#include "emscripten.h"
#include <math.h>

double saturn_x0(double t) {
  return (
     9.52312533591 * cos(0.87401491487 +     213.54291292150 * t)
  +  0.79501390398 * cos(4.76580713096 +       0.24381748350 * t)
  +  0.26427074351 * cos(0.12339999915 +     426.84200835950 * t)
  +  0.06836881382 * cos(4.14537914189 +     206.42936592071 * t)
  +  0.06628914946 * cos(0.75057317755 +     220.65645992230 * t)
  +  0.02340967916 * cos(2.01979283929 +       7.35736448430 * t)
  +  0.01250581159 * cos(2.17392657526 +     110.45013870291 * t)
  +  0.01141539711 * cos(3.03345312296 +     419.72846135871 * t)
  +  0.01098217124 * cos(5.65720860592 +     640.14110379750 * t)
  +  0.00773784455 * cos(3.50285419449 +     213.05527795450 * t)
  +  0.00708587042 * cos(2.70922969272 +     316.63568714010 * t)
  +  0.00434227030 * cos(0.71624098563 +     529.93478257810 * t)
  +  0.00373110880 * cos(0.00103492669 +     433.95555536030 * t)
  +  0.00413446294 * cos(5.12392705512 +     102.84895673509 * t)
  +  0.00169743473 * cos(6.19449424436 +     205.94173095370 * t)
  +  0.00122184772 * cos(4.36825124039 +     103.33659170210 * t)
  +  0.00141571884 * cos(4.84926431365 +     419.24082639170 * t)
  +  0.00097840616 * cos(1.01545569510 +     323.74923414091 * t)
  +  0.00080586098 * cos(5.62239507032 +      11.28951774740 * t)
  +  0.00083840998 * cos(0.62002007163 +     227.77000692311 * t)
  +  0.00072499120 * cos(2.42001514073 +     633.02755679670 * t)
  +  0.00070188882 * cos(0.88664463373 +     209.61075965840 * t)
  +  0.00068920772 * cos(4.01663904384 +     217.47506618460 * t)
  +  0.00065633219 * cos(2.76404999091 +     202.49721265760 * t)
  +  0.00058340081 * cos(2.16106790491 +     224.58861318540 * t)
  +  0.00054036331 * cos(4.90882849644 +     853.44019923550 * t)
  +  0.00045670301 * cos(1.87822014512 +      14.47091148511 * t)
  +  0.00039957906 * cos(4.29286414022 +     199.31581891990 * t)
  +  0.00044623718 * cos(5.61332771211 +      63.49208081989 * t)
  +  0.00025182378 * cos(0.37762569174 +     216.72430665921 * t)
  +  0.00024597547 * cos(4.52837189964 +     210.36151918381 * t)
  +  0.00024755958 * cos(5.60048517853 +     415.79630809560 * t)
  +  0.00025518626 * cos(1.63814026860 +     117.56368570370 * t)
  +  0.00030420785 * cos(4.58036001246 +     735.63269604830 * t)
  +  0.00022261024 * cos(5.81339199632 +     522.33360061030 * t)
  +  0.00023384603 * cos(5.53454487341 +     647.25465079831 * t)
  +  0.00019921860 * cos(2.52438740442 +     426.35437339250 * t)
  +  0.00023368080 * cos(0.18801837763 +     149.80701461810 * t)
  +  0.00024816783 * cos(5.50044242809 +      75.02541605080 * t)
  +  0.00015057730 * cos(4.67637379107 +     277.27881122490 * t)
  +  0.00013291291 * cos(0.78826176081 +     309.03450517230 * t)
  +  0.00012028365 * cos(1.02934559031 +    1059.62574767270 * t)
  +  0.00012408238 * cos(4.19692495275 +     490.57790666290 * t)
  +  0.00012037260 * cos(5.66358935866 +     352.06040979221 * t)
  +  0.00007880259 * cos(2.60324364809 +     743.23387801611 * t)
  +  0.00007428823 * cos(4.26427762571 +       6.86972951729 * t)
  +  0.00006985779 * cos(3.88380796193 +     309.52214013930 * t)
  +  0.00009059376 * cos(4.31626349433 +    1052.02456570489 * t)
  +  0.00006626180 * cos(5.53666910204 +     838.72547026689 * t)
  +  0.00008285289 * cos(2.03028865010 +      95.73540973430 * t)
  +  0.00007908600 * cos(2.91633632242 +     316.14805217309 * t)
  +  0.00006284835 * cos(1.10258326823 +       3.68833577960 * t)
  +  0.00006078527 * cos(6.15871885410 +     441.06910236111 * t)
  +  0.00005628724 * cos(2.47826941808 +     846.32665223470 * t)
  +  0.00005274108 * cos(3.40288166935 +     220.16882495529 * t)
  +  0.00005584926 * cos(3.11230524128 +     412.61491435790 * t)
  +  0.00004423799 * cos(0.00561711784 +     198.82818395289 * t)
  +  0.00004849319 * cos(0.26891980614 +     537.04832957890 * t)
  +  0.00004179381 * cos(0.45517914787 +       4.17597074660 * t)
  +  0.00005772348 * cos(5.30786967696 +      38.37685312130 * t)
  +  0.00005198014 * cos(4.54573443270 +     211.09523236671 * t)
  +  0.00005154525 * cos(0.34613786659 +     215.99059347631 * t)
  +  0.00003792407 * cos(5.99326135433 +     422.90985509640 * t)
  +  0.00004380719 * cos(1.15696233721 +     202.00957769060 * t)
  +  0.00004838174 * cos(2.03403080585 +     109.96250373590 * t)
  +  0.00003765792 * cos(3.72073369090 +     212.57970507500 * t)
  +  0.00003749721 * cos(1.16925812858 +     214.50612076800 * t)
  +  0.00003116757 * cos(0.84596173223 +     213.49472881170 * t)
  +  0.00003115849 * cos(4.04374864852 +     213.59109703130 * t)
  +  0.00003119049 * cos(0.50950816465 +     625.42637482889 * t)
  +  0.00003235633 * cos(1.36565416054 +     632.53992182970 * t)
  +  0.00004077069 * cos(5.95933511847 +     136.78920667889 * t)
  +  0.00003290391 * cos(0.32712024501 +     522.82123557730 * t)
  +  0.00002828736 * cos(0.73223929578 +     330.86278114170 * t)
  +  0.00003365297 * cos(1.42074759163 +     437.88770862340 * t)
  +  0.00002888976 * cos(1.14066267703 +      86.07111631471 * t)
  +  0.00002748221 * cos(5.42931189203 +     138.76131435421 * t)
  +  0.00002742545 * cos(0.93548005709 +     203.98168536590 * t)
  +  0.00002636395 * cos(5.40701545041 +     288.32451148881 * t)
  +  0.00003170535 * cos(5.76636557141 +      76.50988875911 * t)
  +  0.00002530060 * cos(5.09730517007 +     629.09540353360 * t)
  +  0.00002985976 * cos(4.15644325876 +    1066.73929467350 * t)
  +  0.00002617358 * cos(5.45160906944 +     127.22797912329 * t)
  +  0.00002504577 * cos(1.49069183275 +       9.80504503910 * t)
  +  0.00002459199 * cos(5.26431553671 +    1155.11733992350 * t)
  +  0.00002429561 * cos(3.97256605696 +     223.10414047710 * t)
  +  0.00003133467 * cos(4.05731806661 +    1368.41643536150 * t)
  +  0.00002289072 * cos(3.68644263049 +     430.77416162260 * t)
  +  0.00002651422 * cos(5.01550706453 +     412.12727939089 * t)
  +  0.00002791618 * cos(1.76104978670 +       3.42521122121 * t)
  +  0.00002086473 * cos(3.54266754065 +     423.66061462181 * t)
  +  0.00002337517 * cos(5.86744835115 +     388.70897272171 * t)
  +  0.00001735774 * cos(5.67596672079 +     736.12033101530 * t)
  +  0.00001617760 * cos(4.44174561688 +      96.22304470130 * t)
  +  0.00001635420 * cos(4.54438827357 +      12.77399045571 * t)
  +  0.00001637578 * cos(2.19935832842 +     213.02164805970 * t)
  +  0.00001633497 * cos(2.69143754521 +     214.06417778330 * t)
  +  0.00001703439 * cos(2.42595077461 +     529.44714761109 * t)
  +  0.00001499174 * cos(3.59977145410 +      52.44638055600 * t)
  +  0.00001462063 * cos(5.92411007321 +     430.02340209721 * t)
  +  0.00001975850 * cos(2.02313657577 +       1.72829019180 * t)
  +  0.00001422179 * cos(4.89979449865 +     625.91400979590 * t)
  +  0.00001539334 * cos(4.78536735793 +     860.55374623631 * t)
  +  0.00001400317 * cos(3.72256803400 +     341.01470952831 * t)
  +  0.00001337694 * cos(6.25839826307 +     948.93179148630 * t)
  +  0.00001427589 * cos(5.41396429448 +     350.57593708390 * t)
  +  0.00001149795 * cos(0.20404714120 +     941.81824448550 * t)
  +  0.00001112160 * cos(0.47891380184 +     234.88355392390 * t)
  +  0.00001015231 * cos(4.99599119065 +    1471.50920958009 * t)
  +  0.00001090238 * cos(5.82704347671 +     363.10611005610 * t)
  +  0.00001091460 * cos(1.13704115272 +     174.18603700630 * t)
  +  0.00001152320 * cos(3.83459893564 +     201.01273994931 * t)
  +  0.00000874317 * cos(5.95988532860 +     515.22005360950 * t)
  +  0.00001180011 * cos(3.80422455282 +    1684.80830501809 * t)
  +  0.00001058128 * cos(1.29841878389 +     742.74624304909 * t)
  +  0.00000850822 * cos(4.55296025129 +     949.41942645330 * t)
  +  0.00000869178 * cos(3.23528200552 +     210.62215161470 * t)
  +  0.00001119594 * cos(3.46591203463 +     703.87700210090 * t)
  +  0.00000868384 * cos(1.65138396031 +     216.46367422830 * t)
  +  0.00000830815 * cos(0.58110190109 +     212.79215339611 * t)
  +  0.00000825441 * cos(4.30721839854 +     214.29367244690 * t)
  +  0.00000881196 * cos(1.46906794476 +     209.35012722751 * t)
  +  0.00000866345 * cos(3.41432821062 +     217.73569861551 * t)
  +  0.00000789515 * cos(0.23961241737 +     223.83785366000 * t)
  +  0.00001091862 * cos(2.67346837599 +     340.52707456129 * t)
  +  0.00001008329 * cos(1.08917861648 +     226.07308589371 * t)
  +  0.00000919088 * cos(4.86163770046 +     565.35950523021 * t)
  +  0.00000820108 * cos(2.19486077696 +      88.62186273350 * t)
  +  0.00000716162 * cos(5.81233216238 +    1265.32366114289 * t)
  +  0.00000860928 * cos(3.70614582002 +     252.89978883670 * t)
  +  0.00000710939 * cos(3.41349088844 +     417.28078080390 * t)
  +  0.00000701898 * cos(1.91952059017 +     956.53297345411 * t)
  +  0.00000918630 * cos(4.57690637056 +     563.87503252191 * t)
  +  0.00000711475 * cos(0.90576159835 +     207.91383862900 * t)
  +  0.00000797153 * cos(2.01469397505 +     208.12628695010 * t)
  +  0.00000758732 * cos(4.77442040057 +     728.51914904750 * t)
  +  0.00000642018 * cos(1.92693340665 +     639.65346883050 * t)
  +  0.00000769629 * cos(2.89427987517 +     218.95953889290 * t)
  +  0.00000811029 * cos(6.22246903964 +    1162.71852189130 * t)
  +  0.00000692909 * cos(3.97674040211 +     219.17198721400 * t)
  +  0.00000798757 * cos(1.35424808982 +      22.33521801130 * t)
  +  0.00000834309 * cos(2.96244339722 +     160.85271488200 * t)
  +  0.00000655277 * cos(0.92079690947 +     301.92095817150 * t)
  +  0.00000762632 * cos(1.72094446975 +      21.58445848590 * t)
  +  0.00000576036 * cos(3.10166158268 +      99.40443843901 * t)
  +  0.00000615654 * cos(2.27550746905 +     845.83901726770 * t)
  +  0.00000578589 * cos(0.80405181178 +     265.74547599400 * t)
  +  0.00000626782 * cos(2.79771540666 +      18.40306474821 * t)
  +  0.00000589499 * cos(3.90740268282 +     554.31380496631 * t)
  +  0.00000700182 * cos(0.40018815531 +      62.00760811160 * t)
  +  0.00000697691 * cos(0.57105547911 +     124.67723270450 * t)
  +  0.00000613843 * cos(4.42239495907 +     218.20877936750 * t)
  +  0.00000581263 * cos(2.07871172739 +     231.70216018621 * t)
  +  0.00000666749 * cos(2.82369459311 +     425.35753565121 * t)
  +  0.00000516903 * cos(0.38857203410 +     414.31183538731 * t)
  +  0.00000499031 * cos(2.54039255853 +     408.68276109481 * t)
  +  0.00000502357 * cos(6.19770250859 +    1258.21011414209 * t)
  +  0.00000531983 * cos(2.53130210328 +     215.02738562980 * t)
  +  0.00000643415 * cos(1.39270825866 +      64.97655352819 * t)
  +  0.00000518385 * cos(2.70002198759 +     142.69346761730 * t)
  +  0.00000550972 * cos(0.47047442681 +     208.87704647550 * t)
  +  0.00000469313 * cos(0.32930418795 +      71.09326278771 * t)
  +  0.00000456002 * cos(4.67119057391 +     203.24797218300 * t)
  +  0.00000592362 * cos(1.86789317281 +     266.23311096100 * t)
  +  0.00000465459 * cos(5.40811702089 +     654.36819779910 * t)
  +  0.00000444956 * cos(4.73192251220 +    1787.90107923670 * t)
  +  0.00000502683 * cos(4.37046140723 +     251.67594855930 * t)
  +  0.00000522764 * cos(2.19701769819 +     212.05844021321 * t)
  +  0.00000422458 * cos(2.13565038243 +     479.53220639900 * t)
  +  0.00000437134 * cos(1.32836524720 +    1589.31671276730 * t)
  +  0.00000414039 * cos(3.63548652605 +     148.32254190981 * t)
  +  0.00000398994 * cos(1.64973433253 +     213.65478750610 * t)
  +  0.00000398994 * cos(3.23989183406 +     213.43103833690 * t)
  +  0.00000373088 * cos(5.46010584090 +    1581.71553079950 * t)
  +  0.00000469097 * cos(3.55737355039 +    2001.20017467470 * t)
  +  0.00000361258 * cos(4.90274855427 +     302.40859313851 * t)
  +  0.00000345920 * cos(5.01286731480 +     198.56505939450 * t)
  +  0.00000350777 * cos(5.86079095869 +      98.65617104110 * t)
  +  0.00000335274 * cos(1.03009229022 +     213.75536124260 * t)
  +  0.00000335274 * cos(3.85953387637 +     213.33046460040 * t)
  +  0.00000367346 * cos(5.91088479684 +     750.34742501690 * t)
  +  0.00000369973 * cos(5.39933070480 +     151.29148732640 * t)
  +  0.00000399230 * cos(1.04833113678 +    1059.13811270570 * t)
  +  0.00000318144 * cos(6.15035386620 +     228.52076644850 * t)
  +  0.00000315586 * cos(5.68724533460 +     831.61192326610 * t)
  +  0.00000337834 * cos(0.66798086530 +     175.40987728371 * t)
  +  0.00000313433 * cos(3.54547785742 +       2.20386307129 * t)
  +  0.00000330040 * cos(1.38038349450 +     276.79117625789 * t)
  +  0.00000383783 * cos(2.57160924287 +      56.37853381910 * t)
  +  0.00000350135 * cos(4.75975448170 +     114.38229196601 * t)
  +  0.00000401239 * cos(4.28930925743 +     178.11819026941 * t)
  +  0.00000404631 * cos(6.03696917524 +    1479.11039154791 * t)
  +  0.00000404539 * cos(1.52309497166 +     311.95526647910 * t)
  +  0.00000304876 * cos(6.11535489175 +     195.38366565681 * t)
  +  0.00000289344 * cos(4.48279316993 +     192.20227191910 * t)
  +  0.00000270250 * cos(5.14035236650 +     636.20895053440 * t)
  +  0.00000271661 * cos(1.28934639885 +     278.76328393321 * t)
  +  0.00000283573 * cos(0.04390160982 +     191.45151239371 * t)
  +  0.00000294112 * cos(1.97767959737 +    1162.23088692429 * t)
  +  0.00000266932 * cos(5.65493346800 +     205.46615807421 * t)
  +  0.00000269475 * cos(2.14597987484 +     327.68138740401 * t)
  +  0.00000348053 * cos(0.61890667474 +     248.96763557360 * t)
  +  0.00000296599 * cos(1.51525625285 +      10.53875822200 * t)
  +  0.00000252084 * cos(1.67555502838 +     213.80354535241 * t)
  +  0.00000252084 * cos(3.21407113821 +     213.28228049061 * t)
  +  0.00000250282 * cos(2.61655820302 +     433.46792039329 * t)
  +  0.00000294321 * cos(2.01870159642 +     106.51798543980 * t)
  +  0.00000270973 * cos(4.53462056041 +    1044.91101870410 * t)
  +  0.00000263820 * cos(3.76320728541 +      63.97971578690 * t)
  +  0.00000238275 * cos(5.91316475830 +    1574.60198379870 * t)
  +  0.00000305244 * cos(1.10529286976 +     483.46435966210 * t)
  +  0.00000241411 * cos(5.74870980326 +     221.61966776881 * t)
  +  0.00000314980 * cos(4.37056119892 +     479.04457143200 * t)
  +  0.00000223277 * cos(4.01771641783 +      13.98327651810 * t)
  +  0.00000292846 * cos(3.86376968180 +     424.39432780471 * t)
  +  0.00000304942 * cos(1.75360932249 +    6283.31966747490 * t)
  +  0.00000237167 * cos(4.96019200454 +     235.63431344930 * t)
  +  0.00000240608 * cos(5.75032033143 +     275.79433851660 * t)
  +  0.00000263455 * cos(5.51056104098 +      70.60562782070 * t)
  +  0.00000211236 * cos(0.02154252782 +     544.16187657970 * t)
  +  0.00000205878 * cos(4.46555623121 +     842.39449897160 * t)
  +  0.00000282395 * cos(3.56598534931 +     404.75060783170 * t)
  +  0.00000203077 * cos(4.47228022052 +    2104.29294889330 * t)
  +  0.00000267955 * cos(3.49559055839 +     121.49583896680 * t)
  +  0.00000238411 * cos(4.99775321682 +     138.27367938720 * t)
  +  0.00000230884 * cos(4.03701073645 +     497.69145366371 * t)
  +  0.00000203254 * cos(2.93667823303 +     284.39235822571 * t)
  +  0.00000216423 * cos(2.44114933526 +       8.32057233081 * t)
  +  0.00000194279 * cos(5.27870729321 +     190.96387742670 * t)
  +  0.00000216822 * cos(6.14885127819 +     429.28968891431 * t)
  +  0.00000191411 * cos(5.14394229637 +    1898.10740045609 * t)
  +  0.00000212655 * cos(0.67418560513 +     651.18680406140 * t)
  +  0.00000214969 * cos(2.97753864449 +     425.87880051300 * t)
  +  0.00000236822 * cos(3.57393144724 +     219.69325207580 * t)
  +  0.00000229348 * cos(1.65487599461 +     270.16526422410 * t)
  +  0.00000174163 * cos(3.29103993348 +     426.89019246930 * t)
  +  0.00000202398 * cos(2.42508237402 +      39.60069339870 * t)
  +  0.00000179962 * cos(2.48812846406 +     404.26297286470 * t)
  +  0.00000169610 * cos(4.78044354700 +     501.62360692681 * t)
  +  0.00000174157 * cos(0.09324510966 +     426.79382424970 * t)
  +  0.00000165778 * cos(0.76098657662 +     312.70353387701 * t)
  +  0.00000178798 * cos(4.30679581382 +     355.99256305531 * t)
  +  0.00000180904 * cos(0.63787759163 +     618.31282782810 * t)
  +  0.00000182548 * cos(1.24685071391 +     210.83459993580 * t)
  +  0.00000179529 * cos(3.64276765573 +     216.25122590720 * t)
  +  0.00000187071 * cos(0.50925452549 +     427.80521620600 * t)
  +  0.00000180856 * cos(3.08033197166 +      84.58664360640 * t)
  +  0.00000196496 * cos(5.26678343139 +     489.09343395460 * t)
  +  0.00000151676 * cos(0.75207673924 +     213.38285422711 * t)
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  +  0.00000000899 * cos(2.86831464473 +    9896.64985907089 * t)
  +  0.00000001114 * cos(1.71021700338 +     210.08633253789 * t)
  +  0.00000000935 * cos(1.95269050544 +      97.21988244259 * t)
  +  0.00000000909 * cos(2.84341068430 +     981.17512040070 * t)
  +  0.00000000907 * cos(3.53818082973 +    3679.13875017550 * t)
  +  0.00000001078 * cos(2.11362323812 +     429.53576713020 * t)
  +  0.00000001223 * cos(5.59274764012 +     876.85850590470 * t)
  +  0.00000001053 * cos(5.34256956029 +     828.16740497000 * t)
  +  0.00000001159 * cos(1.80620732752 +     979.42752313400 * t)
  +  0.00000001179 * cos(5.56984888168 +     261.23717611490 * t)
  +  0.00000000872 * cos(1.92760134845 +     102.68889804070 * t)
  +  0.00000000902 * cos(6.00836364296 +    1407.51018671831 * t)
  +  0.00000000970 * cos(0.92585247141 +   51322.36608391289 * t)
  +  0.00000000954 * cos(4.49316887147 +    1527.86843632430 * t)
  +  0.00000000870 * cos(5.19978000768 +     103.00901542950 * t)
  +  0.00000001100 * cos(5.62879482377 +    1229.89893849079 * t)
  +  0.00000000980 * cos(1.25124342498 +    1246.90128931980 * t)
  +  0.00000000980 * cos(4.39283607857 +    1246.41365435280 * t)
  +  0.00000001025 * cos(3.23838487665 +    1187.09754427950 * t)
  +  0.00000000899 * cos(0.54202019063 +     663.55941046670 * t)
  +  0.00000000966 * cos(1.79575119893 +     607.00400300581 * t)
  +  0.00000000974 * cos(0.27626387870 +     600.78422788230 * t)
  +  0.00000001052 * cos(6.22307301865 +    1901.77642916080 * t)
  +  0.00000000939 * cos(4.72156953852 +   12573.50906446710 * t)
  +  0.00000000875 * cos(2.22995963009 +     521.85802773080 * t)
  +  0.00000000927 * cos(0.12921366968 +    3583.64715792471 * t)
  +  0.00000000999 * cos(5.03574675925 +    2442.51309451930 * t)
  +  0.00000000868 * cos(2.01963693018 +     449.73655803940 * t)
  +  0.00000000920 * cos(0.32639183017 +     184.60108995130 * t)
  +  0.00000000916 * cos(1.52011458512 +     860.06611126930 * t)
  +  0.00000001151 * cos(1.92144343659 +     775.68965525160 * t)
  +  0.00000001064 * cos(0.14103713575 +    9775.39783758759 * t)
  +  0.00000000991 * cos(1.62300930873 +     447.55200204300 * t)
  +  0.00000000934 * cos(1.28685601483 +   52168.93655363109 * t)
  +  0.00000000852 * cos(6.16455890838 +    4760.34895633411 * t)
  +  0.00000000879 * cos(3.35373437012 +     260.60403666850 * t)
  +  0.00000000961 * cos(2.59929190647 +   10529.92123335110 * t)
  +  0.00000000878 * cos(1.53529030972 +     166.48178917450 * t)
  +  0.00000001023 * cos(3.25205599061 +     517.40460960590 * t)
  +  0.00000001056 * cos(0.94712347846 +     622.24498109120 * t)
  +  0.00000000857 * cos(3.62784678051 +     905.64276230799 * t)
  +  0.00000000858 * cos(4.37974924972 +     866.77352135980 * t)
  +  0.00000000960 * cos(0.24582787127 +    5842.00674763030 * t)
  +  0.00000001006 * cos(1.79633164069 +    1332.72858815100 * t)
  +  0.00000000859 * cos(2.62618934557 +    1886.79857563380 * t)
  +  0.00000001053 * cos(4.19119124113 +     527.48710202330 * t)
  +  0.00000000937 * cos(1.00314188520 +     597.60283414461 * t)
  +  0.00000000858 * cos(0.41037816799 +    1035.24672528451 * t)
  +  0.00000001183 * cos(2.27973890086 +     115.37912970730 * t)
  +  0.00000000920 * cos(1.30633459352 +     589.73852761840 * t)
  +  0.00000000920 * cos(4.44792724711 +     589.25089265140 * t)
  +  0.00000000852 * cos(0.72219554639 +     146.13798591339 * t)
  +  0.00000000852 * cos(3.86378819998 +     146.62562088040 * t)
  +  0.00000000844 * cos(2.53592267944 +      10.27812579110 * t)
  +  0.00000000844 * cos(5.67751533303 +       9.79049082409 * t)
  +  0.00000000959 * cos(1.94261627589 +     177.15498242291 * t)
  +  0.00000000959 * cos(2.94700989070 +     249.93084342011 * t)
  +  0.00000001035 * cos(4.17393929319 +     507.35574708330 * t)
  +  0.00000000988 * cos(5.11539514032 +      67.94549894479 * t)
  +  0.00000001133 * cos(4.92435407900 +      36.40474544600 * t)
  +  0.00000000843 * cos(0.19283077743 +     178.37882270030 * t)
  +  0.00000000843 * cos(4.69679538916 +     248.70700314271 * t)
  +  0.00000000836 * cos(6.26008270853 +     951.21941334670 * t)
  +  0.00000001000 * cos(0.00060532281 +     598.59967188590 * t)
  +  0.00000000870 * cos(1.56871527769 +    2520.33307447240 * t)
  +  0.00000001010 * cos(3.29456379641 +     525.26891613211 * t)
  +  0.00000000869 * cos(1.69757216185 +     803.30074761480 * t)
  +  0.00000000862 * cos(0.89788175589 +    1336.66074141410 * t)
  +  0.00000000865 * cos(2.71043672332 +    1535.24510788349 * t)
  +  0.00000001156 * cos(0.63783988377 +     988.02554284310 * t)
  +  0.00000000854 * cos(3.20756177408 +    3119.95596677750 * t)
  +  0.00000000854 * cos(3.20756177408 +    3120.44360174450 * t)
  +  0.00000000959 * cos(0.01125319100 +     167.80869531589 * t)
  +  0.00000000843 * cos(5.93933593135 +     769.57294599210 * t)
  +  0.00000000819 * cos(5.32247266092 +   20006.84263106329 * t)
  +  0.00000000871 * cos(2.39559363846 +    2015.91490364330 * t)
  +  0.00000001145 * cos(2.59566377091 +     982.39646855060 * t)
  +  0.00000000967 * cos(1.79131153995 +     274.09741748721 * t)
  +  0.00000000811 * cos(3.51067946836 +     310.95842873781 * t)
  +  0.00000001076 * cos(0.55295132771 +     195.64679021520 * t)
  +  0.00000000973 * cos(0.39005913258 +     480.00777927849 * t)
  +  0.00000000927 * cos(2.26192813378 +     221.92848430950 * t)
  +  0.00000000927 * cos(5.76929068640 +     205.15734153350 * t)
  +  0.00000001043 * cos(3.80833299490 +    1054.47224625970 * t)
  +  0.00000001118 * cos(5.22401073053 +     241.36645360580 * t)
  +  0.00000001087 * cos(0.94496532019 +   26404.53882871430 * t)
  +  0.00000000843 * cos(5.30493118625 +    9470.05166819489 * t)
  +  0.00000000799 * cos(2.23950305681 +     556.27385055410 * t)
  +  0.00000000916 * cos(1.67106075742 +     454.66554904380 * t)
  +  0.00000000867 * cos(0.75856039322 +     155.43608891061 * t)
  +  0.00000001078 * cos(5.29407779979 +     903.16145185841 * t)
  +  0.00000000950 * cos(0.01679256709 +     469.48334387639 * t)
  +  0.00000000972 * cos(1.35094632973 +     317.15695200191 * t)
  +  0.00000000793 * cos(3.97038609207 +     529.88659846831 * t)
  +  0.00000000798 * cos(2.46893889261 +     438.14834105430 * t)
  +  0.00000000885 * cos(0.81574627494 +     685.23011986920 * t)
  +  0.00000000791 * cos(4.63298065332 +     206.46299581550 * t)
  +  0.00000000919 * cos(2.21054616872 +     524.25752417581 * t)
  +  0.00000000919 * cos(5.35213882231 +     523.76988920880 * t)
  +  0.00000000841 * cos(5.71772687954 +    3590.76070492550 * t)
  +  0.00000000841 * cos(5.71772687954 +    3590.27306995850 * t)
  +  0.00000001022 * cos(3.33436205114 +     731.92754532131 * t)
  +  0.00000000978 * cos(4.52983537485 +     443.61984877990 * t)
  +  0.00000000923 * cos(3.89253221329 +     261.81332273089 * t)
  +  0.00000000860 * cos(5.19233645312 +    1784.71968549900 * t)
  +  0.00000000803 * cos(2.43021611713 +   19992.61553706169 * t)
  +  0.00000000948 * cos(2.63670367258 +    3280.99474730270 * t)
  +  0.00000000852 * cos(1.68072750753 +     548.09402984280 * t)
  +  0.00000000873 * cos(5.56384706144 +      63.60395540450 * t)
  +  0.00000000956 * cos(4.90457947532 +     108.47803102759 * t)
  +  0.00000000972 * cos(3.15655108462 +     892.79707515070 * t)
  +  0.00000000926 * cos(4.87388996442 +    1025.68549772890 * t)
  +  0.00000000914 * cos(0.82646186068 +     832.34563644899 * t)
  +  0.00000001030 * cos(1.54922251715 +     586.55713388070 * t)
  +  0.00000000809 * cos(0.02318871977 +    1235.36795408890 * t)
  +  0.00000000809 * cos(2.35631924662 +    1310.14955265620 * t)
  +  0.00000000784 * cos(1.33531692413 +    1699.52303398670 * t)
  +  0.00000001020 * cos(3.91431359487 +     102.96083131970 * t)
  +  0.00000000817 * cos(0.58884416481 +       5.90652167079 * t)
  +  0.00000001007 * cos(5.89584195442 +     740.05248427840 * t)
  +  0.00000000872 * cos(2.51565061639 +      63.38020623529 * t)
  +  0.00000000934 * cos(0.00461953261 +     721.89323701370 * t)
  +  0.00000000780 * cos(4.93205218405 +     930.77254422160 * t)
  +  0.00000001031 * cos(0.90633658665 +     738.08037660310 * t)
  +  0.00000000793 * cos(5.83091384800 +     746.41527175380 * t)
  +  0.00000001085 * cos(2.59531505198 +     592.44684060410 * t)
  +  0.00000000961 * cos(4.24333704051 +    1120.39270055950 * t)
  +  0.00000000888 * cos(3.27274826634 +   26514.74514993370 * t)
  +  0.00000000782 * cos(0.97176938732 +     519.63984183961 * t)
  +  0.00000000800 * cos(4.78070775485 +    4113.33812301930 * t)
  +  0.00000000945 * cos(2.48989407033 +    1673.76260475420 * t)
  +  0.00000000850 * cos(1.88127295930 +     580.33735875721 * t)
  +  0.00000001030 * cos(2.74042787073 +    3657.24811383991 * t)
  +  0.00000000775 * cos(1.42999892472 +     735.58451193849 * t)
  +  0.00000000775 * cos(4.57159157831 +     736.07214690550 * t)
  +  0.00000000951 * cos(2.79912666955 +     604.22874617840 * t)
  +  0.00000000760 * cos(0.06105636609 +    3267.25528826810 * t)
  +  0.00000000802 * cos(2.87236079717 +     362.61847508910 * t)
  +  0.00000000866 * cos(3.55253106731 +    1293.63483679419 * t)
  +  0.00000000766 * cos(0.39602652848 +     188.67625556630 * t)
  +  0.00000000768 * cos(3.19838844999 +     845.57589270931 * t)
  +  0.00000000766 * cos(6.03837318319 +    2439.33170078160 * t)
  +  0.00000000769 * cos(4.30008269962 +    1051.97638159510 * t)
  +  0.00000000776 * cos(4.35680451630 +    2014.27037224060 * t)
  +  0.00000000771 * cos(1.21518951297 +    1052.07274981469 * t)
  +  0.00000000822 * cos(4.41913668940 +     582.62498061761 * t)
  +  0.00000001002 * cos(4.18366137124 +   52183.16364763270 * t)
  +  0.00000000828 * cos(2.60868899519 +     631.78916230430 * t)
  +  0.00000000973 * cos(5.48773198848 +     519.14971474510 * t)
  +  0.00000000839 * cos(0.93524853813 +   13362.69352428270 * t)
  +  0.00000000842 * cos(3.25093404707 +     204.45725824539 * t)
  +  0.00000000756 * cos(0.00983905715 +     693.82813957829 * t)
  +  0.00000000756 * cos(3.15143171073 +     694.31577454531 * t)
  +  0.00000000747 * cos(6.11050160069 +     962.75274857760 * t)
  +  0.00000000916 * cos(5.24490716330 +     688.41151360689 * t)
  +  0.00000000769 * cos(1.54076301375 +    6058.48723680599 * t)
  +  0.00000000756 * cos(2.12064124784 +     545.71578525720 * t)
  +  0.00000000830 * cos(1.92350323862 +     595.47066777489 * t)
  +  0.00000000831 * cos(0.77280313250 +     436.87631666710 * t)
  +  0.00000000776 * cos(1.38249726509 +     187.99493201010 * t)
  +  0.00000000757 * cos(4.23072662628 +    5496.22546986590 * t)
  +  0.00000000977 * cos(6.20713264303 +    1055.43296197871 * t)
  +  0.00000000737 * cos(3.54155313450 +     225.58545092669 * t)
  +  0.00000000940 * cos(2.94283899053 +     462.00609858071 * t)
  +  0.00000000881 * cos(5.71084129732 +     157.67132114430 * t)
  +  0.00000000881 * cos(5.46197017645 +     269.41450469871 * t)
  +  0.00000000768 * cos(2.97725228498 +    2093.24724862940 * t)
  +  0.00000000945 * cos(5.11643863868 +     347.65517577710 * t)
  +  0.00000000789 * cos(2.80405308992 +     678.27413943531 * t)
  +  0.00000000894 * cos(5.28864466497 +     185.08872491831 * t)
  +  0.00000000887 * cos(0.33081399998 +     938.63685074779 * t)
  +  0.00000000848 * cos(0.16881037460 +    1016.59984305279 * t)
  +  0.00000000778 * cos(0.01629844158 +    5753.62870238030 * t)
  +  0.00000000778 * cos(3.15789109517 +    5753.14106741329 * t)
  +  0.00000000843 * cos(1.02624495037 +     976.49220761220 * t)
  +  0.00000000900 * cos(2.19862220278 +     655.17383907870 * t)
  +  0.00000000730 * cos(3.17028402119 +     497.95457822210 * t)
  +  0.00000000879 * cos(3.20284714972 +     494.23487328010 * t)
  +  0.00000000728 * cos(4.17683406683 +     995.88984936931 * t)
  +  0.00000000729 * cos(5.48820634686 +     632.58810593949 * t)
  +  0.00000000729 * cos(2.34661369327 +     633.07574090651 * t)
  +  0.00000000841 * cos(0.88660531241 +    1051.06135785839 * t)
  +  0.00000000810 * cos(6.22385696664 +    3900.03902758130 * t)
  +  0.00000000774 * cos(1.63307607705 +     451.48415530609 * t)
  +  0.00000000792 * cos(1.63932414999 +     193.93282284329 * t)
  +  0.00000000894 * cos(1.22695933225 +     103.28840759231 * t)
  +  0.00000000744 * cos(5.76295987616 +     662.77502104650 * t)
  +  0.00000001019 * cos(4.06927095682 +    7232.49527644471 * t)
  +  0.00000000720 * cos(6.27725825901 +  103711.47146249928 * t)
  +  0.00000000776 * cos(1.68634145832 +    1703.45518724980 * t)
  +  0.00000001001 * cos(2.29066167531 +    1126.54303971381 * t)
  +  0.00000000860 * cos(1.85082345148 +    2748.61002343740 * t)
  +  0.00000000716 * cos(2.80780296922 +    4319.03603648950 * t)
  +  0.00000000716 * cos(5.94939562281 +    4319.52367145650 * t)
  +  0.00000000797 * cos(0.88312421788 +     529.98296668790 * t)
  +  0.00000000729 * cos(3.08861395930 +    1649.38358236600 * t)
  +  0.00000000803 * cos(2.56866081755 +     151.01630068050 * t)
  +  0.00000000765 * cos(1.92150517901 +    1379.46213562540 * t)
  +  0.00000000765 * cos(5.06309783260 +    1379.94977059240 * t)
  +  0.00000000749 * cos(3.86728999613 +     785.77214766900 * t)
  +  0.00000000836 * cos(4.09079447369 +    4010.24534880071 * t)
  +  0.00000000727 * cos(1.76200509604 +     608.16089944150 * t)
  +  0.00000000727 * cos(1.76200509604 +     608.64853440851 * t)
  +  0.00000000719 * cos(1.08122225861 +     467.68335698301 * t)
  +  0.00000000709 * cos(2.16805792847 +     103.54904002320 * t)
  +  0.00000000709 * cos(2.16805792847 +     103.06140505620 * t)
  +  0.00000000920 * cos(3.37948839250 +     870.70567462290 * t)
  +  0.00000000716 * cos(3.01984388520 +     664.78325074409 * t)
  +  0.00000000857 * cos(4.73776093669 +    2306.54634406740 * t)
  +  0.00000000724 * cos(4.70354725719 +     740.52556503041 * t)
  +  0.00000000708 * cos(4.72112546056 +    2431.46739425540 * t)
  +  0.00000000706 * cos(4.95679658990 +     102.63650841399 * t)
  +  0.00000000706 * cos(4.95679658990 +     103.12414338101 * t)
  +  0.00000000824 * cos(0.35265072853 +    1163.68172973780 * t)
  +  0.00000000722 * cos(3.07523457584 +     171.21709158970 * t)
  +  0.00000000723 * cos(0.74571067860 +     829.37669103239 * t)
  +  0.00000000720 * cos(1.80911156979 +     255.86873425330 * t)
  +  0.00000000956 * cos(1.61313021087 +    3068.18328683170 * t)
  +  0.00000000800 * cos(4.60599313494 +     279.72649177971 * t)
  +  0.00000000800 * cos(0.28363303165 +     147.35933406330 * t)
  +  0.00000000868 * cos(5.08886004770 +     669.40093308030 * t)
  +  0.00000000769 * cos(4.42409463602 +    3465.83965473750 * t)
  +  0.00000000745 * cos(4.41268882152 +     843.14525849700 * t)
  +  0.00000000848 * cos(4.34921581475 +     103.38477581190 * t)
  +  0.00000000703 * cos(0.03980855697 +    4003.13180179990 * t)
  +  0.00000000719 * cos(2.96421431820 +    9988.69693302559 * t)
  +  0.00000000818 * cos(3.58195947060 +     311.48218572709 * t)
  +  0.00000000901 * cos(5.50487267537 +     937.88609122240 * t)
  +  0.00000000783 * cos(0.40400095682 +     199.83708378171 * t)
  +  0.00000000783 * cos(1.34403255618 +     227.24874206131 * t)
  +  0.00000000909 * cos(5.35487801471 +    4009.75771383370 * t)
  +  0.00000000711 * cos(0.19813010381 +     457.37386202950 * t)
  +  0.00000000705 * cos(1.55599502521 +    5653.98044645779 * t)
  +  0.00000000712 * cos(4.50433897135 +     354.28108781090 * t)
  +  0.00000000733 * cos(4.93048865178 +      37.62858572340 * t)
  +  0.00000000708 * cos(2.84637541601 +     840.69757794220 * t)
  +  0.00000000708 * cos(5.98796806961 +     840.20994297520 * t)
  +  0.00000000695 * cos(4.51136204527 +     812.70191647599 * t)
  +  0.00000000695 * cos(4.51136204527 +     813.18955144300 * t)
  +  0.00000000736 * cos(1.20053248385 +     403.94745867960 * t)
  +  0.00000000733 * cos(0.72827400906 +     182.03578931750 * t)
  +  0.00000000836 * cos(3.44633331041 +    2331.81913833290 * t)
  +  0.00000000928 * cos(2.16436836139 +     842.13386654071 * t)
  +  0.00000000768 * cos(5.27501406783 +    1460.20038475780 * t)
  +  0.00000000685 * cos(5.86089797553 +     455.29619636271 * t)
  +  0.00000000792 * cos(1.62315871295 +    5422.52210375510 * t)
  +  0.00000000837 * cos(5.42340126188 +     570.77613120160 * t)
  +  0.00000000682 * cos(4.88563990270 +    3693.85347914410 * t)
  +  0.00000000752 * cos(2.13635874109 +     413.34862754081 * t)
  +  0.00000000817 * cos(1.53257391407 +     391.73279989249 * t)
  +  0.00000000681 * cos(2.40403440268 +     458.33457774851 * t)
  +  0.00000000803 * cos(5.00204662708 +     418.49006686629 * t)
  +  0.00000000681 * cos(0.38545629971 +     414.57495994570 * t)
  );
}

double saturn_x1(double t) {
  return (
     0.09285877988 * cos(0.61678993503 +       0.24381748350 * t)
  +  0.03086501680 * cos(4.27493632359 +     426.84200835950 * t)
  +  0.02728479923 * cos(5.84476389020 +     206.42936592071 * t)
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  +  0.00000001724 * cos(1.33166239973 +    1037.79747170330 * t)
  +  0.00000001477 * cos(4.36052585434 +     208.38941150850 * t)
  +  0.00000001657 * cos(1.83865415601 +     552.82933225800 * t)
  +  0.00000001520 * cos(2.73911257161 +    2318.07967929830 * t)
  +  0.00000001443 * cos(1.98940467508 +     910.06255053810 * t)
  +  0.00000001446 * cos(1.10349996175 +     204.94489321240 * t)
  +  0.00000001446 * cos(0.64453355125 +     222.14093263061 * t)
  +  0.00000001850 * cos(3.79242867450 +     699.94484883781 * t)
  +  0.00000001439 * cos(4.66881004427 +     393.70490756781 * t)
  +  0.00000001452 * cos(6.27116384237 +    1130.47519297691 * t)
  +  0.00000001874 * cos(2.34112858987 +     770.06058095910 * t)
  +  0.00000001782 * cos(1.54447498730 +     835.54407652920 * t)
  +  0.00000001639 * cos(5.07308302027 +     427.10264079041 * t)
  +  0.00000001565 * cos(0.60414645629 +     392.90175841570 * t)
  +  0.00000001395 * cos(5.81501189133 +    9146.54625153749 * t)
  +  0.00000001516 * cos(3.58009173951 +     397.90018538930 * t)
  +  0.00000001684 * cos(6.24638766723 +    1479.11039154791 * t)
  +  0.00000001659 * cos(1.59176755278 +     721.89323701370 * t)
  +  0.00000001514 * cos(5.91645211455 +     319.06881347989 * t)
  +  0.00000001397 * cos(2.98224235085 +    3163.67487908250 * t)
  +  0.00000001747 * cos(2.27656402390 +      37.88921815429 * t)
  +  0.00000001492 * cos(3.04531836360 +     263.94548910060 * t)
  +  0.00000001354 * cos(4.57495887478 +     140.24578706250 * t)
  +  0.00000001506 * cos(0.27404631561 +     251.41531612840 * t)
  +  0.00000001365 * cos(4.69515666017 +     694.31577454531 * t)
  +  0.00000001352 * cos(4.48933959673 +      60.79832204921 * t)
  +  0.00000001352 * cos(4.48933959673 +      60.31068708220 * t)
  +  0.00000001531 * cos(0.64877553761 +     907.09360512150 * t)
  +  0.00000001783 * cos(0.81801801901 +     185.08872491831 * t)
  +  0.00000001550 * cos(4.05055802538 +     170.51700830159 * t)
  +  0.00000001524 * cos(0.15234864850 +     921.32069912310 * t)
  +  0.00000001541 * cos(2.73990779933 +      31.73638687251 * t)
  +  0.00000001578 * cos(5.98549196472 +     190.64836324160 * t)
  +  0.00000001578 * cos(5.18731950905 +     236.43746260140 * t)
  +  0.00000001732 * cos(0.64736011209 +    1126.54303971381 * t)
  +  0.00000001540 * cos(0.36379616132 +    2833.05591542430 * t)
  +  0.00000001323 * cos(4.87522768351 +     460.78225830330 * t)
  +  0.00000001312 * cos(5.10594513264 +     448.98829064149 * t)
  +  0.00000001724 * cos(5.39037296555 +      78.46993434690 * t)
  +  0.00000001472 * cos(4.26339575699 +      34.18406742730 * t)
  +  0.00000001296 * cos(5.62129859108 +    2325.19322629910 * t)
  +  0.00000001309 * cos(5.45522580580 +     349.09146437560 * t)
  +  0.00000001818 * cos(4.16411482533 +     100.40127618030 * t)
  +  0.00000001290 * cos(2.36413128544 +    1176.94561589290 * t)
  +  0.00000001334 * cos(2.44221382511 +     282.90788551740 * t)
  +  0.00000001287 * cos(0.26504708130 +     286.84003878050 * t)
  +  0.00000001392 * cos(4.87830155415 +      69.12115511239 * t)
  +  0.00000001515 * cos(3.62072467848 +      12.28635548869 * t)
  +  0.00000001247 * cos(4.64664167702 +     187.67941782501 * t)
  +  0.00000001247 * cos(0.24298448957 +     239.40640801801 * t)
  +  0.00000001246 * cos(1.79539178116 +    2487.17222746430 * t)
  +  0.00000001511 * cos(1.66615367049 +     213.00709384469 * t)
  +  0.00000001479 * cos(0.68803218820 +    2516.66404576769 * t)
  +  0.00000001233 * cos(1.65114888447 +    2531.37877473630 * t)
  +  0.00000001632 * cos(2.90714941935 +     906.13039727500 * t)
  +  0.00000001387 * cos(0.55195474062 +     401.56921409400 * t)
  +  0.00000001352 * cos(0.63301755055 +     351.57277482520 * t)
  +  0.00000001313 * cos(0.13852930132 +     350.08830211689 * t)
  +  0.00000001236 * cos(3.39882375572 +   11926.01059618529 * t)
  +  0.00000001227 * cos(5.24375477429 +    4127.56521702090 * t)
  +  0.00000001304 * cos(0.28979853169 +     203.49405039889 * t)
  +  0.00000001478 * cos(4.80872386721 +     264.26100328570 * t)
  +  0.00000001254 * cos(6.19414707054 +     827.67977000299 * t)
  +  0.00000001230 * cos(2.44616325751 +   51535.66517935089 * t)
  +  0.00000001385 * cos(4.26128512958 +      41.29761442810 * t)
  +  0.00000001364 * cos(4.18584755012 +      65.46418849521 * t)
  +  0.00000001395 * cos(2.64686968582 +     629.35852809199 * t)
  +  0.00000001284 * cos(5.37115714123 +     168.29633028290 * t)
  +  0.00000001435 * cos(5.84382021042 +     617.56206830270 * t)
  +  0.00000001411 * cos(5.88687181276 +     188.27011865600 * t)
  +  0.00000001191 * cos(0.70400726689 +     606.51636803880 * t)
  +  0.00000001193 * cos(1.77967286420 +     274.30986580831 * t)
  +  0.00000001197 * cos(2.05343251093 +    1062.80714141041 * t)
  +  0.00000001356 * cos(1.22316379022 +      50.64639366260 * t)
  +  0.00000001356 * cos(4.36475644381 +      50.15875869559 * t)
  +  0.00000001276 * cos(0.30928416823 +    2090.06585489169 * t)
  +  0.00000001195 * cos(2.85953206146 +     681.29796660610 * t)
  +  0.00000001603 * cos(1.64227556935 +    1560.37488979710 * t)
  +  0.00000001191 * cos(3.68583487315 +    9594.99527173989 * t)
  +  0.00000001168 * cos(1.08249837425 +      74.39476873190 * t)
  +  0.00000001165 * cos(4.67802137668 +     674.18441960530 * t)
  +  0.00000001242 * cos(5.63232378165 +    1902.52718868620 * t)
  +  0.00000001330 * cos(0.04908988755 +     200.27902676641 * t)
  +  0.00000001330 * cos(1.69894362545 +     226.80679907661 * t)
  +  0.00000001154 * cos(1.32466818176 +    2847.77064439291 * t)
  +  0.00000001150 * cos(5.63834183266 +      17.65230522280 * t)
  +  0.00000001152 * cos(1.92670632990 +     740.05248427840 * t)
  +  0.00000001247 * cos(5.13783491688 +     348.39138108750 * t)
  +  0.00000001387 * cos(5.73885801869 +     527.48710202330 * t)
  +  0.00000001250 * cos(1.98100336387 +     184.60108995130 * t)
  +  0.00000001328 * cos(4.49802504301 +    2957.48933064529 * t)
  +  0.00000001587 * cos(1.96187033145 +    1243.98302014049 * t)
  +  0.00000001176 * cos(1.80593057083 +     747.16603127920 * t)
  +  0.00000001223 * cos(0.59493067511 +    1773.67398523510 * t)
  +  0.00000001161 * cos(0.01398952175 +    2435.39954751850 * t)
  +  0.00000001570 * cos(4.69885872763 +    3060.58210486390 * t)
  +  0.00000001303 * cos(3.48272421278 +     393.21727260080 * t)
  +  0.00000001126 * cos(0.75321492124 +     305.10235190919 * t)
  +  0.00000001534 * cos(1.87537098734 +      81.99595069970 * t)
  +  0.00000001117 * cos(4.61546207470 +     526.00262931501 * t)
  +  0.00000001307 * cos(5.84787741027 +      72.09010052900 * t)
  +  0.00000001114 * cos(0.00680453000 +   25234.46294233869 * t)
  +  0.00000001118 * cos(1.34292799669 +     511.77553531340 * t)
  +  0.00000001242 * cos(2.97258589350 +     145.38722638800 * t)
  +  0.00000001397 * cos(4.30533366512 +     336.59492129820 * t)
  +  0.00000001401 * cos(2.28518305813 +    2118.52004289490 * t)
  +  0.00000001139 * cos(5.01671933650 +    1055.20595944260 * t)
  +  0.00000001096 * cos(3.93031837723 +     739.30172475301 * t)
  +  0.00000001092 * cos(1.72033976580 +     234.39591895690 * t)
  +  0.00000001197 * cos(0.70790588748 +     306.34074640161 * t)
  +  0.00000001126 * cos(5.90717690029 +    1144.07163965960 * t)
  +  0.00000001351 * cos(3.03970702934 +     179.60266297770 * t)
  +  0.00000001165 * cos(0.13814938960 +     746.67839631219 * t)
  +  0.00000001167 * cos(4.32162909656 +     634.72447782610 * t)
  +  0.00000001121 * cos(3.70393028752 +     366.28750379380 * t)
  +  0.00000001051 * cos(2.77078069512 +     383.81610373959 * t)
  +  0.00000001053 * cos(3.41928600573 +    2107.96197759801 * t)
  +  0.00000001051 * cos(2.99910636875 +   10000.23026825651 * t)
  +  0.00000001288 * cos(1.85993541573 +     247.48316286530 * t)
  +  0.00000001045 * cos(4.77749523511 +    1680.87615175499 * t)
  +  0.00000001070 * cos(5.83029249500 +    3472.95320173830 * t)
  +  0.00000001043 * cos(5.10256961747 +     151.50393564750 * t)
  +  0.00000001033 * cos(1.59445268426 +    6070.02057203690 * t)
  +  0.00000001282 * cos(3.59113162781 +     141.94270809190 * t)
  +  0.00000001167 * cos(5.76598251731 +    2920.88396534110 * t)
  +  0.00000001100 * cos(2.52155794298 +    2634.47154895491 * t)
  +  0.00000001035 * cos(5.30771361050 +    3369.86042751970 * t)
  +  0.00000001091 * cos(0.54826165686 +    1314.56934088630 * t)
  +  0.00000001274 * cos(3.38359403787 +     691.34682912870 * t)
  +  0.00000001079 * cos(4.20190952106 +    1044.64789414570 * t)
  +  0.00000001085 * cos(2.22740147584 +     141.20899490900 * t)
  +  0.00000001245 * cos(5.83769374356 +     179.91817716280 * t)
  +  0.00000001146 * cos(0.33774172888 +     220.54458533771 * t)
  +  0.00000001196 * cos(3.17156910173 +    1460.20038475780 * t)
  +  0.00000001136 * cos(2.05466340621 +     480.00777927849 * t)
  +  0.00000001119 * cos(5.41354135574 +    1534.98198332510 * t)
  +  0.00000001056 * cos(3.62871723489 +     437.40007365639 * t)
  +  0.00000001032 * cos(2.32675902580 +     184.97110483931 * t)
  +  0.00000001032 * cos(2.56286714079 +     242.11472100371 * t)
  +  0.00000001039 * cos(2.32832376555 +    1791.08247297440 * t)
  +  0.00000001061 * cos(2.50615202413 +     938.63685074779 * t)
  +  0.00000001123 * cos(3.96404102873 +   25668.17468021549 * t)
  +  0.00000001103 * cos(5.86207947745 +     210.60759739969 * t)
  +  0.00000001015 * cos(4.05475486800 +     252.41215386970 * t)
  +  0.00000000979 * cos(5.22245385112 +     610.44852130189 * t)
  +  0.00000000979 * cos(2.08086119753 +     610.93615626891 * t)
  +  0.00000001043 * cos(3.45408554292 +      17.91542978119 * t)
  +  0.00000001128 * cos(3.92351069480 +     398.53083270820 * t)
  +  0.00000001035 * cos(3.02168366647 +     235.68919520349 * t)
  +  0.00000001072 * cos(4.53150424448 +     746.15463932291 * t)
  +  0.00000001131 * cos(3.37345520465 +    5481.99837586430 * t)
  +  0.00000000986 * cos(5.28602240316 +     192.44835013500 * t)
  +  0.00000001287 * cos(1.95273113714 +     314.18800658530 * t)
  +  0.00000000973 * cos(3.85435039011 +     561.69047652550 * t)
  +  0.00000001298 * cos(1.08374685926 +     614.38067456499 * t)
  +  0.00000001151 * cos(1.20704230584 +     905.64276230799 * t)
  +  0.00000001279 * cos(5.88520431436 +     322.36782729660 * t)
  +  0.00000000963 * cos(3.50426087646 +     782.59075393131 * t)
  +  0.00000001064 * cos(5.75961632886 +    1372.34858862460 * t)
  +  0.00000000973 * cos(3.52289496745 +      24.62283987170 * t)
  +  0.00000001096 * cos(5.06936627625 +     731.92754532131 * t)
  +  0.00000001080 * cos(6.27980868199 +    2906.65687133950 * t)
  +  0.00000001200 * cos(2.31102641105 +     195.64679021520 * t)
  +  0.00000000993 * cos(1.95529510745 +    6062.90702503610 * t)
  +  0.00000001039 * cos(1.07426067099 +    1159.04949318660 * t)
  +  0.00000000952 * cos(2.30173432343 +     239.88198089750 * t)
  +  0.00000001181 * cos(0.98375947358 +    1468.32781584240 * t)
  +  0.00000001137 * cos(2.73354004808 +       2.69149803831 * t)
  +  0.00000000941 * cos(1.23572643410 +     124.18959773749 * t)
  +  0.00000000942 * cos(3.50129097588 +     115.11600514891 * t)
  +  0.00000001020 * cos(1.79568687186 +     196.38050339810 * t)
  +  0.00000001065 * cos(1.53835988752 +     494.23487328010 * t)
  +  0.00000000945 * cos(4.39156950811 +     121.00820399980 * t)
  +  0.00000000941 * cos(3.67244160492 +     120.01136625851 * t)
  +  0.00000000996 * cos(3.06866654160 +    4863.44173055270 * t)
  +  0.00000001059 * cos(4.47767598624 +   25653.94758621389 * t)
  +  0.00000000936 * cos(1.21580989528 +     307.07445958451 * t)
  +  0.00000000986 * cos(1.95558000476 +    5842.00674763030 * t)
  +  0.00000001061 * cos(3.92781056471 +     418.97770183331 * t)
  +  0.00000000941 * cos(5.52302459792 +      97.17169833279 * t)
  +  0.00000001049 * cos(3.59730911706 +     416.79314583689 * t)
  +  0.00000000956 * cos(2.39282306271 +     141.45507312490 * t)
  +  0.00000000922 * cos(4.97372856088 +    1364.48428209840 * t)
  +  0.00000001090 * cos(1.18314786349 +    1151.93594618579 * t)
  +  0.00000000945 * cos(5.48577517665 +     220.86890824340 * t)
  +  0.00000000945 * cos(2.54544364353 +     206.21691759960 * t)
  +  0.00000000906 * cos(2.01210100437 +   12779.69461290430 * t)
  +  0.00000000913 * cos(6.06812377280 +     285.61619850311 * t)
  +  0.00000000993 * cos(0.00718300554 +      73.05330837550 * t)
  +  0.00000000923 * cos(3.95449289739 +    1048.58004740881 * t)
  +  0.00000000910 * cos(2.91944659858 +    1250.83344258291 * t)
  +  0.00000001055 * cos(2.96570583025 +     287.69386416990 * t)
  +  0.00000000891 * cos(4.95995674723 +    4443.95708667750 * t)
  +  0.00000000890 * cos(3.44861046216 +     952.34018776010 * t)
  +  0.00000001011 * cos(3.98082100593 +     138.90432670610 * t)
  +  0.00000000943 * cos(2.88169222264 +    1368.41643536150 * t)
  +  0.00000001240 * cos(2.96642006057 +     105.78427225690 * t)
  +  0.00000001240 * cos(2.96642006057 +     105.29663728990 * t)
  +  0.00000000975 * cos(1.42837247530 +     700.90805668431 * t)
  +  0.00000000963 * cos(2.83983881025 +    5378.90560164571 * t)
  +  0.00000001131 * cos(3.49207338910 +     640.09291968770 * t)
  +  0.00000001014 * cos(3.84499571511 +     246.68001371321 * t)
  +  0.00000000922 * cos(3.37907074746 +    9772.21644384989 * t)
  +  0.00000000896 * cos(4.52407069260 +    1571.15746550260 * t)
  +  0.00000001121 * cos(5.34360557183 +    6467.68194047809 * t)
  +  0.00000000872 * cos(2.88021294314 +     519.63984183961 * t)
  +  0.00000001164 * cos(0.08165804323 +     739.04109232210 * t)
  +  0.00000001090 * cos(2.12969540273 +    1699.03539901970 * t)
  +  0.00000001180 * cos(2.44363933993 +     636.47207509279 * t)
  +  0.00000000912 * cos(4.11625838132 +      31.26330612050 * t)
  +  0.00000000892 * cos(3.93430854425 +     212.57970507500 * t)
  +  0.00000000892 * cos(3.93430854425 +     212.09207010800 * t)
  +  0.00000000985 * cos(5.09403476262 +     988.02554284310 * t)
  +  0.00000000860 * cos(4.51926390946 +    1585.38455950421 * t)
  +  0.00000000990 * cos(0.10745457981 +    3149.44778508089 * t)
  +  0.00000001177 * cos(0.16333880643 +    1328.79643488791 * t)
  +  0.00000000864 * cos(1.23920060185 +   12146.42323862409 * t)
  +  0.00000001007 * cos(2.26868943041 +     685.23011986920 * t)
  +  0.00000001007 * cos(5.41028208400 +     685.71775483620 * t)
  +  0.00000000853 * cos(5.50195803246 +    2641.58509595570 * t)
  +  0.00000000993 * cos(2.58838169596 +    2111.89413086110 * t)
  +  0.00000000844 * cos(4.99931164886 +    1239.78774231901 * t)
  +  0.00000000846 * cos(3.17548903050 +    2115.07552459880 * t)
  +  0.00000000964 * cos(2.75317670197 +     756.56720014041 * t)
  +  0.00000000981 * cos(1.46114906045 +    1471.24608502170 * t)
  +  0.00000001164 * cos(6.03626063674 +    3391.68870348911 * t)
  +  0.00000000885 * cos(3.21468341749 +     609.12161516050 * t)
  +  0.00000000821 * cos(0.43214580939 +     388.22133775470 * t)
  +  0.00000000906 * cos(2.38644851609 +     327.19375243699 * t)
  +  0.00000000903 * cos(3.04044650688 +     477.24458453860 * t)
  +  0.00000000841 * cos(3.88859140273 +     473.31243127551 * t)
  +  0.00000000904 * cos(0.75775511775 +     635.47523735150 * t)
  +  0.00000000822 * cos(0.09352704461 +    1365.23504162379 * t)
  +  0.00000000997 * cos(0.25000097268 +     123.29582586020 * t)
  +  0.00000000879 * cos(5.54528283460 +    3362.74688051889 * t)
  +  0.00000000846 * cos(1.99050608386 +     227.81819103291 * t)
  +  0.00000000846 * cos(6.04071273632 +     199.26763481011 * t)
  +  0.00000000947 * cos(4.80416752233 +     222.61650551010 * t)
  +  0.00000000875 * cos(3.48686422480 +    9993.11672125570 * t)
  +  0.00000001117 * cos(0.69343471577 +     319.08336769490 * t)
  +  0.00000000800 * cos(5.83577165546 +     834.79331700380 * t)
  +  0.00000000839 * cos(6.01134529585 +     206.64181424181 * t)
  +  0.00000000839 * cos(2.01987352433 +     220.44401160121 * t)
  +  0.00000000838 * cos(3.26925163574 +    2442.51309451930 * t)
  +  0.00000000830 * cos(2.56385471112 +    1891.48148842230 * t)
  +  0.00000000841 * cos(1.50960565043 +      60.04756252381 * t)
  +  0.00000000826 * cos(3.67482294787 +     220.13519506050 * t)
  +  0.00000000854 * cos(1.21615128625 +     540.22972331660 * t)
  +  0.00000000842 * cos(5.83341675596 +    2854.39655642670 * t)
  +  0.00000000858 * cos(5.69541304884 +     781.83999440590 * t)
  +  0.00000000860 * cos(2.63629505046 +    5436.74919775670 * t)
  +  0.00000000785 * cos(2.62141651385 +    3494.29384274070 * t)
  ) * t;
}

double saturn_x2(double t) {
  return (
     0.00862721930 * cos(2.44701762869 +     213.54291292150 * t)
  +  0.00611630287 * cos(2.28479450822 +       0.24381748350 * t)
  +  0.00561413805 * cos(1.25489421778 +     206.42936592071 * t)
  +  0.00547271370 * cos(3.61668298145 +     220.65645992230 * t)
  +  0.00234984093 * cos(2.44660941367 +     426.84200835950 * t)
  +  0.00088108317 * cos(4.86838582414 +       7.35736448430 * t)
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  +  0.00000003544 * cos(2.13015052882 +     114.64292439690 * t)
  +  0.00000003999 * cos(3.22701633780 +     326.93062787860 * t)
  +  0.00000003152 * cos(1.19755571878 +     151.29148732640 * t)
  +  0.00000003262 * cos(5.70768338968 +    1272.43720814370 * t)
  +  0.00000003054 * cos(0.93612488497 +     749.85979004990 * t)
  +  0.00000003350 * cos(5.35233532300 +     212.57970507500 * t)
  +  0.00000003340 * cos(2.68186323180 +     214.50612076800 * t)
  +  0.00000003138 * cos(0.69922169045 +     320.56784040320 * t)
  +  0.00000003732 * cos(4.18854031121 +     611.19928082730 * t)
  +  0.00000003741 * cos(0.62303283965 +     849.50804597240 * t)
  +  0.00000003047 * cos(1.79037915226 +     230.80838830890 * t)
  +  0.00000003048 * cos(5.94415826698 +      21.09682351890 * t)
  +  0.00000002851 * cos(4.73186877358 +    6069.53293706989 * t)
  +  0.00000002864 * cos(6.09139978110 +    9999.74263328950 * t)
  +  0.00000002898 * cos(2.37720286549 +     213.49472881170 * t)
  +  0.00000002898 * cos(5.65686211315 +     213.59109703130 * t)
  +  0.00000002819 * cos(6.19576518658 +     431.50787480550 * t)
  +  0.00000003469 * cos(4.96542567369 +     526.75338884040 * t)
  +  0.00000003327 * cos(3.15421993340 +    1581.71553079950 * t)
  +  0.00000002927 * cos(2.32768555098 +     395.82251972250 * t)
  +  0.00000003762 * cos(0.62502984773 +      38.37685312130 * t)
  +  0.00000002893 * cos(6.25258908606 +     381.59542572090 * t)
  +  0.00000003707 * cos(1.85956087078 +     215.99059347631 * t)
  +  0.00000002804 * cos(3.11861161896 +     260.01333583751 * t)
  +  0.00000002799 * cos(0.07347298152 +     129.67565967810 * t)
  +  0.00000003378 * cos(1.60714359099 +     299.37021175271 * t)
  +  0.00000002783 * cos(5.69238885511 +    1287.15193711231 * t)
  +  0.00000003526 * cos(6.21925842594 +     211.09523236671 * t)
  +  0.00000002541 * cos(5.29829781548 +     414.31183538731 * t)
  +  0.00000002607 * cos(3.83630269401 +     276.79117625789 * t)
  +  0.00000002465 * cos(1.10299698027 +     572.47305223100 * t)
  +  0.00000002461 * cos(3.95494769587 +     409.43352062020 * t)
  +  0.00000002462 * cos(5.12829780057 +      59.55992755679 * t)
  +  0.00000002579 * cos(4.98684783023 +    1493.33748554950 * t)
  +  0.00000002414 * cos(5.95835828919 +     343.46239008310 * t)
  +  0.00000002533 * cos(3.91175931336 +     696.76345510010 * t)
  +  0.00000002390 * cos(5.50027750787 +    1588.82907780029 * t)
  +  0.00000002433 * cos(3.53308752088 +    6070.02057203690 * t)
  +  0.00000002747 * cos(3.63141908197 +     216.98743121760 * t)
  +  0.00000002420 * cos(4.62294661622 +      45.33283355520 * t)
  +  0.00000002297 * cos(2.61803220390 +      99.66756299740 * t)
  +  0.00000002813 * cos(5.66780576556 +     422.17614191350 * t)
  +  0.00000002913 * cos(2.14239548593 +     551.27542358051 * t)
  +  0.00000002860 * cos(5.75550548585 +      69.39634175830 * t)
  +  0.00000002387 * cos(3.66176528516 +    1169.83206889211 * t)
  +  0.00000002258 * cos(3.42521115550 +     188.27011865600 * t)
  +  0.00000002293 * cos(4.30779033149 +      98.91680347199 * t)
  +  0.00000002711 * cos(4.38875028285 +    1795.01462623750 * t)
  +  0.00000002337 * cos(4.98618107601 +   10000.23026825651 * t)
  +  0.00000002777 * cos(1.92096933827 +     100.15519796440 * t)
  +  0.00000003022 * cos(4.27657430351 +     190.96387742670 * t)
  +  0.00000002327 * cos(2.43188651345 +     143.90275367970 * t)
  +  0.00000002152 * cos(4.96770554275 +     189.16389053330 * t)
  +  0.00000002147 * cos(5.81368882353 +     265.74547599400 * t)
  +  0.00000002162 * cos(4.60033037919 +     238.81570718700 * t)
  +  0.00000002184 * cos(4.98321991931 +     917.17609753890 * t)
  +  0.00000002297 * cos(5.88374894966 +     533.11617631580 * t)
  +  0.00000002099 * cos(3.63180133150 +     275.79433851660 * t)
  +  0.00000002122 * cos(0.04103472829 +      93.18466331550 * t)
  +  0.00000002068 * cos(3.90345993566 +     221.61966776881 * t)
  +  0.00000002635 * cos(4.32616395006 +     646.76701583129 * t)
  +  0.00000002175 * cos(5.63002332525 +     432.47108265200 * t)
  +  0.00000002049 * cos(4.11329374307 +     205.46615807421 * t)
  +  0.00000002103 * cos(3.07406244371 +     554.31380496631 * t)
  +  0.00000002036 * cos(4.06354766916 +     415.30867312860 * t)
  +  0.00000002045 * cos(4.55001787181 +     547.20025796550 * t)
  +  0.00000001996 * cos(4.73453786942 +    5642.93474619389 * t)
  +  0.00000002709 * cos(2.90208204814 +     174.18603700630 * t)
  +  0.00000002499 * cos(3.91734791042 +     927.59115048390 * t)
  +  0.00000002481 * cos(2.24814867939 +      91.80325647120 * t)
  +  0.00000002555 * cos(1.49254264738 +     196.86813836510 * t)
  +  0.00000002555 * cos(0.25549086562 +     230.21768747790 * t)
  +  0.00000002082 * cos(3.81823920275 +     832.09955823310 * t)
  +  0.00000002231 * cos(2.05013884781 +    2097.17940189250 * t)
  +  0.00000002095 * cos(2.74501129194 +    1140.89024592190 * t)
  +  0.00000001920 * cos(1.50789835321 +      99.40443843901 * t)
  +  0.00000001910 * cos(2.52768436921 +     106.78110999820 * t)
  +  0.00000002301 * cos(3.33597408639 +    2008.31372167550 * t)
  +  0.00000002228 * cos(0.13234013389 +     219.69325207580 * t)
  +  0.00000002219 * cos(1.60488882515 +     207.39257376720 * t)
  +  0.00000002444 * cos(2.58833940963 +      71.09326278771 * t)
  +  0.00000001950 * cos(5.91966225582 +     417.28078080390 * t)
  +  0.00000001941 * cos(3.37602923994 +     374.15181032000 * t)
  +  0.00000001900 * cos(3.19545181564 +     333.41352756050 * t)
  +  0.00000002353 * cos(1.38929393306 +     650.43604453600 * t)
  +  0.00000001819 * cos(3.03945359046 +     120.74507944141 * t)
  +  0.00000001992 * cos(1.67941763290 +    2413.57127154910 * t)
  +  0.00000001805 * cos(6.12365686072 +    9573.14444241349 * t)
  +  0.00000002272 * cos(6.07077392017 +     135.57992061650 * t)
  +  0.00000001823 * cos(5.32795961259 +     425.87880051300 * t)
  +  0.00000002143 * cos(5.66066380057 +     347.64062156210 * t)
  +  0.00000001841 * cos(0.46818772275 +     220.70464403210 * t)
  +  0.00000001834 * cos(1.26884124633 +     206.38118181090 * t)
  +  0.00000001777 * cos(2.67341880565 +     116.18227885939 * t)
  +  0.00000002138 * cos(2.15400406449 +    2104.29294889330 * t)
  +  0.00000001887 * cos(4.94905172419 +     556.76148552110 * t)
  +  0.00000002390 * cos(0.57829722827 +     856.62159297321 * t)
  +  0.00000001825 * cos(1.86446865071 +     345.08987514331 * t)
  +  0.00000001730 * cos(6.28021453291 +     237.92193530970 * t)
  +  0.00000002103 * cos(2.59628252508 +    2207.38572311189 * t)
  +  0.00000001779 * cos(2.78871624346 +     427.80521620600 * t)
  +  0.00000001911 * cos(2.02159497354 +     145.87486135500 * t)
  +  0.00000001811 * cos(1.03042062457 +     570.98857952271 * t)
  +  0.00000001710 * cos(2.50465838575 +     423.17297965479 * t)
  +  0.00000002261 * cos(3.11062462322 +     421.42538238810 * t)
  +  0.00000001681 * cos(4.98403310748 +     305.85311143459 * t)
  +  0.00000002093 * cos(1.52224482636 +    1169.34443392509 * t)
  +  0.00000002071 * cos(2.14859681048 +     942.30587945250 * t)
  +  0.00000001691 * cos(2.43995589654 +     455.29619636271 * t)
  +  0.00000002080 * cos(3.36200869452 +     405.01373239010 * t)
  +  0.00000001764 * cos(2.79871492543 +     186.71620997851 * t)
  +  0.00000001662 * cos(5.22917796645 +     305.58998687620 * t)
  +  0.00000001748 * cos(3.36057980101 +     899.01685027420 * t)
  +  0.00000001696 * cos(1.59892728325 +      85.17734443740 * t)
  +  0.00000002142 * cos(1.99415297086 +    2001.20017467470 * t)
  +  0.00000002282 * cos(2.04372303495 +     439.37218133171 * t)
  +  0.00000001748 * cos(0.82946401625 +    1066.25165970650 * t)
  +  0.00000001908 * cos(6.13391971195 +     131.64776735340 * t)
  +  0.00000001808 * cos(2.51335072478 +    1457.28211557850 * t)
  +  0.00000001794 * cos(5.82136110186 +     913.24394427581 * t)
  +  0.00000002167 * cos(6.18131622353 +     563.87503252191 * t)
  +  0.00000001602 * cos(3.41843479847 +     327.68138740401 * t)
  +  0.00000001891 * cos(3.37025921442 +    1155.60497489050 * t)
  +  0.00000002205 * cos(1.14231592076 +     388.70897272171 * t)
  +  0.00000001597 * cos(5.72890255976 +     281.21096448800 * t)
  +  0.00000001719 * cos(2.72910423965 +     312.44290144610 * t)
  +  0.00000002158 * cos(0.71647260532 +     224.10097821840 * t)
  +  0.00000001659 * cos(0.02762995097 +     561.42735196710 * t)
  +  0.00000001737 * cos(1.74569938692 +     167.96626188280 * t)
  +  0.00000001501 * cos(4.96905771055 +     312.96665843540 * t)
  +  0.00000001587 * cos(2.37695905463 +     732.45130231059 * t)
  +  0.00000001488 * cos(1.15017207061 +      12.28635548869 * t)
  +  0.00000001460 * cos(3.68257556907 +    2627.35800195410 * t)
  +  0.00000001835 * cos(4.46496396099 +     206.47755003051 * t)
  +  0.00000001708 * cos(5.28688437379 +      82.13896305161 * t)
  +  0.00000001842 * cos(3.55522181358 +     220.60827581251 * t)
  +  0.00000001895 * cos(5.04728306015 +     291.50590522650 * t)
  +  0.00000001423 * cos(0.90600055739 +     225.32232636830 * t)
  +  0.00000001423 * cos(0.84203295561 +     201.76349947470 * t)
  +  0.00000001568 * cos(0.17276009703 +     685.71775483620 * t)
  +  0.00000001663 * cos(2.39240670265 +    3597.87425192630 * t)
  +  0.00000001491 * cos(2.09091136066 +     240.36961586451 * t)
  +  0.00000001913 * cos(1.64595427075 +     295.43805848960 * t)
  +  0.00000001496 * cos(3.10700890764 +    1045.39865367110 * t)
  +  0.00000001477 * cos(5.34776911444 +     440.58146739410 * t)
  +  0.00000001410 * cos(3.85254018400 +     137.27684164590 * t)
  +  0.00000001748 * cos(3.62192812061 +     519.15220687259 * t)
  +  0.00000001325 * cos(2.98811767557 +     980.91199584231 * t)
  +  0.00000001352 * cos(5.53324653057 +    5429.63565075589 * t)
  +  0.00000001414 * cos(6.21378141122 +    1371.59782909919 * t)
  +  0.00000001697 * cos(2.96957793002 +    1898.10740045609 * t)
  +  0.00000001424 * cos(3.32164076256 +     721.40560204669 * t)
  +  0.00000001424 * cos(3.32164076256 +     721.89323701370 * t)
  +  0.00000001295 * cos(5.37619224276 +    1905.22094745690 * t)
  +  0.00000001272 * cos(5.72341064428 +     127.71561409031 * t)
  +  0.00000001740 * cos(2.98134401594 +    1883.88030645450 * t)
  +  0.00000001435 * cos(1.83931362023 +     699.94484883781 * t)
  +  0.00000001260 * cos(0.96015330455 +     850.25880549781 * t)
  +  0.00000001316 * cos(0.48574200131 +    1382.64352936309 * t)
  +  0.00000001303 * cos(4.34276081528 +      28.69800548670 * t)
  +  0.00000001701 * cos(3.01361282532 +     312.70353387701 * t)
  +  0.00000001245 * cos(0.67360153650 +    9359.84534697549 * t)
  +  0.00000001240 * cos(1.28978443782 +    1994.08662767389 * t)
  +  0.00000001286 * cos(2.12726478428 +    1048.84317196720 * t)
  +  0.00000001240 * cos(0.05914920282 +     148.32254190981 * t)
  +  0.00000001365 * cos(2.52639842443 +     212.79215339611 * t)
  +  0.00000001362 * cos(5.50511551601 +     214.29367244690 * t)
  +  0.00000001206 * cos(2.27873859730 +     739.56484931140 * t)
  +  0.00000001503 * cos(3.64035751539 +    1243.98302014049 * t)
  +  0.00000001305 * cos(3.14322057429 +     259.11956396020 * t)
  +  0.00000001167 * cos(3.43763509907 +     233.18663289450 * t)
  +  0.00000001167 * cos(4.59358372111 +     193.89919294850 * t)
  +  0.00000001155 * cos(2.09477644020 +     153.73916788121 * t)
  +  0.00000001220 * cos(4.50978581010 +     283.90472325870 * t)
  +  0.00000001153 * cos(1.49807886709 +     525.74199688410 * t)
  +  0.00000001188 * cos(1.37272384469 +     258.63192899320 * t)
  +  0.00000001558 * cos(6.24300347417 +    4216.43089723790 * t)
  +  0.00000001423 * cos(2.20117675779 +    2420.68481854989 * t)
  +  0.00000001138 * cos(5.47453297293 +      17.91542978119 * t)
  +  0.00000001133 * cos(1.27426244635 +     841.90686400460 * t)
  +  0.00000001109 * cos(5.77014938471 +     121.00820399980 * t)
  +  0.00000001109 * cos(1.74252937792 +     629.84616305900 * t)
  +  0.00000001434 * cos(2.33577168517 +    6062.41939006910 * t)
  +  0.00000001122 * cos(4.02937359406 +     128.60938596760 * t)
  +  0.00000001123 * cos(4.63883211615 +    3178.38960805111 * t)
  +  0.00000001154 * cos(5.89138208590 +      67.91186905000 * t)
  +  0.00000001130 * cos(3.68532102062 +     731.70054278519 * t)
  +  0.00000001305 * cos(3.82341882270 +      97.11681657861 * t)
  +  0.00000001248 * cos(2.25171827957 +    2523.77759276850 * t)
  +  0.00000001161 * cos(3.82920355830 +      81.99595069970 * t)
  +  0.00000001178 * cos(2.27177304436 +    1056.44435393500 * t)
  +  0.00000001342 * cos(0.90865804529 +     355.99256305531 * t)
  +  0.00000001249 * cos(3.35095586398 +     526.26575387340 * t)
  +  0.00000001034 * cos(6.13425127848 +     777.17412795991 * t)
  +  0.00000001332 * cos(3.33641634482 +     835.54407652920 * t)
  +  0.00000001024 * cos(4.46551378693 +    5635.82119919310 * t)
  +  0.00000001173 * cos(2.59368230210 +      74.53778108379 * t)
  +  0.00000001173 * cos(1.88536238484 +    2317.59204433130 * t)
  +  0.00000001012 * cos(4.43552013111 +     215.23983395090 * t)
  +  0.00000001186 * cos(4.99759781142 +    1272.92484311070 * t)
  +  0.00000001049 * cos(2.89184213238 +    6062.90702503610 * t)
  +  0.00000001154 * cos(1.74865938292 +    2406.45772454830 * t)
  +  0.00000001062 * cos(4.97332239252 +     906.13039727500 * t)
  +  0.00000001124 * cos(2.19046669320 +    3914.26612158291 * t)
  +  0.00000000993 * cos(3.56282013143 +     211.84599189210 * t)
  +  0.00000000986 * cos(4.64695151983 +     525.51499434800 * t)
  +  0.00000000986 * cos(1.18009463616 +     602.00806815971 * t)
  +  0.00000000992 * cos(1.73454490947 +     306.34074640161 * t)
  +  0.00000001239 * cos(2.83323142368 +    2193.15862911030 * t)
  +  0.00000001134 * cos(1.51692947764 +    2729.96314120569 * t)
  +  0.00000001041 * cos(0.96856014126 +     945.75039774860 * t)
  +  0.00000001025 * cos(4.65212942292 +      32.48714639791 * t)
  +  0.00000001044 * cos(3.13333997041 +     472.41865939820 * t)
  +  0.00000001335 * cos(3.23250354837 +    2324.70559133209 * t)
  +  0.00000001199 * cos(5.97883679965 +    4113.33812301930 * t)
  +  0.00000001174 * cos(6.24416585602 +    1176.94561589290 * t)
  +  0.00000001213 * cos(1.85427016032 +     252.89978883670 * t)
  +  0.00000000973 * cos(3.32855151003 +     245.03548231051 * t)
  +  0.00000000973 * cos(1.56107465656 +     182.05034353251 * t)
  +  0.00000001167 * cos(4.51079844988 +     635.72131556739 * t)
  +  0.00000000936 * cos(4.89205060352 +     220.13519506050 * t)
  +  0.00000001073 * cos(2.28404354413 +    1773.67398523510 * t)
  +  0.00000000931 * cos(3.12796311727 +     206.95063078250 * t)
  +  0.00000000931 * cos(4.22108011413 +    1582.20316576650 * t)
  +  0.00000001237 * cos(5.91198768163 +    2964.60287764609 * t)
  +  0.00000001074 * cos(3.43802549251 +     738.81408978600 * t)
  +  0.00000000976 * cos(4.61137219155 +      31.99951143090 * t)
  +  0.00000000907 * cos(5.15190704681 +    1802.61580820530 * t)
  +  0.00000000925 * cos(4.33653627215 +    3494.78147770770 * t)
  +  0.00000000999 * cos(5.63756377401 +     171.89841514590 * t)
  +  0.00000000931 * cos(3.19108655615 +    1037.79747170330 * t)
  +  0.00000001094 * cos(2.28588137520 +    2516.66404576769 * t)
  +  0.00000000949 * cos(5.39859475117 +    1809.72935520611 * t)
  +  0.00000000964 * cos(4.14879961487 +    2641.58509595570 * t)
  +  0.00000000947 * cos(4.37174355210 +    2111.40649589409 * t)
  +  0.00000000898 * cos(5.87505951681 +    9566.03089541269 * t)
  +  0.00000001029 * cos(4.83213149276 +     519.63984183961 * t)
  +  0.00000000989 * cos(5.52532133338 +     255.18741069710 * t)
  +  0.00000001003 * cos(2.89315844222 +      60.52313540329 * t)
  +  0.00000000886 * cos(5.44090853481 +     305.10235190919 * t)
  +  0.00000000920 * cos(3.26822857927 +     459.08533727390 * t)
  +  0.00000000888 * cos(6.08377383987 +    3259.65410630030 * t)
  +  0.00000000888 * cos(6.08377383987 +    3260.14174126730 * t)
  +  0.00000000960 * cos(4.90164911800 +      84.68970947040 * t)
  +  0.00000000881 * cos(5.34840991118 +     397.90018538930 * t)
  +  0.00000000924 * cos(0.50062273312 +     731.92754532131 * t)
  +  0.00000000960 * cos(4.40263473154 +    5856.72147659890 * t)
  +  0.00000000886 * cos(4.84941446555 +     471.93102443120 * t)
  +  0.00000000909 * cos(2.87462833456 +     746.15463932291 * t)
  ) * pow(t, 2);
}

double saturn_x3(double t) {
  return (
     0.00076886822 * cos(2.95726755259 +     206.42936592071 * t)
  +  0.00075865107 * cos(1.87343394188 +     220.65645992230 * t)
  +  0.00028377246 * cos(3.86557149479 +       0.24381748350 * t)
  +  0.00011451297 * cos(0.52950959639 +     426.84200835950 * t)
  +  0.00009043324 * cos(0.90644151923 +     433.95555536030 * t)
  +  0.00007419530 * cos(1.78113005821 +     227.77000692311 * t)
  +  0.00008292033 * cos(3.07262247518 +       7.35736448430 * t)
  +  0.00004421142 * cos(2.21157518590 +     419.72846135871 * t)
  +  0.00003519324 * cos(3.11036333131 +     199.31581891990 * t)
  +  0.00003064445 * cos(5.96466087519 +     640.14110379750 * t)
  +  0.00002363042 * cos(3.04029814628 +      14.47091148511 * t)
  +  0.00001027777 * cos(0.00466674598 +     647.25465079831 * t)
  +  0.00000789743 * cos(0.89493947314 +     441.06910236111 * t)
  +  0.00000810744 * cos(1.27206560500 +     216.72430665921 * t)
  +  0.00000766386 * cos(3.60274923273 +     210.36151918381 * t)
  +  0.00000673097 * cos(3.76715088659 +     213.05527795450 * t)
  +  0.00000506614 * cos(3.74427289102 +     213.54291292150 * t)
  +  0.00000384956 * cos(3.04387305073 +     117.56368570370 * t)
  +  0.00000463540 * cos(5.12353455374 +     853.44019923550 * t)
  +  0.00000411246 * cos(3.75278799309 +     110.45013870291 * t)
  +  0.00000324142 * cos(1.64931862119 +     234.88355392390 * t)
  +  0.00000285917 * cos(1.98200727487 +     412.61491435790 * t)
  +  0.00000238406 * cos(3.32280489930 +     103.33659170210 * t)
  +  0.00000192441 * cos(0.61468306333 +     316.63568714010 * t)
  +  0.00000189600 * cos(5.40892808690 +       6.86972951729 * t)
  +  0.00000189610 * cos(2.26186337972 +     633.02755679670 * t)
  +  0.00000213874 * cos(5.57078419443 +     205.94173095370 * t)
  +  0.00000153605 * cos(2.27746123288 +     323.74923414091 * t)
  +  0.00000154083 * cos(2.88123748841 +      21.58445848590 * t)
  +  0.00000130169 * cos(1.38079516386 +     209.61075965840 * t)
  +  0.00000121811 * cos(5.19039452998 +     198.82818395289 * t)
  +  0.00000112652 * cos(4.50657670209 +     220.16882495529 * t)
  +  0.00000109203 * cos(3.33018599514 +     217.47506618460 * t)
  +  0.00000111589 * cos(5.41300222633 +     860.55374623631 * t)
  +  0.00000097336 * cos(0.97161200873 +      95.73540973430 * t)
  +  0.00000114728 * cos(1.16141976921 +     223.83785366000 * t)
  +  0.00000085497 * cos(1.88744465241 +     330.86278114170 * t)
  +  0.00000103793 * cos(2.96083959404 +     309.52214013930 * t)
  +  0.00000085243 * cos(0.03105121395 +     654.36819779910 * t)
  +  0.00000081972 * cos(3.29167838280 +     192.20227191910 * t)
  +  0.00000093735 * cos(3.09844453957 +     426.35437339250 * t)
  +  0.00000078232 * cos(1.55716671048 +     124.67723270450 * t)
  +  0.00000073732 * cos(1.05194572850 +      88.62186273350 * t)
  +  0.00000068659 * cos(3.09861369147 +     109.96250373590 * t)
  +  0.00000087657 * cos(0.36385164600 +     430.02340209721 * t)
  +  0.00000057790 * cos(1.70437193383 +     224.58861318540 * t)
  +  0.00000050888 * cos(3.09413498180 +     202.49721265760 * t)
  +  0.00000048029 * cos(3.83068266955 +     302.40859313851 * t)
  +  0.00000057606 * cos(3.83723480361 +     203.24797218300 * t)
  +  0.00000056960 * cos(4.32645734701 +    1066.73929467350 * t)
  +  0.00000045308 * cos(3.25423824441 +      96.22304470130 * t)
  +  0.00000048067 * cos(6.08559382039 +     309.03450517230 * t)
  +  0.00000036732 * cos(0.80231221541 +     448.18264936190 * t)
  +  0.00000038865 * cos(3.77730274172 +     625.91400979590 * t)
  +  0.00000043853 * cos(0.20832317981 +     422.90985509640 * t)
  +  0.00000036680 * cos(5.09355802388 +      13.98327651810 * t)
  +  0.00000035412 * cos(5.54558308698 +     522.82123557730 * t)
  +  0.00000030232 * cos(3.87085631365 +     412.12727939089 * t)
  +  0.00000034292 * cos(6.06837760251 +     301.92095817150 * t)
  +  0.00000025919 * cos(5.31578501663 +       4.17597074660 * t)
  +  0.00000026527 * cos(3.52104928312 +     423.66061462181 * t)
  +  0.00000023623 * cos(4.82567426056 +     515.22005360950 * t)
  +  0.00000017831 * cos(5.24620312943 +      11.28951774740 * t)
  +  0.00000017289 * cos(0.98528821511 +     537.04832957890 * t)
  +  0.00000016881 * cos(5.38329398416 +     195.38366565681 * t)
  +  0.00000013511 * cos(5.72506783696 +     515.70768857651 * t)
  +  0.00000012893 * cos(1.12369483024 +     437.88770862340 * t)
  +  0.00000011197 * cos(2.55648325655 +     742.74624304909 * t)
  +  0.00000013451 * cos(5.19262853301 +     522.33360061030 * t)
  +  0.00000010292 * cos(0.86377999055 +     337.97632814250 * t)
  +  0.00000011481 * cos(5.27139699788 +     191.71463695210 * t)
  +  0.00000011394 * cos(5.93878680228 +     625.42637482889 * t)
  +  0.00000011380 * cos(4.58881936707 +    1073.85284167431 * t)
  +  0.00000009884 * cos(0.96968966802 +     131.79077970531 * t)
  +  0.00000009268 * cos(1.28597973750 +      81.50831573269 * t)
  +  0.00000010374 * cos(0.94317330721 +     544.16187657970 * t)
  +  0.00000011913 * cos(0.32742179509 +     437.13694909800 * t)
  +  0.00000008626 * cos(3.66458258994 +     728.51914904750 * t)
  +  0.00000008671 * cos(4.32466808269 +     419.24082639170 * t)
  +  0.00000008821 * cos(4.57655314696 +     831.61192326610 * t)
  +  0.00000008112 * cos(0.50007270362 +     149.80701461810 * t)
  +  0.00000009768 * cos(5.81884437871 +     618.31282782810 * t)
  +  0.00000008329 * cos(5.47343196835 +     867.66729323710 * t)
  +  0.00000007645 * cos(2.39585916890 +     846.32665223470 * t)
  +  0.00000008659 * cos(5.79445660573 +     643.32249753521 * t)
  +  0.00000007205 * cos(4.39953882951 +     227.28237195610 * t)
  +  0.00000007157 * cos(5.63667649779 +     636.20895053440 * t)
  +  0.00000007036 * cos(2.63239333334 +     231.70216018621 * t)
  +  0.00000007083 * cos(4.84184174066 +      89.10949770051 * t)
  +  0.00000006556 * cos(2.67135559119 +     743.23387801611 * t)
  +  0.00000005903 * cos(0.87375775835 +     270.16526422410 * t)
  +  0.00000006615 * cos(3.63831273611 +     433.46792039329 * t)
  +  0.00000006469 * cos(2.05411382166 +     408.68276109481 * t)
  +  0.00000005426 * cos(1.51765079988 +     241.99710092470 * t)
  +  0.00000005648 * cos(2.55416366478 +     529.93478257810 * t)
  +  0.00000007105 * cos(3.01903914273 +      18.40306474821 * t)
  +  0.00000005052 * cos(5.18252086135 +     416.54706762100 * t)
  +  0.00000006189 * cos(4.68404979693 +     736.12033101530 * t)
  +  0.00000005821 * cos(3.50616955116 +    1280.03839011150 * t)
  +  0.00000005043 * cos(3.76766161323 +     277.27881122490 * t)
  +  0.00000004744 * cos(1.46479508366 +      56.37853381910 * t)
  +  0.00000005705 * cos(4.87015493433 +     430.77416162260 * t)
  +  0.00000005226 * cos(5.29097572967 +     415.79630809560 * t)
  +  0.00000005511 * cos(3.59570699682 +     529.44714761109 * t)
  +  0.00000004520 * cos(2.36588968635 +    1059.13811270570 * t)
  +  0.00000004583 * cos(0.00787099904 +     294.80741117069 * t)
  +  0.00000004789 * cos(4.15071050239 +     295.29504613770 * t)
  +  0.00000004026 * cos(0.04020873612 +     483.46435966210 * t)
  +  0.00000003728 * cos(0.24380479533 +     185.08872491831 * t)
  +  0.00000003578 * cos(2.51284387407 +     405.50136735710 * t)
  +  0.00000003890 * cos(0.29060160988 +     750.34742501690 * t)
  +  0.00000004291 * cos(5.60521207533 +     941.81824448550 * t)
  +  0.00000003758 * cos(6.26818424862 +     661.48174479990 * t)
  +  0.00000003547 * cos(0.40358942005 +      70.60562782070 * t)
  +  0.00000003641 * cos(3.81013693999 +     839.21310523390 * t)
  +  0.00000004196 * cos(3.97690464270 +     618.80046279510 * t)
  +  0.00000003709 * cos(4.96509425454 +     508.10650660869 * t)
  +  0.00000004193 * cos(5.05036487395 +     838.72547026689 * t)
  +  0.00000003571 * cos(4.46056188614 +    1148.00379292269 * t)
  +  0.00000003647 * cos(5.59898306379 +     934.70469748469 * t)
  +  0.00000002978 * cos(3.43782247022 +    1044.91101870410 * t)
  +  0.00000002876 * cos(5.29356968989 +     398.38782035631 * t)
  +  0.00000002643 * cos(5.23820067295 +     497.69145366371 * t)
  +  0.00000002725 * cos(5.89016060143 +     363.10611005610 * t)
  +  0.00000003246 * cos(2.57150474119 +     639.65346883050 * t)
  +  0.00000002721 * cos(4.14564904530 +    1464.39566257930 * t)
  +  0.00000002917 * cos(2.38362703069 +     113.63153244060 * t)
  +  0.00000002560 * cos(4.95049691984 +     729.00678401450 * t)
  +  0.00000002380 * cos(6.24323945584 +      86.07111631471 * t)
  +  0.00000002667 * cos(0.09012233039 +      10.80188278040 * t)
  +  0.00000002238 * cos(2.26341623480 +      10.53875822200 * t)
  +  0.00000002305 * cos(2.02658716121 +     956.53297345411 * t)
  +  0.00000002316 * cos(2.01244422105 +       3.42521122121 * t)
  +  0.00000002282 * cos(5.91510901442 +     611.19928082730 * t)
  +  0.00000001988 * cos(0.28661492755 +     651.18680406140 * t)
  +  0.00000002365 * cos(5.33155242941 +    2111.40649589409 * t)
  +  0.00000002485 * cos(4.32833388537 +     316.14805217309 * t)
  +  0.00000002670 * cos(0.63080955086 +     196.13442518220 * t)
  +  0.00000002670 * cos(1.11722396213 +     230.95140066080 * t)
  +  0.00000001974 * cos(3.29767644397 +    1059.62574767270 * t)
  +  0.00000002440 * cos(2.29714766763 +     106.03035047280 * t)
  +  0.00000002032 * cos(2.08292611476 +    1375.52998236229 * t)
  +  0.00000002151 * cos(4.69823758687 +     824.49837626530 * t)
  +  0.00000001875 * cos(1.50694339603 +     344.94686279140 * t)
  +  0.00000002440 * cos(1.37504875250 +     323.26159917390 * t)
  +  0.00000002034 * cos(5.64959382524 +     927.59115048390 * t)
  +  0.00000002310 * cos(4.84647061416 +      99.66756299740 * t)
  +  0.00000001764 * cos(1.86111058424 +     191.45151239371 * t)
  +  0.00000002032 * cos(3.74188450688 +     636.95971005981 * t)
  +  0.00000001993 * cos(5.41370582068 +    1258.21011414209 * t)
  +  0.00000001921 * cos(4.30051805390 +    2641.09746098870 * t)
  +  0.00000001620 * cos(5.90686570991 +    1596.43025976811 * t)
  +  0.00000001903 * cos(3.15206555826 +    2634.47154895491 * t)
  +  0.00000001568 * cos(3.03962897704 +     235.63431344930 * t)
  +  0.00000001835 * cos(0.46838409843 +     536.56069461190 * t)
  +  0.00000001523 * cos(4.48022908171 +     956.04533848709 * t)
  +  0.00000002086 * cos(1.63830662169 +     445.00125562421 * t)
  +  0.00000001666 * cos(1.70124586487 +    1876.76675945369 * t)
  +  0.00000001479 * cos(2.77539985198 +    6290.43321447570 * t)
  +  0.00000001479 * cos(5.26668359322 +    5849.12029463110 * t)
  +  0.00000001439 * cos(3.22610898757 +    2538.49232173710 * t)
  +  0.00000001464 * cos(4.18005026025 +    5863.34738863270 * t)
  +  0.00000001464 * cos(3.86203316672 +    6276.20612047410 * t)
  +  0.00000001676 * cos(5.34747324592 +    1251.09656714130 * t)
  +  0.00000001945 * cos(3.48549478580 +     845.83901726770 * t)
  +  0.00000001436 * cos(6.23499570787 +     508.59414157570 * t)
  +  0.00000001481 * cos(4.49861202018 +     284.39235822571 * t)
  +  0.00000001709 * cos(3.35714658968 +    2318.07967929830 * t)
  +  0.00000001305 * cos(4.10818846677 +     107.26874496520 * t)
  +  0.00000001548 * cos(2.81939196041 +    2943.74987161071 * t)
  +  0.00000001465 * cos(2.76905277973 +    2531.37877473630 * t)
  +  0.00000001494 * cos(3.94286053931 +    1780.78753223589 * t)
  +  0.00000001243 * cos(5.53319819376 +     218.20877936750 * t)
  +  0.00000001234 * cos(2.48191739575 +     208.87704647550 * t)
  +  0.00000001359 * cos(1.84182551916 +     142.69346761730 * t)
  +  0.00000001217 * cos(5.17100163408 +    1052.51220067191 * t)
  +  0.00000001352 * cos(0.35400553171 +     209.87388421679 * t)
  +  0.00000001391 * cos(5.36503473377 +    1243.98302014049 * t)
  +  0.00000001426 * cos(0.53946388105 +     852.95256426850 * t)
  +  0.00000001501 * cos(2.10731420473 +    1691.92185201890 * t)
  +  0.00000001326 * cos(6.28017468529 +    2751.79141717511 * t)
  +  0.00000001171 * cos(1.32902114795 +      67.91186905000 * t)
  +  0.00000001462 * cos(1.51066849209 +     160.85271488200 * t)
  +  0.00000001164 * cos(4.63302622392 +     117.07605073670 * t)
  +  0.00000001337 * cos(3.11900326329 +    2627.35800195410 * t)
  +  0.00000001509 * cos(4.93045095005 +    1574.60198379870 * t)
  +  0.00000001213 * cos(4.31502095540 +    1354.67697632690 * t)
  +  0.00000001241 * cos(4.40235607417 +    1140.89024592190 * t)
  +  0.00000001288 * cos(2.87027499482 +    2950.86341861150 * t)
  +  0.00000001337 * cos(3.78093252376 +    2421.17245351690 * t)
  +  0.00000001327 * cos(4.98650305262 +    1567.48843679789 * t)
  +  0.00000001118 * cos(3.03705756384 +     209.12312469139 * t)
  +  0.00000001043 * cos(3.94898504220 +     156.92056161890 * t)
  +  0.00000001069 * cos(3.08968284008 +     194.89603068979 * t)
  +  0.00000001088 * cos(2.53876092916 +    1272.92484311070 * t)
  +  0.00000001270 * cos(4.16462693224 +    2516.66404576769 * t)
  +  0.00000001032 * cos(3.44230149136 +    1361.30288836070 * t)
  +  0.00000001009 * cos(4.86702032393 +      52.44638055600 * t)
  +  0.00000001100 * cos(4.02565365863 +    1671.06884598351 * t)
  +  0.00000001071 * cos(2.74654865620 +    1354.18934135989 * t)
  +  0.00000001120 * cos(2.93643432204 +    1037.79747170330 * t)
  +  0.00000001271 * cos(1.45604360323 +     721.40560204669 * t)
  +  0.00000001009 * cos(2.57702574321 +    1670.58121101650 * t)
  +  0.00000001145 * cos(1.75945733161 +    3157.04896704871 * t)
  +  0.00000001072 * cos(0.27481402100 +    2435.39954751850 * t)
  +  0.00000001044 * cos(5.08425663596 +    1560.37488979710 * t)
  +  0.00000001195 * cos(2.65932688138 +     632.53992182970 * t)
  +  0.00000001043 * cos(3.11389723945 +    2729.96314120569 * t)
  +  0.00000000889 * cos(0.42212522834 +     359.17395679300 * t)
  +  0.00000000881 * cos(5.64403825823 +    1148.49142788971 * t)
  +  0.00000001040 * cos(3.92524025620 +    1773.67398523510 * t)
  +  0.00000001118 * cos(4.70881220655 +    1890.99385345530 * t)
  +  0.00000001047 * cos(2.54344637059 +    3260.14174126730 * t)
  +  0.00000001087 * cos(3.60856902528 +    2001.20017467470 * t)
  +  0.00000001087 * cos(3.60856902527 +    2001.68780964171 * t)
  +  0.00000000974 * cos(3.71347864898 +    1987.46071564010 * t)
  +  0.00000000869 * cos(1.74331052904 +     621.98185653281 * t)
  +  0.00000001085 * cos(2.89917981696 +    2214.98690507971 * t)
  +  0.00000000841 * cos(4.92696318078 +     629.09540353360 * t)
  +  0.00000000875 * cos(2.65002330643 +    2847.77064439291 * t)
  +  0.00000001063 * cos(4.38870058058 +    2200.27217611110 * t)
  +  0.00000000853 * cos(5.24982533241 +     288.32451148881 * t)
  +  0.00000001056 * cos(1.76497744402 +    2332.30677329990 * t)
  +  0.00000000888 * cos(5.03418369313 +    1155.11733992350 * t)
  +  0.00000001045 * cos(4.85721663734 +       2.93757625420 * t)
  +  0.00000000793 * cos(4.83325249319 +     341.01470952831 * t)
  +  0.00000000817 * cos(5.39128218727 +    1802.12817323829 * t)
  +  0.00000000780 * cos(5.10185484903 +    1382.64352936309 * t)
  +  0.00000000798 * cos(1.50816477183 +    2015.42726867629 * t)
  +  0.00000000798 * cos(4.64975742542 +    2015.91490364330 * t)
  +  0.00000000834 * cos(3.90981062264 +    1802.61580820530 * t)
  +  0.00000000766 * cos(5.01481205403 +    1471.50920958009 * t)
  +  0.00000000875 * cos(4.28307795111 +    2523.77759276850 * t)
  +  0.00000000829 * cos(2.87306260461 +    1162.23088692429 * t)
  +  0.00000000749 * cos(3.65030777836 +    1809.72935520611 * t)
  +  0.00000000942 * cos(1.83557306265 +    2008.31372167550 * t)
  +  0.00000000730 * cos(5.63130452905 +     138.76131435421 * t)
  +  0.00000000734 * cos(5.54620111084 +     749.85979004990 * t)
  +  0.00000000727 * cos(2.38685285770 +     181.29958400710 * t)
  +  0.00000000727 * cos(2.50277330889 +     245.78624183590 * t)
  +  0.00000000986 * cos(2.62709892303 +    1795.01462623750 * t)
  +  0.00000000914 * cos(3.38925031218 +     266.23311096100 * t)
  +  0.00000000774 * cos(0.28234439952 +    2840.16946242510 * t)
  +  0.00000000774 * cos(3.42393705311 +    2840.65709739210 * t)
  +  0.00000000806 * cos(4.44962138010 +    1912.82212942470 * t)
  +  0.00000000828 * cos(1.60210145147 +     100.15519796440 * t)
  +  0.00000000700 * cos(0.41140636858 +    9779.32999085069 * t)
  +  0.00000000700 * cos(4.19439623716 +   10220.64291069530 * t)
  +  0.00000000687 * cos(4.43661173924 +     102.84895673509 * t)
  +  0.00000000801 * cos(4.16672540134 +    1457.28211557850 * t)
  ) * pow(t, 3);
}

double saturn_x4(double t) {
  return (
     0.00007957923 * cos(0.10292939767 +     220.65645992230 * t)
  +  0.00007883034 * cos(4.66633773762 +     206.42936592071 * t)
  +  0.00001517028 * cos(0.05577219527 +     227.77000692311 * t)
  +  0.00001235695 * cos(5.39600292264 +     433.95555536030 * t)
  +  0.00001152216 * cos(5.24396587079 +     213.54291292150 * t)
  +  0.00000879616 * cos(5.34174983557 +       0.24381748350 * t)
  +  0.00000709628 * cos(4.81919971142 +     199.31581891990 * t)
  +  0.00000602013 * cos(1.23511363469 +       7.35736448430 * t)
  +  0.00000507367 * cos(4.78792568609 +     426.84200835950 * t)
  +  0.00000386382 * cos(1.30105603325 +      14.47091148511 * t)
  +  0.00000338827 * cos(4.08599989607 +     419.72846135871 * t)
  +  0.00000186029 * cos(5.42685623154 +     441.06910236111 * t)
  +  0.00000220262 * cos(4.07756916511 +     640.14110379750 * t)
  +  0.00000173210 * cos(4.46238384072 +     647.25465079831 * t)
  +  0.00000084974 * cos(6.19195566472 +     234.88355392390 * t)
  +  0.00000085340 * cos(2.82637979462 +     213.05527795450 * t)
  +  0.00000044264 * cos(1.34743358639 +     117.56368570370 * t)
  +  0.00000045849 * cos(3.59457316555 +       6.86972951729 * t)
  +  0.00000047835 * cos(3.21421968827 +     853.44019923550 * t)
  +  0.00000041104 * cos(3.75480601059 +     412.61491435790 * t)
  +  0.00000030735 * cos(1.14073508300 +      21.58445848590 * t)
  +  0.00000022639 * cos(4.54040624066 +     654.36819779910 * t)
  +  0.00000021067 * cos(4.91324359260 +     103.33659170210 * t)
  +  0.00000020230 * cos(1.74358717590 +     110.45013870291 * t)
  +  0.00000021389 * cos(0.96555928483 +     205.94173095370 * t)
  +  0.00000016854 * cos(5.95101073162 +     124.67723270450 * t)
  +  0.00000021739 * cos(3.56778546142 +     860.55374623631 * t)
  +  0.00000017501 * cos(2.66582523466 +     220.16882495529 * t)
  +  0.00000014506 * cos(2.82815343470 +      88.62186273350 * t)
  +  0.00000017401 * cos(0.69153050158 +     198.82818395289 * t)
  +  0.00000013517 * cos(4.90527630680 +     309.52214013930 * t)
  +  0.00000011814 * cos(0.44837969058 +     323.74923414091 * t)
  +  0.00000012071 * cos(5.31212364211 +     448.18264936190 * t)
  +  0.00000011725 * cos(0.04357660859 +     330.86278114170 * t)
  +  0.00000010174 * cos(2.85692484188 +      95.73540973430 * t)
  +  0.00000011491 * cos(5.22879894174 +     192.20227191910 * t)
  +  0.00000010611 * cos(5.64300353639 +     302.40859313851 * t)
  +  0.00000012147 * cos(4.23365602535 +     633.02755679670 * t)
  +  0.00000009067 * cos(2.69785298236 +      13.98327651810 * t)
  +  0.00000008918 * cos(1.46910827681 +     426.35437339250 * t)
  +  0.00000008311 * cos(4.67543017537 +     430.02340209721 * t)
  +  0.00000007296 * cos(2.34933784290 +     316.63568714010 * t)
  +  0.00000007890 * cos(2.51218274353 +    1066.73929467350 * t)
  +  0.00000006699 * cos(1.49841716625 +     109.96250373590 * t)
  +  0.00000006339 * cos(5.32790301740 +     216.72430665921 * t)
  +  0.00000006254 * cos(2.70033795328 +     210.36151918381 * t)
  +  0.00000006126 * cos(1.64892191331 +     301.92095817150 * t)
  +  0.00000006725 * cos(5.51198561168 +     625.91400979590 * t)
  +  0.00000006784 * cos(5.78945551800 +     223.83785366000 * t)
  +  0.00000006868 * cos(2.22797475448 +     203.24797218300 * t)
  +  0.00000006111 * cos(5.16124898313 +      96.22304470130 * t)
  +  0.00000004468 * cos(1.72149500008 +     309.03450517230 * t)
  +  0.00000004160 * cos(1.03429820392 +     522.82123557730 * t)
  +  0.00000003681 * cos(0.94893010872 +     423.66061462181 * t)
  +  0.00000003615 * cos(0.40952028826 +     405.50136735710 * t)
  +  0.00000003079 * cos(5.63647951312 +     412.12727939089 * t)
  +  0.00000003614 * cos(0.37301132942 +     515.22005360950 * t)
  +  0.00000002896 * cos(1.28921720639 +     515.70768857651 * t)
  +  0.00000003000 * cos(4.72788705186 +     422.90985509640 * t)
  +  0.00000002685 * cos(5.00319133132 +     209.61075965840 * t)
  +  0.00000002918 * cos(0.73261775434 +      89.10949770051 * t)
  +  0.00000002617 * cos(2.98014804776 +     217.47506618460 * t)
  +  0.00000002884 * cos(0.63120048927 +     191.71463695210 * t)
  +  0.00000002281 * cos(0.61985347120 +     316.14805217309 * t)
  +  0.00000002717 * cos(5.35927194820 +     131.79077970531 * t)
  +  0.00000002556 * cos(4.65487521363 +     337.97632814250 * t)
  +  0.00000001782 * cos(6.08157929050 +     241.99710092470 * t)
  +  0.00000001782 * cos(1.94963952968 +     185.08872491831 * t)
  +  0.00000001856 * cos(1.22219785032 +     618.31282782810 * t)
  +  0.00000001713 * cos(1.39863052168 +     625.42637482889 * t)
  +  0.00000001632 * cos(5.57529252306 +     728.51914904750 * t)
  +  0.00000001980 * cos(0.12344871269 +     831.61192326610 * t)
  +  0.00000001607 * cos(4.53783680441 +     611.19928082730 * t)
  +  0.00000001801 * cos(2.70567446780 +     227.28237195610 * t)
  +  0.00000001532 * cos(0.60049717130 +    1052.51220067191 * t)
  +  0.00000001510 * cos(1.01685015001 +     742.74624304909 * t)
  +  0.00000001531 * cos(4.91027438516 +     529.44714761109 * t)
  +  0.00000001394 * cos(2.02930508328 +    1361.30288836070 * t)
  +  0.00000001427 * cos(0.73295227059 +    1251.09656714130 * t)
  +  0.00000001649 * cos(5.83036907174 +     295.29504613770 * t)
  +  0.00000001249 * cos(5.31804281913 +     743.23387801611 * t)
  +  0.00000001353 * cos(5.64535868524 +    1678.18239298430 * t)
  +  0.00000001674 * cos(0.75228934735 +     231.70216018621 * t)
  +  0.00000001646 * cos(0.97572157001 +     195.38366565681 * t)
  +  0.00000001305 * cos(1.00406093433 +     934.70469748469 * t)
  +  0.00000001160 * cos(6.07115885491 +      81.50831573269 * t)
  +  0.00000001537 * cos(0.07816179599 +      21.09682351890 * t)
  +  0.00000001096 * cos(1.15801707287 +     832.09955823310 * t)
  +  0.00000001156 * cos(0.08524385094 +     508.10650660869 * t)
  +  0.00000001062 * cos(1.72268908914 +     294.80741117069 * t)
  +  0.00000001285 * cos(5.87120310708 +    1464.39566257930 * t)
  +  0.00000001079 * cos(6.04015764687 +    1368.90407032850 * t)
  +  0.00000001006 * cos(0.12126175121 +    1361.79052332771 * t)
  +  0.00000001290 * cos(6.26123764935 +     736.12033101530 * t)
  +  0.00000001051 * cos(1.11902862643 +     941.81824448550 * t)
  +  0.00000001027 * cos(2.13247533522 +     433.46792039329 * t)
  +  0.00000001021 * cos(0.91271229263 +     522.33360061030 * t)
  +  0.00000001137 * cos(4.47891183265 +    1891.48148842230 * t)
  +  0.00000000991 * cos(5.35089033439 +    1994.57426264090 * t)
  +  0.00000001038 * cos(6.06703363765 +    1148.00379292269 * t)
  +  0.00000000865 * cos(1.97882029045 +     750.34742501690 * t)
  +  0.00000000859 * cos(1.14491409094 +     416.54706762100 * t)
  +  0.00000000862 * cos(4.75102573016 +     437.13694909800 * t)
  +  0.00000000776 * cos(6.05032387495 +     102.84895673509 * t)
  +  0.00000000797 * cos(0.47611886612 +    1375.52998236229 * t)
  +  0.00000000824 * cos(2.96565494557 +     639.65346883050 * t)
  +  0.00000000881 * cos(5.02815372820 +    1258.69774910910 * t)
  +  0.00000000686 * cos(0.20449337417 +     234.39591895690 * t)
  +  0.00000000684 * cos(5.09702256485 +     661.48174479990 * t)
  +  0.00000000859 * cos(5.20905469515 +     537.04832957890 * t)
  ) * pow(t, 4);
}

double saturn_x5(double t) {
  return (
     0.00000605503 * cos(4.59646585232 +     220.65645992230 * t)
  +  0.00000576439 * cos(0.06437124594 +     206.42936592071 * t)
  +  0.00000227348 * cos(4.59085116990 +     227.77000692311 * t)
  +  0.00000133503 * cos(3.58841633128 +     433.95555536030 * t)
  +  0.00000094765 * cos(0.27215838233 +     199.31581891990 * t)
  +  0.00000039851 * cos(5.86635990391 +      14.47091148511 * t)
  +  0.00000034190 * cos(3.64452029703 +     441.06910236111 * t)
  +  0.00000024941 * cos(5.41093732098 +       0.24381748350 * t)
  +  0.00000023155 * cos(2.64207066157 +     647.25465079831 * t)
  +  0.00000016208 * cos(2.39130620524 +     426.84200835950 * t)
  +  0.00000012333 * cos(2.18222106376 +     640.14110379750 * t)
  +  0.00000010358 * cos(4.50067908167 +     234.88355392390 * t)
  +  0.00000010534 * cos(0.41421931470 +     419.72846135871 * t)
  +  0.00000008668 * cos(3.51972888423 +     192.20227191910 * t)
  +  0.00000008840 * cos(5.55216757332 +     213.54291292150 * t)
  +  0.00000004707 * cos(4.57538541908 +      88.62186273350 * t)
  +  0.00000005904 * cos(4.73107708292 +       7.35736448430 * t)
  +  0.00000003895 * cos(2.30231207024 +     405.50136735710 * t)
  +  0.00000003976 * cos(1.96984083585 +       6.86972951729 * t)
  +  0.00000003675 * cos(0.47302446664 +     213.05527795450 * t)
  +  0.00000003472 * cos(1.35605117518 +     853.44019923550 * t)
  +  0.00000004393 * cos(2.75554415948 +     654.36819779910 * t)
  +  0.00000003290 * cos(3.89078522206 +     124.67723270450 * t)
  +  0.00000002569 * cos(5.91571375440 +     109.96250373590 * t)
  +  0.00000002467 * cos(3.15983568463 +     515.70768857651 * t)
  +  0.00000002708 * cos(1.73056604662 +     860.55374623631 * t)
  +  0.00000002138 * cos(3.58678888073 +     448.18264936190 * t)
  +  0.00000002447 * cos(0.90027079514 +     220.16882495529 * t)
  +  0.00000001979 * cos(0.98519013325 +     302.40859313851 * t)
  +  0.00000002238 * cos(5.57282036056 +     198.82818395289 * t)
  +  0.00000001727 * cos(0.08010225619 +     301.92095817150 * t)
  +  0.00000001398 * cos(1.62923220404 +     309.52214013930 * t)
  +  0.00000001536 * cos(2.37774872925 +     205.94173095370 * t)
  +  0.00000001195 * cos(5.50915521926 +     117.56368570370 * t)
  +  0.00000001000 * cos(4.01529701865 +     223.83785366000 * t)
  +  0.00000000984 * cos(3.95579224093 +     203.24797218300 * t)
  +  0.00000000791 * cos(2.18561862902 +     330.86278114170 * t)
  +  0.00000000979 * cos(5.20989352885 +      95.73540973430 * t)
  +  0.00000000784 * cos(3.19070192516 +     522.82123557730 * t)
  +  0.00000000910 * cos(2.05287501643 +      96.22304470130 * t)
  ) * pow(t, 5);
}

double saturn_y0(double t) {
  return (
     9.52312533591 * cos(5.58640389526 +     213.54291292150 * t)
  +  0.79501390398 * cos(3.19501080417 +       0.24381748350 * t)
  +  0.26427074351 * cos(4.83578897954 +     426.84200835950 * t)
  +  0.06836881382 * cos(2.57458281509 +     206.42936592071 * t)
  +  0.06628914946 * cos(5.46296215793 +     220.65645992230 * t)
  +  0.02340967916 * cos(0.44899651249 +       7.35736448430 * t)
  +  0.01250581159 * cos(0.60313024847 +     110.45013870291 * t)
  +  0.01141539711 * cos(1.46265679616 +     419.72846135871 * t)
  +  0.01098217124 * cos(4.08641227912 +     640.14110379750 * t)
  +  0.00773784455 * cos(5.07365052128 +     213.05527795450 * t)
  +  0.00708587042 * cos(1.13843336592 +     316.63568714010 * t)
  +  0.00434227030 * cos(5.42862996601 +     529.93478257810 * t)
  +  0.00373110880 * cos(4.71342390707 +     433.95555536030 * t)
  +  0.00413446294 * cos(0.41153807474 +     102.84895673509 * t)
  +  0.00169743473 * cos(1.48210526398 +     205.94173095370 * t)
  +  0.00122184772 * cos(2.79745491359 +     103.33659170210 * t)
  +  0.00141571884 * cos(0.13687533326 +     419.24082639170 * t)
  +  0.00097840616 * cos(5.72784467548 +     323.74923414091 * t)
  +  0.00080586098 * cos(4.05159874352 +      11.28951774740 * t)
  +  0.00083840998 * cos(5.33240905202 +     227.77000692311 * t)
  +  0.00072499120 * cos(0.84921881394 +     633.02755679670 * t)
  +  0.00070188882 * cos(5.59903361411 +     209.61075965840 * t)
  +  0.00068920772 * cos(2.44584271705 +     217.47506618460 * t)
  +  0.00065633219 * cos(1.19325366411 +     202.49721265760 * t)
  +  0.00058340081 * cos(0.59027157812 +     224.58861318540 * t)
  +  0.00054036331 * cos(3.33803216964 +     853.44019923550 * t)
  +  0.00045670301 * cos(0.30742381833 +      14.47091148511 * t)
  +  0.00039957906 * cos(2.72206781342 +     199.31581891990 * t)
  +  0.00044623718 * cos(0.90093873172 +      63.49208081989 * t)
  +  0.00025182378 * cos(5.09001467212 +     216.72430665921 * t)
  +  0.00024597547 * cos(2.95757557284 +     210.36151918381 * t)
  +  0.00024755958 * cos(4.02968885174 +     415.79630809560 * t)
  +  0.00025518626 * cos(0.06734394180 +     117.56368570370 * t)
  +  0.00030420785 * cos(6.15115633926 +     735.63269604830 * t)
  +  0.00022261024 * cos(1.10100301594 +     522.33360061030 * t)
  +  0.00023384603 * cos(3.96374854662 +     647.25465079831 * t)
  +  0.00019921860 * cos(4.09518373122 +     426.35437339250 * t)
  +  0.00023368080 * cos(4.90040735801 +     149.80701461810 * t)
  +  0.00024816783 * cos(3.92964610129 +      75.02541605080 * t)
  +  0.00015057730 * cos(3.10557746427 +     277.27881122490 * t)
  +  0.00013291291 * cos(2.35905808760 +     309.03450517230 * t)
  +  0.00012028365 * cos(5.74173457069 +    1059.62574767270 * t)
  +  0.00012408238 * cos(2.62612862596 +     490.57790666290 * t)
  +  0.00012037260 * cos(4.09279303186 +     352.06040979221 * t)
  +  0.00007880259 * cos(1.03244732130 +     743.23387801611 * t)
  +  0.00007428823 * cos(5.83507395250 +       6.86972951729 * t)
  +  0.00006985779 * cos(2.31301163514 +     309.52214013930 * t)
  +  0.00009059376 * cos(5.88705982112 +    1052.02456570489 * t)
  +  0.00006626180 * cos(0.82428012166 +     838.72547026689 * t)
  +  0.00008285289 * cos(3.60108497690 +      95.73540973430 * t)
  +  0.00007908600 * cos(4.48713264921 +     316.14805217309 * t)
  +  0.00006284835 * cos(2.67337959503 +       3.68833577960 * t)
  +  0.00006078527 * cos(4.58792252731 +     441.06910236111 * t)
  +  0.00005628724 * cos(0.90747309129 +     846.32665223470 * t)
  +  0.00005274108 * cos(4.97367799615 +     220.16882495529 * t)
  +  0.00005584926 * cos(1.54150891449 +     412.61491435790 * t)
  +  0.00004423799 * cos(1.57641344464 +     198.82818395289 * t)
  +  0.00004849319 * cos(4.98130878652 +     537.04832957890 * t)
  +  0.00004179381 * cos(5.16756812825 +       4.17597074660 * t)
  +  0.00005772348 * cos(3.73707335017 +      38.37685312130 * t)
  +  0.00005198014 * cos(2.97493810590 +     211.09523236671 * t)
  +  0.00005154525 * cos(5.05852684698 +     215.99059347631 * t)
  +  0.00003792407 * cos(4.42246502754 +     422.90985509640 * t)
  +  0.00004380719 * cos(2.72775866401 +     202.00957769060 * t)
  +  0.00004838174 * cos(3.60482713264 +     109.96250373590 * t)
  +  0.00003765792 * cos(2.14993736411 +     212.57970507500 * t)
  +  0.00003749721 * cos(5.88164710896 +     214.50612076800 * t)
  +  0.00003116757 * cos(5.55835071261 +     213.49472881170 * t)
  +  0.00003115849 * cos(2.47295232173 +     213.59109703130 * t)
  +  0.00003119049 * cos(2.08030449144 +     625.42637482889 * t)
  +  0.00003235633 * cos(2.93645048734 +     632.53992182970 * t)
  +  0.00004077069 * cos(1.24694613809 +     136.78920667889 * t)
  +  0.00003290391 * cos(5.03950922540 +     522.82123557730 * t)
  +  0.00002828736 * cos(5.44462827617 +     330.86278114170 * t)
  +  0.00003365297 * cos(6.13313657202 +     437.88770862340 * t)
  +  0.00002888976 * cos(5.85305165742 +      86.07111631471 * t)
  +  0.00002748221 * cos(3.85851556523 +     138.76131435421 * t)
  +  0.00002742545 * cos(5.64786903747 +     203.98168536590 * t)
  +  0.00002636395 * cos(3.83621912362 +     288.32451148881 * t)
  +  0.00003170535 * cos(4.19556924462 +      76.50988875911 * t)
  +  0.00002530060 * cos(3.52650884327 +     629.09540353360 * t)
  +  0.00002985976 * cos(2.58564693197 +    1066.73929467350 * t)
  +  0.00002617358 * cos(0.73922008905 +     127.22797912329 * t)
  +  0.00002504577 * cos(6.20308081313 +       9.80504503910 * t)
  +  0.00002459199 * cos(0.55192655633 +    1155.11733992350 * t)
  +  0.00002429561 * cos(2.40176973016 +     223.10414047710 * t)
  +  0.00003133467 * cos(5.62811439341 +    1368.41643536150 * t)
  +  0.00002289072 * cos(2.11564630370 +     430.77416162260 * t)
  +  0.00002651422 * cos(0.30311808414 +     412.12727939089 * t)
  +  0.00002791618 * cos(0.19025345990 +       3.42521122121 * t)
  +  0.00002086473 * cos(1.97187121386 +     423.66061462181 * t)
  +  0.00002337517 * cos(4.29665202435 +     388.70897272171 * t)
  +  0.00001735774 * cos(4.10517039399 +     736.12033101530 * t)
  +  0.00001617760 * cos(2.87094929008 +      96.22304470130 * t)
  +  0.00001635420 * cos(2.97359194678 +      12.77399045571 * t)
  +  0.00001637578 * cos(0.62856200162 +     213.02164805970 * t)
  +  0.00001633497 * cos(1.12064121841 +     214.06417778330 * t)
  +  0.00001703439 * cos(3.99674710141 +     529.44714761109 * t)
  +  0.00001499174 * cos(5.17056778089 +      52.44638055600 * t)
  +  0.00001462063 * cos(4.35331374641 +     430.02340209721 * t)
  +  0.00001975850 * cos(0.45234024897 +       1.72829019180 * t)
  +  0.00001422179 * cos(3.32899817186 +     625.91400979590 * t)
  +  0.00001539334 * cos(3.21457103113 +     860.55374623631 * t)
  +  0.00001400317 * cos(2.15177170721 +     341.01470952831 * t)
  +  0.00001337694 * cos(1.54600928268 +     948.93179148630 * t)
  +  0.00001427589 * cos(3.84316796768 +     350.57593708390 * t)
  +  0.00001149795 * cos(1.77484346800 +     941.81824448550 * t)
  +  0.00001112160 * cos(5.19130278223 +     234.88355392390 * t)
  +  0.00001015231 * cos(0.28360221027 +    1471.50920958009 * t)
  +  0.00001090238 * cos(4.25624714992 +     363.10611005610 * t)
  +  0.00001091460 * cos(5.84943013311 +     174.18603700630 * t)
  +  0.00001152320 * cos(2.26380260884 +     201.01273994931 * t)
  +  0.00000874317 * cos(1.24749634822 +     515.22005360950 * t)
  +  0.00001180011 * cos(5.37502087961 +    1684.80830501809 * t)
  +  0.00001058128 * cos(2.86921511069 +     742.74624304909 * t)
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  +  0.00000001031 * cos(2.47713291345 +     738.08037660310 * t)
  +  0.00000000793 * cos(4.26011752121 +     746.41527175380 * t)
  +  0.00000001085 * cos(1.02451872519 +     592.44684060410 * t)
  +  0.00000000961 * cos(2.67254071371 +    1120.39270055950 * t)
  +  0.00000000888 * cos(1.70195193954 +   26514.74514993370 * t)
  +  0.00000000782 * cos(5.68415836770 +     519.63984183961 * t)
  +  0.00000000800 * cos(3.20991142806 +    4113.33812301930 * t)
  +  0.00000000945 * cos(4.06069039712 +    1673.76260475420 * t)
  +  0.00000000850 * cos(0.31047663250 +     580.33735875721 * t)
  +  0.00000001030 * cos(1.16963154394 +    3657.24811383991 * t)
  +  0.00000000775 * cos(3.00079525151 +     735.58451193849 * t)
  +  0.00000000775 * cos(3.00079525151 +     736.07214690550 * t)
  +  0.00000000951 * cos(4.36992299634 +     604.22874617840 * t)
  +  0.00000000760 * cos(4.77344534648 +    3267.25528826810 * t)
  +  0.00000000802 * cos(4.44315712396 +     362.61847508910 * t)
  +  0.00000000866 * cos(5.12332739411 +    1293.63483679419 * t)
  +  0.00000000766 * cos(1.96682285527 +     188.67625556630 * t)
  +  0.00000000768 * cos(1.62759212320 +     845.57589270931 * t)
  +  0.00000000766 * cos(4.46757685640 +    2439.33170078160 * t)
  +  0.00000000769 * cos(5.87087902642 +    1051.97638159510 * t)
  +  0.00000000776 * cos(2.78600818951 +    2014.27037224060 * t)
  +  0.00000000771 * cos(2.78598583977 +    1052.07274981469 * t)
  +  0.00000000822 * cos(2.84834036260 +     582.62498061761 * t)
  +  0.00000001002 * cos(2.61286504444 +   52183.16364763270 * t)
  +  0.00000000828 * cos(4.17948532199 +     631.78916230430 * t)
  +  0.00000000973 * cos(3.91693566169 +     519.14971474510 * t)
  +  0.00000000839 * cos(5.64763751852 +   13362.69352428270 * t)
  +  0.00000000842 * cos(4.82173037387 +     204.45725824539 * t)
  +  0.00000000756 * cos(1.58063538394 +     693.82813957829 * t)
  +  0.00000000756 * cos(1.58063538394 +     694.31577454531 * t)
  +  0.00000000747 * cos(4.53970527389 +     962.75274857760 * t)
  +  0.00000000916 * cos(0.53251818292 +     688.41151360689 * t)
  +  0.00000000769 * cos(3.11155934055 +    6058.48723680599 * t)
  +  0.00000000756 * cos(0.54984492104 +     545.71578525720 * t)
  +  0.00000000830 * cos(3.49429956542 +     595.47066777489 * t)
  +  0.00000000831 * cos(5.48519211288 +     436.87631666710 * t)
  +  0.00000000776 * cos(2.95329359189 +     187.99493201010 * t)
  +  0.00000000757 * cos(2.65993029948 +    5496.22546986590 * t)
  +  0.00000000977 * cos(4.63633631623 +    1055.43296197871 * t)
  +  0.00000000737 * cos(5.11234946130 +     225.58545092669 * t)
  +  0.00000000940 * cos(1.37204266374 +     462.00609858071 * t)
  +  0.00000000881 * cos(4.14004497053 +     157.67132114430 * t)
  +  0.00000000881 * cos(3.89117384965 +     269.41450469871 * t)
  +  0.00000000768 * cos(4.54804861178 +    2093.24724862940 * t)
  +  0.00000000945 * cos(3.54564231189 +     347.65517577710 * t)
  +  0.00000000789 * cos(1.23325676313 +     678.27413943531 * t)
  +  0.00000000894 * cos(3.71784833817 +     185.08872491831 * t)
  +  0.00000000887 * cos(1.90161032677 +     938.63685074779 * t)
  +  0.00000000848 * cos(1.73960670139 +    1016.59984305279 * t)
  +  0.00000000778 * cos(4.72868742196 +    5753.62870238030 * t)
  +  0.00000000778 * cos(4.72868742196 +    5753.14106741329 * t)
  +  0.00000000843 * cos(2.59704127717 +     976.49220761220 * t)
  +  0.00000000900 * cos(3.76941852958 +     655.17383907870 * t)
  +  0.00000000730 * cos(4.74108034798 +     497.95457822210 * t)
  +  0.00000000879 * cos(4.77364347651 +     494.23487328010 * t)
  +  0.00000000728 * cos(2.60603774003 +     995.88984936931 * t)
  +  0.00000000729 * cos(0.77581736648 +     632.58810593949 * t)
  +  0.00000000729 * cos(0.77581736648 +     633.07574090651 * t)
  +  0.00000000841 * cos(2.45740163920 +    1051.06135785839 * t)
  +  0.00000000810 * cos(4.65306063985 +    3900.03902758130 * t)
  +  0.00000000774 * cos(3.20387240385 +     451.48415530609 * t)
  +  0.00000000792 * cos(3.21012047679 +     193.93282284329 * t)
  +  0.00000000894 * cos(5.93934831263 +     103.28840759231 * t)
  +  0.00000000744 * cos(4.19216354937 +     662.77502104650 * t)
  +  0.00000001019 * cos(2.49847463002 +    7232.49527644471 * t)
  +  0.00000000720 * cos(1.56486927863 +  103711.47146249928 * t)
  +  0.00000000776 * cos(0.11554513153 +    1703.45518724980 * t)
  +  0.00000001001 * cos(0.71986534852 +    1126.54303971381 * t)
  +  0.00000000860 * cos(0.28002712469 +    2748.61002343740 * t)
  +  0.00000000716 * cos(4.37859929602 +    4319.03603648950 * t)
  +  0.00000000716 * cos(4.37859929602 +    4319.52367145650 * t)
  +  0.00000000797 * cos(5.59551319827 +     529.98296668790 * t)
  +  0.00000000729 * cos(4.65941028609 +    1649.38358236600 * t)
  +  0.00000000803 * cos(4.13945714434 +     151.01630068050 * t)
  +  0.00000000765 * cos(3.49230150581 +    1379.46213562540 * t)
  +  0.00000000765 * cos(3.49230150581 +    1379.94977059240 * t)
  +  0.00000000749 * cos(2.29649366933 +     785.77214766900 * t)
  +  0.00000000836 * cos(2.51999814689 +    4010.24534880071 * t)
  +  0.00000000727 * cos(3.33280142284 +     608.16089944150 * t)
  +  0.00000000727 * cos(0.19120876925 +     608.64853440851 * t)
  +  0.00000000719 * cos(5.79361123899 +     467.68335698301 * t)
  +  0.00000000709 * cos(0.59726160167 +     103.54904002320 * t)
  +  0.00000000709 * cos(3.73885425526 +     103.06140505620 * t)
  +  0.00000000920 * cos(1.80869206570 +     870.70567462290 * t)
  +  0.00000000716 * cos(4.59064021199 +     664.78325074409 * t)
  +  0.00000000857 * cos(0.02537195630 +    2306.54634406740 * t)
  +  0.00000000724 * cos(3.13275093039 +     740.52556503041 * t)
  +  0.00000000708 * cos(3.15032913377 +    2431.46739425540 * t)
  +  0.00000000706 * cos(0.24440760951 +     102.63650841399 * t)
  +  0.00000000706 * cos(3.38600026310 +     103.12414338101 * t)
  +  0.00000000824 * cos(5.06503970891 +    1163.68172973780 * t)
  +  0.00000000722 * cos(1.50443824904 +     171.21709158970 * t)
  +  0.00000000723 * cos(2.31650700540 +     829.37669103239 * t)
  +  0.00000000720 * cos(0.23831524300 +     255.86873425330 * t)
  +  0.00000000956 * cos(0.04233388408 +    3068.18328683170 * t)
  +  0.00000000800 * cos(3.03519680815 +     279.72649177971 * t)
  +  0.00000000800 * cos(4.99602201203 +     147.35933406330 * t)
  +  0.00000000868 * cos(0.37647106732 +     669.40093308030 * t)
  +  0.00000000769 * cos(5.99489096281 +    3465.83965473750 * t)
  +  0.00000000745 * cos(2.84189249473 +     843.14525849700 * t)
  +  0.00000000848 * cos(2.77841948796 +     103.38477581190 * t)
  +  0.00000000703 * cos(4.75219753735 +    4003.13180179990 * t)
  +  0.00000000719 * cos(4.53501064500 +    9988.69693302559 * t)
  +  0.00000000818 * cos(5.15275579739 +     311.48218572709 * t)
  +  0.00000000901 * cos(0.79248369499 +     937.88609122240 * t)
  +  0.00000000783 * cos(5.11638993720 +     199.83708378171 * t)
  +  0.00000000783 * cos(6.05642153657 +     227.24874206131 * t)
  +  0.00000000909 * cos(0.64248903432 +    4009.75771383370 * t)
  +  0.00000000711 * cos(1.76892643060 +     457.37386202950 * t)
  +  0.00000000705 * cos(3.12679135200 +    5653.98044645779 * t)
  +  0.00000000712 * cos(6.07513529815 +     354.28108781090 * t)
  +  0.00000000733 * cos(0.21809967139 +      37.62858572340 * t)
  +  0.00000000708 * cos(1.27557908922 +     840.69757794220 * t)
  +  0.00000000708 * cos(1.27557908922 +     840.20994297520 * t)
  +  0.00000000695 * cos(6.08215837207 +     812.70191647599 * t)
  +  0.00000000695 * cos(2.94056571848 +     813.18955144300 * t)
  +  0.00000000736 * cos(5.91292146424 +     403.94745867960 * t)
  +  0.00000000733 * cos(2.29907033586 +     182.03578931750 * t)
  +  0.00000000836 * cos(5.01712963721 +    2331.81913833290 * t)
  +  0.00000000928 * cos(0.59357203459 +     842.13386654071 * t)
  +  0.00000000768 * cos(3.70421774103 +    1460.20038475780 * t)
  +  0.00000000685 * cos(4.29010164874 +     455.29619636271 * t)
  +  0.00000000792 * cos(3.19395503975 +    5422.52210375510 * t)
  +  0.00000000837 * cos(3.85260493508 +     570.77613120160 * t)
  +  0.00000000682 * cos(3.31484357591 +    3693.85347914410 * t)
  +  0.00000000752 * cos(0.56556241430 +     413.34862754081 * t)
  +  0.00000000817 * cos(3.10337024087 +     391.73279989249 * t)
  +  0.00000000681 * cos(0.83323807589 +     458.33457774851 * t)
  +  0.00000000803 * cos(0.28965764669 +     418.49006686629 * t)
  +  0.00000000681 * cos(1.95625262651 +     414.57495994570 * t)
  );
}

double saturn_y1(double t) {
  return (
     0.09285877988 * cos(5.32917891541 +       0.24381748350 * t)
  +  0.03086501680 * cos(2.70413999679 +     426.84200835950 * t)
  +  0.02728479923 * cos(4.27396756341 +     206.42936592071 * t)
  +  0.02644990371 * cos(3.76176749725 +     220.65645992230 * t)
  +  0.00629201988 * cos(5.03696656027 +       7.35736448430 * t)
  +  0.00256626023 * cos(1.95374338915 +     640.14110379750 * t)
  +  0.00312353889 * cos(3.25876676291 +     419.72846135871 * t)
  +  0.00189297041 * cos(2.91534956216 +     433.95555536030 * t)
  +  0.00204465020 * cos(5.78983620425 +     213.54291292150 * t)
  +  0.00118113185 * cos(5.87589622232 +     110.45013870291 * t)
  +  0.00067024295 * cos(2.16159727865 +     316.63568714010 * t)
  +  0.00066948413 * cos(3.63141659236 +     227.77000692311 * t)
  +  0.00031931062 * cos(4.42042826334 +     199.31581891990 * t)
  +  0.00024548187 * cos(3.29398145587 +     205.94173095370 * t)
  +  0.00030521021 * cos(4.89424590805 +      14.47091148511 * t)
  +  0.00022265017 * cos(4.62323431127 +     103.33659170210 * t)
  +  0.00018939520 * cos(1.20474851114 +     853.44019923550 * t)
  +  0.00018082904 * cos(3.51824365057 +     209.61075965840 * t)
  +  0.00017786477 * cos(4.53241903621 +     217.47506618460 * t)
  +  0.00016307253 * cos(3.29827125771 +     216.72430665921 * t)
  +  0.00016919177 * cos(3.01391698262 +     633.02755679670 * t)
  +  0.00015920273 * cos(4.74692264945 +     210.36151918381 * t)
  +  0.00016167186 * cos(4.03963160527 +     323.74923414091 * t)
  +  0.00014472589 * cos(2.10335699916 +     647.25465079831 * t)
  +  0.00011071575 * cos(4.74242577082 +     117.56368570370 * t)
  +  0.00009887534 * cos(3.61558352957 +     202.49721265760 * t)
  +  0.00008713930 * cos(4.46375520442 +     224.58861318540 * t)
  +  0.00006197025 * cos(2.93543981790 +     213.05527795450 * t)
  +  0.00005502258 * cos(2.83240853648 +     441.06910236111 * t)
  +  0.00005466098 * cos(1.03278600709 +      11.28951774740 * t)
  +  0.00003484091 * cos(4.11221224874 +       6.86972951729 * t)
  +  0.00003596198 * cos(4.07360530172 +     309.03450517230 * t)
  +  0.00003029001 * cos(2.81952991155 +     522.33360061030 * t)
  +  0.00003353859 * cos(5.31984150246 +      95.73540973430 * t)
  +  0.00002987715 * cos(4.07245500326 +     309.52214013930 * t)
  +  0.00002732424 * cos(2.53884637625 +     149.80701461810 * t)
  +  0.00003741808 * cos(3.25277228789 +     412.61491435790 * t)
  +  0.00002374342 * cos(3.28677124286 +     198.82818395289 * t)
  +  0.00002875345 * cos(1.68013950973 +     426.35437339250 * t)
  +  0.00002121841 * cos(3.27302778600 +     220.16882495529 * t)
  +  0.00002386687 * cos(1.79649482549 +     109.96250373590 * t)
  +  0.00001755551 * cos(5.48701989649 +     277.27881122490 * t)
  +  0.00001690652 * cos(2.40558615589 +     422.90985509640 * t)
  +  0.00001545396 * cos(3.73180599039 +     330.86278114170 * t)
  +  0.00001447492 * cos(0.46419209839 +       4.17597074660 * t)
  +  0.00001392451 * cos(0.46330792664 +    1066.73929467350 * t)
  +  0.00001331483 * cos(3.49216178249 +     234.88355392390 * t)
  +  0.00001452348 * cos(4.64285489428 +       3.42521122121 * t)
  +  0.00001285559 * cos(0.83411182275 +     415.79630809560 * t)
  +  0.00001159539 * cos(3.03310034622 +     537.04832957890 * t)
  +  0.00001128476 * cos(3.88012638153 +     423.66061462181 * t)
  +  0.00001131769 * cos(4.43729716045 +     529.93478257810 * t)
  +  0.00001127023 * cos(1.31091242342 +     860.55374623631 * t)
  +  0.00001101803 * cos(2.50576870008 +     430.02340209721 * t)
  +  0.00001061927 * cos(2.81261932039 +     846.32665223470 * t)
  +  0.00001343360 * cos(1.41831229286 +     211.09523236671 * t)
  +  0.00001331640 * cos(0.33818120038 +     215.99059347631 * t)
  +  0.00001287848 * cos(0.51354213126 +     522.82123557730 * t)
  +  0.00001050973 * cos(1.98569718820 +     412.12727939089 * t)
  +  0.00000900723 * cos(2.55020173482 +     838.72547026689 * t)
  +  0.00000882663 * cos(3.84497584849 +     437.88770862340 * t)
  +  0.00000924505 * cos(5.02323714134 +     743.23387801611 * t)
  +  0.00000876882 * cos(4.58871940602 +      96.22304470130 * t)
  +  0.00000905253 * cos(4.94395759972 +       3.68833577960 * t)
  +  0.00000820808 * cos(3.17476222193 +     223.83785366000 * t)
  +  0.00000844907 * cos(3.81271524339 +     625.42637482889 * t)
  +  0.00000760731 * cos(5.03884679059 +     625.91400979590 * t)
  +  0.00000657423 * cos(3.32272595203 +     316.14805217309 * t)
  +  0.00000813631 * cos(4.73875446278 +      21.58445848590 * t)
  +  0.00000642768 * cos(4.79907912774 +    1059.62574767270 * t)
  +  0.00000657845 * cos(5.47081914900 +      88.62186273350 * t)
  +  0.00000715042 * cos(4.55303572982 +     430.77416162260 * t)
  +  0.00000596876 * cos(3.52791235957 +     124.67723270450 * t)
  +  0.00000472020 * cos(2.03831166729 +     654.36819779910 * t)
  +  0.00000467656 * cos(2.94972694776 +     515.22005360950 * t)
  +  0.00000472526 * cos(4.89215133877 +     203.24797218300 * t)
  +  0.00000487417 * cos(5.85503954683 +     736.12033101530 * t)
  +  0.00000402114 * cos(2.85533132593 +      86.07111631471 * t)
  +  0.00000376954 * cos(2.14121779282 +      76.50988875911 * t)
  +  0.00000419410 * cos(1.17666971099 +     742.74624304909 * t)
  +  0.00000439384 * cos(4.19607195732 +     301.92095817150 * t)
  +  0.00000458871 * cos(2.23384913618 +     529.44714761109 * t)
  +  0.00000345395 * cos(4.60405141742 +     192.20227191910 * t)
  +  0.00000334209 * cos(2.28268923760 +    1155.11733992350 * t)
  +  0.00000330276 * cos(5.07000098007 +     302.40859313851 * t)
  +  0.00000339713 * cos(1.16737882478 +     218.20877936750 * t)
  +  0.00000304950 * cos(4.89660174852 +     231.70216018621 * t)
  +  0.00000312395 * cos(0.79548009041 +     629.09540353360 * t)
  +  0.00000311746 * cos(3.50532316923 +     941.81824448550 * t)
  +  0.00000299095 * cos(0.58884669599 +     208.87704647550 * t)
  +  0.00000299955 * cos(1.74484418656 +     728.51914904750 * t)
  +  0.00000271105 * cos(1.13283461800 +     288.32451148881 * t)
  +  0.00000260779 * cos(5.58254809430 +      18.40306474821 * t)
  +  0.00000278736 * cos(0.64654515892 +     632.53992182970 * t)
  +  0.00000335527 * cos(1.50873501393 +     203.98168536590 * t)
  +  0.00000259607 * cos(4.43314622304 +      10.53875822200 * t)
  +  0.00000263983 * cos(1.98364017133 +     363.10611005610 * t)
  +  0.00000291544 * cos(0.24051609787 +     223.10414047710 * t)
  +  0.00000214376 * cos(4.46071700955 +     208.12628695010 * t)
  +  0.00000208551 * cos(3.59347779220 +     218.95953889290 * t)
  +  0.00000208257 * cos(2.81646625431 +     408.68276109481 * t)
  +  0.00000211653 * cos(0.53562740874 +     138.76131435421 * t)
  +  0.00000199845 * cos(3.86657932388 +      13.98327651810 * t)
  +  0.00000195781 * cos(1.92507988390 +      52.44638055600 * t)
  +  0.00000192346 * cos(4.64457398897 +     201.01273994931 * t)
  +  0.00000191573 * cos(5.16049975639 +     341.01470952831 * t)
  +  0.00000185995 * cos(0.07444798265 +     948.93179148630 * t)
  +  0.00000168803 * cos(2.67981533571 +     831.61192326610 * t)
  +  0.00000170172 * cos(5.89341892618 +     350.57593708390 * t)
  +  0.00000167553 * cos(3.43189093041 +     226.07308589371 * t)
  +  0.00000177510 * cos(3.37006198906 +     210.62215161470 * t)
  +  0.00000177755 * cos(4.64994019967 +     216.46367422830 * t)
  +  0.00000157494 * cos(0.14772881381 +     195.38366565681 * t)
  +  0.00000162215 * cos(4.44587835630 +     956.53297345411 * t)
  +  0.00000160622 * cos(3.78223230286 +     127.22797912329 * t)
  +  0.00000147298 * cos(5.02251206802 +       9.80504503910 * t)
  +  0.00000177635 * cos(4.69945913164 +     160.85271488200 * t)
  +  0.00000170308 * cos(1.06394430192 +     207.91383862900 * t)
  +  0.00000158062 * cos(0.92038060554 +    1059.13811270570 * t)
  +  0.00000138665 * cos(2.01815199316 +    1471.50920958009 * t)
  +  0.00000150976 * cos(1.56848256275 +     636.20895053440 * t)
  +  0.00000136839 * cos(2.94611079491 +     544.16187657970 * t)
  +  0.00000163932 * cos(0.66823863663 +     219.17198721400 * t)
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  +  0.00000001167 * cos(1.05359353693 +    2920.88396534110 * t)
  +  0.00000001100 * cos(0.95076161618 +    2634.47154895491 * t)
  +  0.00000001035 * cos(0.59532463011 +    3369.86042751970 * t)
  +  0.00000001091 * cos(5.26065063725 +    1314.56934088630 * t)
  +  0.00000001274 * cos(1.81279771107 +     691.34682912870 * t)
  +  0.00000001079 * cos(2.63111319426 +    1044.64789414570 * t)
  +  0.00000001085 * cos(0.65660514905 +     141.20899490900 * t)
  +  0.00000001245 * cos(1.12530476318 +     179.91817716280 * t)
  +  0.00000001146 * cos(5.05013070926 +     220.54458533771 * t)
  +  0.00000001196 * cos(1.60077277494 +    1460.20038475780 * t)
  +  0.00000001136 * cos(3.62545973301 +     480.00777927849 * t)
  +  0.00000001119 * cos(3.84274502894 +    1534.98198332510 * t)
  +  0.00000001056 * cos(5.19951356169 +     437.40007365639 * t)
  +  0.00000001032 * cos(0.75596269901 +     184.97110483931 * t)
  +  0.00000001032 * cos(0.99207081399 +     242.11472100371 * t)
  +  0.00000001039 * cos(3.89912009234 +    1791.08247297440 * t)
  +  0.00000001061 * cos(4.07694835092 +     938.63685074779 * t)
  +  0.00000001123 * cos(5.53483735553 +   25668.17468021549 * t)
  +  0.00000001103 * cos(1.14969049707 +     210.60759739969 * t)
  +  0.00000001015 * cos(5.62555119479 +     252.41215386970 * t)
  +  0.00000000979 * cos(0.51006487073 +     610.44852130189 * t)
  +  0.00000000979 * cos(0.51006487073 +     610.93615626891 * t)
  +  0.00000001043 * cos(5.02488186971 +      17.91542978119 * t)
  +  0.00000001128 * cos(2.35271436800 +     398.53083270820 * t)
  +  0.00000001035 * cos(4.59247999326 +     235.68919520349 * t)
  +  0.00000001072 * cos(2.96070791769 +     746.15463932291 * t)
  +  0.00000001131 * cos(1.80265887785 +    5481.99837586430 * t)
  +  0.00000000986 * cos(0.57363342277 +     192.44835013500 * t)
  +  0.00000001287 * cos(0.38193481035 +     314.18800658530 * t)
  +  0.00000000973 * cos(5.42514671691 +     561.69047652550 * t)
  +  0.00000001298 * cos(2.65454318605 +     614.38067456499 * t)
  +  0.00000001151 * cos(2.77783863264 +     905.64276230799 * t)
  +  0.00000001279 * cos(1.17281533398 +     322.36782729660 * t)
  +  0.00000000963 * cos(1.93346454966 +     782.59075393131 * t)
  +  0.00000001064 * cos(1.04722734848 +    1372.34858862460 * t)
  +  0.00000000973 * cos(1.95209864065 +      24.62283987170 * t)
  +  0.00000001096 * cos(3.49856994945 +     731.92754532131 * t)
  +  0.00000001080 * cos(1.56741970160 +    2906.65687133950 * t)
  +  0.00000001200 * cos(3.88182273784 +     195.64679021520 * t)
  +  0.00000000993 * cos(0.38449878066 +    6062.90702503610 * t)
  +  0.00000001039 * cos(2.64505699779 +    1159.04949318660 * t)
  +  0.00000000952 * cos(3.87253065022 +     239.88198089750 * t)
  +  0.00000001181 * cos(2.55455580038 +    1468.32781584240 * t)
  +  0.00000001137 * cos(1.16274372128 +       2.69149803831 * t)
  +  0.00000000941 * cos(2.80652276090 +     124.18959773749 * t)
  +  0.00000000942 * cos(1.93049464908 +     115.11600514891 * t)
  +  0.00000001020 * cos(3.36648319866 +     196.38050339810 * t)
  +  0.00000001065 * cos(3.10915621431 +     494.23487328010 * t)
  +  0.00000000945 * cos(5.96236583490 +     121.00820399980 * t)
  +  0.00000000941 * cos(2.10164527812 +     120.01136625851 * t)
  +  0.00000000996 * cos(1.49787021480 +    4863.44173055270 * t)
  +  0.00000001059 * cos(6.04847231304 +   25653.94758621389 * t)
  +  0.00000000936 * cos(5.92819887567 +     307.07445958451 * t)
  +  0.00000000986 * cos(3.52637633155 +    5842.00674763030 * t)
  +  0.00000001061 * cos(2.35701423791 +     418.97770183331 * t)
  +  0.00000000941 * cos(0.81063561753 +      97.17169833279 * t)
  +  0.00000001049 * cos(5.16810544385 +     416.79314583689 * t)
  +  0.00000000956 * cos(3.96361938951 +     141.45507312490 * t)
  +  0.00000000922 * cos(0.26133958050 +    1364.48428209840 * t)
  +  0.00000001090 * cos(2.75394419028 +    1151.93594618579 * t)
  +  0.00000000945 * cos(3.91497884985 +     220.86890824340 * t)
  +  0.00000000945 * cos(0.97464731674 +     206.21691759960 * t)
  +  0.00000000906 * cos(0.44130467758 +   12779.69461290430 * t)
  +  0.00000000913 * cos(4.49732744600 +     285.61619850311 * t)
  +  0.00000000993 * cos(1.57797933233 +      73.05330837550 * t)
  +  0.00000000923 * cos(2.38369657059 +    1048.58004740881 * t)
  +  0.00000000910 * cos(1.34865027178 +    1250.83344258291 * t)
  +  0.00000001055 * cos(4.53650215705 +     287.69386416990 * t)
  +  0.00000000891 * cos(3.38916042044 +    4443.95708667750 * t)
  +  0.00000000890 * cos(1.87781413537 +     952.34018776010 * t)
  +  0.00000001011 * cos(2.41002467914 +     138.90432670610 * t)
  +  0.00000000943 * cos(4.45248854943 +    1368.41643536150 * t)
  +  0.00000001240 * cos(1.39562373377 +     105.78427225690 * t)
  +  0.00000001240 * cos(4.53721638736 +     105.29663728990 * t)
  +  0.00000000975 * cos(6.14076145568 +     700.90805668431 * t)
  +  0.00000000963 * cos(1.26904248346 +    5378.90560164571 * t)
  +  0.00000001131 * cos(1.92127706230 +     640.09291968770 * t)
  +  0.00000001014 * cos(2.27419938832 +     246.68001371321 * t)
  +  0.00000000922 * cos(4.94986707425 +    9772.21644384989 * t)
  +  0.00000000896 * cos(2.95327436580 +    1571.15746550260 * t)
  +  0.00000001121 * cos(0.63121659144 +    6467.68194047809 * t)
  +  0.00000000872 * cos(1.30941661635 +     519.63984183961 * t)
  +  0.00000001164 * cos(4.79404702362 +     739.04109232210 * t)
  +  0.00000001090 * cos(3.70049172953 +    1699.03539901970 * t)
  +  0.00000001180 * cos(4.01443566672 +     636.47207509279 * t)
  +  0.00000000912 * cos(2.54546205453 +      31.26330612050 * t)
  +  0.00000000892 * cos(2.36351221746 +     212.57970507500 * t)
  +  0.00000000892 * cos(5.50510487105 +     212.09207010800 * t)
  +  0.00000000985 * cos(3.52323843583 +     988.02554284310 * t)
  +  0.00000000860 * cos(2.94846758267 +    1585.38455950421 * t)
  +  0.00000000990 * cos(1.67825090661 +    3149.44778508089 * t)
  +  0.00000001177 * cos(4.87572778682 +    1328.79643488791 * t)
  +  0.00000000864 * cos(2.80999692865 +   12146.42323862409 * t)
  +  0.00000001007 * cos(3.83948575721 +     685.23011986920 * t)
  +  0.00000001007 * cos(3.83948575721 +     685.71775483620 * t)
  +  0.00000000853 * cos(3.93116170567 +    2641.58509595570 * t)
  +  0.00000000993 * cos(1.01758536916 +    2111.89413086110 * t)
  +  0.00000000844 * cos(3.42851532207 +    1239.78774231901 * t)
  +  0.00000000846 * cos(1.60469270371 +    2115.07552459880 * t)
  +  0.00000000964 * cos(1.18238037517 +     756.56720014041 * t)
  +  0.00000000981 * cos(6.17353804084 +    1471.24608502170 * t)
  +  0.00000001164 * cos(4.46546430995 +    3391.68870348911 * t)
  +  0.00000000885 * cos(1.64388709070 +     609.12161516050 * t)
  +  0.00000000821 * cos(2.00294213618 +     388.22133775470 * t)
  +  0.00000000906 * cos(3.95724484289 +     327.19375243699 * t)
  +  0.00000000903 * cos(1.46965018009 +     477.24458453860 * t)
  +  0.00000000841 * cos(2.31779507594 +     473.31243127551 * t)
  +  0.00000000904 * cos(5.47014409814 +     635.47523735150 * t)
  +  0.00000000822 * cos(1.66432337141 +    1365.23504162379 * t)
  +  0.00000000997 * cos(1.82079729948 +     123.29582586020 * t)
  +  0.00000000879 * cos(0.83289385422 +    3362.74688051889 * t)
  +  0.00000000846 * cos(0.41970975707 +     227.81819103291 * t)
  +  0.00000000846 * cos(4.46991640952 +     199.26763481011 * t)
  +  0.00000000947 * cos(0.09177854194 +     222.61650551010 * t)
  +  0.00000000875 * cos(1.91606789801 +    9993.11672125570 * t)
  +  0.00000001117 * cos(5.40582369615 +     319.08336769490 * t)
  +  0.00000000800 * cos(1.12338267507 +     834.79331700380 * t)
  +  0.00000000839 * cos(4.44054896906 +     206.64181424181 * t)
  +  0.00000000839 * cos(0.44907719753 +     220.44401160121 * t)
  +  0.00000000838 * cos(1.69845530894 +    2442.51309451930 * t)
  +  0.00000000830 * cos(0.99305838433 +    1891.48148842230 * t)
  +  0.00000000841 * cos(6.22199463081 +      60.04756252381 * t)
  +  0.00000000826 * cos(2.10402662108 +     220.13519506050 * t)
  +  0.00000000854 * cos(5.92854026664 +     540.22972331660 * t)
  +  0.00000000842 * cos(1.12102777557 +    2854.39655642670 * t)
  +  0.00000000858 * cos(4.12461672205 +     781.83999440590 * t)
  +  0.00000000860 * cos(4.20709137726 +    5436.74919775670 * t)
  +  0.00000000785 * cos(4.19221284065 +    3494.29384274070 * t)
  ) * t;
}

double saturn_y2(double t) {
  return (
     0.00862721930 * cos(0.87622130189 +     213.54291292150 * t)
  +  0.00611630287 * cos(0.71399818143 +       0.24381748350 * t)
  +  0.00561413805 * cos(5.96728319816 +     206.42936592071 * t)
  +  0.00547271370 * cos(2.04588665465 +     220.65645992230 * t)
  +  0.00234984093 * cos(0.87581308687 +     426.84200835950 * t)
  +  0.00088108317 * cos(3.29758949735 +       7.35736448430 * t)
  +  0.00050142527 * cos(1.12650721735 +     433.95555536030 * t)
  +  0.00045054746 * cos(5.06577813923 +     419.72846135871 * t)
  +  0.00033335009 * cos(0.01047584776 +     640.14110379750 * t)
  +  0.00027185514 * cos(1.92525242054 +     227.77000692311 * t)
  +  0.00018651786 * cos(1.59992516931 +     213.05527795450 * t)
  +  0.00012946617 * cos(6.11930195692 +     199.31581891990 * t)
  +  0.00010383025 * cos(3.18830710215 +      14.47091148511 * t)
  +  0.00006684574 * cos(4.09620079950 +     110.45013870291 * t)
  +  0.00004661903 * cos(0.26368341105 +     647.25465079831 * t)
  +  0.00004933834 * cos(1.51097568839 +     216.72430665921 * t)
  +  0.00004778577 * cos(0.24213059962 +     210.36151918381 * t)
  +  0.00004377928 * cos(3.66946155930 +     316.63568714010 * t)
  +  0.00003532396 * cos(5.48934411728 +     853.44019923550 * t)
  +  0.00002688895 * cos(1.58317658973 +     209.61075965840 * t)
  +  0.00002540548 * cos(1.07874150891 +     441.06910236111 * t)
  +  0.00002540549 * cos(0.15899514683 +     217.47506618460 * t)
  +  0.00002506252 * cos(3.11588688157 +     117.56368570370 * t)
  +  0.00002582753 * cos(0.02782240807 +     103.33659170210 * t)
  +  0.00002111683 * cos(4.98775349171 +     633.02755679670 * t)
  +  0.00002306046 * cos(5.24765858946 +     205.94173095370 * t)
  +  0.00001843706 * cos(2.39971312535 +     323.74923414091 * t)
  +  0.00001272298 * cos(4.96900516981 +     412.61491435790 * t)
  +  0.00000940336 * cos(2.42501300855 +       6.86972951729 * t)
  +  0.00000804980 * cos(1.78590189490 +     234.88355392390 * t)
  +  0.00000698973 * cos(0.77208908956 +      95.73540973430 * t)
  +  0.00000653010 * cos(5.01381847221 +     198.82818395289 * t)
  +  0.00000766827 * cos(5.79919197548 +     202.49721265760 * t)
  +  0.00000662176 * cos(0.42004956009 +     426.35437339250 * t)
  +  0.00000565841 * cos(1.55419890490 +     220.16882495529 * t)
  +  0.00000765788 * cos(2.28516505694 +     224.58861318540 * t)
  +  0.00000672412 * cos(5.85676090936 +     309.52214013930 * t)
  +  0.00000490992 * cos(0.10668768793 +     109.96250373590 * t)
  +  0.00000440264 * cos(2.02435630765 +     330.86278114170 * t)
  +  0.00000426768 * cos(5.42227433044 +      11.28951774740 * t)
  +  0.00000427613 * cos(5.71584342304 +     860.55374623631 * t)
  +  0.00000505832 * cos(5.83465733982 +     309.03450517230 * t)
  +  0.00000559499 * cos(5.12833446634 +     102.84895673509 * t)
  +  0.00000439569 * cos(3.04587045996 +      21.58445848590 * t)
  +  0.00000404335 * cos(1.38184466479 +     223.83785366000 * t)
  +  0.00000400108 * cos(0.64688754335 +     430.02340209721 * t)
  +  0.00000338086 * cos(4.72348149737 +    1066.73929467350 * t)
  +  0.00000310691 * cos(2.86856110459 +       3.42521122121 * t)
  +  0.00000356340 * cos(0.50093637409 +     422.90985509640 * t)
  +  0.00000268315 * cos(0.90238113501 +      88.62186273350 * t)
  +  0.00000265067 * cos(5.80890278675 +     423.66061462181 * t)
  +  0.00000249792 * cos(2.21289242997 +       4.17597074660 * t)
  +  0.00000244377 * cos(0.24702615370 +     654.36819779910 * t)
  +  0.00000305650 * cos(4.74789522190 +     419.24082639170 * t)
  +  0.00000263490 * cos(1.75719781150 +     124.67723270450 * t)
  +  0.00000243362 * cos(0.01260786807 +      96.22304470130 * t)
  +  0.00000228016 * cos(4.72661469203 +     522.33360061030 * t)
  +  0.00000208205 * cos(0.02609578112 +     192.20227191910 * t)
  +  0.00000262941 * cos(2.24919351561 +     522.82123557730 * t)
  +  0.00000217559 * cos(3.69816995653 +     412.12727939089 * t)
  +  0.00000204218 * cos(0.74740242459 +     149.80701461810 * t)
  +  0.00000207097 * cos(0.47214424781 +     625.91400979590 * t)
  +  0.00000226266 * cos(0.43162189178 +     203.24797218300 * t)
  +  0.00000164818 * cos(1.21105459258 +     537.04832957890 * t)
  +  0.00000154166 * cos(0.52313104707 +     302.40859313851 * t)
  +  0.00000159821 * cos(3.57691788014 +     529.93478257810 * t)
  +  0.00000127987 * cos(4.67133129306 +     515.22005360950 * t)
  +  0.00000150521 * cos(5.90883755804 +     301.92095817150 * t)
  +  0.00000109809 * cos(0.87108590696 +     277.27881122490 * t)
  +  0.00000107126 * cos(2.60669435864 +      10.53875822200 * t)
  +  0.00000125246 * cos(1.70701686068 +     437.88770862340 * t)
  +  0.00000119913 * cos(5.60277656541 +     625.42637482889 * t)
  +  0.00000095870 * cos(2.12616183050 +      13.98327651810 * t)
  +  0.00000093192 * cos(0.34445551196 +     430.77416162260 * t)
  +  0.00000082653 * cos(0.98307709174 +     448.18264936190 * t)
  +  0.00000080395 * cos(3.02174862119 +     231.70216018621 * t)
  +  0.00000086059 * cos(5.78308214520 +     742.74624304909 * t)
  +  0.00000078439 * cos(2.37542883243 +     415.79630809560 * t)
  +  0.00000095719 * cos(5.10971036152 +     846.32665223470 * t)
  +  0.00000069822 * cos(4.50382031149 +     838.72547026689 * t)
  +  0.00000088159 * cos(3.12349955672 +     743.23387801611 * t)
  +  0.00000062703 * cos(3.46541693301 +     728.51914904750 * t)
  +  0.00000061768 * cos(0.31223820367 +       3.68833577960 * t)
  +  0.00000059007 * cos(2.35866131486 +     316.14805217309 * t)
  +  0.00000057483 * cos(3.58195443098 +      18.40306474821 * t)
  +  0.00000068064 * cos(1.33121226452 +     736.12033101530 * t)
  +  0.00000073156 * cos(4.57295172048 +     735.63269604830 * t)
  +  0.00000066143 * cos(0.61450499024 +     529.44714761109 * t)
  +  0.00000046643 * cos(4.39908344730 +     831.61192326610 * t)
  +  0.00000046381 * cos(1.16571256843 +     544.16187657970 * t)
  +  0.00000049127 * cos(2.41446662828 +     515.70768857651 * t)
  +  0.00000045075 * cos(2.04400929715 +     195.38366565681 * t)
  +  0.00000045874 * cos(4.71561784201 +     408.68276109481 * t)
  +  0.00000039597 * cos(4.90149000270 +    1073.85284167431 * t)
  +  0.00000037898 * cos(3.62258524288 +    1059.62574767270 * t)
  +  0.00000044466 * cos(5.29067071105 +     941.81824448550 * t)
  +  0.00000034788 * cos(6.24281796552 +     363.10611005610 * t)
  +  0.00000032598 * cos(0.67708460723 +     433.46792039329 * t)
  +  0.00000033292 * cos(5.12527889351 +     191.71463695210 * t)
  +  0.00000041206 * cos(5.63757151016 +     618.31282782810 * t)
  +  0.00000032714 * cos(5.53677499538 +    1059.13811270570 * t)
  +  0.00000041218 * cos(5.90724265736 +     636.20895053440 * t)
  +  0.00000036847 * cos(4.86141709685 +     223.10414047710 * t)
  +  0.00000028979 * cos(2.88486726124 +     113.63153244060 * t)
  +  0.00000030445 * cos(1.28493169701 +      56.37853381910 * t)
  +  0.00000038514 * cos(0.59603887895 +      86.07111631471 * t)
  +  0.00000033922 * cos(0.59559025853 +     437.13694909800 * t)
  +  0.00000029740 * cos(3.76166810670 +     270.16526422410 * t)
  +  0.00000034418 * cos(6.09770226922 +     643.32249753521 * t)
  +  0.00000031920 * cos(1.14730009415 +     337.97632814250 * t)
  +  0.00000035309 * cos(3.07697728911 +     203.98168536590 * t)
  +  0.00000026923 * cos(1.15025307434 +     131.79077970531 * t)
  +  0.00000026272 * cos(0.57392625326 +     750.34742501690 * t)
  +  0.00000025940 * cos(0.39280055678 +      76.50988875911 * t)
  +  0.00000029423 * cos(3.94515878782 +    1280.03839011150 * t)
  +  0.00000026782 * cos(4.26801091908 +    1155.11733992350 * t)
  +  0.00000024375 * cos(1.05933381750 +      81.50831573269 * t)
  +  0.00000025294 * cos(3.01418609936 +     483.46435966210 * t)
  +  0.00000023209 * cos(5.71293607821 +     867.66729323710 * t)
  +  0.00000022169 * cos(5.57360559022 +     288.32451148881 * t)
  +  0.00000023117 * cos(1.43000944484 +     227.28237195610 * t)
  +  0.00000021350 * cos(2.23904444472 +     160.85271488200 * t)
  +  0.00000022067 * cos(3.22469653238 +    1044.91101870410 * t)
  +  0.00000022088 * cos(3.66393393785 +      70.60562782070 * t)
  +  0.00000020601 * cos(0.57364692423 +      22.33521801130 * t)
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  +  0.00000001891 * cos(1.79946288763 +    1155.60497489050 * t)
  +  0.00000002205 * cos(5.85470490114 +     388.70897272171 * t)
  +  0.00000001597 * cos(4.15810623296 +     281.21096448800 * t)
  +  0.00000001719 * cos(1.15830791285 +     312.44290144610 * t)
  +  0.00000002158 * cos(2.28726893212 +     224.10097821840 * t)
  +  0.00000001659 * cos(4.74001893135 +     561.42735196710 * t)
  +  0.00000001737 * cos(0.17490306013 +     167.96626188280 * t)
  +  0.00000001501 * cos(0.25666873016 +     312.96665843540 * t)
  +  0.00000001587 * cos(3.94775538143 +     732.45130231059 * t)
  +  0.00000001488 * cos(2.72096839740 +      12.28635548869 * t)
  +  0.00000001460 * cos(2.11177924228 +    2627.35800195410 * t)
  +  0.00000001835 * cos(2.89416763419 +     206.47755003051 * t)
  +  0.00000001708 * cos(3.71608804699 +      82.13896305161 * t)
  +  0.00000001842 * cos(1.98442548678 +     220.60827581251 * t)
  +  0.00000001895 * cos(3.47648673336 +     291.50590522650 * t)
  +  0.00000001423 * cos(5.61838953778 +     225.32232636830 * t)
  +  0.00000001423 * cos(5.55442193599 +     201.76349947470 * t)
  +  0.00000001568 * cos(4.88514907741 +     685.71775483620 * t)
  +  0.00000001663 * cos(0.82161037585 +    3597.87425192630 * t)
  +  0.00000001491 * cos(0.52011503386 +     240.36961586451 * t)
  +  0.00000001913 * cos(0.07515794396 +     295.43805848960 * t)
  +  0.00000001496 * cos(1.53621258084 +    1045.39865367110 * t)
  +  0.00000001477 * cos(0.63538013406 +     440.58146739410 * t)
  +  0.00000001410 * cos(2.28174385720 +     137.27684164590 * t)
  +  0.00000001748 * cos(5.19272444741 +     519.15220687259 * t)
  +  0.00000001325 * cos(1.41732134877 +     980.91199584231 * t)
  +  0.00000001352 * cos(0.82085755018 +    5429.63565075589 * t)
  +  0.00000001414 * cos(1.50139243083 +    1371.59782909919 * t)
  +  0.00000001697 * cos(4.54037425682 +    1898.10740045609 * t)
  +  0.00000001424 * cos(4.89243708936 +     721.40560204669 * t)
  +  0.00000001424 * cos(1.75084443577 +     721.89323701370 * t)
  +  0.00000001295 * cos(0.66380326238 +    1905.22094745690 * t)
  +  0.00000001272 * cos(4.15261431749 +     127.71561409031 * t)
  +  0.00000001740 * cos(4.55214034273 +    1883.88030645450 * t)
  +  0.00000001435 * cos(0.26851729343 +     699.94484883781 * t)
  +  0.00000001260 * cos(5.67254228493 +     850.25880549781 * t)
  +  0.00000001316 * cos(2.05653832811 +    1382.64352936309 * t)
  +  0.00000001303 * cos(2.77196448848 +      28.69800548670 * t)
  +  0.00000001701 * cos(1.44281649853 +     312.70353387701 * t)
  +  0.00000001245 * cos(2.24439786330 +    9359.84534697549 * t)
  +  0.00000001240 * cos(2.86058076462 +    1994.08662767389 * t)
  +  0.00000001286 * cos(3.69806111108 +    1048.84317196720 * t)
  +  0.00000001240 * cos(4.77153818320 +     148.32254190981 * t)
  +  0.00000001365 * cos(0.95560209763 +     212.79215339611 * t)
  +  0.00000001362 * cos(3.93431918921 +     214.29367244690 * t)
  +  0.00000001206 * cos(3.84953492409 +     739.56484931140 * t)
  +  0.00000001503 * cos(5.21115384219 +    1243.98302014049 * t)
  +  0.00000001305 * cos(1.57242424750 +     259.11956396020 * t)
  +  0.00000001167 * cos(1.86683877227 +     233.18663289450 * t)
  +  0.00000001167 * cos(3.02278739432 +     193.89919294850 * t)
  +  0.00000001155 * cos(0.52398011340 +     153.73916788121 * t)
  +  0.00000001220 * cos(6.08058213690 +     283.90472325870 * t)
  +  0.00000001153 * cos(6.21046784748 +     525.74199688410 * t)
  +  0.00000001188 * cos(2.94352017149 +     258.63192899320 * t)
  +  0.00000001558 * cos(4.67220714738 +    4216.43089723790 * t)
  +  0.00000001423 * cos(3.77197308459 +    2420.68481854989 * t)
  +  0.00000001138 * cos(0.76214399254 +      17.91542978119 * t)
  +  0.00000001133 * cos(2.84505877314 +     841.90686400460 * t)
  +  0.00000001109 * cos(1.05776040432 +     121.00820399980 * t)
  +  0.00000001109 * cos(0.17173305113 +     629.84616305900 * t)
  +  0.00000001434 * cos(3.90656801196 +    6062.41939006910 * t)
  +  0.00000001122 * cos(2.45857726727 +     128.60938596760 * t)
  +  0.00000001123 * cos(3.06803578936 +    3178.38960805111 * t)
  +  0.00000001154 * cos(4.32058575911 +      67.91186905000 * t)
  +  0.00000001130 * cos(5.25611734741 +     731.70054278519 * t)
  +  0.00000001305 * cos(2.25262249590 +      97.11681657861 * t)
  +  0.00000001248 * cos(3.82251460637 +    2523.77759276850 * t)
  +  0.00000001161 * cos(2.25840723150 +      81.99595069970 * t)
  +  0.00000001178 * cos(0.70097671757 +    1056.44435393500 * t)
  +  0.00000001342 * cos(5.62104702567 +     355.99256305531 * t)
  +  0.00000001249 * cos(4.92175219077 +     526.26575387340 * t)
  +  0.00000001034 * cos(4.56345495168 +     777.17412795991 * t)
  +  0.00000001332 * cos(4.90721267162 +     835.54407652920 * t)
  +  0.00000001024 * cos(6.03631011372 +    5635.82119919310 * t)
  +  0.00000001173 * cos(4.16447862889 +      74.53778108379 * t)
  +  0.00000001173 * cos(3.45615871164 +    2317.59204433130 * t)
  +  0.00000001012 * cos(2.86472380431 +     215.23983395090 * t)
  +  0.00000001186 * cos(3.42680148463 +    1272.92484311070 * t)
  +  0.00000001049 * cos(1.32104580559 +    6062.90702503610 * t)
  +  0.00000001154 * cos(3.31945570971 +    2406.45772454830 * t)
  +  0.00000001062 * cos(3.40252606572 +     906.13039727500 * t)
  +  0.00000001124 * cos(0.61967036641 +    3914.26612158291 * t)
  +  0.00000000993 * cos(1.99202380463 +     211.84599189210 * t)
  +  0.00000000986 * cos(6.21774784663 +     525.51499434800 * t)
  +  0.00000000986 * cos(5.89248361654 +     602.00806815971 * t)
  +  0.00000000992 * cos(0.16374858268 +     306.34074640161 * t)
  +  0.00000001239 * cos(4.40402775047 +    2193.15862911030 * t)
  +  0.00000001134 * cos(3.08772580443 +    2729.96314120569 * t)
  +  0.00000001041 * cos(2.53935646805 +     945.75039774860 * t)
  +  0.00000001025 * cos(3.08133309612 +      32.48714639791 * t)
  +  0.00000001044 * cos(1.56254364362 +     472.41865939820 * t)
  +  0.00000001335 * cos(4.80329987516 +    2324.70559133209 * t)
  +  0.00000001199 * cos(4.40804047285 +    4113.33812301930 * t)
  +  0.00000001174 * cos(4.67336952922 +    1176.94561589290 * t)
  +  0.00000001213 * cos(0.28347383353 +     252.89978883670 * t)
  +  0.00000000973 * cos(1.75775518324 +     245.03548231051 * t)
  +  0.00000000973 * cos(6.27346363694 +     182.05034353251 * t)
  +  0.00000001167 * cos(6.08159477667 +     635.72131556739 * t)
  +  0.00000000936 * cos(3.32125427673 +     220.13519506050 * t)
  +  0.00000001073 * cos(3.85483987093 +    1773.67398523510 * t)
  +  0.00000000931 * cos(1.55716679047 +     206.95063078250 * t)
  +  0.00000000931 * cos(2.65028378733 +    1582.20316576650 * t)
  +  0.00000001237 * cos(1.19959870124 +    2964.60287764609 * t)
  +  0.00000001074 * cos(5.00882181931 +     738.81408978600 * t)
  +  0.00000000976 * cos(6.18216851835 +      31.99951143090 * t)
  +  0.00000000907 * cos(3.58111072001 +    1802.61580820530 * t)
  +  0.00000000925 * cos(2.76573994536 +    3494.78147770770 * t)
  +  0.00000000999 * cos(4.06676744721 +     171.89841514590 * t)
  +  0.00000000931 * cos(4.76188288294 +    1037.79747170330 * t)
  +  0.00000001094 * cos(3.85667770199 +    2516.66404576769 * t)
  +  0.00000000949 * cos(3.82779842438 +    1809.72935520611 * t)
  +  0.00000000964 * cos(2.57800328808 +    2641.58509595570 * t)
  +  0.00000000947 * cos(5.94253987889 +    2111.40649589409 * t)
  +  0.00000000898 * cos(1.16267053643 +    9566.03089541269 * t)
  +  0.00000001029 * cos(3.26133516597 +     519.63984183961 * t)
  +  0.00000000989 * cos(3.95452500658 +     255.18741069710 * t)
  +  0.00000001003 * cos(4.46395476902 +      60.52313540329 * t)
  +  0.00000000886 * cos(0.72851955442 +     305.10235190919 * t)
  +  0.00000000920 * cos(1.69743225247 +     459.08533727390 * t)
  +  0.00000000888 * cos(1.37138485948 +    3259.65410630030 * t)
  +  0.00000000888 * cos(4.51297751307 +    3260.14174126730 * t)
  +  0.00000000960 * cos(0.18926013762 +      84.68970947040 * t)
  +  0.00000000881 * cos(0.63602093080 +     397.90018538930 * t)
  +  0.00000000924 * cos(5.21301171350 +     731.92754532131 * t)
  +  0.00000000960 * cos(2.83183840474 +    5856.72147659890 * t)
  +  0.00000000886 * cos(0.13702548516 +     471.93102443120 * t)
  +  0.00000000909 * cos(1.30383200776 +     746.15463932291 * t)
  ) * pow(t, 2);
}

double saturn_y3(double t) {
  return (
     0.00076886822 * cos(1.38647122579 +     206.42936592071 * t)
  +  0.00075865107 * cos(0.30263761509 +     220.65645992230 * t)
  +  0.00028377246 * cos(2.29477516800 +       0.24381748350 * t)
  +  0.00011451297 * cos(5.24189857677 +     426.84200835950 * t)
  +  0.00009043324 * cos(5.61883049962 +     433.95555536030 * t)
  +  0.00007419530 * cos(0.21033373142 +     227.77000692311 * t)
  +  0.00008292033 * cos(1.50182614839 +       7.35736448430 * t)
  +  0.00004421142 * cos(0.64077885911 +     419.72846135871 * t)
  +  0.00003519324 * cos(1.53956700451 +     199.31581891990 * t)
  +  0.00003064445 * cos(4.39386454839 +     640.14110379750 * t)
  +  0.00002363042 * cos(1.46950181949 +      14.47091148511 * t)
  +  0.00001027777 * cos(4.71705572637 +     647.25465079831 * t)
  +  0.00000789743 * cos(5.60732845352 +     441.06910236111 * t)
  +  0.00000810744 * cos(5.98445458539 +     216.72430665921 * t)
  +  0.00000766386 * cos(2.03195290594 +     210.36151918381 * t)
  +  0.00000673097 * cos(5.33794721338 +     213.05527795450 * t)
  +  0.00000506614 * cos(2.17347656423 +     213.54291292150 * t)
  +  0.00000384956 * cos(1.47307672393 +     117.56368570370 * t)
  +  0.00000463540 * cos(3.55273822694 +     853.44019923550 * t)
  +  0.00000411246 * cos(2.18199166630 +     110.45013870291 * t)
  +  0.00000324142 * cos(0.07852229440 +     234.88355392390 * t)
  +  0.00000285917 * cos(0.41121094808 +     412.61491435790 * t)
  +  0.00000238406 * cos(1.75200857251 +     103.33659170210 * t)
  +  0.00000192441 * cos(5.32707204371 +     316.63568714010 * t)
  +  0.00000189600 * cos(0.69653910652 +       6.86972951729 * t)
  +  0.00000189610 * cos(0.69106705292 +     633.02755679670 * t)
  +  0.00000213874 * cos(0.85839521405 +     205.94173095370 * t)
  +  0.00000153605 * cos(0.70666490608 +     323.74923414091 * t)
  +  0.00000154083 * cos(1.31044116162 +      21.58445848590 * t)
  +  0.00000130169 * cos(6.09318414425 +     209.61075965840 * t)
  +  0.00000121811 * cos(0.47800554959 +     198.82818395289 * t)
  +  0.00000112652 * cos(6.07737302889 +     220.16882495529 * t)
  +  0.00000109203 * cos(1.75938966834 +     217.47506618460 * t)
  +  0.00000111589 * cos(3.84220589954 +     860.55374623631 * t)
  +  0.00000097336 * cos(2.54240833553 +      95.73540973430 * t)
  +  0.00000114728 * cos(5.87380874959 +     223.83785366000 * t)
  +  0.00000085497 * cos(0.31664832561 +     330.86278114170 * t)
  +  0.00000103793 * cos(1.39004326725 +     309.52214013930 * t)
  +  0.00000085243 * cos(4.74344019433 +     654.36819779910 * t)
  +  0.00000081972 * cos(1.72088205600 +     192.20227191910 * t)
  +  0.00000093735 * cos(4.66924086636 +     426.35437339250 * t)
  +  0.00000078232 * cos(6.26955569087 +     124.67723270450 * t)
  +  0.00000073732 * cos(2.62274205530 +      88.62186273350 * t)
  +  0.00000068659 * cos(4.66941001827 +     109.96250373590 * t)
  +  0.00000087657 * cos(5.07624062638 +     430.02340209721 * t)
  +  0.00000057790 * cos(0.13357560704 +     224.58861318540 * t)
  +  0.00000050888 * cos(1.52333865500 +     202.49721265760 * t)
  +  0.00000048029 * cos(2.25988634275 +     302.40859313851 * t)
  +  0.00000057606 * cos(2.26643847681 +     203.24797218300 * t)
  +  0.00000056960 * cos(2.75566102022 +    1066.73929467350 * t)
  +  0.00000045308 * cos(1.68344191762 +      96.22304470130 * t)
  +  0.00000048067 * cos(1.37320484001 +     309.03450517230 * t)
  +  0.00000036732 * cos(5.51470119579 +     448.18264936190 * t)
  +  0.00000038865 * cos(2.20650641493 +     625.91400979590 * t)
  +  0.00000043853 * cos(4.92071216020 +     422.90985509640 * t)
  +  0.00000036680 * cos(0.38116904350 +      13.98327651810 * t)
  +  0.00000035412 * cos(3.97478676019 +     522.82123557730 * t)
  +  0.00000030232 * cos(5.44165264045 +     412.12727939089 * t)
  +  0.00000034292 * cos(1.35598862213 +     301.92095817150 * t)
  +  0.00000025919 * cos(3.74498868983 +       4.17597074660 * t)
  +  0.00000026527 * cos(1.95025295633 +     423.66061462181 * t)
  +  0.00000023623 * cos(0.11328528018 +     515.22005360950 * t)
  +  0.00000017831 * cos(3.67540680263 +      11.28951774740 * t)
  +  0.00000017289 * cos(5.69767719550 +     537.04832957890 * t)
  +  0.00000016881 * cos(3.81249765736 +     195.38366565681 * t)
  +  0.00000013511 * cos(4.15427151016 +     515.70768857651 * t)
  +  0.00000012893 * cos(5.83608381063 +     437.88770862340 * t)
  +  0.00000011197 * cos(4.12727958334 +     742.74624304909 * t)
  +  0.00000013451 * cos(0.48023955262 +     522.33360061030 * t)
  +  0.00000010292 * cos(5.57616897093 +     337.97632814250 * t)
  +  0.00000011481 * cos(0.55900801750 +     191.71463695210 * t)
  +  0.00000011394 * cos(1.22639782189 +     625.42637482889 * t)
  +  0.00000011380 * cos(3.01802304028 +    1073.85284167431 * t)
  +  0.00000009884 * cos(5.68207864841 +     131.79077970531 * t)
  +  0.00000009268 * cos(2.85677606430 +      81.50831573269 * t)
  +  0.00000010374 * cos(5.65556228759 +     544.16187657970 * t)
  +  0.00000011913 * cos(5.03981077547 +     437.13694909800 * t)
  +  0.00000008626 * cos(5.23537891674 +     728.51914904750 * t)
  +  0.00000008671 * cos(5.89546440948 +     419.24082639170 * t)
  +  0.00000008821 * cos(6.14734947376 +     831.61192326610 * t)
  +  0.00000008112 * cos(5.21246168400 +     149.80701461810 * t)
  +  0.00000009768 * cos(1.10645539833 +     618.31282782810 * t)
  +  0.00000008329 * cos(3.90263564155 +     867.66729323710 * t)
  +  0.00000007645 * cos(0.82506284210 +     846.32665223470 * t)
  +  0.00000008659 * cos(4.22366027894 +     643.32249753521 * t)
  +  0.00000007205 * cos(5.97033515631 +     227.28237195610 * t)
  +  0.00000007157 * cos(4.06588017100 +     636.20895053440 * t)
  +  0.00000007036 * cos(1.06159700654 +     231.70216018621 * t)
  +  0.00000007083 * cos(3.27104541387 +      89.10949770051 * t)
  +  0.00000006556 * cos(1.10055926440 +     743.23387801611 * t)
  +  0.00000005903 * cos(5.58614673874 +     270.16526422410 * t)
  +  0.00000006615 * cos(5.20910906290 +     433.46792039329 * t)
  +  0.00000006469 * cos(0.48331749487 +     408.68276109481 * t)
  +  0.00000005426 * cos(6.23003978027 +     241.99710092470 * t)
  +  0.00000005648 * cos(0.98336733799 +     529.93478257810 * t)
  +  0.00000007105 * cos(1.44824281594 +      18.40306474821 * t)
  +  0.00000005052 * cos(3.61172453455 +     416.54706762100 * t)
  +  0.00000006189 * cos(3.11325347013 +     736.12033101530 * t)
  +  0.00000005821 * cos(1.93537322437 +    1280.03839011150 * t)
  +  0.00000005043 * cos(2.19686528643 +     277.27881122490 * t)
  +  0.00000004744 * cos(3.03559141046 +      56.37853381910 * t)
  +  0.00000005705 * cos(3.29935860753 +     430.77416162260 * t)
  +  0.00000005226 * cos(3.72017940288 +     415.79630809560 * t)
  +  0.00000005511 * cos(5.16650332361 +     529.44714761109 * t)
  +  0.00000004520 * cos(3.93668601315 +    1059.13811270570 * t)
  +  0.00000004583 * cos(1.57866732584 +     294.80741117069 * t)
  +  0.00000004789 * cos(2.57991417560 +     295.29504613770 * t)
  +  0.00000004026 * cos(4.75259771651 +     483.46435966210 * t)
  +  0.00000003728 * cos(4.95619377571 +     185.08872491831 * t)
  +  0.00000003578 * cos(0.94204754728 +     405.50136735710 * t)
  +  0.00000003890 * cos(5.00299059027 +     750.34742501690 * t)
  +  0.00000004291 * cos(0.89282309495 +     941.81824448550 * t)
  +  0.00000003758 * cos(4.69738792182 +     661.48174479990 * t)
  +  0.00000003547 * cos(1.97438574685 +      70.60562782070 * t)
  +  0.00000003641 * cos(2.23934061320 +     839.21310523390 * t)
  +  0.00000004196 * cos(2.40610831590 +     618.80046279510 * t)
  +  0.00000003709 * cos(0.25270527416 +     508.10650660869 * t)
  +  0.00000004193 * cos(0.33797589356 +     838.72547026689 * t)
  +  0.00000003571 * cos(6.03135821293 +    1148.00379292269 * t)
  +  0.00000003647 * cos(0.88659408340 +     934.70469748469 * t)
  +  0.00000002978 * cos(5.00861879701 +    1044.91101870410 * t)
  +  0.00000002876 * cos(3.72277336310 +     398.38782035631 * t)
  +  0.00000002643 * cos(3.66740434616 +     497.69145366371 * t)
  +  0.00000002725 * cos(4.31936427464 +     363.10611005610 * t)
  +  0.00000003246 * cos(4.14230106799 +     639.65346883050 * t)
  +  0.00000002721 * cos(5.71644537210 +    1464.39566257930 * t)
  +  0.00000002917 * cos(0.81283070390 +     113.63153244060 * t)
  +  0.00000002560 * cos(3.37970059304 +     729.00678401450 * t)
  +  0.00000002380 * cos(4.67244312905 +      86.07111631471 * t)
  +  0.00000002667 * cos(1.66091865719 +      10.80188278040 * t)
  +  0.00000002238 * cos(0.69261990800 +      10.53875822200 * t)
  +  0.00000002305 * cos(0.45579083441 +     956.53297345411 * t)
  +  0.00000002316 * cos(0.44164789425 +       3.42521122121 * t)
  +  0.00000002282 * cos(1.20272003403 +     611.19928082730 * t)
  +  0.00000001988 * cos(4.99900390794 +     651.18680406140 * t)
  +  0.00000002365 * cos(0.61916344902 +    2111.40649589409 * t)
  +  0.00000002485 * cos(5.89913021216 +     316.14805217309 * t)
  +  0.00000002670 * cos(5.34319853125 +     196.13442518220 * t)
  +  0.00000002670 * cos(5.82961294252 +     230.95140066080 * t)
  +  0.00000001974 * cos(1.72688011717 +    1059.62574767270 * t)
  +  0.00000002440 * cos(3.86794399442 +     106.03035047280 * t)
  +  0.00000002032 * cos(3.65372244155 +    1375.52998236229 * t)
  +  0.00000002151 * cos(6.26903391366 +     824.49837626530 * t)
  +  0.00000001875 * cos(6.21933237642 +     344.94686279140 * t)
  +  0.00000002440 * cos(2.94584507929 +     323.26159917390 * t)
  +  0.00000002034 * cos(0.93720484486 +     927.59115048390 * t)
  +  0.00000002310 * cos(0.13408163378 +      99.66756299740 * t)
  +  0.00000001764 * cos(0.29031425745 +     191.45151239371 * t)
  +  0.00000002032 * cos(2.17108818008 +     636.95971005981 * t)
  +  0.00000001993 * cos(0.70131684029 +    1258.21011414209 * t)
  +  0.00000001921 * cos(5.87131438069 +    2641.09746098870 * t)
  +  0.00000001620 * cos(4.33606938312 +    1596.43025976811 * t)
  +  0.00000001903 * cos(1.58126923147 +    2634.47154895491 * t)
  +  0.00000001568 * cos(1.46883265025 +     235.63431344930 * t)
  +  0.00000001835 * cos(2.03918042522 +     536.56069461190 * t)
  +  0.00000001523 * cos(6.05102540851 +     956.04533848709 * t)
  +  0.00000002086 * cos(0.06751029490 +     445.00125562421 * t)
  +  0.00000001666 * cos(3.27204219166 +    1876.76675945369 * t)
  +  0.00000001479 * cos(1.20460352519 +    6290.43321447570 * t)
  +  0.00000001479 * cos(0.55429461283 +    5849.12029463110 * t)
  +  0.00000001439 * cos(1.65531266077 +    2538.49232173710 * t)
  +  0.00000001464 * cos(5.75084658705 +    5863.34738863270 * t)
  +  0.00000001464 * cos(2.29123683992 +    6276.20612047410 * t)
  +  0.00000001676 * cos(0.63508426553 +    1251.09656714130 * t)
  +  0.00000001945 * cos(5.05629111259 +     845.83901726770 * t)
  +  0.00000001436 * cos(4.66419938107 +     508.59414157570 * t)
  +  0.00000001481 * cos(2.92781569338 +     284.39235822571 * t)
  +  0.00000001709 * cos(1.78635026289 +    2318.07967929830 * t)
  +  0.00000001305 * cos(2.53739213998 +     107.26874496520 * t)
  +  0.00000001548 * cos(1.24859563362 +    2943.74987161071 * t)
  +  0.00000001465 * cos(1.19825645294 +    2531.37877473630 * t)
  +  0.00000001494 * cos(5.51365686610 +    1780.78753223589 * t)
  +  0.00000001243 * cos(3.96240186696 +     218.20877936750 * t)
  +  0.00000001234 * cos(0.91112106896 +     208.87704647550 * t)
  +  0.00000001359 * cos(0.27102919236 +     142.69346761730 * t)
  +  0.00000001217 * cos(3.60020530728 +    1052.51220067191 * t)
  +  0.00000001352 * cos(1.92480185850 +     209.87388421679 * t)
  +  0.00000001391 * cos(0.65264575339 +    1243.98302014049 * t)
  +  0.00000001426 * cos(2.11026020785 +     852.95256426850 * t)
  +  0.00000001501 * cos(3.67811053153 +    1691.92185201890 * t)
  +  0.00000001326 * cos(4.70937835849 +    2751.79141717511 * t)
  +  0.00000001171 * cos(6.04141012834 +      67.91186905000 * t)
  +  0.00000001462 * cos(6.22305747248 +     160.85271488200 * t)
  +  0.00000001164 * cos(6.20382255072 +     117.07605073670 * t)
  +  0.00000001337 * cos(1.54820693649 +    2627.35800195410 * t)
  +  0.00000001509 * cos(0.21806196966 +    1574.60198379870 * t)
  +  0.00000001213 * cos(2.74422462860 +    1354.67697632690 * t)
  +  0.00000001241 * cos(5.97315240097 +    1140.89024592190 * t)
  +  0.00000001288 * cos(1.29947866802 +    2950.86341861150 * t)
  +  0.00000001337 * cos(2.21013619697 +    2421.17245351690 * t)
  +  0.00000001327 * cos(0.27411407224 +    1567.48843679789 * t)
  +  0.00000001118 * cos(4.60785389063 +     209.12312469139 * t)
  +  0.00000001043 * cos(2.37818871541 +     156.92056161890 * t)
  +  0.00000001069 * cos(4.66047916687 +     194.89603068979 * t)
  +  0.00000001088 * cos(0.96796460237 +    1272.92484311070 * t)
  +  0.00000001270 * cos(5.73542325903 +    2516.66404576769 * t)
  +  0.00000001032 * cos(5.01309781815 +    1361.30288836070 * t)
  +  0.00000001009 * cos(0.15463134354 +      52.44638055600 * t)
  +  0.00000001100 * cos(2.45485733183 +    1671.06884598351 * t)
  +  0.00000001071 * cos(4.31734498299 +    1354.18934135989 * t)
  +  0.00000001120 * cos(4.50723064884 +    1037.79747170330 * t)
  +  0.00000001271 * cos(3.02683993003 +     721.40560204669 * t)
  +  0.00000001009 * cos(4.14782207001 +    1670.58121101650 * t)
  +  0.00000001145 * cos(0.18866100481 +    3157.04896704871 * t)
  +  0.00000001072 * cos(4.98720300139 +    2435.39954751850 * t)
  +  0.00000001044 * cos(0.37186765557 +    1560.37488979710 * t)
  +  0.00000001195 * cos(4.23012320818 +     632.53992182970 * t)
  +  0.00000001043 * cos(4.68469356625 +    2729.96314120569 * t)
  +  0.00000000889 * cos(5.13451420872 +     359.17395679300 * t)
  +  0.00000000881 * cos(4.07324193143 +    1148.49142788971 * t)
  +  0.00000001040 * cos(5.49603658299 +    1773.67398523510 * t)
  +  0.00000001118 * cos(6.27960853334 +    1890.99385345530 * t)
  +  0.00000001047 * cos(0.97265004380 +    3260.14174126730 * t)
  +  0.00000001087 * cos(5.17936535207 +    2001.20017467470 * t)
  +  0.00000001087 * cos(2.03777269848 +    2001.68780964171 * t)
  +  0.00000000974 * cos(2.14268232218 +    1987.46071564010 * t)
  +  0.00000000869 * cos(0.17251420225 +     621.98185653281 * t)
  +  0.00000001085 * cos(1.32838349016 +    2214.98690507971 * t)
  +  0.00000000841 * cos(3.35616685398 +     629.09540353360 * t)
  +  0.00000000875 * cos(1.07922697964 +    2847.77064439291 * t)
  +  0.00000001063 * cos(5.95949690738 +    2200.27217611110 * t)
  +  0.00000000853 * cos(3.67902900562 +     288.32451148881 * t)
  +  0.00000001056 * cos(0.19418111722 +    2332.30677329990 * t)
  +  0.00000000888 * cos(0.32179471274 +    1155.11733992350 * t)
  +  0.00000001045 * cos(0.14482765695 +       2.93757625420 * t)
  +  0.00000000793 * cos(3.26245616640 +     341.01470952831 * t)
  +  0.00000000817 * cos(0.67889320689 +    1802.12817323829 * t)
  +  0.00000000780 * cos(0.38946586865 +    1382.64352936309 * t)
  +  0.00000000798 * cos(3.07896109863 +    2015.42726867629 * t)
  +  0.00000000798 * cos(3.07896109863 +    2015.91490364330 * t)
  +  0.00000000834 * cos(2.33901429584 +    1802.61580820530 * t)
  +  0.00000000766 * cos(0.30242307365 +    1471.50920958009 * t)
  +  0.00000000875 * cos(5.85387427791 +    2523.77759276850 * t)
  +  0.00000000829 * cos(4.44385893140 +    1162.23088692429 * t)
  +  0.00000000749 * cos(2.07951145157 +    1809.72935520611 * t)
  +  0.00000000942 * cos(3.40636938944 +    2008.31372167550 * t)
  +  0.00000000730 * cos(4.06050820225 +     138.76131435421 * t)
  +  0.00000000734 * cos(0.83381213045 +     749.85979004990 * t)
  +  0.00000000727 * cos(0.81605653091 +     181.29958400710 * t)
  +  0.00000000727 * cos(0.93197698209 +     245.78624183590 * t)
  +  0.00000000986 * cos(4.19789524983 +    1795.01462623750 * t)
  +  0.00000000914 * cos(1.81845398539 +     266.23311096100 * t)
  +  0.00000000774 * cos(1.85314072632 +    2840.16946242510 * t)
  +  0.00000000774 * cos(1.85314072632 +    2840.65709739210 * t)
  +  0.00000000806 * cos(2.87882505331 +    1912.82212942470 * t)
  +  0.00000000828 * cos(0.03130512468 +     100.15519796440 * t)
  +  0.00000000700 * cos(1.98220269537 +    9779.32999085069 * t)
  +  0.00000000700 * cos(2.62359991037 +   10220.64291069530 * t)
  +  0.00000000687 * cos(6.00740806604 +     102.84895673509 * t)
  +  0.00000000801 * cos(5.73752172813 +    1457.28211557850 * t)
  ) * pow(t, 3);
}

double saturn_y4(double t) {
  return (
     0.00007957923 * cos(4.81531837805 +     220.65645992230 * t)
  +  0.00007883034 * cos(3.09554141083 +     206.42936592071 * t)
  +  0.00001517028 * cos(4.76816117565 +     227.77000692311 * t)
  +  0.00001235695 * cos(3.82520659584 +     433.95555536030 * t)
  +  0.00001152216 * cos(3.67316954399 +     213.54291292150 * t)
  +  0.00000879616 * cos(3.77095350877 +       0.24381748350 * t)
  +  0.00000709628 * cos(3.24840338462 +     199.31581891990 * t)
  +  0.00000602013 * cos(5.94750261507 +       7.35736448430 * t)
  +  0.00000507367 * cos(3.21712935929 +     426.84200835950 * t)
  +  0.00000386382 * cos(6.01344501364 +      14.47091148511 * t)
  +  0.00000338827 * cos(2.51520356928 +     419.72846135871 * t)
  +  0.00000186029 * cos(3.85605990474 +     441.06910236111 * t)
  +  0.00000220262 * cos(2.50677283832 +     640.14110379750 * t)
  +  0.00000173210 * cos(2.89158751393 +     647.25465079831 * t)
  +  0.00000084974 * cos(4.62115933793 +     234.88355392390 * t)
  +  0.00000085340 * cos(4.39717612141 +     213.05527795450 * t)
  +  0.00000044264 * cos(6.05982256678 +     117.56368570370 * t)
  +  0.00000045849 * cos(5.16536949235 +       6.86972951729 * t)
  +  0.00000047835 * cos(1.64342336148 +     853.44019923550 * t)
  +  0.00000041104 * cos(2.18400968380 +     412.61491435790 * t)
  +  0.00000030735 * cos(5.85312406338 +      21.58445848590 * t)
  +  0.00000022639 * cos(2.96960991387 +     654.36819779910 * t)
  +  0.00000021067 * cos(3.34244726581 +     103.33659170210 * t)
  +  0.00000020230 * cos(0.17279084911 +     110.45013870291 * t)
  +  0.00000021389 * cos(2.53635561163 +     205.94173095370 * t)
  +  0.00000016854 * cos(4.38021440482 +     124.67723270450 * t)
  +  0.00000021739 * cos(1.99698913462 +     860.55374623631 * t)
  +  0.00000017501 * cos(4.23662156145 +     220.16882495529 * t)
  +  0.00000014506 * cos(4.39894976150 +      88.62186273350 * t)
  +  0.00000017401 * cos(2.26232682838 +     198.82818395289 * t)
  +  0.00000013517 * cos(3.33447998001 +     309.52214013930 * t)
  +  0.00000011814 * cos(5.16076867097 +     323.74923414091 * t)
  +  0.00000012071 * cos(3.74132731532 +     448.18264936190 * t)
  +  0.00000011725 * cos(4.75596558897 +     330.86278114170 * t)
  +  0.00000010174 * cos(4.42772116867 +      95.73540973430 * t)
  +  0.00000011491 * cos(3.65800261495 +     192.20227191910 * t)
  +  0.00000010611 * cos(4.07220720960 +     302.40859313851 * t)
  +  0.00000012147 * cos(2.66285969856 +     633.02755679670 * t)
  +  0.00000009067 * cos(4.26864930915 +      13.98327651810 * t)
  +  0.00000008918 * cos(3.03990460360 +     426.35437339250 * t)
  +  0.00000008311 * cos(3.10463384858 +     430.02340209721 * t)
  +  0.00000007296 * cos(0.77854151610 +     316.63568714010 * t)
  +  0.00000007890 * cos(0.94138641674 +    1066.73929467350 * t)
  +  0.00000006699 * cos(3.06921349305 +     109.96250373590 * t)
  +  0.00000006339 * cos(3.75710669061 +     216.72430665921 * t)
  +  0.00000006254 * cos(1.12954162648 +     210.36151918381 * t)
  +  0.00000006126 * cos(3.21971824010 +     301.92095817150 * t)
  +  0.00000006725 * cos(3.94118928489 +     625.91400979590 * t)
  +  0.00000006784 * cos(4.21865919120 +     223.83785366000 * t)
  +  0.00000006868 * cos(0.65717842769 +     203.24797218300 * t)
  +  0.00000006111 * cos(3.59045265634 +      96.22304470130 * t)
  +  0.00000004468 * cos(3.29229132687 +     309.03450517230 * t)
  +  0.00000004160 * cos(5.74668718431 +     522.82123557730 * t)
  +  0.00000003681 * cos(5.66131908910 +     423.66061462181 * t)
  +  0.00000003615 * cos(5.12190926865 +     405.50136735710 * t)
  +  0.00000003079 * cos(0.92409053273 +     412.12727939089 * t)
  +  0.00000003614 * cos(1.94380765622 +     515.22005360950 * t)
  +  0.00000002896 * cos(6.00160618678 +     515.70768857651 * t)
  +  0.00000003000 * cos(3.15709072507 +     422.90985509640 * t)
  +  0.00000002685 * cos(3.43239500452 +     209.61075965840 * t)
  +  0.00000002918 * cos(5.44500673473 +      89.10949770051 * t)
  +  0.00000002617 * cos(1.40935172097 +     217.47506618460 * t)
  +  0.00000002884 * cos(2.20199681607 +     191.71463695210 * t)
  +  0.00000002281 * cos(2.19064979800 +     316.14805217309 * t)
  +  0.00000002717 * cos(3.78847562141 +     131.79077970531 * t)
  +  0.00000002556 * cos(3.08407888684 +     337.97632814250 * t)
  +  0.00000001782 * cos(4.51078296370 +     241.99710092470 * t)
  +  0.00000001782 * cos(0.37884320289 +     185.08872491831 * t)
  +  0.00000001856 * cos(2.79299417712 +     618.31282782810 * t)
  +  0.00000001713 * cos(2.96942684848 +     625.42637482889 * t)
  +  0.00000001632 * cos(0.86290354268 +     728.51914904750 * t)
  +  0.00000001980 * cos(1.69424503948 +     831.61192326610 * t)
  +  0.00000001607 * cos(6.10863313121 +     611.19928082730 * t)
  +  0.00000001801 * cos(4.27647079459 +     227.28237195610 * t)
  +  0.00000001532 * cos(5.31288615169 +    1052.51220067191 * t)
  +  0.00000001510 * cos(2.58764647681 +     742.74624304909 * t)
  +  0.00000001531 * cos(0.19788540477 +     529.44714761109 * t)
  +  0.00000001394 * cos(3.60010141007 +    1361.30288836070 * t)
  +  0.00000001427 * cos(2.30374859738 +    1251.09656714130 * t)
  +  0.00000001649 * cos(4.25957274495 +     295.29504613770 * t)
  +  0.00000001249 * cos(3.74724649234 +     743.23387801611 * t)
  +  0.00000001353 * cos(4.07456235845 +    1678.18239298430 * t)
  +  0.00000001674 * cos(5.46467832773 +     231.70216018621 * t)
  +  0.00000001646 * cos(5.68811055040 +     195.38366565681 * t)
  +  0.00000001305 * cos(2.57485726113 +     934.70469748469 * t)
  +  0.00000001160 * cos(1.35876987453 +      81.50831573269 * t)
  +  0.00000001537 * cos(1.64895812279 +      21.09682351890 * t)
  +  0.00000001096 * cos(5.87040605326 +     832.09955823310 * t)
  +  0.00000001156 * cos(1.65604017773 +     508.10650660869 * t)
  +  0.00000001062 * cos(3.29348541593 +     294.80741117069 * t)
  +  0.00000001285 * cos(1.15881412669 +    1464.39566257930 * t)
  +  0.00000001079 * cos(4.46936132008 +    1368.90407032850 * t)
  +  0.00000001006 * cos(4.83365073160 +    1361.79052332771 * t)
  +  0.00000001290 * cos(4.69044132255 +     736.12033101530 * t)
  +  0.00000001051 * cos(2.68982495323 +     941.81824448550 * t)
  +  0.00000001027 * cos(3.70327166201 +     433.46792039329 * t)
  +  0.00000001021 * cos(2.48350861942 +     522.33360061030 * t)
  +  0.00000001137 * cos(2.90811550586 +    1891.48148842230 * t)
  +  0.00000000991 * cos(3.78009400759 +    1994.57426264090 * t)
  +  0.00000001038 * cos(1.35464465726 +    1148.00379292269 * t)
  +  0.00000000865 * cos(0.40802396366 +     750.34742501690 * t)
  +  0.00000000859 * cos(5.85730307132 +     416.54706762100 * t)
  +  0.00000000862 * cos(3.18022940336 +     437.13694909800 * t)
  +  0.00000000776 * cos(1.33793489456 +     102.84895673509 * t)
  +  0.00000000797 * cos(2.04691519292 +    1375.52998236229 * t)
  +  0.00000000824 * cos(4.53645127236 +     639.65346883050 * t)
  +  0.00000000881 * cos(3.45735740140 +    1258.69774910910 * t)
  +  0.00000000686 * cos(1.77528970097 +     234.39591895690 * t)
  +  0.00000000684 * cos(3.52622623805 +     661.48174479990 * t)
  +  0.00000000859 * cos(3.63825836835 +     537.04832957890 * t)
  ) * pow(t, 4);
}

double saturn_y5(double t) {
  return (
     0.00000605503 * cos(3.02566952553 +     220.65645992230 * t)
  +  0.00000576439 * cos(4.77676022633 +     206.42936592071 * t)
  +  0.00000227348 * cos(3.02005484310 +     227.77000692311 * t)
  +  0.00000133503 * cos(2.01762000448 +     433.95555536030 * t)
  +  0.00000094765 * cos(4.98454736271 +     199.31581891990 * t)
  +  0.00000039851 * cos(4.29556357711 +      14.47091148511 * t)
  +  0.00000034190 * cos(2.07372397023 +     441.06910236111 * t)
  +  0.00000024941 * cos(3.84014099419 +       0.24381748350 * t)
  +  0.00000023155 * cos(1.07127433478 +     647.25465079831 * t)
  +  0.00000016208 * cos(0.82050987845 +     426.84200835950 * t)
  +  0.00000012333 * cos(0.61142473697 +     640.14110379750 * t)
  +  0.00000010358 * cos(2.92988275487 +     234.88355392390 * t)
  +  0.00000010534 * cos(5.12660829509 +     419.72846135871 * t)
  +  0.00000008668 * cos(1.94893255744 +     192.20227191910 * t)
  +  0.00000008840 * cos(3.98137124653 +     213.54291292150 * t)
  +  0.00000004707 * cos(6.14618174587 +      88.62186273350 * t)
  +  0.00000005904 * cos(3.16028075613 +       7.35736448430 * t)
  +  0.00000003895 * cos(0.73151574345 +     405.50136735710 * t)
  +  0.00000003976 * cos(3.54063716264 +       6.86972951729 * t)
  +  0.00000003675 * cos(2.04382079343 +     213.05527795450 * t)
  +  0.00000003472 * cos(6.06844015557 +     853.44019923550 * t)
  +  0.00000004393 * cos(1.18474783269 +     654.36819779910 * t)
  +  0.00000003290 * cos(2.31998889526 +     124.67723270450 * t)
  +  0.00000002569 * cos(1.20332477401 +     109.96250373590 * t)
  +  0.00000002467 * cos(1.58903935784 +     515.70768857651 * t)
  +  0.00000002708 * cos(0.15976971982 +     860.55374623631 * t)
  +  0.00000002138 * cos(2.01599255393 +     448.18264936190 * t)
  +  0.00000002447 * cos(2.47106712193 +     220.16882495529 * t)
  +  0.00000001979 * cos(5.69757911363 +     302.40859313851 * t)
  +  0.00000002238 * cos(0.86043138018 +     198.82818395289 * t)
  +  0.00000001727 * cos(1.65089858299 +     301.92095817150 * t)
  +  0.00000001398 * cos(0.05843587724 +     309.52214013930 * t)
  +  0.00000001536 * cos(3.94854505604 +     205.94173095370 * t)
  +  0.00000001195 * cos(3.93835889247 +     117.56368570370 * t)
  +  0.00000001000 * cos(2.44450069185 +     223.83785366000 * t)
  +  0.00000000984 * cos(2.38499591413 +     203.24797218300 * t)
  +  0.00000000791 * cos(0.61482230222 +     330.86278114170 * t)
  +  0.00000000979 * cos(0.49750454847 +      95.73540973430 * t)
  +  0.00000000784 * cos(1.61990559836 +     522.82123557730 * t)
  +  0.00000000910 * cos(0.48207868964 +      96.22304470130 * t)
  ) * pow(t, 5);
}

double saturn_z0(double t) {
  return (
     0.41356950940 * cos(3.60234142982 +     213.29909543800 * t)
  +  0.01148283576 * cos(2.85128367469 +     426.59819087600 * t)
  +  0.01214249867
  +  0.00329280791 * cos(0.57121407104 +     206.18554843720 * t)
  +  0.00286934048 * cos(3.48073526693 +     220.41264243880 * t)
  +  0.00099076584 * cos(4.73369511264 +       7.11354700080 * t)
  +  0.00057361820 * cos(4.92611225093 +     110.20632121940 * t)
  +  0.00047738127 * cos(2.10039779728 +     639.89728631400 * t)
  +  0.00043458803 * cos(5.84904978051 +     419.48464387520 * t)
  +  0.00034565673 * cos(5.42614229590 +     316.39186965660 * t)
  +  0.00016185391 * cos(2.72987173675 +     433.71173787680 * t)
  +  0.00009001270 * cos(1.38140102737 +     103.09277421860 * t)
  +  0.00011433574 * cos(3.71662021072 +     529.69096509460 * t)
  +  0.00005398708 * cos(5.13204892363 +     202.25339517410 * t)
  +  0.00003902467 * cos(3.71499738796 +     323.50541665740 * t)
  +  0.00003709212 * cos(5.05549348785 +     632.78373931320 * t)
  +  0.00003614100 * cos(3.35210451276 +     227.52618943960 * t)
  +  0.00003379953 * cos(2.13868919206 +      11.04570026390 * t)
  +  0.00003089874 * cos(3.62572857085 +     209.36694217490 * t)
  +  0.00002683064 * cos(4.87689555581 +     224.34479570190 * t)
  +  0.00002963493 * cos(0.46490184985 +     217.23124870110 * t)
  +  0.00002343367 * cos(1.34558278340 +     853.19638175200 * t)
  +  0.00002423663 * cos(2.92907094760 +      63.73589830340 * t)
  +  0.00001701916 * cos(1.89892525654 +     735.87651353180 * t)
  +  0.00001941205 * cos(4.59421314662 +      14.22709400160 * t)
  +  0.00001990145 * cos(0.73166053611 +     199.07200143640 * t)
  +  0.00001460265 * cos(3.12851339724 +     522.57741809380 * t)
  +  0.00001148341 * cos(4.41139213915 +     117.31986822020 * t)
  +  0.00001092809 * cos(3.10679381209 +     216.48048917570 * t)
  +  0.00001015179 * cos(1.97897195994 +     647.01083331480 * t)
  +  0.00001098254 * cos(0.96097709156 +     210.11770170030 * t)
  +  0.00000991030 * cos(2.99610026682 +     846.08283475120 * t)
  +  0.00001028743 * cos(2.11933059243 +     415.55249061210 * t)
  +  0.00000907817 * cos(4.68576278610 +     309.27832265580 * t)
  +  0.00000818092 * cos(2.91497656196 +     149.56319713460 * t)
  +  0.00000733443 * cos(2.10018715614 +      74.78159856730 * t)
  +  0.00000631275 * cos(1.30557255814 +     277.03499374140 * t)
  +  0.00000574266 * cos(0.63353925382 +     490.33408917940 * t)
  +  0.00000471645 * cos(1.62329782277 +    1052.26838318840 * t)
  +  0.00000416292 * cos(5.88171380023 +      95.97922721780 * t)
  +  0.00000412467 * cos(2.56322277221 +    1162.47470440780 * t)
  +  0.00000381934 * cos(2.83850532211 +     838.96928775040 * t)
  +  0.00000370902 * cos(2.22356953874 +     351.81659230870 * t)
  +  0.00000337338 * cos(4.12487690436 +       3.93215326310 * t)
  +  0.00000263173 * cos(2.60594324261 +     440.82528487760 * t)
  +  0.00000245414 * cos(3.87716027424 +    1059.38193018920 * t)
  +  0.00000231186 * cos(2.79137518143 +     127.47179660680 * t)
  +  0.00000232835 * cos(1.69429632635 +      38.13303563780 * t)
  +  0.00000226218 * cos(0.98981012262 +     210.85141488320 * t)
  +  0.00000252287 * cos(3.04205345262 +     137.03302416240 * t)
  +  0.00000213656 * cos(3.00046819587 +     536.80451209540 * t)
  +  0.00000223924 * cos(3.07498346391 +     215.74677599280 * t)
  +  0.00000189917 * cos(5.75255233102 +     742.99006053260 * t)
  +  0.00000162873 * cos(3.89762690585 +     214.26230328450 * t)
  +  0.00000164510 * cos(2.45697452905 +     422.66603761290 * t)
  +  0.00000158304 * cos(2.31306407231 +    1478.86657406440 * t)
  +  0.00000156454 * cos(1.35680198123 +    1368.66025284500 * t)
  +  0.00000202699 * cos(3.85581899880 +     949.17560896980 * t)
  +  0.00000150079 * cos(4.14045329244 +     437.64389113990 * t)
  +  0.00000142705 * cos(2.58383947868 +    1155.36115740700 * t)
  +  0.00000163551 * cos(0.16578976592 +     212.33588759150 * t)
  +  0.00000135335 * cos(0.48883402314 +     213.34727954780 * t)
  +  0.00000129140 * cos(2.17035714121 +      76.26607127560 * t)
  +  0.00000128206 * cos(0.59415255592 +    1066.49547719000 * t)
  +  0.00000140534 * cos(3.97289861748 +     625.67019231240 * t)
  +  0.00000121564 * cos(4.51381049808 +       3.18139373770 * t)
  +  0.00000119190 * cos(1.61391416177 +     628.85158605010 * t)
  +  0.00000115147 * cos(3.43459040245 +     330.61896365820 * t)
  +  0.00000135375 * cos(3.57424025701 +     213.25091132820 * t)
  +  0.00000103727 * cos(6.17639441368 +     200.76892246580 * t)
  +  0.00000107498 * cos(3.52498564069 +     138.51749687070 * t)
  +  0.00000107560 * cos(3.99837836470 +      85.82729883120 * t)
  +  0.00000113808 * cos(0.43922136441 +     222.86032299360 * t)
  +  0.00000094920 * cos(2.26222536028 +     388.46515523820 * t)
  +  0.00000110037 * cos(3.51152757685 +    1265.56747862640 * t)
  +  0.00000101425 * cos(0.14126238472 +     430.53034413910 * t)
  +  0.00000101928 * cos(0.21047731069 +     412.37109687440 * t)
  +  0.00000104973 * cos(4.19518394917 +       9.56122755560 * t)
  +  0.00000083620 * cos(4.82013591775 +       1.48447270830 * t)
  +  0.00000071104 * cos(4.92741306047 +     212.77783057620 * t)
  +  0.00000070089 * cos(1.05108025259 +      12.53017297220 * t)
  +  0.00000066662 * cos(1.22617152895 +     860.30992875280 * t)
  +  0.00000077048 * cos(0.80511279723 +      52.69019803950 * t)
  +  0.00000090986 * cos(6.28198480720 +     423.41679713830 * t)
  +  0.00000062746 * cos(2.06105893244 +    1795.25844372100 * t)
  +  0.00000063467 * cos(2.36959372262 +     429.77958461370 * t)
  +  0.00000058999 * cos(2.31882650737 +    1471.75302706360 * t)
  +  0.00000076181 * cos(2.67435759741 +     191.20769491020 * t)
  +  0.00000063389 * cos(1.81556177589 +     350.33211960040 * t)
  +  0.00000056601 * cos(1.11303957705 +    1685.05212250160 * t)
  +  0.00000057837 * cos(3.29043420072 +     515.46387109300 * t)
  +  0.00000070959 * cos(5.41979944279 +     213.82036029980 * t)
  +  0.00000070150 * cos(3.82574373735 +     942.06206196900 * t)
  +  0.00000051149 * cos(3.86030131690 +     173.94221952280 * t)
  +  0.00000051666 * cos(3.49111344070 +     203.73786788240 * t)
  +  0.00000050128 * cos(1.98273693937 +     195.13984817330 * t)
  +  0.00000048091 * cos(3.20971334548 +     234.63973644040 * t)
  +  0.00000049761 * cos(6.18808156638 +     703.63318461740 * t)
  +  0.00000046488 * cos(3.80768518798 +     225.82926841020 * t)
  +  0.00000054298 * cos(3.18076013146 +    1581.95934828300 * t)
  +  0.00000047483 * cos(1.53655093485 +     265.98929347750 * t)
  +  0.00000039354 * cos(2.10537295968 +     728.76296653100 * t)
  +  0.00000039602 * cos(2.27507746067 +     288.08069400530 * t)
  +  0.00000041716 * cos(1.05111221485 +     563.63121503840 * t)
  +  0.00000037614 * cos(6.14179074602 +     217.49188113200 * t)
  +  0.00000042785 * cos(0.11273484212 +     252.65597135320 * t)
  +  0.00000037718 * cos(5.96333653993 +     210.37833413120 * t)
  +  0.00000036792 * cos(1.35292393469 +     565.11568774670 * t)
  +  0.00000037862 * cos(4.00773869969 +      62.25142559510 * t)
  +  0.00000036057 * cos(3.30899953753 +     212.54833591260 * t)
  +  0.00000035460 * cos(5.01105830246 +      65.22037101170 * t)
  +  0.00000034852 * cos(4.75445504646 +     207.88246946660 * t)
  +  0.00000040506 * cos(2.20073759144 +     362.86229257260 * t)
  +  0.00000032560 * cos(6.14806301843 +     417.03696332040 * t)
  +  0.00000037967 * cos(4.57075294928 +     302.16477565500 * t)
  +  0.00000032818 * cos(5.79538785685 +      99.16062095550 * t)
  +  0.00000030744 * cos(3.64317302294 +     207.67002114550 * t)
  +  0.00000032548 * cos(2.95740474962 +      70.84944530420 * t)
  +  0.00000035830 * cos(0.75230512173 +     214.04985496340 * t)
  +  0.00000034253 * cos(2.96835157474 +     223.59403617650 * t)
  +  0.00000032939 * cos(4.45144712576 +      21.34064100240 * t)
  +  0.00000037689 * cos(4.37977418287 +     216.21985674480 * t)
  +  0.00000032421 * cos(5.78559756829 +     160.60889739850 * t)
  +  0.00000028902 * cos(5.81529149124 +      88.86568021700 * t)
  +  0.00000033335 * cos(5.62401622695 +     218.71572140940 * t)
  +  0.00000038185 * cos(4.19997816879 +     209.10630974400 * t)
  +  0.00000027693 * cos(5.55618950213 +      18.15924726470 * t)
  +  0.00000028922 * cos(5.58858980738 +     425.11371816770 * t)
  +  0.00000032330 * cos(4.22794944092 +      22.09140052780 * t)
  +  0.00000029913 * cos(3.31182307103 +     124.43341522100 * t)
  +  0.00000029455 * cos(5.83042047243 +     956.28915597060 * t)
  +  0.00000026648 * cos(0.86666603224 +     217.96496188400 * t)
  +  0.00000025659 * cos(5.10869894674 +     479.28838891550 * t)
  +  0.00000025652 * cos(4.80215156054 +     231.45834270270 * t)
  +  0.00000026011 * cos(2.05589181933 +    1788.14489672020 * t)
  +  0.00000025663 * cos(1.81564756635 +    2111.65031337760 * t)
  +  0.00000022977 * cos(5.44037839738 +     142.44965013380 * t)
  +  0.00000031283 * cos(3.54881062563 +    1258.45393162560 * t)
  +  0.00000030192 * cos(0.42929684303 +     218.92816973050 * t)
  +  0.00000026495 * cos(2.86288115466 +    1898.35121793960 * t)
  +  0.00000029523 * cos(0.37961341545 +     554.06998748280 * t)
  +  0.00000022228 * cos(5.48142509504 +     408.43894361130 * t)
  +  0.00000021237 * cos(0.87139429027 +    2001.44399215820 * t)
  +  0.00000020174 * cos(1.85380647370 +     654.12438031560 * t)
  +  0.00000020521 * cos(6.16117414568 +      56.62235130260 * t)
  +  0.00000023744 * cos(3.20046265011 +     208.63322899200 * t)
  +  0.00000021685 * cos(3.17871482760 +     414.06801790380 * t)
  +  0.00000019856 * cos(3.13857572740 +     175.16605980020 * t)
  +  0.00000017347 * cos(5.96946168051 +     213.18722085340 * t)
  +  0.00000017925 * cos(1.14556340660 +     203.00415469950 * t)
  +  0.00000018247 * cos(3.00127995342 +     831.85574074960 * t)
  +  0.00000017378 * cos(0.74127655202 +     177.87437278590 * t)
  +  0.00000016401 * cos(1.36402971878 +     211.81462272970 * t)
  +  0.00000016228 * cos(3.17582194781 +      98.89998852460 * t)
  +  0.00000016107 * cos(0.54971362869 +     251.43213107580 * t)
  +  0.00000015546 * cos(2.29108586908 +     750.10360753340 * t)
  +  0.00000014801 * cos(0.20111341190 +     148.07872442630 * t)
  +  0.00000015320 * cos(3.80296373340 +     483.22054217860 * t)
  +  0.00000014467 * cos(1.32549449124 +     114.13847448250 * t)
  +  0.00000014146 * cos(4.85276668809 +     327.43756992050 * t)
  +  0.00000015436 * cos(1.48161033604 +     198.32124191100 * t)
  +  0.00000014576 * cos(3.75966213667 +     213.51154375910 * t)
  +  0.00000014820 * cos(3.34957428396 +     248.72381809010 * t)
  +  0.00000013743 * cos(4.77276011938 +     106.27416795630 * t)
  +  0.00000017347 * cos(4.37930417897 +     213.41097002260 * t)
  +  0.00000014576 * cos(0.30591841563 +     213.08664711690 * t)
  +  0.00000013755 * cos(2.59733474149 +     228.27694896500 * t)
  +  0.00000012945 * cos(1.84552645547 +    1045.15483618760 * t)
  +  0.00000012834 * cos(4.24597463890 +      10.29494073850 * t)
  +  0.00000012885 * cos(4.86095700310 +      39.35687591520 * t)
  +  0.00000016969 * cos(1.27721722241 +     214.78356814630 * t)
  +  0.00000012706 * cos(0.31024660308 +     424.15051032120 * t)
  +  0.00000012558 * cos(0.03128357867 +    1272.68102562720 * t)
  +  0.00000014310 * cos(2.34661407283 +    1375.77379984580 * t)
  +  0.00000011808 * cos(1.79617614059 +    2104.53676637680 * t)
  +  0.00000013258 * cos(2.56724178887 +    2214.74308759620 * t)
  +  0.00000011158 * cos(0.45949551763 +     497.44763618020 * t)
  +  0.00000014798 * cos(1.03056978581 +       2.44768055480 * t)
  +  0.00000014861 * cos(3.26343762010 +    1574.84580128220 * t)
  +  0.00000011978 * cos(6.22486801109 +     121.25202148330 * t)
  +  0.00000010959 * cos(1.31570222417 +     235.39049596580 * t)
  +  0.00000011901 * cos(1.58846496072 +     635.96513305090 * t)
  +  0.00000011080 * cos(5.37041305935 +    1169.58825140860 * t)
  +  0.00000010475 * cos(2.19368288733 +     221.37585028530 * t)
  +  0.00000012129 * cos(4.63783219973 +     269.92144674060 * t)
  +  0.00000010959 * cos(4.40512358221 +     213.55972786890 * t)
  +  0.00000010673 * cos(1.60141035946 +    2428.04218303420 * t)
  +  0.00000013041 * cos(1.87126265057 +     151.04766984290 * t)
  +  0.00000011521 * cos(2.11579255167 +     205.22234059070 * t)
  +  0.00000010228 * cos(2.41342516828 +     275.55052103310 * t)
  +  0.00000010229 * cos(0.96548776504 +     842.15068148810 * t)
  +  0.00000010959 * cos(5.94363969204 +     213.03846300710 * t)
  +  0.00000009406 * cos(3.39740548756 +     650.94298657790 * t)
  +  0.00000010284 * cos(0.01930234298 +     219.44943459230 * t)
  +  0.00000009424 * cos(1.68112701238 +     488.84961647110 * t)
  +  0.00000008939 * cos(5.28697277625 +     340.77089204480 * t)
  +  0.00000009017 * cos(2.70864683669 +    1692.16566950240 * t)
  +  0.00000009979 * cos(3.97256303244 +     278.51946644970 * t)
  +  0.00000008356 * cos(0.65143790392 +    2317.83586181480 * t)
  +  0.00000009107 * cos(0.33774330802 +   10213.28554621100 * t)
  +  0.00000008169 * cos(3.23957036879 +     427.56139872250 * t)
  +  0.00000009044 * cos(0.23054654773 +     312.19908396260 * t)
  +  0.00000007927 * cos(3.97539997718 +     210.59078245230 * t)
  +  0.00000010063 * cos(4.21498692120 +     618.55664531160 * t)
  +  0.00000009335 * cos(5.70779396792 +     425.63498302950 * t)
  +  0.00000008385 * cos(0.64196694648 +     188.92007304980 * t)
  +  0.00000008670 * cos(2.75601079050 +     491.81856188770 * t)
  +  0.00000008100 * cos(4.06039030284 +     207.14875628370 * t)
  +  0.00000009452 * cos(2.59277908129 +     429.04587143080 * t)
  +  0.00000007738 * cos(1.55361395079 +     601.76425067620 * t)
  +  0.00000007577 * cos(6.02114380426 +     426.64637498580 * t)
  +  0.00000009275 * cos(5.16642875471 +       8.07675484730 * t)
  +  0.00000007638 * cos(2.70476229552 +     543.91805909620 * t)
  +  0.00000007663 * cos(2.73399784358 +    1148.24761040620 * t)
  +  0.00000007158 * cos(5.84039229615 +      84.34282612290 * t)
  +  0.00000008033 * cos(4.20065885029 +     767.36908292080 * t)
  +  0.00000006822 * cos(6.12047591103 +    1279.79457262800 * t)
  +  0.00000008887 * cos(4.87842237223 +    1589.07289528380 * t)
  +  0.00000006961 * cos(3.34826318442 +     237.67811782620 * t)
  +  0.00000006580 * cos(5.81874339759 +     284.14854074220 * t)
  +  0.00000006629 * cos(1.53732206945 +     289.56516671360 * t)
  +  0.00000006283 * cos(3.84796221759 +     125.98732389850 * t)
  +  0.00000007796 * cos(0.08813581424 +     216.00740842370 * t)
  +  0.00000008282 * cos(1.90022750359 +     134.58534360760 * t)
  +  0.00000006576 * cos(0.35050721605 +     220.46082654860 * t)
  +  0.00000006587 * cos(0.58291546593 +     213.45915413240 * t)
  +  0.00000006378 * cos(6.14309601319 +      73.29712585900 * t)
  +  0.00000006626 * cos(3.37506241952 +     312.45971639350 * t)
  +  0.00000006587 * cos(3.48062808501 +     213.13903674360 * t)
  +  0.00000007576 * cos(2.82334902636 +     426.55000676620 * t)
  +  0.00000005988 * cos(5.47551169354 +      35.42472265210 * t)
  +  0.00000005723 * cos(5.22938546212 +     212.02707105080 * t)
  +  0.00000006565 * cos(5.18423527980 +      67.66805156650 * t)
  +  0.00000005704 * cos(5.31164037710 +    1485.98012106520 * t)
  +  0.00000006842 * cos(6.15429926594 +     179.35884549420 * t)
  +  0.00000007349 * cos(0.73079523905 +     355.74874557180 * t)
  +  0.00000005590 * cos(4.19082216094 +     247.23934538180 * t)
  +  0.00000006488 * cos(2.29038019982 +    2531.13495725280 * t)
  +  0.00000007413 * cos(2.98595847215 +    1891.23767093880 * t)
  +  0.00000005491 * cos(2.70527999156 +    2008.55753915900 * t)
  +  0.00000005820 * cos(2.98199777797 +       5.41662597140 * t)
  +  0.00000005622 * cos(1.45901882320 +     501.37978944330 * t)
  +  0.00000005473 * cos(0.81641753389 +     181.05576652360 * t)
  +  0.00000005454 * cos(6.12211624341 +     643.82943957710 * t)
  +  0.00000005407 * cos(1.53066536154 +    2420.92863603340 * t)
  +  0.00000005442 * cos(0.02368001914 +     404.50679034820 * t)
  +  0.00000005436 * cos(4.67977840196 +     621.73803904930 * t)
  +  0.00000006267 * cos(5.43877709236 +     636.71589257630 * t)
  +  0.00000005068 * cos(4.33978904750 +     113.38771495710 * t)
  +  0.00000004865 * cos(5.10809843245 +      69.15252427480 * t)
  +  0.00000005070 * cos(3.27536823314 +     144.14657116320 * t)
  +  0.00000004738 * cos(0.53669462342 +    1073.60902419080 * t)
  +  0.00000005183 * cos(2.18841260581 +     107.02492748170 * t)
  +  0.00000005310 * cos(0.66732715963 +     116.42609634290 * t)
  +  0.00000005141 * cos(2.42998599018 +     692.58748435350 * t)
  +  0.00000006231 * cos(5.93759865879 +     436.15941843160 * t)
  +  0.00000006367 * cos(3.45785496152 +     220.36445832900 * t)
  +  0.00000004541 * cos(0.61777794179 +     206.23373254700 * t)
  +  0.00000004528 * cos(1.65756596310 +    1361.54670584420 * t)
  +  0.00000005172 * cos(4.96799695932 +     342.25536475310 * t)
  +  0.00000005805 * cos(2.10740836405 +       4.66586644600 * t)
  +  0.00000004639 * cos(1.63821364676 +       5.62907429250 * t)
  +  0.00000004731 * cos(1.44641985940 +    2744.43405269080 * t)
  +  0.00000004756 * cos(3.73287086188 +     206.13736432740 * t)
  +  0.00000004322 * cos(4.15153138812 +     426.07692601420 * t)
  +  0.00000004167 * cos(1.65241802351 +     191.95845443560 * t)
  +  0.00000004164 * cos(2.47912208303 +     447.93883187840 * t)
  +  0.00000005676 * cos(5.11706007934 +     214.57111982520 * t)
  +  0.00000003966 * cos(0.05086647098 +     206.70681329900 * t)
  +  0.00000004603 * cos(5.52562693778 +      78.71375183040 * t)
  +  0.00000003802 * cos(0.43628874694 +     617.80588578620 * t)
  +  0.00000004800 * cos(5.54041183899 +     344.70304530790 * t)
  +  0.00000004743 * cos(0.53760335914 +     128.95626931510 * t)
  +  0.00000004130 * cos(1.61538042826 +     643.07868005170 * t)
  +  0.00000004686 * cos(3.97383030786 +     934.94851496820 * t)
  +  0.00000004043 * cos(2.18819710124 +     358.93013930950 * t)
  +  0.00000003906 * cos(5.19970623343 +     630.33605875840 * t)
  +  0.00000003883 * cos(5.39147665291 +     320.32402291970 * t)
  +  0.00000004913 * cos(1.03288629446 +      32.24332891440 * t)
  +  0.00000003689 * cos(5.45822055399 +     916.93228005540 * t)
  +  0.00000004228 * cos(4.28360558940 +       4.19278569400 * t)
  +  0.00000004020 * cos(4.88073386744 +      54.17467074780 * t)
  +  0.00000004185 * cos(3.32405342181 +     245.54242435240 * t)
  +  0.00000004583 * cos(1.85097979187 +     114.39910691340 * t)
  +  0.00000004596 * cos(4.18504944347 +     219.89137757700 * t)
  +  0.00000003552 * cos(5.98005739127 +      20.60692781950 * t)
  +  0.00000003975 * cos(5.80157206371 +      14.97785352700 * t)
  +  0.00000003475 * cos(2.47178960968 +    1464.63948006280 * t)
  +  0.00000004395 * cos(0.85418906454 +     525.49817940060 * t)
  +  0.00000003187 * cos(2.61148353061 +    2324.94940881560 * t)
  +  0.00000003966 * cos(4.66662911986 +     427.11945573780 * t)
  +  0.00000003124 * cos(0.10655817305 +      14.01464568050 * t)
  +  0.00000003104 * cos(0.38849805992 +    2634.22773147140 * t)
  +  0.00000003508 * cos(2.85265213502 +      87.31177153950 * t)
  +  0.00000002979 * cos(3.04084830124 +     420.96911658350 * t)
  +  0.00000003143 * cos(1.71420147928 +       0.96320784650 * t)
  +  0.00000003169 * cos(1.34499488466 +     159.12442469020 * t)
  +  0.00000003871 * cos(2.71348462732 +    2207.62954059540 * t)
  +  0.00000002814 * cos(0.52649713800 +     778.41478318470 * t)
  +  0.00000002890 * cos(1.29415320006 +    2737.32050569000 * t)
  +  0.00000002831 * cos(4.45595764630 +     518.64526483070 * t)
  +  0.00000002757 * cos(2.05371431350 +     214.52293571540 * t)
  +  0.00000002757 * cos(2.83591185309 +     212.07525516060 * t)
  +  0.00000003187 * cos(2.00772012188 +    2847.52682690940 * t)
  +  0.00000002712 * cos(5.27492060596 +     305.34616939270 * t)
  +  0.00000002771 * cos(2.54360038772 +     319.57326339430 * t)
  +  0.00000002630 * cos(5.50124179878 +     423.67742956920 * t)
  +  0.00000002626 * cos(0.49212317679 +     153.49535039770 * t)
  +  0.00000002828 * cos(3.04457317761 +     211.60217440860 * t)
  +  0.00000002650 * cos(2.71849987794 +     145.63104387150 * t)
  +  0.00000002589 * cos(5.18248239650 +    1802.37199072180 * t)
  +  0.00000002579 * cos(1.68789924795 +       6.15033915430 * t)
  +  0.00000003452 * cos(0.69033243447 +     776.93031047640 * t)
  +  0.00000002527 * cos(3.47384786002 +     184.98791978670 * t)
  +  0.00000002496 * cos(5.96218386110 +       2.92076130680 * t)
  +  0.00000003222 * cos(3.60809233593 +    1251.34038462480 * t)
  +  0.00000002684 * cos(5.48972047825 +     391.17346822390 * t)
  +  0.00000002370 * cos(1.54660575926 +      51.20572533120 * t)
  +  0.00000002310 * cos(0.63846192912 +     416.30325013750 * t)
  +  0.00000002444 * cos(3.87972666346 +     182.27960680100 * t)
  +  0.00000002435 * cos(2.71829697900 +     627.36711334180 * t)
  +  0.00000002236 * cos(1.31003501645 +     241.61027108930 * t)
  +  0.00000002653 * cos(5.70255270090 +     220.93390730060 * t)
  +  0.00000002646 * cos(3.30185009916 +     696.51963761660 * t)
  +  0.00000002211 * cos(4.72699183302 +     387.24131496080 * t)
  +  0.00000002313 * cos(2.81517281649 +     738.79727483860 * t)
  +  0.00000002197 * cos(2.63929129920 +     436.89313161450 * t)
  +  0.00000002348 * cos(1.83689902078 +     214.99601646740 * t)
  +  0.00000002842 * cos(2.88171478117 +     337.73251065900 * t)
  +  0.00000002195 * cos(1.58125142363 +    1677.93857550080 * t)
  +  0.00000002609 * cos(1.41922918177 +     329.72519178090 * t)
  +  0.00000002207 * cos(5.67197607780 +     905.88657979150 * t)
  +  0.00000002182 * cos(3.15263816837 +     439.12836384820 * t)
  +  0.00000002060 * cos(5.78919528834 +     120.35824960600 * t)
  +  0.00000002079 * cos(5.08007114480 +       7.06536289100 * t)
  +  0.00000002351 * cos(0.26849523535 +     140.00196957900 * t)
  +  0.00000002770 * cos(4.57559729641 +      24.37902238820 * t)
  +  0.00000002705 * cos(4.32491993913 +      46.47042291600 * t)
  +  0.00000002052 * cos(1.22649156182 +      92.04707395470 * t)
  +  0.00000002046 * cos(5.19173373776 +     347.88443904560 * t)
  +  0.00000002036 * cos(2.88971262431 +     980.66817835880 * t)
  +  0.00000002481 * cos(1.55318712059 +     576.16138801060 * t)
  +  0.00000002024 * cos(4.32935289944 +      31.01948863700 * t)
  +  0.00000002006 * cos(2.01138855049 +     211.86280683950 * t)
  +  0.00000002006 * cos(2.87823761610 +     214.73538403650 * t)
  +  0.00000002026 * cos(2.42235724251 +    2641.34127847220 * t)
  +  0.00000001938 * cos(2.48016602910 +     487.36514376280 * t)
  +  0.00000002065 * cos(1.16081214330 +     192.69216761850 * t)
  +  0.00000002254 * cos(5.99623174740 +    1905.46476494040 * t)
  +  0.00000001922 * cos(5.98223148262 +      96.87299909510 * t)
  +  0.00000002534 * cos(2.62272549680 +     421.93232443000 * t)
  +  0.00000002106 * cos(1.84883841490 +     299.12639426920 * t)
  +  0.00000002211 * cos(1.86083014117 +     221.16340196420 * t)
  +  0.00000002083 * cos(6.14443432076 +      59.80374504030 * t)
  +  0.00000001909 * cos(1.13231253998 +     282.45161971280 * t)
  +  0.00000001898 * cos(3.53454927143 +     219.66188291340 * t)
  +  0.00000002007 * cos(4.35167828920 +     444.75743814070 * t)
  +  0.00000001974 * cos(5.78637079670 +     430.79097657000 * t)
  +  0.00000001937 * cos(4.03561100629 +     429.51895218280 * t)
  +  0.00000001838 * cos(2.97004270413 +     425.84743135060 * t)
  +  0.00000001880 * cos(3.59058053053 +    3340.61242669980 * t)
  +  0.00000001858 * cos(5.83605607376 +     280.96714700450 * t)
  +  0.00000001768 * cos(4.86059839675 +    2118.76386037840 * t)
  +  0.00000002128 * cos(3.95375781114 +     831.10498122420 * t)
  +  0.00000002111 * cos(5.51034879271 +     428.08266358430 * t)
  +  0.00000002359 * cos(3.95534711749 +       2.96894541660 * t)
  +  0.00000002084 * cos(4.99656154667 +     254.94359321360 * t)
  +  0.00000002189 * cos(5.75843317256 +     418.52143602870 * t)
  +  0.00000002225 * cos(5.22774546552 +     638.41281360570 * t)
  +  0.00000002362 * cos(0.10821349524 +     131.40394986990 * t)
  +  0.00000001938 * cos(3.62212314488 +     267.47376618580 * t)
  +  0.00000002349 * cos(2.45602769901 +    2524.02141025200 * t)
  +  0.00000001752 * cos(0.17721513623 +     969.62247809490 * t)
  +  0.00000002216 * cos(4.46378373321 +     353.30106501700 * t)
  +  0.00000001697 * cos(3.74680430424 +     421.18156490460 * t)
  +  0.00000001692 * cos(1.29673821700 +    2840.41327990860 * t)
  +  0.00000001698 * cos(2.09387250037 +     292.01284726840 * t)
  +  0.00000002118 * cos(2.90133577623 +     205.43478891180 * t)
  +  0.00000002049 * cos(1.88559014939 +     199.28444975750 * t)
  +  0.00000001712 * cos(2.97477489664 +     273.10284047830 * t)
  +  0.00000001828 * cos(2.23147050409 +    1781.03134971940 * t)
  +  0.00000001933 * cos(3.33016281296 +     533.62311835770 * t)
  +  0.00000001737 * cos(2.59432238776 +     264.50482076920 * t)
  +  0.00000001676 * cos(2.73737546375 +    3480.31056622260 * t)
  +  0.00000001935 * cos(2.01080991907 +       7.16173111060 * t)
  +  0.00000001602 * cos(4.81017819939 +    1382.88734684660 * t)
  +  0.00000001894 * cos(4.74702697079 +     558.00214074590 * t)
  +  0.00000001589 * cos(0.85622467383 +    1044.40407666220 * t)
  +  0.00000001565 * cos(5.03064453644 +     458.84151979040 * t)
  +  0.00000001648 * cos(5.00766073214 +    2648.45482547300 * t)
  +  0.00000001562 * cos(4.62304098893 +     543.02428721890 * t)
  +  0.00000001794 * cos(2.92299868481 +     227.31374111850 * t)
  +  0.00000001844 * cos(6.25012647811 +     432.22726516850 * t)
  +  0.00000001821 * cos(5.47892889469 +     205.66428357540 * t)
  +  0.00000001605 * cos(2.57251520836 +    3127.31333126180 * t)
  +  0.00000001477 * cos(1.36669731999 +     206.93630796260 * t)
  +  0.00000001468 * cos(4.67912895132 +     339.28641933650 * t)
  +  0.00000001481 * cos(0.92457754588 +    1994.33044515740 * t)
  +  0.00000001547 * cos(0.13419340100 +     465.95506679120 * t)
  +  0.00000001457 * cos(0.52628058703 +     427.34895040140 * t)
  +  0.00000001902 * cos(1.24600006636 +     166.82867252200 * t)
  +  0.00000001529 * cos(2.85370771355 +     209.15449385380 * t)
  +  0.00000001494 * cos(3.66845408834 +    1182.92157353290 * t)
  +  0.00000001588 * cos(1.63988438811 +    3163.91869656600 * t)
  +  0.00000001502 * cos(4.96348459770 +     373.90799283650 * t)
  +  0.00000001608 * cos(3.59138122093 +     233.90602325750 * t)
  +  0.00000001460 * cos(1.17818401345 +      92.94084583200 * t)
  +  0.00000001462 * cos(5.05747764334 +      33.94024994380 * t)
  +  0.00000001490 * cos(2.03601440129 +     217.44369702220 * t)
  +  0.00000001688 * cos(1.50928274793 +     815.06334611420 * t)
  +  0.00000001778 * cos(0.24563726151 +       6.59228213900 * t)
  +  0.00000001834 * cos(3.98017256784 +     212.40532356070 * t)
  +  0.00000001834 * cos(0.90945359875 +     214.19286731530 * t)
  +  0.00000001451 * cos(3.59438611623 +     494.26624244250 * t)
  +  0.00000001474 * cos(4.97772142978 +    1699.27921650320 * t)
  +  0.00000001388 * cos(4.77847833406 +    2854.64037391020 * t)
  +  0.00000001589 * cos(5.43527416407 +    2538.24850425360 * t)
  +  0.00000001390 * cos(4.08155384651 +     894.84087952760 * t)
  +  0.00000001435 * cos(1.51395699369 +     867.42347575360 * t)
  +  0.00000001404 * cos(4.02343833901 +     300.61086697750 * t)
  );
}

double saturn_z1(double t) {
  return (
     0.03810308320 * cos(5.33520316778 +     213.29909543800 * t)
  -  0.00707598508
  +  0.00144960439 * cos(2.30149367100 +     206.18554843720 * t)
  +  0.00089591263 * cos(1.69286730496 +     220.41264243880 * t)
  +  0.00088982080 * cos(6.09698706089 +     426.59819087600 * t)
  +  0.00018761941 * cos(1.23200112053 +     419.48464387520 * t)
  +  0.00018103257 * cos(2.90933498453 +       7.11354700080 * t)
  +  0.00006860076 * cos(0.84862244997 +     433.71173787680 * t)
  +  0.00008398809 * cos(5.89715948074 +     639.89728631400 * t)
  +  0.00005939993 * cos(0.42396560640 +     316.39186965660 * t)
  +  0.00002571420 * cos(1.61235344206 +     227.52618943960 * t)
  +  0.00002030372 * cos(5.19792292680 +     110.20632121940 * t)
  +  0.00001632449 * cos(2.43938017095 +     199.07200143640 * t)
  +  0.00001126250 * cos(2.85739547477 +      14.22709400160 * t)
  +  0.00001025703 * cos(0.77676708535 +     632.78373931320 * t)
  +  0.00001035641 * cos(2.45710665385 +     217.23124870110 * t)
  +  0.00000919338 * cos(5.69490380320 +     529.69096509460 * t)
  +  0.00001025261 * cos(3.40455226241 +     103.09277421860 * t)
  +  0.00000788013 * cos(2.75643752556 +     210.11770170030 * t)
  +  0.00000652471 * cos(1.66305264153 +     202.25339517410 * t)
  +  0.00000678403 * cos(5.28303371104 +     853.19638175200 * t)
  +  0.00000546618 * cos(0.04231005132 +     647.01083331480 * t)
  +  0.00000616068 * cos(1.25272437511 +     216.48048917570 * t)
  +  0.00000589338 * cos(1.25138980225 +     209.36694217490 * t)
  +  0.00000398211 * cos(2.75660806272 +     117.31986822020 * t)
  +  0.00000342895 * cos(1.80589354512 +     224.34479570190 * t)
  +  0.00000383087 * cos(4.43945576495 +      11.04570026390 * t)
  +  0.00000315596 * cos(1.62252525888 +     323.50541665740 * t)
  +  0.00000215621 * cos(0.81176116742 +     440.82528487760 * t)
  +  0.00000208871 * cos(1.21651777785 +      63.73589830340 * t)
  +  0.00000180311 * cos(0.93555501458 +     309.27832265580 * t)
  +  0.00000172362 * cos(0.22156069668 +     735.87651353180 * t)
  +  0.00000132928 * cos(1.49015865779 +      95.97922721780 * t)
  +  0.00000141627 * cos(1.38605092643 +     412.37109687440 * t)
  +  0.00000114025 * cos(4.13401798874 +     415.55249061210 * t)
  +  0.00000107829 * cos(4.67440616464 +     846.08283475120 * t)
  +  0.00000113250 * cos(3.23797737561 +     277.03499374140 * t)
  +  0.00000096663 * cos(5.13321545536 +     522.57741809380 * t)
  +  0.00000080905 * cos(5.97207598010 +     149.56319713460 * t)
  +  0.00000078248 * cos(4.68235800719 +     215.74677599280 * t)
  +  0.00000073767 * cos(3.76912541093 +      74.78159856730 * t)
  +  0.00000058294 * cos(4.12074427198 +    1162.47470440780 * t)
  +  0.00000059154 * cos(0.00909087388 +    1052.26838318840 * t)
  +  0.00000054000 * cos(2.63292711570 +       3.18139373770 * t)
  +  0.00000053374 * cos(1.48573267831 +     234.63973644040 * t)
  +  0.00000057043 * cos(1.87312646111 +     423.41679713830 * t)
  +  0.00000052955 * cos(1.65323274690 +     330.61896365820 * t)
  +  0.00000050894 * cos(2.68041943186 +     742.99006053260 * t)
  +  0.00000049329 * cos(4.95750749572 +       3.93215326310 * t)
  +  0.00000061047 * cos(0.29238361571 +     422.66603761290 * t)
  +  0.00000053719 * cos(2.46146211746 +     490.33408917940 * t)
  +  0.00000051705 * cos(4.60792983851 +    1066.49547719000 * t)
  +  0.00000043576 * cos(5.53983423151 +     860.30992875280 * t)
  +  0.00000038478 * cos(2.42479516896 +     430.53034413910 * t)
  +  0.00000037913 * cos(5.63475884335 +     210.85141488320 * t)
  +  0.00000042636 * cos(0.46334621133 +     429.77958461370 * t)
  +  0.00000038288 * cos(3.94527342286 +     351.81659230870 * t)
  +  0.00000032052 * cos(2.73490028872 +      21.34064100240 * t)
  +  0.00000037226 * cos(0.77640416852 +     536.80451209540 * t)
  +  0.00000034303 * cos(5.53964443183 +     949.17560896980 * t)
  +  0.00000032486 * cos(1.51592537935 +     437.64389113990 * t)
  +  0.00000025209 * cos(5.61832461480 +     203.73786788240 * t)
  +  0.00000032600 * cos(1.15985496536 +     223.59403617650 * t)
  +  0.00000028157 * cos(5.03992835097 +     515.46387109300 * t)
  +  0.00000025365 * cos(1.63357066215 +     137.03302416240 * t)
  +  0.00000022772 * cos(3.87097220542 +    1478.86657406440 * t)
  +  0.00000022874 * cos(1.52589628823 +     124.43341522100 * t)
  +  0.00000021781 * cos(1.25479228248 +      88.86568021700 * t)
  +  0.00000021071 * cos(2.91498706203 +     203.00415469950 * t)
  +  0.00000022077 * cos(6.03637528612 +    1368.66025284500 * t)
  +  0.00000021851 * cos(3.47826348846 +      38.13303563780 * t)
  +  0.00000022636 * cos(0.42502415739 +     127.47179660680 * t)
  +  0.00000018793 * cos(0.02824698856 +     654.12438031560 * t)
  +  0.00000018132 * cos(0.35264011886 +      85.82729883120 * t)
  +  0.00000019127 * cos(4.85094487248 +     838.96928775040 * t)
  +  0.00000015811 * cos(0.06549781548 +     302.16477565500 * t)
  +  0.00000014993 * cos(5.63243246457 +     214.26230328450 * t)
  +  0.00000016073 * cos(5.40920567275 +    1265.56747862640 * t)
  +  0.00000014177 * cos(2.06003944064 +     138.51749687070 * t)
  +  0.00000014570 * cos(5.68093007156 +     942.06206196900 * t)
  +  0.00000012460 * cos(2.22381807104 +     213.34727954780 * t)
  +  0.00000012340 * cos(5.42069314117 +     217.96496188400 * t)
  +  0.00000011994 * cos(3.89295080099 +     728.76296653100 * t)
  +  0.00000015172 * cos(4.88775469732 +     208.63322899200 * t)
  +  0.00000014560 * cos(4.02541618429 +     195.13984817330 * t)
  +  0.00000012463 * cos(5.30921040178 +     213.25091132820 * t)
  +  0.00000011186 * cos(1.39522203481 +     210.37833413120 * t)
  +  0.00000011627 * cos(2.81135897939 +     231.45834270270 * t)
  +  0.00000015326 * cos(4.31191275758 +     628.85158605010 * t)
  +  0.00000012272 * cos(2.46356221718 +     200.76892246580 * t)
  +  0.00000015060 * cos(1.90080442413 +     212.33588759150 * t)
  +  0.00000011799 * cos(1.46416357606 +     218.71572140940 * t)
  +  0.00000010790 * cos(0.87460319256 +     408.43894361130 * t)
  +  0.00000010282 * cos(5.35193913607 +     207.67002114550 * t)
  +  0.00000013027 * cos(3.77267768832 +     350.33211960040 * t)
  +  0.00000010032 * cos(2.41897316373 +      10.29494073850 * t)
  +  0.00000012485 * cos(2.56988226727 +     340.77089204480 * t)
  +  0.00000011155 * cos(4.46475107308 +      52.69019803950 * t)
  +  0.00000011678 * cos(5.99973973452 +     191.20769491020 * t)
  +  0.00000009985 * cos(5.55354944984 +      76.26607127560 * t)
  +  0.00000009222 * cos(3.47198476691 +      18.15924726470 * t)
  +  0.00000008684 * cos(3.59341160996 +    1795.25844372100 * t)
  +  0.00000008772 * cos(2.84157598451 +     191.95845443560 * t)
  +  0.00000008792 * cos(5.77952076653 +    1685.05212250160 * t)
  +  0.00000010212 * cos(4.67919299694 +    1155.36115740700 * t)
  +  0.00000007416 * cos(2.34743956282 +     160.60889739850 * t)
  +  0.00000008681 * cos(3.66196489035 +     222.86032299360 * t)
  +  0.00000008204 * cos(4.00167578990 +     388.46515523820 * t)
  +  0.00000007229 * cos(0.85694899722 +     142.44965013380 * t)
  +  0.00000007962 * cos(6.12384852532 +     209.10630974400 * t)
  +  0.00000008152 * cos(0.17850883770 +       1.48447270830 * t)
  +  0.00000007462 * cos(4.54643529511 +     625.67019231240 * t)
  +  0.00000008149 * cos(4.75191185936 +     831.85574074960 * t)
  +  0.00000007464 * cos(5.87758421420 +     362.86229257260 * t)
  +  0.00000006550 * cos(0.37942895236 +     212.77783057620 * t)
  +  0.00000007220 * cos(5.21944812420 +    1581.95934828300 * t)
  +  0.00000006436 * cos(0.63886589467 +      22.09140052780 * t)
  +  0.00000007311 * cos(0.07712493176 +     265.98929347750 * t)
  +  0.00000007040 * cos(5.39023352132 +    1258.45393162560 * t)
  +  0.00000006246 * cos(6.10782448635 +     618.55664531160 * t)
  +  0.00000005540 * cos(1.63194253275 +      56.62235130260 * t)
  +  0.00000007460 * cos(2.16123164874 +     207.88246946660 * t)
  +  0.00000006689 * cos(5.61849505042 +     483.22054217860 * t)
  +  0.00000005366 * cos(2.54918207389 +     554.06998748280 * t)
  +  0.00000007245 * cos(3.44291004853 +      12.53017297220 * t)
  +  0.00000005769 * cos(0.85039589871 +     225.82926841020 * t)
  +  0.00000006530 * cos(0.87136105335 +     213.82036029980 * t)
  +  0.00000005249 * cos(0.71690429208 +     447.93883187840 * t)
  +  0.00000004793 * cos(4.97423814367 +     212.54833591260 * t)
  +  0.00000005801 * cos(0.02624779337 +     269.92144674060 * t)
  +  0.00000004710 * cos(3.07134751984 +    1375.77379984580 * t)
  +  0.00000005649 * cos(5.76570118321 +     635.96513305090 * t)
  +  0.00000004366 * cos(4.43717368507 +     235.39049596580 * t)
  +  0.00000005595 * cos(1.00573470142 +      70.84944530420 * t)
  +  0.00000005094 * cos(0.10066001708 +     750.10360753340 * t)
  +  0.00000004487 * cos(4.79200734443 +     218.92816973050 * t)
  +  0.00000004220 * cos(3.11074964024 +     703.63318461740 * t)
  +  0.00000004530 * cos(2.43215667228 +     216.21985674480 * t)
  +  0.00000004076 * cos(1.21943503644 +     417.03696332040 * t)
  +  0.00000004075 * cos(5.52140305637 +    2001.44399215820 * t)
  +  0.00000004489 * cos(5.12835463313 +    1574.84580128220 * t)
  +  0.00000003835 * cos(4.59484102776 +     424.15051032120 * t)
  +  0.00000004075 * cos(4.07912904262 +    1279.79457262800 * t)
  +  0.00000004918 * cos(4.36928157904 +    1471.75302706360 * t)
  +  0.00000003719 * cos(3.42064399733 +    1045.15483618760 * t)
  +  0.00000004734 * cos(5.61204474661 +       9.56122755560 * t)
  +  0.00000004537 * cos(0.79869612235 +     543.91805909620 * t)
  +  0.00000003610 * cos(5.94058751363 +     934.94851496820 * t)
  +  0.00000004230 * cos(5.90345986772 +     173.94221952280 * t)
  +  0.00000003444 * cos(2.86327846707 +     106.27416795630 * t)
  +  0.00000003432 * cos(4.89216582171 +     497.44763618020 * t)
  +  0.00000003553 * cos(4.80761740206 +    1073.60902419080 * t)
  +  0.00000004601 * cos(4.77897976995 +     288.08069400530 * t)
  +  0.00000003314 * cos(3.41625676576 +    2111.65031337760 * t)
  +  0.00000003264 * cos(4.45520175360 +     107.02492748170 * t)
  +  0.00000003442 * cos(2.57824148394 +     113.38771495710 * t)
  +  0.00000003664 * cos(4.49847588517 +    1148.24761040620 * t)
  +  0.00000003349 * cos(1.27990783834 +     344.70304530790 * t)
  +  0.00000002971 * cos(4.31371705105 +     219.44943459230 * t)
  +  0.00000002920 * cos(1.64503980864 +     636.71589257630 * t)
  +  0.00000002971 * cos(2.61742682364 +     404.50679034820 * t)
  +  0.00000003051 * cos(5.10422803245 +    1898.35121793960 * t)
  +  0.00000002774 * cos(3.14101665470 +     217.49188113200 * t)
  +  0.00000002950 * cos(5.37168308363 +     175.16605980020 * t)
  +  0.00000002822 * cos(1.33413781392 +     650.94298657790 * t)
  +  0.00000003174 * cos(1.19063213567 +     337.73251065900 * t)
  +  0.00000003041 * cos(6.26099119193 +     207.14875628370 * t)
  +  0.00000002591 * cos(4.52751512849 +     565.11568774670 * t)
  +  0.00000003416 * cos(5.97202994093 +     643.07868005170 * t)
  +  0.00000002507 * cos(0.83753919585 +     436.89313161450 * t)
  +  0.00000002350 * cos(2.16713733034 +     177.87437278590 * t)
  +  0.00000002755 * cos(3.61967991567 +     114.13847448250 * t)
  +  0.00000002495 * cos(4.64668211731 +     429.04587143080 * t)
  +  0.00000002768 * cos(4.77439427919 +    1891.23767093880 * t)
  +  0.00000002238 * cos(4.00121267561 +     284.14854074220 * t)
  +  0.00000002251 * cos(4.90436209991 +    2214.74308759620 * t)
  +  0.00000002409 * cos(3.56267761888 +    1169.58825140860 * t)
  +  0.00000002157 * cos(3.02442510484 +    1692.16566950240 * t)
  +  0.00000002003 * cos(2.47564274875 +     416.30325013750 * t)
  +  0.00000002085 * cos(4.09277149039 +    1272.68102562720 * t)
  +  0.00000001945 * cos(0.97841451672 +     114.39910691340 * t)
  +  0.00000001907 * cos(3.36673783584 +    1059.38193018920 * t)
  +  0.00000001861 * cos(4.45402970588 +     508.35032409220 * t)
  +  0.00000001874 * cos(2.73629728926 +     214.04985496340 * t)
  +  0.00000001905 * cos(2.99492664264 +    1361.54670584420 * t)
  +  0.00000002064 * cos(5.39674851006 +     245.54242435240 * t)
  +  0.00000001878 * cos(0.56676085326 +     621.73803904930 * t)
  +  0.00000002525 * cos(1.19036969669 +     479.28838891550 * t)
  +  0.00000001966 * cos(2.58393370207 +      99.16062095550 * t)
  +  0.00000001908 * cos(2.85404393589 +     355.74874557180 * t)
  +  0.00000002056 * cos(2.39618093351 +    2435.15573003500 * t)
  +  0.00000002158 * cos(4.97710925643 +    2317.83586181480 * t)
  +  0.00000002202 * cos(0.84567094644 +     358.93013930950 * t)
  +  0.00000001881 * cos(1.13062277248 +     757.21715453420 * t)
  +  0.00000001707 * cos(1.57935987501 +    6069.77675455340 * t)
  +  0.00000002151 * cos(4.06616159617 +    1788.14489672020 * t)
  +  0.00000001746 * cos(3.06455575770 +    2008.55753915900 * t)
  +  0.00000001746 * cos(5.09056895026 +     220.46082654860 * t)
  +  0.00000001795 * cos(2.95316519456 +    1781.03134971940 * t)
  +  0.00000001700 * cos(6.05669760153 +     206.13736432740 * t)
  +  0.00000001614 * cos(5.96461527769 +     867.42347575360 * t)
  +  0.00000001956 * cos(2.13214810643 +     252.65597135320 * t)
  +  0.00000001739 * cos(5.77930712282 +     181.05576652360 * t)
  +  0.00000001553 * cos(1.32350368373 +     131.54696222180 * t)
  +  0.00000001599 * cos(0.86145918975 +      81.75213321620 * t)
  +  0.00000001792 * cos(0.86879017108 +       4.66586644600 * t)
  +  0.00000001548 * cos(4.47085375766 +     121.25202148330 * t)
  +  0.00000001619 * cos(4.79891754382 +     842.15068148810 * t)
  +  0.00000001513 * cos(3.01415732754 +    2428.04218303420 * t)
  +  0.00000001822 * cos(2.62978911169 +     643.82943957710 * t)
  +  0.00000002085 * cos(3.00604517701 +     563.63121503840 * t)
  +  0.00000001939 * cos(2.25124681713 +    1677.93857550080 * t)
  +  0.00000001472 * cos(3.39986301851 +     956.28915597060 * t)
  +  0.00000001467 * cos(4.24274724035 +      98.89998852460 * t)
  +  0.00000001384 * cos(2.33959628851 +     444.75743814070 * t)
  +  0.00000001810 * cos(2.02611183018 +    2420.92863603340 * t)
  +  0.00000001628 * cos(4.47984535594 +     251.43213107580 * t)
  +  0.00000001593 * cos(1.97508934614 +      62.25142559510 * t)
  +  0.00000001516 * cos(1.25225067905 +     425.11371816770 * t)
  +  0.00000001181 * cos(5.09622518839 +     414.06801790380 * t)
  +  0.00000001211 * cos(0.96174816662 +     214.78356814630 * t)
  +  0.00000001429 * cos(2.95386700663 +      65.22037101170 * t)
  +  0.00000001042 * cos(5.99222596459 +     151.04766984290 * t)
  +  0.00000001200 * cos(0.65918491217 +     211.81462272970 * t)
  +  0.00000000967 * cos(6.01089625149 +    1589.07289528380 * t)
  +  0.00000000904 * cos(0.07909774752 +     213.41097002260 * t)
  +  0.00000000904 * cos(1.66925524906 +     213.18722085340 * t)
  +  0.00000001071 * cos(3.60798747502 +     248.72381809010 * t)
  +  0.00000000815 * cos(4.93878023673 +       2.44768055480 * t)
  +  0.00000000775 * cos(3.45264409045 +     198.32124191100 * t)
  +  0.00000000983 * cos(3.20558404998 +     312.19908396260 * t)
  +  0.00000000760 * cos(2.28889729136 +     213.08664711690 * t)
  +  0.00000000760 * cos(5.74264101239 +     213.51154375910 * t)
  +  0.00000000724 * cos(4.57593199965 +     228.27694896500 * t)
  ) * t;
}

double saturn_z2(double t) {
  return (
     0.00195192259 * cos(0.50946874402 +     213.29909543800 * t)
  +  0.00036491216 * cos(3.99604491617 +     206.18554843720 * t)
  +  0.00015091412 * cos(6.17687148383 +     220.41264243880 * t)
  +  0.00019236496
  +  0.00003420562 * cos(3.04256365132 +     419.48464387520 * t)
  +  0.00001903731 * cos(1.01852901874 +       7.11354700080 * t)
  +  0.00001553807 * cos(5.27527652115 +     433.71173787680 * t)
  +  0.00001658586 * cos(5.05753354015 +     426.59819087600 * t)
  +  0.00000939968 * cos(6.15093957163 +     227.52618943960 * t)
  +  0.00000665875 * cos(1.95823182523 +     316.39186965660 * t)
  +  0.00000727405 * cos(3.86689219213 +     639.89728631400 * t)
  +  0.00000708634 * cos(4.14159824503 +     199.07200143640 * t)
  +  0.00000332785 * cos(1.11013701815 +      14.22709400160 * t)
  +  0.00000276129 * cos(4.52772200630 +     210.11770170030 * t)
  +  0.00000246881 * cos(4.50860976295 +     103.09277421860 * t)
  +  0.00000236419 * cos(1.02568314619 +     110.20632121940 * t)
  +  0.00000193411 * cos(4.35154385844 +     217.23124870110 * t)
  +  0.00000170756 * cos(2.72871130039 +     632.78373931320 * t)
  +  0.00000154811 * cos(4.42812217496 +     647.01083331480 * t)
  +  0.00000159221 * cos(5.67806982371 +     216.48048917570 * t)
  +  0.00000100473 * cos(3.17382026227 +     853.19638175200 * t)
  +  0.00000090850 * cos(5.30427538537 +     440.82528487760 * t)
  +  0.00000077600 * cos(3.28475417716 +     202.25339517410 * t)
  +  0.00000072917 * cos(1.06686891373 +     117.31986822020 * t)
  +  0.00000061331 * cos(1.61343080245 +     529.69096509460 * t)
  +  0.00000064246 * cos(3.02694204128 +     412.37109687440 * t)
  +  0.00000063778 * cos(5.55207588103 +     209.36694217490 * t)
  +  0.00000041451 * cos(3.33188411884 +     309.27832265580 * t)
  +  0.00000033437 * cos(0.11560358087 +     323.50541665740 * t)
  +  0.00000029893 * cos(6.03701243746 +     234.63973644040 * t)
  +  0.00000025877 * cos(3.50813571651 +      95.97922721780 * t)
  +  0.00000017574 * cos(0.22180355628 +       3.93215326310 * t)
  +  0.00000016154 * cos(3.77501334464 +     423.41679713830 * t)
  +  0.00000015793 * cos(1.02173188447 +      21.34064100240 * t)
  +  0.00000014438 * cos(5.60523358660 +     223.59403617650 * t)
  +  0.00000013542 * cos(4.81528922933 +     429.77958461370 * t)
  +  0.00000015398 * cos(5.52110630605 +     224.34479570190 * t)
  +  0.00000011511 * cos(4.71374175861 +     203.00415469950 * t)
  +  0.00000014090 * cos(5.07886462834 +     277.03499374140 * t)
  +  0.00000014469 * cos(3.60157016903 +     860.30992875280 * t)
  +  0.00000012120 * cos(0.05423484257 +     415.55249061210 * t)
  +  0.00000013400 * cos(0.51901182147 +     522.57741809380 * t)
  +  0.00000010074 * cos(4.55389948936 +     422.66603761290 * t)
  +  0.00000012614 * cos(6.15368985726 +     330.61896365820 * t)
  +  0.00000010793 * cos(2.51124542537 +    1066.49547719000 * t)
  +  0.00000008990 * cos(6.00345025989 +     124.43341522100 * t)
  +  0.00000010308 * cos(6.00841164198 +      11.04570026390 * t)
  +  0.00000008308 * cos(0.68581626528 +       3.18139373770 * t)
  +  0.00000009597 * cos(5.80785895962 +      63.73589830340 * t)
  +  0.00000007930 * cos(5.51468008833 +     735.87651353180 * t)
  +  0.00000008053 * cos(3.03363150224 +      88.86568021700 * t)
  +  0.00000008834 * cos(4.47705749563 +     654.12438031560 * t)
  +  0.00000007356 * cos(4.43315310489 +     191.95845443560 * t)
  +  0.00000006543 * cos(4.88541538755 +     625.67019231240 * t)
  +  0.00000008411 * cos(1.49318798287 +     742.99006053260 * t)
  +  0.00000006909 * cos(4.48978383769 +     430.53034413910 * t)
  +  0.00000006388 * cos(0.08457977809 +     215.74677599280 * t)
  +  0.00000007107 * cos(0.70220678131 +     949.17560896980 * t)
  +  0.00000005669 * cos(0.46049062500 +     515.46387109300 * t)
  +  0.00000005034 * cos(5.23865643179 +      74.78159856730 * t)
  +  0.00000004315 * cos(1.63053592014 +    1059.38193018920 * t)
  +  0.00000004299 * cos(1.18161521312 +     210.85141488320 * t)
  +  0.00000003314 * cos(5.42600783265 +     437.64389113990 * t)
  +  0.00000003489 * cos(0.53174386810 +      10.29494073850 * t)
  +  0.00000003355 * cos(5.23729212209 +     447.93883187840 * t)
  +  0.00000003056 * cos(1.18250311873 +     942.06206196900 * t)
  +  0.00000002996 * cos(5.62814654221 +     728.76296653100 * t)
  +  0.00000003361 * cos(5.11461252953 +     536.80451209540 * t)
  +  0.00000002396 * cos(1.84582366198 +    1471.75302706360 * t)
  +  0.00000002280 * cos(0.09630660324 +     195.13984817330 * t)
  +  0.00000002351 * cos(1.27223026559 +     231.45834270270 * t)
  +  0.00000002515 * cos(0.03375128717 +     838.96928775040 * t)
  +  0.00000002748 * cos(1.32449995239 +     203.73786788240 * t)
  +  0.00000002290 * cos(3.07698270979 +     408.43894361130 * t)
  +  0.00000002040 * cos(5.80760536835 +    1162.47470440780 * t)
  +  0.00000002084 * cos(0.74674443126 +    1265.56747862640 * t)
  +  0.00000002283 * cos(1.77539793334 +     846.08283475120 * t)
  +  0.00000001868 * cos(0.23989474559 +    1898.35121793960 * t)
  +  0.00000001720 * cos(1.98614962644 +      18.15924726470 * t)
  +  0.00000001849 * cos(0.68415972849 +    1258.45393162560 * t)
  +  0.00000001575 * cos(2.31138086283 +     302.16477565500 * t)
  +  0.00000001874 * cos(0.84722174143 +    1375.77379984580 * t)
  +  0.00000001401 * cos(3.28871251562 +    1073.60902419080 * t)
  +  0.00000001369 * cos(4.66184064286 +     490.33408917940 * t)
  +  0.00000001319 * cos(0.58131415395 +     618.55664531160 * t)
  +  0.00000001430 * cos(2.32626814584 +    1368.66025284500 * t)
  +  0.00000001519 * cos(0.21611173188 +     831.85574074960 * t)
  +  0.00000001250 * cos(5.97999895371 +     351.81659230870 * t)
  +  0.00000000966 * cos(2.64913416683 +      85.82729883120 * t)
  +  0.00000000771 * cos(1.16732337173 +     217.96496188400 * t)
  +  0.00000000697 * cos(0.53637719953 +     628.85158605010 * t)
  ) * pow(t, 2);
}

double saturn_z3(double t) {
  return (
     0.00006552316 * cos(1.98918006303 +     213.29909543800 * t)
  +  0.00006205120 * cos(5.69682939522 +     206.18554843720 * t)
  +  0.00005692884
  +  0.00001736879 * cos(4.32959476351 +     220.41264243880 * t)
  +  0.00000450555 * cos(4.83582005306 +     419.48464387520 * t)
  +  0.00000231881 * cos(4.39490786964 +     227.52618943960 * t)
  +  0.00000199865 * cos(2.33322152046 +     426.59819087600 * t)
  +  0.00000205985 * cos(5.84743845970 +     199.07200143640 * t)
  +  0.00000242710 * cos(3.41690207168 +     433.71173787680 * t)
  +  0.00000139339 * cos(5.28736351227 +       7.11354700080 * t)
  +  0.00000067206 * cos(5.62860360986 +      14.22709400160 * t)
  +  0.00000056299 * cos(1.93019307649 +     639.89728631400 * t)
  +  0.00000055780 * cos(0.01778616215 +     210.11770170030 * t)
  +  0.00000050857 * cos(3.44381337767 +     316.39186965660 * t)
  +  0.00000029135 * cos(0.23714193891 +     103.09277421860 * t)
  +  0.00000030392 * cos(2.54675335277 +     647.01083331480 * t)
  +  0.00000025847 * cos(3.51464713160 +     440.82528487760 * t)
  +  0.00000020480 * cos(3.72108337650 +     216.48048917570 * t)
  +  0.00000018853 * cos(6.10978933980 +     217.23124870110 * t)
  +  0.00000018881 * cos(4.62069633304 +     632.78373931320 * t)
  +  0.00000017464 * cos(4.72219191592 +     412.37109687440 * t)
  +  0.00000010821 * cos(1.21499195673 +     853.19638175200 * t)
  +  0.00000010927 * cos(4.30569213091 +     234.63973644040 * t)
  +  0.00000009297 * cos(5.60250826661 +     117.31986822020 * t)
  +  0.00000007656 * cos(5.66078016942 +     309.27832265580 * t)
  +  0.00000007303 * cos(5.47485612817 +     202.25339517410 * t)
  +  0.00000005000 * cos(5.51413752856 +      21.34064100240 * t)
  +  0.00000004259 * cos(5.49035642189 +      95.97922721780 * t)
  +  0.00000004838 * cos(0.29619340824 +     110.20632121940 * t)
  +  0.00000003957 * cos(6.09695713906 +     191.95845443560 * t)
  +  0.00000003467 * cos(3.73810181850 +     223.59403617650 * t)
  +  0.00000003322 * cos(1.65077341966 +     860.30992875280 * t)
  +  0.00000002905 * cos(4.28100382746 +     323.50541665740 * t)
  +  0.00000002380 * cos(2.83328075768 +     429.77958461370 * t)
  +  0.00000002398 * cos(4.14927979178 +     124.43341522100 * t)
  +  0.00000002780 * cos(2.64718847967 +     654.12438031560 * t)
  +  0.00000002787 * cos(0.65101567800 +     203.00415469950 * t)
  +  0.00000001947 * cos(1.53880195116 +     209.36694217490 * t)
  +  0.00000001856 * cos(5.62026724615 +     302.16477565500 * t)
  +  0.00000001819 * cos(4.80294039631 +      88.86568021700 * t)
  +  0.00000001959 * cos(4.38771818896 +     330.61896365820 * t)
  +  0.00000001487 * cos(3.12393556594 +     529.69096509460 * t)
  +  0.00000001276 * cos(3.91936027558 +     447.93883187840 * t)
  +  0.00000001374 * cos(1.28276260217 +    1066.49547719000 * t)
  +  0.00000000804 * cos(4.10158366806 +     224.34479570190 * t)
  ) * pow(t, 3);
}

double saturn_z4(double t) {
  return (
     0.00000789033 * cos(1.11928782644 +     206.18554843720 * t)
  +  0.00000281365 * cos(3.13274851308 +     213.29909543800 * t)
  -  0.00000169515
  +  0.00000157511 * cos(2.46634171520 +     220.41264243880 * t)
  +  0.00000046995 * cos(1.27259130638 +     199.07200143640 * t)
  +  0.00000043842 * cos(0.38587829145 +     419.48464387520 * t)
  +  0.00000043114 * cos(2.62919688921 +     227.52618943960 * t)
  +  0.00000028988 * cos(1.55482750505 +     433.71173787680 * t)
  +  0.00000009447 * cos(3.85114048856 +      14.22709400160 * t)
  +  0.00000006018 * cos(1.29220324867 +     426.59819087600 * t)
  +  0.00000007462 * cos(3.20599530963 +       7.11354700080 * t)
  +  0.00000004617 * cos(0.67712478942 +     647.01083331480 * t)
  +  0.00000005282 * cos(1.71952902559 +     440.82528487760 * t)
  +  0.00000003522 * cos(6.19992669453 +     639.89728631400 * t)
  +  0.00000002258 * cos(0.44292528032 +     412.37109687440 * t)
  +  0.00000002256 * cos(2.11084590211 +     210.11770170030 * t)
  +  0.00000002460 * cos(2.50380847653 +     234.63973644040 * t)
  +  0.00000001239 * cos(5.78004218066 +     110.20632121940 * t)
  +  0.00000001449 * cos(5.96384491391 +     216.48048917570 * t)
  +  0.00000001322 * cos(0.54271370335 +     853.19638175200 * t)
  +  0.00000001151 * cos(4.86229315211 +     117.31986822020 * t)
  +  0.00000001045 * cos(5.61649418233 +     316.39186965660 * t)
  ) * pow(t, 4);
}

double saturn_z5(double t) {
  return (
     0.00000077433 * cos(2.81859989913 +     206.18554843720 * t)
  -  0.00000013826
  +  0.00000009303 * cos(0.47844462514 +     220.41264243880 * t)
  +  0.00000007840 * cos(2.99415198633 +     199.07200143640 * t)
  +  0.00000005604 * cos(0.80222427065 +     227.52618943960 * t)
  +  0.00000002881 * cos(6.00054088318 +     433.71173787680 * t)
  +  0.00000001362 * cos(2.58324584516 +     419.48464387520 * t)
  +  0.00000000968 * cos(5.23916441152 +     213.29909543800 * t)
  +  0.00000000867 * cos(5.81659714144 +       7.11354700080 * t)
  ) * pow(t, 5);
}

EMSCRIPTEN_KEEPALIVE
double saturn_x(double t) {
  return saturn_x0(t) + saturn_x1(t) + saturn_x2(t) + saturn_x3(t) + saturn_x4(t) + saturn_x5(t);
}

EMSCRIPTEN_KEEPALIVE
double saturn_y(double t) {
  return saturn_y0(t) + saturn_y1(t) + saturn_y2(t) + saturn_y3(t) + saturn_y4(t) + saturn_y5(t);
}

EMSCRIPTEN_KEEPALIVE
double saturn_z(double t) {
  return saturn_z0(t) + saturn_z1(t) + saturn_z2(t) + saturn_z3(t) + saturn_z4(t) + saturn_z5(t);
}
