Table of coefficients c13(n) of the weight 13 newform on S13(Gamma_0(3),chi3) for n up to 1000

{1, 1}
{2, 0}
{3, 729}
{4, 4096}
{5, 0}
{6, 0}
{7, -153502}
{8, 0}
{9, 531441}
{10, 0}
{11, 0}
{12, 2985984}
{13, -9397582}
{14, 0}
{15, 0}
{16, 16777216}
{17, 0}
{18, 0}
{19, 17886962}
{20, 0}
{21, -111902958}
{22, 0}
{23, 0}
{24, 0}
{25, 244140625}
{26, 0}
{27, 387420489}
{28, -628744192}
{29, 0}
{30, 0}
{31, -530187838}
{32, 0}
{33, 0}
{34, 0}
{35, 0}
{36, 2176782336}
{37, 2826257618}
{38, 0}
{39, -6850837278}
{40, 0}
{41, 0}
{42, 0}
{43, -235885102}
{44, 0}
{45, 0}
{46, 0}
{47, 0}
{48, 12230590464}
{49, 9721576803}
{50, 0}
{51, 0}
{52, -38492495872}
{53, 0}
{54, 0}
{55, 0}
{56, 0}
{57, 13039595298}
{58, 0}
{59, 0}
{60, 0}
{61, 74063873522}
{62, 0}
{63, -81577256382}
{64, 68719476736}
{65, 0}
{66, 0}
{67, -151031344462}
{68, 0}
{69, 0}
{70, 0}
{71, 0}
{72, 0}
{73, 104459767778}
{74, 0}
{75, 177978515625}
{76, 73264996352}
{77, 0}
{78, 0}
{79, -444304748158}
{80, 0}
{81, 282429536481}
{82, 0}
{83, 0}
{84, -458354515968}
{85, 0}
{86, 0}
{87, 0}
{88, 0}
{89, 0}
{90, 0}
{91, 1442547632164}
{92, 0}
{93, -386506933902}
{94, 0}
{95, 0}
{96, 0}
{97, -1662757858942}
{98, 0}
{99, 0}
{100, 1000000000000}
{101, 0}
{102, 0}
{103, -1118097306142}
{104, 0}
{105, 0}
{106, 0}
{107, 0}
{108, 1586874322944}
{109, 1366607576882}
{110, 0}
{111, 2060341803522}
{112, -2575336210432}
{113, 0}
{114, 0}
{115, 0}
{116, 0}
{117, -4994260375662}
{118, 0}
{119, 0}
{120, 0}
{121, 3138428376721}
{122, 0}
{123, 0}
{124, -2171649384448}
{125, 0}
{126, 0}
{127, 7229451168578}
{128, 0}
{129, -171960239358}
{130, 0}
{131, 0}
{132, 0}
{133, -2745684440924}
{134, 0}
{135, 0}
{136, 0}
{137, 0}
{138, 0}
{139, -12826042472878}
{140, 0}
{141, 0}
{142, 0}
{143, 0}
{144, 8916100448256}
{145, 0}
{146, 0}
{147, 7087029489387}
{148, 11576351203328}
{149, 0}
{150, 0}
{151, -9035874338398}
{152, 0}
{153, 0}
{154, 0}
{155, 0}
{156, -28061029490688}
{157, 20212693942898}
{158, 0}
{159, 0}
{160, 0}
{161, 0}
{162, 0}
{163, -29109402123982}
{164, 0}
{165, 0}
{166, 0}
{167, 0}
{168, 0}
{169, 65016462324243}
{170, 0}
{171, 9505864972242}
{172, -966185377792}
{173, 0}
{174, 0}
{175, -37476074218750}
{176, 0}
{177, 0}
{178, 0}
{179, 0}
{180, 0}
{181, -70313997302638}
{182, 0}
{183, 53992563797538}
{184, 0}
{185, 0}
{186, 0}
{187, 0}
{188, 0}
{189, -59469819902478}
{190, 0}
{191, 0}
{192, 50096498540544}
{193, 67083975818498}
{194, 0}
{195, 0}
{196, 39819578585088}
{197, 0}
{198, 0}
{199, 11619642434402}
{200, 0}
{201, -110101850112798}
{202, 0}
{203, 0}
{204, 0}
{205, 0}
{206, 0}
{207, 0}
{208, -157665263091712}
{209, 0}
{210, 0}
{211, 133168231188722}
{212, 0}
{213, 0}
{214, 0}
{215, 0}
{216, 0}
{217, 81384893508676}
{218, 0}
{219, 76151170710162}
{220, 0}
{221, 0}
{222, 0}
{223, -106463554876222}
{224, 0}
{225, 129746337890625}
{226, 0}
{227, 0}
{228, 53410182340608}
{229, -271843754560558}
{230, 0}
{231, 0}
{232, 0}
{233, 0}
{234, 0}
{235, 0}
{236, 0}
{237, -323898161407182}
{238, 0}
{239, 0}
{240, 0}
{241, 307204056694082}
{242, 0}
{243, 205891132094649}
{244, 303365625946112}
{245, 0}
{246, 0}
{247, -168094192125884}
{248, 0}
{249, 0}
{250, 0}
{251, 0}
{252, -334140442140672}
{253, 0}
{254, 0}
{255, 0}
{256, 281474976710656}
{257, 0}
{258, 0}
{259, -433836196878236}
{260, 0}
{261, 0}
{262, 0}
{263, 0}
{264, 0}
{265, 0}
{266, 0}
{267, 0}
{268, -618624386916352}
{269, 0}
{270, 0}
{271, 740164217869442}
{272, 0}
{273, 1051617223847556}
{274, 0}
{275, 0}
{276, 0}
{277, -213505833091822}
{278, 0}
{279, -281763554814558}
{280, 0}
{281, 0}
{282, 0}
{283, -832250053790062}
{284, 0}
{285, 0}
{286, 0}
{287, 0}
{288, 0}
{289, 582622237229761}
{290, 0}
{291, -1212150479168718}
{292, 427867208818688}
{293, 0}
{294, 0}
{295, 0}
{296, 0}
{297, 0}
{298, 0}
{299, 0}
{300, 729000000000000}
{301, 36208834927204}
{302, 0}
{303, 0}
{304, 300093425057792}
{305, 0}
{306, 0}
{307, 1388190642589298}
{308, 0}
{309, -815092936177518}
{310, 0}
{311, 0}
{312, 0}
{313, -369604242300382}
{314, 0}
{315, 0}
{316, -1819872248455168}
{317, 0}
{318, 0}
{319, 0}
{320, 0}
{321, 0}
{322, 0}
{323, 0}
{324, 1156831381426176}
{325, -2294331542968750}
{326, 0}
{327, 996256923546978}
{328, 0}
{329, 0}
{330, 0}
{331, 2488476901070162}
{332, 0}
{333, 1501989174767538}
{334, 0}
{335, 0}
{336, -1877420097404928}
{337, -200526329150782}
{338, 0}
{339, 0}
{340, 0}
{341, 0}
{342, 0}
{343, 632383785513796}
{344, 0}
{345, 0}
{346, 0}
{347, 0}
{348, 0}
{349, -373350072185998}
{350, 0}
{351, -3640815813857598}
{352, 0}
{353, 0}
{354, 0}
{355, 0}
{356, 0}
{357, 0}
{358, 0}
{359, 0}
{360, 0}
{361, -1893371509476717}
{362, 0}
{363, 2287914286629609}
{364, 5908675101343744}
{365, 0}
{366, 0}
{367, 1517360408718338}
{368, 0}
{369, 0}
{370, 0}
{371, 0}
{372, -1583132401262592}
{373, -3011372587392622}
{374, 0}
{375, 0}
{376, 0}
{377, 0}
{378, 0}
{379, -4688738421035758}
{380, 0}
{381, 5270269901893362}
{382, 0}
{383, 0}
{384, 0}
{385, 0}
{386, 0}
{387, -125359014491982}
{388, -6810656190226432}
{389, 0}
{390, 0}
{391, 0}
{392, 0}
{393, 0}
{394, 0}
{395, 0}
{396, 0}
{397, 7477782720263858}
{398, 0}
{399, -2001603957433596}
{400, 4096000000000000}
{401, 0}
{402, 0}
{403, 4982483683007716}
{404, 0}
{405, 0}
{406, 0}
{407, 0}
{408, 0}
{409, -4623171010305118}
{410, 0}
{411, 0}
{412, -4579726565957632}
{413, 0}
{414, 0}
{415, 0}
{416, 0}
{417, -9350184962728062}
{418, 0}
{419, 0}
{420, 0}
{421, 9736942483653842}
{422, 0}
{423, 0}
{424, 0}
{425, 0}
{426, 0}
{427, -11368952713374044}
{428, 0}
{429, 0}
{430, 0}
{431, 0}
{432, 6499837226778624}
{433, 11047944506953538}
{434, 0}
{435, 0}
{436, 5597624634908672}
{437, 0}
{438, 0}
{439, -11451808024282078}
{440, 0}
{441, 5166444497763123}
{442, 0}
{443, 0}
{444, 8439160027226112}
{445, 0}
{446, 0}
{447, 0}
{448, -10548577117929472}
{449, 0}
{450, 0}
{451, 0}
{452, 0}
{453, -6587152392692142}
{454, 0}
{455, 0}
{456, 0}
{457, -17358047953987102}
{458, 0}
{459, 0}
{460, 0}
{461, 0}
{462, 0}
{463, 17447495440991618}
{464, 0}
{465, 0}
{466, 0}
{467, 0}
{468, -20456490498711552}
{469, 23183613437605924}
{470, 0}
{471, 14735053884372642}
{472, 0}
{473, 0}
{474, 0}
{475, 4366934082031250}
{476, 0}
{477, 0}
{478, 0}
{479, 0}
{480, 0}
{481, -26559987718279676}
{482, 0}
{483, 0}
{484, 12855002631049216}
{485, 0}
{486, 0}
{487, 15675581435675618}
{488, 0}
{489, -21220754148382878}
{490, 0}
{491, 0}
{492, 0}
{493, 0}
{494, 0}
{495, 0}
{496, -8895075878699008}
{497, 0}
{498, 0}
{499, -30500335309625998}
{500, 0}
{501, 0}
{502, 0}
{503, 0}
{504, 0}
{505, 0}
{506, 0}
{507, 47397001034373147}
{508, 29611831986495488}
{509, 0}
{510, 0}
{511, -16034783273458556}
{512, 0}
{513, 6929775564764418}
{514, 0}
{515, 0}
{516, -704349140410368}
{517, 0}
{518, 0}
{519, 0}
{520, 0}
{521, 0}
{522, 0}
{523, -21006600313359022}
{524, 0}
{525, -27320058105468750}
{526, 0}
{527, 0}
{528, 0}
{529, 21914624432020321}
{530, 0}
{531, 0}
{532, -11246323470024704}
{533, 0}
{534, 0}
{535, 0}
{536, 0}
{537, 0}
{538, 0}
{539, 0}
{540, 0}
{541, -11093332968965518}
{542, 0}
{543, -51258904033623102}
{544, 0}
{545, 0}
{546, 0}
{547, 51820420656369458}
{548, 0}
{549, 39360579008405202}
{550, 0}
{551, 0}
{552, 0}
{553, 68201667451749316}
{554, 0}
{555, 0}
{556, -52535469968908288}
{557, 0}
{558, 0}
{559, 2216749588623364}
{560, 0}
{561, 0}
{562, 0}
{563, 0}
{564, 0}
{565, 0}
{566, 0}
{567, -43353498708906462}
{568, 0}
{569, 0}
{570, 0}
{571, -40039288445061358}
{572, 0}
{573, 0}
{574, 0}
{575, 0}
{576, 36520347436056576}
{577, -68826701019009022}
{578, 0}
{579, 48904218371685042}
{580, 0}
{581, 0}
{582, 0}
{583, 0}
{584, 0}
{585, 0}
{586, 0}
{587, 0}
{588, 29028472788529152}
{589, -9483449711168156}
{590, 0}
{591, 0}
{592, 47416734528831488}
{593, 0}
{594, 0}
{595, 0}
{596, 0}
{597, 8470719334679058}
{598, 0}
{599, 0}
{600, 0}
{601, 85903354627927202}
{602, 0}
{603, -80264248732229742}
{604, -37010941290078208}
{605, 0}
{606, 0}
{607, 29850323959624898}
{608, 0}
{609, 0}
{610, 0}
{611, 0}
{612, 0}
{613, -81066147128641582}
{614, 0}
{615, 0}
{616, 0}
{617, 0}
{618, 0}
{619, -56720282925000238}
{620, 0}
{621, 0}
{622, 0}
{623, 0}
{624, -114937976793858048}
{625, 59604644775390625}
{626, 0}
{627, 0}
{628, 82791194390110208}
{629, 0}
{630, 0}
{631, 122658064888937762}
{632, 0}
{633, 97079640536578338}
{634, 0}
{635, 0}
{636, 0}
{637, -91359315175490346}
{638, 0}
{639, 0}
{640, 0}
{641, 0}
{642, 0}
{643, -12820719900001102}
{644, 0}
{645, 0}
{646, 0}
{647, 0}
{648, 0}
{649, 0}
{650, 0}
{651, 59329587367824804}
{652, -119232111099830272}
{653, 0}
{654, 0}
{655, 0}
{656, 0}
{657, 55514203447708098}
{658, 0}
{659, 0}
{660, 0}
{661, -141821666393687278}
{662, 0}
{663, 0}
{664, 0}
{665, 0}
{666, 0}
{667, 0}
{668, 0}
{669, -77611931504765838}
{670, 0}
{671, 0}
{672, 0}
{673, -184856015190397822}
{674, 0}
{675, 94585080322265625}
{676, 266307429680099328}
{677, 0}
{678, 0}
{679, 255236656863314884}
{680, 0}
{681, 0}
{682, 0}
{683, 0}
{684, 38936022926303232}
{685, 0}
{686, 0}
{687, -198174097074646782}
{688, -3957495307436032}
{689, 0}
{690, 0}
{691, -56461867159435918}
{692, 0}
{693, 0}
{694, 0}
{695, 0}
{696, 0}
{697, 0}
{698, 0}
{699, 0}
{700, -153502000000000000}
{701, 0}
{702, 0}
{703, 50553162615376516}
{704, 0}
{705, 0}
{706, 0}
{707, 0}
{708, 0}
{709, 98474179887654482}
{710, 0}
{711, -236121759665835678}
{712, 0}
{713, 0}
{714, 0}
{715, 0}
{716, 0}
{717, 0}
{718, 0}
{719, 0}
{720, 0}
{721, 171630172687409284}
{722, 0}
{723, 223951757329985778}
{724, -288006132951605248}
{725, 0}
{726, 0}
{727, 130178110016930978}
{728, 0}
{729, 150094635296999121}
{730, 0}
{731, 0}
{732, 221153541314715648}
{733, 4695500854817138}
{734, 0}
{735, 0}
{736, 0}
{737, 0}
{738, 0}
{739, -294328635627433678}
{740, 0}
{741, -122540666059769436}
{742, 0}
{743, 0}
{744, 0}
{745, 0}
{746, 0}
{747, 0}
{748, 0}
{749, 0}
{750, 0}
{751, -270526059225676798}
{752, 0}
{753, 0}
{754, 0}
{755, 0}
{756, -243588382320549888}
{757, 349823128805828498}
{758, 0}
{759, 0}
{760, 0}
{761, 0}
{762, 0}
{763, -209776996266540764}
{764, 0}
{765, 0}
{766, 0}
{767, 0}
{768, 205195258022068224}
{769, 375466157966914562}
{770, 0}
{771, 0}
{772, 274775964952567808}
{773, 0}
{774, 0}
{775, -129440390136718750}
{776, 0}
{777, -316266587524234044}
{778, 0}
{779, 0}
{780, 0}
{781, 0}
{782, 0}
{783, 0}
{784, 163100993884520448}
{785, 0}
{786, 0}
{787, 350484831237720818}
{788, 0}
{789, 0}
{790, 0}
{791, 0}
{792, 0}
{793, -696021324660623804}
{794, 0}
{795, 0}
{796, 47594055411310592}
{797, 0}
{798, 0}
{799, 0}
{800, 0}
{801, 0}
{802, 0}
{803, 0}
{804, -450977178062020608}
{805, 0}
{806, 0}
{807, 0}
{808, 0}
{809, 0}
{810, 0}
{811, -335751729990047278}
{812, 0}
{813, 539579714826823218}
{814, 0}
{815, 0}
{816, 0}
{817, -4219267855840124}
{818, 0}
{819, 766628956184868324}
{820, 0}
{821, 0}
{822, 0}
{823, 310814069601593378}
{824, 0}
{825, 0}
{826, 0}
{827, 0}
{828, 0}
{829, 70270414796640242}
{830, 0}
{831, -155645752323938238}
{832, -645796917623652352}
{833, 0}
{834, 0}
{835, 0}
{836, 0}
{837, -205405631459812782}
{838, 0}
{839, 0}
{840, 0}
{841, 353814783205469041}
{842, 0}
{843, 0}
{844, 545457074949005312}
{845, 0}
{846, 0}
{847, -481755032683426942}
{848, 0}
{849, -606710289212955198}
{850, 0}
{851, 0}
{852, 0}
{853, 110659453911626258}
{854, 0}
{855, 0}
{856, 0}
{857, 0}
{858, 0}
{859, -720711917046641518}
{860, 0}
{861, 0}
{862, 0}
{863, 0}
{864, 0}
{865, 0}
{866, 0}
{867, 424731610940495769}
{868, 333352523811536896}
{869, 0}
{870, 0}
{871, 1419329444151890884}
{872, 0}
{873, -883657699313995422}
{874, 0}
{875, 0}
{876, 311915195228823552}
{877, 449515578374147378}
{878, 0}
{879, 0}
{880, 0}
{881, 0}
{882, 0}
{883, -46858732317515662}
{884, 0}
{885, 0}
{886, 0}
{887, 0}
{888, 0}
{889, -1109735213279060156}
{890, 0}
{891, 0}
{892, -436074720773005312}
{893, 0}
{894, 0}
{895, 0}
{896, 0}
{897, 0}
{898, 0}
{899, 0}
{900, 531441000000000000}
{901, 0}
{902, 0}
{903, 26396240661931716}
{904, 0}
{905, 0}
{906, 0}
{907, -844781006288432302}
{908, 0}
{909, 0}
{910, 0}
{911, 0}
{912, 218768106867130368}
{913, 0}
{914, 0}
{915, 0}
{916, -1113472018680045568}
{917, 0}
{918, 0}
{919, 1181299028812025762}
{920, 0}
{921, 1011990978447598242}
{922, 0}
{923, 0}
{924, 0}
{925, 690004301269531250}
{926, 0}
{927, -594202750473410622}
{928, 0}
{929, 0}
{930, 0}
{931, 173889474855342486}
{932, 0}
{933, 0}
{934, 0}
{935, 0}
{936, 0}
{937, 708699746663397218}
{938, 0}
{939, -269441492636978478}
{940, 0}
{941, 0}
{942, 0}
{943, 0}
{944, 0}
{945, 0}
{946, 0}
{947, 0}
{948, -1326686869123817472}
{949, -981669233394712796}
{950, 0}
{951, 0}
{952, 0}
{953, 0}
{954, 0}
{955, 0}
{956, 0}
{957, 0}
{958, 0}
{959, 0}
{960, 0}
{961, -506563640225435517}
{962, 0}
{963, 0}
{964, 1258307816218959872}
{965, 0}
{966, 0}
{967, -1154272293085320862}
{968, 0}
{969, 0}
{970, 0}
{971, 0}
{972, 843330077059682304}
{973, 1968823171671718756}
{974, 0}
{975, -1672567694824218750}
{976, 1242585603875274752}
{977, 0}
{978, 0}
{979, 0}
{980, 0}
{981, 726271297265746962}
{982, 0}
{983, 0}
{984, 0}
{985, 0}
{986, 0}
{987, 0}
{988, -688513810947620864}
{989, 0}
{990, 0}
{991, -1876059794018329918}
{992, 0}
{993, 1814099660880148098}
{994, 0}
{995, 0}
{996, 0}
{997, -650343532720989742}
{998, 0}
{999, 1094950108405535202}
,{1000,0}}