Formats: - HTML - YAML - JSON - 2026-09-16T10:38:56.764749
  • lfunc_lfunctions • Show schema
    {'Lhash': '1250823820722093596733742295396,1488239099425160040779106498510,1954898806716569759500903768575', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 380137.2649529088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '9072.1', 'coefficient_field': '1.1.1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'euler_factors': [[1], [1], [1, 0, 0, 2, 0, 0, 125], [1, 3, 3, 1], [1, -3, 15, -30, 165, -363, 1331], [1, 6, 36, 132, 468, 1014, 2197], [1, 6, 42, 154, 714, 1734, 4913], [1, 0, 33, -8, 627, 0, 6859], [1, -6, 33, -68, 759, -3174, 12167], [1, 6, 42, 86, 1218, 5046, 24389], [1, 0, 69, -8, 2139, 0, 29791], [1, 15, 162, 1107, 5994, 20535, 50653], [1, -6, 135, -500, 5535, -10086, 68921], [1, 3, 9, -142, 387, 5547, 79507], [1, 6, -15, -572, -705, 13254, 103823], [1, 9, 39, 110, 2067, 25281, 148877], [1, -24, 345, -3144, 20355, -83544, 205379], [1, 6, 120, 344, 7320, 22326, 226981], [1, -9, 171, -1218, 11457, -40401, 300763], [1, -21, 345, -3222, 24495, -105861, 357911], [1, 12, 246, 1748, 17958, 63948, 389017], [1, 15, 291, 2374, 22989, 93615, 493039], [1, 12, 273, 1968, 22659, 82668, 571787], [1, 0, 162, 388, 14418, 0, 704969], [1, -30, 399, -3940, 38703, -282270, 912673], [1, 24, 411, 4560, 41511, 244824, 1030301], [1, 18, 189, 1308, 19467, 190962, 1092727], [1, -15, 381, -3258, 40767, -171735, 1225043], [1, 18, 330, 3122, 35970, 213858, 1295029], [1, 15, 174, 2187, 19662, 191535, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 0, 0, 2, 0, 0, 125], 1]], [[[1, 1], 3]], [[[1, -3, 15, -30, 165, -363, 1331], 1]], [[[1, 6, 36, 132, 468, 1014, 2197], 1]], [[[1, 6, 42, 154, 714, 1734, 4913], 1]], [[[1, 0, 33, -8, 627, 0, 6859], 1]], [[[1, -6, 33, -68, 759, -3174, 12167], 1]], [[[1, 6, 42, 86, 1218, 5046, 24389], 1]], [[[1, 0, 69, -8, 2139, 0, 29791], 1]], [[[1, 15, 162, 1107, 5994, 20535, 50653], 1]], [[[1, -2, 41], 3]], [[[1, 3, 9, -142, 387, 5547, 79507], 1]], [[[1, 6, -15, -572, -705, 13254, 103823], 1]], [[[1, 9, 39, 110, 2067, 25281, 148877], 1]], [[[1, -24, 345, -3144, 20355, -83544, 205379], 1]], [[[1, 6, 120, 344, 7320, 22326, 226981], 1]], [[[1, -9, 171, -1218, 11457, -40401, 300763], 1]], [[[1, -21, 345, -3222, 24495, -105861, 357911], 1]], [[[1, 12, 246, 1748, 17958, 63948, 389017], 1]], [[[1, 15, 291, 2374, 22989, 93615, 493039], 1]], [[[1, 12, 273, 1968, 22659, 82668, 571787], 1]], [[[1, 0, 162, 388, 14418, 0, 704969], 1]], [[[1, -30, 399, -3940, 38703, -282270, 912673], 1]], [[[1, 24, 411, 4560, 41511, 244824, 1030301], 1]], [[[1, 18, 189, 1308, 19467, 190962, 1092727], 1]], [[[1, -15, 381, -3258, 40767, -171735, 1225043], 1]], [[[1, 18, 330, 3122, 35970, 213858, 1295029], 1]], [[[1, 15, 174, 2187, 19662, 191535, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 8, 'label': '6-9072e3-1.1-c1e3-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bx', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 17}, 'plot_values': [-5.881612879008895e-181, 0.0002630442337100076, 0.0021012618053210153, 0.007074387188772202, 0.01671133107928417, 0.03249469721516944, 0.05584557147092786, 0.08810850084391493, 0.13053580239203968, 0.18427333880704735, 0.250346424750914, 0.3296437941696344, 0.4229057236504807, 0.5307117818014884, 0.6534647895947779, 0.7913830742935386, 0.9444913927010156, 1.1126060747729523, 1.2953332497352057, 1.4920646283007915, 1.7019660938709973, 1.9239833148074512, 2.156844222334738, 2.399054341169394, 2.6489102425890345, 2.9045103676073443, 3.163761054483882, 3.424396843196403, 3.6840006676885997, 3.9400245409660495, 4.189813937959452, 4.43063728574742, 4.659724395665805, 4.874290268789891, 5.071572317156641, 5.248887830026393, 5.4036508846371865, 5.533414017573325, 5.635943424352889, 5.709221585675367, 5.751488468755729, 5.761330143993532, 5.737659617622471, 5.679751447310467, 5.587336554550423, 5.460554879319818, 5.299976927192972, 5.1066953984912, 4.88224578863442, 4.628609161861125, 4.34829042506928, 4.044206803696244, 3.719668215927958, 3.378433045377429, 3.0245691681670634, 2.6624115960584644, 2.296589602724836, 1.9318700281121082, 1.5730959963582691, 1.2251839796392052, 0.8929636057914405, 0.5811055852568041, 0.2940930748163285, 0.03607521128335894, -0.1892039534629507, -0.3784496533834618, -0.5289313037517294, -0.6385386707795879, -0.7058270044964144, -0.7300848549882879, -0.7113617260216603, -0.6504975300999541, -0.5491332116774982, -0.40969931993528586, -0.2354146469653254, -0.030237480556009434, 0.20118970971825495, 0.45358233729424, 0.7211146711533538, 0.9975160806210912, 1.2761551087986187, 1.5501764916592298, 1.8126268978438254, 2.056571701127768, 2.2752450491677267, 2.4621861549009476, 2.611368799121476, 2.7173386425201977, 2.7753363770958908, 2.7814116415183783, 2.732524193991954, 2.62662972764037, 2.462746078900868, 2.241002801830752, 1.962669968893825, 1.6301468665093228, 1.246957000973025, 0.8177095064929749, 0.3479893763600437, -0.15569014407785559, -0.6859912141922936, -1.2349661964963916, -1.7941215996001496, -2.3545707400172375, -2.907342642353002, -3.4434257086104365, -3.953941543264438, -4.430519902154587, -4.865282118649683, -5.2510013646140665, -5.581502675126529, -5.851551577646255, -6.056966267419535, -6.194996338638267, -6.264096256683458, -6.263963016641936, -6.195851252245434, -6.06223209155574, -5.86674483201751, -5.614419429716612, -5.311244938158464, -4.964042758395768, -4.580587702929515, -4.16913151335912, -3.738224170479598, -3.2967474027257313, -2.8534525163962354, -2.4167704487343755, -1.994791315010365, -1.594877976724192, -1.2235110122496091, -0.8862594596140735, -0.5875205629632573, -0.3304404000830045, -0.11692078480670373, 0.052487104254288104, 0.17856173131327702, 0.2633359728757524, 0.3100519113495281, 0.32303829563109804, 0.30755777615797925, 0.26964297742375504, 0.2158968717971586, 0.15328098038581814, 0.08888919390547874, 0.029716795714368274, -0.017566679628492978, -0.04683909174475019, -0.05273134853597278, -0.030810821433527577, 0.022261910885784435, 0.10860621779217754, 0.22904103546946933, 0.3830309384002749, 0.5686739454191, 0.7827669371239997, 1.0208590124381955, 1.2773612605144335, 1.545770303153825, 1.8187974146725598, 2.088575068477367, 2.347013681791333, 2.5859462679829743, 2.797378716699453, 2.973920465622745, 3.108871641180919, 3.1964489521914556, 3.2322093857476837, 3.213014736172315, 3.1371679249995634, 3.0047470569440753, 2.8174103212202466, 2.5783990868368067, 2.2927198887631777, 1.966794486820015, 1.608321552316755, 1.2262823972833978, 0.830485582158699, 0.4313193286102831, 0.03960353651317057, -0.3338869015716702, -0.6787129052423072, -0.9850079100361585, -1.2438776041629418, -1.4476506904019246, -1.590113713694582, -1.6667479070814308, -1.6748624247414936, -1.6137365261427705, -1.4846447007318553, -1.290823629616038, -1.037457944796782, -0.7314977220623506, -0.38145531802974936, 0.0027811904095733885, 0.41027969900704836, 0.8293923471365869, 1.24807451432731, 1.654267327184119, 2.036267448676284, 2.3830913172828057, 2.6847972904419675, 2.932797309049301, 3.1201553227901155, 3.241757606818127, 3.2944793893247097, 3.2773148609639713, 3.191352321609611, 3.039748281234875, 2.827626760040176, 2.5618793529823147, 2.2509549749364393, 1.9045279480479216, 1.5332031103388166, 1.1481850781959975, 0.7607801055394623, 0.38212410793471824, 0.02283376249278205, -0.30754382515296325, -0.6006600447707892, -0.8496213518788606, -1.0494614050804154, -1.1970429108145302, -1.2911377665566939, -1.3327138655097563, -1.3245912594060167, -1.271316292907629, -1.1792134263329126, -1.0558528818151773, -0.9097559289034044, -0.7502370033944415, -0.5868026252795886, -0.42878307534645344, -0.2850588624409965, -0.16353944904860182, -0.07084652892219848, -0.01205835912894863, 0.009599342384022568, -0.0070970076185851785, -0.06125966402602865, -0.14986681752804967, -0.2678470320356395, -0.4081944785510684, -0.5622234690998438, -0.7198799018685509, -0.8700762514969913, -1.0011320587281973, -1.1012290424187834, -1.1588720639809869, -1.1633705403483616, -1.1053004378150624, -0.9769313692985859, -0.7725982274425999, -0.48902200333166357, -0.1255241796445405, 0.31581520229438886, 0.8300886045429352, 1.4097000359873215, 2.044437889456378, 2.721692079143622, 3.427000343883204, 4.144270807727669, 4.856226988906777, 5.545304571106613, 6.193865442515677, 6.784734211974019, 7.3022889030921405, 7.732481176884468, 8.063291258171711, 8.285800090630008, 8.393866865252052, 8.384348739422146, 8.257950035470117, 8.018500733675316, 7.672859575449287, 7.231407580946957, 6.706992730364925, 6.114538273159949, 5.471161395254542, 4.794961013986937, 4.104453782955595, 3.41841721589031, 2.7547612370254058, 2.1299779053801124, 1.558891566905286, 1.0538463374675624, 0.6243583486871275, 0.276974004720121, 0.01492384836227153, -0.1618956617202776, -0.256809068096381, -0.27622243618239556, -0.22929294929989513, -0.1275242268024817, 0.015739068174839853, 0.18589079795124447, 0.3676686383184237, 0.5458053207682086, 0.7056696244038192, 0.8338815417490419, 0.9188623581023182, 0.9513235202250031, 0.924667132388312, 0.8352450149521833, 0.6825301377424383, 0.46912585210423996, 0.20066697078074974, -0.11438352336667719, -0.465176448277506, -0.8388538345568497, -1.2210526803365154, -1.5967114883905782, -1.9505287307855155, -2.267584047475798, -2.534297940299359, -2.738728018291515, -2.8710787797035033, -2.9245465250171088, -2.895255492149747, -2.7824634969675324, -2.589059682557742, -2.321065813698442, -1.9874531710714765, -1.6001796531295647, -1.1733399570518896, -0.7226524309838303, -0.26508445350308263, 0.1821282277390454, 0.6021388611504457, 0.9790790460883706, 1.2988868316116378, 1.5498592582755208, 1.7231811319699508, 1.8133538818026629, 1.8184211436197648, 1.7401852713594248, 1.5841172981615954, 1.3591444077658668, 1.0774239599305335, 0.7537885689540357, 0.40514176041337, 0.049837733362856025, -0.29312705378554627, -0.6049164529040235, -0.8676496326625541, -1.0651699855463983, -1.1837705757084682, -1.212845002271802, -1.1453513825581543, -0.9782023990979822, -0.7124665704606445, -0.3533922140197032, 0.08968257659423268, 0.603756481711511, 1.1725287947773595, 1.7769426385660907, 2.3962180476953843, 3.0083765632061192, 3.591043251779486, 4.122863364446617, 4.583866193588658, 4.9562309402262725, 5.225733915419023, 5.381656475579063, 5.417226288260573, 5.330733352162988, 5.124830101116167, 4.806474400916373, 4.387471600442401, 3.8832266538852838, 3.3121985810404313, 2.6958311409756988, 2.057020447321302, 1.4192756880042474, 0.8062182313508177, 0.24014699567041548, -0.25878275942804707, -0.6731638231182798, -0.989305237229576, -1.1977206214849072, -1.2934851907987988, -1.2765139768981435, -1.1515173977920574, -0.9278727979837447, -0.6192152134697719, -0.24285235360394059, 0.18088035429812252, 0.6294893830615158, 1.0792585163661481, 1.5062177804264971, 1.887107086098483, 2.2003425864116872, 2.426962354944779, 2.551316491958913, 2.561734158295081, 2.451072852549777, 2.216905152519335, 1.8616686083261282, 1.3925594839520332, 0.821210448692254, 0.16329868966998456, -0.5622635888516853, -1.3339421157137836, -2.128338964461976, -2.92152418138293, -3.6895841552949205, -4.40944148390798, -5.06036778670701, -5.624116579531592, -6.08548916794564, -6.433655666265162, -6.6616657571054425, -6.7665564892913075, -6.75021230330152, -6.618275122046245, -6.3797768802017645, -6.047463321074569, -5.636347283553589, -5.163035529761894, -4.645644823504279, -4.102371921550193, -3.5507958334477836, -3.007646206990098, -2.487750538722266, -2.00358598627695, -1.5651696741167809, -1.179595606007848, -0.8509906347310582, -0.5806870791123862, -0.3673406781289533, -0.2072663544768838, -0.09487966848443355, -0.023183619361499496, 0.015700867772461484, 0.029995084230369798, 0.02772318540523713, 0.016245192748085457, 0.0018561179909427753, -0.010523663051888562, -0.017539029195675158, -0.017479588767927618, -0.010228727757325513, 0.002892706380435386, 0.01939835325772788, 0.03598103457905805, 0.048912430862330325, 0.0545179334045959, 0.04959500904971702, 0.03182763553012892, 0.00019780292978493187, -0.04478093607871177, -0.10087817326924696, -0.16405873332899873, -0.22859769023203036, -0.2872616030075671, -0.331666606582599, -0.35272098189317397, -0.34112615740287244, -0.2880880379117245, -0.18587792773286818, -0.028427958905334987, 0.18789307023427237, 0.4639093978055827, 0.7972603444786474, 1.1819279269471987, 1.6083228334633943, 2.063380112753604, 2.530667037234631, 2.9910145416997933, 3.4231561686253746, 3.8044502397697935, 4.111910556471817, 4.323213559530293, 4.417764355359205, 4.3777945927277795, 4.189365957816491, 3.843270833686728, 3.33582387684136, 2.669435125083564, 1.8527755821765017, 0.901028542719342, -0.1642678253524841, -1.3161947496217268, -2.5226993908764257, -3.7475121250369634, -4.952319285215943, -6.0971639417706935, -7.141840939456563, -8.04892327680852, -8.783782915975445, -9.315959168379601, -9.62239019396868, -9.686540445437874, -9.499206537981244, -9.061227829633912, -8.381457662573412, -7.476658034466607, -6.37315286982372, -5.10378119148699, -3.706874857901035, -2.2267089485421536, -0.7099755785942513, 0.7957946704137079, 2.242689456098582, 3.585644619406228, 4.783978298584451, 5.802143103420231, 6.611918541365283, 7.193290615639795, 7.534826851620104, 7.634398470405015, 7.499030315778783, 7.144447107477771, 6.594366851182445, 5.879337690294181, 5.035417616696432, 4.102540205460714, 3.122748399100366, 2.1384057304457196, 1.1904002578565096, 0.31642023483998843, -0.45063000256743674, -1.0838574214739578, -1.5634393331646785, -1.8773332005904464, -2.021525237099318, -2.000072113974876, -1.8245513511811664, -1.513394262764246, -1.0909688816863254, -0.5858358672201055, -0.029659169309375552, 0.5442308626505103, 1.1032811716519944, 1.616525432058996, 2.055908849652669, 2.3987041100963573, 2.6274371383953223, 2.7305408039591432, 2.7040745241195867, 2.5505244205403823, 2.2785313949834127, 1.9035658310939871, 1.4458303704494206, 0.9292114244761989, 0.38100161647211894, -0.17048880801369948, -0.6972788184924064, -1.1724806358952424, -1.5722484206629155, -1.876830168211377, -2.0712031562326967, -2.1460297491378566, -2.097965279200379, -1.9296792432392829, -1.6496674279838053, -1.2717019571579016, -0.8140918957559153, -0.298652196005396, 0.25044244338106486, 0.8079147126669219, 1.348650980965685, 1.84893229172265, 2.287705698544827, 2.6474408189521452, 2.914917726916774, 3.0819928396511007, 3.14563971503618, 3.1079836440236988, 2.97627278734599, 2.7620963512936885, 2.480703892344748, 2.150257439424339, 1.7905963305540378, 1.4221970595883338, 1.0651091396638905, 0.7378219993755126, 0.45636485423299694, 0.2334650886645037, 0.0779930846360494, -0.005389920406890905, -0.016429118650733935, 0.040925650440353296, 0.15884590954736746, 0.32618111322891635, 0.5292295286581395, 0.752543284582406, 0.9799904195614985, 1.1956458193019168, 1.3846521078172447, 1.5343059682199962, 1.6345856253012068, 1.678629942929646, 1.6633703700076887, 1.589413483827722, 1.4608988595192924, 1.285432981474743, 1.0733791442866105, 0.8371661152189322, 0.5906325516394344, 0.3480744663934822, 0.12334779500822901, -0.07097110043119456, -0.2243166740804615, -0.32879721636233494, -0.3797169846290976, -0.37574973800248507, -0.3190509661608761, -0.21511532690874022, -0.07236013639241214, 0.09834573935844473, 0.28450739305121786, 0.47271592116530975, 0.6494340454898695, 0.8021811272513936, 0.9200650204349761, 0.994447563828086, 1.0199829064439068, 0.9945564300210145, 0.9194529555351222, 0.7998137241254892, 0.6438541437307274, 0.46241511306354854, 0.2686992569604465, 0.07700895640767152, -0.09810699762404392, -0.2426033631938136, -0.34416887848130445, -0.39303448586841416, -0.38271274846209324, -0.3106580238145652, -0.17856415100685524, 0.007412200268010408, 0.23685934269999379, 0.49556175648270834, 0.7660345642743285, 1.028496126627266, 1.2619382851049228, 1.445242930288427, 1.5584500778101045, 1.5839869466107999, 1.5078237289283465, 1.3204238820004315, 1.0175492386055012, 0.6007866373735897, 0.07773070940025553, -0.5380568479380311, -1.2276195517983437, -1.9672342148854247, -2.7293365196534847, -3.4842132039372813, -4.201025693682724, -4.849230415337372, -5.40091491350455, -5.831518952109465, -6.121092901583185, -6.256494245498505, -6.231155905638221, -6.045562732332261, -5.708565108593276, -5.235923294036917, -4.649721788894913, -3.9784426870800744, -3.254562932981627, -2.513121059066592, -1.7907552837701892, -1.1230937755376615, -0.5431071870935948, -0.07979350363604107, 0.2437467847384709, 0.4114008284742842, 0.4148693821437036, 0.2542621193244029, -0.061919716333838255, -0.5170451783469349, -1.0871856476105124, -1.7423000338313925, -2.447638736861526, -3.165501061082957, -3.8571134258195587, -4.4846362830866395, -5.01297210566044, -5.411533377387578, -5.6559538347350955, -5.729106175164555, -5.621995764201045, -5.334330829222785, -4.874339983535153, -4.258423509023812, -3.5101889186685726, -2.659286349410316, -1.7400203491052126, -0.7891023799711263, 0.15575145729880877, 1.0575678694943171, 1.8828581322558393, 2.602344086269531, 3.192229174350439, 3.636470196112141, 3.9261884783544336, 4.059871895760277, 4.044481369067272, 3.8935038205923105, 3.626019115780643, 3.2665286289911113, 2.842240280701024, 2.3814910160397296, 1.9127971514695787, 1.462330783757028, 1.052504843845565, 0.7010873357552949, 0.4197546163898737, 0.21356665989812645, 0.0808906634083623, 0.01343538794536453, -0.0030940877122879826, 0.011992963707859183, 0.035637209648626746, 0.04256897248313823, 0.006980055495332405, -0.09574340779814515, -0.28733301355677043, -0.5851366239115774, -1.000795501101753, -1.5392257347409752, -2.1981984521768463, -2.9679755387076985, -3.8314545561962037, -4.7653479933763165, -5.740717858474362, -6.724207477087826, -7.680672872379929, -8.573979291571584, -9.368706570095645, -10.03346936828025, -10.541089599254382, -10.86992620065673, -11.006850552320554, -10.946123670067859, -10.68968610039125, -10.24896192482677, -9.642351541165286, -8.894332331622513, -8.035842607286064, -7.10097105677097, -6.125314444563505, -5.145364822037016, -4.195389437582198, -3.3058561546136844, -2.5026586311148717, -1.8051737361082718, -1.225555891982759, -0.7686315773738228, -0.43155676056316516, -0.20432038420622264, -0.07067912263606518, -0.009311228772256127, 0.004717467475748388, -0.0016692066795371595, -0.00133676037355122, 0.03120523478944934, 0.11834034263555993, 0.27838999120282026, 0.5243660845125659, 0.8605370714940529, 1.2803882842240333, 1.7702243818282708, 2.3290215127856078], 'positive_zeros': ['0.986726011486835339083871197503373', '1.17401364315783513978712248973651', '1.54214324228190901364517818211414', '2.10408031028959127198137007551726', '2.27483505286464357705728411369992', '2.33828572313983749006856065609626', '2.79848938136265470565714156184639', '3.03114092542283969911619040342173', '3.39165685186836478211059322319645', '3.69305404981113201081732807960824', '3.71523032979897543448890864928759', '3.97347868062664212677888061351009', '4.50107856665445790571406803120567', '4.59219205522045890101382261190528', '4.79143264090657412237094585999698', '5.10292980211848295314302535717452', '5.33034136662350122109509034526984', '5.49704443379439214687099721842009', '5.86659910343364783929703059347571', '6.02474073092625862023752878416709', '6.25362965360793324834918312897877', '6.75787394866519458692759703067951', '6.83020763803188123139176981967842', '6.90322675043134280697617053563858', '7.01570705661680822260656346439393', '7.18982845431720678679478050718847', '7.51330538908799565031015989319796'], 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1e3-0', 'trace_hash': 2173141273981339347, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.986726011486835339083871197503', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.17401364315783513978712248974', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.54214324228190901364517818211', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 380137.2649529088, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 746636341248, 'conductor_radical': 42, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 3, 0, -6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, -15, 0, 0, 0, 6, 0, -3, 0, 0, 0, -6, 0, 6, 0, 0, 0, -9, 0, 0, 0, 0, 0, 24, 0, -6, 0, 0, 0, 0, 0, 9, 0, 0, 0, 21, 0, -12, 0, 0, 0, -9, 0, -15, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 30, 0, 0, 0], 'euler11': [1, -3, 15, -30, 165, -363, 1331], 'euler13': [1, 6, 36, 132, 468, 1014, 2197], 'euler17': [1, 6, 42, 154, 714, 1734, 4913], 'euler19': [1, 0, 33, -8, 627, 0, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -6, 33, -68, 759, -3174, 12167], 'euler29': [1, 6, 42, 86, 1218, 5046, 24389], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 69, -8, 2139, 0, 29791], 'euler37': [1, 15, 162, 1107, 5994, 20535, 50653], 'euler41': [1, -6, 135, -500, 5535, -10086, 68921], 'euler43': [1, 3, 9, -142, 387, 5547, 79507], 'euler47': [1, 6, -15, -572, -705, 13254, 103823], 'euler5': [1, 0, 0, 2, 0, 0, 125], 'euler53': [1, 9, 39, 110, 2067, 25281, 148877], 'euler59': [1, -24, 345, -3144, 20355, -83544, 205379], 'euler61': [1, 6, 120, 344, 7320, 22326, 226981], 'euler67': [1, -9, 171, -1218, 11457, -40401, 300763], 'euler7': [1, 3, 3, 1, 0, 0, 0], 'euler71': [1, -21, 345, -3222, 24495, -105861, 357911], 'euler73': [1, 12, 246, 1748, 17958, 63948, 389017], 'euler79': [1, 15, 291, 2374, 22989, 93615, 493039], 'euler83': [1, 12, 273, 1968, 22659, 82668, 571787], 'euler89': [1, 0, 162, 388, 14418, 0, 704969], 'euler97': [1, -30, 399, -3940, 38703, -282270, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 2, 0, 0, 125], [1, 3, 3, 1, 0, 0, 0], [1, -3, 15, -30, 165, -363, 1331], [1, 6, 36, 132, 468, 1014, 2197], [1, 6, 42, 154, 714, 1734, 4913], [1, 0, 33, -8, 627, 0, 6859], [1, -6, 33, -68, 759, -3174, 12167], [1, 6, 42, 86, 1218, 5046, 24389], [1, 0, 69, -8, 2139, 0, 29791], [1, 15, 162, 1107, 5994, 20535, 50653], [1, -6, 135, -500, 5535, -10086, 68921], [1, 3, 9, -142, 387, 5547, 79507], [1, 6, -15, -572, -705, 13254, 103823], [1, 9, 39, 110, 2067, 25281, 148877], [1, -24, 345, -3144, 20355, -83544, 205379], [1, 6, 120, 344, 7320, 22326, 226981], [1, -9, 171, -1218, 11457, -40401, 300763], [1, -21, 345, -3222, 24495, -105861, 357911], [1, 12, 246, 1748, 17958, 63948, 389017], [1, 15, 291, 2374, 22989, 93615, 493039], [1, 12, 273, 1968, 22659, 82668, 571787], [1, 0, 162, 388, 14418, 0, 704969], [1, -30, 399, -3940, 38703, -282270, 912673]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9072/2/a/bx'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-9072e3-1.1-c1e3-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-9072e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.511185858251809, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 2173141273981339347, 'z1': {'__RealLiteral__': 0, 'data': '0.986726011486835339083871197503', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1250823820722093596733742295396,1488239099425160040779106498510,1954898806716569759500903768575', 'Lhash_array': ['1250823820722093596733742295396', '1488239099425160040779106498510', '1954898806716569759500903768575'], 'factors': ['2-9072-1.1-c1-0-76', '2-9072-1.1-c1-0-97', '2-9072-1.1-c1-0-140'], 'label': '6-9072e3-1.1-c1e3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9072/2/a/bx'}