-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '588672211295716981685036277003,685697346731286254491899474954,2211983987794812559268256814427,2242335734623303208029513597661', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 5, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 152548.95646688485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, 4, 6, 4, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 37523281640625, 'conductor_radical': 165, 'degree': 8, 'euler_factors': [[1, 0, -5, 0, 13, 0, -20, 0, 16], [1], [1], [1, 0, -5, 0, 93, 0, -245, 0, 2401], [1, 4, 6, 4, 1], [1, 0, -10, 0, 43, 0, -1690, 0, 28561], [1, 0, -65, 0, 1633, 0, -18785, 0, 83521], [1, 0, -14, 0, 771, 0, -5054, 0, 130321], [1, 0, -25, 0, 933, 0, -13225, 0, 279841], [1, 10, 151, 920, 7101, 26680, 126991, 243890, 707281], [1, 12, 178, 1224, 9195, 37944, 171058, 357492, 923521], [1, 0, -10, 0, 1483, 0, -13690, 0, 1874161], [1, -12, 218, -1584, 14595, -64944, 366458, -827052, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 0, -10, 0, 1563, 0, -22090, 0, 4879681], [1, 0, -85, 0, 6873, 0, -238765, 0, 7890481], [1, -20, 346, -3640, 33891, -214760, 1204426, -4107580, 12117361], [1, 22, 363, 4004, 36845, 244244, 1350723, 4993582, 13845841], [1, 0, -140, 0, 13878, 0, -628460, 0, 20151121], [1, -12, 88, -1164, 15870, -82644, 443608, -4294932, 25411681], [1, 0, -25, 0, 10153, 0, -133225, 0, 28398241], [1, 10, 331, 2320, 39841, 183280, 2065771, 4930390, 38950081], [1, 0, 55, 0, 6333, 0, 378895, 0, 47458321], [1, 50, 1231, 19600, 218901, 1744400, 9750751, 35248450, 62742241], [1, 0, -385, 0, 55873, 0, -3622465, 0, 88529281], [1, -2, 343, -544, 49845, -54944, 3498943, -2060602, 104060401], [1, 0, -325, 0, 47413, 0, -3447925, 0, 112550881], [1, 0, -410, 0, 64843, 0, -4694090, 0, 131079601], [1, 10, 411, 3020, 66461, 329180, 4883091, 12950290, 141158161], [1, 0, 70, 0, 11083, 0, 893830, 0, 163047361]], 'euler_factors_factorization': [[[[1, 0, -5, 0, 13, 0, -20, 0, 16], 1]], [1], [1], [[[1, 0, -5, 0, 93, 0, -245, 0, 2401], 1]], [[[1, 1], 4]], [[[1, 0, -10, 0, 43, 0, -1690, 0, 28561], 1]], [[[1, 0, -65, 0, 1633, 0, -18785, 0, 83521], 1]], [[[1, 0, -7, 0, 361], 2]], [[[1, 0, -25, 0, 933, 0, -13225, 0, 279841], 1]], [[[1, 5, 63, 145, 841], 2]], [[[1, 3, 31], 4]], [[[1, 0, -10, 0, 1483, 0, -13690, 0, 1874161], 1]], [[[1, -3, 41], 4]], [[[1, 0, -50, 0, 1849], 2]], [[[1, 0, -10, 0, 1563, 0, -22090, 0, 4879681], 1]], [[[1, 0, -85, 0, 6873, 0, -238765, 0, 7890481], 1]], [[[1, -10, 123, -590, 3481], 2]], [[[1, 11, 121, 671, 3721], 2]], [[[1, 0, -70, 0, 4489], 2]], [[[1, -6, 26, -426, 5041], 2]], [[[1, 0, -25, 0, 10153, 0, -133225, 0, 28398241], 1]], [[[1, 5, 153, 395, 6241], 2]], [[[1, 0, 55, 0, 6333, 0, 378895, 0, 47458321], 1]], [[[1, 25, 303, 2225, 7921], 2]], [[[1, 0, -385, 0, 55873, 0, -3622465, 0, 88529281], 1]], [[[1, -1, 171, -101, 10201], 2]], [[[1, 0, -325, 0, 47413, 0, -3447925, 0, 112550881], 1]], [[[1, 0, -410, 0, 64843, 0, -4694090, 0, 131079601], 1]], [[[1, 5, 193, 545, 11881], 2]], [[[1, 0, 70, 0, 11083, 0, 893830, 0, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 9, 'label': '8-2475e4-1.1-c1e4-0-9', 'leading_term': '6.3828005951678013912897766592586088148035746717910960695056853358825894134934049516791149', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2475/2/c/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [6.382800595167802, 6.371569934358526, 6.336588272837709, 6.278290623593588, 6.197246266209218, 6.094039509209507, 5.9692038026481775, 5.823385018056707, 5.657381125986301, 5.472166555140184, 5.2688625299123135, 5.048727630349873, 4.813154678388597, 4.563662353532062, 4.301879599634952, 4.029566156860414, 3.7486218646665583, 3.461062239615443, 3.169002636983977, 2.874675231815072, 2.5804147353718396, 2.288634327116278, 2.001817086029741, 1.7225187326374196, 1.4533356560310626, 1.196885752837158, 0.9558012436272347, 0.7327021194684329, 0.5301663838910585, 0.3507130475433348, 0.1967792771840611, 0.07068423528319924, -0.025396076625167074, -0.08945206113374658, -0.11967513647862703, -0.11448637461209626, -0.0725624328680326, 0.007134014406391733, 0.12532886113583283, 0.282414645758498, 0.4784230159869005, 0.7130069621587147, 0.9854290267250302, 1.2945451316918821, 1.638792246533646, 2.016191942631247, 2.4243524416455533, 2.8604683580213823, 3.3213364386512816, 3.803376340288264, 4.302656012151189, 4.814918843298593, 5.33561696821093, 5.85995515861673, 6.382952800880394, 6.89947975396939, 7.404304064989164, 7.892174696182917, 8.357895587251152, 8.796355882761796, 9.202602393663742, 9.57194842597305, 9.900016587886842, 10.18277307283635, 10.416637332626712, 10.598532406519821, 10.725915055595731, 10.796826288638108, 10.809979796303349, 10.76471876900612, 10.661062518709523, 10.499774807041149, 10.28231297943624, 10.010765999496273, 9.687926263810226, 9.317280970195082, 8.90284894450152, 8.449142983931385, 7.9612493917198215, 7.444653093544747, 6.905089404186745, 6.348538489350967, 5.781208597513853, 5.209303418371654, 4.6389306897455524, 4.076107078672004, 3.52661971731701, 2.9958712783899957, 2.4888476330939953, 2.0100673043087687, 1.5634578518231455, 1.1522965609928681, 0.7792152471710827, 0.4461289124717809, 0.15420784691614586, -0.09610187982531744, -0.3050643295755873, -0.473651571107264, -0.6034956326764238, -0.6968177217566605, -0.7563750765768439, -0.7853825455119485, -0.7874229006355934, -0.7663491287000535, -0.7261843379016044, -0.6710170419222806, -0.6049034950933125, -0.5317609075456916, -0.45526771443395625, -0.3787773196211187, -0.3052414934936631, -0.23713659439232762, -0.17640941439131613, -0.12444029325896888, -0.08201934750045259, -0.04933931206384845, -0.02600797854156182, -0.011076698401006734, -0.0030855113289798837, -0.00012408015062485752, 9.379406260257313e-05, 0.00014380625965008083, 0.0027951503515678895, 0.010907914727454332, 0.027326509623982077, 0.054772214961434446, 0.09573919533229487, 0.1523956821940609, 0.22649228229914858, 0.3192823164112334, 0.4314638790552901, 0.5631291516569283, 0.7137281095941117, 0.8820605570592256, 1.0663049909242672, 1.26403201121847, 1.4722430648792646, 1.6874562065821168, 1.9058129295099144, 2.1231438293698246, 2.335078348073163, 2.537185130575744, 2.7251167038549706, 2.89469491083595, 3.042049805510578, 3.163723891515643, 3.2568195706329433, 3.3190647756662734, 3.3488742587712736, 3.345379803095018, 3.308541133567563, 3.23913330273338, 3.138661247977245, 3.0093292412816504, 2.854090840052502, 2.676490528672953, 2.4804972230024185, 2.270429561750643, 2.0509228721952173, 1.8266800869732482, 1.60231242583495, 1.382257410895015, 1.170678409821323, 0.9712694240344373, 0.7871579960334316, 0.6208522903258573, 0.4741787078151568, 0.3482158583298729, 0.24329544890692914, 0.15902430989530172, 0.09433394862242492, 0.04754297919746209, 0.016454626378935928, -0.0015259878277962, -0.00925681146680764, -0.009718674969019575, -0.005865102804286768, -0.0004714064684375551, 0.004007937923340794, 0.0055701320790053485, 0.0027778910967599223, -0.0051514018697235734, -0.018282779837536036, -0.03593278364229664, -0.056673670926659724, -0.07837141090562676, -0.09825616353733499, -0.11303055392277146, -0.11900755889189299, -0.11226983007676918, -0.08885315433353114, -0.044947591133803984, 0.022902636247871477, 0.1176041123253746, 0.2413126919225587, 0.39525760841911745, 0.5796195346489832, 0.7934044990190123, 1.0343593114613345, 1.2989735482959488, 1.5825218108806274, 1.8790875837737204, 2.1817159287936674, 2.4826691792574143, 2.7735697640965253, 3.0456224634724074, 3.290056167287332, 3.4984322186991936, 3.6628268684262837, 3.7762084295409735, 3.8329896188250507, 3.829100424581699, 3.7621610664914917, 3.6318840202098364, 3.4402818622879225, 3.1914990866695496, 2.8918616153657872, 2.5499916251754575, 2.176515104562862, 1.7837194254602722, 1.3853883008145238, 0.9963908746070571, 0.6321646212500222, 0.308249503212976, 0.03984682461865219, -0.1588035148976216, -0.27493760135987927, -0.2977184483876109, -0.21871181290073852, -0.032282293317151455, 0.26407216787715754, 0.6695143563513495, 1.1797764939809046, 1.7871638743919318, 2.4805887313904647, 3.2458559312318855, 4.066044473043521, 4.9219308833004725, 5.792483802882036, 6.655537441530999, 7.488466425799058, 8.268905596010004, 8.975456890416144, 9.588383172606235, 10.09029832641859, 10.466800832943468, 10.706948745205104, 10.803635915563785, 10.753949534557162, 10.559239734834263, 10.225125547980573, 9.761354390109743, 9.181486634199532, 8.50237037758541, 7.743659368479536, 6.927137793873163, 6.075865048896595, 5.21337292075991, 4.362905642203674, 3.546523301706255, 2.784285102083913, 2.0935548051978987, 1.4883869799200415, 0.9790269916974635, 0.5715793062674286, 0.26781899158432426, 0.06521517156954224, -0.042865357932892194, -0.06680851958239357, -0.02019581110332356, 0.08088483447495581, 0.21861702174127512, 0.3744158422989236, 0.5299065644578266, 0.6678291071121719, 0.7730260252700082, 0.8334769117599027, 0.8409355186519608, 0.791557659741975, 0.6865721057805865, 0.5324740197980158, 0.3409416417690977, 0.12879075633809486, -0.08234188841086312, -0.2668536497239858, -0.395983475213904, -0.4387349203494141, -0.363197459025116, -0.13785156272382876, 0.2671169339296725, 0.8783271127207506, 1.717909720623259, 2.8023421873109426, 4.141117120539558, 5.735944598791718, 7.580277851803781, 9.658718183516962, 11.946697466654161, 14.411234713112696, 17.011433501275913, 19.698828196380134, 22.418799027223912, 25.11251745945382, 27.718142429159112, 30.172350540782315, 32.4125898599659, 34.379424674516905, 36.01796024232377, 37.27961977460119, 38.12393322865619, 38.52038562641766, 38.44921752051718, 37.90207070435425, 36.88258642532182, 35.40690823269768, 33.50292468314636, 31.209476777811208, 28.57558140609627, 25.658973607212697, 22.524187476322776, 19.240818037899885, 15.881566444244806, 12.519559872469065, 9.226430967050756, 6.070451873509765, 3.1142864051417134, 0.4127885812152383, -1.988010755444042, -4.052053944065827, -5.754295231903054, -7.081433525690168, -8.03162192858987, -8.614072374089012, -8.848396101649822, -8.763812989815833, -8.397608484875333, -7.793362465335262, -6.99928282190855, -6.066478856504945, -5.046846746367304, -3.991198744362065, -2.947614312335674, -1.9596741437982257, -1.0651398848215425, -0.29502108775637714, 0.32724161924640965, 0.7864998344881331, 1.0757064919094466, 1.1956242462075641, 1.1544409437748167, 0.9670432443126604, 0.6537340293389418, 0.23909211790959006, -0.24932378176884998, -0.7824382597608958, -1.3310826011027355, -1.8672340373519642, -2.3652306354177703, -2.8029605695762965, -3.1625747748094506, -3.4309783470244994, -3.6001763798967814, -3.667569166542114, -3.6355777078031166, -3.5111100771232198, -3.305004614123747, -3.0314527972278076, -2.7068667170382876, -2.348847893899798, -1.9752825550098299, -1.6034642271695672, -1.2490778806176235, -0.9254464345163382, -0.642977367355489, -0.40875749561845826, -0.22630649330620378, -0.09557666354944884, -0.013151328542807168, 0.027377936509978443, 0.03488188597776176, 0.020036468690473805, -0.005424602072936283, -0.02949327733766339, -0.040663999698482785, -0.028675003256404742, 0.014834473894649489, 0.09582284490268914, 0.21746859834164253, 0.37993124689236846, 0.5803092515470467, 0.8129117285254814, 1.069518284812027, 1.3397562982241802, 1.6117211180852447, 1.8729168336275595, 2.1107751199710587, 2.3132663988081648, 2.4697293620810985, 2.571799719619487, 2.613594507673883, 2.5920055347867264, 2.5070567319656734, 2.3622185839126426, 2.1639210837690968, 1.9212014418035814, 1.645307965985662, 1.3493451462722108, 1.0472915592448635, 0.753178267618073, 0.48037909944670343, 0.24100552453397087, 0.04501788968698864, -0.10038757774243566, -0.19115533595226034, -0.22661712925794894, -0.20966940589095084, -0.14665046980378732, -0.04702913808144748, 0.07705348978644497, 0.21142031199310193, 0.3406190715760817, 0.44875730092841787, 0.5204100160635028, 0.5415033481562257, 0.5001308344190868, 0.387291441690348, 0.19753672708779565, -0.07062700338984194, -0.4145264418672276, -0.8273000388273809, -1.298046287380169, -1.8122582937843068, -2.3524430083178896, -2.8988674372647947, -3.4304668665966225, -3.9258136180461856, -4.364091145182423, -4.72609710037712, -4.9952994790758, -5.158521180515653, -5.206548365881587, -5.134686083045146, -4.943127309123167, -4.636795557004747, -4.225181256846227, -3.721953140922984, -3.1443633363873045, -2.5124575431172813, -1.8481948792015528, -1.1742432283096345, -0.5131774562128563, 0.11343673571746624, 0.6861794671641305, 1.188706932408988, 1.608068998128884, 1.93521784800212, 2.1656518298260243, 2.2991190330765887, 2.3394065026292394, 2.2942039743324614, 2.174559891949505, 1.9938742722311227, 1.7673332743116823, 1.5112204067482746, 1.2417373625553558, 0.9741820358458955, 0.7224458925094523, 0.49826191548220167, 0.31059414115740125, 0.16542760447685262, 0.06570086526467914, 0.011250955937815943, -0.0009287185365520193, 0.023724510187690617, 0.0778296147346526, 0.152675074955701, 0.23888600149112107, 0.3270725055460064, 0.4084887727863552, 0.4756079269337625, 0.5225682014319931, 0.5455147298769905, 0.5428128520018143, 0.5150642252358859, 0.4649735864444485, 0.39710055331592353, 0.3174776560141504, 0.23311085929842926, 0.15144406934250818, 0.0798015263118198, 0.024825433377615922, -0.008019747543568151, -0.014846777679800137, 0.006343506078279192, 0.05551044659144052, 0.13056684982315653, 0.22747532942381862, 0.3405070769783033, 0.46271970661036094, 0.5863643507664574, 0.7033587069980918, 0.8059152488075428, 0.8871921102928136, 0.941625096647685, 0.9653071503041835, 0.9563447322837753, 0.9150871945421523, 0.8439581144837786, 0.7473096594085225, 0.6311149204987775, 0.5026629050153235, 0.36991415036372155, 0.24088278838934624, 0.12306559674704713, 0.022982281494509666, -0.0544312314349869, -0.10622437215439548, -0.13160848093980107, -0.13199677665947288, -0.11093958897866417, -0.0737828029040283, -0.027166663613371084, 0.02159075881550914, 0.06525468897226784, 0.0974939027698981, 0.11369295891653187, 0.11172712950504257, 0.09262851488136499, 0.0610764790246913, 0.02567912931230595, -0.0010078456364462714, -0.00273563739935034, 0.03989633036944038, 0.14861175893990664, 0.3464005279802186, 0.6562486430673857, 1.099696103679844, 1.6953410075184512, 2.4574627131433155, 3.3946269489436065, 4.508415894840498, 5.792480417195674, 7.232333508509738, 8.805067287648074, 10.479261461778288, 12.215696354507696, 13.969522802151632, 15.69113471806314, 17.32739686835682, 18.824219589389696, 20.130391319999067, 21.198335092396118, 21.985798917875837, 22.459025473686026, 22.59561078808823, 22.383980766802097, 21.82420012759457, 20.929055048295435, 19.724550301312444, 18.247523498652416, 16.544437925917098, 14.669354591348085, 12.682670476167054, 10.647520530535477, 8.626664862927273, 6.67971281933427, 4.861461354035594, 3.2187425079292695, 1.7880330333772252, 0.5943805541366599, -0.34898024307961334, -1.041357295055687, -1.4940632716521325, -1.7290453919590147, -1.777142824405139, -1.6758658098016652, -1.466663371536969, -1.1920983281066628, -0.8929090397548523, -0.605096061816754, -0.35740577229506815, -0.16926310687339685, -0.049189171011330586, 0.006049458802514517, 0.011529136298998767, -0.006487313516266731, -0.011971748393375961, 0.03875905872867583, 0.19434624300231096, 0.5052335855641823, 1.0202992036366958, 1.7833777844448582, 2.8298224852230183, 4.183389679884945, 5.854033606744837, 7.835980874758962, 10.106292309257558, 12.624621437299052, 15.335212477720798, 18.167876725925183, 21.039659802279196, 23.85855084175932, 26.52965217713228, 28.957425990294688, 31.049159721276972, 32.72074769830621, 33.903128904949895, 34.543050955587226, 34.605516948631056, 34.077068656296305, 32.96902223238891, 31.31463397233815, 29.167885544591247, 26.60162621186253, 23.706937874643675, 20.58697552941346, 17.35178334561993, 14.113837281013772, 10.985000120230783, 8.069811873782761, 5.460303250153574, 3.2327958488548743, 1.4455361837544822, 0.1353749622350713, -0.6833264422660738, -1.0183465925693291, -0.8986796008498211, -0.3726027987502789, 0.4954890242672293, 1.6288397296847035, 2.942387922420432, 4.347395000473818, 5.756048679095467, 7.085937942390571, 8.264020169996524, 9.229730118538518, 9.937492303304913, 10.358463573870631, 10.481476211767161, 10.31214624313299, 9.87150968414911, 9.19412617544948, 8.325793718948887, 7.319483480533763, 6.231713841616357, 5.11925791355639, 4.035952239689068, 3.0289163168747093, 2.1361307550565503, 1.3847478005897762, 0.7899730170503697, 0.35461308720897056, 0.06973936435749686, -0.08396774554306402, -0.13424325440725812, -0.11469258256024906, -0.06190385339017255, -0.01241605499209221, 0.0002431856568848161, -0.05166946062327912, -0.18780524075964716, -0.4180532253393041, -0.7414119537965526, -1.1456871362444807, -1.6081810216402823, -2.096875808076935, -2.5721519797173276, -2.989515386428958, -3.3026045127253045, -3.4659504152750538, -3.438176296384124, -3.1852996479404503, -2.6829641685753107, -1.9183908017072469, -0.8921645926702759, 0.3812783398722163, 1.8740127214403985, 3.545434624323445, 5.343945518568133, 7.209414976649816, 9.075910097181866, 10.875159849428755, 12.540090603001085, 14.007818180184225, 15.222814306699895, 16.140192536854958, 16.727731216521917, 16.967045811511664, 16.854535689194474, 16.401533307323284, 15.63367954972726, 14.588984820907408, 13.31549840162925, 11.869140090778412, 10.311016999743611, 8.70326641254071, 7.1062713026554665, 5.576380566274379, 4.162901566528122, 2.905268645213195, 1.83261448189452, 0.9628632822344617, 0.30165697982868156, -0.15653438172992304, -0.42696452793132744, -0.5335445219589299, -0.5068869515433528, -0.38153943813920016, -0.19388857491415884, 0.02013776581756088, 0.227424882924644, 0.3993145653240522, 0.5131332483932393, 0.5534307071150091, 0.5120783709902951, 0.38818677732159945, 0.18807412202966875, -0.07602639339101042, -0.38742775780441757, -0.7261829683445159, -1.0706764797203285, -1.3995435206675784, -1.6930916269569123, -1.93449491606913, -2.1109549454011867, -2.2143323381652995, -2.2415191412788955, -2.1944192157841425, -2.079432760668186, -1.906765690565798, -1.6896735497578943, -1.4432182611885003, -1.1830691143546626, -0.9244858143574417, -0.6812698369637272, -0.4648352011079248, -0.2836180637425846, -0.14273688843901655, -0.04386055113443973, 0.01459391385866929, 0.03704894876996191, 0.030156287542902158, 0.0020369427936099793, -0.03851974621882171, -0.08286639020047151, -0.12324652116921186, -0.15341992136602675, -0.16910909807282004, -0.16823492091684022, -0.15093793060579921, -0.11942326171090088, -0.07760119472152303, -0.030561701034157698, 0.016001886411771794, 0.05644586246140859, 0.08578944881566525, 0.10021246686307513, 0.09747273090550475, 0.07720191119246096, 0.040883939555850735, -0.00829192662332886, -0.06567150567199452, -0.12565039894177227, -0.18228407908508446, -0.2298514390182261, -0.26345821074553827, -0.2796686932479809, -0.27688232048429084, -0.2555468315684968, -0.21824245047942517, -0.16953765216462732, -0.11555407999935358, -0.06338628441540547, -0.0203765120356548, 0.00671690885599366, 0.012590927227491609, -0.005791574775777125, -0.04851234146663235, -0.11219696997062496, -0.18977153338330532, -0.27050379401097024, -0.34035794710474687, -0.38269577565022334, -0.3792130533377964, -0.31111145296615195, -0.16046495609146086, 0.08834895418370296, 0.4472845870745545, 0.9233287627339534, 1.5174861000239788, 2.22418559465858, 3.0308299059832713, 3.917873327988864, 4.8594449889017195, 5.824651356387099, 6.778667442340438, 7.684483059974525, 8.504687591368128, 9.204228352245169, 9.752160222208257, 10.123017251617231, 10.29828923846816, 10.268951659086339, 10.035529621292694, 9.607250166407908, 9.002028468242658, 8.24711769137815, 7.376169226892885, 6.426800503297394, 5.439181879201888, 4.454507325013088, 3.5113262317211134, 2.643365504619851, 1.8781763757881127, 1.235632665646384, 0.7264703571403551, 0.35206618000859397, 0.10479134611978765, -0.031231042843370867, -0.07878422413903981, -0.06564261176292648, -0.022392190928878047, 0.019914573640034582, 0.03217944107433307, -0.010500260809569546, -0.1269182220780428, -0.32822968386469664, -0.6170212460628755, -0.9870209686940477, -1.4234193374716322, -1.9038216564716675, -2.3998109845645113, -2.8788953958705035, -3.3068383636318535, -3.65027170434687, -3.8790304508666833, -3.96839474331239, -3.9010905892867402, -3.6688479833018386, -3.273103487586361, -2.725169863218527, -2.0455928742646696, -1.2633158345631785, -0.4139421469192914, 0.46287246113378894, 1.32578080749073, 2.133909309310451, 2.8497069194899836, 3.44187416919247, 3.886383039945873, 4.16799924733526, 4.281851456140195, 4.232970143315678, 4.035105721002822, 3.7103509378698902, 3.2875774689878483, 2.7992333594695795, 2.2791446018691386, 1.7608721382319856, 1.274659386504868, 0.8451444931819032, 0.4901824660257808, 0.21992742134985013, 0.03609353277886129, -0.06758068811235815, -0.10422584733495993, -0.09240791470060056, -0.054106573328739055, -0.01237128713816061, 0.011060316496245554, -0.0019332544509645902, -0.06381958300025305, -0.17988331763309154, -0.3472853091085905, -0.5548077533817235, -0.7833005791010752, -1.006826692082664, -1.194546153590293, -1.3133644607042625, -1.3311592006653163, -1.2190203857640722, -0.9535121648326488, -0.5186689372428834, 0.09039923302702761, 0.8636514830149632, 1.775827827363891, 2.797523757051457, 3.904520068811746], 'positive_zeros': ['0.46438049348119402901010710630441', '0.54091982965008847509965374484607', '1.38568465391928222869429663086431', '1.74494769094619936449408969548510', '1.76240417828612586298479929448114', '1.76889099742436147182389627532833', '2.53245702393390904258852037014663', '2.59408464708222606013377943234568', '2.64305368563454441458485811317635', '2.80813566977082935146137594382545', '3.28379230514534594698192230935464', '3.35639636267667604518408838064032', '3.90379843168599400456502953223412', '3.94398583472337731991702966749806', '4.13968070942314629719524474459137', '4.22457129521533049983783528262684', '4.77777673164639708579564786535823', '5.04555203664522979998740174837249', '5.16364347829369655213113917528693', '5.52594788836928962383101823468136', '5.57809095556498022714021825097305', '5.63580742160780555687085883781654', '6.02451457361668432536057251976139', '6.11420726679279898764888689438736', '6.25140904766786369078729666870967', '6.60371047182712143846748673060362', '6.90694604212870691826303078236532', '6.91554397814595457614189976976237', '7.18759743660634433783195403069756', '7.21882920574107084530687591632866', '7.53320026579072264094046945590089', '7.63993557368343087438653231026764', '7.76284666761449316578431500140649', '7.78031707847052671849768591605434', '8.343719319119956368408760831480216', '8.537254338273337482237509078416053', '8.564515002728500332927087327589844', '8.590217278732133964010609384572967', '9.127897466695342161611682767871741', '9.191502336406037440201175796239469'], 'prelabel': '8-2475e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.4455567143235175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1056287305183517018, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46438049348119402901010710630', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.54091982965008847509965374485', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.38568465391928222869429663086', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 152548.95646688485, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 37523281640625, 'conductor_radical': 165, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 5, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, -20, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, -22, 0, 0, 15, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler13': [1, 0, -10, 0, 43, 0, -1690, 0, 28561], 'euler17': [1, 0, -65, 0, 1633, 0, -18785, 0, 83521], 'euler19': [1, 0, -14, 0, 771, 0, -5054, 0, 130321], 'euler2': [1, 0, -5, 0, 13, 0, -20, 0, 16], 'euler23': [1, 0, -25, 0, 933, 0, -13225, 0, 279841], 'euler29': [1, 10, 151, 920, 7101, 26680, 126991, 243890, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 12, 178, 1224, 9195, 37944, 171058, 357492, 923521], 'euler37': [1, 0, -10, 0, 1483, 0, -13690, 0, 1874161], 'euler41': [1, -12, 218, -1584, 14595, -64944, 366458, -827052, 2825761], 'euler43': [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], 'euler47': [1, 0, -10, 0, 1563, 0, -22090, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -85, 0, 6873, 0, -238765, 0, 7890481], 'euler59': [1, -20, 346, -3640, 33891, -214760, 1204426, -4107580, 12117361], 'euler61': [1, 22, 363, 4004, 36845, 244244, 1350723, 4993582, 13845841], 'euler67': [1, 0, -140, 0, 13878, 0, -628460, 0, 20151121], 'euler7': [1, 0, -5, 0, 93, 0, -245, 0, 2401], 'euler71': [1, -12, 88, -1164, 15870, -82644, 443608, -4294932, 25411681], 'euler73': [1, 0, -25, 0, 10153, 0, -133225, 0, 28398241], 'euler79': [1, 10, 331, 2320, 39841, 183280, 2065771, 4930390, 38950081], 'euler83': [1, 0, 55, 0, 6333, 0, 378895, 0, 47458321], 'euler89': [1, 50, 1231, 19600, 218901, 1744400, 9750751, 35248450, 62742241], 'euler97': [1, 0, -385, 0, 55873, 0, -3622465, 0, 88529281], 'euler_factors': [[1, 0, -5, 0, 13, 0, -20, 0, 16], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -5, 0, 93, 0, -245, 0, 2401], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, 0, -10, 0, 43, 0, -1690, 0, 28561], [1, 0, -65, 0, 1633, 0, -18785, 0, 83521], [1, 0, -14, 0, 771, 0, -5054, 0, 130321], [1, 0, -25, 0, 933, 0, -13225, 0, 279841], [1, 10, 151, 920, 7101, 26680, 126991, 243890, 707281], [1, 12, 178, 1224, 9195, 37944, 171058, 357492, 923521], [1, 0, -10, 0, 1483, 0, -13690, 0, 1874161], [1, -12, 218, -1584, 14595, -64944, 366458, -827052, 2825761], [1, 0, -100, 0, 6198, 0, -184900, 0, 3418801], [1, 0, -10, 0, 1563, 0, -22090, 0, 4879681], [1, 0, -85, 0, 6873, 0, -238765, 0, 7890481], [1, -20, 346, -3640, 33891, -214760, 1204426, -4107580, 12117361], [1, 22, 363, 4004, 36845, 244244, 1350723, 4993582, 13845841], [1, 0, -140, 0, 13878, 0, -628460, 0, 20151121], [1, -12, 88, -1164, 15870, -82644, 443608, -4294932, 25411681], [1, 0, -25, 0, 10153, 0, -133225, 0, 28398241], [1, 10, 331, 2320, 39841, 183280, 2065771, 4930390, 38950081], [1, 0, 55, 0, 6333, 0, 378895, 0, 47458321], [1, 50, 1231, 19600, 218901, 1744400, 9750751, 35248450, 62742241], [1, 0, -385, 0, 55873, 0, -3622465, 0, 88529281]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/2/c/p'], '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': '8-2475e4-1.1-c1e4-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-2475e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.4455567143235175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1056287305183517018, 'z1': {'__RealLiteral__': 0, 'data': '0.46438049348119402901010710630', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '588672211295716981685036277003,685697346731286254491899474954,2211983987794812559268256814427,2242335734623303208029513597661', 'Lhash_array': ['588672211295716981685036277003', '685697346731286254491899474954', '2211983987794812559268256814427', '2242335734623303208029513597661'], 'label': '8-2475e4-1.1-c1e4-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/c/p'}