-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4974986380799921433225880744346', 'a10': [25.727922061357855, 0.0], 'a2': [-2.414213562373095, 0.0], 'a3': [-0.7573593128807149, 0.0], 'a4': [-2.1715728752538097, 0.0], 'a5': [-10.65685424949238, 0.0], 'a6': [1.82842712474619, 0.0], 'a7': [-22.14213562373095, 0.0], 'a8': [24.556349186104047, 0.0], 'a9': [-26.426406871192853, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7110553901664787, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [-29.0, 0]]]], 'bad_primes': [29], 'central_character': '29.1', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'conjugate': '4974986380799921433225880744346', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.414213562373095, 0], [8.0, 0]], [[1.0, 0], [0.7573593128807149, 0], [27.0, 0]], [[1.0, 0], [10.65685424949238, 0], [125.0, 0]], [[1.0, 0], [22.14213562373095, 0], [343.0, 0]], [[1.0, 0], [-39.32590180780452, 0], [1331.0, 0]], [[1.0, 0], [-23.76955262170047, 0], [2197.0, 0]], [[1.0, 0], [-4.544155877284289, 0], [4913.0, 0]], [[1.0, 0], [155.25483399593904, 0], [6859.0, 0]], [[1.0, 0], [41.88225099390856, 0], [12167.0, 0]], [[1.0, 0], [-29.0, 0]], [[1.0, 0], [57.90454557049501, 0], [29791.0, 0]], [[1.0, 0], [-235.1959594928933, 0], [50653.0, 0]], [[1.0, 0], [175.16147160748713, 0], [68921.0, 0]], [[1.0, 0], [402.8305191657993, 0], [79507.0, 0]], [[1.0, 0], [-227.74220741123068, 0], [103823.0, 0]], [[1.0, 0], [-673.5340546095176, 0], [148877.0, 0]], [[1.0, 0], [800.7249634685276, 0], [205379.0, 0]], [[1.0, 0], [222.2699858975891, 0], [226981.0, 0]], [[1.0, 0], [524.479364188578, 0], [300763.0, 0]], [[1.0, 0], [281.9167388793148, 0], [357911.0, 0]], [[1.0, 0], [-1229.0966799187809, 0], [389017.0, 0]], [[1.0, 0], [-611.2468247692254, 0], [493039.0, 0]], [[1.0, 0], [-515.4903320081219, 0], [571787.0, 0]], [[1.0, 0], [358.2194795587556, 0], [704969.0, 0]], [[1.0, 0], [-829.415439051649, 0], [912673.0, 0]], [[1.0, 0], [978.0101012677667, 0], [1030301.0, 0]], [[1.0, 0], [1217.3279938488577, 0], [1092727.0, 0]], [[1.0, 0], [707.0437226013956, 0], [1225043.0, 0]], [[1.0, 0], [1496.1353518862932, 0], [1295029.0, 0]], [[1.0, 0], [1067.2346314604056, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-29-1.1-c3-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/29/4/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.13932303079586572, 0.28135083328310223, 0.4285133714082693, 0.5827000006549147, 0.7450096076555571, 0.9155212414016962, 1.0930892571117996, 1.2751693973414813, 1.4576871081572758, 1.6349652425803038, 1.7997334165731516, 1.9432442008848336, 2.0555210044867134, 2.125758235582832, 2.1428857199185667, 2.0962963421891883, 1.9767187938417243, 1.7771970208566115, 1.4941159436165476, 1.1281913894145867, 0.6853236464512211, 0.1772017448869298, -0.3784572475504778, -0.9581399803385133, -1.5333213656009117, -2.071843742724805, -2.539877885826897, -2.9043868645889908, -3.135941398527516, -3.2116645092622513, -3.1180234144084373, -2.853148015834895, -2.428347904309263, -1.8685314816669925, -1.2113059594147988, -0.5046549038796425, 0.19675626718776337, 0.8364204327399848, 1.3615695797700482, 1.7289343671146125, 1.9100113479079903, 1.895129703501869, 1.6956629640269028, 1.3438840933534744, 0.890209767199136, 0.3979016502521961, -0.06434619289741654, -0.43115159660146957, -0.6494482890955552, -0.6865053780986036, -0.5357087523546478, -0.2190309379054319, 0.21451403907679786, 0.6946048403241469, 1.1390830153991407, 1.4660690189772236, 1.6070895990328076, 1.5192337989159095, 1.1942876609070485, 0.6630613429894505, -0.006283541301634813, -0.7162318741342895, -1.3535384231687941, -1.806750503082895, -1.9850559340895788, -1.8353845774648463, -1.3546750712714473, -0.5947434331185256, 0.3417737976562429, 1.314510878222577, 2.1660222372186744, 2.7470332971263676, 2.9422457268716347, 2.6921933037149333, 2.0069722615182517, 0.9687996937922616, -0.2778497561084089, -1.547593542176275, -2.643851127046665, -3.3920142977184535, -3.6702025768181152, -3.431810250656764, -2.7152617662296534, -1.6385806690645588, -0.37918149925433114, 0.8578055156016103, 1.8769535169872351, 2.5285807895364334, 2.7362708954198793, 2.510173196371521, 1.9430912982263182, 1.1898348140377257, 0.4338421509357114, -0.15208258155241458, -0.44259744854375427, -0.386177139368046, -0.015034786289621278, 0.5638421898595659, 1.194782501117956, 1.7108974502968026, 1.9743435802140403, 1.9098598949407362, 1.5233316313000638, 0.900442039693707, 0.18513842088028482, -0.45739481425725437, -0.8844920294183986, -1.0156082320634046, -0.8573631152462344, -0.5067442495750221, -0.13033480017036037, 0.07655895972934151, -0.058401567916177115, -0.6347494044508762, -1.644270547538076, -2.961059396775108, -4.360943241649334, -5.567418415695891, -6.314269704488711, -6.410146205508159, -5.788941155567157, -4.532461758079116, -2.8581495083247845, -1.0731164044979837, 0.49558089750890943, 1.577945862982706, 2.026208988649718, 1.8512368221121465, 1.2199663508027996, 0.41331917129709805, -0.2457232391785468, -0.47610537004153264, -0.11325050024247678, 0.8454708531928746, 2.236875290538912, 3.7715165987555905, 5.106952371223379, 5.9358112177611, 6.065416721126826, 5.467625725204278, 4.285326770297347, 2.793719373221917, 1.326896250647605, 0.18991067800489264, -0.4193659717828179, -0.45700050800652703, -0.03567642294894222, 0.6167494914355102, 1.2300802946283256, 1.5741166042978751, 1.5258645459986142, 1.1015797435102206, 0.4443230483522385, -0.22860364842203956, -0.7014287381674228, -0.834486563122802, -0.6132278193032569, -0.15506094011375302, 0.32928698361696984, 0.6084137319966059, 0.513797044690224, 0.006575255512101509, -0.7959214533559646, -1.6453055412960471, -2.2339630693261356, -2.2929823643773926, -1.6858017161043937, -0.4667341278938202, 1.116978580787851, 2.684015936447507, 3.8238955922189595, 4.217574397525029, 3.7367254574544955, 2.4895526577015445, 0.7963670667261662, -0.9004283925341449, -2.166414022342938, -2.7061284157382586, -2.454087158265101, -1.5962408125764203, -0.5133420836397747, 0.3378358496651492, 0.5693783691906703, -0.011977900074227098, -1.338213279177483, -3.094550061415609, -4.811622913662241, -6.006965452371839, -6.33144884949042, -5.674443909086591, -4.194606478139521, -2.267178303255928, -0.3657390647358032, 1.0825101006904463, 1.82069681624761, 1.8258547614948935, 1.293397540423293, 0.5507987343091753, -0.06727621066785638, -0.3375846647618818, -0.2190742929067675, 0.1479272549429246, 0.5116126297176034, 0.6199686423411467, 0.3305767026806753, -0.32334452842966765, -1.1366948790601736, -1.8059036481358872, -2.045243226687921, -1.702156285415347, -0.8266948920745948, 0.33386924584391875, 1.416721164950472, 2.0738566403473695, 2.1037383615461254, 1.5342181044152448, 0.6228280325603414, -0.22980579583332916, -0.6250887388225349, -0.31837843431468504, 0.6790775458058461, 2.0889386098001297, 3.4540434629278174, 4.298182091939551, 4.301480198418652, 3.427183928374881, 1.950802420812363, 0.3765295496651889, -0.7332624528638196, -0.9567886452996037, -0.16878720696718957, 1.4041505087268544, 3.2517054028981485, 4.750002945739525, 5.374933818602634, 4.88301064000477, 3.394827025915664, 1.3508153547743866, -0.6448583098368286, -2.035725958456909, -2.503163853546796, -2.066827743671976, -1.0604964809755832, 0.005150485618807642, 0.6394835246437044, 0.5538462218645137, -0.2392444331427392, -1.4446005471472614, -2.609879105189971, -3.3065270831250935, -3.294313787427906, -2.6057551853227006, -1.5198571519038357, -0.4393722234804974, 0.27579821674808364, 0.44976600258141397], 'positive_zeros': ['3.92457225982003136766281733809045', '6.45363169599506477439245978795443', '8.235515118369237279416647585399605', '9.233686056546093846184361494432642', '10.72109520463557624017405549538926', '12.06699832388332366568260854879765', '13.49720619638542510200395714814857', '14.99362885371431321175005214260216', '16.46976932620168704908211552686508'], 'prelabel': '2-29-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3080731593326418, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.92457225982003136766281733809', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.45363169599506477439245978795', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.235515118369237279416647585400', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.7110553901664787, 'bad_primes': [29], 'central_character': '1.1', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/4/a/a/1/1'], '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': '2-29-1.1-c3-0-5', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-29-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3080731593326418, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.92457225982003136766281733809', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4974986380799921433225880744346', 'Lhash_array': ['4974986380799921433225880744346'], 'label': '2-29-1.1-c3-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/4/a/a/1/1'}