-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2031632868699548461802165803546', 'a10': [0.5739779522395382, 0.0], 'a2': [-1.2855752193730787, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.3472963553338607, 0.0], 'a5': [-0.44647558819579863, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.5320888862379562, 0.0], 'a8': [3.017626026941956, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2031632868699548461802165803546', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2855752193730787, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.44647558819579863, 0], [5.0, 0]], [[1.0, 0], [3.5320888862379562, 0], [7.0, 0]], [[1.0, 0], [-2.780061328486417, 0], [11.0, 0]], [[1.0, 0], [-3.2908593693815895, 0], [13.0, 0]], [[1.0, 0], [-7.039362392920385, 0], [17.0, 0]], [[1.0, 0], [5.184792530904096, 0], [19.0, 0]], [[1.0, 0], [7.276927091375923, 0], [23.0, 0]], [[1.0, 0], [3.6191609596636973, 0], [29.0, 0]], [[1.0, 0], [1.935822227524088, 0], [31.0, 0]], [[1.0, 0], [3.2266815969056775, 0], [37.0, 0]], [[1.0, 0], [-4.860835997155709, 0], [41.0, 0]], [[1.0, 0], [5.758770483143634, 0], [43.0, 0]], [[1.0, 0], [3.017626026941956, 0], [47.0, 0]], [[1.0, 0], [8.771413200489262, 0], [53.0, 0]], [[1.0, 0], [2.9637744817276386, 0], [59.0, 0]], [[1.0, 0], [-7.887126028095458, 0], [61.0, 0]], [[1.0, 0], [9.438815273860666, 0], [67.0, 0]], [[1.0, 0], [5.307311585351507, 0], [71.0, 0]], [[1.0, 0], [1.554377592712286, 0], [73.0, 0]], [[1.0, 0], [11.901673948046147, 0], [79.0, 0]], [[1.0, 0], [-16.257251181605444, 0], [83.0, 0]], [[1.0, 0], [18.42582621403687, 0], [89.0, 0]], [[1.0, 0], [-10.113807625001135, 0], [97.0, 0]], [[1.0, 0], [-2.0807746686692914, 0], [101.0, 0]], [[1.0, 0], [1.448310754234792, 0], [103.0, 0]], [[1.0, 0], [-2.235834013195234, 0], [107.0, 0]], [[1.0, 0], [11.502993046336577, 0], [109.0, 0]], [[1.0, 0], [1.68815062568781, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-3e6-1.1-c1-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/729/2/a/c/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1330418321653452e-120, 0.16754190955987974, 0.33523475045849505, 0.5016383325685592, 0.662491756486143, 0.8100687171717661, 0.9331723698118786, 1.0177206851381035, 1.0478435385616187, 1.0074126600450692, 0.881915152562, 0.6605472705923303, 0.3383539172883448, -0.0818147656655203, -0.5877997627683823, -1.1573674279164265, -1.7584439530359814, -2.3505456946762644, -2.8874890785958973, -3.321312506802265, -3.6071653779540753, -3.7087366099201193, -3.6036332152920427, -3.288007603651642, -2.7796981508285694, -2.1192128370406462, -1.3680610079098883, -0.604218925709768, 0.08512159837718511, 0.6129656465703106, 0.9031381535757261, 0.9008472095683377, 0.581735828608224, -0.042021763285320916, -0.9197958241629854, -1.965519319379723, -3.065791850884803, -4.092476798687968, -4.918457743103117, -5.43459213716124, -5.565503083777067, -5.281779410453422, -4.606463261556042, -3.6143885921550307, -2.4239234836609795, -1.1818325255358169, -0.04313446452521762, 0.8512137895412915, 1.3954087010025782, 1.5352283168407412, 1.2769015495178644, 0.6866084574267002, -0.11971578653036981, -0.9949529706799741, -1.7849026744802197, -2.3539475686342475, -2.607850344980432, -2.5095654067942412, -2.085046193430744, -1.417754255514718, -0.6326396444477191, 0.12761493629687648, 0.7297113339318246, 1.0750392272113745, 1.1181802203698923, 0.8748287980051697, 0.41737241814465625, -0.14114721332888902, -0.6715289105211367, -1.0563165321695025, -1.215174955165035, -1.1221481860664402, -0.8107961991229214, -0.36575343137246685, 0.0977497391503852, 0.4620551902386448, 0.6366197075631651, 0.5819878405459212, 0.32219066638886074, -0.05803914727523987, -0.4314552104984297, -0.6584454546941652, -0.6226048505295231, -0.26344332013083666, 0.4019645396207394, 1.274523345972492, 2.1883158055307135, 2.9433848210392144, 3.349654519501297, 3.2723923670773973, 2.6685258983374105, 1.604516737552108, 0.2502083668558765, -1.1516228736820262, -2.3345366162271945, -3.0662121884592093, -3.201760716743572, -2.7198352039886373, -1.7321327623085767, -0.46266805219943896, 0.7998066610855991, 1.7662769444270687, 2.2143365722659256, 2.041673960324254, 1.2928759829619676, 0.1520850656929765, -1.0980218805127822, -2.142278384402931, -2.7090101609343282, -2.6378597832402346, -1.922680409162696, -0.7182329614704362, 0.692078489582354, 1.96070847823702, 2.757842935350906, 2.8510766855448937, 2.163371452371952, 0.7946968482136962, -0.9985326108930063, -2.8617244554731025, -4.424121095792844, -5.384513937592114, -5.5795353989480265, -5.017708846772734, -3.8710975704159574, -2.4272200364782677, -1.0140801635885812, 0.08199340173212129, 0.6843434741356392, 0.7624669958062009, 0.42826922085995156, -0.10567790747093214, -0.593356624544133, -0.8286976019869937, -0.7044411903525594, -0.24015715012342675, 0.4279069055549507, 1.0914485731164683, 1.5355701151911925, 1.6054671729776504, 1.2544900255781926, 0.5593097306169722, -0.3022451911363402, -1.1039104199856562, -1.6382457658064484, -1.7779259248902157, -1.5122584722358505, -0.9476089660353533, -0.27149774852378855, 0.308515084636329, 0.631927929582001, 0.636888020570822, 0.3792487662850483, 0.012077815460040582, -0.2688087110387811, -0.2964194165224706, 0.001954228547831853, 0.5678001352496894, 1.2173037044192045, 1.6913386124643377, 1.7364843979083946, 1.1930814730218797, 0.0623589829048105, -1.4706866510225074, -3.0696939600381086, -4.329130304399818, -4.884961156436334, -4.522311277259048, -3.2475883829091305, -1.3014183156843055, 0.8946917357628348, 2.8455114813062887, 4.113974112673488, 4.440171244158175, 3.8123669410813528, 2.468180011069843, 0.8243640130610378, -0.6450359985817008, -1.5464619472732068, -1.6794423930377094, -1.0899123659195094, -0.047763494943965173, 1.0448385073447206, 1.7863940502557132, 1.9091317969405657, 1.370440125951811, 0.3732858685385858, -0.6920183130113966, -1.3678503509001207, -1.2746644979643509, -0.23677094786563688, 1.6510075765146783, 4.037462417165311, 6.406760818780229, 8.220671062120257, 9.068409217542497, 8.77893523706447, 7.462309775143976, 5.468898336226158, 3.2807188190042997, 1.3699384401627626, 0.06885606390182551, -0.5092260424638488, -0.4762674950543551, -0.1050140685299045, 0.28131565190748264, 0.42628924034183074, 0.22486619889498155, -0.25167052490496095, -0.7960891597573491, -1.1537441433712217, -1.1257961077546872, -0.6493208606034232, 0.17443192560458431, 1.113239873917133, 1.8858090477242997, 2.261983518757017, 2.1442900976800185, 1.6007082820420384, 0.8364496067270505, 0.11503898117183467, -0.34205577314139773, -0.4396038023699089, -0.24439816910697645, 0.04199150491364252, 0.16466308910111743, -0.0786682843313564, -0.747306430980721, -1.7186133661209766, -2.7183654739925167, -3.4129238280525716, -3.531910978981212, -2.976796901615731, -1.8734321472798205, -0.5449185920206578, 0.5907072435482883, 1.1655083895899527, 0.9992672683280559, 0.17918554452916233, -0.9509289605470241, -1.8939596597244934, -2.1643207530911392, -1.4598916559236477, 0.2186748721803383, 2.545375056410957, 4.955299263850548, 6.815030103172446, 7.6220097636750515, 7.166219088589287, 5.598739797908465, 3.3825865982576313, 1.1412533784308085, -0.5441605052396981, -1.3201484333692328, -1.1649157993387995, -0.3760029702043585, 0.553300787899144], 'positive_zeros': ['1.60267574387908682091371094118424', '3.48319650034324299815555660692509', '4.11804420121259399366825220900424', '5.75522192822413679222060617235479', '6.48262804058891677369048992075018', '7.60268935526527204223706508838944', '8.343949114742025274853597721085527', '9.222386586803199988926810602388584', '9.856868679589171670763357500048726'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60267574387908682091371094118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.48319650034324299815555660693', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11804420121259399366825220900', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/c/1/2'], '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': '2-3e6-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60267574387908682091371094118', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2031632868699548461802165803546', 'Lhash_array': ['2031632868699548461802165803546'], 'label': '2-3e6-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/c/1/2'}