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lfunc_lfunctions • Show schema
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{'Lhash': '186702505792582996927589746060', 'a10': [8.0, 0], 'a2': [0, -1.4142135623730951], 'a3': [0, 0], 'a4': [2.0, 0], 'a5': [0, 5.656854249492381], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [0, -8.48528137423857], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '2249202786687652808519672070706', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.656854249492381], [-25.0, 0]], [[1.0, 0], [1.0, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [16.0, 0], [169.0, 0]], [[1.0, 0], [0, -11.313708498984761], [-289.0, 0]], [[1.0, 0], [33.0, 0], [361.0, 0]], [[1.0, 0], [0, -24.041630560342615], [-529.0, 0]], 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'2-33e2-3.2-c2-0-3', 'leading_term': '0.557325380869568063359336161703982518743752903045642289', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1089/3/b/a/485/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.5573253808695681, 0.3389055721655722, 0.11586087677054548, -0.11027448456288222, -0.33788366949197324, -0.5652477366922418, -0.7905291895429651, -1.0117601691939435, -1.2268367470202346, -1.4335205287785904, -1.6294485006314905, -1.812151735349686, -1.979083248621591, -2.1276549613274507, -2.255283392214998, -2.359443382805222, -2.43772884719398, -2.4879192475567837, -2.5080502254095607, -2.4964865733210755, -2.4519955169356864, -2.3738180989052564, -2.261736321531681, -2.1161336210229162, -1.938046220849463, -1.7292029520026067, -1.4920512403887474, 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'6.82678411706001966354791793640973', '7.71163392046260910560159710945771', '8.521736553846322655351591783423666', '9.085985262835343717118712015007503'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.6959132760153036, 'root_number': '-0.5773502691896257645091487805019574556476017512701268760 - 0.816496580927726032732428024901963797321982493552223377*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14728230772656822312402314515', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.81960435233667253479874611678', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86935628219156447016442233487', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/a/485/1'], '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': '2-33e2-3.2-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.14728230772656822312402314515', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '186702505792582996927589746060', 'Lhash_array': ['186702505792582996927589746060'], 'label': '2-33e2-3.2-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/a/485/1'}