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lfunc_lfunctions • Show schema
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{'Lhash': '2947824738790346742682148047713', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7096212045130694, 0.2778404885528416], 'a4': [0.7839332197201502, -1.8399588873176485], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.86778881960956, -1.0220414211387379], 'a8': [0.0, 0.0], 'a9': [2.8456093258414366, -0.9500039814044176], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7096212045130694, -0.2778404885528416]]], [13, [[1.0, 0], [2.598076211353316, -2.5]]]], 'bad_primes': [3, 13], 'central_character': '507.362', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '129894979034602078897718823676', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.7839332197201502, 1.8399588873176485]], [[1.0, 0], [1.7096212045130694, -0.2778404885528416]], [[1.0, 0], [0, 0], [2.3236158602188426, -4.42728012826605]], [[1.0, 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-35.78348329956639]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-507-507.362-c1-0-50', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/507/2/x/a/362/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.16556130310860107, 0.37364501233069397, 0.5924580227875422, 0.8249163718243016, 1.0713206924609673, 1.3285419144105586, 1.5896839048438283, 1.844171407706253, 2.078206865680362, 2.2755660396600277, 2.418719272776925, 2.4902571784180023, 2.4745687107041068, 2.359675071152249, 2.139074800944759, 1.8134131511816904, 1.391761022957152, 0.892282985925876, 0.3420960189964127, -0.2238260131298249, -0.7647627935072091, -1.2373228869122543, -1.5993064111434299, -1.81404694584543, -1.8548084400180016, -1.7087301670061437, -1.379781667393541, 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'8.621401954691243837435498050930676', '9.803218988123580608243310519726464', '10.55109306026231288217971198613149', '11.53064260626520222343211424005575'], 'prelabel': '2-507-507.362-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.9483065598891758, 'root_number': '-0.9868421202156847 - 0.16168682620489516*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.474153279945', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32542369187504560425345313685', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55267544386246654529625163901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.81158780027768143676343109924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '507.362', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/x/a/362/1'], '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': '2-507-507.362-c1-0-50', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-507-507.362-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.4741532799445879, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32542369187504560425345313685', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2947824738790346742682148047713', 'Lhash_array': ['2947824738790346742682148047713'], 'label': '2-507-507.362-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/x/a/362/1'}