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lfunc_lfunctions • Show schema
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{'Lhash': '454392221659014930330015320631', 'a10': [-2.0, -1.0], 'a2': [0.7071067811865476, 0.7071067811865476], 'a3': [0.2928932188134525, 1.7071067811865475], 'a4': [0.0, 1.0], 'a5': [-2.1213203435596424, 0.7071067811865476], 'a6': [-1.0, 1.4142135623730951], 'a7': [0.0, 0.0], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-2.8284271247461903, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [-0.2928932188134525, -1.7071067811865475]]], [5, [[1.0, 0], [2.1213203435596424, -0.7071067811865476]]], [31, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.683', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '3329146934207460611860408782268', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7071067811865476, 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-0.1591309803985952], 'positive_zeros': ['0.35845225930331716462255307627035', '1.78449513312604381026496152831773', '3.10199337933578825288728933139028', '3.89076450321693730876667080314530', '5.15497109352716466242633866705818', '6.02703724300821650857947394985407', '7.08232546690759435107189515270438', '7.79739742810154540762501862706161', '8.675894411162824492333883841830872', '9.407574252983029967659291355764491'], 'prelabel': '2-930-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.7697050848405202, 'root_number': '-0.7494980401428052 + 0.6620065617666444*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.38485254242', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35845225930331716462255307627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78449513312604381026496152832', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10199337933578825288728933139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '15.8', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/j/a/683/2'], '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': '2-930-15.8-c1-0-5', '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': '2-930-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.3848525424202601, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35845225930331716462255307627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '454392221659014930330015320631', 'Lhash_array': ['454392221659014930330015320631'], 'label': '2-930-15.8-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/j/a/683/2'}