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lfunc_lfunctions • Show schema
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{'Lhash': '2247513436576172941860711294709', 'a10': [0.0, 0.0], 'a2': [-0.6548607339452851, 0.7557495743542583], 'a3': [0.0, 0.0], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.9594929736144974, -0.28173255684142967], 'a8': [0.8412535328311812, 0.5406408174555976], 'a9': [-0.41541501300188644, -0.9096319953545183], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3213978681356536, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6548607339452851, -0.7557495743542583]]], [7, [[1.0, 0], [0.9594929736144974, 0.28173255684142967]]], [23, [[1.0, 0], [-0.41541501300188644, 0.9096319953545183]]]], 'bad_primes': [2, 7, 23], 'central_character': '644.447', 'coefficient_field': 'CDF', 'conductor': 644, 'conductor_radical': 322, 'conjugate': '1122370817084125500915801351818', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6548607339452851, -0.7557495743542583]], [[1.0, 0], 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'2.93815142393270950057337894038286', '4.04483504661900090591572218571865', '5.21539064037664156272850239579242', '6.70950811635892691012171654146685', '7.32776460808480176744802113935501', '8.522171466762660008881792341698377', '9.235108423954795057282310129638602', '9.924184084142438597935648003081318', '10.72903260424697544079592693869064'], 'prelabel': '2-644-644.447-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5669196311080201, 'root_angle': 0.12840591055863929, 'root_number': '0.91973201738099667260119963964374 + 0.39254683313495478323353175488514*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.06420295527931964', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77297548407386689065757158046', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.93815142393270950057337894038', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04483504661900090591572218572', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3213978681356536, 'bad_primes': [2, 7, 23], 'central_character': '644.447', 'conductor': 644, 'conductor_radical': 322, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/644/1/r/a/447/1'], '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': '2-644-644.447-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-644-644.447-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5669196311080201, 'root_angle': 0.06420295527931964, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77297548407386689065757158046', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2247513436576172941860711294709', 'Lhash_array': ['2247513436576172941860711294709'], 'label': '2-644-644.447-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/644/1/r/a/447/1'}