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lfunc_lfunctions • Show schema
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{'Lhash': '3080908464348356090322797634043', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.0, 0.0], 'a5': [-0.4270509831248423, -1.314327780297834], 'a6': [0.0, 0.0], 'a7': [-3.4270509831248424, -2.48989828488278], 'a8': [0.0, 0.0], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.108050613361803, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [11, [[1.0, 0], [3.3090169943749475, 0.2245139882897927]]]], 'bad_primes': [2, 3, 11], 'central_character': '264.97', 'coefficient_field': 'CDF', 'conductor': 264, 'conductor_radical': 66, 'conjugate': '483710136609869640768347209637', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0.4270509831248423, 1.314327780297834], 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'positive_zeros': ['2.43040824008892156268821023382175', '3.66119059307798381225726804830569', '5.61865639120173605737251025895189', '6.07754986535200997213033164830186', '7.37385290319372791007784453274625', '8.256444503846197228215747827569360', '9.718950673255643679009956104632310', '10.31209555751091452301792920190559', '11.42868843753162788512976272934462', '12.47856927487417298743941999922364'], 'prelabel': '2-264-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.451912743026179, 'root_angle': 0.3534991328282215, 'root_number': '-0.605428570850402 + 0.7958996454315329*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.353499132828', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43040824008892156268821023382', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66119059307798381225726804831', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.61865639120173605737251025895', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.108050613361803, 'bad_primes': [2, 3, 11], 'central_character': '11.9', 'conductor': 264, 'conductor_radical': 66, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/264/2/q/c/97/1'], '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': '2-264-11.9-c1-0-4', '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': '2-264-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.451912743026179, 'root_angle': 0.3534991328282215, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43040824008892156268821023382', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3080908464348356090322797634043', 'Lhash_array': ['3080908464348356090322797634043'], 'factors': ['2-264-11.9-c1-0-4'], 'label': '2-264-11.9-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/264/2/q/c/97/1'}