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lfunc_lfunctions • Show schema
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{'Lhash': '1184043865120963580609954822400', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 0.27246037750067315], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [0.27246037750067315, 0], 'a7': [4.198225720192863, 0], 'a8': [0, 1.0], 'a9': [2.925765342692191, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.57830829308566, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [0.08621141657070035, -5.384474681122836]]]], 'bad_primes': [2, 5, 29], 'central_character': '1450.1101', 'coefficient_field': 'CDF', 'conductor': 1450, 'conductor_radical': 290, 'conjugate': '1927225791610538852646588606166', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -0.27246037750067315], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.198225720192863, 0], [7.0, 0]], [[1.0, 0], [0, -2.7819151781354075], [-11.0, 0]], [[1.0, 0], [-2.5094548006347344, 0], [13.0, 0]], [[1.0, 0], [0, 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['0.934045915260708936989074799315587', '2.16371924661641938320783140134795', '3.82195250824128874425252070262651', '4.53961300027868554834213695288476', '5.46127578882881780283662789808946', '6.20162755056758319659792780142632', '7.30598667136621930137575025318052', '7.86715801320662500440625232287629', '8.441018463201094337242751239389319', '9.397641348162760714007546658862661'], 'prelabel': '2-1450-29.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4026913308564533, 'root_angle': 0.002548029586549071, 'root_number': '0.999871846816878641260968636291884132241945185607526903793 + 0.01600905815481889432805600354918988312692862768494751774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0025480295865490717', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.934045915260708936989074799316', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.16371924661641938320783140135', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82195250824128874425252070263', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.57830829308566, 'bad_primes': [2, 5, 29], 'central_character': '29.28', 'conductor': 1450, 'conductor_radical': 290, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1450/2/c/e/1101/3'], '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': '2-1450-29.28-c1-0-20', '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': '2-1450-29.28-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4026913308564533, 'root_angle': 0.002548029586549071, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.934045915260708936989074799316', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1184043865120963580609954822400', 'Lhash_array': ['1184043865120963580609954822400'], 'factors': ['2-1450-29.28-c1-0-20'], 'label': '2-1450-29.28-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1450/2/c/e/1101/3'}