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lfunc_lfunctions • Show schema
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{'Lhash': '946057205743368283417869820200', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 2.288245611270737], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-2.23606797749979, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 39.126696990427405, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '4900.2549', 'coefficient_field': 'CDF', 'conductor': 4900, 'conductor_radical': 70, 'conjugate': '643251411481521086377030343093', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.288245611270737], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.47213595499958, 0], [11.0, 0]], [[1.0, 0], [0, 0.8740320488976422], [-13.0, 0]], [[1.0, 0], [0, 4.576491222541474], [-17.0, 0]], [[1.0, 0], [5.99070478491457, 0], [19.0, 0]], [[1.0, 0], [0, 3.4721359549995796], [-23.0, 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'4.59786130508674770343915341837261', '5.41797278677712374240062289686992', '6.31140467331692787418685436005911', '6.65259299864858846924781701016934', '7.64099346998034946267355651959934', '8.099129658555408359509400836839802'], 'prelabel': '2-70e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': -0.14758361765043326, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74630754371357451286943424663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.97464729928448389761696059499', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.42166350431996341884067691103', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 39.126696990427405, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 4900, 'conductor_radical': 70, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4900/2/e/u/2549/7'], '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': '2-70e2-5.4-c1-0-25', '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': '2-70e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.25513365088448, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74630754371357451286943424663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '946057205743368283417869820200', 'Lhash_array': ['946057205743368283417869820200'], 'label': '2-70e2-5.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4900/2/e/u/2549/7'}