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lfunc_lfunctions • Show schema
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{'Lhash': '1199236294616093361083284378090', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.4753525681732881, 0.0], 'a6': [0.0, 0.0], 'a7': [4.555385607153361, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.77464611966268, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 13], 'central_character': '8112.1', 'coefficient_field': 'CDF', 'conductor': 8112, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.4753525681732881, 0], [5.0, 0]], [[1.0, 0], [-4.555385607153361, 0], [7.0, 0]], [[1.0, 0], [-1.6520177685888047, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-7.939454183311042, 0], [17.0, 0]], [[1.0, 0], [-2.602722904935381, 0], [19.0, 0]], [[1.0, 0], [3.81208384654895, 0], [23.0, 0]], 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'4.34857700665391432104084683314957', '5.15578346352130098777199900152020', '5.68397258891038633727578768844258', '6.21461934314574331580931752329301', '7.38700130316501506739814130166151', '7.77482842064112541911960843118884'], 'prelabel': '2-8112-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.048269759374538, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.946030628944743414977025909671', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.53389970177540414461071328127', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.50891372336262160921061599014', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.77464611966268, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 8112, 'conductor_radical': 78, 'degree': 2, 'index': 70, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8112/2/a/cq/1/3'], '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': '2-8112-1.1-c1-0-70', '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': '2-8112-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.048269759374538, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.946030628944743414977025909671', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1199236294616093361083284378090', 'Lhash_array': ['1199236294616093361083284378090'], 'label': '2-8112-1.1-c1-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8112/2/a/cq/1/3'}