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lfunc_lfunctions • Show schema
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{'Lhash': '750008685865402815313483012028', 'a10': [10.0, 0.0], 'a2': [2.0, 0.0], 'a3': [0.0, 0.0], 'a4': [4.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-35.422898862423146, 0.0], 'a8': [8.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 122.13395371188312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '2070.1', 'coefficient_field': 'CDF', 'conductor': 2070, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [35.422898862423146, 0], [343.0, 0]], [[1.0, 0], [-16.629835759987728, 0], [1331.0, 0]], [[1.0, 0], [79.91316193036589, 0], [2197.0, 0]], [[1.0, 0], [-46.82190482380407, 0], [4913.0, 0]], [[1.0, 0], [110.65331121618112, 0], [6859.0, 0]], [[1.0, 0], 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'2.86229806421714376891858656026878', '3.82820270861479506528859621877777', '4.66025198416688089646774880671793', '5.79399871380085064876019243066165', '6.23629001997672875113452356278086', '7.03488983972451791985354318786015', '7.67282084948072386443599003765193', '9.124105540437047103299145200312491'], 'prelabel': '2-2070-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.051423153236108, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59165253085540314681533273102', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24959710240942508583289448674', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86229806421714376891858656027', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 122.13395371188312, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 2070, 'conductor_radical': 690, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2070/4/a/bj/1/1'], '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': '2-2070-1.1-c3-0-18', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-2070-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.051423153236108, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59165253085540314681533273102', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '750008685865402815313483012028', 'Lhash_array': ['750008685865402815313483012028'], 'label': '2-2070-1.1-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2070/4/a/bj/1/1'}