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lfunc_lfunctions • Show schema
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{'Lhash': '331899364380800858425039227894', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.1967624782450272, -3.8049042244813074], 'a6': [0, 0], 'a7': [1.449489742783178, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [3.348469228349534, -18.702613556046018]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.217', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '2003425803162886956931945582429', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1967624782450272, 3.8049042244813074], [-12.5, -21.650635094610966]], [[1.0, 0], [-1.449489742783178, 0], [49.0, 0]], [[1.0, 0], [15.15541927207435, 0], [121.0, 0]], [[1.0, 0], [14.848469228349535, -8.572767706041478], [84.5, 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'10.14810546877935423782821594827805'], 'prelabel': '2-684-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.6414348214417481, 'root_number': '-0.4298535727145923790921861036212523900525570474953464999 - 0.902898613369463892951702615854847517068329886722002880*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32071741072087406', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26182243302771700753875927416', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.43164709314542113442842171321', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88648179682267841225486944030', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '19.8', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/y/g/217/3'], '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': '2-684-19.8-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-684-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': -0.32071741072087406, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26182243302771700753875927416', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '331899364380800858425039227894', 'Lhash_array': ['331899364380800858425039227894'], 'label': '2-684-19.8-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/y/g/217/3'}