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lfunc_lfunctions • Show schema
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{'Lhash': '614389205624754262603209387488', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.4142135623730951], 'a6': [0, 0], 'a7': [-2.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, -4.242640687119285]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1025', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '1293429680190349244029235178743', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-5.0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-11.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-13.0, 0]], [[1.0, 0], [0, -7.0710678118654755], [-17.0, 0]], [[1.0, 0], [-1.0, -4.242640687119285]], [[1.0, 0], [0, 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'7.71865709717719150320283949744244', '8.906418544850366507911922198744176'], 'prelabel': '2-2736-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': -0.26959480939477504, 'root_number': '0.66226617853252190326637586025843132089668374601959475 - 0.74926864926535517268852799758566390359875703645337405*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13479740469738752', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48466762490716200556038009173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19305119089552562109018607698', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.95036380937654436880837791093', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/f/c/1025/1'], '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': '2-2736-57.56-c1-0-6', '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': '2-2736-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': -0.13479740469738752, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48466762490716200556038009173', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '614389205624754262603209387488', 'Lhash_array': ['614389205624754262603209387488'], 'label': '2-2736-57.56-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/f/c/1025/1'}