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lfunc_lfunctions • Show schema
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{'Lhash': '98791465537432992157137961027', 'a10': [0, 0], 'a2': [0, 1.9032119259115532], 'a3': [0, 0], 'a4': [-1.6222156349319639, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 4.4286394867550705], 'a8': [0, 0.7190037090204106], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.199', 'coefficient_field': 'CDF', 'conductor': 2475, 'conductor_radical': 165, 'conjugate': '2813931715461309647852360762192', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.9032119259115532], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.4286394867550705], [-7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0.6222156349319637], [-13.0, 0]], [[1.0, 0], [0, 5.184208216891143], [-17.0, 0]], [[1.0, 0], [7.050855121687034, 0], [19.0, 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'3.63026384621231595027956916337726', '3.78888817661061832529700081076925', '4.70374699561850029766653023902628', '5.96301599622954239757438993453631', '6.88102829081873141914332729521876', '7.54266605097704084001826076658195', '8.411721118428434053253878151216487'], 'prelabel': '2-2475-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.07793272493196978172763638318', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.39298710667495261494377066939', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.12963505941075567247049638619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/2/c/r/199/5'], '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': '2-2475-5.4-c1-0-0', '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': '2-2475-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.07793272493196978172763638318', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '98791465537432992157137961027', 'Lhash_array': ['98791465537432992157137961027'], 'label': '2-2475-5.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/c/r/199/5'}