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lfunc_lfunctions • Show schema
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{'Lhash': '2768315397302626091437969442937', 'a10': [0.0, 0.0], 'a2': [-2.1700864866260337, 0.0], 'a3': [1.7092753594369228, 0.0], 'a4': [2.7092753594369228, 0.0], 'a5': [0.0, 0.0], 'a6': [-3.7092753594369228, 0.0], 'a7': [-1.0783777456217782, 0.0], 'a8': [-1.5391888728108891, 0.0], 'a9': [-0.07837774562177824, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2768315397302626091437969442937', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1700864866260337, 0], [2.0, 0]], [[1.0, 0], [-1.7092753594369228, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0783777456217782, 0], [7.0, 0]], [[1.0, 0], [6.340172973252067, 0], [11.0, 0]], [[1.0, 0], [1.3691023861848555, 0], [13.0, 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'6.24145341271270623921407924605789', '7.48024771249110438457370552182316', '8.028091385468656552884780165313413', '8.726054419556630194650702462318219', '9.538426248023707266528190880262254', '10.31803516712566130100771050541334'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18381579025341456127530937661', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96067152540332391416046639408', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.73287086874634028716202162561', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/f/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': '2-475-1.1-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.18381579025341456127530937661', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2768315397302626091437969442937', 'Lhash_array': ['2768315397302626091437969442937'], 'label': '2-475-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/f/1/1'}