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lfunc_lfunctions • Show schema
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{'Lhash': '1051869768536248540944066233999', 'a10': [1.1961449706358898, 0.0], 'a2': [-0.30873585558228867, 0.0], 'a3': [-2.954377064770962, 0.0], 'a4': [-1.904682171477872, 0.0], 'a5': [-3.874331241442334, 0.0], 'a6': [0.9121221308047536, 0.0], 'a7': [-1.0, 0.0], 'a8': [1.2055153909881298, 0.0], 'a9': [5.728343840844683, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.352857192692081, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [7, 13, 17], 'central_character': '1547.1', 'coefficient_field': 'CDF', 'conductor': 1547, 'conductor_radical': 1547, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30873585558228867, 0], [2.0, 0]], [[1.0, 0], [2.954377064770962, 0], [3.0, 0]], [[1.0, 0], [3.874331241442334, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.742061295338687, 0], [11.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 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'4.29357928319863582455100568632937', '4.83385495535320922363563992846401', '5.52602946444443797451199764681743', '6.77307182042551117905231874880576', '7.31988771037947630637213355299254', '8.233059794539154057993503315536279', '8.948820542857137253243446303448069'], 'prelabel': '2-1547-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.514663169166013, 'root_angle': 0.5, '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': '0.829778937782121185916278972359', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.22561922506862898459818590706', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29357928319863582455100568633', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.352857192692081, 'bad_primes': [7, 13, 17], 'central_character': '1.1', 'conductor': 1547, 'conductor_radical': 1547, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1547/2/a/i/1/7'], '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': '2-1547-1.1-c1-0-26', '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': '2-1547-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.514663169166013, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829778937782121185916278972359', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1051869768536248540944066233999', 'Lhash_array': ['1051869768536248540944066233999'], 'factors': ['2-1547-1.1-c1-0-26'], 'label': '2-1547-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1547/2/a/i/1/7'}