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lfunc_lfunctions • Show schema
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{'Lhash': '1236037637706995958476181669822', 'a10': [0.0, 0.0], 'a2': [-1.5225997589481977, 0.0], 'a3': [1.0, 0.0], 'a4': [0.3183100259491094, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.5225997589481977, 0.0], 'a7': [-0.9909851137249969, 0.0], 'a8': [2.5605407491154866, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5225997589481977, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9909851137249969, 0], [7.0, 0]], [[1.0, 0], [-5.973487053570643, 0], [11.0, 0]], [[1.0, 0], [-4.029922718721167, 0], [13.0, 0]], [[1.0, 0], [-0.47617559490155753, 0], [17.0, 0]], [[1.0, 0], [-2.8232247717721966, 0], [19.0, 0]], 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'5.14476284157472806151080061262149', '6.54800146501137124639923884536937', '6.82965534504925837809423139768563', '8.068994008288444731720190506913566', '8.523333306902368452326369081114171', '9.149380948135333689580358200721893'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.975061769768781866501334334119', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.82740767757816540804184779295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42775251076730872544131980689', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/2'], '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': '2-1875-1.1-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': 0, 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.975061769768781866501334334119', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1236037637706995958476181669822', 'Lhash_array': ['1236037637706995958476181669822'], 'label': '2-1875-1.1-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/2'}