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lfunc_lfunctions • Show schema
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{'Lhash': '711169759485894465856190434767', 'a10': [-0.488065823162717, 6.2170842754751705], 'a2': [-0.502745270166972, -1.3218347829153], 'a3': [-2.9273308320613842, 0.733258201597341], 'a4': [-1.4944943866494766, 1.3290923701057067], 'a5': [-3.9862927297568205, -1.8853760475666326], 'a6': [2.4409479257620923, 3.500805622254921], 'a7': [0.3867495961430459, 1.274942555968938], 'a8': [2.5081905086921727, 1.3072797604592907], 'a9': [5.385834417082364, -2.8787884723175643], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.044170291744779, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.502745270166972, 1.3218347829153]]]], 'bad_primes': [2], 'central_character': '256.101', 'coefficient_field': 'CDF', 'conductor': 256, 'conductor_radical': 2, 'conjugate': '1101175611301365223042660630131', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.502745270166972, 1.3218347829153]], [[1.0, 0], [2.9273308320613842, 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'root_analytic_conductor': 1.4297448344878811, 'root_angle': 0.06668706970630181, 'root_number': '0.9781342719926707 + 0.20797438773408658*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0333435348532', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56101402023385195556800829891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.09149181773510771825361600912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91271070687932396030096008701', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.044170291744779, 'bad_primes': [2], 'central_character': '256.101', 'conductor': 256, 'conductor_radical': 2, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/2/m/a/101/13'], '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': '2-2e8-256.101-c1-0-3', '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': '2-2e8-256.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4297448344878811, 'root_angle': 0.033343534853150905, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56101402023385195556800829891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '711169759485894465856190434767', 'Lhash_array': ['711169759485894465856190434767'], 'label': '2-2e8-256.101-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/2/m/a/101/13'}