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lfunc_lfunctions • Show schema
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{'Lhash': '1474503047861897042527817317034', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.6690790882822886, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.6690790882822886, 0.0], 'a8': [0.0, 0.0], 'a9': [4.123983179505812, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.692473971915598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.6690790882822886, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.6690790882822886, 0], [7.0, 0]], [[1.0, 0], [-1.214174997058765, 0], [11.0, 0]], [[1.0, 0], [-2.2141749970587647, 0], [13.0, 0]], [[1.0, 0], [-1.214174997058765, 0], [17.0, 0]], [[1.0, 0], [-2.5788872707293353, 0], [19.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-1840-1.1-c1-0-18', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1840/2/a/t/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-5.651761922276232e-61, 0.08418738456579929, 0.16782907870948266, 0.2503484523742916, 0.3311087681100277, 0.40938742442330195, 0.4843550054598865, 0.5550602137885726, 0.6204214135331473, 0.6792251706968667, 0.7301318760209148, 0.7716882891887438, 0.8023466545795666, 0.8204899011579541, 0.8244623399837935, 0.8126051982620772, 0.7832962663438383, 0.734992874357467, 0.6662773526995578, 0.5759040635435467, 0.46284701989558336, 0.32634703778792584, 0.16595730062064745, -0.018413842121548594, -0.2264640608624988, -0.4574634560477225, -0.7102274260752668, 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'6.82377209018436714601766899280010', '7.988367821801163022835933366548064', '8.954024069073385062795153787427158'], 'prelabel': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, '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': '1.16317780908747699667837173688', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.03818114620558777499039094258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89303622839608625433553678016', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.692473971915598, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/2/a/t/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': '2-1840-1.1-c1-0-18', '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': '2-1840-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.833076306560515, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16317780908747699667837173688', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1474503047861897042527817317034', 'Lhash_array': ['1474503047861897042527817317034'], 'label': '2-1840-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/2/a/t/1/1'}