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lfunc_lfunctions • Show schema
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{'Lhash': '2410397776802801368703275851429', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.035276180410083], 'a6': [0.0, 0.0], 'a7': [0.0, -0.2679491924311227], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.899074734638629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '864.863', 'coefficient_field': 'CDF', 'conductor': 864, 'conductor_radical': 6, 'conjugate': '429172717578468852137522287247', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.035276180410083], [-5.0, 0]], [[1.0, 0], [0, 0.2679491924311227], [-7.0, 0]], [[1.0, 0], [3.8637033051562732, 0], [11.0, 0]], [[1.0, 0], [2.4641016151377544, 0], [13.0, 0]], [[1.0, 0], [0, 6.6921304299024635], [-17.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-19.0, 0]], [[1.0, 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'7.972164347979550472766996351405040', '8.645497817451599605190804926553140', '9.884990808803224054028926282396211', '10.45098744941138433947883460453060'], 'prelabel': '2-864-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': 0.75, 'root_number': '-0.7071067811865475 + 0.7071067811865476*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90146857215137225866210874258', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01257550723240714869896775119', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13945554139826556990152162582', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.899074734638629, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 864, 'conductor_radical': 6, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/864/2/c/b/863/3'], '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': '2-864-12.11-c1-0-13', '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': '2-864-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6266089801564734, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90146857215137225866210874258', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2410397776802801368703275851429', 'Lhash_array': ['2410397776802801368703275851429'], 'label': '2-864-12.11-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/864/2/c/b/863/3'}