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lfunc_lfunctions • Show schema
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{'Lhash': '558168309005847365430603236863', 'a10': [-0.810144764666133, 0.3355729490102717], 'a2': [-1.1041845831180515, 1.1041845831180515], 'a3': [0.3826834323650898, -0.9238795325112867], 'a4': [0.0, -0.4384471871911697], 'a5': [0.5188071501782202, 0.2148969578599539], 'a6': [0.5975803902250437, 1.442686682689507], 'a7': [0.0, 0.0], 'a8': [-1.7242425416281388, -1.7242425416281388], 'a9': [-0.7071067811865476, -0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.923029855245012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.3826834323650898, 0.9238795325112867]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 17], 'central_character': '867.688', 'coefficient_field': 'CDF', 'conductor': 867, 'conductor_radical': 51, 'conjugate': '1899410028499049209717280791005', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1041845831180515, -1.1041845831180515], [0, -2.0]], [[1.0, 0], [-0.3826834323650898, 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'4.38151777174656631667912146279039', '5.29974027592731069394208755310755', '6.30530174413950921909016176952079', '7.60339013231414717571071017950452', '8.526991519789883497869886564314935', '9.113555873939936649120996309122505', '9.980882528649449051498080615026000'], 'prelabel': '2-867-17.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': -0.38512589351804466, 'root_number': '-0.7506339407249885 - 0.6607183114093891*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.385125893518', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44031715750803418868244530297', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.17654130465354694433044895781', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90643088958057667153357763697', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.923029855245012, 'bad_primes': [3, 17], 'central_character': '17.8', 'conductor': 867, 'conductor_radical': 51, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/867/2/h/j/688/2'], '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': '2-867-17.8-c1-0-7', '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': '2-867-17.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.631165113641676, 'root_angle': -0.38512589351804466, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44031715750803418868244530297', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '558168309005847365430603236863', 'Lhash_array': ['558168309005847365430603236863'], 'factors': ['2-867-17.8-c1-0-7'], 'label': '2-867-17.8-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/867/2/h/j/688/2'}