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lfunc_lfunctions • Show schema
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{'Lhash': '1024447585921076609351918460983', 'a10': [1.0, 0.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.0, -1.0], 'a5': [-0.7071067811865476, -0.7071067811865476], 'a6': [0.0, -1.0], 'a7': [0.0, 1.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.41921461061172205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '840.293', 'coefficient_field': 'CDF', 'conductor': 840, 'conductor_radical': 210, 'conjugate': '1700024422652599463642571140794', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], 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'7.60830839848579287449144212331909', '8.280410840573720331898018058078660', '9.588533819693222175183673687479901', '10.28575046308627946864190954219059'], 'prelabel': '2-840-840.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6474678452338171, 'root_angle': -0.5737918088252166, 'root_number': '-0.22975292054736118352393736938184 - 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2868959044126083', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.808146649981180763141789924352', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.25844481267753838998040089743', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74190083982064994031321079220', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.41921461061172205, 'bad_primes': [2, 3, 5, 7], 'central_character': '840.293', 'conductor': 840, 'conductor_radical': 210, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/840/1/bp/b/293/1'], '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': '2-840-840.293-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-840-840.293-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6474678452338171, 'root_angle': -0.2868959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.808146649981180763141789924352', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1024447585921076609351918460983', 'Lhash_array': ['1024447585921076609351918460983'], 'label': '2-840-840.293-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/840/1/bp/b/293/1'}