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lfunc_lfunctions • Show schema
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{'Lhash': '2333486618774178431944568576032', 'a10': [8.807347496902475, 0.0], 'a2': [2.7031960820050687, 0.0], 'a3': [-0.3459491735225414, 0.0], 'a4': [5.307269057767554, 0.0], 'a5': [3.258123802239944, 0.0], 'a6': [-0.9351684504390256, 0.0], 'a7': [-1.0, 0.0], 'a8': [8.94019675909385, 0.0], 'a9': [-2.8803191693390704, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.446302559117473, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 13], 'central_character': '1183.1', 'coefficient_field': 'CDF', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.7031960820050687, 0], [2.0, 0]], [[1.0, 0], [0.3459491735225414, 0], [3.0, 0]], [[1.0, 0], [-3.258123802239944, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.846027612657462, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.1531397921551756, 0], [17.0, 0]], [[1.0, 0], 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'3.52586849597655241413870142371818', '4.97198756547918707475596748079982', '5.38214148681914448056464508528459', '6.18855320772094710507074814287951', '6.63234187601328730482727216846195', '7.81554528285669634769456335050651', '9.040631196154107389098727669982026', '10.18563410189934767763023775303322'], 'prelabel': '2-1183-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84079636640731647897466443701', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73130567511854820079895814731', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52586849597655241413870142372', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.446302559117473, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 1183, 'conductor_radical': 91, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1183/2/a/p/1/6'], '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': '2-1183-1.1-c1-0-57', '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': '2-1183-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0734837821464867, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84079636640731647897466443701', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2333486618774178431944568576032', 'Lhash_array': ['2333486618774178431944568576032'], 'label': '2-1183-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1183/2/a/p/1/6'}