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lfunc_lfunctions • Show schema
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{'Lhash': '1876499486039950937705134833884', 'a10': [4.268189295753665, 0.0], 'a2': [-2.490863615361032, 0.0], 'a3': [-1.0, 0.0], 'a4': [4.204401550329432, 0.0], 'a5': [-1.7135379349683995, 0.0], 'a6': [2.490863615361032, 0.0], 'a7': [1.0, 0.0], 'a8': [-5.490863615361032, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.623338277032136, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [193, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 193], 'central_character': '579.1', 'coefficient_field': 'CDF', 'conductor': 579, 'conductor_radical': 579, 'conjugate': '1876499486039950937705134833884', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.490863615361032, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.7135379349683995, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0], [7.0, 0]], [[1.0, 0], [3.0, 0], [11.0, 0]], [[1.0, 0], [-1.2044015503294316, 0], [13.0, 0]], [[1.0, 0], [-2.490863615361032, 0], 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'7.14485305668778484838957450098303', '7.73217450685809061484570551660374', '8.464299276487119940130721612920705', '9.381319435541491782358012072991866', '10.34662799054845299615719069945609'], 'prelabel': '2-579-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.150194939309489, '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': '1.48029708320423910213754158820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09123110207663081906554914272', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75033806039549903062951810546', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.623338277032136, 'bad_primes': [3, 193], 'central_character': '1.1', 'conductor': 579, 'conductor_radical': 579, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/579/2/a/d/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': '2-579-1.1-c1-0-14', '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': '2-579-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.150194939309489, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48029708320423910213754158820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1876499486039950937705134833884', 'Lhash_array': ['1876499486039950937705134833884'], 'label': '2-579-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/579/2/a/d/1/1'}