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lfunc_lfunctions • Show schema
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{'Lhash': '3370716497290834336604644320939', 'a10': [-2.1368973850531505, 0.0], 'a2': [1.552533731067022, 0.0], 'a3': [0.4679681892984895, 0.0], 'a4': [0.4103609861008884, 0.0], 'a5': [-1.3763935316139693, 0.0], 'a6': [0.7265363989522623, 0.0], 'a7': [-3.3515727246108504, 0.0], 'a8': [-2.4679681892984893, 0.0], 'a9': [-2.781005773804693, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.837064387755599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [17, 43], 'central_character': '731.1', 'coefficient_field': 'CDF', 'conductor': 731, 'conductor_radical': 731, 'conjugate': '3370716497290834336604644320939', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.552533731067022, 0], [2.0, 0]], [[1.0, 0], [-0.4679681892984895, 0], [3.0, 0]], [[1.0, 0], [1.3763935316139693, 0], [5.0, 0]], [[1.0, 0], [3.3515727246108504, 0], [7.0, 0]], [[1.0, 0], [-2.057607203197601, 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'5.50115242423230845791444184146311', '6.14386475681703177786822373728180', '7.16382076688123639464718917725058', '8.213159074108972597148798098600205', '9.334888056856925858937426460117106', '9.636356672510607432848327470142368'], 'prelabel': '2-731-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, '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': '2.65902646729624576157635952031', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50560523527321925559032479873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17760811363505970694803797222', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.837064387755599, 'bad_primes': [17, 43], 'central_character': '1.1', 'conductor': 731, 'conductor_radical': 731, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/731/2/a/c/1/5'], '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': '2-731-1.1-c1-0-55', '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': '2-731-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.416001735875949, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.65902646729624576157635952031', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3370716497290834336604644320939', 'Lhash_array': ['3370716497290834336604644320939'], 'label': '2-731-1.1-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/731/2/a/c/1/5'}