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lfunc_lfunctions • Show schema
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{'Lhash': '370306110351954059601629518407', 'a10': [-109028.23693321265, 0], 'a2': [-19.595917942265423, 11.313708498984761], 'a3': [0, 0], 'a4': [256.0, -443.40500673763256], 'a5': [4172.867938150601, 2409.2064273840083], 'a6': [0, 0], 'a7': [-335.26480832579097, -580.6956820101111], 'a8': [0, 11585.237502960395], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 102.92787493314336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [19.595917942265423, -11.313708498984761]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.53', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1784838592457813961332045633814', 'degree': 2, 'euler_factors': [[[1.0, 0], [19.595917942265423, -11.313708498984761]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4172.867938150601, -2409.2064273840083], [4882812.5, 8457279.33383241]], [[1.0, 0], [335.26480832579097, 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-4.51718928719658, -4.429268540019177, -4.222037597903051], 'positive_zeros': ['0.29212001342111436997964555688555', '1.55775362319940372850606041069808', '2.22797816407952610130335995620215', '3.92063589939593618978670806833096', '5.27348408014613244752135247045727', '6.32199326784568535522705425037594', '7.56199891210200113718379022285347', '8.876100602689127579347428917997926', '9.545184479567050328329111056187244', '10.17680008882065861066849327969604'], 'prelabel': '2-162-9.5-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.145337595819242, 'root_angle': -0.8888888888888888, 'root_number': '-0.9396926207859083840541092773247314699362081342644646331 - 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4444444444444444', 'prec': 64}, 'spectral_label': 'c10-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29212001342111436997964555689', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 102.92787493314336, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/11/d/d/53/2'], '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': '2-162-9.5-c10-0-7', 'motivic_weight': 10, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [10], 'order_of_vanishing': 0, 'prelabel': '2-162-9.5-c10-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.145337595819242, 'root_angle': -0.4444444444444444, 'self_dual': False, 'spectral_label': 'c10-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29212001342111436997964555689', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '370306110351954059601629518407', 'Lhash_array': ['370306110351954059601629518407'], 'label': '2-162-9.5-c10-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/11/d/d/53/2'}