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lfunc_lfunctions • Show schema
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{'Lhash': '1317321044535825496175271891704', 'a10': [2.3382397603499676, -1.9620161205137097], 'a2': [0.32614009210243955, -1.37609325277156], 'a3': [-0.028119266252437138, 2.999868214916353], 'a4': [-1.7872652806468246, -0.8975983604009243], 'a5': [1.731255438033036, 1.2888719196644838], 'a6': [4.118927589664834, 1.0170720284708659], 'a7': [3.6768133571824704, 2.4182781877398734], 'a8': [-1.8180779106881748, 2.1667008816788074], 'a9': [-8.998418613730848, -0.16870818611491248], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.41418028263681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.32614009210243955, 1.37609325277156]]], [3, [[1.0, 0], [0.028119266252437138, -2.999868214916353]]]], 'bad_primes': [2, 3], 'central_character': '162.65', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '2659956246859705779095022412557', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.25967057626492485, 'root_number': '0.6853011599048111 - 0.7282597889717106*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.129835288132', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03918307165922010819462590687', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21836044366142509943133480177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.20860187205088687390825630570', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.41418028263681, 'bad_primes': [2, 3], 'central_character': '81.65', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/3/h/a/65/14'], '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': '2-162-81.65-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-162-81.65-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.100995069636483, 'root_angle': -0.12983528813246242, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03918307165922010819462590687', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1317321044535825496175271891704', 'Lhash_array': ['1317321044535825496175271891704'], 'label': '2-162-81.65-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/3/h/a/65/14'}