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lfunc_lfunctions • Show schema
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{'Lhash': '2717831242075206436993527291089', 'a10': [1.8367776387165178, 3.1813921924634], 'a2': [-0.632804240207218, 1.096049095283922], 'a3': [1.3136399888037744, 2.2752912034623485], 'a4': [0.19911758715153094, 0.34488177762697547], 'a5': [1.4513000403687613, -2.5137254069454573], 'a6': [-3.3251078200831636, -5.6094782716366846e-61], 'a7': [-1.2953581502487999, -2.306956276695336], 'a8': [-3.0352267746261483, 0.0], 'a9': [-1.9513000403687613, 3.379750810729896], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [1.2953581502487999, 2.306956276695336]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '91.79', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '4204160904094382536705277486348', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.632804240207218, -1.096049095283922], [-1.0, 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'9.478256401013718356347095440273601', '10.55649675326800644554919584106189', '11.68032019869949282574962877609594', '12.82949986531904994234632257471363', '13.54569818539315467539018983890806'], 'prelabel': '2-91-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.5163632425735892, 'root_number': '-0.05138400408296696 - 0.9986789695014117*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.258181621287', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.14399081386139421756398149636', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75840817566795589164627141121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.16618870871093693955849088181', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '7.2', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/e/c/79/3'], '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': '2-91-7.2-c1-0-3', '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': '2-91-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.2581816212867946, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.14399081386139421756398149636', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2717831242075206436993527291089', 'Lhash_array': ['2717831242075206436993527291089'], 'label': '2-91-7.2-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/e/c/79/3'}