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lfunc_lfunctions • Show schema
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{'Lhash': '2519539361904286987541757946121', 'a10': [5.65252661403614, 3.913099906105934], 'a2': [1.808073599630165, -0.8549092690574939], 'a3': [1.3512412286883855, 0.78013948712336], 'a4': [2.538260283359163, -3.091477758923952], 'a5': [1.7187096903919148, 2.976892507219771], 'a6': [3.1100920710228155, 0.2553609595584266], 'a7': [0.0, 0.0], 'a8': [1.9464284161423087, -7.7596015632784745], 'a9': [-3.282764761261802, -5.685915355802156], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.34061318146182, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.808073599630165, 0.8549092690574939]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '196.67', 'coefficient_field': 'CDF', 'conductor': 196, 'conductor_radical': 14, 'conjugate': '2357245587880440464235374167493', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.808073599630165, 0.8549092690574939]], [[1.0, 0], [-1.3512412286883855, 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'8.707769572644930136250563394840303', '10.68988622156330014999168795338712', '11.50971819295901317777567417833427', '12.71084725477574648874867889329693'], 'prelabel': '2-14e2-28.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.310976672634715, 'root_angle': 0.13284589023937593, 'root_number': '0.9141672414553347 + 0.40533721103538456*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0664229451197', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98756610177178629955229592967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.54803300798335900030899205303', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.84922237305552748274417419146', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.34061318146182, 'bad_primes': [2, 7], 'central_character': '28.11', 'conductor': 196, 'conductor_radical': 14, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/196/3/g/j/67/6'], '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': '2-14e2-28.11-c2-0-22', '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': '2-14e2-28.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.310976672634715, 'root_angle': 0.06642294511968796, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98756610177178629955229592967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2519539361904286987541757946121', 'Lhash_array': ['2519539361904286987541757946121'], 'label': '2-14e2-28.11-c2-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/196/3/g/j/67/6'}