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lfunc_lfunctions • Show schema
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{'Lhash': '1556765344331451566054914968044', 'a10': [168.0, -290.9845356715714], 'a2': [2.0, 3.4641016151377544], 'a3': [-5.0, 8.660254037844387], 'a4': [-8.0, 13.856406460551018], 'a5': [-42.0, -72.74613391789285], 'a6': [-40.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-64.0, 0.0], 'a9': [71.5, 123.84163274117472], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.717614341672105, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, -3.4641016151377544]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.67', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '985778120342603668257348877612', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, -3.4641016151377544]], [[1.0, 0], [5.0, -8.660254037844387], [-121.5, -210.4441731196186]], [[1.0, 0], [42.0, 72.74613391789285], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [-168.0, 290.9845356715714], 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-0.020172953053946126, 'root_number': '0.9919779164085226 - 0.12641128651274003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0201729530539', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22807131874600902171485289198', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07045766800819100790285523428', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22188121943707209568416426724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.717614341672105, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/6/c/c/67/1'], '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': '2-98-7.4-c5-0-9', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-98-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9645446575454417, 'root_angle': -0.020172953053946126, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22807131874600902171485289198', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1556765344331451566054914968044', 'Lhash_array': ['1556765344331451566054914968044'], 'factors': ['2-98-7.4-c5-0-9'], 'label': '2-98-7.4-c5-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/6/c/c/67/1'}