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lfunc_lfunctions • Show schema
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{'Lhash': '3310368189452911245865557651456', 'a10': [0.0, -1542201.8195682014], 'a2': [0.0, -110.06906208033482], 'a3': [1258.4626280110385, 0.0], 'a4': [-8019.198427244601, 0.0], 'a5': [14011.219778020937, 0.0], 'a6': [0.0, -138517.8011283283], 'a7': [0.0, -131084.90476358196], 'a8': [0.0, 431822.77124185784], 'a9': [1052287.1861004496, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.053931990039143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '6.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1398872.4665263675, -1087006.9912909654]]]], 'bad_primes': [11], 'central_character': '11.10', 'coefficient_field': 'CDF', 'conductor': 11, 'conductor_radical': 11, 'conjugate': '1831440992364671568915128853567', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 110.06906208033482], [-4096.0, 0]], [[1.0, 0], [-1258.4626280110385, 0], [531441.0, 0]], [[1.0, 0], [-14011.219778020937, 0], [244140625.0, 0]], [[1.0, 0], [0, 131084.90476358196], [-13841287201.0, 0]], 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0.7897259519108715, 'root_number': '-0.7896270388241597 + 0.6135871083699437*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.394862975955', 'prec': 47}, 'spectral_label': 'c12-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.61142004654666547042672433941', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.25060057668144635018352723148', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.12101329862969705465991007262', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.053931990039143, 'bad_primes': [11], 'central_character': '11.10', 'conductor': 11, 'conductor_radical': 11, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/11/13/b/b/10/1'], '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': '2-11-11.10-c12-0-9', 'motivic_weight': 12, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [12], 'order_of_vanishing': 0, 'prelabel': '2-11-11.10-c12-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1707935899454482, 'root_angle': 0.39486297595543574, 'self_dual': False, 'spectral_label': 'c12-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61142004654666547042672433941', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3310368189452911245865557651456', 'Lhash_array': ['3310368189452911245865557651456'], 'label': '2-11-11.10-c12-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/11/13/b/b/10/1'}