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lfunc_lfunctions • Show schema
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{'Lhash': '2522401330726372244333381119963', 'a10': [21.510199044748923, 21.510199044748923], 'a2': [0.0, 2.1178341881786844], 'a3': [-5.927584280907147, 5.927584280907147], 'a4': [3.514778351381533, 0.0], 'a5': [10.156696480212869, -10.156696480212869], 'a6': [-12.553640643415717, -12.553640643415717], 'a7': [3.215999845202429, 3.215999845202429], 'a8': [0.0, 24.3863912618556], 'a9': [0.0, -43.27251081451499], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.003032470097591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [51.739268260597115, 47.28687048069441]]]], 'bad_primes': [17], 'central_character': '17.4', 'coefficient_field': 'CDF', 'conductor': 17, 'conductor_radical': 17, 'conjugate': '6556650255890634253124698956373', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.1178341881786844], [-8.0, 0]], [[1.0, 0], [5.927584280907147, -5.927584280907147], [0, -27.0]], [[1.0, 0], [-10.156696480212869, 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'0.07748001798584941 - 0.996993905103192*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.237656300889', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98982379708749078810849432379', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.07904238286820764077112287950', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.16939616777459365669093710526', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.003032470097591, 'bad_primes': [17], 'central_character': '17.4', 'conductor': 17, 'conductor_radical': 17, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/17/4/c/a/4/3'], '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': '2-17-17.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-17-17.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0015150873040262, 'root_angle': -0.2376563008891779, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98982379708749078810849432379', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2522401330726372244333381119963', 'Lhash_array': ['2522401330726372244333381119963'], 'label': '2-17-17.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/17/4/c/a/4/3'}