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lfunc_lfunctions • Show schema
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{'Lhash': '2438099379118652883052812156828', 'a10': [0.0, -2.9061701120214436], 'a2': [0.0, -0.7265425280053609], 'a3': [1.381966011250105, 0.0], 'a4': [3.4721359549995796, 0.0], 'a5': [4.0, 0.0], 'a6': [0.0, -1.0040570794311363], 'a7': [0.0, 9.95959313953112], 'a8': [0.0, -5.428824546345146], 'a9': [-7.0901699437494745, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2970111987595927, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [0, 0]]]], 'bad_primes': [11], 'central_character': '121.120', 'coefficient_field': 'CDF', 'conductor': 121, 'conductor_radical': 11, 'conjugate': '2739587772754615564875905150574', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.7265425280053609], [-4.0, 0]], [[1.0, 0], [-1.381966011250105, 0], [9.0, 0]], [[1.0, 0], [-4.0, 0], [25.0, 0]], [[1.0, 0], [0, -9.95959313953112], [-49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 5.257311121191336], [-169.0, 0]], [[1.0, 0], [0, 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'5.56706524303702039138541083858164', '6.69825847467274651509432689244203', '7.68334536665281264052958723840735', '8.879142777423662526629275551819059', '10.29842618935403553320467484534042', '10.93983234661696636053166761896773', '12.26245876059873233647934925114585', '13.68678868615251856083302143564778'], 'prelabel': '2-11e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.815767385641562, 'root_angle': 0.07029931173052668, 'root_number': '0.9757112070410057 + 0.2190608145118239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0351496558653', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92332128323032736125812850306', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61988003535187609757778686332', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.56706524303702039138541083858', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.2970111987595927, 'bad_primes': [11], 'central_character': '11.10', 'conductor': 121, 'conductor_radical': 11, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/3/b/b/120/2'], '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': '2-11e2-11.10-c2-0-6', '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': '2-11e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.815767385641562, 'root_angle': 0.03514965586526334, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92332128323032736125812850306', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2438099379118652883052812156828', 'Lhash_array': ['2438099379118652883052812156828'], 'label': '2-11e2-11.10-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/3/b/b/120/2'}