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lfunc_lfunctions • Show schema
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{'Lhash': '2974273917315084363007593884441,3616863215301261957384682330152', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': -5, 'a8': -1, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.82191556911358, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [11, [1, 2, 1]]], 'bad_primes': [5, 11], 'central_character': '275.1', 'coefficient_field': '1.1.1.1', 'conductor': 75625, 'conductor_radical': 55, 'degree': 4, 'euler_factors': [[1, 1, 1, 2, 4], [1, 1, 3, 3, 9], [1], [1, 5, 17, 35, 49], [1, 2, 1], [1, 10, 51, 130, 169], [1, 3, 7, 51, 289], [1, 2, 39, 38, 361], [1, -11, 73, -253, 529], [1, 9, 49, 261, 841], [1, -6, 19, -186, 961], [1, 12, 97, 444, 1369], [1, 4, 73, 164, 1681], [1, 0, 34, 0, 1849], [1, -6, 103, -282, 2209], [1, 1, 103, 53, 2809], [1, 14, 115, 826, 3481], [1, 5, 99, 305, 3721], [1, -8, 150, -536, 4489], [1, -2, 130, -142, 5041], [1, -5, 123, -365, 5329], [1, 11, 159, 869, 6241], [1, 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[[[1, -5, 143, -545, 11881], 1]], [[[1, 0, 109, 0, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 14, 'label': '4-275e2-1.1-c1e2-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/275/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [2.6747390464034134e-239, 0.005904836994875755, 0.023818760236571517, 0.054334924023331684, 0.09839945294320929, 0.15728405966477255, 0.23247648565367623, 0.32564780843117863, 0.43845998979987, 0.5725376840084215, 0.7291925363698036, 0.9094079867207736, 1.113496342141106, 1.3411106958556889, 1.5908699882140718, 1.860420559145874, 2.1460860800783608, 2.443005983111083, 2.7448875937868107, 3.044243458276572, 3.3323348269708783, 3.5995102208989977, 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0.3762365712371977, 1.1742908934140195], 'positive_zeros': ['2.34628841478842226900834011508233', '2.85320199008313282448555336254071', '3.39743855585965294744355267594207', '4.66495966213269380614410498206073', '4.96521826308231203896098221581515', '5.64031011464947950521292302591377', '6.24236146899732046281076286266346', '6.92346215499356070623832759681521', '7.05460335950302119734931810000186', '7.61296540418524370081381517166468', '8.605904675749065979491153211911381', '8.819873036028638500292269708526923', '9.443182157871460324338093872423398', '9.714380402320605627927132262200263', '10.00820008617195022368519186425072', '10.75770470419501364913570977746691', '11.01779809857128900000577135766972', '11.67020501557625141701675509836864'], 'prelabel': '4-275e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 767742156726772763, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34628841478842226900834011508', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85320199008313282448555336254', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39743855585965294744355267594', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.82191556911358, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 75625, 'conductor_radical': 55, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 0, 0, 1, -5, -1, -2, 0, -2, 0, -10, 5, 0, -1, -3, 2, -2, 0, 5, 2, 11, 1, 0, 10, 2, 0, -9, 0, 6, 6, 2, 3, 0, 0, -12, 2, 10, 0, -4, -5, 0, 0, 0, -11, 6, 1, 8, 0, 3, 0, -1, -2, 0, 5, 2, 9, -14, 0, -5, -6, 10, -3, 0, -2, 8, 0, -11, 0, 2, 2, 5, 12, 0, 0, 10, -10, -11, 0, -2, 4, -11, 0, 0, 0, 9, 2, 7, 0, 50, 0, -6, -6, 0, -6, -27, -8, 4, 0], 'euler11': [1, 2, 1, 0, 0], 'euler13': [1, 10, 51, 130, 169], 'euler17': [1, 3, 7, 51, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 1, 1, 2, 4], 'euler23': [1, -11, 73, -253, 529], 'euler29': [1, 9, 49, 261, 841], 'euler3': [1, 1, 3, 3, 9], 'euler31': [1, -6, 19, -186, 961], 'euler37': [1, 12, 97, 444, 1369], 'euler41': [1, 4, 73, 164, 1681], 'euler43': [1, 0, 34, 0, 1849], 'euler47': [1, -6, 103, -282, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 1, 103, 53, 2809], 'euler59': [1, 14, 115, 826, 3481], 'euler61': [1, 5, 99, 305, 3721], 'euler67': [1, -8, 150, -536, 4489], 'euler7': [1, 5, 17, 35, 49], 'euler71': [1, -2, 130, -142, 5041], 'euler73': [1, -5, 123, -365, 5329], 'euler79': [1, 11, 159, 869, 6241], 'euler83': [1, 11, 115, 913, 6889], 'euler89': [1, -7, 187, -623, 7921], 'euler97': [1, 27, 373, 2619, 9409], 'euler_factors': [[1, 1, 1, 2, 4], [1, 1, 3, 3, 9], [1, 0, 0, 0, 0], [1, 5, 17, 35, 49], [1, 2, 1, 0, 0], [1, 10, 51, 130, 169], [1, 3, 7, 51, 289], [1, 2, 39, 38, 361], [1, -11, 73, -253, 529], [1, 9, 49, 261, 841], [1, -6, 19, -186, 961], [1, 12, 97, 444, 1369], [1, 4, 73, 164, 1681], [1, 0, 34, 0, 1849], [1, -6, 103, -282, 2209], [1, 1, 103, 53, 2809], [1, 14, 115, 826, 3481], [1, 5, 99, 305, 3721], [1, -8, 150, -536, 4489], [1, -2, 130, -142, 5041], [1, -5, 123, -365, 5329], [1, 11, 159, 869, 6241], [1, 11, 115, 913, 6889], [1, -7, 187, -623, 7921], [1, 27, 373, 2619, 9409]], 'index': 14, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/75625/b', 'ModularForm/GL2/Q/holomorphic/275/2/a/e'], '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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-275e2-1.1-c1e2-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-275e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 767742156726772763, 'z1': {'__RealLiteral__': 0, 'data': '2.34628841478842226900834011508', 'prec': 103}}
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id: 10154648
{'Lhash': '2974273917315084363007593884441,3616863215301261957384682330152', 'Lhash_array': ['2974273917315084363007593884441', '3616863215301261957384682330152'], 'label': '4-275e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/a/e'}
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id: 1237598
{'Lhash': '767742156726772763', 'Lhash_array': ['767742156726772763'], 'label': '4-275e2-1.1-c1e2-0-14', 'type': 'G2Q', 'url': 'Genus2Curve/Q/75625/b'}