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lfunc_lfunctions • Show schema
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{'Lhash': '821899538294353974876597283832,2291631092226201190762168250469', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 259.1404863902583, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -1, 7]]], 'bad_primes': [2, 3, 7], 'central_character': '2016.1', 'coefficient_field': '1.1.1.1', 'conductor': 4064256, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, -3, 4, -15, 25], [1, -1, 7], [1, 5, 14, 55, 121], [1, -4, 30, -52, 169], [1, -2, -13, -34, 289], [1, -6, 17, -114, 361], [1, 2, -19, 46, 529], [1, 2, 59, 58, 841], [1, -1, -30, -31, 961], [1, 10, 63, 370, 1369], [1, 8, 98, 328, 1681], [1, -8, 102, -344, 1849], [1, -8, 17, -376, 2209], [1, -5, -28, -265, 2809], [1, 13, 110, 767, 3481], [1, -8, 3, -488, 3721], [1, -14, 129, -938, 4489], [1, 24, 286, 1704, 5041], [1, -6, -37, -438, 5329], [1, 11, 42, 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'2.99938453640640460508747082894922', '3.40943219604235664577552860875774', '3.93798226426328505923379919355176', '4.66948933101685461394439327788373', '5.03700057765526876492813317456349', '5.46896932051028645702667004198628', '5.67423549159683224908794303725156', '6.07935480851325592963968882749640', '6.43638663487877139478220909891211', '7.20361048881376163126012316128809', '7.38534481682280194667432039612412', '7.65793701233622131700668379038690', '8.346747057119739796582791129875202', '8.685204516555070348500925097757818', '8.736691780547568924835719545975365', '9.525774627127339485037275891585405'], 'prelabel': '4-2016e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1913619558068594370, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64836441377961573383700110765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51261375670747518773645512088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.80777817784617706108728586105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.1404863902583, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 4064256, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 3, 0, 1, 0, 0, 0, -5, 0, 4, 0, 0, 0, 2, 0, 6, 0, 0, 0, -2, 0, 5, 0, 0, 0, -2, 0, 1, 0, 0, 0, 3, 0, -10, 0, 0, 0, -8, 0, 8, 0, 0, 0, 8, 0, -6, 0, 0, 0, 5, 0, -15, 0, 0, 0, -13, 0, 8, 0, 0, 0, 12, 0, 14, 0, 0, 0, -24, 0, 6, 0, 0, 0, -5, 0, -11, 0, 0, 0, -14, 0, 6, 0, 0, 0, -6, 0, 4, 0, 0, 0, 18, 0, 38, 0, 0, 0], 'euler11': [1, 5, 14, 55, 121], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, -2, -13, -34, 289], 'euler19': [1, -6, 17, -114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, -19, 46, 529], 'euler29': [1, 2, 59, 58, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -1, -30, -31, 961], 'euler37': [1, 10, 63, 370, 1369], 'euler41': [1, 8, 98, 328, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, -8, 17, -376, 2209], 'euler5': [1, -3, 4, -15, 25], 'euler53': [1, -5, -28, -265, 2809], 'euler59': [1, 13, 110, 767, 3481], 'euler61': [1, -8, 3, -488, 3721], 'euler67': [1, -14, 129, -938, 4489], 'euler7': [1, -1, 7, 0, 0], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, -6, -37, -438, 5329], 'euler79': [1, 11, 42, 869, 6241], 'euler83': [1, 14, 215, 1162, 6889], 'euler89': [1, 6, -53, 534, 7921], 'euler97': [1, -38, 555, -3686, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, -3, 4, -15, 25], [1, -1, 7, 0, 0], [1, 5, 14, 55, 121], [1, -4, 30, -52, 169], [1, -2, -13, -34, 289], [1, -6, 17, -114, 361], [1, 2, -19, 46, 529], [1, 2, 59, 58, 841], [1, -1, -30, -31, 961], [1, 10, 63, 370, 1369], [1, 8, 98, 328, 1681], [1, -8, 102, -344, 1849], [1, -8, 17, -376, 2209], [1, -5, -28, -265, 2809], [1, 13, 110, 767, 3481], [1, -8, 3, -488, 3721], [1, -14, 129, -938, 4489], [1, 24, 286, 1704, 5041], [1, -6, -37, -438, 5329], [1, 11, 42, 869, 6241], [1, 14, 215, 1162, 6889], [1, 6, -53, 534, 7921], [1, -38, 555, -3686, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2016/2/s/m'], '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': '4-2016e2-1.1-c1e2-0-7', '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': 0, 'prelabel': '4-2016e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.0122114908726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1913619558068594370, 'z1': {'__RealLiteral__': 0, 'data': '0.64836441377961573383700110765', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '821899538294353974876597283832,2291631092226201190762168250469', 'Lhash_array': ['821899538294353974876597283832', '2291631092226201190762168250469'], 'label': '4-2016e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2016/2/s/m'}