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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 3, 'A9': 2, 'Lhash': '1796049827911077013488758375928', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [1.0606601717798214, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4856027632974416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 2]], [7, [1, -1, 7, -7]], [17, [1, 5, 11, -17]]], 'bad_primes': [2, 7, 17], 'central_character': '7616.1', 'coefficient_field': '1.1.1.1', 'conductor': 7616, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 0, -2, 0, 9], [1, 0, -2, 0, 25], [1, -1, 7, -7], [1, 0, 6, 0, 121], [1, 0, 6, 0, 169], [1, 5, 11, -17], [1, 0, -10, 0, 361], [1, -16, 110, -368, 529], [1, 0, 38, 0, 841], [1, 0, 62, 0, 961], [1, 0, 22, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 6, 0, 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'symplectic', 'trace_hash': 1976775346107681852, 'z1': {'__RealLiteral__': 0, 'data': '1.41683349306797468746149066882827', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.97566938692753315409261641346808', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.20074021204333954966211858673772', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4856027632974416, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 7616, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 1, 3, 2, 0, 0, 0, 0, -1, 0, -1, -5, -2, 0, 0, 0, 0, 16, 0, 2, 0, 0, -1, 0, 0, 0, -5, 0, 5, 0, -2, 0, 0, 0, 0, -12, 0, 0, 0, 0, -16, 8, 0, -6, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 7, 0, 0, 0, 5, 0, 0, -8, 6, -4, 0, 0, 0, 0, 0, -8, 0, -5, 12, 0, 0, 0, 0, 0, 0, -12, 0, 0, -16, 0, -8, 0, 0, 4, 6, 0, -2], 'euler11': [1, 0, 6, 0, 121], 'euler13': [1, 0, 6, 0, 169], 'euler17': [1, 5, 11, -17, 0], 'euler19': [1, 0, -10, 0, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, -16, 110, -368, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, 0, 22, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, 6, 0, 1849], 'euler47': [1, -8, 94, -376, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 6, 0, 2809], 'euler59': [1, 0, -42, 0, 3481], 'euler61': [1, 0, 62, 0, 3721], 'euler67': [1, 0, 22, 0, 4489], 'euler7': [1, -1, 7, -7, 0], 'euler71': [1, 8, 142, 568, 5041], 'euler73': [1, 4, 6, 292, 5329], 'euler79': [1, 8, 158, 632, 6241], 'euler83': [1, 0, 38, 0, 6889], 'euler89': [1, 12, 214, 1068, 7921], 'euler97': [1, -4, -58, -388, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 0, -2, 0, 9], [1, 0, -2, 0, 25], [1, -1, 7, -7, 0], [1, 0, 6, 0, 121], [1, 0, 6, 0, 169], [1, 5, 11, -17, 0], [1, 0, -10, 0, 361], [1, -16, 110, -368, 529], [1, 0, 38, 0, 841], [1, 0, 62, 0, 961], [1, 0, 22, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, 6, 0, 1849], [1, -8, 94, -376, 2209], [1, 0, 6, 0, 2809], [1, 0, -42, 0, 3481], [1, 0, 62, 0, 3721], [1, 0, 22, 0, 4489], [1, 8, 142, 568, 5041], [1, 4, 6, 292, 5329], [1, 8, 158, 632, 6241], [1, 0, 38, 0, 6889], [1, 12, 214, 1068, 7921], [1, -4, -58, -388, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-119.4-b', 'EllipticCurve/2.2.8.1/119.4/b', 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-119.1-b', 'EllipticCurve/2.2.8.1/119.1/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-7616-1.1-c1e2-0-0', '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': '4-7616-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.8347766397728551, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1976775346107681852, 'z1': {'__RealLiteral__': 0, 'data': '1.41683349306797468746149066882827', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9551644
{'Lhash': '1796049827911077013488758375928', 'Lhash_array': ['1796049827911077013488758375928'], 'label': '4-7616-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/119.1/b'}
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id: 9551570
{'Lhash': '1796049827911077013488758375928', 'Lhash_array': ['1796049827911077013488758375928'], 'label': '4-7616-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-119.1-b'}
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id: 9551260
{'Lhash': '1796049827911077013488758375928', 'Lhash_array': ['1796049827911077013488758375928'], 'label': '4-7616-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.8.1/119.4/b'}
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id: 9551103
{'Lhash': '1796049827911077013488758375928', 'Lhash_array': ['1796049827911077013488758375928'], 'label': '4-7616-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-119.4-b'}