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lfunc_lfunctions • Show schema
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{'A10': -12, 'A2': 2, 'A3': -2, 'A4': 2, 'A5': -6, 'A6': -4, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1017608200157608638860020978911', 'a10': [-3.794733192202055, 0], 'a2': [1.4142135623730951, 0], 'a3': [-1.1547005383792515, 0], 'a4': [1.0, 0], 'a5': [-2.6832815729997477, 0], 'a6': [-1.6329931618554518, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.56221492352006, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 2]], [11, [1, 0, -1]], [19, [1, 0, 19]]], 'bad_primes': [2, 11, 19], 'central_character': '698896.1', 'coefficient_field': '1.1.1.1', 'conductor': 698896, 'conductor_radical': 418, 'degree': 4, 'euler_factors': [[1, -2, 2], [1, 2, 3, 6, 9], [1, 6, 19, 30, 25], [1, 0, -2, 0, 49], [1, 0, -1], [1, 0, 14, 0, 169], [1, -4, 34, -68, 289], [1, 0, 19], [1, 0, -3, 0, 529], [1, 0, -2, 0, 841], [1, 2, 59, 62, 961], [1, 0, 45, 0, 1369], [1, 0, -14, 0, 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'trace_hash': 138538084395100161, 'z1': {'__RealLiteral__': 0, 'data': '0.802751325936655719005547051771654', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.19731876267553041800621884523259', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.12875467287827706433861893011937', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.56221492352006, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 698896, 'conductor_radical': 418, 'degree': 4, 'dirichlet_coefficients': [1, 2, -2, 2, -6, -4, 0, 0, 1, -12, 0, -4, 0, 0, 12, -4, 4, 2, 0, -12, 0, 0, 0, 0, 17, 0, -2, 0, 0, 24, -2, -8, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 8, 2, 34, -8, 0, 0, -4, 0, 0, 0, 0, 10, 24, 0, -4, 0, -8, 0, 0, 10, 8, 0, 0, -6, 0, -8, 0, -34, 0, 0, 0, 12, 24, 4, 0, 0, 0, -24, 0, 0, 0, 0, -12, 0, 0, 4, 0, 0, 16, 0, 4, 0, 34], 'euler11': [1, 0, -1, 0, 0], 'euler13': [1, 0, 14, 0, 169], 'euler17': [1, -4, 34, -68, 289], 'euler19': [1, 0, 19, 0, 0], 'euler2': [1, -2, 2, 0, 0], 'euler23': [1, 0, -3, 0, 529], 'euler29': [1, 0, -2, 0, 841], 'euler3': [1, 2, 3, 6, 9], 'euler31': [1, 2, 59, 62, 961], 'euler37': [1, 0, 45, 0, 1369], 'euler41': [1, 0, -14, 0, 1681], 'euler43': [1, 0, -30, 0, 1849], 'euler47': [1, 0, 46, 0, 2209], 'euler5': [1, 6, 19, 30, 25], 'euler53': [1, 0, -74, 0, 2809], 'euler59': [1, -10, 43, -590, 3481], 'euler61': [1, 0, 118, 0, 3721], 'euler67': [1, -10, 155, -670, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 6, 147, 426, 5041], 'euler73': [1, 8, 146, 584, 5329], 'euler79': [1, -12, 190, -948, 6241], 'euler83': [1, 0, 86, 0, 6889], 'euler89': [1, 0, -19, 0, 7921], 'euler97': [1, 0, 125, 0, 9409], 'euler_factors': [[1, -2, 2, 0, 0], [1, 2, 3, 6, 9], [1, 6, 19, 30, 25], [1, 0, -2, 0, 49], [1, 0, -1, 0, 0], [1, 0, 14, 0, 169], [1, -4, 34, -68, 289], [1, 0, 19, 0, 0], [1, 0, -3, 0, 529], [1, 0, -2, 0, 841], [1, 2, 59, 62, 961], [1, 0, 45, 0, 1369], [1, 0, -14, 0, 1681], [1, 0, -30, 0, 1849], [1, 0, 46, 0, 2209], [1, 0, -74, 0, 2809], [1, -10, 43, -590, 3481], [1, 0, 118, 0, 3721], [1, -10, 155, -670, 4489], [1, 6, 147, 426, 5041], [1, 8, 146, 584, 5329], [1, -12, 190, -948, 6241], [1, 0, 86, 0, 6889], [1, 0, -19, 0, 7921], [1, 0, 125, 0, 9409]], 'index': 6, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-121.1-e', 'ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-121.1-a', 'EllipticCurve/2.2.76.1/121.1/a', 'EllipticCurve/2.2.76.1/121.1/e'], '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': '4-836e2-1.1-c1e2-0-6', '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': 1, 'prelabel': '4-836e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.583697662068657, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 138538084395100161, 'z1': {'__RealLiteral__': 0, 'data': '0.802751325936655719005547051771654', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9480266
{'Lhash': '1017608200157608638860020978911', 'Lhash_array': ['1017608200157608638860020978911'], 'label': '4-836e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.76.1/121.1/e'}
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id: 9480264
{'Lhash': '1017608200157608638860020978911', 'Lhash_array': ['1017608200157608638860020978911'], 'label': '4-836e2-1.1-c1e2-0-6', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.76.1/121.1/a'}
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id: 9479908
{'Lhash': '1017608200157608638860020978911', 'Lhash_array': ['1017608200157608638860020978911'], 'label': '4-836e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-121.1-a'}
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id: 9479741
{'Lhash': '1017608200157608638860020978911', 'Lhash_array': ['1017608200157608638860020978911'], 'label': '4-836e2-1.1-c1e2-0-6', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.76.1/holomorphic/2.2.76.1-121.1-e'}