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lfunc_lfunctions • Show schema
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{'Lhash': '529700326222027337569859598809,566047647630320856823974977532,599618642782047289007154909545,1400197912569840882836285292892,1519040173170184967744249196689,1542309983203365647143870402627,1618711523370112244158272001459,1741607930602245385419053269945,1785332908360639533767171855645,2352018330155757785153149367202', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 711.1192268531736, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]], [3, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]], [7, [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [23, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.1', 'coefficient_field': '1.1.1.1', 'conductor': 741944085990901508095773947751038976, 'conductor_radical': 966, 'degree': 20, 'euler_factors': [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 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1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 711.1192268531736, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 741944085990901508095773947751038976, 'conductor_radical': 966, 'degree': 20, 'dirichlet_coefficients': [1, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2, -1, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, -1, -2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, -9, -1, 9, 0, 0, 1, 0, 0, 0, -1, 2, 0, 2, 0, 0, 0, 0, 2, -9, 0, -2, -2, 0, 0, 0, 0, -2, 0, 1, 0, 2, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, -9, 2, 0, 0, 9, 2, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler13': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], 'euler17': [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], 'euler19': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler2': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -1, 1, -1, 1, -1, 1, -1, 1, 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5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, -1, 9, -36, 84, -126, 126, -84, 36, -9, 1], [1, 0, -10, 0, 45, 0, -120, 0, 210, 0, -252, 0, 210, 0, -120, 0, 45, 0, -10, 0, 1], [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '20-3864e10-1.1-c0e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3886638213815174, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e10-0', 'trace_hash': 2220727289919957454, 'z1': {'__RealLiteral__': 0, 'data': '0.41785987883937374187561179182', 'prec': 103}}
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lfunc_instances • Show schema
Hide schema
{'Lhash': '529700326222027337569859598809,566047647630320856823974977532,599618642782047289007154909545,1400197912569840882836285292892,1519040173170184967744249196689,1542309983203365647143870402627,1618711523370112244158272001459,1741607930602245385419053269945,1785332908360639533767171855645,2352018330155757785153149367202', 'Lhash_array': ['529700326222027337569859598809', '566047647630320856823974977532', '599618642782047289007154909545', '1400197912569840882836285292892', '1519040173170184967744249196689', '1542309983203365647143870402627', '1618711523370112244158272001459', '1741607930602245385419053269945', '1785332908360639533767171855645', '2352018330155757785153149367202'], 'label': '20-3864e10-1.1-c0e10-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3864/1/dl/d'}