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lfunc_lfunctions • Show schema
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{'Lhash': '1853811336460284914545709892404', 'a10': -1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.27826216393724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, -1]], [31, [1, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '2790.1', 'coefficient_field': '1.1.1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -1], [1, 2, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, 8, 29], [1, 1], [1, -4, 37], [1, 10, 41], [1, -8, 43], [1, -4, 47], [1, -14, 53], [1, 14, 59], [1, 6, 61], [1, 10, 67], [1, 6, 71], [1, 8, 73], [1, -8, 79], [1, -12, 83], [1, 16, 89], [1, 10, 97], [1, -6, 101], [1, 6, 103], [1, 8, 107], [1, -18, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -1], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 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1.298925422173718, 0.6013934171660793, -0.08808458361464917, -0.7374193847577603, -1.3170834639041593, -1.8017104224998528, -2.17148657536401, -2.413255881866455, -2.521273840958326], 'positive_zeros': ['1.46239928898903404461019333123305', '2.45848603266431580474701776073649', '3.45847952437465463730423854322952', '4.37755450809302032813521596800799', '5.65751449219398047877913070624794', '6.21881102965997724253631115668432', '6.91025413756572000512757594118155', '7.68378196833310505351006793317809', '8.736880779463300026877543577553679'], 'prelabel': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 496430524854672593, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46239928898903404461019333123', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45848603266431580474701776074', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.45847952437465463730423854323', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.27826216393724, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 2790, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 1, 0, -2, -1, 0, -1, 0, 0, 4, 2, 0, 1, -6, 0, 0, 1, 0, 0, 0, 0, 1, -4, 0, -2, -8, 0, -1, -1, 0, 6, -2, 0, 4, 0, 0, -1, -10, 0, 8, 0, 0, 0, 4, 0, -3, -1, 0, 4, 14, 0, 0, 2, 0, 8, -14, 0, -6, 1, 0, 1, 4, 0, -10, -6, 0, 2, -6, 0, -8, -4, 0, 0, 0, 0, 8, 1, 0, 10, 12, 0, -6, -8, 0, 0, -16, 0, -8, 0, 0, -4, 0, 0, -10, 3, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 1, 0], 'euler37': [1, -4, 37], 'euler41': [1, 10, 41], 'euler43': [1, -8, 43], 'euler47': [1, -4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -14, 53], 'euler59': [1, 14, 59], 'euler61': [1, 6, 61], 'euler67': [1, 10, 67], 'euler7': [1, 2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 8, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 16, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 2, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, 8, 29], [1, 1, 0], [1, -4, 37], [1, 10, 41], [1, -8, 43], [1, -4, 47], [1, -14, 53], [1, 14, 59], [1, 6, 61], [1, 10, 67], [1, 6, 71], [1, 8, 73], [1, -8, 79], [1, -12, 83], [1, 16, 89], [1, 10, 97]], 'index': 37, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2790/f', 'ModularForm/GL2/Q/holomorphic/2790/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/2790/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2790-1.1-c1-0-37', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2790-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.71998539869958, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 496430524854672593, 'z1': {'__RealLiteral__': 0, 'data': '1.46239928898903404461019333123', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20041968
{'Lhash': '1853811336460284914545709892404', 'Lhash_array': ['1853811336460284914545709892404'], 'factors': ['2-2790-1.1-c1-0-37'], 'label': '2-2790-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/f'}
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id: 24558774
{'Lhash': '1853811336460284914545709892404', 'Lhash_array': ['1853811336460284914545709892404'], 'factors': ['2-2790-1.1-c1-0-37'], 'label': '2-2790-1.1-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2790/2/a/f/1/1'}
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id: 23465
{'Lhash': '496430524854672593', 'Lhash_array': ['496430524854672593'], 'factors': ['2-2790-1.1-c1-0-37'], 'label': '2-2790-1.1-c1-0-37', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2790/f'}