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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': -2, 'A3': 3, 'A4': 0, 'A5': 2, 'A6': -6, 'A7': 2, 'A8': 4, 'A9': 2, 'Lhash': '585636855749534129', 'a10': [-0.041237113402061855, 0.0], 'a2': [-0.020618556701030927, 0.0], 'a3': [0.030927835051546393, 0.0], 'a4': [0.0, 0.0], 'a5': [0.020618556701030927, 0.0], 'a6': [-0.061855670103092786, 0.0], 'a7': [0.020618556701030927, 0.0], 'a8': [0.041237113402061855, 0.0], 'a9': [0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.2914509231923064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[7, [1, -2, 4, 7]], [653, [1, 2, 654, 653]]], 'bad_primes': [7, 653], 'central_character': '4571.1', 'coefficient_field': '1.1.1.1', 'conductor': 4571, 'conductor_radical': 4571, 'degree': 4, 'euler_factors': [[1, 2, 4, 4, 4], [1, -3, 7, -9, 9], [1, -2, 6, -10, 25], [1, -2, 4, 7], [1, 3, 17, 33, 121], [1, 2, 22, 26, 169], [1, 0, 10, 0, 289], [1, 2, 18, 38, 361], [1, -3, -3, -69, 529], [1, 6, 18, 174, 841], [1, -2, 2, -62, 961], [1, 0, 10, 0, 1369], [1, -9, 71, -369, 1681], [1, -3, -8, -129, 1849], [1, -1, 18, -47, 2209], [1, 1, 11, 53, 2809], [1, -6, 58, -354, 3481], [1, 5, 43, 305, 3721], [1, 0, -100, 0, 4489], [1, 6, 76, 426, 5041], [1, -7, -22, -511, 5329], [1, 16, 178, 1264, 6241], [1, 4, 34, 332, 6889], [1, -5, -27, -445, 7921], [1, -2, 46, -194, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-4571-1.1-c1e2-0-0', 'leading_term': '0.634991203209', 'load_key': 'G2Q', '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, 'origin': 'Genus2Curve/Q/4571/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.6349912032085627, 0.6535911494294548, 0.707135481292963, 0.7883410343237951, 0.8836026732705418, 0.9716866857350873, 1.023644081815138, 1.005458425094692, 0.8847858064818281, 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-6.919470847115933, -8.424217750333423, -3.928419444273135], 'positive_zeros': [2.0032642245859, 2.845876736459309, 4.18793618209331, 5.146645835022202, 5.961707768229135, 7.440146046270906, 7.70930887671239, 8.338611295422012, 8.833019936538449, 9.13748871302178, 9.795954872298754, 10.10895379877338, 10.92622176421845, 11.45910601531741, 12.64470246052944, 13.0652593545353, 13.70898577300905, 13.95560267043083, 14.48208107031767, 14.95108635989904, 15.41317264059797, 16.29347692298667, 16.90618138607376, 17.42696807340614, 17.63156544062245, 18.09385230087278, 18.77631560047269, 18.97947678499341, 19.48637179195981, 19.93041692794471], 'prelabel': '4-4571-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7347529845276214, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 585636855749534129, 'z1': {'__RealLiteral__': 0, 'data': '2.00326422459', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.84587673646', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.18793618209', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2914509231923064, 'bad_primes': [7, 653], 'central_character': '1.1', 'conductor': 4571, 'conductor_radical': 4571, 'degree': 4, 'dirichlet_coefficients': [1, -2, 3, 0, 2, -6, 2, 4, 2, -4, -3, 0, -2, -4, 6, -4, 0, -4, -2, 0, 6, 6, 3, 12, -2, 4, -6, 0, -6, -12, 2, 0, -9, 0, 4, 0, 0, 4, -6, 8, 9, -12, 3, 0, 4, -6, 1, -12, 0, 4, 0, 0, -1, 12, -6, 8, -6, 12, 6, 0, -5, -4, 4, 0, -4, 18, 0, 0, 9, -8, -6, 8, 7, 0, -6, 0, -6, 12, -16, -8, -14, -18, -4, 0, 0, -6, -18, -12, 5, -8, -4, 0, 6, -2, -4, 0, 2, 0, -6, 0], 'euler11': [1, 3, 17, 33, 121], 'euler13': [1, 2, 22, 26, 169], 'euler17': [1, 0, 10, 0, 289], 'euler19': [1, 2, 18, 38, 361], 'euler2': [1, 2, 4, 4, 4], 'euler23': [1, -3, -3, -69, 529], 'euler29': [1, 6, 18, 174, 841], 'euler3': [1, -3, 7, -9, 9], 'euler31': [1, -2, 2, -62, 961], 'euler37': [1, 0, 10, 0, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, -3, -8, -129, 1849], 'euler47': [1, -1, 18, -47, 2209], 'euler5': [1, -2, 6, -10, 25], 'euler53': [1, 1, 11, 53, 2809], 'euler59': [1, -6, 58, -354, 3481], 'euler61': [1, 5, 43, 305, 3721], 'euler67': [1, 0, -100, 0, 4489], 'euler7': [1, -2, 4, 7, 0], 'euler71': [1, 6, 76, 426, 5041], 'euler73': [1, -7, -22, -511, 5329], 'euler79': [1, 16, 178, 1264, 6241], 'euler83': [1, 4, 34, 332, 6889], 'euler89': [1, -5, -27, -445, 7921], 'euler97': [1, -2, 46, -194, 9409], 'euler_factors': [[1, 2, 4, 4, 4], [1, -3, 7, -9, 9], [1, -2, 6, -10, 25], [1, -2, 4, 7, 0], [1, 3, 17, 33, 121], [1, 2, 22, 26, 169], [1, 0, 10, 0, 289], [1, 2, 18, 38, 361], [1, -3, -3, -69, 529], [1, 6, 18, 174, 841], [1, -2, 2, -62, 961], [1, 0, 10, 0, 1369], [1, -9, 71, -369, 1681], [1, -3, -8, -129, 1849], [1, -1, 18, -47, 2209], [1, 1, 11, 53, 2809], [1, -6, 58, -354, 3481], [1, 5, 43, 305, 3721], [1, 0, -100, 0, 4489], [1, 6, 76, 426, 5041], [1, -7, -22, -511, 5329], [1, 16, 178, 1264, 6241], [1, 4, 34, 332, 6889], [1, -5, -27, -445, 7921], [1, -2, 46, -194, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/4571/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-4571-1.1-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': '4-4571-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.7347529845276214, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 585636855749534129, 'z1': {'__RealLiteral__': 0, 'data': '2.00326422459', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '585636855749534129', 'Lhash_array': ['585636855749534129'], 'label': '4-4571-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/4571/a'}