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lfunc_lfunctions • Show schema
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{'A10': 12, 'A2': -3, 'A3': -1, 'A4': 4, 'A5': -4, 'A6': 3, 'A7': -5, 'A8': -3, 'A9': -2, 'Lhash': '69981569533283134', 'a10': [0.12371134020618557, 0.0], 'a2': [-0.030927835051546393, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [0.041237113402061855, 0.0], 'a5': [-0.041237113402061855, 0.0], 'a6': [0.030927835051546393, 0.0], 'a7': [-0.05154639175257732, 0.0], 'a8': [-0.030927835051546393, 0.0], 'a9': [-0.020618556701030927, 0.0], 'algebraic': True, 'analytic_conductor': 0.7350990359842705, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1, 1, 3]], [7, [1, 5, 11, 7]], [61, [1, 1, 61, 61]]], 'bad_primes': [3, 7, 61], 'central_character': '11529.1', 'coefficient_field': '1.1.1.1', 'conductor': 11529, 'conductor_radical': 1281, 'degree': 4, 'euler_factors': [[1, 3, 5, 6, 4], [1, 1, 3], [1, 4, 11, 20, 25], [1, 5, 11, 7], [1, 2, 7, 22, 121], [1, 1, -5, 13, 169], [1, 7, 43, 119, 289], [1, 0, 15, 0, 361], [1, 6, 29, 138, 529], [1, -6, 42, -174, 841], [1, 6, 18, 186, 961], [1, 0, -5, 0, 1369], [1, -1, -12, -41, 1681], [1, 3, 37, 129, 1849], [1, -1, 15, -47, 2209], [1, -1, 47, -53, 2809], [1, 16, 152, 944, 3481], [1, 1, 61, 61], [1, 1, 103, 67, 4489], [1, -3, -8, -213, 5041], [1, 0, -20, 0, 5329], [1, -3, 29, -237, 6241], [1, -9, 139, -747, 6889], [1, 2, 40, 178, 7921], [1, 21, 285, 2037, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-11529-1.1-c1e2-0-0', 'leading_term': '0.41249695976', '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': 2, 'origin': 'Genus2Curve/Q/11529/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.01500669396385272, 0.06602218644275987, 0.1704626461424373, 0.3548788099245276, 0.649470657136957, 1.077773063467518, 1.641011346742492, 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0.5160818674481468, -1.304860998362957, -7.575465064575613, -12.25589750016022, -6.82904750517924], 'positive_zeros': [2.700358494180648, 3.609207550978282, 4.44444096365608, 5.64411925088902, 6.465770658035855, 6.861281056950111, 7.70035215600033, 8.058923194266807, 8.601080981489835, 9.17611646620501, 9.569992531324878, 10.20159618613451, 10.84669003114264, 10.96510244592793, 11.90675171931031, 12.15014125664773, 12.60271800327275, 13.37035906869838, 13.86866573683501, 14.84275846259141, 15.40269368996558, 15.74937249895082, 16.09815826934012, 16.4813354791709, 16.85270894494011, 17.48087811493938, 17.90947045055197, 18.24071605346602, 18.72196543809506, 19.23608823272798, 19.56566105348592, 19.79450070654308], 'prelabel': '4-11529-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9259477128799191, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 69981569533283134, 'z1': {'__RealLiteral__': 0, 'data': '2.70035849418', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.60920755098', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.44444096366', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7350990359842705, 'bad_primes': [3, 7, 61], 'central_character': '1.1', 'conductor': 11529, 'conductor_radical': 1281, 'degree': 4, 'dirichlet_coefficients': [1, -3, -1, 4, -4, 3, -5, -3, -2, 12, -2, -4, -1, 15, 4, 3, -7, 6, 0, -16, 5, 6, -6, 3, 5, 3, 5, -20, 6, -12, -6, -6, 2, 21, 20, -8, 0, 0, 1, 12, 1, -15, -3, -8, 8, 18, 1, -3, 14, -15, 7, -4, 1, -15, 8, 15, 0, -18, -16, 16, -1, 18, 10, 5, 4, -6, -1, -28, 6, -60, 3, 6, 0, 0, -5, 0, 10, -3, 3, -12, 1, -3, 9, 20, 28, 9, -6, 6, -2, -24, 5, -24, 6, -3, 0, 6, -21, -42, 4, 20], 'euler11': [1, 2, 7, 22, 121], 'euler13': [1, 1, -5, 13, 169], 'euler17': [1, 7, 43, 119, 289], 'euler19': [1, 0, 15, 0, 361], 'euler2': [1, 3, 5, 6, 4], 'euler23': [1, 6, 29, 138, 529], 'euler29': [1, -6, 42, -174, 841], 'euler3': [1, 1, 3, 0, 0], 'euler31': [1, 6, 18, 186, 961], 'euler37': [1, 0, -5, 0, 1369], 'euler41': [1, -1, -12, -41, 1681], 'euler43': [1, 3, 37, 129, 1849], 'euler47': [1, -1, 15, -47, 2209], 'euler5': [1, 4, 11, 20, 25], 'euler53': [1, -1, 47, -53, 2809], 'euler59': [1, 16, 152, 944, 3481], 'euler61': [1, 1, 61, 61, 0], 'euler67': [1, 1, 103, 67, 4489], 'euler7': [1, 5, 11, 7, 0], 'euler71': [1, -3, -8, -213, 5041], 'euler73': [1, 0, -20, 0, 5329], 'euler79': [1, -3, 29, -237, 6241], 'euler83': [1, -9, 139, -747, 6889], 'euler89': [1, 2, 40, 178, 7921], 'euler97': [1, 21, 285, 2037, 9409], 'euler_factors': [[1, 3, 5, 6, 4], [1, 1, 3, 0, 0], [1, 4, 11, 20, 25], [1, 5, 11, 7, 0], [1, 2, 7, 22, 121], [1, 1, -5, 13, 169], [1, 7, 43, 119, 289], [1, 0, 15, 0, 361], [1, 6, 29, 138, 529], [1, -6, 42, -174, 841], [1, 6, 18, 186, 961], [1, 0, -5, 0, 1369], [1, -1, -12, -41, 1681], [1, 3, 37, 129, 1849], [1, -1, 15, -47, 2209], [1, -1, 47, -53, 2809], [1, 16, 152, 944, 3481], [1, 1, 61, 61, 0], [1, 1, 103, 67, 4489], [1, -3, -8, -213, 5041], [1, 0, -20, 0, 5329], [1, -3, 29, -237, 6241], [1, -9, 139, -747, 6889], [1, 2, 40, 178, 7921], [1, 21, 285, 2037, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/11529/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': '4-11529-1.1-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': 2, 'prelabel': '4-11529-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.9259477128799191, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 69981569533283134, 'z1': {'__RealLiteral__': 0, 'data': '2.70035849418', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '69981569533283134', 'Lhash_array': ['69981569533283134'], 'label': '4-11529-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/11529/a'}