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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': -1, 'A3': 0, 'A4': -2, 'A5': 3, 'A6': 0, 'A7': -5, 'A8': 3, 'A9': 0, 'Lhash': '351041983347545524', 'a10': [-0.030927835051546393, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.020618556701030927, 0.0], 'a5': [0.030927835051546393, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.05154639175257732, 0.0], 'a8': [0.030927835051546393, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 27.10914407410845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[3, [1]], [29, [1, -5, 23, 29]], [181, [1, -16, 164, 181]]], 'bad_primes': [3, 29, 181], 'central_character': '425169.1', 'coefficient_field': '1.1.1.1', 'conductor': 425169, 'conductor_radical': 15747, 'degree': 4, 'euler_factors': [[1, 1, 3, 2, 4], [1], [1, -3, 9, -15, 25], [1, 5, 18, 35, 49], [1, 2, -6, 22, 121], [1, 3, 15, 39, 169], [1, 5, 16, 85, 289], [1, 4, 13, 76, 361], [1, 8, 39, 184, 529], [1, -5, 23, 29], [1, 6, 42, 186, 961], [1, 13, 96, 481, 1369], [1, -9, 71, -369, 1681], [1, 12, 91, 516, 1849], [1, -8, 56, -376, 2209], [1, 7, 24, 371, 2809], [1, -6, 43, -354, 3481], [1, -2, 28, -122, 3721], [1, 6, 36, 402, 4489], [1, 20, 224, 1420, 5041], [1, 1, -44, 73, 5329], [1, 0, 131, 0, 6241], [1, -17, 188, -1411, 6889], [1, 1, 163, 89, 7921], [1, -3, 105, -291, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-425169-1.1-c1e2-0-0', 'leading_term': '3.00892949938', '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/425169/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.1070085385341798, 0.4393416981917509, 1.00720932187832, 1.760274524312836, 2.528277672160937, 3.016489693938567, 2.904397538266943, 2.042856317301173, 0.6521337927548237, 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-0.3660673735542816, -6.571376239183596], 'positive_zeros': [1.773060992854121, 2.307101185923745, 2.939381895956614, 3.784841949071393, 4.154875237000092, 4.964221311683277, 5.227193793170909, 6.070106713794337, 6.239981731611256, 6.61818534296885, 7.341513162214688, 7.699101680038687, 8.447810296048944, 8.86457212905743, 8.994609168023562, 9.56890780292141, 9.882984432619281, 10.18377819998569, 10.32793884152402, 10.84172211752805, 11.61951355003012, 12.13283023281708, 12.53409298367586, 12.96546860873101, 13.1260906313287, 13.58282543834919, 13.79485069658861, 14.1848053096581, 14.60270699999735, 15.24593503154775, 15.57134988132504, 16.01602832513948, 16.37221116587771, 16.59072288822423, 17.22844058691617, 17.59160623459687, 17.67788451052183, 17.93767462338853, 18.33851758662534, 18.95394185146755, 19.11999099992204, 19.38458067724321, 19.7244326719319], 'prelabel': '4-425169-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.281807227590527, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 351041983347545524, 'z1': {'__RealLiteral__': 0, 'data': '1.77306099285', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.30710118592', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.93938189596', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.10914407410845, 'bad_primes': [3, 29, 181], 'central_character': '1.1', 'conductor': 425169, 'conductor_radical': 15747, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -2, 3, 0, -5, 3, 0, -3, -2, 0, -3, 5, 0, 1, -5, 0, -4, -6, 0, 2, -8, 0, 0, 3, 0, 10, 5, 0, -6, -2, 0, 5, -15, 0, -13, 4, 0, 9, 9, 0, -12, 4, 0, 8, 8, 0, 7, 0, 0, 6, -7, 0, -6, -15, 0, -5, 6, 0, 2, 6, 0, 1, -9, 0, -6, 10, 0, 15, -20, 0, -1, 13, 0, 8, 10, 0, 0, 3, 0, -9, 17, 0, -15, 12, 0, -6, -1, 0, 15, 16, 0, -8, -12, 0, 3, -7, 0, 0], 'euler11': [1, 2, -6, 22, 121], 'euler13': [1, 3, 15, 39, 169], 'euler17': [1, 5, 16, 85, 289], 'euler19': [1, 4, 13, 76, 361], 'euler2': [1, 1, 3, 2, 4], 'euler23': [1, 8, 39, 184, 529], 'euler29': [1, -5, 23, 29, 0], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6, 42, 186, 961], 'euler37': [1, 13, 96, 481, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 12, 91, 516, 1849], 'euler47': [1, -8, 56, -376, 2209], 'euler5': [1, -3, 9, -15, 25], 'euler53': [1, 7, 24, 371, 2809], 'euler59': [1, -6, 43, -354, 3481], 'euler61': [1, -2, 28, -122, 3721], 'euler67': [1, 6, 36, 402, 4489], 'euler7': [1, 5, 18, 35, 49], 'euler71': [1, 20, 224, 1420, 5041], 'euler73': [1, 1, -44, 73, 5329], 'euler79': [1, 0, 131, 0, 6241], 'euler83': [1, -17, 188, -1411, 6889], 'euler89': [1, 1, 163, 89, 7921], 'euler97': [1, -3, 105, -291, 9409], 'euler_factors': [[1, 1, 3, 2, 4], [1, 0, 0, 0, 0], [1, -3, 9, -15, 25], [1, 5, 18, 35, 49], [1, 2, -6, 22, 121], [1, 3, 15, 39, 169], [1, 5, 16, 85, 289], [1, 4, 13, 76, 361], [1, 8, 39, 184, 529], [1, -5, 23, 29, 0], [1, 6, 42, 186, 961], [1, 13, 96, 481, 1369], [1, -9, 71, -369, 1681], [1, 12, 91, 516, 1849], [1, -8, 56, -376, 2209], [1, 7, 24, 371, 2809], [1, -6, 43, -354, 3481], [1, -2, 28, -122, 3721], [1, 6, 36, 402, 4489], [1, 20, 224, 1420, 5041], [1, 1, -44, 73, 5329], [1, 0, 131, 0, 6241], [1, -17, 188, -1411, 6889], [1, 1, 163, 89, 7921], [1, -3, 105, -291, 9409]], 'index': 0, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/425169/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': '4-425169-1.1-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': '4-425169-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.281807227590527, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 351041983347545524, 'z1': {'__RealLiteral__': 0, 'data': '1.77306099285', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '351041983347545524', 'Lhash_array': ['351041983347545524'], 'label': '4-425169-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/425169/a'}