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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 3, 'A9': -3, 'Lhash': '1297672526402308054', 'a10': [0.0, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.010309278350515464, 0.0], 'a8': [0.030927835051546393, 0.0], 'a9': [-0.030927835051546393, 0.0], 'algebraic': True, 'analytic_conductor': 2.065852091759074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1, 2]], [3, [1, 0, 3]], [5, [1, 0, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '32400.1', 'coefficient_field': '1.1.1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 1, 2], [1, 0, 3], [1, 0, 5], [1, -1, 5, -7, 49], [1, 5, 25, 55, 121], [1, -1, 15, -13, 169], [1, -5, 19, -85, 289], [1, 4, 6, 76, 361], [1, 3, 37, 69, 529], [1, 4, 22, 116, 841], [1, 5, 38, 155, 961], [1, -9, 91, -333, 1369], [1, 7, 61, 287, 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[1.761361758159681, 2.781767273186283, 3.696520554465796, 4.462049491622455, 5.196933857193609, 5.746062048206558, 6.119478056363566, 7.460216603605721, 7.557484787979119, 8.2012943536501, 8.493002356353662, 9.095298414621078, 9.735570977835048, 10.12288394983556, 10.60063663467579, 11.14112670537221, 11.45952934327171, 12.20455159336421, 12.69067975126122, 13.27327522807583, 13.44643619258159, 14.13258886444317, 14.57677349765151, 14.78444733146175, 15.54316578743221, 15.96931903497593, 16.47079759291812, 16.82908872482091, 17.30293175242019, 17.60236245666255, 18.12271261267392, 18.52102969066828, 18.76296925328724, 19.17125424653227, 19.76677393950724], 'prelabel': '4-180e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 1297672526402308054, 'z1': {'__RealLiteral__': 0, 'data': '1.76136175816', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.78176727319', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.69652055447', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.065852091759074, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 1, 3, -3, 0, -5, 0, 1, -1, 0, -1, 5, 3, -4, 0, 0, 5, -3, 0, -5, -1, 0, -1, -4, 0, -5, -5, 0, -5, 0, 3, 9, 4, 0, 0, -7, 0, 3, 5, 0, 3, 5, 0, -4, 5, 0, -1, -7, 0, 0, 3, 0, 4, 1, 0, -3, 5, -3, 7, 0, 0, 1, -5, 0, 0, -19, -9, 1, -9, 0, 4, -5, 0, -8, 0, 9, 7, -15, 0, 0, -3, 0, -15, 0, 0, 1, 3, 0, -5, 0, 0, 12, 4, 15, 5], 'euler11': [1, 5, 25, 55, 121], 'euler13': [1, -1, 15, -13, 169], 'euler17': [1, -5, 19, -85, 289], 'euler19': [1, 4, 6, 76, 361], 'euler2': [1, 1, 2, 0, 0], 'euler23': [1, 3, 37, 69, 529], 'euler29': [1, 4, 22, 116, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 5, 38, 155, 961], 'euler37': [1, -9, 91, -333, 1369], 'euler41': [1, 7, 61, 287, 1681], 'euler43': [1, -3, 1, -129, 1849], 'euler47': [1, -5, -2, -235, 2209], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 7, 67, 371, 2809], 'euler59': [1, -1, -17, -59, 3481], 'euler61': [1, 3, 13, 183, 3721], 'euler67': [1, -1, -46, -67, 4489], 'euler7': [1, -1, 5, -7, 49], 'euler71': [1, 19, 214, 1349, 5041], 'euler73': [1, -1, -12, -73, 5329], 'euler79': [1, 8, 122, 632, 6241], 'euler83': [1, 15, 154, 1245, 6889], 'euler89': [1, 0, -50, 0, 7921], 'euler97': [1, -12, 82, -1164, 9409], 'euler_factors': [[1, 1, 2, 0, 0], [1, 0, 3, 0, 0], [1, 0, 5, 0, 0], [1, -1, 5, -7, 49], [1, 5, 25, 55, 121], [1, -1, 15, -13, 169], [1, -5, 19, -85, 289], [1, 4, 6, 76, 361], [1, 3, 37, 69, 529], [1, 4, 22, 116, 841], [1, 5, 38, 155, 961], [1, -9, 91, -333, 1369], [1, 7, 61, 287, 1681], [1, -3, 1, -129, 1849], [1, -5, -2, -235, 2209], [1, 7, 67, 371, 2809], [1, -1, -17, -59, 3481], [1, 3, 13, 183, 3721], [1, -1, -46, -67, 4489], [1, 19, 214, 1349, 5041], [1, -1, -12, -73, 5329], [1, 8, 122, 632, 6241], [1, 15, 154, 1245, 6889], [1, 0, -50, 0, 7921], [1, -12, 82, -1164, 9409]], 'index': 7, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/32400/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': '4-180e2-1.1-c1e2-0-7', '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': 1, 'prelabel': '4-180e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.198877490147783, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1297672526402308054, 'z1': {'__RealLiteral__': 0, 'data': '1.76136175816', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1297672526402308054', 'Lhash_array': ['1297672526402308054'], 'label': '4-180e2-1.1-c1e2-0-7', 'type': 'G2Q', 'url': 'Genus2Curve/Q/32400/a'}