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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '1981683618597372744', 'a10': [0.0, 0.0], 'a2': [0.010309278350515464, 0.0], 'a3': [-0.010309278350515464, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.010309278350515464, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.030927835051546393, 0.0], 'a9': [0.010309278350515464, 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, 1]], [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, 1], [1, 0, 5], [1, 0, 8, 0, 49], [1, 2, -8, 22, 121], [1, 2, -8, 26, 169], [1, 3, 8, 51, 289], [1, 7, 42, 133, 361], [1, 3, 46, 69, 529], [1, -10, 76, -290, 841], [1, 3, 30, 93, 961], [1, -2, 34, -74, 1369], [1, 0, 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2.996263043877344, 3.972022108499313, 4.569537550971558, 4.900774668493113, 5.696089789433214, 6.344191703438324, 6.538800736086737, 7.536353698763418, 8.093335185040543, 8.575700719756272, 9.184089205091611, 9.774955742737175, 10.23491864912651, 10.73028148361377, 11.23202040300101, 12.00102565334691, 12.09806427567835, 12.81765087676682, 12.98987378258232, 13.57581960957283, 13.97988938877838, 14.47983032304041, 14.96999317978373, 15.3690900110448, 15.79495417786874, 16.21211747265951, 16.82393965305843, 17.33786673578179, 17.60736074021476, 17.96841942351791, 18.37257875733157, 18.97947284010585, 19.22766483811934, 19.85300283422629], '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': 1981683618597372744, 'z1': {'__RealLiteral__': 0, 'data': '2.08233427794', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.99626304388', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.9720221085', 'prec': 40}}
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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, -1, -1, 0, -1, 0, -3, 1, 0, -2, 1, -2, 0, 0, -1, -3, 1, -7, 0, 0, -2, -3, 3, -5, -2, -1, 0, 10, 0, -3, 5, 2, -3, 0, -1, 2, -7, 2, 0, 0, 0, -2, 2, 0, -3, 0, 1, -8, -5, 3, 2, -1, -1, 0, 0, 7, 10, -8, 0, -9, -3, 0, 7, 0, 2, 8, 3, 3, 0, -6, -3, 0, 2, 5, 7, 0, 2, -7, 0, 1, 0, 9, 0, 0, -2, -10, 6, 12, 0, 0, 3, 3, 0, 0, -5, -2, -8, -2, 5], 'euler11': [1, 2, -8, 22, 121], 'euler13': [1, 2, -8, 26, 169], 'euler17': [1, 3, 8, 51, 289], 'euler19': [1, 7, 42, 133, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 3, 46, 69, 529], 'euler29': [1, -10, 76, -290, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, 3, 30, 93, 961], 'euler37': [1, -2, 34, -74, 1369], 'euler41': [1, 0, 8, 0, 1681], 'euler43': [1, 2, 68, 86, 1849], 'euler47': [1, 0, 10, 0, 2209], 'euler5': [1, 0, 5, 0, 0], 'euler53': [1, 1, 76, 53, 2809], 'euler59': [1, 8, 28, 472, 3481], 'euler61': [1, 9, 120, 549, 3721], 'euler67': [1, -8, 54, -536, 4489], 'euler7': [1, 0, 8, 0, 49], 'euler71': [1, 6, 48, 426, 5041], 'euler73': [1, 0, 60, 0, 5329], 'euler79': [1, 7, 142, 553, 6241], 'euler83': [1, -9, 66, -747, 6889], 'euler89': [1, -12, 160, -1068, 7921], 'euler97': [1, 2, -30, 194, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 1, 0, 0, 0], [1, 0, 5, 0, 0], [1, 0, 8, 0, 49], [1, 2, -8, 22, 121], [1, 2, -8, 26, 169], [1, 3, 8, 51, 289], [1, 7, 42, 133, 361], [1, 3, 46, 69, 529], [1, -10, 76, -290, 841], [1, 3, 30, 93, 961], [1, -2, 34, -74, 1369], [1, 0, 8, 0, 1681], [1, 2, 68, 86, 1849], [1, 0, 10, 0, 2209], [1, 1, 76, 53, 2809], [1, 8, 28, 472, 3481], [1, 9, 120, 549, 3721], [1, -8, 54, -536, 4489], [1, 6, 48, 426, 5041], [1, 0, 60, 0, 5329], [1, 7, 142, 553, 6241], [1, -9, 66, -747, 6889], [1, -12, 160, -1068, 7921], [1, 2, -30, 194, 9409]], 'index': 11, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/32400/d'], '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-c1e2-0-11', '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': 1981683618597372744, 'z1': {'__RealLiteral__': 0, 'data': '2.08233427794', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '1981683618597372744', 'Lhash_array': ['1981683618597372744'], 'label': '4-180e2-1.1-c1e2-0-11', 'type': 'G2Q', 'url': 'Genus2Curve/Q/32400/d'}