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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -2, 'A4': -1, 'A5': 0, 'A6': -2, 'A7': -1, 'A8': -3, 'A9': 0, 'Lhash': '879736290182210232', 'a10': [0.0, 0.0], 'a2': [0.010309278350515464, 0.0], 'a3': [-0.020618556701030927, 0.0], 'a4': [-0.010309278350515464, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.020618556701030927, 0.0], 'a7': [-0.010309278350515464, 0.0], 'a8': [-0.030927835051546393, 0.0], 'a9': [0.0, 0.0], 'algebraic': True, 'analytic_conductor': 20.48509135927023, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, -1, 2]], [5, [1, 0, 4, -5]], [251, [1, -14, 236, 251]]], 'bad_primes': [2, 5, 251], 'central_character': '321280.1', 'coefficient_field': '1.1.1.1', 'conductor': 321280, 'conductor_radical': 2510, 'degree': 4, 'euler_factors': [[1, -1, 2], [1, 2, 4, 6, 9], [1, 0, 4, -5], [1, 1, -2, 7, 49], [1, 3, 22, 33, 121], [1, 3, 12, 39, 169], [1, 3, 32, 51, 289], [1, 6, 24, 114, 361], [1, 3, 7, 69, 529], [1, -7, 57, -203, 841], [1, 6, 62, 186, 961], [1, 4, 8, 148, 1369], [1, -9, 71, -369, 1681], [1, 3, 79, 129, 1849], [1, 12, 86, 564, 2209], [1, -10, 82, -530, 2809], [1, 19, 184, 1121, 3481], [1, 9, 36, 549, 3721], [1, 14, 120, 938, 4489], [1, 10, 86, 710, 5041], [1, 9, 28, 657, 5329], [1, 8, -4, 632, 6241], [1, -11, 74, -913, 6889], [1, -4, 122, -356, 7921], [1, -3, 47, -291, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 5, 'label': '4-321280-1.1-c1e2-0-5', 'leading_term': '3.74213436935', '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/321280/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.1336790219953375, 0.556407983133269, 1.306470158470326, 2.367250142588386, 3.58113985687725, 4.60297079016724, 4.956840588299463, 4.228792196772115, 2.343645333824687, 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-4.697409010689008], 'positive_zeros': [1.858670282994493, 2.717836834411809, 3.151065924457085, 4.145030858042265, 4.394337086359114, 4.956179380967375, 5.399073616053681, 5.913863430383556, 6.270814292637047, 6.539981742442379, 7.463005731306172, 7.674121942527727, 8.425309121135172, 8.783060412860051, 9.233909165814708, 9.725010491844248, 10.2948820124084, 10.59407157278904, 10.88121891263552, 11.54937063285935, 11.95838149954213, 12.15468370060851, 12.54371463285028, 13.08292304619875, 13.35540894788698, 13.57266929815601, 14.35289905719263, 14.44321539525469, 15.01730645165599, 15.32798209324852, 15.71143331305808, 16.23254834584481, 16.47374719562521, 16.96213418388494, 17.36795362159813, 17.67415473655964, 17.84479196425042, 18.28623702923984, 18.66877880184406, 19.11256007696274, 19.59421701063778, 19.86234647871544], 'prelabel': '4-321280-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1274505601021203, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'USp(4)', 'trace_hash': 879736290182210232, 'z1': {'__RealLiteral__': 0, 'data': '1.85867028299', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.71783683441', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15106592446', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.48509135927023, 'bad_primes': [2, 5, 251], 'central_character': '1.1', 'conductor': 321280, 'conductor_radical': 2510, 'degree': 4, 'dirichlet_coefficients': [1, 1, -2, -1, 0, -2, -1, -3, 0, 0, -3, 2, -3, -1, 0, -1, -3, 0, -6, 0, 2, -3, -3, 6, -4, -3, 2, 1, 7, 0, -6, 5, 6, -3, 0, 0, -4, -6, 6, 0, 9, 2, -3, 3, 0, -3, -12, 2, 3, -4, 6, 3, 10, 2, 0, 3, 12, 7, -19, 0, -9, -6, 0, 7, 0, 6, -14, 3, 6, 0, -10, 0, -9, -4, 8, 6, 3, 6, -8, 0, -1, 9, 11, -2, 0, -3, -14, 9, 4, 0, 3, 3, 12, -12, 0, -10, 3, 3, 0, 4], 'euler11': [1, 3, 22, 33, 121], 'euler13': [1, 3, 12, 39, 169], 'euler17': [1, 3, 32, 51, 289], 'euler19': [1, 6, 24, 114, 361], 'euler2': [1, -1, 2, 0, 0], 'euler23': [1, 3, 7, 69, 529], 'euler29': [1, -7, 57, -203, 841], 'euler3': [1, 2, 4, 6, 9], 'euler31': [1, 6, 62, 186, 961], 'euler37': [1, 4, 8, 148, 1369], 'euler41': [1, -9, 71, -369, 1681], 'euler43': [1, 3, 79, 129, 1849], 'euler47': [1, 12, 86, 564, 2209], 'euler5': [1, 0, 4, -5, 0], 'euler53': [1, -10, 82, -530, 2809], 'euler59': [1, 19, 184, 1121, 3481], 'euler61': [1, 9, 36, 549, 3721], 'euler67': [1, 14, 120, 938, 4489], 'euler7': [1, 1, -2, 7, 49], 'euler71': [1, 10, 86, 710, 5041], 'euler73': [1, 9, 28, 657, 5329], 'euler79': [1, 8, -4, 632, 6241], 'euler83': [1, -11, 74, -913, 6889], 'euler89': [1, -4, 122, -356, 7921], 'euler97': [1, -3, 47, -291, 9409], 'euler_factors': [[1, -1, 2, 0, 0], [1, 2, 4, 6, 9], [1, 0, 4, -5, 0], [1, 1, -2, 7, 49], [1, 3, 22, 33, 121], [1, 3, 12, 39, 169], [1, 3, 32, 51, 289], [1, 6, 24, 114, 361], [1, 3, 7, 69, 529], [1, -7, 57, -203, 841], [1, 6, 62, 186, 961], [1, 4, 8, 148, 1369], [1, -9, 71, -369, 1681], [1, 3, 79, 129, 1849], [1, 12, 86, 564, 2209], [1, -10, 82, -530, 2809], [1, 19, 184, 1121, 3481], [1, 9, 36, 549, 3721], [1, 14, 120, 938, 4489], [1, 10, 86, 710, 5041], [1, 9, 28, 657, 5329], [1, 8, -4, 632, 6241], [1, -11, 74, -913, 6889], [1, -4, 122, -356, 7921], [1, -3, 47, -291, 9409]], 'index': 5, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/321280/f'], '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': '4-321280-1.1-c1e2-0-5', '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': '4-321280-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1274505601021203, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 879736290182210232, 'z1': {'__RealLiteral__': 0, 'data': '1.85867028299', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': '879736290182210232', 'Lhash_array': ['879736290182210232'], 'label': '4-321280-1.1-c1e2-0-5', 'type': 'G2Q', 'url': 'Genus2Curve/Q/321280/f'}