-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 2, 'A2': -1, 'A3': -4, 'A4': 1, 'A5': -2, 'A6': 4, 'A7': 2, 'A8': -1, 'A9': 7, 'Lhash': '563433189856627425', 'a10': [0.020618556701030927, 0.0], 'a2': [-0.010309278350515464, 0.0], 'a3': [-0.041237113402061855, 0.0], 'a4': [0.010309278350515464, 0.0], 'a5': [-0.020618556701030927, 0.0], 'a6': [0.041237113402061855, 0.0], 'a7': [0.020618556701030927, 0.0], 'a8': [-0.010309278350515464, 0.0], 'a9': [0.07216494845360824, 0.0], 'algebraic': True, 'analytic_conductor': 13.727459628004988, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.500000000000000', 'prec': 57}, 'bad_lfactors': [[2, [1, 1]], [29, [1, 0, -1]]], 'bad_primes': [2, 29], 'central_character': '215296.1', 'coefficient_field': '1.1.1.1', 'conductor': 215296, 'conductor_radical': 58, 'degree': 4, 'euler_factors': [[1, 1], [1, 4, 9, 12, 9], [1, 2, 7, 10, 25], [1, -2, 6, -14, 49], [1, 4, 25, 44, 121], [1, -6, 35, -78, 169], [1, 4, 34, 68, 289], [1, 12, 70, 228, 361], [1, -8, 46, -184, 529], [1, 0, -1], [1, -8, 77, -248, 961], [1, 12, 106, 444, 1369], [1, 4, 86, 164, 1681], [1, -8, 93, -344, 1849], [1, -16, 149, -752, 2209], [1, -2, 107, -106, 2809], [1, 0, 102, 0, 3481], [1, -12, 154, -732, 3721], [1, 6, 142, 402, 4489], [1, -10, 118, -710, 5041], [1, 6, 74, 438, 5329], [1, 0, 109, 0, 6241], [1, 12, 166, 996, 6889], [1, -2, 130, -178, 7921], [1, 18, 266, 1746, 9409]], 'gamma_factors': [[], [0, 0]], 'index': 4, 'label': '4-464e2-1.1-c1e2-0-4', 'leading_term': '0.850879586542', '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': 1, 'origin': 'Genus2Curve/Q/215296/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.1875', 'prec': 20}, 'plot_values': [0.0, 0.1546116478763794, 0.2740121711132872, 0.2991742923471648, 0.1435187648824659, -0.2743692724803616, -0.9588151012506007, -1.751429902218106, -2.292284246523636, -2.103586702487552, -0.8323413375697505, 1.417745898798958, 3.863876858510017, 5.177868886507644, 4.084656217868247, 0.213568298105362, -5.329350955461842, -10.22185561958056, -12.12123899094588, -10.16536417943347, -5.694955044597053, -1.468724898318567, 0.2461422508407918, -0.7170851987393746, -2.493509228634952, -2.957453753581919, -1.636185933156125, 0.03794089619013424, 0.3768224677860076, -0.7347217248695382, -1.809112133448373, -1.558972319649079, -0.4332355806557211, -0.001896013919148804, -0.8792469448940675, -1.82996128188192, -1.400324901644183, -0.1183566594398997, -0.193216072205572, -2.641098204481634, -5.420068940656579, -5.428296386484778, -2.314724402393083, 0.8287121129634726, 1.218579421229902, -0.135929386841405, -0.1275666919266049, 1.495602759191179, 0.8593105686690721, -5.051657791503893, -13.32906911683099, -17.21715465288906, -13.47027990721742, -5.858064210229556, -0.519337809364738, 0.5482959179701552, -0.1311199862934573, -0.2046280533266682, 0.07927621614436622, 0.01087802236334698, 0.1565610857997903, 0.7718478312798243, 0.7139779547933589, -0.3308851857334183, -0.485041266690326, 1.180677902371428, 2.04351415652135, -0.2002405155867507, -2.569855210786213, -0.5966366041445753, 3.096852753212878, 0.5677230477116333, -8.3158185582496, -11.39183190019654, 0.3289705376649332, 17.12463681833346, 19.88176490946097, 4.458038536070137, -12.72155356723324, -15.84561450810308, -7.539036518817976, -0.506471954949673, 0.4548328162118018, -0.1474507503251696, 0.2141433998180475, -0.7502220660589616, -3.120428469060936, -3.48177708673509, -1.259735011448717, 0.2488497658649022, -0.2041956433036223, -0.4793821201072553, 0.1669888934747325, 0.2669382681289408, -0.05460947699534877, 0.4104189419351266, 0.4161368386695367, -1.539944697517579, -3.085083564982407, -1.686765583308168, 0.06506805418044688, -0.7875078025879131, -1.490211192882437, -0.05010725066519708, -2.373977102053956, -12.32178309060024, -20.1251793032108, -14.17737865343305, -0.1703516843988562, 6.315888934993428, 2.807370378911015, -0.3244899695966474, 0.2420993614711665, -1.321172898205514, -4.33430541171244, -2.015644248018645, 3.252776677153492, 2.364048032926608, -3.554694190991828, -4.829111358494251, -0.3588398328094097, 2.174955304833273, 0.7488314843664136, -0.2075909515289006, 0.1636090997447957, 0.0235941798777587, 0.4236135082098233, 1.331718776996716, 0.09243030533729436, -0.9455789797273741, 2.704530159289947, 5.037752247247287, -3.361369481259762, -15.26029888545132, -14.6570266404612, -3.752026558865689, 1.49793900012395, -0.01835095512868787, 3.661057429231418, 11.15214953365251, 10.08929652323823, 1.8223310690724, -1.367450256984943, 1.451663793954553, 1.9265341255994, -0.4473551516829298, -0.8120766101063356, 0.04547710391039038, -0.3364577523219952, -0.4760092535196932, 0.1307912495239591, -0.06346390196919961, -0.1497573451637891, 0.5344558670791792, -0.01590164766709147, -0.7834115551594711, 1.023322355056722, 2.320033293621984, 0.3319546700762165, 0.7038969325367378, 5.288462761972004], 'positive_zeros': [0.8301424842220264, 1.951854907005511, 2.820420287429813, 4.060157679799393, 4.221463272161603, 5.05667172197396, 5.332575493695205, 6.117550642980299, 6.186248684097992, 6.962786977629977, 7.092294954930529, 7.999330472257728, 8.416163402295368, 8.643506374817898, 9.04191846872012, 10.16283382881085, 10.46054334513251, 10.80330214098309, 11.0825708266304, 11.14914256918044, 11.75608341854126, 12.07048630043892, 12.55084053898538, 12.96417955859964, 13.3272522232886, 13.87145344236654, 14.47947443791115, 15.21769316783365, 15.47776366797874, 15.65077303673302, 15.84934678481967, 16.62484669541971, 16.82608394495314, 17.20333055790643, 17.56071922513726, 17.68188315517846, 18.05709366328594, 18.73133200854964, 18.8260295844526, 19.32344043338399, 19.37542430604861], 'prelabel': '4-464e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9248528914666212, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'G_{3,3}', 'trace_hash': 563433189856627425, 'z1': {'__RealLiteral__': 0, 'data': '0.830142484222', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.95185490701', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.82042028743', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.727459628004988, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 215296, 'conductor_radical': 58, 'degree': 4, 'dirichlet_coefficients': [1, -1, -4, 1, -2, 4, 2, -1, 7, 2, -4, -4, 6, -2, 8, 1, -4, -7, -12, -2, -8, 4, 8, 4, -3, -6, -4, 2, 0, -8, 8, -1, 16, 4, -4, 7, -12, 12, -24, 2, -4, 8, 8, -4, -14, -8, 16, -4, -2, 3, 16, 6, 2, 4, 8, -2, 48, 0, 0, 8, 12, -8, 14, 1, -12, -16, -6, -4, -32, 4, 10, -7, -6, 12, 12, -12, -8, 24, 0, -2, -8, 4, -12, -8, 8, -8, 0, 4, 2, 14, 12, 8, -32, -16, 24, 4, -18, 2, -28, -3], 'euler11': [1, 4, 25, 44, 121], 'euler13': [1, -6, 35, -78, 169], 'euler17': [1, 4, 34, 68, 289], 'euler19': [1, 12, 70, 228, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, -8, 46, -184, 529], 'euler29': [1, 0, -1, 0, 0], 'euler3': [1, 4, 9, 12, 9], 'euler31': [1, -8, 77, -248, 961], 'euler37': [1, 12, 106, 444, 1369], 'euler41': [1, 4, 86, 164, 1681], 'euler43': [1, -8, 93, -344, 1849], 'euler47': [1, -16, 149, -752, 2209], 'euler5': [1, 2, 7, 10, 25], 'euler53': [1, -2, 107, -106, 2809], 'euler59': [1, 0, 102, 0, 3481], 'euler61': [1, -12, 154, -732, 3721], 'euler67': [1, 6, 142, 402, 4489], 'euler7': [1, -2, 6, -14, 49], 'euler71': [1, -10, 118, -710, 5041], 'euler73': [1, 6, 74, 438, 5329], 'euler79': [1, 0, 109, 0, 6241], 'euler83': [1, 12, 166, 996, 6889], 'euler89': [1, -2, 130, -178, 7921], 'euler97': [1, 18, 266, 1746, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 4, 9, 12, 9], [1, 2, 7, 10, 25], [1, -2, 6, -14, 49], [1, 4, 25, 44, 121], [1, -6, 35, -78, 169], [1, 4, 34, 68, 289], [1, 12, 70, 228, 361], [1, -8, 46, -184, 529], [1, 0, -1, 0, 0], [1, -8, 77, -248, 961], [1, 12, 106, 444, 1369], [1, 4, 86, 164, 1681], [1, -8, 93, -344, 1849], [1, -16, 149, -752, 2209], [1, -2, 107, -106, 2809], [1, 0, 102, 0, 3481], [1, -12, 154, -732, 3721], [1, 6, 142, 402, 4489], [1, -10, 118, -710, 5041], [1, 6, 74, 438, 5329], [1, 0, 109, 0, 6241], [1, 12, 166, 996, 6889], [1, -2, 130, -178, 7921], [1, 18, 266, 1746, 9409]], 'index': 4, 'instance_types': ['G2Q'], 'instance_urls': ['Genus2Curve/Q/215296/b'], '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': '4-464e2-1.1-c1e2-0-4', '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': '4-464e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.9248528914666212, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 563433189856627425, 'z1': {'__RealLiteral__': 0, 'data': '0.830142484222', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9953910
{'Lhash': '563433189856627425', 'Lhash_array': ['563433189856627425'], 'label': '4-464e2-1.1-c1e2-0-4', 'type': 'ECQP', 'url': 'EllipticCurve/Q/58/a|EllipticCurve/Q/3712/h'}
-
id: 827532
{'Lhash': '563433189856627425', 'Lhash_array': ['563433189856627425'], 'label': '4-464e2-1.1-c1e2-0-4', 'type': 'G2Q', 'url': 'Genus2Curve/Q/215296/b'}