-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1590713900044183900354828051917', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.129426657363098, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [19, [1, -1]]], 'bad_primes': [2, 3, 19], 'central_character': '3648.1', 'coefficient_field': '1.1.1.1', 'conductor': 3648, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 0, 5], [1, 4, 7], [1, -4, 11], [1, 0, 13], [1, 2, 17], [1, -1], [1, -2, 23], [1, -6, 29], [1, 6, 31], [1, -8, 37], [1, -10, 41], [1, 12, 43], [1, 10, 47], [1, 2, 53], [1, -4, 59], [1, -10, 61], [1, 0, 67], [1, -16, 71], [1, 2, 73], [1, 10, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97], [1, 8, 101], [1, -6, 103], [1, 4, 107], [1, -4, 109], [1, 14, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 0, 5], 1]], [[[1, 4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 0, 13], 1]], [[[1, 2, 17], 1]], [[[1, -1], 1]], [[[1, -2, 23], 1]], [[[1, -6, 29], 1]], [[[1, 6, 31], 1]], [[[1, -8, 37], 1]], [[[1, -10, 41], 1]], [[[1, 12, 43], 1]], [[[1, 10, 47], 1]], [[[1, 2, 53], 1]], [[[1, -4, 59], 1]], [[[1, -10, 61], 1]], [[[1, 0, 67], 1]], [[[1, -16, 71], 1]], [[[1, 2, 73], 1]], [[[1, 10, 79], 1]], [[[1, 16, 83], 1]], [[[1, 2, 89], 1]], [[[1, 10, 97], 1]], [[[1, 8, 101], 1]], [[[1, -6, 103], 1]], [[[1, 4, 107], 1]], [[[1, -4, 109], 1]], [[[1, 14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 42, 'label': '2-3648-1.1-c1-0-42', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3648/2/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.1084745963690159e-60, 0.1403015824805059, 0.2796843801808066, 0.4171855712712023, 0.5517574903757005, 0.682233028778112, 0.8072997473873732, 0.9254845901315816, 1.0351503984481292, 1.1345047466467593, 1.2216209999241703, 1.2944709745030192, 1.3509681624207313, 1.3890201640549475, 1.4065887317468928, 1.4017556472465627, 1.372792515950407, 1.3182324492151776, 1.2369415159361616, 1.128187775485289, 0.9917056600621441, 0.8277534626552342, 0.6371617158422214, 0.4213703255049656, 0.18245246026921252, -0.07687660152579084, -0.35326719620868824, -0.6427607604568223, -0.9408338614157589, -1.2424610846503727, -1.5421965688074912, -1.8342734079138223, -2.1127195451152474, -2.3714881723195527, -2.6046000478034204, -2.8062945692610435, -2.9711859149561053, -3.094420112893987, -3.171828539115507, -3.2000731018901694, -3.1767782571438388, -3.100645037228098, -2.971542471565614, -2.790572140557857, -2.5601021348525848, -2.2837673862111796, -1.966434183150993, -1.6141276672689249, -1.2339222014102247, -0.8337956794193737, -0.42245007453123984, -0.00910176045168992, 0.3967536566654191, 0.7855961304283382, 1.1481487216503092, 1.4756501948861012, 1.7601243289832287, 1.9946372226969695, 2.1735337681226747, 2.292644654535193, 2.3494557663400073, 2.3432326537696633, 2.27509387474954, 2.1480284100748457, 1.9668540087127948, 1.7381151810718676, 1.4699215701455506, 1.1717295288997283, 0.8540718450366585, 0.5282426040882103, 0.20594608894021713, -0.10107970088025296, -0.38145293913779293, -0.6245382796713032, -0.8208239914233928, -0.9622722078271375, -1.042628952543715, -1.0576814930410068, -1.0054519696860467, -0.8863181236915045, -0.7030542548046105, -0.4607882117551857, -0.16687316975216931, 0.16932392142404518, 0.5367121416133133, 0.9228364439948958, 1.3142963741838591, 1.697209858798479, 2.0577060447342124, 2.3824294942740485, 2.6590369931649374, 2.876667879057142, 3.0263691911506014, 3.101458094973041, 3.0978059347483895, 3.01403086400553, 2.8515892258390605, 2.6147595908763206, 2.310517480298583, 1.9483031478145973, 1.5396891963046437, 1.0979590799522583, 0.6376115064340976, 0.173809226753865, -0.2782064835369982, -0.7037123336779896, -1.0890861036083814, -1.4223517965443877, -1.693663294004239, -1.8957049341726346, -2.023990411260072, -2.0770452686119136, -2.0564628950315362, -1.9668291561590219, -1.8155163917964263, -1.612353251699602, -1.369182476841873, -1.099324005763493, -0.816965447947095, -0.5365057876896406, -0.27188096131987516, -0.03590152606705888, 0.1603671026988497, 0.3081524850243456, 0.4014241865577226, 0.43722092199246193, 0.41583769412504007, 0.34086076324139164, 0.21904497956241648, 0.06003517066593503, -0.12405942023817676, -0.3192215352804684, -0.5101904461501519, -0.6812062128144906, -0.8168006456373788, -0.9025987812680869, -0.9260931041402031, -0.8773528942661528, -0.7496330081650996, -0.5398500704223792, -0.24889935151990783, 0.11820766554010867, 0.5523971455503235, 1.040781606019418, 1.5670977591649704, 2.1123186539002643, 2.6554165839427064, 3.174245394771973, 3.6465042551646287, 4.050740013165106, 4.367342219086232, 4.579483973285316, 4.673963051375838, 4.641901276563935, 4.47926574170876, 4.187183019348245, 3.7720266233071666, 3.2452683000549127, 2.6230947606871227, 1.9258026950000284, 1.1769957924914625, 0.4026174877582995, -0.3701382649557562, -1.1139891604265235, -1.8027461469496169, -2.41245899964014, -2.9224711141354565, -3.3163321972324598, -3.582523554840056, -3.7149590592737254, -3.713235251000125, -3.5826159180722255, -3.3337493346160683, -2.9821295006507893, -2.547325550485303, -2.052015328691839, -1.5208693494383214, -0.9793394035639501, -0.4524115040179918, 0.03661466489079383, 0.46725828916637896, 0.8228442725798015, 1.0912935459046584, 1.2656755565511908, 1.3444934930621886, 1.3316863311062184, 1.236346337993955, 1.0721654955870557, 0.8566386213814444, 0.6100640201259332, 0.35439357121592474, 0.11199262924755081, -0.09562450780054371, -0.2490158644885573, -0.3319237395568032, -0.3322165084939868, -0.2426079966175001, -0.06111362947592857, 0.20878358730264326, 0.5582687169966078, 0.9736273108006627, 1.4369534706568239, 1.9270971026941315, 2.4208003768560884, 2.8939624450996395, 3.322963719933453, 3.6859769555775754, 3.9641922882057044, 4.142887346348165, 4.212281380476108, 4.168123705302432, 4.011981019707726, 3.751204613233645, 3.398576195062557, 2.971649113568455, 2.491819059621409, 1.9831739747622592, 1.471185904863027, 0.9813171719089525, 0.5376188812929746, 0.16140105676630986, -0.12994953957384217, -0.32393547267756634, -0.41364180578728427, -0.39811466161397285, -0.2824011185633593, -0.07724566519818638, 0.2015417598619205, 0.5340119260153375, 0.8972450000916475, 1.2666954327571252, 1.6176357210251506, 1.9266151199083779, 2.172847605565098, 2.3394466361122297, 2.4144324020162875, 2.3914499023120777, 2.270152649925725, 2.056226185230841, 1.7610467592888912, 1.4009923078514943, 0.9964438886732835, 0.5705348315960866, 0.14772078167811079, -0.247744404578467, -0.5933350961284763, -0.8696894102219878, -1.0618647392010416, -1.1603338086249402, -1.1616563629868377, -1.0687803116693344, -0.8909480137839825, -0.6432070709726303, -0.34554913191589753, -0.021723337911500138, 0.30220826405220813, 0.5994890448968315], 'positive_zeros': ['1.25485200713650100256263649356457', '2.59096801605995758443809230130732', '3.58834969751350496793839399628726', '4.18996617241742471056324636486805', '5.24974769470397520513045103465142', '6.15303436289493204195564662977335', '6.56793180927898505204276009439467', '7.14484973381679933288499588457087', '8.202111681048451602860500584502512'], 'prelabel': '2-3648-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.397168392533542, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1221038204671136056, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25485200713650100256263649356', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59096801605995758443809230131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58834969751350496793839399629', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.129426657363098, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 3648, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -4, 0, 1, 0, 4, 0, 0, 0, 0, 0, -2, 0, 1, 0, 4, 0, 2, 0, -5, 0, -1, 0, 6, 0, -6, 0, -4, 0, 0, 0, 8, 0, 0, 0, 10, 0, -12, 0, 0, 0, -10, 0, 9, 0, 2, 0, -2, 0, 0, 0, -1, 0, 4, 0, 10, 0, -4, 0, 0, 0, 0, 0, -2, 0, 16, 0, -2, 0, 5, 0, -16, 0, -10, 0, 1, 0, -16, 0, 0, 0, -6, 0, -2, 0, 0, 0, 6, 0, 0, 0, -10, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 0, 13], 'euler17': [1, 2, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -8, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 5], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 0, 67], 'euler7': [1, 4, 7], 'euler71': [1, -16, 71], 'euler73': [1, 2, 73], 'euler79': [1, 10, 79], 'euler83': [1, 16, 83], 'euler89': [1, 2, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 5], [1, 4, 7], [1, -4, 11], [1, 0, 13], [1, 2, 17], [1, -1, 0], [1, -2, 23], [1, -6, 29], [1, 6, 31], [1, -8, 37], [1, -10, 41], [1, 12, 43], [1, 10, 47], [1, 2, 53], [1, -4, 59], [1, -10, 61], [1, 0, 67], [1, -16, 71], [1, 2, 73], [1, 10, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97]], 'index': 42, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3648/j', 'ModularForm/GL2/Q/holomorphic/3648/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/3648/2/a/j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-3648-1.1-c1-0-42', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3648-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.397168392533542, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1221038204671136056, 'z1': {'__RealLiteral__': 0, 'data': '1.25485200713650100256263649356', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20524678
{'Lhash': '1590713900044183900354828051917', 'Lhash_array': ['1590713900044183900354828051917'], 'label': '2-3648-1.1-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3648/2/a/j'}
-
id: 24562426
{'Lhash': '1590713900044183900354828051917', 'Lhash_array': ['1590713900044183900354828051917'], 'label': '2-3648-1.1-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3648/2/a/j/1/1'}
-
id: 91153
{'Lhash': '1221038204671136056', 'Lhash_array': ['1221038204671136056'], 'label': '2-3648-1.1-c1-0-42', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3648/j'}