-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2881572533478861958804546968490', 'a10': [3.246979603717467, 0.0], 'a2': [-2.246979603717467, 0.0], 'a3': [-0.5549581320873712, 0.0], 'a4': [3.0489173395223053, 0.0], 'a5': [-1.445041867912629, 0.0], 'a6': [1.246979603717467, 0.0], 'a7': [2.0489173395223053, 0.0], 'a8': [-2.3568958678922094, 0.0], 'a9': [-2.692021471630096, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3494717941596392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.1', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '2881572533478861958804546968490', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.246979603717467, 0], [2.0, 0]], [[1.0, 0], [0.5549581320873712, 0], [3.0, 0]], [[1.0, 0], [1.445041867912629, 0], [5.0, 0]], [[1.0, 0], [-2.0489173395223053, 0], [7.0, 0]], [[1.0, 0], [2.5549581320873713, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.2958969432397724, 0], [17.0, 0]], [[1.0, 0], [5.850855075327144, 0], [19.0, 0]], [[1.0, 0], [1.8900837358252576, 0], [23.0, 0]], [[1.0, 0], [-2.26874986787179, 0], [29.0, 0]], [[1.0, 0], [4.26874986787179, 0], [31.0, 0]], [[1.0, 0], [-5.356895867892209, 0], [37.0, 0]], [[1.0, 0], [-1.2741266790854493, 0], [41.0, 0]], [[1.0, 0], [-6.137063339542725, 0], [43.0, 0]], [[1.0, 0], [2.9510826604776947, 0], [47.0, 0]], [[1.0, 0], [-5.521106282802917, 0], [53.0, 0]], [[1.0, 0], [12.207750943219352, 0], [59.0, 0]], [[1.0, 0], [-8.564646811111562, 0], [61.0, 0]], [[1.0, 0], [-0.5767283962416943, 0], [67.0, 0]], [[1.0, 0], [4.594186792585485, 0], [71.0, 0]], [[1.0, 0], [10.55256522598143, 0], [73.0, 0]], [[1.0, 0], [15.777774565544576, 0], [79.0, 0]], [[1.0, 0], [-7.72348041480861, 0], [83.0, 0]], [[1.0, 0], [-6.613564150633867, 0], [89.0, 0]], [[1.0, 0], [-11.926919490217431, 0], [97.0, 0]], [[1.0, 0], [-13.063982829760155, 0], [101.0, 0]], [[1.0, 0], [-9.16852228272124, 0], [103.0, 0]], [[1.0, 0], [6.899772414849449, 0], [107.0, 0]], [[1.0, 0], [-0.12199784930487415, 0], [109.0, 0]], [[1.0, 0], [-7.307978528369904, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-13e2-1.1-c1-0-3', '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/169/2/a/b/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.915745562873095e-120, 0.08455309942584724, 0.17195563120175456, 0.26454806735225384, 0.36373489104995826, 0.4696797741786667, 0.5811159579384626, 0.6952432855829106, 0.8076895139751876, 0.9125316763833529, 1.002389348606072, 1.0686100800552762, 1.1015680236558705, 1.091091703770305, 1.0270275209061186, 0.8999331443907124, 0.7018802853636384, 0.4273304132096315, 0.07403094290596818, -0.3561352765305002, -0.8564260152921397, -1.4147269371052864, -2.0133360090241816, -2.6291230907559, -3.2341257658536566, -3.7966161094437316, -4.282637992673239, -4.657972434431864, -4.890442274199525, -4.952420942645117, -4.8233680559602785, -4.4921821213755075, -3.959142945344624, -3.237217885815418, -2.352530123692203, -1.3438350036522395, -0.26092117845028096, 0.8380569587087322, 1.8902067569946293, 2.8322700286491362, 3.605427735441166, 4.160143807163824, 4.460606123264624, 4.488313601447887, 4.2443957119836755, 3.7503365090545775, 3.0469059838427, 2.1912679718434283, 1.2524212913584623, 0.3053201255235321, -0.5758108979251804, -1.3243239966418965, -1.8874490493074763, -2.231349066045673, -2.3443238220778917, -2.2377268539945145, -1.9443985337443546, -1.5146979169452, -1.0105072032681, -0.49784894823367815, -0.03896124069361725, 0.3152119787259632, 0.5311619719880518, 0.5967625525312193, 0.522444684276013, 0.3393589872386419, 0.09468098465382142, -0.15538781680743505, -0.3540230960663385, -0.45244292066696873, -0.41759770285353554, -0.23772480434994953, 0.07514100680960671, 0.48620835615441643, 0.9425246420245704, 1.3805912748394231, 1.735970669797046, 1.953487056919888, 1.9964435899471578, 1.8533318430344878, 1.5408068190699091, 1.1022139066197074, 0.6016200790423478, 0.11402644012573981, -0.28688826060031125, -0.5416359470899025, -0.6162955393271942, -0.510369957676365, -0.2595113095340312, 0.0677837974619592, 0.3794839557103239, 0.5743148341192387, 0.5590948595244525, 0.2665009683914139, -0.3296526752193338, -1.204389753493653, -2.278949743757626, -3.4266955022874575, -4.487385315853741, -5.288273651245027, -5.669275014688699, -5.508549781348307, -4.744520698329643, -3.390600623259241, -1.5398060099214288, 0.642157053155572, 2.935014428960083, 5.0911442728988785, 6.868233609774759, 8.062660716384359, 8.538552413738559, 8.247926574787842, 7.238557025737971, 5.648022886323534, 3.6845494121989595, 1.5973667233963296, -0.3589508024385495, -1.960655004470282, -3.0458379316365254, -3.5354092175848466, -3.440776645460446, -2.857164084714575, -1.9439010164611241, -0.8952075686752612, 0.09341122774115752, 0.8573496800964417, 1.2881809497012624, 1.3478568444805368, 1.0697104727037037, 0.5465780136761176, -0.09128461181837282, -0.7039726643332922, -1.1699016180417081, -1.4085726024352478, -1.3938672522528408, -1.1555684933081125, -0.7692110067000364, -0.3367365425986651, 0.037714870608859925, 0.27158936254440846, 0.32213730823704684, 0.19515442105683986, -0.0575941550459413, -0.3516241855206443, -0.5906447029831831, -0.6903767915150436, -0.5998000730410453, -0.3148294400254127, 0.1189616734404888, 0.6155312576710231, 1.0677099734678428, 1.3725104437870477, 1.4566569660903959, 1.2962705736349796, 0.9257034900876985, 0.4327804750197594, -0.05927862529018068, -0.4198543878498354, -0.5429079123125485, -0.3756820758650161, 0.06289304949380317, 0.679243419834597, 1.319633029289383, 1.8002433295528886, 1.9473258797018933, 1.6392043147452278, 0.8408512836728363, -0.3772951688066527, -1.8417641746069793, -3.3009749101497916, -4.469091816502422, -5.080921372550116, -4.94706722428702, -3.997820555194787, -2.305954283005616, -0.08247536675643095, 2.355258888937152, 4.637919555507901, 6.411035921305404, 7.4012498115345515, 7.468621351145653, 6.634074841742293, 5.075911594900797, 3.0955685632461667, 1.0591667987277786, -0.6734914207904886, -1.8180814818989708, -2.2189545014504843, -1.8755424873959172, -0.9367616310957545, 0.33502750296362377, 1.6224962492440145, 2.621538907172915, 3.1045185783343854, 2.9651802592055128, 2.2360453601520516, 1.075290618019484, -0.27310430084002235, -1.5363142503394758, -2.4735202764676996, -2.926915782967708, -2.8517448708906206, -2.3193733801375043, -1.4937975278602726, -0.5881618822806284, 0.18766585348046466, 0.6756716736951353, 0.8029966231426618, 0.5926305693331425, 0.14995077044415986, -0.3704171570465166, -0.808171075875475, -1.0397591196655693, -1.00874295971792, -0.7366288935427284, -0.3120244841400589, 0.13821452680838806, 0.48741681239200413, 0.6462085702196915, 0.5878946201764438, 0.3550183137873317, 0.04529569498302565, -0.21904887938351456, -0.3297264261952743, -0.22737406696738824, 0.07744776034773362, 0.5040964477580406, 0.9235975980397029, 1.197051690636835, 1.2203091613637256, 0.9620655756510662, 0.4835610502636561, -0.06750679557622243, -0.4894635279133003, -0.578730210403201, -0.188647769627066, 0.7207161036897722, 2.0563757718502593, 3.5992327798075823, 5.0451381336014345, 6.0724371502922825, 6.420616082348262, 5.960592997068254, 4.737935869363474, 2.9759423527313684, 1.034893000242666, -0.6653246180218204, -1.7423502593663203, -1.945452547200822, -1.2233309440069722, 0.2523080077714896, 2.1152700821301376, 3.880932037450175, 5.053520896581512, 5.2401649636485805, 4.244910027397344, 2.120050603188798], 'positive_zeros': ['2.27315991722013939124163957550679', '4.52958182550039471163474635583111', '6.16677339140566145731511886703920', '7.51191873285717262157202617449543', '8.296094328891065865091021257589340', '8.973815934188217580884209870241545', '10.40712211024041910491450461924094', '11.09985480453711155356091186659229', '11.68876898935071458998037617007851'], 'prelabel': '2-13e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1616676780214035, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27315991722013939124163957551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.52958182550039471163474635583', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.16677339140566145731511886704', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.3494717941596392, 'bad_primes': [13], 'central_character': '1.1', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/2/a/b/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-13e2-1.1-c1-0-3', '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': '2-13e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1616676780214035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27315991722013939124163957551', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2881572533478861958804546968490', 'Lhash_array': ['2881572533478861958804546968490'], 'label': '2-13e2-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/2/a/b/1/1'}