-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2926868619710159891485471692135', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [6.130083814555983, -6.130083814555983], 'a4': [0.0, 0.0], 'a5': [3.859309191160408, 10.493127873376213], 'a6': [0.0, 0.0], 'a7': [-24.756432761452142, -24.756432761452142], 'a8': [0.0, 0.0], 'a9': [0.0, -48.155855146962445], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.440305600918503, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-3.859309191160408, -10.493127873376213]]]], 'bad_primes': [2, 5], 'central_character': '160.63', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '1187504619691657937773367925202', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-6.130083814555983, 6.130083814555983], [0, -27.0]], [[1.0, 0], [-3.859309191160408, -10.493127873376213]], [[1.0, 0], [24.756432761452142, 24.756432761452142], [0, 343.0]], [[1.0, 0], [0, 39.896882735242194], [-1331.0, 0]], [[1.0, 0], [-3.9140050825032744, -3.9140050825032744], [0, 2197.0]], [[1.0, 0], [-42.30711266348776, 42.30711266348776], [0, -4913.0]], [[1.0, 0], [-61.016584422998136, 0], [6859.0, 0]], [[1.0, 0], [-41.125510503150764, 41.125510503150764], [0, -12167.0]], [[1.0, 0], [0, -57.29512587092676], [-24389.0, 0]], [[1.0, 0], [0, -228.7678413431523], [-29791.0, 0]], [[1.0, 0], [-231.47785102692563, 231.47785102692563], [0, -50653.0]], [[1.0, 0], [-78.1642562873483, 0], [68921.0, 0]], [[1.0, 0], [147.05605137058834, -147.05605137058834], [0, -79507.0]], [[1.0, 0], [-34.75890376943136, -34.75890376943136], [0, 103823.0]], [[1.0, 0], [-132.875162757544, -132.875162757544], [0, 148877.0]], [[1.0, 0], [275.6829606126334, 0], [205379.0, 0]], [[1.0, 0], [322.19493742243344, 0], [226981.0, 0]], [[1.0, 0], [-89.63965943274258, -89.63965943274258], [0, 300763.0]], [[1.0, 0], [0, -292.2318086059588], [-357911.0, 0]], [[1.0, 0], [-299.66925097802965, -299.66925097802965], [0, 389017.0]], [[1.0, 0], [-227.28023503835132, 0], [493039.0, 0]], [[1.0, 0], [-287.6630734580816, 287.6630734580816], [0, -571787.0]], [[1.0, 0], [0, -471.69513871764224], [-704969.0, 0]], [[1.0, 0], [-1200.491827614585, 1200.491827614585], [0, -912673.0]], [[1.0, 0], [767.393409731762, 0], [1030301.0, 0]], [[1.0, 0], [-931.5046436060827, 931.5046436060827], [0, -1092727.0]], [[1.0, 0], [-647.000062379336, -647.000062379336], [0, 1225043.0]], [[1.0, 0], [0, 764.4888633250371], [-1295029.0, 0]], [[1.0, 0], [-1621.219418947419, -1621.219418947419], [0, 1442897.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-160-20.3-c3-0-14', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/160/4/n/c/63/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.1887033511776695, 2.4141586902931964, 2.6141542222108645, 2.7853154649060374, 2.9238386823128373, 3.0255305101922993, 3.0859565857282374, 3.1006949142473816, 3.0656809513246794, 2.9776234756415083, 2.834463343901519, 2.635841180696868, 2.3835351201883204, 2.081826258730882, 1.737748085788173, 1.3611775485133457, 0.9647302815765216, 0.5634314524713266, 0.17414689050366752, -0.18522347815092569, -0.4967670488835303, -0.7437489141986007, -0.9119017742661167, -0.9907241985767631, -0.9746786093553097, -0.8641698833679614, -0.666184447917214, -0.3944801706527575, -0.0692403831228632, 0.28385891841226624, 0.635172601310623, 0.953148973021455, 1.2068198805493564, 1.3685482592516836, 1.4168122373496632, 1.3387685503500737, 1.1323224577090254, 0.807441676648764, 0.3864911042621155, -0.09656642672824926, -0.5981634157274961, -1.0682606011240354, -1.4544407124514591, -1.7066623437419655, -1.7822678250222141, -1.6507643156711154, -1.297866110577681, -0.7283076897450522, 0.03298426299388438, 0.9416376547966308, 1.9365978568974602, 2.944792442791857, 3.887362492207849, 4.686919696176249, 5.275125072974878, 5.599788106828563, 5.630673508807789, 5.363286960002406, 4.820090531982398, 4.048860144456718, 3.118216556117873, 2.1107030104038875, 1.1141051796453871, 0.2119691133449144, -0.5255689377632592, -1.0495003878621387, -1.3371893263700867, -1.3943868206011816, -1.253638600303221, -0.9691691823980437, -0.6088046784308354, -0.24393113858102958, 0.06118895567244633, 0.25925699615534276, 0.32748697466455085, 0.27166020342642305, 0.12591940442813843, -0.05188764711647747, -0.18886065571319247, -0.20861974295583588, -0.04421801586772655, 0.34949136081092197, 0.9859616955670031, 1.8412166292388112, 2.853439029507685, 3.9283235381871586, 4.9497851466439275, 5.794774214425178, 6.350240703505074, 6.529835966937133, 6.287827292205958, 5.627969446590101, 4.60571223230584, 3.3230479612422745, 1.9163908394018636, 0.5389698492761468, -0.6598648430945554, -1.5554310277605943, -2.0654582205768026, -2.161984887307031, -1.8754092782356404, -1.2898514519919937, -0.5303272858188691, 0.25644641815520386, 0.92472140686365, 1.3523248572735862, 1.4595824735332525, 1.2214498195862347, 0.670793016972042, -0.10781114619927659, -0.9928059545097834, -1.8465021076985872, -2.538536317815027, -2.9679225681907204, -3.0798536432885895, -2.8742701632145016, -2.404628814589173, -1.7670365908264458, -1.0816710875602311, -0.46985913780950006, -0.031059448501440025, 0.17589382401799294, 0.14363028780807227, -0.08307790199412296, -0.41715327535664026, -0.7478978651980445, -0.9650764808967459, -0.9837630225132629, -0.7649766091349471, -0.3277483374479451, 0.25024951188066424, 0.844259929846825, 1.3045640863835861, 1.4853854864439129, 1.2752570166383597, 0.6229616508499155, -0.44629318705520915, -1.828191638330058, -3.3514217706201803, -4.803104412552068, -5.963431711485105, -6.643460394875998, -6.719144532272442, -6.155133608836195, -5.013569511552045, -3.445804589368863, -1.6681409251400223, 0.07424869219574284, 1.5487206231911252, 2.5742525929461495, 3.050932281472062, 2.97431424114884, 2.4320024343534543, 1.5832651721671738, 0.6258197490218183, -0.24354119063623073, -0.8666010964735458, -1.1521559503862575, -1.0896714407974866, -0.7456880171925333, -0.24412441279313613, 0.2649715763247842, 0.6412295543390155, 0.7863684399711544, 0.6660264800073808, 0.31617005345291405, -0.1673120365757457, -0.6534167463724567, -1.0094981027400858, -1.135567688280835, -0.9912307380472221, -0.6085695689403343, -0.08737202661392937, 0.4268800521592125, 0.777780687143813, 0.8378551479646994, 0.5442737979553771, -0.07830091096593624, -0.9139321378282959, -1.7728268390756363, -2.427352255208261, -2.659680943063028, -2.3111017617429317, -1.322149128556103, 0.245789478553718, 2.2130721373861113, 4.30922679395848, 6.22043039199765, 7.647750258783347, 8.364240314182355, 8.258917147630337, 7.358205473964715, 5.8201313620220825, 3.9023535988367524, 1.9107785772943362, 0.13972920186957213, -1.1835400066751882, -1.9382139433560726, -2.125074964396865, -1.8548472653409036, -1.3132060506089347, -0.7111887229114984, -0.23295650601414514, 0.0067426204028618415, -0.014428265689280845, -0.22793061720182337, -0.49938707169160534, -0.6703236224354824, -0.6057221398111553, -0.23506656007646007, 0.4238027789352498, 1.2643975971123997, 2.115263191203843, 2.781900099013168, 3.096404319768121, 2.962100778250802, 2.3814360310253857, 1.4594044656458813, 0.38086539555494137, -0.6332235210862771, -1.3800566819891624, -1.7260835263284238, -1.6416925603518246, -1.2099698907742304, -0.6063473077840078, -0.05330903627227947, 0.23912216425930358, 0.13234118196875758, -0.39766830164344236, -1.2447776050644774, -2.1900856805103106, -2.9494394760100504, -3.2406341058130725, -2.8544923158262887, -1.7124559228131695, 0.10397431118070799, 2.360194553664926, 4.7114620191754115, 6.77273185002143, 8.199540624401092, 8.76118028884339, 8.389028578598042, 7.188737928505681, 5.413630396302143, 3.40597045152924, 1.5204646402247906, 0.048437116333908396, -0.8393818975084892, -1.1185048853461212, -0.900001020539943, -0.38796094205095205, 0.1824593888428799, 0.6094146185391528, 0.7741342032793223, 0.6635292053715689, 0.3608703570906155, 0.008717315870481685], 'positive_zeros': ['2.30889222880753008753700742542978', '3.52498072883615748661478342056928', '4.85076643559975961732569745604432', '5.99509718575553152122499575191760', '7.907814093646970764767799608099878', '8.971639218404035033984019509143527', '9.587963114167670564685050270951366', '10.01895452225938394840557352162084', '11.92808671908459148613566774020329', '12.83326400786682281433026953230043'], 'prelabel': '2-160-20.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': 0.5640236470413371, 'root_number': '-0.19978277277909892 + 0.9798402133514907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.282011823521', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30889222880753008753700742543', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52498072883615748661478342057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85076643559975961732569745604', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.440305600918503, 'bad_primes': [2, 5], 'central_character': '20.3', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/4/n/c/63/4'], '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': '2-160-20.3-c3-0-14', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-160-20.3-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': 0.28201182352066856, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30889222880753008753700742543', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2926868619710159891485471692135', 'Lhash_array': ['2926868619710159891485471692135'], 'label': '2-160-20.3-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/4/n/c/63/4'}