-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1783641925543960843059138057783', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [3.23606797749979, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': 'CDF', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.23606797749979, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.47213595499958, 0], [11.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [13.0, 0]], [[1.0, 0], [3.23606797749979, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [8.47213595499958, 0], [23.0, 0]], [[1.0, 0], [2.76393202250021, 0], [29.0, 0]], [[1.0, 0], [2.4721359549995796, 0], [31.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [37.0, 0]], [[1.0, 0], [-2.0, 0], [41.0, 0]], [[1.0, 0], [-8.0, 0], [43.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [47.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [53.0, 0]], [[1.0, 0], [-4.0, 0], [59.0, 0]], [[1.0, 0], [12.47213595499958, 0], [61.0, 0]], [[1.0, 0], [10.47213595499958, 0], [67.0, 0]], [[1.0, 0], [0.7639320225002103, 0], [71.0, 0]], [[1.0, 0], [4.47213595499958, 0], [73.0, 0]], [[1.0, 0], [12.0, 0], [79.0, 0]], [[1.0, 0], [7.708203932499369, 0], [83.0, 0]], [[1.0, 0], [-6.944271909999159, 0], [89.0, 0]], [[1.0, 0], [-12.47213595499958, 0], [97.0, 0]], [[1.0, 0], [-4.180339887498948, 0], [101.0, 0]], [[1.0, 0], [-8.94427190999916, 0], [103.0, 0]], [[1.0, 0], [5.708203932499369, 0], [107.0, 0]], [[1.0, 0], [2.9442719099991588, 0], [109.0, 0]], [[1.0, 0], [10.76393202250021, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 120, 'label': '2-9576-1.1-c1-0-120', '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/9576/2/a/bq/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.1388604131554472e-60, 0.2427111618165901, 0.48390142764673716, 0.7220059861218021, 0.955376085245636, 1.1822464934766235, 1.4007134920588171, 1.6087257003039148, 1.8040891811715365, 1.9844873904456246, 2.147515688632695, 2.290729380509969, 2.4117036115935666, 2.5081029432570157, 2.5777580446827955, 2.6187466685074154, 2.6294759038534203, 2.608762612854659, 2.5559089457592297, 2.4707698903441235, 2.3538099424069636, 2.206146186681498, 2.029575353880652, 1.826582771599983, 1.6003315548665835, 1.354630884038983, 1.093882788212122, 0.8230074823298149, 0.5473479831986395, 0.2725554372430724, 0.004457311532506404, -0.2510886930801849, -0.4883514765128855, -0.701889981999743, -0.8867185855548725, -1.038469363686107, -1.1535459007851332, -1.2292631864814094, -1.263968218028941, -1.257136175705425, -1.2094374865903685, -1.122771733679169, -1.000265195624455, -0.8462298024992011, -0.6660824422959947, -0.46622482151609457, -0.2538854344592392, -0.03692658705003775, 0.17637919521011036, 0.37759772007858056, 0.5583997722971872, 0.7108379263732311, 0.8276247674173344, 0.9024031781563351, 0.9299990666534256, 0.9066469535023686, 0.8301792295334557, 0.7001706437420941, 0.5180306815618743, 0.28703792731117383, 0.012312239180874008, -0.2992774456866758, -0.6392696736831669, -0.9978290924522113, -1.3640224561044938, -1.7261450359692962, -2.0720882722785094, -2.3897375419763507, -2.6673872677861925, -2.8941593345695806, -3.060409981144708, -3.1581100553023282, -3.181183795784546, -3.1257921566732523, -2.990548114371093, -2.776653369559993, -2.487948327301001, -2.130870136247841, -1.714316800210698, -1.2494188310353234, -0.7492234650879639, -0.22829998019204065, 0.2977220161421645, 0.8126664445316225, 1.3003593207905872, 1.7451926224867538, 2.132682758932794, 2.4500024312870337, 2.6864649755542613, 2.8339414335409527, 2.8871925837950667, 2.8441009394176806, 2.7057912004018263, 2.4766317195230982, 2.1641140574719864, 1.778612494405037, 1.3330302419289892, 0.8423438605650521, 0.323061828325866, -0.20738287320915622, -0.7312830731979356, -1.2313251956205713, -1.6912477324949957, -2.096463366901636, -2.434618588188403, -2.696066664752694, -2.874232955028506, -2.9658556456162444, -2.9710899601092327, -2.893469493306385, -2.739724367139066, -2.519462123278477, -2.244723392415828, -1.9294301355125283, -1.5887493686592207, -1.238399510755721, -0.8939296138632796, -0.5700035745051832, -0.2797218577227059, -0.034012231918948435, 0.15888148554078377, 0.2937875636093766, 0.36885141281246603, 0.3856238022124398, 0.34898548111274214, 0.26690894611292754, 0.15006575238032427, 0.011295232759716035, -0.13504259702157648, -0.27380114648403325, -0.38983475228358727, -0.4688026023782938, -0.4979504285623104, -0.46683142955698, -0.367929848527609, -0.1971543960869478, 0.04582584565042537, 0.3574234937041221, 0.7301652829617908, 1.1529183068879993, 1.6113042445094081, 2.0882864580006992, 2.5649060465025104, 3.0211350663525223, 3.436808585897915, 3.792592391682563, 4.070940286947116, 4.2569942192196715, 4.339382036255481, 4.310871484535839, 4.168845005977654, 3.915567721465129, 3.5582303787168232, 3.1087595643828236, 2.5833986453200657, 2.0020741751528512, 1.387573322784661, 0.7645677000891277, 0.15852727241902453, -0.40542562406942534, -0.9036681249574138, -1.31517908545092, -1.6225375791166106, -1.812767513096465, -1.8779848267153498, -1.8158126494002047, -1.6295406130215593, -1.3280167386137998, -0.9252733595179348, -0.4399017581574129, 0.10579708619393889, 0.6868466742502054, 1.2767653235378773, 1.8488164035627805, 2.377277443049446, 2.838665347794725, 3.212856408096786, 3.484044374795287, 3.6414874616312614, 3.6800053484196935, 3.6001996287831903, 3.408385059476755, 3.116233723843664, 2.7401490596971887, 2.3004008429010243, 1.8200649051909603, 1.323821904440857, 0.8366772652930153, 0.38266901105764567, -0.01636867974719572, -0.34192084840382153, -0.5797267297312949, -0.7204842518525038, -0.7602860454066829, -0.7007631847401046, -0.5489285631395003, -0.316728089956188, -0.020323907706981607, 0.3208513199494216, 0.6852171364166614, 1.0502829901085693, 1.3939320502287562, 1.6956792361429316, 1.9378324806208724, 2.1064911543972697, 2.1923242526432296, 2.1910829516226036, 2.103816859843001, 1.93677992284362, 1.7010295827470994, 1.411740458188544, 1.087270493840325, 0.7480322658845776, 0.4152340482437192, 0.10956361683873207, -0.15010794249242632, -0.3479252668864113, -0.47207801137722666, -0.5155966836296267, -0.4768639963616585, -0.3598065933319504, -0.17375019932435717, 0.06705925567392462, 0.3442462889835477, 0.6363672860027619, 0.9201849673784676, 1.172084522258872, 1.3695502752215403, 1.4926165499099717, 1.5252061247730901, 1.4562744555086202, 1.2806874832938357, 0.9997748893141681, 0.6215183609542134, 0.16035484212308723, -0.3634032876503723, -0.924506873705583, -1.4940219450982886, -2.0408303579473137, -2.5332988259896667, -2.941024722230722, -3.2365608192576194, -3.397020474540826, -3.4054697961900238, -3.2520238483834563, -2.9345794526913447, -2.459136789678862, -1.839684724858362, -1.0976492963149873, -0.26092970403592436, 0.6374300161908089, 1.5608640778712337, 2.47111561233271, 3.3301749630426407, 4.102218515413022, 4.7554399780292105, 5.263671308801576], 'positive_zeros': ['1.40704538397475749011271734053890', '2.21113185854446894071579297139156', '2.81445499711354156946386247002357', '3.81719112521580628574694423563830', '4.62231608038667603239056930204534', '5.58549832141792829673213412357894', '5.95676842864901874450457831268523', '6.36711393436554598551836789273214', '7.41899486715441144324200888190771'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, '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': '1.40704538397475749011271734054', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21113185854446894071579297139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81445499711354156946386247002', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'index': 120, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bq/1/2'], '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': '2-9576-1.1-c1-0-120', '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': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40704538397475749011271734054', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1783641925543960843059138057783', 'Lhash_array': ['1783641925543960843059138057783'], 'label': '2-9576-1.1-c1-0-120', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bq/1/2'}