-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '668155298128751493807487886058,2600763448384637846421332880423', 'a10': 3, 'a2': 1, 'a3': 0, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.99366952191765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1, 1]], [3, [1]], [7, [1, 1, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '1134.1', 'coefficient_field': '1.1.1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1, -1, 1], [1], [1, -3, 4, -15, 25], [1, 1, 1], [1, 3, -2, 33, 121], [1, -4, 3, -52, 169], [1, 12, 70, 204, 289], [1, 14, 87, 266, 361], [1, -3, -14, -69, 529], [1, 0, -29, 0, 841], [1, 5, -6, 155, 961], [1, 14, 123, 518, 1369], [1, -9, 40, -369, 1681], [1, -10, 57, -430, 1849], [1, 6, -11, 282, 2209], [1, -24, 250, -1272, 2809], [1, -6, -23, -354, 3481], [1, 8, 3, 488, 3721], [1, -4, -51, -268, 4489], [1, -18, 223, -1278, 5041], [1, -4, 150, -292, 5329], [1, -10, 21, -790, 6241], [1, 0, -83, 0, 6889], [1, -30, 403, -2670, 7921], [1, 8, -33, 776, 9409], [1, -6, -65, -606, 10201], [1, 5, -78, 515, 10609], [1, 24, 358, 2568, 11449], [1, -22, 339, -2398, 11881], [1, -18, 211, -2034, 12769]], 'euler_factors_factorization': [[[[1, -1, 1], 1]], [1], [[[1, -3, 4, -15, 25], 1]], [[[1, 1, 1], 1]], [[[1, 3, -2, 33, 121], 1]], [[[1, -4, 3, -52, 169], 1]], [[[1, 6, 17], 2]], [[[1, 7, 19], 2]], [[[1, -3, -14, -69, 529], 1]], [[[1, 0, -29, 0, 841], 1]], [[[1, 5, -6, 155, 961], 1]], [[[1, 7, 37], 2]], [[[1, -9, 40, -369, 1681], 1]], [[[1, -10, 57, -430, 1849], 1]], [[[1, 6, -11, 282, 2209], 1]], [[[1, -12, 53], 2]], [[[1, -6, -23, -354, 3481], 1]], [[[1, 8, 3, 488, 3721], 1]], [[[1, -4, -51, -268, 4489], 1]], [[[1, -9, 71], 2]], [[[1, -2, 73], 2]], [[[1, -10, 21, -790, 6241], 1]], [[[1, 0, -83, 0, 6889], 1]], [[[1, -15, 89], 2]], [[[1, 8, -33, 776, 9409], 1]], [[[1, -6, -65, -606, 10201], 1]], [[[1, 5, -78, 515, 10609], 1]], [[[1, 12, 107], 2]], [[[1, -11, 109], 2]], [[[1, -18, 211, -2034, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 20, 'label': '4-1134e2-1.1-c1e2-0-20', 'leading_term': '2.12421935149959912752349494074321128671958561481160154057050202526510796915407052897007229', 'load_key': 'CMFs-workshop', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1134/2/f/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [2.124219351499599, 2.116645290272285, 2.096460126307216, 2.061711192136801, 2.0124637866233788, 1.948947050026015, 1.8707876102710415, 1.777570310386138, 1.6689905100863232, 1.5447487073765331, 1.4045260006352456, 1.2480613359112604, 1.0751592367565732, 0.8857268725457328, 0.6797740850804289, 0.45746763997404677, 0.21912408030156574, -0.03473600321634564, -0.30340124051519207, -0.5859188918824404, -0.8811115471784079, -1.1875394589128048, -1.5035169101666523, -1.8270946501163567, -2.1560741958240457, -2.4880145022051177, -2.8202451358656084, -3.1498968969139103, -3.4739178824074854, -3.7891230829131595, -4.0922197348447895, -4.379866929447215, -4.648717426209054, -4.895476233529479, -5.1169640521443265, -5.310164944652316, -5.472311154662529, -5.600913964519381, -5.693863190276841, -5.749439360297049, -5.766416255450439, -5.744055195227921, -5.682196768466071, -5.581238780936699, -5.442204294550877, -5.266703692516015, -5.056970182509379, -4.815804073079392, -4.546573001971941, -4.2531344703223155, -3.9398037593691666, -3.6112518166144336, -3.272446742569628, -2.9285285570371054, -2.584730879375084, -2.2462401698150383, -1.9181040485226306, -1.6050883878636444, -1.311578689700298, -1.0414521609127851, -0.797979473820275, -0.5837294184206735, -0.4004804306624433, -0.24917207627272206, -0.12983851257463533, -0.04161445537495534, 0.017295186584424714, 0.04955504296410979, 0.058680253594611737, 0.04892878150748195, 0.025224695714592897, -0.006985020065196268, -0.041865390637409974, -0.07335652307511821, -0.09535848143348354, -0.10189574114535233, -0.08733593346944678, -0.046535001702872725, 0.02493179743861522, 0.13066552241495796, 0.27322488799704747, 0.4540820908955683, 0.6734422005059512, 0.9302722739606976, 1.2221841591405946, 1.545539531213579, 1.89541909554583, 2.2657934413438787, 2.6495958838370774, 3.0389371898023834, 3.4252886544716623, 3.7997114442792284, 4.1531401778109736, 4.476597381385048, 4.761547782556254, 5.000073414363363, 5.1852522815025175, 5.311274901821172, 5.373793601840536, 5.369965141732881, 5.298720460938126, 5.160720638667183, 4.958510832163853, 4.6963794180418965, 4.380380951496071, 4.018093252526815, 3.6185171994949625, 3.1917363082131693, 2.7487198567871607, 2.30090608502786, 1.8599442418572179, 1.437244382102503, 1.0436945552172339, 0.6892371764174089, 0.3825971217970882, 0.13094807539732817, -0.060311595038306506, -0.18775137758404142, -0.2500467393457023, -0.24800432024811067, -0.1845779710265051, -0.06473088495003404, 0.10469620425207839, 0.315254613581143, 0.5571712292822377, 0.8197020396665358, 1.0915402866016541, 1.3612006373160621, 1.617494802447459, 1.8498934525484216, 2.0489935328431015, 2.2068076219455386, 2.3171463060373303, 2.37578849378937, 2.380719564893751, 2.3321431464324043, 2.2325460373249832, 2.0865260062434943, 1.9006879784164084, 1.6832879297822225, 1.443990204718344, 1.1933651695814387, 0.9425509524982498, 0.7026794131107219, 0.4844942443972066, 0.2978009004662641, 0.15110107481575238, 0.051159710225914895, 0.0027225356726047352, 0.008267835947110077, 0.06787381018262928, 0.17918326764975384, 0.33747318363106116, 0.5358211978024259, 0.7653947011123128, 1.015780976630299, 1.2754618125651145, 1.532255573603109, 1.7738919286465307, 1.9885076174323353, 2.165202702116447, 2.294526448164194, 2.368893974438589, 2.3829926865410522, 2.3339686810182623, 2.2216813002027, 2.0486231836145863, 1.8199592096540562, 1.5432037313499, 1.228012016154326, 0.8856786464873884, 0.5287107905921201, 0.1702234742209555, -0.17660822960205763, -0.49918236163328567, -0.7859975513417343, -1.0272419771530896, -1.2151553816027834, -1.3445008036511221, -1.4126555660270288, -1.4198935287239045, -1.3691704209527837, -1.266155521714305, -1.1187554147272076, -0.9368671445470618, -0.7317422548842718, -0.5154944485874244, -0.3004269271142877, -0.09839745654160087, 0.07977450477175553, 0.22493296738425603, 0.33000373205156003, 0.39044852290373677, 0.4044428892965846, 0.37303469078210155, 0.3000495449669974, 0.19190021727931467, 0.05722863335689876, -0.09360443926017864, -0.24908070927386214, -0.39725635246325885, -0.5264097606998914, -0.6258567657101172, -0.6865262899362702, -0.7017050724069003, -0.6673792209450798, -0.5827599028470619, -0.45027256300770163, -0.27574054061108055, -0.06798552489814695, 0.16140437825149434, 0.39880417725178985, 0.6291958844329244, 0.8370915128176085, 1.007485588833552, 1.1267960326714492, 1.1839236350721716, 1.1710344946946587, 1.0844646035959324, 0.9251935102069341, 0.6993366544397667, 0.41820470699713386, 0.09819950744528118, -0.23958498931398714, -0.5701246642060238, -0.8652873057510473, -1.0951770046501221, -1.2292488022218266, -1.238045728775754, -1.0943794127386444, -0.7751994789106055, -0.2625502625215442, 0.4547188077769719, 1.38049823858043, 2.510163039526304, 3.830795306312366, 5.320654009454902, 6.950083784644279, 8.681908415687388, 10.472856542547738, 12.274942403364099, 14.037114994964822, 15.707489214021669, 17.234899877011802, 18.571617624199177, 19.67454662548078, 20.507902156776172, 21.043865050439543, 21.264686725613174, 21.16267466343951, 20.741334730984082, 20.01461024736166, 19.006927141124883, 17.751663606508792, 16.290247925341482, 14.669925412414484, 12.94227453975815, 11.160482333600623, 9.377716763176023, 7.644306102269901, 6.0063288838957005, 4.503232419993771, 3.1668588643065827, 2.0200262418448514, 1.0760867076879923, 0.33880270225669695, -0.19754605599961503, -0.5469709321834659, -0.7311540178555551, -0.777251611750758, -0.7168501257185004, -0.5833153333208417, -0.41049306400530605, -0.2302244859516069, -0.07106335079412554, 0.043542844545236756, 0.09616137726504494, 0.0762665731519612, -0.019560675212368026, -0.18768862567317782, -0.4181148726126924, -0.6953074172403766, -0.9996847849407733, -1.3089594037892713, -1.600095565653843, -1.8508037600247695, -2.041510969520546, -2.1566278180097007, -2.186070529121271, -2.1259454799687965, -1.9792972450987851, -1.755959635516492, -1.472400274324526, -1.150682489965732, -0.8174741884551634, -0.5023059611496081, -0.2359800557951441, -0.048517376498654605, 0.03267099045661585, -0.015341225649481146, -0.2093694625322745, -0.5588555355312057, -1.0648963617395293, -1.7198394060747362, -2.507338204850977, -3.402806819705775, -4.374675450514701, -5.385494451697136, -6.39427298602912, -7.3578945787059045, -8.234126667778954, -8.982965457730984, -9.569706205557841, -9.965858881737693, -10.151640116324039, -10.116175587361262, -9.858928147154868, -9.389020776511112, -8.725397257494793, -7.895267912939117, -6.933100551608661, -5.878416226924386, -4.773932161969467, -3.663153731456032, -2.588117458720988, -1.5873438316483264, -0.6936634075151066, 0.06694729199175267, 0.6770203838018477, 1.1275594640888424, 1.4188594762348516, 1.5592559560719739, 1.5649816053534467, 1.4579976490777058, 1.2649936813790048, 1.0148080650181774, 0.73691635680084, 0.4590108966517008, 0.20548636387957667, -0.0043243956135623285, -0.1571437663372456, -0.24652956967158093, -0.2729759241148906, -0.24360427623298136, -0.17127589173189672, -0.07332639590209226, 0.030098283729878796, 0.11791316384284517, 0.17008424229417315, 0.16959754384603123, 0.10422059890927908, -0.03198031560056548, -0.2376258573798197, -0.503389592255875, -0.8121032849326997, -1.1391743557831326, -1.4539573151112215, -1.7210613024297983, -1.9028609831976453, -1.9612461248925772, -1.8608670129888922, -1.570730734017667, -1.0675517202696858, -0.3366338559538678, 0.6254009911965712, 1.8108189753835828, 3.1993024971039072, 4.759353456315093, 6.44842793246028, 8.21537038166588, 10.00210712163931, 11.746701298028714, 13.38617721999434, 14.859602475755317, 16.111375427115494, 17.093646226360963, 17.76936912205113, 18.113403185255063, 18.1147926038214, 17.77608288933042, 17.11454352107315, 16.15961914399454, 14.953046561247868, 13.544831032882687, 11.992418830068557, 10.35597669534008, 8.696959611913066, 7.073641008486543, 5.5395469418648515, 4.140080808382565, 2.9113473255341136, 1.878383010851645, 1.0548249861374381, 0.4428248320397394, 0.03380129928224126, -0.1902645654621992, -0.255089074493944, -0.1919404623059436, -0.035342057876496344, 0.1793161274988103, 0.41800661544758494, 0.6501319144648056, 0.8500892757160737, 0.9985845843229554, 1.0831672689795195, 1.0985553594368094, 1.0461128774687256, 0.9331955196411196, 0.7718512112116144, 0.5774578921506598, 0.3670966222045207, 0.15796729352147526, -0.03410876811083339, -0.1959451512146925, -0.31799986525130497, -0.3948879368879661, -0.42570122817250045, -0.4136460040480707, -0.36565426980372484, -0.2913363956939739, -0.20204945466105517, -0.10958725575342124, -0.02502600117849163, 0.0423663564991391, 0.08610386419822048, 0.10298983238149076, 0.0935445284665257, 0.06178897123400247, 0.014939704423232458, -0.03743235800596072, -0.08436088009565604, -0.1146598650454148, -0.11820968761551207, -0.08706802335558618, -0.016628851085846608, 0.09373564339081634, 0.2400571158976797, 0.41389023998604063, 0.6024691363173273, 0.7896552092636845, 0.9568592945763355, 1.084597171904547, 1.1539433449942906, 1.1482223463704297, 1.0545980691884875, 0.8653264726918679, 0.5790125256831934, 0.20095614590703795, -0.2563549699400776, -0.7739843199306952, -1.3270947096294268, -1.886582401871038, -2.420677331954927, -2.8969816629165073, -3.28480012977704, -3.5569732159357144, -3.6923155728786328, -3.676713309704295, -3.504927729803551, -3.1806355980512624, -2.7169954002344654, -2.1355821654927967, -1.4654757736196746, -0.7413246783999401, -0.0011680011839494892, 0.7158903004222962, 1.3725385075259995, 1.9353271033888242, 2.377449960056244, 2.6798846887427743, 2.8334210033845, 2.8383886466982213, 2.7054544337352295, 2.4537931643573176, 2.1107537787164996, 1.708811224149042, 1.2835210292847128, 0.8705183367204705, 0.5049834664522712, 0.2162106349529279], 'positive_zeros': ['0.52708159331006191865992390189973', '2.05164060815842562480150541530895', '2.21237225023772979770243576228854', '2.42810963841338972513826963496160', '3.61397700878471967169425439184485', '3.79421652203593157403378953867450', '4.62988275667730495171662040456155', '4.64501113420199188984415023812766', '5.39013433183998221583354016950926', '5.89162690390824851179670978583514', '6.16837736391229946838681691161386', '6.54074369264001809800659256991370', '6.94665877024398364258631591236200', '7.23127755651231028803050604544065', '8.299611877144388942130204100970931', '8.580036781848298818569007847199345', '8.682706816228100642796548089708858', '9.294385969806531741035839376068829', '9.339331760542930896811336916456160', '10.21573703022119596023887242262726'], 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1712271117780885824, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52708159331006191865992390190', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05164060815842562480150541531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.21237225023772979770243576229', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 81.99366952191765, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1285956, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 0, 3, 0, -1, -1, 0, 3, -3, 0, 4, -1, 0, -1, -12, 0, -14, 0, 0, -3, 3, 0, 5, 4, 0, 0, 0, 0, -5, 0, 0, -12, -3, 0, -14, -14, 0, -3, 9, 0, 10, 0, 0, 3, -6, 0, 0, 5, 0, 0, 24, 0, -9, 1, 0, 0, 6, 0, -8, -5, 0, 1, 12, 0, 4, 0, 0, -3, 18, 0, 4, -14, 0, 0, 3, 0, 10, -3, 0, 9, 0, 0, -36, 10, 0, 3, 30, 0, -4, 0, 0, -6, -42, 0, -8, 0, 0, 0], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, -4, 3, -52, 169], 'euler17': [1, 12, 70, 204, 289], 'euler19': [1, 14, 87, 266, 361], 'euler2': [1, -1, 1, 0, 0], 'euler23': [1, -3, -14, -69, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 5, -6, 155, 961], 'euler37': [1, 14, 123, 518, 1369], 'euler41': [1, -9, 40, -369, 1681], 'euler43': [1, -10, 57, -430, 1849], 'euler47': [1, 6, -11, 282, 2209], 'euler5': [1, -3, 4, -15, 25], 'euler53': [1, -24, 250, -1272, 2809], 'euler59': [1, -6, -23, -354, 3481], 'euler61': [1, 8, 3, 488, 3721], 'euler67': [1, -4, -51, -268, 4489], 'euler7': [1, 1, 1, 0, 0], 'euler71': [1, -18, 223, -1278, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, -10, 21, -790, 6241], 'euler83': [1, 0, -83, 0, 6889], 'euler89': [1, -30, 403, -2670, 7921], 'euler97': [1, 8, -33, 776, 9409], 'euler_factors': [[1, -1, 1, 0, 0], [1, 0, 0, 0, 0], [1, -3, 4, -15, 25], [1, 1, 1, 0, 0], [1, 3, -2, 33, 121], [1, -4, 3, -52, 169], [1, 12, 70, 204, 289], [1, 14, 87, 266, 361], [1, -3, -14, -69, 529], [1, 0, -29, 0, 841], [1, 5, -6, 155, 961], [1, 14, 123, 518, 1369], [1, -9, 40, -369, 1681], [1, -10, 57, -430, 1849], [1, 6, -11, 282, 2209], [1, -24, 250, -1272, 2809], [1, -6, -23, -354, 3481], [1, 8, 3, 488, 3721], [1, -4, -51, -268, 4489], [1, -18, 223, -1278, 5041], [1, -4, 150, -292, 5329], [1, -10, 21, -790, 6241], [1, 0, -83, 0, 6889], [1, -30, 403, -2670, 7921], [1, 8, -33, 776, 9409]], 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1134/2/f/o'], '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': '4-1134e2-1.1-c1e2-0-20', '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': 0, 'prelabel': '4-1134e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.00915861815445, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1712271117780885824, 'z1': {'__RealLiteral__': 0, 'data': '0.52708159331006191865992390190', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '668155298128751493807487886058,2600763448384637846421332880423', 'Lhash_array': ['668155298128751493807487886058', '2600763448384637846421332880423'], 'label': '4-1134e2-1.1-c1e2-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1134/2/f/o'}