-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '107831285071555453079244743942,1957075020085287059269690984342', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -8, 'a6': 0, 'a7': 20, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5557.792009410902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 38, 361]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 8, 66, 200, 625], [1, -20, 198, -980, 2401], [1, -20, 342, -2420, 14641], [1, 0, 250, 0, 28561], [1, 20, 678, 5780, 83521], [1, 38, 361], [1, 40, 1458, 21160, 279841], [1, 0, -482, 0, 707281], [1, 0, -1622, 0, 923521], [1, 0, -2630, 0, 1874161], [1, 0, -2162, 0, 2825761], [1, -20, 3798, -36980, 3418801], [1, 160, 10818, 353440, 4879681], [1, 0, -3890, 0, 7890481], [1, 0, -5762, 0, 12117361], [1, 20, 7542, 74420, 13845841], [1, 0, -3170, 0, 20151121], [1, 0, 718, 0, 25411681], [1, 20, 10758, 106580, 28398241], [1, 0, -12182, 0, 38950081], [1, -140, 18678, -964460, 47458321], [1, 0, -5042, 0, 62742241], [1, 0, -13010, 0, 88529281], [1, None, None, None, 104060401], [1, 0, 12490, 0, 112550881], [1, 0, -19010, 0, 131079601], [1, 0, 538, 0, 141158161], [1, 0, -25490, 0, 163047361]], 'euler_factors_factorization': [[1], [1], [[[1, 4, 25], 2]], [[[1, -10, 49], 2]], [[[1, -10, 121], 2]], [[[1, 0, 250, 0, 28561], 1]], [[[1, 10, 289], 2]], [[[1, 19], 2]], [[[1, 20, 529], 2]], [[[1, 0, -482, 0, 707281], 1]], [[[1, 0, -1622, 0, 923521], 1]], [[[1, 0, -2630, 0, 1874161], 1]], [[[1, 0, -2162, 0, 2825761], 1]], [[[1, -10, 1849], 2]], [[[1, 80, 2209], 2]], [[[1, 0, -3890, 0, 7890481], 1]], [[[1, 0, -5762, 0, 12117361], 1]], [[[1, 10, 3721], 2]], [[[1, 0, -3170, 0, 20151121], 1]], [[[1, 0, 718, 0, 25411681], 1]], [[[1, 10, 5329], 2]], [[[1, 0, -12182, 0, 38950081], 1]], [[[1, -70, 6889], 2]], [[[1, 0, -5042, 0, 62742241], 1]], [[[1, 0, -13010, 0, 88529281], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 2, 'label': '4-2736e2-1.1-c2e2-0-2', 'leading_term': '0.139273410343032360693554519049371614597465769757412416872477548609287441059471038627890376', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2736/3/o/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [0.13927341034303234, 0.1267708429498224, 0.08932169393473173, 0.027371246141366927, -0.058428767348848505, -0.16718087095052542, -0.2977245407367231, -0.4486561325255884, -0.6183468583330561, -0.8049512441510913, -1.0064218893852934, -1.2205249895202053, -1.444863176572293, -1.6768923567580774, -1.9139506607690837, -2.153276899321754, -2.3920472256946534, -2.6273933466584998, -2.856447356591158, -3.076357874391717, -3.28434344159152, -3.477704248636449, -3.6538839367813316, -3.810474335247661, -3.94528491853301, -4.056337847331785, -4.141943640780021, -4.2006838968318085, -4.231491037651242, -4.2336163957452175, -4.206711248040404, -4.150778511279253, -4.066251780834597, -3.9539296762918283, -3.81504932431703, -3.651203405298223, -3.4644045349269375, -3.2569862334028032, -3.031655016856456, -2.7913777671336306, -2.539419062519828, -2.279218673594618, -2.0144127286978177, -1.748706190147212, -1.485877810416811, -1.2296533365287168, -0.9836957755438986, -0.7514856194300448, -0.5362995749894337, -0.3411041974615007, -0.16852779444213928, -0.02077343062664885, 0.10040998395585633, 0.19379033886654906, 0.25867516458643364, 0.29494647664193907, 0.30307036227161865, 0.2841025818179064, 0.2396781109658536, 0.17198842424478722, 0.08374534894511858, -0.021866493261201655, -0.14125527947107358, -0.2704883907818121, -0.4053886794273899, -0.5416114824088138, -0.6747697862055312, -0.8005118917355125, -0.9146704764587543, -1.0133299896300618, -1.0929914782221284, -1.1506187656247935, -1.1838082102191696, -1.1908037441522457, -1.1706588188181202, -1.1232124697626364, -1.0492298830589395, -0.9503347150153244, -0.8291152236514371, -0.6890119004617377, -0.5343780767107992, -0.3703262043002468, -0.20273525205818474, -0.038063301497667006, 0.11670127871247796, 0.2542493357801146, 0.3670533821828228, 0.4475845675165744, 0.488460080049425, 0.4826512201712832, 0.4236611246903891, 0.30570748127789793, 0.12391074027606336, -0.12556324418621193, -0.445328176463422, -0.8366858654577409, -1.2994899212356874, -1.8321113381421525, -2.4313660584364984, -3.0925369138685275, -3.8093872473343002, -4.574231328078433, -5.378050833223197, -6.2105986969224825, -7.060627756785937, -7.916006698295811, -8.764061168428714, -9.59167582896579, -10.385738551644742, -11.13320029137272, -11.821603570037764, -12.439072423580456, -12.974898268488756, -13.41943579376982, -13.76471343253378, -14.004217662839803, -14.13349244201744, -14.14980350228987, -14.052691726159782, -13.843519896134, -13.525949208057376, -13.105382510658734, -12.589340675004909, -11.986827417881504, -11.308592372071026, -10.566451863233961, -9.773437213296333, -8.943112172257038, -8.08961694823499, -7.22702547329104, -6.369306500506692, -5.529761977519121, -4.720934960779609, -3.954164028811731, -3.23947264999946, -2.5852642553344816, -1.9982283610512297, -1.4831876043898171, -1.0430521706868827, -0.6788151599745366, -0.3895790620802253, -0.1726809266831677, -0.023803675250585434, 0.0628005609004989, 0.09411424546925905, 0.07807426849773257, 0.02330369137257555, -0.06117889708912001, -0.1662756280704304, -0.28306453473527604, -0.4031317169935644, -0.5187510769798486, -0.6231967927923867, -0.7108185036349183, -0.777300095568634, -0.8196157706868046, -0.8362078779890091, -0.8268256938921502, -0.792606119000003, -0.7358131233049251, -0.659819142107329, -0.5687768286192606, -0.46751397956124097, -0.36117856718846875, -0.2550738094793471, -0.15432102502684156, -0.0636718840138792, 0.012769206476406492, 0.07171335873029785, 0.11087259431531167, 0.12906729019824129, 0.12630071681250069, 0.10377187485881376, 0.06383777324446609, 0.00991118062659629, -0.05367284284730535, -0.121877280626689, -0.18915989969541958, -0.24979545656064508, -0.2980917359929605, -0.32877930939996514, -0.33719781778425634, -0.3197048820445668, -0.2737859933368683, -0.19842663312929498, -0.09410904640294518, 0.03690765236296673, 0.19072430059636625, 0.36165924431510105, 0.5425188602180064, 0.7246206962354691, 0.8981762956885045, 1.0524839643845814, 1.176383222616512, 1.2585943067521272, 1.2881897676914387, 1.2550316283948646, 1.1501999142625874, 0.9664569420502299, 0.6985764305621979, 0.34375128127474064, -0.0982194992147009, -0.6246653351556346, -1.2300202076968896, -1.905775363656774, -2.640611924608016, -3.4206261002806686, -4.2295826596717205, -5.049436194040899, -5.860643585743113, -6.6429686605156295, -7.375772705304244, -8.039053127396796, -8.613622715958194, -9.082300974870549, -9.429897375061628, -9.644451749825341, -9.716954601506385, -9.642524091983415, -9.419825892483743, -9.052080829355358, -8.546184249118719, -7.913460063869011, -7.168520117435039, -6.329714713064355, -5.417810182138662, -4.456128448905589, -3.4691501364708524, -2.4823803761164376, -1.5210004896087888, -0.6095375371151038, 0.22931321578137215, 0.9751077620107748, 1.610556042881763, 2.1219087645572587, 2.4995148650370957, 2.738057619652243, 2.8367414813410536, 2.79928101029988, 2.6337418086486433, 2.3522226332447542, 1.9704232073389119, 1.5070066917385199, 0.9830059426515075, 0.4209033597570714, -0.15598942025562837, -0.7246520770969213, -1.262863407710454, -1.750406681078264, -2.1693422686641353, -2.505166190342059, -2.746759824310229, -2.887374354782602, -2.9242183273176394, -2.859165181861301, -2.6979943636014623, -2.450760355050795, -2.1307560432053316, -1.7545334863884703, -1.3407009795789084, -0.9096401829313416, -0.48227393769738636, -0.07957271133380744, 0.2785656199061638, 0.573892642138027, 0.7906947006472494, 0.9163109913711268, 0.9416990587468147, 0.8617596488545973, 0.675549543195596, 0.3863077994780388, 0.0013407446931368557, -0.468309688415734, -1.0082299708493605, -1.6013280738492335, -2.228326217071122, -2.8687624989004696, -3.5014702718111597, -4.105787549198413, -4.66188247895161, -5.152038376257164, -5.560709779013627, -5.875741220938795, -6.088082862764863, -6.192814605714797, -6.188507023684938, -6.077956736249156, -5.867237873778027, -5.566103805831856, -5.1868266168332955, -4.744275754512844, -4.254679068046022, -3.735441022315121, -3.2039725302227544, -2.6773509802220707, -2.171354969912515, -1.7000886432959945, -1.2753233872722713, -0.9062064790889479, -0.5989607493772178, -0.35677304382196706, -0.1798437292983349, -0.06550877145957062, -0.008574189516433102, -0.0016746537406009008, -0.03578363471411519, -0.1007611098440207, -0.18590606721463881, -0.2806059127203269, -0.3747983866068226, -0.45961342733215454, -0.5276361759316863, -0.5734327978839231, -0.593550334988278, -0.5868413799621364, -0.5541916690984264, -0.49860014421413534, -0.4246808004034192, -0.338506423898985, -0.24697657545046023, -0.15748478325308546, -0.07727077498605556, -0.013011484235880904, 0.02972253094200875, 0.04683105924289394, 0.03602684729129454, -0.002962620438000506, -0.06830648585222007, -0.15611884521875793, -0.2606212470112565, -0.3744793794099287, -0.4891571372113214, -0.5955190495106185, -0.6842704478128688, -0.7467429315127857, -0.7752899741528222, -0.7641259591778825, -0.7095481150301631, -0.6106767991755301, -0.4694037853021853, -0.29088896298447975, -0.08318694192240315, 0.1426060816319396, 0.37303035240985083, 0.592507514666025, 0.7842408394178728, 0.9308149656130593, 1.0151838308363292, 1.0215089048494121, 0.9360732578782199, 0.7481781352600748, 0.4508268187055229, 0.041464573731850154, -0.4776853190545153, -1.099250045010685, -1.8107699222347593, -2.5948637534892747, -3.429657714991411, -4.289577822473095, -5.146028135189302, -5.968799866689516, -6.726813218269221, -7.390026784322503, -7.930018955624541, -8.322189563601276, -8.545958585355223, -8.586992222898166, -8.436841169813382, -8.094908312093363, -7.567430549594239, -6.868940160749177, -6.020600089992361, -5.050991883391981, -3.9939260422970926, -2.888503787666587, -1.776620978648158, -0.7023795759894442, 0.2904331572668666, 1.1593873623258375, 1.8656583804614844, 2.3752375161340367, 2.6606456703841066, 2.7019834852351567, 2.48793456764167, 2.016340222301811, 1.2944358753273308, 0.33870492218662734, -0.8255736831144865, -2.1653243000469202, -3.640612932385086, -5.206492107224856, -6.814129678494645, -8.413353813067278, -9.953634465036421, -11.387067455679638, -12.66888766795873, -13.760560731356417, -14.629581401759143, -15.25232805668967, -15.613019433665094, -15.70603309253192, -15.534037843955275, -15.109573728283713, -14.45252040281729, -13.590864927077677, -12.55778232636392, -11.391654604243143, -10.133107640125917, -8.824465114625003, -7.507093565379294, -6.220556586005072, -5.000566132428696, -3.8781314044926414, -2.878309650034605, -2.0196168597683264, -1.3136351252884337, -0.7648759215239043, -0.3711590095017132, -0.12401028606937485, -0.009605556386007094, -0.009666303836960299, -0.10268239562902647, -0.26516463479824165, -0.4728371057778918, -0.70203549193594, -0.930594763372881, -1.1391598531992813, -1.3115787837066708, -1.435920146434714, -1.5042971368951927, -1.5134566018247313, -1.464081754109623, -1.3609138239612035, -1.2116857158863175, -1.0268379028300745, -0.8183015935827974, -0.598953387423378, -0.3814827501196122, -0.1777773809201404, 0.001925147630893966, 0.14952694560836077, 0.2595105243854208, 0.3291509184809938, 0.35852477869627336, 0.35036854720811716, 0.3097317203236787, 0.24349607703437207, 0.1598266446376946, 0.06745250955648215, -0.024892220743771495, -0.10926617853494078, -0.17890555370143704, -0.2289216330010162, -0.25637914940038914, -0.2607409912941803, -0.2435907184798162, -0.20873726746572435, -0.16162594755905618, -0.10910529485160865, -0.05865269202652835, -0.017897278001504827, 0.00616364860571597, 0.0077202747331774, -0.017238656252605258, -0.07048961209957336, -0.15127640486584173, -0.25617499011948625, -0.3791707019689698, -0.5119417301258234, -0.6442751013649483, -0.7647877174036215, -0.8615505316006685, -0.9231543858474534, -0.9393451291114198, -0.9022432892606997, -0.8067714759145532, -0.6517770021739884, -0.44006454869348405, -0.17916671303352041, 0.11912500797868864, 0.438539422809811, 0.7592911906280201, 1.058496769976343, 1.3115122287327572, 1.4929298193142528, 1.578065850260052, 1.5443360238896657, 1.372619373260709, 1.0486945669992072, 0.564216059592317, -0.08216445786632773, -0.8843990420954185, -1.8285959079984275, -2.8932600499020467, -4.049783880354116, -5.263237261914782, -6.493908129970283, -7.698398411866742, -8.832122293376546, -9.850380360180662, -10.711598268672523, -11.377903751291038, -11.818510874314935, -12.00980401411535, -11.939094699131704, -11.602577988329108, -11.006481511146399, -10.168181467866347, -9.123137833052924, -7.909702161797512, -6.553052226250132, -5.103194535171254], 'positive_zeros': ['0.085063885152692211467309290560327', '1.29889896153095985114723183450600', '1.54385997192990941027552130606120', '2.11347530713007540101659571773927', '2.34942641025673812072461627161428', '3.61096462915241623382695676981783', '3.71485947343092483477021546397708', '4.23558673262339735914459964559110', '4.42214055269399308662618963455692', '4.71596957154463816108555574342630', '5.09827804762983624473892201320562', '5.85803290473776230659147779265037', '6.21384291701002508986663312583762', '6.65767758222565868448497478834635', '6.88093828368026515409070534188544', '7.70419885108029885613329107262603', '7.71532754222860423244608047130659', '8.182192272491092724713868251433031', '8.275894058089597159868054884041957', '8.939740459607827378890608954137420'], 'prelabel': '4-2736e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 1303467320394376548, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.085063885152692211467309290560', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.29889896153095985114723183451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.54385997192990941027552130606', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5557.792009410902, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -8, 0, 20, 0, 0, 0, 20, 0, 0, 0, 0, 0, -20, 0, -38, 0, 0, 0, -40, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -160, 0, 202, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 0, 0, 0, 400, 0, 0, 0, 0, 0, 140, 0, 160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 304, 0, 0, 0, 0, 0], 'euler11': [1, -20, 342, -2420, 14641], 'euler13': [1, 0, 250, 0, 28561], 'euler17': [1, 20, 678, 5780, 83521], 'euler19': [1, 38, 361, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 40, 1458, 21160, 279841], 'euler29': [1, 0, -482, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -1622, 0, 923521], 'euler37': [1, 0, -2630, 0, 1874161], 'euler41': [1, 0, -2162, 0, 2825761], 'euler43': [1, -20, 3798, -36980, 3418801], 'euler47': [1, 160, 10818, 353440, 4879681], 'euler5': [1, 8, 66, 200, 625], 'euler53': [1, 0, -3890, 0, 7890481], 'euler59': [1, 0, -5762, 0, 12117361], 'euler61': [1, 20, 7542, 74420, 13845841], 'euler67': [1, 0, -3170, 0, 20151121], 'euler7': [1, -20, 198, -980, 2401], 'euler71': [1, 0, 718, 0, 25411681], 'euler73': [1, 20, 10758, 106580, 28398241], 'euler79': [1, 0, -12182, 0, 38950081], 'euler83': [1, -140, 18678, -964460, 47458321], 'euler89': [1, 0, -5042, 0, 62742241], 'euler97': [1, 0, -13010, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 8, 66, 200, 625], [1, -20, 198, -980, 2401], [1, -20, 342, -2420, 14641], [1, 0, 250, 0, 28561], [1, 20, 678, 5780, 83521], [1, 38, 361, 0, 0], [1, 40, 1458, 21160, 279841], [1, 0, -482, 0, 707281], [1, 0, -1622, 0, 923521], [1, 0, -2630, 0, 1874161], [1, 0, -2162, 0, 2825761], [1, -20, 3798, -36980, 3418801], [1, 160, 10818, 353440, 4879681], [1, 0, -3890, 0, 7890481], [1, 0, -5762, 0, 12117361], [1, 20, 7542, 74420, 13845841], [1, 0, -3170, 0, 20151121], [1, 0, 718, 0, 25411681], [1, 20, 10758, 106580, 28398241], [1, 0, -12182, 0, 38950081], [1, -140, 18678, -964460, 47458321], [1, 0, -5042, 0, 62742241], [1, 0, -13010, 0, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/o/e'], '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': '4-2736e2-1.1-c2e2-0-2', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1303467320394376548, 'z1': {'__RealLiteral__': 0, 'data': '0.085063885152692211467309290560', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '107831285071555453079244743942,1957075020085287059269690984342', 'Lhash_array': ['107831285071555453079244743942', '1957075020085287059269690984342'], 'label': '4-2736e2-1.1-c2e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/o/e'}