-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1522596315276628942747484469675,2386653263961102339429173170754', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 357.53421604259364, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [37, [1, -2, 1]]], 'bad_primes': [2, 37], 'central_character': '2368.1', 'coefficient_field': '1.1.1.1', 'conductor': 5607424, 'conductor_radical': 74, 'degree': 4, 'euler_factors': [[1], [1, 1, 5, 3, 9], [1, 1, -1, 5, 25], [1, -2, 10, -14, 49], [1, 5, 27, 55, 121], [1, 1, 15, 13, 169], [1, 0, 14, 0, 289], [1, 0, 18, 0, 361], [1, -1, 35, -23, 529], [1, -3, -1, -87, 841], [1, 17, 133, 527, 961], [1, -2, 1], [1, -17, 153, -697, 1681], [1, 6, 90, 258, 1849], [1, 2, 90, 94, 2209], [1, -8, 102, -424, 2809], [1, 14, 162, 826, 3481], [1, 19, 211, 1159, 3721], [1, 9, 123, 603, 4489], [1, -12, 98, -852, 5041], [1, -3, 117, -219, 5329], [1, 3, 59, 237, 6241], [1, 20, 246, 1660, 6889], [1, 12, 194, 1068, 7921], [1, -8, 190, -776, 9409], [1, 16, 246, 1616, 10201], [1, 1, -75, 103, 10609], [1, -1, 153, -107, 11449], [1, -12, 174, -1308, 11881], [1, -4, 150, -452, 12769]], 'euler_factors_factorization': [[1], [[[1, 1, 5, 3, 9], 1]], [[[1, 1, -1, 5, 25], 1]], [[[1, -2, 10, -14, 49], 1]], [[[1, 5, 27, 55, 121], 1]], [[[1, 1, 15, 13, 169], 1]], [[[1, 0, 14, 0, 289], 1]], [[[1, 0, 18, 0, 361], 1]], [[[1, -1, 35, -23, 529], 1]], [[[1, -3, -1, -87, 841], 1]], [[[1, 17, 133, 527, 961], 1]], [[[1, -1], 2]], [[[1, -17, 153, -697, 1681], 1]], [[[1, 6, 90, 258, 1849], 1]], [[[1, 2, 90, 94, 2209], 1]], [[[1, -8, 102, -424, 2809], 1]], [[[1, 14, 162, 826, 3481], 1]], [[[1, 19, 211, 1159, 3721], 1]], [[[1, 9, 123, 603, 4489], 1]], [[[1, -12, 98, -852, 5041], 1]], [[[1, -3, 117, -219, 5329], 1]], [[[1, 3, 59, 237, 6241], 1]], [[[1, 20, 246, 1660, 6889], 1]], [[[1, 12, 194, 1068, 7921], 1]], [[[1, -8, 190, -776, 9409], 1]], [[[1, 16, 246, 1616, 10201], 1]], [[[1, 1, -75, 103, 10609], 1]], [[[1, -1, 153, -107, 11449], 1]], [[[1, -12, 174, -1308, 11881], 1]], [[[1, -4, 150, -452, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 12, 'label': '4-2368e2-1.1-c1e2-0-12', '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': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/2368/2/a/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [1.0844598728711683e-120, 0.004813940475451238, 0.01923941084132009, 0.04322700228221589, 0.07669221161655336, 0.11951371795533848, 0.17152819706060576, 0.23252839757755986, 0.30225442667126623, 0.38039280983665386, 0.46656432474501225, 0.5603251306385533, 0.6611517227930324, 0.7684450239845333, 0.8815135198172738, 0.9995809378091539, 1.1217690572315722, 1.2471092818761311, 1.3745269545534797, 1.5028567750032615, 1.630830653966163, 1.7570965518666142, 1.880211955005278, 1.9986653255436286, 2.1108771577129244, 2.2152228478133904, 2.31004298689088, 2.393666096549108, 2.464429342837959, 2.520699260052537, 2.5609034467450273, 2.583547140963503, 2.587255713681608, 2.5707847949847675, 2.5330725556273004, 2.4732410462962133, 2.390656409273321, 2.284919212342913, 2.155929924831844, 2.0038663284419678, 1.829250897688902, 1.6329138660673927, 1.4160586451180153, 1.1802098153231193, 0.9272724721848594, 0.6594652782541554, 0.37936969947473437, 0.08984925829953073, -0.20591493848823744, -0.5045165261436269, -0.8023048438693925, -1.0954855459776538, -1.3801196530846112, -1.6522281778630417, -1.9078093711758528, -2.142942320864611, -2.3538207816300503, -2.5368502425801407, -2.68869491421296, -2.806362700394452, -2.887260154584943, -2.9292602067267186, -2.9307583646091193, -2.890718974929068, -2.8087248087275833, -2.6849990748413064, -2.5204399515264155, -2.316617465856988, -2.0757846459937577, -1.800850624971587, -1.4953609687848874, -1.1634507995783627, -0.8097885177626175, -0.43951516675048075, -0.058148150513809754, 0.3284847510490714, 0.7143821069864692, 1.0934300547570144, 1.4595765865745685, 1.8068768938313098, 2.129698940660876, 2.4227417286204385, 2.6812627420195487, 2.901058860565333, 3.078703712376046, 3.2114829625737586, 3.29762797368185, 3.3362002044010697, 3.3273071155109366, 3.271934253100235, 3.1721302202465993, 3.0307894134991598, 2.8517951526179575, 2.639760617084413, 2.4001227912566647, 2.138853473900951, 1.8625013081752224, 1.5778883506654866, 1.2921027289516354, 1.0121987170859372, 0.7451479995679859, 0.49756213815579187, 0.2756154513737277, 0.08480792311583008, -0.07012325104772564, -0.18538495869482252, -0.2582083841342418, -0.2869636082560615, -0.27121142228420025, -0.2117462510176681, -0.11060099544280506, 0.028979813995265908, 0.20259693730995185, 0.404783918562382, 0.629134819161122, 0.8684364324275534, 1.1148686570936435, 1.360159884741058, 1.5958538253918058, 1.813462785192729, 2.0047867986549015, 2.1620382275518297, 2.278192074373265, 2.3470568297794747, 2.3636297284302703, 2.32409309963302, 2.2261458301141444, 2.0689113593505324, 1.8532172428179534, 1.5814097908270115, 1.257557564439854, 0.8871776177740378, 0.47734581512777774, 0.036349634990682216, -0.4263022074128422, -0.9002765580650904, -1.374503205343299, -1.8375908027022965, -2.2779959404443137, -2.6844242508557143, -3.0460551581001916, -3.3528945652611846, -3.5960208231942303, -3.7678597682382016, -3.8624124129400466, -3.8754312496940995, -3.8045893634100714, -3.6495481111287815, -3.412031157645619, -3.095786728938603, -2.706538307641805, -2.2518581675524003, -1.7409784125646977, -1.184604802829453, -0.5945862510226854, 0.016292543562903605, 0.6347697233362881, 1.2472909575511288, 1.8405684115852996, 2.401698593769078, 2.918782251925723, 3.380936357007436, 3.7789281674099864, 4.1050525583123845, 4.35373151788486, 4.521242383232341, 4.606237878048491, 4.6093277190896815, 4.533483695908868, 4.383494579414989, 4.166234671697537, 3.8900278071062533, 3.564774615338581, 3.2012735685863802, 2.8112198029794184, 2.4065379123063337, 1.9992812680118368, 1.6010314867974438, 1.2227395937347934, 0.8742404928594942, 0.5640842624055956, 0.2992011146859629, 0.08477150782239266, -0.07594057012270082, -0.18163636601541616, -0.23298323498531862, -0.23255240985369602, -0.18467690081101248, -0.09526529048012979, 0.028442726991891296, 0.17818045045809136, 0.3449477418374729, 0.5194084409991773, 0.6921741183337207, 0.8542549661277826, 0.9972770572076333, 1.1139372684400017, 1.1981074338859967, 1.2452415122249287, 1.2523366842475412, 1.2182465212996247, 1.1434901328327756, 1.0304379959428405, 0.8829827959198726, 0.7065831725352361, 0.5078306818088798, 0.29435839600619046, 0.07435435349117886, -0.14363648710125704, -0.35119334371343464, -0.5402777007913854, -0.7036502249312174, -0.8351306396027646, -0.9299010328049545, -0.9847061837813453, -0.9980110694355784, -0.9700867429695775, -0.9030126294032123, -0.8006084871883569, -0.6682970880609397, -0.5128652810820022, -0.3422260686045151, -0.16501818250975062, 0.00967532991125145, 0.1728532638930884, 0.3158543212823258, 0.430951122497014, 0.5115186162039437, 0.5526239095050393, 0.5510498739326113, 0.5058052960861961, 0.4179689992147649, 0.2910532516468211, 0.13066065598329454, -0.05534651030911786, -0.2573550114941755, -0.4640440740550024, -0.6630108850426906, -0.8410118848715931, -0.9846357148149794, -1.0806939151706985, -1.1168618475359824, -1.0821419964775347, -0.9673958266911802, -0.7657845108631242, -0.47312999756332236, -0.08823299287428532, 0.38697204287071973, 0.9473119315280607, 1.5844272125524486, 2.286946404117148, 3.040710892360968, 3.829259373178358, 4.634157196160427, 5.4357803777705405, 6.2136572254722955, 6.9474995178067385, 7.6174533190903295, 8.205289289087093, 8.69446447366974, 9.071359935272733, 9.325076104994386, 9.448598082274321, 9.438281449638877, 9.294835392429084, 9.02249901040278, 8.629758848360252, 8.12826134272131, 7.533220752406592, 6.862154401080059, 6.134983493052108, 5.372707600091251, 4.597247262013648, 3.8301875617809635, 3.092450370316583, 2.4032310936780115, 1.7796135520176832, 1.2357992581326152, 0.782784927121512, 0.4279431932271778, 0.17487019347478752, 0.023326330513290444, -0.030668985705096883, 0.005419602135642242, 0.12101897237212832, 0.3029303886468912, 0.5359701741843147, 0.8035554873467614, 1.088547206102807, 1.3738019915073465, 1.643117648713043, 1.8816229287220447, 2.0767056244327007, 2.218140341890315, 2.2988802228473837, 2.3148679673474546, 2.2655936990592873, 2.153588581145777, 1.9846906818329255, 1.767274652494253, 1.5122180568398396, 1.2319656171287914, 0.9402417320402391, 0.6510759299825525, 0.3783538854015862, 0.13493685731462168, -0.06782502108814188, -0.22076380248014338, -0.3172840765948617, -0.3537470467220381, -0.32964375453917016, -0.2476671698415341, -0.11358282304468528, 0.0639782007331951, 0.2739850280994516, 0.5034071232672188, 0.7379909835308219, 0.9627287858774776, 1.162864055342085, 1.3242874169442012, 1.4346458523809333, 1.4835327914320802, 1.4635534778093735, 1.3702099443928575, 1.2027789645601221, 0.9638451526505308, 0.6598781515536482, 0.30043023677633723, -0.10164880014575363, -0.5312707230379394, -0.971253060139702, -1.4035056688878516, -1.8094645085424297, -2.17124782391037, -2.4722541701006158, -2.6981293015850407, -2.8373685319800126, -2.881963194062071, -2.827841170142509, -2.67511434642604, -2.428215526139259, -2.0957369418651486, -1.690173496575773, -1.2274151878088906, -0.7260772795668177, -0.20677332925172465, 0.30890978979890904, 0.7991885992420145, 1.2433352596134586, 1.6223207579599181, 1.9201171909567853, 2.124043328394655, 2.2259210408201353, 2.2220085442087516, 2.1138319637028666, 1.9076630400589143, 1.6148978534661085, 1.2511167857444445, 0.8359599169750148, 0.39188286488389074, -0.0564305073368522, -0.48344638034094534, -0.8637013730642982, -1.1731191993514998, -1.3900638552833111, -1.4964095688833865, -1.4784873516831611, -1.3277695765454334, -1.0414711416604125, -0.6227847258664683, -0.08093964132333384, 0.5689861308990644, 1.3066692815652794, 2.1070371682001547, 2.9415533425793026, 3.77883500428627, 4.586534704317744, 5.331853082927486, 5.983836800078366, 6.513561274457081, 6.896599393290815, 7.11269190924649, 7.148115997152287, 6.994739827308207, 6.652039158656169, 6.125534471278637, 5.4282641967839895, 4.5787101249211, 3.6016268561679876, 2.5256549461490727, 1.3835114999269205, 0.20955357970784513, -0.9605642421388785, -2.092093276591251, -3.1518818243015194, -4.110089191467277, -4.940998519901374, -5.624055259427649, -6.144575144085381, -6.49402246473565, -6.67042870832575, -6.6779414222318065, -6.52684384582019, -6.2325143566635495, -5.815029827625737, -5.297759484343826, -4.706626406478142, -4.068603622248256, -3.410781200735921, -2.759029418269159, -2.1370591937274304, -1.5654687221113217, -1.06098515107301, -0.6360271120690957, -0.2982761805544028, -0.05078464694087393, 0.10804494474738344, 0.18387993176073938, 0.18607792708971635, 0.1267906567058785, 0.020276602283684716, -0.11810788048565789, -0.27274667416574716, -0.4286769388549839, -0.572389486548069, -0.6924745707406329, -0.7802044074249046, -0.8298105587774843, -0.8387151102458351, -0.8074263199181707, -0.7393601516615204, -0.6404274716140764, -0.5184755864057959, -0.3827074654883826, -0.24285494160861648, -0.10860438649929707, 0.0113284056639019, 0.10959756990990284, 0.18105882425983258, 0.22286909903894936, 0.23505318699731553, 0.2202503501423987, 0.18390320078063993, 0.13368089696838958, 0.07926303551356545, 0.03154461872573679, 0.002082302244053067, 0.002237213068468031, 0.04243435960090105, 0.13141353466754815, 0.27550680903261754, 0.47814109355271983, 0.7393509301405562, 1.0556138077724848, 1.4197820414198576, 1.8212468207089623, 2.2463995487557975, 2.6790315522027943, 3.1013361970213262, 3.4943784835842737, 3.839544719164567, 4.1188773167496056, 4.3167905810854625, 4.420071630751565, 4.419627775421408, 4.310005953707226, 4.090931008619631, 3.7662847518940894, 3.345237191656125, 2.8407351619734067, 2.270111806922591, 1.6532413828887427, 1.012618775013664, 0.37141878748005897, -0.24685547499159488, -0.8201322231031202, -1.3283704857680205, -1.7548771479022391, -2.086928085296804, -2.3164487638870983, -2.440439284294758, -2.460932809182377, -2.385065847518797, -2.224356497483446, -1.9943586257140808, -1.7134235804401377, -1.401991368234655, -1.0810900128100205, -0.7714226868227996, -0.49189915083481517, -0.25875033589418983, -0.08436722808002181, 0.02330473938301802, 0.06141872521865138, 0.03233823535778372, -0.05630294256223559, -0.19210463055096932, -0.35838748352577654, -0.5353051875769865, -0.7007133822155238, -0.8317439432584848, -0.9058084548284208, -0.9023771016642759, -0.8038466421783882, -0.5971189378850738, -0.27414641435458187, 0.16661733276932114, 0.7205383953641171, 1.37799214170613, 2.1228656616623813, 2.9257312247522043, 3.7553239756553913], 'positive_zeros': ['1.20111670755529859367750701856683', '1.88273745425703762303955273290787', '2.62835604648112675911862417268033', '2.81358716855355318974090931266901', '3.37898508990300207671263441878195', '3.93487574639646458794843975015467', '4.63340670909118477644036268773307', '4.79349275179450951857527691564916', '5.26444465352941903649710666134711', '5.66066900696456155223540626054435', '5.93413699195548337040859199668316', '6.25118871682023166550125613830698', '7.14141541810912673276885485047748', '7.18371038650827330023163554763538', '7.76037241063182108831191156876595', '7.938719086852026653062089827405573', '8.321906214625450307925073386963316', '8.769864460941078009362586251491069'], 'prelabel': '4-2368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.348399153555157, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1777774265831742234, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20111670755529859367750701857', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88273745425703762303955273291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62835604648112675911862417268', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 357.53421604259364, 'bad_primes': [2, 37], 'central_character': '1.1', 'conductor': 5607424, 'conductor_radical': 74, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 2, 0, -4, 0, -5, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 1, 0, 2, 0, 6, 0, 3, 0, -17, 0, 5, 0, -2, 0, 2, 0, 1, 0, 17, 0, -6, 0, 4, 0, -2, 0, -6, 0, 0, 0, 8, 0, 5, 0, 0, 0, -14, 0, -19, 0, -8, 0, 1, 0, -9, 0, -1, 0, 12, 0, 3, 0, -2, 0, -10, 0, -3, 0, 8, 0, -20, 0, 0, 0, -3, 0, -12, 0, -2, 0, 17, 0, 0, 0, 8, 0, 20, 0], 'euler11': [1, 5, 27, 55, 121], 'euler13': [1, 1, 15, 13, 169], 'euler17': [1, 0, 14, 0, 289], 'euler19': [1, 0, 18, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -1, 35, -23, 529], 'euler29': [1, -3, -1, -87, 841], 'euler3': [1, 1, 5, 3, 9], 'euler31': [1, 17, 133, 527, 961], 'euler37': [1, -2, 1, 0, 0], 'euler41': [1, -17, 153, -697, 1681], 'euler43': [1, 6, 90, 258, 1849], 'euler47': [1, 2, 90, 94, 2209], 'euler5': [1, 1, -1, 5, 25], 'euler53': [1, -8, 102, -424, 2809], 'euler59': [1, 14, 162, 826, 3481], 'euler61': [1, 19, 211, 1159, 3721], 'euler67': [1, 9, 123, 603, 4489], 'euler7': [1, -2, 10, -14, 49], 'euler71': [1, -12, 98, -852, 5041], 'euler73': [1, -3, 117, -219, 5329], 'euler79': [1, 3, 59, 237, 6241], 'euler83': [1, 20, 246, 1660, 6889], 'euler89': [1, 12, 194, 1068, 7921], 'euler97': [1, -8, 190, -776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 5, 3, 9], [1, 1, -1, 5, 25], [1, -2, 10, -14, 49], [1, 5, 27, 55, 121], [1, 1, 15, 13, 169], [1, 0, 14, 0, 289], [1, 0, 18, 0, 361], [1, -1, 35, -23, 529], [1, -3, -1, -87, 841], [1, 17, 133, 527, 961], [1, -2, 1, 0, 0], [1, -17, 153, -697, 1681], [1, 6, 90, 258, 1849], [1, 2, 90, 94, 2209], [1, -8, 102, -424, 2809], [1, 14, 162, 826, 3481], [1, 19, 211, 1159, 3721], [1, 9, 123, 603, 4489], [1, -12, 98, -852, 5041], [1, -3, 117, -219, 5329], [1, 3, 59, 237, 6241], [1, 20, 246, 1660, 6889], [1, 12, 194, 1068, 7921], [1, -8, 190, -776, 9409]], 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2368/2/a/u'], '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': '4-2368e2-1.1-c1e2-0-12', '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': 2, 'prelabel': '4-2368e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.348399153555157, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1777774265831742234, 'z1': {'__RealLiteral__': 0, 'data': '1.20111670755529859367750701857', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1522596315276628942747484469675,2386653263961102339429173170754', 'Lhash_array': ['1522596315276628942747484469675', '2386653263961102339429173170754'], 'label': '4-2368e2-1.1-c1e2-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2368/2/a/u'}