-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1298840637980920379073186460746,2036550352754001209340295601785', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6178390655285312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1, 1, 1]]], 'bad_primes': [3, 5, 7], 'central_character': '1575.1', 'coefficient_field': '1.1.1.1', 'conductor': 2480625, 'conductor_radical': 105, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 1], [1], [1], [1, 1, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 3, 4, 3, 1], [1, 1, 0, 1, 1], [1, 0, 2, 0, 1], [1, 3, 4, 3, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 3, 4, 3, 1], [1, 0, -1, 0, 1], [1, 1, 0, 1, 1], [1, 0, 2, 0, 1]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1], 1]], [1], [1], [[[1, 1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, -1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 4]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, 0, 1], 2]], [[[1, 1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, 1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, 0, 1], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 1, 'label': '4-1575e2-1.1-c0e2-0-1', 'leading_term': '1.41028668942721621728721127078661057658750494718500319652914276000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1575/1/x/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [1.4102866894272161, 1.414550464308008, 1.4223191758628184, 1.4367745914268373, 1.4573178273462777, 1.4825882357849136, 1.5120266931315032, 1.5451709369167999, 1.5811562037157036, 1.618977296637354, 1.6575955124649842, 1.6959075654322697, 1.7327214798709067, 1.7667822289284065, 1.7968116980604876, 1.821503517006126, 1.8395654177750729, 1.8497137980063414, 1.850729329901913, 1.8414464889024162, 1.8208150267158383, 1.7878868829471868, 1.7418822498052717, 1.682172409608366, 1.6083478210173492, 1.520195354616449, 1.4177659810787924, 1.3013444490179455, 1.1715135977795796, 1.0291147825629876, 0.8753054095200917, 0.711508984721554, 0.5394621816980927, 0.3611542875726825, 0.17886014930835112, -0.004930087845599149, -0.18749536123931246, -0.36596150736021466, -0.5373052613867311, -0.6984362013564263, -0.8462212819169594, -0.9775663238440517, -1.089460224313793, -1.1790505245341347, -1.243704394977027, -1.2810723494817515, -1.289160972549456, -1.2663789389164566, -1.2116144589842628, -1.1242585078247624, -1.0042783665739232, -0.8522144087917648, -0.6692401608630362, -0.45713110961234127, -0.21830161100384513, 0.04425313952158748, 0.3269521019781906, 0.6257090757637095, 0.9359663640810815, 1.2527908017615659, 1.5709498674225846, 1.8850128720101051, 2.1894695064797505, 2.478823762082434, 2.7477506368783535, 2.9911691042544617, 3.2044284015495053, 3.383346409026706, 3.5244131177295843, 3.6247823320399966, 3.6824770871429506, 3.696325700836102, 3.666152558971947, 3.5926540914414407, 3.477558821107131, 3.323444503750846, 3.133853809985954, 2.9130601407725414, 2.666129712559916, 2.39864977772944, 2.1167338766749273, 1.8267316045538162, 1.535180788188396, 1.248521788608024, 0.9730075488955665, 0.7144470403031763, 0.4780905682505028, 0.26842588673582346, 0.08906087925145834, -0.05740810406404932, -0.16949191166100339, -0.24685516787605916, -0.2903670221159656, -0.30205864611411687, -0.28511024672768753, -0.24372563202193703, -0.18304432943689433, -0.10894960471927595, -0.027904720597174054, 0.053280219144709116, 0.12767725066176883, 0.1884830948489174, 0.22929126958701615, 0.2443095268841671, 0.22864326095659965, 0.17845507755471418, 0.0912213218121643, -0.034192593187801885, -0.19734232800920462, -0.39622929714752264, -0.6272133306768923, -0.8851393958817597, -1.163379019056822, -1.4540458774591787, -1.7481776292753142, -2.036012598656052, -2.3073055872351933, -2.551626077890747, -2.758782227997096, -2.919094077404886, -3.023881877845919, -3.065667266666335, -3.0386680967029163, -2.9388872090512574, -2.7645484272156144, -2.5160462212878945, -2.19625826016463, -1.8103486272588933, -1.3659019939603962, -0.8725958461804908, -0.3421194086568677, 0.2122464695304768, 0.7759378910534122, 1.3335615662788396, 1.8694149700600824, 2.3679009555355646, 2.8142156658509796, 3.1946468169448483, 3.4973620252780373, 3.7125194542989215, 3.8330739327824483, 3.8546454781488357, 3.776256438697196, 3.599929571252823, 3.331277909081276, 2.9788365259832927, 2.5544475601800753, 2.0723642440459695, 1.5494042321584196, 1.0038959291004985, 0.45560997655876867, -0.07535858482863982, -0.5688333635807884, -1.0056336736048113, -1.3679123752310538, -1.640090482321399, -1.809188026840648, -1.8655330368188794, -1.8029761758067675, -1.6193227747873784, -1.316331185564278, -0.8998577147389492, -0.3795640911139511, 0.23119022442781648, 0.9159673478029287, 1.655535527334482, 2.4288045084406455, 3.213179982397033, 3.985756725959183, 4.7236203830439525, 5.405199103806956, 6.010393520526685, 6.521960051162744, 6.925372864082378, 7.210102924230107, 7.369155527750791, 7.400120804943412, 7.304381457974311, 7.087841714578385, 6.759854449834085, 6.333582094534426, 5.824741582559538, 5.251605281907978, 4.6336978103864945, 3.9914988253475996, 3.3452411784487786, 2.714421295729374, 2.1168399619601668, 1.5680523165186746, 1.0807611748509356, 0.6643424013404569, 0.32465047278685655, 0.0637349953835019, -0.11994300100822752, -0.23152835805990302, -0.2792084689793031, -0.2739439686384984, -0.22867465802534276, -0.1578021122201036, -0.07631473311435016, 0.0008866734910523919, 0.05978648476974768, 0.0879584850938633, 0.07514681045259093, 0.013860188378155428, -0.10035959910495397, -0.26857905192647924, -0.48855221438430346, -0.7546840298544667, -1.0584255443367938, -1.3885882117260653, -1.7319620450926456, -2.0739442996147863, -2.3992437482109588, -2.6927259853552217, -2.940049217040378, -3.1285835523212957, -3.2478359598449393, -3.290281662634496, -3.2514766132816217, -3.1306501914503055, -2.930465534824074, -2.6572631249597203, -2.320501039686193, -1.9326018614000275, -1.5081725214732933, -1.0634807125848997, -0.6156039036108506, -0.181631877600147, 0.2220838816674628, 0.580851903864103, 0.882131806224864, 1.1164062881202805, 1.2772980377625038, 1.3622282218856459, 1.3721139077029523, 1.3116930905029394, 1.1888383336498758, 1.014498024477371, 0.8017386743943874, 0.5653340739339128, 0.32070534949922624, 0.08326734875613503, -0.13254026113095654, -0.3139832352702064, -0.45073186137927307, -0.535478679296048, -0.5642408589964673, -0.5366935263579216, -0.4560283232246324, -0.32888632043974636, -0.16481810570419866, 0.024215309513678642, 0.22464931590237755, 0.4221820584259959, 0.6026549753666292, 0.753133589823304, 0.8626455203637975, 0.9232627324991628, 0.9305028709994628, 0.8841826578974589, 0.7883528810607757, 0.6517248496764141, 0.4871043351432434, 0.31127140231759626, 0.1439849910391835, 0.007307640751412606, -0.07565227410115621, -0.08185660695257437, 0.010372392990612066, 0.22001896246408, 0.5622962072839733, 1.0473919308422486, 1.6798095567433824, 2.457506583638269, 3.3717723382741287, 4.407028699440702, 5.5412426171835625, 6.7465582694291975, 7.990113346153802, 9.235532102589532, 10.443904260508647, 11.57601568106223, 12.593182367482266, 13.45995979486179, 14.144519026978456, 14.621485005598092, 14.871602363436578, 14.884326946886068, 14.656646933469126, 14.195097671309819, 13.513757976956875, 12.63546853951581, 11.589183799746637, 10.410327630237772, 9.137815168696424, 7.813645604641093, 6.479986960198647, 5.1782505551475095, 3.9466365111266173, 2.8190275628484947, 1.823320203283303, 0.9804970542685092, 0.3039303529122833, -0.20106287866942443, -0.5369355202001599, -0.7136881973171101, -0.747773551671334, -0.6611822691417918, -0.4798559040350332, -0.23222010602343932, 0.05249163345021088, 0.3459866178169495, 0.6222745088576936, 0.8593568517555712, 1.039951425858036, 1.1527902123247795, 1.1925308094013052, 1.1604168206518608, 1.0633814753728095, 0.9139704181249774, 0.7288183291679236, 0.5279074044786748, 0.33272969075811026, 0.16511588737430652, 0.04545510535922636, -0.008559513578610232, 0.016691023826111172, 0.12979574426233545, 0.33357525898405255, 0.6247546342772716, 0.9939399144311262, 1.4261207521976336, 1.9012567439882304, 2.395631899095471, 2.882789427644744, 3.335570900338134, 3.7270433592281305, 4.032899622111397, 4.232011783848118, 4.308782092714599, 4.2530361364735345, 4.061917436024114, 3.738985048656159, 3.2953403453003918, 2.747983165361112, 2.120025812717856, 1.438545213099627, 0.7339396711726504, 0.037648005327912154, -0.6191068522426041, -1.207310064559972, -1.7016476935928924, -2.081834945079446, -2.333923319220882, -2.4507246508098386, -2.4325640008466682, -2.286753421603488, -2.027562352057458, -1.6749040114641407, -1.2534896522270813, -0.7910654577187073, -0.31691968323138964, 0.13989286186745, 0.5523597366955875, 0.8968628550552652, 1.1548907077248567, 1.313633432794742, 1.3672049222245657, 1.316328428900962, 1.1687920186524898, 0.9382889446457037, 0.6440168677853528, 0.30893829033018955, -0.041354084187536916, -0.3805548487951888, -0.683207104504889, -0.9263571934923893, -1.0911235441985496, -1.163717505545314, -1.1365914041037515, -1.0086159453703756, -0.7854757551790763, -0.47900830548912554, -0.1066956914128628, 0.30961541509842194, 0.7450564987208839, 1.173255778080626, 1.568240287300198, 1.9057463329565971, 2.1652664148025336, 2.330751455445641, 2.39235140955875, 2.3462583878387626, 2.1957666753246636, 1.9502215607506688, 1.6251970162149705, 1.2407434161397268, 0.8207066890320893, 0.3906510930308863, -0.023434867006904232, -0.3970745329746576, -0.7088049842417098, -0.9415339741854504, -1.0837881147493171, -1.1301937973688712, -1.0820748220141536, -0.9469806933416138, -0.7384079291924994, -0.4745432529497956, -0.1771177844324464, 0.13026199713574377, 0.4238796297475113, 0.6815045759605489, 0.8843511322577526, 1.0181274944438166, 1.0746930792570655, 1.052222489269117, 0.9561288498949251, 0.7982309596202002, 0.5966932606871483, 0.3743446010597754, 0.15764513870881103, -0.025469071860450873, -0.14731105186619947, -0.1825677342252638, -0.11022447041817113, 0.08484315811454349, 0.4103309841993592, 0.8658111163935535, 1.4421114146318832, 2.1216377866054565, 2.8790095630582933, 3.682234166560464, 4.494647578922327, 5.27652232238553, 5.988048742497954, 6.590804209592043, 7.051252366112092, 7.341494457407109, 7.442627911048212, 7.3443479796603, 7.047532284645522, 6.562530397830986, 5.910525016460852, 5.120673266793579, 4.230094553513206, 3.2803274346849793, 2.316134469673109, 1.3819334754119237, 0.5199040166002363, -0.23291266574236727, -0.8465494213218043, -1.2997889599727106, -1.581483699640937, -1.6907342444053117, -1.6371055798008425, -1.4393934169238298, -1.1245498038767854, -0.7254661626127319, -0.27877508981676885, 0.1776804259113012, 0.6076887812605545, 0.9787710511896155, 1.2649974441340426, 1.448030559673308, 1.5192370386846505, 1.4793205077453062, 1.3392235431817836, 1.1183658679737039, 0.8441494082084406, 0.549181433360703, 0.26957484810332843, 0.04180034480277594, -0.09968471612512855, -0.12521778394288638, -0.012229424642705836, 0.25297392207025954, 0.6737494721808945, 1.242688176803837, 1.941577270883177, 2.74229755139905, 3.6084561987399546, 4.497204482801907, 5.3623776042864675, 6.156545902882633, 6.835121985114276, 7.357856537043439, 7.6931301872902855, 7.818212231097268, 7.72291171133125, 7.408208951657035, 6.888610877172447, 6.18916799585034, 5.346222546530627, 4.403228298979239, 3.4100023915700426, 2.4180785614630818, 1.4789804667650381, 0.6399304187465963, -0.058095873444865276, -0.5834977506719633, -0.9153667464809316, -1.045151839149063, -0.9765534234349579, -0.7254344274628859, -0.3189884653429961, 0.20605407789122282, 0.8106827816366634, 1.4507034551692692, 2.0622663093200932, 2.5903653621003526], 'positive_zeros': ['1.02460460141546533731090149360495', '1.60655495480169230664533452450567', '2.59511306074975866219956695346739', '2.88104399043898628402685523471927', '3.12760345105075596315641598121098', '3.82677478317679182518084185679029', '4.41956878938508141687838840019191', '4.76475524543023702655972934511445', '5.63389040558050400263991941960857', '5.85900599019417237478912698898064', '5.98100840600319990675127526827922', '6.69253119144104813150899422308868', '7.10070670875801345571919352381981', '7.37919937047148341501953087265285', '7.79488126140241289617004408679374', '7.87874864765669193479236167158277', '8.893357507536551178093015173587160', '9.106073597725074568894866773614892', '9.541884241741345333064276369542937', '9.571165917370971600287195208812868'], 'prelabel': '4-1575e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8865818602345634, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 860117999244892860, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02460460141546533731090149360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60655495480169230664533452451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59511306074975866219956695347', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6178390655285312, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 2480625, 'conductor_radical': 105, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -1, 0, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, 0, 1, 0, 1], 'euler19': [1, -3, 4, -3, 1], 'euler2': [1, 0, -1, 0, 1], 'euler23': [1, 0, -1, 0, 1], 'euler29': [1, 0, 2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, -1, 0, -1, 1], 'euler41': [1, 0, -2, 0, 1], 'euler43': [1, -4, 6, -4, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, -1, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, 3, 4, 3, 1], 'euler67': [1, 1, 0, 1, 1], 'euler7': [1, 1, 1, 0, 0], 'euler71': [1, 0, 2, 0, 1], 'euler73': [1, 3, 4, 3, 1], 'euler79': [1, -1, 0, -1, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, 1, 0, 1], 'euler97': [1, 0, 1, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, -1, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 3, 4, 3, 1], [1, 1, 0, 1, 1], [1, 0, 2, 0, 1], [1, 3, 4, 3, 1], [1, -1, 0, -1, 1], [1, 0, -2, 0, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1575/1/x/a'], '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': '4-1575e2-1.1-c0e2-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-1575e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8865818602345634, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 860117999244892860, 'z1': {'__RealLiteral__': 0, 'data': '1.02460460141546533731090149360', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1298840637980920379073186460746,2036550352754001209340295601785', 'Lhash_array': ['1298840637980920379073186460746', '2036550352754001209340295601785'], 'label': '4-1575e2-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1575/1/x/a'}