-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1223454986923476694418920336000,3072184073449728867011592275018', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.529112783831148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 2, 5]]], 'bad_primes': [2, 5], 'central_character': '320.1', 'coefficient_field': '1.1.1.1', 'conductor': 102400, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, -2, 2, -6, 9], [1, 2, 5], [1, 2, 2, 14, 49], [1, 0, 14, 0, 121], [1, -2, 2, -26, 169], [1, -2, 2, -34, 289], [1, 8, 54, 152, 361], [1, -10, 50, -230, 529], [1, 0, 6, 0, 841], [1, 0, -58, 0, 961], [1, -10, 50, -370, 1369], [1, -12, 118, -492, 1681], [1, 6, 18, 258, 1849], [1, -14, 98, -658, 2209], [1, -2, 2, -106, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, -14, 98, -938, 4489], [1, 0, -106, 0, 5041], [1, -18, 162, -1314, 5329], [1, 16, 222, 1264, 6241], [1, -10, 50, -830, 6889], [1, 0, -178, 0, 7921], [1, 6, 18, 582, 9409], [1, 12, 238, 1212, 10201], [1, 6, 18, 618, 10609], [1, -6, 18, -642, 11449], [1, 0, -202, 0, 11881], [1, 6, 18, 678, 12769]], 'euler_factors_factorization': [[1], [[[1, -2, 2, -6, 9], 1]], [[[1, 2, 5], 1]], [[[1, 2, 2, 14, 49], 1]], [[[1, 0, 14, 0, 121], 1]], [[[1, -6, 13], 1], [[1, 4, 13], 1]], [[[1, -2, 2, -34, 289], 1]], [[[1, 4, 19], 2]], [[[1, -10, 50, -230, 529], 1]], [[[1, 0, 6, 0, 841], 1]], [[[1, 0, -58, 0, 961], 1]], [[[1, -12, 37], 1], [[1, 2, 37], 1]], [[[1, -6, 41], 2]], [[[1, 6, 18, 258, 1849], 1]], [[[1, -14, 98, -658, 2209], 1]], [[[1, -2, 2, -106, 2809], 1]], [[[1, 4, 59], 2]], [[[1, 2, 61], 2]], [[[1, -14, 98, -938, 4489], 1]], [[[1, 0, -106, 0, 5041], 1]], [[[1, -18, 162, -1314, 5329], 1]], [[[1, 8, 79], 2]], [[[1, -10, 50, -830, 6889], 1]], [[[1, 0, -89], 2]], [[[1, 6, 18, 582, 9409], 1]], [[[1, 6, 101], 2]], [[[1, 6, 18, 618, 10609], 1]], [[[1, -6, 18, -642, 11449], 1]], [[[1, 0, -202, 0, 11881], 1]], [[[1, 6, 18, 678, 12769], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 10, 'label': '4-320e2-1.1-c1e2-0-10', '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/320/2/n/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.8062565158524417, 1.8045203496405247, 1.7955247519881075, 1.7805759067661735, 1.7577427904213514, 1.724146071861905, 1.6769907156463018, 1.6132762784414225, 1.5295757090556008, 1.4223688961820715, 1.2883748035632732, 1.1246348152325534, 0.9288864973738369, 0.6996196276144883, 0.43657224822482443, 0.14067086932085401, -0.1854622652683719, -0.5377029442919395, -0.9099957750777066, -1.2947180563617144, -1.6824406314134914, -2.0624676140908074, -2.4228849185145584, -2.7512373148779887, -3.03492043522483, -3.2618961985951476, -3.421409645419903, -3.504585023278337, -3.505354495802443, -3.420741474556132, -3.25179835167979, -3.003394593730438, -2.684908472858845, -2.3094114693222663, -1.8938767951096616, -1.4577887112156422, -1.022736327324177, -0.6106525134897607, -0.24284540275516084, 0.06176196388073009, 0.28789174198298473, 0.42520676646855404, 0.46941211388321, 0.4226612021156399, 0.2939905285402733, 0.09861249503919738, -0.14270137430937604, -0.40532893740660253, -0.6625405254566873, -0.8877145626365692, -1.0568579344706663, -1.1505422383825255, -1.1564583949586291, -1.0702268131333705, -0.8970541261867123, -0.6508305703074152, -0.35411106667202324, -0.03547197025943597, 0.2724355279059515, 0.5365952608840314, 0.7269846866622638, 0.8200942148869735, 0.8024478763083321, 0.6724918222299392, 0.44266392268693866, 0.13860639363549523, -0.2015598967835624, -0.530805438844836, -0.7971154267036542, -0.9487596341632945, -0.9404605067112201, -0.7383201308813486, -0.3260296438837903, 0.292827169805642, 1.0912739179068067, 2.0207837603794903, 3.0126700486059637, 3.9839746461460894, 4.844258065705365, 5.503521316145045, 5.882666289122886, 5.920075266336963, 5.582127027574836, 4.865005287331128, 3.8010619107089396, 2.4539721701609247, 0.9179379051172823, -0.6929734667922972, -2.2530596970304573, -3.6378138503757835, -4.736645500943299, -5.462660302367049, -5.764680667602561, -5.629378757778497, -5.0873302951788615, -4.205764014747094, -3.0857822320521144, -1.8480227190549396, -0.6221649216973664, 0.46879747160633917, 1.3218780870901874, 1.8644845566929655, 2.0640407230546316, 1.9284090810288594, 1.5068038472260634, 0.8801304026058797, 0.15234984704068597, -0.5645388925752085, -1.1646549918044031, -1.5611509147909286, -1.6988131746255661, -1.5583645918135482, -1.16096918980894, -0.5617938323813041, 0.15605175653489933, 0.8951376428294002, 1.5572103390892549, 2.0564739339896447, 2.3332997826710673, 2.359675560421149, 2.1457121003390833, 1.73400355601225, 1.1955498939806355, 0.6160035921038998, 0.08375865133486972, -0.32422326011258906, -0.5547005007512911, -0.5847051674971747, -0.42638233712793255, -0.12233153901620995, 0.26039412947028096, 0.6429684536370465, 0.9482684222825191, 1.1133429828014567, 1.102040267399602, 0.9090003247172536, 0.5632295878372234, 0.12067000884517569, -0.34402158421315204, -0.7516855587123656, -1.033829838286701, -1.1439151613979588, -1.0698194701167116, -0.8334871654884691, -0.4924973969310589, -0.12625709836401225, 0.17417874274482184, 0.32654221080424717, 0.27137481844066214, -0.012443977253064939, -0.5019905667822906, -1.1284102482324134, -1.7879271415982882, -2.353257318497783, -2.699559847592628, -2.719149734316018, -2.3502249353877125, -1.581351243229065, -0.4672682540663597, 0.884593570292745, 2.320426435882165, 3.6670980963599407, 4.756609966345379, 5.451588760875167, 5.67234531864791, 5.404018397607758, 4.70872221399079, 3.707200157622398, 2.5683206752087617, 1.473657187797338, 0.5923148331547523, 0.048278165740968756, -0.10021630188951948, 0.12839717494910818, 0.6406680435478829, 1.2843111014924884, 1.8756676821614935, 2.230444786129521, 2.2024888363099246, 1.7063293717444479, 0.7432890870020296, -0.6018503864865431, -2.1650043855864016, -3.7319556906719655, -5.071433451801818, -5.971422518377945, -6.280654567678601, -5.926917319137179, -4.940324609308568, -3.439545953391828, -1.6219502092078215, 0.2746357415335922, 2.0078075953946843, 3.3682139484662765, 4.217225465540747, 4.4981927605512935, 4.251572384892176, 3.591267054637296, 2.6900458049288045, 1.7358154827074648, 0.9022863587749714, 0.31305599563812575, 0.02330782318839787, 0.012839379577147177, 0.19594689486898015, 0.44288543647236006, 0.6132253983866969, 0.5846679475954811, 0.28646937644071246, -0.28957771089952333, -1.0801728411247569, -1.9671133216955856, -2.7995799942625936, -3.4249576753530557, -3.7259139321833374, -3.6393036436103126, -3.180713864015609, -2.433263586427871, -1.54255679066269, -0.6800736525974941, -0.015193380133190836, 0.3221214744574087, 0.2669242115155032, -0.16841499562676127, -0.894936797759458, -1.7661376212998197, -2.608367256144445, -3.2526844738393392, -3.5747459012254517, -3.5104005221694097, -3.0775602549874845, -2.3590231472618495, -1.493985247361953, -0.6374492365554725, 0.0654228888028831, 0.5156953748733427, 0.6754869556679952, 0.5769526733616513, 0.30706484650888227, -0.01040812315576029, -0.253815528765107, -0.32525533289885405, -0.18570833718198804, 0.14564473214328752, 0.5858857555076233, 1.0164416765182624, 1.3090988334923817, 1.3597255558880061, 1.1216724333622798, 0.614113007728273, -0.06674071349016342, -0.7778627754632997, -1.3486660565100428, -1.6318729857562535, -1.53100703916089, -1.0362184250374191, -0.22516156926758782, 0.739613621063733, 1.6526292796171946, 2.2962438962635234, 2.5053432720946427, 2.189395657668882, 1.3764035673158939, 0.1944030642764675, -1.13691630452707, -2.362041258346906, -3.241680506910861, -3.6060827140107565, -3.40590920816381, -2.7176187821311246, -1.7481012101694633, -0.7803555050662684, -0.12581149735017505, -0.04589442764817394, -0.6936282146772887, -2.068081991758056, -4.002667594045796, -6.184525155073142, -8.214691655297054, -9.671243382094989, -10.2099293301215, -9.611834916006217, -7.857934240158282, -5.112247791852227, -1.7201653063662088, 1.8697229922553946, 5.1774768785026355, 7.776017914233389, 9.376071520315358, 9.852608374446891, 9.28102233974618, 7.88498915355168, 6.006093606318782, 4.011809333389853, 2.235723840919599, 0.9116180719645776, 0.1413575091779306, -0.10508595821890901, 0.0334034319795818, 0.35942724045719476, 0.6721428206496624, 0.8152928966228294, 0.7148848194768282, 0.3833358241449734, -0.09010971605713552, -0.5752226025091985, -0.9426365740207036, -1.098999549098818, -1.0184664759812878, -0.7410253194623179, -0.3653633004101181, -0.012947784014881777, 0.20538442410919364, 0.22301116700860305, 0.03836764353737981, -0.286678808926133, -0.6438251001750209, -0.9110982223102095, -0.9931052468645823, -0.8480078379093778, -0.5106027540160197, -0.08131016094793475, 0.29293742600702644, 0.4613115437844593, 0.31242906528981046, -0.19185545385401487, -0.9948169945672746, -1.954243672685558, -2.871436055311823, -3.5353754804353845, -3.7830328078366833, -3.5318650867783186, -2.819147560344363, -1.7826768200609855, -0.6437382329442123, 0.35575628977026974, 1.0084037609122498, 1.1944581681360724, 0.9175728557189922, 0.2990564667976951, -0.4474246091206576, -1.0761332231008247, -1.3777966468761607, -1.2363427645444558, -0.6760520942497429, 0.14393254881951809, 0.9543394368240967, 1.4448895467409406, 1.3447608580826351, 0.49391397049784835, -1.0948230218186263, -3.2304406055180412, -5.565725750928017, -7.666203798820427, -9.10973483850186, -9.565380541342254, -8.892735577507123, -7.151243234037864, -4.617974964538721, -1.7085799780619142, 1.0975033967842724, 3.3608358397236637, 4.780263847822504, 5.2311603097315595, 4.80248885059587, 3.7354721490484315, 2.3772474732243696, 1.0739458181854395, 0.0987706856518377, -0.4090453256200067, -0.4634082589974117, -0.20288193830110177, 0.16380742397364878, 0.4330281762708655, 0.4784611477637963, 0.2887721030282696, -0.01681846438799939, -0.23080022951362808, -0.11324826566988666, 0.525602965889566, 1.7615038785053356, 3.5121722246496474, 5.5458846717061885, 7.512177812145176, 9.038632613101775, 9.791737647780815, 9.5926240533702, 8.42804571023274, 6.493886817208073, 4.124307086282287, 1.735432049922565, -0.27408560259368187, -1.6191408686889817, -2.1662854924751147, -1.9824314334935385, -1.2721774314653502, -0.3490978171971175, 0.47780139201771865, 0.9590092983550946, 0.9779422624891805, 0.5573979725057482, -0.15225904435652915, -0.9349215657740821, -1.566443232060729, -1.8913901397635031, -1.8491887275382946, -1.4979863547113088, -0.9749306598594109, -0.4569240216363422, -0.09551880469363588, 0.02912830582784002, -0.06803362500687132, -0.2841454693935037, -0.46478918934844055, -0.46206453217072013, -0.18192830218075462, 0.3690415459127971, 1.086314725600818, 1.7848617546703558, 2.2551612146643505, 2.327950520397051, 1.923330619692055, 1.0915785930747086, -0.0022739896295741113, -1.1101360265865055, -1.9692444692119286, -2.3770061941072336, -2.23963067334176, -1.6117015901482412, -0.6687671826267151, 0.3311327338842655, 1.1266666230499929, 1.5279862158615896, 1.4647716708549383, 1.0142002333935378, 0.36464733160810364, -0.235976732778571, -0.5638821969167334, -0.49317302191590195, -0.03616575694847384, 0.648860075675034, 1.3066695825754502, 1.663127630367924, 1.5104891648980918, 0.7931663046406163, -0.3695353583339405, -1.6872552012807702, -2.774461388037056, -3.2526942292174783, -2.8518289559196828, -1.511545135832206, 0.6025246742505534, 3.1078162257466104, 5.5016880787963505, 7.284428237609008, 8.075196425786269, 7.735358934507253, 6.3780818926632294, 4.374301236536239, 2.2298139046093026, 0.4750455304712038, -0.4838122427370883, -0.4686539041272125, 0.43063207835908385, 1.8778791123306058, 3.385745330925156, 4.454504254239837, 4.6925726893894595, 3.9428958337025315, 2.2973341241714973, 0.09226757811269477, -2.2003282495181753, -4.095469360671062, -5.213781273948385, -5.3958488020159745, -4.7061462530095435, -3.4326644815261336, -1.9699411127843685, -0.724999913501234, 0.006059034549597682, 0.10784532450435737, -0.3365350237779155, -1.0838437026651442, -1.81348806757134, -2.2360092015042805, -2.168736573011531, -1.6020204376701082, -0.6795224125637591, 0.33911680718787146, 1.1689645147345311, 1.5875197872525584, 1.4943828888307347, 0.9467170678140759, 0.12632212957425676, -0.7136980338072442, -1.3293204562478693, -1.5626757451444784, -1.3749188300293194, -0.8606784564700002, -0.19885950577294945, 0.40363387957203317, 0.7814549195472612, 0.8641293130979265, 0.6840891216048697, 0.362947877139734, 0.05464377019846999, -0.1123269187561576, -0.08586515875065083, 0.09095341466385203, 0.2978666715710223, 0.3687387536218557, 0.17493896643856172], 'positive_zeros': ['0.965135808481614986405658292942896', '2.42352590918712853466567242206663', '2.83914565713673064494934908550961', '3.56947203076070380168261943173674', '4.08831241527517536506397399518433', '4.53537320768920545153705018768903', '5.41066169742392480345008753508256', '6.15927039959388504878409697851313', '6.63788300244926264859356528383641', '7.11186202054915336867025013044971', '7.76114321371533072991784338574948', '8.083294707773213364670804230381917', '8.578585476202832637249814237152791', '9.086184361996998785091766103785683', '9.310491780430194098450854394124255', '9.897535205114377250911723937344623', '10.69693638849651829150433791637935', '10.78840241851468527504478962394020', '11.28628376592839010459808379064035', '11.92828920887095361776041972633358'], 'prelabel': '4-320e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.598503320197044, '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': 1148464560044160078, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.965135808481614986405658292943', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.42352590918712853466567242207', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83914565713673064494934908551', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.529112783831148, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 102400, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, -2, 0, 2, 0, 0, 0, 2, 0, -4, 0, 2, 0, -8, 0, -4, 0, 10, 0, -1, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 10, 0, 4, 0, 12, 0, -6, 0, -4, 0, 14, 0, 2, 0, 4, 0, 2, 0, 0, 0, -16, 0, -8, 0, -4, 0, -4, 0, -4, 0, 14, 0, 20, 0, 0, 0, 18, 0, -2, 0, 0, 0, -16, 0, 11, 0, 10, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 16, 0, -6, 0, 0, 0], 'euler11': [1, 0, 14, 0, 121], 'euler13': [1, -2, 2, -26, 169], 'euler17': [1, -2, 2, -34, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -10, 50, -230, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, -2, 2, -6, 9], 'euler31': [1, 0, -58, 0, 961], 'euler37': [1, -10, 50, -370, 1369], 'euler41': [1, -12, 118, -492, 1681], 'euler43': [1, 6, 18, 258, 1849], 'euler47': [1, -14, 98, -658, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, -2, 2, -106, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, 4, 126, 244, 3721], 'euler67': [1, -14, 98, -938, 4489], 'euler7': [1, 2, 2, 14, 49], 'euler71': [1, 0, -106, 0, 5041], 'euler73': [1, -18, 162, -1314, 5329], 'euler79': [1, 16, 222, 1264, 6241], 'euler83': [1, -10, 50, -830, 6889], 'euler89': [1, 0, -178, 0, 7921], 'euler97': [1, 6, 18, 582, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 2, -6, 9], [1, 2, 5, 0, 0], [1, 2, 2, 14, 49], [1, 0, 14, 0, 121], [1, -2, 2, -26, 169], [1, -2, 2, -34, 289], [1, 8, 54, 152, 361], [1, -10, 50, -230, 529], [1, 0, 6, 0, 841], [1, 0, -58, 0, 961], [1, -10, 50, -370, 1369], [1, -12, 118, -492, 1681], [1, 6, 18, 258, 1849], [1, -14, 98, -658, 2209], [1, -2, 2, -106, 2809], [1, 8, 134, 472, 3481], [1, 4, 126, 244, 3721], [1, -14, 98, -938, 4489], [1, 0, -106, 0, 5041], [1, -18, 162, -1314, 5329], [1, 16, 222, 1264, 6241], [1, -10, 50, -830, 6889], [1, 0, -178, 0, 7921], [1, 6, 18, 582, 9409]], 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/2/n/f'], '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': '4-320e2-1.1-c1e2-0-10', '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': '4-320e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.598503320197044, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1148464560044160078, 'z1': {'__RealLiteral__': 0, 'data': '0.965135808481614986405658292943', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1223454986923476694418920336000,3072184073449728867011592275018', 'Lhash_array': ['1223454986923476694418920336000', '3072184073449728867011592275018'], 'label': '4-320e2-1.1-c1e2-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/2/n/f'}