-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '740657835657222728184050450207,1537128162500829003670109577057,1682254917186462775147652248731,3520040747217253705333775611369', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': -3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 268.6211879468495, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 3, -2, 1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': '1.1.1.1', 'conductor': 66074188401, 'conductor_radical': 39, 'degree': 8, 'euler_factors': [[1, 0, 3, 0, 5, 0, 12, 0, 16], [1, -2, 3, -2, 1], [1, 0, -12, 0, 86, 0, -300, 0, 625], [1, 0, -2, 0, -45, 0, -98, 0, 2401], [1, 0, 6, 0, -85, 0, 726, 0, 14641], [1], [1, -4, -22, -16, 883, -272, -6358, -19652, 83521], [1, 0, 38, 0, 1083, 0, 13718, 0, 130321], [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], [1, -20, 242, -2000, 12523, -58000, 203522, -487780, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, 70, 0, 3531, 0, 95830, 0, 1874161], [1, 0, 46, 0, 435, 0, 77326, 0, 2825761], [1, 24, 346, 3456, 26283, 148608, 639754, 1908168, 3418801], [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], [1, -24, 428, -4680, 41046, -248040, 1202252, -3573048, 7890481], [1, 0, -26, 0, -2805, 0, -90506, 0, 12117361], [1, -4, -110, -16, 11179, -976, -409310, -907924, 13845841], [1, 0, 70, 0, 411, 0, 314230, 0, 20151121], [1, 0, 142, 0, 15123, 0, 715822, 0, 25411681], [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], [1, -32, 700, -9632, 102214, -760928, 4368700, -15777248, 38950081], [1, 0, -300, 0, 36278, 0, -2066700, 0, 47458321], [1, 0, 174, 0, 22355, 0, 1378254, 0, 62742241], [1, 0, 94, 0, -573, 0, 884446, 0, 88529281], [1, 36, 770, 11664, 135579, 1178064, 7854770, 37090836, 104060401], [1, 0, 412, 0, 63654, 0, 4370908, 0, 112550881], [1, 24, 218, 3456, 55083, 369792, 2495882, 29401032, 131079601], [1, 0, -428, 0, 69558, 0, -5085068, 0, 141158161], [1, -12, -118, -432, 39603, -48816, -1506742, -17314764, 163047361]], 'euler_factors_factorization': [[[[1, 0, 3, 0, 5, 0, 12, 0, 16], 1]], [[[1, -1, 1], 2]], [[[1, -4, 5], 2], [[1, 4, 5], 2]], [[[1, 0, -13, 0, 49], 1], [[1, 0, 11, 0, 49], 1]], [[[1, 0, 6, 0, -85, 0, 726, 0, 14641], 1]], [1], [[[1, -2, -13, -34, 289], 2]], [[[1, 0, 19, 0, 361], 2]], [[[1, 0, -23, 0, 529], 2]], [[[1, -10, 71, -290, 841], 2]], [[[1, 0, -46, 0, 961], 2]], [[[1, -12, 107, -444, 1369], 1], [[1, 12, 107, 444, 1369], 1]], [[[1, 0, 46, 0, 435, 0, 77326, 0, 2825761], 1]], [[[1, 12, 101, 516, 1849], 2]], [[[1, 0, -47], 4]], [[[1, -6, 53], 4]], [[[1, 0, -26, 0, -2805, 0, -90506, 0, 12117361], 1]], [[[1, -2, -57, -122, 3721], 2]], [[[1, 0, 70, 0, 411, 0, 314230, 0, 20151121], 1]], [[[1, 0, 71, 0, 5041], 2]], [[[1, 0, -142, 0, 5329], 2]], [[[1, -8, 79], 4]], [[[1, 0, -150, 0, 6889], 2]], [[[1, 0, 174, 0, 22355, 0, 1378254, 0, 62742241], 1]], [[[1, 0, 94, 0, -573, 0, 884446, 0, 88529281], 1]], [[[1, 18, 223, 1818, 10201], 2]], [[[1, 0, 103], 4]], [[[1, 12, 37, 1284, 11449], 2]], [[[1, 0, -214, 0, 11881], 2]], [[[1, -6, -77, -678, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 9, 'label': '8-507e4-1.1-c1e4-0-9', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/507/2/j/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [2.5881261414824634, 2.5803255449091673, 2.5587946483900668, 2.5230185989776905, 2.4724788701851725, 2.406702209386796, 2.325316008544496, 2.2280248955710205, 2.114614031892898, 1.9849378482776734, 1.8388917469377417, 1.6765854049991362, 1.4984171931140513, 1.3051271733750396, 1.0978894851890957, 0.8783258108558643, 0.6485191206917263, 0.41106423946116805, 0.16917983591056043, -0.07339947873512422, -0.31249222806449123, -0.543493687923802, -0.7613801454787799, -0.9609553578981516, -1.1370312035581613, -1.284582563638849, -1.3989433943114362, -1.4761240286979072, -1.51305657683187, -1.5078431936383863, -1.4600832801645705, -1.3710782710494014, -1.2439758805411463, -1.083927692160255, -0.8982897309267404, -0.6964695064955555, -0.4897449537397388, -0.2910801971283822, -0.11487932019987376, 0.023643222363628383, 0.10905677378853759, 0.12632824184520483, 0.061590592670940796, -0.09699679169347362, -0.35851029956306724, -0.7285351422206514, -1.2083241759826422, -1.794336355147705, -2.4779638036706264, -3.24536788670942, -4.077427508777417, -4.950261382066009, -5.835923183804794, -6.703331733694698, -7.519619006220504, -8.251461219603273, -8.866489755158987, -9.335024294916574, -9.632392358707522, -9.739814278564157, -9.645342482486921, -9.345170615078855, -8.845440911720216, -8.161114495074626, -7.315161308295357, -6.338232712102848, -5.268630868109273, -4.148880067519979, -3.0232309284456518, -1.9359100563808707, -0.929632733864254, -0.04178283801424582, 0.6978490947027135, 1.2683134345561053, 1.6583111282530794, 1.8675917342616541, 1.9067441969854897, 1.796068178410624, 1.5640028011697071, 1.2452376362194377, 0.878009446216651, 0.5011515167161162, 0.15125523982995998, -0.14003815182152335, -0.34845282926032767, -0.458857101406483, -0.46607324687227814, -0.37502969593885654, -0.20016582822155987, 0.03613300507723336, 0.3063525530732961, 0.5803563339966363, 0.8281155209365899, 1.0228852050929873, 1.1448778994418667, 1.1826260228642809, 1.1339453392134151, 1.0066714186290153, 0.8189015213309992, 0.596319021285443, 0.36950236596440744, 0.1711722923996416, 0.033012760316919035, -0.018447086104475846, 0.03515282642003753, 0.2018110640188391, 0.4776560786814066, 0.8467152958006865, 1.2820713219366808, 1.7481359827430627, 2.20413375419184, 2.608064640439366, 2.9208238864125615, 3.110477787825874, 3.156687556439422, 3.052527283801062, 2.805337244211887, 2.436793671829235, 1.9819283594390507, 1.4846523933405844, 0.9931927068172449, 0.5554389166691313, 0.21396525214184567, 0.0006222328041915014, -0.06706119432723098, 0.011997380612376972, 0.22186825691953466, 0.5311634117237273, 0.8963356406736395, 1.2663930027096686, 1.5892226283359874, 1.8176580437845153, 1.9149071488855327, 1.8594407356621314, 1.6492614644393762, 1.3019042218001127, 0.8526705131288811, 0.35151257020904647, -0.1416416061179202, -0.5647550218501112, -0.8610284104448188, -0.9855297677148267, -0.9109750701526425, -0.6318061663274323, -0.16547413944889217, 0.44890546823928507, 1.1549074253348328, 1.8849096556144462, 2.5673134577161503, 3.134873315424403, 3.53415673510404, 3.7304028090747443, 3.7106152258130902, 3.485397284784808, 3.089095460294617, 2.572511161388692, 1.995485247993163, 1.419692123868231, 0.9012525596866883, 0.48177426527859785, 0.18354005692867592, 0.008038476681177601, -0.06265177085680362, -0.06135430909920987, -0.02806705526069125, -0.0007193243968796907, -0.005643981994672299, -0.049248048776640005, -0.11247551922976186, -0.1491182352326675, -0.08893869715969649, 0.15456292835701457, 0.6724355812743721, 1.5454983268493057, 2.8285389157599714, 4.536187541905049, 6.631222738438383, 9.018077587365683, 11.54703483881585, 14.021471354620958, 16.210347061603716, 17.869605615464927, 18.777141088078533, 18.752159476479875, 17.673923166698696, 15.502834265346225, 12.303240650452382, 8.233220972214962, 3.5316831382021445, -1.4972082571868357, -6.506814688561244, -11.14693190023756, -15.096603898399296, -18.094702477163906, -19.971409941856418, -20.658790367415044, -20.191971158400964, -18.705435775887043, -16.423629886149154, -13.622136772444772, -10.594128248112806, -7.621610004176613, -4.94836088748594, -2.7492147945219334, -1.117724884464636, -0.06568490381548178, 0.4691259531340687, 0.604794687962544, 0.4892585987953046, 0.27288388979843886, 0.08262261226222677, 2.6678674151682914e-05, 0.049127329138973365, 0.19467562416890866, 0.3504376176261587, 0.397006388973774, 0.20595467876345308, -0.33361633373697436, -1.290921378097809, -2.674949787147638, -4.424009136510868, -6.4066648522084, -8.438966087104138, -10.304495571185162, -11.77973794117544, -12.666339713174253, -12.82990581193279, -12.21397254629396, -10.848289450808208, -8.852444397701321, -6.430530260030172, -3.838051896641765, -1.3502108938780246, 0.7696106842570434, 2.3042189598213896, 3.111482642958576, 3.1390212369157067, 2.429126582544654, 1.1145956950825884, -0.60521506788118, -2.4932756394670035, -4.3055995457335765, -5.823504787746047, -6.881954726972197, -7.386451827614671, -7.320483361564145, -6.743900291757236, -5.775813787511938, -4.572246175284424, -3.301550403025115, -2.1191455189679256, -1.145414870036039, -0.45249872558179177, -0.059077581025277416, 0.06645368537702646, -0.006786364918005725, -0.18849857124904318, -0.3850906421479098, -0.5176845172515419, -0.5345476979028053, -0.4169590663431089, -0.17940091086328977, 0.13644559542588466, 0.47368775557837933, 0.7727680451965724, 0.9834918901608536, 1.075866265096589, 1.0440234362276843, 0.9050735766060028, 0.6943479586832254, 0.4575951037722007, 0.23979873991751102, 0.07604733496074753, -0.014706643531236076, -0.032262884484284264, 0.006956751431257376, 0.07547900229851896, 0.14246837580308436, 0.18236031650884774, 0.18121610473681596, 0.13957101723115112, 0.07171543587645383, 0.0009536845481798903, -0.04893707175822832, -0.06252738195901505, -0.04048125995088222, -0.004528032961403261, 0.0031204572566449107, -0.07461939898950072, -0.2997691603129066, -0.7254169804744411, -1.3819792060272102, -2.266216805759576, -3.334895475870003, -4.506212511843133, -5.6679498242508295, -6.690904093187825, -7.448303079955309, -7.841779361604343, -7.814083783027149, -7.357587070177687, -6.5198413150977865, -5.404011961990231, -4.145084045835418, -2.887359638977208, -1.764135189157257, -0.8782814671098785, -0.28184314516918724, 0.029551149751862824, 0.11152463166551072, 0.057442192401473025, -0.022308548213362152, -0.024477423987074524, 0.12485257766217298, 0.45393244279881384, 0.9393738592497635, 1.5108427010031011, 2.0656245890930847, 2.4918562999885476, 2.6930148821094444, 2.6093750511082425, 2.233377191228344, 1.6144956077998787, 0.8493797555599804, 0.06374249035012924, -0.6127676120365203, -1.0769903374224457, -1.2729880045207238, -1.2030463857222162, -0.9286963209085565, -0.5588785139914653, -0.21957485432872775, -0.021432964990911584, -0.028937951887414517, -0.2357585318287369, -0.5549507226634225, -0.8276224345887973, -0.8488194279928571, -0.41125213871669025, 0.647030589344038, 2.3985578650754285, 4.792284259315541, 7.6401970882205665, 10.633658265525018, 13.38055693964834, 15.465717970548578, 16.53795292111321, 16.371824340242593, 14.916260035632874, 12.330531383305974, 8.996967484210312, 5.456351667489483, 2.330093658366622, 0.23179795663669803, -0.33327985119582126, 0.9309123119763463, 4.050121212961323, 8.757180597742073, 14.520647734070796, 20.613163544211176, 26.20618310320168, 30.4908790297478, 32.83027654890013, 32.83580866829638, 30.412111834888492, 25.78148035935262, 19.48157541269667, 12.246196356430163, 4.888831694239284, -1.805586948384739, -7.187217526233358, -10.839579481285433, -12.617845257864838, -12.645200371104805, -11.275888139377804, -9.00566836706053, -6.374621729724954, -3.877109768729315, -1.8861717416835457, -0.6020667108755107, -0.0447548679783293, -0.0796345166352235, -0.47053308504393043, -0.9481194262448653, -1.2746766987165783, -1.2960035479745906, -0.9735353010667842, -0.3800204142868605, 0.32875900350283416, 0.9573821483196587, 1.3224730052457414, 1.3024911439670182, 0.8682027640358285, 0.09082642542053151, -0.8754366700120921, -1.8292857551823878, -2.568025992297359, -2.9356365081716644, -2.865173954311259, -2.3915621065644705, -1.6439158918086803, -0.8193230334919608, -0.14008598906442973, 0.20000431737750826, 0.08123314265325307, -0.5111282307508946, -1.4810634631555557, -2.6376686790123176, -3.7285581620809083, -4.4900397910099565, -4.711050108468853, -4.270004645311353, -3.1579621414122214, -1.487342976502995, 0.5240730147838122, 2.6000692535517658, 4.452793060890951, 5.831507183137607, 6.575778337438494, 6.632375253388387, 6.053027205299752, 4.980876020624617, 3.6252920841577048, 2.2101935052138533, 0.9338488638114749, -0.06055356507157031, -0.7047542973585419, -1.0033234459664568, -1.017573076355616, -0.8438560771228074, -0.5890224039463141, -0.3405977075982156, -0.15245864199872772, -0.0426499228273864, 0.0002920906710050361, 0.004823838803064503, -0.0004706331689416219, -0.00039635598639435935, 0.0004268351091878173, -0.02054683022283615, -0.09414375872861883, -0.24508043887881073, -0.47865480043596476, -0.771941944217649, -1.0719918810164313, -1.3038396378386528, -1.3906307440479342, -1.2719217666929563, -0.9204171210485578, -0.35515697825162135, 0.3540671767371569, 1.1005529544612656, 1.760693840359555, 2.2191891932275403, 2.3987312588862006, 2.2761887470606266, 1.887547629562508, 1.323148616999456, 0.7115612707444962, 0.18598946211128392, -0.1452376743750874, -0.22166900134175668, -0.04438470251665553, 0.32552944211940305, 0.783154571494338, 1.205775713262778, 1.486089099340347, 1.557659689843701, 1.4089553357449387, 1.085889762094209, 0.6813935017777879, 0.3058695966631887, 0.05705892098453889, -0.0053788434743997455, 0.12374382284317449, 0.39362904507113666, 0.7122494979747124, 0.9727298549549019, 1.0868658394425577, 1.0107224153912513, 0.7576602510176936, 0.39673161188097444, 0.03378628871533844, -0.2257894432985142, -0.3139791350386976, -0.22954737459738395, -0.051905417623676356, 0.07137477352142003, -0.03886090006339947, -0.5391476181898108, -1.500231017561758, -2.855990992991536, -4.3771106431509, -5.678241825441597, -6.269265333547809, -5.64037131558314, -3.365238580311466, 0.7930610576396359, 6.8031010789950095, 14.327041765624573, 22.72561852105881, 31.129882537745683, 38.613274846551555, 44.302982246218804, 47.492339513588796, 47.7760827414834, 45.201141649245905, 40.177094821355, 33.38122568462442, 25.673696549385003, 18.000924938979754, 11.174499863345261, 5.750666734280174, 1.98598961155388, -0.15672087827130507, -0.9737969197861597, -0.918888949658648, -0.47888744847353937, -0.0605096628841521, 0.08303131501588182, -0.11497215524010806, -0.5495110768463396, -1.01136885400873, -1.2701462297870598, -1.1495446760899972, -0.5904051271380449, 0.3127079572741963, 1.3477370975838177, 2.2445240679303082, 2.744116385828073, 2.676587817060847, 2.021919350595595, 0.9202853159939537, -0.3571440073115383, -1.468798190752324, -2.093630929695417, -2.018548492875217, -1.2007313421124317, 0.20668159302075667, 1.8826849437060302, 3.4089981955337056, 4.368625880182075, 4.44492135557211, 3.502980422321766, 1.6354092912626867, -0.8436726638615544, -3.480917629408049, -5.778557349728038, -7.293188000983449, -7.739979522831353, -7.090245713931388, -5.558756425308449, -3.550086433258232, -1.5798609985538674, -0.1697277809208537, 0.2828328857827938, -0.40844685109530404, -2.180722314093595, -4.74041028957611, -7.626280015474963, -10.30322986375088, -12.276720121225503, -13.213895755693207, -12.98354059449622, -11.66289756802874, -9.517552082975076, -6.9458701256933715, -4.3650397110281745, -2.1287048779351814, -0.47090003280896375, 0.5271592455462073, 0.9275435022478006, 0.8908527614663047, 0.6200860347302273, 0.3040935109909209, 0.06960023618358217, -0.035885326983960755, -0.03454189651259705, 0.01106016286258851, 0.037883489179535164, 0.017650113906257706, -0.023687331921945942, -0.008540034520720071, 0.1680632338840114, 0.6011817934341261, 1.336287090898904, 2.3426648973459767, 3.5073898874580207, 4.649554943835861, 5.5578408102689565, 6.053520154211445, 6.029146622026331, 5.47264473532487, 4.478907169835422, 3.242352411245354, 1.9964474754167658, 0.9566623867670045, 0.27447931783209367, 0.0042765700996358754, 0.09004708623833133, 0.38833950737027717, 0.7140880539964615, 0.8941446686829053, 0.8172671788066186, 0.46841177174317944, -0.06492908021891085, -0.6272053450427075, -1.0377089941494442, -1.137994669259147, -0.8430032672455133, -0.18668479514055092, 0.6967175016036511, 1.6091297636461996, 2.3338429025425995, 2.6898988776802994, 2.592912814054531, 2.0793948695826057, 1.2988882126564003, 0.4778556903756288, -0.1389520328624534, -0.3530163150643734, -0.06623118067583741, 0.6904727500559716, 1.7654382643785083, 2.9215623604241188, 3.8947867676684225, 4.469909214690933, 4.527025867262536, 4.0635721541404575, 3.1944256941408073, 2.12449398150459, 1.0794134855350799, 0.24733479985581192, -0.2629301204811789, -0.444381973415377, -0.3808666375332929, -0.20640697541413572, -0.05296084031042147, 0.0003167553917522054, -0.03897420089952816, -0.07424870003171993, 0.05121410896277439, 0.5007100282182846, 1.3824075769458837, 2.697014654767725, 4.311563115319959, 5.97878459033827, 7.383759982517221, 8.210587393106762, 8.225328562277744, 7.3614386297040655, 5.7296925498728815, 3.5975689587998176, 1.3415279420848036, -0.6360678352242211, -2.015405673347269, -2.629869313532761, -2.50179760124692, -1.8404258711814252, -0.9734351090692253, -0.25253719110108525, 0.04238362321440267, -0.21553564574295747, -0.9568546924771864, -1.9302450473447303, -2.76629623781873, -3.079270325149819, -2.5717670674765483, -1.1206131724814163, 1.174720169657474, 4.006663724226548, 6.927971034704715, 9.443139710583857, 11.118966511845857, 11.705531515577626, 11.168413140794046, 9.677178634780923, 7.564429546130901, 5.253955719921557, 3.139655409916599, 1.502514550869757, 0.4671529542582787, -0.002642595686682243, -0.06368914759401122, 0.07414967390745464, 0.21931837117730804, 0.25633161596507853, 0.16728624044912135, 0.01458209909273631, -0.10420647472147543, -0.11688909058337933, -0.02896882025629218, 0.05395651220289463, -0.05998710517682199, -0.596022285575055, -1.7371745859595713, -3.5498614097295724, -5.930658141204614, -8.60092025917048, -11.147606587825265, -13.098991316926968, -14.032083774392271, -13.701747600871785, -12.089228747856522, -9.410953862157964, -6.08935933934632, -2.6722354855768145, 0.3065382688462051, 2.436789247682596, 3.512681788853393, 3.578479499949363, 2.8849419856590317, 1.8044346962198334, 0.7318809867581375, -0.01593462881127506, -0.28549847350695035, -0.10639781372424194, 0.34194757813228543, 0.804310846346197, 1.0431658972946825, 0.9226254946769303, 0.45932008553042114, -0.1772035488873629, -0.7160112129899997, -0.8661945322042165, -0.40998969289871623, 0.7196557766728806, 2.4109341916277516, 4.387442311281666, 6.269846824109113, 7.690854300413674, 8.376723570940454, 8.20320400927791, 7.23135435336537, 5.709955841918287, 3.9736757657025956, 2.351160390676163, 1.0930221782924125, 0.3183458563033195, -0.009479892863728011, -0.046004849686333185, 0.0009852316124076734, -0.053238221062841304, -0.30699426026164706, -0.7431558437830798, -1.241337933408872, -1.6282312172582256, -1.7440529943517704, -1.5033556083010604, -0.9337066837191933, -0.17468576324960577, 0.5710128574589133, 1.1027611217126407, 1.2900370659591025, 1.126402320080717, 0.7279435849737328, 0.2856221450002298, -0.012922109574124936, -0.07779295984221009, 0.0023419595688756916, -0.06494054999123287, -0.7368889553807082, -2.5333163844512194, -5.889983290870165, -11.002273784968072, -17.704924938931725, -25.456062908689255, -33.38104190999299, -40.386326504415685, -45.36652700686032, -47.51732903340963, -46.44752579498785, -42.23578068636522, -35.45348139827208, -27.128415748331964, -18.45263462729817, -10.537222094731804, -4.228739316930328, 0.014529076213972484, 2.187161142777987, 2.6708923638964084, 2.085975269262041, 1.1010752032321942, 0.2628145444072837, -0.11802287810858379, -0.010091920849766537, 0.38920638840198185, 0.7668374607338048, 0.8148259715944133, 0.34275584812533055, -0.6355044834222724, -1.91871326372015, -3.1869953292311317, -4.0966248315564435, -4.390107967021141, -3.9749469933374737, -2.944504648356628, -1.5497478578841095, -0.12909660750920868, 1.0018917174023207, 1.6361107371098291, 1.7233412450754804, 1.372591672737925, 0.7989487464431225, 0.24431924110958, -0.10337604311771455, -0.17171283032388188, -0.018164685903680814, 0.20334636885826726, 0.308636576724163, 0.1660936329623802, -0.2390459431148857, -0.7807080727990888, -1.2134607945494995, -1.243995852515742, -0.6259790439449976, 0.7552248093961398, 2.825051958143664, 5.307558882778352, 7.784440939862013, 9.790088736062835, 10.922757867004398, 10.948816904006893, 9.856962687272203, 7.86066656360435, 5.34684449921547, 2.7680392531126707, 0.538386953279031, -1.0473034967264436, -1.8711606140064188, -2.012841470476136, -1.6776573931235375, -1.1188155255976708, -0.5679834324578611, -0.1779368411743284, 0.009185999591003831, 0.04187499430930527, 0.01239289016894558, 0.0016097328122411127, 0.03333925127736657, 0.05702286886244016, -0.03607790830929805, -0.36910026600422197, -1.0255104249628098, -2.0020463556036034, -3.1866154337711734, -4.38278595338378, -5.354059178473406, -5.87909639229, -5.816721950791029, -5.170426907259471, -4.070618367259186, -2.7342988154753285, -1.4159650611063022, -0.35021598955331823, 0.32192591511484453, 0.5788980782001966, 0.5051823765964953, 0.24987394121245177, -0.025688372813126886, -0.20033087609261782, -0.22704856742472815, -0.13633893734951527, -0.005496898303888291, 0.08384808646360016, 0.08781182608852135, 0.027009066318250643, -0.019497509708813275, 0.05337003108809653, 0.3288647996540305, 0.8199256601066984, 1.4451493438924892, 2.0375553373650437, 2.3870597271965037, 2.3151680707727214, 1.7400670860216363, 0.7170076350268936, -0.5550594939447904, -1.772784536794353, -2.6206413021649824, -2.868678101550206, -2.4517189564652737, -1.4972453816200388, -0.3037657050149521, 0.7296291454478352, 1.2259382998902255, 0.9953193460639996, 0.07595260890858847, -1.2682371969526725, -2.5804518294430445, -3.3034373572580757, -2.987634405344493, -1.4223918955468766, 1.3033805102848925, 4.789891762767082, 8.405220421534185, 11.44935545045969, 13.333140908964491, 13.717139988293365, 12.58744777504379, 10.25375205827236, 7.261216093417452, 4.221696202443262, 1.6582489494495987, -0.09984577391721447, -0.9739242832499794, -1.129862294414198, -0.861284470098665, -0.46768754436815785, -0.1619110635886958, -0.020882920982780325, 0.002631848106001837, -0.0002654249459983509, 0.0026199403966960483, -0.09790454820603087, -0.5759432508163196, -1.8124038452386109, -4.16319006487731, -7.801810670215898, -12.575685080219673, -17.919554147888245, -22.893422979662464, -26.42535983251566, -27.52196033162154, -25.493608941943805, -20.206897584021526, -12.307853191163664, -3.0289268298605223, 6.069362656754182, 13.384464618627655, 17.60402575109418, 18.081789639289088, 14.978763440147208, 9.20460166468446, 2.180531372870293, -4.499437393897712, -9.441999173657127, -11.783860852746134, -11.401289273191486, -8.838056484421157, -5.106084314907751, -1.3970660580440442, 1.259352179422922, 2.2728916836831177, 1.6037642377905539, -0.2720285002118192, -2.54827310128155, -4.372328329310483, -5.09824339544988, -4.470364669023744, -2.700411954863144, -0.35925043821925073, 1.8187613571992758, 3.163329800005619, 3.283826552440427, 2.175952027283461, 0.20568037438760506, -2.0070221324094017, -3.786442102594715, -4.6103922610963695, -4.250943873178433, -2.829476299370949, -0.7648926369798996, 1.375436857298094, 3.04385967210393, 3.870213243297636, 3.77640720476432, 2.9551704513644355, 1.783565077396099, 0.7005720726492842, 0.06742817531097489, 0.05413729745995381, 0.6086342272050698, 1.492902496065237, 2.380945253599383, 2.973908616331069, 3.0882536317861065, 2.704049567218713, 1.966916196583318, 1.1130479733453051, 0.37946959361027227, -0.0747115349524761, -0.21717360619821277, -0.1367703983650491, 0.0022515665133975484, 0.02700401296606076, -0.17330683411392883, -0.6015020848045061, -1.1555417482412016, -1.6665721041933332, -1.9605455627958621, -1.925588085304526, -1.5531267454009574, -0.9406497359375919, -0.2564059173665311, 0.3152865823224135, 0.6351511809150393, 0.6552082412797741, 0.42844758962096935, 0.07834922058330163, -0.24677970467998192, -0.4284890710510391, -0.42789847681794935, -0.28636543348750676, -0.09843719818861868, 0.030229899630759872, 0.032975097977581524, -0.07637509548846265, -0.20148312560772755, -0.19578453610011326, 0.08587230344849661, 0.7260682728632659, 1.6951873077248065, 2.837894457716735, 3.924194895609277, 4.702675901088952, 4.957343968631137, 4.573680072132431, 3.611761648232843, 2.2778737356342056, 0.8626156544446848, -0.35038124264450266, -1.2053537563087762, -1.6697494052767676], 'positive_zeros': ['0.58427601069559211659278518919953', '1.21258031371111450142897206750607', '1.32706513678421127496192652455301', '2.22035890197502677009601545076923', '2.57776087182548201477794171579172', '2.77682253026464955026954085099894', '3.20042096471468075968969185058838', '3.23733454865177329590224391855345', '3.84388913374310136613066332041143', '3.90362739056643014903956334909593', '4.30324775280008398674875661607683', '4.50907840137758826199335631565724', '5.03343672835818185234682035604923', '5.15793714502192657356880132516648', '5.17828559136724514226844144432973', '5.32759007511666517854498648748425', '5.89703178190644632425152677083839', '6.40896089649131685023041641185199', '6.59380417041481276008485035464189', '6.60092293847460045573578207565696', '6.76475613307462198498448976831979', '7.26902923345936071442047001961485', '7.45832661107519511001384848081107', '7.914854382130781075196214412133117', '7.967242877284151867198205796654203', '8.174592963637014901234646926138434', '8.523772592159863876121282326894651', '8.589947577738212527438042482678383', '8.812968544246956760293060853274625', '8.942579938555328393974933150966255', '8.972105478683061547030849688736445', '9.620408432861726135263780124584789', '9.708459303304471877678323976374367', '9.758777023120490532268167020652740', '10.12766739455584385987827426668481', '10.38516686379216812754785710299452', '10.39387809811603231696194845844312', '10.57716475040532129221519695907359', '11.03703227081171774483274474939247', '11.07653171725581739287371986266812'], 'prelabel': '8-507e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 2081836496521347633, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58427601069559211659278518920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.21258031371111450142897206751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.32706513678421127496192652455', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 268.6211879468495, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 66074188401, 'conductor_radical': 39, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, -3, 0, 0, 0, 0, 1, 0, 0, -6, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 12, 0, -2, 0, 20, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 8, 2, 0, 8, 0, 24, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -9, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 32, 0, -4, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36], 'euler11': [1, 0, 6, 0, -85, 0, 726, 0, 14641], 'euler13': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler17': [1, -4, -22, -16, 883, -272, -6358, -19652, 83521], 'euler19': [1, 0, 38, 0, 1083, 0, 13718, 0, 130321], 'euler2': [1, 0, 3, 0, 5, 0, 12, 0, 16], 'euler23': [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], 'euler29': [1, -20, 242, -2000, 12523, -58000, 203522, -487780, 707281], 'euler3': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler31': [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], 'euler37': [1, 0, 70, 0, 3531, 0, 95830, 0, 1874161], 'euler41': [1, 0, 46, 0, 435, 0, 77326, 0, 2825761], 'euler43': [1, 24, 346, 3456, 26283, 148608, 639754, 1908168, 3418801], 'euler47': [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], 'euler5': [1, 0, -12, 0, 86, 0, -300, 0, 625], 'euler53': [1, -24, 428, -4680, 41046, -248040, 1202252, -3573048, 7890481], 'euler59': [1, 0, -26, 0, -2805, 0, -90506, 0, 12117361], 'euler61': [1, -4, -110, -16, 11179, -976, -409310, -907924, 13845841], 'euler67': [1, 0, 70, 0, 411, 0, 314230, 0, 20151121], 'euler7': [1, 0, -2, 0, -45, 0, -98, 0, 2401], 'euler71': [1, 0, 142, 0, 15123, 0, 715822, 0, 25411681], 'euler73': [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], 'euler79': [1, -32, 700, -9632, 102214, -760928, 4368700, -15777248, 38950081], 'euler83': [1, 0, -300, 0, 36278, 0, -2066700, 0, 47458321], 'euler89': [1, 0, 174, 0, 22355, 0, 1378254, 0, 62742241], 'euler97': [1, 0, 94, 0, -573, 0, 884446, 0, 88529281], 'euler_factors': [[1, 0, 3, 0, 5, 0, 12, 0, 16], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, -12, 0, 86, 0, -300, 0, 625], [1, 0, -2, 0, -45, 0, -98, 0, 2401], [1, 0, 6, 0, -85, 0, 726, 0, 14641], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, -22, -16, 883, -272, -6358, -19652, 83521], [1, 0, 38, 0, 1083, 0, 13718, 0, 130321], [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], [1, -20, 242, -2000, 12523, -58000, 203522, -487780, 707281], [1, 0, -92, 0, 4038, 0, -88412, 0, 923521], [1, 0, 70, 0, 3531, 0, 95830, 0, 1874161], [1, 0, 46, 0, 435, 0, 77326, 0, 2825761], [1, 24, 346, 3456, 26283, 148608, 639754, 1908168, 3418801], [1, 0, -188, 0, 13254, 0, -415292, 0, 4879681], [1, -24, 428, -4680, 41046, -248040, 1202252, -3573048, 7890481], [1, 0, -26, 0, -2805, 0, -90506, 0, 12117361], [1, -4, -110, -16, 11179, -976, -409310, -907924, 13845841], [1, 0, 70, 0, 411, 0, 314230, 0, 20151121], [1, 0, 142, 0, 15123, 0, 715822, 0, 25411681], [1, 0, -284, 0, 30822, 0, -1513436, 0, 28398241], [1, -32, 700, -9632, 102214, -760928, 4368700, -15777248, 38950081], [1, 0, -300, 0, 36278, 0, -2066700, 0, 47458321], [1, 0, 174, 0, 22355, 0, 1378254, 0, 62742241], [1, 0, 94, 0, -573, 0, 884446, 0, 88529281]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/j/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': '8-507e4-1.1-c1e4-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-507e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 2081836496521347633, 'z1': {'__RealLiteral__': 0, 'data': '0.58427601069559211659278518920', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '740657835657222728184050450207,1537128162500829003670109577057,1682254917186462775147652248731,3520040747217253705333775611369', 'Lhash_array': ['740657835657222728184050450207', '1537128162500829003670109577057', '1682254917186462775147652248731', '3520040747217253705333775611369'], 'label': '8-507e4-1.1-c1e4-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/j/e'}