-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '458566174490006322573476514776,1300141463231923341172681123120,1518835339360741707514712242626,2468467533762027883719797301170', 'a10': 0, 'a2': -6, 'a3': 0, 'a4': 17, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -30, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 669.3698663148037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, 0, -13, 0, 169]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'euler_factors': [[1, 6, 19, 42, 69, 84, 76, 48, 16], [1, 0, -6, 0, 27, 0, -54, 0, 81], [1, 0, 6, 0, 59, 0, 150, 0, 625], [1], [1, -12, 82, -408, 1563, -4488, 9922, -15972, 14641], [1, 0, -13, 0, 169], [1, 0, 5, 0, -264, 0, 1445, 0, 83521], [1, 0, -14, 0, -165, 0, -5054, 0, 130321], [1, 8, 2, 128, 1843, 2944, 1058, 97336, 279841], [1, 2, -55, 2, 2524, 58, -46255, 48778, 707281], [1, 0, -124, 0, 5766, 0, -119164, 0, 923521], [1, 6, 89, 462, 5004, 17094, 121841, 303918, 1874161], [1, 0, 69, 0, 3080, 0, 115989, 0, 2825761], [1, 12, 22, 432, 6843, 18576, 40678, 954084, 3418801], [1, 0, -84, 0, 6182, 0, -185556, 0, 4879681], [1, -20, 362, -3680, 33379, -195040, 1016858, -2977540, 7890481], [1, 0, 66, 0, 875, 0, 229746, 0, 12117361], [1, 0, -83, 0, 3168, 0, -308843, 0, 13845841], [1, -48, 1094, -15648, 153243, -1048416, 4910966, -14436624, 20151121], [1, 36, 682, 9000, 88131, 639000, 3437962, 12884796, 25411681], [1, 0, -58, 0, 11499, 0, -309082, 0, 28398241], [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], [1, 0, -228, 0, 26774, 0, -1570692, 0, 47458321], [1, 0, 126, 0, 7955, 0, 998046, 0, 62742241], [1, 0, 142, 0, 10755, 0, 1336078, 0, 88529281], [1, 0, -163, 0, 16368, 0, -1662763, 0, 104060401], [1, 0, 100, 0, 23718, 0, 1060900, 0, 112550881], [1, 4, -202, 16, 34363, 1712, -2312698, 4900172, 131079601], [1, 0, -340, 0, 52662, 0, -4039540, 0, 141158161], [1, 10, -151, 250, 38932, 28250, -1928119, 14428970, 163047361]], 'euler_factors_factorization': [[[[1, 3, 5, 6, 4], 2]], [[[1, -3, 3], 2], [[1, 3, 3], 2]], [[[1, 0, 3, 0, 25], 2]], [1], [[[1, -6, 23, -66, 121], 2]], [[[1, 0, -13, 0, 169], 1]], [[[1, 0, 5, 0, -264, 0, 1445, 0, 83521], 1]], [[[1, 0, -14, 0, -165, 0, -5054, 0, 130321], 1]], [[[1, 4, -7, 92, 529], 2]], [[[1, 1, -28, 29, 841], 2]], [[[1, 0, -31], 4]], [[[1, 3, 40, 111, 1369], 2]], [[[1, 0, 69, 0, 3080, 0, 115989, 0, 2825761], 1]], [[[1, 6, -7, 258, 1849], 2]], [[[1, 0, -42, 0, 2209], 2]], [[[1, -5, 53], 4]], [[[1, 0, 66, 0, 875, 0, 229746, 0, 12117361], 1]], [[[1, 0, -83, 0, 3168, 0, -308843, 0, 13845841], 1]], [[[1, -24, 259, -1608, 4489], 2]], [[[1, 18, 179, 1278, 5041], 2]], [[[1, 0, -29, 0, 5329], 2]], [[[1, 6, 79], 4]], [[[1, 0, -114, 0, 6889], 2]], [[[1, 0, 126, 0, 7955, 0, 998046, 0, 62742241], 1]], [[[1, 0, 142, 0, 10755, 0, 1336078, 0, 88529281], 1]], [[[1, 0, -163, 0, 16368, 0, -1662763, 0, 104060401], 1]], [[[1, 0, 50, 0, 10609], 2]], [[[1, 2, -103, 214, 11449], 2]], [[[1, 0, -170, 0, 11881], 2]], [[[1, 5, -88, 565, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 6, 'label': '8-637e4-1.1-c1e4-0-6', '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/637/2/q/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.2059407733197099, 0.20380932240694127, 0.1986720070542323, 0.19036371326410348, 0.17875768690046517, 0.1638196470023867, 0.1457091477650265, 0.12466774660400112, 0.10098115893886518, 0.07497209116290383, 0.047000266503541825, 0.017493396646433058, -0.013047728592720792, -0.04404588156458145, -0.07483413610044427, -0.10468999984913754, -0.13285933235283512, -0.15856926569208626, -0.1810320926745514, -0.19949878873353385, -0.21329908413579113, -0.22187296250979902, -0.2248042634864035, -0.2218711466797771, -0.2130781288371467, -0.19868128617648623, -0.17921579662691736, -0.15549244230943107, -0.12857839046102945, -0.09977213987207534, -0.07057177956523947, -0.04258277042221522, -0.01742652720378344, 0.003349928288560547, 0.018375583016609482, 0.02658741299665749, 0.02733099631196038, 0.020440095188997285, 0.006308411642464519, -0.014083025953976374, -0.03919508241439525, -0.06700227885888163, -0.09510331961583551, -0.12090529869365124, -0.1418453613794961, -0.15563897574345367, -0.1605512713889999, -0.15563511240794523, -0.1409266713261914, -0.11758786356079731, -0.08796740305509751, -0.05545048066201317, -0.02419250978850241, 0.001280926165091704, 0.016654117516992063, 0.018597212587190597, 0.005585898535713773, -0.021223268810399435, -0.05708147876667553, -0.09293145205495774, -0.11491624464006603, -0.1041482765694166, -0.03691852015008955, 0.11446564838429586, 0.3803852548438376, 0.792073220359137, 1.3790039086209387, 2.1659008891647615, 3.1695270500733925, 4.395293706097709, 5.833864855561279, 7.458252400410029, 9.221549066683808, 11.055834478046782, 12.873384504514119, 14.56784044969888, 16.01691967132093, 17.08802953168318, 17.6487709922586, 17.572552109356508, 16.74590004920193, 15.079425369474233, 12.52404297328331, 9.073378638608498, 4.767549620192338, -0.30021221299933737, -5.974587330999458, -12.049628073679317, -18.27796179553267, -24.378130531714614, -30.0431361653046, -34.96537045613183, -38.85618439510017, -41.4627370546343, -42.58596621523876, -42.10040124613441, -39.965669511777854, -36.23307815458377, -31.04912294773006, -24.649400021032932, -17.345901603228768, -9.509229372020387, -1.5447101819644002, 6.1343210096665235, 13.133203607561466, 19.10422016563036, 23.778179066446086, 26.977152786320488, 28.623038368904318, 28.74495645344822, 27.48503548752298, 25.07193454382861, 21.796471300764978, 17.98999323172458, 14.002267748608409, 10.15832932899096, 6.7299204906009535, 3.917439661032391, 1.837984525997546, 0.5140182799664723, -0.12028679003431876, -0.20226691417729628, 0.08207825458046711, 0.5259583777545523, 0.9337290822698547, 1.1507887407307573, 1.087704700277076, 0.7363195543860568, 0.1747917801901508, -0.4400392485835296, -0.8935210753908083, -0.9431525608499498, -0.3560091733380448, 1.049542995454139, 3.3640656542433445, 6.5572062629476795, 10.457254634475774, 14.746180820828172, 18.98129111140049, 22.62753310757859, 25.102198986763675, 25.83838190287391, 24.37312431458393, 20.40317876383797, 13.835718046409266, 4.83713927983853, -6.127704646456463, -18.32476233764072, -30.792838641828197, -42.40170360087466, -51.94124324408135, -58.238720898778624, -60.26646604239679, -57.24784378211339, -48.766752073149846, -34.82263500009284, -15.854062631033006, 7.266054831472063, 33.27554508491696, 60.62310999708491, 87.582454841095, 112.39104362829002, 133.4296387330641, 149.33823793795898, 159.11383386192355, 162.20901379281256, 158.63323051581258, 148.88567875149855, 133.8850321863698, 114.90359962769003, 93.48990374551504, 71.26257771267694, 49.759823149143614, 30.32670219557596, 14.017952296225465, 1.4949088890642181, -7.000117589225059, -11.624386181603748, -12.887958192860085, -11.56574285638247, -8.584644327775967, -4.908215239662953, -1.429011391766873, 1.132584797199387, 2.2964999241742543, 1.8558741091507172, -0.12766705615972868, -3.3563016601685973, -7.354355677551071, -11.546630471484626, -15.351878075623903, -18.255983683560626, -19.872787658185946, -19.990706504297417, -18.59752451247204, -15.861785386539925, -12.100898062657125, -7.735385456649663, -3.224645550383375, 0.9924780831195891, 4.544826546093093, 7.169279745476306, 8.74485475163353, 9.28247349754756, 8.904877506821514, 7.821894835880298, 6.299673055432048, 4.6095870172130535, 2.991474210975391, 1.6284905907287426, 0.630932795276656, 0.031143819199421385, -0.2069044643261396, -0.16977782302536318, 0.02807572186473536, 0.2697671032944784, 0.4569261655204352, 0.5245044246346785, 0.44783855429518105, 0.24089546623492777, -0.05198960266806335, -0.36899569690801876, -0.6473570873513341, -0.8364829755974731, -0.9068100820413065, -0.8547806199354404, -0.7033944530553401, -0.4934571890460798, -0.27305681548386934, -0.08696222169849602, 0.03329873179208561, 0.07738683131553266, 0.05833881151075909, 0.00983607138480724, -0.020816261969880852, 0.017208101804795595, 0.16726933829850282, 0.45533158756692643, 0.8833591357975461, 1.4271973590236624, 2.0385890092405936, 2.65192010727608, 3.1967029809713896, 3.60751275591895, 3.8330272859970083, 3.84481260950304, 3.6451698807782877, 3.262675490517576, 2.7460701783028734, 2.157514998057248, 1.5645558550060636, 1.0270600904816205, 0.589045088116836, 0.2744520016291765, 0.08599823526123249, 0.007113751266109812, 0.007690324639471184, 0.05148608517968721, 0.10380841522709064, 0.13796541782252272, 0.13932665621840912, 0.10661889431970431, 0.050241893501307755, -0.011859225129190708, -0.05932944795482931, -0.0747602713483837, -0.04826204667482624, 0.020493326293637096, 0.12222191739809793, 0.23991592014353763, 0.35295857089806587, 0.4415692167749044, 0.4905352531077635, 0.49220999111543107, 0.44847198044581904, 0.36927451666872024, 0.27000635766266357, 0.16824387769264787, 0.08012580595099796, 0.016988399791756738, -0.016415108552797725, -0.02222003317449352, -0.008245072043536137, 0.014710916852036352, 0.035761638053783414, 0.046644153709938775, 0.043838879873968555, 0.02901538125715411, 0.008176372735113999, -0.010113657125703874, -0.01731083722782439, -0.0074985349028574445, 0.020967211093657703, 0.0648036036549727, 0.11624116322481817, 0.16500739641793966, 0.20080377418498568, 0.21576161106587333, 0.2065187552492403, 0.17502212445912282, 0.12803861866524854, 0.0756192608356472, 0.028709785852685528, -0.0035802457693205436, -0.016035600247909426, -0.008469419351391063, 0.014354725043535237, 0.044237586815633556, 0.07174747634871272, 0.08868625762041807, 0.09043013325410622, 0.07690833751896639, 0.05233569942997418, 0.02395832928032087, -3.356921064394928e-05, -0.013186889534072887, -0.012660268885793713, 1.5124317773823148e-05, 0.01948782035171267, 0.03837389294029014, 0.049757425291391336, 0.04965523286820981, 0.03868430610678141, 0.021850257217883917, 0.00666789404849971, -8.280018365788117e-05, 0.003732825948769636, 0.012425257653317387, 0.011353658225333803, -0.02125554727392139, -0.10884738848981779, -0.2686769152029049, -0.5027415112059205, -0.7892936710320471, -1.0790773781990437, -1.2970396742312433, -1.349371306866246, -1.137971525973472, -0.5854668066524009, 0.34596817608171215, 1.6389495538879724, 3.2089550279019847, 4.900455163717881, 6.505260501489834, 7.788847066329703, 8.525038513001213, 8.540433728228468, 7.746298294787497, 6.160062420768932, 3.9163991998533327, 1.2610613156745176, -1.491367853014052, -4.003252897525184, -5.964146122943534, -7.148402154029276, -7.453211421816337, -6.911195658952982, -5.685384065446326, -4.045557437264072, -2.306926428018333, -0.7689869522395221, 0.3386677779012471, 0.9013823193844195, 0.9404572849983154, 0.6017612309460402, 0.120504050378176, -0.23264080242364152, -0.2183482134041483, 0.3140271045251884, 1.3880500267526714, 2.890796090824196, 4.593981888482816, 6.198855377583781, 7.400905168177939, 7.97002121813726, 7.794597639944706, 6.902313716017791, 5.460555233673969, 3.750526255011764, 2.085254643931409, 0.7361132731559598, -0.12496392587636769, -0.4648617047897248, -0.3964391292262028, -0.13723139042515833, 0.06127754641486305, -0.00025448717459052153, -0.38551398941525034, -0.9718484031386704, -1.4474848333329482, -1.359243785278175, -0.21524819444352927, 2.376189222690307, 6.565174510494823, 12.175389464323166, 18.656797997047946, 25.10595028940052, 30.39385072511208, 33.44499458532403, 33.434441084319886, 29.980861270154204, 23.343119152028923, 14.572836410473055, 5.354004894258504, -2.225001688719588, -5.959898529851972, -3.9141910373383073, 5.1563397685853385, 21.512090985521148, 44.27726518258117, 71.46861010593351, 100.22767004452022, 127.19111336956949, 148.99984377676864, 162.9546404828533, 167.34955429624523, 161.6875939221537, 146.82087973832824, 124.96419072762441, 99.09765330314617, 72.42910483569716, 47.933822719377844, 27.929412709706586, 13.614629608559438, 4.988675784860741, 1.0245210087576992, 0.013997628043089485, 0.043696121147829406, -0.4729618175260716, -2.350099392411482, -5.366317213444701, -8.24223510940607, -8.86441883670332, -4.726871992149964, 6.477264878408127, 26.290492956991166, 55.015038335161535, 91.4306791444036, 132.88075855699523, 175.55743330642775, 214.95335906428394, 246.54618026612016, 266.7655011662725, 273.3663493124499, 265.6628973950343, 244.70654569560466, 213.35012166210745, 175.47053376062723, 135.29137024834856, 96.82916380629227, 63.405283839317484, 37.09638041892047, 18.59383343847122, 7.335915663916966, 1.81881253682102, 0.03447022291650309, -0.05139402750632602, -0.0888136457200515, -1.074733385984893, -3.275273252082804, -6.320663531548998, -9.43506139395305, -11.765145852971228, -12.655781508004218, -11.836453518295526, -9.505760505100428, -6.286290269079418, -3.0048768960931835, -0.4453833924232746, 0.8851322995542283, 0.9408996844642868, 0.19397139420880868, -0.45062087496967884, 0.1498031034243784, 3.1000458624228733, 9.177043523065006, 18.596422529265144, 30.8863658356651, 44.94164375465656, 59.175083092400854, 71.75183688774113, 80.91960906826267, 85.43245955023642, 84.68635064695596, 78.77750654082809, 68.51305406418484, 55.3398635473553, 40.967366496440945, 27.064336764945303, 15.025002888142394, 5.781048589692304, -0.31883541076318755, -3.4689616445619658, -4.277489409397278, -3.586888965019005, -2.2532763162794307, -0.9696602826877984, -0.15654841811810183, 0.07205455975461524, -0.13364517555127575, -0.4607785818317377, -0.5604641197339406, -0.1666323888932793, 0.826082135319107, 2.3328809174248, 4.1026226907268075, 5.801047581428755, 7.095557663276246, 7.7303682497192225, 7.589724949127221, 6.738214355042836, 5.3777181631421005, 3.7874782486079437, 2.2598677247608783, 1.0350930012573245, 0.24273453557803626, -0.11478857139047373, -0.14630398356138619, -0.03150433879076283, 0.0356574682230059, -0.09884942746497857, -0.5093598646650389, -1.1763380938750145, -1.9973008314682863, -2.8154773037187004, -3.4622696888460247, -3.8085564982239024, -3.7890778110913828, -3.411466184443596, -2.7532012875889795, -1.9440441322217883, -1.1259737581268041, -0.4218001760819016, 0.08665067261545004, 0.3709946835597888, 0.45316496504675324, 0.3900808427407932, 0.25352835622876024, 0.1096954266309836, 0.0037433921639725646, -0.04611046552258361, -0.0463604889212355, -0.019349345616599057, 0.009223354025284854, 0.020314808057433954, 0.007450633848813147, -0.02278459660382058, -0.05578546802519898, -0.07587002195794287, -0.07289515285190741, -0.04692413736945117, -0.007503247993950647, 0.030644279625231828, 0.05350404507902866, 0.053678424372236105, 0.03398676214258034, 0.0068285154436990465, -0.010107120378221809, -0.0004176103353436978, 0.044212528257809344, 0.11949547108263453, 0.2079624127600787, 0.28387013310849063, 0.3202494333725495, 0.29654473098314643, 0.20593162347343522, 0.060319878040825094, -0.1134323216193897, -0.28027258676786443, -0.4051166725538313, -0.46197575323088436, -0.4418466078287928, -0.3544411894817101, -0.22479250087758915, -0.08622598697102583, 0.02876664491431191, 0.09735169088641676, 0.11212648672103717, 0.08134625368659874, 0.02475712247870999, -0.03282260410953491, -0.06956585625806884, -0.07444702257840811, -0.04882526479973123, -0.004617717972172104, 0.040002368930172484, 0.06759267654508651, 0.06815431915611432, 0.04213310115902192, -8.812709056313672e-05, -0.0419836150380462, -0.06702592672735781, -0.06451763028494528, -0.03388838629652712, 0.014017773550930897, 0.06223790845702277, 0.09381095401940369, 0.09742121969201266, 0.07186769503191753, 0.02809458198461445, -0.014533707370410497, -0.035133314063341366, -0.01897927871075816, 0.03673331224650987, 0.12045793430130759, 0.20879292191655394, 0.27448670720851176, 0.295526447399386, 0.2629484080156681, 0.1858301997311591, 0.0913183474237231, 0.016255058628373262, -0.003894619494725758, 0.05366680230967969, 0.19062031423752504, 0.38502101829068724, 0.595628910076903, 0.7726026332560275, 0.8738338116740472, 0.8756509098362554, 0.7783909463079148, 0.6069463611094151, 0.4048562446202432, 0.21771467176374903, 0.07955265857705347, 0.004298208977753621, -0.016571989190621493, -0.00820509676588044, 3.472558108798018e-06, -0.012258681774975966, -0.04692650803161784, -0.08680543352066705, -0.10426398713612943, -0.07711378541387272, -0.006727989165294097, 0.07163167867401023, 0.0902274678738564, -0.03549673843574219, -0.3764735281279554, -0.9570289022302892, -1.729394289326642, -2.564462007781632, -3.272693130326746, -3.649105283312781, -3.5295863537101857, -2.8522938956040114, -1.710945789748581, -0.34669762065193294, 0.8983349557443234, 1.6617298567259158, 1.6745133107905843, 0.8694221386292467, -0.5579757374897144, -2.1467923668358533, -3.246427097658669, -3.178827294552598, -1.4283575303201128, 2.1722270225977467, 7.312298558869445, 13.192400018418299, 18.62317042288319, 22.24492621491785, 22.89234995927587, 19.882427476183977, 13.223376392342617, 3.7411026068658892, -6.9269991916753035, -16.677616117357775, -23.35544264709023, -25.186050566138377, -21.191029766837822, -11.466026463548081, 2.774932612842843, 19.386729233206694, 35.74599078244754, 49.250220013593434, 57.78553875315837, 60.15838415840819, 56.434735993787875, 47.73469510803904, 35.90827616048007, 23.161597541833913, 11.616899518130909, 2.785443096739646, -2.653075310452071, -4.848914365007202, -4.6205027759375366, -3.115272410928148, -1.4256014139651565, -0.28795533228932846, 0.07594673321408799, -0.05504556495646733, -0.09159930560623882, 0.5803948740951715, 2.3251130448676025, 5.07810133040652, 8.307760161178807, 11.149792221438242, 12.727824271160346, 12.426038464956521, 10.091930843205759, 6.146772538958369, 1.5425841314818687, -2.5758291651117924, -5.224097171325072, -5.878414479637795, -4.672309037877337, -2.365075627114363, -0.060886815123497716, 1.2209426403635217, 1.0174581513624397, -0.20545827823835944, -0.9496284778536656, 1.0821799581557623, 8.425746789028091, 23.112224304874907, 45.87614450795744, 75.53660979819325, 108.96115409587833, 141.3787791483993, 167.0307440588923, 180.30511309333184, 177.4651582322502, 157.33248419275927, 121.59661660856453, 74.85529825449665, 24.194641591397, -22.523481675391587, -58.237829658798645, -78.01980281752861, -80.10561796955537, -66.20884045593218, -41.07626966037092, -11.41148287134832, 15.797796334219576, 34.75042266502782, 41.89194712990377, 36.65715951074926, 21.738685602227125, 1.8048673690208128, -17.80887096843487, -32.25080817731753, -38.23608753910962, -35.02600796461644, -24.33642766989654, -9.633430680394735, 4.833787853145073, 15.247827824108617, 19.32598752900428, 16.901286541294102, 9.851396660485479, 1.5987367337808798, -3.8449813503265275, -3.067519567608943, 5.773152164207319, 22.46889785949271, 44.64865536870281, 68.21550906207028, 88.55840143993962, 101.51357954093075, 104.14445627732209, 95.43312864527799, 76.78267197545136, 51.385511722515986, 23.418617304568436, -2.777973391207598, -23.51677689879724, -36.503268981263595, -41.130759131948174, -38.38468478890407, -30.381954204225693, -19.754498287106493, -9.076106389962794, -0.34397016394883756, 5.42494150364542, 8.093887467308656, 8.181561447706516, 6.607727203177547, 4.409710869828891, 2.382189597505854, 0.9520019356593651, 0.200987664656039, -0.032792000334013166, -0.016144986039026706, 0.023493492701737798, -0.016465831420317597, -0.10445219068329395, -0.12658685509729362, 0.032906535813545475, 0.4165552038322503, 0.9591925530406353, 1.5060139085900823, 1.8660355668079933, 1.8865753129330614, 1.5275390861592137, 0.87704736288378, 0.1247224494527854, -0.49693579077361294, -0.795299706585864, -0.6920203800302287, -0.25291189051745167, 0.3277102498613142, 0.7861501650184467, 0.8822494767200716, 0.48441924052413404, -0.3764362740547054, -1.5064367607097775, -2.597844222363082, -3.311425651407874, -3.376843153917406, -2.6859534806191396, -1.3178336532153259, 0.47815052097570265, 2.339714151538132, 3.894494858608298, 4.855310154026142, 5.079797501861767, 4.59928992860411, 3.611201750672768, 2.399027419636095, 1.2505666644174716, 0.38909293583115645, -0.07542368701022284, -0.1590457341559162, 0.023507032437679494, 0.3084078515698353, 0.5416994966838322, 0.6251338358878653, 0.5355782881158796, 0.31996779877236114, 0.06898450061079425, -0.12397278729518903, -0.19647557359115672, -0.13605019951877648, 0.020860746332685434, 0.2073510956093444, 0.35196969414308654, 0.4046890083229469, 0.3555764475935193, 0.2321373244870267, 0.08527486002059168, -0.030680578975306596, -0.07953412152566934, -0.056555181397886206, 0.011855393947726289, 0.07921744570146667, 0.09727697439700357, 0.03515508650115294, -0.10880155169046961, -0.3053357413385917, -0.5053488967949215, -0.6562473517306194, -0.7178183678615583, -0.6752347393416059, -0.5458874538854295, -0.36965597727748756, -0.19497997787038399, -0.06458414603791246, -0.0033626535418802015, -0.012347306888930359, -0.07153367248991033, -0.14879704066161106, -0.21267696399423106, -0.2420082391041002, -0.23028376674317183, -0.18546375116905234, -0.12548162480923092, -0.06884194661991401, -0.028017698034946102, -0.006625814702782358, -0.0002212252354736227, -0.00010057587917221752, 0.001584704653406884, 0.007979957740481108, 0.016668688730947324, 0.021708692873550792, 0.017060979959833484, 0.00010125354263737976, -0.025999681004432965, -0.05365285806798263, -0.07408559301854506, -0.0808895791941174, -0.07259159587737428, -0.05324292755323021, -0.030417005097885415, -0.011721274616425158, -0.0013683009708883047, 0.0011891805533435426, 0.00018573320448428903, 0.0006778726509892164, 0.005219844423929252, 0.0121615936037487, 0.016712025986384303, 0.014474268646003608, 0.006111405168870936, -9.987122063291762e-05, 0.010235877917051609, 0.051590667019710296, 0.1296157547484371, 0.23328774600843782, 0.33200984721409743, 0.3822989079363339, 0.34793075721382927, 0.22018986694279516, 0.03653560139344368, -0.10715648014060092, -0.06547903416173265, 0.3206826776642071, 1.180702731795498, 2.5662426858802534, 4.402938247190856, 6.482972796966019, 8.492069005419955, 10.06966649618321, 10.903853302914698, 10.804528535208126, 9.753473622405616, 7.929503205550257, 5.691648120384843, 3.4593036211280905, 1.6057650924221292, 0.37314548004232506, -0.18884601058011768, -0.23101036401624003, -0.03385897699235764, 0.09967904040202144, -0.03819037263678442, -0.46690713538089496, -0.991952265552265, -1.2532524451287086, -0.8331647501830809, 0.5972778580778185, 3.140971512402145, 6.594961351655455, 10.485564427010729, 14.157030762729987, 16.907841066808842, 18.174580003970913, 17.739189270084122, 15.734695567269037, 12.58779519885074, 8.924726455402704, 5.4313680880745565, 2.6367973377183263, 0.8045023780305156, -0.08338376139164033, -0.2694439119770197, -0.10161083245940805, 0.10522571315567385, 0.17153503303005485, 0.0872296302585416, -0.02905526638983252, -0.023188749057005673, 0.1866886214586037, 0.5415588574181017, 0.847826962020006, 0.8445293741614619, 0.3221587466458633, -0.7303119196513285, -2.0751044546789297, -3.261870233534431, -3.737964746015571, -3.0305797634909992, -0.9501090216144252, 2.29439070031622, 6.099411845661692, 9.61722501429847, 11.989112743345014, 12.593706307132269, 11.262313365706916, 8.388495418212363, 4.758596941966997, 1.3022101958963561, -1.18442691027905, -2.303016439510181, -2.1753400398052016, -1.330653019052178, -0.4462612183995648, -0.018825532891273117, -0.07708744100836283, -0.11656043332881998, 0.6936375316009467, 3.0727423893089525, 7.07355363984755, 11.596682393192102, 14.210145882850213, 11.57700231437797, 0.18843745487535174, -22.64700481527941, -57.63402677580313, -102.4299032494105, -151.75110167615108, -198.07877978363223, -232.97783351286964, -249.18032060311327, -242.52160043899545, -213.13496678652757, -165.88225472596417, -109.77401611433167, -55.58947813752361, -13.163859845929398, 11.218178955726458, 16.93479438093879, 9.700901865353948, 0.5500314990800902, 3.4276539555334486, 31.75002786789846, 94.79736323118573, 194.85653079519864, 325.75845261768626, 473.83611941312637, 620.2059664052127, 743.9522747757376, 826.4361895037673, 856.6884597552379, 831.9451802863001, 757.2052007100092, 644.3168572771863, 510.4221588650593, 373.734255337366, 249.97417423659007, 149.9570930335435, 78.15197740167064, 32.899104856114185], 'positive_zeros': ['0.36174492751192283920582065736580', '1.02563077160050588388763888263621', '1.19814982068977736533655416662493', '1.65438281468056873717286811130993', '1.75789193504972211826357711750812', '1.94727753319219183722341688458174', '2.65451630707336712811170433743397', '3.19363821162491801652653090674407', '3.74091289655486929302239605028545', '3.80574935754804569119346087585847', '4.00872987438536625854239342655422', '4.13504431006134506523862720970039', '4.54563447999940184406540278293268', '4.89692257069560783077233991617117', '5.47332365673608099628079144604456', '5.70310504524885945680930765127637', '5.81097095487179657548977896476242', '6.21101416090532414378092411036341', '6.59621244688971070378589983007263', '6.68379195279553670757359955368941', '6.86981878470427440821554762111773', '7.17662170439854535957314117326932', '7.28794309194263491909331314502424', '7.33662940912575958561207768540255', '7.980029677477025086783119041861432', '7.986663527885752340171478667087658', '8.212496328520291359051336539214810', '8.336062824914152418965226577610023', '8.731270374047983744168272588969388', '8.824323120490776585586525113888990', '9.012566800554134632786260172048416', '9.104224237915395871696287799958786', '9.464132850657816959264814818985856', '9.544833005724576413440401206659573', '9.812486113865712994980755152818164', '9.906197617094972028072972426981050', '10.15454927376622673651805779244224', '10.16499447752018331100702999557217', '10.26612761494226351619666636902581', '10.58359883048553925214582927054499'], 'prelabel': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, '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': 142190657755996743, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36174492751192283920582065737', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.02563077160050588388763888264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.19814982068977736533655416662', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 669.3698663148037, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, -6, 0, 17, 0, 0, 0, -30, 6, 0, 12, 0, 0, 0, 0, 40, 0, -36, 0, 0, 0, -72, -8, 0, -6, 0, 0, 0, -2, 0, 0, -54, 0, 0, 0, 102, -6, 0, 0, 0, 0, 0, -12, 204, 0, 48, 0, 0, 0, 36, 0, 0, 20, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 79, 0, 0, 48, 0, 0, 0, -36, -180, 0, 36, 0, 0, 0, 0, -24, 0, 9, 0, 0, 0, 0, 72, 0, -360, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 72, -102], 'euler11': [1, -12, 82, -408, 1563, -4488, 9922, -15972, 14641], 'euler13': [1, 0, -13, 0, 169, 0, 0, 0, 0], 'euler17': [1, 0, 5, 0, -264, 0, 1445, 0, 83521], 'euler19': [1, 0, -14, 0, -165, 0, -5054, 0, 130321], 'euler2': [1, 6, 19, 42, 69, 84, 76, 48, 16], 'euler23': [1, 8, 2, 128, 1843, 2944, 1058, 97336, 279841], 'euler29': [1, 2, -55, 2, 2524, 58, -46255, 48778, 707281], 'euler3': [1, 0, -6, 0, 27, 0, -54, 0, 81], 'euler31': [1, 0, -124, 0, 5766, 0, -119164, 0, 923521], 'euler37': [1, 6, 89, 462, 5004, 17094, 121841, 303918, 1874161], 'euler41': [1, 0, 69, 0, 3080, 0, 115989, 0, 2825761], 'euler43': [1, 12, 22, 432, 6843, 18576, 40678, 954084, 3418801], 'euler47': [1, 0, -84, 0, 6182, 0, -185556, 0, 4879681], 'euler5': [1, 0, 6, 0, 59, 0, 150, 0, 625], 'euler53': [1, -20, 362, -3680, 33379, -195040, 1016858, -2977540, 7890481], 'euler59': [1, 0, 66, 0, 875, 0, 229746, 0, 12117361], 'euler61': [1, 0, -83, 0, 3168, 0, -308843, 0, 13845841], 'euler67': [1, -48, 1094, -15648, 153243, -1048416, 4910966, -14436624, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 36, 682, 9000, 88131, 639000, 3437962, 12884796, 25411681], 'euler73': [1, 0, -58, 0, 11499, 0, -309082, 0, 28398241], 'euler79': [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], 'euler83': [1, 0, -228, 0, 26774, 0, -1570692, 0, 47458321], 'euler89': [1, 0, 126, 0, 7955, 0, 998046, 0, 62742241], 'euler97': [1, 0, 142, 0, 10755, 0, 1336078, 0, 88529281], 'euler_factors': [[1, 6, 19, 42, 69, 84, 76, 48, 16], [1, 0, -6, 0, 27, 0, -54, 0, 81], [1, 0, 6, 0, 59, 0, 150, 0, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -12, 82, -408, 1563, -4488, 9922, -15972, 14641], [1, 0, -13, 0, 169, 0, 0, 0, 0], [1, 0, 5, 0, -264, 0, 1445, 0, 83521], [1, 0, -14, 0, -165, 0, -5054, 0, 130321], [1, 8, 2, 128, 1843, 2944, 1058, 97336, 279841], [1, 2, -55, 2, 2524, 58, -46255, 48778, 707281], [1, 0, -124, 0, 5766, 0, -119164, 0, 923521], [1, 6, 89, 462, 5004, 17094, 121841, 303918, 1874161], [1, 0, 69, 0, 3080, 0, 115989, 0, 2825761], [1, 12, 22, 432, 6843, 18576, 40678, 954084, 3418801], [1, 0, -84, 0, 6182, 0, -185556, 0, 4879681], [1, -20, 362, -3680, 33379, -195040, 1016858, -2977540, 7890481], [1, 0, 66, 0, 875, 0, 229746, 0, 12117361], [1, 0, -83, 0, 3168, 0, -308843, 0, 13845841], [1, -48, 1094, -15648, 153243, -1048416, 4910966, -14436624, 20151121], [1, 36, 682, 9000, 88131, 639000, 3437962, 12884796, 25411681], [1, 0, -58, 0, 11499, 0, -309082, 0, 28398241], [1, 24, 532, 6552, 72870, 517608, 3320212, 11832936, 38950081], [1, 0, -228, 0, 26774, 0, -1570692, 0, 47458321], [1, 0, 126, 0, 7955, 0, 998046, 0, 62742241], [1, 0, 142, 0, 10755, 0, 1336078, 0, 88529281]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/q/d'], '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': '8-637e4-1.1-c1e4-0-6', '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': '8-637e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 142190657755996743, 'z1': {'__RealLiteral__': 0, 'data': '0.36174492751192283920582065737', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '458566174490006322573476514776,1300141463231923341172681123120,1518835339360741707514712242626,2468467533762027883719797301170', 'Lhash_array': ['458566174490006322573476514776', '1300141463231923341172681123120', '1518835339360741707514712242626', '2468467533762027883719797301170'], 'label': '8-637e4-1.1-c1e4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/q/d'}