LMFDB - Embedded newform 1.118.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,118,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 118, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 118);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 118 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$86.6887159558$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} + \cdots - 93\!\cdots\!48 $ x^9 - 4x^8 - 13110209693586334768127463752564x^7 + 961959021967063293867723377335462302581919896x^6 + 53383138974519780468109264227534066137403399462186048406629046x^5 - 7886152195725511854557238129603023033602862368862473496411083807595526363808x^4 - 72917920795128143242856941749636730961132131295260116889911930937209741611729276800382652948x^3 + 22157012071569318718773078129357357824093042139248672069646947035525467947998275307925179426162382252807112x^2 + 24053174556766387224127627447888998434889723820057005020310902670145653966494958904002713154169084764320833732601723771217x - 9346051287821343799089168466447240879550280090808193066564417274871778929250409866977510633146139989369900758641999156219534993785477948
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{151}\cdot 3^{56}\cdot 5^{18}\cdot 7^{7}\cdot 11^{4}\cdot 13^{4}\cdot 17^{2}\cdot 19\cdot 23\cdot 29^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.13220e15$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.09583e17 q^{2} -4.19687e27 q^{3} +2.05438e35 q^{4} -4.17042e40 q^{5} +2.55834e45 q^{6} +1.99165e49 q^{7} -2.39470e52 q^{8} -4.89422e55 q^{9} +O(q^{10})$	\(q-6.09583e17 q^{2} -4.19687e27 q^{3} +2.05438e35 q^{4} -4.17042e40 q^{5} +2.55834e45 q^{6} +1.99165e49 q^{7} -2.39470e52 q^{8} -4.89422e55 q^{9} +2.54222e58 q^{10} +4.20232e60 q^{11} -8.62195e62 q^{12} -4.76447e64 q^{13} -1.21407e67 q^{14} +1.75027e68 q^{15} -1.95365e70 q^{16} +1.78036e71 q^{17} +2.98343e73 q^{18} +1.28093e74 q^{19} -8.56762e75 q^{20} -8.35868e76 q^{21} -2.56166e78 q^{22} -7.88451e79 q^{23} +1.00502e80 q^{24} -4.27929e81 q^{25} +2.90434e82 q^{26} +4.84731e83 q^{27} +4.09159e84 q^{28} -2.32635e85 q^{29} -1.06693e86 q^{30} +1.41201e87 q^{31} +1.58880e88 q^{32} -1.76366e88 q^{33} -1.08528e89 q^{34} -8.30601e89 q^{35} -1.00546e91 q^{36} +7.07097e91 q^{37} -7.80831e91 q^{38} +1.99959e92 q^{39} +9.98689e92 q^{40} +1.87523e94 q^{41} +5.09531e94 q^{42} +2.34273e95 q^{43} +8.63314e95 q^{44} +2.04110e96 q^{45} +4.80626e97 q^{46} +1.28689e98 q^{47} +8.19923e97 q^{48} -3.55772e98 q^{49} +2.60858e99 q^{50} -7.47195e98 q^{51} -9.78801e99 q^{52} -8.93863e100 q^{53} -2.95483e101 q^{54} -1.75254e101 q^{55} -4.76939e101 q^{56} -5.37588e101 q^{57} +1.41811e103 q^{58} +3.88197e103 q^{59} +3.59572e103 q^{60} +4.21493e104 q^{61} -8.60737e104 q^{62} -9.74757e104 q^{63} -6.43899e105 q^{64} +1.98698e105 q^{65} +1.07509e106 q^{66} -5.05518e106 q^{67} +3.65754e106 q^{68} +3.30902e107 q^{69} +5.06320e107 q^{70} +1.62423e108 q^{71} +1.17202e108 q^{72} -1.32357e109 q^{73} -4.31034e109 q^{74} +1.79596e109 q^{75} +2.63151e109 q^{76} +8.36953e109 q^{77} -1.21891e110 q^{78} +7.88152e110 q^{79} +8.14756e110 q^{80} +1.22305e111 q^{81} -1.14311e112 q^{82} -3.02315e112 q^{83} -1.71719e112 q^{84} -7.42487e111 q^{85} -1.42809e113 q^{86} +9.76340e112 q^{87} -1.00633e113 q^{88} -8.52895e113 q^{89} -1.24422e114 q^{90} -9.48914e113 q^{91} -1.61977e115 q^{92} -5.92602e114 q^{93} -7.84463e115 q^{94} -5.34200e114 q^{95} -6.66799e115 q^{96} +1.14814e116 q^{97} +2.16873e116 q^{98} -2.05671e116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 40\!\cdots\!52 q^{2}+ \cdots + 22\!\cdots\!97 q^{9}+O(q^{10}) $ 9 * q + 40417036685158752 * q^2 + 10302905323878152966875623636 * q^3 + 679626474486553930371683615220261888 * q^4 + 38453607070720263635688515692568185914150 * q^5 - 4850209982284354841792124153951223028275738752 * q^6 - 33936637323452994043236135663221508618375503117208 * q^7 + 84807426568136809852447254974619690045330359678238720 * q^8 + 228322388396621838147039528942639942618778890580268310597 * q^9	$ 9 q + 40\!\cdots\!52 q^{2}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) $ 9 * q + 40417036685158752 * q^2 + 10302905323878152966875623636 * q^3 + 679626474486553930371683615220261888 * q^4 + 38453607070720263635688515692568185914150 * q^5 - 4850209982284354841792124153951223028275738752 * q^6 - 33936637323452994043236135663221508618375503117208 * q^7 + 84807426568136809852447254974619690045330359678238720 * q^8 + 228322388396621838147039528942639942618778890580268310597 * q^9 - 116795550914172753602500302406542633798241819198212925771200 * q^10 - 18850526893652982349030077823189856392436130547985552802563652 * q^11 + 3227106826098906050636969251983952779002958811977260223984586752 * q^12 - 98574936372230476445754809314443731682386957493373954090363278834 * q^13 + 35258972517405629268130631622450754971434643685593795240367372736256 * q^14 - 915629885182684846104756133008435145438889653925288537510093151318600 * q^15 + 61702437097071514242829543900966314104457520182055990902400499737165824 * q^16 - 680002505828907486847031510246007941006426153324907295268216079884418078 * q^17 - 41733213100034654524842848551561180884346520214587575830257187744066967584 * q^18 - 160689510555833725295714486201244011986205134154473703462344729085218574940 * q^19 - 2238340134838118789188928650249499474871086998961353735072744834498868275200 * q^20 - 325231066595782226476051172214780538694781261136602948155806527762690471674592 * q^21 - 13112988820785042404307735263630112517712749663800581417200667121255782067843456 * q^22 - 58153519408904797009281866377912077673911181772550205922884346377262357403061704 * q^23 - 3038238801938958809634055377152977696212679179273938957003033953876165693929553920 * q^24 + 5528673600140129203782645127829908484096231088932064383194690227200862517083894375 * q^25 + 56682227661992970696514878061752865405652252745109723390003965691218585268522989888 * q^26 + 1827774475813800388315702586366166077051345533885606497916848989661362329232290194120 * q^27 - 6468486093767359175378792181544485287676854914825022016113590703460551157550283513856 * q^28 - 48386553564988730519261358531155605067882474797775404905351553453290924873675961170210 * q^29 - 933061727033306076487821089990705907034760165404132848486598428012292996783024527379200 * q^30 - 621957331647921924682092054631242956130629654943098483596990494053452820493965659370592 * q^31 + 5001840478035603540410109619911952695496967661900989837684340698950683681301601905016832 * q^32 + 121811126973553577276247861343842508235672706892636830990043974788533005362046408289426992 * q^33 - 739829614062010739581951319533134982709290713812079124382329752841795383755334475547959104 * q^34 - 4738290388179207473702786515865081056559422688400941664804502829786561878838282647304413200 * q^35 + 45099229254587225493722800395751937761885426855646977453280381634636333644471918552752149504 * q^36 - 34964212885413714773919749832666304501127253457648317866689087418325240609603845719432098618 * q^37 + 721325600351264057185221862351496532134128096990026176343425219143447708368813195315354449280 * q^38 - 5256181041389152420659051237224453246783624348532029963454064662671494105217119495256720274216 * q^39 - 3971440606190340326438464214808272022762933594464202348081080358302577556396774721686560768000 * q^40 + 10020257933125498318762169522473576122868342311015731314988395755981139260089136547294206867738 * q^41 + 252970816117377205232172452762620886935079264765511703102710428456975064426237455951343632231424 * q^42 + 50615459145440588569921800707258109935625533244654510855325763075886611210775326812060053355356 * q^43 - 4005524110904096730553185857622707642025685539352197636568303886000422137318429894399607389425664 * q^44 + 5473276137456663664850729608899955954082083355607725618741940940860469618299772760360253073375950 * q^45 + 1478376152522396457093466079811724410922025958141013781241190503228240084745237352373452997174528 * q^46 + 16685567512808747231645711437000622991513185216117548515196412601564484313290777292415784238201712 * q^47 - 216224080066172714935125828338658772066778469688001789861117569570442266773620007884590970572898304 * q^48 + 169974231907168786505678866260391714519211137411643020101217953968783780867359385345616236202809313 * q^49 - 2469575139897634839277498689855848621914551651256318080857839988659447958716938283028005975429980000 * q^50 + 22542359242748231968428303678420614483799317368695374408674201779527797470892277868165393834070628328 * q^51 - 3641374884516561660680840591520895881667064402106525036999341733309771062927915917819681324515084288 * q^52 - 213846929196927043507342255756620254016567403070821501560181236631146130543117495693232522403826884714 * q^53 + 70368920588017409616903857310987095626556658223669990059448426800295554432360247812557938014199560960 * q^54 + 148096007032108307991537648756429447360412191714871283455777374803615140028070019602170536767368773800 * q^55 + 4912754841589119447020005683504898647317892135202904974904770520342259478270647905318907285925688770560 * q^56 + 4725267742102384458969291922476649493908095234626754028721076337022388939733447041972841854747117257040 * q^57 - 61691450689404126451745332477746935968828799400881738634159938087335342513296447359674633686816855103680 * q^58 - 7764769731115259168900983283133365701920906050369948450392029627233204947390357923079821008349713252820 * q^59 + 242167860317000066114168168973610808827817432218852606538275645995232520514013583121633628591005079756800 * q^60 - 222929606503067710799398508192199729986190593058228065549044227683974026321115005709568884316645733270402 * q^61 + 1827141305370492398064568813635835649207511770956919266173894646721039854569012442466628721293062130637824 * q^62 - 6149430428052066771901587011857473350643630395143732809634023246996722252441575455955324150064952541470264 * q^63 + 1713574251954623356255571860783147114735206198681534690227478857137685402094507991899117111923895957454848 * q^64 + 12869386968955442746581655138229434721016903840553054939904074922997747298934225413734850521793432682742900 * q^65 - 19801437990698690478552825543250876645747446443556478809261957366009300212043482490741679345707416428383744 * q^66 + 107684064602401021489570577643707663917970871646716750467969519975118177172469237075867827266943410721303572 * q^67 - 251444068481959286401052998092041093692640408644327131004605869607770327086902833194726609492888262105757696 * q^68 - 636551002833346124243317331997139947630296871486667493370629456953598473495382187316694584320495561912206496 * q^69 + 2445861734303677525943378629352934810152324980084761531508197481523725822715645101402879849637685872106969600 * q^70 + 1502419505224176558531294169685503912214338337110158873961577642731392413889415756979097582494411807941436328 * q^71 - 14190460126457652958916758648699640896837300874267064764308762389188142317932680769710235258136844562310922240 * q^72 - 3680626529239964132564912872164428299172360038443306444645976164259015478054371367373032231078544242855946054 * q^73 + 18995030812524563839649408435663136474226268660391755695671253594362128606663820760673799433403903696813952576 * q^74 - 5954144082365263500038634316183618316282448578954739961163265060170444211914471312789969527239069427687252500 * q^75 + 75521635038824380969585182658956176528723379098044694676717523275104397685022044564398827919896405931443589120 * q^76 - 240771158437798357271369248931142348166973346297260790267580673145058666334232888264118432356615568402288764576 * q^77 - 1477784208875012842343990522137891883864267581783960725138689920617516099527473962194409706068146624342516014848 * q^78 - 2285355792246583755429666361022638813506260919808216029514856597259553412365830319339899046809462718803389829360 * q^79 + 731147255618903270849902761914980040425478725108304832815559424615479093332325975905808837098967573706466918400 * q^80 - 3532367670468406933076216472986157092840312801374884126730791036696135691770424326872669760546172592566341977631 * q^81 - 25860102286736164243905760962310812415991288634659729695499047849150555031014924251023990367180912563898028431936 * q^82 - 26117732855991809313933081725190177898263990806499246105780578093346337131589033812952875783820862626814896023324 * q^83 - 303841612882842424652673770557081077080232195176517190811304259946807947644403425630681019724069771858331742470144 * q^84 - 271784820026506038543716236739677268739946655832804497399888502506585385926171661627342672703869328144134352799700 * q^85 - 159145514743719971775182317155196763266785145636471136796587486856422371505286708178643130744777323230578900292992 * q^86 - 1355100613113558654481164729536860328574661378469179428445142384013367192233258069363369980837305546640235173931240 * q^87 - 5330018914167959490555492640418721613119677246727591406115888524964039124470757411539029636129427474678220869468160 * q^88 - 4395897084707064164421802509143573377632162722728879042427722619171467149720889139563855226466565875308146508794230 * q^89 - 23411936176011976544246884681770302612989489885021236648740047507452430500242447452152815918439699794497873950801600 * q^90 - 17606324029223302595865761669828668634914557724735380270289077831587010762982273184351868955067224006438510779110352 * q^91 - 55772404313727512066859492963963844589319577918377808030728482638027588994319973465872892384865446342595251431088128 * q^92 - 116072789390555091884134123921208861440848184837899694086563014238934971188422968399738169216529674194608920356995968 * q^93 - 215603007291864892759964647694822697504579441834466411893750448780856116572052774856258753465664728162623916745168384 * q^94 - 363311345030338353402396700470528946025867499164153062121513673791488768341279059764913540333394357951818599838481000 * q^95 - 701671877550835095764080820751918498721447481909785429122092358416515475269177135171212459682250091038670024691679232 * q^96 - 298117805360022175643266169567709680719740267556363080426954452630296899863133621017987146964797348637751058662202638 * q^97 - 2126339804064355593061344246003551033537506779034582996212286410224706625784123846976709615330292659973382337208735136 * q^98 - 1520953441055457260978457109220493407200764700486006435781344466290947949395060067028631646046107176946794789660596916 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−6.09583e17	−1.49547	−0.747735	−	0.663997i	$-0.768859\pi$
$2$	−6.09583e17	−1.49547	−0.747735	+	0.663997i	$0.768859\pi$
$3$	−4.19687e27	−0.514437	−0.257218	−	0.966353i	$-0.582806\pi$
$3$	−4.19687e27	−0.514437	−0.257218	+	0.966353i	$0.582806\pi$
$4$	2.05438e35	1.23643
$5$	−4.17042e40	−0.537569	−0.268785	−	0.963200i	$-0.586622\pi$
$5$	−4.17042e40	−0.537569	−0.268785	+	0.963200i	$0.586622\pi$
$6$	2.55834e45	0.769325
$7$	1.99165e49	0.726068	0.363034	−	0.931776i	$-0.381741\pi$
$7$	1.99165e49	0.726068	0.363034	+	0.931776i	$0.381741\pi$
$8$	−2.39470e52	−0.353579
$9$	−4.89422e55	−0.735355
$10$	2.54222e58	0.803919
$11$	4.20232e60	0.503520	0.251760	−	0.967790i	$-0.418991\pi$
$11$	4.20232e60	0.503520	0.251760	+	0.967790i	$0.418991\pi$
$12$	−8.62195e62	−0.636067
$13$	−4.76447e64	−0.325333	−0.162667	−	0.986681i	$-0.552009\pi$
$13$	−4.76447e64	−0.325333	−0.162667	+	0.986681i	$0.552009\pi$
$14$	−1.21407e67	−1.08581
$15$	1.75027e68	0.276545
$16$	−1.95365e70	−0.707666
$17$	1.78036e71	0.185886	0.0929431	−	0.995671i	$-0.470373\pi$
$17$	1.78036e71	0.185886	0.0929431	+	0.995671i	$0.470373\pi$
$18$	2.98343e73	1.09970
$19$	1.28093e74	0.199728	0.0998640	−	0.995001i	$-0.468159\pi$
$19$	1.28093e74	0.199728	0.0998640	+	0.995001i	$0.468159\pi$
$20$	−8.56762e75	−0.664669
$21$	−8.35868e76	−0.373516
$22$	−2.56166e78	−0.752999
$23$	−7.88451e79	−1.72066	−0.860332	−	0.509734i	$-0.829744\pi$
$23$	−7.88451e79	−1.72066	−0.860332	+	0.509734i	$0.829744\pi$
$24$	1.00502e80	0.181894
$25$	−4.27929e81	−0.711019
$26$	2.90434e82	0.486526
$27$	4.84731e83	0.892730
$28$	4.09159e84	0.897734
$29$	−2.32635e85	−0.655229	−0.327614	−	0.944812i	$-0.606245\pi$
$29$	−2.32635e85	−0.655229	−0.327614	+	0.944812i	$0.606245\pi$
$30$	−1.06693e86	−0.413566
$31$	1.41201e87	0.803857	0.401928	−	0.915671i	$-0.368340\pi$
$31$	1.41201e87	0.803857	0.401928	+	0.915671i	$0.368340\pi$
$32$	1.58880e88	1.41187
$33$	−1.76366e88	−0.259029
$34$	−1.08528e89	−0.277987
$35$	−8.30601e89	−0.390312
$36$	−1.00546e91	−0.909217
$37$	7.07097e91	1.28730	0.643648	−	0.765322i	$-0.277420\pi$
$37$	7.07097e91	1.28730	0.643648	+	0.765322i	$0.277420\pi$
$38$	−7.80831e91	−0.298687
$39$	1.99959e92	0.167363
$40$	9.98689e92	0.190073
$41$	1.87523e94	0.841779	0.420889	−	0.907112i	$-0.361718\pi$
$41$	1.87523e94	0.841779	0.420889	+	0.907112i	$0.361718\pi$
$42$	5.09531e94	0.558582
$43$	2.34273e95	0.648361	0.324181	−	0.945995i	$-0.394911\pi$
$43$	2.34273e95	0.648361	0.324181	+	0.945995i	$0.394911\pi$
$44$	8.63314e95	0.622569
$45$	2.04110e96	0.395304
$46$	4.80626e97	2.57320
$47$	1.28689e98	1.95801	0.979006	−	0.203832i	$-0.0653398\pi$
$47$	1.28689e98	1.95801	0.979006	+	0.203832i	$0.0653398\pi$
$48$	8.19923e97	0.364050
$49$	−3.55772e98	−0.472826
$50$	2.60858e99	1.06331
$51$	−7.47195e98	−0.0956266
$52$	−9.78801e99	−0.402253
$53$	−8.93863e100	−1.20540	−0.602702	−	0.797966i	$-0.705909\pi$
$53$	−8.93863e100	−1.20540	−0.602702	+	0.797966i	$0.705909\pi$
$54$	−2.95483e101	−1.33505
$55$	−1.75254e101	−0.270677
$56$	−4.76939e101	−0.256722
$57$	−5.37588e101	−0.102747
$58$	1.41811e103	0.979876
$59$	3.88197e103	0.986756	0.493378	−	0.869815i	$-0.335762\pi$
$59$	3.88197e103	0.986756	0.493378	+	0.869815i	$0.335762\pi$
$60$	3.59572e103	0.341930
$61$	4.21493e104	1.52404	0.762018	−	0.647555i	$-0.224209\pi$
$61$	4.21493e104	1.52404	0.762018	+	0.647555i	$0.224209\pi$
$62$	−8.60737e104	−1.20214
$63$	−9.74757e104	−0.533917
$64$	−6.43899e105	−1.40375
$65$	1.98698e105	0.174889
$66$	1.07509e106	0.387370
$67$	−5.05518e106	−0.755719	−0.377860	−	0.925863i	$-0.623340\pi$
$67$	−5.05518e106	−0.755719	−0.377860	+	0.925863i	$0.623340\pi$
$68$	3.65754e106	0.229836
$69$	3.30902e107	0.885173
$70$	5.06320e107	0.583700
$71$	1.62423e108	0.816648	0.408324	−	0.912837i	$-0.366113\pi$
$71$	1.62423e108	0.816648	0.408324	+	0.912837i	$0.366113\pi$
$72$	1.17202e108	0.260006
$73$	−1.32357e109	−1.31027	−0.655133	−	0.755514i	$-0.727387\pi$
$73$	−1.32357e109	−1.31027	−0.655133	+	0.755514i	$0.727387\pi$
$74$	−4.31034e109	−1.92511
$75$	1.79596e109	0.365774
$76$	2.63151e109	0.246950
$77$	8.36953e109	0.365589
$78$	−1.21891e110	−0.250287
$79$	7.88152e110	0.768113	0.384057	−	0.923310i	$-0.374527\pi$
$79$	7.88152e110	0.768113	0.384057	+	0.923310i	$0.374527\pi$
$80$	8.14756e110	0.380420
$81$	1.22305e111	0.276102
$82$	−1.14311e112	−1.25886
$83$	−3.02315e112	−1.63829	−0.819147	−	0.573583i	$-0.805553\pi$
$83$	−3.02315e112	−1.63829	−0.819147	+	0.573583i	$0.805553\pi$
$84$	−1.71719e112	−0.461827
$85$	−7.42487e111	−0.0999267
$86$	−1.42809e113	−0.969606
$87$	9.76340e112	0.337074
$88$	−1.00633e113	−0.178034
$89$	−8.52895e113	−0.779076	−0.389538	−	0.921010i	$-0.627365\pi$
$89$	−8.52895e113	−0.779076	−0.389538	+	0.921010i	$0.627365\pi$
$90$	−1.24422e114	−0.591166
$91$	−9.48914e113	−0.236214
$92$	−1.61977e115	−2.12749
$93$	−5.92602e114	−0.413533
$94$	−7.84463e115	−2.92815
$95$	−5.34200e114	−0.107368
$96$	−6.66799e115	−0.726319
$97$	1.14814e116	0.682102	0.341051	−	0.940045i	$-0.389217\pi$
$97$	1.14814e116	0.682102	0.341051	+	0.940045i	$0.389217\pi$
$98$	2.16873e116	0.707097
$99$	−2.05671e116	−0.370266
$100$	−8.79127e116	−0.879127
$101$	−2.38478e117	−1.33244	−0.666221	−	0.745754i	$-0.732089\pi$
$101$	−2.38478e117	−1.33244	−0.666221	+	0.745754i	$0.732089\pi$
$102$	4.55477e116	0.143007
$103$	4.19355e117	0.744053	0.372026	−	0.928222i	$-0.378663\pi$
$103$	4.19355e117	0.744053	0.372026	+	0.928222i	$0.378663\pi$
$104$	1.14095e117	0.115031
$105$	3.48592e117	0.200791
$106$	5.44883e118	1.80265
$107$	3.39022e118	0.647555	0.323777	−	0.946133i	$-0.395047\pi$
$107$	3.39022e118	0.647555	0.323777	+	0.946133i	$0.395047\pi$
$108$	9.95819e118	1.10380
$109$	1.40342e119	0.907271	0.453635	−	0.891187i	$-0.350127\pi$
$109$	1.40342e119	0.907271	0.453635	+	0.891187i	$0.350127\pi$
$110$	1.06832e119	0.404789
$111$	−2.96759e119	−0.662232
$112$	−3.89099e119	−0.513814
$113$	−7.04666e119	−0.553216	−0.276608	−	0.960983i	$-0.589210\pi$
$113$	−7.04666e119	−0.553216	−0.276608	+	0.960983i	$0.589210\pi$
$114$	3.27705e119	0.153656
$115$	3.28817e120	0.924977
$116$	−4.77921e120	−0.810147
$117$	2.33184e120	0.239235
$118$	−2.36638e121	−1.47567
$119$	3.54586e120	0.134966
$120$	−4.19137e120	−0.0977806
$121$	−5.19942e121	−0.746468
$122$	−2.56935e122	−2.27915
$123$	−7.87008e121	−0.433042
$124$	2.90080e122	0.993915
$125$	4.29462e122	0.919792
$126$	5.94195e122	0.798458
$127$	1.77034e123	1.49809	0.749047	−	0.662517i	$-0.230512\pi$
$127$	1.77034e123	1.49809	0.749047	+	0.662517i	$0.230512\pi$
$128$	1.28525e123	0.687392
$129$	−9.83212e122	−0.333541
$130$	−1.21123e123	−0.261542
$131$	5.21402e122	0.0719121	0.0359561	−	0.999353i	$-0.488552\pi$
$131$	5.21402e122	0.0719121	0.0359561	+	0.999353i	$0.488552\pi$
$132$	−3.62322e123	−0.320272
$133$	2.55115e123	0.145016
$134$	3.08155e124	1.13016
$135$	−2.02153e124	−0.479905
$136$	−4.26343e123	−0.0657254
$137$	−2.10681e124	−0.211579	−0.105789	−	0.994389i	$-0.533737\pi$
$137$	−2.10681e124	−0.211579	−0.105789	+	0.994389i	$0.533737\pi$
$138$	−2.01712e125	−1.32375
$139$	1.14160e125	0.491073	0.245537	−	0.969387i	$-0.421036\pi$
$139$	1.14160e125	0.491073	0.245537	+	0.969387i	$0.421036\pi$
$140$	−1.70637e125	−0.482594
$141$	−5.40089e125	−1.00727
$142$	−9.90104e125	−1.22127
$143$	−2.00218e125	−0.163812
$144$	9.56162e125	0.520386
$145$	9.70188e125	0.352231
$146$	8.06825e126	1.95946
$147$	1.49313e126	0.243239
$148$	1.45264e127	1.59165
$149$	−8.52611e126	−0.630020	−0.315010	−	0.949088i	$-0.602008\pi$
$149$	−8.52611e126	−0.630020	−0.315010	+	0.949088i	$0.602008\pi$
$150$	−1.09479e127	−0.547005
$151$	9.13801e126	0.309528	0.154764	−	0.987951i	$-0.450538\pi$
$151$	9.13801e126	0.309528	0.154764	+	0.987951i	$0.450538\pi$
$152$	−3.06743e126	−0.0706195
$153$	−8.71350e126	−0.136692
$154$	−5.10192e127	−0.546728
$155$	−5.88868e127	−0.432129
$156$	4.10790e127	0.206934
$157$	2.23077e128	0.773261	0.386630	−	0.922235i	$-0.373639\pi$
$157$	2.23077e128	0.773261	0.386630	+	0.922235i	$0.373639\pi$
$158$	−4.80444e128	−1.14869
$159$	3.75143e128	0.620104
$160$	−6.62597e128	−0.758980
$161$	−1.57032e129	−1.24932
$162$	−7.45547e128	−0.412902
$163$	−2.06942e129	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$163$	−2.06942e129	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$164$	3.85242e129	1.04080
$165$	7.35519e128	0.139246
$166$	1.84286e130	2.45002
$167$	1.14161e130	1.06808	0.534042	−	0.845458i	$-0.320672\pi$
$167$	1.14161e130	1.06808	0.534042	+	0.845458i	$0.320672\pi$
$168$	2.00165e129	0.132067
$169$	−1.91773e130	−0.894158
$170$	4.52607e129	0.149437
$171$	−6.26914e129	−0.146871
$172$	4.81285e130	0.801655
$173$	−1.19631e131	−1.41953	−0.709767	−	0.704437i	$-0.751200\pi$
$173$	−1.19631e131	−1.41953	−0.709767	+	0.704437i	$0.751200\pi$
$174$	−5.95160e130	−0.504084
$175$	−8.52284e130	−0.516248
$176$	−8.20987e130	−0.356324
$177$	−1.62921e131	−0.507624
$178$	5.19910e131	1.16509
$179$	−3.80069e131	−0.613705	−0.306853	−	0.951757i	$-0.599276\pi$
$179$	−3.80069e131	−0.613705	−0.306853	+	0.951757i	$0.599276\pi$
$180$	4.19318e131	0.488767
$181$	−3.77160e131	−0.317928	−0.158964	−	0.987284i	$-0.550815\pi$
$181$	−3.77160e131	−0.317928	−0.158964	+	0.987284i	$0.550815\pi$
$182$	5.78442e131	0.353251
$183$	−1.76895e132	−0.784021
$184$	1.88810e132	0.608390
$185$	−2.94889e132	−0.692011
$186$	3.61240e132	0.618427
$187$	7.48165e131	0.0935974
$188$	2.64375e133	2.42095
$189$	9.65412e132	0.648182
$190$	3.25639e132	0.160565
$191$	−4.97321e133	−1.80379	−0.901893	−	0.431960i	$-0.857822\pi$
$191$	−4.97321e133	−1.80379	−0.901893	+	0.431960i	$0.857822\pi$
$192$	2.70236e133	0.722140
$193$	−6.56183e133	−1.29397	−0.646983	−	0.762505i	$-0.723969\pi$
$193$	−6.56183e133	−1.29397	−0.646983	+	0.762505i	$0.723969\pi$
$194$	−6.99887e133	−1.02006
$195$	−8.33911e132	−0.0899694
$196$	−7.30890e133	−0.584618
$197$	−1.69685e134	−1.00779	−0.503895	−	0.863765i	$-0.668100\pi$
$197$	−1.69685e134	−1.00779	−0.503895	+	0.863765i	$0.668100\pi$
$198$	1.25373e134	0.553722
$199$	1.48641e134	0.488915	0.244457	−	0.969660i	$-0.421390\pi$
$199$	1.48641e134	0.488915	0.244457	+	0.969660i	$0.421390\pi$
$200$	1.02476e134	0.251401
$201$	2.12159e134	0.388770
$202$	1.45372e135	1.99263
$203$	−4.63328e134	−0.475740
$204$	−1.53502e134	−0.118236
$205$	−7.82048e134	−0.452515
$206$	−2.55631e135	−1.11271
$207$	3.85885e135	1.26530
$208$	9.30812e134	0.230227
$209$	5.38286e134	0.100567
$210$	−2.12496e135	−0.300277
$211$	1.76147e136	1.88518	0.942590	−	0.333952i	$-0.108382\pi$
$211$	1.76147e136	1.88518	0.942590	+	0.333952i	$0.108382\pi$
$212$	−1.83633e136	−1.49040
$213$	−6.81669e135	−0.420113
$214$	−2.06662e136	−0.968399
$215$	−9.77016e135	−0.348539
$216$	−1.16078e136	−0.315650
$217$	2.81223e136	0.583654
$218$	−8.55499e136	−1.35680
$219$	5.55485e136	0.674049
$220$	−3.60038e136	−0.334674
$221$	−8.48249e135	−0.0604749
$222$	1.80899e137	0.990349
$223$	2.38591e137	1.00420	0.502100	−	0.864810i	$-0.332561\pi$
$223$	2.38591e137	1.00420	0.502100	+	0.864810i	$0.332561\pi$
$224$	3.16433e137	1.02512
$225$	2.09438e137	0.522851
$226$	4.29552e137	0.827318
$227$	−4.55977e137	−0.678313	−0.339157	−	0.940730i	$-0.610142\pi$
$227$	−4.55977e137	−0.678313	−0.339157	+	0.940730i	$0.610142\pi$
$228$	−1.10441e137	−0.127040
$229$	−1.79565e138	−1.59899	−0.799494	−	0.600674i	$-0.794899\pi$
$229$	−1.79565e138	−1.59899	−0.799494	+	0.600674i	$0.794899\pi$
$230$	−2.00441e138	−1.38328
$231$	−3.51258e137	−0.188073
$232$	5.57091e137	0.231675
$233$	3.67399e138	1.18800	0.594000	−	0.804465i	$-0.297548\pi$
$233$	3.67399e138	1.18800	0.594000	+	0.804465i	$0.297548\pi$
$234$	−1.42145e138	−0.357770
$235$	−5.36685e138	−1.05257
$236$	7.97504e138	1.22006
$237$	−3.30777e138	−0.395146
$238$	−2.16149e138	−0.201838
$239$	5.34425e138	0.390489	0.195245	−	0.980755i	$-0.437450\pi$
$239$	5.34425e138	0.390489	0.195245	+	0.980755i	$0.437450\pi$
$240$	−3.41942e138	−0.195702
$241$	−1.92612e139	−0.864343	−0.432172	−	0.901791i	$-0.642252\pi$
$241$	−1.92612e139	−0.864343	−0.432172	+	0.901791i	$0.642252\pi$
$242$	3.16948e139	1.11632
$243$	−3.73947e139	−1.03477
$244$	8.65906e139	1.88437
$245$	1.48372e139	0.254177
$246$	4.79746e139	0.647602
$247$	−6.10294e138	−0.0649781
$248$	−3.38133e139	−0.284227
$249$	1.26878e140	0.842799
$250$	−2.61793e140	−1.37552
$251$	9.37891e139	0.390157	0.195079	−	0.980788i	$-0.437504\pi$
$251$	9.37891e139	0.390157	0.195079	+	0.980788i	$0.437504\pi$
$252$	−2.00252e140	−0.660153
$253$	−3.31332e140	−0.866389
$254$	−1.07917e141	−2.24036
$255$	3.11612e139	0.0514060
$256$	2.86394e140	0.375774
$257$	8.85139e140	0.924536	0.462268	−	0.886740i	$-0.347036\pi$
$257$	8.85139e140	0.924536	0.462268	+	0.886740i	$0.347036\pi$
$258$	5.99349e140	0.498801
$259$	1.40829e141	0.934663
$260$	4.08201e140	0.216239
$261$	1.13857e141	0.481826
$262$	−3.17838e140	−0.107543
$263$	−2.78721e140	−0.0754671	−0.0377336	−	0.999288i	$-0.512014\pi$
$263$	−2.78721e140	−0.0754671	−0.0377336	+	0.999288i	$0.512014\pi$
$264$	4.22342e140	0.0915872
$265$	3.72778e141	0.647988
$266$	−1.55514e141	−0.216867
$267$	3.57949e141	0.400785
$268$	−1.03852e142	−0.934396
$269$	−2.17860e142	−1.57641	−0.788203	−	0.615415i	$-0.788988\pi$
$269$	−2.17860e142	−1.57641	−0.788203	+	0.615415i	$0.788988\pi$
$270$	1.23229e142	0.717683
$271$	5.11470e140	0.0239948	0.0119974	−	0.999928i	$-0.496181\pi$
$271$	5.11470e140	0.0239948	0.0119974	+	0.999928i	$0.496181\pi$
$272$	−3.47821e141	−0.131545
$273$	3.98247e141	0.121517
$274$	1.28427e142	0.316410
$275$	−1.79829e142	−0.358012
$276$	6.79798e142	1.09446
$277$	−1.08280e143	−1.41086	−0.705429	−	0.708781i	$-0.749246\pi$
$277$	−1.08280e143	−1.41086	−0.705429	+	0.708781i	$0.749246\pi$
$278$	−6.95897e142	−0.734386
$279$	−6.91069e142	−0.591120
$280$	1.98904e142	0.138006
$281$	−4.11966e142	−0.232028	−0.116014	−	0.993248i	$-0.537012\pi$
$281$	−4.11966e142	−0.232028	−0.116014	+	0.993248i	$0.537012\pi$
$282$	3.29229e143	1.50635
$283$	3.47032e143	1.29081	0.645406	−	0.763840i	$-0.276688\pi$
$283$	3.47032e143	1.29081	0.645406	+	0.763840i	$0.276688\pi$
$284$	3.33678e143	1.00973
$285$	2.24197e142	0.0552339
$286$	1.22049e143	0.244976
$287$	3.73479e143	0.611188
$288$	−7.77595e143	−1.03823
$289$	−8.85629e143	−0.965446
$290$	−5.91410e143	−0.526751
$291$	−4.81860e143	−0.350898
$292$	−2.71911e144	−1.62006
$293$	2.35753e144	1.15001	0.575004	−	0.818151i	$-0.305001\pi$
$293$	2.35753e144	1.15001	0.575004	+	0.818151i	$0.305001\pi$
$294$	−9.10186e143	−0.363757
$295$	−1.61895e144	−0.530450
$296$	−1.69328e144	−0.455160
$297$	2.03699e144	0.449507
$298$	5.19737e144	0.942177
$299$	3.75655e144	0.559789
$300$	3.68958e144	0.452255
$301$	4.66589e144	0.470754
$302$	−5.57038e144	−0.462891
$303$	1.00086e145	0.685457
$304$	−2.50249e144	−0.141341
$305$	−1.75780e145	−0.819276
$306$	5.31160e144	0.204419
$307$	−9.30696e144	−0.295946	−0.147973	−	0.988991i	$-0.547275\pi$
$307$	−9.30696e144	−0.295946	−0.147973	+	0.988991i	$0.547275\pi$
$308$	1.71942e145	0.452027
$309$	−1.75998e145	−0.382768
$310$	3.58964e145	0.646236
$311$	2.44097e145	0.363982	0.181991	−	0.983300i	$-0.441746\pi$
$311$	2.44097e145	0.363982	0.181991	+	0.983300i	$0.441746\pi$
$312$	−4.78840e144	−0.0591761
$313$	−8.15693e145	−0.835955	−0.417977	−	0.908457i	$-0.637261\pi$
$313$	−8.15693e145	−0.835955	−0.417977	+	0.908457i	$0.637261\pi$
$314$	−1.35984e146	−1.15639
$315$	4.06514e145	0.287018
$316$	1.61916e146	0.949721
$317$	−2.49915e146	−1.21850	−0.609250	−	0.792978i	$-0.708529\pi$
$317$	−2.49915e146	−1.21850	−0.609250	+	0.792978i	$0.708529\pi$
$318$	−2.28680e146	−0.927347
$319$	−9.77608e145	−0.329921
$320$	2.68533e146	0.754613
$321$	−1.42283e146	−0.333126
$322$	9.57237e146	1.86832
$323$	2.28052e145	0.0371266
$324$	2.51260e146	0.341381
$325$	2.03885e146	0.231318
$326$	1.26149e147	1.19578
$327$	−5.88996e146	−0.466733
$328$	−4.49060e146	−0.297635
$329$	2.56302e147	1.42165
$330$	−4.48360e146	−0.208239
$331$	−1.59205e147	−0.619468	−0.309734	−	0.950823i	$-0.600240\pi$
$331$	−1.59205e147	−0.619468	−0.309734	+	0.950823i	$0.600240\pi$
$332$	−6.21070e147	−2.02564
$333$	−3.46069e147	−0.946619
$334$	−6.95907e147	−1.59729
$335$	2.10822e147	0.406252
$336$	1.63300e147	0.264325
$337$	5.78875e147	0.787473	0.393737	−	0.919223i	$-0.371182\pi$
$337$	5.78875e147	0.787473	0.393737	+	0.919223i	$0.371182\pi$
$338$	1.16901e148	1.33719
$339$	2.95739e147	0.284595
$340$	−1.52535e147	−0.123553
$341$	5.93371e147	0.404758
$342$	3.82156e147	0.219641
$343$	−2.20716e148	−1.06937
$344$	−5.61012e147	−0.229247
$345$	−1.38000e148	−0.475842
$346$	7.29248e148	2.12287
$347$	−3.88532e148	−0.955329	−0.477664	−	0.878542i	$-0.658517\pi$
$347$	−3.88532e148	−0.955329	−0.477664	+	0.878542i	$0.658517\pi$
$348$	2.00577e148	0.416769
$349$	−1.08995e148	−0.191478	−0.0957392	−	0.995406i	$-0.530521\pi$
$349$	−1.08995e148	−0.191478	−0.0957392	+	0.995406i	$0.530521\pi$
$350$	5.19537e148	0.772034
$351$	−2.30948e148	−0.290435
$352$	6.67664e148	0.710906
$353$	−1.61261e149	−1.45448	−0.727241	−	0.686382i	$-0.759198\pi$
$353$	−1.61261e149	−1.45448	−0.727241	+	0.686382i	$0.759198\pi$
$354$	9.93140e148	0.759136
$355$	−6.77373e148	−0.439005
$356$	−1.75217e149	−0.963276
$357$	−1.48815e148	−0.0694314
$358$	2.31683e149	0.917779
$359$	−4.29380e149	−1.44483	−0.722415	−	0.691459i	$-0.756968\pi$
$359$	−4.29380e149	−1.44483	−0.722415	+	0.691459i	$0.756968\pi$
$360$	−4.88781e148	−0.139771
$361$	−3.94904e149	−0.960109
$362$	2.29910e149	0.475452
$363$	2.18213e149	0.384010
$364$	−1.94943e149	−0.292063
$365$	5.51984e149	0.704359
$366$	1.07832e150	1.17248
$367$	9.41755e149	0.872917	0.436459	−	0.899724i	$-0.356233\pi$
$367$	9.41755e149	0.872917	0.436459	+	0.899724i	$0.356233\pi$
$368$	1.54036e150	1.21766
$369$	−9.17777e149	−0.619006
$370$	1.79759e150	1.03488
$371$	−1.78026e150	−0.875205
$372$	−1.21743e150	−0.511306
$373$	−2.41784e150	−0.867883	−0.433942	−	0.900941i	$-0.642878\pi$
$373$	−2.41784e150	−0.867883	−0.433942	+	0.900941i	$0.642878\pi$
$374$	−4.56069e149	−0.139972
$375$	−1.80240e150	−0.473175
$376$	−3.08170e150	−0.692311
$377$	1.10838e150	0.213168
$378$	−5.88499e150	−0.969338
$379$	2.56529e150	0.362029	0.181014	−	0.983480i	$-0.442062\pi$
$379$	2.56529e150	0.362029	0.181014	+	0.983480i	$0.442062\pi$
$380$	−1.09745e150	−0.132753
$381$	−7.42988e150	−0.770674
$382$	3.03158e151	2.69751
$383$	−1.16014e151	−0.885894	−0.442947	−	0.896548i	$-0.646067\pi$
$383$	−1.16014e151	−0.885894	−0.442947	+	0.896548i	$0.646067\pi$
$384$	−5.39403e150	−0.353620
$385$	−3.49045e150	−0.196530
$386$	3.99998e151	1.93509
$387$	−1.14658e151	−0.476776
$388$	2.35872e151	0.843373
$389$	−5.26500e151	−1.61937	−0.809686	−	0.586863i	$-0.800363\pi$
$389$	−5.26500e151	−1.61937	−0.809686	+	0.586863i	$0.800363\pi$
$390$	5.08338e150	0.134547
$391$	−1.40373e151	−0.319848
$392$	8.51966e150	0.167181
$393$	−2.18826e150	−0.0369942
$394$	1.03437e152	1.50712
$395$	−3.28693e151	−0.412914
$396$	−4.22525e151	−0.457809
$397$	1.53229e152	1.43250	0.716252	−	0.697842i	$-0.245856\pi$
$397$	1.53229e152	1.43250	0.716252	+	0.697842i	$0.245856\pi$
$398$	−9.06089e151	−0.731158
$399$	−1.07069e151	−0.0746015
$400$	8.36025e151	0.503164
$401$	−3.47222e152	−1.80577	−0.902883	−	0.429886i	$-0.858554\pi$
$401$	−3.47222e152	−1.80577	−0.902883	+	0.429886i	$0.858554\pi$
$402$	−1.29329e152	−0.581394
$403$	−6.72748e151	−0.261521
$404$	−4.89924e152	−1.64748
$405$	−5.10061e151	−0.148424
$406$	2.82437e152	0.711456
$407$	2.97145e152	0.648179
$408$	1.78931e151	0.0338115
$409$	9.81431e152	1.60711	0.803556	−	0.595229i	$-0.202939\pi$
$409$	9.81431e152	1.60711	0.803556	+	0.595229i	$0.202939\pi$
$410$	4.76723e152	0.676722
$411$	8.84200e151	0.108844
$412$	8.61512e152	0.919971
$413$	7.73152e152	0.716452
$414$	−2.35229e153	−1.89222
$415$	1.26078e153	0.880697
$416$	−7.56979e152	−0.459329
$417$	−4.79113e152	−0.252626
$418$	−3.28130e152	−0.150395
$419$	1.42621e152	0.0568410	0.0284205	−	0.999596i	$-0.490952\pi$
$419$	1.42621e152	0.0568410	0.0284205	+	0.999596i	$0.490952\pi$
$420$	7.16140e152	0.248264
$421$	2.48106e153	0.748402	0.374201	−	0.927348i	$-0.377917\pi$
$421$	2.48106e153	0.748402	0.374201	+	0.927348i	$0.377917\pi$
$422$	−1.07376e154	−2.81923
$423$	−6.29831e153	−1.43983
$424$	2.14053e153	0.426205
$425$	−7.61870e152	−0.132169
$426$	4.15534e153	0.628267
$427$	8.39466e153	1.10655
$428$	6.96478e153	0.800658
$429$	8.40289e152	0.0842708
$430$	5.95572e153	0.521230
$431$	−8.85383e153	−0.676411	−0.338205	−	0.941072i	$-0.609820\pi$
$431$	−8.85383e153	−0.676411	−0.338205	+	0.941072i	$0.609820\pi$
$432$	−9.46996e153	−0.631755
$433$	1.78830e154	1.04207	0.521036	−	0.853534i	$-0.325546\pi$
$433$	1.78830e154	1.04207	0.521036	+	0.853534i	$0.325546\pi$
$434$	−1.71428e154	−0.872838
$435$	−4.07175e153	−0.181201
$436$	2.88315e154	1.12178
$437$	−1.00995e154	−0.343665
$438$	−3.38614e154	−1.00802
$439$	5.13149e154	1.33681	0.668404	−	0.743799i	$-0.266978\pi$
$439$	5.13149e154	1.33681	0.668404	+	0.743799i	$0.266978\pi$
$440$	4.19681e153	0.0957056
$441$	1.74123e154	0.347695
$442$	5.17078e153	0.0904385
$443$	3.21825e154	0.493176	0.246588	−	0.969120i	$-0.420691\pi$
$443$	3.21825e154	0.493176	0.246588	+	0.969120i	$0.420691\pi$
$444$	−6.09655e154	−0.818805
$445$	3.55693e154	0.418808
$446$	−1.45441e155	−1.50175
$447$	3.57830e154	0.324105
$448$	−1.28242e155	−1.01922
$449$	−7.90834e153	−0.0551663	−0.0275832	−	0.999620i	$-0.508781\pi$
$449$	−7.90834e153	−0.0551663	−0.0275832	+	0.999620i	$0.508781\pi$
$450$	−1.27670e155	−0.781909
$451$	7.88029e154	0.423852
$452$	−1.44765e155	−0.684014
$453$	−3.83510e154	−0.159233
$454$	2.77956e155	1.01440
$455$	3.95737e154	0.126981
$456$	1.28736e154	0.0363293
$457$	−3.73202e154	−0.0926502	−0.0463251	−	0.998926i	$-0.514751\pi$
$457$	−3.73202e154	−0.0926502	−0.0463251	+	0.998926i	$0.514751\pi$
$458$	1.09460e156	2.39124
$459$	8.62997e154	0.165946
$460$	6.75514e155	1.14367
$461$	−7.73552e153	−0.0115341	−0.00576707	−	0.999983i	$-0.501836\pi$
$461$	−7.73552e153	−0.0115341	−0.00576707	+	0.999983i	$0.501836\pi$
$462$	2.14121e155	0.281257
$463$	−1.52789e156	−1.76849	−0.884247	−	0.467019i	$-0.845328\pi$
$463$	−1.52789e156	−1.76849	−0.884247	+	0.467019i	$0.845328\pi$
$464$	4.54489e155	0.463683
$465$	2.47140e155	0.222303
$466$	−2.23960e156	−1.77662
$467$	−2.55372e156	−1.78705	−0.893523	−	0.449018i	$-0.851774\pi$
$467$	−2.55372e156	−1.78705	−0.893523	+	0.449018i	$0.851774\pi$
$468$	4.79047e155	0.295799
$469$	−1.00681e156	−0.548703
$470$	3.27154e156	1.57408
$471$	−9.36227e155	−0.397794
$472$	−9.29615e155	−0.348896
$473$	9.84488e155	0.326463
$474$	2.01636e156	0.590929
$475$	−5.48146e155	−0.142010
$476$	7.28453e155	0.166876
$477$	4.37477e156	0.886400
$478$	−3.25776e156	−0.583966
$479$	−5.49037e156	−0.870912	−0.435456	−	0.900210i	$-0.643413\pi$
$479$	−5.49037e156	−0.870912	−0.435456	+	0.900210i	$0.643413\pi$
$480$	2.78083e156	0.390447
$481$	−3.36894e156	−0.418800
$482$	1.17413e157	1.29260
$483$	6.59041e156	0.642695
$484$	−1.06816e157	−0.922957
$485$	−4.78823e156	−0.366677
$486$	2.27951e157	1.54746
$487$	−3.40722e156	−0.205096	−0.102548	−	0.994728i	$-0.532699\pi$
$487$	−3.40722e156	−0.205096	−0.102548	+	0.994728i	$0.532699\pi$
$488$	−1.00935e157	−0.538867
$489$	8.68510e156	0.411346
$490$	−9.04450e156	−0.380114
$491$	3.85358e156	0.143746	0.0718732	−	0.997414i	$-0.477102\pi$
$491$	3.85358e156	0.143746	0.0718732	+	0.997414i	$0.477102\pi$
$492$	−1.61681e157	−0.535427
$493$	−4.14176e156	−0.121798
$494$	3.72025e156	0.0971729
$495$	8.57733e156	0.199044
$496$	−2.75858e157	−0.568862
$497$	3.23490e157	0.592941
$498$	−7.73425e157	−1.26038
$499$	−1.13135e158	−1.63952	−0.819759	−	0.572709i	$-0.805893\pi$
$499$	−1.13135e158	−1.63952	−0.819759	+	0.572709i	$0.805893\pi$
$500$	8.82278e157	1.13726
$501$	−4.79120e157	−0.549461
$502$	−5.71722e157	−0.583468
$503$	6.51518e157	0.591834	0.295917	−	0.955214i	$-0.404375\pi$
$503$	6.51518e157	0.591834	0.295917	+	0.955214i	$0.404375\pi$
$504$	2.33425e157	0.188782
$505$	9.94554e157	0.716280
$506$	2.01974e158	1.29566
$507$	8.04845e157	0.459988
$508$	3.63694e158	1.85229
$509$	1.60312e158	0.727741	0.363871	−	0.931450i	$-0.381455\pi$
$509$	1.60312e158	0.727741	0.363871	+	0.931450i	$0.381455\pi$
$510$	−1.89953e157	−0.0768761
$511$	−2.63608e158	−0.951341
$512$	−3.88130e158	−1.24935
$513$	6.20905e157	0.178303
$514$	−5.39566e158	−1.38262
$515$	−1.74888e158	−0.399980
$516$	−2.01989e158	−0.412401
$517$	5.40790e158	0.985898
$518$	−8.58468e158	−1.39776
$519$	5.02074e158	0.730260
$520$	−4.75822e157	−0.0618371
$521$	−7.80911e158	−0.906974	−0.453487	−	0.891263i	$-0.649820\pi$
$521$	−7.80911e158	−0.906974	−0.453487	+	0.891263i	$0.649820\pi$
$522$	−6.94053e158	−0.720556
$523$	1.57083e159	1.45808	0.729039	−	0.684472i	$-0.239967\pi$
$523$	1.57083e159	1.45808	0.729039	+	0.684472i	$0.239967\pi$
$524$	1.07116e158	0.0889146
$525$	3.57692e158	0.265577
$526$	1.69903e158	0.112859
$527$	2.51389e158	0.149426
$528$	3.44557e158	0.183306
$529$	4.11685e159	1.96069
$530$	−2.27239e159	−0.969048
$531$	−1.89992e159	−0.725616
$532$	5.24103e158	0.179303
$533$	−8.93446e158	−0.273859
$534$	−2.18199e159	−0.599363
$535$	−1.41386e159	−0.348106
$536$	1.21056e159	0.267206
$537$	1.59510e159	0.315713
$538$	1.32803e160	2.35747
$539$	−1.49507e159	−0.238077
$540$	−4.15299e159	−0.593370
$541$	−6.04286e159	−0.774823	−0.387411	−	0.921907i	$-0.626631\pi$
$541$	−6.04286e159	−0.774823	−0.387411	+	0.921907i	$0.626631\pi$
$542$	−3.11784e158	−0.0358835
$543$	1.58289e159	0.163554
$544$	2.82864e159	0.262448
$545$	−5.85284e159	−0.487721
$546$	−2.42764e159	−0.181725
$547$	−2.10732e160	−1.41733	−0.708666	−	0.705544i	$-0.750703\pi$
$547$	−2.10732e160	−1.41733	−0.708666	+	0.705544i	$0.750703\pi$
$548$	−4.32818e159	−0.261603
$549$	−2.06288e160	−1.12071
$550$	1.09621e160	0.535397
$551$	−2.97989e159	−0.130867
$552$	−7.92411e159	−0.312978
$553$	1.56972e160	0.557702
$554$	6.60058e160	2.10990
$555$	1.23761e160	0.355996
$556$	2.34527e160	0.607179
$557$	−3.92569e160	−0.914929	−0.457465	−	0.889228i	$-0.651242\pi$
$557$	−3.92569e160	−0.914929	−0.457465	+	0.889228i	$0.651242\pi$
$558$	4.21264e160	0.884003
$559$	−1.11619e160	−0.210934
$560$	1.62271e160	0.276211
$561$	−3.13995e159	−0.0481499
$562$	2.51127e160	0.346992
$563$	1.10246e161	1.37284	0.686421	−	0.727204i	$-0.259181\pi$
$563$	1.10246e161	1.37284	0.686421	+	0.727204i	$0.259181\pi$
$564$	−1.10955e161	−1.24543
$565$	2.93876e160	0.297392
$566$	−2.11545e161	−1.93037
$567$	2.43587e160	0.200468
$568$	−3.88954e160	−0.288749
$569$	−1.29272e161	−0.865840	−0.432920	−	0.901432i	$-0.642517\pi$
$569$	−1.29272e161	−0.865840	−0.432920	+	0.901432i	$0.642517\pi$
$570$	−1.36667e160	−0.0826006
$571$	−2.26996e161	−1.23825	−0.619123	−	0.785294i	$-0.712512\pi$
$571$	−2.26996e161	−1.23825	−0.619123	+	0.785294i	$0.712512\pi$
$572$	−4.11323e160	−0.202542
$573$	2.08719e161	0.927934
$574$	−2.27666e161	−0.914014
$575$	3.37401e161	1.22343
$576$	3.15139e161	1.03225
$577$	−2.31802e161	−0.686012	−0.343006	−	0.939333i	$-0.611445\pi$
$577$	−2.31802e161	−0.686012	−0.343006	+	0.939333i	$0.611445\pi$
$578$	5.39864e161	1.44380
$579$	2.75392e161	0.665663
$580$	1.99313e161	0.435510
$581$	−6.02106e161	−1.18951
$582$	2.93734e161	0.524758
$583$	−3.75629e161	−0.606945
$584$	3.16955e161	0.463282
$585$	−9.72474e160	−0.128606
$586$	−1.43711e162	−1.71980
$587$	3.67223e161	0.397742	0.198871	−	0.980026i	$-0.436273\pi$
$587$	3.67223e161	0.397742	0.198871	+	0.980026i	$0.436273\pi$
$588$	3.06745e161	0.300749
$589$	1.80868e161	0.160553
$590$	9.86882e161	0.793273
$591$	7.12147e161	0.518444
$592$	−1.38142e162	−0.910975
$593$	2.93135e162	1.75133	0.875666	−	0.482917i	$-0.160423\pi$
$593$	2.93135e162	1.75133	0.875666	+	0.482917i	$0.160423\pi$
$594$	−1.24171e162	−0.672225
$595$	−1.47877e161	−0.0725535
$596$	−1.75159e162	−0.778978
$597$	−6.23826e161	−0.251516
$598$	−2.28993e162	−0.837149
$599$	−2.08913e162	−0.692623	−0.346312	−	0.938119i	$-0.612566\pi$
$599$	−2.08913e162	−0.692623	−0.346312	+	0.938119i	$0.612566\pi$
$600$	−4.30078e161	−0.129330
$601$	−2.35481e160	−0.00642391	−0.00321195	−	0.999995i	$-0.501022\pi$
$601$	−2.35481e160	−0.00642391	−0.00321195	+	0.999995i	$0.501022\pi$
$602$	−2.84424e162	−0.703999
$603$	2.47412e162	0.555722
$604$	1.87729e162	0.382711
$605$	2.16838e162	0.401278
$606$	−6.10108e162	−1.02508
$607$	7.90941e162	1.20672	0.603358	−	0.797470i	$-0.293829\pi$
$607$	7.90941e162	1.20672	0.603358	+	0.797470i	$0.293829\pi$
$608$	2.03514e162	0.281990
$609$	1.94453e162	0.244738
$610$	1.07153e163	1.22520
$611$	−6.13133e162	−0.637006
$612$	−1.79008e162	−0.169011
$613$	2.25474e163	1.93490	0.967451	−	0.253060i	$-0.0814369\pi$
$613$	2.25474e163	1.93490	0.967451	+	0.253060i	$0.0814369\pi$
$614$	5.67336e162	0.442579
$615$	3.28215e162	0.232790
$616$	−2.00425e162	−0.129265
$617$	−2.87605e163	−1.68700	−0.843499	−	0.537130i	$-0.819508\pi$
$617$	−2.87605e163	−1.68700	−0.843499	+	0.537130i	$0.819508\pi$
$618$	1.07285e163	0.572418
$619$	−1.93525e163	−0.939366	−0.469683	−	0.882835i	$-0.655632\pi$
$619$	−1.93525e163	−0.939366	−0.469683	+	0.882835i	$0.655632\pi$
$620$	−1.20976e163	−0.534298
$621$	−3.82186e163	−1.53609
$622$	−1.48797e163	−0.544325
$623$	−1.69867e163	−0.565662
$624$	−3.90650e162	−0.118437
$625$	7.84465e162	0.216567
$626$	4.97232e163	1.25015
$627$	−2.25912e162	−0.0517353
$628$	4.58285e163	0.956085
$629$	1.25889e163	0.239290
$630$	−2.47804e163	−0.429227
$631$	3.54315e163	0.559335	0.279667	−	0.960097i	$-0.409776\pi$
$631$	3.54315e163	0.559335	0.279667	+	0.960097i	$0.409776\pi$
$632$	−1.88738e163	−0.271589
$633$	−7.39268e163	−0.969806
$634$	1.52344e164	1.82223
$635$	−7.38306e163	−0.805329
$636$	7.70684e163	0.766717
$637$	1.69507e163	0.153826
$638$	5.95933e163	0.493387
$639$	−7.94935e163	−0.600526
$640$	−5.36004e163	−0.369521
$641$	1.11842e164	0.703735	0.351867	−	0.936050i	$-0.385547\pi$
$641$	1.11842e164	0.703735	0.351867	+	0.936050i	$0.385547\pi$
$642$	8.67332e163	0.498180
$643$	−1.66574e164	−0.873507	−0.436753	−	0.899581i	$-0.643872\pi$
$643$	−1.66574e164	−0.873507	−0.436753	+	0.899581i	$0.643872\pi$
$644$	−3.22602e164	−1.54470
$645$	4.10041e163	0.179301
$646$	−1.39016e163	−0.0555218
$647$	3.04650e164	1.11148	0.555739	−	0.831357i	$-0.312435\pi$
$647$	3.04650e164	1.11148	0.555739	+	0.831357i	$0.312435\pi$
$648$	−2.92882e163	−0.0976237
$649$	1.63133e164	0.496851
$650$	−1.24285e164	−0.345929
$651$	−1.18025e164	−0.300253
$652$	−4.25138e164	−0.988657
$653$	3.44273e163	0.0731952	0.0365976	−	0.999330i	$-0.488348\pi$
$653$	3.44273e163	0.0731952	0.0365976	+	0.999330i	$0.488348\pi$
$654$	3.59042e164	0.697986
$655$	−2.17447e163	−0.0386578
$656$	−3.66354e164	−0.595698
$657$	6.47784e164	0.963510
$658$	−1.56237e165	−2.12603
$659$	−4.45437e164	−0.554613	−0.277306	−	0.960782i	$-0.589442\pi$
$659$	−4.45437e164	−0.554613	−0.277306	+	0.960782i	$0.589442\pi$
$660$	1.51103e164	0.172169
$661$	3.79355e164	0.395604	0.197802	−	0.980242i	$-0.436620\pi$
$661$	3.79355e164	0.395604	0.197802	+	0.980242i	$0.436620\pi$
$662$	9.70486e164	0.926396
$663$	3.55999e163	0.0311105
$664$	7.23954e164	0.579266
$665$	−1.06394e164	−0.0779562
$666$	2.10958e165	1.41564
$667$	1.83422e165	1.12743
$668$	2.34530e165	1.32061
$669$	−1.00134e165	−0.516597
$670$	−1.28514e165	−0.607538
$671$	1.77125e165	0.767383
$672$	−1.32803e165	−0.527357
$673$	−4.59246e165	−1.67172	−0.835861	−	0.548941i	$-0.815031\pi$
$673$	−4.59246e165	−1.67172	−0.835861	+	0.548941i	$0.815031\pi$
$674$	−3.52872e165	−1.17764
$675$	−2.07430e165	−0.634748
$676$	−3.93973e165	−1.10557
$677$	1.89717e165	0.488280	0.244140	−	0.969740i	$-0.421494\pi$
$677$	1.89717e165	0.488280	0.244140	+	0.969740i	$0.421494\pi$
$678$	−1.80278e165	−0.425603
$679$	2.28669e165	0.495252
$680$	1.77803e164	0.0353320
$681$	1.91368e165	0.348949
$682$	−3.61709e165	−0.605304
$683$	2.29671e164	0.0352772	0.0176386	−	0.999844i	$-0.494385\pi$
$683$	2.29671e164	0.0352772	0.0176386	+	0.999844i	$0.494385\pi$
$684$	−1.28792e165	−0.181596
$685$	8.78628e164	0.113738
$686$	1.34545e166	1.59921
$687$	7.53609e165	0.822578
$688$	−4.57688e165	−0.458824
$689$	4.25878e165	0.392158
$690$	8.41226e165	0.711608
$691$	5.74742e165	0.446691	0.223345	−	0.974739i	$-0.428302\pi$
$691$	5.74742e165	0.446691	0.223345	+	0.974739i	$0.428302\pi$
$692$	−2.45767e166	−1.75516
$693$	−4.09624e165	−0.268838
$694$	2.36843e166	1.42867
$695$	−4.76093e165	−0.263986
$696$	−2.33804e165	−0.119182
$697$	3.33858e165	0.156475
$698$	6.64416e165	0.286350
$699$	−1.54192e166	−0.611150
$700$	−1.75091e166	−0.638306
$701$	−3.29581e166	−1.10524	−0.552622	−	0.833432i	$-0.686373\pi$
$701$	−3.29581e166	−1.10524	−0.552622	+	0.833432i	$0.686373\pi$
$702$	1.40782e166	0.434337
$703$	9.05740e165	0.257109
$704$	−2.70587e166	−0.706815
$705$	2.25240e166	0.541479
$706$	9.83017e166	2.17513
$707$	−4.74964e166	−0.967443
$708$	−3.34702e166	−0.627643
$709$	−3.59644e166	−0.620966	−0.310483	−	0.950579i	$-0.600491\pi$
$709$	−3.59644e166	−0.620966	−0.310483	+	0.950579i	$0.600491\pi$
$710$	4.12915e166	0.656519
$711$	−3.85739e166	−0.564836
$712$	2.04242e166	0.275465
$713$	−1.11330e167	−1.38317
$714$	9.07150e165	0.103833
$715$	8.34994e165	0.0880602
$716$	−7.80805e166	−0.758806
$717$	−2.24291e166	−0.200882
$718$	2.61743e167	2.16070
$719$	1.74998e165	0.0133166	0.00665828	−	0.999978i	$-0.497881\pi$
$719$	1.74998e165	0.0133166	0.00665828	+	0.999978i	$0.497881\pi$
$720$	−3.98760e166	−0.279744
$721$	8.35206e166	0.540233
$722$	2.40727e167	1.43581
$723$	8.08367e166	0.444650
$724$	−7.74829e166	−0.393097
$725$	9.95515e166	0.465880
$726$	−1.33019e167	−0.574276
$727$	−3.75828e166	−0.149701	−0.0748507	−	0.997195i	$-0.523848\pi$
$727$	−3.75828e166	−0.149701	−0.0748507	+	0.997195i	$0.523848\pi$
$728$	2.27236e166	0.0835202
$729$	7.55395e166	0.256221
$730$	−3.36480e167	−1.05335
$731$	4.17091e166	0.120521
$732$	−3.63410e167	−0.969389
$733$	7.75842e167	1.91069	0.955346	−	0.295490i	$-0.0954829\pi$
$733$	7.75842e167	1.91069	0.955346	+	0.295490i	$0.0954829\pi$
$734$	−5.74078e167	−1.30542
$735$	−6.22698e166	−0.130758
$736$	−1.25269e168	−2.42936
$737$	−2.12435e167	−0.380520
$738$	5.59461e167	0.925706
$739$	−5.05055e167	−0.772039	−0.386020	−	0.922491i	$-0.626150\pi$
$739$	−5.05055e167	−0.772039	−0.386020	+	0.922491i	$0.626150\pi$
$740$	−6.05814e167	−0.855625
$741$	2.56132e166	0.0334271
$742$	1.08522e168	1.30884
$743$	9.39974e167	1.04778	0.523890	−	0.851786i	$-0.324480\pi$
$743$	9.39974e167	1.04778	0.523890	+	0.851786i	$0.324480\pi$
$744$	1.41910e167	0.146217
$745$	3.55575e167	0.338680
$746$	1.47387e168	1.29789
$747$	1.47960e168	1.20473
$748$	1.53701e167	0.115727
$749$	6.75211e167	0.470168
$750$	1.09871e168	0.707619
$751$	−2.51483e168	−1.49821	−0.749104	−	0.662453i	$-0.769515\pi$
$751$	−2.51483e168	−1.49821	−0.749104	+	0.662453i	$0.769515\pi$
$752$	−2.51413e168	−1.38562
$753$	−3.93620e167	−0.200711
$754$	−6.75652e167	−0.318786
$755$	−3.81094e167	−0.166393
$756$	1.98332e168	0.801434
$757$	−2.73040e168	−1.02122	−0.510608	−	0.859814i	$-0.670580\pi$
$757$	−2.73040e168	−1.02122	−0.510608	+	0.859814i	$0.670580\pi$
$758$	−1.56376e168	−0.541404
$759$	1.39056e168	0.445702
$760$	1.27925e167	0.0379629
$761$	−3.07125e167	−0.0843942	−0.0421971	−	0.999109i	$-0.513436\pi$
$761$	−3.07125e167	−0.0843942	−0.0421971	+	0.999109i	$0.513436\pi$
$762$	4.52913e168	1.15252
$763$	2.79511e168	0.658740
$764$	−1.02168e169	−2.23026
$765$	3.63390e167	0.0734816
$766$	7.07200e168	1.32483
$767$	−1.84955e168	−0.321025
$768$	−1.20196e168	−0.193312
$769$	−2.81890e168	−0.420135	−0.210068	−	0.977687i	$-0.567368\pi$
$769$	−2.81890e168	−0.420135	−0.210068	+	0.977687i	$0.567368\pi$
$770$	2.12772e168	0.293904
$771$	−3.71481e168	−0.475615
$772$	−1.34805e169	−1.59990
$773$	9.61364e168	1.05776	0.528880	−	0.848697i	$-0.322612\pi$
$773$	9.61364e168	1.05776	0.528880	+	0.848697i	$0.322612\pi$
$774$	6.98937e168	0.713004
$775$	−6.04240e168	−0.571558
$776$	−2.74945e168	−0.241177
$777$	−5.91040e168	−0.480825
$778$	3.20945e169	2.42172
$779$	2.40203e168	0.168127
$780$	−1.71317e168	−0.111241
$781$	6.82554e168	0.411198
$782$	8.55689e168	0.478323
$783$	−1.12766e169	−0.584943
$784$	6.95055e168	0.334603
$785$	−9.30327e168	−0.415681
$786$	1.33392e168	0.0553238
$787$	2.99359e169	1.15258	0.576289	−	0.817246i	$-0.304500\pi$
$787$	2.99359e169	1.15258	0.576289	+	0.817246i	$0.304500\pi$
$788$	−3.48598e169	−1.24607
$789$	1.16975e168	0.0388231
$790$	2.00365e169	0.617501
$791$	−1.40345e169	−0.401672
$792$	4.92519e168	0.130918
$793$	−2.00819e169	−0.495820
$794$	−9.34056e169	−2.14227
$795$	−1.56450e169	−0.333349
$796$	3.05364e169	0.604511
$797$	−9.55809e169	−1.75816	−0.879082	−	0.476671i	$-0.841843\pi$
$797$	−9.55809e169	−1.75816	−0.879082	+	0.476671i	$0.841843\pi$
$798$	6.52672e168	0.111564
$799$	2.29113e169	0.363967
$800$	−6.79894e169	−1.00387
$801$	4.17426e169	0.572898
$802$	2.11661e170	2.70047
$803$	−5.56206e169	−0.659745
$804$	4.35855e169	0.480688
$805$	6.54888e169	0.671596
$806$	4.10096e169	0.391098
$807$	9.14328e169	0.810961
$808$	5.71083e169	0.471123
$809$	−8.00742e169	−0.614475	−0.307237	−	0.951633i	$-0.599405\pi$
$809$	−8.00742e169	−0.614475	−0.307237	+	0.951633i	$0.599405\pi$
$810$	3.10925e169	0.221963
$811$	8.12469e169	0.539618	0.269809	−	0.962914i	$-0.413039\pi$
$811$	8.12469e169	0.539618	0.269809	+	0.962914i	$0.413039\pi$
$812$	−9.51850e169	−0.588221
$813$	−2.14657e168	−0.0123438
$814$	−1.81134e170	−0.969332
$815$	8.63037e169	0.429843
$816$	1.45976e169	0.0676718
$817$	3.00086e169	0.129496
$818$	−5.98263e170	−2.40339
$819$	4.64420e169	0.173701
$820$	−1.60662e170	−0.559504
$821$	3.91906e170	1.27089	0.635443	−	0.772147i	$-0.280817\pi$
$821$	3.91906e170	1.27089	0.635443	+	0.772147i	$0.280817\pi$
$822$	−5.38993e169	−0.162773
$823$	−1.59265e169	−0.0447950	−0.0223975	−	0.999749i	$-0.507130\pi$
$823$	−1.59265e169	−0.0447950	−0.0223975	+	0.999749i	$0.507130\pi$
$824$	−1.00423e170	−0.263081
$825$	7.54720e169	0.184175
$826$	−4.71300e170	−1.07143
$827$	5.60852e169	0.118789	0.0593944	−	0.998235i	$-0.481083\pi$
$827$	5.60852e169	0.118789	0.0593944	+	0.998235i	$0.481083\pi$
$828$	7.92754e170	1.56446
$829$	8.86046e169	0.162936	0.0814679	−	0.996676i	$-0.474039\pi$
$829$	8.86046e169	0.162936	0.0814679	+	0.996676i	$0.474039\pi$
$830$	−7.68551e170	−1.31706
$831$	4.54438e170	0.725797
$832$	3.06784e170	0.456686
$833$	−6.33404e169	−0.0878918
$834$	2.92059e170	0.377795
$835$	−4.76101e170	−0.574169
$836$	1.10584e170	0.124344
$837$	6.84445e170	0.717627
$838$	−8.69390e169	−0.0850041
$839$	−8.79135e170	−0.801642	−0.400821	−	0.916156i	$-0.631275\pi$
$839$	−8.79135e170	−0.801642	−0.400821	+	0.916156i	$0.631275\pi$
$840$	−8.34772e169	−0.0709953
$841$	−7.19374e170	−0.570675
$842$	−1.51241e171	−1.11921
$843$	1.72897e170	0.119364
$844$	3.61873e171	2.33090
$845$	7.99773e170	0.480672
$846$	3.83934e171	2.15323
$847$	−1.03554e171	−0.541986
$848$	1.74630e171	0.853024
$849$	−1.45645e171	−0.664041
$850$	4.64423e170	0.197654
$851$	−5.57511e171	−2.21500
$852$	−1.40040e171	−0.519442
$853$	1.21294e171	0.420068	0.210034	−	0.977694i	$-0.432642\pi$
$853$	1.21294e171	0.420068	0.210034	+	0.977694i	$0.432642\pi$
$854$	−5.11724e171	−1.65482
$855$	2.61450e170	0.0789533
$856$	−8.11854e170	−0.228962
$857$	−4.24515e171	−1.11819	−0.559094	−	0.829104i	$-0.688851\pi$
$857$	−4.24515e171	−1.11819	−0.559094	+	0.829104i	$0.688851\pi$
$858$	−5.12226e170	−0.126024
$859$	−4.12134e169	−0.00947194	−0.00473597	−	0.999989i	$-0.501508\pi$
$859$	−4.12134e169	−0.00947194	−0.00473597	+	0.999989i	$0.501508\pi$
$860$	−2.00716e171	−0.430946
$861$	−1.56744e171	−0.314418
$862$	5.39714e171	1.01155
$863$	6.81136e171	1.19290	0.596448	−	0.802652i	$-0.296578\pi$
$863$	6.81136e171	1.19290	0.596448	+	0.802652i	$0.296578\pi$
$864$	7.70140e171	1.26042
$865$	4.98910e171	0.763098
$866$	−1.09012e172	−1.55839
$867$	3.71687e171	0.496661
$868$	5.77737e171	0.721650
$869$	3.31206e171	0.386760
$870$	2.48207e171	0.270980
$871$	2.40852e171	0.245861
$872$	−3.36076e171	−0.320792
$873$	−5.61926e171	−0.501587
$874$	6.15647e171	0.513941
$875$	8.55338e171	0.667831
$876$	1.14117e172	0.833416
$877$	2.14592e171	0.146601	0.0733005	−	0.997310i	$-0.476647\pi$
$877$	2.14592e171	0.146601	0.0733005	+	0.997310i	$0.476647\pi$
$878$	−3.12807e172	−1.99916
$879$	−9.89423e171	−0.591606
$880$	3.42386e171	0.191549
$881$	−3.01849e172	−1.58015	−0.790075	−	0.613010i	$-0.789959\pi$
$881$	−3.01849e172	−1.58015	−0.790075	+	0.613010i	$0.789959\pi$
$882$	−1.06142e172	−0.519967
$883$	1.34856e172	0.618255	0.309127	−	0.951021i	$-0.399963\pi$
$883$	1.34856e172	0.618255	0.309127	+	0.951021i	$0.399963\pi$
$884$	−1.74262e171	−0.0747732
$885$	6.79451e171	0.272883
$886$	−1.96179e172	−0.737530
$887$	−1.63205e172	−0.574383	−0.287191	−	0.957873i	$-0.592722\pi$
$887$	−1.63205e172	−0.574383	−0.287191	+	0.957873i	$0.592722\pi$
$888$	7.10648e171	0.234151
$889$	3.52589e172	1.08772
$890$	−2.16824e172	−0.626315
$891$	5.13962e171	0.139023
$892$	4.90156e172	1.24163
$893$	1.64841e172	0.391070
$894$	−2.18127e172	−0.484690
$895$	1.58505e172	0.329909
$896$	2.55977e172	0.499093
$897$	−1.57657e172	−0.287976
$898$	4.82079e171	0.0824997
$899$	−3.28484e172	−0.526710
$900$	4.30265e172	0.646471
$901$	−1.59140e172	−0.224068
$902$	−4.80369e172	−0.633859
$903$	−1.95821e172	−0.242173
$904$	1.68746e172	0.195605
$905$	1.57292e172	0.170908
$906$	2.33781e172	0.238128
$907$	4.60827e172	0.440059	0.220030	−	0.975493i	$-0.429385\pi$
$907$	4.60827e172	0.440059	0.220030	+	0.975493i	$0.429385\pi$
$908$	−9.36749e172	−0.838689
$909$	1.16717e173	0.979818
$910$	−2.41235e172	−0.189897
$911$	2.03580e173	1.50283	0.751415	−	0.659830i	$-0.229372\pi$
$911$	2.03580e173	1.50283	0.751415	+	0.659830i	$0.229372\pi$
$912$	1.05026e172	0.0727109
$913$	−1.27043e173	−0.824914
$914$	2.27498e172	0.138556
$915$	7.37728e172	0.421466
$916$	−3.68893e173	−1.97704
$917$	1.03845e172	0.0522131
$918$	−5.26068e172	−0.248168
$919$	−2.27320e173	−1.00619	−0.503095	−	0.864231i	$-0.667805\pi$
$919$	−2.27320e173	−1.00619	−0.503095	+	0.864231i	$0.667805\pi$
$920$	−7.87417e172	−0.327052
$921$	3.90601e172	0.152246
$922$	4.71544e171	0.0172490
$923$	−7.73860e172	−0.265683
$924$	−7.21617e172	−0.232539
$925$	−3.02587e173	−0.915291
$926$	9.31374e173	2.64473
$927$	−2.05241e173	−0.547143
$928$	−3.69611e173	−0.925100
$929$	2.84056e173	0.667550	0.333775	−	0.942653i	$-0.391677\pi$
$929$	2.84056e173	0.667550	0.333775	+	0.942653i	$0.391677\pi$
$930$	−1.50652e173	−0.332448
$931$	−4.55718e172	−0.0944365
$932$	7.54775e173	1.46888
$933$	−1.02444e173	−0.187246
$934$	1.55670e174	2.67247
$935$	−3.12016e172	−0.0503151
$936$	−5.58404e172	−0.0845885
$937$	2.63396e172	0.0374837	0.0187419	−	0.999824i	$-0.494034\pi$
$937$	2.63396e172	0.0374837	0.0187419	+	0.999824i	$0.494034\pi$
$938$	6.13736e173	0.820570
$939$	3.42335e173	0.430046
$940$	−1.10255e174	−1.30143
$941$	−8.79032e173	−0.975016	−0.487508	−	0.873119i	$-0.662094\pi$
$941$	−8.79032e173	−0.975016	−0.487508	+	0.873119i	$0.662094\pi$
$942$	5.70708e173	0.594889
$943$	−1.47852e174	−1.44842
$944$	−7.58403e173	−0.698294
$945$	−4.02618e173	−0.348443
$946$	−6.00127e173	−0.488216
$947$	−1.60070e174	−1.22415	−0.612077	−	0.790798i	$-0.709666\pi$
$947$	−1.60070e174	−1.22415	−0.612077	+	0.790798i	$0.709666\pi$
$948$	−6.79541e173	−0.488571
$949$	6.30610e173	0.426273
$950$	3.34140e173	0.212372
$951$	1.04886e174	0.626841
$952$	−8.49125e172	−0.0477211
$953$	2.02788e174	1.07179	0.535893	−	0.844286i	$-0.319975\pi$
$953$	2.02788e174	1.07179	0.535893	+	0.844286i	$0.319975\pi$
$954$	−2.66678e174	−1.32558
$955$	2.07404e174	0.969660
$956$	1.09791e174	0.482814
$957$	4.10289e173	0.169723
$958$	3.34683e174	1.30242
$959$	−4.19602e173	−0.153620
$960$	−1.12700e174	−0.388200
$961$	−1.09168e174	−0.353814
$962$	2.05365e174	0.626303
$963$	−1.65925e174	−0.476182
$964$	−3.95697e174	−1.06870
$965$	2.73656e174	0.695596
$966$	−4.01740e174	−0.961132
$967$	4.60221e174	1.03638	0.518188	−	0.855267i	$-0.326607\pi$
$967$	4.60221e174	1.03638	0.518188	+	0.855267i	$0.326607\pi$
$968$	1.24510e174	0.263935
$969$	−9.57103e172	−0.0190993
$970$	2.91882e174	0.548355
$971$	6.41185e174	1.13412	0.567059	−	0.823677i	$-0.308081\pi$
$971$	6.41185e174	1.13412	0.567059	+	0.823677i	$0.308081\pi$
$972$	−7.68227e174	−1.27942
$973$	2.27365e174	0.356552
$974$	2.07698e174	0.306714
$975$	−8.55680e173	−0.118999
$976$	−8.23452e174	−1.07851
$977$	1.61853e174	0.199660	0.0998298	−	0.995005i	$-0.468170\pi$
$977$	1.61853e174	0.199660	0.0998298	+	0.995005i	$0.468170\pi$
$978$	−5.29429e174	−0.615155
$979$	−3.58413e174	−0.392280
$980$	3.04812e174	0.314273
$981$	−6.86864e174	−0.667166
$982$	−2.34908e174	−0.214969
$983$	1.16375e175	1.00341	0.501704	−	0.865039i	$-0.332707\pi$
$983$	1.16375e175	1.00341	0.501704	+	0.865039i	$0.332707\pi$
$984$	1.88464e174	0.153114
$985$	7.07659e174	0.541757
$986$	2.52474e174	0.182145
$987$	−1.07567e175	−0.731348
$988$	−1.25377e174	−0.0803411
$989$	−1.84713e175	−1.11561
$990$	−5.22860e174	−0.297664
$991$	−2.33120e175	−1.25104	−0.625520	−	0.780208i	$-0.715113\pi$
$991$	−2.33120e175	−1.25104	−0.625520	+	0.780208i	$0.715113\pi$
$992$	2.24340e175	1.13494
$993$	6.68162e174	0.318677
$994$	−1.97194e175	−0.886726
$995$	−6.19895e174	−0.262826
$996$	2.60655e175	1.04206
$997$	−6.39777e174	−0.241191	−0.120596	−	0.992702i	$-0.538480\pi$
$997$	−6.39777e174	−0.241191	−0.120596	+	0.992702i	$0.538480\pi$
$998$	6.89653e175	2.45185
$999$	3.42752e175	1.14921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.118.a.a.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.118.a.a.1.2	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 118 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-6.09583e17 q^{2} -4.19687e27 q^{3} +2.05438e35 q^{4} -4.17042e40 q^{5} +2.55834e45 q^{6} +1.99165e49 q^{7} -2.39470e52 q^{8} -4.89422e55 q^{9} +O(q^{10})\)	\(q-6.09583e17 q^{2} -4.19687e27 q^{3} +2.05438e35 q^{4} -4.17042e40 q^{5} +2.55834e45 q^{6} +1.99165e49 q^{7} -2.39470e52 q^{8} -4.89422e55 q^{9} +2.54222e58 q^{10} +4.20232e60 q^{11} -8.62195e62 q^{12} -4.76447e64 q^{13} -1.21407e67 q^{14} +1.75027e68 q^{15} -1.95365e70 q^{16} +1.78036e71 q^{17} +2.98343e73 q^{18} +1.28093e74 q^{19} -8.56762e75 q^{20} -8.35868e76 q^{21} -2.56166e78 q^{22} -7.88451e79 q^{23} +1.00502e80 q^{24} -4.27929e81 q^{25} +2.90434e82 q^{26} +4.84731e83 q^{27} +4.09159e84 q^{28} -2.32635e85 q^{29} -1.06693e86 q^{30} +1.41201e87 q^{31} +1.58880e88 q^{32} -1.76366e88 q^{33} -1.08528e89 q^{34} -8.30601e89 q^{35} -1.00546e91 q^{36} +7.07097e91 q^{37} -7.80831e91 q^{38} +1.99959e92 q^{39} +9.98689e92 q^{40} +1.87523e94 q^{41} +5.09531e94 q^{42} +2.34273e95 q^{43} +8.63314e95 q^{44} +2.04110e96 q^{45} +4.80626e97 q^{46} +1.28689e98 q^{47} +8.19923e97 q^{48} -3.55772e98 q^{49} +2.60858e99 q^{50} -7.47195e98 q^{51} -9.78801e99 q^{52} -8.93863e100 q^{53} -2.95483e101 q^{54} -1.75254e101 q^{55} -4.76939e101 q^{56} -5.37588e101 q^{57} +1.41811e103 q^{58} +3.88197e103 q^{59} +3.59572e103 q^{60} +4.21493e104 q^{61} -8.60737e104 q^{62} -9.74757e104 q^{63} -6.43899e105 q^{64} +1.98698e105 q^{65} +1.07509e106 q^{66} -5.05518e106 q^{67} +3.65754e106 q^{68} +3.30902e107 q^{69} +5.06320e107 q^{70} +1.62423e108 q^{71} +1.17202e108 q^{72} -1.32357e109 q^{73} -4.31034e109 q^{74} +1.79596e109 q^{75} +2.63151e109 q^{76} +8.36953e109 q^{77} -1.21891e110 q^{78} +7.88152e110 q^{79} +8.14756e110 q^{80} +1.22305e111 q^{81} -1.14311e112 q^{82} -3.02315e112 q^{83} -1.71719e112 q^{84} -7.42487e111 q^{85} -1.42809e113 q^{86} +9.76340e112 q^{87} -1.00633e113 q^{88} -8.52895e113 q^{89} -1.24422e114 q^{90} -9.48914e113 q^{91} -1.61977e115 q^{92} -5.92602e114 q^{93} -7.84463e115 q^{94} -5.34200e114 q^{95} -6.66799e115 q^{96} +1.14814e116 q^{97} +2.16873e116 q^{98} -2.05671e116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 40\!\cdots\!52 q^{2}+ \cdots + 22\!\cdots\!97 q^{9}+O(q^{10}) \) 9 * q + 40417036685158752 * q^2 + 10302905323878152966875623636 * q^3 + 679626474486553930371683615220261888 * q^4 + 38453607070720263635688515692568185914150 * q^5 - 4850209982284354841792124153951223028275738752 * q^6 - 33936637323452994043236135663221508618375503117208 * q^7 + 84807426568136809852447254974619690045330359678238720 * q^8 + 228322388396621838147039528942639942618778890580268310597 * q^9	\( 9 q + 40\!\cdots\!52 q^{2}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) \) 9 * q + 40417036685158752 * q^2 + 10302905323878152966875623636 * q^3 + 679626474486553930371683615220261888 * q^4 + 38453607070720263635688515692568185914150 * q^5 - 4850209982284354841792124153951223028275738752 * q^6 - 33936637323452994043236135663221508618375503117208 * q^7 + 84807426568136809852447254974619690045330359678238720 * q^8 + 228322388396621838147039528942639942618778890580268310597 * q^9 - 116795550914172753602500302406542633798241819198212925771200 * q^10 - 18850526893652982349030077823189856392436130547985552802563652 * q^11 + 3227106826098906050636969251983952779002958811977260223984586752 * q^12 - 98574936372230476445754809314443731682386957493373954090363278834 * q^13 + 35258972517405629268130631622450754971434643685593795240367372736256 * q^14 - 915629885182684846104756133008435145438889653925288537510093151318600 * q^15 + 61702437097071514242829543900966314104457520182055990902400499737165824 * q^16 - 680002505828907486847031510246007941006426153324907295268216079884418078 * q^17 - 41733213100034654524842848551561180884346520214587575830257187744066967584 * q^18 - 160689510555833725295714486201244011986205134154473703462344729085218574940 * q^19 - 2238340134838118789188928650249499474871086998961353735072744834498868275200 * q^20 - 325231066595782226476051172214780538694781261136602948155806527762690471674592 * q^21 - 13112988820785042404307735263630112517712749663800581417200667121255782067843456 * q^22 - 58153519408904797009281866377912077673911181772550205922884346377262357403061704 * q^23 - 3038238801938958809634055377152977696212679179273938957003033953876165693929553920 * q^24 + 5528673600140129203782645127829908484096231088932064383194690227200862517083894375 * q^25 + 56682227661992970696514878061752865405652252745109723390003965691218585268522989888 * q^26 + 1827774475813800388315702586366166077051345533885606497916848989661362329232290194120 * q^27 - 6468486093767359175378792181544485287676854914825022016113590703460551157550283513856 * q^28 - 48386553564988730519261358531155605067882474797775404905351553453290924873675961170210 * q^29 - 933061727033306076487821089990705907034760165404132848486598428012292996783024527379200 * q^30 - 621957331647921924682092054631242956130629654943098483596990494053452820493965659370592 * q^31 + 5001840478035603540410109619911952695496967661900989837684340698950683681301601905016832 * q^32 + 121811126973553577276247861343842508235672706892636830990043974788533005362046408289426992 * q^33 - 739829614062010739581951319533134982709290713812079124382329752841795383755334475547959104 * q^34 - 4738290388179207473702786515865081056559422688400941664804502829786561878838282647304413200 * q^35 + 45099229254587225493722800395751937761885426855646977453280381634636333644471918552752149504 * q^36 - 34964212885413714773919749832666304501127253457648317866689087418325240609603845719432098618 * q^37 + 721325600351264057185221862351496532134128096990026176343425219143447708368813195315354449280 * q^38 - 5256181041389152420659051237224453246783624348532029963454064662671494105217119495256720274216 * q^39 - 3971440606190340326438464214808272022762933594464202348081080358302577556396774721686560768000 * q^40 + 10020257933125498318762169522473576122868342311015731314988395755981139260089136547294206867738 * q^41 + 252970816117377205232172452762620886935079264765511703102710428456975064426237455951343632231424 * q^42 + 50615459145440588569921800707258109935625533244654510855325763075886611210775326812060053355356 * q^43 - 4005524110904096730553185857622707642025685539352197636568303886000422137318429894399607389425664 * q^44 + 5473276137456663664850729608899955954082083355607725618741940940860469618299772760360253073375950 * q^45 + 1478376152522396457093466079811724410922025958141013781241190503228240084745237352373452997174528 * q^46 + 16685567512808747231645711437000622991513185216117548515196412601564484313290777292415784238201712 * q^47 - 216224080066172714935125828338658772066778469688001789861117569570442266773620007884590970572898304 * q^48 + 169974231907168786505678866260391714519211137411643020101217953968783780867359385345616236202809313 * q^49 - 2469575139897634839277498689855848621914551651256318080857839988659447958716938283028005975429980000 * q^50 + 22542359242748231968428303678420614483799317368695374408674201779527797470892277868165393834070628328 * q^51 - 3641374884516561660680840591520895881667064402106525036999341733309771062927915917819681324515084288 * q^52 - 213846929196927043507342255756620254016567403070821501560181236631146130543117495693232522403826884714 * q^53 + 70368920588017409616903857310987095626556658223669990059448426800295554432360247812557938014199560960 * q^54 + 148096007032108307991537648756429447360412191714871283455777374803615140028070019602170536767368773800 * q^55 + 4912754841589119447020005683504898647317892135202904974904770520342259478270647905318907285925688770560 * q^56 + 4725267742102384458969291922476649493908095234626754028721076337022388939733447041972841854747117257040 * q^57 - 61691450689404126451745332477746935968828799400881738634159938087335342513296447359674633686816855103680 * q^58 - 7764769731115259168900983283133365701920906050369948450392029627233204947390357923079821008349713252820 * q^59 + 242167860317000066114168168973610808827817432218852606538275645995232520514013583121633628591005079756800 * q^60 - 222929606503067710799398508192199729986190593058228065549044227683974026321115005709568884316645733270402 * q^61 + 1827141305370492398064568813635835649207511770956919266173894646721039854569012442466628721293062130637824 * q^62 - 6149430428052066771901587011857473350643630395143732809634023246996722252441575455955324150064952541470264 * q^63 + 1713574251954623356255571860783147114735206198681534690227478857137685402094507991899117111923895957454848 * q^64 + 12869386968955442746581655138229434721016903840553054939904074922997747298934225413734850521793432682742900 * q^65 - 19801437990698690478552825543250876645747446443556478809261957366009300212043482490741679345707416428383744 * q^66 + 107684064602401021489570577643707663917970871646716750467969519975118177172469237075867827266943410721303572 * q^67 - 251444068481959286401052998092041093692640408644327131004605869607770327086902833194726609492888262105757696 * q^68 - 636551002833346124243317331997139947630296871486667493370629456953598473495382187316694584320495561912206496 * q^69 + 2445861734303677525943378629352934810152324980084761531508197481523725822715645101402879849637685872106969600 * q^70 + 1502419505224176558531294169685503912214338337110158873961577642731392413889415756979097582494411807941436328 * q^71 - 14190460126457652958916758648699640896837300874267064764308762389188142317932680769710235258136844562310922240 * q^72 - 3680626529239964132564912872164428299172360038443306444645976164259015478054371367373032231078544242855946054 * q^73 + 18995030812524563839649408435663136474226268660391755695671253594362128606663820760673799433403903696813952576 * q^74 - 5954144082365263500038634316183618316282448578954739961163265060170444211914471312789969527239069427687252500 * q^75 + 75521635038824380969585182658956176528723379098044694676717523275104397685022044564398827919896405931443589120 * q^76 - 240771158437798357271369248931142348166973346297260790267580673145058666334232888264118432356615568402288764576 * q^77 - 1477784208875012842343990522137891883864267581783960725138689920617516099527473962194409706068146624342516014848 * q^78 - 2285355792246583755429666361022638813506260919808216029514856597259553412365830319339899046809462718803389829360 * q^79 + 731147255618903270849902761914980040425478725108304832815559424615479093332325975905808837098967573706466918400 * q^80 - 3532367670468406933076216472986157092840312801374884126730791036696135691770424326872669760546172592566341977631 * q^81 - 25860102286736164243905760962310812415991288634659729695499047849150555031014924251023990367180912563898028431936 * q^82 - 26117732855991809313933081725190177898263990806499246105780578093346337131589033812952875783820862626814896023324 * q^83 - 303841612882842424652673770557081077080232195176517190811304259946807947644403425630681019724069771858331742470144 * q^84 - 271784820026506038543716236739677268739946655832804497399888502506585385926171661627342672703869328144134352799700 * q^85 - 159145514743719971775182317155196763266785145636471136796587486856422371505286708178643130744777323230578900292992 * q^86 - 1355100613113558654481164729536860328574661378469179428445142384013367192233258069363369980837305546640235173931240 * q^87 - 5330018914167959490555492640418721613119677246727591406115888524964039124470757411539029636129427474678220869468160 * q^88 - 4395897084707064164421802509143573377632162722728879042427722619171467149720889139563855226466565875308146508794230 * q^89 - 23411936176011976544246884681770302612989489885021236648740047507452430500242447452152815918439699794497873950801600 * q^90 - 17606324029223302595865761669828668634914557724735380270289077831587010762982273184351868955067224006438510779110352 * q^91 - 55772404313727512066859492963963844589319577918377808030728482638027588994319973465872892384865446342595251431088128 * q^92 - 116072789390555091884134123921208861440848184837899694086563014238934971188422968399738169216529674194608920356995968 * q^93 - 215603007291864892759964647694822697504579441834466411893750448780856116572052774856258753465664728162623916745168384 * q^94 - 363311345030338353402396700470528946025867499164153062121513673791488768341279059764913540333394357951818599838481000 * q^95 - 701671877550835095764080820751918498721447481909785429122092358416515475269177135171212459682250091038670024691679232 * q^96 - 298117805360022175643266169567709680719740267556363080426954452630296899863133621017987146964797348637751058662202638 * q^97 - 2126339804064355593061344246003551033537506779034582996212286410224706625784123846976709615330292659973382337208735136 * q^98 - 1520953441055457260978457109220493407200764700486006435781344466290947949395060067028631646046107176946794789660596916 * q^99

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