LMFDB - Embedded newform 1.86.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,86,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, 86, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 86);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 86 $
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:	$45.7549576907$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 17\!\cdots\!50 $ x^6 - 3x^5 - 20125264230072359909772x^4 - 314483190102207151531480871396326x^3 + 90192008136736578291529572869233310390975625x^2 + 2091285328888251081155130451204419887619836339467659225*x - 17301527721628842869681120067092990846953613013306724567953408750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{65}\cdot 3^{23}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.73032e10$ 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)

$f(q)$	$=$	$q-8.02060e12 q^{2} +1.02906e20 q^{3} +2.56443e25 q^{4} +8.73356e29 q^{5} -8.25371e32 q^{6} +1.26096e35 q^{7} +1.04599e38 q^{8} -2.53278e40 q^{9} +O(q^{10})$	\(q-8.02060e12 q^{2} +1.02906e20 q^{3} +2.56443e25 q^{4} +8.73356e29 q^{5} -8.25371e32 q^{6} +1.26096e35 q^{7} +1.04599e38 q^{8} -2.53278e40 q^{9} -7.00484e42 q^{10} +5.36289e42 q^{11} +2.63897e45 q^{12} -2.69728e47 q^{13} -1.01137e48 q^{14} +8.98740e49 q^{15} -1.83101e51 q^{16} -1.84892e52 q^{17} +2.03144e53 q^{18} -1.42794e54 q^{19} +2.23967e55 q^{20} +1.29761e55 q^{21} -4.30136e55 q^{22} +1.16043e58 q^{23} +1.07639e58 q^{24} +5.04257e59 q^{25} +2.16338e60 q^{26} -6.30254e60 q^{27} +3.23365e60 q^{28} -1.62505e61 q^{29} -7.20843e62 q^{30} -2.67104e63 q^{31} +1.06393e64 q^{32} +5.51876e62 q^{33} +1.48294e65 q^{34} +1.10127e65 q^{35} -6.49515e65 q^{36} -7.87622e66 q^{37} +1.14530e67 q^{38} -2.77568e67 q^{39} +9.13521e67 q^{40} +1.54694e68 q^{41} -1.04076e68 q^{42} -3.44599e69 q^{43} +1.37528e68 q^{44} -2.21202e70 q^{45} -9.30736e70 q^{46} +1.94993e71 q^{47} -1.88423e71 q^{48} -6.65392e71 q^{49} -4.04444e72 q^{50} -1.90265e72 q^{51} -6.91701e72 q^{52} -2.32907e73 q^{53} +5.05501e73 q^{54} +4.68372e72 q^{55} +1.31895e73 q^{56} -1.46944e74 q^{57} +1.30339e74 q^{58} +2.41420e75 q^{59} +2.30476e75 q^{60} +3.93274e75 q^{61} +2.14233e76 q^{62} -3.19374e75 q^{63} -1.45000e76 q^{64} -2.35569e77 q^{65} -4.42638e75 q^{66} -1.23494e77 q^{67} -4.74143e77 q^{68} +1.19416e78 q^{69} -8.83282e77 q^{70} -3.56162e78 q^{71} -2.64926e78 q^{72} -2.16699e78 q^{73} +6.31720e79 q^{74} +5.18913e79 q^{75} -3.66187e79 q^{76} +6.76240e77 q^{77} +2.22626e80 q^{78} -3.82923e80 q^{79} -1.59913e81 q^{80} +2.61141e80 q^{81} -1.24074e81 q^{82} +3.91847e81 q^{83} +3.32763e80 q^{84} -1.61476e82 q^{85} +2.76389e82 q^{86} -1.67228e81 q^{87} +5.60953e80 q^{88} -3.41411e81 q^{89} +1.77417e83 q^{90} -3.40117e82 q^{91} +2.97585e83 q^{92} -2.74867e83 q^{93} -1.56396e84 q^{94} -1.24710e84 q^{95} +1.09486e84 q^{96} -2.02668e84 q^{97} +5.33684e84 q^{98} -1.35830e83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) $ 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9	$ 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 14\!\cdots\!76 q^{99}+O(q^{100}) $ 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9 + 94651165962435813693946284861726959764800 * q^10 - 56344805701335918998354740625397619012956888 * q^11 - 38113762524253328553901066462492282955462553600 * q^12 - 380409468466294979156527797290184755501373645900 * q^13 + 7432102291035232990382031969981134697595704847104 * q^14 + 144434402836684505734903243186122115181592351080400 * q^15 + 2636948568634008151994191667083023793288011486068736 * q^16 - 51365945458144838311659694040021464865555671618554900 * q^17 + 463507663069864508791700717104909645587637083805192800 * q^18 + 2653138201866103222242250000135395331152453781661358360 * q^19 - 52474536419792695778976723338965188133980339812187187200 * q^20 - 58207920650233869679987953151176418416472072173047654208 * q^21 + 3581897081140779531372538339240606543513118132263441718400 * q^22 - 2885510207115801266245992081450013398631817932489294263600 * q^23 - 68567070931993796242748985500475684139954880414010505297920 * q^24 + 669968020810517762245853029111649576216707129701526846916250 * q^25 - 145338677717367061512932551412743816475529536844287947743168 * q^26 - 2889483981995895623844053829009837579840855941832615148040400 * q^27 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 - 126005957659709196887223202461409590769523616790635653593969260 * q^29 + 136086353401335907485123608360817834511749084976435568495980800 * q^30 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 + 18707915462589185913352646999729455863851090555123851448234803200 * q^32 + 41065540677287661644797365484571058991908764323686266561418093600 * q^33 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 - 54720272714504178732776803597096361295121671934223039039646799200 * q^35 + 3399696315710870996405230044380107361656113863069854483749794804736 * q^36 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 - 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 + 110170203428145375146126906937514681017464730369816703999974469819536 * q^39 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 - 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 3196148185952018443143303103341158979894551408731781313074799986918400 * q^42 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 - 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 86500611154071576329235297315912364271843998646281427040496904001252300 * q^45 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 - 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 2011644131471271504966965322061354320977669648116299895717796775041433600 * q^48 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 - 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 10328830658918507785729550461151529723270274866387219032022415269933043728 * q^51 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 - 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 - 127995453221656133194026073100343370388415314716409270018601938523610333440 * q^54 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 + 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 609918064048630066051419788625468329088455176450389301471226460423851647200 * q^57 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 + 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 31689950181369930414484676957647463168779067278456560490215008364167133388800 * q^60 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 + 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 + 35795966074431291550182082060995682584043172792907267107900820593108358481200 * q^63 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 - 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 1499689309727229977020921941751495239601349525904665530644129573530308780586496 * q^66 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 - 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 745502955929877889390374691705185133399296067237471890306223900077423420825024 * q^69 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 - 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 42205813302686543920197586259094606661421265173628042056899709260796372565196800 * q^72 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 + 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 145624067696916644200840962911775023608813806434012931341647651068546287549085000 * q^75 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 + 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 + 171841231286923953547335431872475383039854385588725970844304858012728142132768000 * q^78 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 - 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 4310060020996155465671846173285816617646939986231807893561334612249450355160008554 * q^81 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 - 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 - 12398071481018763514585592745934914502465484593761365063657562420201819291615461376 * q^84 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 + 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 50876914632638320845048890401340559827753840179451919522781964204571716769119542800 * q^87 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 + 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 + 84790751750172409977703550300414634726575284296402896259290449409557083536687630400 * q^90 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 - 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 593175476050386740279600068063559704679480457431525655959184215070525871275273350400 * q^93 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 - 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 - 8776777977440964474954793317935829637440571398014671264365724282514189936233386344448 * q^96 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 + 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98 + 14740689076241711017386038088080153281412276754860625822798307085897192961497015786376 * 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 $

$2$	−8.02060e12	−1.28953	−0.644766	−	0.764380i	$-0.723045\pi$
$2$	−8.02060e12	−1.28953	−0.644766	+	0.764380i	$0.723045\pi$
$3$	1.02906e20	0.542987	0.271493	−	0.962440i	$-0.412483\pi$
$3$	1.02906e20	0.542987	0.271493	+	0.962440i	$0.412483\pi$
$4$	2.56443e25	0.662891
$5$	8.73356e29	1.71778	0.858888	−	0.512164i	$-0.171156\pi$
$5$	8.73356e29	1.71778	0.858888	+	0.512164i	$0.171156\pi$
$6$	−8.25371e32	−0.700198
$7$	1.26096e35	0.152769	0.0763844	−	0.997078i	$-0.475662\pi$
$7$	1.26096e35	0.152769	0.0763844	+	0.997078i	$0.475662\pi$
$8$	1.04599e38	0.434713
$9$	−2.53278e40	−0.705166
$10$	−7.00484e42	−2.21512
$11$	5.36289e42	0.0295264	0.0147632	−	0.999891i	$-0.495301\pi$
$11$	5.36289e42	0.0295264	0.0147632	+	0.999891i	$0.495301\pi$
$12$	2.63897e45	0.359941
$13$	−2.69728e47	−1.22556	−0.612779	−	0.790254i	$-0.709949\pi$
$13$	−2.69728e47	−1.22556	−0.612779	+	0.790254i	$0.709949\pi$
$14$	−1.01137e48	−0.197000
$15$	8.98740e49	0.932729
$16$	−1.83101e51	−1.22347
$17$	−1.84892e52	−0.939374	−0.469687	−	0.882833i	$-0.655633\pi$
$17$	−1.84892e52	−0.939374	−0.469687	+	0.882833i	$0.655633\pi$
$18$	2.03144e53	0.909333
$19$	−1.42794e54	−0.642219	−0.321109	−	0.947042i	$-0.604056\pi$
$19$	−1.42794e54	−0.642219	−0.321109	+	0.947042i	$0.604056\pi$
$20$	2.23967e55	1.13870
$21$	1.29761e55	0.0829514
$22$	−4.30136e55	−0.0380752
$23$	1.16043e58	1.55305	0.776527	−	0.630084i	$-0.216979\pi$
$23$	1.16043e58	1.55305	0.776527	+	0.630084i	$0.216979\pi$
$24$	1.07639e58	0.236043
$25$	5.04257e59	1.95075
$26$	2.16338e60	1.58040
$27$	−6.30254e60	−0.925882
$28$	3.23365e60	0.101269
$29$	−1.62505e61	−0.114538	−0.0572692	−	0.998359i	$-0.518239\pi$
$29$	−1.62505e61	−0.114538	−0.0572692	+	0.998359i	$0.518239\pi$
$30$	−7.20843e62	−1.20278
$31$	−2.67104e63	−1.10613	−0.553067	−	0.833137i	$-0.686543\pi$
$31$	−2.67104e63	−1.10613	−0.553067	+	0.833137i	$0.686543\pi$
$32$	1.06393e64	1.14299
$33$	5.51876e62	0.0160324
$34$	1.48294e65	1.21135
$35$	1.10127e65	0.262422
$36$	−6.49515e65	−0.467448
$37$	−7.87622e66	−1.76907	−0.884534	−	0.466476i	$-0.845523\pi$
$37$	−7.87622e66	−1.76907	−0.884534	+	0.466476i	$0.845523\pi$
$38$	1.14530e67	0.828161
$39$	−2.77568e67	−0.665462
$40$	9.13521e67	0.746739
$41$	1.54694e68	0.442752	0.221376	−	0.975189i	$-0.428945\pi$
$41$	1.54694e68	0.442752	0.221376	+	0.975189i	$0.428945\pi$
$42$	−1.04076e68	−0.106968
$43$	−3.44599e69	−1.30288	−0.651441	−	0.758700i	$-0.725835\pi$
$43$	−3.44599e69	−1.30288	−0.651441	+	0.758700i	$0.725835\pi$
$44$	1.37528e68	0.0195728
$45$	−2.21202e70	−1.21132
$46$	−9.30736e70	−2.00271
$47$	1.94993e71	1.68213	0.841065	−	0.540933i	$-0.181929\pi$
$47$	1.94993e71	1.68213	0.841065	+	0.540933i	$0.181929\pi$
$48$	−1.88423e71	−0.664326
$49$	−6.65392e71	−0.976662
$50$	−4.04444e72	−2.51555
$51$	−1.90265e72	−0.510067
$52$	−6.91701e72	−0.812411
$53$	−2.32907e73	−1.21747	−0.608734	−	0.793374i	$-0.708322\pi$
$53$	−2.32907e73	−1.21747	−0.608734	+	0.793374i	$0.708322\pi$
$54$	5.05501e73	1.19395
$55$	4.68372e72	0.0507197
$56$	1.31895e73	0.0664106
$57$	−1.46944e74	−0.348716
$58$	1.30339e74	0.147701
$59$	2.41420e75	1.32301	0.661503	−	0.749942i	$-0.269919\pi$
$59$	2.41420e75	1.32301	0.661503	+	0.749942i	$0.269919\pi$
$60$	2.30476e75	0.618297
$61$	3.93274e75	0.522609	0.261305	−	0.965256i	$-0.415847\pi$
$61$	3.93274e75	0.522609	0.261305	+	0.965256i	$0.415847\pi$
$62$	2.14233e76	1.42640
$63$	−3.19374e75	−0.107727
$64$	−1.45000e76	−0.250449
$65$	−2.35569e77	−2.10523
$66$	−4.42638e75	−0.0206743
$67$	−1.23494e77	−0.304417	−0.152208	−	0.988348i	$-0.548638\pi$
$67$	−1.23494e77	−0.304417	−0.152208	+	0.988348i	$0.548638\pi$
$68$	−4.74143e77	−0.622702
$69$	1.19416e78	0.843288
$70$	−8.83282e77	−0.338402
$71$	−3.56162e78	−0.746738	−0.373369	−	0.927683i	$-0.621797\pi$
$71$	−3.56162e78	−0.746738	−0.373369	+	0.927683i	$0.621797\pi$
$72$	−2.64926e78	−0.306545
$73$	−2.16699e78	−0.139520	−0.0697599	−	0.997564i	$-0.522223\pi$
$73$	−2.16699e78	−0.139520	−0.0697599	+	0.997564i	$0.522223\pi$
$74$	6.31720e79	2.28127
$75$	5.18913e79	1.05923
$76$	−3.66187e79	−0.425721
$77$	6.76240e77	0.00451071
$78$	2.22626e80	0.858134
$79$	−3.82923e80	−0.858934	−0.429467	−	0.903083i	$-0.641299\pi$
$79$	−3.82923e80	−0.858934	−0.429467	+	0.903083i	$0.641299\pi$
$80$	−1.59913e81	−2.10164
$81$	2.61141e80	0.202424
$82$	−1.24074e81	−0.570943
$83$	3.91847e81	1.07720	0.538602	−	0.842560i	$-0.318953\pi$
$83$	3.91847e81	1.07720	0.538602	+	0.842560i	$0.318953\pi$
$84$	3.32763e80	0.0549877
$85$	−1.61476e82	−1.61363
$86$	2.76389e82	1.68011
$87$	−1.67228e81	−0.0621928
$88$	5.60953e80	0.0128355
$89$	−3.41411e81	−0.0483283	−0.0241642	−	0.999708i	$-0.507692\pi$
$89$	−3.41411e81	−0.0483283	−0.0241642	+	0.999708i	$0.507692\pi$
$90$	1.77417e83	1.56203
$91$	−3.40117e82	−0.187227
$92$	2.97585e83	1.02951
$93$	−2.74867e83	−0.600616
$94$	−1.56396e84	−2.16916
$95$	−1.24710e84	−1.10319
$96$	1.09486e84	0.620626
$97$	−2.02668e84	−0.739582	−0.369791	−	0.929115i	$-0.620571\pi$
$97$	−2.02668e84	−0.739582	−0.369791	+	0.929115i	$0.620571\pi$
$98$	5.33684e84	1.25944
$99$	−1.35830e83	−0.0208210
$100$	1.29313e85	1.29313
$101$	−1.34906e85	−0.883837	−0.441919	−	0.897055i	$-0.645702\pi$
$101$	−1.34906e85	−0.883837	−0.441919	+	0.897055i	$0.645702\pi$
$102$	1.52604e85	0.657748
$103$	8.42778e84	0.239956	0.119978	−	0.992777i	$-0.461718\pi$
$103$	8.42778e84	0.239956	0.119978	+	0.992777i	$0.461718\pi$
$104$	−2.82133e85	−0.532766
$105$	1.13328e85	0.142492
$106$	1.86805e86	1.56996
$107$	−2.81973e86	−1.59000	−0.795000	−	0.606610i	$-0.792529\pi$
$107$	−2.81973e86	−1.59000	−0.795000	+	0.606610i	$0.792529\pi$
$108$	−1.61625e86	−0.613759
$109$	1.04253e85	0.0267584	0.0133792	−	0.999910i	$-0.495741\pi$
$109$	1.04253e85	0.0267584	0.0133792	+	0.999910i	$0.495741\pi$
$110$	−3.75662e85	−0.0654046
$111$	−8.10513e86	−0.960580
$112$	−2.30883e86	−0.186908
$113$	−4.17811e86	−0.231817	−0.115909	−	0.993260i	$-0.536978\pi$
$113$	−4.17811e86	−0.231817	−0.115909	+	0.993260i	$0.536978\pi$
$114$	1.17858e87	0.449680
$115$	1.01347e88	2.66780
$116$	−4.16733e86	−0.0759265
$117$	6.83163e87	0.864222
$118$	−1.93633e88	−1.70606
$119$	−2.33141e87	−0.143507
$120$	9.40071e87	0.405469
$121$	−3.29609e88	−0.999128
$122$	−3.15429e88	−0.673921
$123$	1.59190e88	0.240408
$124$	−6.84970e88	−0.733247
$125$	2.14639e89	1.63318
$126$	2.56157e88	0.138918
$127$	−1.75380e89	−0.679708	−0.339854	−	0.940478i	$-0.610378\pi$
$127$	−1.75380e89	−0.679708	−0.339854	+	0.940478i	$0.610378\pi$
$128$	−2.95291e89	−0.820024
$129$	−3.54615e89	−0.707447
$130$	1.88940e90	2.71476
$131$	4.13091e89	0.428564	0.214282	−	0.976772i	$-0.431259\pi$
$131$	4.13091e89	0.428564	0.214282	+	0.976772i	$0.431259\pi$
$132$	1.41525e88	0.0106277
$133$	−1.80058e89	−0.0981110
$134$	9.90499e89	0.392555
$135$	−5.50436e90	−1.59046
$136$	−1.93395e90	−0.408358
$137$	5.29962e89	0.0819636	0.0409818	−	0.999160i	$-0.486951\pi$
$137$	5.29962e89	0.0819636	0.0409818	+	0.999160i	$0.486951\pi$
$138$	−9.57787e90	−1.08745
$139$	−3.68316e90	−0.307674	−0.153837	−	0.988096i	$-0.549163\pi$
$139$	−3.68316e90	−0.307674	−0.153837	+	0.988096i	$0.549163\pi$
$140$	2.82413e90	0.173957
$141$	2.00660e91	0.913374
$142$	2.85664e91	0.962942
$143$	−1.44652e90	−0.0361863
$144$	4.63756e91	0.862747
$145$	−1.41925e91	−0.196751
$146$	1.73806e91	0.179915
$147$	−6.84731e91	−0.530314
$148$	−2.01980e92	−1.17270
$149$	2.89543e92	1.26269	0.631346	−	0.775502i	$-0.282503\pi$
$149$	2.89543e92	1.26269	0.631346	+	0.775502i	$0.282503\pi$
$150$	−4.16199e92	−1.36591
$151$	2.21750e92	0.548711	0.274356	−	0.961628i	$-0.411535\pi$
$151$	2.21750e92	0.548711	0.274356	+	0.961628i	$0.411535\pi$
$152$	−1.49361e92	−0.279181
$153$	4.68291e92	0.662414
$154$	−5.42385e90	−0.00581670
$155$	−2.33277e93	−1.90009
$156$	−7.11804e92	−0.441129
$157$	2.72439e93	1.28687	0.643435	−	0.765501i	$-0.277509\pi$
$157$	2.72439e93	1.28687	0.643435	+	0.765501i	$0.277509\pi$
$158$	3.07127e93	1.10762
$159$	−2.39676e93	−0.661069
$160$	9.29194e93	1.96339
$161$	1.46326e93	0.237258
$162$	−2.09451e93	−0.261032
$163$	−1.28376e94	−1.23171	−0.615856	−	0.787859i	$-0.711190\pi$
$163$	−1.28376e94	−1.23171	−0.615856	+	0.787859i	$0.711190\pi$
$164$	3.96704e93	0.293496
$165$	4.81985e92	0.0275401
$166$	−3.14285e94	−1.38909
$167$	−4.31089e94	−1.47610	−0.738052	−	0.674744i	$-0.764254\pi$
$167$	−4.31089e94	−1.47610	−0.738052	+	0.674744i	$0.764254\pi$
$168$	1.35728e93	0.0360600
$169$	2.43155e94	0.501994
$170$	1.29514e95	2.08083
$171$	3.61667e94	0.452870
$172$	−8.83702e94	−0.863668
$173$	3.57238e93	0.0272897	0.0136448	−	0.999907i	$-0.495657\pi$
$173$	3.57238e93	0.0272897	0.0136448	+	0.999907i	$0.495657\pi$
$174$	1.34127e94	0.0801996
$175$	6.35849e94	0.298014
$176$	−9.81953e93	−0.0361245
$177$	2.48436e95	0.718375
$178$	2.73832e94	0.0623209
$179$	−5.48467e95	−0.983777	−0.491889	−	0.870658i	$-0.663693\pi$
$179$	−5.48467e95	−0.983777	−0.491889	+	0.870658i	$0.663693\pi$
$180$	−5.67258e95	−0.802970
$181$	2.02214e95	0.226190	0.113095	−	0.993584i	$-0.463924\pi$
$181$	2.02214e95	0.226190	0.113095	+	0.993584i	$0.463924\pi$
$182$	2.72794e95	0.241435
$183$	4.04704e95	0.283770
$184$	1.21380e96	0.675133
$185$	−6.87874e96	−3.03886
$186$	2.20460e96	0.774513
$187$	−9.91555e94	−0.0277363
$188$	5.00046e96	1.11507
$189$	−7.94725e95	−0.141446
$190$	1.00025e97	1.42259
$191$	8.50271e96	0.967474	0.483737	−	0.875213i	$-0.339279\pi$
$191$	8.50271e96	0.967474	0.483737	+	0.875213i	$0.339279\pi$
$192$	−1.49214e96	−0.135990
$193$	−1.30166e97	−0.951284	−0.475642	−	0.879639i	$-0.657784\pi$
$193$	−1.30166e97	−0.951284	−0.475642	+	0.879639i	$0.657784\pi$
$194$	1.62552e97	0.953713
$195$	−2.42415e97	−1.14311
$196$	−1.70635e97	−0.647420
$197$	−5.78095e97	−1.76679	−0.883394	−	0.468632i	$-0.844747\pi$
$197$	−5.78095e97	−1.76679	−0.883394	+	0.468632i	$0.844747\pi$
$198$	1.08944e96	0.0268493
$199$	1.47974e97	0.294395	0.147198	−	0.989107i	$-0.452975\pi$
$199$	1.47974e97	0.294395	0.147198	+	0.989107i	$0.452975\pi$
$200$	5.27447e97	0.848016
$201$	−1.27084e97	−0.165294
$202$	1.08202e98	1.13974
$203$	−2.04912e96	−0.0174979
$204$	−4.87923e97	−0.338119
$205$	1.35103e98	0.760549
$206$	−6.75958e97	−0.309430
$207$	−2.93912e98	−1.09516
$208$	4.93876e98	1.49943
$209$	−7.65791e96	−0.0189624
$210$	−9.08954e97	−0.183748
$211$	3.76349e97	0.0621709	0.0310854	−	0.999517i	$-0.490104\pi$
$211$	3.76349e97	0.0621709	0.0310854	+	0.999517i	$0.490104\pi$
$212$	−5.97274e98	−0.807049
$213$	−3.66514e98	−0.405469
$214$	2.26159e99	2.05035
$215$	−3.00958e99	−2.23806
$216$	−6.59238e98	−0.402493
$217$	−3.36807e98	−0.168983
$218$	−8.36168e97	−0.0345059
$219$	−2.22997e98	−0.0757574
$220$	1.20111e98	0.0336216
$221$	4.98705e99	1.15126
$222$	6.50080e99	1.23870
$223$	4.24047e99	0.667510	0.333755	−	0.942660i	$-0.391684\pi$
$223$	4.24047e99	0.667510	0.333755	+	0.942660i	$0.391684\pi$
$224$	1.34158e99	0.174613
$225$	−1.27717e100	−1.37560
$226$	3.35109e99	0.298936
$227$	−8.66689e98	−0.0640862	−0.0320431	−	0.999486i	$-0.510201\pi$
$227$	−8.66689e98	−0.0640862	−0.0320431	+	0.999486i	$0.510201\pi$
$228$	−3.76830e99	−0.231161
$229$	2.41769e100	1.23138	0.615691	−	0.787988i	$-0.288877\pi$
$229$	2.41769e100	1.23138	0.615691	+	0.787988i	$0.288877\pi$
$230$	−8.12864e100	−3.44021
$231$	6.95894e97	0.00244925
$232$	−1.69978e99	−0.0497913
$233$	1.65769e100	0.404460	0.202230	−	0.979338i	$-0.435181\pi$
$233$	1.65769e100	0.404460	0.202230	+	0.979338i	$0.435181\pi$
$234$	−5.47937e100	−1.11444
$235$	1.70298e101	2.88952
$236$	6.19105e100	0.877009
$237$	−3.94052e100	−0.466390
$238$	1.86993e100	0.185057
$239$	−6.68826e100	−0.553863	−0.276932	−	0.960890i	$-0.589318\pi$
$239$	−6.68826e100	−0.553863	−0.276932	+	0.960890i	$0.589318\pi$
$240$	−1.64560e101	−1.14116
$241$	−5.36341e100	−0.311686	−0.155843	−	0.987782i	$-0.549809\pi$
$241$	−5.36341e100	−0.311686	−0.155843	+	0.987782i	$0.549809\pi$
$242$	2.64366e101	1.28841
$243$	2.53245e101	1.03580
$244$	1.00852e101	0.346433
$245$	−5.81124e101	−1.67769
$246$	−1.27680e101	−0.310014
$247$	3.85157e101	0.787076
$248$	−2.79387e101	−0.480851
$249$	4.03236e101	0.584908
$250$	−1.72153e102	−2.10603
$251$	1.30922e101	0.135170	0.0675850	−	0.997714i	$-0.478471\pi$
$251$	1.30922e101	0.135170	0.0675850	+	0.997714i	$0.478471\pi$
$252$	−8.19013e100	−0.0714115
$253$	6.22328e100	0.0458561
$254$	1.40665e102	0.876505
$255$	−1.66170e102	−0.876181
$256$	2.92935e102	1.30790
$257$	4.04708e102	1.53103	0.765516	−	0.643417i	$-0.222484\pi$
$257$	4.04708e102	1.53103	0.765516	+	0.643417i	$0.222484\pi$
$258$	2.84422e102	0.912275
$259$	−9.93160e101	−0.270258
$260$	−6.04101e102	−1.39554
$261$	4.11589e101	0.0807686
$262$	−3.31324e102	−0.552647
$263$	2.53494e102	0.359624	0.179812	−	0.983701i	$-0.442451\pi$
$263$	2.53494e102	0.359624	0.179812	+	0.983701i	$0.442451\pi$
$264$	5.77256e100	0.00696950
$265$	−2.03411e103	−2.09134
$266$	1.44417e102	0.126517
$267$	−3.51334e101	−0.0262416
$268$	−3.16693e102	−0.201795
$269$	2.17675e102	0.118396	0.0591979	−	0.998246i	$-0.481146\pi$
$269$	2.17675e102	0.118396	0.0591979	+	0.998246i	$0.481146\pi$
$270$	4.41483e103	2.05094
$271$	−2.62828e103	−1.04346	−0.521732	−	0.853109i	$-0.674714\pi$
$271$	−2.62828e103	−1.04346	−0.521732	+	0.853109i	$0.674714\pi$
$272$	3.38539e103	1.14929
$273$	−3.50002e102	−0.101662
$274$	−4.25061e102	−0.105695
$275$	2.70428e102	0.0575986
$276$	3.06234e103	0.559008
$277$	−9.07350e103	−1.42032	−0.710158	−	0.704043i	$-0.751376\pi$
$277$	−9.07350e103	−1.42032	−0.710158	+	0.704043i	$0.751376\pi$
$278$	2.95411e103	0.396756
$279$	6.76515e103	0.780008
$280$	1.15191e103	0.114078
$281$	−7.27690e103	−0.619338	−0.309669	−	0.950844i	$-0.600218\pi$
$281$	−7.27690e103	−0.619338	−0.309669	+	0.950844i	$0.600218\pi$
$282$	−1.60941e104	−1.17782
$283$	2.31141e104	1.45530	0.727650	−	0.685948i	$-0.240612\pi$
$283$	2.31141e104	1.45530	0.727650	+	0.685948i	$0.240612\pi$
$284$	−9.13355e103	−0.495006
$285$	−1.28335e104	−0.599016
$286$	1.16020e103	0.0466634
$287$	1.95063e103	0.0676387
$288$	−2.69471e104	−0.805994
$289$	−4.55491e103	−0.117577
$290$	1.13832e104	0.253717
$291$	−2.08558e104	−0.401583
$292$	−5.55711e103	−0.0924864
$293$	1.30031e105	1.87142	0.935711	−	0.352767i	$-0.114759\pi$
$293$	1.30031e105	1.87142	0.935711	+	0.352767i	$0.114759\pi$
$294$	5.49195e104	0.683857
$295$	2.10845e105	2.27263
$296$	−8.23843e104	−0.769036
$297$	−3.37999e103	−0.0273379
$298$	−2.32231e105	−1.62828
$299$	−3.13001e105	−1.90336
$300$	1.33072e105	0.702155
$301$	−4.34526e104	−0.199040
$302$	−1.77857e105	−0.707581
$303$	−1.38827e105	−0.479912
$304$	2.61458e105	0.785733
$305$	3.43468e105	0.897725
$306$	−3.75597e105	−0.854204
$307$	−6.59511e104	−0.130569	−0.0652847	−	0.997867i	$-0.520796\pi$
$307$	−6.59511e104	−0.130569	−0.0652847	+	0.997867i	$0.520796\pi$
$308$	1.73417e103	0.00299011
$309$	8.67273e104	0.130293
$310$	1.87102e106	2.45023
$311$	−3.84525e105	−0.439145	−0.219573	−	0.975596i	$-0.570466\pi$
$311$	−3.84525e105	−0.439145	−0.219573	+	0.975596i	$0.570466\pi$
$312$	−2.90333e105	−0.289285
$313$	1.06825e106	0.929047	0.464523	−	0.885561i	$-0.346226\pi$
$313$	1.06825e106	0.929047	0.464523	+	0.885561i	$0.346226\pi$
$314$	−2.18512e106	−1.65946
$315$	−2.78927e105	−0.185051
$316$	−9.81980e105	−0.569379
$317$	1.42747e106	0.723680	0.361840	−	0.932240i	$-0.382149\pi$
$317$	1.42747e106	0.723680	0.361840	+	0.932240i	$0.382149\pi$
$318$	1.92234e106	0.852469
$319$	−8.71496e103	−0.00338190
$320$	−1.26637e106	−0.430215
$321$	−2.90168e106	−0.863348
$322$	−1.17362e106	−0.305952
$323$	2.64015e106	0.603283
$324$	6.69680e105	0.134185
$325$	−1.36012e107	−2.39076
$326$	1.02965e107	1.58833
$327$	1.07283e105	0.0145295
$328$	1.61809e106	0.192470
$329$	2.45878e106	0.256977
$330$	−3.86580e105	−0.0355138
$331$	−9.70151e106	−0.783699	−0.391850	−	0.920029i	$-0.628165\pi$
$331$	−9.70151e106	−0.783699	−0.391850	+	0.920029i	$0.628165\pi$
$332$	1.00487e107	0.714069
$333$	1.99487e107	1.24749
$334$	3.45759e107	1.90348
$335$	−1.07855e107	−0.522919
$336$	−2.37594e106	−0.101488
$337$	−3.12398e107	−1.17608	−0.588041	−	0.808831i	$-0.700101\pi$
$337$	−3.12398e107	−1.17608	−0.588041	+	0.808831i	$0.700101\pi$
$338$	−1.95025e107	−0.647336
$339$	−4.29954e106	−0.125874
$340$	−4.14096e107	−1.06966
$341$	−1.43245e106	−0.0326601
$342$	−2.90078e107	−0.583991
$343$	−1.69812e107	−0.301972
$344$	−3.60447e107	−0.566379
$345$	1.04293e108	1.44858
$346$	−2.86526e106	−0.0351909
$347$	8.72324e107	0.947710	0.473855	−	0.880603i	$-0.342862\pi$
$347$	8.72324e107	0.947710	0.473855	+	0.880603i	$0.342862\pi$
$348$	−4.28845e106	−0.0412271
$349$	1.06941e108	0.910051	0.455025	−	0.890479i	$-0.349630\pi$
$349$	1.06941e108	0.910051	0.455025	+	0.890479i	$0.349630\pi$
$350$	−5.09988e107	−0.384298
$351$	1.69997e108	1.13472
$352$	5.70577e106	0.0337482
$353$	−4.25520e107	−0.223098	−0.111549	−	0.993759i	$-0.535581\pi$
$353$	−4.25520e107	−0.223098	−0.111549	+	0.993759i	$0.535581\pi$
$354$	−1.99261e108	−0.926366
$355$	−3.11057e108	−1.28273
$356$	−8.75526e106	−0.0320364
$357$	−2.39917e107	−0.0779224
$358$	4.39903e108	1.26861
$359$	3.53844e108	0.906353	0.453177	−	0.891421i	$-0.350291\pi$
$359$	3.53844e108	0.906353	0.453177	+	0.891421i	$0.350291\pi$
$360$	−2.31375e108	−0.526575
$361$	−2.90472e108	−0.587555
$362$	−1.62188e108	−0.291678
$363$	−3.39189e108	−0.542513
$364$	−8.72207e107	−0.124111
$365$	−1.89256e108	−0.239664
$366$	−3.24597e108	−0.365930
$367$	1.26974e109	1.27469	0.637347	−	0.770577i	$-0.280032\pi$
$367$	1.26974e109	1.27469	0.637347	+	0.770577i	$0.280032\pi$
$368$	−2.12477e109	−1.90011
$369$	−3.91807e108	−0.312214
$370$	5.51716e109	3.91871
$371$	−2.93686e108	−0.185991
$372$	−7.04878e108	−0.398143
$373$	−2.28944e109	−1.15373	−0.576864	−	0.816841i	$-0.695724\pi$
$373$	−2.28944e109	−1.15373	−0.576864	+	0.816841i	$0.695724\pi$
$374$	7.95286e107	0.0357668
$375$	2.20877e109	0.886793
$376$	2.03960e109	0.731244
$377$	4.38321e108	0.140374
$378$	6.37417e108	0.182399
$379$	−2.40874e109	−0.616061	−0.308030	−	0.951377i	$-0.599670\pi$
$379$	−2.40874e109	−0.616061	−0.308030	+	0.951377i	$0.599670\pi$
$380$	−3.19811e109	−0.731293
$381$	−1.80478e109	−0.369073
$382$	−6.81968e109	−1.24759
$383$	−6.10887e109	−1.00003	−0.500015	−	0.866017i	$-0.666672\pi$
$383$	−6.10887e109	−1.00003	−0.500015	+	0.866017i	$0.666672\pi$
$384$	−3.03873e109	−0.445262
$385$	5.90598e107	0.00774838
$386$	1.04401e110	1.22671
$387$	8.72795e109	0.918747
$388$	−5.19728e109	−0.490262
$389$	1.57517e110	1.33190	0.665948	−	0.745998i	$-0.268027\pi$
$389$	1.57517e110	1.33190	0.665948	+	0.745998i	$0.268027\pi$
$390$	1.94432e110	1.47408
$391$	−2.14554e110	−1.45890
$392$	−6.95992e109	−0.424567
$393$	4.25097e109	0.232704
$394$	4.63666e110	2.27833
$395$	−3.34428e110	−1.47546
$396$	−3.48328e108	−0.0138020
$397$	−4.15199e109	−0.147795	−0.0738974	−	0.997266i	$-0.523544\pi$
$397$	−4.15199e109	−0.147795	−0.0738974	+	0.997266i	$0.523544\pi$
$398$	−1.18684e110	−0.379632
$399$	−1.85291e109	−0.0532729
$400$	−9.23302e110	−2.38668
$401$	2.99636e110	0.696558	0.348279	−	0.937391i	$-0.386766\pi$
$401$	2.99636e110	0.696558	0.348279	+	0.937391i	$0.386766\pi$
$402$	1.01929e110	0.213152
$403$	7.20454e110	1.35563
$404$	−3.45957e110	−0.585887
$405$	2.28069e110	0.347719
$406$	1.64352e109	0.0225641
$407$	−4.22393e109	−0.0522342
$408$	−1.99015e110	−0.221733
$409$	−2.65793e110	−0.266872	−0.133436	−	0.991057i	$-0.542601\pi$
$409$	−2.65793e110	−0.266872	−0.133436	+	0.991057i	$0.542601\pi$
$410$	−1.08361e111	−0.980751
$411$	5.45365e109	0.0445051
$412$	2.16125e110	0.159064
$413$	3.04420e110	0.202114
$414$	2.35735e111	1.41224
$415$	3.42222e111	1.85039
$416$	−2.86973e111	−1.40080
$417$	−3.79021e110	−0.167063
$418$	6.14210e109	0.0244526
$419$	1.86967e111	0.672466	0.336233	−	0.941779i	$-0.390847\pi$
$419$	1.86967e111	0.672466	0.336233	+	0.941779i	$0.390847\pi$
$420$	2.90621e110	0.0944566
$421$	1.96564e110	0.0577451	0.0288725	−	0.999583i	$-0.490808\pi$
$421$	1.96564e110	0.0577451	0.0288725	+	0.999583i	$0.490808\pi$
$422$	−3.01855e110	−0.0801713
$423$	−4.93874e111	−1.18618
$424$	−2.43618e111	−0.529249
$425$	−9.32330e111	−1.83248
$426$	2.93966e111	0.522865
$427$	4.95903e110	0.0798384
$428$	−7.23101e111	−1.05400
$429$	−1.48857e110	−0.0196487
$430$	2.41386e112	2.88604
$431$	−1.62112e112	−1.75602	−0.878012	−	0.478638i	$-0.841131\pi$
$431$	−1.62112e112	−1.75602	−0.878012	+	0.478638i	$0.841131\pi$
$432$	1.15400e112	1.13279
$433$	1.50861e112	1.34227	0.671136	−	0.741334i	$-0.265807\pi$
$433$	1.50861e112	1.34227	0.671136	+	0.741334i	$0.265807\pi$
$434$	2.70140e111	0.217909
$435$	−1.46050e111	−0.106833
$436$	2.67349e110	0.0177379
$437$	−1.65703e112	−0.997401
$438$	1.78857e111	0.0976915
$439$	2.25334e112	1.11708	0.558540	−	0.829477i	$-0.311362\pi$
$439$	2.25334e112	1.11708	0.558540	+	0.829477i	$0.311362\pi$
$440$	4.89911e110	0.0220485
$441$	1.68529e112	0.688708
$442$	−3.99992e112	−1.48458
$443$	−2.26776e112	−0.764608	−0.382304	−	0.924037i	$-0.624869\pi$
$443$	−2.26776e112	−0.764608	−0.382304	+	0.924037i	$0.624869\pi$
$444$	−2.07851e112	−0.636760
$445$	−2.98173e111	−0.0830172
$446$	−3.40111e112	−0.860775
$447$	2.97959e112	0.685624
$448$	−1.82839e111	−0.0382608
$449$	−2.75326e112	−0.524057	−0.262028	−	0.965060i	$-0.584391\pi$
$449$	−2.75326e112	−0.524057	−0.262028	+	0.965060i	$0.584391\pi$
$450$	1.02437e113	1.77388
$451$	8.29610e110	0.0130729
$452$	−1.07145e112	−0.153670
$453$	2.28195e112	0.297943
$454$	6.95136e111	0.0826411
$455$	−2.97043e112	−0.321614
$456$	−1.53702e112	−0.151591
$457$	−3.86985e112	−0.347741	−0.173870	−	0.984769i	$-0.555627\pi$
$457$	−3.86985e112	−0.347741	−0.173870	+	0.984769i	$0.555627\pi$
$458$	−1.93913e113	−1.58790
$459$	1.16529e113	0.869749
$460$	2.59898e113	1.76846
$461$	1.78941e113	1.11025	0.555123	−	0.831768i	$-0.312671\pi$
$461$	1.78941e113	1.11025	0.555123	+	0.831768i	$0.312671\pi$
$462$	−5.58148e110	−0.00315839
$463$	−5.64251e112	−0.291260	−0.145630	−	0.989339i	$-0.546521\pi$
$463$	−5.64251e112	−0.291260	−0.145630	+	0.989339i	$0.546521\pi$
$464$	2.97548e112	0.140134
$465$	−2.40057e113	−1.03172
$466$	−1.32956e113	−0.521564
$467$	1.76225e113	0.631102	0.315551	−	0.948909i	$-0.397811\pi$
$467$	1.76225e113	0.631102	0.315551	+	0.948909i	$0.397811\pi$
$468$	1.75193e113	0.572885
$469$	−1.55722e112	−0.0465054
$470$	−1.36589e114	−3.72613
$471$	2.80357e113	0.698753
$472$	2.52522e113	0.575128
$473$	−1.84805e112	−0.0384694
$474$	3.16053e113	0.601424
$475$	−7.20051e113	−1.25281
$476$	−5.97875e112	−0.0951295
$477$	5.89902e113	0.858517
$478$	5.36439e113	0.714224
$479$	−1.70471e113	−0.207679	−0.103839	−	0.994594i	$-0.533113\pi$
$479$	−1.70471e113	−0.207679	−0.103839	+	0.994594i	$0.533113\pi$
$480$	9.56200e113	1.06610
$481$	2.12444e114	2.16810
$482$	4.30178e113	0.401929
$483$	1.50579e113	0.128828
$484$	−8.45262e113	−0.662313
$485$	−1.77001e114	−1.27043
$486$	−2.03118e114	−1.33569
$487$	−1.16489e114	−0.701944	−0.350972	−	0.936386i	$-0.614149\pi$
$487$	−1.16489e114	−0.701944	−0.350972	+	0.936386i	$0.614149\pi$
$488$	4.11360e113	0.227185
$489$	−1.32107e114	−0.668803
$490$	4.66096e114	2.16343
$491$	−3.69129e114	−1.57114	−0.785569	−	0.618774i	$-0.787630\pi$
$491$	−3.69129e114	−1.57114	−0.785569	+	0.618774i	$0.787630\pi$
$492$	4.08233e113	0.159365
$493$	3.00458e113	0.107594
$494$	−3.08919e114	−1.01496
$495$	−1.18628e113	−0.0357658
$496$	4.89070e114	1.35332
$497$	−4.49107e113	−0.114078
$498$	−3.23419e114	−0.754257
$499$	2.40006e114	0.513983	0.256992	−	0.966414i	$-0.417269\pi$
$499$	2.40006e114	0.513983	0.256992	+	0.966414i	$0.417269\pi$
$500$	5.50428e114	1.08262
$501$	−4.43618e114	−0.801504
$502$	−1.05007e114	−0.174306
$503$	1.19763e115	1.82677	0.913387	−	0.407092i	$-0.133457\pi$
$503$	1.19763e115	1.82677	0.913387	+	0.407092i	$0.133457\pi$
$504$	−3.34061e113	−0.0468304
$505$	−1.17821e115	−1.51823
$506$	−4.99144e113	−0.0591328
$507$	2.50222e114	0.272576
$508$	−4.49751e114	−0.450573
$509$	9.67368e114	0.891427	0.445714	−	0.895176i	$-0.352950\pi$
$509$	9.67368e114	0.891427	0.445714	+	0.895176i	$0.352950\pi$
$510$	1.33278e115	1.12986
$511$	−2.73249e113	−0.0213143
$512$	−1.20716e115	−0.866548
$513$	8.99967e114	0.594619
$514$	−3.24600e115	−1.97431
$515$	7.36046e114	0.412190
$516$	−9.09386e114	−0.468960
$517$	1.04573e114	0.0496672
$518$	7.96573e114	0.348507
$519$	3.67621e113	0.0148179
$520$	−2.46402e115	−0.915172
$521$	−6.53524e114	−0.223696	−0.111848	−	0.993725i	$-0.535677\pi$
$521$	−6.53524e114	−0.223696	−0.111848	+	0.993725i	$0.535677\pi$
$522$	−3.30119e114	−0.104154
$523$	6.19684e114	0.180239	0.0901194	−	0.995931i	$-0.471275\pi$
$523$	6.19684e114	0.180239	0.0901194	+	0.995931i	$0.471275\pi$
$524$	1.05934e115	0.284091
$525$	6.54329e114	0.161818
$526$	−2.03317e115	−0.463746
$527$	4.93853e115	1.03907
$528$	−1.01049e114	−0.0196151
$529$	7.88305e115	1.41198
$530$	1.63147e116	2.69684
$531$	−6.11463e115	−0.932938
$532$	−4.61747e114	−0.0650369
$533$	−4.17255e115	−0.542619
$534$	2.81790e114	0.0338394
$535$	−2.46263e116	−2.73126
$536$	−1.29174e115	−0.132334
$537$	−5.64408e115	−0.534178
$538$	−1.74588e115	−0.152675
$539$	−3.56843e114	−0.0288373
$540$	−1.41156e116	−1.05430
$541$	1.13376e116	0.782775	0.391388	−	0.920226i	$-0.371995\pi$
$541$	1.13376e116	0.782775	0.391388	+	0.920226i	$0.371995\pi$
$542$	2.10804e116	1.34558
$543$	2.08091e115	0.122818
$544$	−1.96713e116	−1.07369
$545$	9.10497e114	0.0459650
$546$	2.80722e115	0.131096
$547$	3.62140e116	1.56464	0.782321	−	0.622875i	$-0.214036\pi$
$547$	3.62140e116	1.56464	0.782321	+	0.622875i	$0.214036\pi$
$548$	1.35905e115	0.0543329
$549$	−9.96076e115	−0.368526
$550$	−2.16899e115	−0.0742752
$551$	2.32048e115	0.0735587
$552$	1.24908e116	0.366588
$553$	−4.82850e115	−0.131218
$554$	7.27749e116	1.83154
$555$	−7.07867e116	−1.65006
$556$	−9.44522e115	−0.203955
$557$	−3.07616e116	−0.615408	−0.307704	−	0.951482i	$-0.599561\pi$
$557$	−3.07616e116	−0.615408	−0.307704	+	0.951482i	$0.599561\pi$
$558$	−5.42606e116	−1.00584
$559$	9.29482e116	1.59676
$560$	−2.01644e116	−0.321065
$561$	−1.02037e115	−0.0150604
$562$	5.83651e116	0.798656
$563$	−1.92104e116	−0.243742	−0.121871	−	0.992546i	$-0.538889\pi$
$563$	−1.92104e116	−0.243742	−0.121871	+	0.992546i	$0.538889\pi$
$564$	5.14580e116	0.605468
$565$	−3.64898e116	−0.398210
$566$	−1.85388e117	−1.87666
$567$	3.29289e115	0.0309241
$568$	−3.72542e116	−0.324617
$569$	1.23067e116	0.0995109	0.0497555	−	0.998761i	$-0.484156\pi$
$569$	1.23067e116	0.0995109	0.0497555	+	0.998761i	$0.484156\pi$
$570$	1.02932e117	0.772450
$571$	−2.47416e117	−1.72343	−0.861714	−	0.507395i	$-0.830608\pi$
$571$	−2.47416e117	−1.72343	−0.861714	+	0.507395i	$0.830608\pi$
$572$	−3.70952e115	−0.0239876
$573$	8.74984e116	0.525325
$574$	−1.56453e116	−0.0872222
$575$	5.85156e117	3.02962
$576$	3.67254e116	0.176608
$577$	−6.89222e116	−0.307884	−0.153942	−	0.988080i	$-0.549197\pi$
$577$	−6.89222e116	−0.307884	−0.153942	+	0.988080i	$0.549197\pi$
$578$	3.65331e116	0.151619
$579$	−1.33949e117	−0.516535
$580$	−3.63956e116	−0.130425
$581$	4.94104e116	0.164563
$582$	1.67276e117	0.517854
$583$	−1.24905e116	−0.0359474
$584$	−2.26665e116	−0.0606511
$585$	5.96645e117	1.48454
$586$	−1.04292e118	−2.41326
$587$	−7.37134e116	−0.158645	−0.0793226	−	0.996849i	$-0.525276\pi$
$587$	−7.37134e116	−0.158645	−0.0793226	+	0.996849i	$0.525276\pi$
$588$	−1.75595e117	−0.351540
$589$	3.81409e117	0.710380
$590$	−1.69110e118	−2.93062
$591$	−5.94896e117	−0.959342
$592$	1.44215e118	2.16440
$593$	−4.84529e117	−0.676855	−0.338427	−	0.940992i	$-0.609895\pi$
$593$	−4.84529e117	−0.676855	−0.338427	+	0.940992i	$0.609895\pi$
$594$	2.71095e116	0.0352531
$595$	−2.03615e117	−0.246513
$596$	7.42515e117	0.837026
$597$	1.52275e117	0.159853
$598$	2.51046e118	2.45444
$599$	4.36053e117	0.397100	0.198550	−	0.980091i	$-0.436377\pi$
$599$	4.36053e117	0.397100	0.198550	+	0.980091i	$0.436377\pi$
$600$	5.42777e117	0.460462
$601$	−2.11839e118	−1.67433	−0.837164	−	0.546953i	$-0.815788\pi$
$601$	−2.11839e118	−1.67433	−0.837164	+	0.546953i	$0.815788\pi$
$602$	3.48516e117	0.256668
$603$	3.12784e117	0.214664
$604$	5.68664e117	0.363736
$605$	−2.87866e118	−1.71628
$606$	1.11347e118	0.618861
$607$	2.97983e118	1.54409	0.772045	−	0.635568i	$-0.219234\pi$
$607$	2.97983e118	1.54409	0.772045	+	0.635568i	$0.219234\pi$
$608$	−1.51924e118	−0.734047
$609$	−2.10868e116	−0.00950113
$610$	−2.75482e118	−1.15764
$611$	−5.25951e118	−2.06155
$612$	1.20090e118	0.439108
$613$	3.54440e118	1.20913	0.604565	−	0.796556i	$-0.293347\pi$
$613$	3.54440e118	1.20913	0.604565	+	0.796556i	$0.293347\pi$
$614$	5.28967e117	0.168373
$615$	1.39030e118	0.412968
$616$	7.07339e115	0.00196086
$617$	4.96700e118	1.28521	0.642606	−	0.766197i	$-0.277853\pi$
$617$	4.96700e118	1.28521	0.642606	+	0.766197i	$0.277853\pi$
$618$	−6.95604e117	−0.168017
$619$	−3.47146e118	−0.782817	−0.391408	−	0.920217i	$-0.628012\pi$
$619$	−3.47146e118	−0.782817	−0.391408	+	0.920217i	$0.628012\pi$
$620$	−5.98223e118	−1.25955
$621$	−7.31367e118	−1.43795
$622$	3.08412e118	0.566291
$623$	−4.30505e116	−0.00738306
$624$	5.08230e118	0.814170
$625$	5.71089e118	0.854679
$626$	−8.56799e118	−1.19804
$627$	−7.88048e116	−0.0102963
$628$	6.98653e118	0.853054
$629$	1.45625e119	1.66182
$630$	2.23716e118	0.238629
$631$	1.04076e119	1.03778	0.518888	−	0.854842i	$-0.326346\pi$
$631$	1.04076e119	1.03778	0.518888	+	0.854842i	$0.326346\pi$
$632$	−4.00533e118	−0.373390
$633$	3.87288e117	0.0337579
$634$	−1.14491e119	−0.933209
$635$	−1.53169e119	−1.16759
$636$	−6.14634e118	−0.438217
$637$	1.79475e119	1.19696
$638$	6.98992e116	0.00436107
$639$	9.02082e118	0.526574
$640$	−2.57894e119	−1.40862
$641$	−2.21225e119	−1.13075	−0.565376	−	0.824833i	$-0.691269\pi$
$641$	−2.21225e119	−1.13075	−0.565376	+	0.824833i	$0.691269\pi$
$642$	2.32732e119	1.11331
$643$	−3.58461e119	−1.60500	−0.802502	−	0.596650i	$-0.796498\pi$
$643$	−3.58461e119	−1.60500	−0.802502	+	0.596650i	$0.796498\pi$
$644$	3.75243e118	0.157276
$645$	−3.09705e119	−1.21523
$646$	−2.11756e119	−0.777953
$647$	4.91588e119	1.69110	0.845550	−	0.533896i	$-0.179273\pi$
$647$	4.91588e119	1.69110	0.845550	+	0.533896i	$0.179273\pi$
$648$	2.73151e118	0.0879964
$649$	1.29471e118	0.0390636
$650$	1.09090e120	3.08296
$651$	−3.46596e118	−0.0917554
$652$	−3.29211e119	−0.816490
$653$	3.29630e119	0.765978	0.382989	−	0.923753i	$-0.374895\pi$
$653$	3.29630e119	0.765978	0.382989	+	0.923753i	$0.374895\pi$
$654$	−8.60471e117	−0.0187362
$655$	3.60776e119	0.736176
$656$	−2.83247e119	−0.541692
$657$	5.48852e118	0.0983846
$658$	−1.97209e119	−0.331380
$659$	−4.04990e119	−0.637991	−0.318995	−	0.947756i	$-0.603345\pi$
$659$	−4.04990e119	−0.637991	−0.318995	+	0.947756i	$0.603345\pi$
$660$	1.23602e118	0.0182561
$661$	−1.24585e120	−1.72545	−0.862726	−	0.505672i	$-0.831244\pi$
$661$	−1.24585e120	−1.72545	−0.862726	+	0.505672i	$0.831244\pi$
$662$	7.78119e119	1.01060
$663$	5.13200e119	0.625117
$664$	4.09868e119	0.468275
$665$	−1.57255e119	−0.168533
$666$	−1.60001e120	−1.60867
$667$	−1.88576e119	−0.177884
$668$	−1.10550e120	−0.978495
$669$	4.36372e119	0.362449
$670$	8.65059e119	0.674321
$671$	2.10909e118	0.0154307
$672$	1.38057e119	0.0948123
$673$	6.48786e119	0.418275	0.209137	−	0.977886i	$-0.432934\pi$
$673$	6.48786e119	0.418275	0.209137	+	0.977886i	$0.432934\pi$
$674$	2.50562e120	1.51660
$675$	−3.17810e120	−1.80617
$676$	6.23555e119	0.332767
$677$	1.52546e120	0.764506	0.382253	−	0.924058i	$-0.375148\pi$
$677$	1.52546e120	0.764506	0.382253	+	0.924058i	$0.375148\pi$
$678$	3.44849e119	0.162318
$679$	−2.55556e119	−0.112985
$680$	−1.68902e120	−0.701467
$681$	−8.91878e118	−0.0347979
$682$	1.14891e119	0.0421163
$683$	−1.36446e120	−0.469980	−0.234990	−	0.971998i	$-0.575506\pi$
$683$	−1.36446e120	−0.469980	−0.234990	+	0.971998i	$0.575506\pi$
$684$	9.27471e119	0.300204
$685$	4.62846e119	0.140795
$686$	1.36199e120	0.389403
$687$	2.48796e120	0.668623
$688$	6.30966e120	1.59403
$689$	6.28216e120	1.49208
$690$	−8.36489e120	−1.86799
$691$	−6.04346e120	−1.26902	−0.634511	−	0.772914i	$-0.718798\pi$
$691$	−6.04346e120	−1.26902	−0.634511	+	0.772914i	$0.718798\pi$
$692$	9.16114e118	0.0180901
$693$	−1.71277e118	−0.00318080
$694$	−6.99656e120	−1.22210
$695$	−3.21671e120	−0.528515
$696$	−1.74918e119	−0.0270360
$697$	−2.86017e120	−0.415910
$698$	−8.57734e120	−1.17354
$699$	1.70587e120	0.219617
$700$	1.63059e120	0.197551
$701$	1.22391e121	1.39551	0.697757	−	0.716334i	$-0.254181\pi$
$701$	1.22391e121	1.39551	0.697757	+	0.716334i	$0.254181\pi$
$702$	−1.36348e121	−1.46326
$703$	1.12468e121	1.13613
$704$	−7.77620e118	−0.00739485
$705$	1.75248e121	1.56897
$706$	3.41293e120	0.287692
$707$	−1.70111e120	−0.135023
$708$	6.37098e120	0.476204
$709$	−6.68793e120	−0.470789	−0.235395	−	0.971900i	$-0.575638\pi$
$709$	−6.68793e120	−0.470789	−0.235395	+	0.971900i	$0.575638\pi$
$710$	2.49486e121	1.65412
$711$	9.69860e120	0.605691
$712$	−3.57112e119	−0.0210089
$713$	−3.09956e121	−1.71789
$714$	1.92428e120	0.100483
$715$	−1.26333e120	−0.0621599
$716$	−1.40651e121	−0.652137
$717$	−6.88265e120	−0.300740
$718$	−2.83804e121	−1.16877
$719$	−4.15426e121	−1.61256	−0.806280	−	0.591534i	$-0.798523\pi$
$719$	−4.15426e121	−1.61256	−0.806280	+	0.591534i	$0.798523\pi$
$720$	4.05024e121	1.48200
$721$	1.06271e120	0.0366578
$722$	2.32976e121	0.757671
$723$	−5.51930e120	−0.169241
$724$	5.18565e120	0.149939
$725$	−8.19442e120	−0.223436
$726$	2.72050e121	0.699588
$727$	−7.26538e121	−1.76216	−0.881081	−	0.472965i	$-0.843184\pi$
$727$	−7.26538e121	−1.76216	−0.881081	+	0.472965i	$0.843184\pi$
$728$	−3.55758e120	−0.0813900
$729$	1.66810e121	0.359999
$730$	1.51794e121	0.309054
$731$	6.37136e121	1.22389
$732$	1.03784e121	0.188108
$733$	8.42735e121	1.44136	0.720680	−	0.693268i	$-0.243830\pi$
$733$	8.42735e121	1.44136	0.720680	+	0.693268i	$0.243830\pi$
$734$	−1.01841e122	−1.64376
$735$	−5.98014e121	−0.910960
$736$	1.23462e122	1.77512
$737$	−6.62288e119	−0.00898832
$738$	3.14253e121	0.402609
$739$	−3.94992e120	−0.0477748	−0.0238874	−	0.999715i	$-0.507604\pi$
$739$	−3.94992e120	−0.0477748	−0.0238874	+	0.999715i	$0.507604\pi$
$740$	−1.76401e122	−2.01443
$741$	3.96351e121	0.427372
$742$	2.35554e121	0.239842
$743$	−1.01255e122	−0.973627	−0.486813	−	0.873506i	$-0.661841\pi$
$743$	−1.01255e122	−0.973627	−0.486813	+	0.873506i	$0.661841\pi$
$744$	−2.87508e121	−0.261096
$745$	2.52875e122	2.16902
$746$	1.83626e122	1.48777
$747$	−9.92464e121	−0.759607
$748$	−2.54278e120	−0.0183861
$749$	−3.55557e121	−0.242902
$750$	−1.77157e122	−1.14355
$751$	−6.49853e121	−0.396386	−0.198193	−	0.980163i	$-0.563507\pi$
$751$	−6.49853e121	−0.396386	−0.198193	+	0.980163i	$0.563507\pi$
$752$	−3.57034e122	−2.05803
$753$	1.34727e121	0.0733955
$754$	−3.51560e121	−0.181016
$755$	1.93667e122	0.942563
$756$	−2.03802e121	−0.0937632
$757$	4.46168e120	0.0194054	0.00970272	−	0.999953i	$-0.496911\pi$
$757$	4.46168e120	0.0194054	0.00970272	+	0.999953i	$0.496911\pi$
$758$	1.93195e122	0.794430
$759$	6.40415e120	0.0248992
$760$	−1.30446e122	−0.479570
$761$	−1.62320e121	−0.0564318	−0.0282159	−	0.999602i	$-0.508983\pi$
$761$	−1.62320e121	−0.0564318	−0.0282159	+	0.999602i	$0.508983\pi$
$762$	1.44754e122	0.475931
$763$	1.31458e120	0.00408786
$764$	2.18047e122	0.641330
$765$	4.08984e122	1.13788
$766$	4.89968e122	1.28957
$767$	−6.51177e122	−1.62142
$768$	3.01449e122	0.710170
$769$	4.31367e121	0.0961563	0.0480782	−	0.998844i	$-0.484690\pi$
$769$	4.31367e121	0.0961563	0.0480782	+	0.998844i	$0.484690\pi$
$770$	−4.73695e120	−0.00999178
$771$	4.16471e122	0.831330
$772$	−3.33801e122	−0.630598
$773$	6.62830e122	1.18515	0.592575	−	0.805515i	$-0.298111\pi$
$773$	6.62830e122	1.18515	0.592575	+	0.805515i	$0.298111\pi$
$774$	−7.00033e122	−1.18475
$775$	−1.34689e123	−2.15779
$776$	−2.11988e122	−0.321506
$777$	−1.02203e122	−0.146747
$778$	−1.26338e123	−1.71752
$779$	−2.20895e122	−0.284344
$780$	−6.21659e122	−0.757760
$781$	−1.91006e121	−0.0220485
$782$	1.72085e123	1.88130
$783$	1.02419e122	0.106049
$784$	1.21834e123	1.19491
$785$	2.37936e123	2.21055
$786$	−3.40953e122	−0.300080
$787$	−1.45463e123	−1.21291	−0.606453	−	0.795119i	$-0.707408\pi$
$787$	−1.45463e123	−1.21291	−0.606453	+	0.795119i	$0.707408\pi$
$788$	−1.48249e123	−1.17119
$789$	2.60861e122	0.195271
$790$	2.68231e123	1.90265
$791$	−5.26843e121	−0.0354145
$792$	−1.42077e121	−0.00905115
$793$	−1.06077e123	−0.640488
$794$	3.33014e122	0.190586
$795$	−2.09323e123	−1.13557
$796$	3.79471e122	0.195152
$797$	1.84086e123	0.897516	0.448758	−	0.893653i	$-0.351867\pi$
$797$	1.84086e123	0.897516	0.448758	+	0.893653i	$0.351867\pi$
$798$	1.48615e122	0.0686971
$799$	−3.60526e123	−1.58015
$800$	5.36497e123	2.22968
$801$	8.64719e121	0.0340795
$802$	−2.40326e123	−0.898234
$803$	−1.16214e121	−0.00411951
$804$	−3.25898e122	−0.109572
$805$	1.27795e123	0.407556
$806$	−5.77847e123	−1.74813
$807$	2.24001e122	0.0642874
$808$	−1.41110e123	−0.384215
$809$	5.34857e123	1.38174	0.690868	−	0.722981i	$-0.257228\pi$
$809$	5.34857e123	1.38174	0.690868	+	0.722981i	$0.257228\pi$
$810$	−1.82925e123	−0.448395
$811$	1.49607e123	0.347990	0.173995	−	0.984747i	$-0.444332\pi$
$811$	1.49607e123	0.347990	0.173995	+	0.984747i	$0.444332\pi$
$812$	−5.25484e121	−0.0115992
$813$	−2.70467e123	−0.566587
$814$	3.38785e122	0.0673576
$815$	−1.12118e124	−2.11580
$816$	3.48379e123	0.624050
$817$	4.92068e123	0.836735
$818$	2.13182e123	0.344140
$819$	8.61441e122	0.132026
$820$	3.46464e123	0.504161
$821$	−4.28921e123	−0.592643	−0.296322	−	0.955088i	$-0.595760\pi$
$821$	−4.28921e123	−0.592643	−0.296322	+	0.955088i	$0.595760\pi$
$822$	−4.37415e122	−0.0573908
$823$	1.46435e124	1.82453	0.912266	−	0.409599i	$-0.134331\pi$
$823$	1.46435e124	1.82453	0.912266	+	0.409599i	$0.134331\pi$
$824$	8.81536e122	0.104312
$825$	2.78288e122	0.0312753
$826$	−2.44163e123	−0.260632
$827$	1.52786e124	1.54917	0.774585	−	0.632470i	$-0.217959\pi$
$827$	1.52786e124	1.54917	0.774585	+	0.632470i	$0.217959\pi$
$828$	−7.53719e123	−0.725972
$829$	1.72896e124	1.58204	0.791021	−	0.611789i	$-0.209550\pi$
$829$	1.72896e124	1.58204	0.791021	+	0.611789i	$0.209550\pi$
$830$	−2.74483e124	−2.38614
$831$	−9.33722e123	−0.771212
$832$	3.91106e123	0.306940
$833$	1.23026e124	0.917450
$834$	3.03997e123	0.215433
$835$	−3.76494e124	−2.53561
$836$	−1.96382e122	−0.0125700
$837$	1.68343e124	1.02415
$838$	−1.49959e124	−0.867166
$839$	−1.39624e124	−0.767494	−0.383747	−	0.923438i	$-0.625367\pi$
$839$	−1.39624e124	−0.767494	−0.383747	+	0.923438i	$0.625367\pi$
$840$	1.18539e123	0.0619430
$841$	−1.98653e124	−0.986881
$842$	−1.57656e123	−0.0744641
$843$	−7.48840e123	−0.336292
$844$	9.65123e122	0.0412125
$845$	2.12361e124	0.862312
$846$	3.96117e124	1.52962
$847$	−4.15624e123	−0.152636
$848$	4.26455e124	1.48953
$849$	2.37858e124	0.790208
$850$	7.47785e124	2.36305
$851$	−9.13982e124	−2.74746
$852$	−9.39901e123	−0.268782
$853$	−2.71677e123	−0.0739127	−0.0369563	−	0.999317i	$-0.511766\pi$
$853$	−2.71677e123	−0.0739127	−0.0369563	+	0.999317i	$0.511766\pi$
$854$	−3.97743e123	−0.102954
$855$	3.15864e124	0.777930
$856$	−2.94941e124	−0.691193
$857$	2.46992e124	0.550805	0.275402	−	0.961329i	$-0.411189\pi$
$857$	2.46992e124	0.550805	0.275402	+	0.961329i	$0.411189\pi$
$858$	1.19392e123	0.0253376
$859$	−8.99118e124	−1.81596	−0.907982	−	0.419010i	$-0.862377\pi$
$859$	−8.99118e124	−1.81596	−0.907982	+	0.419010i	$0.862377\pi$
$860$	−7.71787e124	−1.48359
$861$	2.00733e123	0.0367269
$862$	1.30023e125	2.26445
$863$	6.78801e124	1.12534	0.562669	−	0.826682i	$-0.309774\pi$
$863$	6.78801e124	1.12534	0.562669	+	0.826682i	$0.309774\pi$
$864$	−6.70549e124	−1.05827
$865$	3.11996e123	0.0468775
$866$	−1.20999e125	−1.73090
$867$	−4.68730e123	−0.0638426
$868$	−8.63720e123	−0.112017
$869$	−2.05357e123	−0.0253612
$870$	1.17140e124	0.137765
$871$	3.33099e124	0.373080
$872$	1.09047e123	0.0116322
$873$	5.13313e124	0.521527
$874$	1.32904e125	1.28618
$875$	2.70651e124	0.249498
$876$	−5.71862e123	−0.0502189
$877$	−1.94609e125	−1.62810	−0.814050	−	0.580794i	$-0.802742\pi$
$877$	−1.94609e125	−1.62810	−0.814050	+	0.580794i	$0.802742\pi$
$878$	−1.80731e125	−1.44051
$879$	1.33810e125	1.01616
$880$	−8.57595e123	−0.0620538
$881$	1.01589e124	0.0700442	0.0350221	−	0.999387i	$-0.488850\pi$
$881$	1.01589e124	0.0700442	0.0350221	+	0.999387i	$0.488850\pi$
$882$	−1.35171e125	−0.888111
$883$	2.03107e124	0.127173	0.0635866	−	0.997976i	$-0.479746\pi$
$883$	2.03107e124	0.127173	0.0635866	+	0.997976i	$0.479746\pi$
$884$	1.27890e125	0.763158
$885$	2.16973e125	1.23401
$886$	1.81888e125	0.985986
$887$	2.54535e125	1.31520	0.657602	−	0.753366i	$-0.271571\pi$
$887$	2.54535e125	1.31520	0.657602	+	0.753366i	$0.271571\pi$
$888$	−8.47787e124	−0.417576
$889$	−2.21148e124	−0.103838
$890$	2.39153e124	0.107053
$891$	1.40047e123	0.00597685
$892$	1.08744e125	0.442486
$893$	−2.78439e125	−1.08030
$894$	−2.38981e125	−0.884134
$895$	−4.79007e125	−1.68991
$896$	−3.72350e124	−0.125274
$897$	−3.22098e125	−1.03350
$898$	2.20828e125	0.675788
$899$	4.34056e124	0.126695
$900$	−3.27523e125	−0.911874
$901$	4.30626e125	1.14366
$902$	−6.65396e123	−0.0168579
$903$	−4.47155e124	−0.108076
$904$	−4.37025e124	−0.100774
$905$	1.76605e125	0.388543
$906$	−1.83026e125	−0.384207
$907$	−1.07143e125	−0.214612	−0.107306	−	0.994226i	$-0.534222\pi$
$907$	−1.07143e125	−0.214612	−0.107306	+	0.994226i	$0.534222\pi$
$908$	−2.22257e124	−0.0424821
$909$	3.41687e125	0.623251
$910$	2.38246e125	0.414731
$911$	5.95619e125	0.989549	0.494775	−	0.869021i	$-0.335251\pi$
$911$	5.95619e125	0.989549	0.494775	+	0.869021i	$0.335251\pi$
$912$	2.69057e125	0.426642
$913$	2.10144e124	0.0318059
$914$	3.10385e125	0.448422
$915$	3.53451e125	0.487452
$916$	6.20001e125	0.816271
$917$	5.20891e124	0.0654712
$918$	−9.34630e125	−1.12157
$919$	−9.94343e125	−1.13927	−0.569635	−	0.821898i	$-0.692916\pi$
$919$	−9.94343e125	−1.13927	−0.569635	+	0.821898i	$0.692916\pi$
$920$	1.06008e126	1.15973
$921$	−6.78679e124	−0.0708974
$922$	−1.43521e126	−1.43170
$923$	9.60671e125	0.915171
$924$	1.78457e123	0.00162359
$925$	−3.97164e126	−3.45101
$926$	4.52563e125	0.375588
$927$	−2.13457e125	−0.169209
$928$	−1.72894e125	−0.130916
$929$	4.38107e125	0.316892	0.158446	−	0.987368i	$-0.449352\pi$
$929$	4.38107e125	0.316892	0.158446	+	0.987368i	$0.449352\pi$
$930$	1.92540e126	1.33044
$931$	9.50142e125	0.627230
$932$	4.25103e125	0.268113
$933$	−3.95701e125	−0.238450
$934$	−1.41343e126	−0.813826
$935$	−8.65981e124	−0.0476447
$936$	7.14580e125	0.375688
$937$	−1.39168e126	−0.699208	−0.349604	−	0.936897i	$-0.613684\pi$
$937$	−1.39168e126	−0.699208	−0.349604	+	0.936897i	$0.613684\pi$
$938$	1.24898e125	0.0599701
$939$	1.09930e126	0.504460
$940$	4.36719e126	1.91544
$941$	6.53069e125	0.273779	0.136890	−	0.990586i	$-0.456289\pi$
$941$	6.53069e125	0.273779	0.136890	+	0.990586i	$0.456289\pi$
$942$	−2.24863e126	−0.901063
$943$	1.79512e126	0.687618
$944$	−4.42042e126	−1.61865
$945$	−6.94078e125	−0.242972
$946$	1.48225e125	0.0496074
$947$	6.16860e125	0.197384	0.0986922	−	0.995118i	$-0.468534\pi$
$947$	6.16860e125	0.197384	0.0986922	+	0.995118i	$0.468534\pi$
$948$	−1.01052e126	−0.309165
$949$	5.84499e125	0.170990
$950$	5.77524e126	1.61554
$951$	1.46895e126	0.392949
$952$	−2.43863e125	−0.0623843
$953$	−3.66331e126	−0.896243	−0.448121	−	0.893973i	$-0.647907\pi$
$953$	−3.66331e126	−0.896243	−0.448121	+	0.893973i	$0.647907\pi$
$954$	−4.73137e126	−1.10708
$955$	7.42590e126	1.66190
$956$	−1.71516e126	−0.367151
$957$	−8.96825e123	−0.00183633
$958$	1.36728e126	0.267808
$959$	6.68262e124	0.0125215
$960$	−1.30317e126	−0.233601
$961$	1.30343e126	0.223534
$962$	−1.70393e127	−2.79583
$963$	7.14176e126	1.12121
$964$	−1.37541e126	−0.206614
$965$	−1.13681e127	−1.63409
$966$	−1.20773e126	−0.166128
$967$	−2.99920e126	−0.394802	−0.197401	−	0.980323i	$-0.563250\pi$
$967$	−2.99920e126	−0.394802	−0.197401	+	0.980323i	$0.563250\pi$
$968$	−3.44768e126	−0.434334
$969$	2.71688e126	0.327575
$970$	1.41966e127	1.63827
$971$	1.07598e127	1.18846	0.594231	−	0.804294i	$-0.297456\pi$
$971$	1.07598e127	1.18846	0.594231	+	0.804294i	$0.297456\pi$
$972$	6.49430e126	0.686619
$973$	−4.64432e125	−0.0470031
$974$	9.34308e126	0.905179
$975$	−1.39966e127	−1.29815
$976$	−7.20089e126	−0.639395
$977$	2.26510e127	1.92561	0.962804	−	0.270200i	$-0.0870899\pi$
$977$	2.26510e127	1.92561	0.962804	+	0.270200i	$0.0870899\pi$
$978$	1.05957e127	0.862442
$979$	−1.83095e124	−0.00142696
$980$	−1.49026e127	−1.11212
$981$	−2.64049e125	−0.0188691
$982$	2.96063e127	2.02603
$983$	9.87724e125	0.0647308	0.0323654	−	0.999476i	$-0.489696\pi$
$983$	9.87724e125	0.0647308	0.0323654	+	0.999476i	$0.489696\pi$
$984$	1.66511e126	0.104509
$985$	−5.04883e127	−3.03494
$986$	−2.40985e126	−0.138746
$987$	2.53025e126	0.139535
$988$	9.87709e126	0.521746
$989$	−3.99884e127	−2.02345
$990$	9.51470e125	0.0461211
$991$	6.53433e126	0.303439	0.151719	−	0.988424i	$-0.451519\pi$
$991$	6.53433e126	0.303439	0.151719	+	0.988424i	$0.451519\pi$
$992$	−2.84181e127	−1.26430
$993$	−9.98347e126	−0.425538
$994$	3.60210e126	0.147108
$995$	1.29234e127	0.505705
$996$	1.03407e127	0.387730
$997$	1.86520e127	0.670165	0.335083	−	0.942189i	$-0.391236\pi$
$997$	1.86520e127	0.670165	0.335083	+	0.942189i	$0.391236\pi$
$998$	−1.92499e127	−0.662797
$999$	4.96402e127	1.63795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.86.a.a.1.2	✓	6
3.2	odd	2		9.86.a.a.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.86.a.a.1.2	✓	6	1.1	even	1	trivial
9.86.a.a.1.5		6	3.2	odd	2

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:	\( k \)	\(=\)	\( 86 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-8.02060e12 q^{2} +1.02906e20 q^{3} +2.56443e25 q^{4} +8.73356e29 q^{5} -8.25371e32 q^{6} +1.26096e35 q^{7} +1.04599e38 q^{8} -2.53278e40 q^{9} +O(q^{10})\)	\(q-8.02060e12 q^{2} +1.02906e20 q^{3} +2.56443e25 q^{4} +8.73356e29 q^{5} -8.25371e32 q^{6} +1.26096e35 q^{7} +1.04599e38 q^{8} -2.53278e40 q^{9} -7.00484e42 q^{10} +5.36289e42 q^{11} +2.63897e45 q^{12} -2.69728e47 q^{13} -1.01137e48 q^{14} +8.98740e49 q^{15} -1.83101e51 q^{16} -1.84892e52 q^{17} +2.03144e53 q^{18} -1.42794e54 q^{19} +2.23967e55 q^{20} +1.29761e55 q^{21} -4.30136e55 q^{22} +1.16043e58 q^{23} +1.07639e58 q^{24} +5.04257e59 q^{25} +2.16338e60 q^{26} -6.30254e60 q^{27} +3.23365e60 q^{28} -1.62505e61 q^{29} -7.20843e62 q^{30} -2.67104e63 q^{31} +1.06393e64 q^{32} +5.51876e62 q^{33} +1.48294e65 q^{34} +1.10127e65 q^{35} -6.49515e65 q^{36} -7.87622e66 q^{37} +1.14530e67 q^{38} -2.77568e67 q^{39} +9.13521e67 q^{40} +1.54694e68 q^{41} -1.04076e68 q^{42} -3.44599e69 q^{43} +1.37528e68 q^{44} -2.21202e70 q^{45} -9.30736e70 q^{46} +1.94993e71 q^{47} -1.88423e71 q^{48} -6.65392e71 q^{49} -4.04444e72 q^{50} -1.90265e72 q^{51} -6.91701e72 q^{52} -2.32907e73 q^{53} +5.05501e73 q^{54} +4.68372e72 q^{55} +1.31895e73 q^{56} -1.46944e74 q^{57} +1.30339e74 q^{58} +2.41420e75 q^{59} +2.30476e75 q^{60} +3.93274e75 q^{61} +2.14233e76 q^{62} -3.19374e75 q^{63} -1.45000e76 q^{64} -2.35569e77 q^{65} -4.42638e75 q^{66} -1.23494e77 q^{67} -4.74143e77 q^{68} +1.19416e78 q^{69} -8.83282e77 q^{70} -3.56162e78 q^{71} -2.64926e78 q^{72} -2.16699e78 q^{73} +6.31720e79 q^{74} +5.18913e79 q^{75} -3.66187e79 q^{76} +6.76240e77 q^{77} +2.22626e80 q^{78} -3.82923e80 q^{79} -1.59913e81 q^{80} +2.61141e80 q^{81} -1.24074e81 q^{82} +3.91847e81 q^{83} +3.32763e80 q^{84} -1.61476e82 q^{85} +2.76389e82 q^{86} -1.67228e81 q^{87} +5.60953e80 q^{88} -3.41411e81 q^{89} +1.77417e83 q^{90} -3.40117e82 q^{91} +2.97585e83 q^{92} -2.74867e83 q^{93} -1.56396e84 q^{94} -1.24710e84 q^{95} +1.09486e84 q^{96} -2.02668e84 q^{97} +5.33684e84 q^{98} -1.35830e83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 57\!\cdots\!38 q^{9}+O(q^{10}) \) 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9	\( 6 q - 3596910688800 q^{2} - 15\!\cdots\!00 q^{3}+ \cdots + 14\!\cdots\!76 q^{99}+O(q^{100}) \) 6 * q - 3596910688800 * q^2 - 158574346104614272200 * q^3 + 140991407339885551387640832 * q^4 - 937371071374809475998758615100 * q^5 - 2163199670798237803919272036318848 * q^6 + 376764526445862177226143056468406000 * q^7 + 444573639427992844351424894916577689600 * q^8 + 57207108743130009711910898489373895669038 * q^9 + 94651165962435813693946284861726959764800 * q^10 - 56344805701335918998354740625397619012956888 * q^11 - 38113762524253328553901066462492282955462553600 * q^12 - 380409468466294979156527797290184755501373645900 * q^13 + 7432102291035232990382031969981134697595704847104 * q^14 + 144434402836684505734903243186122115181592351080400 * q^15 + 2636948568634008151994191667083023793288011486068736 * q^16 - 51365945458144838311659694040021464865555671618554900 * q^17 + 463507663069864508791700717104909645587637083805192800 * q^18 + 2653138201866103222242250000135395331152453781661358360 * q^19 - 52474536419792695778976723338965188133980339812187187200 * q^20 - 58207920650233869679987953151176418416472072173047654208 * q^21 + 3581897081140779531372538339240606543513118132263441718400 * q^22 - 2885510207115801266245992081450013398631817932489294263600 * q^23 - 68567070931993796242748985500475684139954880414010505297920 * q^24 + 669968020810517762245853029111649576216707129701526846916250 * q^25 - 145338677717367061512932551412743816475529536844287947743168 * q^26 - 2889483981995895623844053829009837579840855941832615148040400 * q^27 + 26317831788111975278561322769557791839073407987295193709977600 * q^28 - 126005957659709196887223202461409590769523616790635653593969260 * q^29 + 136086353401335907485123608360817834511749084976435568495980800 * q^30 - 5173343222869174361945421290475955243870433981978751385509914688 * q^31 + 18707915462589185913352646999729455863851090555123851448234803200 * q^32 + 41065540677287661644797365484571058991908764323686266561418093600 * q^33 - 261567067349813682388055634030637558284890219695677173368549801536 * q^34 - 54720272714504178732776803597096361295121671934223039039646799200 * q^35 + 3399696315710870996405230044380107361656113863069854483749794804736 * q^36 - 5097772448818865838142977649516403030637492688710699135052039832700 * q^37 - 48700117286552805406633697613393636582143669921611431061746550761600 * q^38 + 110170203428145375146126906937514681017464730369816703999974469819536 * q^39 - 142216395874814214555238931398128417040750190812408712268526706688000 * q^40 - 37443196175066827621993378286362463826782697218192853395514169611588 * q^41 - 3196148185952018443143303103341158979894551408731781313074799986918400 * q^42 - 1200203503033233321208433978807766368170132198490662545566874292959000 * q^43 - 18639061742892206758508411691062975986004422355135358223957061170139136 * q^44 - 86500611154071576329235297315912364271843998646281427040496904001252300 * q^45 - 191201172378193769791517179835271412887470991983918549920785652631609088 * q^46 - 239424902055614885318194585971856964272866563499240512979067317687189600 * q^47 - 2011644131471271504966965322061354320977669648116299895717796775041433600 * q^48 - 3550036072199457619495079372134003262477445775089732177587676397325457258 * q^49 - 11494548593012586974824937998111766287236762210273483206149818153415980000 * q^50 - 10328830658918507785729550461151529723270274866387219032022415269933043728 * q^51 - 58712069233310142887861446777253810318205781466445594810258784313124096000 * q^52 - 50490336878498884627542374457418517146058176491360508941999343448428076700 * q^53 - 127995453221656133194026073100343370388415314716409270018601938523610333440 * q^54 + 39301939079139487846929886085782264562447760597309570618345636737530354800 * q^55 + 587681993552427976427603903951469305598093495610137163751240432058398146560 * q^56 + 609918064048630066051419788625468329088455176450389301471226460423851647200 * q^57 + 1968773654564353990385431635289950834066592911242318428340655057560215041600 * q^58 + 6616590288827867291331513194467053420958403068835561414972249041164074836680 * q^59 + 31689950181369930414484676957647463168779067278456560490215008364167133388800 * q^60 + 14357623272339506273937696878826484910577784548921932472541795844444520630612 * q^61 + 6341655988756470271607502111666483932112595649902706601178034698608656870400 * q^62 + 35795966074431291550182082060995682584043172792907267107900820593108358481200 * q^63 - 15036793202050903912474653273096694719068286214625123977211579195245857865728 * q^64 - 207821434856417257245443053802293031083793273150318306362240037299645012878600 * q^65 - 1499689309727229977020921941751495239601349525904665530644129573530308780586496 * q^66 - 676342476586532149280756429155984326543089556982073869153059292790609382659400 * q^67 - 3163312242521042817824168546059434229649323239544821535981619303392310998579200 * q^68 - 745502955929877889390374691705185133399296067237471890306223900077423420825024 * q^69 - 6084039126370540917643976340500810012180196811570702685650569892863510961958400 * q^70 - 6034633570006156478287618014555933721359683069405109018337202921275711590822288 * q^71 + 42205813302686543920197586259094606661421265173628042056899709260796372565196800 * q^72 + 35801030708258502256835696755718519936386302900895514245440128302587327554955900 * q^73 + 107340388271157498582387358259935699803904453010588240913436902735784529206718784 * q^74 + 145624067696916644200840962911775023608813806434012931341647651068546287549085000 * q^75 + 161366039234563681095121956921292746446621209914504282248055858395547636251627520 * q^76 + 251398792676383195671611646509617352303457127744134928661968949244057263571048000 * q^77 + 171841231286923953547335431872475383039854385588725970844304858012728142132768000 * q^78 - 1371264739680910465180747804297591457073099822996075412863178473301594188074547360 * q^79 - 4133302113696354289363675864719400535772990320893278365909081697225137404615065600 * q^80 - 4310060020996155465671846173285816617646939986231807893561334612249450355160008554 * q^81 - 1521817925451755348555955193889971681134404529402094946034920762170082779676769600 * q^82 - 6003587143963376493630220870754035373224271946820478343977301287860006839810301800 * q^83 - 12398071481018763514585592745934914502465484593761365063657562420201819291615461376 * q^84 + 17517819416067376478784379475048913828437460883636030543204171384490930355142297800 * q^85 + 21492879965867203934779808388379416439833228958041181100627630027642419671434758272 * q^86 + 50876914632638320845048890401340559827753840179451919522781964204571716769119542800 * q^87 + 272530707230233729788642007241687387343090541246894873629875449706966387853783859200 * q^88 + 160168600498492831669414330089333488062247500152820008689246769174592053409073033820 * q^89 + 84790751750172409977703550300414634726575284296402896259290449409557083536687630400 * q^90 - 25835286532054033379869466839714977397623074555127707439218236615589791891497666528 * q^91 - 409168494351117176400001947891440713569740400895293133641599839567086438014810726400 * q^92 - 593175476050386740279600068063559704679480457431525655959184215070525871275273350400 * q^93 - 1363919087472816080652148503710266001883533236220476628035821611168261836377449504256 * q^94 - 5333227198671761899795642368410473530089556162431166206847226445312136951029790006000 * q^95 - 8776777977440964474954793317935829637440571398014671264365724282514189936233386344448 * q^96 + 1982258923770441792809455137165411551481047984016852591852301644261535493014975149900 * q^97 + 4998389537167322966144480371748484731963375313000939154777788888434561052122410226400 * q^98 + 14740689076241711017386038088080153281412276754860625822798307085897192961497015786376 * q^99

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