LMFDB - Embedded newform 2.80.a.a.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,80,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 80); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 80, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 80 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$79.0474097443$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5157021731103247543589585180x + 141562397820564875200991893221092433132672 $ x^3 - x^2 - 5157021731103247543589585180*x + 141562397820564875200991893221092433132672
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{9}\cdot 5^{4}\cdot 7\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.86202e13$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.49756e11 q^{2} +7.60629e18 q^{3} +3.02231e23 q^{4} -2.65106e27 q^{5} +4.18160e30 q^{6} -1.85699e33 q^{7} +1.66153e35 q^{8} +8.58611e36 q^{9} -1.45744e39 q^{10} +1.28066e40 q^{11} +2.29886e42 q^{12} +9.72252e42 q^{13} -1.02089e45 q^{14} -2.01648e46 q^{15} +9.13439e46 q^{16} +5.80157e48 q^{17} +4.72026e48 q^{18} -1.76912e50 q^{19} -8.01235e50 q^{20} -1.41248e52 q^{21} +7.04052e51 q^{22} -3.63643e53 q^{23} +1.26381e54 q^{24} -9.51547e54 q^{25} +5.34501e54 q^{26} -3.09451e56 q^{27} -5.61242e56 q^{28} -6.59091e57 q^{29} -1.10857e58 q^{30} -5.88368e58 q^{31} +5.02168e58 q^{32} +9.74109e58 q^{33} +3.18945e60 q^{34} +4.92301e60 q^{35} +2.59499e60 q^{36} -9.06879e61 q^{37} -9.72584e61 q^{38} +7.39524e61 q^{39} -4.40484e62 q^{40} -9.50622e63 q^{41} -7.76521e63 q^{42} +2.02221e64 q^{43} +3.87056e63 q^{44} -2.27623e64 q^{45} -1.99915e65 q^{46} -1.19680e66 q^{47} +6.94788e65 q^{48} -2.34246e66 q^{49} -5.23119e66 q^{50} +4.41285e67 q^{51} +2.93845e66 q^{52} +2.24366e68 q^{53} -1.70122e68 q^{54} -3.39512e67 q^{55} -3.08546e68 q^{56} -1.34565e69 q^{57} -3.62339e69 q^{58} +4.05370e69 q^{59} -6.09443e69 q^{60} +2.62524e70 q^{61} -3.23459e70 q^{62} -1.59444e70 q^{63} +2.76070e70 q^{64} -2.57750e70 q^{65} +5.35522e70 q^{66} +3.14459e71 q^{67} +1.75342e72 q^{68} -2.76597e72 q^{69} +2.70645e72 q^{70} -1.14540e73 q^{71} +1.42661e72 q^{72} -2.75743e73 q^{73} -4.98562e73 q^{74} -7.23775e73 q^{75} -5.34684e73 q^{76} -2.37818e73 q^{77} +4.06558e73 q^{78} +9.08613e74 q^{79} -2.42158e74 q^{80} -2.77681e75 q^{81} -5.22610e75 q^{82} -1.14994e76 q^{83} -4.26897e75 q^{84} -1.53803e76 q^{85} +1.11172e76 q^{86} -5.01324e76 q^{87} +2.12787e75 q^{88} -1.62121e77 q^{89} -1.25137e76 q^{90} -1.80547e76 q^{91} -1.09904e77 q^{92} -4.47530e77 q^{93} -6.57950e77 q^{94} +4.69005e77 q^{95} +3.81964e77 q^{96} +1.53312e78 q^{97} -1.28778e78 q^{98} +1.09959e77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3} + 90\!\cdots\!32 q^{4} - 40\!\cdots\!50 q^{5} - 25\!\cdots\!68 q^{6} + 14\!\cdots\!12 q^{7} + 49\!\cdots\!16 q^{8} - 66\!\cdots\!69 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots + 43\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 1649267441664 * q^2 - 4584969341748725436 * q^3 + 906694364710971881029632 * q^4 - 4059262187174651001136305750 * q^5 - 2520613552124598169254827655168 * q^6 + 1483415167701865205633594539244712 * q^7 + 498460498419343452338927647605129216 * q^8 - 6672177462878166486769127437981485969 * q^9 - 2231602987494983256332043780416864256000 * q^10 - 124415627894002097981147146385015573568084 * q^11 - 1385721954845381178123642556040054449373184 * q^12 + 42751290531030108169653302093972335572078354 * q^13 + 815516112853742916658765248637469002360160256 * q^14 + 12130195395785681466027262600593952860024579000 * q^15 + 274031556999544297163190906134303066185487351808 * q^16 + 946712075921587263895141601588172960900304679382 * q^17 - 3668068351509757323918927238219104062763247337472 * q^18 + 20257201468438772377828741263164304940521204158100 * q^19 - 1226836716665196806401755258077521564978095587328000 * q^20 - 43631041707758317195716974587393663148235360312109344 * q^21 - 68398214773253678769205071140782913654477159600750592 * q^22 + 82529324959900375708064647869197163323144742475087224 * q^23 - 761808701108492914776959414090992784142990461361979392 * q^24 + 21083927432436875746692985513144812516022059835070953125 * q^25 + 23502770520648804835840429075458496001384189590977380352 * q^26 + 274892147371249163933625876457102532152743271603258606440 * q^27 + 448334724360687495454854442833822454444881294443390435328 * q^28 + 1495670726099376746574980522811287146529994291477752261730 * q^29 + 6668645442430627599572534772986232026773917767829553152000 * q^30 - 95179276352007712146226202833884603073380381912216918148704 * q^31 + 150650441649280338332058946156983993986456530667136828309504 * q^32 + 992822698008241864790090731991207114961142366072700744254608 * q^33 + 520460467815870253931488608270113859514661800240826302857216 * q^34 - 21607610499914207082682499103219854780050992252308433934818000 * q^35 - 2016541901981061111184418693574995613694576474265768360411136 * q^36 - 144566050902862740859885196306965987391617821343191168676139958 * q^37 + 11136514280374746053268812699409461656846054022858075327692800 * q^38 + 228190042825724963101591896942117207549963869755940875240057752 * q^39 - 674460617677956923507095330616191354152404416503766019211264000 * q^40 - 8990031028114195750037275993147973941443305064257192760778706994 * q^41 - 23986418844829947113932651151989616268711842899364606112769769472 * q^42 - 95593681974303841410795644029721502703583992143632618507356214196 * q^43 - 37602316231156301545654439995778051325641119291417114840657821696 * q^44 - 301087420222926180530726149020081890688604646091994014416774832750 * q^45 + 45370976212957264010784064774650611487856300647019740393910566912 * q^46 - 1196991457557369832323664024412035293457581150671216623337274714768 * q^47 - 418808762504859650152288744683537353736464821656275597627643396096 * q^48 + 979527459006508007750478947254655464139388961590111701782059182619 * q^49 + 11591011685574864757307129975239519727150876544791666881462272000000 * q^50 + 54835677094941655265769813003495680021307623179495147480345912211016 * q^51 + 12920784736202177212341925318873824836005358723163067556811899928576 * q^52 + 125345260867666016932298670205922091626639085968719891046717117688474 * q^53 + 151123556209501123809570029322571740481897066012165273816362878238720 * q^54 + 218552253106716091346953706059417254940663339263001756619683362801000 * q^55 + 246474621285161894535007804980680832577435519262273080715899268235264 * q^56 - 3717966118204647103187961905025238537942233258324174220458365486643600 * q^57 + 822253677335218786882869933735866915073470126715345596892208944906240 * q^58 - 11972958248068544720959454962966912784485227241028887059908129310352740 * q^59 + 3666126602733951524981634615014227304097506969423520216337115774976000 * q^60 - 64131246374258928284376769397123814135901710973884122711218411370114814 * q^61 - 52325360536168871373801409406694002027278058045563085607243845732401152 * q^62 + 70051688514428937815669910467509313829077855679613962909546987100234824 * q^63 + 82820956161486765449217070347324305429413307666044638661950290685591552 * q^64 + 891137435602017208473142837371223459080944333869708385766316087294741500 * q^65 + 545810050390001042909631180643191746345039202954535635835955360934395904 * q^66 + 1066530064121225601134341646949007968554017501968094906567414396182674052 * q^67 + 286126168080642981173114751630936852583911790660458738532906761933815808 * q^68 - 8157044315638375005795679302675007882029666940395500924677412200323240288 * q^69 - 11878909496555229468914291404784461386008100471809805344642547931152384000 * q^70 - 11965128429849499869561209311265966495949289765114193633775048728088683544 * q^71 - 1108605634562853770741055758550483389972691928261434972195503389978656768 * q^72 - 21000617554059015243660635152162850086671731600300702395695797742856222866 * q^73 - 79476026974677343330576619065978738282412401561571438302725214096488136704 * q^74 - 292290092969427932732653354537557410364081060335887189482606343379537062500 * q^75 + 6122363472082753142156111928411278890127331396457557757688967569237606400 * q^76 - 313088925468723418800569716492755177099175159696850088390493982222779568736 * q^77 + 125448802714794002433554422131839463862520205642671303790805016830883659776 * q^78 - 752771845175749719716095680259956103143909956608587888174845776003401815280 * q^79 - 370788645806948409159647752825708722452803938387153627308606284137234432000 * q^80 - 5430810619867098975054002966228960820045900884810688198506068573048487508357 * q^81 - 4942321824739293094368293269951547925396379429009385144359999748146747932672 * q^82 - 26574910236679674809554404156731348191995217371417312252463281001984618227756 * q^83 - 13186673214297948356576041298479632282330484902484582711586284526041496027136 * q^84 - 61899665747197215566012671763299618265748666908061238888083245866423505095500 * q^85 - 52553182436334043036996837433204672780783210015490947984376227250456439554048 * q^86 - 113886925506447843297583002913412072306835473772896532524712459437309650171560 * q^87 - 20672091963733285299571209049479821890334470859452313822118604199797664514048 * q^88 - 298553979180856324945701053715618937701373783711334946928152981953765466232770 * q^89 - 165524559756093052774612573846179093471923695979362367916518453818511327232000 * q^90 - 325469734796585461839474806271975513931239639583395403663965991364192518458384 * q^91 + 24942957954847408687610284739208958229343323190591158381856773431790042873856 * q^92 + 202912930249066039233266302287024066236035757547578650004667495188619949592448 * q^93 - 658053012966435260621714005982903963417353447091062252257938595545124893097984 * q^94 - 2764634158440341917915731742585889802219731536972926191181370883821066211265000 * q^95 - 230242552094285214524682441979479910898239975893526559356618697188184841781248 * q^96 - 3594992107094973275749338803035652864766054361504256609082707972538374192841498 * q^97 + 538500915451767365689653965669792537884976176057975029266028685937292368412672 * q^98 + 438106251552810720132252327913477796137507348924505662619110697139172583981532 * q^99

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 $

$2$	5.49756e11	0.707107
$2$	5.49756e11	0.707107
$3$	7.60629e18	1.08364	0.541818	−	0.840496i	$-0.317736\pi$
$3$	7.60629e18	1.08364	0.541818	+	0.840496i	$0.317736\pi$
$4$	3.02231e23	0.500000
$5$	−2.65106e27	−0.651786	−0.325893	−	0.945407i	$-0.605665\pi$
$5$	−2.65106e27	−0.651786	−0.325893	+	0.945407i	$0.605665\pi$
$6$	4.18160e30	0.766247
$7$	−1.85699e33	−0.771681	−0.385841	−	0.922565i	$-0.626089\pi$
$7$	−1.85699e33	−0.771681	−0.385841	+	0.922565i	$0.626089\pi$
$8$	1.66153e35	0.353553
$9$	8.58611e36	0.174268
$10$	−1.45744e39	−0.460882
$11$	1.28066e40	0.0938477	0.0469238	−	0.998898i	$-0.485058\pi$
$11$	1.28066e40	0.0938477	0.0469238	+	0.998898i	$0.485058\pi$
$12$	2.29886e42	0.541818
$13$	9.72252e42	0.0970547	0.0485274	−	0.998822i	$-0.484547\pi$
$13$	9.72252e42	0.0970547	0.0485274	+	0.998822i	$0.484547\pi$
$14$	−1.02089e45	−0.545661
$15$	−2.01648e46	−0.706299
$16$	9.13439e46	0.250000
$17$	5.80157e48	1.44815	0.724075	−	0.689721i	$-0.242267\pi$
$17$	5.80157e48	1.44815	0.724075	+	0.689721i	$0.242267\pi$
$18$	4.72026e48	0.123226
$19$	−1.76912e50	−0.545746	−0.272873	−	0.962050i	$-0.587974\pi$
$19$	−1.76912e50	−0.545746	−0.272873	+	0.962050i	$0.587974\pi$
$20$	−8.01235e50	−0.325893
$21$	−1.41248e52	−0.836222
$22$	7.04052e51	0.0663603
$23$	−3.63643e53	−0.592141	−0.296071	−	0.955166i	$-0.595676\pi$
$23$	−3.63643e53	−0.592141	−0.296071	+	0.955166i	$0.595676\pi$
$24$	1.26381e54	0.383123
$25$	−9.51547e54	−0.575175
$26$	5.34501e54	0.0686280
$27$	−3.09451e56	−0.894793
$28$	−5.61242e56	−0.385841
$29$	−6.59091e57	−1.13299	−0.566493	−	0.824066i	$-0.691700\pi$
$29$	−6.59091e57	−1.13299	−0.566493	+	0.824066i	$0.691700\pi$
$30$	−1.10857e58	−0.499429
$31$	−5.88368e58	−0.725876	−0.362938	−	0.931813i	$-0.618226\pi$
$31$	−5.88368e58	−0.725876	−0.362938	+	0.931813i	$0.618226\pi$
$32$	5.02168e58	0.176777
$33$	9.74109e58	0.101697
$34$	3.18945e60	1.02400
$35$	4.92301e60	0.502971
$36$	2.59499e60	0.0871339
$37$	−9.06879e61	−1.03177	−0.515883	−	0.856659i	$-0.672536\pi$
$37$	−9.06879e61	−1.03177	−0.515883	+	0.856659i	$0.672536\pi$
$38$	−9.72584e61	−0.385900
$39$	7.39524e61	0.105172
$40$	−4.40484e62	−0.230441
$41$	−9.50622e63	−1.87519	−0.937595	−	0.347729i	$-0.886953\pi$
$41$	−9.50622e63	−1.87519	−0.937595	+	0.347729i	$0.886953\pi$
$42$	−7.76521e63	−0.591298
$43$	2.02221e64	0.607887	0.303944	−	0.952690i	$-0.401697\pi$
$43$	2.02221e64	0.607887	0.303944	+	0.952690i	$0.401697\pi$
$44$	3.87056e63	0.0469238
$45$	−2.27623e64	−0.113585
$46$	−1.99915e65	−0.418707
$47$	−1.19680e66	−1.07191	−0.535954	−	0.844247i	$-0.680048\pi$
$47$	−1.19680e66	−1.07191	−0.535954	+	0.844247i	$0.680048\pi$
$48$	6.94788e65	0.270909
$49$	−2.34246e66	−0.404508
$50$	−5.23119e66	−0.406710
$51$	4.41285e67	1.56927
$52$	2.93845e66	0.0485274
$53$	2.24366e68	1.74607	0.873033	−	0.487662i	$-0.162150\pi$
$53$	2.24366e68	1.74607	0.873033	+	0.487662i	$0.162150\pi$
$54$	−1.70122e68	−0.632715
$55$	−3.39512e67	−0.0611686
$56$	−3.08546e68	−0.272831
$57$	−1.34565e69	−0.591390
$58$	−3.62339e69	−0.801143
$59$	4.05370e69	0.456244	0.228122	−	0.973633i	$-0.426741\pi$
$59$	4.05370e69	0.456244	0.228122	+	0.973633i	$0.426741\pi$
$60$	−6.09443e69	−0.353150
$61$	2.62524e70	0.791845	0.395922	−	0.918284i	$-0.370425\pi$
$61$	2.62524e70	0.791845	0.395922	+	0.918284i	$0.370425\pi$
$62$	−3.23459e70	−0.513272
$63$	−1.59444e70	−0.134479
$64$	2.76070e70	0.125000
$65$	−2.57750e70	−0.0632589
$66$	5.35522e70	0.0719105
$67$	3.14459e71	0.233136	0.116568	−	0.993183i	$-0.462811\pi$
$67$	3.14459e71	0.233136	0.116568	+	0.993183i	$0.462811\pi$
$68$	1.75342e72	0.724075
$69$	−2.76597e72	−0.641666
$70$	2.70645e72	0.355654
$71$	−1.14540e73	−0.859511	−0.429756	−	0.902945i	$-0.641400\pi$
$71$	−1.14540e73	−0.859511	−0.429756	+	0.902945i	$0.641400\pi$
$72$	1.42661e72	0.0616130
$73$	−2.75743e73	−0.690639	−0.345320	−	0.938485i	$-0.612230\pi$
$73$	−2.75743e73	−0.690639	−0.345320	+	0.938485i	$0.612230\pi$
$74$	−4.98562e73	−0.729569
$75$	−7.23775e73	−0.623280
$76$	−5.34684e73	−0.272873
$77$	−2.37818e73	−0.0724205
$78$	4.06558e73	0.0743678
$79$	9.08613e74	1.00487	0.502434	−	0.864616i	$-0.332438\pi$
$79$	9.08613e74	1.00487	0.502434	+	0.864616i	$0.332438\pi$
$80$	−2.42158e74	−0.162947
$81$	−2.77681e75	−1.14390
$82$	−5.22610e75	−1.32596
$83$	−1.14994e76	−1.80756	−0.903779	−	0.428000i	$-0.859218\pi$
$83$	−1.14994e76	−1.80756	−0.903779	+	0.428000i	$0.859218\pi$
$84$	−4.26897e75	−0.418111
$85$	−1.53803e76	−0.943884
$86$	1.11172e76	0.429841
$87$	−5.01324e76	−1.22775
$88$	2.12787e75	0.0331802
$89$	−1.62121e77	−1.61783	−0.808917	−	0.587923i	$-0.799946\pi$
$89$	−1.62121e77	−1.61783	−0.808917	+	0.587923i	$0.799946\pi$
$90$	−1.25137e76	−0.0803170
$91$	−1.80547e76	−0.0748953
$92$	−1.09904e77	−0.296071
$93$	−4.47530e77	−0.786586
$94$	−6.57950e77	−0.757953
$95$	4.69005e77	0.355709
$96$	3.81964e77	0.191562
$97$	1.53312e78	0.510613	0.255306	−	0.966860i	$-0.417824\pi$
$97$	1.53312e78	0.510613	0.255306	+	0.966860i	$0.417824\pi$
$98$	−1.28778e78	−0.286030
$99$	1.09959e77	0.0163546
$100$	−2.87587e78	−0.287587
$101$	−4.96241e78	−0.334964	−0.167482	−	0.985875i	$-0.553564\pi$
$101$	−4.96241e78	−0.334964	−0.167482	+	0.985875i	$0.553564\pi$
$102$	2.42599e79	1.10964
$103$	5.86895e79	1.82595	0.912977	−	0.408011i	$-0.133778\pi$
$103$	5.86895e79	1.82595	0.912977	+	0.408011i	$0.133778\pi$
$104$	1.61543e78	0.0343140
$105$	3.74459e79	0.545038
$106$	1.23347e80	1.23465
$107$	1.14263e80	0.789308	0.394654	−	0.918830i	$-0.370864\pi$
$107$	1.14263e80	0.789308	0.394654	+	0.918830i	$0.370864\pi$
$108$	−9.35257e79	−0.447397
$109$	7.14271e79	0.237420	0.118710	−	0.992929i	$-0.462124\pi$
$109$	7.14271e79	0.237420	0.118710	+	0.992929i	$0.462124\pi$
$110$	−1.86649e79	−0.0432527
$111$	−6.89799e80	−1.11806
$112$	−1.69625e80	−0.192920
$113$	1.77984e80	0.142490	0.0712449	−	0.997459i	$-0.477303\pi$
$113$	1.77984e80	0.142490	0.0712449	+	0.997459i	$0.477303\pi$
$114$	−7.39776e80	−0.418176
$115$	9.64040e80	0.385949
$116$	−1.99198e81	−0.566493
$117$	8.34786e79	0.0169135
$118$	2.22855e81	0.322613
$119$	−1.07735e82	−1.11751
$120$	−3.35045e81	−0.249714
$121$	−1.84578e82	−0.991193
$122$	1.44324e82	0.559919
$123$	−7.23071e82	−2.03202
$124$	−1.77823e82	−0.362938
$125$	6.90843e82	1.02668
$126$	−8.76550e81	−0.0950912
$127$	1.79973e83	1.42876	0.714381	−	0.699757i	$-0.246709\pi$
$127$	1.79973e83	1.42876	0.714381	+	0.699757i	$0.246709\pi$
$128$	1.51771e82	0.0883883
$129$	1.53815e83	0.658729
$130$	−1.41700e82	−0.0447308
$131$	2.21880e83	0.517490	0.258745	−	0.965946i	$-0.416691\pi$
$131$	2.21880e83	0.517490	0.258745	+	0.965946i	$0.416691\pi$
$132$	2.94407e82	0.0508484
$133$	3.28525e83	0.421142
$134$	1.72876e83	0.164852
$135$	8.20374e83	0.583214
$136$	9.63952e83	0.511998
$137$	1.95925e84	0.779162	0.389581	−	0.920992i	$-0.372620\pi$
$137$	1.95925e84	0.779162	0.389581	+	0.920992i	$0.372620\pi$
$138$	−1.52061e84	−0.453726
$139$	−6.77992e84	−1.52104	−0.760519	−	0.649316i	$-0.775055\pi$
$139$	−6.77992e84	−1.52104	−0.760519	+	0.649316i	$0.775055\pi$
$140$	1.48789e84	0.251486
$141$	−9.10324e84	−1.16156
$142$	−6.29689e84	−0.607766
$143$	1.24513e83	0.00910836
$144$	7.84288e83	0.0435670
$145$	1.74729e85	0.738465
$146$	−1.51591e85	−0.488356
$147$	−1.78175e85	−0.438340
$148$	−2.74087e85	−0.515883
$149$	3.82174e85	0.551320	0.275660	−	0.961255i	$-0.411104\pi$
$149$	3.82174e85	0.551320	0.275660	+	0.961255i	$0.411104\pi$
$150$	−3.97899e85	−0.440726
$151$	−4.09858e85	−0.349176	−0.174588	−	0.984642i	$-0.555859\pi$
$151$	−4.09858e85	−0.349176	−0.174588	+	0.984642i	$0.555859\pi$
$152$	−2.93946e85	−0.192950
$153$	4.98129e85	0.252366
$154$	−1.30742e85	−0.0512090
$155$	1.55980e86	0.473116
$156$	2.23507e85	0.0525860
$157$	4.89833e86	0.895388	0.447694	−	0.894187i	$-0.352245\pi$
$157$	4.89833e86	0.895388	0.447694	+	0.894187i	$0.352245\pi$
$158$	4.99515e86	0.710549
$159$	1.70659e87	1.89210
$160$	−1.33128e86	−0.115221
$161$	6.75282e86	0.456944
$162$	−1.52657e87	−0.808858
$163$	−5.59731e86	−0.232578	−0.116289	−	0.993215i	$-0.537100\pi$
$163$	−5.59731e86	−0.232578	−0.116289	+	0.993215i	$0.537100\pi$
$164$	−2.87308e87	−0.937595
$165$	−2.58243e86	−0.0662845
$166$	−6.32188e87	−1.27814
$167$	7.11513e87	1.13470	0.567352	−	0.823476i	$-0.307968\pi$
$167$	7.11513e87	1.13470	0.567352	+	0.823476i	$0.307968\pi$
$168$	−2.34689e87	−0.295649
$169$	−9.94064e87	−0.990580
$170$	−8.45544e87	−0.667427
$171$	−1.51899e87	−0.0951059
$172$	6.11176e87	0.303944
$173$	1.42338e88	0.562990	0.281495	−	0.959563i	$-0.409170\pi$
$173$	1.42338e88	0.562990	0.281495	+	0.959563i	$0.409170\pi$
$174$	−2.75606e88	−0.868147
$175$	1.76702e88	0.443852
$176$	1.16981e87	0.0234619
$177$	3.08336e88	0.494403
$178$	−8.91269e88	−1.14398
$179$	2.86107e88	0.294330	0.147165	−	0.989112i	$-0.452985\pi$
$179$	2.86107e88	0.294330	0.147165	+	0.989112i	$0.452985\pi$
$180$	−6.87949e87	−0.0567927
$181$	2.53194e89	1.67938	0.839692	−	0.543062i	$-0.182735\pi$
$181$	2.53194e89	1.67938	0.839692	+	0.543062i	$0.182735\pi$
$182$	−9.92566e87	−0.0529590
$183$	1.99683e89	0.858072
$184$	−6.04205e88	−0.209353
$185$	2.40420e89	0.672491
$186$	−2.46032e89	−0.556200
$187$	7.42986e88	0.135906
$188$	−3.61712e89	−0.535954
$189$	5.74648e89	0.690495
$190$	2.57838e89	0.251525
$191$	−1.06863e90	−0.847250	−0.423625	−	0.905838i	$-0.639242\pi$
$191$	−1.06863e90	−0.847250	−0.423625	+	0.905838i	$0.639242\pi$
$192$	2.09987e89	0.135455
$193$	−1.46911e90	−0.771862	−0.385931	−	0.922528i	$-0.626120\pi$
$193$	−1.46911e90	−0.771862	−0.385931	+	0.922528i	$0.626120\pi$
$194$	8.42839e89	0.361058
$195$	−1.96053e89	−0.0685497
$196$	−7.07965e89	−0.202254
$197$	−4.21707e90	−0.985361	−0.492680	−	0.870210i	$-0.663983\pi$
$197$	−4.21707e90	−0.985361	−0.492680	+	0.870210i	$0.663983\pi$
$198$	6.04506e88	0.0115645
$199$	−1.10898e91	−1.73872	−0.869358	−	0.494183i	$-0.835467\pi$
$199$	−1.10898e91	−1.73872	−0.869358	+	0.494183i	$0.835467\pi$
$200$	−1.58103e90	−0.203355
$201$	2.39187e90	0.252635
$202$	−2.72811e90	−0.236856
$203$	1.22393e91	0.874304
$204$	1.33370e91	0.784634
$205$	2.52016e91	1.22222
$206$	3.22649e91	1.29114
$207$	−3.12227e90	−0.103191
$208$	8.88093e89	0.0242637
$209$	−2.26565e90	−0.0512170
$210$	2.05861e91	0.385400
$211$	−8.61013e91	−1.33614	−0.668071	−	0.744098i	$-0.732880\pi$
$211$	−8.61013e91	−1.33614	−0.668071	+	0.744098i	$0.732880\pi$
$212$	6.78105e91	0.873033
$213$	−8.71223e91	−0.931398
$214$	6.28168e91	0.558125
$215$	−5.36102e91	−0.396212
$216$	−5.14163e91	−0.316357
$217$	1.09260e92	0.560145
$218$	3.92675e91	0.167881
$219$	−2.09738e92	−0.748402
$220$	−1.02611e91	−0.0305843
$221$	5.64060e91	0.140550
$222$	−3.79221e92	−0.790588
$223$	−2.22142e91	−0.0387783	−0.0193892	−	0.999812i	$-0.506172\pi$
$223$	−2.22142e91	−0.0387783	−0.0193892	+	0.999812i	$0.506172\pi$
$224$	−9.32523e91	−0.136415
$225$	−8.17009e91	−0.100234
$226$	9.78480e91	0.100755
$227$	−1.60869e93	−1.39140	−0.695698	−	0.718335i	$-0.744905\pi$
$227$	−1.60869e93	−1.39140	−0.695698	+	0.718335i	$0.744905\pi$
$228$	−4.06696e92	−0.295695
$229$	1.79947e93	1.10064	0.550318	−	0.834955i	$-0.314507\pi$
$229$	1.79947e93	1.10064	0.550318	+	0.834955i	$0.314507\pi$
$230$	5.29986e92	0.272907
$231$	−1.80892e92	−0.0784775
$232$	−1.09510e93	−0.400571
$233$	6.04403e93	1.86538	0.932691	−	0.360677i	$-0.117454\pi$
$233$	6.04403e93	1.86538	0.932691	+	0.360677i	$0.117454\pi$
$234$	4.58929e91	0.0119597
$235$	3.17280e93	0.698655
$236$	1.22516e93	0.228122
$237$	6.91118e93	1.08891
$238$	−5.92279e93	−0.790199
$239$	−7.72957e93	−0.873853	−0.436926	−	0.899497i	$-0.643933\pi$
$239$	−7.72957e93	−0.873853	−0.436926	+	0.899497i	$0.643933\pi$
$240$	−1.84193e93	−0.176575
$241$	1.51645e94	1.23355	0.616773	−	0.787141i	$-0.288440\pi$
$241$	1.51645e94	1.23355	0.616773	+	0.787141i	$0.288440\pi$
$242$	−1.01473e94	−0.700879
$243$	−5.87470e93	−0.344777
$244$	7.93429e93	0.395922
$245$	6.21002e93	0.263653
$246$	−3.97512e94	−1.43686
$247$	−1.72003e93	−0.0529672
$248$	−9.77595e93	−0.256636
$249$	−8.74681e94	−1.95873
$250$	3.79795e94	0.725970
$251$	8.82095e92	0.0144013	0.00720067	−	0.999974i	$-0.497708\pi$
$251$	8.82095e92	0.0144013	0.00720067	+	0.999974i	$0.497708\pi$
$252$	−4.81888e93	−0.0672396
$253$	−4.65703e93	−0.0555711
$254$	9.89410e94	1.01029
$255$	−1.16987e95	−1.02283
$256$	8.34370e93	0.0625000
$257$	1.61155e95	1.03487	0.517435	−	0.855723i	$-0.326887\pi$
$257$	1.61155e95	1.03487	0.517435	+	0.855723i	$0.326887\pi$
$258$	8.45610e94	0.465791
$259$	1.68407e95	0.796195
$260$	−7.79003e93	−0.0316295
$261$	−5.65903e94	−0.197443
$262$	1.21980e95	0.365921
$263$	4.78228e95	1.23419	0.617096	−	0.786888i	$-0.288309\pi$
$263$	4.78228e95	1.23419	0.617096	+	0.786888i	$0.288309\pi$
$264$	1.61852e94	0.0359552
$265$	−5.94809e95	−1.13806
$266$	1.80608e95	0.297792
$267$	−1.23314e96	−1.75314
$268$	9.50394e94	0.116568
$269$	3.32626e95	0.352161	0.176080	−	0.984376i	$-0.443658\pi$
$269$	3.32626e95	0.352161	0.176080	+	0.984376i	$0.443658\pi$
$270$	4.51005e95	0.412394
$271$	1.95121e95	0.154176	0.0770882	−	0.997024i	$-0.475438\pi$
$271$	1.95121e95	0.154176	0.0770882	+	0.997024i	$0.475438\pi$
$272$	5.29938e95	0.362037
$273$	−1.37329e95	−0.0811593
$274$	1.07711e96	0.550951
$275$	−1.21861e95	−0.0539788
$276$	−8.35964e95	−0.320833
$277$	−4.41915e96	−1.47024	−0.735119	−	0.677938i	$-0.762874\pi$
$277$	−4.41915e96	−1.47024	−0.735119	+	0.677938i	$0.762874\pi$
$278$	−3.72730e96	−1.07554
$279$	−5.05179e95	−0.126497
$280$	8.17975e95	0.177827
$281$	−3.47444e96	−0.656123	−0.328061	−	0.944656i	$-0.606395\pi$
$281$	−3.47444e96	−0.656123	−0.328061	+	0.944656i	$0.606395\pi$
$282$	−5.00456e96	−0.821346
$283$	1.17873e97	1.68209	0.841046	−	0.540964i	$-0.181940\pi$
$283$	1.17873e97	1.68209	0.841046	+	0.540964i	$0.181940\pi$
$284$	−3.46175e96	−0.429756
$285$	3.56739e96	0.385460
$286$	6.84516e94	0.00644058
$287$	1.76530e97	1.44705
$288$	4.31167e95	0.0308065
$289$	1.76086e97	1.09714
$290$	9.60585e96	0.522174
$291$	1.16613e97	0.553318
$292$	−8.33382e96	−0.345320
$293$	−9.28581e96	−0.336162	−0.168081	−	0.985773i	$-0.553757\pi$
$293$	−9.28581e96	−0.336162	−0.168081	+	0.985773i	$0.553757\pi$
$294$	−9.79525e96	−0.309953
$295$	−1.07466e97	−0.297374
$296$	−1.50681e97	−0.364785
$297$	−3.96302e96	−0.0839743
$298$	2.10103e97	0.389842
$299$	−3.53552e96	−0.0574701
$300$	−2.18748e97	−0.311640
$301$	−3.75524e97	−0.469095
$302$	−2.25322e97	−0.246905
$303$	−3.77456e97	−0.362979
$304$	−1.61598e97	−0.136436
$305$	−6.95967e97	−0.516113
$306$	2.73850e97	0.178450
$307$	−2.56749e98	−1.47076	−0.735382	−	0.677653i	$-0.762997\pi$
$307$	−2.56749e98	−1.47076	−0.735382	+	0.677653i	$0.762997\pi$
$308$	−7.18761e96	−0.0362102
$309$	4.46409e98	1.97867
$310$	8.57510e97	0.334543
$311$	−1.55032e98	−0.532581	−0.266290	−	0.963893i	$-0.585798\pi$
$311$	−1.55032e98	−0.532581	−0.266290	+	0.963893i	$0.585798\pi$
$312$	1.22874e97	0.0371839
$313$	−1.78061e98	−0.474861	−0.237431	−	0.971405i	$-0.576305\pi$
$313$	−1.78061e98	−0.474861	−0.237431	+	0.971405i	$0.576305\pi$
$314$	2.69288e98	0.633135
$315$	4.22695e97	0.0876517
$316$	2.74612e98	0.502434
$317$	−2.78466e98	−0.449709	−0.224855	−	0.974392i	$-0.572191\pi$
$317$	−2.78466e98	−0.449709	−0.224855	+	0.974392i	$0.572191\pi$
$318$	9.38210e98	1.33792
$319$	−8.44074e97	−0.106328
$320$	−7.31879e97	−0.0814733
$321$	8.69119e98	0.855323
$322$	3.71240e98	0.323108
$323$	−1.02637e99	−0.790321
$324$	−8.39239e98	−0.571949
$325$	−9.25144e97	−0.0558234
$326$	−3.07715e98	−0.164457
$327$	5.43296e98	0.257276
$328$	−1.57949e99	−0.662980
$329$	2.22246e99	0.827171
$330$	−1.41970e98	−0.0468702
$331$	−4.91173e98	−0.143889	−0.0719447	−	0.997409i	$-0.522921\pi$
$331$	−4.91173e98	−0.143889	−0.0719447	+	0.997409i	$0.522921\pi$
$332$	−3.47549e99	−0.903779
$333$	−7.78656e98	−0.179804
$334$	3.91159e99	0.802356
$335$	−8.33651e98	−0.151955
$336$	−1.29022e99	−0.209055
$337$	−8.39998e99	−1.21031	−0.605156	−	0.796107i	$-0.706889\pi$
$337$	−8.39998e99	−1.21031	−0.605156	+	0.796107i	$0.706889\pi$
$338$	−5.46493e99	−0.700446
$339$	1.35380e99	0.154407
$340$	−4.64842e99	−0.471942
$341$	−7.53501e98	−0.0681218
$342$	−8.35071e98	−0.0672500
$343$	1.51036e100	1.08383
$344$	3.35998e99	0.214921
$345$	7.33277e99	0.418229
$346$	7.82513e99	0.398094
$347$	3.42021e100	1.55252	0.776262	−	0.630411i	$-0.217113\pi$
$347$	3.42021e100	1.55252	0.776262	+	0.630411i	$0.217113\pi$
$348$	−1.51516e100	−0.613873
$349$	3.77841e100	1.36680	0.683399	−	0.730045i	$-0.260501\pi$
$349$	3.77841e100	1.36680	0.683399	+	0.730045i	$0.260501\pi$
$350$	9.71428e99	0.313851
$351$	−3.00864e99	−0.0868439
$352$	6.43108e98	0.0165901
$353$	−4.09635e100	−0.944706	−0.472353	−	0.881410i	$-0.656595\pi$
$353$	−4.09635e100	−0.944706	−0.472353	+	0.881410i	$0.656595\pi$
$354$	1.69510e100	0.349595
$355$	3.03652e100	0.560217
$356$	−4.89980e100	−0.808917
$357$	−8.19463e100	−1.21097
$358$	1.57289e100	0.208122
$359$	−1.14485e101	−1.35680	−0.678402	−	0.734691i	$-0.737327\pi$
$359$	−1.14485e101	−1.35680	−0.678402	+	0.734691i	$0.737327\pi$
$360$	−3.78204e99	−0.0401585
$361$	−7.37856e100	−0.702162
$362$	1.39195e101	1.18750
$363$	−1.40396e101	−1.07409
$364$	−5.45669e99	−0.0374476
$365$	7.31012e100	0.450149
$366$	1.09777e101	0.606748
$367$	1.62596e101	0.806866	0.403433	−	0.915009i	$-0.367817\pi$
$367$	1.62596e101	0.806866	0.403433	+	0.915009i	$0.367817\pi$
$368$	−3.32165e100	−0.148035
$369$	−8.16214e100	−0.326785
$370$	1.32172e101	0.475523
$371$	−4.16647e101	−1.34741
$372$	−1.35258e101	−0.393293
$373$	−3.50179e100	−0.0915781	−0.0457890	−	0.998951i	$-0.514580\pi$
$373$	−3.50179e100	−0.0915781	−0.0457890	+	0.998951i	$0.514580\pi$
$374$	4.08461e100	0.0960997
$375$	5.25476e101	1.11254
$376$	−1.98853e101	−0.378977
$377$	−6.40803e100	−0.109962
$378$	3.15916e101	0.488254
$379$	1.04790e102	1.45905	0.729524	−	0.683955i	$-0.239741\pi$
$379$	1.04790e102	1.45905	0.729524	+	0.683955i	$0.239741\pi$
$380$	1.41748e101	0.177855
$381$	1.36893e102	1.54826
$382$	−5.87488e101	−0.599096
$383$	−1.41594e102	−1.30224	−0.651121	−	0.758974i	$-0.725701\pi$
$383$	−1.41594e102	−1.30224	−0.651121	+	0.758974i	$0.725701\pi$
$384$	1.15441e101	0.0957808
$385$	6.30471e100	0.0472027
$386$	−8.07650e101	−0.545789
$387$	1.73629e101	0.105935
$388$	4.63356e101	0.255306
$389$	−4.18185e99	−0.00208142	−0.00104071	−	0.999999i	$-0.500331\pi$
$389$	−4.18185e99	−0.00208142	−0.00104071	+	0.999999i	$0.500331\pi$
$390$	−1.07781e101	−0.0484719
$391$	−2.10970e102	−0.857509
$392$	−3.89208e101	−0.143015
$393$	1.68769e102	0.560771
$394$	−2.31836e102	−0.696755
$395$	−2.40879e102	−0.654959
$396$	3.32331e100	0.00817732
$397$	2.75148e102	0.612833	0.306416	−	0.951898i	$-0.400870\pi$
$397$	2.75148e102	0.612833	0.306416	+	0.951898i	$0.400870\pi$
$398$	−6.09670e102	−1.22946
$399$	2.49886e102	0.456364
$400$	−8.69180e101	−0.143794
$401$	−3.11049e102	−0.466258	−0.233129	−	0.972446i	$-0.574896\pi$
$401$	−3.11049e102	−0.466258	−0.233129	+	0.972446i	$0.574896\pi$
$402$	1.31494e102	0.178640
$403$	−5.72043e101	−0.0704497
$404$	−1.49980e102	−0.167482
$405$	7.36149e102	0.745577
$406$	6.72862e102	0.618227
$407$	−1.16141e102	−0.0968289
$408$	7.33210e102	0.554820
$409$	−7.44587e102	−0.511499	−0.255749	−	0.966743i	$-0.582322\pi$
$409$	−7.44587e102	−0.511499	−0.255749	+	0.966743i	$0.582322\pi$
$410$	1.38547e103	0.864242
$411$	1.49026e103	0.844328
$412$	1.77378e103	0.912977
$413$	−7.52770e102	−0.352075
$414$	−1.71649e102	−0.0729671
$415$	3.04858e103	1.17814
$416$	4.88234e101	0.0171570
$417$	−5.15701e103	−1.64825
$418$	−1.24555e102	−0.0362159
$419$	−2.51989e103	−0.666696	−0.333348	−	0.942804i	$-0.608178\pi$
$419$	−2.51989e103	−0.666696	−0.333348	+	0.942804i	$0.608178\pi$
$420$	1.13173e103	0.272519
$421$	−1.54376e103	−0.338404	−0.169202	−	0.985581i	$-0.554119\pi$
$421$	−1.54376e103	−0.338404	−0.169202	+	0.985581i	$0.554119\pi$
$422$	−4.73347e103	−0.944795
$423$	−1.02759e103	−0.186799
$424$	3.72792e103	0.617327
$425$	−5.52047e103	−0.832940
$426$	−4.78960e103	−0.658598
$427$	−4.87505e103	−0.611052
$428$	3.45339e103	0.394654
$429$	9.47080e101	0.00987015
$430$	−2.94725e103	−0.280164
$431$	7.28283e103	0.631609	0.315804	−	0.948824i	$-0.397726\pi$
$431$	7.28283e103	0.631609	0.315804	+	0.948824i	$0.397726\pi$
$432$	−2.82664e103	−0.223698
$433$	1.57500e104	1.13765	0.568826	−	0.822458i	$-0.307398\pi$
$433$	1.57500e104	1.13765	0.568826	+	0.822458i	$0.307398\pi$
$434$	6.00661e103	0.396082
$435$	1.32904e104	0.800227
$436$	2.15875e103	0.118710
$437$	6.43328e103	0.323158
$438$	−1.15305e104	−0.529200
$439$	−3.12712e104	−1.31158	−0.655791	−	0.754943i	$-0.727665\pi$
$439$	−3.12712e104	−1.31158	−0.655791	+	0.754943i	$0.727665\pi$
$440$	−5.64111e102	−0.0216264
$441$	−2.01126e103	−0.0704928
$442$	3.10095e103	0.0993837
$443$	1.81541e104	0.532141	0.266070	−	0.963954i	$-0.414275\pi$
$443$	1.81541e104	0.532141	0.266070	+	0.963954i	$0.414275\pi$
$444$	−2.08479e104	−0.559030
$445$	4.29793e104	1.05448
$446$	−1.22124e103	−0.0274204
$447$	2.90693e104	0.597431
$448$	−5.12660e103	−0.0964601
$449$	7.43824e104	1.28156	0.640781	−	0.767723i	$-0.278611\pi$
$449$	7.43824e104	1.28156	0.640781	+	0.767723i	$0.278611\pi$
$450$	−4.49155e103	−0.0708765
$451$	−1.21743e104	−0.175982
$452$	5.37925e103	0.0712449
$453$	−3.11750e104	−0.378380
$454$	−8.84386e104	−0.983865
$455$	4.78641e103	0.0488157
$456$	−2.23584e104	−0.209088
$457$	−7.65689e104	−0.656693	−0.328347	−	0.944557i	$-0.606491\pi$
$457$	−7.65689e104	−0.656693	−0.328347	+	0.944557i	$0.606491\pi$
$458$	9.89270e104	0.778267
$459$	−1.79530e105	−1.29579
$460$	2.91363e104	0.192975
$461$	−1.66389e105	−1.01143	−0.505717	−	0.862700i	$-0.668772\pi$
$461$	−1.66389e105	−1.01143	−0.505717	+	0.862700i	$0.668772\pi$
$462$	−9.94462e103	−0.0554920
$463$	−1.71678e105	−0.879561	−0.439780	−	0.898105i	$-0.644944\pi$
$463$	−1.71678e105	−0.879561	−0.439780	+	0.898105i	$0.644944\pi$
$464$	−6.02040e104	−0.283247
$465$	1.18643e105	0.512685
$466$	3.32274e105	1.31902
$467$	−9.15884e104	−0.334059	−0.167030	−	0.985952i	$-0.553418\pi$
$467$	−9.15884e104	−0.334059	−0.167030	+	0.985952i	$0.553418\pi$
$468$	2.52299e103	0.00845676
$469$	−5.83948e104	−0.179907
$470$	1.74427e105	0.494023
$471$	3.72581e105	0.970275
$472$	6.73537e104	0.161307
$473$	2.58977e104	0.0570488
$474$	3.79946e105	0.769977
$475$	1.68340e105	0.313899
$476$	−3.25609e105	−0.558755
$477$	1.92643e105	0.304283
$478$	−4.24938e105	−0.617907
$479$	4.15143e105	0.555834	0.277917	−	0.960605i	$-0.410356\pi$
$479$	4.15143e105	0.555834	0.277917	+	0.960605i	$0.410356\pi$
$480$	−1.01261e105	−0.124857
$481$	−8.81716e104	−0.100138
$482$	8.33678e105	0.872249
$483$	5.13639e105	0.495161
$484$	−5.57853e105	−0.495596
$485$	−4.06439e105	−0.332810
$486$	−3.22965e105	−0.243794
$487$	−8.11230e105	−0.564612	−0.282306	−	0.959324i	$-0.591099\pi$
$487$	−8.11230e105	−0.564612	−0.282306	+	0.959324i	$0.591099\pi$
$488$	4.36192e105	0.279959
$489$	−4.25748e105	−0.252030
$490$	3.41399e105	0.186431
$491$	−4.62762e105	−0.233152	−0.116576	−	0.993182i	$-0.537192\pi$
$491$	−4.62762e105	−0.233152	−0.116576	+	0.993182i	$0.537192\pi$
$492$	−2.18535e106	−1.01601
$493$	−3.82377e106	−1.64073
$494$	−9.45598e104	−0.0374535
$495$	−2.91508e104	−0.0106597
$496$	−5.37438e105	−0.181469
$497$	2.12700e106	0.663269
$498$	−4.80861e106	−1.38503
$499$	4.53291e106	1.20616	0.603081	−	0.797680i	$-0.293940\pi$
$499$	4.53291e106	1.20616	0.603081	+	0.797680i	$0.293940\pi$
$500$	2.08794e106	0.513339
$501$	5.41198e106	1.22961
$502$	4.84937e104	0.0101833
$503$	4.84227e106	0.939969	0.469984	−	0.882675i	$-0.344260\pi$
$503$	4.84227e106	0.939969	0.469984	+	0.882675i	$0.344260\pi$
$504$	−2.64921e105	−0.0475456
$505$	1.31557e106	0.218325
$506$	−2.56023e105	−0.0392947
$507$	−7.56115e106	−1.07343
$508$	5.43934e106	0.714381
$509$	−1.80631e106	−0.219503	−0.109752	−	0.993959i	$-0.535006\pi$
$509$	−1.80631e106	−0.219503	−0.109752	+	0.993959i	$0.535006\pi$
$510$	−6.43145e106	−0.723248
$511$	5.12053e106	0.532953
$512$	4.58700e105	0.0441942
$513$	5.47456e106	0.488330
$514$	8.85959e106	0.731763
$515$	−1.55590e107	−1.19013
$516$	4.64879e106	0.329364
$517$	−1.53270e106	−0.100596
$518$	9.25827e106	0.562995
$519$	1.08267e107	0.610077
$520$	−4.28261e105	−0.0223654
$521$	−1.62831e107	−0.788220	−0.394110	−	0.919063i	$-0.628947\pi$
$521$	−1.62831e107	−0.788220	−0.394110	+	0.919063i	$0.628947\pi$
$522$	−3.11109e106	−0.139613
$523$	−2.15324e107	−0.895932	−0.447966	−	0.894051i	$-0.647851\pi$
$523$	−2.15324e107	−0.895932	−0.447966	+	0.894051i	$0.647851\pi$
$524$	6.70592e106	0.258745
$525$	1.34405e107	0.480974
$526$	2.62909e107	0.872706
$527$	−3.41346e107	−1.05118
$528$	8.89789e105	0.0254242
$529$	−2.44901e107	−0.649369
$530$	−3.27000e107	−0.804731
$531$	3.48055e106	0.0795087
$532$	9.92905e106	0.210571
$533$	−9.24244e106	−0.181996
$534$	−6.77926e107	−1.23966
$535$	−3.02919e107	−0.514460
$536$	5.22485e106	0.0824260
$537$	2.17622e107	0.318946
$538$	1.82863e107	0.249015
$539$	−2.99990e106	−0.0379622
$540$	2.47943e107	0.291607
$541$	1.13893e108	1.24510	0.622550	−	0.782580i	$-0.286097\pi$
$541$	1.13893e108	1.24510	0.622550	+	0.782580i	$0.286097\pi$
$542$	1.07269e107	0.109019
$543$	1.92587e108	1.81984
$544$	2.91337e107	0.255999
$545$	−1.89358e107	−0.154747
$546$	−7.54975e106	−0.0573883
$547$	1.69864e107	0.120116	0.0600580	−	0.998195i	$-0.480871\pi$
$547$	1.69864e107	0.120116	0.0600580	+	0.998195i	$0.480871\pi$
$548$	5.92147e107	0.389581
$549$	2.25406e107	0.137993
$550$	−6.69938e106	−0.0381688
$551$	1.16601e108	0.618322
$552$	−4.59576e107	−0.226863
$553$	−1.68729e108	−0.775438
$554$	−2.42945e108	−1.03962
$555$	1.82870e108	0.728736
$556$	−2.04911e108	−0.760519
$557$	−3.33058e108	−1.15143	−0.575717	−	0.817649i	$-0.695277\pi$
$557$	−3.33058e108	−1.15143	−0.575717	+	0.817649i	$0.695277\pi$
$558$	−2.77725e107	−0.0894468
$559$	1.96610e107	0.0589983
$560$	4.49687e107	0.125743
$561$	5.65137e107	0.147272
$562$	−1.91009e108	−0.463949
$563$	−9.48166e107	−0.214686	−0.107343	−	0.994222i	$-0.534234\pi$
$563$	−9.48166e107	−0.214686	−0.107343	+	0.994222i	$0.534234\pi$
$564$	−2.75129e108	−0.580779
$565$	−4.71848e107	−0.0928728
$566$	6.48013e108	1.18942
$567$	5.15651e108	0.882725
$568$	−1.90312e108	−0.303883
$569$	−6.27566e108	−0.934813	−0.467407	−	0.884042i	$-0.654812\pi$
$569$	−6.27566e108	−0.934813	−0.467407	+	0.884042i	$0.654812\pi$
$570$	1.96119e108	0.272561
$571$	−6.73753e108	−0.873724	−0.436862	−	0.899529i	$-0.643910\pi$
$571$	−6.73753e108	−0.873724	−0.436862	+	0.899529i	$0.643910\pi$
$572$	3.76317e106	0.00455418
$573$	−8.12835e108	−0.918110
$574$	9.70483e108	1.02322
$575$	3.46023e108	0.340585
$576$	2.37037e107	0.0217835
$577$	7.80864e108	0.670086	0.335043	−	0.942203i	$-0.391249\pi$
$577$	7.80864e108	0.670086	0.335043	+	0.942203i	$0.391249\pi$
$578$	9.68046e108	0.775794
$579$	−1.11745e109	−0.836418
$580$	5.28087e108	0.369232
$581$	2.13544e109	1.39486
$582$	6.41089e108	0.391255
$583$	2.87337e108	0.163864
$584$	−4.58156e108	−0.244178
$585$	−2.21307e107	−0.0110240
$586$	−5.10493e108	−0.237702
$587$	−7.66662e108	−0.333733	−0.166866	−	0.985980i	$-0.553365\pi$
$587$	−7.66662e108	−0.333733	−0.166866	+	0.985980i	$0.553365\pi$
$588$	−5.38499e108	−0.219170
$589$	1.04089e109	0.396144
$590$	−5.90802e108	−0.210275
$591$	−3.20763e109	−1.06777
$592$	−8.28379e108	−0.257942
$593$	1.67799e109	0.488798	0.244399	−	0.969675i	$-0.421409\pi$
$593$	1.67799e109	0.488798	0.244399	+	0.969675i	$0.421409\pi$
$594$	−2.17869e108	−0.0593788
$595$	2.85612e109	0.728377
$596$	1.15505e109	0.275660
$597$	−8.43525e109	−1.88414
$598$	−1.94367e108	−0.0406375
$599$	6.70787e109	1.31288	0.656441	−	0.754378i	$-0.272061\pi$
$599$	6.70787e109	1.31288	0.656441	+	0.754378i	$0.272061\pi$
$600$	−1.20258e109	−0.220363
$601$	−6.31266e109	−1.08311	−0.541553	−	0.840667i	$-0.682163\pi$
$601$	−6.31266e109	−1.08311	−0.541553	+	0.840667i	$0.682163\pi$
$602$	−2.06446e109	−0.331700
$603$	2.69998e108	0.0406281
$604$	−1.23872e109	−0.174588
$605$	4.89328e109	0.646046
$606$	−2.07508e109	−0.256665
$607$	−2.26276e109	−0.262231	−0.131116	−	0.991367i	$-0.541856\pi$
$607$	−2.26276e109	−0.262231	−0.131116	+	0.991367i	$0.541856\pi$
$608$	−8.88396e108	−0.0964751
$609$	9.30956e109	0.947428
$610$	−3.82612e109	−0.364947
$611$	−1.16359e109	−0.104034
$612$	1.50550e109	0.126183
$613$	−1.94266e110	−1.52654	−0.763270	−	0.646080i	$-0.776407\pi$
$613$	−1.94266e110	−1.52654	−0.763270	+	0.646080i	$0.776407\pi$
$614$	−1.41149e110	−1.03999
$615$	1.91691e110	1.32445
$616$	−3.95143e108	−0.0256045
$617$	4.39287e109	0.266983	0.133492	−	0.991050i	$-0.457381\pi$
$617$	4.39287e109	0.266983	0.133492	+	0.991050i	$0.457381\pi$
$618$	2.45416e110	1.39913
$619$	2.75144e110	1.47157	0.735784	−	0.677217i	$-0.236814\pi$
$619$	2.75144e110	1.47157	0.735784	+	0.677217i	$0.236814\pi$
$620$	4.71421e109	0.236558
$621$	1.12529e110	0.529844
$622$	−8.52297e109	−0.376592
$623$	3.01058e110	1.24845
$624$	6.75510e108	0.0262930
$625$	−2.57266e109	−0.0939989
$626$	−9.78899e109	−0.335778
$627$	−1.72332e109	−0.0555006
$628$	1.48043e110	0.447694
$629$	−5.26133e110	−1.49415
$630$	2.32379e109	0.0619791
$631$	−4.89104e110	−1.22530	−0.612648	−	0.790356i	$-0.709896\pi$
$631$	−4.89104e110	−1.22530	−0.612648	+	0.790356i	$0.709896\pi$
$632$	1.50969e110	0.355274
$633$	−6.54912e110	−1.44789
$634$	−1.53088e110	−0.317992
$635$	−4.77119e110	−0.931247
$636$	5.15787e110	0.946050
$637$	−2.27746e109	−0.0392594
$638$	−4.64034e109	−0.0751854
$639$	−9.83451e109	−0.149785
$640$	−4.02355e109	−0.0576103
$641$	−1.17078e111	−1.57609	−0.788046	−	0.615617i	$-0.788907\pi$
$641$	−1.17078e111	−1.57609	−0.788046	+	0.615617i	$0.788907\pi$
$642$	4.77803e110	0.604805
$643$	1.54290e111	1.83656	0.918280	−	0.395932i	$-0.129578\pi$
$643$	1.54290e111	1.83656	0.918280	+	0.395932i	$0.129578\pi$
$644$	2.04091e110	0.228472
$645$	−4.07775e110	−0.429350
$646$	−5.64252e110	−0.558842
$647$	1.15657e111	1.07759	0.538796	−	0.842437i	$-0.318880\pi$
$647$	1.15657e111	1.07759	0.538796	+	0.842437i	$0.318880\pi$
$648$	−4.61376e110	−0.404429
$649$	5.19142e109	0.0428174
$650$	−5.08603e109	−0.0394731
$651$	8.31061e110	0.606993
$652$	−1.69168e110	−0.116289
$653$	1.68990e111	1.09343	0.546714	−	0.837320i	$-0.315879\pi$
$653$	1.68990e111	1.09343	0.546714	+	0.837320i	$0.315879\pi$
$654$	2.98680e110	0.181922
$655$	−5.88219e110	−0.337293
$656$	−8.68335e110	−0.468798
$657$	−2.36756e110	−0.120356
$658$	1.22181e111	0.584898
$659$	1.23391e111	0.556300	0.278150	−	0.960538i	$-0.410279\pi$
$659$	1.23391e111	0.556300	0.278150	+	0.960538i	$0.410279\pi$
$660$	−7.80491e109	−0.0331423
$661$	−8.39203e110	−0.335668	−0.167834	−	0.985815i	$-0.553677\pi$
$661$	−8.39203e110	−0.335668	−0.167834	+	0.985815i	$0.553677\pi$
$662$	−2.70025e110	−0.101745
$663$	4.29040e110	0.152305
$664$	−1.91067e111	−0.639068
$665$	−8.70940e110	−0.274494
$666$	−4.28071e110	−0.127140
$667$	2.39674e111	0.670888
$668$	2.15042e111	0.567352
$669$	−1.68968e110	−0.0420216
$670$	−4.58304e110	−0.107448
$671$	3.36204e110	0.0743128
$672$	−7.09305e110	−0.147825
$673$	1.10154e111	0.216474	0.108237	−	0.994125i	$-0.465479\pi$
$673$	1.10154e111	0.216474	0.108237	+	0.994125i	$0.465479\pi$
$674$	−4.61794e111	−0.855819
$675$	2.94457e111	0.514663
$676$	−3.00438e111	−0.495290
$677$	−7.61922e111	−1.18483	−0.592417	−	0.805631i	$-0.701826\pi$
$677$	−7.61922e111	−1.18483	−0.592417	+	0.805631i	$0.701826\pi$
$678$	7.44261e110	0.109182
$679$	−2.84699e111	−0.394030
$680$	−2.55550e111	−0.333713
$681$	−1.22362e112	−1.50777
$682$	−4.14242e110	−0.0481694
$683$	1.15611e112	1.26877	0.634383	−	0.773019i	$-0.281254\pi$
$683$	1.15611e112	1.26877	0.634383	+	0.773019i	$0.281254\pi$
$684$	−4.59085e110	−0.0475530
$685$	−5.19410e111	−0.507847
$686$	8.30328e111	0.766385
$687$	1.36873e112	1.19269
$688$	1.84717e111	0.151972
$689$	2.18140e111	0.169464
$690$	4.03123e111	0.295732
$691$	−1.40879e112	−0.976030	−0.488015	−	0.872835i	$-0.662279\pi$
$691$	−1.40879e112	−0.976030	−0.488015	+	0.872835i	$0.662279\pi$
$692$	4.30191e111	0.281495
$693$	−2.04193e110	−0.0126206
$694$	1.88028e112	1.09780
$695$	1.79740e112	0.991391
$696$	−8.32968e111	−0.434074
$697$	−5.51510e112	−2.71556
$698$	2.07720e112	0.966472
$699$	4.59727e112	2.02140
$700$	5.34048e111	0.221926
$701$	−1.92210e112	−0.754944	−0.377472	−	0.926021i	$-0.623206\pi$
$701$	−1.92210e112	−0.754944	−0.377472	+	0.926021i	$0.623206\pi$
$702$	−1.65402e111	−0.0614079
$703$	1.60438e112	0.563082
$704$	3.53552e110	0.0117310
$705$	2.41333e112	0.757087
$706$	−2.25199e112	−0.668008
$707$	9.21517e111	0.258486
$708$	9.31890e111	0.247201
$709$	−6.34877e112	−1.59281	−0.796404	−	0.604766i	$-0.793267\pi$
$709$	−6.34877e112	−1.59281	−0.796404	+	0.604766i	$0.793267\pi$
$710$	1.66935e112	0.396134
$711$	7.80145e111	0.175116
$712$	−2.69370e112	−0.571990
$713$	2.13956e112	0.429821
$714$	−4.50505e112	−0.856288
$715$	−3.30091e110	−0.00593670
$716$	8.64706e111	0.147165
$717$	−5.87934e112	−0.946939
$718$	−6.29387e112	−0.959406
$719$	−3.22984e112	−0.466004	−0.233002	−	0.972476i	$-0.574855\pi$
$719$	−3.22984e112	−0.466004	−0.233002	+	0.972476i	$0.574855\pi$
$720$	−2.07920e111	−0.0283963
$721$	−1.08986e113	−1.40905
$722$	−4.05641e112	−0.496503
$723$	1.15346e113	1.33672
$724$	7.65233e112	0.839692
$725$	6.27157e112	0.651666
$726$	−7.71833e112	−0.759498
$727$	8.06731e112	0.751829	0.375915	−	0.926654i	$-0.377329\pi$
$727$	8.06731e112	0.751829	0.375915	+	0.926654i	$0.377329\pi$
$728$	−2.99985e111	−0.0264795
$729$	9.21275e112	0.770286
$730$	4.01878e112	0.318303
$731$	1.17320e113	0.880312
$732$	6.03506e112	0.429036
$733$	7.27076e112	0.489748	0.244874	−	0.969555i	$-0.421253\pi$
$733$	7.27076e112	0.489748	0.244874	+	0.969555i	$0.421253\pi$
$734$	8.93884e112	0.570541
$735$	4.72352e112	0.285704
$736$	−1.82610e112	−0.104677
$737$	4.02716e111	0.0218793
$738$	−4.48718e112	−0.231072
$739$	−3.85731e113	−1.88291	−0.941453	−	0.337144i	$-0.890539\pi$
$739$	−3.85731e113	−1.88291	−0.941453	+	0.337144i	$0.890539\pi$
$740$	7.26624e112	0.336246
$741$	−1.30831e112	−0.0573972
$742$	−2.29054e113	−0.952760
$743$	4.29894e113	1.69552	0.847760	−	0.530381i	$-0.177951\pi$
$743$	4.29894e113	1.69552	0.847760	+	0.530381i	$0.177951\pi$
$744$	−7.43587e112	−0.278100
$745$	−1.01317e113	−0.359343
$746$	−1.92513e112	−0.0647555
$747$	−9.87354e112	−0.314999
$748$	2.24554e112	0.0679528
$749$	−2.12186e113	−0.609094
$750$	2.88883e113	0.786688
$751$	−1.59275e113	−0.411501	−0.205750	−	0.978605i	$-0.565963\pi$
$751$	−1.59275e113	−0.411501	−0.205750	+	0.978605i	$0.565963\pi$
$752$	−1.09321e113	−0.267977
$753$	6.70947e111	0.0156058
$754$	−3.52285e112	−0.0777547
$755$	1.08656e113	0.227588
$756$	1.73677e113	0.345248
$757$	−5.65100e113	−1.06620	−0.533099	−	0.846053i	$-0.678973\pi$
$757$	−5.65100e113	−1.06620	−0.533099	+	0.846053i	$0.678973\pi$
$758$	5.76088e113	1.03170
$759$	−3.54228e112	−0.0602188
$760$	7.79269e112	0.125762
$761$	−1.01296e114	−1.55202	−0.776011	−	0.630719i	$-0.782760\pi$
$761$	−1.01296e114	−1.55202	−0.776011	+	0.630719i	$0.782760\pi$
$762$	7.52575e113	1.09478
$763$	−1.32640e113	−0.183212
$764$	−3.22975e113	−0.423625
$765$	−1.32057e113	−0.164489
$766$	−7.78419e113	−0.920825
$767$	3.94122e112	0.0442806
$768$	6.34646e112	0.0677273
$769$	−1.08013e114	−1.09493	−0.547464	−	0.836829i	$-0.684407\pi$
$769$	−1.08013e114	−1.09493	−0.547464	+	0.836829i	$0.684407\pi$
$770$	3.46605e112	0.0333773
$771$	1.22579e114	1.12142
$772$	−4.44010e113	−0.385931
$773$	1.88313e114	1.55521	0.777606	−	0.628752i	$-0.216434\pi$
$773$	1.88313e114	1.55521	0.777606	+	0.628752i	$0.216434\pi$
$774$	9.54538e112	0.0749075
$775$	5.59860e113	0.417506
$776$	2.54733e113	0.180529
$777$	1.28095e114	0.862786
$778$	−2.29900e111	−0.00147178
$779$	1.68176e114	1.02338
$780$	−5.92532e112	−0.0342748
$781$	−1.46687e113	−0.0806631
$782$	−1.15982e114	−0.606350
$783$	2.03956e114	1.01379
$784$	−2.13969e113	−0.101127
$785$	−1.29858e114	−0.583602
$786$	9.27815e113	0.396525
$787$	−3.84579e114	−1.56309	−0.781543	−	0.623851i	$-0.785567\pi$
$787$	−3.84579e114	−1.56309	−0.781543	+	0.623851i	$0.785567\pi$
$788$	−1.27453e114	−0.492680
$789$	3.63754e114	1.33742
$790$	−1.32425e114	−0.463126
$791$	−3.30516e113	−0.109957
$792$	1.82701e112	0.00578224
$793$	2.55239e113	0.0768522
$794$	1.51264e114	0.433338
$795$	−4.52429e114	−1.23324
$796$	−3.35170e114	−0.869358
$797$	2.51884e114	0.621724	0.310862	−	0.950455i	$-0.399382\pi$
$797$	2.51884e114	0.621724	0.310862	+	0.950455i	$0.399382\pi$
$798$	1.37376e114	0.322698
$799$	−6.94334e114	−1.55228
$800$	−4.77837e113	−0.101678
$801$	−1.39199e114	−0.281936
$802$	−1.71001e114	−0.329694
$803$	−3.53133e113	−0.0648149
$804$	7.22898e113	0.126317
$805$	−1.79022e114	−0.297830
$806$	−3.14484e113	−0.0498154
$807$	2.53005e114	0.381614
$808$	−8.24522e113	−0.118428
$809$	1.26046e115	1.72410	0.862048	−	0.506827i	$-0.169182\pi$
$809$	1.26046e115	1.72410	0.862048	+	0.506827i	$0.169182\pi$
$810$	4.04702e114	0.527203
$811$	−6.26846e114	−0.777745	−0.388873	−	0.921292i	$-0.627135\pi$
$811$	−6.26846e114	−0.777745	−0.388873	+	0.921292i	$0.627135\pi$
$812$	3.69910e114	0.437152
$813$	1.48415e114	0.167071
$814$	−6.38490e113	−0.0684684
$815$	1.48388e114	0.151591
$816$	4.03087e114	0.392317
$817$	−3.57754e114	−0.331752
$818$	−4.09341e114	−0.361684
$819$	−1.55019e113	−0.0130518
$820$	7.61671e114	0.611112
$821$	2.01591e115	1.54140	0.770701	−	0.637197i	$-0.219906\pi$
$821$	2.01591e115	1.54140	0.770701	+	0.637197i	$0.219906\pi$
$822$	8.19281e114	0.597030
$823$	−2.32205e115	−1.61279	−0.806397	−	0.591374i	$-0.798586\pi$
$823$	−2.32205e115	−1.61279	−0.806397	+	0.591374i	$0.798586\pi$
$824$	9.75146e114	0.645572
$825$	−9.26911e113	−0.0584934
$826$	−4.13840e114	−0.248955
$827$	2.17296e115	1.24619	0.623096	−	0.782145i	$-0.285875\pi$
$827$	2.17296e115	1.24619	0.623096	+	0.782145i	$0.285875\pi$
$828$	−9.43649e113	−0.0515956
$829$	−4.50498e114	−0.234849	−0.117425	−	0.993082i	$-0.537464\pi$
$829$	−4.50498e114	−0.234849	−0.117425	+	0.993082i	$0.537464\pi$
$830$	1.67597e115	0.833071
$831$	−3.36134e115	−1.59320
$832$	2.68410e113	0.0121318
$833$	−1.35900e115	−0.585788
$834$	−2.83509e115	−1.16549
$835$	−1.88627e115	−0.739584
$836$	−6.84750e113	−0.0256085
$837$	1.82071e115	0.649509
$838$	−1.38533e115	−0.471425
$839$	−1.56998e115	−0.509678	−0.254839	−	0.966984i	$-0.582022\pi$
$839$	−1.56998e115	−0.509678	−0.254839	+	0.966984i	$0.582022\pi$
$840$	6.22176e114	0.192700
$841$	9.59927e114	0.283659
$842$	−8.48688e114	−0.239288
$843$	−2.64276e115	−0.710998
$844$	−2.60225e115	−0.668071
$845$	2.63533e115	0.645646
$846$	−5.64923e114	−0.132087
$847$	3.42760e115	0.764885
$848$	2.04945e115	0.436516
$849$	8.96576e115	1.82278
$850$	−3.03491e115	−0.588977
$851$	3.29780e115	0.610951
$852$	−2.63311e115	−0.465699
$853$	6.34354e114	0.107114	0.0535569	−	0.998565i	$-0.482944\pi$
$853$	6.34354e114	0.107114	0.0535569	+	0.998565i	$0.482944\pi$
$854$	−2.68009e115	−0.432079
$855$	4.02693e114	0.0619887
$856$	1.89852e115	0.279063
$857$	−1.23961e116	−1.73997	−0.869984	−	0.493080i	$-0.835871\pi$
$857$	−1.23961e116	−1.73997	−0.869984	+	0.493080i	$0.835871\pi$
$858$	5.20663e113	0.00697925
$859$	−4.17377e115	−0.534316	−0.267158	−	0.963653i	$-0.586085\pi$
$859$	−4.17377e115	−0.534316	−0.267158	+	0.963653i	$0.586085\pi$
$860$	−1.62027e115	−0.198106
$861$	1.34274e116	1.56808
$862$	4.00378e115	0.446615
$863$	−4.00523e115	−0.426778	−0.213389	−	0.976967i	$-0.568450\pi$
$863$	−4.00523e115	−0.426778	−0.213389	+	0.976967i	$0.568450\pi$
$864$	−1.55396e115	−0.158179
$865$	−3.77348e115	−0.366949
$866$	8.65866e115	0.804441
$867$	1.33937e116	1.18890
$868$	3.30217e115	0.280072
$869$	1.16363e115	0.0943045
$870$	7.30649e115	0.565846
$871$	3.05734e114	0.0226269
$872$	1.18679e115	0.0839405
$873$	1.31635e115	0.0889833
$874$	3.53673e115	0.228507
$875$	−1.28289e116	−0.792267
$876$	−6.33895e115	−0.374201
$877$	2.16879e116	1.22387	0.611933	−	0.790909i	$-0.290392\pi$
$877$	2.16879e116	1.22387	0.611933	+	0.790909i	$0.290392\pi$
$878$	−1.71915e116	−0.927428
$879$	−7.06306e115	−0.364277
$880$	−3.10123e114	−0.0152922
$881$	−8.73866e115	−0.411999	−0.206000	−	0.978552i	$-0.566045\pi$
$881$	−8.73866e115	−0.411999	−0.206000	+	0.978552i	$0.566045\pi$
$882$	−1.10570e115	−0.0498459
$883$	−4.21269e116	−1.81598	−0.907990	−	0.418991i	$-0.862384\pi$
$883$	−4.21269e116	−1.81598	−0.907990	+	0.418991i	$0.862384\pi$
$884$	1.70477e115	0.0702749
$885$	−8.17420e115	−0.322245
$886$	9.98030e115	0.376280
$887$	−2.64676e116	−0.954401	−0.477200	−	0.878795i	$-0.658348\pi$
$887$	−2.64676e116	−0.954401	−0.477200	+	0.878795i	$0.658348\pi$
$888$	−1.14613e116	−0.395294
$889$	−3.34208e116	−1.10255
$890$	2.36281e116	0.745631
$891$	−3.55615e115	−0.107352
$892$	−6.71383e114	−0.0193892
$893$	2.11729e116	0.584989
$894$	1.59810e116	0.422447
$895$	−7.58488e115	−0.191840
$896$	−2.81838e115	−0.0682076
$897$	−2.68922e115	−0.0622767
$898$	4.08922e116	0.906202
$899$	3.87789e116	0.822408
$900$	−2.46926e115	−0.0501172
$901$	1.30168e117	2.52856
$902$	−6.69287e115	−0.124438
$903$	−2.85634e116	−0.508328
$904$	2.95727e115	0.0503777
$905$	−6.71234e116	−1.09460
$906$	−1.71387e116	−0.267555
$907$	7.58959e116	1.13431	0.567153	−	0.823612i	$-0.308045\pi$
$907$	7.58959e116	1.13431	0.567153	+	0.823612i	$0.308045\pi$
$908$	−4.86196e116	−0.695698
$909$	−4.26078e115	−0.0583735
$910$	2.63136e115	0.0345179
$911$	1.28882e117	1.61889	0.809445	−	0.587196i	$-0.199768\pi$
$911$	1.28882e117	1.61889	0.809445	+	0.587196i	$0.199768\pi$
$912$	−1.22916e116	−0.147847
$913$	−1.47269e116	−0.169635
$914$	−4.20942e116	−0.464352
$915$	−5.29373e116	−0.559279
$916$	5.43857e116	0.550318
$917$	−4.12030e116	−0.399338
$918$	−9.86977e116	−0.916265
$919$	2.01359e117	1.79064	0.895319	−	0.445425i	$-0.146947\pi$
$919$	2.01359e117	1.79064	0.895319	+	0.445425i	$0.146947\pi$
$920$	1.60179e116	0.136454
$921$	−1.95291e117	−1.59377
$922$	−9.14731e116	−0.715191
$923$	−1.11362e116	−0.0834196
$924$	−5.46711e115	−0.0392387
$925$	8.62938e116	0.593446
$926$	−9.43810e116	−0.621943
$927$	5.03914e116	0.318205
$928$	−3.30975e116	−0.200286
$929$	−2.63868e117	−1.53026	−0.765132	−	0.643873i	$-0.777326\pi$
$929$	−2.63868e117	−1.53026	−0.765132	+	0.643873i	$0.777326\pi$
$930$	6.52248e116	0.362523
$931$	4.14410e116	0.220759
$932$	1.82670e117	0.932691
$933$	−1.17922e117	−0.577124
$934$	−5.03512e116	−0.236216
$935$	−1.96970e116	−0.0885813
$936$	1.38703e115	0.00597983
$937$	−6.56474e116	−0.271334	−0.135667	−	0.990755i	$-0.543318\pi$
$937$	−6.56474e116	−0.271334	−0.135667	+	0.990755i	$0.543318\pi$
$938$	−3.21029e116	−0.127213
$939$	−1.35438e117	−0.514577
$940$	9.58921e116	0.349327
$941$	−9.13472e116	−0.319084	−0.159542	−	0.987191i	$-0.551002\pi$
$941$	−9.13472e116	−0.319084	−0.159542	+	0.987191i	$0.551002\pi$
$942$	2.04829e117	0.686088
$943$	3.45686e117	1.11038
$944$	3.70281e116	0.114061
$945$	−1.52343e117	−0.450055
$946$	1.42374e116	0.0403396
$947$	5.03010e117	1.36695	0.683475	−	0.729974i	$-0.260468\pi$
$947$	5.03010e117	1.36695	0.683475	+	0.729974i	$0.260468\pi$
$948$	2.08878e117	0.544456
$949$	−2.68092e116	−0.0670298
$950$	9.25460e116	0.221960
$951$	−2.11810e117	−0.487321
$952$	−1.79005e117	−0.395099
$953$	2.05186e116	0.0434487	0.0217244	−	0.999764i	$-0.493084\pi$
$953$	2.05186e116	0.0434487	0.0217244	+	0.999764i	$0.493084\pi$
$954$	1.05907e117	0.215161
$955$	2.83302e117	0.552225
$956$	−2.33612e117	−0.436926
$957$	−6.42027e116	−0.115221
$958$	2.28227e117	0.393034
$959$	−3.63832e117	−0.601265
$960$	−5.56689e116	−0.0882874
$961$	−3.10836e117	−0.473104
$962$	−4.84728e116	−0.0708081
$963$	9.81075e116	0.137551
$964$	4.58320e117	0.616773
$965$	3.89470e117	0.503089
$966$	2.82376e117	0.350132
$967$	3.90525e117	0.464840	0.232420	−	0.972616i	$-0.425336\pi$
$967$	3.90525e117	0.464840	0.232420	+	0.972616i	$0.425336\pi$
$968$	−3.06683e117	−0.350440
$969$	−7.80686e117	−0.856421
$970$	−2.23442e117	−0.235332
$971$	−1.02887e118	−1.04040	−0.520201	−	0.854044i	$-0.674143\pi$
$971$	−1.02887e118	−1.04040	−0.520201	+	0.854044i	$0.674143\pi$
$972$	−1.77552e117	−0.172388
$973$	1.25903e118	1.17376
$974$	−4.45979e117	−0.399241
$975$	−7.03692e116	−0.0604923
$976$	2.39799e117	0.197961
$977$	−2.13644e118	−1.69377	−0.846886	−	0.531774i	$-0.821526\pi$
$977$	−2.13644e118	−1.69377	−0.846886	+	0.531774i	$0.821526\pi$
$978$	−2.34057e117	−0.178212
$979$	−2.07622e117	−0.151830
$980$	1.87686e117	0.131826
$981$	6.13281e116	0.0413746
$982$	−2.54406e117	−0.164863
$983$	1.29011e118	0.803088	0.401544	−	0.915840i	$-0.368474\pi$
$983$	1.29011e118	0.803088	0.401544	+	0.915840i	$0.368474\pi$
$984$	−1.20141e118	−0.718429
$985$	1.11797e118	0.642245
$986$	−2.10214e118	−1.16017
$987$	1.69047e118	0.896353
$988$	−5.19848e116	−0.0264836
$989$	−7.35363e117	−0.359955
$990$	−1.60258e116	−0.00753756
$991$	−4.92128e117	−0.222417	−0.111209	−	0.993797i	$-0.535472\pi$
$991$	−4.92128e117	−0.222417	−0.111209	+	0.993797i	$0.535472\pi$
$992$	−2.95460e117	−0.128318
$993$	−3.73601e117	−0.155924
$994$	1.16933e118	0.469002
$995$	2.93999e118	1.13327
$996$	−2.64356e118	−0.979367
$997$	4.52649e118	1.61177	0.805885	−	0.592072i	$-0.201690\pi$
$997$	4.52649e118	1.61177	0.805885	+	0.592072i	$0.201690\pi$
$998$	2.49199e118	0.852885
$999$	2.80634e118	0.923218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.80.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.80.a.a.1.3	✓	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 80 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+5.49756e11 q^{2} +7.60629e18 q^{3} +3.02231e23 q^{4} -2.65106e27 q^{5} +4.18160e30 q^{6} -1.85699e33 q^{7} +1.66153e35 q^{8} +8.58611e36 q^{9} -1.45744e39 q^{10} +1.28066e40 q^{11} +2.29886e42 q^{12} +9.72252e42 q^{13} -1.02089e45 q^{14} -2.01648e46 q^{15} +9.13439e46 q^{16} +5.80157e48 q^{17} +4.72026e48 q^{18} -1.76912e50 q^{19} -8.01235e50 q^{20} -1.41248e52 q^{21} +7.04052e51 q^{22} -3.63643e53 q^{23} +1.26381e54 q^{24} -9.51547e54 q^{25} +5.34501e54 q^{26} -3.09451e56 q^{27} -5.61242e56 q^{28} -6.59091e57 q^{29} -1.10857e58 q^{30} -5.88368e58 q^{31} +5.02168e58 q^{32} +9.74109e58 q^{33} +3.18945e60 q^{34} +4.92301e60 q^{35} +2.59499e60 q^{36} -9.06879e61 q^{37} -9.72584e61 q^{38} +7.39524e61 q^{39} -4.40484e62 q^{40} -9.50622e63 q^{41} -7.76521e63 q^{42} +2.02221e64 q^{43} +3.87056e63 q^{44} -2.27623e64 q^{45} -1.99915e65 q^{46} -1.19680e66 q^{47} +6.94788e65 q^{48} -2.34246e66 q^{49} -5.23119e66 q^{50} +4.41285e67 q^{51} +2.93845e66 q^{52} +2.24366e68 q^{53} -1.70122e68 q^{54} -3.39512e67 q^{55} -3.08546e68 q^{56} -1.34565e69 q^{57} -3.62339e69 q^{58} +4.05370e69 q^{59} -6.09443e69 q^{60} +2.62524e70 q^{61} -3.23459e70 q^{62} -1.59444e70 q^{63} +2.76070e70 q^{64} -2.57750e70 q^{65} +5.35522e70 q^{66} +3.14459e71 q^{67} +1.75342e72 q^{68} -2.76597e72 q^{69} +2.70645e72 q^{70} -1.14540e73 q^{71} +1.42661e72 q^{72} -2.75743e73 q^{73} -4.98562e73 q^{74} -7.23775e73 q^{75} -5.34684e73 q^{76} -2.37818e73 q^{77} +4.06558e73 q^{78} +9.08613e74 q^{79} -2.42158e74 q^{80} -2.77681e75 q^{81} -5.22610e75 q^{82} -1.14994e76 q^{83} -4.26897e75 q^{84} -1.53803e76 q^{85} +1.11172e76 q^{86} -5.01324e76 q^{87} +2.12787e75 q^{88} -1.62121e77 q^{89} -1.25137e76 q^{90} -1.80547e76 q^{91} -1.09904e77 q^{92} -4.47530e77 q^{93} -6.57950e77 q^{94} +4.69005e77 q^{95} +3.81964e77 q^{96} +1.53312e78 q^{97} -1.28778e78 q^{98} +1.09959e77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3} + 90\!\cdots\!32 q^{4} - 40\!\cdots\!50 q^{5} - 25\!\cdots\!68 q^{6} + 14\!\cdots\!12 q^{7} + 49\!\cdots\!16 q^{8} - 66\!\cdots\!69 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots + 43\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 1649267441664 * q^2 - 4584969341748725436 * q^3 + 906694364710971881029632 * q^4 - 4059262187174651001136305750 * q^5 - 2520613552124598169254827655168 * q^6 + 1483415167701865205633594539244712 * q^7 + 498460498419343452338927647605129216 * q^8 - 6672177462878166486769127437981485969 * q^9 - 2231602987494983256332043780416864256000 * q^10 - 124415627894002097981147146385015573568084 * q^11 - 1385721954845381178123642556040054449373184 * q^12 + 42751290531030108169653302093972335572078354 * q^13 + 815516112853742916658765248637469002360160256 * q^14 + 12130195395785681466027262600593952860024579000 * q^15 + 274031556999544297163190906134303066185487351808 * q^16 + 946712075921587263895141601588172960900304679382 * q^17 - 3668068351509757323918927238219104062763247337472 * q^18 + 20257201468438772377828741263164304940521204158100 * q^19 - 1226836716665196806401755258077521564978095587328000 * q^20 - 43631041707758317195716974587393663148235360312109344 * q^21 - 68398214773253678769205071140782913654477159600750592 * q^22 + 82529324959900375708064647869197163323144742475087224 * q^23 - 761808701108492914776959414090992784142990461361979392 * q^24 + 21083927432436875746692985513144812516022059835070953125 * q^25 + 23502770520648804835840429075458496001384189590977380352 * q^26 + 274892147371249163933625876457102532152743271603258606440 * q^27 + 448334724360687495454854442833822454444881294443390435328 * q^28 + 1495670726099376746574980522811287146529994291477752261730 * q^29 + 6668645442430627599572534772986232026773917767829553152000 * q^30 - 95179276352007712146226202833884603073380381912216918148704 * q^31 + 150650441649280338332058946156983993986456530667136828309504 * q^32 + 992822698008241864790090731991207114961142366072700744254608 * q^33 + 520460467815870253931488608270113859514661800240826302857216 * q^34 - 21607610499914207082682499103219854780050992252308433934818000 * q^35 - 2016541901981061111184418693574995613694576474265768360411136 * q^36 - 144566050902862740859885196306965987391617821343191168676139958 * q^37 + 11136514280374746053268812699409461656846054022858075327692800 * q^38 + 228190042825724963101591896942117207549963869755940875240057752 * q^39 - 674460617677956923507095330616191354152404416503766019211264000 * q^40 - 8990031028114195750037275993147973941443305064257192760778706994 * q^41 - 23986418844829947113932651151989616268711842899364606112769769472 * q^42 - 95593681974303841410795644029721502703583992143632618507356214196 * q^43 - 37602316231156301545654439995778051325641119291417114840657821696 * q^44 - 301087420222926180530726149020081890688604646091994014416774832750 * q^45 + 45370976212957264010784064774650611487856300647019740393910566912 * q^46 - 1196991457557369832323664024412035293457581150671216623337274714768 * q^47 - 418808762504859650152288744683537353736464821656275597627643396096 * q^48 + 979527459006508007750478947254655464139388961590111701782059182619 * q^49 + 11591011685574864757307129975239519727150876544791666881462272000000 * q^50 + 54835677094941655265769813003495680021307623179495147480345912211016 * q^51 + 12920784736202177212341925318873824836005358723163067556811899928576 * q^52 + 125345260867666016932298670205922091626639085968719891046717117688474 * q^53 + 151123556209501123809570029322571740481897066012165273816362878238720 * q^54 + 218552253106716091346953706059417254940663339263001756619683362801000 * q^55 + 246474621285161894535007804980680832577435519262273080715899268235264 * q^56 - 3717966118204647103187961905025238537942233258324174220458365486643600 * q^57 + 822253677335218786882869933735866915073470126715345596892208944906240 * q^58 - 11972958248068544720959454962966912784485227241028887059908129310352740 * q^59 + 3666126602733951524981634615014227304097506969423520216337115774976000 * q^60 - 64131246374258928284376769397123814135901710973884122711218411370114814 * q^61 - 52325360536168871373801409406694002027278058045563085607243845732401152 * q^62 + 70051688514428937815669910467509313829077855679613962909546987100234824 * q^63 + 82820956161486765449217070347324305429413307666044638661950290685591552 * q^64 + 891137435602017208473142837371223459080944333869708385766316087294741500 * q^65 + 545810050390001042909631180643191746345039202954535635835955360934395904 * q^66 + 1066530064121225601134341646949007968554017501968094906567414396182674052 * q^67 + 286126168080642981173114751630936852583911790660458738532906761933815808 * q^68 - 8157044315638375005795679302675007882029666940395500924677412200323240288 * q^69 - 11878909496555229468914291404784461386008100471809805344642547931152384000 * q^70 - 11965128429849499869561209311265966495949289765114193633775048728088683544 * q^71 - 1108605634562853770741055758550483389972691928261434972195503389978656768 * q^72 - 21000617554059015243660635152162850086671731600300702395695797742856222866 * q^73 - 79476026974677343330576619065978738282412401561571438302725214096488136704 * q^74 - 292290092969427932732653354537557410364081060335887189482606343379537062500 * q^75 + 6122363472082753142156111928411278890127331396457557757688967569237606400 * q^76 - 313088925468723418800569716492755177099175159696850088390493982222779568736 * q^77 + 125448802714794002433554422131839463862520205642671303790805016830883659776 * q^78 - 752771845175749719716095680259956103143909956608587888174845776003401815280 * q^79 - 370788645806948409159647752825708722452803938387153627308606284137234432000 * q^80 - 5430810619867098975054002966228960820045900884810688198506068573048487508357 * q^81 - 4942321824739293094368293269951547925396379429009385144359999748146747932672 * q^82 - 26574910236679674809554404156731348191995217371417312252463281001984618227756 * q^83 - 13186673214297948356576041298479632282330484902484582711586284526041496027136 * q^84 - 61899665747197215566012671763299618265748666908061238888083245866423505095500 * q^85 - 52553182436334043036996837433204672780783210015490947984376227250456439554048 * q^86 - 113886925506447843297583002913412072306835473772896532524712459437309650171560 * q^87 - 20672091963733285299571209049479821890334470859452313822118604199797664514048 * q^88 - 298553979180856324945701053715618937701373783711334946928152981953765466232770 * q^89 - 165524559756093052774612573846179093471923695979362367916518453818511327232000 * q^90 - 325469734796585461839474806271975513931239639583395403663965991364192518458384 * q^91 + 24942957954847408687610284739208958229343323190591158381856773431790042873856 * q^92 + 202912930249066039233266302287024066236035757547578650004667495188619949592448 * q^93 - 658053012966435260621714005982903963417353447091062252257938595545124893097984 * q^94 - 2764634158440341917915731742585889802219731536972926191181370883821066211265000 * q^95 - 230242552094285214524682441979479910898239975893526559356618697188184841781248 * q^96 - 3594992107094973275749338803035652864766054361504256609082707972538374192841498 * q^97 + 538500915451767365689653965669792537884976176057975029266028685937292368412672 * q^98 + 438106251552810720132252327913477796137507348924505662619110697139172583981532 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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