LMFDB - Embedded newform 2.80.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,80,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 80, names="a")

//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);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 80 $
Character orbit:	$[\chi]$	$=$	2.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:	$79.0474097443$
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			1.2
Root			$4.42382e13$ 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)

$f(q)$	$=$	$q+5.49756e11 q^{2} -3.97815e18 q^{3} +3.02231e23 q^{4} +4.89479e27 q^{5} -2.18701e30 q^{6} -4.89031e32 q^{7} +1.66153e35 q^{8} -3.34439e37 q^{9} +O(q^{10})$	\(q+5.49756e11 q^{2} -3.97815e18 q^{3} +3.02231e23 q^{4} +4.89479e27 q^{5} -2.18701e30 q^{6} -4.89031e32 q^{7} +1.66153e35 q^{8} -3.34439e37 q^{9} +2.69094e39 q^{10} -5.46900e40 q^{11} -1.20232e42 q^{12} +1.00475e44 q^{13} -2.68848e44 q^{14} -1.94722e46 q^{15} +9.13439e46 q^{16} -6.88703e48 q^{17} -1.83860e49 q^{18} -1.77793e50 q^{19} +1.47936e51 q^{20} +1.94544e51 q^{21} -3.00662e52 q^{22} -4.07703e53 q^{23} -6.60983e53 q^{24} +7.41536e54 q^{25} +5.52365e55 q^{26} +3.29047e56 q^{27} -1.47801e56 q^{28} +6.28477e56 q^{29} -1.07050e58 q^{30} +8.31077e58 q^{31} +5.02168e58 q^{32} +2.17565e59 q^{33} -3.78619e60 q^{34} -2.39370e60 q^{35} -1.01078e61 q^{36} +3.89836e61 q^{37} -9.77426e61 q^{38} -3.99703e62 q^{39} +8.13286e62 q^{40} -2.06553e63 q^{41} +1.06952e63 q^{42} -6.18778e64 q^{43} -1.65290e64 q^{44} -1.63701e65 q^{45} -2.24137e65 q^{46} +1.50856e66 q^{47} -3.63379e65 q^{48} -5.55174e66 q^{49} +4.07663e66 q^{50} +2.73976e67 q^{51} +3.03666e67 q^{52} -4.87601e67 q^{53} +1.80895e68 q^{54} -2.67696e68 q^{55} -8.12542e67 q^{56} +7.07286e68 q^{57} +3.45509e68 q^{58} -2.11219e69 q^{59} -5.88511e69 q^{60} -5.88931e70 q^{61} +4.56889e70 q^{62} +1.63551e70 q^{63} +2.76070e70 q^{64} +4.91802e71 q^{65} +1.19608e71 q^{66} -7.00026e70 q^{67} -2.08148e72 q^{68} +1.62190e72 q^{69} -1.31595e72 q^{70} -8.38692e72 q^{71} -5.55683e72 q^{72} -3.60236e73 q^{73} +2.14315e73 q^{74} -2.94994e73 q^{75} -5.37346e73 q^{76} +2.67451e73 q^{77} -2.19739e74 q^{78} -1.26900e75 q^{79} +4.47109e74 q^{80} +3.38773e74 q^{81} -1.13554e75 q^{82} -1.04441e76 q^{83} +5.87973e74 q^{84} -3.37106e76 q^{85} -3.40177e76 q^{86} -2.50017e75 q^{87} -9.08694e75 q^{88} -8.09056e76 q^{89} -8.99956e76 q^{90} -4.91352e76 q^{91} -1.23221e77 q^{92} -3.30615e77 q^{93} +8.29341e77 q^{94} -8.70258e77 q^{95} -1.99770e77 q^{96} -1.98469e78 q^{97} -3.05210e78 q^{98} +1.82905e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3}+ \cdots - 66\!\cdots\!69 q^{9}+O(q^{10}) $ 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	$ 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3}+ \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

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 $

$2$	5.49756e11	0.707107
$2$	5.49756e11	0.707107
$3$	−3.97815e18	−0.566750	−0.283375	−	0.959009i	$-0.591454\pi$
$3$	−3.97815e18	−0.566750	−0.283375	+	0.959009i	$0.591454\pi$
$4$	3.02231e23	0.500000
$5$	4.89479e27	1.20342	0.601712	−	0.798713i	$-0.294485\pi$
$5$	4.89479e27	1.20342	0.601712	+	0.798713i	$0.294485\pi$
$6$	−2.18701e30	−0.400753
$7$	−4.89031e32	−0.203219	−0.101609	−	0.994824i	$-0.532399\pi$
$7$	−4.89031e32	−0.203219	−0.101609	+	0.994824i	$0.532399\pi$
$8$	1.66153e35	0.353553
$9$	−3.34439e37	−0.678795
$10$	2.69094e39	0.850950
$11$	−5.46900e40	−0.400772	−0.200386	−	0.979717i	$-0.564220\pi$
$11$	−5.46900e40	−0.400772	−0.200386	+	0.979717i	$0.564220\pi$
$12$	−1.20232e42	−0.283375
$13$	1.00475e44	1.00298	0.501492	−	0.865162i	$-0.332785\pi$
$13$	1.00475e44	1.00298	0.501492	+	0.865162i	$0.332785\pi$
$14$	−2.68848e44	−0.143697
$15$	−1.94722e46	−0.682041
$16$	9.13439e46	0.250000
$17$	−6.88703e48	−1.71909	−0.859547	−	0.511056i	$-0.829254\pi$
$17$	−6.88703e48	−1.71909	−0.859547	+	0.511056i	$0.829254\pi$
$18$	−1.83860e49	−0.479980
$19$	−1.77793e50	−0.548462	−0.274231	−	0.961664i	$-0.588423\pi$
$19$	−1.77793e50	−0.548462	−0.274231	+	0.961664i	$0.588423\pi$
$20$	1.47936e51	0.601712
$21$	1.94544e51	0.115174
$22$	−3.00662e52	−0.283388
$23$	−4.07703e53	−0.663888	−0.331944	−	0.943299i	$-0.607705\pi$
$23$	−4.07703e53	−0.663888	−0.331944	+	0.943299i	$0.607705\pi$
$24$	−6.60983e53	−0.200376
$25$	7.41536e54	0.448231
$26$	5.52365e55	0.709217
$27$	3.29047e56	0.951457
$28$	−1.47801e56	−0.101609
$29$	6.28477e56	0.108036	0.0540180	−	0.998540i	$-0.482797\pi$
$29$	6.28477e56	0.108036	0.0540180	+	0.998540i	$0.482797\pi$
$30$	−1.07050e58	−0.482276
$31$	8.31077e58	1.02531	0.512654	−	0.858595i	$-0.328662\pi$
$31$	8.31077e58	1.02531	0.512654	+	0.858595i	$0.328662\pi$
$32$	5.02168e58	0.176777
$33$	2.17565e59	0.227137
$34$	−3.78619e60	−1.21558
$35$	−2.39370e60	−0.244559
$36$	−1.01078e61	−0.339397
$37$	3.89836e61	0.443521	0.221760	−	0.975101i	$-0.428820\pi$
$37$	3.89836e61	0.443521	0.221760	+	0.975101i	$0.428820\pi$
$38$	−9.77426e61	−0.387821
$39$	−3.99703e62	−0.568441
$40$	8.13286e62	0.425475
$41$	−2.06553e63	−0.407445	−0.203723	−	0.979029i	$-0.565304\pi$
$41$	−2.06553e63	−0.407445	−0.203723	+	0.979029i	$0.565304\pi$
$42$	1.06952e63	0.0814405
$43$	−6.18778e64	−1.86008	−0.930039	−	0.367462i	$-0.880227\pi$
$43$	−6.18778e64	−1.86008	−0.930039	+	0.367462i	$0.880227\pi$
$44$	−1.65290e64	−0.200386
$45$	−1.63701e65	−0.816878
$46$	−2.24137e65	−0.469440
$47$	1.50856e66	1.35113	0.675567	−	0.737299i	$-0.263899\pi$
$47$	1.50856e66	1.35113	0.675567	+	0.737299i	$0.263899\pi$
$48$	−3.63379e65	−0.141687
$49$	−5.55174e66	−0.958702
$50$	4.07663e66	0.316947
$51$	2.73976e67	0.974296
$52$	3.03666e67	0.501492
$53$	−4.87601e67	−0.379462	−0.189731	−	0.981836i	$-0.560762\pi$
$53$	−4.87601e67	−0.379462	−0.189731	+	0.981836i	$0.560762\pi$
$54$	1.80895e68	0.672781
$55$	−2.67696e68	−0.482299
$56$	−8.12542e67	−0.0718487
$57$	7.07286e68	0.310841
$58$	3.45509e68	0.0763930
$59$	−2.11219e69	−0.237727	−0.118864	−	0.992911i	$-0.537925\pi$
$59$	−2.11219e69	−0.237727	−0.118864	+	0.992911i	$0.537925\pi$
$60$	−5.88511e69	−0.341020
$61$	−5.88931e70	−1.77638	−0.888189	−	0.459477i	$-0.848037\pi$
$61$	−5.88931e70	−1.77638	−0.888189	+	0.459477i	$0.848037\pi$
$62$	4.56889e70	0.725002
$63$	1.63551e70	0.137944
$64$	2.76070e70	0.125000
$65$	4.91802e71	1.20702
$66$	1.19608e71	0.160610
$67$	−7.00026e70	−0.0518990	−0.0259495	−	0.999663i	$-0.508261\pi$
$67$	−7.00026e70	−0.0518990	−0.0259495	+	0.999663i	$0.508261\pi$
$68$	−2.08148e72	−0.859547
$69$	1.62190e72	0.376258
$70$	−1.31595e72	−0.172929
$71$	−8.38692e72	−0.629358	−0.314679	−	0.949198i	$-0.601897\pi$
$71$	−8.38692e72	−0.629358	−0.314679	+	0.949198i	$0.601897\pi$
$72$	−5.55683e72	−0.239990
$73$	−3.60236e73	−0.902264	−0.451132	−	0.892457i	$-0.648980\pi$
$73$	−3.60236e73	−0.902264	−0.451132	+	0.892457i	$0.648980\pi$
$74$	2.14315e73	0.313617
$75$	−2.94994e73	−0.254035
$76$	−5.37346e73	−0.274231
$77$	2.67451e73	0.0814444
$78$	−2.19739e74	−0.401948
$79$	−1.26900e75	−1.40344	−0.701718	−	0.712455i	$-0.747583\pi$
$79$	−1.26900e75	−1.40344	−0.701718	+	0.712455i	$0.747583\pi$
$80$	4.47109e74	0.300856
$81$	3.38773e74	0.139557
$82$	−1.13554e75	−0.288107
$83$	−1.04441e76	−1.64168	−0.820838	−	0.571161i	$-0.806493\pi$
$83$	−1.04441e76	−1.64168	−0.820838	+	0.571161i	$0.806493\pi$
$84$	5.87973e74	0.0575871
$85$	−3.37106e76	−2.06880
$86$	−3.40177e76	−1.31527
$87$	−2.50017e75	−0.0612294
$88$	−9.08694e75	−0.141694
$89$	−8.09056e76	−0.807371	−0.403685	−	0.914898i	$-0.632271\pi$
$89$	−8.09056e76	−0.807371	−0.403685	+	0.914898i	$0.632271\pi$
$90$	−8.99956e76	−0.577620
$91$	−4.91352e76	−0.203825
$92$	−1.23221e77	−0.331944
$93$	−3.30615e77	−0.581093
$94$	8.29341e77	0.955395
$95$	−8.70258e77	−0.660033
$96$	−1.99770e77	−0.100188
$97$	−1.98469e78	−0.661013	−0.330506	−	0.943804i	$-0.607220\pi$
$97$	−1.98469e78	−0.661013	−0.330506	+	0.943804i	$0.607220\pi$
$98$	−3.05210e78	−0.677905
$99$	1.82905e78	0.272042
$100$	2.24115e78	0.224115
$101$	2.10600e79	1.42156	0.710778	−	0.703416i	$-0.248343\pi$
$101$	2.10600e79	1.42156	0.710778	+	0.703416i	$0.248343\pi$
$102$	1.50620e79	0.688932
$103$	4.55537e79	1.41727	0.708635	−	0.705575i	$-0.249311\pi$
$103$	4.55537e79	1.41727	0.708635	+	0.705575i	$0.249311\pi$
$104$	1.66942e79	0.354608
$105$	9.52251e78	0.138604
$106$	−2.68062e79	−0.268320
$107$	8.59982e79	0.594060	0.297030	−	0.954868i	$-0.404004\pi$
$107$	8.59982e79	0.594060	0.297030	+	0.954868i	$0.404004\pi$
$108$	9.94483e79	0.475728
$109$	2.52913e80	0.840667	0.420333	−	0.907370i	$-0.361913\pi$
$109$	2.52913e80	0.840667	0.420333	+	0.907370i	$0.361913\pi$
$110$	−1.47168e80	−0.341037
$111$	−1.55083e80	−0.251365
$112$	−4.46700e79	−0.0508047
$113$	−9.71549e80	−0.777797	−0.388898	−	0.921281i	$-0.627144\pi$
$113$	−9.71549e80	−0.777797	−0.388898	+	0.921281i	$0.627144\pi$
$114$	3.88835e80	0.219798
$115$	−1.99562e81	−0.798939
$116$	1.89946e80	0.0540180
$117$	−3.36027e81	−0.680820
$118$	−1.16119e81	−0.168099
$119$	3.36797e81	0.349352
$120$	−3.23537e81	−0.241138
$121$	−1.56308e82	−0.839382
$122$	−3.23768e82	−1.25609
$123$	8.21699e81	0.230920
$124$	2.51178e82	0.512654
$125$	−4.46809e82	−0.664013
$126$	8.99133e81	0.0975410
$127$	−3.39778e82	−0.269741	−0.134871	−	0.990863i	$-0.543062\pi$
$127$	−3.39778e82	−0.269741	−0.134871	+	0.990863i	$0.543062\pi$
$128$	1.51771e82	0.0883883
$129$	2.46159e83	1.05420
$130$	2.70371e83	0.853489
$131$	6.62131e83	1.54429	0.772143	−	0.635449i	$-0.219185\pi$
$131$	6.62131e83	1.54429	0.772143	+	0.635449i	$0.219185\pi$
$132$	6.57550e82	0.113569
$133$	8.69462e82	0.111458
$134$	−3.84843e82	−0.0366981
$135$	1.61061e84	1.14501
$136$	−1.14430e84	−0.607792
$137$	−4.00220e84	−1.59161	−0.795804	−	0.605555i	$-0.792951\pi$
$137$	−4.00220e84	−1.59161	−0.795804	+	0.605555i	$0.792951\pi$
$138$	8.91652e83	0.266055
$139$	3.64079e84	0.816790	0.408395	−	0.912805i	$-0.366089\pi$
$139$	3.64079e84	0.816790	0.408395	+	0.912805i	$0.366089\pi$
$140$	−7.23453e83	−0.122279
$141$	−6.00129e84	−0.765754
$142$	−4.61076e84	−0.445023
$143$	−5.49496e84	−0.401968
$144$	−3.05490e84	−0.169699
$145$	3.07626e84	0.130013
$146$	−1.98042e85	−0.637997
$147$	2.20856e85	0.543344
$148$	1.17821e85	0.221760
$149$	−1.06970e86	−1.54313	−0.771567	−	0.636148i	$-0.780527\pi$
$149$	−1.06970e86	−1.54313	−0.771567	+	0.636148i	$0.780527\pi$
$150$	−1.62175e85	−0.179630
$151$	−3.70109e85	−0.315312	−0.157656	−	0.987494i	$-0.550394\pi$
$151$	−3.70109e85	−0.315312	−0.157656	+	0.987494i	$0.550394\pi$
$152$	−2.95409e85	−0.193911
$153$	2.30330e86	1.16691
$154$	1.47033e85	0.0575899
$155$	4.06795e86	1.23388
$156$	−1.20803e86	−0.284220
$157$	9.97348e86	1.82310	0.911550	−	0.411190i	$-0.134887\pi$
$157$	9.97348e86	1.82310	0.911550	+	0.411190i	$0.134887\pi$
$158$	−6.97642e86	−0.992379
$159$	1.93975e86	0.215060
$160$	2.45801e86	0.212737
$161$	1.99380e86	0.134915
$162$	1.86243e86	0.0986816
$163$	2.64776e87	1.10019	0.550096	−	0.835101i	$-0.314591\pi$
$163$	2.64776e87	1.10019	0.550096	+	0.835101i	$0.314591\pi$
$164$	−6.24269e86	−0.203723
$165$	1.06494e87	0.273343
$166$	−5.74172e87	−1.16084
$167$	−1.10962e88	−1.76960	−0.884800	−	0.465972i	$-0.845705\pi$
$167$	−1.10962e88	−1.76960	−0.884800	+	0.465972i	$0.845705\pi$
$168$	3.23241e86	0.0407202
$169$	5.99757e85	0.00597655
$170$	−1.85326e88	−1.46286
$171$	5.94609e87	0.372293
$172$	−1.87014e88	−0.930039
$173$	4.71445e88	1.86471	0.932353	−	0.361550i	$-0.117752\pi$
$173$	4.71445e88	1.86471	0.932353	+	0.361550i	$0.117752\pi$
$174$	−1.37449e87	−0.0432957
$175$	−3.62634e87	−0.0910889
$176$	−4.99560e87	−0.100193
$177$	8.40262e87	0.134732
$178$	−4.44783e88	−0.570897
$179$	1.13158e89	1.16410	0.582052	−	0.813152i	$-0.302250\pi$
$179$	1.13158e89	1.16410	0.582052	+	0.813152i	$0.302250\pi$
$180$	−4.94756e88	−0.408439
$181$	4.17898e88	0.277183	0.138591	−	0.990350i	$-0.455743\pi$
$181$	4.17898e88	0.277183	0.138591	+	0.990350i	$0.455743\pi$
$182$	−2.70124e88	−0.144126
$183$	2.34285e89	1.00676
$184$	−6.77414e88	−0.234720
$185$	1.90817e89	0.533744
$186$	−1.81757e89	−0.410895
$187$	3.76652e89	0.688964
$188$	4.55935e89	0.675567
$189$	−1.60914e89	−0.193354
$190$	−4.78430e89	−0.466714
$191$	1.03324e90	0.819189	0.409594	−	0.912268i	$-0.365670\pi$
$191$	1.03324e90	0.819189	0.409594	+	0.912268i	$0.365670\pi$
$192$	−1.09825e89	−0.0708437
$193$	−3.15305e90	−1.65660	−0.828299	−	0.560287i	$-0.810691\pi$
$193$	−3.15305e90	−1.65660	−0.828299	+	0.560287i	$0.810691\pi$
$194$	−1.09110e90	−0.467407
$195$	−1.95646e90	−0.684076
$196$	−1.67791e90	−0.479351
$197$	−6.64923e89	−0.155366	−0.0776829	−	0.996978i	$-0.524752\pi$
$197$	−6.64923e89	−0.155366	−0.0776829	+	0.996978i	$0.524752\pi$
$198$	1.00553e90	0.192363
$199$	−5.17517e90	−0.811388	−0.405694	−	0.914009i	$-0.632970\pi$
$199$	−5.17517e90	−0.811388	−0.405694	+	0.914009i	$0.632970\pi$
$200$	1.23209e90	0.158473
$201$	2.78481e89	0.0294138
$202$	1.15779e91	1.00519
$203$	−3.07345e89	−0.0219549
$204$	8.28043e90	0.487148
$205$	−1.01103e91	−0.490330
$206$	2.50434e91	1.00216
$207$	1.36352e91	0.450644
$208$	9.17774e90	0.250746
$209$	9.72349e90	0.219808
$210$	5.23506e90	0.0980075
$211$	2.46092e91	0.381892	0.190946	−	0.981601i	$-0.438844\pi$
$211$	2.46092e91	0.381892	0.190946	+	0.981601i	$0.438844\pi$
$212$	−1.47369e91	−0.189731
$213$	3.33644e91	0.356688
$214$	4.72780e91	0.420064
$215$	−3.02879e92	−2.23846
$216$	5.46723e91	0.336391
$217$	−4.06423e91	−0.208362
$218$	1.39040e92	0.594441
$219$	1.43307e92	0.511358
$220$	−8.09062e91	−0.241149
$221$	−6.91972e92	−1.72422
$222$	−8.52576e91	−0.177742
$223$	4.78744e91	0.0835720	0.0417860	−	0.999127i	$-0.486695\pi$
$223$	4.78744e91	0.0835720	0.0417860	+	0.999127i	$0.486695\pi$
$224$	−2.45576e91	−0.0359244
$225$	−2.47999e92	−0.304257
$226$	−5.34115e92	−0.549985
$227$	1.82027e93	1.57440	0.787199	−	0.616699i	$-0.211530\pi$
$227$	1.82027e93	1.57440	0.787199	+	0.616699i	$0.211530\pi$
$228$	2.13764e92	0.155420
$229$	−5.98845e92	−0.366280	−0.183140	−	0.983087i	$-0.558626\pi$
$229$	−5.98845e92	−0.366280	−0.183140	+	0.983087i	$0.558626\pi$
$230$	−1.09711e93	−0.564935
$231$	−1.06396e92	−0.0461586
$232$	1.04424e92	0.0381965
$233$	1.18342e93	0.365242	0.182621	−	0.983183i	$-0.441542\pi$
$233$	1.18342e93	0.365242	0.182621	+	0.983183i	$0.441542\pi$
$234$	−1.84733e93	−0.481412
$235$	7.38410e93	1.62599
$236$	−6.38371e92	−0.118864
$237$	5.04828e93	0.795397
$238$	1.85156e93	0.247029
$239$	1.64788e94	1.86298	0.931492	−	0.363761i	$-0.118508\pi$
$239$	1.64788e94	1.86298	0.931492	+	0.363761i	$0.118508\pi$
$240$	−1.77867e93	−0.170510
$241$	−4.71709e93	−0.383708	−0.191854	−	0.981423i	$-0.561450\pi$
$241$	−4.71709e93	−0.383708	−0.191854	+	0.981423i	$0.561450\pi$
$242$	−8.59313e93	−0.593533
$243$	−1.75597e94	−1.03055
$244$	−1.77993e94	−0.888189
$245$	−2.71746e94	−1.15373
$246$	4.51734e93	0.163285
$247$	−1.78637e94	−0.550099
$248$	1.38086e94	0.362501
$249$	4.15483e94	0.930420
$250$	−2.45636e94	−0.469528
$251$	−7.60187e94	−1.24110	−0.620552	−	0.784165i	$-0.713092\pi$
$251$	−7.60187e94	−1.24110	−0.620552	+	0.784165i	$0.713092\pi$
$252$	4.94304e93	0.0689719
$253$	2.22973e94	0.266068
$254$	−1.86795e94	−0.190736
$255$	1.34106e95	1.17249
$256$	8.34370e93	0.0625000
$257$	−5.57775e94	−0.358180	−0.179090	−	0.983833i	$-0.557315\pi$
$257$	−5.57775e94	−0.358180	−0.179090	+	0.983833i	$0.557315\pi$
$258$	1.35327e95	0.745431
$259$	−1.90642e94	−0.0901318
$260$	1.48638e95	0.603508
$261$	−2.10188e94	−0.0733343
$262$	3.64010e95	1.09198
$263$	−2.83880e95	−0.732627	−0.366314	−	0.930491i	$-0.619380\pi$
$263$	−2.83880e95	−0.732627	−0.366314	+	0.930491i	$0.619380\pi$
$264$	3.61492e94	0.0803052
$265$	−2.38671e95	−0.456654
$266$	4.77992e94	0.0788126
$267$	3.21854e95	0.457577
$268$	−2.11570e94	−0.0259495
$269$	1.25150e95	0.132500	0.0662499	−	0.997803i	$-0.478897\pi$
$269$	1.25150e95	0.132500	0.0662499	+	0.997803i	$0.478897\pi$
$270$	8.85445e95	0.809642
$271$	−9.12378e95	−0.720921	−0.360461	−	0.932774i	$-0.617381\pi$
$271$	−9.12378e95	−0.720921	−0.360461	+	0.932774i	$0.617381\pi$
$272$	−6.29088e95	−0.429774
$273$	1.95467e95	0.115518
$274$	−2.20023e96	−1.12544
$275$	−4.05546e95	−0.179638
$276$	4.90191e95	0.188129
$277$	−2.66373e96	−0.886215	−0.443108	−	0.896468i	$-0.646124\pi$
$277$	−2.66373e96	−0.886215	−0.443108	+	0.896468i	$0.646124\pi$
$278$	2.00154e96	0.577558
$279$	−2.77945e96	−0.695974
$280$	−3.97722e95	−0.0864645
$281$	9.97999e95	0.188465	0.0942325	−	0.995550i	$-0.469960\pi$
$281$	9.97999e95	0.188465	0.0942325	+	0.995550i	$0.469960\pi$
$282$	−3.29924e96	−0.541470
$283$	6.54735e96	0.934332	0.467166	−	0.884170i	$-0.345275\pi$
$283$	6.54735e96	0.934332	0.467166	+	0.884170i	$0.345275\pi$
$284$	−2.53479e96	−0.314679
$285$	3.46202e96	0.374074
$286$	−3.02089e96	−0.284234
$287$	1.01011e96	0.0828006
$288$	−1.67945e96	−0.119995
$289$	3.13816e97	1.95529
$290$	1.69119e96	0.0919332
$291$	7.89540e96	0.374629
$292$	−1.08875e97	−0.451132
$293$	2.94703e97	1.06688	0.533438	−	0.845839i	$-0.320900\pi$
$293$	2.94703e97	1.06688	0.533438	+	0.845839i	$0.320900\pi$
$294$	1.21417e97	0.384202
$295$	−1.03387e97	−0.286087
$296$	6.47727e96	0.156808
$297$	−1.79956e97	−0.381317
$298$	−5.88073e97	−1.09116
$299$	−4.09639e97	−0.665869
$300$	−8.91564e96	−0.127017
$301$	3.02602e97	0.378003
$302$	−2.03470e97	−0.222959
$303$	−8.37798e97	−0.805667
$304$	−1.62403e97	−0.137116
$305$	−2.88269e98	−2.13774
$306$	1.26625e98	0.825131
$307$	2.25783e98	1.29338	0.646689	−	0.762753i	$-0.276153\pi$
$307$	2.25783e98	1.29338	0.646689	+	0.762753i	$0.276153\pi$
$308$	8.08322e96	0.0407222
$309$	−1.81219e98	−0.803238
$310$	2.23638e98	0.872486
$311$	5.42095e97	0.186226	0.0931129	−	0.995656i	$-0.470318\pi$
$311$	5.42095e97	0.186226	0.0931129	+	0.995656i	$0.470318\pi$
$312$	−6.64120e97	−0.200974
$313$	1.18148e98	0.315084	0.157542	−	0.987512i	$-0.449643\pi$
$313$	1.18148e98	0.315084	0.157542	+	0.987512i	$0.449643\pi$
$314$	5.48298e98	1.28913
$315$	8.00549e97	0.166005
$316$	−3.83533e98	−0.701718
$317$	−2.14263e98	−0.346024	−0.173012	−	0.984920i	$-0.555350\pi$
$317$	−2.14263e98	−0.346024	−0.173012	+	0.984920i	$0.555350\pi$
$318$	1.06639e98	0.152070
$319$	−3.43714e97	−0.0432978
$320$	1.35130e98	0.150428
$321$	−3.42114e98	−0.336683
$322$	1.09610e98	0.0953990
$323$	1.22446e99	0.942859
$324$	1.02388e98	0.0697784
$325$	7.45055e98	0.449568
$326$	1.45562e99	0.777953
$327$	−1.00612e99	−0.476448
$328$	−3.43195e98	−0.144054
$329$	−7.37734e98	−0.274576
$330$	5.85454e98	0.193282
$331$	−4.17466e99	−1.22297	−0.611484	−	0.791257i	$-0.709427\pi$
$331$	−4.17466e99	−1.22297	−0.611484	+	0.791257i	$0.709427\pi$
$332$	−3.15654e99	−0.820838
$333$	−1.30377e99	−0.301060
$334$	−6.10022e99	−1.25130
$335$	−3.42648e98	−0.0624566
$336$	1.77704e98	0.0287936
$337$	1.04448e100	1.50494	0.752469	−	0.658628i	$-0.228863\pi$
$337$	1.04448e100	1.50494	0.752469	+	0.658628i	$0.228863\pi$
$338$	3.29720e97	0.00422606
$339$	3.86497e99	0.440816
$340$	−1.01884e100	−1.03440
$341$	−4.54516e99	−0.410915
$342$	3.26890e99	0.263251
$343$	5.54690e99	0.398045
$344$	−1.02812e100	−0.657637
$345$	7.93888e99	0.452799
$346$	2.59180e100	1.31855
$347$	5.51655e99	0.250411	0.125205	−	0.992131i	$-0.460041\pi$
$347$	5.51655e99	0.250411	0.125205	+	0.992131i	$0.460041\pi$
$348$	−7.55631e98	−0.0306147
$349$	3.56359e100	1.28909	0.644545	−	0.764566i	$-0.277047\pi$
$349$	3.56359e100	1.28909	0.644545	+	0.764566i	$0.277047\pi$
$350$	−1.99360e99	−0.0644096
$351$	3.30608e100	0.954296
$352$	−2.74636e99	−0.0708471
$353$	−3.47437e100	−0.801264	−0.400632	−	0.916239i	$-0.631209\pi$
$353$	−3.47437e100	−0.801264	−0.400632	+	0.916239i	$0.631209\pi$
$354$	4.61939e99	0.0952699
$355$	−4.10522e100	−0.757385
$356$	−2.44522e100	−0.403685
$357$	−1.33983e100	−0.197995
$358$	6.22094e100	0.823145
$359$	−1.07000e101	−1.26810	−0.634051	−	0.773291i	$-0.718609\pi$
$359$	−1.07000e101	−1.26810	−0.634051	+	0.773291i	$0.718609\pi$
$360$	−2.71995e100	−0.288810
$361$	−7.34732e100	−0.699189
$362$	2.29742e100	0.195998
$363$	6.21817e100	0.475720
$364$	−1.48502e100	−0.101913
$365$	−1.76328e101	−1.08581
$366$	1.28800e101	0.711889
$367$	−1.54635e101	−0.767358	−0.383679	−	0.923467i	$-0.625343\pi$
$367$	−1.54635e101	−0.767358	−0.383679	+	0.923467i	$0.625343\pi$
$368$	−3.72412e100	−0.165972
$369$	6.90795e100	0.276572
$370$	1.04903e101	0.377414
$371$	2.38452e100	0.0771138
$372$	−9.99222e100	−0.290547
$373$	4.26617e101	1.11568	0.557840	−	0.829949i	$-0.311630\pi$
$373$	4.26617e101	1.11568	0.557840	+	0.829949i	$0.311630\pi$
$374$	2.07067e101	0.487171
$375$	1.77747e101	0.376329
$376$	2.50653e101	0.477698
$377$	6.31460e100	0.108358
$378$	−8.84635e100	−0.136722
$379$	−9.99664e101	−1.39189	−0.695946	−	0.718094i	$-0.745015\pi$
$379$	−9.99664e101	−1.39189	−0.695946	+	0.718094i	$0.745015\pi$
$380$	−2.63019e101	−0.330017
$381$	1.35169e101	0.152876
$382$	5.68031e101	0.579254
$383$	1.36150e102	1.25218	0.626091	−	0.779750i	$-0.284654\pi$
$383$	1.36150e102	1.25218	0.626091	+	0.779750i	$0.284654\pi$
$384$	−6.03768e100	−0.0500941
$385$	1.30912e101	0.0980121
$386$	−1.73341e102	−1.17139
$387$	2.06944e102	1.26261
$388$	−5.99837e101	−0.330506
$389$	−4.48106e101	−0.223034	−0.111517	−	0.993763i	$-0.535571\pi$
$389$	−4.48106e101	−0.223034	−0.111517	+	0.993763i	$0.535571\pi$
$390$	−1.07558e102	−0.483715
$391$	2.80787e102	1.14129
$392$	−9.22440e101	−0.338952
$393$	−2.63406e102	−0.875224
$394$	−3.65545e101	−0.109860
$395$	−6.21151e102	−1.68893
$396$	5.52797e101	0.136021
$397$	1.71294e101	0.0381520	0.0190760	−	0.999818i	$-0.493928\pi$
$397$	1.71294e101	0.0381520	0.0190760	+	0.999818i	$0.493928\pi$
$398$	−2.84508e102	−0.573738
$399$	−3.45885e101	−0.0631687
$400$	6.77347e101	0.112058
$401$	−4.65242e102	−0.697391	−0.348696	−	0.937236i	$-0.613375\pi$
$401$	−4.65242e102	−0.697391	−0.348696	+	0.937236i	$0.613375\pi$
$402$	1.53096e101	0.0207987
$403$	8.35022e102	1.02837
$404$	6.36499e102	0.710778
$405$	1.65822e102	0.167946
$406$	−1.68965e101	−0.0155245
$407$	−2.13202e102	−0.177751
$408$	4.55221e102	0.344466
$409$	2.33176e103	1.60182	0.800908	−	0.598787i	$-0.204350\pi$
$409$	2.33176e103	1.60182	0.800908	+	0.598787i	$0.204350\pi$
$410$	−5.55822e102	−0.346716
$411$	1.59213e103	0.902043
$412$	1.37677e103	0.708635
$413$	1.03293e102	0.0483107
$414$	7.49604e102	0.318653
$415$	−5.11218e103	−1.97563
$416$	5.04551e102	0.177304
$417$	−1.44836e103	−0.462916
$418$	5.34555e102	0.155428
$419$	−1.95542e103	−0.517352	−0.258676	−	0.965964i	$-0.583286\pi$
$419$	−1.95542e103	−0.517352	−0.258676	+	0.965964i	$0.583286\pi$
$420$	2.87800e102	0.0693018
$421$	2.45727e102	0.0538655	0.0269328	−	0.999637i	$-0.491426\pi$
$421$	2.45727e102	0.0538655	0.0269328	+	0.999637i	$0.491426\pi$
$422$	1.35291e103	0.270038
$423$	−5.04523e103	−0.917142
$424$	−8.10167e102	−0.134160
$425$	−5.10698e103	−0.770551
$426$	1.83423e103	0.252217
$427$	2.88005e103	0.360994
$428$	2.59914e103	0.297030
$429$	2.18598e103	0.227815
$430$	−1.66509e104	−1.58283
$431$	−2.52250e103	−0.218766	−0.109383	−	0.994000i	$-0.534887\pi$
$431$	−2.52250e103	−0.218766	−0.109383	+	0.994000i	$0.534887\pi$
$432$	3.00564e103	0.237864
$433$	4.62118e103	0.333796	0.166898	−	0.985974i	$-0.446625\pi$
$433$	4.62118e103	0.333796	0.166898	+	0.985974i	$0.446625\pi$
$434$	−2.23433e103	−0.147334
$435$	−1.22378e103	−0.0736849
$436$	7.64382e103	0.420333
$437$	7.24867e103	0.364118
$438$	7.87839e103	0.361585
$439$	3.70824e104	1.55532	0.777659	−	0.628686i	$-0.216407\pi$
$439$	3.70824e104	1.55532	0.777659	+	0.628686i	$0.216407\pi$
$440$	−4.44787e103	−0.170518
$441$	1.85672e104	0.650762
$442$	−3.80416e104	−1.21921
$443$	1.98367e104	0.581464	0.290732	−	0.956804i	$-0.406101\pi$
$443$	1.98367e104	0.581464	0.290732	+	0.956804i	$0.406101\pi$
$444$	−4.68709e103	−0.125683
$445$	−3.96016e104	−0.971610
$446$	2.63192e103	0.0590944
$447$	4.25542e104	0.874571
$448$	−1.35007e103	−0.0254024
$449$	−1.53692e103	−0.0264801	−0.0132401	−	0.999912i	$-0.504215\pi$
$449$	−1.53692e103	−0.0264801	−0.0132401	+	0.999912i	$0.504215\pi$
$450$	−1.36339e104	−0.215142
$451$	1.12964e104	0.163293
$452$	−2.93633e104	−0.388898
$453$	1.47235e104	0.178703
$454$	1.00070e105	1.11327
$455$	−2.40507e104	−0.245288
$456$	1.17518e104	0.109899
$457$	−6.47448e104	−0.555284	−0.277642	−	0.960685i	$-0.589553\pi$
$457$	−6.47448e104	−0.555284	−0.277642	+	0.960685i	$0.589553\pi$
$458$	−3.29218e104	−0.258999
$459$	−2.26616e105	−1.63564
$460$	−6.03140e104	−0.399470
$461$	3.27201e104	0.198897	0.0994486	−	0.995043i	$-0.468292\pi$
$461$	3.27201e104	0.198897	0.0994486	+	0.995043i	$0.468292\pi$
$462$	−5.84919e103	−0.0326390
$463$	−1.52312e105	−0.780342	−0.390171	−	0.920743i	$-0.627584\pi$
$463$	−1.52312e105	−0.780342	−0.390171	+	0.920743i	$0.627584\pi$
$464$	5.74075e103	0.0270090
$465$	−1.61829e105	−0.699302
$466$	6.50592e104	0.258265
$467$	4.27864e105	1.56059	0.780296	−	0.625411i	$-0.215069\pi$
$467$	4.27864e105	1.56059	0.780296	+	0.625411i	$0.215069\pi$
$468$	−1.01558e105	−0.340410
$469$	3.42334e103	0.0105469
$470$	4.05945e105	1.14975
$471$	−3.96760e105	−1.03324
$472$	−3.50948e104	−0.0840493
$473$	3.38410e105	0.745466
$474$	2.77532e105	0.562431
$475$	−1.31840e105	−0.245838
$476$	1.01791e105	0.174676
$477$	1.63073e105	0.257577
$478$	9.05933e105	1.31733
$479$	5.99734e105	0.802982	0.401491	−	0.915863i	$-0.368492\pi$
$479$	5.99734e105	0.802982	0.401491	+	0.915863i	$0.368492\pi$
$480$	−9.77832e104	−0.120569
$481$	3.91686e105	0.444844
$482$	−2.59325e105	−0.271322
$483$	−7.93162e104	−0.0764628
$484$	−4.72413e105	−0.419691
$485$	−9.71465e105	−0.795479
$486$	−9.65355e105	−0.728709
$487$	−9.70453e105	−0.675430	−0.337715	−	0.941248i	$-0.609654\pi$
$487$	−9.70453e105	−0.675430	−0.337715	+	0.941248i	$0.609654\pi$
$488$	−9.78529e105	−0.628045
$489$	−1.05332e106	−0.623534
$490$	−1.49394e106	−0.815807
$491$	2.30647e106	1.16206	0.581031	−	0.813881i	$-0.302650\pi$
$491$	2.30647e106	1.16206	0.581031	+	0.813881i	$0.302650\pi$
$492$	2.48343e105	0.115460
$493$	−4.32834e105	−0.185724
$494$	−9.82065e105	−0.388979
$495$	8.95282e105	0.327382
$496$	7.59138e105	0.256327
$497$	4.10147e105	0.127897
$498$	2.28414e106	0.657906
$499$	−1.71471e106	−0.456267	−0.228134	−	0.973630i	$-0.573262\pi$
$499$	−1.71471e106	−0.456267	−0.228134	+	0.973630i	$0.573262\pi$
$500$	−1.35040e106	−0.332006
$501$	4.41425e106	1.00292
$502$	−4.17917e106	−0.877593
$503$	−4.85813e106	−0.943047	−0.471523	−	0.881854i	$-0.656296\pi$
$503$	−4.85813e106	−0.943047	−0.471523	+	0.881854i	$0.656296\pi$
$504$	2.71746e105	0.0487705
$505$	1.03084e107	1.71074
$506$	1.22581e106	0.188138
$507$	−2.38592e104	−0.00338721
$508$	−1.02691e106	−0.134871
$509$	−2.97109e106	−0.361046	−0.180523	−	0.983571i	$-0.557779\pi$
$509$	−2.97109e106	−0.361046	−0.180523	+	0.983571i	$0.557779\pi$
$510$	7.37254e106	0.829077
$511$	1.76166e106	0.183357
$512$	4.58700e105	0.0441942
$513$	−5.85021e106	−0.521838
$514$	−3.06640e106	−0.253271
$515$	2.22976e107	1.70558
$516$	7.43970e106	0.527099
$517$	−8.25034e106	−0.541496
$518$	−1.04807e106	−0.0637328
$519$	−1.87548e107	−1.05682
$520$	8.17146e106	0.426744
$521$	−2.30322e107	−1.11492	−0.557461	−	0.830203i	$-0.688224\pi$
$521$	−2.30322e107	−1.11492	−0.557461	+	0.830203i	$0.688224\pi$
$522$	−1.15552e106	−0.0518551
$523$	1.79475e107	0.746772	0.373386	−	0.927676i	$-0.378197\pi$
$523$	1.79475e107	0.746772	0.373386	+	0.927676i	$0.378197\pi$
$524$	2.00117e107	0.772143
$525$	1.44261e106	0.0516246
$526$	−1.56065e107	−0.518046
$527$	−5.72366e107	−1.76260
$528$	1.98732e106	0.0567843
$529$	−2.10915e107	−0.559253
$530$	−1.31211e107	−0.322903
$531$	7.06401e106	0.161368
$532$	2.62779e106	0.0557289
$533$	−2.07533e107	−0.408661
$534$	1.76941e107	0.323556
$535$	4.20943e107	0.714906
$536$	−1.16312e106	−0.0183491
$537$	−4.50160e107	−0.659755
$538$	6.88019e106	0.0936916
$539$	3.03625e107	0.384221
$540$	4.86778e107	0.572503
$541$	4.85269e107	0.530507	0.265253	−	0.964179i	$-0.414544\pi$
$541$	4.85269e107	0.530507	0.265253	+	0.964179i	$0.414544\pi$
$542$	−5.01585e107	−0.509768
$543$	−1.66246e107	−0.157093
$544$	−3.45845e107	−0.303896
$545$	1.23795e108	1.01168
$546$	1.07459e107	0.0816835
$547$	2.28510e108	1.61587	0.807935	−	0.589272i	$-0.200585\pi$
$547$	2.28510e108	1.61587	0.807935	+	0.589272i	$0.200585\pi$
$548$	−1.20959e108	−0.795804
$549$	1.96962e108	1.20580
$550$	−2.22951e107	−0.127023
$551$	−1.11739e107	−0.0592537
$552$	2.69485e107	0.133027
$553$	6.20582e107	0.285205
$554$	−1.46440e108	−0.626649
$555$	−7.59097e107	−0.302499
$556$	1.10036e108	0.408395
$557$	−1.17658e108	−0.406763	−0.203381	−	0.979100i	$-0.565193\pi$
$557$	−1.17658e108	−0.406763	−0.203381	+	0.979100i	$0.565193\pi$
$558$	−1.52802e108	−0.492128
$559$	−6.21715e108	−1.86563
$560$	−2.18650e107	−0.0611396
$561$	−1.49838e108	−0.390470
$562$	5.48656e107	0.133265
$563$	−1.27725e108	−0.289197	−0.144598	−	0.989490i	$-0.546189\pi$
$563$	−1.27725e108	−0.289197	−0.144598	+	0.989490i	$0.546189\pi$
$564$	−1.81378e108	−0.382877
$565$	−4.75553e108	−0.936020
$566$	3.59944e108	0.660673
$567$	−1.65671e107	−0.0283606
$568$	−1.39352e108	−0.222512
$569$	9.69265e108	1.44380	0.721902	−	0.691996i	$-0.243268\pi$
$569$	9.69265e108	1.44380	0.721902	+	0.691996i	$0.243268\pi$
$570$	1.90326e108	0.264510
$571$	1.01163e109	1.31188	0.655941	−	0.754812i	$-0.272272\pi$
$571$	1.01163e109	1.31188	0.655941	+	0.754812i	$0.272272\pi$
$572$	−1.66075e108	−0.200984
$573$	−4.11039e108	−0.464275
$574$	5.55313e107	0.0585489
$575$	−3.02327e108	−0.297575
$576$	−9.23287e107	−0.0848493
$577$	−1.82860e109	−1.56918	−0.784592	−	0.620012i	$-0.787128\pi$
$577$	−1.82860e109	−1.56918	−0.784592	+	0.620012i	$0.787128\pi$
$578$	1.72522e109	1.38260
$579$	1.25433e109	0.938876
$580$	9.29743e107	0.0650066
$581$	5.10750e108	0.333620
$582$	4.34054e108	0.264903
$583$	2.66669e108	0.152078
$584$	−5.98544e108	−0.318998
$585$	−1.64478e109	−0.819316
$586$	1.62015e109	0.754396
$587$	6.79134e108	0.295631	0.147816	−	0.989015i	$-0.452776\pi$
$587$	6.79134e108	0.295631	0.147816	+	0.989015i	$0.452776\pi$
$588$	6.67497e108	0.271672
$589$	−1.47760e109	−0.562343
$590$	−5.68378e108	−0.202294
$591$	2.64516e108	0.0880535
$592$	3.56091e108	0.110880
$593$	−6.06804e108	−0.176762	−0.0883808	−	0.996087i	$-0.528169\pi$
$593$	−6.06804e108	−0.176762	−0.0883808	+	0.996087i	$0.528169\pi$
$594$	−9.89317e108	−0.269632
$595$	1.64855e109	0.420419
$596$	−3.23297e109	−0.771567
$597$	2.05876e109	0.459854
$598$	−2.25201e109	−0.470841
$599$	−1.34300e109	−0.262854	−0.131427	−	0.991326i	$-0.541956\pi$
$599$	−1.34300e109	−0.262854	−0.131427	+	0.991326i	$0.541956\pi$
$600$	−4.90143e108	−0.0898148
$601$	8.18477e108	0.140432	0.0702158	−	0.997532i	$-0.477631\pi$
$601$	8.18477e108	0.140432	0.0702158	+	0.997532i	$0.477631\pi$
$602$	1.66357e109	0.267288
$603$	2.34116e108	0.0352288
$604$	−1.11859e109	−0.157656
$605$	−7.65096e109	−1.01013
$606$	−4.60584e109	−0.569693
$607$	−5.35707e109	−0.620832	−0.310416	−	0.950601i	$-0.600468\pi$
$607$	−5.35707e109	−0.620832	−0.310416	+	0.950601i	$0.600468\pi$
$608$	−8.92819e108	−0.0969554
$609$	1.22266e108	0.0124430
$610$	−1.58478e110	−1.51161
$611$	1.51572e110	1.35516
$612$	6.96128e109	0.583456
$613$	1.02717e110	0.807152	0.403576	−	0.914946i	$-0.367767\pi$
$613$	1.02717e110	0.807152	0.403576	+	0.914946i	$0.367767\pi$
$614$	1.24126e110	0.914557
$615$	4.02204e109	0.277894
$616$	4.44380e108	0.0287949
$617$	1.92725e110	1.17132	0.585658	−	0.810558i	$-0.300836\pi$
$617$	1.92725e110	1.17132	0.585658	+	0.810558i	$0.300836\pi$
$618$	−9.96263e109	−0.567975
$619$	1.71413e110	0.916773	0.458387	−	0.888753i	$-0.348428\pi$
$619$	1.71413e110	0.916773	0.458387	+	0.888753i	$0.348428\pi$
$620$	1.22946e110	0.616941
$621$	−1.34154e110	−0.631661
$622$	2.98020e109	0.131682
$623$	3.95653e109	0.164073
$624$	−3.65104e109	−0.142110
$625$	−3.41380e110	−1.24732
$626$	6.49527e109	0.222798
$627$	−3.86815e109	−0.124576
$628$	3.01430e110	0.911550
$629$	−2.68482e110	−0.762454
$630$	4.40107e109	0.117383
$631$	1.26048e110	0.315774	0.157887	−	0.987457i	$-0.449532\pi$
$631$	1.26048e110	0.315774	0.157887	+	0.987457i	$0.449532\pi$
$632$	−2.10849e110	−0.496190
$633$	−9.78990e109	−0.216437
$634$	−1.17792e110	−0.244676
$635$	−1.66314e110	−0.324614
$636$	5.86254e109	0.107530
$637$	−5.57809e110	−0.961563
$638$	−1.88959e109	−0.0306161
$639$	2.80492e110	0.427205
$640$	7.42887e109	0.106369
$641$	−1.34704e111	−1.81338	−0.906691	−	0.421796i	$-0.861400\pi$
$641$	−1.34704e111	−1.81338	−0.906691	+	0.421796i	$0.861400\pi$
$642$	−1.88079e110	−0.238071
$643$	−1.06147e111	−1.26349	−0.631746	−	0.775176i	$-0.717661\pi$
$643$	−1.06147e111	−1.26349	−0.631746	+	0.775176i	$0.717661\pi$
$644$	6.02588e109	0.0674573
$645$	1.20490e111	1.26865
$646$	6.73157e110	0.666702
$647$	1.67610e111	1.56164	0.780821	−	0.624754i	$-0.214801\pi$
$647$	1.67610e111	1.56164	0.780821	+	0.624754i	$0.214801\pi$
$648$	5.62884e109	0.0493408
$649$	1.15516e110	0.0952744
$650$	4.09598e110	0.317893
$651$	1.61681e110	0.118089
$652$	8.00237e110	0.550096
$653$	−2.48695e111	−1.60915	−0.804576	−	0.593849i	$-0.797608\pi$
$653$	−2.48695e111	−1.60915	−0.804576	+	0.593849i	$0.797608\pi$
$654$	−5.53123e110	−0.336899
$655$	3.24099e111	1.85843
$656$	−1.88674e110	−0.101861
$657$	1.20477e111	0.612452
$658$	−4.05574e110	−0.194154
$659$	4.85740e110	0.218993	0.109497	−	0.993987i	$-0.465076\pi$
$659$	4.85740e110	0.218993	0.109497	+	0.993987i	$0.465076\pi$
$660$	3.21857e110	0.136671
$661$	−4.55920e110	−0.182361	−0.0911804	−	0.995834i	$-0.529064\pi$
$661$	−4.55920e110	−0.182361	−0.0911804	+	0.995834i	$0.529064\pi$
$662$	−2.29504e111	−0.864769
$663$	2.75277e111	0.977204
$664$	−1.73533e111	−0.580420
$665$	4.25583e110	0.134131
$666$	−7.16753e110	−0.212881
$667$	−2.56232e110	−0.0717238
$668$	−3.35363e111	−0.884800
$669$	−1.90451e110	−0.0473644
$670$	−1.88373e110	−0.0441635
$671$	3.22086e111	0.711922
$672$	9.76937e109	0.0203601
$673$	−9.83245e111	−1.93226	−0.966132	−	0.258047i	$-0.916921\pi$
$673$	−9.83245e111	−1.93226	−0.966132	+	0.258047i	$0.916921\pi$
$674$	5.74208e111	1.06415
$675$	2.44000e111	0.426472
$676$	1.81265e109	0.00298828
$677$	−6.06797e110	−0.0943606	−0.0471803	−	0.998886i	$-0.515024\pi$
$677$	−6.06797e110	−0.0943606	−0.0471803	+	0.998886i	$0.515024\pi$
$678$	2.12479e111	0.311704
$679$	9.70577e110	0.134330
$680$	−5.60113e111	−0.731431
$681$	−7.24130e111	−0.892290
$682$	−2.49873e111	−0.290560
$683$	1.05684e112	1.15983	0.579914	−	0.814678i	$-0.303086\pi$
$683$	1.05684e112	1.15983	0.579914	+	0.814678i	$0.303086\pi$
$684$	1.79710e111	0.186147
$685$	−1.95899e112	−1.91538
$686$	3.04944e111	0.281460
$687$	2.38229e111	0.207589
$688$	−5.65216e111	−0.465019
$689$	−4.89916e111	−0.380594
$690$	4.36445e111	0.320177
$691$	6.73270e111	0.466451	0.233226	−	0.972423i	$-0.425072\pi$
$691$	6.73270e111	0.466451	0.233226	+	0.972423i	$0.425072\pi$
$692$	1.42486e112	0.932353
$693$	−8.94463e110	−0.0552840
$694$	3.03275e111	0.177067
$695$	1.78209e112	0.982945
$696$	−4.15413e110	−0.0216479
$697$	1.42254e112	0.700437
$698$	1.95910e112	0.911525
$699$	−4.70782e111	−0.207001
$700$	−1.09599e111	−0.0455445
$701$	1.16482e112	0.457508	0.228754	−	0.973484i	$-0.426535\pi$
$701$	1.16482e112	0.457508	0.228754	+	0.973484i	$0.426535\pi$
$702$	1.81754e112	0.674789
$703$	−6.93101e111	−0.243255
$704$	−1.50983e111	−0.0500965
$705$	−2.93750e112	−0.921528
$706$	−1.91006e112	−0.566579
$707$	−1.02990e112	−0.288887
$708$	2.53954e111	0.0673660
$709$	−2.47067e112	−0.619854	−0.309927	−	0.950760i	$-0.600305\pi$
$709$	−2.47067e112	−0.619854	−0.309927	+	0.950760i	$0.600305\pi$
$710$	−2.25687e112	−0.535552
$711$	4.24405e112	0.952645
$712$	−1.34427e112	−0.285449
$713$	−3.38833e112	−0.680690
$714$	−7.36579e111	−0.140004
$715$	−2.68967e112	−0.483738
$716$	3.42000e112	0.582052
$717$	−6.55552e112	−1.05585
$718$	−5.88240e112	−0.896684
$719$	6.57218e112	0.948239	0.474120	−	0.880460i	$-0.342766\pi$
$719$	6.57218e112	0.948239	0.474120	+	0.880460i	$0.342766\pi$
$720$	−1.49531e112	−0.204220
$721$	−2.22772e112	−0.288016
$722$	−4.03923e112	−0.494401
$723$	1.87653e112	0.217466
$724$	1.26302e112	0.138591
$725$	4.66038e111	0.0484251
$726$	3.41848e112	0.336385
$727$	6.76758e112	0.630702	0.315351	−	0.948975i	$-0.397878\pi$
$727$	6.76758e112	0.630702	0.315351	+	0.948975i	$0.397878\pi$
$728$	−8.16399e111	−0.0720631
$729$	5.31638e112	0.444507
$730$	−9.69372e112	−0.767781
$731$	4.26155e113	3.19765
$732$	7.08084e112	0.503381
$733$	−2.31755e113	−1.56107	−0.780535	−	0.625113i	$-0.785053\pi$
$733$	−2.31755e113	−1.56107	−0.780535	+	0.625113i	$0.785053\pi$
$734$	−8.50114e112	−0.542604
$735$	1.08105e113	0.653874
$736$	−2.04736e112	−0.117360
$737$	3.82844e111	0.0207997
$738$	3.79769e112	0.195566
$739$	−2.43476e111	−0.0118850	−0.00594252	−	0.999982i	$-0.501892\pi$
$739$	−2.43476e111	−0.0118850	−0.00594252	+	0.999982i	$0.501892\pi$
$740$	5.76708e112	0.266872
$741$	7.10643e112	0.311768
$742$	1.31091e112	0.0545277
$743$	−1.37580e113	−0.542623	−0.271312	−	0.962492i	$-0.587457\pi$
$743$	−1.37580e113	−0.542623	−0.271312	+	0.962492i	$0.587457\pi$
$744$	−5.49328e112	−0.205447
$745$	−5.23595e113	−1.85705
$746$	2.34535e113	0.788905
$747$	3.49293e113	1.11436
$748$	1.13836e113	0.344482
$749$	−4.20558e112	−0.120724
$750$	9.77176e112	0.266105
$751$	−6.50645e113	−1.68100	−0.840498	−	0.541815i	$-0.817737\pi$
$751$	−6.50645e113	−1.68100	−0.840498	+	0.541815i	$0.817737\pi$
$752$	1.37798e113	0.337783
$753$	3.02414e113	0.703396
$754$	3.47149e112	0.0766209
$755$	−1.81161e113	−0.379454
$756$	−4.86333e112	−0.0966769
$757$	−6.36602e113	−1.20110	−0.600552	−	0.799586i	$-0.705053\pi$
$757$	−6.36602e113	−1.20110	−0.600552	+	0.799586i	$0.705053\pi$
$758$	−5.49571e113	−0.984216
$759$	−8.87020e112	−0.150794
$760$	−1.44596e113	−0.233357
$761$	−2.38873e112	−0.0365994	−0.0182997	−	0.999833i	$-0.505825\pi$
$761$	−2.38873e112	−0.0365994	−0.0182997	+	0.999833i	$0.505825\pi$
$762$	7.43097e112	0.108100
$763$	−1.23682e113	−0.170839
$764$	3.12278e113	0.409594
$765$	1.12741e114	1.40429
$766$	7.48495e113	0.885426
$767$	−2.12222e113	−0.238437
$768$	−3.31925e112	−0.0354219
$769$	−4.88929e113	−0.495628	−0.247814	−	0.968808i	$-0.579712\pi$
$769$	−4.88929e113	−0.495628	−0.247814	+	0.968808i	$0.579712\pi$
$770$	7.19695e112	0.0693051
$771$	2.21891e113	0.202998
$772$	−9.52950e113	−0.828299
$773$	−3.54645e113	−0.292889	−0.146445	−	0.989219i	$-0.546783\pi$
$773$	−3.54645e113	−0.292889	−0.146445	+	0.989219i	$0.546783\pi$
$774$	1.13769e114	0.892800
$775$	6.16273e113	0.459575
$776$	−3.29764e113	−0.233703
$777$	7.58402e112	0.0510822
$778$	−2.46349e113	−0.157709
$779$	3.67237e113	0.223469
$780$	−5.91304e113	−0.342038
$781$	4.58681e113	0.252229
$782$	1.54364e114	0.807011
$783$	2.06798e113	0.102792
$784$	−5.07117e113	−0.239676
$785$	4.88181e114	2.19396
$786$	−1.44809e114	−0.618877
$787$	1.15764e114	0.470513	0.235257	−	0.971933i	$-0.424407\pi$
$787$	1.15764e114	0.470513	0.235257	+	0.971933i	$0.424407\pi$
$788$	−2.00961e113	−0.0776829
$789$	1.12932e114	0.415216
$790$	−3.41481e114	−1.19425
$791$	4.75118e113	0.158063
$792$	3.03903e113	0.0961813
$793$	−5.91726e114	−1.78168
$794$	9.41700e112	0.0269776
$795$	9.49467e113	0.258808
$796$	−1.56410e114	−0.405694
$797$	−2.73245e114	−0.674449	−0.337224	−	0.941424i	$-0.609488\pi$
$797$	−2.73245e114	−0.674449	−0.337224	+	0.941424i	$0.609488\pi$
$798$	−1.90152e113	−0.0446670
$799$	−1.03895e115	−2.32273
$800$	3.72376e113	0.0792367
$801$	2.70580e114	0.548039
$802$	−2.55770e114	−0.493130
$803$	1.97013e114	0.361602
$804$	8.41656e112	0.0147069
$805$	9.75922e113	0.162360
$806$	4.59058e114	0.727166
$807$	−4.97865e113	−0.0750943
$808$	3.49919e114	0.502596
$809$	5.73262e114	0.784127	0.392063	−	0.919938i	$-0.371761\pi$
$809$	5.73262e114	0.784127	0.392063	+	0.919938i	$0.371761\pi$
$810$	9.11619e113	0.118756
$811$	−1.19603e115	−1.48395	−0.741976	−	0.670427i	$-0.766111\pi$
$811$	−1.19603e115	−1.48395	−0.741976	+	0.670427i	$0.766111\pi$
$812$	−9.28893e112	−0.0109775
$813$	3.62958e114	0.408582
$814$	−1.17209e114	−0.125689
$815$	1.29602e115	1.32400
$816$	2.50261e114	0.243574
$817$	1.10014e115	1.02018
$818$	1.28190e115	1.13266
$819$	1.64328e114	0.138355
$820$	−3.05566e114	−0.245165
$821$	−5.25239e114	−0.401608	−0.200804	−	0.979631i	$-0.564355\pi$
$821$	−5.25239e114	−0.401608	−0.200804	+	0.979631i	$0.564355\pi$
$822$	8.75284e114	0.637841
$823$	−1.95872e115	−1.36044	−0.680219	−	0.733009i	$-0.738115\pi$
$823$	−1.95872e115	−1.36044	−0.680219	+	0.733009i	$0.738115\pi$
$824$	7.56890e114	0.501081
$825$	1.61332e114	0.101810
$826$	5.67858e113	0.0341608
$827$	−2.24516e115	−1.28760	−0.643799	−	0.765194i	$-0.722643\pi$
$827$	−2.24516e115	−1.28760	−0.643799	+	0.765194i	$0.722643\pi$
$828$	4.12099e114	0.225322
$829$	−1.93714e114	−0.100985	−0.0504926	−	0.998724i	$-0.516079\pi$
$829$	−1.93714e114	−0.100985	−0.0504926	+	0.998724i	$0.516079\pi$
$830$	−2.81045e115	−1.39698
$831$	1.05967e115	0.502262
$832$	2.77380e114	0.125373
$833$	3.82350e115	1.64810
$834$	−7.96243e114	−0.327331
$835$	−5.43137e115	−2.12958
$836$	2.93874e114	0.109904
$837$	2.73463e115	0.975536
$838$	−1.07500e115	−0.365823
$839$	1.82782e115	0.593384	0.296692	−	0.954973i	$-0.404116\pi$
$839$	1.82782e115	0.593384	0.296692	+	0.954973i	$0.404116\pi$
$840$	1.58220e114	0.0490037
$841$	−3.34459e115	−0.988328
$842$	1.35090e114	0.0380887
$843$	−3.97019e114	−0.106812
$844$	7.43767e114	0.190946
$845$	2.93569e113	0.00719233
$846$	−2.77365e115	−0.648517
$847$	7.64396e114	0.170578
$848$	−4.45394e114	−0.0948655
$849$	−2.60463e115	−0.529533
$850$	−2.80759e115	−0.544862
$851$	−1.58938e115	−0.294448
$852$	1.00838e115	0.178344
$853$	4.74639e115	0.801451	0.400725	−	0.916198i	$-0.368758\pi$
$853$	4.74639e115	0.801451	0.400725	+	0.916198i	$0.368758\pi$
$854$	1.58333e115	0.255261
$855$	2.91049e115	0.448027
$856$	1.42889e115	0.210032
$857$	1.20258e116	1.68799	0.843996	−	0.536350i	$-0.180197\pi$
$857$	1.20258e116	1.68799	0.843996	+	0.536350i	$0.180197\pi$
$858$	1.20175e115	0.161090
$859$	−1.14226e115	−0.146229	−0.0731145	−	0.997324i	$-0.523294\pi$
$859$	−1.14226e115	−0.146229	−0.0731145	+	0.997324i	$0.523294\pi$
$860$	−9.15395e115	−1.11923
$861$	−4.01836e114	−0.0469272
$862$	−1.38676e115	−0.154691
$863$	−6.75444e115	−0.719718	−0.359859	−	0.933007i	$-0.617175\pi$
$863$	−6.75444e115	−0.719718	−0.359859	+	0.933007i	$0.617175\pi$
$864$	1.65237e115	0.168195
$865$	2.30763e116	2.24403
$866$	2.54052e115	0.236029
$867$	−1.24841e116	−1.10816
$868$	−1.22834e115	−0.104181
$869$	6.94018e115	0.562458
$870$	−6.72782e114	−0.0521031
$871$	−7.03348e114	−0.0520539
$872$	4.20223e115	0.297221
$873$	6.63760e115	0.448692
$874$	3.98500e115	0.257470
$875$	2.18504e115	0.134940
$876$	4.33119e115	0.255679
$877$	−3.48116e116	−1.96445	−0.982223	−	0.187720i	$-0.939890\pi$
$877$	−3.48116e116	−1.96445	−0.982223	+	0.187720i	$0.939890\pi$
$878$	2.03863e116	1.09978
$879$	−1.17237e116	−0.604652
$880$	−2.44524e115	−0.120575
$881$	−3.49904e116	−1.64968	−0.824841	−	0.565365i	$-0.808735\pi$
$881$	−3.49904e116	−1.64968	−0.824841	+	0.565365i	$0.808735\pi$
$882$	1.02074e116	0.460158
$883$	1.11374e116	0.480106	0.240053	−	0.970760i	$-0.422835\pi$
$883$	1.11374e116	0.480106	0.240053	+	0.970760i	$0.422835\pi$
$884$	−2.09136e116	−0.862112
$885$	4.11291e115	0.162140
$886$	1.09054e116	0.411157
$887$	−3.98786e116	−1.43799	−0.718996	−	0.695014i	$-0.755398\pi$
$887$	−3.98786e116	−1.43799	−0.718996	+	0.695014i	$0.755398\pi$
$888$	−2.57675e115	−0.0888711
$889$	1.66162e115	0.0548165
$890$	−2.17712e116	−0.687032
$891$	−1.85275e115	−0.0559304
$892$	1.44691e115	0.0417860
$893$	−2.68212e116	−0.741046
$894$	2.33944e116	0.618415
$895$	5.53886e116	1.40091
$896$	−7.42208e114	−0.0179622
$897$	1.62960e116	0.377381
$898$	−8.44929e114	−0.0187243
$899$	5.22313e115	0.110770
$900$	−7.49530e115	−0.152128
$901$	3.35813e116	0.652331
$902$	6.21026e115	0.115465
$903$	−1.20379e116	−0.214233
$904$	−1.61426e116	−0.274993
$905$	2.04552e116	0.333569
$906$	8.09432e115	0.126362
$907$	8.34265e116	1.24686	0.623428	−	0.781881i	$-0.285740\pi$
$907$	8.34265e116	1.24686	0.623428	+	0.781881i	$0.285740\pi$
$908$	5.50143e116	0.787199
$909$	−7.04330e116	−0.964945
$910$	−1.32220e116	−0.173445
$911$	8.37500e116	1.05198	0.525992	−	0.850490i	$-0.323694\pi$
$911$	8.37500e116	1.05198	0.525992	+	0.850490i	$0.323694\pi$
$912$	6.46062e115	0.0777102
$913$	5.71190e116	0.657937
$914$	−3.55938e116	−0.392645
$915$	1.14678e117	1.21156
$916$	−1.80990e116	−0.183140
$917$	−3.23803e116	−0.313828
$918$	−1.24583e117	−1.15657
$919$	−1.19879e117	−1.06605	−0.533027	−	0.846099i	$-0.678945\pi$
$919$	−1.19879e117	−1.06605	−0.533027	+	0.846099i	$0.678945\pi$
$920$	−3.31580e116	−0.282468
$921$	−8.98199e116	−0.733022
$922$	1.79881e116	0.140642
$923$	−8.42673e116	−0.631236
$924$	−3.21562e115	−0.0230793
$925$	2.89077e116	0.198800
$926$	−8.37344e116	−0.551785
$927$	−1.52349e117	−0.962036
$928$	3.15601e115	0.0190982
$929$	−3.36229e115	−0.0194991	−0.00974955	−	0.999952i	$-0.503103\pi$
$929$	−3.36229e115	−0.0194991	−0.00974955	+	0.999952i	$0.503103\pi$
$930$	−8.89664e116	−0.494481
$931$	9.87059e116	0.525812
$932$	3.57667e116	0.182621
$933$	−2.15653e116	−0.105543
$934$	2.35221e117	1.10350
$935$	1.84363e117	0.829117
$936$	−5.58320e116	−0.240706
$937$	2.01314e117	0.832072	0.416036	−	0.909348i	$-0.363419\pi$
$937$	2.01314e117	0.832072	0.416036	+	0.909348i	$0.363419\pi$
$938$	1.88200e115	0.00745776
$939$	−4.70011e116	−0.178574
$940$	2.23171e117	0.812993
$941$	−4.68874e117	−1.63782	−0.818910	−	0.573922i	$-0.805421\pi$
$941$	−4.68874e117	−1.63782	−0.818910	+	0.573922i	$0.805421\pi$
$942$	−2.18121e117	−0.730612
$943$	8.42124e116	0.270498
$944$	−1.92936e116	−0.0594319
$945$	−7.87641e116	−0.232687
$946$	1.86043e117	0.527124
$947$	2.62277e117	0.712748	0.356374	−	0.934343i	$-0.384013\pi$
$947$	2.62277e117	0.712748	0.356374	+	0.934343i	$0.384013\pi$
$948$	1.52575e117	0.397699
$949$	−3.61945e117	−0.904956
$950$	−7.24796e116	−0.173833
$951$	8.52370e116	0.196109
$952$	5.59601e116	0.123515
$953$	−2.14786e117	−0.454817	−0.227409	−	0.973799i	$-0.573025\pi$
$953$	−2.14786e117	−0.454817	−0.227409	+	0.973799i	$0.573025\pi$
$954$	8.96504e116	0.182134
$955$	5.05750e117	0.985832
$956$	4.98042e117	0.931492
$957$	1.36735e116	0.0245390
$958$	3.29707e117	0.567794
$959$	1.95720e117	0.323445
$960$	−5.37569e116	−0.0852551
$961$	3.36764e116	0.0512569
$962$	2.15332e117	0.314552
$963$	−2.87612e117	−0.403245
$964$	−1.42565e117	−0.191854
$965$	−1.54335e118	−1.99359
$966$	−4.36045e116	−0.0540674
$967$	1.10219e118	1.31193	0.655967	−	0.754789i	$-0.272261\pi$
$967$	1.10219e118	1.31193	0.655967	+	0.754789i	$0.272261\pi$
$968$	−2.59712e117	−0.296766
$969$	−4.87110e117	−0.534365
$970$	−5.34069e117	−0.562489
$971$	9.46321e117	0.956927	0.478464	−	0.878107i	$-0.341194\pi$
$971$	9.46321e117	0.956927	0.478464	+	0.878107i	$0.341194\pi$
$972$	−5.30709e117	−0.515275
$973$	−1.78046e117	−0.165987
$974$	−5.33512e117	−0.477601
$975$	−2.96394e117	−0.254793
$976$	−5.37952e117	−0.444095
$977$	6.33104e117	0.501926	0.250963	−	0.967997i	$-0.419253\pi$
$977$	6.33104e117	0.501926	0.250963	+	0.967997i	$0.419253\pi$
$978$	−5.79068e117	−0.440905
$979$	4.42473e117	0.323571
$980$	−8.21301e117	−0.576863
$981$	−8.45840e117	−0.570640
$982$	1.26800e118	0.821702
$983$	−2.21813e118	−1.38078	−0.690389	−	0.723439i	$-0.742560\pi$
$983$	−2.21813e118	−1.38078	−0.690389	+	0.723439i	$0.742560\pi$
$984$	1.36528e117	0.0816424
$985$	−3.25466e117	−0.186971
$986$	−2.37953e117	−0.131327
$987$	2.93482e117	0.155616
$988$	−5.39896e117	−0.275049
$989$	2.52278e118	1.23488
$990$	4.92186e117	0.231494
$991$	2.82670e118	1.27753	0.638765	−	0.769402i	$-0.279446\pi$
$991$	2.82670e118	1.27753	0.638765	+	0.769402i	$0.279446\pi$
$992$	4.17340e117	0.181251
$993$	1.66074e118	0.693117
$994$	2.25480e117	0.0904371
$995$	−2.53314e118	−0.976444
$996$	1.25572e118	0.465210
$997$	2.50563e118	0.892192	0.446096	−	0.894985i	$-0.352814\pi$
$997$	2.50563e118	0.892192	0.446096	+	0.894985i	$0.352814\pi$
$998$	−9.42672e117	−0.322630
$999$	1.28274e118	0.421991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.80.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.80.a.a.1.2	✓	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+5.49756e11 q^{2} -3.97815e18 q^{3} +3.02231e23 q^{4} +4.89479e27 q^{5} -2.18701e30 q^{6} -4.89031e32 q^{7} +1.66153e35 q^{8} -3.34439e37 q^{9} +O(q^{10})\)	\(q+5.49756e11 q^{2} -3.97815e18 q^{3} +3.02231e23 q^{4} +4.89479e27 q^{5} -2.18701e30 q^{6} -4.89031e32 q^{7} +1.66153e35 q^{8} -3.34439e37 q^{9} +2.69094e39 q^{10} -5.46900e40 q^{11} -1.20232e42 q^{12} +1.00475e44 q^{13} -2.68848e44 q^{14} -1.94722e46 q^{15} +9.13439e46 q^{16} -6.88703e48 q^{17} -1.83860e49 q^{18} -1.77793e50 q^{19} +1.47936e51 q^{20} +1.94544e51 q^{21} -3.00662e52 q^{22} -4.07703e53 q^{23} -6.60983e53 q^{24} +7.41536e54 q^{25} +5.52365e55 q^{26} +3.29047e56 q^{27} -1.47801e56 q^{28} +6.28477e56 q^{29} -1.07050e58 q^{30} +8.31077e58 q^{31} +5.02168e58 q^{32} +2.17565e59 q^{33} -3.78619e60 q^{34} -2.39370e60 q^{35} -1.01078e61 q^{36} +3.89836e61 q^{37} -9.77426e61 q^{38} -3.99703e62 q^{39} +8.13286e62 q^{40} -2.06553e63 q^{41} +1.06952e63 q^{42} -6.18778e64 q^{43} -1.65290e64 q^{44} -1.63701e65 q^{45} -2.24137e65 q^{46} +1.50856e66 q^{47} -3.63379e65 q^{48} -5.55174e66 q^{49} +4.07663e66 q^{50} +2.73976e67 q^{51} +3.03666e67 q^{52} -4.87601e67 q^{53} +1.80895e68 q^{54} -2.67696e68 q^{55} -8.12542e67 q^{56} +7.07286e68 q^{57} +3.45509e68 q^{58} -2.11219e69 q^{59} -5.88511e69 q^{60} -5.88931e70 q^{61} +4.56889e70 q^{62} +1.63551e70 q^{63} +2.76070e70 q^{64} +4.91802e71 q^{65} +1.19608e71 q^{66} -7.00026e70 q^{67} -2.08148e72 q^{68} +1.62190e72 q^{69} -1.31595e72 q^{70} -8.38692e72 q^{71} -5.55683e72 q^{72} -3.60236e73 q^{73} +2.14315e73 q^{74} -2.94994e73 q^{75} -5.37346e73 q^{76} +2.67451e73 q^{77} -2.19739e74 q^{78} -1.26900e75 q^{79} +4.47109e74 q^{80} +3.38773e74 q^{81} -1.13554e75 q^{82} -1.04441e76 q^{83} +5.87973e74 q^{84} -3.37106e76 q^{85} -3.40177e76 q^{86} -2.50017e75 q^{87} -9.08694e75 q^{88} -8.09056e76 q^{89} -8.99956e76 q^{90} -4.91352e76 q^{91} -1.23221e77 q^{92} -3.30615e77 q^{93} +8.29341e77 q^{94} -8.70258e77 q^{95} -1.99770e77 q^{96} -1.98469e78 q^{97} -3.05210e78 q^{98} +1.82905e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3}+ \cdots - 66\!\cdots\!69 q^{9}+O(q^{10}) \) 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	\( 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3}+ \cdots + 43\!\cdots\!32 q^{99}+O(q^{100}) \) 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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