LMFDB - Embedded newform 2.80.a.a.1.1

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			1.1
Root			$-8.28584e13$ 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)

$f(q)$	$=$	\(q+5.49756e11 q^{2} -8.21312e18 q^{3} +3.02231e23 q^{4} -6.30299e27 q^{5} -4.51521e30 q^{6} +3.82944e33 q^{7} +1.66153e35 q^{8} +1.81857e37 q^{9} -3.46510e39 q^{10} -8.25322e40 q^{11} -2.48226e42 q^{12} -6.74458e43 q^{13} +2.10526e45 q^{14} +5.17672e46 q^{15} +9.13439e46 q^{16} +2.03217e48 q^{17} +9.99767e48 q^{18} +3.74962e50 q^{19} -1.90496e51 q^{20} -3.14516e52 q^{21} -4.53726e52 q^{22} +8.53875e53 q^{23} -1.36464e54 q^{24} +2.31840e55 q^{25} -3.70787e55 q^{26} +2.55296e56 q^{27} +1.15738e57 q^{28} +7.45811e57 q^{29} +2.84593e58 q^{30} -1.19450e59 q^{31} +5.02168e58 q^{32} +6.77847e59 q^{33} +1.11720e60 q^{34} -2.41369e61 q^{35} +5.49628e60 q^{36} -9.28617e61 q^{37} +2.06138e62 q^{38} +5.53941e62 q^{39} -1.04726e63 q^{40} +2.58172e63 q^{41} -1.72907e64 q^{42} -5.39380e64 q^{43} -2.49438e64 q^{44} -1.14624e65 q^{45} +4.69423e65 q^{46} -1.50875e66 q^{47} -7.50218e65 q^{48} +8.87373e66 q^{49} +1.27456e67 q^{50} -1.66904e67 q^{51} -2.03843e67 q^{52} -5.02607e67 q^{53} +1.40350e68 q^{54} +5.20200e68 q^{55} +6.36275e68 q^{56} -3.07961e69 q^{57} +4.10014e69 q^{58} -1.39145e70 q^{59} +1.56457e70 q^{60} -3.14906e70 q^{61} -6.56684e70 q^{62} +6.96409e70 q^{63} +2.76070e70 q^{64} +4.25110e71 q^{65} +3.72650e71 q^{66} +8.22074e71 q^{67} +6.14186e71 q^{68} -7.01298e72 q^{69} -1.32694e73 q^{70} +7.87577e72 q^{71} +3.02161e72 q^{72} +4.25972e73 q^{73} -5.10513e73 q^{74} -1.90413e74 q^{75} +1.13325e74 q^{76} -3.16052e74 q^{77} +3.04532e74 q^{78} -3.92382e74 q^{79} -5.75739e74 q^{80} -2.99278e75 q^{81} +1.41931e75 q^{82} -4.63134e75 q^{83} -9.50567e75 q^{84} -1.28087e76 q^{85} -2.96527e76 q^{86} -6.12543e76 q^{87} -1.37130e76 q^{88} -5.55275e76 q^{89} -6.30152e76 q^{90} -2.58280e77 q^{91} +2.58068e77 q^{92} +9.81058e77 q^{93} -8.29445e77 q^{94} -2.36338e78 q^{95} -4.12437e77 q^{96} -3.14342e78 q^{97} +4.87838e78 q^{98} -1.50090e78 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−8.21312e18	−1.17009	−0.585044	−	0.811002i	$-0.698923\pi$
$3$	−8.21312e18	−1.17009	−0.585044	+	0.811002i	$0.698923\pi$
$4$	3.02231e23	0.500000
$5$	−6.30299e27	−1.54964	−0.774821	−	0.632181i	$-0.782160\pi$
$5$	−6.30299e27	−1.54964	−0.774821	+	0.632181i	$0.782160\pi$
$6$	−4.51521e30	−0.827377
$7$	3.82944e33	1.59134	0.795670	−	0.605731i	$-0.207119\pi$
$7$	3.82944e33	1.59134	0.795670	+	0.605731i	$0.207119\pi$
$8$	1.66153e35	0.353553
$9$	1.81857e37	0.369105
$10$	−3.46510e39	−1.09576
$11$	−8.25322e40	−0.604801	−0.302400	−	0.953181i	$-0.597788\pi$
$11$	−8.25322e40	−0.604801	−0.302400	+	0.953181i	$0.597788\pi$
$12$	−2.48226e42	−0.585044
$13$	−6.74458e43	−0.673275	−0.336638	−	0.941634i	$-0.609290\pi$
$13$	−6.74458e43	−0.673275	−0.336638	+	0.941634i	$0.609290\pi$
$14$	2.10526e45	1.12525
$15$	5.17672e46	1.81322
$16$	9.13439e46	0.250000
$17$	2.03217e48	0.507256	0.253628	−	0.967302i	$-0.418376\pi$
$17$	2.03217e48	0.507256	0.253628	+	0.967302i	$0.418376\pi$
$18$	9.99767e48	0.260997
$19$	3.74962e50	1.15670	0.578349	−	0.815789i	$-0.303697\pi$
$19$	3.74962e50	1.15670	0.578349	+	0.815789i	$0.303697\pi$
$20$	−1.90496e51	−0.774821
$21$	−3.14516e52	−1.86201
$22$	−4.53726e52	−0.427659
$23$	8.53875e53	1.39042	0.695208	−	0.718808i	$-0.255312\pi$
$23$	8.53875e53	1.39042	0.695208	+	0.718808i	$0.255312\pi$
$24$	−1.36464e54	−0.413688
$25$	2.31840e55	1.40139
$26$	−3.70787e55	−0.476078
$27$	2.55296e56	0.738202
$28$	1.15738e57	0.795670
$29$	7.45811e57	1.28206	0.641029	−	0.767517i	$-0.278508\pi$
$29$	7.45811e57	1.28206	0.641029	+	0.767517i	$0.278508\pi$
$30$	2.84593e58	1.28214
$31$	−1.19450e59	−1.47367	−0.736834	−	0.676073i	$-0.763680\pi$
$31$	−1.19450e59	−1.47367	−0.736834	+	0.676073i	$0.763680\pi$
$32$	5.02168e58	0.176777
$33$	6.77847e59	0.707670
$34$	1.11720e60	0.358684
$35$	−2.41369e61	−2.46601
$36$	5.49628e60	0.184553
$37$	−9.28617e61	−1.05650	−0.528249	−	0.849089i	$-0.677151\pi$
$37$	−9.28617e61	−1.05650	−0.528249	+	0.849089i	$0.677151\pi$
$38$	2.06138e62	0.817909
$39$	5.53941e62	0.787791
$40$	−1.04726e63	−0.547881
$41$	2.58172e63	0.509268	0.254634	−	0.967037i	$-0.418045\pi$
$41$	2.58172e63	0.509268	0.254634	+	0.967037i	$0.418045\pi$
$42$	−1.72907e64	−1.31664
$43$	−5.39380e64	−1.62140	−0.810701	−	0.585460i	$-0.800914\pi$
$43$	−5.39380e64	−1.62140	−0.810701	+	0.585460i	$0.800914\pi$
$44$	−2.49438e64	−0.302400
$45$	−1.14624e65	−0.571981
$46$	4.69423e65	0.983173
$47$	−1.50875e66	−1.35130	−0.675651	−	0.737222i	$-0.736137\pi$
$47$	−1.50875e66	−1.35130	−0.675651	+	0.737222i	$0.736137\pi$
$48$	−7.50218e65	−0.292522
$49$	8.87373e66	1.53236
$50$	1.27456e67	0.990932
$51$	−1.66904e67	−0.593535
$52$	−2.03843e67	−0.336638
$53$	−5.02607e67	−0.391140	−0.195570	−	0.980690i	$-0.562656\pi$
$53$	−5.02607e67	−0.391140	−0.195570	+	0.980690i	$0.562656\pi$
$54$	1.40350e68	0.521988
$55$	5.20200e68	0.937225
$56$	6.36275e68	0.562623
$57$	−3.07961e69	−1.35344
$58$	4.10014e69	0.906552
$59$	−1.39145e70	−1.56607	−0.783037	−	0.621976i	$-0.786330\pi$
$59$	−1.39145e70	−1.56607	−0.783037	+	0.621976i	$0.786330\pi$
$60$	1.56457e70	0.906608
$61$	−3.14906e70	−0.949843	−0.474921	−	0.880028i	$-0.657524\pi$
$61$	−3.14906e70	−0.949843	−0.474921	+	0.880028i	$0.657524\pi$
$62$	−6.56684e70	−1.04204
$63$	6.96409e70	0.587371
$64$	2.76070e70	0.125000
$65$	4.25110e71	1.04334
$66$	3.72650e71	0.500398
$67$	8.22074e71	0.609475	0.304738	−	0.952436i	$-0.401431\pi$
$67$	8.22074e71	0.609475	0.304738	+	0.952436i	$0.401431\pi$
$68$	6.14186e71	0.253628
$69$	−7.01298e72	−1.62691
$70$	−1.32694e73	−1.74373
$71$	7.87577e72	0.591001	0.295500	−	0.955343i	$-0.404514\pi$
$71$	7.87577e72	0.591001	0.295500	+	0.955343i	$0.404514\pi$
$72$	3.02161e72	0.130498
$73$	4.25972e73	1.06691	0.533456	−	0.845828i	$-0.320893\pi$
$73$	4.25972e73	1.06691	0.533456	+	0.845828i	$0.320893\pi$
$74$	−5.10513e73	−0.747057
$75$	−1.90413e74	−1.63975
$76$	1.13325e74	0.578349
$77$	−3.16052e74	−0.962443
$78$	3.04532e74	0.557053
$79$	−3.92382e74	−0.433949	−0.216974	−	0.976177i	$-0.569619\pi$
$79$	−3.92382e74	−0.433949	−0.216974	+	0.976177i	$0.569619\pi$
$80$	−5.75739e74	−0.387410
$81$	−2.99278e75	−1.23287
$82$	1.41931e75	0.360107
$83$	−4.63134e75	−0.727985	−0.363992	−	0.931402i	$-0.618587\pi$
$83$	−4.63134e75	−0.727985	−0.363992	+	0.931402i	$0.618587\pi$
$84$	−9.50567e75	−0.931003
$85$	−1.28087e76	−0.786066
$86$	−2.96527e76	−1.14650
$87$	−6.12543e76	−1.50012
$88$	−1.37130e76	−0.213829
$89$	−5.55275e76	−0.554119	−0.277059	−	0.960853i	$-0.589360\pi$
$89$	−5.55275e76	−0.554119	−0.277059	+	0.960853i	$0.589360\pi$
$90$	−6.30152e76	−0.404451
$91$	−2.58280e77	−1.07141
$92$	2.58068e77	0.695208
$93$	9.81058e77	1.72432
$94$	−8.29445e77	−0.955515
$95$	−2.36338e78	−1.79247
$96$	−4.12437e77	−0.206844
$97$	−3.14342e78	−1.04693	−0.523466	−	0.852047i	$-0.675361\pi$
$97$	−3.14342e78	−1.04693	−0.523466	+	0.852047i	$0.675361\pi$
$98$	4.87838e78	1.08354
$99$	−1.50090e78	−0.223235
$100$	7.00695e78	0.700695
$101$	2.63770e79	1.78045	0.890227	−	0.455517i	$-0.150546\pi$
$101$	2.63770e79	1.78045	0.890227	+	0.455517i	$0.150546\pi$
$102$	−9.17567e78	−0.419692
$103$	2.28078e79	0.709600	0.354800	−	0.934942i	$-0.384549\pi$
$103$	2.28078e79	0.709600	0.354800	+	0.934942i	$0.384549\pi$
$104$	−1.12064e79	−0.238039
$105$	1.98239e80	2.88544
$106$	−2.76311e79	−0.276577
$107$	−5.16285e79	−0.356640	−0.178320	−	0.983973i	$-0.557066\pi$
$107$	−5.16285e79	−0.356640	−0.178320	+	0.983973i	$0.557066\pi$
$108$	7.71585e79	0.369101
$109$	−4.16854e80	−1.38560	−0.692800	−	0.721130i	$-0.743623\pi$
$109$	−4.16854e80	−1.38560	−0.692800	+	0.721130i	$0.743623\pi$
$110$	2.85983e80	0.662718
$111$	7.62684e80	1.23620
$112$	3.49796e80	0.397835
$113$	−1.74584e80	−0.139768	−0.0698838	−	0.997555i	$-0.522263\pi$
$113$	−1.74584e80	−0.139768	−0.0698838	+	0.997555i	$0.522263\pi$
$114$	−1.69303e81	−0.957025
$115$	−5.38197e81	−2.15465
$116$	2.25408e81	0.641029
$117$	−1.22655e81	−0.248509
$118$	−7.64956e81	−1.10738
$119$	7.78207e81	0.807217
$120$	8.60130e81	0.641069
$121$	−1.18103e82	−0.634216
$122$	−1.73121e82	−0.671640
$123$	−2.12039e82	−0.595888
$124$	−3.61016e82	−0.736834
$125$	−4.18546e82	−0.622010
$126$	3.82855e82	0.415334
$127$	4.46335e82	0.354335	0.177167	−	0.984181i	$-0.443307\pi$
$127$	4.46335e82	0.354335	0.177167	+	0.984181i	$0.443307\pi$
$128$	1.51771e82	0.0883883
$129$	4.42999e83	1.89718
$130$	2.33707e83	0.737750
$131$	−2.66669e83	−0.621952	−0.310976	−	0.950418i	$-0.600656\pi$
$131$	−2.66669e83	−0.621952	−0.310976	+	0.950418i	$0.600656\pi$
$132$	2.04867e83	0.353835
$133$	1.43589e84	1.84070
$134$	4.51940e83	0.430964
$135$	−1.60913e84	−1.14395
$136$	3.37652e83	0.179342
$137$	2.69740e84	1.07271	0.536356	−	0.843992i	$-0.319801\pi$
$137$	2.69740e84	1.07271	0.536356	+	0.843992i	$0.319801\pi$
$138$	−3.85542e84	−1.15040
$139$	−6.92728e84	−1.55410	−0.777048	−	0.629441i	$-0.783284\pi$
$139$	−6.92728e84	−1.55410	−0.777048	+	0.629441i	$0.783284\pi$
$140$	−7.29494e84	−1.23300
$141$	1.23915e85	1.58114
$142$	4.32975e84	0.417901
$143$	5.56646e84	0.407198
$144$	1.66115e84	0.0922763
$145$	−4.70084e85	−1.98673
$146$	2.34181e85	0.754420
$147$	−7.28809e85	−1.79300
$148$	−2.80657e85	−0.528249
$149$	8.99610e85	1.29777	0.648884	−	0.760888i	$-0.275236\pi$
$149$	8.99610e85	1.29777	0.648884	+	0.760888i	$0.275236\pi$
$150$	−1.04681e86	−1.15948
$151$	5.00768e85	0.426626	0.213313	−	0.976984i	$-0.431575\pi$
$151$	5.00768e85	0.426626	0.213313	+	0.976984i	$0.431575\pi$
$152$	6.23013e85	0.408955
$153$	3.69564e85	0.187231
$154$	−1.73752e86	−0.680550
$155$	7.52893e86	2.28366
$156$	1.67418e86	0.393896
$157$	−2.12281e86	−0.388039	−0.194020	−	0.980998i	$-0.562153\pi$
$157$	−2.12281e86	−0.388039	−0.194020	+	0.980998i	$0.562153\pi$
$158$	−2.15714e86	−0.306848
$159$	4.12797e86	0.457668
$160$	−3.16516e86	−0.273941
$161$	3.26986e87	2.21262
$162$	−1.64530e87	−0.871768
$163$	1.08655e87	0.451483	0.225741	−	0.974187i	$-0.427520\pi$
$163$	1.08655e87	0.451483	0.225741	+	0.974187i	$0.427520\pi$
$164$	7.80276e86	0.254634
$165$	−4.27246e87	−1.09664
$166$	−2.54611e87	−0.514763
$167$	−1.89691e87	−0.302515	−0.151257	−	0.988494i	$-0.548332\pi$
$167$	−1.89691e87	−0.302515	−0.151257	+	0.988494i	$0.548332\pi$
$168$	−5.22580e87	−0.658319
$169$	−5.48623e87	−0.546700
$170$	−7.04168e87	−0.555832
$171$	6.81893e87	0.426943
$172$	−1.63018e88	−0.810701
$173$	−8.50105e87	−0.336242	−0.168121	−	0.985766i	$-0.553770\pi$
$173$	−8.50105e87	−0.336242	−0.168121	+	0.985766i	$0.553770\pi$
$174$	−3.36749e88	−1.06075
$175$	8.87819e88	2.23009
$176$	−7.53881e87	−0.151200
$177$	1.14281e89	1.83244
$178$	−3.05266e88	−0.391821
$179$	1.38245e88	0.142218	0.0711090	−	0.997469i	$-0.477346\pi$
$179$	1.38245e88	0.142218	0.0711090	+	0.997469i	$0.477346\pi$
$180$	−3.46430e88	−0.285990
$181$	−2.33673e89	−1.54990	−0.774951	−	0.632022i	$-0.782225\pi$
$181$	−2.33673e89	−1.54990	−0.774951	+	0.632022i	$0.782225\pi$
$182$	−1.41991e89	−0.757601
$183$	2.58636e89	1.11140
$184$	1.41874e89	0.491587
$185$	5.85306e89	1.63719
$186$	5.39342e89	1.21928
$187$	−1.67719e89	−0.306789
$188$	−4.55992e89	−0.675651
$189$	9.77641e89	1.17473
$190$	−1.29928e90	−1.26747
$191$	−1.09703e90	−0.869759	−0.434880	−	0.900489i	$-0.643209\pi$
$191$	−1.09703e90	−0.869759	−0.434880	+	0.900489i	$0.643209\pi$
$192$	−2.26739e89	−0.146261
$193$	1.32482e90	0.696054	0.348027	−	0.937484i	$-0.386852\pi$
$193$	1.32482e90	0.696054	0.348027	+	0.937484i	$0.386852\pi$
$194$	−1.72811e90	−0.740292
$195$	−3.49148e90	−1.22079
$196$	2.68192e90	0.766180
$197$	−6.08806e90	−1.42253	−0.711267	−	0.702922i	$-0.751878\pi$
$197$	−6.08806e90	−1.42253	−0.711267	+	0.702922i	$0.751878\pi$
$198$	−8.25130e89	−0.157851
$199$	−5.10486e90	−0.800363	−0.400182	−	0.916436i	$-0.631053\pi$
$199$	−5.10486e90	−0.800363	−0.400182	+	0.916436i	$0.631053\pi$
$200$	3.85211e90	0.495466
$201$	−6.75179e90	−0.713139
$202$	1.45009e91	1.25897
$203$	2.85604e91	2.04019
$204$	−5.04438e90	−0.296767
$205$	−1.62725e91	−0.789183
$206$	1.25387e91	0.501763
$207$	1.55283e91	0.513210
$208$	−6.16076e90	−0.168319
$209$	−3.09465e91	−0.699572
$210$	1.08983e92	2.04032
$211$	−1.42596e91	−0.221285	−0.110642	−	0.993860i	$-0.535291\pi$
$211$	−1.42596e91	−0.221285	−0.110642	+	0.993860i	$0.535291\pi$
$212$	−1.51904e91	−0.195570
$213$	−6.46846e91	−0.691523
$214$	−2.83831e91	−0.252183
$215$	3.39971e92	2.51259
$216$	4.24183e91	0.260994
$217$	−4.57427e92	−2.34511
$218$	−2.29168e92	−0.979767
$219$	−3.49856e92	−1.24838
$220$	1.57221e92	0.468612
$221$	−1.37061e92	−0.341523
$222$	4.19290e92	0.874122
$223$	−2.27052e92	−0.396355	−0.198177	−	0.980166i	$-0.563502\pi$
$223$	−2.27052e92	−0.396355	−0.198177	+	0.980166i	$0.563502\pi$
$224$	1.92302e92	0.281312
$225$	4.21617e92	0.517260
$226$	−9.59787e91	−0.0988306
$227$	−3.35766e92	−0.290413	−0.145206	−	0.989401i	$-0.546385\pi$
$227$	−3.35766e92	−0.290413	−0.145206	+	0.989401i	$0.546385\pi$
$228$	−9.30754e92	−0.676719
$229$	4.88971e92	0.299076	0.149538	−	0.988756i	$-0.452221\pi$
$229$	4.88971e92	0.299076	0.149538	+	0.988756i	$0.452221\pi$
$230$	−2.95877e93	−1.52357
$231$	2.59577e93	1.12614
$232$	1.23919e93	0.453276
$233$	2.60425e92	0.0803754	0.0401877	−	0.999192i	$-0.487204\pi$
$233$	2.60425e92	0.0803754	0.0401877	+	0.999192i	$0.487204\pi$
$234$	−6.74302e92	−0.175723
$235$	9.50964e93	2.09403
$236$	−4.20539e93	−0.783037
$237$	3.22268e93	0.507758
$238$	4.27824e93	0.570789
$239$	6.47603e93	0.732136	0.366068	−	0.930588i	$-0.380704\pi$
$239$	6.47603e93	0.732136	0.366068	+	0.930588i	$0.380704\pi$
$240$	4.72861e93	0.453304
$241$	−7.71719e93	−0.627749	−0.313874	−	0.949465i	$-0.601627\pi$
$241$	−7.71719e93	−0.627749	−0.313874	+	0.949465i	$0.601627\pi$
$242$	−6.49275e93	−0.448458
$243$	1.20017e94	0.704359
$244$	−9.51744e93	−0.474921
$245$	−5.59310e94	−2.37461
$246$	−1.16570e94	−0.421357
$247$	−2.52896e94	−0.778777
$248$	−1.98471e94	−0.521021
$249$	3.80378e94	0.851806
$250$	−2.30098e94	−0.439827
$251$	5.59683e94	0.913756	0.456878	−	0.889529i	$-0.348968\pi$
$251$	5.59683e94	0.913756	0.456878	+	0.889529i	$0.348968\pi$
$252$	2.10477e94	0.293686
$253$	−7.04722e94	−0.840925
$254$	2.45375e94	0.250553
$255$	1.05200e95	0.919766
$256$	8.34370e93	0.0625000
$257$	−2.35450e94	−0.151196	−0.0755982	−	0.997138i	$-0.524087\pi$
$257$	−2.35450e94	−0.151196	−0.0755982	+	0.997138i	$0.524087\pi$
$258$	2.43541e95	1.34151
$259$	−3.55608e95	−1.68125
$260$	1.28482e95	0.521668
$261$	1.35631e95	0.473214
$262$	−1.46603e95	−0.439786
$263$	1.52001e94	0.0392280	0.0196140	−	0.999808i	$-0.493756\pi$
$263$	1.52001e94	0.0392280	0.0196140	+	0.999808i	$0.493756\pi$
$264$	1.12627e95	0.250199
$265$	3.16793e95	0.606126
$266$	7.89391e95	1.30157
$267$	4.56054e95	0.648368
$268$	2.48457e95	0.304738
$269$	−1.48094e96	−1.56792	−0.783960	−	0.620812i	$-0.786803\pi$
$269$	−1.48094e96	−1.56792	−0.783960	+	0.620812i	$0.786803\pi$
$270$	−8.84627e95	−0.808894
$271$	−2.26883e96	−1.79273	−0.896366	−	0.443315i	$-0.853802\pi$
$271$	−2.26883e96	−1.79273	−0.896366	+	0.443315i	$0.853802\pi$
$272$	1.85626e95	0.126814
$273$	2.12128e96	1.25364
$274$	1.48291e96	0.758521
$275$	−1.91343e96	−0.847562
$276$	−2.11954e96	−0.813455
$277$	4.00584e96	1.33273	0.666365	−	0.745625i	$-0.267849\pi$
$277$	4.00584e96	1.33273	0.666365	+	0.745625i	$0.267849\pi$
$278$	−3.80831e96	−1.09891
$279$	−2.17228e96	−0.543939
$280$	−4.01043e96	−0.871865
$281$	−2.14515e96	−0.405095	−0.202548	−	0.979272i	$-0.564922\pi$
$281$	−2.14515e96	−0.405095	−0.202548	+	0.979272i	$0.564922\pi$
$282$	6.81233e96	1.11804
$283$	−9.57649e96	−1.36660	−0.683301	−	0.730136i	$-0.739456\pi$
$283$	−9.57649e96	−1.36660	−0.683301	+	0.730136i	$0.739456\pi$
$284$	2.38031e96	0.295500
$285$	1.94107e97	2.09734
$286$	3.06019e96	0.287932
$287$	9.88653e96	0.810418
$288$	9.13226e95	0.0652492
$289$	−1.19199e97	−0.742691
$290$	−2.58431e97	−1.40483
$291$	2.58172e97	1.22500
$292$	1.28742e97	0.533456
$293$	3.05995e97	1.10775	0.553876	−	0.832599i	$-0.313148\pi$
$293$	3.05995e97	1.10775	0.553876	+	0.832599i	$0.313148\pi$
$294$	−4.00667e97	−1.26784
$295$	8.77027e97	2.42685
$296$	−1.54293e97	−0.373528
$297$	−2.10702e97	−0.446466
$298$	4.94566e97	0.917660
$299$	−5.75903e97	−0.936133
$300$	−5.75489e97	−0.819874
$301$	−2.06552e98	−2.58020
$302$	2.75300e97	0.301670
$303$	−2.16637e98	−2.08329
$304$	3.42505e97	0.289175
$305$	1.98485e98	1.47192
$306$	2.03170e97	0.132392
$307$	7.77058e97	0.445131	0.222565	−	0.974918i	$-0.428557\pi$
$307$	7.77058e97	0.445131	0.222565	+	0.974918i	$0.428557\pi$
$308$	−9.55209e97	−0.481222
$309$	−1.87323e98	−0.830294
$310$	4.13907e98	1.61479
$311$	3.47624e98	1.19419	0.597097	−	0.802169i	$-0.296321\pi$
$311$	3.47624e98	1.19419	0.597097	+	0.802169i	$0.296321\pi$
$312$	9.20392e97	0.278526
$313$	−2.20496e98	−0.588029	−0.294015	−	0.955801i	$-0.594991\pi$
$313$	−2.20496e98	−0.588029	−0.294015	+	0.955801i	$0.594991\pi$
$314$	−1.16703e98	−0.274385
$315$	−4.38946e98	−0.910215
$316$	−1.18590e98	−0.216974
$317$	7.00574e98	1.13139	0.565696	−	0.824614i	$-0.308608\pi$
$317$	7.00574e98	1.13139	0.565696	+	0.824614i	$0.308608\pi$
$318$	2.26938e98	0.323620
$319$	−6.15534e98	−0.775390
$320$	−1.74006e98	−0.193705
$321$	4.24031e98	0.417300
$322$	1.79763e99	1.56456
$323$	7.61987e98	0.586743
$324$	−9.04511e98	−0.616433
$325$	−1.56367e99	−0.943521
$326$	5.97340e98	0.319246
$327$	3.42367e99	1.62127
$328$	4.28961e98	0.180053
$329$	−5.77767e99	−2.15038
$330$	−2.34881e99	−0.775438
$331$	2.76926e99	0.811255	0.405628	−	0.914038i	$-0.367053\pi$
$331$	2.76926e99	0.811255	0.405628	+	0.914038i	$0.367053\pi$
$332$	−1.39974e99	−0.363992
$333$	−1.68875e99	−0.389959
$334$	−1.04284e99	−0.213910
$335$	−5.18152e99	−0.944468
$336$	−2.87291e99	−0.465502
$337$	1.60789e99	0.231672	0.115836	−	0.993268i	$-0.463045\pi$
$337$	1.60789e99	0.231672	0.115836	+	0.993268i	$0.463045\pi$
$338$	−3.01609e99	−0.386575
$339$	1.43388e99	0.163540
$340$	−3.87120e99	−0.393033
$341$	9.85849e99	0.891276
$342$	3.74875e99	0.301894
$343$	1.18055e100	0.847165
$344$	−8.96199e99	−0.573252
$345$	4.42027e100	2.52113
$346$	−4.67350e99	−0.237759
$347$	−2.28429e100	−1.03690	−0.518450	−	0.855108i	$-0.673491\pi$
$347$	−2.28429e100	−1.03690	−0.518450	+	0.855108i	$0.673491\pi$
$348$	−1.85130e100	−0.750060
$349$	−4.51784e99	−0.163428	−0.0817140	−	0.996656i	$-0.526039\pi$
$349$	−4.51784e99	−0.163428	−0.0817140	+	0.996656i	$0.526039\pi$
$350$	4.88084e100	1.57691
$351$	−1.72187e100	−0.497014
$352$	−4.14451e99	−0.106915
$353$	5.92330e100	1.36604	0.683020	−	0.730400i	$-0.260666\pi$
$353$	5.92330e100	1.36604	0.683020	+	0.730400i	$0.260666\pi$
$354$	6.28267e100	1.29573
$355$	−4.96409e100	−0.915840
$356$	−1.67822e100	−0.277059
$357$	−6.39151e100	−0.944515
$358$	7.60010e99	0.100563
$359$	−1.17034e101	−1.38702	−0.693508	−	0.720449i	$-0.743936\pi$
$359$	−1.17034e101	−1.38702	−0.693508	+	0.720449i	$0.743936\pi$
$360$	−1.90452e100	−0.202226
$361$	3.55130e100	0.337951
$362$	−1.28463e101	−1.09595
$363$	9.69990e100	0.742088
$364$	−7.80603e100	−0.535705
$365$	−2.68490e101	−1.65333
$366$	1.42186e101	0.785878
$367$	1.67047e100	0.0828951	0.0414475	−	0.999141i	$-0.486803\pi$
$367$	1.67047e100	0.0828951	0.0414475	+	0.999141i	$0.486803\pi$
$368$	7.79963e100	0.347604
$369$	4.69502e100	0.187973
$370$	3.21776e101	1.15767
$371$	−1.92470e101	−0.622436
$372$	2.96507e101	0.862161
$373$	−1.64281e100	−0.0429624	−0.0214812	−	0.999769i	$-0.506838\pi$
$373$	−1.64281e100	−0.0429624	−0.0214812	+	0.999769i	$0.506838\pi$
$374$	−9.22048e100	−0.216933
$375$	3.43756e101	0.727806
$376$	−2.50684e101	−0.477757
$377$	−5.03018e101	−0.863178
$378$	5.37464e101	0.830660
$379$	1.18470e102	1.64953	0.824763	−	0.565478i	$-0.191308\pi$
$379$	1.18470e102	1.64953	0.824763	+	0.565478i	$0.191308\pi$
$380$	−7.14288e101	−0.896234
$381$	−3.66580e101	−0.414603
$382$	−6.03096e101	−0.615013
$383$	4.39756e101	0.404446	0.202223	−	0.979340i	$-0.435183\pi$
$383$	4.39756e101	0.404446	0.202223	+	0.979340i	$0.435183\pi$
$384$	−1.24651e101	−0.103422
$385$	1.99207e102	1.49144
$386$	7.28327e101	0.492185
$387$	−9.80898e101	−0.598468
$388$	−9.50039e101	−0.523466
$389$	−1.30405e102	−0.649063	−0.324531	−	0.945875i	$-0.605207\pi$
$389$	−1.30405e102	−0.649063	−0.324531	+	0.945875i	$0.605207\pi$
$390$	−1.91946e102	−0.863232
$391$	1.73522e102	0.705298
$392$	1.47440e102	0.541771
$393$	2.19019e102	0.727738
$394$	−3.34694e102	−1.00588
$395$	2.47318e102	0.672465
$396$	−4.53620e101	−0.111618
$397$	−7.99431e102	−1.78056	−0.890278	−	0.455417i	$-0.849490\pi$
$397$	−7.99431e102	−1.78056	−0.890278	+	0.455417i	$0.849490\pi$
$398$	−2.80642e102	−0.565942
$399$	−1.17932e103	−2.15378
$400$	2.11772e102	0.350347
$401$	−2.55804e102	−0.383447	−0.191724	−	0.981449i	$-0.561408\pi$
$401$	−2.55804e102	−0.383447	−0.191724	+	0.981449i	$0.561408\pi$
$402$	−3.71183e102	−0.504266
$403$	8.05642e102	0.992185
$404$	7.97195e102	0.890227
$405$	1.88634e103	1.91050
$406$	1.57012e103	1.44263
$407$	7.66409e102	0.638971
$408$	−2.77318e102	−0.209846
$409$	2.16051e103	1.48418	0.742090	−	0.670300i	$-0.233835\pi$
$409$	2.16051e103	1.48418	0.742090	+	0.670300i	$0.233835\pi$
$410$	−8.94592e102	−0.558037
$411$	−2.21541e103	−1.25517
$412$	6.89324e102	0.354800
$413$	−5.32846e103	−2.49215
$414$	8.53677e102	0.362894
$415$	2.91913e103	1.12812
$416$	−3.38692e102	−0.119019
$417$	5.68945e103	1.81843
$418$	−1.70130e103	−0.494672
$419$	−5.50337e103	−1.45604	−0.728022	−	0.685554i	$-0.759560\pi$
$419$	−5.50337e103	−1.45604	−0.728022	+	0.685554i	$0.759560\pi$
$420$	5.99141e103	1.44272
$421$	−6.95144e103	−1.52381	−0.761907	−	0.647686i	$-0.775737\pi$
$421$	−6.95144e103	−1.52381	−0.761907	+	0.647686i	$0.775737\pi$
$422$	−7.83932e102	−0.156472
$423$	−2.74376e103	−0.498772
$424$	−8.35099e102	−0.138289
$425$	4.71139e103	0.710864
$426$	−3.55607e103	−0.488981
$427$	−1.20591e104	−1.51152
$428$	−1.56038e103	−0.178320
$429$	−4.57179e103	−0.476457
$430$	1.86901e104	1.77667
$431$	3.22243e103	0.279468	0.139734	−	0.990189i	$-0.455375\pi$
$431$	3.22243e103	0.279468	0.139734	+	0.990189i	$0.455375\pi$
$432$	2.33197e103	0.184551
$433$	−1.40100e104	−1.01196	−0.505982	−	0.862544i	$-0.668870\pi$
$433$	−1.40100e104	−1.01196	−0.505982	+	0.862544i	$0.668870\pi$
$434$	−2.51473e104	−1.65824
$435$	3.86085e104	2.32465
$436$	−1.25987e104	−0.692800
$437$	3.20171e104	1.60829
$438$	−1.92335e104	−0.882738
$439$	6.97672e103	0.292619	0.146310	−	0.989239i	$-0.453260\pi$
$439$	6.97672e103	0.292619	0.146310	+	0.989239i	$0.453260\pi$
$440$	8.64330e103	0.331359
$441$	1.61375e104	0.565602
$442$	−7.53503e103	−0.241493
$443$	7.02654e103	0.205965	0.102983	−	0.994683i	$-0.467161\pi$
$443$	7.02654e103	0.205965	0.102983	+	0.994683i	$0.467161\pi$
$444$	2.30507e104	0.618098
$445$	3.49989e104	0.858686
$446$	−1.24823e104	−0.280265
$447$	−7.38860e104	−1.51850
$448$	1.05719e104	0.198917
$449$	2.55988e103	0.0441052	0.0220526	−	0.999757i	$-0.492980\pi$
$449$	2.55988e103	0.0441052	0.0220526	+	0.999757i	$0.492980\pi$
$450$	2.31786e104	0.365758
$451$	−2.13075e104	−0.308006
$452$	−5.27648e103	−0.0698838
$453$	−4.11287e104	−0.499190
$454$	−1.84589e104	−0.205353
$455$	1.62793e105	1.66030
$456$	−5.11687e104	−0.478513
$457$	−1.40981e105	−1.20912	−0.604562	−	0.796558i	$-0.706652\pi$
$457$	−1.40981e105	−1.20912	−0.604562	+	0.796558i	$0.706652\pi$
$458$	2.68814e104	0.211479
$459$	5.18805e104	0.374458
$460$	−1.62660e105	−1.07732
$461$	−8.17494e104	−0.496933	−0.248467	−	0.968640i	$-0.579927\pi$
$461$	−8.17494e104	−0.496933	−0.248467	+	0.968640i	$0.579927\pi$
$462$	1.42704e105	0.796303
$463$	1.15708e105	0.592809	0.296405	−	0.955062i	$-0.404212\pi$
$463$	1.15708e105	0.592809	0.296405	+	0.955062i	$0.404212\pi$
$464$	6.81252e104	0.320515
$465$	−6.18360e105	−2.67208
$466$	1.43170e104	0.0568340
$467$	−3.86650e105	−1.41027	−0.705133	−	0.709075i	$-0.749113\pi$
$467$	−3.86650e105	−1.41027	−0.705133	+	0.709075i	$0.749113\pi$
$468$	−3.70701e104	−0.124255
$469$	3.14808e105	0.969882
$470$	5.22798e105	1.48071
$471$	1.74349e105	0.454040
$472$	−2.31194e105	−0.553690
$473$	4.45162e105	0.980626
$474$	1.77168e105	0.359039
$475$	8.69314e105	1.62098
$476$	2.35199e105	0.403609
$477$	−9.14024e104	−0.144372
$478$	3.56023e105	0.517698
$479$	−4.66249e105	−0.624260	−0.312130	−	0.950039i	$-0.601042\pi$
$479$	−4.66249e105	−0.624260	−0.312130	+	0.950039i	$0.601042\pi$
$480$	2.59958e105	0.320534
$481$	6.26314e105	0.711314
$482$	−4.24257e105	−0.443885
$483$	−2.68558e106	−2.58896
$484$	−3.56943e105	−0.317108
$485$	1.98129e106	1.62237
$486$	6.59800e105	0.498057
$487$	−1.15665e106	−0.805026	−0.402513	−	0.915414i	$-0.631863\pi$
$487$	−1.15665e106	−0.805026	−0.402513	+	0.915414i	$0.631863\pi$
$488$	−5.23227e105	−0.335820
$489$	−8.92400e105	−0.528274
$490$	−3.07484e106	−1.67910
$491$	3.67125e105	0.184967	0.0924836	−	0.995714i	$-0.470519\pi$
$491$	3.67125e105	0.184967	0.0924836	+	0.995714i	$0.470519\pi$
$492$	−6.40850e105	−0.297944
$493$	1.51561e106	0.650332
$494$	−1.39031e106	−0.550678
$495$	9.46017e105	0.345934
$496$	−1.09110e106	−0.368417
$497$	3.01598e106	0.940483
$498$	2.09115e106	0.602318
$499$	−2.49648e106	−0.664287	−0.332144	−	0.943229i	$-0.607772\pi$
$499$	−2.49648e106	−0.664287	−0.332144	+	0.943229i	$0.607772\pi$
$500$	−1.26498e106	−0.311005
$501$	1.55796e106	0.353969
$502$	3.07689e106	0.646123
$503$	8.98748e106	1.74463	0.872313	−	0.488948i	$-0.162619\pi$
$503$	8.98748e106	1.74463	0.872313	+	0.488948i	$0.162619\pi$
$504$	1.15711e106	0.207667
$505$	−1.66254e107	−2.75907
$506$	−3.87425e106	−0.594624
$507$	4.50590e106	0.639687
$508$	1.34896e106	0.177167
$509$	−6.54652e106	−0.795533	−0.397767	−	0.917487i	$-0.630215\pi$
$509$	−6.54652e106	−0.795533	−0.397767	+	0.917487i	$0.630215\pi$
$510$	5.78341e106	0.650373
$511$	1.63124e107	1.69782
$512$	4.58700e105	0.0441942
$513$	9.57263e106	0.853877
$514$	−1.29440e106	−0.106912
$515$	−1.43757e107	−1.09963
$516$	1.33888e107	0.948591
$517$	1.24521e107	0.817269
$518$	−1.95498e107	−1.18882
$519$	6.98201e106	0.393432
$520$	7.06336e106	0.368875
$521$	−3.19837e106	−0.154824	−0.0774122	−	0.996999i	$-0.524666\pi$
$521$	−3.19837e106	−0.154824	−0.0774122	+	0.996999i	$0.524666\pi$
$522$	7.45637e106	0.334613
$523$	−1.84452e107	−0.767480	−0.383740	−	0.923441i	$-0.625364\pi$
$523$	−1.84452e107	−0.767480	−0.383740	+	0.923441i	$0.625364\pi$
$524$	−8.05958e106	−0.310976
$525$	−7.29176e107	−2.60940
$526$	8.35637e105	0.0277384
$527$	−2.42743e107	−0.747528
$528$	6.19171e106	0.176918
$529$	3.51966e107	0.933258
$530$	1.74159e107	0.428596
$531$	−2.53044e107	−0.578046
$532$	4.33973e107	0.920350
$533$	−1.74126e107	−0.342878
$534$	2.50718e107	0.458465
$535$	3.25414e107	0.552665
$536$	1.36590e107	0.215482
$537$	−1.13542e107	−0.166408
$538$	−8.14158e107	−1.10869
$539$	−7.32368e107	−0.926773
$540$	−4.86329e107	−0.571975
$541$	4.78952e107	0.523600	0.261800	−	0.965122i	$-0.415684\pi$
$541$	4.78952e107	0.523600	0.261800	+	0.965122i	$0.415684\pi$
$542$	−1.24730e108	−1.26765
$543$	1.91918e108	1.81352
$544$	1.02049e107	0.0896711
$545$	2.62743e108	2.14718
$546$	1.16619e108	0.886460
$547$	4.04694e107	0.286172	0.143086	−	0.989710i	$-0.454297\pi$
$547$	4.04694e107	0.286172	0.143086	+	0.989710i	$0.454297\pi$
$548$	8.15239e107	0.536356
$549$	−5.72677e107	−0.350592
$550$	−1.05192e108	−0.599317
$551$	2.79651e108	1.48295
$552$	−1.16523e108	−0.575199
$553$	−1.50260e108	−0.690560
$554$	2.20223e108	0.942383
$555$	−4.80719e108	−1.91566
$556$	−2.09364e108	−0.777048
$557$	−1.61844e108	−0.559521	−0.279760	−	0.960070i	$-0.590255\pi$
$557$	−1.61844e108	−0.559521	−0.279760	+	0.960070i	$0.590255\pi$
$558$	−1.19422e108	−0.384623
$559$	3.63789e108	1.09165
$560$	−2.20476e108	−0.616501
$561$	1.37750e108	0.358970
$562$	−1.17931e108	−0.286446
$563$	−4.79605e108	−1.08593	−0.542965	−	0.839755i	$-0.682698\pi$
$563$	−4.79605e108	−1.08593	−0.542965	+	0.839755i	$0.682698\pi$
$564$	3.74512e108	0.790571
$565$	1.10040e108	0.216590
$566$	−5.26473e108	−0.966334
$567$	−1.14607e109	−1.96191
$568$	1.30859e108	0.208950
$569$	−4.57641e108	−0.681695	−0.340847	−	0.940119i	$-0.610714\pi$
$569$	−4.57641e108	−0.681695	−0.340847	+	0.940119i	$0.610714\pi$
$570$	1.06712e109	1.48305
$571$	5.56713e108	0.721947	0.360973	−	0.932576i	$-0.382445\pi$
$571$	5.56713e108	0.721947	0.360973	+	0.932576i	$0.382445\pi$
$572$	1.68236e108	0.203599
$573$	9.01000e108	1.01769
$574$	5.43518e108	0.573052
$575$	1.97963e109	1.94852
$576$	5.02051e107	0.0461381
$577$	−2.39008e108	−0.205101	−0.102551	−	0.994728i	$-0.532700\pi$
$577$	−2.39008e108	−0.205101	−0.102551	+	0.994728i	$0.532700\pi$
$578$	−6.55304e108	−0.525162
$579$	−1.08809e109	−0.814444
$580$	−1.42074e109	−0.993366
$581$	−1.77355e109	−1.15847
$582$	1.41932e109	0.866207
$583$	4.14813e108	0.236562
$584$	7.07768e108	0.377210
$585$	7.73091e108	0.385101
$586$	1.68222e109	0.783300
$587$	5.56169e108	0.242104	0.121052	−	0.992646i	$-0.461373\pi$
$587$	5.56169e108	0.242104	0.121052	+	0.992646i	$0.461373\pi$
$588$	−2.20269e109	−0.896498
$589$	−4.47893e109	−1.70459
$590$	4.82151e109	1.71604
$591$	5.00019e109	1.66449
$592$	−8.48235e108	−0.264125
$593$	−1.68614e109	−0.491172	−0.245586	−	0.969375i	$-0.578980\pi$
$593$	−1.68614e109	−0.491172	−0.245586	+	0.969375i	$0.578980\pi$
$594$	−1.15834e109	−0.315699
$595$	−4.90503e109	−1.25090
$596$	2.71891e109	0.648884
$597$	4.19268e109	0.936495
$598$	−3.16606e109	−0.661946
$599$	1.24027e109	0.242748	0.121374	−	0.992607i	$-0.461270\pi$
$599$	1.24027e109	0.242748	0.121374	+	0.992607i	$0.461270\pi$
$600$	−3.16378e109	−0.579739
$601$	−5.87933e109	−1.00876	−0.504378	−	0.863483i	$-0.668278\pi$
$601$	−5.87933e109	−1.00876	−0.504378	+	0.863483i	$0.668278\pi$
$602$	−1.13553e110	−1.82448
$603$	1.49500e109	0.224960
$604$	1.51348e109	0.213313
$605$	7.44399e109	0.982807
$606$	−1.19098e110	−1.47311
$607$	1.04727e110	1.21368	0.606841	−	0.794823i	$-0.292436\pi$
$607$	1.04727e110	1.21368	0.606841	+	0.794823i	$0.292436\pi$
$608$	1.88294e109	0.204477
$609$	−2.34570e110	−2.38720
$610$	1.09118e110	1.04080
$611$	1.01759e110	0.909798
$612$	1.11694e109	0.0936155
$613$	1.00038e110	0.786095	0.393048	−	0.919518i	$-0.371421\pi$
$613$	1.00038e110	0.786095	0.393048	+	0.919518i	$0.371421\pi$
$614$	4.27192e109	0.314755
$615$	1.33648e110	0.923413
$616$	−5.25132e109	−0.340275
$617$	6.42669e109	0.390592	0.195296	−	0.980744i	$-0.437433\pi$
$617$	6.42669e109	0.390592	0.195296	+	0.980744i	$0.437433\pi$
$618$	−1.02982e110	−0.587107
$619$	−8.63865e109	−0.462025	−0.231012	−	0.972951i	$-0.574204\pi$
$619$	−8.63865e109	−0.462025	−0.231012	+	0.972951i	$0.574204\pi$
$620$	2.27548e110	1.14183
$621$	2.17991e110	1.02641
$622$	1.91109e110	0.844423
$623$	−2.12639e110	−0.881791
$624$	5.05991e109	0.196948
$625$	−1.19739e110	−0.437497
$626$	−1.21219e110	−0.415800
$627$	2.54167e110	0.818561
$628$	−6.41581e109	−0.194020
$629$	−1.88711e110	−0.535915
$630$	−2.41313e110	−0.643619
$631$	−4.06248e110	−1.01773	−0.508864	−	0.860847i	$-0.669935\pi$
$631$	−4.06248e110	−1.01773	−0.508864	+	0.860847i	$0.669935\pi$
$632$	−6.51956e109	−0.153424
$633$	1.17116e110	0.258923
$634$	3.85144e110	0.800015
$635$	−2.81324e110	−0.549092
$636$	1.24760e110	0.228834
$637$	−5.98496e110	−1.03170
$638$	−3.38394e110	−0.548284
$639$	1.43226e110	0.218141
$640$	−9.56611e109	−0.136970
$641$	1.85524e110	0.249752	0.124876	−	0.992172i	$-0.460147\pi$
$641$	1.85524e110	0.249752	0.124876	+	0.992172i	$0.460147\pi$
$642$	2.33114e110	0.295076
$643$	1.40624e110	0.167389	0.0836946	−	0.996491i	$-0.473328\pi$
$643$	1.40624e110	0.167389	0.0836946	+	0.996491i	$0.473328\pi$
$644$	9.88256e110	1.10631
$645$	−2.79222e111	−2.93995
$646$	4.18907e110	0.414890
$647$	−7.93419e110	−0.739237	−0.369618	−	0.929184i	$-0.620512\pi$
$647$	−7.93419e110	−0.739237	−0.369618	+	0.929184i	$0.620512\pi$
$648$	−4.97260e110	−0.435884
$649$	1.14839e111	0.947163
$650$	−8.59635e110	−0.667170
$651$	3.75690e111	2.74398
$652$	3.28391e110	0.225741
$653$	1.35943e110	0.0879602	0.0439801	−	0.999032i	$-0.485996\pi$
$653$	1.35943e110	0.0879602	0.0439801	+	0.999032i	$0.485996\pi$
$654$	1.88218e111	1.14641
$655$	1.68081e111	0.963802
$656$	2.35824e110	0.127317
$657$	7.74659e110	0.393802
$658$	−3.17631e111	−1.52055
$659$	3.54015e111	1.59605	0.798027	−	0.602621i	$-0.205877\pi$
$659$	3.54015e111	1.59605	0.798027	+	0.602621i	$0.205877\pi$
$660$	−1.29127e111	−0.548318
$661$	−4.21617e111	−1.68640	−0.843199	−	0.537602i	$-0.819330\pi$
$661$	−4.21617e111	−1.68640	−0.843199	+	0.537602i	$0.819330\pi$
$662$	1.52242e111	0.573644
$663$	1.12570e111	0.399612
$664$	−7.69514e110	−0.257381
$665$	−9.05043e111	−2.85242
$666$	−9.28401e110	−0.275742
$667$	6.36830e111	1.78260
$668$	−5.73307e110	−0.151257
$669$	1.86481e111	0.463770
$670$	−2.84857e111	−0.667840
$671$	2.59899e111	0.574466
$672$	−1.57940e111	−0.329159
$673$	−2.68247e110	−0.0527157	−0.0263578	−	0.999653i	$-0.508391\pi$
$673$	−2.68247e110	−0.0527157	−0.0263578	+	0.999653i	$0.508391\pi$
$674$	8.83945e110	0.163817
$675$	5.91880e111	1.03451
$676$	−1.65811e111	−0.273350
$677$	1.61023e111	0.250400	0.125200	−	0.992132i	$-0.460043\pi$
$677$	1.61023e111	0.250400	0.125200	+	0.992132i	$0.460043\pi$
$678$	7.88284e110	0.115640
$679$	−1.20375e112	−1.66602
$680$	−2.12822e111	−0.277916
$681$	2.75768e111	0.339808
$682$	5.41976e111	0.630227
$683$	−1.41196e112	−1.54955	−0.774773	−	0.632240i	$-0.782136\pi$
$683$	−1.41196e112	−1.54955	−0.774773	+	0.632240i	$0.782136\pi$
$684$	2.06090e111	0.213472
$685$	−1.70017e112	−1.66232
$686$	6.49017e111	0.599036
$687$	−4.01597e111	−0.349945
$688$	−4.92690e111	−0.405351
$689$	3.38988e111	0.263345
$690$	2.43007e112	1.78271
$691$	1.55517e112	1.07744	0.538722	−	0.842483i	$-0.318907\pi$
$691$	1.55517e112	1.07744	0.538722	+	0.842483i	$0.318907\pi$
$692$	−2.56929e111	−0.168121
$693$	−5.74762e111	−0.355243
$694$	−1.25580e112	−0.733199
$695$	4.36625e112	2.40829
$696$	−1.01776e112	−0.530373
$697$	5.24649e111	0.258330
$698$	−2.48371e111	−0.115561
$699$	−2.13890e111	−0.0940463
$700$	2.68327e112	1.11504
$701$	3.52460e112	1.38436	0.692178	−	0.721727i	$-0.256651\pi$
$701$	3.52460e112	1.38436	0.692178	+	0.721727i	$0.256651\pi$
$702$	−9.46606e111	−0.351442
$703$	−3.48196e112	−1.22205
$704$	−2.27847e111	−0.0756001
$705$	−7.81038e112	−2.45020
$706$	3.25637e112	0.965936
$707$	1.01009e113	2.83331
$708$	3.45393e112	0.916221
$709$	−7.33733e112	−1.84082	−0.920412	−	0.390951i	$-0.872146\pi$
$709$	−7.33733e112	−1.84082	−0.920412	+	0.390951i	$0.872146\pi$
$710$	−2.72904e112	−0.647596
$711$	−7.13572e111	−0.160173
$712$	−9.22609e111	−0.195911
$713$	−1.01996e113	−2.04901
$714$	−3.51377e112	−0.667873
$715$	−3.50853e112	−0.631011
$716$	4.17820e111	0.0711090
$717$	−5.31884e112	−0.856663
$718$	−6.43401e112	−0.980768
$719$	1.11527e113	1.60913	0.804564	−	0.593866i	$-0.202399\pi$
$719$	1.11527e113	1.60913	0.804564	+	0.593866i	$0.202399\pi$
$720$	−1.04702e112	−0.142995
$721$	8.73412e112	1.12921
$722$	1.95235e112	0.238967
$723$	6.33821e112	0.734521
$724$	−7.06232e112	−0.774951
$725$	1.72909e113	1.79666
$726$	5.33257e112	0.524735
$727$	−3.69443e112	−0.344301	−0.172151	−	0.985071i	$-0.555072\pi$
$727$	−3.69443e112	−0.344301	−0.172151	+	0.985071i	$0.555072\pi$
$728$	−4.29141e112	−0.378800
$729$	4.88817e112	0.408704
$730$	−1.47604e113	−1.16908
$731$	−1.09611e113	−0.822467
$732$	7.81678e112	0.555700
$733$	−2.41435e113	−1.62628	−0.813138	−	0.582072i	$-0.802242\pi$
$733$	−2.41435e113	−1.62628	−0.813138	+	0.582072i	$0.802242\pi$
$734$	9.18350e111	0.0586157
$735$	4.59368e113	2.77850
$736$	4.28789e112	0.245793
$737$	−6.78476e112	−0.368611
$738$	2.58112e112	0.132917
$739$	2.42273e113	1.18263	0.591315	−	0.806441i	$-0.298609\pi$
$739$	2.42273e113	1.18263	0.591315	+	0.806441i	$0.298609\pi$
$740$	1.76898e113	0.818597
$741$	2.07707e113	0.911237
$742$	−1.05812e113	−0.440128
$743$	−3.00886e113	−1.18671	−0.593354	−	0.804941i	$-0.702197\pi$
$743$	−3.00886e113	−1.18671	−0.593354	+	0.804941i	$0.702197\pi$
$744$	1.63006e113	0.609640
$745$	−5.67023e113	−2.01107
$746$	−9.03145e111	−0.0303790
$747$	−8.42240e112	−0.268703
$748$	−5.06901e112	−0.153395
$749$	−1.97708e113	−0.567536
$750$	1.88982e113	0.514637
$751$	5.94779e113	1.53666	0.768330	−	0.640054i	$-0.221088\pi$
$751$	5.94779e113	1.53666	0.768330	+	0.640054i	$0.221088\pi$
$752$	−1.37815e113	−0.337825
$753$	−4.59674e113	−1.06917
$754$	−2.76537e113	−0.610359
$755$	−3.15634e113	−0.661118
$756$	2.95474e113	0.587365
$757$	−8.35816e113	−1.57697	−0.788485	−	0.615053i	$-0.789134\pi$
$757$	−8.35816e113	−1.57697	−0.788485	+	0.615053i	$0.789134\pi$
$758$	6.51295e113	1.16639
$759$	5.78797e113	0.983956
$760$	−3.92684e113	−0.633733
$761$	8.03890e113	1.23169	0.615847	−	0.787866i	$-0.288814\pi$
$761$	8.03890e113	1.23169	0.615847	+	0.787866i	$0.288814\pi$
$762$	−2.01530e113	−0.293169
$763$	−1.59632e114	−2.20496
$764$	−3.31556e113	−0.434880
$765$	−2.32935e113	−0.290141
$766$	2.41758e113	0.285986
$767$	9.38473e113	1.05440
$768$	−6.85278e112	−0.0731305
$769$	9.45083e113	0.958031	0.479015	−	0.877806i	$-0.340994\pi$
$769$	9.45083e113	0.958031	0.479015	+	0.877806i	$0.340994\pi$
$770$	1.09515e114	1.05461
$771$	1.93378e113	0.176913
$772$	4.00402e113	0.348027
$773$	1.29252e113	0.106745	0.0533724	−	0.998575i	$-0.483003\pi$
$773$	1.29252e113	0.106745	0.0533724	+	0.998575i	$0.483003\pi$
$774$	−5.39254e113	−0.423181
$775$	−2.76934e114	−2.06518
$776$	−5.22289e113	−0.370146
$777$	2.92065e114	1.96721
$778$	−7.16912e113	−0.458957
$779$	9.68046e113	0.589069
$780$	−1.05524e114	−0.610397
$781$	−6.50005e113	−0.357438
$782$	9.53947e113	0.498721
$783$	1.90403e114	0.946419
$784$	8.10560e113	0.383090
$785$	1.33801e114	0.601322
$786$	1.20407e114	0.514589
$787$	−3.27904e113	−0.133274	−0.0666368	−	0.997777i	$-0.521227\pi$
$787$	−3.27904e113	−0.133274	−0.0666368	+	0.997777i	$0.521227\pi$
$788$	−1.84000e114	−0.711267
$789$	−1.24841e113	−0.0459002
$790$	1.35964e114	0.475505
$791$	−6.68560e113	−0.222418
$792$	−2.49380e113	−0.0789255
$793$	2.12391e114	0.639506
$794$	−4.39492e114	−1.25904
$795$	−2.60185e114	−0.709221
$796$	−1.54285e114	−0.400182
$797$	3.20452e114	0.790968	0.395484	−	0.918473i	$-0.370577\pi$
$797$	3.20452e114	0.790968	0.395484	+	0.918473i	$0.370577\pi$
$798$	−6.48336e114	−1.52295
$799$	−3.06604e114	−0.685456
$800$	1.16423e114	0.247733
$801$	−1.00980e114	−0.204528
$802$	−1.40630e114	−0.271138
$803$	−3.51564e114	−0.645269
$804$	−2.04060e114	−0.356570
$805$	−2.06099e115	−3.42877
$806$	4.42906e114	0.701581
$807$	1.21632e115	1.83460
$808$	4.38263e114	0.629486
$809$	6.00066e114	0.820791	0.410395	−	0.911908i	$-0.365391\pi$
$809$	6.00066e114	0.820791	0.410395	+	0.911908i	$0.365391\pi$
$810$	1.03703e115	1.35093
$811$	1.44248e114	0.178973	0.0894865	−	0.995988i	$-0.471477\pi$
$811$	1.44248e114	0.178973	0.0894865	+	0.995988i	$0.471477\pi$
$812$	8.63185e114	1.02009
$813$	1.86342e115	2.09765
$814$	4.21338e114	0.451821
$815$	−6.84854e114	−0.699636
$816$	−1.52457e114	−0.148384
$817$	−2.02247e115	−1.87547
$818$	1.18776e115	1.04947
$819$	−4.69699e114	−0.395463
$820$	−4.91807e114	−0.394591
$821$	2.34612e115	1.79389	0.896945	−	0.442143i	$-0.145781\pi$
$821$	2.34612e115	1.79389	0.896945	+	0.442143i	$0.145781\pi$
$822$	−1.21793e115	−0.887536
$823$	−1.74822e115	−1.21423	−0.607116	−	0.794613i	$-0.707674\pi$
$823$	−1.74822e115	−1.21423	−0.607116	+	0.794613i	$0.707674\pi$
$824$	3.78960e114	0.250881
$825$	1.57152e115	0.991721
$826$	−2.92935e115	−1.76222
$827$	1.49217e115	0.855756	0.427878	−	0.903837i	$-0.359261\pi$
$827$	1.49217e115	0.855756	0.427878	+	0.903837i	$0.359261\pi$
$828$	4.69314e114	0.256605
$829$	−6.82432e114	−0.355759	−0.177879	−	0.984052i	$-0.556924\pi$
$829$	−6.82432e114	−0.355759	−0.177879	+	0.984052i	$0.556924\pi$
$830$	1.60481e115	0.797698
$831$	−3.29004e115	−1.55941
$832$	−1.86198e114	−0.0841594
$833$	1.80329e115	0.777300
$834$	3.12781e115	1.28582
$835$	1.19562e115	0.468790
$836$	−9.35299e114	−0.349786
$837$	−3.04952e115	−1.08787
$838$	−3.02551e115	−1.02958
$839$	−5.82530e115	−1.89113	−0.945565	−	0.325434i	$-0.894489\pi$
$839$	−5.82530e115	−1.89113	−0.945565	+	0.325434i	$0.894489\pi$
$840$	3.29382e115	1.02016
$841$	2.17825e115	0.643674
$842$	−3.82159e115	−1.07750
$843$	1.76183e115	0.473997
$844$	−4.30971e114	−0.110642
$845$	3.45796e115	0.847189
$846$	−1.50840e115	−0.352685
$847$	−4.52267e115	−1.00925
$848$	−4.59101e114	−0.0977849
$849$	7.86528e115	1.59904
$850$	2.59011e115	0.502657
$851$	−7.92923e115	−1.46897
$852$	−1.95497e115	−0.345761
$853$	1.07883e116	1.82165	0.910827	−	0.412789i	$-0.135445\pi$
$853$	1.07883e116	1.82165	0.910827	+	0.412789i	$0.135445\pi$
$854$	−6.62957e115	−1.06881
$855$	−4.29797e115	−0.661609
$856$	−8.57826e114	−0.126091
$857$	6.82144e115	0.957488	0.478744	−	0.877955i	$-0.341092\pi$
$857$	6.82144e115	0.957488	0.478744	+	0.877955i	$0.341092\pi$
$858$	−2.51337e115	−0.336906
$859$	4.27541e114	0.0547329	0.0273664	−	0.999625i	$-0.491288\pi$
$859$	4.27541e114	0.0547329	0.0273664	+	0.999625i	$0.491288\pi$
$860$	1.02750e116	1.25630
$861$	−8.11992e115	−0.948260
$862$	1.77155e115	0.197614
$863$	1.47735e116	1.57419	0.787093	−	0.616835i	$-0.211585\pi$
$863$	1.47735e116	1.57419	0.787093	+	0.616835i	$0.211585\pi$
$864$	1.28202e115	0.130497
$865$	5.35820e115	0.521054
$866$	−7.70206e115	−0.715566
$867$	9.78996e115	0.869013
$868$	−1.38249e116	−1.17255
$869$	3.23841e115	0.262453
$870$	2.12253e116	1.64378
$871$	−5.54455e115	−0.410345
$872$	−6.92618e115	−0.489883
$873$	−5.71651e115	−0.386428
$874$	1.76016e116	1.13723
$875$	−1.60280e116	−0.989829
$876$	−1.05737e116	−0.624190
$877$	−1.63499e116	−0.922640	−0.461320	−	0.887234i	$-0.652624\pi$
$877$	−1.63499e116	−0.922640	−0.461320	+	0.887234i	$0.652624\pi$
$878$	3.83549e115	0.206913
$879$	−2.51317e116	−1.29617
$880$	4.75170e115	0.234306
$881$	1.32327e116	0.623881	0.311940	−	0.950102i	$-0.399021\pi$
$881$	1.32327e116	0.623881	0.311940	+	0.950102i	$0.399021\pi$
$882$	8.87166e115	0.399941
$883$	1.91608e116	0.825975	0.412987	−	0.910737i	$-0.364485\pi$
$883$	1.91608e116	0.825975	0.412987	+	0.910737i	$0.364485\pi$
$884$	−4.14243e115	−0.170762
$885$	−7.20312e116	−2.83963
$886$	3.86288e115	0.145640
$887$	2.58557e115	0.0932339	0.0466169	−	0.998913i	$-0.485156\pi$
$887$	2.58557e115	0.0932339	0.0466169	+	0.998913i	$0.485156\pi$
$888$	1.26723e116	0.437061
$889$	1.70921e116	0.563867
$890$	1.92409e116	0.607182
$891$	2.47001e116	0.745639
$892$	−6.86224e115	−0.198177
$893$	−5.65724e116	−1.56305
$894$	−4.06193e116	−1.07374
$895$	−8.71357e115	−0.220387
$896$	5.81198e115	0.140656
$897$	4.72996e116	1.09536
$898$	1.40731e115	0.0311871
$899$	−8.90872e116	−1.88933
$900$	1.27426e116	0.258630
$901$	−1.02138e116	−0.198408
$902$	−1.17139e116	−0.217793
$903$	1.69644e117	3.01906
$904$	−2.90078e115	−0.0494153
$905$	1.47284e117	2.40179
$906$	−2.26107e116	−0.352981
$907$	4.93689e116	0.737846	0.368923	−	0.929460i	$-0.379727\pi$
$907$	4.93689e116	0.737846	0.368923	+	0.929460i	$0.379727\pi$
$908$	−1.01479e116	−0.145206
$909$	4.79683e116	0.657175
$910$	8.94967e116	1.17401
$911$	−7.50189e116	−0.942312	−0.471156	−	0.882050i	$-0.656163\pi$
$911$	−7.50189e116	−0.942312	−0.471156	+	0.882050i	$0.656163\pi$
$912$	−2.81303e116	−0.338360
$913$	3.82235e116	0.440286
$914$	−7.75052e116	−0.854980
$915$	−1.63018e117	−1.72227
$916$	1.47782e116	0.149538
$917$	−1.02119e117	−0.989736
$918$	2.85216e116	0.264782
$919$	1.40402e117	1.24857	0.624283	−	0.781198i	$-0.285391\pi$
$919$	1.40402e117	1.24857	0.624283	+	0.781198i	$0.285391\pi$
$920$	−8.94232e116	−0.761783
$921$	−6.38207e116	−0.520842
$922$	−4.49422e116	−0.351385
$923$	−5.31188e116	−0.397906
$924$	7.84524e116	0.563072
$925$	−2.15291e117	−1.48057
$926$	6.36112e116	0.419179
$927$	4.14775e116	0.261917
$928$	3.74522e116	0.226638
$929$	3.32782e116	0.192992	0.0964960	−	0.995333i	$-0.469237\pi$
$929$	3.32782e116	0.192992	0.0964960	+	0.995333i	$0.469237\pi$
$930$	−3.39947e117	−1.88945
$931$	3.32731e117	1.77248
$932$	7.87085e115	0.0401877
$933$	−2.85508e117	−1.39731
$934$	−2.12563e117	−0.997208
$935$	1.05713e117	0.475413
$936$	−2.03795e116	−0.0878613
$937$	1.14649e117	0.473866	0.236933	−	0.971526i	$-0.423858\pi$
$937$	1.14649e117	0.473866	0.236933	+	0.971526i	$0.423858\pi$
$938$	1.73068e117	0.685810
$939$	1.81096e117	0.688046
$940$	2.87411e117	1.04702
$941$	2.64667e117	0.924507	0.462253	−	0.886748i	$-0.347041\pi$
$941$	2.64667e117	0.924507	0.462253	+	0.886748i	$0.347041\pi$
$942$	9.58494e116	0.321055
$943$	2.20447e117	0.708095
$944$	−1.27100e117	−0.391518
$945$	−6.16206e117	−1.82041
$946$	2.44731e117	0.693407
$947$	−6.09833e117	−1.65724	−0.828622	−	0.559809i	$-0.810875\pi$
$947$	−6.09833e117	−1.65724	−0.828622	+	0.559809i	$0.810875\pi$
$948$	9.73994e116	0.253879
$949$	−2.87301e117	−0.718325
$950$	4.77910e117	1.14621
$951$	−5.75389e117	−1.32383
$952$	1.29302e117	0.285394
$953$	−2.86861e117	−0.607438	−0.303719	−	0.952762i	$-0.598228\pi$
$953$	−2.86861e117	−0.607438	−0.303719	+	0.952762i	$0.598228\pi$
$954$	−5.02490e116	−0.102086
$955$	6.91454e117	1.34781
$956$	1.95726e117	0.366068
$957$	5.05545e117	0.907274
$958$	−2.56323e117	−0.441419
$959$	1.03295e118	1.70705
$960$	1.42914e117	0.226652
$961$	7.69821e117	1.17170
$962$	3.44320e117	0.502975
$963$	−9.38899e116	−0.131638
$964$	−2.33238e117	−0.313874
$965$	−8.35032e117	−1.07863
$966$	−1.47641e118	−1.83067
$967$	4.09752e117	0.487725	0.243862	−	0.969810i	$-0.421585\pi$
$967$	4.09752e117	0.487725	0.243862	+	0.969810i	$0.421585\pi$
$968$	−1.96231e117	−0.224229
$969$	−6.25828e117	−0.686540
$970$	1.08923e118	1.14719
$971$	−9.47250e117	−0.957867	−0.478933	−	0.877851i	$-0.658976\pi$
$971$	−9.47250e117	−0.957867	−0.478933	+	0.877851i	$0.658976\pi$
$972$	3.62729e117	0.352180
$973$	−2.65276e118	−2.47309
$974$	−6.35877e117	−0.569239
$975$	1.28426e118	1.10400
$976$	−2.87647e117	−0.237461
$977$	8.95310e117	0.709804	0.354902	−	0.934904i	$-0.384514\pi$
$977$	8.95310e117	0.709804	0.354902	+	0.934904i	$0.384514\pi$
$978$	−4.90602e117	−0.373546
$979$	4.58281e117	0.335132
$980$	−1.69041e118	−1.18730
$981$	−7.58077e117	−0.511432
$982$	2.01829e117	0.130792
$983$	−1.68447e118	−1.04857	−0.524287	−	0.851542i	$-0.675668\pi$
$983$	−1.68447e118	−1.04857	−0.524287	+	0.851542i	$0.675668\pi$
$984$	−3.52311e117	−0.210678
$985$	3.83729e118	2.20442
$986$	8.33218e117	0.459854
$987$	4.74527e118	2.51613
$988$	−7.64332e117	−0.389388
$989$	−4.60563e118	−2.25442
$990$	5.20079e117	0.244613
$991$	1.36583e118	0.617287	0.308643	−	0.951178i	$-0.400125\pi$
$991$	1.36583e118	0.617287	0.308643	+	0.951178i	$0.400125\pi$
$992$	−5.99841e117	−0.260510
$993$	−2.27442e118	−0.949240
$994$	1.65805e118	0.665022
$995$	3.21759e118	1.24028
$996$	1.14962e118	0.425903
$997$	2.34775e118	0.835973	0.417987	−	0.908453i	$-0.362736\pi$
$997$	2.34775e118	0.835973	0.417987	+	0.908453i	$0.362736\pi$
$998$	−1.37245e118	−0.469722
$999$	−2.37072e118	−0.779909

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.80.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+5.49756e11 q^{2} -8.21312e18 q^{3} +3.02231e23 q^{4} -6.30299e27 q^{5} -4.51521e30 q^{6} +3.82944e33 q^{7} +1.66153e35 q^{8} +1.81857e37 q^{9} -3.46510e39 q^{10} -8.25322e40 q^{11} -2.48226e42 q^{12} -6.74458e43 q^{13} +2.10526e45 q^{14} +5.17672e46 q^{15} +9.13439e46 q^{16} +2.03217e48 q^{17} +9.99767e48 q^{18} +3.74962e50 q^{19} -1.90496e51 q^{20} -3.14516e52 q^{21} -4.53726e52 q^{22} +8.53875e53 q^{23} -1.36464e54 q^{24} +2.31840e55 q^{25} -3.70787e55 q^{26} +2.55296e56 q^{27} +1.15738e57 q^{28} +7.45811e57 q^{29} +2.84593e58 q^{30} -1.19450e59 q^{31} +5.02168e58 q^{32} +6.77847e59 q^{33} +1.11720e60 q^{34} -2.41369e61 q^{35} +5.49628e60 q^{36} -9.28617e61 q^{37} +2.06138e62 q^{38} +5.53941e62 q^{39} -1.04726e63 q^{40} +2.58172e63 q^{41} -1.72907e64 q^{42} -5.39380e64 q^{43} -2.49438e64 q^{44} -1.14624e65 q^{45} +4.69423e65 q^{46} -1.50875e66 q^{47} -7.50218e65 q^{48} +8.87373e66 q^{49} +1.27456e67 q^{50} -1.66904e67 q^{51} -2.03843e67 q^{52} -5.02607e67 q^{53} +1.40350e68 q^{54} +5.20200e68 q^{55} +6.36275e68 q^{56} -3.07961e69 q^{57} +4.10014e69 q^{58} -1.39145e70 q^{59} +1.56457e70 q^{60} -3.14906e70 q^{61} -6.56684e70 q^{62} +6.96409e70 q^{63} +2.76070e70 q^{64} +4.25110e71 q^{65} +3.72650e71 q^{66} +8.22074e71 q^{67} +6.14186e71 q^{68} -7.01298e72 q^{69} -1.32694e73 q^{70} +7.87577e72 q^{71} +3.02161e72 q^{72} +4.25972e73 q^{73} -5.10513e73 q^{74} -1.90413e74 q^{75} +1.13325e74 q^{76} -3.16052e74 q^{77} +3.04532e74 q^{78} -3.92382e74 q^{79} -5.75739e74 q^{80} -2.99278e75 q^{81} +1.41931e75 q^{82} -4.63134e75 q^{83} -9.50567e75 q^{84} -1.28087e76 q^{85} -2.96527e76 q^{86} -6.12543e76 q^{87} -1.37130e76 q^{88} -5.55275e76 q^{89} -6.30152e76 q^{90} -2.58280e77 q^{91} +2.58068e77 q^{92} +9.81058e77 q^{93} -8.29445e77 q^{94} -2.36338e78 q^{95} -4.12437e77 q^{96} -3.14342e78 q^{97} +4.87838e78 q^{98} -1.50090e78 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 1649267441664 q^{2} - 45\!\cdots\!36 q^{3} + 90\!\cdots\!32 q^{4} - 40\!\cdots\!50 q^{5} - 25\!\cdots\!68 q^{6} + 14\!\cdots\!12 q^{7} + 49\!\cdots\!16 q^{8} - 66\!\cdots\!69 q^{9} - 22\!\cdots\!00 q^{10}+ \cdots + 43\!\cdots\!32 q^{99}+O(q^{100}) \) 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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