LMFDB - Embedded newform 3.70.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,70,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 70, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 70);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	3.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:	$90.4544859877$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 40\!\cdots\!00 $ x^6 - 3x^5 - 8785036246714673132x^4 - 489946547045174855374556256x^3 + 19187418488273751521495823450187335040x^2 + 711105729064303642253694769744270208387385600*x - 4081433259823761741733687714132191037604592129279360000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{33}\cdot 5^{5}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.38628e9$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.96695e10 q^{2} +1.66772e16 q^{3} +9.83375e20 q^{4} +1.65867e24 q^{5} -6.61576e26 q^{6} +4.47127e28 q^{7} -1.55933e31 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q-3.96695e10 q^{2} +1.66772e16 q^{3} +9.83375e20 q^{4} +1.65867e24 q^{5} -6.61576e26 q^{6} +4.47127e28 q^{7} -1.55933e31 q^{8} +2.78128e32 q^{9} -6.57985e34 q^{10} -2.74899e35 q^{11} +1.63999e37 q^{12} -3.14018e38 q^{13} -1.77373e39 q^{14} +2.76619e40 q^{15} +3.80952e40 q^{16} -2.63495e42 q^{17} -1.10332e43 q^{18} +2.13084e44 q^{19} +1.63109e45 q^{20} +7.45682e44 q^{21} +1.09051e46 q^{22} +1.06019e47 q^{23} -2.60052e47 q^{24} +1.05711e48 q^{25} +1.24569e49 q^{26} +4.63840e48 q^{27} +4.39694e49 q^{28} +1.54570e50 q^{29} -1.09733e51 q^{30} -3.83638e51 q^{31} +7.69342e51 q^{32} -4.58454e51 q^{33} +1.04527e53 q^{34} +7.41635e52 q^{35} +2.73505e53 q^{36} +2.33975e54 q^{37} -8.45294e54 q^{38} -5.23693e54 q^{39} -2.58640e55 q^{40} +2.64500e55 q^{41} -2.95809e55 q^{42} +1.73336e55 q^{43} -2.70329e56 q^{44} +4.61322e56 q^{45} -4.20572e57 q^{46} -7.32804e57 q^{47} +6.35321e56 q^{48} -1.85013e58 q^{49} -4.19349e58 q^{50} -4.39436e58 q^{51} -3.08797e59 q^{52} -6.18818e58 q^{53} -1.84003e59 q^{54} -4.55966e59 q^{55} -6.97217e59 q^{56} +3.55364e60 q^{57} -6.13172e60 q^{58} +1.09613e61 q^{59} +2.72020e61 q^{60} +5.00925e61 q^{61} +1.52187e62 q^{62} +1.24359e61 q^{63} -3.27682e62 q^{64} -5.20851e62 q^{65} +1.81867e62 q^{66} +1.85894e63 q^{67} -2.59115e63 q^{68} +1.76810e63 q^{69} -2.94203e63 q^{70} -3.06540e63 q^{71} -4.33693e63 q^{72} -4.48131e63 q^{73} -9.28168e64 q^{74} +1.76296e64 q^{75} +2.09542e65 q^{76} -1.22915e64 q^{77} +2.07747e65 q^{78} +5.32048e65 q^{79} +6.31873e64 q^{80} +7.73554e64 q^{81} -1.04926e66 q^{82} +1.21310e66 q^{83} +7.33285e65 q^{84} -4.37051e66 q^{85} -6.87615e65 q^{86} +2.57779e66 q^{87} +4.28657e66 q^{88} +3.85757e66 q^{89} -1.83004e67 q^{90} -1.40406e67 q^{91} +1.04256e68 q^{92} -6.39799e67 q^{93} +2.90700e68 q^{94} +3.53435e68 q^{95} +1.28305e68 q^{96} +1.26654e68 q^{97} +7.33937e68 q^{98} -7.64572e67 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) $ 6 * q + 19700962938 * q^2 + 100063090197999414 * q^3 + 2215616615832949213668 * q^4 + 628080806150898444057636 * q^5 + 328556538575422922826619722 * q^6 + 47913495403332419035526232336 * q^7 + 24457375972572426935219376797544 * q^8 + 1668770336662161067543714657390566 * q^9	$ 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 38\!\cdots\!64 q^{99}+O(q^{100}) $ 6 * q + 19700962938 * q^2 + 100063090197999414 * q^3 + 2215616615832949213668 * q^4 + 628080806150898444057636 * q^5 + 328556538575422922826619722 * q^6 + 47913495403332419035526232336 * q^7 + 24457375972572426935219376797544 * q^8 + 1668770336662161067543714657390566 * q^9 - 22202946094182786607107040591714596 * q^10 + 1390130418743494007545256289087169224 * q^11 + 36950240879046435619379563386337465092 * q^12 + 133509121614335990365965211432000729332 * q^13 - 2841394212247933581409064272690567131408 * q^14 + 10474617726251589358520780625360618370884 * q^15 + 297926539143537140116723472619801199364880 * q^16 - 274151565383473524836430571365328624168788 * q^17 + 5479397092435836303110872860016484759473818 * q^18 + 138429394829044356269800544348434108061745912 * q^19 + 138597243063668969619157527013420360089172824 * q^20 + 799062068707513693070181199972452904025975184 * q^21 + 41357320156815766506190949808834631301146379064 * q^22 + 218317639771339979005196930422301057686492438608 * q^23 + 407880102991649733080716879327968269719818106536 * q^24 + 3158503477944939899259768424552979678128936846746 * q^25 + 23013722899099212942495329191134948082985267735052 * q^26 + 27830386119528611875968901007343548725913806188054 * q^27 - 22620517010064241205747099942016845775787346540448 * q^28 + 386749858303620975828595276373219723661271736500404 * q^29 - 370282566280588494739921166576105524382557210541124 * q^30 - 406800617338554840921365551900230681176672582694624 * q^31 + 8820058315615156467775375743923825115981231801768096 * q^32 + 23183457579618822681041348155744625937569376878472456 * q^33 + 281687660915944724759468852907875788491074366030810196 * q^34 + 890666754256698409309143705814565889896130721823553120 * q^35 + 616225880986304773795203687785611855657221329076909348 * q^36 - 1034952541392536641085376764904786871274360452152204924 * q^37 - 5285525891153406695181497436406602451158488826469402872 * q^38 + 2226555879725162556253661663326679211189300189218101908 * q^39 - 82332680986716259050086980186058027597204731237577012112 * q^40 - 75922269693086975847370108328993717966577053054061574404 * q^41 - 47386447558039744873106666160656130217031504344407499152 * q^42 + 517689066199516372636612583654794159251763191323866573320 * q^43 + 635179531764405639585838952451726338367638421474019771824 * q^44 + 174687103055246053382755708023577718190895841278777776996 * q^45 + 5002677415477463005074915765236526191711825419441207632816 * q^46 + 2453203952295844591600634297438375000618428764145129219680 * q^47 + 4968575026449593322551787829369140395486935424990568696720 * q^48 + 2425144461879979131295388929466673195687370332650760871830 * q^49 + 37635665810544549850117129516993646830506493536524891294694 * q^50 - 4572075469148207520239238457234666663632976056294376848372 * q^51 + 5305218099159647316820834640268608261939453873644307186232 * q^52 + 74471113644675549895227882174052653368560896469248975574788 * q^53 + 91380900915177136766508328597711019880437502648894485390442 * q^54 - 2409654567830037488585083843998013931798965138034800503971664 * q^55 - 1152362306928674739149660784650028044220707470519808104718400 * q^56 + 2308612170138856515323754812102347865320528660571074398815928 * q^57 + 15022887190676434515518320415561940276213411853028154366072396 * q^58 + 11415146769011619472046632564776870018333102937631875861541928 * q^59 + 2311411405645659457638507670716384370296951624465227816120856 * q^60 + 33238256339320993820472102641365032387601740714468466667170260 * q^61 - 124525378061521437222478334616477802775494912101377589859538208 * q^62 + 13326103309146657949938227725670548487445834719016647868423696 * q^63 - 766655384080592585753942434682913694288086896286784450843059648 * q^64 - 1033047386671074609986337778384229107631858701816226280998392392 * q^65 + 689723542866499218831313407015589656876016041998031390482311416 * q^66 + 1829841882595431765701319157889272255403856626816125827498086232 * q^67 + 2317663971913472593763546580441523937519238504690538745057995656 * q^68 + 3640922946708989413397256792395290653432177770376246213302495952 * q^69 + 21667344061607294216951596756563208633436583684026130660066187680 * q^70 - 13440911053044271064593659636588909406794279924608753124634255248 * q^71 + 6802290589270456310723007400658664216160810865509880920119594984 * q^72 - 10455717435803652258126612179458660840472081585301779921081767812 * q^73 - 161664876015117679845821922240487717737273356359281171995837108868 * q^74 + 52674936400716562322380194260642699522996671253949886206452634474 * q^75 + 71090965276426447702322949472042826997822238537703230080293688528 * q^76 - 43362153841256194511002835681080956828831169900379264481733785408 * q^77 + 383804038374054851929016706651242398292482671566351802142233876588 * q^78 + 849706277580491574368053093245214288882224299075364357356727921600 * q^79 - 189522757413920765612591740266335581479125703002325048006012452256 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 1548665779897056733086309454028318283362331255484057489512257090052 * q^82 - 147710286880885756653308105230523797327053885776686380979324732296 * q^83 - 377246472317239697653688739971600940182916419912051144657271882912 * q^84 + 900129278829088984191830889400611488683994113651840432684483124232 * q^85 + 20081029605597770660724545035979232318223218281164495480965241306104 * q^86 + 6449897659249786389820756834246397993926418977011658135033733793876 * q^87 + 42299661882900410851288517995075665379682018856186665678192374320864 * q^88 + 63907211385846533401519989675721990056288572539740159493298948890332 * q^89 - 6175269638080203823349656636276052054009049469739079836962862483556 * q^90 + 44568583318227431253455625104560122172317657855744447513981633586656 * q^91 + 407516989708923645515294364601926415744249719108325034482775450006496 * q^92 - 6784287810891609560820397041997675504562492646751100945260348825056 * q^93 + 543732799316328297398198809151553350012212421132175473218873964726688 * q^94 + 727302843727922318056572996599295364559054812190980909735896231363024 * q^95 + 147093715131169030822786258830983491108570311615658180154147861982624 * q^96 + 947436775360467753919340697699840040468393082746311551117424599367372 * q^97 + 2424310569772600455357151217191683340027129070175336157909473058804458 * q^98 + 386634734481815239147577824740950727802459268187074272255289250523464 * 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 $

$2$	−3.96695e10	−1.63276	−0.816380	−	0.577516i	$-0.804022\pi$
$2$	−3.96695e10	−1.63276	−0.816380	+	0.577516i	$0.804022\pi$
$3$	1.66772e16	0.577350
$3$	1.66772e16	0.577350
$4$	9.83375e20	1.66590
$5$	1.65867e24	1.27436	0.637182	−	0.770713i	$-0.280100\pi$
$5$	1.65867e24	1.27436	0.637182	+	0.770713i	$0.280100\pi$
$6$	−6.61576e26	−0.942674
$7$	4.47127e28	0.312283	0.156142	−	0.987735i	$-0.450094\pi$
$7$	4.47127e28	0.312283	0.156142	+	0.987735i	$0.450094\pi$
$8$	−1.55933e31	−1.08726
$9$	2.78128e32	0.333333
$10$	−6.57985e34	−2.08073
$11$	−2.74899e35	−0.324433	−0.162217	−	0.986755i	$-0.551864\pi$
$11$	−2.74899e35	−0.324433	−0.162217	+	0.986755i	$0.551864\pi$
$12$	1.63999e37	0.961809
$13$	−3.14018e38	−1.16388	−0.581941	−	0.813231i	$-0.697706\pi$
$13$	−3.14018e38	−1.16388	−0.581941	+	0.813231i	$0.697706\pi$
$14$	−1.77373e39	−0.509883
$15$	2.76619e40	0.735755
$16$	3.80952e40	0.109328
$17$	−2.63495e42	−0.933867	−0.466934	−	0.884292i	$-0.654641\pi$
$17$	−2.63495e42	−0.933867	−0.466934	+	0.884292i	$0.654641\pi$
$18$	−1.10332e43	−0.544253
$19$	2.13084e44	1.62762	0.813808	−	0.581135i	$-0.197391\pi$
$19$	2.13084e44	1.62762	0.813808	+	0.581135i	$0.197391\pi$
$20$	1.63109e45	2.12297
$21$	7.45682e44	0.180297
$22$	1.09051e46	0.529722
$23$	1.06019e47	1.11115	0.555576	−	0.831466i	$-0.312498\pi$
$23$	1.06019e47	1.11115	0.555576	+	0.831466i	$0.312498\pi$
$24$	−2.60052e47	−0.627729
$25$	1.05711e48	0.624006
$26$	1.24569e49	1.90034
$27$	4.63840e48	0.192450
$28$	4.39694e49	0.520233
$29$	1.54570e50	0.544997	0.272499	−	0.962156i	$-0.412150\pi$
$29$	1.54570e50	0.544997	0.272499	+	0.962156i	$0.412150\pi$
$30$	−1.09733e51	−1.20131
$31$	−3.83638e51	−1.35501	−0.677505	−	0.735518i	$-0.736939\pi$
$31$	−3.83638e51	−1.35501	−0.677505	+	0.735518i	$0.736939\pi$
$32$	7.69342e51	0.908752
$33$	−4.58454e51	−0.187312
$34$	1.04527e53	1.52478
$35$	7.41635e52	0.397963
$36$	2.73505e53	0.555301
$37$	2.33975e54	1.84591	0.922954	−	0.384909i	$-0.125767\pi$
$37$	2.33975e54	1.84591	0.922954	+	0.384909i	$0.125767\pi$
$38$	−8.45294e54	−2.65750
$39$	−5.23693e54	−0.671967
$40$	−2.58640e55	−1.38556
$41$	2.64500e55	0.604480	0.302240	−	0.953232i	$-0.402266\pi$
$41$	2.64500e55	0.604480	0.302240	+	0.953232i	$0.402266\pi$
$42$	−2.95809e55	−0.294381
$43$	1.73336e55	0.0765997	0.0382998	−	0.999266i	$-0.487806\pi$
$43$	1.73336e55	0.0765997	0.0382998	+	0.999266i	$0.487806\pi$
$44$	−2.70329e56	−0.540474
$45$	4.61322e56	0.424788
$46$	−4.20572e57	−1.81424
$47$	−7.32804e57	−1.50526	−0.752630	−	0.658443i	$-0.771215\pi$
$47$	−7.32804e57	−1.50526	−0.752630	+	0.658443i	$0.771215\pi$
$48$	6.35321e56	0.0631205
$49$	−1.85013e58	−0.902479
$50$	−4.19349e58	−1.01885
$51$	−4.39436e58	−0.539169
$52$	−3.08797e59	−1.93891
$53$	−6.18818e58	−0.201393	−0.100697	−	0.994917i	$-0.532107\pi$
$53$	−6.18818e58	−0.201393	−0.100697	+	0.994917i	$0.532107\pi$
$54$	−1.84003e59	−0.314225
$55$	−4.55966e59	−0.413447
$56$	−6.97217e59	−0.339532
$57$	3.55364e60	0.939704
$58$	−6.13172e60	−0.889849
$59$	1.09613e61	0.881997	0.440999	−	0.897508i	$-0.354624\pi$
$59$	1.09613e61	0.881997	0.440999	+	0.897508i	$0.354624\pi$
$60$	2.72020e61	1.22570
$61$	5.00925e61	1.27613	0.638063	−	0.769984i	$-0.279736\pi$
$61$	5.00925e61	1.27613	0.638063	+	0.769984i	$0.279736\pi$
$62$	1.52187e62	2.21241
$63$	1.24359e61	0.104094
$64$	−3.27682e62	−1.59310
$65$	−5.20851e62	−1.48321
$66$	1.81867e62	0.305835
$67$	1.85894e63	1.86074	0.930369	−	0.366625i	$-0.119487\pi$
$67$	1.85894e63	1.86074	0.930369	+	0.366625i	$0.119487\pi$
$68$	−2.59115e63	−1.55573
$69$	1.76810e63	0.641524
$70$	−2.94203e63	−0.649778
$71$	−3.06540e63	−0.415025	−0.207512	−	0.978232i	$-0.566537\pi$
$71$	−3.06540e63	−0.415025	−0.207512	+	0.978232i	$0.566537\pi$
$72$	−4.33693e63	−0.362419
$73$	−4.48131e63	−0.232684	−0.116342	−	0.993209i	$-0.537117\pi$
$73$	−4.48131e63	−0.232684	−0.116342	+	0.993209i	$0.537117\pi$
$74$	−9.28168e64	−3.01392
$75$	1.76296e64	0.360270
$76$	2.09542e65	2.71145
$77$	−1.22915e64	−0.101315
$78$	2.07747e65	1.09716
$79$	5.32048e65	1.81057	0.905287	−	0.424800i	$-0.139656\pi$
$79$	5.32048e65	1.81057	0.905287	+	0.424800i	$0.139656\pi$
$80$	6.31873e64	0.139324
$81$	7.73554e64	0.111111
$82$	−1.04926e66	−0.986971
$83$	1.21310e66	0.751107	0.375553	−	0.926801i	$-0.377453\pi$
$83$	1.21310e66	0.751107	0.375553	+	0.926801i	$0.377453\pi$
$84$	7.33285e65	0.300357
$85$	−4.37051e66	−1.19009
$86$	−6.87615e65	−0.125069
$87$	2.57779e66	0.314654
$88$	4.28657e66	0.352743
$89$	3.85757e66	0.214961	0.107480	−	0.994207i	$-0.465722\pi$
$89$	3.85757e66	0.214961	0.107480	+	0.994207i	$0.465722\pi$
$90$	−1.83004e67	−0.693577
$91$	−1.40406e67	−0.363461
$92$	1.04256e68	1.85107
$93$	−6.39799e67	−0.782316
$94$	2.90700e68	2.45773
$95$	3.53435e68	2.07418
$96$	1.28305e68	0.524668
$97$	1.26654e68	0.362239	0.181120	−	0.983461i	$-0.442028\pi$
$97$	1.26654e68	0.362239	0.181120	+	0.983461i	$0.442028\pi$
$98$	7.33937e68	1.47353
$99$	−7.64572e67	−0.108144
$100$	1.03953e69	1.03953
$101$	−2.51827e69	−1.78655	−0.893276	−	0.449508i	$-0.851599\pi$
$101$	−2.51827e69	−1.78655	−0.893276	+	0.449508i	$0.851599\pi$
$102$	1.74322e69	0.880332
$103$	2.80294e67	0.0101095	0.00505475	−	0.999987i	$-0.498391\pi$
$103$	2.80294e67	0.0101095	0.00505475	+	0.999987i	$0.498391\pi$
$104$	4.89656e69	1.26544
$105$	1.23684e69	0.229764
$106$	2.45482e69	0.328827
$107$	−8.90279e69	−0.862553	−0.431277	−	0.902220i	$-0.641937\pi$
$107$	−8.90279e69	−0.862553	−0.431277	+	0.902220i	$0.641937\pi$
$108$	4.56128e69	0.320603
$109$	2.02921e70	1.03780	0.518900	−	0.854835i	$-0.326342\pi$
$109$	2.02921e70	1.03780	0.518900	+	0.854835i	$0.326342\pi$
$110$	1.80879e70	0.675059
$111$	3.90205e70	1.06574
$112$	1.70334e69	0.0341413
$113$	−1.20871e70	−0.178286	−0.0891430	−	0.996019i	$-0.528413\pi$
$113$	−1.20871e70	−0.178286	−0.0891430	+	0.996019i	$0.528413\pi$
$114$	−1.40971e71	−1.53431
$115$	1.75850e71	1.41601
$116$	1.52000e71	0.907912
$117$	−8.73373e70	−0.387960
$118$	−4.34829e71	−1.44009
$119$	−1.17816e71	−0.291631
$120$	−4.31339e71	−0.799955
$121$	−6.42382e71	−0.894743
$122$	−1.98715e72	−2.08361
$123$	4.41111e71	0.348997
$124$	−3.77260e72	−2.25732
$125$	−1.05650e72	−0.479154
$126$	−4.93325e71	−0.169961
$127$	4.67754e72	1.22684	0.613422	−	0.789755i	$-0.289793\pi$
$127$	4.67754e72	1.22684	0.613422	+	0.789755i	$0.289793\pi$
$128$	8.45758e72	1.69240
$129$	2.89075e71	0.0442248
$130$	2.06619e73	2.42172
$131$	−1.84457e73	−1.65972	−0.829861	−	0.557971i	$-0.811580\pi$
$131$	−1.84457e73	−1.65972	−0.829861	+	0.557971i	$0.811580\pi$
$132$	−4.50832e72	−0.312043
$133$	9.52757e72	0.508277
$134$	−7.37433e73	−3.03814
$135$	7.69355e72	0.245252
$136$	4.10875e73	1.01535
$137$	8.38342e73	1.60902	0.804511	−	0.593938i	$-0.202428\pi$
$137$	8.38342e73	1.60902	0.804511	+	0.593938i	$0.202428\pi$
$138$	−7.01396e73	−1.04745
$139$	8.54470e73	0.994686	0.497343	−	0.867554i	$-0.334309\pi$
$139$	8.54470e73	0.994686	0.497343	+	0.867554i	$0.334309\pi$
$140$	7.29305e73	0.662967
$141$	−1.22211e74	−0.869063
$142$	1.21603e74	0.677636
$143$	8.63232e73	0.377602
$144$	1.05954e73	0.0364426
$145$	2.56380e74	0.694525
$146$	1.77772e74	0.379917
$147$	−3.08549e74	−0.521047
$148$	2.30085e75	3.07510
$149$	−1.69199e72	−0.00179255	−0.000896275	−	1.00000i	$-0.500285\pi$
$149$	−1.69199e72	−0.00179255	−0.000896275		1.00000i	$0.500285\pi$
$150$	−6.99357e74	−0.588234
$151$	1.96760e74	0.131593	0.0657964	−	0.997833i	$-0.479041\pi$
$151$	1.96760e74	0.131593	0.0657964	+	0.997833i	$0.479041\pi$
$152$	−3.32268e75	−1.76964
$153$	−7.32855e74	−0.311289
$154$	4.87597e74	0.165423
$155$	−6.36327e75	−1.72678
$156$	−5.14987e75	−1.11943
$157$	5.37741e75	0.937637	0.468819	−	0.883294i	$-0.344680\pi$
$157$	5.37741e75	0.937637	0.468819	+	0.883294i	$0.344680\pi$
$158$	−2.11061e76	−2.95623
$159$	−1.03201e75	−0.116275
$160$	1.27608e76	1.15808
$161$	4.74040e75	0.346994
$162$	−3.06865e75	−0.181418
$163$	7.81716e75	0.373746	0.186873	−	0.982384i	$-0.440165\pi$
$163$	7.81716e75	0.373746	0.186873	+	0.982384i	$0.440165\pi$
$164$	2.60102e76	1.00701
$165$	−7.60422e75	−0.238704
$166$	−4.81230e76	−1.22638
$167$	2.45916e76	0.509411	0.254706	−	0.967019i	$-0.418021\pi$
$167$	2.45916e76	0.509411	0.254706	+	0.967019i	$0.418021\pi$
$168$	−1.16276e76	−0.196029
$169$	2.58139e76	0.354619
$170$	1.73376e77	1.94313
$171$	5.92647e76	0.542538
$172$	1.70454e76	0.127608
$173$	−1.39145e77	−0.852861	−0.426430	−	0.904520i	$-0.640229\pi$
$173$	−1.39145e77	−0.852861	−0.426430	+	0.904520i	$0.640229\pi$
$174$	−1.02260e77	−0.513755
$175$	4.72661e76	0.194867
$176$	−1.04723e76	−0.0354696
$177$	1.82803e77	0.509221
$178$	−1.53028e77	−0.350979
$179$	−1.31065e77	−0.247774	−0.123887	−	0.992296i	$-0.539536\pi$
$179$	−1.31065e77	−0.247774	−0.123887	+	0.992296i	$0.539536\pi$
$180$	4.53653e77	0.707656
$181$	−2.64680e77	−0.341044	−0.170522	−	0.985354i	$-0.554545\pi$
$181$	−2.64680e77	−0.341044	−0.170522	+	0.985354i	$0.554545\pi$
$182$	5.56984e77	0.593444
$183$	8.35402e77	0.736772
$184$	−1.65318e78	−1.20811
$185$	3.88087e78	2.35236
$186$	2.53805e78	1.27733
$187$	7.24346e77	0.302978
$188$	−7.20621e78	−2.50762
$189$	2.07395e77	0.0600990
$190$	−1.40206e79	−3.38663
$191$	6.26371e78	1.26235	0.631176	−	0.775640i	$-0.282573\pi$
$191$	6.26371e78	1.26235	0.631176	+	0.775640i	$0.282573\pi$
$192$	−5.46481e78	−0.919777
$193$	−1.63342e78	−0.229811	−0.114905	−	0.993376i	$-0.536657\pi$
$193$	−1.63342e78	−0.229811	−0.114905	+	0.993376i	$0.536657\pi$
$194$	−5.02432e78	−0.591450
$195$	−8.68632e78	−0.856331
$196$	−1.81937e79	−1.50344
$197$	1.14744e79	0.795512	0.397756	−	0.917491i	$-0.369789\pi$
$197$	1.14744e79	0.795512	0.397756	+	0.917491i	$0.369789\pi$
$198$	3.03302e78	0.176574
$199$	2.13921e79	1.04670	0.523350	−	0.852118i	$-0.324682\pi$
$199$	2.13921e79	1.04670	0.523350	+	0.852118i	$0.324682\pi$
$200$	−1.64838e79	−0.678455
$201$	3.10019e79	1.07430
$202$	9.98988e79	2.91701
$203$	6.91125e78	0.170194
$204$	−4.32130e79	−0.898202
$205$	4.38717e79	0.770329
$206$	−1.11191e78	−0.0165064
$207$	2.94869e79	0.370384
$208$	−1.19626e79	−0.127245
$209$	−5.85766e79	−0.528053
$210$	−4.90648e79	−0.375149
$211$	1.31242e80	0.851784	0.425892	−	0.904774i	$-0.359960\pi$
$211$	1.31242e80	0.851784	0.425892	+	0.904774i	$0.359960\pi$
$212$	−6.08530e79	−0.335502
$213$	−5.11222e79	−0.239615
$214$	3.53170e80	1.40834
$215$	2.87506e79	0.0976159
$216$	−7.23278e79	−0.209243
$217$	−1.71535e80	−0.423147
$218$	−8.04979e80	−1.69448
$219$	−7.47357e79	−0.134340
$220$	−4.48385e80	−0.688762
$221$	8.27422e80	1.08691
$222$	−1.54792e81	−1.74009
$223$	9.06031e80	0.872218	0.436109	−	0.899894i	$-0.356356\pi$
$223$	9.06031e80	0.872218	0.436109	+	0.899894i	$0.356356\pi$
$224$	3.43994e80	0.283788
$225$	2.94012e80	0.208002
$226$	4.79491e80	0.291098
$227$	2.12382e81	1.10720	0.553600	−	0.832783i	$-0.313254\pi$
$227$	2.12382e81	1.10720	0.553600	+	0.832783i	$0.313254\pi$
$228$	3.49456e81	1.56545
$229$	−4.51571e81	−1.73941	−0.869704	−	0.493573i	$-0.835691\pi$
$229$	−4.51571e81	−1.73941	−0.869704	+	0.493573i	$0.835691\pi$
$230$	−6.97589e81	−2.31201
$231$	−2.04987e80	−0.0584943
$232$	−2.41025e81	−0.592552
$233$	−3.86484e81	−0.819130	−0.409565	−	0.912281i	$-0.634319\pi$
$233$	−3.86484e81	−0.819130	−0.409565	+	0.912281i	$0.634319\pi$
$234$	3.46463e81	0.633446
$235$	−1.21548e82	−1.91825
$236$	1.07791e82	1.46932
$237$	8.87306e81	1.04534
$238$	4.67370e81	0.476163
$239$	3.95101e81	0.348322	0.174161	−	0.984717i	$-0.444279\pi$
$239$	3.95101e81	0.348322	0.174161	+	0.984717i	$0.444279\pi$
$240$	1.05379e81	0.0804386
$241$	8.51783e81	0.563302	0.281651	−	0.959517i	$-0.409118\pi$
$241$	8.51783e81	0.563302	0.281651	+	0.959517i	$0.409118\pi$
$242$	2.54830e82	1.46090
$243$	1.29007e81	0.0641500
$244$	4.92597e82	2.12590
$245$	−3.06875e82	−1.15009
$246$	−1.74987e82	−0.569828
$247$	−6.69122e82	−1.89435
$248$	5.98216e82	1.47325
$249$	2.02310e82	0.433652
$250$	4.19109e82	0.782342
$251$	3.89785e82	0.633988	0.316994	−	0.948427i	$-0.397326\pi$
$251$	3.89785e82	0.633988	0.316994	+	0.948427i	$0.397326\pi$
$252$	1.22291e82	0.173411
$253$	−2.91445e82	−0.360495
$254$	−1.85556e83	−2.00314
$255$	−7.28878e82	−0.687097
$256$	−1.42079e83	−1.17018
$257$	−1.81467e83	−1.30648	−0.653242	−	0.757149i	$-0.726591\pi$
$257$	−1.81467e83	−1.30648	−0.653242	+	0.757149i	$0.726591\pi$
$258$	−1.14675e82	−0.0722085
$259$	1.04617e83	0.576447
$260$	−5.12192e83	−2.47088
$261$	4.29903e82	0.181666
$262$	7.31732e83	2.70992
$263$	−1.12415e83	−0.365050	−0.182525	−	0.983201i	$-0.558427\pi$
$263$	−1.12415e83	−0.365050	−0.182525	+	0.983201i	$0.558427\pi$
$264$	7.14880e82	0.203656
$265$	−1.02641e83	−0.256649
$266$	−3.77954e83	−0.829894
$267$	6.43334e82	0.124108
$268$	1.82804e84	3.09981
$269$	7.99034e83	1.19155	0.595774	−	0.803152i	$-0.296845\pi$
$269$	7.99034e83	1.19155	0.595774	+	0.803152i	$0.296845\pi$
$270$	−3.05200e83	−0.400437
$271$	9.96976e82	0.115145	0.0575724	−	0.998341i	$-0.481664\pi$
$271$	9.96976e82	0.115145	0.0575724	+	0.998341i	$0.481664\pi$
$272$	−1.00379e83	−0.102098
$273$	−2.34158e83	−0.209844
$274$	−3.32566e84	−2.62714
$275$	−2.90598e83	−0.202448
$276$	1.73870e84	1.06872
$277$	2.47067e84	1.34049	0.670244	−	0.742141i	$-0.266190\pi$
$277$	2.47067e84	1.34049	0.670244	+	0.742141i	$0.266190\pi$
$278$	−3.38964e84	−1.62408
$279$	−1.06701e84	−0.451670
$280$	−1.15645e84	−0.432688
$281$	5.00138e84	1.65471	0.827355	−	0.561680i	$-0.189845\pi$
$281$	5.00138e84	1.65471	0.827355	+	0.561680i	$0.189845\pi$
$282$	4.84805e84	1.41897
$283$	6.82334e83	0.176752	0.0883762	−	0.996087i	$-0.471832\pi$
$283$	6.82334e83	0.176752	0.0883762	+	0.996087i	$0.471832\pi$
$284$	−3.01444e84	−0.691391
$285$	5.89430e84	1.19753
$286$	−3.42440e84	−0.616533
$287$	1.18265e84	0.188769
$288$	2.13976e84	0.302917
$289$	−1.01817e84	−0.127892
$290$	−1.01705e85	−1.13399
$291$	2.11224e84	0.209139
$292$	−4.40681e84	−0.387629
$293$	−2.19285e85	−1.71426	−0.857128	−	0.515103i	$-0.827754\pi$
$293$	−2.19285e85	−1.71426	−0.857128	+	0.515103i	$0.827754\pi$
$294$	1.22400e85	0.850744
$295$	1.81811e85	1.12399
$296$	−3.64844e85	−2.00698
$297$	−1.27509e84	−0.0624372
$298$	6.71204e82	0.00292680
$299$	−3.32919e85	−1.29325
$300$	1.73365e85	0.600175
$301$	7.75032e83	0.0239208
$302$	−7.80538e84	−0.214859
$303$	−4.19977e85	−1.03147
$304$	8.11749e84	0.177944
$305$	8.30868e85	1.62625
$306$	2.90720e85	0.508260
$307$	−4.26941e85	−0.666952	−0.333476	−	0.942759i	$-0.608222\pi$
$307$	−4.26941e85	−0.666952	−0.333476	+	0.942759i	$0.608222\pi$
$308$	−1.20871e85	−0.168781
$309$	4.67452e83	0.00583673
$310$	2.52428e86	2.81941
$311$	−1.27687e86	−1.27618	−0.638090	−	0.769961i	$-0.720275\pi$
$311$	−1.27687e86	−1.27618	−0.638090	+	0.769961i	$0.720275\pi$
$312$	8.16609e85	0.730602
$313$	1.62653e86	1.30312	0.651558	−	0.758599i	$-0.274116\pi$
$313$	1.62653e86	1.30312	0.651558	+	0.758599i	$0.274116\pi$
$314$	−2.13319e86	−1.53094
$315$	2.06270e85	0.132654
$316$	5.23203e86	3.01624
$317$	1.26399e86	0.653432	0.326716	−	0.945123i	$-0.394058\pi$
$317$	1.26399e86	0.653432	0.326716	+	0.945123i	$0.394058\pi$
$318$	4.09395e85	0.189848
$319$	−4.24911e85	−0.176815
$320$	−5.43515e86	−2.03019
$321$	−1.48474e86	−0.497995
$322$	−1.88049e86	−0.566558
$323$	−5.61467e86	−1.51998
$324$	7.60694e85	0.185100
$325$	−3.31951e86	−0.726269
$326$	−3.10103e86	−0.610237
$327$	3.38416e86	0.599174
$328$	−4.12442e86	−0.657226
$329$	−3.27657e86	−0.470068
$330$	3.01656e86	0.389745
$331$	−1.21372e87	−1.41271	−0.706356	−	0.707857i	$-0.749662\pi$
$331$	−1.21372e87	−1.41271	−0.706356	+	0.707857i	$0.749662\pi$
$332$	1.19293e87	1.25127
$333$	6.50751e86	0.615303
$334$	−9.75537e86	−0.831746
$335$	3.08336e87	2.37126
$336$	2.84069e85	0.0197115
$337$	1.98898e87	1.24566	0.622830	−	0.782357i	$-0.285983\pi$
$337$	1.98898e87	1.24566	0.622830	+	0.782357i	$0.285983\pi$
$338$	−1.02403e87	−0.579008
$339$	−2.01579e86	−0.102934
$340$	−4.29785e87	−1.98257
$341$	1.05462e87	0.439611
$342$	−2.35100e87	−0.885834
$343$	−1.74388e87	−0.594112
$344$	−2.70287e86	−0.0832836
$345$	2.93269e87	0.817536
$346$	5.51983e87	1.39252
$347$	3.43340e85	0.00784075	0.00392038	−	0.999992i	$-0.498752\pi$
$347$	3.43340e85	0.00784075	0.00392038	+	0.999992i	$0.498752\pi$
$348$	2.53494e87	0.524183
$349$	5.04778e87	0.945417	0.472708	−	0.881219i	$-0.343276\pi$
$349$	5.04778e87	0.945417	0.472708	+	0.881219i	$0.343276\pi$
$350$	−1.87503e87	−0.318170
$351$	−1.45654e87	−0.223989
$352$	−2.11491e87	−0.294829
$353$	−4.19996e86	−0.0530906	−0.0265453	−	0.999648i	$-0.508451\pi$
$353$	−4.19996e86	−0.0530906	−0.0265453	+	0.999648i	$0.508451\pi$
$354$	−7.25173e87	−0.831436
$355$	−5.08448e87	−0.528893
$356$	3.79344e87	0.358103
$357$	−1.96484e87	−0.168373
$358$	5.19927e87	0.404555
$359$	2.61698e88	1.84945	0.924725	−	0.380636i	$-0.124295\pi$
$359$	2.61698e88	1.84945	0.924725	+	0.380636i	$0.124295\pi$
$360$	−7.19352e87	−0.461854
$361$	2.82653e88	1.64913
$362$	1.04997e88	0.556842
$363$	−1.07131e88	−0.516580
$364$	−1.38072e88	−0.605490
$365$	−7.43300e87	−0.296524
$366$	−3.31400e88	−1.20297
$367$	1.54132e88	0.509228	0.254614	−	0.967043i	$-0.418052\pi$
$367$	1.54132e88	0.509228	0.254614	+	0.967043i	$0.418052\pi$
$368$	4.03882e87	0.121480
$369$	7.35649e87	0.201493
$370$	−1.53952e89	−3.84084
$371$	−2.76690e87	−0.0628918
$372$	−6.29163e88	−1.30326
$373$	−2.30885e88	−0.435955	−0.217977	−	0.975954i	$-0.569946\pi$
$373$	−2.30885e88	−0.435955	−0.217977	+	0.975954i	$0.569946\pi$
$374$	−2.87345e88	−0.494690
$375$	−1.76195e88	−0.276639
$376$	1.14268e89	1.63661
$377$	−4.85377e88	−0.634312
$378$	−8.22728e87	−0.0981271
$379$	1.38008e89	1.50263	0.751317	−	0.659942i	$-0.229419\pi$
$379$	1.38008e89	1.50263	0.751317	+	0.659942i	$0.229419\pi$
$380$	3.47559e89	3.45537
$381$	7.80082e88	0.708319
$382$	−2.48478e89	−2.06112
$383$	4.21450e88	0.319439	0.159720	−	0.987162i	$-0.448941\pi$
$383$	4.21450e88	0.319439	0.159720	+	0.987162i	$0.448941\pi$
$384$	1.41049e89	0.977106
$385$	−2.03875e88	−0.129112
$386$	6.47970e88	0.375226
$387$	4.82096e87	0.0255332
$388$	1.24549e89	0.603455
$389$	−2.02335e89	−0.897036	−0.448518	−	0.893774i	$-0.648048\pi$
$389$	−2.02335e89	−0.897036	−0.448518	+	0.893774i	$0.648048\pi$
$390$	3.44582e89	1.39818
$391$	−2.79355e89	−1.03767
$392$	2.88495e89	0.981228
$393$	−3.07622e89	−0.958240
$394$	−4.55186e89	−1.29888
$395$	8.82490e89	2.30733
$396$	−7.51861e88	−0.180158
$397$	−3.09203e89	−0.679158	−0.339579	−	0.940578i	$-0.610285\pi$
$397$	−3.09203e89	−0.679158	−0.339579	+	0.940578i	$0.610285\pi$
$398$	−8.48614e89	−1.70901
$399$	1.58893e89	0.293454
$400$	4.02707e88	0.0682213
$401$	8.08721e89	1.25695	0.628475	−	0.777830i	$-0.283680\pi$
$401$	8.08721e89	1.25695	0.628475	+	0.777830i	$0.283680\pi$
$402$	−1.22983e90	−1.75407
$403$	1.20469e90	1.57707
$404$	−2.47641e90	−2.97622
$405$	1.28307e89	0.141596
$406$	−2.74166e89	−0.277885
$407$	−6.43195e89	−0.598875
$408$	6.85224e89	0.586215
$409$	1.60064e90	1.25846	0.629229	−	0.777220i	$-0.283371\pi$
$409$	1.60064e90	1.25846	0.629229	+	0.777220i	$0.283371\pi$
$410$	−1.74037e90	−1.25776
$411$	1.39812e90	0.928969
$412$	2.75634e88	0.0168414
$413$	4.90109e89	0.275433
$414$	−1.16973e90	−0.604748
$415$	2.01212e90	0.957184
$416$	−2.41587e90	−1.05768
$417$	1.42501e90	0.574282
$418$	2.32371e90	0.862183
$419$	1.44039e90	0.492147	0.246074	−	0.969251i	$-0.420860\pi$
$419$	1.44039e90	0.492147	0.246074	+	0.969251i	$0.420860\pi$
$420$	1.21628e90	0.382764
$421$	1.44085e90	0.417722	0.208861	−	0.977945i	$-0.433024\pi$
$421$	1.44085e90	0.417722	0.208861	+	0.977945i	$0.433024\pi$
$422$	−5.20632e90	−1.39076
$423$	−2.03814e90	−0.501754
$424$	9.64939e89	0.218967
$425$	−2.78543e90	−0.582739
$426$	2.02799e90	0.391233
$427$	2.23977e90	0.398513
$428$	−8.75479e90	−1.43693
$429$	1.43963e90	0.218009
$430$	−1.14052e90	−0.159383
$431$	9.75545e90	1.25829	0.629146	−	0.777287i	$-0.283405\pi$
$431$	9.75545e90	1.25829	0.629146	+	0.777287i	$0.283405\pi$
$432$	1.76701e89	0.0210402
$433$	−2.64456e90	−0.290750	−0.145375	−	0.989377i	$-0.546439\pi$
$433$	−2.64456e90	−0.290750	−0.145375	+	0.989377i	$0.546439\pi$
$434$	6.80471e90	0.690898
$435$	4.27570e90	0.400984
$436$	1.99548e91	1.72887
$437$	2.25910e91	1.80853
$438$	2.96473e90	0.219345
$439$	−2.75187e91	−1.88192	−0.940961	−	0.338516i	$-0.890075\pi$
$439$	−2.75187e91	−1.88192	−0.940961	+	0.338516i	$0.890075\pi$
$440$	7.11000e90	0.449523
$441$	−5.14573e90	−0.300826
$442$	−3.28235e91	−1.77466
$443$	−2.42199e91	−1.21128	−0.605640	−	0.795739i	$-0.707083\pi$
$443$	−2.42199e91	−1.21128	−0.605640	+	0.795739i	$0.707083\pi$
$444$	3.83718e91	1.77541
$445$	6.39842e90	0.273938
$446$	−3.59418e91	−1.42412
$447$	−2.82176e88	−0.00103493
$448$	−1.46515e91	−0.497499
$449$	−3.70665e91	−1.16542	−0.582710	−	0.812680i	$-0.698008\pi$
$449$	−3.70665e91	−1.16542	−0.582710	+	0.812680i	$0.698008\pi$
$450$	−1.16633e91	−0.339617
$451$	−7.27107e90	−0.196114
$452$	−1.18862e91	−0.297007
$453$	3.28140e90	0.0759752
$454$	−8.42510e91	−1.80779
$455$	−2.32887e91	−0.463182
$456$	−5.54129e91	−1.02170
$457$	4.36078e91	0.745513	0.372756	−	0.927929i	$-0.378413\pi$
$457$	4.36078e91	0.745513	0.372756	+	0.927929i	$0.378413\pi$
$458$	1.79136e92	2.84004
$459$	−1.22220e91	−0.179723
$460$	1.72927e92	2.35894
$461$	1.86277e91	0.235764	0.117882	−	0.993028i	$-0.462390\pi$
$461$	1.86277e91	0.235764	0.117882	+	0.993028i	$0.462390\pi$
$462$	8.13175e90	0.0955071
$463$	−2.24020e91	−0.244198	−0.122099	−	0.992518i	$-0.538963\pi$
$463$	−2.24020e91	−0.244198	−0.122099	+	0.992518i	$0.538963\pi$
$464$	5.88838e90	0.0595834
$465$	−1.06121e92	−0.996956
$466$	1.53317e92	1.33744
$467$	−5.84323e91	−0.473391	−0.236696	−	0.971584i	$-0.576064\pi$
$467$	−5.84323e91	−0.473391	−0.236696	+	0.971584i	$0.576064\pi$
$468$	−8.58853e91	−0.646304
$469$	8.31184e91	0.581077
$470$	4.82174e92	3.13204
$471$	8.96800e91	0.541345
$472$	−1.70922e92	−0.958959
$473$	−4.76499e90	−0.0248515
$474$	−3.51990e92	−1.70678
$475$	2.25253e92	1.01564
$476$	−1.15857e92	−0.485829
$477$	−1.72111e91	−0.0671311
$478$	−1.56735e92	−0.568725
$479$	1.13789e92	0.384172	0.192086	−	0.981378i	$-0.438475\pi$
$479$	1.13789e92	0.384172	0.192086	+	0.981378i	$0.438475\pi$
$480$	2.12814e92	0.668619
$481$	−7.34724e92	−2.14842
$482$	−3.37898e92	−0.919736
$483$	7.90565e91	0.200337
$484$	−6.31703e92	−1.49055
$485$	2.10077e92	0.461625
$486$	−5.11765e91	−0.104742
$487$	−1.24619e91	−0.0237594	−0.0118797	−	0.999929i	$-0.503782\pi$
$487$	−1.24619e91	−0.0237594	−0.0118797	+	0.999929i	$0.503782\pi$
$488$	−7.81106e92	−1.38748
$489$	1.30368e92	0.215782
$490$	1.21736e93	1.87782
$491$	−2.02174e92	−0.290679	−0.145339	−	0.989382i	$-0.546427\pi$
$491$	−2.02174e92	−0.290679	−0.145339	+	0.989382i	$0.546427\pi$
$492$	4.33778e92	0.581395
$493$	−4.07285e92	−0.508955
$494$	2.65437e93	3.09302
$495$	−1.26817e92	−0.137816
$496$	−1.46148e92	−0.148141
$497$	−1.37062e92	−0.129605
$498$	−8.02556e92	−0.708049
$499$	−9.22082e92	−0.759103	−0.379551	−	0.925171i	$-0.623922\pi$
$499$	−9.22082e92	−0.759103	−0.379551	+	0.925171i	$0.623922\pi$
$500$	−1.03894e93	−0.798223
$501$	4.10119e92	0.294109
$502$	−1.54626e93	−1.03515
$503$	1.55278e93	0.970541	0.485271	−	0.874364i	$-0.338721\pi$
$503$	1.55278e93	0.970541	0.485271	+	0.874364i	$0.338721\pi$
$504$	−1.93916e92	−0.113177
$505$	−4.17698e93	−2.27672
$506$	1.15615e93	0.588601
$507$	4.30503e92	0.204740
$508$	4.59978e93	2.04380
$509$	−3.09379e93	−1.28448	−0.642241	−	0.766503i	$-0.721995\pi$
$509$	−3.09379e93	−1.28448	−0.642241	+	0.766503i	$0.721995\pi$
$510$	2.89142e93	1.12186
$511$	−2.00372e92	−0.0726634
$512$	6.43735e92	0.218220
$513$	9.88369e92	0.313235
$514$	7.19869e93	2.13317
$515$	4.64915e91	0.0128832
$516$	2.84270e92	0.0736742
$517$	2.01447e93	0.488357
$518$	−4.15009e93	−0.941198
$519$	−2.32055e93	−0.492399
$520$	8.12176e93	1.61263
$521$	−9.05822e93	−1.68322	−0.841611	−	0.540084i	$-0.818392\pi$
$521$	−9.05822e93	−1.68322	−0.841611	+	0.540084i	$0.818392\pi$
$522$	−1.70540e93	−0.296616
$523$	3.50366e93	0.570446	0.285223	−	0.958461i	$-0.407932\pi$
$523$	3.50366e93	0.570446	0.285223	+	0.958461i	$0.407932\pi$
$524$	−1.81390e94	−2.76493
$525$	7.88266e92	0.112506
$526$	4.45946e93	0.596038
$527$	1.01087e94	1.26540
$528$	−1.74649e92	−0.0204784
$529$	2.13628e93	0.234659
$530$	4.07173e93	0.419045
$531$	3.04865e93	0.293999
$532$	9.36917e93	0.846740
$533$	−8.30576e93	−0.703543
$534$	−2.55208e93	−0.202638
$535$	−1.47668e94	−1.09921
$536$	−2.89870e94	−2.02310
$537$	−2.18579e93	−0.143052
$538$	−3.16973e94	−1.94551
$539$	5.08599e93	0.292794
$540$	7.56565e93	0.408565
$541$	−1.53075e94	−0.775531	−0.387766	−	0.921758i	$-0.626753\pi$
$541$	−1.53075e94	−0.775531	−0.387766	+	0.921758i	$0.626753\pi$
$542$	−3.95496e93	−0.188004
$543$	−4.41411e93	−0.196902
$544$	−2.02718e94	−0.848653
$545$	3.36579e94	1.32254
$546$	9.28892e93	0.342625
$547$	1.58908e94	0.550281	0.275140	−	0.961404i	$-0.411276\pi$
$547$	1.58908e94	0.550281	0.275140	+	0.961404i	$0.411276\pi$
$548$	8.24405e94	2.68047
$549$	1.39322e94	0.425375
$550$	1.15279e94	0.330549
$551$	3.29364e94	0.887045
$552$	−2.75704e94	−0.697502
$553$	2.37893e94	0.565412
$554$	−9.80103e94	−2.18869
$555$	6.47219e94	1.35814
$556$	8.40264e94	1.65705
$557$	8.44184e94	1.56471	0.782353	−	0.622835i	$-0.214019\pi$
$557$	8.44184e94	1.56471	0.782353	+	0.622835i	$0.214019\pi$
$558$	4.23276e94	0.737469
$559$	−5.44306e93	−0.0891529
$560$	2.82527e93	0.0435085
$561$	1.20801e94	0.174924
$562$	−1.98402e95	−2.70174
$563$	−4.40991e94	−0.564793	−0.282397	−	0.959298i	$-0.591129\pi$
$563$	−4.40991e94	−0.564793	−0.282397	+	0.959298i	$0.591129\pi$
$564$	−1.20179e95	−1.44777
$565$	−2.00485e94	−0.227202
$566$	−2.70679e94	−0.288594
$567$	3.45877e93	0.0346981
$568$	4.77996e94	0.451239
$569$	3.19912e94	0.284222	0.142111	−	0.989851i	$-0.454611\pi$
$569$	3.19912e94	0.284222	0.142111	+	0.989851i	$0.454611\pi$
$570$	−2.33824e95	−1.95527
$571$	−6.34941e94	−0.499790	−0.249895	−	0.968273i	$-0.580396\pi$
$571$	−6.34941e94	−0.499790	−0.249895	+	0.968273i	$0.580396\pi$
$572$	8.48881e94	0.629048
$573$	1.04461e95	0.728819
$574$	−4.69152e94	−0.308215
$575$	1.12074e95	0.693366
$576$	−9.11376e94	−0.531033
$577$	−1.91689e95	−1.05204	−0.526019	−	0.850473i	$-0.676316\pi$
$577$	−1.91689e95	−1.05204	−0.526019	+	0.850473i	$0.676316\pi$
$578$	4.03901e94	0.208817
$579$	−2.72408e94	−0.132681
$580$	2.52118e95	1.15701
$581$	5.42409e94	0.234558
$582$	−8.37915e94	−0.341474
$583$	1.70112e94	0.0653387
$584$	6.98783e94	0.252988
$585$	−1.44863e95	−0.494403
$586$	8.69893e95	2.79897
$587$	2.30000e95	0.697773	0.348886	−	0.937165i	$-0.386560\pi$
$587$	2.30000e95	0.697773	0.348886	+	0.937165i	$0.386560\pi$
$588$	−3.03420e95	−0.868013
$589$	−8.17471e95	−2.20544
$590$	−7.21236e95	−1.83520
$591$	1.91361e95	0.459289
$592$	8.91334e94	0.201809
$593$	4.81215e95	1.02790	0.513952	−	0.857819i	$-0.328181\pi$
$593$	4.81215e95	1.02790	0.513952	+	0.857819i	$0.328181\pi$
$594$	5.05823e94	0.101945
$595$	−1.95417e95	−0.371645
$596$	−1.66386e93	−0.00298621
$597$	3.56760e95	0.604312
$598$	1.32067e96	2.11156
$599$	−8.45412e95	−1.27598	−0.637989	−	0.770046i	$-0.720233\pi$
$599$	−8.45412e95	−1.27598	−0.637989	+	0.770046i	$0.720233\pi$
$600$	−2.74903e95	−0.391706
$601$	−2.30766e95	−0.310458	−0.155229	−	0.987878i	$-0.549612\pi$
$601$	−2.30766e95	−0.310458	−0.155229	+	0.987878i	$0.549612\pi$
$602$	−3.07452e94	−0.0390569
$603$	5.17025e95	0.620246
$604$	1.93489e95	0.219221
$605$	−1.06550e96	−1.14023
$606$	1.66603e96	1.68414
$607$	−8.71771e95	−0.832516	−0.416258	−	0.909247i	$-0.636659\pi$
$607$	−8.71771e95	−0.832516	−0.416258	+	0.909247i	$0.636659\pi$
$608$	1.63935e96	1.47910
$609$	1.15260e95	0.0982613
$610$	−3.29601e96	−2.65528
$611$	2.30114e96	1.75194
$612$	−7.20672e95	−0.518577
$613$	1.05504e96	0.717598	0.358799	−	0.933415i	$-0.383186\pi$
$613$	1.05504e96	0.717598	0.358799	+	0.933415i	$0.383186\pi$
$614$	1.69366e96	1.08897
$615$	7.31656e95	0.444749
$616$	1.91664e95	0.110156
$617$	1.00230e96	0.544701	0.272350	−	0.962198i	$-0.412199\pi$
$617$	1.00230e96	0.544701	0.272350	+	0.962198i	$0.412199\pi$
$618$	−1.85436e94	−0.00952997
$619$	−3.03655e96	−1.47589	−0.737944	−	0.674862i	$-0.764203\pi$
$619$	−3.03655e96	−1.47589	−0.737944	+	0.674862i	$0.764203\pi$
$620$	−6.25748e96	−2.87664
$621$	4.91758e95	0.213841
$622$	5.06527e96	2.08370
$623$	1.72483e95	0.0671286
$624$	−1.99502e95	−0.0734648
$625$	−3.54319e96	−1.23462
$626$	−6.45238e96	−2.12768
$627$	−9.76893e95	−0.304871
$628$	5.28801e96	1.56201
$629$	−6.16514e96	−1.72383
$630$	−8.18262e95	−0.216593
$631$	2.53534e96	0.635365	0.317683	−	0.948197i	$-0.397095\pi$
$631$	2.53534e96	0.635365	0.317683	+	0.948197i	$0.397095\pi$
$632$	−8.29637e96	−1.96856
$633$	2.18875e96	0.491778
$634$	−5.01420e96	−1.06690
$635$	7.75848e96	1.56345
$636$	−1.01486e96	−0.193702
$637$	5.80973e96	1.05038
$638$	1.68560e96	0.288697
$639$	−8.52575e95	−0.138342
$640$	1.40283e97	2.15673
$641$	2.30765e96	0.336177	0.168088	−	0.985772i	$-0.446241\pi$
$641$	2.30765e96	0.336177	0.168088	+	0.985772i	$0.446241\pi$
$642$	5.88987e96	0.813107
$643$	−1.01724e97	−1.33090	−0.665452	−	0.746441i	$-0.731761\pi$
$643$	−1.01724e97	−1.33090	−0.665452	+	0.746441i	$0.731761\pi$
$644$	4.66159e96	0.578059
$645$	4.79480e95	0.0563586
$646$	2.22731e97	2.48176
$647$	−7.41201e96	−0.782957	−0.391479	−	0.920187i	$-0.628036\pi$
$647$	−7.41201e96	−0.782957	−0.391479	+	0.920187i	$0.628036\pi$
$648$	−1.20622e96	−0.120806
$649$	−3.01325e96	−0.286149
$650$	1.31683e97	1.18582
$651$	−2.86072e96	−0.244304
$652$	7.68720e96	0.622625
$653$	9.81252e96	0.753834	0.376917	−	0.926247i	$-0.376984\pi$
$653$	9.81252e96	0.753834	0.376917	+	0.926247i	$0.376984\pi$
$654$	−1.34248e97	−0.978307
$655$	−3.05952e97	−2.11509
$656$	1.00762e96	0.0660866
$657$	−1.24638e96	−0.0775614
$658$	1.29980e97	0.767508
$659$	−3.09533e97	−1.73444	−0.867221	−	0.497923i	$-0.834096\pi$
$659$	−3.09533e97	−1.73444	−0.867221	+	0.497923i	$0.834096\pi$
$660$	−7.47780e96	−0.397657
$661$	−2.88598e97	−1.45661	−0.728304	−	0.685254i	$-0.759691\pi$
$661$	−2.88598e97	−1.45661	−0.728304	+	0.685254i	$0.759691\pi$
$662$	4.81478e97	2.30662
$663$	1.37991e97	0.627528
$664$	−1.89162e97	−0.816646
$665$	1.58031e97	0.647730
$666$	−2.58150e97	−1.00464
$667$	1.63874e97	0.605575
$668$	2.41828e97	0.848629
$669$	1.51100e97	0.503576
$670$	−1.22316e98	−3.87169
$671$	−1.37704e97	−0.414018
$672$	5.73685e96	0.163845
$673$	6.11464e96	0.165902	0.0829509	−	0.996554i	$-0.473566\pi$
$673$	6.11464e96	0.165902	0.0829509	+	0.996554i	$0.473566\pi$
$674$	−7.89020e97	−2.03386
$675$	4.90328e96	0.120090
$676$	2.53848e97	0.590761
$677$	1.98833e97	0.439723	0.219862	−	0.975531i	$-0.429439\pi$
$677$	1.98833e97	0.439723	0.219862	+	0.975531i	$0.429439\pi$
$678$	7.99656e96	0.168066
$679$	5.66307e96	0.113121
$680$	6.81505e97	1.29393
$681$	3.54194e97	0.639242
$682$	−4.18361e97	−0.717779
$683$	7.70165e97	1.25623	0.628115	−	0.778120i	$-0.283827\pi$
$683$	7.70165e97	1.25623	0.628115	+	0.778120i	$0.283827\pi$
$684$	5.82795e97	0.903816
$685$	1.39053e98	2.05048
$686$	6.91788e97	0.970043
$687$	−7.53093e97	−1.00425
$688$	6.60327e95	0.00837448
$689$	1.94320e97	0.234398
$690$	−1.16338e98	−1.33484
$691$	−8.91781e97	−0.973342	−0.486671	−	0.873585i	$-0.661789\pi$
$691$	−8.91781e97	−0.973342	−0.486671	+	0.873585i	$0.661789\pi$
$692$	−1.36832e98	−1.42078
$693$	−3.41861e96	−0.0337717
$694$	−1.36201e96	−0.0128021
$695$	1.41728e98	1.26759
$696$	−4.01962e97	−0.342110
$697$	−6.96945e97	−0.564505
$698$	−2.00243e98	−1.54364
$699$	−6.44547e97	−0.472925
$700$	4.64804e97	0.324629
$701$	−2.19700e97	−0.146069	−0.0730347	−	0.997329i	$-0.523268\pi$
$701$	−2.19700e97	−0.146069	−0.0730347	+	0.997329i	$0.523268\pi$
$702$	5.77802e97	0.365720
$703$	4.98564e98	3.00443
$704$	9.00794e97	0.516855
$705$	−2.02707e98	−1.10750
$706$	1.66610e97	0.0866842
$707$	−1.12599e98	−0.557910
$708$	1.79764e98	0.848313
$709$	4.05220e98	1.82136	0.910680	−	0.413113i	$-0.135559\pi$
$709$	4.05220e98	1.82136	0.910680	+	0.413113i	$0.135559\pi$
$710$	2.01699e98	0.863555
$711$	1.47978e98	0.603525
$712$	−6.01521e97	−0.233718
$713$	−4.06729e98	−1.50562
$714$	7.79442e97	0.274913
$715$	1.43181e98	0.481203
$716$	−1.28886e98	−0.412767
$717$	6.58917e97	0.201104
$718$	−1.03815e99	−3.01971
$719$	−1.83648e98	−0.509143	−0.254571	−	0.967054i	$-0.581934\pi$
$719$	−1.83648e98	−0.509143	−0.254571	+	0.967054i	$0.581934\pi$
$720$	1.75742e97	0.0464412
$721$	1.25327e96	0.00315703
$722$	−1.12127e99	−2.69263
$723$	1.42053e98	0.325222
$724$	−2.60279e98	−0.568145
$725$	1.63397e98	0.340081
$726$	4.24985e98	0.843451
$727$	7.32794e96	0.0138690	0.00693450	−	0.999976i	$-0.497793\pi$
$727$	7.32794e96	0.0138690	0.00693450	+	0.999976i	$0.497793\pi$
$728$	2.18939e98	0.395175
$729$	2.15147e97	0.0370370
$730$	2.94864e98	0.484153
$731$	−4.56732e97	−0.0715339
$732$	8.21514e98	1.22739
$733$	−1.16739e99	−1.66390	−0.831951	−	0.554849i	$-0.812776\pi$
$733$	−1.16739e99	−1.66390	−0.831951	+	0.554849i	$0.812776\pi$
$734$	−6.11433e98	−0.831447
$735$	−5.11780e98	−0.664003
$736$	8.15649e98	1.00976
$737$	−5.11021e98	−0.603686
$738$	−2.91828e98	−0.328990
$739$	5.82977e98	0.627218	0.313609	−	0.949552i	$-0.398462\pi$
$739$	5.82977e98	0.627218	0.313609	+	0.949552i	$0.398462\pi$
$740$	3.81635e99	3.91880
$741$	−1.11591e99	−1.09370
$742$	1.09762e98	0.102687
$743$	2.40668e98	0.214934	0.107467	−	0.994209i	$-0.465726\pi$
$743$	2.40668e98	0.214934	0.107467	+	0.994209i	$0.465726\pi$
$744$	9.97656e98	0.850579
$745$	−2.80645e96	−0.00228436
$746$	9.15910e98	0.711809
$747$	3.37397e98	0.250369
$748$	7.12304e98	0.504731
$749$	−3.98068e98	−0.269361
$750$	6.98956e98	0.451686
$751$	−1.47818e99	−0.912327	−0.456164	−	0.889896i	$-0.650777\pi$
$751$	−1.47818e99	−0.912327	−0.456164	+	0.889896i	$0.650777\pi$
$752$	−2.79163e98	−0.164567
$753$	6.50051e98	0.366033
$754$	1.92547e99	1.03568
$755$	3.26359e98	0.167697
$756$	2.03947e98	0.100119
$757$	2.78733e99	1.30732	0.653659	−	0.756789i	$-0.273233\pi$
$757$	2.78733e99	1.30732	0.653659	+	0.756789i	$0.273233\pi$
$758$	−5.47473e99	−2.45344
$759$	−4.86049e98	−0.208132
$760$	−5.51121e99	−2.25516
$761$	−2.48114e99	−0.970244	−0.485122	−	0.874446i	$-0.661225\pi$
$761$	−2.48114e99	−0.970244	−0.485122	+	0.874446i	$0.661225\pi$
$762$	−3.09455e99	−1.15651
$763$	9.07317e98	0.324088
$764$	6.15957e99	2.10295
$765$	−1.21556e99	−0.396696
$766$	−1.67187e99	−0.521567
$767$	−3.44204e99	−1.02654
$768$	−2.36948e99	−0.675602
$769$	5.68885e99	1.55084	0.775418	−	0.631449i	$-0.217539\pi$
$769$	5.68885e99	1.55084	0.775418	+	0.631449i	$0.217539\pi$
$770$	8.08761e98	0.210810
$771$	−3.02635e99	−0.754299
$772$	−1.60626e99	−0.382842
$773$	−2.68030e99	−0.610928	−0.305464	−	0.952204i	$-0.598812\pi$
$773$	−2.68030e99	−0.610928	−0.305464	+	0.952204i	$0.598812\pi$
$774$	−1.91245e98	−0.0416896
$775$	−4.05546e99	−0.845535
$776$	−1.97496e99	−0.393848
$777$	1.74471e99	0.332812
$778$	8.02654e99	1.46464
$779$	5.63607e99	0.983861
$780$	−8.54191e99	−1.42656
$781$	8.42676e98	0.134648
$782$	1.10819e100	1.69426
$783$	7.16957e98	0.104885
$784$	−7.04811e98	−0.0986662
$785$	8.91932e99	1.19489
$786$	1.22032e100	1.56458
$787$	8.96553e98	0.110014	0.0550069	−	0.998486i	$-0.482482\pi$
$787$	8.96553e98	0.110014	0.0550069	+	0.998486i	$0.482482\pi$
$788$	1.12837e100	1.32525
$789$	−1.87477e99	−0.210762
$790$	−3.50080e100	−3.76732
$791$	−5.40449e98	−0.0556758
$792$	1.19222e99	0.117581
$793$	−1.57299e100	−1.48526
$794$	1.22659e100	1.10890
$795$	−1.71177e99	−0.148176
$796$	2.10364e100	1.74370
$797$	−1.54221e100	−1.22414	−0.612070	−	0.790804i	$-0.709663\pi$
$797$	−1.54221e100	−1.22414	−0.612070	+	0.790804i	$0.709663\pi$
$798$	−6.30321e99	−0.479139
$799$	1.93090e100	1.40571
$800$	8.13277e99	0.567066
$801$	1.07290e99	0.0716535
$802$	−3.20816e100	−2.05229
$803$	1.23191e99	0.0754905
$804$	3.04865e100	1.78967
$805$	7.86274e99	0.442197
$806$	−4.77895e100	−2.57498
$807$	1.33256e100	0.687940
$808$	3.92681e100	1.94244
$809$	4.54953e98	0.0215647	0.0107823	−	0.999942i	$-0.496568\pi$
$809$	4.54953e98	0.0215647	0.0107823	+	0.999942i	$0.496568\pi$
$810$	−5.08987e99	−0.231192
$811$	−3.61873e100	−1.57520	−0.787602	−	0.616184i	$-0.788678\pi$
$811$	−3.61873e100	−1.57520	−0.787602	+	0.616184i	$0.788678\pi$
$812$	6.79635e99	0.283526
$813$	1.66268e99	0.0664789
$814$	2.55153e100	0.977818
$815$	1.29661e100	0.476289
$816$	−1.67404e99	−0.0589462
$817$	3.69351e99	0.124675
$818$	−6.34965e100	−2.05476
$819$	−3.90509e99	−0.121154
$820$	4.31423e100	1.28329
$821$	3.34462e100	0.953912	0.476956	−	0.878927i	$-0.341740\pi$
$821$	3.34462e100	0.953912	0.476956	+	0.878927i	$0.341740\pi$
$822$	−5.54627e100	−1.51678
$823$	−2.43442e100	−0.638411	−0.319206	−	0.947685i	$-0.603416\pi$
$823$	−2.43442e100	−0.638411	−0.319206	+	0.947685i	$0.603416\pi$
$824$	−4.37070e98	−0.0109916
$825$	−4.84635e99	−0.116884
$826$	−1.94424e100	−0.449716
$827$	−3.11543e100	−0.691160	−0.345580	−	0.938389i	$-0.612318\pi$
$827$	−3.11543e100	−0.691160	−0.345580	+	0.938389i	$0.612318\pi$
$828$	2.89967e100	0.617024
$829$	−2.52368e100	−0.515114	−0.257557	−	0.966263i	$-0.582917\pi$
$829$	−2.52368e100	−0.515114	−0.257557	+	0.966263i	$0.582917\pi$
$830$	−7.98200e100	−1.56285
$831$	4.12038e100	0.773931
$832$	1.02898e101	1.85418
$833$	4.87500e100	0.842796
$834$	−5.65296e100	−0.937664
$835$	4.07893e100	0.649176
$836$	−5.76028e100	−0.879684
$837$	−1.77946e100	−0.260772
$838$	−5.71394e100	−0.803558
$839$	−7.37095e100	−0.994800	−0.497400	−	0.867521i	$-0.665712\pi$
$839$	−7.37095e100	−0.994800	−0.497400	+	0.867521i	$0.665712\pi$
$840$	−1.92863e100	−0.249813
$841$	−5.65462e100	−0.702978
$842$	−5.71580e100	−0.682040
$843$	8.34089e100	0.955347
$844$	1.29061e101	1.41899
$845$	4.28167e100	0.451915
$846$	8.08519e100	0.819243
$847$	−2.87227e100	−0.279413
$848$	−2.35740e99	−0.0220179
$849$	1.13794e100	0.102048
$850$	1.10497e101	0.951472
$851$	2.48058e101	2.05109
$852$	−5.02723e100	−0.399175
$853$	2.28074e101	1.73914	0.869568	−	0.493814i	$-0.164398\pi$
$853$	2.28074e101	1.73914	0.869568	+	0.493814i	$0.164398\pi$
$854$	−8.88508e100	−0.650676
$855$	9.83004e100	0.691392
$856$	1.38824e101	0.937818
$857$	9.87627e100	0.640847	0.320424	−	0.947274i	$-0.396175\pi$
$857$	9.87627e100	0.640847	0.320424	+	0.947274i	$0.396175\pi$
$858$	−5.71093e100	−0.355956
$859$	−1.05058e101	−0.629021	−0.314510	−	0.949254i	$-0.601840\pi$
$859$	−1.05058e101	−0.629021	−0.314510	+	0.949254i	$0.601840\pi$
$860$	2.82727e100	0.162619
$861$	1.97233e100	0.108986
$862$	−3.86994e101	−2.05449
$863$	1.10814e101	0.565228	0.282614	−	0.959234i	$-0.408798\pi$
$863$	1.10814e101	0.565228	0.282614	+	0.959234i	$0.408798\pi$
$864$	3.56851e100	0.174889
$865$	−2.30796e101	−1.08686
$866$	1.04908e101	0.474725
$867$	−1.69801e100	−0.0738384
$868$	−1.68683e101	−0.704922
$869$	−1.46260e101	−0.587411
$870$	−1.69615e101	−0.654711
$871$	−5.83741e101	−2.16568
$872$	−3.16421e101	−1.12836
$873$	3.52262e100	0.120746
$874$	−8.96173e101	−2.95289
$875$	−4.72391e100	−0.149632
$876$	−7.34932e100	−0.223798
$877$	2.81425e101	0.823904	0.411952	−	0.911205i	$-0.364847\pi$
$877$	2.81425e101	0.823904	0.411952	+	0.911205i	$0.364847\pi$
$878$	1.09165e102	3.07272
$879$	−3.65705e101	−0.989726
$880$	−1.73701e100	−0.0452013
$881$	3.15971e101	0.790640	0.395320	−	0.918543i	$-0.370634\pi$
$881$	3.15971e101	0.790640	0.395320	+	0.918543i	$0.370634\pi$
$882$	2.04129e101	0.491177
$883$	3.11171e100	0.0720037	0.0360018	−	0.999352i	$-0.488538\pi$
$883$	3.11171e100	0.0720037	0.0360018	+	0.999352i	$0.488538\pi$
$884$	8.13667e101	1.81069
$885$	3.03210e101	0.648934
$886$	9.60793e101	1.97773
$887$	−5.02818e101	−0.995510	−0.497755	−	0.867318i	$-0.665842\pi$
$887$	−5.02818e101	−0.995510	−0.497755	+	0.867318i	$0.665842\pi$
$888$	−6.08456e101	−1.15873
$889$	2.09146e101	0.383123
$890$	−2.53822e101	−0.447275
$891$	−2.12649e100	−0.0360482
$892$	8.90968e101	1.45303
$893$	−1.56149e102	−2.44999
$894$	1.11938e99	0.00168979
$895$	−2.17392e101	−0.315754
$896$	3.78162e101	0.528508
$897$	−5.55215e101	−0.746658
$898$	1.47041e102	1.90285
$899$	−5.92989e101	−0.738477
$900$	2.89124e101	0.346511
$901$	1.63056e101	0.188075
$902$	2.88440e101	0.320206
$903$	1.29254e100	0.0138107
$904$	1.88478e101	0.193843
$905$	−4.39015e101	−0.434614
$906$	−1.30172e101	−0.124049
$907$	−5.01012e101	−0.459617	−0.229809	−	0.973236i	$-0.573810\pi$
$907$	−5.01012e101	−0.459617	−0.229809	+	0.973236i	$0.573810\pi$
$908$	2.08851e102	1.84449
$909$	−7.00404e101	−0.595517
$910$	9.23850e101	0.756264
$911$	1.66499e102	1.31229	0.656143	−	0.754637i	$-0.272187\pi$
$911$	1.66499e102	1.31229	0.656143	+	0.754637i	$0.272187\pi$
$912$	1.35377e101	0.102736
$913$	−3.33479e101	−0.243684
$914$	−1.72990e102	−1.21724
$915$	1.38565e102	0.938916
$916$	−4.44063e102	−2.89768
$917$	−8.24757e101	−0.518303
$918$	4.84839e101	0.293444
$919$	7.04590e101	0.410725	0.205363	−	0.978686i	$-0.434163\pi$
$919$	7.04590e101	0.410725	0.205363	+	0.978686i	$0.434163\pi$
$920$	−2.74208e102	−1.53957
$921$	−7.12018e101	−0.385065
$922$	−7.38951e101	−0.384945
$923$	9.62590e101	0.483040
$924$	−2.01579e101	−0.0974458
$925$	2.47337e102	1.15186
$926$	8.88676e101	0.398717
$927$	7.79578e99	0.00336984
$928$	1.18917e102	0.495267
$929$	2.77489e102	1.11353	0.556767	−	0.830669i	$-0.312042\pi$
$929$	2.77489e102	1.11353	0.556767	+	0.830669i	$0.312042\pi$
$930$	4.20978e102	1.62779
$931$	−3.94233e102	−1.46889
$932$	−3.80059e102	−1.36459
$933$	−2.12945e102	−0.736803
$934$	2.31798e102	0.772934
$935$	1.20145e102	0.386104
$936$	1.36187e102	0.421813
$937$	3.66771e102	1.09491	0.547456	−	0.836835i	$-0.315596\pi$
$937$	3.66771e102	1.09491	0.547456	+	0.836835i	$0.315596\pi$
$938$	−3.29727e102	−0.948759
$939$	2.71260e102	0.752355
$940$	−1.19527e103	−3.19562
$941$	−5.19971e102	−1.34010	−0.670049	−	0.742316i	$-0.733727\pi$
$941$	−5.19971e102	−1.34010	−0.670049	+	0.742316i	$0.733727\pi$
$942$	−3.55756e102	−0.883886
$943$	2.80420e102	0.671670
$944$	4.17573e101	0.0964270
$945$	3.44000e101	0.0765880
$946$	1.89025e101	0.0405765
$947$	−1.17133e101	−0.0242440	−0.0121220	−	0.999927i	$-0.503859\pi$
$947$	−1.17133e101	−0.0242440	−0.0121220	+	0.999927i	$0.503859\pi$
$948$	8.72555e102	1.74143
$949$	1.40721e102	0.270817
$950$	−8.93567e102	−1.65830
$951$	2.10799e102	0.377259
$952$	1.83714e102	0.317078
$953$	−5.09310e102	−0.847768	−0.423884	−	0.905716i	$-0.639334\pi$
$953$	−5.09310e102	−0.847768	−0.423884	+	0.905716i	$0.639334\pi$
$954$	6.82755e101	0.109609
$955$	1.03894e103	1.60870
$956$	3.88532e102	0.580270
$957$	−7.08632e101	−0.102084
$958$	−4.51397e102	−0.627261
$959$	3.74846e102	0.502471
$960$	−9.06429e102	−1.17213
$961$	6.70180e102	0.836055
$962$	2.91461e103	3.50785
$963$	−2.47612e102	−0.287518
$964$	8.37622e102	0.938406
$965$	−2.70930e102	−0.292863
$966$	−3.13613e102	−0.327102
$967$	2.64925e102	0.266630	0.133315	−	0.991074i	$-0.457438\pi$
$967$	2.64925e102	0.266630	0.133315	+	0.991074i	$0.457438\pi$
$968$	1.00168e103	0.972816
$969$	−9.36368e102	−0.877559
$970$	−8.33367e102	−0.753723
$971$	−2.35670e102	−0.205703	−0.102852	−	0.994697i	$-0.532797\pi$
$971$	−2.35670e102	−0.205703	−0.102852	+	0.994697i	$0.532797\pi$
$972$	1.26862e102	0.106868
$973$	3.82057e102	0.310624
$974$	4.94358e101	0.0387934
$975$	−5.53600e102	−0.419312
$976$	1.90829e102	0.139516
$977$	−4.18214e102	−0.295146	−0.147573	−	0.989051i	$-0.547146\pi$
$977$	−4.18214e102	−0.295146	−0.147573	+	0.989051i	$0.547146\pi$
$978$	−5.17165e102	−0.352321
$979$	−1.06044e102	−0.0697404
$980$	−3.01773e103	−1.91593
$981$	5.64382e102	0.345933
$982$	8.02013e102	0.474608
$983$	−1.71477e103	−0.979738	−0.489869	−	0.871796i	$-0.662955\pi$
$983$	−1.71477e103	−0.979738	−0.489869	+	0.871796i	$0.662955\pi$
$984$	−6.87836e102	−0.379450
$985$	1.90323e103	1.01377
$986$	1.61568e103	0.831001
$987$	−5.46439e102	−0.271394
$988$	−6.57998e103	−3.15580
$989$	1.83769e102	0.0851139
$990$	5.03077e102	0.225020
$991$	−4.57217e103	−1.97506	−0.987531	−	0.157423i	$-0.949681\pi$
$991$	−4.57217e103	−1.97506	−0.987531	+	0.157423i	$0.949681\pi$
$992$	−2.95149e103	−1.23137
$993$	−2.02415e103	−0.815629
$994$	5.43720e102	0.211614
$995$	3.54823e103	1.33388
$996$	1.98947e103	0.722421
$997$	3.49680e103	1.22656	0.613279	−	0.789867i	$-0.289850\pi$
$997$	3.49680e103	1.22656	0.613279	+	0.789867i	$0.289850\pi$
$998$	3.65785e103	1.23943
$999$	1.08527e103	0.355245

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.70.a.b.1.1	✓	6
3.2	odd	2		9.70.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.70.a.b.1.1	✓	6	1.1	even	1	trivial
9.70.a.c.1.6		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-3.96695e10 q^{2} +1.66772e16 q^{3} +9.83375e20 q^{4} +1.65867e24 q^{5} -6.61576e26 q^{6} +4.47127e28 q^{7} -1.55933e31 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q-3.96695e10 q^{2} +1.66772e16 q^{3} +9.83375e20 q^{4} +1.65867e24 q^{5} -6.61576e26 q^{6} +4.47127e28 q^{7} -1.55933e31 q^{8} +2.78128e32 q^{9} -6.57985e34 q^{10} -2.74899e35 q^{11} +1.63999e37 q^{12} -3.14018e38 q^{13} -1.77373e39 q^{14} +2.76619e40 q^{15} +3.80952e40 q^{16} -2.63495e42 q^{17} -1.10332e43 q^{18} +2.13084e44 q^{19} +1.63109e45 q^{20} +7.45682e44 q^{21} +1.09051e46 q^{22} +1.06019e47 q^{23} -2.60052e47 q^{24} +1.05711e48 q^{25} +1.24569e49 q^{26} +4.63840e48 q^{27} +4.39694e49 q^{28} +1.54570e50 q^{29} -1.09733e51 q^{30} -3.83638e51 q^{31} +7.69342e51 q^{32} -4.58454e51 q^{33} +1.04527e53 q^{34} +7.41635e52 q^{35} +2.73505e53 q^{36} +2.33975e54 q^{37} -8.45294e54 q^{38} -5.23693e54 q^{39} -2.58640e55 q^{40} +2.64500e55 q^{41} -2.95809e55 q^{42} +1.73336e55 q^{43} -2.70329e56 q^{44} +4.61322e56 q^{45} -4.20572e57 q^{46} -7.32804e57 q^{47} +6.35321e56 q^{48} -1.85013e58 q^{49} -4.19349e58 q^{50} -4.39436e58 q^{51} -3.08797e59 q^{52} -6.18818e58 q^{53} -1.84003e59 q^{54} -4.55966e59 q^{55} -6.97217e59 q^{56} +3.55364e60 q^{57} -6.13172e60 q^{58} +1.09613e61 q^{59} +2.72020e61 q^{60} +5.00925e61 q^{61} +1.52187e62 q^{62} +1.24359e61 q^{63} -3.27682e62 q^{64} -5.20851e62 q^{65} +1.81867e62 q^{66} +1.85894e63 q^{67} -2.59115e63 q^{68} +1.76810e63 q^{69} -2.94203e63 q^{70} -3.06540e63 q^{71} -4.33693e63 q^{72} -4.48131e63 q^{73} -9.28168e64 q^{74} +1.76296e64 q^{75} +2.09542e65 q^{76} -1.22915e64 q^{77} +2.07747e65 q^{78} +5.32048e65 q^{79} +6.31873e64 q^{80} +7.73554e64 q^{81} -1.04926e66 q^{82} +1.21310e66 q^{83} +7.33285e65 q^{84} -4.37051e66 q^{85} -6.87615e65 q^{86} +2.57779e66 q^{87} +4.28657e66 q^{88} +3.85757e66 q^{89} -1.83004e67 q^{90} -1.40406e67 q^{91} +1.04256e68 q^{92} -6.39799e67 q^{93} +2.90700e68 q^{94} +3.53435e68 q^{95} +1.28305e68 q^{96} +1.26654e68 q^{97} +7.33937e68 q^{98} -7.64572e67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 6 * q + 19700962938 * q^2 + 100063090197999414 * q^3 + 2215616615832949213668 * q^4 + 628080806150898444057636 * q^5 + 328556538575422922826619722 * q^6 + 47913495403332419035526232336 * q^7 + 24457375972572426935219376797544 * q^8 + 1668770336662161067543714657390566 * q^9	\( 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 38\!\cdots\!64 q^{99}+O(q^{100}) \) 6 * q + 19700962938 * q^2 + 100063090197999414 * q^3 + 2215616615832949213668 * q^4 + 628080806150898444057636 * q^5 + 328556538575422922826619722 * q^6 + 47913495403332419035526232336 * q^7 + 24457375972572426935219376797544 * q^8 + 1668770336662161067543714657390566 * q^9 - 22202946094182786607107040591714596 * q^10 + 1390130418743494007545256289087169224 * q^11 + 36950240879046435619379563386337465092 * q^12 + 133509121614335990365965211432000729332 * q^13 - 2841394212247933581409064272690567131408 * q^14 + 10474617726251589358520780625360618370884 * q^15 + 297926539143537140116723472619801199364880 * q^16 - 274151565383473524836430571365328624168788 * q^17 + 5479397092435836303110872860016484759473818 * q^18 + 138429394829044356269800544348434108061745912 * q^19 + 138597243063668969619157527013420360089172824 * q^20 + 799062068707513693070181199972452904025975184 * q^21 + 41357320156815766506190949808834631301146379064 * q^22 + 218317639771339979005196930422301057686492438608 * q^23 + 407880102991649733080716879327968269719818106536 * q^24 + 3158503477944939899259768424552979678128936846746 * q^25 + 23013722899099212942495329191134948082985267735052 * q^26 + 27830386119528611875968901007343548725913806188054 * q^27 - 22620517010064241205747099942016845775787346540448 * q^28 + 386749858303620975828595276373219723661271736500404 * q^29 - 370282566280588494739921166576105524382557210541124 * q^30 - 406800617338554840921365551900230681176672582694624 * q^31 + 8820058315615156467775375743923825115981231801768096 * q^32 + 23183457579618822681041348155744625937569376878472456 * q^33 + 281687660915944724759468852907875788491074366030810196 * q^34 + 890666754256698409309143705814565889896130721823553120 * q^35 + 616225880986304773795203687785611855657221329076909348 * q^36 - 1034952541392536641085376764904786871274360452152204924 * q^37 - 5285525891153406695181497436406602451158488826469402872 * q^38 + 2226555879725162556253661663326679211189300189218101908 * q^39 - 82332680986716259050086980186058027597204731237577012112 * q^40 - 75922269693086975847370108328993717966577053054061574404 * q^41 - 47386447558039744873106666160656130217031504344407499152 * q^42 + 517689066199516372636612583654794159251763191323866573320 * q^43 + 635179531764405639585838952451726338367638421474019771824 * q^44 + 174687103055246053382755708023577718190895841278777776996 * q^45 + 5002677415477463005074915765236526191711825419441207632816 * q^46 + 2453203952295844591600634297438375000618428764145129219680 * q^47 + 4968575026449593322551787829369140395486935424990568696720 * q^48 + 2425144461879979131295388929466673195687370332650760871830 * q^49 + 37635665810544549850117129516993646830506493536524891294694 * q^50 - 4572075469148207520239238457234666663632976056294376848372 * q^51 + 5305218099159647316820834640268608261939453873644307186232 * q^52 + 74471113644675549895227882174052653368560896469248975574788 * q^53 + 91380900915177136766508328597711019880437502648894485390442 * q^54 - 2409654567830037488585083843998013931798965138034800503971664 * q^55 - 1152362306928674739149660784650028044220707470519808104718400 * q^56 + 2308612170138856515323754812102347865320528660571074398815928 * q^57 + 15022887190676434515518320415561940276213411853028154366072396 * q^58 + 11415146769011619472046632564776870018333102937631875861541928 * q^59 + 2311411405645659457638507670716384370296951624465227816120856 * q^60 + 33238256339320993820472102641365032387601740714468466667170260 * q^61 - 124525378061521437222478334616477802775494912101377589859538208 * q^62 + 13326103309146657949938227725670548487445834719016647868423696 * q^63 - 766655384080592585753942434682913694288086896286784450843059648 * q^64 - 1033047386671074609986337778384229107631858701816226280998392392 * q^65 + 689723542866499218831313407015589656876016041998031390482311416 * q^66 + 1829841882595431765701319157889272255403856626816125827498086232 * q^67 + 2317663971913472593763546580441523937519238504690538745057995656 * q^68 + 3640922946708989413397256792395290653432177770376246213302495952 * q^69 + 21667344061607294216951596756563208633436583684026130660066187680 * q^70 - 13440911053044271064593659636588909406794279924608753124634255248 * q^71 + 6802290589270456310723007400658664216160810865509880920119594984 * q^72 - 10455717435803652258126612179458660840472081585301779921081767812 * q^73 - 161664876015117679845821922240487717737273356359281171995837108868 * q^74 + 52674936400716562322380194260642699522996671253949886206452634474 * q^75 + 71090965276426447702322949472042826997822238537703230080293688528 * q^76 - 43362153841256194511002835681080956828831169900379264481733785408 * q^77 + 383804038374054851929016706651242398292482671566351802142233876588 * q^78 + 849706277580491574368053093245214288882224299075364357356727921600 * q^79 - 189522757413920765612591740266335581479125703002325048006012452256 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 1548665779897056733086309454028318283362331255484057489512257090052 * q^82 - 147710286880885756653308105230523797327053885776686380979324732296 * q^83 - 377246472317239697653688739971600940182916419912051144657271882912 * q^84 + 900129278829088984191830889400611488683994113651840432684483124232 * q^85 + 20081029605597770660724545035979232318223218281164495480965241306104 * q^86 + 6449897659249786389820756834246397993926418977011658135033733793876 * q^87 + 42299661882900410851288517995075665379682018856186665678192374320864 * q^88 + 63907211385846533401519989675721990056288572539740159493298948890332 * q^89 - 6175269638080203823349656636276052054009049469739079836962862483556 * q^90 + 44568583318227431253455625104560122172317657855744447513981633586656 * q^91 + 407516989708923645515294364601926415744249719108325034482775450006496 * q^92 - 6784287810891609560820397041997675504562492646751100945260348825056 * q^93 + 543732799316328297398198809151553350012212421132175473218873964726688 * q^94 + 727302843727922318056572996599295364559054812190980909735896231363024 * q^95 + 147093715131169030822786258830983491108570311615658180154147861982624 * q^96 + 947436775360467753919340697699840040468393082746311551117424599367372 * q^97 + 2424310569772600455357151217191683340027129070175336157909473058804458 * q^98 + 386634734481815239147577824740950727802459268187074272255289250523464 * q^99

Introduction

L-functions

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