LMFDB - Embedded newform 3.70.a.b.1.6

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			1.6
Root			$-2.19909e9$ 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)

$f(q)$	$=$	$q+4.28672e10 q^{2} +1.66772e16 q^{3} +1.24730e21 q^{4} -1.81509e24 q^{5} +7.14904e26 q^{6} -1.63830e29 q^{7} +2.81639e31 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q+4.28672e10 q^{2} +1.66772e16 q^{3} +1.24730e21 q^{4} -1.81509e24 q^{5} +7.14904e26 q^{6} -1.63830e29 q^{7} +2.81639e31 q^{8} +2.78128e32 q^{9} -7.78079e34 q^{10} +1.04682e36 q^{11} +2.08014e37 q^{12} +4.05400e38 q^{13} -7.02295e39 q^{14} -3.02706e40 q^{15} +4.71031e41 q^{16} +4.76202e40 q^{17} +1.19226e43 q^{18} -9.69137e42 q^{19} -2.26397e45 q^{20} -2.73223e45 q^{21} +4.48741e46 q^{22} +1.42285e47 q^{23} +4.69694e47 q^{24} +1.60050e48 q^{25} +1.73783e49 q^{26} +4.63840e48 q^{27} -2.04346e50 q^{28} +5.47213e50 q^{29} -1.29762e51 q^{30} -1.63102e51 q^{31} +3.56675e51 q^{32} +1.74580e52 q^{33} +2.04134e51 q^{34} +2.97368e53 q^{35} +3.46909e53 q^{36} -5.47216e53 q^{37} -4.15442e53 q^{38} +6.76092e54 q^{39} -5.11201e55 q^{40} +5.82103e55 q^{41} -1.17123e56 q^{42} +2.95770e56 q^{43} +1.30570e57 q^{44} -5.04829e56 q^{45} +6.09936e57 q^{46} -4.26617e57 q^{47} +7.85547e57 q^{48} +6.33990e57 q^{49} +6.86089e58 q^{50} +7.94170e56 q^{51} +5.05655e59 q^{52} +4.66607e59 q^{53} +1.98835e59 q^{54} -1.90007e60 q^{55} -4.61410e60 q^{56} -1.61625e59 q^{57} +2.34575e61 q^{58} -6.52176e60 q^{59} -3.77566e61 q^{60} -3.35534e61 q^{61} -6.99172e61 q^{62} -4.55659e61 q^{63} -1.25151e62 q^{64} -7.35838e62 q^{65} +7.48374e62 q^{66} +1.01983e63 q^{67} +5.93966e61 q^{68} +2.37291e63 q^{69} +1.27473e64 q^{70} -2.25332e63 q^{71} +7.83318e63 q^{72} -1.79742e64 q^{73} -2.34576e64 q^{74} +2.66918e64 q^{75} -1.20880e64 q^{76} -1.71501e65 q^{77} +2.89822e65 q^{78} -1.94393e65 q^{79} -8.54966e65 q^{80} +7.73554e64 q^{81} +2.49531e66 q^{82} -1.58132e66 q^{83} -3.40791e66 q^{84} -8.64351e64 q^{85} +1.26788e67 q^{86} +9.12597e66 q^{87} +2.94825e67 q^{88} +1.53541e67 q^{89} -2.16406e67 q^{90} -6.64168e67 q^{91} +1.77472e68 q^{92} -2.72008e67 q^{93} -1.82879e68 q^{94} +1.75908e67 q^{95} +5.94833e67 q^{96} +3.95713e68 q^{97} +2.71774e68 q^{98} +2.91150e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.28672e10	1.76437	0.882186	−	0.470901i	$-0.156071\pi$
$2$	4.28672e10	1.76437	0.882186	+	0.470901i	$0.156071\pi$
$3$	1.66772e16	0.577350
$3$	1.66772e16	0.577350
$4$	1.24730e21	2.11301
$5$	−1.81509e24	−1.39455	−0.697275	−	0.716804i	$-0.745604\pi$
$5$	−1.81509e24	−1.39455	−0.697275	+	0.716804i	$0.745604\pi$
$6$	7.14904e26	1.01866
$7$	−1.63830e29	−1.14423	−0.572114	−	0.820174i	$-0.693876\pi$
$7$	−1.63830e29	−1.14423	−0.572114	+	0.820174i	$0.693876\pi$
$8$	2.81639e31	1.96376
$9$	2.78128e32	0.333333
$10$	−7.78079e34	−2.46050
$11$	1.04682e36	1.23544	0.617722	−	0.786396i	$-0.288056\pi$
$11$	1.04682e36	1.23544	0.617722	+	0.786396i	$0.288056\pi$
$12$	2.08014e37	1.21995
$13$	4.05400e38	1.50258	0.751290	−	0.659972i	$-0.229432\pi$
$13$	4.05400e38	1.50258	0.751290	+	0.659972i	$0.229432\pi$
$14$	−7.02295e39	−2.01884
$15$	−3.02706e40	−0.805143
$16$	4.71031e41	1.35179
$17$	4.76202e40	0.0168773	0.00843865	−	0.999964i	$-0.497314\pi$
$17$	4.76202e40	0.0168773	0.00843865	+	0.999964i	$0.497314\pi$
$18$	1.19226e43	0.588124
$19$	−9.69137e42	−0.0740263	−0.0370132	−	0.999315i	$-0.511784\pi$
$19$	−9.69137e42	−0.0740263	−0.0370132	+	0.999315i	$0.511784\pi$
$20$	−2.26397e45	−2.94669
$21$	−2.73223e45	−0.660620
$22$	4.48741e46	2.17978
$23$	1.42285e47	1.49124	0.745622	−	0.666369i	$-0.232152\pi$
$23$	1.42285e47	1.49124	0.745622	+	0.666369i	$0.232152\pi$
$24$	4.69694e47	1.13378
$25$	1.60050e48	0.944768
$26$	1.73783e49	2.65111
$27$	4.63840e48	0.192450
$28$	−2.04346e50	−2.41776
$29$	5.47213e50	1.92941	0.964707	−	0.263327i	$-0.0848197\pi$
$29$	5.47213e50	1.92941	0.964707	+	0.263327i	$0.0848197\pi$
$30$	−1.29762e51	−1.42057
$31$	−1.63102e51	−0.576077	−0.288038	−	0.957619i	$-0.593003\pi$
$31$	−1.63102e51	−0.576077	−0.288038	+	0.957619i	$0.593003\pi$
$32$	3.56675e51	0.421307
$33$	1.74580e52	0.713284
$34$	2.04134e51	0.0297778
$35$	2.97368e53	1.59568
$36$	3.46909e53	0.704336
$37$	−5.47216e53	−0.431717	−0.215859	−	0.976425i	$-0.569255\pi$
$37$	−5.47216e53	−0.431717	−0.215859	+	0.976425i	$0.569255\pi$
$38$	−4.15442e53	−0.130610
$39$	6.76092e54	0.867515
$40$	−5.11201e55	−2.73856
$41$	5.82103e55	1.33032	0.665161	−	0.746700i	$-0.268363\pi$
$41$	5.82103e55	1.33032	0.665161	+	0.746700i	$0.268363\pi$
$42$	−1.17123e56	−1.16558
$43$	2.95770e56	1.30705	0.653525	−	0.756905i	$-0.273289\pi$
$43$	2.95770e56	1.30705	0.653525	+	0.756905i	$0.273289\pi$
$44$	1.30570e57	2.61050
$45$	−5.04829e56	−0.464850
$46$	6.09936e57	2.63111
$47$	−4.26617e57	−0.876318	−0.438159	−	0.898897i	$-0.644369\pi$
$47$	−4.26617e57	−0.876318	−0.438159	+	0.898897i	$0.644369\pi$
$48$	7.85547e57	0.780458
$49$	6.33990e57	0.309256
$50$	6.86089e58	1.66692
$51$	7.94170e56	0.00974412
$52$	5.05655e59	3.17496
$53$	4.66607e59	1.51857	0.759283	−	0.650760i	$-0.225550\pi$
$53$	4.66607e59	1.51857	0.759283	+	0.650760i	$0.225550\pi$
$54$	1.98835e59	0.339553
$55$	−1.90007e60	−1.72289
$56$	−4.61410e60	−2.24699
$57$	−1.61625e59	−0.0427391
$58$	2.34575e61	3.40420
$59$	−6.52176e60	−0.524772	−0.262386	−	0.964963i	$-0.584509\pi$
$59$	−6.52176e60	−0.524772	−0.262386	+	0.964963i	$0.584509\pi$
$60$	−3.77566e61	−1.70127
$61$	−3.35534e61	−0.854786	−0.427393	−	0.904066i	$-0.640568\pi$
$61$	−3.35534e61	−0.854786	−0.427393	+	0.904066i	$0.640568\pi$
$62$	−6.99172e61	−1.01641
$63$	−4.55659e61	−0.381409
$64$	−1.25151e62	−0.608452
$65$	−7.35838e62	−2.09542
$66$	7.48374e62	1.25850
$67$	1.01983e63	1.02082	0.510409	−	0.859932i	$-0.329494\pi$
$67$	1.01983e63	1.02082	0.510409	+	0.859932i	$0.329494\pi$
$68$	5.93966e61	0.0356619
$69$	2.37291e63	0.860971
$70$	1.27473e64	2.81537
$71$	−2.25332e63	−0.305077	−0.152538	−	0.988298i	$-0.548745\pi$
$71$	−2.25332e63	−0.305077	−0.152538	+	0.988298i	$0.548745\pi$
$72$	7.83318e63	0.654586
$73$	−1.79742e64	−0.933276	−0.466638	−	0.884448i	$-0.654535\pi$
$73$	−1.79742e64	−0.933276	−0.466638	+	0.884448i	$0.654535\pi$
$74$	−2.34576e64	−0.761710
$75$	2.66918e64	0.545462
$76$	−1.20880e64	−0.156418
$77$	−1.71501e65	−1.41363
$78$	2.89822e65	1.53062
$79$	−1.94393e65	−0.661524	−0.330762	−	0.943714i	$-0.607306\pi$
$79$	−1.94393e65	−0.661524	−0.330762	+	0.943714i	$0.607306\pi$
$80$	−8.54966e65	−1.88514
$81$	7.73554e64	0.111111
$82$	2.49531e66	2.34718
$83$	−1.58132e66	−0.979099	−0.489549	−	0.871976i	$-0.662839\pi$
$83$	−1.58132e66	−0.979099	−0.489549	+	0.871976i	$0.662839\pi$
$84$	−3.40791e66	−1.39589
$85$	−8.64351e64	−0.0235362
$86$	1.26788e67	2.30612
$87$	9.12597e66	1.11395
$88$	2.94825e67	2.42612
$89$	1.53541e67	0.855598	0.427799	−	0.903874i	$-0.359289\pi$
$89$	1.53541e67	0.855598	0.427799	+	0.903874i	$0.359289\pi$
$90$	−2.16406e67	−0.820168
$91$	−6.64168e67	−1.71929
$92$	1.77472e68	3.15101
$93$	−2.72008e67	−0.332598
$94$	−1.82879e68	−1.54615
$95$	1.75908e67	0.103233
$96$	5.94833e67	0.243242
$97$	3.95713e68	1.13176	0.565882	−	0.824486i	$-0.308536\pi$
$97$	3.95713e68	1.13176	0.565882	+	0.824486i	$0.308536\pi$
$98$	2.71774e68	0.545642
$99$	2.91150e68	0.411815
$100$	1.99630e69	1.99630
$101$	−1.28051e69	−0.908441	−0.454220	−	0.890889i	$-0.650082\pi$
$101$	−1.28051e69	−0.908441	−0.454220	+	0.890889i	$0.650082\pi$
$102$	3.40438e67	0.0171922
$103$	9.87174e67	0.0356049	0.0178024	−	0.999842i	$-0.494333\pi$
$103$	9.87174e67	0.0356049	0.0178024	+	0.999842i	$0.494333\pi$
$104$	1.14176e70	2.95071
$105$	4.95925e69	0.921267
$106$	2.00021e70	2.67932
$107$	−4.38557e69	−0.424899	−0.212449	−	0.977172i	$-0.568144\pi$
$107$	−4.38557e69	−0.424899	−0.212449	+	0.977172i	$0.568144\pi$
$108$	5.78547e69	0.406648
$109$	2.12641e70	1.08751	0.543754	−	0.839244i	$-0.317002\pi$
$109$	2.12641e70	1.08751	0.543754	+	0.839244i	$0.317002\pi$
$110$	−8.14507e70	−3.03982
$111$	−9.12603e69	−0.249252
$112$	−7.71692e70	−1.54676
$113$	−1.96866e70	−0.290378	−0.145189	−	0.989404i	$-0.546379\pi$
$113$	−1.96866e70	−0.290378	−0.145189	+	0.989404i	$0.546379\pi$
$114$	−6.92840e69	−0.0754077
$115$	−2.58261e71	−2.07961
$116$	6.82538e71	4.07686
$117$	1.12753e71	0.500860
$118$	−2.79570e71	−0.925893
$119$	−7.80163e69	−0.0193115
$120$	−8.52539e71	−1.58111
$121$	3.77875e71	0.526324
$122$	−1.43834e72	−1.50816
$123$	9.70783e71	0.768062
$124$	−2.03437e72	−1.21725
$125$	1.69833e71	0.0770240
$126$	−1.95328e72	−0.672947
$127$	5.93387e72	1.55636	0.778179	−	0.628043i	$-0.216144\pi$
$127$	5.93387e72	1.55636	0.778179	+	0.628043i	$0.216144\pi$
$128$	−7.47032e72	−1.49484
$129$	4.93261e72	0.754626
$130$	−3.15433e73	−3.69710
$131$	−1.18270e73	−1.06418	−0.532091	−	0.846687i	$-0.678594\pi$
$131$	−1.18270e73	−1.06418	−0.532091	+	0.846687i	$0.678594\pi$
$132$	2.17753e73	1.50718
$133$	1.58774e72	0.0847029
$134$	4.37173e73	1.80110
$135$	−8.41913e72	−0.268381
$136$	1.34117e72	0.0331430
$137$	−6.88834e72	−0.132207	−0.0661036	−	0.997813i	$-0.521057\pi$
$137$	−6.88834e72	−0.132207	−0.0661036	+	0.997813i	$0.521057\pi$
$138$	1.01720e74	1.51907
$139$	3.13718e73	0.365198	0.182599	−	0.983187i	$-0.441549\pi$
$139$	3.13718e73	0.365198	0.182599	+	0.983187i	$0.441549\pi$
$140$	3.70906e74	3.37169
$141$	−7.11477e73	−0.505943
$142$	−9.65933e73	−0.538269
$143$	4.24379e74	1.85636
$144$	1.31007e74	0.450598
$145$	−9.93242e74	−2.69066
$146$	−7.70502e74	−1.64665
$147$	1.05732e74	0.178549
$148$	−6.82543e74	−0.912222
$149$	1.62415e75	1.72068	0.860339	−	0.509723i	$-0.170252\pi$
$149$	1.62415e75	1.72068	0.860339	+	0.509723i	$0.170252\pi$
$150$	1.14420e75	0.962398
$151$	−6.71687e74	−0.449223	−0.224612	−	0.974448i	$-0.572111\pi$
$151$	−6.71687e74	−0.449223	−0.224612	+	0.974448i	$0.572111\pi$
$152$	−2.72947e74	−0.145370
$153$	1.32445e73	0.00562577
$154$	−7.35175e75	−2.49417
$155$	2.96045e75	0.803368
$156$	8.43290e75	1.83307
$157$	−8.53620e74	−0.148842	−0.0744212	−	0.997227i	$-0.523711\pi$
$157$	−8.53620e74	−0.148842	−0.0744212	+	0.997227i	$0.523711\pi$
$158$	−8.33308e75	−1.16717
$159$	7.78169e75	0.876745
$160$	−6.47398e75	−0.587533
$161$	−2.33106e76	−1.70632
$162$	3.31601e75	0.196041
$163$	−3.59591e76	−1.71924	−0.859621	−	0.510932i	$-0.829300\pi$
$163$	−3.59591e76	−1.71924	−0.859621	+	0.510932i	$0.829300\pi$
$164$	7.26057e76	2.81098
$165$	−3.16878e76	−0.994710
$166$	−6.77869e76	−1.72749
$167$	−1.71281e76	−0.354805	−0.177403	−	0.984138i	$-0.556770\pi$
$167$	−1.71281e76	−0.354805	−0.177403	+	0.984138i	$0.556770\pi$
$168$	−7.69502e76	−1.29730
$169$	9.15556e76	1.25775
$170$	−3.70523e75	−0.0415267
$171$	−2.69545e75	−0.0246754
$172$	3.68914e77	2.76181
$173$	1.86387e77	1.14242	0.571209	−	0.820805i	$-0.306475\pi$
$173$	1.86387e77	1.14242	0.571209	+	0.820805i	$0.306475\pi$
$174$	3.91204e77	1.96542
$175$	−2.62210e77	−1.08103
$176$	4.93084e77	1.67007
$177$	−1.08765e77	−0.302977
$178$	6.58188e77	1.50959
$179$	−8.75816e77	−1.65571	−0.827853	−	0.560945i	$-0.810438\pi$
$179$	−8.75816e77	−1.65571	−0.827853	+	0.560945i	$0.810438\pi$
$180$	−6.29673e77	−0.982231
$181$	5.51204e76	0.0710234	0.0355117	−	0.999369i	$-0.488694\pi$
$181$	5.51204e76	0.0710234	0.0355117	+	0.999369i	$0.488694\pi$
$182$	−2.84710e78	−3.03347
$183$	−5.59577e77	−0.493511
$184$	4.00730e78	2.92845
$185$	9.93249e77	0.602051
$186$	−1.16602e78	−0.586827
$187$	4.98496e76	0.0208510
$188$	−5.32119e78	−1.85167
$189$	−7.59911e77	−0.220207
$190$	7.54066e77	0.182142
$191$	−6.92451e77	−0.139553	−0.0697763	−	0.997563i	$-0.522229\pi$
$191$	−6.92451e77	−0.139553	−0.0697763	+	0.997563i	$0.522229\pi$
$192$	−2.08717e78	−0.351290
$193$	−1.17108e79	−1.64763	−0.823815	−	0.566858i	$-0.808159\pi$
$193$	−1.17108e79	−1.64763	−0.823815	+	0.566858i	$0.808159\pi$
$194$	1.69631e79	1.99685
$195$	−1.22717e79	−1.20979
$196$	7.90775e78	0.653459
$197$	−9.00204e78	−0.624103	−0.312051	−	0.950065i	$-0.601016\pi$
$197$	−9.00204e78	−0.624103	−0.312051	+	0.950065i	$0.601016\pi$
$198$	1.24808e79	0.726595
$199$	1.97443e79	0.966077	0.483038	−	0.875599i	$-0.339533\pi$
$199$	1.97443e79	0.966077	0.483038	+	0.875599i	$0.339533\pi$
$200$	4.50763e79	1.85530
$201$	1.70079e79	0.589369
$202$	−5.48920e79	−1.60283
$203$	−8.96501e79	−2.20769
$204$	9.90568e77	0.0205894
$205$	−1.05657e80	−1.85520
$206$	4.23174e78	0.0628202
$207$	3.95735e79	0.497082
$208$	1.90956e80	2.03118
$209$	−1.01451e79	−0.0914554
$210$	2.12589e80	1.62546
$211$	2.00728e79	0.130275	0.0651377	−	0.997876i	$-0.479251\pi$
$211$	2.00728e79	0.130275	0.0651377	+	0.997876i	$0.479251\pi$
$212$	5.81999e80	3.20874
$213$	−3.75790e79	−0.176136
$214$	−1.87997e80	−0.749679
$215$	−5.36850e80	−1.82275
$216$	1.30635e80	0.377926
$217$	2.67211e80	0.659163
$218$	9.11532e80	1.91877
$219$	−2.99758e80	−0.538827
$220$	−2.36996e81	−3.64048
$221$	1.93052e79	0.0253595
$222$	−3.91207e80	−0.439773
$223$	−1.09587e81	−1.05497	−0.527487	−	0.849563i	$-0.676866\pi$
$223$	−1.09587e81	−1.05497	−0.527487	+	0.849563i	$0.676866\pi$
$224$	−5.84342e80	−0.482070
$225$	4.45144e80	0.314923
$226$	−8.43909e80	−0.512335
$227$	2.47125e80	0.128832	0.0644162	−	0.997923i	$-0.479481\pi$
$227$	2.47125e80	0.128832	0.0644162	+	0.997923i	$0.479481\pi$
$228$	−2.01595e80	−0.0903081
$229$	3.09746e81	1.19311	0.596557	−	0.802571i	$-0.296535\pi$
$229$	3.09746e81	1.19311	0.596557	+	0.802571i	$0.296535\pi$
$230$	−1.10709e82	−3.66921
$231$	−2.86015e81	−0.816159
$232$	1.54116e82	3.78890
$233$	4.42177e81	0.937168	0.468584	−	0.883419i	$-0.344764\pi$
$233$	4.42177e81	0.937168	0.468584	+	0.883419i	$0.344764\pi$
$234$	4.83341e81	0.883703
$235$	7.74350e81	1.22207
$236$	−8.13459e81	−1.10885
$237$	−3.24193e81	−0.381931
$238$	−3.34434e80	−0.0340726
$239$	9.15609e81	0.807202	0.403601	−	0.914935i	$-0.367758\pi$
$239$	9.15609e81	0.807202	0.403601	+	0.914935i	$0.367758\pi$
$240$	−1.42584e82	−1.08839
$241$	2.19840e82	1.45385	0.726925	−	0.686717i	$-0.240949\pi$
$241$	2.19840e82	1.45385	0.726925	+	0.686717i	$0.240949\pi$
$242$	1.61984e82	0.928631
$243$	1.29007e81	0.0641500
$244$	−4.18512e82	−1.80617
$245$	−1.15075e82	−0.431272
$246$	4.16148e82	1.35515
$247$	−3.92888e81	−0.111230
$248$	−4.59358e82	−1.13128
$249$	−2.63720e82	−0.565283
$250$	7.28025e81	0.135899
$251$	−2.13329e82	−0.346981	−0.173490	−	0.984836i	$-0.555505\pi$
$251$	−2.13329e82	−0.346981	−0.173490	+	0.984836i	$0.555505\pi$
$252$	−5.68343e82	−0.805920
$253$	1.48946e83	1.84235
$254$	2.54368e83	2.74599
$255$	−1.44149e81	−0.0135887
$256$	−2.46355e83	−2.02900
$257$	2.88143e82	0.207451	0.103725	−	0.994606i	$-0.466924\pi$
$257$	2.88143e82	0.207451	0.103725	+	0.994606i	$0.466924\pi$
$258$	2.11447e83	1.33144
$259$	8.96507e82	0.493983
$260$	−9.17811e83	−4.42764
$261$	1.52195e83	0.643138
$262$	−5.06992e83	−1.87761
$263$	−3.96861e82	−0.128874	−0.0644370	−	0.997922i	$-0.520525\pi$
$263$	−3.96861e82	−0.128874	−0.0644370	+	0.997922i	$0.520525\pi$
$264$	4.91684e83	1.40072
$265$	−8.46935e83	−2.11772
$266$	6.80620e82	0.149447
$267$	2.56063e83	0.493980
$268$	1.27204e84	2.15699
$269$	9.84406e82	0.146798	0.0733991	−	0.997303i	$-0.476615\pi$
$269$	9.84406e82	0.146798	0.0733991	+	0.997303i	$0.476615\pi$
$270$	−3.60904e83	−0.473524
$271$	1.47855e83	0.170764	0.0853820	−	0.996348i	$-0.472789\pi$
$271$	1.47855e83	0.170764	0.0853820	+	0.996348i	$0.472789\pi$
$272$	2.24306e82	0.0228146
$273$	−1.10765e84	−0.992634
$274$	−2.95284e83	−0.233263
$275$	1.67543e84	1.16721
$276$	2.95973e84	1.81924
$277$	−4.17597e83	−0.226571	−0.113286	−	0.993562i	$-0.536138\pi$
$277$	−4.17597e83	−0.226571	−0.113286	+	0.993562i	$0.536138\pi$
$278$	1.34482e84	0.644345
$279$	−4.53633e83	−0.192026
$280$	8.37503e84	3.13353
$281$	−5.01765e84	−1.66009	−0.830047	−	0.557694i	$-0.811686\pi$
$281$	−5.01765e84	−1.66009	−0.830047	+	0.557694i	$0.811686\pi$
$282$	−3.04990e84	−0.892671
$283$	1.07413e84	0.278244	0.139122	−	0.990275i	$-0.455572\pi$
$283$	1.07413e84	0.278244	0.139122	+	0.990275i	$0.455572\pi$
$284$	−2.81056e84	−0.644630
$285$	2.93364e83	0.0596018
$286$	1.81920e85	3.27530
$287$	−9.53662e84	−1.52219
$288$	9.92014e83	0.140436
$289$	−7.95888e84	−0.999715
$290$	−4.25775e85	−4.74733
$291$	6.59938e84	0.653424
$292$	−2.24192e85	−1.97202
$293$	−5.69255e84	−0.445015	−0.222507	−	0.974931i	$-0.571424\pi$
$293$	−5.69255e84	−0.445015	−0.222507	+	0.974931i	$0.571424\pi$
$294$	4.53242e84	0.315026
$295$	1.18376e85	0.731820
$296$	−1.54117e85	−0.847789
$297$	4.85556e84	0.237761
$298$	6.96227e85	3.03591
$299$	5.76823e85	2.24071
$300$	3.32927e85	1.15257
$301$	−4.84561e85	−1.49556
$302$	−2.87933e85	−0.792597
$303$	−2.13554e85	−0.524489
$304$	−4.56494e84	−0.100068
$305$	6.09026e85	1.19204
$306$	5.67755e83	0.00992595
$307$	−5.79059e85	−0.904584	−0.452292	−	0.891870i	$-0.649394\pi$
$307$	−5.79059e85	−0.904584	−0.452292	+	0.891870i	$0.649394\pi$
$308$	−2.13913e86	−2.98701
$309$	1.64633e84	0.0205565
$310$	1.26906e86	1.41744
$311$	8.08625e85	0.808190	0.404095	−	0.914717i	$-0.367586\pi$
$311$	8.08625e85	0.808190	0.404095	+	0.914717i	$0.367586\pi$
$312$	1.90414e86	1.70359
$313$	−4.81889e85	−0.386071	−0.193036	−	0.981192i	$-0.561833\pi$
$313$	−4.81889e85	−0.386071	−0.193036	+	0.981192i	$0.561833\pi$
$314$	−3.65923e85	−0.262613
$315$	8.27064e85	0.531894
$316$	−2.42466e86	−1.39781
$317$	−1.49602e86	−0.773378	−0.386689	−	0.922210i	$-0.626381\pi$
$317$	−1.49602e86	−0.773378	−0.386689	+	0.922210i	$0.626381\pi$
$318$	3.33579e86	1.54690
$319$	5.72832e86	2.38368
$320$	2.27161e86	0.848516
$321$	−7.31389e85	−0.245315
$322$	−9.99261e86	−3.01059
$323$	−4.61505e83	−0.00124936
$324$	9.64854e85	0.234779
$325$	6.48842e86	1.41959
$326$	−1.54147e87	−3.03338
$327$	3.54625e86	0.627874
$328$	1.63943e87	2.61243
$329$	6.98928e86	1.00271
$330$	−1.35837e87	−1.75504
$331$	1.15925e86	0.134931	0.0674657	−	0.997722i	$-0.478509\pi$
$331$	1.15925e86	0.134931	0.0674657	+	0.997722i	$0.478509\pi$
$332$	−1.97238e87	−2.06884
$333$	−1.52196e86	−0.143906
$334$	−7.34232e86	−0.626009
$335$	−1.85109e87	−1.42358
$336$	−1.28697e87	−0.893021
$337$	−1.51114e87	−0.946398	−0.473199	−	0.880956i	$-0.656901\pi$
$337$	−1.51114e87	−0.946398	−0.473199	+	0.880956i	$0.656901\pi$
$338$	3.92473e87	2.21913
$339$	−3.28317e86	−0.167650
$340$	−1.07810e86	−0.0497322
$341$	−1.70738e87	−0.711711
$342$	−1.15546e86	−0.0435366
$343$	2.31994e87	0.790369
$344$	8.33004e87	2.56673
$345$	−4.30706e87	−1.20067
$346$	7.98988e87	2.01565
$347$	1.91934e87	0.438314	0.219157	−	0.975690i	$-0.429669\pi$
$347$	1.91934e87	0.438314	0.219157	+	0.975690i	$0.429669\pi$
$348$	1.13828e88	2.35378
$349$	−1.87686e87	−0.351524	−0.175762	−	0.984433i	$-0.556239\pi$
$349$	−1.87686e87	−0.351524	−0.175762	+	0.984433i	$0.556239\pi$
$350$	−1.12402e88	−1.90734
$351$	1.88040e87	0.289172
$352$	3.73374e87	0.520501
$353$	−4.55945e87	−0.576348	−0.288174	−	0.957578i	$-0.593048\pi$
$353$	−4.55945e87	−0.576348	−0.288174	+	0.957578i	$0.593048\pi$
$354$	−4.66243e87	−0.534564
$355$	4.08998e87	0.425445
$356$	1.91512e88	1.80788
$357$	−1.30109e86	−0.0111495
$358$	−3.75438e88	−2.92128
$359$	1.86689e88	1.31935	0.659675	−	0.751551i	$-0.270694\pi$
$359$	1.86689e88	1.31935	0.659675	+	0.751551i	$0.270694\pi$
$360$	−1.42180e88	−0.912853
$361$	−1.70456e88	−0.994520
$362$	2.36286e87	0.125312
$363$	6.30190e87	0.303873
$364$	−8.28416e88	−3.63288
$365$	3.26248e88	1.30150
$366$	−2.39875e88	−0.870737
$367$	3.12420e88	1.03219	0.516095	−	0.856531i	$-0.327385\pi$
$367$	3.12420e88	1.03219	0.516095	+	0.856531i	$0.327385\pi$
$368$	6.70207e88	2.01585
$369$	1.61899e88	0.443441
$370$	4.25778e88	1.06224
$371$	−7.64444e88	−1.73758
$372$	−3.39275e88	−0.702782
$373$	−4.34646e88	−0.820694	−0.410347	−	0.911929i	$-0.634592\pi$
$373$	−4.34646e88	−0.820694	−0.410347	+	0.911929i	$0.634592\pi$
$374$	2.13691e87	0.0367889
$375$	2.83233e87	0.0444698
$376$	−1.20152e89	−1.72088
$377$	2.21840e89	2.89910
$378$	−3.25752e88	−0.388526
$379$	9.33495e88	1.01639	0.508194	−	0.861243i	$-0.330313\pi$
$379$	9.33495e88	1.01639	0.508194	+	0.861243i	$0.330313\pi$
$380$	2.19409e88	0.218133
$381$	9.89602e88	0.898564
$382$	−2.96834e88	−0.246223
$383$	−1.30657e89	−0.990322	−0.495161	−	0.868801i	$-0.664891\pi$
$383$	−1.30657e89	−0.990322	−0.495161	+	0.868801i	$0.664891\pi$
$384$	−1.24584e89	−0.863047
$385$	3.11290e89	1.97138
$386$	−5.02010e89	−2.90703
$387$	8.22620e88	0.435684
$388$	4.93573e89	2.39142
$389$	8.24396e88	0.365489	0.182745	−	0.983160i	$-0.441502\pi$
$389$	8.24396e88	0.365489	0.182745	+	0.983160i	$0.441502\pi$
$390$	−5.26054e89	−2.13452
$391$	6.77564e87	0.0251682
$392$	1.78556e89	0.607303
$393$	−1.97242e89	−0.614406
$394$	−3.85892e89	−1.10115
$395$	3.52841e89	0.922528
$396$	3.63151e89	0.870168
$397$	1.95927e89	0.430351	0.215175	−	0.976575i	$-0.430968\pi$
$397$	1.95927e89	0.430351	0.215175	+	0.976575i	$0.430968\pi$
$398$	8.46385e89	1.70452
$399$	2.64791e88	0.0489032
$400$	7.53885e89	1.27713
$401$	7.27279e89	1.13037	0.565184	−	0.824965i	$-0.308805\pi$
$401$	7.27279e89	1.13037	0.565184	+	0.824965i	$0.308805\pi$
$402$	7.29082e89	1.03987
$403$	−6.61214e89	−0.865602
$404$	−1.59718e90	−1.91954
$405$	−1.40407e89	−0.154950
$406$	−3.84305e90	−3.89518
$407$	−5.72836e89	−0.533363
$408$	2.23669e88	0.0191351
$409$	1.69012e89	0.132881	0.0664405	−	0.997790i	$-0.478836\pi$
$409$	1.69012e89	0.132881	0.0664405	+	0.997790i	$0.478836\pi$
$410$	−4.52922e90	−3.27326
$411$	−1.14878e89	−0.0763299
$412$	1.23130e89	0.0752334
$413$	1.06846e90	0.600458
$414$	1.69640e90	0.877037
$415$	2.87025e90	1.36540
$416$	1.44596e90	0.633047
$417$	5.23193e89	0.210847
$418$	−4.34892e89	−0.161361
$419$	−2.89598e90	−0.989491	−0.494745	−	0.869038i	$-0.664739\pi$
$419$	−2.89598e90	−0.989491	−0.494745	+	0.869038i	$0.664739\pi$
$420$	6.18567e90	1.94664
$421$	−1.66190e90	−0.481805	−0.240903	−	0.970549i	$-0.577443\pi$
$421$	−1.66190e90	−0.481805	−0.240903	+	0.970549i	$0.577443\pi$
$422$	8.60463e89	0.229854
$423$	−1.18654e90	−0.292106
$424$	1.31415e91	2.98210
$425$	7.62160e88	0.0159451
$426$	−1.61090e90	−0.310770
$427$	5.49707e90	0.978070
$428$	−5.47011e90	−0.897814
$429$	7.07745e90	1.07177
$430$	−2.30133e91	−3.21600
$431$	9.02329e90	1.16386	0.581928	−	0.813241i	$-0.302299\pi$
$431$	9.02329e90	1.16386	0.581928	+	0.813241i	$0.302299\pi$
$432$	2.18483e90	0.260153
$433$	−3.90248e90	−0.429050	−0.214525	−	0.976718i	$-0.568820\pi$
$433$	−3.90248e90	−0.429050	−0.214525	+	0.976718i	$0.568820\pi$
$434$	1.14546e91	1.16301
$435$	−1.65645e91	−1.55345
$436$	2.65227e91	2.29791
$437$	−1.37894e90	−0.110391
$438$	−1.28498e91	−0.950691
$439$	2.03523e91	1.39184	0.695919	−	0.718121i	$-0.254997\pi$
$439$	2.03523e91	1.39184	0.695919	+	0.718121i	$0.254997\pi$
$440$	−5.35134e91	−3.38334
$441$	1.76331e90	0.103085
$442$	8.27559e89	0.0447436
$443$	3.55938e90	0.178011	0.0890054	−	0.996031i	$-0.471631\pi$
$443$	3.55938e90	0.178011	0.0890054	+	0.996031i	$0.471631\pi$
$444$	−1.13829e91	−0.526672
$445$	−2.78692e91	−1.19317
$446$	−4.69770e91	−1.86137
$447$	2.70862e91	0.993433
$448$	2.05036e91	0.696207
$449$	−2.24070e91	−0.704507	−0.352253	−	0.935905i	$-0.614584\pi$
$449$	−2.24070e91	−0.704507	−0.352253	+	0.935905i	$0.614584\pi$
$450$	1.90821e91	0.555641
$451$	6.09355e91	1.64354
$452$	−2.45551e91	−0.613572
$453$	−1.12018e91	−0.259359
$454$	1.05936e91	0.227308
$455$	1.20553e92	2.39764
$456$	−4.55198e90	−0.0839293
$457$	4.50782e91	0.770650	0.385325	−	0.922781i	$-0.374089\pi$
$457$	4.50782e91	0.770650	0.385325	+	0.922781i	$0.374089\pi$
$458$	1.32779e92	2.10510
$459$	2.20881e89	0.00324804
$460$	−3.22128e92	−4.39424
$461$	−1.32991e92	−1.68322	−0.841609	−	0.540088i	$-0.818391\pi$
$461$	−1.32991e92	−1.68322	−0.841609	+	0.540088i	$0.818391\pi$
$462$	−1.22606e92	−1.44001
$463$	−1.58450e92	−1.72722	−0.863609	−	0.504163i	$-0.831801\pi$
$463$	−1.58450e92	−1.72722	−0.863609	+	0.504163i	$0.831801\pi$
$464$	2.57754e92	2.60817
$465$	4.93720e91	0.463825
$466$	1.89549e92	1.65351
$467$	−4.13498e91	−0.334997	−0.167499	−	0.985872i	$-0.553569\pi$
$467$	−4.13498e91	−0.334997	−0.167499	+	0.985872i	$0.553569\pi$
$468$	1.40637e92	1.05832
$469$	−1.67080e92	−1.16805
$470$	3.31942e92	2.15618
$471$	−1.42360e91	−0.0859342
$472$	−1.83678e92	−1.03053
$473$	3.09617e92	1.61479
$474$	−1.38972e92	−0.673869
$475$	−1.55110e91	−0.0699377
$476$	−9.73097e90	−0.0408053
$477$	1.29777e92	0.506189
$478$	3.92496e92	1.42421
$479$	−4.88540e92	−1.64940	−0.824698	−	0.565573i	$-0.808655\pi$
$479$	−4.88540e92	−1.64940	−0.824698	+	0.565573i	$0.808655\pi$
$480$	−1.07968e92	−0.339212
$481$	−2.21841e92	−0.648690
$482$	9.42394e92	2.56513
$483$	−3.88755e92	−0.985146
$484$	4.71324e92	1.11213
$485$	−7.18256e92	−1.57830
$486$	5.53017e91	0.113184
$487$	9.32954e91	0.177873	0.0889367	−	0.996037i	$-0.471653\pi$
$487$	9.32954e91	0.177873	0.0889367	+	0.996037i	$0.471653\pi$
$488$	−9.44995e92	−1.67859
$489$	−5.99697e92	−0.992605
$490$	−4.93294e92	−0.760924
$491$	−5.04505e92	−0.725361	−0.362680	−	0.931914i	$-0.618138\pi$
$491$	−5.04505e92	−0.725361	−0.362680	+	0.931914i	$0.618138\pi$
$492$	1.21086e93	1.62292
$493$	2.60584e91	0.0325633
$494$	−1.68420e92	−0.196252
$495$	−5.28464e92	−0.574296
$496$	−7.68261e92	−0.778737
$497$	3.69162e92	0.349077
$498$	−1.13049e93	−0.997369
$499$	8.52537e91	0.0701850	0.0350925	−	0.999384i	$-0.488827\pi$
$499$	8.52537e91	0.0701850	0.0350925	+	0.999384i	$0.488827\pi$
$500$	2.11832e92	0.162752
$501$	−2.85648e92	−0.204847
$502$	−9.14480e92	−0.612203
$503$	−8.75642e91	−0.0547307	−0.0273653	−	0.999625i	$-0.508712\pi$
$503$	−8.75642e91	−0.0547307	−0.0273653	+	0.999625i	$0.508712\pi$
$504$	−1.28331e93	−0.748995
$505$	2.32425e93	1.26687
$506$	6.38492e93	3.25059
$507$	1.52689e93	0.726161
$508$	7.40131e93	3.28860
$509$	−3.07352e93	−1.27606	−0.638032	−	0.770010i	$-0.720251\pi$
$509$	−3.07352e93	−1.27606	−0.638032	+	0.770010i	$0.720251\pi$
$510$	−6.17928e91	−0.0239754
$511$	2.94472e93	1.06788
$512$	−6.15086e93	−2.08508
$513$	−4.49524e91	−0.0142464
$514$	1.23519e93	0.366020
$515$	−1.79181e92	−0.0496528
$516$	6.15244e93	1.59453
$517$	−4.46590e93	−1.08264
$518$	3.84307e93	0.871569
$519$	3.10841e93	0.659575
$520$	−2.07241e94	−4.11490
$521$	8.73170e92	0.162255	0.0811274	−	0.996704i	$-0.474148\pi$
$521$	8.73170e92	0.162255	0.0811274	+	0.996704i	$0.474148\pi$
$522$	6.52419e93	1.13473
$523$	−1.74888e93	−0.284743	−0.142371	−	0.989813i	$-0.545473\pi$
$523$	−1.74888e93	−0.284743	−0.142371	+	0.989813i	$0.545473\pi$
$524$	−1.47519e94	−2.24863
$525$	−4.37293e93	−0.624132
$526$	−1.70123e93	−0.227382
$527$	−7.76694e91	−0.00972263
$528$	8.22325e93	0.964213
$529$	1.11413e94	1.22381
$530$	−3.63057e94	−3.73644
$531$	−1.81389e93	−0.174924
$532$	1.98039e93	0.178978
$533$	2.35984e94	1.99892
$534$	1.09767e94	0.871564
$535$	7.96021e93	0.592542
$536$	2.87224e94	2.00464
$537$	−1.46061e94	−0.955922
$538$	4.21987e93	0.259006
$539$	6.63672e93	0.382068
$540$	−1.05012e94	−0.567091
$541$	−1.24256e94	−0.629523	−0.314761	−	0.949171i	$-0.601925\pi$
$541$	−1.24256e94	−0.629523	−0.314761	+	0.949171i	$0.601925\pi$
$542$	6.33814e93	0.301291
$543$	9.19253e92	0.0410054
$544$	1.69849e92	0.00711052
$545$	−3.85963e94	−1.51658
$546$	−4.74816e94	−1.75138
$547$	−1.61111e94	−0.557908	−0.278954	−	0.960304i	$-0.589988\pi$
$547$	−1.61111e94	−0.557908	−0.278954	+	0.960304i	$0.589988\pi$
$548$	−8.59183e93	−0.279355
$549$	−9.33216e93	−0.284929
$550$	7.18210e94	2.05939
$551$	−5.30324e93	−0.142827
$552$	6.68305e94	1.69074
$553$	3.18475e94	0.756934
$554$	−1.79012e94	−0.399756
$555$	1.65646e94	0.347594
$556$	3.91300e94	0.771666
$557$	−7.31844e94	−1.35648	−0.678242	−	0.734839i	$-0.737258\pi$
$557$	−7.31844e94	−1.35648	−0.678242	+	0.734839i	$0.737258\pi$
$558$	−1.94460e94	−0.338805
$559$	1.19905e95	1.96395
$560$	1.40069e95	2.15703
$561$	8.31351e92	0.0120383
$562$	−2.15093e95	−2.92902
$563$	1.58652e94	0.203192	0.101596	−	0.994826i	$-0.467605\pi$
$563$	1.58652e94	0.203192	0.101596	+	0.994826i	$0.467605\pi$
$564$	−8.87425e94	−1.06906
$565$	3.57330e94	0.404947
$566$	4.60450e94	0.490925
$567$	−1.26732e94	−0.127136
$568$	−6.34622e94	−0.599097
$569$	−1.58138e95	−1.40495	−0.702477	−	0.711706i	$-0.747923\pi$
$569$	−1.58138e95	−1.40495	−0.702477	+	0.711706i	$0.747923\pi$
$570$	1.25757e94	0.105160
$571$	1.01458e95	0.798622	0.399311	−	0.916816i	$-0.369249\pi$
$571$	1.01458e95	0.798622	0.399311	+	0.916816i	$0.369249\pi$
$572$	5.29328e95	3.92249
$573$	−1.15481e94	−0.0805707
$574$	−4.08808e95	−2.68571
$575$	2.27727e95	1.40888
$576$	−3.48081e94	−0.202817
$577$	3.04636e95	1.67192	0.835960	−	0.548790i	$-0.184911\pi$
$577$	3.04636e95	1.67192	0.835960	+	0.548790i	$0.184911\pi$
$578$	−3.41175e95	−1.76387
$579$	−1.95303e95	−0.951260
$580$	−1.23887e96	−5.68539
$581$	2.59069e95	1.12031
$582$	2.82897e95	1.15288
$583$	4.88452e95	1.87610
$584$	−5.06223e95	−1.83273
$585$	−2.04658e95	−0.698474
$586$	−2.44024e95	−0.785171
$587$	−1.13468e95	−0.344238	−0.172119	−	0.985076i	$-0.555061\pi$
$587$	−1.13468e95	−0.344238	−0.172119	+	0.985076i	$0.555061\pi$
$588$	1.31879e95	0.377275
$589$	1.58068e94	0.0426449
$590$	5.07445e95	1.29120
$591$	−1.50129e95	−0.360326
$592$	−2.57756e95	−0.583593
$593$	7.57763e94	0.161863	0.0809313	−	0.996720i	$-0.474211\pi$
$593$	7.57763e94	0.161863	0.0809313	+	0.996720i	$0.474211\pi$
$594$	2.08144e95	0.419500
$595$	1.41607e94	0.0269308
$596$	2.02580e96	3.63580
$597$	3.29280e95	0.557765
$598$	2.47268e96	3.95345
$599$	−5.96172e95	−0.899801	−0.449901	−	0.893079i	$-0.648541\pi$
$599$	−5.96172e95	−0.899801	−0.449901	+	0.893079i	$0.648541\pi$
$600$	7.51745e95	1.07116
$601$	−4.26513e95	−0.573804	−0.286902	−	0.957960i	$-0.592625\pi$
$601$	−4.26513e95	−0.573804	−0.286902	+	0.957960i	$0.592625\pi$
$602$	−2.07718e96	−2.63873
$603$	2.83644e95	0.340272
$604$	−8.37795e95	−0.949212
$605$	−6.85879e95	−0.733985
$606$	−9.15444e95	−0.925393
$607$	1.79258e96	1.71186	0.855931	−	0.517091i	$-0.172985\pi$
$607$	1.79258e96	1.71186	0.855931	+	0.517091i	$0.172985\pi$
$608$	−3.45667e94	−0.0311878
$609$	−1.49511e96	−1.27461
$610$	2.61072e96	2.10320
$611$	−1.72950e96	−1.31674
$612$	1.65199e94	0.0118873
$613$	2.69155e96	1.83069	0.915346	−	0.402668i	$-0.131917\pi$
$613$	2.69155e96	1.83069	0.915346	+	0.402668i	$0.131917\pi$
$614$	−2.48226e96	−1.59602
$615$	−1.76206e96	−1.07110
$616$	−4.83012e96	−2.77603
$617$	1.28215e96	0.696789	0.348394	−	0.937348i	$-0.386727\pi$
$617$	1.28215e96	0.696789	0.348394	+	0.937348i	$0.386727\pi$
$618$	7.05735e94	0.0362693
$619$	−3.62718e96	−1.76296	−0.881479	−	0.472223i	$-0.843452\pi$
$619$	−3.62718e96	−1.76296	−0.881479	+	0.472223i	$0.843452\pi$
$620$	3.69257e96	1.69752
$621$	6.59975e95	0.286990
$622$	3.46635e96	1.42595
$623$	−2.51547e96	−0.978998
$624$	3.18461e96	1.17270
$625$	−3.01961e96	−1.05218
$626$	−2.06572e96	−0.681173
$627$	−1.69192e95	−0.0528018
$628$	−1.06472e96	−0.314505
$629$	−2.60585e94	−0.00728623
$630$	3.54539e96	0.938458
$631$	5.56599e96	1.39486	0.697428	−	0.716655i	$-0.254328\pi$
$631$	5.56599e96	1.39486	0.697428	+	0.716655i	$0.254328\pi$
$632$	−5.47486e96	−1.29907
$633$	3.34757e95	0.0752145
$634$	−6.41300e96	−1.36453
$635$	−1.07705e97	−2.17042
$636$	9.70610e96	1.85257
$637$	2.57019e96	0.464681
$638$	2.45557e97	4.20570
$639$	−6.26711e95	−0.101692
$640$	1.35593e97	2.08463
$641$	3.43716e96	0.500723	0.250361	−	0.968152i	$-0.419451\pi$
$641$	3.43716e96	0.500723	0.250361	+	0.968152i	$0.419451\pi$
$642$	−3.13526e96	−0.432827
$643$	−7.73727e96	−1.01230	−0.506150	−	0.862446i	$-0.668932\pi$
$643$	−7.73727e96	−1.01230	−0.506150	+	0.862446i	$0.668932\pi$
$644$	−2.90753e97	−3.60547
$645$	−8.95315e96	−1.05236
$646$	−1.97834e94	−0.00220434
$647$	−1.05926e97	−1.11894	−0.559469	−	0.828851i	$-0.688995\pi$
$647$	−1.05926e97	−1.11894	−0.559469	+	0.828851i	$0.688995\pi$
$648$	2.17863e96	0.218195
$649$	−6.82710e96	−0.648327
$650$	2.78140e97	2.50468
$651$	4.45632e96	0.380568
$652$	−4.48518e97	−3.63277
$653$	1.60344e97	1.23182	0.615911	−	0.787816i	$-0.288788\pi$
$653$	1.60344e97	1.23182	0.615911	+	0.787816i	$0.288788\pi$
$654$	1.52018e97	1.10780
$655$	2.14672e97	1.48406
$656$	2.74189e97	1.79832
$657$	−4.99913e96	−0.311092
$658$	2.99611e97	1.76915
$659$	1.97541e97	1.10691	0.553454	−	0.832880i	$-0.313310\pi$
$659$	1.97541e97	1.10691	0.553454	+	0.832880i	$0.313310\pi$
$660$	−3.95242e97	−2.10183
$661$	8.88677e96	0.448532	0.224266	−	0.974528i	$-0.428001\pi$
$661$	8.88677e96	0.448532	0.224266	+	0.974528i	$0.428001\pi$
$662$	4.96940e96	0.238069
$663$	3.21956e95	0.0146413
$664$	−4.45362e97	−1.92271
$665$	−2.88190e96	−0.118122
$666$	−6.52423e96	−0.253903
$667$	7.78602e97	2.87723
$668$	−2.13638e97	−0.749707
$669$	−1.82761e97	−0.609090
$670$	−7.93510e97	−2.51172
$671$	−3.51243e97	−1.05604
$672$	−9.74518e96	−0.278324
$673$	4.14286e96	0.112404	0.0562018	−	0.998419i	$-0.482101\pi$
$673$	4.14286e96	0.112404	0.0562018	+	0.998419i	$0.482101\pi$
$674$	−6.47784e97	−1.66980
$675$	7.42375e96	0.181821
$676$	1.14197e98	2.65763
$677$	−6.09855e97	−1.34871	−0.674353	−	0.738409i	$-0.735577\pi$
$677$	−6.09855e97	−1.34871	−0.674353	+	0.738409i	$0.735577\pi$
$678$	−1.40740e97	−0.295797
$679$	−6.48299e97	−1.29499
$680$	−2.43435e96	−0.0462195
$681$	4.12135e96	0.0743814
$682$	−7.31905e97	−1.25572
$683$	3.38375e97	0.551929	0.275965	−	0.961168i	$-0.411003\pi$
$683$	3.38375e97	0.551929	0.275965	+	0.961168i	$0.411003\pi$
$684$	−3.36203e96	−0.0521394
$685$	1.25030e97	0.184370
$686$	9.94493e97	1.39450
$687$	5.16569e97	0.688845
$688$	1.39317e98	1.76686
$689$	1.89162e98	2.28177
$690$	−1.84632e98	−2.11842
$691$	−1.20829e98	−1.31880	−0.659399	−	0.751793i	$-0.729189\pi$
$691$	−1.20829e98	−1.31880	−0.659399	+	0.751793i	$0.729189\pi$
$692$	2.32480e98	2.41394
$693$	−4.76992e97	−0.471210
$694$	8.22767e97	0.773348
$695$	−5.69427e97	−0.509287
$696$	2.57023e98	2.18752
$697$	2.77198e96	0.0224522
$698$	−8.04557e97	−0.620219
$699$	7.37427e97	0.541074
$700$	−3.27055e98	−2.28422
$701$	3.80821e97	0.253191	0.126596	−	0.991954i	$-0.459595\pi$
$701$	3.80821e97	0.253191	0.126596	+	0.991954i	$0.459595\pi$
$702$	8.06077e97	0.510206
$703$	5.30328e96	0.0319584
$704$	−1.31011e98	−0.751708
$705$	1.29140e98	0.705562
$706$	−1.95451e98	−1.01689
$707$	2.09787e98	1.03946
$708$	−1.35662e98	−0.640193
$709$	−4.54779e97	−0.204411	−0.102206	−	0.994763i	$-0.532590\pi$
$709$	−4.54779e97	−0.204411	−0.102206	+	0.994763i	$0.532590\pi$
$710$	1.75326e98	0.750642
$711$	−5.40662e97	−0.220508
$712$	4.32432e98	1.68019
$713$	−2.32070e98	−0.859072
$714$	−5.57742e96	−0.0196718
$715$	−7.70288e98	−2.58878
$716$	−1.09240e99	−3.49852
$717$	1.52698e98	0.466039
$718$	8.00283e98	2.32782
$719$	−2.65984e98	−0.737411	−0.368705	−	0.929546i	$-0.620199\pi$
$719$	−2.65984e98	−0.737411	−0.368705	+	0.929546i	$0.620199\pi$
$720$	−2.37790e98	−0.628381
$721$	−1.61729e97	−0.0407401
$722$	−7.30696e98	−1.75470
$723$	3.66632e98	0.839381
$724$	6.87516e97	0.150073
$725$	8.75813e98	1.82285
$726$	2.70144e98	0.536146
$727$	6.20908e98	1.17514	0.587570	−	0.809173i	$-0.300085\pi$
$727$	6.20908e98	1.17514	0.587570	+	0.809173i	$0.300085\pi$
$728$	−1.87056e99	−3.37628
$729$	2.15147e97	0.0370370
$730$	1.39853e99	2.29633
$731$	1.40846e97	0.0220595
$732$	−6.97960e98	−1.04279
$733$	1.69381e97	0.0241422	0.0120711	−	0.999927i	$-0.496158\pi$
$733$	1.69381e97	0.0241422	0.0120711	+	0.999927i	$0.496158\pi$
$734$	1.33926e99	1.82117
$735$	−1.91913e98	−0.248995
$736$	5.07495e98	0.628271
$737$	1.06758e99	1.26116
$738$	6.94017e98	0.782394
$739$	1.35143e99	1.45399	0.726994	−	0.686643i	$-0.240917\pi$
$739$	1.35143e99	1.45399	0.726994	+	0.686643i	$0.240917\pi$
$740$	1.23888e99	1.27214
$741$	−6.55226e97	−0.0642189
$742$	−3.27696e99	−3.06574
$743$	−4.50753e98	−0.402554	−0.201277	−	0.979534i	$-0.564509\pi$
$743$	−4.50753e98	−0.402554	−0.201277	+	0.979534i	$0.564509\pi$
$744$	−7.66080e98	−0.653143
$745$	−2.94798e99	−2.39957
$746$	−1.86321e99	−1.44801
$747$	−4.39811e98	−0.326366
$748$	6.21774e97	0.0440583
$749$	7.18489e98	0.486180
$750$	1.21414e98	0.0784613
$751$	1.20159e99	0.741617	0.370808	−	0.928709i	$-0.379081\pi$
$751$	1.20159e99	0.741617	0.370808	+	0.928709i	$0.379081\pi$
$752$	−2.00950e99	−1.18460
$753$	−3.55772e98	−0.200330
$754$	9.50965e99	5.11509
$755$	1.21917e99	0.626464
$756$	−9.47836e98	−0.465298
$757$	−3.41198e99	−1.60029	−0.800144	−	0.599808i	$-0.795244\pi$
$757$	−3.41198e99	−1.60029	−0.800144	+	0.599808i	$0.795244\pi$
$758$	4.00163e99	1.79328
$759$	2.48401e99	1.06368
$760$	4.95424e98	0.202725
$761$	−3.15412e99	−1.23341	−0.616704	−	0.787195i	$-0.711533\pi$
$761$	−3.15412e99	−1.23341	−0.616704	+	0.787195i	$0.711533\pi$
$762$	4.24214e99	1.58540
$763$	−3.48371e99	−1.24436
$764$	−8.63693e98	−0.294876
$765$	−2.40400e97	−0.00784541
$766$	−5.60091e99	−1.74730
$767$	−2.64392e99	−0.788512
$768$	−4.10851e99	−1.17145
$769$	−2.01292e99	−0.548742	−0.274371	−	0.961624i	$-0.588470\pi$
$769$	−2.01292e99	−0.548742	−0.274371	+	0.961624i	$0.588470\pi$
$770$	1.33441e100	3.47824
$771$	4.80541e98	0.119772
$772$	−1.46069e100	−3.48146
$773$	−5.80485e99	−1.32312	−0.661558	−	0.749894i	$-0.730105\pi$
$773$	−5.80485e99	−1.32312	−0.661558	+	0.749894i	$0.730105\pi$
$774$	3.52634e99	0.768708
$775$	−2.61044e99	−0.544259
$776$	1.11448e100	2.22251
$777$	1.49512e99	0.285201
$778$	3.53395e99	0.644859
$779$	−5.64138e98	−0.0984788
$780$	−1.53065e100	−2.55630
$781$	−2.35881e99	−0.376906
$782$	2.90452e98	0.0444060
$783$	2.53819e99	0.371316
$784$	2.98629e99	0.418049
$785$	1.54940e99	0.207568
$786$	−8.45519e99	−1.08404
$787$	8.33657e99	1.02296	0.511480	−	0.859295i	$-0.329097\pi$
$787$	8.33657e99	1.02296	0.511480	+	0.859295i	$0.329097\pi$
$788$	−1.12282e100	−1.31873
$789$	−6.61852e98	−0.0744054
$790$	1.51253e100	1.62768
$791$	3.22526e99	0.332259
$792$	8.19991e99	0.808705
$793$	−1.36025e100	−1.28439
$794$	8.39885e99	0.759298
$795$	−1.41245e100	−1.22266
$796$	2.46271e100	2.04133
$797$	1.96662e100	1.56102	0.780508	−	0.625145i	$-0.214960\pi$
$797$	1.96662e100	1.56102	0.780508	+	0.625145i	$0.214960\pi$
$798$	1.13508e99	0.0862835
$799$	−2.03156e98	−0.0147899
$800$	5.70858e99	0.398037
$801$	4.27042e99	0.285199
$802$	3.11764e100	1.99439
$803$	−1.88157e100	−1.15301
$804$	2.12140e100	1.24534
$805$	4.23110e100	2.37955
$806$	−2.83444e100	−1.52724
$807$	1.64171e99	0.0847539
$808$	−3.60642e100	−1.78396
$809$	2.62199e99	0.124282	0.0621408	−	0.998067i	$-0.480207\pi$
$809$	2.62199e99	0.124282	0.0621408	+	0.998067i	$0.480207\pi$
$810$	−6.01887e99	−0.273389
$811$	−3.75645e99	−0.163515	−0.0817576	−	0.996652i	$-0.526053\pi$
$811$	−3.75645e99	−0.163515	−0.0817576	+	0.996652i	$0.526053\pi$
$812$	−1.11821e101	−4.66486
$813$	2.46581e99	0.0985906
$814$	−2.45558e100	−0.941051
$815$	6.52692e100	2.39757
$816$	3.74079e98	0.0131720
$817$	−2.86642e99	−0.0967562
$818$	7.24506e99	0.234452
$819$	−1.84724e100	−0.573098
$820$	−1.31786e101	−3.92005
$821$	−2.68505e100	−0.765796	−0.382898	−	0.923791i	$-0.625074\pi$
$821$	−2.68505e100	−0.765796	−0.382898	+	0.923791i	$0.625074\pi$
$822$	−4.92450e99	−0.134674
$823$	2.66214e100	0.698131	0.349065	−	0.937098i	$-0.386499\pi$
$823$	2.66214e100	0.698131	0.349065	+	0.937098i	$0.386499\pi$
$824$	2.78027e99	0.0699194
$825$	2.79415e100	0.673888
$826$	4.58020e100	1.05943
$827$	−1.03882e100	−0.230463	−0.115231	−	0.993339i	$-0.536761\pi$
$827$	−1.03882e100	−0.230463	−0.115231	+	0.993339i	$0.536761\pi$
$828$	4.93600e100	1.05034
$829$	3.00951e100	0.614278	0.307139	−	0.951665i	$-0.400628\pi$
$829$	3.00951e100	0.614278	0.307139	+	0.951665i	$0.400628\pi$
$830$	1.23040e101	2.40908
$831$	−6.96433e99	−0.130811
$832$	−5.07363e100	−0.914247
$833$	3.01907e98	0.00521940
$834$	2.24278e100	0.372013
$835$	3.10891e100	0.494794
$836$	−1.26540e100	−0.193246
$837$	−7.56531e99	−0.110866
$838$	−1.24143e101	−1.74583
$839$	−7.14754e100	−0.964648	−0.482324	−	0.875993i	$-0.660207\pi$
$839$	−7.14754e100	−0.964648	−0.482324	+	0.875993i	$0.660207\pi$
$840$	1.39672e101	1.80915
$841$	2.19004e101	2.72264
$842$	−7.12408e100	−0.850083
$843$	−8.36803e100	−0.958455
$844$	2.50367e100	0.275273
$845$	−1.66182e101	−1.75399
$846$	−5.08637e100	−0.515384
$847$	−6.19075e100	−0.602234
$848$	2.19786e101	2.05279
$849$	1.79135e100	0.160644
$850$	3.26717e99	0.0281331
$851$	−7.78607e100	−0.643796
$852$	−4.68722e100	−0.372177
$853$	1.60020e101	1.22021	0.610103	−	0.792322i	$-0.291128\pi$
$853$	1.60020e101	1.22021	0.610103	+	0.792322i	$0.291128\pi$
$854$	2.35644e101	1.72568
$855$	4.89249e99	0.0344111
$856$	−1.23515e101	−0.834398
$857$	5.84263e100	0.379114	0.189557	−	0.981870i	$-0.439295\pi$
$857$	5.84263e100	0.379114	0.189557	+	0.981870i	$0.439295\pi$
$858$	3.03390e101	1.89100
$859$	−1.39086e101	−0.832760	−0.416380	−	0.909191i	$-0.636701\pi$
$859$	−1.39086e101	−0.832760	−0.416380	+	0.909191i	$0.636701\pi$
$860$	−6.69613e101	−3.85148
$861$	−1.59044e101	−0.878837
$862$	3.86803e101	2.05347
$863$	3.45201e101	1.76076	0.880378	−	0.474272i	$-0.157289\pi$
$863$	3.45201e101	1.76076	0.880378	+	0.474272i	$0.157289\pi$
$864$	1.65440e100	0.0810805
$865$	−3.38310e101	−1.59316
$866$	−1.67288e101	−0.757004
$867$	−1.32732e101	−0.577186
$868$	3.33292e101	1.39282
$869$	−2.03494e101	−0.817277
$870$	−7.10073e101	−2.74087
$871$	4.13440e101	1.53386
$872$	5.98880e101	2.13561
$873$	1.10059e101	0.377255
$874$	−5.91112e100	−0.194771
$875$	−2.78238e100	−0.0881329
$876$	−3.73889e101	−1.13855
$877$	−3.30378e101	−0.967221	−0.483610	−	0.875283i	$-0.660675\pi$
$877$	−3.30378e101	−0.967221	−0.483610	+	0.875283i	$0.660675\pi$
$878$	8.72447e101	2.45572
$879$	−9.49358e100	−0.256929
$880$	−8.94993e101	−2.32899
$881$	5.07976e101	1.27108	0.635542	−	0.772067i	$-0.280777\pi$
$881$	5.07976e101	1.27108	0.635542	+	0.772067i	$0.280777\pi$
$882$	7.55879e100	0.181881
$883$	4.42021e101	1.02282	0.511409	−	0.859338i	$-0.329124\pi$
$883$	4.42021e101	1.02282	0.511409	+	0.859338i	$0.329124\pi$
$884$	2.40794e100	0.0535848
$885$	1.97418e101	0.422517
$886$	1.52581e101	0.314077
$887$	−8.55007e101	−1.69280	−0.846398	−	0.532551i	$-0.821234\pi$
$887$	−8.55007e101	−1.69280	−0.846398	+	0.532551i	$0.821234\pi$
$888$	−2.57024e101	−0.489471
$889$	−9.72148e101	−1.78083
$890$	−1.19467e102	−2.10520
$891$	8.09770e100	0.137272
$892$	−1.36688e102	−2.22917
$893$	4.13450e100	0.0648706
$894$	1.16111e102	1.75279
$895$	1.58969e102	2.30896
$896$	1.22387e102	1.71044
$897$	9.61978e101	1.29368
$898$	−9.60525e101	−1.24301
$899$	−8.92514e101	−1.11149
$900$	5.55228e101	0.665434
$901$	2.22199e100	0.0256293
$902$	2.61214e102	2.89981
$903$	−8.08112e101	−0.863464
$904$	−5.54451e101	−0.570233
$905$	−1.00049e101	−0.0990456
$906$	−4.80191e101	−0.457606
$907$	−1.35223e102	−1.24051	−0.620253	−	0.784402i	$-0.712970\pi$
$907$	−1.35223e102	−1.24051	−0.620253	+	0.784402i	$0.712970\pi$
$908$	3.08239e101	0.272224
$909$	−3.56147e101	−0.302814
$910$	5.16775e102	4.23033
$911$	7.78436e101	0.613535	0.306767	−	0.951785i	$-0.400753\pi$
$911$	7.78436e101	0.613535	0.306767	+	0.951785i	$0.400753\pi$
$912$	−7.61303e100	−0.0577744
$913$	−1.65536e102	−1.20962
$914$	1.93237e102	1.35971
$915$	1.01568e102	0.688226
$916$	3.86346e102	2.52106
$917$	1.93763e102	1.21767
$918$	9.46856e99	0.00573075
$919$	−4.38204e101	−0.255441	−0.127721	−	0.991810i	$-0.540766\pi$
$919$	−4.38204e101	−0.255441	−0.127721	+	0.991810i	$0.540766\pi$
$920$	−7.27363e102	−4.08386
$921$	−9.65708e101	−0.522262
$922$	−5.70095e102	−2.96982
$923$	−9.13494e101	−0.458402
$924$	−3.56746e102	−1.72455
$925$	−8.75819e101	−0.407873
$926$	−6.79229e102	−3.04745
$927$	2.74561e100	0.0118683
$928$	1.95177e102	0.812875
$929$	−6.99250e100	−0.0280602	−0.0140301	−	0.999902i	$-0.504466\pi$
$929$	−6.99250e100	−0.0280602	−0.0140301	+	0.999902i	$0.504466\pi$
$930$	2.11644e102	0.818359
$931$	−6.14423e100	−0.0228930
$932$	5.51528e102	1.98024
$933$	1.34856e102	0.466609
$934$	−1.77255e102	−0.591059
$935$	−9.04817e100	−0.0290777
$936$	3.17557e102	0.983569
$937$	−1.77154e102	−0.528852	−0.264426	−	0.964406i	$-0.585182\pi$
$937$	−1.77154e102	−0.528852	−0.264426	+	0.964406i	$0.585182\pi$
$938$	−7.16223e102	−2.06087
$939$	−8.03655e101	−0.222898
$940$	9.65846e102	2.58224
$941$	−4.03005e102	−1.03865	−0.519324	−	0.854578i	$-0.673816\pi$
$941$	−4.03005e102	−1.03865	−0.519324	+	0.854578i	$0.673816\pi$
$942$	−6.10256e101	−0.151620
$943$	8.28245e102	1.98384
$944$	−3.07195e102	−0.709383
$945$	1.37931e102	0.307089
$946$	1.32724e103	2.84909
$947$	−4.21960e101	−0.0873368	−0.0436684	−	0.999046i	$-0.513905\pi$
$947$	−4.21960e101	−0.0873368	−0.0436684	+	0.999046i	$0.513905\pi$
$948$	−4.04365e102	−0.807023
$949$	−7.28672e102	−1.40232
$950$	−6.64914e101	−0.123396
$951$	−2.49493e102	−0.446510
$952$	−2.19724e101	−0.0379231
$953$	2.68329e102	0.446644	0.223322	−	0.974745i	$-0.428310\pi$
$953$	2.68329e102	0.446644	0.223322	+	0.974745i	$0.428310\pi$
$954$	5.56316e102	0.893105
$955$	1.25686e102	0.194613
$956$	1.14204e103	1.70562
$957$	9.55322e102	1.37622
$958$	−2.09423e103	−2.91015
$959$	1.12852e102	0.151275
$960$	3.78841e102	0.489891
$961$	−5.35576e102	−0.668135
$962$	−9.50971e102	−1.14453
$963$	−1.21975e102	−0.141633
$964$	2.74207e103	3.07200
$965$	2.12562e103	2.29770
$966$	−1.66649e103	−1.73816
$967$	−1.48385e103	−1.49340	−0.746699	−	0.665162i	$-0.768363\pi$
$967$	−1.48385e103	−1.49340	−0.746699	+	0.665162i	$0.768363\pi$
$968$	1.06424e103	1.03357
$969$	−7.69660e99	−0.000721321 0
$970$	−3.07896e103	−2.78471
$971$	−5.58536e102	−0.487515	−0.243758	−	0.969836i	$-0.578380\pi$
$971$	−5.58536e102	−0.487515	−0.243758	+	0.969836i	$0.578380\pi$
$972$	1.60910e102	0.135549
$973$	−5.13965e102	−0.417870
$974$	3.99931e102	0.313835
$975$	1.08209e103	0.819600
$976$	−1.58047e103	−1.15549
$977$	7.51754e102	0.530534	0.265267	−	0.964175i	$-0.414540\pi$
$977$	7.51754e102	0.530534	0.265267	+	0.964175i	$0.414540\pi$
$978$	−2.57073e103	−1.75132
$979$	1.60730e103	1.05704
$980$	−1.43533e103	−0.911281
$981$	5.91415e102	0.362503
$982$	−2.16267e103	−1.27981
$983$	1.05747e103	0.604186	0.302093	−	0.953279i	$-0.402315\pi$
$983$	1.05747e103	0.604186	0.302093	+	0.953279i	$0.402315\pi$
$984$	2.73410e103	1.50829
$985$	1.63395e103	0.870342
$986$	1.11705e102	0.0574538
$987$	1.16562e103	0.578913
$988$	−4.90049e102	−0.235031
$989$	4.20837e103	1.94913
$990$	−2.26538e103	−1.01327
$991$	1.61452e103	0.697433	0.348717	−	0.937228i	$-0.386618\pi$
$991$	1.61452e103	0.697433	0.348717	+	0.937228i	$0.386618\pi$
$992$	−5.81744e102	−0.242705
$993$	1.93331e102	0.0779027
$994$	1.58249e103	0.615902
$995$	−3.58378e103	−1.34724
$996$	−3.28938e103	−1.19445
$997$	−1.36566e103	−0.479028	−0.239514	−	0.970893i	$-0.576988\pi$
$997$	−1.36566e103	−0.479028	−0.239514	+	0.970893i	$0.576988\pi$
$998$	3.65458e102	0.123832
$999$	−2.53821e102	−0.0830840

Twists

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

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

\(f(q)\)	\(=\)	\(q+4.28672e10 q^{2} +1.66772e16 q^{3} +1.24730e21 q^{4} -1.81509e24 q^{5} +7.14904e26 q^{6} -1.63830e29 q^{7} +2.81639e31 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q+4.28672e10 q^{2} +1.66772e16 q^{3} +1.24730e21 q^{4} -1.81509e24 q^{5} +7.14904e26 q^{6} -1.63830e29 q^{7} +2.81639e31 q^{8} +2.78128e32 q^{9} -7.78079e34 q^{10} +1.04682e36 q^{11} +2.08014e37 q^{12} +4.05400e38 q^{13} -7.02295e39 q^{14} -3.02706e40 q^{15} +4.71031e41 q^{16} +4.76202e40 q^{17} +1.19226e43 q^{18} -9.69137e42 q^{19} -2.26397e45 q^{20} -2.73223e45 q^{21} +4.48741e46 q^{22} +1.42285e47 q^{23} +4.69694e47 q^{24} +1.60050e48 q^{25} +1.73783e49 q^{26} +4.63840e48 q^{27} -2.04346e50 q^{28} +5.47213e50 q^{29} -1.29762e51 q^{30} -1.63102e51 q^{31} +3.56675e51 q^{32} +1.74580e52 q^{33} +2.04134e51 q^{34} +2.97368e53 q^{35} +3.46909e53 q^{36} -5.47216e53 q^{37} -4.15442e53 q^{38} +6.76092e54 q^{39} -5.11201e55 q^{40} +5.82103e55 q^{41} -1.17123e56 q^{42} +2.95770e56 q^{43} +1.30570e57 q^{44} -5.04829e56 q^{45} +6.09936e57 q^{46} -4.26617e57 q^{47} +7.85547e57 q^{48} +6.33990e57 q^{49} +6.86089e58 q^{50} +7.94170e56 q^{51} +5.05655e59 q^{52} +4.66607e59 q^{53} +1.98835e59 q^{54} -1.90007e60 q^{55} -4.61410e60 q^{56} -1.61625e59 q^{57} +2.34575e61 q^{58} -6.52176e60 q^{59} -3.77566e61 q^{60} -3.35534e61 q^{61} -6.99172e61 q^{62} -4.55659e61 q^{63} -1.25151e62 q^{64} -7.35838e62 q^{65} +7.48374e62 q^{66} +1.01983e63 q^{67} +5.93966e61 q^{68} +2.37291e63 q^{69} +1.27473e64 q^{70} -2.25332e63 q^{71} +7.83318e63 q^{72} -1.79742e64 q^{73} -2.34576e64 q^{74} +2.66918e64 q^{75} -1.20880e64 q^{76} -1.71501e65 q^{77} +2.89822e65 q^{78} -1.94393e65 q^{79} -8.54966e65 q^{80} +7.73554e64 q^{81} +2.49531e66 q^{82} -1.58132e66 q^{83} -3.40791e66 q^{84} -8.64351e64 q^{85} +1.26788e67 q^{86} +9.12597e66 q^{87} +2.94825e67 q^{88} +1.53541e67 q^{89} -2.16406e67 q^{90} -6.64168e67 q^{91} +1.77472e68 q^{92} -2.72008e67 q^{93} -1.82879e68 q^{94} +1.75908e67 q^{95} +5.94833e67 q^{96} +3.95713e68 q^{97} +2.71774e68 q^{98} +2.91150e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

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Groups

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