LMFDB - Embedded newform 3.70.a.b.1.3

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			1.3
Root			$4.68489e8$ 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)

$f(q)$	$=$	$q-5.14931e9 q^{2} +1.66772e16 q^{3} -5.63780e20 q^{4} +5.32454e23 q^{5} -8.58759e25 q^{6} +1.60190e29 q^{7} +5.94269e30 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q-5.14931e9 q^{2} +1.66772e16 q^{3} -5.63780e20 q^{4} +5.32454e23 q^{5} -8.58759e25 q^{6} +1.60190e29 q^{7} +5.94269e30 q^{8} +2.78128e32 q^{9} -2.74177e33 q^{10} +8.01269e35 q^{11} -9.40227e36 q^{12} +4.97458e38 q^{13} -8.24868e38 q^{14} +8.87984e39 q^{15} +3.02197e41 q^{16} -3.55776e42 q^{17} -1.43217e42 q^{18} +1.29809e44 q^{19} -3.00187e44 q^{20} +2.67152e45 q^{21} -4.12598e45 q^{22} -1.58861e47 q^{23} +9.91073e46 q^{24} -1.41056e48 q^{25} -2.56156e48 q^{26} +4.63840e48 q^{27} -9.03120e49 q^{28} +5.31660e50 q^{29} -4.57250e49 q^{30} +3.63108e51 q^{31} -5.06405e51 q^{32} +1.33629e52 q^{33} +1.83200e52 q^{34} +8.52939e52 q^{35} -1.56803e53 q^{36} -6.48838e53 q^{37} -6.68425e53 q^{38} +8.29619e54 q^{39} +3.16421e54 q^{40} -5.06527e55 q^{41} -1.37565e55 q^{42} +3.76782e55 q^{43} -4.51740e56 q^{44} +1.48091e56 q^{45} +8.18022e56 q^{46} -1.66171e55 q^{47} +5.03979e57 q^{48} +5.16034e57 q^{49} +7.26340e57 q^{50} -5.93334e58 q^{51} -2.80457e59 q^{52} +7.77253e58 q^{53} -2.38845e58 q^{54} +4.26639e59 q^{55} +9.51960e59 q^{56} +2.16484e60 q^{57} -2.73768e60 q^{58} -2.15460e59 q^{59} -5.00628e60 q^{60} +1.95680e61 q^{61} -1.86976e61 q^{62} +4.45534e61 q^{63} -1.52309e62 q^{64} +2.64873e62 q^{65} -6.88097e61 q^{66} -5.83429e62 q^{67} +2.00580e63 q^{68} -2.64935e63 q^{69} -4.39204e62 q^{70} -5.86844e62 q^{71} +1.65283e63 q^{72} +1.18218e64 q^{73} +3.34107e63 q^{74} -2.35241e64 q^{75} -7.31836e64 q^{76} +1.28355e65 q^{77} -4.27196e64 q^{78} +9.48481e64 q^{79} +1.60906e65 q^{80} +7.73554e64 q^{81} +2.60826e65 q^{82} +2.22522e66 q^{83} -1.50615e66 q^{84} -1.89434e66 q^{85} -1.94017e65 q^{86} +8.86660e66 q^{87} +4.76169e66 q^{88} -2.87703e67 q^{89} -7.62564e65 q^{90} +7.96878e67 q^{91} +8.95626e67 q^{92} +6.05563e67 q^{93} +8.55663e64 q^{94} +6.91172e67 q^{95} -8.44540e67 q^{96} +4.12944e68 q^{97} -2.65722e67 q^{98} +2.22856e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.14931e9	−0.211940	−0.105970	−	0.994369i	$-0.533795\pi$
$2$	−5.14931e9	−0.211940	−0.105970	+	0.994369i	$0.533795\pi$
$3$	1.66772e16	0.577350
$3$	1.66772e16	0.577350
$4$	−5.63780e20	−0.955081
$5$	5.32454e23	0.409088	0.204544	−	0.978857i	$-0.434429\pi$
$5$	5.32454e23	0.409088	0.204544	+	0.978857i	$0.434429\pi$
$6$	−8.58759e25	−0.122364
$7$	1.60190e29	1.11880	0.559401	−	0.828897i	$-0.311031\pi$
$7$	1.60190e29	1.11880	0.559401	+	0.828897i	$0.311031\pi$
$8$	5.94269e30	0.414361
$9$	2.78128e32	0.333333
$10$	−2.74177e33	−0.0867024
$11$	8.01269e35	0.945651	0.472825	−	0.881156i	$-0.343234\pi$
$11$	8.01269e35	0.945651	0.472825	+	0.881156i	$0.343234\pi$
$12$	−9.40227e36	−0.551416
$13$	4.97458e38	1.84379	0.921893	−	0.387445i	$-0.126642\pi$
$13$	4.97458e38	1.84379	0.921893	+	0.387445i	$0.126642\pi$
$14$	−8.24868e38	−0.237119
$15$	8.87984e39	0.236187
$16$	3.02197e41	0.867261
$17$	−3.55776e42	−1.26092	−0.630462	−	0.776220i	$-0.717135\pi$
$17$	−3.55776e42	−1.26092	−0.630462	+	0.776220i	$0.717135\pi$
$18$	−1.43217e42	−0.0706468
$19$	1.29809e44	0.991528	0.495764	−	0.868457i	$-0.334888\pi$
$19$	1.29809e44	0.991528	0.495764	+	0.868457i	$0.334888\pi$
$20$	−3.00187e44	−0.390713
$21$	2.67152e45	0.645941
$22$	−4.12598e45	−0.200422
$23$	−1.58861e47	−1.66497	−0.832484	−	0.554048i	$-0.813082\pi$
$23$	−1.58861e47	−1.66497	−0.832484	+	0.554048i	$0.813082\pi$
$24$	9.91073e46	0.239231
$25$	−1.41056e48	−0.832647
$26$	−2.56156e48	−0.390773
$27$	4.63840e48	0.192450
$28$	−9.03120e49	−1.06855
$29$	5.31660e50	1.87458	0.937289	−	0.348554i	$-0.113327\pi$
$29$	5.31660e50	1.87458	0.937289	+	0.348554i	$0.113327\pi$
$30$	−4.57250e49	−0.0500576
$31$	3.63108e51	1.28250	0.641251	−	0.767331i	$-0.278416\pi$
$31$	3.63108e51	1.28250	0.641251	+	0.767331i	$0.278416\pi$
$32$	−5.06405e51	−0.598168
$33$	1.33629e52	0.545972
$34$	1.83200e52	0.267241
$35$	8.52939e52	0.457689
$36$	−1.56803e53	−0.318360
$37$	−6.48838e53	−0.511891	−0.255945	−	0.966691i	$-0.582387\pi$
$37$	−6.48838e53	−0.511891	−0.255945	+	0.966691i	$0.582387\pi$
$38$	−6.68425e53	−0.210145
$39$	8.29619e54	1.06451
$40$	3.16421e54	0.169510
$41$	−5.06527e55	−1.15760	−0.578802	−	0.815468i	$-0.696479\pi$
$41$	−5.06527e55	−1.15760	−0.578802	+	0.815468i	$0.696479\pi$
$42$	−1.37565e55	−0.136901
$43$	3.76782e55	0.166506	0.0832528	−	0.996528i	$-0.473469\pi$
$43$	3.76782e55	0.166506	0.0832528	+	0.996528i	$0.473469\pi$
$44$	−4.51740e56	−0.903173
$45$	1.48091e56	0.136363
$46$	8.18022e56	0.352874
$47$	−1.66171e55	−0.00341333	−0.00170666	−	0.999999i	$-0.500543\pi$
$47$	−1.66171e55	−0.00341333	−0.00170666	+	0.999999i	$0.500543\pi$
$48$	5.03979e57	0.500714
$49$	5.16034e57	0.251718
$50$	7.26340e57	0.176471
$51$	−5.93334e58	−0.727995
$52$	−2.80457e59	−1.76097
$53$	7.77253e58	0.252956	0.126478	−	0.991969i	$-0.459633\pi$
$53$	7.77253e58	0.252956	0.126478	+	0.991969i	$0.459633\pi$
$54$	−2.38845e58	−0.0407880
$55$	4.26639e59	0.386855
$56$	9.51960e59	0.463588
$57$	2.16484e60	0.572459
$58$	−2.73768e60	−0.397299
$59$	−2.15460e59	−0.0173369	−0.00866847	−	0.999962i	$-0.502759\pi$
$59$	−2.15460e59	−0.0173369	−0.00866847	+	0.999962i	$0.502759\pi$
$60$	−5.00628e60	−0.225578
$61$	1.95680e61	0.498503	0.249251	−	0.968439i	$-0.419815\pi$
$61$	1.95680e61	0.498503	0.249251	+	0.968439i	$0.419815\pi$
$62$	−1.86976e61	−0.271814
$63$	4.45534e61	0.372934
$64$	−1.52309e62	−0.740485
$65$	2.64873e62	0.754271
$66$	−6.88097e61	−0.115713
$67$	−5.83429e62	−0.583993	−0.291996	−	0.956419i	$-0.594320\pi$
$67$	−5.83429e62	−0.583993	−0.291996	+	0.956419i	$0.594320\pi$
$68$	2.00580e63	1.20429
$69$	−2.64935e63	−0.961270
$70$	−4.39204e62	−0.0970028
$71$	−5.86844e62	−0.0794528	−0.0397264	−	0.999211i	$-0.512649\pi$
$71$	−5.86844e62	−0.0794528	−0.0397264	+	0.999211i	$0.512649\pi$
$72$	1.65283e63	0.138120
$73$	1.18218e64	0.613825	0.306913	−	0.951738i	$-0.400704\pi$
$73$	1.18218e64	0.613825	0.306913	+	0.951738i	$0.400704\pi$
$74$	3.34107e63	0.108490
$75$	−2.35241e64	−0.480729
$76$	−7.31836e64	−0.946989
$77$	1.28355e65	1.05800
$78$	−4.27196e64	−0.225613
$79$	9.48481e64	0.322771	0.161385	−	0.986891i	$-0.448404\pi$
$79$	9.48481e64	0.322771	0.161385	+	0.986891i	$0.448404\pi$
$80$	1.60906e65	0.354787
$81$	7.73554e64	0.111111
$82$	2.60826e65	0.245343
$83$	2.22522e66	1.37778	0.688889	−	0.724867i	$-0.258099\pi$
$83$	2.22522e66	1.37778	0.688889	+	0.724867i	$0.258099\pi$
$84$	−1.50615e66	−0.616926
$85$	−1.89434e66	−0.515829
$86$	−1.94017e65	−0.0352893
$87$	8.86660e66	1.08229
$88$	4.76169e66	0.391841
$89$	−2.87703e67	−1.60321	−0.801603	−	0.597857i	$-0.796019\pi$
$89$	−2.87703e67	−1.60321	−0.801603	+	0.597857i	$0.796019\pi$
$90$	−7.62564e65	−0.0289008
$91$	7.96878e67	2.06283
$92$	8.95626e67	1.59018
$93$	6.05563e67	0.740453
$94$	8.55663e64	0.000723422 0
$95$	6.91172e67	0.405622
$96$	−8.44540e67	−0.345353
$97$	4.12944e68	1.18104	0.590522	−	0.807022i	$-0.298922\pi$
$97$	4.12944e68	1.18104	0.590522	+	0.807022i	$0.298922\pi$
$98$	−2.65722e67	−0.0533492
$99$	2.22856e68	0.315217
$100$	7.95245e68	0.795245
$101$	2.39298e69	1.69766	0.848830	−	0.528665i	$-0.177307\pi$
$101$	2.39298e69	1.69766	0.848830	+	0.528665i	$0.177307\pi$
$102$	3.05526e68	0.154292
$103$	1.37225e69	0.494936	0.247468	−	0.968896i	$-0.420402\pi$
$103$	1.37225e69	0.494936	0.247468	+	0.968896i	$0.420402\pi$
$104$	2.95624e69	0.763992
$105$	1.42246e69	0.264247
$106$	−4.00231e68	−0.0536116
$107$	9.85792e69	0.955092	0.477546	−	0.878607i	$-0.341526\pi$
$107$	9.85792e69	0.955092	0.477546	+	0.878607i	$0.341526\pi$
$108$	−2.61504e69	−0.183805
$109$	−1.58563e68	−0.00810937	−0.00405468	−	0.999992i	$-0.501291\pi$
$109$	−1.58563e68	−0.00810937	−0.00405468	+	0.999992i	$0.501291\pi$
$110$	−2.19690e69	−0.0819902
$111$	−1.08208e70	−0.295540
$112$	4.84089e70	0.970294
$113$	7.66522e70	1.13062	0.565312	−	0.824877i	$-0.308756\pi$
$113$	7.66522e70	1.13062	0.565312	+	0.824877i	$0.308756\pi$
$114$	−1.11474e70	−0.121327
$115$	−8.45861e70	−0.681119
$116$	−2.99740e71	−1.79037
$117$	1.38357e71	0.614595
$118$	1.10947e69	0.00367440
$119$	−5.69918e71	−1.41072
$120$	5.27701e70	0.0978667
$121$	−7.59196e70	−0.105745
$122$	−1.00762e71	−0.105653
$123$	−8.44745e71	−0.668343
$124$	−2.04713e72	−1.22489
$125$	−1.65307e72	−0.749714
$126$	−2.29419e71	−0.0790398
$127$	−2.23143e72	−0.585269	−0.292635	−	0.956224i	$-0.594532\pi$
$127$	−2.23143e72	−0.585269	−0.292635	+	0.956224i	$0.594532\pi$
$128$	3.77357e72	0.755107
$129$	6.28367e71	0.0961320
$130$	−1.36391e72	−0.159861
$131$	1.99353e71	0.0179375	0.00896877	−	0.999960i	$-0.497145\pi$
$131$	1.99353e71	0.0179375	0.00896877	+	0.999960i	$0.497145\pi$
$132$	−7.53375e72	−0.521447
$133$	2.07941e73	1.10932
$134$	3.00425e72	0.123772
$135$	2.46973e72	0.0787291
$136$	−2.11427e73	−0.522477
$137$	1.04290e73	0.200162	0.100081	−	0.994979i	$-0.468090\pi$
$137$	1.04290e73	0.200162	0.100081	+	0.994979i	$0.468090\pi$
$138$	1.36423e73	0.203732
$139$	1.35356e74	1.57568	0.787838	−	0.615883i	$-0.211201\pi$
$139$	1.35356e74	1.57568	0.787838	+	0.615883i	$0.211201\pi$
$140$	−4.80870e73	−0.437130
$141$	−2.77126e71	−0.00197069
$142$	3.02184e72	0.0168393
$143$	3.98597e74	1.74358
$144$	8.40494e73	0.289087
$145$	2.83085e74	0.766868
$146$	−6.08740e73	−0.130094
$147$	8.60600e73	0.145329
$148$	3.65802e74	0.488897
$149$	−1.69781e75	−1.79871	−0.899356	−	0.437216i	$-0.855964\pi$
$149$	−1.69781e75	−1.79871	−0.899356	+	0.437216i	$0.855964\pi$
$150$	1.21133e74	0.101886
$151$	−8.03331e74	−0.537267	−0.268633	−	0.963243i	$-0.586572\pi$
$151$	−8.03331e74	−0.537267	−0.268633	+	0.963243i	$0.586572\pi$
$152$	7.71413e74	0.410850
$153$	−9.89514e74	−0.420308
$154$	−6.60941e74	−0.224232
$155$	1.93339e75	0.524657
$156$	−4.67723e75	−1.01669
$157$	−2.28371e75	−0.398201	−0.199100	−	0.979979i	$-0.563802\pi$
$157$	−2.28371e75	−0.398201	−0.199100	+	0.979979i	$0.563802\pi$
$158$	−4.88402e74	−0.0684081
$159$	1.29624e75	0.146044
$160$	−2.69637e75	−0.244704
$161$	−2.54479e76	−1.86277
$162$	−3.98327e74	−0.0235489
$163$	−1.34703e76	−0.644027	−0.322013	−	0.946735i	$-0.604360\pi$
$163$	−1.34703e76	−0.644027	−0.322013	+	0.946735i	$0.604360\pi$
$164$	2.85570e76	1.10561
$165$	7.11514e75	0.223351
$166$	−1.14583e76	−0.292007
$167$	−4.04568e76	−0.838057	−0.419028	−	0.907973i	$-0.637629\pi$
$167$	−4.04568e76	−0.838057	−0.419028	+	0.907973i	$0.637629\pi$
$168$	1.58760e76	0.267652
$169$	1.74671e77	2.39955
$170$	9.75456e75	0.109325
$171$	3.61035e76	0.330509
$172$	−2.12422e76	−0.159026
$173$	8.39010e76	0.514253	0.257126	−	0.966378i	$-0.417224\pi$
$173$	8.39010e76	0.514253	0.257126	+	0.966378i	$0.417224\pi$
$174$	−4.56568e76	−0.229380
$175$	−2.25957e77	−0.931567
$176$	2.42141e77	0.820126
$177$	−3.59327e75	−0.0100095
$178$	1.48147e77	0.339784
$179$	4.58651e77	0.867067	0.433534	−	0.901137i	$-0.357267\pi$
$179$	4.58651e77	0.867067	0.433534	+	0.901137i	$0.357267\pi$
$180$	−8.34906e76	−0.130238
$181$	8.29664e77	1.06903	0.534517	−	0.845158i	$-0.320494\pi$
$181$	8.29664e77	1.06903	0.534517	+	0.845158i	$0.320494\pi$
$182$	−4.10337e77	−0.437197
$183$	3.26339e77	0.287811
$184$	−9.44060e77	−0.689898
$185$	−3.45477e77	−0.209408
$186$	−3.11823e77	−0.156932
$187$	−2.85072e78	−1.19239
$188$	9.36837e75	0.00326001
$189$	7.43025e77	0.215314
$190$	−3.55906e77	−0.0859678
$191$	−2.49882e78	−0.503598	−0.251799	−	0.967780i	$-0.581022\pi$
$191$	−2.49882e78	−0.503598	−0.251799	+	0.967780i	$0.581022\pi$
$192$	−2.54009e78	−0.427519
$193$	−5.30933e78	−0.746986	−0.373493	−	0.927633i	$-0.621840\pi$
$193$	−5.30933e78	−0.746986	−0.373493	+	0.927633i	$0.621840\pi$
$194$	−2.12637e78	−0.250311
$195$	4.41734e78	0.435479
$196$	−2.90930e78	−0.240411
$197$	−1.84118e79	−1.27647	−0.638237	−	0.769840i	$-0.720336\pi$
$197$	−1.84118e79	−1.27647	−0.638237	+	0.769840i	$0.720336\pi$
$198$	−1.14755e78	−0.0668072
$199$	3.48687e79	1.70610	0.853050	−	0.521830i	$-0.174750\pi$
$199$	3.48687e79	1.70610	0.853050	+	0.521830i	$0.174750\pi$
$200$	−8.38251e78	−0.345016
$201$	−9.72995e78	−0.337168
$202$	−1.23222e79	−0.359803
$203$	8.51667e79	2.09728
$204$	3.34510e79	0.695294
$205$	−2.69703e79	−0.473562
$206$	−7.06613e78	−0.104897
$207$	−4.41837e79	−0.554990
$208$	1.50330e80	1.59904
$209$	1.04012e80	0.937639
$210$	−7.32469e78	−0.0560046
$211$	−1.33893e80	−0.868984	−0.434492	−	0.900676i	$-0.643072\pi$
$211$	−1.33893e80	−0.868984	−0.434492	+	0.900676i	$0.643072\pi$
$212$	−4.38200e79	−0.241593
$213$	−9.78690e78	−0.0458721
$214$	−5.07614e79	−0.202423
$215$	2.00619e79	0.0681155
$216$	2.75646e79	0.0797438
$217$	5.81664e80	1.43487
$218$	8.16488e77	0.00171870
$219$	1.97154e80	0.354392
$220$	−2.40531e80	−0.369478
$221$	−1.76984e81	−2.32487
$222$	5.57196e79	0.0626369
$223$	−4.46096e80	−0.429448	−0.214724	−	0.976675i	$-0.568885\pi$
$223$	−4.46096e80	−0.429448	−0.214724	+	0.976675i	$0.568885\pi$
$224$	−8.11210e80	−0.669232
$225$	−3.92316e80	−0.277549
$226$	−3.94706e80	−0.239625
$227$	2.50707e81	1.30700	0.653499	−	0.756928i	$-0.273301\pi$
$227$	2.50707e81	1.30700	0.653499	+	0.756928i	$0.273301\pi$
$228$	−1.22050e81	−0.546745
$229$	−3.68716e81	−1.42026	−0.710130	−	0.704071i	$-0.751364\pi$
$229$	−3.68716e81	−1.42026	−0.710130	+	0.704071i	$0.751364\pi$
$230$	4.35559e80	0.144357
$231$	2.14061e81	0.610834
$232$	3.15949e81	0.776751
$233$	−4.98076e80	−0.105564	−0.0527820	−	0.998606i	$-0.516809\pi$
$233$	−4.98076e80	−0.105564	−0.0527820	+	0.998606i	$0.516809\pi$
$234$	−7.12443e80	−0.130258
$235$	−8.84782e78	−0.00139635
$236$	1.21472e80	0.0165582
$237$	1.58180e81	0.186352
$238$	2.93468e81	0.298990
$239$	4.06081e81	0.358001	0.179001	−	0.983849i	$-0.442714\pi$
$239$	4.06081e81	0.358001	0.179001	+	0.983849i	$0.442714\pi$
$240$	2.68346e81	0.204836
$241$	7.79740e81	0.515658	0.257829	−	0.966191i	$-0.416993\pi$
$241$	7.79740e81	0.515658	0.257829	+	0.966191i	$0.416993\pi$
$242$	3.90933e80	0.0224116
$243$	1.29007e81	0.0641500
$244$	−1.10321e82	−0.476111
$245$	2.74765e81	0.102975
$246$	4.34985e81	0.141649
$247$	6.45744e82	1.82816
$248$	2.15784e82	0.531418
$249$	3.71104e82	0.795461
$250$	8.51216e81	0.158895
$251$	−1.12311e83	−1.82675	−0.913373	−	0.407123i	$-0.866532\pi$
$251$	−1.12311e83	−1.82675	−0.913373	+	0.407123i	$0.866532\pi$
$252$	−2.51183e82	−0.356182
$253$	−1.27290e83	−1.57448
$254$	1.14903e82	0.124042
$255$	−3.15923e82	−0.297814
$256$	7.04761e82	0.580448
$257$	−1.58528e83	−1.14133	−0.570666	−	0.821182i	$-0.693315\pi$
$257$	−1.58528e83	−1.14133	−0.570666	+	0.821182i	$0.693315\pi$
$258$	−3.23565e81	−0.0203743
$259$	−1.03937e83	−0.572704
$260$	−1.49330e83	−0.720390
$261$	1.47870e83	0.624859
$262$	−1.02653e81	−0.00380169
$263$	1.40913e83	0.457593	0.228796	−	0.973474i	$-0.426521\pi$
$263$	1.40913e83	0.457593	0.228796	+	0.973474i	$0.426521\pi$
$264$	7.94116e82	0.226229
$265$	4.13851e82	0.103481
$266$	−1.07075e83	−0.235110
$267$	−4.79808e83	−0.925611
$268$	3.28926e83	0.557761
$269$	6.34257e82	0.0945826	0.0472913	−	0.998881i	$-0.484941\pi$
$269$	6.34257e82	0.0945826	0.0472913	+	0.998881i	$0.484941\pi$
$270$	−1.27174e82	−0.0166859
$271$	1.03148e84	1.19130	0.595651	−	0.803243i	$-0.296894\pi$
$271$	1.03148e84	1.19130	0.595651	+	0.803243i	$0.296894\pi$
$272$	−1.07514e84	−1.09355
$273$	1.32897e84	1.19098
$274$	−5.37020e82	−0.0424225
$275$	−1.13024e84	−0.787393
$276$	1.49365e84	0.918091
$277$	2.08935e84	1.13360	0.566800	−	0.823855i	$-0.308181\pi$
$277$	2.08935e84	1.13360	0.566800	+	0.823855i	$0.308181\pi$
$278$	−6.96989e83	−0.333949
$279$	1.00991e84	0.427501
$280$	5.06875e83	0.189648
$281$	−2.64608e83	−0.0875457	−0.0437729	−	0.999042i	$-0.513938\pi$
$281$	−2.64608e83	−0.0875457	−0.0437729	+	0.999042i	$0.513938\pi$
$282$	1.42700e81	0.000417668 0
$283$	4.87066e83	0.126170	0.0630849	−	0.998008i	$-0.479906\pi$
$283$	4.87066e83	0.126170	0.0630849	+	0.998008i	$0.479906\pi$
$284$	3.30851e83	0.0758839
$285$	1.15268e84	0.234186
$286$	−2.05250e84	−0.369535
$287$	−8.11407e84	−1.29513
$288$	−1.40846e84	−0.199389
$289$	4.69652e84	0.589930
$290$	−1.45769e84	−0.162530
$291$	6.88674e84	0.681876
$292$	−6.66490e84	−0.586253
$293$	−1.48720e85	−1.16262	−0.581309	−	0.813683i	$-0.697459\pi$
$293$	−1.48720e85	−1.16262	−0.581309	+	0.813683i	$0.697459\pi$
$294$	−4.43149e83	−0.0308012
$295$	−1.14723e83	−0.00709234
$296$	−3.85585e84	−0.212107
$297$	3.71660e84	0.181991
$298$	8.74252e84	0.381220
$299$	−7.90265e85	−3.06985
$300$	1.32624e85	0.459135
$301$	6.03568e84	0.186287
$302$	4.13660e84	0.113869
$303$	3.99081e85	0.980145
$304$	3.92278e85	0.859914
$305$	1.04191e85	0.203932
$306$	5.09531e84	0.0890803
$307$	8.32322e85	1.30022	0.650111	−	0.759839i	$-0.274722\pi$
$307$	8.32322e85	1.30022	0.650111	+	0.759839i	$0.274722\pi$
$308$	−7.23642e85	−1.01047
$309$	2.28852e85	0.285751
$310$	−9.95560e84	−0.111196
$311$	−2.43662e85	−0.243531	−0.121765	−	0.992559i	$-0.538856\pi$
$311$	−2.43662e85	−0.243531	−0.121765	+	0.992559i	$0.538856\pi$
$312$	4.93017e85	0.441091
$313$	9.97380e85	0.799063	0.399532	−	0.916719i	$-0.369173\pi$
$313$	9.97380e85	0.799063	0.399532	+	0.916719i	$0.369173\pi$
$314$	1.17595e85	0.0843949
$315$	2.37227e85	0.152563
$316$	−5.34735e85	−0.308272
$317$	−8.62919e85	−0.446093	−0.223046	−	0.974808i	$-0.571600\pi$
$317$	−8.62919e85	−0.446093	−0.223046	+	0.974808i	$0.571600\pi$
$318$	−6.67473e84	−0.0309527
$319$	4.26003e86	1.77270
$320$	−8.10976e85	−0.302924
$321$	1.64402e86	0.551422
$322$	1.31039e86	0.394796
$323$	−4.61829e86	−1.25024
$324$	−4.36115e85	−0.106120
$325$	−7.01693e86	−1.53522
$326$	6.93625e85	0.136495
$327$	−2.64438e84	−0.00468195
$328$	−3.01014e86	−0.479665
$329$	−2.66189e84	−0.00381884
$330$	−3.66380e85	−0.0473370
$331$	−3.17780e86	−0.369880	−0.184940	−	0.982750i	$-0.559209\pi$
$331$	−3.17780e86	−0.369880	−0.184940	+	0.982750i	$0.559209\pi$
$332$	−1.25454e87	−1.31589
$333$	−1.80460e86	−0.170630
$334$	2.08325e86	0.177618
$335$	−3.10649e86	−0.238905
$336$	8.07324e86	0.560199
$337$	8.68193e86	0.543732	0.271866	−	0.962335i	$-0.412359\pi$
$337$	8.68193e86	0.543732	0.271866	+	0.962335i	$0.412359\pi$
$338$	−8.99433e86	−0.508561
$339$	1.27834e87	0.652767
$340$	1.06799e87	0.492659
$341$	2.90948e87	1.21280
$342$	−1.85908e86	−0.0700483
$343$	−2.45734e87	−0.837180
$344$	2.23910e86	0.0689934
$345$	−1.41066e87	−0.393244
$346$	−4.32032e86	−0.108991
$347$	3.57974e87	0.817493	0.408747	−	0.912648i	$-0.365966\pi$
$347$	3.57974e87	0.817493	0.408747	+	0.912648i	$0.365966\pi$
$348$	−4.99881e87	−1.03367
$349$	5.32830e87	0.997957	0.498978	−	0.866614i	$-0.333709\pi$
$349$	5.32830e87	0.997957	0.498978	+	0.866614i	$0.333709\pi$
$350$	1.16352e87	0.197437
$351$	2.30741e87	0.354837
$352$	−4.05766e87	−0.565658
$353$	9.57571e87	1.21044	0.605220	−	0.796058i	$-0.293085\pi$
$353$	9.57571e87	1.21044	0.605220	+	0.796058i	$0.293085\pi$
$354$	1.85028e85	0.00212142
$355$	−3.12467e86	−0.0325032
$356$	1.62201e88	1.53119
$357$	−9.50463e87	−0.814482
$358$	−2.36173e87	−0.183767
$359$	−1.59077e87	−0.112422	−0.0562108	−	0.998419i	$-0.517902\pi$
$359$	−1.59077e87	−0.112422	−0.0562108	+	0.998419i	$0.517902\pi$
$360$	8.80057e86	0.0565034
$361$	−2.89196e86	−0.0168731
$362$	−4.27219e87	−0.226571
$363$	−1.26612e87	−0.0610517
$364$	−4.49264e88	−1.97017
$365$	6.29456e87	0.251109
$366$	−1.68042e87	−0.0609987
$367$	2.66598e88	0.880801	0.440400	−	0.897801i	$-0.354836\pi$
$367$	2.66598e88	0.880801	0.440400	+	0.897801i	$0.354836\pi$
$368$	−4.80072e88	−1.44396
$369$	−1.40880e88	−0.385868
$370$	1.77897e87	0.0443821
$371$	1.24508e88	0.283007
$372$	−3.41404e88	−0.707192
$373$	−5.75002e88	−1.08571	−0.542856	−	0.839826i	$-0.682657\pi$
$373$	−5.75002e88	−1.08571	−0.542856	+	0.839826i	$0.682657\pi$
$374$	1.46792e88	0.252716
$375$	−2.75686e88	−0.432848
$376$	−9.87500e85	−0.00141435
$377$	2.64479e89	3.45632
$378$	−3.82606e87	−0.0456336
$379$	−5.68009e88	−0.618446	−0.309223	−	0.950989i	$-0.600069\pi$
$379$	−5.68009e88	−0.618446	−0.309223	+	0.950989i	$0.600069\pi$
$380$	−3.89669e88	−0.387402
$381$	−3.72140e88	−0.337905
$382$	1.28672e88	0.106733
$383$	1.22895e88	0.0931488	0.0465744	−	0.998915i	$-0.485170\pi$
$383$	1.22895e88	0.0931488	0.0465744	+	0.998915i	$0.485170\pi$
$384$	6.29325e88	0.435961
$385$	6.83434e88	0.432814
$386$	2.73393e88	0.158316
$387$	1.04794e88	0.0555019
$388$	−2.32810e89	−1.12799
$389$	2.39646e89	1.06245	0.531226	−	0.847230i	$-0.321732\pi$
$389$	2.39646e89	1.06245	0.531226	+	0.847230i	$0.321732\pi$
$390$	−2.27462e88	−0.0922956
$391$	5.65188e89	2.09940
$392$	3.06663e88	0.104302
$393$	3.32464e87	0.0103562
$394$	9.48081e88	0.270536
$395$	5.05023e88	0.132042
$396$	−1.25642e89	−0.301058
$397$	−8.98950e89	−1.97453	−0.987263	−	0.159096i	$-0.949142\pi$
$397$	−8.98950e89	−1.97453	−0.987263	+	0.159096i	$0.949142\pi$
$398$	−1.79549e89	−0.361591
$399$	3.46787e89	0.640468
$400$	−4.26266e89	−0.722122
$401$	−4.90883e89	−0.762952	−0.381476	−	0.924379i	$-0.624584\pi$
$401$	−4.90883e89	−0.762952	−0.381476	+	0.924379i	$0.624584\pi$
$402$	5.01025e88	0.0714596
$403$	1.80631e90	2.36466
$404$	−1.34911e90	−1.62140
$405$	4.11882e88	0.0454543
$406$	−4.38549e89	−0.444499
$407$	−5.19894e89	−0.484070
$408$	−3.52600e89	−0.301653
$409$	−4.23313e89	−0.332819	−0.166409	−	0.986057i	$-0.553217\pi$
$409$	−4.23313e89	−0.332819	−0.166409	+	0.986057i	$0.553217\pi$
$410$	1.38878e89	0.100367
$411$	1.73926e89	0.115564
$412$	−7.73647e89	−0.472704
$413$	−3.45146e88	−0.0193966
$414$	2.27515e89	0.117625
$415$	1.18483e90	0.563633
$416$	−2.51915e90	−1.10289
$417$	2.25736e90	0.909717
$418$	−5.35588e89	−0.198724
$419$	−6.06631e89	−0.207272	−0.103636	−	0.994615i	$-0.533048\pi$
$419$	−6.06631e89	−0.207272	−0.103636	+	0.994615i	$0.533048\pi$
$420$	−8.01956e89	−0.252377
$421$	4.48971e90	1.30162	0.650812	−	0.759239i	$-0.274428\pi$
$421$	4.48971e90	1.30162	0.650812	+	0.759239i	$0.274428\pi$
$422$	6.89454e89	0.184173
$423$	−4.62168e87	−0.00113778
$424$	4.61897e89	0.104815
$425$	5.01843e90	1.04990
$426$	5.03957e88	0.00972216
$427$	3.13460e90	0.557726
$428$	−5.55770e90	−0.912190
$429$	6.64748e90	1.00665
$430$	−1.03305e89	−0.0144364
$431$	−7.99006e90	−1.03059	−0.515293	−	0.857014i	$-0.672317\pi$
$431$	−7.99006e90	−1.03059	−0.515293	+	0.857014i	$0.672317\pi$
$432$	1.40171e90	0.166905
$433$	1.26386e91	1.38953	0.694764	−	0.719238i	$-0.255509\pi$
$433$	1.26386e91	1.38953	0.694764	+	0.719238i	$0.255509\pi$
$434$	−2.99516e90	−0.304106
$435$	4.72106e90	0.442751
$436$	8.93946e88	0.00774510
$437$	−2.06215e91	−1.65086
$438$	−1.01521e90	−0.0751100
$439$	−1.22942e91	−0.840761	−0.420381	−	0.907348i	$-0.638103\pi$
$439$	−1.22942e91	−0.840761	−0.420381	+	0.907348i	$0.638103\pi$
$440$	2.53538e90	0.160297
$441$	1.43524e90	0.0839059
$442$	9.11342e90	0.492735
$443$	2.60056e91	1.30058	0.650292	−	0.759684i	$-0.274647\pi$
$443$	2.60056e91	1.30058	0.650292	+	0.759684i	$0.274647\pi$
$444$	6.10055e90	0.282265
$445$	−1.53189e91	−0.655853
$446$	2.29708e90	0.0910173
$447$	−2.83146e91	−1.03849
$448$	−2.43984e91	−0.828457
$449$	2.89562e89	0.00910423	0.00455212	−	0.999990i	$-0.498551\pi$
$449$	2.89562e89	0.00910423	0.00455212	+	0.999990i	$0.498551\pi$
$450$	2.02016e90	0.0588238
$451$	−4.05865e91	−1.09469
$452$	−4.32150e91	−1.07984
$453$	−1.33973e91	−0.310191
$454$	−1.29097e91	−0.277005
$455$	4.24301e91	0.843880
$456$	1.28650e91	0.237204
$457$	4.97909e90	0.0851219	0.0425609	−	0.999094i	$-0.486448\pi$
$457$	4.97909e90	0.0851219	0.0425609	+	0.999094i	$0.486448\pi$
$458$	1.89863e91	0.301010
$459$	−1.65023e91	−0.242665
$460$	4.76880e91	0.650524
$461$	−3.36324e91	−0.425673	−0.212836	−	0.977088i	$-0.568270\pi$
$461$	−3.36324e91	−0.425673	−0.212836	+	0.977088i	$0.568270\pi$
$462$	−1.10226e91	−0.129460
$463$	1.50898e92	1.64490	0.822449	−	0.568838i	$-0.192607\pi$
$463$	1.50898e92	1.64490	0.822449	+	0.568838i	$0.192607\pi$
$464$	1.60666e92	1.62575
$465$	3.22434e91	0.302911
$466$	2.56474e90	0.0223733
$467$	7.47538e91	0.605621	0.302810	−	0.953051i	$-0.402075\pi$
$467$	7.47538e91	0.605621	0.302810	+	0.953051i	$0.402075\pi$
$468$	−7.80030e91	−0.586988
$469$	−9.34596e91	−0.653372
$470$	4.55601e88	0.000295944 0
$471$	−3.80858e91	−0.229901
$472$	−1.28041e90	−0.00718375
$473$	3.01904e91	0.157456
$474$	−8.14516e90	−0.0394954
$475$	−1.83103e92	−0.825592
$476$	3.21309e92	1.34736
$477$	2.16176e91	0.0843186
$478$	−2.09103e91	−0.0758750
$479$	8.18296e91	0.276271	0.138135	−	0.990413i	$-0.455889\pi$
$479$	8.18296e91	0.276271	0.138135	+	0.990413i	$0.455889\pi$
$480$	−4.49679e91	−0.141280
$481$	−3.22770e92	−0.943817
$482$	−4.01512e91	−0.109289
$483$	−4.24399e92	−1.07547
$484$	4.28020e91	0.100995
$485$	2.19874e92	0.483151
$486$	−6.64296e90	−0.0135960
$487$	1.81183e92	0.345436	0.172718	−	0.984971i	$-0.444745\pi$
$487$	1.81183e92	0.345436	0.172718	+	0.984971i	$0.444745\pi$
$488$	1.16287e92	0.206560
$489$	−2.24646e92	−0.371829
$490$	−1.41485e91	−0.0218245
$491$	−5.69097e92	−0.818229	−0.409114	−	0.912483i	$-0.634162\pi$
$491$	−5.69097e92	−0.818229	−0.409114	+	0.912483i	$0.634162\pi$
$492$	4.76251e92	0.638322
$493$	−1.89152e93	−2.36370
$494$	−3.32513e92	−0.387462
$495$	1.18660e92	0.128952
$496$	1.09730e93	1.11226
$497$	−9.40065e91	−0.0888920
$498$	−1.91093e92	−0.168590
$499$	−3.22281e92	−0.265317	−0.132659	−	0.991162i	$-0.542351\pi$
$499$	−3.22281e92	−0.265317	−0.132659	+	0.991162i	$0.542351\pi$
$500$	9.31969e92	0.716038
$501$	−6.74706e92	−0.483852
$502$	5.78323e92	0.387161
$503$	3.27709e91	0.0204829	0.0102415	−	0.999948i	$-0.496740\pi$
$503$	3.27709e91	0.0204829	0.0102415	+	0.999948i	$0.496740\pi$
$504$	2.64767e92	0.154529
$505$	1.27415e93	0.694493
$506$	6.55456e92	0.333696
$507$	2.91302e93	1.38538
$508$	1.25804e93	0.558980
$509$	−2.88130e93	−1.19626	−0.598129	−	0.801400i	$-0.704089\pi$
$509$	−2.88130e93	−1.19626	−0.598129	+	0.801400i	$0.704089\pi$
$510$	1.62679e92	0.0631189
$511$	1.89373e93	0.686749
$512$	−2.59043e93	−0.878128
$513$	6.02105e92	0.190820
$514$	8.16307e92	0.241894
$515$	7.30660e92	0.202472
$516$	−3.54261e92	−0.0918139
$517$	−1.33147e91	−0.00322782
$518$	5.35206e92	0.121379
$519$	1.39923e93	0.296904
$520$	1.57406e93	0.312540
$521$	2.46295e93	0.457671	0.228836	−	0.973465i	$-0.426508\pi$
$521$	2.46295e93	0.457671	0.228836	+	0.973465i	$0.426508\pi$
$522$	−7.61427e92	−0.132433
$523$	−4.98137e93	−0.811036	−0.405518	−	0.914087i	$-0.632909\pi$
$523$	−4.98137e93	−0.811036	−0.405518	+	0.914087i	$0.632909\pi$
$524$	−1.12391e92	−0.0171318
$525$	−3.76833e93	−0.537840
$526$	−7.25606e92	−0.0969824
$527$	−1.29185e94	−1.61714
$528$	4.03823e93	0.473500
$529$	1.61330e94	1.77212
$530$	−2.13105e92	−0.0219319
$531$	−5.99256e91	−0.00577898
$532$	−1.17233e94	−1.05949
$533$	−2.51976e94	−2.13437
$534$	2.47068e93	0.196174
$535$	5.24889e93	0.390717
$536$	−3.46714e93	−0.241984
$537$	7.64900e93	0.500601
$538$	−3.26598e92	−0.0200459
$539$	4.13482e93	0.238037
$540$	−1.39239e93	−0.0751927
$541$	−3.11290e94	−1.57710	−0.788551	−	0.614969i	$-0.789169\pi$
$541$	−3.11290e94	−1.57710	−0.788551	+	0.614969i	$0.789169\pi$
$542$	−5.31143e93	−0.252485
$543$	1.38364e94	0.617207
$544$	1.80167e94	0.754245
$545$	−8.44274e91	−0.00331745
$546$	−6.84326e93	−0.252416
$547$	3.11139e94	1.07744	0.538719	−	0.842486i	$-0.318909\pi$
$547$	3.11139e94	1.07744	0.538719	+	0.842486i	$0.318909\pi$
$548$	−5.87966e93	−0.191171
$549$	5.44242e93	0.166168
$550$	5.81993e93	0.166880
$551$	6.90142e94	1.85870
$552$	−1.57443e94	−0.398313
$553$	1.51937e94	0.361116
$554$	−1.07587e94	−0.240256
$555$	−5.76158e93	−0.120902
$556$	−7.63110e94	−1.50490
$557$	8.79669e94	1.63048	0.815239	−	0.579124i	$-0.196605\pi$
$557$	8.79669e94	1.63048	0.815239	+	0.579124i	$0.196605\pi$
$558$	−5.20032e93	−0.0906046
$559$	1.87433e94	0.307001
$560$	2.57755e94	0.396936
$561$	−4.75420e94	−0.688429
$562$	1.36255e93	0.0185545
$563$	7.78317e94	0.996821	0.498410	−	0.866941i	$-0.333917\pi$
$563$	7.78317e94	0.996821	0.498410	+	0.866941i	$0.333917\pi$
$564$	1.56238e92	0.00188216
$565$	4.08138e94	0.462526
$566$	−2.50805e93	−0.0267405
$567$	1.23916e94	0.124311
$568$	−3.48743e93	−0.0329221
$569$	−9.94223e94	−0.883305	−0.441653	−	0.897186i	$-0.645608\pi$
$569$	−9.94223e94	−0.883305	−0.441653	+	0.897186i	$0.645608\pi$
$570$	−5.93550e93	−0.0496335
$571$	−2.14253e95	−1.68648	−0.843241	−	0.537535i	$-0.819355\pi$
$571$	−2.14253e95	−1.68648	−0.843241	+	0.537535i	$0.819355\pi$
$572$	−2.24721e95	−1.66526
$573$	−4.16733e94	−0.290753
$574$	4.17818e94	0.274490
$575$	2.24082e95	1.38633
$576$	−4.23615e94	−0.246828
$577$	−1.33908e95	−0.734924	−0.367462	−	0.930039i	$-0.619773\pi$
$577$	−1.33908e95	−0.734924	−0.367462	+	0.930039i	$0.619773\pi$
$578$	−2.41838e94	−0.125030
$579$	−8.85446e94	−0.431272
$580$	−1.59598e95	−0.732421
$581$	3.56459e95	1.54146
$582$	−3.54619e94	−0.144517
$583$	6.22789e94	0.239208
$584$	7.02533e94	0.254345
$585$	7.36688e94	0.251424
$586$	7.65806e94	0.246406
$587$	−1.46328e95	−0.443929	−0.221964	−	0.975055i	$-0.571247\pi$
$587$	−1.46328e95	−0.443929	−0.221964	+	0.975055i	$0.571247\pi$
$588$	−4.85189e94	−0.138801
$589$	4.71347e95	1.27164
$590$	5.90742e92	0.00150315
$591$	−3.07057e95	−0.736972
$592$	−1.96077e95	−0.443943
$593$	−7.20546e95	−1.53913	−0.769564	−	0.638569i	$-0.779526\pi$
$593$	−7.20546e95	−1.53913	−0.769564	+	0.638569i	$0.779526\pi$
$594$	−1.91379e94	−0.0385712
$595$	−3.03455e95	−0.577111
$596$	9.57190e95	1.71792
$597$	5.81511e95	0.985017
$598$	4.06931e95	0.650624
$599$	7.65357e95	1.15515	0.577575	−	0.816337i	$-0.303999\pi$
$599$	7.65357e95	1.15515	0.577575	+	0.816337i	$0.303999\pi$
$600$	−1.39797e95	−0.199195
$601$	−6.43040e95	−0.865105	−0.432553	−	0.901609i	$-0.642387\pi$
$601$	−6.43040e95	−0.865105	−0.432553	+	0.901609i	$0.642387\pi$
$602$	−3.10795e94	−0.0394817
$603$	−1.62268e95	−0.194664
$604$	4.52902e95	0.513133
$605$	−4.04237e94	−0.0432589
$606$	−2.05499e95	−0.207732
$607$	1.61041e96	1.53790	0.768948	−	0.639311i	$-0.220780\pi$
$607$	1.61041e96	1.53790	0.768948	+	0.639311i	$0.220780\pi$
$608$	−6.57358e95	−0.593101
$609$	1.42034e96	1.21087
$610$	−5.36510e94	−0.0432214
$611$	−8.26628e93	−0.00629345
$612$	5.57869e95	0.401428
$613$	−1.54880e96	−1.05344	−0.526718	−	0.850040i	$-0.676578\pi$
$613$	−1.54880e96	−1.05344	−0.526718	+	0.850040i	$0.676578\pi$
$614$	−4.28588e95	−0.275569
$615$	−4.49788e95	−0.273411
$616$	7.62776e95	0.438392
$617$	−3.47655e96	−1.88934	−0.944672	−	0.328017i	$-0.893620\pi$
$617$	−3.47655e96	−1.88934	−0.944672	+	0.328017i	$0.893620\pi$
$618$	−1.17843e95	−0.0605622
$619$	−9.74011e95	−0.473409	−0.236704	−	0.971582i	$-0.576067\pi$
$619$	−9.74011e95	−0.473409	−0.236704	+	0.971582i	$0.576067\pi$
$620$	−1.09001e96	−0.501090
$621$	−7.36859e95	−0.320423
$622$	1.25469e95	0.0516140
$623$	−4.60872e96	−1.79367
$624$	2.50708e96	0.923209
$625$	1.50939e96	0.525947
$626$	−5.13582e95	−0.169354
$627$	1.73462e96	0.541346
$628$	1.28751e96	0.380314
$629$	2.30841e96	0.645455
$630$	−1.22155e95	−0.0323343
$631$	−2.16054e96	−0.541438	−0.270719	−	0.962658i	$-0.587261\pi$
$631$	−2.16054e96	−0.541438	−0.270719	+	0.962658i	$0.587261\pi$
$632$	5.63653e95	0.133743
$633$	−2.23295e96	−0.501708
$634$	4.44343e95	0.0945451
$635$	−1.18814e96	−0.239427
$636$	−7.30794e95	−0.139484
$637$	2.56705e96	0.464114
$638$	−2.19362e96	−0.375706
$639$	−1.63218e95	−0.0264843
$640$	2.00925e96	0.308906
$641$	−5.33136e95	−0.0776669	−0.0388334	−	0.999246i	$-0.512364\pi$
$641$	−5.33136e95	−0.0776669	−0.0388334	+	0.999246i	$0.512364\pi$
$642$	−8.46558e95	−0.116869
$643$	−5.65858e95	−0.0740336	−0.0370168	−	0.999315i	$-0.511786\pi$
$643$	−5.65858e95	−0.0740336	−0.0370168	+	0.999315i	$0.511786\pi$
$644$	1.43470e97	1.77910
$645$	3.34577e95	0.0393265
$646$	2.37810e96	0.264977
$647$	5.16548e95	0.0545648	0.0272824	−	0.999628i	$-0.491315\pi$
$647$	5.16548e95	0.0545648	0.0272824	+	0.999628i	$0.491315\pi$
$648$	4.59699e95	0.0460401
$649$	−1.72642e95	−0.0163947
$650$	3.61323e96	0.325376
$651$	9.70051e96	0.828420
$652$	7.59428e96	0.615098
$653$	−3.76314e96	−0.289099	−0.144549	−	0.989498i	$-0.546173\pi$
$653$	−3.76314e96	−0.289099	−0.144549	+	0.989498i	$0.546173\pi$
$654$	1.36167e94	0.000992293 0
$655$	1.06146e95	0.00733804
$656$	−1.53071e97	−1.00394
$657$	3.28798e96	0.204608
$658$	1.37069e94	0.000809366 0
$659$	3.78460e96	0.212067	0.106034	−	0.994363i	$-0.466185\pi$
$659$	3.78460e96	0.212067	0.106034	+	0.994363i	$0.466185\pi$
$660$	−4.01138e96	−0.213318
$661$	−2.48052e96	−0.125197	−0.0625983	−	0.998039i	$-0.519939\pi$
$661$	−2.48052e96	−0.125197	−0.0625983	+	0.998039i	$0.519939\pi$
$662$	1.63635e96	0.0783925
$663$	−2.95159e97	−1.34227
$664$	1.32238e97	0.570897
$665$	1.10719e97	0.453811
$666$	9.29246e95	0.0361634
$667$	−8.44599e97	−3.12111
$668$	2.28088e97	0.800412
$669$	−7.43962e96	−0.247942
$670$	1.59963e96	0.0506335
$671$	1.56793e97	0.471410
$672$	−1.35287e97	−0.386381
$673$	2.19107e97	0.594479	0.297239	−	0.954803i	$-0.403934\pi$
$673$	2.19107e97	0.594479	0.297239	+	0.954803i	$0.403934\pi$
$674$	−4.47059e96	−0.115239
$675$	−6.54273e96	−0.160243
$676$	−9.84760e97	−2.29176
$677$	3.20061e97	0.707821	0.353910	−	0.935279i	$-0.384852\pi$
$677$	3.20061e97	0.707821	0.353910	+	0.935279i	$0.384852\pi$
$678$	−6.58258e96	−0.138348
$679$	6.61495e97	1.32135
$680$	−1.12575e97	−0.213739
$681$	4.18109e97	0.754595
$682$	−1.49818e97	−0.257041
$683$	5.88966e97	0.960673	0.480337	−	0.877084i	$-0.340515\pi$
$683$	5.88966e97	0.960673	0.480337	+	0.877084i	$0.340515\pi$
$684$	−2.03545e97	−0.315663
$685$	5.55296e96	0.0818841
$686$	1.26536e97	0.177432
$687$	−6.14914e97	−0.819987
$688$	1.13862e97	0.144404
$689$	3.86650e97	0.466396
$690$	7.26390e96	0.0833444
$691$	1.07178e97	0.116980	0.0584901	−	0.998288i	$-0.481371\pi$
$691$	1.07178e97	0.116980	0.0584901	+	0.998288i	$0.481371\pi$
$692$	−4.73017e97	−0.491153
$693$	3.56993e97	0.352665
$694$	−1.84332e97	−0.173260
$695$	7.20708e97	0.644590
$696$	5.26914e97	0.448458
$697$	1.80210e98	1.45965
$698$	−2.74371e97	−0.211507
$699$	−8.30650e96	−0.0609475
$700$	1.27390e98	0.889722
$701$	−1.65328e98	−1.09920	−0.549598	−	0.835429i	$-0.685219\pi$
$701$	−1.65328e98	−1.09920	−0.549598	+	0.835429i	$0.685219\pi$
$702$	−1.18815e97	−0.0752042
$703$	−8.42249e97	−0.507554
$704$	−1.22041e98	−0.700241
$705$	−1.47557e95	−0.000806185 0
$706$	−4.93082e97	−0.256541
$707$	3.83331e98	1.89935
$708$	2.02581e96	0.00955988
$709$	−3.96232e96	−0.0178096	−0.00890481	−	0.999960i	$-0.502835\pi$
$709$	−3.96232e96	−0.0178096	−0.00890481	+	0.999960i	$0.502835\pi$
$710$	1.60899e96	0.00688875
$711$	2.63799e97	0.107590
$712$	−1.70973e98	−0.664305
$713$	−5.76837e98	−2.13533
$714$	4.89422e97	0.172622
$715$	2.12235e98	0.713277
$716$	−2.58578e98	−0.828119
$717$	6.77228e97	0.206692
$718$	8.19137e96	0.0238267
$719$	4.28219e97	0.118719	0.0593593	−	0.998237i	$-0.481094\pi$
$719$	4.28219e97	0.118719	0.0593593	+	0.998237i	$0.481094\pi$
$720$	4.47525e97	0.118262
$721$	2.19821e98	0.553735
$722$	1.48916e96	0.00357609
$723$	1.30039e98	0.297715
$724$	−4.67748e98	−1.02101
$725$	−7.49938e98	−1.56086
$726$	6.51966e96	0.0129393
$727$	−6.82395e98	−1.29151	−0.645756	−	0.763544i	$-0.723458\pi$
$727$	−6.82395e98	−1.29151	−0.645756	+	0.763544i	$0.723458\pi$
$728$	4.73560e98	0.854756
$729$	2.15147e97	0.0370370
$730$	−3.24126e97	−0.0532201
$731$	−1.34050e98	−0.209951
$732$	−1.83984e98	−0.274883
$733$	9.72133e98	1.38560	0.692801	−	0.721129i	$-0.256377\pi$
$733$	9.72133e98	1.38560	0.692801	+	0.721129i	$0.256377\pi$
$734$	−1.37279e98	−0.186677
$735$	4.58230e97	0.0594525
$736$	8.04478e98	0.995932
$737$	−4.67484e98	−0.552253
$738$	7.25432e97	0.0817810
$739$	7.64044e98	0.822026	0.411013	−	0.911630i	$-0.365175\pi$
$739$	7.64044e98	0.822026	0.411013	+	0.911630i	$0.365175\pi$
$740$	1.94773e98	0.200002
$741$	1.07692e99	1.05549
$742$	−6.41130e97	−0.0599807
$743$	−5.03918e98	−0.450034	−0.225017	−	0.974355i	$-0.572244\pi$
$743$	−5.03918e98	−0.450034	−0.225017	+	0.974355i	$0.572244\pi$
$744$	3.59867e98	0.306815
$745$	−9.04004e98	−0.735833
$746$	2.96086e98	0.230106
$747$	6.18898e98	0.459259
$748$	1.60718e99	1.13883
$749$	1.57914e99	1.06856
$750$	1.41959e98	0.0917380
$751$	1.04907e99	0.647481	0.323741	−	0.946146i	$-0.395059\pi$
$751$	1.04907e99	0.647481	0.323741	+	0.946146i	$0.395059\pi$
$752$	−5.02162e96	−0.00296025
$753$	−1.87303e99	−1.05467
$754$	−1.36188e99	−0.732534
$755$	−4.27737e98	−0.219790
$756$	−4.18903e98	−0.205642
$757$	−3.73086e99	−1.74985	−0.874925	−	0.484258i	$-0.839090\pi$
$757$	−3.73086e99	−1.74985	−0.874925	+	0.484258i	$0.839090\pi$
$758$	2.92485e98	0.131074
$759$	−2.12284e99	−0.909026
$760$	4.10742e98	0.168074
$761$	2.16870e99	0.848065	0.424033	−	0.905647i	$-0.360614\pi$
$761$	2.16870e99	0.848065	0.424033	+	0.905647i	$0.360614\pi$
$762$	1.91626e98	0.0716158
$763$	−2.54002e97	−0.00907278
$764$	1.40879e99	0.480977
$765$	−5.26871e98	−0.171943
$766$	−6.32825e97	−0.0197420
$767$	−1.07182e98	−0.0319656
$768$	1.17534e99	0.335122
$769$	−3.51618e99	−0.958544	−0.479272	−	0.877666i	$-0.659099\pi$
$769$	−3.51618e99	−0.958544	−0.479272	+	0.877666i	$0.659099\pi$
$770$	−3.51921e98	−0.0917307
$771$	−2.64379e99	−0.658948
$772$	2.99329e99	0.713432
$773$	1.94236e99	0.442728	0.221364	−	0.975191i	$-0.428949\pi$
$773$	1.94236e99	0.442728	0.221364	+	0.975191i	$0.428949\pi$
$774$	−5.39616e97	−0.0117631
$775$	−5.12186e99	−1.06787
$776$	2.45400e99	0.489378
$777$	−1.73338e99	−0.330651
$778$	−1.23401e99	−0.225176
$779$	−6.57517e99	−1.14780
$780$	−2.49041e99	−0.415918
$781$	−4.70220e98	−0.0751346
$782$	−2.91033e99	−0.444948
$783$	2.46605e99	0.360763
$784$	1.55944e99	0.218305
$785$	−1.21597e99	−0.162899
$786$	−1.71196e97	−0.00219491
$787$	7.76774e99	0.953162	0.476581	−	0.879131i	$-0.341876\pi$
$787$	7.76774e99	0.953162	0.476581	+	0.879131i	$0.341876\pi$
$788$	1.03802e100	1.21914
$789$	2.35004e99	0.264191
$790$	−2.60052e98	−0.0279850
$791$	1.22789e100	1.26495
$792$	1.32436e99	0.130614
$793$	9.73426e99	0.919132
$794$	4.62897e99	0.418482
$795$	6.90188e98	0.0597450
$796$	−1.96583e100	−1.62946
$797$	4.88527e99	0.387772	0.193886	−	0.981024i	$-0.437891\pi$
$797$	4.88527e99	0.387772	0.193886	+	0.981024i	$0.437891\pi$
$798$	−1.78571e99	−0.135741
$799$	5.91195e97	0.00430395
$800$	7.14313e99	0.498063
$801$	−8.00184e99	−0.534402
$802$	2.52771e99	0.161700
$803$	9.47244e99	0.580464
$804$	5.48556e99	0.322023
$805$	−1.35498e100	−0.762038
$806$	−9.30125e99	−0.501167
$807$	1.05776e99	0.0546073
$808$	1.42207e100	0.703444
$809$	−1.30775e100	−0.619869	−0.309935	−	0.950758i	$-0.600307\pi$
$809$	−1.30775e100	−0.619869	−0.309935	+	0.950758i	$0.600307\pi$
$810$	−2.12091e98	−0.00963360
$811$	1.39710e100	0.608148	0.304074	−	0.952648i	$-0.401653\pi$
$811$	1.39710e100	0.608148	0.304074	+	0.952648i	$0.401653\pi$
$812$	−4.80153e100	−2.00307
$813$	1.72022e100	0.687799
$814$	2.67709e99	0.102594
$815$	−7.17230e99	−0.263464
$816$	−1.79304e100	−0.631362
$817$	4.89096e99	0.165095
$818$	2.17977e99	0.0705377
$819$	2.21634e100	0.687610
$820$	1.52053e100	0.452290
$821$	−1.50706e100	−0.429825	−0.214912	−	0.976633i	$-0.568947\pi$
$821$	−1.50706e100	−0.429825	−0.214912	+	0.976633i	$0.568947\pi$
$822$	−8.95598e98	−0.0244926
$823$	−3.63966e100	−0.954480	−0.477240	−	0.878773i	$-0.658363\pi$
$823$	−3.63966e100	−0.954480	−0.477240	+	0.878773i	$0.658363\pi$
$824$	8.15485e99	0.205082
$825$	−1.88492e100	−0.454602
$826$	1.77726e98	0.00411093
$827$	−6.70641e100	−1.48782	−0.743909	−	0.668281i	$-0.767031\pi$
$827$	−6.70641e100	−1.48782	−0.743909	+	0.668281i	$0.767031\pi$
$828$	2.49099e100	0.530060
$829$	5.72549e100	1.16864	0.584321	−	0.811523i	$-0.301361\pi$
$829$	5.72549e100	1.16864	0.584321	+	0.811523i	$0.301361\pi$
$830$	−6.10105e99	−0.119457
$831$	3.48445e100	0.654484
$832$	−7.57673e100	−1.36530
$833$	−1.83593e100	−0.317397
$834$	−1.16238e100	−0.192806
$835$	−2.15414e100	−0.342839
$836$	−5.86398e100	−0.895521
$837$	1.68424e100	0.246818
$838$	3.12373e99	0.0439293
$839$	4.67178e99	0.0630514	0.0315257	−	0.999503i	$-0.489963\pi$
$839$	4.67178e99	0.0630514	0.0315257	+	0.999503i	$0.489963\pi$
$840$	8.45325e99	0.109493
$841$	2.02225e101	2.51404
$842$	−2.31189e100	−0.275867
$843$	−4.41292e99	−0.0505446
$844$	7.54861e100	0.829951
$845$	9.30042e100	0.981626
$846$	2.37984e97	0.000241141 0
$847$	−1.21616e100	−0.118307
$848$	2.34883e100	0.219379
$849$	8.12288e99	0.0728442
$850$	−2.58414e100	−0.222517
$851$	1.03075e101	0.852282
$852$	5.51766e99	0.0438116
$853$	−2.08194e101	−1.58755	−0.793775	−	0.608212i	$-0.791887\pi$
$853$	−2.08194e101	−1.58755	−0.793775	+	0.608212i	$0.791887\pi$
$854$	−1.61410e100	−0.118205
$855$	1.92235e100	0.135207
$856$	5.85826e100	0.395752
$857$	1.88710e101	1.22449	0.612246	−	0.790667i	$-0.290266\pi$
$857$	1.88710e101	1.22449	0.612246	+	0.790667i	$0.290266\pi$
$858$	−3.42299e100	−0.213351
$859$	7.81045e100	0.467640	0.233820	−	0.972280i	$-0.424877\pi$
$859$	7.81045e100	0.467640	0.233820	+	0.972280i	$0.424877\pi$
$860$	−1.13105e100	−0.0650558
$861$	−1.35320e101	−0.747743
$862$	4.11433e100	0.218423
$863$	−7.44003e100	−0.379491	−0.189746	−	0.981833i	$-0.560766\pi$
$863$	−7.44003e100	−0.379491	−0.189746	+	0.981833i	$0.560766\pi$
$864$	−2.34891e100	−0.115118
$865$	4.46734e100	0.210375
$866$	−6.50801e100	−0.294497
$867$	7.83247e100	0.340596
$868$	−3.27931e101	−1.37041
$869$	7.59988e100	0.305228
$870$	−2.43102e100	−0.0938369
$871$	−2.90231e101	−1.07676
$872$	−9.42289e98	−0.00336020
$873$	1.14851e101	0.393681
$874$	1.06186e101	0.349884
$875$	−2.64805e101	−0.838782
$876$	−1.11152e101	−0.338473
$877$	−5.09689e101	−1.49217	−0.746087	−	0.665849i	$-0.768070\pi$
$877$	−5.09689e101	−1.49217	−0.746087	+	0.665849i	$0.768070\pi$
$878$	6.33064e100	0.178191
$879$	−2.48023e101	−0.671238
$880$	1.28929e101	0.335504
$881$	−7.35235e100	−0.183974	−0.0919871	−	0.995760i	$-0.529322\pi$
$881$	−7.35235e100	−0.183974	−0.0919871	+	0.995760i	$0.529322\pi$
$882$	−7.39048e99	−0.0177831
$883$	4.26855e101	0.987725	0.493863	−	0.869540i	$-0.335585\pi$
$883$	4.26855e101	0.987725	0.493863	+	0.869540i	$0.335585\pi$
$884$	9.97799e101	2.22044
$885$	−1.91325e99	−0.00409477
$886$	−1.33911e101	−0.275646
$887$	−5.06049e101	−1.00191	−0.500954	−	0.865474i	$-0.667017\pi$
$887$	−5.06049e101	−1.00191	−0.500954	+	0.865474i	$0.667017\pi$
$888$	−6.43047e100	−0.122460
$889$	−3.57454e101	−0.654800
$890$	7.88815e100	0.139002
$891$	6.19825e100	0.105072
$892$	2.51500e101	0.410157
$893$	−2.15704e99	−0.00338441
$894$	1.45801e101	0.220097
$895$	2.44211e101	0.354707
$896$	6.04489e101	0.844815
$897$	−1.31794e102	−1.77238
$898$	−1.49104e99	−0.00192955
$899$	1.93050e102	2.40415
$900$	2.21180e101	0.265082
$901$	−2.76528e101	−0.318958
$902$	2.08992e101	0.232009
$903$	1.00658e101	0.107553
$904$	4.55521e101	0.468487
$905$	4.41758e101	0.437329
$906$	6.89868e100	0.0657420
$907$	−3.29000e101	−0.301818	−0.150909	−	0.988548i	$-0.548220\pi$
$907$	−3.29000e101	−0.301818	−0.150909	+	0.988548i	$0.548220\pi$
$908$	−1.41344e102	−1.24829
$909$	6.65554e101	0.565887
$910$	−2.18486e101	−0.178852
$911$	−2.43324e102	−1.91779	−0.958893	−	0.283767i	$-0.908416\pi$
$911$	−2.43324e102	−1.91779	−0.958893	+	0.283767i	$0.908416\pi$
$912$	6.54208e101	0.496471
$913$	1.78300e102	1.30290
$914$	−2.56389e100	−0.0180408
$915$	1.73761e101	0.117740
$916$	2.07875e102	1.35646
$917$	3.19343e100	0.0200685
$918$	8.49754e100	0.0514305
$919$	−2.62898e102	−1.53251	−0.766254	−	0.642537i	$-0.777882\pi$
$919$	−2.62898e102	−1.53251	−0.766254	+	0.642537i	$0.777882\pi$
$920$	−5.02669e101	−0.282229
$921$	1.38808e102	0.750683
$922$	1.73183e101	0.0902173
$923$	−2.91930e101	−0.146494
$924$	−1.20683e102	−0.583396
$925$	9.15225e101	0.426224
$926$	−7.77020e101	−0.348621
$927$	3.81661e101	0.164979
$928$	−2.69235e102	−1.12131
$929$	−2.75628e102	−1.10607	−0.553033	−	0.833160i	$-0.686530\pi$
$929$	−2.75628e102	−1.10607	−0.553033	+	0.833160i	$0.686530\pi$
$930$	−1.66031e101	−0.0641990
$931$	6.69858e101	0.249585
$932$	2.80805e101	0.100822
$933$	−4.06359e101	−0.140603
$934$	−3.84930e101	−0.128356
$935$	−1.51788e102	−0.487795
$936$	8.22213e101	0.254664
$937$	−3.79577e102	−1.13314	−0.566571	−	0.824013i	$-0.691730\pi$
$937$	−3.79577e102	−1.13314	−0.566571	+	0.824013i	$0.691730\pi$
$938$	4.81252e101	0.138476
$939$	1.66335e102	0.461339
$940$	4.98823e99	0.00133363
$941$	−7.07790e102	−1.82416	−0.912080	−	0.410013i	$-0.865524\pi$
$941$	−7.07790e102	−1.82416	−0.912080	+	0.410013i	$0.865524\pi$
$942$	1.96115e101	0.0487254
$943$	8.04673e102	1.92737
$944$	−6.51113e100	−0.0150357
$945$	3.95627e101	0.0880823
$946$	−1.55460e101	−0.0333713
$947$	9.27922e102	1.92060	0.960300	−	0.278969i	$-0.0899926\pi$
$947$	9.27922e102	1.92060	0.960300	+	0.278969i	$0.0899926\pi$
$948$	−8.91787e101	−0.177981
$949$	5.88084e102	1.13176
$950$	9.42852e101	0.174976
$951$	−1.43911e102	−0.257552
$952$	−3.38685e102	−0.584549
$953$	−1.95220e102	−0.324953	−0.162476	−	0.986712i	$-0.551948\pi$
$953$	−1.95220e102	−0.324953	−0.162476	+	0.986712i	$0.551948\pi$
$954$	−1.11316e101	−0.0178705
$955$	−1.33051e102	−0.206016
$956$	−2.28940e102	−0.341920
$957$	7.10453e102	1.02347
$958$	−4.21365e101	−0.0585530
$959$	1.67062e102	0.223942
$960$	−1.35248e102	−0.174893
$961$	5.16879e102	0.644811
$962$	1.66204e102	0.200033
$963$	2.74177e102	0.318364
$964$	−4.39602e102	−0.492495
$965$	−2.82697e102	−0.305583
$966$	2.18536e102	0.227936
$967$	−3.46197e102	−0.348425	−0.174213	−	0.984708i	$-0.555738\pi$
$967$	−3.46197e102	−0.348425	−0.174213	+	0.984708i	$0.555738\pi$
$968$	−4.51167e101	−0.0438164
$969$	−7.70200e102	−0.721827
$970$	−1.13220e102	−0.102399
$971$	1.58896e103	1.38691	0.693457	−	0.720498i	$-0.256087\pi$
$971$	1.58896e103	1.38691	0.693457	+	0.720498i	$0.256087\pi$
$972$	−7.27316e101	−0.0612685
$973$	2.16827e103	1.76287
$974$	−9.32966e101	−0.0732119
$975$	−1.17023e103	−0.886361
$976$	5.91339e102	0.432332
$977$	−6.46717e102	−0.456407	−0.228203	−	0.973613i	$-0.573285\pi$
$977$	−6.46717e102	−0.456407	−0.228203	+	0.973613i	$0.573285\pi$
$978$	1.15677e102	0.0788056
$979$	−2.30528e103	−1.51607
$980$	−1.54907e102	−0.0983493
$981$	−4.41008e100	−0.00270312
$982$	2.93045e102	0.173416
$983$	2.58982e102	0.147970	0.0739850	−	0.997259i	$-0.476428\pi$
$983$	2.58982e102	0.147970	0.0739850	+	0.997259i	$0.476428\pi$
$984$	−5.02006e102	−0.276935
$985$	−9.80345e102	−0.522191
$986$	9.74002e102	0.500964
$987$	−4.43928e100	−0.00220481
$988$	−3.64058e103	−1.74605
$989$	−5.98559e102	−0.277227
$990$	−6.11019e101	−0.0273301
$991$	−2.31880e103	−1.00166	−0.500831	−	0.865545i	$-0.666972\pi$
$991$	−2.31880e103	−1.00166	−0.500831	+	0.865545i	$0.666972\pi$
$992$	−1.83880e103	−0.767152
$993$	−5.29967e102	−0.213550
$994$	4.84068e101	0.0188398
$995$	1.85660e103	0.697945
$996$	−2.09221e103	−0.759729
$997$	1.95399e103	0.685393	0.342697	−	0.939446i	$-0.388660\pi$
$997$	1.95399e103	0.685393	0.342697	+	0.939446i	$0.388660\pi$
$998$	1.65952e102	0.0562315
$999$	−3.00957e102	−0.0985134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.70.a.b.1.3	✓	6
3.2	odd	2		9.70.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.70.a.b.1.3	✓	6	1.1	even	1	trivial
9.70.a.c.1.4		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)

\(f(q)\)	\(=\)	\(q-5.14931e9 q^{2} +1.66772e16 q^{3} -5.63780e20 q^{4} +5.32454e23 q^{5} -8.58759e25 q^{6} +1.60190e29 q^{7} +5.94269e30 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q-5.14931e9 q^{2} +1.66772e16 q^{3} -5.63780e20 q^{4} +5.32454e23 q^{5} -8.58759e25 q^{6} +1.60190e29 q^{7} +5.94269e30 q^{8} +2.78128e32 q^{9} -2.74177e33 q^{10} +8.01269e35 q^{11} -9.40227e36 q^{12} +4.97458e38 q^{13} -8.24868e38 q^{14} +8.87984e39 q^{15} +3.02197e41 q^{16} -3.55776e42 q^{17} -1.43217e42 q^{18} +1.29809e44 q^{19} -3.00187e44 q^{20} +2.67152e45 q^{21} -4.12598e45 q^{22} -1.58861e47 q^{23} +9.91073e46 q^{24} -1.41056e48 q^{25} -2.56156e48 q^{26} +4.63840e48 q^{27} -9.03120e49 q^{28} +5.31660e50 q^{29} -4.57250e49 q^{30} +3.63108e51 q^{31} -5.06405e51 q^{32} +1.33629e52 q^{33} +1.83200e52 q^{34} +8.52939e52 q^{35} -1.56803e53 q^{36} -6.48838e53 q^{37} -6.68425e53 q^{38} +8.29619e54 q^{39} +3.16421e54 q^{40} -5.06527e55 q^{41} -1.37565e55 q^{42} +3.76782e55 q^{43} -4.51740e56 q^{44} +1.48091e56 q^{45} +8.18022e56 q^{46} -1.66171e55 q^{47} +5.03979e57 q^{48} +5.16034e57 q^{49} +7.26340e57 q^{50} -5.93334e58 q^{51} -2.80457e59 q^{52} +7.77253e58 q^{53} -2.38845e58 q^{54} +4.26639e59 q^{55} +9.51960e59 q^{56} +2.16484e60 q^{57} -2.73768e60 q^{58} -2.15460e59 q^{59} -5.00628e60 q^{60} +1.95680e61 q^{61} -1.86976e61 q^{62} +4.45534e61 q^{63} -1.52309e62 q^{64} +2.64873e62 q^{65} -6.88097e61 q^{66} -5.83429e62 q^{67} +2.00580e63 q^{68} -2.64935e63 q^{69} -4.39204e62 q^{70} -5.86844e62 q^{71} +1.65283e63 q^{72} +1.18218e64 q^{73} +3.34107e63 q^{74} -2.35241e64 q^{75} -7.31836e64 q^{76} +1.28355e65 q^{77} -4.27196e64 q^{78} +9.48481e64 q^{79} +1.60906e65 q^{80} +7.73554e64 q^{81} +2.60826e65 q^{82} +2.22522e66 q^{83} -1.50615e66 q^{84} -1.89434e66 q^{85} -1.94017e65 q^{86} +8.86660e66 q^{87} +4.76169e66 q^{88} -2.87703e67 q^{89} -7.62564e65 q^{90} +7.96878e67 q^{91} +8.95626e67 q^{92} +6.05563e67 q^{93} +8.55663e64 q^{94} +6.91172e67 q^{95} -8.44540e67 q^{96} +4.12944e68 q^{97} -2.65722e67 q^{98} +2.22856e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 19700962938 q^{2} + 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 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

Fields

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Groups

Database

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