LMFDB - Embedded newform 432.2.l.b.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	432.107
Dual form			432.2.l.b.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12975 - 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(-1.26575 + 1.26575i) q^{5} +1.47880 q^{7} +(1.01076 - 2.64166i) q^{8} +O(q^{10})$	\(q+(-1.12975 - 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(-1.26575 + 1.26575i) q^{5} +1.47880 q^{7} +(1.01076 - 2.64166i) q^{8} +(2.50674 - 0.353222i) q^{10} +(-1.16753 - 1.16753i) q^{11} +(-0.842585 + 0.842585i) q^{13} +(-1.67068 - 1.25800i) q^{14} +(-3.38913 + 2.12458i) q^{16} +4.56781i q^{17} +(2.78873 + 2.78873i) q^{19} +(-3.13246 - 1.73340i) q^{20} +(0.325812 + 2.31221i) q^{22} +5.13786i q^{23} +1.79575i q^{25} +(1.66869 - 0.235133i) q^{26} +(0.817282 + 2.84245i) q^{28} +(0.161370 + 0.161370i) q^{29} +9.34223i q^{31} +(5.63621 + 0.482847i) q^{32} +(3.88578 - 5.16048i) q^{34} +(-1.87180 + 1.87180i) q^{35} +(-6.53108 - 6.53108i) q^{37} +(-0.778227 - 5.52290i) q^{38} +(2.06432 + 4.62305i) q^{40} +9.35455 q^{41} +(3.98100 - 3.98100i) q^{43} +(1.59888 - 2.88939i) q^{44} +(4.37071 - 5.80449i) q^{46} +5.75824 q^{47} -4.81314 q^{49} +(1.52762 - 2.02875i) q^{50} +(-2.08522 - 1.15389i) q^{52} +(-7.87488 + 7.87488i) q^{53} +2.95560 q^{55} +(1.49471 - 3.90650i) q^{56} +(-0.0450322 - 0.319583i) q^{58} +(1.12227 + 1.12227i) q^{59} +(0.396250 - 0.396250i) q^{61} +(7.94732 - 10.5544i) q^{62} +(-5.95675 - 5.34015i) q^{64} -2.13300i q^{65} +(6.11749 + 6.11749i) q^{67} +(-8.77991 + 2.52446i) q^{68} +(3.70697 - 0.522347i) q^{70} +15.9291i q^{71} -12.6493i q^{73} +(1.82257 + 12.9344i) q^{74} +(-3.81905 + 6.90151i) q^{76} +(-1.72655 - 1.72655i) q^{77} -4.38560i q^{79} +(1.60060 - 6.97897i) q^{80} +(-10.5683 - 7.95779i) q^{82} +(4.10414 - 4.10414i) q^{83} +(-5.78171 - 5.78171i) q^{85} +(-7.88412 + 1.11095i) q^{86} +(-4.26430 + 1.90413i) q^{88} -0.815713 q^{89} +(-1.24602 + 1.24602i) q^{91} +(-9.87561 + 2.83951i) q^{92} +(-6.50536 - 4.89846i) q^{94} -7.05966 q^{95} -12.3377 q^{97} +(5.43763 + 4.09447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) $ 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.12975	−	0.850687i	−0.798853	−	0.601526i
$2$	−1.12975	−	0.850687i	−0.798853	−	0.601526i
$3$		0			0
$3$		0			0
$4$	0.552664	+	1.92212i	0.276332	+	0.961062i
$5$	−1.26575	+	1.26575i	−0.566061	+	0.566061i	−0.931022	−	0.364962i	$-0.881082\pi$
$5$	−1.26575	+	1.26575i	−0.566061	+	0.566061i	0.364962	+	0.931022i	$0.381082\pi$
$6$		0			0
$7$	1.47880			0.558936			0.279468	−	0.960155i	$-0.409842\pi$
$7$	1.47880			0.558936			0.279468	+	0.960155i	$0.409842\pi$
$8$	1.01076	−	2.64166i	0.357356	−	0.933968i
$9$		0			0
$10$	2.50674	−	0.353222i	0.792700	−	0.111699i
$11$	−1.16753	−	1.16753i	−0.352023	−	0.352023i	0.508839	−	0.860862i	$-0.330075\pi$
$11$	−1.16753	−	1.16753i	−0.352023	−	0.352023i	−0.860862	+	0.508839i	$0.830075\pi$
$12$		0			0
$13$	−0.842585	+	0.842585i	−0.233691	+	0.233691i	−0.814231	−	0.580540i	$-0.802841\pi$
$13$	−0.842585	+	0.842585i	−0.233691	+	0.233691i	0.580540	+	0.814231i	$0.302841\pi$
$14$	−1.67068	−	1.25800i	−0.446507	−	0.336215i
$15$		0			0
$16$	−3.38913	+	2.12458i	−0.847281	+	0.531144i
$17$			4.56781i			1.10786i	0.832564	+	0.553929i	$0.186872\pi$
$17$			4.56781i			1.10786i	−0.832564	+	0.553929i	$0.813128\pi$
$18$		0			0
$19$	2.78873	+	2.78873i	0.639778	+	0.639778i	0.950501	−	0.310723i	$-0.100571\pi$
$19$	2.78873	+	2.78873i	0.639778	+	0.639778i	−0.310723	+	0.950501i	$0.600571\pi$
$20$	−3.13246	−	1.73340i	−0.700440	−	0.387599i
$21$		0			0
$22$	0.325812	+	2.31221i	0.0694634	+	0.492966i
$23$			5.13786i			1.07132i	0.844434	+	0.535659i	$0.179937\pi$
$23$			5.13786i			1.07132i	−0.844434	+	0.535659i	$0.820063\pi$
$24$		0			0
$25$			1.79575i			0.359151i
$26$	1.66869	−	0.235133i	0.327256	−	0.0461134i
$27$		0			0
$28$	0.817282	+	2.84245i	0.154452	+	0.537172i
$29$	0.161370	+	0.161370i	0.0299657	+	0.0299657i	0.721931	−	0.691965i	$-0.243255\pi$
$29$	0.161370	+	0.161370i	0.0299657	+	0.0299657i	−0.691965	+	0.721931i	$0.743255\pi$
$30$		0			0
$31$			9.34223i			1.67791i	0.544197	+	0.838957i	$0.316834\pi$
$31$			9.34223i			1.67791i	−0.544197	+	0.838957i	$0.683166\pi$
$32$	5.63621	+	0.482847i	0.996351	+	0.0853562i
$33$		0			0
$34$	3.88578	−	5.16048i	0.666406	−	0.885015i
$35$	−1.87180	+	1.87180i	−0.316391	+	0.316391i
$36$		0			0
$37$	−6.53108	−	6.53108i	−1.07370	−	1.07370i	−0.997059	−	0.0766437i	$-0.975580\pi$
$37$	−6.53108	−	6.53108i	−1.07370	−	1.07370i	−0.0766437	−	0.997059i	$-0.524420\pi$
$38$	−0.778227	−	5.52290i	−0.126245	−	0.895932i
$39$		0			0
$40$	2.06432	+	4.62305i	0.326398	+	0.730968i
$41$	9.35455			1.46094			0.730468	−	0.682947i	$-0.239302\pi$
$41$	9.35455			1.46094			0.730468	+	0.682947i	$0.239302\pi$
$42$		0			0
$43$	3.98100	−	3.98100i	0.607097	−	0.607097i	−0.335089	−	0.942186i	$-0.608766\pi$
$43$	3.98100	−	3.98100i	0.607097	−	0.607097i	0.942186	+	0.335089i	$0.108766\pi$
$44$	1.59888	−	2.88939i	0.241041	−	0.435591i
$45$		0			0
$46$	4.37071	−	5.80449i	0.644426	−	0.855826i
$47$	5.75824			0.839925			0.419963	−	0.907541i	$-0.362043\pi$
$47$	5.75824			0.839925			0.419963	+	0.907541i	$0.362043\pi$
$48$		0			0
$49$	−4.81314			−0.687591
$50$	1.52762	−	2.02875i	0.216039	−	0.286909i
$51$		0			0
$52$	−2.08522	−	1.15389i	−0.289168	−	0.160015i
$53$	−7.87488	+	7.87488i	−1.08170	+	1.08170i	−0.0853469	+	0.996351i	$0.527200\pi$
$53$	−7.87488	+	7.87488i	−1.08170	+	1.08170i	−0.996351	+	0.0853469i	$0.972800\pi$
$54$		0			0
$55$	2.95560			0.398533
$56$	1.49471	−	3.90650i	0.199739	−	0.522028i
$57$		0			0
$58$	−0.0450322	−	0.319583i	−0.00591302	−	0.0419633i
$59$	1.12227	+	1.12227i	0.146107	+	0.146107i	0.776377	−	0.630269i	$-0.217056\pi$
$59$	1.12227	+	1.12227i	0.146107	+	0.146107i	−0.630269	+	0.776377i	$0.717056\pi$
$60$		0			0
$61$	0.396250	−	0.396250i	0.0507346	−	0.0507346i	−0.681284	−	0.732019i	$-0.738578\pi$
$61$	0.396250	−	0.396250i	0.0507346	−	0.0507346i	0.732019	+	0.681284i	$0.238578\pi$
$62$	7.94732	−	10.5544i	1.00931	−	1.34041i
$63$		0			0
$64$	−5.95675	−	5.34015i	−0.744593	−	0.667518i
$65$		−	2.13300i		−	0.264567i
$66$		0			0
$67$	6.11749	+	6.11749i	0.747370	+	0.747370i	0.973985	−	0.226614i	$-0.0727657\pi$
$67$	6.11749	+	6.11749i	0.747370	+	0.747370i	−0.226614	+	0.973985i	$0.572766\pi$
$68$	−8.77991	+	2.52446i	−1.06472	+	0.306136i
$69$		0			0
$70$	3.70697	−	0.522347i	0.443068	−	0.0624324i
$71$			15.9291i			1.89043i	0.326444	+	0.945216i	$0.394149\pi$
$71$			15.9291i			1.89043i	−0.326444	+	0.945216i	$0.605851\pi$
$72$		0			0
$73$		−	12.6493i		−	1.48048i	−0.672340	−	0.740242i	$-0.734711\pi$
$73$		−	12.6493i		−	1.48048i	0.672340	−	0.740242i	$-0.265289\pi$
$74$	1.82257	+	12.9344i	0.211870	+	1.50359i
$75$		0			0
$76$	−3.81905	+	6.90151i	−0.438076	+	0.791658i
$77$	−1.72655	−	1.72655i	−0.196758	−	0.196758i
$78$		0			0
$79$		−	4.38560i		−	0.493419i	−0.969090	−	0.246709i	$-0.920651\pi$
$79$		−	4.38560i		−	0.493419i	0.969090	−	0.246709i	$-0.0793493\pi$
$80$	1.60060	−	6.97897i	0.178953	−	0.780272i
$81$		0			0
$82$	−10.5683	−	7.95779i	−1.16707	−	0.878791i
$83$	4.10414	−	4.10414i	0.450488	−	0.450488i	−0.445029	−	0.895516i	$-0.646807\pi$
$83$	4.10414	−	4.10414i	0.450488	−	0.450488i	0.895516	+	0.445029i	$0.146807\pi$
$84$		0			0
$85$	−5.78171	−	5.78171i	−0.627114	−	0.627114i
$86$	−7.88412	+	1.11095i	−0.850166	+	0.119796i
$87$		0			0
$88$	−4.26430	+	1.90413i	−0.454576	+	0.202981i
$89$	−0.815713			−0.0864654			−0.0432327	−	0.999065i	$-0.513766\pi$
$89$	−0.815713			−0.0864654			−0.0432327	+	0.999065i	$0.513766\pi$
$90$		0			0
$91$	−1.24602	+	1.24602i	−0.130618	+	0.130618i
$92$	−9.87561	+	2.83951i	−1.02960	+	0.296039i
$93$		0			0
$94$	−6.50536	−	4.89846i	−0.670977	−	0.505237i
$95$	−7.05966			−0.724306
$96$		0			0
$97$	−12.3377			−1.25270			−0.626350	−	0.779542i	$-0.715452\pi$
$97$	−12.3377			−1.25270			−0.626350	+	0.779542i	$0.715452\pi$
$98$	5.43763	+	4.09447i	0.549284	+	0.413604i
$99$		0			0
$100$	−3.45166	+	0.992448i	−0.345166	+	0.0992448i
$101$	0.195337	−	0.195337i	0.0194367	−	0.0194367i	−0.697322	−	0.716758i	$-0.745625\pi$
$101$	0.195337	−	0.195337i	0.0194367	−	0.0194367i	0.716758	+	0.697322i	$0.245625\pi$
$102$		0			0
$103$	7.40614			0.729749			0.364874	−	0.931057i	$-0.381112\pi$
$103$	7.40614			0.729749			0.364874	+	0.931057i	$0.381112\pi$
$104$	1.37418	+	3.07747i	0.134749	+	0.301771i
$105$		0			0
$106$	15.5957	−	2.19758i	1.51479	−	0.213448i
$107$	−12.0499	−	12.0499i	−1.16491	−	1.16491i	−0.983387	−	0.181519i	$-0.941899\pi$
$107$	−12.0499	−	12.0499i	−1.16491	−	1.16491i	−0.181519	−	0.983387i	$-0.558101\pi$
$108$		0			0
$109$	−2.33845	+	2.33845i	−0.223983	+	0.223983i	−0.810173	−	0.586190i	$-0.800627\pi$
$109$	−2.33845	+	2.33845i	−0.223983	+	0.223983i	0.586190	+	0.810173i	$0.300627\pi$
$110$	−3.33908	−	2.51429i	−0.318369	−	0.239728i
$111$		0			0
$112$	−5.01186	+	3.14183i	−0.473576	+	0.296875i
$113$		−	17.6709i		−	1.66234i	−0.556021	−	0.831168i	$-0.687672\pi$
$113$		−	17.6709i		−	1.66234i	0.556021	−	0.831168i	$-0.312328\pi$
$114$		0			0
$115$	−6.50325	−	6.50325i	−0.606431	−	0.606431i
$116$	−0.220990	+	0.399357i	−0.0205184	+	0.0370793i
$117$		0			0
$118$	−0.313183	−	2.22259i	−0.0288308	−	0.204606i
$119$			6.75490i			0.619221i
$120$		0			0
$121$		−	8.27376i		−	0.752160i
$122$	−0.784748	+	0.110578i	−0.0710477	+	0.0100113i
$123$		0			0
$124$	−17.9569	+	5.16311i	−1.61258	+	0.463661i
$125$	−8.60173	−	8.60173i	−0.769362	−	0.769362i
$126$		0			0
$127$		−	2.51234i		−	0.222934i	−0.993768	−	0.111467i	$-0.964445\pi$
$127$		−	2.51234i		−	0.222934i	0.993768	−	0.111467i	$-0.0355550\pi$
$128$	2.18683	+	11.1003i	0.193291	+	0.981142i
$129$		0			0
$130$	−1.81452	+	2.40976i	−0.159144	+	0.211350i
$131$	12.9471	−	12.9471i	1.13119	−	1.13119i	0.141209	−	0.989980i	$-0.454901\pi$
$131$	12.9471	−	12.9471i	1.13119	−	1.13119i	0.989980	−	0.141209i	$-0.0450991\pi$
$132$		0			0
$133$	4.12398	+	4.12398i	0.357595	+	0.357595i
$134$	−1.70716	−	12.1153i	−0.147476	−	1.04660i
$135$		0			0
$136$	12.0666	+	4.61694i	1.03470	+	0.395899i
$137$	18.2869			1.56235			0.781176	−	0.624310i	$-0.214620\pi$
$137$	18.2869			1.56235			0.781176	+	0.624310i	$0.214620\pi$
$138$		0			0
$139$	−9.14289	+	9.14289i	−0.775490	+	0.775490i	−0.979060	−	0.203570i	$-0.934745\pi$
$139$	−9.14289	+	9.14289i	−0.775490	+	0.775490i	0.203570	+	0.979060i	$0.434745\pi$
$140$	−4.63230	−	2.56335i	−0.391501	−	0.216643i
$141$		0			0
$142$	13.5507	−	17.9958i	1.13715	−	1.51018i
$143$	1.96748			0.164529
$144$		0			0
$145$	−0.408508			−0.0339248
$146$	−10.7606	+	14.2905i	−0.890550	+	1.18269i
$147$		0			0
$148$	8.94405	−	16.1630i	0.735197	−	1.32859i
$149$	−15.0435	+	15.0435i	−1.23241	+	1.23241i	−0.269381	+	0.963034i	$0.586819\pi$
$149$	−15.0435	+	15.0435i	−1.23241	+	1.23241i	−0.963034	+	0.269381i	$0.913181\pi$
$150$		0			0
$151$	1.62721			0.132421			0.0662104	−	0.997806i	$-0.478909\pi$
$151$	1.62721			0.132421			0.0662104	+	0.997806i	$0.478909\pi$
$152$	10.1856	−	4.54815i	0.826161	−	0.368904i
$153$		0			0
$154$	0.481813	+	3.41931i	0.0388256	+	0.275536i
$155$	−11.8249	−	11.8249i	−0.949802	−	0.949802i
$156$		0			0
$157$	8.31389	−	8.31389i	0.663521	−	0.663521i	−0.292688	−	0.956208i	$-0.594550\pi$
$157$	8.31389	−	8.31389i	0.663521	−	0.663521i	0.956208	+	0.292688i	$0.0945496\pi$
$158$	−3.73077	+	4.95463i	−0.296804	+	0.394169i
$159$		0			0
$160$	−7.74520	+	6.52287i	−0.612312	+	0.515678i
$161$			7.59789i			0.598798i
$162$		0			0
$163$	10.0962	+	10.0962i	0.790797	+	0.790797i	0.981624	−	0.190827i	$-0.0611170\pi$
$163$	10.0962	+	10.0962i	0.790797	+	0.790797i	−0.190827	+	0.981624i	$0.561117\pi$
$164$	5.16992	+	17.9806i	0.403703	+	1.40405i
$165$		0			0
$166$	−8.12798	+	1.14531i	−0.630854	+	0.0888931i
$167$		−	13.3585i		−	1.03371i	−0.856073	−	0.516856i	$-0.827102\pi$
$167$		−	13.3585i		−	1.03371i	0.856073	−	0.516856i	$-0.172898\pi$
$168$		0			0
$169$			11.5801i			0.890777i
$170$	1.61345	+	11.4503i	0.123746	+	0.878198i
$171$		0			0
$172$	9.85214	+	5.45183i	0.751219	+	0.415698i
$173$	−4.10881	−	4.10881i	−0.312387	−	0.312387i	0.533447	−	0.845834i	$-0.320896\pi$
$173$	−4.10881	−	4.10881i	−0.312387	−	0.312387i	−0.845834	+	0.533447i	$0.820896\pi$
$174$		0			0
$175$			2.65557i			0.200742i
$176$	6.43740	+	1.47640i	0.485238	+	0.111288i
$177$		0			0
$178$	0.921551	+	0.693917i	0.0690732	+	0.0520112i
$179$	−0.0730717	+	0.0730717i	−0.00546164	+	0.00546164i	−0.709832	−	0.704371i	$-0.751229\pi$
$179$	−0.0730717	+	0.0730717i	−0.00546164	+	0.00546164i	0.704371	+	0.709832i	$0.251229\pi$
$180$		0			0
$181$	4.05639	+	4.05639i	0.301509	+	0.301509i	0.841604	−	0.540095i	$-0.181612\pi$
$181$	4.05639	+	4.05639i	0.301509	+	0.301509i	−0.540095	+	0.841604i	$0.681612\pi$
$182$	2.46766	−	0.347716i	0.182915	−	0.0257744i
$183$		0			0
$184$	13.5725	+	5.19312i	1.00058	+	0.382842i
$185$	16.5334			1.21556
$186$		0			0
$187$	5.33305	−	5.33305i	0.389991	−	0.389991i
$188$	3.18237	+	11.0681i	0.232098	+	0.807221i
$189$		0			0
$190$	7.97565	+	6.00556i	0.578614	+	0.435689i
$191$	14.2421			1.03052			0.515261	−	0.857033i	$-0.327695\pi$
$191$	14.2421			1.03052			0.515261	+	0.857033i	$0.327695\pi$
$192$		0			0
$193$	−2.49549			−0.179630			−0.0898148	−	0.995958i	$-0.528628\pi$
$193$	−2.49549			−0.179630			−0.0898148	+	0.995958i	$0.528628\pi$
$194$	13.9385	+	10.4955i	1.00072	+	0.753533i
$195$		0			0
$196$	−2.66005	−	9.25145i	−0.190003	−	0.660818i
$197$	7.01941	−	7.01941i	0.500113	−	0.500113i	−0.411360	−	0.911473i	$-0.634946\pi$
$197$	7.01941	−	7.01941i	0.500113	−	0.500113i	0.911473	+	0.411360i	$0.134946\pi$
$198$		0			0
$199$	0.00885227			0.000627521			0.000313760	−	1.00000i	$-0.499900\pi$
$199$	0.00885227			0.000627521			0.000313760		1.00000i	$0.499900\pi$
$200$	4.74377	+	1.81507i	0.335435	+	0.128345i
$201$		0			0
$202$	−0.386852	+	0.0545110i	−0.0272188	+	0.00383538i
$203$	0.238635	+	0.238635i	0.0167489	+	0.0167489i
$204$		0			0
$205$	−11.8405	+	11.8405i	−0.826978	+	0.826978i
$206$	−8.36707	−	6.30030i	−0.582962	−	0.438963i
$207$		0			0
$208$	1.06549	−	4.64576i	0.0738785	−	0.322126i
$209$		−	6.51184i		−	0.450433i
$210$		0			0
$211$	5.34136	+	5.34136i	0.367714	+	0.367714i	0.866643	−	0.498929i	$-0.166273\pi$
$211$	5.34136	+	5.34136i	0.367714	+	0.367714i	−0.498929	+	0.866643i	$0.666273\pi$
$212$	−19.4887	−	10.7843i	−1.33849	−	0.740672i
$213$		0			0
$214$	3.36266	+	23.8640i	0.229867	+	1.63131i
$215$			10.0779i			0.687308i
$216$		0			0
$217$			13.8153i			0.937847i
$218$	4.63116	−	0.652573i	0.313662	−	0.0441978i
$219$		0			0
$220$	1.63345	+	5.68103i	0.110127	+	0.383015i
$221$	−3.84877	−	3.84877i	−0.258896	−	0.258896i
$222$		0			0
$223$		−	9.03492i		−	0.605023i	−0.953146	−	0.302512i	$-0.902175\pi$
$223$		−	9.03492i		−	0.605023i	0.953146	−	0.302512i	$-0.0978251\pi$
$224$	8.33485	+	0.714037i	0.556896	+	0.0477086i
$225$		0			0
$226$	−15.0324	+	19.9637i	−0.999940	+	1.32796i
$227$	8.78561	−	8.78561i	0.583121	−	0.583121i	−0.352638	−	0.935760i	$-0.614715\pi$
$227$	8.78561	−	8.78561i	0.583121	−	0.583121i	0.935760	+	0.352638i	$0.114715\pi$
$228$		0			0
$229$	−3.05241	−	3.05241i	−0.201709	−	0.201709i	0.599023	−	0.800732i	$-0.295556\pi$
$229$	−3.05241	−	3.05241i	−0.201709	−	0.201709i	−0.800732	+	0.599023i	$0.795556\pi$
$230$	1.81481	+	12.8793i	0.119665	+	0.849234i
$231$		0			0
$232$	0.589391	−	0.263179i	0.0386954	−	0.0172786i
$233$	−0.628345			−0.0411642			−0.0205821	−	0.999788i	$-0.506552\pi$
$233$	−0.628345			−0.0411642			−0.0205821	+	0.999788i	$0.506552\pi$
$234$		0			0
$235$	−7.28849	+	7.28849i	−0.475449	+	0.475449i
$236$	−1.53691	+	2.77738i	−0.100044	+	0.180792i
$237$		0			0
$238$	5.74631	−	7.63134i	0.372478	−	0.494666i
$239$	−2.31962			−0.150043			−0.0750217	−	0.997182i	$-0.523903\pi$
$239$	−2.31962			−0.150043			−0.0750217	+	0.997182i	$0.523903\pi$
$240$		0			0
$241$	24.8731			1.60222			0.801109	−	0.598518i	$-0.204244\pi$
$241$	24.8731			1.60222			0.801109	+	0.598518i	$0.204244\pi$
$242$	−7.03838	+	9.34726i	−0.452444	+	0.600865i
$243$		0			0
$244$	0.980635	+	0.542649i	0.0627787	+	0.0347395i
$245$	6.09223	−	6.09223i	0.389218	−	0.389218i
$246$		0			0
$247$	−4.69948			−0.299021
$248$	24.6790	+	9.44271i	1.56712	+	0.599613i
$249$		0			0
$250$	2.40041	+	17.0352i	0.151815	+	1.07740i
$251$	−15.2526	−	15.2526i	−0.962737	−	0.962737i	0.0365936	−	0.999330i	$-0.488349\pi$
$251$	−15.2526	−	15.2526i	−0.962737	−	0.962737i	−0.999330	+	0.0365936i	$0.988349\pi$
$252$		0			0
$253$	5.99860	−	5.99860i	0.377129	−	0.377129i
$254$	−2.13722	+	2.83832i	−0.134101	+	0.178092i
$255$		0			0
$256$	6.97235	−	14.4009i	0.435772	−	0.900057i
$257$		−	11.8747i		−	0.740722i	−0.928888	−	0.370361i	$-0.879234\pi$
$257$		−	11.8747i		−	0.740722i	0.928888	−	0.370361i	$-0.120766\pi$
$258$		0			0
$259$	−9.65819	−	9.65819i	−0.600131	−	0.600131i
$260$	4.09990	−	1.17883i	0.254265	−	0.0731082i
$261$		0			0
$262$	−25.6408	+	3.61303i	−1.58409	+	0.223213i
$263$			7.44522i			0.459092i	0.973298	+	0.229546i	$0.0737241\pi$
$263$			7.44522i			0.459092i	−0.973298	+	0.229546i	$0.926276\pi$
$264$		0			0
$265$		−	19.9353i		−	1.22461i
$266$	−1.15085	−	8.16728i	−0.0705629	−	0.500768i
$267$		0			0
$268$	−8.37766	+	15.1395i	−0.511747	+	0.924792i
$269$	0.822509	+	0.822509i	0.0501492	+	0.0501492i	0.731737	−	0.681587i	$-0.238710\pi$
$269$	0.822509	+	0.822509i	0.0501492	+	0.0501492i	−0.681587	+	0.731737i	$0.738710\pi$
$270$		0			0
$271$			13.8535i			0.841543i	0.907167	+	0.420771i	$0.138241\pi$
$271$			13.8535i			0.841543i	−0.907167	+	0.420771i	$0.861759\pi$
$272$	−9.70467	−	15.4809i	−0.588432	−	0.938667i
$273$		0			0
$274$	−20.6596	−	15.5564i	−1.24809	−	0.939797i
$275$	2.09659	−	2.09659i	0.126429	−	0.126429i
$276$		0			0
$277$	22.7763	+	22.7763i	1.36849	+	1.36849i	0.862589	+	0.505906i	$0.168842\pi$
$277$	22.7763	+	22.7763i	1.36849	+	1.36849i	0.505906	+	0.862589i	$0.331158\pi$
$278$	18.1069	−	2.55143i	1.08598	−	0.153025i
$279$		0			0
$280$	3.05273	+	6.83658i	0.182435	+	0.408564i
$281$	−8.02293			−0.478608			−0.239304	−	0.970945i	$-0.576919\pi$
$281$	−8.02293			−0.478608			−0.239304	+	0.970945i	$0.576919\pi$
$282$		0			0
$283$	9.94633	−	9.94633i	0.591248	−	0.591248i	−0.346721	−	0.937968i	$-0.612705\pi$
$283$	9.94633	−	9.94633i	0.591248	−	0.591248i	0.937968	+	0.346721i	$0.112705\pi$
$284$	−30.6177	+	8.80342i	−1.81682	+	0.522387i
$285$		0			0
$286$	−2.22276	−	1.67371i	−0.131435	−	0.0989687i
$287$	13.8336			0.816569
$288$		0			0
$289$	−3.86492			−0.227348
$290$	0.461512	+	0.347513i	0.0271009	+	0.0204066i
$291$		0			0
$292$	24.3135	−	6.99079i	1.42284	−	0.409105i
$293$	−17.8928	+	17.8928i	−1.04531	+	1.04531i	−0.0463831	+	0.998924i	$0.514769\pi$
$293$	−17.8928	+	17.8928i	−1.04531	+	1.04531i	−0.998924	+	0.0463831i	$0.985231\pi$
$294$		0			0
$295$	−2.84103			−0.165411
$296$	−23.8542	+	10.6516i	−1.38650	+	0.619110i
$297$		0			0
$298$	29.7928	−	4.19807i	1.72585	−	0.243188i
$299$	−4.32909	−	4.32909i	−0.250358	−	0.250358i
$300$		0			0
$301$	5.88713	−	5.88713i	0.339328	−	0.339328i
$302$	−1.83834	−	1.38425i	−0.105785	−	0.0796547i
$303$		0			0
$304$	−15.3762	−	3.52648i	−0.881886	−	0.202258i
$305$			1.00311i			0.0574377i
$306$		0			0
$307$	−11.9244	−	11.9244i	−0.680562	−	0.680562i	0.279565	−	0.960127i	$-0.409810\pi$
$307$	−11.9244	−	11.9244i	−0.680562	−	0.680562i	−0.960127	+	0.279565i	$0.909810\pi$
$308$	2.36444	−	4.27284i	0.134726	−	0.243467i
$309$		0			0
$310$	3.29989	+	23.4185i	0.187421	+	1.33008i
$311$			0.125339i			0.00710734i	0.999994	+	0.00355367i	$0.00113117\pi$
$311$			0.125339i			0.00710734i	−0.999994	+	0.00355367i	$0.998869\pi$
$312$		0			0
$313$			28.8410i			1.63019i	0.579329	+	0.815094i	$0.303315\pi$
$313$			28.8410i			1.63019i	−0.579329	+	0.815094i	$0.696685\pi$
$314$	−16.4651	+	2.32009i	−0.929180	+	0.130930i
$315$		0			0
$316$	8.42967	−	2.42376i	0.474206	−	0.136347i
$317$	−18.4600	−	18.4600i	−1.03682	−	1.03682i	−0.999296	−	0.0375227i	$-0.988053\pi$
$317$	−18.4600	−	18.4600i	−1.03682	−	1.03682i	−0.0375227	−	0.999296i	$-0.511947\pi$
$318$		0			0
$319$		−	0.376808i		−	0.0210972i
$320$	14.2990	−	0.780464i	0.799341	−	0.0436292i
$321$		0			0
$322$	6.46343	−	8.58371i	0.360193	−	0.478351i
$323$	−12.7384	+	12.7384i	−0.708783	+	0.708783i
$324$		0			0
$325$	−1.51308	−	1.51308i	−0.0839303	−	0.0839303i
$326$	−2.81747	−	19.9949i	−0.156045	−	1.10742i
$327$		0			0
$328$	9.45516	−	24.7116i	0.522074	−	1.36447i
$329$	8.51531			0.469464
$330$		0			0
$331$	4.25015	−	4.25015i	0.233609	−	0.233609i	−0.580588	−	0.814197i	$-0.697177\pi$
$331$	4.25015	−	4.25015i	0.233609	−	0.233609i	0.814197	+	0.580588i	$0.197177\pi$
$332$	10.1569	+	5.62046i	0.557431	+	0.308463i
$333$		0			0
$334$	−11.3639	+	15.0917i	−0.621805	+	0.825783i
$335$	−15.4864			−0.846114
$336$		0			0
$337$	12.7546			0.694789			0.347394	−	0.937719i	$-0.387067\pi$
$337$	12.7546			0.694789			0.347394	+	0.937719i	$0.387067\pi$
$338$	9.85104	−	13.0826i	0.535826	−	0.711600i
$339$		0			0
$340$	7.91783	−	14.3085i	0.429404	−	0.775988i
$341$	10.9073	−	10.9073i	0.590665	−	0.590665i
$342$		0			0
$343$	−17.4693			−0.943255
$344$	−6.49264	−	14.5403i	−0.350060	−	0.783959i
$345$		0			0
$346$	1.14661	+	8.13723i	0.0616422	+	0.437460i
$347$	24.3745	+	24.3745i	1.30849	+	1.30849i	0.922504	+	0.385988i	$0.126139\pi$
$347$	24.3745	+	24.3745i	1.30849	+	1.30849i	0.385988	+	0.922504i	$0.373861\pi$
$348$		0			0
$349$	−5.14223	+	5.14223i	−0.275257	+	0.275257i	−0.831212	−	0.555955i	$-0.812353\pi$
$349$	−5.14223	+	5.14223i	−0.275257	+	0.275257i	0.555955	+	0.831212i	$0.312353\pi$
$350$	2.25906	−	3.00013i	0.120752	−	0.160363i
$351$		0			0
$352$	−6.01670	−	7.14417i	−0.320691	−	0.380786i
$353$			22.1829i			1.18068i	0.807156	+	0.590338i	$0.201005\pi$
$353$			22.1829i			1.18068i	−0.807156	+	0.590338i	$0.798995\pi$
$354$		0			0
$355$	−20.1622	−	20.1622i	−1.07010	−	1.07010i
$356$	−0.450815	−	1.56790i	−0.0238932	−	0.0830987i
$357$		0			0
$358$	0.144714	−	0.0203915i	0.00764836	−	0.00107772i
$359$			8.55209i			0.451362i	0.974201	+	0.225681i	$0.0724607\pi$
$359$			8.55209i			0.451362i	−0.974201	+	0.225681i	$0.927539\pi$
$360$		0			0
$361$		−	3.44599i		−	0.181368i
$362$	−1.13198	−	8.03343i	−0.0594958	−	0.422228i
$363$		0			0
$364$	−3.08363	−	1.70637i	−0.161626	−	0.0894383i
$365$	16.0108	+	16.0108i	0.838044	+	0.838044i
$366$		0			0
$367$		−	27.9033i		−	1.45654i	−0.685291	−	0.728270i	$-0.740325\pi$
$367$		−	27.9033i		−	1.45654i	0.685291	−	0.728270i	$-0.259675\pi$
$368$	−10.9158	−	17.4129i	−0.569024	−	0.907708i
$369$		0			0
$370$	−18.6786	−	14.0648i	−0.971055	−	0.731192i
$371$	−11.6454	+	11.6454i	−0.604600	+	0.604600i
$372$		0			0
$373$	2.32666	+	2.32666i	0.120470	+	0.120470i	0.764771	−	0.644302i	$-0.222852\pi$
$373$	2.32666	+	2.32666i	0.120470	+	0.120470i	−0.644302	+	0.764771i	$0.722852\pi$
$374$	−10.5618	+	1.48825i	−0.546136	+	0.0769556i
$375$		0			0
$376$	5.82017	−	15.2113i	0.300152	−	0.784464i
$377$	−0.271936			−0.0140054
$378$		0			0
$379$	−0.522727	+	0.522727i	−0.0268507	+	0.0268507i	−0.720405	−	0.693554i	$-0.756044\pi$
$379$	−0.522727	+	0.522727i	−0.0268507	+	0.0268507i	0.693554	+	0.720405i	$0.256044\pi$
$380$	−3.90162	−	13.5696i	−0.200149	−	0.696103i
$381$		0			0
$382$	−16.0900	−	12.1156i	−0.823235	−	0.619886i
$383$	−25.8856			−1.32269			−0.661346	−	0.750081i	$-0.730015\pi$
$383$	−25.8856			−1.32269			−0.661346	+	0.750081i	$0.730015\pi$
$384$		0			0
$385$	4.37075			0.222754
$386$	2.81928	+	2.12288i	0.143498	+	0.108052i
$387$		0			0
$388$	−6.81858	−	23.7145i	−0.346161	−	1.20392i
$389$	−1.95484	+	1.95484i	−0.0991144	+	0.0991144i	−0.754925	−	0.655811i	$-0.772327\pi$
$389$	−1.95484	+	1.95484i	−0.0991144	+	0.0991144i	0.655811	+	0.754925i	$0.272327\pi$
$390$		0			0
$391$	−23.4688			−1.18687
$392$	−4.86490	+	12.7147i	−0.245715	+	0.642188i
$393$		0			0
$394$	−13.9015	+	1.95885i	−0.700347	+	0.0986854i
$395$	5.55107	+	5.55107i	0.279305	+	0.279305i
$396$		0			0
$397$	−3.86800	+	3.86800i	−0.194129	+	0.194129i	−0.797478	−	0.603348i	$-0.793833\pi$
$397$	−3.86800	+	3.86800i	−0.194129	+	0.194129i	0.603348	+	0.797478i	$0.293833\pi$
$398$	−0.0100008	−	0.00753051i	−0.000501297	−	0.000377470i
$399$		0			0
$400$	−3.81522	−	6.08603i	−0.190761	−	0.304302i
$401$		−	16.1774i		−	0.807863i	−0.914789	−	0.403931i	$-0.867643\pi$
$401$		−	16.1774i		−	0.807863i	0.914789	−	0.403931i	$-0.132357\pi$
$402$		0			0
$403$	−7.87163	−	7.87163i	−0.392114	−	0.392114i
$404$	0.483417	+	0.267506i	0.0240509	+	0.0133089i
$405$		0			0
$406$	−0.0665938	−	0.472601i	−0.00330500	−	0.0234548i
$407$			15.2504i			0.755936i
$408$		0			0
$409$			15.1738i			0.750295i	0.926965	+	0.375148i	$0.122408\pi$
$409$			15.1738i			0.750295i	−0.926965	+	0.375148i	$0.877592\pi$
$410$	23.4494	−	3.30424i	1.15808	−	0.163185i
$411$		0			0
$412$	4.09310	+	14.2355i	0.201653	+	0.701334i
$413$	1.65962	+	1.65962i	0.0816646	+	0.0816646i
$414$		0			0
$415$			10.3896i			0.510007i
$416$	−5.15583	+	4.34215i	−0.252785	+	0.212891i
$417$		0			0
$418$	−5.53953	+	7.35674i	−0.270947	+	0.359830i
$419$	−6.32294	+	6.32294i	−0.308896	+	0.308896i	−0.844481	−	0.535585i	$-0.820091\pi$
$419$	−6.32294	+	6.32294i	−0.308896	+	0.308896i	0.535585	+	0.844481i	$0.320091\pi$
$420$		0			0
$421$	−18.1865	−	18.1865i	−0.886356	−	0.886356i	0.107815	−	0.994171i	$-0.465615\pi$
$421$	−18.1865	−	18.1865i	−0.886356	−	0.886356i	−0.994171	+	0.107815i	$0.965615\pi$
$422$	−1.49057	−	10.5782i	−0.0725597	−	0.514939i
$423$		0			0
$424$	12.8432	+	28.7623i	0.623720	+	1.39682i
$425$	−8.20267			−0.397888
$426$		0			0
$427$	0.585976	−	0.585976i	0.0283574	−	0.0283574i
$428$	16.5018	−	29.8209i	0.797647	−	1.44145i
$429$		0			0
$430$	8.57315	−	11.3855i	0.413434	−	0.549058i
$431$	33.2536			1.60177			0.800884	−	0.598820i	$-0.204363\pi$
$431$	33.2536			1.60177			0.800884	+	0.598820i	$0.204363\pi$
$432$		0			0
$433$	21.2087			1.01922			0.509612	−	0.860404i	$-0.329789\pi$
$433$	21.2087			1.01922			0.509612	+	0.860404i	$0.329789\pi$
$434$	11.7525	−	15.6079i	0.564139	−	0.749201i
$435$		0			0
$436$	−5.78718	−	3.20242i	−0.277156	−	0.153368i
$437$	−14.3281	+	14.3281i	−0.685406	+	0.685406i
$438$		0			0
$439$	−34.3580			−1.63982			−0.819908	−	0.572495i	$-0.805976\pi$
$439$	−34.3580			−1.63982			−0.819908	+	0.572495i	$0.805976\pi$
$440$	2.98739	−	7.80769i	0.142418	−	0.372217i
$441$		0			0
$442$	1.07404	+	7.62224i	0.0510871	+	0.362553i
$443$	−6.79175	−	6.79175i	−0.322686	−	0.322686i	0.527111	−	0.849797i	$-0.323275\pi$
$443$	−6.79175	−	6.79175i	−0.322686	−	0.322686i	−0.849797	+	0.527111i	$0.823275\pi$
$444$		0			0
$445$	1.03249	−	1.03249i	0.0489447	−	0.0489447i
$446$	−7.68589	+	10.2072i	−0.363937	+	0.483324i
$447$		0			0
$448$	−8.80887	−	7.89703i	−0.416180	−	0.373100i
$449$			24.1062i			1.13764i	0.822461	+	0.568821i	$0.192600\pi$
$449$			24.1062i			1.13764i	−0.822461	+	0.568821i	$0.807400\pi$
$450$		0			0
$451$	−10.9217	−	10.9217i	−0.514283	−	0.514283i
$452$	33.9656	−	9.76605i	1.59761	−	0.459357i
$453$		0			0
$454$	−17.3993	+	2.45173i	−0.816591	+	0.115065i
$455$		−	3.15430i		−	0.147876i
$456$		0			0
$457$			1.51672i			0.0709493i	0.999371	+	0.0354746i	$0.0112943\pi$
$457$			1.51672i			0.0709493i	−0.999371	+	0.0354746i	$0.988706\pi$
$458$	0.851811	+	6.04511i	0.0398025	+	0.282469i
$459$		0			0
$460$	8.90595	−	16.0942i	0.415242	−	0.750394i
$461$	23.6025	+	23.6025i	1.09928	+	1.09928i	0.994495	+	0.104783i	$0.0334148\pi$
$461$	23.6025	+	23.6025i	1.09928	+	1.09928i	0.104783	+	0.994495i	$0.466585\pi$
$462$		0			0
$463$		−	15.2915i		−	0.710655i	−0.934742	−	0.355328i	$-0.884369\pi$
$463$		−	15.2915i		−	0.710655i	0.934742	−	0.355328i	$-0.115631\pi$
$464$	−0.889746	−	0.204060i	−0.0413054	−	0.00947326i
$465$		0			0
$466$	0.709872	+	0.534525i	0.0328842	+	0.0247614i
$467$	24.2269	−	24.2269i	1.12109	−	1.12109i	0.129507	−	0.991579i	$-0.458661\pi$
$467$	24.2269	−	24.2269i	1.12109	−	1.12109i	0.991579	−	0.129507i	$-0.0413393\pi$
$468$		0			0
$469$	9.04657	+	9.04657i	0.417732	+	0.417732i
$470$	14.4344	−	2.03394i	0.665809	−	0.0938186i
$471$		0			0
$472$	4.09900	−	1.83032i	0.188672	−	0.0842473i
$473$	−9.29587			−0.427424
$474$		0			0
$475$	−5.00787	+	5.00787i	−0.229777	+	0.229777i
$476$	−12.9838	+	3.73319i	−0.595110	+	0.171110i
$477$		0			0
$478$	2.62058	+	1.97327i	0.119863	+	0.0902551i
$479$	10.7866			0.492852			0.246426	−	0.969162i	$-0.420744\pi$
$479$	10.7866			0.492852			0.246426	+	0.969162i	$0.420744\pi$
$480$		0			0
$481$	11.0060			0.501829
$482$	−28.1004	−	21.1592i	−1.27994	−	0.963777i
$483$		0			0
$484$	15.9032	−	4.57260i	0.722872	−	0.207846i
$485$	15.6164	−	15.6164i	0.709105	−	0.709105i
$486$		0			0
$487$	19.6195			0.889044			0.444522	−	0.895768i	$-0.353374\pi$
$487$	19.6195			0.889044			0.444522	+	0.895768i	$0.353374\pi$
$488$	−0.646247	−	1.44727i	−0.0292542	−	0.0655148i
$489$		0			0
$490$	−12.0653	+	1.70011i	−0.545053	+	0.0768030i
$491$	25.7673	+	25.7673i	1.16286	+	1.16286i	0.983846	+	0.179017i	$0.0572917\pi$
$491$	25.7673	+	25.7673i	1.16286	+	1.16286i	0.179017	+	0.983846i	$0.442708\pi$
$492$		0			0
$493$	−0.737108	+	0.737108i	−0.0331977	+	0.0331977i
$494$	5.30923	+	3.99779i	0.238874	+	0.179869i
$495$		0			0
$496$	−19.8483	−	31.6620i	−0.891215	−	1.42167i
$497$			23.5560i			1.05663i
$498$		0			0
$499$	16.7571	+	16.7571i	0.750152	+	0.750152i	0.974507	−	0.224355i	$-0.0720275\pi$
$499$	16.7571	+	16.7571i	0.750152	+	0.750152i	−0.224355	+	0.974507i	$0.572028\pi$
$500$	11.7797	−	21.2874i	0.526805	−	0.952004i
$501$		0			0
$502$	4.25642	+	30.2068i	0.189973	+	1.34820i
$503$		−	27.0368i		−	1.20551i	−0.797926	−	0.602755i	$-0.794070\pi$
$503$		−	27.0368i		−	1.20551i	0.797926	−	0.602755i	$-0.205930\pi$
$504$		0			0
$505$			0.494495i			0.0220047i
$506$	−11.8798	+	1.67398i	−0.528123	+	0.0744174i
$507$		0			0
$508$	4.82904	−	1.38848i	0.214254	−	0.0616039i
$509$	17.4927	+	17.4927i	0.775351	+	0.775351i	0.979036	−	0.203685i	$-0.0652919\pi$
$509$	17.4927	+	17.4927i	0.775351	+	0.775351i	−0.203685	+	0.979036i	$0.565292\pi$
$510$		0			0
$511$		−	18.7058i		−	0.827495i
$512$	−20.1277	+	10.3381i	−0.889526	+	0.456885i
$513$		0			0
$514$	−10.1016	+	13.4154i	−0.445564	+	0.591728i
$515$	−9.37432	+	9.37432i	−0.413082	+	0.413082i
$516$		0			0
$517$	−6.72291	−	6.72291i	−0.295673	−	0.295673i
$518$	2.69523	+	19.1274i	0.118422	+	0.840410i
$519$		0			0
$520$	−5.63468	−	2.15595i	−0.247097	−	0.0945445i
$521$	−15.8879			−0.696063			−0.348032	−	0.937483i	$-0.613150\pi$
$521$	−15.8879			−0.696063			−0.348032	+	0.937483i	$0.613150\pi$
$522$		0			0
$523$	15.6815	−	15.6815i	0.685703	−	0.685703i	−0.275576	−	0.961279i	$-0.588869\pi$
$523$	15.6815	−	15.6815i	0.685703	−	0.685703i	0.961279	+	0.275576i	$0.0888687\pi$
$524$	32.0412	+	17.7305i	1.39973	+	0.774560i
$525$		0			0
$526$	6.33355	−	8.41122i	0.276156	−	0.366747i
$527$	−42.6736			−1.85889
$528$		0			0
$529$	−3.39762			−0.147723
$530$	−16.9587	+	22.5218i	−0.736637	+	0.978286i
$531$		0			0
$532$	−5.64764	+	10.2060i	−0.244856	+	0.442486i
$533$	−7.88201	+	7.88201i	−0.341408	+	0.341408i
$534$		0			0
$535$	30.5043			1.31882
$536$	22.3436	−	9.97705i	0.965097	−	0.430943i
$537$		0			0
$538$	−0.229531	−	1.62893i	−0.00989577	−	0.0702280i
$539$	5.61947	+	5.61947i	0.242048	+	0.242048i
$540$		0			0
$541$	28.8331	−	28.8331i	1.23963	−	1.23963i	0.279482	−	0.960151i	$-0.409837\pi$
$541$	28.8331	−	28.8331i	1.23963	−	1.23963i	0.960151	−	0.279482i	$-0.0901627\pi$
$542$	11.7850	−	15.6510i	0.506210	−	0.672269i
$543$		0			0
$544$	−2.20556	+	25.7452i	−0.0945625	+	1.10381i
$545$		−	5.91980i		−	0.253576i
$546$		0			0
$547$	7.25520	+	7.25520i	0.310210	+	0.310210i	0.844991	−	0.534781i	$-0.179606\pi$
$547$	7.25520	+	7.25520i	0.310210	+	0.310210i	−0.534781	+	0.844991i	$0.679606\pi$
$548$	10.1065	+	35.1496i	0.431728	+	1.50152i
$549$		0			0
$550$	−4.15217	+	0.585079i	−0.177049	+	0.0249478i
$551$			0.900034i			0.0383427i
$552$		0			0
$553$		−	6.48545i		−	0.275789i
$554$	−6.35599	−	45.1070i	−0.270040	−	1.91641i
$555$		0			0
$556$	−22.6267	−	12.5208i	−0.959587	−	0.531002i
$557$	2.08325	+	2.08325i	0.0882703	+	0.0882703i	0.749863	−	0.661593i	$-0.230119\pi$
$557$	2.08325	+	2.08325i	0.0882703	+	0.0882703i	−0.661593	+	0.749863i	$0.730119\pi$
$558$		0			0
$559$			6.70867i			0.283746i
$560$	2.36698	−	10.3205i	0.100023	−	0.436122i
$561$		0			0
$562$	9.06390	+	6.82501i	0.382338	+	0.287895i
$563$	−18.1884	+	18.1884i	−0.766549	+	0.766549i	−0.977497	−	0.210948i	$-0.932345\pi$
$563$	−18.1884	+	18.1884i	−0.766549	+	0.766549i	0.210948	+	0.977497i	$0.432345\pi$
$564$		0			0
$565$	22.3669	+	22.3669i	0.940983	+	0.940983i
$566$	−19.6981	+	2.77564i	−0.827971	+	0.116669i
$567$		0			0
$568$	42.0792	+	16.1004i	1.76560	+	0.675557i
$569$	−24.1971			−1.01440			−0.507198	−	0.861829i	$-0.669319\pi$
$569$	−24.1971			−1.01440			−0.507198	+	0.861829i	$0.669319\pi$
$570$		0			0
$571$	−24.4026	+	24.4026i	−1.02122	+	1.02122i	−0.0214492	+	0.999770i	$0.506828\pi$
$571$	−24.4026	+	24.4026i	−1.02122	+	1.02122i	−0.999770	+	0.0214492i	$0.993172\pi$
$572$	1.08736	+	3.78175i	0.0454647	+	0.158123i
$573$		0			0
$574$	−15.6284	−	11.7680i	−0.652318	−	0.491188i
$575$	−9.22633			−0.384765
$576$		0			0
$577$	−44.9453			−1.87110			−0.935548	−	0.353200i	$-0.885094\pi$
$577$	−44.9453			−1.87110			−0.935548	+	0.353200i	$0.885094\pi$
$578$	4.36638	+	3.28783i	0.181618	+	0.136756i
$579$		0			0
$580$	−0.225768	−	0.785204i	−0.00937449	−	0.0326038i
$581$	6.06922	−	6.06922i	0.251794	−	0.251794i
$582$		0			0
$583$	18.3883			0.761565
$584$	−33.4151	−	12.7853i	−1.38273	−	0.529060i
$585$		0			0
$586$	35.4355	−	4.99319i	1.46383	−	0.206267i
$587$	15.6677	+	15.6677i	0.646676	+	0.646676i	0.952188	−	0.305512i	$-0.0988277\pi$
$587$	15.6677	+	15.6677i	0.646676	+	0.646676i	−0.305512	+	0.952188i	$0.598828\pi$
$588$		0			0
$589$	−26.0529	+	26.0529i	−1.07349	+	1.07349i
$590$	3.20965	+	2.41683i	0.132139	+	0.0994992i
$591$		0			0
$592$	36.0104	+	8.25887i	1.48002	+	0.339437i
$593$			0.259633i			0.0106618i	0.999986	+	0.00533092i	$0.00169689\pi$
$593$			0.259633i			0.0106618i	−0.999986	+	0.00533092i	$0.998303\pi$
$594$		0			0
$595$	−8.55002	−	8.55002i	−0.350517	−	0.350517i
$596$	−37.2296	−	20.6015i	−1.52498	−	0.843872i
$597$		0			0
$598$	1.20808	+	8.57348i	0.0494021	+	0.350596i
$599$		−	33.6422i		−	1.37458i	−0.726382	−	0.687291i	$-0.758800\pi$
$599$		−	33.6422i		−	1.37458i	0.726382	−	0.687291i	$-0.241200\pi$
$600$		0			0
$601$		−	21.8534i		−	0.891419i	−0.895178	−	0.445710i	$-0.852951\pi$
$601$		−	21.8534i		−	0.891419i	0.895178	−	0.445710i	$-0.147049\pi$
$602$	−11.6591	+	1.64287i	−0.475188	+	0.0669584i
$603$		0			0
$604$	0.899302	+	3.12771i	0.0365921	+	0.127265i
$605$	10.4725	+	10.4725i	0.425768	+	0.425768i
$606$		0			0
$607$			19.4186i			0.788177i	0.919073	+	0.394088i	$0.128940\pi$
$607$			19.4186i			0.788177i	−0.919073	+	0.394088i	$0.871060\pi$
$608$	14.3713	+	17.0644i	0.582834	+	0.692052i
$609$		0			0
$610$	0.853330	−	1.13326i	0.0345503	−	0.0458843i
$611$	−4.85181	+	4.85181i	−0.196283	+	0.196283i
$612$		0			0
$613$	11.1127	+	11.1127i	0.448839	+	0.448839i	0.894968	−	0.446129i	$-0.147198\pi$
$613$	11.1127	+	11.1127i	0.448839	+	0.448839i	−0.446129	+	0.894968i	$0.647198\pi$
$614$	3.32764	+	23.6155i	0.134293	+	0.953044i
$615$		0			0
$616$	−6.30607	+	2.81583i	−0.254079	+	0.113453i
$617$	−4.27564			−0.172131			−0.0860654	−	0.996289i	$-0.527429\pi$
$617$	−4.27564			−0.172131			−0.0860654	+	0.996289i	$0.527429\pi$
$618$		0			0
$619$	−6.85100	+	6.85100i	−0.275365	+	0.275365i	−0.831255	−	0.555891i	$-0.812377\pi$
$619$	−6.85100	+	6.85100i	−0.275365	+	0.275365i	0.555891	+	0.831255i	$0.312377\pi$
$620$	16.1938	−	29.2642i	0.650358	−	1.17528i
$621$		0			0
$622$	0.106625	−	0.141602i	0.00427525	−	0.00567772i
$623$	−1.20628			−0.0483286
$624$		0			0
$625$	12.7965			0.511860
$626$	24.5346	−	32.5830i	0.980601	−	1.30228i
$627$		0			0
$628$	20.5751	+	11.3855i	0.821036	+	0.454333i
$629$	29.8327	−	29.8327i	1.18951	−	1.18951i
$630$		0			0
$631$	−1.73528			−0.0690802			−0.0345401	−	0.999403i	$-0.510997\pi$
$631$	−1.73528			−0.0690802			−0.0345401	+	0.999403i	$0.510997\pi$
$632$	−11.5853	−	4.43277i	−0.460837	−	0.176326i
$633$		0			0
$634$	5.15149	+	36.5589i	0.204592	+	1.45194i
$635$	3.18000	+	3.18000i	0.126194	+	0.126194i
$636$		0			0
$637$	4.05548	−	4.05548i	0.160684	−	0.160684i
$638$	−0.320546	+	0.425698i	−0.0126905	+	0.0168536i
$639$		0			0
$640$	−16.8183	−	11.2823i	−0.664800	−	0.445971i
$641$			3.07469i			0.121443i	0.998155	+	0.0607214i	$0.0193401\pi$
$641$			3.07469i			0.121443i	−0.998155	+	0.0607214i	$0.980660\pi$
$642$		0			0
$643$	7.18763	+	7.18763i	0.283452	+	0.283452i	0.834484	−	0.551032i	$-0.185766\pi$
$643$	7.18763	+	7.18763i	0.283452	+	0.283452i	−0.551032	+	0.834484i	$0.685766\pi$
$644$	−14.6041	+	4.19908i	−0.575482	+	0.165467i
$645$		0			0
$646$	25.2276	−	3.55480i	0.992565	−	0.139862i
$647$		−	11.1585i		−	0.438685i	−0.975648	−	0.219342i	$-0.929609\pi$
$647$		−	11.1585i		−	0.438685i	0.975648	−	0.219342i	$-0.0703912\pi$
$648$		0			0
$649$		−	2.62057i		−	0.102866i
$650$	0.422241	+	2.99655i	0.0165617	+	0.117534i
$651$		0			0
$652$	−13.8264	+	24.9860i	−0.541483	+	0.978527i
$653$	−24.1318	−	24.1318i	−0.944349	−	0.944349i	0.0541822	−	0.998531i	$-0.482745\pi$
$653$	−24.1318	−	24.1318i	−0.944349	−	0.944349i	−0.998531	+	0.0541822i	$0.982745\pi$
$654$		0			0
$655$			32.7755i			1.28064i
$656$	−31.7037	+	19.8745i	−1.23782	+	0.775967i
$657$		0			0
$658$	−9.62016	−	7.24386i	−0.375033	−	0.282395i
$659$	−14.1846	+	14.1846i	−0.552552	+	0.552552i	−0.927177	−	0.374625i	$-0.877772\pi$
$659$	−14.1846	+	14.1846i	−0.552552	+	0.552552i	0.374625	+	0.927177i	$0.377772\pi$
$660$		0			0
$661$	21.3432	+	21.3432i	0.830153	+	0.830153i	0.987537	−	0.157385i	$-0.0503062\pi$
$661$	21.3432	+	21.3432i	0.830153	+	0.830153i	−0.157385	+	0.987537i	$0.550306\pi$
$662$	−8.41715	+	1.18605i	−0.327142	+	0.0460973i
$663$		0			0
$664$	−6.69346	−	14.9900i	−0.259757	−	0.581726i
$665$	−10.4399			−0.404841
$666$		0			0
$667$	−0.829097	+	0.829097i	−0.0321028	+	0.0321028i
$668$	25.6767	−	7.38275i	0.993461	−	0.285647i
$669$		0			0
$670$	17.4958	+	13.1741i	0.675920	+	0.508960i
$671$	−0.925266			−0.0357195
$672$		0			0
$673$	−13.7772			−0.531071			−0.265536	−	0.964101i	$-0.585549\pi$
$673$	−13.7772			−0.531071			−0.265536	+	0.964101i	$0.585549\pi$
$674$	−14.4095	−	10.8502i	−0.555034	−	0.417934i
$675$		0			0
$676$	−22.2584	+	6.39990i	−0.856092	+	0.246150i
$677$	18.7732	−	18.7732i	0.721514	−	0.721514i	−0.247400	−	0.968914i	$-0.579576\pi$
$677$	18.7732	−	18.7732i	0.721514	−	0.721514i	0.968914	+	0.247400i	$0.0795760\pi$
$678$		0			0
$679$	−18.2450			−0.700179
$680$	−21.1172	+	9.42942i	−0.809808	+	0.361602i
$681$		0			0
$682$	−21.6012	+	3.04382i	−0.827155	+	0.116554i
$683$	−32.0134	−	32.0134i	−1.22496	−	1.22496i	−0.965847	−	0.259112i	$-0.916570\pi$
$683$	−32.0134	−	32.0134i	−1.22496	−	1.22496i	−0.259112	−	0.965847i	$-0.583430\pi$
$684$		0			0
$685$	−23.1466	+	23.1466i	−0.884386	+	0.884386i
$686$	19.7359	+	14.8609i	0.753522	+	0.567393i
$687$		0			0
$688$	−5.03417	+	21.9501i	−0.191926	+	0.836838i
$689$		−	13.2705i		−	0.505566i
$690$		0			0
$691$	16.3176	+	16.3176i	0.620752	+	0.620752i	0.945724	−	0.324972i	$-0.105355\pi$
$691$	16.3176	+	16.3176i	0.620752	+	0.620752i	−0.324972	+	0.945724i	$0.605355\pi$
$692$	5.62685	−	10.1684i	0.213901	−	0.386546i
$693$		0			0
$694$	−6.80199	−	48.2721i	−0.258200	−	1.83238i
$695$		−	23.1452i		−	0.877949i
$696$		0			0
$697$			42.7298i			1.61851i
$698$	10.1839	−	1.43500i	0.385464	−	0.0543155i
$699$		0			0
$700$	−5.10433	+	1.46764i	−0.192926	+	0.0554714i
$701$	4.92514	+	4.92514i	0.186020	+	0.186020i	0.793973	−	0.607953i	$-0.208009\pi$
$701$	4.92514	+	4.92514i	0.186020	+	0.186020i	−0.607953	+	0.793973i	$0.708009\pi$
$702$		0			0
$703$		−	36.4268i		−	1.37386i
$704$	0.719900	+	13.1894i	0.0271323	+	0.497096i
$705$		0			0
$706$	18.8707	−	25.0611i	0.710207	−	0.943186i
$707$	0.288865	−	0.288865i	0.0108639	−	0.0108639i
$708$		0			0
$709$	−17.8267	−	17.8267i	−0.669497	−	0.669497i	0.288103	−	0.957599i	$-0.406976\pi$
$709$	−17.8267	−	17.8267i	−0.669497	−	0.669497i	−0.957599	+	0.288103i	$0.906976\pi$
$710$	5.62650	+	39.9300i	0.211159	+	1.49855i
$711$		0			0
$712$	−0.824487	+	2.15484i	−0.0308989	+	0.0807560i
$713$	−47.9991			−1.79758
$714$		0			0
$715$	−2.49034	+	2.49034i	−0.0931336	+	0.0931336i
$716$	−0.180837	−	0.100069i	−0.00675820	−	0.00373975i
$717$		0			0
$718$	7.27515	−	9.66171i	0.271506	−	0.360572i
$719$	39.2431			1.46352			0.731761	−	0.681561i	$-0.238699\pi$
$719$	39.2431			1.46352			0.731761	+	0.681561i	$0.238699\pi$
$720$		0			0
$721$	10.9522			0.407882
$722$	−2.93146	+	3.89311i	−0.109098	+	0.144886i
$723$		0			0
$724$	−5.55507	+	10.0387i	−0.206453	+	0.373086i
$725$	−0.289781	+	0.289781i	−0.0107622	+	0.0107622i
$726$		0			0
$727$	39.9286			1.48087			0.740435	−	0.672128i	$-0.234620\pi$
$727$	39.9286			1.48087			0.740435	+	0.672128i	$0.234620\pi$
$728$	2.03214	+	4.55098i	0.0753161	+	0.168671i
$729$		0			0
$730$	−4.46800	−	31.7084i	−0.165368	−	1.17358i
$731$	18.1845	+	18.1845i	0.672577	+	0.672577i
$732$		0			0
$733$	15.5110	−	15.5110i	0.572912	−	0.572912i	−0.360029	−	0.932941i	$-0.617233\pi$
$733$	15.5110	−	15.5110i	0.572912	−	0.572912i	0.932941	+	0.360029i	$0.117233\pi$
$734$	−23.7370	+	31.5237i	−0.876147	+	1.16356i
$735$		0			0
$736$	−2.48080	+	28.9581i	−0.0914436	+	1.06741i
$737$		−	14.2847i		−	0.526183i
$738$		0			0
$739$	21.9310	+	21.9310i	0.806744	+	0.806744i	0.984140	−	0.177396i	$-0.0567673\pi$
$739$	21.9310	+	21.9310i	0.806744	+	0.806744i	−0.177396	+	0.984140i	$0.556767\pi$
$740$	9.13742	+	31.7793i	0.335898	+	1.16823i
$741$		0			0
$742$	23.0630	−	3.24979i	0.846669	−	0.119303i
$743$		−	16.0670i		−	0.589439i	−0.955584	−	0.294720i	$-0.904774\pi$
$743$		−	16.0670i		−	0.589439i	0.955584	−	0.294720i	$-0.0952263\pi$
$744$		0			0
$745$		−	38.0827i		−	1.39524i
$746$	−0.649281	−	4.60779i	−0.0237718	−	0.168703i
$747$		0			0
$748$	13.1982	+	7.30340i	0.482573	+	0.267039i
$749$	−17.8194	−	17.8194i	−0.651108	−	0.651108i
$750$		0			0
$751$			2.33565i			0.0852289i	0.999092	+	0.0426145i	$0.0135687\pi$
$751$			2.33565i			0.0852289i	−0.999092	+	0.0426145i	$0.986431\pi$
$752$	−19.5154	+	12.2338i	−0.711653	+	0.446121i
$753$		0			0
$754$	0.307219	+	0.231332i	0.0111883	+	0.00842463i
$755$	−2.05965	+	2.05965i	−0.0749582	+	0.0749582i
$756$		0			0
$757$	−9.89049	−	9.89049i	−0.359476	−	0.359476i	0.504144	−	0.863620i	$-0.331808\pi$
$757$	−9.89049	−	9.89049i	−0.359476	−	0.359476i	−0.863620	+	0.504144i	$0.831808\pi$
$758$	1.03523	−	0.145873i	0.0376011	−	0.00529835i
$759$		0			0
$760$	−7.13559	+	18.6492i	−0.258835	+	0.676479i
$761$	5.73919			0.208045			0.104023	−	0.994575i	$-0.466829\pi$
$761$	5.73919			0.208045			0.104023	+	0.994575i	$0.466829\pi$
$762$		0			0
$763$	−3.45812	+	3.45812i	−0.125192	+	0.125192i
$764$	7.87109	+	27.3751i	0.284766	+	0.990396i
$765$		0			0
$766$	29.2442	+	22.0205i	1.05664	+	0.795634i
$767$	−1.89122			−0.0682880
$768$		0			0
$769$	−53.0430			−1.91278			−0.956391	−	0.292091i	$-0.905649\pi$
$769$	−53.0430			−1.91278			−0.956391	+	0.292091i	$0.905649\pi$
$770$	−4.93785	−	3.71814i	−0.177948	−	0.133993i
$771$		0			0
$772$	−1.37917	−	4.79665i	−0.0496374	−	0.172635i
$773$	23.4184	−	23.4184i	0.842300	−	0.842300i	−0.146858	−	0.989158i	$-0.546916\pi$
$773$	23.4184	−	23.4184i	0.842300	−	0.842300i	0.989158	+	0.146858i	$0.0469160\pi$
$774$		0			0
$775$	−16.7764			−0.602624
$776$	−12.4704	+	32.5919i	−0.447660	+	1.16998i
$777$		0			0
$778$	3.87144	−	0.545522i	0.138798	−	0.0195579i
$779$	26.0873	+	26.0873i	0.934674	+	0.934674i
$780$		0			0
$781$	18.5976	−	18.5976i	0.665476	−	0.665476i
$782$	26.5138	+	19.9646i	0.948133	+	0.713932i
$783$		0			0
$784$	16.3123	−	10.2259i	0.582583	−	0.365210i
$785$			21.0466i			0.751186i
$786$		0			0
$787$	−0.858162	−	0.858162i	−0.0305902	−	0.0305902i	0.691646	−	0.722236i	$-0.256886\pi$
$787$	−0.858162	−	0.858162i	−0.0305902	−	0.0305902i	−0.722236	+	0.691646i	$0.756886\pi$
$788$	17.3716	+	9.61281i	0.618836	+	0.342442i
$789$		0			0
$790$	−1.54909	−	10.9935i	−0.0551142	−	0.391133i
$791$		−	26.1318i		−	0.929139i
$792$		0			0
$793$			0.667749i			0.0237125i
$794$	7.66032	−	1.07941i	0.271855	−	0.0383068i
$795$		0			0
$796$	0.00489233	+	0.0170152i	0.000173404	+	0.000603087i
$797$	5.26955	+	5.26955i	0.186657	+	0.186657i	0.794249	−	0.607592i	$-0.207864\pi$
$797$	5.26955	+	5.26955i	0.186657	+	0.186657i	−0.607592	+	0.794249i	$0.707864\pi$
$798$		0			0
$799$			26.3026i			0.930518i
$800$	−0.867075	+	10.1212i	−0.0306557	+	0.357840i
$801$		0			0
$802$	−13.7619	+	18.2764i	−0.485951	+	0.645364i
$803$	−14.7684	+	14.7684i	−0.521165	+	0.521165i
$804$		0			0
$805$	−9.61704	−	9.61704i	−0.338956	−	0.338956i
$806$	2.19667	+	15.5893i	0.0773744	+	0.549108i
$807$		0			0
$808$	−0.318576	−	0.713451i	−0.0112075	−	0.0250991i
$809$	7.20874			0.253446			0.126723	−	0.991938i	$-0.459554\pi$
$809$	7.20874			0.253446			0.126723	+	0.991938i	$0.459554\pi$
$810$		0			0
$811$	5.72509	−	5.72509i	0.201035	−	0.201035i	−0.599408	−	0.800443i	$-0.704597\pi$
$811$	5.72509	−	5.72509i	0.201035	−	0.201035i	0.800443	+	0.599408i	$0.204597\pi$
$812$	−0.326801	+	0.590571i	−0.0114685	+	0.0207250i
$813$		0			0
$814$	12.9733	−	17.2292i	0.454715	−	0.603882i
$815$	−25.5586			−0.895278
$816$		0			0
$817$	22.2039			0.776815
$818$	12.9081	−	17.1426i	0.451322	−	0.599376i
$819$		0			0
$820$	−29.3028	−	16.2151i	−1.02330	−	0.566257i
$821$	28.9487	−	28.9487i	1.01032	−	1.01032i	0.0103699	−	0.999946i	$-0.496699\pi$
$821$	28.9487	−	28.9487i	1.01032	−	1.01032i	0.999946	−	0.0103699i	$-0.00330090\pi$
$822$		0			0
$823$	23.9244			0.833953			0.416976	−	0.908917i	$-0.363090\pi$
$823$	23.9244			0.833953			0.416976	+	0.908917i	$0.363090\pi$
$824$	7.48579	−	19.5645i	0.260780	−	0.681562i
$825$		0			0
$826$	−0.463136	−	3.28677i	−0.0161146	−	0.114361i
$827$	29.2738	+	29.2738i	1.01795	+	1.01795i	0.999836	+	0.0181126i	$0.00576574\pi$
$827$	29.2738	+	29.2738i	1.01795	+	1.01795i	0.0181126	+	0.999836i	$0.494234\pi$
$828$		0			0
$829$	4.28147	−	4.28147i	0.148702	−	0.148702i	−0.628836	−	0.777538i	$-0.716468\pi$
$829$	4.28147	−	4.28147i	0.148702	−	0.148702i	0.777538	+	0.628836i	$0.216468\pi$
$830$	8.83832	−	11.7377i	0.306782	−	0.407420i
$831$		0			0
$832$	9.51860	−	0.519540i	0.329998	−	0.0180118i
$833$		−	21.9855i		−	0.761753i
$834$		0			0
$835$	16.9085	+	16.9085i	0.585143	+	0.585143i
$836$	12.5166	−	3.59886i	0.432894	−	0.124469i
$837$		0			0
$838$	12.5222	−	1.76449i	0.432572	−	0.0609533i
$839$		−	41.0260i		−	1.41638i	−0.706024	−	0.708188i	$-0.749513\pi$
$839$		−	41.0260i		−	1.41638i	0.706024	−	0.708188i	$-0.250487\pi$
$840$		0			0
$841$		−	28.9479i		−	0.998204i
$842$	5.07515	+	36.0172i	0.174901	+	1.24123i
$843$		0			0
$844$	−7.31478	+	13.2187i	−0.251785	+	0.455007i
$845$	−14.6575	−	14.6575i	−0.504234	−	0.504234i
$846$		0			0
$847$		−	12.2353i		−	0.420409i
$848$	9.95817	−	43.4198i	0.341965	−	1.49104i
$849$		0			0
$850$	9.26695	+	6.97790i	0.317854	+	0.239340i
$851$	33.5558	−	33.5558i	1.15028	−	1.15028i
$852$		0			0
$853$	−35.5411	−	35.5411i	−1.21690	−	1.21690i	−0.968711	−	0.248193i	$-0.920163\pi$
$853$	−35.5411	−	35.5411i	−1.21690	−	1.21690i	−0.248193	−	0.968711i	$-0.579837\pi$
$854$	−1.16049	+	0.163524i	−0.0397111	+	0.00559566i
$855$		0			0
$856$	−44.0112	+	19.6522i	−1.50427	+	0.671699i
$857$	8.85223			0.302386			0.151193	−	0.988504i	$-0.451688\pi$
$857$	8.85223			0.302386			0.151193	+	0.988504i	$0.451688\pi$
$858$		0			0
$859$	31.1164	−	31.1164i	1.06168	−	1.06168i	0.0637080	−	0.997969i	$-0.479707\pi$
$859$	31.1164	−	31.1164i	1.06168	−	1.06168i	0.997969	−	0.0637080i	$-0.0202926\pi$
$860$	−19.3710	+	5.56969i	−0.660546	+	0.189925i
$861$		0			0
$862$	−37.5682	−	28.2884i	−1.27958	−	0.963506i
$863$	−11.6345			−0.396043			−0.198022	−	0.980198i	$-0.563452\pi$
$863$	−11.6345			−0.396043			−0.198022	+	0.980198i	$0.563452\pi$
$864$		0			0
$865$	10.4014			0.353660
$866$	−23.9605	−	18.0420i	−0.814210	−	0.613091i
$867$		0			0
$868$	−26.5548	+	7.63524i	−0.901329	+	0.259157i
$869$	−5.12031	+	5.12031i	−0.173695	+	0.173695i
$870$		0			0
$871$	−10.3090			−0.349308
$872$	3.81380	+	8.54101i	0.129152	+	0.289235i
$873$		0			0
$874$	28.3759	−	3.99842i	0.959828	−	0.135249i
$875$	−12.7203	−	12.7203i	−0.430024	−	0.430024i
$876$		0			0
$877$	−27.8544	+	27.8544i	−0.940576	+	0.940576i	−0.998331	−	0.0577553i	$-0.981606\pi$
$877$	−27.8544	+	27.8544i	−0.940576	+	0.940576i	0.0577553	+	0.998331i	$0.481606\pi$
$878$	38.8159	+	29.2279i	1.30997	+	0.986393i
$879$		0			0
$880$	−10.0169	+	6.27939i	−0.337669	+	0.211678i
$881$			18.4567i			0.621823i	0.950439	+	0.310912i	$0.100634\pi$
$881$			18.4567i			0.621823i	−0.950439	+	0.310912i	$0.899366\pi$
$882$		0			0
$883$	−2.68187	−	2.68187i	−0.0902521	−	0.0902521i	0.660539	−	0.750791i	$-0.270328\pi$
$883$	−2.68187	−	2.68187i	−0.0902521	−	0.0902521i	−0.750791	+	0.660539i	$0.770328\pi$
$884$	5.27074	−	9.52489i	0.177274	−	0.320357i
$885$		0			0
$886$	1.89532	+	13.4506i	0.0636744	+	0.451882i
$887$		−	0.308340i		−	0.0103531i	−0.999987	−	0.00517653i	$-0.998352\pi$
$887$		−	0.308340i		−	0.0103531i	0.999987	−	0.00517653i	$-0.00164775\pi$
$888$		0			0
$889$		−	3.71526i		−	0.124606i
$890$	−2.04478	+	0.288128i	−0.0685411	+	0.00965808i
$891$		0			0
$892$	17.3662	−	4.99327i	0.581465	−	0.167187i
$893$	16.0582	+	16.0582i	0.537366	+	0.537366i
$894$		0			0
$895$		−	0.184981i		−	0.00618323i
$896$	3.23390	+	16.4153i	0.108037	+	0.548395i
$897$		0			0
$898$	20.5068	−	27.2340i	0.684322	−	0.908809i
$899$	−1.50756	+	1.50756i	−0.0502798	+	0.0502798i
$900$		0			0
$901$	−35.9710	−	35.9710i	−1.19837	−	1.19837i
$902$	3.04783	+	21.6297i	0.101482	+	0.720191i
$903$		0			0
$904$	−46.6805	−	17.8609i	−1.55257	−	0.594046i
$905$	−10.2688			−0.341345
$906$		0			0
$907$	11.5311	−	11.5311i	0.382882	−	0.382882i	−0.489257	−	0.872140i	$-0.662732\pi$
$907$	11.5311	−	11.5311i	0.382882	−	0.382882i	0.872140	+	0.489257i	$0.162732\pi$
$908$	21.7425	+	12.0315i	0.721551	+	0.399281i
$909$		0			0
$910$	−2.68332	+	3.56356i	−0.0889512	+	0.118131i
$911$	4.72201			0.156447			0.0782236	−	0.996936i	$-0.475075\pi$
$911$	4.72201			0.156447			0.0782236	+	0.996936i	$0.475075\pi$
$912$		0			0
$913$	−9.58339			−0.317164
$914$	1.29026	−	1.71351i	0.0426779	−	0.0566780i
$915$		0			0
$916$	4.18016	−	7.55407i	0.138116	−	0.249594i
$917$	19.1462	−	19.1462i	0.632262	−	0.632262i
$918$		0			0
$919$	35.4646			1.16987			0.584935	−	0.811080i	$-0.301120\pi$
$919$	35.4646			1.16987			0.584935	+	0.811080i	$0.301120\pi$
$920$	−23.7526	+	10.6062i	−0.783099	+	0.349676i
$921$		0			0
$922$	−6.58655	−	46.7432i	−0.216917	−	1.53941i
$923$	−13.4216	−	13.4216i	−0.441777	−	0.441777i
$924$		0			0
$925$	11.7282	−	11.7282i	0.385621	−	0.385621i
$926$	−13.0083	+	17.2755i	−0.427478	+	0.567709i
$927$		0			0
$928$	0.831598	+	0.987432i	0.0272985	+	0.0324141i
$929$		−	59.4380i		−	1.95010i	−0.221993	−	0.975048i	$-0.571256\pi$
$929$		−	59.4380i		−	1.95010i	0.221993	−	0.975048i	$-0.428744\pi$
$930$		0			0
$931$	−13.4225	−	13.4225i	−0.439906	−	0.439906i
$932$	−0.347263	−	1.20776i	−0.0113750	−	0.0395614i
$933$		0			0
$934$	−47.9797	+	6.76079i	−1.56994	+	0.221220i
$935$			13.5006i			0.441517i
$936$		0			0
$937$		−	20.2422i		−	0.661283i	−0.943756	−	0.330642i	$-0.892735\pi$
$937$		−	20.2422i		−	0.661283i	0.943756	−	0.330642i	$-0.107265\pi$
$938$	−2.52455	−	17.9162i	−0.0824295	−	0.584983i
$939$		0			0
$940$	−18.0375	−	9.98130i	−0.588317	−	0.325554i
$941$	26.7386	+	26.7386i	0.871654	+	0.871654i	0.992653	−	0.120999i	$-0.0386097\pi$
$941$	26.7386	+	26.7386i	0.871654	+	0.871654i	−0.120999	+	0.992653i	$0.538610\pi$
$942$		0			0
$943$			48.0624i			1.56513i
$944$	−6.18787	−	1.41917i	−0.201398	−	0.0461900i
$945$		0			0
$946$	10.5020	+	7.90787i	0.341449	+	0.257107i
$947$	−5.67631	+	5.67631i	−0.184455	+	0.184455i	−0.793294	−	0.608839i	$-0.791636\pi$
$947$	−5.67631	+	5.67631i	−0.184455	+	0.184455i	0.608839	+	0.793294i	$0.291636\pi$
$948$		0			0
$949$	10.6581	+	10.6581i	0.345976	+	0.345976i
$950$	9.91776	−	1.39750i	0.321775	−	0.0453410i
$951$		0			0
$952$	17.8442	+	6.82755i	0.578333	+	0.221282i
$953$	−57.8320			−1.87336			−0.936680	−	0.350185i	$-0.886119\pi$
$953$	−57.8320			−1.87336			−0.936680	+	0.350185i	$0.886119\pi$
$954$		0			0
$955$	−18.0269	+	18.0269i	−0.583338	+	0.583338i
$956$	−1.28197	−	4.45859i	−0.0414618	−	0.144201i
$957$		0			0
$958$	−12.1861	−	9.17602i	−0.393717	−	0.296464i
$959$	27.0427			0.873255
$960$		0			0
$961$	−56.2773			−1.81540
$962$	−12.4340	−	9.36264i	−0.400888	−	0.301864i
$963$		0			0
$964$	13.7465	+	47.8092i	0.442744	+	1.53983i
$965$	3.15867	−	3.15867i	0.101681	−	0.101681i
$966$		0			0
$967$	−19.5761			−0.629526			−0.314763	−	0.949170i	$-0.601925\pi$
$967$	−19.5761			−0.629526			−0.314763	+	0.949170i	$0.601925\pi$
$968$	−21.8565	−	8.36274i	−0.702493	−	0.268789i
$969$		0			0
$970$	−30.9273	+	4.35794i	−0.993015	+	0.139925i
$971$	2.78950	+	2.78950i	0.0895194	+	0.0895194i	0.750448	−	0.660929i	$-0.229838\pi$
$971$	2.78950	+	2.78950i	0.0895194	+	0.0895194i	−0.660929	+	0.750448i	$0.729838\pi$
$972$		0			0
$973$	−13.5206	+	13.5206i	−0.433449	+	0.433449i
$974$	−22.1651	−	16.6900i	−0.710215	−	0.534783i
$975$		0			0
$976$	−0.501078	+	2.18480i	−0.0160391	+	0.0699339i
$977$			38.5087i			1.23200i	0.787745	+	0.616001i	$0.211248\pi$
$977$			38.5087i			1.23200i	−0.787745	+	0.616001i	$0.788752\pi$
$978$		0			0
$979$	0.952368	+	0.952368i	0.0304378	+	0.0304378i
$980$	15.0770	+	8.34307i	0.481616	+	0.266510i
$981$		0			0
$982$	−7.19067	−	51.0305i	−0.229464	−	1.62845i
$983$		−	1.26237i		−	0.0402634i	−0.999797	−	0.0201317i	$-0.993591\pi$
$983$		−	1.26237i		−	0.0402634i	0.999797	−	0.0201317i	$-0.00640855\pi$
$984$		0			0
$985$			17.7696i			0.566188i
$986$	1.45979	−	0.205699i	0.0464893	−	0.00655078i
$987$		0			0
$988$	−2.59723	−	9.03299i	−0.0826290	−	0.287378i
$989$	20.4538	+	20.4538i	0.650394	+	0.650394i
$990$		0			0
$991$			7.56646i			0.240357i	0.992752	+	0.120178i	$0.0383466\pi$
$991$			7.56646i			0.240357i	−0.992752	+	0.120178i	$0.961653\pi$
$992$	−4.51087	+	52.6548i	−0.143220	+	1.67179i
$993$		0			0
$994$	20.0388	−	26.6123i	0.635591	−	0.844092i
$995$	−0.0112048	+	0.0112048i	−0.000355215	+	0.000355215i
$996$		0			0
$997$	−32.4462	−	32.4462i	−1.02758	−	1.02758i	−0.999609	−	0.0279715i	$-0.991095\pi$
$997$	−32.4462	−	32.4462i	−1.02758	−	1.02758i	−0.0279715	−	0.999609i	$-0.508905\pi$
$998$	−4.67627	−	33.1864i	−0.148025	−	1.05050i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.b.107.4	✓	32
3.2	odd	2	inner	432.2.l.b.107.13	yes	32
4.3	odd	2		1728.2.l.b.1295.6		32
12.11	even	2		1728.2.l.b.1295.11		32
16.3	odd	4	inner	432.2.l.b.323.13	yes	32
16.13	even	4		1728.2.l.b.431.11		32
48.29	odd	4		1728.2.l.b.431.6		32
48.35	even	4	inner	432.2.l.b.323.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.b.107.4	✓	32	1.1	even	1	trivial
432.2.l.b.107.13	yes	32	3.2	odd	2	inner
432.2.l.b.323.4	yes	32	48.35	even	4	inner
432.2.l.b.323.13	yes	32	16.3	odd	4	inner
1728.2.l.b.431.6		32	48.29	odd	4
1728.2.l.b.431.11		32	16.13	even	4
1728.2.l.b.1295.6		32	4.3	odd	2
1728.2.l.b.1295.11		32	12.11	even	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12975 - 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(-1.26575 + 1.26575i) q^{5} +1.47880 q^{7} +(1.01076 - 2.64166i) q^{8} +O(q^{10})\)	\(q+(-1.12975 - 0.850687i) q^{2} +(0.552664 + 1.92212i) q^{4} +(-1.26575 + 1.26575i) q^{5} +1.47880 q^{7} +(1.01076 - 2.64166i) q^{8} +(2.50674 - 0.353222i) q^{10} +(-1.16753 - 1.16753i) q^{11} +(-0.842585 + 0.842585i) q^{13} +(-1.67068 - 1.25800i) q^{14} +(-3.38913 + 2.12458i) q^{16} +4.56781i q^{17} +(2.78873 + 2.78873i) q^{19} +(-3.13246 - 1.73340i) q^{20} +(0.325812 + 2.31221i) q^{22} +5.13786i q^{23} +1.79575i q^{25} +(1.66869 - 0.235133i) q^{26} +(0.817282 + 2.84245i) q^{28} +(0.161370 + 0.161370i) q^{29} +9.34223i q^{31} +(5.63621 + 0.482847i) q^{32} +(3.88578 - 5.16048i) q^{34} +(-1.87180 + 1.87180i) q^{35} +(-6.53108 - 6.53108i) q^{37} +(-0.778227 - 5.52290i) q^{38} +(2.06432 + 4.62305i) q^{40} +9.35455 q^{41} +(3.98100 - 3.98100i) q^{43} +(1.59888 - 2.88939i) q^{44} +(4.37071 - 5.80449i) q^{46} +5.75824 q^{47} -4.81314 q^{49} +(1.52762 - 2.02875i) q^{50} +(-2.08522 - 1.15389i) q^{52} +(-7.87488 + 7.87488i) q^{53} +2.95560 q^{55} +(1.49471 - 3.90650i) q^{56} +(-0.0450322 - 0.319583i) q^{58} +(1.12227 + 1.12227i) q^{59} +(0.396250 - 0.396250i) q^{61} +(7.94732 - 10.5544i) q^{62} +(-5.95675 - 5.34015i) q^{64} -2.13300i q^{65} +(6.11749 + 6.11749i) q^{67} +(-8.77991 + 2.52446i) q^{68} +(3.70697 - 0.522347i) q^{70} +15.9291i q^{71} -12.6493i q^{73} +(1.82257 + 12.9344i) q^{74} +(-3.81905 + 6.90151i) q^{76} +(-1.72655 - 1.72655i) q^{77} -4.38560i q^{79} +(1.60060 - 6.97897i) q^{80} +(-10.5683 - 7.95779i) q^{82} +(4.10414 - 4.10414i) q^{83} +(-5.78171 - 5.78171i) q^{85} +(-7.88412 + 1.11095i) q^{86} +(-4.26430 + 1.90413i) q^{88} -0.815713 q^{89} +(-1.24602 + 1.24602i) q^{91} +(-9.87561 + 2.83951i) q^{92} +(-6.50536 - 4.89846i) q^{94} -7.05966 q^{95} -12.3377 q^{97} +(5.43763 + 4.09447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{10} - 8 q^{16} - 16 q^{19} + 16 q^{22} + 24 q^{28} + 24 q^{34} - 24 q^{40} - 16 q^{43} + 32 q^{46} + 32 q^{49} + 48 q^{52} - 32 q^{55} + 32 q^{61} - 24 q^{64} - 32 q^{67} - 48 q^{76} - 80 q^{82} + 32 q^{85} - 24 q^{88} - 48 q^{91}+O(q^{100}) \) 32 * q + 8 * q^10 - 8 * q^16 - 16 * q^19 + 16 * q^22 + 24 * q^28 + 24 * q^34 - 24 * q^40 - 16 * q^43 + 32 * q^46 + 32 * q^49 + 48 * q^52 - 32 * q^55 + 32 * q^61 - 24 * q^64 - 32 * q^67 - 48 * q^76 - 80 * q^82 + 32 * q^85 - 24 * q^88 - 48 * q^91

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