LMFDB - Embedded newform 387.2.v.a.242.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(8,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 13]))

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

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

chi := DirichletCharacter("387.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.v (of order $14$, degree $6$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			242.9
Character	$\chi$	$=$	387.242
Dual form			387.2.v.a.8.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0211977 + 0.0928730i) q^{2} +(1.79376 - 0.863830i) q^{4} +(1.55851 + 1.95431i) q^{5} +1.70699i q^{7} +(0.237039 + 0.297238i) q^{8} +O(q^{10})$	\(q+(0.0211977 + 0.0928730i) q^{2} +(1.79376 - 0.863830i) q^{4} +(1.55851 + 1.95431i) q^{5} +1.70699i q^{7} +(0.237039 + 0.297238i) q^{8} +(-0.148466 + 0.186171i) q^{10} +(-2.28056 + 4.73563i) q^{11} +(0.699719 + 0.877420i) q^{13} +(-0.158533 + 0.0361841i) q^{14} +(2.46006 - 3.08482i) q^{16} +(-0.976839 - 0.779003i) q^{17} +(-2.78424 - 5.78154i) q^{19} +(4.48380 + 2.15928i) q^{20} +(-0.488155 - 0.111418i) q^{22} +(1.12903 - 2.34445i) q^{23} +(-0.277773 + 1.21701i) q^{25} +(-0.0666563 + 0.0835843i) q^{26} +(1.47455 + 3.06193i) q^{28} +(0.142833 + 0.625794i) q^{29} +(1.17079 + 5.12954i) q^{31} +(1.02371 + 0.492991i) q^{32} +(0.0516417 - 0.107235i) q^{34} +(-3.33599 + 2.66036i) q^{35} -5.00015i q^{37} +(0.477930 - 0.381136i) q^{38} +(-0.211467 + 0.926497i) q^{40} +(6.93264 - 1.58233i) q^{41} +(6.55610 + 0.132524i) q^{43} +10.4646i q^{44} +(0.241669 + 0.0551593i) q^{46} +(-4.65908 - 9.67467i) q^{47} +4.08620 q^{49} -0.118915 q^{50} +(2.01307 + 0.969444i) q^{52} +(-5.75575 - 4.59006i) q^{53} +(-12.8092 + 2.92361i) q^{55} +(-0.507381 + 0.404623i) q^{56} +(-0.0550916 + 0.0265307i) q^{58} +(-3.32207 - 2.64926i) q^{59} +(8.14746 + 1.85960i) q^{61} +(-0.451578 + 0.217469i) q^{62} +(1.73189 - 7.58789i) q^{64} +(-0.624232 + 2.73494i) q^{65} +(-12.9293 + 6.22641i) q^{67} +(-2.42514 - 0.553523i) q^{68} +(-0.317791 - 0.253430i) q^{70} +(6.29542 - 3.03172i) q^{71} +(-7.19395 + 5.73699i) q^{73} +(0.464379 - 0.105991i) q^{74} +(-9.98854 - 7.96560i) q^{76} +(-8.08365 - 3.89288i) q^{77} -7.65734 q^{79} +9.86275 q^{80} +(0.293912 + 0.610314i) q^{82} +(-2.82251 - 0.644219i) q^{83} -3.12313i q^{85} +(0.126666 + 0.611694i) q^{86} +(-1.94819 + 0.444661i) q^{88} +(2.41919 - 10.5992i) q^{89} +(-1.49774 + 1.19441i) q^{91} -5.18067i q^{92} +(0.799755 - 0.637783i) q^{94} +(6.95967 - 14.4519i) q^{95} +(2.17060 + 1.04531i) q^{97} +(0.0866178 + 0.379497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 20 q^{4}+O(q^{10}) $ 96 * q - 20 * q^4	$ 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) $ 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$-1$

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 $

$2$	0.0211977	+	0.0928730i	0.0149890	+	0.0656711i	0.981869	−	0.189559i	$-0.0607059\pi$
$2$	0.0211977	+	0.0928730i	0.0149890	+	0.0656711i	−0.966880	+	0.255230i	$0.917849\pi$
$3$		0			0
$3$		0			0
$4$	1.79376	−	0.863830i	0.896881	−	0.431915i
$5$	1.55851	+	1.95431i	0.696988	+	0.873995i	0.996794	−	0.0800046i	$-0.0254935\pi$
$5$	1.55851	+	1.95431i	0.696988	+	0.873995i	−0.299806	+	0.954000i	$0.596922\pi$
$6$		0			0
$7$			1.70699i			0.645180i	0.946539	+	0.322590i	$0.104554\pi$
$7$			1.70699i			0.645180i	−0.946539	+	0.322590i	$0.895446\pi$
$8$	0.237039	+	0.297238i	0.0838060	+	0.105089i
$9$		0			0
$10$	−0.148466	+	0.186171i	−0.0469491	+	0.0588723i
$11$	−2.28056	+	4.73563i	−0.687614	+	1.42785i	0.205792	+	0.978596i	$0.434023\pi$
$11$	−2.28056	+	4.73563i	−0.687614	+	1.42785i	−0.893406	+	0.449250i	$0.851691\pi$
$12$		0			0
$13$	0.699719	+	0.877420i	0.194067	+	0.243353i	0.869339	−	0.494217i	$-0.164545\pi$
$13$	0.699719	+	0.877420i	0.194067	+	0.243353i	−0.675272	+	0.737569i	$0.735974\pi$
$14$	−0.158533	+	0.0361841i	−0.0423697	+	0.00967061i
$15$		0			0
$16$	2.46006	−	3.08482i	0.615016	−	0.771205i
$17$	−0.976839	−	0.779003i	−0.236918	−	0.188936i	0.497833	−	0.867273i	$-0.334129\pi$
$17$	−0.976839	−	0.779003i	−0.236918	−	0.188936i	−0.734751	+	0.678337i	$0.762701\pi$
$18$		0			0
$19$	−2.78424	−	5.78154i	−0.638750	−	1.32638i	−0.929232	−	0.369497i	$-0.879530\pi$
$19$	−2.78424	−	5.78154i	−0.638750	−	1.32638i	0.290483	−	0.956880i	$-0.406184\pi$
$20$	4.48380	+	2.15928i	1.00261	+	0.482830i
$21$		0			0
$22$	−0.488155	−	0.111418i	−0.104075	−	0.0237544i
$23$	1.12903	−	2.34445i	0.235418	−	0.488851i	−0.749471	−	0.662037i	$-0.769692\pi$
$23$	1.12903	−	2.34445i	0.235418	−	0.488851i	0.984889	+	0.173186i	$0.0554063\pi$
$24$		0			0
$25$	−0.277773	+	1.21701i	−0.0555547	+	0.243401i
$26$	−0.0666563	+	0.0835843i	−0.0130724	+	0.0163922i
$27$		0			0
$28$	1.47455	+	3.06193i	0.278663	+	0.578650i
$29$	0.142833	+	0.625794i	0.0265235	+	0.116207i	0.986457	−	0.164022i	$-0.0524468\pi$
$29$	0.142833	+	0.625794i	0.0265235	+	0.116207i	−0.959933	+	0.280229i	$0.909590\pi$
$30$		0			0
$31$	1.17079	+	5.12954i	0.210279	+	0.921293i	0.964377	+	0.264531i	$0.0852173\pi$
$31$	1.17079	+	5.12954i	0.210279	+	0.921293i	−0.754098	+	0.656762i	$0.771926\pi$
$32$	1.02371	+	0.492991i	0.180968	+	0.0871494i
$33$		0			0
$34$	0.0516417	−	0.107235i	0.00885647	−	0.0183907i
$35$	−3.33599	+	2.66036i	−0.563885	+	0.449683i
$36$		0			0
$37$		−	5.00015i		−	0.822019i	−0.911631	−	0.411010i	$-0.865176\pi$
$37$		−	5.00015i		−	0.822019i	0.911631	−	0.411010i	$-0.134824\pi$
$38$	0.477930	−	0.381136i	0.0775305	−	0.0618285i
$39$		0			0
$40$	−0.211467	+	0.926497i	−0.0334359	+	0.146492i
$41$	6.93264	−	1.58233i	1.08270	−	0.247119i	0.356285	−	0.934378i	$-0.384043\pi$
$41$	6.93264	−	1.58233i	1.08270	−	0.247119i	0.726412	+	0.687259i	$0.241186\pi$
$42$		0			0
$43$	6.55610	+	0.132524i	0.999796	+	0.0202098i
$43$	6.55610	+	0.132524i	0.999796	+	0.0202098i
$44$			10.4646i			1.57760i
$45$		0			0
$46$	0.241669	+	0.0551593i	0.0356321	+	0.00813280i
$47$	−4.65908	−	9.67467i	−0.679596	−	1.41120i	−0.900045	−	0.435797i	$-0.856466\pi$
$47$	−4.65908	−	9.67467i	−0.679596	−	1.41120i	0.220449	−	0.975399i	$-0.429248\pi$
$48$		0			0
$49$	4.08620			0.583742
$50$	−0.118915			−0.0168171
$51$		0			0
$52$	2.01307	+	0.969444i	0.279163	+	0.134438i
$53$	−5.75575	−	4.59006i	−0.790614	−	0.630493i	0.142614	−	0.989778i	$-0.454449\pi$
$53$	−5.75575	−	4.59006i	−0.790614	−	0.630493i	−0.933228	+	0.359285i	$0.883021\pi$
$54$		0			0
$55$	−12.8092	+	2.92361i	−1.72719	+	0.394220i
$56$	−0.507381	+	0.404623i	−0.0678016	+	0.0540700i
$57$		0			0
$58$	−0.0550916	+	0.0265307i	−0.00723388	+	0.00348365i
$59$	−3.32207	−	2.64926i	−0.432497	−	0.344905i	0.382918	−	0.923783i	$-0.374919\pi$
$59$	−3.32207	−	2.64926i	−0.432497	−	0.344905i	−0.815414	+	0.578878i	$0.803491\pi$
$60$		0			0
$61$	8.14746	+	1.85960i	1.04318	+	0.238098i	0.709585	−	0.704620i	$-0.248883\pi$
$61$	8.14746	+	1.85960i	1.04318	+	0.238098i	0.333591	+	0.942718i	$0.391740\pi$
$62$	−0.451578	+	0.217469i	−0.0573505	+	0.0276186i
$63$		0			0
$64$	1.73189	−	7.58789i	0.216486	−	0.948487i
$65$	−0.624232	+	2.73494i	−0.0774265	+	0.339228i
$66$		0			0
$67$	−12.9293	+	6.22641i	−1.57956	+	0.760677i	−0.998582	−	0.0532399i	$-0.983045\pi$
$67$	−12.9293	+	6.22641i	−1.57956	+	0.760677i	−0.580981	+	0.813917i	$0.697331\pi$
$68$	−2.42514	−	0.553523i	−0.294092	−	0.0671245i
$69$		0			0
$70$	−0.317791	−	0.253430i	−0.0379833	−	0.0302906i
$71$	6.29542	−	3.03172i	0.747129	−	0.359798i	−0.0212662	−	0.999774i	$-0.506770\pi$
$71$	6.29542	−	3.03172i	0.747129	−	0.359798i	0.768395	+	0.639975i	$0.221055\pi$
$72$		0			0
$73$	−7.19395	+	5.73699i	−0.841988	+	0.671463i	−0.946374	−	0.323074i	$-0.895284\pi$
$73$	−7.19395	+	5.73699i	−0.841988	+	0.671463i	0.104385	+	0.994537i	$0.466712\pi$
$74$	0.464379	−	0.105991i	0.0539829	−	0.0123213i
$75$		0			0
$76$	−9.98854	−	7.96560i	−1.14576	−	0.913717i
$77$	−8.08365	−	3.89288i	−0.921218	−	0.443635i
$78$		0			0
$79$	−7.65734			−0.861518			−0.430759	−	0.902467i	$-0.641754\pi$
$79$	−7.65734			−0.861518			−0.430759	+	0.902467i	$0.641754\pi$
$80$	9.86275			1.10269
$81$		0			0
$82$	0.293912	+	0.610314i	0.0324571	+	0.0673979i
$83$	−2.82251	−	0.644219i	−0.309810	−	0.0707122i	0.0647889	−	0.997899i	$-0.479363\pi$
$83$	−2.82251	−	0.644219i	−0.309810	−	0.0707122i	−0.374599	+	0.927187i	$0.622220\pi$
$84$		0			0
$85$		−	3.12313i		−	0.338752i
$86$	0.126666	+	0.611694i	0.0136588	+	0.0659607i
$87$		0			0
$88$	−1.94819	+	0.444661i	−0.207678	+	0.0474011i
$89$	2.41919	−	10.5992i	0.256434	−	1.12351i	−0.668599	−	0.743624i	$-0.733105\pi$
$89$	2.41919	−	10.5992i	0.256434	−	1.12351i	0.925033	−	0.379888i	$-0.124037\pi$
$90$		0			0
$91$	−1.49774	+	1.19441i	−0.157006	+	0.125208i
$92$		−	5.18067i		−	0.540122i
$93$		0			0
$94$	0.799755	−	0.637783i	0.0824884	−	0.0657823i
$95$	6.95967	−	14.4519i	0.714047	−	1.48273i
$96$		0			0
$97$	2.17060	+	1.04531i	0.220391	+	0.106135i	0.540822	−	0.841137i	$-0.318113\pi$
$97$	2.17060	+	1.04531i	0.220391	+	0.106135i	−0.320431	+	0.947272i	$0.603828\pi$
$98$	0.0866178	+	0.379497i	0.00874972	+	0.0383350i
$99$		0			0
$100$	0.553026	+	2.42297i	0.0553026	+	0.242297i
$101$	−5.72464	−	11.8873i	−0.569623	−	1.18283i	−0.964496	−	0.264098i	$-0.914926\pi$
$101$	−5.72464	−	11.8873i	−0.569623	−	1.18283i	0.394873	−	0.918736i	$-0.370788\pi$
$102$		0			0
$103$	−0.305003	+	0.382462i	−0.0300529	+	0.0376851i	−0.796631	−	0.604466i	$-0.793386\pi$
$103$	−0.305003	+	0.382462i	−0.0300529	+	0.0376851i	0.766578	+	0.642151i	$0.221958\pi$
$104$	−0.0949415	+	0.415966i	−0.00930978	+	0.0407888i
$105$		0			0
$106$	0.304284	−	0.631853i	0.0295547	−	0.0613710i
$107$	−11.3806	−	2.59754i	−1.10020	−	0.251114i	−0.366386	−	0.930463i	$-0.619405\pi$
$107$	−11.3806	−	2.59754i	−1.10020	−	0.251114i	−0.733815	+	0.679349i	$0.762262\pi$
$108$		0			0
$109$	1.01630	+	0.489425i	0.0973440	+	0.0468784i	0.481922	−	0.876214i	$-0.339939\pi$
$109$	1.01630	+	0.489425i	0.0973440	+	0.0468784i	−0.384578	+	0.923092i	$0.625653\pi$
$110$	−0.543049	−	1.12765i	−0.0517777	−	0.107518i
$111$		0			0
$112$	5.26575	+	4.19929i	0.497566	+	0.396796i
$113$	−8.97062	+	11.2488i	−0.843885	+	1.05820i	0.153657	+	0.988124i	$0.450895\pi$
$113$	−8.97062	+	11.2488i	−0.843885	+	1.05820i	−0.997542	+	0.0700741i	$0.977676\pi$
$114$		0			0
$115$	6.34139	−	1.44738i	0.591338	−	0.134969i
$116$	0.796788	+	0.999141i	0.0739799	+	0.0927679i
$117$		0			0
$118$	0.175625	−	0.364689i	0.0161676	−	0.0335723i
$119$	1.32975	−	1.66745i	0.121898	−	0.152855i
$120$		0			0
$121$	−10.3668	−	12.9996i	−0.942440	−	1.18178i
$122$			0.796099i			0.0720754i
$123$		0			0
$124$	6.53116	+	8.18982i	0.586516	+	0.735468i
$125$	8.44926	−	4.06895i	0.755725	−	0.363938i
$126$		0			0
$127$	3.28565	+	14.3954i	0.291555	+	1.27738i	0.882362	+	0.470572i	$0.155952\pi$
$127$	3.28565	+	14.3954i	0.291555	+	1.27738i	−0.590807	+	0.806813i	$0.701191\pi$
$128$	3.01388			0.266392
$129$		0			0
$130$	−0.267235			−0.0234380
$131$	1.24530	+	5.45600i	0.108802	+	0.476693i	0.999745	+	0.0225778i	$0.00718736\pi$
$131$	1.24530	+	5.45600i	0.108802	+	0.476693i	−0.890943	+	0.454115i	$0.849956\pi$
$132$		0			0
$133$	9.86902	−	4.75267i	0.855752	−	0.412109i
$134$	−0.852336	−	1.06880i	−0.0736306	−	0.0923299i
$135$		0			0
$136$		−	0.475007i		−	0.0407315i
$137$	13.2924	+	16.6682i	1.13565	+	1.42406i	0.890740	+	0.454514i	$0.150187\pi$
$137$	13.2924	+	16.6682i	1.13565	+	1.42406i	0.244910	+	0.969546i	$0.421242\pi$
$138$		0			0
$139$	−9.05029	+	11.3487i	−0.767636	+	0.962585i	−0.999949	−	0.0100560i	$-0.996799\pi$
$139$	−9.05029	+	11.3487i	−0.767636	+	0.962585i	0.232314	+	0.972641i	$0.425370\pi$
$140$	−3.68587	+	7.65378i	−0.311512	+	0.646862i
$141$		0			0
$142$	0.415013	+	0.520410i	0.0348271	+	0.0436718i
$143$	−5.75089	+	1.31260i	−0.480913	+	0.109765i
$144$		0			0
$145$	−1.00039	+	1.25445i	−0.0830778	+	0.104176i
$146$	−0.685306	−	0.546513i	−0.0567163	−	0.0452298i
$147$		0			0
$148$	−4.31928	−	8.96907i	−0.355042	−	0.737253i
$149$	0.735200	+	0.354054i	0.0602300	+	0.0290052i	0.463756	−	0.885963i	$-0.346501\pi$
$149$	0.735200	+	0.354054i	0.0602300	+	0.0290052i	−0.403526	+	0.914968i	$0.632216\pi$
$150$		0			0
$151$	20.4797	+	4.67437i	1.66662	+	0.380395i	0.948810	−	0.315847i	$-0.102289\pi$
$151$	20.4797	+	4.67437i	1.66662	+	0.380395i	0.717808	+	0.696242i	$0.245146\pi$
$152$	1.05852	−	2.19803i	0.0858571	−	0.178284i
$153$		0			0
$154$	0.190189	−	0.833273i	0.0153259	−	0.0671471i
$155$	−8.20005	+	10.2825i	−0.658644	+	0.825914i
$156$		0			0
$157$	−9.53931	−	19.8086i	−0.761320	−	1.58090i	−0.813021	−	0.582234i	$-0.802179\pi$
$157$	−9.53931	−	19.8086i	−0.761320	−	1.58090i	0.0517016	−	0.998663i	$-0.483536\pi$
$158$	−0.162318	−	0.711160i	−0.0129133	−	0.0565769i
$159$		0			0
$160$	0.632001	+	2.76898i	0.0499641	+	0.218907i
$161$	4.00194	+	1.92723i	0.315397	+	0.151887i
$162$		0			0
$163$	−2.23376	+	4.63844i	−0.174961	+	0.363311i	−0.969947	−	0.243318i	$-0.921764\pi$
$163$	−2.23376	+	4.63844i	−0.174961	+	0.363311i	0.794985	+	0.606629i	$0.207478\pi$
$164$	11.0686	−	8.82695i	0.864316	−	0.689269i
$165$		0			0
$166$		−	0.275791i		−	0.0214055i
$167$	−14.9973	+	11.9600i	−1.16053	+	0.925491i	−0.998124	−	0.0612325i	$-0.980497\pi$
$167$	−14.9973	+	11.9600i	−1.16053	+	0.925491i	−0.162406	+	0.986724i	$0.551925\pi$
$168$		0			0
$169$	2.61251	−	11.4462i	0.200963	−	0.880474i
$170$	0.290055	−	0.0662032i	0.0222462	−	0.00507755i
$171$		0			0
$172$	11.8746	−	5.42564i	0.905427	−	0.413701i
$173$			19.1628i			1.45692i	0.685086	+	0.728462i	$0.259764\pi$
$173$			19.1628i			1.45692i	−0.685086	+	0.728462i	$0.740236\pi$
$174$		0			0
$175$	−2.07741	−	0.474156i	−0.157038	−	0.0358428i
$176$	8.99825	+	18.6851i	0.678268	+	1.40844i
$177$		0			0
$178$	1.03566			0.0776260
$179$	9.26725			0.692666			0.346333	−	0.938112i	$-0.387427\pi$
$179$	9.26725			0.692666			0.346333	+	0.938112i	$0.387427\pi$
$180$		0			0
$181$	−13.5373	−	6.51921i	−1.00622	−	0.484569i	−0.143174	−	0.989698i	$-0.545731\pi$
$181$	−13.5373	−	6.51921i	−1.00622	−	0.484569i	−0.863044	+	0.505128i	$0.831445\pi$
$182$	−0.142677	−	0.113781i	−0.0105759	−	0.00843403i
$183$		0			0
$184$	0.964482	−	0.220137i	0.0711025	−	0.0162287i
$185$	9.77185	−	7.79279i	0.718441	−	0.572938i
$186$		0			0
$187$	5.91680	−	2.84938i	0.432680	−	0.208368i
$188$	−16.7145	−	13.3294i	−1.21903	−	0.972147i
$189$		0			0
$190$	1.48972	+	0.340019i	0.108076	+	0.0246676i
$191$	−11.2465	+	5.41602i	−0.813767	+	0.391889i	−0.794002	−	0.607915i	$-0.792006\pi$
$191$	−11.2465	+	5.41602i	−0.813767	+	0.391889i	−0.0197647	+	0.999805i	$0.506292\pi$
$192$		0			0
$193$	−1.95193	+	8.55196i	−0.140503	+	0.615583i	0.854815	+	0.518932i	$0.173670\pi$
$193$	−1.95193	+	8.55196i	−0.140503	+	0.615583i	−0.995318	+	0.0966513i	$0.969187\pi$
$194$	−0.0510691	+	0.223748i	−0.00366655	+	0.0160642i
$195$		0			0
$196$	7.32966	−	3.52978i	0.523547	−	0.252127i
$197$	3.20557	+	0.731650i	0.228387	+	0.0521279i	0.335183	−	0.942153i	$-0.391202\pi$
$197$	3.20557	+	0.731650i	0.228387	+	0.0521279i	−0.106796	+	0.994281i	$0.534059\pi$
$198$		0			0
$199$	−1.54601	−	1.23290i	−0.109593	−	0.0873978i	0.567160	−	0.823608i	$-0.308042\pi$
$199$	−1.54601	−	1.23290i	−0.109593	−	0.0873978i	−0.676753	+	0.736210i	$0.736614\pi$
$200$	−0.427583	+	0.205913i	−0.0302347	+	0.0145603i
$201$		0			0
$202$	0.982663	−	0.783648i	0.0691400	−	0.0551373i
$203$	−1.06822	+	0.243815i	−0.0749744	+	0.0171124i
$204$		0			0
$205$	13.8970	+	11.0825i	0.970607	+	0.774034i
$206$	−0.0419858	−	0.0202193i	−0.00292529	−	0.00140874i
$207$		0			0
$208$	4.42804			0.307029
$209$	33.7289			2.33307
$210$		0			0
$211$	3.45573	+	7.17589i	0.237902	+	0.494009i	0.985400	−	0.170255i	$-0.0544592\pi$
$211$	3.45573	+	7.17589i	0.237902	+	0.494009i	−0.747498	+	0.664264i	$0.768745\pi$
$212$	−14.2895	−	3.26148i	−0.981406	−	0.223999i
$213$		0			0
$214$		−	1.11201i		−	0.0760154i
$215$	9.95877	+	13.0192i	0.679183	+	0.887903i
$216$		0			0
$217$	−8.75606	+	1.99851i	−0.594400	+	0.135668i
$218$	−0.0239112	+	0.104762i	−0.00161947	+	0.00709536i
$219$		0			0
$220$	−20.4511	+	16.3092i	−1.37881	+	1.09957i
$221$		−	1.40218i		−	0.0943209i
$222$		0			0
$223$	0.978809	−	0.780574i	0.0655459	−	0.0522711i	−0.590169	−	0.807280i	$-0.700939\pi$
$223$	0.978809	−	0.780574i	0.0655459	−	0.0522711i	0.655715	+	0.755009i	$0.272367\pi$
$224$	−0.841530	+	1.74745i	−0.0562271	+	0.116757i
$225$		0			0
$226$	−1.23487	−	0.594680i	−0.0821421	−	0.0395576i
$227$	−4.69517	−	20.5709i	−0.311630	−	1.36534i	−0.851837	−	0.523807i	$-0.824511\pi$
$227$	−4.69517	−	20.5709i	−0.311630	−	1.36534i	0.540207	−	0.841532i	$-0.318346\pi$
$228$		0			0
$229$	−1.05524	−	4.62332i	−0.0697323	−	0.305517i	0.928020	−	0.372531i	$-0.121510\pi$
$229$	−1.05524	−	4.62332i	−0.0697323	−	0.305517i	−0.997752	+	0.0670137i	$0.978653\pi$
$230$	0.268845	+	0.558263i	0.0177271	+	0.0368108i
$231$		0			0
$232$	−0.152152	+	0.190793i	−0.00998929	+	0.0125262i
$233$	−1.94034	+	8.50119i	−0.127116	+	0.556932i	0.870755	+	0.491717i	$0.163630\pi$
$233$	−1.94034	+	8.50119i	−0.127116	+	0.556932i	−0.997871	+	0.0652149i	$0.979227\pi$
$234$		0			0
$235$	11.6461	−	24.1834i	0.759708	−	1.57755i
$236$	−8.24751	−	1.88244i	−0.536867	−	0.122537i
$237$		0			0
$238$	0.183049	+	0.0881516i	0.0118653	+	0.00571402i
$239$	5.18144	+	10.7594i	0.335159	+	0.695965i	0.998635	−	0.0522326i	$-0.0166337\pi$
$239$	5.18144	+	10.7594i	0.335159	+	0.695965i	−0.663476	+	0.748198i	$0.730919\pi$
$240$		0			0
$241$	18.6153	+	14.8452i	1.19912	+	0.956265i	0.999720	−	0.0236540i	$-0.00753000\pi$
$241$	18.6153	+	14.8452i	1.19912	+	0.956265i	0.199398	+	0.979919i	$0.436101\pi$
$242$	0.987560	−	1.23836i	0.0634827	−	0.0796048i
$243$		0			0
$244$	16.2210	−	3.70233i	1.03844	−	0.237018i
$245$	6.36839	+	7.98571i	0.406862	+	0.510188i
$246$		0			0
$247$	3.12465	−	6.48841i	0.198817	−	0.412848i
$248$	−1.24717	+	1.56390i	−0.0791955	+	0.0993080i
$249$		0			0
$250$	0.557000	+	0.698456i	0.0352278	+	0.0441742i
$251$		−	0.107418i		−	0.00678015i	−0.999994	−	0.00339008i	$-0.998921\pi$
$251$		−	0.107418i		−	0.00678015i	0.999994	−	0.00339008i	$-0.00107910\pi$
$252$		0			0
$253$	8.52762	+	10.6933i	0.536127	+	0.672282i
$254$	−1.26730	+	0.610297i	−0.0795172	+	0.0382935i
$255$		0			0
$256$	−3.39989	−	14.8959i	−0.212493	−	0.930992i
$257$	14.3888			0.897547			0.448773	−	0.893646i	$-0.351861\pi$
$257$	14.3888			0.897547			0.448773	+	0.893646i	$0.351861\pi$
$258$		0			0
$259$	8.53518			0.530350
$260$	1.24280	+	5.44506i	0.0770752	+	0.337688i
$261$		0			0
$262$	−0.480318	+	0.231309i	−0.0296741	+	0.0142903i
$263$	−16.5501	−	20.7532i	−1.02052	−	1.27970i	−0.959544	−	0.281557i	$-0.909149\pi$
$263$	−16.5501	−	20.7532i	−1.02052	−	1.27970i	−0.0609793	−	0.998139i	$-0.519422\pi$
$264$		0			0
$265$		−	18.4022i		−	1.13044i
$266$	0.650595	+	0.815820i	0.0398905	+	0.0500211i
$267$		0			0
$268$	−17.8135	+	22.3374i	−1.08813	+	1.36447i
$269$	1.74321	−	3.61980i	0.106285	−	0.220703i	−0.841043	−	0.540969i	$-0.818058\pi$
$269$	1.74321	−	3.61980i	0.106285	−	0.220703i	0.947328	+	0.320265i	$0.103772\pi$
$270$		0			0
$271$	2.23880	+	2.80736i	0.135997	+	0.170535i	0.845166	−	0.534503i	$-0.179501\pi$
$271$	2.23880	+	2.80736i	0.135997	+	0.170535i	−0.709169	+	0.705038i	$0.750930\pi$
$272$	−4.80617	+	1.09698i	−0.291417	+	0.0665140i
$273$		0			0
$274$	−1.26626	+	1.58784i	−0.0764974	+	0.0959247i
$275$	−5.12980	−	4.09088i	−0.309339	−	0.246689i
$276$		0			0
$277$	3.40070	+	7.06163i	0.204328	+	0.424292i	0.977800	−	0.209538i	$-0.0671961\pi$
$277$	3.40070	+	7.06163i	0.204328	+	0.424292i	−0.773472	+	0.633830i	$0.781482\pi$
$278$	−1.24583	−	0.599962i	−0.0747202	−	0.0359833i
$279$		0			0
$280$	−1.58152	−	0.360971i	−0.0945138	−	0.0215722i
$281$	−8.07441	+	16.7667i	−0.481679	+	1.00022i	0.508584	+	0.861012i	$0.330169\pi$
$281$	−8.07441	+	16.7667i	−0.481679	+	1.00022i	−0.990264	+	0.139205i	$0.955545\pi$
$282$		0			0
$283$	2.95518	−	12.9475i	0.175667	−	0.769647i	−0.807932	−	0.589276i	$-0.799413\pi$
$283$	2.95518	−	12.9475i	0.175667	−	0.769647i	0.983599	−	0.180371i	$-0.0577299\pi$
$284$	8.67360	−	10.8764i	0.514684	−	0.645393i
$285$		0			0
$286$	−0.243811	−	0.506278i	−0.0144168	−	0.0299368i
$287$	2.70102	+	11.8339i	0.159436	+	0.698535i
$288$		0			0
$289$	−3.43549	−	15.0519i	−0.202088	−	0.885403i
$290$	−0.137710	−	0.0663178i	−0.00808663	−	0.00389432i
$291$		0			0
$292$	−7.94846	+	16.5051i	−0.465148	+	0.965890i
$293$	−3.91142	+	3.11925i	−0.228508	+	0.182229i	−0.731050	−	0.682324i	$-0.760969\pi$
$293$	−3.91142	+	3.11925i	−0.228508	+	0.182229i	0.502543	+	0.864552i	$0.332398\pi$
$294$		0			0
$295$		−	10.6213i		−	0.618395i
$296$	1.48623	−	1.18523i	0.0863855	−	0.0688901i
$297$		0			0
$298$	−0.0172975	+	0.0757854i	−0.00100202	+	0.00439013i
$299$	2.84707	−	0.649825i	0.164650	−	0.0375803i
$300$		0			0
$301$	−0.226217	+	11.1912i	−0.0130389	+	0.645049i
$302$			2.00110i			0.115150i
$303$		0			0
$304$	−24.6844	−	5.63406i	−1.41575	−	0.323136i
$305$	9.06367	+	18.8209i	0.518984	+	1.07768i
$306$		0			0
$307$	−11.8129			−0.674198			−0.337099	−	0.941469i	$-0.609446\pi$
$307$	−11.8129			−0.674198			−0.337099	+	0.941469i	$0.609446\pi$
$308$	−17.8629			−1.01784
$309$		0			0
$310$	−1.12879	−	0.543598i	−0.0641111	−	0.0308743i
$311$	−23.5922	−	18.8141i	−1.33779	−	1.06685i	−0.991689	−	0.128655i	$-0.958934\pi$
$311$	−23.5922	−	18.8141i	−1.33779	−	1.06685i	−0.346101	−	0.938197i	$-0.612494\pi$
$312$		0			0
$313$	−7.75676	+	1.77043i	−0.438438	+	0.100071i	−0.436042	−	0.899926i	$-0.643620\pi$
$313$	−7.75676	+	1.77043i	−0.438438	+	0.100071i	−0.00239647	+	0.999997i	$0.500763\pi$
$314$	1.63747	−	1.30584i	0.0924079	−	0.0736928i
$315$		0			0
$316$	−13.7354	+	6.61464i	−0.772679	+	0.372103i
$317$	22.0289	+	17.5674i	1.23726	+	0.986685i	0.999883	+	0.0152688i	$0.00486040\pi$
$317$	22.0289	+	17.5674i	1.23726	+	0.986685i	0.237381	+	0.971417i	$0.423711\pi$
$318$		0			0
$319$	−3.28927	−	0.750753i	−0.184164	−	0.0420341i
$320$	17.5283	−	8.44118i	0.979861	−	0.471876i
$321$		0			0
$322$	−0.0941562	+	0.412525i	−0.00524712	+	0.0229891i
$323$	−1.78408	+	7.81657i	−0.0992689	+	0.434926i
$324$		0			0
$325$	−1.26219	+	0.607838i	−0.0700136	+	0.0337168i
$326$	−0.478136	−	0.109132i	−0.0264815	−	0.00604424i
$327$		0			0
$328$	2.11364	+	1.68557i	0.116706	+	0.0930699i
$329$	16.5145	−	7.95298i	0.910476	−	0.438462i
$330$		0			0
$331$	−6.99322	+	5.57691i	−0.384382	+	0.306535i	−0.796549	−	0.604574i	$-0.793344\pi$
$331$	−6.99322	+	5.57691i	−0.384382	+	0.306535i	0.412167	+	0.911108i	$0.364772\pi$
$332$	−5.61940	+	1.28259i	−0.308405	+	0.0703914i
$333$		0			0
$334$	−1.42867	−	1.13933i	−0.0781733	−	0.0623411i
$335$	−32.3188	−	15.5639i	−1.76576	−	0.850348i
$336$		0			0
$337$	17.4270			0.949308			0.474654	−	0.880172i	$-0.342573\pi$
$337$	17.4270			0.949308			0.474654	+	0.880172i	$0.342573\pi$
$338$	1.11842			0.0608340
$339$		0			0
$340$	−2.69786	−	5.60216i	−0.146312	−	0.303820i
$341$	−26.9617	−	6.15382i	−1.46006	−	0.333248i
$342$		0			0
$343$			18.9240i			1.02180i
$344$	1.51466	+	1.98013i	0.0816650	+	0.106762i
$345$		0			0
$346$	−1.77971	+	0.406207i	−0.0956779	+	0.0218378i
$347$	4.88099	−	21.3850i	0.262025	−	1.14801i	−0.657026	−	0.753868i	$-0.728186\pi$
$347$	4.88099	−	21.3850i	0.262025	−	1.14801i	0.919051	−	0.394139i	$-0.128957\pi$
$348$		0			0
$349$	21.4158	−	17.0786i	1.14636	−	0.914194i	0.149151	−	0.988814i	$-0.452346\pi$
$349$	21.4158	−	17.0786i	1.14636	−	0.914194i	0.997212	+	0.0746200i	$0.0237744\pi$
$350$		−	0.202986i		−	0.0108501i
$351$		0			0
$352$	−4.66925	+	3.72360i	−0.248872	+	0.198469i
$353$	12.5727	−	26.1074i	0.669176	−	1.38956i	−0.239020	−	0.971015i	$-0.576826\pi$
$353$	12.5727	−	26.1074i	0.669176	−	1.38956i	0.908196	−	0.418544i	$-0.137460\pi$
$354$		0			0
$355$	15.7364	+	7.57826i	0.835202	+	0.402212i
$356$	−4.81644	−	21.1022i	−0.255271	−	1.11841i
$357$		0			0
$358$	0.196444	+	0.860677i	0.0103824	+	0.0454882i
$359$	−0.263648	−	0.547471i	−0.0139148	−	0.0288944i	0.893896	−	0.448275i	$-0.147962\pi$
$359$	−0.263648	−	0.547471i	−0.0139148	−	0.0288944i	−0.907810	+	0.419381i	$0.862247\pi$
$360$		0			0
$361$	−13.8279	+	17.3397i	−0.727785	+	0.912614i
$362$	0.318500	−	1.39544i	0.0167400	−	0.0733427i
$363$		0			0
$364$	−1.65483	+	3.43629i	−0.0867366	+	0.180110i
$365$	−22.4237	−	5.11807i	−1.17371	−	0.267892i
$366$		0			0
$367$	−4.73635	−	2.28091i	−0.247236	−	0.119062i	0.306163	−	0.951979i	$-0.400955\pi$
$367$	−4.73635	−	2.28091i	−0.247236	−	0.119062i	−0.553398	+	0.832917i	$0.686669\pi$
$368$	−4.45473	−	9.25033i	−0.232219	−	0.482207i
$369$		0			0
$370$	0.930881	+	0.742353i	0.0483942	+	0.0385931i
$371$	7.83517	−	9.82500i	0.406782	−	0.510088i
$372$		0			0
$373$	−30.0907	+	6.86800i	−1.55804	+	0.355611i	−0.912811	−	0.408382i	$-0.866093\pi$
$373$	−30.0907	+	6.86800i	−1.55804	+	0.355611i	−0.645224	+	0.763993i	$0.723236\pi$
$374$	0.390053	+	0.489111i	0.0201692	+	0.0252913i
$375$		0			0
$376$	1.77129	−	3.67813i	0.0913475	−	0.189685i
$377$	−0.449141	+	0.563205i	−0.0231319	+	0.0290065i
$378$		0			0
$379$	−7.87336	−	9.87288i	−0.404427	−	0.507136i	0.537356	−	0.843355i	$-0.319423\pi$
$379$	−7.87336	−	9.87288i	−0.404427	−	0.507136i	−0.941784	+	0.336219i	$0.890852\pi$
$380$		−	31.9352i		−	1.63824i
$381$		0			0
$382$	−0.741401	−	0.929688i	−0.0379334	−	0.0475670i
$383$	17.3355	−	8.34832i	0.885801	−	0.426579i	0.0650612	−	0.997881i	$-0.479276\pi$
$383$	17.3355	−	8.34832i	0.885801	−	0.426579i	0.820740	+	0.571302i	$0.193561\pi$
$384$		0			0
$385$	−4.99057	−	21.8651i	−0.254343	−	1.11435i
$386$	−0.835623			−0.0425321
$387$		0			0
$388$	4.79651			0.243506
$389$	2.03597	+	8.92019i	0.103228	+	0.452271i	0.999953	+	0.00968353i	$0.00308241\pi$
$389$	2.03597	+	8.92019i	0.103228	+	0.452271i	−0.896725	+	0.442588i	$0.854060\pi$
$390$		0			0
$391$	−2.92921	+	1.41063i	−0.148136	+	0.0713387i
$392$	0.968589	+	1.21457i	0.0489211	+	0.0613451i
$393$		0			0
$394$			0.313220i			0.0157798i
$395$	−11.9341	−	14.9648i	−0.600468	−	0.752963i
$396$		0			0
$397$	6.71499	−	8.42034i	0.337016	−	0.422605i	−0.584228	−	0.811589i	$-0.698603\pi$
$397$	6.71499	−	8.42034i	0.337016	−	0.422605i	0.921244	+	0.388985i	$0.127174\pi$
$398$	0.0817313	−	0.169717i	0.00409682	−	0.00850713i
$399$		0			0
$400$	3.07090	+	3.85079i	0.153545	+	0.192540i
$401$	23.4047	−	5.34196i	1.16877	−	0.266765i	0.406272	−	0.913752i	$-0.366829\pi$
$401$	23.4047	−	5.34196i	1.16877	−	0.266765i	0.762501	+	0.646987i	$0.223971\pi$
$402$		0			0
$403$	−3.68154	+	4.61651i	−0.183391	+	0.229965i
$404$	−20.5373	−	16.3779i	−1.02177	−	0.814832i
$405$		0			0
$406$	−0.0452876	−	0.0940407i	−0.00224759	−	0.00466716i
$407$	23.6788	+	11.4031i	1.17372	+	0.565232i
$408$		0			0
$409$	1.74392	+	0.398039i	0.0862314	+	0.0196818i	0.265419	−	0.964133i	$-0.414490\pi$
$409$	1.74392	+	0.398039i	0.0862314	+	0.0196818i	−0.179188	+	0.983815i	$0.557347\pi$
$410$	−0.734679	+	1.52558i	−0.0362832	+	0.0753429i
$411$		0			0
$412$	−0.216721	+	0.949517i	−0.0106771	+	0.0467794i
$413$	4.52226	−	5.67073i	0.222526	−	0.279038i
$414$		0			0
$415$	−3.13991	−	6.52009i	−0.154132	−	0.320058i
$416$	0.283747	+	1.24318i	0.0139118	+	0.0609518i
$417$		0			0
$418$	0.714973	+	3.13250i	0.0349705	+	0.153216i
$419$	36.4916	+	17.5734i	1.78273	+	0.858519i	0.954544	+	0.298069i	$0.0963426\pi$
$419$	36.4916	+	17.5734i	1.78273	+	0.858519i	0.828188	+	0.560450i	$0.189372\pi$
$420$		0			0
$421$	−8.64071	+	17.9426i	−0.421122	+	0.874469i	0.577202	+	0.816601i	$0.304145\pi$
$421$	−8.64071	+	17.9426i	−0.421122	+	0.874469i	−0.998324	+	0.0578680i	$0.981570\pi$
$422$	−0.593194	+	0.473056i	−0.0288762	+	0.0230280i
$423$		0			0
$424$		−	2.79885i		−	0.135924i
$425$	1.21939	−	0.972431i	0.0591491	−	0.0471698i
$426$		0			0
$427$	−3.17432	+	13.9076i	−0.153616	+	0.673036i
$428$	−22.6579	+	5.17151i	−1.09521	+	0.249974i
$429$		0			0
$430$	−0.998031	+	1.20088i	−0.0481293	+	0.0579115i
$431$			19.4573i			0.937225i	0.883404	+	0.468613i	$0.155246\pi$
$431$			19.4573i			0.937225i	−0.883404	+	0.468613i	$0.844754\pi$
$432$		0			0
$433$	−19.9197	−	4.54654i	−0.957279	−	0.218493i	−0.284782	−	0.958592i	$-0.591921\pi$
$433$	−19.9197	−	4.54654i	−0.957279	−	0.218493i	−0.672497	+	0.740100i	$0.734778\pi$
$434$	−0.371216	−	0.770838i	−0.0178189	−	0.0370014i
$435$		0			0
$436$	2.24578			0.107553
$437$	−16.6980			−0.798774
$438$		0			0
$439$	−28.5619	−	13.7547i	−1.36319	−	0.656476i	−0.397841	−	0.917454i	$-0.630240\pi$
$439$	−28.5619	−	13.7547i	−1.36319	−	0.656476i	−0.965345	+	0.260979i	$0.915955\pi$
$440$	−3.90528	−	3.11436i	−0.186177	−	0.148471i
$441$		0			0
$442$	0.130225	−	0.0297230i	0.00619416	−	0.00141378i
$443$	−16.2988	+	12.9978i	−0.774379	+	0.617546i	−0.928852	−	0.370451i	$-0.879203\pi$
$443$	−16.2988	+	12.9978i	−0.774379	+	0.617546i	0.154474	+	0.987997i	$0.450632\pi$
$444$		0			0
$445$	24.4845	−	11.7911i	1.16068	−	0.558952i
$446$	0.0932427	+	0.0743586i	0.00441517	+	0.00352098i
$447$		0			0
$448$	12.9524	+	2.95631i	0.611945	+	0.139672i
$449$	36.5422	−	17.5978i	1.72453	−	0.830491i	0.736465	−	0.676476i	$-0.236494\pi$
$449$	36.5422	−	17.5978i	1.72453	−	0.830491i	0.988068	−	0.154015i	$-0.0492205\pi$
$450$		0			0
$451$	−8.31697	+	36.4390i	−0.391631	+	1.71585i
$452$	−6.37410	+	27.9268i	−0.299813	+	1.31356i
$453$		0			0
$454$	1.81096	−	0.872110i	0.0849923	−	0.0409302i
$455$	−4.66851	−	1.06556i	−0.218863	−	0.0499541i
$456$		0			0
$457$	−1.36701	−	1.09015i	−0.0639459	−	0.0509951i	0.590995	−	0.806675i	$-0.298735\pi$
$457$	−1.36701	−	1.09015i	−0.0639459	−	0.0509951i	−0.654941	+	0.755680i	$0.727307\pi$
$458$	0.407013	−	0.196007i	0.0190185	−	0.00915881i
$459$		0			0
$460$	10.1246	−	8.07414i	0.472064	−	0.376459i
$461$	−21.4777	+	4.90215i	−1.00032	+	0.228316i	−0.691165	−	0.722697i	$-0.742902\pi$
$461$	−21.4777	+	4.90215i	−1.00032	+	0.228316i	−0.309152	+	0.951013i	$0.600045\pi$
$462$		0			0
$463$	31.6815	+	25.2651i	1.47236	+	1.17417i	0.946111	+	0.323842i	$0.104975\pi$
$463$	31.6815	+	25.2651i	1.47236	+	1.17417i	0.526252	+	0.850329i	$0.323597\pi$
$464$	2.28184	+	1.09888i	0.105932	+	0.0510141i
$465$		0			0
$466$	−0.830662			−0.0384797
$467$	−22.2524			−1.02972			−0.514860	−	0.857274i	$-0.672156\pi$
$467$	−22.2524			−1.02972			−0.514860	+	0.857274i	$0.672156\pi$
$468$		0			0
$469$	−10.6284	−	22.0701i	−0.490774	−	1.01910i
$470$	2.49286	+	0.568978i	0.114987	+	0.0262450i
$471$		0			0
$472$		−	1.61542i		−	0.0743559i
$473$	−15.5792	+	30.7450i	−0.716330	+	1.41366i
$474$		0			0
$475$	7.80956	−	1.78248i	0.358327	−	0.0817858i
$476$	0.944856	−	4.13968i	0.0433074	−	0.189742i
$477$		0			0
$478$	−0.889420	+	0.709289i	−0.0406811	+	0.0324421i
$479$			8.07399i			0.368910i	0.982841	+	0.184455i	$0.0590520\pi$
$479$			8.07399i			0.368910i	−0.982841	+	0.184455i	$0.940948\pi$
$480$		0			0
$481$	4.38723	−	3.49870i	0.200040	−	0.159527i
$482$	−0.984119	+	2.04354i	−0.0448254	+	0.0930809i
$483$		0			0
$484$	−29.8251	−	14.3630i	−1.35569	−	0.652864i
$485$	1.34005	+	5.87116i	0.0608487	+	0.266596i
$486$		0			0
$487$	−6.11115	−	26.7747i	−0.276922	−	1.21328i	−0.901661	−	0.432443i	$-0.857652\pi$
$487$	−6.11115	−	26.7747i	−0.276922	−	1.21328i	0.624739	−	0.780834i	$-0.285205\pi$
$488$	1.37852	+	2.86253i	0.0624028	+	0.129581i
$489$		0			0
$490$	−0.606662	+	0.760730i	−0.0274062	+	0.0343663i
$491$	−0.582009	+	2.54995i	−0.0262657	+	0.115078i	−0.986361	−	0.164594i	$-0.947369\pi$
$491$	−0.582009	+	2.54995i	−0.0262657	+	0.115078i	0.960096	+	0.279672i	$0.0902257\pi$
$492$		0			0
$493$	0.347970	−	0.722567i	0.0156718	−	0.0325428i
$494$	0.668834	+	0.152657i	0.0300922	+	0.00686836i
$495$		0			0
$496$	18.7039	+	9.00734i	0.839831	+	0.404441i
$497$	5.17510	+	10.7462i	0.232135	+	0.482033i
$498$		0			0
$499$	−10.9176	−	8.70647i	−0.488738	−	0.389755i	0.347883	−	0.937538i	$-0.386901\pi$
$499$	−10.9176	−	8.70647i	−0.488738	−	0.389755i	−0.836621	+	0.547783i	$0.815472\pi$
$500$	11.6411	−	14.5974i	0.520605	−	0.652818i
$501$		0			0
$502$	0.00997622	−	0.00227701i	0.000445260	−	0.000101628i
$503$	−2.02750	−	2.54241i	−0.0904020	−	0.113360i	0.734573	−	0.678529i	$-0.237382\pi$
$503$	−2.02750	−	2.54241i	−0.0904020	−	0.113360i	−0.824975	+	0.565169i	$0.808811\pi$
$504$		0			0
$505$	14.3096	−	29.7143i	0.636771	−	1.32227i
$506$	−0.812353	+	1.01866i	−0.0361135	+	0.0452849i
$507$		0			0
$508$	18.3289	+	22.9837i	0.813212	+	1.01974i
$509$			36.2085i			1.60492i	0.596709	+	0.802458i	$0.296475\pi$
$509$			36.2085i			1.60492i	−0.596709	+	0.802458i	$0.703525\pi$
$510$		0			0
$511$	−9.79296	−	12.2800i	−0.433215	−	0.543234i
$512$	6.74218	−	3.24686i	0.297965	−	0.143492i
$513$		0			0
$514$	0.305008	+	1.33633i	0.0134533	+	0.0589429i
$515$	−1.22280			−0.0538831
$516$		0			0
$517$	56.4409			2.48227
$518$	0.180926	+	0.792688i	0.00794943	+	0.0348287i
$519$		0			0
$520$	−0.960895	+	0.462743i	−0.0421380	+	0.0202926i
$521$	−5.77342	−	7.23965i	−0.252938	−	0.317175i	0.639109	−	0.769116i	$-0.279303\pi$
$521$	−5.77342	−	7.23965i	−0.252938	−	0.317175i	−0.892048	+	0.451941i	$0.850732\pi$
$522$		0			0
$523$			37.9226i			1.65824i	0.559072	+	0.829119i	$0.311158\pi$
$523$			37.9226i			1.65824i	−0.559072	+	0.829119i	$0.688842\pi$
$524$	6.94682	+	8.71104i	0.303473	+	0.380543i
$525$		0			0
$526$	1.57659	−	1.97698i	0.0687425	−	0.0862003i
$527$	2.85226	−	5.92278i	0.124246	−	0.258000i
$528$		0			0
$529$	10.1185	+	12.6882i	0.439936	+	0.551662i
$530$	1.70907	−	0.390084i	0.0742372	−	0.0169442i
$531$		0			0
$532$	13.5972	−	17.0503i	0.589512	−	0.739225i
$533$	6.23927	+	4.97565i	0.270253	+	0.215519i
$534$		0			0
$535$	−12.6604	−	26.2895i	−0.547355	−	1.13659i
$536$	−4.91547	−	2.36717i	−0.212316	−	0.102246i
$537$		0			0
$538$	0.373134	+	0.0851654i	0.0160869	+	0.00367174i
$539$	−9.31881	+	19.3507i	−0.401390	+	0.833494i
$540$		0			0
$541$	−5.94808	+	26.0603i	−0.255728	+	1.12042i	0.670040	+	0.742325i	$0.266277\pi$
$541$	−5.94808	+	26.0603i	−0.255728	+	1.12042i	−0.925768	+	0.378093i	$0.876580\pi$
$542$	−0.213271	+	0.267433i	−0.00916077	+	0.0114872i
$543$		0			0
$544$	−0.615955	−	1.27904i	−0.0264089	−	0.0548386i
$545$	0.627429	+	2.74895i	0.0268761	+	0.117752i
$546$		0			0
$547$	4.27529	+	18.7313i	0.182798	+	0.800891i	0.980290	+	0.197562i	$0.0633023\pi$
$547$	4.27529	+	18.7313i	0.182798	+	0.800891i	−0.797492	+	0.603329i	$0.793841\pi$
$548$	38.2420	+	18.4164i	1.63362	+	0.786708i
$549$		0			0
$550$	0.271193	−	0.563138i	0.0115637	−	0.0240123i
$551$	3.22037	−	2.56816i	0.137192	−	0.109407i
$552$		0			0
$553$		−	13.0710i		−	0.555834i
$554$	−0.583748	+	0.465523i	−0.0248011	+	0.0197782i
$555$		0			0
$556$	−6.43071	+	28.1748i	−0.272723	+	1.19488i
$557$	23.3315	−	5.32525i	0.988585	−	0.225638i	0.302492	−	0.953152i	$-0.402181\pi$
$557$	23.3315	−	5.32525i	0.988585	−	0.225638i	0.686093	+	0.727514i	$0.259324\pi$
$558$		0			0
$559$	4.47115	+	5.84518i	0.189109	+	0.247225i
$560$			16.8356i			0.711433i
$561$		0			0
$562$	−1.72833	−	0.394481i	−0.0729053	−	0.0166402i
$563$	−3.57697	−	7.42765i	−0.150751	−	0.313038i	0.811894	−	0.583805i	$-0.198437\pi$
$563$	−3.57697	−	7.42765i	−0.150751	−	0.313038i	−0.962645	+	0.270767i	$0.912723\pi$
$564$		0			0
$565$	−35.9645			−1.51304
$566$	1.26511			0.0531767
$567$		0			0
$568$	2.39340	+	1.15260i	0.100425	+	0.0483621i
$569$	−14.7686	−	11.7776i	−0.619131	−	0.493741i	0.262968	−	0.964805i	$-0.415299\pi$
$569$	−14.7686	−	11.7776i	−0.619131	−	0.493741i	−0.882099	+	0.471064i	$0.843870\pi$
$570$		0			0
$571$	17.8657	−	4.07774i	0.747658	−	0.170648i	0.168316	−	0.985733i	$-0.446167\pi$
$571$	17.8657	−	4.07774i	0.747658	−	0.170648i	0.579341	+	0.815085i	$0.303310\pi$
$572$	−9.18185	+	7.32228i	−0.383913	+	0.306160i
$573$		0			0
$574$	−1.04180	+	0.501703i	−0.0434838	+	0.0209407i
$575$	2.53959	+	2.02526i	0.105908	+	0.0844590i
$576$		0			0
$577$	−11.2297	−	2.56311i	−0.467499	−	0.106704i	−0.0177190	−	0.999843i	$-0.505640\pi$
$577$	−11.2297	−	2.56311i	−0.467499	−	0.106704i	−0.449780	+	0.893139i	$0.648498\pi$
$578$	1.32509	−	0.638128i	0.0551164	−	0.0265426i
$579$		0			0
$580$	−0.710830	+	3.11435i	−0.0295156	+	0.129316i
$581$	1.09967	−	4.81798i	0.0456221	−	0.199884i
$582$		0			0
$583$	34.8632	−	16.7892i	1.44388	−	0.695338i
$584$	−3.41050	−	0.778424i	−0.141127	−	0.0322114i
$585$		0			0
$586$	−0.372607	−	0.297144i	−0.0153923	−	0.0122749i
$587$	39.4541	−	19.0001i	1.62844	−	0.784217i	0.628463	−	0.777839i	$-0.283684\pi$
$587$	39.4541	−	19.0001i	1.62844	−	0.784217i	0.999980	−	0.00637774i	$-0.00203011\pi$
$588$		0			0
$589$	26.3969	−	21.0509i	1.08767	−	0.867385i
$590$	0.986430	−	0.225146i	0.0406107	−	0.00926912i
$591$		0			0
$592$	−15.4246	−	12.3007i	−0.633945	−	0.505555i
$593$	−12.8904	−	6.20770i	−0.529346	−	0.254920i	0.150067	−	0.988676i	$-0.452051\pi$
$593$	−12.8904	−	6.20770i	−0.529346	−	0.254920i	−0.679413	+	0.733756i	$0.737765\pi$
$594$		0			0
$595$	5.33115			0.218556
$596$	1.62462			0.0665469
$597$		0			0
$598$	0.120702	+	0.250641i	0.00493589	+	0.0102495i
$599$	−3.86711	−	0.882642i	−0.158006	−	0.0360638i	0.142786	−	0.989754i	$-0.454394\pi$
$599$	−3.86711	−	0.882642i	−0.158006	−	0.0360638i	−0.300792	+	0.953690i	$0.597251\pi$
$600$		0			0
$601$		−	35.0155i		−	1.42831i	−0.699986	−	0.714156i	$-0.746811\pi$
$601$		−	35.0155i		−	1.42831i	0.699986	−	0.714156i	$-0.253189\pi$
$602$	−1.04415	+	0.216217i	−0.0425565	+	0.00881236i
$603$		0			0
$604$	40.7736	−	9.30632i	1.65906	−	0.378669i
$605$	9.24845	−	40.5201i	0.376003	−	1.64738i
$606$		0			0
$607$	−34.9733	+	27.8903i	−1.41952	+	1.13203i	−0.448293	+	0.893887i	$0.647968\pi$
$607$	−34.9733	+	27.8903i	−1.41952	+	1.13203i	−0.971230	+	0.238145i	$0.923461\pi$
$608$		−	7.29122i		−	0.295698i
$609$		0			0
$610$	−1.55583	+	1.24073i	−0.0629936	+	0.0502357i
$611$	5.22871	−	10.8575i	0.211531	−	0.439248i
$612$		0			0
$613$	5.20489	+	2.50654i	0.210223	+	0.101238i	0.536033	−	0.844197i	$-0.319922\pi$
$613$	5.20489	+	2.50654i	0.210223	+	0.101238i	−0.325809	+	0.945436i	$0.605637\pi$
$614$	−0.250406	−	1.09710i	−0.0101056	−	0.0442754i
$615$		0			0
$616$	−0.759031	−	3.32553i	−0.0305822	−	0.133989i
$617$	17.9784	+	37.3326i	0.723785	+	1.50295i	0.858910	+	0.512126i	$0.171142\pi$
$617$	17.9784	+	37.3326i	0.723785	+	1.50295i	−0.135126	+	0.990828i	$0.543144\pi$
$618$		0			0
$619$	−2.11787	+	2.65573i	−0.0851244	+	0.106743i	−0.822570	−	0.568664i	$-0.807460\pi$
$619$	−2.11787	+	2.65573i	−0.0851244	+	0.106743i	0.737445	+	0.675407i	$0.236032\pi$
$620$	−5.82657	+	25.5279i	−0.234001	+	1.02522i
$621$		0			0
$622$	1.24723	−	2.58989i	0.0500093	−	0.103845i
$623$	18.0927	+	4.12953i	0.724867	+	0.165446i
$624$		0			0
$625$	26.7437	+	12.8791i	1.06975	+	0.515163i
$626$	−0.328850	−	0.682865i	−0.0131435	−	0.0272928i
$627$		0			0
$628$	−34.2225	−	27.2915i	−1.36563	−	1.08905i
$629$	−3.89513	+	4.88434i	−0.155309	+	0.194751i
$630$		0			0
$631$	17.9463	−	4.09613i	0.714432	−	0.163065i	0.150170	−	0.988660i	$-0.452018\pi$
$631$	17.9463	−	4.09613i	0.714432	−	0.163065i	0.564262	+	0.825596i	$0.309161\pi$
$632$	−1.81509	−	2.27605i	−0.0722004	−	0.0905364i
$633$		0			0
$634$	−1.16458	+	2.41828i	−0.0462514	+	0.0960420i
$635$	−23.0124	+	28.8566i	−0.913218	+	1.14514i
$636$		0			0
$637$	2.85919	+	3.58531i	0.113285	+	0.142055i
$638$		−	0.321398i		−	0.0127243i
$639$		0			0
$640$	4.69717	+	5.89007i	0.185672	+	0.232825i
$641$	−38.7456	+	18.6589i	−1.53036	+	0.736983i	−0.994242	−	0.107160i	$-0.965824\pi$
$641$	−38.7456	+	18.6589i	−1.53036	+	0.736983i	−0.536118	+	0.844143i	$0.680110\pi$
$642$		0			0
$643$	3.05868	+	13.4010i	0.120623	+	0.528483i	0.998747	+	0.0500495i	$0.0159379\pi$
$643$	3.05868	+	13.4010i	0.120623	+	0.528483i	−0.878124	+	0.478433i	$0.841205\pi$
$644$	8.84333			0.348476
$645$		0			0
$646$	−0.763767			−0.0300500
$647$	−1.47073	−	6.44371i	−0.0578205	−	0.253328i	0.937754	−	0.347299i	$-0.112901\pi$
$647$	−1.47073	−	6.44371i	−0.0578205	−	0.253328i	−0.995575	+	0.0939708i	$0.970044\pi$
$648$		0			0
$649$	20.1221	−	9.69029i	0.789861	−	0.380377i
$650$	−0.0832072	−	0.104339i	−0.00326365	−	0.00409249i
$651$		0			0
$652$			10.2498i			0.401415i
$653$	−24.4319	−	30.6366i	−0.956094	−	1.19890i	−0.979961	−	0.199189i	$-0.936169\pi$
$653$	−24.4319	−	30.6366i	−0.956094	−	1.19890i	0.0238669	−	0.999715i	$-0.492402\pi$
$654$		0			0
$655$	−8.72192	+	10.9369i	−0.340794	+	0.427342i
$656$	12.1735	−	25.2786i	0.475296	−	0.986963i
$657$		0			0
$658$	1.08869	+	1.36517i	0.0424414	+	0.0532199i
$659$	39.6703	−	9.05448i	1.54533	−	0.352712i	0.636968	−	0.770890i	$-0.280188\pi$
$659$	39.6703	−	9.05448i	1.54533	−	0.352712i	0.908365	+	0.418178i	$0.137331\pi$
$660$		0			0
$661$	−4.23646	+	5.31235i	−0.164779	+	0.206626i	−0.857365	−	0.514709i	$-0.827900\pi$
$661$	−4.23646	+	5.31235i	−0.164779	+	0.206626i	0.692586	+	0.721335i	$0.256471\pi$
$662$	−0.666185	−	0.531264i	−0.0258920	−	0.0206482i
$663$		0			0
$664$	−0.477559	−	0.991661i	−0.0185329	−	0.0384839i
$665$	24.6692	+	11.8801i	0.956630	+	0.460689i
$666$		0			0
$667$	1.62840	+	0.371672i	0.0630520	+	0.0143912i
$668$	−16.5703	+	34.4085i	−0.641123	+	1.33131i
$669$		0			0
$670$	0.760385	−	3.33146i	0.0293762	−	0.128706i
$671$	−27.3872	+	34.3424i	−1.05727	+	1.32577i
$672$		0			0
$673$	−6.16604	−	12.8039i	−0.237683	−	0.493554i	0.747672	−	0.664068i	$-0.231172\pi$
$673$	−6.16604	−	12.8039i	−0.237683	−	0.493554i	−0.985355	+	0.170514i	$0.945457\pi$
$674$	0.369411	+	1.61850i	0.0142292	+	0.0623421i
$675$		0			0
$676$	−5.20132	−	22.7885i	−0.200051	−	0.876479i
$677$	−30.1761	−	14.5320i	−1.15976	−	0.558512i	−0.247810	−	0.968809i	$-0.579711\pi$
$677$	−30.1761	−	14.5320i	−1.15976	−	0.558512i	−0.911952	+	0.410297i	$0.865425\pi$
$678$		0			0
$679$	−1.78432	+	3.70519i	−0.0684761	+	0.142192i
$680$	0.928313	−	0.740305i	0.0355992	−	0.0283894i
$681$		0			0
$682$		−	2.63446i		−	0.100879i
$683$	−22.2838	+	17.7707i	−0.852664	+	0.679977i	−0.948967	−	0.315375i	$-0.897870\pi$
$683$	−22.2838	+	17.7707i	−0.852664	+	0.679977i	0.0963030	+	0.995352i	$0.469298\pi$
$684$		0			0
$685$	−11.8584	+	51.9552i	−0.453087	+	1.98511i
$686$	−1.75753	+	0.401144i	−0.0671027	+	0.0153158i
$687$		0			0
$688$	16.5372	−	19.8984i	0.630476	−	0.758618i
$689$		−	8.26197i		−	0.314756i
$690$		0			0
$691$	−19.9899	−	4.56256i	−0.760452	−	0.173568i	−0.175326	−	0.984511i	$-0.556098\pi$
$691$	−19.9899	−	4.56256i	−0.760452	−	0.173568i	−0.585126	+	0.810942i	$0.698955\pi$
$692$	16.5534	+	34.3736i	0.629267	+	1.30669i
$693$		0			0
$694$	2.08955			0.0793184
$695$	−36.2839			−1.37633
$696$		0			0
$697$	−8.00471	−	3.85487i	−0.303200	−	0.146013i
$698$	2.04010	+	1.62693i	0.0772190	+	0.0615801i
$699$		0			0
$700$	−4.13597	+	0.944008i	−0.156325	+	0.0356802i
$701$	−38.4720	+	30.6804i	−1.45307	+	1.15878i	−0.496221	+	0.868196i	$0.665279\pi$
$701$	−38.4720	+	30.6804i	−1.45307	+	1.15878i	−0.956848	+	0.290588i	$0.906149\pi$
$702$		0			0
$703$	−28.9086	+	13.9216i	−1.09031	+	0.525064i
$704$	31.9838	+	25.5062i	1.20543	+	0.961301i
$705$		0			0
$706$	2.69119	+	0.614246i	0.101284	+	0.0231175i
$707$	20.2915	−	9.77188i	0.763141	−	0.367509i
$708$		0			0
$709$	−6.11809	+	26.8051i	−0.229770	+	1.00669i	0.720058	+	0.693914i	$0.244115\pi$
$709$	−6.11809	+	26.8051i	−0.229770	+	1.00669i	−0.949828	+	0.312774i	$0.898742\pi$
$710$	−0.370241	+	1.62213i	−0.0138949	+	0.0608775i
$711$		0			0
$712$	3.72392	−	1.79335i	0.139560	−	0.0672085i
$713$	13.3478	+	3.04655i	0.499879	+	0.114094i
$714$		0			0
$715$	−11.5281	−	9.19332i	−0.431125	−	0.343811i
$716$	16.6232	−	8.00533i	0.621239	−	0.299173i
$717$		0			0
$718$	0.0452566	−	0.0360909i	0.00168896	−	0.00134690i
$719$	46.2076	−	10.5466i	1.72325	−	0.393321i	0.757511	−	0.652823i	$-0.226415\pi$
$719$	46.2076	−	10.5466i	1.72325	−	0.393321i	0.965743	+	0.259501i	$0.0835582\pi$
$720$		0			0
$721$	−0.652858	−	0.520637i	−0.0243137	−	0.0193895i
$722$	−1.90351	−	0.916681i	−0.0708412	−	0.0341153i
$723$		0			0
$724$	−29.9141			−1.11175
$725$	−0.801269			−0.0297584
$726$		0			0
$727$	−2.06806	−	4.29436i	−0.0767000	−	0.159269i	0.859093	−	0.511820i	$-0.171029\pi$
$727$	−2.06806	−	4.29436i	−0.0767000	−	0.159269i	−0.935793	+	0.352551i	$0.885314\pi$
$728$	−0.710048	−	0.162064i	−0.0263161	−	0.00600649i
$729$		0			0
$730$		−	2.19105i		−	0.0810944i
$731$	−6.30101	−	5.23667i	−0.233051	−	0.193685i
$732$		0			0
$733$	17.6578	−	4.03027i	0.652205	−	0.148862i	0.116399	−	0.993203i	$-0.462865\pi$
$733$	17.6578	−	4.03027i	0.652205	−	0.148862i	0.535806	+	0.844341i	$0.320008\pi$
$734$	0.111435	−	0.488229i	0.00411315	−	0.0180209i
$735$		0			0
$736$	2.31159	−	1.84343i	0.0852062	−	0.0679496i
$737$		−	75.4279i		−	2.77842i
$738$		0			0
$739$	31.4165	−	25.0538i	1.15567	−	0.921620i	0.157845	−	0.987464i	$-0.449545\pi$
$739$	31.4165	−	25.0538i	1.15567	−	0.921620i	0.997830	+	0.0658440i	$0.0209740\pi$
$740$	10.7967	−	22.4196i	0.396896	−	0.824162i
$741$		0			0
$742$	1.07856	+	0.519409i	0.0395953	+	0.0190681i
$743$	3.38743	+	14.8413i	0.124273	+	0.544474i	0.998283	+	0.0585676i	$0.0186533\pi$
$743$	3.38743	+	14.8413i	0.124273	+	0.544474i	−0.874011	+	0.485907i	$0.838490\pi$
$744$		0			0
$745$	0.453887	+	1.98861i	0.0166291	+	0.0728570i
$746$	−1.27570	−	2.64903i	−0.0467068	−	0.0969877i
$747$		0			0
$748$	8.15195	−	10.2222i	0.298065	−	0.373762i
$749$	4.43397	−	19.4265i	0.162014	−	0.709828i
$750$		0			0
$751$	−4.71611	+	9.79311i	−0.172093	+	0.357356i	−0.969120	−	0.246588i	$-0.920691\pi$
$751$	−4.71611	+	9.79311i	−0.172093	+	0.357356i	0.797027	+	0.603944i	$0.206405\pi$
$752$	−41.3063	−	9.42788i	−1.50628	−	0.343800i
$753$		0			0
$754$	−0.0618273	−	0.0297744i	−0.00225162	−	0.00108432i
$755$	22.7828	+	47.3089i	0.829150	+	1.72175i
$756$		0			0
$757$	−12.5925	−	10.0421i	−0.457681	−	0.364988i	0.367344	−	0.930085i	$-0.380267\pi$
$757$	−12.5925	−	10.0421i	−0.457681	−	0.364988i	−0.825024	+	0.565097i	$0.808839\pi$
$758$	0.750028	−	0.940505i	0.0272422	−	0.0341607i
$759$		0			0
$760$	5.94536	−	1.35699i	0.215661	−	0.0492232i
$761$	13.4795	+	16.9027i	0.488631	+	0.612723i	0.963623	−	0.267267i	$-0.0861205\pi$
$761$	13.4795	+	16.9027i	0.488631	+	0.612723i	−0.474992	+	0.879990i	$0.657549\pi$
$762$		0			0
$763$	−0.835442	+	1.73481i	−0.0302450	+	0.0628045i
$764$	−15.4950	+	19.4301i	−0.560589	+	0.702956i
$765$		0			0
$766$	1.14281	+	1.43303i	0.0412912	+	0.0517776i
$767$		−	4.76859i		−	0.172184i
$768$		0			0
$769$	5.73708	+	7.19407i	0.206884	+	0.259425i	0.874438	−	0.485137i	$-0.161230\pi$
$769$	5.73708	+	7.19407i	0.206884	+	0.259425i	−0.667554	+	0.744561i	$0.732659\pi$
$770$	1.92489	−	0.926978i	0.0693682	−	0.0334060i
$771$		0			0
$772$	3.88614	+	17.0263i	0.139865	+	0.612790i
$773$	−45.5195			−1.63722			−0.818612	−	0.574347i	$-0.805256\pi$
$773$	−45.5195			−1.63722			−0.818612	+	0.574347i	$0.805256\pi$
$774$		0			0
$775$	−6.56789			−0.235926
$776$	0.203813	+	0.892963i	0.00731646	+	0.0320555i
$777$		0			0
$778$	−0.785287	+	0.378174i	−0.0281539	+	0.0135582i
$779$	−28.4505	−	35.6758i	−1.01934	−	1.27822i
$780$		0			0
$781$			36.7268i			1.31419i
$782$	−0.193102	−	0.242142i	−0.00690532	−	0.00865899i
$783$		0			0
$784$	10.0523	−	12.6052i	0.359011	−	0.450185i
$785$	23.8450	−	49.5147i	0.851066	−	1.76726i
$786$		0			0
$787$	−18.9160	−	23.7200i	−0.674284	−	0.845526i	0.320530	−	0.947238i	$-0.396139\pi$
$787$	−18.9160	−	23.7200i	−0.674284	−	0.845526i	−0.994814	+	0.101713i	$0.967568\pi$
$788$	6.38204	−	1.45666i	0.227351	−	0.0518913i
$789$		0			0
$790$	1.13686	−	1.42557i	0.0404475	−	0.0507196i
$791$	−19.2016	−	15.3127i	−0.682729	−	0.544458i
$792$		0			0
$793$	4.06928	+	8.44995i	0.144504	+	0.300066i
$794$	0.924364	+	0.445150i	0.0328045	+	0.0157978i
$795$		0			0
$796$	−3.83818	−	0.876040i	−0.136041	−	0.0310504i
$797$	−0.696900	+	1.44713i	−0.0246855	+	0.0512599i	−0.912947	−	0.408078i	$-0.866199\pi$
$797$	−0.696900	+	1.44713i	−0.0246855	+	0.0512599i	0.888262	+	0.459338i	$0.151913\pi$
$798$		0			0
$799$	−2.98543	+	13.0800i	−0.105617	+	0.462738i
$800$	−0.884332	+	1.10892i	−0.0312658	+	0.0392061i
$801$		0			0
$802$	0.992248	+	2.06042i	0.0350375	+	0.0727561i
$803$	−10.7620	−	47.1514i	−0.379783	−	1.66394i
$804$		0			0
$805$	2.47066	+	10.8247i	0.0870793	+	0.381519i
$806$	−0.506790	−	0.244057i	−0.0178509	−	0.00859654i
$807$		0			0
$808$	2.17640	−	4.51934i	0.0765655	−	0.158990i
$809$	33.0027	−	26.3188i	1.16031	−	0.925319i	0.162202	−	0.986758i	$-0.448140\pi$
$809$	33.0027	−	26.3188i	1.16031	−	0.925319i	0.998111	+	0.0614390i	$0.0195690\pi$
$810$		0			0
$811$			20.8788i			0.733154i	0.930388	+	0.366577i	$0.119470\pi$
$811$			20.8788i			0.733154i	−0.930388	+	0.366577i	$0.880530\pi$
$812$	−1.70552	+	1.36011i	−0.0598520	+	0.0477304i
$813$		0			0
$814$	−0.557107	+	2.44084i	−0.0195266	+	0.0855516i
$815$	−12.5463	+	2.86361i	−0.439478	+	0.100308i
$816$		0			0
$817$	−17.4876	−	38.2734i	−0.611813	−	1.33902i
$818$			0.170401i			0.00595793i
$819$		0			0
$820$	34.5013	+	7.87469i	1.20484	+	0.274996i
$821$	−2.11058	−	4.38267i	−0.0736599	−	0.152956i	0.860887	−	0.508796i	$-0.169909\pi$
$821$	−2.11058	−	4.38267i	−0.0736599	−	0.152956i	−0.934547	+	0.355840i	$0.884195\pi$
$822$		0			0
$823$	−0.256601			−0.00894455			−0.00447227	−	0.999990i	$-0.501424\pi$
$823$	−0.256601			−0.00894455			−0.00447227	+	0.999990i	$0.501424\pi$
$824$	−0.185980			−0.00647892
$825$		0			0
$826$	0.622519	+	0.299789i	0.0216602	+	0.0104310i
$827$	−33.9334	−	27.0610i	−1.17998	−	0.941002i	−0.180883	−	0.983505i	$-0.557896\pi$
$827$	−33.9334	−	27.0610i	−1.17998	−	0.941002i	−0.999096	+	0.0425026i	$0.986467\pi$
$828$		0			0
$829$	−27.5989	+	6.29927i	−0.958550	+	0.218783i	−0.673051	−	0.739596i	$-0.735017\pi$
$829$	−27.5989	+	6.29927i	−0.958550	+	0.218783i	−0.285499	+	0.958379i	$0.592159\pi$
$830$	0.538982	−	0.429823i	0.0187083	−	0.0149194i
$831$		0			0
$832$	7.86960	−	3.78980i	0.272829	−	0.131388i
$833$	−3.99156	−	3.18316i	−0.138299	−	0.110290i
$834$		0			0
$835$	−46.7471	−	10.6697i	−1.61775	−	0.369241i
$836$	60.5016	−	29.1360i	2.09249	−	1.00769i
$837$		0			0
$838$	−0.858562	+	3.76160i	−0.0296585	+	0.129942i
$839$	−2.75718	+	12.0800i	−0.0951885	+	0.417048i	−0.999961	−	0.00884752i	$-0.997184\pi$
$839$	−2.75718	+	12.0800i	−0.0951885	+	0.417048i	0.904772	+	0.425895i	$0.140041\pi$
$840$		0			0
$841$	25.7569	−	12.4039i	0.888168	−	0.427719i
$842$	−1.84955	−	0.422147i	−0.0637396	−	0.0145482i
$843$		0			0
$844$	12.3975	+	9.88668i	0.426740	+	0.340314i
$845$	26.4410	−	12.7333i	0.909599	−	0.438040i
$846$		0			0
$847$	22.1901	−	17.6960i	0.762462	−	0.608043i
$848$	−28.3190	+	6.46363i	−0.972480	+	0.221962i
$849$		0			0
$850$	0.116161	+	0.0926352i	0.00398428	+	0.00317736i
$851$	−11.7226	−	5.64530i	−0.401845	−	0.193518i
$852$		0			0
$853$	−53.6595			−1.83726			−0.918632	−	0.395113i	$-0.870705\pi$
$853$	−53.6595			−1.83726			−0.918632	+	0.395113i	$0.870705\pi$
$854$	−1.35893			−0.0465016
$855$		0			0
$856$	−1.92555	−	3.99845i	−0.0658141	−	0.136664i
$857$	17.7755	+	4.05714i	0.607200	+	0.138589i	0.515056	−	0.857156i	$-0.327771\pi$
$857$	17.7755	+	4.05714i	0.607200	+	0.138589i	0.0921435	+	0.995746i	$0.470628\pi$
$858$		0			0
$859$		−	26.8204i		−	0.915102i	−0.889183	−	0.457551i	$-0.848727\pi$
$859$		−	26.8204i		−	0.915102i	0.889183	−	0.457551i	$-0.151273\pi$
$860$	29.1100	+	14.7507i	0.992644	+	0.502994i
$861$		0			0
$862$	−1.80706	+	0.412449i	−0.0615486	+	0.0140481i
$863$	5.58790	−	24.4822i	0.190214	−	0.833384i	−0.786285	−	0.617864i	$-0.787998\pi$
$863$	5.58790	−	24.4822i	0.190214	−	0.833384i	0.976499	−	0.215520i	$-0.0691446\pi$
$864$		0			0
$865$	−37.4502	+	29.8655i	−1.27334	+	1.01546i
$866$		−	1.94638i		−	0.0661406i
$867$		0			0
$868$	−13.9799	+	11.1486i	−0.474509	+	0.378408i
$869$	17.4630	−	36.2623i	0.592392	−	1.23011i
$870$		0			0
$871$	−14.5100	−	6.98767i	−0.491654	−	0.236768i
$872$	0.0954277	+	0.418096i	0.00323159	+	0.0141585i
$873$		0			0
$874$	−0.353959	−	1.55080i	−0.0119728	−	0.0524564i
$875$	6.94564	+	14.4228i	0.234806	+	0.487579i
$876$		0			0
$877$	−30.9474	+	38.8068i	−1.04502	+	1.31041i	−0.0959344	+	0.995388i	$0.530584\pi$
$877$	−30.9474	+	38.8068i	−1.04502	+	1.31041i	−0.949084	+	0.315024i	$0.897988\pi$
$878$	0.671994	−	2.94420i	0.0226787	−	0.0993619i
$879$		0			0
$880$	−22.4926	+	46.7063i	−0.758224	+	1.57447i
$881$	−47.8544	−	10.9225i	−1.61226	−	0.367987i	−0.680981	−	0.732301i	$-0.738446\pi$
$881$	−47.8544	−	10.9225i	−1.61226	−	0.367987i	−0.931276	+	0.364314i	$0.881304\pi$
$882$		0			0
$883$	5.46398	+	2.63131i	0.183877	+	0.0885507i	0.523558	−	0.851990i	$-0.324605\pi$
$883$	5.46398	+	2.63131i	0.183877	+	0.0885507i	−0.339680	+	0.940541i	$0.610319\pi$
$884$	−1.21125	−	2.51518i	−0.0407386	−	0.0845946i
$885$		0			0
$886$	−1.55265	−	1.23819i	−0.0521621	−	0.0415979i
$887$	15.9347	−	19.9814i	0.535034	−	0.670911i	−0.438691	−	0.898638i	$-0.644558\pi$
$887$	15.9347	−	19.9814i	0.535034	−	0.670911i	0.973725	+	0.227727i	$0.0731293\pi$
$888$		0			0
$889$	−24.5727	+	5.60857i	−0.824143	+	0.188105i
$890$	1.61409	+	2.02400i	0.0541044	+	0.0678447i
$891$		0			0
$892$	1.08147	−	2.24569i	0.0362102	−	0.0751912i
$893$	−42.9625	+	53.8733i	−1.43769	+	1.80280i
$894$		0			0
$895$	14.4431	+	18.1111i	0.482780	+	0.605387i
$896$			5.14465i			0.171871i
$897$		0			0
$898$	2.40897	+	3.02075i	0.0803884	+	0.100804i
$899$	−3.04281	+	1.46534i	−0.101483	+	0.0488718i
$900$		0			0
$901$	2.04677	+	8.96750i	0.0681879	+	0.298751i
$902$	−3.56050			−0.118552
$903$		0			0
$904$	−5.46996			−0.181928
$905$	−8.35745	−	36.6164i	−0.277811	−	1.21717i
$906$		0			0
$907$	14.8489	−	7.15087i	0.493051	−	0.237441i	−0.170800	−	0.985306i	$-0.554635\pi$
$907$	14.8489	−	7.15087i	0.493051	−	0.237441i	0.663851	+	0.747865i	$0.268921\pi$
$908$	−26.1918	−	32.8435i	−0.869205	−	1.08995i
$909$		0			0
$910$		−	0.456166i		−	0.0151217i
$911$	−2.37766	−	2.98150i	−0.0787755	−	0.0987813i	0.740882	−	0.671635i	$-0.234408\pi$
$911$	−2.37766	−	2.98150i	−0.0787755	−	0.0987813i	−0.819658	+	0.572854i	$0.805836\pi$
$912$		0			0
$913$	9.48767	−	11.8972i	0.313996	−	0.393739i
$914$	0.0722683	−	0.150067i	0.00239042	−	0.00496377i
$915$		0			0
$916$	−5.88661	−	7.38158i	−0.194499	−	0.243894i
$917$	−9.31332	+	2.12570i	−0.307553	+	0.0701969i
$918$		0			0
$919$	1.15150	−	1.44394i	0.0379846	−	0.0476312i	−0.762476	−	0.647016i	$-0.776017\pi$
$919$	1.15150	−	1.44394i	0.0379846	−	0.0476312i	0.800461	+	0.599385i	$0.204588\pi$
$920$	1.93337	+	1.54181i	0.0637414	+	0.0508321i
$921$		0			0
$922$	−0.910555	−	1.89079i	−0.0299875	−	0.0622698i
$923$	7.06512	+	3.40238i	0.232551	+	0.111991i
$924$		0			0
$925$	6.08520	+	1.38891i	0.200080	+	0.0456670i
$926$	−1.67488	+	3.47792i	−0.0550399	+	0.114291i
$927$		0			0
$928$	−0.162291	+	0.711045i	−0.00532748	+	0.0233412i
$929$	−22.5432	+	28.2683i	−0.739618	+	0.927452i	−0.999268	−	0.0382511i	$-0.987821\pi$
$929$	−22.5432	+	28.2683i	−0.739618	+	0.927452i	0.259650	+	0.965703i	$0.416393\pi$
$930$		0			0
$931$	−11.3770	−	23.6245i	−0.372865	−	0.774263i
$932$	3.86307	+	16.9252i	0.126539	+	0.554405i
$933$		0			0
$934$	−0.471700	−	2.06665i	−0.0154345	−	0.0676229i
$935$	14.7900	+	7.12249i	0.483685	+	0.232930i
$936$		0			0
$937$	5.24318	−	10.8876i	0.171287	−	0.355681i	−0.797599	−	0.603188i	$-0.793897\pi$
$937$	5.24318	−	10.8876i	0.171287	−	0.355681i	0.968886	+	0.247506i	$0.0796112\pi$
$938$	1.82442	−	1.45493i	0.0595694	−	0.0475050i
$939$		0			0
$940$		−	53.4395i		−	1.74300i
$941$	9.11347	−	7.26775i	0.297091	−	0.236922i	−0.463587	−	0.886051i	$-0.653438\pi$
$941$	9.11347	−	7.26775i	0.297091	−	0.236922i	0.760678	+	0.649129i	$0.224867\pi$
$942$		0			0
$943$	4.11745	−	18.0397i	0.134083	−	0.587454i
$944$	−16.3450	+	3.73064i	−0.531984	+	0.121422i
$945$		0			0
$946$	−3.18562	−	0.795160i	−0.103574	−	0.0258529i
$947$			5.71880i			0.185836i	0.995674	+	0.0929180i	$0.0296194\pi$
$947$			5.71880i			0.185836i	−0.995674	+	0.0929180i	$0.970381\pi$
$948$		0			0
$949$	−10.0675	−	2.29784i	−0.326805	−	0.0745910i
$950$	0.331089	+	0.687513i	0.0107419	+	0.0223059i
$951$		0			0
$952$	0.810831			0.0262792
$953$	−2.54644			−0.0824874			−0.0412437	−	0.999149i	$-0.513132\pi$
$953$	−2.54644			−0.0824874			−0.0412437	+	0.999149i	$0.513132\pi$
$954$		0			0
$955$	−28.1124	−	13.5382i	−0.909695	−	0.438086i
$956$	18.5885	+	14.8238i	0.601196	+	0.479438i
$957$		0			0
$958$	−0.749855	+	0.171150i	−0.0242267	+	0.00552959i
$959$	−28.4524	+	22.6900i	−0.918775	+	0.732699i
$960$		0			0
$961$	2.98855	−	1.43921i	0.0964047	−	0.0464261i
$962$	0.417934	+	0.333291i	0.0134747	+	0.0107457i
$963$		0			0
$964$	46.2152	+	10.5483i	1.48849	+	0.339738i
$965$	−19.7553	+	9.51366i	−0.635946	+	0.306255i
$966$		0			0
$967$	−5.20875	+	22.8210i	−0.167502	+	0.733875i	0.819488	+	0.573096i	$0.194258\pi$
$967$	−5.20875	+	22.8210i	−0.167502	+	0.733875i	−0.986990	+	0.160779i	$0.948599\pi$
$968$	1.40663	−	6.16283i	0.0452106	−	0.198081i
$969$		0			0
$970$	−0.516866	+	0.248910i	−0.0165956	+	0.00799201i
$971$	−5.27455	−	1.20388i	−0.169268	−	0.0386344i	0.137047	−	0.990565i	$-0.456239\pi$
$971$	−5.27455	−	1.20388i	−0.169268	−	0.0386344i	−0.306315	+	0.951930i	$0.599096\pi$
$972$		0			0
$973$	−19.3721	−	15.4487i	−0.621041	−	0.495264i
$974$	2.35710	−	1.13512i	0.0755265	−	0.0363716i
$975$		0			0
$976$	25.7798	−	20.5587i	0.825192	−	0.658068i
$977$	30.4310	−	6.94567i	0.973572	−	0.222212i	0.293988	−	0.955809i	$-0.405017\pi$
$977$	30.4310	−	6.94567i	0.973572	−	0.222212i	0.679584	+	0.733598i	$0.262160\pi$
$978$		0			0
$979$	44.6767	+	35.6285i	1.42787	+	1.13869i
$980$	18.3217	+	8.82325i	0.585264	+	0.281848i
$981$		0			0
$982$	−0.249159			−0.00795097
$983$	23.0007			0.733608			0.366804	−	0.930298i	$-0.380452\pi$
$983$	23.0007			0.733608			0.366804	+	0.930298i	$0.380452\pi$
$984$		0			0
$985$	3.56604	+	7.40497i	0.113624	+	0.235942i
$986$	0.0744831	+	0.0170003i	0.00237203	+	0.000541400i
$987$		0			0
$988$		−	14.3378i		−	0.456147i
$989$	7.71271	−	15.2208i	0.245250	−	0.483994i
$990$		0			0
$991$	8.32697	−	1.90058i	0.264515	−	0.0603738i	−0.0882064	−	0.996102i	$-0.528114\pi$
$991$	8.32697	−	1.90058i	0.264515	−	0.0603738i	0.352721	+	0.935728i	$0.385256\pi$
$992$	−1.33028	+	5.82834i	−0.0422364	+	0.185050i
$993$		0			0
$994$	−0.888332	+	0.708421i	−0.0281762	+	0.0224698i
$995$		−	4.94287i		−	0.156699i
$996$		0			0
$997$	−18.8412	+	15.0253i	−0.596706	+	0.475857i	−0.874660	−	0.484737i	$-0.838915\pi$
$997$	−18.8412	+	15.0253i	−0.596706	+	0.475857i	0.277954	+	0.960594i	$0.410344\pi$
$998$	0.577170	−	1.19851i	0.0182700	−	0.0379380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.v.a.242.9	yes	96
3.2	odd	2	inner	387.2.v.a.242.8	yes	96
43.8	odd	14	inner	387.2.v.a.8.8	✓	96
129.8	even	14	inner	387.2.v.a.8.9	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.v.a.8.8	✓	96	43.8	odd	14	inner
387.2.v.a.8.9	yes	96	129.8	even	14	inner
387.2.v.a.242.8	yes	96	3.2	odd	2	inner
387.2.v.a.242.9	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0211977 + 0.0928730i) q^{2} +(1.79376 - 0.863830i) q^{4} +(1.55851 + 1.95431i) q^{5} +1.70699i q^{7} +(0.237039 + 0.297238i) q^{8} +O(q^{10})\)	\(q+(0.0211977 + 0.0928730i) q^{2} +(1.79376 - 0.863830i) q^{4} +(1.55851 + 1.95431i) q^{5} +1.70699i q^{7} +(0.237039 + 0.297238i) q^{8} +(-0.148466 + 0.186171i) q^{10} +(-2.28056 + 4.73563i) q^{11} +(0.699719 + 0.877420i) q^{13} +(-0.158533 + 0.0361841i) q^{14} +(2.46006 - 3.08482i) q^{16} +(-0.976839 - 0.779003i) q^{17} +(-2.78424 - 5.78154i) q^{19} +(4.48380 + 2.15928i) q^{20} +(-0.488155 - 0.111418i) q^{22} +(1.12903 - 2.34445i) q^{23} +(-0.277773 + 1.21701i) q^{25} +(-0.0666563 + 0.0835843i) q^{26} +(1.47455 + 3.06193i) q^{28} +(0.142833 + 0.625794i) q^{29} +(1.17079 + 5.12954i) q^{31} +(1.02371 + 0.492991i) q^{32} +(0.0516417 - 0.107235i) q^{34} +(-3.33599 + 2.66036i) q^{35} -5.00015i q^{37} +(0.477930 - 0.381136i) q^{38} +(-0.211467 + 0.926497i) q^{40} +(6.93264 - 1.58233i) q^{41} +(6.55610 + 0.132524i) q^{43} +10.4646i q^{44} +(0.241669 + 0.0551593i) q^{46} +(-4.65908 - 9.67467i) q^{47} +4.08620 q^{49} -0.118915 q^{50} +(2.01307 + 0.969444i) q^{52} +(-5.75575 - 4.59006i) q^{53} +(-12.8092 + 2.92361i) q^{55} +(-0.507381 + 0.404623i) q^{56} +(-0.0550916 + 0.0265307i) q^{58} +(-3.32207 - 2.64926i) q^{59} +(8.14746 + 1.85960i) q^{61} +(-0.451578 + 0.217469i) q^{62} +(1.73189 - 7.58789i) q^{64} +(-0.624232 + 2.73494i) q^{65} +(-12.9293 + 6.22641i) q^{67} +(-2.42514 - 0.553523i) q^{68} +(-0.317791 - 0.253430i) q^{70} +(6.29542 - 3.03172i) q^{71} +(-7.19395 + 5.73699i) q^{73} +(0.464379 - 0.105991i) q^{74} +(-9.98854 - 7.96560i) q^{76} +(-8.08365 - 3.89288i) q^{77} -7.65734 q^{79} +9.86275 q^{80} +(0.293912 + 0.610314i) q^{82} +(-2.82251 - 0.644219i) q^{83} -3.12313i q^{85} +(0.126666 + 0.611694i) q^{86} +(-1.94819 + 0.444661i) q^{88} +(2.41919 - 10.5992i) q^{89} +(-1.49774 + 1.19441i) q^{91} -5.18067i q^{92} +(0.799755 - 0.637783i) q^{94} +(6.95967 - 14.4519i) q^{95} +(2.17060 + 1.04531i) q^{97} +(0.0866178 + 0.379497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 20 q^{4}+O(q^{10}) \) 96 * q - 20 * q^4	\( 96 q - 20 q^{4} + 16 q^{10} - 4 q^{13} - 36 q^{16} - 16 q^{25} - 48 q^{31} - 104 q^{40} + 28 q^{43} - 28 q^{46} - 160 q^{49} - 44 q^{52} + 84 q^{55} + 20 q^{58} + 52 q^{64} + 40 q^{67} - 140 q^{70} - 28 q^{73} + 112 q^{76} + 64 q^{79} + 168 q^{88} + 56 q^{91} + 112 q^{94} - 108 q^{97}+O(q^{100}) \) 96 * q - 20 * q^4 + 16 * q^10 - 4 * q^13 - 36 * q^16 - 16 * q^25 - 48 * q^31 - 104 * q^40 + 28 * q^43 - 28 * q^46 - 160 * q^49 - 44 * q^52 + 84 * q^55 + 20 * q^58 + 52 * q^64 + 40 * q^67 - 140 * q^70 - 28 * q^73 + 112 * q^76 + 64 * q^79 + 168 * q^88 + 56 * q^91 + 112 * q^94 - 108 * q^97

Introduction

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