LMFDB - Embedded newform 480.2.v.d.353.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,2,Mod(257,480)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(480, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("480.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	480.v (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:	$3.83281929702$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.7
Character	$\chi$	$=$	480.353
Dual form			480.2.v.d.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.391016 - 1.68734i) q^{3} +(-1.95188 + 1.09094i) q^{5} +(0.246506 - 0.246506i) q^{7} +(-2.69421 - 1.31955i) q^{9} +O(q^{10})$	\(q+(0.391016 - 1.68734i) q^{3} +(-1.95188 + 1.09094i) q^{5} +(0.246506 - 0.246506i) q^{7} +(-2.69421 - 1.31955i) q^{9} -1.86613i q^{11} +(-3.25879 - 3.25879i) q^{13} +(1.07757 + 3.72006i) q^{15} +(-2.34560 - 2.34560i) q^{17} -5.02774i q^{19} +(-0.319551 - 0.512326i) q^{21} +(-3.94448 + 3.94448i) q^{23} +(2.61968 - 4.25879i) q^{25} +(-3.28001 + 4.03008i) q^{27} -7.57031 q^{29} +10.7060 q^{31} +(-3.14878 - 0.729685i) q^{33} +(-0.212226 + 0.750074i) q^{35} +(-0.619684 + 0.619684i) q^{37} +(-6.77291 + 4.22443i) q^{39} +3.66655i q^{41} +(-3.73142 - 3.73142i) q^{43} +(6.69834 - 0.363628i) q^{45} +(1.11605 + 1.11605i) q^{47} +6.87847i q^{49} +(-4.87499 + 3.04065i) q^{51} +(2.80561 - 2.80561i) q^{53} +(2.03584 + 3.64246i) q^{55} +(-8.48350 - 1.96593i) q^{57} +7.94743 q^{59} +3.87847 q^{61} +(-0.989416 + 0.338862i) q^{63} +(9.91592 + 2.80561i) q^{65} +(6.81708 - 6.81708i) q^{67} +(5.11331 + 8.19802i) q^{69} -9.81356i q^{71} +(-6.23937 - 6.23937i) q^{73} +(-6.16167 - 6.08554i) q^{75} +(-0.460011 - 0.460011i) q^{77} -9.09942i q^{79} +(5.51757 + 7.11030i) q^{81} +(5.27276 - 5.27276i) q^{83} +(7.13726 + 2.01942i) q^{85} +(-2.96011 + 12.7737i) q^{87} +9.52940 q^{89} -1.60662 q^{91} +(4.18623 - 18.0647i) q^{93} +(5.48498 + 9.81356i) q^{95} +(-11.5176 + 11.5176i) q^{97} +(-2.46245 + 5.02774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 16 q^{13} + 16 q^{21} + 16 q^{25} + 24 q^{33} + 32 q^{37} + 32 q^{45} + 16 q^{57} - 48 q^{61} - 56 q^{73} - 56 q^{81} - 64 q^{85} - 96 q^{93} - 88 q^{97}+O(q^{100}) $ 24 * q + 16 * q^13 + 16 * q^21 + 16 * q^25 + 24 * q^33 + 32 * q^37 + 32 * q^45 + 16 * q^57 - 48 * q^61 - 56 * q^73 - 56 * q^81 - 64 * q^85 - 96 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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			0
$2$		0			0
$3$	0.391016	−	1.68734i	0.225753	−	0.974185i
$3$	0.391016	−	1.68734i	0.225753	−	0.974185i
$4$		0			0
$5$	−1.95188	+	1.09094i	−0.872908	+	0.487885i
$5$	−1.95188	+	1.09094i	−0.872908	+	0.487885i
$6$		0			0
$7$	0.246506	−	0.246506i	0.0931705	−	0.0931705i	−0.658985	−	0.752156i	$-0.729014\pi$
$7$	0.246506	−	0.246506i	0.0931705	−	0.0931705i	0.752156	+	0.658985i	$0.229014\pi$
$8$		0			0
$9$	−2.69421	−	1.31955i	−0.898071	−	0.439850i
$10$		0			0
$11$		−	1.86613i		−	0.562658i	−0.959611	−	0.281329i	$-0.909225\pi$
$11$		−	1.86613i		−	0.562658i	0.959611	−	0.281329i	$-0.0907753\pi$
$12$		0			0
$13$	−3.25879	−	3.25879i	−0.903825	−	0.903825i	0.0919400	−	0.995765i	$-0.470693\pi$
$13$	−3.25879	−	3.25879i	−0.903825	−	0.903825i	−0.995765	+	0.0919400i	$0.970693\pi$
$14$		0			0
$15$	1.07757	+	3.72006i	0.278228	+	0.960515i
$16$		0			0
$17$	−2.34560	−	2.34560i	−0.568892	−	0.568892i	0.362926	−	0.931818i	$-0.381778\pi$
$17$	−2.34560	−	2.34560i	−0.568892	−	0.568892i	−0.931818	+	0.362926i	$0.881778\pi$
$18$		0			0
$19$		−	5.02774i		−	1.15344i	−0.816941	−	0.576722i	$-0.804332\pi$
$19$		−	5.02774i		−	1.15344i	0.816941	−	0.576722i	$-0.195668\pi$
$20$		0			0
$21$	−0.319551	−	0.512326i	−0.0697317	−	0.111799i
$22$		0			0
$23$	−3.94448	+	3.94448i	−0.822481	+	0.822481i	−0.986463	−	0.163982i	$-0.947566\pi$
$23$	−3.94448	+	3.94448i	−0.822481	+	0.822481i	0.163982	+	0.986463i	$0.447566\pi$
$24$		0			0
$25$	2.61968	−	4.25879i	0.523937	−	0.851757i
$26$		0			0
$27$	−3.28001	+	4.03008i	−0.631238	+	0.775589i
$28$		0			0
$29$	−7.57031			−1.40577			−0.702886	−	0.711303i	$-0.748106\pi$
$29$	−7.57031			−1.40577			−0.702886	+	0.711303i	$0.748106\pi$
$30$		0			0
$31$	10.7060			1.92286			0.961431	−	0.275047i	$-0.0886934\pi$
$31$	10.7060			1.92286			0.961431	+	0.275047i	$0.0886934\pi$
$32$		0			0
$33$	−3.14878	−	0.729685i	−0.548133	−	0.127022i
$34$		0			0
$35$	−0.212226	+	0.750074i	−0.0358728	+	0.126786i
$36$		0			0
$37$	−0.619684	+	0.619684i	−0.101875	+	0.101875i	−0.756207	−	0.654332i	$-0.772950\pi$
$37$	−0.619684	+	0.619684i	−0.101875	+	0.101875i	0.654332	+	0.756207i	$0.272950\pi$
$38$		0			0
$39$	−6.77291	+	4.22443i	−1.08453	+	0.676451i
$40$		0			0
$41$			3.66655i			0.572619i	0.958137	+	0.286310i	$0.0924286\pi$
$41$			3.66655i			0.572619i	−0.958137	+	0.286310i	$0.907571\pi$
$42$		0			0
$43$	−3.73142	−	3.73142i	−0.569037	−	0.569037i	0.362822	−	0.931858i	$-0.381813\pi$
$43$	−3.73142	−	3.73142i	−0.569037	−	0.569037i	−0.931858	+	0.362822i	$0.881813\pi$
$44$		0			0
$45$	6.69834	−	0.363628i	0.998530	−	0.0542064i
$46$		0			0
$47$	1.11605	+	1.11605i	0.162793	+	0.162793i	0.783803	−	0.621010i	$-0.213277\pi$
$47$	1.11605	+	1.11605i	0.162793	+	0.162793i	−0.621010	+	0.783803i	$0.713277\pi$
$48$		0			0
$49$			6.87847i			0.982639i
$50$		0			0
$51$	−4.87499	+	3.04065i	−0.682635	+	0.425777i
$52$		0			0
$53$	2.80561	−	2.80561i	0.385381	−	0.385381i	−0.487656	−	0.873036i	$-0.662148\pi$
$53$	2.80561	−	2.80561i	0.385381	−	0.385381i	0.873036	+	0.487656i	$0.162148\pi$
$54$		0			0
$55$	2.03584	+	3.64246i	0.274512	+	0.491149i
$56$		0			0
$57$	−8.48350	−	1.96593i	−1.12367	−	0.260393i
$58$		0			0
$59$	7.94743			1.03467			0.517334	−	0.855784i	$-0.326925\pi$
$59$	7.94743			1.03467			0.517334	+	0.855784i	$0.326925\pi$
$60$		0			0
$61$	3.87847			0.496587			0.248294	−	0.968685i	$-0.420130\pi$
$61$	3.87847			0.496587			0.248294	+	0.968685i	$0.420130\pi$
$62$		0			0
$63$	−0.989416	+	0.338862i	−0.124655	+	0.0426926i
$64$		0			0
$65$	9.91592	+	2.80561i	1.22992	+	0.347993i
$66$		0			0
$67$	6.81708	−	6.81708i	0.832838	−	0.832838i	−0.155066	−	0.987904i	$-0.549559\pi$
$67$	6.81708	−	6.81708i	0.832838	−	0.832838i	0.987904	+	0.155066i	$0.0495589\pi$
$68$		0			0
$69$	5.11331	+	8.19802i	0.615571	+	0.986926i
$70$		0			0
$71$		−	9.81356i		−	1.16466i	−0.812954	−	0.582328i	$-0.802142\pi$
$71$		−	9.81356i		−	1.16466i	0.812954	−	0.582328i	$-0.197858\pi$
$72$		0			0
$73$	−6.23937	−	6.23937i	−0.730263	−	0.730263i	0.240409	−	0.970672i	$-0.422718\pi$
$73$	−6.23937	−	6.23937i	−0.730263	−	0.730263i	−0.970672	+	0.240409i	$0.922718\pi$
$74$		0			0
$75$	−6.16167	−	6.08554i	−0.711488	−	0.702698i
$76$		0			0
$77$	−0.460011	−	0.460011i	−0.0524231	−	0.0524231i
$78$		0			0
$79$		−	9.09942i		−	1.02376i	−0.859056	−	0.511882i	$-0.828948\pi$
$79$		−	9.09942i		−	1.02376i	0.859056	−	0.511882i	$-0.171052\pi$
$80$		0			0
$81$	5.51757	+	7.11030i	0.613063	+	0.790034i
$82$		0			0
$83$	5.27276	−	5.27276i	0.578760	−	0.578760i	−0.355801	−	0.934562i	$-0.615792\pi$
$83$	5.27276	−	5.27276i	0.578760	−	0.578760i	0.934562	+	0.355801i	$0.115792\pi$
$84$		0			0
$85$	7.13726	+	2.01942i	0.774144	+	0.219037i
$86$		0			0
$87$	−2.96011	+	12.7737i	−0.317357	+	1.36948i
$88$		0			0
$89$	9.52940			1.01011			0.505057	−	0.863086i	$-0.331471\pi$
$89$	9.52940			1.01011			0.505057	+	0.863086i	$0.331471\pi$
$90$		0			0
$91$	−1.60662			−0.168419
$92$		0			0
$93$	4.18623	−	18.0647i	0.434092	−	1.87322i
$94$		0			0
$95$	5.48498	+	9.81356i	0.562748	+	1.00685i
$96$		0			0
$97$	−11.5176	+	11.5176i	−1.16943	+	1.16943i	−0.187089	+	0.982343i	$0.559905\pi$
$97$	−11.5176	+	11.5176i	−1.16943	+	1.16943i	−0.982343	+	0.187089i	$0.940095\pi$
$98$		0			0
$99$	−2.46245	+	5.02774i	−0.247485	+	0.505307i
$100$		0			0
$101$		−	2.87911i		−	0.286482i	−0.989688	−	0.143241i	$-0.954248\pi$
$101$		−	2.87911i		−	0.286482i	0.989688	−	0.143241i	$-0.0457524\pi$
$102$		0			0
$103$	0.739518	+	0.739518i	0.0728668	+	0.0728668i	0.742601	−	0.669734i	$-0.233592\pi$
$103$	0.739518	+	0.739518i	0.0728668	+	0.0728668i	−0.669734	+	0.742601i	$0.733592\pi$
$104$		0			0
$105$	1.18264	+	0.651388i	0.115414	+	0.0635690i
$106$		0			0
$107$	−10.9296	−	10.9296i	−1.05661	−	1.05661i	−0.998299	−	0.0583068i	$-0.981430\pi$
$107$	−10.9296	−	10.9296i	−1.05661	−	1.05661i	−0.0583068	−	0.998299i	$-0.518570\pi$
$108$		0			0
$109$			10.3960i			0.995760i	0.867246	+	0.497880i	$0.165888\pi$
$109$			10.3960i			0.995760i	−0.867246	+	0.497880i	$0.834112\pi$
$110$		0			0
$111$	0.803310	+	1.28792i	0.0762468	+	0.122244i
$112$		0			0
$113$	12.7950	−	12.7950i	1.20365	−	1.20365i	0.230608	−	0.973047i	$-0.425928\pi$
$113$	12.7950	−	12.7950i	1.20365	−	1.20365i	0.973047	−	0.230608i	$-0.0740715\pi$
$114$		0			0
$115$	3.39595	−	12.0024i	0.316674	−	1.11923i
$116$		0			0
$117$	4.47973	+	13.0800i	0.414151	+	1.20925i
$118$		0			0
$119$	−1.15641			−0.106008
$120$		0			0
$121$	7.51757			0.683416
$122$		0			0
$123$	6.18671	+	1.43368i	0.557837	+	0.129270i
$124$		0			0
$125$	−0.467218	+	11.1706i	−0.0417893	+	0.999126i
$126$		0			0
$127$	4.78124	−	4.78124i	0.424266	−	0.424266i	−0.462403	−	0.886670i	$-0.653013\pi$
$127$	4.78124	−	4.78124i	0.424266	−	0.424266i	0.886670	+	0.462403i	$0.153013\pi$
$128$		0			0
$129$	−7.75521	+	4.83712i	−0.682808	+	0.425885i
$130$		0			0
$131$			16.5683i			1.44758i	0.690019	+	0.723792i	$0.257602\pi$
$131$			16.5683i			1.44758i	−0.690019	+	0.723792i	$0.742398\pi$
$132$		0			0
$133$	−1.23937	−	1.23937i	−0.107467	−	0.107467i
$134$		0			0
$135$	2.00559	−	11.4445i	0.172614	−	0.984990i
$136$		0			0
$137$	4.76470	+	4.76470i	0.407076	+	0.407076i	0.880718	−	0.473642i	$-0.157061\pi$
$137$	4.76470	+	4.76470i	0.407076	+	0.407076i	−0.473642	+	0.880718i	$0.657061\pi$
$138$		0			0
$139$			16.3843i			1.38970i	0.719154	+	0.694851i	$0.244530\pi$
$139$			16.3843i			1.38970i	−0.719154	+	0.694851i	$0.755470\pi$
$140$		0			0
$141$	2.31955	−	1.44676i	0.195341	−	0.121839i
$142$		0			0
$143$	−6.08131	+	6.08131i	−0.508544	+	0.508544i
$144$		0			0
$145$	14.7764	−	8.25879i	1.22711	−	0.685855i
$146$		0			0
$147$	11.6063	+	2.68959i	0.957271	+	0.221834i
$148$		0			0
$149$	−8.26754			−0.677303			−0.338652	−	0.940912i	$-0.609971\pi$
$149$	−8.26754			−0.677303			−0.338652	+	0.940912i	$0.609971\pi$
$150$		0			0
$151$	−13.4766			−1.09671			−0.548356	−	0.836245i	$-0.684746\pi$
$151$	−13.4766			−1.09671			−0.548356	+	0.836245i	$0.684746\pi$
$152$		0			0
$153$	3.22441	+	9.41469i	0.260678	+	0.761133i
$154$		0			0
$155$	−20.8969	+	11.6797i	−1.67848	+	0.938135i
$156$		0			0
$157$	−3.25879	+	3.25879i	−0.260079	+	0.260079i	−0.825086	−	0.565007i	$-0.808874\pi$
$157$	−3.25879	+	3.25879i	−0.260079	+	0.260079i	0.565007	+	0.825086i	$0.308874\pi$
$158$		0			0
$159$	−3.63698	−	5.83105i	−0.288431	−	0.462433i
$160$		0			0
$161$			1.94467i			0.153262i
$162$		0			0
$163$	16.0441	+	16.0441i	1.25667	+	1.25667i	0.952673	+	0.303996i	$0.0983210\pi$
$163$	16.0441	+	16.0441i	1.25667	+	1.25667i	0.303996	+	0.952673i	$0.401679\pi$
$164$		0			0
$165$	6.94210	−	2.01089i	0.540442	−	0.156547i
$166$		0			0
$167$	−6.34845	−	6.34845i	−0.491258	−	0.491258i	0.417444	−	0.908702i	$-0.362926\pi$
$167$	−6.34845	−	6.34845i	−0.491258	−	0.491258i	−0.908702	+	0.417444i	$0.862926\pi$
$168$		0			0
$169$			8.23937i			0.633798i
$170$		0			0
$171$	−6.63436	+	13.5458i	−0.507342	+	1.03587i
$172$		0			0
$173$	−0.0734985	+	0.0734985i	−0.00558798	+	0.00558798i	−0.709895	−	0.704307i	$-0.751258\pi$
$173$	−0.0734985	+	0.0734985i	−0.00558798	+	0.00558798i	0.704307	+	0.709895i	$0.251258\pi$
$174$		0			0
$175$	−0.404048	−	1.69558i	−0.0305432	−	0.128174i
$176$		0			0
$177$	3.10757	−	13.4100i	0.233579	−	1.00796i
$178$		0			0
$179$	15.4119			1.15194			0.575971	−	0.817470i	$-0.304624\pi$
$179$	15.4119			1.15194			0.575971	+	0.817470i	$0.304624\pi$
$180$		0			0
$181$	−7.27820			−0.540985			−0.270492	−	0.962722i	$-0.587186\pi$
$181$	−7.27820			−0.540985			−0.270492	+	0.962722i	$0.587186\pi$
$182$		0			0
$183$	1.51654	−	6.54429i	0.112106	−	0.483768i
$184$		0			0
$185$	0.533510	−	1.88559i	0.0392244	−	0.138631i
$186$		0			0
$187$	−4.37719	+	4.37719i	−0.320092	+	0.320092i
$188$		0			0
$189$	0.184898	+	1.80198i	0.0134493	+	0.131075i
$190$		0			0
$191$		−	20.7835i		−	1.50384i	−0.659252	−	0.751922i	$-0.729127\pi$
$191$		−	20.7835i		−	1.50384i	0.659252	−	0.751922i	$-0.270873\pi$
$192$		0			0
$193$	−14.1567	−	14.1567i	−1.01902	−	1.01902i	−0.999816	−	0.0192040i	$-0.993887\pi$
$193$	−14.1567	−	14.1567i	−1.01902	−	1.01902i	−0.0192040	−	0.999816i	$-0.506113\pi$
$194$		0			0
$195$	8.61129	−	15.6345i	0.616668	−	1.11961i
$196$		0			0
$197$	−12.3350	−	12.3350i	−0.878833	−	0.878833i	0.114581	−	0.993414i	$-0.463448\pi$
$197$	−12.3350	−	12.3350i	−0.878833	−	0.878833i	−0.993414	+	0.114581i	$0.963448\pi$
$198$		0			0
$199$			1.81450i			0.128627i	0.997930	+	0.0643134i	$0.0204857\pi$
$199$			1.81450i			0.128627i	−0.997930	+	0.0643134i	$0.979514\pi$
$200$		0			0
$201$	−8.83712	−	14.1683i	−0.623323	−	0.999354i
$202$		0			0
$203$	−1.86613	+	1.86613i	−0.130976	+	0.130976i
$204$		0			0
$205$	−4.00000	−	7.15667i	−0.279372	−	0.499844i
$206$		0			0
$207$	15.8322	−	5.42233i	1.10041	−	0.376878i
$208$		0			0
$209$	−9.38241			−0.648995
$210$		0			0
$211$	−7.93547			−0.546300			−0.273150	−	0.961971i	$-0.588066\pi$
$211$	−7.93547			−0.546300			−0.273150	+	0.961971i	$0.588066\pi$
$212$		0			0
$213$	−16.5588	−	3.83726i	−1.13459	−	0.262924i
$214$		0			0
$215$	11.3541	+	3.21252i	0.774341	+	0.219092i
$216$		0			0
$217$	2.63910	−	2.63910i	0.179154	−	0.179154i
$218$		0			0
$219$	−12.9676	+	8.08823i	−0.876270	+	0.546552i
$220$		0			0
$221$			15.2876i			1.02836i
$222$		0			0
$223$	−17.1239	−	17.1239i	−1.14670	−	1.14670i	−0.987198	−	0.159500i	$-0.949012\pi$
$223$	−17.1239	−	17.1239i	−1.14670	−	1.14670i	−0.159500	−	0.987198i	$-0.550988\pi$
$224$		0			0
$225$	−12.6777	+	8.01727i	−0.845178	+	0.534485i
$226$		0			0
$227$	−1.34640	−	1.34640i	−0.0893635	−	0.0893635i	0.661012	−	0.750375i	$-0.270127\pi$
$227$	−1.34640	−	1.34640i	−0.0893635	−	0.0893635i	−0.750375	+	0.661012i	$0.770127\pi$
$228$		0			0
$229$		−	17.7958i		−	1.17598i	−0.808869	−	0.587989i	$-0.799920\pi$
$229$		−	17.7958i		−	1.17598i	0.808869	−	0.587989i	$-0.200080\pi$
$230$		0			0
$231$	−0.956065	+	0.596322i	−0.0629045	+	0.0392351i
$232$		0			0
$233$	−8.10382	+	8.10382i	−0.530899	+	0.530899i	−0.920840	−	0.389941i	$-0.872495\pi$
$233$	−8.10382	+	8.10382i	−0.530899	+	0.530899i	0.389941	+	0.920840i	$0.372495\pi$
$234$		0			0
$235$	−3.39595	−	0.960852i	−0.221528	−	0.0626791i
$236$		0			0
$237$	−15.3538	−	3.55802i	−0.997336	−	0.231118i
$238$		0			0
$239$	23.3594			1.51099			0.755496	−	0.655153i	$-0.227396\pi$
$239$	23.3594			1.51099			0.755496	+	0.655153i	$0.227396\pi$
$240$		0			0
$241$	7.36090			0.474157			0.237079	−	0.971490i	$-0.423810\pi$
$241$	7.36090			0.474157			0.237079	+	0.971490i	$0.423810\pi$
$242$		0			0
$243$	14.1549	−	6.52976i	0.908040	−	0.418884i
$244$		0			0
$245$	−7.50402	−	13.4260i	−0.479414	−	0.857753i
$246$		0			0
$247$	−16.3843	+	16.3843i	−1.04251	+	1.04251i
$248$		0			0
$249$	−6.83519	−	10.9587i	−0.433163	−	0.694476i
$250$		0			0
$251$		−	6.79102i		−	0.428646i	−0.976763	−	0.214323i	$-0.931246\pi$
$251$		−	6.79102i		−	0.428646i	0.976763	−	0.214323i	$-0.0687545\pi$
$252$		0			0
$253$	7.36090	+	7.36090i	0.462776	+	0.462776i
$254$		0			0
$255$	6.19822	−	11.2533i	0.388147	−	0.704711i
$256$		0			0
$257$	−7.18380	−	7.18380i	−0.448113	−	0.448113i	0.446614	−	0.894727i	$-0.352630\pi$
$257$	−7.18380	−	7.18380i	−0.448113	−	0.448113i	−0.894727	+	0.446614i	$0.852630\pi$
$258$		0			0
$259$			0.305511i			0.0189836i
$260$		0			0
$261$	20.3960	+	9.98941i	1.26248	+	0.618329i
$262$		0			0
$263$	−0.212226	+	0.212226i	−0.0130864	+	0.0130864i	−0.713620	−	0.700533i	$-0.752946\pi$
$263$	−0.212226	+	0.212226i	−0.0130864	+	0.0130864i	0.700533	+	0.713620i	$0.252946\pi$
$264$		0			0
$265$	−2.41546	+	8.53699i	−0.148380	+	0.524423i
$266$		0			0
$267$	3.72615	−	16.0793i	0.228036	−	0.984038i
$268$		0			0
$269$	−6.87309			−0.419060			−0.209530	−	0.977802i	$-0.567193\pi$
$269$	−6.87309			−0.419060			−0.209530	+	0.977802i	$0.567193\pi$
$270$		0			0
$271$	6.63436			0.403009			0.201504	−	0.979488i	$-0.435417\pi$
$271$	6.63436			0.403009			0.201504	+	0.979488i	$0.435417\pi$
$272$		0			0
$273$	−0.628214	+	2.71091i	−0.0380212	+	0.164072i
$274$		0			0
$275$	−7.94743	−	4.88866i	−0.479248	−	0.294797i
$276$		0			0
$277$	13.2588	−	13.2588i	0.796643	−	0.796643i	−0.185921	−	0.982565i	$-0.559527\pi$
$277$	13.2588	−	13.2588i	0.796643	−	0.796643i	0.982565	+	0.185921i	$0.0595270\pi$
$278$		0			0
$279$	−28.8444	−	14.1272i	−1.72687	−	0.845771i
$280$		0			0
$281$			2.09167i			0.124779i	0.998052	+	0.0623893i	$0.0198720\pi$
$281$			2.09167i			0.124779i	−0.998052	+	0.0623893i	$0.980128\pi$
$282$		0			0
$283$	12.8308	+	12.8308i	0.762714	+	0.762714i	0.976812	−	0.214098i	$-0.0686811\pi$
$283$	12.8308	+	12.8308i	0.762714	+	0.762714i	−0.214098	+	0.976812i	$0.568681\pi$
$284$		0			0
$285$	18.7035	−	5.41776i	1.10790	−	0.320921i
$286$		0			0
$287$	0.903826	+	0.903826i	0.0533512	+	0.0533512i
$288$		0			0
$289$		−	5.99631i		−	0.352724i
$290$		0			0
$291$	14.9305	+	23.9376i	0.875240	+	1.40325i
$292$		0			0
$293$	−14.6071	+	14.6071i	−0.853357	+	0.853357i	−0.990545	−	0.137188i	$-0.956194\pi$
$293$	−14.6071	+	14.6071i	−0.853357	+	0.853357i	0.137188	+	0.990545i	$0.456194\pi$
$294$		0			0
$295$	−15.5124	+	8.67020i	−0.903170	+	0.504799i
$296$		0			0
$297$	7.52064	+	6.12091i	0.436392	+	0.355171i
$298$		0			0
$299$	25.7084			1.48676
$300$		0			0
$301$	−1.83963			−0.106035
$302$		0			0
$303$	−4.85803	−	1.12578i	−0.279087	−	0.0646742i
$304$		0			0
$305$	−7.57031	+	4.23119i	−0.433475	+	0.242277i
$306$		0			0
$307$	−5.86101	+	5.86101i	−0.334506	+	0.334506i	−0.854295	−	0.519789i	$-0.826011\pi$
$307$	−5.86101	+	5.86101i	−0.334506	+	0.334506i	0.519789	+	0.854295i	$0.326011\pi$
$308$		0			0
$309$	1.53698	−	0.958652i	0.0874356	−	0.0545358i
$310$		0			0
$311$		−	9.81356i		−	0.556476i	−0.960512	−	0.278238i	$-0.910250\pi$
$311$		−	9.81356i		−	0.556476i	0.960512	−	0.278238i	$-0.0897504\pi$
$312$		0			0
$313$	−1.12153	−	1.12153i	−0.0633926	−	0.0633926i	0.674700	−	0.738092i	$-0.264273\pi$
$313$	−1.12153	−	1.12153i	−0.0633926	−	0.0633926i	−0.738092	+	0.674700i	$0.764273\pi$
$314$		0			0
$315$	1.56154	−	1.74082i	0.0879830	−	0.0980839i
$316$		0			0
$317$	−2.34560	−	2.34560i	−0.131742	−	0.131742i	0.638161	−	0.769903i	$-0.279695\pi$
$317$	−2.34560	−	2.34560i	−0.131742	−	0.131742i	−0.769903	+	0.638161i	$0.779695\pi$
$318$		0			0
$319$			14.1272i			0.790969i
$320$		0			0
$321$	−22.7156	+	14.1683i	−1.26786	+	0.790797i
$322$		0			0
$323$	−11.7931	+	11.7931i	−0.656185	+	0.656185i
$324$		0			0
$325$	−22.4155	+	5.34148i	−1.24339	+	0.296292i
$326$		0			0
$327$	17.5416	+	4.06502i	0.970054	+	0.224796i
$328$		0			0
$329$	0.550227			0.0303350
$330$		0			0
$331$	−21.6200			−1.18834			−0.594170	−	0.804339i	$-0.702520\pi$
$331$	−21.6200			−1.18834			−0.594170	+	0.804339i	$0.702520\pi$
$332$		0			0
$333$	2.48727	−	0.851856i	0.136301	−	0.0466814i
$334$		0			0
$335$	−5.86908	+	20.7432i	−0.320662	+	1.13332i
$336$		0			0
$337$	1.51757	−	1.51757i	0.0826674	−	0.0826674i	−0.664564	−	0.747231i	$-0.731383\pi$
$337$	1.51757	−	1.51757i	0.0826674	−	0.0826674i	0.747231	+	0.664564i	$0.231383\pi$
$338$		0			0
$339$	−16.5865	−	26.5926i	−0.900853	−	1.44431i
$340$		0			0
$341$		−	19.9788i		−	1.08191i
$342$		0			0
$343$	3.42112	+	3.42112i	0.184723	+	0.184723i
$344$		0			0
$345$	−18.9242	−	10.4232i	−1.01884	−	0.561168i
$346$		0			0
$347$	−12.3164	−	12.3164i	−0.661177	−	0.661177i	0.294480	−	0.955658i	$-0.404853\pi$
$347$	−12.3164	−	12.3164i	−0.661177	−	0.661177i	−0.955658	+	0.294480i	$0.904853\pi$
$348$		0			0
$349$		−	9.96116i		−	0.533209i	−0.963806	−	0.266604i	$-0.914098\pi$
$349$		−	9.96116i		−	0.533209i	0.963806	−	0.266604i	$-0.0859017\pi$
$350$		0			0
$351$	23.8220	−	2.44433i	1.27152	−	0.130469i
$352$		0			0
$353$	4.76470	−	4.76470i	0.253599	−	0.253599i	−0.568845	−	0.822445i	$-0.692610\pi$
$353$	4.76470	−	4.76470i	0.253599	−	0.253599i	0.822445	+	0.568845i	$0.192610\pi$
$354$		0			0
$355$	10.7060	+	19.1549i	0.568218	+	1.01664i
$356$		0			0
$357$	−0.452174	+	1.95125i	−0.0239316	+	0.103271i
$358$		0			0
$359$	−18.4345			−0.972934			−0.486467	−	0.873699i	$-0.661715\pi$
$359$	−18.4345			−0.972934			−0.486467	+	0.873699i	$0.661715\pi$
$360$		0			0
$361$	−6.27820			−0.330432
$362$		0			0
$363$	2.93949	−	12.6847i	0.154283	−	0.665773i
$364$		0			0
$365$	18.9853	+	5.37171i	0.993736	+	0.281168i
$366$		0			0
$367$	−2.52406	+	2.52406i	−0.131755	+	0.131755i	−0.769909	−	0.638154i	$-0.779698\pi$
$367$	−2.52406	+	2.52406i	−0.131755	+	0.131755i	0.638154	+	0.769909i	$0.279698\pi$
$368$		0			0
$369$	4.83820	−	9.87847i	0.251867	−	0.514253i
$370$		0			0
$371$		−	1.38320i		−	0.0718122i
$372$		0			0
$373$	23.6548	+	23.6548i	1.22480	+	1.22480i	0.965905	+	0.258895i	$0.0833584\pi$
$373$	23.6548	+	23.6548i	1.22480	+	1.22480i	0.258895	+	0.965905i	$0.416642\pi$
$374$		0			0
$375$	18.6658	+	5.15622i	0.963900	+	0.266266i
$376$		0			0
$377$	24.6700	+	24.6700i	1.27057	+	1.27057i
$378$		0			0
$379$			16.3843i			0.841607i	0.907152	+	0.420803i	$0.138252\pi$
$379$			16.3843i			0.841607i	−0.907152	+	0.420803i	$0.861748\pi$
$380$		0			0
$381$	−6.19802	−	9.93710i	−0.317534	−	0.509093i
$382$		0			0
$383$	−15.0863	+	15.0863i	−0.770875	+	0.770875i	−0.978259	−	0.207385i	$-0.933505\pi$
$383$	−15.0863	+	15.0863i	−0.770875	+	0.770875i	0.207385	+	0.978259i	$0.433505\pi$
$384$		0			0
$385$	1.39973	+	0.396041i	0.0713370	+	0.0201841i
$386$		0			0
$387$	5.12945	+	14.9770i	0.260744	+	0.761326i
$388$		0			0
$389$	33.7106			1.70919			0.854597	−	0.519291i	$-0.173804\pi$
$389$	33.7106			1.70919			0.854597	+	0.519291i	$0.173804\pi$
$390$		0			0
$391$	18.5044			0.935805
$392$		0			0
$393$	27.9564	+	6.47849i	1.41021	+	0.326796i
$394$		0			0
$395$	9.92696	+	17.7610i	0.499479	+	0.893653i
$396$		0			0
$397$	1.85905	−	1.85905i	0.0933032	−	0.0933032i	−0.658915	−	0.752218i	$-0.728984\pi$
$397$	1.85905	−	1.85905i	0.0933032	−	0.0933032i	0.752218	+	0.658915i	$0.228984\pi$
$398$		0			0
$399$	−2.57584	+	1.60662i	−0.128954	+	0.0804316i
$400$		0			0
$401$		−	36.0395i		−	1.79973i	−0.436173	−	0.899863i	$-0.643666\pi$
$401$		−	36.0395i		−	1.79973i	0.436173	−	0.899863i	$-0.356334\pi$
$402$		0			0
$403$	−34.8887	−	34.8887i	−1.73793	−	1.73793i
$404$		0			0
$405$	−18.5266	−	7.85911i	−0.920593	−	0.390522i
$406$		0			0
$407$	1.15641	+	1.15641i	0.0573211	+	0.0573211i
$408$		0			0
$409$			19.1567i			0.947237i	0.880730	+	0.473618i	$0.157052\pi$
$409$			19.1567i			0.947237i	−0.880730	+	0.473618i	$0.842948\pi$
$410$		0			0
$411$	9.90273	−	6.17658i	0.488466	−	0.304668i
$412$		0			0
$413$	1.95909	−	1.95909i	0.0964005	−	0.0964005i
$414$		0			0
$415$	−4.53952	+	16.0441i	−0.222836	+	0.787573i
$416$		0			0
$417$	27.6459	+	6.40653i	1.35383	+	0.313729i
$418$		0			0
$419$	−3.02254			−0.147661			−0.0738303	−	0.997271i	$-0.523522\pi$
$419$	−3.02254			−0.147661			−0.0738303	+	0.997271i	$0.523522\pi$
$420$		0			0
$421$	−18.6003			−0.906522			−0.453261	−	0.891378i	$-0.649739\pi$
$421$	−18.6003			−0.906522			−0.453261	+	0.891378i	$0.649739\pi$
$422$		0			0
$423$	−1.53420	−	4.47957i	−0.0745951	−	0.217804i
$424$		0			0
$425$	−16.1341	+	3.84468i	−0.782621	+	0.186494i
$426$		0			0
$427$	0.956065	−	0.956065i	0.0462673	−	0.0462673i
$428$		0			0
$429$	7.88333	+	12.6391i	0.380611	+	0.610222i
$430$		0			0
$431$		−	22.2030i		−	1.06948i	−0.845017	−	0.534740i	$-0.820410\pi$
$431$		−	22.2030i		−	1.06948i	0.845017	−	0.534740i	$-0.179590\pi$
$432$		0			0
$433$	9.27451	+	9.27451i	0.445705	+	0.445705i	0.893924	−	0.448219i	$-0.147942\pi$
$433$	9.27451	+	9.27451i	0.445705	+	0.445705i	−0.448219	+	0.893924i	$0.647942\pi$
$434$		0			0
$435$	−8.15757	−	28.1620i	−0.391125	−	1.35027i
$436$		0			0
$437$	19.8318	+	19.8318i	0.948685	+	0.948685i
$438$		0			0
$439$		−	27.7409i		−	1.32400i	−0.749503	−	0.662001i	$-0.769707\pi$
$439$		−	27.7409i		−	1.32400i	0.749503	−	0.662001i	$-0.230293\pi$
$440$		0			0
$441$	9.07649	−	18.5321i	0.432214	−	0.882479i
$442$		0			0
$443$	5.81061	−	5.81061i	0.276070	−	0.276070i	−0.555468	−	0.831538i	$-0.687461\pi$
$443$	5.81061	−	5.81061i	0.276070	−	0.276070i	0.831538	+	0.555468i	$0.187461\pi$
$444$		0			0
$445$	−18.6003	+	10.3960i	−0.881737	+	0.492820i
$446$		0			0
$447$	−3.23274	+	13.9501i	−0.152903	+	0.659818i
$448$		0			0
$449$	4.91400			0.231906			0.115953	−	0.993255i	$-0.463008\pi$
$449$	4.91400			0.231906			0.115953	+	0.993255i	$0.463008\pi$
$450$		0			0
$451$	6.84225			0.322189
$452$		0			0
$453$	−5.26957	+	22.7396i	−0.247586	+	1.06840i
$454$		0			0
$455$	3.13593	−	1.75273i	0.147015	−	0.0821693i
$456$		0			0
$457$	4.15667	−	4.15667i	0.194441	−	0.194441i	−0.603171	−	0.797612i	$-0.706096\pi$
$457$	4.15667	−	4.15667i	0.194441	−	0.194441i	0.797612	+	0.603171i	$0.206096\pi$
$458$		0			0
$459$	17.1466	−	1.75938i	0.800333	−	0.0821206i
$460$		0			0
$461$			21.6439i			1.00806i	0.863687	+	0.504029i	$0.168150\pi$
$461$			21.6439i			1.00806i	−0.863687	+	0.504029i	$0.831850\pi$
$462$		0			0
$463$	18.4154	+	18.4154i	0.855836	+	0.855836i	0.990844	−	0.135009i	$-0.0431062\pi$
$463$	18.4154	+	18.4154i	0.855836	+	0.855836i	−0.135009	+	0.990844i	$0.543106\pi$
$464$		0			0
$465$	11.5365	+	39.8271i	0.534994	+	1.84694i
$466$		0			0
$467$	1.23300	+	1.23300i	0.0570565	+	0.0570565i	0.735059	−	0.678003i	$-0.237154\pi$
$467$	1.23300	+	1.23300i	0.0570565	+	0.0570565i	−0.678003	+	0.735059i	$0.737154\pi$
$468$		0			0
$469$		−	3.36090i		−	0.155192i
$470$		0			0
$471$	4.22443	+	6.77291i	0.194652	+	0.312079i
$472$		0			0
$473$	−6.96331	+	6.96331i	−0.320173	+	0.320173i
$474$		0			0
$475$	−21.4121	−	13.1711i	−0.982454	−	0.604331i
$476$		0			0
$477$	−11.2611	+	3.85677i	−0.515609	+	0.176589i
$478$		0			0
$479$	15.8949			0.726255			0.363128	−	0.931739i	$-0.381709\pi$
$479$	15.8949			0.726255			0.363128	+	0.931739i	$0.381709\pi$
$480$		0			0
$481$	4.03884			0.184155
$482$		0			0
$483$	3.28132	+	0.760398i	0.149305	+	0.0345993i
$484$		0			0
$485$	9.91592	−	35.0460i	0.450259	−	1.59135i
$486$		0			0
$487$	−8.48749	+	8.48749i	−0.384605	+	0.384605i	−0.872758	−	0.488153i	$-0.837671\pi$
$487$	−8.48749	+	8.48749i	−0.384605	+	0.384605i	0.488153	+	0.872758i	$0.337671\pi$
$488$		0			0
$489$	33.3453	−	20.7983i	1.50792	−	0.940531i
$490$		0			0
$491$		−	20.3006i		−	0.916153i	−0.888913	−	0.458077i	$-0.848539\pi$
$491$		−	20.3006i		−	0.916153i	0.888913	−	0.458077i	$-0.151461\pi$
$492$		0			0
$493$	17.7569	+	17.7569i	0.799732	+	0.799732i
$494$		0			0
$495$	−0.678576	−	12.5000i	−0.0304997	−	0.561831i
$496$		0			0
$497$	−2.41910	−	2.41910i	−0.108511	−	0.108511i
$498$		0			0
$499$		−	18.2965i		−	0.819062i	−0.912296	−	0.409531i	$-0.865692\pi$
$499$		−	18.2965i		−	0.819062i	0.912296	−	0.409531i	$-0.134308\pi$
$500$		0			0
$501$	−13.1943	+	8.22964i	−0.589479	+	0.367673i
$502$		0			0
$503$	−7.84860	+	7.84860i	−0.349952	+	0.349952i	−0.860092	−	0.510140i	$-0.829594\pi$
$503$	−7.84860	+	7.84860i	−0.349952	+	0.349952i	0.510140	+	0.860092i	$0.329594\pi$
$504$		0			0
$505$	3.14095	+	5.61968i	0.139770	+	0.250073i
$506$		0			0
$507$	13.9026	+	3.22172i	0.617436	+	0.143082i
$508$		0			0
$509$	20.8709			0.925086			0.462543	−	0.886597i	$-0.346937\pi$
$509$	20.8709			0.925086			0.462543	+	0.886597i	$0.346937\pi$
$510$		0			0
$511$	−3.07608			−0.136078
$512$		0			0
$513$	20.2622	+	16.4910i	0.894599	+	0.728097i
$514$		0			0
$515$	−2.25022	−	0.636679i	−0.0991567	−	0.0280554i
$516$		0			0
$517$	2.08270	−	2.08270i	0.0915968	−	0.0915968i
$518$		0			0
$519$	0.0952776	+	0.152756i	0.00418222	+	0.00670523i
$520$		0			0
$521$			18.1388i			0.794675i	0.917673	+	0.397337i	$0.130066\pi$
$521$			18.1388i			0.794675i	−0.917673	+	0.397337i	$0.869934\pi$
$522$		0			0
$523$	−11.0163	−	11.0163i	−0.481711	−	0.481711i	0.423967	−	0.905678i	$-0.360637\pi$
$523$	−11.0163	−	11.0163i	−0.481711	−	0.481711i	−0.905678	+	0.423967i	$0.860637\pi$
$524$		0			0
$525$	−3.01901	+	0.0187658i	−0.131760	+	0.000819005i
$526$		0			0
$527$	−25.1121	−	25.1121i	−1.09390	−	1.09390i
$528$		0			0
$529$		−	8.11784i		−	0.352949i
$530$		0			0
$531$	−21.4121	−	10.4870i	−0.929205	−	0.455099i
$532$		0			0
$533$	11.9485	−	11.9485i	0.517547	−	0.517547i
$534$		0			0
$535$	33.2569	+	9.40972i	1.43782	+	0.406818i
$536$		0			0
$537$	6.02631	−	26.0051i	0.260055	−	1.12220i
$538$		0			0
$539$	12.8361			0.552890
$540$		0			0
$541$	9.75694			0.419484			0.209742	−	0.977757i	$-0.432738\pi$
$541$	9.75694			0.419484			0.209742	+	0.977757i	$0.432738\pi$
$542$		0			0
$543$	−2.84589	+	12.2808i	−0.122129	+	0.527019i
$544$		0			0
$545$	−11.3415	−	20.2918i	−0.485816	−	0.869207i
$546$		0			0
$547$	−7.77314	+	7.77314i	−0.332356	+	0.332356i	−0.853480	−	0.521125i	$-0.825513\pi$
$547$	−7.77314	+	7.77314i	−0.332356	+	0.332356i	0.521125	+	0.853480i	$0.325513\pi$
$548$		0			0
$549$	−10.4494	−	5.11784i	−0.445971	−	0.218424i
$550$		0			0
$551$			38.0616i			1.62148i
$552$		0			0
$553$	−2.24306	−	2.24306i	−0.0953846	−	0.0953846i
$554$		0			0
$555$	−2.97302	−	1.63751i	−0.126198	−	0.0695083i
$556$		0			0
$557$	8.56383	+	8.56383i	0.362861	+	0.362861i	0.864865	−	0.502004i	$-0.167404\pi$
$557$	8.56383	+	8.56383i	0.362861	+	0.362861i	−0.502004	+	0.864865i	$0.667404\pi$
$558$		0			0
$559$			24.3198i			1.02862i
$560$		0			0
$561$	5.67424	+	9.09734i	0.239567	+	0.384090i
$562$		0			0
$563$	24.4170	−	24.4170i	1.02905	−	1.02905i	0.0294866	−	0.999565i	$-0.490613\pi$
$563$	24.4170	−	24.4170i	1.02905	−	1.02905i	0.999565	−	0.0294866i	$-0.00938725\pi$
$564$		0			0
$565$	−11.0157	+	38.9330i	−0.463435	+	1.63792i
$566$		0			0
$567$	3.11284	+	0.392618i	0.130727	+	0.0164884i
$568$		0			0
$569$	3.07396			0.128867			0.0644335	−	0.997922i	$-0.479476\pi$
$569$	3.07396			0.128867			0.0644335	+	0.997922i	$0.479476\pi$
$570$		0			0
$571$	28.0464			1.17371			0.586854	−	0.809693i	$-0.300366\pi$
$571$	28.0464			1.17371			0.586854	+	0.809693i	$0.300366\pi$
$572$		0			0
$573$	−35.0688	−	8.12669i	−1.46502	−	0.339497i
$574$		0			0
$575$	6.46540	+	27.1320i	0.269626	+	1.13148i
$576$		0			0
$577$	−6.39973	+	6.39973i	−0.266424	+	0.266424i	−0.827658	−	0.561233i	$-0.810327\pi$
$577$	−6.39973	+	6.39973i	−0.266424	+	0.266424i	0.561233	+	0.827658i	$0.310327\pi$
$578$		0			0
$579$	−29.4226	+	18.3516i	−1.22276	+	0.762666i
$580$		0			0
$581$		−	2.59953i		−	0.107847i
$582$		0			0
$583$	−5.23563	−	5.23563i	−0.216838	−	0.216838i
$584$		0			0
$585$	−23.0134	−	20.6435i	−0.951489	−	0.853503i
$586$		0			0
$587$	−4.36893	−	4.36893i	−0.180325	−	0.180325i	0.611172	−	0.791498i	$-0.290698\pi$
$587$	−4.36893	−	4.36893i	−0.180325	−	0.180325i	−0.791498	+	0.611172i	$0.790698\pi$
$588$		0			0
$589$		−	53.8272i		−	2.21791i
$590$		0			0
$591$	−25.6365	+	15.9901i	−1.05455	+	0.657747i
$592$		0			0
$593$	−15.2141	+	15.2141i	−0.624769	+	0.624769i	−0.946747	−	0.321978i	$-0.895652\pi$
$593$	−15.2141	+	15.2141i	−0.624769	+	0.624769i	0.321978	+	0.946747i	$0.395652\pi$
$594$		0			0
$595$	2.25717	−	1.26158i	0.0925351	−	0.0517196i
$596$		0			0
$597$	3.06168	+	0.709500i	0.125306	+	0.0290379i
$598$		0			0
$599$	−3.50546			−0.143229			−0.0716147	−	0.997432i	$-0.522815\pi$
$599$	−3.50546			−0.143229			−0.0716147	+	0.997432i	$0.522815\pi$
$600$		0			0
$601$	−29.9488			−1.22164			−0.610818	−	0.791771i	$-0.709159\pi$
$601$	−29.9488			−1.22164			−0.610818	+	0.791771i	$0.709159\pi$
$602$		0			0
$603$	−27.3621	+	9.37118i	−1.11427	+	0.381624i
$604$		0			0
$605$	−14.6734	+	8.20125i	−0.596559	+	0.333428i
$606$		0			0
$607$	18.9084	−	18.9084i	0.767468	−	0.767468i	−0.210192	−	0.977660i	$-0.567409\pi$
$607$	18.9084	−	18.9084i	0.767468	−	0.767468i	0.977660	+	0.210192i	$0.0674088\pi$
$608$		0			0
$609$	2.41910	+	3.87847i	0.0980269	+	0.157164i
$610$		0			0
$611$		−	7.27395i		−	0.294273i
$612$		0			0
$613$	13.2588	+	13.2588i	0.535517	+	0.535517i	0.922209	−	0.386692i	$-0.126382\pi$
$613$	13.2588	+	13.2588i	0.535517	+	0.535517i	−0.386692	+	0.922209i	$0.626382\pi$
$614$		0			0
$615$	−13.6398	+	3.95098i	−0.550009	+	0.159319i
$616$		0			0
$617$	−22.3244	−	22.3244i	−0.898748	−	0.898748i	0.0965778	−	0.995325i	$-0.469210\pi$
$617$	−22.3244	−	22.3244i	−0.898748	−	0.898748i	−0.995325	+	0.0965778i	$0.969210\pi$
$618$		0			0
$619$		−	33.2821i		−	1.33772i	−0.743389	−	0.668860i	$-0.766783\pi$
$619$		−	33.2821i		−	1.33772i	0.743389	−	0.668860i	$-0.233217\pi$
$620$		0			0
$621$	−2.95865	−	28.8345i	−0.118727	−	1.15709i
$622$		0			0
$623$	2.34905	−	2.34905i	0.0941128	−	0.0941128i
$624$		0			0
$625$	−11.2745	−	22.3133i	−0.450980	−	0.892534i
$626$		0			0
$627$	−3.66867	+	15.8313i	−0.146513	+	0.632241i
$628$		0			0
$629$	2.90706			0.115912
$630$		0			0
$631$	9.40493			0.374404			0.187202	−	0.982321i	$-0.440058\pi$
$631$	9.40493			0.374404			0.187202	+	0.982321i	$0.440058\pi$
$632$		0			0
$633$	−3.10289	+	13.3898i	−0.123329	+	0.532197i
$634$		0			0
$635$	−4.11635	+	14.5485i	−0.163352	+	0.577338i
$636$		0			0
$637$	22.4155	−	22.4155i	0.888133	−	0.888133i
$638$		0			0
$639$	−12.9495	+	26.4398i	−0.512274	+	1.04594i
$640$		0			0
$641$			3.66655i			0.144820i	0.997375	+	0.0724100i	$0.0230690\pi$
$641$			3.66655i			0.144820i	−0.997375	+	0.0724100i	$0.976931\pi$
$642$		0			0
$643$	31.8078	+	31.8078i	1.25438	+	1.25438i	0.953737	+	0.300641i	$0.0972005\pi$
$643$	31.8078	+	31.8078i	1.25438	+	1.25438i	0.300641	+	0.953737i	$0.402800\pi$
$644$		0			0
$645$	9.86023	−	17.9020i	0.388246	−	0.704890i
$646$		0			0
$647$	25.3793	+	25.3793i	0.997761	+	0.997761i	0.999997	−	0.00223615i	$-0.000711788\pi$
$647$	25.3793	+	25.3793i	0.997761	+	0.997761i	−0.00223615	+	0.999997i	$0.500712\pi$
$648$		0			0
$649$		−	14.8309i		−	0.582164i
$650$		0			0
$651$	−3.42112	−	5.48498i	−0.134084	−	0.214973i
$652$		0			0
$653$	−11.2959	+	11.2959i	−0.442045	+	0.442045i	−0.892699	−	0.450654i	$-0.851191\pi$
$653$	−11.2959	+	11.2959i	−0.442045	+	0.442045i	0.450654	+	0.892699i	$0.351191\pi$
$654$		0			0
$655$	−18.0751	−	32.3395i	−0.706254	−	1.26361i
$656$		0			0
$657$	8.57703	+	25.0434i	0.334622	+	0.977034i
$658$		0			0
$659$	−13.9925			−0.545071			−0.272535	−	0.962146i	$-0.587862\pi$
$659$	−13.9925			−0.545071			−0.272535	+	0.962146i	$0.587862\pi$
$660$		0			0
$661$	−6.67794			−0.259742			−0.129871	−	0.991531i	$-0.541456\pi$
$661$	−6.67794			−0.259742			−0.129871	+	0.991531i	$0.541456\pi$
$662$		0			0
$663$	25.7954	+	5.97770i	1.00181	+	0.232155i
$664$		0			0
$665$	3.77118	+	1.06702i	0.146240	+	0.0413772i
$666$		0			0
$667$	29.8609	−	29.8609i	1.15622	−	1.15622i
$668$		0			0
$669$	−35.5894	+	22.1980i	−1.37597	+	0.858225i
$670$		0			0
$671$		−	7.23772i		−	0.279409i
$672$		0			0
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	0.796877	−	0.604141i	$-0.206484\pi$
$673$	5.00000	+	5.00000i	0.192736	+	0.192736i	−0.604141	+	0.796877i	$0.706484\pi$
$674$		0			0
$675$	8.57067	+	24.5264i	0.329885	+	0.944021i
$676$		0			0
$677$	−8.53588	−	8.53588i	−0.328061	−	0.328061i	0.523788	−	0.851849i	$-0.324518\pi$
$677$	−8.53588	−	8.53588i	−0.328061	−	0.328061i	−0.851849	+	0.523788i	$0.824518\pi$
$678$		0			0
$679$			5.67830i			0.217913i
$680$		0			0
$681$	−2.79829	+	1.74536i	−0.107231	+	0.0668824i
$682$		0			0
$683$	−21.7639	+	21.7639i	−0.832774	+	0.832774i	−0.987895	−	0.155121i	$-0.950423\pi$
$683$	−21.7639	+	21.7639i	−0.832774	+	0.832774i	0.155121	+	0.987895i	$0.450423\pi$
$684$		0			0
$685$	−14.4982	−	4.10211i	−0.553946	−	0.156734i
$686$		0			0
$687$	−30.0275	−	6.95843i	−1.14562	−	0.265481i
$688$		0			0
$689$	−18.2858			−0.696633
$690$		0			0
$691$	−33.5876			−1.27773			−0.638866	−	0.769318i	$-0.720596\pi$
$691$	−33.5876			−1.27773			−0.638866	+	0.769318i	$0.720596\pi$
$692$		0			0
$693$	0.632360	+	1.84638i	0.0240214	+	0.0701380i
$694$		0			0
$695$	−17.8744	−	31.9803i	−0.678014	−	1.21308i
$696$		0			0
$697$	8.60027	−	8.60027i	0.325758	−	0.325758i
$698$		0			0
$699$	10.5052	+	16.8426i	0.397342	+	0.637046i
$700$		0			0
$701$		−	23.7356i		−	0.896481i	−0.893913	−	0.448241i	$-0.852051\pi$
$701$		−	23.7356i		−	0.896481i	0.893913	−	0.448241i	$-0.147949\pi$
$702$		0			0
$703$	3.11561	+	3.11561i	0.117508	+	0.117508i
$704$		0			0
$705$	−2.94915	+	5.35441i	−0.111071	+	0.201659i
$706$		0			0
$707$	−0.709718	−	0.709718i	−0.0266917	−	0.0266917i
$708$		0			0
$709$			1.96116i			0.0736531i	0.999322	+	0.0368265i	$0.0117249\pi$
$709$			1.96116i			0.0736531i	−0.999322	+	0.0368265i	$0.988275\pi$
$710$		0			0
$711$	−12.0071	+	24.5158i	−0.450303	+	0.919414i
$712$		0			0
$713$	−42.2298	+	42.2298i	−1.58152	+	1.58152i
$714$		0			0
$715$	5.23563	−	18.5044i	0.195801	−	0.692024i
$716$		0			0
$717$	9.13388	−	39.4151i	0.341111	−	1.47199i
$718$		0			0
$719$	21.9399			0.818222			0.409111	−	0.912485i	$-0.365839\pi$
$719$	21.9399			0.818222			0.409111	+	0.912485i	$0.365839\pi$
$720$		0			0
$721$	0.364591			0.0135781
$722$		0			0
$723$	2.87823	−	12.4203i	0.107042	−	0.461917i
$724$		0			0
$725$	−19.8318	+	32.2403i	−0.736536	+	1.19738i
$726$		0			0
$727$	26.1933	−	26.1933i	0.971456	−	0.971456i	−0.0281474	−	0.999604i	$-0.508961\pi$
$727$	26.1933	−	26.1933i	0.971456	−	0.971456i	0.999604	+	0.0281474i	$0.00896077\pi$
$728$		0			0
$729$	−5.48311	−	26.4374i	−0.203078	−	0.979163i
$730$		0			0
$731$			17.5049i			0.647441i
$732$		0			0
$733$	14.1021	+	14.1021i	0.520873	+	0.520873i	0.917835	−	0.396962i	$-0.129935\pi$
$733$	14.1021	+	14.1021i	0.520873	+	0.520873i	−0.396962	+	0.917835i	$0.629935\pi$
$734$		0			0
$735$	−25.5883	+	7.41205i	−0.943839	+	0.273398i
$736$		0			0
$737$	−12.7215	−	12.7215i	−0.468604	−	0.468604i
$738$		0			0
$739$			6.93987i			0.255287i	0.991820	+	0.127644i	$0.0407414\pi$
$739$			6.93987i			0.255287i	−0.991820	+	0.127644i	$0.959259\pi$
$740$		0			0
$741$	21.2394	+	34.0524i	0.780248	+	1.25095i
$742$		0			0
$743$	26.7075	−	26.7075i	0.979804	−	0.979804i	−0.0199958	−	0.999800i	$-0.506365\pi$
$743$	26.7075	−	26.7075i	0.979804	−	0.979804i	0.999800	+	0.0199958i	$0.00636528\pi$
$744$		0			0
$745$	16.1373	−	9.01942i	0.591223	−	0.330446i
$746$		0			0
$747$	−21.1636	+	7.24826i	−0.774336	+	0.265200i
$748$		0			0
$749$	−5.38843			−0.196889
$750$		0			0
$751$	−17.1325			−0.625174			−0.312587	−	0.949889i	$-0.601196\pi$
$751$	−17.1325			−0.625174			−0.312587	+	0.949889i	$0.601196\pi$
$752$		0			0
$753$	−11.4587	−	2.65540i	−0.417580	−	0.0967681i
$754$		0			0
$755$	26.3047	−	14.7022i	0.957328	−	0.535069i
$756$		0			0
$757$	23.8152	−	23.8152i	0.865578	−	0.865578i	−0.126401	−	0.991979i	$-0.540343\pi$
$757$	23.8152	−	23.8152i	0.865578	−	0.865578i	0.991979	+	0.126401i	$0.0403427\pi$
$758$		0			0
$759$	15.2985	−	9.54209i	0.555302	−	0.346356i
$760$		0			0
$761$		−	3.91818i		−	0.142034i	−0.997475	−	0.0710169i	$-0.977376\pi$
$761$		−	3.91818i		−	0.142034i	0.997475	−	0.0710169i	$-0.0226244\pi$
$762$		0			0
$763$	2.56268	+	2.56268i	0.0927754	+	0.0927754i
$764$		0			0
$765$	−16.5646	−	14.8587i	−0.598893	−	0.537218i
$766$		0			0
$767$	−25.8990	−	25.8990i	−0.935158	−	0.935158i
$768$		0			0
$769$			14.9963i			0.540781i	0.962751	+	0.270390i	$0.0871528\pi$
$769$			14.9963i			0.540781i	−0.962751	+	0.270390i	$0.912847\pi$
$770$		0			0
$771$	−14.9305	+	9.31252i	−0.537708	+	0.335382i
$772$		0			0
$773$	12.7950	−	12.7950i	0.460205	−	0.460205i	−0.438518	−	0.898723i	$-0.644496\pi$
$773$	12.7950	−	12.7950i	0.460205	−	0.460205i	0.898723	+	0.438518i	$0.144496\pi$
$774$		0			0
$775$	28.0464	−	45.5947i	1.00746	−	1.63781i
$776$		0			0
$777$	0.515501	+	0.119460i	0.0184935	+	0.00428560i
$778$		0			0
$779$	18.4345			0.660484
$780$		0			0
$781$	−18.3133			−0.655303
$782$		0			0
$783$	24.8307	−	30.5090i	0.887376	−	1.09030i
$784$		0			0
$785$	2.80561	−	9.91592i	0.100137	−	0.353914i
$786$		0			0
$787$	−16.3592	+	16.3592i	−0.583141	+	0.583141i	−0.935765	−	0.352624i	$-0.885290\pi$
$787$	−16.3592	+	16.3592i	−0.583141	+	0.583141i	0.352624	+	0.935765i	$0.385290\pi$
$788$		0			0
$789$	0.275113	+	0.441081i	0.00979430	+	0.0157029i
$790$		0			0
$791$		−	6.30810i		−	0.224290i
$792$		0			0
$793$	−12.6391	−	12.6391i	−0.448828	−	0.448828i
$794$		0			0
$795$	13.4603	+	7.41379i	0.477388	+	0.262940i
$796$		0			0
$797$	31.8538	+	31.8538i	1.12832	+	1.12832i	0.990450	+	0.137870i	$0.0440257\pi$
$797$	31.8538	+	31.8538i	1.12832	+	1.12832i	0.137870	+	0.990450i	$0.455974\pi$
$798$		0			0
$799$		−	5.23563i		−	0.185223i
$800$		0			0
$801$	−25.6742	−	12.5745i	−0.907155	−	0.444299i
$802$		0			0
$803$	−11.6435	+	11.6435i	−0.410888	+	0.410888i
$804$		0			0
$805$	−2.12153	−	3.79577i	−0.0747741	−	0.133783i
$806$		0			0
$807$	−2.68749	+	11.5972i	−0.0946040	+	0.408241i
$808$		0			0
$809$	−45.2749			−1.59178			−0.795890	−	0.605441i	$-0.792997\pi$
$809$	−45.2749			−1.59178			−0.795890	+	0.605441i	$0.792997\pi$
$810$		0			0
$811$	36.1898			1.27080			0.635398	−	0.772185i	$-0.280836\pi$
$811$	36.1898			1.27080			0.635398	+	0.772185i	$0.280836\pi$
$812$		0			0
$813$	2.59414	−	11.1944i	0.0909805	−	0.392605i
$814$		0			0
$815$	−48.8193	−	13.8130i	−1.71007	−	0.483847i
$816$		0			0
$817$	−18.7606	+	18.7606i	−0.656351	+	0.656351i
$818$		0			0
$819$	4.32858	+	2.12002i	0.151253	+	0.0740794i
$820$		0			0
$821$		−	52.1768i		−	1.82098i	−0.413528	−	0.910492i	$-0.635704\pi$
$821$		−	52.1768i		−	1.82098i	0.413528	−	0.910492i	$-0.364296\pi$
$822$		0			0
$823$	−2.03105	−	2.03105i	−0.0707980	−	0.0707980i	0.670821	−	0.741619i	$-0.265942\pi$
$823$	−2.03105	−	2.03105i	−0.0707980	−	0.0707980i	−0.741619	+	0.670821i	$0.765942\pi$
$824$		0			0
$825$	−11.3564	+	11.4985i	−0.395379	+	0.400325i
$826$		0			0
$827$	11.7200	+	11.7200i	0.407546	+	0.407546i	0.880882	−	0.473336i	$-0.156950\pi$
$827$	11.7200	+	11.7200i	0.407546	+	0.407546i	−0.473336	+	0.880882i	$0.656950\pi$
$828$		0			0
$829$		−	17.3609i		−	0.602969i	−0.953471	−	0.301484i	$-0.902518\pi$
$829$		−	17.3609i		−	0.602969i	0.953471	−	0.301484i	$-0.0974821\pi$
$830$		0			0
$831$	−17.1876	−	27.5564i	−0.596233	−	0.955922i
$832$		0			0
$833$	16.1341	−	16.1341i	0.559015	−	0.559015i
$834$		0			0
$835$	19.3172	+	5.46563i	0.668501	+	0.189146i
$836$		0			0
$837$	−35.1159	+	43.1462i	−1.21378	+	1.49135i
$838$		0			0
$839$	25.8990			0.894132			0.447066	−	0.894501i	$-0.352469\pi$
$839$	25.8990			0.894132			0.447066	+	0.894501i	$0.352469\pi$
$840$		0			0
$841$	28.3097			0.976195
$842$		0			0
$843$	3.52935	+	0.817876i	0.121557	+	0.0281692i
$844$		0			0
$845$	−8.98869	−	16.0823i	−0.309220	−	0.553247i
$846$		0			0
$847$	1.85313	−	1.85313i	0.0636741	−	0.0636741i
$848$		0			0
$849$	26.6670	−	16.6329i	0.915210	−	0.570840i
$850$		0			0
$851$		−	4.88866i		−	0.167581i
$852$		0			0
$853$	−30.3328	−	30.3328i	−1.03857	−	1.03857i	−0.999226	−	0.0393485i	$-0.987472\pi$
$853$	−30.3328	−	30.3328i	−1.03857	−	1.03857i	−0.0393485	−	0.999226i	$-0.512528\pi$
$854$		0			0
$855$	−1.82823	−	33.6775i	−0.0625241	−	1.15175i
$856$		0			0
$857$	4.76470	+	4.76470i	0.162759	+	0.162759i	0.783788	−	0.621029i	$-0.213285\pi$
$857$	4.76470	+	4.76470i	0.162759	+	0.162759i	−0.621029	+	0.783788i	$0.713285\pi$
$858$		0			0
$859$			16.3843i			0.559026i	0.960142	+	0.279513i	$0.0901731\pi$
$859$			16.3843i			0.559026i	−0.960142	+	0.279513i	$0.909827\pi$
$860$		0			0
$861$	1.87847	−	1.17165i	0.0640181	−	0.0399297i
$862$		0			0
$863$	−3.88956	+	3.88956i	−0.132402	+	0.132402i	−0.770202	−	0.637800i	$-0.779845\pi$
$863$	−3.88956	+	3.88956i	−0.132402	+	0.132402i	0.637800	+	0.770202i	$0.279845\pi$
$864$		0			0
$865$	0.0632776	−	0.223643i	0.00215150	−	0.00760409i
$866$		0			0
$867$	−10.1178	−	2.34465i	−0.343618	−	0.0796285i
$868$		0			0
$869$	−16.9807			−0.576030
$870$		0			0
$871$	−44.4308			−1.50548
$872$		0			0
$873$	46.2288	−	15.8328i	1.56461	−	0.535858i
$874$		0			0
$875$	2.63844	+	2.86878i	0.0891955	+	0.0969826i
$876$		0			0
$877$	−25.7375	+	25.7375i	−0.869094	+	0.869094i	−0.992372	−	0.123278i	$-0.960659\pi$
$877$	−25.7375	+	25.7375i	−0.869094	+	0.869094i	0.123278	+	0.992372i	$0.460659\pi$
$878$		0			0
$879$	18.9355	+	30.3587i	0.638679	+	1.02398i
$880$		0			0
$881$			37.8660i			1.27574i	0.770145	+	0.637869i	$0.220184\pi$
$881$			37.8660i			1.27574i	−0.770145	+	0.637869i	$0.779816\pi$
$882$		0			0
$883$	2.77536	+	2.77536i	0.0933982	+	0.0933982i	0.752262	−	0.658864i	$-0.228963\pi$
$883$	2.77536	+	2.77536i	0.0933982	+	0.0933982i	−0.658864	+	0.752262i	$0.728963\pi$
$884$		0			0
$885$	8.56394	+	29.5649i	0.287874	+	0.993814i
$886$		0			0
$887$	25.3793	+	25.3793i	0.852152	+	0.852152i	0.990398	−	0.138246i	$-0.0441465\pi$
$887$	25.3793	+	25.3793i	0.852152	+	0.852152i	−0.138246	+	0.990398i	$0.544146\pi$
$888$		0			0
$889$		−	2.35721i		−	0.0790582i
$890$		0			0
$891$	13.2687	−	10.2965i	0.444519	−	0.344945i
$892$		0			0
$893$	5.61123	−	5.61123i	0.187772	−	0.187772i
$894$		0			0
$895$	−30.0823	+	16.8136i	−1.00554	+	0.562015i
$896$		0			0
$897$	10.0524	−	43.3788i	0.335640	−	1.44838i
$898$		0			0
$899$	−81.0481			−2.70311
$900$		0			0
$901$	−13.1617			−0.438480
$902$		0			0
$903$	−0.719326	+	3.10408i	−0.0239377	+	0.103297i
$904$		0			0
$905$	14.2062	−	7.94011i	0.472230	−	0.263938i
$906$		0			0
$907$	25.4586	−	25.4586i	0.845339	−	0.845339i	−0.144209	−	0.989547i	$-0.546064\pi$
$907$	25.4586	−	25.4586i	0.845339	−	0.845339i	0.989547	+	0.144209i	$0.0460637\pi$
$908$		0			0
$909$	−3.79913	+	7.75694i	−0.126009	+	0.257281i
$910$		0			0
$911$			45.3355i			1.50203i	0.660283	+	0.751017i	$0.270436\pi$
$911$			45.3355i			1.50203i	−0.660283	+	0.751017i	$0.729564\pi$
$912$		0			0
$913$	−9.83963	−	9.83963i	−0.325644	−	0.325644i
$914$		0			0
$915$	4.17934	+	14.4281i	0.138165	+	0.476979i
$916$		0			0
$917$	4.08419	+	4.08419i	0.134872	+	0.134872i
$918$		0			0
$919$		−	22.3681i		−	0.737857i	−0.929458	−	0.368929i	$-0.879725\pi$
$919$		−	22.3681i		−	0.737857i	0.929458	−	0.368929i	$-0.120275\pi$
$920$		0			0
$921$	7.59775	+	12.1812i	0.250355	+	0.401386i
$922$		0			0
$923$	−31.9803	+	31.9803i	−1.05264	+	1.05264i
$924$		0			0
$925$	1.01573	+	4.26248i	0.0333968	+	0.140149i
$926$		0			0
$927$	−1.01659	−	2.96825i	−0.0333891	−	0.0974901i
$928$		0			0
$929$	30.2055			0.991009			0.495504	−	0.868605i	$-0.334983\pi$
$929$	30.2055			0.991009			0.495504	+	0.868605i	$0.334983\pi$
$930$		0			0
$931$	34.5832			1.13342
$932$		0			0
$933$	−16.5588	−	3.83726i	−0.542110	−	0.125626i
$934$		0			0
$935$	3.76849	−	13.3190i	0.123243	−	0.435579i
$936$		0			0
$937$	−18.4312	+	18.4312i	−0.602121	+	0.602121i	−0.940875	−	0.338754i	$-0.889994\pi$
$937$	−18.4312	+	18.4312i	−0.602121	+	0.602121i	0.338754	+	0.940875i	$0.389994\pi$
$938$		0			0
$939$	−2.33094	+	1.45386i	−0.0760672	+	0.0474450i
$940$		0			0
$941$			53.1392i			1.73229i	0.499794	+	0.866144i	$0.333409\pi$
$941$			53.1392i			1.73229i	−0.499794	+	0.866144i	$0.666591\pi$
$942$		0			0
$943$	−14.4626	−	14.4626i	−0.470968	−	0.470968i
$944$		0			0
$945$	−2.32676	−	3.31554i	−0.0756894	−	0.107854i
$946$		0			0
$947$	7.31075	+	7.31075i	0.237568	+	0.237568i	0.815842	−	0.578275i	$-0.196274\pi$
$947$	7.31075	+	7.31075i	0.237568	+	0.237568i	−0.578275	+	0.815842i	$0.696274\pi$
$948$		0			0
$949$			40.6655i			1.32006i
$950$		0			0
$951$	−4.87499	+	3.04065i	−0.158082	+	0.0985999i
$952$		0			0
$953$	21.2574	−	21.2574i	0.688595	−	0.688595i	−0.273326	−	0.961921i	$-0.588124\pi$
$953$	21.2574	−	21.2574i	0.688595	−	0.688595i	0.961921	+	0.273326i	$0.0881239\pi$
$954$		0			0
$955$	22.6737	+	40.5670i	0.733702	+	1.31272i
$956$		0			0
$957$	23.8373	+	5.52394i	0.770550	+	0.178564i
$958$		0			0
$959$	2.34905			0.0758549
$960$		0			0
$961$	83.6193			2.69740
$962$		0			0
$963$	15.0245	+	43.8689i	0.484159	+	1.41366i
$964$		0			0
$965$	43.0763	+	12.1880i	1.38667	+	0.392346i
$966$		0			0
$967$	23.5707	−	23.5707i	0.757983	−	0.757983i	−0.217972	−	0.975955i	$-0.569944\pi$
$967$	23.5707	−	23.5707i	0.757983	−	0.757983i	0.975955	+	0.217972i	$0.0699441\pi$
$968$		0			0
$969$	15.2876	+	24.5102i	0.491109	+	0.787381i
$970$		0			0
$971$		−	52.0903i		−	1.67166i	−0.548990	−	0.835829i	$-0.684987\pi$
$971$		−	52.0903i		−	1.67166i	0.548990	−	0.835829i	$-0.315013\pi$
$972$		0			0
$973$	4.03884	+	4.03884i	0.129479	+	0.129479i
$974$		0			0
$975$	0.248082	+	39.9110i	0.00794497	+	1.27818i
$976$		0			0
$977$	−20.0523	−	20.0523i	−0.641531	−	0.641531i	0.309401	−	0.950932i	$-0.399871\pi$
$977$	−20.0523	−	20.0523i	−0.641531	−	0.641531i	−0.950932	+	0.309401i	$0.899871\pi$
$978$		0			0
$979$		−	17.7831i		−	0.568349i
$980$		0			0
$981$	13.7181	−	28.0092i	0.437985	−	0.894263i
$982$		0			0
$983$	19.2430	−	19.2430i	0.613757	−	0.613757i	−0.330166	−	0.943923i	$-0.607105\pi$
$983$	19.2430	−	19.2430i	0.613757	−	0.613757i	0.943923	+	0.330166i	$0.107105\pi$
$984$		0			0
$985$	37.5333	+	10.6197i	1.19591	+	0.338371i
$986$		0			0
$987$	0.215147	−	0.928418i	0.00684822	−	0.0295519i
$988$		0			0
$989$	29.4370			0.936043
$990$		0			0
$991$	−0.207885			−0.00660369			−0.00330184	−	0.999995i	$-0.501051\pi$
$991$	−0.207885			−0.00660369			−0.00330184	+	0.999995i	$0.501051\pi$
$992$		0			0
$993$	−8.45375	+	36.4802i	−0.268272	+	1.15766i
$994$		0			0
$995$	−1.97952	−	3.54170i	−0.0627551	−	0.112279i
$996$		0			0
$997$	11.4630	−	11.4630i	0.363037	−	0.363037i	−0.501893	−	0.864930i	$-0.667363\pi$
$997$	11.4630	−	11.4630i	0.363037	−	0.363037i	0.864930	+	0.501893i	$0.167363\pi$
$998$		0			0
$999$	−0.464809	−	4.52995i	−0.0147059	−	0.143321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.2.v.d.353.7	yes	24
3.2	odd	2	inner	480.2.v.d.353.1	yes	24
4.3	odd	2	inner	480.2.v.d.353.6	yes	24
5.2	odd	4	inner	480.2.v.d.257.1	✓	24
8.3	odd	2		960.2.v.n.833.7		24
8.5	even	2		960.2.v.n.833.6		24
12.11	even	2	inner	480.2.v.d.353.12	yes	24
15.2	even	4	inner	480.2.v.d.257.7	yes	24
20.7	even	4	inner	480.2.v.d.257.12	yes	24
24.5	odd	2		960.2.v.n.833.12		24
24.11	even	2		960.2.v.n.833.1		24
40.27	even	4		960.2.v.n.257.1		24
40.37	odd	4		960.2.v.n.257.12		24
60.47	odd	4	inner	480.2.v.d.257.6	yes	24
120.77	even	4		960.2.v.n.257.6		24
120.107	odd	4		960.2.v.n.257.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.v.d.257.1	✓	24	5.2	odd	4	inner
480.2.v.d.257.6	yes	24	60.47	odd	4	inner
480.2.v.d.257.7	yes	24	15.2	even	4	inner
480.2.v.d.257.12	yes	24	20.7	even	4	inner
480.2.v.d.353.1	yes	24	3.2	odd	2	inner
480.2.v.d.353.6	yes	24	4.3	odd	2	inner
480.2.v.d.353.7	yes	24	1.1	even	1	trivial
480.2.v.d.353.12	yes	24	12.11	even	2	inner
960.2.v.n.257.1		24	40.27	even	4
960.2.v.n.257.6		24	120.77	even	4
960.2.v.n.257.7		24	120.107	odd	4
960.2.v.n.257.12		24	40.37	odd	4
960.2.v.n.833.1		24	24.11	even	2
960.2.v.n.833.6		24	8.5	even	2
960.2.v.n.833.7		24	8.3	odd	2
960.2.v.n.833.12		24	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.391016 - 1.68734i) q^{3} +(-1.95188 + 1.09094i) q^{5} +(0.246506 - 0.246506i) q^{7} +(-2.69421 - 1.31955i) q^{9} +O(q^{10})\)	\(q+(0.391016 - 1.68734i) q^{3} +(-1.95188 + 1.09094i) q^{5} +(0.246506 - 0.246506i) q^{7} +(-2.69421 - 1.31955i) q^{9} -1.86613i q^{11} +(-3.25879 - 3.25879i) q^{13} +(1.07757 + 3.72006i) q^{15} +(-2.34560 - 2.34560i) q^{17} -5.02774i q^{19} +(-0.319551 - 0.512326i) q^{21} +(-3.94448 + 3.94448i) q^{23} +(2.61968 - 4.25879i) q^{25} +(-3.28001 + 4.03008i) q^{27} -7.57031 q^{29} +10.7060 q^{31} +(-3.14878 - 0.729685i) q^{33} +(-0.212226 + 0.750074i) q^{35} +(-0.619684 + 0.619684i) q^{37} +(-6.77291 + 4.22443i) q^{39} +3.66655i q^{41} +(-3.73142 - 3.73142i) q^{43} +(6.69834 - 0.363628i) q^{45} +(1.11605 + 1.11605i) q^{47} +6.87847i q^{49} +(-4.87499 + 3.04065i) q^{51} +(2.80561 - 2.80561i) q^{53} +(2.03584 + 3.64246i) q^{55} +(-8.48350 - 1.96593i) q^{57} +7.94743 q^{59} +3.87847 q^{61} +(-0.989416 + 0.338862i) q^{63} +(9.91592 + 2.80561i) q^{65} +(6.81708 - 6.81708i) q^{67} +(5.11331 + 8.19802i) q^{69} -9.81356i q^{71} +(-6.23937 - 6.23937i) q^{73} +(-6.16167 - 6.08554i) q^{75} +(-0.460011 - 0.460011i) q^{77} -9.09942i q^{79} +(5.51757 + 7.11030i) q^{81} +(5.27276 - 5.27276i) q^{83} +(7.13726 + 2.01942i) q^{85} +(-2.96011 + 12.7737i) q^{87} +9.52940 q^{89} -1.60662 q^{91} +(4.18623 - 18.0647i) q^{93} +(5.48498 + 9.81356i) q^{95} +(-11.5176 + 11.5176i) q^{97} +(-2.46245 + 5.02774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 16 q^{13} + 16 q^{21} + 16 q^{25} + 24 q^{33} + 32 q^{37} + 32 q^{45} + 16 q^{57} - 48 q^{61} - 56 q^{73} - 56 q^{81} - 64 q^{85} - 96 q^{93} - 88 q^{97}+O(q^{100}) \) 24 * q + 16 * q^13 + 16 * q^21 + 16 * q^25 + 24 * q^33 + 32 * q^37 + 32 * q^45 + 16 * q^57 - 48 * q^61 - 56 * q^73 - 56 * q^81 - 64 * q^85 - 96 * q^93 - 88 * q^97

Introduction

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