LMFDB - Embedded newform 1170.2.cu.c.1151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.cu (of order $12$, degree $4$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1151.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1170.1151
Dual form			1170.2.cu.c.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.866025 - 0.232051i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.866025 - 0.232051i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{10} +(0.965926 - 0.258819i) q^{11} +(-2.59808 - 2.50000i) q^{13} +0.896575i q^{14} +(0.500000 - 0.866025i) q^{16} +(2.44949 + 4.24264i) q^{17} +(0.232051 - 0.866025i) q^{19} +(0.258819 - 0.965926i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.63896 + 4.57081i) q^{23} -1.00000i q^{25} +(-1.74238 + 3.15660i) q^{26} +(0.866025 - 0.232051i) q^{28} +(2.44949 + 1.41421i) q^{29} +(1.26795 + 1.26795i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.46410 - 3.46410i) q^{34} +(0.776457 - 0.448288i) q^{35} +(1.59808 + 5.96410i) q^{37} -0.896575 q^{38} -1.00000 q^{40} +(1.03528 + 3.86370i) q^{41} +(-3.92820 + 2.26795i) q^{43} +(-0.707107 + 0.707107i) q^{44} +(5.09808 + 1.36603i) q^{46} +(7.02030 + 7.02030i) q^{47} +(-5.36603 - 3.09808i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.8666i q^{53} +(-0.500000 + 0.866025i) q^{55} +(-0.448288 - 0.776457i) q^{56} +(0.732051 - 2.73205i) q^{58} +(-1.03528 + 3.86370i) q^{59} +(2.46410 + 4.26795i) q^{61} +(0.896575 - 1.55291i) q^{62} +1.00000i q^{64} +(3.60488 - 0.0693504i) q^{65} +(10.1962 - 2.73205i) q^{67} +(-4.24264 - 2.44949i) q^{68} +(-0.633975 - 0.633975i) q^{70} +(-1.93185 - 0.517638i) q^{71} +(2.53590 - 2.53590i) q^{73} +(5.34727 - 3.08725i) q^{74} +(0.232051 + 0.866025i) q^{76} -0.896575 q^{77} +2.00000 q^{79} +(0.258819 + 0.965926i) q^{80} +(3.46410 - 2.00000i) q^{82} +(-9.52056 + 9.52056i) q^{83} +(-4.73205 - 1.26795i) q^{85} +(3.20736 + 3.20736i) q^{86} +(0.866025 + 0.500000i) q^{88} +(11.7112 - 3.13801i) q^{89} +(1.66987 + 2.76795i) q^{91} -5.27792i q^{92} +(4.96410 - 8.59808i) q^{94} +(0.448288 + 0.776457i) q^{95} +(-1.66025 + 6.19615i) q^{97} +(-1.60368 + 5.98502i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{16} - 12 q^{19} - 4 q^{22} + 24 q^{31} - 8 q^{37} - 8 q^{40} + 24 q^{43} + 20 q^{46} - 36 q^{49} + 28 q^{52} - 4 q^{55} - 8 q^{58} - 8 q^{61} + 40 q^{67} - 12 q^{70} + 48 q^{73} - 12 q^{76} + 16 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{94} + 56 q^{97}+O(q^{100}) $ 8 * q + 4 * q^16 - 12 * q^19 - 4 * q^22 + 24 * q^31 - 8 * q^37 - 8 * q^40 + 24 * q^43 + 20 * q^46 - 36 * q^49 + 28 * q^52 - 4 * q^55 - 8 * q^58 - 8 * q^61 + 40 * q^67 - 12 * q^70 + 48 * q^73 - 12 * q^76 + 16 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$	−0.866025	−	0.232051i	−0.327327	−	0.0877070i	0.0914134	−	0.995813i	$-0.470862\pi$
$7$	−0.866025	−	0.232051i	−0.327327	−	0.0877070i	−0.418740	+	0.908106i	$0.637528\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	0.965926	−	0.258819i	0.291238	−	0.0780369i	−0.110242	−	0.993905i	$-0.535163\pi$
$11$	0.965926	−	0.258819i	0.291238	−	0.0780369i	0.401480	+	0.915868i	$0.368496\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$			0.896575i			0.239620i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.44949	+	4.24264i	0.594089	+	1.02899i	0.993675	+	0.112296i	$0.0358205\pi$
$17$	2.44949	+	4.24264i	0.594089	+	1.02899i	−0.399586	+	0.916696i	$0.630846\pi$
$18$		0			0
$19$	0.232051	−	0.866025i	0.0532361	−	0.198680i	−0.934186	−	0.356787i	$-0.883872\pi$
$19$	0.232051	−	0.866025i	0.0532361	−	0.198680i	0.987422	+	0.158107i	$0.0505390\pi$
$20$	0.258819	−	0.965926i	0.0578737	−	0.215988i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−2.63896	+	4.57081i	−0.550261	+	0.953080i	0.447995	+	0.894036i	$0.352138\pi$
$23$	−2.63896	+	4.57081i	−0.550261	+	0.953080i	−0.998255	+	0.0590435i	$0.981195\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−1.74238	+	3.15660i	−0.341709	+	0.619060i
$27$		0			0
$28$	0.866025	−	0.232051i	0.163663	−	0.0438535i
$29$	2.44949	+	1.41421i	0.454859	+	0.262613i	0.709880	−	0.704323i	$-0.248749\pi$
$29$	2.44949	+	1.41421i	0.454859	+	0.262613i	−0.255021	+	0.966935i	$0.582082\pi$
$30$		0			0
$31$	1.26795	+	1.26795i	0.227730	+	0.227730i	0.811744	−	0.584014i	$-0.198519\pi$
$31$	1.26795	+	1.26795i	0.227730	+	0.227730i	−0.584014	+	0.811744i	$0.698519\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	3.46410	−	3.46410i	0.594089	−	0.594089i
$35$	0.776457	−	0.448288i	0.131245	−	0.0757745i
$36$		0			0
$37$	1.59808	+	5.96410i	0.262722	+	0.980492i	0.963630	+	0.267240i	$0.0861118\pi$
$37$	1.59808	+	5.96410i	0.262722	+	0.980492i	−0.700908	+	0.713252i	$0.747222\pi$
$38$	−0.896575			−0.145444
$39$		0			0
$40$	−1.00000			−0.158114
$41$	1.03528	+	3.86370i	0.161683	+	0.603409i	0.998440	+	0.0558348i	$0.0177820\pi$
$41$	1.03528	+	3.86370i	0.161683	+	0.603409i	−0.836757	+	0.547574i	$0.815551\pi$
$42$		0			0
$43$	−3.92820	+	2.26795i	−0.599045	+	0.345859i	−0.768666	−	0.639650i	$-0.779079\pi$
$43$	−3.92820	+	2.26795i	−0.599045	+	0.345859i	0.169621	+	0.985509i	$0.445746\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$		0			0
$46$	5.09808	+	1.36603i	0.751670	+	0.201409i
$47$	7.02030	+	7.02030i	1.02402	+	1.02402i	0.999704	+	0.0243115i	$0.00773937\pi$
$47$	7.02030	+	7.02030i	1.02402	+	1.02402i	0.0243115	+	0.999704i	$0.492261\pi$
$48$		0			0
$49$	−5.36603	−	3.09808i	−0.766575	−	0.442582i
$50$	−0.965926	+	0.258819i	−0.136603	+	0.0366025i
$51$		0			0
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$			12.8666i			1.76737i	0.468085	+	0.883683i	$0.344944\pi$
$53$			12.8666i			1.76737i	−0.468085	+	0.883683i	$0.655056\pi$
$54$		0			0
$55$	−0.500000	+	0.866025i	−0.0674200	+	0.116775i
$56$	−0.448288	−	0.776457i	−0.0599050	−	0.103758i
$57$		0			0
$58$	0.732051	−	2.73205i	0.0961230	−	0.358736i
$59$	−1.03528	+	3.86370i	−0.134781	+	0.503011i	0.865217	+	0.501397i	$0.167180\pi$
$59$	−1.03528	+	3.86370i	−0.134781	+	0.503011i	−0.999999	+	0.00161411i	$0.999486\pi$
$60$		0			0
$61$	2.46410	+	4.26795i	0.315496	+	0.546455i	0.979543	−	0.201236i	$-0.0644958\pi$
$61$	2.46410	+	4.26795i	0.315496	+	0.546455i	−0.664047	+	0.747691i	$0.731162\pi$
$62$	0.896575	−	1.55291i	0.113865	−	0.197220i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	3.60488	−	0.0693504i	0.447131	−	0.00860185i
$66$		0			0
$67$	10.1962	−	2.73205i	1.24566	−	0.333773i	0.425000	−	0.905193i	$-0.360274\pi$
$67$	10.1962	−	2.73205i	1.24566	−	0.333773i	0.820658	+	0.571420i	$0.193607\pi$
$68$	−4.24264	−	2.44949i	−0.514496	−	0.297044i
$69$		0			0
$70$	−0.633975	−	0.633975i	−0.0757745	−	0.0757745i
$71$	−1.93185	−	0.517638i	−0.229269	−	0.0614323i	0.142356	−	0.989816i	$-0.454532\pi$
$71$	−1.93185	−	0.517638i	−0.229269	−	0.0614323i	−0.371624	+	0.928383i	$0.621199\pi$
$72$		0			0
$73$	2.53590	−	2.53590i	0.296804	−	0.296804i	−0.542956	−	0.839761i	$-0.682695\pi$
$73$	2.53590	−	2.53590i	0.296804	−	0.296804i	0.839761	+	0.542956i	$0.182695\pi$
$74$	5.34727	−	3.08725i	0.621607	−	0.358885i
$75$		0			0
$76$	0.232051	+	0.866025i	0.0266181	+	0.0993399i
$77$	−0.896575			−0.102174
$78$		0			0
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$	0.258819	+	0.965926i	0.0289368	+	0.107994i
$81$		0			0
$82$	3.46410	−	2.00000i	0.382546	−	0.220863i
$83$	−9.52056	+	9.52056i	−1.04502	+	1.04502i	−0.0460792	+	0.998938i	$0.514673\pi$
$83$	−9.52056	+	9.52056i	−1.04502	+	1.04502i	−0.998938	+	0.0460792i	$0.985327\pi$
$84$		0			0
$85$	−4.73205	−	1.26795i	−0.513263	−	0.137528i
$86$	3.20736	+	3.20736i	0.345859	+	0.345859i
$87$		0			0
$88$	0.866025	+	0.500000i	0.0923186	+	0.0533002i
$89$	11.7112	−	3.13801i	1.24139	−	0.332629i	0.422384	−	0.906417i	$-0.361193\pi$
$89$	11.7112	−	3.13801i	1.24139	−	0.332629i	0.819004	+	0.573788i	$0.194527\pi$
$90$		0			0
$91$	1.66987	+	2.76795i	0.175050	+	0.290160i
$92$		−	5.27792i		−	0.550261i
$93$		0			0
$94$	4.96410	−	8.59808i	0.512008	−	0.886824i
$95$	0.448288	+	0.776457i	0.0459934	+	0.0796628i
$96$		0			0
$97$	−1.66025	+	6.19615i	−0.168573	+	0.629124i	0.828984	+	0.559272i	$0.188919\pi$
$97$	−1.66025	+	6.19615i	−0.168573	+	0.629124i	−0.997557	+	0.0698518i	$0.977747\pi$
$98$	−1.60368	+	5.98502i	−0.161996	+	0.604579i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.82843	−	4.89898i	0.281439	−	0.487467i	−0.690300	−	0.723523i	$-0.742522\pi$
$101$	2.82843	−	4.89898i	0.281439	−	0.487467i	0.971739	+	0.236056i	$0.0758550\pi$
$102$		0			0
$103$			0.660254i			0.0650568i	0.999471	+	0.0325284i	$0.0103559\pi$
$103$			0.660254i			0.0650568i	−0.999471	+	0.0325284i	$0.989644\pi$
$104$	−0.0693504	−	3.60488i	−0.00680036	−	0.353488i
$105$		0			0
$106$	12.4282	−	3.33013i	1.20713	−	0.323451i
$107$	−10.6945	−	6.17449i	−1.03388	−	0.596911i	−0.115786	−	0.993274i	$-0.536939\pi$
$107$	−10.6945	−	6.17449i	−1.03388	−	0.596911i	−0.918094	+	0.396363i	$0.870272\pi$
$108$		0			0
$109$	3.26795	+	3.26795i	0.313013	+	0.313013i	0.846076	−	0.533063i	$-0.178959\pi$
$109$	3.26795	+	3.26795i	0.313013	+	0.313013i	−0.533063	+	0.846076i	$0.678959\pi$
$110$	0.965926	+	0.258819i	0.0920974	+	0.0246774i
$111$		0			0
$112$	−0.633975	+	0.633975i	−0.0599050	+	0.0599050i
$113$	−1.79315	+	1.03528i	−0.168685	+	0.0973906i	−0.581966	−	0.813213i	$-0.697716\pi$
$113$	−1.79315	+	1.03528i	−0.168685	+	0.0973906i	0.413280	+	0.910604i	$0.364383\pi$
$114$		0			0
$115$	−1.36603	−	5.09808i	−0.127383	−	0.475398i
$116$	−2.82843			−0.262613
$117$		0			0
$118$	4.00000			0.368230
$119$	−1.13681	−	4.24264i	−0.104211	−	0.388922i
$120$		0			0
$121$	−8.66025	+	5.00000i	−0.787296	+	0.454545i
$122$	3.48477	−	3.48477i	0.315496	−	0.315496i
$123$		0			0
$124$	−1.73205	−	0.464102i	−0.155543	−	0.0416776i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	10.9641	+	6.33013i	0.972907	+	0.561708i	0.900121	−	0.435640i	$-0.143478\pi$
$127$	10.9641	+	6.33013i	0.972907	+	0.561708i	0.0727855	+	0.997348i	$0.476811\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−1.00000	−	3.46410i	−0.0877058	−	0.303822i
$131$		−	4.38134i		−	0.382800i	−0.981512	−	0.191400i	$-0.938697\pi$
$131$		−	4.38134i		−	0.382800i	0.981512	−	0.191400i	$-0.0613027\pi$
$132$		0			0
$133$	−0.401924	+	0.696152i	−0.0348512	+	0.0603641i
$134$	−5.27792	−	9.14162i	−0.455943	−	0.789716i
$135$		0			0
$136$	−1.26795	+	4.73205i	−0.108726	+	0.405770i
$137$	2.07055	−	7.72741i	0.176899	−	0.660197i	−0.819321	−	0.573335i	$-0.805649\pi$
$137$	2.07055	−	7.72741i	0.176899	−	0.660197i	0.996220	−	0.0868620i	$-0.0276839\pi$
$138$		0			0
$139$	−8.33013	−	14.4282i	−0.706552	−	1.22378i	−0.966128	−	0.258062i	$-0.916916\pi$
$139$	−8.33013	−	14.4282i	−0.706552	−	1.22378i	0.259576	−	0.965723i	$-0.416417\pi$
$140$	−0.448288	+	0.776457i	−0.0378872	+	0.0656226i
$141$		0			0
$142$			2.00000i			0.167836i
$143$	−3.15660	−	1.74238i	−0.263968	−	0.145705i
$144$		0			0
$145$	−2.73205	+	0.732051i	−0.226884	+	0.0607935i
$146$	−3.10583	−	1.79315i	−0.257040	−	0.148402i
$147$		0			0
$148$	−4.36603	−	4.36603i	−0.358885	−	0.358885i
$149$	−2.31079	−	0.619174i	−0.189307	−	0.0507247i	0.162920	−	0.986639i	$-0.447909\pi$
$149$	−2.31079	−	0.619174i	−0.189307	−	0.0507247i	−0.352227	+	0.935915i	$0.614575\pi$
$150$		0			0
$151$	10.1962	−	10.1962i	0.829751	−	0.829751i	−0.157731	−	0.987482i	$-0.550418\pi$
$151$	10.1962	−	10.1962i	0.829751	−	0.829751i	0.987482	+	0.157731i	$0.0504179\pi$
$152$	0.776457	−	0.448288i	0.0629790	−	0.0363609i
$153$		0			0
$154$	0.232051	+	0.866025i	0.0186992	+	0.0697863i
$155$	−1.79315			−0.144029
$156$		0			0
$157$	−6.80385			−0.543006			−0.271503	−	0.962438i	$-0.587521\pi$
$157$	−6.80385			−0.543006			−0.271503	+	0.962438i	$0.587521\pi$
$158$	−0.517638	−	1.93185i	−0.0411811	−	0.153690i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	3.34607	−	3.34607i	0.263707	−	0.263707i
$162$		0			0
$163$	−19.6603	−	5.26795i	−1.53991	−	0.412618i	−0.613673	−	0.789560i	$-0.710309\pi$
$163$	−19.6603	−	5.26795i	−1.53991	−	0.412618i	−0.926237	+	0.376942i	$0.876975\pi$
$164$	−2.82843	−	2.82843i	−0.220863	−	0.220863i
$165$		0			0
$166$	11.6603	+	6.73205i	0.905011	+	0.522508i
$167$	7.32989	−	1.96404i	0.567204	−	0.151982i	0.0361899	−	0.999345i	$-0.488478\pi$
$167$	7.32989	−	1.96404i	0.567204	−	0.151982i	0.531014	+	0.847363i	$0.321811\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$			4.89898i			0.375735i
$171$		0			0
$172$	2.26795	−	3.92820i	0.172930	−	0.299523i
$173$	5.86491	+	10.1583i	0.445900	+	0.772322i	0.998114	−	0.0613801i	$-0.0195502\pi$
$173$	5.86491	+	10.1583i	0.445900	+	0.772322i	−0.552214	+	0.833702i	$0.686217\pi$
$174$		0			0
$175$	−0.232051	+	0.866025i	−0.0175414	+	0.0654654i
$176$	0.258819	−	0.965926i	0.0195092	−	0.0728094i
$177$		0			0
$178$	−6.06218	−	10.5000i	−0.454379	−	0.787008i
$179$	0.189469	−	0.328169i	0.0141616	−	0.0245285i	−0.858858	−	0.512214i	$-0.828825\pi$
$179$	0.189469	−	0.328169i	0.0141616	−	0.0245285i	0.873019	+	0.487686i	$0.162159\pi$
$180$		0			0
$181$			19.8564i			1.47592i	0.674847	+	0.737958i	$0.264210\pi$
$181$			19.8564i			1.47592i	−0.674847	+	0.737958i	$0.735790\pi$
$182$	2.24144	−	2.32937i	0.166146	−	0.172664i
$183$		0			0
$184$	−5.09808	+	1.36603i	−0.375835	+	0.100705i
$185$	−5.34727	−	3.08725i	−0.393139	−	0.226979i
$186$		0			0
$187$	3.46410	+	3.46410i	0.253320	+	0.253320i
$188$	−9.58991	−	2.56961i	−0.699416	−	0.187408i
$189$		0			0
$190$	0.633975	−	0.633975i	0.0459934	−	0.0459934i
$191$	20.9730	−	12.1087i	1.51755	−	0.876158i	0.517764	−	0.855524i	$-0.326765\pi$
$191$	20.9730	−	12.1087i	1.51755	−	0.876158i	0.999787	−	0.0206345i	$-0.00656863\pi$
$192$		0			0
$193$	−0.339746	−	1.26795i	−0.0244554	−	0.0912690i	0.952620	−	0.304165i	$-0.0983773\pi$
$193$	−0.339746	−	1.26795i	−0.0244554	−	0.0912690i	−0.977075	+	0.212896i	$0.931711\pi$
$194$	6.41473			0.460551
$195$		0			0
$196$	6.19615			0.442582
$197$	1.96404	+	7.32989i	0.139932	+	0.522233i	0.999929	+	0.0119336i	$0.00379868\pi$
$197$	1.96404	+	7.32989i	0.139932	+	0.522233i	−0.859997	+	0.510299i	$0.829535\pi$
$198$		0			0
$199$	−3.92820	+	2.26795i	−0.278463	+	0.160771i	−0.632727	−	0.774375i	$-0.718065\pi$
$199$	−3.92820	+	2.26795i	−0.278463	+	0.160771i	0.354264	+	0.935145i	$0.384731\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$		0			0
$202$	−5.46410	−	1.46410i	−0.384453	−	0.103014i
$203$	−1.79315	−	1.79315i	−0.125855	−	0.125855i
$204$		0			0
$205$	−3.46410	−	2.00000i	−0.241943	−	0.139686i
$206$	0.637756	−	0.170886i	0.0444346	−	0.0119062i
$207$		0			0
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$		−	0.896575i		−	0.0620174i
$210$		0			0
$211$	4.96410	−	8.59808i	0.341743	−	0.591916i	−0.643014	−	0.765855i	$-0.722316\pi$
$211$	4.96410	−	8.59808i	0.341743	−	0.591916i	0.984756	+	0.173939i	$0.0556495\pi$
$212$	−6.43331	−	11.1428i	−0.441842	−	0.765292i
$213$		0			0
$214$	−3.19615	+	11.9282i	−0.218484	+	0.815395i
$215$	1.17398	−	4.38134i	0.0800646	−	0.298805i
$216$		0			0
$217$	−0.803848	−	1.39230i	−0.0545687	−	0.0945158i
$218$	2.31079	−	4.00240i	0.156506	−	0.271077i
$219$		0			0
$220$		−	1.00000i		−	0.0674200i
$221$	4.24264	−	17.1464i	0.285391	−	1.15339i
$222$		0			0
$223$	−2.33013	+	0.624356i	−0.156037	+	0.0418099i	−0.335992	−	0.941865i	$-0.609071\pi$
$223$	−2.33013	+	0.624356i	−0.156037	+	0.0418099i	0.179955	+	0.983675i	$0.442405\pi$
$224$	0.776457	+	0.448288i	0.0518792	+	0.0299525i
$225$		0			0
$226$	1.46410	+	1.46410i	0.0973906	+	0.0973906i
$227$	−10.9348	−	2.92996i	−0.725766	−	0.194468i	−0.123023	−	0.992404i	$-0.539259\pi$
$227$	−10.9348	−	2.92996i	−0.725766	−	0.194468i	−0.602743	+	0.797935i	$0.705926\pi$
$228$		0			0
$229$	−0.339746	+	0.339746i	−0.0224510	+	0.0224510i	−0.718243	−	0.695792i	$-0.755053\pi$
$229$	−0.339746	+	0.339746i	−0.0224510	+	0.0224510i	0.695792	+	0.718243i	$0.255053\pi$
$230$	−4.57081	+	2.63896i	−0.301390	+	0.174008i
$231$		0			0
$232$	0.732051	+	2.73205i	0.0480615	+	0.179368i
$233$	−8.76268			−0.574062			−0.287031	−	0.957921i	$-0.592668\pi$
$233$	−8.76268			−0.574062			−0.287031	+	0.957921i	$0.592668\pi$
$234$		0			0
$235$	−9.92820			−0.647645
$236$	−1.03528	−	3.86370i	−0.0673907	−	0.251506i
$237$		0			0
$238$	−3.80385	+	2.19615i	−0.246567	+	0.142355i
$239$	−10.4543	+	10.4543i	−0.676232	+	0.676232i	−0.959146	−	0.282913i	$-0.908699\pi$
$239$	−10.4543	+	10.4543i	−0.676232	+	0.676232i	0.282913	+	0.959146i	$0.408699\pi$
$240$		0			0
$241$	−5.96410	−	1.59808i	−0.384182	−	0.102941i	0.0615587	−	0.998103i	$-0.480393\pi$
$241$	−5.96410	−	1.59808i	−0.384182	−	0.102941i	−0.445740	+	0.895162i	$0.647060\pi$
$242$	7.07107	+	7.07107i	0.454545	+	0.454545i
$243$		0			0
$244$	−4.26795	−	2.46410i	−0.273227	−	0.157748i
$245$	5.98502	−	1.60368i	0.382369	−	0.102456i
$246$		0			0
$247$	−2.76795	+	1.66987i	−0.176120	+	0.106251i
$248$			1.79315i			0.113865i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−11.4710	−	19.8683i	−0.724043	−	1.25408i	−0.959367	−	0.282162i	$-0.908949\pi$
$251$	−11.4710	−	19.8683i	−0.724043	−	1.25408i	0.235324	−	0.971917i	$-0.424385\pi$
$252$		0			0
$253$	−1.36603	+	5.09808i	−0.0858813	+	0.320513i
$254$	3.27671	−	12.2289i	0.205599	−	0.767307i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.6617	+	23.6627i	−0.852191	+	1.47604i	0.0270355	+	0.999634i	$0.491393\pi$
$257$	−13.6617	+	23.6627i	−0.852191	+	1.47604i	−0.879227	+	0.476404i	$0.841940\pi$
$258$		0			0
$259$		−	5.53590i		−	0.343984i
$260$	−3.08725	+	1.86250i	−0.191463	+	0.115507i
$261$		0			0
$262$	−4.23205	+	1.13397i	−0.261457	+	0.0700572i
$263$	−14.0728	−	8.12493i	−0.867765	−	0.501004i	−0.00116020	−	0.999999i	$-0.500369\pi$
$263$	−14.0728	−	8.12493i	−0.867765	−	0.501004i	−0.866605	+	0.498995i	$0.833703\pi$
$264$		0			0
$265$	−9.09808	−	9.09808i	−0.558890	−	0.558890i
$266$	0.776457	+	0.208051i	0.0476076	+	0.0127564i
$267$		0			0
$268$	−7.46410	+	7.46410i	−0.455943	+	0.455943i
$269$	17.6269	−	10.1769i	1.07473	−	0.620496i	0.145261	−	0.989393i	$-0.453598\pi$
$269$	17.6269	−	10.1769i	1.07473	−	0.620496i	0.929470	+	0.368897i	$0.120265\pi$
$270$		0			0
$271$	5.07180	+	18.9282i	0.308090	+	1.14981i	0.930253	+	0.366919i	$0.119587\pi$
$271$	5.07180	+	18.9282i	0.308090	+	1.14981i	−0.622163	+	0.782888i	$0.713746\pi$
$272$	4.89898			0.297044
$273$		0			0
$274$	−8.00000			−0.483298
$275$	−0.258819	−	0.965926i	−0.0156074	−	0.0582475i
$276$		0			0
$277$	−18.0622	+	10.4282i	−1.08525	+	0.626570i	−0.932308	−	0.361665i	$-0.882208\pi$
$277$	−18.0622	+	10.4282i	−1.08525	+	0.626570i	−0.152943	+	0.988235i	$0.548875\pi$
$278$	−11.7806	+	11.7806i	−0.706552	+	0.706552i
$279$		0			0
$280$	0.866025	+	0.232051i	0.0517549	+	0.0138677i
$281$	−5.55532	−	5.55532i	−0.331403	−	0.331403i	0.521716	−	0.853119i	$-0.325292\pi$
$281$	−5.55532	−	5.55532i	−0.331403	−	0.331403i	−0.853119	+	0.521716i	$0.825292\pi$
$282$		0			0
$283$	−25.3923	−	14.6603i	−1.50942	−	0.871462i	−0.999940	−	0.0109768i	$-0.996506\pi$
$283$	−25.3923	−	14.6603i	−1.50942	−	0.871462i	−0.509476	−	0.860485i	$-0.670161\pi$
$284$	1.93185	−	0.517638i	0.114634	−	0.0307162i
$285$		0			0
$286$	−0.866025	+	3.50000i	−0.0512092	+	0.206959i
$287$		−	3.58630i		−	0.211693i
$288$		0			0
$289$	−3.50000	+	6.06218i	−0.205882	+	0.356599i
$290$	1.41421	+	2.44949i	0.0830455	+	0.143839i
$291$		0			0
$292$	−0.928203	+	3.46410i	−0.0543190	+	0.202721i
$293$	−3.60488	+	13.4536i	−0.210600	+	0.785968i	0.777070	+	0.629414i	$0.216705\pi$
$293$	−3.60488	+	13.4536i	−0.210600	+	0.785968i	−0.987669	+	0.156554i	$0.949961\pi$
$294$		0			0
$295$	−2.00000	−	3.46410i	−0.116445	−	0.201688i
$296$	−3.08725	+	5.34727i	−0.179443	+	0.310804i
$297$		0			0
$298$			2.39230i			0.138582i
$299$	18.2832	−	5.27792i	1.05735	−	0.305230i
$300$		0			0
$301$	3.92820	−	1.05256i	0.226418	−	0.0606685i
$302$	−12.4877	−	7.20977i	−0.718586	−	0.414876i
$303$		0			0
$304$	−0.633975	−	0.633975i	−0.0363609	−	0.0363609i
$305$	−4.76028	−	1.27551i	−0.272573	−	0.0730357i
$306$		0			0
$307$	16.1962	−	16.1962i	0.924363	−	0.924363i	−0.0729708	−	0.997334i	$-0.523248\pi$
$307$	16.1962	−	16.1962i	0.924363	−	0.924363i	0.997334	+	0.0729708i	$0.0232480\pi$
$308$	0.776457	−	0.448288i	0.0442428	−	0.0255436i
$309$		0			0
$310$	0.464102	+	1.73205i	0.0263592	+	0.0983739i
$311$	−0.554803			−0.0314600			−0.0157300	−	0.999876i	$-0.505007\pi$
$311$	−0.554803			−0.0314600			−0.0157300	+	0.999876i	$0.505007\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	1.76097	+	6.57201i	0.0993770	+	0.370880i
$315$		0			0
$316$	−1.73205	+	1.00000i	−0.0974355	+	0.0562544i
$317$	11.3645	−	11.3645i	0.638293	−	0.638293i	−0.311842	−	0.950134i	$-0.600946\pi$
$317$	11.3645	−	11.3645i	0.638293	−	0.638293i	0.950134	+	0.311842i	$0.100946\pi$
$318$		0			0
$319$	2.73205	+	0.732051i	0.152965	+	0.0409870i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$		0			0
$322$	−4.09808	−	2.36603i	−0.228377	−	0.131853i
$323$	4.24264	−	1.13681i	0.236067	−	0.0632539i
$324$		0			0
$325$	−2.50000	+	2.59808i	−0.138675	+	0.144115i
$326$			20.3538i			1.12729i
$327$		0			0
$328$	−2.00000	+	3.46410i	−0.110432	+	0.191273i
$329$	−4.45069	−	7.70882i	−0.245375	−	0.425001i
$330$		0			0
$331$	0.294229	−	1.09808i	0.0161723	−	0.0603557i	−0.957368	−	0.288871i	$-0.906720\pi$
$331$	0.294229	−	1.09808i	0.0161723	−	0.0603557i	0.973540	+	0.228515i	$0.0733869\pi$
$332$	3.48477	−	13.0053i	0.191251	−	0.713760i
$333$		0			0
$334$	−3.79423	−	6.57180i	−0.207611	−	0.359593i
$335$	−5.27792	+	9.14162i	−0.288363	+	0.499460i
$336$		0			0
$337$		−	4.53590i		−	0.247086i	−0.992339	−	0.123543i	$-0.960574\pi$
$337$		−	4.53590i		−	0.247086i	0.992339	−	0.123543i	$-0.0394257\pi$
$338$	12.4183	−	3.84512i	0.675468	−	0.209147i
$339$		0			0
$340$	4.73205	−	1.26795i	0.256631	−	0.0687642i
$341$	1.55291	+	0.896575i	0.0840950	+	0.0485523i
$342$		0			0
$343$	8.36603	+	8.36603i	0.451723	+	0.451723i
$344$	−4.38134	−	1.17398i	−0.236226	−	0.0632966i
$345$		0			0
$346$	8.29423	−	8.29423i	0.445900	−	0.445900i
$347$	−3.76217	+	2.17209i	−0.201964	+	0.116604i	−0.597571	−	0.801816i	$-0.703867\pi$
$347$	−3.76217	+	2.17209i	−0.201964	+	0.116604i	0.395607	+	0.918420i	$0.370534\pi$
$348$		0			0
$349$	−0.679492	−	2.53590i	−0.0363724	−	0.135744i	0.945352	−	0.326051i	$-0.105718\pi$
$349$	−0.679492	−	2.53590i	−0.0363724	−	0.135744i	−0.981725	+	0.190308i	$0.939051\pi$
$350$	0.896575			0.0479240
$351$		0			0
$352$	−1.00000			−0.0533002
$353$	6.86800	+	25.6317i	0.365547	+	1.36424i	0.866678	+	0.498867i	$0.166250\pi$
$353$	6.86800	+	25.6317i	0.365547	+	1.36424i	−0.501132	+	0.865371i	$0.667083\pi$
$354$		0			0
$355$	1.73205	−	1.00000i	0.0919277	−	0.0530745i
$356$	−8.57321	+	8.57321i	−0.454379	+	0.454379i
$357$		0			0
$358$	−0.366025	−	0.0980762i	−0.0193450	−	0.00518349i
$359$	−3.76217	−	3.76217i	−0.198560	−	0.198560i	0.600823	−	0.799382i	$-0.294840\pi$
$359$	−3.76217	−	3.76217i	−0.198560	−	0.198560i	−0.799382	+	0.600823i	$0.794840\pi$
$360$		0			0
$361$	15.7583	+	9.09808i	0.829386	+	0.478846i
$362$	19.1798	−	5.13922i	1.00807	−	0.270111i
$363$		0			0
$364$	−2.83013	−	1.56218i	−0.148339	−	0.0818804i
$365$			3.58630i			0.187716i
$366$		0			0
$367$	−4.66025	+	8.07180i	−0.243263	+	0.421344i	−0.961642	−	0.274308i	$-0.911551\pi$
$367$	−4.66025	+	8.07180i	−0.243263	+	0.421344i	0.718379	+	0.695652i	$0.244885\pi$
$368$	2.63896	+	4.57081i	0.137565	+	0.238270i
$369$		0			0
$370$	−1.59808	+	5.96410i	−0.0830800	+	0.310059i
$371$	2.98571	−	11.1428i	0.155010	−	0.578507i
$372$		0			0
$373$	−18.3923	−	31.8564i	−0.952317	−	1.64946i	−0.740391	−	0.672177i	$-0.765360\pi$
$373$	−18.3923	−	31.8564i	−0.952317	−	1.64946i	−0.211927	−	0.977286i	$-0.567974\pi$
$374$	2.44949	−	4.24264i	0.126660	−	0.219382i
$375$		0			0
$376$			9.92820i			0.512008i
$377$	−2.82843	−	9.79796i	−0.145671	−	0.504621i
$378$		0			0
$379$	36.5526	−	9.79423i	1.87758	−	0.503096i	0.877872	−	0.478896i	$-0.158963\pi$
$379$	36.5526	−	9.79423i	1.87758	−	0.503096i	0.999707	−	0.0241998i	$-0.00770379\pi$
$380$	−0.776457	−	0.448288i	−0.0398314	−	0.0229967i
$381$		0			0
$382$	−17.1244	−	17.1244i	−0.876158	−	0.876158i
$383$	−30.1146	−	8.06918i	−1.53878	−	0.412316i	−0.612911	−	0.790152i	$-0.710002\pi$
$383$	−30.1146	−	8.06918i	−1.53878	−	0.412316i	−0.925872	+	0.377836i	$0.876668\pi$
$384$		0			0
$385$	0.633975	−	0.633975i	0.0323103	−	0.0323103i
$386$	−1.13681	+	0.656339i	−0.0578622	+	0.0334068i
$387$		0			0
$388$	−1.66025	−	6.19615i	−0.0842866	−	0.314562i
$389$	−26.0106			−1.31879			−0.659396	−	0.751796i	$-0.729188\pi$
$389$	−26.0106			−1.31879			−0.659396	+	0.751796i	$0.729188\pi$
$390$		0			0
$391$	−25.8564			−1.30761
$392$	−1.60368	−	5.98502i	−0.0809982	−	0.302289i
$393$		0			0
$394$	6.57180	−	3.79423i	0.331082	−	0.191150i
$395$	−1.41421	+	1.41421i	−0.0711568	+	0.0711568i
$396$		0			0
$397$	30.3564	+	8.13397i	1.52354	+	0.408232i	0.920907	−	0.389783i	$-0.127450\pi$
$397$	30.3564	+	8.13397i	1.52354	+	0.408232i	0.602637	+	0.798015i	$0.294117\pi$
$398$	3.20736	+	3.20736i	0.160771	+	0.160771i
$399$		0			0
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	32.7721	−	8.78127i	1.63656	−	0.438515i	0.680755	−	0.732511i	$-0.261652\pi$
$401$	32.7721	−	8.78127i	1.63656	−	0.438515i	0.955807	+	0.293996i	$0.0949851\pi$
$402$		0			0
$403$	−0.124356	−	6.46410i	−0.00619460	−	0.322000i
$404$			5.65685i			0.281439i
$405$		0			0
$406$	−1.26795	+	2.19615i	−0.0629273	+	0.108993i
$407$	3.08725	+	5.34727i	0.153029	+	0.265054i
$408$		0			0
$409$	−5.64359	+	21.0622i	−0.279058	+	1.04146i	0.674015	+	0.738717i	$0.264568\pi$
$409$	−5.64359	+	21.0622i	−0.279058	+	1.04146i	−0.953073	+	0.302740i	$0.902099\pi$
$410$	−1.03528	+	3.86370i	−0.0511286	+	0.190815i
$411$		0			0
$412$	−0.330127	−	0.571797i	−0.0162642	−	0.0281704i
$413$	1.79315	−	3.10583i	0.0882352	−	0.152828i
$414$		0			0
$415$		−	13.4641i		−	0.660927i
$416$	1.86250	+	3.08725i	0.0913166	+	0.151365i
$417$		0			0
$418$	−0.866025	+	0.232051i	−0.0423587	+	0.0113500i
$419$	6.53983	+	3.77577i	0.319491	+	0.184458i	0.651166	−	0.758935i	$-0.274280\pi$
$419$	6.53983	+	3.77577i	0.319491	+	0.184458i	−0.331674	+	0.943394i	$0.607614\pi$
$420$		0			0
$421$	2.53590	+	2.53590i	0.123592	+	0.123592i	0.766197	−	0.642605i	$-0.222146\pi$
$421$	2.53590	+	2.53590i	0.123592	+	0.123592i	−0.642605	+	0.766197i	$0.722146\pi$
$422$	−9.58991	−	2.56961i	−0.466829	−	0.125087i
$423$		0			0
$424$	−9.09808	+	9.09808i	−0.441842	+	0.441842i
$425$	4.24264	−	2.44949i	0.205798	−	0.118818i
$426$		0			0
$427$	−1.14359	−	4.26795i	−0.0553424	−	0.206541i
$428$	12.3490			0.596911
$429$		0			0
$430$	−4.53590			−0.218740
$431$	−2.44949	−	9.14162i	−0.117988	−	0.440336i	0.881505	−	0.472174i	$-0.156531\pi$
$431$	−2.44949	−	9.14162i	−0.117988	−	0.440336i	−0.999493	+	0.0318378i	$0.989864\pi$
$432$		0			0
$433$	−23.6603	+	13.6603i	−1.13704	+	0.656470i	−0.945696	−	0.325053i	$-0.894618\pi$
$433$	−23.6603	+	13.6603i	−1.13704	+	0.656470i	−0.191344	+	0.981523i	$0.561284\pi$
$434$	−1.13681	+	1.13681i	−0.0545687	+	0.0545687i
$435$		0			0
$436$	−4.46410	−	1.19615i	−0.213792	−	0.0572853i
$437$	3.34607	+	3.34607i	0.160064	+	0.160064i
$438$		0			0
$439$	12.8038	+	7.39230i	0.611094	+	0.352815i	0.773394	−	0.633926i	$-0.218558\pi$
$439$	12.8038	+	7.39230i	0.611094	+	0.352815i	−0.162299	+	0.986742i	$0.551891\pi$
$440$	−0.965926	+	0.258819i	−0.0460487	+	0.0123387i
$441$		0			0
$442$	−17.6603	+	0.339746i	−0.840013	+	0.0161601i
$443$		−	10.2784i		−	0.488343i	−0.969732	−	0.244172i	$-0.921484\pi$
$443$		−	10.2784i		−	0.488343i	0.969732	−	0.244172i	$-0.0785160\pi$
$444$		0			0
$445$	−6.06218	+	10.5000i	−0.287375	+	0.497748i
$446$	1.20616	+	2.08913i	0.0571134	+	0.0989234i
$447$		0			0
$448$	0.232051	−	0.866025i	0.0109634	−	0.0409159i
$449$	−0.448288	+	1.67303i	−0.0211560	+	0.0789553i	−0.975697	−	0.219125i	$-0.929680\pi$
$449$	−0.448288	+	1.67303i	−0.0211560	+	0.0789553i	0.954541	+	0.298080i	$0.0963464\pi$
$450$		0			0
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	1.03528	−	1.79315i	0.0486953	−	0.0843427i
$453$		0			0
$454$			11.3205i			0.531298i
$455$	−3.13801	−	0.776457i	−0.147112	−	0.0364009i
$456$		0			0
$457$	37.0526	−	9.92820i	1.73325	−	0.464422i	0.752319	−	0.658799i	$-0.228935\pi$
$457$	37.0526	−	9.92820i	1.73325	−	0.464422i	0.980927	+	0.194377i	$0.0622687\pi$
$458$	0.416102	+	0.240237i	0.0194432	+	0.0112255i
$459$		0			0
$460$	3.73205	+	3.73205i	0.174008	+	0.174008i
$461$	−13.0053	−	3.48477i	−0.605718	−	0.162302i	−0.0570913	−	0.998369i	$-0.518183\pi$
$461$	−13.0053	−	3.48477i	−0.605718	−	0.162302i	−0.548627	+	0.836067i	$0.684849\pi$
$462$		0			0
$463$	16.1244	−	16.1244i	0.749362	−	0.749362i	−0.224997	−	0.974359i	$-0.572237\pi$
$463$	16.1244	−	16.1244i	0.749362	−	0.749362i	0.974359	+	0.224997i	$0.0722373\pi$
$464$	2.44949	−	1.41421i	0.113715	−	0.0656532i
$465$		0			0
$466$	2.26795	+	8.46410i	0.105061	+	0.392092i
$467$	−4.14110			−0.191627			−0.0958137	−	0.995399i	$-0.530545\pi$
$467$	−4.14110			−0.191627			−0.0958137	+	0.995399i	$0.530545\pi$
$468$		0			0
$469$	−9.46410			−0.437012
$470$	2.56961	+	9.58991i	0.118527	+	0.442349i
$471$		0			0
$472$	−3.46410	+	2.00000i	−0.159448	+	0.0920575i
$473$	−3.20736	+	3.20736i	−0.147475	+	0.147475i
$474$		0			0
$475$	−0.866025	−	0.232051i	−0.0397360	−	0.0106472i
$476$	3.10583	+	3.10583i	0.142355	+	0.142355i
$477$		0			0
$478$	12.8038	+	7.39230i	0.585634	+	0.338116i
$479$	−9.89949	+	2.65256i	−0.452319	+	0.121199i	−0.477784	−	0.878477i	$-0.658560\pi$
$479$	−9.89949	+	2.65256i	−0.452319	+	0.121199i	0.0254650	+	0.999676i	$0.491893\pi$
$480$		0			0
$481$	10.7583	−	19.4904i	0.490538	−	0.888685i
$482$			6.17449i			0.281240i
$483$		0			0
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−3.20736	−	5.55532i	−0.145639	−	0.252254i
$486$		0			0
$487$	4.20577	−	15.6962i	0.190582	−	0.711261i	−0.802785	−	0.596269i	$-0.796649\pi$
$487$	4.20577	−	15.6962i	0.190582	−	0.711261i	0.993366	−	0.114992i	$-0.0366841\pi$
$488$	−1.27551	+	4.76028i	−0.0577398	+	0.215488i
$489$		0			0
$490$	−3.09808	−	5.36603i	−0.139957	−	0.242412i
$491$	0.877993	−	1.52073i	0.0396233	−	0.0686295i	−0.845534	−	0.533922i	$-0.820718\pi$
$491$	0.877993	−	1.52073i	0.0396233	−	0.0686295i	0.885157	+	0.465293i	$0.154051\pi$
$492$		0			0
$493$			13.8564i			0.624061i
$494$	2.32937	+	2.24144i	0.104803	+	0.100847i
$495$		0			0
$496$	1.73205	−	0.464102i	0.0777714	−	0.0208388i
$497$	1.55291	+	0.896575i	0.0696577	+	0.0402169i
$498$		0			0
$499$	23.1962	+	23.1962i	1.03840	+	1.03840i	0.999233	+	0.0391698i	$0.0124713\pi$
$499$	23.1962	+	23.1962i	1.03840	+	1.03840i	0.0391698	+	0.999233i	$0.487529\pi$
$500$	−0.965926	−	0.258819i	−0.0431975	−	0.0115747i
$501$		0			0
$502$	−16.2224	+	16.2224i	−0.724043	+	0.724043i
$503$	30.5629	−	17.6455i	1.36273	−	0.786773i	0.372745	−	0.927934i	$-0.378417\pi$
$503$	30.5629	−	17.6455i	1.36273	−	0.786773i	0.989987	+	0.141161i	$0.0450834\pi$
$504$		0			0
$505$	1.46410	+	5.46410i	0.0651517	+	0.243149i
$506$	5.27792			0.234632
$507$		0			0
$508$	−12.6603			−0.561708
$509$	1.17398	+	4.38134i	0.0520356	+	0.194200i	0.987051	−	0.160408i	$-0.0512811\pi$
$509$	1.17398	+	4.38134i	0.0520356	+	0.194200i	−0.935015	+	0.354608i	$0.884614\pi$
$510$		0			0
$511$	−2.78461	+	1.60770i	−0.123184	+	0.0711202i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	26.3923	+	7.07180i	1.16411	+	0.311924i
$515$	−0.466870	−	0.466870i	−0.0205728	−	0.0205728i
$516$		0			0
$517$	8.59808	+	4.96410i	0.378143	+	0.218321i
$518$	−5.34727	+	1.43280i	−0.234945	+	0.0629534i
$519$		0			0
$520$	2.59808	+	2.50000i	0.113933	+	0.109632i
$521$		−	3.72500i		−	0.163195i	−0.996665	−	0.0815977i	$-0.973998\pi$
$521$		−	3.72500i		−	0.163195i	0.996665	−	0.0815977i	$-0.0260023\pi$
$522$		0			0
$523$	19.7846	−	34.2679i	0.865121	−	1.49843i	−0.00180682	−	0.999998i	$-0.500575\pi$
$523$	19.7846	−	34.2679i	0.865121	−	1.49843i	0.866927	−	0.498434i	$-0.166092\pi$
$524$	2.19067	+	3.79435i	0.0956999	+	0.165757i
$525$		0			0
$526$	−4.20577	+	15.6962i	−0.183380	+	0.684385i
$527$	−2.27362	+	8.48528i	−0.0990406	+	0.369625i
$528$		0			0
$529$	−2.42820	−	4.20577i	−0.105574	−	0.182860i
$530$	−6.43331	+	11.1428i	−0.279445	+	0.484013i
$531$		0			0
$532$		−	0.803848i		−	0.0348512i
$533$	6.96953	−	12.6264i	0.301884	−	0.546909i
$534$		0			0
$535$	11.9282	−	3.19615i	0.515701	−	0.138182i
$536$	9.14162	+	5.27792i	0.394858	+	0.227971i
$537$		0			0
$538$	−14.3923	−	14.3923i	−0.620496	−	0.620496i
$539$	−5.98502	−	1.60368i	−0.257793	−	0.0690755i
$540$		0			0
$541$	7.80385	−	7.80385i	0.335514	−	0.335514i	−0.519162	−	0.854676i	$-0.673756\pi$
$541$	7.80385	−	7.80385i	0.335514	−	0.335514i	0.854676	+	0.519162i	$0.173756\pi$
$542$	16.9706	−	9.79796i	0.728948	−	0.420858i
$543$		0			0
$544$	−1.26795	−	4.73205i	−0.0543629	−	0.202885i
$545$	−4.62158			−0.197967
$546$		0			0
$547$	33.7128			1.44146			0.720728	−	0.693218i	$-0.243808\pi$
$547$	33.7128			1.44146			0.720728	+	0.693218i	$0.243808\pi$
$548$	2.07055	+	7.72741i	0.0884496	+	0.330098i
$549$		0			0
$550$	−0.866025	+	0.500000i	−0.0369274	+	0.0213201i
$551$	1.79315	−	1.79315i	0.0763908	−	0.0763908i
$552$		0			0
$553$	−1.73205	−	0.464102i	−0.0736543	−	0.0197356i
$554$	14.7477	+	14.7477i	0.626570	+	0.626570i
$555$		0			0
$556$	14.4282	+	8.33013i	0.611892	+	0.353276i
$557$	2.19067	−	0.586988i	0.0928217	−	0.0248715i	−0.212109	−	0.977246i	$-0.568033\pi$
$557$	2.19067	−	0.586988i	0.0928217	−	0.0248715i	0.304931	+	0.952374i	$0.401367\pi$
$558$		0			0
$559$	15.8756	+	3.92820i	0.671468	+	0.166145i
$560$		−	0.896575i		−	0.0378872i
$561$		0			0
$562$	−3.92820	+	6.80385i	−0.165701	+	0.287003i
$563$	0.757875	+	1.31268i	0.0319406	+	0.0553228i	0.881554	−	0.472084i	$-0.156498\pi$
$563$	0.757875	+	1.31268i	0.0319406	+	0.0553228i	−0.849613	+	0.527406i	$0.823165\pi$
$564$		0			0
$565$	0.535898	−	2.00000i	0.0225454	−	0.0841406i
$566$	−7.58871	+	28.3214i	−0.318977	+	1.19044i
$567$		0			0
$568$	−1.00000	−	1.73205i	−0.0419591	−	0.0726752i
$569$	−18.3018	+	31.6997i	−0.767252	+	1.32892i	0.171795	+	0.985133i	$0.445043\pi$
$569$	−18.3018	+	31.6997i	−0.767252	+	1.32892i	−0.939048	+	0.343787i	$0.888290\pi$
$570$		0			0
$571$		−	32.6603i		−	1.36679i	−0.730049	−	0.683395i	$-0.760503\pi$
$571$		−	32.6603i		−	1.36679i	0.730049	−	0.683395i	$-0.239497\pi$
$572$	3.60488	−	0.0693504i	0.150728	−	0.00289968i
$573$		0			0
$574$	−3.46410	+	0.928203i	−0.144589	+	0.0387425i
$575$	4.57081	+	2.63896i	0.190616	+	0.110052i
$576$		0			0
$577$	7.66025	+	7.66025i	0.318901	+	0.318901i	0.848345	−	0.529444i	$-0.177600\pi$
$577$	7.66025	+	7.66025i	0.318901	+	0.318901i	−0.529444	+	0.848345i	$0.677600\pi$
$578$	6.76148	+	1.81173i	0.281241	+	0.0753582i
$579$		0			0
$580$	2.00000	−	2.00000i	0.0830455	−	0.0830455i
$581$	10.4543	−	6.03579i	0.433717	−	0.250407i
$582$		0			0
$583$	3.33013	+	12.4282i	0.137920	+	0.514724i
$584$	3.58630			0.148402
$585$		0			0
$586$	13.9282			0.575369
$587$	10.5930	+	39.5336i	0.437220	+	1.63173i	0.735698	+	0.677310i	$0.236854\pi$
$587$	10.5930	+	39.5336i	0.437220	+	1.63173i	−0.298478	+	0.954417i	$0.596479\pi$
$588$		0			0
$589$	1.39230	−	0.803848i	0.0573689	−	0.0331220i
$590$	−2.82843	+	2.82843i	−0.116445	+	0.116445i
$591$		0			0
$592$	5.96410	+	1.59808i	0.245123	+	0.0656805i
$593$	28.0812	+	28.0812i	1.15316	+	1.15316i	0.985916	+	0.167241i	$0.0534856\pi$
$593$	28.0812	+	28.0812i	1.15316	+	1.15316i	0.167241	+	0.985916i	$0.446514\pi$
$594$		0			0
$595$	3.80385	+	2.19615i	0.155943	+	0.0900335i
$596$	2.31079	−	0.619174i	0.0946536	−	0.0253624i
$597$		0			0
$598$	−9.83013	−	16.2942i	−0.401984	−	0.666321i
$599$			26.4911i			1.08240i	0.840895	+	0.541199i	$0.182029\pi$
$599$			26.4911i			1.08240i	−0.840895	+	0.541199i	$0.817971\pi$
$600$		0			0
$601$	−9.42820	+	16.3301i	−0.384584	+	0.666120i	−0.991711	−	0.128485i	$-0.958989\pi$
$601$	−9.42820	+	16.3301i	−0.384584	+	0.666120i	0.607127	+	0.794605i	$0.292322\pi$
$602$	−2.03339	−	3.52193i	−0.0828747	−	0.143543i
$603$		0			0
$604$	−3.73205	+	13.9282i	−0.151855	+	0.566731i
$605$	2.58819	−	9.65926i	0.105225	−	0.392705i
$606$		0			0
$607$	−5.93782	−	10.2846i	−0.241009	−	0.417439i	0.719993	−	0.693981i	$-0.244145\pi$
$607$	−5.93782	−	10.2846i	−0.241009	−	0.417439i	−0.961002	+	0.276542i	$0.910812\pi$
$608$	−0.448288	+	0.776457i	−0.0181805	+	0.0314895i
$609$		0			0
$610$			4.92820i			0.199537i
$611$	−0.688524	−	35.7900i	−0.0278547	−	1.44791i
$612$		0			0
$613$	8.89230	−	2.38269i	0.359157	−	0.0962358i	−0.0747284	−	0.997204i	$-0.523809\pi$
$613$	8.89230	−	2.38269i	0.359157	−	0.0962358i	0.433885	+	0.900968i	$0.357142\pi$
$614$	−19.8362	−	11.4524i	−0.800522	−	0.462182i
$615$		0			0
$616$	−0.633975	−	0.633975i	−0.0255436	−	0.0255436i
$617$	−12.8666	−	3.44760i	−0.517991	−	0.138795i	−0.00965369	−	0.999953i	$-0.503073\pi$
$617$	−12.8666	−	3.44760i	−0.517991	−	0.138795i	−0.508337	+	0.861158i	$0.669740\pi$
$618$		0			0
$619$	26.8827	−	26.8827i	1.08051	−	1.08051i	0.0840444	−	0.996462i	$-0.473216\pi$
$619$	26.8827	−	26.8827i	1.08051	−	1.08051i	0.996462	−	0.0840444i	$-0.0267837\pi$
$620$	1.55291	−	0.896575i	0.0623665	−	0.0360073i
$621$		0			0
$622$	0.143594	+	0.535898i	0.00575758	+	0.0214876i
$623$	−10.8704			−0.435513
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	2.58819	+	9.65926i	0.103445	+	0.386062i
$627$		0			0
$628$	5.89230	−	3.40192i	0.235129	−	0.135752i
$629$	−21.3891	+	21.3891i	−0.852838	+	0.852838i
$630$		0			0
$631$	14.1962	+	3.80385i	0.565140	+	0.151429i	0.530067	−	0.847956i	$-0.322167\pi$
$631$	14.1962	+	3.80385i	0.565140	+	0.151429i	0.0350732	+	0.999385i	$0.488834\pi$
$632$	1.41421	+	1.41421i	0.0562544	+	0.0562544i
$633$		0			0
$634$	−13.9186	−	8.03590i	−0.552778	−	0.319146i
$635$	−12.2289	+	3.27671i	−0.485288	+	0.130032i
$636$		0			0
$637$	6.19615	+	21.4641i	0.245500	+	0.850439i
$638$		−	2.82843i		−	0.111979i
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−2.62038	−	4.53862i	−0.103499	−	0.179265i	0.809625	−	0.586947i	$-0.199670\pi$
$641$	−2.62038	−	4.53862i	−0.103499	−	0.179265i	−0.913124	+	0.407682i	$0.866337\pi$
$642$		0			0
$643$	5.66025	−	21.1244i	0.223219	−	0.833063i	−0.759892	−	0.650050i	$-0.774748\pi$
$643$	5.66025	−	21.1244i	0.223219	−	0.833063i	0.983110	−	0.183014i	$-0.0585852\pi$
$644$	−1.22474	+	4.57081i	−0.0482617	+	0.180115i
$645$		0			0
$646$	−2.19615	−	3.80385i	−0.0864065	−	0.149660i
$647$	−4.17329	+	7.22835i	−0.164069	+	0.284176i	−0.936324	−	0.351137i	$-0.885795\pi$
$647$	−4.17329	+	7.22835i	−0.164069	+	0.284176i	0.772255	+	0.635312i	$0.219129\pi$
$648$		0			0
$649$			4.00000i			0.157014i
$650$	3.15660	+	1.74238i	0.123812	+	0.0683419i
$651$		0			0
$652$	19.6603	−	5.26795i	0.769955	−	0.206309i
$653$	4.29839	+	2.48168i	0.168209	+	0.0971155i	0.581741	−	0.813374i	$-0.302372\pi$
$653$	4.29839	+	2.48168i	0.168209	+	0.0971155i	−0.413532	+	0.910490i	$0.635705\pi$
$654$		0			0
$655$	3.09808	+	3.09808i	0.121052	+	0.121052i
$656$	3.86370	+	1.03528i	0.150852	+	0.0404207i
$657$		0			0
$658$	−6.29423	+	6.29423i	−0.245375	+	0.245375i
$659$	−34.2693	+	19.7854i	−1.33494	+	0.770729i	−0.986053	−	0.166435i	$-0.946775\pi$
$659$	−34.2693	+	19.7854i	−1.33494	+	0.770729i	−0.348890	+	0.937164i	$0.613441\pi$
$660$		0			0
$661$	−6.41154	−	23.9282i	−0.249380	−	0.930699i	−0.971131	−	0.238546i	$-0.923329\pi$
$661$	−6.41154	−	23.9282i	−0.249380	−	0.930699i	0.721751	−	0.692153i	$-0.243338\pi$
$662$	−1.13681			−0.0441835
$663$		0			0
$664$	−13.4641			−0.522508
$665$	−0.208051	−	0.776457i	−0.00806787	−	0.0301097i
$666$		0			0
$667$	−12.9282	+	7.46410i	−0.500582	+	0.289011i
$668$	−5.36585	+	5.36585i	−0.207611	+	0.207611i
$669$		0			0
$670$	10.1962	+	2.73205i	0.393912	+	0.105548i
$671$	3.48477	+	3.48477i	0.134528	+	0.134528i
$672$		0			0
$673$	37.1769	+	21.4641i	1.43306	+	0.827380i	0.997353	−	0.0727061i	$-0.0231635\pi$
$673$	37.1769	+	21.4641i	1.43306	+	0.827380i	0.435711	+	0.900086i	$0.356497\pi$
$674$	−4.38134	+	1.17398i	−0.168763	+	0.0452199i
$675$		0			0
$676$	−6.92820	−	11.0000i	−0.266469	−	0.423077i
$677$			30.8081i			1.18405i	0.805919	+	0.592026i	$0.201672\pi$
$677$			30.8081i			1.18405i	−0.805919	+	0.592026i	$0.798328\pi$
$678$		0			0
$679$	2.87564	−	4.98076i	0.110357	−	0.191144i
$680$	−2.44949	−	4.24264i	−0.0939336	−	0.162698i
$681$		0			0
$682$	0.464102	−	1.73205i	0.0177714	−	0.0663237i
$683$	2.20925	−	8.24504i	0.0845347	−	0.315488i	−0.910691	−	0.413088i	$-0.864450\pi$
$683$	2.20925	−	8.24504i	0.0845347	−	0.315488i	0.995226	+	0.0976005i	$0.0311167\pi$
$684$		0			0
$685$	4.00000	+	6.92820i	0.152832	+	0.264713i
$686$	5.91567	−	10.2462i	0.225861	−	0.391204i
$687$		0			0
$688$			4.53590i			0.172930i
$689$	32.1666	−	33.4285i	1.22545	−	1.27352i
$690$		0			0
$691$	12.1603	−	3.25833i	0.462598	−	0.123953i	−0.0199902	−	0.999800i	$-0.506364\pi$
$691$	12.1603	−	3.25833i	0.462598	−	0.123953i	0.482588	+	0.875847i	$0.339697\pi$
$692$	−10.1583	−	5.86491i	−0.386161	−	0.222950i
$693$		0			0
$694$	3.07180	+	3.07180i	0.116604	+	0.116604i
$695$	16.0926	+	4.31199i	0.610426	+	0.163563i
$696$		0			0
$697$	−13.8564	+	13.8564i	−0.524849	+	0.524849i
$698$	−2.27362	+	1.31268i	−0.0860579	+	0.0496856i
$699$		0			0
$700$	−0.232051	−	0.866025i	−0.00877070	−	0.0327327i
$701$	34.4959			1.30289			0.651447	−	0.758694i	$-0.274162\pi$
$701$	34.4959			1.30289			0.651447	+	0.758694i	$0.274162\pi$
$702$		0			0
$703$	5.53590			0.208790
$704$	0.258819	+	0.965926i	0.00975461	+	0.0364047i
$705$		0			0
$706$	22.9808	−	13.2679i	0.864892	−	0.499346i
$707$	−3.58630	+	3.58630i	−0.134877	+	0.134877i
$708$		0			0
$709$	23.6603	+	6.33975i	0.888579	+	0.238094i	0.674105	−	0.738635i	$-0.264529\pi$
$709$	23.6603	+	6.33975i	0.888579	+	0.238094i	0.214474	+	0.976730i	$0.431196\pi$
$710$	−1.41421	−	1.41421i	−0.0530745	−	0.0530745i
$711$		0			0
$712$	10.5000	+	6.06218i	0.393504	+	0.227190i
$713$	−9.14162	+	2.44949i	−0.342356	+	0.0917341i
$714$		0			0
$715$	3.46410	−	1.00000i	0.129550	−	0.0373979i
$716$			0.378937i			0.0141616i
$717$		0			0
$718$	−2.66025	+	4.60770i	−0.0992798	+	0.171958i
$719$	−4.79744	−	8.30942i	−0.178914	−	0.309889i	0.762595	−	0.646877i	$-0.223925\pi$
$719$	−4.79744	−	8.30942i	−0.178914	−	0.309889i	−0.941509	+	0.336988i	$0.890592\pi$
$720$		0			0
$721$	0.153212	−	0.571797i	0.00570593	−	0.0212948i
$722$	4.70951	−	17.5761i	0.175270	−	0.654116i
$723$		0			0
$724$	−9.92820	−	17.1962i	−0.368979	−	0.639090i
$725$	1.41421	−	2.44949i	0.0525226	−	0.0909718i
$726$		0			0
$727$		−	7.92820i		−	0.294041i	−0.989133	−	0.147020i	$-0.953032\pi$
$727$		−	7.92820i		−	0.294041i	0.989133	−	0.147020i	$-0.0469683\pi$
$728$	−0.776457	+	3.13801i	−0.0287774	+	0.116303i
$729$		0			0
$730$	3.46410	−	0.928203i	0.128212	−	0.0343543i
$731$	−19.2442	−	11.1106i	−0.711772	−	0.410942i
$732$		0			0
$733$	14.8301	+	14.8301i	0.547763	+	0.547763i	0.925793	−	0.378030i	$-0.123398\pi$
$733$	14.8301	+	14.8301i	0.547763	+	0.547763i	−0.378030	+	0.925793i	$0.623398\pi$
$734$	9.00292	+	2.41233i	0.332304	+	0.0890405i
$735$		0			0
$736$	3.73205	−	3.73205i	0.137565	−	0.137565i
$737$	9.14162	−	5.27792i	0.336736	−	0.194415i
$738$		0			0
$739$	−10.3301	−	38.5526i	−0.380000	−	1.41818i	−0.845900	−	0.533342i	$-0.820936\pi$
$739$	−10.3301	−	38.5526i	−0.380000	−	1.41818i	0.465900	−	0.884837i	$-0.345731\pi$
$740$	6.17449			0.226979
$741$		0			0
$742$	−11.5359			−0.423496
$743$	2.13492	+	7.96764i	0.0783228	+	0.292304i	0.993966	−	0.109687i	$-0.0349848\pi$
$743$	2.13492	+	7.96764i	0.0783228	+	0.292304i	−0.915643	+	0.401991i	$0.868318\pi$
$744$		0			0
$745$	2.07180	−	1.19615i	0.0759048	−	0.0438236i
$746$	−26.0106	+	26.0106i	−0.952317	+	0.952317i
$747$		0			0
$748$	−4.73205	−	1.26795i	−0.173021	−	0.0463608i
$749$	7.82894	+	7.82894i	0.286063	+	0.286063i
$750$		0			0
$751$	−12.9282	−	7.46410i	−0.471757	−	0.272369i	0.245218	−	0.969468i	$-0.421140\pi$
$751$	−12.9282	−	7.46410i	−0.471757	−	0.272369i	−0.716975	+	0.697099i	$0.754474\pi$
$752$	9.58991	−	2.56961i	0.349708	−	0.0937040i
$753$		0			0
$754$	−8.73205	+	5.26795i	−0.318003	+	0.191847i
$755$			14.4195i			0.524781i
$756$		0			0
$757$	−7.50000	+	12.9904i	−0.272592	+	0.472143i	−0.969525	−	0.244993i	$-0.921214\pi$
$757$	−7.50000	+	12.9904i	−0.272592	+	0.472143i	0.696933	+	0.717137i	$0.254548\pi$
$758$	−18.9210	−	32.7721i	−0.687242	−	1.19034i
$759$		0			0
$760$	−0.232051	+	0.866025i	−0.00841737	+	0.0314140i
$761$	−7.89829	+	29.4768i	−0.286313	+	1.06853i	0.661562	+	0.749891i	$0.269894\pi$
$761$	−7.89829	+	29.4768i	−0.286313	+	1.06853i	−0.947875	+	0.318644i	$0.896773\pi$
$762$		0			0
$763$	−2.07180	−	3.58846i	−0.0750041	−	0.129911i
$764$	−12.1087	+	20.9730i	−0.438079	+	0.758775i
$765$		0			0
$766$			31.1769i			1.12647i
$767$	12.3490	−	7.45001i	0.445896	−	0.269004i
$768$		0			0
$769$	−7.56218	+	2.02628i	−0.272699	+	0.0730695i	−0.392577	−	0.919719i	$-0.628416\pi$
$769$	−7.56218	+	2.02628i	−0.272699	+	0.0730695i	0.119878	+	0.992789i	$0.461750\pi$
$770$	−0.776457	−	0.448288i	−0.0279816	−	0.0161552i
$771$		0			0
$772$	0.928203	+	0.928203i	0.0334068	+	0.0334068i
$773$	−7.79676	−	2.08913i	−0.280430	−	0.0751410i	0.115863	−	0.993265i	$-0.463037\pi$
$773$	−7.79676	−	2.08913i	−0.280430	−	0.0751410i	−0.396293	+	0.918124i	$0.629703\pi$
$774$		0			0
$775$	1.26795	−	1.26795i	0.0455461	−	0.0455461i
$776$	−5.55532	+	3.20736i	−0.199424	+	0.115138i
$777$		0			0
$778$	6.73205	+	25.1244i	0.241356	+	0.900752i
$779$	3.58630			0.128493
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	6.69213	+	24.9754i	0.239310	+	0.893117i
$783$		0			0
$784$	−5.36603	+	3.09808i	−0.191644	+	0.110646i
$785$	4.81105	−	4.81105i	0.171714	−	0.171714i
$786$		0			0
$787$	−29.6603	−	7.94744i	−1.05727	−	0.283296i	−0.312019	−	0.950076i	$-0.601005\pi$
$787$	−29.6603	−	7.94744i	−1.05727	−	0.283296i	−0.745255	+	0.666780i	$0.767672\pi$
$788$	−5.36585	−	5.36585i	−0.191150	−	0.191150i
$789$		0			0
$790$	1.73205	+	1.00000i	0.0616236	+	0.0355784i
$791$	1.79315	−	0.480473i	0.0637571	−	0.0170837i
$792$		0			0
$793$	4.26795	−	17.2487i	0.151559	−	0.612520i
$794$		−	31.4273i		−	1.11531i
$795$		0			0
$796$	2.26795	−	3.92820i	0.0803853	−	0.139231i
$797$	5.50455	+	9.53416i	0.194981	+	0.337717i	0.946894	−	0.321545i	$-0.104202\pi$
$797$	5.50455	+	9.53416i	0.194981	+	0.337717i	−0.751913	+	0.659262i	$0.770869\pi$
$798$		0			0
$799$	−12.5885	+	46.9808i	−0.445348	+	1.66206i
$800$	−0.258819	+	0.965926i	−0.00915064	+	0.0341506i
$801$		0			0
$802$	−16.9641	−	29.3827i	−0.599023	−	1.03754i
$803$	1.79315	−	3.10583i	0.0632789	−	0.109602i
$804$		0			0
$805$			4.73205i			0.166783i
$806$	−6.21166	+	1.79315i	−0.218796	+	0.0631610i
$807$		0			0
$808$	5.46410	−	1.46410i	0.192226	−	0.0515069i
$809$	23.7506	+	13.7124i	0.835028	+	0.482103i	0.855571	−	0.517686i	$-0.173206\pi$
$809$	23.7506	+	13.7124i	0.835028	+	0.482103i	−0.0205434	+	0.999789i	$0.506540\pi$
$810$		0			0
$811$	−8.16987	−	8.16987i	−0.286883	−	0.286883i	0.548963	−	0.835846i	$-0.315023\pi$
$811$	−8.16987	−	8.16987i	−0.286883	−	0.286883i	−0.835846	+	0.548963i	$0.815023\pi$
$812$	2.44949	+	0.656339i	0.0859602	+	0.0230330i
$813$		0			0
$814$	4.36603	−	4.36603i	0.153029	−	0.153029i
$815$	17.6269	−	10.1769i	0.617443	−	0.356481i
$816$		0			0
$817$	1.05256	+	3.92820i	0.0368244	+	0.137430i
$818$	21.8052			0.762400
$819$		0			0
$820$	4.00000			0.139686
$821$	12.4877	+	46.6047i	0.435823	+	1.62651i	0.739089	+	0.673608i	$0.235256\pi$
$821$	12.4877	+	46.6047i	0.435823	+	1.62651i	−0.303265	+	0.952906i	$0.598077\pi$
$822$		0			0
$823$	−33.8205	+	19.5263i	−1.17891	+	0.680643i	−0.955762	−	0.294142i	$-0.904966\pi$
$823$	−33.8205	+	19.5263i	−1.17891	+	0.680643i	−0.223147	+	0.974785i	$0.571633\pi$
$824$	−0.466870	+	0.466870i	−0.0162642	+	0.0162642i
$825$		0			0
$826$	−3.46410	−	0.928203i	−0.120532	−	0.0322963i
$827$	−24.1160	−	24.1160i	−0.838594	−	0.838594i	0.150080	−	0.988674i	$-0.452047\pi$
$827$	−24.1160	−	24.1160i	−0.838594	−	0.838594i	−0.988674	+	0.150080i	$0.952047\pi$
$828$		0			0
$829$	−35.9090	−	20.7321i	−1.24717	−	0.720054i	−0.276626	−	0.960978i	$-0.589216\pi$
$829$	−35.9090	−	20.7321i	−1.24717	−	0.720054i	−0.970544	+	0.240924i	$0.922550\pi$
$830$	−13.0053	+	3.48477i	−0.451421	+	0.120958i
$831$		0			0
$832$	2.50000	−	2.59808i	0.0866719	−	0.0900721i
$833$		−	30.3548i		−	1.05173i
$834$		0			0
$835$	−3.79423	+	6.57180i	−0.131305	+	0.227426i
$836$	0.448288	+	0.776457i	0.0155044	+	0.0268543i
$837$		0			0
$838$	1.95448	−	7.29423i	0.0675165	−	0.251975i
$839$	−11.4524	+	42.7410i	−0.395381	+	1.47558i	0.425749	+	0.904841i	$0.360011\pi$
$839$	−11.4524	+	42.7410i	−0.395381	+	1.47558i	−0.821130	+	0.570741i	$0.806656\pi$
$840$		0			0
$841$	−10.5000	−	18.1865i	−0.362069	−	0.627122i
$842$	1.79315	−	3.10583i	0.0617961	−	0.107034i
$843$		0			0
$844$			9.92820i			0.341743i
$845$	−9.53914	−	8.83203i	−0.328156	−	0.303831i
$846$		0			0
$847$	8.66025	−	2.32051i	0.297570	−	0.0797336i
$848$	11.1428	+	6.43331i	0.382646	+	0.220921i
$849$		0			0
$850$	−3.46410	−	3.46410i	−0.118818	−	0.118818i
$851$	−31.4780	−	8.43451i	−1.07905	−	0.289131i
$852$		0			0
$853$	15.0000	−	15.0000i	0.513590	−	0.513590i	−0.402034	−	0.915625i	$-0.631697\pi$
$853$	15.0000	−	15.0000i	0.513590	−	0.513590i	0.915625	+	0.402034i	$0.131697\pi$
$854$	−3.82654	+	2.20925i	−0.130941	+	0.0755991i
$855$		0			0
$856$	−3.19615	−	11.9282i	−0.109242	−	0.407698i
$857$	28.7647			0.982585			0.491292	−	0.870995i	$-0.336525\pi$
$857$	28.7647			0.982585			0.491292	+	0.870995i	$0.336525\pi$
$858$		0			0
$859$	−3.00000			−0.102359			−0.0511793	−	0.998689i	$-0.516298\pi$
$859$	−3.00000			−0.102359			−0.0511793	+	0.998689i	$0.516298\pi$
$860$	1.17398	+	4.38134i	0.0400323	+	0.149403i
$861$		0			0
$862$	−8.19615	+	4.73205i	−0.279162	+	0.161174i
$863$	25.6317	−	25.6317i	0.872514	−	0.872514i	−0.120232	−	0.992746i	$-0.538364\pi$
$863$	25.6317	−	25.6317i	0.872514	−	0.872514i	0.992746	+	0.120232i	$0.0383639\pi$
$864$		0			0
$865$	−11.3301	−	3.03590i	−0.385236	−	0.103224i
$866$	19.3185	+	19.3185i	0.656470	+	0.656470i
$867$		0			0
$868$	1.39230	+	0.803848i	0.0472579	+	0.0272844i
$869$	1.93185	−	0.517638i	0.0655336	−	0.0175597i
$870$		0			0
$871$	−33.3205	−	18.3923i	−1.12902	−	0.623199i
$872$			4.62158i			0.156506i
$873$		0			0
$874$	2.36603	−	4.09808i	0.0800320	−	0.138619i
$875$	−0.448288	−	0.776457i	−0.0151549	−	0.0262490i
$876$		0			0
$877$	3.63397	−	13.5622i	0.122711	−	0.457962i	−0.877037	−	0.480423i	$-0.840483\pi$
$877$	3.63397	−	13.5622i	0.122711	−	0.457962i	0.999748	+	0.0224604i	$0.00714997\pi$
$878$	3.82654	−	14.2808i	0.129139	−	0.481955i
$879$		0			0
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	3.51695	−	6.09154i	0.118489	−	0.205229i	−0.800680	−	0.599092i	$-0.795528\pi$
$881$	3.51695	−	6.09154i	0.118489	−	0.205229i	0.919169	+	0.393863i	$0.128862\pi$
$882$		0			0
$883$			25.3205i			0.852103i	0.904699	+	0.426051i	$0.140096\pi$
$883$			25.3205i			0.852103i	−0.904699	+	0.426051i	$0.859904\pi$
$884$	4.89898	+	16.9706i	0.164771	+	0.570782i
$885$		0			0
$886$	−9.92820	+	2.66025i	−0.333545	+	0.0893730i
$887$	−45.5880	−	26.3202i	−1.53069	−	0.883747i	−0.999330	−	0.0366039i	$-0.988346\pi$
$887$	−45.5880	−	26.3202i	−1.53069	−	0.883747i	−0.531365	−	0.847143i	$-0.678321\pi$
$888$		0			0
$889$	−8.02628	−	8.02628i	−0.269193	−	0.269193i
$890$	11.7112	+	3.13801i	0.392561	+	0.105186i
$891$		0			0
$892$	1.70577	−	1.70577i	0.0571134	−	0.0571134i
$893$	7.70882	−	4.45069i	0.257966	−	0.148937i
$894$		0			0
$895$	0.0980762	+	0.366025i	0.00327833	+	0.0122349i
$896$	−0.896575			−0.0299525
$897$		0			0
$898$	1.73205			0.0577993
$899$	1.31268	+	4.89898i	0.0437802	+	0.163390i
$900$		0			0
$901$	−54.5885	+	31.5167i	−1.81861	+	1.04997i
$902$	2.82843	−	2.82843i	0.0941763	−	0.0941763i
$903$		0			0
$904$	−2.00000	−	0.535898i	−0.0665190	−	0.0178237i
$905$	−14.0406	−	14.0406i	−0.466725	−	0.466725i
$906$		0			0
$907$	−8.32051	−	4.80385i	−0.276278	−	0.159509i	0.355459	−	0.934692i	$-0.384324\pi$
$907$	−8.32051	−	4.80385i	−0.276278	−	0.159509i	−0.631737	+	0.775183i	$0.717658\pi$
$908$	10.9348	−	2.92996i	0.362883	−	0.0972342i
$909$		0			0
$910$	0.0621778	+	3.23205i	0.00206117	+	0.107141i
$911$		−	12.8295i		−	0.425059i	−0.977155	−	0.212529i	$-0.931830\pi$
$911$		−	12.8295i		−	0.425059i	0.977155	−	0.212529i	$-0.0681701\pi$
$912$		0			0
$913$	−6.73205	+	11.6603i	−0.222798	+	0.385898i
$914$	−19.1798	−	33.2204i	−0.634412	−	1.09883i
$915$		0			0
$916$	0.124356	−	0.464102i	0.00410883	−	0.0153343i
$917$	−1.01669	+	3.79435i	−0.0335742	+	0.125301i
$918$		0			0
$919$	9.58846	+	16.6077i	0.316294	+	0.547837i	0.979712	−	0.200412i	$-0.0642281\pi$
$919$	9.58846	+	16.6077i	0.316294	+	0.547837i	−0.663418	+	0.748249i	$0.730895\pi$
$920$	2.63896	−	4.57081i	0.0870039	−	0.150695i
$921$		0			0
$922$			13.4641i			0.443417i
$923$	3.72500	+	6.17449i	0.122610	+	0.203236i
$924$		0			0
$925$	5.96410	−	1.59808i	0.196098	−	0.0525444i
$926$	−19.7482	−	11.4016i	−0.648967	−	0.374681i
$927$		0			0
$928$	−2.00000	−	2.00000i	−0.0656532	−	0.0656532i
$929$	−50.8473	−	13.6245i	−1.66825	−	0.447005i	−0.703609	−	0.710587i	$-0.748429\pi$
$929$	−50.8473	−	13.6245i	−1.66825	−	0.447005i	−0.964637	+	0.263582i	$0.915096\pi$
$930$		0			0
$931$	−3.92820	+	3.92820i	−0.128742	+	0.128742i
$932$	7.58871	−	4.38134i	0.248576	−	0.143516i
$933$		0			0
$934$	1.07180	+	4.00000i	0.0350703	+	0.130884i
$935$	−4.89898			−0.160214
$936$		0			0
$937$	−4.92820			−0.160997			−0.0804987	−	0.996755i	$-0.525651\pi$
$937$	−4.92820			−0.160997			−0.0804987	+	0.996755i	$0.525651\pi$
$938$	2.44949	+	9.14162i	0.0799787	+	0.298484i
$939$		0			0
$940$	8.59808	−	4.96410i	0.280438	−	0.161911i
$941$	0.277401	−	0.277401i	0.00904303	−	0.00904303i	−0.702571	−	0.711614i	$-0.747965\pi$
$941$	0.277401	−	0.277401i	0.00904303	−	0.00904303i	0.711614	+	0.702571i	$0.247965\pi$
$942$		0			0
$943$	−20.3923	−	5.46410i	−0.664065	−	0.177936i
$944$	2.82843	+	2.82843i	0.0920575	+	0.0920575i
$945$		0			0
$946$	3.92820	+	2.26795i	0.127717	+	0.0737374i
$947$	1.65445	−	0.443309i	0.0537624	−	0.0144056i	−0.231838	−	0.972755i	$-0.574474\pi$
$947$	1.65445	−	0.443309i	0.0537624	−	0.0144056i	0.285600	+	0.958349i	$0.407807\pi$
$948$		0			0
$949$	−12.9282	+	0.248711i	−0.419667	+	0.00807351i
$950$			0.896575i			0.0290887i
$951$		0			0
$952$	2.19615	−	3.80385i	0.0711777	−	0.123283i
$953$	0.896575	+	1.55291i	0.0290429	+	0.0503038i	0.880182	−	0.474637i	$-0.157421\pi$
$953$	0.896575	+	1.55291i	0.0290429	+	0.0503038i	−0.851139	+	0.524941i	$0.824087\pi$
$954$		0			0
$955$	−6.26795	+	23.3923i	−0.202826	+	0.756957i
$956$	3.82654	−	14.2808i	0.123759	−	0.461875i
$957$		0			0
$958$	5.12436	+	8.87564i	0.165560	+	0.286759i
$959$	−3.58630	+	6.21166i	−0.115808	+	0.200585i
$960$		0			0
$961$		−	27.7846i		−	0.896278i
$962$	−21.6107	−	5.34727i	−0.696758	−	0.172403i
$963$		0			0
$964$	5.96410	−	1.59808i	0.192091	−	0.0514706i
$965$	1.13681	+	0.656339i	0.0365953	+	0.0211283i
$966$		0			0
$967$	31.5429	+	31.5429i	1.01435	+	1.01435i	0.999895	+	0.0144571i	$0.00460199\pi$
$967$	31.5429	+	31.5429i	1.01435	+	1.01435i	0.0144571	+	0.999895i	$0.495398\pi$
$968$	−9.65926	−	2.58819i	−0.310460	−	0.0831876i
$969$		0			0
$970$	−4.53590	+	4.53590i	−0.145639	+	0.145639i
$971$	26.0800	−	15.0573i	0.836947	−	0.483212i	−0.0192783	−	0.999814i	$-0.506137\pi$
$971$	26.0800	−	15.0573i	0.836947	−	0.483212i	0.856225	+	0.516603i	$0.172804\pi$
$972$		0			0
$973$	3.86603	+	14.4282i	0.123939	+	0.462547i
$974$	−16.2499			−0.520679
$975$		0			0
$976$	4.92820			0.157748
$977$	3.66063	+	13.6617i	0.117114	+	0.437075i	0.999436	−	0.0335702i	$-0.0106877\pi$
$977$	3.66063	+	13.6617i	0.117114	+	0.437075i	−0.882322	+	0.470646i	$0.844021\pi$
$978$		0			0
$979$	10.5000	−	6.06218i	0.335581	−	0.193748i
$980$	−4.38134	+	4.38134i	−0.139957	+	0.139957i
$981$		0			0
$982$	−1.69615	−	0.454483i	−0.0541264	−	0.0145031i
$983$	−10.0890	−	10.0890i	−0.321788	−	0.321788i	0.527665	−	0.849453i	$-0.323068\pi$
$983$	−10.0890	−	10.0890i	−0.321788	−	0.321788i	−0.849453	+	0.527665i	$0.823068\pi$
$984$		0			0
$985$	−6.57180	−	3.79423i	−0.209395	−	0.120894i
$986$	13.3843	−	3.58630i	0.426242	−	0.114211i
$987$		0			0
$988$	1.56218	−	2.83013i	0.0496995	−	0.0900383i
$989$		−	23.9401i		−	0.761251i
$990$		0			0
$991$	−25.1962	+	43.6410i	−0.800382	+	1.38630i	0.118983	+	0.992896i	$0.462037\pi$
$991$	−25.1962	+	43.6410i	−0.800382	+	1.38630i	−0.919365	+	0.393406i	$0.871297\pi$
$992$	−0.896575	−	1.55291i	−0.0284663	−	0.0493051i
$993$		0			0
$994$	0.464102	−	1.73205i	0.0147204	−	0.0549373i
$995$	1.17398	−	4.38134i	0.0372176	−	0.138898i
$996$		0			0
$997$	−17.3564	−	30.0622i	−0.549683	−	0.952079i	−0.998296	−	0.0583527i	$-0.981415\pi$
$997$	−17.3564	−	30.0622i	−0.549683	−	0.952079i	0.448613	−	0.893726i	$-0.351918\pi$
$998$	16.4022	−	28.4094i	0.519201	−	0.899283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.c.1151.1	yes	8
3.2	odd	2	inner	1170.2.cu.c.1151.2	yes	8
13.2	odd	12	inner	1170.2.cu.c.431.2	yes	8
39.2	even	12	inner	1170.2.cu.c.431.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.c.431.1	✓	8	39.2	even	12	inner
1170.2.cu.c.431.2	yes	8	13.2	odd	12	inner
1170.2.cu.c.1151.1	yes	8	1.1	even	1	trivial
1170.2.cu.c.1151.2	yes	8	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.866025 - 0.232051i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.866025 - 0.232051i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{10} +(0.965926 - 0.258819i) q^{11} +(-2.59808 - 2.50000i) q^{13} +0.896575i q^{14} +(0.500000 - 0.866025i) q^{16} +(2.44949 + 4.24264i) q^{17} +(0.232051 - 0.866025i) q^{19} +(0.258819 - 0.965926i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.63896 + 4.57081i) q^{23} -1.00000i q^{25} +(-1.74238 + 3.15660i) q^{26} +(0.866025 - 0.232051i) q^{28} +(2.44949 + 1.41421i) q^{29} +(1.26795 + 1.26795i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.46410 - 3.46410i) q^{34} +(0.776457 - 0.448288i) q^{35} +(1.59808 + 5.96410i) q^{37} -0.896575 q^{38} -1.00000 q^{40} +(1.03528 + 3.86370i) q^{41} +(-3.92820 + 2.26795i) q^{43} +(-0.707107 + 0.707107i) q^{44} +(5.09808 + 1.36603i) q^{46} +(7.02030 + 7.02030i) q^{47} +(-5.36603 - 3.09808i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.8666i q^{53} +(-0.500000 + 0.866025i) q^{55} +(-0.448288 - 0.776457i) q^{56} +(0.732051 - 2.73205i) q^{58} +(-1.03528 + 3.86370i) q^{59} +(2.46410 + 4.26795i) q^{61} +(0.896575 - 1.55291i) q^{62} +1.00000i q^{64} +(3.60488 - 0.0693504i) q^{65} +(10.1962 - 2.73205i) q^{67} +(-4.24264 - 2.44949i) q^{68} +(-0.633975 - 0.633975i) q^{70} +(-1.93185 - 0.517638i) q^{71} +(2.53590 - 2.53590i) q^{73} +(5.34727 - 3.08725i) q^{74} +(0.232051 + 0.866025i) q^{76} -0.896575 q^{77} +2.00000 q^{79} +(0.258819 + 0.965926i) q^{80} +(3.46410 - 2.00000i) q^{82} +(-9.52056 + 9.52056i) q^{83} +(-4.73205 - 1.26795i) q^{85} +(3.20736 + 3.20736i) q^{86} +(0.866025 + 0.500000i) q^{88} +(11.7112 - 3.13801i) q^{89} +(1.66987 + 2.76795i) q^{91} -5.27792i q^{92} +(4.96410 - 8.59808i) q^{94} +(0.448288 + 0.776457i) q^{95} +(-1.66025 + 6.19615i) q^{97} +(-1.60368 + 5.98502i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{16} - 12 q^{19} - 4 q^{22} + 24 q^{31} - 8 q^{37} - 8 q^{40} + 24 q^{43} + 20 q^{46} - 36 q^{49} + 28 q^{52} - 4 q^{55} - 8 q^{58} - 8 q^{61} + 40 q^{67} - 12 q^{70} + 48 q^{73} - 12 q^{76} + 16 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{94} + 56 q^{97}+O(q^{100}) \) 8 * q + 4 * q^16 - 12 * q^19 - 4 * q^22 + 24 * q^31 - 8 * q^37 - 8 * q^40 + 24 * q^43 + 20 * q^46 - 36 * q^49 + 28 * q^52 - 4 * q^55 - 8 * q^58 - 8 * q^61 + 40 * q^67 - 12 * q^70 + 48 * q^73 - 12 * q^76 + 16 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^94 + 56 * q^97

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