LMFDB - Embedded newform 460.2.x.a.337.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			337.8
Character	$\chi$	$=$	460.337
Dual form			460.2.x.a.273.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.545609 + 0.203502i) q^{3} +(-2.21096 - 0.334147i) q^{5} +(-0.553657 + 0.120441i) q^{7} +(-2.01097 - 1.74252i) q^{9} +O(q^{10})$	\(q+(0.545609 + 0.203502i) q^{3} +(-2.21096 - 0.334147i) q^{5} +(-0.553657 + 0.120441i) q^{7} +(-2.01097 - 1.74252i) q^{9} +(-5.19477 + 0.746895i) q^{11} +(-0.730177 + 3.35657i) q^{13} +(-1.13832 - 0.632248i) q^{15} +(-1.58760 + 2.90746i) q^{17} +(1.26818 + 0.372372i) q^{19} +(-0.326591 - 0.0469566i) q^{21} +(-2.97831 - 3.75894i) q^{23} +(4.77669 + 1.47757i) q^{25} +(-1.57984 - 2.89325i) q^{27} +(-1.89944 - 6.46890i) q^{29} +(-3.66812 + 8.03205i) q^{31} +(-2.98631 - 0.649632i) q^{33} +(1.26436 - 0.0812868i) q^{35} +(-0.454586 - 6.35594i) q^{37} +(-1.08146 + 1.68278i) q^{39} +(3.48811 + 4.02549i) q^{41} +(1.19610 - 3.20688i) q^{43} +(3.86392 + 4.52460i) q^{45} +(3.04315 + 3.04315i) q^{47} +(-6.07539 + 2.77454i) q^{49} +(-1.45788 + 1.26326i) q^{51} +(-2.03251 - 9.34330i) q^{53} +(11.7350 + 0.0844615i) q^{55} +(0.616153 + 0.461246i) q^{57} +(2.57751 + 4.01068i) q^{59} +(-4.51493 - 2.06190i) q^{61} +(1.32326 + 0.722554i) q^{63} +(2.73598 - 7.17725i) q^{65} +(3.28997 + 4.39488i) q^{67} +(-0.860043 - 2.65701i) q^{69} +(-0.947935 + 6.59304i) q^{71} +(12.0925 - 6.60300i) q^{73} +(2.30552 + 1.77824i) q^{75} +(2.78616 - 1.03919i) q^{77} +(-5.12614 + 3.29437i) q^{79} +(0.862864 + 6.00135i) q^{81} +(-17.0986 + 1.22291i) q^{83} +(4.48163 - 5.89780i) q^{85} +(0.280080 - 3.91603i) q^{87} +(-3.81099 - 8.34491i) q^{89} -1.94633i q^{91} +(-3.63590 + 3.63590i) q^{93} +(-2.67947 - 1.24706i) q^{95} +(12.9709 + 0.927698i) q^{97} +(11.7480 + 7.54999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

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			0
$2$		0			0
$3$	0.545609	+	0.203502i	0.315008	+	0.117492i	0.501995	−	0.864871i	$-0.332600\pi$
$3$	0.545609	+	0.203502i	0.315008	+	0.117492i	−0.186987	+	0.982362i	$0.559872\pi$
$4$		0			0
$5$	−2.21096	−	0.334147i	−0.988772	−	0.149435i
$5$	−2.21096	−	0.334147i	−0.988772	−	0.149435i
$6$		0			0
$7$	−0.553657	+	0.120441i	−0.209263	+	0.0455223i	−0.315975	−	0.948768i	$-0.602331\pi$
$7$	−0.553657	+	0.120441i	−0.209263	+	0.0455223i	0.106712	+	0.994290i	$0.465968\pi$
$8$		0			0
$9$	−2.01097	−	1.74252i	−0.670324	−	0.580839i
$10$		0			0
$11$	−5.19477	+	0.746895i	−1.56628	+	0.225197i	−0.870176	−	0.492742i	$-0.835995\pi$
$11$	−5.19477	+	0.746895i	−1.56628	+	0.225197i	−0.696106	+	0.717939i	$0.745086\pi$
$12$		0			0
$13$	−0.730177	+	3.35657i	−0.202515	+	0.930945i	0.757900	+	0.652371i	$0.226225\pi$
$13$	−0.730177	+	3.35657i	−0.202515	+	0.930945i	−0.960415	+	0.278574i	$0.910138\pi$
$14$		0			0
$15$	−1.13832	−	0.632248i	−0.293913	−	0.163246i
$16$		0			0
$17$	−1.58760	+	2.90746i	−0.385049	+	0.705164i	−0.996270	−	0.0862962i	$-0.972497\pi$
$17$	−1.58760	+	2.90746i	−0.385049	+	0.705164i	0.611221	+	0.791460i	$0.290679\pi$
$18$		0			0
$19$	1.26818	+	0.372372i	0.290941	+	0.0854279i	0.423946	−	0.905687i	$-0.360645\pi$
$19$	1.26818	+	0.372372i	0.290941	+	0.0854279i	−0.133005	+	0.991115i	$0.542463\pi$
$20$		0			0
$21$	−0.326591	−	0.0469566i	−0.0712679	−	0.0102468i
$22$		0			0
$23$	−2.97831	−	3.75894i	−0.621021	−	0.783794i
$23$	−2.97831	−	3.75894i	−0.621021	−	0.783794i
$24$		0			0
$25$	4.77669	+	1.47757i	0.955338	+	0.295514i
$26$		0			0
$27$	−1.57984	−	2.89325i	−0.304040	−	0.556807i
$28$		0			0
$29$	−1.89944	−	6.46890i	−0.352717	−	1.20124i	−0.924610	−	0.380916i	$-0.875609\pi$
$29$	−1.89944	−	6.46890i	−0.352717	−	1.20124i	0.571893	−	0.820329i	$-0.306209\pi$
$30$		0			0
$31$	−3.66812	+	8.03205i	−0.658813	+	1.44260i	0.224811	+	0.974402i	$0.427824\pi$
$31$	−3.66812	+	8.03205i	−0.658813	+	1.44260i	−0.883624	+	0.468197i	$0.844904\pi$
$32$		0			0
$33$	−2.98631	−	0.649632i	−0.519850	−	0.113086i
$34$		0			0
$35$	1.26436	−	0.0812868i	0.213716	−	0.0137400i
$36$		0			0
$37$	−0.454586	−	6.35594i	−0.0747335	−	1.04491i	−0.887044	−	0.461685i	$-0.847245\pi$
$37$	−0.454586	−	6.35594i	−0.0747335	−	1.04491i	0.812310	−	0.583225i	$-0.198209\pi$
$38$		0			0
$39$	−1.08146	+	1.68278i	−0.173172	+	0.269461i
$40$		0			0
$41$	3.48811	+	4.02549i	0.544751	+	0.628677i	0.959652	−	0.281190i	$-0.0907292\pi$
$41$	3.48811	+	4.02549i	0.544751	+	0.628677i	−0.414901	+	0.909867i	$0.636184\pi$
$42$		0			0
$43$	1.19610	−	3.20688i	0.182404	−	0.489044i	−0.813278	−	0.581876i	$-0.802319\pi$
$43$	1.19610	−	3.20688i	0.182404	−	0.489044i	0.995682	+	0.0928314i	$0.0295917\pi$
$44$		0			0
$45$	3.86392	+	4.52460i	0.576000	+	0.674487i
$46$		0			0
$47$	3.04315	+	3.04315i	0.443889	+	0.443889i	0.893317	−	0.449428i	$-0.148372\pi$
$47$	3.04315	+	3.04315i	0.443889	+	0.443889i	−0.449428	+	0.893317i	$0.648372\pi$
$48$		0			0
$49$	−6.07539	+	2.77454i	−0.867913	+	0.396363i
$50$		0			0
$51$	−1.45788	+	1.26326i	−0.204144	+	0.176892i
$52$		0			0
$53$	−2.03251	−	9.34330i	−0.279187	−	1.28340i	−0.876503	−	0.481396i	$-0.840130\pi$
$53$	−2.03251	−	9.34330i	−0.279187	−	1.28340i	0.597316	−	0.802006i	$-0.296234\pi$
$54$		0			0
$55$	11.7350	+	0.0844615i	1.58235	+	0.0113888i
$56$		0			0
$57$	0.616153	+	0.461246i	0.0816115	+	0.0610936i
$58$		0			0
$59$	2.57751	+	4.01068i	0.335563	+	0.522146i	0.967499	−	0.252875i	$-0.0813760\pi$
$59$	2.57751	+	4.01068i	0.335563	+	0.522146i	−0.631936	+	0.775020i	$0.717740\pi$
$60$		0			0
$61$	−4.51493	−	2.06190i	−0.578078	−	0.263999i	0.104846	−	0.994488i	$-0.466565\pi$
$61$	−4.51493	−	2.06190i	−0.578078	−	0.263999i	−0.682924	+	0.730489i	$0.739292\pi$
$62$		0			0
$63$	1.32326	+	0.722554i	0.166715	+	0.0910333i
$64$		0			0
$65$	2.73598	−	7.17725i	0.339356	−	0.890229i
$66$		0			0
$67$	3.28997	+	4.39488i	0.401933	+	0.536920i	0.955152	−	0.296116i	$-0.0956915\pi$
$67$	3.28997	+	4.39488i	0.401933	+	0.536920i	−0.553219	+	0.833036i	$0.686601\pi$
$68$		0			0
$69$	−0.860043	−	2.65701i	−0.103537	−	0.319866i
$70$		0			0
$71$	−0.947935	+	6.59304i	−0.112499	+	0.782449i	0.852975	+	0.521951i	$0.174796\pi$
$71$	−0.947935	+	6.59304i	−0.112499	+	0.782449i	−0.965474	+	0.260498i	$0.916113\pi$
$72$		0			0
$73$	12.0925	−	6.60300i	1.41532	−	0.772822i	0.424170	−	0.905582i	$-0.360566\pi$
$73$	12.0925	−	6.60300i	1.41532	−	0.772822i	0.991148	+	0.132760i	$0.0423839\pi$
$74$		0			0
$75$	2.30552	+	1.77824i	0.266218	+	0.205334i
$76$		0			0
$77$	2.78616	−	1.03919i	0.317513	−	0.118426i
$78$		0			0
$79$	−5.12614	+	3.29437i	−0.576735	+	0.370645i	−0.796254	−	0.604963i	$-0.793188\pi$
$79$	−5.12614	+	3.29437i	−0.576735	+	0.370645i	0.219518	+	0.975608i	$0.429552\pi$
$80$		0			0
$81$	0.862864	+	6.00135i	0.0958738	+	0.666817i
$82$		0			0
$83$	−17.0986	+	1.22291i	−1.87681	+	0.134232i	−0.962586	−	0.270975i	$-0.912654\pi$
$83$	−17.0986	+	1.22291i	−1.87681	+	0.134232i	−0.914225	+	0.405207i	$0.867199\pi$
$84$		0			0
$85$	4.48163	−	5.89780i	0.486101	−	0.639706i
$86$		0			0
$87$	0.280080	−	3.91603i	0.0300277	−	0.419843i
$88$		0			0
$89$	−3.81099	−	8.34491i	−0.403964	−	0.884559i	−0.996853	−	0.0792741i	$-0.974740\pi$
$89$	−3.81099	−	8.34491i	−0.403964	−	0.884559i	0.592888	−	0.805285i	$-0.297988\pi$
$90$		0			0
$91$		−	1.94633i		−	0.204031i
$92$		0			0
$93$	−3.63590	+	3.63590i	−0.377025	+	0.377025i
$94$		0			0
$95$	−2.67947	−	1.24706i	−0.274908	−	0.127945i
$96$		0			0
$97$	12.9709	+	0.927698i	1.31700	+	0.0941935i	0.712082	−	0.702097i	$-0.247753\pi$
$97$	12.9709	+	0.927698i	1.31700	+	0.0941935i	0.604915	+	0.796290i	$0.293207\pi$
$98$		0			0
$99$	11.7480	+	7.54999i	1.18072	+	0.758802i
$100$		0			0
$101$	2.81012	−	3.24305i	0.279617	−	0.322696i	−0.598517	−	0.801110i	$-0.704243\pi$
$101$	2.81012	−	3.24305i	0.279617	−	0.322696i	0.878134	+	0.478415i	$0.158788\pi$
$102$		0			0
$103$	−4.87709	+	6.51503i	−0.480554	+	0.641945i	−0.973655	−	0.228027i	$-0.926772\pi$
$103$	−4.87709	+	6.51503i	−0.480554	+	0.641945i	0.493101	+	0.869972i	$0.335863\pi$
$104$		0			0
$105$	0.706388	+	0.212949i	0.0689365	+	0.0207817i
$106$		0			0
$107$	3.72416	+	9.98485i	0.360028	+	0.965272i	0.983094	+	0.183103i	$0.0586142\pi$
$107$	3.72416	+	9.98485i	0.360028	+	0.965272i	−0.623066	+	0.782169i	$0.714113\pi$
$108$		0			0
$109$	−11.6137	+	3.41008i	−1.11239	+	0.326626i	−0.785763	−	0.618528i	$-0.787729\pi$
$109$	−11.6137	+	3.41008i	−1.11239	+	0.326626i	−0.326624	+	0.945154i	$0.605911\pi$
$110$		0			0
$111$	1.04542	−	3.56037i	0.0992268	−	0.337935i
$112$		0			0
$113$	7.76252	−	5.81095i	0.730236	−	0.546648i	−0.168200	−	0.985753i	$-0.553795\pi$
$113$	7.76252	−	5.81095i	0.730236	−	0.546648i	0.898436	+	0.439105i	$0.144704\pi$
$114$		0			0
$115$	5.32889	+	9.30607i	0.496921	+	0.867796i
$116$		0			0
$117$	7.31724	−	5.47762i	0.676479	−	0.506406i
$118$		0			0
$119$	0.528807	−	1.80095i	0.0484756	−	0.165093i
$120$		0			0
$121$	15.8733	−	4.66083i	1.44303	−	0.423712i
$122$		0			0
$123$	1.08395	+	2.90618i	0.0977365	+	0.262042i
$124$		0			0
$125$	−10.0673	−	4.86297i	−0.900451	−	0.434957i
$126$		0			0
$127$	6.78029	−	9.05741i	0.601653	−	0.803715i	−0.391544	−	0.920159i	$-0.628059\pi$
$127$	6.78029	−	9.05741i	0.601653	−	0.803715i	0.993197	+	0.116445i	$0.0371498\pi$
$128$		0			0
$129$	1.30521	−	1.50629i	0.114917	−	0.132622i
$130$		0			0
$131$	12.2670	+	7.88354i	1.07177	+	0.688788i	0.952643	−	0.304091i	$-0.0983525\pi$
$131$	12.2670	+	7.88354i	1.07177	+	0.688788i	0.119132	+	0.992878i	$0.461989\pi$
$132$		0			0
$133$	−0.746986	−	0.0534255i	−0.0647719	−	0.00463258i
$134$		0			0
$135$	2.52618	+	6.92477i	0.217419	+	0.595989i
$136$		0			0
$137$	2.70034	−	2.70034i	0.230706	−	0.230706i	−0.582281	−	0.812987i	$-0.697840\pi$
$137$	2.70034	−	2.70034i	0.230706	−	0.230706i	0.812987	+	0.582281i	$0.197840\pi$
$138$		0			0
$139$		−	10.4722i		−	0.888243i	−0.895967	−	0.444121i	$-0.853516\pi$
$139$		−	10.4722i		−	0.888243i	0.895967	−	0.444121i	$-0.146484\pi$
$140$		0			0
$141$	1.04108	+	2.27966i	0.0876751	+	0.191982i
$142$		0			0
$143$	1.28610	−	17.9820i	0.107549	−	1.50373i
$144$		0			0
$145$	2.03802	+	14.9372i	0.169249	+	1.24046i
$146$		0			0
$147$	−3.87942	+	0.277461i	−0.319969	+	0.0228846i
$148$		0			0
$149$	−0.111781	−	0.777451i	−0.00915742	−	0.0636912i	0.984730	−	0.174087i	$-0.0556973\pi$
$149$	−0.111781	−	0.777451i	−0.00915742	−	0.0636912i	−0.993888	+	0.110396i	$0.964788\pi$
$150$		0			0
$151$	−10.6948	+	6.87316i	−0.870334	+	0.559330i	−0.897855	−	0.440291i	$-0.854875\pi$
$151$	−10.6948	+	6.87316i	−0.870334	+	0.559330i	0.0275207	+	0.999621i	$0.491239\pi$
$152$		0			0
$153$	8.25892	−	3.08042i	0.667694	−	0.249037i
$154$		0			0
$155$	10.7939	−	16.5329i	0.866991	−	1.32795i
$156$		0			0
$157$	−8.71955	+	4.76124i	−0.695896	+	0.379988i	−0.787927	−	0.615768i	$-0.788846\pi$
$157$	−8.71955	+	4.76124i	−0.695896	+	0.379988i	0.0920314	+	0.995756i	$0.470664\pi$
$158$		0			0
$159$	0.792422	−	5.51141i	0.0628431	−	0.437084i
$160$		0			0
$161$	2.10169	+	1.72246i	0.165637	+	0.135749i
$162$		0			0
$163$	2.23712	+	2.98845i	0.175225	+	0.234073i	0.879552	−	0.475802i	$-0.157842\pi$
$163$	2.23712	+	2.98845i	0.175225	+	0.234073i	−0.704327	+	0.709875i	$0.748751\pi$
$164$		0			0
$165$	6.38554	+	2.43418i	0.497113	+	0.189500i
$166$		0			0
$167$	−8.34846	−	4.55860i	−0.646023	−	0.352755i	0.122601	−	0.992456i	$-0.460876\pi$
$167$	−8.34846	−	4.55860i	−0.646023	−	0.352755i	−0.768624	+	0.639701i	$0.779058\pi$
$168$		0			0
$169$	1.09182	+	0.498619i	0.0839863	+	0.0383553i
$170$		0			0
$171$	−1.90141	−	2.95866i	−0.145405	−	0.226254i
$172$		0			0
$173$	−12.7864	−	9.57181i	−0.972135	−	0.727731i	−0.00989983	−	0.999951i	$-0.503151\pi$
$173$	−12.7864	−	9.57181i	−0.972135	−	0.727731i	−0.962235	+	0.272220i	$0.912242\pi$
$174$		0			0
$175$	−2.82261	−	0.242760i	−0.213369	−	0.0183509i
$176$		0			0
$177$	0.590131	+	2.71279i	0.0443570	+	0.203906i
$178$		0			0
$179$	−17.8696	+	15.4841i	−1.33563	+	1.15733i	−0.361242	+	0.932472i	$0.617647\pi$
$179$	−17.8696	+	15.4841i	−1.33563	+	1.15733i	−0.974391	+	0.224861i	$0.927807\pi$
$180$		0			0
$181$	−24.2285	+	11.0648i	−1.80089	+	0.822438i	−0.841548	+	0.540182i	$0.818356\pi$
$181$	−24.2285	+	11.0648i	−1.80089	+	0.822438i	−0.959339	+	0.282256i	$0.908917\pi$
$182$		0			0
$183$	−2.04379	−	2.04379i	−0.151081	−	0.151081i
$184$		0			0
$185$	−1.11875	+	14.2046i	−0.0822520	+	1.04435i
$186$		0			0
$187$	6.07562	−	16.2894i	0.444293	−	1.19120i
$188$		0			0
$189$	1.22315	+	1.41159i	0.0889713	+	0.102678i
$190$		0			0
$191$	−11.9079	+	18.5290i	−0.861623	+	1.34071i	0.0774505	+	0.996996i	$0.475322\pi$
$191$	−11.9079	+	18.5290i	−0.861623	+	1.34071i	−0.939074	+	0.343716i	$0.888314\pi$
$192$		0			0
$193$	0.0798857	+	1.11695i	0.00575030	+	0.0803997i	0.999517	−	0.0310814i	$-0.00989510\pi$
$193$	0.0798857	+	1.11695i	0.00575030	+	0.0803997i	−0.993767	+	0.111481i	$0.964441\pi$
$194$		0			0
$195$	2.95336	−	3.35920i	0.211495	−	0.240557i
$196$		0			0
$197$	−3.44132	−	0.748614i	−0.245184	−	0.0533366i	0.0882937	−	0.996094i	$-0.471859\pi$
$197$	−3.44132	−	0.748614i	−0.245184	−	0.0533366i	−0.333478	+	0.942758i	$0.608222\pi$
$198$		0			0
$199$	−0.746590	+	1.63480i	−0.0529243	+	0.115888i	−0.934247	−	0.356627i	$-0.883927\pi$
$199$	−0.746590	+	1.63480i	−0.0529243	+	0.115888i	0.881322	+	0.472515i	$0.156654\pi$
$200$		0			0
$201$	0.900671	+	3.06740i	0.0635284	+	0.216358i
$202$		0			0
$203$	1.83076	+	3.35278i	0.128494	+	0.235319i
$204$		0			0
$205$	−6.36697	−	10.0657i	−0.444688	−	0.703022i
$206$		0			0
$207$	−0.560725	+	12.7489i	−0.0389731	+	0.886109i
$208$		0			0
$209$	−6.86603	−	0.987186i	−0.474933	−	0.0682851i
$210$		0			0
$211$	10.3575	+	3.04125i	0.713043	+	0.209368i	0.618083	−	0.786113i	$-0.287910\pi$
$211$	10.3575	+	3.04125i	0.713043	+	0.209368i	0.0949599	+	0.995481i	$0.469728\pi$
$212$		0			0
$213$	−1.85890	+	3.40432i	−0.127370	+	0.233260i
$214$		0			0
$215$	−3.71611	+	6.69061i	−0.253436	+	0.456296i
$216$		0			0
$217$	1.06349	−	4.88880i	0.0721946	−	0.331873i
$218$		0			0
$219$	7.94150	−	1.14181i	0.536637	−	0.0771567i
$220$		0			0
$221$	−8.59988	−	7.45184i	−0.578490	−	0.501265i
$222$		0			0
$223$	13.2891	−	2.89088i	0.889907	−	0.193587i	0.255705	−	0.966755i	$-0.417692\pi$
$223$	13.2891	−	2.89088i	0.889907	−	0.193587i	0.634202	+	0.773167i	$0.281329\pi$
$224$		0			0
$225$	−7.03110	−	11.2948i	−0.468740	−	0.752988i
$226$		0			0
$227$	−22.1259	−	8.25252i	−1.46855	−	0.547739i	−0.517200	−	0.855865i	$-0.673026\pi$
$227$	−22.1259	−	8.25252i	−1.46855	−	0.547739i	−0.951346	+	0.308126i	$0.900298\pi$
$228$		0			0
$229$	−2.74833			−0.181615			−0.0908075	−	0.995868i	$-0.528945\pi$
$229$	−2.74833			−0.181615			−0.0908075	+	0.995868i	$0.528945\pi$
$230$		0			0
$231$	1.73163			0.113933
$232$		0			0
$233$	−20.5283	−	7.65665i	−1.34485	−	0.501604i	−0.429067	−	0.903273i	$-0.641157\pi$
$233$	−20.5283	−	7.65665i	−1.34485	−	0.501604i	−0.915785	+	0.401669i	$0.868430\pi$
$234$		0			0
$235$	−5.71142	−	7.74513i	−0.372572	−	0.505237i
$236$		0			0
$237$	−3.46728	+	0.754260i	−0.225224	+	0.0489945i
$238$		0			0
$239$	−12.6499	−	10.9612i	−0.818252	−	0.709020i	0.141478	−	0.989941i	$-0.454814\pi$
$239$	−12.6499	−	10.9612i	−0.818252	−	0.709020i	−0.959731	+	0.280922i	$0.909360\pi$
$240$		0			0
$241$	−9.08549	+	1.30630i	−0.585248	+	0.0841459i	−0.428578	−	0.903505i	$-0.640985\pi$
$241$	−9.08549	+	1.30630i	−0.585248	+	0.0841459i	−0.156670	+	0.987651i	$0.550076\pi$
$242$		0			0
$243$	−2.85265	+	13.1134i	−0.182998	+	0.841227i
$244$		0			0
$245$	14.3596	−	4.10432i	0.917399	−	0.262215i
$246$		0			0
$247$	−2.17589	+	3.98484i	−0.138448	+	0.253549i
$248$		0			0
$249$	−9.57800	−	2.81236i	−0.606981	−	0.178226i
$250$		0			0
$251$	−9.91073	−	1.42495i	−0.625560	−	0.0899419i	−0.177757	−	0.984074i	$-0.556884\pi$
$251$	−9.91073	−	1.42495i	−0.625560	−	0.0899419i	−0.447803	+	0.894132i	$0.647793\pi$
$252$		0			0
$253$	18.2792	+	17.3024i	1.14920	+	1.08779i
$254$		0			0
$255$	3.64543	−	2.30587i	0.228286	−	0.144399i
$256$		0			0
$257$	9.11681	+	16.6962i	0.568691	+	1.04148i	0.990851	+	0.134958i	$0.0430900\pi$
$257$	9.11681	+	16.6962i	0.568691	+	1.04148i	−0.422161	+	0.906521i	$0.638728\pi$
$258$		0			0
$259$	1.01720	+	3.46426i	0.0632057	+	0.215259i
$260$		0			0
$261$	−7.45245	+	16.3186i	−0.461295	+	1.01009i
$262$		0			0
$263$	−8.30118	−	1.80581i	−0.511873	−	0.111351i	−0.0507921	−	0.998709i	$-0.516175\pi$
$263$	−8.30118	−	1.80581i	−0.511873	−	0.111351i	−0.461081	+	0.887358i	$0.652538\pi$
$264$		0			0
$265$	1.37176	+	21.3368i	0.0842668	+	1.31071i
$266$		0			0
$267$	−0.381109	−	5.32861i	−0.0233235	−	0.326105i
$268$		0			0
$269$	3.82936	−	5.95860i	0.233480	−	0.363302i	−0.704668	−	0.709538i	$-0.748904\pi$
$269$	3.82936	−	5.95860i	0.233480	−	0.363302i	0.938148	+	0.346236i	$0.112540\pi$
$270$		0			0
$271$	−1.58734	−	1.83189i	−0.0964241	−	0.111279i	0.705487	−	0.708723i	$-0.250728\pi$
$271$	−1.58734	−	1.83189i	−0.0964241	−	0.111279i	−0.801911	+	0.597444i	$0.796183\pi$
$272$		0			0
$273$	0.396082	−	1.06194i	0.0239720	−	0.0642714i
$274$		0			0
$275$	−25.9174	−	4.10796i	−1.56288	−	0.247719i
$276$		0			0
$277$	−18.9746	−	18.9746i	−1.14007	−	1.14007i	−0.988437	−	0.151635i	$-0.951546\pi$
$277$	−18.9746	−	18.9746i	−1.14007	−	1.14007i	−0.151635	−	0.988437i	$-0.548454\pi$
$278$		0			0
$279$	21.3725	−	9.76048i	1.27954	−	0.584345i
$280$		0			0
$281$	15.2896	−	13.2485i	0.912102	−	0.790341i	−0.0661397	−	0.997810i	$-0.521068\pi$
$281$	15.2896	−	13.2485i	0.912102	−	0.790341i	0.978241	+	0.207470i	$0.0665228\pi$
$282$		0			0
$283$	−3.08858	−	14.1980i	−0.183597	−	0.843982i	−0.973127	−	0.230270i	$-0.926039\pi$
$283$	−3.08858	−	14.1980i	−0.183597	−	0.843982i	0.789530	−	0.613712i	$-0.210325\pi$
$284$		0			0
$285$	−1.20817	−	1.22568i	−0.0715656	−	0.0726032i
$286$		0			0
$287$	−2.41605	−	1.80863i	−0.142615	−	0.106760i
$288$		0			0
$289$	3.25800	+	5.06955i	0.191647	+	0.298209i
$290$		0			0
$291$	6.88826	+	3.14576i	0.403797	+	0.184408i
$292$		0			0
$293$	27.4088	+	14.9664i	1.60124	+	0.874344i	0.996988	+	0.0775509i	$0.0247100\pi$
$293$	27.4088	+	14.9664i	1.60124	+	0.874344i	0.604253	+	0.796793i	$0.293472\pi$
$294$		0			0
$295$	−4.35861	−	9.72871i	−0.253768	−	0.566428i
$296$		0			0
$297$	10.3678	+	13.8498i	0.601603	+	0.803648i
$298$		0			0
$299$	14.7918	−	7.25221i	0.855435	−	0.419406i
$300$		0			0
$301$	−0.275993	+	1.91957i	−0.0159080	+	0.110642i
$302$		0			0
$303$	2.19319	−	1.19757i	0.125996	−	0.0687988i
$304$		0			0
$305$	9.29336	+	6.06743i	0.532136	+	0.347420i
$306$		0			0
$307$	−6.69926	+	2.49870i	−0.382347	+	0.142608i	−0.533286	−	0.845935i	$-0.679043\pi$
$307$	−6.69926	+	2.49870i	−0.382347	+	0.142608i	0.150939	+	0.988543i	$0.451770\pi$
$308$		0			0
$309$	−3.98681	+	2.56216i	−0.226801	+	0.145756i
$310$		0			0
$311$	−2.59332	−	18.0370i	−0.147054	−	1.02278i	−0.921009	−	0.389542i	$-0.872633\pi$
$311$	−2.59332	−	18.0370i	−0.147054	−	1.02278i	0.773955	−	0.633241i	$-0.218276\pi$
$312$		0			0
$313$	−24.2983	+	1.73785i	−1.37342	+	0.0982291i	−0.738451	−	0.674307i	$-0.764442\pi$
$313$	−24.2983	+	1.73785i	−1.37342	+	0.0982291i	−0.634971	+	0.772536i	$0.718988\pi$
$314$		0			0
$315$	−2.68424	−	2.03970i	−0.151240	−	0.114924i
$316$		0			0
$317$	1.07789	−	15.0709i	0.0605406	−	0.846468i	−0.872937	−	0.487833i	$-0.837788\pi$
$317$	1.07789	−	15.0709i	0.0605406	−	0.846468i	0.933478	−	0.358635i	$-0.116758\pi$
$318$		0			0
$319$	14.6987	+	32.1857i	0.822971	+	1.80206i
$320$		0			0
$321$			6.20570i			0.346369i
$322$		0			0
$323$	−3.09602	+	3.09602i	−0.172267	+	0.172267i
$324$		0			0
$325$	−8.44740	+	14.9544i	−0.468577	+	0.829521i
$326$		0			0
$327$	−7.03048	−	0.502830i	−0.388786	−	0.0278065i
$328$		0			0
$329$	−2.05138	−	1.31834i	−0.113096	−	0.0726825i
$330$		0			0
$331$	10.4223	−	12.0280i	0.572862	−	0.661118i	−0.393192	−	0.919456i	$-0.628629\pi$
$331$	10.4223	−	12.0280i	0.572862	−	0.661118i	0.966055	+	0.258338i	$0.0831748\pi$
$332$		0			0
$333$	−10.1612	+	13.5737i	−0.556829	+	0.743837i
$334$		0			0
$335$	−5.80545	−	10.8162i	−0.317186	−	0.590954i
$336$		0			0
$337$	4.54406	+	12.1831i	0.247531	+	0.663656i	0.999987	+	0.00501416i	$0.00159606\pi$
$337$	4.54406	+	12.1831i	0.247531	+	0.663656i	−0.752457	+	0.658642i	$0.771131\pi$
$338$		0			0
$339$	5.41784	−	1.59082i	0.294257	−	0.0864016i
$340$		0			0
$341$	13.0559	−	44.4644i	0.707017	−	2.40788i
$342$		0			0
$343$	6.20466	−	4.64475i	0.335020	−	0.250793i
$344$		0			0
$345$	1.01369	+	6.16192i	0.0545752	+	0.331747i
$346$		0			0
$347$	−21.0911	+	15.7886i	−1.13223	+	0.847576i	−0.989833	−	0.142234i	$-0.954572\pi$
$347$	−21.0911	+	15.7886i	−1.13223	+	0.847576i	−0.142396	+	0.989810i	$0.545481\pi$
$348$		0			0
$349$	3.74417	−	12.7515i	0.200421	−	0.682570i	−0.796534	−	0.604593i	$-0.793336\pi$
$349$	3.74417	−	12.7515i	0.200421	−	0.682570i	0.996955	−	0.0779771i	$-0.0248461\pi$
$350$		0			0
$351$	10.8650	−	3.19024i	0.579929	−	0.170282i
$352$		0			0
$353$	10.1535	+	27.2226i	0.540416	+	1.44891i	0.864379	+	0.502841i	$0.167712\pi$
$353$	10.1535	+	27.2226i	0.540416	+	1.44891i	−0.323964	+	0.946070i	$0.605016\pi$
$354$		0			0
$355$	4.29889	−	14.2602i	0.228161	−	0.756852i
$356$		0			0
$357$	0.655019	−	0.875002i	0.0346673	−	0.0463100i
$358$		0			0
$359$	−1.55250	+	1.79168i	−0.0819376	+	0.0945611i	−0.795238	−	0.606297i	$-0.792654\pi$
$359$	−1.55250	+	1.79168i	−0.0819376	+	0.0945611i	0.713300	+	0.700858i	$0.247200\pi$
$360$		0			0
$361$	−14.5142	−	9.32771i	−0.763905	−	0.490932i
$362$		0			0
$363$	9.60913	+	0.687259i	0.504349	+	0.0360717i
$364$		0			0
$365$	−28.9424	+	10.5583i	−1.51491	+	0.552647i
$366$		0			0
$367$	7.80773	−	7.80773i	0.407560	−	0.407560i	−0.473327	−	0.880887i	$-0.656947\pi$
$367$	7.80773	−	7.80773i	0.407560	−	0.407560i	0.880887	+	0.473327i	$0.156947\pi$
$368$		0			0
$369$		−	14.1732i		−	0.737830i
$370$		0			0
$371$	2.25063	+	4.92819i	0.116847	+	0.255859i
$372$		0			0
$373$	−1.25359	+	17.5274i	−0.0649082	+	0.907535i	0.855806	+	0.517297i	$0.173062\pi$
$373$	−1.25359	+	17.5274i	−0.0649082	+	0.907535i	−0.920714	+	0.390238i	$0.872393\pi$
$374$		0			0
$375$	−4.50322	−	4.70201i	−0.232545	−	0.242811i
$376$		0			0
$377$	23.1002	−	1.65216i	1.18972	−	0.0850906i
$378$		0			0
$379$	0.00971592	+	0.0675757i	0.000499073	+	0.00347113i	0.990069	−	0.140579i	$-0.0448964\pi$
$379$	0.00971592	+	0.0675757i	0.000499073	+	0.00347113i	−0.989570	+	0.144050i	$0.953987\pi$
$380$		0			0
$381$	5.54259	−	3.56200i	0.283955	−	0.182487i
$382$		0			0
$383$	14.4007	−	5.37117i	0.735839	−	0.274454i	0.0465257	−	0.998917i	$-0.485185\pi$
$383$	14.4007	−	5.37117i	0.735839	−	0.274454i	0.689313	+	0.724463i	$0.257912\pi$
$384$		0			0
$385$	−6.50734	+	1.36661i	−0.331645	+	0.0696489i
$386$		0			0
$387$	−7.99337	+	4.36471i	−0.406326	+	0.221871i
$388$		0			0
$389$	−3.87056	+	26.9204i	−0.196245	+	1.36492i	0.618814	+	0.785538i	$0.287614\pi$
$389$	−3.87056	+	26.9204i	−0.196245	+	1.36492i	−0.815059	+	0.579378i	$0.803295\pi$
$390$		0			0
$391$	15.6574	−	2.69165i	0.791826	−	0.136123i
$392$		0			0
$393$	5.08869	+	6.79769i	0.256690	+	0.342898i
$394$		0			0
$395$	12.4345	−	5.57083i	0.625647	−	0.280299i
$396$		0			0
$397$	14.4967	+	7.91582i	0.727570	+	0.397283i	0.799928	−	0.600095i	$-0.204871\pi$
$397$	14.4967	+	7.91582i	0.727570	+	0.397283i	−0.0723583	+	0.997379i	$0.523053\pi$
$398$		0			0
$399$	−0.396691	−	0.181163i	−0.0198594	−	0.00906947i
$400$		0			0
$401$	−8.53988	−	13.2883i	−0.426461	−	0.663586i	0.559829	−	0.828608i	$-0.310867\pi$
$401$	−8.53988	−	13.2883i	−0.426461	−	0.663586i	−0.986290	+	0.165022i	$0.947231\pi$
$402$		0			0
$403$	−24.2818	−	18.1771i	−1.20956	−	0.905466i
$404$		0			0
$405$	0.0975758	−	13.5571i	0.00484858	−	0.673657i
$406$		0			0
$407$	7.10869	+	32.6781i	0.352365	+	1.61979i
$408$		0			0
$409$	0.407552	−	0.353146i	0.0201522	−	0.0174620i	−0.644726	−	0.764413i	$-0.723029\pi$
$409$	0.407552	−	0.353146i	0.0201522	−	0.0174620i	0.664879	+	0.746951i	$0.268483\pi$
$410$		0			0
$411$	2.02286	−	0.923808i	0.0997802	−	0.0455681i
$412$		0			0
$413$	−1.91010	−	1.91010i	−0.0939901	−	0.0939901i
$414$		0			0
$415$	38.2129	+	3.00962i	1.87580	+	0.147737i
$416$		0			0
$417$	2.13112	−	5.71375i	0.104361	−	0.279803i
$418$		0			0
$419$	3.12462	+	3.60600i	0.152647	+	0.176165i	0.826923	−	0.562316i	$-0.190089\pi$
$419$	3.12462	+	3.60600i	0.152647	+	0.176165i	−0.674275	+	0.738480i	$0.735544\pi$
$420$		0			0
$421$	12.3736	−	19.2537i	0.603051	−	0.938366i	−0.396740	−	0.917931i	$-0.629858\pi$
$421$	12.3736	−	19.2537i	0.603051	−	0.938366i	0.999791	−	0.0204351i	$-0.00650516\pi$
$422$		0			0
$423$	−0.816947	−	11.4224i	−0.0397213	−	0.555377i
$424$		0			0
$425$	−11.8794	+	11.5423i	−0.576238	+	0.559883i
$426$		0			0
$427$	2.74806	+	0.597804i	0.132988	+	0.0289298i
$428$		0			0
$429$	4.36107	−	9.54940i	0.210554	−	0.461050i
$430$		0			0
$431$	0.316858	+	1.07912i	0.0152625	+	0.0519793i	0.966772	−	0.255640i	$-0.0822860\pi$
$431$	0.316858	+	1.07912i	0.0152625	+	0.0519793i	−0.951510	+	0.307619i	$0.900468\pi$
$432$		0			0
$433$	−3.84788	−	7.04686i	−0.184917	−	0.338650i	0.768732	−	0.639571i	$-0.220888\pi$
$433$	−3.84788	−	7.04686i	−0.184917	−	0.338650i	−0.953649	+	0.300920i	$0.902706\pi$
$434$		0			0
$435$	−1.92778	+	8.56460i	−0.0924298	+	0.410641i
$436$		0			0
$437$	−2.37731	−	5.87606i	−0.113722	−	0.281090i
$438$		0			0
$439$	16.5984	+	2.38649i	0.792200	+	0.113901i	0.526523	−	0.850161i	$-0.323495\pi$
$439$	16.5984	+	2.38649i	0.792200	+	0.113901i	0.265677	+	0.964062i	$0.414405\pi$
$440$		0			0
$441$	17.0521	+	5.00696i	0.812006	+	0.238427i
$442$		0			0
$443$	18.9835	−	34.7657i	0.901933	−	1.65177i	0.153921	−	0.988083i	$-0.450810\pi$
$443$	18.9835	−	34.7657i	0.901933	−	1.65177i	0.748012	−	0.663685i	$-0.231008\pi$
$444$		0			0
$445$	5.63753	+	19.7237i	0.267244	+	0.934993i
$446$		0			0
$447$	0.0972241	−	0.446932i	0.00459854	−	0.0211392i
$448$		0			0
$449$	−6.73763	+	0.968725i	−0.317968	+	0.0457170i	−0.299451	−	0.954112i	$-0.596804\pi$
$449$	−6.73763	+	0.968725i	−0.317968	+	0.0457170i	−0.0185171	+	0.999829i	$0.505895\pi$
$450$		0			0
$451$	−21.1265	−	18.3063i	−0.994810	−	0.862008i
$452$		0			0
$453$	−7.23391	+	1.57364i	−0.339879	+	0.0739361i
$454$		0			0
$455$	−0.650361	+	4.30326i	−0.0304894	+	0.201740i
$456$		0			0
$457$	33.0079	+	12.3113i	1.54404	+	0.575899i	0.970038	−	0.242952i	$-0.0781158\pi$
$457$	33.0079	+	12.3113i	1.54404	+	0.575899i	0.574006	+	0.818851i	$0.305388\pi$
$458$		0			0
$459$	10.9202			0.509710
$460$		0			0
$461$	30.8961			1.43897			0.719487	−	0.694506i	$-0.244377\pi$
$461$	30.8961			1.43897			0.719487	+	0.694506i	$0.244377\pi$
$462$		0			0
$463$	4.50457	+	1.68012i	0.209345	+	0.0780817i	0.451949	−	0.892044i	$-0.350729\pi$
$463$	4.50457	+	1.68012i	0.209345	+	0.0780817i	−0.242604	+	0.970125i	$0.578002\pi$
$464$		0			0
$465$	9.25375	−	6.82390i	0.429132	−	0.316451i
$466$		0			0
$467$	9.07573	−	1.97430i	0.419975	−	0.0913599i	0.00238842	−	0.999997i	$-0.499240\pi$
$467$	9.07573	−	1.97430i	0.419975	−	0.0913599i	0.417586	+	0.908637i	$0.362876\pi$
$468$		0			0
$469$	−2.35084	−	2.03701i	−0.108552	−	0.0940605i
$470$		0			0
$471$	−5.72639	+	0.823330i	−0.263858	+	0.0379371i
$472$		0			0
$473$	−3.81828	+	17.5523i	−0.175565	+	0.807058i
$474$		0			0
$475$	5.50750	+	3.65253i	0.252702	+	0.167590i
$476$		0			0
$477$	−12.1935	+	22.3308i	−0.558304	+	1.02246i
$478$		0			0
$479$	5.53376	+	1.62486i	0.252844	+	0.0742417i	0.405698	−	0.914007i	$-0.367028\pi$
$479$	5.53376	+	1.62486i	0.252844	+	0.0742417i	−0.152854	+	0.988249i	$0.548847\pi$
$480$		0			0
$481$	21.6661	+	3.11511i	0.987888	+	0.142037i
$482$		0			0
$483$	0.796181	+	1.36749i	0.0362275	+	0.0622228i
$484$		0			0
$485$	−28.3682	−	6.38530i	−1.28813	−	0.289941i
$486$		0			0
$487$	−0.474941	−	0.869790i	−0.0215217	−	0.0394140i	0.866697	−	0.498835i	$-0.166239\pi$
$487$	−0.474941	−	0.869790i	−0.0215217	−	0.0394140i	−0.888219	+	0.459421i	$0.848057\pi$
$488$		0			0
$489$	0.612442	+	2.08578i	0.0276956	+	0.0943224i
$490$		0			0
$491$	−14.2899	+	31.2905i	−0.644894	+	1.41212i	0.251059	+	0.967972i	$0.419221\pi$
$491$	−14.2899	+	31.2905i	−0.644894	+	1.41212i	−0.895953	+	0.444149i	$0.853506\pi$
$492$		0			0
$493$	21.8236	+	4.74744i	0.982887	+	0.213814i
$494$		0			0
$495$	−23.4516	−	20.6183i	−1.05407	−	0.926723i
$496$		0			0
$497$	−0.269239	−	3.76445i	−0.0120770	−	0.168859i
$498$		0			0
$499$	−11.2204	+	17.4593i	−0.502295	+	0.781586i	−0.996123	−	0.0879739i	$-0.971961\pi$
$499$	−11.2204	+	17.4593i	−0.502295	+	0.781586i	0.493828	+	0.869559i	$0.335597\pi$
$500$		0			0
$501$	−3.62731	−	4.18614i	−0.162056	−	0.187023i
$502$		0			0
$503$	−4.28408	+	11.4861i	−0.191018	+	0.512139i	−0.996788	−	0.0800902i	$-0.974479\pi$
$503$	−4.28408	+	11.4861i	−0.191018	+	0.512139i	0.805770	+	0.592229i	$0.201752\pi$
$504$		0			0
$505$	−7.29672	+	6.23126i	−0.324700	+	0.277288i
$506$		0			0
$507$	0.494239	+	0.494239i	0.0219499	+	0.0219499i
$508$		0			0
$509$	16.1361	−	7.36913i	0.715222	−	0.326631i	−0.0243548	−	0.999703i	$-0.507753\pi$
$509$	16.1361	−	7.36913i	0.715222	−	0.326631i	0.739576	+	0.673073i	$0.235026\pi$
$510$		0			0
$511$	−5.89982	+	5.11223i	−0.260993	+	0.226152i
$512$		0			0
$513$	−0.926153	−	4.25746i	−0.0408906	−	0.187971i
$514$		0			0
$515$	12.9600	−	12.7748i	0.571087	−	0.562925i
$516$		0			0
$517$	−18.0813	−	13.5355i	−0.795217	−	0.595292i
$518$		0			0
$519$	−5.02852	−	7.82453i	−0.220728	−	0.343459i
$520$		0			0
$521$	−14.2308	−	6.49898i	−0.623462	−	0.284726i	0.0785285	−	0.996912i	$-0.474978\pi$
$521$	−14.2308	−	6.49898i	−0.623462	−	0.284726i	−0.701991	+	0.712186i	$0.747705\pi$
$522$		0			0
$523$	30.4317	+	16.6170i	1.33069	+	0.726610i	0.977896	−	0.209092i	$-0.0670508\pi$
$523$	30.4317	+	16.6170i	1.33069	+	0.726610i	0.352791	+	0.935702i	$0.385233\pi$
$524$		0			0
$525$	−1.49064	−	0.706858i	−0.0650569	−	0.0308498i
$526$		0			0
$527$	−17.5294	−	23.4166i	−0.763594	−	1.02004i
$528$		0			0
$529$	−5.25933	+	22.3906i	−0.228666	+	0.973505i
$530$		0			0
$531$	1.80538	−	12.5567i	0.0783469	−	0.544915i
$532$		0			0
$533$	−16.0588	+	8.76876i	−0.695583	+	0.379817i
$534$		0			0
$535$	−4.89756	−	23.3205i	−0.211740	−	1.00823i
$536$		0			0
$537$	−12.9008	+	4.81176i	−0.556712	+	0.207643i
$538$		0			0
$539$	29.4880	−	18.9508i	1.27014	−	0.816267i
$540$		0			0
$541$	−4.86485	−	33.8358i	−0.209156	−	1.45471i	−0.775919	−	0.630832i	$-0.782714\pi$
$541$	−4.86485	−	33.8358i	−0.209156	−	1.45471i	0.566763	−	0.823881i	$-0.308195\pi$
$542$		0			0
$543$	−15.4710	+	1.10651i	−0.663923	+	0.0474847i
$544$		0			0
$545$	26.8168	−	3.65888i	1.14871	−	0.156729i
$546$		0			0
$547$	0.0795944	−	1.11288i	0.00340321	−	0.0475831i	−0.995467	−	0.0951104i	$-0.969680\pi$
$547$	0.0795944	−	1.11288i	0.00340321	−	0.0475831i	0.998870	+	0.0475273i	$0.0151341\pi$
$548$		0			0
$549$	5.48651	+	12.0138i	0.234158	+	0.512735i
$550$		0			0
$551$		−	8.91103i		−	0.379623i
$552$		0			0
$553$	2.44135	−	2.44135i	0.103817	−	0.103817i
$554$		0			0
$555$	−3.50107	+	7.52251i	−0.148612	+	0.319313i
$556$		0			0
$557$	7.47030	+	0.534287i	0.316527	+	0.0226384i	0.228699	−	0.973497i	$-0.426553\pi$
$557$	7.47030	+	0.534287i	0.316527	+	0.0226384i	0.0878280	+	0.996136i	$0.472007\pi$
$558$		0			0
$559$	9.89074	+	6.35639i	0.418334	+	0.268847i
$560$		0			0
$561$	6.62983	−	7.65123i	0.279912	−	0.323035i
$562$		0			0
$563$	−0.491504	+	0.656573i	−0.0207144	+	0.0276712i	−0.810779	−	0.585353i	$-0.800956\pi$
$563$	−0.491504	+	0.656573i	−0.0207144	+	0.0276712i	0.790064	+	0.613024i	$0.210047\pi$
$564$		0			0
$565$	−19.1043	+	10.2540i	−0.803725	+	0.431387i
$566$		0			0
$567$	−1.20054	−	3.21877i	−0.0504179	−	0.135176i
$568$		0			0
$569$	−5.85906	+	1.72037i	−0.245624	+	0.0721219i	−0.402227	−	0.915540i	$-0.631764\pi$
$569$	−5.85906	+	1.72037i	−0.245624	+	0.0721219i	0.156603	+	0.987662i	$0.449946\pi$
$570$		0			0
$571$	5.96905	−	20.3287i	0.249797	−	0.850730i	−0.735155	−	0.677899i	$-0.762890\pi$
$571$	5.96905	−	20.3287i	0.249797	−	0.850730i	0.984952	−	0.172831i	$-0.0552913\pi$
$572$		0			0
$573$	−10.2677	+	7.68633i	−0.428941	+	0.321101i
$574$		0			0
$575$	−8.67236	−	22.3560i	−0.361663	−	0.932309i
$576$		0			0
$577$	6.60953	−	4.94783i	0.275158	−	0.205981i	−0.452782	−	0.891621i	$-0.649569\pi$
$577$	6.60953	−	4.94783i	0.275158	−	0.205981i	0.727941	+	0.685640i	$0.240478\pi$
$578$		0			0
$579$	−0.183715	+	0.625674i	−0.00763492	+	0.0260021i
$580$		0			0
$581$	9.31946	−	2.73644i	0.386636	−	0.113527i
$582$		0			0
$583$	17.5369	+	47.0182i	0.726304	+	1.94730i
$584$		0			0
$585$	−18.0085	+	9.66576i	−0.744558	+	0.399630i
$586$		0			0
$587$	−15.2827	+	20.4153i	−0.630786	+	0.842631i	−0.996098	−	0.0882537i	$-0.971871\pi$
$587$	−15.2827	+	20.4153i	−0.630786	+	0.842631i	0.365312	+	0.930885i	$0.380962\pi$
$588$		0			0
$589$	−7.64274	+	8.82020i	−0.314914	+	0.363430i
$590$		0			0
$591$	−1.72527	−	1.10877i	−0.0709683	−	0.0456086i
$592$		0			0
$593$	−7.96734	−	0.569835i	−0.327179	−	0.0234003i	−0.0932165	−	0.995646i	$-0.529715\pi$
$593$	−7.96734	−	0.569835i	−0.327179	−	0.0234003i	−0.233963	+	0.972246i	$0.575169\pi$
$594$		0			0
$595$	−1.77095	+	3.80513i	−0.0726020	+	0.155995i
$596$		0			0
$597$	−0.740032	+	0.740032i	−0.0302875	+	0.0302875i
$598$		0			0
$599$			25.6597i			1.04843i	0.851587	+	0.524214i	$0.175641\pi$
$599$			25.6597i			1.04843i	−0.851587	+	0.524214i	$0.824359\pi$
$600$		0			0
$601$	5.42484	+	11.8787i	0.221284	+	0.484544i	0.987417	−	0.158138i	$-0.0505491\pi$
$601$	5.42484	+	11.8787i	0.221284	+	0.484544i	−0.766133	+	0.642682i	$0.777822\pi$
$602$		0			0
$603$	1.04212	−	14.5708i	0.0424386	−	0.593369i
$604$		0			0
$605$	−36.6527	+	5.00089i	−1.49015	+	0.203315i
$606$		0			0
$607$	−37.0462	+	2.64960i	−1.50366	+	0.107544i	−0.798710	−	0.601716i	$-0.794484\pi$
$607$	−37.0462	+	2.64960i	−1.50366	+	0.107544i	−0.704948	+	0.709259i	$0.749030\pi$
$608$		0			0
$609$	0.316582	+	2.20187i	0.0128285	+	0.0892244i
$610$		0			0
$611$	−12.4366	+	7.99249i	−0.503130	+	0.323342i
$612$		0			0
$613$	−3.59100	+	1.33937i	−0.145039	+	0.0540967i	−0.420935	−	0.907091i	$-0.638298\pi$
$613$	−3.59100	+	1.33937i	−0.145039	+	0.0540967i	0.275896	+	0.961187i	$0.411025\pi$
$614$		0			0
$615$	−1.42548	−	6.78766i	−0.0574809	−	0.273705i
$616$		0			0
$617$	30.0272	−	16.3961i	1.20885	−	0.660081i	0.256929	−	0.966430i	$-0.417289\pi$
$617$	30.0272	−	16.3961i	1.20885	−	0.660081i	0.951919	+	0.306349i	$0.0991076\pi$
$618$		0			0
$619$	1.52877	−	10.6328i	0.0614464	−	0.427369i	−0.935758	−	0.352643i	$-0.885283\pi$
$619$	1.52877	−	10.6328i	0.0614464	−	0.427369i	0.997204	−	0.0747255i	$-0.0238081\pi$
$620$		0			0
$621$	−6.17034	+	14.5555i	−0.247607	+	0.584093i
$622$		0			0
$623$	3.11505	+	4.16122i	0.124802	+	0.166716i
$624$		0			0
$625$	20.6336	+	14.1158i	0.825343	+	0.564632i
$626$		0			0
$627$	−3.54528	−	1.93587i	−0.141585	−	0.0773111i
$628$		0			0
$629$	19.2014	+	8.76897i	0.765609	+	0.349642i
$630$		0			0
$631$	−20.8422	−	32.4311i	−0.829715	−	1.29106i	−0.954299	−	0.298852i	$-0.903396\pi$
$631$	−20.8422	−	32.4311i	−0.829715	−	1.29106i	0.124585	−	0.992209i	$-0.460240\pi$
$632$		0			0
$633$	5.03228	+	3.76711i	0.200015	+	0.149729i
$634$		0			0
$635$	−18.0175	+	17.7600i	−0.715001	+	0.704782i
$636$		0			0
$637$	−4.87682	−	22.4184i	−0.193227	−	0.888248i
$638$		0			0
$639$	13.3947	−	11.6066i	0.529888	−	0.459151i
$640$		0			0
$641$	−13.4291	+	6.13286i	−0.530417	+	0.242233i	−0.662575	−	0.748995i	$-0.730536\pi$
$641$	−13.4291	+	6.13286i	−0.530417	+	0.242233i	0.132158	+	0.991229i	$0.457809\pi$
$642$		0			0
$643$	6.76925	+	6.76925i	0.266953	+	0.266953i	0.827871	−	0.560918i	$-0.189552\pi$
$643$	6.76925	+	6.76925i	0.266953	+	0.266953i	−0.560918	+	0.827871i	$0.689552\pi$
$644$		0			0
$645$	−3.38909	+	2.89422i	−0.133445	+	0.113960i
$646$		0			0
$647$	−1.47172	+	3.94582i	−0.0578591	+	0.155126i	−0.962663	−	0.270702i	$-0.912744\pi$
$647$	−1.47172	+	3.94582i	−0.0578591	+	0.155126i	0.904804	+	0.425828i	$0.140017\pi$
$648$		0			0
$649$	−16.3851	−	18.9094i	−0.643171	−	0.742259i
$650$		0			0
$651$	1.57513	−	2.45095i	0.0617342	−	0.0960603i
$652$		0			0
$653$	1.86878	+	26.1289i	0.0731309	+	1.02250i	0.893030	+	0.449996i	$0.148575\pi$
$653$	1.86878	+	26.1289i	0.0731309	+	1.02250i	−0.819899	+	0.572507i	$0.805971\pi$
$654$		0			0
$655$	−24.4876	−	21.5292i	−0.956811	−	0.841215i
$656$		0			0
$657$	−35.8235	−	7.79292i	−1.39761	−	0.304031i
$658$		0			0
$659$	11.8191	−	25.8801i	0.460405	−	1.00815i	−0.526990	−	0.849872i	$-0.676679\pi$
$659$	11.8191	−	25.8801i	0.460405	−	1.00815i	0.987395	−	0.158275i	$-0.0505933\pi$
$660$		0			0
$661$	0.287359	+	0.978654i	0.0111770	+	0.0380652i	0.964893	−	0.262645i	$-0.0845946\pi$
$661$	0.287359	+	0.978654i	0.0111770	+	0.0380652i	−0.953716	+	0.300710i	$0.902776\pi$
$662$		0			0
$663$	−3.17571	−	5.81588i	−0.123334	−	0.225870i
$664$		0			0
$665$	1.63371	+	0.367725i	0.0633524	+	0.0142598i
$666$		0			0
$667$	−18.6591	+	26.4063i	−0.722484	+	1.02246i
$668$		0			0
$669$	7.83898	+	1.12708i	0.303073	+	0.0435753i
$670$		0			0
$671$	24.9941	+	7.33892i	0.964885	+	0.283316i
$672$		0			0
$673$	10.2178	−	18.7125i	0.393868	−	0.721315i	−0.603220	−	0.797575i	$-0.706116\pi$
$673$	10.2178	−	18.7125i	0.393868	−	0.721315i	0.997088	+	0.0762595i	$0.0242977\pi$
$674$		0			0
$675$	−3.27140	−	16.1545i	−0.125916	−	0.621787i
$676$		0			0
$677$	−7.19615	+	33.0802i	−0.276571	+	1.27137i	0.603818	+	0.797122i	$0.293645\pi$
$677$	−7.19615	+	33.0802i	−0.276571	+	1.27137i	−0.880389	+	0.474253i	$0.842718\pi$
$678$		0			0
$679$	−7.29317	+	1.04860i	−0.279886	+	0.0402416i
$680$		0			0
$681$	−10.3927	−	9.00531i	−0.398248	−	0.345084i
$682$		0			0
$683$	15.5403	−	3.38059i	0.594634	−	0.129355i	0.0948301	−	0.995493i	$-0.469769\pi$
$683$	15.5403	−	3.38059i	0.594634	−	0.129355i	0.499803	+	0.866139i	$0.333406\pi$
$684$		0			0
$685$	−6.87266	+	5.06804i	−0.262591	+	0.193640i
$686$		0			0
$687$	−1.49952	−	0.559291i	−0.0572101	−	0.0213383i
$688$		0			0
$689$	32.8455			1.25132
$690$		0			0
$691$	−22.5355			−0.857292			−0.428646	−	0.903473i	$-0.641009\pi$
$691$	−22.5355			−0.857292			−0.428646	+	0.903473i	$0.641009\pi$
$692$		0			0
$693$	−7.41370	−	2.76517i	−0.281623	−	0.105040i
$694$		0			0
$695$	−3.49926	+	23.1537i	−0.132735	+	0.878269i
$696$		0			0
$697$	−17.2417	+	3.75070i	−0.653076	+	0.142068i
$698$		0			0
$699$	−9.64228	−	8.35508i	−0.364704	−	0.316018i
$700$		0			0
$701$	5.39595	−	0.775820i	0.203802	−	0.0293023i	−0.0396576	−	0.999213i	$-0.512627\pi$
$701$	5.39595	−	0.775820i	0.203802	−	0.0293023i	0.243460	+	0.969911i	$0.421718\pi$
$702$		0			0
$703$	1.79027	−	8.22976i	0.0675215	−	0.310391i
$704$		0			0
$705$	−1.54005	−	5.38810i	−0.0580018	−	0.202928i
$706$		0			0
$707$	−1.16525	+	2.13399i	−0.0438236	+	0.0802570i
$708$		0			0
$709$	−31.4823	−	9.24403i	−1.18234	−	0.347167i	−0.369266	−	0.929324i	$-0.620391\pi$
$709$	−31.4823	−	9.24403i	−1.18234	−	0.347167i	−0.813076	+	0.582157i	$0.802209\pi$
$710$		0			0
$711$	16.0490	+	2.30750i	0.601885	+	0.0865380i
$712$		0			0
$713$	41.1168	−	10.1337i	1.53984	−	0.379510i
$714$		0			0
$715$	−8.85212	+	39.3277i	−0.331051	+	1.47077i
$716$		0			0
$717$	−4.67127	−	8.55479i	−0.174452	−	0.319485i
$718$		0			0
$719$	−1.58346	−	5.39278i	−0.0590532	−	0.201117i	0.924682	−	0.380739i	$-0.124331\pi$
$719$	−1.58346	−	5.39278i	−0.0590532	−	0.201117i	−0.983736	+	0.179623i	$0.942512\pi$
$720$		0			0
$721$	1.91556	−	4.19449i	0.0713392	−	0.156211i
$722$		0			0
$723$	−5.22296	−	1.13619i	−0.194244	−	0.0422552i
$724$		0			0
$725$	0.485224	−	33.7065i	0.0180208	−	1.25183i
$726$		0			0
$727$	−3.79903	−	53.1174i	−0.140898	−	1.97001i	−0.227523	−	0.973773i	$-0.573063\pi$
$727$	−3.79903	−	53.1174i	−0.140898	−	1.97001i	0.0866252	−	0.996241i	$-0.472392\pi$
$728$		0			0
$729$	5.60878	−	8.72744i	0.207733	−	0.323238i
$730$		0			0
$731$	7.42496	+	8.56886i	0.274622	+	0.316931i
$732$		0			0
$733$	−0.914344	+	2.45145i	−0.0337721	+	0.0905465i	−0.952741	−	0.303783i	$-0.901750\pi$
$733$	−0.914344	+	2.45145i	−0.0337721	+	0.0905465i	0.918969	+	0.394329i	$0.129023\pi$
$734$		0			0
$735$	8.66995	+	0.682839i	0.319796	+	0.0251869i
$736$		0			0
$737$	−20.3731	−	20.3731i	−0.750454	−	0.750454i
$738$		0			0
$739$	−44.3157	+	20.2383i	−1.63018	+	0.744478i	−0.999502	−	0.0315656i	$-0.989951\pi$
$739$	−44.3157	+	20.2383i	−1.63018	+	0.744478i	−0.630679	+	0.776044i	$0.717223\pi$
$740$		0			0
$741$	−1.99811	+	1.73137i	−0.0734023	+	0.0636034i
$742$		0			0
$743$	3.12084	+	14.3463i	0.114493	+	0.526314i	0.998291	+	0.0584451i	$0.0186143\pi$
$743$	3.12084	+	14.3463i	0.114493	+	0.526314i	−0.883798	+	0.467868i	$0.845022\pi$
$744$		0			0
$745$	−0.0126405	+	1.75626i	−0.000463113	+	0.0643445i
$746$		0			0
$747$	36.5157	+	27.3353i	1.33604	+	1.00015i
$748$		0			0
$749$	−3.26449	−	5.07965i	−0.119282	−	0.185606i
$750$		0			0
$751$	43.1089	+	19.6872i	1.57307	+	0.718396i	0.995212	−	0.0977436i	$-0.0311625\pi$
$751$	43.1089	+	19.6872i	1.57307	+	0.718396i	0.577855	+	0.816139i	$0.303890\pi$
$752$		0			0
$753$	−5.11741	−	2.79432i	−0.186489	−	0.101831i
$754$		0			0
$755$	25.9425	−	11.6226i	0.944145	−	0.422991i
$756$		0			0
$757$	−13.3771	−	17.8697i	−0.486198	−	0.649485i	0.488617	−	0.872498i	$-0.337502\pi$
$757$	−13.3771	−	17.8697i	−0.486198	−	0.649485i	−0.974815	+	0.223014i	$0.928411\pi$
$758$		0			0
$759$	6.45223	+	13.1602i	0.234201	+	0.477684i
$760$		0			0
$761$	−4.87753	+	33.9240i	−0.176810	+	1.22974i	0.687275	+	0.726398i	$0.258807\pi$
$761$	−4.87753	+	33.9240i	−0.176810	+	1.22974i	−0.864085	+	0.503346i	$0.832102\pi$
$762$		0			0
$763$	6.01927	−	3.28677i	0.217912	−	0.118989i
$764$		0			0
$765$	−19.2895	+	4.05099i	−0.697412	+	0.146464i
$766$		0			0
$767$	−15.3441	+	5.72307i	−0.554045	+	0.206648i
$768$		0			0
$769$	−30.1670	+	19.3872i	−1.08785	+	0.699119i	−0.956358	−	0.292198i	$-0.905613\pi$
$769$	−30.1670	+	19.3872i	−1.08785	+	0.699119i	−0.131493	+	0.991317i	$0.541977\pi$
$770$		0			0
$771$	1.57651	+	10.9649i	0.0567767	+	0.394891i
$772$		0			0
$773$	−11.1622	+	0.798339i	−0.401478	+	0.0287143i	−0.270618	−	0.962687i	$-0.587228\pi$
$773$	−11.1622	+	0.798339i	−0.401478	+	0.0287143i	−0.130859	+	0.991401i	$0.541774\pi$
$774$		0			0
$775$	−29.3894	+	32.9467i	−1.05570	+	1.18348i
$776$		0			0
$777$	−0.149990	+	2.09714i	−0.00538087	+	0.0752343i
$778$		0			0
$779$	2.92458	+	6.40393i	0.104784	+	0.229445i
$780$		0			0
$781$		−	34.9573i		−	1.25087i
$782$		0			0
$783$	−15.7154	+	15.7154i	−0.561621	+	0.561621i
$784$		0			0
$785$	20.8695	−	7.61329i	0.744866	−	0.271730i
$786$		0			0
$787$	26.5221	+	1.89690i	0.945410	+	0.0676170i	0.535524	−	0.844520i	$-0.320114\pi$
$787$	26.5221	+	1.89690i	0.945410	+	0.0676170i	0.409886	+	0.912137i	$0.365569\pi$
$788$		0			0
$789$	−4.16172	−	2.67457i	−0.148161	−	0.0952174i
$790$		0			0
$791$	−3.59790	+	4.15220i	−0.127927	+	0.147635i
$792$		0			0
$793$	10.2176	−	13.6491i	0.362838	−	0.484695i
$794$		0			0
$795$	−3.59364	+	11.9207i	−0.127453	+	0.422785i
$796$		0			0
$797$	−2.82258	−	7.56764i	−0.0999810	−	0.268059i	0.877323	−	0.479900i	$-0.159327\pi$
$797$	−2.82258	−	7.56764i	−0.0999810	−	0.268059i	−0.977304	+	0.211840i	$0.932054\pi$
$798$		0			0
$799$	−13.6791	+	4.01655i	−0.483933	+	0.142095i
$800$		0			0
$801$	−6.87735	+	23.4221i	−0.242999	+	0.827579i
$802$		0			0
$803$	−57.8859	+	43.3329i	−2.04275	+	1.52918i
$804$		0			0
$805$	−4.07121	−	4.51056i	−0.143491	−	0.158976i
$806$		0			0
$807$	3.30192	−	2.47179i	0.116233	−	0.0870110i
$808$		0			0
$809$	9.56006	−	32.5586i	0.336114	−	1.14470i	−0.602036	−	0.798469i	$-0.705644\pi$
$809$	9.56006	−	32.5586i	0.336114	−	1.14470i	0.938150	−	0.346229i	$-0.112538\pi$
$810$		0			0
$811$	−22.0840	+	6.48445i	−0.775475	+	0.227700i	−0.645441	−	0.763810i	$-0.723327\pi$
$811$	−22.0840	+	6.48445i	−0.775475	+	0.227700i	−0.130033	+	0.991510i	$0.541508\pi$
$812$		0			0
$813$	−0.493275	−	1.32252i	−0.0172999	−	0.0463829i
$814$		0			0
$815$	−3.94761	−	7.35487i	−0.138279	−	0.257630i
$816$		0			0
$817$	2.71103	−	3.62151i	0.0948468	−	0.126700i
$818$		0			0
$819$	−3.39152	+	3.91402i	−0.118509	+	0.136767i
$820$		0			0
$821$	−5.79081	−	3.72153i	−0.202101	−	0.129882i	0.435676	−	0.900104i	$-0.356509\pi$
$821$	−5.79081	−	3.72153i	−0.202101	−	0.129882i	−0.637777	+	0.770221i	$0.720146\pi$
$822$		0			0
$823$	−55.4710	−	3.96737i	−1.93360	−	0.138294i	−0.949250	−	0.314524i	$-0.898155\pi$
$823$	−55.4710	−	3.96737i	−1.93360	−	0.138294i	−0.984349	+	0.176230i	$0.943610\pi$
$824$		0			0
$825$	−13.3048	−	7.51558i	−0.463214	−	0.261659i
$826$		0			0
$827$	1.09707	−	1.09707i	0.0381488	−	0.0381488i	−0.687775	−	0.725924i	$-0.741412\pi$
$827$	1.09707	−	1.09707i	0.0381488	−	0.0381488i	0.725924	+	0.687775i	$0.241412\pi$
$828$		0			0
$829$		−	49.0868i		−	1.70486i	−0.522845	−	0.852428i	$-0.675129\pi$
$829$		−	49.0868i		−	1.70486i	0.522845	−	0.852428i	$-0.324871\pi$
$830$		0			0
$831$	−6.49134	−	14.2141i	−0.225182	−	0.493080i
$832$		0			0
$833$	1.57839	−	22.0688i	0.0546881	−	0.764640i
$834$		0			0
$835$	16.9349	+	12.8685i	0.586055	+	0.445333i
$836$		0			0
$837$	29.0338	−	2.07654i	1.00355	−	0.0717757i
$838$		0			0
$839$	3.10620	+	21.6041i	0.107238	+	0.745856i	0.970500	+	0.241101i	$0.0775084\pi$
$839$	3.10620	+	21.6041i	0.107238	+	0.745856i	−0.863262	+	0.504756i	$0.831583\pi$
$840$		0			0
$841$	−13.8424	+	8.89599i	−0.477325	+	0.306758i
$842$		0			0
$843$	11.0383	−	4.11706i	0.380178	−	0.141799i
$844$		0			0
$845$	−2.24736	−	1.46725i	−0.0773117	−	0.0504751i
$846$		0			0
$847$	−8.22704	+	4.49230i	−0.282684	+	0.154357i
$848$		0			0
$849$	1.20416	−	8.37508i	0.0413265	−	0.287432i
$850$		0			0
$851$	−22.5377	+	20.6387i	−0.772583	+	0.707487i
$852$		0			0
$853$	−19.3073	−	25.7915i	−0.661068	−	0.883083i	0.337229	−	0.941423i	$-0.390510\pi$
$853$	−19.3073	−	25.7915i	−0.661068	−	0.883083i	−0.998297	+	0.0583395i	$0.981419\pi$
$854$		0			0
$855$	3.21532	+	7.17682i	0.109962	+	0.245442i
$856$		0			0
$857$	43.7149	+	23.8701i	1.49327	+	0.815389i	0.998559	−	0.0536673i	$-0.0170910\pi$
$857$	43.7149	+	23.8701i	1.49327	+	0.815389i	0.494714	+	0.869056i	$0.335273\pi$
$858$		0			0
$859$	−46.9493	−	21.4410i	−1.60189	−	0.731559i	−0.604032	−	0.796960i	$-0.706440\pi$
$859$	−46.9493	−	21.4410i	−1.60189	−	0.731559i	−0.997859	+	0.0654009i	$0.979167\pi$
$860$		0			0
$861$	−0.950160	−	1.47848i	−0.0323814	−	0.0503864i
$862$		0			0
$863$	46.4555	+	34.7762i	1.58136	+	1.18379i	0.884445	+	0.466644i	$0.154537\pi$
$863$	46.4555	+	34.7762i	1.58136	+	1.18379i	0.696919	+	0.717150i	$0.254554\pi$
$864$		0			0
$865$	25.0719	+	25.4354i	0.852471	+	0.864831i
$866$		0			0
$867$	0.745934	+	3.42900i	0.0253333	+	0.116455i
$868$		0			0
$869$	24.1685	−	20.9422i	0.819862	−	0.710414i
$870$		0			0
$871$	−17.1540	+	7.83396i	−0.581240	+	0.265444i
$872$		0			0
$873$	−24.4676	−	24.4676i	−0.828103	−	0.828103i
$874$		0			0
$875$	6.15956	+	1.47990i	0.208231	+	0.0500297i
$876$		0			0
$877$	−1.05628	+	2.83200i	−0.0356680	+	0.0956297i	−0.953563	−	0.301194i	$-0.902615\pi$
$877$	−1.05628	+	2.83200i	−0.0356680	+	0.0956297i	0.917895	+	0.396824i	$0.129888\pi$
$878$		0			0
$879$	11.9088	+	13.7435i	0.401675	+	0.463558i
$880$		0			0
$881$	−20.3432	+	31.6546i	−0.685379	+	1.06647i	0.307977	+	0.951394i	$0.400348\pi$
$881$	−20.3432	+	31.6546i	−0.685379	+	1.06647i	−0.993357	+	0.115077i	$0.963288\pi$
$882$		0			0
$883$	−1.12501	−	15.7297i	−0.0378595	−	0.529345i	−0.980626	−	0.195891i	$-0.937240\pi$
$883$	−1.12501	−	15.7297i	−0.0378595	−	0.529345i	0.942766	−	0.333454i	$-0.108214\pi$
$884$		0			0
$885$	−0.398286	−	6.19506i	−0.0133882	−	0.208245i
$886$		0			0
$887$	26.3498	+	5.73204i	0.884739	+	0.192463i	0.631904	−	0.775046i	$-0.282274\pi$
$887$	26.3498	+	5.73204i	0.884739	+	0.192463i	0.252835	+	0.967510i	$0.418637\pi$
$888$		0			0
$889$	−2.66308	+	5.83132i	−0.0893167	+	0.195576i
$890$		0			0
$891$	−8.96476	−	30.5312i	−0.300331	−	1.02283i
$892$		0			0
$893$	2.72608	+	4.99244i	0.0912248	+	0.167066i
$894$		0			0
$895$	44.6828	−	28.2636i	1.49358	−	0.944747i
$896$		0			0
$897$	9.54641	−	0.946707i	0.318745	−	0.0316096i
$898$		0			0
$899$	58.9259	+	8.47227i	1.96529	+	0.282566i
$900$		0			0
$901$	30.3921	+	8.92394i	1.01251	+	0.297299i
$902$		0			0
$903$	−0.541220	+	0.991171i	−0.0180107	+	0.0329841i
$904$		0			0
$905$	57.2654	−	16.3679i	1.90357	−	0.544087i
$906$		0			0
$907$	11.5071	−	52.8975i	0.382088	−	1.75643i	−0.237387	−	0.971415i	$-0.576291\pi$
$907$	11.5071	−	52.8975i	0.382088	−	1.75643i	0.619475	−	0.785016i	$-0.287346\pi$
$908$		0			0
$909$	−11.3021	+	1.62500i	−0.374868	+	0.0538979i
$910$		0			0
$911$	30.6171	+	26.5299i	1.01439	+	0.878974i	0.992678	−	0.120790i	$-0.0385428\pi$
$911$	30.6171	+	26.5299i	1.01439	+	0.878974i	0.0217123	+	0.999764i	$0.493088\pi$
$912$		0			0
$913$	87.9097	−	19.1236i	2.90939	−	0.632898i
$914$		0			0
$915$	3.83581	+	5.20166i	0.126808	+	0.171962i
$916$		0			0
$917$	−7.74123	−	2.88733i	−0.255638	−	0.0953480i
$918$		0			0
$919$	−28.1291			−0.927892			−0.463946	−	0.885864i	$-0.653567\pi$
$919$	−28.1291			−0.927892			−0.463946	+	0.885864i	$0.653567\pi$
$920$		0			0
$921$	−4.16367			−0.137198
$922$		0			0
$923$	−21.4378	−	7.99589i	−0.705634	−	0.263188i
$924$		0			0
$925$	7.21994	−	31.0321i	0.237390	−	1.02033i
$926$		0			0
$927$	21.1602	−	4.60313i	0.694993	−	0.151187i
$928$		0			0
$929$	6.21116	+	5.38200i	0.203781	+	0.176578i	0.750773	−	0.660561i	$-0.229681\pi$
$929$	6.21116	+	5.38200i	0.203781	+	0.176578i	−0.546991	+	0.837138i	$0.684227\pi$
$930$		0			0
$931$	−8.73786	+	1.25631i	−0.286372	+	0.0411740i
$932$		0			0
$933$	2.25561	−	10.3689i	0.0738454	−	0.339462i
$934$		0			0
$935$	−18.8760	+	33.9850i	−0.617311	+	1.11143i
$936$		0			0
$937$	−3.82893	+	7.01216i	−0.125086	+	0.229077i	−0.932716	−	0.360612i	$-0.882568\pi$
$937$	−3.82893	+	7.01216i	−0.125086	+	0.229077i	0.807630	+	0.589689i	$0.200750\pi$
$938$		0			0
$939$	−13.6110	−	3.99656i	−0.444180	−	0.130423i
$940$		0			0
$941$	48.7618	+	7.01089i	1.58959	+	0.228548i	0.879617	−	0.475682i	$-0.157799\pi$
$941$	48.7618	+	7.01089i	1.58959	+	0.228548i	0.709972	+	0.704230i	$0.248708\pi$
$942$		0			0
$943$	4.74293	−	25.1008i	0.154451	−	0.817394i
$944$		0			0
$945$	−2.23266	−	3.52969i	−0.0726286	−	0.114821i
$946$		0			0
$947$	1.95130	+	3.57353i	0.0634086	+	0.116124i	0.907461	−	0.420137i	$-0.138018\pi$
$947$	1.95130	+	3.57353i	0.0634086	+	0.116124i	−0.844052	+	0.536261i	$0.819836\pi$
$948$		0			0
$949$	13.3338	+	45.4106i	0.432832	+	1.47409i
$950$		0			0
$951$	3.65507	−	8.00349i	0.118524	−	0.259531i
$952$		0			0
$953$	−27.4210	−	5.96508i	−0.888254	−	0.193228i	−0.254787	−	0.966997i	$-0.582005\pi$
$953$	−27.4210	−	5.96508i	−0.888254	−	0.193228i	−0.633467	+	0.773769i	$0.718369\pi$
$954$		0			0
$955$	32.5192	−	36.9879i	1.05230	−	1.19690i
$956$		0			0
$957$	1.46991	+	20.5521i	0.0475155	+	0.664354i
$958$		0			0
$959$	−1.16983	+	1.82030i	−0.0377759	+	0.0587804i
$960$		0			0
$961$	−30.7581	−	35.4968i	−0.992198	−	1.14506i
$962$		0			0
$963$	9.90960	−	26.5687i	0.319332	−	0.856164i
$964$		0			0
$965$	0.196601	−	2.49622i	0.00632880	−	0.0803562i
$966$		0			0
$967$	33.6606	+	33.6606i	1.08245	+	1.08245i	0.996280	+	0.0861707i	$0.0274630\pi$
$967$	33.6606	+	33.6606i	1.08245	+	1.08245i	0.0861707	+	0.996280i	$0.472537\pi$
$968$		0			0
$969$	−2.31926	+	1.05917i	−0.0745054	+	0.0340255i
$970$		0			0
$971$	18.6198	−	16.1342i	0.597539	−	0.517771i	−0.302746	−	0.953071i	$-0.597903\pi$
$971$	18.6198	−	16.1342i	0.597539	−	0.517771i	0.900285	+	0.435301i	$0.143358\pi$
$972$		0			0
$973$	1.26128	+	5.79803i	0.0404349	+	0.185876i
$974$		0			0
$975$	−7.65223	+	6.44020i	−0.245067	+	0.206252i
$976$		0			0
$977$	18.3901	+	13.7666i	0.588350	+	0.440433i	0.851524	−	0.524315i	$-0.175679\pi$
$977$	18.3901	+	13.7666i	0.588350	+	0.440433i	−0.263174	+	0.964748i	$0.584769\pi$
$978$		0			0
$979$	26.0300	+	40.5035i	0.831922	+	1.29450i
$980$		0			0
$981$	29.2969	+	13.3794i	0.935376	+	0.427172i
$982$		0			0
$983$	24.6568	+	13.4636i	0.786429	+	0.429423i	0.821675	−	0.569956i	$-0.193040\pi$
$983$	24.6568	+	13.4636i	0.786429	+	0.429423i	−0.0352460	+	0.999379i	$0.511221\pi$
$984$		0			0
$985$	7.35848	+	2.80506i	0.234461	+	0.0893768i
$986$		0			0
$987$	−0.850967	−	1.13676i	−0.0270866	−	0.0361834i
$988$		0			0
$989$	−15.6168	+	5.05499i	−0.496587	+	0.160739i
$990$		0			0
$991$	0.616456	−	4.28755i	0.0195824	−	0.136198i	−0.977685	−	0.210077i	$-0.932629\pi$
$991$	0.616456	−	4.28755i	0.0195824	−	0.136198i	0.997267	+	0.0738784i	$0.0235377\pi$
$992$		0			0
$993$	8.13423	−	4.44163i	0.258132	−	0.140951i
$994$		0			0
$995$	2.19695	−	3.36501i	0.0696478	−	0.106678i
$996$		0			0
$997$	−22.6212	+	8.43727i	−0.716420	+	0.267211i	−0.681126	−	0.732166i	$-0.738510\pi$
$997$	−22.6212	+	8.43727i	−0.716420	+	0.267211i	−0.0352941	+	0.999377i	$0.511237\pi$
$998$		0			0
$999$	−17.6712	+	11.3566i	−0.559091	+	0.359306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.337.8	yes	240
5.3	odd	4	inner	460.2.x.a.153.5	✓	240
23.20	odd	22	inner	460.2.x.a.457.5	yes	240
115.43	even	44	inner	460.2.x.a.273.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.153.5	✓	240	5.3	odd	4	inner
460.2.x.a.273.8	yes	240	115.43	even	44	inner
460.2.x.a.337.8	yes	240	1.1	even	1	trivial
460.2.x.a.457.5	yes	240	23.20	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.545609 + 0.203502i) q^{3} +(-2.21096 - 0.334147i) q^{5} +(-0.553657 + 0.120441i) q^{7} +(-2.01097 - 1.74252i) q^{9} +O(q^{10})\)	\(q+(0.545609 + 0.203502i) q^{3} +(-2.21096 - 0.334147i) q^{5} +(-0.553657 + 0.120441i) q^{7} +(-2.01097 - 1.74252i) q^{9} +(-5.19477 + 0.746895i) q^{11} +(-0.730177 + 3.35657i) q^{13} +(-1.13832 - 0.632248i) q^{15} +(-1.58760 + 2.90746i) q^{17} +(1.26818 + 0.372372i) q^{19} +(-0.326591 - 0.0469566i) q^{21} +(-2.97831 - 3.75894i) q^{23} +(4.77669 + 1.47757i) q^{25} +(-1.57984 - 2.89325i) q^{27} +(-1.89944 - 6.46890i) q^{29} +(-3.66812 + 8.03205i) q^{31} +(-2.98631 - 0.649632i) q^{33} +(1.26436 - 0.0812868i) q^{35} +(-0.454586 - 6.35594i) q^{37} +(-1.08146 + 1.68278i) q^{39} +(3.48811 + 4.02549i) q^{41} +(1.19610 - 3.20688i) q^{43} +(3.86392 + 4.52460i) q^{45} +(3.04315 + 3.04315i) q^{47} +(-6.07539 + 2.77454i) q^{49} +(-1.45788 + 1.26326i) q^{51} +(-2.03251 - 9.34330i) q^{53} +(11.7350 + 0.0844615i) q^{55} +(0.616153 + 0.461246i) q^{57} +(2.57751 + 4.01068i) q^{59} +(-4.51493 - 2.06190i) q^{61} +(1.32326 + 0.722554i) q^{63} +(2.73598 - 7.17725i) q^{65} +(3.28997 + 4.39488i) q^{67} +(-0.860043 - 2.65701i) q^{69} +(-0.947935 + 6.59304i) q^{71} +(12.0925 - 6.60300i) q^{73} +(2.30552 + 1.77824i) q^{75} +(2.78616 - 1.03919i) q^{77} +(-5.12614 + 3.29437i) q^{79} +(0.862864 + 6.00135i) q^{81} +(-17.0986 + 1.22291i) q^{83} +(4.48163 - 5.89780i) q^{85} +(0.280080 - 3.91603i) q^{87} +(-3.81099 - 8.34491i) q^{89} -1.94633i q^{91} +(-3.63590 + 3.63590i) q^{93} +(-2.67947 - 1.24706i) q^{95} +(12.9709 + 0.927698i) q^{97} +(11.7480 + 7.54999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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