LMFDB - Embedded newform 637.2.bc.a.460.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			460.5
Character	$\chi$	$=$	637.460
Dual form			637.2.bc.a.619.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.312819 + 1.16746i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(0.466951 - 0.269594i) q^{4} +(-0.837372 + 0.224373i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(2.17009 + 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +O(q^{10})$	\(q+(0.312819 + 1.16746i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(0.466951 - 0.269594i) q^{4} +(-0.837372 + 0.224373i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(2.17009 + 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +(-0.523892 - 0.907408i) q^{10} +(-0.678845 + 2.53348i) q^{11} +(-0.612999 + 1.06175i) q^{12} +(0.104263 + 3.60404i) q^{13} +(1.39383 - 1.39383i) q^{15} +(-1.31545 + 2.27842i) q^{16} +(-1.52363 - 2.63901i) q^{17} +(2.53348 + 0.678845i) q^{18} +(0.142426 - 0.0381629i) q^{19} +(-0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +(-5.63805 - 3.25513i) q^{23} +(-6.74039 - 1.80608i) q^{24} +(-3.67928 + 2.12423i) q^{25} +(-4.17495 + 1.24914i) q^{26} -1.88704i q^{27} -3.78765 q^{29} +(2.06325 + 1.19122i) q^{30} +(-2.47920 + 9.25250i) q^{31} +(2.85733 + 0.765619i) q^{32} +(-1.54354 - 5.76059i) q^{33} +(2.60430 - 2.60430i) q^{34} -1.17009i q^{36} +(2.76582 - 0.741100i) q^{37} +(0.0891070 + 0.154338i) q^{38} +(-4.30271 - 6.97838i) q^{39} +(-2.30408 - 1.33026i) q^{40} +(2.27378 + 2.27378i) q^{41} -3.18342i q^{43} +(0.366025 + 1.36603i) q^{44} +(-0.486909 + 1.81717i) q^{45} +(2.03653 - 7.60045i) q^{46} +(-1.90947 - 7.12626i) q^{47} -5.98209i q^{48} +(-3.63090 - 3.63090i) q^{50} +(6.00053 + 3.46441i) q^{51} +(1.02032 + 1.65480i) q^{52} +(-1.71594 - 2.97210i) q^{53} +(2.20304 - 0.590303i) q^{54} -2.27378i q^{55} +(-0.237071 + 0.237071i) q^{57} +(-1.18485 - 4.42192i) q^{58} +(-12.5010 - 3.34963i) q^{59} +(0.275081 - 1.02662i) q^{60} +(7.97398 + 4.60378i) q^{61} -11.5774 q^{62} +8.83710i q^{64} +(-0.895958 - 2.99453i) q^{65} +(6.24239 - 3.60404i) q^{66} +(1.43357 + 0.384125i) q^{67} +(-1.42292 - 0.821525i) q^{68} +14.8029 q^{69} +(-4.10310 + 4.10310i) q^{71} +(6.43299 - 1.72371i) q^{72} +(9.46056 + 2.53495i) q^{73} +(1.73041 + 2.99715i) q^{74} +(4.83004 - 8.36588i) q^{75} +(0.0562174 - 0.0562174i) q^{76} +(6.80098 - 7.20620i) q^{78} +(-8.79791 + 15.2384i) q^{79} +(0.590303 - 2.20304i) q^{80} +(5.40049 + 9.35393i) q^{81} +(-1.94326 + 3.36583i) q^{82} +(10.5474 + 10.5474i) q^{83} +(1.86797 + 1.86797i) q^{85} +(3.71650 - 0.995834i) q^{86} +(7.45847 - 4.30615i) q^{87} +(-6.97103 + 4.02472i) q^{88} +(-1.24285 - 4.63836i) q^{89} -2.27378 q^{90} -3.51026 q^{92} +(-5.63716 - 21.0382i) q^{93} +(7.72228 - 4.45846i) q^{94} +(-0.110701 + 0.0639130i) q^{95} +(-6.49694 + 1.74085i) q^{96} +(-4.44330 - 4.44330i) q^{97} +(4.02472 + 4.02472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.312819	+	1.16746i	0.221197	+	0.825517i	0.983893	+	0.178760i	$0.0572085\pi$
$2$	0.312819	+	1.16746i	0.221197	+	0.825517i	−0.762696	+	0.646757i	$0.776125\pi$
$3$	−1.96915	+	1.13689i	−1.13689	+	0.656384i	−0.945659	−	0.325160i	$-0.894582\pi$
$3$	−1.96915	+	1.13689i	−1.13689	+	0.656384i	−0.191232	+	0.981545i	$0.561248\pi$
$4$	0.466951	−	0.269594i	0.233476	−	0.134797i
$5$	−0.837372	+	0.224373i	−0.374484	+	0.100343i	−0.441152	−	0.897432i	$-0.645430\pi$
$5$	−0.837372	+	0.224373i	−0.374484	+	0.100343i	0.0666675	+	0.997775i	$0.478763\pi$
$6$	−1.94326	−	1.94326i	−0.793333	−	0.793333i
$7$		0			0
$7$		0			0
$8$	2.17009	+	2.17009i	0.767241	+	0.767241i
$9$	1.08504	−	1.87935i	0.361681	−	0.626450i
$10$	−0.523892	−	0.907408i	−0.165669	−	0.286948i
$11$	−0.678845	+	2.53348i	−0.204679	+	0.763874i	0.784868	+	0.619663i	$0.212731\pi$
$11$	−0.678845	+	2.53348i	−0.204679	+	0.763874i	−0.989547	+	0.144210i	$0.953936\pi$
$12$	−0.612999	+	1.06175i	−0.176958	+	0.306500i
$13$	0.104263	+	3.60404i	0.0289173	+	0.999582i
$13$	0.104263	+	3.60404i	0.0289173	+	0.999582i
$14$		0			0
$15$	1.39383	−	1.39383i	0.359884	−	0.359884i
$16$	−1.31545	+	2.27842i	−0.328862	+	0.569606i
$17$	−1.52363	−	2.63901i	−0.369535	−	0.640053i	0.619958	−	0.784635i	$-0.287150\pi$
$17$	−1.52363	−	2.63901i	−0.369535	−	0.640053i	−0.989493	+	0.144582i	$0.953816\pi$
$18$	2.53348	+	0.678845i	0.597147	+	0.160005i
$19$	0.142426	−	0.0381629i	0.0326747	−	0.00875516i	−0.242445	−	0.970165i	$-0.577949\pi$
$19$	0.142426	−	0.0381629i	0.0326747	−	0.00875516i	0.275119	+	0.961410i	$0.411283\pi$
$20$	−0.330522	+	0.330522i	−0.0739070	+	0.0739070i
$21$		0			0
$22$	−3.17009			−0.675865
$23$	−5.63805	−	3.25513i	−1.17561	−	0.678741i	−0.220619	−	0.975360i	$-0.570808\pi$
$23$	−5.63805	−	3.25513i	−1.17561	−	0.678741i	−0.954996	+	0.296619i	$0.904141\pi$
$24$	−6.74039	−	1.80608i	−1.37588	−	0.368665i
$25$	−3.67928	+	2.12423i	−0.735856	+	0.424846i
$26$	−4.17495	+	1.24914i	−0.818775	+	0.244976i
$27$		−	1.88704i		−	0.363162i
$28$		0			0
$29$	−3.78765			−0.703350			−0.351675	−	0.936122i	$-0.614388\pi$
$29$	−3.78765			−0.703350			−0.351675	+	0.936122i	$0.614388\pi$
$30$	2.06325	+	1.19122i	0.376696	+	0.217485i
$31$	−2.47920	+	9.25250i	−0.445278	+	1.66180i	0.269925	+	0.962881i	$0.413001\pi$
$31$	−2.47920	+	9.25250i	−0.445278	+	1.66180i	−0.715203	+	0.698917i	$0.753666\pi$
$32$	2.85733	+	0.765619i	0.505109	+	0.135344i
$33$	−1.54354	−	5.76059i	−0.268697	−	1.00279i
$34$	2.60430	−	2.60430i	0.446635	−	0.446635i
$35$		0			0
$36$		−	1.17009i		−	0.195014i
$37$	2.76582	−	0.741100i	0.454699	−	0.121836i	−0.0241984	−	0.999707i	$-0.507703\pi$
$37$	2.76582	−	0.741100i	0.454699	−	0.121836i	0.478897	+	0.877871i	$0.341037\pi$
$38$	0.0891070	+	0.154338i	0.0144551	+	0.0250369i
$39$	−4.30271	−	6.97838i	−0.688986	−	1.11743i
$40$	−2.30408	−	1.33026i	−0.364307	−	0.210333i
$41$	2.27378	+	2.27378i	0.355105	+	0.355105i	0.862005	−	0.506900i	$-0.169209\pi$
$41$	2.27378	+	2.27378i	0.355105	+	0.355105i	−0.506900	+	0.862005i	$0.669209\pi$
$42$		0			0
$43$		−	3.18342i		−	0.485467i	−0.970093	−	0.242733i	$-0.921956\pi$
$43$		−	3.18342i		−	0.485467i	0.970093	−	0.242733i	$-0.0780440\pi$
$44$	0.366025	+	1.36603i	0.0551804	+	0.205936i
$45$	−0.486909	+	1.81717i	−0.0725842	+	0.270888i
$46$	2.03653	−	7.60045i	0.300270	−	1.12062i
$47$	−1.90947	−	7.12626i	−0.278525	−	1.03947i	−0.953442	−	0.301577i	$-0.902487\pi$
$47$	−1.90947	−	7.12626i	−0.278525	−	1.03947i	0.674916	−	0.737894i	$-0.264180\pi$
$48$		−	5.98209i		−	0.863440i
$49$		0			0
$50$	−3.63090	−	3.63090i	−0.513486	−	0.513486i
$51$	6.00053	+	3.46441i	0.840242	+	0.485114i
$52$	1.02032	+	1.65480i	0.141492	+	0.229480i
$53$	−1.71594	−	2.97210i	−0.235703	−	0.408249i	0.723774	−	0.690037i	$-0.242406\pi$
$53$	−1.71594	−	2.97210i	−0.235703	−	0.408249i	−0.959477	+	0.281788i	$0.909072\pi$
$54$	2.20304	−	0.590303i	0.299796	−	0.0803301i
$55$		−	2.27378i		−	0.306597i
$56$		0			0
$57$	−0.237071	+	0.237071i	−0.0314008	+	0.0314008i
$58$	−1.18485	−	4.42192i	−0.155578	−	0.580627i
$59$	−12.5010	−	3.34963i	−1.62749	−	0.436084i	−0.674299	−	0.738459i	$-0.735554\pi$
$59$	−12.5010	−	3.34963i	−1.62749	−	0.436084i	−0.953189	+	0.302375i	$0.902221\pi$
$60$	0.275081	−	1.02662i	0.0355128	−	0.132536i
$61$	7.97398	+	4.60378i	1.02096	+	0.589454i	0.914383	−	0.404850i	$-0.132676\pi$
$61$	7.97398	+	4.60378i	1.02096	+	0.589454i	0.106581	+	0.994304i	$0.466010\pi$
$62$	−11.5774			−1.47034
$63$		0			0
$64$			8.83710i			1.10464i
$65$	−0.895958	−	2.99453i	−0.111130	−	0.371426i
$66$	6.24239	−	3.60404i	0.768385	−	0.443627i
$67$	1.43357	+	0.384125i	0.175139	+	0.0469283i	0.345323	−	0.938484i	$-0.387769\pi$
$67$	1.43357	+	0.384125i	0.175139	+	0.0469283i	−0.170184	+	0.985412i	$0.554436\pi$
$68$	−1.42292	−	0.821525i	−0.172555	−	0.0996245i
$69$	14.8029			1.78206
$70$		0			0
$71$	−4.10310	+	4.10310i	−0.486949	+	0.486949i	−0.907342	−	0.420393i	$-0.861892\pi$
$71$	−4.10310	+	4.10310i	−0.486949	+	0.486949i	0.420393	+	0.907342i	$0.361892\pi$
$72$	6.43299	−	1.72371i	0.758135	−	0.203142i
$73$	9.46056	+	2.53495i	1.10727	+	0.296693i	0.765724	−	0.643170i	$-0.222381\pi$
$73$	9.46056	+	2.53495i	1.10727	+	0.296693i	0.341551	+	0.939863i	$0.389048\pi$
$74$	1.73041	+	2.99715i	0.201156	+	0.348412i
$75$	4.83004	−	8.36588i	0.557725	−	0.966008i
$76$	0.0562174	−	0.0562174i	0.00644858	−	0.00644858i
$77$		0			0
$78$	6.80098	−	7.20620i	0.770060	−	0.815942i
$79$	−8.79791	+	15.2384i	−0.989842	+	1.71446i	−0.371800	+	0.928313i	$0.621259\pi$
$79$	−8.79791	+	15.2384i	−0.989842	+	1.71446i	−0.618043	+	0.786145i	$0.712074\pi$
$80$	0.590303	−	2.20304i	0.0659979	−	0.246307i
$81$	5.40049	+	9.35393i	0.600055	+	1.03933i
$82$	−1.94326	+	3.36583i	−0.214597	+	0.371693i
$83$	10.5474	+	10.5474i	1.15773	+	1.15773i	0.984963	+	0.172763i	$0.0552694\pi$
$83$	10.5474	+	10.5474i	1.15773	+	1.15773i	0.172763	+	0.984963i	$0.444731\pi$
$84$		0			0
$85$	1.86797	+	1.86797i	0.202610	+	0.202610i
$86$	3.71650	−	0.995834i	0.400761	−	0.107384i
$87$	7.45847	−	4.30615i	0.799632	−	0.461668i
$88$	−6.97103	+	4.02472i	−0.743114	+	0.429037i
$89$	−1.24285	−	4.63836i	−0.131741	−	0.491666i	0.868249	−	0.496129i	$-0.165246\pi$
$89$	−1.24285	−	4.63836i	−0.131741	−	0.491666i	−0.999990	+	0.00446375i	$0.998579\pi$
$90$	−2.27378			−0.239678
$91$		0			0
$92$	−3.51026			−0.365970
$93$	−5.63716	−	21.0382i	−0.584547	−	2.18156i
$94$	7.72228	−	4.45846i	0.796492	−	0.459855i
$95$	−0.110701	+	0.0639130i	−0.0113576	+	0.00655734i
$96$	−6.49694	+	1.74085i	−0.663091	+	0.177675i
$97$	−4.44330	−	4.44330i	−0.451149	−	0.451149i	0.444587	−	0.895736i	$-0.353351\pi$
$97$	−4.44330	−	4.44330i	−0.451149	−	0.451149i	−0.895736	+	0.444587i	$0.853351\pi$
$98$		0			0
$99$	4.02472	+	4.02472i	0.404500	+	0.404500i
$100$	−1.14536	+	1.98383i	−0.114536	+	0.198383i
$101$	0.580109	+	1.00478i	0.0577231	+	0.0999793i	0.893443	−	0.449177i	$-0.148283\pi$
$101$	0.580109	+	1.00478i	0.0577231	+	0.0999793i	−0.835720	+	0.549156i	$0.814949\pi$
$102$	−2.16746	+	8.08909i	−0.214611	+	0.800939i
$103$	−2.66052	+	4.60816i	−0.262149	+	0.454055i	−0.966813	−	0.255486i	$-0.917765\pi$
$103$	−2.66052	+	4.60816i	−0.262149	+	0.454055i	0.704664	+	0.709541i	$0.251098\pi$
$104$	−7.59483	+	8.04735i	−0.744734	+	0.789107i
$105$		0			0
$106$	2.93302	−	2.93302i	0.284880	−	0.284880i
$107$	−5.12423	+	8.87543i	−0.495378	+	0.858020i	−0.999986	−	0.00532858i	$-0.998304\pi$
$107$	−5.12423	+	8.87543i	−0.495378	+	0.858020i	0.504608	+	0.863349i	$0.331637\pi$
$108$	−0.508736	−	0.881157i	−0.0489532	−	0.0847894i
$109$	7.99758	+	2.14295i	0.766030	+	0.205257i	0.620617	−	0.784114i	$-0.286882\pi$
$109$	7.99758	+	2.14295i	0.766030	+	0.205257i	0.145413	+	0.989371i	$0.453549\pi$
$110$	2.65454	−	0.711283i	0.253101	−	0.0678181i
$111$	−4.60378	+	4.60378i	−0.436972	+	0.436972i
$112$		0			0
$113$	5.74539			0.540481			0.270241	−	0.962793i	$-0.412897\pi$
$113$	5.74539			0.540481			0.270241	+	0.962793i	$0.412897\pi$
$114$	−0.350931	−	0.202610i	−0.0328677	−	0.0189762i
$115$	5.45151	+	1.46073i	0.508356	+	0.136214i
$116$	−1.76865	+	1.02113i	−0.164215	+	0.0948096i
$117$	6.88639	+	3.71460i	0.636647	+	0.343415i
$118$		−	15.6422i		−	1.43998i
$119$		0			0
$120$	6.04945			0.552237
$121$	3.56858	+	2.06032i	0.324416	+	0.187302i
$122$	−2.88030	+	10.7494i	−0.260770	+	0.973208i
$123$	−7.06247	−	1.89238i	−0.636801	−	0.170630i
$124$	1.33676	+	4.98885i	0.120044	+	0.448012i
$125$	5.66930	−	5.66930i	0.507078	−	0.507078i
$126$		0			0
$127$		−	7.37629i		−	0.654540i	−0.944931	−	0.327270i	$-0.893871\pi$
$127$		−	7.37629i		−	0.654540i	0.944931	−	0.327270i	$-0.106129\pi$
$128$	−4.60228	+	1.23318i	−0.406788	+	0.108998i
$129$	3.61920	+	6.26864i	0.318653	+	0.551923i
$130$	3.21571	−	1.98274i	0.282037	−	0.173898i
$131$	10.3613	+	5.98209i	0.905269	+	0.522658i	0.878906	−	0.476995i	$-0.158274\pi$
$131$	10.3613	+	5.98209i	0.905269	+	0.522658i	0.0263633	+	0.999652i	$0.491607\pi$
$132$	−2.27378	−	2.27378i	−0.197907	−	0.197907i
$133$		0			0
$134$			1.79380i			0.154960i
$135$	0.423402	+	1.58016i	0.0364406	+	0.135998i
$136$	2.42046	−	9.03328i	0.207553	−	0.774598i
$137$	0.689433	−	2.57300i	0.0589023	−	0.219826i	−0.930201	−	0.367051i	$-0.880367\pi$
$137$	0.689433	−	2.57300i	0.0589023	−	0.219826i	0.989103	+	0.147225i	$0.0470341\pi$
$138$	4.63063	+	17.2818i	0.394186	+	1.47112i
$139$			6.36883i			0.540197i	0.962833	+	0.270098i	$0.0870563\pi$
$139$			6.36883i			0.540197i	−0.962833	+	0.270098i	$0.912944\pi$
$140$		0			0
$141$	11.8618	+	11.8618i	0.998946	+	0.998946i
$142$	−6.07372	−	3.50667i	−0.509695	−	0.294273i
$143$	−9.20156	−	2.18244i	−0.769473	−	0.182505i
$144$	2.85464	+	4.94438i	0.237886	+	0.412031i
$145$	3.17168	−	0.849848i	0.263393	−	0.0705760i
$146$			11.8378i			0.979701i
$147$		0			0
$148$	1.09171	−	1.09171i	0.0897379	−	0.0897379i
$149$	4.88130	+	18.2173i	0.399892	+	1.49242i	0.813286	+	0.581865i	$0.197677\pi$
$149$	4.88130	+	18.2173i	0.399892	+	1.49242i	−0.413394	+	0.910552i	$0.635657\pi$
$150$	11.2777	+	3.02186i	0.920823	+	0.246734i
$151$	2.79727	−	10.4396i	0.227639	−	0.849560i	−0.753691	−	0.657229i	$-0.771729\pi$
$151$	2.79727	−	10.4396i	0.227639	−	0.849560i	0.981330	−	0.192331i	$-0.0616047\pi$
$152$	0.391893	+	0.226259i	0.0317867	+	0.0183521i
$153$	−6.61282			−0.534615
$154$		0			0
$155$		−	8.30406i		−	0.666998i
$156$	−3.89049	−	2.09857i	−0.311489	−	0.168020i
$157$	18.2116	−	10.5145i	1.45345	−	0.839148i	0.454772	−	0.890608i	$-0.349721\pi$
$157$	18.2116	−	10.5145i	1.45345	−	0.839148i	0.998675	+	0.0514594i	$0.0163873\pi$
$158$	−20.5424	−	5.50431i	−1.63426	−	0.437899i
$159$	6.75790	+	3.90168i	0.535936	+	0.309423i
$160$	−2.56443			−0.202736
$161$		0			0
$162$	−9.23093	+	9.23093i	−0.725250	+	0.725250i
$163$	9.61152	−	2.57540i	0.752832	−	0.201721i	0.138058	−	0.990424i	$-0.455914\pi$
$163$	9.61152	−	2.57540i	0.752832	−	0.201721i	0.614774	+	0.788703i	$0.289247\pi$
$164$	1.67474	+	0.448746i	0.130776	+	0.0350412i
$165$	2.58504	+	4.47743i	0.201245	+	0.348567i
$166$	−9.01419	+	15.6130i	−0.699637	+	1.21181i
$167$	−12.0684	+	12.0684i	−0.933884	+	0.933884i	−0.997946	−	0.0640620i	$-0.979594\pi$
$167$	−12.0684	+	12.0684i	−0.933884	+	0.933884i	0.0640620	+	0.997946i	$0.479594\pi$
$168$		0			0
$169$	−12.9783	+	0.751536i	−0.998328	+	0.0578104i
$170$	−1.59644	+	2.76511i	−0.122441	+	0.212074i
$171$	0.0828167	−	0.309076i	0.00633315	−	0.0236356i
$172$	−0.858232	−	1.48650i	−0.0654395	−	0.113345i
$173$	−3.74120	+	6.47994i	−0.284438	+	0.492661i	−0.972473	−	0.233017i	$-0.925140\pi$
$173$	−3.74120	+	6.47994i	−0.284438	+	0.492661i	0.688035	+	0.725678i	$0.258474\pi$
$174$	7.36040	+	7.36040i	0.557990	+	0.557990i
$175$		0			0
$176$	−4.87936	−	4.87936i	−0.367796	−	0.367796i
$177$	28.4245	−	7.61632i	2.13652	−	0.572478i
$178$	5.02630	−	2.90194i	0.376737	−	0.217509i
$179$	19.6595	−	11.3504i	1.46942	−	0.848371i	0.470010	−	0.882661i	$-0.344250\pi$
$179$	19.6595	−	11.3504i	1.46942	−	0.848371i	0.999412	+	0.0342899i	$0.0109170\pi$
$180$	0.262536	+	0.979798i	0.0195683	+	0.0730298i
$181$	1.91735			0.142516			0.0712579	−	0.997458i	$-0.477299\pi$
$181$	1.91735			0.142516			0.0712579	+	0.997458i	$0.477299\pi$
$182$		0			0
$183$	−20.9360			−1.54763
$184$	−5.17114	−	19.2990i	−0.381222	−	1.42274i
$185$	−2.14974	+	1.24115i	−0.158052	+	0.0912515i
$186$	22.7978	−	13.1623i	1.67161	−	0.965106i
$187$	7.72018	−	2.06862i	0.564556	−	0.151272i
$188$	−2.81283	−	2.81283i	−0.205147	−	0.205147i
$189$		0			0
$190$	−0.109245	−	0.109245i	−0.00792546	−	0.00792546i
$191$	5.00359	−	8.66648i	0.362047	−	0.627084i	−0.626250	−	0.779622i	$-0.715411\pi$
$191$	5.00359	−	8.66648i	0.362047	−	0.627084i	0.988298	+	0.152538i	$0.0487445\pi$
$192$	−10.0468	−	17.4016i	−0.725067	−	1.25585i
$193$	−3.74632	+	13.9815i	−0.269666	+	1.00641i	0.689666	+	0.724127i	$0.257757\pi$
$193$	−3.74632	+	13.9815i	−0.269666	+	1.00641i	−0.959332	+	0.282280i	$0.908909\pi$
$194$	3.79741	−	6.57731i	0.272638	−	0.472224i
$195$	5.16874	+	4.87809i	0.370141	+	0.349327i
$196$		0			0
$197$	15.2690	−	15.2690i	1.08787	−	1.08787i	0.0921223	−	0.995748i	$-0.470635\pi$
$197$	15.2690	−	15.2690i	1.08787	−	1.08787i	0.995748	−	0.0921223i	$-0.0293651\pi$
$198$	−3.43968	+	5.95770i	−0.244447	+	0.423395i
$199$	11.2318	+	19.4540i	0.796198	+	1.37906i	0.922075	+	0.387010i	$0.126492\pi$
$199$	11.2318	+	19.4540i	0.796198	+	1.37906i	−0.125877	+	0.992046i	$0.540175\pi$
$200$	−12.5941	−	3.37458i	−0.890539	−	0.238619i
$201$	−3.25963	+	0.873416i	−0.229917	+	0.0616060i
$202$	−0.991567	+	0.991567i	−0.0697664	+	0.0697664i
$203$		0			0
$204$	3.73594			0.261568
$205$	−2.41418	−	1.39383i	−0.168614	−	0.0973491i
$206$	−6.21209	−	1.66452i	−0.432817	−	0.115973i
$207$	−12.2351	+	7.06391i	−0.850395	+	0.490976i
$208$	−8.34869	−	4.50338i	−0.578878	−	0.312253i
$209$			0.386740i			0.0267513i
$210$		0			0
$211$	−18.8504			−1.29772			−0.648859	−	0.760909i	$-0.724753\pi$
$211$	−18.8504			−1.29772			−0.648859	+	0.760909i	$0.724753\pi$
$212$	−1.60252	−	0.925216i	−0.110062	−	0.0635441i
$213$	3.41486	−	12.7444i	0.233982	−	0.873233i
$214$	−11.9646	−	3.20592i	−0.817886	−	0.219152i
$215$	0.714274	+	2.66571i	0.0487131	+	0.181800i
$216$	4.09505	−	4.09505i	0.278633	−	0.278633i
$217$		0			0
$218$			10.0072i			0.677772i
$219$	−21.5113	+	5.76392i	−1.45360	+	0.389490i
$220$	−0.612999	−	1.06175i	−0.0413284	−	0.0715829i
$221$	9.35223	−	5.76638i	0.629099	−	0.387889i
$222$	−6.81487	−	3.93457i	−0.457384	−	0.264071i
$223$	−4.32131	−	4.32131i	−0.289376	−	0.289376i	0.547457	−	0.836833i	$-0.315596\pi$
$223$	−4.32131	−	4.32131i	−0.289376	−	0.289376i	−0.836833	+	0.547457i	$0.815596\pi$
$224$		0			0
$225$			9.21953i			0.614636i
$226$	1.79727	+	6.70750i	0.119553	+	0.446176i
$227$	1.71677	−	6.40708i	0.113946	−	0.425253i	−0.885260	−	0.465097i	$-0.846019\pi$
$227$	1.71677	−	6.40708i	0.113946	−	0.425253i	0.999206	+	0.0398440i	$0.0126861\pi$
$228$	−0.0467876	+	0.174614i	−0.00309858	+	0.0115641i
$229$	0.0969027	+	0.361646i	0.00640351	+	0.0238982i	0.969054	−	0.246850i	$-0.0793955\pi$
$229$	0.0969027	+	0.361646i	0.00640351	+	0.0238982i	−0.962650	+	0.270748i	$0.912729\pi$
$230$			6.82135i			0.449786i
$231$		0			0
$232$	−8.21953	−	8.21953i	−0.539639	−	0.539639i
$233$	−5.33723	−	3.08145i	−0.349653	−	0.201872i	0.314879	−	0.949132i	$-0.398036\pi$
$233$	−5.33723	−	3.08145i	−0.349653	−	0.201872i	−0.664533	+	0.747259i	$0.731369\pi$
$234$	−2.18244	+	9.20156i	−0.142670	+	0.601525i
$235$	3.19788	+	5.53889i	0.208607	+	0.361318i
$236$	−6.74039	+	1.80608i	−0.438762	+	0.117566i
$237$		−	40.0091i		−	2.59887i
$238$		0			0
$239$	−5.63090	+	5.63090i	−0.364232	+	0.364232i	−0.865369	−	0.501136i	$-0.832916\pi$
$239$	−5.63090	+	5.63090i	−0.364232	+	0.364232i	0.501136	+	0.865369i	$0.332916\pi$
$240$	1.34222	+	5.00924i	0.0866400	+	0.323345i
$241$	1.51926	+	0.407084i	0.0978640	+	0.0262226i	0.307419	−	0.951574i	$-0.400535\pi$
$241$	1.51926	+	0.407084i	0.0978640	+	0.0262226i	−0.209555	+	0.977797i	$0.567201\pi$
$242$	−1.28901	+	4.81067i	−0.0828610	+	0.309241i
$243$	−16.3661	−	9.44898i	−1.04989	−	0.606152i
$244$	4.96462			0.317827
$245$		0			0
$246$		−	8.83710i		−	0.563433i
$247$	0.152390	+	0.509330i	0.00969636	+	0.0324079i
$248$	−25.4588	+	14.6987i	−1.61664	+	0.933365i
$249$	−32.7607	−	8.77819i	−2.07612	−	0.556295i
$250$	8.39213	+	4.84520i	0.530765	+	0.306437i
$251$	−12.1069			−0.764182			−0.382091	−	0.924125i	$-0.624796\pi$
$251$	−12.1069			−0.764182			−0.382091	+	0.924125i	$0.624796\pi$
$252$		0			0
$253$	12.0742	−	12.0742i	0.759097	−	0.759097i
$254$	8.61150	−	2.30744i	0.540334	−	0.144782i
$255$	−5.80199	−	1.55464i	−0.363335	−	0.0973553i
$256$	5.95774	+	10.3191i	0.372359	+	0.644944i
$257$	8.78794	−	15.2212i	0.548176	−	0.949469i	−0.450223	−	0.892916i	$-0.648656\pi$
$257$	8.78794	−	15.2212i	0.548176	−	0.949469i	0.998400	−	0.0565532i	$-0.0180111\pi$
$258$	−6.18621	+	6.18621i	−0.385137	+	0.385137i
$259$		0			0
$260$	−1.22568	−	1.15676i	−0.0760133	−	0.0717389i
$261$	−4.10977	+	7.11833i	−0.254388	+	0.440613i
$262$	−3.74262	+	13.9677i	−0.231220	+	0.862925i
$263$	7.26293	+	12.5798i	0.447851	+	0.775701i	0.998246	−	0.0592033i	$-0.0188560\pi$
$263$	7.26293	+	12.5798i	0.447851	+	0.775701i	−0.550395	+	0.834905i	$0.685523\pi$
$264$	9.15135	−	15.8506i	0.563226	−	0.975537i
$265$	2.10374	+	2.10374i	0.129232	+	0.129232i
$266$		0			0
$267$	7.72067	+	7.72067i	0.472497	+	0.472497i
$268$	0.772967	−	0.207116i	0.0472165	−	0.0126516i
$269$	−20.2782	+	11.7076i	−1.23638	+	0.713825i	−0.968353	−	0.249585i	$-0.919706\pi$
$269$	−20.2782	+	11.7076i	−1.23638	+	0.713825i	−0.268029	+	0.963411i	$0.586372\pi$
$270$	−1.71232	+	0.988607i	−0.104208	+	0.0601647i
$271$	−0.884511	−	3.30104i	−0.0537302	−	0.200524i	0.933843	−	0.357683i	$-0.116433\pi$
$271$	−0.884511	−	3.30104i	−0.0537302	−	0.200524i	−0.987573	+	0.157159i	$0.949766\pi$
$272$	8.01703			0.486104
$273$		0			0
$274$	3.21953			0.194499
$275$	−2.88405	−	10.7634i	−0.173915	−	0.649058i
$276$	6.91224	−	3.99078i	0.416068	−	0.240217i
$277$	25.1773	−	14.5361i	1.51276	−	0.873391i	0.512868	−	0.858467i	$-0.328583\pi$
$277$	25.1773	−	14.5361i	1.51276	−	0.873391i	0.999889	−	0.0149234i	$-0.00475043\pi$
$278$	−7.43533	+	1.99229i	−0.445942	+	0.119490i
$279$	14.6987	+	14.6987i	0.879985	+	0.879985i
$280$		0			0
$281$	9.68455	+	9.68455i	0.577732	+	0.577732i	0.934278	−	0.356546i	$-0.116046\pi$
$281$	9.68455	+	9.68455i	0.577732	+	0.577732i	−0.356546	+	0.934278i	$0.616046\pi$
$282$	−10.1376	+	17.5588i	−0.603683	+	1.04561i
$283$	−2.15179	−	3.72700i	−0.127910	−	0.221547i	0.794956	−	0.606667i	$-0.207494\pi$
$283$	−2.15179	−	3.72700i	−0.127910	−	0.221547i	−0.922867	+	0.385119i	$0.874160\pi$
$284$	−0.809775	+	3.02212i	−0.0480513	+	0.179330i
$285$	0.145324	−	0.251709i	0.00860827	−	0.0149100i
$286$	−0.330522	−	11.4251i	−0.0195442	−	0.675582i
$287$		0			0
$288$	4.53919	−	4.53919i	0.267474	−	0.267474i
$289$	3.85710	−	6.68069i	0.226888	−	0.392982i
$290$	1.98432	+	3.43695i	0.116523	+	0.201824i
$291$	13.8011	+	3.69799i	0.809034	+	0.216780i
$292$	5.10103	−	1.36682i	0.298515	−	0.0799869i
$293$	−3.57373	+	3.57373i	−0.208780	+	0.208780i	−0.803749	−	0.594969i	$-0.797164\pi$
$293$	−3.57373	+	3.57373i	−0.208780	+	0.208780i	0.594969	+	0.803749i	$0.297164\pi$
$294$		0			0
$295$	11.2195			0.653227
$296$	7.61033	+	4.39383i	0.442341	+	0.255386i
$297$	4.78079	+	1.28101i	0.277410	+	0.0743317i
$298$	−19.7409	+	11.3974i	−1.14356	+	0.660235i
$299$	11.1438	−	20.6592i	0.644462	−	1.19475i
$300$		−	5.20861i		−	0.300719i
$301$		0			0
$302$	13.0628			0.751678
$303$	−2.28465	−	1.31904i	−0.131250	−	0.0757770i
$304$	−0.100403	+	0.374707i	−0.00575848	+	0.0214909i
$305$	−7.71016	−	2.06593i	−0.441482	−	0.118295i
$306$	−2.06862	−	7.72018i	−0.118255	−	0.441334i
$307$	8.59457	−	8.59457i	0.490518	−	0.490518i	−0.417952	−	0.908469i	$-0.637252\pi$
$307$	8.59457	−	8.59457i	0.490518	−	0.490518i	0.908469	+	0.417952i	$0.137252\pi$
$308$		0			0
$309$		−	12.0989i		−	0.688282i
$310$	9.69463	−	2.59767i	0.550618	−	0.147538i
$311$	−11.2702	−	19.5206i	−0.639077	−	1.10691i	−0.985636	−	0.168885i	$-0.945983\pi$
$311$	−11.2702	−	19.5206i	−0.639077	−	1.10691i	0.346559	−	0.938028i	$-0.387350\pi$
$312$	5.80642	−	24.4809i	0.328724	−	1.38596i
$313$	3.73147	+	2.15436i	0.210915	+	0.121772i	0.601737	−	0.798695i	$-0.294476\pi$
$313$	3.73147	+	2.15436i	0.210915	+	0.121772i	−0.390822	+	0.920466i	$0.627809\pi$
$314$	17.9722	+	17.9722i	1.01423	+	1.01423i
$315$		0			0
$316$			9.48747i			0.533712i
$317$	1.45351	+	5.42458i	0.0816374	+	0.304675i	0.994656	−	0.103243i	$-0.0329218\pi$
$317$	1.45351	+	5.42458i	0.0816374	+	0.304675i	−0.913019	+	0.407917i	$0.866255\pi$
$318$	−2.44104	+	9.11008i	−0.136887	+	0.510868i
$319$	2.57123	−	9.59595i	0.143961	−	0.537270i
$320$	−1.98281	−	7.39994i	−0.110842	−	0.413669i
$321$		−	23.3028i		−	1.30063i
$322$		0			0
$323$	−0.317716	−	0.317716i	−0.0176782	−	0.0176782i
$324$	5.04353	+	2.91189i	0.280196	+	0.161771i
$325$	−8.03944	−	13.0388i	−0.445948	−	0.723262i
$326$	6.01333	+	10.4154i	0.333048	+	0.576855i
$327$	−18.1848	+	4.87259i	−1.00562	+	0.269455i
$328$			9.86861i			0.544903i
$329$		0			0
$330$	−4.41855	+	4.41855i	−0.243233	+	0.243233i
$331$	0.625638	+	2.33491i	0.0343882	+	0.128338i	0.980986	−	0.194078i	$-0.0621715\pi$
$331$	0.625638	+	2.33491i	0.0343882	+	0.128338i	−0.946598	+	0.322417i	$0.895505\pi$
$332$	7.76863	+	2.08160i	0.426359	+	0.114243i
$333$	1.60825	−	6.00208i	0.0881317	−	0.328912i
$334$	−17.8646	−	10.3141i	−0.977509	−	0.564365i
$335$	−1.28662			−0.0702957
$336$		0			0
$337$			23.1327i			1.26012i	0.776546	+	0.630061i	$0.216970\pi$
$337$			23.1327i			1.26012i	−0.776546	+	0.630061i	$0.783030\pi$
$338$	−4.93723	−	14.9165i	−0.268550	−	0.811349i
$339$	−11.3136	+	6.53189i	−0.614468	+	0.354763i
$340$	1.37584	+	0.368656i	0.0746156	+	0.0199932i
$341$	−21.7581	−	12.5620i	−1.17826	−	0.680272i
$342$	0.386740			0.0209125
$343$		0			0
$344$	6.90829	−	6.90829i	0.372470	−	0.372470i
$345$	−12.3956	+	3.32138i	−0.667354	+	0.178817i
$346$	−8.73537	−	2.34064i	−0.469616	−	0.125833i
$347$	4.30212	+	7.45149i	0.230950	+	0.400017i	0.958088	−	0.286474i	$-0.0924834\pi$
$347$	4.30212	+	7.45149i	0.230950	+	0.400017i	−0.727138	+	0.686491i	$0.759150\pi$
$348$	2.32183	−	4.02152i	0.124463	−	0.215576i
$349$	19.0680	−	19.0680i	1.02069	−	1.02069i	0.0209053	−	0.999781i	$-0.493345\pi$
$349$	19.0680	−	19.0680i	1.02069	−	1.02069i	0.999781	−	0.0209053i	$-0.00665484\pi$
$350$		0			0
$351$	6.80098	−	0.196748i	0.363010	−	0.0105017i
$352$	−3.87936	+	6.71925i	−0.206771	+	0.358137i
$353$	1.76143	−	6.57373i	0.0937513	−	0.349885i	−0.903076	−	0.429481i	$-0.858696\pi$
$353$	1.76143	−	6.57373i	0.0937513	−	0.349885i	0.996827	+	0.0795964i	$0.0253632\pi$
$354$	17.7834	+	30.8018i	0.945180	+	1.63710i
$355$	2.51520	−	4.35645i	0.133493	−	0.231216i
$356$	−1.83083	−	1.83083i	−0.0970336	−	0.0970336i
$357$		0			0
$358$	19.4010	+	19.4010i	1.02538	+	1.02538i
$359$	17.1444	−	4.59383i	0.904848	−	0.242453i	0.223751	−	0.974646i	$-0.428170\pi$
$359$	17.1444	−	4.59383i	0.904848	−	0.242453i	0.681097	+	0.732193i	$0.261503\pi$
$360$	−5.00005	+	2.88678i	−0.263526	+	0.152147i
$361$	−16.4357	+	9.48913i	−0.865034	+	0.499428i
$362$	0.599785	+	2.23843i	0.0315240	+	0.117649i
$363$	−9.36943			−0.491768
$364$		0			0
$365$	−8.49079			−0.444428
$366$	−6.54918	−	24.4419i	−0.342331	−	1.27760i
$367$	−19.8152	+	11.4403i	−1.03434	+	0.597178i	−0.918226	−	0.396058i	$-0.870378\pi$
$367$	−19.8152	+	11.4403i	−1.03434	+	0.597178i	−0.116117	+	0.993236i	$0.537045\pi$
$368$	14.8331	−	8.56391i	0.773230	−	0.446425i
$369$	6.74039	−	1.80608i	0.350890	−	0.0940208i
$370$	−2.12147	−	2.12147i	−0.110290	−	0.110290i
$371$		0			0
$372$	−8.30406	−	8.30406i	−0.430545	−	0.430545i
$373$	−5.25206	+	9.09683i	−0.271941	+	0.471016i	−0.969359	−	0.245649i	$-0.920999\pi$
$373$	−5.25206	+	9.09683i	−0.271941	+	0.471016i	0.697418	+	0.716665i	$0.254332\pi$
$374$	4.83004	+	8.36588i	0.249756	+	0.432589i
$375$	−4.71834	+	17.6091i	−0.243654	+	0.909330i
$376$	11.3209	−	19.6083i	0.583829	−	1.01122i
$377$	−0.394912	−	13.6509i	−0.0203390	−	0.703055i
$378$		0			0
$379$	3.64229	−	3.64229i	0.187092	−	0.187092i	−0.607346	−	0.794438i	$-0.707766\pi$
$379$	3.64229	−	3.64229i	0.187092	−	0.187092i	0.794438	+	0.607346i	$0.207766\pi$
$380$	−0.0344612	+	0.0596885i	−0.00176782	+	0.00306196i
$381$	8.38604	+	14.5250i	0.429630	+	0.744141i
$382$	11.6830	+	3.13044i	0.597752	+	0.160167i
$383$	−33.5483	+	8.98925i	−1.71424	+	0.459329i	−0.976458	−	0.215709i	$-0.930794\pi$
$383$	−33.5483	+	8.98925i	−1.71424	+	0.459329i	−0.737782	+	0.675039i	$0.764127\pi$
$384$	7.66061	−	7.66061i	0.390929	−	0.390929i
$385$		0			0
$386$	−17.4947			−0.890455
$387$	−5.98276	−	3.45415i	−0.304121	−	0.175584i
$388$	−3.27269	−	0.876916i	−0.166146	−	0.0445187i
$389$	−5.62028	+	3.24487i	−0.284960	+	0.164521i	−0.635667	−	0.771964i	$-0.719275\pi$
$389$	−5.62028	+	3.24487i	−0.284960	+	0.164521i	0.350707	+	0.936485i	$0.385941\pi$
$390$	−4.07808	+	7.56023i	−0.206501	+	0.382827i
$391$			19.8385i			1.00327i
$392$		0			0
$393$	−27.2039			−1.37226
$394$	22.6023	+	13.0494i	1.13869	+	0.657422i
$395$	3.94803	−	14.7343i	0.198647	−	0.741361i
$396$	2.96439	+	0.794307i	0.148966	+	0.0399154i
$397$	2.52385	+	9.41915i	0.126669	+	0.472734i	0.999894	−	0.0145835i	$-0.00464222\pi$
$397$	2.52385	+	9.41915i	0.126669	+	0.472734i	−0.873225	+	0.487317i	$0.837976\pi$
$398$	−19.1982	+	19.1982i	−0.962317	+	0.962317i
$399$		0			0
$400$		−	11.1773i		−	0.558864i
$401$	−12.3254	+	3.30257i	−0.615499	+	0.164922i	−0.553081	−	0.833128i	$-0.686548\pi$
$401$	−12.3254	+	3.30257i	−0.615499	+	0.164922i	−0.0624181	+	0.998050i	$0.519881\pi$
$402$	−2.03935	−	3.53226i	−0.101714	−	0.176173i
$403$	−33.6049	−	7.97045i	−1.67398	−	0.397037i
$404$	0.541766	+	0.312789i	0.0269539	+	0.0155618i
$405$	−6.62099	−	6.62099i	−0.329000	−	0.329000i
$406$		0			0
$407$			7.51026i			0.372270i
$408$	5.50360	+	20.5397i	0.272469	+	1.01687i
$409$	−1.04715	+	3.90803i	−0.0517784	+	0.193240i	−0.986971	−	0.160901i	$-0.948560\pi$
$409$	−1.04715	+	3.90803i	−0.0517784	+	0.193240i	0.935192	+	0.354141i	$0.115227\pi$
$410$	0.872031	−	3.25446i	0.0430665	−	0.160727i
$411$	1.56762	+	5.85044i	0.0773251	+	0.288581i
$412$			2.86905i			0.141348i
$413$		0			0
$414$	−12.0742	−	12.0742i	−0.593413	−	0.593413i
$415$	−11.1986	−	6.46554i	−0.549720	−	0.317381i
$416$	−2.46141	+	10.3778i	−0.120681	+	0.508811i
$417$	−7.24067	−	12.5412i	−0.354577	−	0.614145i
$418$	−0.451502	+	0.120980i	−0.0220837	+	0.00591730i
$419$			35.4097i			1.72988i	0.501878	+	0.864939i	$0.332643\pi$
$419$			35.4097i			1.72988i	−0.501878	+	0.864939i	$0.667357\pi$
$420$		0			0
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	−0.0745864	−	0.997215i	$-0.523764\pi$
$421$	18.9307	−	18.9307i	0.922628	−	0.922628i	0.997215	+	0.0745864i	$0.0237636\pi$
$422$	−5.89678	−	22.0071i	−0.287051	−	1.07129i
$423$	−15.4646	−	4.14372i	−0.751914	−	0.201475i
$424$	2.72597	−	10.1734i	0.132385	−	0.494066i
$425$	11.2117	+	6.47309i	0.543848	+	0.313991i
$426$	15.9468			0.772624
$427$		0			0
$428$			5.52586i			0.267102i
$429$	20.6005	−	6.16362i	0.994600	−	0.297582i
$430$	−2.88866	+	1.66777i	−0.139303	+	0.0804269i
$431$	−17.2177	−	4.61347i	−0.829348	−	0.222223i	−0.180919	−	0.983498i	$-0.557907\pi$
$431$	−17.2177	−	4.61347i	−0.829348	−	0.222223i	−0.648429	+	0.761275i	$0.724574\pi$
$432$	4.29948	+	2.48231i	0.206859	+	0.119430i
$433$	−14.3392			−0.689098			−0.344549	−	0.938768i	$-0.611968\pi$
$433$	−14.3392			−0.689098			−0.344549	+	0.938768i	$0.611968\pi$
$434$		0			0
$435$	−5.27933	+	5.27933i	−0.253125	+	0.253125i
$436$	4.31221	−	1.15545i	0.206517	−	0.0553361i
$437$	−0.927228	−	0.248450i	−0.0443553	−	0.0118850i
$438$	−13.4583	−	23.3104i	−0.643061	−	1.11381i
$439$	−9.99061	+	17.3042i	−0.476826	+	0.825886i	−0.999647	−	0.0265559i	$-0.991546\pi$
$439$	−9.99061	+	17.3042i	−0.476826	+	0.825886i	0.522822	+	0.852442i	$0.324879\pi$
$440$	4.93430	−	4.93430i	0.235234	−	0.235234i
$441$		0			0
$442$	9.65756	+	9.11450i	0.459363	+	0.433532i
$443$	2.81904	−	4.88273i	0.133937	−	0.231985i	−0.791254	−	0.611488i	$-0.790571\pi$
$443$	2.81904	−	4.88273i	0.133937	−	0.231985i	0.925191	+	0.379502i	$0.123905\pi$
$444$	−0.908588	+	3.39090i	−0.0431197	+	0.160925i
$445$	2.08145	+	3.60518i	0.0986702	+	0.170902i
$446$	3.69315	−	6.39672i	0.174876	−	0.302894i
$447$	−30.3231	−	30.3231i	−1.43423	−	1.43423i
$448$		0			0
$449$	−12.9060	−	12.9060i	−0.609073	−	0.609073i	0.333631	−	0.942704i	$-0.391726\pi$
$449$	−12.9060	−	12.9060i	−0.609073	−	0.609073i	−0.942704	+	0.333631i	$0.891726\pi$
$450$	−10.7634	+	2.88405i	−0.507392	+	0.135955i
$451$	−7.30413	+	4.21704i	−0.343938	+	0.198573i
$452$	2.68282	−	1.54893i	0.126189	−	0.0728553i
$453$	6.36039	+	23.7373i	0.298837	+	1.11528i
$454$	8.01703			0.376258
$455$		0			0
$456$	−1.02893			−0.0481840
$457$	2.55005	+	9.51692i	0.119286	+	0.445183i	0.999572	−	0.0292619i	$-0.00931567\pi$
$457$	2.55005	+	9.51692i	0.119286	+	0.445183i	−0.880285	+	0.474444i	$0.842649\pi$
$458$	−0.391893	+	0.226259i	−0.0183119	+	0.0105724i
$459$	−4.97992	+	2.87516i	−0.232443	+	0.134201i
$460$	2.93939	−	0.787608i	0.137050	−	0.0367224i
$461$	−7.20809	−	7.20809i	−0.335714	−	0.335714i	0.519037	−	0.854752i	$-0.326291\pi$
$461$	−7.20809	−	7.20809i	−0.335714	−	0.335714i	−0.854752	+	0.519037i	$0.826291\pi$
$462$		0			0
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	0.606421	−	0.795144i	$-0.292605\pi$
$463$	−4.06084	−	4.06084i	−0.188723	−	0.188723i	−0.795144	+	0.606421i	$0.792605\pi$
$464$	4.98246	−	8.62988i	0.231305	−	0.400632i
$465$	9.44081	+	16.3520i	0.437807	+	0.758304i
$466$	1.92787	−	7.19492i	0.0893070	−	0.333298i
$467$	−8.68367	+	15.0406i	−0.401832	+	0.695994i	−0.993947	−	0.109860i	$-0.964960\pi$
$467$	−8.68367	+	15.0406i	−0.401832	+	0.695994i	0.592115	+	0.805854i	$0.298293\pi$
$468$	4.21704	−	0.121997i	0.194933	−	0.00563929i
$469$		0			0
$470$	−5.46606	+	5.46606i	−0.252131	+	0.252131i
$471$	−23.9077	+	41.4093i	−1.10161	+	1.90804i
$472$	−19.8592	−	34.3972i	−0.914094	−	1.58326i
$473$	8.06513	+	2.16105i	0.370835	+	0.0993650i
$474$	46.7089	−	12.5156i	2.14541	−	0.574861i
$475$	−0.442957	+	0.442957i	−0.0203243	+	0.0203243i
$476$		0			0
$477$	−7.44748			−0.340997
$478$	−8.33528	−	4.81238i	−0.381247	−	0.220113i
$479$	13.5050	+	3.61865i	0.617059	+	0.165340i	0.553790	−	0.832656i	$-0.313181\pi$
$479$	13.5050	+	3.61865i	0.617059	+	0.165340i	0.0632685	+	0.997997i	$0.479848\pi$
$480$	5.04976	−	2.91548i	0.230489	−	0.133073i
$481$	2.95933	+	9.89088i	0.134934	+	0.450985i
$482$			1.90101i			0.0865887i
$483$		0			0
$484$	2.22180			0.100991
$485$	4.71766	+	2.72374i	0.214218	+	0.123679i
$486$	5.91164	−	22.0626i	0.268158	−	1.00078i
$487$	17.2244	+	4.61527i	0.780513	+	0.209138i	0.627011	−	0.779010i	$-0.284278\pi$
$487$	17.2244	+	4.61527i	0.780513	+	0.209138i	0.153502	+	0.988148i	$0.450945\pi$
$488$	7.31363	+	27.2948i	0.331073	+	1.23558i
$489$	−15.9986	+	15.9986i	−0.723482	+	0.723482i
$490$		0			0
$491$		−	1.72487i		−	0.0778425i	−0.999242	−	0.0389212i	$-0.987608\pi$
$491$		−	1.72487i		−	0.0778425i	0.999242	−	0.0389212i	$-0.0123921\pi$
$492$	−3.80800	+	1.02035i	−0.171678	+	0.0460010i
$493$	5.77099	+	9.99564i	0.259912	+	0.450181i
$494$	−0.546950	+	0.337237i	−0.0246084	+	0.0151730i
$495$	−4.27323	−	2.46715i	−0.192068	−	0.110890i
$496$	−17.8199	−	17.8199i	−0.800135	−	0.800135i
$497$		0			0
$498$		−	40.9926i		−	1.83692i
$499$	−10.0860	−	37.6415i	−0.451512	−	1.68507i	−0.698145	−	0.715957i	$-0.745991\pi$
$499$	−10.0860	−	37.6415i	−0.451512	−	1.68507i	0.246633	−	0.969109i	$-0.420676\pi$
$500$	1.11888	−	4.17570i	0.0500376	−	0.186743i
$501$	10.0441	−	37.4851i	0.448738	−	1.67471i
$502$	−3.78728	−	14.1343i	−0.169034	−	0.630845i
$503$			20.8862i			0.931272i	0.884976	+	0.465636i	$0.154174\pi$
$503$			20.8862i			0.931272i	−0.884976	+	0.465636i	$0.845826\pi$
$504$		0			0
$505$	−0.711213	−	0.711213i	−0.0316486	−	0.0316486i
$506$	17.8731	+	10.3190i	0.794556	+	0.458737i
$507$	24.7018	−	16.2348i	1.09704	−	0.721011i
$508$	−1.98861	−	3.44437i	−0.0882302	−	0.152819i
$509$	20.8281	−	5.58088i	0.923191	−	0.247368i	0.234242	−	0.972178i	$-0.424739\pi$
$509$	20.8281	−	5.58088i	0.923191	−	0.247368i	0.688949	+	0.724810i	$0.258072\pi$
$510$		−	7.25990i		−	0.321474i
$511$		0			0
$512$	−16.9216	+	16.9216i	−0.747837	+	0.747837i
$513$	−0.0720149	−	0.268763i	−0.00317954	−	0.0118662i
$514$	20.5191	+	5.49807i	0.905057	+	0.242509i
$515$	1.19390	−	4.45570i	0.0526095	−	0.196341i
$516$	3.37998	+	1.95143i	0.148795	+	0.0859070i
$517$	19.3505			0.851033
$518$		0			0
$519$		−	17.0133i		−	0.746802i
$520$	4.55409	−	8.44270i	0.199710	−	0.370237i
$521$	17.4541	−	10.0771i	0.764678	−	0.441487i	−0.0662945	−	0.997800i	$-0.521118\pi$
$521$	17.4541	−	10.0771i	0.764678	−	0.441487i	0.830973	+	0.556313i	$0.187784\pi$
$522$	−9.59595	−	2.57123i	−0.420003	−	0.112540i
$523$	−9.78880	−	5.65157i	−0.428034	−	0.247126i	0.270475	−	0.962727i	$-0.412819\pi$
$523$	−9.78880	−	5.65157i	−0.428034	−	0.247126i	−0.698509	+	0.715601i	$0.746153\pi$
$524$	6.45095			0.281811
$525$		0			0
$526$	−12.4143	+	12.4143i	−0.541291	+	0.541291i
$527$	28.1948	−	7.55477i	1.22818	−	0.329091i
$528$	15.1555	+	4.06091i	0.659559	+	0.176728i
$529$	9.69174	+	16.7866i	0.421380	+	0.729852i
$530$	−1.79794	+	3.11412i	−0.0780973	+	0.135269i
$531$	−19.8592	+	19.8592i	−0.861817	+	0.861817i
$532$		0			0
$533$	−7.95774	+	8.43188i	−0.344688	+	0.365225i
$534$	−6.59837	+	11.4287i	−0.285540	+	0.494569i
$535$	2.29948	−	8.58178i	0.0994152	−	0.371023i
$536$	2.27739	+	3.94456i	0.0983684	+	0.170379i
$537$	−25.8084	+	44.7015i	−1.11372	+	1.92901i
$538$	−20.0115	−	20.0115i	−0.862758	−	0.862758i
$539$		0			0
$540$	0.623710	+	0.623710i	0.0268402	+	0.0268402i
$541$	12.6887	−	3.39993i	0.545531	−	0.146174i	0.0244801	−	0.999700i	$-0.492207\pi$
$541$	12.6887	−	3.39993i	0.545531	−	0.146174i	0.521051	+	0.853526i	$0.325540\pi$
$542$	3.57713	−	2.06526i	0.153651	−	0.0887104i
$543$	−3.77557	+	2.17982i	−0.162025	+	0.0935452i
$544$	−2.33304	−	8.70702i	−0.100028	−	0.373311i
$545$	−7.17778			−0.307462
$546$		0			0
$547$	12.8999			0.551559			0.275780	−	0.961221i	$-0.411064\pi$
$547$	12.8999			0.551559			0.275780	+	0.961221i	$0.411064\pi$
$548$	−0.371735	−	1.38733i	−0.0158797	−	0.0592639i
$549$	17.3042	−	9.99061i	0.738527	−	0.426389i
$550$	11.6636	−	6.73400i	0.497339	−	0.287139i
$551$	−0.539459	+	0.144548i	−0.0229817	+	0.00615794i
$552$	32.1236	+	32.1236i	1.36727	+	1.36727i
$553$		0			0
$554$	24.8462	+	24.8462i	1.05562	+	1.05562i
$555$	2.82211	−	4.88805i	0.119792	−	0.207486i
$556$	1.71700	+	2.97393i	0.0728170	+	0.126123i
$557$	−6.08162	+	22.6969i	−0.257687	+	0.961699i	0.708890	+	0.705320i	$0.249196\pi$
$557$	−6.08162	+	22.6969i	−0.257687	+	0.961699i	−0.966576	+	0.256380i	$0.917470\pi$
$558$	−12.5620	+	21.7581i	−0.531793	+	0.921092i
$559$	11.4732	−	0.331912i	0.485264	−	0.0140384i
$560$		0			0
$561$	−12.8504	+	12.8504i	−0.542546	+	0.542546i
$562$	−8.27678	+	14.3358i	−0.349135	+	0.604720i
$563$	−10.8380	−	18.7720i	−0.456769	−	0.791147i	0.542019	−	0.840366i	$-0.317660\pi$
$563$	−10.8380	−	18.7720i	−0.456769	−	0.791147i	−0.998788	+	0.0492194i	$0.984327\pi$
$564$	8.73678	+	2.34101i	0.367885	+	0.0985744i
$565$	−4.81103	+	1.28911i	−0.202402	+	0.0542334i
$566$	3.67799	−	3.67799i	0.154598	−	0.154598i
$567$		0			0
$568$	−17.8082			−0.747214
$569$	−15.6524	−	9.03692i	−0.656183	−	0.378847i	0.134638	−	0.990895i	$-0.457013\pi$
$569$	−15.6524	−	9.03692i	−0.656183	−	0.378847i	−0.790821	+	0.612047i	$0.790346\pi$
$570$	0.339320	+	0.0909205i	0.0142125	+	0.00380824i
$571$	−7.39319	+	4.26846i	−0.309395	+	0.178630i	−0.646656	−	0.762782i	$-0.723833\pi$
$571$	−7.39319	+	4.26846i	−0.309395	+	0.178630i	0.337260	+	0.941411i	$0.390500\pi$
$572$	−4.88505	+	1.46160i	−0.204254	+	0.0611124i
$573$			22.7542i			0.950569i
$574$		0			0
$575$	27.6586			1.15344
$576$	16.6080	+	9.58864i	0.692000	+	0.399527i
$577$	3.13524	−	11.7009i	0.130522	−	0.487114i	−0.869454	−	0.494013i	$-0.835529\pi$
$577$	3.13524	−	11.7009i	0.130522	−	0.487114i	0.999976	+	0.00689906i	$0.00219606\pi$
$578$	9.00599	+	2.41315i	0.374600	+	0.100374i
$579$	−8.51831	−	31.7908i	−0.354009	−	1.32118i
$580$	1.25190	−	1.25190i	0.0519825	−	0.0519825i
$581$		0			0
$582$			17.2690i			0.715822i
$583$	8.69461	−	2.32971i	0.360094	−	0.0964869i
$584$	15.0292	+	26.0313i	0.621912	+	1.07718i
$585$	−6.59993	−	1.56538i	−0.272873	−	0.0647205i
$586$	−5.29011	−	3.05425i	−0.218532	−	0.126170i
$587$	0.308382	+	0.308382i	0.0127283	+	0.0127283i	0.713442	−	0.700714i	$-0.247135\pi$
$587$	0.308382	+	0.308382i	0.0127283	+	0.0127283i	−0.700714	+	0.713442i	$0.747135\pi$
$588$		0			0
$589$			1.41241i			0.0581972i
$590$	3.50968	+	13.0983i	0.144491	+	0.539249i
$591$	−12.7078	+	47.4261i	−0.522729	+	1.95085i
$592$	−1.94976	+	7.27660i	−0.0801346	+	0.299066i
$593$	1.81257	+	6.76461i	0.0744334	+	0.277789i	0.993104	−	0.117235i	$-0.0374030\pi$
$593$	1.81257	+	6.76461i	0.0744334	+	0.277789i	−0.918671	+	0.395024i	$0.870736\pi$
$594$			5.98209i			0.245448i
$595$		0			0
$596$	7.19061	+	7.19061i	0.294539	+	0.294539i
$597$	−44.2341	−	25.5386i	−1.81038	−	1.04522i
$598$	27.6047	+	6.54731i	1.12884	+	0.267739i
$599$	8.81545	+	15.2688i	0.360189	+	0.623866i	0.987992	−	0.154506i	$-0.0493787\pi$
$599$	8.81545	+	15.2688i	0.360189	+	0.623866i	−0.627802	+	0.778373i	$0.716045\pi$
$600$	28.6363	−	7.67307i	1.16907	−	0.313252i
$601$			7.14746i			0.291551i	0.989318	+	0.145776i	$0.0465677\pi$
$601$			7.14746i			0.291551i	−0.989318	+	0.145776i	$0.953432\pi$
$602$		0			0
$603$	2.27739	−	2.27739i	0.0927426	−	0.0927426i
$604$	−1.50826	−	5.62890i	−0.0613702	−	0.229037i
$605$	−3.45051	−	0.924561i	−0.140283	−	0.0375887i
$606$	0.825244	−	3.07985i	0.0335232	−	0.125110i
$607$	25.8552	+	14.9275i	1.04943	+	0.605888i	0.922489	−	0.386022i	$-0.126151\pi$
$607$	25.8552	+	14.9275i	1.04943	+	0.605888i	0.126939	+	0.991910i	$0.459485\pi$
$608$	0.436175			0.0176892
$609$		0			0
$610$		−	9.64754i		−	0.390618i
$611$	25.4842	−	7.62483i	1.03098	−	0.308468i
$612$	−3.08787	+	1.78278i	−0.124820	+	0.0720646i
$613$	8.79593	+	2.35686i	0.355264	+	0.0951928i	0.432037	−	0.901856i	$-0.357795\pi$
$613$	8.79593	+	2.35686i	0.355264	+	0.0951928i	−0.0767728	+	0.997049i	$0.524462\pi$
$614$	12.7223	+	7.34524i	0.513431	+	0.296430i
$615$	6.33852			0.255594
$616$		0			0
$617$	16.4908	−	16.4908i	0.663894	−	0.663894i	−0.292402	−	0.956296i	$-0.594454\pi$
$617$	16.4908	−	16.4908i	0.663894	−	0.663894i	0.956296	+	0.292402i	$0.0944544\pi$
$618$	14.1249	−	3.78477i	0.568188	−	0.152246i
$619$	−30.4907	−	8.16997i	−1.22553	−	0.328379i	−0.412690	−	0.910871i	$-0.635411\pi$
$619$	−30.4907	−	8.16997i	−1.22553	−	0.328379i	−0.812836	+	0.582493i	$0.802078\pi$
$620$	−2.23873	−	3.87759i	−0.0899094	−	0.155728i
$621$	−6.14257	+	10.6392i	−0.246493	+	0.426938i
$622$	19.2639	−	19.2639i	0.772414	−	0.772414i
$623$		0			0
$624$	21.5597	−	0.623710i	0.863079	−	0.0249684i
$625$	7.14588	−	12.3770i	0.285835	−	0.495081i
$626$	−1.34785	+	5.03025i	−0.0538710	+	0.201049i
$627$	−0.439681	−	0.761550i	−0.0175592	−	0.0304134i
$628$	5.66930	−	9.81952i	0.226230	−	0.391841i
$629$	−6.16986	−	6.16986i	−0.246009	−	0.246009i
$630$		0			0
$631$	3.75154	+	3.75154i	0.149346	+	0.149346i	0.777826	−	0.628480i	$-0.216322\pi$
$631$	3.75154	+	3.75154i	0.149346	+	0.149346i	−0.628480	+	0.777826i	$0.716322\pi$
$632$	−52.1609	+	13.9765i	−2.07485	+	0.555955i
$633$	37.1194	−	21.4309i	1.47536	−	0.851801i
$634$	−5.87828	+	3.39383i	−0.233456	+	0.134786i
$635$	1.65504	+	6.17670i	0.0656783	+	0.245115i
$636$	4.20748			0.166837
$637$		0			0
$638$	12.0072			0.475369
$639$	3.25912	+	12.1632i	0.128929	+	0.481169i
$640$	3.57713	−	2.06526i	0.141398	−	0.0816364i
$641$	−22.2523	+	12.8474i	−0.878912	+	0.507440i	−0.870300	−	0.492523i	$-0.836075\pi$
$641$	−22.2523	+	12.8474i	−0.878912	+	0.507440i	−0.00861267	+	0.999963i	$0.502742\pi$
$642$	27.2050	−	7.28955i	1.07370	−	0.287696i
$643$	−22.1537	−	22.1537i	−0.873658	−	0.873658i	0.119211	−	0.992869i	$-0.461964\pi$
$643$	−22.1537	−	22.1537i	−0.873658	−	0.873658i	−0.992869	+	0.119211i	$0.961964\pi$
$644$		0			0
$645$	−4.43713	−	4.43713i	−0.174712	−	0.174712i
$646$	0.271532	−	0.470308i	0.0106833	−	0.0185040i
$647$	16.2223	+	28.0978i	0.637764	+	1.10464i	0.985922	+	0.167204i	$0.0534737\pi$
$647$	16.2223	+	28.0978i	0.637764	+	1.10464i	−0.348159	+	0.937436i	$0.613193\pi$
$648$	−8.57929	+	32.0184i	−0.337027	+	1.25780i
$649$	16.9724	−	29.3971i	0.666226	−	1.15394i
$650$	12.7073	−	13.4645i	0.498423	−	0.528120i
$651$		0			0
$652$	3.79380	−	3.79380i	0.148577	−	0.148577i
$653$	−15.8257	+	27.4109i	−0.619308	+	1.07267i	0.370304	+	0.928910i	$0.379253\pi$
$653$	−15.8257	+	27.4109i	−0.619308	+	1.07267i	−0.989612	+	0.143762i	$0.954080\pi$
$654$	−11.3771	−	19.7057i	−0.444879	−	0.770553i
$655$	−10.0185	−	2.68444i	−0.391454	−	0.104890i
$656$	−8.17169	+	2.18960i	−0.319051	+	0.0854894i
$657$	15.0292	−	15.0292i	0.586344	−	0.586344i
$658$		0			0
$659$	30.5330			1.18940			0.594699	−	0.803948i	$-0.297271\pi$
$659$	30.5330			1.18940			0.594699	+	0.803948i	$0.297271\pi$
$660$	2.41418	+	1.39383i	0.0939718	+	0.0542546i
$661$	12.5797	+	3.37071i	0.489292	+	0.131105i	0.495026	−	0.868878i	$-0.335158\pi$
$661$	12.5797	+	3.37071i	0.489292	+	0.131105i	−0.00573384	+	0.999984i	$0.501825\pi$
$662$	−2.53020	+	1.46081i	−0.0983390	+	0.0567760i
$663$	−11.8602	+	21.9874i	−0.460613	+	0.853918i
$664$			45.7775i			1.77651i
$665$		0			0
$666$	7.51026			0.291017
$667$	21.3550	+	12.3293i	0.826868	+	0.477392i
$668$	−2.38179	+	8.88896i	−0.0921542	+	0.343924i
$669$	13.4222	+	3.59646i	0.518931	+	0.139047i
$670$	−0.402480	−	1.50208i	−0.0155492	−	0.0580302i
$671$	−17.0767	+	17.0767i	−0.659239	+	0.659239i
$672$		0			0
$673$			22.6319i			0.872397i	0.899850	+	0.436199i	$0.143675\pi$
$673$			22.6319i			0.872397i	−0.899850	+	0.436199i	$0.856325\pi$
$674$	−27.0065	+	7.23637i	−1.04025	+	0.278734i
$675$	4.00852	+	6.94295i	0.154288	+	0.267234i
$676$	−5.85760	+	3.84980i	−0.225292	+	0.148069i
$677$	−9.28744	−	5.36211i	−0.356945	−	0.206082i	0.310795	−	0.950477i	$-0.399405\pi$
$677$	−9.28744	−	5.36211i	−0.356945	−	0.206082i	−0.667740	+	0.744395i	$0.732738\pi$
$678$	−11.1648	−	11.1648i	−0.428781	−	0.428781i
$679$		0			0
$680$			8.10731i			0.310901i
$681$	3.90357	+	14.5683i	0.149585	+	0.558259i
$682$	7.85928	−	29.3312i	0.300947	−	1.12315i
$683$	−1.35686	+	5.06387i	−0.0519188	+	0.193763i	−0.987014	−	0.160632i	$-0.948647\pi$
$683$	−1.35686	+	5.06387i	−0.0519188	+	0.193763i	0.935096	+	0.354396i	$0.115313\pi$
$684$	−0.0446538	−	0.166650i	−0.00170738	−	0.00637204i
$685$			2.30925i			0.0882319i
$686$		0			0
$687$	−0.601968	−	0.601968i	−0.0229665	−	0.0229665i
$688$	7.25318	+	4.18762i	0.276525	+	0.159652i
$689$	10.5327	−	6.49420i	0.401262	−	0.247409i
$690$	−7.75513	−	13.4323i	−0.295233	−	0.511358i
$691$	−0.363544	+	0.0974114i	−0.0138299	+	0.00370571i	−0.265727	−	0.964048i	$-0.585612\pi$
$691$	−0.363544	+	0.0974114i	−0.0138299	+	0.00370571i	0.251897	+	0.967754i	$0.418945\pi$
$692$			4.03442i			0.153366i
$693$		0			0
$694$	−7.35350	+	7.35350i	−0.279135	+	0.279135i
$695$	−1.42899	−	5.33308i	−0.0542049	−	0.202295i
$696$	25.5302	+	6.84081i	0.967721	+	0.259300i
$697$	2.53612	−	9.46493i	0.0960624	−	0.358510i
$698$	28.2259	+	16.2962i	1.06837	+	0.616822i
$699$	14.0131			0.530024
$700$		0			0
$701$		−	34.0349i		−	1.28548i	−0.766084	−	0.642740i	$-0.777798\pi$
$701$		−	34.0349i		−	1.28548i	0.766084	−	0.642740i	$-0.222202\pi$
$702$	2.35717	+	7.87831i	0.0889658	+	0.297348i
$703$	0.365642	−	0.211104i	0.0137905	−	0.00796192i
$704$	−22.3886	−	5.99902i	−0.843804	−	0.226096i
$705$	−12.5942	−	7.27129i	−0.474327	−	0.273853i
$706$	8.22556			0.309573
$707$		0			0
$708$	11.2195	−	11.2195i	0.421656	−	0.421656i
$709$	−15.7077	+	4.20888i	−0.589917	+	0.158068i	−0.541415	−	0.840755i	$-0.682111\pi$
$709$	−15.7077	+	4.20888i	−0.589917	+	0.158068i	−0.0485016	+	0.998823i	$0.515445\pi$
$710$	5.87277	+	1.57360i	0.220401	+	0.0590563i
$711$	19.0922	+	33.0687i	0.716015	+	1.24017i
$712$	7.36857	−	12.7627i	0.276149	−	0.478304i
$713$	44.0960	−	44.0960i	1.65141	−	1.65141i
$714$		0			0
$715$	8.19481	−	0.237071i	0.306469	−	0.00886596i
$716$	6.12003	−	10.6002i	0.228716	−	0.396148i
$717$	4.68638	−	17.4898i	0.175016	−	0.653169i
$718$	10.7262	+	18.5783i	0.400298	+	0.693337i
$719$	17.5222	−	30.3494i	0.653469	−	1.13184i	−0.328806	−	0.944397i	$-0.606646\pi$
$719$	17.5222	−	30.3494i	0.653469	−	1.13184i	0.982275	−	0.187444i	$-0.0600203\pi$
$720$	−3.49978	−	3.49978i	−0.130429	−	0.130429i
$721$		0			0
$722$	−16.2195	−	16.2195i	−0.603629	−	0.603629i
$723$	−3.45446	+	0.925620i	−0.128473	+	0.0344242i
$724$	0.895311	−	0.516908i	0.0332740	−	0.0192107i
$725$	13.9358	−	8.04585i	0.517564	−	0.298816i
$726$	−2.93094	−	10.9384i	−0.108777	−	0.405962i
$727$	−15.0936			−0.559789			−0.279895	−	0.960031i	$-0.590300\pi$
$727$	−15.0936			−0.559789			−0.279895	+	0.960031i	$0.590300\pi$
$728$		0			0
$729$	10.5669			0.391367
$730$	−2.65608	−	9.91262i	−0.0983059	−	0.366883i
$731$	−8.40106	+	4.85035i	−0.310724	+	0.179397i
$732$	−9.77609	+	5.64423i	−0.361335	+	0.208617i
$733$	−20.2383	+	5.42285i	−0.747520	+	0.200297i	−0.612418	−	0.790534i	$-0.709803\pi$
$733$	−20.2383	+	5.42285i	−0.747520	+	0.200297i	−0.135102	+	0.990832i	$0.543136\pi$
$734$	−19.5546	−	19.5546i	−0.721773	−	0.721773i
$735$		0			0
$736$	−13.6176	−	13.6176i	−0.501950	−	0.501950i
$737$	−1.94635	+	3.37117i	−0.0716946	+	0.124179i
$738$	4.21704	+	7.30413i	0.155231	+	0.268869i
$739$	5.90653	−	22.0435i	0.217275	−	0.810883i	−0.768078	−	0.640357i	$-0.778787\pi$
$739$	5.90653	−	22.0435i	0.217275	−	0.810883i	0.985353	−	0.170526i	$-0.0545467\pi$
$740$	−0.669216	+	1.15912i	−0.0246009	+	0.0426100i
$741$	−0.879132	−	0.829697i	−0.0322957	−	0.0304797i
$742$		0			0
$743$	−24.1350	+	24.1350i	−0.885428	+	0.885428i	−0.994080	−	0.108652i	$-0.965347\pi$
$743$	−24.1350	+	24.1350i	−0.885428	+	0.885428i	0.108652	+	0.994080i	$0.465347\pi$
$744$	33.4215	−	57.8878i	1.22529	−	2.12227i
$745$	−8.17494	−	14.1594i	−0.299506	−	0.518760i
$746$	−12.2631	−	3.28589i	−0.448984	−	0.120305i
$747$	31.2666	−	8.37786i	1.14399	−	0.306530i
$748$	3.04726	−	3.04726i	0.111419	−	0.111419i
$749$		0			0
$750$	−22.0338			−0.804562
$751$	14.5293	+	8.38849i	0.530181	+	0.306100i	0.741090	−	0.671405i	$-0.234309\pi$
$751$	14.5293	+	8.38849i	0.530181	+	0.306100i	−0.210909	+	0.977506i	$0.567642\pi$
$752$	18.7484	+	5.02363i	0.683686	+	0.183193i
$753$	23.8404	−	13.7643i	0.868792	−	0.501597i
$754$	15.8133	−	4.73129i	0.575885	−	0.172304i
$755$			9.36943i			0.340989i
$756$		0			0
$757$	−20.7321			−0.753520			−0.376760	−	0.926311i	$-0.622962\pi$
$757$	−20.7321			−0.753520			−0.376760	+	0.926311i	$0.622962\pi$
$758$	5.39160	+	3.11284i	0.195832	+	0.113063i
$759$	−10.0489	+	37.5029i	−0.364751	+	1.36127i
$760$	−0.378927	−	0.101533i	−0.0137451	−	0.00368299i
$761$	0.773522	+	2.88682i	0.0280402	+	0.104647i	0.978528	−	0.206115i	$-0.0660822\pi$
$761$	0.773522	+	2.88682i	0.0280402	+	0.104647i	−0.950488	+	0.310763i	$0.899416\pi$
$762$	−14.3341	+	14.3341i	−0.519268	+	0.519268i
$763$		0			0
$764$		−	5.39576i		−	0.195212i
$765$	5.53739	−	1.48374i	0.200205	−	0.0536447i
$766$	−20.9891	−	36.3542i	−0.758368	−	1.31353i
$767$	10.7688	−	45.4033i	0.388839	−	1.63942i
$768$	−23.4634	−	13.5466i	−0.846663	−	0.488821i
$769$	25.9456	+	25.9456i	0.935621	+	0.935621i	0.998049	−	0.0624284i	$-0.0198845\pi$
$769$	25.9456	+	25.9456i	0.935621	+	0.935621i	−0.0624284	+	0.998049i	$0.519885\pi$
$770$		0			0
$771$			39.9637i			1.43926i
$772$	2.01997	+	7.53864i	0.0727004	+	0.271322i
$773$	0.348344	−	1.30004i	0.0125291	−	0.0467591i	−0.959378	−	0.282123i	$-0.908961\pi$
$773$	0.348344	−	1.30004i	0.0125291	−	0.0467591i	0.971907	+	0.235364i	$0.0756281\pi$
$774$	2.16105	−	8.06513i	0.0776772	−	0.289895i
$775$	−10.5328	−	39.3089i	−0.378349	−	1.41202i
$776$		−	19.2847i		−	0.692280i
$777$		0			0
$778$	−5.54638	−	5.54638i	−0.198847	−	0.198847i
$779$	0.410619	+	0.237071i	0.0147120	+	0.00849395i
$780$	3.72865	+	0.884367i	0.133507	+	0.0316654i
$781$	−7.60977	−	13.1805i	−0.272299	−	0.471636i
$782$	−23.1606	+	6.20585i	−0.828220	+	0.221921i
$783$			7.14746i			0.255430i
$784$		0			0
$785$	−12.8908	+	12.8908i	−0.460091	+	0.460091i
$786$	−8.50991	−	31.7594i	−0.303538	−	1.13282i
$787$	−33.8797	−	9.07805i	−1.20768	−	0.323597i	−0.401830	−	0.915714i	$-0.631626\pi$
$787$	−33.8797	−	9.07805i	−1.20768	−	0.323597i	−0.805852	+	0.592117i	$0.798292\pi$
$788$	3.01344	−	11.2463i	0.107349	−	0.400633i
$789$	−28.6036	−	16.5143i	−1.01832	−	0.587925i
$790$	18.4366			0.655946
$791$		0			0
$792$			17.4680i			0.620698i
$793$	−15.7608	+	29.2186i	−0.559684	+	1.03758i
$794$	−10.2069	+	5.89298i	−0.362231	+	0.209134i
$795$	−6.53431	−	1.75086i	−0.231748	−	0.0620967i
$796$	10.4894	+	6.05604i	0.371786	+	0.214651i
$797$	−34.9017			−1.23628			−0.618141	−	0.786067i	$-0.712114\pi$
$797$	−34.9017			−1.23628			−0.618141	+	0.786067i	$0.712114\pi$
$798$		0			0
$799$	−15.8969	+	15.8969i	−0.562392	+	0.562392i
$800$	−12.1393	+	3.25270i	−0.429187	+	0.115000i
$801$	−10.0656	−	2.69708i	−0.355652	−	0.0952967i
$802$	−7.71121	−	13.3562i	−0.272292	−	0.471624i
$803$	−12.8445	+	22.2473i	−0.453272	+	0.785091i
$804$	−1.28662	+	1.28662i	−0.0453757	+	0.0453757i
$805$		0			0
$806$	−1.20710	−	41.7256i	−0.0425182	−	1.46972i
$807$	26.6205	−	46.1081i	0.937088	−	1.62308i
$808$	−0.921570	+	3.43935i	−0.0324207	+	0.120996i
$809$	−5.13090	−	8.88698i	−0.180393	−	0.312449i	0.761622	−	0.648022i	$-0.224404\pi$
$809$	−5.13090	−	8.88698i	−0.180393	−	0.312449i	−0.942014	+	0.335573i	$0.891070\pi$
$810$	5.65855	−	9.80090i	0.198821	−	0.344368i
$811$	13.3684	+	13.3684i	0.469428	+	0.469428i	0.901729	−	0.432301i	$-0.142298\pi$
$811$	13.3684	+	13.3684i	0.469428	+	0.469428i	−0.432301	+	0.901729i	$0.642298\pi$
$812$		0			0
$813$	5.49466	+	5.49466i	0.192706	+	0.192706i
$814$	−8.76790	+	2.34935i	−0.307315	+	0.0823448i
$815$	−7.47057	+	4.31313i	−0.261683	+	0.151082i
$816$	−15.7868	+	9.11450i	−0.552647	+	0.319071i
$817$	−0.121488	−	0.453401i	−0.00425034	−	0.0158625i
$818$	−4.89002			−0.170976
$819$		0			0
$820$	−1.50307			−0.0524895
$821$	6.33494	+	23.6423i	0.221091	+	0.825122i	0.983933	+	0.178538i	$0.0571366\pi$
$821$	6.33494	+	23.6423i	0.221091	+	0.825122i	−0.762842	+	0.646585i	$0.776197\pi$
$822$	−6.33976	+	3.66026i	−0.221124	+	0.127666i
$823$	30.3777	−	17.5386i	1.05890	−	0.611356i	0.133772	−	0.991012i	$-0.457291\pi$
$823$	30.3777	−	17.5386i	1.05890	−	0.611356i	0.925128	+	0.379656i	$0.123958\pi$
$824$	−15.7737	+	4.22654i	−0.549502	+	0.147239i
$825$	17.9160	+	17.9160i	0.623753	+	0.623753i
$826$		0			0
$827$	−19.4173	−	19.4173i	−0.675207	−	0.675207i	0.283705	−	0.958912i	$-0.408436\pi$
$827$	−19.4173	−	19.4173i	−0.675207	−	0.675207i	−0.958912	+	0.283705i	$0.908436\pi$
$828$	−3.80878	+	6.59701i	−0.132364	+	0.229262i
$829$	4.58045	+	7.93358i	0.159086	+	0.275545i	0.934539	−	0.355860i	$-0.115812\pi$
$829$	4.58045	+	7.93358i	0.159086	+	0.275545i	−0.775453	+	0.631405i	$0.782479\pi$
$830$	4.04509	−	15.0965i	0.140407	−	0.524006i
$831$	−33.0520	+	57.2477i	−1.14656	+	1.98590i
$832$	−31.8493	+	0.921381i	−1.10418	+	0.0319432i
$833$		0			0
$834$	12.3763	−	12.3763i	0.428556	−	0.428556i
$835$	7.39794	−	12.8136i	0.256016	−	0.443433i
$836$	0.104263	+	0.180589i	0.00360601	+	0.00624579i
$837$	17.4599	+	4.67836i	0.603501	+	0.161708i
$838$	−41.3393	+	11.0768i	−1.42804	+	0.382643i
$839$	26.1882	−	26.1882i	0.904116	−	0.904116i	−0.0916731	−	0.995789i	$-0.529221\pi$
$839$	26.1882	−	26.1882i	0.904116	−	0.904116i	0.995789	+	0.0916731i	$0.0292215\pi$
$840$		0			0
$841$	−14.6537			−0.505299
$842$	28.0227	+	16.1789i	0.965727	+	0.557563i
$843$	−30.0806	−	8.06009i	−1.03603	−	0.277604i
$844$	−8.80223	+	5.08197i	−0.302985	+	0.174929i
$845$	10.6990	−	3.54129i	0.368057	−	0.121824i
$846$		−	19.3505i		−	0.665283i
$847$		0			0
$848$	9.02893			0.310055
$849$	8.47439	+	4.89269i	0.290840	+	0.167917i
$850$	−4.04981	+	15.1141i	−0.138907	+	0.518410i
$851$	−18.0062	−	4.82476i	−0.617246	−	0.165391i
$852$	−1.84125	−	6.87165i	−0.0630803	−	0.235419i
$853$	−7.70865	+	7.70865i	−0.263939	+	0.263939i	−0.826652	−	0.562713i	$-0.809758\pi$
$853$	−7.70865	+	7.70865i	−0.263939	+	0.263939i	0.562713	+	0.826652i	$0.309758\pi$
$854$		0			0
$855$			0.277394i			0.00948666i
$856$	−30.3805	+	8.14042i	−1.03838	+	0.278234i
$857$	11.2070	+	19.4112i	0.382825	+	0.663073i	0.991465	−	0.130374i	$-0.0416178\pi$
$857$	11.2070	+	19.4112i	0.382825	+	0.663073i	−0.608640	+	0.793447i	$0.708284\pi$
$858$	13.6400	+	22.1221i	0.465661	+	0.755235i
$859$	37.7323	+	21.7847i	1.28741	+	0.743286i	0.978191	−	0.207706i	$-0.0665996\pi$
$859$	37.7323	+	21.7847i	1.28741	+	0.743286i	0.309217	+	0.950991i	$0.399933\pi$
$860$	1.05219	+	1.05219i	0.0358794	+	0.0358794i
$861$		0			0
$862$		−	21.5441i		−	0.733795i
$863$	−3.30482	−	12.3337i	−0.112497	−	0.419846i	0.886590	−	0.462556i	$-0.153067\pi$
$863$	−3.30482	−	12.3337i	−0.112497	−	0.419846i	−0.999088	+	0.0427101i	$0.986401\pi$
$864$	1.44475	−	5.39190i	0.0491516	−	0.183436i
$865$	1.67885	−	6.26555i	0.0570826	−	0.213035i
$866$	−4.48558	−	16.7404i	−0.152426	−	0.568862i
$867$			17.5404i			0.595703i
$868$		0			0
$869$	−32.6339	−	32.6339i	−1.10703	−	1.10703i
$870$	−7.81487	−	4.51192i	−0.264949	−	0.152968i
$871$	−1.23493	+	5.20671i	−0.0418441	+	0.176423i
$872$	12.7051	+	22.0058i	0.430248	+	0.745211i
$873$	−13.1717	+	3.52934i	−0.445794	+	0.119450i
$874$		−	1.16022i		−	0.0392450i
$875$		0			0
$876$	−8.49079	+	8.49079i	−0.286877	+	0.286877i
$877$	−1.76408	−	6.58365i	−0.0595689	−	0.222314i	0.929724	−	0.368257i	$-0.120045\pi$
$877$	−1.76408	−	6.58365i	−0.0595689	−	0.222314i	−0.989293	+	0.145943i	$0.953379\pi$
$878$	−23.3272	−	6.25050i	−0.787255	−	0.210944i
$879$	2.97428	−	11.1002i	0.100320	−	0.374399i
$880$	5.18064	+	2.99104i	0.174639	+	0.100828i
$881$	−3.46947			−0.116889			−0.0584447	−	0.998291i	$-0.518614\pi$
$881$	−3.46947			−0.116889			−0.0584447	+	0.998291i	$0.518614\pi$
$882$		0			0
$883$		−	47.0772i		−	1.58427i	−0.610344	−	0.792136i	$-0.708969\pi$
$883$		−	47.0772i		−	1.58427i	0.610344	−	0.792136i	$-0.291031\pi$
$884$	2.81245	−	5.21393i	0.0945930	−	0.175363i
$885$	−22.0930	+	12.7554i	−0.742648	+	0.428768i
$886$	6.58222	+	1.76370i	0.221134	+	0.0592527i
$887$	4.98590	+	2.87861i	0.167410	+	0.0966543i	0.581364	−	0.813644i	$-0.302519\pi$
$887$	4.98590	+	2.87861i	0.167410	+	0.0966543i	−0.413954	+	0.910298i	$0.635853\pi$
$888$	−19.9812			−0.670526
$889$		0			0
$890$	−3.55777	+	3.55777i	−0.119257	+	0.119257i
$891$	−27.3641	+	7.33219i	−0.916732	+	0.245638i
$892$	−3.18284	−	0.852839i	−0.106569	−	0.0285552i
$893$	−0.543917	−	0.942091i	−0.0182015	−	0.0315259i
$894$	25.9153	−	44.8865i	0.866736	−	1.50123i
$895$	−13.9156	+	13.9156i	−0.465148	+	0.465148i
$896$		0			0
$897$	1.54339	+	53.3503i	0.0515324	+	1.78132i
$898$	11.0300	−	19.1045i	0.368075	−	0.637525i
$899$	9.39035	−	35.0453i	0.313186	−	1.16883i
$900$	2.48554	+	4.30507i	0.0828512	+	0.143502i
$901$	−5.22892	+	9.05676i	−0.174201	+	0.301724i
$902$	−7.20809	−	7.20809i	−0.240003	−	0.240003i
$903$		0			0
$904$	12.4680	+	12.4680i	0.414679	+	0.414679i
$905$	−1.60554	+	0.430203i	−0.0533699	+	0.0143004i
$906$	−25.7226	+	14.8510i	−0.854577	+	0.493390i
$907$	−11.3806	+	6.57058i	−0.377886	+	0.218172i	−0.676898	−	0.736077i	$-0.736676\pi$
$907$	−11.3806	+	6.57058i	−0.377886	+	0.218172i	0.299012	+	0.954249i	$0.403343\pi$
$908$	−0.925665	−	3.45463i	−0.0307193	−	0.114646i
$909$	2.51778			0.0835093
$910$		0			0
$911$	22.8394			0.756702			0.378351	−	0.925662i	$-0.376491\pi$
$911$	22.8394			0.756702			0.378351	+	0.925662i	$0.376491\pi$
$912$	−0.228294	−	0.852003i	−0.00755956	−	0.0282126i
$913$	−33.8817	+	19.5616i	−1.12132	+	0.647394i
$914$	−10.3129	+	5.95415i	−0.341120	+	0.196946i
$915$	17.5312	−	4.69748i	0.579564	−	0.155294i
$916$	0.142747	+	0.142747i	0.00471648	+	0.00471648i
$917$		0			0
$918$	−4.91443	−	4.91443i	−0.162201	−	0.162201i
$919$	−17.5132	+	30.3338i	−0.577709	+	1.00062i	0.418033	+	0.908432i	$0.362720\pi$
$919$	−17.5132	+	30.3338i	−0.577709	+	1.00062i	−0.995742	+	0.0921887i	$0.970614\pi$
$920$	8.66034	+	15.0002i	0.285523	+	0.494541i
$921$	−7.15293	+	26.6951i	−0.235697	+	0.879634i
$922$	6.16030	−	10.6700i	0.202879	−	0.351396i
$923$	−15.2156	−	14.3600i	−0.500826	−	0.472664i
$924$		0			0
$925$	−8.60197	+	8.60197i	−0.282831	+	0.282831i
$926$	3.47055	−	6.01117i	0.114049	−	0.197539i
$927$	5.77356	+	10.0001i	0.189629	+	0.328447i
$928$	−10.8226	−	2.89990i	−0.355268	−	0.0951938i
$929$	−21.8787	+	5.86238i	−0.717817	+	0.192339i	−0.599198	−	0.800601i	$-0.704514\pi$
$929$	−21.8787	+	5.86238i	−0.717817	+	0.192339i	−0.118620	+	0.992940i	$0.537847\pi$
$930$	−16.1369	+	16.1369i	−0.529151	+	0.529151i
$931$		0			0
$932$	−3.32297			−0.108847
$933$	44.3857	+	25.6261i	1.45312	+	0.838960i
$934$	−20.2756	−	5.43284i	−0.663439	−	0.177768i
$935$	−6.00053	+	3.46441i	−0.196238	+	0.113298i
$936$	6.88306	+	23.0051i	0.224980	+	0.751944i
$937$		−	39.2356i		−	1.28177i	−0.767636	−	0.640886i	$-0.778567\pi$
$937$		−	39.2356i		−	1.28177i	0.767636	−	0.640886i	$-0.221433\pi$
$938$		0			0
$939$	−9.79711			−0.319717
$940$	2.98651	+	1.72426i	0.0974092	+	0.0562392i
$941$	11.5919	−	43.2616i	0.377886	−	1.41029i	−0.471197	−	0.882028i	$-0.656178\pi$
$941$	11.5919	−	43.2616i	0.377886	−	1.41029i	0.849083	−	0.528260i	$-0.177155\pi$
$942$	−55.8224	−	14.9576i	−1.81879	−	0.487344i
$943$	−5.41824	−	20.2212i	−0.176442	−	0.658491i
$944$	24.0763	−	24.0763i	0.783615	−	0.783615i
$945$		0			0
$946$			10.0917i			0.328110i
$947$	15.8388	−	4.24398i	0.514691	−	0.137911i	0.00788104	−	0.999969i	$-0.497491\pi$
$947$	15.8388	−	4.24398i	0.514691	−	0.137911i	0.506810	+	0.862058i	$0.330825\pi$
$948$	−10.7862	−	18.6823i	−0.350320	−	0.606773i
$949$	−8.14968	+	34.3606i	−0.264550	+	1.11539i
$950$	−0.655699	−	0.378568i	−0.0212737	−	0.0122824i
$951$	−9.02935	−	9.02935i	−0.292797	−	0.292797i
$952$		0			0
$953$			37.1939i			1.20483i	0.798183	+	0.602415i	$0.205795\pi$
$953$			37.1939i			1.20483i	−0.798183	+	0.602415i	$0.794205\pi$
$954$	−2.32971	−	8.69461i	−0.0754273	−	0.281498i
$955$	−2.24535	+	8.37974i	−0.0726577	+	0.271162i
$956$	−1.11130	+	4.14741i	−0.0359419	+	0.134137i
$957$	5.84641	+	21.8191i	0.188988	+	0.705312i
$958$			16.8985i			0.545965i
$959$		0			0
$960$	12.3174	+	12.3174i	0.397542	+	0.397542i
$961$	−52.6156	−	30.3776i	−1.69728	−	0.979923i
$962$	−10.6214	+	6.54895i	−0.342449	+	0.211147i
$963$	11.1200	+	19.2605i	0.358338	+	0.620659i
$964$	0.819167	−	0.219495i	0.0263836	−	0.00706946i
$965$		−	12.5483i		−	0.403943i
$966$		0			0
$967$	34.8785	−	34.8785i	1.12162	−	1.12162i	0.130117	−	0.991499i	$-0.458465\pi$
$967$	34.8785	−	34.8785i	1.12162	−	1.12162i	0.991499	−	0.130117i	$-0.0415354\pi$
$968$	3.27305	+	12.2152i	0.105200	+	0.392611i
$969$	0.986841	+	0.264423i	0.0317019	+	0.00849450i
$970$	−1.70408	+	6.35970i	−0.0547146	+	0.204198i
$971$	11.8674	+	6.85166i	0.380844	+	0.219880i	0.678185	−	0.734891i	$-0.262767\pi$
$971$	11.8674	+	6.85166i	0.380844	+	0.219880i	−0.297342	+	0.954771i	$0.596100\pi$
$972$	−10.1896			−0.326831
$973$		0			0
$974$			21.5525i			0.690587i
$975$	30.6546	+	16.5354i	0.981732	+	0.529558i
$976$	−20.9787	+	12.1121i	−0.671513	+	0.387698i
$977$	−7.93676	−	2.12665i	−0.253919	−	0.0680375i	0.129614	−	0.991565i	$-0.458626\pi$
$977$	−7.93676	−	2.12665i	−0.253919	−	0.0680375i	−0.383533	+	0.923527i	$0.625293\pi$
$978$	−23.6823	−	13.6730i	−0.757278	−	0.437215i
$979$	12.5949			0.402535
$980$		0			0
$981$	12.7051	−	12.7051i	0.405642	−	0.405642i
$982$	2.01372	−	0.539573i	0.0642602	−	0.0172185i
$983$	16.7554	+	4.48959i	0.534413	+	0.143196i	0.515925	−	0.856634i	$-0.327448\pi$
$983$	16.7554	+	4.48959i	0.534413	+	0.143196i	0.0184877	+	0.999829i	$0.494115\pi$
$984$	−11.2195	−	19.4328i	−0.357666	−	0.619495i
$985$	−9.35987	+	16.2118i	−0.298230	+	0.516550i
$986$	−9.86420	+	9.86420i	−0.314140	+	0.314140i
$987$		0			0
$988$	0.208471	+	0.196748i	0.00663235	+	0.00625940i
$989$	−10.3624	+	17.9483i	−0.329506	+	0.570722i
$990$	1.54354	−	5.76059i	0.0490571	−	0.183083i
$991$	−20.2787	−	35.1238i	−0.644175	−	1.11574i	−0.984491	−	0.175433i	$-0.943868\pi$
$991$	−20.2787	−	35.1238i	−0.644175	−	1.11574i	0.340317	−	0.940311i	$-0.389466\pi$
$992$	−14.1678	+	24.5393i	−0.449827	+	0.779124i
$993$	−3.88652	−	3.88652i	−0.123335	−	0.123335i
$994$		0			0
$995$	−13.7701	−	13.7701i	−0.436542	−	0.436542i
$996$	−17.6642	+	4.73310i	−0.559711	+	0.149974i
$997$	−15.1282	+	8.73430i	−0.479116	+	0.276618i	−0.720048	−	0.693924i	$-0.755880\pi$
$997$	−15.1282	+	8.73430i	−0.479116	+	0.276618i	0.240932	+	0.970542i	$0.422547\pi$
$998$	40.7897	−	23.5500i	1.29118	−	0.745461i
$999$	−1.39849	−	5.21923i	−0.0442462	−	0.165129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.460.5		24
7.2	even	3		91.2.i.a.83.5	yes	12
7.3	odd	6	inner	637.2.bc.a.31.1		24
7.4	even	3	inner	637.2.bc.a.31.2		24
7.5	odd	6		91.2.i.a.83.6	yes	12
7.6	odd	2	inner	637.2.bc.a.460.6		24
13.8	odd	4	inner	637.2.bc.a.411.1		24
21.2	odd	6		819.2.y.h.811.1		12
21.5	even	6		819.2.y.h.811.2		12
91.34	even	4	inner	637.2.bc.a.411.2		24
91.47	even	12		91.2.i.a.34.6	yes	12
91.60	odd	12	inner	637.2.bc.a.619.6		24
91.73	even	12	inner	637.2.bc.a.619.5		24
91.86	odd	12		91.2.i.a.34.5	✓	12
273.47	odd	12		819.2.y.h.307.1		12
273.86	even	12		819.2.y.h.307.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.5	✓	12	91.86	odd	12
91.2.i.a.34.6	yes	12	91.47	even	12
91.2.i.a.83.5	yes	12	7.2	even	3
91.2.i.a.83.6	yes	12	7.5	odd	6
637.2.bc.a.31.1		24	7.3	odd	6	inner
637.2.bc.a.31.2		24	7.4	even	3	inner
637.2.bc.a.411.1		24	13.8	odd	4	inner
637.2.bc.a.411.2		24	91.34	even	4	inner
637.2.bc.a.460.5		24	1.1	even	1	trivial
637.2.bc.a.460.6		24	7.6	odd	2	inner
637.2.bc.a.619.5		24	91.73	even	12	inner
637.2.bc.a.619.6		24	91.60	odd	12	inner
819.2.y.h.307.1		12	273.47	odd	12
819.2.y.h.307.2		12	273.86	even	12
819.2.y.h.811.1		12	21.2	odd	6
819.2.y.h.811.2		12	21.5	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.312819 + 1.16746i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(0.466951 - 0.269594i) q^{4} +(-0.837372 + 0.224373i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(2.17009 + 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +O(q^{10})\)	\(q+(0.312819 + 1.16746i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(0.466951 - 0.269594i) q^{4} +(-0.837372 + 0.224373i) q^{5} +(-1.94326 - 1.94326i) q^{6} +(2.17009 + 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +(-0.523892 - 0.907408i) q^{10} +(-0.678845 + 2.53348i) q^{11} +(-0.612999 + 1.06175i) q^{12} +(0.104263 + 3.60404i) q^{13} +(1.39383 - 1.39383i) q^{15} +(-1.31545 + 2.27842i) q^{16} +(-1.52363 - 2.63901i) q^{17} +(2.53348 + 0.678845i) q^{18} +(0.142426 - 0.0381629i) q^{19} +(-0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +(-5.63805 - 3.25513i) q^{23} +(-6.74039 - 1.80608i) q^{24} +(-3.67928 + 2.12423i) q^{25} +(-4.17495 + 1.24914i) q^{26} -1.88704i q^{27} -3.78765 q^{29} +(2.06325 + 1.19122i) q^{30} +(-2.47920 + 9.25250i) q^{31} +(2.85733 + 0.765619i) q^{32} +(-1.54354 - 5.76059i) q^{33} +(2.60430 - 2.60430i) q^{34} -1.17009i q^{36} +(2.76582 - 0.741100i) q^{37} +(0.0891070 + 0.154338i) q^{38} +(-4.30271 - 6.97838i) q^{39} +(-2.30408 - 1.33026i) q^{40} +(2.27378 + 2.27378i) q^{41} -3.18342i q^{43} +(0.366025 + 1.36603i) q^{44} +(-0.486909 + 1.81717i) q^{45} +(2.03653 - 7.60045i) q^{46} +(-1.90947 - 7.12626i) q^{47} -5.98209i q^{48} +(-3.63090 - 3.63090i) q^{50} +(6.00053 + 3.46441i) q^{51} +(1.02032 + 1.65480i) q^{52} +(-1.71594 - 2.97210i) q^{53} +(2.20304 - 0.590303i) q^{54} -2.27378i q^{55} +(-0.237071 + 0.237071i) q^{57} +(-1.18485 - 4.42192i) q^{58} +(-12.5010 - 3.34963i) q^{59} +(0.275081 - 1.02662i) q^{60} +(7.97398 + 4.60378i) q^{61} -11.5774 q^{62} +8.83710i q^{64} +(-0.895958 - 2.99453i) q^{65} +(6.24239 - 3.60404i) q^{66} +(1.43357 + 0.384125i) q^{67} +(-1.42292 - 0.821525i) q^{68} +14.8029 q^{69} +(-4.10310 + 4.10310i) q^{71} +(6.43299 - 1.72371i) q^{72} +(9.46056 + 2.53495i) q^{73} +(1.73041 + 2.99715i) q^{74} +(4.83004 - 8.36588i) q^{75} +(0.0562174 - 0.0562174i) q^{76} +(6.80098 - 7.20620i) q^{78} +(-8.79791 + 15.2384i) q^{79} +(0.590303 - 2.20304i) q^{80} +(5.40049 + 9.35393i) q^{81} +(-1.94326 + 3.36583i) q^{82} +(10.5474 + 10.5474i) q^{83} +(1.86797 + 1.86797i) q^{85} +(3.71650 - 0.995834i) q^{86} +(7.45847 - 4.30615i) q^{87} +(-6.97103 + 4.02472i) q^{88} +(-1.24285 - 4.63836i) q^{89} -2.27378 q^{90} -3.51026 q^{92} +(-5.63716 - 21.0382i) q^{93} +(7.72228 - 4.45846i) q^{94} +(-0.110701 + 0.0639130i) q^{95} +(-6.49694 + 1.74085i) q^{96} +(-4.44330 - 4.44330i) q^{97} +(4.02472 + 4.02472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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