LMFDB - Embedded newform 637.2.bc.a.411.1

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			411.1
Character	$\chi$	$=$	637.411
Dual form			637.2.bc.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16746 + 0.312819i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(-0.466951 + 0.269594i) q^{4} +(-0.224373 - 0.837372i) q^{5} +(1.94326 - 1.94326i) q^{6} +(2.17009 - 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +O(q^{10})$	\(q+(-1.16746 + 0.312819i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(-0.466951 + 0.269594i) q^{4} +(-0.224373 - 0.837372i) 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} +(2.53348 + 0.678845i) 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} +(-0.678845 + 2.53348i) q^{18} +(0.0381629 + 0.142426i) q^{19} +(0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +(5.63805 + 3.25513i) q^{23} +(-1.80608 + 6.74039i) q^{24} +(3.67928 - 2.12423i) q^{25} +(-1.00569 - 4.24018i) q^{26} -1.88704i q^{27} -3.78765 q^{29} +(-2.06325 - 1.19122i) q^{30} +(-9.25250 - 2.47920i) q^{31} +(-0.765619 + 2.85733i) q^{32} +(-5.76059 + 1.54354i) q^{33} +(-2.60430 - 2.60430i) q^{34} +1.17009i q^{36} +(-0.741100 - 2.76582i) q^{37} +(-0.0891070 - 0.154338i) q^{38} +(-3.89210 - 7.21545i) q^{39} +(-2.30408 - 1.33026i) q^{40} +(-2.27378 + 2.27378i) q^{41} +3.18342i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-1.81717 - 0.486909i) q^{45} +(-7.60045 - 2.03653i) q^{46} +(-7.12626 + 1.90947i) q^{47} -5.98209i q^{48} +(-3.63090 + 3.63090i) q^{50} +(-6.00053 - 3.46441i) q^{51} +(-0.922944 - 1.71102i) q^{52} +(-1.71594 - 2.97210i) q^{53} +(0.590303 + 2.20304i) q^{54} -2.27378i q^{55} +(-0.237071 - 0.237071i) q^{57} +(4.42192 - 1.18485i) q^{58} +(-3.34963 + 12.5010i) q^{59} +(-1.02662 - 0.275081i) q^{60} +(7.97398 + 4.60378i) q^{61} +11.5774 q^{62} -8.83710i q^{64} +(3.04132 - 0.721344i) q^{65} +(6.24239 - 3.60404i) q^{66} +(-0.384125 + 1.43357i) q^{67} +(-1.42292 - 0.821525i) q^{68} -14.8029 q^{69} +(-4.10310 - 4.10310i) q^{71} +(-1.72371 - 6.43299i) q^{72} +(2.53495 - 9.46056i) 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} +(2.20304 + 0.590303i) 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} +(-0.995834 - 3.71650i) q^{86} +(7.45847 - 4.30615i) q^{87} +(6.97103 - 4.02472i) q^{88} +(-4.63836 + 1.24285i) q^{89} +2.27378 q^{90} -3.51026 q^{92} +(21.0382 - 5.63716i) q^{93} +(7.72228 - 4.45846i) q^{94} +(0.110701 - 0.0639130i) q^{95} +(-1.74085 - 6.49694i) 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.16746	+	0.312819i	−0.825517	+	0.221197i	−0.646757	−	0.762696i	$-0.723875\pi$
$2$	−1.16746	+	0.312819i	−0.825517	+	0.221197i	−0.178760	+	0.983893i	$0.557208\pi$
$3$	−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
$5$	−0.224373	−	0.837372i	−0.100343	−	0.374484i	0.897432	−	0.441152i	$-0.145430\pi$
$5$	−0.224373	−	0.837372i	−0.100343	−	0.374484i	−0.997775	+	0.0666675i	$0.978763\pi$
$6$	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
$11$	2.53348	+	0.678845i	0.763874	+	0.204679i	0.619663	−	0.784868i	$-0.287269\pi$
$11$	2.53348	+	0.678845i	0.763874	+	0.204679i	0.144210	+	0.989547i	$0.453936\pi$
$12$	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	0.989493	−	0.144582i	$-0.0461837\pi$
$17$	1.52363	+	2.63901i	0.369535	+	0.640053i	−0.619958	+	0.784635i	$0.712850\pi$
$18$	−0.678845	+	2.53348i	−0.160005	+	0.597147i
$19$	0.0381629	+	0.142426i	0.00875516	+	0.0326747i	0.970165	−	0.242445i	$-0.0779493\pi$
$19$	0.0381629	+	0.142426i	0.00875516	+	0.0326747i	−0.961410	+	0.275119i	$0.911283\pi$
$20$	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	0.954996	−	0.296619i	$-0.0958590\pi$
$23$	5.63805	+	3.25513i	1.17561	+	0.678741i	0.220619	+	0.975360i	$0.429192\pi$
$24$	−1.80608	+	6.74039i	−0.368665	+	1.37588i
$25$	3.67928	−	2.12423i	0.735856	−	0.424846i
$26$	−1.00569	−	4.24018i	−0.197232	−	0.831568i
$27$		−	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
$31$	−9.25250	−	2.47920i	−1.66180	−	0.445278i	−0.698917	−	0.715203i	$-0.746334\pi$
$31$	−9.25250	−	2.47920i	−1.66180	−	0.445278i	−0.962881	+	0.269925i	$0.913001\pi$
$32$	−0.765619	+	2.85733i	−0.135344	+	0.505109i
$33$	−5.76059	+	1.54354i	−1.00279	+	0.268697i
$34$	−2.60430	−	2.60430i	−0.446635	−	0.446635i
$35$		0			0
$36$			1.17009i			0.195014i
$37$	−0.741100	−	2.76582i	−0.121836	−	0.454699i	0.877871	−	0.478897i	$-0.158963\pi$
$37$	−0.741100	−	2.76582i	−0.121836	−	0.454699i	−0.999707	+	0.0241984i	$0.992297\pi$
$38$	−0.0891070	−	0.154338i	−0.0144551	−	0.0250369i
$39$	−3.89210	−	7.21545i	−0.623234	−	1.15540i
$40$	−2.30408	−	1.33026i	−0.364307	−	0.210333i
$41$	−2.27378	+	2.27378i	−0.355105	+	0.355105i	−0.862005	−	0.506900i	$-0.830791\pi$
$41$	−2.27378	+	2.27378i	−0.355105	+	0.355105i	0.506900	+	0.862005i	$0.330791\pi$
$42$		0			0
$43$			3.18342i			0.485467i	0.970093	+	0.242733i	$0.0780440\pi$
$43$			3.18342i			0.485467i	−0.970093	+	0.242733i	$0.921956\pi$
$44$	−1.36603	+	0.366025i	−0.205936	+	0.0551804i
$45$	−1.81717	−	0.486909i	−0.270888	−	0.0725842i
$46$	−7.60045	−	2.03653i	−1.12062	−	0.300270i
$47$	−7.12626	+	1.90947i	−1.03947	+	0.278525i	−0.737894	−	0.674916i	$-0.764180\pi$
$47$	−7.12626	+	1.90947i	−1.03947	+	0.278525i	−0.301577	+	0.953442i	$0.597513\pi$
$48$		−	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
$52$	−0.922944	−	1.71102i	−0.127989	−	0.237276i
$53$	−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	$0.909072\pi$
$54$	0.590303	+	2.20304i	0.0803301	+	0.299796i
$55$		−	2.27378i		−	0.306597i
$56$		0			0
$57$	−0.237071	−	0.237071i	−0.0314008	−	0.0314008i
$58$	4.42192	−	1.18485i	0.580627	−	0.155578i
$59$	−3.34963	+	12.5010i	−0.436084	+	1.62749i	0.302375	+	0.953189i	$0.402221\pi$
$59$	−3.34963	+	12.5010i	−0.436084	+	1.62749i	−0.738459	+	0.674299i	$0.764446\pi$
$60$	−1.02662	−	0.275081i	−0.132536	−	0.0355128i
$61$	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
$65$	3.04132	−	0.721344i	0.377229	−	0.0894717i
$66$	6.24239	−	3.60404i	0.768385	−	0.443627i
$67$	−0.384125	+	1.43357i	−0.0469283	+	0.175139i	−0.985412	−	0.170184i	$-0.945564\pi$
$67$	−0.384125	+	1.43357i	−0.0469283	+	0.175139i	0.938484	+	0.345323i	$0.112231\pi$
$68$	−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	0.420393	−	0.907342i	$-0.361892\pi$
$71$	−4.10310	−	4.10310i	−0.486949	−	0.486949i	−0.907342	+	0.420393i	$0.861892\pi$
$72$	−1.72371	−	6.43299i	−0.203142	−	0.758135i
$73$	2.53495	−	9.46056i	0.296693	−	1.10727i	−0.643170	−	0.765724i	$-0.722381\pi$
$73$	2.53495	−	9.46056i	0.296693	−	1.10727i	0.939863	−	0.341551i	$-0.110952\pi$
$74$	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	$0.712074\pi$
$80$	2.20304	+	0.590303i	0.246307	+	0.0659979i
$81$	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	−0.172763	+	0.984963i	$0.555269\pi$
$83$	−10.5474	+	10.5474i	−1.15773	+	1.15773i	−0.984963	+	0.172763i	$0.944731\pi$
$84$		0			0
$85$	1.86797	−	1.86797i	0.202610	−	0.202610i
$86$	−0.995834	−	3.71650i	−0.107384	−	0.400761i
$87$	7.45847	−	4.30615i	0.799632	−	0.461668i
$88$	6.97103	−	4.02472i	0.743114	−	0.429037i
$89$	−4.63836	+	1.24285i	−0.491666	+	0.131741i	−0.496129	−	0.868249i	$-0.665246\pi$
$89$	−4.63836	+	1.24285i	−0.491666	+	0.131741i	0.00446375	+	0.999990i	$0.498579\pi$
$90$	2.27378			0.239678
$91$		0			0
$92$	−3.51026			−0.365970
$93$	21.0382	−	5.63716i	2.18156	−	0.584547i
$94$	7.72228	−	4.45846i	0.796492	−	0.459855i
$95$	0.110701	−	0.0639130i	0.0113576	−	0.00655734i
$96$	−1.74085	−	6.49694i	−0.177675	−	0.663091i
$97$	4.44330	−	4.44330i	0.451149	−	0.451149i	−0.444587	−	0.895736i	$-0.646649\pi$
$97$	4.44330	−	4.44330i	0.451149	−	0.451149i	0.895736	+	0.444587i	$0.146649\pi$
$98$		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	0.835720	−	0.549156i	$-0.185051\pi$
$101$	−0.580109	−	1.00478i	−0.0577231	−	0.0999793i	−0.893443	+	0.449177i	$0.851717\pi$
$102$	8.08909	+	2.16746i	0.800939	+	0.214611i
$103$	2.66052	−	4.60816i	0.262149	−	0.454055i	−0.704664	−	0.709541i	$-0.748902\pi$
$103$	2.66052	−	4.60816i	0.262149	−	0.454055i	0.966813	+	0.255486i	$0.0822355\pi$
$104$	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
$109$	−2.14295	+	7.99758i	−0.205257	+	0.766030i	0.784114	+	0.620617i	$0.213118\pi$
$109$	−2.14295	+	7.99758i	−0.205257	+	0.766030i	−0.989371	+	0.145413i	$0.953549\pi$
$110$	0.711283	+	2.65454i	0.0678181	+	0.253101i
$111$	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
$115$	1.46073	−	5.45151i	0.136214	−	0.508356i
$116$	1.76865	−	1.02113i	0.164215	−	0.0948096i
$117$	6.66013	+	4.10649i	0.615729	+	0.379645i
$118$		−	15.6422i		−	1.43998i
$119$		0			0
$120$	6.04945			0.552237
$121$	−3.56858	−	2.06032i	−0.324416	−	0.187302i
$122$	−10.7494	−	2.88030i	−0.973208	−	0.260770i
$123$	1.89238	−	7.06247i	0.170630	−	0.636801i
$124$	4.98885	−	1.33676i	0.448012	−	0.120044i
$125$	−5.66930	−	5.66930i	−0.507078	−	0.507078i
$126$		0			0
$127$			7.37629i			0.654540i	0.944931	+	0.327270i	$0.106129\pi$
$127$			7.37629i			0.654540i	−0.944931	+	0.327270i	$0.893871\pi$
$128$	1.23318	+	4.60228i	0.108998	+	0.406788i
$129$	−3.61920	−	6.26864i	−0.318653	−	0.551923i
$130$	−3.32496	+	1.79352i	−0.291618	+	0.157302i
$131$	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
$135$	−1.58016	+	0.423402i	−0.135998	+	0.0364406i
$136$	9.03328	+	2.42046i	0.774598	+	0.207553i
$137$	−2.57300	−	0.689433i	−0.219826	−	0.0589023i	0.147225	−	0.989103i	$-0.452966\pi$
$137$	−2.57300	−	0.689433i	−0.219826	−	0.0589023i	−0.367051	+	0.930201i	$0.619633\pi$
$138$	17.2818	−	4.63063i	1.47112	−	0.394186i
$139$			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
$143$	−2.71073	+	9.06000i	−0.226683	+	0.757635i
$144$	2.85464	+	4.94438i	0.237886	+	0.412031i
$145$	0.849848	+	3.17168i	0.0705760	+	0.263393i
$146$			11.8378i			0.979701i
$147$		0			0
$148$	1.09171	+	1.09171i	0.0897379	+	0.0897379i
$149$	−18.2173	+	4.88130i	−1.49242	+	0.399892i	−0.910552	−	0.413394i	$-0.864343\pi$
$149$	−18.2173	+	4.88130i	−1.49242	+	0.399892i	−0.581865	+	0.813286i	$0.697677\pi$
$150$	3.02186	−	11.2777i	0.246734	−	0.920823i
$151$	−10.4396	−	2.79727i	−0.849560	−	0.227639i	−0.192331	−	0.981330i	$-0.561605\pi$
$151$	−10.4396	−	2.79727i	−0.849560	−	0.227639i	−0.657229	+	0.753691i	$0.728271\pi$
$152$	0.391893	+	0.226259i	0.0317867	+	0.0183521i
$153$	6.61282			0.534615
$154$		0			0
$155$			8.30406i			0.666998i
$156$	3.76266	+	2.31998i	0.301254	+	0.185747i
$157$	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	$0.0163873\pi$
$158$	5.50431	−	20.5424i	0.437899	−	1.63426i
$159$	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
$163$	−2.57540	−	9.61152i	−0.201721	−	0.752832i	−0.990424	−	0.138058i	$-0.955914\pi$
$163$	−2.57540	−	9.61152i	−0.201721	−	0.752832i	0.788703	−	0.614774i	$-0.210753\pi$
$164$	0.448746	−	1.67474i	0.0350412	−	0.130776i
$165$	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	$-0.0204055\pi$
$167$	12.0684	+	12.0684i	0.933884	+	0.933884i	−0.0640620	+	0.997946i	$0.520406\pi$
$168$		0			0
$169$	−12.9783	−	0.751536i	−0.998328	−	0.0578104i
$170$	−1.59644	+	2.76511i	−0.122441	+	0.212074i
$171$	0.309076	+	0.0828167i	0.0236356	+	0.00633315i
$172$	−0.858232	−	1.48650i	−0.0654395	−	0.113345i
$173$	3.74120	−	6.47994i	0.284438	−	0.492661i	−0.688035	−	0.725678i	$-0.741526\pi$
$173$	3.74120	−	6.47994i	0.284438	−	0.492661i	0.972473	+	0.233017i	$0.0748597\pi$
$174$	−7.36040	+	7.36040i	−0.557990	+	0.557990i
$175$		0			0
$176$	−4.87936	+	4.87936i	−0.367796	+	0.367796i
$177$	−7.61632	−	28.4245i	−0.572478	−	2.13652i
$178$	5.02630	−	2.90194i	0.376737	−	0.217509i
$179$	−19.6595	+	11.3504i	−1.46942	+	0.848371i	−0.999412	−	0.0342899i	$-0.989083\pi$
$179$	−19.6595	+	11.3504i	−1.46942	+	0.848371i	−0.470010	+	0.882661i	$0.655750\pi$
$180$	0.979798	−	0.262536i	0.0730298	−	0.0195683i
$181$	−1.91735			−0.142516			−0.0712579	−	0.997458i	$-0.522701\pi$
$181$	−1.91735			−0.142516			−0.0712579	+	0.997458i	$0.522701\pi$
$182$		0			0
$183$	−20.9360			−1.54763
$184$	19.2990	−	5.17114i	1.42274	−	0.381222i
$185$	−2.14974	+	1.24115i	−0.158052	+	0.0912515i
$186$	−22.7978	+	13.1623i	−1.67161	+	0.965106i
$187$	2.06862	+	7.72018i	0.151272	+	0.564556i
$188$	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
$193$	13.9815	+	3.74632i	1.00641	+	0.269666i	0.724127	−	0.689666i	$-0.242243\pi$
$193$	13.9815	+	3.74632i	1.00641	+	0.269666i	0.282280	+	0.959332i	$0.408909\pi$
$194$	−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	0.995748	+	0.0921223i	$0.0293651\pi$
$197$	15.2690	+	15.2690i	1.08787	+	1.08787i	0.0921223	+	0.995748i	$0.470635\pi$
$198$	−3.43968	+	5.95770i	−0.244447	+	0.423395i
$199$	−11.2318	−	19.4540i	−0.796198	−	1.37906i	−0.922075	−	0.387010i	$-0.873508\pi$
$199$	−11.2318	−	19.4540i	−0.796198	−	1.37906i	0.125877	−	0.992046i	$-0.459825\pi$
$200$	3.37458	−	12.5941i	0.238619	−	0.890539i
$201$	−0.873416	−	3.25963i	−0.0616060	−	0.229917i
$202$	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
$206$	−1.66452	+	6.21209i	−0.115973	+	0.432817i
$207$	12.2351	−	7.06391i	0.850395	−	0.490976i
$208$	−8.07439	−	4.97849i	−0.559858	−	0.345196i
$209$			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
$213$	12.7444	+	3.41486i	0.873233	+	0.233982i
$214$	3.20592	−	11.9646i	0.219152	−	0.817886i
$215$	2.66571	−	0.714274i	0.181800	−	0.0487131i
$216$	−4.09505	−	4.09505i	−0.278633	−	0.278633i
$217$		0			0
$218$		−	10.0072i		−	0.677772i
$219$	5.76392	+	21.5113i	0.389490	+	1.45360i
$220$	0.612999	+	1.06175i	0.0413284	+	0.0715829i
$221$	−9.66995	+	5.21608i	−0.650471	+	0.350872i
$222$	−6.81487	−	3.93457i	−0.457384	−	0.264071i
$223$	4.32131	−	4.32131i	0.289376	−	0.289376i	−0.547457	−	0.836833i	$-0.684404\pi$
$223$	4.32131	−	4.32131i	0.289376	−	0.289376i	0.836833	+	0.547457i	$0.184404\pi$
$224$		0			0
$225$		−	9.21953i		−	0.614636i
$226$	−6.70750	+	1.79727i	−0.446176	+	0.119553i
$227$	6.40708	+	1.71677i	0.425253	+	0.113946i	0.465097	−	0.885260i	$-0.346019\pi$
$227$	6.40708	+	1.71677i	0.425253	+	0.113946i	−0.0398440	+	0.999206i	$0.512686\pi$
$228$	0.174614	+	0.0467876i	0.0115641	+	0.00309858i
$229$	0.361646	−	0.0969027i	0.0238982	−	0.00640351i	−0.246850	−	0.969054i	$-0.579396\pi$
$229$	0.361646	−	0.0969027i	0.0238982	−	0.00640351i	0.270748	+	0.962650i	$0.412729\pi$
$230$			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	0.664533	−	0.747259i	$-0.268631\pi$
$233$	5.33723	+	3.08145i	0.349653	+	0.201872i	−0.314879	+	0.949132i	$0.601964\pi$
$234$	−9.06000	−	2.71073i	−0.592271	−	0.177206i
$235$	3.19788	+	5.53889i	0.208607	+	0.361318i
$236$	−1.80608	−	6.74039i	−0.117566	−	0.438762i
$237$		−	40.0091i		−	2.59887i
$238$		0			0
$239$	−5.63090	−	5.63090i	−0.364232	−	0.364232i	0.501136	−	0.865369i	$-0.332916\pi$
$239$	−5.63090	−	5.63090i	−0.364232	−	0.364232i	−0.865369	+	0.501136i	$0.832916\pi$
$240$	−5.00924	+	1.34222i	−0.323345	+	0.0866400i
$241$	0.407084	−	1.51926i	0.0262226	−	0.0978640i	−0.951574	−	0.307419i	$-0.900535\pi$
$241$	0.407084	−	1.51926i	0.0262226	−	0.0978640i	0.977797	+	0.209555i	$0.0672014\pi$
$242$	4.81067	+	1.28901i	0.309241	+	0.0828610i
$243$	−16.3661	−	9.44898i	−1.04989	−	0.606152i
$244$	−4.96462			−0.317827
$245$		0			0
$246$			8.83710i			0.563433i
$247$	−0.517287	+	0.122691i	−0.0329142	+	0.00780663i
$248$	−25.4588	+	14.6987i	−1.61664	+	0.933365i
$249$	8.77819	−	32.7607i	0.556295	−	2.07612i
$250$	8.39213	+	4.84520i	0.530765	+	0.306437i
$251$	12.1069			0.764182			0.382091	−	0.924125i	$-0.375204\pi$
$251$	12.1069			0.764182			0.382091	+	0.924125i	$0.375204\pi$
$252$		0			0
$253$	12.0742	+	12.0742i	0.759097	+	0.759097i
$254$	−2.30744	−	8.61150i	−0.144782	−	0.540334i
$255$	−1.55464	+	5.80199i	−0.0973553	+	0.363335i
$256$	5.95774	+	10.3191i	0.372359	+	0.644944i
$257$	−8.78794	+	15.2212i	−0.548176	+	0.949469i	0.450223	+	0.892916i	$0.351344\pi$
$257$	−8.78794	+	15.2212i	−0.548176	+	0.949469i	−0.998400	+	0.0565532i	$0.981989\pi$
$258$	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
$262$	−13.9677	−	3.74262i	−0.862925	−	0.231220i
$263$	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
$268$	−0.207116	−	0.772967i	−0.0126516	−	0.0472165i
$269$	−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
$271$	−3.30104	+	0.884511i	−0.200524	+	0.0537302i	−0.357683	−	0.933843i	$-0.616433\pi$
$271$	−3.30104	+	0.884511i	−0.200524	+	0.0537302i	0.157159	+	0.987573i	$0.449766\pi$
$272$	−8.01703			−0.486104
$273$		0			0
$274$	3.21953			0.194499
$275$	10.7634	−	2.88405i	0.649058	−	0.173915i
$276$	6.91224	−	3.99078i	0.416068	−	0.240217i
$277$	−25.1773	+	14.5361i	−1.51276	+	0.873391i	−0.512868	+	0.858467i	$0.671417\pi$
$277$	−25.1773	+	14.5361i	−1.51276	+	0.873391i	−0.999889	+	0.0149234i	$0.995250\pi$
$278$	−1.99229	−	7.43533i	−0.119490	−	0.445942i
$279$	−14.6987	+	14.6987i	−0.879985	+	0.879985i
$280$		0			0
$281$	9.68455	−	9.68455i	0.577732	−	0.577732i	−0.356546	−	0.934278i	$-0.616046\pi$
$281$	9.68455	−	9.68455i	0.577732	−	0.577732i	0.934278	+	0.356546i	$0.116046\pi$
$282$	−10.1376	+	17.5588i	−0.603683	+	1.04561i
$283$	2.15179	+	3.72700i	0.127910	+	0.221547i	0.922867	−	0.385119i	$-0.125840\pi$
$283$	2.15179	+	3.72700i	0.127910	+	0.221547i	−0.794956	+	0.606667i	$0.792506\pi$
$284$	3.02212	+	0.809775i	0.179330	+	0.0480513i
$285$	−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
$291$	−3.69799	+	13.8011i	−0.216780	+	0.809034i
$292$	1.36682	+	5.10103i	0.0799869	+	0.298515i
$293$	3.57373	+	3.57373i	0.208780	+	0.208780i	0.803749	−	0.594969i	$-0.202836\pi$
$293$	3.57373	+	3.57373i	0.208780	+	0.208780i	−0.594969	+	0.803749i	$0.702836\pi$
$294$		0			0
$295$	11.2195			0.653227
$296$	−7.61033	−	4.39383i	−0.442341	−	0.255386i
$297$	1.28101	−	4.78079i	0.0743317	−	0.277410i
$298$	19.7409	−	11.3974i	1.14356	−	0.660235i
$299$	−12.3195	+	19.9804i	−0.712453	+	1.15550i
$300$		−	5.20861i		−	0.300719i
$301$		0			0
$302$	13.0628			0.751678
$303$	2.28465	+	1.31904i	0.131250	+	0.0757770i
$304$	−0.374707	−	0.100403i	−0.0214909	−	0.00575848i
$305$	2.06593	−	7.71016i	0.118295	−	0.441482i
$306$	−7.72018	+	2.06862i	−0.441334	+	0.118255i
$307$	−8.59457	−	8.59457i	−0.490518	−	0.490518i	0.417952	−	0.908469i	$-0.362748\pi$
$307$	−8.59457	−	8.59457i	−0.490518	−	0.490518i	−0.908469	+	0.417952i	$0.862748\pi$
$308$		0			0
$309$			12.0989i			0.688282i
$310$	−2.59767	−	9.69463i	−0.147538	−	0.550618i
$311$	11.2702	+	19.5206i	0.639077	+	1.10691i	0.985636	+	0.168885i	$0.0540168\pi$
$311$	11.2702	+	19.5206i	0.639077	+	1.10691i	−0.346559	+	0.938028i	$0.612650\pi$
$312$	−24.1043	−	7.21197i	−1.36464	−	0.408297i
$313$	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
$317$	−5.42458	+	1.45351i	−0.304675	+	0.0816374i	−0.407917	−	0.913019i	$-0.633745\pi$
$317$	−5.42458	+	1.45351i	−0.304675	+	0.0816374i	0.103243	+	0.994656i	$0.467078\pi$
$318$	−9.11008	−	2.44104i	−0.510868	−	0.136887i
$319$	−9.59595	−	2.57123i	−0.537270	−	0.143961i
$320$	−7.39994	+	1.98281i	−0.413669	+	0.110842i
$321$		−	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
$325$	7.27221	+	13.4818i	0.403390	+	0.747833i
$326$	6.01333	+	10.4154i	0.333048	+	0.576855i
$327$	−4.87259	−	18.1848i	−0.269455	−	1.00562i
$328$			9.86861i			0.544903i
$329$		0			0
$330$	−4.41855	−	4.41855i	−0.243233	−	0.243233i
$331$	−2.33491	+	0.625638i	−0.128338	+	0.0343882i	−0.322417	−	0.946598i	$-0.604495\pi$
$331$	−2.33491	+	0.625638i	−0.128338	+	0.0343882i	0.194078	+	0.980986i	$0.437828\pi$
$332$	2.08160	−	7.76863i	0.114243	−	0.426359i
$333$	−6.00208	−	1.60825i	−0.328912	−	0.0881317i
$334$	−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	$-0.783030\pi$
$337$		−	23.1327i		−	1.26012i	0.776546	−	0.630061i	$-0.216970\pi$
$338$	15.3867	−	3.18246i	0.836923	−	0.173103i
$339$	−11.3136	+	6.53189i	−0.614468	+	0.354763i
$340$	−0.368656	+	1.37584i	−0.0199932	+	0.0746156i
$341$	−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
$345$	3.32138	+	12.3956i	0.178817	+	0.667354i
$346$	−2.34064	+	8.73537i	−0.125833	+	0.469616i
$347$	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	−0.999781	−	0.0209053i	$-0.993345\pi$
$349$	−19.0680	−	19.0680i	−1.02069	−	1.02069i	−0.0209053	−	0.999781i	$-0.506655\pi$
$350$		0			0
$351$	6.80098	+	0.196748i	0.363010	+	0.0105017i
$352$	−3.87936	+	6.71925i	−0.206771	+	0.358137i
$353$	6.57373	+	1.76143i	0.349885	+	0.0937513i	0.429481	−	0.903076i	$-0.358696\pi$
$353$	6.57373	+	1.76143i	0.349885	+	0.0937513i	−0.0795964	+	0.996827i	$0.525363\pi$
$354$	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
$359$	−4.59383	−	17.1444i	−0.242453	−	0.904848i	−0.974646	−	0.223751i	$-0.928170\pi$
$359$	−4.59383	−	17.1444i	−0.242453	−	0.904848i	0.732193	−	0.681097i	$-0.238497\pi$
$360$	−5.00005	+	2.88678i	−0.263526	+	0.152147i
$361$	16.4357	−	9.48913i	0.865034	−	0.499428i
$362$	2.23843	−	0.599785i	0.117649	−	0.0315240i
$363$	9.36943			0.491768
$364$		0			0
$365$	−8.49079			−0.444428
$366$	24.4419	−	6.54918i	1.27760	−	0.342331i
$367$	−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
$369$	1.80608	+	6.74039i	0.0940208	+	0.350890i
$370$	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
$375$	17.6091	+	4.71834i	0.909330	+	0.243654i
$376$	−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	0.794438	−	0.607346i	$-0.207766\pi$
$379$	3.64229	+	3.64229i	0.187092	+	0.187092i	−0.607346	+	0.794438i	$0.707766\pi$
$380$	−0.0344612	+	0.0596885i	−0.00176782	+	0.00306196i
$381$	−8.38604	−	14.5250i	−0.429630	−	0.744141i
$382$	−3.13044	+	11.6830i	−0.160167	+	0.597752i
$383$	−8.98925	−	33.5483i	−0.459329	−	1.71424i	−0.675039	−	0.737782i	$-0.735873\pi$
$383$	−8.98925	−	33.5483i	−0.459329	−	1.71424i	0.215709	−	0.976458i	$-0.430794\pi$
$384$	−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
$388$	−0.876916	+	3.27269i	−0.0445187	+	0.166146i
$389$	5.62028	−	3.24487i	0.284960	−	0.164521i	−0.350707	−	0.936485i	$-0.614059\pi$
$389$	5.62028	−	3.24487i	0.284960	−	0.164521i	0.635667	+	0.771964i	$0.280725\pi$
$390$	4.50832	−	7.31184i	0.228287	−	0.370249i
$391$			19.8385i			1.00327i
$392$		0			0
$393$	−27.2039			−1.37226
$394$	−22.6023	−	13.0494i	−1.13869	−	0.657422i
$395$	14.7343	+	3.94803i	0.741361	+	0.198647i
$396$	−0.794307	+	2.96439i	−0.0399154	+	0.148966i
$397$	9.41915	−	2.52385i	0.472734	−	0.126669i	−0.0145835	−	0.999894i	$-0.504642\pi$
$397$	9.41915	−	2.52385i	0.472734	−	0.126669i	0.487317	+	0.873225i	$0.337976\pi$
$398$	19.1982	+	19.1982i	0.962317	+	0.962317i
$399$		0			0
$400$			11.1773i			0.558864i
$401$	3.30257	+	12.3254i	0.164922	+	0.615499i	0.998050	+	0.0624181i	$0.0198812\pi$
$401$	3.30257	+	12.3254i	0.164922	+	0.615499i	−0.833128	+	0.553081i	$0.813452\pi$
$402$	2.03935	+	3.53226i	0.101714	+	0.176173i
$403$	9.89984	−	33.0879i	0.493146	−	1.64823i
$404$	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
$408$	−20.5397	+	5.50360i	−1.01687	+	0.272469i
$409$	−3.90803	−	1.04715i	−0.193240	−	0.0517784i	0.160901	−	0.986971i	$-0.448560\pi$
$409$	−3.90803	−	1.04715i	−0.193240	−	0.0517784i	−0.354141	+	0.935192i	$0.615227\pi$
$410$	−3.25446	−	0.872031i	−0.160727	−	0.0430665i
$411$	5.85044	−	1.56762i	0.288581	−	0.0773251i
$412$			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
$416$	−10.2181	−	3.05724i	−0.500984	−	0.149893i
$417$	−7.24067	−	12.5412i	−0.354577	−	0.614145i
$418$	−0.120980	−	0.451502i	−0.00591730	−	0.0220837i
$419$			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	0.997215	−	0.0745864i	$-0.0237636\pi$
$421$	18.9307	+	18.9307i	0.922628	+	0.922628i	−0.0745864	+	0.997215i	$0.523764\pi$
$422$	22.0071	−	5.89678i	1.07129	−	0.287051i
$423$	−4.14372	+	15.4646i	−0.201475	+	0.751914i
$424$	−10.1734	−	2.72597i	−0.494066	−	0.132385i
$425$	11.2117	+	6.47309i	0.543848	+	0.313991i
$426$	−15.9468			−0.772624
$427$		0			0
$428$		−	5.52586i		−	0.267102i
$429$	−4.96239	−	20.9223i	−0.239586	−	1.01014i
$430$	−2.88866	+	1.66777i	−0.139303	+	0.0804269i
$431$	4.61347	−	17.2177i	0.222223	−	0.829348i	−0.761275	−	0.648429i	$-0.775426\pi$
$431$	4.61347	−	17.2177i	0.222223	−	0.829348i	0.983498	−	0.180919i	$-0.0579071\pi$
$432$	4.29948	+	2.48231i	0.206859	+	0.119430i
$433$	14.3392			0.689098			0.344549	−	0.938768i	$-0.388032\pi$
$433$	14.3392			0.689098			0.344549	+	0.938768i	$0.388032\pi$
$434$		0			0
$435$	−5.27933	−	5.27933i	−0.253125	−	0.253125i
$436$	−1.15545	−	4.31221i	−0.0553361	−	0.206517i
$437$	−0.248450	+	0.927228i	−0.0118850	+	0.0443553i
$438$	−13.4583	−	23.3104i	−0.643061	−	1.11381i
$439$	9.99061	−	17.3042i	0.476826	−	0.825886i	−0.522822	−	0.852442i	$-0.675121\pi$
$439$	9.99061	−	17.3042i	0.476826	−	0.825886i	0.999647	+	0.0265559i	$0.00845400\pi$
$440$	−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	$0.123905\pi$
$444$	−3.39090	−	0.908588i	−0.160925	−	0.0431197i
$445$	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	−0.942704	−	0.333631i	$-0.891726\pi$
$449$	−12.9060	+	12.9060i	−0.609073	+	0.609073i	0.333631	+	0.942704i	$0.391726\pi$
$450$	2.88405	+	10.7634i	0.135955	+	0.507392i
$451$	−7.30413	+	4.21704i	−0.343938	+	0.198573i
$452$	−2.68282	+	1.54893i	−0.126189	+	0.0728553i
$453$	23.7373	−	6.36039i	1.11528	−	0.298837i
$454$	−8.01703			−0.376258
$455$		0			0
$456$	−1.02893			−0.0481840
$457$	−9.51692	+	2.55005i	−0.445183	+	0.119286i	−0.474444	−	0.880285i	$-0.657351\pi$
$457$	−9.51692	+	2.55005i	−0.445183	+	0.119286i	0.0292619	+	0.999572i	$0.490684\pi$
$458$	−0.391893	+	0.226259i	−0.0183119	+	0.0105724i
$459$	4.97992	−	2.87516i	0.232443	−	0.134201i
$460$	0.787608	+	2.93939i	0.0367224	+	0.137050i
$461$	7.20809	−	7.20809i	0.335714	−	0.335714i	−0.519037	−	0.854752i	$-0.673709\pi$
$461$	7.20809	−	7.20809i	0.335714	−	0.335714i	0.854752	+	0.519037i	$0.173709\pi$
$462$		0			0
$463$	−4.06084	+	4.06084i	−0.188723	+	0.188723i	−0.795144	−	0.606421i	$-0.792605\pi$
$463$	−4.06084	+	4.06084i	−0.188723	+	0.188723i	0.606421	+	0.795144i	$0.292605\pi$
$464$	4.98246	−	8.62988i	0.231305	−	0.400632i
$465$	−9.44081	−	16.3520i	−0.437807	−	0.758304i
$466$	−7.19492	−	1.92787i	−0.333298	−	0.0893070i
$467$	8.68367	−	15.0406i	0.401832	−	0.695994i	−0.592115	−	0.805854i	$-0.701707\pi$
$467$	8.68367	−	15.0406i	0.401832	−	0.695994i	0.993947	+	0.109860i	$0.0350401\pi$
$468$	−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
$473$	−2.16105	+	8.06513i	−0.0993650	+	0.370835i
$474$	12.5156	+	46.7089i	0.574861	+	2.14541i
$475$	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
$479$	3.61865	−	13.5050i	0.165340	−	0.617059i	−0.832656	−	0.553790i	$-0.813181\pi$
$479$	3.61865	−	13.5050i	0.165340	−	0.617059i	0.997997	−	0.0632685i	$-0.0201525\pi$
$480$	−5.04976	+	2.91548i	−0.230489	+	0.133073i
$481$	10.0454	−	2.38259i	0.458032	−	0.108637i
$482$			1.90101i			0.0865887i
$483$		0			0
$484$	2.22180			0.100991
$485$	−4.71766	−	2.72374i	−0.214218	−	0.123679i
$486$	22.0626	+	5.91164i	1.00078	+	0.268158i
$487$	−4.61527	+	17.2244i	−0.209138	+	0.780513i	0.779010	+	0.627011i	$0.215722\pi$
$487$	−4.61527	+	17.2244i	−0.209138	+	0.780513i	−0.988148	+	0.153502i	$0.950945\pi$
$488$	27.2948	−	7.31363i	1.23558	−	0.331073i
$489$	15.9986	+	15.9986i	0.723482	+	0.723482i
$490$		0			0
$491$			1.72487i			0.0778425i	0.999242	+	0.0389212i	$0.0123921\pi$
$491$			1.72487i			0.0778425i	−0.999242	+	0.0389212i	$0.987608\pi$
$492$	1.02035	+	3.80800i	0.0460010	+	0.171678i
$493$	−5.77099	−	9.99564i	−0.259912	−	0.450181i
$494$	0.565531	−	0.305054i	0.0254444	−	0.0137250i
$495$	−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
$499$	37.6415	−	10.0860i	1.68507	−	0.451512i	0.715957	−	0.698145i	$-0.245991\pi$
$499$	37.6415	−	10.0860i	1.68507	−	0.451512i	0.969109	+	0.246633i	$0.0793241\pi$
$500$	4.17570	+	1.11888i	0.186743	+	0.0500376i
$501$	−37.4851	−	10.0441i	−1.67471	−	0.448738i
$502$	−14.1343	+	3.78728i	−0.630845	+	0.169034i
$503$			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
$507$	26.4106	−	13.2750i	1.17294	−	0.589563i
$508$	−1.98861	−	3.44437i	−0.0882302	−	0.152819i
$509$	5.58088	+	20.8281i	0.247368	+	0.923191i	0.972178	+	0.234242i	$0.0752609\pi$
$509$	5.58088	+	20.8281i	0.247368	+	0.923191i	−0.724810	+	0.688949i	$0.758072\pi$
$510$		−	7.25990i		−	0.321474i
$511$		0			0
$512$	−16.9216	−	16.9216i	−0.747837	−	0.747837i
$513$	0.268763	−	0.0720149i	0.0118662	−	0.00317954i
$514$	5.49807	−	20.5191i	0.242509	−	0.905057i
$515$	−4.45570	−	1.19390i	−0.196341	−	0.0526095i
$516$	3.37998	+	1.95143i	0.148795	+	0.0859070i
$517$	−19.3505			−0.851033
$518$		0			0
$519$			17.0133i			0.746802i
$520$	5.03455	−	8.16531i	0.220780	−	0.358072i
$521$	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	$0.187784\pi$
$522$	2.57123	−	9.59595i	0.112540	−	0.420003i
$523$	−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
$527$	−7.55477	−	28.1948i	−0.329091	−	1.22818i
$528$	4.06091	−	15.1555i	0.176728	−	0.659559i
$529$	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
$535$	8.58178	+	2.29948i	0.371023	+	0.0994152i
$536$	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
$541$	−3.39993	−	12.6887i	−0.146174	−	0.545531i	−0.999700	−	0.0244801i	$-0.992207\pi$
$541$	−3.39993	−	12.6887i	−0.146174	−	0.545531i	0.853526	−	0.521051i	$-0.174460\pi$
$542$	3.57713	−	2.06526i	0.153651	−	0.0887104i
$543$	3.77557	−	2.17982i	0.162025	−	0.0935452i
$544$	−8.70702	+	2.33304i	−0.373311	+	0.100028i
$545$	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	$0.411064\pi$
$548$	1.38733	−	0.371735i	0.0592639	−	0.0158797i
$549$	17.3042	−	9.99061i	0.738527	−	0.426389i
$550$	−11.6636	+	6.73400i	−0.497339	+	0.287139i
$551$	−0.144548	−	0.539459i	−0.00615794	−	0.0229817i
$552$	−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
$557$	22.6969	+	6.08162i	0.961699	+	0.257687i	0.705320	−	0.708890i	$-0.250804\pi$
$557$	22.6969	+	6.08162i	0.961699	+	0.257687i	0.256380	+	0.966576i	$0.417470\pi$
$558$	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	0.998788	−	0.0492194i	$-0.0156733\pi$
$563$	10.8380	+	18.7720i	0.456769	+	0.791147i	−0.542019	+	0.840366i	$0.682340\pi$
$564$	−2.34101	+	8.73678i	−0.0985744	+	0.367885i
$565$	−1.28911	−	4.81103i	−0.0542334	−	0.202402i
$566$	−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	0.790821	−	0.612047i	$-0.209654\pi$
$569$	15.6524	+	9.03692i	0.656183	+	0.378847i	−0.134638	+	0.990895i	$0.542987\pi$
$570$	0.0909205	−	0.339320i	0.00380824	−	0.0142125i
$571$	7.39319	−	4.26846i	0.309395	−	0.178630i	−0.337260	−	0.941411i	$-0.609500\pi$
$571$	7.39319	−	4.26846i	0.309395	−	0.178630i	0.646656	+	0.762782i	$0.276167\pi$
$572$	−1.17675	−	4.96138i	−0.0492022	−	0.207446i
$573$			22.7542i			0.950569i
$574$		0			0
$575$	27.6586			1.15344
$576$	−16.6080	−	9.58864i	−0.692000	−	0.399527i
$577$	11.7009	+	3.13524i	0.487114	+	0.130522i	0.494013	−	0.869454i	$-0.335529\pi$
$577$	11.7009	+	3.13524i	0.487114	+	0.130522i	−0.00689906	+	0.999976i	$0.502196\pi$
$578$	−2.41315	+	9.00599i	−0.100374	+	0.374600i
$579$	−31.7908	+	8.51831i	−1.32118	+	0.354009i
$580$	−1.25190	−	1.25190i	−0.0519825	−	0.0519825i
$581$		0			0
$582$		−	17.2690i		−	0.715822i
$583$	−2.32971	−	8.69461i	−0.0964869	−	0.360094i
$584$	−15.0292	−	26.0313i	−0.621912	−	1.07718i
$585$	1.94431	−	6.49839i	0.0803872	−	0.268676i
$586$	−5.29011	−	3.05425i	−0.218532	−	0.126170i
$587$	−0.308382	+	0.308382i	−0.0127283	+	0.0127283i	−0.713442	−	0.700714i	$-0.752865\pi$
$587$	−0.308382	+	0.308382i	−0.0127283	+	0.0127283i	0.700714	+	0.713442i	$0.252865\pi$
$588$		0			0
$589$		−	1.41241i		−	0.0581972i
$590$	−13.0983	+	3.50968i	−0.539249	+	0.144491i
$591$	−47.4261	−	12.7078i	−1.95085	−	0.522729i
$592$	7.27660	+	1.94976i	0.299066	+	0.0801346i
$593$	6.76461	−	1.81257i	0.277789	−	0.0744334i	−0.117235	−	0.993104i	$-0.537403\pi$
$593$	6.76461	−	1.81257i	0.277789	−	0.0744334i	0.395024	+	0.918671i	$0.370736\pi$
$594$			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
$598$	8.13220	−	27.1800i	0.332550	−	1.11147i
$599$	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	$0.716045\pi$
$600$	7.67307	+	28.6363i	0.313252	+	1.16907i
$601$			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
$604$	5.62890	−	1.50826i	0.229037	−	0.0613702i
$605$	−0.924561	+	3.45051i	−0.0375887	+	0.140283i
$606$	−3.07985	−	0.825244i	−0.125110	−	0.0335232i
$607$	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
$611$	−6.13883	−	25.8824i	−0.248350	−	1.04709i
$612$	−3.08787	+	1.78278i	−0.124820	+	0.0720646i
$613$	−2.35686	+	8.79593i	−0.0951928	+	0.355264i	−0.997049	−	0.0767728i	$-0.975538\pi$
$613$	−2.35686	+	8.79593i	−0.0951928	+	0.355264i	0.901856	+	0.432037i	$0.142205\pi$
$614$	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	0.956296	−	0.292402i	$-0.0944544\pi$
$617$	16.4908	+	16.4908i	0.663894	+	0.663894i	−0.292402	+	0.956296i	$0.594454\pi$
$618$	−3.78477	−	14.1249i	−0.152246	−	0.568188i
$619$	−8.16997	+	30.4907i	−0.328379	+	1.22553i	0.582493	+	0.812836i	$0.302078\pi$
$619$	−8.16997	+	30.4907i	−0.328379	+	1.22553i	−0.910871	+	0.412690i	$0.864589\pi$
$620$	−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
$626$	−5.03025	−	1.34785i	−0.201049	−	0.0538710i
$627$	−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	−0.628480	−	0.777826i	$-0.716322\pi$
$631$	3.75154	−	3.75154i	0.149346	−	0.149346i	0.777826	+	0.628480i	$0.216322\pi$
$632$	13.9765	+	52.1609i	0.555955	+	2.07485i
$633$	37.1194	−	21.4309i	1.47536	−	0.851801i
$634$	5.87828	−	3.39383i	0.233456	−	0.134786i
$635$	6.17670	−	1.65504i	0.245115	−	0.0656783i
$636$	−4.20748			−0.166837
$637$		0			0
$638$	12.0072			0.475369
$639$	−12.1632	+	3.25912i	−0.481169	+	0.128929i
$640$	3.57713	−	2.06526i	0.141398	−	0.0816364i
$641$	22.2523	−	12.8474i	0.878912	−	0.507440i	0.00861267	−	0.999963i	$-0.497258\pi$
$641$	22.2523	−	12.8474i	0.878912	−	0.507440i	0.870300	+	0.492523i	$0.163925\pi$
$642$	7.28955	+	27.2050i	0.287696	+	1.07370i
$643$	22.1537	−	22.1537i	0.873658	−	0.873658i	−0.119211	−	0.992869i	$-0.538036\pi$
$643$	22.1537	−	22.1537i	0.873658	−	0.873658i	0.992869	+	0.119211i	$0.0380363\pi$
$644$		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	$-0.946526\pi$
$647$	−16.2223	−	28.0978i	−0.637764	−	1.10464i	0.348159	−	0.937436i	$-0.386807\pi$
$648$	32.0184	+	8.57929i	1.25780	+	0.337027i
$649$	−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
$655$	2.68444	−	10.0185i	0.104890	−	0.391454i
$656$	−2.18960	−	8.17169i	−0.0854894	−	0.319051i
$657$	−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
$661$	3.37071	−	12.5797i	0.131105	−	0.489292i	−0.868878	−	0.495026i	$-0.835158\pi$
$661$	3.37071	−	12.5797i	0.131105	−	0.489292i	0.999984	+	0.00573384i	$0.00182515\pi$
$662$	2.53020	−	1.46081i	0.0983390	−	0.0567760i
$663$	13.1115	−	21.2649i	0.509208	−	0.825862i
$664$			45.7775i			1.77651i
$665$		0			0
$666$	7.51026			0.291017
$667$	−21.3550	−	12.3293i	−0.826868	−	0.477392i
$668$	−8.88896	−	2.38179i	−0.343924	−	0.0921542i
$669$	−3.59646	+	13.4222i	−0.139047	+	0.518931i
$670$	−1.50208	+	0.402480i	−0.0580302	+	0.0155492i
$671$	17.0767	+	17.0767i	0.659239	+	0.659239i
$672$		0			0
$673$		−	22.6319i		−	0.872397i	−0.899850	−	0.436199i	$-0.856325\pi$
$673$		−	22.6319i		−	0.872397i	0.899850	−	0.436199i	$-0.143675\pi$
$674$	7.23637	+	27.0065i	0.278734	+	1.04025i
$675$	−4.00852	−	6.94295i	−0.154288	−	0.267234i
$676$	6.26282	−	3.14794i	0.240878	−	0.121074i
$677$	−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
$681$	−14.5683	+	3.90357i	−0.558259	+	0.149585i
$682$	29.3312	+	7.85928i	1.12315	+	0.300947i
$683$	5.06387	+	1.35686i	0.193763	+	0.0519188i	0.354396	−	0.935096i	$-0.384687\pi$
$683$	5.06387	+	1.35686i	0.193763	+	0.0519188i	−0.160632	+	0.987014i	$0.551353\pi$
$684$	−0.166650	+	0.0446538i	−0.00637204	+	0.00170738i
$685$			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
$689$	10.8905	−	5.87445i	0.414894	−	0.223799i
$690$	−7.75513	−	13.4323i	−0.295233	−	0.511358i
$691$	−0.0974114	−	0.363544i	−0.00370571	−	0.0138299i	0.964048	−	0.265727i	$-0.0856121\pi$
$691$	−0.0974114	−	0.363544i	−0.00370571	−	0.0138299i	−0.967754	+	0.251897i	$0.918945\pi$
$692$			4.03442i			0.153366i
$693$		0			0
$694$	−7.35350	−	7.35350i	−0.279135	−	0.279135i
$695$	5.33308	−	1.42899i	0.202295	−	0.0542049i
$696$	6.84081	−	25.5302i	0.259300	−	0.967721i
$697$	−9.46493	−	2.53612i	−0.358510	−	0.0960624i
$698$	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	$0.222202\pi$
$701$			34.0349i			1.28548i	−0.766084	+	0.642740i	$0.777798\pi$
$702$	−8.00140	+	1.89778i	−0.301993	+	0.0716272i
$703$	0.365642	−	0.211104i	0.0137905	−	0.00796192i
$704$	5.99902	−	22.3886i	0.226096	−	0.843804i
$705$	−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
$709$	4.20888	+	15.7077i	0.158068	+	0.589917i	0.998823	+	0.0485016i	$0.0154446\pi$
$709$	4.20888	+	15.7077i	0.158068	+	0.589917i	−0.840755	+	0.541415i	$0.817889\pi$
$710$	1.57360	−	5.87277i	0.0590563	−	0.220401i
$711$	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
$717$	17.4898	+	4.68638i	0.653169	+	0.175016i
$718$	10.7262	+	18.5783i	0.400298	+	0.693337i
$719$	−17.5222	+	30.3494i	−0.653469	+	1.13184i	0.328806	+	0.944397i	$0.393354\pi$
$719$	−17.5222	+	30.3494i	−0.653469	+	1.13184i	−0.982275	+	0.187444i	$0.939980\pi$
$720$	3.49978	−	3.49978i	0.130429	−	0.130429i
$721$		0			0
$722$	−16.2195	+	16.2195i	−0.603629	+	0.603629i
$723$	0.925620	+	3.45446i	0.0344242	+	0.128473i
$724$	0.895311	−	0.516908i	0.0332740	−	0.0192107i
$725$	−13.9358	+	8.04585i	−0.517564	+	0.298816i
$726$	−10.9384	+	2.93094i	−0.405962	+	0.108777i
$727$	15.0936			0.559789			0.279895	−	0.960031i	$-0.409700\pi$
$727$	15.0936			0.559789			0.279895	+	0.960031i	$0.409700\pi$
$728$		0			0
$729$	10.5669			0.391367
$730$	9.91262	−	2.65608i	0.366883	−	0.0983059i
$731$	−8.40106	+	4.85035i	−0.310724	+	0.179397i
$732$	9.77609	−	5.64423i	0.361335	−	0.208617i
$733$	−5.42285	−	20.2383i	−0.200297	−	0.747520i	−0.990832	−	0.135102i	$-0.956864\pi$
$733$	−5.42285	−	20.2383i	−0.200297	−	0.747520i	0.790534	−	0.612418i	$-0.209803\pi$
$734$	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
$739$	−22.0435	−	5.90653i	−0.810883	−	0.217275i	−0.170526	−	0.985353i	$-0.554547\pi$
$739$	−22.0435	−	5.90653i	−0.810883	−	0.217275i	−0.640357	+	0.768078i	$0.721213\pi$
$740$	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	0.108652	−	0.994080i	$-0.465347\pi$
$743$	−24.1350	−	24.1350i	−0.885428	−	0.885428i	−0.994080	+	0.108652i	$0.965347\pi$
$744$	33.4215	−	57.8878i	1.22529	−	2.12227i
$745$	8.17494	+	14.1594i	0.299506	+	0.518760i
$746$	3.28589	−	12.2631i	0.120305	−	0.448984i
$747$	8.37786	+	31.2666i	0.306530	+	1.14399i
$748$	−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	0.210909	−	0.977506i	$-0.432358\pi$
$751$	−14.5293	−	8.38849i	−0.530181	−	0.306100i	−0.741090	+	0.671405i	$0.765691\pi$
$752$	5.02363	−	18.7484i	0.183193	−	0.683686i
$753$	−23.8404	+	13.7643i	−0.868792	+	0.501597i
$754$	3.80921	+	16.0603i	0.138723	+	0.584883i
$755$			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
$759$	−37.5029	−	10.0489i	−1.36127	−	0.364751i
$760$	0.101533	−	0.378927i	0.00368299	−	0.0137451i
$761$	2.88682	−	0.773522i	0.104647	−	0.0280402i	−0.206115	−	0.978528i	$-0.566082\pi$
$761$	2.88682	−	0.773522i	0.104647	−	0.0280402i	0.310763	+	0.950488i	$0.399416\pi$
$762$	14.3341	+	14.3341i	0.519268	+	0.519268i
$763$		0			0
$764$			5.39576i			0.195212i
$765$	−1.48374	−	5.53739i	−0.0536447	−	0.200205i
$766$	20.9891	+	36.3542i	0.758368	+	1.31353i
$767$	−44.7048	−	13.3756i	−1.61420	−	0.482964i
$768$	−23.4634	−	13.5466i	−0.846663	−	0.488821i
$769$	−25.9456	+	25.9456i	−0.935621	+	0.935621i	−0.998049	−	0.0624284i	$-0.980115\pi$
$769$	−25.9456	+	25.9456i	−0.935621	+	0.935621i	0.0624284	+	0.998049i	$0.480115\pi$
$770$		0			0
$771$		−	39.9637i		−	1.43926i
$772$	−7.53864	+	2.01997i	−0.271322	+	0.0727004i
$773$	1.30004	+	0.348344i	0.0467591	+	0.0125291i	0.282123	−	0.959378i	$-0.408961\pi$
$773$	1.30004	+	0.348344i	0.0467591	+	0.0125291i	−0.235364	+	0.971907i	$0.575628\pi$
$774$	−8.06513	−	2.16105i	−0.289895	−	0.0776772i
$775$	−39.3089	+	10.5328i	−1.41202	+	0.378349i
$776$		−	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
$780$	1.09844	−	3.67129i	0.0393306	−	0.131453i
$781$	−7.60977	−	13.1805i	−0.272299	−	0.471636i
$782$	−6.20585	−	23.1606i	−0.221921	−	0.828220i
$783$			7.14746i			0.255430i
$784$		0			0
$785$	−12.8908	−	12.8908i	−0.460091	−	0.460091i
$786$	31.7594	−	8.50991i	1.13282	−	0.303538i
$787$	−9.07805	+	33.8797i	−0.323597	+	1.20768i	0.592117	+	0.805852i	$0.298292\pi$
$787$	−9.07805	+	33.8797i	−0.323597	+	1.20768i	−0.915714	+	0.401830i	$0.868374\pi$
$788$	−11.2463	−	3.01344i	−0.400633	−	0.107349i
$789$	−28.6036	−	16.5143i	−1.01832	−	0.587925i
$790$	−18.4366			−0.655946
$791$		0			0
$792$		−	17.4680i		−	0.620698i
$793$	−17.4236	+	28.2586i	−0.618731	+	1.00349i
$794$	−10.2069	+	5.89298i	−0.362231	+	0.209134i
$795$	1.75086	−	6.53431i	0.0620967	−	0.231748i
$796$	10.4894	+	6.05604i	0.371786	+	0.214651i
$797$	34.9017			1.23628			0.618141	−	0.786067i	$-0.287886\pi$
$797$	34.9017			1.23628			0.618141	+	0.786067i	$0.287886\pi$
$798$		0			0
$799$	−15.8969	−	15.8969i	−0.562392	−	0.562392i
$800$	3.25270	+	12.1393i	0.115000	+	0.429187i
$801$	−2.69708	+	10.0656i	−0.0952967	+	0.355652i
$802$	−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
$808$	−3.43935	−	0.921570i	−0.120996	−	0.0324207i
$809$	−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	$-0.857702\pi$
$811$	−13.3684	+	13.3684i	−0.469428	+	0.469428i	0.432301	+	0.901729i	$0.357702\pi$
$812$		0			0
$813$	5.49466	−	5.49466i	0.192706	−	0.192706i
$814$	2.34935	+	8.76790i	0.0823448	+	0.307315i
$815$	−7.47057	+	4.31313i	−0.261683	+	0.151082i
$816$	15.7868	−	9.11450i	0.552647	−	0.319071i
$817$	−0.453401	+	0.121488i	−0.0158625	+	0.00425034i
$818$	4.89002			0.170976
$819$		0			0
$820$	−1.50307			−0.0524895
$821$	−23.6423	+	6.33494i	−0.825122	+	0.221091i	−0.646585	−	0.762842i	$-0.723803\pi$
$821$	−23.6423	+	6.33494i	−0.825122	+	0.221091i	−0.178538	+	0.983933i	$0.557137\pi$
$822$	−6.33976	+	3.66026i	−0.221124	+	0.127666i
$823$	−30.3777	+	17.5386i	−1.05890	+	0.611356i	−0.925128	−	0.379656i	$-0.876042\pi$
$823$	−30.3777	+	17.5386i	−1.05890	+	0.611356i	−0.133772	+	0.991012i	$0.542709\pi$
$824$	−4.22654	−	15.7737i	−0.147239	−	0.549502i
$825$	−17.9160	+	17.9160i	−0.623753	+	0.623753i
$826$		0			0
$827$	−19.4173	+	19.4173i	−0.675207	+	0.675207i	−0.958912	−	0.283705i	$-0.908436\pi$
$827$	−19.4173	+	19.4173i	−0.675207	+	0.675207i	0.283705	+	0.958912i	$0.408436\pi$
$828$	−3.80878	+	6.59701i	−0.132364	+	0.229262i
$829$	−4.58045	−	7.93358i	−0.159086	−	0.275545i	0.775453	−	0.631405i	$-0.217521\pi$
$829$	−4.58045	−	7.93358i	−0.159086	−	0.275545i	−0.934539	+	0.355860i	$0.884188\pi$
$830$	−15.0965	−	4.04509i	−0.524006	−	0.140407i
$831$	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
$837$	−4.67836	+	17.4599i	−0.161708	+	0.603501i
$838$	−11.0768	−	41.3393i	−0.382643	−	1.42804i
$839$	−26.1882	−	26.1882i	−0.904116	−	0.904116i	0.0916731	−	0.995789i	$-0.470779\pi$
$839$	−26.1882	−	26.1882i	−0.904116	−	0.904116i	−0.995789	+	0.0916731i	$0.970779\pi$
$840$		0			0
$841$	−14.6537			−0.505299
$842$	−28.0227	−	16.1789i	−0.965727	−	0.557563i
$843$	−8.06009	+	30.0806i	−0.277604	+	1.03603i
$844$	8.80223	−	5.08197i	0.302985	−	0.174929i
$845$	2.28266	+	11.0363i	0.0785258	+	0.379659i
$846$		−	19.3505i		−	0.665283i
$847$		0			0
$848$	9.02893			0.310055
$849$	−8.47439	−	4.89269i	−0.290840	−	0.167917i
$850$	−15.1141	−	4.04981i	−0.518410	−	0.138907i
$851$	4.82476	−	18.0062i	0.165391	−	0.617246i
$852$	−6.87165	+	1.84125i	−0.235419	+	0.0630803i
$853$	7.70865	+	7.70865i	0.263939	+	0.263939i	0.826652	−	0.562713i	$-0.190242\pi$
$853$	7.70865	+	7.70865i	0.263939	+	0.263939i	−0.562713	+	0.826652i	$0.690242\pi$
$854$		0			0
$855$		−	0.277394i		−	0.00948666i
$856$	8.14042	+	30.3805i	0.278234	+	1.03838i
$857$	−11.2070	−	19.4112i	−0.382825	−	0.663073i	0.608640	−	0.793447i	$-0.291716\pi$
$857$	−11.2070	−	19.4112i	−0.382825	−	0.663073i	−0.991465	+	0.130374i	$0.958382\pi$
$858$	12.3383	+	22.8736i	0.421222	+	0.780892i
$859$	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
$863$	12.3337	−	3.30482i	0.419846	−	0.112497i	−0.0427101	−	0.999088i	$-0.513599\pi$
$863$	12.3337	−	3.30482i	0.419846	−	0.112497i	0.462556	+	0.886590i	$0.346933\pi$
$864$	5.39190	+	1.44475i	0.183436	+	0.0491516i
$865$	−6.26555	−	1.67885i	−0.213035	−	0.0570826i
$866$	−16.7404	+	4.48558i	−0.568862	+	0.152426i
$867$			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
$871$	−5.12661	−	1.53387i	−0.173709	−	0.0519732i
$872$	12.7051	+	22.0058i	0.430248	+	0.745211i
$873$	−3.52934	−	13.1717i	−0.119450	−	0.445794i
$874$		−	1.16022i		−	0.0392450i
$875$		0			0
$876$	−8.49079	−	8.49079i	−0.286877	−	0.286877i
$877$	6.58365	−	1.76408i	0.222314	−	0.0595689i	−0.145943	−	0.989293i	$-0.546621\pi$
$877$	6.58365	−	1.76408i	0.222314	−	0.0595689i	0.368257	+	0.929724i	$0.379955\pi$
$878$	−6.25050	+	23.3272i	−0.210944	+	0.787255i
$879$	−11.1002	−	2.97428i	−0.374399	−	0.100320i
$880$	5.18064	+	2.99104i	0.174639	+	0.100828i
$881$	3.46947			0.116889			0.0584447	−	0.998291i	$-0.481386\pi$
$881$	3.46947			0.116889			0.0584447	+	0.998291i	$0.481386\pi$
$882$		0			0
$883$			47.0772i			1.58427i	0.610344	+	0.792136i	$0.291031\pi$
$883$			47.0772i			1.58427i	−0.610344	+	0.792136i	$0.708969\pi$
$884$	3.10917	−	5.04262i	0.104573	−	0.169602i
$885$	−22.0930	+	12.7554i	−0.742648	+	0.428768i
$886$	−1.76370	+	6.58222i	−0.0592527	+	0.221134i
$887$	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
$891$	7.33219	+	27.3641i	0.245638	+	0.916732i
$892$	−0.852839	+	3.18284i	−0.0285552	+	0.106569i
$893$	−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
$899$	35.0453	+	9.39035i	1.16883	+	0.313186i
$900$	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
$905$	0.430203	+	1.60554i	0.0143004	+	0.0533699i
$906$	−25.7226	+	14.8510i	−0.854577	+	0.493390i
$907$	11.3806	−	6.57058i	0.377886	−	0.218172i	−0.299012	−	0.954249i	$-0.596657\pi$
$907$	11.3806	−	6.57058i	0.377886	−	0.218172i	0.676898	+	0.736077i	$0.263324\pi$
$908$	−3.45463	+	0.925665i	−0.114646	+	0.0307193i
$909$	−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	$0.376491\pi$
$912$	0.852003	−	0.228294i	0.0282126	−	0.00755956i
$913$	−33.8817	+	19.5616i	−1.12132	+	0.647394i
$914$	10.3129	−	5.95415i	0.341120	−	0.196946i
$915$	4.69748	+	17.5312i	0.155294	+	0.579564i
$916$	−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
$921$	26.6951	+	7.15293i	0.879634	+	0.235697i
$922$	−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
$928$	2.89990	−	10.8226i	0.0951938	−	0.355268i
$929$	−5.86238	−	21.8787i	−0.192339	−	0.717817i	−0.992940	−	0.118620i	$-0.962153\pi$
$929$	−5.86238	−	21.8787i	−0.192339	−	0.717817i	0.800601	−	0.599198i	$-0.204514\pi$
$930$	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
$934$	−5.43284	+	20.2756i	−0.177768	+	0.663439i
$935$	6.00053	−	3.46441i	0.196238	−	0.113298i
$936$	23.3645	−	5.54162i	0.763692	−	0.181134i
$937$		−	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
$941$	43.2616	+	11.5919i	1.41029	+	0.377886i	0.882028	−	0.471197i	$-0.156178\pi$
$941$	43.2616	+	11.5919i	1.41029	+	0.377886i	0.528260	+	0.849083i	$0.322845\pi$
$942$	14.9576	−	55.8224i	0.487344	−	1.81879i
$943$	−20.2212	+	5.41824i	−0.658491	+	0.176442i
$944$	−24.0763	−	24.0763i	−0.783615	−	0.783615i
$945$		0			0
$946$		−	10.0917i		−	0.328110i
$947$	−4.24398	−	15.8388i	−0.137911	−	0.514691i	−0.999969	−	0.00788104i	$-0.997491\pi$
$947$	−4.24398	−	15.8388i	−0.137911	−	0.514691i	0.862058	−	0.506810i	$-0.169175\pi$
$948$	10.7862	+	18.6823i	0.350320	+	0.606773i
$949$	33.8320	+	10.1225i	1.09823	+	0.328589i
$950$	−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	$-0.794205\pi$
$953$		−	37.1939i		−	1.20483i	0.798183	−	0.602415i	$-0.205795\pi$
$954$	8.69461	−	2.32971i	0.281498	−	0.0754273i
$955$	−8.37974	−	2.24535i	−0.271162	−	0.0726577i
$956$	4.14741	+	1.11130i	0.134137	+	0.0359419i
$957$	21.8191	−	5.84641i	0.705312	−	0.188988i
$958$			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
$962$	−10.9823	+	5.92397i	−0.354083	+	0.190996i
$963$	11.1200	+	19.2605i	0.358338	+	0.620659i
$964$	0.219495	+	0.819167i	0.00706946	+	0.0263836i
$965$		−	12.5483i		−	0.403943i
$966$		0			0
$967$	34.8785	+	34.8785i	1.12162	+	1.12162i	0.991499	+	0.130117i	$0.0415354\pi$
$967$	34.8785	+	34.8785i	1.12162	+	1.12162i	0.130117	+	0.991499i	$0.458465\pi$
$968$	−12.2152	+	3.27305i	−0.392611	+	0.105200i
$969$	0.264423	−	0.986841i	0.00849450	−	0.0317019i
$970$	6.35970	+	1.70408i	0.204198	+	0.0547146i
$971$	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
$975$	−29.6474	−	18.2799i	−0.949476	−	0.585426i
$976$	−20.9787	+	12.1121i	−0.671513	+	0.387698i
$977$	2.12665	−	7.93676i	0.0680375	−	0.253919i	−0.923527	−	0.383533i	$-0.874707\pi$
$977$	2.12665	−	7.93676i	0.0680375	−	0.253919i	0.991565	+	0.129614i	$0.0413738\pi$
$978$	−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
$982$	−0.539573	−	2.01372i	−0.0172185	−	0.0642602i
$983$	4.48959	−	16.7554i	0.143196	−	0.534413i	−0.856634	−	0.515925i	$-0.827448\pi$
$983$	4.48959	−	16.7554i	0.143196	−	0.534413i	0.999829	−	0.0184877i	$-0.00588516\pi$
$984$	−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
$990$	5.76059	+	1.54354i	0.183083	+	0.0490571i
$991$	−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
$996$	4.73310	+	17.6642i	0.149974	+	0.559711i
$997$	−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
$999$	−5.21923	+	1.39849i	−0.165129	+	0.0442462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.411.1		24
7.2	even	3		91.2.i.a.34.5	✓	12
7.3	odd	6	inner	637.2.bc.a.619.5		24
7.4	even	3	inner	637.2.bc.a.619.6		24
7.5	odd	6		91.2.i.a.34.6	yes	12
7.6	odd	2	inner	637.2.bc.a.411.2		24
13.5	odd	4	inner	637.2.bc.a.460.5		24
21.2	odd	6		819.2.y.h.307.2		12
21.5	even	6		819.2.y.h.307.1		12
91.5	even	12		91.2.i.a.83.6	yes	12
91.18	odd	12	inner	637.2.bc.a.31.2		24
91.31	even	12	inner	637.2.bc.a.31.1		24
91.44	odd	12		91.2.i.a.83.5	yes	12
91.83	even	4	inner	637.2.bc.a.460.6		24
273.5	odd	12		819.2.y.h.811.2		12
273.44	even	12		819.2.y.h.811.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.5	✓	12	7.2	even	3
91.2.i.a.34.6	yes	12	7.5	odd	6
91.2.i.a.83.5	yes	12	91.44	odd	12
91.2.i.a.83.6	yes	12	91.5	even	12
637.2.bc.a.31.1		24	91.31	even	12	inner
637.2.bc.a.31.2		24	91.18	odd	12	inner
637.2.bc.a.411.1		24	1.1	even	1	trivial
637.2.bc.a.411.2		24	7.6	odd	2	inner
637.2.bc.a.460.5		24	13.5	odd	4	inner
637.2.bc.a.460.6		24	91.83	even	4	inner
637.2.bc.a.619.5		24	7.3	odd	6	inner
637.2.bc.a.619.6		24	7.4	even	3	inner
819.2.y.h.307.1		12	21.5	even	6
819.2.y.h.307.2		12	21.2	odd	6
819.2.y.h.811.1		12	273.44	even	12
819.2.y.h.811.2		12	273.5	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-1.16746 + 0.312819i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(-0.466951 + 0.269594i) q^{4} +(-0.224373 - 0.837372i) q^{5} +(1.94326 - 1.94326i) q^{6} +(2.17009 - 2.17009i) q^{8} +(1.08504 - 1.87935i) q^{9} +O(q^{10})\)	\(q+(-1.16746 + 0.312819i) q^{2} +(-1.96915 + 1.13689i) q^{3} +(-0.466951 + 0.269594i) q^{4} +(-0.224373 - 0.837372i) 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} +(2.53348 + 0.678845i) 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} +(-0.678845 + 2.53348i) q^{18} +(0.0381629 + 0.142426i) q^{19} +(0.330522 + 0.330522i) q^{20} -3.17009 q^{22} +(5.63805 + 3.25513i) q^{23} +(-1.80608 + 6.74039i) q^{24} +(3.67928 - 2.12423i) q^{25} +(-1.00569 - 4.24018i) q^{26} -1.88704i q^{27} -3.78765 q^{29} +(-2.06325 - 1.19122i) q^{30} +(-9.25250 - 2.47920i) q^{31} +(-0.765619 + 2.85733i) q^{32} +(-5.76059 + 1.54354i) q^{33} +(-2.60430 - 2.60430i) q^{34} +1.17009i q^{36} +(-0.741100 - 2.76582i) q^{37} +(-0.0891070 - 0.154338i) q^{38} +(-3.89210 - 7.21545i) q^{39} +(-2.30408 - 1.33026i) q^{40} +(-2.27378 + 2.27378i) q^{41} +3.18342i q^{43} +(-1.36603 + 0.366025i) q^{44} +(-1.81717 - 0.486909i) q^{45} +(-7.60045 - 2.03653i) q^{46} +(-7.12626 + 1.90947i) q^{47} -5.98209i q^{48} +(-3.63090 + 3.63090i) q^{50} +(-6.00053 - 3.46441i) q^{51} +(-0.922944 - 1.71102i) q^{52} +(-1.71594 - 2.97210i) q^{53} +(0.590303 + 2.20304i) q^{54} -2.27378i q^{55} +(-0.237071 - 0.237071i) q^{57} +(4.42192 - 1.18485i) q^{58} +(-3.34963 + 12.5010i) q^{59} +(-1.02662 - 0.275081i) q^{60} +(7.97398 + 4.60378i) q^{61} +11.5774 q^{62} -8.83710i q^{64} +(3.04132 - 0.721344i) q^{65} +(6.24239 - 3.60404i) q^{66} +(-0.384125 + 1.43357i) q^{67} +(-1.42292 - 0.821525i) q^{68} -14.8029 q^{69} +(-4.10310 - 4.10310i) q^{71} +(-1.72371 - 6.43299i) q^{72} +(2.53495 - 9.46056i) 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} +(2.20304 + 0.590303i) 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} +(-0.995834 - 3.71650i) q^{86} +(7.45847 - 4.30615i) q^{87} +(6.97103 - 4.02472i) q^{88} +(-4.63836 + 1.24285i) q^{89} +2.27378 q^{90} -3.51026 q^{92} +(21.0382 - 5.63716i) q^{93} +(7.72228 - 4.45846i) q^{94} +(0.110701 - 0.0639130i) q^{95} +(-1.74085 - 6.49694i) 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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