LMFDB - Embedded newform 507.2.k.k.188.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(80,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.80"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.12
Character	$\chi$	$=$	507.188
Dual form			507.2.k.k.89.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.340435 + 0.0912193i) q^{2} +(0.839735 + 1.51487i) q^{3} +(-1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.424061 - 0.439116i) q^{6} +(-0.300747 + 1.12240i) q^{7} +(0.965906 - 0.965906i) q^{8} +(-1.58969 + 2.54419i) q^{9} +(-1.06066 - 0.612371i) q^{10} +(0.485362 + 1.81140i) q^{11} +(-2.78492 - 1.67330i) q^{12} -0.409539i q^{14} +(-1.65895 + 5.78573i) q^{15} +(1.63506 - 2.83201i) q^{16} +(-2.95083 - 5.11099i) q^{17} +(0.309108 - 1.01114i) q^{18} +(4.75906 + 1.27519i) q^{19} +(-6.29623 - 1.68707i) q^{20} +(-1.95284 + 0.486926i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(1.35482 - 2.34662i) q^{23} +(2.27433 + 0.652122i) q^{24} +7.07560i q^{25} +(-5.18904 - 0.271740i) q^{27} +(-0.564135 - 2.10538i) q^{28} +(-2.32707 - 1.34353i) q^{29} +(0.0369941 - 2.12099i) q^{30} +(3.22500 - 3.22500i) q^{31} +(-1.00539 + 3.75217i) q^{32} +(-2.33646 + 2.25635i) q^{33} +(1.47079 + 1.47079i) q^{34} +(-3.49695 + 2.01896i) q^{35} +(0.196243 - 5.62393i) q^{36} +(2.08708 - 0.559232i) q^{37} -1.73647 q^{38} +4.74684 q^{40} +(-6.57436 + 1.76159i) q^{41} +(0.620400 - 0.343904i) q^{42} +(-4.80750 + 2.77561i) q^{43} +(-2.48735 - 2.48735i) q^{44} +(-10.1577 + 2.34538i) q^{45} +(-0.247172 + 0.922459i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(5.66317 + 0.0987761i) q^{48} +(4.89284 + 2.82488i) q^{49} +(-0.645431 - 2.40878i) q^{50} +(5.26460 - 8.76202i) q^{51} +2.46136i q^{53} +(1.79132 - 0.380831i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(0.793642 + 1.37463i) q^{56} +(2.06460 + 8.28020i) q^{57} +(0.914771 + 0.245112i) q^{58} +(9.66677 + 2.59020i) q^{59} +(-2.73147 - 10.9547i) q^{60} +(1.33134 + 2.30596i) q^{61} +(-0.803720 + 1.39208i) q^{62} +(-2.37750 - 2.54943i) q^{63} +5.17117i q^{64} +(0.589590 - 0.981273i) q^{66} +(-1.76087 - 6.57167i) q^{67} +(9.58711 + 5.53512i) q^{68} +(4.69254 + 0.0818465i) q^{69} +(1.00632 - 1.00632i) q^{70} +(3.00415 - 11.2116i) q^{71} +(0.921953 + 3.99294i) q^{72} +(9.13263 + 9.13263i) q^{73} +(-0.659503 + 0.380764i) q^{74} +(-10.7186 + 5.94163i) q^{75} +(-8.92696 + 2.39197i) q^{76} -2.17908 q^{77} +1.10008 q^{79} +(10.9765 - 2.94114i) q^{80} +(-3.94577 - 8.08894i) q^{81} +(2.07745 - 1.19942i) q^{82} +(-4.58922 - 4.58922i) q^{83} +(2.71567 - 2.62256i) q^{84} +(5.30793 - 19.8095i) q^{85} +(1.38345 - 1.38345i) q^{86} +(0.0811644 - 4.65342i) q^{87} +(2.21845 + 1.28082i) q^{88} +(1.10619 + 4.12834i) q^{89} +(3.24410 - 1.72503i) q^{90} +5.08271i q^{92} +(7.59361 + 2.17732i) q^{93} +(0.556230 - 0.963419i) q^{94} +(8.56055 + 14.8273i) q^{95} +(-6.52833 + 1.62779i) q^{96} +(11.8495 + 3.17506i) q^{97} +(-1.92338 - 0.515368i) q^{98} +(-5.38010 - 1.64471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.340435	+	0.0912193i	−0.240724	+	0.0645018i	−0.377164	−	0.926147i	$-0.623101\pi$
$2$	−0.340435	+	0.0912193i	−0.240724	+	0.0645018i	0.136440	+	0.990648i	$0.456434\pi$
$3$	0.839735	+	1.51487i	0.484821	+	0.874613i
$3$	0.839735	+	1.51487i	0.484821	+	0.874613i
$4$	−1.62448	+	0.937892i	−0.812238	+	0.468946i
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.994541	+	0.104350i	$0.0332761\pi$
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.104350	+	0.994541i	$0.466724\pi$
$6$	−0.424061	−	0.439116i	−0.173122	−	0.179269i
$7$	−0.300747	+	1.12240i	−0.113672	+	0.424228i	−0.999184	−	0.0403875i	$-0.987141\pi$
$7$	−0.300747	+	1.12240i	−0.113672	+	0.424228i	0.885513	+	0.464615i	$0.153807\pi$
$8$	0.965906	−	0.965906i	0.341499	−	0.341499i
$9$	−1.58969	+	2.54419i	−0.529897	+	0.848062i
$10$	−1.06066	−	0.612371i	−0.335410	−	0.193649i
$11$	0.485362	+	1.81140i	0.146342	+	0.546156i	0.999692	+	0.0248176i	$0.00790049\pi$
$11$	0.485362	+	1.81140i	0.146342	+	0.546156i	−0.853350	+	0.521339i	$0.825433\pi$
$12$	−2.78492	−	1.67330i	−0.803936	−	0.483039i
$13$		0			0
$13$		0			0
$14$		−	0.409539i		−	0.109454i
$15$	−1.65895	+	5.78573i	−0.428339	+	1.49387i
$16$	1.63506	−	2.83201i	0.408766	−	0.708003i
$17$	−2.95083	−	5.11099i	−0.715682	−	1.23960i	−0.962696	−	0.270586i	$-0.912783\pi$
$17$	−2.95083	−	5.11099i	−0.715682	−	1.23960i	0.247014	−	0.969012i	$-0.420551\pi$
$18$	0.309108	−	1.01114i	0.0728573	−	0.238328i
$19$	4.75906	+	1.27519i	1.09180	+	0.292548i	0.759423	−	0.650598i	$-0.225482\pi$
$19$	4.75906	+	1.27519i	1.09180	+	0.292548i	0.332381	+	0.943145i	$0.392148\pi$
$20$	−6.29623	−	1.68707i	−1.40788	−	0.377240i
$21$	−1.95284	+	0.486926i	−0.426146	+	0.106256i
$22$	−0.330468	−	0.572388i	−0.0704561	−	0.122034i
$23$	1.35482	−	2.34662i	0.282500	−	0.489305i	−0.689500	−	0.724286i	$-0.742169\pi$
$23$	1.35482	−	2.34662i	0.282500	−	0.489305i	0.972000	+	0.234981i	$0.0755028\pi$
$24$	2.27433	+	0.652122i	0.464246	+	0.133114i
$25$			7.07560i			1.41512i
$26$		0			0
$27$	−5.18904	−	0.271740i	−0.998632	−	0.0522964i
$28$	−0.564135	−	2.10538i	−0.106612	−	0.397880i
$29$	−2.32707	−	1.34353i	−0.432125	−	0.249488i	0.268126	−	0.963384i	$-0.413596\pi$
$29$	−2.32707	−	1.34353i	−0.432125	−	0.249488i	−0.700252	+	0.713896i	$0.746929\pi$
$30$	0.0369941	−	2.12099i	0.00675416	−	0.387239i
$31$	3.22500	−	3.22500i	0.579227	−	0.579227i	−0.355463	−	0.934690i	$-0.615677\pi$
$31$	3.22500	−	3.22500i	0.579227	−	0.579227i	0.934690	+	0.355463i	$0.115677\pi$
$32$	−1.00539	+	3.75217i	−0.177730	+	0.663296i
$33$	−2.33646	+	2.25635i	−0.406726	+	0.392781i
$34$	1.47079	+	1.47079i	0.252238	+	0.252238i
$35$	−3.49695	+	2.01896i	−0.591092	+	0.341267i
$36$	0.196243	−	5.62393i	0.0327072	−	0.937321i
$37$	2.08708	−	0.559232i	0.343114	−	0.0919372i	−0.0831470	−	0.996537i	$-0.526497\pi$
$37$	2.08708	−	0.559232i	0.343114	−	0.0919372i	0.426261	+	0.904600i	$0.359830\pi$
$38$	−1.73647			−0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	−6.57436	+	1.76159i	−1.02674	+	0.275115i	−0.732609	−	0.680650i	$-0.761698\pi$
$41$	−6.57436	+	1.76159i	−1.02674	+	0.275115i	−0.294133	+	0.955764i	$0.595031\pi$
$42$	0.620400	−	0.343904i	0.0957298	−	0.0530655i
$43$	−4.80750	+	2.77561i	−0.733136	+	0.423276i	−0.819568	−	0.572981i	$-0.805787\pi$
$43$	−4.80750	+	2.77561i	−0.733136	+	0.423276i	0.0864321	+	0.996258i	$0.472453\pi$
$44$	−2.48735	−	2.48735i	−0.374982	−	0.374982i
$45$	−10.1577	+	2.34538i	−1.51423	+	0.349629i
$46$	−0.247172	+	0.922459i	−0.0364436	+	0.136009i
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	−0.850895	−	0.525336i	$-0.823940\pi$
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	0.525336	+	0.850895i	$0.323940\pi$
$48$	5.66317	+	0.0987761i	0.817408	+	0.0142571i
$49$	4.89284	+	2.82488i	0.698977	+	0.403555i
$50$	−0.645431	−	2.40878i	−0.0912777	−	0.340653i
$51$	5.26460	−	8.76202i	0.737191	−	1.22693i
$52$		0			0
$53$			2.46136i			0.338093i	0.985608	+	0.169047i	$0.0540689\pi$
$53$			2.46136i			0.338093i	−0.985608	+	0.169047i	$0.945931\pi$
$54$	1.79132	−	0.380831i	0.243768	−	0.0518245i
$55$	−3.25832	+	5.64358i	−0.439352	+	0.760980i
$56$	0.793642	+	1.37463i	0.106055	+	0.183692i
$57$	2.06460	+	8.28020i	0.273463	+	1.09674i
$58$	0.914771	+	0.245112i	0.120115	+	0.0321848i
$59$	9.66677	+	2.59020i	1.25851	+	0.337216i	0.825617	−	0.564231i	$-0.190827\pi$
$59$	9.66677	+	2.59020i	1.25851	+	0.337216i	0.432890	+	0.901447i	$0.357494\pi$
$60$	−2.73147	−	10.9547i	−0.352631	−	1.41424i
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	0.938581	−	0.345058i	$-0.112141\pi$
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	−0.768120	+	0.640306i	$0.778808\pi$
$62$	−0.803720	+	1.39208i	−0.102073	+	0.176795i
$63$	−2.37750	−	2.54943i	−0.299537	−	0.321198i
$64$			5.17117i			0.646397i
$65$		0			0
$66$	0.589590	−	0.981273i	0.0725736	−	0.120786i
$67$	−1.76087	−	6.57167i	−0.215125	−	0.802857i	−0.986123	−	0.166019i	$-0.946909\pi$
$67$	−1.76087	−	6.57167i	−0.215125	−	0.802857i	0.770998	−	0.636838i	$-0.219758\pi$
$68$	9.58711	+	5.53512i	1.16261	+	0.671232i
$69$	4.69254	+	0.0818465i	0.564915	+	0.00985317i
$70$	1.00632	−	1.00632i	0.120278	−	0.120278i
$71$	3.00415	−	11.2116i	0.356527	−	1.33058i	−0.522025	−	0.852930i	$-0.674823\pi$
$71$	3.00415	−	11.2116i	0.356527	−	1.33058i	0.878552	−	0.477647i	$-0.158510\pi$
$72$	0.921953	+	3.99294i	0.108653	+	0.470572i
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.997444	+	0.0714492i	$0.0227624\pi$
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.0714492	+	0.997444i	$0.477238\pi$
$74$	−0.659503	+	0.380764i	−0.0766657	+	0.0442630i
$75$	−10.7186	+	5.94163i	−1.23768	+	0.686080i
$76$	−8.92696	+	2.39197i	−1.02399	+	0.274378i
$77$	−2.17908			−0.248330
$78$		0			0
$79$	1.10008			0.123769			0.0618844	−	0.998083i	$-0.480289\pi$
$79$	1.10008			0.123769			0.0618844	+	0.998083i	$0.480289\pi$
$80$	10.9765	−	2.94114i	1.22721	−	0.328829i
$81$	−3.94577	−	8.08894i	−0.438419	−	0.898771i
$82$	2.07745	−	1.19942i	0.229416	−	0.132453i
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	0.408864	−	0.912596i	$-0.365925\pi$
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	−0.912596	+	0.408864i	$0.865925\pi$
$84$	2.71567	−	2.62256i	0.296303	−	0.286144i
$85$	5.30793	−	19.8095i	0.575726	−	2.14864i
$86$	1.38345	−	1.38345i	0.149181	−	0.149181i
$87$	0.0811644	−	4.65342i	0.00870173	−	0.498899i
$88$	2.21845	+	1.28082i	0.236488	+	0.136536i
$89$	1.10619	+	4.12834i	0.117256	+	0.437604i	0.999446	−	0.0332896i	$-0.0105984\pi$
$89$	1.10619	+	4.12834i	0.117256	+	0.437604i	−0.882190	+	0.470893i	$0.843932\pi$
$90$	3.24410	−	1.72503i	0.341959	−	0.181834i
$91$		0			0
$92$			5.08271i			0.529909i
$93$	7.59361	+	2.17732i	0.787421	+	0.225778i
$94$	0.556230	−	0.963419i	0.0573708	−	0.0993691i
$95$	8.56055	+	14.8273i	0.878294	+	1.52125i
$96$	−6.52833	+	1.62779i	−0.666295	+	0.166135i
$97$	11.8495	+	3.17506i	1.20313	+	0.322379i	0.804065	−	0.594542i	$-0.202667\pi$
$97$	11.8495	+	3.17506i	1.20313	+	0.322379i	0.399070	+	0.916921i	$0.369333\pi$
$98$	−1.92338	−	0.515368i	−0.194291	−	0.0520600i
$99$	−5.38010	−	1.64471i	−0.540721	−	0.165299i
$100$	−6.63614	−	11.4941i	−0.663614	−	1.14941i
$101$	−5.54779	+	9.60905i	−0.552026	+	0.956137i	0.446103	+	0.894982i	$0.352812\pi$
$101$	−5.54779	+	9.60905i	−0.552026	+	0.956137i	−0.998128	+	0.0611547i	$0.980522\pi$
$102$	−0.992988	+	3.46313i	−0.0983204	+	0.342901i
$103$		−	4.43285i		−	0.436782i	−0.975861	−	0.218391i	$-0.929919\pi$
$103$		−	4.43285i		−	0.436782i	0.975861	−	0.218391i	$-0.0700808\pi$
$104$		0			0
$105$	−5.99499	−	3.60205i	−0.585051	−	0.351524i
$106$	−0.224523	−	0.837932i	−0.0218076	−	0.0813872i
$107$	−11.3063	−	6.52769i	−1.09302	−	0.631055i	−0.158641	−	0.987336i	$-0.550711\pi$
$107$	−11.3063	−	6.52769i	−1.09302	−	0.631055i	−0.934379	+	0.356281i	$0.884045\pi$
$108$	8.68434	−	4.42532i	0.835651	−	0.425827i
$109$	−4.48829	+	4.48829i	−0.429901	+	0.429901i	−0.888594	−	0.458694i	$-0.848318\pi$
$109$	−4.48829	+	4.48829i	−0.429901	+	0.429901i	0.458694	+	0.888594i	$0.348318\pi$
$110$	0.594443	−	2.21849i	0.0566780	−	0.211525i
$111$	2.59976	+	2.69206i	0.246759	+	0.255519i
$112$	2.68692	+	2.68692i	0.253890	+	0.253890i
$113$	11.2693	−	6.50632i	1.06012	−	0.612063i	0.134657	−	0.990892i	$-0.457007\pi$
$113$	11.2693	−	6.50632i	1.06012	−	0.612063i	0.925467	+	0.378829i	$0.123673\pi$
$114$	−1.45818	−	2.63054i	−0.136571	−	0.246372i
$115$	9.09518	−	2.43705i	0.848130	−	0.227256i
$116$	5.04035			0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	6.62404	−	1.77491i	0.607225	−	0.162705i
$120$	3.98608	+	7.19086i	0.363878	+	0.656433i
$121$	6.48070	−	3.74164i	0.589155	−	0.340149i
$122$	−0.663584	−	0.663584i	−0.0600781	−	0.0600781i
$123$	−8.18931	−	8.48005i	−0.738405	−	0.764621i
$124$	−2.21423	+	8.26363i	−0.198844	+	0.742096i
$125$	−5.10014	+	5.10014i	−0.456171	+	0.456171i
$126$	1.04194	+	0.651040i	0.0928236	+	0.0579992i
$127$	6.74982	+	3.89701i	0.598950	+	0.345804i	0.768628	−	0.639696i	$-0.220940\pi$
$127$	6.74982	+	3.89701i	0.598950	+	0.345804i	−0.169679	+	0.985499i	$0.554273\pi$
$128$	−2.48249	−	9.26479i	−0.219423	−	0.818900i
$129$	−8.24172	−	4.95198i	−0.725643	−	0.435997i
$130$		0			0
$131$		−	18.5420i		−	1.62003i	−0.586412	−	0.810013i	$-0.699460\pi$
$131$		−	18.5420i		−	1.62003i	0.586412	−	0.810013i	$-0.300540\pi$
$132$	1.67931	−	5.85674i	0.146165	−	0.509764i
$133$	−2.86254	+	4.95807i	−0.248214	+	0.429919i
$134$	1.19893	+	2.07660i	0.103571	+	0.179391i
$135$	−12.0828	−	13.4182i	−1.03992	−	1.15485i
$136$	−7.78697	−	2.08651i	−0.667727	−	0.178917i
$137$	7.27811	+	1.95016i	0.621811	+	0.166614i	0.555951	−	0.831215i	$-0.312354\pi$
$137$	7.27811	+	1.95016i	0.621811	+	0.166614i	0.0658600	+	0.997829i	$0.479021\pi$
$138$	−1.60497	+	0.400186i	−0.136624	+	0.0340661i
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	0.957419	−	0.288703i	$-0.0932239\pi$
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	−0.728733	+	0.684798i	$0.759891\pi$
$140$	3.78714	−	6.55952i	0.320072	−	0.554381i
$141$	−5.25531	−	1.50686i	−0.442577	−	0.126900i
$142$			4.09087i			0.343298i
$143$		0			0
$144$	4.60592	+	8.66193i	0.383827	+	0.721828i
$145$	−2.41673	−	9.01937i	−0.200699	−	0.749018i
$146$	−3.94214	−	2.27600i	−0.326254	−	0.188363i
$147$	−0.170655	+	9.78419i	−0.0140753	+	0.806987i
$148$	−2.86592	+	2.86592i	−0.235577	+	0.235577i
$149$	−5.90444	+	22.0357i	−0.483710	+	1.80523i	0.102088	+	0.994775i	$0.467448\pi$
$149$	−5.90444	+	22.0357i	−0.483710	+	1.80523i	−0.585798	+	0.810457i	$0.699219\pi$
$150$	3.10701	−	3.00049i	0.253686	−	0.244989i
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	0.384500	−	0.923125i	$-0.374374\pi$
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	−0.923125	+	0.384500i	$0.874374\pi$
$152$	5.82852	−	3.36510i	0.472755	−	0.272945i
$153$	17.6942	+	0.617428i	1.43049	+	0.0499161i
$154$	0.741836	−	0.198774i	0.0597789	−	0.0160177i
$155$	15.8489			1.27301
$156$		0			0
$157$	15.6785			1.25128			0.625640	−	0.780112i	$-0.284838\pi$
$157$	15.6785			1.25128			0.625640	+	0.780112i	$0.284838\pi$
$158$	−0.374506	+	0.100349i	−0.0297941	+	0.00798331i
$159$	−3.72865	+	2.06689i	−0.295701	+	0.163915i
$160$	−11.6902	+	6.74937i	−0.924195	+	0.533584i
$161$	2.22640	+	2.22640i	0.175465	+	0.175465i
$162$	2.08114	+	2.39383i	0.163510	+	0.188077i
$163$	−0.894579	+	3.33861i	−0.0700688	+	0.261500i	−0.992070	−	0.125687i	$-0.959887\pi$
$163$	−0.894579	+	3.33861i	−0.0700688	+	0.261500i	0.922001	+	0.387187i	$0.126553\pi$
$164$	9.02770	−	9.02770i	0.704945	−	0.704945i
$165$	−11.2854	−	0.196839i	−0.878570	−	0.0153239i
$166$	1.98096	+	1.14371i	0.153752	+	0.0887687i
$167$	−1.35706	−	5.06462i	−0.105012	−	0.391912i	0.893334	−	0.449393i	$-0.148360\pi$
$167$	−1.35706	−	5.06462i	−0.105012	−	0.391912i	−0.998347	+	0.0574813i	$0.981693\pi$
$168$	−1.41594	+	2.35659i	−0.109242	+	0.181815i
$169$		0			0
$170$			7.22802i			0.554364i
$171$	−10.8097	+	10.0808i	−0.826642	+	0.770897i
$172$	5.20644	−	9.01782i	0.396987	−	0.687602i
$173$	−7.12562	−	12.3419i	−0.541751	−	0.938339i	−0.998804	−	0.0489001i	$-0.984428\pi$
$173$	−7.12562	−	12.3419i	−0.541751	−	0.938339i	0.457053	−	0.889439i	$-0.348905\pi$
$174$	0.396851	+	1.59159i	0.0300852	+	0.120658i
$175$	−7.94166	−	2.12796i	−0.600333	−	0.160859i
$176$	5.92349	+	1.58720i	0.446500	+	0.119639i
$177$	4.19369	+	16.8190i	0.315217	+	1.26420i
$178$	−0.753169	−	1.30453i	−0.0564524	−	0.0977785i
$179$	2.18334	−	3.78165i	0.163190	−	0.282654i	−0.772821	−	0.634624i	$-0.781155\pi$
$179$	2.18334	−	3.78165i	0.163190	−	0.282654i	0.936011	+	0.351970i	$0.114488\pi$
$180$	14.3013	−	13.3369i	1.06595	−	0.994071i
$181$			2.10738i			0.156640i	0.996928	+	0.0783201i	$0.0249556\pi$
$181$			2.10738i			0.156640i	−0.996928	+	0.0783201i	$0.975044\pi$
$182$		0			0
$183$	−2.37526	+	3.95321i	−0.175584	+	0.292230i
$184$	−0.957986	−	3.57525i	−0.0706237	−	0.263571i
$185$	6.50251	+	3.75422i	0.478074	+	0.276016i
$186$	−2.78375	−	0.0485537i	−0.204114	−	0.00356013i
$187$	7.82581	−	7.82581i	0.572280	−	0.572280i
$188$	1.53240	−	5.71901i	0.111762	−	0.417101i
$189$	1.86559	−	5.74246i	0.135702	−	0.417703i
$190$	−4.26685	−	4.26685i	−0.309550	−	0.309550i
$191$	−5.88706	+	3.39890i	−0.425973	+	0.245935i	−0.697629	−	0.716459i	$-0.745762\pi$
$191$	−5.88706	+	3.39890i	−0.425973	+	0.245935i	0.271657	+	0.962394i	$0.412428\pi$
$192$	−7.83368	+	4.34242i	−0.565347	+	0.313387i
$193$	−10.7374	+	2.87709i	−0.772898	+	0.207098i	−0.623652	−	0.781702i	$-0.714352\pi$
$193$	−10.7374	+	2.87709i	−0.772898	+	0.207098i	−0.149247	+	0.988800i	$0.547685\pi$
$194$	−4.32361			−0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	−2.20602	+	0.591102i	−0.157173	+	0.0421143i	−0.336547	−	0.941667i	$-0.609259\pi$
$197$	−2.20602	+	0.591102i	−0.157173	+	0.0421143i	0.179375	+	0.983781i	$0.442593\pi$
$198$	1.98160	+	0.0691468i	0.140826	+	0.00491405i
$199$	15.8856	−	9.17157i	1.12610	−	0.650155i	0.183150	−	0.983085i	$-0.441371\pi$
$199$	15.8856	−	9.17157i	1.12610	−	0.650155i	0.942952	+	0.332930i	$0.108037\pi$
$200$	6.83436	+	6.83436i	0.483262	+	0.483262i
$201$	8.47659	−	8.18597i	0.597893	−	0.577393i
$202$	1.01213	−	3.77732i	0.0712133	−	0.265772i
$203$	2.20784	−	2.20784i	0.154960	−	0.154960i
$204$	−0.334383	+	19.1713i	−0.0234115	+	1.34226i
$205$	−20.4830	−	11.8259i	−1.43060	−	0.825956i
$206$	0.404361	+	1.50910i	0.0281732	+	0.105144i
$207$	3.81650	+	7.17733i	0.265265	+	0.498859i
$208$		0			0
$209$			9.23947i			0.639107i
$210$	2.36948	+	0.679404i	0.163510	+	0.0468833i
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	−0.694671	−	0.719327i	$-0.744450\pi$
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	0.970291	+	0.241939i	$0.0777834\pi$
$212$	−2.30849	−	3.99842i	−0.158548	−	0.274612i
$213$	19.5069	−	4.86389i	1.33659	−	0.333269i
$214$	4.44451	+	1.19090i	0.303820	+	0.0814084i
$215$	−18.6332	−	4.99274i	−1.27077	−	0.340502i
$216$	−5.27460	+	4.74965i	−0.358891	+	0.323173i
$217$	2.64984	+	4.58965i	0.179883	+	0.311566i
$218$	1.11855	−	1.93739i	0.0757580	−	0.131217i
$219$	−6.16580	+	21.5038i	−0.416646	+	1.45309i
$220$		−	12.2238i		−	0.824129i
$221$		0			0
$222$	−1.13062	−	0.679324i	−0.0758821	−	0.0455932i
$223$	7.32834	+	27.3497i	0.490742	+	1.83147i	0.552680	+	0.833393i	$0.313605\pi$
$223$	7.32834	+	27.3497i	0.490742	+	1.83147i	−0.0619383	+	0.998080i	$0.519728\pi$
$224$	−3.90907	−	2.25691i	−0.261186	−	0.150796i
$225$	−18.0016	−	11.2480i	−1.20011	−	0.749867i
$226$	−3.24295	+	3.24295i	−0.215718	+	0.215718i
$227$	1.90366	−	7.10455i	0.126350	−	0.471546i	−0.873534	−	0.486763i	$-0.838177\pi$
$227$	1.90366	−	7.10455i	0.126350	−	0.471546i	0.999884	+	0.0152176i	$0.00484411\pi$
$228$	−11.1198	−	11.5146i	−0.736428	−	0.762574i
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	0.221263	−	0.975214i	$-0.428982\pi$
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	−0.975214	+	0.221263i	$0.928982\pi$
$230$	−2.87401	+	1.65931i	−0.189507	+	0.109412i
$231$	−1.82985	−	3.30104i	−0.120395	−	0.217192i
$232$	−3.54545	+	0.950001i	−0.232770	+	0.0623706i
$233$	−18.1554			−1.18940			−0.594700	−	0.803947i	$-0.702729\pi$
$233$	−18.1554			−1.18940			−0.594700	+	0.803947i	$0.702729\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	−18.1328	+	4.85866i	−1.18034	+	0.316272i
$237$	0.923776	+	1.66648i	0.0600057	+	0.108250i
$238$	−2.09315	+	1.20848i	−0.135679	+	0.0783341i
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	0.886306	−	0.463099i	$-0.153263\pi$
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	−0.463099	+	0.886306i	$0.653263\pi$
$240$	13.6728	+	14.1582i	0.882574	+	0.913908i
$241$	−7.16336	+	26.7340i	−0.461433	+	1.72209i	0.207021	+	0.978337i	$0.433623\pi$
$241$	−7.16336	+	26.7340i	−0.461433	+	1.72209i	−0.668453	+	0.743754i	$0.733043\pi$
$242$	−1.86495	+	1.86495i	−0.119883	+	0.119883i
$243$	8.94033	−	12.7699i	0.573522	−	0.819190i
$244$	−4.32547	−	2.49731i	−0.276910	−	0.159874i
$245$	5.08137	+	18.9639i	0.324637	+	1.21156i
$246$	3.56147	+	2.13988i	0.227071	+	0.136434i
$247$		0			0
$248$		−	6.23009i		−	0.395611i
$249$	3.09836	−	10.8058i	0.196351	−	0.684791i
$250$	1.27104	−	2.20150i	0.0803874	−	0.139235i
$251$	−2.80003	−	4.84979i	−0.176736	−	0.306116i	0.764025	−	0.645187i	$-0.223221\pi$
$251$	−2.80003	−	4.84979i	−0.176736	−	0.306116i	−0.940761	+	0.339071i	$0.889887\pi$
$252$	6.25328	+	1.91164i	0.393920	+	0.120422i
$253$	4.90825	+	1.31516i	0.308579	+	0.0826834i
$254$	−2.65336	−	0.710965i	−0.166486	−	0.0446099i
$255$	34.4661	−	8.59385i	2.15835	−	0.538168i
$256$	−3.48092	−	6.02913i	−0.217557	−	0.376821i
$257$	−3.40679	+	5.90073i	−0.212510	+	0.368077i	−0.952499	−	0.304541i	$-0.901497\pi$
$257$	−3.40679	+	5.90073i	−0.212510	+	0.368077i	0.739990	+	0.672618i	$0.234830\pi$
$258$	3.25749	+	0.934023i	0.202802	+	0.0581497i
$259$			2.51073i			0.156009i
$260$		0			0
$261$	7.11751	−	3.78469i	0.440563	−	0.234266i
$262$	1.69139	+	6.31236i	0.104495	+	0.389979i
$263$	19.5996	+	11.3159i	1.20857	+	0.697765i	0.962446	−	0.271474i	$-0.0875111\pi$
$263$	19.5996	+	11.3159i	1.20857	+	0.697765i	0.246119	+	0.969240i	$0.420844\pi$
$264$	−0.0773761	+	4.43623i	−0.00476217	+	0.273031i
$265$	−6.04803	+	6.04803i	−0.371528	+	0.371528i
$266$	0.522238	−	1.94902i	0.0320205	−	0.119502i
$267$	−5.32502	+	5.14245i	−0.325886	+	0.314713i
$268$	9.02401	+	9.02401i	0.551229	+	0.551229i
$269$	−22.6058	+	13.0515i	−1.37830	+	0.795762i	−0.991955	−	0.126593i	$-0.959596\pi$
$269$	−22.6058	+	13.0515i	−1.37830	+	0.795762i	−0.386345	+	0.922354i	$0.626262\pi$
$270$	5.33739	+	3.46584i	0.324823	+	0.210925i
$271$	17.0798	−	4.57652i	1.03753	−	0.278004i	0.300438	−	0.953801i	$-0.402867\pi$
$271$	17.0798	−	4.57652i	1.03753	−	0.278004i	0.737087	+	0.675797i	$0.236201\pi$
$272$	−19.2992			−1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	−12.8167	+	3.43423i	−0.772876	+	0.207092i
$276$	−7.69967	+	4.26813i	−0.463466	+	0.256911i
$277$	−19.6593	+	11.3503i	−1.18122	+	0.681975i	−0.956295	−	0.292402i	$-0.905545\pi$
$277$	−19.6593	+	11.3503i	−1.18122	+	0.681975i	−0.224920	+	0.974377i	$0.572212\pi$
$278$	−1.34385	−	1.34385i	−0.0805989	−	0.0805989i
$279$	3.07825	+	13.3317i	0.184290	+	0.798151i
$280$	−1.42759	+	5.32786i	−0.0853151	+	0.318400i
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	−0.914679	−	0.404181i	$-0.867557\pi$
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	0.404181	+	0.914679i	$0.367557\pi$
$282$	1.92655	+	0.0336025i	0.114724	+	0.00200100i
$283$	−6.15361	−	3.55279i	−0.365794	−	0.211192i	0.305825	−	0.952088i	$-0.401068\pi$
$283$	−6.15361	−	3.55279i	−0.365794	−	0.211192i	−0.671620	+	0.740896i	$0.734401\pi$
$284$	5.63513	+	21.0306i	0.334384	+	1.24794i
$285$	−15.2729	+	25.4192i	−0.904690	+	1.50570i
$286$		0			0
$287$		−	7.90886i		−	0.466845i
$288$	−7.94796	−	8.52269i	−0.468338	−	0.502205i
$289$	−8.91483	+	15.4409i	−0.524402	+	0.908291i
$290$	1.64548	+	2.85006i	0.0966260	+	0.167361i
$291$	5.14061	+	20.6167i	0.301348	+	1.20857i
$292$	−23.4012	−	6.27032i	−1.36945	−	0.366943i
$293$	−15.3534	−	4.11392i	−0.896953	−	0.240338i	−0.219245	−	0.975670i	$-0.570360\pi$
$293$	−15.3534	−	4.11392i	−0.896953	−	0.240338i	−0.677707	+	0.735332i	$0.737026\pi$
$294$	−0.834411	−	3.34645i	−0.0486638	−	0.195169i
$295$	17.3885	+	30.1178i	1.01240	+	1.75352i
$296$	1.47576	−	2.55609i	0.0857768	−	0.148570i
$297$	−2.02633	−	9.53130i	−0.117580	−	0.553062i
$298$		−	8.04031i		−	0.465763i
$299$		0			0
$300$	11.8396	−	19.7050i	0.683558	−	1.13767i
$301$	−1.66951	−	6.23070i	−0.0962289	−	0.359131i
$302$	2.85701	+	1.64949i	0.164402	+	0.0949176i
$303$	−19.2152	−	0.335149i	−1.10388	−	0.0192538i
$304$	11.3927	−	11.3927i	0.653417	−	0.653417i
$305$	−2.39481	+	8.93755i	−0.137126	+	0.511763i
$306$	−6.08006	+	1.40386i	−0.347574	+	0.0802534i
$307$	−14.3846	−	14.3846i	−0.820970	−	0.820970i	0.165277	−	0.986247i	$-0.447148\pi$
$307$	−14.3846	−	14.3846i	−0.820970	−	0.820970i	−0.986247	+	0.165277i	$0.947148\pi$
$308$	3.53987	−	2.04374i	0.201703	−	0.116453i
$309$	6.71521	−	3.72242i	0.382015	−	0.211761i
$310$	−5.39552	+	1.44572i	−0.306445	+	0.0821116i
$311$	7.62181			0.432193			0.216097	−	0.976372i	$-0.430667\pi$
$311$	7.62181			0.432193			0.216097	+	0.976372i	$0.430667\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	−5.33751	+	1.43018i	−0.301213	+	0.0807099i
$315$	0.422445	−	12.1064i	0.0238021	−	0.682120i
$316$	−1.78705	+	1.03176i	−0.100530	+	0.0580408i
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	0.507901	−	0.861416i	$-0.330422\pi$
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	−0.861416	+	0.507901i	$0.830422\pi$
$318$	1.08082	−	1.04377i	0.0606095	−	0.0585315i
$319$	1.30420	−	4.86734i	0.0730211	−	0.272518i
$320$	−12.7066	+	12.7066i	−0.710319	+	0.710319i
$321$	0.394345	−	22.6091i	0.0220102	−	1.26192i
$322$	−0.961034	−	0.554853i	−0.0535563	−	0.0309207i
$323$	−7.52572	−	28.0864i	−0.418743	−	1.56277i
$324$	13.9963	+	9.43958i	0.777575	+	0.524421i
$325$		0			0
$326$		−	1.21818i		−	0.0674689i
$327$	−10.5682	−	3.03023i	−0.584422	−	0.167572i
$328$	−4.64868	+	8.05175i	−0.256680	+	0.444583i
$329$	−1.83387	−	3.17636i	−0.101105	−	0.175118i
$330$	3.85991	−	0.962439i	0.212481	−	0.0529805i
$331$	−15.5288	−	4.16094i	−0.853541	−	0.228706i	−0.194584	−	0.980886i	$-0.562336\pi$
$331$	−15.5288	−	4.16094i	−0.853541	−	0.228706i	−0.658958	+	0.752180i	$0.729002\pi$
$332$	11.7593	+	3.15088i	0.645373	+	0.172927i
$333$	−1.89502	+	6.19893i	−0.103847	+	0.339699i
$334$	0.923981	+	1.60038i	0.0505580	+	0.0875690i
$335$	11.8211	−	20.4747i	0.645853	−	1.11865i
$336$	−1.81404	+	6.32664i	−0.0989642	+	0.345146i
$337$		−	28.3556i		−	1.54463i	−0.635243	−	0.772313i	$-0.719100\pi$
$337$		−	28.3556i		−	1.54463i	0.635243	−	0.772313i	$-0.280900\pi$
$338$		0			0
$339$	19.3195	+	11.6080i	1.04929	+	0.630457i
$340$	9.95653	+	37.1583i	0.539968	+	2.01519i
$341$	7.40704	+	4.27646i	0.401114	+	0.231583i
$342$	2.76045	−	4.41791i	0.149268	−	0.238893i
$343$	−10.3937	+	10.3937i	−0.561209	+	0.561209i
$344$	−1.96261	+	7.32457i	−0.105817	+	0.394914i
$345$	11.3294	+	11.7316i	0.609952	+	0.631607i
$346$	3.55163	+	3.55163i	0.190937	+	0.190937i
$347$	−9.59025	+	5.53693i	−0.514831	+	0.297238i	−0.734817	−	0.678265i	$-0.762732\pi$
$347$	−9.59025	+	5.53693i	−0.514831	+	0.297238i	0.219986	+	0.975503i	$0.429399\pi$
$348$	4.23256	+	7.63550i	0.226889	+	0.409306i
$349$	28.8980	−	7.74319i	1.54687	−	0.414483i	0.618394	−	0.785868i	$-0.287784\pi$
$349$	28.8980	−	7.74319i	1.54687	−	0.414483i	0.928479	+	0.371385i	$0.121117\pi$
$350$	2.89773			0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	12.2442	−	3.28082i	0.651692	−	0.174620i	0.0821982	−	0.996616i	$-0.473806\pi$
$353$	12.2442	−	3.28082i	0.651692	−	0.174620i	0.569494	+	0.821996i	$0.307139\pi$
$354$	−2.96190	−	5.34324i	−0.157423	−	0.283990i
$355$	34.9309	−	20.1674i	1.85394	−	1.07037i
$356$	−5.66891	−	5.66891i	−0.300452	−	0.300452i
$357$	8.25120	+	8.54414i	0.436700	+	0.452204i
$358$	−0.398325	+	1.48657i	−0.0210521	+	0.0785676i
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.0790589	−	0.996870i	$-0.474808\pi$
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.996870	−	0.0790589i	$-0.0251915\pi$
$360$	−7.54600	+	12.0768i	−0.397709	+	0.636505i
$361$	4.56807	+	2.63738i	0.240425	+	0.138809i
$362$	−0.192234	−	0.717426i	−0.0101036	−	0.0377071i
$363$	11.1102	+	6.67547i	0.583133	+	0.350371i
$364$		0			0
$365$			44.8813i			2.34919i
$366$	0.448012	−	1.56248i	0.0234180	−	0.0816722i
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	−0.388299	−	0.921533i	$-0.626937\pi$
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	0.992221	−	0.124490i	$-0.0397295\pi$
$368$	−4.43045	−	7.67376i	−0.230953	−	0.400023i
$369$	5.96937	−	19.5268i	0.310753	−	1.01652i
$370$	−2.55614	−	0.684915i	−0.132887	−	0.0356071i
$371$	−2.76263	−	0.740245i	−0.143429	−	0.0384316i
$372$	−14.3777	+	3.58497i	−0.745451	+	0.185872i
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	−0.999377	−	0.0352886i	$-0.988765\pi$
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	0.469128	−	0.883130i	$-0.344568\pi$
$374$	−1.95031	+	3.37804i	−0.100848	+	0.174674i
$375$	−12.0088	−	3.44331i	−0.620134	−	0.177812i
$376$			4.31166i			0.222357i
$377$		0			0
$378$	−0.111288	+	2.12511i	−0.00572404	+	0.109304i
$379$	−1.02786	−	3.83602i	−0.0527975	−	0.197043i	0.934489	−	0.355991i	$-0.115857\pi$
$379$	−1.02786	−	3.83602i	−0.0527975	−	0.197043i	−0.987287	+	0.158948i	$0.949190\pi$
$380$	−27.8128	−	16.0577i	−1.42677	−	0.823744i
$381$	−0.235423	+	13.4976i	−0.0120611	+	0.691502i
$382$	1.69412	−	1.69412i	0.0866785	−	0.0866785i
$383$	6.88748	−	25.7044i	0.351934	−	1.31344i	−0.532365	−	0.846515i	$-0.678697\pi$
$383$	6.88748	−	25.7044i	0.351934	−	1.31344i	0.884299	−	0.466921i	$-0.154637\pi$
$384$	11.9504	−	11.5406i	0.609839	−	0.588931i
$385$	−5.35443	−	5.35443i	−0.272887	−	0.272887i
$386$	3.39296	−	1.95893i	0.172697	−	0.0997067i
$387$	0.580765	−	16.6435i	0.0295219	−	0.846038i
$388$	−22.2271	+	5.95573i	−1.12841	+	0.302356i
$389$	6.17335			0.313001			0.156501	−	0.987678i	$-0.449979\pi$
$389$	6.17335			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	7.45460	−	1.99745i	0.376514	−	0.100887i
$393$	28.0889	−	15.5704i	1.41690	−	0.785423i
$394$	0.697088	−	0.402464i	0.0351188	−	0.0202758i
$395$	2.70311	+	2.70311i	0.136008	+	0.136008i
$396$	10.2824	−	2.37417i	0.516710	−	0.119306i
$397$	6.17560	−	23.0477i	0.309945	−	1.15673i	−0.618660	−	0.785659i	$-0.712324\pi$
$397$	6.17560	−	23.0477i	0.309945	−	1.15673i	0.928605	−	0.371071i	$-0.121009\pi$
$398$	−4.57140	+	4.57140i	−0.229143	+	0.229143i
$399$	−9.91463	−	0.172930i	−0.496352	−	0.00865730i
$400$	20.0382	+	11.5691i	1.00191	+	0.578453i
$401$	−6.00499	−	22.4109i	−0.299875	−	1.11915i	−0.937268	−	0.348610i	$-0.886654\pi$
$401$	−6.00499	−	22.4109i	−0.299875	−	1.11915i	0.637393	−	0.770539i	$-0.280013\pi$
$402$	−2.13901	+	3.56002i	−0.106684	+	0.177558i
$403$		0			0
$404$		−	20.8129i		−	1.03548i
$405$	10.1806	−	29.5716i	0.505877	−	1.46942i
$406$	−0.550228	+	0.953023i	−0.0273074	+	0.0472978i
$407$	2.02598	+	3.50910i	0.100424	+	0.173940i
$408$	−3.37818	−	13.5484i	−0.167245	−	0.670746i
$409$	12.1401	+	3.25292i	0.600288	+	0.160847i	0.546151	−	0.837687i	$-0.316093\pi$
$409$	12.1401	+	3.25292i	0.600288	+	0.160847i	0.0541371	+	0.998534i	$0.482759\pi$
$410$	8.05189	+	2.15750i	0.397655	+	0.106551i
$411$	3.15743	+	12.6630i	0.155744	+	0.624622i
$412$	4.15753	+	7.20106i	0.204827	+	0.354771i
$413$	−5.81450	+	10.0710i	−0.286113	+	0.495562i
$414$	−1.95398	−	2.09528i	−0.0960329	−	0.102977i
$415$		−	22.5532i		−	1.10709i
$416$		0			0
$417$	−4.81024	+	8.00582i	−0.235558	+	0.392047i
$418$	−0.842818	−	3.14544i	−0.0412236	−	0.153848i
$419$	−23.2172	−	13.4045i	−1.13424	−	0.654851i	−0.189239	−	0.981931i	$-0.560602\pi$
$419$	−23.2172	−	13.4045i	−1.13424	−	0.654851i	−0.944997	+	0.327080i	$0.893935\pi$
$420$	13.1170	+	0.228786i	0.640046	+	0.0111636i
$421$	8.93430	−	8.93430i	0.435431	−	0.435431i	−0.455040	−	0.890471i	$-0.650375\pi$
$421$	8.93430	−	8.93430i	0.435431	−	0.435431i	0.890471	+	0.455040i	$0.150375\pi$
$422$	−0.730414	+	2.72594i	−0.0355560	+	0.132697i
$423$	−2.13036	−	9.22649i	−0.103582	−	0.448607i
$424$	2.37744	+	2.37744i	0.115459	+	0.115459i
$425$	36.1633	−	20.8789i	1.75418	−	1.01278i
$426$	−6.19716	+	3.43525i	−0.300253	+	0.166438i
$427$	−2.98861	+	0.800795i	−0.144629	+	0.0387532i
$428$	24.4891			1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	20.5028	−	5.49370i	0.987583	−	0.264622i	0.271348	−	0.962481i	$-0.412531\pi$
$431$	20.5028	−	5.49370i	0.987583	−	0.264622i	0.716235	+	0.697859i	$0.245864\pi$
$432$	−9.25399	+	14.2511i	−0.445233	+	0.685658i
$433$	1.60537	−	0.926859i	0.0771490	−	0.0445420i	−0.460929	−	0.887437i	$-0.652484\pi$
$433$	1.60537	−	0.926859i	0.0771490	−	0.0445420i	0.538078	+	0.842895i	$0.319150\pi$
$434$	−1.32076	−	1.32076i	−0.0633986	−	0.0633986i
$435$	11.6338	−	11.2349i	0.557798	−	0.538673i
$436$	3.08159	−	11.5007i	0.147582	−	0.550782i
$437$	9.44007	−	9.44007i	0.451580	−	0.451580i
$438$	0.137496	−	7.88308i	0.00656979	−	0.376668i
$439$	−12.4753	−	7.20264i	−0.595415	−	0.343763i	0.171820	−	0.985128i	$-0.445035\pi$
$439$	−12.4753	−	7.20264i	−0.595415	−	0.343763i	−0.767236	+	0.641365i	$0.778368\pi$
$440$	2.30393	+	8.59840i	0.109836	+	0.409913i
$441$	−14.9651	+	7.95761i	−0.712625	+	0.378934i
$442$		0			0
$443$		−	22.2330i		−	1.05632i	−0.849144	−	0.528162i	$-0.822881\pi$
$443$		−	22.2330i		−	1.05632i	0.849144	−	0.528162i	$-0.177119\pi$
$444$	−6.74811	−	1.93489i	−0.320251	−	0.0918260i
$445$	−7.42603	+	12.8623i	−0.352027	+	0.609729i
$446$	−4.98965	−	8.64232i	−0.236267	−	0.409226i
$447$	−38.3394	+	9.55963i	−1.81339	+	0.452155i
$448$	−5.80413	−	1.55521i	−0.274220	−	0.0734769i
$449$	23.7458	+	6.36268i	1.12064	+	0.300273i	0.771141	−	0.636665i	$-0.219687\pi$
$449$	23.7458	+	6.36268i	1.12064	+	0.300273i	0.349495	+	0.936938i	$0.386353\pi$
$450$	7.15442	+	2.18712i	0.337263	+	0.103102i
$451$	−6.38188	−	11.0537i	−0.300511	−	0.520501i
$452$	−12.2044	+	21.1387i	−0.574048	+	0.994281i
$453$	4.46857	−	15.5845i	0.209952	−	0.732225i
$454$			2.59229i			0.121662i
$455$		0			0
$456$	9.99211	+	6.00368i	0.467923	+	0.281148i
$457$	1.75192	+	6.53825i	0.0819513	+	0.305847i	0.994719	−	0.102632i	$-0.0327263\pi$
$457$	1.75192	+	6.53825i	0.0819513	+	0.305847i	−0.912768	+	0.408478i	$0.866060\pi$
$458$	4.92490	+	2.84339i	0.230125	+	0.132863i
$459$	13.9231	+	27.3230i	0.649876	+	1.27533i
$460$	−12.4892	+	12.4892i	−0.582312	+	0.582312i
$461$	−3.20695	+	11.9685i	−0.149363	+	0.557429i	0.850160	+	0.526525i	$0.176505\pi$
$461$	−3.20695	+	11.9685i	−0.149363	+	0.557429i	−0.999522	+	0.0309044i	$0.990161\pi$
$462$	0.924064	+	0.956871i	0.0429914	+	0.0445177i
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	0.526236	−	0.850339i	$-0.323603\pi$
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	−0.850339	+	0.526236i	$0.823603\pi$
$464$	−7.60980	+	4.39352i	−0.353276	+	0.203964i
$465$	13.3089	+	24.0091i	0.617184	+	1.11339i
$466$	6.18074	−	1.65612i	0.286317	−	0.0767185i
$467$	9.19934			0.425695			0.212847	−	0.977085i	$-0.431726\pi$
$467$	9.19934			0.425695			0.212847	+	0.977085i	$0.431726\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	3.73407	−	1.00054i	0.172240	−	0.0461515i
$471$	13.1658	+	23.7510i	0.606647	+	1.09439i
$472$	11.8391	−	6.83530i	0.544938	−	0.314620i
$473$	−7.36110	−	7.36110i	−0.338464	−	0.338464i
$474$	−0.466501	−	0.483064i	−0.0214271	−	0.0221878i
$475$	−9.02270	+	33.6732i	−0.413990	+	1.54503i
$476$	−9.09592	+	9.09592i	−0.416911	+	0.416911i
$477$	−6.26215	−	3.91280i	−0.286724	−	0.179155i
$478$	−2.82415	−	1.63052i	−0.129174	−	0.0745784i
$479$	5.93980	+	22.1676i	0.271396	+	1.01287i	0.958218	+	0.286039i	$0.0923388\pi$
$479$	5.93980	+	22.1676i	0.271396	+	1.01287i	−0.686821	+	0.726826i	$0.740995\pi$
$480$	−20.0412	−	12.0416i	−0.914750	−	0.549621i
$481$		0			0
$482$		−	9.75464i		−	0.444312i
$483$	−1.50313	+	5.24229i	−0.0683947	+	0.238533i
$484$	−7.01850	+	12.1564i	−0.319023	+	0.552563i
$485$	21.3148	+	36.9183i	0.967854	+	1.67637i
$486$	−1.87874	+	5.16285i	−0.0852213	+	0.234192i
$487$	−28.4656	−	7.62733i	−1.28990	−	0.345627i	−0.452277	−	0.891878i	$-0.649388\pi$
$487$	−28.4656	−	7.62733i	−1.28990	−	0.345627i	−0.837622	+	0.546250i	$0.816055\pi$
$488$	3.51329	+	0.941384i	0.159039	+	0.0426144i
$489$	−5.80879	+	1.44838i	−0.262682	+	0.0654978i
$490$	−3.45975	−	5.99247i	−0.156296	−	0.270712i
$491$	−7.66195	+	13.2709i	−0.345779	+	0.598907i	−0.985495	−	0.169705i	$-0.945719\pi$
$491$	−7.66195	+	13.2709i	−0.345779	+	0.598907i	0.639716	+	0.768611i	$0.279052\pi$
$492$	21.2567	+	6.09496i	0.958326	+	0.274782i
$493$			15.8582i			0.714215i
$494$		0			0
$495$	−9.17859	−	17.2613i	−0.412547	−	0.775838i
$496$	−3.86016	−	14.4063i	−0.173326	−	0.646863i
$497$	11.6805	+	6.74372i	0.523941	+	0.302497i
$498$	−0.0690926	+	3.96131i	−0.00309611	+	0.177510i
$499$	−29.5332	+	29.5332i	−1.32209	+	1.32209i	−0.410004	+	0.912084i	$0.634473\pi$
$499$	−29.5332	+	29.5332i	−1.32209	+	1.32209i	−0.912084	+	0.410004i	$0.865527\pi$
$500$	3.50168	−	13.0684i	0.156600	−	0.584439i
$501$	6.53269	−	6.30871i	0.291859	−	0.281852i
$502$	1.39562	+	1.39562i	0.0622897	+	0.0622897i
$503$	30.1073	−	17.3825i	1.34242	−	0.775046i	0.355257	−	0.934768i	$-0.384393\pi$
$503$	30.1073	−	17.3825i	1.34242	−	0.775046i	0.987162	+	0.159722i	$0.0510599\pi$
$504$	−4.75895	−	0.166060i	−0.211981	−	0.00739692i
$505$	−37.2433	+	9.97931i	−1.65730	+	0.444073i
$506$	−1.79091			−0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	42.7871	−	11.4648i	1.89651	−	0.508167i	0.898969	−	0.438011i	$-0.144317\pi$
$509$	42.7871	−	11.4648i	1.89651	−	0.508167i	0.997536	−	0.0701558i	$-0.0223497\pi$
$510$	−10.9495	+	6.06962i	−0.484854	+	0.268767i
$511$	−12.9971	+	7.50387i	−0.574957	+	0.331952i
$512$	15.2996	+	15.2996i	0.676153	+	0.676153i
$513$	−24.3484	−	7.91022i	−1.07501	−	0.349245i
$514$	0.621529	−	2.31958i	0.0274145	−	0.102312i
$515$	10.8924	−	10.8924i	0.479975	−	0.479975i
$516$	18.0329	+	0.314527i	0.793854	+	0.0138463i
$517$	−5.12618	−	2.95960i	−0.225449	−	0.130163i
$518$	−0.229027	−	0.854741i	−0.0100629	−	0.0375552i
$519$	12.7128	−	21.1584i	0.558032	−	0.928749i
$520$		0			0
$521$		−	1.93372i		−	0.0847179i	−0.999102	−	0.0423590i	$-0.986513\pi$
$521$		−	1.93372i		−	0.0847179i	0.999102	−	0.0423590i	$-0.0134873\pi$
$522$	−2.07781	+	1.93769i	−0.0909434	+	0.0848106i
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	−0.882020	−	0.471212i	$-0.843817\pi$
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	0.849091	+	0.528246i	$0.177150\pi$
$524$	17.3904	+	30.1211i	0.759705	+	1.31585i
$525$	−3.44529	−	13.8175i	−0.150365	−	0.603047i
$526$	−7.70463	−	2.06445i	−0.335938	−	0.0900142i
$527$	−25.9994	−	6.96651i	−1.13255	−	0.303466i
$528$	2.56976	+	10.3062i	0.111835	+	0.448519i
$529$	7.82890	+	13.5601i	0.340387	+	0.589568i
$530$	1.50726	−	2.61066i	0.0654714	−	0.113400i
$531$	−21.9571	+	20.4764i	−0.952859	+	0.888602i
$532$		−	10.7390i		−	0.465595i
$533$		0			0
$534$	1.34373	−	2.23641i	0.0581490	−	0.0967791i
$535$	−11.7419	−	43.8215i	−0.507648	−	1.89457i
$536$	−8.04846	−	4.64678i	−0.347640	−	0.200710i
$537$	7.56215	+	0.131898i	0.326331	+	0.00569182i
$538$	6.50526	−	6.50526i	0.280462	−	0.280462i
$539$	−2.74218	+	10.2340i	−0.118114	+	0.440808i
$540$	32.2130	+	10.4652i	1.38623	+	0.450351i
$541$	2.56375	+	2.56375i	0.110224	+	0.110224i	0.760068	−	0.649844i	$-0.225166\pi$
$541$	2.56375	+	2.56375i	0.110224	+	0.110224i	−0.649844	+	0.760068i	$0.725166\pi$
$542$	−5.39710	+	3.11602i	−0.231825	+	0.133844i
$543$	−3.19242	+	1.76964i	−0.137000	+	0.0759425i
$544$	22.1441	−	5.93348i	0.949419	−	0.254396i
$545$	−22.0572			−0.944827
$546$		0			0
$547$	23.1549			0.990030			0.495015	−	0.868884i	$-0.335163\pi$
$547$	23.1549			0.990030			0.495015	+	0.868884i	$0.335163\pi$
$548$	−13.6522	+	3.65808i	−0.583191	+	0.156266i
$549$	−7.98321	−	0.278569i	−0.340715	−	0.0118890i
$550$	4.04999	−	2.33826i	0.172692	−	0.0997038i
$551$	−9.36139	−	9.36139i	−0.398809	−	0.398809i
$552$	4.61161	−	4.45349i	0.196283	−	0.189553i
$553$	−0.330846	+	1.23473i	−0.0140690	+	0.0525062i
$554$	5.65736	−	5.65736i	0.240358	−	0.240358i
$555$	−0.226797	+	13.0030i	−0.00962700	+	0.551948i
$556$	−8.75970	−	5.05741i	−0.371494	−	0.214482i
$557$	−0.926129	−	3.45636i	−0.0392414	−	0.146451i	0.943526	−	0.331300i	$-0.107487\pi$
$557$	−0.926129	−	3.45636i	−0.0392414	−	0.146451i	−0.982767	+	0.184849i	$0.940820\pi$
$558$	−2.26406	−	4.25780i	−0.0958451	−	0.180247i
$559$		0			0
$560$			13.2045i			0.557994i
$561$	18.4267	+	5.28351i	0.777977	+	0.223070i
$562$	2.13267	−	3.69389i	0.0899611	−	0.155817i
$563$	−9.83710	−	17.0384i	−0.414585	−	0.718081i	0.580800	−	0.814046i	$-0.302740\pi$
$563$	−9.83710	−	17.0384i	−0.414585	−	0.718081i	−0.995385	+	0.0959647i	$0.969406\pi$
$564$	9.95039	−	2.48105i	0.418987	−	0.104471i
$565$	43.6781	+	11.7035i	1.83755	+	0.492370i
$566$	2.41899	+	0.648166i	0.101678	+	0.0272445i
$567$	10.2657	−	1.99601i	0.431119	−	0.0838247i
$568$	−7.92766	−	13.7311i	−0.332637	−	0.576145i
$569$	4.78231	−	8.28321i	0.200485	−	0.347250i	−0.748200	−	0.663473i	$-0.769082\pi$
$569$	4.78231	−	8.28321i	0.200485	−	0.347250i	0.948685	+	0.316223i	$0.102415\pi$
$570$	2.88072	−	10.0468i	0.120660	−	0.420813i
$571$			17.9785i			0.752375i	0.926544	+	0.376187i	$0.122765\pi$
$571$			17.9785i			0.752375i	−0.926544	+	0.376187i	$0.877235\pi$
$572$		0			0
$573$	−10.0925	−	6.06399i	−0.421619	−	0.253327i
$574$	0.721441	+	2.69245i	0.0301124	+	0.112381i
$575$	16.6038	+	9.58619i	0.692425	+	0.399772i
$576$	−13.1564	−	8.22057i	−0.548185	−	0.342524i
$577$	6.37509	−	6.37509i	0.265398	−	0.265398i	−0.561844	−	0.827243i	$-0.689908\pi$
$577$	6.37509	−	6.37509i	0.265398	−	0.265398i	0.827243	+	0.561844i	$0.189908\pi$
$578$	1.62641	−	6.06984i	0.0676497	−	0.252472i
$579$	−13.3750	−	13.8499i	−0.555848	−	0.575582i
$580$	12.3851	+	12.3851i	0.514264	+	0.514264i
$581$	6.53113	−	3.77075i	0.270957	−	0.156437i
$582$	−3.63069	−	6.54973i	−0.150497	−	0.271495i
$583$	−4.45849	+	1.19465i	−0.184652	+	0.0494773i
$584$	17.6425			0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	−30.3129	+	8.12231i	−1.25115	+	0.335243i	−0.822779	−	0.568362i	$-0.807577\pi$
$587$	−30.3129	+	8.12231i	−1.25115	+	0.335243i	−0.428367	+	0.903605i	$0.640911\pi$
$588$	−8.89929	−	16.0542i	−0.367000	−	0.662066i
$589$	19.4604	−	11.2355i	0.801853	−	0.462950i
$590$	−8.66697	−	8.66697i	−0.356814	−	0.356814i
$591$	−2.74792	−	2.84548i	−0.113034	−	0.117047i
$592$	1.82876	−	6.82503i	0.0751616	−	0.280507i
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	−0.999673	−	0.0255650i	$-0.991862\pi$
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	0.0255650	+	0.999673i	$0.491862\pi$
$594$	1.55927	+	3.05995i	0.0639778	+	0.125551i
$595$	20.6378	+	11.9153i	0.846069	+	0.488478i
$596$	−11.0754	−	41.3341i	−0.453668	−	1.69311i
$597$	27.2335	+	16.3630i	1.11459	+	0.669695i
$598$		0			0
$599$			33.7915i			1.38068i	0.723484	+	0.690341i	$0.242540\pi$
$599$			33.7915i			1.38068i	−0.723484	+	0.690341i	$0.757460\pi$
$600$	−4.61415	+	16.0923i	−0.188372	+	0.656964i
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	−0.375516	−	0.926816i	$-0.622534\pi$
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	0.990404	−	0.138202i	$-0.0441323\pi$
$602$	1.13672	+	1.96886i	0.0463292	+	0.0802446i
$603$	19.5188	+	5.96693i	0.794867	+	0.242992i
$604$	16.9596	+	4.54432i	0.690077	+	0.184906i
$605$	25.1183	+	6.73042i	1.02120	+	0.273630i
$606$	6.57209	−	1.63870i	0.266973	−	0.0665676i
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	0.550927	−	0.834553i	$-0.314274\pi$
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	−0.998208	+	0.0598403i	$0.980941\pi$
$608$	−9.56943	+	16.5747i	−0.388092	+	0.672195i
$609$	5.19860	+	1.49060i	0.210658	+	0.0604022i
$610$		−	3.26111i		−	0.132038i
$611$		0			0
$612$	−29.3229	+	15.5923i	−1.18531	+	0.630280i
$613$	−0.153064	−	0.571244i	−0.00618221	−	0.0230723i	0.962766	−	0.270337i	$-0.0871350\pi$
$613$	−0.153064	−	0.571244i	−0.00618221	−	0.0230723i	−0.968948	+	0.247264i	$0.920468\pi$
$614$	6.20916	+	3.58486i	0.250581	+	0.144673i
$615$	0.714416	−	40.9599i	0.0288080	−	1.65166i
$616$	−2.10479	+	2.10479i	−0.0848044	+	0.0848044i
$617$	7.52400	−	28.0800i	0.302905	−	1.13046i	−0.631829	−	0.775108i	$-0.717695\pi$
$617$	7.52400	−	28.0800i	0.302905	−	1.13046i	0.934734	−	0.355349i	$-0.115638\pi$
$618$	−1.94654	+	1.87980i	−0.0783012	+	0.0756166i
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	0.0808459	−	0.996727i	$-0.474238\pi$
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	−0.996727	+	0.0808459i	$0.974238\pi$
$620$	−25.7461	+	14.8645i	−1.03399	+	0.596974i
$621$	−7.66791	+	11.8086i	−0.307703	+	0.473862i
$622$	−2.59473	+	0.695256i	−0.104039	+	0.0278772i
$623$	−4.96634			−0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	2.21789	−	0.594282i	0.0886448	−	0.0237523i
$627$	−13.9966	+	7.75870i	−0.558972	+	0.309853i
$628$	−25.4694	+	14.7047i	−1.01634	+	0.586783i
$629$	−9.01686	−	9.01686i	−0.359526	−	0.359526i
$630$	0.960524	+	4.15999i	0.0382682	+	0.165738i
$631$	10.5019	−	39.1937i	0.418075	−	1.56028i	−0.360521	−	0.932751i	$-0.617401\pi$
$631$	10.5019	−	39.1937i	0.418075	−	1.56028i	0.778596	−	0.627526i	$-0.215932\pi$
$632$	1.06258	−	1.06258i	0.0422670	−	0.0422670i
$633$	13.8668	+	0.241863i	0.551157	+	0.00961320i
$634$	2.71690	+	1.56860i	0.107902	+	0.0622971i
$635$	7.00990	+	26.1613i	0.278180	+	1.03818i
$636$	4.11858	−	6.85468i	0.163312	−	0.271806i
$637$		0			0
$638$			1.77598i			0.0703117i
$639$	23.7488	+	25.4662i	0.939489	+	1.00743i
$640$	16.6654	−	28.8653i	0.658758	−	1.14100i
$641$	−12.8560	−	22.2673i	−0.507783	−	0.879506i	−0.999959	−	0.00901077i	$-0.997132\pi$
$641$	−12.8560	−	22.2673i	−0.507783	−	0.879506i	0.492176	−	0.870496i	$-0.336202\pi$
$642$	1.92814	+	7.73291i	0.0760976	+	0.305194i
$643$	−0.612124	−	0.164018i	−0.0241398	−	0.00646824i	0.246729	−	0.969085i	$-0.420644\pi$
$643$	−0.612124	−	0.164018i	−0.0241398	−	0.00646824i	−0.270869	+	0.962616i	$0.587311\pi$
$644$	−5.70484	−	1.52861i	−0.224802	−	0.0602356i
$645$	−8.08354	−	32.4195i	−0.318289	−	1.27652i
$646$	5.12404	+	8.87510i	0.201603	+	0.349186i
$647$	23.5124	−	40.7247i	0.924368	−	1.60105i	0.131794	−	0.991277i	$-0.457926\pi$
$647$	23.5124	−	40.7247i	0.924368	−	1.60105i	0.792574	−	0.609776i	$-0.208740\pi$
$648$	−11.6244	−	4.00191i	−0.456649	−	0.157210i
$649$			18.7675i			0.736690i
$650$		0			0
$651$	−4.72758	+	7.86826i	−0.185289	+	0.308381i
$652$	−1.67804	−	6.26251i	−0.0657169	−	0.245259i
$653$	−25.0935	−	14.4877i	−0.981984	−	0.566949i	−0.0791154	−	0.996865i	$-0.525210\pi$
$653$	−25.0935	−	14.4877i	−0.981984	−	0.566949i	−0.902869	+	0.429917i	$0.858543\pi$
$654$	3.87419	+	0.0675732i	0.151493	+	0.00264232i
$655$	45.5614	−	45.5614i	1.78023	−	1.78023i
$656$	−5.76064	+	21.4990i	−0.224915	+	0.839394i
$657$	−37.7532	+	8.71705i	−1.47289	+	0.340085i
$658$	0.914059	+	0.914059i	0.0356337	+	0.0356337i
$659$	−40.4280	+	23.3411i	−1.57485	+	0.909241i	−0.579290	+	0.815121i	$0.696670\pi$
$659$	−40.4280	+	23.3411i	−1.57485	+	0.909241i	−0.995561	+	0.0941194i	$0.969996\pi$
$660$	18.5175	−	10.2648i	0.720794	−	0.399555i
$661$	−6.70655	+	1.79701i	−0.260854	+	0.0698957i	−0.386876	−	0.922132i	$-0.626446\pi$
$661$	−6.70655	+	1.79701i	−0.260854	+	0.0698957i	0.126021	+	0.992028i	$0.459779\pi$
$662$	5.66611			0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	−19.2167	+	5.14911i	−0.745194	+	0.199674i
$666$	0.0796706	−	2.28320i	0.00308717	−	0.0884721i
$667$	−6.30553	+	3.64050i	−0.244151	+	0.140961i
$668$	6.95457	+	6.95457i	0.269080	+	0.269080i
$669$	−35.2776	+	34.0680i	−1.36391	+	1.31715i
$670$	−2.15662	+	8.04861i	−0.0833174	+	0.310945i
$671$	−3.53081	+	3.53081i	−0.136306	+	0.136306i
$672$	0.136342	−	7.81696i	0.00525952	−	0.301546i
$673$	−22.6855	−	13.0975i	−0.874460	−	0.504870i	−0.00563228	−	0.999984i	$-0.501793\pi$
$673$	−22.6855	−	13.0975i	−0.874460	−	0.504870i	−0.868828	+	0.495114i	$0.835126\pi$
$674$	2.58657	+	9.65322i	0.0996311	+	0.371828i
$675$	1.92272	−	36.7156i	0.0740057	−	1.41318i
$676$		0			0
$677$		−	21.9298i		−	0.842829i	−0.906868	−	0.421415i	$-0.861534\pi$
$677$		−	21.9298i		−	0.842829i	0.906868	−	0.421415i	$-0.138466\pi$
$678$	−7.63589	−	2.18945i	−0.293255	−	0.0840852i
$679$	−7.12739	+	12.3450i	−0.273524	+	0.473758i
$680$	−14.0071	−	24.2610i	−0.537149	−	0.930369i
$681$	12.3611	−	3.08213i	0.473677	−	0.118108i
$682$	−2.91171	−	0.780190i	−0.111495	−	0.0298750i
$683$	7.36335	+	1.97300i	0.281751	+	0.0754949i	0.396927	−	0.917850i	$-0.370077\pi$
$683$	7.36335	+	1.97300i	0.281751	+	0.0754949i	−0.115176	+	0.993345i	$0.536743\pi$
$684$	8.10549	−	26.5144i	0.309921	−	1.01380i
$685$	13.0918	+	22.6757i	0.500212	+	0.866392i
$686$	2.59028	−	4.48650i	0.0988975	−	0.171296i
$687$	7.70291	−	26.8646i	0.293884	−	1.02495i
$688$			18.1532i			0.692084i
$689$		0			0
$690$	−4.92706	−	2.96039i	−0.187570	−	0.112700i
$691$	4.12878	+	15.4088i	0.157066	+	0.586179i	0.998920	+	0.0464729i	$0.0147981\pi$
$691$	4.12878	+	15.4088i	0.157066	+	0.586179i	−0.841853	+	0.539707i	$0.818535\pi$
$692$	23.1508	+	13.3661i	0.880061	+	0.508103i
$693$	3.46407	−	5.54399i	0.131589	−	0.210599i
$694$	2.75978	−	2.75978i	0.104760	−	0.104760i
$695$	−4.84983	+	18.0998i	−0.183965	+	0.686565i
$696$	−4.41637	−	4.57317i	−0.167402	−	0.173345i
$697$	28.4033	+	28.4033i	1.07585	+	1.07585i
$698$	−9.13155	+	5.27210i	−0.345634	+	0.199552i
$699$	−15.2457	−	27.5032i	−0.576647	−	1.04027i
$700$	14.8968	−	3.99159i	0.563047	−	0.150868i
$701$	−30.3059			−1.14464			−0.572319	−	0.820031i	$-0.693956\pi$
$701$	−30.3059			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	−9.36704	+	2.50989i	−0.353034	+	0.0945951i
$705$	−9.21066	−	16.6160i	−0.346893	−	0.625793i
$706$	−3.86907	+	2.23381i	−0.145615	+	0.0840706i
$707$	−9.11674	−	9.11674i	−0.342870	−	0.342870i
$708$	−22.5870	−	23.3889i	−0.848871	−	0.879008i
$709$	−8.80249	+	32.8514i	−0.330585	+	1.23376i	0.577993	+	0.816042i	$0.303836\pi$
$709$	−8.80249	+	32.8514i	−0.330585	+	1.23376i	−0.908577	+	0.417717i	$0.862830\pi$
$710$	−10.0521	+	10.0521i	−0.377247	+	0.377247i
$711$	−1.74879	+	2.79881i	−0.0655847	+	0.104964i
$712$	5.05607	+	2.91912i	0.189484	+	0.109399i
$713$	−3.19855	−	11.9372i	−0.119787	−	0.447050i
$714$	−3.58839	−	2.15606i	−0.134292	−	0.0806884i
$715$		0			0
$716$			8.19093i			0.306110i
$717$	−4.41718	+	15.4053i	−0.164963	+	0.575322i
$718$	−5.08050	+	8.79968i	−0.189602	+	0.328401i
$719$	3.94839	+	6.83882i	0.147250	+	0.255045i	0.930210	−	0.367027i	$-0.119624\pi$
$719$	3.94839	+	6.83882i	0.147250	+	0.255045i	−0.782960	+	0.622072i	$0.786291\pi$
$720$	−9.96640	+	32.6017i	−0.371426	+	1.21499i
$721$	4.97544	+	1.33316i	0.185295	+	0.0496496i
$722$	−1.79571	−	0.481159i	−0.0668294	−	0.0179069i
$723$	−46.5140	+	11.5979i	−1.72988	+	0.431331i
$724$	−1.97649	−	3.42339i	−0.0734558	−	0.127229i
$725$	9.50629	−	16.4654i	0.353055	−	0.611509i
$726$	−4.39123	−	1.25910i	−0.162974	−	0.0467296i
$727$			24.6824i			0.915420i	0.889102	+	0.457710i	$0.151330\pi$
$727$			24.6824i			0.915420i	−0.889102	+	0.457710i	$0.848670\pi$
$728$		0			0
$729$	26.8523	+	2.82014i	0.994530	+	0.104450i
$730$	−4.09404	−	15.2792i	−0.151527	−	0.565507i
$731$	28.3722	+	16.3807i	1.04939	+	0.605863i
$732$	0.150866	−	8.64963i	0.00557616	−	0.319700i
$733$	−34.3405	+	34.3405i	−1.26839	+	1.26839i	−0.321476	+	0.946918i	$0.604179\pi$
$733$	−34.3405	+	34.3405i	−1.26839	+	1.26839i	−0.946918	+	0.321476i	$0.895821\pi$
$734$	−2.11072	+	7.87731i	−0.0779081	+	0.290757i
$735$	−24.4610	+	23.6223i	−0.902257	+	0.871323i
$736$	7.44281	+	7.44281i	0.274346	+	0.274346i
$737$	11.0492	−	6.37928i	0.407004	−	0.234984i
$738$	−0.250964	+	7.19212i	−0.00923812	+	0.264746i
$739$	37.5261	−	10.0551i	1.38042	−	0.369882i	0.509146	−	0.860680i	$-0.329961\pi$
$739$	37.5261	−	10.0551i	1.38042	−	0.369882i	0.871273	+	0.490798i	$0.163295\pi$
$740$	−14.0842			−0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	−50.3503	+	13.4913i	−1.84717	+	0.494949i	−0.999374	−	0.0353674i	$-0.988740\pi$
$743$	−50.3503	+	13.4913i	−1.84717	+	0.494949i	−0.847800	+	0.530316i	$0.822073\pi$
$744$	9.43781	−	5.23162i	0.346007	−	0.191801i
$745$	−68.6542	+	39.6375i	−2.51530	+	1.45221i
$746$	5.10435	+	5.10435i	0.186883	+	0.186883i
$747$	18.9713	−	4.38039i	0.694122	−	0.160270i
$748$	−5.37308	+	20.0526i	−0.196459	+	0.733195i
$749$	10.7270	−	10.7270i	0.391957	−	0.391957i
$750$	4.40233	+	0.0767848i	0.160750	+	0.00280378i
$751$	42.7471	+	24.6801i	1.55986	+	0.900588i	0.997269	+	0.0738552i	$0.0235303\pi$
$751$	42.7471	+	24.6801i	1.55986	+	0.900588i	0.562595	+	0.826733i	$0.309803\pi$
$752$	2.67150	+	9.97017i	0.0974196	+	0.363575i
$753$	4.99555	−	8.31423i	0.182048	−	0.302987i
$754$		0			0
$755$		−	32.5270i		−	1.18378i
$756$	2.35521	+	11.0782i	0.0856580	+	0.402911i
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	−0.984928	−	0.172964i	$-0.944666\pi$
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	0.642255	+	0.766491i	$0.277999\pi$
$758$	0.699838	+	1.21216i	0.0254193	+	0.0440275i
$759$	2.12932	+	8.53976i	0.0772895	+	0.309974i
$760$	22.5905	+	6.05310i	0.819443	+	0.219569i
$761$	−37.1766	−	9.96144i	−1.34765	−	0.361102i	−0.488384	−	0.872629i	$-0.662413\pi$
$761$	−37.1766	−	9.96144i	−1.34765	−	0.361102i	−0.859267	+	0.511527i	$0.829080\pi$
$762$	−1.15109	−	4.61653i	−0.0416997	−	0.167239i
$763$	−3.68783	−	6.38751i	−0.133508	−	0.231243i
$764$	6.37559	−	11.0428i	0.230661	−	0.399516i
$765$	41.9610	+	44.9953i	1.51710	+	1.62681i
$766$			9.37896i			0.338876i
$767$		0			0
$768$	6.21032	−	10.3360i	0.224096	−	0.372969i
$769$	0.738559	+	2.75634i	0.0266331	+	0.0993962i	0.977963	−	0.208778i	$-0.0669487\pi$
$769$	0.738559	+	2.75634i	0.0266331	+	0.0993962i	−0.951330	+	0.308174i	$0.900282\pi$
$770$	2.31126	+	1.33441i	0.0832921	+	0.0480887i
$771$	−11.7997	−	0.205808i	−0.424954	−	0.00741200i
$772$	14.7443	−	14.7443i	0.530660	−	0.530660i
$773$	−1.66335	+	6.20770i	−0.0598265	+	0.223275i	−0.989366	−	0.145447i	$-0.953538\pi$
$773$	−1.66335	+	6.20770i	−0.0598265	+	0.223275i	0.929540	+	0.368722i	$0.120205\pi$
$774$	1.32050	+	5.71902i	0.0474643	+	0.205566i
$775$	22.8188	+	22.8188i	0.819675	+	0.819675i
$776$	14.5123	−	8.37869i	0.520962	−	0.300777i
$777$	−3.80344	+	2.10835i	−0.136448	+	0.0756366i
$778$	−2.10162	+	0.563129i	−0.0753469	+	0.0201891i
$779$	−33.5341			−1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	5.44405	−	1.45873i	0.194679	−	0.0521640i
$783$	11.7102	+	7.60400i	0.418487	+	0.271745i
$784$	16.0002	−	9.23773i	0.571436	−	0.329919i
$785$	38.5251	+	38.5251i	1.37502	+	1.37502i
$786$	−8.14212	+	7.86296i	−0.290420	+	0.280463i
$787$	3.92580	−	14.6513i	0.139940	−	0.522262i	−0.859989	−	0.510313i	$-0.829530\pi$
$787$	3.92580	−	14.6513i	0.139940	−	0.522262i	0.999929	−	0.0119493i	$-0.00380368\pi$
$788$	3.02924	−	3.02924i	0.107912	−	0.107912i
$789$	−0.683604	+	39.1933i	−0.0243370	+	1.39532i
$790$	−1.16681	−	0.673658i	−0.0415132	−	0.0239677i
$791$	3.91350	+	14.6054i	0.139148	+	0.519308i
$792$	−6.78531	+	3.60804i	−0.241105	+	0.128206i
$793$		0			0
$794$			8.40957i			0.298444i
$795$	−14.2408	−	4.08327i	−0.505067	−	0.144819i
$796$	−17.2039	+	29.7980i	−0.609775	+	1.05616i
$797$	−0.789625	−	1.36767i	−0.0279700	−	0.0484454i	0.851702	−	0.524027i	$-0.175571\pi$
$797$	−0.789625	−	1.36767i	−0.0279700	−	0.0484454i	−0.879672	+	0.475582i	$0.842238\pi$
$798$	3.39106	−	0.845534i	0.120042	−	0.0299316i
$799$	17.9934	+	4.82131i	0.636560	+	0.170566i
$800$	−26.5489	−	7.11374i	−0.938644	−	0.251509i
$801$	−12.2618	−	3.74845i	−0.433248	−	0.132445i
$802$	4.08862	+	7.08170i	0.144374	+	0.250063i
$803$	−12.1102	+	20.9754i	−0.427359	+	0.740207i
$804$	−6.09247	+	21.2480i	−0.214865	+	0.749360i
$805$			10.9414i			0.385633i
$806$		0			0
$807$	−38.7542	−	23.2852i	−1.36421	−	0.819677i
$808$	3.92280	+	14.6401i	0.138004	+	0.515037i
$809$	−10.5758	−	6.10595i	−0.371826	−	0.214674i	0.302430	−	0.953172i	$-0.402202\pi$
$809$	−10.5758	−	6.10595i	−0.371826	−	0.214674i	−0.674256	+	0.738498i	$0.735536\pi$
$810$	−0.768323	+	10.9959i	−0.0269961	+	0.386356i
$811$	29.6037	−	29.6037i	1.03952	−	1.03952i	0.0403387	−	0.999186i	$-0.487156\pi$
$811$	29.6037	−	29.6037i	1.03952	−	1.03952i	0.999186	−	0.0403387i	$-0.0128437\pi$
$812$	−1.51587	+	5.65729i	−0.0531965	+	0.198532i
$813$	21.2754	+	22.0307i	0.746160	+	0.772651i
$814$	−1.00981	−	1.00981i	−0.0353939	−	0.0353939i
$815$	−10.4018	+	6.00546i	−0.364358	+	0.210362i
$816$	−16.2062	−	29.2359i	−0.567331	−	1.02346i
$817$	−26.4186	+	7.07884i	−0.924269	+	0.247657i
$818$	−4.42964			−0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	17.9749	−	4.81637i	0.627330	−	0.168093i	0.0688721	−	0.997625i	$-0.478060\pi$
$821$	17.9749	−	4.81637i	0.627330	−	0.168093i	0.558458	+	0.829533i	$0.311393\pi$
$822$	−2.23001	−	4.02293i	−0.0777807	−	0.140316i
$823$	0.447230	−	0.258209i	0.0155895	−	0.00900059i	−0.492185	−	0.870491i	$-0.663802\pi$
$823$	0.447230	−	0.258209i	0.0155895	−	0.00900059i	0.507774	+	0.861490i	$0.330468\pi$
$824$	−4.28172	−	4.28172i	−0.149161	−	0.149161i
$825$	−15.9651	−	16.5319i	−0.555832	−	0.575566i
$826$	1.06079	−	3.95892i	0.0369096	−	0.137748i
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	−0.238472	−	0.971149i	$-0.576646\pi$
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	0.971149	+	0.238472i	$0.0766464\pi$
$828$	−12.9314	−	8.07994i	−0.449396	−	0.280797i
$829$	−1.46119	−	0.843616i	−0.0507491	−	0.0293000i	0.474411	−	0.880304i	$-0.342661\pi$
$829$	−1.46119	−	0.843616i	−0.0507491	−	0.0293000i	−0.525160	+	0.851004i	$0.675994\pi$
$830$	2.05729	+	7.67790i	0.0714094	+	0.266504i
$831$	−33.7030	−	20.2502i	−1.16914	−	0.702471i
$832$		0			0
$833$		−	33.3430i		−	1.15527i
$834$	0.907288	−	3.16425i	0.0314168	−	0.109569i
$835$	9.11018	−	15.7793i	0.315271	−	0.546065i
$836$	−8.66562	−	15.0093i	−0.299707	−	0.519107i
$837$	−17.6110	+	15.8583i	−0.608726	+	0.548143i
$838$	9.12670	+	2.44549i	0.315277	+	0.0844781i
$839$	−10.4663	−	2.80444i	−0.361337	−	0.0968199i	0.0735829	−	0.997289i	$-0.476557\pi$
$839$	−10.4663	−	2.80444i	−0.361337	−	0.0968199i	−0.434920	+	0.900469i	$0.643223\pi$
$840$	−9.26984	+	2.31136i	−0.319840	+	0.0797495i
$841$	−10.8898	−	18.8618i	−0.375512	−	0.650406i
$842$	−2.22657	+	3.85653i	−0.0767326	+	0.132905i
$843$	−20.1496	−	5.77751i	−0.693989	−	0.198988i
$844$			15.0198i			0.517004i
$845$		0			0
$846$	1.56688	+	2.94669i	0.0538706	+	0.101309i
$847$	2.25057	+	8.39923i	0.0773304	+	0.288601i
$848$	6.97060	+	4.02448i	0.239371	+	0.138201i
$849$	0.214628	−	12.3054i	0.00736602	−	0.422319i
$850$	−10.4067	+	10.4067i	−0.356947	+	0.356947i
$851$	1.51532	−	5.65526i	0.0519446	−	0.193860i
$852$	−27.1267	+	26.1966i	−0.929346	+	0.897482i
$853$	30.1644	+	30.1644i	1.03281	+	1.03281i	0.999443	+	0.0333670i	$0.0106230\pi$
$853$	30.1644	+	30.1644i	1.03281	+	1.03281i	0.0333670	+	0.999443i	$0.489377\pi$
$854$	0.944378	−	0.545237i	0.0323160	−	0.0186576i
$855$	−51.3321	−	1.79120i	−1.75552	−	0.0612577i
$856$	−17.2259	+	4.61568i	−0.588771	+	0.157761i
$857$	36.7949			1.25689			0.628444	−	0.777855i	$-0.283692\pi$
$857$	36.7949			1.25689			0.628444	+	0.777855i	$0.283692\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	34.9518	−	9.36529i	1.19185	−	0.319354i
$861$	11.9809	−	6.64135i	0.408309	−	0.226336i
$862$	−6.47872	+	3.74049i	−0.220666	+	0.127402i
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	0.991931	−	0.126779i	$-0.0404637\pi$
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	−0.126779	+	0.991931i	$0.540464\pi$
$864$	6.23663	−	19.1970i	0.212175	−	0.653094i
$865$	12.8175	−	47.8355i	0.435808	−	1.62646i
$866$	−0.461976	+	0.461976i	−0.0156986	+	0.0156986i
$867$	−30.8772	−	0.538556i	−1.04864	−	0.0182903i
$868$	−8.60919	−	4.97052i	−0.292215	−	0.168710i
$869$	0.533937	+	1.99268i	0.0181126	+	0.0675971i
$870$	−2.93571	+	4.88599i	−0.0995299	+	0.165651i
$871$		0			0
$872$			8.67054i			0.293622i
$873$	−26.9150	+	25.1000i	−0.910934	+	0.849505i
$874$	−2.35262	+	4.07485i	−0.0795784	+	0.137834i
$875$	−4.19056	−	7.25826i	−0.141667	−	0.245374i
$876$	−10.1520	−	40.7152i	−0.343005	−	1.37564i
$877$	17.6992	+	4.74247i	0.597658	+	0.160142i	0.544951	−	0.838468i	$-0.316548\pi$
$877$	17.6992	+	4.74247i	0.597658	+	0.160142i	0.0527071	+	0.998610i	$0.483215\pi$
$878$	4.90406	+	1.31404i	0.165504	+	0.0443467i
$879$	−6.66068	−	26.7130i	−0.224659	−	0.901007i
$880$	10.6551	+	18.4552i	0.359184	+	0.622125i
$881$	−15.5539	+	26.9401i	−0.524023	+	0.907635i	0.475586	+	0.879669i	$0.342236\pi$
$881$	−15.5539	+	26.9401i	−0.524023	+	0.907635i	−0.999609	+	0.0279654i	$0.991097\pi$
$882$	4.36877	−	4.07416i	0.147104	−	0.137184i
$883$		−	9.56660i		−	0.321942i	−0.986959	−	0.160971i	$-0.948537\pi$
$883$		−	9.56660i		−	0.321942i	0.986959	−	0.160971i	$-0.0514625\pi$
$884$		0			0
$885$	−31.0229	+	51.6323i	−1.04282	+	1.73560i
$886$	2.02808	+	7.56891i	0.0681348	+	0.254282i
$887$	−21.3515	−	12.3273i	−0.716913	−	0.413910i	0.0967027	−	0.995313i	$-0.469170\pi$
$887$	−21.3515	−	12.3273i	−0.716913	−	0.413910i	−0.813615	+	0.581404i	$0.802504\pi$
$888$	5.11141	+	0.0891524i	0.171528	+	0.00299176i
$889$	−6.40399	+	6.40399i	−0.214783	+	0.214783i
$890$	1.35479	−	5.05616i	0.0454128	−	0.169483i
$891$	12.7371	−	11.0734i	0.426710	−	0.370973i
$892$	−37.5558	−	37.5558i	−1.25746	−	1.25746i
$893$	−13.4680	+	7.77574i	−0.450688	+	0.260205i
$894$	12.1801	−	6.75173i	0.407362	−	0.225812i
$895$	14.6571	−	3.92737i	0.489934	−	0.131277i
$896$	11.1454			0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	−11.8377	+	3.17189i	−0.394808	+	0.105789i
$900$	39.7926	+	1.38854i	1.32642	+	0.0462846i
$901$	12.5800	−	7.26306i	0.419100	−	0.241967i
$902$	3.18093	+	3.18093i	0.105913	+	0.105913i
$903$	8.03678	−	7.76123i	0.267447	−	0.258278i
$904$	4.60057	−	17.1696i	0.153013	−	0.571051i
$905$	−5.17824	+	5.17824i	−0.172130	+	0.172130i
$906$	−0.0996478	+	5.71314i	−0.00331058	+	0.189806i
$907$	1.45939	+	0.842581i	0.0484584	+	0.0279775i	0.524033	−	0.851698i	$-0.324427\pi$
$907$	1.45939	+	0.842581i	0.0484584	+	0.0279775i	−0.475575	+	0.879675i	$0.657760\pi$
$908$	3.57085	+	13.3266i	0.118503	+	0.442259i
$909$	−15.6280	−	29.3900i	−0.518346	−	0.974806i
$910$		0			0
$911$			43.9421i			1.45587i	0.685648	+	0.727933i	$0.259519\pi$
$911$			43.9421i			1.45587i	−0.685648	+	0.727933i	$0.740481\pi$
$912$	26.8254	+	7.69167i	0.888277	+	0.254697i
$913$	6.08545	−	10.5403i	0.201399	−	0.348834i
$914$	−1.19283	−	2.06604i	−0.0394553	−	0.0683386i
$915$	−15.5503	+	3.87734i	−0.514076	+	0.128181i
$916$	29.2350	+	7.83348i	0.965950	+	0.258826i
$917$	20.8116	+	5.57646i	0.687260	+	0.184151i
$918$	−7.23231	−	8.03165i	−0.238702	−	0.265084i
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	0.788254	−	0.615349i	$-0.210985\pi$
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	−0.927035	+	0.374974i	$0.877652\pi$
$920$	6.43113	−	11.1390i	0.212028	−	0.367243i
$921$	9.71159	−	33.8700i	0.320008	−	1.11606i
$922$		−	4.36704i		−	0.143821i
$923$		0			0
$924$	6.06857	+	3.64625i	0.199641	+	0.119953i
$925$	3.95690	+	14.7674i	0.130102	+	0.485548i
$926$	3.01029	+	1.73799i	0.0989244	+	0.0571140i
$927$	11.2780	+	7.04686i	0.370418	+	0.231449i
$928$	7.38077	−	7.38077i	0.242286	−	0.242286i
$929$	0.593828	−	2.21620i	0.0194829	−	0.0727110i	−0.955500	−	0.294991i	$-0.904683\pi$
$929$	0.593828	−	2.21620i	0.0194829	−	0.0727110i	0.974983	+	0.222280i	$0.0713500\pi$
$930$	−6.72089	−	6.95951i	−0.220387	−	0.228211i
$931$	19.6831	+	19.6831i	0.645087	+	0.645087i
$932$	29.4930	−	17.0278i	0.966076	−	0.557764i
$933$	6.40030	+	11.5461i	0.209536	+	0.378002i
$934$	−3.13178	+	0.839158i	−0.102475	+	0.0274581i
$935$	38.4590			1.25775
$936$		0			0
$937$	7.10985			0.232269			0.116134	−	0.993234i	$-0.462950\pi$
$937$	7.10985			0.232269			0.116134	+	0.993234i	$0.462950\pi$
$938$	−2.69135	+	0.721146i	−0.0878758	+	0.0235463i
$939$	−5.47077	−	9.86922i	−0.178532	−	0.322070i
$940$	17.8181	−	10.2873i	0.581163	−	0.335534i
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	0.972266	−	0.233877i	$-0.0751412\pi$
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	−0.233877	+	0.972266i	$0.575141\pi$
$942$	−6.64864	−	6.88469i	−0.216624	−	0.224315i
$943$	−4.77330	+	17.8142i	−0.155440	+	0.580110i
$944$	23.1413	−	23.1413i	0.753185	−	0.753185i
$945$	18.6945	−	9.52623i	0.608131	−	0.309888i
$946$	3.17745	+	1.83450i	0.103308	+	0.0596448i
$947$	−3.46107	−	12.9169i	−0.112470	−	0.419742i	0.886616	−	0.462507i	$-0.153050\pi$
$947$	−3.46107	−	12.9169i	−0.112470	−	0.419742i	−0.999085	+	0.0427648i	$0.986383\pi$
$948$	−3.06363	−	1.84076i	−0.0995022	−	0.0597852i
$949$		0			0
$950$		−	12.2866i		−	0.398629i
$951$	4.24943	−	14.8203i	0.137797	−	0.480580i
$952$	4.68381	−	8.11259i	0.151803	−	0.262931i
$953$	−8.89415	−	15.4051i	−0.288110	−	0.499021i	0.685249	−	0.728309i	$-0.259693\pi$
$953$	−8.89415	−	15.4051i	−0.288110	−	0.499021i	−0.973359	+	0.229288i	$0.926360\pi$
$954$	2.48878	+	0.760824i	0.0805772	+	0.0246326i
$955$	−22.8174	−	6.11390i	−0.738353	−	0.197841i
$956$	−16.7646	−	4.49206i	−0.542206	−	0.145284i
$957$	8.46858	−	2.11157i	0.273750	−	0.0682575i
$958$	−4.04423	−	7.00482i	−0.130663	−	0.226315i
$959$	−4.37773	+	7.58246i	−0.141364	+	0.244850i
$960$	−29.9190	−	8.57871i	−0.965632	−	0.276877i
$961$			10.1988i			0.328993i
$962$		0			0
$963$	34.5812	−	18.3883i	1.11436	−	0.592555i
$964$	−13.4369	−	50.1473i	−0.432774	−	1.61513i
$965$	−33.4536	−	19.3144i	−1.07691	−	0.621753i
$966$	0.0335193	−	1.92177i	0.00107847	−	0.0618321i
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	−0.0648250	−	0.997897i	$-0.520649\pi$
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	0.997897	+	0.0648250i	$0.0206489\pi$
$968$	2.64568	−	9.87382i	0.0850354	−	0.317357i
$969$	36.2277	−	34.9856i	1.16380	−	1.12390i
$970$	−10.6239	−	10.6239i	−0.341114	−	0.341114i
$971$	19.5631	−	11.2948i	0.627810	−	0.362466i	−0.152093	−	0.988366i	$-0.548601\pi$
$971$	19.5631	−	11.2948i	0.627810	−	0.362466i	0.779904	+	0.625900i	$0.215268\pi$
$972$	−2.54656	+	29.1295i	−0.0816810	+	0.934328i
$973$	−6.05235	+	1.62172i	−0.194029	+	0.0519900i
$974$	10.3864			0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	2.57462	−	0.689868i	0.0823694	−	0.0220708i	−0.217399	−	0.976083i	$-0.569757\pi$
$977$	2.57462	−	0.689868i	0.0823694	−	0.0220708i	0.299768	+	0.954012i	$0.403091\pi$
$978$	1.84540	−	1.02295i	0.0590092	−	0.0327104i
$979$	−6.94116	+	4.00748i	−0.221841	+	0.128080i
$980$	−26.0407	−	26.0407i	−0.831839	−	0.831839i
$981$	−4.28406	−	18.5541i	−0.136779	−	0.592385i
$982$	1.39784	−	5.21679i	0.0446067	−	0.166475i
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.263440	+	0.964676i	$0.584857\pi$
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.964676	+	0.263440i	$0.915143\pi$
$984$	−16.1010	−	0.280832i	−0.513282	−	0.00895260i
$985$	−6.87308	−	3.96818i	−0.218995	−	0.126437i
$986$	−1.44657	−	5.39867i	−0.0460682	−	0.171929i
$987$	3.27182	−	5.44538i	0.104143	−	0.173328i
$988$		0			0
$989$			15.0419i			0.478303i
$990$	4.69928	+	5.03909i	0.149353	+	0.160153i
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	−0.951827	−	0.306635i	$-0.900797\pi$
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	0.741467	+	0.670989i	$0.234130\pi$
$992$	8.85836	+	15.3431i	0.281253	+	0.487145i
$993$	−6.73680	−	27.0183i	−0.213786	−	0.857400i
$994$	−4.59160	−	1.23032i	−0.145637	−	0.0390232i
$995$	61.5704	+	16.4977i	1.95191	+	0.523013i
$996$	5.10147	+	20.4597i	0.161646	+	0.648291i
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	1.00000		0.000107105i	$3.40926e-5\pi$
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	−0.499907	+	0.866079i	$0.666633\pi$
$998$	7.36014	−	12.7481i	0.232981	−	0.403535i
$999$	−10.9819	+	2.33473i	−0.347453	+	0.0738677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.188.12		96
3.2	odd	2	inner	507.2.k.k.188.13		96
13.2	odd	12	inner	507.2.k.k.89.11		96
13.3	even	3	inner	507.2.k.k.80.13		96
13.4	even	6		507.2.f.g.239.11	✓	48
13.5	odd	4	inner	507.2.k.k.488.14		96
13.6	odd	12		507.2.f.g.437.13	yes	48
13.7	odd	12		507.2.f.g.437.11	yes	48
13.8	odd	4	inner	507.2.k.k.488.12		96
13.9	even	3		507.2.f.g.239.13	yes	48
13.10	even	6	inner	507.2.k.k.80.11		96
13.11	odd	12	inner	507.2.k.k.89.13		96
13.12	even	2	inner	507.2.k.k.188.14		96
39.2	even	12	inner	507.2.k.k.89.14		96
39.5	even	4	inner	507.2.k.k.488.11		96
39.8	even	4	inner	507.2.k.k.488.13		96
39.11	even	12	inner	507.2.k.k.89.12		96
39.17	odd	6		507.2.f.g.239.14	yes	48
39.20	even	12		507.2.f.g.437.14	yes	48
39.23	odd	6	inner	507.2.k.k.80.14		96
39.29	odd	6	inner	507.2.k.k.80.12		96
39.32	even	12		507.2.f.g.437.12	yes	48
39.35	odd	6		507.2.f.g.239.12	yes	48
39.38	odd	2	inner	507.2.k.k.188.11		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.11	✓	48	13.4	even	6
507.2.f.g.239.12	yes	48	39.35	odd	6
507.2.f.g.239.13	yes	48	13.9	even	3
507.2.f.g.239.14	yes	48	39.17	odd	6
507.2.f.g.437.11	yes	48	13.7	odd	12
507.2.f.g.437.12	yes	48	39.32	even	12
507.2.f.g.437.13	yes	48	13.6	odd	12
507.2.f.g.437.14	yes	48	39.20	even	12
507.2.k.k.80.11		96	13.10	even	6	inner
507.2.k.k.80.12		96	39.29	odd	6	inner
507.2.k.k.80.13		96	13.3	even	3	inner
507.2.k.k.80.14		96	39.23	odd	6	inner
507.2.k.k.89.11		96	13.2	odd	12	inner
507.2.k.k.89.12		96	39.11	even	12	inner
507.2.k.k.89.13		96	13.11	odd	12	inner
507.2.k.k.89.14		96	39.2	even	12	inner
507.2.k.k.188.11		96	39.38	odd	2	inner
507.2.k.k.188.12		96	1.1	even	1	trivial
507.2.k.k.188.13		96	3.2	odd	2	inner
507.2.k.k.188.14		96	13.12	even	2	inner
507.2.k.k.488.11		96	39.5	even	4	inner
507.2.k.k.488.12		96	13.8	odd	4	inner
507.2.k.k.488.13		96	39.8	even	4	inner
507.2.k.k.488.14		96	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.340435 + 0.0912193i) q^{2} +(0.839735 + 1.51487i) q^{3} +(-1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.424061 - 0.439116i) q^{6} +(-0.300747 + 1.12240i) q^{7} +(0.965906 - 0.965906i) q^{8} +(-1.58969 + 2.54419i) q^{9} +(-1.06066 - 0.612371i) q^{10} +(0.485362 + 1.81140i) q^{11} +(-2.78492 - 1.67330i) q^{12} -0.409539i q^{14} +(-1.65895 + 5.78573i) q^{15} +(1.63506 - 2.83201i) q^{16} +(-2.95083 - 5.11099i) q^{17} +(0.309108 - 1.01114i) q^{18} +(4.75906 + 1.27519i) q^{19} +(-6.29623 - 1.68707i) q^{20} +(-1.95284 + 0.486926i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(1.35482 - 2.34662i) q^{23} +(2.27433 + 0.652122i) q^{24} +7.07560i q^{25} +(-5.18904 - 0.271740i) q^{27} +(-0.564135 - 2.10538i) q^{28} +(-2.32707 - 1.34353i) q^{29} +(0.0369941 - 2.12099i) q^{30} +(3.22500 - 3.22500i) q^{31} +(-1.00539 + 3.75217i) q^{32} +(-2.33646 + 2.25635i) q^{33} +(1.47079 + 1.47079i) q^{34} +(-3.49695 + 2.01896i) q^{35} +(0.196243 - 5.62393i) q^{36} +(2.08708 - 0.559232i) q^{37} -1.73647 q^{38} +4.74684 q^{40} +(-6.57436 + 1.76159i) q^{41} +(0.620400 - 0.343904i) q^{42} +(-4.80750 + 2.77561i) q^{43} +(-2.48735 - 2.48735i) q^{44} +(-10.1577 + 2.34538i) q^{45} +(-0.247172 + 0.922459i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(5.66317 + 0.0987761i) q^{48} +(4.89284 + 2.82488i) q^{49} +(-0.645431 - 2.40878i) q^{50} +(5.26460 - 8.76202i) q^{51} +2.46136i q^{53} +(1.79132 - 0.380831i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(0.793642 + 1.37463i) q^{56} +(2.06460 + 8.28020i) q^{57} +(0.914771 + 0.245112i) q^{58} +(9.66677 + 2.59020i) q^{59} +(-2.73147 - 10.9547i) q^{60} +(1.33134 + 2.30596i) q^{61} +(-0.803720 + 1.39208i) q^{62} +(-2.37750 - 2.54943i) q^{63} +5.17117i q^{64} +(0.589590 - 0.981273i) q^{66} +(-1.76087 - 6.57167i) q^{67} +(9.58711 + 5.53512i) q^{68} +(4.69254 + 0.0818465i) q^{69} +(1.00632 - 1.00632i) q^{70} +(3.00415 - 11.2116i) q^{71} +(0.921953 + 3.99294i) q^{72} +(9.13263 + 9.13263i) q^{73} +(-0.659503 + 0.380764i) q^{74} +(-10.7186 + 5.94163i) q^{75} +(-8.92696 + 2.39197i) q^{76} -2.17908 q^{77} +1.10008 q^{79} +(10.9765 - 2.94114i) q^{80} +(-3.94577 - 8.08894i) q^{81} +(2.07745 - 1.19942i) q^{82} +(-4.58922 - 4.58922i) q^{83} +(2.71567 - 2.62256i) q^{84} +(5.30793 - 19.8095i) q^{85} +(1.38345 - 1.38345i) q^{86} +(0.0811644 - 4.65342i) q^{87} +(2.21845 + 1.28082i) q^{88} +(1.10619 + 4.12834i) q^{89} +(3.24410 - 1.72503i) q^{90} +5.08271i q^{92} +(7.59361 + 2.17732i) q^{93} +(0.556230 - 0.963419i) q^{94} +(8.56055 + 14.8273i) q^{95} +(-6.52833 + 1.62779i) q^{96} +(11.8495 + 3.17506i) q^{97} +(-1.92338 - 0.515368i) q^{98} +(-5.38010 - 1.64471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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