LMFDB - Embedded newform 507.2.k.k.488.12

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			488.12
Character	$\chi$	$=$	507.488
Dual form			507.2.k.k.80.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0912193 - 0.340435i) q^{2} +(0.839735 + 1.51487i) q^{3} +(1.62448 - 0.937892i) q^{4} +(-2.45719 + 2.45719i) q^{5} +(0.439116 - 0.424061i) q^{6} +(1.12240 + 0.300747i) q^{7} +(-0.965906 - 0.965906i) q^{8} +(-1.58969 + 2.54419i) q^{9} +(1.06066 + 0.612371i) q^{10} +(1.81140 - 0.485362i) q^{11} +(2.78492 + 1.67330i) q^{12} -0.409539i q^{14} +(-5.78573 - 1.65895i) q^{15} +(1.63506 - 2.83201i) q^{16} +(2.95083 + 5.11099i) q^{17} +(1.01114 + 0.309108i) q^{18} +(-1.27519 + 4.75906i) q^{19} +(-1.68707 + 6.29623i) q^{20} +(0.486926 + 1.95284i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(-1.35482 + 2.34662i) q^{23} +(0.652122 - 2.27433i) q^{24} -7.07560i q^{25} +(-5.18904 - 0.271740i) q^{27} +(2.10538 - 0.564135i) q^{28} +(-2.32707 - 1.34353i) q^{29} +(-0.0369941 + 2.12099i) q^{30} +(3.22500 + 3.22500i) q^{31} +(-3.75217 - 1.00539i) q^{32} +(2.25635 + 2.33646i) q^{33} +(1.47079 - 1.47079i) q^{34} +(-3.49695 + 2.01896i) q^{35} +(-0.196243 + 5.62393i) q^{36} +(-0.559232 - 2.08708i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(-1.76159 - 6.57436i) q^{41} +(0.620400 - 0.343904i) q^{42} +(4.80750 - 2.77561i) q^{43} +(2.48735 - 2.48735i) q^{44} +(-2.34538 - 10.1577i) q^{45} +(0.922459 + 0.247172i) q^{46} +(2.23192 + 2.23192i) q^{47} +(5.66317 + 0.0987761i) q^{48} +(-4.89284 - 2.82488i) q^{49} +(-2.40878 + 0.645431i) q^{50} +(-5.26460 + 8.76202i) q^{51} +2.46136i q^{53} +(0.380831 + 1.79132i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(-0.793642 - 1.37463i) q^{56} +(-8.28020 + 2.06460i) q^{57} +(-0.245112 + 0.914771i) q^{58} +(2.59020 - 9.66677i) q^{59} +(-10.9547 + 2.73147i) q^{60} +(1.33134 + 2.30596i) q^{61} +(0.803720 - 1.39208i) q^{62} +(-2.54943 + 2.37750i) q^{63} -5.17117i q^{64} +(0.589590 - 0.981273i) q^{66} +(6.57167 - 1.76087i) q^{67} +(9.58711 + 5.53512i) q^{68} +(-4.69254 - 0.0818465i) q^{69} +(1.00632 + 1.00632i) q^{70} +(11.2116 + 3.00415i) q^{71} +(3.99294 - 0.921953i) q^{72} +(9.13263 - 9.13263i) q^{73} +(-0.659503 + 0.380764i) q^{74} +(10.7186 - 5.94163i) q^{75} +(2.39197 + 8.92696i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(2.94114 + 10.9765i) q^{80} +(-3.94577 - 8.08894i) q^{81} +(-2.07745 + 1.19942i) q^{82} +(4.58922 - 4.58922i) q^{83} +(2.62256 + 2.71567i) q^{84} +(-19.8095 - 5.30793i) q^{85} +(-1.38345 - 1.38345i) q^{86} +(0.0811644 - 4.65342i) q^{87} +(-2.21845 - 1.28082i) q^{88} +(4.12834 - 1.10619i) q^{89} +(-3.24410 + 1.72503i) q^{90} +5.08271i q^{92} +(-2.17732 + 7.59361i) q^{93} +(0.556230 - 0.963419i) q^{94} +(-8.56055 - 14.8273i) q^{95} +(-1.62779 - 6.52833i) q^{96} +(-3.17506 + 11.8495i) q^{97} +(-0.515368 + 1.92338i) q^{98} +(-1.64471 + 5.38010i) 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.0912193	−	0.340435i	−0.0645018	−	0.240724i	0.926147	−	0.377164i	$-0.123101\pi$
$2$	−0.0912193	−	0.340435i	−0.0645018	−	0.240724i	−0.990648	+	0.136440i	$0.956434\pi$
$3$	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	−0.104350	+	0.994541i	$0.533276\pi$
$5$	−2.45719	+	2.45719i	−1.09889	+	1.09889i	−0.994541	+	0.104350i	$0.966724\pi$
$6$	0.439116	−	0.424061i	0.179269	−	0.173122i
$7$	1.12240	+	0.300747i	0.424228	+	0.113672i	0.464615	−	0.885513i	$-0.346193\pi$
$7$	1.12240	+	0.300747i	0.424228	+	0.113672i	−0.0403875	+	0.999184i	$0.512859\pi$
$8$	−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
$11$	1.81140	−	0.485362i	0.546156	−	0.146342i	0.0248176	−	0.999692i	$-0.492100\pi$
$11$	1.81140	−	0.485362i	0.546156	−	0.146342i	0.521339	+	0.853350i	$0.325433\pi$
$12$	2.78492	+	1.67330i	0.803936	+	0.483039i
$13$		0			0
$13$		0			0
$14$		−	0.409539i		−	0.109454i
$15$	−5.78573	−	1.65895i	−1.49387	−	0.428339i
$16$	1.63506	−	2.83201i	0.408766	−	0.708003i
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	0.962696	+	0.270586i	$0.0872174\pi$
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	−0.247014	+	0.969012i	$0.579449\pi$
$18$	1.01114	+	0.309108i	0.238328	+	0.0728573i
$19$	−1.27519	+	4.75906i	−0.292548	+	1.09180i	0.650598	+	0.759423i	$0.274518\pi$
$19$	−1.27519	+	4.75906i	−0.292548	+	1.09180i	−0.943145	+	0.332381i	$0.892148\pi$
$20$	−1.68707	+	6.29623i	−0.377240	+	1.40788i
$21$	0.486926	+	1.95284i	0.106256	+	0.426146i
$22$	−0.330468	−	0.572388i	−0.0704561	−	0.122034i
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	−0.972000	−	0.234981i	$-0.924497\pi$
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	0.689500	+	0.724286i	$0.257831\pi$
$24$	0.652122	−	2.27433i	0.133114	−	0.464246i
$25$		−	7.07560i		−	1.41512i
$26$		0			0
$27$	−5.18904	−	0.271740i	−0.998632	−	0.0522964i
$28$	2.10538	−	0.564135i	0.397880	−	0.106612i
$29$	−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	0.934690	−	0.355463i	$-0.115677\pi$
$31$	3.22500	+	3.22500i	0.579227	+	0.579227i	−0.355463	+	0.934690i	$0.615677\pi$
$32$	−3.75217	−	1.00539i	−0.663296	−	0.177730i
$33$	2.25635	+	2.33646i	0.392781	+	0.406726i
$34$	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
$37$	−0.559232	−	2.08708i	−0.0919372	−	0.343114i	0.904600	−	0.426261i	$-0.140170\pi$
$37$	−0.559232	−	2.08708i	−0.0919372	−	0.343114i	−0.996537	+	0.0831470i	$0.973503\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	−1.76159	−	6.57436i	−0.275115	−	1.02674i	−0.955764	−	0.294133i	$-0.904969\pi$
$41$	−1.76159	−	6.57436i	−0.275115	−	1.02674i	0.680650	−	0.732609i	$-0.261698\pi$
$42$	0.620400	−	0.343904i	0.0957298	−	0.0530655i
$43$	4.80750	−	2.77561i	0.733136	−	0.423276i	−0.0864321	−	0.996258i	$-0.527547\pi$
$43$	4.80750	−	2.77561i	0.733136	−	0.423276i	0.819568	+	0.572981i	$0.194213\pi$
$44$	2.48735	−	2.48735i	0.374982	−	0.374982i
$45$	−2.34538	−	10.1577i	−0.349629	−	1.51423i
$46$	0.922459	+	0.247172i	0.136009	+	0.0364436i
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	0.850895	−	0.525336i	$-0.176060\pi$
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	−0.525336	+	0.850895i	$0.676060\pi$
$48$	5.66317	+	0.0987761i	0.817408	+	0.0142571i
$49$	−4.89284	−	2.82488i	−0.698977	−	0.403555i
$50$	−2.40878	+	0.645431i	−0.340653	+	0.0912777i
$51$	−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	$0.945931\pi$
$54$	0.380831	+	1.79132i	0.0518245	+	0.243768i
$55$	−3.25832	+	5.64358i	−0.439352	+	0.760980i
$56$	−0.793642	−	1.37463i	−0.106055	−	0.183692i
$57$	−8.28020	+	2.06460i	−1.09674	+	0.273463i
$58$	−0.245112	+	0.914771i	−0.0321848	+	0.120115i
$59$	2.59020	−	9.66677i	0.337216	−	1.25851i	−0.564231	−	0.825617i	$-0.690827\pi$
$59$	2.59020	−	9.66677i	0.337216	−	1.25851i	0.901447	−	0.432890i	$-0.142506\pi$
$60$	−10.9547	+	2.73147i	−1.41424	+	0.352631i
$61$	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
$63$	−2.54943	+	2.37750i	−0.321198	+	0.299537i
$64$		−	5.17117i		−	0.646397i
$65$		0			0
$66$	0.589590	−	0.981273i	0.0725736	−	0.120786i
$67$	6.57167	−	1.76087i	0.802857	−	0.215125i	0.166019	−	0.986123i	$-0.446909\pi$
$67$	6.57167	−	1.76087i	0.802857	−	0.215125i	0.636838	+	0.770998i	$0.280242\pi$
$68$	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
$71$	11.2116	+	3.00415i	1.33058	+	0.356527i	0.852930	−	0.522025i	$-0.174823\pi$
$71$	11.2116	+	3.00415i	1.33058	+	0.356527i	0.477647	+	0.878552i	$0.341490\pi$
$72$	3.99294	−	0.921953i	0.470572	−	0.108653i
$73$	9.13263	−	9.13263i	1.06889	−	1.06889i	0.0714492	−	0.997444i	$-0.477238\pi$
$73$	9.13263	−	9.13263i	1.06889	−	1.06889i	0.997444	−	0.0714492i	$-0.0227624\pi$
$74$	−0.659503	+	0.380764i	−0.0766657	+	0.0442630i
$75$	10.7186	−	5.94163i	1.23768	−	0.686080i
$76$	2.39197	+	8.92696i	0.274378	+	1.02399i
$77$	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	$0.480289\pi$
$80$	2.94114	+	10.9765i	0.328829	+	1.22721i
$81$	−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	$-0.634075\pi$
$83$	4.58922	−	4.58922i	0.503732	−	0.503732i	0.912596	+	0.408864i	$0.134075\pi$
$84$	2.62256	+	2.71567i	0.286144	+	0.296303i
$85$	−19.8095	−	5.30793i	−2.14864	−	0.575726i
$86$	−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
$89$	4.12834	−	1.10619i	0.437604	−	0.117256i	−0.0332896	−	0.999446i	$-0.510598\pi$
$89$	4.12834	−	1.10619i	0.437604	−	0.117256i	0.470893	+	0.882190i	$0.343932\pi$
$90$	−3.24410	+	1.72503i	−0.341959	+	0.181834i
$91$		0			0
$92$			5.08271i			0.529909i
$93$	−2.17732	+	7.59361i	−0.225778	+	0.787421i
$94$	0.556230	−	0.963419i	0.0573708	−	0.0993691i
$95$	−8.56055	−	14.8273i	−0.878294	−	1.52125i
$96$	−1.62779	−	6.52833i	−0.166135	−	0.666295i
$97$	−3.17506	+	11.8495i	−0.322379	+	1.20313i	0.594542	+	0.804065i	$0.297333\pi$
$97$	−3.17506	+	11.8495i	−0.322379	+	1.20313i	−0.916921	+	0.399070i	$0.869333\pi$
$98$	−0.515368	+	1.92338i	−0.0520600	+	0.194291i
$99$	−1.64471	+	5.38010i	−0.165299	+	0.540721i
$100$	−6.63614	−	11.4941i	−0.663614	−	1.14941i
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	−0.446103	−	0.894982i	$-0.647188\pi$
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	0.998128	−	0.0611547i	$-0.0194783\pi$
$102$	3.46313	+	0.992988i	0.342901	+	0.0983204i
$103$			4.43285i			0.436782i	0.975861	+	0.218391i	$0.0700808\pi$
$103$			4.43285i			0.436782i	−0.975861	+	0.218391i	$0.929919\pi$
$104$		0			0
$105$	−5.99499	−	3.60205i	−0.585051	−	0.351524i
$106$	0.837932	−	0.224523i	0.0813872	−	0.0218076i
$107$	−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	0.458694	−	0.888594i	$-0.348318\pi$
$109$	−4.48829	−	4.48829i	−0.429901	−	0.429901i	−0.888594	+	0.458694i	$0.848318\pi$
$110$	2.21849	+	0.594443i	0.211525	+	0.0566780i
$111$	2.69206	−	2.59976i	0.255519	−	0.246759i
$112$	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
$115$	−2.43705	−	9.09518i	−0.227256	−	0.848130i
$116$	−5.04035			−0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	1.77491	+	6.62404i	0.162705	+	0.607225i
$120$	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
$123$	8.48005	−	8.18931i	0.764621	−	0.738405i
$124$	8.26363	+	2.21423i	0.742096	+	0.198844i
$125$	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	0.169679	−	0.985499i	$-0.445727\pi$
$127$	−6.74982	−	3.89701i	−0.598950	−	0.345804i	−0.768628	+	0.639696i	$0.779060\pi$
$128$	−9.26479	+	2.48249i	−0.818900	+	0.219423i
$129$	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	$-0.300540\pi$
$132$	5.85674	+	1.67931i	0.509764	+	0.146165i
$133$	−2.86254	+	4.95807i	−0.248214	+	0.429919i
$134$	−1.19893	−	2.07660i	−0.103571	−	0.179391i
$135$	13.4182	−	12.0828i	1.15485	−	1.03992i
$136$	2.08651	−	7.78697i	0.178917	−	0.667727i
$137$	1.95016	−	7.27811i	0.166614	−	0.621811i	−0.831215	−	0.555951i	$-0.812354\pi$
$137$	1.95016	−	7.27811i	0.166614	−	0.621811i	0.997829	−	0.0658600i	$-0.0209791\pi$
$138$	0.400186	+	1.60497i	0.0340661	+	0.136624i
$139$	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
$141$	−1.50686	+	5.25531i	−0.126900	+	0.442577i
$142$		−	4.09087i		−	0.343298i
$143$		0			0
$144$	4.60592	+	8.66193i	0.383827	+	0.721828i
$145$	9.01937	−	2.41673i	0.749018	−	0.200699i
$146$	−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
$149$	−22.0357	−	5.90444i	−1.80523	−	0.483710i	−0.810457	−	0.585798i	$-0.800781\pi$
$149$	−22.0357	−	5.90444i	−1.80523	−	0.483710i	−0.994775	+	0.102088i	$0.967448\pi$
$150$	−3.00049	−	3.10701i	−0.244989	−	0.253686i
$151$	−6.61873	+	6.61873i	−0.538625	+	0.538625i	−0.923125	−	0.384500i	$-0.874374\pi$
$151$	−6.61873	+	6.61873i	−0.538625	+	0.538625i	0.384500	+	0.923125i	$0.374374\pi$
$152$	5.82852	−	3.36510i	0.472755	−	0.272945i
$153$	−17.6942	−	0.617428i	−1.43049	−	0.0499161i
$154$	−0.198774	−	0.741836i	−0.0160177	−	0.0597789i
$155$	−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	$0.284838\pi$
$158$	−0.100349	−	0.374506i	−0.00798331	−	0.0297941i
$159$	−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
$162$	−2.39383	+	2.08114i	−0.188077	+	0.163510i
$163$	3.33861	+	0.894579i	0.261500	+	0.0700688i	0.387187	−	0.922001i	$-0.373447\pi$
$163$	3.33861	+	0.894579i	0.261500	+	0.0700688i	−0.125687	+	0.992070i	$0.540113\pi$
$164$	−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
$167$	−5.06462	+	1.35706i	−0.391912	+	0.105012i	−0.449393	−	0.893334i	$-0.648360\pi$
$167$	−5.06462	+	1.35706i	−0.391912	+	0.105012i	0.0574813	+	0.998347i	$0.481693\pi$
$168$	1.41594	−	2.35659i	0.109242	−	0.181815i
$169$		0			0
$170$			7.22802i			0.554364i
$171$	−10.0808	−	10.8097i	−0.770897	−	0.826642i
$172$	5.20644	−	9.01782i	0.396987	−	0.687602i
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	0.998804	+	0.0489001i	$0.0155716\pi$
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	−0.457053	+	0.889439i	$0.651095\pi$
$174$	−1.59159	+	0.396851i	−0.120658	+	0.0300852i
$175$	2.12796	−	7.94166i	0.160859	−	0.600333i
$176$	1.58720	−	5.92349i	0.119639	−	0.446500i
$177$	16.8190	−	4.19369i	1.26420	−	0.315217i
$178$	−0.753169	−	1.30453i	−0.0564524	−	0.0977785i
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	−0.936011	−	0.351970i	$-0.885512\pi$
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	0.772821	+	0.634624i	$0.218845\pi$
$180$	−13.3369	−	14.3013i	−0.994071	−	1.06595i
$181$		−	2.10738i		−	0.156640i	−0.996928	−	0.0783201i	$-0.975044\pi$
$181$		−	2.10738i		−	0.156640i	0.996928	−	0.0783201i	$-0.0249556\pi$
$182$		0			0
$183$	−2.37526	+	3.95321i	−0.175584	+	0.292230i
$184$	3.57525	−	0.957986i	0.263571	−	0.0706237i
$185$	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
$188$	5.71901	+	1.53240i	0.417101	+	0.111762i
$189$	−5.74246	−	1.86559i	−0.417703	−	0.135702i
$190$	−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
$193$	2.87709	+	10.7374i	0.207098	+	0.772898i	0.988800	+	0.149247i	$0.0476849\pi$
$193$	2.87709	+	10.7374i	0.207098	+	0.772898i	−0.781702	+	0.623652i	$0.785648\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	−0.591102	−	2.20602i	−0.0421143	−	0.157173i	0.941667	−	0.336547i	$-0.109259\pi$
$197$	−0.591102	−	2.20602i	−0.0421143	−	0.157173i	−0.983781	+	0.179375i	$0.942593\pi$
$198$	1.98160	+	0.0691468i	0.140826	+	0.00491405i
$199$	−15.8856	+	9.17157i	−1.12610	+	0.650155i	−0.942952	−	0.332930i	$-0.891963\pi$
$199$	−15.8856	+	9.17157i	−1.12610	+	0.650155i	−0.183150	+	0.983085i	$0.558629\pi$
$200$	−6.83436	+	6.83436i	−0.483262	+	0.483262i
$201$	8.18597	+	8.47659i	0.577393	+	0.597893i
$202$	−3.77732	−	1.01213i	−0.265772	−	0.0712133i
$203$	−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
$206$	1.50910	−	0.404361i	0.105144	−	0.0281732i
$207$	−3.81650	−	7.17733i	−0.265265	−	0.498859i
$208$		0			0
$209$			9.23947i			0.639107i
$210$	−0.679404	+	2.36948i	−0.0468833	+	0.163510i
$211$	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
$213$	4.86389	+	19.5069i	0.333269	+	1.33659i
$214$	−1.19090	+	4.44451i	−0.0814084	+	0.303820i
$215$	−4.99274	+	18.6332i	−0.340502	+	1.27077i
$216$	4.74965	+	5.27460i	0.323173	+	0.358891i
$217$	2.64984	+	4.58965i	0.179883	+	0.311566i
$218$	−1.11855	+	1.93739i	−0.0757580	+	0.131217i
$219$	21.5038	+	6.16580i	1.45309	+	0.416646i
$220$			12.2238i			0.824129i
$221$		0			0
$222$	−1.13062	−	0.679324i	−0.0758821	−	0.0455932i
$223$	−27.3497	+	7.32834i	−1.83147	+	0.490742i	−0.998080	−	0.0619383i	$-0.980272\pi$
$223$	−27.3497	+	7.32834i	−1.83147	+	0.490742i	−0.833393	+	0.552680i	$0.813605\pi$
$224$	−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
$227$	7.10455	+	1.90366i	0.471546	+	0.126350i	0.486763	−	0.873534i	$-0.338177\pi$
$227$	7.10455	+	1.90366i	0.471546	+	0.126350i	−0.0152176	+	0.999884i	$0.504844\pi$
$228$	−11.5146	+	11.1198i	−0.762574	+	0.736428i
$229$	−11.4094	+	11.4094i	−0.753951	+	0.753951i	−0.975214	−	0.221263i	$-0.928982\pi$
$229$	−11.4094	+	11.4094i	−0.753951	+	0.753951i	0.221263	+	0.975214i	$0.428982\pi$
$230$	−2.87401	+	1.65931i	−0.189507	+	0.109412i
$231$	1.82985	+	3.30104i	0.120395	+	0.217192i
$232$	0.950001	+	3.54545i	0.0623706	+	0.232770i
$233$	18.1554			1.18940			0.594700	−	0.803947i	$-0.297271\pi$
$233$	18.1554			1.18940			0.594700	+	0.803947i	$0.297271\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	−4.85866	−	18.1328i	−0.316272	−	1.18034i
$237$	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	$-0.846737\pi$
$239$	−6.54262	+	6.54262i	−0.423207	+	0.423207i	0.463099	+	0.886306i	$0.346737\pi$
$240$	−14.1582	+	13.6728i	−0.913908	+	0.882574i
$241$	26.7340	+	7.16336i	1.72209	+	0.461433i	0.978337	−	0.207021i	$-0.0663767\pi$
$241$	26.7340	+	7.16336i	1.72209	+	0.461433i	0.743754	+	0.668453i	$0.233043\pi$
$242$	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
$245$	18.9639	−	5.08137i	1.21156	−	0.324637i
$246$	−3.56147	−	2.13988i	−0.227071	−	0.136434i
$247$		0			0
$248$		−	6.23009i		−	0.395611i
$249$	10.8058	+	3.09836i	0.684791	+	0.196351i
$250$	1.27104	−	2.20150i	0.0803874	−	0.139235i
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	0.940761	−	0.339071i	$-0.110113\pi$
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	−0.764025	+	0.645187i	$0.776779\pi$
$252$	−1.91164	+	6.25328i	−0.120422	+	0.393920i
$253$	−1.31516	+	4.90825i	−0.0826834	+	0.308579i
$254$	−0.710965	+	2.65336i	−0.0446099	+	0.166486i
$255$	−8.59385	−	34.4661i	−0.538168	−	2.15835i
$256$	−3.48092	−	6.02913i	−0.217557	−	0.376821i
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	−0.739990	−	0.672618i	$-0.765170\pi$
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	0.952499	+	0.304541i	$0.0985030\pi$
$258$	0.934023	−	3.25749i	0.0581497	−	0.202802i
$259$		−	2.51073i		−	0.156009i
$260$		0			0
$261$	7.11751	−	3.78469i	0.440563	−	0.234266i
$262$	−6.31236	+	1.69139i	−0.389979	+	0.104495i
$263$	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
$266$	1.94902	+	0.522238i	0.119502	+	0.0320205i
$267$	5.14245	+	5.32502i	0.314713	+	0.325886i
$268$	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
$271$	−4.57652	−	17.0798i	−0.278004	−	1.03753i	−0.953801	−	0.300438i	$-0.902867\pi$
$271$	−4.57652	−	17.0798i	−0.278004	−	1.03753i	0.675797	−	0.737087i	$-0.263799\pi$
$272$	19.2992			1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	−3.43423	−	12.8167i	−0.207092	−	0.772876i
$276$	−7.69967	+	4.26813i	−0.463466	+	0.256911i
$277$	19.6593	−	11.3503i	1.18122	−	0.681975i	0.224920	−	0.974377i	$-0.427788\pi$
$277$	19.6593	−	11.3503i	1.18122	−	0.681975i	0.956295	+	0.292402i	$0.0944546\pi$
$278$	1.34385	−	1.34385i	0.0805989	−	0.0805989i
$279$	−13.3317	+	3.07825i	−0.798151	+	0.184290i
$280$	5.32786	+	1.42759i	0.318400	+	0.0853151i
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	0.914679	−	0.404181i	$-0.132443\pi$
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	−0.404181	+	0.914679i	$0.632443\pi$
$282$	1.92655	+	0.0336025i	0.114724	+	0.00200100i
$283$	6.15361	+	3.55279i	0.365794	+	0.211192i	0.671620	−	0.740896i	$-0.265599\pi$
$283$	6.15361	+	3.55279i	0.365794	+	0.211192i	−0.305825	+	0.952088i	$0.598932\pi$
$284$	21.0306	−	5.63513i	1.24794	−	0.334384i
$285$	15.2729	−	25.4192i	0.904690	−	1.50570i
$286$		0			0
$287$		−	7.90886i		−	0.466845i
$288$	8.52269	−	7.94796i	0.502205	−	0.468338i
$289$	−8.91483	+	15.4409i	−0.524402	+	0.908291i
$290$	−1.64548	−	2.85006i	−0.0966260	−	0.167361i
$291$	−20.6167	+	5.14061i	−1.20857	+	0.301348i
$292$	6.27032	−	23.4012i	0.366943	−	1.36945i
$293$	−4.11392	+	15.3534i	−0.240338	+	0.896953i	0.735332	+	0.677707i	$0.237026\pi$
$293$	−4.11392	+	15.3534i	−0.240338	+	0.896953i	−0.975670	+	0.219245i	$0.929640\pi$
$294$	−3.34645	+	0.834411i	−0.195169	+	0.0486638i
$295$	17.3885	+	30.1178i	1.01240	+	1.75352i
$296$	−1.47576	+	2.55609i	−0.0857768	+	0.148570i
$297$	−9.53130	+	2.02633i	−0.553062	+	0.117580i
$298$			8.04031i			0.465763i
$299$		0			0
$300$	11.8396	−	19.7050i	0.683558	−	1.13767i
$301$	6.23070	−	1.66951i	0.359131	−	0.0962289i
$302$	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
$305$	−8.93755	−	2.39481i	−0.511763	−	0.137126i
$306$	1.40386	+	6.08006i	0.0802534	+	0.347574i
$307$	−14.3846	+	14.3846i	−0.820970	+	0.820970i	−0.986247	−	0.165277i	$-0.947148\pi$
$307$	−14.3846	+	14.3846i	−0.820970	+	0.820970i	0.165277	+	0.986247i	$0.447148\pi$
$308$	3.53987	−	2.04374i	0.201703	−	0.116453i
$309$	−6.71521	+	3.72242i	−0.382015	+	0.211761i
$310$	1.44572	+	5.39552i	0.0821116	+	0.306445i
$311$	−7.62181			−0.432193			−0.216097	−	0.976372i	$-0.569333\pi$
$311$	−7.62181			−0.432193			−0.216097	+	0.976372i	$0.569333\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	−1.43018	−	5.33751i	−0.0807099	−	0.301213i
$315$	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	$-0.669578\pi$
$317$	6.29415	−	6.29415i	0.353515	−	0.353515i	0.861416	+	0.507901i	$0.169578\pi$
$318$	1.04377	+	1.08082i	0.0585315	+	0.0606095i
$319$	−4.86734	−	1.30420i	−0.272518	−	0.0730211i
$320$	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
$323$	−28.0864	+	7.52572i	−1.56277	+	0.418743i
$324$	−13.9963	−	9.43958i	−0.777575	−	0.524421i
$325$		0			0
$326$		−	1.21818i		−	0.0674689i
$327$	3.03023	−	10.5682i	0.167572	−	0.584422i
$328$	−4.64868	+	8.05175i	−0.256680	+	0.444583i
$329$	1.83387	+	3.17636i	0.101105	+	0.175118i
$330$	0.962439	+	3.85991i	0.0529805	+	0.212481i
$331$	4.16094	−	15.5288i	0.228706	−	0.853541i	−0.752180	−	0.658958i	$-0.770998\pi$
$331$	4.16094	−	15.5288i	0.228706	−	0.853541i	0.980886	−	0.194584i	$-0.0623356\pi$
$332$	3.15088	−	11.7593i	0.172927	−	0.645373i
$333$	6.19893	+	1.89502i	0.339699	+	0.103847i
$334$	0.923981	+	1.60038i	0.0505580	+	0.0875690i
$335$	−11.8211	+	20.4747i	−0.645853	+	1.11865i
$336$	6.32664	+	1.81404i	0.345146	+	0.0989642i
$337$			28.3556i			1.54463i	0.635243	+	0.772313i	$0.280900\pi$
$337$			28.3556i			1.54463i	−0.635243	+	0.772313i	$0.719100\pi$
$338$		0			0
$339$	19.3195	+	11.6080i	1.04929	+	0.630457i
$340$	−37.1583	+	9.95653i	−2.01519	+	0.539968i
$341$	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
$344$	−7.32457	−	1.96261i	−0.394914	−	0.105817i
$345$	11.7316	−	11.3294i	0.631607	−	0.609952i
$346$	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
$349$	−7.74319	−	28.8980i	−0.414483	−	1.54687i	−0.785868	−	0.618394i	$-0.787784\pi$
$349$	−7.74319	−	28.8980i	−0.414483	−	1.54687i	0.371385	−	0.928479i	$-0.378883\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	3.28082	+	12.2442i	0.174620	+	0.651692i	0.996616	+	0.0821982i	$0.0261940\pi$
$353$	3.28082	+	12.2442i	0.174620	+	0.651692i	−0.821996	+	0.569494i	$0.807139\pi$
$354$	−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
$357$	−8.54414	+	8.25120i	−0.452204	+	0.436700i
$358$	1.48657	+	0.398325i	0.0785676	+	0.0210521i
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.996870	−	0.0790589i	$-0.974808\pi$
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.0790589	−	0.996870i	$-0.525192\pi$
$360$	−7.54600	+	12.0768i	−0.397709	+	0.636505i
$361$	−4.56807	−	2.63738i	−0.240425	−	0.138809i
$362$	−0.717426	+	0.192234i	−0.0377071	+	0.0101036i
$363$	−11.1102	−	6.67547i	−0.583133	−	0.350371i
$364$		0			0
$365$			44.8813i			2.34919i
$366$	1.56248	+	0.448012i	0.0816722	+	0.0234180i
$367$	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
$369$	19.5268	+	5.96937i	1.01652	+	0.310753i
$370$	0.684915	−	2.55614i	0.0356071	−	0.132887i
$371$	−0.740245	+	2.76263i	−0.0384316	+	0.143429i
$372$	3.58497	+	14.3777i	0.185872	+	0.745451i
$373$	−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
$375$	−3.44331	+	12.0088i	−0.177812	+	0.620134i
$376$		−	4.31166i		−	0.222357i
$377$		0			0
$378$	−0.111288	+	2.12511i	−0.00572404	+	0.109304i
$379$	3.83602	−	1.02786i	0.197043	−	0.0527975i	−0.158948	−	0.987287i	$-0.550810\pi$
$379$	3.83602	−	1.02786i	0.197043	−	0.0527975i	0.355991	+	0.934489i	$0.384143\pi$
$380$	−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
$383$	25.7044	+	6.88748i	1.31344	+	0.351934i	0.846515	−	0.532365i	$-0.178697\pi$
$383$	25.7044	+	6.88748i	1.31344	+	0.351934i	0.466921	+	0.884299i	$0.345363\pi$
$384$	−11.5406	−	11.9504i	−0.588931	−	0.609839i
$385$	−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
$388$	5.95573	+	22.2271i	0.302356	+	1.12841i
$389$	−6.17335			−0.313001			−0.156501	−	0.987678i	$-0.550021\pi$
$389$	−6.17335			−0.313001			−0.156501	+	0.987678i	$0.550021\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	1.99745	+	7.45460i	0.100887	+	0.376514i
$393$	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
$396$	2.37417	+	10.2824i	0.119306	+	0.516710i
$397$	−23.0477	−	6.17560i	−1.15673	−	0.309945i	−0.371071	−	0.928605i	$-0.621009\pi$
$397$	−23.0477	−	6.17560i	−1.15673	−	0.309945i	−0.785659	+	0.618660i	$0.787676\pi$
$398$	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
$401$	−22.4109	+	6.00499i	−1.11915	+	0.299875i	−0.770539	−	0.637393i	$-0.780013\pi$
$401$	−22.4109	+	6.00499i	−1.11915	+	0.299875i	−0.348610	+	0.937268i	$0.613346\pi$
$402$	2.13901	−	3.56002i	0.106684	−	0.177558i
$403$		0			0
$404$		−	20.8129i		−	1.03548i
$405$	29.5716	+	10.1806i	1.46942	+	0.505877i
$406$	−0.550228	+	0.953023i	−0.0273074	+	0.0472978i
$407$	−2.02598	−	3.50910i	−0.100424	−	0.173940i
$408$	13.5484	−	3.37818i	0.670746	−	0.167245i
$409$	−3.25292	+	12.1401i	−0.160847	+	0.600288i	0.837687	+	0.546151i	$0.183907\pi$
$409$	−3.25292	+	12.1401i	−0.160847	+	0.600288i	−0.998534	+	0.0541371i	$0.982759\pi$
$410$	2.15750	−	8.05189i	0.106551	−	0.397655i
$411$	12.6630	−	3.15743i	0.624622	−	0.155744i
$412$	4.15753	+	7.20106i	0.204827	+	0.354771i
$413$	5.81450	−	10.0710i	0.286113	−	0.495562i
$414$	−2.09528	+	1.95398i	−0.102977	+	0.0960329i
$415$			22.5532i			1.10709i
$416$		0			0
$417$	−4.81024	+	8.00582i	−0.235558	+	0.392047i
$418$	3.14544	−	0.842818i	0.153848	−	0.0412236i
$419$	−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	0.890471	−	0.455040i	$-0.150375\pi$
$421$	8.93430	+	8.93430i	0.435431	+	0.435431i	−0.455040	+	0.890471i	$0.650375\pi$
$422$	−2.72594	−	0.730414i	−0.132697	−	0.0355560i
$423$	−9.22649	+	2.13036i	−0.448607	+	0.103582i
$424$	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
$427$	0.800795	+	2.98861i	0.0387532	+	0.144629i
$428$	−24.4891			−1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	5.49370	+	20.5028i	0.264622	+	0.987583i	0.962481	+	0.271348i	$0.0874694\pi$
$431$	5.49370	+	20.5028i	0.264622	+	0.987583i	−0.697859	+	0.716235i	$0.745864\pi$
$432$	−9.25399	+	14.2511i	−0.445233	+	0.685658i
$433$	−1.60537	+	0.926859i	−0.0771490	+	0.0445420i	−0.538078	−	0.842895i	$-0.680850\pi$
$433$	−1.60537	+	0.926859i	−0.0771490	+	0.0445420i	0.460929	+	0.887437i	$0.347516\pi$
$434$	1.32076	−	1.32076i	0.0633986	−	0.0633986i
$435$	11.2349	+	11.6338i	0.538673	+	0.557798i
$436$	−11.5007	−	3.08159i	−0.550782	−	0.147582i
$437$	−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	0.767236	−	0.641365i	$-0.221632\pi$
$439$	12.4753	+	7.20264i	0.595415	+	0.343763i	−0.171820	+	0.985128i	$0.554965\pi$
$440$	8.59840	−	2.30393i	0.409913	−	0.109836i
$441$	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	$-0.177119\pi$
$444$	1.93489	−	6.74811i	0.0918260	−	0.320251i
$445$	−7.42603	+	12.8623i	−0.352027	+	0.609729i
$446$	4.98965	+	8.64232i	0.236267	+	0.409226i
$447$	−9.55963	−	38.3394i	−0.452155	−	1.81339i
$448$	1.55521	−	5.80413i	0.0734769	−	0.274220i
$449$	6.36268	−	23.7458i	0.300273	−	1.12064i	−0.636665	−	0.771141i	$-0.719687\pi$
$449$	6.36268	−	23.7458i	0.300273	−	1.12064i	0.936938	−	0.349495i	$-0.113647\pi$
$450$	2.18712	−	7.15442i	0.103102	−	0.337263i
$451$	−6.38188	−	11.0537i	−0.300511	−	0.520501i
$452$	12.2044	−	21.1387i	0.574048	−	0.994281i
$453$	−15.5845	−	4.46857i	−0.732225	−	0.209952i
$454$		−	2.59229i		−	0.121662i
$455$		0			0
$456$	9.99211	+	6.00368i	0.467923	+	0.281148i
$457$	−6.53825	+	1.75192i	−0.305847	+	0.0819513i	−0.408478	−	0.912768i	$-0.633940\pi$
$457$	−6.53825	+	1.75192i	−0.305847	+	0.0819513i	0.102632	+	0.994719i	$0.467274\pi$
$458$	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
$461$	−11.9685	−	3.20695i	−0.557429	−	0.149363i	−0.0309044	−	0.999522i	$-0.509839\pi$
$461$	−11.9685	−	3.20695i	−0.557429	−	0.149363i	−0.526525	+	0.850160i	$0.676505\pi$
$462$	0.956871	−	0.924064i	0.0445177	−	0.0429914i
$463$	−6.97385	+	6.97385i	−0.324102	+	0.324102i	−0.850339	−	0.526236i	$-0.823603\pi$
$463$	−6.97385	+	6.97385i	−0.324102	+	0.324102i	0.526236	+	0.850339i	$0.323603\pi$
$464$	−7.60980	+	4.39352i	−0.353276	+	0.203964i
$465$	−13.3089	−	24.0091i	−0.617184	−	1.11339i
$466$	−1.65612	−	6.18074i	−0.0767185	−	0.286317i
$467$	−9.19934			−0.425695			−0.212847	−	0.977085i	$-0.568274\pi$
$467$	−9.19934			−0.425695			−0.212847	+	0.977085i	$0.568274\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	1.00054	+	3.73407i	0.0461515	+	0.172240i
$471$	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
$474$	0.483064	−	0.466501i	0.0221878	−	0.0214271i
$475$	33.6732	+	9.02270i	1.54503	+	0.413990i
$476$	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
$479$	22.1676	−	5.93980i	1.01287	−	0.271396i	0.286039	−	0.958218i	$-0.407661\pi$
$479$	22.1676	−	5.93980i	1.01287	−	0.271396i	0.726826	+	0.686821i	$0.240995\pi$
$480$	20.0412	+	12.0416i	0.914750	+	0.549621i
$481$		0			0
$482$		−	9.75464i		−	0.444312i
$483$	−5.24229	−	1.50313i	−0.238533	−	0.0683947i
$484$	−7.01850	+	12.1564i	−0.319023	+	0.552563i
$485$	−21.3148	−	36.9183i	−0.967854	−	1.67637i
$486$	−5.16285	−	1.87874i	−0.234192	−	0.0852213i
$487$	7.62733	−	28.4656i	0.345627	−	1.28990i	−0.546250	−	0.837622i	$-0.683945\pi$
$487$	7.62733	−	28.4656i	0.345627	−	1.28990i	0.891878	−	0.452277i	$-0.149388\pi$
$488$	0.941384	−	3.51329i	0.0426144	−	0.159039i
$489$	1.44838	+	5.80879i	0.0654978	+	0.262682i
$490$	−3.45975	−	5.99247i	−0.156296	−	0.270712i
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	−0.639716	−	0.768611i	$-0.720948\pi$
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	0.985495	+	0.169705i	$0.0542814\pi$
$492$	6.09496	−	21.2567i	0.274782	−	0.958326i
$493$		−	15.8582i		−	0.714215i
$494$		0			0
$495$	−9.17859	−	17.2613i	−0.412547	−	0.775838i
$496$	14.4063	−	3.86016i	0.646863	−	0.173326i
$497$	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	−0.912084	−	0.410004i	$-0.865527\pi$
$499$	−29.5332	−	29.5332i	−1.32209	−	1.32209i	−0.410004	−	0.912084i	$-0.634473\pi$
$500$	13.0684	+	3.50168i	0.584439	+	0.156600i
$501$	−6.30871	−	6.53269i	−0.281852	−	0.291859i
$502$	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
$505$	9.97931	+	37.2433i	0.444073	+	1.65730i
$506$	1.79091			0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	11.4648	+	42.7871i	0.508167	+	1.89651i	0.438011	+	0.898969i	$0.355683\pi$
$509$	11.4648	+	42.7871i	0.508167	+	1.89651i	0.0701558	+	0.997536i	$0.477650\pi$
$510$	−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
$513$	7.91022	−	24.3484i	0.349245	−	1.07501i
$514$	−2.31958	−	0.621529i	−0.102312	−	0.0274145i
$515$	−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
$518$	−0.854741	+	0.229027i	−0.0375552	+	0.0100629i
$519$	−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	$-0.0134873\pi$
$522$	−1.93769	−	2.07781i	−0.0848106	−	0.0909434i
$523$	−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
$525$	13.8175	−	3.44529i	0.603047	−	0.150365i
$526$	2.06445	−	7.70463i	0.0900142	−	0.335938i
$527$	−6.96651	+	25.9994i	−0.303466	+	1.13255i
$528$	10.3062	−	2.56976i	0.448519	−	0.111835i
$529$	7.82890	+	13.5601i	0.340387	+	0.589568i
$530$	−1.50726	+	2.61066i	−0.0654714	+	0.113400i
$531$	20.4764	+	21.9571i	0.888602	+	0.952859i
$532$			10.7390i			0.465595i
$533$		0			0
$534$	1.34373	−	2.23641i	0.0581490	−	0.0967791i
$535$	43.8215	−	11.7419i	1.89457	−	0.507648i
$536$	−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
$539$	−10.2340	−	2.74218i	−0.440808	−	0.118114i
$540$	10.4652	−	32.2130i	0.450351	−	1.38623i
$541$	2.56375	−	2.56375i	0.110224	−	0.110224i	−0.649844	−	0.760068i	$-0.725166\pi$
$541$	2.56375	−	2.56375i	0.110224	−	0.110224i	0.760068	+	0.649844i	$0.225166\pi$
$542$	−5.39710	+	3.11602i	−0.231825	+	0.133844i
$543$	3.19242	−	1.76964i	0.137000	−	0.0759425i
$544$	−5.93348	−	22.1441i	−0.254396	−	0.949419i
$545$	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	$0.335163\pi$
$548$	−3.65808	−	13.6522i	−0.156266	−	0.583191i
$549$	−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
$552$	4.45349	+	4.61161i	0.189553	+	0.196283i
$553$	1.23473	+	0.330846i	0.0525062	+	0.0140690i
$554$	−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
$557$	−3.45636	+	0.926129i	−0.146451	+	0.0392414i	−0.331300	−	0.943526i	$-0.607487\pi$
$557$	−3.45636	+	0.926129i	−0.146451	+	0.0392414i	0.184849	+	0.982767i	$0.440820\pi$
$558$	2.26406	+	4.25780i	0.0958451	+	0.180247i
$559$		0			0
$560$			13.2045i			0.557994i
$561$	−5.28351	+	18.4267i	−0.223070	+	0.777977i
$562$	2.13267	−	3.69389i	0.0899611	−	0.155817i
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	0.995385	−	0.0959647i	$-0.0305936\pi$
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	−0.580800	+	0.814046i	$0.697260\pi$
$564$	2.48105	+	9.95039i	0.104471	+	0.418987i
$565$	−11.7035	+	43.6781i	−0.492370	+	1.83755i
$566$	0.648166	−	2.41899i	0.0272445	−	0.101678i
$567$	−1.99601	−	10.2657i	−0.0838247	−	0.431119i
$568$	−7.92766	−	13.7311i	−0.332637	−	0.576145i
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	−0.948685	−	0.316223i	$-0.897585\pi$
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	0.748200	+	0.663473i	$0.230918\pi$
$570$	−10.0468	−	2.88072i	−0.420813	−	0.120660i
$571$		−	17.9785i		−	0.752375i	−0.926544	−	0.376187i	$-0.877235\pi$
$571$		−	17.9785i		−	0.752375i	0.926544	−	0.376187i	$-0.122765\pi$
$572$		0			0
$573$	−10.0925	−	6.06399i	−0.421619	−	0.253327i
$574$	−2.69245	+	0.721441i	−0.112381	+	0.0301124i
$575$	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	0.827243	−	0.561844i	$-0.189908\pi$
$577$	6.37509	+	6.37509i	0.265398	+	0.265398i	−0.561844	+	0.827243i	$0.689908\pi$
$578$	6.06984	+	1.62641i	0.252472	+	0.0676497i
$579$	−13.8499	+	13.3750i	−0.575582	+	0.555848i
$580$	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
$583$	1.19465	+	4.45849i	0.0494773	+	0.184652i
$584$	−17.6425			−0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	−8.12231	−	30.3129i	−0.335243	−	1.25115i	−0.903605	−	0.428367i	$-0.859089\pi$
$587$	−8.12231	−	30.3129i	−0.335243	−	1.25115i	0.568362	−	0.822779i	$-0.307577\pi$
$588$	−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
$591$	2.84548	−	2.74792i	0.117047	−	0.113034i
$592$	−6.82503	−	1.82876i	−0.280507	−	0.0751616i
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	0.999673	−	0.0255650i	$-0.00813848\pi$
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	−0.0255650	+	0.999673i	$0.508138\pi$
$594$	1.55927	+	3.05995i	0.0639778	+	0.125551i
$595$	−20.6378	−	11.9153i	−0.846069	−	0.488478i
$596$	−41.3341	+	11.0754i	−1.69311	+	0.453668i
$597$	−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	$0.757460\pi$
$600$	−16.0923	−	4.61415i	−0.656964	−	0.188372i
$601$	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
$603$	−5.96693	+	19.5188i	−0.242992	+	0.794867i
$604$	−4.54432	+	16.9596i	−0.184906	+	0.690077i
$605$	6.73042	−	25.1183i	0.273630	−	1.02120i
$606$	−1.63870	−	6.57209i	−0.0665676	−	0.266973i
$607$	−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
$609$	1.49060	−	5.19860i	0.0604022	−	0.210658i
$610$			3.26111i			0.132038i
$611$		0			0
$612$	−29.3229	+	15.5923i	−1.18531	+	0.630280i
$613$	0.571244	−	0.153064i	0.0230723	−	0.00618221i	−0.247264	−	0.968948i	$-0.579532\pi$
$613$	0.571244	−	0.153064i	0.0230723	−	0.00618221i	0.270337	+	0.962766i	$0.412865\pi$
$614$	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
$617$	28.0800	+	7.52400i	1.13046	+	0.302905i	0.775108	−	0.631829i	$-0.217695\pi$
$617$	28.0800	+	7.52400i	1.13046	+	0.302905i	0.355349	+	0.934734i	$0.384362\pi$
$618$	1.87980	+	1.94654i	0.0756166	+	0.0783012i
$619$	−22.7868	+	22.7868i	−0.915881	+	0.915881i	−0.996727	−	0.0808459i	$-0.974238\pi$
$619$	−22.7868	+	22.7868i	−0.915881	+	0.915881i	0.0808459	+	0.996727i	$0.474238\pi$
$620$	−25.7461	+	14.8645i	−1.03399	+	0.596974i
$621$	7.66791	−	11.8086i	0.307703	−	0.473862i
$622$	0.695256	+	2.59473i	0.0278772	+	0.104039i
$623$	4.96634			0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	0.594282	+	2.21789i	0.0237523	+	0.0886448i
$627$	−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
$630$	−4.15999	+	0.960524i	−0.165738	+	0.0382682i
$631$	−39.1937	−	10.5019i	−1.56028	−	0.418075i	−0.627526	−	0.778596i	$-0.715932\pi$
$631$	−39.1937	−	10.5019i	−1.56028	−	0.418075i	−0.932751	+	0.360521i	$0.882599\pi$
$632$	−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
$635$	26.1613	−	7.00990i	1.03818	−	0.278180i
$636$	−4.11858	+	6.85468i	−0.163312	+	0.271806i
$637$		0			0
$638$			1.77598i			0.0703117i
$639$	−25.4662	+	23.7488i	−1.00743	+	0.939489i
$640$	16.6654	−	28.8653i	0.658758	−	1.14100i
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	0.999959	+	0.00901077i	$0.00286825\pi$
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	−0.492176	+	0.870496i	$0.663798\pi$
$642$	−7.73291	+	1.92814i	−0.305194	+	0.0760976i
$643$	0.164018	−	0.612124i	0.00646824	−	0.0241398i	−0.962616	−	0.270869i	$-0.912689\pi$
$643$	0.164018	−	0.612124i	0.00646824	−	0.0241398i	0.969085	+	0.246729i	$0.0793557\pi$
$644$	−1.52861	+	5.70484i	−0.0602356	+	0.224802i
$645$	−32.4195	+	8.08354i	−1.27652	+	0.318289i
$646$	5.12404	+	8.87510i	0.201603	+	0.349186i
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.131794	+	0.991277i	$0.542074\pi$
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.792574	+	0.609776i	$0.791260\pi$
$648$	−4.00191	+	11.6244i	−0.157210	+	0.456649i
$649$		−	18.7675i		−	0.736690i
$650$		0			0
$651$	−4.72758	+	7.86826i	−0.185289	+	0.308381i
$652$	6.26251	−	1.67804i	0.245259	−	0.0657169i
$653$	−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
$656$	−21.4990	−	5.76064i	−0.839394	−	0.224915i
$657$	8.71705	+	37.7532i	0.340085	+	1.47289i
$658$	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
$661$	1.79701	+	6.70655i	0.0698957	+	0.260854i	0.992028	−	0.126021i	$-0.0402208\pi$
$661$	1.79701	+	6.70655i	0.0698957	+	0.260854i	−0.922132	+	0.386876i	$0.873554\pi$
$662$	−5.66611			−0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	−5.14911	−	19.2167i	−0.199674	−	0.745194i
$666$	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
$669$	−34.0680	−	35.2776i	−1.31715	−	1.36391i
$670$	8.04861	+	2.15662i	0.310945	+	0.0833174i
$671$	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	0.868828	−	0.495114i	$-0.164874\pi$
$673$	22.6855	+	13.0975i	0.874460	+	0.504870i	0.00563228	+	0.999984i	$0.498207\pi$
$674$	9.65322	−	2.58657i	0.371828	−	0.0996311i
$675$	−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	$-0.138466\pi$
$678$	2.18945	−	7.63589i	0.0840852	−	0.293255i
$679$	−7.12739	+	12.3450i	−0.273524	+	0.473758i
$680$	14.0071	+	24.2610i	0.537149	+	0.930369i
$681$	3.08213	+	12.3611i	0.118108	+	0.473677i
$682$	0.780190	−	2.91171i	0.0298750	−	0.111495i
$683$	1.97300	−	7.36335i	0.0754949	−	0.281751i	−0.917850	−	0.396927i	$-0.870077\pi$
$683$	1.97300	−	7.36335i	0.0754949	−	0.281751i	0.993345	+	0.115176i	$0.0367433\pi$
$684$	−26.5144	−	8.10549i	−1.01380	−	0.309921i
$685$	13.0918	+	22.6757i	0.500212	+	0.866392i
$686$	−2.59028	+	4.48650i	−0.0988975	+	0.171296i
$687$	−26.8646	−	7.70291i	−1.02495	−	0.293884i
$688$		−	18.1532i		−	0.692084i
$689$		0			0
$690$	−4.92706	−	2.96039i	−0.187570	−	0.112700i
$691$	−15.4088	+	4.12878i	−0.586179	+	0.157066i	−0.539707	−	0.841853i	$-0.681465\pi$
$691$	−15.4088	+	4.12878i	−0.586179	+	0.157066i	−0.0464729	+	0.998920i	$0.514798\pi$
$692$	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
$695$	−18.0998	−	4.84983i	−0.686565	−	0.183965i
$696$	−4.57317	+	4.41637i	−0.173345	+	0.167402i
$697$	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
$700$	−3.99159	−	14.8968i	−0.150868	−	0.563047i
$701$	30.3059			1.14464			0.572319	−	0.820031i	$-0.306044\pi$
$701$	30.3059			1.14464			0.572319	+	0.820031i	$0.306044\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	−2.50989	−	9.36704i	−0.0945951	−	0.353034i
$705$	−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
$708$	23.3889	−	22.5870i	0.879008	−	0.848871i
$709$	32.8514	+	8.80249i	1.23376	+	0.330585i	0.816042	−	0.577993i	$-0.196164\pi$
$709$	32.8514	+	8.80249i	1.23376	+	0.330585i	0.417717	+	0.908577i	$0.362830\pi$
$710$	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
$713$	−11.9372	+	3.19855i	−0.447050	+	0.119787i
$714$	3.58839	+	2.15606i	0.134292	+	0.0806884i
$715$		0			0
$716$			8.19093i			0.306110i
$717$	−15.4053	−	4.41718i	−0.575322	−	0.164963i
$718$	−5.08050	+	8.79968i	−0.189602	+	0.328401i
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	0.782960	−	0.622072i	$-0.213709\pi$
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	−0.930210	+	0.367027i	$0.880376\pi$
$720$	−32.6017	−	9.96640i	−1.21499	−	0.371426i
$721$	−1.33316	+	4.97544i	−0.0496496	+	0.185295i
$722$	−0.481159	+	1.79571i	−0.0179069	+	0.0668294i
$723$	11.5979	+	46.5140i	0.431331	+	1.72988i
$724$	−1.97649	−	3.42339i	−0.0734558	−	0.127229i
$725$	−9.50629	+	16.4654i	−0.353055	+	0.611509i
$726$	−1.25910	+	4.39123i	−0.0467296	+	0.162974i
$727$		−	24.6824i		−	0.915420i	−0.889102	−	0.457710i	$-0.848670\pi$
$727$		−	24.6824i		−	0.915420i	0.889102	−	0.457710i	$-0.151330\pi$
$728$		0			0
$729$	26.8523	+	2.82014i	0.994530	+	0.104450i
$730$	15.2792	−	4.09404i	0.565507	−	0.151527i
$731$	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	−0.946918	−	0.321476i	$-0.895821\pi$
$733$	−34.3405	−	34.3405i	−1.26839	−	1.26839i	−0.321476	−	0.946918i	$-0.604179\pi$
$734$	−7.87731	−	2.11072i	−0.290757	−	0.0779081i
$735$	23.6223	+	24.4610i	0.871323	+	0.902257i
$736$	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
$739$	−10.0551	−	37.5261i	−0.369882	−	1.38042i	−0.860680	−	0.509146i	$-0.829961\pi$
$739$	−10.0551	−	37.5261i	−0.369882	−	1.38042i	0.490798	−	0.871273i	$-0.336705\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	−13.4913	−	50.3503i	−0.494949	−	1.84717i	−0.530316	−	0.847800i	$-0.677927\pi$
$743$	−13.4913	−	50.3503i	−0.494949	−	1.84717i	0.0353674	−	0.999374i	$-0.488740\pi$
$744$	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
$747$	4.38039	+	18.9713i	0.160270	+	0.694122i
$748$	20.0526	+	5.37308i	0.733195	+	0.196459i
$749$	−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	$-0.976470\pi$
$751$	−42.7471	−	24.6801i	−1.55986	−	0.900588i	−0.562595	−	0.826733i	$-0.690197\pi$
$752$	9.97017	−	2.67150i	0.363575	−	0.0974196i
$753$	−4.99555	+	8.31423i	−0.182048	+	0.302987i
$754$		0			0
$755$		−	32.5270i		−	1.18378i
$756$	−11.0782	+	2.35521i	−0.402911	+	0.0856580i
$757$	−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
$759$	−8.53976	+	2.12932i	−0.309974	+	0.0772895i
$760$	−6.05310	+	22.5905i	−0.219569	+	0.819443i
$761$	−9.96144	+	37.1766i	−0.361102	+	1.34765i	0.511527	+	0.859267i	$0.329080\pi$
$761$	−9.96144	+	37.1766i	−0.361102	+	1.34765i	−0.872629	+	0.488384i	$0.837587\pi$
$762$	−4.61653	+	1.15109i	−0.167239	+	0.0416997i
$763$	−3.68783	−	6.38751i	−0.133508	−	0.231243i
$764$	−6.37559	+	11.0428i	−0.230661	+	0.399516i
$765$	44.9953	−	41.9610i	1.62681	−	1.51710i
$766$		−	9.37896i		−	0.338876i
$767$		0			0
$768$	6.21032	−	10.3360i	0.224096	−	0.372969i
$769$	−2.75634	+	0.738559i	−0.0993962	+	0.0266331i	−0.308174	−	0.951330i	$-0.599718\pi$
$769$	−2.75634	+	0.738559i	−0.0993962	+	0.0266331i	0.208778	+	0.977963i	$0.433051\pi$
$770$	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
$773$	−6.20770	−	1.66335i	−0.223275	−	0.0598265i	0.145447	−	0.989366i	$-0.453538\pi$
$773$	−6.20770	−	1.66335i	−0.223275	−	0.0598265i	−0.368722	+	0.929540i	$0.620205\pi$
$774$	5.71902	−	1.32050i	0.205566	−	0.0474643i
$775$	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
$778$	0.563129	+	2.10162i	0.0201891	+	0.0753469i
$779$	33.5341			1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	1.45873	+	5.44405i	0.0521640	+	0.194679i
$783$	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
$786$	−7.86296	−	8.14212i	−0.280463	−	0.290420i
$787$	−14.6513	−	3.92580i	−0.522262	−	0.139940i	−0.0119493	−	0.999929i	$-0.503804\pi$
$787$	−14.6513	−	3.92580i	−0.522262	−	0.139940i	−0.510313	+	0.859989i	$0.670470\pi$
$788$	−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
$791$	14.6054	−	3.91350i	0.519308	−	0.139148i
$792$	6.78531	−	3.60804i	0.241105	−	0.128206i
$793$		0			0
$794$			8.40957i			0.298444i
$795$	4.08327	−	14.2408i	0.144819	−	0.505067i
$796$	−17.2039	+	29.7980i	−0.609775	+	1.05616i
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	0.879672	−	0.475582i	$-0.157762\pi$
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	−0.851702	+	0.524027i	$0.824429\pi$
$798$	0.845534	+	3.39106i	0.0299316	+	0.120042i
$799$	−4.82131	+	17.9934i	−0.170566	+	0.636560i
$800$	−7.11374	+	26.5489i	−0.251509	+	0.938644i
$801$	−3.74845	+	12.2618i	−0.132445	+	0.433248i
$802$	4.08862	+	7.08170i	0.144374	+	0.250063i
$803$	12.1102	−	20.9754i	0.427359	−	0.740207i
$804$	21.2480	+	6.09247i	0.749360	+	0.214865i
$805$		−	10.9414i		−	0.385633i
$806$		0			0
$807$	−38.7542	−	23.2852i	−1.36421	−	0.819677i
$808$	−14.6401	+	3.92280i	−0.515037	+	0.138004i
$809$	−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	0.999186	+	0.0403387i	$0.0128437\pi$
$811$	29.6037	+	29.6037i	1.03952	+	1.03952i	0.0403387	+	0.999186i	$0.487156\pi$
$812$	−5.65729	−	1.51587i	−0.198532	−	0.0531965i
$813$	22.0307	−	21.2754i	0.772651	−	0.746160i
$814$	−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
$817$	7.07884	+	26.4186i	0.247657	+	0.924269i
$818$	4.42964			0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	4.81637	+	17.9749i	0.168093	+	0.627330i	0.997625	+	0.0688721i	$0.0219400\pi$
$821$	4.81637	+	17.9749i	0.168093	+	0.627330i	−0.829533	+	0.558458i	$0.811393\pi$
$822$	−2.23001	−	4.02293i	−0.0777807	−	0.140316i
$823$	−0.447230	+	0.258209i	−0.0155895	+	0.00900059i	−0.507774	−	0.861490i	$-0.669532\pi$
$823$	−0.447230	+	0.258209i	−0.0155895	+	0.00900059i	0.492185	+	0.870491i	$0.336198\pi$
$824$	4.28172	−	4.28172i	0.149161	−	0.149161i
$825$	16.5319	−	15.9651i	0.575566	−	0.555832i
$826$	−3.95892	−	1.06079i	−0.137748	−	0.0369096i
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	0.238472	−	0.971149i	$-0.423354\pi$
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	−0.971149	+	0.238472i	$0.923354\pi$
$828$	−12.9314	−	8.07994i	−0.449396	−	0.280797i
$829$	1.46119	+	0.843616i	0.0507491	+	0.0293000i	0.525160	−	0.851004i	$-0.324006\pi$
$829$	1.46119	+	0.843616i	0.0507491	+	0.0293000i	−0.474411	+	0.880304i	$0.657339\pi$
$830$	7.67790	−	2.05729i	0.266504	−	0.0714094i
$831$	33.7030	+	20.2502i	1.16914	+	0.702471i
$832$		0			0
$833$		−	33.3430i		−	1.15527i
$834$	3.16425	+	0.907288i	0.109569	+	0.0314168i
$835$	9.11018	−	15.7793i	0.315271	−	0.546065i
$836$	8.66562	+	15.0093i	0.299707	+	0.519107i
$837$	−15.8583	−	17.6110i	−0.548143	−	0.608726i
$838$	−2.44549	+	9.12670i	−0.0844781	+	0.315277i
$839$	−2.80444	+	10.4663i	−0.0968199	+	0.361337i	−0.997289	−	0.0735829i	$-0.976557\pi$
$839$	−2.80444	+	10.4663i	−0.0968199	+	0.361337i	0.900469	+	0.434920i	$0.143223\pi$
$840$	2.31136	+	9.26984i	0.0797495	+	0.319840i
$841$	−10.8898	−	18.8618i	−0.375512	−	0.650406i
$842$	2.22657	−	3.85653i	0.0767326	−	0.132905i
$843$	−5.77751	+	20.1496i	−0.198988	+	0.693989i
$844$		−	15.0198i		−	0.517004i
$845$		0			0
$846$	1.56688	+	2.94669i	0.0538706	+	0.101309i
$847$	−8.39923	+	2.25057i	−0.288601	+	0.0773304i
$848$	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
$851$	5.65526	+	1.51532i	0.193860	+	0.0519446i
$852$	26.1966	+	27.1267i	0.897482	+	0.929346i
$853$	30.1644	−	30.1644i	1.03281	−	1.03281i	0.0333670	−	0.999443i	$-0.489377\pi$
$853$	30.1644	−	30.1644i	1.03281	−	1.03281i	0.999443	−	0.0333670i	$-0.0106230\pi$
$854$	0.944378	−	0.545237i	0.0323160	−	0.0186576i
$855$	51.3321	+	1.79120i	1.75552	+	0.0612577i
$856$	4.61568	+	17.2259i	0.157761	+	0.588771i
$857$	−36.7949			−1.25689			−0.628444	−	0.777855i	$-0.716308\pi$
$857$	−36.7949			−1.25689			−0.628444	+	0.777855i	$0.716308\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	9.36529	+	34.9518i	0.319354	+	1.19185i
$861$	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	$-0.959536\pi$
$863$	−25.4155	+	25.4155i	−0.865153	+	0.865153i	0.126779	+	0.991931i	$0.459536\pi$
$864$	19.1970	+	6.23663i	0.653094	+	0.212175i
$865$	−47.8355	−	12.8175i	−1.62646	−	0.435808i
$866$	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
$869$	1.99268	−	0.533937i	0.0675971	−	0.0181126i
$870$	2.93571	−	4.88599i	0.0995299	−	0.165651i
$871$		0			0
$872$			8.67054i			0.293622i
$873$	−25.1000	−	26.9150i	−0.849505	−	0.910934i
$874$	−2.35262	+	4.07485i	−0.0795784	+	0.137834i
$875$	4.19056	+	7.25826i	0.141667	+	0.245374i
$876$	40.7152	−	10.1520i	1.37564	−	0.343005i
$877$	−4.74247	+	17.6992i	−0.160142	+	0.597658i	0.838468	+	0.544951i	$0.183452\pi$
$877$	−4.74247	+	17.6992i	−0.160142	+	0.597658i	−0.998610	+	0.0527071i	$0.983215\pi$
$878$	1.31404	−	4.90406i	0.0443467	−	0.165504i
$879$	−26.7130	+	6.66068i	−0.901007	+	0.224659i
$880$	10.6551	+	18.4552i	0.359184	+	0.622125i
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	−0.475586	−	0.879669i	$-0.657764\pi$
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	0.999609	−	0.0279654i	$-0.00890283\pi$
$882$	−4.07416	−	4.36877i	−0.137184	−	0.147104i
$883$			9.56660i			0.321942i	0.986959	+	0.160971i	$0.0514625\pi$
$883$			9.56660i			0.321942i	−0.986959	+	0.160971i	$0.948537\pi$
$884$		0			0
$885$	−31.0229	+	51.6323i	−1.04282	+	1.73560i
$886$	−7.56891	+	2.02808i	−0.254282	+	0.0681348i
$887$	−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
$890$	5.05616	+	1.35479i	0.169483	+	0.0454128i
$891$	−11.0734	−	12.7371i	−0.370973	−	0.426710i
$892$	−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
$895$	−3.92737	−	14.6571i	−0.131277	−	0.489934i
$896$	−11.1454			−0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	−3.17189	−	11.8377i	−0.105789	−	0.394808i
$900$	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
$903$	7.76123	+	8.03678i	0.258278	+	0.267447i
$904$	−17.1696	−	4.60057i	−0.571051	−	0.153013i
$905$	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	0.475575	−	0.879675i	$-0.342240\pi$
$907$	−1.45939	−	0.842581i	−0.0484584	−	0.0279775i	−0.524033	+	0.851698i	$0.675573\pi$
$908$	13.3266	−	3.57085i	0.442259	−	0.118503i
$909$	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	$0.740481\pi$
$912$	−7.69167	+	26.8254i	−0.254697	+	0.888277i
$913$	6.08545	−	10.5403i	0.201399	−	0.348834i
$914$	1.19283	+	2.06604i	0.0394553	+	0.0683386i
$915$	−3.87734	−	15.5503i	−0.128181	−	0.514076i
$916$	−7.83348	+	29.2350i	−0.258826	+	0.965950i
$917$	5.57646	−	20.8116i	0.184151	−	0.687260i
$918$	−8.03165	+	7.23231i	−0.265084	+	0.238702i
$919$	−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
$921$	−33.8700	−	9.71159i	−1.11606	−	0.320008i
$922$			4.36704i			0.143821i
$923$		0			0
$924$	6.06857	+	3.64625i	0.199641	+	0.119953i
$925$	−14.7674	+	3.95690i	−0.485548	+	0.130102i
$926$	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
$929$	2.21620	+	0.593828i	0.0727110	+	0.0194829i	0.294991	−	0.955500i	$-0.404683\pi$
$929$	2.21620	+	0.593828i	0.0727110	+	0.0194829i	−0.222280	+	0.974983i	$0.571350\pi$
$930$	−6.95951	+	6.72089i	−0.228211	+	0.220387i
$931$	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
$934$	0.839158	+	3.13178i	0.0274581	+	0.102475i
$935$	−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	$0.462950\pi$
$938$	−0.721146	−	2.69135i	−0.0235463	−	0.0878758i
$939$	−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	$-0.924859\pi$
$941$	−22.6506	+	22.6506i	−0.738390	+	0.738390i	0.233877	+	0.972266i	$0.424859\pi$
$942$	6.88469	−	6.64864i	0.224315	−	0.216624i
$943$	17.8142	+	4.77330i	0.580110	+	0.155440i
$944$	−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
$947$	−12.9169	+	3.46107i	−0.419742	+	0.112470i	−0.462507	−	0.886616i	$-0.653050\pi$
$947$	−12.9169	+	3.46107i	−0.419742	+	0.112470i	0.0427648	+	0.999085i	$0.486383\pi$
$948$	3.06363	+	1.84076i	0.0995022	+	0.0597852i
$949$		0			0
$950$		−	12.2866i		−	0.398629i
$951$	14.8203	+	4.24943i	0.480580	+	0.137797i
$952$	4.68381	−	8.11259i	0.151803	−	0.262931i
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	0.973359	−	0.229288i	$-0.0736399\pi$
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	−0.685249	+	0.728309i	$0.740307\pi$
$954$	−0.760824	+	2.48878i	−0.0246326	+	0.0805772i
$955$	6.11390	−	22.8174i	0.197841	−	0.738353i
$956$	−4.49206	+	16.7646i	−0.145284	+	0.542206i
$957$	−2.11157	−	8.46858i	−0.0682575	−	0.273750i
$958$	−4.04423	−	7.00482i	−0.130663	−	0.226315i
$959$	4.37773	−	7.58246i	0.141364	−	0.244850i
$960$	−8.57871	+	29.9190i	−0.276877	+	0.965632i
$961$		−	10.1988i		−	0.328993i
$962$		0			0
$963$	34.5812	−	18.3883i	1.11436	−	0.592555i
$964$	50.1473	−	13.4369i	1.61513	−	0.432774i
$965$	−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	0.997897	−	0.0648250i	$-0.0206489\pi$
$967$	29.0154	+	29.0154i	0.933072	+	0.933072i	−0.0648250	+	0.997897i	$0.520649\pi$
$968$	9.87382	+	2.64568i	0.317357	+	0.0850354i
$969$	−34.9856	−	36.2277i	−1.12390	−	1.16380i
$970$	−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
$973$	1.62172	+	6.05235i	0.0519900	+	0.194029i
$974$	−10.3864			−0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	0.689868	+	2.57462i	0.0220708	+	0.0823694i	0.976083	−	0.217399i	$-0.0697573\pi$
$977$	0.689868	+	2.57462i	0.0220708	+	0.0823694i	−0.954012	+	0.299768i	$0.903091\pi$
$978$	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
$981$	18.5541	−	4.28406i	0.592385	−	0.136779i
$982$	−5.21679	−	1.39784i	−0.166475	−	0.0446067i
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.964676	+	0.263440i	$0.0848571\pi$
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.263440	+	0.964676i	$0.415143\pi$
$984$	−16.1010	−	0.280832i	−0.513282	−	0.00895260i
$985$	6.87308	+	3.96818i	0.218995	+	0.126437i
$986$	−5.39867	+	1.44657i	−0.171929	+	0.0460682i
$987$	−3.27182	+	5.44538i	−0.104143	+	0.173328i
$988$		0			0
$989$			15.0419i			0.478303i
$990$	−5.03909	+	4.69928i	−0.160153	+	0.149353i
$991$	−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
$993$	27.0183	−	6.73680i	0.857400	−	0.213786i
$994$	1.23032	−	4.59160i	0.0390232	−	0.145637i
$995$	16.4977	−	61.5704i	0.523013	−	1.95191i
$996$	20.4597	−	5.10147i	0.648291	−	0.161646i
$997$	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
$999$	2.33473	+	10.9819i	0.0738677	+	0.347453i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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