LMFDB - Embedded newform 507.2.k.k.80.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			80.12
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0912193 + 0.340435i) q^{2} +(0.839735 - 1.51487i) q^{3} +(1.62448 + 0.937892i) q^{4} +(-2.45719 - 2.45719i) q^{5} +(0.439116 + 0.424061i) q^{6} +(1.12240 - 0.300747i) q^{7} +(-0.965906 + 0.965906i) q^{8} +(-1.58969 - 2.54419i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 96 * q + 24 * q^9	$ 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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.990648	−	0.136440i	$-0.956434\pi$
$2$	−0.0912193	+	0.340435i	−0.0645018	+	0.240724i	0.926147	+	0.377164i	$0.123101\pi$
$3$	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	$-0.966724\pi$
$5$	−2.45719	−	2.45719i	−1.09889	−	1.09889i	−0.104350	−	0.994541i	$-0.533276\pi$
$6$	0.439116	+	0.424061i	0.179269	+	0.173122i
$7$	1.12240	−	0.300747i	0.424228	−	0.113672i	−0.0403875	−	0.999184i	$-0.512859\pi$
$7$	1.12240	−	0.300747i	0.424228	−	0.113672i	0.464615	+	0.885513i	$0.346193\pi$
$8$	−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	0.521339	−	0.853350i	$-0.325433\pi$
$11$	1.81140	+	0.485362i	0.546156	+	0.146342i	0.0248176	+	0.999692i	$0.492100\pi$
$12$	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	−0.247014	−	0.969012i	$-0.579449\pi$
$17$	2.95083	−	5.11099i	0.715682	−	1.23960i	0.962696	−	0.270586i	$-0.0872174\pi$
$18$	1.01114	−	0.309108i	0.238328	−	0.0728573i
$19$	−1.27519	−	4.75906i	−0.292548	−	1.09180i	−0.943145	−	0.332381i	$-0.892148\pi$
$19$	−1.27519	−	4.75906i	−0.292548	−	1.09180i	0.650598	−	0.759423i	$-0.274518\pi$
$20$	−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	0.689500	−	0.724286i	$-0.257831\pi$
$23$	−1.35482	−	2.34662i	−0.282500	−	0.489305i	−0.972000	+	0.234981i	$0.924497\pi$
$24$	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	−0.700252	−	0.713896i	$-0.746929\pi$
$29$	−2.32707	+	1.34353i	−0.432125	+	0.249488i	0.268126	+	0.963384i	$0.413596\pi$
$30$	−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	$0.115677\pi$
$32$	−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	−0.996537	−	0.0831470i	$-0.973503\pi$
$37$	−0.559232	+	2.08708i	−0.0919372	+	0.343114i	0.904600	+	0.426261i	$0.140170\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	−1.76159	+	6.57436i	−0.275115	+	1.02674i	0.680650	+	0.732609i	$0.261698\pi$
$41$	−1.76159	+	6.57436i	−0.275115	+	1.02674i	−0.955764	+	0.294133i	$0.904969\pi$
$42$	0.620400	+	0.343904i	0.0957298	+	0.0530655i
$43$	4.80750	+	2.77561i	0.733136	+	0.423276i	0.819568	−	0.572981i	$-0.194213\pi$
$43$	4.80750	+	2.77561i	0.733136	+	0.423276i	−0.0864321	+	0.996258i	$0.527547\pi$
$44$	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	−0.525336	−	0.850895i	$-0.676060\pi$
$47$	2.23192	−	2.23192i	0.325559	−	0.325559i	0.850895	+	0.525336i	$0.176060\pi$
$48$	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	$-0.945931\pi$
$53$		−	2.46136i		−	0.338093i	0.985608	−	0.169047i	$-0.0540689\pi$
$54$	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	0.901447	+	0.432890i	$0.142506\pi$
$59$	2.59020	+	9.66677i	0.337216	+	1.25851i	−0.564231	+	0.825617i	$0.690827\pi$
$60$	−10.9547	−	2.73147i	−1.41424	−	0.352631i
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	−0.768120	−	0.640306i	$-0.778808\pi$
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	0.938581	+	0.345058i	$0.112141\pi$
$62$	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	0.636838	−	0.770998i	$-0.280242\pi$
$67$	6.57167	+	1.76087i	0.802857	+	0.215125i	0.166019	+	0.986123i	$0.446909\pi$
$68$	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	0.477647	−	0.878552i	$-0.341490\pi$
$71$	11.2116	−	3.00415i	1.33058	−	0.356527i	0.852930	+	0.522025i	$0.174823\pi$
$72$	3.99294	+	0.921953i	0.470572	+	0.108653i
$73$	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
$76$	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	0.912596	−	0.408864i	$-0.134075\pi$
$83$	4.58922	+	4.58922i	0.503732	+	0.503732i	−0.408864	+	0.912596i	$0.634075\pi$
$84$	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	0.470893	−	0.882190i	$-0.343932\pi$
$89$	4.12834	+	1.10619i	0.437604	+	0.117256i	−0.0332896	+	0.999446i	$0.510598\pi$
$90$	−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	−0.916921	−	0.399070i	$-0.869333\pi$
$97$	−3.17506	−	11.8495i	−0.322379	−	1.20313i	0.594542	−	0.804065i	$-0.297333\pi$
$98$	−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	0.998128	+	0.0611547i	$0.0194783\pi$
$101$	5.54779	+	9.60905i	0.552026	+	0.956137i	−0.446103	+	0.894982i	$0.647188\pi$
$102$	3.46313	−	0.992988i	0.342901	−	0.0983204i
$103$		−	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
$106$	0.837932	+	0.224523i	0.0813872	+	0.0218076i
$107$	−11.3063	+	6.52769i	−1.09302	+	0.631055i	−0.934379	−	0.356281i	$-0.884045\pi$
$107$	−11.3063	+	6.52769i	−1.09302	+	0.631055i	−0.158641	+	0.987336i	$0.550711\pi$
$108$	−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	$0.348318\pi$
$110$	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	0.925467	−	0.378829i	$-0.123673\pi$
$113$	11.2693	+	6.50632i	1.06012	+	0.612063i	0.134657	+	0.990892i	$0.457007\pi$
$114$	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	−0.768628	−	0.639696i	$-0.779060\pi$
$127$	−6.74982	+	3.89701i	−0.598950	+	0.345804i	0.169679	+	0.985499i	$0.445727\pi$
$128$	−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	$0.300540\pi$
$131$			18.5420i			1.62003i	−0.586412	+	0.810013i	$0.699460\pi$
$132$	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	0.997829	+	0.0658600i	$0.0209791\pi$
$137$	1.95016	+	7.27811i	0.166614	+	0.621811i	−0.831215	+	0.555951i	$0.812354\pi$
$138$	0.400186	−	1.60497i	0.0340661	−	0.136624i
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	−0.728733	−	0.684798i	$-0.759891\pi$
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	0.957419	+	0.288703i	$0.0932239\pi$
$140$	−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	−0.994775	−	0.102088i	$-0.967448\pi$
$149$	−22.0357	+	5.90444i	−1.80523	+	0.483710i	−0.810457	+	0.585798i	$0.800781\pi$
$150$	−3.00049	+	3.10701i	−0.244989	+	0.253686i
$151$	−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
$154$	−0.198774	+	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	−0.125687	−	0.992070i	$-0.540113\pi$
$163$	3.33861	−	0.894579i	0.261500	−	0.0700688i	0.387187	+	0.922001i	$0.373447\pi$
$164$	−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	0.0574813	−	0.998347i	$-0.481693\pi$
$167$	−5.06462	−	1.35706i	−0.391912	−	0.105012i	−0.449393	+	0.893334i	$0.648360\pi$
$168$	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	−0.457053	−	0.889439i	$-0.651095\pi$
$173$	7.12562	−	12.3419i	0.541751	−	0.938339i	0.998804	−	0.0489001i	$-0.0155716\pi$
$174$	−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	0.772821	−	0.634624i	$-0.218845\pi$
$179$	−2.18334	−	3.78165i	−0.163190	−	0.282654i	−0.936011	+	0.351970i	$0.885512\pi$
$180$	−13.3369	+	14.3013i	−0.994071	+	1.06595i
$181$			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
$184$	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	0.271657	−	0.962394i	$-0.412428\pi$
$191$	−5.88706	−	3.39890i	−0.425973	−	0.245935i	−0.697629	+	0.716459i	$0.745762\pi$
$192$	7.83368	+	4.34242i	0.565347	+	0.313387i
$193$	2.87709	−	10.7374i	0.207098	−	0.772898i	−0.781702	−	0.623652i	$-0.785648\pi$
$193$	2.87709	−	10.7374i	0.207098	−	0.772898i	0.988800	−	0.149247i	$-0.0476849\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	−0.591102	+	2.20602i	−0.0421143	+	0.157173i	−0.983781	−	0.179375i	$-0.942593\pi$
$197$	−0.591102	+	2.20602i	−0.0421143	+	0.157173i	0.941667	+	0.336547i	$0.109259\pi$
$198$	1.98160	−	0.0691468i	0.140826	−	0.00491405i
$199$	−15.8856	−	9.17157i	−1.12610	−	0.650155i	−0.183150	−	0.983085i	$-0.558629\pi$
$199$	−15.8856	−	9.17157i	−1.12610	−	0.650155i	−0.942952	+	0.332930i	$0.891963\pi$
$200$	−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	0.970291	−	0.241939i	$-0.0777834\pi$
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	−0.694671	+	0.719327i	$0.744450\pi$
$212$	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	−0.833393	−	0.552680i	$-0.813605\pi$
$223$	−27.3497	−	7.32834i	−1.83147	−	0.490742i	−0.998080	+	0.0619383i	$0.980272\pi$
$224$	−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	−0.0152176	−	0.999884i	$-0.504844\pi$
$227$	7.10455	−	1.90366i	0.471546	−	0.126350i	0.486763	+	0.873534i	$0.338177\pi$
$228$	−11.5146	−	11.1198i	−0.762574	−	0.736428i
$229$	−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
$232$	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	0.463099	−	0.886306i	$-0.346737\pi$
$239$	−6.54262	−	6.54262i	−0.423207	−	0.423207i	−0.886306	+	0.463099i	$0.846737\pi$
$240$	−14.1582	−	13.6728i	−0.913908	−	0.882574i
$241$	26.7340	−	7.16336i	1.72209	−	0.461433i	0.743754	−	0.668453i	$-0.233043\pi$
$241$	26.7340	−	7.16336i	1.72209	−	0.461433i	0.978337	+	0.207021i	$0.0663767\pi$
$242$	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	−0.764025	−	0.645187i	$-0.776779\pi$
$251$	2.80003	−	4.84979i	0.176736	−	0.306116i	0.940761	+	0.339071i	$0.110113\pi$
$252$	−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	0.952499	−	0.304541i	$-0.0985030\pi$
$257$	3.40679	+	5.90073i	0.212510	+	0.368077i	−0.739990	+	0.672618i	$0.765170\pi$
$258$	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	0.246119	−	0.969240i	$-0.420844\pi$
$263$	19.5996	−	11.3159i	1.20857	−	0.697765i	0.962446	+	0.271474i	$0.0875111\pi$
$264$	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	−0.386345	−	0.922354i	$-0.626262\pi$
$269$	−22.6058	−	13.0515i	−1.37830	−	0.795762i	−0.991955	+	0.126593i	$0.959596\pi$
$270$	−5.33739	+	3.46584i	−0.324823	+	0.210925i
$271$	−4.57652	+	17.0798i	−0.278004	+	1.03753i	0.675797	+	0.737087i	$0.263799\pi$
$271$	−4.57652	+	17.0798i	−0.278004	+	1.03753i	−0.953801	+	0.300438i	$0.902867\pi$
$272$	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	0.956295	−	0.292402i	$-0.0944546\pi$
$277$	19.6593	+	11.3503i	1.18122	+	0.681975i	0.224920	+	0.974377i	$0.427788\pi$
$278$	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	−0.404181	−	0.914679i	$-0.632443\pi$
$281$	8.55751	−	8.55751i	0.510498	−	0.510498i	0.914679	+	0.404181i	$0.132443\pi$
$282$	1.92655	−	0.0336025i	0.114724	−	0.00200100i
$283$	6.15361	−	3.55279i	0.365794	−	0.211192i	−0.305825	−	0.952088i	$-0.598932\pi$
$283$	6.15361	−	3.55279i	0.365794	−	0.211192i	0.671620	+	0.740896i	$0.265599\pi$
$284$	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	−0.975670	−	0.219245i	$-0.929640\pi$
$293$	−4.11392	−	15.3534i	−0.240338	−	0.896953i	0.735332	−	0.677707i	$-0.237026\pi$
$294$	−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	0.165277	−	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
$310$	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	0.861416	−	0.507901i	$-0.169578\pi$
$317$	6.29415	+	6.29415i	0.353515	+	0.353515i	−0.507901	+	0.861416i	$0.669578\pi$
$318$	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	0.980886	+	0.194584i	$0.0623356\pi$
$331$	4.16094	+	15.5288i	0.228706	+	0.853541i	−0.752180	+	0.658958i	$0.770998\pi$
$332$	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	$-0.719100\pi$
$337$		−	28.3556i		−	1.54463i	0.635243	−	0.772313i	$-0.280900\pi$
$338$		0			0
$339$	19.3195	−	11.6080i	1.04929	−	0.630457i
$340$	−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	0.219986	−	0.975503i	$-0.429399\pi$
$347$	−9.59025	−	5.53693i	−0.514831	−	0.297238i	−0.734817	+	0.678265i	$0.762732\pi$
$348$	−4.23256	+	7.63550i	−0.226889	+	0.409306i
$349$	−7.74319	+	28.8980i	−0.414483	+	1.54687i	0.371385	+	0.928479i	$0.378883\pi$
$349$	−7.74319	+	28.8980i	−0.414483	+	1.54687i	−0.785868	+	0.618394i	$0.787784\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	3.28082	−	12.2442i	0.174620	−	0.651692i	−0.821996	−	0.569494i	$-0.807139\pi$
$353$	3.28082	−	12.2442i	0.174620	−	0.651692i	0.996616	−	0.0821982i	$-0.0261940\pi$
$354$	−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	−0.0790589	+	0.996870i	$0.525192\pi$
$359$	−20.3859	+	20.3859i	−1.07593	+	1.07593i	−0.996870	+	0.0790589i	$0.974808\pi$
$360$	−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	0.992221	+	0.124490i	$0.0397295\pi$
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	−0.388299	+	0.921533i	$0.626937\pi$
$368$	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	0.469128	+	0.883130i	$0.344568\pi$
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	−0.999377	+	0.0352886i	$0.988765\pi$
$374$	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	0.355991	−	0.934489i	$-0.384143\pi$
$379$	3.83602	+	1.02786i	0.197043	+	0.0527975i	−0.158948	+	0.987287i	$0.550810\pi$
$380$	−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	0.466921	−	0.884299i	$-0.345363\pi$
$383$	25.7044	−	6.88748i	1.31344	−	0.351934i	0.846515	+	0.532365i	$0.178697\pi$
$384$	−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	−0.785659	−	0.618660i	$-0.787676\pi$
$397$	−23.0477	+	6.17560i	−1.15673	+	0.309945i	−0.371071	+	0.928605i	$0.621009\pi$
$398$	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	−0.348610	−	0.937268i	$-0.613346\pi$
$401$	−22.4109	−	6.00499i	−1.11915	−	0.299875i	−0.770539	+	0.637393i	$0.780013\pi$
$402$	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	−0.998534	−	0.0541371i	$-0.982759\pi$
$409$	−3.25292	−	12.1401i	−0.160847	−	0.600288i	0.837687	−	0.546151i	$-0.183907\pi$
$410$	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	−0.944997	−	0.327080i	$-0.893935\pi$
$419$	−23.2172	+	13.4045i	−1.13424	+	0.654851i	−0.189239	+	0.981931i	$0.560602\pi$
$420$	−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	$0.150375\pi$
$422$	−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	−0.697859	−	0.716235i	$-0.745864\pi$
$431$	5.49370	−	20.5028i	0.264622	−	0.987583i	0.962481	−	0.271348i	$-0.0874694\pi$
$432$	−9.25399	−	14.2511i	−0.445233	−	0.685658i
$433$	−1.60537	−	0.926859i	−0.0771490	−	0.0445420i	0.460929	−	0.887437i	$-0.347516\pi$
$433$	−1.60537	−	0.926859i	−0.0771490	−	0.0445420i	−0.538078	+	0.842895i	$0.680850\pi$
$434$	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	−0.171820	−	0.985128i	$-0.554965\pi$
$439$	12.4753	−	7.20264i	0.595415	−	0.343763i	0.767236	+	0.641365i	$0.221632\pi$
$440$	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	$0.177119\pi$
$443$			22.2330i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$444$	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	0.936938	+	0.349495i	$0.113647\pi$
$449$	6.36268	+	23.7458i	0.300273	+	1.12064i	−0.636665	+	0.771141i	$0.719687\pi$
$450$	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	0.102632	−	0.994719i	$-0.467274\pi$
$457$	−6.53825	−	1.75192i	−0.305847	−	0.0819513i	−0.408478	+	0.912768i	$0.633940\pi$
$458$	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	−0.526525	−	0.850160i	$-0.676505\pi$
$461$	−11.9685	+	3.20695i	−0.557429	+	0.149363i	−0.0309044	+	0.999522i	$0.509839\pi$
$462$	0.956871	+	0.924064i	0.0445177	+	0.0429914i
$463$	−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
$466$	−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	0.726826	−	0.686821i	$-0.240995\pi$
$479$	22.1676	+	5.93980i	1.01287	+	0.271396i	0.286039	+	0.958218i	$0.407661\pi$
$480$	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	0.891878	+	0.452277i	$0.149388\pi$
$487$	7.62733	+	28.4656i	0.345627	+	1.28990i	−0.546250	+	0.837622i	$0.683945\pi$
$488$	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	0.985495	−	0.169705i	$-0.0542814\pi$
$491$	7.66195	+	13.2709i	0.345779	+	0.598907i	−0.639716	+	0.768611i	$0.720948\pi$
$492$	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	−0.410004	+	0.912084i	$0.634473\pi$
$499$	−29.5332	+	29.5332i	−1.32209	+	1.32209i	−0.912084	+	0.410004i	$0.865527\pi$
$500$	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	0.987162	−	0.159722i	$-0.0510599\pi$
$503$	30.1073	+	17.3825i	1.34242	+	0.775046i	0.355257	+	0.934768i	$0.384393\pi$
$504$	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	0.0701558	−	0.997536i	$-0.477650\pi$
$509$	11.4648	−	42.7871i	0.508167	−	1.89651i	0.438011	−	0.898969i	$-0.355683\pi$
$510$	−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	$0.0134873\pi$
$521$			1.93372i			0.0847179i	−0.999102	+	0.0423590i	$0.986513\pi$
$522$	−1.93769	+	2.07781i	−0.0848106	+	0.0909434i
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	0.849091	−	0.528246i	$-0.177150\pi$
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	−0.882020	+	0.471212i	$0.843817\pi$
$524$	−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	0.760068	−	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
$544$	−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	0.184849	−	0.982767i	$-0.440820\pi$
$557$	−3.45636	−	0.926129i	−0.146451	−	0.0392414i	−0.331300	+	0.943526i	$0.607487\pi$
$558$	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	−0.580800	−	0.814046i	$-0.697260\pi$
$563$	9.83710	−	17.0384i	0.414585	−	0.718081i	0.995385	+	0.0959647i	$0.0305936\pi$
$564$	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	0.748200	−	0.663473i	$-0.230918\pi$
$569$	−4.78231	−	8.28321i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$570$	−10.0468	+	2.88072i	−0.420813	+	0.120660i
$571$			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
$574$	−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	−0.561844	−	0.827243i	$-0.689908\pi$
$577$	6.37509	−	6.37509i	0.265398	−	0.265398i	0.827243	+	0.561844i	$0.189908\pi$
$578$	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	0.568362	+	0.822779i	$0.307577\pi$
$587$	−8.12231	+	30.3129i	−0.335243	+	1.25115i	−0.903605	+	0.428367i	$0.859089\pi$
$588$	−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	−0.0255650	−	0.999673i	$-0.508138\pi$
$593$	23.7211	−	23.7211i	0.974108	−	0.974108i	0.999673	+	0.0255650i	$0.00813848\pi$
$594$	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	$-0.757460\pi$
$599$		−	33.7915i		−	1.38068i	0.723484	−	0.690341i	$-0.242540\pi$
$600$	−16.0923	+	4.61415i	−0.656964	+	0.188372i
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	0.990404	+	0.138202i	$0.0441323\pi$
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	−0.375516	+	0.926816i	$0.622534\pi$
$602$	−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	−0.998208	−	0.0598403i	$-0.980941\pi$
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	0.550927	+	0.834553i	$0.314274\pi$
$608$	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	0.270337	−	0.962766i	$-0.412865\pi$
$613$	0.571244	+	0.153064i	0.0230723	+	0.00618221i	−0.247264	+	0.968948i	$0.579532\pi$
$614$	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	0.355349	−	0.934734i	$-0.384362\pi$
$617$	28.0800	−	7.52400i	1.13046	−	0.302905i	0.775108	+	0.631829i	$0.217695\pi$
$618$	1.87980	−	1.94654i	0.0756166	−	0.0783012i
$619$	−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
$622$	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	−0.932751	−	0.360521i	$-0.882599\pi$
$631$	−39.1937	+	10.5019i	−1.56028	+	0.418075i	−0.627526	+	0.778596i	$0.715932\pi$
$632$	−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	−0.492176	−	0.870496i	$-0.663798\pi$
$641$	12.8560	−	22.2673i	0.507783	−	0.879506i	0.999959	−	0.00901077i	$-0.00286825\pi$
$642$	−7.73291	−	1.92814i	−0.305194	−	0.0760976i
$643$	0.164018	+	0.612124i	0.00646824	+	0.0241398i	0.969085	−	0.246729i	$-0.0793557\pi$
$643$	0.164018	+	0.612124i	0.00646824	+	0.0241398i	−0.962616	+	0.270869i	$0.912689\pi$
$644$	−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	−0.792574	−	0.609776i	$-0.791260\pi$
$647$	−23.5124	−	40.7247i	−0.924368	−	1.60105i	−0.131794	−	0.991277i	$-0.542074\pi$
$648$	−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	−0.902869	−	0.429917i	$-0.858543\pi$
$653$	−25.0935	+	14.4877i	−0.981984	+	0.566949i	−0.0791154	+	0.996865i	$0.525210\pi$
$654$	−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	−0.995561	−	0.0941194i	$-0.969996\pi$
$659$	−40.4280	−	23.3411i	−1.57485	−	0.909241i	−0.579290	−	0.815121i	$-0.696670\pi$
$660$	−18.5175	−	10.2648i	−0.720794	−	0.399555i
$661$	1.79701	−	6.70655i	0.0698957	−	0.260854i	−0.922132	−	0.386876i	$-0.873554\pi$
$661$	1.79701	−	6.70655i	0.0698957	−	0.260854i	0.992028	+	0.126021i	$0.0402208\pi$
$662$	−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	0.00563228	−	0.999984i	$-0.498207\pi$
$673$	22.6855	−	13.0975i	0.874460	−	0.504870i	0.868828	+	0.495114i	$0.164874\pi$
$674$	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	$0.138466\pi$
$677$			21.9298i			0.842829i	−0.906868	+	0.421415i	$0.861534\pi$
$678$	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	0.993345	−	0.115176i	$-0.0367433\pi$
$683$	1.97300	+	7.36335i	0.0754949	+	0.281751i	−0.917850	+	0.396927i	$0.870077\pi$
$684$	−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	−0.0464729	−	0.998920i	$-0.514798\pi$
$691$	−15.4088	−	4.12878i	−0.586179	−	0.157066i	−0.539707	+	0.841853i	$0.681465\pi$
$692$	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	0.417717	−	0.908577i	$-0.362830\pi$
$709$	32.8514	−	8.80249i	1.23376	−	0.330585i	0.816042	+	0.577993i	$0.196164\pi$
$710$	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	−0.930210	−	0.367027i	$-0.880376\pi$
$719$	−3.94839	+	6.83882i	−0.147250	+	0.255045i	0.782960	+	0.622072i	$0.213709\pi$
$720$	−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	$0.151330\pi$
$727$			24.6824i			0.915420i	−0.889102	+	0.457710i	$0.848670\pi$
$728$		0			0
$729$	26.8523	−	2.82014i	0.994530	−	0.104450i
$730$	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	−0.321476	+	0.946918i	$0.604179\pi$
$733$	−34.3405	+	34.3405i	−1.26839	+	1.26839i	−0.946918	+	0.321476i	$0.895821\pi$
$734$	−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	0.490798	+	0.871273i	$0.336705\pi$
$739$	−10.0551	+	37.5261i	−0.369882	+	1.38042i	−0.860680	+	0.509146i	$0.829961\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	−13.4913	+	50.3503i	−0.494949	+	1.84717i	0.0353674	+	0.999374i	$0.488740\pi$
$743$	−13.4913	+	50.3503i	−0.494949	+	1.84717i	−0.530316	+	0.847800i	$0.677927\pi$
$744$	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	−0.562595	+	0.826733i	$0.690197\pi$
$751$	−42.7471	+	24.6801i	−1.55986	+	0.900588i	−0.997269	+	0.0738552i	$0.976470\pi$
$752$	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	0.642255	−	0.766491i	$-0.277999\pi$
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	−0.984928	+	0.172964i	$0.944666\pi$
$758$	−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	−0.872629	−	0.488384i	$-0.837587\pi$
$761$	−9.96144	−	37.1766i	−0.361102	−	1.34765i	0.511527	−	0.859267i	$-0.329080\pi$
$762$	−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	0.208778	−	0.977963i	$-0.433051\pi$
$769$	−2.75634	−	0.738559i	−0.0993962	−	0.0266331i	−0.308174	+	0.951330i	$0.599718\pi$
$770$	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	−0.368722	−	0.929540i	$-0.620205\pi$
$773$	−6.20770	+	1.66335i	−0.223275	+	0.0598265i	0.145447	+	0.989366i	$0.453538\pi$
$774$	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	−0.510313	−	0.859989i	$-0.670470\pi$
$787$	−14.6513	+	3.92580i	−0.522262	+	0.139940i	−0.0119493	+	0.999929i	$0.503804\pi$
$788$	−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	−0.851702	−	0.524027i	$-0.824429\pi$
$797$	0.789625	−	1.36767i	0.0279700	−	0.0484454i	0.879672	+	0.475582i	$0.157762\pi$
$798$	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	−0.674256	−	0.738498i	$-0.735536\pi$
$809$	−10.5758	+	6.10595i	−0.371826	+	0.214674i	0.302430	+	0.953172i	$0.402202\pi$
$810$	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	$-0.0128437\pi$
$812$	−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	−0.829533	−	0.558458i	$-0.811393\pi$
$821$	4.81637	−	17.9749i	0.168093	−	0.627330i	0.997625	−	0.0688721i	$-0.0219400\pi$
$822$	−2.23001	+	4.02293i	−0.0777807	+	0.140316i
$823$	−0.447230	−	0.258209i	−0.0155895	−	0.00900059i	0.492185	−	0.870491i	$-0.336198\pi$
$823$	−0.447230	−	0.258209i	−0.0155895	−	0.00900059i	−0.507774	+	0.861490i	$0.669532\pi$
$824$	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	−0.971149	−	0.238472i	$-0.923354\pi$
$827$	−21.0701	+	21.0701i	−0.732678	+	0.732678i	0.238472	+	0.971149i	$0.423354\pi$
$828$	−12.9314	+	8.07994i	−0.449396	+	0.280797i
$829$	1.46119	−	0.843616i	0.0507491	−	0.0293000i	−0.474411	−	0.880304i	$-0.657339\pi$
$829$	1.46119	−	0.843616i	0.0507491	−	0.0293000i	0.525160	+	0.851004i	$0.324006\pi$
$830$	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	0.900469	−	0.434920i	$-0.143223\pi$
$839$	−2.80444	−	10.4663i	−0.0968199	−	0.361337i	−0.997289	+	0.0735829i	$0.976557\pi$
$840$	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	0.999443	+	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
$856$	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	0.126779	−	0.991931i	$-0.459536\pi$
$863$	−25.4155	−	25.4155i	−0.865153	−	0.865153i	−0.991931	+	0.126779i	$0.959536\pi$
$864$	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	−0.998610	−	0.0527071i	$-0.983215\pi$
$877$	−4.74247	−	17.6992i	−0.160142	−	0.597658i	0.838468	−	0.544951i	$-0.183452\pi$
$878$	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	0.999609	+	0.0279654i	$0.00890283\pi$
$881$	15.5539	+	26.9401i	0.524023	+	0.907635i	−0.475586	+	0.879669i	$0.657764\pi$
$882$	−4.07416	+	4.36877i	−0.137184	+	0.147104i
$883$		−	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
$886$	−7.56891	−	2.02808i	−0.254282	−	0.0681348i
$887$	−21.3515	+	12.3273i	−0.716913	+	0.413910i	−0.813615	−	0.581404i	$-0.802504\pi$
$887$	−21.3515	+	12.3273i	−0.716913	+	0.413910i	0.0967027	+	0.995313i	$0.469170\pi$
$888$	−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	−0.524033	−	0.851698i	$-0.675573\pi$
$907$	−1.45939	+	0.842581i	−0.0484584	+	0.0279775i	0.475575	+	0.879675i	$0.342240\pi$
$908$	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	$-0.740481\pi$
$911$		−	43.9421i		−	1.45587i	0.685648	−	0.727933i	$-0.259519\pi$
$912$	−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	−0.927035	−	0.374974i	$-0.877652\pi$
$919$	−4.20715	+	7.28699i	−0.138781	+	0.240376i	0.788254	+	0.615349i	$0.210985\pi$
$920$	−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	−0.222280	−	0.974983i	$-0.571350\pi$
$929$	2.21620	−	0.593828i	0.0727110	−	0.0194829i	0.294991	+	0.955500i	$0.404683\pi$
$930$	−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	0.233877	−	0.972266i	$-0.424859\pi$
$941$	−22.6506	−	22.6506i	−0.738390	−	0.738390i	−0.972266	+	0.233877i	$0.924859\pi$
$942$	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	0.0427648	−	0.999085i	$-0.486383\pi$
$947$	−12.9169	−	3.46107i	−0.419742	−	0.112470i	−0.462507	+	0.886616i	$0.653050\pi$
$948$	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	−0.685249	−	0.728309i	$-0.740307\pi$
$953$	8.89415	−	15.4051i	0.288110	−	0.499021i	0.973359	+	0.229288i	$0.0736399\pi$
$954$	−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	−0.0648250	−	0.997897i	$-0.520649\pi$
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	0.997897	+	0.0648250i	$0.0206489\pi$
$968$	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	0.779904	−	0.625900i	$-0.215268\pi$
$971$	19.5631	+	11.2948i	0.627810	+	0.362466i	−0.152093	+	0.988366i	$0.548601\pi$
$972$	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	−0.954012	−	0.299768i	$-0.903091\pi$
$977$	0.689868	−	2.57462i	0.0220708	−	0.0823694i	0.976083	+	0.217399i	$0.0697573\pi$
$978$	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	0.263440	−	0.964676i	$-0.415143\pi$
$983$	38.5049	−	38.5049i	1.22812	−	1.22812i	0.964676	−	0.263440i	$-0.0848571\pi$
$984$	−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	0.741467	−	0.670989i	$-0.234130\pi$
$991$	−6.62217	−	11.4699i	−0.210360	−	0.364354i	−0.951827	+	0.306635i	$0.900797\pi$
$992$	−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	−0.499907	−	0.866079i	$-0.666633\pi$
$997$	15.7906	−	27.3501i	0.500093	−	0.866186i	1.00000		0.000107105i	$-3.40926e-5\pi$
$998$	−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.80.12		96
3.2	odd	2	inner	507.2.k.k.80.13		96
13.2	odd	12		507.2.f.g.437.12	yes	48
13.3	even	3		507.2.f.g.239.12	yes	48
13.4	even	6	inner	507.2.k.k.188.11		96
13.5	odd	4	inner	507.2.k.k.89.14		96
13.6	odd	12	inner	507.2.k.k.488.11		96
13.7	odd	12	inner	507.2.k.k.488.13		96
13.8	odd	4	inner	507.2.k.k.89.12		96
13.9	even	3	inner	507.2.k.k.188.13		96
13.10	even	6		507.2.f.g.239.14	yes	48
13.11	odd	12		507.2.f.g.437.14	yes	48
13.12	even	2	inner	507.2.k.k.80.14		96
39.2	even	12		507.2.f.g.437.13	yes	48
39.5	even	4	inner	507.2.k.k.89.11		96
39.8	even	4	inner	507.2.k.k.89.13		96
39.11	even	12		507.2.f.g.437.11	yes	48
39.17	odd	6	inner	507.2.k.k.188.14		96
39.20	even	12	inner	507.2.k.k.488.12		96
39.23	odd	6		507.2.f.g.239.11	✓	48
39.29	odd	6		507.2.f.g.239.13	yes	48
39.32	even	12	inner	507.2.k.k.488.14		96
39.35	odd	6	inner	507.2.k.k.188.12		96
39.38	odd	2	inner	507.2.k.k.80.11		96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0912193 + 0.340435i) q^{2} +(0.839735 - 1.51487i) q^{3} +(1.62448 + 0.937892i) q^{4} +(-2.45719 - 2.45719i) q^{5} +(0.439116 + 0.424061i) q^{6} +(1.12240 - 0.300747i) q^{7} +(-0.965906 + 0.965906i) q^{8} +(-1.58969 - 2.54419i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 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

Introduction

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