LMFDB - Embedded newform 507.2.k.k.89.14

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			89.14
Character	$\chi$	$=$	507.89
Dual form			507.2.k.k.188.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

Coefficient data

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

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

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

$2$	0.340435	+	0.0912193i	0.240724	+	0.0645018i	0.377164	−	0.926147i	$-0.376899\pi$
$2$	0.340435	+	0.0912193i	0.240724	+	0.0645018i	−0.136440	+	0.990648i	$0.543566\pi$
$3$	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	$0.966724\pi$
$6$	0.424061	−	0.439116i	0.173122	−	0.179269i
$7$	0.300747	+	1.12240i	0.113672	+	0.424228i	0.999184	−	0.0403875i	$-0.0128593\pi$
$7$	0.300747	+	1.12240i	0.113672	+	0.424228i	−0.885513	+	0.464615i	$0.846193\pi$
$8$	−0.965906	−	0.965906i	−0.341499	−	0.341499i
$9$	−1.58969	−	2.54419i	−0.529897	−	0.848062i
$10$	−1.06066	+	0.612371i	−0.335410	+	0.193649i
$11$	−0.485362	+	1.81140i	−0.146342	+	0.546156i	0.853350	+	0.521339i	$0.174567\pi$
$11$	−0.485362	+	1.81140i	−0.146342	+	0.546156i	−0.999692	+	0.0248176i	$0.992100\pi$
$12$	−2.78492	+	1.67330i	−0.803936	+	0.483039i
$13$		0			0
$13$		0			0
$14$			0.409539i			0.109454i
$15$	1.65895	+	5.78573i	0.428339	+	1.49387i
$16$	1.63506	+	2.83201i	0.408766	+	0.708003i
$17$	−2.95083	+	5.11099i	−0.715682	+	1.23960i	0.247014	+	0.969012i	$0.420551\pi$
$17$	−2.95083	+	5.11099i	−0.715682	+	1.23960i	−0.962696	+	0.270586i	$0.912783\pi$
$18$	−0.309108	−	1.01114i	−0.0728573	−	0.238328i
$19$	−4.75906	+	1.27519i	−1.09180	+	0.292548i	−0.759423	−	0.650598i	$-0.774518\pi$
$19$	−4.75906	+	1.27519i	−1.09180	+	0.292548i	−0.332381	+	0.943145i	$0.607852\pi$
$20$	6.29623	−	1.68707i	1.40788	−	0.377240i
$21$	1.95284	+	0.486926i	0.426146	+	0.106256i
$22$	−0.330468	+	0.572388i	−0.0704561	+	0.122034i
$23$	1.35482	+	2.34662i	0.282500	+	0.489305i	0.972000	−	0.234981i	$-0.0755028\pi$
$23$	1.35482	+	2.34662i	0.282500	+	0.489305i	−0.689500	+	0.724286i	$0.742169\pi$
$24$	−2.27433	+	0.652122i	−0.464246	+	0.133114i
$25$		−	7.07560i		−	1.41512i
$26$		0			0
$27$	−5.18904	+	0.271740i	−0.998632	+	0.0522964i
$28$	0.564135	−	2.10538i	0.106612	−	0.397880i
$29$	−2.32707	+	1.34353i	−0.432125	+	0.249488i	−0.700252	−	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	$-0.384323\pi$
$31$	−3.22500	−	3.22500i	−0.579227	−	0.579227i	−0.934690	+	0.355463i	$0.884323\pi$
$32$	1.00539	+	3.75217i	0.177730	+	0.663296i
$33$	2.33646	+	2.25635i	0.406726	+	0.392781i
$34$	−1.47079	+	1.47079i	−0.252238	+	0.252238i
$35$	−3.49695	−	2.01896i	−0.591092	−	0.341267i
$36$	0.196243	+	5.62393i	0.0327072	+	0.937321i
$37$	−2.08708	−	0.559232i	−0.343114	−	0.0919372i	0.0831470	−	0.996537i	$-0.473503\pi$
$37$	−2.08708	−	0.559232i	−0.343114	−	0.0919372i	−0.426261	+	0.904600i	$0.640170\pi$
$38$	−1.73647			−0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	6.57436	+	1.76159i	1.02674	+	0.275115i	0.732609	−	0.680650i	$-0.238302\pi$
$41$	6.57436	+	1.76159i	1.02674	+	0.275115i	0.294133	+	0.955764i	$0.404969\pi$
$42$	0.620400	+	0.343904i	0.0957298	+	0.0530655i
$43$	−4.80750	−	2.77561i	−0.733136	−	0.423276i	0.0864321	−	0.996258i	$-0.472453\pi$
$43$	−4.80750	−	2.77561i	−0.733136	−	0.423276i	−0.819568	+	0.572981i	$0.805787\pi$
$44$	2.48735	−	2.48735i	0.374982	−	0.374982i
$45$	10.1577	+	2.34538i	1.51423	+	0.349629i
$46$	0.247172	+	0.922459i	0.0364436	+	0.136009i
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	0.850895	−	0.525336i	$-0.176060\pi$
$47$	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
$50$	0.645431	−	2.40878i	0.0912777	−	0.340653i
$51$	5.26460	+	8.76202i	0.737191	+	1.22693i
$52$		0			0
$53$		−	2.46136i		−	0.338093i	−0.985608	−	0.169047i	$-0.945931\pi$
$53$		−	2.46136i		−	0.338093i	0.985608	−	0.169047i	$-0.0540689\pi$
$54$	−1.79132	−	0.380831i	−0.243768	−	0.0518245i
$55$	−3.25832	−	5.64358i	−0.439352	−	0.760980i
$56$	0.793642	−	1.37463i	0.106055	−	0.183692i
$57$	−2.06460	+	8.28020i	−0.273463	+	1.09674i
$58$	−0.914771	+	0.245112i	−0.120115	+	0.0321848i
$59$	−9.66677	+	2.59020i	−1.25851	+	0.337216i	−0.825617	−	0.564231i	$-0.809173\pi$
$59$	−9.66677	+	2.59020i	−1.25851	+	0.337216i	−0.432890	+	0.901447i	$0.642506\pi$
$60$	2.73147	−	10.9547i	0.352631	−	1.41424i
$61$	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
$63$	2.37750	−	2.54943i	0.299537	−	0.321198i
$64$		−	5.17117i		−	0.646397i
$65$		0			0
$66$	0.589590	+	0.981273i	0.0725736	+	0.120786i
$67$	1.76087	−	6.57167i	0.215125	−	0.802857i	−0.770998	−	0.636838i	$-0.780242\pi$
$67$	1.76087	−	6.57167i	0.215125	−	0.802857i	0.986123	−	0.166019i	$-0.0530914\pi$
$68$	9.58711	−	5.53512i	1.16261	−	0.671232i
$69$	4.69254	−	0.0818465i	0.564915	−	0.00985317i
$70$	−1.00632	−	1.00632i	−0.120278	−	0.120278i
$71$	−3.00415	−	11.2116i	−0.356527	−	1.33058i	−0.878552	−	0.477647i	$-0.841490\pi$
$71$	−3.00415	−	11.2116i	−0.356527	−	1.33058i	0.522025	−	0.852930i	$-0.325177\pi$
$72$	−0.921953	+	3.99294i	−0.108653	+	0.470572i
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.0714492	+	0.997444i	$0.522762\pi$
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.997444	+	0.0714492i	$0.977238\pi$
$74$	−0.659503	−	0.380764i	−0.0766657	−	0.0442630i
$75$	−10.7186	−	5.94163i	−1.23768	−	0.686080i
$76$	8.92696	+	2.39197i	1.02399	+	0.274378i
$77$	−2.17908			−0.248330
$78$		0			0
$79$	1.10008			0.123769			0.0618844	−	0.998083i	$-0.480289\pi$
$79$	1.10008			0.123769			0.0618844	+	0.998083i	$0.480289\pi$
$80$	−10.9765	−	2.94114i	−1.22721	−	0.328829i
$81$	−3.94577	+	8.08894i	−0.438419	+	0.898771i
$82$	2.07745	+	1.19942i	0.229416	+	0.132453i
$83$	4.58922	−	4.58922i	0.503732	−	0.503732i	−0.408864	−	0.912596i	$-0.634075\pi$
$83$	4.58922	−	4.58922i	0.503732	−	0.503732i	0.912596	+	0.408864i	$0.134075\pi$
$84$	−2.71567	−	2.62256i	−0.296303	−	0.286144i
$85$	−5.30793	−	19.8095i	−0.575726	−	2.14864i
$86$	−1.38345	−	1.38345i	−0.149181	−	0.149181i
$87$	0.0811644	+	4.65342i	0.00870173	+	0.498899i
$88$	2.21845	−	1.28082i	0.236488	−	0.136536i
$89$	−1.10619	+	4.12834i	−0.117256	+	0.437604i	−0.999446	−	0.0332896i	$-0.989402\pi$
$89$	−1.10619	+	4.12834i	−0.117256	+	0.437604i	0.882190	+	0.470893i	$0.156068\pi$
$90$	3.24410	+	1.72503i	0.341959	+	0.181834i
$91$		0			0
$92$		−	5.08271i		−	0.529909i
$93$	−7.59361	+	2.17732i	−0.787421	+	0.225778i
$94$	0.556230	+	0.963419i	0.0573708	+	0.0993691i
$95$	8.56055	−	14.8273i	0.878294	−	1.52125i
$96$	6.52833	+	1.62779i	0.666295	+	0.166135i
$97$	−11.8495	+	3.17506i	−1.20313	+	0.322379i	−0.804065	−	0.594542i	$-0.797333\pi$
$97$	−11.8495	+	3.17506i	−1.20313	+	0.322379i	−0.399070	+	0.916921i	$0.630667\pi$
$98$	1.92338	−	0.515368i	0.194291	−	0.0520600i
$99$	5.38010	−	1.64471i	0.540721	−	0.165299i
$100$	−6.63614	+	11.4941i	−0.663614	+	1.14941i
$101$	−5.54779	−	9.60905i	−0.552026	−	0.956137i	−0.998128	−	0.0611547i	$-0.980522\pi$
$101$	−5.54779	−	9.60905i	−0.552026	−	0.956137i	0.446103	−	0.894982i	$-0.352812\pi$
$102$	0.992988	+	3.46313i	0.0983204	+	0.342901i
$103$			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
$106$	0.224523	−	0.837932i	0.0218076	−	0.0813872i
$107$	−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	$-0.151682\pi$
$109$	4.48829	+	4.48829i	0.429901	+	0.429901i	−0.458694	+	0.888594i	$0.651682\pi$
$110$	−0.594443	−	2.21849i	−0.0566780	−	0.211525i
$111$	−2.59976	+	2.69206i	−0.246759	+	0.255519i
$112$	−2.68692	+	2.68692i	−0.253890	+	0.253890i
$113$	11.2693	+	6.50632i	1.06012	+	0.612063i	0.925467	−	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
$115$	−9.09518	−	2.43705i	−0.848130	−	0.227256i
$116$	5.04035			0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	−6.62404	−	1.77491i	−0.607225	−	0.162705i
$120$	3.98608	−	7.19086i	0.363878	−	0.656433i
$121$	6.48070	+	3.74164i	0.589155	+	0.340149i
$122$	0.663584	−	0.663584i	0.0600781	−	0.0600781i
$123$	8.18931	−	8.48005i	0.738405	−	0.764621i
$124$	2.21423	+	8.26363i	0.198844	+	0.742096i
$125$	5.10014	+	5.10014i	0.456171	+	0.456171i
$126$	1.04194	−	0.651040i	0.0928236	−	0.0579992i
$127$	6.74982	−	3.89701i	0.598950	−	0.345804i	−0.169679	−	0.985499i	$-0.554273\pi$
$127$	6.74982	−	3.89701i	0.598950	−	0.345804i	0.768628	+	0.639696i	$0.220940\pi$
$128$	2.48249	−	9.26479i	0.219423	−	0.818900i
$129$	−8.24172	+	4.95198i	−0.725643	+	0.435997i
$130$		0			0
$131$			18.5420i			1.62003i	0.586412	+	0.810013i	$0.300540\pi$
$131$			18.5420i			1.62003i	−0.586412	+	0.810013i	$0.699460\pi$
$132$	−1.67931	−	5.85674i	−0.146165	−	0.509764i
$133$	−2.86254	−	4.95807i	−0.248214	−	0.429919i
$134$	1.19893	−	2.07660i	0.103571	−	0.179391i
$135$	12.0828	−	13.4182i	1.03992	−	1.15485i
$136$	7.78697	−	2.08651i	0.667727	−	0.178917i
$137$	−7.27811	+	1.95016i	−0.621811	+	0.166614i	−0.555951	−	0.831215i	$-0.687646\pi$
$137$	−7.27811	+	1.95016i	−0.621811	+	0.166614i	−0.0658600	+	0.997829i	$0.520979\pi$
$138$	1.60497	+	0.400186i	0.136624	+	0.0340661i
$139$	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
$141$	5.25531	−	1.50686i	0.442577	−	0.126900i
$142$		−	4.09087i		−	0.343298i
$143$		0			0
$144$	4.60592	−	8.66193i	0.383827	−	0.721828i
$145$	2.41673	−	9.01937i	0.200699	−	0.749018i
$146$	−3.94214	+	2.27600i	−0.326254	+	0.188363i
$147$	−0.170655	−	9.78419i	−0.0140753	−	0.806987i
$148$	2.86592	+	2.86592i	0.235577	+	0.235577i
$149$	5.90444	+	22.0357i	0.483710	+	1.80523i	0.585798	+	0.810457i	$0.300781\pi$
$149$	5.90444	+	22.0357i	0.483710	+	1.80523i	−0.102088	+	0.994775i	$0.532552\pi$
$150$	−3.10701	−	3.00049i	−0.253686	−	0.244989i
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	−0.384500	−	0.923125i	$-0.625626\pi$
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	0.923125	+	0.384500i	$0.125626\pi$
$152$	5.82852	+	3.36510i	0.472755	+	0.272945i
$153$	17.6942	−	0.617428i	1.43049	−	0.0499161i
$154$	−0.741836	−	0.198774i	−0.0597789	−	0.0160177i
$155$	15.8489			1.27301
$156$		0			0
$157$	15.6785			1.25128			0.625640	−	0.780112i	$-0.284838\pi$
$157$	15.6785			1.25128			0.625640	+	0.780112i	$0.284838\pi$
$158$	0.374506	+	0.100349i	0.0297941	+	0.00798331i
$159$	−3.72865	−	2.06689i	−0.295701	−	0.163915i
$160$	−11.6902	−	6.74937i	−0.924195	−	0.533584i
$161$	−2.22640	+	2.22640i	−0.175465	+	0.175465i
$162$	−2.08114	+	2.39383i	−0.163510	+	0.188077i
$163$	0.894579	+	3.33861i	0.0700688	+	0.261500i	0.992070	−	0.125687i	$-0.0401134\pi$
$163$	0.894579	+	3.33861i	0.0700688	+	0.261500i	−0.922001	+	0.387187i	$0.873447\pi$
$164$	−9.02770	−	9.02770i	−0.704945	−	0.704945i
$165$	−11.2854	+	0.196839i	−0.878570	+	0.0153239i
$166$	1.98096	−	1.14371i	0.153752	−	0.0887687i
$167$	1.35706	−	5.06462i	0.105012	−	0.391912i	−0.893334	−	0.449393i	$-0.851640\pi$
$167$	1.35706	−	5.06462i	0.105012	−	0.391912i	0.998347	+	0.0574813i	$0.0183070\pi$
$168$	−1.41594	−	2.35659i	−0.109242	−	0.181815i
$169$		0			0
$170$		−	7.22802i		−	0.554364i
$171$	10.8097	+	10.0808i	0.826642	+	0.770897i
$172$	5.20644	+	9.01782i	0.396987	+	0.687602i
$173$	−7.12562	+	12.3419i	−0.541751	+	0.938339i	0.457053	+	0.889439i	$0.348905\pi$
$173$	−7.12562	+	12.3419i	−0.541751	+	0.938339i	−0.998804	+	0.0489001i	$0.984428\pi$
$174$	−0.396851	+	1.59159i	−0.0300852	+	0.120658i
$175$	7.94166	−	2.12796i	0.600333	−	0.160859i
$176$	−5.92349	+	1.58720i	−0.446500	+	0.119639i
$177$	−4.19369	+	16.8190i	−0.315217	+	1.26420i
$178$	−0.753169	+	1.30453i	−0.0564524	+	0.0977785i
$179$	2.18334	+	3.78165i	0.163190	+	0.282654i	0.936011	−	0.351970i	$-0.114488\pi$
$179$	2.18334	+	3.78165i	0.163190	+	0.282654i	−0.772821	+	0.634624i	$0.781155\pi$
$180$	−14.3013	−	13.3369i	−1.06595	−	0.994071i
$181$		−	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
$184$	0.957986	−	3.57525i	0.0706237	−	0.263571i
$185$	6.50251	−	3.75422i	0.478074	−	0.276016i
$186$	−2.78375	+	0.0485537i	−0.204114	+	0.00356013i
$187$	−7.82581	−	7.82581i	−0.572280	−	0.572280i
$188$	−1.53240	−	5.71901i	−0.111762	−	0.417101i
$189$	−1.86559	−	5.74246i	−0.135702	−	0.417703i
$190$	4.26685	−	4.26685i	0.309550	−	0.309550i
$191$	−5.88706	−	3.39890i	−0.425973	−	0.245935i	0.271657	−	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
$193$	10.7374	+	2.87709i	0.772898	+	0.207098i	0.623652	−	0.781702i	$-0.285648\pi$
$193$	10.7374	+	2.87709i	0.772898	+	0.207098i	0.149247	+	0.988800i	$0.452315\pi$
$194$	−4.32361			−0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	2.20602	+	0.591102i	0.157173	+	0.0421143i	0.336547	−	0.941667i	$-0.390741\pi$
$197$	2.20602	+	0.591102i	0.157173	+	0.0421143i	−0.179375	+	0.983781i	$0.557407\pi$
$198$	1.98160	−	0.0691468i	0.140826	−	0.00491405i
$199$	15.8856	+	9.17157i	1.12610	+	0.650155i	0.942952	−	0.332930i	$-0.108037\pi$
$199$	15.8856	+	9.17157i	1.12610	+	0.650155i	0.183150	+	0.983085i	$0.441371\pi$
$200$	−6.83436	+	6.83436i	−0.483262	+	0.483262i
$201$	−8.47659	−	8.18597i	−0.597893	−	0.577393i
$202$	−1.01213	−	3.77732i	−0.0712133	−	0.265772i
$203$	−2.20784	−	2.20784i	−0.154960	−	0.154960i
$204$	−0.334383	−	19.1713i	−0.0234115	−	1.34226i
$205$	−20.4830	+	11.8259i	−1.43060	+	0.825956i
$206$	−0.404361	+	1.50910i	−0.0281732	+	0.105144i
$207$	3.81650	−	7.17733i	0.265265	−	0.498859i
$208$		0			0
$209$		−	9.23947i		−	0.639107i
$210$	−2.36948	+	0.679404i	−0.163510	+	0.0468833i
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	0.970291	−	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
$213$	−19.5069	−	4.86389i	−1.33659	−	0.333269i
$214$	−4.44451	+	1.19090i	−0.303820	+	0.0814084i
$215$	18.6332	−	4.99274i	1.27077	−	0.340502i
$216$	5.27460	+	4.74965i	0.358891	+	0.323173i
$217$	2.64984	−	4.58965i	0.179883	−	0.311566i
$218$	1.11855	+	1.93739i	0.0757580	+	0.131217i
$219$	6.16580	+	21.5038i	0.416646	+	1.45309i
$220$			12.2238i			0.824129i
$221$		0			0
$222$	−1.13062	+	0.679324i	−0.0758821	+	0.0455932i
$223$	−7.32834	+	27.3497i	−0.490742	+	1.83147i	0.0619383	+	0.998080i	$0.480272\pi$
$223$	−7.32834	+	27.3497i	−0.490742	+	1.83147i	−0.552680	+	0.833393i	$0.686395\pi$
$224$	−3.90907	+	2.25691i	−0.261186	+	0.150796i
$225$	−18.0016	+	11.2480i	−1.20011	+	0.749867i
$226$	3.24295	+	3.24295i	0.215718	+	0.215718i
$227$	−1.90366	−	7.10455i	−0.126350	−	0.471546i	0.873534	−	0.486763i	$-0.161823\pi$
$227$	−1.90366	−	7.10455i	−0.126350	−	0.471546i	−0.999884	+	0.0152176i	$0.995156\pi$
$228$	11.1198	−	11.5146i	0.736428	−	0.762574i
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	−0.221263	−	0.975214i	$-0.571018\pi$
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	0.975214	+	0.221263i	$0.0710179\pi$
$230$	−2.87401	−	1.65931i	−0.189507	−	0.109412i
$231$	−1.82985	+	3.30104i	−0.120395	+	0.217192i
$232$	3.54545	+	0.950001i	0.232770	+	0.0623706i
$233$	−18.1554			−1.18940			−0.594700	−	0.803947i	$-0.702729\pi$
$233$	−18.1554			−1.18940			−0.594700	+	0.803947i	$0.702729\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	18.1328	+	4.85866i	1.18034	+	0.316272i
$237$	0.923776	−	1.66648i	0.0600057	−	0.108250i
$238$	−2.09315	−	1.20848i	−0.135679	−	0.0783341i
$239$	−6.54262	+	6.54262i	−0.423207	+	0.423207i	−0.886306	−	0.463099i	$-0.846737\pi$
$239$	−6.54262	+	6.54262i	−0.423207	+	0.423207i	0.463099	+	0.886306i	$0.346737\pi$
$240$	−13.6728	+	14.1582i	−0.882574	+	0.913908i
$241$	7.16336	+	26.7340i	0.461433	+	1.72209i	0.668453	+	0.743754i	$0.266957\pi$
$241$	7.16336	+	26.7340i	0.461433	+	1.72209i	−0.207021	+	0.978337i	$0.566377\pi$
$242$	1.86495	+	1.86495i	0.119883	+	0.119883i
$243$	8.94033	+	12.7699i	0.573522	+	0.819190i
$244$	−4.32547	+	2.49731i	−0.276910	+	0.159874i
$245$	−5.08137	+	18.9639i	−0.324637	+	1.21156i
$246$	3.56147	−	2.13988i	0.227071	−	0.136434i
$247$		0			0
$248$			6.23009i			0.395611i
$249$	−3.09836	−	10.8058i	−0.196351	−	0.684791i
$250$	1.27104	+	2.20150i	0.0803874	+	0.139235i
$251$	−2.80003	+	4.84979i	−0.176736	+	0.306116i	−0.940761	−	0.339071i	$-0.889887\pi$
$251$	−2.80003	+	4.84979i	−0.176736	+	0.306116i	0.764025	+	0.645187i	$0.223221\pi$
$252$	−6.25328	+	1.91164i	−0.393920	+	0.120422i
$253$	−4.90825	+	1.31516i	−0.308579	+	0.0826834i
$254$	2.65336	−	0.710965i	0.166486	−	0.0446099i
$255$	−34.4661	−	8.59385i	−2.15835	−	0.538168i
$256$	−3.48092	+	6.02913i	−0.217557	+	0.376821i
$257$	−3.40679	−	5.90073i	−0.212510	−	0.368077i	0.739990	−	0.672618i	$-0.234830\pi$
$257$	−3.40679	−	5.90073i	−0.212510	−	0.368077i	−0.952499	+	0.304541i	$0.901497\pi$
$258$	−3.25749	+	0.934023i	−0.202802	+	0.0581497i
$259$		−	2.51073i		−	0.156009i
$260$		0			0
$261$	7.11751	+	3.78469i	0.440563	+	0.234266i
$262$	−1.69139	+	6.31236i	−0.104495	+	0.389979i
$263$	19.5996	−	11.3159i	1.20857	−	0.697765i	0.246119	−	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
$266$	−0.522238	−	1.94902i	−0.0320205	−	0.119502i
$267$	5.32502	+	5.14245i	0.325886	+	0.314713i
$268$	−9.02401	+	9.02401i	−0.551229	+	0.551229i
$269$	−22.6058	−	13.0515i	−1.37830	−	0.795762i	−0.386345	−	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
$271$	−17.0798	−	4.57652i	−1.03753	−	0.278004i	−0.300438	−	0.953801i	$-0.597133\pi$
$271$	−17.0798	−	4.57652i	−1.03753	−	0.278004i	−0.737087	+	0.675797i	$0.763799\pi$
$272$	−19.2992			−1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	12.8167	+	3.43423i	0.772876	+	0.207092i
$276$	−7.69967	−	4.26813i	−0.463466	−	0.256911i
$277$	−19.6593	−	11.3503i	−1.18122	−	0.681975i	−0.224920	−	0.974377i	$-0.572212\pi$
$277$	−19.6593	−	11.3503i	−1.18122	−	0.681975i	−0.956295	+	0.292402i	$0.905545\pi$
$278$	1.34385	−	1.34385i	0.0805989	−	0.0805989i
$279$	−3.07825	+	13.3317i	−0.184290	+	0.798151i
$280$	1.42759	+	5.32786i	0.0853151	+	0.318400i
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	0.914679	−	0.404181i	$-0.132443\pi$
$281$	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	$-0.734401\pi$
$283$	−6.15361	+	3.55279i	−0.365794	+	0.211192i	0.305825	+	0.952088i	$0.401068\pi$
$284$	−5.63513	+	21.0306i	−0.334384	+	1.24794i
$285$	−15.2729	−	25.4192i	−0.904690	−	1.50570i
$286$		0			0
$287$			7.90886i			0.466845i
$288$	7.94796	−	8.52269i	0.468338	−	0.502205i
$289$	−8.91483	−	15.4409i	−0.524402	−	0.908291i
$290$	1.64548	−	2.85006i	0.0966260	−	0.167361i
$291$	−5.14061	+	20.6167i	−0.301348	+	1.20857i
$292$	23.4012	−	6.27032i	1.36945	−	0.366943i
$293$	15.3534	−	4.11392i	0.896953	−	0.240338i	0.219245	−	0.975670i	$-0.429640\pi$
$293$	15.3534	−	4.11392i	0.896953	−	0.240338i	0.677707	+	0.735332i	$0.262974\pi$
$294$	0.834411	−	3.34645i	0.0486638	−	0.195169i
$295$	17.3885	−	30.1178i	1.01240	−	1.75352i
$296$	1.47576	+	2.55609i	0.0857768	+	0.148570i
$297$	2.02633	−	9.53130i	0.117580	−	0.553062i
$298$			8.04031i			0.465763i
$299$		0			0
$300$	11.8396	+	19.7050i	0.683558	+	1.13767i
$301$	1.66951	−	6.23070i	0.0962289	−	0.359131i
$302$	2.85701	−	1.64949i	0.164402	−	0.0949176i
$303$	−19.2152	+	0.335149i	−1.10388	+	0.0192538i
$304$	−11.3927	−	11.3927i	−0.653417	−	0.653417i
$305$	2.39481	+	8.93755i	0.137126	+	0.511763i
$306$	6.08006	+	1.40386i	0.347574	+	0.0802534i
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	−0.165277	−	0.986247i	$-0.552852\pi$
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	0.986247	+	0.165277i	$0.0528518\pi$
$308$	3.53987	+	2.04374i	0.201703	+	0.116453i
$309$	6.71521	+	3.72242i	0.382015	+	0.211761i
$310$	5.39552	+	1.44572i	0.306445	+	0.0821116i
$311$	7.62181			0.432193			0.216097	−	0.976372i	$-0.430667\pi$
$311$	7.62181			0.432193			0.216097	+	0.976372i	$0.430667\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	5.33751	+	1.43018i	0.301213	+	0.0807099i
$315$	0.422445	+	12.1064i	0.0238021	+	0.682120i
$316$	−1.78705	−	1.03176i	−0.100530	−	0.0580408i
$317$	6.29415	−	6.29415i	0.353515	−	0.353515i	−0.507901	−	0.861416i	$-0.669578\pi$
$317$	6.29415	−	6.29415i	0.353515	−	0.353515i	0.861416	+	0.507901i	$0.169578\pi$
$318$	−1.08082	−	1.04377i	−0.0606095	−	0.0585315i
$319$	−1.30420	−	4.86734i	−0.0730211	−	0.272518i
$320$	12.7066	+	12.7066i	0.710319	+	0.710319i
$321$	0.394345	+	22.6091i	0.0220102	+	1.26192i
$322$	−0.961034	+	0.554853i	−0.0535563	+	0.0309207i
$323$	7.52572	−	28.0864i	0.418743	−	1.56277i
$324$	13.9963	−	9.43958i	0.777575	−	0.524421i
$325$		0			0
$326$			1.21818i			0.0674689i
$327$	10.5682	−	3.03023i	0.584422	−	0.167572i
$328$	−4.64868	−	8.05175i	−0.256680	−	0.444583i
$329$	−1.83387	+	3.17636i	−0.101105	+	0.175118i
$330$	−3.85991	−	0.962439i	−0.212481	−	0.0529805i
$331$	15.5288	−	4.16094i	0.853541	−	0.228706i	0.194584	−	0.980886i	$-0.437664\pi$
$331$	15.5288	−	4.16094i	0.853541	−	0.228706i	0.658958	+	0.752180i	$0.270998\pi$
$332$	−11.7593	+	3.15088i	−0.645373	+	0.172927i
$333$	1.89502	+	6.19893i	0.103847	+	0.339699i
$334$	0.923981	−	1.60038i	0.0505580	−	0.0875690i
$335$	11.8211	+	20.4747i	0.645853	+	1.11865i
$336$	1.81404	+	6.32664i	0.0989642	+	0.345146i
$337$			28.3556i			1.54463i	0.635243	+	0.772313i	$0.280900\pi$
$337$			28.3556i			1.54463i	−0.635243	+	0.772313i	$0.719100\pi$
$338$		0			0
$339$	19.3195	−	11.6080i	1.04929	−	0.630457i
$340$	−9.95653	+	37.1583i	−0.539968	+	2.01519i
$341$	7.40704	−	4.27646i	0.401114	−	0.231583i
$342$	2.76045	+	4.41791i	0.149268	+	0.238893i
$343$	10.3937	+	10.3937i	0.561209	+	0.561209i
$344$	1.96261	+	7.32457i	0.105817	+	0.394914i
$345$	−11.3294	+	11.7316i	−0.609952	+	0.631607i
$346$	−3.55163	+	3.55163i	−0.190937	+	0.190937i
$347$	−9.59025	−	5.53693i	−0.514831	−	0.297238i	0.219986	−	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
$349$	−28.8980	−	7.74319i	−1.54687	−	0.414483i	−0.618394	−	0.785868i	$-0.712216\pi$
$349$	−28.8980	−	7.74319i	−1.54687	−	0.414483i	−0.928479	+	0.371385i	$0.878883\pi$
$350$	2.89773			0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	−12.2442	−	3.28082i	−0.651692	−	0.174620i	−0.0821982	−	0.996616i	$-0.526194\pi$
$353$	−12.2442	−	3.28082i	−0.651692	−	0.174620i	−0.569494	+	0.821996i	$0.692861\pi$
$354$	−2.96190	+	5.34324i	−0.157423	+	0.283990i
$355$	34.9309	+	20.1674i	1.85394	+	1.07037i
$356$	5.66891	−	5.66891i	0.300452	−	0.300452i
$357$	−8.25120	+	8.54414i	−0.436700	+	0.452204i
$358$	0.398325	+	1.48657i	0.0210521	+	0.0785676i
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.996870	−	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
$362$	0.192234	−	0.717426i	0.0101036	−	0.0377071i
$363$	11.1102	−	6.67547i	0.583133	−	0.350371i
$364$		0			0
$365$		−	44.8813i		−	2.34919i
$366$	−0.448012	−	1.56248i	−0.0234180	−	0.0816722i
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	0.992221	+	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
$369$	−5.96937	−	19.5268i	−0.310753	−	1.01652i
$370$	2.55614	−	0.684915i	0.132887	−	0.0356071i
$371$	2.76263	−	0.740245i	0.143429	−	0.0384316i
$372$	14.3777	+	3.58497i	0.745451	+	0.185872i
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	0.469128	+	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
$375$	12.0088	−	3.44331i	0.620134	−	0.177812i
$376$		−	4.31166i		−	0.222357i
$377$		0			0
$378$	−0.111288	−	2.12511i	−0.00572404	−	0.109304i
$379$	1.02786	−	3.83602i	0.0527975	−	0.197043i	−0.934489	−	0.355991i	$-0.884143\pi$
$379$	1.02786	−	3.83602i	0.0527975	−	0.197043i	0.987287	+	0.158948i	$0.0508101\pi$
$380$	−27.8128	+	16.0577i	−1.42677	+	0.823744i
$381$	−0.235423	−	13.4976i	−0.0120611	−	0.691502i
$382$	−1.69412	−	1.69412i	−0.0866785	−	0.0866785i
$383$	−6.88748	−	25.7044i	−0.351934	−	1.31344i	−0.884299	−	0.466921i	$-0.845363\pi$
$383$	−6.88748	−	25.7044i	−0.351934	−	1.31344i	0.532365	−	0.846515i	$-0.321303\pi$
$384$	−11.9504	−	11.5406i	−0.609839	−	0.588931i
$385$	5.35443	−	5.35443i	0.272887	−	0.272887i
$386$	3.39296	+	1.95893i	0.172697	+	0.0997067i
$387$	0.580765	+	16.6435i	0.0295219	+	0.846038i
$388$	22.2271	+	5.95573i	1.12841	+	0.302356i
$389$	6.17335			0.313001			0.156501	−	0.987678i	$-0.449979\pi$
$389$	6.17335			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	−7.45460	−	1.99745i	−0.376514	−	0.100887i
$393$	28.0889	+	15.5704i	1.41690	+	0.785423i
$394$	0.697088	+	0.402464i	0.0351188	+	0.0202758i
$395$	−2.70311	+	2.70311i	−0.136008	+	0.136008i
$396$	−10.2824	−	2.37417i	−0.516710	−	0.119306i
$397$	−6.17560	−	23.0477i	−0.309945	−	1.15673i	−0.928605	−	0.371071i	$-0.878991\pi$
$397$	−6.17560	−	23.0477i	−0.309945	−	1.15673i	0.618660	−	0.785659i	$-0.287676\pi$
$398$	4.57140	+	4.57140i	0.229143	+	0.229143i
$399$	−9.91463	+	0.172930i	−0.496352	+	0.00865730i
$400$	20.0382	−	11.5691i	1.00191	−	0.578453i
$401$	6.00499	−	22.4109i	0.299875	−	1.11915i	−0.637393	−	0.770539i	$-0.719987\pi$
$401$	6.00499	−	22.4109i	0.299875	−	1.11915i	0.937268	−	0.348610i	$-0.113346\pi$
$402$	−2.13901	−	3.56002i	−0.106684	−	0.177558i
$403$		0			0
$404$			20.8129i			1.03548i
$405$	−10.1806	−	29.5716i	−0.505877	−	1.46942i
$406$	−0.550228	−	0.953023i	−0.0273074	−	0.0472978i
$407$	2.02598	−	3.50910i	0.100424	−	0.173940i
$408$	3.37818	−	13.5484i	0.167245	−	0.670746i
$409$	−12.1401	+	3.25292i	−0.600288	+	0.160847i	−0.546151	−	0.837687i	$-0.683907\pi$
$409$	−12.1401	+	3.25292i	−0.600288	+	0.160847i	−0.0541371	+	0.998534i	$0.517241\pi$
$410$	−8.05189	+	2.15750i	−0.397655	+	0.106551i
$411$	−3.15743	+	12.6630i	−0.155744	+	0.624622i
$412$	4.15753	−	7.20106i	0.204827	−	0.354771i
$413$	−5.81450	−	10.0710i	−0.286113	−	0.495562i
$414$	1.95398	−	2.09528i	0.0960329	−	0.102977i
$415$			22.5532i			1.10709i
$416$		0			0
$417$	−4.81024	−	8.00582i	−0.235558	−	0.392047i
$418$	0.842818	−	3.14544i	0.0412236	−	0.153848i
$419$	−23.2172	+	13.4045i	−1.13424	+	0.654851i	−0.944997	−	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	$-0.349625\pi$
$421$	−8.93430	−	8.93430i	−0.435431	−	0.435431i	−0.890471	+	0.455040i	$0.849625\pi$
$422$	0.730414	+	2.72594i	0.0355560	+	0.132697i
$423$	2.13036	−	9.22649i	0.103582	−	0.448607i
$424$	−2.37744	+	2.37744i	−0.115459	+	0.115459i
$425$	36.1633	+	20.8789i	1.75418	+	1.01278i
$426$	−6.19716	−	3.43525i	−0.300253	−	0.166438i
$427$	2.98861	+	0.800795i	0.144629	+	0.0387532i
$428$	24.4891			1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	−20.5028	−	5.49370i	−0.987583	−	0.264622i	−0.271348	−	0.962481i	$-0.587469\pi$
$431$	−20.5028	−	5.49370i	−0.987583	−	0.264622i	−0.716235	+	0.697859i	$0.754136\pi$
$432$	−9.25399	−	14.2511i	−0.445233	−	0.685658i
$433$	1.60537	+	0.926859i	0.0771490	+	0.0445420i	0.538078	−	0.842895i	$-0.319150\pi$
$433$	1.60537	+	0.926859i	0.0771490	+	0.0445420i	−0.460929	+	0.887437i	$0.652484\pi$
$434$	1.32076	−	1.32076i	0.0633986	−	0.0633986i
$435$	−11.6338	−	11.2349i	−0.557798	−	0.538673i
$436$	−3.08159	−	11.5007i	−0.147582	−	0.550782i
$437$	−9.44007	−	9.44007i	−0.451580	−	0.451580i
$438$	0.137496	+	7.88308i	0.00656979	+	0.376668i
$439$	−12.4753	+	7.20264i	−0.595415	+	0.343763i	−0.767236	−	0.641365i	$-0.778368\pi$
$439$	−12.4753	+	7.20264i	−0.595415	+	0.343763i	0.171820	+	0.985128i	$0.445035\pi$
$440$	−2.30393	+	8.59840i	−0.109836	+	0.409913i
$441$	−14.9651	−	7.95761i	−0.712625	−	0.378934i
$442$		0			0
$443$			22.2330i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$443$			22.2330i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$444$	6.74811	−	1.93489i	0.320251	−	0.0918260i
$445$	−7.42603	−	12.8623i	−0.352027	−	0.609729i
$446$	−4.98965	+	8.64232i	−0.236267	+	0.409226i
$447$	38.3394	+	9.55963i	1.81339	+	0.452155i
$448$	5.80413	−	1.55521i	0.274220	−	0.0734769i
$449$	−23.7458	+	6.36268i	−1.12064	+	0.300273i	−0.771141	−	0.636665i	$-0.780313\pi$
$449$	−23.7458	+	6.36268i	−1.12064	+	0.300273i	−0.349495	+	0.936938i	$0.613647\pi$
$450$	−7.15442	+	2.18712i	−0.337263	+	0.103102i
$451$	−6.38188	+	11.0537i	−0.300511	+	0.520501i
$452$	−12.2044	−	21.1387i	−0.574048	−	0.994281i
$453$	−4.46857	−	15.5845i	−0.209952	−	0.732225i
$454$		−	2.59229i		−	0.121662i
$455$		0			0
$456$	9.99211	−	6.00368i	0.467923	−	0.281148i
$457$	−1.75192	+	6.53825i	−0.0819513	+	0.305847i	−0.994719	−	0.102632i	$-0.967274\pi$
$457$	−1.75192	+	6.53825i	−0.0819513	+	0.305847i	0.912768	+	0.408478i	$0.133940\pi$
$458$	4.92490	−	2.84339i	0.230125	−	0.132863i
$459$	13.9231	−	27.3230i	0.649876	−	1.27533i
$460$	12.4892	+	12.4892i	0.582312	+	0.582312i
$461$	3.20695	+	11.9685i	0.149363	+	0.557429i	0.999522	+	0.0309044i	$0.00983873\pi$
$461$	3.20695	+	11.9685i	0.149363	+	0.557429i	−0.850160	+	0.526525i	$0.823495\pi$
$462$	−0.924064	+	0.956871i	−0.0429914	+	0.0445177i
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	−0.526236	−	0.850339i	$-0.676397\pi$
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	0.850339	+	0.526236i	$0.176397\pi$
$464$	−7.60980	−	4.39352i	−0.353276	−	0.203964i
$465$	13.3089	−	24.0091i	0.617184	−	1.11339i
$466$	−6.18074	−	1.65612i	−0.286317	−	0.0767185i
$467$	9.19934			0.425695			0.212847	−	0.977085i	$-0.431726\pi$
$467$	9.19934			0.425695			0.212847	+	0.977085i	$0.431726\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	−3.73407	−	1.00054i	−0.172240	−	0.0461515i
$471$	13.1658	−	23.7510i	0.606647	−	1.09439i
$472$	11.8391	+	6.83530i	0.544938	+	0.314620i
$473$	7.36110	−	7.36110i	0.338464	−	0.338464i
$474$	0.466501	−	0.483064i	0.0214271	−	0.0221878i
$475$	9.02270	+	33.6732i	0.413990	+	1.54503i
$476$	9.09592	+	9.09592i	0.416911	+	0.416911i
$477$	−6.26215	+	3.91280i	−0.286724	+	0.179155i
$478$	−2.82415	+	1.63052i	−0.129174	+	0.0745784i
$479$	−5.93980	+	22.1676i	−0.271396	+	1.01287i	0.686821	+	0.726826i	$0.259005\pi$
$479$	−5.93980	+	22.1676i	−0.271396	+	1.01287i	−0.958218	+	0.286039i	$0.907661\pi$
$480$	−20.0412	+	12.0416i	−0.914750	+	0.549621i
$481$		0			0
$482$			9.75464i			0.444312i
$483$	1.50313	+	5.24229i	0.0683947	+	0.238533i
$484$	−7.01850	−	12.1564i	−0.319023	−	0.552563i
$485$	21.3148	−	36.9183i	0.967854	−	1.67637i
$486$	1.87874	+	5.16285i	0.0852213	+	0.234192i
$487$	28.4656	−	7.62733i	1.28990	−	0.345627i	0.452277	−	0.891878i	$-0.350612\pi$
$487$	28.4656	−	7.62733i	1.28990	−	0.345627i	0.837622	+	0.546250i	$0.183945\pi$
$488$	−3.51329	+	0.941384i	−0.159039	+	0.0426144i
$489$	5.80879	+	1.44838i	0.262682	+	0.0654978i
$490$	−3.45975	+	5.99247i	−0.156296	+	0.270712i
$491$	−7.66195	−	13.2709i	−0.345779	−	0.598907i	0.639716	−	0.768611i	$-0.279052\pi$
$491$	−7.66195	−	13.2709i	−0.345779	−	0.598907i	−0.985495	+	0.169705i	$0.945719\pi$
$492$	−21.2567	+	6.09496i	−0.958326	+	0.274782i
$493$		−	15.8582i		−	0.714215i
$494$		0			0
$495$	−9.17859	+	17.2613i	−0.412547	+	0.775838i
$496$	3.86016	−	14.4063i	0.173326	−	0.646863i
$497$	11.6805	−	6.74372i	0.523941	−	0.302497i
$498$	−0.0690926	−	3.96131i	−0.00309611	−	0.177510i
$499$	29.5332	+	29.5332i	1.32209	+	1.32209i	0.912084	+	0.410004i	$0.134473\pi$
$499$	29.5332	+	29.5332i	1.32209	+	1.32209i	0.410004	+	0.912084i	$0.365527\pi$
$500$	−3.50168	−	13.0684i	−0.156600	−	0.584439i
$501$	−6.53269	−	6.30871i	−0.291859	−	0.281852i
$502$	−1.39562	+	1.39562i	−0.0622897	+	0.0622897i
$503$	30.1073	+	17.3825i	1.34242	+	0.775046i	0.987162	−	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
$505$	37.2433	+	9.97931i	1.65730	+	0.444073i
$506$	−1.79091			−0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	−42.7871	−	11.4648i	−1.89651	−	0.508167i	−0.997536	−	0.0701558i	$-0.977650\pi$
$509$	−42.7871	−	11.4648i	−1.89651	−	0.508167i	−0.898969	−	0.438011i	$-0.855683\pi$
$510$	−10.9495	−	6.06962i	−0.484854	−	0.268767i
$511$	−12.9971	−	7.50387i	−0.574957	−	0.331952i
$512$	−15.2996	+	15.2996i	−0.676153	+	0.676153i
$513$	24.3484	−	7.91022i	1.07501	−	0.349245i
$514$	−0.621529	−	2.31958i	−0.0274145	−	0.102312i
$515$	−10.8924	−	10.8924i	−0.479975	−	0.479975i
$516$	18.0329	−	0.314527i	0.793854	−	0.0138463i
$517$	−5.12618	+	2.95960i	−0.225449	+	0.130163i
$518$	0.229027	−	0.854741i	0.0100629	−	0.0375552i
$519$	12.7128	+	21.1584i	0.558032	+	0.928749i
$520$		0			0
$521$			1.93372i			0.0847179i	0.999102	+	0.0423590i	$0.0134873\pi$
$521$			1.93372i			0.0847179i	−0.999102	+	0.0423590i	$0.986513\pi$
$522$	2.07781	+	1.93769i	0.0909434	+	0.0848106i
$523$	−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
$525$	3.44529	−	13.8175i	0.150365	−	0.603047i
$526$	7.70463	−	2.06445i	0.335938	−	0.0900142i
$527$	25.9994	−	6.96651i	1.13255	−	0.303466i
$528$	−2.56976	+	10.3062i	−0.111835	+	0.448519i
$529$	7.82890	−	13.5601i	0.340387	−	0.589568i
$530$	1.50726	+	2.61066i	0.0654714	+	0.113400i
$531$	21.9571	+	20.4764i	0.952859	+	0.888602i
$532$			10.7390i			0.465595i
$533$		0			0
$534$	1.34373	+	2.23641i	0.0581490	+	0.0967791i
$535$	11.7419	−	43.8215i	0.507648	−	1.89457i
$536$	−8.04846	+	4.64678i	−0.347640	+	0.200710i
$537$	7.56215	−	0.131898i	0.326331	−	0.00569182i
$538$	−6.50526	−	6.50526i	−0.280462	−	0.280462i
$539$	2.74218	+	10.2340i	0.118114	+	0.440808i
$540$	−32.2130	+	10.4652i	−1.38623	+	0.450351i
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	−0.760068	−	0.649844i	$-0.774834\pi$
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	0.649844	+	0.760068i	$0.274834\pi$
$542$	−5.39710	−	3.11602i	−0.231825	−	0.133844i
$543$	−3.19242	−	1.76964i	−0.137000	−	0.0759425i
$544$	−22.1441	−	5.93348i	−0.949419	−	0.254396i
$545$	−22.0572			−0.944827
$546$		0			0
$547$	23.1549			0.990030			0.495015	−	0.868884i	$-0.335163\pi$
$547$	23.1549			0.990030			0.495015	+	0.868884i	$0.335163\pi$
$548$	13.6522	+	3.65808i	0.583191	+	0.156266i
$549$	−7.98321	+	0.278569i	−0.340715	+	0.0118890i
$550$	4.04999	+	2.33826i	0.172692	+	0.0997038i
$551$	9.36139	−	9.36139i	0.398809	−	0.398809i
$552$	−4.61161	−	4.45349i	−0.196283	−	0.189553i
$553$	0.330846	+	1.23473i	0.0140690	+	0.0525062i
$554$	−5.65736	−	5.65736i	−0.240358	−	0.240358i
$555$	−0.226797	−	13.0030i	−0.00962700	−	0.551948i
$556$	−8.75970	+	5.05741i	−0.371494	+	0.214482i
$557$	0.926129	−	3.45636i	0.0392414	−	0.146451i	−0.943526	−	0.331300i	$-0.892513\pi$
$557$	0.926129	−	3.45636i	0.0392414	−	0.146451i	0.982767	+	0.184849i	$0.0591796\pi$
$558$	−2.26406	+	4.25780i	−0.0958451	+	0.180247i
$559$		0			0
$560$		−	13.2045i		−	0.557994i
$561$	−18.4267	+	5.28351i	−0.777977	+	0.223070i
$562$	2.13267	+	3.69389i	0.0899611	+	0.155817i
$563$	−9.83710	+	17.0384i	−0.414585	+	0.718081i	−0.995385	−	0.0959647i	$-0.969406\pi$
$563$	−9.83710	+	17.0384i	−0.414585	+	0.718081i	0.580800	+	0.814046i	$0.302740\pi$
$564$	−9.95039	−	2.48105i	−0.418987	−	0.104471i
$565$	−43.6781	+	11.7035i	−1.83755	+	0.492370i
$566$	−2.41899	+	0.648166i	−0.101678	+	0.0272445i
$567$	−10.2657	−	1.99601i	−0.431119	−	0.0838247i
$568$	−7.92766	+	13.7311i	−0.332637	+	0.576145i
$569$	4.78231	+	8.28321i	0.200485	+	0.347250i	0.948685	−	0.316223i	$-0.102415\pi$
$569$	4.78231	+	8.28321i	0.200485	+	0.347250i	−0.748200	+	0.663473i	$0.769082\pi$
$570$	−2.88072	−	10.0468i	−0.120660	−	0.420813i
$571$		−	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
$574$	−0.721441	+	2.69245i	−0.0301124	+	0.112381i
$575$	16.6038	−	9.58619i	0.692425	−	0.399772i
$576$	−13.1564	+	8.22057i	−0.548185	+	0.342524i
$577$	−6.37509	−	6.37509i	−0.265398	−	0.265398i	0.561844	−	0.827243i	$-0.310092\pi$
$577$	−6.37509	−	6.37509i	−0.265398	−	0.265398i	−0.827243	+	0.561844i	$0.810092\pi$
$578$	−1.62641	−	6.06984i	−0.0676497	−	0.252472i
$579$	13.3750	−	13.8499i	0.555848	−	0.575582i
$580$	−12.3851	+	12.3851i	−0.514264	+	0.514264i
$581$	6.53113	+	3.77075i	0.270957	+	0.156437i
$582$	−3.63069	+	6.54973i	−0.150497	+	0.271495i
$583$	4.45849	+	1.19465i	0.184652	+	0.0494773i
$584$	17.6425			0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	30.3129	+	8.12231i	1.25115	+	0.335243i	0.822779	−	0.568362i	$-0.192423\pi$
$587$	30.3129	+	8.12231i	1.25115	+	0.335243i	0.428367	+	0.903605i	$0.359089\pi$
$588$	−8.89929	+	16.0542i	−0.367000	+	0.662066i
$589$	19.4604	+	11.2355i	0.801853	+	0.462950i
$590$	8.66697	−	8.66697i	0.356814	−	0.356814i
$591$	2.74792	−	2.84548i	0.113034	−	0.117047i
$592$	−1.82876	−	6.82503i	−0.0751616	−	0.280507i
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	0.999673	−	0.0255650i	$-0.00813848\pi$
$593$	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
$596$	11.0754	−	41.3341i	0.453668	−	1.69311i
$597$	27.2335	−	16.3630i	1.11459	−	0.669695i
$598$		0			0
$599$		−	33.7915i		−	1.38068i	−0.723484	−	0.690341i	$-0.757460\pi$
$599$		−	33.7915i		−	1.38068i	0.723484	−	0.690341i	$-0.242540\pi$
$600$	4.61415	+	16.0923i	0.188372	+	0.656964i
$601$	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
$603$	−19.5188	+	5.96693i	−0.794867	+	0.242992i
$604$	−16.9596	+	4.54432i	−0.690077	+	0.184906i
$605$	−25.1183	+	6.73042i	−1.02120	+	0.273630i
$606$	−6.57209	−	1.63870i	−0.266973	−	0.0665676i
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	−0.998208	−	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
$609$	−5.19860	+	1.49060i	−0.210658	+	0.0604022i
$610$			3.26111i			0.132038i
$611$		0			0
$612$	−29.3229	−	15.5923i	−1.18531	−	0.630280i
$613$	0.153064	−	0.571244i	0.00618221	−	0.0230723i	−0.962766	−	0.270337i	$-0.912865\pi$
$613$	0.153064	−	0.571244i	0.00618221	−	0.0230723i	0.968948	+	0.247264i	$0.0795316\pi$
$614$	6.20916	−	3.58486i	0.250581	−	0.144673i
$615$	0.714416	+	40.9599i	0.0288080	+	1.65166i
$616$	2.10479	+	2.10479i	0.0848044	+	0.0848044i
$617$	−7.52400	−	28.0800i	−0.302905	−	1.13046i	−0.934734	−	0.355349i	$-0.884362\pi$
$617$	−7.52400	−	28.0800i	−0.302905	−	1.13046i	0.631829	−	0.775108i	$-0.282305\pi$
$618$	1.94654	+	1.87980i	0.0783012	+	0.0756166i
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	−0.0808459	−	0.996727i	$-0.525762\pi$
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	0.996727	+	0.0808459i	$0.0257622\pi$
$620$	−25.7461	−	14.8645i	−1.03399	−	0.596974i
$621$	−7.66791	−	11.8086i	−0.307703	−	0.473862i
$622$	2.59473	+	0.695256i	0.104039	+	0.0278772i
$623$	−4.96634			−0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	−2.21789	−	0.594282i	−0.0886448	−	0.0237523i
$627$	−13.9966	−	7.75870i	−0.558972	−	0.309853i
$628$	−25.4694	−	14.7047i	−1.01634	−	0.586783i
$629$	9.01686	−	9.01686i	0.359526	−	0.359526i
$630$	−0.960524	+	4.15999i	−0.0382682	+	0.165738i
$631$	−10.5019	−	39.1937i	−0.418075	−	1.56028i	−0.778596	−	0.627526i	$-0.784068\pi$
$631$	−10.5019	−	39.1937i	−0.418075	−	1.56028i	0.360521	−	0.932751i	$-0.382599\pi$
$632$	−1.06258	−	1.06258i	−0.0422670	−	0.0422670i
$633$	13.8668	−	0.241863i	0.551157	−	0.00961320i
$634$	2.71690	−	1.56860i	0.107902	−	0.0622971i
$635$	−7.00990	+	26.1613i	−0.278180	+	1.03818i
$636$	4.11858	+	6.85468i	0.163312	+	0.271806i
$637$		0			0
$638$		−	1.77598i		−	0.0703117i
$639$	−23.7488	+	25.4662i	−0.939489	+	1.00743i
$640$	16.6654	+	28.8653i	0.658758	+	1.14100i
$641$	−12.8560	+	22.2673i	−0.507783	+	0.879506i	0.492176	+	0.870496i	$0.336202\pi$
$641$	−12.8560	+	22.2673i	−0.507783	+	0.879506i	−0.999959	+	0.00901077i	$0.997132\pi$
$642$	−1.92814	+	7.73291i	−0.0760976	+	0.305194i
$643$	0.612124	−	0.164018i	0.0241398	−	0.00646824i	−0.246729	−	0.969085i	$-0.579356\pi$
$643$	0.612124	−	0.164018i	0.0241398	−	0.00646824i	0.270869	+	0.962616i	$0.412689\pi$
$644$	5.70484	−	1.52861i	0.224802	−	0.0602356i
$645$	8.08354	−	32.4195i	0.318289	−	1.27652i
$646$	5.12404	−	8.87510i	0.201603	−	0.349186i
$647$	23.5124	+	40.7247i	0.924368	+	1.60105i	0.792574	+	0.609776i	$0.208740\pi$
$647$	23.5124	+	40.7247i	0.924368	+	1.60105i	0.131794	+	0.991277i	$0.457926\pi$
$648$	11.6244	−	4.00191i	0.456649	−	0.157210i
$649$		−	18.7675i		−	0.736690i
$650$		0			0
$651$	−4.72758	−	7.86826i	−0.185289	−	0.308381i
$652$	1.67804	−	6.26251i	0.0657169	−	0.245259i
$653$	−25.0935	+	14.4877i	−0.981984	+	0.566949i	−0.902869	−	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
$656$	5.76064	+	21.4990i	0.224915	+	0.839394i
$657$	37.7532	+	8.71705i	1.47289	+	0.340085i
$658$	−0.914059	+	0.914059i	−0.0356337	+	0.0356337i
$659$	−40.4280	−	23.3411i	−1.57485	−	0.909241i	−0.995561	−	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
$661$	6.70655	+	1.79701i	0.260854	+	0.0698957i	0.386876	−	0.922132i	$-0.373554\pi$
$661$	6.70655	+	1.79701i	0.260854	+	0.0698957i	−0.126021	+	0.992028i	$0.540221\pi$
$662$	5.66611			0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	19.2167	+	5.14911i	0.745194	+	0.199674i
$666$	0.0796706	+	2.28320i	0.00308717	+	0.0884721i
$667$	−6.30553	−	3.64050i	−0.244151	−	0.140961i
$668$	−6.95457	+	6.95457i	−0.269080	+	0.269080i
$669$	35.2776	+	34.0680i	1.36391	+	1.31715i
$670$	2.15662	+	8.04861i	0.0833174	+	0.310945i
$671$	3.53081	+	3.53081i	0.136306	+	0.136306i
$672$	0.136342	+	7.81696i	0.00525952	+	0.301546i
$673$	−22.6855	+	13.0975i	−0.874460	+	0.504870i	−0.868828	−	0.495114i	$-0.835126\pi$
$673$	−22.6855	+	13.0975i	−0.874460	+	0.504870i	−0.00563228	+	0.999984i	$0.501793\pi$
$674$	−2.58657	+	9.65322i	−0.0996311	+	0.371828i
$675$	1.92272	+	36.7156i	0.0740057	+	1.41318i
$676$		0			0
$677$			21.9298i			0.842829i	0.906868	+	0.421415i	$0.138466\pi$
$677$			21.9298i			0.842829i	−0.906868	+	0.421415i	$0.861534\pi$
$678$	7.63589	−	2.18945i	0.293255	−	0.0840852i
$679$	−7.12739	−	12.3450i	−0.273524	−	0.473758i
$680$	−14.0071	+	24.2610i	−0.537149	+	0.930369i
$681$	−12.3611	−	3.08213i	−0.473677	−	0.118108i
$682$	2.91171	−	0.780190i	0.111495	−	0.0298750i
$683$	−7.36335	+	1.97300i	−0.281751	+	0.0754949i	−0.396927	−	0.917850i	$-0.629923\pi$
$683$	−7.36335	+	1.97300i	−0.281751	+	0.0754949i	0.115176	+	0.993345i	$0.463257\pi$
$684$	−8.10549	−	26.5144i	−0.309921	−	1.01380i
$685$	13.0918	−	22.6757i	0.500212	−	0.866392i
$686$	2.59028	+	4.48650i	0.0988975	+	0.171296i
$687$	−7.70291	−	26.8646i	−0.293884	−	1.02495i
$688$		−	18.1532i		−	0.692084i
$689$		0			0
$690$	−4.92706	+	2.96039i	−0.187570	+	0.112700i
$691$	−4.12878	+	15.4088i	−0.157066	+	0.586179i	0.841853	+	0.539707i	$0.181465\pi$
$691$	−4.12878	+	15.4088i	−0.157066	+	0.586179i	−0.998920	+	0.0464729i	$0.985202\pi$
$692$	23.1508	−	13.3661i	0.880061	−	0.508103i
$693$	3.46407	+	5.54399i	0.131589	+	0.210599i
$694$	−2.75978	−	2.75978i	−0.104760	−	0.104760i
$695$	4.84983	+	18.0998i	0.183965	+	0.686565i
$696$	4.41637	−	4.57317i	0.167402	−	0.173345i
$697$	−28.4033	+	28.4033i	−1.07585	+	1.07585i
$698$	−9.13155	−	5.27210i	−0.345634	−	0.199552i
$699$	−15.2457	+	27.5032i	−0.576647	+	1.04027i
$700$	−14.8968	−	3.99159i	−0.563047	−	0.150868i
$701$	−30.3059			−1.14464			−0.572319	−	0.820031i	$-0.693956\pi$
$701$	−30.3059			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	9.36704	+	2.50989i	0.353034	+	0.0945951i
$705$	−9.21066	+	16.6160i	−0.346893	+	0.625793i
$706$	−3.86907	−	2.23381i	−0.145615	−	0.0840706i
$707$	9.11674	−	9.11674i	0.342870	−	0.342870i
$708$	22.5870	−	23.3889i	0.848871	−	0.879008i
$709$	8.80249	+	32.8514i	0.330585	+	1.23376i	0.908577	+	0.417717i	$0.137170\pi$
$709$	8.80249	+	32.8514i	0.330585	+	1.23376i	−0.577993	+	0.816042i	$0.696164\pi$
$710$	10.0521	+	10.0521i	0.377247	+	0.377247i
$711$	−1.74879	−	2.79881i	−0.0655847	−	0.104964i
$712$	5.05607	−	2.91912i	0.189484	−	0.109399i
$713$	3.19855	−	11.9372i	0.119787	−	0.447050i
$714$	−3.58839	+	2.15606i	−0.134292	+	0.0806884i
$715$		0			0
$716$		−	8.19093i		−	0.306110i
$717$	4.41718	+	15.4053i	0.164963	+	0.575322i
$718$	−5.08050	−	8.79968i	−0.189602	−	0.328401i
$719$	3.94839	−	6.83882i	0.147250	−	0.255045i	−0.782960	−	0.622072i	$-0.786291\pi$
$719$	3.94839	−	6.83882i	0.147250	−	0.255045i	0.930210	+	0.367027i	$0.119624\pi$
$720$	9.96640	+	32.6017i	0.371426	+	1.21499i
$721$	−4.97544	+	1.33316i	−0.185295	+	0.0496496i
$722$	1.79571	−	0.481159i	0.0668294	−	0.0179069i
$723$	46.5140	+	11.5979i	1.72988	+	0.431331i
$724$	−1.97649	+	3.42339i	−0.0734558	+	0.127229i
$725$	9.50629	+	16.4654i	0.353055	+	0.611509i
$726$	4.39123	−	1.25910i	0.162974	−	0.0467296i
$727$		−	24.6824i		−	0.915420i	−0.889102	−	0.457710i	$-0.848670\pi$
$727$		−	24.6824i		−	0.915420i	0.889102	−	0.457710i	$-0.151330\pi$
$728$		0			0
$729$	26.8523	−	2.82014i	0.994530	−	0.104450i
$730$	4.09404	−	15.2792i	0.151527	−	0.565507i
$731$	28.3722	−	16.3807i	1.04939	−	0.605863i
$732$	0.150866	+	8.64963i	0.00557616	+	0.319700i
$733$	34.3405	+	34.3405i	1.26839	+	1.26839i	0.946918	+	0.321476i	$0.104179\pi$
$733$	34.3405	+	34.3405i	1.26839	+	1.26839i	0.321476	+	0.946918i	$0.395821\pi$
$734$	2.11072	+	7.87731i	0.0779081	+	0.290757i
$735$	24.4610	+	23.6223i	0.902257	+	0.871323i
$736$	−7.44281	+	7.44281i	−0.274346	+	0.274346i
$737$	11.0492	+	6.37928i	0.407004	+	0.234984i
$738$	−0.250964	−	7.19212i	−0.00923812	−	0.264746i
$739$	−37.5261	−	10.0551i	−1.38042	−	0.369882i	−0.509146	−	0.860680i	$-0.670039\pi$
$739$	−37.5261	−	10.0551i	−1.38042	−	0.369882i	−0.871273	+	0.490798i	$0.836705\pi$
$740$	−14.0842			−0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	50.3503	+	13.4913i	1.84717	+	0.494949i	0.999374	−	0.0353674i	$-0.0112601\pi$
$743$	50.3503	+	13.4913i	1.84717	+	0.494949i	0.847800	+	0.530316i	$0.177927\pi$
$744$	9.43781	+	5.23162i	0.346007	+	0.191801i
$745$	−68.6542	−	39.6375i	−2.51530	−	1.45221i
$746$	−5.10435	+	5.10435i	−0.186883	+	0.186883i
$747$	−18.9713	−	4.38039i	−0.694122	−	0.160270i
$748$	5.37308	+	20.0526i	0.196459	+	0.733195i
$749$	−10.7270	−	10.7270i	−0.391957	−	0.391957i
$750$	4.40233	−	0.0767848i	0.160750	−	0.00280378i
$751$	42.7471	−	24.6801i	1.55986	−	0.900588i	0.562595	−	0.826733i	$-0.309803\pi$
$751$	42.7471	−	24.6801i	1.55986	−	0.900588i	0.997269	−	0.0738552i	$-0.0235303\pi$
$752$	−2.67150	+	9.97017i	−0.0974196	+	0.363575i
$753$	4.99555	+	8.31423i	0.182048	+	0.302987i
$754$		0			0
$755$			32.5270i			1.18378i
$756$	−2.35521	+	11.0782i	−0.0856580	+	0.402911i
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	0.642255	−	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
$759$	−2.12932	+	8.53976i	−0.0772895	+	0.309974i
$760$	−22.5905	+	6.05310i	−0.819443	+	0.219569i
$761$	37.1766	−	9.96144i	1.34765	−	0.361102i	0.488384	−	0.872629i	$-0.337587\pi$
$761$	37.1766	−	9.96144i	1.34765	−	0.361102i	0.859267	+	0.511527i	$0.170920\pi$
$762$	1.15109	−	4.61653i	0.0416997	−	0.167239i
$763$	−3.68783	+	6.38751i	−0.133508	+	0.231243i
$764$	6.37559	+	11.0428i	0.230661	+	0.399516i
$765$	−41.9610	+	44.9953i	−1.51710	+	1.62681i
$766$		−	9.37896i		−	0.338876i
$767$		0			0
$768$	6.21032	+	10.3360i	0.224096	+	0.372969i
$769$	−0.738559	+	2.75634i	−0.0266331	+	0.0993962i	−0.977963	−	0.208778i	$-0.933051\pi$
$769$	−0.738559	+	2.75634i	−0.0266331	+	0.0993962i	0.951330	+	0.308174i	$0.0997180\pi$
$770$	2.31126	−	1.33441i	0.0832921	−	0.0480887i
$771$	−11.7997	+	0.205808i	−0.424954	+	0.00741200i
$772$	−14.7443	−	14.7443i	−0.530660	−	0.530660i
$773$	1.66335	+	6.20770i	0.0598265	+	0.223275i	0.989366	−	0.145447i	$-0.0464620\pi$
$773$	1.66335	+	6.20770i	0.0598265	+	0.223275i	−0.929540	+	0.368722i	$0.879795\pi$
$774$	−1.32050	+	5.71902i	−0.0474643	+	0.205566i
$775$	−22.8188	+	22.8188i	−0.819675	+	0.819675i
$776$	14.5123	+	8.37869i	0.520962	+	0.300777i
$777$	−3.80344	−	2.10835i	−0.136448	−	0.0756366i
$778$	2.10162	+	0.563129i	0.0753469	+	0.0201891i
$779$	−33.5341			−1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	−5.44405	−	1.45873i	−0.194679	−	0.0521640i
$783$	11.7102	−	7.60400i	0.418487	−	0.271745i
$784$	16.0002	+	9.23773i	0.571436	+	0.329919i
$785$	−38.5251	+	38.5251i	−1.37502	+	1.37502i
$786$	8.14212	+	7.86296i	0.290420	+	0.280463i
$787$	−3.92580	−	14.6513i	−0.139940	−	0.522262i	−0.999929	−	0.0119493i	$-0.996196\pi$
$787$	−3.92580	−	14.6513i	−0.139940	−	0.522262i	0.859989	−	0.510313i	$-0.170470\pi$
$788$	−3.02924	−	3.02924i	−0.107912	−	0.107912i
$789$	−0.683604	−	39.1933i	−0.0243370	−	1.39532i
$790$	−1.16681	+	0.673658i	−0.0415132	+	0.0239677i
$791$	−3.91350	+	14.6054i	−0.139148	+	0.519308i
$792$	−6.78531	−	3.60804i	−0.241105	−	0.128206i
$793$		0			0
$794$		−	8.40957i		−	0.298444i
$795$	14.2408	−	4.08327i	0.505067	−	0.144819i
$796$	−17.2039	−	29.7980i	−0.609775	−	1.05616i
$797$	−0.789625	+	1.36767i	−0.0279700	+	0.0484454i	−0.879672	−	0.475582i	$-0.842238\pi$
$797$	−0.789625	+	1.36767i	−0.0279700	+	0.0484454i	0.851702	+	0.524027i	$0.175571\pi$
$798$	−3.39106	−	0.845534i	−0.120042	−	0.0299316i
$799$	−17.9934	+	4.82131i	−0.636560	+	0.170566i
$800$	26.5489	−	7.11374i	0.938644	−	0.251509i
$801$	12.2618	−	3.74845i	0.433248	−	0.132445i
$802$	4.08862	−	7.08170i	0.144374	−	0.250063i
$803$	−12.1102	−	20.9754i	−0.427359	−	0.740207i
$804$	6.09247	+	21.2480i	0.214865	+	0.749360i
$805$		−	10.9414i		−	0.385633i
$806$		0			0
$807$	−38.7542	+	23.2852i	−1.36421	+	0.819677i
$808$	−3.92280	+	14.6401i	−0.138004	+	0.515037i
$809$	−10.5758	+	6.10595i	−0.371826	+	0.214674i	−0.674256	−	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	−0.999186	−	0.0403387i	$-0.987156\pi$
$811$	−29.6037	−	29.6037i	−1.03952	−	1.03952i	−0.0403387	−	0.999186i	$-0.512844\pi$
$812$	1.51587	+	5.65729i	0.0531965	+	0.198532i
$813$	−21.2754	+	22.0307i	−0.746160	+	0.772651i
$814$	1.00981	−	1.00981i	0.0353939	−	0.0353939i
$815$	−10.4018	−	6.00546i	−0.364358	−	0.210362i
$816$	−16.2062	+	29.2359i	−0.567331	+	1.02346i
$817$	26.4186	+	7.07884i	0.924269	+	0.247657i
$818$	−4.42964			−0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	−17.9749	−	4.81637i	−0.627330	−	0.168093i	−0.0688721	−	0.997625i	$-0.521940\pi$
$821$	−17.9749	−	4.81637i	−0.627330	−	0.168093i	−0.558458	+	0.829533i	$0.688607\pi$
$822$	−2.23001	+	4.02293i	−0.0777807	+	0.140316i
$823$	0.447230	+	0.258209i	0.0155895	+	0.00900059i	0.507774	−	0.861490i	$-0.330468\pi$
$823$	0.447230	+	0.258209i	0.0155895	+	0.00900059i	−0.492185	+	0.870491i	$0.663802\pi$
$824$	4.28172	−	4.28172i	0.149161	−	0.149161i
$825$	15.9651	−	16.5319i	0.555832	−	0.575566i
$826$	−1.06079	−	3.95892i	−0.0369096	−	0.137748i
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	0.238472	−	0.971149i	$-0.423354\pi$
$827$	−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	$-0.675994\pi$
$829$	−1.46119	+	0.843616i	−0.0507491	+	0.0293000i	0.474411	+	0.880304i	$0.342661\pi$
$830$	−2.05729	+	7.67790i	−0.0714094	+	0.266504i
$831$	−33.7030	+	20.2502i	−1.16914	+	0.702471i
$832$		0			0
$833$			33.3430i			1.15527i
$834$	−0.907288	−	3.16425i	−0.0314168	−	0.109569i
$835$	9.11018	+	15.7793i	0.315271	+	0.546065i
$836$	−8.66562	+	15.0093i	−0.299707	+	0.519107i
$837$	17.6110	+	15.8583i	0.608726	+	0.548143i
$838$	−9.12670	+	2.44549i	−0.315277	+	0.0844781i
$839$	10.4663	−	2.80444i	0.361337	−	0.0968199i	−0.0735829	−	0.997289i	$-0.523443\pi$
$839$	10.4663	−	2.80444i	0.361337	−	0.0968199i	0.434920	+	0.900469i	$0.356777\pi$
$840$	9.26984	+	2.31136i	0.319840	+	0.0797495i
$841$	−10.8898	+	18.8618i	−0.375512	+	0.650406i
$842$	−2.22657	−	3.85653i	−0.0767326	−	0.132905i
$843$	20.1496	−	5.77751i	0.693989	−	0.198988i
$844$		−	15.0198i		−	0.517004i
$845$		0			0
$846$	1.56688	−	2.94669i	0.0538706	−	0.101309i
$847$	−2.25057	+	8.39923i	−0.0773304	+	0.288601i
$848$	6.97060	−	4.02448i	0.239371	−	0.138201i
$849$	0.214628	+	12.3054i	0.00736602	+	0.422319i
$850$	10.4067	+	10.4067i	0.356947	+	0.356947i
$851$	−1.51532	−	5.65526i	−0.0519446	−	0.193860i
$852$	27.1267	+	26.1966i	0.929346	+	0.897482i
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.0333670	+	0.999443i	$0.510623\pi$
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.999443	+	0.0333670i	$0.989377\pi$
$854$	0.944378	+	0.545237i	0.0323160	+	0.0186576i
$855$	−51.3321	+	1.79120i	−1.75552	+	0.0612577i
$856$	17.2259	+	4.61568i	0.588771	+	0.157761i
$857$	36.7949			1.25689			0.628444	−	0.777855i	$-0.283692\pi$
$857$	36.7949			1.25689			0.628444	+	0.777855i	$0.283692\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	−34.9518	−	9.36529i	−1.19185	−	0.319354i
$861$	11.9809	+	6.64135i	0.408309	+	0.226336i
$862$	−6.47872	−	3.74049i	−0.220666	−	0.127402i
$863$	−25.4155	+	25.4155i	−0.865153	+	0.865153i	−0.991931	−	0.126779i	$-0.959536\pi$
$863$	−25.4155	+	25.4155i	−0.865153	+	0.865153i	0.126779	+	0.991931i	$0.459536\pi$
$864$	−6.23663	−	19.1970i	−0.212175	−	0.653094i
$865$	−12.8175	−	47.8355i	−0.435808	−	1.62646i
$866$	0.461976	+	0.461976i	0.0156986	+	0.0156986i
$867$	−30.8772	+	0.538556i	−1.04864	+	0.0182903i
$868$	−8.60919	+	4.97052i	−0.292215	+	0.168710i
$869$	−0.533937	+	1.99268i	−0.0181126	+	0.0675971i
$870$	−2.93571	−	4.88599i	−0.0995299	−	0.165651i
$871$		0			0
$872$		−	8.67054i		−	0.293622i
$873$	26.9150	+	25.1000i	0.910934	+	0.849505i
$874$	−2.35262	−	4.07485i	−0.0795784	−	0.137834i
$875$	−4.19056	+	7.25826i	−0.141667	+	0.245374i
$876$	10.1520	−	40.7152i	0.343005	−	1.37564i
$877$	−17.6992	+	4.74247i	−0.597658	+	0.160142i	−0.544951	−	0.838468i	$-0.683452\pi$
$877$	−17.6992	+	4.74247i	−0.597658	+	0.160142i	−0.0527071	+	0.998610i	$0.516785\pi$
$878$	−4.90406	+	1.31404i	−0.165504	+	0.0443467i
$879$	6.66068	−	26.7130i	0.224659	−	0.901007i
$880$	10.6551	−	18.4552i	0.359184	−	0.622125i
$881$	−15.5539	−	26.9401i	−0.524023	−	0.907635i	−0.999609	−	0.0279654i	$-0.991097\pi$
$881$	−15.5539	−	26.9401i	−0.524023	−	0.907635i	0.475586	−	0.879669i	$-0.342236\pi$
$882$	−4.36877	−	4.07416i	−0.147104	−	0.137184i
$883$			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
$886$	−2.02808	+	7.56891i	−0.0681348	+	0.254282i
$887$	−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
$890$	−1.35479	−	5.05616i	−0.0454128	−	0.169483i
$891$	−12.7371	−	11.0734i	−0.426710	−	0.370973i
$892$	37.5558	−	37.5558i	1.25746	−	1.25746i
$893$	−13.4680	−	7.77574i	−0.450688	−	0.260205i
$894$	12.1801	+	6.75173i	0.407362	+	0.225812i
$895$	−14.6571	−	3.92737i	−0.489934	−	0.131277i
$896$	11.1454			0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	11.8377	+	3.17189i	0.394808	+	0.105789i
$900$	39.7926	−	1.38854i	1.32642	−	0.0462846i
$901$	12.5800	+	7.26306i	0.419100	+	0.241967i
$902$	−3.18093	+	3.18093i	−0.105913	+	0.105913i
$903$	−8.03678	−	7.76123i	−0.267447	−	0.258278i
$904$	−4.60057	−	17.1696i	−0.153013	−	0.571051i
$905$	5.17824	+	5.17824i	0.172130	+	0.172130i
$906$	−0.0996478	−	5.71314i	−0.00331058	−	0.189806i
$907$	1.45939	−	0.842581i	0.0484584	−	0.0279775i	−0.475575	−	0.879675i	$-0.657760\pi$
$907$	1.45939	−	0.842581i	0.0484584	−	0.0279775i	0.524033	+	0.851698i	$0.324427\pi$
$908$	−3.57085	+	13.3266i	−0.118503	+	0.442259i
$909$	−15.6280	+	29.3900i	−0.518346	+	0.974806i
$910$		0			0
$911$		−	43.9421i		−	1.45587i	−0.685648	−	0.727933i	$-0.740481\pi$
$911$		−	43.9421i		−	1.45587i	0.685648	−	0.727933i	$-0.259519\pi$
$912$	−26.8254	+	7.69167i	−0.888277	+	0.254697i
$913$	6.08545	+	10.5403i	0.201399	+	0.348834i
$914$	−1.19283	+	2.06604i	−0.0394553	+	0.0683386i
$915$	15.5503	+	3.87734i	0.514076	+	0.128181i
$916$	−29.2350	+	7.83348i	−0.965950	+	0.258826i
$917$	−20.8116	+	5.57646i	−0.687260	+	0.184151i
$918$	7.23231	−	8.03165i	0.238702	−	0.265084i
$919$	−4.20715	+	7.28699i	−0.138781	+	0.240376i	−0.927035	−	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
$921$	−9.71159	−	33.8700i	−0.320008	−	1.11606i
$922$			4.36704i			0.143821i
$923$		0			0
$924$	6.06857	−	3.64625i	0.199641	−	0.119953i
$925$	−3.95690	+	14.7674i	−0.130102	+	0.485548i
$926$	3.01029	−	1.73799i	0.0989244	−	0.0571140i
$927$	11.2780	−	7.04686i	0.370418	−	0.231449i
$928$	−7.38077	−	7.38077i	−0.242286	−	0.242286i
$929$	−0.593828	−	2.21620i	−0.0194829	−	0.0727110i	0.955500	−	0.294991i	$-0.0953167\pi$
$929$	−0.593828	−	2.21620i	−0.0194829	−	0.0727110i	−0.974983	+	0.222280i	$0.928650\pi$
$930$	6.72089	−	6.95951i	0.220387	−	0.228211i
$931$	−19.6831	+	19.6831i	−0.645087	+	0.645087i
$932$	29.4930	+	17.0278i	0.966076	+	0.557764i
$933$	6.40030	−	11.5461i	0.209536	−	0.378002i
$934$	3.13178	+	0.839158i	0.102475	+	0.0274581i
$935$	38.4590			1.25775
$936$		0			0
$937$	7.10985			0.232269			0.116134	−	0.993234i	$-0.462950\pi$
$937$	7.10985			0.232269			0.116134	+	0.993234i	$0.462950\pi$
$938$	2.69135	+	0.721146i	0.0878758	+	0.0235463i
$939$	−5.47077	+	9.86922i	−0.178532	+	0.322070i
$940$	17.8181	+	10.2873i	0.581163	+	0.335534i
$941$	−22.6506	+	22.6506i	−0.738390	+	0.738390i	−0.972266	−	0.233877i	$-0.924859\pi$
$941$	−22.6506	+	22.6506i	−0.738390	+	0.738390i	0.233877	+	0.972266i	$0.424859\pi$
$942$	6.64864	−	6.88469i	0.216624	−	0.224315i
$943$	4.77330	+	17.8142i	0.155440	+	0.580110i
$944$	−23.1413	−	23.1413i	−0.753185	−	0.753185i
$945$	18.6945	+	9.52623i	0.608131	+	0.309888i
$946$	3.17745	−	1.83450i	0.103308	−	0.0596448i
$947$	3.46107	−	12.9169i	0.112470	−	0.419742i	−0.886616	−	0.462507i	$-0.846950\pi$
$947$	3.46107	−	12.9169i	0.112470	−	0.419742i	0.999085	+	0.0427648i	$0.0136166\pi$
$948$	−3.06363	+	1.84076i	−0.0995022	+	0.0597852i
$949$		0			0
$950$			12.2866i			0.398629i
$951$	−4.24943	−	14.8203i	−0.137797	−	0.480580i
$952$	4.68381	+	8.11259i	0.151803	+	0.262931i
$953$	−8.89415	+	15.4051i	−0.288110	+	0.499021i	−0.973359	−	0.229288i	$-0.926360\pi$
$953$	−8.89415	+	15.4051i	−0.288110	+	0.499021i	0.685249	+	0.728309i	$0.259693\pi$
$954$	−2.48878	+	0.760824i	−0.0805772	+	0.0246326i
$955$	22.8174	−	6.11390i	0.738353	−	0.197841i
$956$	16.7646	−	4.49206i	0.542206	−	0.145284i
$957$	−8.46858	−	2.11157i	−0.273750	−	0.0682575i
$958$	−4.04423	+	7.00482i	−0.130663	+	0.226315i
$959$	−4.37773	−	7.58246i	−0.141364	−	0.244850i
$960$	29.9190	−	8.57871i	0.965632	−	0.276877i
$961$		−	10.1988i		−	0.328993i
$962$		0			0
$963$	34.5812	+	18.3883i	1.11436	+	0.592555i
$964$	13.4369	−	50.1473i	0.432774	−	1.61513i
$965$	−33.4536	+	19.3144i	−1.07691	+	0.621753i
$966$	0.0335193	+	1.92177i	0.00107847	+	0.0618321i
$967$	−29.0154	−	29.0154i	−0.933072	−	0.933072i	0.0648250	−	0.997897i	$-0.479351\pi$
$967$	−29.0154	−	29.0154i	−0.933072	−	0.933072i	−0.997897	+	0.0648250i	$0.979351\pi$
$968$	−2.64568	−	9.87382i	−0.0850354	−	0.317357i
$969$	−36.2277	−	34.9856i	−1.16380	−	1.12390i
$970$	10.6239	−	10.6239i	0.341114	−	0.341114i
$971$	19.5631	+	11.2948i	0.627810	+	0.362466i	0.779904	−	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
$973$	6.05235	+	1.62172i	0.194029	+	0.0519900i
$974$	10.3864			0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	−2.57462	−	0.689868i	−0.0823694	−	0.0220708i	0.217399	−	0.976083i	$-0.430243\pi$
$977$	−2.57462	−	0.689868i	−0.0823694	−	0.0220708i	−0.299768	+	0.954012i	$0.596909\pi$
$978$	1.84540	+	1.02295i	0.0590092	+	0.0327104i
$979$	−6.94116	−	4.00748i	−0.221841	−	0.128080i
$980$	26.0407	−	26.0407i	0.831839	−	0.831839i
$981$	4.28406	−	18.5541i	0.136779	−	0.592385i
$982$	−1.39784	−	5.21679i	−0.0446067	−	0.166475i
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.964676	+	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
$986$	1.44657	−	5.39867i	0.0460682	−	0.171929i
$987$	3.27182	+	5.44538i	0.104143	+	0.173328i
$988$		0			0
$989$		−	15.0419i		−	0.478303i
$990$	−4.69928	+	5.03909i	−0.149353	+	0.160153i
$991$	−6.62217	−	11.4699i	−0.210360	−	0.364354i	0.741467	−	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
$993$	6.73680	−	27.0183i	0.213786	−	0.857400i
$994$	4.59160	−	1.23032i	0.145637	−	0.0390232i
$995$	−61.5704	+	16.4977i	−1.95191	+	0.523013i
$996$	−5.10147	+	20.4597i	−0.161646	+	0.648291i
$997$	15.7906	−	27.3501i	0.500093	−	0.866186i	−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
$999$	10.9819	+	2.33473i	0.347453	+	0.0738677i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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