LMFDB - Embedded newform 507.2.k.k.188.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			188.11
Character	$\chi$	$=$	507.188
Dual form			507.2.k.k.89.11

$q$-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} +(-1.73179 + 0.0302056i) q^{3} +(-1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(0.586806 - 0.168255i) q^{6} +(0.300747 - 1.12240i) q^{7} +(0.965906 - 0.965906i) q^{8} +(2.99818 - 0.104619i) q^{9} +(-1.06066 - 0.612371i) q^{10} +(0.485362 + 1.81140i) q^{11} +(2.78492 - 1.67330i) q^{12} +0.409539i q^{14} +(-4.32956 - 4.18112i) q^{15} +(1.63506 - 2.83201i) q^{16} +(2.95083 + 5.11099i) q^{17} +(-1.01114 + 0.309108i) q^{18} +(-4.75906 - 1.27519i) q^{19} +(-6.29623 - 1.68707i) q^{20} +(-0.486926 + 1.95284i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(-1.35482 + 2.34662i) q^{23} +(-1.64357 + 1.70192i) q^{24} +7.07560i q^{25} +(-5.18904 + 0.271740i) q^{27} +(0.564135 + 2.10538i) q^{28} +(2.32707 + 1.34353i) q^{29} +(1.85533 + 1.02846i) q^{30} +(-3.22500 + 3.22500i) q^{31} +(-1.00539 + 3.75217i) q^{32} +(-0.895258 - 3.12229i) q^{33} +(-1.47079 - 1.47079i) q^{34} +(3.49695 - 2.01896i) q^{35} +(-4.77234 + 2.98191i) q^{36} +(-2.08708 + 0.559232i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(-6.57436 + 1.76159i) q^{41} +(-0.0123704 - 0.709234i) q^{42} +(-4.80750 + 2.77561i) q^{43} +(-2.48735 - 2.48735i) q^{44} +(7.62417 + 7.11003i) q^{45} +(0.247172 - 0.922459i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(-2.74604 + 4.95383i) q^{48} +(4.89284 + 2.82488i) q^{49} +(-0.645431 - 2.40878i) q^{50} +(-5.26460 - 8.76202i) q^{51} -2.46136i q^{53} +(1.74174 - 0.565851i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(-0.793642 - 1.37463i) q^{56} +(8.28020 + 2.06460i) q^{57} +(-0.914771 - 0.245112i) q^{58} +(9.66677 + 2.59020i) q^{59} +(10.9547 + 2.73147i) q^{60} +(1.33134 + 2.30596i) q^{61} +(0.803720 - 1.39208i) q^{62} +(0.784266 - 3.39662i) q^{63} +5.17117i q^{64} +(0.589590 + 0.981273i) q^{66} +(1.76087 + 6.57167i) q^{67} +(-9.58711 - 5.53512i) q^{68} +(2.27539 - 4.10478i) q^{69} +(-1.00632 + 1.00632i) q^{70} +(3.00415 - 11.2116i) q^{71} +(2.79490 - 2.99701i) q^{72} +(-9.13263 - 9.13263i) q^{73} +(0.659503 - 0.380764i) q^{74} +(-0.213723 - 12.2534i) q^{75} +(8.92696 - 2.39197i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(10.9765 - 2.94114i) q^{80} +(8.97811 - 0.627334i) q^{81} +(2.07745 - 1.19942i) q^{82} +(-4.58922 - 4.58922i) q^{83} +(-1.04056 - 3.62903i) q^{84} +(-5.30793 + 19.8095i) q^{85} +(1.38345 - 1.38345i) q^{86} +(-4.07057 - 2.25642i) q^{87} +(2.21845 + 1.28082i) q^{88} +(1.10619 + 4.12834i) q^{89} +(-3.24410 - 1.72503i) q^{90} -5.08271i q^{92} +(5.48760 - 5.68242i) q^{93} +(0.556230 - 0.963419i) q^{94} +(-8.56055 - 14.8273i) q^{95} +(1.62779 - 6.52833i) q^{96} +(-11.8495 - 3.17506i) q^{97} +(-1.92338 - 0.515368i) q^{98} +(1.64471 + 5.38010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

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

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

Coefficient data

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

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

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

$2$	−0.340435	+	0.0912193i	−0.240724	+	0.0645018i	−0.377164	−	0.926147i	$-0.623101\pi$
$2$	−0.340435	+	0.0912193i	−0.240724	+	0.0645018i	0.136440	+	0.990648i	$0.456434\pi$
$3$	−1.73179	+	0.0302056i	−0.999848	+	0.0174392i
$3$	−1.73179	+	0.0302056i	−0.999848	+	0.0174392i
$4$	−1.62448	+	0.937892i	−0.812238	+	0.468946i
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.994541	+	0.104350i	$0.0332761\pi$
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.104350	+	0.994541i	$0.466724\pi$
$6$	0.586806	−	0.168255i	0.239562	−	0.0686900i
$7$	0.300747	−	1.12240i	0.113672	−	0.424228i	−0.885513	−	0.464615i	$-0.846193\pi$
$7$	0.300747	−	1.12240i	0.113672	−	0.424228i	0.999184	+	0.0403875i	$0.0128593\pi$
$8$	0.965906	−	0.965906i	0.341499	−	0.341499i
$9$	2.99818	−	0.104619i	0.999392	−	0.0348731i
$10$	−1.06066	−	0.612371i	−0.335410	−	0.193649i
$11$	0.485362	+	1.81140i	0.146342	+	0.546156i	0.999692	+	0.0248176i	$0.00790049\pi$
$11$	0.485362	+	1.81140i	0.146342	+	0.546156i	−0.853350	+	0.521339i	$0.825433\pi$
$12$	2.78492	−	1.67330i	0.803936	−	0.483039i
$13$		0			0
$13$		0			0
$14$			0.409539i			0.109454i
$15$	−4.32956	−	4.18112i	−1.11789	−	1.07956i
$16$	1.63506	−	2.83201i	0.408766	−	0.708003i
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	0.962696	+	0.270586i	$0.0872174\pi$
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	−0.247014	+	0.969012i	$0.579449\pi$
$18$	−1.01114	+	0.309108i	−0.238328	+	0.0728573i
$19$	−4.75906	−	1.27519i	−1.09180	−	0.292548i	−0.332381	−	0.943145i	$-0.607852\pi$
$19$	−4.75906	−	1.27519i	−1.09180	−	0.292548i	−0.759423	+	0.650598i	$0.774518\pi$
$20$	−6.29623	−	1.68707i	−1.40788	−	0.377240i
$21$	−0.486926	+	1.95284i	−0.106256	+	0.426146i
$22$	−0.330468	−	0.572388i	−0.0704561	−	0.122034i
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	−0.972000	−	0.234981i	$-0.924497\pi$
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	0.689500	+	0.724286i	$0.257831\pi$
$24$	−1.64357	+	1.70192i	−0.335492	+	0.347403i
$25$			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	$-0.253071\pi$
$29$	2.32707	+	1.34353i	0.432125	+	0.249488i	−0.268126	+	0.963384i	$0.586404\pi$
$30$	1.85533	+	1.02846i	0.338736	+	0.187770i
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	−0.934690	−	0.355463i	$-0.884323\pi$
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	0.355463	+	0.934690i	$0.384323\pi$
$32$	−1.00539	+	3.75217i	−0.177730	+	0.663296i
$33$	−0.895258	−	3.12229i	−0.155844	−	0.543521i
$34$	−1.47079	−	1.47079i	−0.252238	−	0.252238i
$35$	3.49695	−	2.01896i	0.591092	−	0.341267i
$36$	−4.77234	+	2.98191i	−0.795390	+	0.496986i
$37$	−2.08708	+	0.559232i	−0.343114	+	0.0919372i	−0.426261	−	0.904600i	$-0.640170\pi$
$37$	−2.08708	+	0.559232i	−0.343114	+	0.0919372i	0.0831470	+	0.996537i	$0.473503\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	−6.57436	+	1.76159i	−1.02674	+	0.275115i	−0.732609	−	0.680650i	$-0.761698\pi$
$41$	−6.57436	+	1.76159i	−1.02674	+	0.275115i	−0.294133	+	0.955764i	$0.595031\pi$
$42$	−0.0123704	−	0.709234i	−0.00190879	−	0.109437i
$43$	−4.80750	+	2.77561i	−0.733136	+	0.423276i	−0.819568	−	0.572981i	$-0.805787\pi$
$43$	−4.80750	+	2.77561i	−0.733136	+	0.423276i	0.0864321	+	0.996258i	$0.472453\pi$
$44$	−2.48735	−	2.48735i	−0.374982	−	0.374982i
$45$	7.62417	+	7.11003i	1.13654	+	1.05990i
$46$	0.247172	−	0.922459i	0.0364436	−	0.136009i
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	−0.850895	−	0.525336i	$-0.823940\pi$
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	0.525336	+	0.850895i	$0.323940\pi$
$48$	−2.74604	+	4.95383i	−0.396357	+	0.715024i
$49$	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	$-0.0540689\pi$
$54$	1.74174	−	0.565851i	0.237021	−	0.0770025i
$55$	−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
$58$	−0.914771	−	0.245112i	−0.120115	−	0.0321848i
$59$	9.66677	+	2.59020i	1.25851	+	0.337216i	0.825617	−	0.564231i	$-0.190827\pi$
$59$	9.66677	+	2.59020i	1.25851	+	0.337216i	0.432890	+	0.901447i	$0.357494\pi$
$60$	10.9547	+	2.73147i	1.41424	+	0.352631i
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	0.938581	−	0.345058i	$-0.112141\pi$
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	−0.768120	+	0.640306i	$0.778808\pi$
$62$	0.803720	−	1.39208i	0.102073	−	0.176795i
$63$	0.784266	−	3.39662i	0.0988082	−	0.427934i
$64$			5.17117i			0.646397i
$65$		0			0
$66$	0.589590	+	0.981273i	0.0725736	+	0.120786i
$67$	1.76087	+	6.57167i	0.215125	+	0.802857i	0.986123	+	0.166019i	$0.0530914\pi$
$67$	1.76087	+	6.57167i	0.215125	+	0.802857i	−0.770998	+	0.636838i	$0.780242\pi$
$68$	−9.58711	−	5.53512i	−1.16261	−	0.671232i
$69$	2.27539	−	4.10478i	0.273924	−	0.494157i
$70$	−1.00632	+	1.00632i	−0.120278	+	0.120278i
$71$	3.00415	−	11.2116i	0.356527	−	1.33058i	−0.522025	−	0.852930i	$-0.674823\pi$
$71$	3.00415	−	11.2116i	0.356527	−	1.33058i	0.878552	−	0.477647i	$-0.158510\pi$
$72$	2.79490	−	2.99701i	0.329383	−	0.353201i
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.997444	−	0.0714492i	$-0.977238\pi$
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.0714492	−	0.997444i	$-0.522762\pi$
$74$	0.659503	−	0.380764i	0.0766657	−	0.0442630i
$75$	−0.213723	−	12.2534i	−0.0246786	−	1.41490i
$76$	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
$81$	8.97811	−	0.627334i	0.997568	−	0.0697038i
$82$	2.07745	−	1.19942i	0.229416	−	0.132453i
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	0.408864	−	0.912596i	$-0.365925\pi$
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	−0.912596	+	0.408864i	$0.865925\pi$
$84$	−1.04056	−	3.62903i	−0.113534	−	0.395960i
$85$	−5.30793	+	19.8095i	−0.575726	+	2.14864i
$86$	1.38345	−	1.38345i	0.149181	−	0.149181i
$87$	−4.07057	−	2.25642i	−0.436410	−	0.241914i
$88$	2.21845	+	1.28082i	0.236488	+	0.136536i
$89$	1.10619	+	4.12834i	0.117256	+	0.437604i	0.999446	−	0.0332896i	$-0.0105984\pi$
$89$	1.10619	+	4.12834i	0.117256	+	0.437604i	−0.882190	+	0.470893i	$0.843932\pi$
$90$	−3.24410	−	1.72503i	−0.341959	−	0.181834i
$91$		0			0
$92$		−	5.08271i		−	0.529909i
$93$	5.48760	−	5.68242i	0.569037	−	0.589240i
$94$	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
$97$	−11.8495	−	3.17506i	−1.20313	−	0.322379i	−0.399070	−	0.916921i	$-0.630667\pi$
$97$	−11.8495	−	3.17506i	−1.20313	−	0.322379i	−0.804065	+	0.594542i	$0.797333\pi$
$98$	−1.92338	−	0.515368i	−0.194291	−	0.0520600i
$99$	1.64471	+	5.38010i	0.165299	+	0.540721i
$100$	−6.63614	−	11.4941i	−0.663614	−	1.14941i
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	−0.446103	−	0.894982i	$-0.647188\pi$
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	0.998128	−	0.0611547i	$-0.0194783\pi$
$102$	2.59152	+	2.50267i	0.256599	+	0.247801i
$103$		−	4.43285i		−	0.436782i	−0.975861	−	0.218391i	$-0.929919\pi$
$103$		−	4.43285i		−	0.436782i	0.975861	−	0.218391i	$-0.0700808\pi$
$104$		0			0
$105$	−5.99499	+	3.60205i	−0.585051	+	0.351524i
$106$	0.224523	+	0.837932i	0.0218076	+	0.0813872i
$107$	11.3063	+	6.52769i	1.09302	+	0.631055i	0.934379	−	0.356281i	$-0.115955\pi$
$107$	11.3063	+	6.52769i	1.09302	+	0.631055i	0.158641	+	0.987336i	$0.449289\pi$
$108$	8.17461	−	5.30819i	0.786602	−	0.510781i
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	−0.458694	−	0.888594i	$-0.651682\pi$
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	0.888594	+	0.458694i	$0.151682\pi$
$110$	0.594443	−	2.21849i	0.0566780	−	0.211525i
$111$	3.59749	−	1.03151i	0.341459	−	0.0979068i
$112$	−2.68692	−	2.68692i	−0.253890	−	0.253890i
$113$	−11.2693	+	6.50632i	−1.06012	+	0.612063i	−0.925467	−	0.378829i	$-0.876327\pi$
$113$	−11.2693	+	6.50632i	−1.06012	+	0.612063i	−0.134657	+	0.990892i	$0.542993\pi$
$114$	−3.00720	+	0.0524512i	−0.281650	+	0.00491250i
$115$	−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
$120$	−8.22051	+	0.143381i	−0.750427	+	0.0130888i
$121$	6.48070	−	3.74164i	0.589155	−	0.340149i
$122$	−0.663584	−	0.663584i	−0.0600781	−	0.0600781i
$123$	11.3322	−	3.24929i	1.02179	−	0.292978i
$124$	2.21423	−	8.26363i	0.198844	−	0.742096i
$125$	−5.10014	+	5.10014i	−0.456171	+	0.456171i
$126$	0.0428457	+	1.22787i	0.00381699	+	0.109387i
$127$	6.74982	+	3.89701i	0.598950	+	0.345804i	0.768628	−	0.639696i	$-0.220940\pi$
$127$	6.74982	+	3.89701i	0.598950	+	0.345804i	−0.169679	+	0.985499i	$0.554273\pi$
$128$	−2.48249	−	9.26479i	−0.219423	−	0.818900i
$129$	8.24172	−	4.95198i	0.725643	−	0.435997i
$130$		0			0
$131$			18.5420i			1.62003i	0.586412	+	0.810013i	$0.300540\pi$
$131$			18.5420i			1.62003i	−0.586412	+	0.810013i	$0.699460\pi$
$132$	4.38269	+	4.23243i	0.381465	+	0.368386i
$133$	−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
$136$	7.78697	+	2.08651i	0.667727	+	0.178917i
$137$	7.27811	+	1.95016i	0.621811	+	0.166614i	0.555951	−	0.831215i	$-0.312354\pi$
$137$	7.27811	+	1.95016i	0.621811	+	0.166614i	0.0658600	+	0.997829i	$0.479021\pi$
$138$	−0.400186	+	1.60497i	−0.0340661	+	0.136624i
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	0.957419	−	0.288703i	$-0.0932239\pi$
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	−0.728733	+	0.684798i	$0.759891\pi$
$140$	−3.78714	+	6.55952i	−0.320072	+	0.554381i
$141$	3.79780	−	3.93263i	0.319832	−	0.331187i
$142$			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
$147$	−8.55869	−	4.74431i	−0.705909	−	0.391304i
$148$	2.86592	−	2.86592i	0.235577	−	0.235577i
$149$	−5.90444	+	22.0357i	−0.483710	+	1.80523i	0.102088	+	0.994775i	$0.467448\pi$
$149$	−5.90444	+	22.0357i	−0.483710	+	1.80523i	−0.585798	+	0.810457i	$0.699219\pi$
$150$	1.19051	+	4.15200i	0.0972046	+	0.339010i
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	0.923125	−	0.384500i	$-0.125626\pi$
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	−0.384500	+	0.923125i	$0.625626\pi$
$152$	−5.82852	+	3.36510i	−0.472755	+	0.272945i
$153$	9.38182	+	15.0149i	0.758476	+	1.21389i
$154$	−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
$159$	0.0743468	+	4.26255i	0.00589608	+	0.338042i
$160$	−11.6902	+	6.74937i	−0.924195	+	0.533584i
$161$	2.22640	+	2.22640i	0.175465	+	0.175465i
$162$	−2.99924	+	1.03254i	−0.235642	+	0.0811243i
$163$	0.894579	−	3.33861i	0.0700688	−	0.261500i	−0.922001	−	0.387187i	$-0.873447\pi$
$163$	0.894579	−	3.33861i	0.0700688	−	0.261500i	0.992070	+	0.125687i	$0.0401134\pi$
$164$	9.02770	−	9.02770i	0.704945	−	0.704945i
$165$	5.47225	−	9.87189i	0.426014	−	0.768526i
$166$	1.98096	+	1.14371i	0.153752	+	0.0887687i
$167$	−1.35706	−	5.06462i	−0.105012	−	0.391912i	0.893334	−	0.449393i	$-0.148360\pi$
$167$	−1.35706	−	5.06462i	−0.105012	−	0.391912i	−0.998347	+	0.0574813i	$0.981693\pi$
$168$	1.41594	+	2.35659i	0.109242	+	0.181815i
$169$		0			0
$170$		−	7.22802i		−	0.554364i
$171$	−14.4019	−	3.32534i	−1.10134	−	0.254295i
$172$	5.20644	−	9.01782i	0.396987	−	0.687602i
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	0.998804	+	0.0489001i	$0.0155716\pi$
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	−0.457053	+	0.889439i	$0.651095\pi$
$174$	1.59159	+	0.396851i	0.120658	+	0.0300852i
$175$	7.94166	+	2.12796i	0.600333	+	0.160859i
$176$	5.92349	+	1.58720i	0.446500	+	0.119639i
$177$	−16.8190	−	4.19369i	−1.26420	−	0.315217i
$178$	−0.753169	−	1.30453i	−0.0564524	−	0.0977785i
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	−0.936011	−	0.351970i	$-0.885512\pi$
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	0.772821	+	0.634624i	$0.218845\pi$
$180$	−19.0537	−	4.39942i	−1.42018	−	0.327914i
$181$			2.10738i			0.156640i	0.996928	+	0.0783201i	$0.0249556\pi$
$181$			2.10738i			0.156640i	−0.996928	+	0.0783201i	$0.975044\pi$
$182$		0			0
$183$	−2.37526	−	3.95321i	−0.175584	−	0.292230i
$184$	0.957986	+	3.57525i	0.0706237	+	0.263571i
$185$	−6.50251	−	3.75422i	−0.478074	−	0.276016i
$186$	−1.34982	+	2.43507i	−0.0989739	+	0.178548i
$187$	−7.82581	+	7.82581i	−0.572280	+	0.572280i
$188$	1.53240	−	5.71901i	0.111762	−	0.417101i
$189$	−1.25559	+	5.90591i	−0.0913304	+	0.429592i
$190$	4.26685	+	4.26685i	0.309550	+	0.309550i
$191$	5.88706	−	3.39890i	0.425973	−	0.245935i	−0.271657	−	0.962394i	$-0.587572\pi$
$191$	5.88706	−	3.39890i	0.425973	−	0.245935i	0.697629	+	0.716459i	$0.254238\pi$
$192$	−0.156198	−	8.95537i	−0.0112726	−	0.646298i
$193$	10.7374	−	2.87709i	0.772898	−	0.207098i	0.149247	−	0.988800i	$-0.452315\pi$
$193$	10.7374	−	2.87709i	0.772898	−	0.207098i	0.623652	+	0.781702i	$0.285648\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	−2.20602	+	0.591102i	−0.157173	+	0.0421143i	−0.336547	−	0.941667i	$-0.609259\pi$
$197$	−2.20602	+	0.591102i	−0.157173	+	0.0421143i	0.179375	+	0.983781i	$0.442593\pi$
$198$	−1.05069	−	1.68155i	−0.0746689	−	0.119502i
$199$	15.8856	−	9.17157i	1.12610	−	0.650155i	0.183150	−	0.983085i	$-0.441371\pi$
$199$	15.8856	−	9.17157i	1.12610	−	0.650155i	0.942952	+	0.332930i	$0.108037\pi$
$200$	6.83436	+	6.83436i	0.483262	+	0.483262i
$201$	−3.24796	−	11.3275i	−0.229093	−	0.798984i
$202$	−1.01213	+	3.77732i	−0.0712133	+	0.265772i
$203$	2.20784	−	2.20784i	0.154960	−	0.154960i
$204$	16.7700	+	9.29607i	1.17414	+	0.650855i
$205$	−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
$210$	1.71233	−	1.77312i	0.118162	−	0.122357i
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	−0.694671	−	0.719327i	$-0.744450\pi$
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	0.970291	+	0.241939i	$0.0777834\pi$
$212$	2.30849	+	3.99842i	0.158548	+	0.274612i
$213$	−4.86389	+	19.5069i	−0.333269	+	1.33659i
$214$	−4.44451	−	1.19090i	−0.303820	−	0.0814084i
$215$	−18.6332	−	4.99274i	−1.27077	−	0.340502i
$216$	−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
$219$	16.0916	+	15.5399i	1.08737	+	1.05009i
$220$		−	12.2238i		−	0.824129i
$221$		0			0
$222$	−1.13062	+	0.679324i	−0.0758821	+	0.0455932i
$223$	−7.32834	−	27.3497i	−0.490742	−	1.83147i	−0.552680	−	0.833393i	$-0.686395\pi$
$223$	−7.32834	−	27.3497i	−0.490742	−	1.83147i	0.0619383	−	0.998080i	$-0.480272\pi$
$224$	3.90907	+	2.25691i	0.261186	+	0.150796i
$225$	0.740244	+	21.2139i	0.0493496	+	1.41426i
$226$	3.24295	−	3.24295i	0.215718	−	0.215718i
$227$	1.90366	−	7.10455i	0.126350	−	0.471546i	−0.873534	−	0.486763i	$-0.838177\pi$
$227$	1.90366	−	7.10455i	0.126350	−	0.471546i	0.999884	+	0.0152176i	$0.00484411\pi$
$228$	−15.3874	+	4.41203i	−1.01905	+	0.292194i
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	0.975214	−	0.221263i	$-0.0710179\pi$
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	−0.221263	+	0.975214i	$0.571018\pi$
$230$	2.87401	−	1.65931i	0.189507	−	0.109412i
$231$	−3.77371	+	0.0658205i	−0.248292	+	0.00433067i
$232$	3.54545	−	0.950001i	0.232770	−	0.0623706i
$233$	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
$236$	−18.1328	+	4.85866i	−1.18034	+	0.316272i
$237$	−1.90511	+	0.0332286i	−0.123750	+	0.00215843i
$238$	−2.09315	+	1.20848i	−0.135679	+	0.0783341i
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	0.886306	−	0.463099i	$-0.153263\pi$
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	−0.463099	+	0.886306i	$0.653263\pi$
$240$	−18.9201	+	5.42498i	−1.22129	+	0.350181i
$241$	7.16336	−	26.7340i	0.461433	−	1.72209i	−0.207021	−	0.978337i	$-0.566377\pi$
$241$	7.16336	−	26.7340i	0.461433	−	1.72209i	0.668453	−	0.743754i	$-0.266957\pi$
$242$	−1.86495	+	1.86495i	−0.119883	+	0.119883i
$243$	−15.5292	+	1.35760i	−0.996200	+	0.0870900i
$244$	−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
$249$	8.08617	+	7.80893i	0.512440	+	0.494871i
$250$	1.27104	−	2.20150i	0.0803874	−	0.139235i
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	0.940761	−	0.339071i	$-0.110113\pi$
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	−0.764025	+	0.645187i	$0.776779\pi$
$252$	1.91164	+	6.25328i	0.120422	+	0.393920i
$253$	−4.90825	−	1.31516i	−0.308579	−	0.0826834i
$254$	−2.65336	−	0.710965i	−0.166486	−	0.0446099i
$255$	8.59385	−	34.4661i	0.538168	−	2.15835i
$256$	−3.48092	−	6.02913i	−0.217557	−	0.376821i
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	−0.739990	−	0.672618i	$-0.765170\pi$
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	0.952499	+	0.304541i	$0.0985030\pi$
$258$	−2.35406	+	2.43763i	−0.146557	+	0.151760i
$259$			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	$-0.579156\pi$
$263$	−19.5996	−	11.3159i	−1.20857	−	0.697765i	−0.962446	+	0.271474i	$0.912489\pi$
$264$	−3.88058	−	2.15111i	−0.238833	−	0.132391i
$265$	6.04803	−	6.04803i	0.371528	−	0.371528i
$266$	0.522238	−	1.94902i	0.0320205	−	0.119502i
$267$	−2.04038	−	7.11600i	−0.124869	−	0.435492i
$268$	−9.02401	−	9.02401i	−0.551229	−	0.551229i
$269$	22.6058	−	13.0515i	1.37830	−	0.795762i	0.386345	−	0.922354i	$-0.373738\pi$
$269$	22.6058	−	13.0515i	1.37830	−	0.795762i	0.991955	+	0.126593i	$0.0404042\pi$
$270$	5.67021	+	2.88940i	0.345078	+	0.175843i
$271$	−17.0798	+	4.57652i	−1.03753	+	0.278004i	−0.737087	−	0.675797i	$-0.763799\pi$
$271$	−17.0798	+	4.57652i	−1.03753	+	0.278004i	−0.300438	+	0.953801i	$0.597133\pi$
$272$	19.2992			1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	−12.8167	+	3.43423i	−0.772876	+	0.207092i
$276$	0.153526	+	8.80218i	0.00924120	+	0.529829i
$277$	−19.6593	+	11.3503i	−1.18122	+	0.681975i	−0.956295	−	0.292402i	$-0.905545\pi$
$277$	−19.6593	+	11.3503i	−1.18122	+	0.681975i	−0.224920	+	0.974377i	$0.572212\pi$
$278$	−1.34385	−	1.34385i	−0.0805989	−	0.0805989i
$279$	−9.33171	+	10.0065i	−0.558675	+	0.599074i
$280$	1.42759	−	5.32786i	0.0853151	−	0.318400i
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	−0.914679	−	0.404181i	$-0.867557\pi$
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	0.404181	+	0.914679i	$0.367557\pi$
$282$	−0.934172	+	1.68524i	−0.0556291	+	0.100354i
$283$	−6.15361	−	3.55279i	−0.365794	−	0.211192i	0.305825	−	0.952088i	$-0.401068\pi$
$283$	−6.15361	−	3.55279i	−0.365794	−	0.211192i	−0.671620	+	0.740896i	$0.734401\pi$
$284$	5.63513	+	21.0306i	0.334384	+	1.24794i
$285$	15.2729	+	25.4192i	0.904690	+	1.50570i
$286$		0			0
$287$			7.90886i			0.466845i
$288$	−2.62179	+	11.3548i	−0.154490	+	0.669091i
$289$	−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
$292$	23.4012	+	6.27032i	1.36945	+	0.366943i
$293$	−15.3534	−	4.11392i	−0.896953	−	0.240338i	−0.219245	−	0.975670i	$-0.570360\pi$
$293$	−15.3534	−	4.11392i	−0.896953	−	0.240338i	−0.677707	+	0.735332i	$0.737026\pi$
$294$	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
$297$	−3.01079	−	9.26751i	−0.174704	−	0.537756i
$298$		−	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
$303$	−9.31734	+	16.8084i	−0.535267	+	0.965618i
$304$	−11.3927	+	11.3927i	−0.653417	+	0.653417i
$305$	−2.39481	+	8.93755i	−0.137126	+	0.511763i
$306$	−4.56355	−	4.25581i	−0.260881	−	0.243288i
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	0.986247	−	0.165277i	$-0.0528518\pi$
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	−0.165277	+	0.986247i	$0.552852\pi$
$308$	−3.53987	+	2.04374i	−0.201703	+	0.116453i
$309$	0.133897	+	7.67675i	0.00761713	+	0.436715i
$310$	5.39552	−	1.44572i	0.306445	−	0.0821116i
$311$	−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	$0.558944\pi$
$314$	−5.33751	+	1.43018i	−0.301213	+	0.0807099i
$315$	10.2732	−	6.41906i	0.578832	−	0.361673i
$316$	−1.78705	+	1.03176i	−0.100530	+	0.0580408i
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	0.507901	−	0.861416i	$-0.330422\pi$
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	−0.861416	+	0.507901i	$0.830422\pi$
$318$	−0.414137	−	1.44434i	−0.0232236	−	0.0809945i
$319$	−1.30420	+	4.86734i	−0.0730211	+	0.272518i
$320$	−12.7066	+	12.7066i	−0.710319	+	0.710319i
$321$	−19.7773	−	10.9631i	−1.10386	−	0.611898i
$322$	−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
$327$	−7.63720	+	7.90834i	−0.422338	+	0.437332i
$328$	−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
$331$	15.5288	+	4.16094i	0.853541	+	0.228706i	0.658958	−	0.752180i	$-0.270998\pi$
$331$	15.5288	+	4.16094i	0.853541	+	0.228706i	0.194584	+	0.980886i	$0.437664\pi$
$332$	11.7593	+	3.15088i	0.645373	+	0.172927i
$333$	−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
$336$	4.73433	+	4.57201i	0.258279	+	0.249424i
$337$		−	28.3556i		−	1.54463i	−0.635243	−	0.772313i	$-0.719100\pi$
$337$		−	28.3556i		−	1.54463i	0.635243	−	0.772313i	$-0.280900\pi$
$338$		0			0
$339$	19.3195	−	11.6080i	1.04929	−	0.630457i
$340$	−9.95653	−	37.1583i	−0.539968	−	2.01519i
$341$	−7.40704	−	4.27646i	−0.401114	−	0.231583i
$342$	5.20625	−	0.181669i	0.281522	−	0.00982351i
$343$	10.3937	−	10.3937i	0.561209	−	0.561209i
$344$	−1.96261	+	7.32457i	−0.105817	+	0.394914i
$345$	15.6773	−	4.49517i	0.844037	−	0.242012i
$346$	−3.55163	−	3.55163i	−0.190937	−	0.190937i
$347$	9.59025	−	5.53693i	0.514831	−	0.297238i	−0.219986	−	0.975503i	$-0.570601\pi$
$347$	9.59025	−	5.53693i	0.514831	−	0.297238i	0.734817	+	0.678265i	$0.237268\pi$
$348$	8.72881	−	0.152247i	0.467913	−	0.00816128i
$349$	−28.8980	+	7.74319i	−1.54687	+	0.414483i	−0.928479	−	0.371385i	$-0.878883\pi$
$349$	−28.8980	+	7.74319i	−1.54687	+	0.414483i	−0.618394	+	0.785868i	$0.712216\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	12.2442	−	3.28082i	0.651692	−	0.174620i	0.0821982	−	0.996616i	$-0.473806\pi$
$353$	12.2442	−	3.28082i	0.651692	−	0.174620i	0.569494	+	0.821996i	$0.307139\pi$
$354$	6.10833	−	0.106541i	0.324654	−	0.00566257i
$355$	34.9309	−	20.1674i	1.85394	−	1.07037i
$356$	−5.66891	−	5.66891i	−0.300452	−	0.300452i
$357$	−11.4178	+	3.27384i	−0.604295	+	0.173270i
$358$	0.398325	−	1.48657i	0.0210521	−	0.0785676i
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.0790589	−	0.996870i	$-0.474808\pi$
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.996870	−	0.0790589i	$-0.0251915\pi$
$360$	14.2318	−	0.496611i	0.750084	−	0.0261737i
$361$	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
$366$	1.16923	+	1.12914i	0.0611167	+	0.0590212i
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	−0.388299	−	0.921533i	$-0.626937\pi$
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	0.992221	−	0.124490i	$-0.0397295\pi$
$368$	4.43045	+	7.67376i	0.230953	+	0.400023i
$369$	−19.5268	+	5.96937i	−1.01652	+	0.310753i
$370$	2.55614	+	0.684915i	0.132887	+	0.0356071i
$371$	−2.76263	−	0.740245i	−0.143429	−	0.0384316i
$372$	−3.58497	+	14.3777i	−0.185872	+	0.745451i
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	−0.999377	−	0.0352886i	$-0.988765\pi$
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	0.469128	−	0.883130i	$-0.344568\pi$
$374$	1.95031	−	3.37804i	0.100848	−	0.174674i
$375$	8.67831	−	8.98642i	0.448146	−	0.464057i
$376$			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	0.987287	−	0.158948i	$-0.0508101\pi$
$379$	1.02786	+	3.83602i	0.0527975	+	0.197043i	−0.934489	+	0.355991i	$0.884143\pi$
$380$	27.8128	+	16.0577i	1.42677	+	0.823744i
$381$	−11.8070	−	6.54491i	−0.604889	−	0.335306i
$382$	−1.69412	+	1.69412i	−0.0866785	+	0.0866785i
$383$	6.88748	−	25.7044i	0.351934	−	1.31344i	−0.532365	−	0.846515i	$-0.678697\pi$
$383$	6.88748	−	25.7044i	0.351934	−	1.31344i	0.884299	−	0.466921i	$-0.154637\pi$
$384$	4.57900	+	15.9697i	0.233671	+	0.814948i
$385$	5.35443	+	5.35443i	0.272887	+	0.272887i
$386$	−3.39296	+	1.95893i	−0.172697	+	0.0997067i
$387$	−14.1233	+	8.82472i	−0.717929	+	0.448586i
$388$	22.2271	−	5.95573i	1.12841	−	0.302356i
$389$	−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
$392$	7.45460	−	1.99745i	0.376514	−	0.100887i
$393$	−0.560074	−	32.1109i	−0.0282520	−	1.61978i
$394$	0.697088	−	0.402464i	0.0351188	−	0.0202758i
$395$	2.70311	+	2.70311i	0.136008	+	0.136008i
$396$	−7.71774	−	7.19729i	−0.387831	−	0.361677i
$397$	−6.17560	+	23.0477i	−0.309945	+	1.15673i	0.618660	+	0.785659i	$0.287676\pi$
$397$	−6.17560	+	23.0477i	−0.309945	+	1.15673i	−0.928605	+	0.371071i	$0.878991\pi$
$398$	−4.57140	+	4.57140i	−0.229143	+	0.229143i
$399$	4.80755	−	8.67278i	0.240679	−	0.434182i
$400$	20.0382	+	11.5691i	1.00191	+	0.578453i
$401$	−6.00499	−	22.4109i	−0.299875	−	1.11915i	−0.937268	−	0.348610i	$-0.886654\pi$
$401$	−6.00499	−	22.4109i	−0.299875	−	1.11915i	0.637393	−	0.770539i	$-0.280013\pi$
$402$	2.13901	+	3.56002i	0.106684	+	0.177558i
$403$		0			0
$404$			20.8129i			1.03548i
$405$	23.6024	+	20.5195i	1.17281	+	1.01962i
$406$	−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
$409$	−12.1401	−	3.25292i	−0.600288	−	0.160847i	−0.0541371	−	0.998534i	$-0.517241\pi$
$409$	−12.1401	−	3.25292i	−0.600288	−	0.160847i	−0.546151	+	0.837687i	$0.683907\pi$
$410$	8.05189	+	2.15750i	0.397655	+	0.106551i
$411$	−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
$414$	0.644559	−	2.79155i	0.0316783	−	0.137197i
$415$		−	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	$-0.106065\pi$
$419$	23.2172	+	13.4045i	1.13424	+	0.654851i	0.189239	+	0.981931i	$0.439398\pi$
$420$	6.36039	−	11.4741i	0.310355	−	0.559878i
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	−0.890471	−	0.455040i	$-0.849625\pi$
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	0.455040	+	0.890471i	$0.349625\pi$
$422$	−0.730414	+	2.72594i	−0.0355560	+	0.132697i
$423$	−6.45819	+	6.92520i	−0.314008	+	0.336715i
$424$	−2.37744	−	2.37744i	−0.115459	−	0.115459i
$425$	−36.1633	+	20.8789i	−1.75418	+	1.01278i
$426$	−0.123567	−	7.08452i	−0.00598685	−	0.343246i
$427$	2.98861	−	0.800795i	0.144629	−	0.0387532i
$428$	−24.4891			−1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	20.5028	−	5.49370i	0.987583	−	0.264622i	0.271348	−	0.962481i	$-0.412531\pi$
$431$	20.5028	−	5.49370i	0.987583	−	0.264622i	0.716235	+	0.697859i	$0.245864\pi$
$432$	−7.71484	+	15.1398i	−0.371181	+	0.728412i
$433$	1.60537	−	0.926859i	0.0771490	−	0.0445420i	−0.460929	−	0.887437i	$-0.652484\pi$
$433$	1.60537	−	0.926859i	0.0771490	−	0.0445420i	0.538078	+	0.842895i	$0.319150\pi$
$434$	−1.32076	−	1.32076i	−0.0633986	−	0.0633986i
$435$	−4.45770	−	15.5466i	−0.213730	−	0.745404i
$436$	−3.08159	+	11.5007i	−0.147582	+	0.550782i
$437$	9.44007	−	9.44007i	0.451580	−	0.451580i
$438$	−6.89569	−	3.82247i	−0.329489	−	0.182644i
$439$	−12.4753	−	7.20264i	−0.595415	−	0.343763i	0.171820	−	0.985128i	$-0.445035\pi$
$439$	−12.4753	−	7.20264i	−0.595415	−	0.343763i	−0.767236	+	0.641365i	$0.778368\pi$
$440$	2.30393	+	8.59840i	0.109836	+	0.409913i
$441$	14.9651	+	7.95761i	0.712625	+	0.378934i
$442$		0			0
$443$			22.2330i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$443$			22.2330i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$444$	−4.87659	+	5.04972i	−0.231433	+	0.239649i
$445$	−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
$448$	5.80413	+	1.55521i	0.274220	+	0.0734769i
$449$	23.7458	+	6.36268i	1.12064	+	0.300273i	0.771141	−	0.636665i	$-0.219687\pi$
$449$	23.7458	+	6.36268i	1.12064	+	0.300273i	0.349495	+	0.936938i	$0.386353\pi$
$450$	−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
$453$	−11.6622	−	11.2623i	−0.547936	−	0.529150i
$454$			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	0.912768	−	0.408478i	$-0.133940\pi$
$457$	−1.75192	−	6.53825i	−0.0819513	−	0.305847i	−0.994719	+	0.102632i	$0.967274\pi$
$458$	−4.92490	−	2.84339i	−0.230125	−	0.132863i
$459$	−16.7009	−	25.7193i	−0.779529	−	1.20047i
$460$	12.4892	−	12.4892i	0.582312	−	0.582312i
$461$	−3.20695	+	11.9685i	−0.149363	+	0.557429i	0.850160	+	0.526525i	$0.176505\pi$
$461$	−3.20695	+	11.9685i	−0.149363	+	0.557429i	−0.999522	+	0.0309044i	$0.990161\pi$
$462$	1.27870	−	0.366643i	0.0594905	−	0.0170578i
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	0.850339	−	0.526236i	$-0.176397\pi$
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	−0.526236	+	0.850339i	$0.676397\pi$
$464$	7.60980	−	4.39352i	0.353276	−	0.203964i
$465$	27.4469	−	0.478725i	1.27282	−	0.0222003i
$466$	−6.18074	+	1.65612i	−0.286317	+	0.0767185i
$467$	−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
$470$	3.73407	−	1.00054i	0.172240	−	0.0461515i
$471$	−27.1518	+	0.473578i	−1.25109	+	0.0218213i
$472$	11.8391	−	6.83530i	0.544938	−	0.314620i
$473$	−7.36110	−	7.36110i	−0.338464	−	0.338464i
$474$	0.645534	−	0.185095i	0.0296504	−	0.00850168i
$475$	9.02270	−	33.6732i	0.413990	−	1.54503i
$476$	−9.09592	+	9.09592i	−0.416911	+	0.416911i
$477$	−0.257506	−	7.37958i	−0.0117904	−	0.337888i
$478$	−2.82415	−	1.63052i	−0.129174	−	0.0745784i
$479$	5.93980	+	22.1676i	0.271396	+	1.01287i	0.958218	+	0.286039i	$0.0923388\pi$
$479$	5.93980	+	22.1676i	0.271396	+	1.01287i	−0.686821	+	0.726826i	$0.740995\pi$
$480$	20.0412	−	12.0416i	0.914750	−	0.549621i
$481$		0			0
$482$			9.75464i			0.444312i
$483$	−3.92289	−	3.78840i	−0.178498	−	0.172378i
$484$	−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
$487$	28.4656	+	7.62733i	1.28990	+	0.345627i	0.837622	−	0.546250i	$-0.183945\pi$
$487$	28.4656	+	7.62733i	1.28990	+	0.345627i	0.452277	+	0.891878i	$0.350612\pi$
$488$	3.51329	+	0.941384i	0.159039	+	0.0426144i
$489$	−1.44838	+	5.80879i	−0.0654978	+	0.262682i
$490$	−3.45975	−	5.99247i	−0.156296	−	0.270712i
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	−0.639716	−	0.768611i	$-0.720948\pi$
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	0.985495	+	0.169705i	$0.0542814\pi$
$492$	−15.3614	+	15.9067i	−0.692544	+	0.717131i
$493$			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
$498$	−3.46514	−	1.92082i	−0.155277	−	0.0860739i
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.410004	−	0.912084i	$-0.365527\pi$
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.912084	−	0.410004i	$-0.134473\pi$
$500$	3.50168	−	13.0684i	0.156600	−	0.584439i
$501$	2.50312	+	8.72985i	0.111831	+	0.390021i
$502$	−1.39562	−	1.39562i	−0.0622897	−	0.0622897i
$503$	−30.1073	+	17.3825i	−1.34242	+	0.775046i	−0.987162	−	0.159722i	$-0.948940\pi$
$503$	−30.1073	+	17.3825i	−1.34242	+	0.775046i	−0.355257	+	0.934768i	$0.615607\pi$
$504$	−2.52329	−	4.03834i	−0.112396	−	0.179882i
$505$	37.2433	−	9.97931i	1.65730	−	0.444073i
$506$	1.79091			0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	42.7871	−	11.4648i	1.89651	−	0.508167i	0.898969	−	0.438011i	$-0.144317\pi$
$509$	42.7871	−	11.4648i	1.89651	−	0.508167i	0.997536	−	0.0701558i	$-0.0223497\pi$
$510$	0.218327	+	12.5174i	0.00966767	+	0.554280i
$511$	−12.9971	+	7.50387i	−0.574957	+	0.331952i
$512$	15.2996	+	15.2996i	0.676153	+	0.676153i
$513$	25.0415	+	5.32377i	1.10561	+	0.235050i
$514$	−0.621529	+	2.31958i	−0.0274145	+	0.102312i
$515$	10.8924	−	10.8924i	0.479975	−	0.479975i
$516$	−8.74406	+	15.7742i	−0.384936	+	0.694421i
$517$	−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	$0.986513\pi$
$522$	−2.76829	−	0.639186i	−0.121165	−	0.0279764i
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	−0.882020	−	0.471212i	$-0.843817\pi$
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	0.849091	+	0.528246i	$0.177150\pi$
$524$	−17.3904	−	30.1211i	−0.759705	−	1.31585i
$525$	−13.8175	−	3.44529i	−0.603047	−	0.150365i
$526$	7.70463	+	2.06445i	0.335938	+	0.0900142i
$527$	−25.9994	−	6.96651i	−1.13255	−	0.303466i
$528$	−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
$531$	29.2537	+	6.75455i	1.26950	+	0.293123i
$532$		−	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
$537$	3.66685	−	6.61497i	0.158236	−	0.285457i
$538$	−6.50526	+	6.50526i	−0.280462	+	0.280462i
$539$	−2.74218	+	10.2340i	−0.118114	+	0.440808i
$540$	33.1299	+	7.04334i	1.42568	+	0.303097i
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	0.649844	−	0.760068i	$-0.274834\pi$
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	−0.760068	+	0.649844i	$0.774834\pi$
$542$	5.39710	−	3.11602i	0.231825	−	0.133844i
$543$	−0.0636546	−	3.64953i	−0.00273168	−	0.156616i
$544$	−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
$549$	4.23285	+	6.77438i	0.180654	+	0.289123i
$550$	4.04999	−	2.33826i	0.172692	−	0.0997038i
$551$	−9.36139	−	9.36139i	−0.398809	−	0.398809i
$552$	−1.76702	−	6.16264i	−0.0752094	−	0.262299i
$553$	0.330846	−	1.23473i	0.0140690	−	0.0525062i
$554$	5.65736	−	5.65736i	0.240358	−	0.240358i
$555$	11.3744	+	6.30511i	0.482815	+	0.267637i
$556$	−8.75970	−	5.05741i	−0.371494	−	0.214482i
$557$	−0.926129	−	3.45636i	−0.0392414	−	0.146451i	0.943526	−	0.331300i	$-0.107487\pi$
$557$	−0.926129	−	3.45636i	−0.0392414	−	0.146451i	−0.982767	+	0.184849i	$0.940820\pi$
$558$	2.26406	−	4.25780i	0.0958451	−	0.180247i
$559$		0			0
$560$		−	13.2045i		−	0.557994i
$561$	13.3163	−	13.7890i	0.562213	−	0.582173i
$562$	2.13267	−	3.69389i	0.0899611	−	0.155817i
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	0.995385	−	0.0959647i	$-0.0305936\pi$
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	−0.580800	+	0.814046i	$0.697260\pi$
$564$	−2.48105	+	9.95039i	−0.104471	+	0.418987i
$565$	−43.6781	−	11.7035i	−1.83755	−	0.492370i
$566$	2.41899	+	0.648166i	0.101678	+	0.0272445i
$567$	1.99601	−	10.2657i	0.0838247	−	0.431119i
$568$	−7.92766	−	13.7311i	−0.332637	−	0.576145i
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	−0.948685	−	0.316223i	$-0.897585\pi$
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	0.748200	+	0.663473i	$0.230918\pi$
$570$	−7.51816	−	7.26039i	−0.314901	−	0.304104i
$571$			17.9785i			0.752375i	0.926544	+	0.376187i	$0.122765\pi$
$571$			17.9785i			0.752375i	−0.926544	+	0.376187i	$0.877235\pi$
$572$		0			0
$573$	−10.0925	+	6.06399i	−0.421619	+	0.253327i
$574$	−0.721441	−	2.69245i	−0.0301124	−	0.112381i
$575$	−16.6038	−	9.58619i	−0.692425	−	0.399772i
$576$	0.541005	+	15.5041i	0.0225419	+	0.646004i
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	−0.827243	−	0.561844i	$-0.810092\pi$
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	0.561844	+	0.827243i	$0.310092\pi$
$578$	1.62641	−	6.06984i	0.0676497	−	0.252472i
$579$	−18.5081	+	5.30684i	−0.769169	+	0.220545i
$580$	−12.3851	−	12.3851i	−0.514264	−	0.514264i
$581$	−6.53113	+	3.77075i	−0.270957	+	0.156437i
$582$	−7.48758	+	0.130597i	−0.310370	+	0.00541343i
$583$	4.45849	−	1.19465i	0.184652	−	0.0494773i
$584$	−17.6425			−0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	−30.3129	+	8.12231i	−1.25115	+	0.335243i	−0.822779	−	0.568362i	$-0.807577\pi$
$587$	−30.3129	+	8.12231i	−1.25115	+	0.335243i	−0.428367	+	0.903605i	$0.640911\pi$
$588$	18.3530	−	0.320111i	0.756866	−	0.0132012i
$589$	19.4604	−	11.2355i	0.801853	−	0.462950i
$590$	−8.66697	−	8.66697i	−0.356814	−	0.356814i
$591$	3.80251	−	1.09030i	0.156414	−	0.0448489i
$592$	−1.82876	+	6.82503i	−0.0751616	+	0.280507i
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	−0.999673	−	0.0255650i	$-0.991862\pi$
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	0.0255650	+	0.999673i	$0.491862\pi$
$594$	1.87036	+	2.88034i	0.0767416	+	0.118182i
$595$	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	$-0.242540\pi$
$600$	−12.0421	−	11.6292i	−0.491617	−	0.474761i
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	−0.375516	−	0.926816i	$-0.622534\pi$
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	0.990404	−	0.138202i	$-0.0441323\pi$
$602$	−1.13672	−	1.96886i	−0.0463292	−	0.0802446i
$603$	5.96693	+	19.5188i	0.242992	+	0.794867i
$604$	−16.9596	−	4.54432i	−0.690077	−	0.184906i
$605$	25.1183	+	6.73042i	1.02120	+	0.273630i
$606$	1.63870	−	6.57209i	0.0665676	−	0.266973i
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	0.550927	−	0.834553i	$-0.314274\pi$
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	−0.998208	+	0.0598403i	$0.980941\pi$
$608$	9.56943	−	16.5747i	0.388092	−	0.672195i
$609$	−3.75682	+	3.89020i	−0.152234	+	0.157639i
$610$		−	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	0.968948	−	0.247264i	$-0.0795316\pi$
$613$	0.153064	+	0.571244i	0.00618221	+	0.0230723i	−0.962766	+	0.270337i	$0.912865\pi$
$614$	−6.20916	−	3.58486i	−0.250581	−	0.144673i
$615$	35.8295	+	19.8612i	1.44478	+	0.800882i
$616$	2.10479	−	2.10479i	0.0848044	−	0.0848044i
$617$	7.52400	−	28.0800i	0.302905	−	1.13046i	−0.631829	−	0.775108i	$-0.717695\pi$
$617$	7.52400	−	28.0800i	0.302905	−	1.13046i	0.934734	−	0.355349i	$-0.115638\pi$
$618$	−0.745851	−	2.60122i	−0.0300025	−	0.104637i
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	0.996727	−	0.0808459i	$-0.0257622\pi$
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	−0.0808459	+	0.996727i	$0.525762\pi$
$620$	25.7461	−	14.8645i	1.03399	−	0.596974i
$621$	6.39257	−	12.5449i	0.256525	−	0.503409i
$622$	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
$627$	0.279084	+	16.0008i	0.0111455	+	0.639010i
$628$	−25.4694	+	14.7047i	−1.01634	+	0.586783i
$629$	−9.01686	−	9.01686i	−0.359526	−	0.359526i
$630$	−2.91183	+	3.12239i	−0.116010	+	0.124399i
$631$	−10.5019	+	39.1937i	−0.418075	+	1.56028i	0.360521	+	0.932751i	$0.382599\pi$
$631$	−10.5019	+	39.1937i	−0.418075	+	1.56028i	−0.778596	+	0.627526i	$0.784068\pi$
$632$	1.06258	−	1.06258i	0.0422670	−	0.0422670i
$633$	−6.72395	+	12.1300i	−0.267253	+	0.482122i
$634$	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
$639$	7.83401	−	33.9287i	0.309909	−	1.34220i
$640$	16.6654	−	28.8653i	0.658758	−	1.14100i
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	0.999959	+	0.00901077i	$0.00286825\pi$
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	−0.492176	+	0.870496i	$0.663798\pi$
$642$	7.73291	+	1.92814i	0.305194	+	0.0760976i
$643$	0.612124	+	0.164018i	0.0241398	+	0.00646824i	0.270869	−	0.962616i	$-0.412689\pi$
$643$	0.612124	+	0.164018i	0.0241398	+	0.00646824i	−0.246729	+	0.969085i	$0.579356\pi$
$644$	−5.70484	−	1.52861i	−0.224802	−	0.0602356i
$645$	32.4195	+	8.08354i	1.27652	+	0.318289i
$646$	5.12404	+	8.87510i	0.201603	+	0.349186i
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.131794	+	0.991277i	$0.542074\pi$
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.792574	+	0.609776i	$0.791260\pi$
$648$	8.06607	−	9.27796i	0.316865	−	0.364473i
$649$			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	$-0.141457\pi$
$653$	25.0935	+	14.4877i	0.981984	+	0.566949i	0.0791154	+	0.996865i	$0.474790\pi$
$654$	1.87858	−	3.38894i	0.0734582	−	0.132518i
$655$	−45.5614	+	45.5614i	−1.78023	+	1.78023i
$656$	−5.76064	+	21.4990i	−0.224915	+	0.839394i
$657$	−28.3367	−	26.4258i	−1.10552	−	1.03097i
$658$	−0.914059	−	0.914059i	−0.0356337	−	0.0356337i
$659$	40.4280	−	23.3411i	1.57485	−	0.909241i	0.579290	−	0.815121i	$-0.303330\pi$
$659$	40.4280	−	23.3411i	1.57485	−	0.909241i	0.995561	−	0.0941194i	$-0.0300035\pi$
$660$	0.369227	+	21.1690i	0.0143721	+	0.824003i
$661$	6.70655	−	1.79701i	0.260854	−	0.0698957i	−0.126021	−	0.992028i	$-0.540221\pi$
$661$	6.70655	−	1.79701i	0.260854	−	0.0698957i	0.386876	+	0.922132i	$0.373554\pi$
$662$	−5.66611			−0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	−19.2167	+	5.14911i	−0.745194	+	0.199674i
$666$	1.93747	−	1.21060i	0.0750755	−	0.0469096i
$667$	−6.30553	+	3.64050i	−0.244151	+	0.140961i
$668$	6.95457	+	6.95457i	0.269080	+	0.269080i
$669$	13.5172	+	47.1426i	0.522607	+	1.82264i
$670$	2.15662	−	8.04861i	0.0833174	−	0.310945i
$671$	−3.53081	+	3.53081i	−0.136306	+	0.136306i
$672$	−6.83786	−	3.79040i	−0.263776	−	0.146218i
$673$	−22.6855	−	13.0975i	−0.874460	−	0.504870i	−0.00563228	−	0.999984i	$-0.501793\pi$
$673$	−22.6855	−	13.0975i	−0.874460	−	0.504870i	−0.868828	+	0.495114i	$0.835126\pi$
$674$	2.58657	+	9.65322i	0.0996311	+	0.371828i
$675$	−1.92272	−	36.7156i	−0.0740057	−	1.41318i
$676$		0			0
$677$			21.9298i			0.842829i	0.906868	+	0.421415i	$0.138466\pi$
$677$			21.9298i			0.842829i	−0.906868	+	0.421415i	$0.861534\pi$
$678$	−5.51815	+	5.71406i	−0.211923	+	0.219447i
$679$	−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
$682$	2.91171	+	0.780190i	0.111495	+	0.0298750i
$683$	7.36335	+	1.97300i	0.281751	+	0.0754949i	0.396927	−	0.917850i	$-0.370077\pi$
$683$	7.36335	+	1.97300i	0.281751	+	0.0754949i	−0.115176	+	0.993345i	$0.536743\pi$
$684$	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
$687$	−20.1032	−	19.4139i	−0.766985	−	0.740688i
$688$			18.1532i			0.692084i
$689$		0			0
$690$	−4.92706	+	2.96039i	−0.187570	+	0.112700i
$691$	−4.12878	−	15.4088i	−0.157066	−	0.586179i	−0.998920	−	0.0464729i	$-0.985202\pi$
$691$	−4.12878	−	15.4088i	−0.157066	−	0.586179i	0.841853	−	0.539707i	$-0.181465\pi$
$692$	−23.1508	−	13.3661i	−0.880061	−	0.508103i
$693$	6.53327	−	0.227974i	0.248179	−	0.00866003i
$694$	−2.75978	+	2.75978i	−0.104760	+	0.104760i
$695$	−4.84983	+	18.0998i	−0.183965	+	0.686565i
$696$	−6.11128	+	1.75229i	−0.231647	+	0.0664205i
$697$	−28.4033	−	28.4033i	−1.07585	−	1.07585i
$698$	9.13155	−	5.27210i	0.345634	−	0.199552i
$699$	−31.4413	+	0.548395i	−1.18922	+	0.0207422i
$700$	−14.8968	+	3.99159i	−0.563047	+	0.150868i
$701$	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
$704$	−9.36704	+	2.50989i	−0.353034	+	0.0945951i
$705$	18.9952	−	0.331311i	0.715399	−	0.0124779i
$706$	−3.86907	+	2.23381i	−0.145615	+	0.0840706i
$707$	−9.11674	−	9.11674i	−0.342870	−	0.342870i
$708$	31.2553	−	8.96188i	1.17465	−	0.336808i
$709$	8.80249	−	32.8514i	0.330585	−	1.23376i	−0.577993	−	0.816042i	$-0.696164\pi$
$709$	8.80249	−	32.8514i	0.330585	−	1.23376i	0.908577	−	0.417717i	$-0.137170\pi$
$710$	−10.0521	+	10.0521i	−0.377247	+	0.377247i
$711$	3.29824	−	0.115090i	0.123694	−	0.00431620i
$712$	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
$717$	−11.5281	−	11.1328i	−0.430523	−	0.415762i
$718$	−5.08050	+	8.79968i	−0.189602	+	0.328401i
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	0.782960	−	0.622072i	$-0.213709\pi$
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	−0.930210	+	0.367027i	$0.880376\pi$
$720$	32.6017	−	9.96640i	1.21499	−	0.371426i
$721$	−4.97544	−	1.33316i	−0.185295	−	0.0496496i
$722$	−1.79571	−	0.481159i	−0.0668294	−	0.0179069i
$723$	−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
$726$	3.17336	−	3.28603i	0.117775	−	0.121956i
$727$			24.6824i			0.915420i	0.889102	+	0.457710i	$0.151330\pi$
$727$			24.6824i			0.915420i	−0.889102	+	0.457710i	$0.848670\pi$
$728$		0			0
$729$	26.8523	−	2.82014i	0.994530	−	0.104450i
$730$	4.09404	+	15.2792i	0.151527	+	0.565507i
$731$	−28.3722	−	16.3807i	−1.04939	−	0.605863i
$732$	7.56623	+	4.19416i	0.279656	+	0.155021i
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.321476	−	0.946918i	$-0.395821\pi$
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.946918	−	0.321476i	$-0.104179\pi$
$734$	−2.11072	+	7.87731i	−0.0779081	+	0.290757i
$735$	−9.37267	−	32.6880i	−0.345716	−	1.20572i
$736$	−7.44281	−	7.44281i	−0.274346	−	0.274346i
$737$	−11.0492	+	6.37928i	−0.407004	+	0.234984i
$738$	6.10308	−	3.81340i	0.224657	−	0.140373i
$739$	−37.5261	+	10.0551i	−1.38042	+	0.369882i	−0.871273	−	0.490798i	$-0.836705\pi$
$739$	−37.5261	+	10.0551i	−1.38042	+	0.369882i	−0.509146	+	0.860680i	$0.670039\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	−50.3503	+	13.4913i	−1.84717	+	0.494949i	−0.999374	−	0.0353674i	$-0.988740\pi$
$743$	−50.3503	+	13.4913i	−1.84717	+	0.494949i	−0.847800	+	0.530316i	$0.822073\pi$
$744$	−0.188184	−	10.7892i	−0.00689914	−	0.395551i
$745$	−68.6542	+	39.6375i	−2.51530	+	1.45221i
$746$	5.10435	+	5.10435i	0.186883	+	0.186883i
$747$	−14.2394	−	13.2792i	−0.520992	−	0.485859i
$748$	5.37308	−	20.0526i	0.196459	−	0.733195i
$749$	10.7270	−	10.7270i	0.391957	−	0.391957i
$750$	−2.13467	+	3.85092i	−0.0779470	+	0.140616i
$751$	42.7471	+	24.6801i	1.55986	+	0.900588i	0.997269	+	0.0738552i	$0.0235303\pi$
$751$	42.7471	+	24.6801i	1.55986	+	0.900588i	0.562595	+	0.826733i	$0.309803\pi$
$752$	2.67150	+	9.97017i	0.0974196	+	0.363575i
$753$	−4.99555	−	8.31423i	−0.182048	−	0.302987i
$754$		0			0
$755$			32.5270i			1.18378i
$756$	−3.49944	−	10.7716i	−0.127273	−	0.391760i
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	−0.984928	−	0.172964i	$-0.944666\pi$
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	0.642255	+	0.766491i	$0.277999\pi$
$758$	−0.699838	−	1.21216i	−0.0254193	−	0.0440275i
$759$	8.53976	+	2.12932i	0.309974	+	0.0772895i
$760$	−22.5905	−	6.05310i	−0.819443	−	0.219569i
$761$	−37.1766	−	9.96144i	−1.34765	−	0.361102i	−0.488384	−	0.872629i	$-0.662413\pi$
$761$	−37.1766	−	9.96144i	−1.34765	−	0.361102i	−0.859267	+	0.511527i	$0.829080\pi$
$762$	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
$765$	−13.8417	+	59.9476i	−0.500446	+	2.16741i
$766$			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	0.951330	−	0.308174i	$-0.0997180\pi$
$769$	−0.738559	−	2.75634i	−0.0266331	−	0.0993962i	−0.977963	+	0.208778i	$0.933051\pi$
$770$	−2.31126	−	1.33441i	−0.0832921	−	0.0480887i
$771$	−5.72160	+	10.3217i	−0.206058	+	0.371727i
$772$	−14.7443	+	14.7443i	−0.530660	+	0.530660i
$773$	−1.66335	+	6.20770i	−0.0598265	+	0.223275i	−0.989366	−	0.145447i	$-0.953538\pi$
$773$	−1.66335	+	6.20770i	−0.0598265	+	0.223275i	0.929540	+	0.368722i	$0.120205\pi$
$774$	4.00309	−	4.29256i	0.143888	−	0.154293i
$775$	−22.8188	−	22.8188i	−0.819675	−	0.819675i
$776$	−14.5123	+	8.37869i	−0.520962	+	0.300777i
$777$	−0.0758381	−	4.34805i	−0.00272068	−	0.155986i
$778$	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
$783$	−12.4403	−	6.33929i	−0.444581	−	0.226548i
$784$	16.0002	−	9.23773i	0.571436	−	0.329919i
$785$	38.5251	+	38.5251i	1.37502	+	1.37502i
$786$	3.11980	+	10.8806i	0.111280	+	0.388098i
$787$	−3.92580	+	14.6513i	−0.139940	+	0.522262i	0.859989	+	0.510313i	$0.170470\pi$
$787$	−3.92580	+	14.6513i	−0.139940	+	0.522262i	−0.999929	+	0.0119493i	$0.996196\pi$
$788$	3.02924	−	3.02924i	0.107912	−	0.107912i
$789$	34.2842	+	19.0046i	1.22055	+	0.676583i
$790$	−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
$795$	−10.2912	+	10.6566i	−0.364992	+	0.377950i
$796$	−17.2039	+	29.7980i	−0.609775	+	1.05616i
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	0.879672	−	0.475582i	$-0.157762\pi$
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	−0.851702	+	0.524027i	$0.824429\pi$
$798$	−0.845534	+	3.39106i	−0.0299316	+	0.120042i
$799$	−17.9934	−	4.82131i	−0.636560	−	0.170566i
$800$	−26.5489	−	7.11374i	−0.938644	−	0.251509i
$801$	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
$804$	15.9002	+	15.3551i	0.560758	+	0.541532i
$805$			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	$-0.264464\pi$
$809$	10.5758	+	6.10595i	0.371826	+	0.214674i	−0.302430	+	0.953172i	$0.597798\pi$
$810$	−9.90687	−	4.83255i	−0.348092	−	0.169798i
$811$	−29.6037	+	29.6037i	−1.03952	+	1.03952i	−0.0403387	+	0.999186i	$0.512844\pi$
$811$	−29.6037	+	29.6037i	−1.03952	+	1.03952i	−0.999186	+	0.0403387i	$0.987156\pi$
$812$	−1.51587	+	5.65729i	−0.0531965	+	0.198532i
$813$	29.4404	−	8.44147i	1.03252	−	0.296055i
$814$	1.00981	+	1.00981i	0.0353939	+	0.0353939i
$815$	10.4018	−	6.00546i	0.364358	−	0.210362i
$816$	−33.4221	+	0.582944i	−1.17001	+	0.0204071i
$817$	26.4186	−	7.07884i	0.924269	−	0.247657i
$818$	4.42964			0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	17.9749	−	4.81637i	0.627330	−	0.168093i	0.0688721	−	0.997625i	$-0.478060\pi$
$821$	17.9749	−	4.81637i	0.627330	−	0.168093i	0.558458	+	0.829533i	$0.311393\pi$
$822$	4.59896	−	0.0802145i	0.160407	−	0.00279780i
$823$	0.447230	−	0.258209i	0.0155895	−	0.00900059i	−0.492185	−	0.870491i	$-0.663802\pi$
$823$	0.447230	−	0.258209i	0.0155895	−	0.00900059i	0.507774	+	0.861490i	$0.330468\pi$
$824$	−4.28172	−	4.28172i	−0.149161	−	0.149161i
$825$	22.0921	−	6.33448i	0.769147	−	0.220538i
$826$	−1.06079	+	3.95892i	−0.0369096	+	0.137748i
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	−0.238472	−	0.971149i	$-0.576646\pi$
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	0.971149	+	0.238472i	$0.0766464\pi$
$828$	−0.531750	−	15.2389i	−0.0184796	−	0.529587i
$829$	−1.46119	−	0.843616i	−0.0507491	−	0.0293000i	0.474411	−	0.880304i	$-0.342661\pi$
$829$	−1.46119	−	0.843616i	−0.0507491	−	0.0293000i	−0.525160	+	0.851004i	$0.675994\pi$
$830$	2.05729	+	7.67790i	0.0714094	+	0.266504i
$831$	33.7030	−	20.2502i	1.16914	−	0.702471i
$832$		0			0
$833$			33.3430i			1.15527i
$834$	2.36786	+	2.28667i	0.0819922	+	0.0791811i
$835$	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
$838$	−9.12670	−	2.44549i	−0.315277	−	0.0844781i
$839$	−10.4663	−	2.80444i	−0.361337	−	0.0968199i	0.0735829	−	0.997289i	$-0.476557\pi$
$839$	−10.4663	−	2.80444i	−0.361337	−	0.0968199i	−0.434920	+	0.900469i	$0.643223\pi$
$840$	−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
$843$	14.5613	−	15.0783i	0.501518	−	0.519323i
$844$			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
$849$	10.7641	+	5.96681i	0.369422	+	0.204780i
$850$	10.4067	−	10.4067i	0.356947	−	0.356947i
$851$	1.51532	−	5.65526i	0.0519446	−	0.193860i
$852$	−10.3941	−	36.2503i	−0.356096	−	1.24192i
$853$	−30.1644	−	30.1644i	−1.03281	−	1.03281i	−0.999443	−	0.0333670i	$-0.989377\pi$
$853$	−30.1644	−	30.1644i	−1.03281	−	1.03281i	−0.0333670	−	0.999443i	$-0.510623\pi$
$854$	−0.944378	+	0.545237i	−0.0323160	+	0.0186576i
$855$	−27.2173	−	43.5593i	−0.930810	−	1.48970i
$856$	17.2259	−	4.61568i	0.588771	−	0.157761i
$857$	−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	$0.812166\pi$
$860$	34.9518	−	9.36529i	1.19185	−	0.319354i
$861$	−0.238892	−	13.6965i	−0.00814141	−	0.466774i
$862$	−6.47872	+	3.74049i	−0.220666	+	0.127402i
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	0.991931	−	0.126779i	$-0.0404637\pi$
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	−0.126779	+	0.991931i	$0.540464\pi$
$864$	4.19740	−	19.7434i	0.142799	−	0.671683i
$865$	−12.8175	+	47.8355i	−0.435808	+	1.62646i
$866$	−0.461976	+	0.461976i	−0.0156986	+	0.0156986i
$867$	14.9722	−	27.0097i	0.508482	−	0.917298i
$868$	−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
$873$	−35.8590	−	8.27971i	−1.21364	−	0.280226i
$874$	−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
$877$	−17.6992	−	4.74247i	−0.597658	−	0.160142i	−0.0527071	−	0.998610i	$-0.516785\pi$
$877$	−17.6992	−	4.74247i	−0.597658	−	0.160142i	−0.544951	+	0.838468i	$0.683452\pi$
$878$	4.90406	+	1.31404i	0.165504	+	0.0443467i
$879$	26.7130	+	6.66068i	0.901007	+	0.224659i
$880$	10.6551	+	18.4552i	0.359184	+	0.622125i
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	−0.475586	−	0.879669i	$-0.657764\pi$
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	0.999609	−	0.0279654i	$-0.00890283\pi$
$882$	−5.82054	−	1.34394i	−0.195988	−	0.0452528i
$883$		−	9.56660i		−	0.321942i	−0.986959	−	0.160971i	$-0.948537\pi$
$883$		−	9.56660i		−	0.321942i	0.986959	−	0.160971i	$-0.0514625\pi$
$884$		0			0
$885$	−31.0229	−	51.6323i	−1.04282	−	1.73560i
$886$	−2.02808	−	7.56891i	−0.0681348	−	0.254282i
$887$	21.3515	+	12.3273i	0.716913	+	0.413910i	0.813615	−	0.581404i	$-0.197496\pi$
$887$	21.3515	+	12.3273i	0.716913	+	0.413910i	−0.0967027	+	0.995313i	$0.530830\pi$
$888$	2.47849	−	4.47118i	0.0831728	−	0.150043i
$889$	6.40399	−	6.40399i	0.214783	−	0.214783i
$890$	1.35479	−	5.05616i	0.0454128	−	0.169483i
$891$	5.49398	+	15.9584i	0.184055	+	0.534627i
$892$	37.5558	+	37.5558i	1.25746	+	1.25746i
$893$	13.4680	−	7.77574i	0.450688	−	0.260205i
$894$	0.242862	+	13.9241i	0.00812253	+	0.465692i
$895$	−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
$900$	−21.0988	−	33.7672i	−0.703294	−	1.12557i
$901$	12.5800	−	7.26306i	0.419100	−	0.241967i
$902$	3.18093	+	3.18093i	0.105913	+	0.105913i
$903$	−3.07944	−	10.7398i	−0.102477	−	0.357399i
$904$	−4.60057	+	17.1696i	−0.153013	+	0.571051i
$905$	−5.17824	+	5.17824i	−0.172130	+	0.172130i
$906$	4.99755	+	2.77027i	0.166032	+	0.0920362i
$907$	1.45939	+	0.842581i	0.0484584	+	0.0279775i	0.524033	−	0.851698i	$-0.324427\pi$
$907$	1.45939	+	0.842581i	0.0484584	+	0.0279775i	−0.475575	+	0.879675i	$0.657760\pi$
$908$	3.57085	+	13.3266i	0.118503	+	0.442259i
$909$	15.6280	−	29.3900i	0.518346	−	0.974806i
$910$		0			0
$911$		−	43.9421i		−	1.45587i	−0.685648	−	0.727933i	$-0.740481\pi$
$911$		−	43.9421i		−	1.45587i	0.685648	−	0.727933i	$-0.259519\pi$
$912$	19.3856	−	20.0739i	0.641922	−	0.664713i
$913$	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
$916$	−29.2350	−	7.83348i	−0.965950	−	0.258826i
$917$	20.8116	+	5.57646i	0.687260	+	0.184151i
$918$	8.03165	+	7.23231i	0.265084	+	0.238702i
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	0.788254	−	0.615349i	$-0.210985\pi$
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	−0.927035	+	0.374974i	$0.877652\pi$
$920$	−6.43113	+	11.1390i	−0.212028	+	0.367243i
$921$	−25.3455	−	24.4765i	−0.835163	−	0.806528i
$922$		−	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
$927$	−0.463762	−	13.2905i	−0.0152319	−	0.436516i
$928$	−7.38077	+	7.38077i	−0.242286	+	0.242286i
$929$	0.593828	−	2.21620i	0.0194829	−	0.0727110i	−0.955500	−	0.294991i	$-0.904683\pi$
$929$	0.593828	−	2.21620i	0.0194829	−	0.0727110i	0.974983	+	0.222280i	$0.0713500\pi$
$930$	−9.30022	+	2.66666i	−0.304966	+	0.0874433i
$931$	−19.6831	−	19.6831i	−0.645087	−	0.645087i
$932$	−29.4930	+	17.0278i	−0.966076	+	0.557764i
$933$	13.1994	−	0.230221i	0.432128	−	0.00753711i
$934$	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
$939$	11.2824	−	0.196786i	0.368187	−	0.00642186i
$940$	17.8181	−	10.2873i	0.581163	−	0.335534i
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	0.972266	−	0.233877i	$-0.0751412\pi$
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	−0.233877	+	0.972266i	$0.575141\pi$
$942$	9.20024	−	2.63799i	0.299760	−	0.0859505i
$943$	4.77330	−	17.8142i	0.155440	−	0.580110i
$944$	23.1413	−	23.1413i	0.753185	−	0.753185i
$945$	−17.5972	+	11.4268i	−0.572436	+	0.371712i
$946$	3.17745	+	1.83450i	0.103308	+	0.0596448i
$947$	−3.46107	−	12.9169i	−0.112470	−	0.419742i	0.886616	−	0.462507i	$-0.153050\pi$
$947$	−3.46107	−	12.9169i	−0.112470	−	0.419742i	−0.999085	+	0.0427648i	$0.986383\pi$
$948$	3.06363	−	1.84076i	0.0995022	−	0.0597852i
$949$		0			0
$950$			12.2866i			0.398629i
$951$	11.0902	+	10.7100i	0.359626	+	0.347296i
$952$	4.68381	−	8.11259i	0.151803	−	0.262931i
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	0.973359	−	0.229288i	$-0.0736399\pi$
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	−0.685249	+	0.728309i	$0.740307\pi$
$954$	0.760824	+	2.48878i	0.0246326	+	0.0805772i
$955$	22.8174	+	6.11390i	0.738353	+	0.197841i
$956$	−16.7646	−	4.49206i	−0.542206	−	0.145284i
$957$	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
$960$	21.6213	−	22.3889i	0.697824	−	0.722598i
$961$			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
$966$	1.68107	+	0.931859i	0.0540874	+	0.0299821i
$967$	−29.0154	+	29.0154i	−0.933072	+	0.933072i	−0.997897	−	0.0648250i	$-0.979351\pi$
$967$	−29.0154	+	29.0154i	−0.933072	+	0.933072i	0.0648250	+	0.997897i	$0.479351\pi$
$968$	2.64568	−	9.87382i	0.0850354	−	0.317357i
$969$	13.8813	+	48.4123i	0.445932	+	1.55523i
$970$	10.6239	+	10.6239i	0.341114	+	0.341114i
$971$	−19.5631	+	11.2948i	−0.627810	+	0.362466i	−0.779904	−	0.625900i	$-0.784732\pi$
$971$	−19.5631	+	11.2948i	−0.627810	+	0.362466i	0.152093	+	0.988366i	$0.451399\pi$
$972$	23.9536	−	16.7701i	0.768311	−	0.537902i
$973$	6.05235	−	1.62172i	0.194029	−	0.0519900i
$974$	−10.3864			−0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	2.57462	−	0.689868i	0.0823694	−	0.0220708i	−0.217399	−	0.976083i	$-0.569757\pi$
$977$	2.57462	−	0.689868i	0.0823694	−	0.0220708i	0.299768	+	0.954012i	$0.403091\pi$
$978$	−0.0367960	−	2.10963i	−0.00117660	−	0.0674587i
$979$	−6.94116	+	4.00748i	−0.221841	+	0.128080i
$980$	−26.0407	−	26.0407i	−0.831839	−	0.831839i
$981$	12.9871	−	13.9263i	0.414647	−	0.444631i
$982$	−1.39784	+	5.21679i	−0.0446067	+	0.166475i
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.263440	+	0.964676i	$0.584857\pi$
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.964676	+	0.263440i	$0.915143\pi$
$984$	7.80731	−	14.0843i	0.248888	−	0.448992i
$985$	−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
$990$	1.55015	−	6.71362i	0.0492669	−	0.213373i
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	−0.951827	−	0.306635i	$-0.900797\pi$
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	0.741467	+	0.670989i	$0.234130\pi$
$992$	−8.85836	−	15.3431i	−0.281253	−	0.487145i
$993$	−27.0183	−	6.73680i	−0.857400	−	0.213786i
$994$	4.59160	+	1.23032i	0.145637	+	0.0390232i
$995$	61.5704	+	16.4977i	1.95191	+	0.523013i
$996$	−20.4597	−	5.10147i	−0.648291	−	0.161646i
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	1.00000		0.000107105i	$3.40926e-5\pi$
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	−0.499907	+	0.866079i	$0.666633\pi$
$998$	−7.36014	+	12.7481i	−0.232981	+	0.403535i
$999$	10.6780	−	3.46902i	0.337837	−	0.109755i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.340435 + 0.0912193i) q^{2} +(-1.73179 + 0.0302056i) q^{3} +(-1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(0.586806 - 0.168255i) q^{6} +(0.300747 - 1.12240i) q^{7} +(0.965906 - 0.965906i) q^{8} +(2.99818 - 0.104619i) q^{9} +(-1.06066 - 0.612371i) q^{10} +(0.485362 + 1.81140i) q^{11} +(2.78492 - 1.67330i) q^{12} +0.409539i q^{14} +(-4.32956 - 4.18112i) q^{15} +(1.63506 - 2.83201i) q^{16} +(2.95083 + 5.11099i) q^{17} +(-1.01114 + 0.309108i) q^{18} +(-4.75906 - 1.27519i) q^{19} +(-6.29623 - 1.68707i) q^{20} +(-0.486926 + 1.95284i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(-1.35482 + 2.34662i) q^{23} +(-1.64357 + 1.70192i) q^{24} +7.07560i q^{25} +(-5.18904 + 0.271740i) q^{27} +(0.564135 + 2.10538i) q^{28} +(2.32707 + 1.34353i) q^{29} +(1.85533 + 1.02846i) q^{30} +(-3.22500 + 3.22500i) q^{31} +(-1.00539 + 3.75217i) q^{32} +(-0.895258 - 3.12229i) q^{33} +(-1.47079 - 1.47079i) q^{34} +(3.49695 - 2.01896i) q^{35} +(-4.77234 + 2.98191i) q^{36} +(-2.08708 + 0.559232i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(-6.57436 + 1.76159i) q^{41} +(-0.0123704 - 0.709234i) q^{42} +(-4.80750 + 2.77561i) q^{43} +(-2.48735 - 2.48735i) q^{44} +(7.62417 + 7.11003i) q^{45} +(0.247172 - 0.922459i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(-2.74604 + 4.95383i) q^{48} +(4.89284 + 2.82488i) q^{49} +(-0.645431 - 2.40878i) q^{50} +(-5.26460 - 8.76202i) q^{51} -2.46136i q^{53} +(1.74174 - 0.565851i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(-0.793642 - 1.37463i) q^{56} +(8.28020 + 2.06460i) q^{57} +(-0.914771 - 0.245112i) q^{58} +(9.66677 + 2.59020i) q^{59} +(10.9547 + 2.73147i) q^{60} +(1.33134 + 2.30596i) q^{61} +(0.803720 - 1.39208i) q^{62} +(0.784266 - 3.39662i) q^{63} +5.17117i q^{64} +(0.589590 + 0.981273i) q^{66} +(1.76087 + 6.57167i) q^{67} +(-9.58711 - 5.53512i) q^{68} +(2.27539 - 4.10478i) q^{69} +(-1.00632 + 1.00632i) q^{70} +(3.00415 - 11.2116i) q^{71} +(2.79490 - 2.99701i) q^{72} +(-9.13263 - 9.13263i) q^{73} +(0.659503 - 0.380764i) q^{74} +(-0.213723 - 12.2534i) q^{75} +(8.92696 - 2.39197i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(10.9765 - 2.94114i) q^{80} +(8.97811 - 0.627334i) q^{81} +(2.07745 - 1.19942i) q^{82} +(-4.58922 - 4.58922i) q^{83} +(-1.04056 - 3.62903i) q^{84} +(-5.30793 + 19.8095i) q^{85} +(1.38345 - 1.38345i) q^{86} +(-4.07057 - 2.25642i) q^{87} +(2.21845 + 1.28082i) q^{88} +(1.10619 + 4.12834i) q^{89} +(-3.24410 - 1.72503i) q^{90} -5.08271i q^{92} +(5.48760 - 5.68242i) q^{93} +(0.556230 - 0.963419i) q^{94} +(-8.56055 - 14.8273i) q^{95} +(1.62779 - 6.52833i) q^{96} +(-11.8495 - 3.17506i) q^{97} +(-1.92338 - 0.515368i) q^{98} +(1.64471 + 5.38010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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