LMFDB - Embedded newform 507.2.k.k.89.13

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			89.13
Character	$\chi$	$=$	507.89
Dual form			507.2.k.k.188.13

$q$-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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

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

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	$0.543566\pi$
$3$	−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	−0.104350	+	0.994541i	$0.533276\pi$
$5$	−2.45719	+	2.45719i	−1.09889	+	1.09889i	−0.994541	+	0.104350i	$0.966724\pi$
$6$	−0.586806	−	0.168255i	−0.239562	−	0.0686900i
$7$	−0.300747	−	1.12240i	−0.113672	−	0.424228i	0.885513	−	0.464615i	$-0.153807\pi$
$7$	−0.300747	−	1.12240i	−0.113672	−	0.424228i	−0.999184	+	0.0403875i	$0.987141\pi$
$8$	−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	0.853350	+	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
$15$	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	−0.247014	−	0.969012i	$-0.579449\pi$
$17$	2.95083	−	5.11099i	0.715682	−	1.23960i	0.962696	−	0.270586i	$-0.0872174\pi$
$18$	1.01114	+	0.309108i	0.238328	+	0.0728573i
$19$	4.75906	−	1.27519i	1.09180	−	0.292548i	0.332381	−	0.943145i	$-0.392148\pi$
$19$	4.75906	−	1.27519i	1.09180	−	0.292548i	0.759423	+	0.650598i	$0.225482\pi$
$20$	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	0.689500	−	0.724286i	$-0.257831\pi$
$23$	−1.35482	−	2.34662i	−0.282500	−	0.489305i	−0.972000	+	0.234981i	$0.924497\pi$
$24$	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	−0.268126	−	0.963384i	$-0.586404\pi$
$29$	2.32707	−	1.34353i	0.432125	−	0.249488i	0.700252	+	0.713896i	$0.253071\pi$
$30$	1.85533	−	1.02846i	0.338736	−	0.187770i
$31$	3.22500	+	3.22500i	0.579227	+	0.579227i	0.934690	−	0.355463i	$-0.115677\pi$
$31$	3.22500	+	3.22500i	0.579227	+	0.579227i	−0.355463	+	0.934690i	$0.615677\pi$
$32$	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	$-0.359830\pi$
$37$	2.08708	+	0.559232i	0.343114	+	0.0919372i	−0.0831470	+	0.996537i	$0.526497\pi$
$38$	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	$0.404969\pi$
$42$	−0.0123704	+	0.709234i	−0.00190879	+	0.109437i
$43$	−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
$45$	−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	$-0.176060\pi$
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	−0.525336	+	0.850895i	$0.676060\pi$
$48$	−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	$0.0540689\pi$
$53$			2.46136i			0.338093i	−0.985608	+	0.169047i	$0.945931\pi$
$54$	−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	$-0.809173\pi$
$59$	−9.66677	+	2.59020i	−1.25851	+	0.337216i	−0.432890	+	0.901447i	$0.642506\pi$
$60$	−10.9547	+	2.73147i	−1.41424	+	0.352631i
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	−0.768120	−	0.640306i	$-0.778808\pi$
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	0.938581	+	0.345058i	$0.112141\pi$
$62$	0.803720	+	1.39208i	0.102073	+	0.176795i
$63$	−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	0.770998	+	0.636838i	$0.219758\pi$
$67$	−1.76087	+	6.57167i	−0.215125	+	0.802857i	−0.986123	+	0.166019i	$0.946909\pi$
$68$	−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	−0.878552	−	0.477647i	$-0.841490\pi$
$71$	−3.00415	−	11.2116i	−0.356527	−	1.33058i	0.522025	−	0.852930i	$-0.325177\pi$
$72$	−2.79490	−	2.99701i	−0.329383	−	0.353201i
$73$	9.13263	−	9.13263i	1.06889	−	1.06889i	0.0714492	−	0.997444i	$-0.477238\pi$
$73$	9.13263	−	9.13263i	1.06889	−	1.06889i	0.997444	−	0.0714492i	$-0.0227624\pi$
$74$	0.659503	+	0.380764i	0.0766657	+	0.0442630i
$75$	−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	$-0.634075\pi$
$83$	4.58922	−	4.58922i	0.503732	−	0.503732i	0.912596	+	0.408864i	$0.134075\pi$
$84$	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	$-0.989402\pi$
$89$	−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
$93$	−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	$-0.369333\pi$
$97$	11.8495	−	3.17506i	1.20313	−	0.322379i	0.804065	+	0.594542i	$0.202667\pi$
$98$	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	0.998128	+	0.0611547i	$0.0194783\pi$
$101$	5.54779	+	9.60905i	0.552026	+	0.956137i	−0.446103	+	0.894982i	$0.647188\pi$
$102$	−2.59152	+	2.50267i	−0.256599	+	0.247801i
$103$			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	0.158641	−	0.987336i	$-0.449289\pi$
$107$	11.3063	−	6.52769i	1.09302	−	0.631055i	0.934379	+	0.356281i	$0.115955\pi$
$108$	8.17461	+	5.30819i	0.786602	+	0.510781i
$109$	−4.48829	−	4.48829i	−0.429901	−	0.429901i	0.458694	−	0.888594i	$-0.348318\pi$
$109$	−4.48829	−	4.48829i	−0.429901	−	0.429901i	−0.888594	+	0.458694i	$0.848318\pi$
$110$	−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	−0.134657	−	0.990892i	$-0.542993\pi$
$113$	−11.2693	−	6.50632i	−1.06012	−	0.612063i	−0.925467	+	0.378829i	$0.876327\pi$
$114$	−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	−0.169679	−	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	$-0.699460\pi$
$131$		−	18.5420i		−	1.62003i	0.586412	−	0.810013i	$-0.300540\pi$
$132$	−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	$-0.687646\pi$
$137$	−7.27811	+	1.95016i	−0.621811	+	0.166614i	−0.0658600	+	0.997829i	$0.520979\pi$
$138$	0.400186	+	1.60497i	0.0340661	+	0.136624i
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	−0.728733	−	0.684798i	$-0.759891\pi$
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	0.957419	+	0.288703i	$0.0932239\pi$
$140$	−3.78714	−	6.55952i	−0.320072	−	0.554381i
$141$	−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	0.585798	+	0.810457i	$0.300781\pi$
$149$	5.90444	+	22.0357i	0.483710	+	1.80523i	−0.102088	+	0.994775i	$0.532552\pi$
$150$	−1.19051	+	4.15200i	−0.0972046	+	0.339010i
$151$	−6.61873	+	6.61873i	−0.538625	+	0.538625i	−0.923125	−	0.384500i	$-0.874374\pi$
$151$	−6.61873	+	6.61873i	−0.538625	+	0.538625i	0.384500	+	0.923125i	$0.374374\pi$
$152$	−5.82852	−	3.36510i	−0.472755	−	0.272945i
$153$	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	$-0.126553\pi$
$163$	−0.894579	−	3.33861i	−0.0700688	−	0.261500i	−0.992070	+	0.125687i	$0.959887\pi$
$164$	−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	$-0.851640\pi$
$167$	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
$171$	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	−0.457053	−	0.889439i	$-0.651095\pi$
$173$	7.12562	−	12.3419i	0.541751	−	0.938339i	0.998804	−	0.0489001i	$-0.0155716\pi$
$174$	−1.59159	+	0.396851i	−0.120658	+	0.0300852i
$175$	−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	0.772821	−	0.634624i	$-0.218845\pi$
$179$	−2.18334	−	3.78165i	−0.163190	−	0.282654i	−0.936011	+	0.351970i	$0.885512\pi$
$180$	19.0537	−	4.39942i	1.42018	−	0.327914i
$181$		−	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
$186$	−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	0.697629	−	0.716459i	$-0.254238\pi$
$191$	5.88706	+	3.39890i	0.425973	+	0.245935i	−0.271657	+	0.962394i	$0.587572\pi$
$192$	−0.156198	+	8.95537i	−0.0112726	+	0.646298i
$193$	−10.7374	−	2.87709i	−0.772898	−	0.207098i	−0.149247	−	0.988800i	$-0.547685\pi$
$193$	−10.7374	−	2.87709i	−0.772898	−	0.207098i	−0.623652	+	0.781702i	$0.714352\pi$
$194$	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	$0.557407\pi$
$198$	−1.05069	+	1.68155i	−0.0746689	+	0.119502i
$199$	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
$201$	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	0.970291	−	0.241939i	$-0.0777834\pi$
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	−0.694671	+	0.719327i	$0.744450\pi$
$212$	2.30849	−	3.99842i	0.158548	−	0.274612i
$213$	4.86389	+	19.5069i	0.333269	+	1.33659i
$214$	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	−0.0619383	−	0.998080i	$-0.519728\pi$
$223$	7.32834	−	27.3497i	0.490742	−	1.83147i	0.552680	−	0.833393i	$-0.313605\pi$
$224$	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	$-0.161823\pi$
$227$	−1.90366	−	7.10455i	−0.126350	−	0.471546i	−0.999884	+	0.0152176i	$0.995156\pi$
$228$	15.3874	+	4.41203i	1.01905	+	0.292194i
$229$	−11.4094	+	11.4094i	−0.753951	+	0.753951i	−0.975214	−	0.221263i	$-0.928982\pi$
$229$	−11.4094	+	11.4094i	−0.753951	+	0.753951i	0.221263	+	0.975214i	$0.428982\pi$
$230$	2.87401	+	1.65931i	0.189507	+	0.109412i
$231$	−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	$-0.846737\pi$
$239$	−6.54262	+	6.54262i	−0.423207	+	0.423207i	0.463099	+	0.886306i	$0.346737\pi$
$240$	18.9201	+	5.42498i	1.22129	+	0.350181i
$241$	−7.16336	−	26.7340i	−0.461433	−	1.72209i	−0.668453	−	0.743754i	$-0.733043\pi$
$241$	−7.16336	−	26.7340i	−0.461433	−	1.72209i	0.207021	−	0.978337i	$-0.433623\pi$
$242$	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	−0.764025	−	0.645187i	$-0.776779\pi$
$251$	2.80003	−	4.84979i	0.176736	−	0.306116i	0.940761	+	0.339071i	$0.110113\pi$
$252$	−1.91164	+	6.25328i	−0.120422	+	0.393920i
$253$	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	0.952499	−	0.304541i	$-0.0985030\pi$
$257$	3.40679	+	5.90073i	0.212510	+	0.368077i	−0.739990	+	0.672618i	$0.765170\pi$
$258$	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	−0.962446	−	0.271474i	$-0.912489\pi$
$263$	−19.5996	+	11.3159i	−1.20857	+	0.697765i	−0.246119	+	0.969240i	$0.579156\pi$
$264$	−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	0.991955	−	0.126593i	$-0.0404042\pi$
$269$	22.6058	+	13.0515i	1.37830	+	0.795762i	0.386345	+	0.922354i	$0.373738\pi$
$270$	5.67021	−	2.88940i	0.345078	−	0.175843i
$271$	17.0798	+	4.57652i	1.03753	+	0.278004i	0.737087	−	0.675797i	$-0.236201\pi$
$271$	17.0798	+	4.57652i	1.03753	+	0.278004i	0.300438	+	0.953801i	$0.402867\pi$
$272$	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	−0.224920	−	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
$279$	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	$-0.132443\pi$
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	−0.404181	+	0.914679i	$0.632443\pi$
$282$	−0.934172	−	1.68524i	−0.0556291	−	0.100354i
$283$	−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
$288$	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	$-0.429640\pi$
$293$	15.3534	−	4.11392i	0.896953	−	0.240338i	0.677707	+	0.735332i	$0.262974\pi$
$294$	−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	$-0.947148\pi$
$307$	−14.3846	+	14.3846i	−0.820970	+	0.820970i	0.165277	+	0.986247i	$0.447148\pi$
$308$	−3.53987	−	2.04374i	−0.201703	−	0.116453i
$309$	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	$-0.669578\pi$
$317$	6.29415	−	6.29415i	0.353515	−	0.353515i	0.861416	+	0.507901i	$0.169578\pi$
$318$	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	$-0.729002\pi$
$331$	−15.5288	+	4.16094i	−0.853541	+	0.228706i	−0.194584	+	0.980886i	$0.562336\pi$
$332$	−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	$0.280900\pi$
$337$			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
$342$	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	0.734817	−	0.678265i	$-0.237268\pi$
$347$	9.59025	+	5.53693i	0.514831	+	0.297238i	−0.219986	+	0.975503i	$0.570601\pi$
$348$	8.72881	+	0.152247i	0.467913	+	0.00816128i
$349$	28.8980	+	7.74319i	1.54687	+	0.414483i	0.928479	−	0.371385i	$-0.121117\pi$
$349$	28.8980	+	7.74319i	1.54687	+	0.414483i	0.618394	+	0.785868i	$0.287784\pi$
$350$	−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	$0.692861\pi$
$354$	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	−0.996870	−	0.0790589i	$-0.974808\pi$
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.0790589	−	0.996870i	$-0.525192\pi$
$360$	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	0.992221	+	0.124490i	$0.0397295\pi$
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	−0.388299	+	0.921533i	$0.626937\pi$
$368$	4.43045	−	7.67376i	0.230953	−	0.400023i
$369$	19.5268	+	5.96937i	1.01652	+	0.310753i
$370$	−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	0.469128	+	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
$375$	−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	$-0.949190\pi$
$379$	−1.02786	+	3.83602i	−0.0527975	+	0.197043i	0.934489	+	0.355991i	$0.115857\pi$
$380$	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	−0.884299	−	0.466921i	$-0.845363\pi$
$383$	−6.88748	−	25.7044i	−0.351934	−	1.31344i	0.532365	−	0.846515i	$-0.321303\pi$
$384$	−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	0.928605	+	0.371071i	$0.121009\pi$
$397$	6.17560	+	23.0477i	0.309945	+	1.15673i	−0.618660	+	0.785659i	$0.712324\pi$
$398$	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	−0.637393	−	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
$405$	−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	$-0.482759\pi$
$409$	12.1401	−	3.25292i	0.600288	−	0.160847i	0.546151	+	0.837687i	$0.316093\pi$
$410$	−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	0.189239	−	0.981931i	$-0.439398\pi$
$419$	23.2172	−	13.4045i	1.13424	−	0.654851i	0.944997	+	0.327080i	$0.106065\pi$
$420$	6.36039	+	11.4741i	0.310355	+	0.559878i
$421$	8.93430	+	8.93430i	0.435431	+	0.435431i	0.890471	−	0.455040i	$-0.150375\pi$
$421$	8.93430	+	8.93430i	0.435431	+	0.435431i	−0.455040	+	0.890471i	$0.650375\pi$
$422$	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	$-0.587469\pi$
$431$	−20.5028	−	5.49370i	−0.987583	−	0.264622i	−0.716235	+	0.697859i	$0.754136\pi$
$432$	−7.71484	−	15.1398i	−0.371181	−	0.728412i
$433$	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
$435$	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	−0.767236	−	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	$-0.822881\pi$
$443$		−	22.2330i		−	1.05632i	0.849144	−	0.528162i	$-0.177119\pi$
$444$	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	$-0.780313\pi$
$449$	−23.7458	+	6.36268i	−1.12064	+	0.300273i	−0.349495	+	0.936938i	$0.613647\pi$
$450$	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	$-0.866060\pi$
$457$	1.75192	−	6.53825i	0.0819513	−	0.305847i	0.994719	+	0.102632i	$0.0327263\pi$
$458$	−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	0.999522	+	0.0309044i	$0.00983873\pi$
$461$	3.20695	+	11.9685i	0.149363	+	0.557429i	−0.850160	+	0.526525i	$0.823495\pi$
$462$	−1.27870	−	0.366643i	−0.0594905	−	0.0170578i
$463$	−6.97385	+	6.97385i	−0.324102	+	0.324102i	−0.850339	−	0.526236i	$-0.823603\pi$
$463$	−6.97385	+	6.97385i	−0.324102	+	0.324102i	0.526236	+	0.850339i	$0.323603\pi$
$464$	7.60980	+	4.39352i	0.353276	+	0.203964i
$465$	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	0.686821	+	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
$483$	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	$-0.816055\pi$
$487$	−28.4656	+	7.62733i	−1.28990	+	0.345627i	−0.452277	+	0.891878i	$0.649388\pi$
$488$	−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	0.985495	−	0.169705i	$-0.0542814\pi$
$491$	7.66195	+	13.2709i	0.345779	+	0.598907i	−0.639716	+	0.768611i	$0.720948\pi$
$492$	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	−0.912084	−	0.410004i	$-0.865527\pi$
$499$	−29.5332	−	29.5332i	−1.32209	−	1.32209i	−0.410004	−	0.912084i	$-0.634473\pi$
$500$	−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	−0.355257	−	0.934768i	$-0.615607\pi$
$503$	−30.1073	−	17.3825i	−1.34242	−	0.775046i	−0.987162	+	0.159722i	$0.948940\pi$
$504$	−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	−0.997536	−	0.0701558i	$-0.977650\pi$
$509$	−42.7871	−	11.4648i	−1.89651	−	0.508167i	−0.898969	−	0.438011i	$-0.855683\pi$
$510$	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	$-0.986513\pi$
$521$		−	1.93372i		−	0.0847179i	0.999102	−	0.0423590i	$-0.0134873\pi$
$522$	2.76829	−	0.639186i	0.121165	−	0.0279764i
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	0.849091	−	0.528246i	$-0.177150\pi$
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	−0.882020	+	0.471212i	$0.843817\pi$
$524$	−17.3904	+	30.1211i	−0.759705	+	1.31585i
$525$	13.8175	−	3.44529i	0.603047	−	0.150365i
$526$	−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	$-0.725166\pi$
$541$	2.56375	−	2.56375i	0.110224	−	0.110224i	0.760068	+	0.649844i	$0.225166\pi$
$542$	5.39710	+	3.11602i	0.231825	+	0.133844i
$543$	−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	$-0.892513\pi$
$557$	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
$561$	−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	−0.580800	−	0.814046i	$-0.697260\pi$
$563$	9.83710	−	17.0384i	0.414585	−	0.718081i	0.995385	+	0.0959647i	$0.0305936\pi$
$564$	2.48105	+	9.95039i	0.104471	+	0.418987i
$565$	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	0.748200	−	0.663473i	$-0.230918\pi$
$569$	−4.78231	−	8.28321i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$570$	7.51816	−	7.26039i	0.314901	−	0.304104i
$571$		−	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
$576$	0.541005	−	15.5041i	0.0225419	−	0.646004i
$577$	6.37509	+	6.37509i	0.265398	+	0.265398i	0.827243	−	0.561844i	$-0.189908\pi$
$577$	6.37509	+	6.37509i	0.265398	+	0.265398i	−0.561844	+	0.827243i	$0.689908\pi$
$578$	−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	$-0.192423\pi$
$587$	30.3129	+	8.12231i	1.25115	+	0.335243i	0.428367	+	0.903605i	$0.359089\pi$
$588$	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	$-0.00813848\pi$
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	−0.0255650	+	0.999673i	$0.508138\pi$
$594$	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	$0.242540\pi$
$599$			33.7915i			1.38068i	−0.723484	+	0.690341i	$0.757460\pi$
$600$	12.0421	−	11.6292i	0.491617	−	0.474761i
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	0.990404	+	0.138202i	$0.0441323\pi$
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	−0.375516	+	0.926816i	$0.622534\pi$
$602$	−1.13672	+	1.96886i	−0.0463292	+	0.0802446i
$603$	−5.96693	+	19.5188i	−0.242992	+	0.794867i
$604$	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	−0.998208	−	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
$609$	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	$-0.920468\pi$
$613$	−0.153064	+	0.571244i	−0.00618221	+	0.0230723i	0.962766	+	0.270337i	$0.0871350\pi$
$614$	−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	−0.934734	−	0.355349i	$-0.884362\pi$
$617$	−7.52400	−	28.0800i	−0.302905	−	1.13046i	0.631829	−	0.775108i	$-0.282305\pi$
$618$	0.745851	−	2.60122i	0.0300025	−	0.104637i
$619$	−22.7868	+	22.7868i	−0.915881	+	0.915881i	−0.996727	−	0.0808459i	$-0.974238\pi$
$619$	−22.7868	+	22.7868i	−0.915881	+	0.915881i	0.0808459	+	0.996727i	$0.474238\pi$
$620$	25.7461	+	14.8645i	1.03399	+	0.596974i
$621$	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	0.778596	+	0.627526i	$0.215932\pi$
$631$	10.5019	+	39.1937i	0.418075	+	1.56028i	−0.360521	+	0.932751i	$0.617401\pi$
$632$	−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	−0.492176	−	0.870496i	$-0.663798\pi$
$641$	12.8560	−	22.2673i	0.507783	−	0.879506i	0.999959	−	0.00901077i	$-0.00286825\pi$
$642$	−7.73291	+	1.92814i	−0.305194	+	0.0760976i
$643$	−0.612124	+	0.164018i	−0.0241398	+	0.00646824i	−0.270869	−	0.962616i	$-0.587311\pi$
$643$	−0.612124	+	0.164018i	−0.0241398	+	0.00646824i	0.246729	+	0.969085i	$0.420644\pi$
$644$	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	−0.792574	−	0.609776i	$-0.791260\pi$
$647$	−23.5124	−	40.7247i	−0.924368	−	1.60105i	−0.131794	−	0.991277i	$-0.542074\pi$
$648$	−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	0.0791154	−	0.996865i	$-0.474790\pi$
$653$	25.0935	−	14.4877i	0.981984	−	0.566949i	0.902869	+	0.429917i	$0.141457\pi$
$654$	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	0.995561	+	0.0941194i	$0.0300035\pi$
$659$	40.4280	+	23.3411i	1.57485	+	0.909241i	0.579290	+	0.815121i	$0.303330\pi$
$660$	0.369227	−	21.1690i	0.0143721	−	0.824003i
$661$	−6.70655	−	1.79701i	−0.260854	−	0.0698957i	0.126021	−	0.992028i	$-0.459779\pi$
$661$	−6.70655	−	1.79701i	−0.260854	−	0.0698957i	−0.386876	+	0.922132i	$0.626446\pi$
$662$	−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	−0.868828	−	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	$-0.861534\pi$
$677$		−	21.9298i		−	0.842829i	0.906868	−	0.421415i	$-0.138466\pi$
$678$	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	$-0.629923\pi$
$683$	−7.36335	+	1.97300i	−0.281751	+	0.0754949i	0.115176	+	0.993345i	$0.463257\pi$
$684$	−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	−0.841853	−	0.539707i	$-0.818535\pi$
$691$	4.12878	−	15.4088i	0.157066	−	0.586179i	0.998920	−	0.0464729i	$-0.0147981\pi$
$692$	−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	−0.908577	−	0.417717i	$-0.862830\pi$
$709$	−8.80249	−	32.8514i	−0.330585	−	1.23376i	0.577993	−	0.816042i	$-0.303836\pi$
$710$	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	−0.930210	−	0.367027i	$-0.880376\pi$
$719$	−3.94839	+	6.83882i	−0.147250	+	0.255045i	0.782960	+	0.622072i	$0.213709\pi$
$720$	−32.6017	−	9.96640i	−1.21499	−	0.371426i
$721$	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	$-0.848670\pi$
$727$		−	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
$732$	7.56623	−	4.19416i	0.279656	−	0.155021i
$733$	−34.3405	−	34.3405i	−1.26839	−	1.26839i	−0.946918	−	0.321476i	$-0.895821\pi$
$733$	−34.3405	−	34.3405i	−1.26839	−	1.26839i	−0.321476	−	0.946918i	$-0.604179\pi$
$734$	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	$-0.163295\pi$
$739$	37.5261	+	10.0551i	1.38042	+	0.369882i	0.509146	+	0.860680i	$0.329961\pi$
$740$	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	$0.177927\pi$
$744$	−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	0.562595	−	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
$756$	3.49944	−	10.7716i	0.127273	−	0.391760i
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	0.642255	−	0.766491i	$-0.277999\pi$
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	−0.984928	+	0.172964i	$0.944666\pi$
$758$	−0.699838	+	1.21216i	−0.0254193	+	0.0440275i
$759$	−8.53976	+	2.12932i	−0.309974	+	0.0772895i
$760$	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	$0.170920\pi$
$762$	−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	$-0.900282\pi$
$769$	0.738559	−	2.75634i	0.0266331	−	0.0993962i	0.977963	+	0.208778i	$0.0669487\pi$
$770$	−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	$-0.0464620\pi$
$773$	1.66335	+	6.20770i	0.0598265	+	0.223275i	−0.929540	+	0.368722i	$0.879795\pi$
$774$	−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	0.999929	+	0.0119493i	$0.00380368\pi$
$787$	3.92580	+	14.6513i	0.139940	+	0.522262i	−0.859989	+	0.510313i	$0.829530\pi$
$788$	−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	−0.851702	−	0.524027i	$-0.824429\pi$
$797$	0.789625	−	1.36767i	0.0279700	−	0.0484454i	0.879672	+	0.475582i	$0.157762\pi$
$798$	0.845534	+	3.39106i	0.0299316	+	0.120042i
$799$	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	−0.302430	−	0.953172i	$-0.597798\pi$
$809$	10.5758	−	6.10595i	0.371826	−	0.214674i	0.674256	+	0.738498i	$0.264464\pi$
$810$	−9.90687	+	4.83255i	−0.348092	+	0.169798i
$811$	29.6037	+	29.6037i	1.03952	+	1.03952i	0.999186	+	0.0403387i	$0.0128437\pi$
$811$	29.6037	+	29.6037i	1.03952	+	1.03952i	0.0403387	+	0.999186i	$0.487156\pi$
$812$	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	$-0.521940\pi$
$821$	−17.9749	−	4.81637i	−0.627330	−	0.168093i	−0.558458	+	0.829533i	$0.688607\pi$
$822$	4.59896	+	0.0802145i	0.160407	+	0.00279780i
$823$	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
$825$	−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	$-0.423354\pi$
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	−0.971149	+	0.238472i	$0.923354\pi$
$828$	−0.531750	+	15.2389i	−0.0184796	+	0.529587i
$829$	−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
$834$	−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	$-0.523443\pi$
$839$	10.4663	−	2.80444i	0.361337	−	0.0968199i	0.434920	+	0.900469i	$0.356777\pi$
$840$	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	0.0333670	−	0.999443i	$-0.489377\pi$
$853$	30.1644	−	30.1644i	1.03281	−	1.03281i	0.999443	−	0.0333670i	$-0.0106230\pi$
$854$	−0.944378	−	0.545237i	−0.0323160	−	0.0186576i
$855$	−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	$-0.959536\pi$
$863$	−25.4155	+	25.4155i	−0.865153	+	0.865153i	0.126779	+	0.991931i	$0.459536\pi$
$864$	−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	$-0.483215\pi$
$877$	17.6992	−	4.74247i	0.597658	−	0.160142i	0.544951	+	0.838468i	$0.316548\pi$
$878$	−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	0.999609	+	0.0279654i	$0.00890283\pi$
$881$	15.5539	+	26.9401i	0.524023	+	0.907635i	−0.475586	+	0.879669i	$0.657764\pi$
$882$	5.82054	−	1.34394i	0.195988	−	0.0452528i
$883$			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	−0.0967027	−	0.995313i	$-0.530830\pi$
$887$	21.3515	−	12.3273i	0.716913	−	0.413910i	0.813615	+	0.581404i	$0.197496\pi$
$888$	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	−0.475575	−	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	$0.259519\pi$
$911$			43.9421i			1.45587i	−0.685648	+	0.727933i	$0.740481\pi$
$912$	−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	−0.927035	−	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
$921$	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	$-0.0953167\pi$
$929$	−0.593828	−	2.21620i	−0.0194829	−	0.0727110i	−0.974983	+	0.222280i	$0.928650\pi$
$930$	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	$-0.924859\pi$
$941$	−22.6506	+	22.6506i	−0.738390	+	0.738390i	0.233877	+	0.972266i	$0.424859\pi$
$942$	−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	$-0.846950\pi$
$947$	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
$951$	−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	−0.685249	−	0.728309i	$-0.740307\pi$
$953$	8.89415	−	15.4051i	0.288110	−	0.499021i	0.973359	+	0.229288i	$0.0736399\pi$
$954$	−0.760824	+	2.48878i	−0.0246326	+	0.0805772i
$955$	−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	$-0.0206489\pi$
$967$	29.0154	+	29.0154i	0.933072	+	0.933072i	−0.0648250	+	0.997897i	$0.520649\pi$
$968$	−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	0.152093	−	0.988366i	$-0.451399\pi$
$971$	−19.5631	−	11.2948i	−0.627810	−	0.362466i	−0.779904	+	0.625900i	$0.784732\pi$
$972$	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	$-0.430243\pi$
$977$	−2.57462	−	0.689868i	−0.0823694	−	0.0220708i	−0.299768	+	0.954012i	$0.596909\pi$
$978$	−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	0.964676	+	0.263440i	$0.0848571\pi$
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.263440	+	0.964676i	$0.415143\pi$
$984$	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	0.741467	−	0.670989i	$-0.234130\pi$
$991$	−6.62217	−	11.4699i	−0.210360	−	0.364354i	−0.951827	+	0.306635i	$0.900797\pi$
$992$	−8.85836	+	15.3431i	−0.281253	+	0.487145i
$993$	27.0183	−	6.73680i	0.857400	−	0.213786i
$994$	−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	−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
$999$	−10.6780	−	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.89.13		96
3.2	odd	2	inner	507.2.k.k.89.12		96
13.2	odd	12		507.2.f.g.239.13	yes	48
13.3	even	3		507.2.f.g.437.11	yes	48
13.4	even	6	inner	507.2.k.k.488.14		96
13.5	odd	4	inner	507.2.k.k.80.13		96
13.6	odd	12	inner	507.2.k.k.188.12		96
13.7	odd	12	inner	507.2.k.k.188.14		96
13.8	odd	4	inner	507.2.k.k.80.11		96
13.9	even	3	inner	507.2.k.k.488.12		96
13.10	even	6		507.2.f.g.437.13	yes	48
13.11	odd	12		507.2.f.g.239.11	✓	48
13.12	even	2	inner	507.2.k.k.89.11		96
39.2	even	12		507.2.f.g.239.12	yes	48
39.5	even	4	inner	507.2.k.k.80.12		96
39.8	even	4	inner	507.2.k.k.80.14		96
39.11	even	12		507.2.f.g.239.14	yes	48
39.17	odd	6	inner	507.2.k.k.488.11		96
39.20	even	12	inner	507.2.k.k.188.11		96
39.23	odd	6		507.2.f.g.437.12	yes	48
39.29	odd	6		507.2.f.g.437.14	yes	48
39.32	even	12	inner	507.2.k.k.188.13		96
39.35	odd	6	inner	507.2.k.k.488.13		96
39.38	odd	2	inner	507.2.k.k.89.14		96

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more