LMFDB - Embedded newform 507.2.k.k.80.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			80.14
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

Coefficient data

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

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

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

$2$	0.0912193	−	0.340435i	0.0645018	−	0.240724i	−0.926147	−	0.377164i	$-0.876899\pi$
$2$	0.0912193	−	0.340435i	0.0645018	−	0.240724i	0.990648	+	0.136440i	$0.0435660\pi$
$3$	0.839735	−	1.51487i	0.484821	−	0.874613i
$3$	0.839735	−	1.51487i	0.484821	−	0.874613i
$4$	1.62448	+	0.937892i	0.812238	+	0.468946i
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.994541	+	0.104350i	$0.0332761\pi$
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.104350	+	0.994541i	$0.466724\pi$
$6$	−0.439116	−	0.424061i	−0.179269	−	0.173122i
$7$	−1.12240	+	0.300747i	−0.424228	+	0.113672i	−0.464615	−	0.885513i	$-0.653807\pi$
$7$	−1.12240	+	0.300747i	−0.424228	+	0.113672i	0.0403875	+	0.999184i	$0.487141\pi$
$8$	0.965906	−	0.965906i	0.341499	−	0.341499i
$9$	−1.58969	−	2.54419i	−0.529897	−	0.848062i
$10$	1.06066	−	0.612371i	0.335410	−	0.193649i
$11$	−1.81140	−	0.485362i	−0.546156	−	0.146342i	−0.0248176	−	0.999692i	$-0.507900\pi$
$11$	−1.81140	−	0.485362i	−0.546156	−	0.146342i	−0.521339	+	0.853350i	$0.674567\pi$
$12$	2.78492	−	1.67330i	0.803936	−	0.483039i
$13$		0			0
$13$		0			0
$14$			0.409539i			0.109454i
$15$	5.78573	−	1.65895i	1.49387	−	0.428339i
$16$	1.63506	+	2.83201i	0.408766	+	0.708003i
$17$	2.95083	−	5.11099i	0.715682	−	1.23960i	−0.247014	−	0.969012i	$-0.579449\pi$
$17$	2.95083	−	5.11099i	0.715682	−	1.23960i	0.962696	−	0.270586i	$-0.0872174\pi$
$18$	−1.01114	+	0.309108i	−0.238328	+	0.0728573i
$19$	1.27519	+	4.75906i	0.292548	+	1.09180i	0.943145	+	0.332381i	$0.107852\pi$
$19$	1.27519	+	4.75906i	0.292548	+	1.09180i	−0.650598	+	0.759423i	$0.725482\pi$
$20$	1.68707	+	6.29623i	0.377240	+	1.40788i
$21$	−0.486926	+	1.95284i	−0.106256	+	0.426146i
$22$	−0.330468	+	0.572388i	−0.0704561	+	0.122034i
$23$	−1.35482	−	2.34662i	−0.282500	−	0.489305i	0.689500	−	0.724286i	$-0.257831\pi$
$23$	−1.35482	−	2.34662i	−0.282500	−	0.489305i	−0.972000	+	0.234981i	$0.924497\pi$
$24$	−0.652122	−	2.27433i	−0.133114	−	0.464246i
$25$			7.07560i			1.41512i
$26$		0			0
$27$	−5.18904	+	0.271740i	−0.998632	+	0.0522964i
$28$	−2.10538	−	0.564135i	−0.397880	−	0.106612i
$29$	−2.32707	+	1.34353i	−0.432125	+	0.249488i	−0.700252	−	0.713896i	$-0.746929\pi$
$29$	−2.32707	+	1.34353i	−0.432125	+	0.249488i	0.268126	+	0.963384i	$0.413596\pi$
$30$	−0.0369941	−	2.12099i	−0.00675416	−	0.387239i
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	−0.934690	−	0.355463i	$-0.884323\pi$
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	0.355463	+	0.934690i	$0.384323\pi$
$32$	3.75217	−	1.00539i	0.663296	−	0.177730i
$33$	−2.25635	+	2.33646i	−0.392781	+	0.406726i
$34$	−1.47079	−	1.47079i	−0.252238	−	0.252238i
$35$	−3.49695	−	2.01896i	−0.591092	−	0.341267i
$36$	−0.196243	−	5.62393i	−0.0327072	−	0.937321i
$37$	0.559232	−	2.08708i	0.0919372	−	0.343114i	−0.904600	−	0.426261i	$-0.859830\pi$
$37$	0.559232	−	2.08708i	0.0919372	−	0.343114i	0.996537	+	0.0831470i	$0.0264971\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	1.76159	−	6.57436i	0.275115	−	1.02674i	−0.680650	−	0.732609i	$-0.738302\pi$
$41$	1.76159	−	6.57436i	0.275115	−	1.02674i	0.955764	−	0.294133i	$-0.0950309\pi$
$42$	0.620400	+	0.343904i	0.0957298	+	0.0530655i
$43$	4.80750	+	2.77561i	0.733136	+	0.423276i	0.819568	−	0.572981i	$-0.194213\pi$
$43$	4.80750	+	2.77561i	0.733136	+	0.423276i	−0.0864321	+	0.996258i	$0.527547\pi$
$44$	−2.48735	−	2.48735i	−0.374982	−	0.374982i
$45$	2.34538	−	10.1577i	0.349629	−	1.51423i
$46$	−0.922459	+	0.247172i	−0.136009	+	0.0364436i
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	−0.850895	−	0.525336i	$-0.823940\pi$
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	0.525336	+	0.850895i	$0.323940\pi$
$48$	5.66317	−	0.0987761i	0.817408	−	0.0142571i
$49$	−4.89284	+	2.82488i	−0.698977	+	0.403555i
$50$	2.40878	+	0.645431i	0.340653	+	0.0912777i
$51$	−5.26460	−	8.76202i	−0.737191	−	1.22693i
$52$		0			0
$53$		−	2.46136i		−	0.338093i	−0.985608	−	0.169047i	$-0.945931\pi$
$53$		−	2.46136i		−	0.338093i	0.985608	−	0.169047i	$-0.0540689\pi$
$54$	−0.380831	+	1.79132i	−0.0518245	+	0.243768i
$55$	−3.25832	−	5.64358i	−0.439352	−	0.760980i
$56$	−0.793642	+	1.37463i	−0.106055	+	0.183692i
$57$	8.28020	+	2.06460i	1.09674	+	0.273463i
$58$	0.245112	+	0.914771i	0.0321848	+	0.120115i
$59$	−2.59020	−	9.66677i	−0.337216	−	1.25851i	−0.901447	−	0.432890i	$-0.857494\pi$
$59$	−2.59020	−	9.66677i	−0.337216	−	1.25851i	0.564231	−	0.825617i	$-0.309173\pi$
$60$	10.9547	+	2.73147i	1.41424	+	0.352631i
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	−0.768120	−	0.640306i	$-0.778808\pi$
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	0.938581	+	0.345058i	$0.112141\pi$
$62$	0.803720	+	1.39208i	0.102073	+	0.176795i
$63$	2.54943	+	2.37750i	0.321198	+	0.299537i
$64$			5.17117i			0.646397i
$65$		0			0
$66$	0.589590	+	0.981273i	0.0725736	+	0.120786i
$67$	−6.57167	−	1.76087i	−0.802857	−	0.215125i	−0.166019	−	0.986123i	$-0.553091\pi$
$67$	−6.57167	−	1.76087i	−0.802857	−	0.215125i	−0.636838	+	0.770998i	$0.719758\pi$
$68$	9.58711	−	5.53512i	1.16261	−	0.671232i
$69$	−4.69254	+	0.0818465i	−0.564915	+	0.00985317i
$70$	−1.00632	+	1.00632i	−0.120278	+	0.120278i
$71$	−11.2116	+	3.00415i	−1.33058	+	0.356527i	−0.852930	−	0.522025i	$-0.825177\pi$
$71$	−11.2116	+	3.00415i	−1.33058	+	0.356527i	−0.477647	+	0.878552i	$0.658510\pi$
$72$	−3.99294	−	0.921953i	−0.470572	−	0.108653i
$73$	−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
$75$	10.7186	+	5.94163i	1.23768	+	0.686080i
$76$	−2.39197	+	8.92696i	−0.274378	+	1.02399i
$77$	2.17908			0.248330
$78$		0			0
$79$	1.10008			0.123769			0.0618844	−	0.998083i	$-0.480289\pi$
$79$	1.10008			0.123769			0.0618844	+	0.998083i	$0.480289\pi$
$80$	−2.94114	+	10.9765i	−0.328829	+	1.22721i
$81$	−3.94577	+	8.08894i	−0.438419	+	0.898771i
$82$	−2.07745	−	1.19942i	−0.229416	−	0.132453i
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	0.408864	−	0.912596i	$-0.365925\pi$
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	−0.912596	+	0.408864i	$0.865925\pi$
$84$	−2.62256	+	2.71567i	−0.286144	+	0.296303i
$85$	19.8095	−	5.30793i	2.14864	−	0.575726i
$86$	1.38345	−	1.38345i	0.149181	−	0.149181i
$87$	0.0811644	+	4.65342i	0.00870173	+	0.498899i
$88$	−2.21845	+	1.28082i	−0.236488	+	0.136536i
$89$	−4.12834	−	1.10619i	−0.437604	−	0.117256i	0.0332896	−	0.999446i	$-0.489402\pi$
$89$	−4.12834	−	1.10619i	−0.437604	−	0.117256i	−0.470893	+	0.882190i	$0.656068\pi$
$90$	−3.24410	−	1.72503i	−0.341959	−	0.181834i
$91$		0			0
$92$		−	5.08271i		−	0.529909i
$93$	2.17732	+	7.59361i	0.225778	+	0.787421i
$94$	0.556230	+	0.963419i	0.0573708	+	0.0993691i
$95$	−8.56055	+	14.8273i	−0.878294	+	1.52125i
$96$	1.62779	−	6.52833i	0.166135	−	0.666295i
$97$	3.17506	+	11.8495i	0.322379	+	1.20313i	0.916921	+	0.399070i	$0.130667\pi$
$97$	3.17506	+	11.8495i	0.322379	+	1.20313i	−0.594542	+	0.804065i	$0.702667\pi$
$98$	0.515368	+	1.92338i	0.0520600	+	0.194291i
$99$	1.64471	+	5.38010i	0.165299	+	0.540721i
$100$	−6.63614	+	11.4941i	−0.663614	+	1.14941i
$101$	5.54779	+	9.60905i	0.552026	+	0.956137i	0.998128	+	0.0611547i	$0.0194783\pi$
$101$	5.54779	+	9.60905i	0.552026	+	0.956137i	−0.446103	+	0.894982i	$0.647188\pi$
$102$	−3.46313	+	0.992988i	−0.342901	+	0.0983204i
$103$		−	4.43285i		−	0.436782i	−0.975861	−	0.218391i	$-0.929919\pi$
$103$		−	4.43285i		−	0.436782i	0.975861	−	0.218391i	$-0.0700808\pi$
$104$		0			0
$105$	−5.99499	+	3.60205i	−0.585051	+	0.351524i
$106$	−0.837932	−	0.224523i	−0.0813872	−	0.0218076i
$107$	−11.3063	+	6.52769i	−1.09302	+	0.631055i	−0.934379	−	0.356281i	$-0.884045\pi$
$107$	−11.3063	+	6.52769i	−1.09302	+	0.631055i	−0.158641	+	0.987336i	$0.550711\pi$
$108$	−8.68434	−	4.42532i	−0.835651	−	0.425827i
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	−0.458694	−	0.888594i	$-0.651682\pi$
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	0.888594	+	0.458694i	$0.151682\pi$
$110$	−2.21849	+	0.594443i	−0.211525	+	0.0566780i
$111$	−2.69206	−	2.59976i	−0.255519	−	0.246759i
$112$	−2.68692	−	2.68692i	−0.253890	−	0.253890i
$113$	11.2693	+	6.50632i	1.06012	+	0.612063i	0.925467	−	0.378829i	$-0.123673\pi$
$113$	11.2693	+	6.50632i	1.06012	+	0.612063i	0.134657	+	0.990892i	$0.457007\pi$
$114$	1.45818	−	2.63054i	0.136571	−	0.246372i
$115$	2.43705	−	9.09518i	0.227256	−	0.848130i
$116$	−5.04035			−0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	−1.77491	+	6.62404i	−0.162705	+	0.607225i
$120$	3.98608	−	7.19086i	0.363878	−	0.656433i
$121$	−6.48070	−	3.74164i	−0.589155	−	0.340149i
$122$	−0.663584	−	0.663584i	−0.0600781	−	0.0600781i
$123$	−8.48005	−	8.18931i	−0.764621	−	0.738405i
$124$	−8.26363	+	2.21423i	−0.742096	+	0.198844i
$125$	−5.10014	+	5.10014i	−0.456171	+	0.456171i
$126$	1.04194	−	0.651040i	0.0928236	−	0.0579992i
$127$	−6.74982	+	3.89701i	−0.598950	+	0.345804i	−0.768628	−	0.639696i	$-0.779060\pi$
$127$	−6.74982	+	3.89701i	−0.598950	+	0.345804i	0.169679	+	0.985499i	$0.445727\pi$
$128$	9.26479	+	2.48249i	0.818900	+	0.219423i
$129$	8.24172	−	4.95198i	0.725643	−	0.435997i
$130$		0			0
$131$			18.5420i			1.62003i	0.586412	+	0.810013i	$0.300540\pi$
$131$			18.5420i			1.62003i	−0.586412	+	0.810013i	$0.699460\pi$
$132$	−5.85674	+	1.67931i	−0.509764	+	0.146165i
$133$	−2.86254	−	4.95807i	−0.248214	−	0.429919i
$134$	−1.19893	+	2.07660i	−0.103571	+	0.179391i
$135$	−13.4182	−	12.0828i	−1.15485	−	1.03992i
$136$	−2.08651	−	7.78697i	−0.178917	−	0.667727i
$137$	−1.95016	−	7.27811i	−0.166614	−	0.621811i	−0.997829	−	0.0658600i	$-0.979021\pi$
$137$	−1.95016	−	7.27811i	−0.166614	−	0.621811i	0.831215	−	0.555951i	$-0.187646\pi$
$138$	−0.400186	+	1.60497i	−0.0340661	+	0.136624i
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	−0.728733	−	0.684798i	$-0.759891\pi$
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	0.957419	+	0.288703i	$0.0932239\pi$
$140$	−3.78714	−	6.55952i	−0.320072	−	0.554381i
$141$	1.50686	+	5.25531i	0.126900	+	0.442577i
$142$			4.09087i			0.343298i
$143$		0			0
$144$	4.60592	−	8.66193i	0.383827	−	0.721828i
$145$	−9.01937	−	2.41673i	−0.749018	−	0.200699i
$146$	−3.94214	+	2.27600i	−0.326254	+	0.188363i
$147$	0.170655	+	9.78419i	0.0140753	+	0.806987i
$148$	2.86592	−	2.86592i	0.235577	−	0.235577i
$149$	22.0357	−	5.90444i	1.80523	−	0.483710i	0.810457	−	0.585798i	$-0.199219\pi$
$149$	22.0357	−	5.90444i	1.80523	−	0.483710i	0.994775	+	0.102088i	$0.0325523\pi$
$150$	3.00049	−	3.10701i	0.244989	−	0.253686i
$151$	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
$153$	−17.6942	+	0.617428i	−1.43049	+	0.0499161i
$154$	0.198774	−	0.741836i	0.0160177	−	0.0597789i
$155$	−15.8489			−1.27301
$156$		0			0
$157$	15.6785			1.25128			0.625640	−	0.780112i	$-0.284838\pi$
$157$	15.6785			1.25128			0.625640	+	0.780112i	$0.284838\pi$
$158$	0.100349	−	0.374506i	0.00798331	−	0.0297941i
$159$	−3.72865	−	2.06689i	−0.295701	−	0.163915i
$160$	11.6902	+	6.74937i	0.924195	+	0.533584i
$161$	2.22640	+	2.22640i	0.175465	+	0.175465i
$162$	2.39383	+	2.08114i	0.188077	+	0.163510i
$163$	−3.33861	+	0.894579i	−0.261500	+	0.0700688i	−0.387187	−	0.922001i	$-0.626553\pi$
$163$	−3.33861	+	0.894579i	−0.261500	+	0.0700688i	0.125687	+	0.992070i	$0.459887\pi$
$164$	9.02770	−	9.02770i	0.704945	−	0.704945i
$165$	−11.2854	+	0.196839i	−0.878570	+	0.0153239i
$166$	−1.98096	+	1.14371i	−0.153752	+	0.0887687i
$167$	5.06462	+	1.35706i	0.391912	+	0.105012i	0.449393	−	0.893334i	$-0.351640\pi$
$167$	5.06462	+	1.35706i	0.391912	+	0.105012i	−0.0574813	+	0.998347i	$0.518307\pi$
$168$	1.41594	+	2.35659i	0.109242	+	0.181815i
$169$		0			0
$170$		−	7.22802i		−	0.554364i
$171$	10.0808	−	10.8097i	0.770897	−	0.826642i
$172$	5.20644	+	9.01782i	0.396987	+	0.687602i
$173$	7.12562	−	12.3419i	0.541751	−	0.938339i	−0.457053	−	0.889439i	$-0.651095\pi$
$173$	7.12562	−	12.3419i	0.541751	−	0.938339i	0.998804	−	0.0489001i	$-0.0155716\pi$
$174$	1.59159	+	0.396851i	0.120658	+	0.0300852i
$175$	−2.12796	−	7.94166i	−0.160859	−	0.600333i
$176$	−1.58720	−	5.92349i	−0.119639	−	0.446500i
$177$	−16.8190	−	4.19369i	−1.26420	−	0.315217i
$178$	−0.753169	+	1.30453i	−0.0564524	+	0.0977785i
$179$	−2.18334	−	3.78165i	−0.163190	−	0.282654i	0.772821	−	0.634624i	$-0.218845\pi$
$179$	−2.18334	−	3.78165i	−0.163190	−	0.282654i	−0.936011	+	0.351970i	$0.885512\pi$
$180$	13.3369	−	14.3013i	0.994071	−	1.06595i
$181$			2.10738i			0.156640i	0.996928	+	0.0783201i	$0.0249556\pi$
$181$			2.10738i			0.156640i	−0.996928	+	0.0783201i	$0.975044\pi$
$182$		0			0
$183$	−2.37526	−	3.95321i	−0.175584	−	0.292230i
$184$	−3.57525	−	0.957986i	−0.263571	−	0.0706237i
$185$	6.50251	−	3.75422i	0.478074	−	0.276016i
$186$	2.78375	−	0.0485537i	0.204114	−	0.00356013i
$187$	−7.82581	+	7.82581i	−0.572280	+	0.572280i
$188$	−5.71901	+	1.53240i	−0.417101	+	0.111762i
$189$	5.74246	−	1.86559i	0.417703	−	0.135702i
$190$	4.26685	+	4.26685i	0.309550	+	0.309550i
$191$	−5.88706	−	3.39890i	−0.425973	−	0.245935i	0.271657	−	0.962394i	$-0.412428\pi$
$191$	−5.88706	−	3.39890i	−0.425973	−	0.245935i	−0.697629	+	0.716459i	$0.745762\pi$
$192$	7.83368	+	4.34242i	0.565347	+	0.313387i
$193$	−2.87709	+	10.7374i	−0.207098	+	0.772898i	0.781702	+	0.623652i	$0.214352\pi$
$193$	−2.87709	+	10.7374i	−0.207098	+	0.772898i	−0.988800	+	0.149247i	$0.952315\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	0.591102	−	2.20602i	0.0421143	−	0.157173i	−0.941667	−	0.336547i	$-0.890741\pi$
$197$	0.591102	−	2.20602i	0.0421143	−	0.157173i	0.983781	+	0.179375i	$0.0574074\pi$
$198$	1.98160	−	0.0691468i	0.140826	−	0.00491405i
$199$	−15.8856	−	9.17157i	−1.12610	−	0.650155i	−0.183150	−	0.983085i	$-0.558629\pi$
$199$	−15.8856	−	9.17157i	−1.12610	−	0.650155i	−0.942952	+	0.332930i	$0.891963\pi$
$200$	6.83436	+	6.83436i	0.483262	+	0.483262i
$201$	−8.18597	+	8.47659i	−0.577393	+	0.597893i
$202$	3.77732	−	1.01213i	0.265772	−	0.0712133i
$203$	2.20784	−	2.20784i	0.154960	−	0.154960i
$204$	−0.334383	−	19.1713i	−0.0234115	−	1.34226i
$205$	20.4830	−	11.8259i	1.43060	−	0.825956i
$206$	−1.50910	−	0.404361i	−0.105144	−	0.0281732i
$207$	−3.81650	+	7.17733i	−0.265265	+	0.498859i
$208$		0			0
$209$		−	9.23947i		−	0.639107i
$210$	0.679404	+	2.36948i	0.0468833	+	0.163510i
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	0.970291	−	0.241939i	$-0.0777834\pi$
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	−0.694671	+	0.719327i	$0.744450\pi$
$212$	2.30849	−	3.99842i	0.158548	−	0.274612i
$213$	−4.86389	+	19.5069i	−0.333269	+	1.33659i
$214$	1.19090	+	4.44451i	0.0814084	+	0.303820i
$215$	4.99274	+	18.6332i	0.340502	+	1.27077i
$216$	−4.74965	+	5.27460i	−0.323173	+	0.358891i
$217$	2.64984	−	4.58965i	0.179883	−	0.311566i
$218$	−1.11855	−	1.93739i	−0.0757580	−	0.131217i
$219$	−21.5038	+	6.16580i	−1.45309	+	0.416646i
$220$		−	12.2238i		−	0.824129i
$221$		0			0
$222$	−1.13062	+	0.679324i	−0.0758821	+	0.0455932i
$223$	27.3497	+	7.32834i	1.83147	+	0.490742i	0.998080	−	0.0619383i	$-0.0197282\pi$
$223$	27.3497	+	7.32834i	1.83147	+	0.490742i	0.833393	+	0.552680i	$0.186395\pi$
$224$	−3.90907	+	2.25691i	−0.261186	+	0.150796i
$225$	18.0016	−	11.2480i	1.20011	−	0.749867i
$226$	3.24295	−	3.24295i	0.215718	−	0.215718i
$227$	−7.10455	+	1.90366i	−0.471546	+	0.126350i	−0.486763	−	0.873534i	$-0.661823\pi$
$227$	−7.10455	+	1.90366i	−0.471546	+	0.126350i	0.0152176	+	0.999884i	$0.495156\pi$
$228$	11.5146	+	11.1198i	0.762574	+	0.736428i
$229$	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
$231$	1.82985	−	3.30104i	0.120395	−	0.217192i
$232$	−0.950001	+	3.54545i	−0.0623706	+	0.232770i
$233$	18.1554			1.18940			0.594700	−	0.803947i	$-0.297271\pi$
$233$	18.1554			1.18940			0.594700	+	0.803947i	$0.297271\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	4.85866	−	18.1328i	0.316272	−	1.18034i
$237$	0.923776	−	1.66648i	0.0600057	−	0.108250i
$238$	2.09315	+	1.20848i	0.135679	+	0.0783341i
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	0.886306	−	0.463099i	$-0.153263\pi$
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	−0.463099	+	0.886306i	$0.653263\pi$
$240$	14.1582	+	13.6728i	0.913908	+	0.882574i
$241$	−26.7340	+	7.16336i	−1.72209	+	0.461433i	−0.978337	−	0.207021i	$-0.933623\pi$
$241$	−26.7340	+	7.16336i	−1.72209	+	0.461433i	−0.743754	+	0.668453i	$0.766957\pi$
$242$	−1.86495	+	1.86495i	−0.119883	+	0.119883i
$243$	8.94033	+	12.7699i	0.573522	+	0.819190i
$244$	4.32547	−	2.49731i	0.276910	−	0.159874i
$245$	−18.9639	−	5.08137i	−1.21156	−	0.324637i
$246$	−3.56147	+	2.13988i	−0.227071	+	0.136434i
$247$		0			0
$248$			6.23009i			0.395611i
$249$	−10.8058	+	3.09836i	−0.684791	+	0.196351i
$250$	1.27104	+	2.20150i	0.0803874	+	0.139235i
$251$	2.80003	−	4.84979i	0.176736	−	0.306116i	−0.764025	−	0.645187i	$-0.776779\pi$
$251$	2.80003	−	4.84979i	0.176736	−	0.306116i	0.940761	+	0.339071i	$0.110113\pi$
$252$	1.91164	+	6.25328i	0.120422	+	0.393920i
$253$	1.31516	+	4.90825i	0.0826834	+	0.308579i
$254$	0.710965	+	2.65336i	0.0446099	+	0.166486i
$255$	8.59385	−	34.4661i	0.538168	−	2.15835i
$256$	−3.48092	+	6.02913i	−0.217557	+	0.376821i
$257$	3.40679	+	5.90073i	0.212510	+	0.368077i	0.952499	−	0.304541i	$-0.0985030\pi$
$257$	3.40679	+	5.90073i	0.212510	+	0.368077i	−0.739990	+	0.672618i	$0.765170\pi$
$258$	−0.934023	−	3.25749i	−0.0581497	−	0.202802i
$259$			2.51073i			0.156009i
$260$		0			0
$261$	7.11751	+	3.78469i	0.440563	+	0.234266i
$262$	6.31236	+	1.69139i	0.389979	+	0.104495i
$263$	19.5996	−	11.3159i	1.20857	−	0.697765i	0.246119	−	0.969240i	$-0.420844\pi$
$263$	19.5996	−	11.3159i	1.20857	−	0.697765i	0.962446	+	0.271474i	$0.0875111\pi$
$264$	0.0773761	+	4.43623i	0.00476217	+	0.273031i
$265$	6.04803	−	6.04803i	0.371528	−	0.371528i
$266$	−1.94902	+	0.522238i	−0.119502	+	0.0320205i
$267$	−5.14245	+	5.32502i	−0.314713	+	0.325886i
$268$	−9.02401	−	9.02401i	−0.551229	−	0.551229i
$269$	−22.6058	−	13.0515i	−1.37830	−	0.795762i	−0.386345	−	0.922354i	$-0.626262\pi$
$269$	−22.6058	−	13.0515i	−1.37830	−	0.795762i	−0.991955	+	0.126593i	$0.959596\pi$
$270$	−5.33739	+	3.46584i	−0.324823	+	0.210925i
$271$	4.57652	−	17.0798i	0.278004	−	1.03753i	−0.675797	−	0.737087i	$-0.736201\pi$
$271$	4.57652	−	17.0798i	0.278004	−	1.03753i	0.953801	−	0.300438i	$-0.0971328\pi$
$272$	19.2992			1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	3.43423	−	12.8167i	0.207092	−	0.772876i
$276$	−7.69967	−	4.26813i	−0.463466	−	0.256911i
$277$	19.6593	+	11.3503i	1.18122	+	0.681975i	0.956295	−	0.292402i	$-0.0944546\pi$
$277$	19.6593	+	11.3503i	1.18122	+	0.681975i	0.224920	+	0.974377i	$0.427788\pi$
$278$	−1.34385	−	1.34385i	−0.0805989	−	0.0805989i
$279$	13.3317	+	3.07825i	0.798151	+	0.184290i
$280$	−5.32786	+	1.42759i	−0.318400	+	0.0853151i
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	−0.914679	−	0.404181i	$-0.867557\pi$
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	0.404181	+	0.914679i	$0.367557\pi$
$282$	1.92655	−	0.0336025i	0.114724	−	0.00200100i
$283$	6.15361	−	3.55279i	0.365794	−	0.211192i	−0.305825	−	0.952088i	$-0.598932\pi$
$283$	6.15361	−	3.55279i	0.365794	−	0.211192i	0.671620	+	0.740896i	$0.265599\pi$
$284$	−21.0306	−	5.63513i	−1.24794	−	0.334384i
$285$	15.2729	+	25.4192i	0.904690	+	1.50570i
$286$		0			0
$287$			7.90886i			0.466845i
$288$	−8.52269	−	7.94796i	−0.502205	−	0.468338i
$289$	−8.91483	−	15.4409i	−0.524402	−	0.908291i
$290$	−1.64548	+	2.85006i	−0.0966260	+	0.167361i
$291$	20.6167	+	5.14061i	1.20857	+	0.301348i
$292$	−6.27032	−	23.4012i	−0.366943	−	1.36945i
$293$	4.11392	+	15.3534i	0.240338	+	0.896953i	0.975670	+	0.219245i	$0.0703596\pi$
$293$	4.11392	+	15.3534i	0.240338	+	0.896953i	−0.735332	+	0.677707i	$0.762974\pi$
$294$	3.34645	+	0.834411i	0.195169	+	0.0486638i
$295$	17.3885	−	30.1178i	1.01240	−	1.75352i
$296$	−1.47576	−	2.55609i	−0.0857768	−	0.148570i
$297$	9.53130	+	2.02633i	0.553062	+	0.117580i
$298$		−	8.04031i		−	0.465763i
$299$		0			0
$300$	11.8396	+	19.7050i	0.683558	+	1.13767i
$301$	−6.23070	−	1.66951i	−0.359131	−	0.0962289i
$302$	2.85701	−	1.64949i	0.164402	−	0.0949176i
$303$	19.2152	−	0.335149i	1.10388	−	0.0192538i
$304$	−11.3927	+	11.3927i	−0.653417	+	0.653417i
$305$	8.93755	−	2.39481i	0.511763	−	0.137126i
$306$	−1.40386	+	6.08006i	−0.0802534	+	0.347574i
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	0.986247	−	0.165277i	$-0.0528518\pi$
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	−0.165277	+	0.986247i	$0.552852\pi$
$308$	3.53987	+	2.04374i	0.201703	+	0.116453i
$309$	−6.71521	−	3.72242i	−0.382015	−	0.211761i
$310$	−1.44572	+	5.39552i	−0.0821116	+	0.306445i
$311$	−7.62181			−0.432193			−0.216097	−	0.976372i	$-0.569333\pi$
$311$	−7.62181			−0.432193			−0.216097	+	0.976372i	$0.569333\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	1.43018	−	5.33751i	0.0807099	−	0.301213i
$315$	0.422445	+	12.1064i	0.0238021	+	0.682120i
$316$	1.78705	+	1.03176i	0.100530	+	0.0580408i
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	0.507901	−	0.861416i	$-0.330422\pi$
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	−0.861416	+	0.507901i	$0.830422\pi$
$318$	−1.04377	+	1.08082i	−0.0585315	+	0.0606095i
$319$	4.86734	−	1.30420i	0.272518	−	0.0730211i
$320$	−12.7066	+	12.7066i	−0.710319	+	0.710319i
$321$	0.394345	+	22.6091i	0.0220102	+	1.26192i
$322$	0.961034	−	0.554853i	0.0535563	−	0.0309207i
$323$	28.0864	+	7.52572i	1.56277	+	0.418743i
$324$	−13.9963	+	9.43958i	−0.777575	+	0.524421i
$325$		0			0
$326$			1.21818i			0.0674689i
$327$	−3.03023	−	10.5682i	−0.167572	−	0.584422i
$328$	−4.64868	−	8.05175i	−0.256680	−	0.444583i
$329$	1.83387	−	3.17636i	0.101105	−	0.175118i
$330$	−0.962439	+	3.85991i	−0.0529805	+	0.212481i
$331$	−4.16094	−	15.5288i	−0.228706	−	0.853541i	−0.980886	−	0.194584i	$-0.937664\pi$
$331$	−4.16094	−	15.5288i	−0.228706	−	0.853541i	0.752180	−	0.658958i	$-0.229002\pi$
$332$	−3.15088	−	11.7593i	−0.172927	−	0.645373i
$333$	−6.19893	+	1.89502i	−0.339699	+	0.103847i
$334$	0.923981	−	1.60038i	0.0505580	−	0.0875690i
$335$	−11.8211	−	20.4747i	−0.645853	−	1.11865i
$336$	−6.32664	+	1.81404i	−0.345146	+	0.0989642i
$337$		−	28.3556i		−	1.54463i	−0.635243	−	0.772313i	$-0.719100\pi$
$337$		−	28.3556i		−	1.54463i	0.635243	−	0.772313i	$-0.280900\pi$
$338$		0			0
$339$	19.3195	−	11.6080i	1.04929	−	0.630457i
$340$	37.1583	+	9.95653i	2.01519	+	0.539968i
$341$	7.40704	−	4.27646i	0.401114	−	0.231583i
$342$	−2.76045	−	4.41791i	−0.149268	−	0.238893i
$343$	10.3937	−	10.3937i	0.561209	−	0.561209i
$344$	7.32457	−	1.96261i	0.394914	−	0.105817i
$345$	−11.7316	−	11.3294i	−0.631607	−	0.609952i
$346$	−3.55163	−	3.55163i	−0.190937	−	0.190937i
$347$	−9.59025	−	5.53693i	−0.514831	−	0.297238i	0.219986	−	0.975503i	$-0.429399\pi$
$347$	−9.59025	−	5.53693i	−0.514831	−	0.297238i	−0.734817	+	0.678265i	$0.762732\pi$
$348$	−4.23256	+	7.63550i	−0.226889	+	0.409306i
$349$	7.74319	−	28.8980i	0.414483	−	1.54687i	−0.371385	−	0.928479i	$-0.621117\pi$
$349$	7.74319	−	28.8980i	0.414483	−	1.54687i	0.785868	−	0.618394i	$-0.212216\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	−3.28082	+	12.2442i	−0.174620	+	0.651692i	0.821996	+	0.569494i	$0.192861\pi$
$353$	−3.28082	+	12.2442i	−0.174620	+	0.651692i	−0.996616	+	0.0821982i	$0.973806\pi$
$354$	−2.96190	+	5.34324i	−0.157423	+	0.283990i
$355$	−34.9309	−	20.1674i	−1.85394	−	1.07037i
$356$	−5.66891	−	5.66891i	−0.300452	−	0.300452i
$357$	8.54414	+	8.25120i	0.452204	+	0.436700i
$358$	−1.48657	+	0.398325i	−0.0785676	+	0.0210521i
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.0790589	−	0.996870i	$-0.474808\pi$
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.996870	−	0.0790589i	$-0.0251915\pi$
$360$	−7.54600	−	12.0768i	−0.397709	−	0.636505i
$361$	−4.56807	+	2.63738i	−0.240425	+	0.138809i
$362$	0.717426	+	0.192234i	0.0377071	+	0.0101036i
$363$	−11.1102	+	6.67547i	−0.583133	+	0.350371i
$364$		0			0
$365$		−	44.8813i		−	2.34919i
$366$	−1.56248	+	0.448012i	−0.0816722	+	0.0234180i
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	0.992221	+	0.124490i	$0.0397295\pi$
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	−0.388299	+	0.921533i	$0.626937\pi$
$368$	4.43045	−	7.67376i	0.230953	−	0.400023i
$369$	−19.5268	+	5.96937i	−1.01652	+	0.310753i
$370$	−0.684915	−	2.55614i	−0.0356071	−	0.132887i
$371$	0.740245	+	2.76263i	0.0384316	+	0.143429i
$372$	−3.58497	+	14.3777i	−0.185872	+	0.745451i
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	0.469128	+	0.883130i	$0.344568\pi$
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	−0.999377	+	0.0352886i	$0.988765\pi$
$374$	1.95031	+	3.37804i	0.100848	+	0.174674i
$375$	3.44331	+	12.0088i	0.177812	+	0.620134i
$376$			4.31166i			0.222357i
$377$		0			0
$378$	−0.111288	−	2.12511i	−0.00572404	−	0.109304i
$379$	−3.83602	−	1.02786i	−0.197043	−	0.0527975i	0.158948	−	0.987287i	$-0.449190\pi$
$379$	−3.83602	−	1.02786i	−0.197043	−	0.0527975i	−0.355991	+	0.934489i	$0.615857\pi$
$380$	−27.8128	+	16.0577i	−1.42677	+	0.823744i
$381$	0.235423	+	13.4976i	0.0120611	+	0.691502i
$382$	−1.69412	+	1.69412i	−0.0866785	+	0.0866785i
$383$	−25.7044	+	6.88748i	−1.31344	+	0.351934i	−0.846515	−	0.532365i	$-0.821303\pi$
$383$	−25.7044	+	6.88748i	−1.31344	+	0.351934i	−0.466921	+	0.884299i	$0.654637\pi$
$384$	11.5406	−	11.9504i	0.588931	−	0.609839i
$385$	5.35443	+	5.35443i	0.272887	+	0.272887i
$386$	3.39296	+	1.95893i	0.172697	+	0.0997067i
$387$	−0.580765	−	16.6435i	−0.0295219	−	0.846038i
$388$	−5.95573	+	22.2271i	−0.302356	+	1.12841i
$389$	−6.17335			−0.313001			−0.156501	−	0.987678i	$-0.550021\pi$
$389$	−6.17335			−0.313001			−0.156501	+	0.987678i	$0.550021\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	−1.99745	+	7.45460i	−0.100887	+	0.376514i
$393$	28.0889	+	15.5704i	1.41690	+	0.785423i
$394$	−0.697088	−	0.402464i	−0.0351188	−	0.0202758i
$395$	2.70311	+	2.70311i	0.136008	+	0.136008i
$396$	−2.37417	+	10.2824i	−0.119306	+	0.516710i
$397$	23.0477	−	6.17560i	1.15673	−	0.309945i	0.371071	−	0.928605i	$-0.378991\pi$
$397$	23.0477	−	6.17560i	1.15673	−	0.309945i	0.785659	+	0.618660i	$0.212324\pi$
$398$	−4.57140	+	4.57140i	−0.229143	+	0.229143i
$399$	−9.91463	+	0.172930i	−0.496352	+	0.00865730i
$400$	−20.0382	+	11.5691i	−1.00191	+	0.578453i
$401$	22.4109	+	6.00499i	1.11915	+	0.299875i	0.770539	−	0.637393i	$-0.219987\pi$
$401$	22.4109	+	6.00499i	1.11915	+	0.299875i	0.348610	+	0.937268i	$0.386654\pi$
$402$	2.13901	+	3.56002i	0.106684	+	0.177558i
$403$		0			0
$404$			20.8129i			1.03548i
$405$	−29.5716	+	10.1806i	−1.46942	+	0.505877i
$406$	−0.550228	−	0.953023i	−0.0273074	−	0.0472978i
$407$	−2.02598	+	3.50910i	−0.100424	+	0.173940i
$408$	−13.5484	−	3.37818i	−0.670746	−	0.167245i
$409$	3.25292	+	12.1401i	0.160847	+	0.600288i	0.998534	+	0.0541371i	$0.0172408\pi$
$409$	3.25292	+	12.1401i	0.160847	+	0.600288i	−0.837687	+	0.546151i	$0.816093\pi$
$410$	−2.15750	−	8.05189i	−0.106551	−	0.397655i
$411$	−12.6630	−	3.15743i	−0.624622	−	0.155744i
$412$	4.15753	−	7.20106i	0.204827	−	0.354771i
$413$	5.81450	+	10.0710i	0.286113	+	0.495562i
$414$	2.09528	+	1.95398i	0.102977	+	0.0960329i
$415$		−	22.5532i		−	1.10709i
$416$		0			0
$417$	−4.81024	−	8.00582i	−0.235558	−	0.392047i
$418$	−3.14544	−	0.842818i	−0.153848	−	0.0412236i
$419$	−23.2172	+	13.4045i	−1.13424	+	0.654851i	−0.944997	−	0.327080i	$-0.893935\pi$
$419$	−23.2172	+	13.4045i	−1.13424	+	0.654851i	−0.189239	+	0.981931i	$0.560602\pi$
$420$	−13.1170	+	0.228786i	−0.640046	+	0.0111636i
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	−0.890471	−	0.455040i	$-0.849625\pi$
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	0.455040	+	0.890471i	$0.349625\pi$
$422$	2.72594	−	0.730414i	0.132697	−	0.0355560i
$423$	9.22649	+	2.13036i	0.448607	+	0.103582i
$424$	−2.37744	−	2.37744i	−0.115459	−	0.115459i
$425$	36.1633	+	20.8789i	1.75418	+	1.01278i
$426$	6.19716	+	3.43525i	0.300253	+	0.166438i
$427$	−0.800795	+	2.98861i	−0.0387532	+	0.144629i
$428$	−24.4891			−1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	−5.49370	+	20.5028i	−0.264622	+	0.987583i	0.697859	+	0.716235i	$0.254136\pi$
$431$	−5.49370	+	20.5028i	−0.264622	+	0.987583i	−0.962481	+	0.271348i	$0.912531\pi$
$432$	−9.25399	−	14.2511i	−0.445233	−	0.685658i
$433$	−1.60537	−	0.926859i	−0.0771490	−	0.0445420i	0.460929	−	0.887437i	$-0.347516\pi$
$433$	−1.60537	−	0.926859i	−0.0771490	−	0.0445420i	−0.538078	+	0.842895i	$0.680850\pi$
$434$	−1.32076	−	1.32076i	−0.0633986	−	0.0633986i
$435$	−11.2349	+	11.6338i	−0.538673	+	0.557798i
$436$	11.5007	−	3.08159i	0.550782	−	0.147582i
$437$	9.44007	−	9.44007i	0.451580	−	0.451580i
$438$	0.137496	+	7.88308i	0.00656979	+	0.376668i
$439$	12.4753	−	7.20264i	0.595415	−	0.343763i	−0.171820	−	0.985128i	$-0.554965\pi$
$439$	12.4753	−	7.20264i	0.595415	−	0.343763i	0.767236	+	0.641365i	$0.221632\pi$
$440$	−8.59840	−	2.30393i	−0.409913	−	0.109836i
$441$	14.9651	+	7.95761i	0.712625	+	0.378934i
$442$		0			0
$443$			22.2330i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$443$			22.2330i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$444$	−1.93489	−	6.74811i	−0.0918260	−	0.320251i
$445$	−7.42603	−	12.8623i	−0.352027	−	0.609729i
$446$	4.98965	−	8.64232i	0.236267	−	0.409226i
$447$	9.55963	−	38.3394i	0.452155	−	1.81339i
$448$	−1.55521	−	5.80413i	−0.0734769	−	0.274220i
$449$	−6.36268	−	23.7458i	−0.300273	−	1.12064i	−0.936938	−	0.349495i	$-0.886353\pi$
$449$	−6.36268	−	23.7458i	−0.300273	−	1.12064i	0.636665	−	0.771141i	$-0.280313\pi$
$450$	−2.18712	−	7.15442i	−0.103102	−	0.337263i
$451$	−6.38188	+	11.0537i	−0.300511	+	0.520501i
$452$	12.2044	+	21.1387i	0.574048	+	0.994281i
$453$	15.5845	−	4.46857i	0.732225	−	0.209952i
$454$			2.59229i			0.121662i
$455$		0			0
$456$	9.99211	−	6.00368i	0.467923	−	0.281148i
$457$	6.53825	+	1.75192i	0.305847	+	0.0819513i	0.408478	−	0.912768i	$-0.366060\pi$
$457$	6.53825	+	1.75192i	0.305847	+	0.0819513i	−0.102632	+	0.994719i	$0.532726\pi$
$458$	4.92490	−	2.84339i	0.230125	−	0.132863i
$459$	−13.9231	+	27.3230i	−0.649876	+	1.27533i
$460$	12.4892	−	12.4892i	0.582312	−	0.582312i
$461$	11.9685	−	3.20695i	0.557429	−	0.149363i	0.0309044	−	0.999522i	$-0.490161\pi$
$461$	11.9685	−	3.20695i	0.557429	−	0.149363i	0.526525	+	0.850160i	$0.323495\pi$
$462$	−0.956871	−	0.924064i	−0.0445177	−	0.0429914i
$463$	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
$465$	−13.3089	+	24.0091i	−0.617184	+	1.11339i
$466$	1.65612	−	6.18074i	0.0767185	−	0.286317i
$467$	−9.19934			−0.425695			−0.212847	−	0.977085i	$-0.568274\pi$
$467$	−9.19934			−0.425695			−0.212847	+	0.977085i	$0.568274\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	−1.00054	+	3.73407i	−0.0461515	+	0.172240i
$471$	13.1658	−	23.7510i	0.606647	−	1.09439i
$472$	−11.8391	−	6.83530i	−0.544938	−	0.314620i
$473$	−7.36110	−	7.36110i	−0.338464	−	0.338464i
$474$	−0.483064	−	0.466501i	−0.0221878	−	0.0214271i
$475$	−33.6732	+	9.02270i	−1.54503	+	0.413990i
$476$	−9.09592	+	9.09592i	−0.416911	+	0.416911i
$477$	−6.26215	+	3.91280i	−0.286724	+	0.179155i
$478$	2.82415	−	1.63052i	0.129174	−	0.0745784i
$479$	−22.1676	−	5.93980i	−1.01287	−	0.271396i	−0.286039	−	0.958218i	$-0.592339\pi$
$479$	−22.1676	−	5.93980i	−1.01287	−	0.271396i	−0.726826	+	0.686821i	$0.759005\pi$
$480$	20.0412	−	12.0416i	0.914750	−	0.549621i
$481$		0			0
$482$			9.75464i			0.444312i
$483$	5.24229	−	1.50313i	0.238533	−	0.0683947i
$484$	−7.01850	−	12.1564i	−0.319023	−	0.552563i
$485$	−21.3148	+	36.9183i	−0.967854	+	1.67637i
$486$	5.16285	−	1.87874i	0.234192	−	0.0852213i
$487$	−7.62733	−	28.4656i	−0.345627	−	1.28990i	−0.891878	−	0.452277i	$-0.850612\pi$
$487$	−7.62733	−	28.4656i	−0.345627	−	1.28990i	0.546250	−	0.837622i	$-0.316055\pi$
$488$	−0.941384	−	3.51329i	−0.0426144	−	0.159039i
$489$	−1.44838	+	5.80879i	−0.0654978	+	0.262682i
$490$	−3.45975	+	5.99247i	−0.156296	+	0.270712i
$491$	7.66195	+	13.2709i	0.345779	+	0.598907i	0.985495	−	0.169705i	$-0.0542814\pi$
$491$	7.66195	+	13.2709i	0.345779	+	0.598907i	−0.639716	+	0.768611i	$0.720948\pi$
$492$	−6.09496	−	21.2567i	−0.274782	−	0.958326i
$493$			15.8582i			0.714215i
$494$		0			0
$495$	−9.17859	+	17.2613i	−0.412547	+	0.775838i
$496$	−14.4063	−	3.86016i	−0.646863	−	0.173326i
$497$	11.6805	−	6.74372i	0.523941	−	0.302497i
$498$	0.0690926	+	3.96131i	0.00309611	+	0.177510i
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.410004	−	0.912084i	$-0.365527\pi$
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.912084	−	0.410004i	$-0.134473\pi$
$500$	−13.0684	+	3.50168i	−0.584439	+	0.156600i
$501$	6.30871	−	6.53269i	0.281852	−	0.291859i
$502$	−1.39562	−	1.39562i	−0.0622897	−	0.0622897i
$503$	30.1073	+	17.3825i	1.34242	+	0.775046i	0.987162	−	0.159722i	$-0.0510599\pi$
$503$	30.1073	+	17.3825i	1.34242	+	0.775046i	0.355257	+	0.934768i	$0.384393\pi$
$504$	4.75895	−	0.166060i	0.211981	−	0.00739692i
$505$	−9.97931	+	37.2433i	−0.444073	+	1.65730i
$506$	1.79091			0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	−11.4648	+	42.7871i	−0.508167	+	1.89651i	−0.0701558	+	0.997536i	$0.522350\pi$
$509$	−11.4648	+	42.7871i	−0.508167	+	1.89651i	−0.438011	+	0.898969i	$0.644317\pi$
$510$	−10.9495	−	6.06962i	−0.484854	−	0.268767i
$511$	12.9971	+	7.50387i	0.574957	+	0.331952i
$512$	15.2996	+	15.2996i	0.676153	+	0.676153i
$513$	−7.91022	−	24.3484i	−0.349245	−	1.07501i
$514$	2.31958	−	0.621529i	0.102312	−	0.0274145i
$515$	10.8924	−	10.8924i	0.479975	−	0.479975i
$516$	18.0329	−	0.314527i	0.793854	−	0.0138463i
$517$	5.12618	−	2.95960i	0.225449	−	0.130163i
$518$	0.854741	+	0.229027i	0.0375552	+	0.0100629i
$519$	−12.7128	−	21.1584i	−0.558032	−	0.928749i
$520$		0			0
$521$			1.93372i			0.0847179i	0.999102	+	0.0423590i	$0.0134873\pi$
$521$			1.93372i			0.0847179i	−0.999102	+	0.0423590i	$0.986513\pi$
$522$	1.93769	−	2.07781i	0.0848106	−	0.0909434i
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	0.849091	−	0.528246i	$-0.177150\pi$
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	−0.882020	+	0.471212i	$0.843817\pi$
$524$	−17.3904	+	30.1211i	−0.759705	+	1.31585i
$525$	−13.8175	−	3.44529i	−0.603047	−	0.150365i
$526$	−2.06445	−	7.70463i	−0.0900142	−	0.335938i
$527$	6.96651	+	25.9994i	0.303466	+	1.13255i
$528$	−10.3062	−	2.56976i	−0.448519	−	0.111835i
$529$	7.82890	−	13.5601i	0.340387	−	0.589568i
$530$	−1.50726	−	2.61066i	−0.0654714	−	0.113400i
$531$	−20.4764	+	21.9571i	−0.888602	+	0.952859i
$532$		−	10.7390i		−	0.465595i
$533$		0			0
$534$	1.34373	+	2.23641i	0.0581490	+	0.0967791i
$535$	−43.8215	−	11.7419i	−1.89457	−	0.507648i
$536$	−8.04846	+	4.64678i	−0.347640	+	0.200710i
$537$	−7.56215	+	0.131898i	−0.326331	+	0.00569182i
$538$	−6.50526	+	6.50526i	−0.280462	+	0.280462i
$539$	10.2340	−	2.74218i	0.440808	−	0.118114i
$540$	−10.4652	−	32.2130i	−0.450351	−	1.38623i
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	0.649844	−	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
$543$	3.19242	+	1.76964i	0.137000	+	0.0759425i
$544$	5.93348	−	22.1441i	0.254396	−	0.949419i
$545$	22.0572			0.944827
$546$		0			0
$547$	23.1549			0.990030			0.495015	−	0.868884i	$-0.335163\pi$
$547$	23.1549			0.990030			0.495015	+	0.868884i	$0.335163\pi$
$548$	3.65808	−	13.6522i	0.156266	−	0.583191i
$549$	−7.98321	+	0.278569i	−0.340715	+	0.0118890i
$550$	−4.04999	−	2.33826i	−0.172692	−	0.0997038i
$551$	−9.36139	−	9.36139i	−0.398809	−	0.398809i
$552$	−4.45349	+	4.61161i	−0.189553	+	0.196283i
$553$	−1.23473	+	0.330846i	−0.0525062	+	0.0140690i
$554$	5.65736	−	5.65736i	0.240358	−	0.240358i
$555$	−0.226797	−	13.0030i	−0.00962700	−	0.551948i
$556$	8.75970	−	5.05741i	0.371494	−	0.214482i
$557$	3.45636	+	0.926129i	0.146451	+	0.0392414i	0.331300	−	0.943526i	$-0.392513\pi$
$557$	3.45636	+	0.926129i	0.146451	+	0.0392414i	−0.184849	+	0.982767i	$0.559180\pi$
$558$	2.26406	−	4.25780i	0.0958451	−	0.180247i
$559$		0			0
$560$		−	13.2045i		−	0.557994i
$561$	5.28351	+	18.4267i	0.223070	+	0.777977i
$562$	2.13267	+	3.69389i	0.0899611	+	0.155817i
$563$	9.83710	−	17.0384i	0.414585	−	0.718081i	−0.580800	−	0.814046i	$-0.697260\pi$
$563$	9.83710	−	17.0384i	0.414585	−	0.718081i	0.995385	+	0.0959647i	$0.0305936\pi$
$564$	−2.48105	+	9.95039i	−0.104471	+	0.418987i
$565$	11.7035	+	43.6781i	0.492370	+	1.83755i
$566$	−0.648166	−	2.41899i	−0.0272445	−	0.101678i
$567$	1.99601	−	10.2657i	0.0838247	−	0.431119i
$568$	−7.92766	+	13.7311i	−0.332637	+	0.576145i
$569$	−4.78231	−	8.28321i	−0.200485	−	0.347250i	0.748200	−	0.663473i	$-0.230918\pi$
$569$	−4.78231	−	8.28321i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$570$	10.0468	−	2.88072i	0.420813	−	0.120660i
$571$			17.9785i			0.752375i	0.926544	+	0.376187i	$0.122765\pi$
$571$			17.9785i			0.752375i	−0.926544	+	0.376187i	$0.877235\pi$
$572$		0			0
$573$	−10.0925	+	6.06399i	−0.421619	+	0.253327i
$574$	2.69245	+	0.721441i	0.112381	+	0.0301124i
$575$	16.6038	−	9.58619i	0.692425	−	0.399772i
$576$	13.1564	−	8.22057i	0.548185	−	0.342524i
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	−0.827243	−	0.561844i	$-0.810092\pi$
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	0.561844	+	0.827243i	$0.310092\pi$
$578$	−6.06984	+	1.62641i	−0.252472	+	0.0676497i
$579$	13.8499	+	13.3750i	0.575582	+	0.555848i
$580$	−12.3851	−	12.3851i	−0.514264	−	0.514264i
$581$	6.53113	+	3.77075i	0.270957	+	0.156437i
$582$	3.63069	−	6.54973i	0.150497	−	0.271495i
$583$	−1.19465	+	4.45849i	−0.0494773	+	0.184652i
$584$	−17.6425			−0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	8.12231	−	30.3129i	0.335243	−	1.25115i	−0.568362	−	0.822779i	$-0.692423\pi$
$587$	8.12231	−	30.3129i	0.335243	−	1.25115i	0.903605	−	0.428367i	$-0.140911\pi$
$588$	−8.89929	+	16.0542i	−0.367000	+	0.662066i
$589$	−19.4604	−	11.2355i	−0.801853	−	0.462950i
$590$	−8.66697	−	8.66697i	−0.356814	−	0.356814i
$591$	−2.84548	−	2.74792i	−0.117047	−	0.113034i
$592$	6.82503	−	1.82876i	0.280507	−	0.0751616i
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	−0.999673	−	0.0255650i	$-0.991862\pi$
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	0.0255650	+	0.999673i	$0.491862\pi$
$594$	1.55927	−	3.05995i	0.0639778	−	0.125551i
$595$	−20.6378	+	11.9153i	−0.846069	+	0.488478i
$596$	41.3341	+	11.0754i	1.69311	+	0.453668i
$597$	−27.2335	+	16.3630i	−1.11459	+	0.669695i
$598$		0			0
$599$		−	33.7915i		−	1.38068i	−0.723484	−	0.690341i	$-0.757460\pi$
$599$		−	33.7915i		−	1.38068i	0.723484	−	0.690341i	$-0.242540\pi$
$600$	16.0923	−	4.61415i	0.656964	−	0.188372i
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	0.990404	+	0.138202i	$0.0441323\pi$
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	−0.375516	+	0.926816i	$0.622534\pi$
$602$	−1.13672	+	1.96886i	−0.0463292	+	0.0802446i
$603$	5.96693	+	19.5188i	0.242992	+	0.794867i
$604$	4.54432	+	16.9596i	0.184906	+	0.690077i
$605$	−6.73042	−	25.1183i	−0.273630	−	1.02120i
$606$	1.63870	−	6.57209i	0.0665676	−	0.266973i
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	−0.998208	−	0.0598403i	$-0.980941\pi$
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	0.550927	+	0.834553i	$0.314274\pi$
$608$	9.56943	+	16.5747i	0.388092	+	0.672195i
$609$	−1.49060	−	5.19860i	−0.0604022	−	0.210658i
$610$		−	3.26111i		−	0.132038i
$611$		0			0
$612$	−29.3229	−	15.5923i	−1.18531	−	0.630280i
$613$	−0.571244	−	0.153064i	−0.0230723	−	0.00618221i	0.247264	−	0.968948i	$-0.420468\pi$
$613$	−0.571244	−	0.153064i	−0.0230723	−	0.00618221i	−0.270337	+	0.962766i	$0.587135\pi$
$614$	6.20916	−	3.58486i	0.250581	−	0.144673i
$615$	−0.714416	−	40.9599i	−0.0288080	−	1.65166i
$616$	2.10479	−	2.10479i	0.0848044	−	0.0848044i
$617$	−28.0800	+	7.52400i	−1.13046	+	0.302905i	−0.775108	−	0.631829i	$-0.782305\pi$
$617$	−28.0800	+	7.52400i	−1.13046	+	0.302905i	−0.355349	+	0.934734i	$0.615638\pi$
$618$	−1.87980	+	1.94654i	−0.0756166	+	0.0783012i
$619$	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
$621$	7.66791	+	11.8086i	0.307703	+	0.473862i
$622$	−0.695256	+	2.59473i	−0.0278772	+	0.104039i
$623$	4.96634			0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	−0.594282	+	2.21789i	−0.0237523	+	0.0886448i
$627$	−13.9966	−	7.75870i	−0.558972	−	0.309853i
$628$	25.4694	+	14.7047i	1.01634	+	0.586783i
$629$	−9.01686	−	9.01686i	−0.359526	−	0.359526i
$630$	4.15999	+	0.960524i	0.165738	+	0.0382682i
$631$	39.1937	−	10.5019i	1.56028	−	0.418075i	0.627526	−	0.778596i	$-0.284068\pi$
$631$	39.1937	−	10.5019i	1.56028	−	0.418075i	0.932751	+	0.360521i	$0.117401\pi$
$632$	1.06258	−	1.06258i	0.0422670	−	0.0422670i
$633$	13.8668	−	0.241863i	0.551157	−	0.00961320i
$634$	−2.71690	+	1.56860i	−0.107902	+	0.0622971i
$635$	−26.1613	−	7.00990i	−1.03818	−	0.278180i
$636$	−4.11858	−	6.85468i	−0.163312	−	0.271806i
$637$		0			0
$638$		−	1.77598i		−	0.0703117i
$639$	25.4662	+	23.7488i	1.00743	+	0.939489i
$640$	16.6654	+	28.8653i	0.658758	+	1.14100i
$641$	12.8560	−	22.2673i	0.507783	−	0.879506i	−0.492176	−	0.870496i	$-0.663798\pi$
$641$	12.8560	−	22.2673i	0.507783	−	0.879506i	0.999959	−	0.00901077i	$-0.00286825\pi$
$642$	7.73291	+	1.92814i	0.305194	+	0.0760976i
$643$	−0.164018	−	0.612124i	−0.00646824	−	0.0241398i	0.962616	−	0.270869i	$-0.0873109\pi$
$643$	−0.164018	−	0.612124i	−0.00646824	−	0.0241398i	−0.969085	+	0.246729i	$0.920644\pi$
$644$	1.52861	+	5.70484i	0.0602356	+	0.224802i
$645$	32.4195	+	8.08354i	1.27652	+	0.318289i
$646$	5.12404	−	8.87510i	0.201603	−	0.349186i
$647$	−23.5124	−	40.7247i	−0.924368	−	1.60105i	−0.792574	−	0.609776i	$-0.791260\pi$
$647$	−23.5124	−	40.7247i	−0.924368	−	1.60105i	−0.131794	−	0.991277i	$-0.542074\pi$
$648$	4.00191	+	11.6244i	0.157210	+	0.456649i
$649$			18.7675i			0.736690i
$650$		0			0
$651$	−4.72758	−	7.86826i	−0.185289	−	0.308381i
$652$	−6.26251	−	1.67804i	−0.245259	−	0.0657169i
$653$	−25.0935	+	14.4877i	−0.981984	+	0.566949i	−0.902869	−	0.429917i	$-0.858543\pi$
$653$	−25.0935	+	14.4877i	−0.981984	+	0.566949i	−0.0791154	+	0.996865i	$0.525210\pi$
$654$	−3.87419	+	0.0675732i	−0.151493	+	0.00264232i
$655$	−45.5614	+	45.5614i	−1.78023	+	1.78023i
$656$	21.4990	−	5.76064i	0.839394	−	0.224915i
$657$	−8.71705	+	37.7532i	−0.340085	+	1.47289i
$658$	−0.914059	−	0.914059i	−0.0356337	−	0.0356337i
$659$	−40.4280	−	23.3411i	−1.57485	−	0.909241i	−0.995561	−	0.0941194i	$-0.969996\pi$
$659$	−40.4280	−	23.3411i	−1.57485	−	0.909241i	−0.579290	−	0.815121i	$-0.696670\pi$
$660$	−18.5175	−	10.2648i	−0.720794	−	0.399555i
$661$	−1.79701	+	6.70655i	−0.0698957	+	0.260854i	−0.992028	−	0.126021i	$-0.959779\pi$
$661$	−1.79701	+	6.70655i	−0.0698957	+	0.260854i	0.922132	+	0.386876i	$0.126446\pi$
$662$	−5.66611			−0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	5.14911	−	19.2167i	0.199674	−	0.745194i
$666$	0.0796706	+	2.28320i	0.00308717	+	0.0884721i
$667$	6.30553	+	3.64050i	0.244151	+	0.140961i
$668$	6.95457	+	6.95457i	0.269080	+	0.269080i
$669$	34.0680	−	35.2776i	1.31715	−	1.36391i
$670$	−8.04861	+	2.15662i	−0.310945	+	0.0833174i
$671$	−3.53081	+	3.53081i	−0.136306	+	0.136306i
$672$	0.136342	+	7.81696i	0.00525952	+	0.301546i
$673$	22.6855	−	13.0975i	0.874460	−	0.504870i	0.00563228	−	0.999984i	$-0.498207\pi$
$673$	22.6855	−	13.0975i	0.874460	−	0.504870i	0.868828	+	0.495114i	$0.164874\pi$
$674$	−9.65322	−	2.58657i	−0.371828	−	0.0996311i
$675$	−1.92272	−	36.7156i	−0.0740057	−	1.41318i
$676$		0			0
$677$			21.9298i			0.842829i	0.906868	+	0.421415i	$0.138466\pi$
$677$			21.9298i			0.842829i	−0.906868	+	0.421415i	$0.861534\pi$
$678$	−2.18945	−	7.63589i	−0.0840852	−	0.293255i
$679$	−7.12739	−	12.3450i	−0.273524	−	0.473758i
$680$	14.0071	−	24.2610i	0.537149	−	0.930369i
$681$	−3.08213	+	12.3611i	−0.118108	+	0.473677i
$682$	−0.780190	−	2.91171i	−0.0298750	−	0.111495i
$683$	−1.97300	−	7.36335i	−0.0754949	−	0.281751i	0.917850	−	0.396927i	$-0.129923\pi$
$683$	−1.97300	−	7.36335i	−0.0754949	−	0.281751i	−0.993345	+	0.115176i	$0.963257\pi$
$684$	26.5144	−	8.10549i	1.01380	−	0.309921i
$685$	13.0918	−	22.6757i	0.500212	−	0.866392i
$686$	−2.59028	−	4.48650i	−0.0988975	−	0.171296i
$687$	26.8646	−	7.70291i	1.02495	−	0.293884i
$688$			18.1532i			0.692084i
$689$		0			0
$690$	−4.92706	+	2.96039i	−0.187570	+	0.112700i
$691$	15.4088	+	4.12878i	0.586179	+	0.157066i	0.539707	−	0.841853i	$-0.318535\pi$
$691$	15.4088	+	4.12878i	0.586179	+	0.157066i	0.0464729	+	0.998920i	$0.485202\pi$
$692$	23.1508	−	13.3661i	0.880061	−	0.508103i
$693$	−3.46407	−	5.54399i	−0.131589	−	0.210599i
$694$	−2.75978	+	2.75978i	−0.104760	+	0.104760i
$695$	18.0998	−	4.84983i	0.686565	−	0.183965i
$696$	4.57317	+	4.41637i	0.173345	+	0.167402i
$697$	−28.4033	−	28.4033i	−1.07585	−	1.07585i
$698$	−9.13155	−	5.27210i	−0.345634	−	0.199552i
$699$	15.2457	−	27.5032i	0.576647	−	1.04027i
$700$	3.99159	−	14.8968i	0.150868	−	0.563047i
$701$	30.3059			1.14464			0.572319	−	0.820031i	$-0.306044\pi$
$701$	30.3059			1.14464			0.572319	+	0.820031i	$0.306044\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	2.50989	−	9.36704i	0.0945951	−	0.353034i
$705$	−9.21066	+	16.6160i	−0.346893	+	0.625793i
$706$	3.86907	+	2.23381i	0.145615	+	0.0840706i
$707$	−9.11674	−	9.11674i	−0.342870	−	0.342870i
$708$	−23.3889	−	22.5870i	−0.879008	−	0.848871i
$709$	−32.8514	+	8.80249i	−1.23376	+	0.330585i	−0.816042	−	0.577993i	$-0.803836\pi$
$709$	−32.8514	+	8.80249i	−1.23376	+	0.330585i	−0.417717	+	0.908577i	$0.637170\pi$
$710$	−10.0521	+	10.0521i	−0.377247	+	0.377247i
$711$	−1.74879	−	2.79881i	−0.0655847	−	0.104964i
$712$	−5.05607	+	2.91912i	−0.189484	+	0.109399i
$713$	11.9372	+	3.19855i	0.447050	+	0.119787i
$714$	3.58839	−	2.15606i	0.134292	−	0.0806884i
$715$		0			0
$716$		−	8.19093i		−	0.306110i
$717$	15.4053	−	4.41718i	0.575322	−	0.164963i
$718$	−5.08050	−	8.79968i	−0.189602	−	0.328401i
$719$	−3.94839	+	6.83882i	−0.147250	+	0.255045i	−0.930210	−	0.367027i	$-0.880376\pi$
$719$	−3.94839	+	6.83882i	−0.147250	+	0.255045i	0.782960	+	0.622072i	$0.213709\pi$
$720$	32.6017	−	9.96640i	1.21499	−	0.371426i
$721$	1.33316	+	4.97544i	0.0496496	+	0.185295i
$722$	0.481159	+	1.79571i	0.0179069	+	0.0668294i
$723$	−11.5979	+	46.5140i	−0.431331	+	1.72988i
$724$	−1.97649	+	3.42339i	−0.0734558	+	0.127229i
$725$	−9.50629	−	16.4654i	−0.353055	−	0.611509i
$726$	1.25910	+	4.39123i	0.0467296	+	0.162974i
$727$			24.6824i			0.915420i	0.889102	+	0.457710i	$0.151330\pi$
$727$			24.6824i			0.915420i	−0.889102	+	0.457710i	$0.848670\pi$
$728$		0			0
$729$	26.8523	−	2.82014i	0.994530	−	0.104450i
$730$	−15.2792	−	4.09404i	−0.565507	−	0.151527i
$731$	28.3722	−	16.3807i	1.04939	−	0.605863i
$732$	−0.150866	−	8.64963i	−0.00557616	−	0.319700i
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.321476	−	0.946918i	$-0.395821\pi$
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.946918	−	0.321476i	$-0.104179\pi$
$734$	7.87731	−	2.11072i	0.290757	−	0.0779081i
$735$	−23.6223	+	24.4610i	−0.871323	+	0.902257i
$736$	−7.44281	−	7.44281i	−0.274346	−	0.274346i
$737$	11.0492	+	6.37928i	0.407004	+	0.234984i
$738$	0.250964	+	7.19212i	0.00923812	+	0.264746i
$739$	10.0551	−	37.5261i	0.369882	−	1.38042i	−0.490798	−	0.871273i	$-0.663295\pi$
$739$	10.0551	−	37.5261i	0.369882	−	1.38042i	0.860680	−	0.509146i	$-0.170039\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	13.4913	−	50.3503i	0.494949	−	1.84717i	−0.0353674	−	0.999374i	$-0.511260\pi$
$743$	13.4913	−	50.3503i	0.494949	−	1.84717i	0.530316	−	0.847800i	$-0.322073\pi$
$744$	9.43781	+	5.23162i	0.346007	+	0.191801i
$745$	68.6542	+	39.6375i	2.51530	+	1.45221i
$746$	5.10435	+	5.10435i	0.186883	+	0.186883i
$747$	−4.38039	+	18.9713i	−0.160270	+	0.694122i
$748$	−20.0526	+	5.37308i	−0.733195	+	0.196459i
$749$	10.7270	−	10.7270i	0.391957	−	0.391957i
$750$	4.40233	−	0.0767848i	0.160750	−	0.00280378i
$751$	−42.7471	+	24.6801i	−1.55986	+	0.900588i	−0.562595	+	0.826733i	$0.690197\pi$
$751$	−42.7471	+	24.6801i	−1.55986	+	0.900588i	−0.997269	+	0.0738552i	$0.976470\pi$
$752$	−9.97017	−	2.67150i	−0.363575	−	0.0974196i
$753$	−4.99555	−	8.31423i	−0.182048	−	0.302987i
$754$		0			0
$755$			32.5270i			1.18378i
$756$	11.0782	+	2.35521i	0.402911	+	0.0856580i
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	0.642255	−	0.766491i	$-0.277999\pi$
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	−0.984928	+	0.172964i	$0.944666\pi$
$758$	−0.699838	+	1.21216i	−0.0254193	+	0.0440275i
$759$	8.53976	+	2.12932i	0.309974	+	0.0772895i
$760$	6.05310	+	22.5905i	0.219569	+	0.819443i
$761$	9.96144	+	37.1766i	0.361102	+	1.34765i	0.872629	+	0.488384i	$0.162413\pi$
$761$	9.96144	+	37.1766i	0.361102	+	1.34765i	−0.511527	+	0.859267i	$0.670920\pi$
$762$	4.61653	+	1.15109i	0.167239	+	0.0416997i
$763$	−3.68783	+	6.38751i	−0.133508	+	0.231243i
$764$	−6.37559	−	11.0428i	−0.230661	−	0.399516i
$765$	−44.9953	−	41.9610i	−1.62681	−	1.51710i
$766$			9.37896i			0.338876i
$767$		0			0
$768$	6.21032	+	10.3360i	0.224096	+	0.372969i
$769$	2.75634	+	0.738559i	0.0993962	+	0.0266331i	0.308174	−	0.951330i	$-0.400282\pi$
$769$	2.75634	+	0.738559i	0.0993962	+	0.0266331i	−0.208778	+	0.977963i	$0.566949\pi$
$770$	2.31126	−	1.33441i	0.0832921	−	0.0480887i
$771$	11.7997	−	0.205808i	0.424954	−	0.00741200i
$772$	−14.7443	+	14.7443i	−0.530660	+	0.530660i
$773$	6.20770	−	1.66335i	0.223275	−	0.0598265i	−0.145447	−	0.989366i	$-0.546462\pi$
$773$	6.20770	−	1.66335i	0.223275	−	0.0598265i	0.368722

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

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