LMFDB - Embedded newform 507.2.k.k.80.11

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			80.11
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0912193	+	0.340435i	−0.0645018	+	0.240724i	−0.990648	−	0.136440i	$-0.956434\pi$
$2$	−0.0912193	+	0.340435i	−0.0645018	+	0.240724i	0.926147	+	0.377164i	$0.123101\pi$
$3$	−1.73179	−	0.0302056i	−0.999848	−	0.0174392i
$3$	−1.73179	−	0.0302056i	−0.999848	−	0.0174392i
$4$	1.62448	+	0.937892i	0.812238	+	0.468946i
$5$	−2.45719	−	2.45719i	−1.09889	−	1.09889i	−0.994541	−	0.104350i	$-0.966724\pi$
$5$	−2.45719	−	2.45719i	−1.09889	−	1.09889i	−0.104350	−	0.994541i	$-0.533276\pi$
$6$	0.168255	−	0.586806i	0.0686900	−	0.239562i
$7$	−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
$9$	2.99818	+	0.104619i	0.999392	+	0.0348731i
$10$	1.06066	−	0.612371i	0.335410	−	0.193649i
$11$	1.81140	+	0.485362i	0.546156	+	0.146342i	0.521339	−	0.853350i	$-0.325433\pi$
$11$	1.81140	+	0.485362i	0.546156	+	0.146342i	0.0248176	+	0.999692i	$0.492100\pi$
$12$	−2.78492	−	1.67330i	−0.803936	−	0.483039i
$13$		0			0
$13$		0			0
$14$		−	0.409539i		−	0.109454i
$15$	4.18112	+	4.32956i	1.07956	+	1.11789i
$16$	1.63506	+	2.83201i	0.408766	+	0.708003i
$17$	−2.95083	+	5.11099i	−0.715682	+	1.23960i	0.247014	+	0.969012i	$0.420551\pi$
$17$	−2.95083	+	5.11099i	−0.715682	+	1.23960i	−0.962696	+	0.270586i	$0.912783\pi$
$18$	−0.309108	+	1.01114i	−0.0728573	+	0.238328i
$19$	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
$21$	1.95284	−	0.486926i	0.426146	−	0.106256i
$22$	−0.330468	+	0.572388i	−0.0704561	+	0.122034i
$23$	1.35482	+	2.34662i	0.282500	+	0.489305i	0.972000	−	0.234981i	$-0.0755028\pi$
$23$	1.35482	+	2.34662i	0.282500	+	0.489305i	−0.689500	+	0.724286i	$0.742169\pi$
$24$	1.70192	−	1.64357i	0.347403	−	0.335492i
$25$			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	−0.268126	−	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	$-0.884323\pi$
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	0.355463	+	0.934690i	$0.384323\pi$
$32$	−3.75217	+	1.00539i	−0.663296	+	0.177730i
$33$	−3.12229	−	0.895258i	−0.543521	−	0.155844i
$34$	−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
$37$	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	$0.261698\pi$
$41$	−1.76159	+	6.57436i	−0.275115	+	1.02674i	−0.955764	+	0.294133i	$0.904969\pi$
$42$	−0.0123704	+	0.709234i	−0.00190879	+	0.109437i
$43$	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
$45$	−7.11003	−	7.62417i	−1.05990	−	1.13654i
$46$	−0.922459	+	0.247172i	−0.136009	+	0.0364436i
$47$	2.23192	−	2.23192i	0.325559	−	0.325559i	−0.525336	−	0.850895i	$-0.676060\pi$
$47$	2.23192	−	2.23192i	0.325559	−	0.325559i	0.850895	+	0.525336i	$0.176060\pi$
$48$	−2.74604	−	4.95383i	−0.396357	−	0.715024i
$49$	−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	$0.0540689\pi$
$53$			2.46136i			0.338093i	−0.985608	+	0.169047i	$0.945931\pi$
$54$	0.565851	−	1.74174i	0.0770025	−	0.237021i
$55$	−3.25832	−	5.64358i	−0.439352	−	0.760980i
$56$	0.793642	−	1.37463i	0.106055	−	0.183692i
$57$	−2.06460	−	8.28020i	−0.273463	−	1.09674i
$58$	0.245112	+	0.914771i	0.0321848	+	0.120115i
$59$	2.59020	+	9.66677i	0.337216	+	1.25851i	0.901447	+	0.432890i	$0.142506\pi$
$59$	2.59020	+	9.66677i	0.337216	+	1.25851i	−0.564231	+	0.825617i	$0.690827\pi$
$60$	2.73147	+	10.9547i	0.352631	+	1.41424i
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	−0.768120	−	0.640306i	$-0.778808\pi$
$61$	1.33134	−	2.30596i	0.170461	−	0.295247i	0.938581	+	0.345058i	$0.112141\pi$
$62$	−0.803720	−	1.39208i	−0.102073	−	0.176795i
$63$	−3.39662	+	0.784266i	−0.427934	+	0.0988082i
$64$			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
$69$	−2.27539	−	4.10478i	−0.273924	−	0.494157i
$70$	−1.00632	+	1.00632i	−0.120278	+	0.120278i
$71$	11.2116	−	3.00415i	1.33058	−	0.356527i	0.477647	−	0.878552i	$-0.341490\pi$
$71$	11.2116	−	3.00415i	1.33058	−	0.356527i	0.852930	+	0.522025i	$0.174823\pi$
$72$	−2.99701	+	2.79490i	−0.353201	+	0.329383i
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.997444	−	0.0714492i	$-0.977238\pi$
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.0714492	−	0.997444i	$-0.522762\pi$
$74$	0.659503	+	0.380764i	0.0766657	+	0.0442630i
$75$	0.213723	−	12.2534i	0.0246786	−	1.41490i
$76$	−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
$81$	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	0.912596	−	0.408864i	$-0.134075\pi$
$83$	4.58922	+	4.58922i	0.503732	+	0.503732i	−0.408864	+	0.912596i	$0.634075\pi$
$84$	3.62903	+	1.04056i	0.395960	+	0.113534i
$85$	19.8095	−	5.30793i	2.14864	−	0.575726i
$86$	−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
$89$	4.12834	+	1.10619i	0.437604	+	0.117256i	0.470893	−	0.882190i	$-0.343932\pi$
$89$	4.12834	+	1.10619i	0.437604	+	0.117256i	−0.0332896	+	0.999446i	$0.510598\pi$
$90$	3.24410	−	1.72503i	0.341959	−	0.181834i
$91$		0			0
$92$			5.08271i			0.529909i
$93$	5.68242	−	5.48760i	0.589240	−	0.569037i
$94$	0.556230	+	0.963419i	0.0573708	+	0.0993691i
$95$	8.56055	−	14.8273i	0.878294	−	1.52125i
$96$	6.52833	−	1.62779i	0.666295	−	0.166135i
$97$	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
$99$	5.38010	+	1.64471i	0.540721	+	0.165299i
$100$	−6.63614	+	11.4941i	−0.663614	+	1.14941i
$101$	−5.54779	−	9.60905i	−0.552026	−	0.956137i	−0.998128	−	0.0611547i	$-0.980522\pi$
$101$	−5.54779	−	9.60905i	−0.552026	−	0.956137i	0.446103	−	0.894982i	$-0.352812\pi$
$102$	2.50267	+	2.59152i	0.247801	+	0.256599i
$103$		−	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	0.158641	−	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	$-0.651682\pi$
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	0.888594	+	0.458694i	$0.151682\pi$
$110$	2.21849	−	0.594443i	0.211525	−	0.0566780i
$111$	−1.03151	+	3.59749i	−0.0979068	+	0.341459i
$112$	−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
$115$	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
$120$	−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
$123$	3.24929	−	11.3322i	0.292978	−	1.02179i
$124$	−8.26363	+	2.21423i	−0.742096	+	0.198844i
$125$	5.10014	−	5.10014i	0.456171	−	0.456171i
$126$	0.0428457	−	1.22787i	0.00381699	−	0.109387i
$127$	−6.74982	+	3.89701i	−0.598950	+	0.345804i	−0.768628	−	0.639696i	$-0.779060\pi$
$127$	−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	$-0.699460\pi$
$131$		−	18.5420i		−	1.62003i	0.586412	−	0.810013i	$-0.300540\pi$
$132$	−4.23243	−	4.38269i	−0.368386	−	0.381465i
$133$	−2.86254	−	4.95807i	−0.248214	−	0.429919i
$134$	1.19893	−	2.07660i	0.103571	−	0.179391i
$135$	12.0828	+	13.4182i	1.03992	+	1.15485i
$136$	−2.08651	−	7.78697i	−0.178917	−	0.667727i
$137$	1.95016	+	7.27811i	0.166614	+	0.621811i	0.997829	+	0.0658600i	$0.0209791\pi$
$137$	1.95016	+	7.27811i	0.166614	+	0.621811i	−0.831215	+	0.555951i	$0.812354\pi$
$138$	1.60497	−	0.400186i	0.136624	−	0.0340661i
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	−0.728733	−	0.684798i	$-0.759891\pi$
$139$	2.69616	−	4.66989i	0.228685	−	0.396095i	0.957419	+	0.288703i	$0.0932239\pi$
$140$	3.78714	+	6.55952i	0.320072	+	0.554381i
$141$	−3.93263	+	3.79780i	−0.331187	+	0.319832i
$142$			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
$147$	8.55869	−	4.74431i	0.705909	−	0.391304i
$148$	2.86592	−	2.86592i	0.235577	−	0.235577i
$149$	−22.0357	+	5.90444i	−1.80523	+	0.483710i	−0.994775	−	0.102088i	$-0.967448\pi$
$149$	−22.0357	+	5.90444i	−1.80523	+	0.483710i	−0.810457	+	0.585798i	$0.800781\pi$
$150$	4.15200	+	1.19051i	0.339010	+	0.0972046i
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	0.923125	−	0.384500i	$-0.125626\pi$
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	−0.384500	+	0.923125i	$0.625626\pi$
$152$	−5.82852	−	3.36510i	−0.472755	−	0.272945i
$153$	−9.38182	+	15.0149i	−0.758476	+	1.21389i
$154$	0.198774	−	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
$159$	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
$162$	−1.03254	+	2.99924i	−0.0811243	+	0.235642i
$163$	−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
$165$	5.47225	+	9.87189i	0.426014	+	0.768526i
$166$	−1.98096	+	1.14371i	−0.153752	+	0.0887687i
$167$	−5.06462	−	1.35706i	−0.391912	−	0.105012i	0.0574813	−	0.998347i	$-0.481693\pi$
$167$	−5.06462	−	1.35706i	−0.391912	−	0.105012i	−0.449393	+	0.893334i	$0.648360\pi$
$168$	−1.41594	+	2.35659i	−0.109242	+	0.181815i
$169$		0			0
$170$			7.22802i			0.554364i
$171$	3.32534	+	14.4019i	0.254295	+	1.10134i
$172$	5.20644	+	9.01782i	0.396987	+	0.687602i
$173$	−7.12562	+	12.3419i	−0.541751	+	0.938339i	0.457053	+	0.889439i	$0.348905\pi$
$173$	−7.12562	+	12.3419i	−0.541751	+	0.938339i	−0.998804	+	0.0489001i	$0.984428\pi$
$174$	−0.396851	−	1.59159i	−0.0300852	−	0.120658i
$175$	−2.12796	−	7.94166i	−0.160859	−	0.600333i
$176$	1.58720	+	5.92349i	0.119639	+	0.446500i
$177$	−4.19369	−	16.8190i	−0.315217	−	1.26420i
$178$	−0.753169	+	1.30453i	−0.0564524	+	0.0977785i
$179$	2.18334	+	3.78165i	0.163190	+	0.282654i	0.936011	−	0.351970i	$-0.114488\pi$
$179$	2.18334	+	3.78165i	0.163190	+	0.282654i	−0.772821	+	0.634624i	$0.781155\pi$
$180$	−4.39942	−	19.0537i	−0.327914	−	1.42018i
$181$			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
$186$	1.34982	+	2.43507i	0.0989739	+	0.178548i
$187$	−7.82581	+	7.82581i	−0.572280	+	0.572280i
$188$	5.71901	−	1.53240i	0.417101	−	0.111762i
$189$	5.90591	−	1.25559i	0.429592	−	0.0913304i
$190$	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
$193$	−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	−0.983781	−	0.179375i	$-0.942593\pi$
$197$	−0.591102	+	2.20602i	−0.0421143	+	0.157173i	0.941667	+	0.336547i	$0.109259\pi$
$198$	−1.05069	+	1.68155i	−0.0746689	+	0.119502i
$199$	−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
$201$	11.3275	+	3.24796i	0.798984	+	0.229093i
$202$	3.77732	−	1.01213i	0.265772	−	0.0712133i
$203$	−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
$206$	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
$210$	1.77312	−	1.71233i	0.122357	−	0.118162i
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	0.970291	−	0.241939i	$-0.0777834\pi$
$211$	4.00362	+	6.93447i	0.275620	+	0.477388i	−0.694671	+	0.719327i	$0.744450\pi$
$212$	−2.30849	+	3.99842i	−0.158548	+	0.274612i
$213$	−19.5069	+	4.86389i	−1.33659	+	0.333269i
$214$	1.19090	+	4.44451i	0.0814084	+	0.303820i
$215$	−4.99274	−	18.6332i	−0.340502	−	1.27077i
$216$	5.27460	−	4.74965i	0.358891	−	0.323173i
$217$	2.64984	−	4.58965i	0.179883	−	0.311566i
$218$	1.11855	+	1.93739i	0.0757580	+	0.131217i
$219$	15.5399	+	16.0916i	1.05009	+	1.08737i
$220$		−	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
$225$	−0.740244	+	21.2139i	−0.0493496	+	1.41426i
$226$	3.24295	−	3.24295i	0.215718	−	0.215718i
$227$	7.10455	−	1.90366i	0.471546	−	0.126350i	−0.0152176	−	0.999884i	$-0.504844\pi$
$227$	7.10455	−	1.90366i	0.471546	−	0.126350i	0.486763	+	0.873534i	$0.338177\pi$
$228$	4.41203	−	15.3874i	0.292194	−	1.01905i
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	0.975214	−	0.221263i	$-0.0710179\pi$
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	−0.221263	+	0.975214i	$0.571018\pi$
$230$	2.87401	+	1.65931i	0.189507	+	0.109412i
$231$	3.77371	+	0.0658205i	0.248292	+	0.00433067i
$232$	−0.950001	+	3.54545i	−0.0623706	+	0.232770i
$233$	−18.1554			−1.18940			−0.594700	−	0.803947i	$-0.702729\pi$
$233$	−18.1554			−1.18940			−0.594700	+	0.803947i	$0.702729\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	−4.85866	+	18.1328i	−0.316272	+	1.18034i
$237$	−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	0.463099	−	0.886306i	$-0.346737\pi$
$239$	−6.54262	−	6.54262i	−0.423207	−	0.423207i	−0.886306	+	0.463099i	$0.846737\pi$
$240$	−5.42498	+	18.9201i	−0.350181	+	1.22129i
$241$	−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
$243$	−15.5292	−	1.35760i	−0.996200	−	0.0870900i
$244$	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
$249$	−7.80893	−	8.08617i	−0.494871	−	0.512440i
$250$	1.27104	+	2.20150i	0.0803874	+	0.139235i
$251$	−2.80003	+	4.84979i	−0.176736	+	0.306116i	−0.940761	−	0.339071i	$-0.889887\pi$
$251$	−2.80003	+	4.84979i	−0.176736	+	0.306116i	0.764025	+	0.645187i	$0.223221\pi$
$252$	−6.25328	−	1.91164i	−0.393920	−	0.120422i
$253$	1.31516	+	4.90825i	0.0826834	+	0.308579i
$254$	−0.710965	−	2.65336i	−0.0446099	−	0.166486i
$255$	−34.4661	+	8.59385i	−2.15835	+	0.538168i
$256$	−3.48092	+	6.02913i	−0.217557	+	0.376821i
$257$	−3.40679	−	5.90073i	−0.212510	−	0.368077i	0.739990	−	0.672618i	$-0.234830\pi$
$257$	−3.40679	−	5.90073i	−0.212510	−	0.368077i	−0.952499	+	0.304541i	$0.901497\pi$
$258$	2.43763	−	2.35406i	0.151760	−	0.146557i
$259$			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	−0.962446	−	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
$266$	1.94902	−	0.522238i	0.119502	−	0.0320205i
$267$	−7.11600	−	2.04038i	−0.435492	−	0.124869i
$268$	−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
$271$	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
$276$	0.153526	−	8.80218i	0.00924120	−	0.529829i
$277$	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
$279$	−10.0065	+	9.33171i	−0.599074	+	0.558675i
$280$	−5.32786	+	1.42759i	−0.318400	+	0.0853151i
$281$	8.55751	−	8.55751i	0.510498	−	0.510498i	−0.404181	−	0.914679i	$-0.632443\pi$
$281$	8.55751	−	8.55751i	0.510498	−	0.510498i	0.914679	+	0.404181i	$0.132443\pi$
$282$	−0.934172	−	1.68524i	−0.0556291	−	0.100354i
$283$	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
$288$	−11.3548	+	2.62179i	−0.669091	+	0.154490i
$289$	−8.91483	−	15.4409i	−0.524402	−	0.908291i
$290$	1.64548	−	2.85006i	0.0966260	−	0.167361i
$291$	−5.14061	−	20.6167i	−0.301348	−	1.20857i
$292$	−6.27032	−	23.4012i	−0.366943	−	1.36945i
$293$	−4.11392	−	15.3534i	−0.240338	−	0.896953i	−0.975670	−	0.219245i	$-0.929640\pi$
$293$	−4.11392	−	15.3534i	−0.240338	−	0.896953i	0.735332	−	0.677707i	$-0.237026\pi$
$294$	0.834411	+	3.34645i	0.0486638	+	0.195169i
$295$	17.3885	−	30.1178i	1.01240	−	1.75352i
$296$	1.47576	+	2.55609i	0.0857768	+	0.148570i
$297$	−9.26751	−	3.01079i	−0.537756	−	0.174704i
$298$		−	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
$303$	9.31734	+	16.8084i	0.535267	+	0.965618i
$304$	−11.3927	+	11.3927i	−0.653417	+	0.653417i
$305$	−8.93755	+	2.39481i	−0.511763	+	0.137126i
$306$	−4.25581	−	4.56355i	−0.243288	−	0.260881i
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	0.986247	−	0.165277i	$-0.0528518\pi$
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	−0.165277	+	0.986247i	$0.552852\pi$
$308$	−3.53987	−	2.04374i	−0.201703	−	0.116453i
$309$	−0.133897	+	7.67675i	−0.00761713	+	0.436715i
$310$	−1.44572	+	5.39552i	−0.0821116	+	0.306445i
$311$	7.62181			0.432193			0.216097	−	0.976372i	$-0.430667\pi$
$311$	7.62181			0.432193			0.216097	+	0.976372i	$0.430667\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	−1.43018	+	5.33751i	−0.0807099	+	0.301213i
$315$	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	0.861416	−	0.507901i	$-0.169578\pi$
$317$	6.29415	+	6.29415i	0.353515	+	0.353515i	−0.507901	+	0.861416i	$0.669578\pi$
$318$	1.44434	+	0.414137i	0.0809945	+	0.0232236i
$319$	4.86734	−	1.30420i	0.272518	−	0.0730211i
$320$	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
$323$	−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
$327$	−7.90834	+	7.63720i	−0.437332	+	0.422338i
$328$	−4.64868	−	8.05175i	−0.256680	−	0.444583i
$329$	−1.83387	+	3.17636i	−0.101105	+	0.175118i
$330$	−3.85991	+	0.962439i	−0.212481	+	0.0529805i
$331$	−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
$333$	1.89502	−	6.19893i	0.103847	−	0.339699i
$334$	0.923981	−	1.60038i	0.0505580	−	0.0875690i
$335$	11.8211	+	20.4747i	0.645853	+	1.11865i
$336$	4.57201	+	4.73433i	0.249424	+	0.258279i
$337$		−	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
$342$	−5.20625	−	0.181669i	−0.281522	−	0.00982351i
$343$	10.3937	−	10.3937i	0.561209	−	0.561209i
$344$	−7.32457	+	1.96261i	−0.394914	+	0.105817i
$345$	−4.49517	+	15.6773i	−0.242012	+	0.844037i
$346$	−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
$349$	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	$-0.807139\pi$
$353$	3.28082	−	12.2442i	0.174620	−	0.651692i	0.996616	−	0.0821982i	$-0.0261940\pi$
$354$	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
$357$	−3.27384	+	11.4178i	−0.173270	+	0.604295i
$358$	−1.48657	+	0.398325i	−0.0785676	+	0.0210521i
$359$	−20.3859	+	20.3859i	−1.07593	+	1.07593i	−0.0790589	+	0.996870i	$0.525192\pi$
$359$	−20.3859	+	20.3859i	−1.07593	+	1.07593i	−0.996870	+	0.0790589i	$0.974808\pi$
$360$	14.2318	+	0.496611i	0.750084	+	0.0261737i
$361$	−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
$366$	−1.12914	−	1.16923i	−0.0590212	−	0.0611167i
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	0.992221	+	0.124490i	$0.0397295\pi$
$367$	11.5695	+	20.0389i	0.603922	+	1.04602i	−0.388299	+	0.921533i	$0.626937\pi$
$368$	−4.43045	+	7.67376i	−0.230953	+	0.400023i
$369$	−5.96937	+	19.5268i	−0.310753	+	1.01652i
$370$	−0.684915	−	2.55614i	−0.0356071	−	0.132887i
$371$	−0.740245	−	2.76263i	−0.0384316	−	0.143429i
$372$	14.3777	−	3.58497i	0.745451	−	0.185872i
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	0.469128	+	0.883130i	$0.344568\pi$
$373$	−10.2408	+	17.7376i	−0.530249	+	0.918419i	−0.999377	+	0.0352886i	$0.988765\pi$
$374$	−1.95031	−	3.37804i	−0.100848	−	0.174674i
$375$	−8.98642	+	8.67831i	−0.464057	+	0.448146i
$376$			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
$381$	11.8070	−	6.54491i	0.604889	−	0.335306i
$382$	−1.69412	+	1.69412i	−0.0866785	+	0.0866785i
$383$	25.7044	−	6.88748i	1.31344	−	0.351934i	0.466921	−	0.884299i	$-0.345363\pi$
$383$	25.7044	−	6.88748i	1.31344	−	0.351934i	0.846515	+	0.532365i	$0.178697\pi$
$384$	15.9697	+	4.57900i	0.814948	+	0.233671i
$385$	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
$388$	−5.95573	+	22.2271i	−0.302356	+	1.12841i
$389$	6.17335			0.313001			0.156501	−	0.987678i	$-0.449979\pi$
$389$	6.17335			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	1.99745	−	7.45460i	0.100887	−	0.376514i
$393$	−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
$396$	7.19729	+	7.71774i	0.361677	+	0.387831i
$397$	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
$399$	4.80755	+	8.67278i	0.240679	+	0.434182i
$400$	−20.0382	+	11.5691i	−1.00191	+	0.578453i
$401$	−22.4109	−	6.00499i	−1.11915	−	0.299875i	−0.348610	−	0.937268i	$-0.613346\pi$
$401$	−22.4109	−	6.00499i	−1.11915	−	0.299875i	−0.770539	+	0.637393i	$0.780013\pi$
$402$	−2.13901	+	3.56002i	−0.106684	+	0.177558i
$403$		0			0
$404$		−	20.8129i		−	1.03548i
$405$	−20.5195	−	23.6024i	−1.01962	−	1.17281i
$406$	−0.550228	−	0.953023i	−0.0273074	−	0.0472978i
$407$	2.02598	−	3.50910i	0.100424	−	0.173940i
$408$	3.37818	+	13.5484i	0.167245	+	0.670746i
$409$	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
$411$	−3.15743	−	12.6630i	−0.155744	−	0.624622i
$412$	4.15753	−	7.20106i	0.204827	−	0.354771i
$413$	−5.81450	−	10.0710i	−0.286113	−	0.495562i
$414$	−2.79155	+	0.644559i	−0.137197	+	0.0316783i
$415$		−	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	0.189239	−	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	$-0.849625\pi$
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	0.455040	+	0.890471i	$0.349625\pi$
$422$	−2.72594	+	0.730414i	−0.132697	+	0.0355560i
$423$	6.92520	−	6.45819i	0.336715	−	0.314008i
$424$	−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
$427$	−0.800795	+	2.98861i	−0.0387532	+	0.144629i
$428$	24.4891			1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	5.49370	−	20.5028i	0.264622	−	0.987583i	−0.697859	−	0.716235i	$-0.745864\pi$
$431$	5.49370	−	20.5028i	0.264622	−	0.987583i	0.962481	−	0.271348i	$-0.0874694\pi$
$432$	−7.71484	−	15.1398i	−0.371181	−	0.728412i
$433$	−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
$435$	15.5466	+	4.45770i	0.745404	+	0.213730i
$436$	11.5007	−	3.08159i	0.550782	−	0.147582i
$437$	−9.44007	+	9.44007i	−0.451580	+	0.451580i
$438$	−6.89569	+	3.82247i	−0.329489	+	0.182644i
$439$	12.4753	−	7.20264i	0.595415	−	0.343763i	−0.171820	−	0.985128i	$-0.554965\pi$
$439$	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	$-0.822881\pi$
$443$		−	22.2330i		−	1.05632i	0.849144	−	0.528162i	$-0.177119\pi$
$444$	−5.04972	+	4.87659i	−0.239649	+	0.231433i
$445$	−7.42603	−	12.8623i	−0.352027	−	0.609729i
$446$	−4.98965	+	8.64232i	−0.236267	+	0.409226i
$447$	38.3394	−	9.55963i	1.81339	−	0.452155i
$448$	−1.55521	−	5.80413i	−0.0734769	−	0.274220i
$449$	6.36268	+	23.7458i	0.300273	+	1.12064i	0.936938	+	0.349495i	$0.113647\pi$
$449$	6.36268	+	23.7458i	0.300273	+	1.12064i	−0.636665	+	0.771141i	$0.719687\pi$
$450$	−7.15442	−	2.18712i	−0.337263	−	0.103102i
$451$	−6.38188	+	11.0537i	−0.300511	+	0.520501i
$452$	−12.2044	−	21.1387i	−0.574048	−	0.994281i
$453$	−11.2623	−	11.6622i	−0.529150	−	0.547936i
$454$			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
$459$	16.7009	−	25.7193i	0.779529	−	1.20047i
$460$	12.4892	−	12.4892i	0.582312	−	0.582312i
$461$	−11.9685	+	3.20695i	−0.557429	+	0.149363i	−0.526525	−	0.850160i	$-0.676505\pi$
$461$	−11.9685	+	3.20695i	−0.557429	+	0.149363i	−0.0309044	+	0.999522i	$0.509839\pi$
$462$	−0.366643	+	1.27870i	−0.0170578	+	0.0594905i
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	0.850339	−	0.526236i	$-0.176397\pi$
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	−0.526236	+	0.850339i	$0.676397\pi$
$464$	7.60980	+	4.39352i	0.353276	+	0.203964i
$465$	−27.4469	−	0.478725i	−1.27282	−	0.0222003i
$466$	1.65612	−	6.18074i	0.0767185	−	0.286317i
$467$	9.19934			0.425695			0.212847	−	0.977085i	$-0.431726\pi$
$467$	9.19934			0.425695			0.212847	+	0.977085i	$0.431726\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	1.00054	−	3.73407i	0.0461515	−	0.172240i
$471$	−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
$474$	0.185095	−	0.645534i	0.00850168	−	0.0296504i
$475$	−33.6732	+	9.02270i	−1.54503	+	0.413990i
$476$	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
$479$	22.1676	+	5.93980i	1.01287	+	0.271396i	0.726826	−	0.686821i	$-0.240995\pi$
$479$	22.1676	+	5.93980i	1.01287	+	0.271396i	0.286039	+	0.958218i	$0.407661\pi$
$480$	−20.0412	−	12.0416i	−0.914750	−	0.549621i
$481$		0			0
$482$		−	9.75464i		−	0.444312i
$483$	3.78840	+	3.92289i	0.172378	+	0.178498i
$484$	−7.01850	−	12.1564i	−0.319023	−	0.552563i
$485$	21.3148	−	36.9183i	0.967854	−	1.67637i
$486$	1.87874	−	5.16285i	0.0852213	−	0.234192i
$487$	−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
$489$	5.80879	−	1.44838i	0.262682	−	0.0654978i
$490$	−3.45975	+	5.99247i	−0.156296	+	0.270712i
$491$	−7.66195	−	13.2709i	−0.345779	−	0.598907i	0.639716	−	0.768611i	$-0.279052\pi$
$491$	−7.66195	−	13.2709i	−0.345779	−	0.598907i	−0.985495	+	0.169705i	$0.945719\pi$
$492$	15.9067	−	15.3614i	0.717131	−	0.692544i
$493$			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
$498$	3.46514	−	1.92082i	0.155277	−	0.0860739i
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.410004	−	0.912084i	$-0.365527\pi$
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.912084	−	0.410004i	$-0.134473\pi$
$500$	13.0684	−	3.50168i	0.584439	−	0.156600i
$501$	8.72985	+	2.50312i	0.390021	+	0.111831i
$502$	−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
$505$	−9.97931	+	37.2433i	−0.444073	+	1.65730i
$506$	−1.79091			−0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	11.4648	−	42.7871i	0.508167	−	1.89651i	0.0701558	−	0.997536i	$-0.477650\pi$
$509$	11.4648	−	42.7871i	0.508167	−	1.89651i	0.438011	−	0.898969i	$-0.355683\pi$
$510$	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
$513$	−5.32377	−	25.0415i	−0.235050	−	1.10561i
$514$	2.31958	−	0.621529i	0.102312	−	0.0274145i
$515$	−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
$518$	−0.854741	−	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	$-0.986513\pi$
$521$		−	1.93372i		−	0.0847179i	0.999102	−	0.0423590i	$-0.0134873\pi$
$522$	0.639186	+	2.76829i	0.0279764	+	0.121165i
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	0.849091	−	0.528246i	$-0.177150\pi$
$523$	−0.753051	−	1.30432i	−0.0329286	−	0.0570340i	−0.882020	+	0.471212i	$0.843817\pi$
$524$	17.3904	−	30.1211i	0.759705	−	1.31585i
$525$	3.44529	+	13.8175i	0.150365	+	0.603047i
$526$	−2.06445	−	7.70463i	−0.0900142	−	0.335938i
$527$	−6.96651	−	25.9994i	−0.303466	−	1.13255i
$528$	−2.56976	−	10.3062i	−0.111835	−	0.448519i
$529$	7.82890	−	13.5601i	0.340387	−	0.589568i
$530$	1.50726	+	2.61066i	0.0654714	+	0.113400i
$531$	6.75455	+	29.2537i	0.293123	+	1.26950i
$532$		−	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
$537$	−3.66685	−	6.61497i	−0.158236	−	0.285457i
$538$	−6.50526	+	6.50526i	−0.280462	+	0.280462i
$539$	−10.2340	+	2.74218i	−0.440808	+	0.118114i
$540$	7.04334	+	33.1299i	0.303097	+	1.42568i
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	0.649844	−	0.760068i	$-0.274834\pi$
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	−0.760068	+	0.649844i	$0.774834\pi$
$542$	5.39710	+	3.11602i	0.231825	+	0.133844i
$543$	0.0636546	−	3.64953i	0.00273168	−	0.156616i
$544$	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
$549$	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
$552$	6.16264	+	1.76702i	0.262299	+	0.0752094i
$553$	−1.23473	+	0.330846i	−0.0525062	+	0.0140690i
$554$	−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
$557$	−3.45636	−	0.926129i	−0.146451	−	0.0392414i	0.184849	−	0.982767i	$-0.440820\pi$
$557$	−3.45636	−	0.926129i	−0.146451	−	0.0392414i	−0.331300	+	0.943526i	$0.607487\pi$
$558$	−2.26406	−	4.25780i	−0.0958451	−	0.180247i
$559$		0			0
$560$			13.2045i			0.557994i
$561$	13.7890	−	13.3163i	0.582173	−	0.562213i
$562$	2.13267	+	3.69389i	0.0899611	+	0.155817i
$563$	−9.83710	+	17.0384i	−0.414585	+	0.718081i	−0.995385	−	0.0959647i	$-0.969406\pi$
$563$	−9.83710	+	17.0384i	−0.414585	+	0.718081i	0.580800	+	0.814046i	$0.302740\pi$
$564$	−9.95039	+	2.48105i	−0.418987	+	0.104471i
$565$	11.7035	+	43.6781i	0.492370	+	1.83755i
$566$	0.648166	+	2.41899i	0.0272445	+	0.101678i
$567$	−10.2657	+	1.99601i	−0.431119	+	0.0838247i
$568$	−7.92766	+	13.7311i	−0.332637	+	0.576145i
$569$	4.78231	+	8.28321i	0.200485	+	0.347250i	0.948685	−	0.316223i	$-0.102415\pi$
$569$	4.78231	+	8.28321i	0.200485	+	0.347250i	−0.748200	+	0.663473i	$0.769082\pi$
$570$	−7.26039	−	7.51816i	−0.304104	−	0.314901i
$571$			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
$576$	−0.541005	+	15.5041i	−0.0225419	+	0.646004i
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	−0.827243	−	0.561844i	$-0.810092\pi$
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	0.561844	+	0.827243i	$0.310092\pi$
$578$	6.06984	−	1.62641i	0.252472	−	0.0676497i
$579$	5.30684	−	18.5081i	0.220545	−	0.769169i
$580$	−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
$583$	−1.19465	+	4.45849i	−0.0494773	+	0.184652i
$584$	17.6425			0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	−8.12231	+	30.3129i	−0.335243	+	1.25115i	0.568362	+	0.822779i	$0.307577\pi$
$587$	−8.12231	+	30.3129i	−0.335243	+	1.25115i	−0.903605	+	0.428367i	$0.859089\pi$
$588$	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
$591$	1.09030	−	3.80251i	0.0448489	−	0.156414i
$592$	6.82503	−	1.82876i	0.280507	−	0.0751616i
$593$	23.7211	−	23.7211i	0.974108	−	0.974108i	−0.0255650	−	0.999673i	$-0.508138\pi$
$593$	23.7211	−	23.7211i	0.974108	−	0.974108i	0.999673	+	0.0255650i	$0.00813848\pi$
$594$	1.87036	−	2.88034i	0.0767416	−	0.118182i
$595$	−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	$0.242540\pi$
$599$			33.7915i			1.38068i	−0.723484	+	0.690341i	$0.757460\pi$
$600$	11.6292	+	12.0421i	0.474761	+	0.491617i
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	0.990404	+	0.138202i	$0.0441323\pi$
$601$	15.0742	+	26.1092i	0.614888	+	1.06502i	−0.375516	+	0.926816i	$0.622534\pi$
$602$	1.13672	−	1.96886i	0.0463292	−	0.0802446i
$603$	−19.5188	−	5.96693i	−0.794867	−	0.242992i
$604$	4.54432	+	16.9596i	0.184906	+	0.690077i
$605$	6.73042	+	25.1183i	0.273630	+	1.02120i
$606$	−6.57209	+	1.63870i	−0.266973	+	0.0665676i
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	−0.998208	−	0.0598403i	$-0.980941\pi$
$607$	−11.0198	+	19.0869i	−0.447281	+	0.774713i	0.550927	+	0.834553i	$0.314274\pi$
$608$	−9.56943	−	16.5747i	−0.388092	−	0.672195i
$609$	3.89020	−	3.75682i	0.157639	−	0.152234i
$610$		−	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
$615$	−35.8295	+	19.8612i	−1.44478	+	0.800882i
$616$	2.10479	−	2.10479i	0.0848044	−	0.0848044i
$617$	28.0800	−	7.52400i	1.13046	−	0.302905i	0.355349	−	0.934734i	$-0.384362\pi$
$617$	28.0800	−	7.52400i	1.13046	−	0.302905i	0.775108	+	0.631829i	$0.217695\pi$
$618$	−2.60122	−	0.745851i	−0.104637	−	0.0300025i
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	0.996727	−	0.0808459i	$-0.0257622\pi$
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	−0.0808459	+	0.996727i	$0.525762\pi$
$620$	25.7461	+	14.8645i	1.03399	+	0.596974i
$621$	−6.39257	−	12.5449i	−0.256525	−	0.503409i
$622$	−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
$627$	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
$630$	−3.12239	+	2.91183i	−0.124399	+	0.116010i
$631$	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
$633$	−6.72395	−	12.1300i	−0.267253	−	0.482122i
$634$	−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
$639$	33.9287	−	7.83401i	1.34220	−	0.309909i
$640$	16.6654	+	28.8653i	0.658758	+	1.14100i
$641$	−12.8560	+	22.2673i	−0.507783	+	0.879506i	0.492176	+	0.870496i	$0.336202\pi$
$641$	−12.8560	+	22.2673i	−0.507783	+	0.879506i	−0.999959	+	0.00901077i	$0.997132\pi$
$642$	−1.92814	−	7.73291i	−0.0760976	−	0.305194i
$643$	−0.164018	−	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
$645$	8.08354	+	32.4195i	0.318289	+	1.27652i
$646$	5.12404	−	8.87510i	0.201603	−	0.349186i
$647$	23.5124	+	40.7247i	0.924368	+	1.60105i	0.792574	+	0.609776i	$0.208740\pi$
$647$	23.5124	+	40.7247i	0.924368	+	1.60105i	0.131794	+	0.991277i	$0.457926\pi$
$648$	−9.27796	+	8.06607i	−0.364473	+	0.316865i
$649$			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	0.0791154	−	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
$656$	−21.4990	+	5.76064i	−0.839394	+	0.224915i
$657$	−26.4258	−	28.3367i	−1.03097	−	1.10552i
$658$	−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
$661$	−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
$666$	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
$669$	−47.1426	−	13.5172i	−1.82264	−	0.522607i
$670$	−8.04861	+	2.15662i	−0.310945	+	0.0833174i
$671$	3.53081	−	3.53081i	0.136306	−	0.136306i
$672$	−6.83786	+	3.79040i	−0.263776	+	0.146218i
$673$	22.6855	−	13.0975i	0.874460	−	0.504870i	0.00563228	−	0.999984i	$-0.498207\pi$
$673$	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	$-0.861534\pi$
$677$		−	21.9298i		−	0.842829i	0.906868	−	0.421415i	$-0.138466\pi$
$678$	−5.71406	+	5.51815i	−0.219447	+	0.211923i
$679$	−7.12739	−	12.3450i	−0.273524	−	0.473758i
$680$	−14.0071	+	24.2610i	−0.537149	+	0.930369i
$681$	−12.3611	+	3.08213i	−0.473677	+	0.118108i
$682$	−0.780190	−	2.91171i	−0.0298750	−	0.111495i
$683$	1.97300	+	7.36335i	0.0754949	+	0.281751i	0.993345	−	0.115176i	$-0.0367433\pi$
$683$	1.97300	+	7.36335i	0.0754949	+	0.281751i	−0.917850	+	0.396927i	$0.870077\pi$
$684$	−8.10549	+	26.5144i	−0.309921	+	1.01380i
$685$	13.0918	−	22.6757i	0.500212	−	0.866392i
$686$	2.59028	+	4.48650i	0.0988975	+	0.171296i
$687$	−19.4139	−	20.1032i	−0.740688	−	0.766985i
$688$			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
$693$	−6.53327	−	0.227974i	−0.248179	−	0.00866003i
$694$	−2.75978	+	2.75978i	−0.104760	+	0.104760i
$695$	−18.0998	+	4.84983i	−0.686565	+	0.183965i
$696$	1.75229	−	6.11128i	0.0664205	−	0.231647i
$697$	−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
$700$	3.99159	−	14.8968i	0.150868	−	0.563047i
$701$	−30.3059			−1.14464			−0.572319	−	0.820031i	$-0.693956\pi$
$701$	−30.3059			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	−2.50989	+	9.36704i	−0.0945951	+	0.353034i
$705$	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
$708$	8.96188	−	31.2553i	0.336808	−	1.17465i
$709$	−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
$711$	3.29824	+	0.115090i	0.123694	+	0.00431620i
$712$	−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
$717$	11.1328	+	11.5281i	0.415762	+	0.430523i
$718$	−5.08050	−	8.79968i	−0.189602	−	0.328401i
$719$	3.94839	−	6.83882i	0.147250	−	0.255045i	−0.782960	−	0.622072i	$-0.786291\pi$
$719$	3.94839	−	6.83882i	0.147250	−	0.255045i	0.930210	+	0.367027i	$0.119624\pi$
$720$	9.96640	−	32.6017i	0.371426	−	1.21499i
$721$	1.33316	+	4.97544i	0.0496496	+	0.185295i
$722$	−0.481159	−	1.79571i	−0.0179069	−	0.0668294i
$723$	46.5140	−	11.5979i	1.72988	−	0.431331i
$724$	−1.97649	+	3.42339i	−0.0734558	+	0.127229i
$725$	9.50629	+	16.4654i	0.353055	+	0.611509i
$726$	−3.28603	+	3.17336i	−0.121956	+	0.117775i
$727$			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
$732$	−7.56623	+	4.19416i	−0.279656	+	0.155021i
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.321476	−	0.946918i	$-0.395821\pi$
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.946918	−	0.321476i	$-0.104179\pi$
$734$	−7.87731	+	2.11072i	−0.290757	+	0.0779081i
$735$	−32.6880	−	9.37267i	−1.20572	−	0.345716i
$736$	−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
$739$	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	$0.488740\pi$
$743$	−13.4913	+	50.3503i	−0.494949	+	1.84717i	−0.530316	+	0.847800i	$0.677927\pi$
$744$	−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
$747$	13.2792	+	14.2394i	0.485859	+	0.520992i
$748$	−20.0526	+	5.37308i	−0.733195	+	0.196459i
$749$	−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	$0.690197\pi$
$751$	−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
$756$	10.7716	+	3.49944i	0.391760	+	0.127273i
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	0.642255	−	0.766491i	$-0.277999\pi$
$757$	−9.42818	−	16.3301i	−0.342673	−	0.593527i	−0.984928	+	0.172964i	$0.944666\pi$
$758$	0.699838	−	1.21216i	0.0254193	−	0.0440275i
$759$	−2.12932	−	8.53976i	−0.0772895	−	0.309974i
$760$	6.05310	+	22.5905i	0.219569	+	0.819443i
$761$	−9.96144	−	37.1766i	−0.361102	−	1.34765i	−0.872629	−	0.488384i	$-0.837587\pi$
$761$	−9.96144	−	37.1766i	−0.361102	−	1.34765i	0.511527	−	0.859267i	$-0.329080\pi$
$762$	1.15109	+	4.61653i	0.0416997	+	0.167239i
$763$	−3.68783	+	6.38751i	−0.133508	+	0.231243i
$764$	6.37559	+	11.0428i	0.230661	+	0.399516i
$765$	59.9476	−	13.8417i	2.16741	−	0.500446i
$766$			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
$771$	5.72160	+	10.3217i	0.206058	+	0.371727i
$772$	−14.7443	+	14.7443i	−0.530660	+	0.530660i
$773$	−6.20770	+	1.66335i	−0.223275	+	0.0598265i	−0.368722	−	0.929540i	$-0.620205\pi$
$773$	−6.20770	+	1.66335i	−0.223275	+	0.0598265i	0.145447	+	0.989366i	$0.453538\pi$

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

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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