LMFDB - Embedded newform 507.2.k.k.80.13

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			80.13
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0912193 - 0.340435i) q^{2} +(-1.73179 - 0.0302056i) q^{3} +(1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.168255 + 0.586806i) q^{6} +(1.12240 - 0.300747i) q^{7} +(0.965906 - 0.965906i) q^{8} +(2.99818 + 0.104619i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 96 * q + 24 * q^9	$ 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

Display 100 coefficients 10 coefficients

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	$0.0435660\pi$
$3$	−1.73179	−	0.0302056i	−0.999848	−	0.0174392i
$3$	−1.73179	−	0.0302056i	−0.999848	−	0.0174392i
$4$	1.62448	+	0.937892i	0.812238	+	0.468946i
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.994541	+	0.104350i	$0.0332761\pi$
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.104350	+	0.994541i	$0.466724\pi$
$6$	−0.168255	+	0.586806i	−0.0686900	+	0.239562i
$7$	1.12240	−	0.300747i	0.424228	−	0.113672i	−0.0403875	−	0.999184i	$-0.512859\pi$
$7$	1.12240	−	0.300747i	0.424228	−	0.113672i	0.464615	+	0.885513i	$0.346193\pi$
$8$	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	−0.0248176	−	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
$15$	−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	$-0.892148\pi$
$19$	−1.27519	−	4.75906i	−0.292548	−	1.09180i	0.650598	−	0.759423i	$-0.274518\pi$
$20$	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	−0.355463	−	0.934690i	$-0.615677\pi$
$31$	3.22500	−	3.22500i	0.579227	−	0.579227i	0.934690	+	0.355463i	$0.115677\pi$
$32$	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	−0.996537	−	0.0831470i	$-0.973503\pi$
$37$	−0.559232	+	2.08708i	−0.0919372	+	0.343114i	0.904600	+	0.426261i	$0.140170\pi$
$38$	−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	$-0.0950309\pi$
$42$	−0.0123704	+	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	−0.850895	−	0.525336i	$-0.823940\pi$
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	0.525336	+	0.850895i	$0.323940\pi$
$48$	−2.74604	−	4.95383i	−0.396357	−	0.715024i
$49$	−4.89284	+	2.82488i	−0.698977	+	0.403555i
$50$	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	$-0.857494\pi$
$59$	−2.59020	−	9.66677i	−0.337216	−	1.25851i	0.564231	−	0.825617i	$-0.309173\pi$
$60$	−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	0.636838	−	0.770998i	$-0.280242\pi$
$67$	6.57167	+	1.76087i	0.802857	+	0.215125i	0.166019	+	0.986123i	$0.446909\pi$
$68$	−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	−0.852930	−	0.522025i	$-0.825177\pi$
$71$	−11.2116	+	3.00415i	−1.33058	+	0.356527i	−0.477647	+	0.878552i	$0.658510\pi$
$72$	2.99701	−	2.79490i	0.353201	−	0.329383i
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.997444	+	0.0714492i	$0.0227624\pi$
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.0714492	+	0.997444i	$0.477238\pi$
$74$	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	0.408864	−	0.912596i	$-0.365925\pi$
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	−0.912596	+	0.408864i	$0.865925\pi$
$84$	−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	0.0332896	−	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
$93$	−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	$-0.869333\pi$
$97$	−3.17506	−	11.8495i	−0.322379	−	1.20313i	0.594542	−	0.804065i	$-0.297333\pi$
$98$	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	−0.888594	−	0.458694i	$-0.848318\pi$
$109$	−4.48829	+	4.48829i	−0.429901	+	0.429901i	0.458694	+	0.888594i	$0.348318\pi$
$110$	−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	$-0.979021\pi$
$137$	−1.95016	−	7.27811i	−0.166614	−	0.621811i	0.831215	−	0.555951i	$-0.187646\pi$
$138$	−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	0.810457	−	0.585798i	$-0.199219\pi$
$149$	22.0357	−	5.90444i	1.80523	−	0.483710i	0.994775	+	0.102088i	$0.0325523\pi$
$150$	−4.15200	−	1.19051i	−0.339010	−	0.0972046i
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	0.384500	−	0.923125i	$-0.374374\pi$
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	−0.923125	+	0.384500i	$0.874374\pi$
$152$	−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	−0.125687	−	0.992070i	$-0.540113\pi$
$163$	3.33861	−	0.894579i	0.261500	−	0.0700688i	0.387187	+	0.922001i	$0.373447\pi$
$164$	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	0.449393	−	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
$171$	−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	$-0.785648\pi$
$193$	2.87709	−	10.7374i	0.207098	−	0.772898i	0.988800	−	0.149247i	$-0.0476849\pi$
$194$	−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	$0.0574074\pi$
$198$	−1.05069	+	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	−0.833393	−	0.552680i	$-0.813605\pi$
$223$	−27.3497	−	7.32834i	−1.83147	−	0.490742i	−0.998080	+	0.0619383i	$0.980272\pi$
$224$	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	−0.486763	−	0.873534i	$-0.661823\pi$
$227$	−7.10455	+	1.90366i	−0.471546	+	0.126350i	0.0152176	+	0.999884i	$0.495156\pi$
$228$	−4.41203	+	15.3874i	−0.292194	+	1.01905i
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	0.221263	−	0.975214i	$-0.428982\pi$
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	−0.975214	+	0.221263i	$0.928982\pi$
$230$	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	0.886306	−	0.463099i	$-0.153263\pi$
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	−0.463099	+	0.886306i	$0.653263\pi$
$240$	5.42498	−	18.9201i	0.350181	−	1.22129i
$241$	26.7340	−	7.16336i	1.72209	−	0.461433i	0.743754	−	0.668453i	$-0.233043\pi$
$241$	26.7340	−	7.16336i	1.72209	−	0.461433i	0.978337	+	0.207021i	$0.0663767\pi$
$242$	−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	$0.263799\pi$
$271$	−4.57652	+	17.0798i	−0.278004	+	1.03753i	−0.953801	+	0.300438i	$0.902867\pi$
$272$	−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	−0.914679	−	0.404181i	$-0.867557\pi$
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	0.404181	+	0.914679i	$0.367557\pi$
$282$	−0.934172	−	1.68524i	−0.0556291	−	0.100354i
$283$	6.15361	−	3.55279i	0.365794	−	0.211192i	−0.305825	−	0.952088i	$-0.598932\pi$
$283$	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	$0.0703596\pi$
$293$	4.11392	+	15.3534i	0.240338	+	0.896953i	−0.735332	+	0.677707i	$0.762974\pi$
$294$	−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	0.165277	−	0.986247i	$-0.447148\pi$
$307$	−14.3846	−	14.3846i	−0.820970	−	0.820970i	−0.986247	+	0.165277i	$0.947148\pi$
$308$	−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	0.507901	−	0.861416i	$-0.330422\pi$
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	−0.861416	+	0.507901i	$0.830422\pi$
$318$	−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	$0.0623356\pi$
$331$	4.16094	+	15.5288i	0.228706	+	0.853541i	−0.752180	+	0.658958i	$0.770998\pi$
$332$	−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	$0.378883\pi$
$349$	−7.74319	+	28.8980i	−0.414483	+	1.54687i	−0.785868	+	0.618394i	$0.787784\pi$
$350$	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	$0.973806\pi$
$354$	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	$-0.474808\pi$
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.996870	−	0.0790589i	$-0.0251915\pi$
$360$	14.2318	+	0.496611i	0.750084	+	0.0261737i
$361$	−4.56807	+	2.63738i	−0.240425	+	0.138809i
$362$	0.717426	+	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	0.355991	−	0.934489i	$-0.384143\pi$
$379$	3.83602	+	1.02786i	0.197043	+	0.0527975i	−0.158948	+	0.987287i	$0.550810\pi$
$380$	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	−0.846515	−	0.532365i	$-0.821303\pi$
$383$	−25.7044	+	6.88748i	−1.31344	+	0.351934i	−0.466921	+	0.884299i	$0.654637\pi$
$384$	−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	−0.785659	−	0.618660i	$-0.787676\pi$
$397$	−23.0477	+	6.17560i	−1.15673	+	0.309945i	−0.371071	+	0.928605i	$0.621009\pi$
$398$	−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	0.770539	−	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
$405$	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	$-0.982759\pi$
$409$	−3.25292	−	12.1401i	−0.160847	−	0.600288i	0.837687	−	0.546151i	$-0.183907\pi$
$410$	−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	−0.455040	−	0.890471i	$-0.650375\pi$
$421$	8.93430	−	8.93430i	0.435431	−	0.435431i	0.890471	+	0.455040i	$0.150375\pi$
$422$	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	$0.254136\pi$
$431$	−5.49370	+	20.5028i	−0.264622	+	0.987583i	−0.962481	+	0.271348i	$0.912531\pi$
$432$	−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	$-0.886353\pi$
$449$	−6.36268	−	23.7458i	−0.300273	−	1.12064i	0.636665	−	0.771141i	$-0.280313\pi$
$450$	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	0.102632	−	0.994719i	$-0.467274\pi$
$457$	−6.53825	−	1.75192i	−0.305847	−	0.0819513i	−0.408478	+	0.912768i	$0.633940\pi$
$458$	−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	0.0309044	−	0.999522i	$-0.490161\pi$
$461$	11.9685	−	3.20695i	0.557429	−	0.149363i	0.526525	+	0.850160i	$0.323495\pi$
$462$	0.366643	−	1.27870i	0.0170578	−	0.0594905i
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	0.526236	−	0.850339i	$-0.323603\pi$
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	−0.850339	+	0.526236i	$0.823603\pi$
$464$	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	−0.286039	−	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
$483$	−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	$0.149388\pi$
$487$	7.62733	+	28.4656i	0.345627	+	1.28990i	−0.546250	+	0.837622i	$0.683945\pi$
$488$	−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	$0.634473\pi$
$499$	−29.5332	+	29.5332i	−1.32209	+	1.32209i	−0.912084	+	0.410004i	$0.865527\pi$
$500$	−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	$0.522350\pi$
$509$	−11.4648	+	42.7871i	−0.508167	+	1.89651i	−0.438011	+	0.898969i	$0.644317\pi$
$510$	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	0.760068	−	0.649844i	$-0.225166\pi$
$541$	2.56375	+	2.56375i	0.110224	+	0.110224i	−0.649844	+	0.760068i	$0.725166\pi$
$542$	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	0.331300	−	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
$561$	−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	−0.561844	−	0.827243i	$-0.689908\pi$
$577$	6.37509	−	6.37509i	0.265398	−	0.265398i	0.827243	+	0.561844i	$0.189908\pi$
$578$	−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	$-0.692423\pi$
$587$	8.12231	−	30.3129i	0.335243	−	1.25115i	0.903605	−	0.428367i	$-0.140911\pi$
$588$	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	−0.999673	−	0.0255650i	$-0.991862\pi$
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	0.0255650	+	0.999673i	$0.491862\pi$
$594$	1.87036	−	2.88034i	0.0767416	−	0.118182i
$595$	−20.6378	+	11.9153i	−0.846069	+	0.488478i
$596$	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	0.270337	−	0.962766i	$-0.412865\pi$
$613$	0.571244	+	0.153064i	0.0230723	+	0.00618221i	−0.247264	+	0.968948i	$0.579532\pi$
$614$	−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	−0.775108	−	0.631829i	$-0.782305\pi$
$617$	−28.0800	+	7.52400i	−1.13046	+	0.302905i	−0.355349	+	0.934734i	$0.615638\pi$
$618$	2.60122	+	0.745851i	0.104637	+	0.0300025i
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	0.0808459	−	0.996727i	$-0.474238\pi$
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	−0.996727	+	0.0808459i	$0.974238\pi$
$620$	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	−0.932751	−	0.360521i	$-0.882599\pi$
$631$	−39.1937	+	10.5019i	−1.56028	+	0.418075i	−0.627526	+	0.778596i	$0.715932\pi$
$632$	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	0.969085	−	0.246729i	$-0.0793557\pi$
$643$	0.164018	+	0.612124i	0.00646824	+	0.0241398i	−0.962616	+	0.270869i	$0.912689\pi$
$644$	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	−0.922132	−	0.386876i	$-0.873554\pi$
$661$	1.79701	−	6.70655i	0.0698957	−	0.260854i	0.992028	+	0.126021i	$0.0402208\pi$
$662$	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	0.917850	−	0.396927i	$-0.129923\pi$
$683$	−1.97300	−	7.36335i	−0.0754949	−	0.281751i	−0.993345	+	0.115176i	$0.963257\pi$
$684$	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	−0.0464729	−	0.998920i	$-0.514798\pi$
$691$	−15.4088	−	4.12878i	−0.586179	−	0.157066i	−0.539707	+	0.841853i	$0.681465\pi$
$692$	−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	0.417717	−	0.908577i	$-0.362830\pi$
$709$	32.8514	−	8.80249i	1.23376	−	0.330585i	0.816042	+	0.577993i	$0.196164\pi$
$710$	−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	$0.604179\pi$
$733$	−34.3405	+	34.3405i	−1.26839	+	1.26839i	−0.946918	+	0.321476i	$0.895821\pi$
$734$	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	$0.336705\pi$
$739$	−10.0551	+	37.5261i	−0.369882	+	1.38042i	−0.860680	+	0.509146i	$0.829961\pi$
$740$	−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	$-0.322073\pi$
$744$	−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	$0.162413\pi$
$761$	9.96144	+	37.1766i	0.361102	+	1.34765i	−0.511527	+	0.859267i	$0.670920\pi$
$762$	−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	0.208778	−	0.977963i	$-0.433051\pi$
$769$	−2.75634	−	0.738559i	−0.0993962	−	0.0266331i	−0.308174	+	0.951330i	$0.599718\pi$
$770$	−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	−0.145447	−	0.989366i	$-0.546462\pi$
$773$	6.20770	−	1.66335i	0.223275	−	0.0598265i	0.368722	+	0.929540i	$0.379795\pi$
$774$	4.29256	−	4.00309i	0.154293	−	0.143888i
$775$	22.8188	+	22.8188i	0.819675	+	0.819675i
$776$	−14.5123	−	8.37869i	−0.520962	−	0.300777i
$777$	0.0758381	−	4.34805i	0.00272068	−	0.155986i
$778$	0.563129	−	2.10162i	0.0201891	−	0.0753469i
$779$	−33.5341			−1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	−1.45873	+	5.44405i	−0.0521640	+	0.194679i
$783$	−12.4403	+	6.33929i	−0.444581	+	0.226548i
$784$	−16.0002	−	9.23773i	−0.571436	−	0.329919i
$785$	38.5251	+	38.5251i	1.37502	+	1.37502i
$786$	10.8806	+	3.11980i	0.388098	+	0.111280i
$787$	−14.6513	+	3.92580i	−0.522262	+	0.139940i	−0.510313	−	0.859989i	$-0.670470\pi$
$787$	−14.6513	+	3.92580i	−0.522262	+	0.139940i	−0.0119493	+	0.999929i	$0.503804\pi$
$788$	3.02924	−	3.02924i	0.107912	−	0.107912i
$789$	34.2842	−	19.0046i	1.22055	−	0.676583i
$790$	1.16681	−	0.673658i	0.0415132	−	0.0239677i
$791$	−14.6054	−	3.91350i	−0.519308	−	0.139148i
$792$	−6.78531	+	3.60804i	−0.241105	+	0.128206i
$793$		0			0
$794$			8.40957i			0.298444i
$795$	10.6566	−	10.2912i	0.377950	−	0.364992i
$796$	−17.2039	−	29.7980i	−0.609775	−	1.05616i
$797$	−0.789625	+	1.36767i	−0.0279700	+	0.0484454i	−0.879672	−	0.475582i	$-0.842238\pi$
$797$	−0.789625	+	1.36767i	−0.0279700	+	0.0484454i	0.851702	+	0.524027i	$0.175571\pi$
$798$	3.39106	−	0.845534i	0.120042	−	0.0299316i
$799$	−4.82131	−	17.9934i	−0.170566	−	0.636560i
$800$	7.11374	+	26.5489i	0.251509	+	0.938644i
$801$	−12.2618	−	3.74845i	−0.433248	−	0.132445i
$802$	4.08862	−	7.08170i	0.144374	−	0.250063i
$803$	−12.1102	−	20.9754i	−0.427359	−	0.740207i
$804$	−15.3551	−	15.9002i	−0.541532	−	0.560758i
$805$			10.9414i			0.385633i
$806$		0			0
$807$	−38.7542	−	23.2852i	−1.36421	−	0.819677i
$808$	−14.6401	−	3.92280i	−0.515037	−	0.138004i
$809$	10.5758	−	6.10595i	0.371826	−	0.214674i	−0.302430	−	0.953172i	$-0.597798\pi$
$809$	10.5758	−	6.10595i	0.371826	−	0.214674i	0.674256	+	0.738498i	$0.264464\pi$
$810$	9.90687	−	4.83255i	0.348092	−	0.169798i
$811$	29.6037	−	29.6037i	1.03952	−	1.03952i	0.0403387	−	0.999186i	$-0.487156\pi$
$811$	29.6037	−	29.6037i	1.03952	−	1.03952i	0.999186	−	0.0403387i	$-0.0128437\pi$
$812$	5.65729	−	1.51587i	0.198532	−	0.0531965i
$813$	8.44147	−	29.4404i	0.296055	−	1.03252i
$814$	−1.00981	−	1.00981i	−0.0353939	−	0.0353939i
$815$	10.4018	+	6.00546i	0.364358	+	0.210362i
$816$	33.4221	+	0.582944i	1.17001	+	0.0204071i
$817$	7.07884	−	26.4186i	0.247657	−	0.924269i
$818$	−4.42964			−0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	−4.81637	+	17.9749i	−0.168093	+	0.627330i	0.829533	+	0.558458i	$0.188607\pi$
$821$	−4.81637	+	17.9749i	−0.168093	+	0.627330i	−0.997625	+	0.0688721i	$0.978060\pi$
$822$	4.59896	+	0.0802145i	0.160407	+	0.00279780i
$823$	−0.447230	−	0.258209i	−0.0155895	−	0.00900059i	0.492185	−	0.870491i	$-0.336198\pi$
$823$	−0.447230	−	0.258209i	−0.0155895	−	0.00900059i	−0.507774	+	0.861490i	$0.669532\pi$
$824$	−4.28172	−	4.28172i	−0.149161	−	0.149161i
$825$	−6.33448	+	22.0921i	−0.220538	+	0.769147i
$826$	−3.95892	+	1.06079i	−0.137748	+	0.0369096i
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	−0.238472	−	0.971149i	$-0.576646\pi$
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	0.971149	+	0.238472i	$0.0766464\pi$
$828$	−0.531750	+	15.2389i	−0.0184796	+	0.529587i
$829$	1.46119	−	0.843616i	0.0507491	−	0.0293000i	−0.474411	−	0.880304i	$-0.657339\pi$
$829$	1.46119	−	0.843616i	0.0507491	−	0.0293000i	0.525160	+	0.851004i	$0.324006\pi$
$830$	−7.67790	−	2.05729i	−0.266504	−	0.0714094i
$831$	−33.7030	−	20.2502i	−1.16914	−	0.702471i
$832$		0			0
$833$		−	33.3430i		−	1.15527i
$834$	2.28667	+	2.36786i	0.0791811	+	0.0819922i
$835$	9.11018	+	15.7793i	0.315271	+	0.546065i
$836$	−8.66562	+	15.0093i	−0.299707	+	0.519107i
$837$	−17.6110	+	15.8583i	−0.608726	+	0.548143i
$838$	−2.44549	−	9.12670i	−0.0844781	−	0.315277i
$839$	2.80444	+	10.4663i	0.0968199	+	0.361337i	0.997289	−	0.0735829i	$-0.0234434\pi$
$839$	2.80444	+	10.4663i	0.0968199	+	0.361337i	−0.900469	+	0.434920i	$0.856777\pi$
$840$	−9.26984	+	2.31136i	−0.319840	+	0.0797495i
$841$	−10.8898	+	18.8618i	−0.375512	+	0.650406i
$842$	−2.22657	−	3.85653i	−0.0767326	−	0.132905i
$843$	15.0783	−	14.5613i	0.519323	−	0.501518i
$844$			15.0198i			0.517004i
$845$		0			0
$846$	1.56688	+	2.94669i	0.0538706	+	0.101309i
$847$	−8.39923	−	2.25057i	−0.288601	−	0.0773304i
$848$	−6.97060	+	4.02448i	−0.239371	+	0.138201i
$849$	−10.7641	+	5.96681i	−0.369422	+	0.204780i
$850$	−10.4067	+	10.4067i	−0.356947	+	0.356947i
$851$	−5.65526	+	1.51532i	−0.193860	+	0.0519446i
$852$	36.2503	+	10.3941i	1.24192	+	0.356096i
$853$	30.1644	+	30.1644i	1.03281	+	1.03281i	0.999443	+	0.0333670i	$0.0106230\pi$
$853$	30.1644	+	30.1644i	1.03281	+	1.03281i	0.0333670	+	0.999443i	$0.489377\pi$
$854$	−0.944378	−	0.545237i	−0.0323160	−	0.0186576i
$855$	27.2173	−	43.5593i	0.930810	−	1.48970i
$856$	4.61568	−	17.2259i	0.157761	−	0.588771i
$857$	36.7949			1.25689			0.628444	−	0.777855i	$-0.283692\pi$
$857$	36.7949			1.25689			0.628444	+	0.777855i	$0.283692\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	−9.36529	+	34.9518i	−0.319354	+	1.19185i
$861$	−0.238892	+	13.6965i	−0.00814141	+	0.466774i
$862$	6.47872	+	3.74049i	0.220666	+	0.127402i
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	0.991931	−	0.126779i	$-0.0404637\pi$
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	−0.126779	+	0.991931i	$0.540464\pi$
$864$	−19.7434	+	4.19740i	−0.671683	+	0.142799i
$865$	−47.8355	+	12.8175i	−1.62646	+	0.435808i
$866$	−0.461976	+	0.461976i	−0.0156986	+	0.0156986i
$867$	14.9722	+	27.0097i	0.508482	+	0.917298i
$868$	8.60919	−	4.97052i	0.292215	−	0.168710i
$869$	−1.99268	−	0.533937i	−0.0675971	−	0.0181126i
$870$	−2.93571	+	4.88599i	−0.0995299	+	0.165651i
$871$		0			0
$872$			8.67054i			0.293622i
$873$	−8.27971	−	35.8590i	−0.280226	−	1.21364i
$874$	−2.35262	−	4.07485i	−0.0795784	−	0.137834i
$875$	−4.19056	+	7.25826i	−0.141667	+	0.245374i
$876$	−10.1520	−	40.7152i	−0.343005	−	1.37564i
$877$	−4.74247	−	17.6992i	−0.160142	−	0.597658i	−0.998610	−	0.0527071i	$-0.983215\pi$
$877$	−4.74247	−	17.6992i	−0.160142	−	0.597658i	0.838468	−	0.544951i	$-0.183452\pi$
$878$	−1.31404	−	4.90406i	−0.0443467	−	0.165504i
$879$	−6.66068	−	26.7130i	−0.224659	−	0.901007i
$880$	10.6551	−	18.4552i	0.359184	−	0.622125i
$881$	−15.5539	−	26.9401i	−0.524023	−	0.907635i	−0.999609	−	0.0279654i	$-0.991097\pi$
$881$	−15.5539	−	26.9401i	−0.524023	−	0.907635i	0.475586	−	0.879669i	$-0.342236\pi$
$882$	1.34394	+	5.82054i	0.0452528	+	0.195988i
$883$		−	9.56660i		−	0.321942i	−0.986959	−	0.160971i	$-0.948537\pi$
$883$		−	9.56660i		−	0.321942i	0.986959	−	0.160971i	$-0.0514625\pi$
$884$		0			0
$885$	−31.0229	+	51.6323i	−1.04282	+	1.73560i
$886$	−7.56891	−	2.02808i	−0.254282	−	0.0681348i
$887$	21.3515	−	12.3273i	0.716913	−	0.413910i	−0.0967027	−	0.995313i	$-0.530830\pi$
$887$	21.3515	−	12.3273i	0.716913	−	0.413910i	0.813615	+	0.581404i	$0.197496\pi$
$888$	−2.47849	−	4.47118i	−0.0831728	−	0.150043i
$889$	−6.40399	+	6.40399i	−0.214783	+	0.214783i
$890$	−5.05616	+	1.35479i	−0.169483	+	0.0454128i
$891$	−15.9584	−	5.49398i	−0.534627	−	0.184055i
$892$	−37.5558	−	37.5558i	−1.25746	−	1.25746i
$893$	13.4680	+	7.77574i	0.450688	+	0.260205i
$894$	−0.242862	+	13.9241i	−0.00812253	+	0.465692i
$895$	−3.92737	+	14.6571i	−0.131277	+	0.489934i
$896$	11.1454			0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	3.17189	−	11.8377i	0.105789	−	0.394808i
$900$	−21.0988	+	33.7672i	−0.703294	+	1.12557i
$901$	−12.5800	−	7.26306i	−0.419100	−	0.241967i
$902$	3.18093	+	3.18093i	0.105913	+	0.105913i
$903$	−10.7398	−	3.07944i	−0.357399	−	0.102477i
$904$	−17.1696	+	4.60057i	−0.571051	+	0.153013i
$905$	−5.17824	+	5.17824i	−0.172130	+	0.172130i
$906$	4.99755	−	2.77027i	0.166032	−	0.0920362i
$907$	−1.45939	+	0.842581i	−0.0484584	+	0.0279775i	−0.524033	−	0.851698i	$-0.675573\pi$
$907$	−1.45939	+	0.842581i	−0.0484584	+	0.0279775i	0.475575	+	0.879675i	$0.342240\pi$
$908$	−13.3266	−	3.57085i	−0.442259	−	0.118503i
$909$	−15.6280	−	29.3900i	−0.518346	−	0.974806i
$910$		0			0
$911$			43.9421i			1.45587i	0.685648	+	0.727933i	$0.259519\pi$
$911$			43.9421i			1.45587i	−0.685648	+	0.727933i	$0.740481\pi$
$912$	−20.0739	+	19.3856i	−0.664713	+	0.641922i
$913$	6.08545	+	10.5403i	0.201399	+	0.348834i
$914$	−1.19283	+	2.06604i	−0.0394553	+	0.0683386i
$915$	−15.5503	+	3.87734i	−0.514076	+	0.128181i
$916$	−7.83348	−	29.2350i	−0.258826	−	0.965950i
$917$	−5.57646	−	20.8116i	−0.184151	−	0.687260i
$918$	−7.23231	−	8.03165i	−0.238702	−	0.265084i
$919$	−4.20715	+	7.28699i	−0.138781	+	0.240376i	−0.927035	−	0.374974i	$-0.877652\pi$
$919$	−4.20715	+	7.28699i	−0.138781	+	0.240376i	0.788254	+	0.615349i	$0.210985\pi$
$920$	6.43113	+	11.1390i	0.212028	+	0.367243i
$921$	24.4765	+	25.3455i	0.806528	+	0.835163i
$922$		−	4.36704i		−	0.143821i
$923$		0			0
$924$	6.06857	+	3.64625i	0.199641	+	0.119953i
$925$	−14.7674	−	3.95690i	−0.485548	−	0.130102i
$926$	−3.01029	+	1.73799i	−0.0989244	+	0.0571140i
$927$	0.463762	−	13.2905i	0.0152319	−	0.436516i
$928$	7.38077	−	7.38077i	0.242286	−	0.242286i
$929$	−2.21620	+	0.593828i	−0.0727110	+	0.0194829i	−0.294991	−	0.955500i	$-0.595317\pi$
$929$	−2.21620	+	0.593828i	−0.0727110	+	0.0194829i	0.222280	+	0.974983i	$0.428650\pi$
$930$	−2.66666	+	9.30022i	−0.0874433	+	0.304966i
$931$	19.6831	+	19.6831i	0.645087	+	0.645087i
$932$	−29.4930	−	17.0278i	−0.966076	−	0.557764i
$933$	−13.1994	−	0.230221i	−0.432128	−	0.00753711i
$934$	0.839158	−	3.13178i	0.0274581	−	0.102475i
$935$	38.4590			1.25775
$936$		0			0
$937$	7.10985			0.232269			0.116134	−	0.993234i	$-0.462950\pi$
$937$	7.10985			0.232269			0.116134	+	0.993234i	$0.462950\pi$
$938$	0.721146	−	2.69135i	0.0235463	−	0.0878758i
$939$	11.2824	+	0.196786i	0.368187	+	0.00642186i
$940$	−17.8181	−	10.2873i	−0.581163	−	0.335534i
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	0.972266	−	0.233877i	$-0.0751412\pi$
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	−0.233877	+	0.972266i	$0.575141\pi$
$942$	−2.63799	+	9.20024i	−0.0859505	+	0.299760i
$943$	17.8142	−	4.77330i	0.580110	−	0.155440i
$944$	23.1413	−	23.1413i	0.753185	−	0.753185i
$945$	−17.5972	−	11.4268i	−0.572436	−	0.371712i
$946$	−3.17745	+	1.83450i	−0.103308	+	0.0596448i
$947$	12.9169	+	3.46107i	0.419742	+	0.112470i	0.462507	−	0.886616i	$-0.346950\pi$
$947$	12.9169	+	3.46107i	0.419742	+	0.112470i	−0.0427648	+	0.999085i	$0.513617\pi$
$948$	−3.06363	−	1.84076i	−0.0995022	−	0.0597852i
$949$		0			0
$950$		−	12.2866i		−	0.398629i
$951$	10.7100	+	11.0902i	0.347296	+	0.359626i
$952$	4.68381	+	8.11259i	0.151803	+	0.262931i
$953$	−8.89415	+	15.4051i	−0.288110	+	0.499021i	−0.973359	−	0.229288i	$-0.926360\pi$
$953$	−8.89415	+	15.4051i	−0.288110	+	0.499021i	0.685249	+	0.728309i	$0.259693\pi$
$954$	2.48878	+	0.760824i	0.0805772	+	0.0246326i
$955$	6.11390	+	22.8174i	0.197841	+	0.738353i
$956$	4.49206	+	16.7646i	0.145284	+	0.542206i
$957$	8.46858	−	2.11157i	0.273750	−	0.0682575i
$958$	−4.04423	+	7.00482i	−0.130663	+	0.226315i
$959$	−4.37773	−	7.58246i	−0.141364	−	0.244850i
$960$	22.3889	−	21.6213i	0.722598	−	0.697824i
$961$			10.1988i			0.328993i
$962$		0			0
$963$	34.5812	−	18.3883i	1.11436	−	0.592555i
$964$	50.1473	+	13.4369i	1.61513	+	0.432774i
$965$	33.4536	−	19.3144i	1.07691	−	0.621753i
$966$	−1.68107	+	0.931859i	−0.0540874	+	0.0299821i
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	−0.0648250	−	0.997897i	$-0.520649\pi$
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	0.997897	+	0.0648250i	$0.0206489\pi$
$968$	−9.87382	+	2.64568i	−0.317357	+	0.0850354i
$969$	−48.4123	−	13.8813i	−1.55523	−	0.445932i
$970$	−10.6239	−	10.6239i	−0.341114	−	0.341114i
$971$	−19.5631	−	11.2948i	−0.627810	−	0.362466i	0.152093	−	0.988366i	$-0.451399\pi$
$971$	−19.5631	−	11.2948i	−0.627810	−	0.362466i	−0.779904	+	0.625900i	$0.784732\pi$
$972$	−23.9536	−	16.7701i	−0.768311	−	0.537902i
$973$	1.62172	−	6.05235i	0.0519900	−	0.194029i
$974$	10.3864			0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	−0.689868	+	2.57462i	−0.0220708	+	0.0823694i	−0.976083	−	0.217399i	$-0.930243\pi$
$977$	−0.689868	+	2.57462i	−0.0220708	+	0.0823694i	0.954012	+	0.299768i	$0.0969094\pi$
$978$	−0.0367960	+	2.10963i	−0.00117660	+	0.0674587i
$979$	6.94116	+	4.00748i	0.221841	+	0.128080i
$980$	−26.0407	−	26.0407i	−0.831839	−	0.831839i
$981$	−13.9263	+	12.9871i	−0.444631	+	0.414647i
$982$	−5.21679	+	1.39784i	−0.166475	+	0.0446067i
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.263440	+	0.964676i	$0.584857\pi$
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.964676	+	0.263440i	$0.915143\pi$
$984$	7.80731	+	14.0843i	0.248888	+	0.448992i
$985$	6.87308	−	3.96818i	0.218995	−	0.126437i
$986$	5.39867	+	1.44657i	0.171929	+	0.0460682i
$987$	3.27182	−	5.44538i	0.104143	−	0.173328i
$988$		0			0
$989$			15.0419i			0.478303i
$990$	−6.71362	+	1.55015i	−0.213373	+	0.0492669i
$991$	−6.62217	−	11.4699i	−0.210360	−	0.364354i	0.741467	−	0.670989i	$-0.234130\pi$
$991$	−6.62217	−	11.4699i	−0.210360	−	0.364354i	−0.951827	+	0.306635i	$0.900797\pi$
$992$	8.85836	−	15.3431i	0.281253	−	0.487145i
$993$	−6.73680	−	27.0183i	−0.213786	−	0.857400i
$994$	1.23032	+	4.59160i	0.0390232	+	0.145637i
$995$	−16.4977	−	61.5704i	−0.523013	−	1.95191i
$996$	5.10147	+	20.4597i	0.161646	+	0.648291i
$997$	15.7906	−	27.3501i	0.500093	−	0.866186i	−0.499907	−	0.866079i	$-0.666633\pi$
$997$	15.7906	−	27.3501i	0.500093	−	0.866186i	1.00000		0.000107105i	$-3.40926e-5\pi$
$998$	7.36014	+	12.7481i	0.232981	+	0.403535i
$999$	3.46902	−	10.6780i	0.109755	−	0.337837i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.0912193 - 0.340435i) q^{2} +(-1.73179 - 0.0302056i) q^{3} +(1.62448 + 0.937892i) q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.168255 + 0.586806i) q^{6} +(1.12240 - 0.300747i) q^{7} +(0.965906 - 0.965906i) q^{8} +(2.99818 + 0.104619i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9}+O(q^{10}) \) 96 * q + 24 * q^9	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 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

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