LMFDB - Embedded newform 476.2.bl.a.465.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, 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:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			465.8
Character	$\chi$	$=$	476.465
Dual form			476.2.bl.a.173.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599246 + 0.203417i) q^{3} +(0.0888400 - 1.35544i) q^{5} +(1.82354 - 1.91695i) q^{7} +(-2.06234 - 1.58249i) q^{9} +O(q^{10})$	\(q+(0.599246 + 0.203417i) q^{3} +(0.0888400 - 1.35544i) q^{5} +(1.82354 - 1.91695i) q^{7} +(-2.06234 - 1.58249i) q^{9} +(-4.46023 - 3.91152i) q^{11} +(-2.54171 - 2.54171i) q^{13} +(0.328955 - 0.794169i) q^{15} +(3.56571 + 2.07019i) q^{17} +(0.0831250 - 0.0109436i) q^{19} +(1.48269 - 0.777791i) q^{21} +(2.88348 + 8.49447i) q^{23} +(3.12791 + 0.411797i) q^{25} +(-1.96869 - 2.94636i) q^{27} +(-3.46580 - 2.31578i) q^{29} +(1.73818 - 5.12051i) q^{31} +(-1.87711 - 3.25125i) q^{33} +(-2.43631 - 2.64199i) q^{35} +(-0.275094 - 0.313685i) q^{37} +(-1.00608 - 2.04014i) q^{39} +(6.27742 - 4.19443i) q^{41} +(5.89411 - 2.44142i) q^{43} +(-2.32818 + 2.65478i) q^{45} +(-2.98842 + 11.1529i) q^{47} +(-0.349432 - 6.99127i) q^{49} +(1.71563 + 1.96588i) q^{51} +(6.32425 - 4.85277i) q^{53} +(-5.69806 + 5.69806i) q^{55} +(0.0520384 + 0.0103511i) q^{57} +(-1.37227 + 10.4234i) q^{59} +(1.69902 - 3.44527i) q^{61} +(-6.79432 + 1.06769i) q^{63} +(-3.67093 + 3.21932i) q^{65} +(9.01789 + 5.20648i) q^{67} +5.67683i q^{69} +(4.09792 - 0.815126i) q^{71} +(-6.85708 + 3.38154i) q^{73} +(1.79062 + 0.883037i) q^{75} +(-15.6316 + 1.41727i) q^{77} +(9.38848 - 3.18696i) q^{79} +(1.43803 + 5.36679i) q^{81} +(4.87919 + 2.02103i) q^{83} +(3.12279 - 4.64918i) q^{85} +(-1.60580 - 2.09272i) q^{87} +(-10.4805 - 2.80823i) q^{89} +(-9.50725 + 0.237444i) q^{91} +(2.08320 - 2.71487i) q^{93} +(-0.00744854 - 0.113643i) q^{95} +(6.11324 - 9.14911i) q^{97} +(3.00858 + 15.1252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	0.599246	+	0.203417i	0.345975	+	0.117443i	0.489018	−	0.872274i	$-0.337355\pi$
$3$	0.599246	+	0.203417i	0.345975	+	0.117443i	−0.143043	+	0.989717i	$0.545689\pi$
$4$		0			0
$5$	0.0888400	−	1.35544i	0.0397304	−	0.606169i	−0.930851	−	0.365398i	$-0.880933\pi$
$5$	0.0888400	−	1.35544i	0.0397304	−	0.606169i	0.970582	−	0.240771i	$-0.0774004\pi$
$6$		0			0
$7$	1.82354	−	1.91695i	0.689232	−	0.724541i
$7$	1.82354	−	1.91695i	0.689232	−	0.724541i
$8$		0			0
$9$	−2.06234	−	1.58249i	−0.687447	−	0.527497i
$10$		0			0
$11$	−4.46023	−	3.91152i	−1.34481	−	1.17937i	−0.967380	−	0.253328i	$-0.918475\pi$
$11$	−4.46023	−	3.91152i	−1.34481	−	1.17937i	−0.377429	−	0.926038i	$-0.623192\pi$
$12$		0			0
$13$	−2.54171	−	2.54171i	−0.704944	−	0.704944i	0.260524	−	0.965467i	$-0.416105\pi$
$13$	−2.54171	−	2.54171i	−0.704944	−	0.704944i	−0.965467	+	0.260524i	$0.916105\pi$
$14$		0			0
$15$	0.328955	−	0.794169i	0.0849359	−	0.205053i
$16$		0			0
$17$	3.56571	+	2.07019i	0.864812	+	0.502095i
$17$	3.56571	+	2.07019i	0.864812	+	0.502095i
$18$		0			0
$19$	0.0831250	−	0.0109436i	0.0190702	−	0.00251064i	−0.120985	−	0.992654i	$-0.538605\pi$
$19$	0.0831250	−	0.0109436i	0.0190702	−	0.00251064i	0.140055	+	0.990144i	$0.455272\pi$
$20$		0			0
$21$	1.48269	−	0.777791i	0.323549	−	0.169728i
$22$		0			0
$23$	2.88348	+	8.49447i	0.601248	+	1.77122i	0.635843	+	0.771818i	$0.280653\pi$
$23$	2.88348	+	8.49447i	0.601248	+	1.77122i	−0.0345951	+	0.999401i	$0.511014\pi$
$24$		0			0
$25$	3.12791	+	0.411797i	0.625582	+	0.0823594i
$26$		0			0
$27$	−1.96869	−	2.94636i	−0.378875	−	0.567026i
$28$		0			0
$29$	−3.46580	−	2.31578i	−0.643584	−	0.430029i	0.190485	−	0.981690i	$-0.438994\pi$
$29$	−3.46580	−	2.31578i	−0.643584	−	0.430029i	−0.834068	+	0.551661i	$0.813994\pi$
$30$		0			0
$31$	1.73818	−	5.12051i	0.312186	−	0.919671i	−0.671692	−	0.740831i	$-0.734432\pi$
$31$	1.73818	−	5.12051i	0.312186	−	0.919671i	0.983878	−	0.178840i	$-0.0572346\pi$
$32$		0			0
$33$	−1.87711	−	3.25125i	−0.326763	−	0.565970i
$34$		0			0
$35$	−2.43631	−	2.64199i	−0.411811	−	0.446578i
$36$		0			0
$37$	−0.275094	−	0.313685i	−0.0452252	−	0.0515695i	0.728785	−	0.684743i	$-0.240085\pi$
$37$	−0.275094	−	0.313685i	−0.0452252	−	0.0515695i	−0.774010	+	0.633173i	$0.781752\pi$
$38$		0			0
$39$	−1.00608	−	2.04014i	−0.161102	−	0.326683i
$40$		0			0
$41$	6.27742	−	4.19443i	0.980368	−	0.655061i	0.0414276	−	0.999142i	$-0.486809\pi$
$41$	6.27742	−	4.19443i	0.980368	−	0.655061i	0.938940	+	0.344081i	$0.111809\pi$
$42$		0			0
$43$	5.89411	−	2.44142i	0.898843	−	0.372313i	0.115068	−	0.993358i	$-0.463291\pi$
$43$	5.89411	−	2.44142i	0.898843	−	0.372313i	0.783775	+	0.621045i	$0.213291\pi$
$44$		0			0
$45$	−2.32818	+	2.65478i	−0.347065	+	0.395752i
$46$		0			0
$47$	−2.98842	+	11.1529i	−0.435906	+	1.62682i	0.302983	+	0.952996i	$0.402017\pi$
$47$	−2.98842	+	11.1529i	−0.435906	+	1.62682i	−0.738889	+	0.673827i	$0.764649\pi$
$48$		0			0
$49$	−0.349432	−	6.99127i	−0.0499189	−	0.998753i
$50$		0			0
$51$	1.71563	+	1.96588i	0.240236	+	0.275278i
$52$		0			0
$53$	6.32425	−	4.85277i	0.868702	−	0.666579i	−0.0750687	−	0.997178i	$-0.523918\pi$
$53$	6.32425	−	4.85277i	0.868702	−	0.666579i	0.943771	+	0.330600i	$0.107251\pi$
$54$		0			0
$55$	−5.69806	+	5.69806i	−0.768326	+	0.768326i
$56$		0			0
$57$	0.0520384	+	0.0103511i	0.00689266	+	0.00137104i
$58$		0			0
$59$	−1.37227	+	10.4234i	−0.178654	+	1.35701i	0.633579	+	0.773678i	$0.281585\pi$
$59$	−1.37227	+	10.4234i	−0.178654	+	1.35701i	−0.812233	+	0.583333i	$0.801748\pi$
$60$		0			0
$61$	1.69902	−	3.44527i	0.217537	−	0.441122i	−0.760561	−	0.649267i	$-0.775076\pi$
$61$	1.69902	−	3.44527i	0.217537	−	0.441122i	0.978098	+	0.208145i	$0.0667425\pi$
$62$		0			0
$63$	−6.79432	+	1.06769i	−0.856004	+	0.134516i
$64$		0			0
$65$	−3.67093	+	3.21932i	−0.455323	+	0.399308i
$66$		0			0
$67$	9.01789	+	5.20648i	1.10171	+	0.636073i	0.936670	−	0.350214i	$-0.113891\pi$
$67$	9.01789	+	5.20648i	1.10171	+	0.636073i	0.165041	+	0.986287i	$0.447224\pi$
$68$		0			0
$69$			5.67683i			0.683410i
$70$		0			0
$71$	4.09792	−	0.815126i	0.486333	−	0.0967377i	0.0541674	−	0.998532i	$-0.482750\pi$
$71$	4.09792	−	0.815126i	0.486333	−	0.0967377i	0.432166	+	0.901794i	$0.357750\pi$
$72$		0			0
$73$	−6.85708	+	3.38154i	−0.802561	+	0.395779i	−0.796829	−	0.604204i	$-0.793491\pi$
$73$	−6.85708	+	3.38154i	−0.802561	+	0.395779i	−0.00573152	+	0.999984i	$0.501824\pi$
$74$		0			0
$75$	1.79062	+	0.883037i	0.206763	+	0.101964i
$76$		0			0
$77$	−15.6316	+	1.41727i	−1.78138	+	0.161513i
$78$		0			0
$79$	9.38848	−	3.18696i	1.05629	−	0.358561i	0.261344	−	0.965246i	$-0.415834\pi$
$79$	9.38848	−	3.18696i	1.05629	−	0.358561i	0.794942	+	0.606685i	$0.207501\pi$
$80$		0			0
$81$	1.43803	+	5.36679i	0.159781	+	0.596310i
$82$		0			0
$83$	4.87919	+	2.02103i	0.535561	+	0.221837i	0.634037	−	0.773303i	$-0.281397\pi$
$83$	4.87919	+	2.02103i	0.535561	+	0.221837i	−0.0984759	+	0.995139i	$0.531397\pi$
$84$		0			0
$85$	3.12279	−	4.64918i	0.338714	−	0.504274i
$86$		0			0
$87$	−1.60580	−	2.09272i	−0.172160	−	0.224363i
$88$		0			0
$89$	−10.4805	−	2.80823i	−1.11093	−	0.297672i	−0.343720	−	0.939072i	$-0.611687\pi$
$89$	−10.4805	−	2.80823i	−1.11093	−	0.297672i	−0.767206	+	0.641401i	$0.778354\pi$
$90$		0			0
$91$	−9.50725	+	0.237444i	−0.996630	+	0.0248909i
$92$		0			0
$93$	2.08320	−	2.71487i	0.216017	−	0.281519i
$94$		0			0
$95$	−0.00744854	−	0.113643i	−0.000764204	−	0.0116595i
$96$		0			0
$97$	6.11324	−	9.14911i	0.620706	−	0.928952i	−0.379288	−	0.925279i	$-0.623831\pi$
$97$	6.11324	−	9.14911i	0.620706	−	0.928952i	0.999993	−	0.00367281i	$-0.00116909\pi$
$98$		0			0
$99$	3.00858	+	15.1252i	0.302374	+	1.52014i
$100$		0			0
$101$	3.26171	−	5.64944i	0.324552	−	0.562141i	−0.656870	−	0.754004i	$-0.728120\pi$
$101$	3.26171	−	5.64944i	0.324552	−	0.562141i	0.981422	+	0.191864i	$0.0614531\pi$
$102$		0			0
$103$	−16.3892	+	9.46233i	−1.61488	+	0.932351i	−0.626663	+	0.779290i	$0.715580\pi$
$103$	−16.3892	+	9.46233i	−1.61488	+	0.932351i	−0.988217	+	0.153061i	$0.951087\pi$
$104$		0			0
$105$	−0.922524	−	2.07879i	−0.0900291	−	0.202869i
$106$		0			0
$107$	−0.290206	−	0.0190211i	−0.0280552	−	0.00183884i	0.0513691	−	0.998680i	$-0.483642\pi$
$107$	−0.290206	−	0.0190211i	−0.0280552	−	0.00183884i	−0.0794243	+	0.996841i	$0.525308\pi$
$108$		0			0
$109$	−0.569950	+	0.0373565i	−0.0545913	+	0.00357810i	−0.0926743	−	0.995696i	$-0.529542\pi$
$109$	−0.569950	+	0.0373565i	−0.0545913	+	0.00357810i	0.0380830	+	0.999275i	$0.487875\pi$
$110$		0			0
$111$	−0.101040	−	0.243933i	−0.00959034	−	0.0231531i
$112$		0			0
$113$	−1.70334	+	8.56325i	−0.160236	+	0.805563i	0.814145	+	0.580661i	$0.197206\pi$
$113$	−1.70334	+	8.56325i	−0.160236	+	0.805563i	−0.974382	+	0.224901i	$0.927794\pi$
$114$		0			0
$115$	11.7699	−	3.15373i	1.09755	−	0.294087i
$116$		0			0
$117$	1.21964	+	9.26411i	0.112756	+	0.856467i
$118$		0			0
$119$	10.4707	−	3.06024i	0.959845	−	0.280532i
$120$		0			0
$121$	3.15790	+	23.9866i	0.287082	+	2.18060i
$122$		0			0
$123$	4.61494	−	1.23657i	0.416115	−	0.111498i
$124$		0			0
$125$	2.16105	−	10.8643i	0.193290	−	0.971734i
$126$		0			0
$127$	2.27158	+	5.48407i	0.201570	+	0.486632i	0.992048	−	0.125857i	$-0.0401681\pi$
$127$	2.27158	+	5.48407i	0.201570	+	0.486632i	−0.790479	+	0.612490i	$0.790168\pi$
$128$		0			0
$129$	4.02865	−	0.264052i	0.354703	−	0.0232484i
$130$		0			0
$131$	−12.7220	−	0.833843i	−1.11153	−	0.0728532i	−0.501443	−	0.865191i	$-0.667197\pi$
$131$	−12.7220	−	0.833843i	−1.11153	−	0.0728532i	−0.610083	+	0.792338i	$0.708864\pi$
$132$		0			0
$133$	0.130603	−	0.179303i	0.0113247	−	0.0155475i
$134$		0			0
$135$	−4.16850	+	2.40668i	−0.358767	+	0.207134i
$136$		0			0
$137$	2.18925	−	3.79189i	0.187040	−	0.323963i	−0.757222	−	0.653158i	$-0.773444\pi$
$137$	2.18925	−	3.79189i	0.187040	−	0.323963i	0.944262	+	0.329195i	$0.106777\pi$
$138$		0			0
$139$	2.42960	+	12.2144i	0.206076	+	1.03601i	0.935870	+	0.352346i	$0.114616\pi$
$139$	2.42960	+	12.2144i	0.206076	+	1.03601i	−0.729794	+	0.683667i	$0.760384\pi$
$140$		0			0
$141$	−4.05949	+	6.07546i	−0.341871	+	0.511646i
$142$		0			0
$143$	1.39467	+	21.2786i	0.116628	+	1.77940i
$144$		0			0
$145$	−3.44679	+	4.49194i	−0.286240	+	0.373035i
$146$		0			0
$147$	1.21275	−	4.26058i	0.100026	−	0.351406i
$148$		0			0
$149$	−5.70255	−	1.52799i	−0.467171	−	0.125178i	0.0175516	−	0.999846i	$-0.494413\pi$
$149$	−5.70255	−	1.52799i	−0.467171	−	0.125178i	−0.484723	+	0.874668i	$0.661080\pi$
$150$		0			0
$151$	−12.5153	−	16.3102i	−1.01848	−	1.32731i	−0.943949	−	0.330090i	$-0.892921\pi$
$151$	−12.5153	−	16.3102i	−1.01848	−	1.32731i	−0.0745304	−	0.997219i	$-0.523746\pi$
$152$		0			0
$153$	−4.07766	−	9.91215i	−0.329659	−	0.801350i
$154$		0			0
$155$	−6.78611	−	2.81090i	−0.545073	−	0.225777i
$156$		0			0
$157$	−5.87576	−	21.9287i	−0.468937	−	1.75010i	−0.643495	−	0.765450i	$-0.722516\pi$
$157$	−5.87576	−	21.9287i	−0.468937	−	1.75010i	0.174558	−	0.984647i	$-0.444150\pi$
$158$		0			0
$159$	4.77692	−	1.62155i	0.378834	−	0.128597i
$160$		0			0
$161$	21.5417	+	9.96247i	1.69772	+	0.785152i
$162$		0			0
$163$	20.6192	+	10.1683i	1.61502	+	0.796441i	0.999968	+	0.00795690i	$0.00253279\pi$
$163$	20.6192	+	10.1683i	1.61502	+	0.796441i	0.615055	+	0.788484i	$0.289134\pi$
$164$		0			0
$165$	−4.57362	+	2.25546i	−0.356056	+	0.175587i
$166$		0			0
$167$	−0.516358	+	0.102710i	−0.0399570	+	0.00794794i	−0.215028	−	0.976608i	$-0.568984\pi$
$167$	−0.516358	+	0.102710i	−0.0399570	+	0.00794794i	0.175071	+	0.984556i	$0.443984\pi$
$168$		0			0
$169$		−	0.0794136i		−	0.00610874i
$170$		0			0
$171$	−0.188750	−	0.108975i	−0.0144341	−	0.00833353i
$172$		0			0
$173$	−12.1532	+	10.6581i	−0.923990	+	0.810317i	−0.982171	−	0.187989i	$-0.939803\pi$
$173$	−12.1532	+	10.6581i	−0.923990	+	0.810317i	0.0581816	+	0.998306i	$0.481470\pi$
$174$		0			0
$175$	6.49325	−	5.24513i	0.490844	−	0.396495i
$176$		0			0
$177$	−2.94262	+	5.96704i	−0.221181	+	0.448510i
$178$		0			0
$179$	−1.38355	+	10.5091i	−0.103412	+	0.785489i	0.858632	+	0.512593i	$0.171315\pi$
$179$	−1.38355	+	10.5091i	−0.103412	+	0.785489i	−0.962043	+	0.272896i	$0.912018\pi$
$180$		0			0
$181$	5.87576	+	1.16876i	0.436742	+	0.0868734i	0.408564	−	0.912730i	$-0.366030\pi$
$181$	5.87576	+	1.16876i	0.436742	+	0.0868734i	0.0281778	+	0.999603i	$0.491030\pi$
$182$		0			0
$183$	1.71896	−	1.71896i	0.127069	−	0.127069i
$184$		0			0
$185$	−0.449619	+	0.345005i	−0.0330567	+	0.0253653i
$186$		0			0
$187$	−7.80630	−	23.1809i	−0.570854	−	1.69515i
$188$		0			0
$189$	−9.23801	−	1.59889i	−0.671966	−	0.116302i
$190$		0			0
$191$	−0.213473	+	0.796691i	−0.0154463	+	0.0576465i	−0.973219	−	0.229881i	$-0.926166\pi$
$191$	−0.213473	+	0.796691i	−0.0154463	+	0.0576465i	0.957773	+	0.287527i	$0.0928331\pi$
$192$		0			0
$193$	12.1498	−	13.8541i	0.874559	−	0.997243i	−0.125428	−	0.992103i	$-0.540030\pi$
$193$	12.1498	−	13.8541i	0.874559	−	0.997243i	0.999987	−	0.00514030i	$-0.00163621\pi$
$194$		0			0
$195$	−2.85466	+	1.18244i	−0.204426	+	0.0846761i
$196$		0			0
$197$	14.7271	−	9.84035i	1.04926	−	0.701096i	0.0936167	−	0.995608i	$-0.470157\pi$
$197$	14.7271	−	9.84035i	1.04926	−	0.701096i	0.955648	+	0.294512i	$0.0951572\pi$
$198$		0			0
$199$	−6.42642	−	13.0315i	−0.455557	−	0.923778i	−0.996569	−	0.0827634i	$-0.973625\pi$
$199$	−6.42642	−	13.0315i	−0.455557	−	0.923778i	0.541012	−	0.841015i	$-0.318041\pi$
$200$		0			0
$201$	4.34485	+	4.95435i	0.306462	+	0.349453i
$202$		0			0
$203$	−10.7593	+	2.42089i	−0.755152	+	0.169913i
$204$		0			0
$205$	−5.12760	−	8.88127i	−0.358127	−	0.620295i
$206$		0			0
$207$	7.49569	−	22.0816i	0.520987	−	1.53478i
$208$		0			0
$209$	−0.413562	−	0.276334i	−0.0286067	−	0.0191144i
$210$		0			0
$211$	12.1753	+	18.2216i	0.838181	+	1.25443i	0.964934	+	0.262493i	$0.0845445\pi$
$211$	12.1753	+	18.2216i	0.838181	+	1.25443i	−0.126753	+	0.991934i	$0.540455\pi$
$212$		0			0
$213$	2.62147	+	0.345123i	0.179620	+	0.0236475i
$214$		0			0
$215$	−2.78556	−	8.20598i	−0.189973	−	0.559643i
$216$		0			0
$217$	−6.64616	−	12.6695i	−0.451171	−	0.860058i
$218$		0			0
$219$	−4.79694	+	0.631530i	−0.324147	+	0.0426748i
$220$		0			0
$221$	−3.80118	−	14.3248i	−0.255695	−	0.963593i
$222$		0			0
$223$	2.15908	−	5.21249i	0.144583	−	0.349054i	−0.834954	−	0.550320i	$-0.814506\pi$
$223$	2.15908	−	5.21249i	0.144583	−	0.349054i	0.979537	+	0.201266i	$0.0645056\pi$
$224$		0			0
$225$	−5.79915	−	5.79915i	−0.386610	−	0.386610i
$226$		0			0
$227$	−10.7462	−	9.42416i	−0.713250	−	0.625503i	0.223826	−	0.974629i	$-0.428145\pi$
$227$	−10.7462	−	9.42416i	−0.713250	−	0.625503i	−0.937076	+	0.349126i	$0.886479\pi$
$228$		0			0
$229$	−10.4361	−	8.00788i	−0.689635	−	0.529176i	0.203438	−	0.979088i	$-0.434789\pi$
$229$	−10.4361	−	8.00788i	−0.689635	−	0.529176i	−0.893073	+	0.449912i	$0.851455\pi$
$230$		0			0
$231$	−9.65547	−	2.33043i	−0.635283	−	0.153331i
$232$		0			0
$233$	−1.63963	+	25.0159i	−0.107416	+	1.63884i	0.515739	+	0.856746i	$0.327517\pi$
$233$	−1.63963	+	25.0159i	−0.107416	+	1.63884i	−0.623155	+	0.782099i	$0.714149\pi$
$234$		0			0
$235$	14.8516	+	5.04144i	0.968812	+	0.328867i
$236$		0			0
$237$	6.27429			0.407559
$238$		0			0
$239$	−1.89315			−0.122458			−0.0612288	−	0.998124i	$-0.519502\pi$
$239$	−1.89315			−0.122458			−0.0612288	+	0.998124i	$0.519502\pi$
$240$		0			0
$241$	24.4022	+	8.28343i	1.57188	+	0.533583i	0.965234	−	0.261387i	$-0.0841798\pi$
$241$	24.4022	+	8.28343i	1.57188	+	0.533583i	0.606650	+	0.794969i	$0.292513\pi$
$242$		0			0
$243$	−0.925240	+	14.1164i	−0.0593542	+	0.905570i
$244$		0			0
$245$	−9.50727	−	0.147472i	−0.607397	−	0.00942161i
$246$		0			0
$247$	−0.239095	−	0.183464i	−0.0152133	−	0.0116735i
$248$		0			0
$249$	2.51273	+	2.20360i	0.159238	+	0.139648i
$250$		0			0
$251$	−7.90281	−	7.90281i	−0.498821	−	0.498821i	0.412250	−	0.911071i	$-0.364743\pi$
$251$	−7.90281	−	7.90281i	−0.498821	−	0.498821i	−0.911071	+	0.412250i	$0.864743\pi$
$252$		0			0
$253$	20.3653	−	49.1661i	1.28035	−	3.09105i
$254$		0			0
$255$	2.81704	−	2.15078i	0.176410	−	0.134687i
$256$		0			0
$257$	11.9968	−	1.57941i	0.748340	−	0.0985208i	0.253296	−	0.967389i	$-0.418485\pi$
$257$	11.9968	−	1.57941i	0.748340	−	0.0985208i	0.495044	+	0.868868i	$0.335152\pi$
$258$		0			0
$259$	−1.10296	−	0.0446724i	−0.0685348	−	0.00277581i
$260$		0			0
$261$	3.48298	+	10.2605i	0.215591	+	0.635110i
$262$		0			0
$263$	4.56559	+	0.601072i	0.281526	+	0.0370637i	0.269967	−	0.962870i	$-0.412987\pi$
$263$	4.56559	+	0.601072i	0.281526	+	0.0370637i	0.0115593	+	0.999933i	$0.496320\pi$
$264$		0			0
$265$	−6.01577	−	9.00324i	−0.369546	−	0.553064i
$266$		0			0
$267$	−5.70913	−	3.81472i	−0.349393	−	0.233457i
$268$		0			0
$269$	−3.33815	+	9.83389i	−0.203531	+	0.599583i	−0.999987	−	0.00511379i	$-0.998372\pi$
$269$	−3.33815	+	9.83389i	−0.203531	+	0.599583i	0.796456	+	0.604696i	$0.206706\pi$
$270$		0			0
$271$	1.94275	+	3.36494i	0.118013	+	0.204405i	0.918980	−	0.394303i	$-0.129014\pi$
$271$	1.94275	+	3.36494i	0.118013	+	0.204405i	−0.800967	+	0.598709i	$0.795681\pi$
$272$		0			0
$273$	−5.74548	−	1.79165i	−0.347732	−	0.108435i
$274$		0			0
$275$	−12.3404	−	14.0716i	−0.744157	−	0.848548i
$276$		0			0
$277$	−3.10484	−	6.29600i	−0.186552	−	0.378290i	0.783425	−	0.621486i	$-0.213471\pi$
$277$	−3.10484	−	6.29600i	−0.186552	−	0.378290i	−0.969977	+	0.243196i	$0.921804\pi$
$278$		0			0
$279$	−11.6879	+	7.80959i	−0.699735	+	0.467548i
$280$		0			0
$281$	−15.6379	+	6.47744i	−0.932881	+	0.386412i	−0.796771	−	0.604282i	$-0.793460\pi$
$281$	−15.6379	+	6.47744i	−0.932881	+	0.386412i	−0.136110	+	0.990694i	$0.543460\pi$
$282$		0			0
$283$	−6.58471	+	7.50842i	−0.391420	+	0.446329i	−0.913666	−	0.406466i	$-0.866761\pi$
$283$	−6.58471	+	7.50842i	−0.391420	+	0.446329i	0.522246	+	0.852795i	$0.325094\pi$
$284$		0			0
$285$	0.0186533	−	0.0696152i	0.00110493	−	0.00412365i
$286$		0			0
$287$	3.40655	−	19.6822i	0.201082	−	1.16181i
$288$		0			0
$289$	8.42861	+	14.7634i	0.495801	+	0.868436i
$290$		0			0
$291$	5.52442	−	4.23904i	0.323847	−	0.248497i
$292$		0			0
$293$	−7.31304	+	7.31304i	−0.427233	+	0.427233i	−0.887685	−	0.460452i	$-0.847687\pi$
$293$	−7.31304	+	7.31304i	−0.427233	+	0.427233i	0.460452	+	0.887685i	$0.347687\pi$
$294$		0			0
$295$	14.0063	+	2.78603i	0.815481	+	0.162209i
$296$		0			0
$297$	−2.74390	+	20.8420i	−0.159217	+	1.20937i
$298$		0			0
$299$	14.2615	−	28.9195i	0.824764	−	1.67246i
$300$		0			0
$301$	6.06803	−	15.7508i	0.349755	−	0.907858i
$302$		0			0
$303$	3.10376	−	2.72192i	0.178306	−	0.156370i
$304$		0			0
$305$	−4.51891	−	2.60899i	−0.258752	−	0.149391i
$306$		0			0
$307$		−	14.9823i		−	0.855084i	−0.903995	−	0.427542i	$-0.859380\pi$
$307$		−	14.9823i		−	0.855084i	0.903995	−	0.427542i	$-0.140620\pi$
$308$		0			0
$309$	−11.7460	+	2.33642i	−0.668206	+	0.132914i
$310$		0			0
$311$	1.75346	−	0.864709i	0.0994294	−	0.0490331i	−0.391894	−	0.920010i	$-0.628180\pi$
$311$	1.75346	−	0.864709i	0.0994294	−	0.0490331i	0.491323	+	0.870977i	$0.336513\pi$
$312$		0			0
$313$	15.5994	+	7.69279i	0.881733	+	0.434822i	0.826031	−	0.563625i	$-0.190594\pi$
$313$	15.5994	+	7.69279i	0.881733	+	0.434822i	0.0557019	+	0.998447i	$0.482260\pi$
$314$		0			0
$315$	0.843576	+	9.30412i	0.0475301	+	0.524228i
$316$		0			0
$317$	15.5717	−	5.28586i	0.874591	−	0.296884i	0.152184	−	0.988352i	$-0.451369\pi$
$317$	15.5717	−	5.28586i	0.874591	−	0.296884i	0.722407	+	0.691468i	$0.243036\pi$
$318$		0			0
$319$	6.40008	+	23.8854i	0.358336	+	1.33733i
$320$		0			0
$321$	−0.170035	−	0.0704310i	−0.00949045	−	0.00393107i
$322$		0			0
$323$	0.319055	+	0.133063i	0.0177527	+	0.00740382i
$324$		0			0
$325$	−6.90357	−	8.99691i	−0.382941	−	0.499059i
$326$		0			0
$327$	−0.349139	−	0.0935516i	−0.0193074	−	0.00517341i
$328$		0			0
$329$	15.9302	+	26.0664i	0.878259	+	1.43709i
$330$		0			0
$331$	5.71747	−	7.45116i	0.314261	−	0.409553i	−0.609340	−	0.792909i	$-0.708565\pi$
$331$	5.71747	−	7.45116i	0.314261	−	0.409553i	0.923600	+	0.383357i	$0.125232\pi$
$332$		0			0
$333$	0.0709350	+	1.08226i	0.00388722	+	0.0593074i
$334$		0			0
$335$	7.85820	−	11.7606i	0.429339	−	0.642552i
$336$		0			0
$337$	−1.47207	−	7.40062i	−0.0801890	−	0.403137i	−0.999943	−	0.0106429i	$-0.996612\pi$
$337$	−1.47207	−	7.40062i	−0.0801890	−	0.403137i	0.919754	−	0.392494i	$-0.128388\pi$
$338$		0			0
$339$	−2.76263	+	4.78501i	−0.150045	+	0.259886i
$340$		0			0
$341$	−27.7816	+	16.0397i	−1.50446	+	0.868601i
$342$		0			0
$343$	−14.0392	−	12.0790i	−0.758043	−	0.652204i
$344$		0			0
$345$	7.69458	+	0.504330i	0.414262	+	0.0271522i
$346$		0			0
$347$	17.5902	−	1.15292i	0.944290	−	0.0618920i	0.414526	−	0.910037i	$-0.363947\pi$
$347$	17.5902	−	1.15292i	0.944290	−	0.0618920i	0.529764	+	0.848145i	$0.322281\pi$
$348$		0			0
$349$	4.90871	+	11.8507i	0.262757	+	0.634352i	0.999107	−	0.0422488i	$-0.0134522\pi$
$349$	4.90871	+	11.8507i	0.262757	+	0.634352i	−0.736350	+	0.676601i	$0.763452\pi$
$350$		0			0
$351$	−2.48494	+	12.4926i	−0.132636	+	0.666807i
$352$		0			0
$353$	−3.76977	+	1.01011i	−0.200644	+	0.0537625i	−0.357742	−	0.933821i	$-0.616453\pi$
$353$	−3.76977	+	1.01011i	−0.200644	+	0.0537625i	0.157097	+	0.987583i	$0.449786\pi$
$354$		0			0
$355$	−0.740793	−	5.62688i	−0.0393172	−	0.298644i
$356$		0			0
$357$	6.89702	+	0.296072i	0.365029	+	0.0156698i
$358$		0			0
$359$	−3.47714	−	26.4115i	−0.183516	−	1.39395i	−0.796877	−	0.604142i	$-0.793516\pi$
$359$	−3.47714	−	26.4115i	−0.183516	−	1.39395i	0.613360	−	0.789803i	$-0.289817\pi$
$360$		0			0
$361$	−18.3458	+	4.91574i	−0.965568	+	0.258723i
$362$		0			0
$363$	−2.98692	+	15.0163i	−0.156773	+	0.788150i
$364$		0			0
$365$	3.97428	+	9.59476i	0.208023	+	0.502212i
$366$		0			0
$367$	−3.87083	+	0.253708i	−0.202056	+	0.0132434i	−0.166095	−	0.986110i	$-0.553116\pi$
$367$	−3.87083	+	0.253708i	−0.202056	+	0.0132434i	−0.0359608	+	0.999353i	$0.511449\pi$
$368$		0			0
$369$	−19.5838	−	1.28359i	−1.01949	−	0.0668211i
$370$		0			0
$371$	2.22996	−	20.9725i	0.115774	−	1.08884i
$372$		0			0
$373$	−4.92596	+	2.84401i	−0.255057	+	0.147257i	−0.622077	−	0.782956i	$-0.713711\pi$
$373$	−4.92596	+	2.84401i	−0.255057	+	0.147257i	0.367021	+	0.930213i	$0.380378\pi$
$374$		0			0
$375$	3.50498	−	6.07081i	0.180997	−	0.313495i
$376$		0			0
$377$	2.92304	+	14.6951i	0.150544	+	0.756836i
$378$		0			0
$379$	4.36799	−	6.53716i	0.224368	−	0.335791i	−0.702158	−	0.712021i	$-0.747780\pi$
$379$	4.36799	−	6.53716i	0.224368	−	0.335791i	0.926526	+	0.376230i	$0.122780\pi$
$380$		0			0
$381$	0.245682	+	3.74838i	0.0125867	+	0.192036i
$382$		0			0
$383$	−14.0843	+	18.3551i	−0.719676	+	0.937900i	−0.999756	−	0.0220769i	$-0.992972\pi$
$383$	−14.0843	+	18.3551i	−0.719676	+	0.937900i	0.280081	+	0.959976i	$0.409639\pi$
$384$		0			0
$385$	0.532306	+	21.3135i	0.0271288	+	1.08624i
$386$		0			0
$387$	−16.0192	−	4.29233i	−0.814301	−	0.218191i
$388$		0			0
$389$	10.0864	+	13.1449i	0.511402	+	0.666472i	0.975675	−	0.219220i	$-0.0703512\pi$
$389$	10.0864	+	13.1449i	0.511402	+	0.666472i	−0.464274	+	0.885692i	$0.653685\pi$
$390$		0			0
$391$	−7.30351	+	36.2582i	−0.369354	+	1.83366i
$392$		0			0
$393$	−7.45399	−	3.08754i	−0.376004	−	0.155746i
$394$		0			0
$395$	−3.48565	−	13.0086i	−0.175382	−	0.654534i
$396$		0			0
$397$	16.9243	−	5.74503i	0.849406	−	0.288335i	0.137407	−	0.990515i	$-0.456123\pi$
$397$	16.9243	−	5.74503i	0.849406	−	0.288335i	0.711999	+	0.702180i	$0.247790\pi$
$398$		0			0
$399$	0.114737	−	0.0808798i	0.00574401	−	0.00404905i
$400$		0			0
$401$	−9.62610	−	4.74707i	−0.480705	−	0.237057i	0.185758	−	0.982595i	$-0.440526\pi$
$401$	−9.62610	−	4.74707i	−0.480705	−	0.237057i	−0.666463	+	0.745538i	$0.732193\pi$
$402$		0			0
$403$	−17.4328	+	8.59691i	−0.868390	+	0.428243i
$404$		0			0
$405$	7.40209	−	1.47237i	0.367813	−	0.0731625i
$406$		0			0
$407$			2.47514i			0.122688i
$408$		0			0
$409$	12.4572	+	7.19218i	0.615970	+	0.355630i	0.775298	−	0.631595i	$-0.217600\pi$
$409$	12.4572	+	7.19218i	0.615970	+	0.355630i	−0.159328	+	0.987226i	$0.550933\pi$
$410$		0			0
$411$	2.08323	−	1.82695i	0.102758	−	0.0901166i
$412$		0			0
$413$	17.4788	+	21.6380i	0.860076	+	1.06474i
$414$		0			0
$415$	3.17284	−	6.43389i	0.155749	−	0.315827i
$416$		0			0
$417$	−1.02869	+	7.81366i	−0.0503751	+	0.382637i
$418$		0			0
$419$	−28.1038	−	5.59020i	−1.37296	−	0.273099i	−0.547145	−	0.837038i	$-0.684285\pi$
$419$	−28.1038	−	5.59020i	−1.37296	−	0.273099i	−0.825817	+	0.563939i	$0.809285\pi$
$420$		0			0
$421$	−12.0444	+	12.0444i	−0.587009	+	0.587009i	−0.936820	−	0.349811i	$-0.886246\pi$
$421$	−12.0444	+	12.0444i	−0.587009	+	0.587009i	0.349811	+	0.936820i	$0.386246\pi$
$422$		0			0
$423$	23.8126	−	18.2720i	1.15781	−	0.888416i
$424$		0			0
$425$	10.3007	+	7.94372i	0.499659	+	0.385327i
$426$		0			0
$427$	−3.50621	−	9.53953i	−0.169677	−	0.461650i
$428$		0			0
$429$	−3.49266	+	13.0348i	−0.168627	+	0.629326i
$430$		0			0
$431$	9.07828	−	10.3518i	0.437285	−	0.498628i	−0.490657	−	0.871353i	$-0.663243\pi$
$431$	9.07828	−	10.3518i	0.437285	−	0.498628i	0.927942	+	0.372725i	$0.121576\pi$
$432$		0			0
$433$	3.48345	−	1.44289i	0.167404	−	0.0693409i	−0.297408	−	0.954751i	$-0.596122\pi$
$433$	3.48345	−	1.44289i	0.167404	−	0.0693409i	0.464812	+	0.885410i	$0.346122\pi$
$434$		0			0
$435$	−2.97921	+	1.99065i	−0.142842	+	0.0954442i
$436$		0			0
$437$	0.332650	+	0.674547i	0.0159128	+	0.0322680i
$438$		0			0
$439$	20.4607	+	23.3310i	0.976538	+	1.11353i	0.993518	+	0.113673i	$0.0362615\pi$
$439$	20.4607	+	23.3310i	0.976538	+	1.11353i	−0.0169801	+	0.999856i	$0.505405\pi$
$440$		0			0
$441$	−10.3430	+	14.9714i	−0.492523	+	0.712922i
$442$		0			0
$443$	−0.812065	−	1.40654i	−0.0385824	−	0.0668266i	0.846089	−	0.533041i	$-0.178951\pi$
$443$	−0.812065	−	1.40654i	−0.0385824	−	0.0668266i	−0.884672	+	0.466214i	$0.845618\pi$
$444$		0			0
$445$	−4.73746	+	13.9561i	−0.224577	+	0.661583i
$446$		0			0
$447$	−3.10641	−	2.07564i	−0.146928	−	0.0981744i
$448$		0			0
$449$	21.0630	+	31.5230i	0.994026	+	1.48766i	0.868571	+	0.495565i	$0.165039\pi$
$449$	21.0630	+	31.5230i	0.994026	+	1.48766i	0.125455	+	0.992099i	$0.459961\pi$
$450$		0			0
$451$	−44.4053	−	5.84607i	−2.09096	−	0.275281i
$452$		0			0
$453$	−4.18197	−	12.3197i	−0.196486	−	0.578829i
$454$		0			0
$455$	−0.522784	+	12.9076i	−0.0245085	+	0.605116i
$456$		0			0
$457$	4.76492	−	0.627313i	0.222893	−	0.0293445i	−0.0182522	−	0.999833i	$-0.505810\pi$
$457$	4.76492	−	0.627313i	0.222893	−	0.0293445i	0.241146	+	0.970489i	$0.422477\pi$
$458$		0			0
$459$	−0.920267	−	14.5814i	−0.0429544	−	0.680603i
$460$		0			0
$461$	−5.81314	+	14.0342i	−0.270745	+	0.653636i	−0.999516	−	0.0311216i	$-0.990092\pi$
$461$	−5.81314	+	14.0342i	−0.270745	+	0.653636i	0.728771	+	0.684758i	$0.240092\pi$
$462$		0			0
$463$	3.77143	+	3.77143i	0.175273	+	0.175273i	0.789292	−	0.614018i	$-0.210448\pi$
$463$	3.77143	+	3.77143i	0.175273	+	0.175273i	−0.614018	+	0.789292i	$0.710448\pi$
$464$		0			0
$465$	−3.49477	−	3.06483i	−0.162066	−	0.142128i
$466$		0			0
$467$	24.4898	+	18.7917i	1.13325	+	0.869577i	0.992714	−	0.120498i	$-0.0384491\pi$
$467$	24.4898	+	18.7917i	1.13325	+	0.869577i	0.140541	+	0.990075i	$0.455116\pi$
$468$		0			0
$469$	26.4250	−	7.79268i	1.22019	−	0.359833i
$470$		0			0
$471$	0.939624	−	14.3359i	0.0432956	−	0.660563i
$472$		0			0
$473$	−35.8387	−	12.1656i	−1.64787	−	0.559375i
$474$		0			0
$475$	0.264514			0.0121367
$476$		0			0
$477$	−20.7222			−0.948805
$478$		0			0
$479$	17.2884	+	5.86861i	0.789925	+	0.268144i	0.687107	−	0.726557i	$-0.258880\pi$
$479$	17.2884	+	5.86861i	0.789925	+	0.268144i	0.102819	+	0.994700i	$0.467214\pi$
$480$		0			0
$481$	−0.0980862	+	1.49651i	−0.00447234	+	0.0682348i
$482$		0			0
$483$	10.8822	+	10.3519i	0.495159	+	0.471028i
$484$		0			0
$485$	−11.8579	−	9.09892i	−0.538441	−	0.413160i
$486$		0			0
$487$	−2.46366	−	2.16057i	−0.111639	−	0.0979050i	0.601706	−	0.798717i	$-0.294488\pi$
$487$	−2.46366	−	2.16057i	−0.111639	−	0.0979050i	−0.713346	+	0.700812i	$0.752821\pi$
$488$		0			0
$489$	10.2876	+	10.2876i	0.465222	+	0.465222i
$490$		0			0
$491$	6.36881	−	15.3757i	0.287420	−	0.693894i	−0.712550	−	0.701622i	$-0.752460\pi$
$491$	6.36881	−	15.3757i	0.287420	−	0.693894i	0.999970	+	0.00772723i	$0.00245968\pi$
$492$		0			0
$493$	−7.56396	−	15.4323i	−0.340664	−	0.695034i
$494$		0			0
$495$	20.7685	−	2.73422i	0.933473	−	0.122894i
$496$		0			0
$497$	5.91014	−	9.34193i	0.265106	−	0.419043i
$498$		0			0
$499$	4.60601	+	13.5689i	0.206193	+	0.607426i	1.00000		0.000744610i	$-0.000237017\pi$
$499$	4.60601	+	13.5689i	0.206193	+	0.607426i	−0.793806	+	0.608171i	$0.791904\pi$
$500$		0			0
$501$	−0.330319	−	0.0434873i	−0.0147576	−	0.00194287i
$502$		0			0
$503$	−2.95621	−	4.42428i	−0.131811	−	0.197269i	0.759693	−	0.650282i	$-0.225349\pi$
$503$	−2.95621	−	4.42428i	−0.131811	−	0.197269i	−0.891504	+	0.453013i	$0.850349\pi$
$504$		0			0
$505$	−7.36769	−	4.92293i	−0.327858	−	0.219068i
$506$		0			0
$507$	0.0161541	−	0.0475883i	0.000717427	−	0.00211347i
$508$		0			0
$509$	−4.79987	−	8.31363i	−0.212751	−	0.368495i	0.739824	−	0.672801i	$-0.234909\pi$
$509$	−4.79987	−	8.31363i	−0.212751	−	0.368495i	−0.952574	+	0.304306i	$0.901576\pi$
$510$		0			0
$511$	−6.02188	+	19.3111i	−0.266392	+	0.854272i
$512$		0			0
$513$	−0.195891	−	0.223371i	−0.00864881	−	0.00986207i
$514$		0			0
$515$	11.3696	+	23.0552i	0.501003	+	1.01593i
$516$		0			0
$517$	56.9539	−	38.0554i	2.50483	−	1.67367i
$518$		0			0
$519$	−9.45078	+	3.91464i	−0.414843	+	0.171834i
$520$		0			0
$521$	14.9205	−	17.0135i	0.653678	−	0.745377i	−0.326128	−	0.945326i	$-0.605744\pi$
$521$	14.9205	−	17.0135i	0.653678	−	0.745377i	0.979806	+	0.199948i	$0.0640775\pi$
$522$		0			0
$523$	2.11656	−	7.89910i	0.0925506	−	0.345403i	−0.904086	−	0.427350i	$-0.859447\pi$
$523$	2.11656	−	7.89910i	0.0925506	−	0.345403i	0.996637	+	0.0819469i	$0.0261138\pi$
$524$		0			0
$525$	4.95801	−	1.82229i	0.216385	−	0.0795313i
$526$		0			0
$527$	16.7983	−	14.6599i	0.731745	−	0.638596i
$528$		0			0
$529$	−45.5944	+	34.9858i	−1.98237	+	1.52112i
$530$		0			0
$531$	19.3250	−	19.3250i	0.838634	−	0.838634i
$532$		0			0
$533$	−26.6164	−	5.29433i	−1.15288	−	0.229323i
$534$		0			0
$535$	−0.0515637	+	0.391665i	−0.00222929	+	0.0169332i
$536$		0			0
$537$	−2.96682	+	6.01612i	−0.128028	+	0.259615i
$538$		0			0
$539$	−25.7879	+	32.5495i	−1.11076	+	1.40201i
$540$		0			0
$541$	−14.6677	+	12.8633i	−0.630616	+	0.553035i	−0.913869	−	0.406010i	$-0.866920\pi$
$541$	−14.6677	+	12.8633i	−0.630616	+	0.553035i	0.283253	+	0.959045i	$0.408586\pi$
$542$		0			0
$543$	3.28328	+	1.89561i	0.140899	+	0.0813482i
$544$		0			0
$545$			0.775849i			0.0332337i
$546$		0			0
$547$	−26.2879	+	5.22898i	−1.12399	+	0.223575i	−0.721881	−	0.692017i	$-0.756722\pi$
$547$	−26.2879	+	5.22898i	−1.12399	+	0.223575i	−0.402107	+	0.915592i	$0.631722\pi$
$548$		0			0
$549$	−8.95608	+	4.41665i	−0.382236	+	0.188498i
$550$		0			0
$551$	−0.313438	−	0.154570i	−0.0133529	−	0.00658492i
$552$		0			0
$553$	11.0110	−	23.8088i	0.468234	−	1.01245i
$554$		0			0
$555$	−0.339612	+	0.115283i	−0.0144157	+	0.00489349i
$556$		0			0
$557$	−0.283943	−	1.05969i	−0.0120311	−	0.0449005i	0.959649	−	0.281199i	$-0.0907322\pi$
$557$	−0.283943	−	1.05969i	−0.0120311	−	0.0449005i	−0.971680	+	0.236299i	$0.924066\pi$
$558$		0			0
$559$	−21.1865	−	8.77573i	−0.896093	−	0.371174i
$560$		0			0
$561$	0.0374776	−	15.4790i	0.00158231	−	0.653523i
$562$		0			0
$563$	17.9116	+	23.3428i	0.754882	+	0.983781i	0.999898	+	0.0142623i	$0.00453997\pi$
$563$	17.9116	+	23.3428i	0.754882	+	0.983781i	−0.245016	+	0.969519i	$0.578793\pi$
$564$		0			0
$565$	11.4556	+	3.06952i	0.481941	+	0.129136i
$566$		0			0
$567$	12.9102	+	7.02990i	0.542177	+	0.295228i
$568$		0			0
$569$	−0.788866	+	1.02807i	−0.0330710	+	0.0430989i	−0.809596	−	0.586987i	$-0.800314\pi$
$569$	−0.788866	+	1.02807i	−0.0330710	+	0.0430989i	0.776525	+	0.630086i	$0.216980\pi$
$570$		0			0
$571$	0.995409	+	15.1870i	0.0416566	+	0.635556i	0.966735	+	0.255780i	$0.0823323\pi$
$571$	0.995409	+	15.1870i	0.0416566	+	0.635556i	−0.925078	+	0.379776i	$0.876001\pi$
$572$		0			0
$573$	−0.289983	+	0.433990i	−0.0121142	+	0.0181302i
$574$		0			0
$575$	5.52128	+	27.7573i	0.230253	+	1.15756i
$576$		0			0
$577$	−12.0731	+	20.9113i	−0.502611	+	0.870547i	0.497385	+	0.867530i	$0.334294\pi$
$577$	−12.0731	+	20.9113i	−0.502611	+	0.870547i	−0.999995	+	0.00301724i	$0.999040\pi$
$578$		0			0
$579$	10.0989	−	5.83058i	0.419694	−	0.242311i
$580$		0			0
$581$	12.7716	−	5.66777i	0.529855	−	0.235139i
$582$		0			0
$583$	−47.1893	−	3.09295i	−1.95438	−	0.128097i
$584$		0			0
$585$	12.6653	−	0.830125i	0.523644	−	0.0343215i
$586$		0			0
$587$	1.31832	+	3.18271i	0.0544130	+	0.131365i	0.948748	−	0.316033i	$-0.102351\pi$
$587$	1.31832	+	3.18271i	0.0544130	+	0.131365i	−0.894335	+	0.447397i	$0.852351\pi$
$588$		0			0
$589$	0.0884492	−	0.444664i	0.00364449	−	0.0183221i
$590$		0			0
$591$	10.8269	−	2.90105i	0.445358	−	0.119333i
$592$		0			0
$593$	−0.398932	−	3.03019i	−0.0163822	−	0.124435i	0.981300	−	0.192486i	$-0.0616551\pi$
$593$	−0.398932	−	3.03019i	−0.0163822	−	0.124435i	−0.997682	+	0.0680514i	$0.978322\pi$
$594$		0			0
$595$	−3.21775	−	14.4642i	−0.131915	−	0.592974i
$596$		0			0
$597$	−1.20019	−	9.11632i	−0.0491203	−	0.373106i
$598$		0			0
$599$	−25.6785	+	6.88054i	−1.04920	+	0.281131i	−0.741919	−	0.670489i	$-0.766084\pi$
$599$	−25.6785	+	6.88054i	−1.04920	+	0.281131i	−0.307276	+	0.951620i	$0.599418\pi$
$600$		0			0
$601$	1.21196	−	6.09294i	0.0494369	−	0.248536i	−0.948162	−	0.317786i	$-0.897061\pi$
$601$	1.21196	−	6.09294i	0.0494369	−	0.248536i	0.997599	+	0.0692500i	$0.0220606\pi$
$602$		0			0
$603$	−10.3588	−	25.0083i	−0.421841	−	1.01842i
$604$		0			0
$605$	32.7929	−	2.14936i	1.33322	−	0.0873839i
$606$		0			0
$607$	−18.7118	−	1.22644i	−0.759489	−	0.0497795i	−0.319263	−	0.947666i	$-0.603435\pi$
$607$	−18.7118	−	1.22644i	−0.759489	−	0.0497795i	−0.440227	+	0.897887i	$0.645102\pi$
$608$		0			0
$609$	−6.93989	−	0.737904i	−0.281219	−	0.0299014i
$610$		0			0
$611$	35.9432	−	20.7518i	1.45411	−	0.839529i
$612$		0			0
$613$	−17.5352	+	30.3719i	−0.708242	+	1.22671i	0.257267	+	0.966340i	$0.417178\pi$
$613$	−17.5352	+	30.3719i	−0.708242	+	1.22671i	−0.965509	+	0.260371i	$0.916155\pi$
$614$		0			0
$615$	−1.26610	−	6.36511i	−0.0510540	−	0.256666i
$616$		0			0
$617$	−0.888598	+	1.32988i	−0.0357736	+	0.0535390i	−0.848925	−	0.528513i	$-0.822750\pi$
$617$	−0.888598	+	1.32988i	−0.0357736	+	0.0535390i	0.813152	+	0.582052i	$0.197750\pi$
$618$		0			0
$619$	0.0676541	+	1.03220i	0.00271925	+	0.0414877i	0.999003	−	0.0446452i	$-0.0142157\pi$
$619$	0.0676541	+	1.03220i	0.00271925	+	0.0414877i	−0.996284	+	0.0861328i	$0.972549\pi$
$620$		0			0
$621$	19.3510	−	25.2188i	0.776530	−	1.01199i
$622$		0			0
$623$	−24.4947	+	14.9697i	−0.981361	+	0.599746i
$624$		0			0
$625$	0.703094	+	0.188394i	0.0281238	+	0.00753574i
$626$		0			0
$627$	−0.191615	−	0.249717i	−0.00765236	−	0.00997275i
$628$		0			0
$629$	−0.331519	−	1.68801i	−0.0132185	−	0.0673053i
$630$		0			0
$631$	7.69306	+	3.18657i	0.306256	+	0.126855i	0.530518	−	0.847673i	$-0.321997\pi$
$631$	7.69306	+	3.18657i	0.306256	+	0.126855i	−0.224263	+	0.974529i	$0.571997\pi$
$632$		0			0
$633$	3.58942	+	13.3959i	0.142667	+	0.532439i
$634$		0			0
$635$	7.63511	−	2.59177i	0.302990	−	0.102851i
$636$		0			0
$637$	−16.8816	+	18.6579i	−0.668875	+	0.739255i
$638$		0			0
$639$	−9.74123	−	4.80385i	−0.385357	−	0.190037i
$640$		0			0
$641$	12.5463	−	6.18717i	0.495551	−	0.244379i	−0.177300	−	0.984157i	$-0.556736\pi$
$641$	12.5463	−	6.18717i	0.495551	−	0.244379i	0.672851	+	0.739778i	$0.265070\pi$
$642$		0			0
$643$	−8.55512	+	1.70172i	−0.337381	+	0.0671093i	−0.360874	−	0.932615i	$-0.617521\pi$
$643$	−8.55512	+	1.70172i	−0.337381	+	0.0671093i	0.0234925	+	0.999724i	$0.492521\pi$
$644$		0			0
$645$		−	5.48403i		−	0.215934i
$646$		0			0
$647$	−21.6332	−	12.4899i	−0.850489	−	0.491030i	0.0103268	−	0.999947i	$-0.496713\pi$
$647$	−21.6332	−	12.4899i	−0.850489	−	0.491030i	−0.860816	+	0.508917i	$0.830046\pi$
$648$		0			0
$649$	46.8919	−	41.1231i	1.84067	−	1.61422i
$650$		0			0
$651$	−1.40551	−	8.94406i	−0.0550862	−	0.350545i
$652$		0			0
$653$	−5.97474	+	12.1156i	−0.233810	+	0.474119i	−0.981881	−	0.189500i	$-0.939313\pi$
$653$	−5.97474	+	12.1156i	−0.233810	+	0.474119i	0.748071	+	0.663618i	$0.230980\pi$
$654$		0			0
$655$	−2.26044	+	17.1698i	−0.0883228	+	0.670878i
$656$		0			0
$657$	19.4929	+	3.87738i	0.760491	+	0.151271i
$658$		0			0
$659$	15.7906	−	15.7906i	0.615114	−	0.615114i	−0.329160	−	0.944274i	$-0.606766\pi$
$659$	15.7906	−	15.7906i	0.615114	−	0.615114i	0.944274	+	0.329160i	$0.106766\pi$
$660$		0			0
$661$	−29.9281	+	22.9646i	−1.16407	+	0.893220i	−0.995712	−	0.0925064i	$-0.970512\pi$
$661$	−29.9281	+	22.9646i	−1.16407	+	0.893220i	−0.168355	+	0.985726i	$0.553845\pi$
$662$		0			0
$663$	0.636069	−	9.35733i	0.0247029	−	0.363409i
$664$		0			0
$665$	−0.231431	−	0.192953i	−0.00897450	−	0.00748241i
$666$		0			0
$667$	9.67770	−	36.1177i	0.374722	−	1.39848i
$668$		0			0
$669$	2.35413	−	2.68437i	0.0910160	−	0.103784i
$670$		0			0
$671$	−21.0543	+	8.72097i	−0.812791	+	0.336669i
$672$		0			0
$673$	25.2059	−	16.8420i	0.971614	−	0.649212i	0.0349312	−	0.999390i	$-0.488879\pi$
$673$	25.2059	−	16.8420i	0.971614	−	0.649212i	0.936683	+	0.350178i	$0.113879\pi$
$674$		0			0
$675$	−4.94459	−	10.0266i	−0.190317	−	0.385925i
$676$		0			0
$677$	−18.6753	−	21.2951i	−0.717749	−	0.818436i	0.271842	−	0.962342i	$-0.412367\pi$
$677$	−18.6753	−	21.2951i	−0.717749	−	0.818436i	−0.989591	+	0.143906i	$0.954034\pi$
$678$		0			0
$679$	−6.39072	−	28.4025i	−0.245253	−	1.08999i
$680$		0			0
$681$	−4.52259	−	7.83335i	−0.173306	−	0.300175i
$682$		0			0
$683$	4.61364	−	13.5914i	0.176536	−	0.520059i	−0.822260	−	0.569112i	$-0.807287\pi$
$683$	4.61364	−	13.5914i	0.176536	−	0.520059i	0.998796	+	0.0490532i	$0.0156204\pi$
$684$		0			0
$685$	−4.94517	−	3.30426i	−0.188945	−	0.126249i
$686$		0			0
$687$	−4.62484	−	6.92157i	−0.176449	−	0.264074i
$688$		0			0
$689$	−28.4087	−	3.74008i	−1.08229	−	0.142486i
$690$		0			0
$691$	−0.0613343	−	0.180685i	−0.00233327	−	0.00687358i	0.945757	−	0.324874i	$-0.105322\pi$
$691$	−0.0613343	−	0.180685i	−0.00233327	−	0.00687358i	−0.948091	+	0.318001i	$0.896989\pi$
$692$		0			0
$693$	34.4805	+	21.8140i	1.30981	+	0.828644i
$694$		0			0
$695$	16.7717	−	2.20804i	0.636187	−	0.0837556i
$696$		0			0
$697$	31.0667	−	1.96069i	1.17674	−	0.0742665i
$698$		0			0
$699$	−6.07119	+	14.6571i	−0.229633	+	0.554384i
$700$		0			0
$701$	−18.0312	−	18.0312i	−0.681030	−	0.681030i	0.279202	−	0.960232i	$-0.409930\pi$
$701$	−18.0312	−	18.0312i	−0.681030	−	0.681030i	−0.960232	+	0.279202i	$0.909930\pi$
$702$		0			0
$703$	−0.0263000	−	0.0230645i	−0.000991925	−	0.000869895i
$704$		0			0
$705$	7.87426	+	6.04213i	0.296562	+	0.227560i
$706$		0			0
$707$	−4.88189	−	16.5545i	−0.183602	−	0.622597i
$708$		0			0
$709$	2.80724	−	42.8301i	0.105428	−	1.60852i	−0.537954	−	0.842974i	$-0.680803\pi$
$709$	2.80724	−	42.8301i	0.105428	−	1.60852i	0.643382	−	0.765545i	$-0.277531\pi$
$710$		0			0
$711$	−24.4056	−	8.28458i	−0.915281	−	0.310696i
$712$		0			0
$713$	48.5081			1.81664
$714$		0			0
$715$	28.9656			1.08325
$716$		0			0
$717$	−1.13446	−	0.385098i	−0.0423673	−	0.0143817i
$718$		0			0
$719$	0.349487	−	5.33214i	0.0130337	−	0.198855i	−0.986376	−	0.164505i	$-0.947397\pi$
$719$	0.349487	−	5.33214i	0.0130337	−	0.198855i	0.999410	−	0.0343499i	$-0.0109361\pi$
$720$		0			0
$721$	−11.7475	+	48.6723i	−0.437500	+	1.81265i
$722$		0			0
$723$	12.9379	+	9.92763i	0.481167	+	0.369213i
$724$		0			0
$725$	−9.88709	−	8.67075i	−0.367197	−	0.322023i
$726$		0			0
$727$	−2.75127	−	2.75127i	−0.102039	−	0.102039i	0.654244	−	0.756283i	$-0.272987\pi$
$727$	−2.75127	−	2.75127i	−0.102039	−	0.102039i	−0.756283	+	0.654244i	$0.772987\pi$
$728$		0			0
$729$	2.95272	−	7.12851i	0.109360	−	0.264019i
$730$		0			0
$731$	26.0709	+	3.49654i	0.964267	+	0.129324i
$732$		0			0
$733$	12.7160	−	1.67410i	0.469678	−	0.0618343i	0.108027	−	0.994148i	$-0.465547\pi$
$733$	12.7160	−	1.67410i	0.469678	−	0.0618343i	0.361651	+	0.932314i	$0.382213\pi$
$734$		0			0
$735$	−5.66720	−	2.02231i	−0.209038	−	0.0745940i
$736$		0			0
$737$	−19.8566	−	58.4957i	−0.731428	−	2.15472i
$738$		0			0
$739$	2.61083	+	0.343723i	0.0960411	+	0.0126440i	0.178394	−	0.983959i	$-0.442910\pi$
$739$	2.61083	+	0.343723i	0.0960411	+	0.0126440i	−0.0823525	+	0.996603i	$0.526243\pi$
$740$		0			0
$741$	−0.105957	−	0.158576i	−0.00389243	−	0.00582544i
$742$		0			0
$743$	42.1745	+	28.1801i	1.54723	+	1.03383i	0.977229	+	0.212187i	$0.0680585\pi$
$743$	42.1745	+	28.1801i	1.54723	+	1.03383i	0.570004	+	0.821642i	$0.306941\pi$
$744$		0			0
$745$	−2.57771	+	7.59370i	−0.0944401	+	0.278212i
$746$		0			0
$747$	−6.86431	−	11.8893i	−0.251152	−	0.435008i
$748$		0			0
$749$	−0.565663	+	0.521625i	−0.0206689	+	0.0190598i
$750$		0			0
$751$	−1.73734	−	1.98105i	−0.0633963	−	0.0722896i	0.719272	−	0.694728i	$-0.244475\pi$
$751$	−1.73734	−	1.98105i	−0.0633963	−	0.0722896i	−0.782669	+	0.622439i	$0.786142\pi$
$752$		0			0
$753$	−3.12817	−	6.34330i	−0.113997	−	0.231163i
$754$		0			0
$755$	−23.2194	+	15.5147i	−0.845039	+	0.564637i
$756$		0			0
$757$	9.45814	−	3.91769i	0.343762	−	0.142391i	−0.204122	−	0.978946i	$-0.565434\pi$
$757$	9.45814	−	3.91769i	0.343762	−	0.142391i	0.547883	+	0.836555i	$0.315434\pi$
$758$		0			0
$759$	22.2050	−	25.3200i	0.805991	−	0.919057i
$760$		0			0
$761$	3.65248	−	13.6312i	0.132402	−	0.494132i	−0.867593	−	0.497275i	$-0.834334\pi$
$761$	3.65248	−	13.6312i	0.132402	−	0.494132i	0.999995	+	0.00314358i	$0.00100063\pi$
$762$		0			0
$763$	−0.967713	+	1.16069i	−0.0350336	+	0.0420197i
$764$		0			0
$765$	−13.7975	+	4.64641i	−0.498851	+	0.167991i
$766$		0			0
$767$	29.9812	−	23.0054i	1.08256	−	0.830675i
$768$		0			0
$769$	−29.1377	+	29.1377i	−1.05073	+	1.05073i	−0.0520916	+	0.998642i	$0.516589\pi$
$769$	−29.1377	+	29.1377i	−1.05073	+	1.05073i	−0.998642	+	0.0520916i	$0.983411\pi$
$770$		0			0
$771$	7.51032	+	1.49390i	0.270478	+	0.0538013i
$772$		0			0
$773$	1.31096	−	9.95770i	0.0471518	−	0.358154i	−0.951562	−	0.307456i	$-0.900522\pi$
$773$	1.31096	−	9.95770i	0.0471518	−	0.358154i	0.998714	−	0.0506974i	$-0.0161444\pi$
$774$		0			0
$775$	7.54548	−	15.3007i	0.271042	−	0.549618i
$776$		0			0
$777$	−0.651860	−	0.251131i	−0.0233853	−	0.00900928i
$778$		0			0
$779$	0.475908	−	0.417360i	0.0170512	−	0.0149535i
$780$		0			0
$781$	−21.4660	−	12.3934i	−0.768115	−	0.443471i
$782$		0			0
$783$			14.7705i			0.527856i
$784$		0			0
$785$	−30.2449	+	6.01608i	−1.07949	+	0.214723i
$786$		0			0
$787$	−15.7600	+	7.77199i	−0.561785	+	0.277042i	−0.700930	−	0.713230i	$-0.747231\pi$
$787$	−15.7600	+	7.77199i	−0.561785	+	0.277042i	0.139145	+	0.990272i	$0.455565\pi$
$788$		0			0
$789$	2.61365	+	1.28891i	0.0930483	+	0.0458863i
$790$		0			0
$791$	13.3093	+	18.8806i	0.473223	+	0.671317i
$792$		0			0
$793$	−13.0753	+	4.43847i	−0.464318	+	0.157615i
$794$		0			0
$795$	−1.77352	−	6.61886i	−0.0629003	−	0.234747i
$796$		0			0
$797$	−47.9992	−	19.8819i	−1.70022	−	0.704254i	−0.700266	−	0.713882i	$-0.746935\pi$
$797$	−47.9992	−	19.8819i	−1.70022	−	0.704254i	−0.999954	+	0.00962795i	$0.996935\pi$
$798$		0			0
$799$	−33.7446	+	33.5816i	−1.19380	+	1.18803i
$800$		0			0
$801$	17.1703	+	22.3768i	0.606682	+	0.790644i
$802$		0			0
$803$	43.8111	+	11.7392i	1.54606	+	0.414266i
$804$		0			0
$805$	15.4172	−	28.3133i	0.543387	−	0.997912i
$806$		0			0
$807$	−4.00075	+	5.21388i	−0.140833	+	0.183537i
$808$		0			0
$809$	0.0517832	+	0.790058i	0.00182060	+	0.0277770i	0.998673	−	0.0515083i	$-0.0164029\pi$
$809$	0.0517832	+	0.790058i	0.00182060	+	0.0277770i	−0.996852	+	0.0792853i	$0.974736\pi$
$810$		0			0
$811$	−2.80149	+	4.19272i	−0.0983736	+	0.147226i	−0.877391	−	0.479775i	$-0.840718\pi$
$811$	−2.80149	+	4.19272i	−0.0983736	+	0.147226i	0.779018	+	0.627002i	$0.215718\pi$
$812$		0			0
$813$	0.479700	+	2.41161i	0.0168238	+	0.0845789i
$814$		0			0
$815$	15.6143	−	27.0447i	0.546944	−	0.947335i
$816$		0			0
$817$	0.463229	−	0.267446i	0.0162063	−	0.00935674i
$818$		0			0
$819$	19.9829	+	14.5554i	0.698261	+	0.508608i
$820$		0			0
$821$	−6.58756	−	0.431772i	−0.229908	−	0.0150689i	−0.0499861	−	0.998750i	$-0.515918\pi$
$821$	−6.58756	−	0.431772i	−0.229908	−	0.0150689i	−0.179921	+	0.983681i	$0.557584\pi$
$822$		0			0
$823$	−41.4960	+	2.71979i	−1.44646	+	0.0948059i	−0.768291	−	0.640101i	$-0.778893\pi$
$823$	−41.4960	+	2.71979i	−1.44646	+	0.0948059i	−0.678168	+	0.734907i	$0.737226\pi$
$824$		0			0
$825$	−4.53257	−	10.9426i	−0.157804	−	0.380972i
$826$		0			0
$827$	1.81293	−	9.11419i	0.0630416	−	0.316931i	−0.936378	−	0.350993i	$-0.885844\pi$
$827$	1.81293	−	9.11419i	0.0630416	−	0.316931i	0.999420	+	0.0340613i	$0.0108442\pi$
$828$		0			0
$829$	−32.8898	+	8.81280i	−1.14231	+	0.306081i	−0.779879	−	0.625930i	$-0.784720\pi$
$829$	−32.8898	+	8.81280i	−1.14231	+	0.306081i	−0.362431	+	0.932011i	$0.618053\pi$
$830$		0			0
$831$	−0.579855	−	4.40443i	−0.0201149	−	0.152788i
$832$		0			0
$833$	13.2273	−	25.6523i	0.458299	−	0.888798i
$834$		0			0
$835$	0.0933436	+	0.709015i	0.00323029	+	0.0245365i
$836$		0			0
$837$	−18.5088	+	4.95941i	−0.639757	+	0.171422i
$838$		0			0
$839$	−2.17086	+	10.9136i	−0.0749464	+	0.376781i	−0.999995	−	0.00306710i	$-0.999024\pi$
$839$	−2.17086	+	10.9136i	−0.0749464	+	0.376781i	0.925049	+	0.379848i	$0.124024\pi$
$840$		0			0
$841$	−4.44884	−	10.7405i	−0.153408	−	0.370361i
$842$		0			0
$843$	−10.6886	+	0.700568i	−0.368135	+	0.0241288i
$844$		0			0
$845$	−0.107640	−	0.00705511i	−0.00370293	−	0.000242703i
$846$		0			0
$847$	51.7398	+	37.6869i	1.77780	+	1.29494i
$848$		0			0
$849$	−5.47320	+	3.15995i	−0.187840	+	0.108449i
$850$		0			0
$851$	1.87136	−	3.24128i	0.0641493	−	0.111110i
$852$		0			0
$853$	−1.13256	−	5.69377i	−0.0387782	−	0.194951i	0.956540	−	0.291600i	$-0.0941876\pi$
$853$	−1.13256	−	5.69377i	−0.0387782	−	0.194951i	−0.995319	+	0.0966489i	$0.969188\pi$
$854$		0			0
$855$	−0.164477	+	0.246158i	−0.00562500	+	0.00841841i
$856$		0			0
$857$	−1.95989	−	29.9021i	−0.0669485	−	1.02144i	−0.890731	−	0.454531i	$-0.849807\pi$
$857$	−1.95989	−	29.9021i	−0.0669485	−	1.02144i	0.823782	−	0.566906i	$-0.191860\pi$
$858$		0			0
$859$	−27.0712	+	35.2799i	−0.923657	+	1.20373i	0.0550529	+	0.998483i	$0.482467\pi$
$859$	−27.0712	+	35.2799i	−0.923657	+	1.20373i	−0.978710	+	0.205250i	$0.934199\pi$
$860$		0			0
$861$	6.04506	−	11.1016i	0.206015	−	0.378340i
$862$		0			0
$863$	−13.6700	−	3.66287i	−0.465332	−	0.124685i	0.0185324	−	0.999828i	$-0.494101\pi$
$863$	−13.6700	−	3.66287i	−0.465332	−	0.124685i	−0.483865	+	0.875143i	$0.660767\pi$
$864$		0			0
$865$	13.3666	+	17.4197i	0.454479	+	0.592289i
$866$		0			0
$867$	2.04769	+	10.5614i	0.0695431	+	0.358686i
$868$		0			0
$869$	−54.3406	−	22.5086i	−1.84338	−	0.763552i
$870$		0			0
$871$	−9.68750	−	36.1542i	−0.328248	−	1.22504i
$872$		0			0
$873$	−27.0860	+	9.19445i	−0.916722	+	0.311185i
$874$		0			0
$875$	−16.8857	−	23.9541i	−0.570840	−	0.809797i
$876$		0			0
$877$	−11.2641	−	5.55482i	−0.380360	−	0.187573i	0.242051	−	0.970264i	$-0.422180\pi$
$877$	−11.2641	−	5.55482i	−0.380360	−	0.187573i	−0.622411	+	0.782691i	$0.713847\pi$
$878$		0			0
$879$	−5.86991	+	2.89472i	−0.197987	+	0.0976365i
$880$		0			0
$881$	38.5010	−	7.65832i	1.29713	−	0.258015i	0.502219	−	0.864740i	$-0.332517\pi$
$881$	38.5010	−	7.65832i	1.29713	−	0.258015i	0.794912	+	0.606725i	$0.207517\pi$
$882$		0			0
$883$			50.6147i			1.70332i	0.524094	+	0.851661i	$0.324404\pi$
$883$			50.6147i			1.70332i	−0.524094	+	0.851661i	$0.675596\pi$
$884$		0			0
$885$	7.82652	+	4.51865i	0.263086	+	0.151893i
$886$		0			0
$887$	29.0131	−	25.4438i	0.974166	−	0.854320i	−0.0151832	−	0.999885i	$-0.504833\pi$
$887$	29.0131	−	25.4438i	0.974166	−	0.854320i	0.989349	+	0.145564i	$0.0464998\pi$
$888$		0			0
$889$	14.6550	+	5.64589i	0.491513	+	0.189357i
$890$		0			0
$891$	14.5784	−	29.5620i	0.488393	−	0.990363i
$892$		0			0
$893$	−0.126359	+	0.959791i	−0.00422844	+	0.0321182i
$894$		0			0
$895$	14.1215	+	2.80895i	0.472031	+	0.0938928i
$896$		0			0
$897$	14.4289	−	14.4289i	0.481766	−	0.481766i
$898$		0			0
$899$	−17.8821	+	13.7215i	−0.596403	+	0.457636i
$900$		0			0
$901$	32.5966	−	4.21116i	1.08595	−	0.140294i
$902$		0			0
$903$	6.84021	−	8.20425i	0.227628	−	0.273020i
$904$		0			0
$905$	2.10619	−	7.86039i	0.0700120	−	0.261288i
$906$		0			0
$907$	−33.5604	+	38.2683i	−1.11435	+	1.27068i	−0.155173	+	0.987887i	$0.549593\pi$
$907$	−33.5604	+	38.2683i	−1.11435	+	1.27068i	−0.959182	+	0.282790i	$0.908740\pi$
$908$		0			0
$909$	−15.6670	+	6.48946i	−0.519640	+	0.215242i
$910$		0			0
$911$	−1.56568	+	1.04615i	−0.0518731	+	0.0346605i	−0.581236	−	0.813735i	$-0.697431\pi$
$911$	−1.56568	+	1.04615i	−0.0518731	+	0.0346605i	0.529363	+	0.848395i	$0.322431\pi$
$912$		0			0
$913$	−13.8570	−	28.0993i	−0.458601	−	0.929951i
$914$		0			0
$915$	−2.17723	−	2.48265i	−0.0719769	−	0.0820739i
$916$		0			0
$917$	−24.7974	+	22.8669i	−0.818884	+	0.755133i
$918$		0			0
$919$	9.44939	+	16.3668i	0.311707	+	0.539892i	0.978732	−	0.205143i	$-0.0657660\pi$
$919$	9.44939	+	16.3668i	0.311707	+	0.539892i	−0.667025	+	0.745035i	$0.732433\pi$
$920$		0			0
$921$	3.04765	−	8.97808i	0.100423	−	0.295838i
$922$		0			0
$923$	−12.4875	−	8.34390i	−0.411032	−	0.274643i
$924$		0			0
$925$	−0.731295	−	1.09446i	−0.0240448	−	0.0359856i
$926$		0			0
$927$	48.7743	+	6.42126i	1.60196	+	0.210902i
$928$		0			0
$929$	9.26825	+	27.3034i	0.304082	+	0.895795i	0.986345	+	0.164689i	$0.0526622\pi$
$929$	9.26825	+	27.3034i	0.304082	+	0.895795i	−0.682264	+	0.731106i	$0.739005\pi$
$930$		0			0
$931$	−0.105556	−	0.577325i	−0.00345947	−	0.0189211i
$932$		0			0
$933$	1.22665	−	0.161491i	0.0401587	−	0.00528699i
$934$		0			0
$935$	−32.1137	+	8.52156i	−1.05023	+	0.278685i
$936$		0			0
$937$	−7.99667	+	19.3057i	−0.261240	+	0.630689i	−0.999016	−	0.0443569i	$-0.985876\pi$
$937$	−7.99667	+	19.3057i	−0.261240	+	0.630689i	0.737776	+	0.675046i	$0.235876\pi$
$938$		0			0
$939$	7.78307	+	7.78307i	0.253991	+	0.253991i
$940$		0			0
$941$	30.8716	+	27.0737i	1.00639	+	0.882576i	0.993092	−	0.117335i	$-0.0374353\pi$
$941$	30.8716	+	27.0737i	1.00639	+	0.882576i	0.0132930	+	0.999912i	$0.495769\pi$
$942$		0			0
$943$	53.7303	+	41.2287i	1.74970	+	1.34259i
$944$		0			0
$945$	−2.98790	+	12.3795i	−0.0971964	+	0.402705i
$946$		0			0
$947$	0.615536	−	9.39126i	0.0200022	−	0.305175i	−0.976122	−	0.217221i	$-0.930301\pi$
$947$	0.615536	−	9.39126i	0.0200022	−	0.305175i	0.996125	−	0.0879536i	$-0.0280327\pi$
$948$		0			0
$949$	26.0236	+	8.83383i	0.844762	+	0.286758i
$950$		0			0
$951$	10.4065			0.337454
$952$		0			0
$953$	−47.6995			−1.54514			−0.772569	−	0.634931i	$-0.781028\pi$
$953$	−47.6995			−1.54514			−0.772569	+	0.634931i	$0.781028\pi$
$954$		0			0
$955$	1.06090	+	0.360126i	0.0343299	+	0.0116534i
$956$		0			0
$957$	−1.02347	+	15.6151i	−0.0330841	+	0.504766i
$958$		0			0
$959$	−3.27671	−	11.1113i	−0.105810	−	0.358804i
$960$		0			0
$961$	1.39558	+	1.07086i	0.0450187	+	0.0345440i
$962$		0			0
$963$	0.568403	+	0.498476i	0.0183165	+	0.0160632i
$964$		0			0
$965$	−17.6990	−	17.6990i	−0.569752	−	0.569752i
$966$		0			0
$967$	−4.65328	+	11.2340i	−0.149639	+	0.361261i	−0.980869	−	0.194667i	$-0.937637\pi$
$967$	−4.65328	+	11.2340i	−0.149639	+	0.361261i	0.831230	+	0.555929i	$0.187637\pi$
$968$		0			0
$969$	0.164125	+	0.144639i	0.00527247	+	0.00464646i
$970$		0			0
$971$	−3.40936	+	0.448851i	−0.109412	+	0.0144043i	−0.185033	−	0.982732i	$-0.559239\pi$
$971$	−3.40936	+	0.448851i	−0.109412	+	0.0144043i	0.0756216	+	0.997137i	$0.475906\pi$
$972$		0			0
$973$	27.8449	+	17.6160i	0.892668	+	0.564743i
$974$		0			0
$975$	−2.30682	−	6.79567i	−0.0738773	−	0.217636i
$976$		0			0
$977$	−10.7225	−	1.41165i	−0.343045	−	0.0451627i	−0.0429642	−	0.999077i	$-0.513680\pi$
$977$	−10.7225	−	1.41165i	−0.343045	−	0.0451627i	−0.300080	+	0.953914i	$0.597013\pi$
$978$		0			0
$979$	35.7608	+	53.5198i	1.14292	+	1.71050i
$980$		0			0
$981$	1.23455	+	0.824898i	0.0394161	+	0.0263370i
$982$		0			0
$983$	8.15261	−	24.0168i	0.260028	−	0.766018i	−0.736000	−	0.676981i	$-0.763288\pi$
$983$	8.15261	−	24.0168i	0.260028	−	0.766018i	0.996028	−	0.0890367i	$-0.0283788\pi$
$984$		0			0
$985$	−12.0296	−	20.8359i	−0.383295	−	0.663887i
$986$		0			0
$987$	4.24375	+	18.8607i	0.135080	+	0.600342i
$988$		0			0
$989$	37.7341	+	43.0275i	1.19988	+	1.36820i
$990$		0			0
$991$	24.5211	+	49.7239i	0.778939	+	1.57953i	0.814499	+	0.580165i	$0.197012\pi$
$991$	24.5211	+	49.7239i	0.778939	+	1.57953i	−0.0355592	+	0.999368i	$0.511321\pi$
$992$		0			0
$993$	4.94187	−	3.30205i	0.156825	−	0.104787i
$994$		0			0
$995$	−18.2343	+	7.55289i	−0.578066	+	0.239443i
$996$		0			0
$997$	−9.84580	+	11.2270i	−0.311820	+	0.355562i	−0.886428	−	0.462866i	$-0.846821\pi$
$997$	−9.84580	+	11.2270i	−0.311820	+	0.355562i	0.574608	+	0.818428i	$0.305154\pi$
$998$		0			0
$999$	−0.382651	+	1.42807i	−0.0121065	+	0.0451823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.465.8	yes	192
7.5	odd	6	inner	476.2.bl.a.397.8	yes	192
17.3	odd	16	inner	476.2.bl.a.241.8	yes	192
119.54	even	48	inner	476.2.bl.a.173.8	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.173.8	✓	192	119.54	even	48	inner
476.2.bl.a.241.8	yes	192	17.3	odd	16	inner
476.2.bl.a.397.8	yes	192	7.5	odd	6	inner
476.2.bl.a.465.8	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599246 + 0.203417i) q^{3} +(0.0888400 - 1.35544i) q^{5} +(1.82354 - 1.91695i) q^{7} +(-2.06234 - 1.58249i) q^{9} +O(q^{10})\)	\(q+(0.599246 + 0.203417i) q^{3} +(0.0888400 - 1.35544i) q^{5} +(1.82354 - 1.91695i) q^{7} +(-2.06234 - 1.58249i) q^{9} +(-4.46023 - 3.91152i) q^{11} +(-2.54171 - 2.54171i) q^{13} +(0.328955 - 0.794169i) q^{15} +(3.56571 + 2.07019i) q^{17} +(0.0831250 - 0.0109436i) q^{19} +(1.48269 - 0.777791i) q^{21} +(2.88348 + 8.49447i) q^{23} +(3.12791 + 0.411797i) q^{25} +(-1.96869 - 2.94636i) q^{27} +(-3.46580 - 2.31578i) q^{29} +(1.73818 - 5.12051i) q^{31} +(-1.87711 - 3.25125i) q^{33} +(-2.43631 - 2.64199i) q^{35} +(-0.275094 - 0.313685i) q^{37} +(-1.00608 - 2.04014i) q^{39} +(6.27742 - 4.19443i) q^{41} +(5.89411 - 2.44142i) q^{43} +(-2.32818 + 2.65478i) q^{45} +(-2.98842 + 11.1529i) q^{47} +(-0.349432 - 6.99127i) q^{49} +(1.71563 + 1.96588i) q^{51} +(6.32425 - 4.85277i) q^{53} +(-5.69806 + 5.69806i) q^{55} +(0.0520384 + 0.0103511i) q^{57} +(-1.37227 + 10.4234i) q^{59} +(1.69902 - 3.44527i) q^{61} +(-6.79432 + 1.06769i) q^{63} +(-3.67093 + 3.21932i) q^{65} +(9.01789 + 5.20648i) q^{67} +5.67683i q^{69} +(4.09792 - 0.815126i) q^{71} +(-6.85708 + 3.38154i) q^{73} +(1.79062 + 0.883037i) q^{75} +(-15.6316 + 1.41727i) q^{77} +(9.38848 - 3.18696i) q^{79} +(1.43803 + 5.36679i) q^{81} +(4.87919 + 2.02103i) q^{83} +(3.12279 - 4.64918i) q^{85} +(-1.60580 - 2.09272i) q^{87} +(-10.4805 - 2.80823i) q^{89} +(-9.50725 + 0.237444i) q^{91} +(2.08320 - 2.71487i) q^{93} +(-0.00744854 - 0.113643i) q^{95} +(6.11324 - 9.14911i) q^{97} +(3.00858 + 15.1252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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