LMFDB - Embedded newform 476.2.bh.a.457.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.3
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20085 + 1.56498i) q^{3} +(0.450909 - 3.42500i) q^{5} +(-0.621265 + 2.57178i) q^{7} +(-0.230659 - 0.860832i) q^{9} +O(q^{10})$	\(q+(-1.20085 + 1.56498i) q^{3} +(0.450909 - 3.42500i) q^{5} +(-0.621265 + 2.57178i) q^{7} +(-0.230659 - 0.860832i) q^{9} +(1.93413 - 0.254633i) q^{11} -1.92804i q^{13} +(4.81857 + 4.81857i) q^{15} +(2.48125 + 3.29293i) q^{17} +(7.08800 - 1.89922i) q^{19} +(-3.27873 - 4.06058i) q^{21} +(5.56777 + 7.25606i) q^{23} +(-6.69766 - 1.79463i) q^{25} +(-3.84320 - 1.59190i) q^{27} +(-1.59872 + 0.662213i) q^{29} +(-0.182278 + 0.237549i) q^{31} +(-1.92411 + 3.33265i) q^{33} +(8.52819 + 3.28747i) q^{35} +(4.46546 + 0.587888i) q^{37} +(3.01734 + 2.31528i) q^{39} +(10.8857 + 4.50902i) q^{41} +(-4.91305 + 4.91305i) q^{43} +(-3.05235 + 0.401850i) q^{45} +(-5.03548 - 2.90724i) q^{47} +(-6.22806 - 3.19551i) q^{49} +(-8.13298 - 0.0712095i) q^{51} +(0.222912 - 0.831918i) q^{53} -6.73921i q^{55} +(-5.53938 + 13.3733i) q^{57} +(10.4348 + 2.79599i) q^{59} +(3.65628 - 2.80557i) q^{61} +(2.35717 - 0.0583987i) q^{63} +(-6.60352 - 0.869370i) q^{65} +(0.0647526 + 0.112155i) q^{67} -18.0416 q^{69} +(0.0493221 + 0.119074i) q^{71} +(-4.93326 - 3.78542i) q^{73} +(10.8514 - 8.32661i) q^{75} +(-0.546749 + 5.13235i) q^{77} +(-9.64016 - 12.5633i) q^{79} +(9.42180 - 5.43968i) q^{81} +(-7.03430 - 7.03430i) q^{83} +(12.3971 - 7.01347i) q^{85} +(0.883478 - 3.29718i) q^{87} +(-4.59019 - 2.65015i) q^{89} +(4.95848 + 1.19782i) q^{91} +(-0.152871 - 0.570521i) q^{93} +(-3.30879 - 25.1328i) q^{95} +(5.70314 - 2.36232i) q^{97} +(-0.665322 - 1.60623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.20085	+	1.56498i	−0.693311	+	0.903541i	−0.998816	−	0.0486498i	$-0.984508\pi$
$3$	−1.20085	+	1.56498i	−0.693311	+	0.903541i	0.305505	+	0.952191i	$0.401175\pi$
$4$		0			0
$5$	0.450909	−	3.42500i	0.201653	−	1.53171i	−0.528802	−	0.848745i	$-0.677359\pi$
$5$	0.450909	−	3.42500i	0.201653	−	1.53171i	0.730455	−	0.682961i	$-0.239308\pi$
$6$		0			0
$7$	−0.621265	+	2.57178i	−0.234816	+	0.972040i
$7$	−0.621265	+	2.57178i	−0.234816	+	0.972040i
$8$		0			0
$9$	−0.230659	−	0.860832i	−0.0768864	−	0.286944i
$10$		0			0
$11$	1.93413	−	0.254633i	0.583163	−	0.0767748i	0.166828	−	0.985986i	$-0.446648\pi$
$11$	1.93413	−	0.254633i	0.583163	−	0.0767748i	0.416335	+	0.909211i	$0.363314\pi$
$12$		0			0
$13$		−	1.92804i		−	0.534741i	−0.963594	−	0.267371i	$-0.913845\pi$
$13$		−	1.92804i		−	0.534741i	0.963594	−	0.267371i	$-0.0861548\pi$
$14$		0			0
$15$	4.81857	+	4.81857i	1.24415	+	1.24415i
$16$		0			0
$17$	2.48125	+	3.29293i	0.601792	+	0.798653i
$17$	2.48125	+	3.29293i	0.601792	+	0.798653i
$18$		0			0
$19$	7.08800	−	1.89922i	1.62610	−	0.435712i	0.673314	−	0.739357i	$-0.264870\pi$
$19$	7.08800	−	1.89922i	1.62610	−	0.435712i	0.952785	+	0.303645i	$0.0982036\pi$
$20$		0			0
$21$	−3.27873	−	4.06058i	−0.715477	−	0.886092i
$22$		0			0
$23$	5.56777	+	7.25606i	1.16096	+	1.51299i	0.819482	+	0.573104i	$0.194261\pi$
$23$	5.56777	+	7.25606i	1.16096	+	1.51299i	0.341479	+	0.939889i	$0.389072\pi$
$24$		0			0
$25$	−6.69766	−	1.79463i	−1.33953	−	0.358927i
$26$		0			0
$27$	−3.84320	−	1.59190i	−0.739624	−	0.306362i
$28$		0			0
$29$	−1.59872	+	0.662213i	−0.296875	+	0.122970i	−0.526149	−	0.850392i	$-0.676365\pi$
$29$	−1.59872	+	0.662213i	−0.296875	+	0.122970i	0.229274	+	0.973362i	$0.426365\pi$
$30$		0			0
$31$	−0.182278	+	0.237549i	−0.0327380	+	0.0426650i	−0.809435	−	0.587209i	$-0.800227\pi$
$31$	−0.182278	+	0.237549i	−0.0327380	+	0.0426650i	0.776697	+	0.629874i	$0.216893\pi$
$32$		0			0
$33$	−1.92411	+	3.33265i	−0.334944	+	0.580140i
$34$		0			0
$35$	8.52819	+	3.28747i	1.44153	+	0.555684i
$36$		0			0
$37$	4.46546	+	0.587888i	0.734116	+	0.0966482i	0.488309	−	0.872671i	$-0.337614\pi$
$37$	4.46546	+	0.587888i	0.734116	+	0.0966482i	0.245807	+	0.969319i	$0.420947\pi$
$38$		0			0
$39$	3.01734	+	2.31528i	0.483160	+	0.370742i
$40$		0			0
$41$	10.8857	+	4.50902i	1.70007	+	0.704191i	0.999952	−	0.00983715i	$-0.00313131\pi$
$41$	10.8857	+	4.50902i	1.70007	+	0.704191i	0.700117	+	0.714028i	$0.253131\pi$
$42$		0			0
$43$	−4.91305	+	4.91305i	−0.749233	+	0.749233i	−0.974335	−	0.225102i	$-0.927728\pi$
$43$	−4.91305	+	4.91305i	−0.749233	+	0.749233i	0.225102	+	0.974335i	$0.427728\pi$
$44$		0			0
$45$	−3.05235	+	0.401850i	−0.455018	+	0.0599043i
$46$		0			0
$47$	−5.03548	−	2.90724i	−0.734500	−	0.424064i	0.0855661	−	0.996332i	$-0.472730\pi$
$47$	−5.03548	−	2.90724i	−0.734500	−	0.424064i	−0.820066	+	0.572269i	$0.806063\pi$
$48$		0			0
$49$	−6.22806	−	3.19551i	−0.889723	−	0.456501i
$50$		0			0
$51$	−8.13298	−	0.0712095i	−1.13884	−	0.00997132i
$52$		0			0
$53$	0.222912	−	0.831918i	0.0306193	−	0.114273i	−0.948925	−	0.315502i	$-0.897827\pi$
$53$	0.222912	−	0.831918i	0.0306193	−	0.114273i	0.979544	+	0.201230i	$0.0644937\pi$
$54$		0			0
$55$		−	6.73921i		−	0.908715i
$56$		0			0
$57$	−5.53938	+	13.3733i	−0.733709	+	1.77133i
$58$		0			0
$59$	10.4348	+	2.79599i	1.35849	+	0.364007i	0.863262	−	0.504756i	$-0.168417\pi$
$59$	10.4348	+	2.79599i	1.35849	+	0.364007i	0.495229	+	0.868762i	$0.335084\pi$
$60$		0			0
$61$	3.65628	−	2.80557i	0.468139	−	0.359216i	−0.347593	−	0.937646i	$-0.613001\pi$
$61$	3.65628	−	2.80557i	0.468139	−	0.359216i	0.815732	+	0.578430i	$0.196334\pi$
$62$		0			0
$63$	2.35717	−	0.0583987i	0.296975	−	0.00735755i
$64$		0			0
$65$	−6.60352	−	0.869370i	−0.819066	−	0.107832i
$66$		0			0
$67$	0.0647526	+	0.112155i	0.00791079	+	0.0137019i	0.869954	−	0.493133i	$-0.164149\pi$
$67$	0.0647526	+	0.112155i	0.00791079	+	0.0137019i	−0.862043	+	0.506835i	$0.830815\pi$
$68$		0			0
$69$	−18.0416			−2.17196
$70$		0			0
$71$	0.0493221	+	0.119074i	0.00585345	+	0.0141315i	0.926779	−	0.375606i	$-0.122566\pi$
$71$	0.0493221	+	0.119074i	0.00585345	+	0.0141315i	−0.920926	+	0.389738i	$0.872566\pi$
$72$		0			0
$73$	−4.93326	−	3.78542i	−0.577394	−	0.443050i	0.278328	−	0.960486i	$-0.410220\pi$
$73$	−4.93326	−	3.78542i	−0.577394	−	0.443050i	−0.855722	+	0.517436i	$0.826886\pi$
$74$		0			0
$75$	10.8514	−	8.32661i	1.25302	−	0.961474i
$76$		0			0
$77$	−0.546749	+	5.13235i	−0.0623079	+	0.584885i
$78$		0			0
$79$	−9.64016	−	12.5633i	−1.08460	−	1.41348i	−0.902755	−	0.430155i	$-0.858459\pi$
$79$	−9.64016	−	12.5633i	−1.08460	−	1.41348i	−0.181848	−	0.983327i	$-0.558208\pi$
$80$		0			0
$81$	9.42180	−	5.43968i	1.04687	−	0.604409i
$82$		0			0
$83$	−7.03430	−	7.03430i	−0.772115	−	0.772115i	0.206361	−	0.978476i	$-0.433838\pi$
$83$	−7.03430	−	7.03430i	−0.772115	−	0.772115i	−0.978476	+	0.206361i	$0.933838\pi$
$84$		0			0
$85$	12.3971	−	7.01347i	1.34465	−	0.760718i
$86$		0			0
$87$	0.883478	−	3.29718i	0.0947188	−	0.353495i
$88$		0			0
$89$	−4.59019	−	2.65015i	−0.486559	−	0.280915i	0.236587	−	0.971610i	$-0.423971\pi$
$89$	−4.59019	−	2.65015i	−0.486559	−	0.280915i	−0.723146	+	0.690695i	$0.757305\pi$
$90$		0			0
$91$	4.95848	+	1.19782i	0.519790	+	0.125566i
$92$		0			0
$93$	−0.152871	−	0.570521i	−0.0158519	−	0.0591603i
$94$		0			0
$95$	−3.30879	−	25.1328i	−0.339475	−	2.57857i
$96$		0			0
$97$	5.70314	−	2.36232i	0.579066	−	0.239857i	−0.0738726	−	0.997268i	$-0.523536\pi$
$97$	5.70314	−	2.36232i	0.579066	−	0.239857i	0.652939	+	0.757411i	$0.273536\pi$
$98$		0			0
$99$	−0.665322	−	1.60623i	−0.0668674	−	0.161432i
$100$		0			0
$101$	−8.33687	−	14.4399i	−0.829549	−	1.43682i	−0.898392	−	0.439194i	$-0.855264\pi$
$101$	−8.33687	−	14.4399i	−0.829549	−	1.43682i	0.0688429	−	0.997628i	$-0.478069\pi$
$102$		0			0
$103$	6.03110	−	10.4462i	0.594262	−	1.02929i	−0.399389	−	0.916782i	$-0.630778\pi$
$103$	6.03110	−	10.4462i	0.594262	−	1.02929i	0.993651	−	0.112510i	$-0.0358891\pi$
$104$		0			0
$105$	−15.3859	+	9.39868i	−1.50151	+	0.917217i
$106$		0			0
$107$	−1.90276	+	14.4529i	−0.183946	+	1.39721i	0.611527	+	0.791223i	$0.290555\pi$
$107$	−1.90276	+	14.4529i	−0.183946	+	1.39721i	−0.795474	+	0.605988i	$0.792778\pi$
$108$		0			0
$109$	−0.209877	−	1.59417i	−0.0201026	−	0.152694i	0.978450	−	0.206486i	$-0.0662027\pi$
$109$	−0.209877	−	1.59417i	−0.0201026	−	0.152694i	−0.998552	+	0.0537915i	$0.982869\pi$
$110$		0			0
$111$	−6.28238	+	6.28238i	−0.596297	+	0.596297i
$112$		0			0
$113$	−1.54027	+	3.71854i	−0.144896	+	0.349811i	−0.979620	−	0.200858i	$-0.935627\pi$
$113$	−1.54027	+	3.71854i	−0.144896	+	0.349811i	0.834724	+	0.550668i	$0.185627\pi$
$114$		0			0
$115$	27.3626	−	15.7978i	2.55157	−	1.47315i
$116$		0			0
$117$	−1.65972	+	0.444719i	−0.153441	+	0.0411143i
$118$		0			0
$119$	−10.0102	+	4.33544i	−0.917633	+	0.397429i
$120$		0			0
$121$	−6.94916	+	1.86202i	−0.631741	+	0.169275i
$122$		0			0
$123$	−20.1287	+	11.6213i	−1.81494	+	1.04786i
$124$		0			0
$125$	−2.55665	+	6.17231i	−0.228674	+	0.552068i
$126$		0			0
$127$	−1.48245	+	1.48245i	−0.131547	+	0.131547i	−0.769814	−	0.638268i	$-0.779651\pi$
$127$	−1.48245	+	1.48245i	−0.131547	+	0.131547i	0.638268	+	0.769814i	$0.279651\pi$
$128$		0			0
$129$	−1.78898	−	13.5887i	−0.157511	−	1.19641i
$130$		0			0
$131$	−2.55658	+	19.4191i	−0.223369	+	1.69666i	0.401445	+	0.915883i	$0.368508\pi$
$131$	−2.55658	+	19.4191i	−0.223369	+	1.69666i	−0.624814	+	0.780773i	$0.714825\pi$
$132$		0			0
$133$	0.480849	+	19.4087i	0.0416949	+	1.68295i
$134$		0			0
$135$	−7.18520	+	12.4451i	−0.618404	+	1.07111i
$136$		0			0
$137$	4.29100	+	7.43223i	0.366605	+	0.634979i	0.989032	−	0.147699i	$-0.0471867\pi$
$137$	4.29100	+	7.43223i	0.366605	+	0.634979i	−0.622427	+	0.782678i	$0.713853\pi$
$138$		0			0
$139$	−3.25378	−	7.85531i	−0.275982	−	0.666279i	0.723735	−	0.690078i	$-0.242424\pi$
$139$	−3.25378	−	7.85531i	−0.275982	−	0.666279i	−0.999717	+	0.0237992i	$0.992424\pi$
$140$		0			0
$141$	10.5966	−	4.38926i	0.892396	−	0.369643i
$142$		0			0
$143$	−0.490942	−	3.72908i	−0.0410547	−	0.311841i
$144$		0			0
$145$	1.54720	+	5.77422i	0.128488	+	0.479523i
$146$		0			0
$147$	12.4799	−	5.90945i	1.02932	−	0.487403i
$148$		0			0
$149$	−7.97067	−	4.60187i	−0.652983	−	0.377000i	0.136615	−	0.990624i	$-0.456378\pi$
$149$	−7.97067	−	4.60187i	−0.652983	−	0.377000i	−0.789598	+	0.613624i	$0.789711\pi$
$150$		0			0
$151$	−2.59735	+	9.69346i	−0.211370	+	0.788843i	0.776043	+	0.630680i	$0.217224\pi$
$151$	−2.59735	+	9.69346i	−0.211370	+	0.788843i	−0.987413	+	0.158163i	$0.949443\pi$
$152$		0			0
$153$	2.26234	−	2.89549i	0.182899	−	0.234086i
$154$		0			0
$155$	0.731413	+	0.731413i	0.0587485	+	0.0587485i
$156$		0			0
$157$	6.73109	−	3.88620i	0.537199	−	0.310152i	−0.206744	−	0.978395i	$-0.566287\pi$
$157$	6.73109	−	3.88620i	0.537199	−	0.310152i	0.743943	+	0.668243i	$0.232953\pi$
$158$		0			0
$159$	1.03425	+	1.34786i	0.0820213	+	0.106892i
$160$		0			0
$161$	−22.1200	+	9.81112i	−1.74330	+	0.773225i
$162$		0			0
$163$	−6.42188	+	4.92768i	−0.503001	+	0.385966i	−0.828863	−	0.559451i	$-0.811012\pi$
$163$	−6.42188	+	4.92768i	−0.503001	+	0.385966i	0.325863	+	0.945417i	$0.394345\pi$
$164$		0			0
$165$	10.5467	+	8.09279i	0.821061	+	0.630023i
$166$		0			0
$167$	6.26093	+	15.1152i	0.484485	+	1.16965i	0.957458	+	0.288574i	$0.0931811\pi$
$167$	6.26093	+	15.1152i	0.484485	+	1.16965i	−0.472972	+	0.881077i	$0.656819\pi$
$168$		0			0
$169$	9.28267			0.714052
$170$		0			0
$171$	−3.26983	−	5.66351i	−0.250050	−	0.433099i
$172$		0			0
$173$	−5.23888	−	0.689712i	−0.398305	−	0.0524378i	−0.0712867	−	0.997456i	$-0.522711\pi$
$173$	−5.23888	−	0.689712i	−0.398305	−	0.0524378i	−0.327018	+	0.945018i	$0.606044\pi$
$174$		0			0
$175$	8.77642	−	16.1099i	0.663435	−	1.21780i
$176$		0			0
$177$	−16.9063	+	12.9726i	−1.27075	+	0.975083i
$178$		0			0
$179$	−3.48406	−	0.933551i	−0.260411	−	0.0697769i	0.126251	−	0.991998i	$-0.459705\pi$
$179$	−3.48406	−	0.933551i	−0.260411	−	0.0697769i	−0.386662	+	0.922221i	$0.626372\pi$
$180$		0			0
$181$	−5.22378	+	12.6113i	−0.388281	+	0.937392i	0.602024	+	0.798478i	$0.294361\pi$
$181$	−5.22378	+	12.6113i	−0.388281	+	0.937392i	−0.990304	+	0.138914i	$0.955639\pi$
$182$		0			0
$183$			9.09107i			0.672031i
$184$		0			0
$185$	4.02703	−	15.0291i	0.296073	−	1.10496i
$186$		0			0
$187$	5.63756	+	5.73715i	0.412259	+	0.419542i
$188$		0			0
$189$	6.48167	−	8.89485i	0.471472	−	0.647005i
$190$		0			0
$191$	−6.01595	−	3.47331i	−0.435299	−	0.251320i	0.266303	−	0.963889i	$-0.414198\pi$
$191$	−6.01595	−	3.47331i	−0.435299	−	0.251320i	−0.701601	+	0.712570i	$0.747531\pi$
$192$		0			0
$193$	7.77477	−	1.02357i	0.559640	−	0.0736780i	0.154600	−	0.987977i	$-0.450591\pi$
$193$	7.77477	−	1.02357i	0.559640	−	0.0736780i	0.405040	+	0.914299i	$0.367258\pi$
$194$		0			0
$195$	9.29039	−	9.29039i	0.665298	−	0.665298i
$196$		0			0
$197$	−0.370946	−	0.153651i	−0.0264288	−	0.0109472i	0.369430	−	0.929259i	$-0.379553\pi$
$197$	−0.370946	−	0.153651i	−0.0264288	−	0.0109472i	−0.395859	+	0.918311i	$0.629553\pi$
$198$		0			0
$199$	−5.37418	−	4.12376i	−0.380966	−	0.292325i	0.400471	−	0.916309i	$-0.368846\pi$
$199$	−5.37418	−	4.12376i	−0.380966	−	0.292325i	−0.781437	+	0.623984i	$0.785513\pi$
$200$		0			0
$201$	−0.253278	−	0.0333447i	−0.0178649	−	0.00235195i
$202$		0			0
$203$	−0.709831	−	4.52297i	−0.0498204	−	0.317450i
$204$		0			0
$205$	20.3519	−	35.2505i	1.42144	−	2.46200i
$206$		0			0
$207$	4.96199	−	6.46660i	0.344882	−	0.449459i
$208$		0			0
$209$	13.2255	−	5.47819i	0.914829	−	0.378934i
$210$		0			0
$211$	23.2681	+	9.63794i	1.60184	+	0.663503i	0.991674	−	0.128771i	$-0.0411033\pi$
$211$	23.2681	+	9.63794i	1.60184	+	0.663503i	0.610165	+	0.792275i	$0.291103\pi$
$212$		0			0
$213$	−0.245577	−	0.0658021i	−0.0168266	−	0.00450868i
$214$		0			0
$215$	14.6118	+	19.0425i	0.996520	+	1.29869i
$216$		0			0
$217$	−0.497679	−	0.616358i	−0.0337847	−	0.0418411i
$218$		0			0
$219$	11.8482	−	3.17472i	0.800627	−	0.214527i
$220$		0			0
$221$	6.34889	−	4.78395i	0.427073	−	0.321803i
$222$		0			0
$223$	−9.25013	−	9.25013i	−0.619434	−	0.619434i	0.325952	−	0.945386i	$-0.394315\pi$
$223$	−9.25013	−	9.25013i	−0.619434	−	0.619434i	−0.945386	+	0.325952i	$0.894315\pi$
$224$		0			0
$225$			6.17951i			0.411967i
$226$		0			0
$227$	8.13074	−	1.07043i	0.539656	−	0.0710471i	0.144229	−	0.989544i	$-0.453930\pi$
$227$	8.13074	−	1.07043i	0.539656	−	0.0710471i	0.395427	+	0.918497i	$0.370597\pi$
$228$		0			0
$229$	−7.58075	−	28.2917i	−0.500950	−	1.86957i	−0.493764	−	0.869596i	$-0.664379\pi$
$229$	−7.58075	−	28.2917i	−0.500950	−	1.86957i	−0.00718613	−	0.999974i	$-0.502287\pi$
$230$		0			0
$231$	−7.37545	−	7.01883i	−0.485269	−	0.461805i
$232$		0			0
$233$	1.67861	−	12.7503i	0.109969	−	0.835301i	−0.844199	−	0.536030i	$-0.819923\pi$
$233$	1.67861	−	12.7503i	0.109969	−	0.835301i	0.954168	−	0.299271i	$-0.0967433\pi$
$234$		0			0
$235$	−12.2278	+	15.9356i	−0.797655	+	1.03952i
$236$		0			0
$237$	31.2377			2.02911
$238$		0			0
$239$	2.43585			0.157562			0.0787810	−	0.996892i	$-0.474897\pi$
$239$	2.43585			0.157562			0.0787810	+	0.996892i	$0.474897\pi$
$240$		0			0
$241$	−14.6319	+	19.0686i	−0.942521	+	1.22832i	0.0309534	+	0.999521i	$0.490146\pi$
$241$	−14.6319	+	19.0686i	−0.942521	+	1.22832i	−0.973474	+	0.228796i	$0.926521\pi$
$242$		0			0
$243$	−1.17228	+	8.90438i	−0.0752021	+	0.571217i
$244$		0			0
$245$	−13.7529	+	19.8902i	−0.878641	+	1.27074i
$246$		0			0
$247$	−3.66177	−	13.6659i	−0.232993	−	0.869542i
$248$		0			0
$249$	19.4557	−	2.56139i	1.23295	−	0.162321i
$250$		0			0
$251$		−	5.21374i		−	0.329089i	−0.986370	−	0.164544i	$-0.947385\pi$
$251$		−	5.21374i		−	0.329089i	0.986370	−	0.164544i	$-0.0526154\pi$
$252$		0			0
$253$	12.6164	+	12.6164i	0.793189	+	0.793189i
$254$		0			0
$255$	−3.91113	+	27.8233i	−0.244924	+	1.74236i
$256$		0			0
$257$	−27.2230	+	7.29437i	−1.69812	+	0.455011i	−0.972466	−	0.233046i	$-0.925131\pi$
$257$	−27.2230	+	7.29437i	−1.69812	+	0.455011i	−0.725657	+	0.688057i	$0.758464\pi$
$258$		0			0
$259$	−4.28615	+	11.1189i	−0.266328	+	0.690896i
$260$		0			0
$261$	0.938814	+	1.22349i	0.0581111	+	0.0757319i
$262$		0			0
$263$	−14.2098	−	3.80751i	−0.876216	−	0.234781i	−0.207442	−	0.978247i	$-0.566514\pi$
$263$	−14.2098	−	3.80751i	−0.876216	−	0.234781i	−0.668774	+	0.743466i	$0.733181\pi$
$264$		0			0
$265$	−2.74880	−	1.13859i	−0.168858	−	0.0699431i
$266$		0			0
$267$	9.65955	−	4.00112i	0.591155	−	0.244864i
$268$		0			0
$269$	9.32924	−	12.1581i	0.568814	−	0.741293i	−0.417042	−	0.908887i	$-0.636933\pi$
$269$	9.32924	−	12.1581i	0.568814	−	0.741293i	0.985856	+	0.167594i	$0.0535999\pi$
$270$		0			0
$271$	0.696303	−	1.20603i	0.0422974	−	0.0732612i	−0.844102	−	0.536183i	$-0.819866\pi$
$271$	0.696303	−	1.20603i	0.0422974	−	0.0732612i	0.886399	+	0.462922i	$0.153199\pi$
$272$		0			0
$273$	−7.82895	+	6.32151i	−0.473830	+	0.382595i
$274$		0			0
$275$	−13.4111	−	1.76561i	−0.808722	−	0.106470i
$276$		0			0
$277$	12.8000	+	9.82182i	0.769080	+	0.590136i	0.917011	−	0.398862i	$-0.130595\pi$
$277$	12.8000	+	9.82182i	0.769080	+	0.590136i	−0.147931	+	0.988998i	$0.547261\pi$
$278$		0			0
$279$	0.246534	+	0.102118i	0.0147596	+	0.00611362i
$280$		0			0
$281$	2.14139	−	2.14139i	0.127745	−	0.127745i	−0.640344	−	0.768088i	$-0.721208\pi$
$281$	2.14139	−	2.14139i	0.127745	−	0.127745i	0.768088	+	0.640344i	$0.221208\pi$
$282$		0			0
$283$	−23.8744	+	3.14312i	−1.41918	+	0.186839i	−0.800751	−	0.598997i	$-0.795566\pi$
$283$	−23.8744	+	3.14312i	−1.41918	+	0.186839i	−0.618434	+	0.785837i	$0.712233\pi$
$284$		0			0
$285$	43.3056	+	25.0025i	2.56520	+	1.48102i
$286$		0			0
$287$	−18.3591	+	25.1944i	−1.08371	+	1.48718i
$288$		0			0
$289$	−4.68678	+	16.3412i	−0.275693	+	0.961246i
$290$		0			0
$291$	−3.15164	+	11.7621i	−0.184752	+	0.689506i
$292$		0			0
$293$			12.3081i			0.719048i	0.933136	+	0.359524i	$0.117061\pi$
$293$			12.3081i			0.719048i	−0.933136	+	0.359524i	$0.882939\pi$
$294$		0			0
$295$	14.2814	−	34.4783i	0.831495	−	2.00741i
$296$		0			0
$297$	−7.83860	−	2.10035i	−0.454842	−	0.121875i
$298$		0			0
$299$	13.9900	−	10.7349i	0.809060	−	0.620814i
$300$		0			0
$301$	−9.58296	−	15.6876i	−0.552352	−	0.904217i
$302$		0			0
$303$	32.6094	+	4.29311i	1.87336	+	0.246633i
$304$		0			0
$305$	−7.96040	−	13.7878i	−0.455811	−	0.789488i
$306$		0			0
$307$	−19.1603			−1.09354			−0.546769	−	0.837283i	$-0.684142\pi$
$307$	−19.1603			−1.09354			−0.546769	+	0.837283i	$0.684142\pi$
$308$		0			0
$309$	9.10559	+	21.9828i	0.517999	+	1.25056i
$310$		0			0
$311$	5.05701	+	3.88038i	0.286757	+	0.220036i	0.742116	−	0.670272i	$-0.233822\pi$
$311$	5.05701	+	3.88038i	0.286757	+	0.220036i	−0.455359	+	0.890308i	$0.650489\pi$
$312$		0			0
$313$	−10.4520	+	8.02008i	−0.590780	+	0.453322i	−0.860382	−	0.509650i	$-0.829775\pi$
$313$	−10.4520	+	8.02008i	−0.590780	+	0.453322i	0.269601	+	0.962972i	$0.413108\pi$
$314$		0			0
$315$	0.862854	−	8.09962i	0.0486163	−	0.456362i
$316$		0			0
$317$	3.51895	+	4.58598i	0.197644	+	0.257574i	0.881652	−	0.471900i	$-0.156432\pi$
$317$	3.51895	+	4.58598i	0.197644	+	0.257574i	−0.684008	+	0.729474i	$0.739765\pi$
$318$		0			0
$319$	−2.92352	+	1.68789i	−0.163686	+	0.0945039i
$320$		0			0
$321$	−20.3335	−	20.3335i	−1.13491	−	1.13491i
$322$		0			0
$323$	23.8411	+	18.6278i	1.32656	+	1.03648i
$324$		0			0
$325$	−3.46012	+	12.9133i	−0.191933	+	0.716303i
$326$		0			0
$327$	2.74688	+	1.58591i	0.151903	+	0.0877011i
$328$		0			0
$329$	10.6051	−	11.1440i	0.584679	−	0.614386i
$330$		0			0
$331$	−4.83866	−	18.0581i	−0.265957	−	0.992565i	−0.961662	−	0.274238i	$-0.911575\pi$
$331$	−4.83866	−	18.0581i	−0.265957	−	0.992565i	0.695705	−	0.718328i	$-0.255092\pi$
$332$		0			0
$333$	−0.523925	−	3.97961i	−0.0287109	−	0.218081i
$334$		0			0
$335$	0.413328	−	0.171206i	0.0225825	−	0.00935398i
$336$		0			0
$337$	−3.49133	−	8.42882i	−0.190185	−	0.459147i	0.799809	−	0.600254i	$-0.204934\pi$
$337$	−3.49133	−	8.42882i	−0.190185	−	0.459147i	−0.989994	+	0.141107i	$0.954934\pi$
$338$		0			0
$339$	−3.96980	−	6.87590i	−0.215610	−	0.373447i
$340$		0			0
$341$	−0.292061	+	0.505864i	−0.0158160	+	0.0273941i
$342$		0			0
$343$	12.0874	−	14.0319i	0.652659	−	0.757652i
$344$		0			0
$345$	−8.13515	+	61.7926i	−0.437982	+	3.32680i
$346$		0			0
$347$	0.697600	+	5.29880i	0.0374491	+	0.284454i	0.999915	+	0.0130510i	$0.00415439\pi$
$347$	0.697600	+	5.29880i	0.0374491	+	0.284454i	−0.962466	+	0.271403i	$0.912512\pi$
$348$		0			0
$349$	−3.28041	+	3.28041i	−0.175597	+	0.175597i	−0.789433	−	0.613837i	$-0.789625\pi$
$349$	−3.28041	+	3.28041i	−0.175597	+	0.175597i	0.613837	+	0.789433i	$0.289625\pi$
$350$		0			0
$351$	−3.06925	+	7.40983i	−0.163824	+	0.395507i
$352$		0			0
$353$	5.29366	−	3.05630i	0.281753	−	0.162670i	−0.352464	−	0.935826i	$-0.614656\pi$
$353$	5.29366	−	3.05630i	0.281753	−	0.162670i	0.634217	+	0.773155i	$0.281323\pi$
$354$		0			0
$355$	0.430068	−	0.115236i	0.0228256	−	0.00611611i
$356$		0			0
$357$	5.23587	−	20.8720i	0.277112	−	1.10466i
$358$		0			0
$359$	6.92543	−	1.85566i	0.365510	−	0.0979382i	−0.0713892	−	0.997449i	$-0.522743\pi$
$359$	6.92543	−	1.85566i	0.365510	−	0.0979382i	0.436899	+	0.899510i	$0.356077\pi$
$360$		0			0
$361$	30.1782	−	17.4234i	1.58833	−	0.917022i
$362$		0			0
$363$	5.43087	−	13.1113i	0.285047	−	0.688164i
$364$		0			0
$365$	−15.1895	+	15.1895i	−0.795055	+	0.795055i
$366$		0			0
$367$	−3.58766	−	27.2510i	−0.187275	−	1.42249i	−0.784356	−	0.620311i	$-0.787007\pi$
$367$	−3.58766	−	27.2510i	−0.187275	−	1.42249i	0.597082	−	0.802180i	$-0.296327\pi$
$368$		0			0
$369$	1.37061	−	10.4108i	0.0713513	−	0.541967i
$370$		0			0
$371$	2.00102	+	1.09012i	0.103888	+	0.0565962i
$372$		0			0
$373$	10.4498	−	18.0996i	0.541069	−	0.937160i	−0.457774	−	0.889069i	$-0.651353\pi$
$373$	10.4498	−	18.0996i	0.541069	−	0.937160i	0.998843	−	0.0480907i	$-0.0153137\pi$
$374$		0			0
$375$	−6.58937	−	11.4131i	−0.340274	−	0.589371i
$376$		0			0
$377$	1.27677	+	3.08240i	0.0657570	+	0.158751i
$378$		0			0
$379$	−20.6877	+	8.56913i	−1.06266	+	0.440167i	−0.844394	−	0.535723i	$-0.820039\pi$
$379$	−20.6877	+	8.56913i	−1.06266	+	0.440167i	−0.218263	+	0.975890i	$0.570039\pi$
$380$		0			0
$381$	−0.539804	−	4.10022i	−0.0276550	−	0.210060i
$382$		0			0
$383$	4.58975	+	17.1292i	0.234525	+	0.875260i	0.978362	+	0.206899i	$0.0663371\pi$
$383$	4.58975	+	17.1292i	0.234525	+	0.875260i	−0.743837	+	0.668361i	$0.766996\pi$
$384$		0			0
$385$	17.3317	+	4.18684i	0.883307	+	0.213381i
$386$		0			0
$387$	5.36255	+	3.09607i	0.272594	+	0.157382i
$388$		0			0
$389$	2.55605	−	9.53932i	0.129597	−	0.483663i	−0.870365	−	0.492408i	$-0.836117\pi$
$389$	2.55605	−	9.53932i	0.129597	−	0.483663i	0.999962	+	0.00874487i	$0.00278361\pi$
$390$		0			0
$391$	−10.0787	+	36.3384i	−0.509700	+	1.83771i
$392$		0			0
$393$	−27.3204	−	27.3204i	−1.37813	−	1.37813i
$394$		0			0
$395$	−47.3761	+	27.3526i	−2.38375	+	1.37626i
$396$		0			0
$397$	0.503681	+	0.656410i	0.0252790	+	0.0329443i	0.805822	−	0.592158i	$-0.201724\pi$
$397$	0.503681	+	0.656410i	0.0252790	+	0.0329443i	−0.780543	+	0.625102i	$0.785057\pi$
$398$		0			0
$399$	−30.9516	−	22.5544i	−1.54952	−	1.12913i
$400$		0			0
$401$	10.3768	−	7.96236i	0.518190	−	0.397621i	−0.316287	−	0.948663i	$-0.602436\pi$
$401$	10.3768	−	7.96236i	0.518190	−	0.397621i	0.834477	+	0.551042i	$0.185770\pi$
$402$		0			0
$403$	0.458003	+	0.351438i	0.0228147	+	0.0175064i
$404$		0			0
$405$	−14.3825	−	34.7225i	−0.714673	−	1.72537i
$406$		0			0
$407$	8.78647			0.435529
$408$		0			0
$409$	−17.0883	−	29.5979i	−0.844964	−	1.46352i	−0.885652	−	0.464349i	$-0.846288\pi$
$409$	−17.0883	−	29.5979i	−0.844964	−	1.46352i	0.0406879	−	0.999172i	$-0.487045\pi$
$410$		0			0
$411$	−16.7841	−	2.20967i	−0.827900	−	0.108995i
$412$		0			0
$413$	−13.6734	+	25.0988i	−0.672825	+	1.23503i
$414$		0			0
$415$	−27.2643	+	20.9206i	−1.33835	+	1.02695i
$416$		0			0
$417$	16.2007	+	4.34096i	0.793351	+	0.212578i
$418$		0			0
$419$	7.08071	−	17.0944i	0.345915	−	0.835114i	−0.651178	−	0.758925i	$-0.725725\pi$
$419$	7.08071	−	17.0944i	0.345915	−	0.835114i	0.997093	−	0.0761887i	$-0.0242751\pi$
$420$		0			0
$421$		−	0.278706i		−	0.0135833i	−0.999977	−	0.00679166i	$-0.997838\pi$
$421$		−	0.278706i		−	0.0135833i	0.999977	−	0.00679166i	$-0.00216187\pi$
$422$		0			0
$423$	−1.34116	+	5.00528i	−0.0652095	+	0.243365i
$424$		0			0
$425$	−10.7090	−	26.5079i	−0.519462	−	1.28582i
$426$		0			0
$427$	4.94376	+	11.1461i	0.239245	+	0.539400i
$428$		0			0
$429$	6.42547	+	3.70975i	0.310225	+	0.179108i
$430$		0			0
$431$	11.9283	−	1.57039i	0.574564	−	0.0756428i	0.162356	−	0.986732i	$-0.448091\pi$
$431$	11.9283	−	1.57039i	0.574564	−	0.0756428i	0.412209	+	0.911089i	$0.364757\pi$
$432$		0			0
$433$	4.14856	−	4.14856i	0.199367	−	0.199367i	−0.600362	−	0.799729i	$-0.704977\pi$
$433$	4.14856	−	4.14856i	0.199367	−	0.199367i	0.799729	+	0.600362i	$0.204977\pi$
$434$		0			0
$435$	−10.8945	−	4.51264i	−0.522350	−	0.216365i
$436$		0			0
$437$	53.2453	+	40.8565i	2.54707	+	1.95443i
$438$		0			0
$439$	−35.2882	−	4.64578i	−1.68421	−	0.221731i	−0.773217	−	0.634142i	$-0.781353\pi$
$439$	−35.2882	−	4.64578i	−1.68421	−	0.221731i	−0.910998	+	0.412411i	$0.864687\pi$
$440$		0			0
$441$	−1.31424	+	6.09839i	−0.0625827	+	0.290399i
$442$		0			0
$443$	10.9219	−	18.9172i	0.518913	−	0.898784i	−0.480845	−	0.876806i	$-0.659670\pi$
$443$	10.9219	−	18.9172i	0.518913	−	0.898784i	0.999758	−	0.0219786i	$-0.00699657\pi$
$444$		0			0
$445$	−11.1465	+	14.5264i	−0.528395	+	0.688618i
$446$		0			0
$447$	16.7734	−	6.94777i	0.793355	−	0.328618i
$448$		0			0
$449$	−28.7765	−	11.9196i	−1.35805	−	0.562522i	−0.419527	−	0.907743i	$-0.637804\pi$
$449$	−28.7765	−	11.9196i	−1.35805	−	0.562522i	−0.938522	+	0.345221i	$0.887804\pi$
$450$		0			0
$451$	22.2026	+	5.94917i	1.04548	+	0.280136i
$452$		0			0
$453$	−12.0510	−	15.7052i	−0.566206	−	0.737895i
$454$		0			0
$455$	6.33836	−	16.4427i	0.297147	−	0.770844i
$456$		0			0
$457$	34.5601	−	9.26034i	1.61665	−	0.433181i	0.666637	−	0.745383i	$-0.267733\pi$
$457$	34.5601	−	9.26034i	1.61665	−	0.433181i	0.950016	+	0.312202i	$0.101067\pi$
$458$		0			0
$459$	−4.29391	−	16.6053i	−0.200423	−	0.775069i
$460$		0			0
$461$	26.0426	+	26.0426i	1.21293	+	1.21293i	0.970060	+	0.242866i	$0.0780875\pi$
$461$	26.0426	+	26.0426i	1.21293	+	1.21293i	0.242866	+	0.970060i	$0.421912\pi$
$462$		0			0
$463$			2.57017i			0.119446i	0.998215	+	0.0597230i	$0.0190217\pi$
$463$			2.57017i			0.119446i	−0.998215	+	0.0597230i	$0.980978\pi$
$464$		0			0
$465$	−2.02296	+	0.266328i	−0.0938127	+	0.0123507i
$466$		0			0
$467$	1.30791	+	4.88120i	0.0605230	+	0.225875i	0.989562	−	0.144106i	$-0.0460308\pi$
$467$	1.30791	+	4.88120i	0.0605230	+	0.225875i	−0.929039	+	0.369981i	$0.879364\pi$
$468$		0			0
$469$	−0.328666	+	0.0968513i	−0.0151764	+	0.00447218i
$470$		0			0
$471$	−2.00122	+	15.2008i	−0.0922112	+	0.700414i
$472$		0			0
$473$	−8.25146	+	10.7535i	−0.379403	+	0.494447i
$474$		0			0
$475$	−50.8814			−2.33460
$476$		0			0
$477$	−0.767558			−0.0351441
$478$		0			0
$479$	−6.78186	+	8.83829i	−0.309871	+	0.403832i	−0.922164	−	0.386799i	$-0.873581\pi$
$479$	−6.78186	+	8.83829i	−0.309871	+	0.403832i	0.612293	+	0.790631i	$0.290247\pi$
$480$		0			0
$481$	1.13347	−	8.60956i	0.0516818	−	0.392562i
$482$		0			0
$483$	11.2086	−	46.3991i	0.510011	−	2.11123i
$484$		0			0
$485$	−5.51934	−	20.5984i	−0.250620	−	0.935327i
$486$		0			0
$487$	−1.96205	+	0.258308i	−0.0889088	+	0.0117051i	−0.174849	−	0.984595i	$-0.555944\pi$
$487$	−1.96205	+	0.258308i	−0.0889088	+	0.0117051i	0.0859405	+	0.996300i	$0.472611\pi$
$488$		0			0
$489$		−	15.9675i		−	0.722076i
$490$		0			0
$491$	−14.4207	−	14.4207i	−0.650798	−	0.650798i	0.302387	−	0.953185i	$-0.402216\pi$
$491$	−14.4207	−	14.4207i	−0.650798	−	0.650798i	−0.953185	+	0.302387i	$0.902216\pi$
$492$		0			0
$493$	−6.14745	−	3.62137i	−0.276867	−	0.163098i
$494$		0			0
$495$	−5.80133	+	1.55446i	−0.260750	+	0.0698679i
$496$		0			0
$497$	−0.336874	+	0.0528687i	−0.0151108	+	0.00237149i
$498$		0			0
$499$	−15.7343	−	20.5054i	−0.704365	−	0.917946i	0.294929	−	0.955519i	$-0.404704\pi$
$499$	−15.7343	−	20.5054i	−0.704365	−	0.917946i	−0.999294	+	0.0375730i	$0.988037\pi$
$500$		0			0
$501$	−31.1734	−	8.35290i	−1.39273	−	0.373180i
$502$		0			0
$503$	22.5802	+	9.35302i	1.00680	+	0.417030i	0.824287	−	0.566173i	$-0.191577\pi$
$503$	22.5802	+	9.35302i	1.00680	+	0.417030i	0.182514	+	0.983203i	$0.441577\pi$
$504$		0			0
$505$	−53.2157	+	22.0427i	−2.36807	+	0.980886i
$506$		0			0
$507$	−11.1471	+	14.5272i	−0.495060	+	0.645175i
$508$		0			0
$509$	10.8165	−	18.7348i	0.479434	−	0.830404i	−0.520288	−	0.853991i	$-0.674175\pi$
$509$	10.8165	−	18.7348i	0.479434	−	0.830404i	0.999722	+	0.0235871i	$0.00750871\pi$
$510$		0			0
$511$	12.8001	−	10.3355i	0.566244	−	0.457215i
$512$		0			0
$513$	−30.2640	−	3.98433i	−1.33619	−	0.175912i
$514$		0			0
$515$	−33.0586	−	25.3668i	−1.45674	−	1.11779i
$516$		0			0
$517$	−10.4796	−	4.34078i	−0.460890	−	0.190907i
$518$		0			0
$519$	7.37050	−	7.37050i	0.323529	−	0.323529i
$520$		0			0
$521$	15.0401	−	1.98007i	0.658919	−	0.0867483i	0.206350	−	0.978478i	$-0.433841\pi$
$521$	15.0401	−	1.98007i	0.658919	−	0.0867483i	0.452568	+	0.891730i	$0.350508\pi$
$522$		0			0
$523$	11.1445	+	6.43425i	0.487313	+	0.281350i	0.723459	−	0.690367i	$-0.242551\pi$
$523$	11.1445	+	6.43425i	0.487313	+	0.281350i	−0.236146	+	0.971718i	$0.575884\pi$
$524$		0			0
$525$	14.6725	+	33.0805i	0.640362	+	1.44375i
$526$		0			0
$527$	−1.23451	−	0.0108089i	−0.0537760	−	0.000470844i
$528$		0			0
$529$	−15.6975	+	58.5840i	−0.682501	+	2.54713i
$530$		0			0
$531$		−	9.62751i		−	0.417798i
$532$		0			0
$533$	8.69356	−	20.9881i	0.376560	−	0.909096i
$534$		0			0
$535$	48.6431	+	13.0339i	2.10302	+	0.563503i
$536$		0			0
$537$	5.64482	−	4.33143i	0.243592	−	0.186915i
$538$		0			0
$539$	−12.8596	−	4.59467i	−0.553901	−	0.197906i
$540$		0			0
$541$	35.4338	+	4.66495i	1.52342	+	0.200562i	0.845261	−	0.534354i	$-0.179445\pi$
$541$	35.4338	+	4.66495i	1.52342	+	0.200562i	0.678158	+	0.734916i	$0.262778\pi$
$542$		0			0
$543$	−13.4635	−	23.3194i	−0.577773	−	1.00073i
$544$		0			0
$545$	−5.55468			−0.237936
$546$		0			0
$547$	−8.37345	−	20.2153i	−0.358023	−	0.864344i	−0.995578	−	0.0939391i	$-0.970054\pi$
$547$	−8.37345	−	20.2153i	−0.358023	−	0.864344i	0.637555	−	0.770405i	$-0.279946\pi$
$548$		0			0
$549$	−3.25848	−	2.50032i	−0.139068	−	0.106711i
$550$		0			0
$551$	−10.0741	+	7.73010i	−0.429169	+	0.329313i
$552$		0			0
$553$	38.2991	−	16.9872i	1.62864	−	0.722369i
$554$		0			0
$555$	18.6843	+	24.3499i	0.793106	+	1.03360i
$556$		0			0
$557$	29.0343	−	16.7630i	1.23022	−	0.710271i	0.263148	−	0.964755i	$-0.415239\pi$
$557$	29.0343	−	16.7630i	1.23022	−	0.710271i	0.967077	+	0.254485i	$0.0819059\pi$
$558$		0			0
$559$	9.47254	+	9.47254i	0.400646	+	0.400646i
$560$		0			0
$561$	−15.7484	+	1.93320i	−0.664897	+	0.0816197i
$562$		0			0
$563$	4.40872	−	16.4536i	0.185806	−	0.693436i	−0.808651	−	0.588288i	$-0.799802\pi$
$563$	4.40872	−	16.4536i	0.185806	−	0.693436i	0.994457	−	0.105147i	$-0.0335314\pi$
$564$		0			0
$565$	12.0415	+	6.95214i	0.506588	+	0.292479i
$566$		0			0
$567$	8.13620	+	27.6102i	0.341688	+	1.15952i
$568$		0			0
$569$	1.50893	+	5.63141i	0.0632577	+	0.236081i	0.990315	−	0.138839i	$-0.0443369\pi$
$569$	1.50893	+	5.63141i	0.0632577	+	0.236081i	−0.927057	+	0.374920i	$0.877670\pi$
$570$		0			0
$571$	−1.12133	−	8.51737i	−0.0469263	−	0.356441i	−0.998758	−	0.0498204i	$-0.984135\pi$
$571$	−1.12133	−	8.51737i	−0.0469263	−	0.356441i	0.951832	−	0.306620i	$-0.0991982\pi$
$572$		0			0
$573$	12.6599	−	5.24391i	0.528875	−	0.219067i
$574$		0			0
$575$	−24.2691	−	58.5908i	−1.01209	−	2.44340i
$576$		0			0
$577$	20.4291	+	35.3842i	0.850473	+	1.47306i	0.880782	+	0.473521i	$0.157017\pi$
$577$	20.4291	+	35.3842i	0.850473	+	1.47306i	−0.0303096	+	0.999541i	$0.509649\pi$
$578$		0			0
$579$	−7.73447	+	13.3965i	−0.321434	+	0.556739i
$580$		0			0
$581$	22.4608	−	13.7205i	0.931831	−	0.569221i
$582$		0			0
$583$	0.219307	−	1.66580i	0.00908275	−	0.0689904i
$584$		0			0
$585$	0.774782	+	5.88505i	0.0320333	+	0.243317i
$586$		0			0
$587$	−21.6261	+	21.6261i	−0.892604	+	0.892604i	−0.994768	−	0.102163i	$-0.967424\pi$
$587$	−21.6261	+	21.6261i	−0.892604	+	0.892604i	0.102163	+	0.994768i	$0.467424\pi$
$588$		0			0
$589$	−0.840825	+	2.02993i	−0.0346456	+	0.0836419i
$590$		0			0
$591$	0.685911	−	0.396011i	0.0282146	−	0.0162897i
$592$		0			0
$593$	23.7838	−	6.37284i	0.976683	−	0.261701i	0.265036	−	0.964239i	$-0.414616\pi$
$593$	23.7838	−	6.37284i	0.976683	−	0.261701i	0.711647	+	0.702537i	$0.247950\pi$
$594$		0			0
$595$	10.3352	+	36.2398i	0.423701	+	1.48569i
$596$		0			0
$597$	12.9072	−	3.45847i	0.528256	−	0.141546i
$598$		0			0
$599$	−18.5754	+	10.7245i	−0.758969	+	0.438191i	−0.828925	−	0.559359i	$-0.811047\pi$
$599$	−18.5754	+	10.7245i	−0.758969	+	0.438191i	0.0699565	+	0.997550i	$0.477714\pi$
$600$		0			0
$601$	−13.9415	+	33.6578i	−0.568686	+	1.37293i	0.333978	+	0.942581i	$0.391609\pi$
$601$	−13.9415	+	33.6578i	−0.568686	+	1.37293i	−0.902663	+	0.430347i	$0.858391\pi$
$602$		0			0
$603$	0.0816107	−	0.0816107i	0.00332344	−	0.00332344i
$604$		0			0
$605$	3.24398	+	24.6404i	0.131886	+	1.00178i
$606$		0			0
$607$	−0.652439	+	4.95576i	−0.0264817	+	0.201148i	−0.999571	−	0.0292787i	$-0.990679\pi$
$607$	−0.652439	+	4.95576i	−0.0264817	+	0.201148i	0.973090	+	0.230427i	$0.0740123\pi$
$608$		0			0
$609$	7.93074	+	4.32053i	0.321370	+	0.175077i
$610$		0			0
$611$	−5.60526	+	9.70859i	−0.226764	+	0.392767i
$612$		0			0
$613$	−17.5559	−	30.4078i	−0.709078	−	1.22816i	−0.965200	−	0.261514i	$-0.915778\pi$
$613$	−17.5559	−	30.4078i	−0.709078	−	1.22816i	0.256122	−	0.966645i	$-0.417555\pi$
$614$		0			0
$615$	30.7267	+	74.1808i	1.23902	+	2.99126i
$616$		0			0
$617$	26.1614	−	10.8364i	1.05322	−	0.436258i	0.212179	−	0.977231i	$-0.431944\pi$
$617$	26.1614	−	10.8364i	1.05322	−	0.436258i	0.841040	+	0.540973i	$0.181944\pi$
$618$		0			0
$619$	−5.05933	−	38.4294i	−0.203352	−	1.54461i	−0.723375	−	0.690456i	$-0.757410\pi$
$619$	−5.05933	−	38.4294i	−0.203352	−	1.54461i	0.520023	−	0.854152i	$-0.325923\pi$
$620$		0			0
$621$	−9.84709	−	36.7499i	−0.395150	−	1.47472i
$622$		0			0
$623$	9.66731	−	10.1585i	0.387312	−	0.406991i
$624$		0			0
$625$	−10.0375	−	5.79514i	−0.401499	−	0.231806i
$626$		0			0
$627$	−7.30862	+	27.2761i	−0.291878	+	1.08930i
$628$		0			0
$629$	9.14405	+	16.1631i	0.364597	+	0.644466i
$630$		0			0
$631$	−14.8565	−	14.8565i	−0.591426	−	0.591426i	0.346590	−	0.938017i	$-0.387339\pi$
$631$	−14.8565	−	14.8565i	−0.591426	−	0.591426i	−0.938017	+	0.346590i	$0.887339\pi$
$632$		0			0
$633$	−43.0246	+	24.8403i	−1.71008	+	0.987312i
$634$		0			0
$635$	4.40895	+	5.74586i	0.174964	+	0.228017i
$636$		0			0
$637$	−6.16106	+	12.0079i	−0.244110	+	0.475771i
$638$		0			0
$639$	0.0911261	−	0.0699235i	0.00360489	−	0.00276613i
$640$		0			0
$641$	−5.88422	−	4.51512i	−0.232413	−	0.178337i	0.485989	−	0.873965i	$-0.338459\pi$
$641$	−5.88422	−	4.51512i	−0.232413	−	0.178337i	−0.718402	+	0.695628i	$0.755126\pi$
$642$		0			0
$643$	−14.6157	−	35.2854i	−0.576387	−	1.39152i	−0.896035	−	0.443984i	$-0.853565\pi$
$643$	−14.6157	−	35.2854i	−0.576387	−	1.39152i	0.319648	−	0.947536i	$-0.396435\pi$
$644$		0			0
$645$	−47.3478			−1.86432
$646$		0			0
$647$	−9.04413	−	15.6649i	−0.355561	−	0.615850i	0.631653	−	0.775252i	$-0.282377\pi$
$647$	−9.04413	−	15.6649i	−0.355561	−	0.615850i	−0.987214	+	0.159401i	$0.949044\pi$
$648$		0			0
$649$	20.8942	+	2.75077i	0.820168	+	0.107977i
$650$		0			0
$651$	1.56222	−	0.0387041i	0.0612284	−	0.00151693i
$652$		0			0
$653$	−31.0263	+	23.8073i	−1.21415	+	0.931653i	−0.998990	−	0.0449255i	$-0.985695\pi$
$653$	−31.0263	+	23.8073i	−1.21415	+	0.931653i	−0.215163	+	0.976578i	$0.569028\pi$
$654$		0			0
$655$	65.3577	+	17.5125i	2.55374	+	0.684271i
$656$		0			0
$657$	−2.12071	+	5.11985i	−0.0827368	+	0.199744i
$658$		0			0
$659$			42.8959i			1.67099i	0.549499	+	0.835494i	$0.314819\pi$
$659$			42.8959i			1.67099i	−0.549499	+	0.835494i	$0.685181\pi$
$660$		0			0
$661$	4.30690	−	16.0736i	0.167519	−	0.625189i	−0.830187	−	0.557486i	$-0.811766\pi$
$661$	4.30690	−	16.0736i	0.167519	−	0.625189i	0.997705	−	0.0677033i	$-0.0215671\pi$
$662$		0			0
$663$	−0.137295	+	15.6807i	−0.00533208	+	0.608987i
$664$		0			0
$665$	66.6915	+	7.10465i	2.58618	+	0.275506i
$666$		0			0
$667$	−13.7064	−	7.91338i	−0.530713	−	0.306407i
$668$		0			0
$669$	25.5843	−	3.36823i	0.989145	−	0.130223i
$670$		0			0
$671$	6.35735	−	6.35735i	0.245423	−	0.245423i
$672$		0			0
$673$	8.98481	+	3.72163i	0.346339	+	0.143458i	0.549070	−	0.835776i	$-0.314982\pi$
$673$	8.98481	+	3.72163i	0.346339	+	0.143458i	−0.202731	+	0.979234i	$0.564982\pi$
$674$		0			0
$675$	22.8835	+	17.5592i	0.880788	+	0.675853i
$676$		0			0
$677$	−23.3682	−	3.07649i	−0.898114	−	0.118239i	−0.332687	−	0.943037i	$-0.607955\pi$
$677$	−23.3682	−	3.07649i	−0.898114	−	0.118239i	−0.565427	+	0.824798i	$0.691289\pi$
$678$		0			0
$679$	2.53219	+	16.1348i	0.0971765	+	0.619198i
$680$		0			0
$681$	−8.08859	+	14.0099i	−0.309956	+	0.536859i
$682$		0			0
$683$	−23.0895	+	30.0909i	−0.883496	+	1.15140i	0.104129	+	0.994564i	$0.466795\pi$
$683$	−23.0895	+	30.0909i	−0.883496	+	1.15140i	−0.987625	+	0.156831i	$0.949872\pi$
$684$		0			0
$685$	27.3902	−	11.3454i	1.04653	−	0.433486i
$686$		0			0
$687$	53.3793	+	22.1104i	2.03655	+	0.843565i
$688$		0			0
$689$	−1.60397	−	0.429782i	−0.0611063	−	0.0163734i
$690$		0			0
$691$	−15.9715	−	20.8145i	−0.607585	−	0.791820i	0.383714	−	0.923452i	$-0.374645\pi$
$691$	−15.9715	−	20.8145i	−0.607585	−	0.791820i	−0.991299	+	0.131632i	$0.957978\pi$
$692$		0			0
$693$	4.54420	−	0.713164i	0.172620	−	0.0270909i
$694$		0			0
$695$	−28.3716	+	7.60214i	−1.07620	+	0.288366i
$696$		0			0
$697$	12.1624	+	47.0340i	0.460683	+	1.78154i
$698$		0			0
$699$	17.9382	+	17.9382i	0.678485	+	0.678485i
$700$		0			0
$701$		−	5.94764i		−	0.224639i	−0.993672	−	0.112320i	$-0.964172\pi$
$701$		−	5.94764i		−	0.224639i	0.993672	−	0.112320i	$-0.0358280\pi$
$702$		0			0
$703$	32.7677	−	4.31395i	1.23586	−	0.162704i
$704$		0			0
$705$	−10.2551	−	38.2725i	−0.386229	−	1.44143i
$706$		0			0
$707$	42.3155	−	12.4696i	1.59144	−	0.468966i
$708$		0			0
$709$	2.09601	−	15.9208i	0.0787172	−	0.597917i	−0.905939	−	0.423409i	$-0.860833\pi$
$709$	2.09601	−	15.9208i	0.0787172	−	0.597917i	0.984656	−	0.174508i	$-0.0558334\pi$
$710$		0			0
$711$	−8.59130	+	11.1964i	−0.322199	+	0.419898i
$712$		0			0
$713$	−2.73855			−0.102559
$714$		0			0
$715$	−12.9935			−0.485928
$716$		0			0
$717$	−2.92509	+	3.81205i	−0.109240	+	0.142364i
$718$		0			0
$719$	1.25967	−	9.56812i	0.0469777	−	0.356831i	−0.951771	−	0.306811i	$-0.900738\pi$
$719$	1.25967	−	9.56812i	0.0469777	−	0.356831i	0.998748	−	0.0500201i	$-0.0159285\pi$
$720$		0			0
$721$	23.1183	+	22.0005i	0.860970	+	0.819341i
$722$		0			0
$723$	−12.2713	−	45.7971i	−0.456374	−	1.70321i
$724$		0			0
$725$	11.8961	−	1.56616i	0.441811	−	0.0581655i
$726$		0			0
$727$			3.12954i			0.116068i	0.998315	+	0.0580340i	$0.0184832\pi$
$727$			3.12954i			0.116068i	−0.998315	+	0.0580340i	$0.981517\pi$
$728$		0			0
$729$	10.5512	+	10.5512i	0.390784	+	0.390784i
$730$		0			0
$731$	−28.3689	−	3.98781i	−1.04926	−	0.147495i
$732$		0			0
$733$	−30.3677	+	8.13700i	−1.12166	+	0.300547i	−0.771553	−	0.636165i	$-0.780520\pi$
$733$	−30.3677	+	8.13700i	−1.12166	+	0.300547i	−0.350103	+	0.936711i	$0.613853\pi$
$734$		0			0
$735$	−14.6126	−	45.4082i	−0.538992	−	1.67490i
$736$		0			0
$737$	0.153798	+	0.200434i	0.00566524	+	0.00738308i
$738$		0			0
$739$	−34.2314	−	9.17228i	−1.25922	−	0.337408i	−0.433330	−	0.901235i	$-0.642662\pi$
$739$	−34.2314	−	9.17228i	−1.25922	−	0.337408i	−0.825893	+	0.563828i	$0.809328\pi$
$740$		0			0
$741$	25.7841	+	10.6801i	0.947204	+	0.392345i
$742$		0			0
$743$	−17.5425	+	7.26635i	−0.643573	+	0.266577i	−0.680508	−	0.732741i	$-0.738241\pi$
$743$	−17.5425	+	7.26635i	−0.643573	+	0.266577i	0.0369347	+	0.999318i	$0.488241\pi$
$744$		0			0
$745$	−19.3554	+	25.2245i	−0.709129	+	0.924154i
$746$		0			0
$747$	−4.43282	+	7.67788i	−0.162189	+	0.280919i
$748$		0			0
$749$	−35.9874	−	13.8725i	−1.31495	−	0.506891i
$750$		0			0
$751$	31.4457	+	4.13991i	1.14747	+	0.151067i	0.680186	−	0.733039i	$-0.261899\pi$
$751$	31.4457	+	4.13991i	1.14747	+	0.151067i	0.467285	+	0.884107i	$0.345232\pi$
$752$		0			0
$753$	8.15940	+	6.26093i	0.297345	+	0.228161i
$754$		0			0
$755$	32.0289	+	13.2668i	1.16565	+	0.482829i
$756$		0			0
$757$	−14.5439	+	14.5439i	−0.528607	+	0.528607i	−0.920157	−	0.391550i	$-0.871939\pi$
$757$	−14.5439	+	14.5439i	−0.528607	+	0.528607i	0.391550	+	0.920157i	$0.371939\pi$
$758$		0			0
$759$	−34.8949	+	4.59400i	−1.26661	+	0.166752i
$760$		0			0
$761$	−14.4429	−	8.33861i	−0.523554	−	0.302274i	0.214833	−	0.976651i	$-0.431079\pi$
$761$	−14.4429	−	8.33861i	−0.523554	−	0.302274i	−0.738388	+	0.674376i	$0.764413\pi$
$762$		0			0
$763$	4.23025	+	0.450649i	0.153145	+	0.0163146i
$764$		0			0
$765$	−8.89692	−	9.05410i	−0.321669	−	0.327352i
$766$		0			0
$767$	5.39077	−	20.1186i	0.194649	−	0.726441i
$768$		0			0
$769$			19.2148i			0.692904i	0.938068	+	0.346452i	$0.112614\pi$
$769$			19.2148i			0.692904i	−0.938068	+	0.346452i	$0.887386\pi$
$770$		0			0
$771$	21.2752	−	51.3628i	0.766207	−	1.84979i
$772$		0			0
$773$	13.6530	+	3.65831i	0.491064	+	0.131580i	0.495850	−	0.868408i	$-0.334857\pi$
$773$	13.6530	+	3.65831i	0.491064	+	0.131580i	−0.00478564	+	0.999989i	$0.501523\pi$
$774$		0			0
$775$	1.64715	−	1.26390i	0.0591672	−	0.0454006i
$776$		0			0
$777$	−12.2538	−	20.0599i	−0.439604	−	0.719644i
$778$		0			0
$779$	85.7219	+	11.2855i	3.07130	+	0.404345i
$780$		0			0
$781$	0.125716	+	0.217746i	0.00449846	+	0.00779156i
$782$		0			0
$783$	7.19839			0.257249
$784$		0			0
$785$	−10.2751	−	24.8063i	−0.366734	−	0.885374i
$786$		0			0
$787$	24.7661	+	19.0037i	0.882818	+	0.677410i	0.947244	−	0.320512i	$-0.103855\pi$
$787$	24.7661	+	19.0037i	0.882818	+	0.677410i	−0.0644264	+	0.997922i	$0.520522\pi$
$788$		0			0
$789$	23.0226	−	17.6658i	0.819625	−	0.628920i
$790$		0			0
$791$	−8.60633	−	6.27143i	−0.306006	−	0.222986i
$792$		0			0
$793$	−5.40923	−	7.04945i	−0.192088	−	0.250333i
$794$		0			0
$795$	5.08277	−	2.93454i	0.180267	−	0.104077i
$796$		0			0
$797$	−15.1919	−	15.1919i	−0.538125	−	0.538125i	0.384853	−	0.922978i	$-0.374252\pi$
$797$	−15.1919	−	15.1919i	−0.538125	−	0.538125i	−0.922978	+	0.384853i	$0.874252\pi$
$798$		0			0
$799$	−2.92097	−	23.7951i	−0.103337	−	0.841809i
$800$		0			0
$801$	−1.22256	+	4.56266i	−0.0431971	+	0.161214i
$802$		0			0
$803$	−10.5055	−	6.06533i	−0.370730	−	0.214041i
$804$		0			0
$805$	23.6289	+	80.1850i	0.832811	+	2.82615i
$806$		0			0
$807$	7.82415	+	29.2001i	0.275423	+	1.02789i
$808$		0			0
$809$	0.993212	+	7.54419i	0.0349195	+	0.265240i	0.999995	+	0.00326670i	$0.00103982\pi$
$809$	0.993212	+	7.54419i	0.0349195	+	0.265240i	−0.965075	+	0.261973i	$0.915627\pi$
$810$		0			0
$811$	12.5470	−	5.19712i	0.440583	−	0.182496i	−0.151354	−	0.988480i	$-0.548363\pi$
$811$	12.5470	−	5.19712i	0.440583	−	0.182496i	0.591937	+	0.805984i	$0.298363\pi$
$812$		0			0
$813$	1.05126	+	2.53796i	0.0368692	+	0.0890102i
$814$		0			0
$815$	13.9816	+	24.2169i	0.489755	+	0.848280i
$816$		0			0
$817$	−25.4927	+	44.1547i	−0.891878	+	1.54478i
$818$		0			0
$819$	−0.112595	−	4.54470i	−0.00393438	−	0.158805i
$820$		0			0
$821$	1.00882	−	7.66272i	0.0352079	−	0.267431i	−0.964782	−	0.263049i	$-0.915272\pi$
$821$	1.00882	−	7.66272i	0.0352079	−	0.267431i	0.999990	−	0.00438173i	$-0.00139475\pi$
$822$		0			0
$823$	−4.46684	−	33.9290i	−0.155704	−	1.18269i	−0.873637	−	0.486578i	$-0.838245\pi$
$823$	−4.46684	−	33.9290i	−0.155704	−	1.18269i	0.717933	−	0.696112i	$-0.245088\pi$
$824$		0			0
$825$	18.8679	−	18.8679i	0.656896	−	0.656896i
$826$		0			0
$827$	19.3737	−	46.7722i	0.673689	−	1.62643i	−0.101602	−	0.994825i	$-0.532397\pi$
$827$	19.3737	−	46.7722i	0.673689	−	1.62643i	0.775291	−	0.631604i	$-0.217603\pi$
$828$		0			0
$829$	−24.3226	+	14.0427i	−0.844758	+	0.487721i	−0.858879	−	0.512179i	$-0.828838\pi$
$829$	−24.3226	+	14.0427i	−0.844758	+	0.487721i	0.0141205	+	0.999900i	$0.495505\pi$
$830$		0			0
$831$	−30.7419	+	8.23726i	−1.06642	+	0.285747i
$832$		0			0
$833$	−4.93079	−	28.4374i	−0.170842	−	0.985298i
$834$		0			0
$835$	54.5927	−	14.6281i	1.88926	−	0.506225i
$836$		0			0
$837$	1.07868	−	0.622778i	0.0372848	−	0.0215264i
$838$		0			0
$839$	−15.1506	+	36.5768i	−0.523056	+	1.26277i	0.412939	+	0.910759i	$0.364502\pi$
$839$	−15.1506	+	36.5768i	−0.523056	+	1.26277i	−0.935996	+	0.352011i	$0.885498\pi$
$840$		0			0
$841$	−18.3887	+	18.3887i	−0.634093	+	0.634093i
$842$		0			0
$843$	0.779740	+	5.92271i	0.0268557	+	0.203989i
$844$		0			0
$845$	4.18565	−	31.7931i	0.143991	−	1.09372i
$846$		0			0
$847$	−0.471430	−	19.0285i	−0.0161985	−	0.653826i
$848$		0			0
$849$	23.7506	−	41.1373i	0.815120	−	1.41183i
$850$		0			0
$851$	20.5969	+	35.6749i	0.706052	+	1.22292i
$852$		0			0
$853$	−12.6537	−	30.5487i	−0.433254	−	1.04597i	−0.978232	−	0.207516i	$-0.933462\pi$
$853$	−12.6537	−	30.5487i	−0.433254	−	1.04597i	0.544978	−	0.838450i	$-0.316538\pi$
$854$		0			0
$855$	−20.8719	+	8.64542i	−0.713803	+	0.295667i
$856$		0			0
$857$	−1.68784	−	12.8204i	−0.0576556	−	0.437937i	−0.995790	−	0.0916658i	$-0.970781\pi$
$857$	−1.68784	−	12.8204i	−0.0576556	−	0.437937i	0.938134	−	0.346272i	$-0.112552\pi$
$858$		0			0
$859$	11.9120	+	44.4562i	0.406432	+	1.51683i	0.801399	+	0.598130i	$0.204089\pi$
$859$	11.9120	+	44.4562i	0.406432	+	1.51683i	−0.394967	+	0.918695i	$0.629244\pi$
$860$		0			0
$861$	−17.3821	−	58.9864i	−0.592381	−	2.01025i
$862$		0			0
$863$	−9.47104	−	5.46811i	−0.322398	−	0.186136i	0.330063	−	0.943959i	$-0.392930\pi$
$863$	−9.47104	−	5.46811i	−0.322398	−	0.186136i	−0.652461	+	0.757822i	$0.726263\pi$
$864$		0			0
$865$	−4.72453	+	17.6322i	−0.160639	+	0.599512i
$866$		0			0
$867$	−19.9455	−	26.9580i	−0.677384	−	0.915542i
$868$		0			0
$869$	−21.8444	−	21.8444i	−0.741020	−	0.741020i
$870$		0			0
$871$	0.216239	−	0.124845i	0.00732697	−	0.00423023i
$872$		0			0
$873$	−3.34904	−	4.36456i	−0.113348	−	0.147718i
$874$		0			0
$875$	−14.2854	−	10.4098i	−0.482936	−	0.351915i
$876$		0			0
$877$	−5.37090	+	4.12124i	−0.181362	+	0.139164i	−0.695453	−	0.718572i	$-0.744796\pi$
$877$	−5.37090	+	4.12124i	−0.181362	+	0.139164i	0.514090	+	0.857736i	$0.328130\pi$
$878$		0			0
$879$	−19.2619	−	14.7802i	−0.649689	−	0.498524i
$880$		0			0
$881$	−19.0610	−	46.0173i	−0.642181	−	1.55036i	−0.823732	−	0.566980i	$-0.808112\pi$
$881$	−19.0610	−	46.0173i	−0.642181	−	1.55036i	0.181551	−	0.983382i	$-0.441888\pi$
$882$		0			0
$883$	23.2088			0.781037			0.390519	−	0.920595i	$-0.372296\pi$
$883$	23.2088			0.781037			0.390519	+	0.920595i	$0.372296\pi$
$884$		0			0
$885$	36.8080	+	63.7534i	1.23729	+	2.14305i
$886$		0			0
$887$	−12.1911	−	1.60499i	−0.409339	−	0.0538904i	−0.0769546	−	0.997035i	$-0.524520\pi$
$887$	−12.1911	−	1.60499i	−0.409339	−	0.0538904i	−0.332384	+	0.943144i	$0.607853\pi$
$888$		0			0
$889$	−2.89154	−	4.73354i	−0.0969792	−	0.158758i
$890$		0			0
$891$	16.8379	−	12.9202i	0.564090	−	0.432842i
$892$		0			0
$893$	−41.2130	−	11.0430i	−1.37914	−	0.369539i
$894$		0			0
$895$	−4.76841	+	11.5120i	−0.159390	+	0.384802i
$896$		0			0
$897$			34.7850i			1.16144i
$898$		0			0
$899$	0.134103	−	0.500481i	0.00447260	−	0.0166920i
$900$		0			0
$901$	3.29255	−	1.33017i	0.109691	−	0.0443142i
$902$		0			0
$903$	36.0584	+	3.84130i	1.19995	+	0.127831i
$904$		0			0
$905$	40.8383	+	23.5780i	1.35751	+	0.783759i
$906$		0			0
$907$	−22.3115	+	2.93736i	−0.740840	+	0.0975335i	−0.491494	−	0.870881i	$-0.663549\pi$
$907$	−22.3115	+	2.93736i	−0.740840	+	0.0975335i	−0.249346	+	0.968414i	$0.580216\pi$
$908$		0			0
$909$	−10.5073	+	10.5073i	−0.348506	+	0.348506i
$910$		0			0
$911$	28.2556	+	11.7039i	0.936150	+	0.387766i	0.798008	−	0.602646i	$-0.205887\pi$
$911$	28.2556	+	11.7039i	0.936150	+	0.387766i	0.138142	+	0.990412i	$0.455887\pi$
$912$		0			0
$913$	−15.3964	−	11.8141i	−0.509547	−	0.390990i
$914$		0			0
$915$	31.1369	+	4.09925i	1.02935	+	0.135517i
$916$		0			0
$917$	−48.3533	−	18.6394i	−1.59677	−	0.615526i
$918$		0			0
$919$	19.6374	−	34.0131i	0.647780	−	1.12199i	−0.335872	−	0.941908i	$-0.609031\pi$
$919$	19.6374	−	34.0131i	0.647780	−	1.12199i	0.983652	−	0.180080i	$-0.0576356\pi$
$920$		0			0
$921$	23.0087	−	29.9855i	0.758162	−	0.988056i
$922$		0			0
$923$	0.229579	−	0.0950947i	0.00755669	−	0.00313008i
$924$		0			0
$925$	−28.8531	−	11.9513i	−0.948683	−	0.392957i
$926$		0			0
$927$	−10.3835	−	2.78226i	−0.341040	−	0.0913813i
$928$		0			0
$929$	23.9053	+	31.1540i	0.784307	+	1.02213i	0.998967	+	0.0454400i	$0.0144690\pi$
$929$	23.9053	+	31.1540i	0.784307	+	1.02213i	−0.214660	+	0.976689i	$0.568864\pi$
$930$		0			0
$931$	−50.2135	−	10.8213i	−1.64568	−	0.354654i
$932$		0			0
$933$	−12.1454	+	3.25436i	−0.397624	+	0.106543i
$934$		0			0
$935$	22.1918	−	16.7217i	0.725748	−	0.546858i
$936$		0			0
$937$	6.78528	+	6.78528i	0.221666	+	0.221666i	0.809200	−	0.587534i	$-0.199901\pi$
$937$	6.78528	+	6.78528i	0.221666	+	0.221666i	−0.587534	+	0.809200i	$0.699901\pi$
$938$		0			0
$939$		−	25.9880i		−	0.848087i
$940$		0			0
$941$	39.9168	−	5.25515i	1.30125	−	0.171313i	0.552137	−	0.833754i	$-0.313813\pi$
$941$	39.9168	−	5.25515i	1.30125	−	0.171313i	0.749114	+	0.662441i	$0.230479\pi$
$942$		0			0
$943$	27.8916	+	104.093i	0.908276	+	3.38973i
$944$		0			0
$945$	−27.5422	−	26.2105i	−0.895947	−	0.852626i
$946$		0			0
$947$	−4.16090	+	31.6052i	−0.135211	+	1.02703i	0.780490	+	0.625169i	$0.214970\pi$
$947$	−4.16090	+	31.6052i	−0.135211	+	1.02703i	−0.915701	+	0.401861i	$0.868364\pi$
$948$		0			0
$949$	−7.29843	+	9.51150i	−0.236917	+	0.308756i
$950$		0			0
$951$	−11.4027			−0.369758
$952$		0			0
$953$	−5.95434			−0.192880			−0.0964401	−	0.995339i	$-0.530746\pi$
$953$	−5.95434			−0.192880			−0.0964401	+	0.995339i	$0.530746\pi$
$954$		0			0
$955$	−14.6087	+	19.0385i	−0.472727	+	0.616070i
$956$		0			0
$957$	0.869190	−	6.60215i	0.0280969	−	0.213417i
$958$		0			0
$959$	−21.7799	+	6.41811i	−0.703309	+	0.207251i
$960$		0			0
$961$	8.00019	+	29.8571i	0.258071	+	0.963132i
$962$		0			0
$963$	12.8804	−	1.69573i	0.415064	−	0.0546443i
$964$		0			0
$965$		−	27.0901i		−	0.872061i
$966$		0			0
$967$	−15.3606	−	15.3606i	−0.493962	−	0.493962i	0.415590	−	0.909552i	$-0.363575\pi$
$967$	−15.3606	−	15.3606i	−0.493962	−	0.493962i	−0.909552	+	0.415590i	$0.863575\pi$
$968$		0			0
$969$	−57.7818	+	14.9416i	−1.85622	+	0.479994i
$970$		0			0
$971$	0.993046	−	0.266086i	0.0318684	−	0.00853910i	−0.242850	−	0.970064i	$-0.578082\pi$
$971$	0.993046	−	0.266086i	0.0318684	−	0.00853910i	0.274718	+	0.961525i	$0.411416\pi$
$972$		0			0
$973$	22.2236	−	3.48775i	0.712454	−	0.111812i
$974$		0			0
$975$	−16.0540	−	20.9220i	−0.514140	−	0.670040i
$976$		0			0
$977$	22.9731	+	6.15561i	0.734973	+	0.196935i	0.606843	−	0.794822i	$-0.292436\pi$
$977$	22.9731	+	6.15561i	0.734973	+	0.196935i	0.128130	+	0.991757i	$0.459102\pi$
$978$		0			0
$979$	−9.55284	−	3.95692i	−0.305310	−	0.126464i
$980$		0			0
$981$	−1.32391	+	0.548380i	−0.0422691	+	0.0175084i
$982$		0			0
$983$	−28.8203	+	37.5594i	−0.919225	+	1.19796i	0.0606123	+	0.998161i	$0.480695\pi$
$983$	−28.8203	+	37.5594i	−0.919225	+	1.19796i	−0.979837	+	0.199796i	$0.935972\pi$
$984$		0			0
$985$	−0.693517	+	1.20121i	−0.0220973	+	0.0382736i
$986$		0			0
$987$	4.70489	+	29.9790i	0.149758	+	0.954243i
$988$		0			0
$989$	−63.0042	−	8.29466i	−2.00342	−	0.263755i
$990$		0			0
$991$	−8.87861	−	6.81279i	−0.282038	−	0.216416i	0.458048	−	0.888927i	$-0.348549\pi$
$991$	−8.87861	−	6.81279i	−0.282038	−	0.216416i	−0.740086	+	0.672512i	$0.765215\pi$
$992$		0			0
$993$	34.0711	+	14.1127i	1.08121	+	0.447854i
$994$		0			0
$995$	−16.5471	+	16.5471i	−0.524579	+	0.524579i
$996$		0			0
$997$	−57.9113	+	7.62417i	−1.83407	+	0.241460i	−0.966647	−	0.256111i	$-0.917559\pi$
$997$	−57.9113	+	7.62417i	−1.83407	+	0.241460i	−0.867423	+	0.497571i	$0.834225\pi$
$998$		0			0
$999$	−16.2258	−	9.36795i	−0.513360	−	0.296389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.3	yes	96
7.4	even	3	inner	476.2.bh.a.389.10	yes	96
17.8	even	8	inner	476.2.bh.a.93.10	yes	96
119.25	even	24	inner	476.2.bh.a.25.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.3	✓	96	119.25	even	24	inner
476.2.bh.a.93.10	yes	96	17.8	even	8	inner
476.2.bh.a.389.10	yes	96	7.4	even	3	inner
476.2.bh.a.457.3	yes	96	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.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20085 + 1.56498i) q^{3} +(0.450909 - 3.42500i) q^{5} +(-0.621265 + 2.57178i) q^{7} +(-0.230659 - 0.860832i) q^{9} +O(q^{10})\)	\(q+(-1.20085 + 1.56498i) q^{3} +(0.450909 - 3.42500i) q^{5} +(-0.621265 + 2.57178i) q^{7} +(-0.230659 - 0.860832i) q^{9} +(1.93413 - 0.254633i) q^{11} -1.92804i q^{13} +(4.81857 + 4.81857i) q^{15} +(2.48125 + 3.29293i) q^{17} +(7.08800 - 1.89922i) q^{19} +(-3.27873 - 4.06058i) q^{21} +(5.56777 + 7.25606i) q^{23} +(-6.69766 - 1.79463i) q^{25} +(-3.84320 - 1.59190i) q^{27} +(-1.59872 + 0.662213i) q^{29} +(-0.182278 + 0.237549i) q^{31} +(-1.92411 + 3.33265i) q^{33} +(8.52819 + 3.28747i) q^{35} +(4.46546 + 0.587888i) q^{37} +(3.01734 + 2.31528i) q^{39} +(10.8857 + 4.50902i) q^{41} +(-4.91305 + 4.91305i) q^{43} +(-3.05235 + 0.401850i) q^{45} +(-5.03548 - 2.90724i) q^{47} +(-6.22806 - 3.19551i) q^{49} +(-8.13298 - 0.0712095i) q^{51} +(0.222912 - 0.831918i) q^{53} -6.73921i q^{55} +(-5.53938 + 13.3733i) q^{57} +(10.4348 + 2.79599i) q^{59} +(3.65628 - 2.80557i) q^{61} +(2.35717 - 0.0583987i) q^{63} +(-6.60352 - 0.869370i) q^{65} +(0.0647526 + 0.112155i) q^{67} -18.0416 q^{69} +(0.0493221 + 0.119074i) q^{71} +(-4.93326 - 3.78542i) q^{73} +(10.8514 - 8.32661i) q^{75} +(-0.546749 + 5.13235i) q^{77} +(-9.64016 - 12.5633i) q^{79} +(9.42180 - 5.43968i) q^{81} +(-7.03430 - 7.03430i) q^{83} +(12.3971 - 7.01347i) q^{85} +(0.883478 - 3.29718i) q^{87} +(-4.59019 - 2.65015i) q^{89} +(4.95848 + 1.19782i) q^{91} +(-0.152871 - 0.570521i) q^{93} +(-3.30879 - 25.1328i) q^{95} +(5.70314 - 2.36232i) q^{97} +(-0.665322 - 1.60623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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