LMFDB - Embedded newform 820.2.bi.a.189.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.12
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.389760 q^{3} +(-0.0716037 + 2.23492i) q^{5} +(-0.300283 - 0.924177i) q^{7} -2.84809 q^{9} +(-2.79647 - 3.84902i) q^{11} +(-1.31080 + 4.03424i) q^{13} +(-0.0279083 + 0.871083i) q^{15} +(-4.26120 + 3.09594i) q^{17} +(-1.78645 + 0.580454i) q^{19} +(-0.117038 - 0.360207i) q^{21} +(2.71321 + 0.881575i) q^{23} +(-4.98975 - 0.320057i) q^{25} -2.27935 q^{27} +(-0.636492 + 0.876056i) q^{29} +(2.33511 - 1.69655i) q^{31} +(-1.08995 - 1.50019i) q^{33} +(2.08696 - 0.604935i) q^{35} +(0.656105 - 0.903051i) q^{37} +(-0.510899 + 1.57238i) q^{39} +(-5.24987 - 3.66591i) q^{41} +(-6.41395 - 2.08402i) q^{43} +(0.203934 - 6.36525i) q^{45} +(-1.49531 + 4.60210i) q^{47} +(4.89919 - 3.55947i) q^{49} +(-1.66085 + 1.20668i) q^{51} +(-3.20899 - 2.33147i) q^{53} +(8.80249 - 5.97430i) q^{55} +(-0.696288 + 0.226238i) q^{57} +(-2.35663 + 7.25296i) q^{59} +(0.967041 + 2.97625i) q^{61} +(0.855233 + 2.63214i) q^{63} +(-8.92235 - 3.21841i) q^{65} +(3.19413 + 2.32067i) q^{67} +(1.05750 + 0.343603i) q^{69} +(-6.73066 - 9.26396i) q^{71} +16.0715i q^{73} +(-1.94480 - 0.124746i) q^{75} +(-2.71744 + 3.74023i) q^{77} +14.2526i q^{79} +7.65586 q^{81} +7.69398i q^{83} +(-6.61407 - 9.74513i) q^{85} +(-0.248079 + 0.341451i) q^{87} +(9.28990 - 3.01847i) q^{89} +4.12196 q^{91} +(0.910131 - 0.661249i) q^{93} +(-1.16935 - 4.03415i) q^{95} +(-2.69462 - 1.95776i) q^{97} +(7.96460 + 10.9623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	0.389760			0.225028			0.112514	−	0.993650i	$-0.464110\pi$
$3$	0.389760			0.225028			0.112514	+	0.993650i	$0.464110\pi$
$4$		0			0
$5$	−0.0716037	+	2.23492i	−0.0320221	+	0.999487i
$5$	−0.0716037	+	2.23492i	−0.0320221	+	0.999487i
$6$		0			0
$7$	−0.300283	−	0.924177i	−0.113496	−	0.349306i	0.878134	−	0.478415i	$-0.158788\pi$
$7$	−0.300283	−	0.924177i	−0.113496	−	0.349306i	−0.991630	+	0.129109i	$0.958788\pi$
$8$		0			0
$9$	−2.84809			−0.949362
$10$		0			0
$11$	−2.79647	−	3.84902i	−0.843169	−	1.16052i	−0.985327	−	0.170678i	$-0.945404\pi$
$11$	−2.79647	−	3.84902i	−0.843169	−	1.16052i	0.142158	−	0.989844i	$-0.454596\pi$
$12$		0			0
$13$	−1.31080	+	4.03424i	−0.363551	+	1.11890i	0.587332	+	0.809346i	$0.300178\pi$
$13$	−1.31080	+	4.03424i	−0.363551	+	1.11890i	−0.950883	+	0.309550i	$0.899822\pi$
$14$		0			0
$15$	−0.0279083	+	0.871083i	−0.00720588	+	0.224913i
$16$		0			0
$17$	−4.26120	+	3.09594i	−1.03349	+	0.750877i	−0.969005	−	0.247042i	$-0.920542\pi$
$17$	−4.26120	+	3.09594i	−1.03349	+	0.750877i	−0.0644884	+	0.997918i	$0.520542\pi$
$18$		0			0
$19$	−1.78645	+	0.580454i	−0.409841	+	0.133165i	−0.506679	−	0.862135i	$-0.669127\pi$
$19$	−1.78645	+	0.580454i	−0.409841	+	0.133165i	0.0968383	+	0.995300i	$0.469127\pi$
$20$		0			0
$21$	−0.117038	−	0.360207i	−0.0255399	−	0.0786037i
$22$		0			0
$23$	2.71321	+	0.881575i	0.565743	+	0.183821i	0.577904	−	0.816105i	$-0.303871\pi$
$23$	2.71321	+	0.881575i	0.565743	+	0.183821i	−0.0121604	+	0.999926i	$0.503871\pi$
$24$		0			0
$25$	−4.98975	−	0.320057i	−0.997949	−	0.0640114i
$26$		0			0
$27$	−2.27935			−0.438661
$28$		0			0
$29$	−0.636492	+	0.876056i	−0.118194	+	0.162679i	−0.864014	−	0.503467i	$-0.832057\pi$
$29$	−0.636492	+	0.876056i	−0.118194	+	0.162679i	0.745821	+	0.666147i	$0.232057\pi$
$30$		0			0
$31$	2.33511	−	1.69655i	0.419397	−	0.304710i	−0.357998	−	0.933722i	$-0.616541\pi$
$31$	2.33511	−	1.69655i	0.419397	−	0.304710i	0.777395	+	0.629012i	$0.216541\pi$
$32$		0			0
$33$	−1.08995	−	1.50019i	−0.189737	−	0.261150i
$34$		0			0
$35$	2.08696	−	0.604935i	0.352761	−	0.102253i
$36$		0			0
$37$	0.656105	−	0.903051i	0.107863	−	0.148461i	−0.751673	−	0.659536i	$-0.770753\pi$
$37$	0.656105	−	0.903051i	0.107863	−	0.148461i	0.859536	+	0.511075i	$0.170753\pi$
$38$		0			0
$39$	−0.510899	+	1.57238i	−0.0818093	+	0.251783i
$40$		0			0
$41$	−5.24987	−	3.66591i	−0.819892	−	0.572519i
$41$	−5.24987	−	3.66591i	−0.819892	−	0.572519i
$42$		0			0
$43$	−6.41395	−	2.08402i	−0.978119	−	0.317810i	−0.224030	−	0.974582i	$-0.571921\pi$
$43$	−6.41395	−	2.08402i	−0.978119	−	0.317810i	−0.754089	+	0.656772i	$0.771921\pi$
$44$		0			0
$45$	0.203934	−	6.36525i	0.0304006	−	0.948875i
$46$		0			0
$47$	−1.49531	+	4.60210i	−0.218114	+	0.671285i	0.780804	+	0.624776i	$0.214810\pi$
$47$	−1.49531	+	4.60210i	−0.218114	+	0.671285i	−0.998918	+	0.0465092i	$0.985190\pi$
$48$		0			0
$49$	4.89919	−	3.55947i	0.699884	−	0.508495i
$50$		0			0
$51$	−1.66085	+	1.20668i	−0.232565	+	0.168968i
$52$		0			0
$53$	−3.20899	−	2.33147i	−0.440788	−	0.320251i	0.345160	−	0.938544i	$-0.387825\pi$
$53$	−3.20899	−	2.33147i	−0.440788	−	0.320251i	−0.785948	+	0.618293i	$0.787825\pi$
$54$		0			0
$55$	8.80249	−	5.97430i	1.18693	−	0.805574i
$56$		0			0
$57$	−0.696288	+	0.226238i	−0.0922256	+	0.0299659i
$58$		0			0
$59$	−2.35663	+	7.25296i	−0.306807	+	0.944255i	0.672190	+	0.740379i	$0.265354\pi$
$59$	−2.35663	+	7.25296i	−0.306807	+	0.944255i	−0.978997	+	0.203876i	$0.934646\pi$
$60$		0			0
$61$	0.967041	+	2.97625i	0.123817	+	0.381069i	0.993684	−	0.112217i	$-0.0357953\pi$
$61$	0.967041	+	2.97625i	0.123817	+	0.381069i	−0.869867	+	0.493287i	$0.835795\pi$
$62$		0			0
$63$	0.855233	+	2.63214i	0.107749	+	0.331618i
$64$		0			0
$65$	−8.92235	−	3.21841i	−1.10668	−	0.399194i
$66$		0			0
$67$	3.19413	+	2.32067i	0.390225	+	0.283515i	0.765548	−	0.643379i	$-0.222468\pi$
$67$	3.19413	+	2.32067i	0.390225	+	0.283515i	−0.375323	+	0.926894i	$0.622468\pi$
$68$		0			0
$69$	1.05750	+	0.343603i	0.127308	+	0.0413649i
$70$		0			0
$71$	−6.73066	−	9.26396i	−0.798783	−	1.09943i	−0.992958	−	0.118463i	$-0.962203\pi$
$71$	−6.73066	−	9.26396i	−0.798783	−	1.09943i	0.194176	−	0.980967i	$-0.437797\pi$
$72$		0			0
$73$			16.0715i			1.88103i	0.339757	+	0.940513i	$0.389655\pi$
$73$			16.0715i			1.88103i	−0.339757	+	0.940513i	$0.610345\pi$
$74$		0			0
$75$	−1.94480	−	0.124746i	−0.224567	−	0.0144044i
$76$		0			0
$77$	−2.71744	+	3.74023i	−0.309681	+	0.426239i
$78$		0			0
$79$			14.2526i			1.60355i	0.597627	+	0.801774i	$0.296110\pi$
$79$			14.2526i			1.60355i	−0.597627	+	0.801774i	$0.703890\pi$
$80$		0			0
$81$	7.65586			0.850651
$82$		0			0
$83$			7.69398i			0.844524i	0.906474	+	0.422262i	$0.138764\pi$
$83$			7.69398i			0.844524i	−0.906474	+	0.422262i	$0.861236\pi$
$84$		0			0
$85$	−6.61407	−	9.74513i	−0.717397	−	1.05701i
$86$		0			0
$87$	−0.248079	+	0.341451i	−0.0265969	+	0.0366074i
$88$		0			0
$89$	9.28990	−	3.01847i	0.984727	−	0.319957i	0.227981	−	0.973666i	$-0.426788\pi$
$89$	9.28990	−	3.01847i	0.984727	−	0.319957i	0.756747	+	0.653708i	$0.226788\pi$
$90$		0			0
$91$	4.12196			0.432099
$92$		0			0
$93$	0.910131	−	0.661249i	0.0943762	−	0.0685683i
$94$		0			0
$95$	−1.16935	−	4.03415i	−0.119973	−	0.413895i
$96$		0			0
$97$	−2.69462	−	1.95776i	−0.273597	−	0.198780i	0.442523	−	0.896757i	$-0.354084\pi$
$97$	−2.69462	−	1.95776i	−0.273597	−	0.198780i	−0.716120	+	0.697977i	$0.754084\pi$
$98$		0			0
$99$	7.96460	+	10.9623i	0.800473	+	1.10176i
$100$		0			0
$101$	−4.75671	+	1.54555i	−0.473310	+	0.153788i	−0.535952	−	0.844248i	$-0.680047\pi$
$101$	−4.75671	+	1.54555i	−0.473310	+	0.153788i	0.0626422	+	0.998036i	$0.480047\pi$
$102$		0			0
$103$	3.80678	−	1.23690i	0.375094	−	0.121875i	−0.115402	−	0.993319i	$-0.536816\pi$
$103$	3.80678	−	1.23690i	0.375094	−	0.121875i	0.490496	+	0.871444i	$0.336816\pi$
$104$		0			0
$105$	0.813415	−	0.235779i	0.0793812	−	0.0230097i
$106$		0			0
$107$	3.08665	−	1.00291i	0.298398	−	0.0969553i	−0.155992	−	0.987758i	$-0.549857\pi$
$107$	3.08665	−	1.00291i	0.298398	−	0.0969553i	0.454390	+	0.890803i	$0.349857\pi$
$108$		0			0
$109$			3.35053i			0.320923i	0.987042	+	0.160461i	$0.0512982\pi$
$109$			3.35053i			0.320923i	−0.987042	+	0.160461i	$0.948702\pi$
$110$		0			0
$111$	0.255724	−	0.351973i	0.0242722	−	0.0334078i
$112$		0			0
$113$	−9.75897	−	13.4321i	−0.918047	−	1.26358i	−0.964343	−	0.264656i	$-0.914742\pi$
$113$	−9.75897	−	13.4321i	−0.918047	−	1.26358i	0.0462959	−	0.998928i	$-0.485258\pi$
$114$		0			0
$115$	−2.16453	+	6.00069i	−0.201843	+	0.559567i
$116$		0			0
$117$	3.73328	−	11.4899i	0.345142	−	1.06224i
$118$		0			0
$119$	4.14077	+	3.00844i	0.379584	+	0.275784i
$120$		0			0
$121$	−3.59547	+	11.0657i	−0.326861	+	1.00598i
$122$		0			0
$123$	−2.04619	−	1.42883i	−0.184499	−	0.128833i
$124$		0			0
$125$	1.07259	−	11.1288i	0.0959351	−	0.995388i
$126$		0			0
$127$	11.8222	−	16.2718i	1.04905	−	1.44389i	0.159418	−	0.987211i	$-0.449038\pi$
$127$	11.8222	−	16.2718i	1.04905	−	1.44389i	0.889631	−	0.456681i	$-0.150962\pi$
$128$		0			0
$129$	−2.49990	−	0.812268i	−0.220104	−	0.0715162i
$130$		0			0
$131$	5.06127	−	3.67723i	0.442205	−	0.321281i	−0.344305	−	0.938858i	$-0.611886\pi$
$131$	5.06127	−	3.67723i	0.442205	−	0.321281i	0.786511	+	0.617577i	$0.211886\pi$
$132$		0			0
$133$	1.07288	+	1.47670i	0.0930309	+	0.128046i
$134$		0			0
$135$	0.163210	−	5.09417i	0.0140469	−	0.438436i
$136$		0			0
$137$	8.81952			0.753503			0.376751	−	0.926314i	$-0.377041\pi$
$137$	8.81952			0.753503			0.376751	+	0.926314i	$0.377041\pi$
$138$		0			0
$139$	2.78275	+	8.56441i	0.236029	+	0.726424i	0.996983	+	0.0776177i	$0.0247314\pi$
$139$	2.78275	+	8.56441i	0.236029	+	0.726424i	−0.760954	+	0.648806i	$0.775269\pi$
$140$		0			0
$141$	−0.582813	+	1.79371i	−0.0490817	+	0.151058i
$142$		0			0
$143$	19.1935	−	6.23634i	1.60504	−	0.521509i
$144$		0			0
$145$	−1.91234	−	1.48524i	−0.158811	−	0.123342i
$146$		0			0
$147$	1.90951	−	1.38734i	0.157493	−	0.114426i
$148$		0			0
$149$	−7.36992	+	10.1438i	−0.603767	+	0.831014i	−0.996047	−	0.0888317i	$-0.971687\pi$
$149$	−7.36992	+	10.1438i	−0.603767	+	0.831014i	0.392279	+	0.919846i	$0.371687\pi$
$150$		0			0
$151$	3.27570	+	1.06434i	0.266572	+	0.0866146i	0.439253	−	0.898363i	$-0.355243\pi$
$151$	3.27570	+	1.06434i	0.266572	+	0.0866146i	−0.172681	+	0.984978i	$0.555243\pi$
$152$		0			0
$153$	12.1363	−	8.81752i	0.981160	−	0.712854i
$154$		0			0
$155$	3.62446	+	5.34026i	0.291124	+	0.428940i
$156$		0			0
$157$	2.57810	+	7.93458i	0.205755	+	0.633249i	0.999682	+	0.0252351i	$0.00803342\pi$
$157$	2.57810	+	7.93458i	0.205755	+	0.633249i	−0.793927	+	0.608014i	$0.791967\pi$
$158$		0			0
$159$	−1.25073	−	0.908712i	−0.0991897	−	0.0720655i
$160$		0			0
$161$		−	2.77221i		−	0.218481i
$162$		0			0
$163$		−	19.6377i		−	1.53814i	−0.639163	−	0.769071i	$-0.720719\pi$
$163$		−	19.6377i		−	1.53814i	0.639163	−	0.769071i	$-0.279281\pi$
$164$		0			0
$165$	3.43086	−	2.32854i	0.267092	−	0.181277i
$166$		0			0
$167$	−16.0937			−1.24537			−0.622685	−	0.782473i	$-0.713958\pi$
$167$	−16.0937			−1.24537			−0.622685	+	0.782473i	$0.713958\pi$
$168$		0			0
$169$	−4.03965	−	2.93498i	−0.310742	−	0.225767i
$170$		0			0
$171$	5.08798	−	1.65318i	0.389087	−	0.126422i
$172$		0			0
$173$			3.37511i			0.256605i	0.991735	+	0.128303i	$0.0409529\pi$
$173$			3.37511i			0.256605i	−0.991735	+	0.128303i	$0.959047\pi$
$174$		0			0
$175$	1.20255	+	4.70751i	0.0909041	+	0.355855i
$176$		0			0
$177$	−0.918520	+	2.82691i	−0.0690402	+	0.212484i
$178$		0			0
$179$	−13.2324	+	18.2128i	−0.989035	+	1.36129i	−0.0572177	+	0.998362i	$0.518223\pi$
$179$	−13.2324	+	18.2128i	−0.989035	+	1.36129i	−0.931817	+	0.362928i	$0.881777\pi$
$180$		0			0
$181$	−5.17108	−	7.11738i	−0.384363	−	0.529030i	0.572371	−	0.819995i	$-0.306024\pi$
$181$	−5.17108	−	7.11738i	−0.384363	−	0.529030i	−0.956734	+	0.290965i	$0.906024\pi$
$182$		0			0
$183$	0.376914	+	1.16002i	0.0278623	+	0.0857513i
$184$		0			0
$185$	1.97127	+	1.53100i	0.144931	+	0.112562i
$186$		0			0
$187$	23.8327	+	7.74371i	1.74282	+	0.566276i
$188$		0			0
$189$	0.684451	+	2.10652i	0.0497865	+	0.153227i
$190$		0			0
$191$		−	2.63743i		−	0.190838i	−0.995437	−	0.0954190i	$-0.969581\pi$
$191$		−	2.63743i		−	0.190838i	0.995437	−	0.0954190i	$-0.0304191\pi$
$192$		0			0
$193$	−1.59264	−	1.15712i	−0.114641	−	0.0832913i	0.528988	−	0.848629i	$-0.322572\pi$
$193$	−1.59264	−	1.15712i	−0.114641	−	0.0832913i	−0.643628	+	0.765338i	$0.722572\pi$
$194$		0			0
$195$	−3.47757	−	1.25441i	−0.249034	−	0.0898299i
$196$		0			0
$197$	−12.7202	−	17.5079i	−0.906278	−	1.24738i	−0.968422	−	0.249318i	$-0.919794\pi$
$197$	−12.7202	−	17.5079i	−0.906278	−	1.24738i	0.0621437	−	0.998067i	$-0.480206\pi$
$198$		0			0
$199$	6.13470	+	1.99329i	0.434877	+	0.141300i	0.518271	−	0.855216i	$-0.326576\pi$
$199$	6.13470	+	1.99329i	0.434877	+	0.141300i	−0.0833936	+	0.996517i	$0.526576\pi$
$200$		0			0
$201$	1.24494	+	0.904505i	0.0878116	+	0.0637988i
$202$		0			0
$203$	1.00076	+	0.325166i	0.0702394	+	0.0228222i
$204$		0			0
$205$	8.56893	−	11.4705i	0.598480	−	0.801138i
$206$		0			0
$207$	−7.72746	−	2.51080i	−0.537095	−	0.174513i
$208$		0			0
$209$	7.22995	+	5.25287i	0.500106	+	0.363348i
$210$		0			0
$211$	19.1949	+	6.23681i	1.32143	+	0.429360i	0.882987	−	0.469397i	$-0.155529\pi$
$211$	19.1949	+	6.23681i	1.32143	+	0.429360i	0.438447	+	0.898757i	$0.355529\pi$
$212$		0			0
$213$	−2.62334	−	3.61072i	−0.179749	−	0.247403i
$214$		0			0
$215$	5.11688	−	14.1855i	0.348968	−	0.967440i
$216$		0			0
$217$	−2.26911	−	1.64860i	−0.154037	−	0.111915i
$218$		0			0
$219$			6.26403i			0.423284i
$220$		0			0
$221$	−6.90418	−	21.2489i	−0.464425	−	1.42935i
$222$		0			0
$223$	8.60718	+	2.79664i	0.576379	+	0.187277i	0.582678	−	0.812703i	$-0.302005\pi$
$223$	8.60718	+	2.79664i	0.576379	+	0.187277i	−0.00629869	+	0.999980i	$0.502005\pi$
$224$		0			0
$225$	14.2112	+	0.911551i	0.947415	+	0.0607700i
$226$		0			0
$227$	6.37101	+	19.6080i	0.422859	+	1.30143i	0.905030	+	0.425349i	$0.139849\pi$
$227$	6.37101	+	19.6080i	0.422859	+	1.30143i	−0.482171	+	0.876077i	$0.660151\pi$
$228$		0			0
$229$	9.92865	+	13.6656i	0.656103	+	0.903049i	0.999345	−	0.0361983i	$-0.0115248\pi$
$229$	9.92865	+	13.6656i	0.656103	+	0.903049i	−0.343241	+	0.939247i	$0.611525\pi$
$230$		0			0
$231$	−1.05915	+	1.45779i	−0.0696869	+	0.0959157i
$232$		0			0
$233$	−1.92125	+	5.91301i	−0.125866	+	0.387374i	−0.994058	−	0.108854i	$-0.965282\pi$
$233$	−1.92125	+	5.91301i	−0.125866	+	0.387374i	0.868192	+	0.496228i	$0.165282\pi$
$234$		0			0
$235$	−10.1783	−	3.67143i	−0.663956	−	0.239498i
$236$		0			0
$237$			5.55511i			0.360843i
$238$		0			0
$239$	11.0326	−	3.58472i	0.713643	−	0.231877i	0.0703779	−	0.997520i	$-0.477579\pi$
$239$	11.0326	−	3.58472i	0.713643	−	0.231877i	0.643265	+	0.765644i	$0.277579\pi$
$240$		0			0
$241$	5.95649	+	4.32764i	0.383691	+	0.278768i	0.762865	−	0.646557i	$-0.223792\pi$
$241$	5.95649	+	4.32764i	0.383691	+	0.278768i	−0.379174	+	0.925325i	$0.623792\pi$
$242$		0			0
$243$	9.82200			0.630082
$244$		0			0
$245$	7.60433	+	11.2042i	0.485823	+	0.715808i
$246$		0			0
$247$		−	7.96784i		−	0.506982i
$248$		0			0
$249$			2.99881i			0.190042i
$250$		0			0
$251$	−5.18927	−	3.77023i	−0.327544	−	0.237975i	0.411844	−	0.911254i	$-0.364885\pi$
$251$	−5.18927	−	3.77023i	−0.327544	−	0.237975i	−0.739388	+	0.673280i	$0.764885\pi$
$252$		0			0
$253$	−4.19422	−	12.9085i	−0.263689	−	0.811550i
$254$		0			0
$255$	−2.57790	−	3.79826i	−0.161434	−	0.237856i
$256$		0			0
$257$	−0.601300	+	0.436870i	−0.0375081	+	0.0272512i	−0.606381	−	0.795174i	$-0.707379\pi$
$257$	−0.601300	+	0.436870i	−0.0375081	+	0.0272512i	0.568873	+	0.822425i	$0.307379\pi$
$258$		0			0
$259$	−1.03160	−	0.335186i	−0.0641003	−	0.0208274i
$260$		0			0
$261$	1.81278	−	2.49508i	0.112208	−	0.154442i
$262$		0			0
$263$	−13.2394	+	9.61902i	−0.816379	+	0.593134i	−0.915673	−	0.401924i	$-0.868342\pi$
$263$	−13.2394	+	9.61902i	−0.816379	+	0.593134i	0.0992938	+	0.995058i	$0.468342\pi$
$264$		0			0
$265$	5.44042	−	7.00489i	0.334202	−	0.430307i
$266$		0			0
$267$	3.62083	−	1.17648i	0.221591	−	0.0719994i
$268$		0			0
$269$	−3.92228	+	12.0715i	−0.239146	+	0.736015i	0.757399	+	0.652953i	$0.226470\pi$
$269$	−3.92228	+	12.0715i	−0.239146	+	0.736015i	−0.996544	+	0.0830620i	$0.973530\pi$
$270$		0			0
$271$	−0.650126	−	2.00088i	−0.0394923	−	0.121545i	0.929367	−	0.369158i	$-0.120354\pi$
$271$	−0.650126	−	2.00088i	−0.0394923	−	0.121545i	−0.968859	+	0.247613i	$0.920354\pi$
$272$		0			0
$273$	1.60658			0.0972344
$274$		0			0
$275$	12.7218	+	20.1006i	0.767153	+	1.21211i
$276$		0			0
$277$	−4.36389	−	6.00638i	−0.262201	−	0.360889i	0.657537	−	0.753423i	$-0.271599\pi$
$277$	−4.36389	−	6.00638i	−0.262201	−	0.360889i	−0.919737	+	0.392534i	$0.871599\pi$
$278$		0			0
$279$	−6.65059	+	4.83193i	−0.398160	+	0.289280i
$280$		0			0
$281$	−9.14590	−	2.97168i	−0.545599	−	0.177276i	0.0232325	−	0.999730i	$-0.492604\pi$
$281$	−9.14590	−	2.97168i	−0.545599	−	0.177276i	−0.568831	+	0.822454i	$0.692604\pi$
$282$		0			0
$283$	4.83158	−	6.65010i	0.287208	−	0.395307i	−0.640897	−	0.767627i	$-0.721437\pi$
$283$	4.83158	−	6.65010i	0.287208	−	0.395307i	0.928105	+	0.372320i	$0.121437\pi$
$284$		0			0
$285$	−0.455767	−	1.57235i	−0.0269973	−	0.0931379i
$286$		0			0
$287$	−1.81150	+	5.95262i	−0.106930	+	0.351372i
$288$		0			0
$289$	3.31968	−	10.2169i	0.195275	−	0.600996i
$290$		0			0
$291$	−1.05026	−	0.763056i	−0.0615671	−	0.0447311i
$292$		0			0
$293$	−9.45667	+	29.1046i	−0.552465	+	1.70031i	0.150082	+	0.988674i	$0.452046\pi$
$293$	−9.45667	+	29.1046i	−0.552465	+	1.70031i	−0.702547	+	0.711637i	$0.747954\pi$
$294$		0			0
$295$	−16.0410	−	5.78622i	−0.933946	−	0.336887i
$296$		0			0
$297$	6.37415	+	8.77326i	0.369865	+	0.509076i
$298$		0			0
$299$	−7.11297	+	9.79016i	−0.411354	+	0.566180i
$300$		0			0
$301$			6.55342i			0.377733i
$302$		0			0
$303$	−1.85397	+	0.602393i	−0.106508	+	0.0346066i
$304$		0			0
$305$	−6.72092	+	1.94815i	−0.384839	+	0.111551i
$306$		0			0
$307$	13.6636	−	4.43957i	0.779823	−	0.253380i	0.108058	−	0.994145i	$-0.465537\pi$
$307$	13.6636	−	4.43957i	0.779823	−	0.253380i	0.671765	+	0.740765i	$0.265537\pi$
$308$		0			0
$309$	1.48373	−	0.482094i	0.0844066	−	0.0274254i
$310$		0			0
$311$	0.251579	+	0.346269i	0.0142658	+	0.0196351i	0.816090	−	0.577924i	$-0.196137\pi$
$311$	0.251579	+	0.346269i	0.0142658	+	0.0196351i	−0.801825	+	0.597560i	$0.796137\pi$
$312$		0			0
$313$	−1.04694	−	0.760647i	−0.0591766	−	0.0429943i	0.557804	−	0.829973i	$-0.311644\pi$
$313$	−1.04694	−	0.760647i	−0.0591766	−	0.0429943i	−0.616980	+	0.786979i	$0.711644\pi$
$314$		0			0
$315$	−5.94385	+	1.72291i	−0.334898	+	0.0970748i
$316$		0			0
$317$	−23.2160	+	16.8674i	−1.30394	+	0.947368i	−0.999986	−	0.00531860i	$-0.998307\pi$
$317$	−23.2160	+	16.8674i	−1.30394	+	0.947368i	−0.303954	+	0.952687i	$0.598307\pi$
$318$		0			0
$319$	5.15188			0.288450
$320$		0			0
$321$	1.20305	−	0.390895i	0.0671478	−	0.0218177i
$322$		0			0
$323$	5.81539	−	8.00419i	0.323577	−	0.445365i
$324$		0			0
$325$	7.83176	−	19.7103i	0.434428	−	1.09333i
$326$		0			0
$327$			1.30590i			0.0722166i
$328$		0			0
$329$	4.70217			0.259239
$330$		0			0
$331$		−	30.0510i		−	1.65175i	−0.563853	−	0.825875i	$-0.690682\pi$
$331$		−	30.0510i		−	1.65175i	0.563853	−	0.825875i	$-0.309318\pi$
$332$		0			0
$333$	−1.86864	+	2.57197i	−0.102401	+	0.140943i
$334$		0			0
$335$	−5.41523	+	6.97246i	−0.295865	+	0.380946i
$336$		0			0
$337$		−	27.5327i		−	1.49980i	−0.661549	−	0.749902i	$-0.730101\pi$
$337$		−	27.5327i		−	1.49980i	0.661549	−	0.749902i	$-0.269899\pi$
$338$		0			0
$339$	−3.80366	−	5.23529i	−0.206586	−	0.284342i
$340$		0			0
$341$	−13.0601	−	4.24349i	−0.707245	−	0.229798i
$342$		0			0
$343$	−10.2638	−	7.45707i	−0.554192	−	0.402644i
$344$		0			0
$345$	−0.843646	+	2.33883i	−0.0454204	+	0.125918i
$346$		0			0
$347$	1.22321	+	3.76467i	0.0656656	+	0.202098i	0.978506	−	0.206219i	$-0.0661159\pi$
$347$	1.22321	+	3.76467i	0.0656656	+	0.202098i	−0.912840	+	0.408317i	$0.866116\pi$
$348$		0			0
$349$	7.15943	+	22.0345i	0.383235	+	1.17948i	0.937752	+	0.347305i	$0.112903\pi$
$349$	7.15943	+	22.0345i	0.383235	+	1.17948i	−0.554517	+	0.832172i	$0.687097\pi$
$350$		0			0
$351$	2.98778	−	9.19544i	0.159476	−	0.490816i
$352$		0			0
$353$	−27.9251	+	9.07342i	−1.48630	+	0.482929i	−0.935989	−	0.352028i	$-0.885492\pi$
$353$	−27.9251	+	9.07342i	−1.48630	+	0.482929i	−0.550314	+	0.834958i	$0.685492\pi$
$354$		0			0
$355$	21.1862	−	14.3792i	1.12445	−	0.763167i
$356$		0			0
$357$	1.61391	+	1.17257i	0.0854169	+	0.0620590i
$358$		0			0
$359$	29.2180	−	21.2282i	1.54207	−	1.12038i	0.593048	−	0.805167i	$-0.297924\pi$
$359$	29.2180	−	21.2282i	1.54207	−	1.12038i	0.949021	−	0.315212i	$-0.102076\pi$
$360$		0			0
$361$	−12.5168	+	9.09401i	−0.658781	+	0.478632i
$362$		0			0
$363$	−1.40137	+	4.31298i	−0.0735529	+	0.226373i
$364$		0			0
$365$	−35.9185	−	1.15078i	−1.88006	−	0.0602345i
$366$		0			0
$367$	−26.9290	−	8.74978i	−1.40568	−	0.456735i	−0.494660	−	0.869087i	$-0.664707\pi$
$367$	−26.9290	−	8.74978i	−1.40568	−	0.456735i	−0.911025	+	0.412352i	$0.864707\pi$
$368$		0			0
$369$	14.9521	+	10.4408i	0.778374	+	0.543528i
$370$		0			0
$371$	−1.19108	+	3.66577i	−0.0618379	+	0.190317i
$372$		0			0
$373$	12.8898	−	17.7413i	0.667409	−	0.918610i	−0.332289	−	0.943178i	$-0.607821\pi$
$373$	12.8898	−	17.7413i	0.667409	−	0.918610i	0.999698	+	0.0245678i	$0.00782095\pi$
$374$		0			0
$375$	0.418051	−	4.33755i	0.0215881	−	0.223990i
$376$		0			0
$377$	−2.69990	−	3.71610i	−0.139052	−	0.191389i
$378$		0			0
$379$	−29.2993	+	21.2872i	−1.50500	+	1.09345i	−0.536670	+	0.843792i	$0.680318\pi$
$379$	−29.2993	+	21.2872i	−1.50500	+	1.09345i	−0.968334	+	0.249658i	$0.919682\pi$
$380$		0			0
$381$	4.60781	−	6.34211i	0.236065	−	0.324916i
$382$		0			0
$383$	−21.0841			−1.07735			−0.538673	−	0.842515i	$-0.681074\pi$
$383$	−21.0841			−1.07735			−0.538673	+	0.842515i	$0.681074\pi$
$384$		0			0
$385$	−8.16454	−	6.34107i	−0.416104	−	0.323171i
$386$		0			0
$387$	18.2675	+	5.93547i	0.928589	+	0.301717i
$388$		0			0
$389$	−8.01697	−	24.6737i	−0.406476	−	1.25101i	−0.919656	−	0.392725i	$-0.871533\pi$
$389$	−8.01697	−	24.6737i	−0.406476	−	1.25101i	0.513180	−	0.858281i	$-0.328467\pi$
$390$		0			0
$391$	−14.2908	+	4.64338i	−0.722719	+	0.234826i
$392$		0			0
$393$	1.97268	−	1.43324i	0.0995086	−	0.0722972i
$394$		0			0
$395$	−31.8535	−	1.02054i	−1.60273	−	0.0513490i
$396$		0			0
$397$	1.80434	−	5.55317i	0.0905570	−	0.278706i	−0.895513	−	0.445035i	$-0.853191\pi$
$397$	1.80434	−	5.55317i	0.0905570	−	0.278706i	0.986070	+	0.166329i	$0.0531913\pi$
$398$		0			0
$399$	0.418167	+	0.575558i	0.0209346	+	0.0288139i
$400$		0			0
$401$	−10.1056			−0.504647			−0.252324	−	0.967643i	$-0.581195\pi$
$401$	−10.1056			−0.504647			−0.252324	+	0.967643i	$0.581195\pi$
$402$		0			0
$403$	3.78344	+	11.6442i	0.188466	+	0.580040i
$404$		0			0
$405$	−0.548188	+	17.1102i	−0.0272397	+	0.850215i
$406$		0			0
$407$	−5.31064			−0.263239
$408$		0			0
$409$	−30.8312			−1.52451			−0.762253	−	0.647279i	$-0.775907\pi$
$409$	−30.8312			−1.52451			−0.762253	+	0.647279i	$0.775907\pi$
$410$		0			0
$411$	3.43750			0.169559
$412$		0			0
$413$	7.41067			0.364655
$414$		0			0
$415$	−17.1954	−	0.550918i	−0.844091	−	0.0270435i
$416$		0			0
$417$	1.08460	+	3.33806i	0.0531132	+	0.163466i
$418$		0			0
$419$	−7.89927			−0.385905			−0.192952	−	0.981208i	$-0.561806\pi$
$419$	−7.89927			−0.385905			−0.192952	+	0.981208i	$0.561806\pi$
$420$		0			0
$421$	15.8068	+	21.7561i	0.770375	+	1.06033i	0.996280	+	0.0861804i	$0.0274661\pi$
$421$	15.8068	+	21.7561i	0.770375	+	1.06033i	−0.225905	+	0.974149i	$0.572534\pi$
$422$		0			0
$423$	4.25878	−	13.1072i	0.207069	−	0.637293i
$424$		0			0
$425$	22.2532	−	14.0841i	1.07944	−	0.683181i
$426$		0			0
$427$	2.46019	−	1.78743i	0.119057	−	0.0865000i
$428$		0			0
$429$	7.48085	−	2.43068i	0.361179	−	0.117354i
$430$		0			0
$431$	−4.70028	−	14.4660i	−0.226404	−	0.696801i	−0.998146	−	0.0608649i	$-0.980614\pi$
$431$	−4.70028	−	14.4660i	−0.226404	−	0.696801i	0.771742	−	0.635936i	$-0.219386\pi$
$432$		0			0
$433$	−4.25062	−	1.38111i	−0.204272	−	0.0663719i	0.205094	−	0.978742i	$-0.434250\pi$
$433$	−4.25062	−	1.38111i	−0.204272	−	0.0663719i	−0.409366	+	0.912370i	$0.634250\pi$
$434$		0			0
$435$	−0.745354	−	0.578886i	−0.0357370	−	0.0277555i
$436$		0			0
$437$	−5.35874			−0.256343
$438$		0			0
$439$	17.7298	−	24.4029i	0.846196	−	1.16469i	−0.138493	−	0.990363i	$-0.544226\pi$
$439$	17.7298	−	24.4029i	0.846196	−	1.16469i	0.984688	−	0.174325i	$-0.0557743\pi$
$440$		0			0
$441$	−13.9533	+	10.1377i	−0.664443	+	0.482746i
$442$		0			0
$443$	21.5689	+	29.6871i	1.02477	+	1.41048i	0.908804	+	0.417222i	$0.136996\pi$
$443$	21.5689	+	29.6871i	1.02477	+	1.41048i	0.115966	+	0.993253i	$0.463004\pi$
$444$		0			0
$445$	6.08085	+	20.9783i	0.288260	+	0.994468i
$446$		0			0
$447$	−2.87250	+	3.95366i	−0.135865	+	0.187002i
$448$		0			0
$449$	−2.19564	+	6.75748i	−0.103619	+	0.318905i	−0.989404	−	0.145190i	$-0.953621\pi$
$449$	−2.19564	+	6.75748i	−0.103619	+	0.318905i	0.885785	+	0.464095i	$0.153621\pi$
$450$		0			0
$451$	0.570973	+	30.4584i	0.0268861	+	1.43423i
$452$		0			0
$453$	1.27674	+	0.414836i	0.0599862	+	0.0194907i
$454$		0			0
$455$	−0.295148	+	9.21226i	−0.0138367	+	0.431877i
$456$		0			0
$457$	−13.1538	+	40.4833i	−0.615310	+	1.89373i	−0.218459	+	0.975846i	$0.570103\pi$
$457$	−13.1538	+	40.4833i	−0.615310	+	1.89373i	−0.396851	+	0.917883i	$0.629897\pi$
$458$		0			0
$459$	9.71277	−	7.05674i	0.453353	−	0.329381i
$460$		0			0
$461$	−9.84494	+	7.15277i	−0.458525	+	0.333138i	−0.792952	−	0.609284i	$-0.791457\pi$
$461$	−9.84494	+	7.15277i	−0.458525	+	0.333138i	0.334428	+	0.942421i	$0.391457\pi$
$462$		0			0
$463$	−25.1585	−	18.2787i	−1.16921	−	0.849484i	−0.178300	−	0.983976i	$-0.557060\pi$
$463$	−25.1585	−	18.2787i	−1.16921	−	0.849484i	−0.990915	+	0.134492i	$0.957060\pi$
$464$		0			0
$465$	1.41267	+	2.08142i	0.0655110	+	0.0965235i
$466$		0			0
$467$	−10.3498	+	3.36284i	−0.478929	+	0.155614i	−0.538526	−	0.842609i	$-0.681019\pi$
$467$	−10.3498	+	3.36284i	−0.478929	+	0.155614i	0.0595965	+	0.998223i	$0.481019\pi$
$468$		0			0
$469$	1.18557	−	3.64880i	0.0547444	−	0.168486i
$470$		0			0
$471$	1.00484	+	3.09258i	0.0463006	+	0.142499i
$472$		0			0
$473$	9.91503	+	30.5153i	0.455893	+	1.40310i
$474$		0			0
$475$	9.09973	−	2.32455i	0.417524	−	0.106658i
$476$		0			0
$477$	9.13947	+	6.64022i	0.418468	+	0.304035i
$478$		0			0
$479$	−23.5229	−	7.64306i	−1.07479	−	0.349220i	−0.282438	−	0.959285i	$-0.591143\pi$
$479$	−23.5229	−	7.64306i	−1.07479	−	0.349220i	−0.792351	+	0.610065i	$0.791143\pi$
$480$		0			0
$481$	2.78310	+	3.83061i	0.126898	+	0.174661i
$482$		0			0
$483$		−	1.08050i		−	0.0491643i
$484$		0			0
$485$	4.56838	−	5.88209i	0.207439	−	0.267092i
$486$		0			0
$487$	−13.4217	+	18.4733i	−0.608193	+	0.837106i	−0.996427	−	0.0844548i	$-0.973085\pi$
$487$	−13.4217	+	18.4733i	−0.608193	+	0.837106i	0.388234	+	0.921561i	$0.373085\pi$
$488$		0			0
$489$		−	7.65398i		−	0.346125i
$490$		0			0
$491$	27.2190			1.22838			0.614189	−	0.789159i	$-0.289483\pi$
$491$	27.2190			1.22838			0.614189	+	0.789159i	$0.289483\pi$
$492$		0			0
$493$		−	5.70359i		−	0.256877i
$494$		0			0
$495$	−25.0702	+	17.0153i	−1.12682	+	0.764781i
$496$		0			0
$497$	−6.54043	+	9.00214i	−0.293379	+	0.403801i
$498$		0			0
$499$	4.46305	−	1.45013i	0.199794	−	0.0649169i	−0.207411	−	0.978254i	$-0.566504\pi$
$499$	4.46305	−	1.45013i	0.199794	−	0.0649169i	0.407204	+	0.913337i	$0.366504\pi$
$500$		0			0
$501$	−6.27269			−0.280243
$502$		0			0
$503$	−20.2787	+	14.7333i	−0.904181	+	0.656926i	−0.939536	−	0.342449i	$-0.888744\pi$
$503$	−20.2787	+	14.7333i	−0.904181	+	0.656926i	0.0353558	+	0.999375i	$0.488744\pi$
$504$		0			0
$505$	−3.11358	−	10.7415i	−0.138552	−	0.477992i
$506$		0			0
$507$	−1.57449	−	1.14394i	−0.0699257	−	0.0508040i
$508$		0			0
$509$	−4.05689	−	5.58383i	−0.179819	−	0.247499i	0.709587	−	0.704618i	$-0.248881\pi$
$509$	−4.05689	−	5.58383i	−0.179819	−	0.247499i	−0.889406	+	0.457119i	$0.848881\pi$
$510$		0			0
$511$	14.8529	−	4.82600i	0.657054	−	0.213490i
$512$		0			0
$513$	4.07195	−	1.32306i	0.179781	−	0.0584145i
$514$		0			0
$515$	2.49179	+	8.59643i	0.109801	+	0.378804i
$516$		0			0
$517$	21.8952	−	7.11417i	0.962948	−	0.312881i
$518$		0			0
$519$			1.31548i			0.0577434i
$520$		0			0
$521$	15.1983	−	20.9186i	0.665848	−	0.916461i	−0.333809	−	0.942641i	$-0.608334\pi$
$521$	15.1983	−	20.9186i	0.665848	−	0.916461i	0.999657	+	0.0261795i	$0.00833416\pi$
$522$		0			0
$523$	6.99067	+	9.62184i	0.305681	+	0.420734i	0.934028	−	0.357199i	$-0.116268\pi$
$523$	6.99067	+	9.62184i	0.305681	+	0.420734i	−0.628347	+	0.777933i	$0.716268\pi$
$524$		0			0
$525$	0.468705	+	1.83480i	0.0204560	+	0.0800773i
$526$		0			0
$527$	−4.69792	+	14.4587i	−0.204645	+	0.629832i
$528$		0			0
$529$	−12.0231	−	8.73526i	−0.522742	−	0.379794i
$530$		0			0
$531$	6.71188	−	20.6571i	0.291271	−	0.896440i
$532$		0			0
$533$	21.6707	−	16.3739i	0.938662	−	0.709233i
$534$		0			0
$535$	2.02042	+	6.97023i	0.0873502	+	0.301349i
$536$		0			0
$537$	−5.15745	+	7.09863i	−0.222561	+	0.306328i
$538$		0			0
$539$	−27.4009	−	8.90309i	−1.18024	−	0.383483i
$540$		0			0
$541$	−23.6856	+	17.2086i	−1.01832	+	0.739855i	−0.965939	−	0.258772i	$-0.916682\pi$
$541$	−23.6856	+	17.2086i	−1.01832	+	0.739855i	−0.0523850	+	0.998627i	$0.516682\pi$
$542$		0			0
$543$	−2.01548	−	2.77407i	−0.0864925	−	0.119047i
$544$		0			0
$545$	−7.48818	−	0.239910i	−0.320758	−	0.0102766i
$546$		0			0
$547$	−42.6269			−1.82260			−0.911298	−	0.411748i	$-0.864918\pi$
$547$	−42.6269			−1.82260			−0.911298	+	0.411748i	$0.864918\pi$
$548$		0			0
$549$	−2.75422	−	8.47661i	−0.117547	−	0.361773i
$550$		0			0
$551$	0.628553	−	1.93449i	0.0267773	−	0.0824119i
$552$		0			0
$553$	13.1720	−	4.27983i	0.560129	−	0.181997i
$554$		0			0
$555$	0.768322	+	0.596725i	0.0326134	+	0.0253295i
$556$		0			0
$557$	30.5453	−	22.1925i	1.29425	−	0.940326i	0.294366	−	0.955693i	$-0.404892\pi$
$557$	30.5453	−	22.1925i	1.29425	−	0.940326i	0.999882	+	0.0153670i	$0.00489165\pi$
$558$		0			0
$559$	16.8149	−	23.1437i	0.711193	−	0.978873i
$560$		0			0
$561$	9.28903	+	3.01819i	0.392183	+	0.127428i
$562$		0			0
$563$	−11.2676	+	8.18637i	−0.474871	+	0.345014i	−0.799337	−	0.600883i	$-0.794816\pi$
$563$	−11.2676	+	8.18637i	−0.474871	+	0.345014i	0.324465	+	0.945898i	$0.394816\pi$
$564$		0			0
$565$	30.7184	−	20.8488i	1.29233	−	0.877114i
$566$		0			0
$567$	−2.29893	−	7.07537i	−0.0965459	−	0.297138i
$568$		0			0
$569$	−16.5837	−	12.0488i	−0.695227	−	0.505112i	0.183147	−	0.983085i	$-0.441371\pi$
$569$	−16.5837	−	12.0488i	−0.695227	−	0.505112i	−0.878374	+	0.477974i	$0.841371\pi$
$570$		0			0
$571$		−	6.00182i		−	0.251168i	−0.992083	−	0.125584i	$-0.959920\pi$
$571$		−	6.00182i		−	0.251168i	0.992083	−	0.125584i	$-0.0400805\pi$
$572$		0			0
$573$		−	1.02797i		−	0.0429439i
$574$		0			0
$575$	−13.2561	−	5.26722i	−0.552816	−	0.219658i
$576$		0			0
$577$	−7.28277			−0.303186			−0.151593	−	0.988443i	$-0.548440\pi$
$577$	−7.28277			−0.303186			−0.151593	+	0.988443i	$0.548440\pi$
$578$		0			0
$579$	−0.620747	−	0.450999i	−0.0257974	−	0.0187429i
$580$		0			0
$581$	7.11060	−	2.31037i	0.294997	−	0.0958505i
$582$		0			0
$583$			18.8713i			0.781570i
$584$		0			0
$585$	25.4116	+	9.16631i	1.05064	+	0.378980i
$586$		0			0
$587$	6.50323	−	20.0149i	0.268417	−	0.826102i	−0.722470	−	0.691403i	$-0.756993\pi$
$587$	6.50323	−	20.0149i	0.268417	−	0.826102i	0.990886	−	0.134700i	$-0.0430069\pi$
$588$		0			0
$589$	−3.18679	+	4.38624i	−0.131309	+	0.180732i
$590$		0			0
$591$	−4.95783	−	6.82387i	−0.203938	−	0.280697i
$592$		0			0
$593$	−14.8763	−	45.7844i	−0.610895	−	1.88014i	−0.449589	−	0.893236i	$-0.648429\pi$
$593$	−14.8763	−	45.7844i	−0.610895	−	1.88014i	−0.161306	−	0.986904i	$-0.551571\pi$
$594$		0			0
$595$	−7.02013	+	9.03887i	−0.287797	+	0.370558i
$596$		0			0
$597$	2.39106	+	0.776903i	0.0978596	+	0.0317965i
$598$		0			0
$599$	−6.46949	−	19.9110i	−0.264336	−	0.813543i	−0.991846	−	0.127446i	$-0.959322\pi$
$599$	−6.46949	−	19.9110i	−0.264336	−	0.813543i	0.727509	−	0.686098i	$-0.240678\pi$
$600$		0			0
$601$			43.3096i			1.76664i	0.468775	+	0.883318i	$0.344696\pi$
$601$			43.3096i			1.76664i	−0.468775	+	0.883318i	$0.655304\pi$
$602$		0			0
$603$	−9.09716	−	6.60947i	−0.370465	−	0.269158i
$604$		0			0
$605$	−24.4736	−	8.82794i	−0.994992	−	0.358907i
$606$		0			0
$607$	5.17468	+	7.12233i	0.210034	+	0.289087i	0.901017	−	0.433784i	$-0.142822\pi$
$607$	5.17468	+	7.12233i	0.210034	+	0.289087i	−0.690983	+	0.722871i	$0.742822\pi$
$608$		0			0
$609$	0.390056	+	0.126737i	0.0158058	+	0.00513563i
$610$		0			0
$611$	−16.6059	−	12.0649i	−0.671803	−	0.488093i
$612$		0			0
$613$	37.8669	+	12.3037i	1.52943	+	0.496941i	0.948436	−	0.316968i	$-0.102665\pi$
$613$	37.8669	+	12.3037i	1.52943	+	0.496941i	0.580992	+	0.813910i	$0.302665\pi$
$614$		0			0
$615$	3.33983	−	4.47076i	0.134675	−	0.180278i
$616$		0			0
$617$	38.9389	+	12.6520i	1.56762	+	0.509351i	0.958830	−	0.283981i	$-0.0916551\pi$
$617$	38.9389	+	12.6520i	1.56762	+	0.509351i	0.608790	+	0.793331i	$0.291655\pi$
$618$		0			0
$619$	−30.7407	−	22.3344i	−1.23557	−	0.897697i	−0.238279	−	0.971197i	$-0.576583\pi$
$619$	−30.7407	−	22.3344i	−1.23557	−	0.897697i	−0.997295	+	0.0734995i	$0.976583\pi$
$620$		0			0
$621$	−6.18436	−	2.00942i	−0.248170	−	0.0806352i
$622$		0			0
$623$	−5.57920	−	7.67911i	−0.223526	−	0.307657i
$624$		0			0
$625$	24.7951	+	3.19401i	0.991805	+	0.127760i
$626$		0			0
$627$	2.81795	+	2.04736i	0.112538	+	0.0817636i
$628$		0			0
$629$			5.87935i			0.234425i
$630$		0			0
$631$	−5.85750	−	18.0275i	−0.233184	−	0.717665i	−0.997357	−	0.0726545i	$-0.976853\pi$
$631$	−5.85750	−	18.0275i	−0.233184	−	0.717665i	0.764174	−	0.645011i	$-0.223147\pi$
$632$		0			0
$633$	7.48142	+	2.43086i	0.297360	+	0.0966180i
$634$		0			0
$635$	35.5198	+	27.5868i	1.40956	+	1.09475i
$636$		0			0
$637$	7.93787	+	24.4302i	0.314510	+	0.967961i
$638$		0			0
$639$	19.1695	+	26.3846i	0.758334	+	1.04376i
$640$		0			0
$641$	−10.2689	+	14.1339i	−0.405596	+	0.558255i	−0.962137	−	0.272565i	$-0.912128\pi$
$641$	−10.2689	+	14.1339i	−0.405596	+	0.558255i	0.556541	+	0.830820i	$0.312128\pi$
$642$		0			0
$643$	−9.86531	+	30.3623i	−0.389050	+	1.19737i	0.544449	+	0.838794i	$0.316739\pi$
$643$	−9.86531	+	30.3623i	−0.389050	+	1.19737i	−0.933499	+	0.358579i	$0.883261\pi$
$644$		0			0
$645$	1.99436	−	5.52892i	0.0785277	−	0.217701i
$646$		0			0
$647$		−	43.9043i		−	1.72606i	−0.505155	−	0.863029i	$-0.668565\pi$
$647$		−	43.9043i		−	1.72606i	0.505155	−	0.863029i	$-0.331435\pi$
$648$		0			0
$649$	34.5070	−	11.2120i	1.35452	−	0.440110i
$650$		0			0
$651$	−0.884408	−	0.642560i	−0.0346627	−	0.0251839i
$652$		0			0
$653$	−38.2042			−1.49505			−0.747523	−	0.664236i	$-0.768757\pi$
$653$	−38.2042			−1.49505			−0.747523	+	0.664236i	$0.768757\pi$
$654$		0			0
$655$	7.85591	+	11.5748i	0.306956	+	0.452267i
$656$		0			0
$657$		−	45.7730i		−	1.78578i
$658$		0			0
$659$			24.4962i			0.954235i	0.878839	+	0.477118i	$0.158318\pi$
$659$			24.4962i			0.954235i	−0.878839	+	0.477118i	$0.841682\pi$
$660$		0			0
$661$	27.1938	+	19.7574i	1.05771	+	0.768475i	0.973664	−	0.227987i	$-0.0732143\pi$
$661$	27.1938	+	19.7574i	1.05771	+	0.768475i	0.0840505	+	0.996461i	$0.473214\pi$
$662$		0			0
$663$	−2.69097	−	8.28196i	−0.104509	−	0.321645i
$664$		0			0
$665$	−3.37713	+	2.29207i	−0.130959	+	0.0888828i
$666$		0			0
$667$	−2.49924	+	1.81581i	−0.0967711	+	0.0703083i
$668$		0			0
$669$	3.35473	+	1.09002i	0.129701	+	0.0421426i
$670$		0			0
$671$	8.75132	−	12.0452i	0.337841	−	0.464998i
$672$		0			0
$673$	0.678170	−	0.492720i	0.0261416	−	0.0189929i	−0.574638	−	0.818408i	$-0.694857\pi$
$673$	0.678170	−	0.492720i	0.0261416	−	0.0189929i	0.600779	+	0.799415i	$0.294857\pi$
$674$		0			0
$675$	11.3734	+	0.729523i	0.437762	+	0.0280793i
$676$		0			0
$677$	17.2073	−	5.59099i	0.661330	−	0.214879i	0.0409267	−	0.999162i	$-0.486969\pi$
$677$	17.2073	−	5.59099i	0.661330	−	0.214879i	0.620403	+	0.784283i	$0.286969\pi$
$678$		0			0
$679$	−1.00016	+	3.07819i	−0.0383828	+	0.118130i
$680$		0			0
$681$	2.48317	+	7.64240i	0.0951551	+	0.292857i
$682$		0			0
$683$	−1.59157			−0.0608999			−0.0304500	−	0.999536i	$-0.509694\pi$
$683$	−1.59157			−0.0608999			−0.0304500	+	0.999536i	$0.509694\pi$
$684$		0			0
$685$	−0.631510	+	19.7109i	−0.0241288	+	0.753116i
$686$		0			0
$687$	3.86979	+	5.32631i	0.147642	+	0.203211i
$688$		0			0
$689$	13.6120	−	9.88972i	0.518577	−	0.376768i
$690$		0			0
$691$	−24.8018	−	8.05859i	−0.943505	−	0.306563i	−0.203431	−	0.979089i	$-0.565209\pi$
$691$	−24.8018	−	8.05859i	−0.943505	−	0.306563i	−0.740074	+	0.672526i	$0.765209\pi$
$692$		0			0
$693$	7.73950	−	10.6525i	0.293999	−	0.404655i
$694$		0			0
$695$	−19.3400	+	5.60597i	−0.733609	+	0.212647i
$696$		0			0
$697$	33.7202	−	0.632117i	1.27724	−	0.0239431i
$698$		0			0
$699$	−0.748828	+	2.30466i	−0.0283233	+	0.0871701i
$700$		0			0
$701$	31.0019	+	22.5242i	1.17093	+	0.850727i	0.991119	−	0.132975i	$-0.0424530\pi$
$701$	31.0019	+	22.5242i	1.17093	+	0.850727i	0.179806	+	0.983702i	$0.442453\pi$
$702$		0			0
$703$	−0.647922	+	1.99410i	−0.0244368	+	0.0752088i
$704$		0			0
$705$	−3.96708	−	1.43098i	−0.149409	−	0.0538937i
$706$		0			0
$707$	2.85672	+	3.93194i	0.107438	+	0.147876i
$708$		0			0
$709$	9.66733	−	13.3059i	0.363064	−	0.499715i	−0.587935	−	0.808908i	$-0.700059\pi$
$709$	9.66733	−	13.3059i	0.363064	−	0.499715i	0.950999	+	0.309193i	$0.100059\pi$
$710$		0			0
$711$		−	40.5928i		−	1.52235i
$712$		0			0
$713$	7.83127	−	2.54453i	0.293283	−	0.0952936i
$714$		0			0
$715$	12.5634	+	43.3424i	0.469845	+	1.62092i
$716$		0			0
$717$	4.30008	−	1.39718i	0.160590	−	0.0521787i
$718$		0			0
$719$	−21.9118	+	7.11957i	−0.817172	+	0.265515i	−0.687632	−	0.726059i	$-0.741350\pi$
$719$	−21.9118	+	7.11957i	−0.817172	+	0.265515i	−0.129539	+	0.991574i	$0.541350\pi$
$720$		0			0
$721$	−2.28623	−	3.14672i	−0.0851435	−	0.117190i
$722$		0			0
$723$	2.32160	+	1.68674i	0.0863413	+	0.0627306i
$724$		0			0
$725$	3.45632	−	4.16758i	0.128364	−	0.154780i
$726$		0			0
$727$	−2.49280	+	1.81112i	−0.0924527	+	0.0671708i	−0.633051	−	0.774110i	$-0.718198\pi$
$727$	−2.49280	+	1.81112i	−0.0924527	+	0.0671708i	0.540599	+	0.841281i	$0.318198\pi$
$728$		0			0
$729$	−19.1394			−0.708865
$730$		0			0
$731$	33.7832	−	10.9768i	1.24952	−	0.405992i
$732$		0			0
$733$	15.0933	−	20.7741i	0.557483	−	0.767309i	−0.433521	−	0.901143i	$-0.642729\pi$
$733$	15.0933	−	20.7741i	0.557483	−	0.767309i	0.991004	+	0.133834i	$0.0427290\pi$
$734$		0			0
$735$	2.96386	+	4.36694i	0.109324	+	0.161077i
$736$		0			0
$737$		−	18.7839i		−	0.691916i
$738$		0			0
$739$	28.2783			1.04024			0.520118	−	0.854094i	$-0.325888\pi$
$739$	28.2783			1.04024			0.520118	+	0.854094i	$0.325888\pi$
$740$		0			0
$741$		−	3.10555i		−	0.114085i
$742$		0			0
$743$	−1.49902	+	2.06322i	−0.0549935	+	0.0756921i	−0.835628	−	0.549296i	$-0.814896\pi$
$743$	−1.49902	+	2.06322i	−0.0549935	+	0.0756921i	0.780635	+	0.624988i	$0.214896\pi$
$744$		0			0
$745$	−22.1429	−	17.1975i	−0.811254	−	0.630069i
$746$		0			0
$747$		−	21.9131i		−	0.801760i
$748$		0			0
$749$	−1.85374	−	2.55145i	−0.0677341	−	0.0932280i
$750$		0			0
$751$	15.3884	+	4.99999i	0.561530	+	0.182452i	0.576009	−	0.817443i	$-0.304609\pi$
$751$	15.3884	+	4.99999i	0.561530	+	0.182452i	−0.0144796	+	0.999895i	$0.504609\pi$
$752$		0			0
$753$	−2.02257	−	1.46948i	−0.0737066	−	0.0535510i
$754$		0			0
$755$	−2.61326	+	7.24471i	−0.0951064	+	0.263662i
$756$		0			0
$757$	−9.99570	−	30.7636i	−0.363300	−	1.11812i	−0.951039	−	0.309071i	$-0.899982\pi$
$757$	−9.99570	−	30.7636i	−0.363300	−	1.11812i	0.587739	−	0.809051i	$-0.300018\pi$
$758$		0			0
$759$	−1.63474	−	5.03121i	−0.0593373	−	0.182622i
$760$		0			0
$761$	−1.99266	+	6.13279i	−0.0722340	+	0.222313i	−0.980655	−	0.195742i	$-0.937288\pi$
$761$	−1.99266	+	6.13279i	−0.0722340	+	0.222313i	0.908421	+	0.418056i	$0.137288\pi$
$762$		0			0
$763$	3.09648	−	1.00611i	0.112100	−	0.0364236i
$764$		0			0
$765$	18.8375	+	27.7550i	0.681070	+	1.00348i
$766$		0			0
$767$	−26.1711	−	19.0144i	−0.944983	−	0.686570i
$768$		0			0
$769$	31.3637	−	22.7871i	1.13101	−	0.821724i	0.145165	−	0.989408i	$-0.453629\pi$
$769$	31.3637	−	22.7871i	1.13101	−	0.821724i	0.985841	+	0.167684i	$0.0536288\pi$
$770$		0			0
$771$	−0.234363	+	0.170274i	−0.00844037	+	0.00613228i
$772$		0			0
$773$	−9.11103	+	28.0409i	−0.327701	+	1.00856i	0.642505	+	0.766281i	$0.277895\pi$
$773$	−9.11103	+	28.0409i	−0.327701	+	1.00856i	−0.970207	+	0.242279i	$0.922105\pi$
$774$		0			0
$775$	−12.1946	+	7.71800i	−0.438042	+	0.277239i
$776$		0			0
$777$	−0.402075	−	0.130642i	−0.0144244	−	0.00468676i
$778$		0			0
$779$	11.5065	+	3.50167i	0.412265	+	0.125460i
$780$		0			0
$781$	−16.8350	+	51.8129i	−0.602404	+	1.85401i
$782$		0			0
$783$	1.45079	−	1.99684i	0.0518469	−	0.0713612i
$784$		0			0
$785$	−17.9178	+	5.19371i	−0.639513	+	0.185371i
$786$		0			0
$787$	−4.22615	−	5.81680i	−0.150646	−	0.207346i	0.727024	−	0.686612i	$-0.240903\pi$
$787$	−4.22615	−	5.81680i	−0.150646	−	0.207346i	−0.877670	+	0.479266i	$0.840903\pi$
$788$		0			0
$789$	−5.16021	+	3.74911i	−0.183708	+	0.133472i
$790$		0			0
$791$	−9.48316	+	13.0524i	−0.337182	+	0.464091i
$792$		0			0
$793$	−13.2745			−0.471391
$794$		0			0
$795$	2.12046	−	2.73023i	0.0752049	−	0.0968312i
$796$		0			0
$797$	0.255219	+	0.0829258i	0.00904033	+	0.00293738i	0.313534	−	0.949577i	$-0.398487\pi$
$797$	0.255219	+	0.0829258i	0.00904033	+	0.00293738i	−0.304493	+	0.952514i	$0.598487\pi$
$798$		0			0
$799$	−7.87601	−	24.2399i	−0.278633	−	0.857545i
$800$		0			0
$801$	−26.4584	+	8.59687i	−0.934863	+	0.303755i
$802$		0			0
$803$	61.8595	−	44.9435i	2.18297	−	1.58602i
$804$		0			0
$805$	6.19567	+	0.198500i	0.218369	+	0.00699622i
$806$		0			0
$807$	−1.52875	+	4.70500i	−0.0538145	+	0.165624i
$808$		0			0
$809$	−6.94984	−	9.56563i	−0.244343	−	0.336310i	0.669177	−	0.743103i	$-0.266647\pi$
$809$	−6.94984	−	9.56563i	−0.244343	−	0.336310i	−0.913520	+	0.406793i	$0.866647\pi$
$810$		0			0
$811$	14.1480			0.496802			0.248401	−	0.968657i	$-0.420095\pi$
$811$	14.1480			0.496802			0.248401	+	0.968657i	$0.420095\pi$
$812$		0			0
$813$	−0.253393	−	0.779864i	−0.00888688	−	0.0273510i
$814$		0			0
$815$	43.8887	+	1.40613i	1.53735	+	0.0492546i
$816$		0			0
$817$	12.6679			0.443194
$818$		0			0
$819$	−11.7397			−0.410218
$820$		0			0
$821$	−15.3090			−0.534287			−0.267143	−	0.963657i	$-0.586080\pi$
$821$	−15.3090			−0.534287			−0.267143	+	0.963657i	$0.586080\pi$
$822$		0			0
$823$	−16.6648			−0.580897			−0.290448	−	0.956891i	$-0.593804\pi$
$823$	−16.6648			−0.580897			−0.290448	+	0.956891i	$0.593804\pi$
$824$		0			0
$825$	4.95845	+	7.83443i	0.172631	+	0.272760i
$826$		0			0
$827$	13.6833	+	42.1130i	0.475817	+	1.46441i	0.844853	+	0.534998i	$0.179688\pi$
$827$	13.6833	+	42.1130i	0.475817	+	1.46441i	−0.369037	+	0.929415i	$0.620312\pi$
$828$		0			0
$829$	5.96168			0.207058			0.103529	−	0.994626i	$-0.466987\pi$
$829$	5.96168			0.207058			0.103529	+	0.994626i	$0.466987\pi$
$830$		0			0
$831$	−1.70087	−	2.34105i	−0.0590026	−	0.0812101i
$832$		0			0
$833$	−9.85651	+	30.3352i	−0.341508	+	1.05105i
$834$		0			0
$835$	1.15237	−	35.9682i	0.0398794	−	1.24473i
$836$		0			0
$837$	−5.32253	+	3.86704i	−0.183973	+	0.133664i
$838$		0			0
$839$	35.6402	−	11.5802i	1.23044	−	0.399793i	0.379564	−	0.925165i	$-0.376074\pi$
$839$	35.6402	−	11.5802i	1.23044	−	0.399793i	0.850873	+	0.525372i	$0.176074\pi$
$840$		0			0
$841$	8.59914	+	26.4654i	0.296522	+	0.912601i
$842$		0			0
$843$	−3.56471	−	1.15824i	−0.122775	−	0.0398920i
$844$		0			0
$845$	6.84869	−	8.81814i	0.235602	−	0.303353i
$846$		0			0
$847$	11.3063			0.388491
$848$		0			0
$849$	1.88316	−	2.59194i	0.0646298	−	0.0889552i
$850$		0			0
$851$	2.57626	−	1.87176i	0.0883130	−	0.0641632i
$852$		0			0
$853$	15.3223	+	21.0893i	0.524625	+	0.722084i	0.986299	−	0.164965i	$-0.0527512\pi$
$853$	15.3223	+	21.0893i	0.524625	+	0.722084i	−0.461674	+	0.887049i	$0.652751\pi$
$854$		0			0
$855$	3.33042	+	11.4896i	0.113898	+	0.392936i
$856$		0			0
$857$	−24.2395	+	33.3627i	−0.828004	+	1.13965i	0.160287	+	0.987070i	$0.448758\pi$
$857$	−24.2395	+	33.3627i	−0.828004	+	1.13965i	−0.988291	+	0.152579i	$0.951242\pi$
$858$		0			0
$859$	−0.340560	+	1.04814i	−0.0116197	+	0.0357619i	−0.956698	−	0.291081i	$-0.905985\pi$
$859$	−0.340560	+	1.04814i	−0.0116197	+	0.0357619i	0.945079	+	0.326843i	$0.105985\pi$
$860$		0			0
$861$	−0.706051	+	2.32009i	−0.0240621	+	0.0790685i
$862$		0			0
$863$	1.58726	+	0.515731i	0.0540309	+	0.0175557i	0.335908	−	0.941895i	$-0.390957\pi$
$863$	1.58726	+	0.515731i	0.0540309	+	0.0175557i	−0.281877	+	0.959451i	$0.590957\pi$
$864$		0			0
$865$	−7.54311	−	0.241671i	−0.256474	−	0.00821705i
$866$		0			0
$867$	1.29388	−	3.98215i	0.0439424	−	0.135241i
$868$		0			0
$869$	54.8587	−	39.8572i	1.86095	−	1.35206i
$870$		0			0
$871$	−13.5490	+	9.84393i	−0.459091	+	0.333549i
$872$		0			0
$873$	7.67452	+	5.57587i	0.259743	+	0.188714i
$874$		0			0
$875$	−10.6070	+	2.35052i	−0.358583	+	0.0794622i
$876$		0			0
$877$	−16.3883	+	5.32489i	−0.553395	+	0.179809i	−0.572347	−	0.820012i	$-0.693967\pi$
$877$	−16.3883	+	5.32489i	−0.553395	+	0.179809i	0.0189523	+	0.999820i	$0.493967\pi$
$878$		0			0
$879$	−3.68583	+	11.3438i	−0.124320	+	0.382618i
$880$		0			0
$881$	9.63739	+	29.6608i	0.324692	+	0.999299i	0.971579	+	0.236714i	$0.0760703\pi$
$881$	9.63739	+	29.6608i	0.324692	+	0.999299i	−0.646888	+	0.762585i	$0.723930\pi$
$882$		0			0
$883$	6.08543	+	18.7290i	0.204791	+	0.630282i	0.999722	+	0.0235821i	$0.00750710\pi$
$883$	6.08543	+	18.7290i	0.204791	+	0.630282i	−0.794931	+	0.606700i	$0.792493\pi$
$884$		0			0
$885$	−6.25216	−	2.25524i	−0.210164	−	0.0758090i
$886$		0			0
$887$	7.85023	+	5.70353i	0.263585	+	0.191506i	0.711726	−	0.702457i	$-0.247914\pi$
$887$	7.85023	+	5.70353i	0.263585	+	0.191506i	−0.448141	+	0.893963i	$0.647914\pi$
$888$		0			0
$889$	−18.5881	−	6.03962i	−0.623423	−	0.202563i
$890$		0			0
$891$	−21.4094	−	29.4675i	−0.717242	−	0.987200i
$892$		0			0
$893$		−	9.08940i		−	0.304165i
$894$		0			0
$895$	−39.7567	−	30.8774i	−1.32892	−	1.03212i
$896$		0			0
$897$	−2.77235	+	3.81581i	−0.0925661	+	0.127406i
$898$		0			0
$899$			3.12553i			0.104242i
$900$		0			0
$901$	20.8922			0.696021
$902$		0			0
$903$			2.55426i			0.0850005i
$904$		0			0
$905$	16.2770	−	11.0473i	0.541067	−	0.367225i
$906$		0			0
$907$	−3.44869	+	4.74672i	−0.114512	+	0.157612i	−0.862426	−	0.506184i	$-0.831056\pi$
$907$	−3.44869	+	4.74672i	−0.114512	+	0.157612i	0.747914	+	0.663796i	$0.231056\pi$
$908$		0			0
$909$	13.5475	−	4.40185i	0.449343	−	0.146000i
$910$		0			0
$911$	40.9448			1.35656			0.678280	−	0.734803i	$-0.262726\pi$
$911$	40.9448			1.35656			0.678280	+	0.734803i	$0.262726\pi$
$912$		0			0
$913$	29.6143	−	21.5160i	0.980089	−	0.712076i
$914$		0			0
$915$	−2.61955	+	0.759311i	−0.0865995	+	0.0251021i
$916$		0			0
$917$	−4.91822	−	3.57330i	−0.162414	−	0.118001i
$918$		0			0
$919$	17.6087	+	24.2363i	0.580857	+	0.799480i	0.993789	−	0.111281i	$-0.0354954\pi$
$919$	17.6087	+	24.2363i	0.580857	+	0.799480i	−0.412932	+	0.910762i	$0.635495\pi$
$920$		0			0
$921$	5.32553	−	1.73037i	0.175482	−	0.0570176i
$922$		0			0
$923$	46.1956	−	15.0099i	1.52055	−	0.494056i
$924$		0			0
$925$	−3.56283	+	4.29600i	−0.117145	+	0.141252i
$926$		0			0
$927$	−10.8421	+	3.52280i	−0.356100	+	0.115704i
$928$		0			0
$929$		−	3.85979i		−	0.126635i	−0.997993	−	0.0633177i	$-0.979832\pi$
$929$		−	3.85979i		−	0.126635i	0.997993	−	0.0633177i	$-0.0201682\pi$
$930$		0			0
$931$	−6.68606	+	9.20258i	−0.219127	+	0.301602i
$932$		0			0
$933$	0.0980556	+	0.134962i	0.00321019	+	0.00441845i
$934$		0			0
$935$	−19.0131	+	52.7097i	−0.621794	+	1.72379i
$936$		0			0
$937$	6.13305	−	18.8756i	0.200358	−	0.616638i	−0.799514	−	0.600647i	$-0.794910\pi$
$937$	6.13305	−	18.8756i	0.200358	−	0.616638i	0.999872	−	0.0159912i	$-0.00509036\pi$
$938$		0			0
$939$	−0.408055	−	0.296470i	−0.0133164	−	0.00967492i
$940$		0			0
$941$	−13.3099	+	40.9635i	−0.433889	+	1.33537i	0.460332	+	0.887747i	$0.347730\pi$
$941$	−13.3099	+	40.9635i	−0.433889	+	1.33537i	−0.894221	+	0.447626i	$0.852270\pi$
$942$		0			0
$943$	−11.0122	−	14.5745i	−0.358607	−	0.474612i
$944$		0			0
$945$	−4.75692	+	1.37886i	−0.154743	+	0.0448543i
$946$		0			0
$947$	3.82391	−	5.26317i	0.124261	−	0.171030i	−0.742354	−	0.670007i	$-0.766291\pi$
$947$	3.82391	−	5.26317i	0.124261	−	0.171030i	0.866615	+	0.498977i	$0.166291\pi$
$948$		0			0
$949$	−64.8362	−	21.0666i	−2.10467	−	0.683850i
$950$		0			0
$951$	−9.04867	+	6.57424i	−0.293423	+	0.213184i
$952$		0			0
$953$	8.16763	+	11.2418i	0.264576	+	0.364157i	0.920549	−	0.390627i	$-0.127742\pi$
$953$	8.16763	+	11.2418i	0.264576	+	0.364157i	−0.655974	+	0.754784i	$0.727742\pi$
$954$		0			0
$955$	5.89446	+	0.188850i	0.190740	+	0.00611104i
$956$		0			0
$957$	2.00800			0.0649094
$958$		0			0
$959$	−2.64835	−	8.15080i	−0.0855198	−	0.263203i
$960$		0			0
$961$	−7.00510	+	21.5595i	−0.225971	+	0.695467i
$962$		0			0
$963$	−8.79104	+	2.85638i	−0.283287	+	0.0920457i
$964$		0			0
$965$	2.70011	−	3.47657i	0.0869197	−	0.111915i
$966$		0			0
$967$	22.0295	−	16.0054i	0.708421	−	0.514698i	−0.174243	−	0.984703i	$-0.555748\pi$
$967$	22.0295	−	16.0054i	0.708421	−	0.514698i	0.882664	+	0.470005i	$0.155748\pi$
$968$		0			0
$969$	2.26661	−	3.11971i	0.0728139	−	0.100220i
$970$		0			0
$971$	11.9317	+	3.87684i	0.382906	+	0.124414i	0.494144	−	0.869380i	$-0.335481\pi$
$971$	11.9317	+	3.87684i	0.382906	+	0.124414i	−0.111238	+	0.993794i	$0.535481\pi$
$972$		0			0
$973$	7.07942	−	5.14350i	0.226956	−	0.164893i
$974$		0			0
$975$	3.05251	−	7.68228i	0.0977585	−	0.246030i
$976$		0			0
$977$	−12.4484	−	38.3122i	−0.398259	−	1.22572i	−0.926394	−	0.376555i	$-0.877109\pi$
$977$	−12.4484	−	38.3122i	−0.398259	−	1.22572i	0.528135	−	0.849160i	$-0.322891\pi$
$978$		0			0
$979$	−37.5971	−	27.3159i	−1.20161	−	0.873020i
$980$		0			0
$981$		−	9.54261i		−	0.304672i
$982$		0			0
$983$		−	54.1831i		−	1.72817i	−0.503343	−	0.864087i	$-0.667897\pi$
$983$		−	54.1831i		−	1.72817i	0.503343	−	0.864087i	$-0.332103\pi$
$984$		0			0
$985$	40.0395	−	27.1751i	1.27577	−	0.865869i
$986$		0			0
$987$	1.83272			0.0583361
$988$		0			0
$989$	−15.5652	−	11.3088i	−0.494944	−	0.359598i
$990$		0			0
$991$	2.97531	−	0.966736i	0.0945138	−	0.0307094i	−0.261378	−	0.965236i	$-0.584177\pi$
$991$	2.97531	−	0.966736i	0.0945138	−	0.0307094i	0.355892	+	0.934527i	$0.384177\pi$
$992$		0			0
$993$		−	11.7127i		−	0.371690i
$994$		0			0
$995$	−4.89410	+	13.5678i	−0.155153	+	0.430130i
$996$		0			0
$997$	−13.4056	+	41.2583i	−0.424560	+	1.30666i	0.478854	+	0.877895i	$0.341052\pi$
$997$	−13.4056	+	41.2583i	−0.424560	+	1.30666i	−0.903415	+	0.428768i	$0.858948\pi$
$998$		0			0
$999$	−1.49549	+	2.05837i	−0.0473153	+	0.0651240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.12	yes	80
5.4	even	2	inner	820.2.bi.a.189.9	✓	80
41.23	even	10	inner	820.2.bi.a.269.9	yes	80
205.64	even	10	inner	820.2.bi.a.269.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.9	✓	80	5.4	even	2	inner
820.2.bi.a.189.12	yes	80	1.1	even	1	trivial
820.2.bi.a.269.9	yes	80	41.23	even	10	inner
820.2.bi.a.269.12	yes	80	205.64	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.389760 q^{3} +(-0.0716037 + 2.23492i) q^{5} +(-0.300283 - 0.924177i) q^{7} -2.84809 q^{9} +(-2.79647 - 3.84902i) q^{11} +(-1.31080 + 4.03424i) q^{13} +(-0.0279083 + 0.871083i) q^{15} +(-4.26120 + 3.09594i) q^{17} +(-1.78645 + 0.580454i) q^{19} +(-0.117038 - 0.360207i) q^{21} +(2.71321 + 0.881575i) q^{23} +(-4.98975 - 0.320057i) q^{25} -2.27935 q^{27} +(-0.636492 + 0.876056i) q^{29} +(2.33511 - 1.69655i) q^{31} +(-1.08995 - 1.50019i) q^{33} +(2.08696 - 0.604935i) q^{35} +(0.656105 - 0.903051i) q^{37} +(-0.510899 + 1.57238i) q^{39} +(-5.24987 - 3.66591i) q^{41} +(-6.41395 - 2.08402i) q^{43} +(0.203934 - 6.36525i) q^{45} +(-1.49531 + 4.60210i) q^{47} +(4.89919 - 3.55947i) q^{49} +(-1.66085 + 1.20668i) q^{51} +(-3.20899 - 2.33147i) q^{53} +(8.80249 - 5.97430i) q^{55} +(-0.696288 + 0.226238i) q^{57} +(-2.35663 + 7.25296i) q^{59} +(0.967041 + 2.97625i) q^{61} +(0.855233 + 2.63214i) q^{63} +(-8.92235 - 3.21841i) q^{65} +(3.19413 + 2.32067i) q^{67} +(1.05750 + 0.343603i) q^{69} +(-6.73066 - 9.26396i) q^{71} +16.0715i q^{73} +(-1.94480 - 0.124746i) q^{75} +(-2.71744 + 3.74023i) q^{77} +14.2526i q^{79} +7.65586 q^{81} +7.69398i q^{83} +(-6.61407 - 9.74513i) q^{85} +(-0.248079 + 0.341451i) q^{87} +(9.28990 - 3.01847i) q^{89} +4.12196 q^{91} +(0.910131 - 0.661249i) q^{93} +(-1.16935 - 4.03415i) q^{95} +(-2.69462 - 1.95776i) q^{97} +(7.96460 + 10.9623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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