LMFDB - Embedded newform 820.2.bq.a.49.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, 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:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142650 + 0.142650i) q^{3} +(1.77418 + 1.36098i) q^{5} +(0.670976 - 4.23638i) q^{7} +2.95930i q^{9} +(-1.96562 + 1.00153i) q^{11} +(2.64628 - 0.419129i) q^{13} +(-0.447231 + 0.0589425i) q^{15} +(6.24745 - 3.18323i) q^{17} +(0.291385 - 1.83973i) q^{19} +(0.508604 + 0.700033i) q^{21} +(-0.316126 + 0.435111i) q^{23} +(1.29544 + 4.82927i) q^{25} +(-0.850094 - 0.850094i) q^{27} +(1.65116 - 3.24059i) q^{29} +(-2.83857 + 8.73621i) q^{31} +(0.137527 - 0.423265i) q^{33} +(6.95607 - 6.60291i) q^{35} +(4.15167 - 1.34896i) q^{37} +(-0.317703 + 0.437280i) q^{39} +(5.88273 - 2.52853i) q^{41} +(-5.48112 - 3.98227i) q^{43} +(-4.02756 + 5.25034i) q^{45} +(-0.372889 - 2.35433i) q^{47} +(-10.8393 - 3.52189i) q^{49} +(-0.437110 + 1.34528i) q^{51} +(4.36779 + 2.22550i) q^{53} +(-4.85045 - 0.898277i) q^{55} +(0.220871 + 0.304003i) q^{57} +(8.79266 + 6.38824i) q^{59} +(6.87237 + 9.45901i) q^{61} +(12.5367 + 1.98562i) q^{63} +(5.26541 + 2.85793i) q^{65} +(-0.712758 + 1.39887i) q^{67} +(-0.0169731 - 0.107164i) q^{69} +(10.6070 - 5.40454i) q^{71} -3.71230 q^{73} +(-0.873689 - 0.504100i) q^{75} +(2.92399 + 8.99912i) q^{77} +(-5.04955 - 5.04955i) q^{79} -8.63537 q^{81} +5.94258i q^{83} +(15.4164 + 2.85504i) q^{85} +(0.226732 + 0.697809i) q^{87} +(-16.8191 - 2.66388i) q^{89} -11.4919i q^{91} +(-0.841298 - 1.65114i) q^{93} +(3.02082 - 2.86745i) q^{95} +(0.513699 - 1.00819i) q^{97} +(-2.96384 - 5.81687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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
$3$	−0.142650	+	0.142650i	−0.0823589	+	0.0823589i	−0.747086	−	0.664727i	$-0.768548\pi$
$3$	−0.142650	+	0.142650i	−0.0823589	+	0.0823589i	0.664727	+	0.747086i	$0.268548\pi$
$4$		0			0
$5$	1.77418	+	1.36098i	0.793438	+	0.608651i
$5$	1.77418	+	1.36098i	0.793438	+	0.608651i
$6$		0			0
$7$	0.670976	−	4.23638i	0.253605	−	1.60120i	−0.451616	−	0.892212i	$-0.649152\pi$
$7$	0.670976	−	4.23638i	0.253605	−	1.60120i	0.705221	−	0.708987i	$-0.250848\pi$
$8$		0			0
$9$			2.95930i			0.986434i
$10$		0			0
$11$	−1.96562	+	1.00153i	−0.592658	+	0.301974i	−0.724476	−	0.689300i	$-0.757918\pi$
$11$	−1.96562	+	1.00153i	−0.592658	+	0.301974i	0.131819	+	0.991274i	$0.457918\pi$
$12$		0			0
$13$	2.64628	−	0.419129i	0.733946	−	0.116246i	0.221737	−	0.975107i	$-0.428827\pi$
$13$	2.64628	−	0.419129i	0.733946	−	0.116246i	0.512209	+	0.858861i	$0.328827\pi$
$14$		0			0
$15$	−0.447231	+	0.0589425i	−0.115475	+	0.0152189i
$16$		0			0
$17$	6.24745	−	3.18323i	1.51523	−	0.772047i	0.518672	−	0.854973i	$-0.326426\pi$
$17$	6.24745	−	3.18323i	1.51523	−	0.772047i	0.996556	+	0.0829259i	$0.0264265\pi$
$18$		0			0
$19$	0.291385	−	1.83973i	0.0668483	−	0.422063i	−0.931456	−	0.363854i	$-0.881461\pi$
$19$	0.291385	−	1.83973i	0.0668483	−	0.422063i	0.998304	−	0.0582096i	$-0.0185392\pi$
$20$		0			0
$21$	0.508604	+	0.700033i	0.110986	+	0.152760i
$22$		0			0
$23$	−0.316126	+	0.435111i	−0.0659169	+	0.0907268i	−0.840703	−	0.541497i	$-0.817858\pi$
$23$	−0.316126	+	0.435111i	−0.0659169	+	0.0907268i	0.774786	+	0.632224i	$0.217858\pi$
$24$		0			0
$25$	1.29544	+	4.82927i	0.259088	+	0.965854i
$26$		0			0
$27$	−0.850094	−	0.850094i	−0.163601	−	0.163601i
$28$		0			0
$29$	1.65116	−	3.24059i	0.306614	−	0.601763i	−0.685361	−	0.728204i	$-0.740355\pi$
$29$	1.65116	−	3.24059i	0.306614	−	0.601763i	0.991974	+	0.126441i	$0.0403554\pi$
$30$		0			0
$31$	−2.83857	+	8.73621i	−0.509822	+	1.56907i	0.282689	+	0.959212i	$0.408773\pi$
$31$	−2.83857	+	8.73621i	−0.509822	+	1.56907i	−0.792511	+	0.609858i	$0.791227\pi$
$32$		0			0
$33$	0.137527	−	0.423265i	0.0239404	−	0.0736809i
$34$		0			0
$35$	6.95607	−	6.60291i	1.17579	−	1.11610i
$36$		0			0
$37$	4.15167	−	1.34896i	0.682531	−	0.221768i	0.0528278	−	0.998604i	$-0.483177\pi$
$37$	4.15167	−	1.34896i	0.682531	−	0.221768i	0.629703	+	0.776836i	$0.283177\pi$
$38$		0			0
$39$	−0.317703	+	0.437280i	−0.0508731	+	0.0700209i
$40$		0			0
$41$	5.88273	−	2.52853i	0.918728	−	0.394890i
$41$	5.88273	−	2.52853i	0.918728	−	0.394890i
$42$		0			0
$43$	−5.48112	−	3.98227i	−0.835863	−	0.607290i	0.0853489	−	0.996351i	$-0.472800\pi$
$43$	−5.48112	−	3.98227i	−0.835863	−	0.607290i	−0.921212	+	0.389061i	$0.872800\pi$
$44$		0			0
$45$	−4.02756	+	5.25034i	−0.600394	+	0.782674i
$46$		0			0
$47$	−0.372889	−	2.35433i	−0.0543915	−	0.343414i	−0.999844	−	0.0176548i	$-0.994380\pi$
$47$	−0.372889	−	2.35433i	−0.0543915	−	0.343414i	0.945453	−	0.325760i	$-0.105620\pi$
$48$		0			0
$49$	−10.8393	−	3.52189i	−1.54847	−	0.503128i
$50$		0			0
$51$	−0.437110	+	1.34528i	−0.0612076	+	0.188378i
$52$		0			0
$53$	4.36779	+	2.22550i	0.599962	+	0.305696i	0.727468	−	0.686142i	$-0.240697\pi$
$53$	4.36779	+	2.22550i	0.599962	+	0.305696i	−0.127505	+	0.991838i	$0.540697\pi$
$54$		0			0
$55$	−4.85045	−	0.898277i	−0.654034	−	0.121124i
$56$		0			0
$57$	0.220871	+	0.304003i	0.0292551	+	0.0402662i
$58$		0			0
$59$	8.79266	+	6.38824i	1.14471	+	0.831678i	0.987768	−	0.155930i	$-0.0498374\pi$
$59$	8.79266	+	6.38824i	1.14471	+	0.831678i	0.156939	+	0.987608i	$0.449837\pi$
$60$		0			0
$61$	6.87237	+	9.45901i	0.879917	+	1.21110i	0.976444	+	0.215772i	$0.0692267\pi$
$61$	6.87237	+	9.45901i	0.879917	+	1.21110i	−0.0965267	+	0.995330i	$0.530773\pi$
$62$		0			0
$63$	12.5367	+	1.98562i	1.57948	+	0.250165i
$64$		0			0
$65$	5.26541	+	2.85793i	0.653094	+	0.354483i
$66$		0			0
$67$	−0.712758	+	1.39887i	−0.0870773	+	0.170899i	−0.930438	−	0.366449i	$-0.880574\pi$
$67$	−0.712758	+	1.39887i	−0.0870773	+	0.170899i	0.843361	+	0.537347i	$0.180574\pi$
$68$		0			0
$69$	−0.0169731	−	0.107164i	−0.00204332	−	0.0129010i
$70$		0			0
$71$	10.6070	−	5.40454i	1.25882	−	0.641401i	0.308071	−	0.951363i	$-0.400316\pi$
$71$	10.6070	−	5.40454i	1.25882	−	0.641401i	0.950749	+	0.309962i	$0.100316\pi$
$72$		0			0
$73$	−3.71230			−0.434491			−0.217246	−	0.976117i	$-0.569707\pi$
$73$	−3.71230			−0.434491			−0.217246	+	0.976117i	$0.569707\pi$
$74$		0			0
$75$	−0.873689	−	0.504100i	−0.100885	−	0.0582084i
$76$		0			0
$77$	2.92399	+	8.99912i	0.333220	+	1.02555i
$78$		0			0
$79$	−5.04955	−	5.04955i	−0.568119	−	0.568119i	0.363482	−	0.931601i	$-0.381588\pi$
$79$	−5.04955	−	5.04955i	−0.568119	−	0.568119i	−0.931601	+	0.363482i	$0.881588\pi$
$80$		0			0
$81$	−8.63537			−0.959486
$82$		0			0
$83$			5.94258i			0.652283i	0.945321	+	0.326141i	$0.105749\pi$
$83$			5.94258i			0.652283i	−0.945321	+	0.326141i	$0.894251\pi$
$84$		0			0
$85$	15.4164	+	2.85504i	1.67215	+	0.309673i
$86$		0			0
$87$	0.226732	+	0.697809i	0.0243082	+	0.0748129i
$88$		0			0
$89$	−16.8191	−	2.66388i	−1.78282	−	0.282371i	−0.824043	−	0.566527i	$-0.808287\pi$
$89$	−16.8191	−	2.66388i	−1.78282	−	0.282371i	−0.958778	+	0.284156i	$0.908287\pi$
$90$		0			0
$91$		−	11.4919i		−	1.20467i
$92$		0			0
$93$	−0.841298	−	1.65114i	−0.0872385	−	0.171215i
$94$		0			0
$95$	3.02082	−	2.86745i	0.309929	−	0.294194i
$96$		0			0
$97$	0.513699	−	1.00819i	0.0521582	−	0.102366i	−0.863456	−	0.504424i	$-0.831705\pi$
$97$	0.513699	−	1.00819i	0.0521582	−	0.102366i	0.915614	+	0.402058i	$0.131705\pi$
$98$		0			0
$99$	−2.96384	−	5.81687i	−0.297878	−	0.584618i
$100$		0			0
$101$	1.14689	−	7.24119i	0.114120	−	0.720526i	−0.862581	−	0.505920i	$-0.831153\pi$
$101$	1.14689	−	7.24119i	0.114120	−	0.720526i	0.976701	−	0.214606i	$-0.0688468\pi$
$102$		0			0
$103$	9.99371	−	7.26086i	0.984710	−	0.715433i	0.0259534	−	0.999663i	$-0.491738\pi$
$103$	9.99371	−	7.26086i	0.984710	−	0.715433i	0.958756	+	0.284230i	$0.0917378\pi$
$104$		0			0
$105$	−0.0503785	+	1.93419i	−0.00491644	+	0.188757i
$106$		0			0
$107$	−2.71223	−	3.73306i	−0.262201	−	0.360889i	0.657536	−	0.753423i	$-0.271599\pi$
$107$	−2.71223	−	3.73306i	−0.262201	−	0.360889i	−0.919738	+	0.392534i	$0.871599\pi$
$108$		0			0
$109$	−5.32740	+	5.32740i	−0.510272	+	0.510272i	−0.914610	−	0.404338i	$-0.867502\pi$
$109$	−5.32740	+	5.32740i	−0.510272	+	0.510272i	0.404338	+	0.914610i	$0.367502\pi$
$110$		0			0
$111$	−0.399807	+	0.784665i	−0.0379480	+	0.0744771i
$112$		0			0
$113$	−10.7438	−	3.49086i	−1.01069	−	0.328392i	−0.243559	−	0.969886i	$-0.578315\pi$
$113$	−10.7438	−	3.49086i	−1.01069	−	0.328392i	−0.767128	+	0.641494i	$0.778315\pi$
$114$		0			0
$115$	−1.15304	+	0.341722i	−0.107522	+	0.0318658i
$116$		0			0
$117$	1.24033	+	7.83114i	0.114669	+	0.723989i
$118$		0			0
$119$	−9.29348	−	28.6024i	−0.851932	−	2.62198i
$120$		0			0
$121$	−3.60504	+	4.96191i	−0.327731	+	0.451083i
$122$		0			0
$123$	−0.478476	+	1.19987i	−0.0431428	+	0.108188i
$124$		0			0
$125$	−4.27421	+	10.3311i	−0.382297	+	0.924040i
$126$		0			0
$127$	−18.4064	+	5.98059i	−1.63330	+	0.530692i	−0.975027	−	0.222087i	$-0.928713\pi$
$127$	−18.4064	+	5.98059i	−1.63330	+	0.530692i	−0.658274	+	0.752779i	$0.728713\pi$
$128$		0			0
$129$	1.34995	−	0.213811i	0.118857	−	0.0188250i
$130$		0			0
$131$	13.8523	+	4.50087i	1.21028	+	0.393243i	0.843532	−	0.537079i	$-0.180472\pi$
$131$	13.8523	+	4.50087i	1.21028	+	0.393243i	0.366745	+	0.930322i	$0.380472\pi$
$132$		0			0
$133$	−7.59828	−	2.46883i	−0.658854	−	0.214075i
$134$		0			0
$135$	−0.351256	−	2.66518i	−0.0302313	−	0.229383i
$136$		0			0
$137$	−15.5097	−	15.5097i	−1.32509	−	1.32509i	−0.909598	−	0.415489i	$-0.863610\pi$
$137$	−15.5097	−	15.5097i	−1.32509	−	1.32509i	−0.415489	−	0.909598i	$-0.636390\pi$
$138$		0			0
$139$	4.28996	−	3.11684i	0.363870	−	0.264367i	−0.390795	−	0.920478i	$-0.627800\pi$
$139$	4.28996	−	3.11684i	0.363870	−	0.264367i	0.754664	+	0.656111i	$0.227800\pi$
$140$		0			0
$141$	0.389037	+	0.282652i	0.0327629	+	0.0238036i
$142$		0			0
$143$	−4.78181	+	3.47419i	−0.399875	+	0.290526i
$144$		0			0
$145$	7.33986	−	3.50219i	0.609542	−	0.290841i
$146$		0			0
$147$	2.04862	−	1.04382i	0.168967	−	0.0860931i
$148$		0			0
$149$	−6.76731	−	3.44811i	−0.554399	−	0.282481i	0.154261	−	0.988030i	$-0.450700\pi$
$149$	−6.76731	−	3.44811i	−0.554399	−	0.282481i	−0.708661	+	0.705550i	$0.750700\pi$
$150$		0			0
$151$	0.475308	+	3.00097i	0.0386800	+	0.244216i	0.999451	−	0.0331265i	$-0.0105464\pi$
$151$	0.475308	+	3.00097i	0.0386800	+	0.244216i	−0.960771	+	0.277342i	$0.910546\pi$
$152$		0			0
$153$	9.42015	+	18.4881i	0.761574	+	1.49467i
$154$		0			0
$155$	−16.9260	+	11.6364i	−1.35953	+	0.934656i
$156$		0			0
$157$	−3.58994	+	22.6660i	−0.286509	+	1.80894i	0.253556	+	0.967321i	$0.418400\pi$
$157$	−3.58994	+	22.6660i	−0.286509	+	1.80894i	−0.540065	+	0.841624i	$0.681600\pi$
$158$		0			0
$159$	−0.940532	+	0.305598i	−0.0745891	+	0.0242355i
$160$		0			0
$161$	1.63118	+	1.63118i	0.128555	+	0.128555i
$162$		0			0
$163$		−	10.6120i		−	0.831194i	−0.909549	−	0.415597i	$-0.863573\pi$
$163$		−	10.6120i		−	0.831194i	0.909549	−	0.415597i	$-0.136427\pi$
$164$		0			0
$165$	0.820054	−	0.563776i	0.0638412	−	0.0438899i
$166$		0			0
$167$	−10.0861	+	10.0861i	−0.780488	+	0.780488i	−0.979913	−	0.199425i	$-0.936092\pi$
$167$	−10.0861	+	10.0861i	−0.780488	+	0.780488i	0.199425	+	0.979913i	$0.436092\pi$
$168$		0			0
$169$	−5.53661	+	1.79895i	−0.425893	+	0.138381i
$170$		0			0
$171$	5.44432	+	0.862296i	0.416338	+	0.0659414i
$172$		0			0
$173$	−14.8793			−1.13125			−0.565625	−	0.824663i	$-0.691365\pi$
$173$	−14.8793			−1.13125			−0.565625	+	0.824663i	$0.691365\pi$
$174$		0			0
$175$	21.3278	−	2.24766i	1.61223	−	0.169907i
$176$		0			0
$177$	−2.16555	+	0.342990i	−0.162773	+	0.0257807i
$178$		0			0
$179$	−3.04641	−	1.55222i	−0.227700	−	0.116019i	0.336419	−	0.941712i	$-0.390784\pi$
$179$	−3.04641	−	1.55222i	−0.227700	−	0.116019i	−0.564119	+	0.825694i	$0.690784\pi$
$180$		0			0
$181$	−6.66193	−	13.0748i	−0.495177	−	0.971840i	−0.994432	−	0.105384i	$-0.966393\pi$
$181$	−6.66193	−	13.0748i	−0.495177	−	0.971840i	0.499254	−	0.866455i	$-0.333607\pi$
$182$		0			0
$183$	−2.32967	−	0.368983i	−0.172214	−	0.0272760i
$184$		0			0
$185$	9.20174	+	3.25706i	0.676525	+	0.239464i
$186$		0			0
$187$	−9.09200	+	12.5141i	−0.664873	+	0.915119i
$188$		0			0
$189$	−4.17171	+	3.03092i	−0.303447	+	0.220467i
$190$		0			0
$191$	−15.1209	+	15.1209i	−1.09411	+	1.09411i	−0.0990225	+	0.995085i	$0.531572\pi$
$191$	−15.1209	+	15.1209i	−1.09411	+	1.09411i	−0.995085	+	0.0990225i	$0.968428\pi$
$192$		0			0
$193$	−6.24563	−	3.18231i	−0.449571	−	0.229068i	0.214520	−	0.976720i	$-0.431181\pi$
$193$	−6.24563	−	3.18231i	−0.449571	−	0.229068i	−0.664091	+	0.747652i	$0.731181\pi$
$194$		0			0
$195$	−1.15879	+	0.343426i	−0.0829829	+	0.0245933i
$196$		0			0
$197$	3.14462	−	9.67813i	0.224045	−	0.689538i	−0.774343	−	0.632767i	$-0.781919\pi$
$197$	3.14462	−	9.67813i	0.224045	−	0.689538i	0.998387	−	0.0567717i	$-0.0180807\pi$
$198$		0			0
$199$	−8.56298	+	1.35624i	−0.607013	+	0.0961415i	−0.452372	−	0.891829i	$-0.649422\pi$
$199$	−8.56298	+	1.35624i	−0.607013	+	0.0961415i	−0.154641	+	0.987971i	$0.549422\pi$
$200$		0			0
$201$	−0.0978733	−	0.301223i	−0.00690345	−	0.0212466i
$202$		0			0
$203$	−12.6205	−	9.16931i	−0.885784	−	0.643560i
$204$		0			0
$205$	13.8783	+	3.52023i	0.969304	+	0.245864i
$206$		0			0
$207$	−1.28762	−	0.935514i	−0.0894960	−	0.0650227i
$208$		0			0
$209$	1.26980	+	3.90805i	0.0878341	+	0.270325i
$210$		0			0
$211$	−18.7809	+	2.97460i	−1.29293	+	0.204780i	−0.764736	−	0.644343i	$-0.777131\pi$
$211$	−18.7809	+	2.97460i	−1.29293	+	0.204780i	−0.528195	+	0.849123i	$0.677131\pi$
$212$		0			0
$213$	−0.742131	+	2.28404i	−0.0508500	+	0.156500i
$214$		0			0
$215$	−4.30470	−	14.5250i	−0.293578	−	0.990596i
$216$		0			0
$217$	35.1053	+	17.8870i	2.38310	+	1.21425i
$218$		0			0
$219$	0.529559	−	0.529559i	0.0357842	−	0.0357842i
$220$		0			0
$221$	15.1983	−	11.0422i	1.02235	−	0.742779i
$222$		0			0
$223$	−13.9665	+	19.2233i	−0.935269	+	1.28729i	0.0224999	+	0.999747i	$0.492837\pi$
$223$	−13.9665	+	19.2233i	−0.935269	+	1.28729i	−0.957769	+	0.287540i	$0.907163\pi$
$224$		0			0
$225$	−14.2913	+	3.83361i	−0.952751	+	0.255574i
$226$		0			0
$227$	6.66878	+	1.05623i	0.442622	+	0.0701045i	0.373768	−	0.927522i	$-0.378066\pi$
$227$	6.66878	+	1.05623i	0.442622	+	0.0701045i	0.0688543	+	0.997627i	$0.478066\pi$
$228$		0			0
$229$	−10.6039	−	20.8113i	−0.700723	−	1.37525i	−0.916989	−	0.398912i	$-0.869388\pi$
$229$	−10.6039	−	20.8113i	−0.700723	−	1.37525i	0.216266	−	0.976335i	$-0.430612\pi$
$230$		0			0
$231$	−1.70083	−	0.866616i	−0.111906	−	0.0570192i
$232$		0			0
$233$	19.6474	−	3.11184i	1.28714	−	0.203863i	0.524904	−	0.851161i	$-0.324101\pi$
$233$	19.6474	−	3.11184i	1.28714	−	0.203863i	0.762237	+	0.647298i	$0.224101\pi$
$234$		0			0
$235$	2.54263	−	4.68451i	0.165863	−	0.305584i
$236$		0			0
$237$	1.44064			0.0935793
$238$		0			0
$239$	3.53925	+	0.560562i	0.228935	+	0.0362597i	0.269848	−	0.962903i	$-0.413027\pi$
$239$	3.53925	+	0.560562i	0.228935	+	0.0362597i	−0.0409129	+	0.999163i	$0.513027\pi$
$240$		0			0
$241$	4.11887	−	1.33830i	0.265320	−	0.0862077i	−0.173336	−	0.984863i	$-0.555455\pi$
$241$	4.11887	−	1.33830i	0.265320	−	0.0862077i	0.438656	+	0.898655i	$0.355455\pi$
$242$		0			0
$243$	3.78212	−	3.78212i	0.242623	−	0.242623i
$244$		0			0
$245$	−14.4376	−	21.0006i	−0.922384	−	1.34168i
$246$		0			0
$247$		−	4.99057i		−	0.317542i
$248$		0			0
$249$	−0.847708	−	0.847708i	−0.0537213	−	0.0537213i
$250$		0			0
$251$	4.92952	−	1.60170i	0.311149	−	0.101098i	−0.149280	−	0.988795i	$-0.547696\pi$
$251$	4.92952	−	1.60170i	0.311149	−	0.101098i	0.460429	+	0.887697i	$0.347696\pi$
$252$		0			0
$253$	0.185607	−	1.17188i	0.0116690	−	0.0736752i
$254$		0			0
$255$	−2.60642	+	1.79188i	−0.163221	+	0.112212i
$256$		0			0
$257$	−10.1777	−	19.9748i	−0.634865	−	1.24599i	−0.954432	−	0.298429i	$-0.903537\pi$
$257$	−10.1777	−	19.9748i	−0.634865	−	1.24599i	0.319566	−	0.947564i	$-0.396463\pi$
$258$		0			0
$259$	−2.92903	−	18.4932i	−0.182001	−	1.14911i
$260$		0			0
$261$	9.58989	+	4.88629i	0.593600	+	0.302454i
$262$		0			0
$263$	10.4063	−	5.30229i	0.641682	−	0.326953i	−0.102695	−	0.994713i	$-0.532747\pi$
$263$	10.4063	−	5.30229i	0.641682	−	0.326953i	0.744377	+	0.667760i	$0.232747\pi$
$264$		0			0
$265$	4.72038	+	9.89294i	0.289971	+	0.607719i
$266$		0			0
$267$	2.77925	−	2.01924i	0.170087	−	0.123575i
$268$		0			0
$269$	−2.82521	−	2.05264i	−0.172256	−	0.125151i	0.498317	−	0.866995i	$-0.333952\pi$
$269$	−2.82521	−	2.05264i	−0.172256	−	0.125151i	−0.670573	+	0.741844i	$0.733952\pi$
$270$		0			0
$271$	−7.82984	+	5.68871i	−0.475629	+	0.345565i	−0.799631	−	0.600492i	$-0.794972\pi$
$271$	−7.82984	+	5.68871i	−0.475629	+	0.345565i	0.324002	+	0.946056i	$0.394972\pi$
$272$		0			0
$273$	1.63931	+	1.63931i	0.0992157	+	0.0992157i
$274$		0			0
$275$	−7.38303	−	8.19509i	−0.445214	−	0.494182i
$276$		0			0
$277$	5.50720	+	1.78940i	0.330895	+	0.107514i	0.469753	−	0.882798i	$-0.344343\pi$
$277$	5.50720	+	1.78940i	0.330895	+	0.107514i	−0.138857	+	0.990312i	$0.544343\pi$
$278$		0			0
$279$	−25.8531	−	8.40018i	−1.54778	−	0.502905i
$280$		0			0
$281$	4.27725	−	0.677450i	0.255159	−	0.0404133i	−0.0275443	−	0.999621i	$-0.508769\pi$
$281$	4.27725	−	0.677450i	0.255159	−	0.0404133i	0.282704	+	0.959207i	$0.408769\pi$
$282$		0			0
$283$	9.32334	−	3.02934i	0.554215	−	0.180075i	−0.0185016	−	0.999829i	$-0.505890\pi$
$283$	9.32334	−	3.02934i	0.554215	−	0.180075i	0.572717	+	0.819753i	$0.305890\pi$
$284$		0			0
$285$	−0.0218779	+	0.839960i	−0.00129593	+	0.0497549i
$286$		0			0
$287$	−6.76463	−	26.6180i	−0.399304	−	1.57121i
$288$		0			0
$289$	18.9053	−	26.0208i	1.11207	−	1.53064i
$290$		0			0
$291$	0.0705392	+	0.217097i	0.00413508	+	0.0127265i
$292$		0			0
$293$	1.58508	+	10.0078i	0.0926014	+	0.584662i	0.989736	+	0.142906i	$0.0456446\pi$
$293$	1.58508	+	10.0078i	0.0926014	+	0.584662i	−0.897135	+	0.441757i	$0.854355\pi$
$294$		0			0
$295$	6.90548	+	23.3006i	0.402053	+	1.35661i
$296$		0			0
$297$	2.52236	+	0.819565i	0.146362	+	0.0475560i
$298$		0			0
$299$	−0.654191	+	1.28392i	−0.0378328	+	0.0742511i
$300$		0			0
$301$	−20.5481	+	20.5481i	−1.18437	+	1.18437i
$302$		0			0
$303$	0.869351	+	1.19656i	0.0499429	+	0.0687405i
$304$		0			0
$305$	−0.680727	+	26.1352i	−0.0389783	+	1.49650i
$306$		0			0
$307$	26.4365	−	19.2072i	1.50881	−	1.09621i	0.542108	−	0.840309i	$-0.317626\pi$
$307$	26.4365	−	19.2072i	1.50881	−	1.09621i	0.966702	−	0.255906i	$-0.0823736\pi$
$308$		0			0
$309$	−0.389841	+	2.46136i	−0.0221773	+	0.140022i
$310$		0			0
$311$	3.74955	+	7.35890i	0.212617	+	0.417285i	0.972542	−	0.232726i	$-0.0747645\pi$
$311$	3.74955	+	7.35890i	0.212617	+	0.417285i	−0.759925	+	0.650011i	$0.774764\pi$
$312$		0			0
$313$	−4.48772	+	8.80765i	−0.253661	+	0.497838i	−0.982361	−	0.186995i	$-0.940125\pi$
$313$	−4.48772	+	8.80765i	−0.253661	+	0.497838i	0.728700	+	0.684833i	$0.240125\pi$
$314$		0			0
$315$	19.5400	+	20.5851i	1.10095	+	1.15984i
$316$		0			0
$317$	0.107691	+	0.211355i	0.00604852	+	0.0118709i	0.894011	−	0.448045i	$-0.147880\pi$
$317$	0.107691	+	0.211355i	0.00604852	+	0.0118709i	−0.887962	+	0.459916i	$0.847880\pi$
$318$		0			0
$319$			8.02348i			0.449229i
$320$		0			0
$321$	0.919420	+	0.145622i	0.0513170	+	0.00812782i
$322$		0			0
$323$	−4.03588	−	12.4212i	−0.224562	−	0.691132i
$324$		0			0
$325$	5.45219	+	12.2366i	0.302433	+	0.678766i
$326$		0			0
$327$		−	1.51990i		−	0.0840509i
$328$		0			0
$329$	−10.2240			−0.563669
$330$		0			0
$331$	24.5994	+	24.5994i	1.35211	+	1.35211i	0.883301	+	0.468806i	$0.155316\pi$
$331$	24.5994	+	24.5994i	1.35211	+	1.35211i	0.468806	+	0.883301i	$0.344684\pi$
$332$		0			0
$333$	3.99198	+	12.2861i	0.218759	+	0.673272i
$334$		0			0
$335$	−3.16840	+	1.51179i	−0.173108	+	0.0825980i
$336$		0			0
$337$	−14.5619			−0.793237			−0.396618	−	0.917984i	$-0.629816\pi$
$337$	−14.5619			−0.793237			−0.396618	+	0.917984i	$0.629816\pi$
$338$		0			0
$339$	2.03057	−	1.03462i	0.110285	−	0.0561931i
$340$		0			0
$341$	−3.17007	−	20.0150i	−0.171669	−	1.08387i
$342$		0			0
$343$	−8.56221	+	16.8043i	−0.462316	+	0.907347i
$344$		0			0
$345$	0.115735	−	0.213228i	0.00623096	−	0.0114798i
$346$		0			0
$347$	−14.1077	−	2.23443i	−0.757339	−	0.119951i	−0.234189	−	0.972191i	$-0.575243\pi$
$347$	−14.1077	−	2.23443i	−0.757339	−	0.119951i	−0.523150	+	0.852240i	$0.675243\pi$
$348$		0			0
$349$	11.3250	+	15.5875i	0.606213	+	0.834381i	0.996259	−	0.0864146i	$-0.0275410\pi$
$349$	11.3250	+	15.5875i	0.606213	+	0.834381i	−0.390046	+	0.920795i	$0.627541\pi$
$350$		0			0
$351$	−2.60588	−	1.89329i	−0.139092	−	0.101056i
$352$		0			0
$353$	2.79686	+	3.84955i	0.148862	+	0.204891i	0.876935	−	0.480608i	$-0.159584\pi$
$353$	2.79686	+	3.84955i	0.148862	+	0.204891i	−0.728074	+	0.685499i	$0.759584\pi$
$354$		0			0
$355$	26.1743	+	4.84733i	1.38919	+	0.257270i
$356$		0			0
$357$	5.40584	+	2.75441i	0.286107	+	0.145779i
$358$		0			0
$359$	−1.81108	+	5.57393i	−0.0955851	+	0.294181i	−0.987406	−	0.158208i	$-0.949428\pi$
$359$	−1.81108	+	5.57393i	−0.0955851	+	0.294181i	0.891821	+	0.452389i	$0.149428\pi$
$360$		0			0
$361$	14.7704	+	4.79918i	0.777388	+	0.252589i
$362$		0			0
$363$	−0.193557	−	1.22207i	−0.0101591	−	0.0641422i
$364$		0			0
$365$	−6.58629	−	5.05238i	−0.344742	−	0.264454i
$366$		0			0
$367$	−10.7686	−	7.82381i	−0.562114	−	0.408400i	0.270118	−	0.962827i	$-0.412937\pi$
$367$	−10.7686	−	7.82381i	−0.562114	−	0.408400i	−0.832232	+	0.554428i	$0.812937\pi$
$368$		0			0
$369$	7.48268	+	17.4088i	0.389533	+	0.906265i
$370$		0			0
$371$	12.3587	−	17.0103i	0.641634	−	0.883133i
$372$		0			0
$373$	−1.04171	+	0.338473i	−0.0539379	+	0.0175255i	−0.335862	−	0.941911i	$-0.609027\pi$
$373$	−1.04171	+	0.338473i	−0.0539379	+	0.0175255i	0.281924	+	0.959437i	$0.409027\pi$
$374$		0			0
$375$	−0.864011	−	2.08344i	−0.0446174	−	0.107588i
$376$		0			0
$377$	3.01121	−	9.26757i	0.155085	−	0.477304i
$378$		0			0
$379$	−5.95092	+	18.3150i	−0.305678	+	0.940780i	0.673745	+	0.738964i	$0.264685\pi$
$379$	−5.95092	+	18.3150i	−0.305678	+	0.940780i	−0.979423	+	0.201817i	$0.935315\pi$
$380$		0			0
$381$	1.77253	−	3.47880i	0.0908097	−	0.178224i
$382$		0			0
$383$	−14.6102	−	14.6102i	−0.746546	−	0.746546i	0.227283	−	0.973829i	$-0.427016\pi$
$383$	−14.6102	−	14.6102i	−0.746546	−	0.746546i	−0.973829	+	0.227283i	$0.927016\pi$
$384$		0			0
$385$	−7.05997	+	19.9456i	−0.359809	+	1.01652i
$386$		0			0
$387$	11.7847	−	16.2203i	0.599052	−	0.824524i
$388$		0			0
$389$	9.93053	+	13.6682i	0.503498	+	0.693006i	0.982806	−	0.184641i	$-0.0591123\pi$
$389$	9.93053	+	13.6682i	0.503498	+	0.693006i	−0.479308	+	0.877647i	$0.659112\pi$
$390$		0			0
$391$	−0.589924	+	3.72463i	−0.0298337	+	0.188363i
$392$		0			0
$393$	−2.61807	+	1.33397i	−0.132064	+	0.0672901i
$394$		0			0
$395$	−2.08646	−	15.8312i	−0.104981	−	0.796553i
$396$		0			0
$397$	−0.999568	+	0.158316i	−0.0501669	+	0.00794566i	−0.181467	−	0.983397i	$-0.558085\pi$
$397$	−0.999568	+	0.158316i	−0.0501669	+	0.00794566i	0.131301	+	0.991343i	$0.458085\pi$
$398$		0			0
$399$	1.43607	−	0.731715i	0.0718935	−	0.0366316i
$400$		0			0
$401$			5.49410i			0.274362i	0.990546	+	0.137181i	$0.0438042\pi$
$401$			5.49410i			0.274362i	−0.990546	+	0.137181i	$0.956196\pi$
$402$		0			0
$403$	−3.85004	+	24.3082i	−0.191784	+	1.21088i
$404$		0			0
$405$	−15.3207	−	11.7526i	−0.761293	−	0.583992i
$406$		0			0
$407$	−6.80959	+	6.80959i	−0.337539	+	0.337539i
$408$		0			0
$409$	−23.6605			−1.16994			−0.584968	−	0.811057i	$-0.698893\pi$
$409$	−23.6605			−1.16994			−0.584968	+	0.811057i	$0.698893\pi$
$410$		0			0
$411$	4.42493			0.218266
$412$		0			0
$413$	32.9627	−	32.9627i	1.62199	−	1.62199i
$414$		0			0
$415$	−8.08776	+	10.5432i	−0.397012	+	0.517546i
$416$		0			0
$417$	−0.167346	+	1.05658i	−0.00819495	+	0.0517409i
$418$		0			0
$419$		−	6.91560i		−	0.337849i	−0.985629	−	0.168924i	$-0.945971\pi$
$419$		−	6.91560i		−	0.337849i	0.985629	−	0.168924i	$-0.0540294\pi$
$420$		0			0
$421$	−13.2138	+	6.73275i	−0.643999	+	0.328134i	−0.745307	−	0.666721i	$-0.767697\pi$
$421$	−13.2138	+	6.73275i	−0.643999	+	0.328134i	0.101308	+	0.994855i	$0.467697\pi$
$422$		0			0
$423$	6.96717	−	1.10349i	0.338756	−	0.0536536i
$424$		0			0
$425$	23.4659	+	26.0469i	1.13826	+	1.26346i
$426$		0			0
$427$	44.6831	−	22.7672i	2.16237	−	1.10178i
$428$		0			0
$429$	0.186532	−	1.17772i	0.00900586	−	0.0568608i
$430$		0			0
$431$	9.78866	+	13.4729i	0.471503	+	0.648968i	0.976844	−	0.213951i	$-0.0686333\pi$
$431$	9.78866	+	13.4729i	0.471503	+	0.648968i	−0.505341	+	0.862920i	$0.668633\pi$
$432$		0			0
$433$	15.1074	−	20.7936i	0.726016	−	0.999276i	−0.273286	−	0.961933i	$-0.588111\pi$
$433$	15.1074	−	20.7936i	0.726016	−	0.999276i	0.999303	−	0.0373431i	$-0.0118894\pi$
$434$		0			0
$435$	−0.547443	+	1.54662i	−0.0262479	+	0.0741546i
$436$		0			0
$437$	0.708372	+	0.708372i	0.0338860	+	0.0338860i
$438$		0			0
$439$	4.07361	−	7.99492i	0.194423	−	0.381576i	−0.773129	−	0.634249i	$-0.781309\pi$
$439$	4.07361	−	7.99492i	0.194423	−	0.381576i	0.967552	+	0.252672i	$0.0813095\pi$
$440$		0			0
$441$	10.4223	−	32.0767i	0.496302	−	1.52746i
$442$		0			0
$443$	10.4004	−	32.0092i	0.494138	−	1.52080i	−0.324157	−	0.946003i	$-0.605081\pi$
$443$	10.4004	−	32.0092i	0.494138	−	1.52080i	0.818295	−	0.574798i	$-0.194919\pi$
$444$		0			0
$445$	−26.2146	−	27.6168i	−1.24269	−	1.30916i
$446$		0			0
$447$	1.45723	−	0.473482i	0.0689245	−	0.0223949i
$448$		0			0
$449$	1.79985	−	2.47728i	0.0849403	−	0.116910i	−0.764432	−	0.644704i	$-0.776981\pi$
$449$	1.79985	−	2.47728i	0.0849403	−	0.116910i	0.849373	+	0.527794i	$0.176981\pi$
$450$		0			0
$451$	−9.03082	+	10.8619i	−0.425245	+	0.511467i
$452$		0			0
$453$	−0.495891	−	0.360286i	−0.0232990	−	0.0169277i
$454$		0			0
$455$	15.6402	−	20.3886i	0.733226	−	0.955834i
$456$		0			0
$457$	1.91764	+	12.1075i	0.0897036	+	0.566366i	0.991074	+	0.133316i	$0.0425626\pi$
$457$	1.91764	+	12.1075i	0.0897036	+	0.566366i	−0.901370	+	0.433050i	$0.857437\pi$
$458$		0			0
$459$	−8.01696	−	2.60487i	−0.374200	−	0.121585i
$460$		0			0
$461$	8.12333	−	25.0011i	0.378341	−	1.16442i	−0.562855	−	0.826556i	$-0.690297\pi$
$461$	8.12333	−	25.0011i	0.378341	−	1.16442i	0.941197	−	0.337860i	$-0.109703\pi$
$462$		0			0
$463$	−13.6320	−	6.94585i	−0.633533	−	0.322801i	0.107565	−	0.994198i	$-0.465695\pi$
$463$	−13.6320	−	6.94585i	−0.633533	−	0.322801i	−0.741098	+	0.671397i	$0.765695\pi$
$464$		0			0
$465$	0.754561	−	4.07442i	0.0349919	−	0.188947i
$466$		0			0
$467$	22.0297	+	30.3213i	1.01941	+	1.40310i	0.912614	+	0.408822i	$0.134060\pi$
$467$	22.0297	+	30.3213i	1.01941	+	1.40310i	0.106800	+	0.994281i	$0.465940\pi$
$468$		0			0
$469$	5.44788	+	3.95812i	0.251560	+	0.182769i
$470$		0			0
$471$	−2.72120	−	3.74541i	−0.125386	−	0.172579i
$472$		0			0
$473$	14.7622	+	2.33810i	0.678766	+	0.107506i
$474$		0			0
$475$	9.26203	−	0.976090i	0.424971	−	0.0447861i
$476$		0			0
$477$	−6.58593	+	12.9256i	−0.301549	+	0.591823i
$478$		0			0
$479$	−4.53168	−	28.6119i	−0.207058	−	1.30731i	−0.843976	−	0.536381i	$-0.819791\pi$
$479$	−4.53168	−	28.6119i	−0.207058	−	1.30731i	0.636918	−	0.770932i	$-0.280209\pi$
$480$		0			0
$481$	10.4211	−	5.30981i	0.475161	−	0.242107i
$482$		0			0
$483$	−0.465375			−0.0211753
$484$		0			0
$485$	2.28353	−	1.08958i	0.103690	−	0.0494752i
$486$		0			0
$487$	8.68449	+	26.7281i	0.393532	+	1.21117i	0.930099	+	0.367309i	$0.119721\pi$
$487$	8.68449	+	26.7281i	0.393532	+	1.21117i	−0.536567	+	0.843858i	$0.680279\pi$
$488$		0			0
$489$	1.51380	+	1.51380i	0.0684562	+	0.0684562i
$490$		0			0
$491$	3.34369			0.150899			0.0754494	−	0.997150i	$-0.475961\pi$
$491$	3.34369			0.150899			0.0754494	+	0.997150i	$0.475961\pi$
$492$		0			0
$493$		−	25.5015i		−	1.14853i
$494$		0			0
$495$	2.65827	−	14.3539i	0.119481	−	0.645161i
$496$		0			0
$497$	−15.7786	−	48.5616i	−0.707767	−	2.17828i
$498$		0			0
$499$	33.2903	+	5.27267i	1.49028	+	0.236037i	0.847821	−	0.530283i	$-0.177914\pi$
$499$	33.2903	+	5.27267i	1.49028	+	0.236037i	0.642459	+	0.766320i	$0.277914\pi$
$500$		0			0
$501$		−	2.87757i		−	0.128560i
$502$		0			0
$503$	11.4294	+	22.4315i	0.509613	+	1.00017i	0.992239	+	0.124346i	$0.0396832\pi$
$503$	11.4294	+	22.4315i	0.509613	+	1.00017i	−0.482625	+	0.875827i	$0.660317\pi$
$504$		0			0
$505$	11.8899	−	11.2863i	0.529096	−	0.502233i
$506$		0			0
$507$	0.533176	−	1.04642i	0.0236792	−	0.0464730i
$508$		0			0
$509$	14.1642	+	27.7989i	0.627819	+	1.23216i	0.957598	+	0.288106i	$0.0930257\pi$
$509$	14.1642	+	27.7989i	0.627819	+	1.23216i	−0.329779	+	0.944058i	$0.606974\pi$
$510$		0			0
$511$	−2.49086	+	15.7267i	−0.110189	+	0.695707i
$512$		0			0
$513$	−1.81165	+	1.31624i	−0.0799862	+	0.0581134i
$514$		0			0
$515$	27.6126	+	0.719207i	1.21676	+	0.0316920i
$516$		0			0
$517$	3.09090	+	4.25426i	0.135938	+	0.187102i
$518$		0			0
$519$	2.12252	−	2.12252i	0.0931685	−	0.0931685i
$520$		0			0
$521$	−6.67481	+	13.1001i	−0.292429	+	0.573924i	−0.989746	−	0.142839i	$-0.954377\pi$
$521$	−6.67481	+	13.1001i	−0.292429	+	0.573924i	0.697317	+	0.716763i	$0.254377\pi$
$522$		0			0
$523$	5.35906	+	1.74126i	0.234335	+	0.0761401i	0.423831	−	0.905742i	$-0.360685\pi$
$523$	5.35906	+	1.74126i	0.234335	+	0.0761401i	−0.189495	+	0.981882i	$0.560685\pi$
$524$		0			0
$525$	−2.72178	+	3.36304i	−0.118788	+	0.146775i
$526$		0			0
$527$	10.0756	+	63.6148i	0.438900	+	2.77110i
$528$		0			0
$529$	7.01801	+	21.5992i	0.305131	+	0.939096i
$530$		0			0
$531$	−18.9047	+	26.0201i	−0.820396	+	1.12918i
$532$		0			0
$533$	14.5076	−	9.15682i	0.628393	−	0.396626i
$534$		0			0
$535$	0.268653	−	10.3144i	0.0116149	−	0.445932i
$536$		0			0
$537$	0.655995	−	0.213146i	0.0283083	−	0.00919791i
$538$		0			0
$539$	24.8332	−	3.93320i	1.06964	−	0.169415i
$540$		0			0
$541$	−41.7059	−	13.5511i	−1.79308	−	0.582606i	−0.793416	−	0.608680i	$-0.791699\pi$
$541$	−41.7059	−	13.5511i	−1.79308	−	0.582606i	−0.999660	+	0.0260745i	$0.991699\pi$
$542$		0			0
$543$	2.81544	+	0.914791i	0.120822	+	0.0392574i
$544$		0			0
$545$	−16.7023	+	2.20127i	−0.715447	+	0.0942919i
$546$		0			0
$547$	−12.1107	−	12.1107i	−0.517817	−	0.517817i	0.399094	−	0.916910i	$-0.369325\pi$
$547$	−12.1107	−	12.1107i	−0.517817	−	0.517817i	−0.916910	+	0.399094i	$0.869325\pi$
$548$		0			0
$549$	−27.9921	+	20.3374i	−1.19467	+	0.867980i
$550$		0			0
$551$	−5.48070	−	3.98196i	−0.233486	−	0.169637i
$552$		0			0
$553$	−24.7799	+	18.0037i	−1.05375	+	0.765594i
$554$		0			0
$555$	−1.77725	+	0.848007i	−0.0754399	+	0.0359959i
$556$		0			0
$557$	4.24094	−	2.16087i	0.179694	−	0.0915588i	−0.361829	−	0.932244i	$-0.617848\pi$
$557$	4.24094	−	2.16087i	0.179694	−	0.0915588i	0.541524	+	0.840686i	$0.317848\pi$
$558$		0			0
$559$	−16.1737	−	8.24089i	−0.684073	−	0.348553i
$560$		0			0
$561$	−0.488157	−	3.08210i	−0.0206100	−	0.130126i
$562$		0			0
$563$	−14.0891	−	27.6514i	−0.593785	−	1.16537i	−0.970963	−	0.239228i	$-0.923106\pi$
$563$	−14.0891	−	27.6514i	−0.593785	−	1.16537i	0.377178	−	0.926141i	$-0.376894\pi$
$564$		0			0
$565$	−14.3104	−	20.8155i	−0.602042	−	0.875715i
$566$		0			0
$567$	−5.79413	+	36.5827i	−0.243331	+	1.53633i
$568$		0			0
$569$	28.9059	−	9.39209i	1.21180	−	0.393737i	0.367709	−	0.929941i	$-0.380142\pi$
$569$	28.9059	−	9.39209i	1.21180	−	0.393737i	0.844089	+	0.536204i	$0.180142\pi$
$570$		0			0
$571$	4.68344	+	4.68344i	0.195996	+	0.195996i	0.798281	−	0.602285i	$-0.205743\pi$
$571$	4.68344	+	4.68344i	0.195996	+	0.195996i	−0.602285	+	0.798281i	$0.705743\pi$
$572$		0			0
$573$		−	4.31398i		−	0.180219i
$574$		0			0
$575$	−2.51079	−	0.962998i	−0.104707	−	0.0401598i
$576$		0			0
$577$	−21.8433	+	21.8433i	−0.909347	+	0.909347i	−0.996219	−	0.0868724i	$-0.972313\pi$
$577$	−21.8433	+	21.8433i	−0.909347	+	0.909347i	0.0868724	+	0.996219i	$0.472313\pi$
$578$		0			0
$579$	1.34490	−	0.436983i	0.0558919	−	0.0181604i
$580$		0			0
$581$	25.1750	+	3.98733i	1.04443	+	0.165422i
$582$		0			0
$583$	−10.8143			−0.447885
$584$		0			0
$585$	−8.45749	+	15.5819i	−0.349674	+	0.644234i
$586$		0			0
$587$	−40.3185	+	6.38583i	−1.66412	+	0.263571i	−0.916349	−	0.400381i	$-0.868878\pi$
$587$	−40.3185	+	6.38583i	−1.66412	+	0.263571i	−0.747775	+	0.663953i	$0.768878\pi$
$588$		0			0
$589$	15.2452	+	7.76780i	0.628166	+	0.320067i
$590$		0			0
$591$	0.932005	+	1.82916i	0.0383376	+	0.0752417i
$592$		0			0
$593$	0.697986	+	0.110550i	0.0286628	+	0.00453975i	0.170749	−	0.985314i	$-0.445381\pi$
$593$	0.697986	+	0.110550i	0.0286628	+	0.00453975i	−0.142087	+	0.989854i	$0.545381\pi$
$594$		0			0
$595$	22.4391	−	63.3941i	0.919913	−	2.59891i
$596$		0			0
$597$	1.02804	−	1.41498i	0.0420749	−	0.0579111i
$598$		0			0
$599$	−19.9946	+	14.5269i	−0.816956	+	0.593553i	−0.915839	−	0.401546i	$-0.868473\pi$
$599$	−19.9946	+	14.5269i	−0.816956	+	0.593553i	0.0988828	+	0.995099i	$0.468473\pi$
$600$		0			0
$601$	16.3652	−	16.3652i	0.667549	−	0.667549i	−0.289599	−	0.957148i	$-0.593522\pi$
$601$	16.3652	−	16.3652i	0.667549	−	0.667549i	0.957148	+	0.289599i	$0.0935219\pi$
$602$		0			0
$603$	−4.13967	−	2.10927i	−0.168580	−	0.0858960i
$604$		0			0
$605$	−13.1491	+	3.89693i	−0.534586	+	0.158433i
$606$		0			0
$607$	1.75150	−	5.39056i	0.0710911	−	0.218796i	−0.909198	−	0.416364i	$-0.863304\pi$
$607$	1.75150	−	5.39056i	0.0710911	−	0.218796i	0.980289	+	0.197568i	$0.0633043\pi$
$608$		0			0
$609$	3.10831	−	0.492308i	0.125955	−	0.0199493i
$610$		0			0
$611$	−1.97354	−	6.07393i	−0.0798408	−	0.245725i
$612$		0			0
$613$	6.13955	+	4.46065i	0.247974	+	0.180164i	0.704828	−	0.709378i	$-0.251024\pi$
$613$	6.13955	+	4.46065i	0.247974	+	0.180164i	−0.456854	+	0.889542i	$0.651024\pi$
$614$		0			0
$615$	−2.48190	+	1.47758i	−0.100080	+	0.0595818i
$616$		0			0
$617$	−11.7723	−	8.55307i	−0.473935	−	0.344334i	0.325038	−	0.945701i	$-0.394623\pi$
$617$	−11.7723	−	8.55307i	−0.473935	−	0.344334i	−0.798973	+	0.601367i	$0.794623\pi$
$618$		0			0
$619$	11.8976	+	36.6171i	0.478206	+	1.47177i	0.841585	+	0.540124i	$0.181623\pi$
$619$	11.8976	+	36.6171i	0.478206	+	1.47177i	−0.363380	+	0.931641i	$0.618377\pi$
$620$		0			0
$621$	0.638622	−	0.101148i	0.0256270	−	0.00405892i
$622$		0			0
$623$	−22.5704	+	69.4646i	−0.904265	+	2.78304i
$624$		0			0
$625$	−21.6437	+	12.5121i	−0.865746	+	0.500483i
$626$		0			0
$627$	−0.738620	−	0.376346i	−0.0294976	−	0.0150298i
$628$		0			0
$629$	21.6433	−	21.6433i	0.862975	−	0.862975i
$630$		0			0
$631$	−18.9644	+	13.7785i	−0.754961	+	0.548512i	−0.897361	−	0.441298i	$-0.854518\pi$
$631$	−18.9644	+	13.7785i	−0.754961	+	0.548512i	0.142399	+	0.989809i	$0.454518\pi$
$632$		0			0
$633$	2.25477	−	3.10342i	0.0896189	−	0.123350i
$634$		0			0
$635$	−40.7957	−	14.4401i	−1.61893	−	0.573039i
$636$		0			0
$637$	−30.1599	−	4.77685i	−1.19498	−	0.189266i
$638$		0			0
$639$	15.9937	+	31.3893i	0.632700	+	1.24174i
$640$		0			0
$641$	28.1730	+	14.3548i	1.11277	+	0.566982i	0.910981	−	0.412448i	$-0.135326\pi$
$641$	28.1730	+	14.3548i	1.11277	+	0.566982i	0.201784	+	0.979430i	$0.435326\pi$
$642$		0			0
$643$	15.1147	−	2.39394i	0.596066	−	0.0944076i	0.148891	−	0.988854i	$-0.452430\pi$
$643$	15.1147	−	2.39394i	0.596066	−	0.0944076i	0.447176	+	0.894446i	$0.352430\pi$
$644$		0			0
$645$	2.68605	+	1.45792i	0.105763	+	0.0574056i
$646$		0			0
$647$	40.6733			1.59903			0.799517	−	0.600644i	$-0.205089\pi$
$647$	40.6733			1.59903			0.799517	+	0.600644i	$0.205089\pi$
$648$		0			0
$649$	−23.6811	−	3.75072i	−0.929565	−	0.147229i
$650$		0			0
$651$	−7.55934	+	2.45618i	−0.296274	+	0.0962652i
$652$		0			0
$653$	12.0240	−	12.0240i	0.470537	−	0.470537i	−0.431551	−	0.902088i	$-0.642034\pi$
$653$	12.0240	−	12.0240i	0.470537	−	0.470537i	0.902088	+	0.431551i	$0.142034\pi$
$654$		0			0
$655$	18.4508	+	26.8381i	0.720932	+	1.04865i
$656$		0			0
$657$		−	10.9858i		−	0.428597i
$658$		0			0
$659$	16.5330	+	16.5330i	0.644033	+	0.644033i	0.951544	−	0.307512i	$-0.0994963\pi$
$659$	16.5330	+	16.5330i	0.644033	+	0.644033i	−0.307512	+	0.951544i	$0.599496\pi$
$660$		0			0
$661$	26.2372	−	8.52498i	1.02051	−	0.331583i	0.249477	−	0.968381i	$-0.419741\pi$
$661$	26.2372	−	8.52498i	1.02051	−	0.331583i	0.771031	+	0.636798i	$0.219741\pi$
$662$		0			0
$663$	−0.592865	+	3.74320i	−0.0230250	+	0.145374i
$664$		0			0
$665$	−10.1207	−	14.7213i	−0.392464	−	0.570867i
$666$		0			0
$667$	0.888040	+	1.74288i	0.0343850	+	0.0674844i
$668$		0			0
$669$	−0.749875	−	4.73453i	−0.0289918	−	0.183047i
$670$		0			0
$671$	−22.9820	−	11.7099i	−0.887211	−	0.452057i
$672$		0			0
$673$	−5.49162	+	2.79812i	−0.211687	+	0.107860i	−0.556619	−	0.830768i	$-0.687902\pi$
$673$	−5.49162	+	2.79812i	−0.211687	+	0.107860i	0.344933	+	0.938627i	$0.387902\pi$
$674$		0			0
$675$	3.00408	−	5.20658i	0.115627	−	0.200401i
$676$		0			0
$677$	−36.1178	+	26.2411i	−1.38812	+	1.00853i	−0.392051	+	0.919943i	$0.628234\pi$
$677$	−36.1178	+	26.2411i	−1.38812	+	1.00853i	−0.996069	+	0.0885847i	$0.971766\pi$
$678$		0			0
$679$	−3.92640	−	2.85269i	−0.150681	−	0.109476i
$680$		0			0
$681$	−1.10197	+	0.800629i	−0.0422276	+	0.0306802i
$682$		0			0
$683$	2.33968	+	2.33968i	0.0895253	+	0.0895253i	0.750451	−	0.660926i	$-0.229836\pi$
$683$	2.33968	+	2.33968i	0.0895253	+	0.0895253i	−0.660926	+	0.750451i	$0.729836\pi$
$684$		0			0
$685$	−6.40859	−	48.6256i	−0.244859	−	1.85789i
$686$		0			0
$687$	4.48136	+	1.45608i	0.170975	+	0.0555531i
$688$		0			0
$689$	12.4912	+	4.05863i	0.475876	+	0.154621i
$690$		0			0
$691$	−38.9592	+	6.17053i	−1.48208	+	0.234738i	−0.844462	−	0.535616i	$-0.820079\pi$
$691$	−38.9592	+	6.17053i	−1.48208	+	0.234738i	−0.637616	+	0.770354i	$0.720079\pi$
$692$		0			0
$693$	−26.6311	+	8.65297i	−1.01163	+	0.328699i
$694$		0			0
$695$	11.8531	+	0.308731i	0.449615	+	0.0117108i
$696$		0			0
$697$	28.7031	−	34.5230i	1.08721	−	1.30765i
$698$		0			0
$699$	−2.35879	+	3.24660i	−0.0892176	+	0.122798i
$700$		0			0
$701$	−11.4969	−	35.3838i	−0.434231	−	1.33643i	−0.893872	−	0.448321i	$-0.852022\pi$
$701$	−11.4969	−	35.3838i	−0.434231	−	1.33643i	0.459641	−	0.888105i	$-0.347978\pi$
$702$		0			0
$703$	−1.27199	−	8.03103i	−0.0479740	−	0.302896i
$704$		0			0
$705$	0.305538	+	1.03095i	0.0115072	+	0.0388278i
$706$		0			0
$707$	−29.9069	−	9.71733i	−1.12476	−	0.365458i
$708$		0			0
$709$	10.2166	−	20.0512i	0.383693	−	0.753040i	−0.615696	−	0.787983i	$-0.711125\pi$
$709$	10.2166	−	20.0512i	0.383693	−	0.753040i	0.999389	+	0.0349439i	$0.0111253\pi$
$710$		0			0
$711$	14.9431	−	14.9431i	0.560412	−	0.560412i
$712$		0			0
$713$	−2.90387	−	3.99684i	−0.108751	−	0.149683i
$714$		0			0
$715$	−13.2121	−	0.344128i	−0.494106	−	0.0128696i
$716$		0			0
$717$	−0.584837	+	0.424909i	−0.0218411	+	0.0158685i
$718$		0			0
$719$	0.504237	−	3.18363i	0.0188049	−	0.118729i	−0.976500	−	0.215516i	$-0.930857\pi$
$719$	0.504237	−	3.18363i	0.0188049	−	0.118729i	0.995305	+	0.0967870i	$0.0308566\pi$
$720$		0			0
$721$	−24.0542	−	47.2090i	−0.895824	−	1.75815i
$722$		0			0
$723$	−0.396648	+	0.778465i	−0.0147515	+	0.0289514i
$724$		0			0
$725$	17.7887	+	3.77592i	0.660655	+	0.140234i
$726$		0			0
$727$	−14.9276	−	29.2970i	−0.553633	−	1.08657i	−0.983029	−	0.183450i	$-0.941274\pi$
$727$	−14.9276	−	29.2970i	−0.553633	−	1.08657i	0.429396	−	0.903116i	$-0.358726\pi$
$728$		0			0
$729$		−	24.8271i		−	0.919522i
$730$		0			0
$731$	−46.9195	−	7.43132i	−1.73538	−	0.274857i
$732$		0			0
$733$	−6.95890	−	21.4173i	−0.257033	−	0.791066i	−0.993422	−	0.114508i	$-0.963471\pi$
$733$	−6.95890	−	21.4173i	−0.257033	−	0.791066i	0.736389	−	0.676558i	$-0.236529\pi$
$734$		0			0
$735$	5.05525	+	0.936206i	0.186466	+	0.0345325i
$736$		0			0
$737$		−	3.46350i		−	0.127580i
$738$		0			0
$739$	0.584696			0.0215084			0.0107542	−	0.999942i	$-0.496577\pi$
$739$	0.584696			0.0215084			0.0107542	+	0.999942i	$0.496577\pi$
$740$		0			0
$741$	0.711904	+	0.711904i	0.0261525	+	0.0261525i
$742$		0			0
$743$	5.67103	+	17.4536i	0.208050	+	0.640312i	0.999574	+	0.0291745i	$0.00928786\pi$
$743$	5.67103	+	17.4536i	0.208050	+	0.640312i	−0.791524	+	0.611138i	$0.790712\pi$
$744$		0			0
$745$	−7.31360	−	15.3278i	−0.267950	−	0.561566i
$746$		0			0
$747$	−17.5859			−0.643434
$748$		0			0
$749$	−17.6345	+	8.98522i	−0.644350	+	0.328313i
$750$		0			0
$751$	5.59826	+	35.3460i	0.204284	+	1.28980i	0.850229	+	0.526412i	$0.176463\pi$
$751$	5.59826	+	35.3460i	0.204284	+	1.28980i	−0.645946	+	0.763383i	$0.723537\pi$
$752$		0			0
$753$	−0.474714	+	0.931678i	−0.0172995	+	0.0339522i
$754$		0			0
$755$	−3.24100	+	5.97116i	−0.117952	+	0.217313i
$756$		0			0
$757$	−18.1007	−	2.86687i	−0.657880	−	0.104198i	−0.181436	−	0.983403i	$-0.558075\pi$
$757$	−18.1007	−	2.86687i	−0.657880	−	0.104198i	−0.476444	+	0.879205i	$0.658075\pi$
$758$		0			0
$759$	0.140691	+	0.193645i	0.00510676	+	0.00702885i
$760$		0			0
$761$	−36.8614	−	26.7814i	−1.33622	−	0.970823i	−0.999574	−	0.0291935i	$-0.990706\pi$
$761$	−36.8614	−	26.7814i	−1.33622	−	0.970823i	−0.336650	−	0.941630i	$-0.609294\pi$
$762$		0			0
$763$	18.9943	+	26.1434i	0.687640	+	0.946455i
$764$		0			0
$765$	−8.44893	+	45.6219i	−0.305472	+	1.64946i
$766$		0			0
$767$	25.9453	+	13.2198i	0.936832	+	0.477340i
$768$		0			0
$769$	7.09298	−	21.8299i	0.255779	−	0.787208i	−0.737896	−	0.674915i	$-0.764180\pi$
$769$	7.09298	−	21.8299i	0.255779	−	0.787208i	0.993675	−	0.112293i	$-0.0358196\pi$
$770$		0			0
$771$	4.30124	+	1.39756i	0.154906	+	0.0503318i
$772$		0			0
$773$	5.21405	+	32.9202i	0.187536	+	1.18406i	0.884357	+	0.466812i	$0.154598\pi$
$773$	5.21405	+	32.9202i	0.187536	+	1.18406i	−0.696820	+	0.717246i	$0.745402\pi$
$774$		0			0
$775$	−45.8667	−	2.39094i	−1.64758	−	0.0858852i
$776$		0			0
$777$	3.05587	+	2.22022i	0.109629	+	0.0796500i
$778$		0			0
$779$	−2.93768	−	11.5594i	−0.105253	−	0.414159i
$780$		0			0
$781$	−15.4365	+	21.2466i	−0.552363	+	0.760262i
$782$		0			0
$783$	−4.15845	+	1.35116i	−0.148611	+	0.0482866i
$784$		0			0
$785$	−37.2173	+	35.3278i	−1.32834	+	1.26090i
$786$		0			0
$787$	12.7638	−	39.2828i	0.454979	−	1.40028i	−0.416180	−	0.909282i	$-0.636631\pi$
$787$	12.7638	−	39.2828i	0.454979	−	1.40028i	0.871160	−	0.491000i	$-0.163369\pi$
$788$		0			0
$789$	−0.728091	+	2.24083i	−0.0259207	+	0.0797758i
$790$		0			0
$791$	−21.9974	+	43.1723i	−0.782137	+	1.53503i
$792$		0			0
$793$	22.1508	+	22.1508i	0.786597	+	0.786597i
$794$		0			0
$795$	−2.08459	−	0.737865i	−0.0739328	−	0.0261694i
$796$		0			0
$797$	10.4137	−	14.3333i	0.368873	−	0.507710i	−0.583721	−	0.811954i	$-0.698404\pi$
$797$	10.4137	−	14.3333i	0.368873	−	0.507710i	0.952594	+	0.304244i	$0.0984038\pi$
$798$		0			0
$799$	−9.82399	−	13.5216i	−0.347548	−	0.478358i
$800$		0			0
$801$	7.88324	−	49.7728i	0.278541	−	1.75864i
$802$		0			0
$803$	7.29697	−	3.71799i	0.257505	−	0.131205i
$804$		0			0
$805$	0.673999	+	5.11402i	0.0237553	+	0.180245i
$806$		0			0
$807$	0.695824	−	0.110208i	0.0244942	−	0.00387950i
$808$		0			0
$809$	8.65220	−	4.40851i	0.304195	−	0.154995i	−0.295230	−	0.955426i	$-0.595396\pi$
$809$	8.65220	−	4.40851i	0.304195	−	0.154995i	0.599425	+	0.800431i	$0.295396\pi$
$810$		0			0
$811$			31.0598i			1.09066i	0.838223	+	0.545328i	$0.183595\pi$
$811$			31.0598i			1.09066i	−0.838223	+	0.545328i	$0.816405\pi$
$812$		0			0
$813$	0.305432	−	1.92842i	0.0107120	−	0.0676326i
$814$		0			0
$815$	14.4427	−	18.8276i	0.505907	−	0.659501i
$816$		0			0
$817$	−8.92342	+	8.92342i	−0.312191	+	0.312191i
$818$		0			0
$819$	34.0079			1.18833
$820$		0			0
$821$	38.7621			1.35281			0.676403	−	0.736532i	$-0.263538\pi$
$821$	38.7621			1.35281			0.676403	+	0.736532i	$0.263538\pi$
$822$		0			0
$823$	19.0788	−	19.0788i	0.665047	−	0.665047i	−0.291518	−	0.956565i	$-0.594160\pi$
$823$	19.0788	−	19.0788i	0.665047	−	0.665047i	0.956565	+	0.291518i	$0.0941605\pi$
$824$		0			0
$825$	2.22222	+	0.115840i	0.0773676	+	0.00403303i
$826$		0			0
$827$	2.76565	−	17.4617i	0.0961712	−	0.607201i	−0.891784	−	0.452461i	$-0.850546\pi$
$827$	2.76565	−	17.4617i	0.0961712	−	0.607201i	0.987955	−	0.154740i	$-0.0494540\pi$
$828$		0			0
$829$			5.31450i			0.184580i	0.995732	+	0.0922901i	$0.0294187\pi$
$829$			5.31450i			0.184580i	−0.995732	+	0.0922901i	$0.970581\pi$
$830$		0			0
$831$	−1.04086	+	0.530344i	−0.0361070	+	0.0183974i
$832$		0			0
$833$	−78.9288	+	12.5011i	−2.73472	+	0.433137i
$834$		0			0
$835$	−31.6217	+	4.16756i	−1.09431	+	0.144224i
$836$		0			0
$837$	9.83964	−	5.01355i	0.340108	−	0.173294i
$838$		0			0
$839$	0.707344	−	4.46599i	0.0244202	−	0.154183i	−0.972465	−	0.233049i	$-0.925130\pi$
$839$	0.707344	−	4.46599i	0.0244202	−	0.154183i	0.996885	+	0.0788656i	$0.0251298\pi$
$840$		0			0
$841$	9.27067	+	12.7600i	0.319678	+	0.440000i
$842$		0			0
$843$	−0.513511	+	0.706787i	−0.0176863	+	0.0243430i
$844$		0			0
$845$	−12.2713	−	4.34357i	−0.422146	−	0.149423i
$846$		0			0
$847$	18.6016	+	18.6016i	0.639159	+	0.639159i
$848$		0			0
$849$	−0.897839	+	1.76211i	−0.0308137	+	0.0604754i
$850$		0			0
$851$	−0.725507	+	2.23288i	−0.0248700	+	0.0765421i
$852$		0			0
$853$	−14.8709	+	45.7680i	−0.509171	+	1.56707i	0.284472	+	0.958684i	$0.408182\pi$
$853$	−14.8709	+	45.7680i	−0.509171	+	1.56707i	−0.793643	+	0.608383i	$0.791818\pi$
$854$		0			0
$855$	8.48564	+	8.93951i	0.290203	+	0.305725i
$856$		0			0
$857$	−13.7062	+	4.45341i	−0.468195	+	0.152126i	−0.533607	−	0.845733i	$-0.679164\pi$
$857$	−13.7062	+	4.45341i	−0.468195	+	0.152126i	0.0654122	+	0.997858i	$0.479164\pi$
$858$		0			0
$859$	31.8377	−	43.8208i	1.08629	−	1.49515i	0.233881	−	0.972265i	$-0.424857\pi$
$859$	31.8377	−	43.8208i	1.08629	−	1.49515i	0.852406	−	0.522881i	$-0.175143\pi$
$860$		0			0
$861$	4.76203	+	2.83209i	0.162290	+	0.0965173i
$862$		0			0
$863$	−31.1859	−	22.6579i	−1.06158	−	0.771282i	−0.0871992	−	0.996191i	$-0.527792\pi$
$863$	−31.1859	−	22.6579i	−1.06158	−	0.771282i	−0.974380	+	0.224909i	$0.927792\pi$
$864$		0			0
$865$	−26.3985	−	20.2504i	−0.897576	−	0.688536i
$866$		0			0
$867$	1.01504	+	6.40870i	0.0344725	+	0.217651i
$868$		0			0
$869$	14.9828	+	4.86821i	0.508257	+	0.165143i
$870$		0			0
$871$	−1.29985	+	4.00053i	−0.0440438	+	0.135553i
$872$		0			0
$873$	2.98354	+	1.52019i	0.100978	+	0.0514507i
$874$		0			0
$875$	40.8984	+	25.0391i	1.38262	+	0.846475i
$876$		0			0
$877$	30.0322	+	41.3358i	1.01412	+	1.39581i	0.916247	+	0.400613i	$0.131203\pi$
$877$	30.0322	+	41.3358i	1.01412	+	1.39581i	0.0978695	+	0.995199i	$0.468797\pi$
$878$		0			0
$879$	−1.65372	−	1.20150i	−0.0557787	−	0.0405256i
$880$		0			0
$881$	−5.31611	−	7.31700i	−0.179104	−	0.246516i	0.710020	−	0.704181i	$-0.248686\pi$
$881$	−5.31611	−	7.31700i	−0.179104	−	0.246516i	−0.889125	+	0.457665i	$0.848686\pi$
$882$		0			0
$883$	−32.1796	−	5.09674i	−1.08293	−	0.171519i	−0.410632	−	0.911801i	$-0.634692\pi$
$883$	−32.1796	−	5.09674i	−1.08293	−	0.171519i	−0.672297	+	0.740282i	$0.734692\pi$
$884$		0			0
$885$	−4.30889	−	2.33876i	−0.144842	−	0.0786165i
$886$		0			0
$887$	−10.5600	+	20.7252i	−0.354571	+	0.695885i	−0.997547	−	0.0700017i	$-0.977700\pi$
$887$	−10.5600	+	20.7252i	−0.354571	+	0.695885i	0.642976	+	0.765886i	$0.277700\pi$
$888$		0			0
$889$	12.9858	+	81.9891i	0.435530	+	2.74983i
$890$		0			0
$891$	16.9739	−	8.64863i	0.568647	−	0.289740i
$892$		0			0
$893$	−4.43999			−0.148579
$894$		0			0
$895$	−3.29234	−	6.90005i	−0.110051	−	0.230643i
$896$		0			0
$897$	−0.0898311	−	0.276472i	−0.00299937	−	0.00923112i
$898$		0			0
$899$	23.6236	+	23.6236i	0.787890	+	0.787890i
$900$		0			0
$901$	34.3718			1.14509
$902$		0			0
$903$		−	5.86236i		−	0.195087i
$904$		0			0
$905$	5.97509	−	32.2638i	0.198619	−	1.07248i
$906$		0			0
$907$	−8.29033	−	25.5150i	−0.275276	−	0.847212i	−0.989146	−	0.146934i	$-0.953059\pi$
$907$	−8.29033	−	25.5150i	−0.275276	−	0.847212i	0.713870	−	0.700278i	$-0.246941\pi$
$908$		0			0
$909$	21.4289	+	3.39400i	0.710751	+	0.112572i
$910$		0			0
$911$		−	48.9178i		−	1.62072i	−0.585933	−	0.810359i	$-0.699272\pi$
$911$		−	48.9178i		−	1.62072i	0.585933	−	0.810359i	$-0.300728\pi$
$912$		0			0
$913$	−5.95170	−	11.6809i	−0.196972	−	0.386580i
$914$		0			0
$915$	−3.63108	−	3.82529i	−0.120040	−	0.126460i
$916$		0			0
$917$	28.3619	−	55.6634i	0.936592	−	1.83817i
$918$		0			0
$919$	11.0254	+	21.6385i	0.363694	+	0.713789i	0.998253	−	0.0590849i	$-0.0188183\pi$
$919$	11.0254	+	21.6385i	0.363694	+	0.713789i	−0.634559	+	0.772874i	$0.718818\pi$
$920$		0			0
$921$	−1.03125	+	6.51107i	−0.0339809	+	0.214547i
$922$		0			0
$923$	25.8039	−	18.7476i	0.849346	−	0.617086i
$924$		0			0
$925$	11.8927	+	18.3020i	0.391031	+	0.601767i
$926$		0			0
$927$	21.4871	+	29.5744i	0.705728	+	0.971351i
$928$		0			0
$929$	−25.8998	+	25.8998i	−0.849744	+	0.849744i	−0.990101	−	0.140357i	$-0.955175\pi$
$929$	−25.8998	+	25.8998i	−0.849744	+	0.849744i	0.140357	+	0.990101i	$0.455175\pi$
$930$		0			0
$931$	−9.63774	+	18.9151i	−0.315864	+	0.619918i
$932$		0			0
$933$	−1.58462	−	0.514874i	−0.0518781	−	0.0168562i
$934$		0			0
$935$	−33.1623	+	9.82816i	−1.08452	+	0.321415i
$936$		0			0
$937$	−0.0661085	−	0.417392i	−0.00215967	−	0.0136356i	0.986585	−	0.163249i	$-0.0521972\pi$
$937$	−0.0661085	−	0.417392i	−0.00215967	−	0.0136356i	−0.988745	+	0.149613i	$0.952197\pi$
$938$		0			0
$939$	−0.616237	−	1.89658i	−0.0201101	−	0.0618927i
$940$		0			0
$941$	20.2935	−	27.9316i	0.661549	−	0.910544i	−0.337983	−	0.941152i	$-0.609745\pi$
$941$	20.2935	−	27.9316i	0.661549	−	0.910544i	0.999531	+	0.0306087i	$0.00974458\pi$
$942$		0			0
$943$	−0.759496	+	3.35897i	−0.0247326	+	0.109383i
$944$		0			0
$945$	−11.5264	−	0.300221i	−0.374954	−	0.00976619i
$946$		0			0
$947$	18.5854	−	6.03875i	0.603943	−	0.196233i	0.00894495	−	0.999960i	$-0.497153\pi$
$947$	18.5854	−	6.03875i	0.603943	−	0.196233i	0.594998	+	0.803727i	$0.297153\pi$
$948$		0			0
$949$	−9.82377	+	1.55593i	−0.318893	+	0.0505077i
$950$		0			0
$951$	−0.0455119	−	0.0147877i	−0.00147582	−	0.000479524i
$952$		0			0
$953$	−9.95505	−	3.23459i	−0.322476	−	0.104779i	0.143306	−	0.989678i	$-0.454227\pi$
$953$	−9.95505	−	3.23459i	−0.322476	−	0.104779i	−0.465781	+	0.884900i	$0.654227\pi$
$954$		0			0
$955$	−47.4064	+	6.24790i	−1.53404	+	0.202177i
$956$		0			0
$957$	−1.14455	−	1.14455i	−0.0369980	−	0.0369980i
$958$		0			0
$959$	−76.1118	+	55.2984i	−2.45778	+	1.78568i
$960$		0			0
$961$	−43.1844	−	31.3753i	−1.39304	−	1.01211i
$962$		0			0
$963$	11.0473	−	8.02630i	0.355993	−	0.258644i
$964$		0			0
$965$	−6.74982	−	14.1462i	−0.217284	−	0.455383i
$966$		0			0
$967$	−50.0803	+	25.5172i	−1.61047	+	0.820578i	−0.610891	+	0.791714i	$0.709189\pi$
$967$	−50.0803	+	25.5172i	−1.61047	+	0.820578i	−0.999583	+	0.0288635i	$0.990811\pi$
$968$		0			0
$969$	2.34760	+	1.19616i	0.0754156	+	0.0384262i
$970$		0			0
$971$	−3.20430	−	20.2311i	−0.102831	−	0.649248i	−0.984232	−	0.176880i	$-0.943399\pi$
$971$	−3.20430	−	20.2311i	−0.102831	−	0.649248i	0.881402	−	0.472368i	$-0.156601\pi$
$972$		0			0
$973$	−10.3256	−	20.2652i	−0.331025	−	0.649672i
$974$		0			0
$975$	−2.52331	−	0.967800i	−0.0808105	−	0.0309944i
$976$		0			0
$977$	−0.316885	+	2.00073i	−0.0101380	+	0.0640090i	−0.992239	−	0.124348i	$-0.960316\pi$
$977$	−0.316885	+	2.00073i	−0.0101380	+	0.0640090i	0.982101	+	0.188357i	$0.0603161\pi$
$978$		0			0
$979$	35.7280	−	11.6087i	1.14187	−	0.371016i
$980$		0			0
$981$	−15.7654	−	15.7654i	−0.503350	−	0.503350i
$982$		0			0
$983$			15.1548i			0.483362i	0.970356	+	0.241681i	$0.0776987\pi$
$983$			15.1548i			0.483362i	−0.970356	+	0.241681i	$0.922301\pi$
$984$		0			0
$985$	18.7509	−	12.8910i	0.597453	−	0.410741i
$986$		0			0
$987$	1.45846	−	1.45846i	0.0464232	−	0.0464232i
$988$		0			0
$989$	3.46545	−	1.12599i	0.110195	−	0.0358045i
$990$		0			0
$991$	−32.5288	−	5.15205i	−1.03331	−	0.163660i	−0.383330	−	0.923611i	$-0.625223\pi$
$991$	−32.5288	−	5.15205i	−1.03331	−	0.163660i	−0.649980	+	0.759951i	$0.725223\pi$
$992$		0			0
$993$	−7.01821			−0.222716
$994$		0			0
$995$	−17.0381	−	9.24786i	−0.540144	−	0.293177i
$996$		0			0
$997$	−61.3485	+	9.71665i	−1.94293	+	0.307729i	−0.999702	−	0.0244252i	$-0.992224\pi$
$997$	−61.3485	+	9.71665i	−1.94293	+	0.307729i	−0.943225	+	0.332155i	$0.892224\pi$
$998$		0			0
$999$	−4.67605	−	2.38257i	−0.147944	−	0.0753811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.11	✓	176
5.4	even	2	inner	820.2.bq.a.49.12	yes	176
41.36	even	20	inner	820.2.bq.a.569.12	yes	176
205.159	even	20	inner	820.2.bq.a.569.11	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.11	✓	176	1.1	even	1	trivial
820.2.bq.a.49.12	yes	176	5.4	even	2	inner
820.2.bq.a.569.11	yes	176	205.159	even	20	inner
820.2.bq.a.569.12	yes	176	41.36	even	20	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.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142650 + 0.142650i) q^{3} +(1.77418 + 1.36098i) q^{5} +(0.670976 - 4.23638i) q^{7} +2.95930i q^{9} +(-1.96562 + 1.00153i) q^{11} +(2.64628 - 0.419129i) q^{13} +(-0.447231 + 0.0589425i) q^{15} +(6.24745 - 3.18323i) q^{17} +(0.291385 - 1.83973i) q^{19} +(0.508604 + 0.700033i) q^{21} +(-0.316126 + 0.435111i) q^{23} +(1.29544 + 4.82927i) q^{25} +(-0.850094 - 0.850094i) q^{27} +(1.65116 - 3.24059i) q^{29} +(-2.83857 + 8.73621i) q^{31} +(0.137527 - 0.423265i) q^{33} +(6.95607 - 6.60291i) q^{35} +(4.15167 - 1.34896i) q^{37} +(-0.317703 + 0.437280i) q^{39} +(5.88273 - 2.52853i) q^{41} +(-5.48112 - 3.98227i) q^{43} +(-4.02756 + 5.25034i) q^{45} +(-0.372889 - 2.35433i) q^{47} +(-10.8393 - 3.52189i) q^{49} +(-0.437110 + 1.34528i) q^{51} +(4.36779 + 2.22550i) q^{53} +(-4.85045 - 0.898277i) q^{55} +(0.220871 + 0.304003i) q^{57} +(8.79266 + 6.38824i) q^{59} +(6.87237 + 9.45901i) q^{61} +(12.5367 + 1.98562i) q^{63} +(5.26541 + 2.85793i) q^{65} +(-0.712758 + 1.39887i) q^{67} +(-0.0169731 - 0.107164i) q^{69} +(10.6070 - 5.40454i) q^{71} -3.71230 q^{73} +(-0.873689 - 0.504100i) q^{75} +(2.92399 + 8.99912i) q^{77} +(-5.04955 - 5.04955i) q^{79} -8.63537 q^{81} +5.94258i q^{83} +(15.4164 + 2.85504i) q^{85} +(0.226732 + 0.697809i) q^{87} +(-16.8191 - 2.66388i) q^{89} -11.4919i q^{91} +(-0.841298 - 1.65114i) q^{93} +(3.02082 - 2.86745i) q^{95} +(0.513699 - 1.00819i) q^{97} +(-2.96384 - 5.81687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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