LMFDB - Embedded newform 400.2.bi.d.303.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			303.8
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.d.367.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04632 - 0.324105i) q^{3} +(1.25149 + 1.85304i) q^{5} +(-1.74263 - 1.74263i) q^{7} +(1.22921 - 0.399395i) q^{9} +(3.97782 + 1.29247i) q^{11} +(1.72939 - 3.39412i) q^{13} +(3.16154 + 3.38630i) q^{15} +(-0.973092 + 6.14386i) q^{17} +(5.07390 - 3.68640i) q^{19} +(-4.13076 - 3.00118i) q^{21} +(-1.78176 - 3.49690i) q^{23} +(-1.86753 + 4.63814i) q^{25} +(-3.15212 + 1.60609i) q^{27} +(-5.30819 + 7.30610i) q^{29} +(-1.52730 - 2.10215i) q^{31} +(8.55880 + 1.35558i) q^{33} +(1.04828 - 5.41004i) q^{35} +(-3.92382 - 1.99929i) q^{37} +(2.43883 - 7.50595i) q^{39} +(-2.43377 - 7.49039i) q^{41} +(-0.559886 + 0.559886i) q^{43} +(2.27845 + 1.77794i) q^{45} +(-0.158140 - 0.998455i) q^{47} -0.926510i q^{49} +12.8877i q^{51} +(0.0860034 + 0.543004i) q^{53} +(2.58321 + 8.98860i) q^{55} +(9.18804 - 9.18804i) q^{57} +(0.0466195 + 0.143480i) q^{59} +(-0.875345 + 2.69404i) q^{61} +(-2.83805 - 1.44606i) q^{63} +(8.45376 - 1.04308i) q^{65} +(-12.5167 - 1.98245i) q^{67} +(-4.77942 - 6.57830i) q^{69} +(-2.76891 + 3.81108i) q^{71} +(4.57470 - 2.33092i) q^{73} +(-2.31832 + 10.0964i) q^{75} +(-4.67956 - 9.18416i) q^{77} +(-1.99771 - 1.45142i) q^{79} +(-9.06660 + 6.58727i) q^{81} +(1.40073 - 8.84384i) q^{83} +(-12.6026 + 5.88581i) q^{85} +(-8.49431 + 16.6710i) q^{87} +(15.7767 + 5.12617i) q^{89} +(-8.92835 + 2.90100i) q^{91} +(-3.80667 - 3.80667i) q^{93} +(13.1810 + 4.78864i) q^{95} +(-10.0535 + 1.59232i) q^{97} +5.40580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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
$3$	2.04632	−	0.324105i	1.18144	−	0.187122i	0.465350	−	0.885127i	$-0.345928\pi$
$3$	2.04632	−	0.324105i	1.18144	−	0.187122i	0.716093	+	0.698004i	$0.245928\pi$
$4$		0			0
$5$	1.25149	+	1.85304i	0.559685	+	0.828706i
$5$	1.25149	+	1.85304i	0.559685	+	0.828706i
$6$		0			0
$7$	−1.74263	−	1.74263i	−0.658651	−	0.658651i	0.296410	−	0.955061i	$-0.404210\pi$
$7$	−1.74263	−	1.74263i	−0.658651	−	0.658651i	−0.955061	+	0.296410i	$0.904210\pi$
$8$		0			0
$9$	1.22921	−	0.399395i	0.409738	−	0.133132i
$10$		0			0
$11$	3.97782	+	1.29247i	1.19936	+	0.389695i	0.839525	−	0.543321i	$-0.182833\pi$
$11$	3.97782	+	1.29247i	1.19936	+	0.389695i	0.359834	+	0.933016i	$0.382833\pi$
$12$		0			0
$13$	1.72939	−	3.39412i	0.479646	−	0.941358i	−0.516718	−	0.856156i	$-0.672846\pi$
$13$	1.72939	−	3.39412i	0.479646	−	0.941358i	0.996364	−	0.0852025i	$-0.0271537\pi$
$14$		0			0
$15$	3.16154	+	3.38630i	0.816305	+	0.874340i
$16$		0			0
$17$	−0.973092	+	6.14386i	−0.236009	+	1.49010i	0.530397	+	0.847749i	$0.322043\pi$
$17$	−0.973092	+	6.14386i	−0.236009	+	1.49010i	−0.766407	+	0.642355i	$0.777957\pi$
$18$		0			0
$19$	5.07390	−	3.68640i	1.16403	−	0.845719i	0.173750	−	0.984790i	$-0.444411\pi$
$19$	5.07390	−	3.68640i	1.16403	−	0.845719i	0.990282	+	0.139071i	$0.0444115\pi$
$20$		0			0
$21$	−4.13076	−	3.00118i	−0.901407	−	0.654910i
$22$		0			0
$23$	−1.78176	−	3.49690i	−0.371523	−	0.729155i	0.627243	−	0.778824i	$-0.284183\pi$
$23$	−1.78176	−	3.49690i	−0.371523	−	0.729155i	−0.998766	+	0.0496691i	$0.984183\pi$
$24$		0			0
$25$	−1.86753	+	4.63814i	−0.373506	+	0.927628i
$26$		0			0
$27$	−3.15212	+	1.60609i	−0.606626	+	0.309091i
$28$		0			0
$29$	−5.30819	+	7.30610i	−0.985706	+	1.35671i	−0.0520085	+	0.998647i	$0.516562\pi$
$29$	−5.30819	+	7.30610i	−0.985706	+	1.35671i	−0.933698	+	0.358062i	$0.883438\pi$
$30$		0			0
$31$	−1.52730	−	2.10215i	−0.274311	−	0.377557i	0.649528	−	0.760338i	$-0.274967\pi$
$31$	−1.52730	−	2.10215i	−0.274311	−	0.377557i	−0.923839	+	0.382780i	$0.874967\pi$
$32$		0			0
$33$	8.55880	+	1.35558i	1.48990	+	0.235976i
$34$		0			0
$35$	1.04828	−	5.41004i	0.177191	−	0.914464i
$36$		0			0
$37$	−3.92382	−	1.99929i	−0.645072	−	0.328680i	0.100666	−	0.994920i	$-0.467903\pi$
$37$	−3.92382	−	1.99929i	−0.645072	−	0.328680i	−0.745738	+	0.666240i	$0.767903\pi$
$38$		0			0
$39$	2.43883	−	7.50595i	0.390526	−	1.20191i
$40$		0			0
$41$	−2.43377	−	7.49039i	−0.380092	−	1.16980i	−0.939979	−	0.341233i	$-0.889155\pi$
$41$	−2.43377	−	7.49039i	−0.380092	−	1.16980i	0.559887	−	0.828569i	$-0.310845\pi$
$42$		0			0
$43$	−0.559886	+	0.559886i	−0.0853818	+	0.0853818i	−0.748508	−	0.663126i	$-0.769229\pi$
$43$	−0.559886	+	0.559886i	−0.0853818	+	0.0853818i	0.663126	+	0.748508i	$0.269229\pi$
$44$		0			0
$45$	2.27845	+	1.77794i	0.339651	+	0.265040i
$46$		0			0
$47$	−0.158140	−	0.998455i	−0.0230670	−	0.145640i	0.973467	−	0.228829i	$-0.0734895\pi$
$47$	−0.158140	−	0.998455i	−0.0230670	−	0.145640i	−0.996534	+	0.0831889i	$0.973490\pi$
$48$		0			0
$49$		−	0.926510i		−	0.132359i
$50$		0			0
$51$			12.8877i			1.80464i
$52$		0			0
$53$	0.0860034	+	0.543004i	0.0118135	+	0.0745873i	0.992891	−	0.119029i	$-0.0379782\pi$
$53$	0.0860034	+	0.543004i	0.0118135	+	0.0745873i	−0.981077	+	0.193617i	$0.937978\pi$
$54$		0			0
$55$	2.58321	+	8.98860i	0.348320	+	1.21202i
$56$		0			0
$57$	9.18804	−	9.18804i	1.21699	−	1.21699i
$58$		0			0
$59$	0.0466195	+	0.143480i	0.00606934	+	0.0186795i	0.954045	−	0.299662i	$-0.0968740\pi$
$59$	0.0466195	+	0.143480i	0.00606934	+	0.0186795i	−0.947976	+	0.318342i	$0.896874\pi$
$60$		0			0
$61$	−0.875345	+	2.69404i	−0.112076	+	0.344936i	−0.991326	−	0.131425i	$-0.958045\pi$
$61$	−0.875345	+	2.69404i	−0.112076	+	0.344936i	0.879250	+	0.476361i	$0.158045\pi$
$62$		0			0
$63$	−2.83805	−	1.44606i	−0.357561	−	0.182187i
$64$		0			0
$65$	8.45376	−	1.04308i	1.04856	−	0.129378i
$66$		0			0
$67$	−12.5167	−	1.98245i	−1.52916	−	0.242195i	−0.665548	−	0.746355i	$-0.731802\pi$
$67$	−12.5167	−	1.98245i	−1.52916	−	0.242195i	−0.863610	+	0.504160i	$0.831802\pi$
$68$		0			0
$69$	−4.77942	−	6.57830i	−0.575374	−	0.791935i
$70$		0			0
$71$	−2.76891	+	3.81108i	−0.328610	+	0.452292i	−0.941071	−	0.338208i	$-0.890179\pi$
$71$	−2.76891	+	3.81108i	−0.328610	+	0.452292i	0.612462	+	0.790500i	$0.290179\pi$
$72$		0			0
$73$	4.57470	−	2.33092i	0.535428	−	0.272814i	−0.165299	−	0.986243i	$-0.552859\pi$
$73$	4.57470	−	2.33092i	0.535428	−	0.272814i	0.700727	+	0.713429i	$0.252859\pi$
$74$		0			0
$75$	−2.31832	+	10.0964i	−0.267697	+	1.16583i
$76$		0			0
$77$	−4.67956	−	9.18416i	−0.533286	−	1.04663i
$78$		0			0
$79$	−1.99771	−	1.45142i	−0.224760	−	0.163297i	0.469707	−	0.882822i	$-0.344360\pi$
$79$	−1.99771	−	1.45142i	−0.224760	−	0.163297i	−0.694467	+	0.719525i	$0.744360\pi$
$80$		0			0
$81$	−9.06660	+	6.58727i	−1.00740	+	0.731919i
$82$		0			0
$83$	1.40073	−	8.84384i	0.153750	−	0.970737i	−0.783326	−	0.621611i	$-0.786478\pi$
$83$	1.40073	−	8.84384i	0.153750	−	0.970737i	0.937076	−	0.349126i	$-0.113522\pi$
$84$		0			0
$85$	−12.6026	+	5.88581i	−1.36695	+	0.638406i
$86$		0			0
$87$	−8.49431	+	16.6710i	−0.910686	+	1.78732i
$88$		0			0
$89$	15.7767	+	5.12617i	1.67233	+	0.543373i	0.983399	−	0.181456i	$-0.0580809\pi$
$89$	15.7767	+	5.12617i	1.67233	+	0.543373i	0.688930	+	0.724828i	$0.258081\pi$
$90$		0			0
$91$	−8.92835	+	2.90100i	−0.935946	+	0.304107i
$92$		0			0
$93$	−3.80667	−	3.80667i	−0.394733	−	0.394733i
$94$		0			0
$95$	13.1810	+	4.78864i	1.35234	+	0.491305i
$96$		0			0
$97$	−10.0535	+	1.59232i	−1.02078	+	0.161675i	−0.644319	−	0.764757i	$-0.722859\pi$
$97$	−10.0535	+	1.59232i	−1.02078	+	0.161675i	−0.376460	+	0.926433i	$0.622859\pi$
$98$		0			0
$99$	5.40580			0.543303
$100$		0			0
$101$	−0.767479			−0.0763670			−0.0381835	−	0.999271i	$-0.512157\pi$
$101$	−0.767479			−0.0763670			−0.0381835	+	0.999271i	$0.512157\pi$
$102$		0			0
$103$	−16.7578	+	2.65417i	−1.65119	+	0.261523i	−0.911463	−	0.411382i	$-0.865046\pi$
$103$	−16.7578	+	2.65417i	−1.65119	+	0.261523i	−0.739728	+	0.672905i	$0.765046\pi$
$104$		0			0
$105$	0.391685	−	11.4104i	0.0382246	−	1.11354i
$106$		0			0
$107$	−8.98836	−	8.98836i	−0.868938	−	0.868938i	0.123417	−	0.992355i	$-0.460615\pi$
$107$	−8.98836	−	8.98836i	−0.868938	−	0.868938i	−0.992355	+	0.123417i	$0.960615\pi$
$108$		0			0
$109$	10.2511	−	3.33078i	0.981875	−	0.319030i	0.226275	−	0.974064i	$-0.427345\pi$
$109$	10.2511	−	3.33078i	0.981875	−	0.319030i	0.755600	+	0.655033i	$0.227345\pi$
$110$		0			0
$111$	−8.67737	−	2.81945i	−0.823619	−	0.267610i
$112$		0			0
$113$	0.976556	−	1.91660i	0.0918666	−	0.180298i	−0.840501	−	0.541810i	$-0.817739\pi$
$113$	0.976556	−	1.91660i	0.0918666	−	0.180298i	0.932368	+	0.361512i	$0.117739\pi$
$114$		0			0
$115$	4.25005	−	7.67803i	0.396319	−	0.715980i
$116$		0			0
$117$	0.770192	−	4.86280i	0.0712043	−	0.449566i
$118$		0			0
$119$	12.4022	−	9.01071i	1.13691	−	0.826011i
$120$		0			0
$121$	5.25341	+	3.81683i	0.477583	+	0.346984i
$122$		0			0
$123$	−7.40796	−	14.5389i	−0.667953	−	1.31093i
$124$		0			0
$125$	−10.9319	+	2.34398i	−0.977776	+	0.209652i
$126$		0			0
$127$	12.9105	−	6.57824i	1.14562	−	0.583725i	0.225071	−	0.974342i	$-0.427739\pi$
$127$	12.9105	−	6.57824i	1.14562	−	0.583725i	0.920553	+	0.390618i	$0.127739\pi$
$128$		0			0
$129$	−0.964244	+	1.32717i	−0.0848969	+	0.116851i
$130$		0			0
$131$	4.91601	+	6.76631i	0.429514	+	0.591176i	0.967842	−	0.251560i	$-0.0809436\pi$
$131$	4.91601	+	6.76631i	0.429514	+	0.591176i	−0.538327	+	0.842736i	$0.680944\pi$
$132$		0			0
$133$	−15.2659	−	2.41789i	−1.32372	−	0.209657i
$134$		0			0
$135$	−6.92100	−	3.83101i	−0.595665	−	0.329721i
$136$		0			0
$137$	5.75021	+	2.92988i	0.491274	+	0.250317i	0.682035	−	0.731320i	$-0.261095\pi$
$137$	5.75021	+	2.92988i	0.491274	+	0.250317i	−0.190760	+	0.981637i	$0.561095\pi$
$138$		0			0
$139$	−6.96377	+	21.4323i	−0.590659	+	1.81786i	−0.0154119	+	0.999881i	$0.504906\pi$
$139$	−6.96377	+	21.4323i	−0.590659	+	1.81786i	−0.575247	+	0.817980i	$0.695094\pi$
$140$		0			0
$141$	−0.647209	−	1.99190i	−0.0545048	−	0.167749i
$142$		0			0
$143$	11.2660	−	11.2660i	0.942111	−	0.942111i
$144$		0			0
$145$	−20.1817	−	0.692775i	−1.67600	−	0.0575319i
$146$		0			0
$147$	−0.300287	−	1.89594i	−0.0247672	−	0.156374i
$148$		0			0
$149$			18.1699i			1.48854i	0.667879	+	0.744270i	$0.267202\pi$
$149$			18.1699i			1.48854i	−0.667879	+	0.744270i	$0.732798\pi$
$150$		0			0
$151$			17.3074i			1.40845i	0.709975	+	0.704227i	$0.248706\pi$
$151$			17.3074i			1.40845i	−0.709975	+	0.704227i	$0.751294\pi$
$152$		0			0
$153$	1.25769	+	7.94076i	0.101678	+	0.641972i
$154$		0			0
$155$	1.98397	−	5.46098i	0.159356	−	0.438637i
$156$		0			0
$157$	14.8688	−	14.8688i	1.18666	−	1.18666i	0.208669	−	0.977986i	$-0.433087\pi$
$157$	14.8688	−	14.8688i	1.18666	−	1.18666i	0.977986	−	0.208669i	$-0.0669132\pi$
$158$		0			0
$159$	0.351981	+	1.08329i	0.0279139	+	0.0859101i
$160$		0			0
$161$	−2.98885	+	9.19873i	−0.235554	+	0.724962i
$162$		0			0
$163$	−4.22896	−	2.15476i	−0.331238	−	0.168774i	0.280460	−	0.959866i	$-0.409513\pi$
$163$	−4.22896	−	2.15476i	−0.331238	−	0.168774i	−0.611697	+	0.791092i	$0.709513\pi$
$164$		0			0
$165$	8.19933	+	17.5563i	0.638317	+	1.36676i
$166$		0			0
$167$	11.4379	+	1.81158i	0.885090	+	0.140184i	0.582398	−	0.812904i	$-0.302115\pi$
$167$	11.4379	+	1.81158i	0.885090	+	0.140184i	0.302692	+	0.953088i	$0.402115\pi$
$168$		0			0
$169$	−0.888031	−	1.22227i	−0.0683101	−	0.0940207i
$170$		0			0
$171$	4.76457	−	6.55787i	0.364356	−	0.501493i
$172$		0			0
$173$	0.135215	−	0.0688953i	0.0102802	−	0.00523801i	−0.448843	−	0.893611i	$-0.648164\pi$
$173$	0.135215	−	0.0688953i	0.0102802	−	0.00523801i	0.459123	+	0.888373i	$0.348164\pi$
$174$		0			0
$175$	11.3369	−	4.82813i	0.856993	−	0.364972i
$176$		0			0
$177$	0.141901	+	0.278496i	0.0106659	+	0.0209331i
$178$		0			0
$179$	−11.0242	−	8.00956i	−0.823989	−	0.598663i	0.0938635	−	0.995585i	$-0.470078\pi$
$179$	−11.0242	−	8.00956i	−0.823989	−	0.598663i	−0.917852	+	0.396922i	$0.870078\pi$
$180$		0			0
$181$	17.3355	−	12.5950i	1.28854	−	0.936178i	0.288764	−	0.957400i	$-0.406756\pi$
$181$	17.3355	−	12.5950i	1.28854	−	0.936178i	0.999775	+	0.0212222i	$0.00675575\pi$
$182$		0			0
$183$	−0.918086	+	5.79656i	−0.0678668	+	0.428494i
$184$		0			0
$185$	−1.20587	−	9.77309i	−0.0886573	−	0.718532i
$186$		0			0
$187$	−11.8116	+	23.1815i	−0.863747	+	1.69520i
$188$		0			0
$189$	8.29177	+	2.69416i	0.603138	+	0.195971i
$190$		0			0
$191$	−6.33371	+	2.05795i	−0.458291	+	0.148908i	−0.529059	−	0.848585i	$-0.677455\pi$
$191$	−6.33371	+	2.05795i	−0.458291	+	0.148908i	0.0707679	+	0.997493i	$0.477455\pi$
$192$		0			0
$193$	8.29523	+	8.29523i	0.597104	+	0.597104i	0.939541	−	0.342437i	$-0.111252\pi$
$193$	8.29523	+	8.29523i	0.597104	+	0.597104i	−0.342437	+	0.939541i	$0.611252\pi$
$194$		0			0
$195$	16.9610	−	4.87439i	1.21460	−	0.349062i
$196$		0			0
$197$	2.14412	−	0.339595i	0.152762	−	0.0241951i	−0.0795850	−	0.996828i	$-0.525360\pi$
$197$	2.14412	−	0.339595i	0.152762	−	0.0241951i	0.232347	+	0.972633i	$0.425360\pi$
$198$		0			0
$199$	13.2655			0.940363			0.470182	−	0.882570i	$-0.344188\pi$
$199$	13.2655			0.940363			0.470182	+	0.882570i	$0.344188\pi$
$200$		0			0
$201$	−26.2557			−1.85193
$202$		0			0
$203$	21.9820	−	3.48160i	1.54283	−	0.244361i
$204$		0			0
$205$	10.8342	−	13.8841i	0.756690	−	0.969704i
$206$		0			0
$207$	−3.58681	−	3.58681i	−0.249300	−	0.249300i
$208$		0			0
$209$	24.9477	−	8.10599i	1.72567	−	0.560703i
$210$		0			0
$211$	21.7098	+	7.05395i	1.49457	+	0.485614i	0.938428	−	0.345476i	$-0.112282\pi$
$211$	21.7098	+	7.05395i	1.49457	+	0.485614i	0.556138	+	0.831090i	$0.312282\pi$
$212$		0			0
$213$	−4.43089	+	8.69612i	−0.303600	+	0.595848i
$214$		0			0
$215$	−1.73818	−	0.336799i	−0.118543	−	0.0229695i
$216$		0			0
$217$	−1.00175	+	6.32478i	−0.0680030	+	0.429354i
$218$		0			0
$219$	8.60583	−	6.25250i	0.581528	−	0.422505i
$220$		0			0
$221$	19.1701	+	13.9279i	1.28952	+	0.936892i
$222$		0			0
$223$	5.06254	+	9.93580i	0.339013	+	0.665350i	0.996078	−	0.0884839i	$-0.0282022\pi$
$223$	5.06254	+	9.93580i	0.339013	+	0.665350i	−0.657065	+	0.753834i	$0.728202\pi$
$224$		0			0
$225$	−0.443144	+	6.44714i	−0.0295429	+	0.429809i
$226$		0			0
$227$	12.8593	−	6.55216i	0.853504	−	0.434882i	0.0282214	−	0.999602i	$-0.491016\pi$
$227$	12.8593	−	6.55216i	0.853504	−	0.434882i	0.825283	+	0.564720i	$0.191016\pi$
$228$		0			0
$229$	−13.4173	+	18.4673i	−0.886637	+	1.22035i	0.0879006	+	0.996129i	$0.471984\pi$
$229$	−13.4173	+	18.4673i	−0.886637	+	1.22035i	−0.974538	+	0.224222i	$0.928016\pi$
$230$		0			0
$231$	−12.5525	−	17.2771i	−0.825895	−	1.13675i
$232$		0			0
$233$	17.5084	+	2.77305i	1.14701	+	0.181669i	0.700866	−	0.713293i	$-0.252797\pi$
$233$	17.5084	+	2.77305i	1.14701	+	0.181669i	0.446144	+	0.894961i	$0.352797\pi$
$234$		0			0
$235$	1.65227	−	1.54260i	0.107782	−	0.100628i
$236$		0			0
$237$	−4.55836	−	2.32260i	−0.296097	−	0.150869i
$238$		0			0
$239$	5.00020	−	15.3890i	0.323436	−	0.995433i	−0.648706	−	0.761039i	$-0.724689\pi$
$239$	5.00020	−	15.3890i	0.323436	−	0.995433i	0.972142	−	0.234394i	$-0.0753105\pi$
$240$		0			0
$241$	1.09681	+	3.37565i	0.0706521	+	0.217445i	0.980148	−	0.198269i	$-0.0635319\pi$
$241$	1.09681	+	3.37565i	0.0706521	+	0.217445i	−0.909496	+	0.415713i	$0.863532\pi$
$242$		0			0
$243$	−8.91358	+	8.91358i	−0.571807	+	0.571807i
$244$		0			0
$245$	1.71686	−	1.15952i	0.109686	−	0.0740791i
$246$		0			0
$247$	−3.73734	−	23.5966i	−0.237801	−	1.50142i
$248$		0			0
$249$		−	18.5513i		−	1.17564i
$250$		0			0
$251$		−	21.8841i		−	1.38131i	−0.723183	−	0.690656i	$-0.757322\pi$
$251$		−	21.8841i		−	1.38131i	0.723183	−	0.690656i	$-0.242678\pi$
$252$		0			0
$253$	−2.56788	−	16.2129i	−0.161441	−	1.01930i
$254$		0			0
$255$	−23.8814	+	16.1288i	−1.49551	+	1.01003i
$256$		0			0
$257$	−11.3492	+	11.3492i	−0.707942	+	0.707942i	−0.966102	−	0.258160i	$-0.916884\pi$
$257$	−11.3492	+	11.3492i	−0.707942	+	0.707942i	0.258160	+	0.966102i	$0.416884\pi$
$258$		0			0
$259$	3.35374	+	10.3218i	0.208391	+	0.641363i
$260$		0			0
$261$	−3.60687	+	11.1008i	−0.223260	+	0.687123i
$262$		0			0
$263$	−3.80598	−	1.93925i	−0.234687	−	0.119579i	0.332693	−	0.943035i	$-0.392043\pi$
$263$	−3.80598	−	1.93925i	−0.234687	−	0.119579i	−0.567380	+	0.823456i	$0.692043\pi$
$264$		0			0
$265$	−0.898577	+	0.838933i	−0.0551991	+	0.0515353i
$266$		0			0
$267$	33.9456	+	5.37646i	2.07744	+	0.329034i
$268$		0			0
$269$	−13.7041	−	18.8621i	−0.835556	−	1.15004i	−0.986863	−	0.161557i	$-0.948348\pi$
$269$	−13.7041	−	18.8621i	−0.835556	−	1.15004i	0.151308	−	0.988487i	$-0.451652\pi$
$270$		0			0
$271$	11.1715	−	15.3762i	0.678618	−	0.934037i	−0.321299	−	0.946978i	$-0.604119\pi$
$271$	11.1715	−	15.3762i	0.678618	−	0.934037i	0.999916	+	0.0129409i	$0.00411932\pi$
$272$		0			0
$273$	−17.3300	+	8.83010i	−1.04886	+	0.534422i
$274$		0			0
$275$	−13.4234	+	16.0360i	−0.809461	+	0.967005i
$276$		0			0
$277$	3.77821	+	7.41516i	0.227011	+	0.445534i	0.976215	−	0.216805i	$-0.0695637\pi$
$277$	3.77821	+	7.41516i	0.227011	+	0.445534i	−0.749204	+	0.662339i	$0.769564\pi$
$278$		0			0
$279$	−2.71697	−	1.97399i	−0.162661	−	0.118180i
$280$		0			0
$281$	7.52487	−	5.46714i	0.448896	−	0.326142i	−0.340264	−	0.940330i	$-0.610516\pi$
$281$	7.52487	−	5.46714i	0.448896	−	0.326142i	0.789160	+	0.614188i	$0.210516\pi$
$282$		0			0
$283$	1.30237	−	8.22282i	0.0774176	−	0.488796i	−0.918264	−	0.395968i	$-0.870409\pi$
$283$	1.30237	−	8.22282i	0.0774176	−	0.488796i	0.995682	−	0.0928282i	$-0.0295907\pi$
$284$		0			0
$285$	28.5246	+	5.52706i	1.68965	+	0.327395i
$286$		0			0
$287$	−8.81179	+	17.2941i	−0.520143	+	1.02084i
$288$		0			0
$289$	−20.6321	−	6.70379i	−1.21365	−	0.394340i
$290$		0			0
$291$	−20.0566	+	6.51679i	−1.17574	+	0.382021i
$292$		0			0
$293$	0.0419460	+	0.0419460i	0.00245051	+	0.00245051i	0.708331	−	0.705880i	$-0.249448\pi$
$293$	0.0419460	+	0.0419460i	0.00245051	+	0.00245051i	−0.705880	+	0.708331i	$0.749448\pi$
$294$		0			0
$295$	−0.207531	+	0.265952i	−0.0120829	+	0.0154843i
$296$		0			0
$297$	−14.6144	+	2.31469i	−0.848014	+	0.134312i
$298$		0			0
$299$	−14.9502			−0.864595
$300$		0			0
$301$	1.95134			0.112474
$302$		0			0
$303$	−1.57051	+	0.248744i	−0.0902233	+	0.0142900i
$304$		0			0
$305$	−6.08765	+	1.74951i	−0.348578	+	0.100177i
$306$		0			0
$307$	−20.4719	−	20.4719i	−1.16839	−	1.16839i	−0.982586	−	0.185806i	$-0.940510\pi$
$307$	−20.4719	−	20.4719i	−1.16839	−	1.16839i	−0.185806	−	0.982586i	$-0.559490\pi$
$308$		0			0
$309$	−33.4315	+	10.8626i	−1.90185	+	0.617949i
$310$		0			0
$311$	21.8505	+	7.09966i	1.23903	+	0.402585i	0.853977	−	0.520311i	$-0.174184\pi$
$311$	21.8505	+	7.09966i	1.23903	+	0.402585i	0.385051	+	0.922895i	$0.374184\pi$
$312$		0			0
$313$	2.24028	−	4.39681i	0.126628	−	0.248522i	−0.818985	−	0.573815i	$-0.805463\pi$
$313$	2.24028	−	4.39681i	0.126628	−	0.248522i	0.945613	+	0.325293i	$0.105463\pi$
$314$		0			0
$315$	−0.872192	−	7.06877i	−0.0491424	−	0.398280i
$316$		0			0
$317$	−3.25054	+	20.5231i	−0.182568	+	1.15269i	0.710809	+	0.703385i	$0.248329\pi$
$317$	−3.25054	+	20.5231i	−0.182568	+	1.15269i	−0.893377	+	0.449307i	$0.851671\pi$
$318$		0			0
$319$	−30.5580	+	22.2017i	−1.71092	+	1.24306i
$320$		0			0
$321$	−21.3062	−	15.4799i	−1.18920	−	0.864003i
$322$		0			0
$323$	17.7114	+	34.7605i	0.985487	+	1.93413i
$324$		0			0
$325$	12.5127	+	14.3598i	0.694079	+	0.796536i
$326$		0			0
$327$	19.8975	−	10.1383i	1.10033	−	0.560647i
$328$		0			0
$329$	−1.46435	+	2.01551i	−0.0807325	+	0.111119i
$330$		0			0
$331$	−10.9135	−	15.0211i	−0.599858	−	0.825634i	0.395837	−	0.918321i	$-0.370454\pi$
$331$	−10.9135	−	15.0211i	−0.599858	−	0.825634i	−0.995695	+	0.0926868i	$0.970454\pi$
$332$		0			0
$333$	−5.62171	−	0.890392i	−0.308068	−	0.0487932i
$334$		0			0
$335$	−11.9910	−	25.6750i	−0.655138	−	1.40278i
$336$		0			0
$337$	−6.52445	−	3.32437i	−0.355409	−	0.181090i	0.267165	−	0.963651i	$-0.413913\pi$
$337$	−6.52445	−	3.32437i	−0.355409	−	0.181090i	−0.622574	+	0.782561i	$0.713913\pi$
$338$		0			0
$339$	1.37717	−	4.23848i	0.0747974	−	0.230203i
$340$		0			0
$341$	−3.35836	−	10.3360i	−0.181866	−	0.559725i
$342$		0			0
$343$	−13.8129	+	13.8129i	−0.745829	+	0.745829i
$344$		0			0
$345$	6.20847	−	17.0892i	0.334253	−	0.920050i
$346$		0			0
$347$	3.01285	+	19.0224i	0.161738	+	1.02117i	0.926345	+	0.376677i	$0.122933\pi$
$347$	3.01285	+	19.0224i	0.161738	+	1.02117i	−0.764607	+	0.644497i	$0.777067\pi$
$348$		0			0
$349$		−	3.60227i		−	0.192825i	−0.995341	−	0.0964126i	$-0.969263\pi$
$349$		−	3.60227i		−	0.192825i	0.995341	−	0.0964126i	$-0.0307368\pi$
$350$		0			0
$351$			13.4762i			0.719307i
$352$		0			0
$353$	−3.42709	−	21.6378i	−0.182405	−	1.15166i	−0.893666	−	0.448734i	$-0.851875\pi$
$353$	−3.42709	−	21.6378i	−0.182405	−	1.15166i	0.711260	−	0.702929i	$-0.248125\pi$
$354$		0			0
$355$	−10.5274	−	0.361373i	−0.558735	−	0.0191797i
$356$		0			0
$357$	22.4584	−	22.4584i	1.18863	−	1.18863i
$358$		0			0
$359$	3.42202	+	10.5319i	0.180607	+	0.555853i	0.999845	−	0.0176016i	$-0.00560306\pi$
$359$	3.42202	+	10.5319i	0.180607	+	0.555853i	−0.819238	+	0.573454i	$0.805603\pi$
$360$		0			0
$361$	6.28356	−	19.3388i	0.330714	−	1.01783i
$362$		0			0
$363$	11.9872	+	6.10779i	0.629166	+	0.320576i
$364$		0			0
$365$	10.0445	+	5.55997i	0.525753	+	0.291022i
$366$		0			0
$367$	−11.2126	−	1.77591i	−0.585295	−	0.0927016i	−0.143237	−	0.989688i	$-0.545751\pi$
$367$	−11.2126	−	1.77591i	−0.585295	−	0.0927016i	−0.442057	+	0.896987i	$0.645751\pi$
$368$		0			0
$369$	−5.98325	−	8.23524i	−0.311476	−	0.428709i
$370$		0			0
$371$	0.796381	−	1.09612i	0.0413460	−	0.0569079i
$372$		0			0
$373$	23.2986	−	11.8712i	1.20635	−	0.614668i	0.269032	−	0.963131i	$-0.413296\pi$
$373$	23.2986	−	11.8712i	1.20635	−	0.614668i	0.937323	+	0.348463i	$0.113296\pi$
$374$		0			0
$375$	−21.6104	+	8.33961i	−1.11596	+	0.430655i
$376$		0			0
$377$	15.6178	+	30.6517i	0.804359	+	1.57864i
$378$		0			0
$379$	−1.78262	−	1.29515i	−0.0915669	−	0.0665273i	0.541060	−	0.840984i	$-0.318023\pi$
$379$	−1.78262	−	1.29515i	−0.0915669	−	0.0665273i	−0.632627	+	0.774457i	$0.718023\pi$
$380$		0			0
$381$	24.2870	−	17.6456i	1.24426	−	0.904010i
$382$		0			0
$383$	−2.81349	+	17.7637i	−0.143763	+	0.907682i	0.805362	+	0.592783i	$0.201971\pi$
$383$	−2.81349	+	17.7637i	−0.143763	+	0.907682i	−0.949125	+	0.314899i	$0.898029\pi$
$384$		0			0
$385$	11.1622	−	20.1653i	0.568878	−	1.02772i
$386$		0			0
$387$	−0.464603	+	0.911834i	−0.0236171	+	0.0463511i
$388$		0			0
$389$	1.15255	+	0.374487i	0.0584367	+	0.0189872i	0.338089	−	0.941114i	$-0.390219\pi$
$389$	1.15255	+	0.374487i	0.0584367	+	0.0189872i	−0.279653	+	0.960101i	$0.590219\pi$
$390$		0			0
$391$	23.2183	−	7.54408i	1.17420	−	0.381521i
$392$		0			0
$393$	12.2527	+	12.2527i	0.618069	+	0.618069i
$394$		0			0
$395$	0.189426	−	5.51828i	0.00953104	−	0.277655i
$396$		0			0
$397$	1.93175	−	0.305959i	0.0969518	−	0.0153557i	−0.107770	−	0.994176i	$-0.534371\pi$
$397$	1.93175	−	0.305959i	0.0969518	−	0.0153557i	0.204722	+	0.978820i	$0.434371\pi$
$398$		0			0
$399$	−32.0226			−1.60314
$400$		0			0
$401$	−4.52511			−0.225973			−0.112987	−	0.993597i	$-0.536042\pi$
$401$	−4.52511			−0.225973			−0.112987	+	0.993597i	$0.536042\pi$
$402$		0			0
$403$	−9.77624	+	1.54840i	−0.486989	+	0.0771315i
$404$		0			0
$405$	−23.5533	−	8.55687i	−1.17037	−	0.425194i
$406$		0			0
$407$	−13.0242	−	13.0242i	−0.645587	−	0.645587i
$408$		0			0
$409$	−9.61896	+	3.12539i	−0.475627	+	0.154540i	−0.537014	−	0.843574i	$-0.680448\pi$
$409$	−9.61896	+	3.12539i	−0.475627	+	0.154540i	0.0613869	+	0.998114i	$0.480448\pi$
$410$		0			0
$411$	12.7164	+	4.13180i	0.627252	+	0.203807i
$412$		0			0
$413$	0.168792	−	0.331272i	0.00830569	−	0.0163008i
$414$		0			0
$415$	18.1410	−	8.47239i	0.890507	−	0.415893i
$416$		0			0
$417$	−7.30378	+	46.1143i	−0.357668	+	2.25823i
$418$		0			0
$419$	−5.54851	+	4.03123i	−0.271062	+	0.196938i	−0.715010	−	0.699115i	$-0.753578\pi$
$419$	−5.54851	+	4.03123i	−0.271062	+	0.196938i	0.443947	+	0.896053i	$0.353578\pi$
$420$		0			0
$421$	18.9116	+	13.7401i	0.921697	+	0.669652i	0.943946	−	0.330101i	$-0.107083\pi$
$421$	18.9116	+	13.7401i	0.921697	+	0.669652i	−0.0222490	+	0.999752i	$0.507083\pi$
$422$		0			0
$423$	−0.593166	−	1.16415i	−0.0288407	−	0.0566031i
$424$		0			0
$425$	−26.6788	−	15.9872i	−1.29411	−	0.775493i
$426$		0			0
$427$	6.22010	−	3.16930i	0.301012	−	0.153373i
$428$		0			0
$429$	19.4025	−	26.7052i	0.936761	−	1.28934i
$430$		0			0
$431$	−9.97612	−	13.7309i	−0.480533	−	0.661396i	0.498075	−	0.867134i	$-0.334041\pi$
$431$	−9.97612	−	13.7309i	−0.480533	−	0.661396i	−0.978607	+	0.205738i	$0.934041\pi$
$432$		0			0
$433$	−22.0597	−	3.49392i	−1.06012	−	0.167907i	−0.398063	−	0.917358i	$-0.630317\pi$
$433$	−22.0597	−	3.49392i	−1.06012	−	0.167907i	−0.662060	+	0.749451i	$0.730317\pi$
$434$		0			0
$435$	−41.5227	+	5.12335i	−1.99086	+	0.245646i
$436$		0			0
$437$	−21.9315	−	11.1746i	−1.04912	−	0.534556i
$438$		0			0
$439$	−9.68976	+	29.8220i	−0.462467	+	1.42333i	0.399673	+	0.916658i	$0.369124\pi$
$439$	−9.68976	+	29.8220i	−0.462467	+	1.42333i	−0.862140	+	0.506670i	$0.830876\pi$
$440$		0			0
$441$	−0.370044	−	1.13888i	−0.0176211	−	0.0542323i
$442$		0			0
$443$	−5.88162	+	5.88162i	−0.279444	+	0.279444i	−0.832887	−	0.553443i	$-0.813314\pi$
$443$	−5.88162	+	5.88162i	−0.279444	+	0.279444i	0.553443	+	0.832887i	$0.313314\pi$
$444$		0			0
$445$	10.2454	+	35.6503i	0.485681	+	1.68999i
$446$		0			0
$447$	5.88897	+	37.1815i	0.278539	+	1.75863i
$448$		0			0
$449$		−	12.7677i		−	0.602545i	−0.953538	−	0.301273i	$-0.902589\pi$
$449$		−	12.7677i		−	0.602545i	0.953538	−	0.301273i	$-0.0974115\pi$
$450$		0			0
$451$		−	32.9410i		−	1.55113i
$452$		0			0
$453$	5.60941	+	35.4164i	0.263553	+	1.66401i
$454$		0			0
$455$	−16.5494	−	12.9140i	−0.775850	−	0.605419i
$456$		0			0
$457$	0.162887	−	0.162887i	0.00761952	−	0.00761952i	−0.703287	−	0.710906i	$-0.748285\pi$
$457$	0.162887	−	0.162887i	0.00761952	−	0.00761952i	0.710906	+	0.703287i	$0.248285\pi$
$458$		0			0
$459$	−6.80026	−	20.9290i	−0.317409	−	0.976884i
$460$		0			0
$461$	7.74811	−	23.8462i	0.360865	−	1.11063i	−0.591665	−	0.806184i	$-0.701529\pi$
$461$	7.74811	−	23.8462i	0.360865	−	1.11063i	0.952530	−	0.304445i	$-0.0984710\pi$
$462$		0			0
$463$	27.1316	+	13.8242i	1.26091	+	0.642466i	0.951262	−	0.308384i	$-0.0997883\pi$
$463$	27.1316	+	13.8242i	1.26091	+	0.642466i	0.309649	+	0.950851i	$0.399788\pi$
$464$		0			0
$465$	2.28990	−	11.8179i	0.106192	−	0.548043i
$466$		0			0
$467$	34.0866	+	5.39878i	1.57734	+	0.249826i	0.882842	−	0.469670i	$-0.155627\pi$
$467$	34.0866	+	5.39878i	1.57734	+	0.249826i	0.694496	+	0.719496i	$0.255627\pi$
$468$		0			0
$469$	18.3573	+	25.2666i	0.847660	+	1.16670i
$470$		0			0
$471$	25.6072	−	35.2453i	1.17992	−	1.62402i
$472$		0			0
$473$	−2.95076	+	1.50349i	−0.135676	+	0.0691305i
$474$		0			0
$475$	7.62238	+	30.4179i	0.349739	+	1.39567i
$476$		0			0
$477$	0.322590	+	0.633118i	0.0147704	+	0.0289885i
$478$		0			0
$479$	14.3448	+	10.4221i	0.655429	+	0.476197i	0.865116	−	0.501571i	$-0.167245\pi$
$479$	14.3448	+	10.4221i	0.655429	+	0.476197i	−0.209687	+	0.977769i	$0.567245\pi$
$480$		0			0
$481$	−13.5716	+	9.86035i	−0.618812	+	0.449593i
$482$		0			0
$483$	−3.13479	+	19.7923i	−0.142638	+	0.900579i
$484$		0			0
$485$	−15.5325	−	16.6368i	−0.705296	−	0.755438i
$486$		0			0
$487$	7.85616	−	15.4186i	0.355997	−	0.698683i	−0.641668	−	0.766982i	$-0.721757\pi$
$487$	7.85616	−	15.4186i	0.355997	−	0.698683i	0.997665	+	0.0682996i	$0.0217574\pi$
$488$		0			0
$489$	−9.35217	−	3.03870i	−0.422920	−	0.137415i
$490$		0			0
$491$	−41.6761	+	13.5414i	−1.88082	+	0.611114i	−0.894295	+	0.447479i	$0.852322\pi$
$491$	−41.6761	+	13.5414i	−1.88082	+	0.611114i	−0.986521	+	0.163635i	$0.947678\pi$
$492$		0			0
$493$	−39.7223	−	39.7223i	−1.78900	−	1.78900i
$494$		0			0
$495$	6.76532	+	10.0172i	0.304078	+	0.450239i
$496$		0			0
$497$	11.4665	−	1.81611i	0.514342	−	0.0814637i
$498$		0			0
$499$	0.883753			0.0395622			0.0197811	−	0.999804i	$-0.493703\pi$
$499$	0.883753			0.0395622			0.0197811	+	0.999804i	$0.493703\pi$
$500$		0			0
$501$	23.9927			1.07192
$502$		0			0
$503$	27.6223	−	4.37494i	1.23162	−	0.195069i	0.493503	−	0.869744i	$-0.335716\pi$
$503$	27.6223	−	4.37494i	1.23162	−	0.195069i	0.738115	+	0.674675i	$0.235716\pi$
$504$		0			0
$505$	−0.960494	−	1.42217i	−0.0427414	−	0.0632858i
$506$		0			0
$507$	−2.21334	−	2.21334i	−0.0982979	−	0.0982979i
$508$		0			0
$509$	−21.7125	+	7.05482i	−0.962389	+	0.312699i	−0.747740	−	0.663992i	$-0.768861\pi$
$509$	−21.7125	+	7.05482i	−0.962389	+	0.312699i	−0.214649	+	0.976691i	$0.568861\pi$
$510$		0			0
$511$	−12.0339	−	3.91005i	−0.532349	−	0.172971i
$512$		0			0
$513$	−10.0729	+	19.7691i	−0.444728	+	0.872827i
$514$		0			0
$515$	−25.8905	−	27.7312i	−1.14087	−	1.22198i
$516$		0			0
$517$	0.661424	−	4.17607i	0.0290894	−	0.183663i
$518$		0			0
$519$	0.254363	−	0.184806i	0.0111653	−	0.00811207i
$520$		0			0
$521$	9.82340	+	7.13712i	0.430371	+	0.312683i	0.781797	−	0.623533i	$-0.214303\pi$
$521$	9.82340	+	7.13712i	0.430371	+	0.312683i	−0.351426	+	0.936216i	$0.614303\pi$
$522$		0			0
$523$	2.19292	+	4.30385i	0.0958898	+	0.188194i	0.933969	−	0.357355i	$-0.116321\pi$
$523$	2.19292	+	4.30385i	0.0958898	+	0.188194i	−0.838079	+	0.545549i	$0.816321\pi$
$524$		0			0
$525$	21.6342	−	13.5543i	0.944194	−	0.591557i
$526$		0			0
$527$	14.4015	−	7.33794i	0.627340	−	0.319646i
$528$		0			0
$529$	4.46541	−	6.14610i	0.194148	−	0.267222i
$530$		0			0
$531$	0.114610	+	0.157748i	0.00497367	+	0.00684567i
$532$		0			0
$533$	−29.6322	−	4.69328i	−1.28351	−	0.203288i
$534$		0			0
$535$	5.40695	−	27.9047i	0.233763	−	1.20642i
$536$		0			0
$537$	−25.1550	−	12.8171i	−1.08552	−	0.553100i
$538$		0			0
$539$	1.19749	−	3.68549i	0.0515795	−	0.158745i
$540$		0			0
$541$	9.98917	+	30.7435i	0.429468	+	1.32177i	0.898651	+	0.438665i	$0.144548\pi$
$541$	9.98917	+	30.7435i	0.429468	+	1.32177i	−0.469183	+	0.883101i	$0.655452\pi$
$542$		0			0
$543$	31.3919	−	31.3919i	1.34716	−	1.34716i
$544$		0			0
$545$	19.0012	+	14.8272i	0.813923	+	0.635129i
$546$		0			0
$547$	−2.77236	−	17.5040i	−0.118537	−	0.748416i	−0.973324	−	0.229436i	$-0.926312\pi$
$547$	−2.77236	−	17.5040i	−0.118537	−	0.748416i	0.854786	−	0.518980i	$-0.173688\pi$
$548$		0			0
$549$			3.66115i			0.156254i
$550$		0			0
$551$			56.6386i			2.41288i
$552$		0			0
$553$	0.951976	+	6.01054i	0.0404821	+	0.255594i
$554$		0			0
$555$	−5.63510	−	19.6080i	−0.239197	−	0.832315i
$556$		0			0
$557$	−1.53075	+	1.53075i	−0.0648598	+	0.0648598i	−0.738793	−	0.673933i	$-0.764604\pi$
$557$	−1.53075	+	1.53075i	−0.0648598	+	0.0648598i	0.673933	+	0.738793i	$0.264604\pi$
$558$		0			0
$559$	0.932057	+	2.86858i	0.0394218	+	0.121328i
$560$		0			0
$561$	−16.6570	+	51.2649i	−0.703259	+	2.16441i
$562$		0			0
$563$	−28.4542	−	14.4981i	−1.19920	−	0.611023i	−0.263788	−	0.964581i	$-0.584972\pi$
$563$	−28.4542	−	14.4981i	−1.19920	−	0.611023i	−0.935413	+	0.353557i	$0.884972\pi$
$564$		0			0
$565$	4.77369	−	0.589010i	0.200831	−	0.0247798i
$566$		0			0
$567$	27.2788	+	4.32054i	1.14560	+	0.181446i
$568$		0			0
$569$	4.66098	+	6.41529i	0.195398	+	0.268943i	0.895462	−	0.445137i	$-0.146845\pi$
$569$	4.66098	+	6.41529i	0.195398	+	0.268943i	−0.700064	+	0.714080i	$0.746845\pi$
$570$		0			0
$571$	27.2326	−	37.4824i	1.13965	−	1.56859i	0.371358	−	0.928490i	$-0.378892\pi$
$571$	27.2326	−	37.4824i	1.13965	−	1.56859i	0.768291	−	0.640101i	$-0.221108\pi$
$572$		0			0
$573$	−12.2938	+	6.26401i	−0.513581	+	0.261683i
$574$		0			0
$575$	19.5466	−	1.73347i	0.815150	−	0.0722908i
$576$		0			0
$577$	9.19356	+	18.0434i	0.382733	+	0.751155i	0.999348	−	0.0361095i	$-0.0114965\pi$
$577$	9.19356	+	18.0434i	0.382733	+	0.751155i	−0.616615	+	0.787265i	$0.711497\pi$
$578$		0			0
$579$	19.6632	+	14.2862i	0.817176	+	0.593713i
$580$		0			0
$581$	−17.8524	+	12.9706i	−0.740644	+	0.538110i
$582$		0			0
$583$	−0.359712	+	2.27113i	−0.0148977	+	0.0940606i
$584$		0			0
$585$	9.97486	−	4.65856i	0.412410	−	0.192608i
$586$		0			0
$587$	−1.93065	+	3.78912i	−0.0796865	+	0.156394i	−0.927412	−	0.374042i	$-0.877972\pi$
$587$	−1.93065	+	3.78912i	−0.0796865	+	0.156394i	0.847725	+	0.530436i	$0.177972\pi$
$588$		0			0
$589$	−15.4988	−	5.03585i	−0.638615	−	0.207499i
$590$		0			0
$591$	4.27749	−	1.38984i	0.175952	−	0.0571704i
$592$		0			0
$593$	23.2329	+	23.2329i	0.954061	+	0.954061i	0.998990	−	0.0449295i	$-0.0143063\pi$
$593$	23.2329	+	23.2329i	0.954061	+	0.954061i	−0.0449295	+	0.998990i	$0.514306\pi$
$594$		0			0
$595$	32.2185	+	11.7049i	1.32083	+	0.479855i
$596$		0			0
$597$	27.1454	−	4.29941i	1.11099	−	0.175963i
$598$		0			0
$599$	−9.62540			−0.393283			−0.196642	−	0.980475i	$-0.563004\pi$
$599$	−9.62540			−0.393283			−0.196642	+	0.980475i	$0.563004\pi$
$600$		0			0
$601$	−6.59716			−0.269104			−0.134552	−	0.990907i	$-0.542959\pi$
$601$	−6.59716			−0.269104			−0.134552	+	0.990907i	$0.542959\pi$
$602$		0			0
$603$	−16.1775	+	2.56226i	−0.658798	+	0.104343i
$604$		0			0
$605$	−0.498136	+	14.5115i	−0.0202521	+	0.589977i
$606$		0			0
$607$	−9.70901	−	9.70901i	−0.394076	−	0.394076i	0.482061	−	0.876138i	$-0.339888\pi$
$607$	−9.70901	−	9.70901i	−0.394076	−	0.394076i	−0.876138	+	0.482061i	$0.839888\pi$
$608$		0			0
$609$	43.8538	−	14.2490i	1.77704	−	0.577397i
$610$		0			0
$611$	−3.66236	−	1.18997i	−0.148163	−	0.0481411i
$612$		0			0
$613$	−2.23292	+	4.38236i	−0.0901870	+	0.177002i	−0.931694	−	0.363244i	$-0.881669\pi$
$613$	−2.23292	+	4.38236i	−0.0901870	+	0.177002i	0.841507	+	0.540246i	$0.181669\pi$
$614$		0			0
$615$	17.6703	−	31.9226i	0.712534	−	1.28724i
$616$		0			0
$617$	6.02851	−	38.0625i	0.242699	−	1.53234i	−0.501958	−	0.864892i	$-0.667387\pi$
$617$	6.02851	−	38.0625i	0.242699	−	1.53234i	0.744657	−	0.667447i	$-0.232613\pi$
$618$		0			0
$619$	−14.2025	+	10.3187i	−0.570845	+	0.414743i	−0.835412	−	0.549624i	$-0.814771\pi$
$619$	−14.2025	+	10.3187i	−0.570845	+	0.414743i	0.264567	+	0.964367i	$0.414771\pi$
$620$		0			0
$621$	11.2326	+	8.16100i	0.450751	+	0.327489i
$622$		0			0
$623$	−18.5599	−	36.4259i	−0.743588	−	1.45937i
$624$		0			0
$625$	−18.0246	−	17.3237i	−0.720986	−	0.692950i
$626$		0			0
$627$	48.4237	−	24.6731i	1.93386	−	0.985349i
$628$		0			0
$629$	16.1016	−	22.1619i	0.642011	−	0.883653i
$630$		0			0
$631$	−18.2439	−	25.1106i	−0.726279	−	0.999638i	−0.999292	−	0.0376272i	$-0.988020\pi$
$631$	−18.2439	−	25.1106i	−0.726279	−	0.999638i	0.273013	−	0.962010i	$-0.411980\pi$
$632$		0			0
$633$	46.7115	+	7.39837i	1.85661	+	0.294059i
$634$		0			0
$635$	28.3472	+	15.6911i	1.12492	+	0.622684i
$636$		0			0
$637$	−3.14468	−	1.60230i	−0.124597	−	0.0634853i
$638$		0			0
$639$	−1.88146	+	5.79052i	−0.0744292	+	0.229070i
$640$		0			0
$641$	−1.92097	−	5.91213i	−0.0758737	−	0.233515i	0.905926	−	0.423437i	$-0.139177\pi$
$641$	−1.92097	−	5.91213i	−0.0758737	−	0.233515i	−0.981799	+	0.189922i	$0.939177\pi$
$642$		0			0
$643$	−20.1458	+	20.1458i	−0.794474	+	0.794474i	−0.982218	−	0.187744i	$-0.939883\pi$
$643$	−20.1458	+	20.1458i	−0.794474	+	0.794474i	0.187744	+	0.982218i	$0.439883\pi$
$644$		0			0
$645$	−3.66604	−	0.125844i	−0.144350	−	0.00495510i
$646$		0			0
$647$	0.821955	+	5.18962i	0.0323144	+	0.204025i	0.998563	−	0.0535853i	$-0.0170649\pi$
$647$	0.821955	+	5.18962i	0.0323144	+	0.204025i	−0.966249	+	0.257610i	$0.917065\pi$
$648$		0			0
$649$			0.630992i			0.0247686i
$650$		0			0
$651$			13.2672i			0.519982i
$652$		0			0
$653$	4.88882	+	30.8668i	0.191314	+	1.20791i	0.877172	+	0.480175i	$0.159427\pi$
$653$	4.88882	+	30.8668i	0.191314	+	1.20791i	−0.685858	+	0.727735i	$0.740573\pi$
$654$		0			0
$655$	−6.38591	+	17.5776i	−0.249518	+	0.686813i
$656$		0			0
$657$	4.69231	−	4.69231i	0.183065	−	0.183065i
$658$		0			0
$659$	1.63532	+	5.03301i	0.0637031	+	0.196058i	0.977842	−	0.209342i	$-0.0671322\pi$
$659$	1.63532	+	5.03301i	0.0637031	+	0.196058i	−0.914139	+	0.405400i	$0.867132\pi$
$660$		0			0
$661$	−1.62510	+	5.00154i	−0.0632090	+	0.194537i	−0.977674	−	0.210128i	$-0.932612\pi$
$661$	−1.62510	+	5.00154i	−0.0632090	+	0.194537i	0.914465	+	0.404665i	$0.132612\pi$
$662$		0			0
$663$	43.7423	+	22.2878i	1.69881	+	0.865587i
$664$		0			0
$665$	−14.6248	−	31.3144i	−0.567124	−	1.21432i
$666$		0			0
$667$	35.0066	+	5.54451i	1.35546	+	0.214684i
$668$		0			0
$669$	13.5798	+	18.6910i	0.525026	+	0.722637i
$670$		0			0
$671$	−6.96394	+	9.58504i	−0.268840	+	0.370026i
$672$		0			0
$673$	−15.3051	+	7.79834i	−0.589969	+	0.300604i	−0.723373	−	0.690458i	$-0.757409\pi$
$673$	−15.3051	+	7.79834i	−0.589969	+	0.300604i	0.133404	+	0.991062i	$0.457409\pi$
$674$		0			0
$675$	−1.56256	−	17.6194i	−0.0601429	−	0.678170i
$676$		0			0
$677$	8.30124	+	16.2921i	0.319043	+	0.626157i	0.993712	−	0.111963i	$-0.0357139\pi$
$677$	8.30124	+	16.2921i	0.319043	+	0.626157i	−0.674670	+	0.738120i	$0.735714\pi$
$678$		0			0
$679$	20.2943	+	14.7447i	0.778824	+	0.565849i
$680$		0			0
$681$	24.1907	−	17.5756i	0.926991	−	0.673498i
$682$		0			0
$683$	0.193581	−	1.22222i	0.00740717	−	0.0467670i	−0.983708	−	0.179774i	$-0.942463\pi$
$683$	0.193581	−	1.22222i	0.00740717	−	0.0467670i	0.991115	+	0.133007i	$0.0424633\pi$
$684$		0			0
$685$	1.76716	+	14.3221i	0.0675196	+	0.547220i
$686$		0			0
$687$	−21.4707	+	42.1386i	−0.819157	+	1.60769i
$688$		0			0
$689$	1.99175	+	0.647159i	0.0758797	+	0.0246548i
$690$		0			0
$691$	16.9206	−	5.49785i	0.643691	−	0.209148i	0.0310607	−	0.999517i	$-0.490111\pi$
$691$	16.9206	−	5.49785i	0.643691	−	0.209148i	0.612630	+	0.790370i	$0.290111\pi$
$692$		0			0
$693$	−9.42029	−	9.42029i	−0.357847	−	0.357847i
$694$		0			0
$695$	−48.4300	+	13.9182i	−1.83705	+	0.527946i
$696$		0			0
$697$	48.3882	−	7.66393i	1.83283	−	0.290292i
$698$		0			0
$699$	36.7265			1.38912
$700$		0			0
$701$	−12.0686			−0.455826			−0.227913	−	0.973681i	$-0.573190\pi$
$701$	−12.0686			−0.455826			−0.227913	+	0.973681i	$0.573190\pi$
$702$		0			0
$703$	−27.2792	+	4.32061i	−1.02886	+	0.162955i
$704$		0			0
$705$	2.88111	−	3.69216i	0.108509	−	0.139055i
$706$		0			0
$707$	1.33743	+	1.33743i	0.0502992	+	0.0502992i
$708$		0			0
$709$	−36.4583	+	11.8460i	−1.36922	+	0.444886i	−0.899110	−	0.437722i	$-0.855785\pi$
$709$	−36.4583	+	11.8460i	−1.36922	+	0.444886i	−0.470109	+	0.882608i	$0.655785\pi$
$710$		0			0
$711$	−3.03530	−	0.986228i	−0.113833	−	0.0369864i
$712$		0			0
$713$	−4.62973	+	9.08635i	−0.173385	+	0.340287i
$714$		0			0
$715$	34.9757	+	6.77707i	1.30802	+	0.253448i
$716$		0			0
$717$	5.24434	−	33.1115i	0.195853	−	1.23657i
$718$		0			0
$719$	−15.8917	+	11.5460i	−0.592662	+	0.430594i	−0.843267	−	0.537495i	$-0.819371\pi$
$719$	−15.8917	+	11.5460i	−0.592662	+	0.430594i	0.250605	+	0.968089i	$0.419371\pi$
$720$		0			0
$721$	33.8277	+	24.5773i	1.25981	+	0.915306i
$722$		0			0
$723$	3.33850	+	6.55218i	0.124160	+	0.243678i
$724$		0			0
$725$	−23.9735	−	38.2645i	−0.890352	−	1.42111i
$726$		0			0
$727$	−30.1021	+	15.3378i	−1.11642	+	0.568846i	−0.912063	−	0.410049i	$-0.865511\pi$
$727$	−30.1021	+	15.3378i	−1.11642	+	0.568846i	−0.204360	+	0.978896i	$0.565511\pi$
$728$		0			0
$729$	4.41070	−	6.07081i	0.163359	−	0.224845i
$730$		0			0
$731$	−2.89504	−	3.98468i	−0.107077	−	0.147379i
$732$		0			0
$733$	−9.31001	−	1.47456i	−0.343873	−	0.0544641i	−0.0178905	−	0.999840i	$-0.505695\pi$
$733$	−9.31001	−	1.47456i	−0.343873	−	0.0544641i	−0.325982	+	0.945376i	$0.605695\pi$
$734$		0			0
$735$	3.13744	−	2.92919i	0.115726	−	0.108045i
$736$		0			0
$737$	−47.2270	−	24.0634i	−1.73963	−	0.886385i
$738$		0			0
$739$	9.33365	−	28.7260i	0.343344	−	1.05670i	−0.619121	−	0.785296i	$-0.712511\pi$
$739$	9.33365	−	28.7260i	0.343344	−	1.05670i	0.962465	−	0.271408i	$-0.0874891\pi$
$740$		0			0
$741$	−15.2956	−	47.0750i	−0.561897	−	1.72934i
$742$		0			0
$743$	−3.50577	+	3.50577i	−0.128614	+	0.128614i	−0.768484	−	0.639869i	$-0.778988\pi$
$743$	−3.50577	+	3.50577i	−0.128614	+	0.128614i	0.639869	+	0.768484i	$0.278988\pi$
$744$		0			0
$745$	−33.6697	+	22.7396i	−1.23356	+	0.833113i
$746$		0			0
$747$	−1.81040	−	11.4304i	−0.0662390	−	0.418217i
$748$		0			0
$749$			31.3267i			1.14465i
$750$		0			0
$751$		−	11.4069i		−	0.416243i	−0.978103	−	0.208121i	$-0.933265\pi$
$751$		−	11.4069i		−	0.416243i	0.978103	−	0.208121i	$-0.0667349\pi$
$752$		0			0
$753$	−7.09275	−	44.7819i	−0.258474	−	1.63194i
$754$		0			0
$755$	−32.0713	+	21.6601i	−1.16719	+	0.788290i
$756$		0			0
$757$	0.478334	−	0.478334i	0.0173853	−	0.0173853i	−0.698361	−	0.715746i	$-0.746087\pi$
$757$	0.478334	−	0.478334i	0.0173853	−	0.0173853i	0.715746	+	0.698361i	$0.246087\pi$
$758$		0			0
$759$	−10.5094	−	32.3446i	−0.381467	−	1.17403i
$760$		0			0
$761$	−5.37866	+	16.5538i	−0.194976	+	0.600075i	0.805001	+	0.593274i	$0.202165\pi$
$761$	−5.37866	+	16.5538i	−0.194976	+	0.600075i	−0.999977	+	0.00680126i	$0.997835\pi$
$762$		0			0
$763$	−23.6681	−	12.0595i	−0.856842	−	0.436583i
$764$		0			0
$765$	−13.1406	+	12.2684i	−0.475098	+	0.443563i
$766$		0			0
$767$	0.567611	+	0.0899007i	0.0204952	+	0.00324613i
$768$		0			0
$769$	25.3991	+	34.9589i	0.915915	+	1.26065i	0.965106	+	0.261860i	$0.0843357\pi$
$769$	25.3991	+	34.9589i	0.915915	+	1.26065i	−0.0491910	+	0.998789i	$0.515664\pi$
$770$		0			0
$771$	−19.5457	+	26.9024i	−0.703922	+	0.968866i
$772$		0			0
$773$	−15.1822	+	7.73571i	−0.546065	+	0.278234i	−0.705183	−	0.709026i	$-0.749135\pi$
$773$	−15.1822	+	7.73571i	−0.546065	+	0.278234i	0.159118	+	0.987260i	$0.449135\pi$
$774$		0			0
$775$	12.6023	−	3.15800i	0.452690	−	0.113439i
$776$		0			0
$777$	10.2082	+	20.0346i	0.366216	+	0.718739i
$778$		0			0
$779$	−39.9613	−	29.0336i	−1.43176	−	1.04024i
$780$		0			0
$781$	−15.9400	+	11.5811i	−0.570377	+	0.414403i
$782$		0			0
$783$	4.99784	−	31.5551i	0.178608	−	1.12769i
$784$		0			0
$785$	46.1606	+	8.94429i	1.64754	+	0.319236i
$786$		0			0
$787$	−10.9088	+	21.4098i	−0.388858	+	0.763176i	−0.999589	−	0.0286614i	$-0.990876\pi$
$787$	−10.9088	+	21.4098i	−0.388858	+	0.763176i	0.610731	+	0.791838i	$0.290876\pi$
$788$		0			0
$789$	−8.41678	−	2.73478i	−0.299645	−	0.0973607i
$790$		0			0
$791$	−5.04169	+	1.63814i	−0.179262	+	0.0582457i
$792$		0			0
$793$	7.63006	+	7.63006i	0.270951	+	0.270951i
$794$		0			0
$795$	−1.56687	+	2.00796i	−0.0555713	+	0.0712150i
$796$		0			0
$797$	−38.7126	+	6.13148i	−1.37127	+	0.217188i	−0.798237	−	0.602343i	$-0.794234\pi$
$797$	−38.7126	+	6.13148i	−1.37127	+	0.217188i	−0.573034	+	0.819531i	$0.694234\pi$
$798$		0			0
$799$	6.28825			0.222462
$800$		0			0
$801$	21.4403			0.757556
$802$		0			0
$803$	21.2100	−	3.35933i	0.748484	−	0.118548i
$804$		0			0
$805$	−20.7862	+	5.97368i	−0.732616	+	0.210545i
$806$		0			0
$807$	−34.1564	−	34.1564i	−1.20236	−	1.20236i
$808$		0			0
$809$	4.10646	−	1.33427i	0.144376	−	0.0469105i	−0.235938	−	0.971768i	$-0.575816\pi$
$809$	4.10646	−	1.33427i	0.144376	−	0.0469105i	0.380313	+	0.924858i	$0.375816\pi$
$810$		0			0
$811$	26.3857	+	8.57325i	0.926529	+	0.301047i	0.733142	−	0.680075i	$-0.238053\pi$
$811$	26.3857	+	8.57325i	0.926529	+	0.301047i	0.193386	+	0.981123i	$0.438053\pi$
$812$		0			0
$813$	17.8769	−	35.0853i	0.626969	−	1.23050i
$814$		0			0
$815$	−1.29964	−	10.5331i	−0.0455246	−	0.368959i
$816$		0			0
$817$	−0.776839	+	4.90477i	−0.0271782	+	0.171596i
$818$		0			0
$819$	−9.81620	+	7.13188i	−0.343006	+	0.249208i
$820$		0			0
$821$	−28.7572	−	20.8933i	−1.00363	−	0.729183i	−0.0407698	−	0.999169i	$-0.512981\pi$
$821$	−28.7572	−	20.8933i	−1.00363	−	0.729183i	−0.962864	+	0.269986i	$0.912981\pi$
$822$		0			0
$823$	−7.67282	−	15.0588i	−0.267458	−	0.524915i	0.717746	−	0.696305i	$-0.245174\pi$
$823$	−7.67282	−	15.0588i	−0.267458	−	0.524915i	−0.985203	+	0.171390i	$0.945174\pi$
$824$		0			0
$825$	−22.2712	+	37.1653i	−0.775384	+	1.29393i
$826$		0			0
$827$	−35.1102	+	17.8896i	−1.22090	+	0.622081i	−0.941149	−	0.337991i	$-0.890253\pi$
$827$	−35.1102	+	17.8896i	−1.22090	+	0.622081i	−0.279753	+	0.960072i	$0.590253\pi$
$828$		0			0
$829$	16.6710	−	22.9457i	0.579008	−	0.796936i	−0.414578	−	0.910014i	$-0.636071\pi$
$829$	16.6710	−	22.9457i	0.579008	−	0.796936i	0.993586	+	0.113078i	$0.0360709\pi$
$830$		0			0
$831$	10.1347	+	13.9493i	0.351570	+	0.483894i
$832$		0			0
$833$	5.69235	+	0.901579i	0.197228	+	0.0312379i
$834$		0			0
$835$	10.9575	+	23.4621i	0.379200	+	0.811938i
$836$		0			0
$837$	8.19047	+	4.17325i	0.283104	+	0.144249i
$838$		0			0
$839$	−2.20988	+	6.80131i	−0.0762935	+	0.234807i	−0.981929	−	0.189250i	$-0.939394\pi$
$839$	−2.20988	+	6.80131i	−0.0762935	+	0.234807i	0.905635	+	0.424057i	$0.139394\pi$
$840$		0			0
$841$	−16.2407	−	49.9837i	−0.560024	−	1.72358i
$842$		0			0
$843$	13.6264	−	13.6264i	0.469317	−	0.469317i
$844$		0			0
$845$	1.15355	−	3.17522i	0.0396834	−	0.109231i
$846$		0			0
$847$	−2.50343	−	15.8060i	−0.0860189	−	0.543102i
$848$		0			0
$849$		−	17.2486i		−	0.591971i
$850$		0			0
$851$			17.2835i			0.592469i
$852$		0			0
$853$	−2.05872	−	12.9982i	−0.0704892	−	0.445051i	−0.997539	−	0.0701130i	$-0.977664\pi$
$853$	−2.05872	−	12.9982i	−0.0704892	−	0.445051i	0.927050	−	0.374938i	$-0.122336\pi$
$854$		0			0
$855$	18.1148	+	0.621827i	0.619514	+	0.0212660i
$856$		0			0
$857$	−8.40804	+	8.40804i	−0.287213	+	0.287213i	−0.835977	−	0.548764i	$-0.815099\pi$
$857$	−8.40804	+	8.40804i	−0.287213	+	0.287213i	0.548764	+	0.835977i	$0.315099\pi$
$858$		0			0
$859$	3.16014	+	9.72591i	0.107823	+	0.331844i	0.990383	−	0.138356i	$-0.0441818\pi$
$859$	3.16014	+	9.72591i	0.107823	+	0.331844i	−0.882560	+	0.470200i	$0.844182\pi$
$860$		0			0
$861$	−12.4266	+	38.2452i	−0.423498	+	1.30339i
$862$		0			0
$863$	−20.2503	−	10.3180i	−0.689328	−	0.351230i	0.0739848	−	0.997259i	$-0.476428\pi$
$863$	−20.2503	−	10.3180i	−0.689328	−	0.351230i	−0.763313	+	0.646029i	$0.776428\pi$
$864$		0			0
$865$	0.296886	+	0.164336i	0.0100944	+	0.00558761i
$866$		0			0
$867$	−44.3927	−	7.03111i	−1.50765	−	0.238789i
$868$		0			0
$869$	−6.07061	−	8.35547i	−0.205931	−	0.283440i
$870$		0			0
$871$	−28.3749	+	39.0547i	−0.961447	+	1.32332i
$872$		0			0
$873$	−11.7219	+	5.97262i	−0.396727	+	0.202143i
$874$		0			0
$875$	23.1348	+	14.9655i	0.782100	+	0.505926i
$876$		0			0
$877$	−11.7991	−	23.1570i	−0.398427	−	0.781956i	0.601429	−	0.798926i	$-0.294598\pi$
$877$	−11.7991	−	23.1570i	−0.398427	−	0.781956i	−0.999856	+	0.0169696i	$0.994598\pi$
$878$		0			0
$879$	0.0994300	+	0.0722401i	0.00335369	+	0.00243660i
$880$		0			0
$881$	11.2752	−	8.19189i	0.379870	−	0.275992i	−0.381422	−	0.924401i	$-0.624565\pi$
$881$	11.2752	−	8.19189i	0.379870	−	0.275992i	0.761292	+	0.648409i	$0.224565\pi$
$882$		0			0
$883$	3.45174	−	21.7934i	0.116160	−	0.733407i	−0.859011	−	0.511957i	$-0.828921\pi$
$883$	3.45174	−	21.7934i	0.116160	−	0.733407i	0.975172	−	0.221451i	$-0.0710792\pi$
$884$		0			0
$885$	−0.338477	+	0.611485i	−0.0113778	+	0.0205548i
$886$		0			0
$887$	−4.09998	+	8.04666i	−0.137664	+	0.270180i	−0.949538	−	0.313652i	$-0.898447\pi$
$887$	−4.09998	+	8.04666i	−0.137664	+	0.270180i	0.811874	+	0.583832i	$0.198447\pi$
$888$		0			0
$889$	−33.9616	−	11.0348i	−1.13904	−	0.370096i
$890$		0			0
$891$	−44.5792	+	14.4847i	−1.49346	+	0.485254i
$892$		0			0
$893$	−4.48309	−	4.48309i	−0.150021	−	0.150021i
$894$		0			0
$895$	1.04533	−	30.4523i	0.0349416	−	1.01791i
$896$		0			0
$897$	−30.5930	+	4.84545i	−1.02147	+	0.161785i
$898$		0			0
$899$	23.4657			0.782626
$900$		0			0
$901$	−3.41983			−0.113931
$902$		0			0
$903$	3.99307	−	0.632441i	0.132881	−	0.0210463i
$904$		0			0
$905$	45.0343	+	16.3609i	1.49699	+	0.543855i
$906$		0			0
$907$	−36.4128	−	36.4128i	−1.20907	−	1.20907i	−0.971330	−	0.237736i	$-0.923595\pi$
$907$	−36.4128	−	36.4128i	−1.20907	−	1.20907i	−0.237736	−	0.971330i	$-0.576405\pi$
$908$		0			0
$909$	−0.943395	+	0.306527i	−0.0312904	+	0.0101669i
$910$		0			0
$911$	16.2401	+	5.27672i	0.538057	+	0.174825i	0.565424	−	0.824800i	$-0.308712\pi$
$911$	16.2401	+	5.27672i	0.538057	+	0.174825i	−0.0273673	+	0.999625i	$0.508712\pi$
$912$		0			0
$913$	17.0023	−	33.3688i	0.562693	−	1.10435i
$914$		0			0
$915$	−11.8903	+	5.55311i	−0.393080	+	0.183580i
$916$		0			0
$917$	3.22438	−	20.3579i	0.106478	−	0.672278i
$918$		0			0
$919$	27.1798	−	19.7473i	0.896578	−	0.651402i	−0.0410069	−	0.999159i	$-0.513057\pi$
$919$	27.1798	−	19.7473i	0.896578	−	0.651402i	0.937585	+	0.347757i	$0.113057\pi$
$920$		0			0
$921$	−48.5271	−	35.2570i	−1.59902	−	1.16176i
$922$		0			0
$923$	8.14673	+	15.9889i	0.268153	+	0.526280i
$924$		0			0
$925$	16.6008	−	14.4655i	0.545832	−	0.475622i
$926$		0			0
$927$	−19.5388	+	9.95551i	−0.641738	+	0.326982i
$928$		0			0
$929$	17.3704	−	23.9083i	0.569903	−	0.784405i	−0.422640	−	0.906298i	$-0.638897\pi$
$929$	17.3704	−	23.9083i	0.569903	−	0.784405i	0.992543	+	0.121893i	$0.0388965\pi$
$930$		0			0
$931$	−3.41549	−	4.70102i	−0.111938	−	0.154070i
$932$		0			0
$933$	47.0141	+	7.44631i	1.53917	+	0.243781i
$934$		0			0
$935$	−57.7384	+	7.12415i	−1.88825	+	0.232984i
$936$		0			0
$937$	49.2964	+	25.1178i	1.61044	+	0.820562i	0.999585	+	0.0288226i	$0.00917579\pi$
$937$	49.2964	+	25.1178i	1.61044	+	0.820562i	0.610859	+	0.791739i	$0.290824\pi$
$938$		0			0
$939$	3.15931	−	9.72336i	0.103100	−	0.317310i
$940$		0			0
$941$	−5.12588	−	15.7758i	−0.167099	−	0.514277i	0.832086	−	0.554647i	$-0.187147\pi$
$941$	−5.12588	−	15.7758i	−0.167099	−	0.514277i	−0.999185	+	0.0403694i	$0.987147\pi$
$942$		0			0
$943$	−21.8568	+	21.8568i	−0.711754	+	0.711754i
$944$		0			0
$945$	5.38470	+	18.7367i	0.175164	+	0.609506i
$946$		0			0
$947$	5.87967	+	37.1228i	0.191064	+	1.20633i	0.877658	+	0.479287i	$0.159105\pi$
$947$	5.87967	+	37.1228i	0.191064	+	1.20633i	−0.686594	+	0.727041i	$0.740895\pi$
$948$		0			0
$949$		−	19.5581i		−	0.634884i
$950$		0			0
$951$			43.0503i			1.39600i
$952$		0			0
$953$	−1.02786	−	6.48965i	−0.0332957	−	0.210220i	0.965432	−	0.260656i	$-0.0839390\pi$
$953$	−1.02786	−	6.48965i	−0.0332957	−	0.210220i	−0.998727	+	0.0504359i	$0.983939\pi$
$954$		0			0
$955$	−11.7401	−	9.16113i	−0.379899	−	0.296447i
$956$		0			0
$957$	−55.3358	+	55.3358i	−1.78875	+	1.78875i
$958$		0			0
$959$	−4.91479	−	15.1262i	−0.158707	−	0.488449i
$960$		0			0
$961$	7.49314	−	23.0615i	0.241714	−	0.743920i
$962$		0			0
$963$	−14.6385	−	7.45870i	−0.471720	−	0.240353i
$964$		0			0
$965$	−4.99000	+	25.7528i	−0.160634	+	0.829013i
$966$		0			0
$967$	3.07254	+	0.486643i	0.0988062	+	0.0156494i	0.205642	−	0.978627i	$-0.434072\pi$
$967$	3.07254	+	0.486643i	0.0988062	+	0.0156494i	−0.106836	+	0.994277i	$0.534072\pi$
$968$		0			0
$969$	47.5092	+	65.3908i	1.52622	+	2.10066i
$970$		0			0
$971$	−10.7163	+	14.7497i	−0.343903	+	0.473342i	−0.945576	−	0.325401i	$-0.894501\pi$
$971$	−10.7163	+	14.7497i	−0.343903	+	0.473342i	0.601673	+	0.798742i	$0.294501\pi$
$972$		0			0
$973$	49.4837	−	25.2132i	1.58637	−	0.808298i
$974$		0			0
$975$	30.2590	+	25.3292i	0.969065	+	0.811185i
$976$		0			0
$977$	−6.28657	−	12.3381i	−0.201125	−	0.394730i	0.768310	−	0.640078i	$-0.221098\pi$
$977$	−6.28657	−	12.3381i	−0.201125	−	0.394730i	−0.969435	+	0.245348i	$0.921098\pi$
$978$		0			0
$979$	56.1316	+	40.7820i	1.79397	+	1.30340i
$980$		0			0
$981$	11.2705	−	8.18846i	0.359838	−	0.261438i
$982$		0			0
$983$	−7.88136	+	49.7609i	−0.251376	+	1.58713i	0.462347	+	0.886699i	$0.347008\pi$
$983$	−7.88136	+	49.7609i	−0.251376	+	1.58713i	−0.713723	+	0.700428i	$0.752992\pi$
$984$		0			0
$985$	3.31263	+	3.54814i	0.105549	+	0.113053i
$986$		0			0
$987$	−2.34330	+	4.59899i	−0.0745881	+	0.146387i
$988$		0			0
$989$	2.95545	+	0.960283i	0.0939778	+	0.0305352i
$990$		0			0
$991$	31.1515	−	10.1217i	0.989561	−	0.321528i	0.230874	−	0.972984i	$-0.425841\pi$
$991$	31.1515	−	10.1217i	0.989561	−	0.321528i	0.758687	+	0.651456i	$0.225841\pi$
$992$		0			0
$993$	−27.2009	−	27.2009i	−0.863193	−	0.863193i
$994$		0			0
$995$	16.6016	+	24.5815i	0.526307	+	0.779285i
$996$		0			0
$997$	12.1665	−	1.92698i	0.385316	−	0.0610281i	0.0392285	−	0.999230i	$-0.487510\pi$
$997$	12.1665	−	1.92698i	0.385316	−	0.0610281i	0.346088	+	0.938202i	$0.387510\pi$
$998$		0			0
$999$	15.5794			0.492909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.303.8	yes	80
4.3	odd	2	inner	400.2.bi.d.303.3	✓	80
25.17	odd	20	inner	400.2.bi.d.367.3	yes	80
100.67	even	20	inner	400.2.bi.d.367.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.303.3	✓	80	4.3	odd	2	inner
400.2.bi.d.303.8	yes	80	1.1	even	1	trivial
400.2.bi.d.367.3	yes	80	25.17	odd	20	inner
400.2.bi.d.367.8	yes	80	100.67	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04632 - 0.324105i) q^{3} +(1.25149 + 1.85304i) q^{5} +(-1.74263 - 1.74263i) q^{7} +(1.22921 - 0.399395i) q^{9} +(3.97782 + 1.29247i) q^{11} +(1.72939 - 3.39412i) q^{13} +(3.16154 + 3.38630i) q^{15} +(-0.973092 + 6.14386i) q^{17} +(5.07390 - 3.68640i) q^{19} +(-4.13076 - 3.00118i) q^{21} +(-1.78176 - 3.49690i) q^{23} +(-1.86753 + 4.63814i) q^{25} +(-3.15212 + 1.60609i) q^{27} +(-5.30819 + 7.30610i) q^{29} +(-1.52730 - 2.10215i) q^{31} +(8.55880 + 1.35558i) q^{33} +(1.04828 - 5.41004i) q^{35} +(-3.92382 - 1.99929i) q^{37} +(2.43883 - 7.50595i) q^{39} +(-2.43377 - 7.49039i) q^{41} +(-0.559886 + 0.559886i) q^{43} +(2.27845 + 1.77794i) q^{45} +(-0.158140 - 0.998455i) q^{47} -0.926510i q^{49} +12.8877i q^{51} +(0.0860034 + 0.543004i) q^{53} +(2.58321 + 8.98860i) q^{55} +(9.18804 - 9.18804i) q^{57} +(0.0466195 + 0.143480i) q^{59} +(-0.875345 + 2.69404i) q^{61} +(-2.83805 - 1.44606i) q^{63} +(8.45376 - 1.04308i) q^{65} +(-12.5167 - 1.98245i) q^{67} +(-4.77942 - 6.57830i) q^{69} +(-2.76891 + 3.81108i) q^{71} +(4.57470 - 2.33092i) q^{73} +(-2.31832 + 10.0964i) q^{75} +(-4.67956 - 9.18416i) q^{77} +(-1.99771 - 1.45142i) q^{79} +(-9.06660 + 6.58727i) q^{81} +(1.40073 - 8.84384i) q^{83} +(-12.6026 + 5.88581i) q^{85} +(-8.49431 + 16.6710i) q^{87} +(15.7767 + 5.12617i) q^{89} +(-8.92835 + 2.90100i) q^{91} +(-3.80667 - 3.80667i) q^{93} +(13.1810 + 4.78864i) q^{95} +(-10.0535 + 1.59232i) q^{97} +5.40580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89}+ \cdots - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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