LMFDB - Embedded newform 820.2.x.a.793.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			793.18
Character	$\chi$	$=$	820.793
Dual form			820.2.x.a.577.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.884872 - 2.13627i) q^{3} +(1.49097 - 1.66644i) q^{5} +(1.45509 + 0.602718i) q^{7} +(-1.65933 - 1.65933i) q^{9} +(-1.39221 + 0.576671i) q^{11} +(1.63915 - 3.95726i) q^{13} +(-2.24065 - 4.65969i) q^{15} +(0.0705774 + 0.170389i) q^{17} +(1.32175 + 0.547487i) q^{19} +(2.57514 - 2.57514i) q^{21} +(0.458474 - 0.458474i) q^{23} +(-0.554042 - 4.96921i) q^{25} +(1.39575 - 0.578137i) q^{27} +(-1.65360 + 0.684943i) q^{29} +6.64937i q^{31} +3.48441i q^{33} +(3.17388 - 1.52619i) q^{35} +(-3.16931 + 3.16931i) q^{37} +(-7.00334 - 7.00334i) q^{39} +(-3.33737 + 5.46461i) q^{41} -11.9749i q^{43} +(-5.23917 + 0.291168i) q^{45} +(4.94377 + 11.9353i) q^{47} +(-3.19573 - 3.19573i) q^{49} +0.426449 q^{51} +(-7.71780 - 3.19682i) q^{53} +(-1.11474 + 3.17982i) q^{55} +(2.33916 - 2.33916i) q^{57} +0.0773468i q^{59} +(-1.35891 - 1.35891i) q^{61} +(-1.41436 - 3.41458i) q^{63} +(-4.15062 - 8.63169i) q^{65} +(1.56827 + 3.78614i) q^{67} +(-0.573734 - 1.38512i) q^{69} +(1.33900 + 3.23263i) q^{71} +5.44939i q^{73} +(-11.1058 - 3.21353i) q^{75} -2.37335 q^{77} +(-2.22709 - 5.37666i) q^{79} -10.5332i q^{81} +(6.71441 + 6.71441i) q^{83} +(0.389172 + 0.136431i) q^{85} +4.13862i q^{87} +(2.22346 - 0.920987i) q^{89} +(4.77023 - 4.77023i) q^{91} +(14.2048 + 5.88384i) q^{93} +(2.88304 - 1.38633i) q^{95} +(-4.88397 + 2.02301i) q^{97} +(3.26701 + 1.35324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.884872	−	2.13627i	0.510881	−	1.23338i	−0.432491	−	0.901638i	$-0.642365\pi$
$3$	0.884872	−	2.13627i	0.510881	−	1.23338i	0.943372	−	0.331737i	$-0.107635\pi$
$4$		0			0
$5$	1.49097	−	1.66644i	0.666780	−	0.745254i
$5$	1.49097	−	1.66644i	0.666780	−	0.745254i
$6$		0			0
$7$	1.45509	+	0.602718i	0.549972	+	0.227806i	0.640325	−	0.768104i	$-0.278800\pi$
$7$	1.45509	+	0.602718i	0.549972	+	0.227806i	−0.0903530	+	0.995910i	$0.528800\pi$
$8$		0			0
$9$	−1.65933	−	1.65933i	−0.553109	−	0.553109i
$10$		0			0
$11$	−1.39221	+	0.576671i	−0.419766	+	0.173873i	−0.582561	−	0.812787i	$-0.697949\pi$
$11$	−1.39221	+	0.576671i	−0.419766	+	0.173873i	0.162795	+	0.986660i	$0.447949\pi$
$12$		0			0
$13$	1.63915	−	3.95726i	0.454619	−	1.09755i	−0.515927	−	0.856633i	$-0.672552\pi$
$13$	1.63915	−	3.95726i	0.454619	−	1.09755i	0.970546	−	0.240915i	$-0.0774476\pi$
$14$		0			0
$15$	−2.24065	−	4.65969i	−0.578533	−	1.20313i
$16$		0			0
$17$	0.0705774	+	0.170389i	0.0171175	+	0.0413254i	0.932207	−	0.361925i	$-0.117880\pi$
$17$	0.0705774	+	0.170389i	0.0171175	+	0.0413254i	−0.915090	+	0.403250i	$0.867880\pi$
$18$		0			0
$19$	1.32175	+	0.547487i	0.303230	+	0.125602i	0.529110	−	0.848553i	$-0.322526\pi$
$19$	1.32175	+	0.547487i	0.303230	+	0.125602i	−0.225880	+	0.974155i	$0.572526\pi$
$20$		0			0
$21$	2.57514	−	2.57514i	0.561941	−	0.561941i
$22$		0			0
$23$	0.458474	−	0.458474i	0.0955985	−	0.0955985i	−0.657690	−	0.753289i	$-0.728466\pi$
$23$	0.458474	−	0.458474i	0.0955985	−	0.0955985i	0.753289	+	0.657690i	$0.228466\pi$
$24$		0			0
$25$	−0.554042	−	4.96921i	−0.110808	−	0.993842i
$26$		0			0
$27$	1.39575	−	0.578137i	0.268612	−	0.111263i
$28$		0			0
$29$	−1.65360	+	0.684943i	−0.307065	+	0.127191i	−0.530895	−	0.847438i	$-0.678144\pi$
$29$	−1.65360	+	0.684943i	−0.307065	+	0.127191i	0.223829	+	0.974628i	$0.428144\pi$
$30$		0			0
$31$			6.64937i			1.19426i	0.802144	+	0.597131i	$0.203693\pi$
$31$			6.64937i			1.19426i	−0.802144	+	0.597131i	$0.796307\pi$
$32$		0			0
$33$			3.48441i			0.606557i
$34$		0			0
$35$	3.17388	−	1.52619i	0.536484	−	0.257973i
$36$		0			0
$37$	−3.16931	+	3.16931i	−0.521032	+	0.521032i	−0.917883	−	0.396851i	$-0.870103\pi$
$37$	−3.16931	+	3.16931i	−0.521032	+	0.521032i	0.396851	+	0.917883i	$0.370103\pi$
$38$		0			0
$39$	−7.00334	−	7.00334i	−1.12143	−	1.12143i
$40$		0			0
$41$	−3.33737	+	5.46461i	−0.521210	+	0.853429i
$41$	−3.33737	+	5.46461i	−0.521210	+	0.853429i
$42$		0			0
$43$		−	11.9749i		−	1.82615i	−0.407791	−	0.913075i	$-0.633701\pi$
$43$		−	11.9749i		−	1.82615i	0.407791	−	0.913075i	$-0.366299\pi$
$44$		0			0
$45$	−5.23917	+	0.291168i	−0.781009	+	0.0434048i
$46$		0			0
$47$	4.94377	+	11.9353i	0.721123	+	1.74094i	0.670127	+	0.742246i	$0.266239\pi$
$47$	4.94377	+	11.9353i	0.721123	+	1.74094i	0.0509955	+	0.998699i	$0.483761\pi$
$48$		0			0
$49$	−3.19573	−	3.19573i	−0.456533	−	0.456533i
$50$		0			0
$51$	0.426449			0.0597148
$52$		0			0
$53$	−7.71780	−	3.19682i	−1.06012	−	0.439116i	−0.216626	−	0.976255i	$-0.569505\pi$
$53$	−7.71780	−	3.19682i	−1.06012	−	0.439116i	−0.843494	+	0.537138i	$0.819505\pi$
$54$		0			0
$55$	−1.11474	+	3.17982i	−0.150312	+	0.428767i
$56$		0			0
$57$	2.33916	−	2.33916i	0.309829	−	0.309829i
$58$		0			0
$59$			0.0773468i			0.0100697i	0.999987	+	0.00503485i	$0.00160265\pi$
$59$			0.0773468i			0.0100697i	−0.999987	+	0.00503485i	$0.998397\pi$
$60$		0			0
$61$	−1.35891	−	1.35891i	−0.173991	−	0.173991i	0.614739	−	0.788730i	$-0.289261\pi$
$61$	−1.35891	−	1.35891i	−0.173991	−	0.173991i	−0.788730	+	0.614739i	$0.789261\pi$
$62$		0			0
$63$	−1.41436	−	3.41458i	−0.178193	−	0.430196i
$64$		0			0
$65$	−4.15062	−	8.63169i	−0.514821	−	1.07063i
$66$		0			0
$67$	1.56827	+	3.78614i	0.191595	+	0.462551i	0.990261	−	0.139224i	$-0.0444607\pi$
$67$	1.56827	+	3.78614i	0.191595	+	0.462551i	−0.798666	+	0.601774i	$0.794461\pi$
$68$		0			0
$69$	−0.573734	−	1.38512i	−0.0690694	−	0.166748i
$70$		0			0
$71$	1.33900	+	3.23263i	0.158910	+	0.383643i	0.983202	−	0.182523i	$-0.0584263\pi$
$71$	1.33900	+	3.23263i	0.158910	+	0.383643i	−0.824292	+	0.566166i	$0.808426\pi$
$72$		0			0
$73$			5.44939i			0.637802i	0.947788	+	0.318901i	$0.103314\pi$
$73$			5.44939i			0.637802i	−0.947788	+	0.318901i	$0.896686\pi$
$74$		0			0
$75$	−11.1058	−	3.21353i	−1.28239	−	0.371066i
$76$		0			0
$77$	−2.37335			−0.270469
$78$		0			0
$79$	−2.22709	−	5.37666i	−0.250567	−	0.604922i	0.747683	−	0.664056i	$-0.231166\pi$
$79$	−2.22709	−	5.37666i	−0.250567	−	0.604922i	−0.998250	+	0.0591337i	$0.981166\pi$
$80$		0			0
$81$		−	10.5332i		−	1.17036i
$82$		0			0
$83$	6.71441	+	6.71441i	0.737003	+	0.737003i	0.971997	−	0.234994i	$-0.0755071\pi$
$83$	6.71441	+	6.71441i	0.737003	+	0.737003i	−0.234994	+	0.971997i	$0.575507\pi$
$84$		0			0
$85$	0.389172	+	0.136431i	0.0422116	+	0.0147980i
$86$		0			0
$87$			4.13862i			0.443706i
$88$		0			0
$89$	2.22346	−	0.920987i	0.235686	−	0.0976244i	−0.261715	−	0.965145i	$-0.584288\pi$
$89$	2.22346	−	0.920987i	0.235686	−	0.0976244i	0.497401	+	0.867521i	$0.334288\pi$
$90$		0			0
$91$	4.77023	−	4.77023i	0.500056	−	0.500056i
$92$		0			0
$93$	14.2048	+	5.88384i	1.47297	+	0.610125i
$94$		0			0
$95$	2.88304	−	1.38633i	0.295794	−	0.142235i
$96$		0			0
$97$	−4.88397	+	2.02301i	−0.495892	+	0.205405i	−0.616590	−	0.787284i	$-0.711487\pi$
$97$	−4.88397	+	2.02301i	−0.495892	+	0.205405i	0.120699	+	0.992689i	$0.461487\pi$
$98$		0			0
$99$	3.26701	+	1.35324i	0.328347	+	0.136006i
$100$		0			0
$101$	2.49187	−	6.01591i	0.247950	−	0.598605i	−0.750079	−	0.661348i	$-0.769985\pi$
$101$	2.49187	−	6.01591i	0.247950	−	0.598605i	0.998030	+	0.0627426i	$0.0199847\pi$
$102$		0			0
$103$	9.09690			0.896344			0.448172	−	0.893947i	$-0.352075\pi$
$103$	9.09690			0.896344			0.448172	+	0.893947i	$0.352075\pi$
$104$		0			0
$105$	−0.451869	−	8.13075i	−0.0440979	−	0.793480i
$106$		0			0
$107$	9.06543	+	9.06543i	0.876388	+	0.876388i	0.993159	−	0.116771i	$-0.0372544\pi$
$107$	9.06543	+	9.06543i	0.876388	+	0.876388i	−0.116771	+	0.993159i	$0.537254\pi$
$108$		0			0
$109$	1.16306	−	2.80788i	0.111401	−	0.268946i	−0.858340	−	0.513081i	$-0.828504\pi$
$109$	1.16306	−	2.80788i	0.111401	−	0.268946i	0.969741	+	0.244135i	$0.0785040\pi$
$110$		0			0
$111$	3.96607	+	9.57494i	0.376443	+	0.908813i
$112$		0			0
$113$	−1.95522	+	1.95522i	−0.183932	+	0.183932i	−0.793067	−	0.609135i	$-0.791517\pi$
$113$	−1.95522	+	1.95522i	−0.183932	+	0.183932i	0.609135	+	0.793067i	$0.291517\pi$
$114$		0			0
$115$	−0.0804502	−	1.44759i	−0.00750202	−	0.134988i
$116$		0			0
$117$	−9.28629	+	3.84651i	−0.858517	+	0.355610i
$118$		0			0
$119$			0.290470i			0.0266273i
$120$		0			0
$121$	−6.17249	+	6.17249i	−0.561135	+	0.561135i
$122$		0			0
$123$	8.72073	+	11.9650i	0.786322	+	1.07885i
$124$		0			0
$125$	−9.10694	−	6.48564i	−0.814550	−	0.580094i
$126$		0			0
$127$	−2.33795	−	2.33795i	−0.207459	−	0.207459i	0.595728	−	0.803187i	$-0.296864\pi$
$127$	−2.33795	−	2.33795i	−0.207459	−	0.207459i	−0.803187	+	0.595728i	$0.796864\pi$
$128$		0			0
$129$	−25.5815	−	10.5962i	−2.25233	−	0.932945i
$130$		0			0
$131$	4.77665	−	4.77665i	0.417338	−	0.417338i	−0.466947	−	0.884285i	$-0.654646\pi$
$131$	4.77665	−	4.77665i	0.417338	−	0.417338i	0.884285	+	0.466947i	$0.154646\pi$
$132$		0			0
$133$	1.59329	+	1.59329i	0.138155	+	0.138155i
$134$		0			0
$135$	1.11758	−	3.18791i	0.0961860	−	0.274372i
$136$		0			0
$137$	6.86468	+	16.5728i	0.586489	+	1.41591i	0.886838	+	0.462081i	$0.152897\pi$
$137$	6.86468	+	16.5728i	0.586489	+	1.41591i	−0.300349	+	0.953829i	$0.597103\pi$
$138$		0			0
$139$			13.3299i			1.13062i	0.824877	+	0.565312i	$0.191244\pi$
$139$			13.3299i			1.13062i	−0.824877	+	0.565312i	$0.808756\pi$
$140$		0			0
$141$	29.8716			2.51565
$142$		0			0
$143$			6.45458i			0.539759i
$144$		0			0
$145$	−1.32404	+	3.77685i	−0.109956	+	0.313650i
$146$		0			0
$147$	−9.65475	+	3.99913i	−0.796310	+	0.329842i
$148$		0			0
$149$	9.93788	+	4.11640i	0.814143	+	0.337229i	0.750606	−	0.660750i	$-0.229762\pi$
$149$	9.93788	+	4.11640i	0.814143	+	0.337229i	0.0635372	+	0.997979i	$0.479762\pi$
$150$		0			0
$151$	7.30445	−	3.02560i	0.594428	−	0.246220i	−0.0651266	−	0.997877i	$-0.520745\pi$
$151$	7.30445	−	3.02560i	0.594428	−	0.246220i	0.659554	+	0.751657i	$0.270745\pi$
$152$		0			0
$153$	0.165620	−	0.399842i	0.0133896	−	0.0323253i
$154$		0			0
$155$	11.0808	+	9.91398i	0.890029	+	0.796310i
$156$		0			0
$157$	3.65098	−	8.81424i	0.291380	−	0.703453i	−0.708618	−	0.705592i	$-0.750681\pi$
$157$	3.65098	−	8.81424i	0.291380	−	0.703453i	0.999998	+	0.00213951i	$0.000681029\pi$
$158$		0			0
$159$	−13.6585	+	13.6585i	−1.08319	+	1.08319i
$160$		0			0
$161$	0.943452	−	0.390791i	0.0743545	−	0.0307986i
$162$		0			0
$163$	1.63616	−	1.63616i	0.128154	−	0.128154i	−0.640121	−	0.768274i	$-0.721116\pi$
$163$	1.63616	−	1.63616i	0.128154	−	0.128154i	0.768274	+	0.640121i	$0.221116\pi$
$164$		0			0
$165$	5.80655	+	5.19513i	0.452039	+	0.404440i
$166$		0			0
$167$	0.346441	+	0.143501i	0.0268084	+	0.0111044i	0.396047	−	0.918230i	$-0.370382\pi$
$167$	0.346441	+	0.143501i	0.0268084	+	0.0111044i	−0.369239	+	0.929334i	$0.620382\pi$
$168$		0			0
$169$	−3.78073	−	3.78073i	−0.290826	−	0.290826i
$170$		0			0
$171$	−1.28476	−	3.10168i	−0.0982478	−	0.237191i
$172$		0			0
$173$	16.2750			1.23736			0.618682	−	0.785641i	$-0.287667\pi$
$173$	16.2750			1.23736			0.618682	+	0.785641i	$0.287667\pi$
$174$		0			0
$175$	2.18885	−	7.56458i	0.165462	−	0.571828i
$176$		0			0
$177$	0.165234	+	0.0684420i	0.0124197	+	0.00514442i
$178$		0			0
$179$	−5.92157	+	14.2959i	−0.442599	+	1.06853i	0.532435	+	0.846471i	$0.321277\pi$
$179$	−5.92157	+	14.2959i	−0.442599	+	1.06853i	−0.975034	+	0.222057i	$0.928723\pi$
$180$		0			0
$181$	9.31005	−	22.4764i	0.692010	−	1.67066i	−0.0486802	−	0.998814i	$-0.515502\pi$
$181$	9.31005	−	22.4764i	0.692010	−	1.67066i	0.740691	−	0.671846i	$-0.234498\pi$
$182$		0			0
$183$	−4.10547	+	1.70054i	−0.303485	+	0.125708i
$184$		0			0
$185$	0.556131	+	10.0068i	0.0408876	+	0.735715i
$186$		0			0
$187$	−0.196517	−	0.196517i	−0.0143707	−	0.0143707i
$188$		0			0
$189$	2.37939			0.173075
$190$		0			0
$191$	−18.3456	−	7.59898i	−1.32744	−	0.549843i	−0.397515	−	0.917596i	$-0.630127\pi$
$191$	−18.3456	−	7.59898i	−1.32744	−	0.549843i	−0.929924	+	0.367753i	$0.880127\pi$
$192$		0			0
$193$	−2.89773	+	6.99575i	−0.208583	+	0.503565i	−0.993201	−	0.116416i	$-0.962860\pi$
$193$	−2.89773	+	6.99575i	−0.208583	+	0.503565i	0.784617	+	0.619981i	$0.212860\pi$
$194$		0			0
$195$	−22.1124	+	1.22890i	−1.58350	+	0.0880035i
$196$		0			0
$197$	−3.21187			−0.228837			−0.114418	−	0.993433i	$-0.536500\pi$
$197$	−3.21187			−0.228837			−0.114418	+	0.993433i	$0.536500\pi$
$198$		0			0
$199$	2.04581	−	4.93901i	0.145023	−	0.350117i	−0.834631	−	0.550809i	$-0.814319\pi$
$199$	2.04581	−	4.93901i	0.145023	−	0.350117i	0.979654	+	0.200692i	$0.0643191\pi$
$200$		0			0
$201$	9.47593			0.668381
$202$		0			0
$203$	−2.81896			−0.197852
$204$		0			0
$205$	4.13054	+	13.7091i	0.288489	+	0.957483i
$206$		0			0
$207$	−1.52152			−0.105753
$208$		0			0
$209$	−2.15587			−0.149125
$210$		0			0
$211$	−4.51324	+	10.8959i	−0.310704	+	0.750106i	0.688975	+	0.724785i	$0.258061\pi$
$211$	−4.51324	+	10.8959i	−0.310704	+	0.750106i	−0.999679	+	0.0253212i	$0.991939\pi$
$212$		0			0
$213$	8.09061			0.554360
$214$		0			0
$215$	−19.9554	−	17.8541i	−1.36095	−	1.21764i
$216$		0			0
$217$	−4.00769	+	9.67543i	−0.272060	+	0.656811i
$218$		0			0
$219$	11.6414	+	4.82201i	0.786650	+	0.325841i
$220$		0			0
$221$	0.789962			0.0531386
$222$		0			0
$223$	16.8381	+	16.8381i	1.12756	+	1.12756i	0.990573	+	0.136987i	$0.0437420\pi$
$223$	16.8381	+	16.8381i	1.12756	+	1.12756i	0.136987	+	0.990573i	$0.456258\pi$
$224$		0			0
$225$	−7.32621	+	9.16488i	−0.488414	+	0.610992i
$226$		0			0
$227$	−16.9742	+	7.03095i	−1.12662	+	0.466660i	−0.866630	−	0.498951i	$-0.833719\pi$
$227$	−16.9742	+	7.03095i	−1.12662	+	0.466660i	−0.259988	+	0.965612i	$0.583719\pi$
$228$		0			0
$229$	6.89561	−	16.6475i	0.455675	−	1.10010i	−0.514456	−	0.857516i	$-0.672006\pi$
$229$	6.89561	−	16.6475i	0.455675	−	1.10010i	0.970131	−	0.242580i	$-0.0779937\pi$
$230$		0			0
$231$	−2.10011	+	5.07012i	−0.138177	+	0.333590i
$232$		0			0
$233$	−15.5700	−	6.44929i	−1.02002	−	0.422507i	−0.190921	−	0.981605i	$-0.561147\pi$
$233$	−15.5700	−	6.44929i	−1.02002	−	0.422507i	−0.829101	+	0.559098i	$0.811147\pi$
$234$		0			0
$235$	27.2605	+	9.55666i	1.77828	+	0.623408i
$236$		0			0
$237$	−13.4567			−0.874106
$238$		0			0
$239$	7.43031	+	17.9384i	0.480627	+	1.16034i	0.959312	+	0.282349i	$0.0911138\pi$
$239$	7.43031	+	17.9384i	0.480627	+	1.16034i	−0.478685	+	0.877987i	$0.658886\pi$
$240$		0			0
$241$	2.83591	+	2.83591i	0.182677	+	0.182677i	0.792521	−	0.609844i	$-0.208768\pi$
$241$	2.83591	+	2.83591i	0.182677	+	0.182677i	−0.609844	+	0.792521i	$0.708768\pi$
$242$		0			0
$243$	−18.3145	−	7.58611i	−1.17488	−	0.486649i
$244$		0			0
$245$	−10.0902	+	0.560766i	−0.644640	+	0.0358260i
$246$		0			0
$247$	4.33310	−	4.33310i	0.275709	−	0.275709i
$248$		0			0
$249$	20.2852	−	8.40240i	1.28552	−	0.532480i
$250$		0			0
$251$	−3.86891	+	3.86891i	−0.244204	+	0.244204i	−0.818587	−	0.574383i	$-0.805242\pi$
$251$	−3.86891	+	3.86891i	−0.244204	+	0.244204i	0.574383	+	0.818587i	$0.305242\pi$
$252$		0			0
$253$	−0.373902	+	0.902679i	−0.0235070	+	0.0567510i
$254$		0			0
$255$	0.635821	−	0.710651i	0.0398166	−	0.0445027i
$256$		0			0
$257$	−6.01724	+	14.5269i	−0.375345	+	0.906163i	0.617480	+	0.786586i	$0.288154\pi$
$257$	−6.01724	+	14.5269i	−0.375345	+	0.906163i	−0.992825	+	0.119576i	$0.961846\pi$
$258$		0			0
$259$	−6.52184	+	2.70143i	−0.405247	+	0.167859i
$260$		0			0
$261$	3.88040	+	1.60732i	0.240191	+	0.0994904i
$262$		0			0
$263$	6.10431	−	2.52849i	0.376408	−	0.155913i	−0.186455	−	0.982463i	$-0.559700\pi$
$263$	6.10431	−	2.52849i	0.376408	−	0.155913i	0.562863	+	0.826550i	$0.309700\pi$
$264$		0			0
$265$	−16.8343	+	8.09490i	−1.03412	+	0.497266i
$266$		0			0
$267$		−	5.56486i		−	0.340564i
$268$		0			0
$269$	1.56828			0.0956195			0.0478098	−	0.998856i	$-0.484776\pi$
$269$	1.56828			0.0956195			0.0478098	+	0.998856i	$0.484776\pi$
$270$		0			0
$271$			0.530860i			0.0322474i	0.999870	+	0.0161237i	$0.00513256\pi$
$271$			0.530860i			0.0322474i	−0.999870	+	0.0161237i	$0.994867\pi$
$272$		0			0
$273$	−5.96945	−	14.4115i	−0.361288	−	0.872226i
$274$		0			0
$275$	3.63694	+	6.59866i	0.219315	+	0.397914i
$276$		0			0
$277$	11.7515	+	11.7515i	0.706081	+	0.706081i	0.965709	−	0.259628i	$-0.0835999\pi$
$277$	11.7515	+	11.7515i	0.706081	+	0.706081i	−0.259628	+	0.965709i	$0.583600\pi$
$278$		0			0
$279$	11.0335	−	11.0335i	0.660557	−	0.660557i
$280$		0			0
$281$	12.6394	+	5.23542i	0.754005	+	0.312319i	0.726375	−	0.687299i	$-0.241204\pi$
$281$	12.6394	+	5.23542i	0.754005	+	0.312319i	0.0276306	+	0.999618i	$0.491204\pi$
$282$		0			0
$283$	21.0340	+	21.0340i	1.25034	+	1.25034i	0.955566	+	0.294776i	$0.0952452\pi$
$283$	21.0340	+	21.0340i	1.25034	+	1.25034i	0.294776	+	0.955566i	$0.404755\pi$
$284$		0			0
$285$	−0.410461	−	7.38567i	−0.0243136	−	0.437489i
$286$		0			0
$287$	−8.14979	+	5.94001i	−0.481067	+	0.350628i
$288$		0			0
$289$	11.9968	−	11.9968i	0.705692	−	0.705692i
$290$		0			0
$291$			12.2236i			0.716558i
$292$		0			0
$293$	−18.0963	+	7.49572i	−1.05720	+	0.437905i	−0.842455	−	0.538766i	$-0.818891\pi$
$293$	−18.0963	+	7.49572i	−1.05720	+	0.437905i	−0.214740	+	0.976671i	$0.568891\pi$
$294$		0			0
$295$	0.128894	+	0.115322i	0.00750449	+	0.00671428i
$296$		0			0
$297$	−1.60977	+	1.60977i	−0.0934084	+	0.0934084i
$298$		0			0
$299$	−1.06279	−	2.56581i	−0.0614630	−	0.148385i
$300$		0			0
$301$	7.21747	−	17.4245i	0.416008	−	1.00433i
$302$		0			0
$303$	−10.6466	−	10.6466i	−0.611632	−	0.611632i
$304$		0			0
$305$	−4.29064	+	0.238454i	−0.245681	+	0.0136538i
$306$		0			0
$307$	−21.9641			−1.25356			−0.626778	−	0.779198i	$-0.715627\pi$
$307$	−21.9641			−1.25356			−0.626778	+	0.779198i	$0.715627\pi$
$308$		0			0
$309$	8.04959	−	19.4334i	0.457925	−	1.10553i
$310$		0			0
$311$	−23.4992	−	9.73369i	−1.33252	−	0.551947i	−0.401145	−	0.916015i	$-0.631388\pi$
$311$	−23.4992	−	9.73369i	−1.33252	−	0.551947i	−0.931372	+	0.364068i	$0.881388\pi$
$312$		0			0
$313$	3.46189	−	1.43396i	0.195678	−	0.0810523i	−0.282693	−	0.959211i	$-0.591228\pi$
$313$	3.46189	−	1.43396i	0.195678	−	0.0810523i	0.478370	+	0.878158i	$0.341228\pi$
$314$		0			0
$315$	−7.79896	−	2.73407i	−0.439421	−	0.154047i
$316$		0			0
$317$	−7.44053	−	3.08197i	−0.417902	−	0.173101i	0.163817	−	0.986491i	$-0.447619\pi$
$317$	−7.44053	−	3.08197i	−0.417902	−	0.173101i	−0.581718	+	0.813390i	$0.697619\pi$
$318$		0			0
$319$	1.90716	−	1.90716i	0.106781	−	0.106781i
$320$		0			0
$321$	27.3879	−	11.3445i	1.52864	−	0.633185i
$322$		0			0
$323$			0.263852i			0.0146811i
$324$		0			0
$325$	−20.5726	−	5.95280i	−1.14116	−	0.330202i
$326$		0			0
$327$	−4.96923	−	4.96923i	−0.274799	−	0.274799i
$328$		0			0
$329$			20.3467i			1.12175i
$330$		0			0
$331$	−0.244976	−	0.591424i	−0.0134651	−	0.0325076i	0.917004	−	0.398878i	$-0.130600\pi$
$331$	−0.244976	−	0.591424i	−0.0134651	−	0.0325076i	−0.930469	+	0.366370i	$0.880600\pi$
$332$		0			0
$333$	10.5179			0.576375
$334$		0			0
$335$	8.64761	+	3.03158i	0.472470	+	0.165633i
$336$		0			0
$337$		−	33.1410i		−	1.80531i	−0.430368	−	0.902653i	$-0.641616\pi$
$337$		−	33.1410i		−	1.80531i	0.430368	−	0.902653i	$-0.358384\pi$
$338$		0			0
$339$	2.44676	+	5.90701i	0.132890	+	0.320825i
$340$		0			0
$341$	−3.83449	−	9.25729i	−0.207650	−	0.501310i
$342$		0			0
$343$	−6.94298	−	16.7618i	−0.374886	−	0.905054i
$344$		0			0
$345$	−3.16363	−	1.10907i	−0.170324	−	0.0597102i
$346$		0			0
$347$	2.99426	+	7.22879i	0.160740	+	0.388062i	0.983645	−	0.180118i	$-0.0576479\pi$
$347$	2.99426	+	7.22879i	0.160740	+	0.388062i	−0.822905	+	0.568179i	$0.807648\pi$
$348$		0			0
$349$	−3.38718	−	3.38718i	−0.181312	−	0.181312i	0.610616	−	0.791927i	$-0.290922\pi$
$349$	−3.38718	−	3.38718i	−0.181312	−	0.181312i	−0.791927	+	0.610616i	$0.790922\pi$
$350$		0			0
$351$		−	6.47099i		−	0.345396i
$352$		0			0
$353$	−18.2189	+	18.2189i	−0.969692	+	0.969692i	−0.999554	−	0.0298623i	$-0.990493\pi$
$353$	−18.2189	+	18.2189i	−0.969692	+	0.969692i	0.0298623	+	0.999554i	$0.490493\pi$
$354$		0			0
$355$	7.38339	+	2.58838i	0.391870	+	0.137377i
$356$		0			0
$357$	0.620521	+	0.257028i	0.0328415	+	0.0136034i
$358$		0			0
$359$	−4.49903			−0.237450			−0.118725	−	0.992927i	$-0.537881\pi$
$359$	−4.49903			−0.237450			−0.118725	+	0.992927i	$0.537881\pi$
$360$		0			0
$361$	−11.9877	−	11.9877i	−0.630934	−	0.630934i
$362$		0			0
$363$	7.72423	+	18.6479i	0.405417	+	0.978764i
$364$		0			0
$365$	9.08107	+	8.12485i	0.475325	+	0.425274i
$366$		0			0
$367$		−	19.3068i		−	1.00781i	−0.863760	−	0.503904i	$-0.831897\pi$
$367$		−	19.3068i		−	1.00781i	0.863760	−	0.503904i	$-0.168103\pi$
$368$		0			0
$369$	14.6054	−	3.52979i	0.760325	−	0.183753i
$370$		0			0
$371$	−9.30331	−	9.30331i	−0.483004	−	0.483004i
$372$		0			0
$373$	−16.4142	+	16.4142i	−0.849893	+	0.849893i	−0.990119	−	0.140227i	$-0.955217\pi$
$373$	−16.4142	+	16.4142i	−0.849893	+	0.849893i	0.140227	+	0.990119i	$0.455217\pi$
$374$		0			0
$375$	−21.9136	+	13.7159i	−1.13161	+	0.708287i
$376$		0			0
$377$			7.66645i			0.394842i
$378$		0			0
$379$		−	24.1645i		−	1.24125i	−0.784109	−	0.620623i	$-0.786880\pi$
$379$		−	24.1645i		−	1.24125i	0.784109	−	0.620623i	$-0.213120\pi$
$380$		0			0
$381$	−7.06326	+	2.92570i	−0.361862	+	0.149888i
$382$		0			0
$383$	17.0831	−	7.07604i	0.872904	−	0.361569i	0.0991635	−	0.995071i	$-0.468383\pi$
$383$	17.0831	−	7.07604i	0.872904	−	0.361569i	0.773741	+	0.633502i	$0.218383\pi$
$384$		0			0
$385$	−3.53859	+	3.95505i	−0.180343	+	0.201568i
$386$		0			0
$387$	−19.8702	+	19.8702i	−1.01006	+	1.01006i
$388$		0			0
$389$	20.5174	−	20.5174i	1.04027	−	1.04027i	0.0411193	−	0.999154i	$-0.486908\pi$
$389$	20.5174	−	20.5174i	1.04027	−	1.04027i	0.999154	−	0.0411193i	$-0.0130924\pi$
$390$		0			0
$391$	0.110477	+	0.0457611i	0.00558706	+	0.00231424i
$392$		0			0
$393$	−5.97749	−	14.4309i	−0.301524	−	0.727944i
$394$		0			0
$395$	−12.2804	−	4.30512i	−0.617894	−	0.216614i
$396$		0			0
$397$	11.0685	−	26.7218i	0.555514	−	1.34113i	−0.357772	−	0.933809i	$-0.616463\pi$
$397$	11.0685	−	26.7218i	0.555514	−	1.34113i	0.913286	−	0.407320i	$-0.133537\pi$
$398$		0			0
$399$	4.81354	−	1.99383i	0.240978	−	0.0998165i
$400$		0			0
$401$	−12.5308	−	12.5308i	−0.625757	−	0.625757i	0.321241	−	0.946998i	$-0.395900\pi$
$401$	−12.5308	−	12.5308i	−0.625757	−	0.625757i	−0.946998	+	0.321241i	$0.895900\pi$
$402$		0			0
$403$	26.3133	+	10.8993i	1.31076	+	0.542934i
$404$		0			0
$405$	−17.5529	−	15.7046i	−0.872212	−	0.780370i
$406$		0			0
$407$	2.58469	−	6.23999i	0.128118	−	0.309305i
$408$		0			0
$409$	−10.4879			−0.518592			−0.259296	−	0.965798i	$-0.583491\pi$
$409$	−10.4879			−0.518592			−0.259296	+	0.965798i	$0.583491\pi$
$410$		0			0
$411$	41.4783			2.04597
$412$		0			0
$413$	−0.0466183	+	0.112547i	−0.00229394	+	0.00553806i
$414$		0			0
$415$	21.2001	−	1.17820i	1.04067	−	0.0578357i
$416$		0			0
$417$	28.4762	+	11.7952i	1.39448	+	0.577614i
$418$		0			0
$419$	3.29605	+	3.29605i	0.161023	+	0.161023i	0.783020	−	0.621997i	$-0.213678\pi$
$419$	3.29605	+	3.29605i	0.161023	+	0.161023i	−0.621997	+	0.783020i	$0.713678\pi$
$420$		0			0
$421$	19.8788	−	8.23406i	0.968833	−	0.401304i	0.158555	−	0.987350i	$-0.449316\pi$
$421$	19.8788	−	8.23406i	0.968833	−	0.401304i	0.810278	+	0.586046i	$0.199316\pi$
$422$		0			0
$423$	11.6013	−	28.0079i	0.564073	−	1.36179i
$424$		0			0
$425$	0.807596	−	0.445117i	0.0391742	−	0.0215913i
$426$		0			0
$427$	−1.15830	−	2.79638i	−0.0560541	−	0.135327i
$428$		0			0
$429$	13.7887	+	5.71147i	0.665725	+	0.275752i
$430$		0			0
$431$	−21.6942	+	21.6942i	−1.04497	+	1.04497i	−0.0460305	+	0.998940i	$0.514657\pi$
$431$	−21.6942	+	21.6942i	−1.04497	+	1.04497i	−0.998940	+	0.0460305i	$0.985343\pi$
$432$		0			0
$433$	16.5381	−	16.5381i	0.794770	−	0.794770i	−0.187495	−	0.982266i	$-0.560037\pi$
$433$	16.5381	−	16.5381i	0.794770	−	0.794770i	0.982266	+	0.187495i	$0.0600369\pi$
$434$		0			0
$435$	6.89676	+	6.17054i	0.330674	+	0.295855i
$436$		0			0
$437$	0.856997	−	0.354980i	0.0409957	−	0.0169810i
$438$		0			0
$439$	−0.192509	+	0.0797398i	−0.00918795	+	0.00380577i	−0.387273	−	0.921965i	$-0.626583\pi$
$439$	−0.192509	+	0.0797398i	−0.00918795	+	0.00380577i	0.378085	+	0.925771i	$0.376583\pi$
$440$		0			0
$441$			10.6055i			0.505025i
$442$		0			0
$443$		−	19.5262i		−	0.927718i	−0.885909	−	0.463859i	$-0.846464\pi$
$443$		−	19.5262i		−	0.927718i	0.885909	−	0.463859i	$-0.153536\pi$
$444$		0			0
$445$	1.78033	−	5.07842i	0.0843958	−	0.240740i
$446$		0			0
$447$	17.5875	−	17.5875i	0.831860	−	0.831860i
$448$		0			0
$449$	−16.7867	−	16.7867i	−0.792215	−	0.792215i	0.189639	−	0.981854i	$-0.439268\pi$
$449$	−16.7867	−	16.7867i	−0.792215	−	0.792215i	−0.981854	+	0.189639i	$0.939268\pi$
$450$		0			0
$451$	1.49503	−	9.53242i	0.0703980	−	0.448864i
$452$		0			0
$453$		−	18.2815i		−	0.858942i
$454$		0			0
$455$	−0.837050	−	15.0615i	−0.0392415	−	0.706096i
$456$		0			0
$457$	5.20775	+	12.5726i	0.243608	+	0.588122i	0.997636	−	0.0687203i	$-0.0218916\pi$
$457$	5.20775	+	12.5726i	0.243608	+	0.588122i	−0.754028	+	0.656843i	$0.771892\pi$
$458$		0			0
$459$	0.197016	+	0.197016i	0.00919594	+	0.00919594i
$460$		0			0
$461$	−37.3704			−1.74051			−0.870256	−	0.492599i	$-0.836047\pi$
$461$	−37.3704			−1.74051			−0.870256	+	0.492599i	$0.836047\pi$
$462$		0			0
$463$	−20.7423	−	8.59176i	−0.963979	−	0.399293i	−0.155511	−	0.987834i	$-0.549702\pi$
$463$	−20.7423	−	8.59176i	−0.963979	−	0.399293i	−0.808467	+	0.588541i	$0.799702\pi$
$464$		0			0
$465$	30.9840	−	14.8989i	1.43685	−	0.690920i
$466$		0			0
$467$	12.6229	−	12.6229i	0.584117	−	0.584117i	−0.351915	−	0.936032i	$-0.614469\pi$
$467$	12.6229	−	12.6229i	0.584117	−	0.584117i	0.936032	+	0.351915i	$0.114469\pi$
$468$		0			0
$469$			6.45440i			0.298037i
$470$		0			0
$471$	−15.5989	−	15.5989i	−0.718761	−	0.718761i
$472$		0			0
$473$	6.90555	+	16.6715i	0.317518	+	0.766556i
$474$		0			0
$475$	1.98827	−	6.87138i	0.0912282	−	0.315281i
$476$		0			0
$477$	7.50178	+	18.1109i	0.343483	+	0.829242i
$478$		0			0
$479$	−0.811220	−	1.95846i	−0.0370656	−	0.0894842i	0.904263	−	0.426977i	$-0.140421\pi$
$479$	−0.811220	−	1.95846i	−0.0370656	−	0.0894842i	−0.941328	+	0.337492i	$0.890421\pi$
$480$		0			0
$481$	7.34682	+	17.7368i	0.334986	+	0.808728i
$482$		0			0
$483$		−	2.36127i		−	0.107441i
$484$		0			0
$485$	−3.91061	+	11.1551i	−0.177572	+	0.506526i
$486$		0			0
$487$	22.8061			1.03344			0.516722	−	0.856153i	$-0.327152\pi$
$487$	22.8061			1.03344			0.516722	+	0.856153i	$0.327152\pi$
$488$		0			0
$489$	−2.04748	−	4.94306i	−0.0925903	−	0.223533i
$490$		0			0
$491$			4.31101i			0.194553i	0.995257	+	0.0972766i	$0.0310131\pi$
$491$			4.31101i			0.194553i	−0.995257	+	0.0972766i	$0.968987\pi$
$492$		0			0
$493$	−0.233413	−	0.233413i	−0.0105124	−	0.0105124i
$494$		0			0
$495$	7.12609	−	3.42664i	0.320294	−	0.154016i
$496$		0			0
$497$			5.51081i			0.247194i
$498$		0			0
$499$	−27.1306	+	11.2379i	−1.21453	+	0.503076i	−0.895668	−	0.444724i	$-0.853302\pi$
$499$	−27.1306	+	11.2379i	−1.21453	+	0.503076i	−0.318866	+	0.947800i	$0.603302\pi$
$500$		0			0
$501$	0.613112	−	0.613112i	0.0273918	−	0.0273918i
$502$		0			0
$503$	−27.0470	−	11.2032i	−1.20597	−	0.499528i	−0.313044	−	0.949739i	$-0.601349\pi$
$503$	−27.0470	−	11.2032i	−1.20597	−	0.499528i	−0.892922	+	0.450211i	$0.851349\pi$
$504$		0			0
$505$	−6.30985	−	13.1221i	−0.280785	−	0.583924i
$506$		0			0
$507$	−11.4221	+	4.73120i	−0.507274	+	0.210120i
$508$		0			0
$509$	−4.15079	−	1.71931i	−0.183980	−	0.0762072i	0.288791	−	0.957392i	$-0.406747\pi$
$509$	−4.15079	−	1.71931i	−0.183980	−	0.0762072i	−0.472772	+	0.881185i	$0.656747\pi$
$510$		0			0
$511$	−3.28444	+	7.92935i	−0.145295	+	0.350774i
$512$		0			0
$513$	2.16135			0.0954260
$514$		0			0
$515$	13.5632	−	15.1594i	0.597664	−	0.668004i
$516$		0			0
$517$	−13.7655	−	13.7655i	−0.605406	−	0.605406i
$518$		0			0
$519$	14.4013	−	34.7678i	0.632146	−	1.52614i
$520$		0			0
$521$	−1.66341	−	4.01583i	−0.0728754	−	0.175937i	0.883244	−	0.468913i	$-0.155354\pi$
$521$	−1.66341	−	4.01583i	−0.0728754	−	0.175937i	−0.956120	+	0.292976i	$0.905354\pi$
$522$		0			0
$523$	5.03989	−	5.03989i	0.220379	−	0.220379i	−0.588279	−	0.808658i	$-0.700194\pi$
$523$	5.03989	−	5.03989i	0.220379	−	0.220379i	0.808658	+	0.588279i	$0.200194\pi$
$524$		0			0
$525$	−14.2231	−	11.3697i	−0.620748	−	0.496213i
$526$		0			0
$527$	−1.13298	+	0.469295i	−0.0493534	+	0.0204428i
$528$		0			0
$529$			22.5796i			0.981722i
$530$		0			0
$531$	0.128344	−	0.128344i	0.00556964	−	0.00556964i
$532$		0			0
$533$	16.1544	+	22.1642i	0.699727	+	0.960037i
$534$		0			0
$535$	28.6232	−	1.59074i	1.23749	−	0.0687738i
$536$		0			0
$537$	25.3001	+	25.3001i	1.09178	+	1.09178i
$538$		0			0
$539$	6.29199	+	2.60623i	0.271015	+	0.112258i
$540$		0			0
$541$	−21.6679	+	21.6679i	−0.931578	+	0.931578i	−0.997805	−	0.0662270i	$-0.978904\pi$
$541$	−21.6679	+	21.6679i	−0.931578	+	0.931578i	0.0662270	+	0.997805i	$0.478904\pi$
$542$		0			0
$543$	−39.7775	−	39.7775i	−1.70702	−	1.70702i
$544$		0			0
$545$	−2.94508	−	6.12463i	−0.126153	−	0.262350i
$546$		0			0
$547$	−7.34027	−	17.7210i	−0.313847	−	0.757695i	−0.999555	−	0.0298180i	$-0.990507\pi$
$547$	−7.34027	−	17.7210i	−0.313847	−	0.757695i	0.685708	−	0.727877i	$-0.259493\pi$
$548$		0			0
$549$			4.50977i			0.192472i
$550$		0			0
$551$	−2.56064			−0.109087
$552$		0			0
$553$		−	9.16584i		−	0.389771i
$554$		0			0
$555$	21.8693	+	7.66669i	0.928302	+	0.325433i
$556$		0			0
$557$	−18.4596	+	7.64622i	−0.782159	+	0.323981i	−0.737786	−	0.675034i	$-0.764129\pi$
$557$	−18.4596	+	7.64622i	−0.782159	+	0.323981i	−0.0443724	+	0.999015i	$0.514129\pi$
$558$		0			0
$559$	−47.3877	−	19.6286i	−2.00429	−	0.830203i
$560$		0			0
$561$	−0.593704	+	0.245920i	−0.0250662	+	0.0103828i
$562$		0			0
$563$	−11.3070	+	27.2976i	−0.476534	+	1.15045i	0.484690	+	0.874686i	$0.338932\pi$
$563$	−11.3070	+	27.2976i	−0.476534	+	1.15045i	−0.961224	+	0.275769i	$0.911068\pi$
$564$		0			0
$565$	0.343090	+	6.17344i	0.0144339	+	0.259718i
$566$		0			0
$567$	6.34855	−	15.3268i	0.266614	−	0.643663i
$568$		0			0
$569$	−28.2444	+	28.2444i	−1.18407	+	1.18407i	−0.205388	+	0.978681i	$0.565846\pi$
$569$	−28.2444	+	28.2444i	−1.18407	+	1.18407i	−0.978681	+	0.205388i	$0.934154\pi$
$570$		0			0
$571$	−2.41510	+	1.00037i	−0.101069	+	0.0418641i	−0.432645	−	0.901564i	$-0.642420\pi$
$571$	−2.41510	+	1.00037i	−0.101069	+	0.0418641i	0.331576	+	0.943428i	$0.392420\pi$
$572$		0			0
$573$	−32.4669	+	32.4669i	−1.35633	+	1.35633i
$574$		0			0
$575$	−2.53227	−	2.02424i	−0.105603	−	0.0844167i
$576$		0			0
$577$	6.22157	+	2.57706i	0.259007	+	0.107284i	0.508409	−	0.861116i	$-0.330234\pi$
$577$	6.22157	+	2.57706i	0.259007	+	0.107284i	−0.249402	+	0.968400i	$0.580234\pi$
$578$		0			0
$579$	12.3807	+	12.3807i	0.514523	+	0.514523i
$580$		0			0
$581$	5.72318	+	13.8170i	0.237437	+	0.573225i
$582$		0			0
$583$	12.5883			0.521353
$584$		0			0
$585$	−7.43557	+	21.2100i	−0.307423	+	0.876927i
$586$		0			0
$587$	−9.87273	−	4.08942i	−0.407491	−	0.168788i	0.169516	−	0.985527i	$-0.445780\pi$
$587$	−9.87273	−	4.08942i	−0.407491	−	0.168788i	−0.577007	+	0.816739i	$0.695780\pi$
$588$		0			0
$589$	−3.64044	+	8.78880i	−0.150002	+	0.362136i
$590$		0			0
$591$	−2.84210	+	6.86143i	−0.116908	+	0.282241i
$592$		0			0
$593$	−32.2481	+	13.3576i	−1.32427	+	0.548531i	−0.929016	−	0.370040i	$-0.879344\pi$
$593$	−32.2481	+	13.3576i	−1.32427	+	0.548531i	−0.395255	+	0.918571i	$0.629344\pi$
$594$		0			0
$595$	0.484050	+	0.433080i	0.0198441	+	0.0177546i
$596$		0			0
$597$	−8.74078	−	8.74078i	−0.357736	−	0.357736i
$598$		0			0
$599$	43.9516			1.79581			0.897906	−	0.440188i	$-0.145088\pi$
$599$	43.9516			1.79581			0.897906	+	0.440188i	$0.145088\pi$
$600$		0			0
$601$	−44.8988	−	18.5977i	−1.83146	−	0.758615i	−0.966447	−	0.256864i	$-0.917311\pi$
$601$	−44.8988	−	18.5977i	−1.83146	−	0.758615i	−0.865012	−	0.501751i	$-0.832689\pi$
$602$		0			0
$603$	3.68017	−	8.88472i	0.149868	−	0.361814i
$604$		0			0
$605$	1.08311	+	19.4890i	0.0440346	+	0.792342i
$606$		0			0
$607$	−10.8953			−0.442227			−0.221114	−	0.975248i	$-0.570969\pi$
$607$	−10.8953			−0.442227			−0.221114	+	0.975248i	$0.570969\pi$
$608$		0			0
$609$	−2.49442	+	6.02206i	−0.101079	+	0.244026i
$610$		0			0
$611$	55.3348			2.23861
$612$		0			0
$613$	−12.8309			−0.518234			−0.259117	−	0.965846i	$-0.583432\pi$
$613$	−12.8309			−0.518234			−0.259117	+	0.965846i	$0.583432\pi$
$614$		0			0
$615$	32.9413	+	3.30683i	1.32832	+	0.133344i
$616$		0			0
$617$	31.5009			1.26818			0.634089	−	0.773260i	$-0.281375\pi$
$617$	31.5009			1.26818			0.634089	+	0.773260i	$0.281375\pi$
$618$		0			0
$619$	−46.0556			−1.85113			−0.925566	−	0.378586i	$-0.876410\pi$
$619$	−46.0556			−1.85113			−0.925566	+	0.378586i	$0.876410\pi$
$620$		0			0
$621$	0.374853	−	0.904975i	0.0150423	−	0.0363154i
$622$		0			0
$623$	3.79043			0.151860
$624$		0			0
$625$	−24.3861	+	5.50630i	−0.975443	+	0.220252i
$626$		0			0
$627$	−1.90767	+	4.60551i	−0.0761849	+	0.183927i
$628$		0			0
$629$	−0.763698	−	0.316334i	−0.0304506	−	0.0126131i
$630$		0			0
$631$	−5.97318			−0.237789			−0.118894	−	0.992907i	$-0.537935\pi$
$631$	−5.97318			−0.237789			−0.118894	+	0.992907i	$0.537935\pi$
$632$		0			0
$633$	19.2830	+	19.2830i	0.766430	+	0.766430i
$634$		0			0
$635$	−7.38184	+	0.410248i	−0.292939	+	0.0162802i
$636$		0			0
$637$	−17.8846	+	7.40806i	−0.708615	+	0.293518i
$638$		0			0
$639$	3.14215	−	7.58583i	0.124302	−	0.300091i
$640$		0			0
$641$	−1.27714	+	3.08329i	−0.0504440	+	0.121783i	−0.947093	−	0.320960i	$-0.895994\pi$
$641$	−1.27714	+	3.08329i	−0.0504440	+	0.121783i	0.896649	+	0.442743i	$0.145994\pi$
$642$		0			0
$643$	9.82483	+	4.06958i	0.387453	+	0.160488i	0.567902	−	0.823096i	$-0.307755\pi$
$643$	9.82483	+	4.06958i	0.387453	+	0.160488i	−0.180449	+	0.983584i	$0.557755\pi$
$644$		0			0
$645$	−55.7992	+	26.8315i	−2.19709	+	1.05649i
$646$		0			0
$647$	33.6866			1.32436			0.662179	−	0.749346i	$-0.269632\pi$
$647$	33.6866			1.32436			0.662179	+	0.749346i	$0.269632\pi$
$648$		0			0
$649$	−0.0446036	−	0.107683i	−0.00175085	−	0.00422692i
$650$		0			0
$651$	17.1230	+	17.1230i	0.671104	+	0.671104i
$652$		0			0
$653$	−23.7395	−	9.83323i	−0.928999	−	0.384804i	−0.133700	−	0.991022i	$-0.542686\pi$
$653$	−23.7395	−	9.83323i	−0.928999	−	0.384804i	−0.795299	+	0.606218i	$0.792686\pi$
$654$		0			0
$655$	−0.838176	−	15.0818i	−0.0327503	−	0.589296i
$656$		0			0
$657$	9.04231	−	9.04231i	0.352774	−	0.352774i
$658$		0			0
$659$	−31.4854	+	13.0417i	−1.22650	+	0.508032i	−0.899470	−	0.436982i	$-0.856047\pi$
$659$	−31.4854	+	13.0417i	−1.22650	+	0.508032i	−0.327029	+	0.945014i	$0.606047\pi$
$660$		0			0
$661$	−13.4561	+	13.4561i	−0.523383	+	0.523383i	−0.918591	−	0.395209i	$-0.870672\pi$
$661$	−13.4561	+	13.4561i	−0.523383	+	0.523383i	0.395209	+	0.918591i	$0.370672\pi$
$662$		0			0
$663$	0.699015	−	1.68757i	0.0271475	−	0.0655398i
$664$		0			0
$665$	5.03065	−	0.279580i	0.195080	−	0.0108416i
$666$		0			0
$667$	−0.444104	+	1.07216i	−0.0171958	+	0.0415142i
$668$		0			0
$669$	50.8702	−	21.0711i	1.96675	−	0.814656i
$670$		0			0
$671$	2.67553	+	1.10824i	0.103288	+	0.0427832i
$672$		0			0
$673$	23.7517	−	9.83826i	0.915559	−	0.379237i	0.125377	−	0.992109i	$-0.459986\pi$
$673$	23.7517	−	9.83826i	0.915559	−	0.379237i	0.790182	+	0.612872i	$0.209986\pi$
$674$		0			0
$675$	−3.64619	−	6.61544i	−0.140342	−	0.254629i
$676$		0			0
$677$			29.7046i			1.14164i	0.821075	+	0.570821i	$0.193375\pi$
$677$			29.7046i			1.14164i	−0.821075	+	0.570821i	$0.806625\pi$
$678$		0			0
$679$	−8.32592			−0.319519
$680$		0			0
$681$			42.4830i			1.62795i
$682$		0			0
$683$	−12.1284	−	29.2807i	−0.464082	−	1.12039i	−0.966706	−	0.255888i	$-0.917632\pi$
$683$	−12.1284	−	29.2807i	−0.464082	−	1.12039i	0.502624	−	0.864505i	$-0.332368\pi$
$684$		0			0
$685$	37.8526	+	13.2699i	1.44627	+	0.507017i
$686$		0			0
$687$	−29.4618	−	29.4618i	−1.12404	−	1.12404i
$688$		0			0
$689$	−25.3013	+	25.3013i	−0.963902	+	0.963902i
$690$		0			0
$691$	−24.5212	−	10.1570i	−0.932830	−	0.386391i	−0.136079	−	0.990698i	$-0.543450\pi$
$691$	−24.5212	−	10.1570i	−0.932830	−	0.386391i	−0.796752	+	0.604307i	$0.793450\pi$
$692$		0			0
$693$	3.93817	+	3.93817i	0.149599	+	0.149599i
$694$		0			0
$695$	22.2134	+	19.8744i	0.842603	+	0.753878i
$696$		0			0
$697$	−1.16665	−	0.182973i	−0.0441901	−	0.00693059i
$698$		0			0
$699$	−27.5548	+	27.5548i	−1.04222	+	1.04222i
$700$		0			0
$701$			34.4360i			1.30063i	0.759665	+	0.650314i	$0.225363\pi$
$701$			34.4360i			1.30063i	−0.759665	+	0.650314i	$0.774637\pi$
$702$		0			0
$703$	−5.92420	+	2.45388i	−0.223435	+	0.0925500i
$704$		0			0
$705$	44.5376	−	49.7793i	1.67738	−	1.87480i
$706$		0			0
$707$	7.25179	−	7.25179i	0.272732	−	0.272732i
$708$		0			0
$709$	17.3721	+	41.9399i	0.652422	+	1.57509i	0.809252	+	0.587461i	$0.199872\pi$
$709$	17.3721	+	41.9399i	0.652422	+	1.57509i	−0.156830	+	0.987626i	$0.550128\pi$
$710$		0			0
$711$	−5.22618	+	12.6171i	−0.195997	+	0.473179i
$712$		0			0
$713$	3.04856	+	3.04856i	0.114170	+	0.114170i
$714$		0			0
$715$	10.7562	+	9.62355i	0.402258	+	0.359901i
$716$		0			0
$717$	44.8960			1.67667
$718$		0			0
$719$	9.15213	−	22.0952i	0.341317	−	0.824012i	−0.656266	−	0.754529i	$-0.727865\pi$
$719$	9.15213	−	22.0952i	0.341317	−	0.824012i	0.997583	−	0.0694827i	$-0.0221349\pi$
$720$		0			0
$721$	13.2368	+	5.48287i	0.492964	+	0.204193i
$722$		0			0
$723$	8.56768	−	3.54885i	0.318636	−	0.131983i
$724$		0			0
$725$	4.31979	+	7.83759i	0.160433	+	0.291081i
$726$		0			0
$727$	3.53535	+	1.46439i	0.131119	+	0.0543112i	0.447278	−	0.894395i	$-0.352393\pi$
$727$	3.53535	+	1.46439i	0.131119	+	0.0543112i	−0.316159	+	0.948706i	$0.602393\pi$
$728$		0			0
$729$	−10.0677	+	10.0677i	−0.372877	+	0.372877i
$730$		0			0
$731$	2.04039	−	0.845156i	0.0754664	−	0.0312592i
$732$		0			0
$733$			16.8384i			0.621939i	0.950420	+	0.310970i	$0.100654\pi$
$733$			16.8384i			0.621939i	−0.950420	+	0.310970i	$0.899346\pi$
$734$		0			0
$735$	−7.73059	+	22.0516i	−0.285147	+	0.813386i
$736$		0			0
$737$	−4.36671	−	4.36671i	−0.160850	−	0.160850i
$738$		0			0
$739$			48.2723i			1.77573i	0.460107	+	0.887863i	$0.347811\pi$
$739$			48.2723i			1.77573i	−0.460107	+	0.887863i	$0.652189\pi$
$740$		0			0
$741$	−5.42243	−	13.0909i	−0.199198	−	0.480906i
$742$		0			0
$743$	35.3649			1.29741			0.648706	−	0.761039i	$-0.275310\pi$
$743$	35.3649			1.29741			0.648706	+	0.761039i	$0.275310\pi$
$744$		0			0
$745$	21.6768	−	10.4235i	0.794176	−	0.381886i
$746$		0			0
$747$		−	22.2828i		−	0.815286i
$748$		0			0
$749$	7.72712	+	18.6549i	0.282343	+	0.681636i
$750$		0			0
$751$	−12.4521	−	30.0621i	−0.454385	−	1.09698i	−0.970638	−	0.240546i	$-0.922674\pi$
$751$	−12.4521	−	30.0621i	−0.454385	−	1.09698i	0.516253	−	0.856436i	$-0.327326\pi$
$752$		0			0
$753$	4.84155	+	11.6885i	0.176436	+	0.425954i
$754$		0			0
$755$	5.84870	−	16.6835i	0.212856	−	0.607174i
$756$		0			0
$757$	−10.1087	−	24.4045i	−0.367406	−	0.886997i	−0.994174	−	0.107790i	$-0.965622\pi$
$757$	−10.1087	−	24.4045i	−0.367406	−	0.886997i	0.626768	−	0.779206i	$-0.284378\pi$
$758$		0			0
$759$	1.59751	+	1.59751i	0.0579860	+	0.0579860i
$760$		0			0
$761$		−	29.7337i		−	1.07785i	−0.842355	−	0.538923i	$-0.818831\pi$
$761$		−	29.7337i		−	1.07785i	0.842355	−	0.538923i	$-0.181169\pi$
$762$		0			0
$763$	3.38472	−	3.38472i	0.122535	−	0.122535i
$764$		0			0
$765$	−0.419379	−	0.872147i	−0.0151627	−	0.0315325i
$766$		0			0
$767$	0.306082	+	0.126783i	0.0110520	+	0.00457788i
$768$		0			0
$769$	−33.1135			−1.19410			−0.597052	−	0.802202i	$-0.703661\pi$
$769$	−33.1135			−1.19410			−0.597052	+	0.802202i	$0.703661\pi$
$770$		0			0
$771$	25.7089	+	25.7089i	0.925882	+	0.925882i
$772$		0			0
$773$	3.63829	+	8.78360i	0.130860	+	0.315924i	0.975705	−	0.219086i	$-0.0703076\pi$
$773$	3.63829	+	8.78360i	0.130860	+	0.315924i	−0.844845	+	0.535011i	$0.820308\pi$
$774$		0			0
$775$	33.0421	−	3.68403i	1.18691	−	0.132334i
$776$		0			0
$777$			16.3228i			0.585578i
$778$		0			0
$779$	−7.40297	+	5.39568i	−0.265239	+	0.193320i
$780$		0			0
$781$	−3.72833	−	3.72833i	−0.133410	−	0.133410i
$782$		0			0
$783$	−1.91201	+	1.91201i	−0.0683298	+	0.0683298i
$784$		0			0
$785$	−9.24491	−	19.2259i	−0.329965	−	0.686200i
$786$		0			0
$787$			32.7988i			1.16915i	0.811340	+	0.584575i	$0.198739\pi$
$787$			32.7988i			1.16915i	−0.811340	+	0.584575i	$0.801261\pi$
$788$		0			0
$789$		−	15.2778i		−	0.543905i
$790$		0			0
$791$	−4.02348	+	1.66658i	−0.143058	+	0.0592567i
$792$		0			0
$793$	−7.60505	+	3.15011i	−0.270063	+	0.111864i
$794$		0			0
$795$	2.39671	+	43.1255i	0.0850025	+	1.52950i
$796$		0			0
$797$	17.2389	−	17.2389i	0.610632	−	0.610632i	−0.332479	−	0.943111i	$-0.607885\pi$
$797$	17.2389	−	17.2389i	0.610632	−	0.610632i	0.943111	+	0.332479i	$0.107885\pi$
$798$		0			0
$799$	−1.68473	+	1.68473i	−0.0596014	+	0.0596014i
$800$		0			0
$801$	−5.21766	−	2.16123i	−0.184357	−	0.0763632i
$802$		0			0
$803$	−3.14250	−	7.58667i	−0.110896	−	0.267728i
$804$		0			0
$805$	0.755426	−	2.15486i	0.0266253	−	0.0759489i
$806$		0			0
$807$	1.38772	−	3.35026i	0.0488502	−	0.117935i
$808$		0			0
$809$	−7.48960	+	3.10230i	−0.263320	+	0.109071i	−0.510438	−	0.859915i	$-0.670517\pi$
$809$	−7.48960	+	3.10230i	−0.263320	+	0.109071i	0.247117	+	0.968986i	$0.420517\pi$
$810$		0			0
$811$	5.69874	+	5.69874i	0.200110	+	0.200110i	0.800047	−	0.599937i	$-0.204808\pi$
$811$	5.69874	+	5.69874i	0.200110	+	0.200110i	−0.599937	+	0.800047i	$0.704808\pi$
$812$		0			0
$813$	1.13406	+	0.469743i	0.0397732	+	0.0164746i
$814$		0			0
$815$	−0.287102	−	5.16601i	−0.0100568	−	0.180957i
$816$		0			0
$817$	6.55609	−	15.8278i	0.229368	−	0.553744i
$818$		0			0
$819$	−15.8307			−0.553171
$820$		0			0
$821$	2.97302			0.103759			0.0518796	−	0.998653i	$-0.483479\pi$
$821$	2.97302			0.103759			0.0518796	+	0.998653i	$0.483479\pi$
$822$		0			0
$823$	7.45013	−	17.9862i	0.259695	−	0.626960i	−0.739223	−	0.673461i	$-0.764807\pi$
$823$	7.45013	−	17.9862i	0.259695	−	0.626960i	0.998918	+	0.0465009i	$0.0148070\pi$
$824$		0			0
$825$	17.3147	−	1.93051i	0.602822	−	0.0672116i
$826$		0			0
$827$	−48.4303	−	20.0605i	−1.68409	−	0.697571i	−0.684577	−	0.728940i	$-0.740013\pi$
$827$	−48.4303	−	20.0605i	−1.68409	−	0.697571i	−0.999508	+	0.0313693i	$0.990013\pi$
$828$		0			0
$829$	37.8392	+	37.8392i	1.31421	+	1.31421i	0.918282	+	0.395926i	$0.129576\pi$
$829$	37.8392	+	37.8392i	1.31421	+	1.31421i	0.395926	+	0.918282i	$0.370424\pi$
$830$		0			0
$831$	35.5030	−	14.7058i	1.23159	−	0.510140i
$832$		0			0
$833$	0.318971	−	0.770064i	0.0110517	−	0.0266811i
$834$		0			0
$835$	0.755668	−	0.363369i	0.0261510	−	0.0125749i
$836$		0			0
$837$	3.84425	+	9.28083i	0.132877	+	0.320792i
$838$		0			0
$839$	−5.31366	−	2.20099i	−0.183448	−	0.0759867i	0.289069	−	0.957308i	$-0.406654\pi$
$839$	−5.31366	−	2.20099i	−0.183448	−	0.0759867i	−0.472517	+	0.881322i	$0.656654\pi$
$840$		0			0
$841$	−18.2409	+	18.2409i	−0.628995	+	0.628995i
$842$		0			0
$843$	22.3685	−	22.3685i	0.770414	−	0.770414i
$844$		0			0
$845$	−11.9373	+	0.663419i	−0.410656	+	0.0228223i
$846$		0			0
$847$	−12.7018	+	5.26126i	−0.436439	+	0.180779i
$848$		0			0
$849$	63.5467	−	26.3219i	2.18092	−	0.903366i
$850$		0			0
$851$			2.90610i			0.0996197i
$852$		0			0
$853$		−	31.1224i		−	1.06561i	−0.846237	−	0.532806i	$-0.821138\pi$
$853$		−	31.1224i		−	1.06561i	0.846237	−	0.532806i	$-0.178862\pi$
$854$		0			0
$855$	−7.08428	−	2.48352i	−0.242277	−	0.0849347i
$856$		0			0
$857$	3.38066	−	3.38066i	0.115481	−	0.115481i	−0.647005	−	0.762486i	$-0.723979\pi$
$857$	3.38066	−	3.38066i	0.115481	−	0.115481i	0.762486	+	0.647005i	$0.223979\pi$
$858$		0			0
$859$	−27.3952	−	27.3952i	−0.934712	−	0.934712i	0.0632836	−	0.997996i	$-0.479843\pi$
$859$	−27.3952	−	27.3952i	−0.934712	−	0.934712i	−0.997996	+	0.0632836i	$0.979843\pi$
$860$		0			0
$861$	5.47793	+	22.6663i	0.186688	+	0.772465i
$862$		0			0
$863$		−	11.9866i		−	0.408028i	−0.978968	−	0.204014i	$-0.934601\pi$
$863$		−	11.9866i		−	0.408028i	0.978968	−	0.204014i	$-0.0653988\pi$
$864$		0			0
$865$	24.2655	−	27.1213i	0.825050	−	0.922151i
$866$		0			0
$867$	−15.0127	−	36.2439i	−0.509859	−	1.23091i
$868$		0			0
$869$	6.20113	+	6.20113i	0.210359	+	0.210359i
$870$		0			0
$871$	17.5534			0.594774
$872$		0			0
$873$	11.4609	+	4.74727i	0.387894	+	0.160671i
$874$		0			0
$875$	−9.34241	−	14.9261i	−0.315831	−	0.504595i
$876$		0			0
$877$	26.7866	−	26.7866i	0.904519	−	0.904519i	−0.0913041	−	0.995823i	$-0.529104\pi$
$877$	26.7866	−	26.7866i	0.904519	−	0.904519i	0.995823	+	0.0913041i	$0.0291035\pi$
$878$		0			0
$879$			45.2913i			1.52764i
$880$		0			0
$881$	−5.31578	−	5.31578i	−0.179093	−	0.179093i	0.611867	−	0.790960i	$-0.290419\pi$
$881$	−5.31578	−	5.31578i	−0.179093	−	0.179093i	−0.790960	+	0.611867i	$0.790419\pi$
$882$		0			0
$883$	18.2598	+	44.0831i	0.614492	+	1.48351i	0.858018	+	0.513620i	$0.171696\pi$
$883$	18.2598	+	44.0831i	0.614492	+	1.48351i	−0.243526	+	0.969894i	$0.578304\pi$
$884$		0			0
$885$	0.360412	−	0.173307i	0.0121151	−	0.00582566i
$886$		0			0
$887$	−12.7795	−	30.8524i	−0.429094	−	1.03592i	−0.979576	−	0.201076i	$-0.935556\pi$
$887$	−12.7795	−	30.8524i	−0.429094	−	1.03592i	0.550482	−	0.834847i	$-0.314444\pi$
$888$		0			0
$889$	−1.99280	−	4.81104i	−0.0668364	−	0.161357i
$890$		0			0
$891$	6.07418	+	14.6644i	0.203493	+	0.491275i
$892$		0			0
$893$			18.4822i			0.618482i
$894$		0			0
$895$	14.9944	+	31.1827i	0.501209	+	1.04232i
$896$		0			0
$897$	−6.42171			−0.214414
$898$		0			0
$899$	−4.55444	−	10.9954i	−0.151899	−	0.366717i
$900$		0			0
$901$		−	1.54065i		−	0.0513265i
$902$		0			0
$903$	−30.8369	−	30.8369i	−1.02619	−	1.02619i
$904$		0			0
$905$	−23.5747	−	49.0262i	−0.783649	−	1.62969i
$906$		0			0
$907$			56.1058i			1.86296i	0.363789	+	0.931481i	$0.381483\pi$
$907$			56.1058i			1.86296i	−0.363789	+	0.931481i	$0.618517\pi$
$908$		0			0
$909$	−14.1172	+	5.84753i	−0.468238	+	0.193950i
$910$		0			0
$911$	15.6177	−	15.6177i	0.517438	−	0.517438i	−0.399357	−	0.916795i	$-0.630767\pi$
$911$	15.6177	−	15.6177i	0.517438	−	0.517438i	0.916795	+	0.399357i	$0.130767\pi$
$912$		0			0
$913$	−13.2198	−	5.47584i	−0.437513	−	0.181224i
$914$		0			0
$915$	−3.28727	+	9.37697i	−0.108674	+	0.309993i
$916$		0			0
$917$	9.82943	−	4.07148i	0.324596	−	0.134452i
$918$		0			0
$919$	−20.2659	−	8.39442i	−0.668511	−	0.276906i	0.0225038	−	0.999747i	$-0.492836\pi$
$919$	−20.2659	−	8.39442i	−0.668511	−	0.276906i	−0.691015	+	0.722840i	$0.742836\pi$
$920$		0			0
$921$	−19.4354	+	46.9212i	−0.640418	+	1.54611i
$922$		0			0
$923$	14.9872			0.493310
$924$		0			0
$925$	17.5049	+	13.9930i	0.575558	+	0.460089i
$926$		0			0
$927$	−15.0947	−	15.0947i	−0.495776	−	0.495776i
$928$		0			0
$929$	9.96672	−	24.0618i	0.326997	−	0.789442i	−0.671815	−	0.740719i	$-0.734485\pi$
$929$	9.96672	−	24.0618i	0.326997	−	0.789442i	0.998812	−	0.0487226i	$-0.0155150\pi$
$930$		0			0
$931$	−2.47434	−	5.97358i	−0.0810931	−	0.195776i
$932$		0			0
$933$	−41.5875	+	41.5875i	−1.36151	+	1.36151i
$934$		0			0
$935$	−0.620483	+	0.0344835i	−0.0202920	+	0.00112773i
$936$		0			0
$937$	51.4402	−	21.3072i	1.68048	−	0.696076i	0.681129	−	0.732164i	$-0.261489\pi$
$937$	51.4402	−	21.3072i	1.68048	−	0.696076i	0.999349	+	0.0360874i	$0.0114895\pi$
$938$		0			0
$939$		−	8.66440i		−	0.282752i
$940$		0			0
$941$	2.58682	−	2.58682i	0.0843280	−	0.0843280i	−0.663685	−	0.748013i	$-0.731008\pi$
$941$	2.58682	−	2.58682i	0.0843280	−	0.0843280i	0.748013	+	0.663685i	$0.231008\pi$
$942$		0			0
$943$	0.975285	+	4.03548i	0.0317597	+	0.131413i
$944$		0			0
$945$	3.54759	−	3.96511i	0.115403	−	0.128985i
$946$		0			0
$947$	25.5399	+	25.5399i	0.829937	+	0.829937i	0.987508	−	0.157571i	$-0.0503664\pi$
$947$	25.5399	+	25.5399i	0.829937	+	0.829937i	−0.157571	+	0.987508i	$0.550366\pi$
$948$		0			0
$949$	21.5647	+	8.93237i	0.700018	+	0.289957i
$950$		0			0
$951$	−13.1678	+	13.1678i	−0.426996	+	0.426996i
$952$		0			0
$953$	31.1622	+	31.1622i	1.00944	+	1.00944i	0.999955	+	0.00948891i	$0.00302046\pi$
$953$	31.1622	+	31.1622i	1.00944	+	1.00944i	0.00948891	+	0.999955i	$0.496980\pi$
$954$		0			0
$955$	−40.0159	+	19.2420i	−1.29488	+	0.622655i
$956$		0			0
$957$	−2.38662	−	5.76181i	−0.0771484	−	0.186253i
$958$		0			0
$959$			28.2524i			0.912317i
$960$		0			0
$961$	−13.2141			−0.426261
$962$		0			0
$963$		−	30.0850i		−	0.969476i
$964$		0			0
$965$	7.33757	+	15.2593i	0.236205	+	0.491215i
$966$		0			0
$967$	22.5462	−	9.33892i	0.725036	−	0.300320i	0.0105254	−	0.999945i	$-0.496650\pi$
$967$	22.5462	−	9.33892i	0.725036	−	0.300320i	0.714510	+	0.699625i	$0.246650\pi$
$968$		0			0
$969$	0.563659	+	0.233475i	0.0181073	+	0.00750030i
$970$		0			0
$971$	3.68538	−	1.52654i	0.118270	−	0.0489889i	−0.322764	−	0.946480i	$-0.604612\pi$
$971$	3.68538	−	1.52654i	0.118270	−	0.0489889i	0.441034	+	0.897491i	$0.354612\pi$
$972$		0			0
$973$	−8.03415	+	19.3962i	−0.257563	+	0.621812i
$974$		0			0
$975$	−30.9209	+	38.6812i	−0.990262	+	1.23879i
$976$		0			0
$977$	3.80550	−	9.18730i	0.121749	−	0.293928i	−0.851241	−	0.524775i	$-0.824150\pi$
$977$	3.80550	−	9.18730i	0.121749	−	0.293928i	0.972990	+	0.230847i	$0.0741496\pi$
$978$		0			0
$979$	−2.56441	+	2.56441i	−0.0819588	+	0.0819588i
$980$		0			0
$981$	−6.58910	+	2.72929i	−0.210374	+	0.0871396i
$982$		0			0
$983$	−12.1643	+	12.1643i	−0.387982	+	0.387982i	−0.873967	−	0.485985i	$-0.838461\pi$
$983$	−12.1643	+	12.1643i	−0.387982	+	0.387982i	0.485985	+	0.873967i	$0.338461\pi$
$984$		0			0
$985$	−4.78879	+	5.35239i	−0.152584	+	0.170541i
$986$		0			0
$987$	43.4659	+	18.0042i	1.38354	+	0.573080i
$988$		0			0
$989$	−5.49017	−	5.49017i	−0.174577	−	0.174577i
$990$		0			0
$991$	17.6998	+	42.7311i	0.562252	+	1.35740i	0.907961	+	0.419055i	$0.137639\pi$
$991$	17.6998	+	42.7311i	0.562252	+	1.35740i	−0.345708	+	0.938342i	$0.612361\pi$
$992$		0			0
$993$	−1.48021			−0.0469731
$994$		0			0
$995$	−5.18034	−	10.7731i	−0.164228	−	0.341531i
$996$		0			0
$997$	−18.8832	−	7.82168i	−0.598037	−	0.247715i	0.0630669	−	0.998009i	$-0.479912\pi$
$997$	−18.8832	−	7.82168i	−0.598037	−	0.247715i	−0.661104	+	0.750294i	$0.729912\pi$
$998$		0			0
$999$	−2.59126	+	6.25586i	−0.0819838	+	0.197926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.793.18	yes	84
5.2	odd	4		820.2.y.a.137.4	yes	84
41.3	odd	8		820.2.y.a.413.4	yes	84
205.167	even	8	inner	820.2.x.a.577.18	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.18	✓	84	205.167	even	8	inner
820.2.x.a.793.18	yes	84	1.1	even	1	trivial
820.2.y.a.137.4	yes	84	5.2	odd	4
820.2.y.a.413.4	yes	84	41.3	odd	8

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.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.884872 - 2.13627i) q^{3} +(1.49097 - 1.66644i) q^{5} +(1.45509 + 0.602718i) q^{7} +(-1.65933 - 1.65933i) q^{9} +(-1.39221 + 0.576671i) q^{11} +(1.63915 - 3.95726i) q^{13} +(-2.24065 - 4.65969i) q^{15} +(0.0705774 + 0.170389i) q^{17} +(1.32175 + 0.547487i) q^{19} +(2.57514 - 2.57514i) q^{21} +(0.458474 - 0.458474i) q^{23} +(-0.554042 - 4.96921i) q^{25} +(1.39575 - 0.578137i) q^{27} +(-1.65360 + 0.684943i) q^{29} +6.64937i q^{31} +3.48441i q^{33} +(3.17388 - 1.52619i) q^{35} +(-3.16931 + 3.16931i) q^{37} +(-7.00334 - 7.00334i) q^{39} +(-3.33737 + 5.46461i) q^{41} -11.9749i q^{43} +(-5.23917 + 0.291168i) q^{45} +(4.94377 + 11.9353i) q^{47} +(-3.19573 - 3.19573i) q^{49} +0.426449 q^{51} +(-7.71780 - 3.19682i) q^{53} +(-1.11474 + 3.17982i) q^{55} +(2.33916 - 2.33916i) q^{57} +0.0773468i q^{59} +(-1.35891 - 1.35891i) q^{61} +(-1.41436 - 3.41458i) q^{63} +(-4.15062 - 8.63169i) q^{65} +(1.56827 + 3.78614i) q^{67} +(-0.573734 - 1.38512i) q^{69} +(1.33900 + 3.23263i) q^{71} +5.44939i q^{73} +(-11.1058 - 3.21353i) q^{75} -2.37335 q^{77} +(-2.22709 - 5.37666i) q^{79} -10.5332i q^{81} +(6.71441 + 6.71441i) q^{83} +(0.389172 + 0.136431i) q^{85} +4.13862i q^{87} +(2.22346 - 0.920987i) q^{89} +(4.77023 - 4.77023i) q^{91} +(14.2048 + 5.88384i) q^{93} +(2.88304 - 1.38633i) q^{95} +(-4.88397 + 2.02301i) q^{97} +(3.26701 + 1.35324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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