LMFDB - Embedded newform 820.2.y.a.413.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (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			413.4
Character	$\chi$	$=$	820.413
Dual form			820.2.y.a.137.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.13627 + 0.884872i) q^{3} +(1.66644 + 1.49097i) q^{5} +(-0.602718 - 1.45509i) q^{7} +(1.65933 - 1.65933i) q^{9} +(-1.39221 - 0.576671i) q^{11} +(-3.95726 + 1.63915i) q^{13} +(-4.87928 - 1.71052i) q^{15} +(-0.170389 - 0.0705774i) q^{17} +(-1.32175 + 0.547487i) q^{19} +(2.57514 + 2.57514i) q^{21} +(-0.458474 + 0.458474i) q^{23} +(0.554042 + 4.96921i) q^{25} +(0.578137 - 1.39575i) q^{27} +(1.65360 + 0.684943i) q^{29} -6.64937i q^{31} +3.48441 q^{33} +(1.16510 - 3.32345i) q^{35} +(-3.16931 + 3.16931i) q^{37} +(7.00334 - 7.00334i) q^{39} +(-3.33737 - 5.46461i) q^{41} -11.9749 q^{43} +(5.23917 - 0.291168i) q^{45} +(-11.9353 - 4.94377i) q^{47} +(3.19573 - 3.19573i) q^{49} +0.426449 q^{51} +(-3.19682 - 7.71780i) q^{53} +(-1.46023 - 3.03672i) q^{55} +(2.33916 - 2.33916i) q^{57} +0.0773468i q^{59} +(-1.35891 + 1.35891i) q^{61} +(-3.41458 - 1.41436i) q^{63} +(-9.03846 - 3.16860i) q^{65} +(-3.78614 - 1.56827i) q^{67} +(0.573734 - 1.38512i) q^{69} +(1.33900 - 3.23263i) q^{71} +5.44939 q^{73} +(-5.58069 - 10.1253i) q^{75} +2.37335i q^{77} +(2.22709 - 5.37666i) q^{79} +10.5332i q^{81} +(6.71441 + 6.71441i) q^{83} +(-0.178714 - 0.371657i) q^{85} -4.13862 q^{87} +(-2.22346 - 0.920987i) q^{89} +(4.77023 + 4.77023i) q^{91} +(5.88384 + 14.2048i) q^{93} +(-3.01890 - 1.05833i) q^{95} +(-2.02301 + 4.88397i) q^{97} +(-3.26701 + 1.35324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

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

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
$3$	−2.13627	+	0.884872i	−1.23338	+	0.510881i	−0.901638	−	0.432491i	$-0.857635\pi$
$3$	−2.13627	+	0.884872i	−1.23338	+	0.510881i	−0.331737	+	0.943372i	$0.607635\pi$
$4$		0			0
$5$	1.66644	+	1.49097i	0.745254	+	0.666780i
$5$	1.66644	+	1.49097i	0.745254	+	0.666780i
$6$		0			0
$7$	−0.602718	−	1.45509i	−0.227806	−	0.549972i	0.768104	−	0.640325i	$-0.221200\pi$
$7$	−0.602718	−	1.45509i	−0.227806	−	0.549972i	−0.995910	+	0.0903530i	$0.971200\pi$
$8$		0			0
$9$	1.65933	−	1.65933i	0.553109	−	0.553109i
$10$		0			0
$11$	−1.39221	−	0.576671i	−0.419766	−	0.173873i	0.162795	−	0.986660i	$-0.447949\pi$
$11$	−1.39221	−	0.576671i	−0.419766	−	0.173873i	−0.582561	+	0.812787i	$0.697949\pi$
$12$		0			0
$13$	−3.95726	+	1.63915i	−1.09755	+	0.454619i	−0.856633	−	0.515927i	$-0.827448\pi$
$13$	−3.95726	+	1.63915i	−1.09755	+	0.454619i	−0.240915	+	0.970546i	$0.577448\pi$
$14$		0			0
$15$	−4.87928	−	1.71052i	−1.25982	−	0.441654i
$16$		0			0
$17$	−0.170389	−	0.0705774i	−0.0413254	−	0.0171175i	0.361925	−	0.932207i	$-0.382120\pi$
$17$	−0.170389	−	0.0705774i	−0.0413254	−	0.0171175i	−0.403250	+	0.915090i	$0.632120\pi$
$18$		0			0
$19$	−1.32175	+	0.547487i	−0.303230	+	0.125602i	−0.529110	−	0.848553i	$-0.677474\pi$
$19$	−1.32175	+	0.547487i	−0.303230	+	0.125602i	0.225880	+	0.974155i	$0.427474\pi$
$20$		0			0
$21$	2.57514	+	2.57514i	0.561941	+	0.561941i
$22$		0			0
$23$	−0.458474	+	0.458474i	−0.0955985	+	0.0955985i	−0.753289	−	0.657690i	$-0.771534\pi$
$23$	−0.458474	+	0.458474i	−0.0955985	+	0.0955985i	0.657690	+	0.753289i	$0.271534\pi$
$24$		0			0
$25$	0.554042	+	4.96921i	0.110808	+	0.993842i
$26$		0			0
$27$	0.578137	−	1.39575i	0.111263	−	0.268612i
$28$		0			0
$29$	1.65360	+	0.684943i	0.307065	+	0.127191i	0.530895	−	0.847438i	$-0.321856\pi$
$29$	1.65360	+	0.684943i	0.307065	+	0.127191i	−0.223829	+	0.974628i	$0.571856\pi$
$30$		0			0
$31$		−	6.64937i		−	1.19426i	−0.802144	−	0.597131i	$-0.796307\pi$
$31$		−	6.64937i		−	1.19426i	0.802144	−	0.597131i	$-0.203693\pi$
$32$		0			0
$33$	3.48441			0.606557
$34$		0			0
$35$	1.16510	−	3.32345i	0.196937	−	0.561766i
$36$		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
$43$	−11.9749			−1.82615			−0.913075	−	0.407791i	$-0.866299\pi$
$43$	−11.9749			−1.82615			−0.913075	+	0.407791i	$0.866299\pi$
$44$		0			0
$45$	5.23917	−	0.291168i	0.781009	−	0.0434048i
$46$		0			0
$47$	−11.9353	−	4.94377i	−1.74094	−	0.721123i	−0.998699	−	0.0509955i	$-0.983761\pi$
$47$	−11.9353	−	4.94377i	−1.74094	−	0.721123i	−0.742246	−	0.670127i	$-0.766239\pi$
$48$		0			0
$49$	3.19573	−	3.19573i	0.456533	−	0.456533i
$50$		0			0
$51$	0.426449			0.0597148
$52$		0			0
$53$	−3.19682	−	7.71780i	−0.439116	−	1.06012i	−0.976255	−	0.216626i	$-0.930495\pi$
$53$	−3.19682	−	7.71780i	−0.439116	−	1.06012i	0.537138	−	0.843494i	$-0.319505\pi$
$54$		0			0
$55$	−1.46023	−	3.03672i	−0.196897	−	0.409471i
$56$		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	−0.788730	−	0.614739i	$-0.789261\pi$
$61$	−1.35891	+	1.35891i	−0.173991	+	0.173991i	0.614739	+	0.788730i	$0.289261\pi$
$62$		0			0
$63$	−3.41458	−	1.41436i	−0.430196	−	0.178193i
$64$		0			0
$65$	−9.03846	−	3.16860i	−1.12108	−	0.393016i
$66$		0			0
$67$	−3.78614	−	1.56827i	−0.462551	−	0.191595i	0.139224	−	0.990261i	$-0.455539\pi$
$67$	−3.78614	−	1.56827i	−0.462551	−	0.191595i	−0.601774	+	0.798666i	$0.705539\pi$
$68$		0			0
$69$	0.573734	−	1.38512i	0.0690694	−	0.166748i
$70$		0			0
$71$	1.33900	−	3.23263i	0.158910	−	0.383643i	−0.824292	−	0.566166i	$-0.808426\pi$
$71$	1.33900	−	3.23263i	0.158910	−	0.383643i	0.983202	+	0.182523i	$0.0584263\pi$
$72$		0			0
$73$	5.44939			0.637802			0.318901	−	0.947788i	$-0.396686\pi$
$73$	5.44939			0.637802			0.318901	+	0.947788i	$0.396686\pi$
$74$		0			0
$75$	−5.58069	−	10.1253i	−0.644403	−	1.16917i
$76$		0			0
$77$			2.37335i			0.270469i
$78$		0			0
$79$	2.22709	−	5.37666i	0.250567	−	0.604922i	−0.747683	−	0.664056i	$-0.768834\pi$
$79$	2.22709	−	5.37666i	0.250567	−	0.604922i	0.998250	+	0.0591337i	$0.0188338\pi$
$80$		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
$85$	−0.178714	−	0.371657i	−0.0193843	−	0.0403119i
$86$		0			0
$87$	−4.13862			−0.443706
$88$		0			0
$89$	−2.22346	−	0.920987i	−0.235686	−	0.0976244i	0.261715	−	0.965145i	$-0.415712\pi$
$89$	−2.22346	−	0.920987i	−0.235686	−	0.0976244i	−0.497401	+	0.867521i	$0.665712\pi$
$90$		0			0
$91$	4.77023	+	4.77023i	0.500056	+	0.500056i
$92$		0			0
$93$	5.88384	+	14.2048i	0.610125	+	1.47297i
$94$		0			0
$95$	−3.01890	−	1.05833i	−0.309733	−	0.108582i
$96$		0			0
$97$	−2.02301	+	4.88397i	−0.205405	+	0.495892i	−0.992689	−	0.120699i	$-0.961487\pi$
$97$	−2.02301	+	4.88397i	−0.205405	+	0.495892i	0.787284	+	0.616590i	$0.211487\pi$
$98$		0			0
$99$	−3.26701	+	1.35324i	−0.328347	+	0.136006i
$100$		0			0
$101$	2.49187	+	6.01591i	0.247950	+	0.598605i	0.998030	−	0.0627426i	$-0.0199847\pi$
$101$	2.49187	+	6.01591i	0.247950	+	0.598605i	−0.750079	+	0.661348i	$0.769985\pi$
$102$		0			0
$103$			9.09690i			0.896344i	0.893947	+	0.448172i	$0.147925\pi$
$103$			9.09690i			0.896344i	−0.893947	+	0.448172i	$0.852075\pi$
$104$		0			0
$105$	0.451869	+	8.13075i	0.0440979	+	0.793480i
$106$		0			0
$107$	−9.06543	−	9.06543i	−0.876388	−	0.876388i	0.116771	−	0.993159i	$-0.462746\pi$
$107$	−9.06543	−	9.06543i	−0.876388	−	0.876388i	−0.993159	+	0.116771i	$0.962746\pi$
$108$		0			0
$109$	−1.16306	−	2.80788i	−0.111401	−	0.268946i	0.858340	−	0.513081i	$-0.171496\pi$
$109$	−1.16306	−	2.80788i	−0.111401	−	0.268946i	−0.969741	+	0.244135i	$0.921496\pi$
$110$		0			0
$111$	3.96607	−	9.57494i	0.376443	−	0.908813i
$112$		0			0
$113$	1.95522	−	1.95522i	0.183932	−	0.183932i	−0.609135	−	0.793067i	$-0.708483\pi$
$113$	1.95522	−	1.95522i	0.183932	−	0.183932i	0.793067	+	0.609135i	$0.208483\pi$
$114$		0			0
$115$	−1.44759	+	0.0804502i	−0.134988	+	0.00750202i
$116$		0			0
$117$	−3.84651	+	9.28629i	−0.355610	+	0.858517i
$118$		0			0
$119$			0.290470i			0.0266273i
$120$		0			0
$121$	−6.17249	−	6.17249i	−0.561135	−	0.561135i
$122$		0			0
$123$	11.9650	+	8.72073i	1.07885	+	0.786322i
$124$		0			0
$125$	−6.48564	+	9.10694i	−0.580094	+	0.814550i
$126$		0			0
$127$	2.33795	+	2.33795i	0.207459	+	0.207459i	0.803187	−	0.595728i	$-0.203136\pi$
$127$	2.33795	+	2.33795i	0.207459	+	0.207459i	−0.595728	+	0.803187i	$0.703136\pi$
$128$		0			0
$129$	25.5815	−	10.5962i	2.25233	−	0.932945i
$130$		0			0
$131$	4.77665	+	4.77665i	0.417338	+	0.417338i	0.884285	−	0.466947i	$-0.154646\pi$
$131$	4.77665	+	4.77665i	0.417338	+	0.417338i	−0.466947	+	0.884285i	$0.654646\pi$
$132$		0			0
$133$	1.59329	+	1.59329i	0.138155	+	0.138155i
$134$		0			0
$135$	3.04444	−	1.46394i	0.262024	−	0.125996i
$136$		0			0
$137$	−16.5728	−	6.86468i	−1.41591	−	0.586489i	−0.462081	−	0.886838i	$-0.652897\pi$
$137$	−16.5728	−	6.86468i	−1.41591	−	0.586489i	−0.953829	+	0.300349i	$0.902897\pi$
$138$		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
$143$	6.45458			0.539759
$144$		0			0
$145$	1.73440	+	3.60687i	0.144034	+	0.299535i
$146$		0			0
$147$	−3.99913	+	9.65475i	−0.329842	+	0.796310i
$148$		0			0
$149$	−9.93788	+	4.11640i	−0.814143	+	0.337229i	−0.750606	−	0.660750i	$-0.770238\pi$
$149$	−9.93788	+	4.11640i	−0.814143	+	0.337229i	−0.0635372	+	0.997979i	$0.520238\pi$
$150$		0			0
$151$	7.30445	+	3.02560i	0.594428	+	0.246220i	0.659554	−	0.751657i	$-0.270745\pi$
$151$	7.30445	+	3.02560i	0.594428	+	0.246220i	−0.0651266	+	0.997877i	$0.520745\pi$
$152$		0			0
$153$	−0.399842	+	0.165620i	−0.0323253	+	0.0133896i
$154$		0			0
$155$	9.91398	−	11.0808i	0.796310	−	0.890029i
$156$		0			0
$157$	8.81424	−	3.65098i	0.703453	−	0.291380i	−0.00213951	−	0.999998i	$-0.500681\pi$
$157$	8.81424	−	3.65098i	0.703453	−	0.291380i	0.705592	+	0.708618i	$0.250681\pi$
$158$		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	−0.768274	−	0.640121i	$-0.778884\pi$
$163$	−1.63616	+	1.63616i	−0.128154	+	0.128154i	0.640121	+	0.768274i	$0.278884\pi$
$164$		0			0
$165$	5.80655	+	5.19513i	0.452039	+	0.404440i
$166$		0			0
$167$	−0.143501	−	0.346441i	−0.0111044	−	0.0268084i	0.918230	−	0.396047i	$-0.129618\pi$
$167$	−0.143501	−	0.346441i	−0.0111044	−	0.0268084i	−0.929334	+	0.369239i	$0.879618\pi$
$168$		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
$173$			16.2750i			1.23736i	0.785641	+	0.618682i	$0.212333\pi$
$173$			16.2750i			1.23736i	−0.785641	+	0.618682i	$0.787667\pi$
$174$		0			0
$175$	6.89672	−	3.80121i	0.521343	−	0.287345i
$176$		0			0
$177$	−0.0684420	−	0.165234i	−0.00514442	−	0.0124197i
$178$		0			0
$179$	5.92157	+	14.2959i	0.442599	+	1.06853i	0.975034	+	0.222057i	$0.0712770\pi$
$179$	5.92157	+	14.2959i	0.442599	+	1.06853i	−0.532435	+	0.846471i	$0.678723\pi$
$180$		0			0
$181$	9.31005	+	22.4764i	0.692010	+	1.67066i	0.740691	+	0.671846i	$0.234498\pi$
$181$	9.31005	+	22.4764i	0.692010	+	1.67066i	−0.0486802	+	0.998814i	$0.515502\pi$
$182$		0			0
$183$	1.70054	−	4.10547i	0.125708	−	0.303485i
$184$		0			0
$185$	−10.0068	+	0.556131i	−0.735715	+	0.0408876i
$186$		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	−0.929924	−	0.367753i	$-0.880127\pi$
$191$	−18.3456	+	7.59898i	−1.32744	+	0.549843i	−0.397515	+	0.917596i	$0.630127\pi$
$192$		0			0
$193$	6.99575	−	2.89773i	0.503565	−	0.208583i	−0.116416	−	0.993201i	$-0.537140\pi$
$193$	6.99575	−	2.89773i	0.503565	−	0.208583i	0.619981	+	0.784617i	$0.287140\pi$
$194$		0			0
$195$	22.1124	−	1.22890i	1.58350	−	0.0880035i
$196$		0			0
$197$			3.21187i			0.228837i	0.993433	+	0.114418i	$0.0365004\pi$
$197$			3.21187i			0.228837i	−0.993433	+	0.114418i	$0.963500\pi$
$198$		0			0
$199$	−2.04581	−	4.93901i	−0.145023	−	0.350117i	0.834631	−	0.550809i	$-0.185681\pi$
$199$	−2.04581	−	4.93901i	−0.145023	−	0.350117i	−0.979654	+	0.200692i	$0.935681\pi$
$200$		0			0
$201$	9.47593			0.668381
$202$		0			0
$203$		−	2.81896i		−	0.197852i
$204$		0			0
$205$	2.58602	−	14.0823i	0.180616	−	0.983554i
$206$		0			0
$207$			1.52152i			0.105753i
$208$		0			0
$209$	2.15587			0.149125
$210$		0			0
$211$	−4.51324	−	10.8959i	−0.310704	−	0.750106i	−0.999679	−	0.0253212i	$-0.991939\pi$
$211$	−4.51324	−	10.8959i	−0.310704	−	0.750106i	0.688975	−	0.724785i	$-0.258061\pi$
$212$		0			0
$213$			8.09061i			0.554360i
$214$		0			0
$215$	−19.9554	−	17.8541i	−1.36095	−	1.21764i
$216$		0			0
$217$	−9.67543	+	4.00769i	−0.656811	+	0.272060i
$218$		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
$225$	9.16488	+	7.32621i	0.610992	+	0.488414i
$226$		0			0
$227$	−7.03095	+	16.9742i	−0.466660	+	1.12662i	0.498951	+	0.866630i	$0.333719\pi$
$227$	−7.03095	+	16.9742i	−0.466660	+	1.12662i	−0.965612	+	0.259988i	$0.916281\pi$
$228$		0			0
$229$	−6.89561	−	16.6475i	−0.455675	−	1.10010i	−0.970131	−	0.242580i	$-0.922006\pi$
$229$	−6.89561	−	16.6475i	−0.455675	−	1.10010i	0.514456	−	0.857516i	$-0.327994\pi$
$230$		0			0
$231$	−2.10011	−	5.07012i	−0.138177	−	0.333590i
$232$		0			0
$233$	−6.44929	−	15.5700i	−0.422507	−	1.02002i	−0.981605	−	0.190921i	$-0.938853\pi$
$233$	−6.44929	−	15.5700i	−0.422507	−	1.02002i	0.559098	−	0.829101i	$-0.311147\pi$
$234$		0			0
$235$	−12.5185	−	26.0336i	−0.816616	−	1.69825i
$236$		0			0
$237$			13.4567i			0.874106i
$238$		0			0
$239$	−7.43031	+	17.9384i	−0.480627	+	1.16034i	0.478685	+	0.877987i	$0.341114\pi$
$239$	−7.43031	+	17.9384i	−0.480627	+	1.16034i	−0.959312	+	0.282349i	$0.908886\pi$
$240$		0			0
$241$	2.83591	−	2.83591i	0.182677	−	0.182677i	−0.609844	−	0.792521i	$-0.708768\pi$
$241$	2.83591	−	2.83591i	0.182677	−	0.182677i	0.792521	+	0.609844i	$0.208768\pi$
$242$		0			0
$243$	−7.58611	−	18.3145i	−0.486649	−	1.17488i
$244$		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	0.574383	−	0.818587i	$-0.305242\pi$
$251$	−3.86891	−	3.86891i	−0.244204	−	0.244204i	−0.818587	+	0.574383i	$0.805242\pi$
$252$		0			0
$253$	0.902679	−	0.373902i	0.0567510	−	0.0235070i
$254$		0			0
$255$	0.710651	+	0.635821i	0.0445027	+	0.0398166i
$256$		0			0
$257$	−14.5269	+	6.01724i	−0.906163	+	0.375345i	−0.786586	−	0.617480i	$-0.788154\pi$
$257$	−14.5269	+	6.01724i	−0.906163	+	0.375345i	−0.119576	+	0.992825i	$0.538154\pi$
$258$		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
$263$	−2.52849	+	6.10431i	−0.155913	+	0.376408i	−0.982463	−	0.186455i	$-0.940300\pi$
$263$	−2.52849	+	6.10431i	−0.155913	+	0.376408i	0.826550	+	0.562863i	$0.190300\pi$
$264$		0			0
$265$	6.17967	−	17.6276i	0.379614	−	1.08285i
$266$		0			0
$267$	5.56486			0.340564
$268$		0			0
$269$	−1.56828			−0.0956195			−0.0478098	−	0.998856i	$-0.515224\pi$
$269$	−1.56828			−0.0956195			−0.0478098	+	0.998856i	$0.515224\pi$
$270$		0			0
$271$		−	0.530860i		−	0.0322474i	−0.999870	−	0.0161237i	$-0.994867\pi$
$271$		−	0.530860i		−	0.0322474i	0.999870	−	0.0161237i	$-0.00513256\pi$
$272$		0			0
$273$	−14.4115	−	5.96945i	−0.872226	−	0.361288i
$274$		0			0
$275$	2.09426	−	7.23766i	0.126288	−	0.436447i
$276$		0			0
$277$	−11.7515	−	11.7515i	−0.706081	−	0.706081i	0.259628	−	0.965709i	$-0.416400\pi$
$277$	−11.7515	−	11.7515i	−0.706081	−	0.706081i	−0.965709	+	0.259628i	$0.916400\pi$
$278$		0			0
$279$	−11.0335	−	11.0335i	−0.660557	−	0.660557i
$280$		0			0
$281$	12.6394	−	5.23542i	0.754005	−	0.312319i	0.0276306	−	0.999618i	$-0.491204\pi$
$281$	12.6394	−	5.23542i	0.754005	−	0.312319i	0.726375	+	0.687299i	$0.241204\pi$
$282$		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
$285$	7.38567	−	0.410461i	0.437489	−	0.0243136i
$286$		0			0
$287$	−5.94001	+	8.14979i	−0.350628	+	0.481067i
$288$		0			0
$289$	−11.9968	−	11.9968i	−0.705692	−	0.705692i
$290$		0			0
$291$		−	12.2236i		−	0.716558i
$292$		0			0
$293$	7.49572	−	18.0963i	0.437905	−	1.05720i	−0.538766	−	0.842455i	$-0.681109\pi$
$293$	7.49572	−	18.0963i	0.437905	−	1.05720i	0.976671	−	0.214740i	$-0.0688905\pi$
$294$		0			0
$295$	−0.115322	+	0.128894i	−0.00671428	+	0.00750449i
$296$		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
$307$			21.9641i			1.25356i	0.779198	+	0.626778i	$0.215627\pi$
$307$			21.9641i			1.25356i	−0.779198	+	0.626778i	$0.784373\pi$
$308$		0			0
$309$	−8.04959	−	19.4334i	−0.457925	−	1.10553i
$310$		0			0
$311$	−23.4992	+	9.73369i	−1.33252	+	0.551947i	−0.931372	−	0.364068i	$-0.881388\pi$
$311$	−23.4992	+	9.73369i	−1.33252	+	0.551947i	−0.401145	+	0.916015i	$0.631388\pi$
$312$		0			0
$313$	−1.43396	+	3.46189i	−0.0810523	+	0.195678i	−0.959211	−	0.282693i	$-0.908772\pi$
$313$	−1.43396	+	3.46189i	−0.0810523	+	0.195678i	0.878158	+	0.478370i	$0.158772\pi$
$314$		0			0
$315$	−3.58142	−	7.44797i	−0.201790	−	0.419646i
$316$		0			0
$317$	3.08197	+	7.44053i	0.173101	+	0.417902i	0.986491	−	0.163817i	$-0.0523805\pi$
$317$	3.08197	+	7.44053i	0.173101	+	0.417902i	−0.813390	+	0.581718i	$0.802381\pi$
$318$		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
$323$	0.263852			0.0146811
$324$		0			0
$325$	−10.3378	−	18.7563i	−0.573437	−	1.04041i
$326$		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	−0.930469	−	0.366370i	$-0.880600\pi$
$331$	−0.244976	+	0.591424i	−0.0134651	+	0.0325076i	0.917004	+	0.398878i	$0.130600\pi$
$332$		0			0
$333$			10.5179i			0.576375i
$334$		0			0
$335$	−3.97114	−	8.25844i	−0.216966	−	0.451207i
$336$		0			0
$337$	33.1410			1.80531			0.902653	−	0.430368i	$-0.141616\pi$
$337$	33.1410			1.80531			0.902653	+	0.430368i	$0.141616\pi$
$338$		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
$343$	−16.7618	−	6.94298i	−0.905054	−	0.374886i
$344$		0			0
$345$	3.02125	−	1.45279i	0.162659	−	0.0782158i
$346$		0			0
$347$	−7.22879	−	2.99426i	−0.388062	−	0.160740i	0.180118	−	0.983645i	$-0.442352\pi$
$347$	−7.22879	−	2.99426i	−0.388062	−	0.160740i	−0.568179	+	0.822905i	$0.692352\pi$
$348$		0			0
$349$	3.38718	−	3.38718i	0.181312	−	0.181312i	−0.610616	−	0.791927i	$-0.709078\pi$
$349$	3.38718	−	3.38718i	0.181312	−	0.181312i	0.791927	+	0.610616i	$0.209078\pi$
$350$		0			0
$351$			6.47099i			0.345396i
$352$		0			0
$353$	18.2189	−	18.2189i	0.969692	−	0.969692i	−0.0298623	−	0.999554i	$-0.509507\pi$
$353$	18.2189	−	18.2189i	0.969692	−	0.969692i	0.999554	+	0.0298623i	$0.00950689\pi$
$354$		0			0
$355$	7.05111	−	3.39058i	0.374234	−	0.179953i
$356$		0			0
$357$	−0.257028	−	0.620521i	−0.0136034	−	0.0328415i
$358$		0			0
$359$	4.49903			0.237450			0.118725	−	0.992927i	$-0.462119\pi$
$359$	4.49903			0.237450			0.118725	+	0.992927i	$0.462119\pi$
$360$		0			0
$361$	−11.9877	+	11.9877i	−0.630934	+	0.630934i
$362$		0			0
$363$	18.6479	+	7.72423i	0.978764	+	0.405417i
$364$		0			0
$365$	9.08107	+	8.12485i	0.475325	+	0.425274i
$366$		0			0
$367$	19.3068			1.00781			0.503904	−	0.863760i	$-0.331897\pi$
$367$	19.3068			1.00781			0.503904	+	0.863760i	$0.331897\pi$
$368$		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	−0.140227	−	0.990119i	$-0.544783\pi$
$373$	16.4142	−	16.4142i	0.849893	−	0.849893i	0.990119	+	0.140227i	$0.0447831\pi$
$374$		0			0
$375$	5.79661	−	25.1938i	0.299335	−	1.30100i
$376$		0			0
$377$	−7.66645			−0.394842
$378$		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
$383$	−7.07604	+	17.0831i	−0.361569	+	0.872904i	0.633502	+	0.773741i	$0.281617\pi$
$383$	−7.07604	+	17.0831i	−0.361569	+	0.872904i	−0.995071	+	0.0991635i	$0.968383\pi$
$384$		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	−0.999154	−	0.0411193i	$-0.986908\pi$
$389$	−20.5174	−	20.5174i	−1.04027	−	1.04027i	−0.0411193	−	0.999154i	$-0.513092\pi$
$390$		0			0
$391$	0.110477	−	0.0457611i	0.00558706	−	0.00231424i
$392$		0			0
$393$	−14.4309	−	5.97749i	−0.727944	−	0.301524i
$394$		0			0
$395$	11.7277	−	5.63937i	0.590086	−	0.283748i
$396$		0			0
$397$	26.7218	−	11.0685i	1.34113	−	0.555514i	0.407320	−	0.913286i	$-0.366463\pi$
$397$	26.7218	−	11.0685i	1.34113	−	0.555514i	0.933809	+	0.357772i	$0.116463\pi$
$398$		0			0
$399$	−4.81354	−	1.99383i	−0.240978	−	0.0998165i
$400$		0			0
$401$	−12.5308	+	12.5308i	−0.625757	+	0.625757i	−0.946998	−	0.321241i	$-0.895900\pi$
$401$	−12.5308	+	12.5308i	−0.625757	+	0.625757i	0.321241	+	0.946998i	$0.395900\pi$
$402$		0			0
$403$	10.8993	+	26.3133i	0.542934	+	1.31076i
$404$		0			0
$405$	−15.7046	+	17.5529i	−0.780370	+	0.872212i
$406$		0			0
$407$	6.23999	−	2.58469i	0.309305	−	0.128118i
$408$		0			0
$409$	10.4879			0.518592			0.259296	−	0.965798i	$-0.416509\pi$
$409$	10.4879			0.518592			0.259296	+	0.965798i	$0.416509\pi$
$410$		0			0
$411$	41.4783			2.04597
$412$		0			0
$413$	0.112547	−	0.0466183i	0.00553806	−	0.00229394i
$414$		0			0
$415$	1.17820	+	21.2001i	0.0578357	+	1.04067i
$416$		0			0
$417$	−11.7952	−	28.4762i	−0.577614	−	1.39448i
$418$		0			0
$419$	−3.29605	+	3.29605i	−0.161023	+	0.161023i	−0.783020	−	0.621997i	$-0.786322\pi$
$419$	−3.29605	+	3.29605i	−0.161023	+	0.161023i	0.621997	+	0.783020i	$0.286322\pi$
$420$		0			0
$421$	19.8788	+	8.23406i	0.968833	+	0.401304i	0.810278	−	0.586046i	$-0.199316\pi$
$421$	19.8788	+	8.23406i	0.968833	+	0.401304i	0.158555	+	0.987350i	$0.449316\pi$
$422$		0			0
$423$	−28.0079	+	11.6013i	−1.36179	+	0.564073i
$424$		0			0
$425$	0.256311	−	0.885802i	0.0124329	−	0.0429677i
$426$		0			0
$427$	2.79638	+	1.15830i	0.135327	+	0.0560541i
$428$		0			0
$429$	−13.7887	+	5.71147i	−0.665725	+	0.275752i
$430$		0			0
$431$	−21.6942	−	21.6942i	−1.04497	−	1.04497i	−0.998940	−	0.0460305i	$-0.985343\pi$
$431$	−21.6942	−	21.6942i	−1.04497	−	1.04497i	−0.0460305	−	0.998940i	$-0.514657\pi$
$432$		0			0
$433$	−16.5381	+	16.5381i	−0.794770	+	0.794770i	−0.982266	−	0.187495i	$-0.939963\pi$
$433$	−16.5381	+	16.5381i	−0.794770	+	0.794770i	0.187495	+	0.982266i	$0.439963\pi$
$434$		0			0
$435$	−6.89676	−	6.17054i	−0.330674	−	0.295855i
$436$		0			0
$437$	0.354980	−	0.856997i	0.0169810	−	0.0409957i
$438$		0			0
$439$	0.192509	+	0.0797398i	0.00918795	+	0.00380577i	0.387273	−	0.921965i	$-0.373417\pi$
$439$	0.192509	+	0.0797398i	0.00918795	+	0.00380577i	−0.378085	+	0.925771i	$0.623417\pi$
$440$		0			0
$441$		−	10.6055i		−	0.505025i
$442$		0			0
$443$	−19.5262			−0.927718			−0.463859	−	0.885909i	$-0.653536\pi$
$443$	−19.5262			−0.927718			−0.463859	+	0.885909i	$0.653536\pi$
$444$		0			0
$445$	−2.33210	−	4.84987i	−0.110552	−	0.229906i
$446$		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	$-0.560732\pi$
$449$	16.7867	−	16.7867i	0.792215	−	0.792215i	0.981854	+	0.189639i	$0.0607316\pi$
$450$		0			0
$451$	1.49503	+	9.53242i	0.0703980	+	0.448864i
$452$		0			0
$453$	−18.2815			−0.858942
$454$		0			0
$455$	0.837050	+	15.0615i	0.0392415	+	0.706096i
$456$		0			0
$457$	−12.5726	−	5.20775i	−0.588122	−	0.243608i	0.0687203	−	0.997636i	$-0.478108\pi$
$457$	−12.5726	−	5.20775i	−0.588122	−	0.243608i	−0.656843	+	0.754028i	$0.728108\pi$
$458$		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
$463$	−8.59176	−	20.7423i	−0.399293	−	0.963979i	−0.987834	−	0.155511i	$-0.950298\pi$
$463$	−8.59176	−	20.7423i	−0.399293	−	0.963979i	0.588541	−	0.808467i	$-0.299702\pi$
$464$		0			0
$465$	−11.3739	+	32.4441i	−0.527451	+	1.50456i
$466$		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
$473$	16.6715	+	6.90555i	0.766556	+	0.317518i
$474$		0			0
$475$	−3.45288	−	6.26472i	−0.158429	−	0.287445i
$476$		0			0
$477$	−18.1109	−	7.50178i	−0.829242	−	0.343483i
$478$		0			0
$479$	0.811220	−	1.95846i	0.0370656	−	0.0894842i	−0.904263	−	0.426977i	$-0.859579\pi$
$479$	0.811220	−	1.95846i	0.0370656	−	0.0894842i	0.941328	+	0.337492i	$0.109579\pi$
$480$		0			0
$481$	7.34682	−	17.7368i	0.334986	−	0.808728i
$482$		0			0
$483$	−2.36127			−0.107441
$484$		0			0
$485$	−10.6530	+	5.12261i	−0.483730	+	0.232606i
$486$		0			0
$487$		−	22.8061i		−	1.03344i	−0.856153	−	0.516722i	$-0.827152\pi$
$487$		−	22.8061i		−	1.03344i	0.856153	−	0.516722i	$-0.172848\pi$
$488$		0			0
$489$	2.04748	−	4.94306i	0.0925903	−	0.223533i
$490$		0			0
$491$		−	4.31101i		−	0.194553i	−0.995257	−	0.0972766i	$-0.968987\pi$
$491$		−	4.31101i		−	0.194553i	0.995257	−	0.0972766i	$-0.0310131\pi$
$492$		0			0
$493$	−0.233413	−	0.233413i	−0.0105124	−	0.0105124i
$494$		0			0
$495$	−7.46191	−	2.61591i	−0.335388	−	0.117576i
$496$		0			0
$497$	−5.51081			−0.247194
$498$		0			0
$499$	27.1306	+	11.2379i	1.21453	+	0.503076i	0.895668	−	0.444724i	$-0.146698\pi$
$499$	27.1306	+	11.2379i	1.21453	+	0.503076i	0.318866	+	0.947800i	$0.396698\pi$
$500$		0			0
$501$	0.613112	+	0.613112i	0.0273918	+	0.0273918i
$502$		0			0
$503$	−11.2032	−	27.0470i	−0.499528	−	1.20597i	−0.949739	−	0.313044i	$-0.898651\pi$
$503$	−11.2032	−	27.0470i	−0.499528	−	1.20597i	0.450211	−	0.892922i	$-0.351349\pi$
$504$		0			0
$505$	−4.81696	+	13.7404i	−0.214352	+	0.611442i
$506$		0			0
$507$	−4.73120	+	11.4221i	−0.210120	+	0.507274i
$508$		0			0
$509$	4.15079	−	1.71931i	0.183980	−	0.0762072i	−0.288791	−	0.957392i	$-0.593253\pi$
$509$	4.15079	−	1.71931i	0.183980	−	0.0762072i	0.472772	+	0.881185i	$0.343253\pi$
$510$		0			0
$511$	−3.28444	−	7.92935i	−0.145295	−	0.350774i
$512$		0			0
$513$			2.16135i			0.0954260i
$514$		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	−0.956120	−	0.292976i	$-0.905354\pi$
$521$	−1.66341	+	4.01583i	−0.0728754	+	0.175937i	0.883244	+	0.468913i	$0.155354\pi$
$522$		0			0
$523$	−5.03989	+	5.03989i	−0.220379	+	0.220379i	−0.808658	−	0.588279i	$-0.799806\pi$
$523$	−5.03989	+	5.03989i	−0.220379	+	0.220379i	0.588279	+	0.808658i	$0.299806\pi$
$524$		0			0
$525$	−11.3697	+	14.2231i	−0.496213	+	0.620748i
$526$		0			0
$527$	−0.469295	+	1.13298i	−0.0204428	+	0.0493534i
$528$		0			0
$529$			22.5796i			0.981722i
$530$		0			0
$531$	0.128344	+	0.128344i	0.00556964	+	0.00556964i
$532$		0			0
$533$	22.1642	+	16.1544i	0.960037	+	0.699727i
$534$		0			0
$535$	−1.59074	−	28.6232i	−0.0687738	−	1.23749i
$536$		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	0.0662270	−	0.997805i	$-0.478904\pi$
$541$	−21.6679	−	21.6679i	−0.931578	−	0.931578i	−0.997805	+	0.0662270i	$0.978904\pi$
$542$		0			0
$543$	−39.7775	−	39.7775i	−1.70702	−	1.70702i
$544$		0			0
$545$	2.24828	−	6.41325i	0.0963059	−	0.274714i
$546$		0			0
$547$	17.7210	+	7.34027i	0.757695	+	0.313847i	0.727877	−	0.685708i	$-0.240507\pi$
$547$	17.7210	+	7.34027i	0.757695	+	0.313847i	0.0298180	+	0.999555i	$0.490507\pi$
$548$		0			0
$549$			4.50977i			0.192472i
$550$		0			0
$551$	−2.56064			−0.109087
$552$		0			0
$553$	−9.16584			−0.389771
$554$		0			0
$555$	20.8851	−	10.0428i	0.886524	−	0.426292i
$556$		0			0
$557$	−7.64622	+	18.4596i	−0.323981	+	0.782159i	0.675034	+	0.737786i	$0.264129\pi$
$557$	−7.64622	+	18.4596i	−0.323981	+	0.782159i	−0.999015	+	0.0443724i	$0.985871\pi$
$558$		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
$563$	27.2976	−	11.3070i	1.15045	−	0.476534i	0.275769	−	0.961224i	$-0.411068\pi$
$563$	27.2976	−	11.3070i	1.15045	−	0.476534i	0.874686	+	0.484690i	$0.161068\pi$
$564$		0			0
$565$	6.17344	−	0.343090i	0.259718	−	0.0144339i
$566$		0			0
$567$	15.3268	−	6.34855i	0.643663	−	0.266614i
$568$		0			0
$569$	28.2444	+	28.2444i	1.18407	+	1.18407i	0.978681	+	0.205388i	$0.0658458\pi$
$569$	28.2444	+	28.2444i	1.18407	+	1.18407i	0.205388	+	0.978681i	$0.434154\pi$
$570$		0			0
$571$	−2.41510	−	1.00037i	−0.101069	−	0.0418641i	0.331576	−	0.943428i	$-0.392420\pi$
$571$	−2.41510	−	1.00037i	−0.101069	−	0.0418641i	−0.432645	+	0.901564i	$0.642420\pi$
$572$		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
$577$	−2.57706	−	6.22157i	−0.107284	−	0.259007i	0.861116	−	0.508409i	$-0.169766\pi$
$577$	−2.57706	−	6.22157i	−0.107284	−	0.259007i	−0.968400	+	0.249402i	$0.919766\pi$
$578$		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
$583$			12.5883i			0.521353i
$584$		0			0
$585$	−20.2555	+	9.74003i	−0.837462	+	0.402701i
$586$		0			0
$587$	4.08942	+	9.87273i	0.168788	+	0.407491i	0.985527	−	0.169516i	$-0.0542205\pi$
$587$	4.08942	+	9.87273i	0.168788	+	0.407491i	−0.816739	+	0.577007i	$0.804220\pi$
$588$		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
$593$	13.3576	−	32.2481i	0.548531	−	1.32427i	−0.370040	−	0.929016i	$-0.620656\pi$
$593$	13.3576	−	32.2481i	0.548531	−	1.32427i	0.918571	−	0.395255i	$-0.129344\pi$
$594$		0			0
$595$	−0.433080	+	0.484050i	−0.0177546	+	0.0198441i
$596$		0			0
$597$	8.74078	+	8.74078i	0.357736	+	0.357736i
$598$		0			0
$599$	−43.9516			−1.79581			−0.897906	−	0.440188i	$-0.854912\pi$
$599$	−43.9516			−1.79581			−0.897906	+	0.440188i	$0.854912\pi$
$600$		0			0
$601$	−44.8988	+	18.5977i	−1.83146	+	0.758615i	−0.865012	+	0.501751i	$0.832689\pi$
$601$	−44.8988	+	18.5977i	−1.83146	+	0.758615i	−0.966447	+	0.256864i	$0.917311\pi$
$602$		0			0
$603$	−8.88472	+	3.68017i	−0.361814	+	0.149868i
$604$		0			0
$605$	−1.08311	−	19.4890i	−0.0440346	−	0.792342i
$606$		0			0
$607$			10.8953i			0.442227i	0.975248	+	0.221114i	$0.0709692\pi$
$607$			10.8953i			0.442227i	−0.975248	+	0.221114i	$0.929031\pi$
$608$		0			0
$609$	2.49442	+	6.02206i	0.101079	+	0.244026i
$610$		0			0
$611$	55.3348			2.23861
$612$		0			0
$613$		−	12.8309i		−	0.518234i	−0.965846	−	0.259117i	$-0.916568\pi$
$613$		−	12.8309i		−	0.518234i	0.965846	−	0.259117i	$-0.0834315\pi$
$614$		0			0
$615$	6.93663	+	32.3720i	0.279712	+	1.30536i
$616$		0			0
$617$		−	31.5009i		−	1.26818i	−0.773260	−	0.634089i	$-0.781375\pi$
$617$		−	31.5009i		−	1.26818i	0.773260	−	0.634089i	$-0.218625\pi$
$618$		0			0
$619$	46.0556			1.85113			0.925566	−	0.378586i	$-0.123590\pi$
$619$	46.0556			1.85113			0.925566	+	0.378586i	$0.123590\pi$
$620$		0			0
$621$	0.374853	+	0.904975i	0.0150423	+	0.0363154i
$622$		0			0
$623$			3.79043i			0.151860i
$624$		0			0
$625$	−24.3861	+	5.50630i	−0.975443	+	0.220252i
$626$		0			0
$627$	−4.60551	+	1.90767i	−0.183927	+	0.0761849i
$628$		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
$635$	0.410248	+	7.38184i	0.0162802	+	0.292939i
$636$		0			0
$637$	−7.40806	+	17.8846i	−0.293518	+	0.708615i
$638$		0			0
$639$	−3.14215	−	7.58583i	−0.124302	−	0.300091i
$640$		0			0
$641$	−1.27714	−	3.08329i	−0.0504440	−	0.121783i	0.896649	−	0.442743i	$-0.145994\pi$
$641$	−1.27714	−	3.08329i	−0.0504440	−	0.121783i	−0.947093	+	0.320960i	$0.895994\pi$
$642$		0			0
$643$	4.06958	+	9.82483i	0.160488	+	0.387453i	0.983584	−	0.180449i	$-0.0577551\pi$
$643$	4.06958	+	9.82483i	0.160488	+	0.387453i	−0.823096	+	0.567902i	$0.807755\pi$
$644$		0			0
$645$	58.4287	+	20.4832i	2.30063	+	0.806527i
$646$		0			0
$647$		−	33.6866i		−	1.32436i	−0.749346	−	0.662179i	$-0.769632\pi$
$647$		−	33.6866i		−	1.32436i	0.749346	−	0.662179i	$-0.230368\pi$
$648$		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
$653$	−9.83323	−	23.7395i	−0.384804	−	0.928999i	−0.991022	−	0.133700i	$-0.957314\pi$
$653$	−9.83323	−	23.7395i	−0.384804	−	0.928999i	0.606218	−	0.795299i	$-0.292686\pi$
$654$		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	$-0.143953\pi$
$659$	31.4854	+	13.0417i	1.22650	+	0.508032i	0.327029	+	0.945014i	$0.393953\pi$
$660$		0			0
$661$	−13.4561	−	13.4561i	−0.523383	−	0.523383i	0.395209	−	0.918591i	$-0.370672\pi$
$661$	−13.4561	−	13.4561i	−0.523383	−	0.523383i	−0.918591	+	0.395209i	$0.870672\pi$
$662$		0			0
$663$	−1.68757	+	0.699015i	−0.0655398	+	0.0271475i
$664$		0			0
$665$	0.279580	+	5.03065i	0.0108416	+	0.195080i
$666$		0			0
$667$	−1.07216	+	0.444104i	−0.0415142	+	0.0171958i
$668$		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
$673$	−9.83826	+	23.7517i	−0.379237	+	0.915559i	0.612872	+	0.790182i	$0.290014\pi$
$673$	−9.83826	+	23.7517i	−0.379237	+	0.915559i	−0.992109	+	0.125377i	$0.959986\pi$
$674$		0			0
$675$	7.25607	+	2.09958i	0.279286	+	0.0808130i
$676$		0			0
$677$	−29.7046			−1.14164			−0.570821	−	0.821075i	$-0.693375\pi$
$677$	−29.7046			−1.14164			−0.570821	+	0.821075i	$0.693375\pi$
$678$		0			0
$679$	8.32592			0.319519
$680$		0			0
$681$		−	42.4830i		−	1.62795i
$682$		0			0
$683$	−29.2807	−	12.1284i	−1.12039	−	0.464082i	−0.255888	−	0.966706i	$-0.582368\pi$
$683$	−29.2807	−	12.1284i	−1.12039	−	0.464082i	−0.864505	+	0.502624i	$0.832368\pi$
$684$		0			0
$685$	−17.3826	−	36.1491i	−0.664154	−	1.38118i
$686$		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	−0.796752	−	0.604307i	$-0.793450\pi$
$691$	−24.5212	+	10.1570i	−0.932830	+	0.386391i	−0.136079	+	0.990698i	$0.543450\pi$
$692$		0			0
$693$	3.93817	+	3.93817i	0.149599	+	0.149599i
$694$		0			0
$695$	−19.8744	+	22.2134i	−0.753878	+	0.842603i
$696$		0			0
$697$	0.182973	+	1.16665i	0.00693059	+	0.0441901i
$698$		0			0
$699$	27.5548	+	27.5548i	1.04222	+	1.04222i
$700$		0			0
$701$		−	34.4360i		−	1.30063i	−0.759665	−	0.650314i	$-0.774637\pi$
$701$		−	34.4360i		−	1.30063i	0.759665	−	0.650314i	$-0.225363\pi$
$702$		0			0
$703$	2.45388	−	5.92420i	0.0925500	−	0.223435i
$704$		0			0
$705$	49.7793	+	44.5376i	1.87480	+	1.67738i
$706$		0			0
$707$	7.25179	−	7.25179i	0.272732	−	0.272732i
$708$		0			0
$709$	−17.3721	+	41.9399i	−0.652422	+	1.57509i	0.156830	+	0.987626i	$0.449872\pi$
$709$	−17.3721	+	41.9399i	−0.652422	+	1.57509i	−0.809252	+	0.587461i	$0.800128\pi$
$710$		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
$717$		−	44.8960i		−	1.67667i
$718$		0			0
$719$	−9.15213	−	22.0952i	−0.341317	−	0.824012i	−0.997583	−	0.0694827i	$-0.977865\pi$
$719$	−9.15213	−	22.0952i	−0.341317	−	0.824012i	0.656266	−	0.754529i	$-0.272135\pi$
$720$		0			0
$721$	13.2368	−	5.48287i	0.492964	−	0.204193i
$722$		0			0
$723$	−3.54885	+	8.56768i	−0.131983	+	0.318636i
$724$		0			0
$725$	−2.48746	+	8.59656i	−0.0923820	+	0.319268i
$726$		0			0
$727$	−1.46439	−	3.53535i	−0.0543112	−	0.131119i	0.894395	−	0.447278i	$-0.147607\pi$
$727$	−1.46439	−	3.53535i	−0.0543112	−	0.131119i	−0.948706	+	0.316159i	$0.897607\pi$
$728$		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
$733$	16.8384			0.621939			0.310970	−	0.950420i	$-0.399346\pi$
$733$	16.8384			0.621939			0.310970	+	0.950420i	$0.399346\pi$
$734$		0			0
$735$	−21.0592	+	10.1265i	−0.776780	+	0.373521i
$736$		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
$743$			35.3649i			1.29741i	0.761039	+	0.648706i	$0.224690\pi$
$743$			35.3649i			1.29741i	−0.761039	+	0.648706i	$0.775310\pi$
$744$		0			0
$745$	−22.6983	−	7.95730i	−0.831601	−	0.291533i
$746$		0			0
$747$	22.2828			0.815286
$748$		0			0
$749$	−7.72712	+	18.6549i	−0.282343	+	0.681636i
$750$		0			0
$751$	−12.4521	+	30.0621i	−0.454385	+	1.09698i	0.516253	+	0.856436i	$0.327326\pi$
$751$	−12.4521	+	30.0621i	−0.454385	+	1.09698i	−0.970638	+	0.240546i	$0.922674\pi$
$752$		0			0
$753$	11.6885	+	4.84155i	0.425954	+	0.176436i
$754$		0			0
$755$	7.66135	+	15.9327i	0.278825	+	0.579849i
$756$		0			0
$757$	24.4045	+	10.1087i	0.886997	+	0.367406i	0.779206	−	0.626768i	$-0.215622\pi$
$757$	24.4045	+	10.1087i	0.886997	+	0.367406i	0.107790	+	0.994174i	$0.465622\pi$
$758$		0			0
$759$	−1.59751	+	1.59751i	−0.0579860	+	0.0579860i
$760$		0			0
$761$			29.7337i			1.07785i	0.842355	+	0.538923i	$0.181169\pi$
$761$			29.7337i			1.07785i	−0.842355	+	0.538923i	$0.818831\pi$
$762$		0			0
$763$	−3.38472	+	3.38472i	−0.122535	+	0.122535i
$764$		0			0
$765$	−0.913247	−	0.320155i	−0.0330185	−	0.0115752i
$766$		0			0
$767$	−0.126783	−	0.306082i	−0.00457788	−	0.0110520i
$768$		0			0
$769$	33.1135			1.19410			0.597052	−	0.802202i	$-0.296339\pi$
$769$	33.1135			1.19410			0.597052	+	0.802202i	$0.296339\pi$
$770$		0			0
$771$	25.7089	−	25.7089i	0.925882	−	0.925882i
$772$		0			0
$773$	8.78360	+	3.63829i	0.315924	+	0.130860i	0.535011	−	0.844845i	$-0.320308\pi$
$773$	8.78360	+	3.63829i	0.315924	+	0.130860i	−0.219086	+	0.975705i	$0.570308\pi$
$774$		0			0
$775$	33.0421	−	3.68403i	1.18691	−	0.132334i
$776$		0			0
$777$	−16.3228			−0.585578
$778$		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
$785$	20.1319	+	7.05760i	0.718538	+	0.251896i
$786$		0			0
$787$	−32.7988			−1.16915			−0.584575	−	0.811340i	$-0.698739\pi$
$787$	−32.7988			−1.16915			−0.584575	+	0.811340i	$0.698739\pi$
$788$		0			0
$789$		−	15.2778i		−	0.543905i
$790$		0			0
$791$	−4.02348	−	1.66658i	−0.143058	−	0.0592567i
$792$		0			0
$793$	3.15011	−	7.60505i	0.111864	−	0.270063i
$794$		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
$803$	−7.58667	−	3.14250i	−0.267728	−	0.110896i
$804$		0			0
$805$	0.989551	+	2.05788i	0.0348771	+	0.0725309i
$806$		0			0
$807$	3.35026	−	1.38772i	0.117935	−	0.0488502i
$808$		0			0
$809$	7.48960	+	3.10230i	0.263320	+	0.109071i	0.510438	−	0.859915i	$-0.329483\pi$
$809$	7.48960	+	3.10230i	0.263320	+	0.109071i	−0.247117	+	0.968986i	$0.579483\pi$
$810$		0			0
$811$	5.69874	−	5.69874i	0.200110	−	0.200110i	−0.599937	−	0.800047i	$-0.704808\pi$
$811$	5.69874	−	5.69874i	0.200110	−	0.200110i	0.800047	+	0.599937i	$0.204808\pi$
$812$		0			0
$813$	0.469743	+	1.13406i	0.0164746	+	0.0397732i
$814$		0			0
$815$	−5.16601	+	0.287102i	−0.180957	+	0.0100568i
$816$		0			0
$817$	15.8278	−	6.55609i	0.553744	−	0.229368i
$818$		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
$823$	−17.9862	+	7.45013i	−0.626960	+	0.259695i	−0.673461	−	0.739223i	$-0.735193\pi$
$823$	−17.9862	+	7.45013i	−0.626960	+	0.259695i	0.0465009	+	0.998918i	$0.485193\pi$
$824$		0			0
$825$	1.93051	+	17.3147i	0.0672116	+	0.602822i
$826$		0			0
$827$	20.0605	+	48.4303i	0.697571	+	1.68409i	0.728940	+	0.684577i	$0.240013\pi$
$827$	20.0605	+	48.4303i	0.697571	+	1.68409i	−0.0313693	+	0.999508i	$0.509987\pi$
$828$		0			0
$829$	−37.8392	+	37.8392i	−1.31421	+	1.31421i	−0.395926	+	0.918282i	$0.629576\pi$
$829$	−37.8392	+	37.8392i	−1.31421	+	1.31421i	−0.918282	+	0.395926i	$0.870424\pi$
$830$		0			0
$831$	35.5030	+	14.7058i	1.23159	+	0.510140i
$832$		0			0
$833$	−0.770064	+	0.318971i	−0.0266811	+	0.0110517i
$834$		0			0
$835$	0.277397	−	0.791278i	0.00959972	−	0.0273833i
$836$		0			0
$837$	−9.28083	−	3.84425i	−0.320792	−	0.132877i
$838$		0			0
$839$	5.31366	−	2.20099i	0.183448	−	0.0759867i	−0.289069	−	0.957308i	$-0.593346\pi$
$839$	5.31366	−	2.20099i	0.183448	−	0.0759867i	0.472517	+	0.881322i	$0.343346\pi$
$840$		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
$847$	−5.26126	+	12.7018i	−0.180779	+	0.436439i
$848$		0			0
$849$	−63.5467	−	26.3219i	−2.18092	−	0.903366i
$850$		0			0
$851$		−	2.90610i		−	0.0996197i
$852$		0			0
$853$	−31.1224			−1.06561			−0.532806	−	0.846237i	$-0.678862\pi$
$853$	−31.1224			−1.06561			−0.532806	+	0.846237i	$0.678862\pi$
$854$		0			0
$855$	−6.76546	+	3.25323i	−0.231374	+	0.111258i
$856$		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	$-0.520157\pi$
$859$	27.3952	−	27.3952i	0.934712	−	0.934712i	0.997996	+	0.0632836i	$0.0201573\pi$
$860$		0			0
$861$	5.47793	−	22.6663i	0.186688	−	0.772465i
$862$		0			0
$863$	−11.9866			−0.408028			−0.204014	−	0.978968i	$-0.565399\pi$
$863$	−11.9866			−0.408028			−0.204014	+	0.978968i	$0.565399\pi$
$864$		0			0
$865$	−24.2655	+	27.1213i	−0.825050	+	0.922151i
$866$		0			0
$867$	36.2439	+	15.0127i	1.23091	+	0.509859i
$868$		0			0
$869$	−6.20113	+	6.20113i	−0.210359	+	0.210359i
$870$		0			0
$871$	17.5534			0.594774
$872$		0			0
$873$	4.74727	+	11.4609i	0.160671	+	0.387894i
$874$		0			0
$875$	17.1604	+	3.94828i	0.580129	+	0.133476i
$876$		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	−0.790960	−	0.611867i	$-0.790419\pi$
$881$	−5.31578	+	5.31578i	−0.179093	+	0.179093i	0.611867	+	0.790960i	$0.290419\pi$
$882$		0			0
$883$	44.0831	+	18.2598i	1.48351	+	0.614492i	0.969894	−	0.243526i	$-0.0783041\pi$
$883$	44.0831	+	18.2598i	1.48351	+	0.614492i	0.513620	+	0.858018i	$0.328304\pi$
$884$		0			0
$885$	0.132303	−	0.377397i	0.00444733	−	0.0126860i
$886$		0			0
$887$	30.8524	+	12.7795i	1.03592	+	0.429094i	0.834847	−	0.550482i	$-0.185556\pi$
$887$	30.8524	+	12.7795i	1.03592	+	0.429094i	0.201076	+	0.979576i	$0.435556\pi$
$888$		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
$893$	18.4822			0.618482
$894$		0			0
$895$	−11.4468	+	32.6521i	−0.382624	+	1.09144i
$896$		0			0
$897$			6.42171i			0.214414i
$898$		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
$905$	−17.9970	+	51.3366i	−0.598240	+	1.70649i
$906$		0			0
$907$	−56.1058			−1.86296			−0.931481	−	0.363789i	$-0.881483\pi$
$907$	−56.1058			−1.86296			−0.931481	+	0.363789i	$0.881483\pi$
$908$		0			0
$909$	14.1172	+	5.84753i	0.468238	+	0.193950i
$910$		0			0
$911$	15.6177	+	15.6177i	0.517438	+	0.517438i	0.916795	−	0.399357i	$-0.130767\pi$
$911$	15.6177	+	15.6177i	0.517438	+	0.517438i	−0.399357	+	0.916795i	$0.630767\pi$
$912$		0			0
$913$	−5.47584	−	13.2198i	−0.181224	−	0.437513i
$914$		0			0
$915$	8.95496	−	4.30607i	0.296042	−	0.142354i
$916$		0			0
$917$	4.07148	−	9.82943i	0.134452	−	0.324596i
$918$		0			0
$919$	20.2659	−	8.39442i	0.668511	−	0.276906i	−0.0225038	−	0.999747i	$-0.507164\pi$
$919$	20.2659	−	8.39442i	0.668511	−	0.276906i	0.691015	+	0.722840i	$0.257164\pi$
$920$		0			0
$921$	−19.4354	−	46.9212i	−0.640418	−	1.54611i
$922$		0			0
$923$			14.9872i			0.493310i
$924$		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	−0.998812	−	0.0487226i	$-0.984485\pi$
$929$	−9.96672	−	24.0618i	−0.326997	−	0.789442i	0.671815	−	0.740719i	$-0.265515\pi$
$930$		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
$935$	0.0344835	+	0.620483i	0.00112773	+	0.0202920i
$936$		0			0
$937$	21.3072	−	51.4402i	0.696076	−	1.68048i	−0.0360874	−	0.999349i	$-0.511489\pi$
$937$	21.3072	−	51.4402i	0.696076	−	1.68048i	0.732164	−	0.681129i	$-0.238511\pi$
$938$		0			0
$939$		−	8.66440i		−	0.282752i
$940$		0			0
$941$	2.58682	+	2.58682i	0.0843280	+	0.0843280i	0.748013	−	0.663685i	$-0.231008\pi$
$941$	2.58682	+	2.58682i	0.0843280	+	0.0843280i	−0.663685	+	0.748013i	$0.731008\pi$
$942$		0			0
$943$	4.03548	+	0.975285i	0.131413	+	0.0317597i
$944$		0			0
$945$	−3.96511	−	3.54759i	−0.128985	−	0.115403i
$946$		0			0
$947$	−25.5399	−	25.5399i	−0.829937	−	0.829937i	0.157571	−	0.987508i	$-0.449634\pi$
$947$	−25.5399	−	25.5399i	−0.829937	−	0.829937i	−0.987508	+	0.157571i	$0.949634\pi$
$948$		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
$955$	−41.9016	−	14.6894i	−1.35590	−	0.475337i
$956$		0			0
$957$	5.76181	+	2.38662i	0.186253	+	0.0771484i
$958$		0			0
$959$			28.2524i			0.912317i
$960$		0			0
$961$	−13.2141			−0.426261
$962$		0			0
$963$	−30.0850			−0.969476
$964$		0			0
$965$	15.9784	+	5.60152i	0.514363	+	0.180319i
$966$		0			0
$967$	9.33892	−	22.5462i	0.300320	−	0.725036i	−0.699625	−	0.714510i	$-0.746650\pi$
$967$	9.33892	−	22.5462i	0.300320	−	0.725036i	0.999945	−	0.0105254i	$-0.00335039\pi$
$968$		0			0
$969$	−0.563659	+	0.233475i	−0.0181073	+	0.00750030i
$970$		0			0
$971$	3.68538	+	1.52654i	0.118270	+	0.0489889i	0.441034	−	0.897491i	$-0.354612\pi$
$971$	3.68538	+	1.52654i	0.118270	+	0.0489889i	−0.322764	+	0.946480i	$0.604612\pi$
$972$		0			0
$973$	19.3962	−	8.03415i	0.621812	−	0.257563i
$974$		0			0
$975$	38.6812	+	30.9209i	1.23879	+	0.990262i
$976$		0			0
$977$	9.18730	−	3.80550i	0.293928	−	0.121749i	−0.230847	−	0.972990i	$-0.574150\pi$
$977$	9.18730	−	3.80550i	0.293928	−	0.121749i	0.524775	+	0.851241i	$0.324150\pi$
$978$		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	−0.485985	−	0.873967i	$-0.661539\pi$
$983$	12.1643	−	12.1643i	0.387982	−	0.387982i	0.873967	+	0.485985i	$0.161539\pi$
$984$		0			0
$985$	−4.78879	+	5.35239i	−0.152584	+	0.170541i
$986$		0			0
$987$	−18.0042	−	43.4659i	−0.573080	−	1.38354i
$988$		0			0
$989$	5.49017	−	5.49017i	0.174577	−	0.174577i
$990$		0			0
$991$	17.6998	−	42.7311i	0.562252	−	1.35740i	−0.345708	−	0.938342i	$-0.612361\pi$
$991$	17.6998	−	42.7311i	0.562252	−	1.35740i	0.907961	−	0.419055i	$-0.137639\pi$
$992$		0			0
$993$		−	1.48021i		−	0.0469731i
$994$		0			0
$995$	3.95469	−	11.2808i	0.125372	−	0.357625i
$996$		0			0
$997$	7.82168	+	18.8832i	0.247715	+	0.598037i	0.998009	−	0.0630669i	$-0.0200882\pi$
$997$	7.82168	+	18.8832i	0.247715	+	0.598037i	−0.750294	+	0.661104i	$0.770088\pi$
$998$		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.y.a.413.4	yes	84
5.2	odd	4		820.2.x.a.577.18	✓	84
41.14	odd	8		820.2.x.a.793.18	yes	84
205.137	even	8	inner	820.2.y.a.137.4	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.18	✓	84	5.2	odd	4
820.2.x.a.793.18	yes	84	41.14	odd	8
820.2.y.a.137.4	yes	84	205.137	even	8	inner
820.2.y.a.413.4	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.13627 + 0.884872i) q^{3} +(1.66644 + 1.49097i) q^{5} +(-0.602718 - 1.45509i) q^{7} +(1.65933 - 1.65933i) q^{9} +(-1.39221 - 0.576671i) q^{11} +(-3.95726 + 1.63915i) q^{13} +(-4.87928 - 1.71052i) q^{15} +(-0.170389 - 0.0705774i) q^{17} +(-1.32175 + 0.547487i) q^{19} +(2.57514 + 2.57514i) q^{21} +(-0.458474 + 0.458474i) q^{23} +(0.554042 + 4.96921i) q^{25} +(0.578137 - 1.39575i) q^{27} +(1.65360 + 0.684943i) q^{29} -6.64937i q^{31} +3.48441 q^{33} +(1.16510 - 3.32345i) q^{35} +(-3.16931 + 3.16931i) q^{37} +(7.00334 - 7.00334i) q^{39} +(-3.33737 - 5.46461i) q^{41} -11.9749 q^{43} +(5.23917 - 0.291168i) q^{45} +(-11.9353 - 4.94377i) q^{47} +(3.19573 - 3.19573i) q^{49} +0.426449 q^{51} +(-3.19682 - 7.71780i) q^{53} +(-1.46023 - 3.03672i) q^{55} +(2.33916 - 2.33916i) q^{57} +0.0773468i q^{59} +(-1.35891 + 1.35891i) q^{61} +(-3.41458 - 1.41436i) q^{63} +(-9.03846 - 3.16860i) q^{65} +(-3.78614 - 1.56827i) q^{67} +(0.573734 - 1.38512i) q^{69} +(1.33900 - 3.23263i) q^{71} +5.44939 q^{73} +(-5.58069 - 10.1253i) q^{75} +2.37335i q^{77} +(2.22709 - 5.37666i) q^{79} +10.5332i q^{81} +(6.71441 + 6.71441i) q^{83} +(-0.178714 - 0.371657i) q^{85} -4.13862 q^{87} +(-2.22346 - 0.920987i) q^{89} +(4.77023 + 4.77023i) q^{91} +(5.88384 + 14.2048i) q^{93} +(-3.01890 - 1.05833i) q^{95} +(-2.02301 + 4.88397i) q^{97} +(-3.26701 + 1.35324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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