LMFDB - Embedded newform 644.2.bc.a.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.869461 - 1.68652i) q^{3} +(-2.83286 + 0.270506i) q^{5} +(2.32176 - 1.26863i) q^{7} +(-0.348215 + 0.489000i) q^{9} +O(q^{10})$	\(q+(-0.869461 - 1.68652i) q^{3} +(-2.83286 + 0.270506i) q^{5} +(2.32176 - 1.26863i) q^{7} +(-0.348215 + 0.489000i) q^{9} +(-1.18042 + 0.408547i) q^{11} +(-0.961267 - 3.27377i) q^{13} +(2.91928 + 4.54248i) q^{15} +(-3.19520 - 1.27917i) q^{17} +(-2.39977 + 0.960722i) q^{19} +(-4.15825 - 2.81268i) q^{21} +(-0.440128 + 4.77559i) q^{23} +(3.04229 - 0.586354i) q^{25} +(-4.50694 - 0.648000i) q^{27} +(1.15149 + 8.00878i) q^{29} +(-4.68192 + 0.223027i) q^{31} +(1.71535 + 1.63558i) q^{33} +(-6.23407 + 4.22189i) q^{35} +(-6.79455 - 4.83838i) q^{37} +(-4.68550 + 4.46761i) q^{39} +(8.85506 + 4.04397i) q^{41} +(-0.760372 + 1.18316i) q^{43} +(0.854168 - 1.47946i) q^{45} +(-7.74681 + 4.47262i) q^{47} +(3.78117 - 5.89090i) q^{49} +(0.620766 + 6.50096i) q^{51} +(-3.31269 - 3.47425i) q^{53} +(3.23345 - 1.47667i) q^{55} +(3.70678 + 3.21194i) q^{57} +(0.486069 + 0.117919i) q^{59} +(0.390850 + 0.201497i) q^{61} +(-0.188115 + 1.57710i) q^{63} +(3.60871 + 9.01412i) q^{65} +(-1.50457 - 7.80643i) q^{67} +(8.43681 - 3.40991i) q^{69} +(-2.01845 - 2.32942i) q^{71} +(-5.18503 + 6.59330i) q^{73} +(-3.63405 - 4.62108i) q^{75} +(-2.22236 + 2.44606i) q^{77} +(8.06847 - 8.46197i) q^{79} +(3.41477 + 9.86634i) q^{81} +(-2.97437 - 6.51296i) q^{83} +(9.39759 + 2.75938i) q^{85} +(12.5058 - 8.90534i) q^{87} +(0.610460 - 12.8151i) q^{89} +(-6.38503 - 6.38144i) q^{91} +(4.44689 + 7.70224i) q^{93} +(6.53833 - 3.37074i) q^{95} +(6.62960 - 14.5168i) q^{97} +(0.211260 - 0.719487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.869461	−	1.68652i	−0.501984	−	0.973713i	−0.994631	−	0.103484i	$-0.967001\pi$
$3$	−0.869461	−	1.68652i	−0.501984	−	0.973713i	0.492647	−	0.870229i	$-0.336029\pi$
$4$		0			0
$5$	−2.83286	+	0.270506i	−1.26689	+	0.120974i	−0.706775	−	0.707438i	$-0.749851\pi$
$5$	−2.83286	+	0.270506i	−1.26689	+	0.120974i	−0.560119	+	0.828412i	$0.689245\pi$
$6$		0			0
$7$	2.32176	−	1.26863i	0.877544	−	0.479496i
$7$	2.32176	−	1.26863i	0.877544	−	0.479496i
$8$		0			0
$9$	−0.348215	+	0.489000i	−0.116072	+	0.163000i
$10$		0			0
$11$	−1.18042	+	0.408547i	−0.355910	+	0.123182i	−0.499171	−	0.866503i	$-0.666362\pi$
$11$	−1.18042	+	0.408547i	−0.355910	+	0.123182i	0.143262	+	0.989685i	$0.454241\pi$
$12$		0			0
$13$	−0.961267	−	3.27377i	−0.266607	−	0.907981i	−0.978596	−	0.205790i	$-0.934023\pi$
$13$	−0.961267	−	3.27377i	−0.266607	−	0.907981i	0.711989	−	0.702191i	$-0.247795\pi$
$14$		0			0
$15$	2.91928	+	4.54248i	0.753754	+	1.17286i
$16$		0			0
$17$	−3.19520	−	1.27917i	−0.774950	−	0.310243i	−0.0497324	−	0.998763i	$-0.515837\pi$
$17$	−3.19520	−	1.27917i	−0.774950	−	0.310243i	−0.725218	+	0.688519i	$0.758261\pi$
$18$		0			0
$19$	−2.39977	+	0.960722i	−0.550544	+	0.220405i	−0.630221	−	0.776416i	$-0.717036\pi$
$19$	−2.39977	+	0.960722i	−0.550544	+	0.220405i	0.0796763	+	0.996821i	$0.474611\pi$
$20$		0			0
$21$	−4.15825	−	2.81268i	−0.907404	−	0.613777i
$22$		0			0
$23$	−0.440128	+	4.77559i	−0.0917730	+	0.995780i
$23$	−0.440128	+	4.77559i	−0.0917730	+	0.995780i
$24$		0			0
$25$	3.04229	−	0.586354i	0.608459	−	0.117271i
$26$		0			0
$27$	−4.50694	−	0.648000i	−0.867361	−	0.124708i
$28$		0			0
$29$	1.15149	+	8.00878i	0.213826	+	1.48719i	0.760220	+	0.649665i	$0.225091\pi$
$29$	1.15149	+	8.00878i	0.213826	+	1.48719i	−0.546394	+	0.837528i	$0.684000\pi$
$30$		0			0
$31$	−4.68192	+	0.223027i	−0.840898	+	0.0400569i	−0.463610	−	0.886039i	$-0.653446\pi$
$31$	−4.68192	+	0.223027i	−0.840898	+	0.0400569i	−0.377288	+	0.926096i	$0.623143\pi$
$32$		0			0
$33$	1.71535	+	1.63558i	0.298604	+	0.284719i
$34$		0			0
$35$	−6.23407	+	4.22189i	−1.05375	+	0.713630i
$36$		0			0
$37$	−6.79455	−	4.83838i	−1.11702	−	0.795424i	−0.136263	−	0.990673i	$-0.543509\pi$
$37$	−6.79455	−	4.83838i	−1.11702	−	0.795424i	−0.980754	+	0.195249i	$0.937449\pi$
$38$		0			0
$39$	−4.68550	+	4.46761i	−0.750280	+	0.715391i
$40$		0			0
$41$	8.85506	+	4.04397i	1.38293	+	0.631562i	0.961375	−	0.275242i	$-0.0887578\pi$
$41$	8.85506	+	4.04397i	1.38293	+	0.631562i	0.421553	+	0.906804i	$0.361485\pi$
$42$		0			0
$43$	−0.760372	+	1.18316i	−0.115956	+	0.180431i	−0.894380	−	0.447308i	$-0.852383\pi$
$43$	−0.760372	+	1.18316i	−0.115956	+	0.180431i	0.778424	+	0.627738i	$0.216019\pi$
$44$		0			0
$45$	0.854168	−	1.47946i	0.127332	−	0.220545i
$46$		0			0
$47$	−7.74681	+	4.47262i	−1.12999	+	0.652399i	−0.943932	−	0.330140i	$-0.892904\pi$
$47$	−7.74681	+	4.47262i	−1.12999	+	0.652399i	−0.186056	+	0.982539i	$0.559571\pi$
$48$		0			0
$49$	3.78117	−	5.89090i	0.540168	−	0.841557i
$50$		0			0
$51$	0.620766	+	6.50096i	0.0869247	+	0.910316i
$52$		0			0
$53$	−3.31269	−	3.47425i	−0.455033	−	0.477225i	0.455751	−	0.890107i	$-0.349371\pi$
$53$	−3.31269	−	3.47425i	−0.455033	−	0.477225i	−0.910784	+	0.412882i	$0.864522\pi$
$54$		0			0
$55$	3.23345	−	1.47667i	0.435998	−	0.199114i
$56$		0			0
$57$	3.70678	+	3.21194i	0.490975	+	0.425432i
$58$		0			0
$59$	0.486069	+	0.117919i	0.0632808	+	0.0153518i	0.267274	−	0.963620i	$-0.413877\pi$
$59$	0.486069	+	0.117919i	0.0632808	+	0.0153518i	−0.203994	+	0.978972i	$0.565392\pi$
$60$		0			0
$61$	0.390850	+	0.201497i	0.0500432	+	0.0257991i	0.483067	−	0.875584i	$-0.339523\pi$
$61$	0.390850	+	0.201497i	0.0500432	+	0.0257991i	−0.433023	+	0.901383i	$0.642553\pi$
$62$		0			0
$63$	−0.188115	+	1.57710i	−0.0237003	+	0.198696i
$64$		0			0
$65$	3.60871	+	9.01412i	0.447605	+	1.11806i
$66$		0			0
$67$	−1.50457	−	7.80643i	−0.183812	−	0.953707i	−0.950273	−	0.311417i	$-0.899197\pi$
$67$	−1.50457	−	7.80643i	−0.183812	−	0.953707i	0.766462	−	0.642290i	$-0.222016\pi$
$68$		0			0
$69$	8.43681	−	3.40991i	1.01567	−	0.410505i
$70$		0			0
$71$	−2.01845	−	2.32942i	−0.239546	−	0.276451i	0.623228	−	0.782040i	$-0.285821\pi$
$71$	−2.01845	−	2.32942i	−0.239546	−	0.276451i	−0.862774	+	0.505589i	$0.831275\pi$
$72$		0			0
$73$	−5.18503	+	6.59330i	−0.606862	+	0.771688i	−0.988270	−	0.152719i	$-0.951197\pi$
$73$	−5.18503	+	6.59330i	−0.606862	+	0.771688i	0.381408	+	0.924407i	$0.375439\pi$
$74$		0			0
$75$	−3.63405	−	4.62108i	−0.419624	−	0.533596i
$76$		0			0
$77$	−2.22236	+	2.44606i	−0.253262	+	0.278755i
$78$		0			0
$79$	8.06847	−	8.46197i	0.907774	−	0.952046i	−0.0912669	−	0.995826i	$-0.529092\pi$
$79$	8.06847	−	8.46197i	0.907774	−	0.952046i	0.999041	+	0.0437802i	$0.0139401\pi$
$80$		0			0
$81$	3.41477	+	9.86634i	0.379419	+	1.09626i
$82$		0			0
$83$	−2.97437	−	6.51296i	−0.326479	−	0.714890i	0.673219	−	0.739443i	$-0.264911\pi$
$83$	−2.97437	−	6.51296i	−0.326479	−	0.714890i	−0.999699	+	0.0245531i	$0.992184\pi$
$84$		0			0
$85$	9.39759	+	2.75938i	1.01931	+	0.299297i
$86$		0			0
$87$	12.5058	−	8.90534i	1.34076	−	0.954752i
$88$		0			0
$89$	0.610460	−	12.8151i	0.0647086	−	1.35840i	−0.700054	−	0.714090i	$-0.746841\pi$
$89$	0.610460	−	12.8151i	0.0647086	−	1.35840i	0.764763	−	0.644312i	$-0.222856\pi$
$90$		0			0
$91$	−6.38503	−	6.38144i	−0.669333	−	0.668957i
$92$		0			0
$93$	4.44689	+	7.70224i	0.461121	+	0.798685i
$94$		0			0
$95$	6.53833	−	3.37074i	0.670819	−	0.345831i
$96$		0			0
$97$	6.62960	−	14.5168i	0.673134	−	1.47396i	−0.196624	−	0.980479i	$-0.562998\pi$
$97$	6.62960	−	14.5168i	0.673134	−	1.47396i	0.869758	−	0.493479i	$-0.164275\pi$
$98$		0			0
$99$	0.211260	−	0.719487i	0.0212325	−	0.0723112i
$100$		0			0
$101$	0.721418	−	7.55503i	0.0717837	−	0.751753i	−0.885890	−	0.463896i	$-0.846451\pi$
$101$	0.721418	−	7.55503i	0.0717837	−	0.751753i	0.957673	−	0.287857i	$-0.0929429\pi$
$102$		0			0
$103$	−10.6845	−	2.05926i	−1.05277	−	0.202905i	−0.366625	−	0.930369i	$-0.619487\pi$
$103$	−10.6845	−	2.05926i	−1.05277	−	0.202905i	−0.686146	+	0.727464i	$0.740699\pi$
$104$		0			0
$105$	12.5406	+	6.84310i	1.22384	+	0.667818i
$106$		0			0
$107$	−5.13702	+	9.96443i	−0.496615	+	0.963298i	0.498715	+	0.866766i	$0.333805\pi$
$107$	−5.13702	+	9.96443i	−0.496615	+	0.963298i	−0.995330	+	0.0965321i	$0.969225\pi$
$108$		0			0
$109$	−0.514269	+	1.28458i	−0.0492580	+	0.123041i	−0.950956	−	0.309325i	$-0.899897\pi$
$109$	−0.514269	+	1.28458i	−0.0492580	+	0.123041i	0.901698	+	0.432366i	$0.142321\pi$
$110$		0			0
$111$	−2.25242	+	15.6659i	−0.213790	+	1.48694i
$112$		0			0
$113$	4.58463	−	3.97261i	0.431286	−	0.373711i	−0.411993	−	0.911187i	$-0.635167\pi$
$113$	4.58463	−	3.97261i	0.431286	−	0.373711i	0.843279	+	0.537475i	$0.180622\pi$
$114$		0			0
$115$	−0.0450024	−	13.6477i	−0.00419650	−	1.27265i
$116$		0			0
$117$	1.93560	+	0.669918i	0.178946	+	0.0619340i
$118$		0			0
$119$	−9.04129	+	1.08360i	−0.828814	+	0.0993332i
$120$		0			0
$121$	−7.42010	+	5.83524i	−0.674555	+	0.530476i
$122$		0			0
$123$	−0.878897	−	18.4503i	−0.0792474	−	1.66361i
$124$		0			0
$125$	5.19259	−	1.52468i	0.464440	−	0.136372i
$126$		0			0
$127$	−2.42478	+	2.79834i	−0.215164	+	0.248313i	−0.853064	−	0.521807i	$-0.825258\pi$
$127$	−2.42478	+	2.79834i	−0.215164	+	0.248313i	0.637899	+	0.770120i	$0.279804\pi$
$128$		0			0
$129$	2.65654	+	0.253669i	0.233895	+	0.0223343i
$130$		0			0
$131$	−18.6407	+	4.52218i	−1.62864	+	0.395105i	−0.942989	−	0.332823i	$-0.891999\pi$
$131$	−18.6407	+	4.52218i	−1.62864	+	0.395105i	−0.685654	+	0.727928i	$0.740484\pi$
$132$		0			0
$133$	−4.35290	+	5.27498i	−0.377444	+	0.457399i
$134$		0			0
$135$	12.9428	+	0.616543i	1.11394	+	0.0530636i
$136$		0			0
$137$	−2.35330	−	1.35868i	−0.201056	−	0.116079i	0.396092	−	0.918211i	$-0.370366\pi$
$137$	−2.35330	−	1.35868i	−0.201056	−	0.116079i	−0.597148	+	0.802131i	$0.703699\pi$
$138$		0			0
$139$		−	11.9523i		−	1.01378i	−0.862010	−	0.506892i	$-0.830794\pi$
$139$		−	11.9523i		−	1.01378i	0.862010	−	0.506892i	$-0.169206\pi$
$140$		0			0
$141$	14.2787	+	9.17638i	1.20249	+	0.772790i
$142$		0			0
$143$	2.47219	+	3.47170i	0.206735	+	0.290318i
$144$		0			0
$145$	−5.42843	−	22.3763i	−0.450807	−	1.85825i
$146$		0			0
$147$	−13.2227	−	1.25511i	−1.09059	−	0.103520i
$148$		0			0
$149$	2.97708	−	15.4466i	0.243892	−	1.26543i	−0.628957	−	0.777440i	$-0.716518\pi$
$149$	2.97708	−	15.4466i	0.243892	−	1.26543i	0.872849	−	0.487991i	$-0.162270\pi$
$150$		0			0
$151$	−3.75446	+	15.4761i	−0.305534	+	1.25943i	0.587421	+	0.809282i	$0.300143\pi$
$151$	−3.75446	+	15.4761i	−0.305534	+	1.25943i	−0.892955	+	0.450147i	$0.851372\pi$
$152$		0			0
$153$	1.73813	−	1.11703i	0.140519	−	0.0903064i
$154$		0			0
$155$	13.2029	−	1.89829i	1.06048	−	0.152474i
$156$		0			0
$157$	5.90476	+	4.64356i	0.471251	+	0.370596i	0.825359	−	0.564609i	$-0.190973\pi$
$157$	5.90476	+	4.64356i	0.471251	+	0.370596i	−0.354108	+	0.935205i	$0.615215\pi$
$158$		0			0
$159$	−2.97913	+	8.60764i	−0.236261	+	0.682630i
$160$		0			0
$161$	5.03657	+	11.6462i	0.396937	+	0.917846i
$162$		0			0
$163$	6.80563	−	19.6636i	0.533058	−	1.54017i	−0.281190	−	0.959652i	$-0.590729\pi$
$163$	6.80563	−	19.6636i	0.533058	−	1.54017i	0.814248	−	0.580518i	$-0.197150\pi$
$164$		0			0
$165$	−5.30179	−	4.16937i	−0.412744	−	0.324585i
$166$		0			0
$167$	12.2336	−	1.75893i	0.946665	−	0.136110i	0.348344	−	0.937367i	$-0.386744\pi$
$167$	12.2336	−	1.75893i	0.946665	−	0.136110i	0.598321	+	0.801257i	$0.295835\pi$
$168$		0			0
$169$	1.14274	−	0.734392i	0.0879028	−	0.0564917i
$170$		0			0
$171$	0.365843	−	1.50802i	0.0279767	−	0.115321i
$172$		0			0
$173$	1.23185	−	6.39144i	0.0936558	−	0.485932i	−0.904567	−	0.426332i	$-0.859805\pi$
$173$	1.23185	−	6.39144i	0.0936558	−	0.485932i	0.998222	−	0.0596000i	$-0.0189825\pi$
$174$		0			0
$175$	6.31962	−	5.22091i	0.477718	−	0.394664i
$176$		0			0
$177$	−0.223745	−	0.922291i	−0.0168177	−	0.0693237i
$178$		0			0
$179$	−0.899521	−	1.26320i	−0.0672333	−	0.0944160i	0.779590	−	0.626290i	$-0.215427\pi$
$179$	−0.899521	−	1.26320i	−0.0672333	−	0.0944160i	−0.846824	+	0.531874i	$0.821488\pi$
$180$		0			0
$181$	13.5109	+	8.68295i	1.00426	+	0.645398i	0.935901	−	0.352263i	$-0.114588\pi$
$181$	13.5109	+	8.68295i	1.00426	+	0.645398i	0.0683581	+	0.997661i	$0.478224\pi$
$182$		0			0
$183$		−	0.834370i		−	0.0616784i
$184$		0			0
$185$	20.5568	+	11.8685i	1.51137	+	0.872589i
$186$		0			0
$187$	4.29428	+	0.204562i	0.314029	+	0.0149590i
$188$		0			0
$189$	−11.2861	+	4.21312i	−0.820944	+	0.306459i
$190$		0			0
$191$	7.84971	−	1.90432i	0.567985	−	0.137792i	0.0585249	−	0.998286i	$-0.481360\pi$
$191$	7.84971	−	1.90432i	0.567985	−	0.137792i	0.509460	+	0.860494i	$0.329845\pi$
$192$		0			0
$193$	20.5671	+	1.96392i	1.48045	+	0.141366i	0.803784	−	0.594921i	$-0.202817\pi$
$193$	20.5671	+	1.96392i	1.48045	+	0.141366i	0.676669	+	0.736287i	$0.263423\pi$
$194$		0			0
$195$	12.0649	−	13.9236i	0.863983	−	0.997089i
$196$		0			0
$197$	−4.22417	+	1.24033i	−0.300960	+	0.0883697i	−0.428726	−	0.903435i	$-0.641037\pi$
$197$	−4.22417	+	1.24033i	−0.300960	+	0.0883697i	0.127766	+	0.991804i	$0.459219\pi$
$198$		0			0
$199$	0.608753	+	12.7793i	0.0431533	+	0.905900i	0.911842	+	0.410542i	$0.134660\pi$
$199$	0.608753	+	12.7793i	0.0431533	+	0.905900i	−0.868689	+	0.495359i	$0.835037\pi$
$200$		0			0
$201$	−11.8575	+	9.32487i	−0.836366	+	0.657725i
$202$		0			0
$203$	12.8336	+	17.1337i	0.900745	+	1.20255i
$204$		0			0
$205$	−26.1791	−	9.06067i	−1.82843	−	0.632825i
$206$		0			0
$207$	−2.18200	−	1.87816i	−0.151660	−	0.130541i
$208$		0			0
$209$	2.44023	−	2.11447i	0.168794	−	0.146261i
$210$		0			0
$211$	−3.21673	+	22.3728i	−0.221449	+	1.54021i	0.511115	+	0.859512i	$0.329232\pi$
$211$	−3.21673	+	22.3728i	−0.221449	+	1.54021i	−0.732564	+	0.680698i	$0.761677\pi$
$212$		0			0
$213$	−2.17364	+	5.42949i	−0.148935	+	0.372023i
$214$		0			0
$215$	1.83398	−	3.55742i	0.125076	−	0.242614i
$216$		0			0
$217$	−10.5874	+	6.45743i	−0.718718	+	0.438359i
$218$		0			0
$219$	15.6279	+	3.01203i	1.05604	+	0.203534i
$220$		0			0
$221$	−1.11626	+	11.6900i	−0.0750877	+	0.786354i
$222$		0			0
$223$	−0.923271	+	3.14437i	−0.0618268	+	0.210563i	−0.984613	−	0.174750i	$-0.944088\pi$
$223$	−0.923271	+	3.14437i	−0.0618268	+	0.210563i	0.922786	+	0.385313i	$0.125906\pi$
$224$		0			0
$225$	−0.772646	+	1.69186i	−0.0515097	+	0.112791i
$226$		0			0
$227$	−10.2167	+	5.26707i	−0.678106	+	0.349588i	−0.762631	−	0.646834i	$-0.776093\pi$
$227$	−10.2167	+	5.26707i	−0.678106	+	0.349588i	0.0845255	+	0.996421i	$0.473063\pi$
$228$		0			0
$229$	7.62832	+	13.2126i	0.504093	+	0.873115i	0.999989	+	0.00473317i	$0.00150662\pi$
$229$	7.62832	+	13.2126i	0.504093	+	0.873115i	−0.495895	+	0.868382i	$0.665160\pi$
$230$		0			0
$231$	6.05759	+	1.62130i	0.398560	+	0.106674i
$232$		0			0
$233$	1.17371	−	24.6393i	0.0768926	−	1.61417i	−0.550066	−	0.835121i	$-0.685397\pi$
$233$	1.17371	−	24.6393i	0.0768926	−	1.61417i	0.626958	−	0.779053i	$-0.284300\pi$
$234$		0			0
$235$	20.7358	−	14.7659i	1.35265	−	0.963220i
$236$		0			0
$237$	−21.2865	−	6.25028i	−1.38271	−	0.406000i
$238$		0			0
$239$	1.59087	+	3.48353i	0.102905	+	0.225331i	0.954080	−	0.299551i	$-0.0968368\pi$
$239$	1.59087	+	3.48353i	0.102905	+	0.225331i	−0.851175	+	0.524882i	$0.824110\pi$
$240$		0			0
$241$	−5.99188	−	17.3124i	−0.385971	−	1.11519i	−0.955950	−	0.293530i	$-0.905170\pi$
$241$	−5.99188	−	17.3124i	−0.385971	−	1.11519i	0.569979	−	0.821659i	$-0.306951\pi$
$242$		0			0
$243$	4.24438	−	4.45138i	0.272277	−	0.285556i
$244$		0			0
$245$	−9.11802	+	17.7109i	−0.582529	+	1.13151i
$246$		0			0
$247$	5.45200	+	6.93279i	0.346903	+	0.441123i
$248$		0			0
$249$	−8.39813	+	10.6791i	−0.532210	+	0.676760i
$250$		0			0
$251$	−13.9687	−	16.1207i	−0.881696	−	1.01753i	−0.999699	−	0.0245178i	$-0.992195\pi$
$251$	−13.9687	−	16.1207i	−0.881696	−	1.01753i	0.118004	−	0.993013i	$-0.462350\pi$
$252$		0			0
$253$	−1.43152	−	5.81702i	−0.0899988	−	0.365713i
$254$		0			0
$255$	−3.51709	−	18.2484i	−0.220249	−	1.14276i
$256$		0			0
$257$	−5.28333	−	13.1971i	−0.329565	−	0.823214i	−0.996916	−	0.0784710i	$-0.974996\pi$
$257$	−5.28333	−	13.1971i	−0.329565	−	0.823214i	0.667351	−	0.744743i	$-0.267428\pi$
$258$		0			0
$259$	−21.9134	−	2.61382i	−1.36163	−	0.162415i
$260$		0			0
$261$	−4.31726	−	2.22570i	−0.267232	−	0.137767i
$262$		0			0
$263$	−12.1970	−	2.95895i	−0.752098	−	0.182457i	−0.158656	−	0.987334i	$-0.550716\pi$
$263$	−12.1970	−	2.95895i	−0.752098	−	0.182457i	−0.593442	+	0.804877i	$0.702231\pi$
$264$		0			0
$265$	10.3242	+	8.94597i	0.634210	+	0.549546i
$266$		0			0
$267$	−22.1437	+	10.1127i	−1.35518	+	0.618888i
$268$		0			0
$269$	−0.991681	−	1.04004i	−0.0604638	−	0.0634127i	0.692807	−	0.721123i	$-0.256374\pi$
$269$	−0.991681	−	1.04004i	−0.0604638	−	0.0634127i	−0.753271	+	0.657710i	$0.771525\pi$
$270$		0			0
$271$	1.79640	+	18.8127i	0.109123	+	1.14279i	0.869713	+	0.493558i	$0.164304\pi$
$271$	1.79640	+	18.8127i	0.109123	+	1.14279i	−0.760590	+	0.649233i	$0.775090\pi$
$272$		0			0
$273$	−5.21089	+	16.3169i	−0.315377	+	0.987543i
$274$		0			0
$275$	−3.35163	+	1.93506i	−0.202111	+	0.116689i
$276$		0			0
$277$	−1.46713	+	2.54114i	−0.0881511	+	0.152682i	−0.906730	−	0.421712i	$-0.861429\pi$
$277$	−1.46713	+	2.54114i	−0.0881511	+	0.152682i	0.818579	+	0.574395i	$0.194763\pi$
$278$		0			0
$279$	1.52126	−	2.36712i	0.0910752	−	0.141716i
$280$		0			0
$281$	−26.7076	−	12.1970i	−1.59324	−	0.727610i	−0.596084	−	0.802922i	$-0.703278\pi$
$281$	−26.7076	−	12.1970i	−1.59324	−	0.727610i	−0.997160	+	0.0753115i	$0.976005\pi$
$282$		0			0
$283$	−5.11632	+	4.87840i	−0.304134	+	0.289991i	−0.826741	−	0.562583i	$-0.809808\pi$
$283$	−5.11632	+	4.87840i	−0.304134	+	0.289991i	0.522607	+	0.852573i	$0.324959\pi$
$284$		0			0
$285$	−11.3697	−	8.09629i	−0.673480	−	0.479583i
$286$		0			0
$287$	25.6896	−	1.84462i	1.51641	−	0.108884i
$288$		0			0
$289$	−3.73042	−	3.55695i	−0.219437	−	0.209233i
$290$		0			0
$291$	−30.2471	+	1.44085i	−1.77311	+	0.0844638i
$292$		0			0
$293$	2.45980	+	17.1083i	0.143703	+	0.999479i	0.926256	+	0.376895i	$0.123008\pi$
$293$	2.45980	+	17.1083i	0.143703	+	0.999479i	−0.782553	+	0.622584i	$0.786083\pi$
$294$		0			0
$295$	−1.40886	−	0.202564i	−0.0820273	−	0.0117937i
$296$		0			0
$297$	5.58482	−	1.07639i	0.324064	−	0.0624582i
$298$		0			0
$299$	16.0573	−	3.14974i	0.928617	−	0.182154i
$300$		0			0
$301$	−0.264414	+	3.71165i	−0.0152406	+	0.213936i
$302$		0			0
$303$	−13.3689	+	5.35212i	−0.768026	+	0.307471i
$304$		0			0
$305$	−1.16173	−	0.465086i	−0.0665205	−	0.0266308i
$306$		0			0
$307$	1.00209	+	1.55929i	0.0571924	+	0.0889932i	0.868672	−	0.495387i	$-0.164974\pi$
$307$	1.00209	+	1.55929i	0.0571924	+	0.0889932i	−0.811480	+	0.584381i	$0.801338\pi$
$308$		0			0
$309$	5.81674	+	19.8100i	0.330903	+	1.12695i
$310$		0			0
$311$	−24.3882	+	8.44084i	−1.38293	+	0.478636i	−0.914400	−	0.404812i	$-0.867337\pi$
$311$	−24.3882	+	8.44084i	−1.38293	+	0.478636i	−0.468528	+	0.883448i	$0.655216\pi$
$312$		0			0
$313$	13.6807	−	19.2119i	0.773281	−	1.08592i	−0.220590	−	0.975367i	$-0.570798\pi$
$313$	13.6807	−	19.2119i	0.773281	−	1.08592i	0.993870	−	0.110554i	$-0.0352625\pi$
$314$		0			0
$315$	0.106291	−	4.51858i	0.00598883	−	0.254593i
$316$		0			0
$317$	−13.4361	+	1.28299i	−0.754648	+	0.0720601i	−0.465287	−	0.885160i	$-0.654049\pi$
$317$	−13.4361	+	1.28299i	−0.754648	+	0.0720601i	−0.289361	+	0.957220i	$0.593443\pi$
$318$		0			0
$319$	−4.63120	−	8.98328i	−0.259298	−	0.502967i
$320$		0			0
$321$	21.2717			1.18727
$322$		0			0
$323$	8.89667			0.495024
$324$		0			0
$325$	−4.84404	−	9.39614i	−0.268699	−	0.521204i
$326$		0			0
$327$	2.61361	−	0.249569i	0.144533	−	0.0138012i
$328$		0			0
$329$	−12.3122	+	20.2122i	−0.678792	+	1.11433i
$330$		0			0
$331$	17.7625	−	24.9439i	0.976315	−	1.37104i	0.0481643	−	0.998839i	$-0.484663\pi$
$331$	17.7625	−	24.9439i	0.976315	−	1.37104i	0.928151	−	0.372204i	$-0.121398\pi$
$332$		0			0
$333$	4.73193	−	1.63774i	0.259308	−	0.0897474i
$334$		0			0
$335$	6.37391	+	21.7075i	0.348244	+	1.18601i
$336$		0			0
$337$	−10.8898	−	16.9448i	−0.593204	−	0.923043i	−0.999955	−	0.00950428i	$-0.996975\pi$
$337$	−10.8898	−	16.9448i	−0.593204	−	0.923043i	0.406751	−	0.913539i	$-0.366662\pi$
$338$		0			0
$339$	−10.6860	−	4.27805i	−0.580386	−	0.232352i
$340$		0			0
$341$	5.43551	−	2.17605i	0.294350	−	0.117840i
$342$		0			0
$343$	1.30564	−	18.4742i	0.0704978	−	0.997512i
$344$		0			0
$345$	−22.9779	+	11.9420i	−1.23709	+	0.642936i
$346$		0			0
$347$	−9.61687	+	1.85350i	−0.516261	+	0.0995011i	−0.440725	−	0.897642i	$-0.645279\pi$
$347$	−9.61687	+	1.85350i	−0.516261	+	0.0995011i	−0.0755354	+	0.997143i	$0.524067\pi$
$348$		0			0
$349$	−22.9124	−	3.29430i	−1.22647	−	0.176340i	−0.501524	−	0.865144i	$-0.667227\pi$
$349$	−22.9124	−	3.29430i	−1.22647	−	0.176340i	−0.724948	+	0.688804i	$0.758136\pi$
$350$		0			0
$351$	2.21096	+	15.3776i	0.118013	+	0.820796i
$352$		0			0
$353$	3.88671	−	0.185147i	0.206869	−	0.00985436i	0.0561081	−	0.998425i	$-0.482131\pi$
$353$	3.88671	−	0.185147i	0.206869	−	0.00985436i	0.150760	+	0.988570i	$0.451828\pi$
$354$		0			0
$355$	6.34811	+	6.05291i	0.336923	+	0.321255i
$356$		0			0
$357$	9.68856	+	14.3062i	0.512773	+	0.757163i
$358$		0			0
$359$	−1.66163	−	1.18324i	−0.0876974	−	0.0624491i	0.535367	−	0.844619i	$-0.320173\pi$
$359$	−1.66163	−	1.18324i	−0.0876974	−	0.0624491i	−0.623065	+	0.782170i	$0.714113\pi$
$360$		0			0
$361$	−8.91505	+	8.50048i	−0.469213	+	0.447394i
$362$		0			0
$363$	16.2927	+	7.44064i	0.855147	+	0.390532i
$364$		0			0
$365$	12.9050	−	20.0805i	0.675476	−	1.05106i
$366$		0			0
$367$	12.5373	−	21.7152i	0.654440	−	1.13352i	−0.327594	−	0.944819i	$-0.606238\pi$
$367$	12.5373	−	21.7152i	0.654440	−	1.13352i	0.982034	−	0.188704i	$-0.0604288\pi$
$368$		0			0
$369$	−5.06097	+	2.92195i	−0.263463	+	0.152111i
$370$		0			0
$371$	−12.0988	−	3.86382i	−0.628139	−	0.200600i
$372$		0			0
$373$	−1.13625	−	11.8993i	−0.0588326	−	0.616123i	−0.976022	−	0.217672i	$-0.930154\pi$
$373$	−1.13625	−	11.8993i	−0.0588326	−	0.616123i	0.917189	−	0.398451i	$-0.130452\pi$
$374$		0			0
$375$	−7.08617	−	7.43176i	−0.365928	−	0.383774i
$376$		0			0
$377$	25.1121	−	11.4683i	1.29334	−	0.590647i
$378$		0			0
$379$	−5.19533	−	4.50178i	−0.266866	−	0.231241i	0.511140	−	0.859497i	$-0.329223\pi$
$379$	−5.19533	−	4.50178i	−0.266866	−	0.231241i	−0.778006	+	0.628257i	$0.783769\pi$
$380$		0			0
$381$	6.82771	+	1.65639i	0.349794	+	0.0848592i
$382$		0			0
$383$	−9.41510	−	4.85382i	−0.481089	−	0.248019i	0.200583	−	0.979677i	$-0.435716\pi$
$383$	−9.41510	−	4.85382i	−0.481089	−	0.248019i	−0.681672	+	0.731658i	$0.738747\pi$
$384$		0			0
$385$	5.63397	−	7.53052i	0.287134	−	0.383791i
$386$		0			0
$387$	−0.313793	−	0.783817i	−0.0159510	−	0.0398437i
$388$		0			0
$389$	−0.563813	−	2.92534i	−0.0285864	−	0.148321i	0.964831	−	0.262871i	$-0.0846694\pi$
$389$	−0.563813	−	2.92534i	−0.0285864	−	0.148321i	−0.993417	+	0.114550i	$0.963457\pi$
$390$		0			0
$391$	7.51507	−	14.6960i	0.380054	−	0.743208i
$392$		0			0
$393$	23.8341	+	27.5060i	1.20227	+	1.38749i
$394$		0			0
$395$	−20.5679	+	26.1542i	−1.03488	+	1.31596i
$396$		0			0
$397$	6.18671	+	7.86704i	0.310502	+	0.394835i	0.916110	−	0.400928i	$-0.131312\pi$
$397$	6.18671	+	7.86704i	0.310502	+	0.394835i	−0.605608	+	0.795763i	$0.707070\pi$
$398$		0			0
$399$	12.6810	+	2.75485i	0.634846	+	0.137915i
$400$		0			0
$401$	13.4814	−	14.1389i	0.673230	−	0.706063i	−0.295176	−	0.955443i	$-0.595378\pi$
$401$	13.4814	−	14.1389i	0.673230	−	0.706063i	0.968406	+	0.249380i	$0.0802268\pi$
$402$		0			0
$403$	5.23072	+	15.1132i	0.260560	+	0.752840i
$404$		0			0
$405$	−12.3425	−	27.0263i	−0.613303	−	1.34295i
$406$		0			0
$407$	9.99712	+	2.93542i	0.495539	+	0.145503i
$408$		0			0
$409$	2.46351	−	1.75425i	0.121813	−	0.0867423i	−0.517527	−	0.855667i	$-0.673147\pi$
$409$	2.46351	−	1.75425i	0.121813	−	0.0867423i	0.639339	+	0.768925i	$0.279208\pi$
$410$		0			0
$411$	−0.245334	+	5.15020i	−0.0121014	+	0.254040i
$412$		0			0
$413$	1.27813	−	0.342860i	0.0628928	−	0.0168710i
$414$		0			0
$415$	10.1878	+	17.6457i	0.500098	+	0.866195i
$416$		0			0
$417$	−20.1578	+	10.3921i	−0.987134	+	0.508903i
$418$		0			0
$419$	−2.25711	+	4.94239i	−0.110267	+	0.241452i	−0.956719	−	0.291014i	$-0.906007\pi$
$419$	−2.25711	+	4.94239i	−0.110267	+	0.241452i	0.846451	+	0.532466i	$0.178735\pi$
$420$		0			0
$421$	−4.89997	+	16.6878i	−0.238810	+	0.813312i	0.749651	+	0.661834i	$0.230221\pi$
$421$	−4.89997	+	16.6878i	−0.238810	+	0.813312i	−0.988461	+	0.151478i	$0.951597\pi$
$422$		0			0
$423$	0.510445	−	5.34562i	0.0248187	−	0.259913i
$424$		0			0
$425$	−10.4708	−	2.01808i	−0.507908	−	0.0978912i
$426$		0			0
$427$	1.16309	−	0.0280138i	0.0562856	−	0.00135568i
$428$		0			0
$429$	3.70562	−	7.18791i	0.178909	−	0.347035i
$430$		0			0
$431$	−8.22545	+	20.5462i	−0.396206	+	0.989675i	0.587392	+	0.809302i	$0.300155\pi$
$431$	−8.22545	+	20.5462i	−0.396206	+	0.989675i	−0.983598	+	0.180373i	$0.942270\pi$
$432$		0			0
$433$	4.62142	−	32.1427i	0.222091	−	1.54468i	−0.508017	−	0.861347i	$-0.669621\pi$
$433$	4.62142	−	32.1427i	0.222091	−	1.54468i	0.730108	−	0.683331i	$-0.239470\pi$
$434$		0			0
$435$	−33.0183	+	28.6105i	−1.58310	+	1.37177i
$436$		0			0
$437$	−3.53181	−	11.8832i	−0.168949	−	0.568448i
$438$		0			0
$439$	−15.8215	−	5.47587i	−0.755119	−	0.261349i	−0.0777301	−	0.996974i	$-0.524767\pi$
$439$	−15.8215	−	5.47587i	−0.755119	−	0.261349i	−0.677389	+	0.735625i	$0.736888\pi$
$440$		0			0
$441$	1.56399	+	3.90029i	0.0744756	+	0.185728i
$442$		0			0
$443$	−23.2575	+	18.2899i	−1.10500	+	0.868980i	−0.992202	−	0.124639i	$-0.960223\pi$
$443$	−23.2575	+	18.2899i	−1.10500	+	0.868980i	−0.112795	+	0.993618i	$0.535980\pi$
$444$		0			0
$445$	1.73722	+	36.4686i	0.0823519	+	1.72878i
$446$		0			0
$447$	−28.6394	+	8.40928i	−1.35460	+	0.397745i
$448$		0			0
$449$	22.1561	−	25.5695i	1.04561	−	1.20670i	0.0676950	−	0.997706i	$-0.478436\pi$
$449$	22.1561	−	25.5695i	1.04561	−	1.20670i	0.977917	−	0.208994i	$-0.0670190\pi$
$450$		0			0
$451$	−12.1048	−	1.15587i	−0.569995	−	0.0544279i
$452$		0			0
$453$	29.3651	−	7.12390i	1.37969	−	0.334710i
$454$		0			0
$455$	19.8141	+	16.3506i	0.928901	+	0.766526i
$456$		0			0
$457$	−18.2646	−	0.870050i	−0.854382	−	0.0406992i	−0.384180	−	0.923258i	$-0.625516\pi$
$457$	−18.2646	−	0.870050i	−0.854382	−	0.0406992i	−0.470202	+	0.882559i	$0.655819\pi$
$458$		0			0
$459$	13.5717	+	7.83562i	0.633472	+	0.365735i
$460$		0			0
$461$			19.9289i			0.928183i	0.885787	+	0.464091i	$0.153619\pi$
$461$			19.9289i			0.928183i	−0.885787	+	0.464091i	$0.846381\pi$
$462$		0			0
$463$	30.8247	+	19.8098i	1.43254	+	0.920641i	0.999817	+	0.0191158i	$0.00608512\pi$
$463$	30.8247	+	19.8098i	1.43254	+	0.920641i	0.432727	+	0.901525i	$0.357551\pi$
$464$		0			0
$465$	−14.6809	−	20.6165i	−0.680812	−	0.956066i
$466$		0			0
$467$	4.91493	+	20.2596i	0.227436	+	0.937504i	0.965005	+	0.262232i	$0.0844585\pi$
$467$	4.91493	+	20.2596i	0.227436	+	0.937504i	−0.737569	+	0.675272i	$0.764026\pi$
$468$		0			0
$469$	−13.3967	−	16.2159i	−0.618601	−	0.748783i
$470$		0			0
$471$	2.69749	−	13.9959i	0.124294	−	0.644896i
$472$		0			0
$473$	0.414181	−	1.70728i	0.0190440	−	0.0785006i
$474$		0			0
$475$	−6.73747	+	4.32991i	−0.309136	+	0.198670i
$476$		0			0
$477$	2.85244	−	0.410118i	0.130604	−	0.0187780i
$478$		0			0
$479$	−6.32402	−	4.97326i	−0.288952	−	0.227234i	0.463152	−	0.886279i	$-0.346718\pi$
$479$	−6.32402	−	4.97326i	−0.288952	−	0.227234i	−0.752104	+	0.659045i	$0.770961\pi$
$480$		0			0
$481$	−9.30837	+	26.8948i	−0.424425	+	1.22630i
$482$		0			0
$483$	15.2624	−	18.6202i	0.694462	−	0.847247i
$484$		0			0
$485$	−14.8539	+	42.9175i	−0.674480	+	1.94878i
$486$		0			0
$487$	−0.912122	−	0.717301i	−0.0413322	−	0.0325040i	0.597279	−	0.802033i	$-0.296248\pi$
$487$	−0.912122	−	0.717301i	−0.0413322	−	0.0325040i	−0.638611	+	0.769529i	$0.720491\pi$
$488$		0			0
$489$	−39.0802	+	5.61889i	−1.76727	+	0.254095i
$490$		0			0
$491$	8.32596	−	5.35077i	0.375745	−	0.241477i	−0.339114	−	0.940745i	$-0.610127\pi$
$491$	8.32596	−	5.35077i	0.375745	−	0.241477i	0.714859	+	0.699269i	$0.246491\pi$
$492$		0			0
$493$	6.56532	−	27.0626i	0.295687	−	1.21884i
$494$		0			0
$495$	−0.403847	+	2.09536i	−0.0181516	+	0.0941792i
$496$		0			0
$497$	−7.64152	−	2.84769i	−0.342769	−	0.127736i
$498$		0			0
$499$	−2.83338	−	11.6793i	−0.126839	−	0.522839i	−0.999410	−	0.0343508i	$-0.989064\pi$
$499$	−2.83338	−	11.6793i	−0.126839	−	0.522839i	0.872570	−	0.488488i	$-0.162452\pi$
$500$		0			0
$501$	−13.6031	−	19.1029i	−0.607742	−	0.853455i
$502$		0			0
$503$	2.20005	+	1.41389i	0.0980953	+	0.0630420i	0.588769	−	0.808301i	$-0.299613\pi$
$503$	2.20005	+	1.41389i	0.0980953	+	0.0630420i	−0.490673	+	0.871344i	$0.663249\pi$
$504$		0			0
$505$			21.5975i			0.961076i
$506$		0			0
$507$	−2.23213	−	1.28872i	−0.0991325	−	0.0572342i
$508$		0			0
$509$	24.1579	+	1.15078i	1.07078	+	0.0510074i	0.575559	−	0.817761i	$-0.304785\pi$
$509$	24.1579	+	1.15078i	1.07078	+	0.0510074i	0.495219	+	0.868768i	$0.335088\pi$
$510$		0			0
$511$	−3.67398	+	21.8860i	−0.162527	+	0.968178i
$512$		0			0
$513$	11.4382	−	2.77487i	0.505007	−	0.122513i
$514$		0			0
$515$	30.8246	+	2.94339i	1.35830	+	0.129701i
$516$		0			0
$517$	7.31721	−	8.44451i	0.321810	−	0.371389i
$518$		0			0
$519$	−11.8503	+	3.47957i	−0.520172	+	0.152736i
$520$		0			0
$521$	1.89243	+	39.7270i	0.0829089	+	1.74047i	0.531786	+	0.846879i	$0.321521\pi$
$521$	1.89243	+	39.7270i	0.0829089	+	1.74047i	−0.448877	+	0.893594i	$0.648176\pi$
$522$		0			0
$523$	17.7478	−	13.9570i	0.776058	−	0.610299i	−0.149562	−	0.988752i	$-0.547787\pi$
$523$	17.7478	−	13.9570i	0.776058	−	0.610299i	0.925620	+	0.378454i	$0.123544\pi$
$524$		0			0
$525$	−14.2998	−	6.11879i	−0.624096	−	0.267046i
$526$		0			0
$527$	15.2450	+	5.27634i	0.664082	+	0.229841i
$528$		0			0
$529$	−22.6126	−	4.20374i	−0.983155	−	0.182771i
$530$		0			0
$531$	−0.226919	+	0.196626i	−0.00984745	+	0.00853286i
$532$		0			0
$533$	4.72697	−	32.8768i	0.204748	−	1.42405i
$534$		0			0
$535$	11.8570	−	29.6175i	0.512625	−	1.28047i
$536$		0			0
$537$	−1.34831	+	2.61536i	−0.0581840	+	0.112861i
$538$		0			0
$539$	−2.05666	+	8.49852i	−0.0885866	+	0.366057i
$540$		0			0
$541$	34.1776	+	6.58720i	1.46941	+	0.283206i	0.860263	−	0.509851i	$-0.170299\pi$
$541$	34.1776	+	6.58720i	1.46941	+	0.283206i	0.609148	+	0.793056i	$0.291511\pi$
$542$		0			0
$543$	2.89673	−	30.3359i	0.124311	−	1.30184i
$544$		0			0
$545$	1.10937	−	3.77815i	0.0475200	−	0.161838i
$546$		0			0
$547$	15.6043	−	34.1687i	0.667194	−	1.46095i	−0.208470	−	0.978029i	$-0.566848\pi$
$547$	15.6043	−	34.1687i	0.667194	−	1.46095i	0.875664	−	0.482921i	$-0.160424\pi$
$548$		0			0
$549$	−0.234632	+	0.120961i	−0.0100138	+	0.00516250i
$550$		0			0
$551$	−10.4575	−	18.1130i	−0.445505	−	0.771638i
$552$		0			0
$553$	7.99801	−	29.8826i	0.340110	−	1.27074i
$554$		0			0
$555$	2.14308	−	44.9887i	0.0909685	−	1.90966i
$556$		0			0
$557$	−3.28386	+	2.33843i	−0.139142	+	0.0990823i	−0.647508	−	0.762058i	$-0.724189\pi$
$557$	−3.28386	+	2.33843i	−0.139142	+	0.0990823i	0.508367	+	0.861141i	$0.330249\pi$
$558$		0			0
$559$	4.60433	+	1.35195i	0.194742	+	0.0571815i
$560$		0			0
$561$	−3.38871	−	7.42024i	−0.143072	−	0.313283i
$562$		0			0
$563$	7.35239	+	21.2433i	0.309866	+	0.895300i	0.987181	+	0.159606i	$0.0510225\pi$
$563$	7.35239	+	21.2433i	0.309866	+	0.895300i	−0.677314	+	0.735694i	$0.736856\pi$
$564$		0			0
$565$	−11.9130	+	12.4940i	−0.501185	+	0.525627i
$566$		0			0
$567$	20.4450	+	18.5752i	0.858609	+	0.780087i
$568$		0			0
$569$	17.1345	+	21.7883i	0.718314	+	0.913411i	0.998922	−	0.0464114i	$-0.0147785\pi$
$569$	17.1345	+	21.7883i	0.718314	+	0.913411i	−0.280608	+	0.959822i	$0.590536\pi$
$570$		0			0
$571$	14.2178	−	18.0795i	0.594998	−	0.756602i	−0.391535	−	0.920163i	$-0.628056\pi$
$571$	14.2178	−	18.0795i	0.594998	−	0.756602i	0.986533	+	0.163561i	$0.0522981\pi$
$572$		0			0
$573$	−10.0367	−	11.5830i	−0.419289	−	0.483885i
$574$		0			0
$575$	1.46119	+	14.7868i	0.0609358	+	0.616653i
$576$		0			0
$577$	6.40796	+	33.2477i	0.266767	+	1.38412i	0.829974	+	0.557802i	$0.188355\pi$
$577$	6.40796	+	33.2477i	0.266767	+	1.38412i	−0.563207	+	0.826316i	$0.690433\pi$
$578$		0			0
$579$	−14.5701	−	36.3944i	−0.605513	−	1.51250i
$580$		0			0
$581$	−15.1683	−	11.3482i	−0.629287	−	0.470802i
$582$		0			0
$583$	5.32976	+	2.74768i	0.220736	+	0.113797i
$584$		0			0
$585$	−5.66451	−	1.37420i	−0.234199	−	0.0568160i
$586$		0			0
$587$	20.5031	+	17.7660i	0.846253	+	0.733283i	0.965728	−	0.259554i	$-0.0835757\pi$
$587$	20.5031	+	17.7660i	0.846253	+	0.733283i	−0.119475	+	0.992837i	$0.538121\pi$
$588$		0			0
$589$	11.0213	−	5.03324i	0.454123	−	0.207391i
$590$		0			0
$591$	5.76459	+	6.04573i	0.237124	+	0.248688i
$592$		0			0
$593$	0.529500	+	5.54518i	0.0217440	+	0.227713i	0.999811	+	0.0194243i	$0.00618334\pi$
$593$	0.529500	+	5.54518i	0.0217440	+	0.227713i	−0.978067	+	0.208289i	$0.933211\pi$
$594$		0			0
$595$	25.3196	−	5.51540i	1.03800	−	0.226109i
$596$		0			0
$597$	21.0232	−	12.1378i	0.860424	−	0.496766i
$598$		0			0
$599$	−18.4396	+	31.9383i	−0.753422	+	1.30496i	0.192734	+	0.981251i	$0.438265\pi$
$599$	−18.4396	+	31.9383i	−0.753422	+	1.30496i	−0.946155	+	0.323713i	$0.895069\pi$
$600$		0			0
$601$	−15.3376	+	23.8658i	−0.625635	+	0.973508i	0.373315	+	0.927705i	$0.378221\pi$
$601$	−15.3376	+	23.8658i	−0.625635	+	0.973508i	−0.998950	+	0.0458031i	$0.985415\pi$
$602$		0			0
$603$	4.34125	+	1.98258i	0.176789	+	0.0807371i
$604$		0			0
$605$	19.4417	−	18.5376i	0.790416	−	0.753661i
$606$		0			0
$607$	30.9583	+	22.0453i	1.25656	+	0.894790i	0.997472	−	0.0710644i	$-0.0226396\pi$
$607$	30.9583	+	22.0453i	1.25656	+	0.894790i	0.259085	+	0.965854i	$0.416579\pi$
$608$		0			0
$609$	17.7380	−	36.5413i	0.718778	−	1.48073i
$610$		0			0
$611$	22.0891	+	21.0619i	0.893630	+	0.852074i
$612$		0			0
$613$	5.28222	−	0.251623i	0.213347	−	0.0101630i	0.0593637	−	0.998236i	$-0.481093\pi$
$613$	5.28222	−	0.251623i	0.213347	−	0.0101630i	0.153983	+	0.988073i	$0.450790\pi$
$614$		0			0
$615$	7.48071	+	52.0294i	0.301651	+	2.09803i
$616$		0			0
$617$	−22.7953	−	3.27748i	−0.917706	−	0.131946i	−0.332754	−	0.943014i	$-0.607978\pi$
$617$	−22.7953	−	3.27748i	−0.917706	−	0.131946i	−0.584953	+	0.811068i	$0.698887\pi$
$618$		0			0
$619$	15.3861	−	2.96543i	0.618420	−	0.119191i	0.129587	−	0.991568i	$-0.458635\pi$
$619$	15.3861	−	2.96543i	0.618420	−	0.119191i	0.488833	+	0.872377i	$0.337423\pi$
$620$		0			0
$621$	5.07821	−	21.2381i	0.203782	−	0.852256i
$622$		0			0
$623$	−14.8403	−	30.5282i	−0.594563	−	1.22308i
$624$		0			0
$625$	−28.6792	+	11.4814i	−1.14717	+	0.459257i
$626$		0			0
$627$	−5.68779	−	2.27705i	−0.227148	−	0.0909365i
$628$		0			0
$629$	15.5209	+	24.1509i	0.618858	+	0.962961i
$630$		0			0
$631$	−6.40276	−	21.8058i	−0.254890	−	0.868076i	−0.983154	−	0.182779i	$-0.941491\pi$
$631$	−6.40276	−	21.8058i	−0.254890	−	0.868076i	0.728264	−	0.685297i	$-0.240327\pi$
$632$		0			0
$633$	40.5291	−	14.0272i	1.61089	−	0.557533i
$634$		0			0
$635$	6.11210	−	8.58324i	0.242551	−	0.340615i
$636$		0			0
$637$	−22.9202	−	6.71598i	−0.908131	−	0.266097i
$638$		0			0
$639$	1.84194	−	0.175884i	0.0728660	−	0.00695786i
$640$		0			0
$641$	−12.7320	−	24.6966i	−0.502883	−	0.975457i	−0.994509	−	0.104651i	$-0.966628\pi$
$641$	−12.7320	−	24.6966i	−0.502883	−	0.975457i	0.491626	−	0.870807i	$-0.336403\pi$
$642$		0			0
$643$	7.88943			0.311129			0.155564	−	0.987826i	$-0.450280\pi$
$643$	7.88943			0.311129			0.155564	+	0.987826i	$0.450280\pi$
$644$		0			0
$645$	−7.59424			−0.299023
$646$		0			0
$647$	−22.3341	−	43.3220i	−0.878042	−	1.70316i	−0.693651	−	0.720312i	$-0.743999\pi$
$647$	−22.3341	−	43.3220i	−0.878042	−	1.70316i	−0.184392	−	0.982853i	$-0.559032\pi$
$648$		0			0
$649$	−0.621941	+	0.0593882i	−0.0244133	+	0.00233119i
$650$		0			0
$651$	20.0959	+	12.2413i	0.787620	+	0.479776i
$652$		0			0
$653$	21.4182	−	30.0776i	0.838157	−	1.17703i	−0.144114	−	0.989561i	$-0.546033\pi$
$653$	21.4182	−	30.0776i	0.838157	−	1.17703i	0.982271	−	0.187466i	$-0.0600275\pi$
$654$		0			0
$655$	51.5832	−	17.8531i	2.01552	−	0.697579i
$656$		0			0
$657$	−1.41862	−	4.83137i	−0.0553455	−	0.188490i
$658$		0			0
$659$	−16.2401	−	25.2702i	−0.632626	−	0.984386i	−0.998555	−	0.0537426i	$-0.982885\pi$
$659$	−16.2401	−	25.2702i	−0.632626	−	0.984386i	0.365929	−	0.930643i	$-0.380751\pi$
$660$		0			0
$661$	32.3114	+	12.9355i	1.25677	+	0.503134i	0.901966	−	0.431808i	$-0.142124\pi$
$661$	32.3114	+	12.9355i	1.25677	+	0.503134i	0.354802	+	0.934941i	$0.384548\pi$
$662$		0			0
$663$	20.6859	−	8.28140i	0.803375	−	0.321623i
$664$		0			0
$665$	10.9042	−	16.1208i	0.422848	−	0.625137i
$666$		0			0
$667$	−38.7535	+	1.97415i	−1.50054	+	0.0764395i
$668$		0			0
$669$	6.10580	−	1.17680i	0.236064	−	0.0454976i
$670$		0			0
$671$	−0.543688	−	0.0781705i	−0.0209888	−	0.00301774i
$672$		0			0
$673$	−5.49284	−	38.2035i	−0.211733	−	1.47264i	−0.767366	−	0.641210i	$-0.778433\pi$
$673$	−5.49284	−	38.2035i	−0.211733	−	1.47264i	0.555633	−	0.831428i	$-0.312476\pi$
$674$		0			0
$675$	−14.0914	+	0.671255i	−0.542378	+	0.0258366i
$676$		0			0
$677$	−30.3982	−	28.9847i	−1.16830	−	1.11397i	−0.991551	−	0.129715i	$-0.958594\pi$
$677$	−30.3982	−	28.9847i	−1.16830	−	1.11397i	−0.176748	−	0.984256i	$-0.556558\pi$
$678$		0			0
$679$	−3.02403	−	42.1151i	−0.116052	−	1.61623i
$680$		0			0
$681$	17.7660	+	12.6511i	0.680796	+	0.484793i
$682$		0			0
$683$	22.6055	−	21.5543i	0.864974	−	0.824751i	−0.120826	−	0.992674i	$-0.538554\pi$
$683$	22.6055	−	21.5543i	0.864974	−	0.824751i	0.985800	+	0.167923i	$0.0537060\pi$
$684$		0			0
$685$	7.03409	+	3.21236i	0.268759	+	0.122738i
$686$		0			0
$687$	15.6508	−	24.3532i	0.597117	−	0.929132i
$688$		0			0
$689$	−8.18953	+	14.1847i	−0.311996	+	0.540393i
$690$		0			0
$691$	−21.8780	+	12.6312i	−0.832277	+	0.480515i	−0.854632	−	0.519235i	$-0.826217\pi$
$691$	−21.8780	+	12.6312i	−0.832277	+	0.480515i	0.0223547	+	0.999750i	$0.492884\pi$
$692$		0			0
$693$	−0.422263	−	1.93849i	−0.0160405	−	0.0736371i
$694$		0			0
$695$	3.23317	+	33.8593i	0.122641	+	1.28436i
$696$		0			0
$697$	−23.1208	−	24.2484i	−0.875763	−	0.918474i
$698$		0			0
$699$	−42.5752	+	19.4434i	−1.61034	+	0.735418i
$700$		0			0
$701$	−14.1484	−	12.2596i	−0.534377	−	0.463040i	0.345381	−	0.938463i	$-0.387750\pi$
$701$	−14.1484	−	12.2596i	−0.534377	−	0.463040i	−0.879758	+	0.475422i	$0.842295\pi$
$702$		0			0
$703$	20.9537	+	5.08330i	0.790283	+	0.191720i
$704$		0			0
$705$	−42.9319	−	22.1329i	−1.61691	−	0.833575i
$706$		0			0
$707$	−7.90955	−	18.4562i	−0.297469	−	0.694117i
$708$		0			0
$709$	6.57595	+	16.4259i	0.246965	+	0.616889i	0.999113	−	0.0421053i	$-0.0134065\pi$
$709$	6.57595	+	16.4259i	0.246965	+	0.616889i	−0.752148	+	0.658994i	$0.770982\pi$
$710$		0			0
$711$	1.32834	+	6.89207i	0.0498165	+	0.258473i
$712$		0			0
$713$	0.995556	−	22.4571i	0.0372839	−	0.841025i
$714$		0			0
$715$	−7.94248	−	9.16612i	−0.297032	−	0.342793i
$716$		0			0
$717$	4.49184	−	5.71183i	0.167751	−	0.213312i
$718$		0			0
$719$	16.5736	+	21.0751i	0.618092	+	0.785968i	0.989813	−	0.142376i	$-0.0454744\pi$
$719$	16.5736	+	21.0751i	0.618092	+	0.785968i	−0.371720	+	0.928345i	$0.621232\pi$
$720$		0			0
$721$	−27.4192	+	8.77346i	−1.02114	+	0.326741i
$722$		0			0
$723$	−23.9880	+	25.1579i	−0.892123	+	0.935632i
$724$		0			0
$725$	8.19915	+	23.6899i	0.304509	+	0.879820i
$726$		0			0
$727$	3.94548	+	8.63940i	0.146330	+	0.320418i	0.968577	−	0.248712i	$-0.0800074\pi$
$727$	3.94548	+	8.63940i	0.146330	+	0.320418i	−0.822248	+	0.569130i	$0.807280\pi$
$728$		0			0
$729$	18.8553	+	5.53641i	0.698343	+	0.205052i
$730$		0			0
$731$	3.94301	−	2.80780i	0.145837	−	0.103850i
$732$		0			0
$733$	−2.20198	+	46.2252i	−0.0813319	+	1.70737i	0.477948	+	0.878388i	$0.341381\pi$
$733$	−2.20198	+	46.2252i	−0.0813319	+	1.70737i	−0.559280	+	0.828979i	$0.688922\pi$
$734$		0			0
$735$	37.7976	−	0.0212554i	1.39419	−	0.000784017i
$736$		0			0
$737$	4.96531	+	8.60017i	0.182900	+	0.316791i
$738$		0			0
$739$	45.8616	−	23.6433i	1.68705	−	0.869733i	0.699084	−	0.715040i	$-0.253592\pi$
$739$	45.8616	−	23.6433i	1.68705	−	0.869733i	0.987963	−	0.154693i	$-0.0494388\pi$
$740$		0			0
$741$	6.95197	−	15.2227i	0.255387	−	0.559220i
$742$		0			0
$743$	−12.1066	+	41.2311i	−0.444146	+	1.51262i	0.368367	+	0.929681i	$0.379917\pi$
$743$	−12.1066	+	41.2311i	−0.444146	+	1.51262i	−0.812513	+	0.582943i	$0.801901\pi$
$744$		0			0
$745$	−4.25528	+	44.5633i	−0.155901	+	1.63267i
$746$		0			0
$747$	4.22055	+	0.813445i	0.154422	+	0.0297624i
$748$		0			0
$749$	0.714192	+	29.6520i	0.0260960	+	1.08346i
$750$		0			0
$751$	−9.28806	+	18.0163i	−0.338926	+	0.657425i	−0.995282	−	0.0970266i	$-0.969067\pi$
$751$	−9.28806	+	18.0163i	−0.338926	+	0.657425i	0.656356	+	0.754452i	$0.272097\pi$
$752$		0			0
$753$	−15.0427	+	37.5748i	−0.548186	+	1.36930i
$754$		0			0
$755$	6.44951	−	44.8573i	0.234722	−	1.63252i
$756$		0			0
$757$	−5.58172	+	4.83659i	−0.202871	+	0.175789i	−0.750371	−	0.661017i	$-0.770125\pi$
$757$	−5.58172	+	4.83659i	−0.202871	+	0.175789i	0.547500	+	0.836806i	$0.315580\pi$
$758$		0			0
$759$	−8.56586	+	7.47196i	−0.310921	+	0.271215i
$760$		0			0
$761$	3.81518	+	1.32045i	0.138300	+	0.0478662i	0.395341	−	0.918534i	$-0.370626\pi$
$761$	3.81518	+	1.32045i	0.138300	+	0.0478662i	−0.257041	+	0.966401i	$0.582748\pi$
$762$		0			0
$763$	0.435643	+	3.63491i	0.0157713	+	0.131593i
$764$		0			0
$765$	−4.62172	+	3.63456i	−0.167099	+	0.131408i
$766$		0			0
$767$	−0.0812016	−	1.70463i	−0.00293202	−	0.0615507i
$768$		0			0
$769$	−39.0537	+	11.4672i	−1.40831	+	0.413518i	−0.895530	−	0.445001i	$-0.853203\pi$
$769$	−39.0537	+	11.4672i	−1.40831	+	0.413518i	−0.512782	+	0.858519i	$0.671385\pi$
$770$		0			0
$771$	−17.6636	+	20.3848i	−0.636138	+	0.734142i
$772$		0			0
$773$	−29.4564	−	2.81275i	−1.05947	−	0.101167i	−0.449257	−	0.893403i	$-0.648311\pi$
$773$	−29.4564	−	2.81275i	−1.05947	−	0.101167i	−0.610216	+	0.792235i	$0.708917\pi$
$774$		0			0
$775$	−14.1130	+	3.42378i	−0.506954	+	0.122986i
$776$		0			0
$777$	14.6446	+	39.2300i	0.525373	+	1.40737i
$778$		0			0
$779$	−25.1352	−	1.19734i	−0.900563	−	0.0428991i
$780$		0			0
$781$	3.33429	+	1.92506i	0.119310	+	0.0688839i
$782$		0			0
$783$		−	36.8413i		−	1.31660i
$784$		0			0
$785$	−17.9835	−	11.5573i	−0.641858	−	0.412497i
$786$		0			0
$787$	29.3234	+	41.1790i	1.04527	+	1.46787i	0.876006	+	0.482300i	$0.160199\pi$
$787$	29.3234	+	41.1790i	1.04527	+	1.46787i	0.169261	+	0.985571i	$0.445862\pi$
$788$		0			0
$789$	5.61447	+	23.1431i	0.199880	+	0.823918i
$790$		0			0
$791$	5.60468	−	15.0396i	0.199280	−	0.534748i
$792$		0			0
$793$	0.283945	−	1.47325i	0.0100832	−	0.0523165i
$794$		0			0
$795$	6.11106	−	25.1901i	0.216737	−	0.893402i
$796$		0			0
$797$	−14.2239	+	9.14114i	−0.503836	+	0.323796i	−0.767749	−	0.640751i	$-0.778623\pi$
$797$	−14.2239	+	9.14114i	−0.503836	+	0.323796i	0.263913	+	0.964547i	$0.414987\pi$
$798$		0			0
$799$	30.4739	−	4.38148i	1.07809	−	0.155006i
$800$		0			0
$801$	6.05403	+	4.76094i	0.213908	+	0.168219i
$802$		0			0
$803$	3.42684	−	9.90119i	0.120930	−	0.349405i
$804$		0			0
$805$	−17.4183	−	31.6295i	−0.613913	−	1.11479i
$806$		0			0
$807$	−0.891828	+	2.57677i	−0.0313938	+	0.0907065i
$808$		0			0
$809$	35.1394	+	27.6339i	1.23544	+	0.971557i	1.00000		0.000332402i	$-0.000105807\pi$
$809$	35.1394	+	27.6339i	1.23544	+	0.971557i	0.235436	+	0.971890i	$0.424348\pi$
$810$		0			0
$811$	−2.48801	+	0.357721i	−0.0873658	+	0.0125613i	−0.185859	−	0.982576i	$-0.559507\pi$
$811$	−2.48801	+	0.357721i	−0.0873658	+	0.0125613i	0.0984933	+	0.995138i	$0.468598\pi$
$812$		0			0
$813$	30.1661	−	19.3866i	1.05797	−	0.679917i
$814$		0			0
$815$	−13.9603	+	57.5452i	−0.489008	+	2.01572i
$816$		0			0
$817$	0.688027	−	3.56982i	0.0240710	−	0.124892i
$818$		0			0
$819$	5.34389	−	0.900164i	0.186731	−	0.0314543i
$820$		0			0
$821$	−3.70585	−	15.2757i	−0.129335	−	0.533127i	−0.999206	−	0.0398469i	$-0.987313\pi$
$821$	−3.70585	−	15.2757i	−0.129335	−	0.533127i	0.869871	−	0.493280i	$-0.164202\pi$
$822$		0			0
$823$	−7.86453	−	11.0442i	−0.274140	−	0.384976i	0.654436	−	0.756117i	$-0.272906\pi$
$823$	−7.86453	−	11.0442i	−0.274140	−	0.384976i	−0.928576	+	0.371141i	$0.878967\pi$
$824$		0			0
$825$	6.17763	+	3.97012i	0.215078	+	0.138222i
$826$		0			0
$827$		−	25.0724i		−	0.871854i	−0.899982	−	0.435927i	$-0.856421\pi$
$827$		−	25.0724i		−	0.871854i	0.899982	−	0.435927i	$-0.143579\pi$
$828$		0			0
$829$	−32.6538	−	18.8527i	−1.13411	−	0.654780i	−0.189147	−	0.981949i	$-0.560572\pi$
$829$	−32.6538	−	18.8527i	−1.13411	−	0.654780i	−0.944966	+	0.327169i	$0.893905\pi$
$830$		0			0
$831$	5.56129	+	0.264917i	0.192919	+	0.00918987i
$832$		0			0
$833$	−19.6171	+	13.9859i	−0.679691	+	0.484582i
$834$		0			0
$835$	−34.1803	+	8.29206i	−1.18286	+	0.286959i
$836$		0			0
$837$	21.2457	+	2.02871i	0.734357	+	0.0701226i
$838$		0			0
$839$	20.9380	−	24.1637i	0.722860	−	0.834225i	−0.268788	−	0.963199i	$-0.586623\pi$
$839$	20.9380	−	24.1637i	0.722860	−	0.834225i	0.991648	+	0.128975i	$0.0411686\pi$
$840$		0			0
$841$	−34.9894	+	10.2738i	−1.20653	+	0.354269i
$842$		0			0
$843$	2.65083	+	55.6478i	0.0912994	+	1.91661i
$844$		0			0
$845$	−3.03856	+	2.38955i	−0.104530	+	0.0822030i
$846$		0			0
$847$	−9.82500	+	22.9614i	−0.337591	+	0.788962i
$848$		0			0
$849$	12.6760	+	4.38719i	0.435038	+	0.150568i
$850$		0			0
$851$	26.0966	−	30.3185i	0.894579	−	1.03930i
$852$		0			0
$853$	−3.43335	+	2.97502i	−0.117556	+	0.101863i	−0.711655	−	0.702529i	$-0.752054\pi$
$853$	−3.43335	+	2.97502i	−0.117556	+	0.101863i	0.594099	+	0.804392i	$0.297509\pi$
$854$		0			0
$855$	−0.628453	+	4.37099i	−0.0214926	+	0.149485i
$856$		0			0
$857$	−8.43236	+	21.0630i	−0.288044	+	0.719499i	0.711809	+	0.702373i	$0.247876\pi$
$857$	−8.43236	+	21.0630i	−0.288044	+	0.719499i	−0.999853	+	0.0171263i	$0.994548\pi$
$858$		0			0
$859$	−18.1157	+	35.1395i	−0.618100	+	1.19895i	0.347198	+	0.937792i	$0.387133\pi$
$859$	−18.1157	+	35.1395i	−0.618100	+	1.19895i	−0.965297	+	0.261154i	$0.915897\pi$
$860$		0			0
$861$	−25.4471	−	41.7223i	−0.867236	−	1.42189i
$862$		0			0
$863$	−2.04459	−	0.394062i	−0.0695986	−	0.0134140i	0.154333	−	0.988019i	$-0.450677\pi$
$863$	−2.04459	−	0.394062i	−0.0695986	−	0.0134140i	−0.223932	+	0.974605i	$0.571889\pi$
$864$		0			0
$865$	−1.76074	+	18.4393i	−0.0598669	+	0.626955i
$866$		0			0
$867$	−2.75541	+	9.38407i	−0.0935787	+	0.318700i
$868$		0			0
$869$	−6.06707	+	13.2850i	−0.205811	+	0.450664i
$870$		0			0
$871$	−24.1102	+	12.4297i	−0.816942	+	0.421163i
$872$		0			0
$873$	4.79019	+	8.29684i	0.162123	+	0.280806i
$874$		0			0
$875$	10.1217	−	10.1274i	0.342177	−	0.342369i
$876$		0			0
$877$	−0.985723	+	20.6929i	−0.0332855	+	0.698749i	0.919132	+	0.393951i	$0.128892\pi$
$877$	−0.985723	+	20.6929i	−0.0332855	+	0.698749i	−0.952417	+	0.304798i	$0.901411\pi$
$878$		0			0
$879$	26.7148	−	19.0235i	0.901068	−	0.641648i
$880$		0			0
$881$	−23.2276	−	6.82022i	−0.782556	−	0.229779i	−0.134036	−	0.990977i	$-0.542794\pi$
$881$	−23.2276	−	6.82022i	−0.782556	−	0.229779i	−0.648520	+	0.761197i	$0.724612\pi$
$882$		0			0
$883$	−9.66357	−	21.1603i	−0.325205	−	0.712100i	0.674451	−	0.738319i	$-0.264380\pi$
$883$	−9.66357	−	21.1603i	−0.325205	−	0.712100i	−0.999656	+	0.0262198i	$0.991653\pi$
$884$		0			0
$885$	0.883325	+	2.55220i	0.0296926	+	0.0857913i
$886$		0			0
$887$	4.13605	−	4.33776i	0.138875	−	0.145648i	−0.650623	−	0.759401i	$-0.725492\pi$
$887$	4.13605	−	4.33776i	0.138875	−	0.145648i	0.789498	+	0.613753i	$0.210341\pi$
$888$		0			0
$889$	−2.07971	+	9.57323i	−0.0697512	+	0.321076i
$890$		0			0
$891$	−8.06173	−	10.2513i	−0.270078	−	0.343432i
$892$		0			0
$893$	14.2936	−	18.1758i	0.478317	−	0.608230i
$894$		0			0
$895$	2.88992	+	3.33515i	0.0965994	+	0.111482i
$896$		0			0
$897$	−19.2733	−	24.3424i	−0.643516	−	0.812768i
$898$		0			0
$899$	−7.17736	−	37.2397i	−0.239378	−	1.24201i
$900$		0			0
$901$	6.14057	+	15.3384i	0.204572	+	0.510997i
$902$		0			0
$903$	6.48967	−	2.78120i	0.215963	−	0.0925525i
$904$		0			0
$905$	−40.6234	−	20.9428i	−1.35037	−	0.696163i
$906$		0			0
$907$	3.35089	+	0.812916i	0.111264	+	0.0269924i	0.291005	−	0.956722i	$-0.406011\pi$
$907$	3.35089	+	0.812916i	0.111264	+	0.0269924i	−0.179740	+	0.983714i	$0.557526\pi$
$908$		0			0
$909$	3.44320	+	2.98355i	0.114204	+	0.0989580i
$910$		0			0
$911$	−8.09030	+	3.69472i	−0.268044	+	0.122411i	−0.544903	−	0.838499i	$-0.683434\pi$
$911$	−8.09030	+	3.69472i	−0.268044	+	0.122411i	0.276860	+	0.960910i	$0.410706\pi$
$912$		0			0
$913$	6.17185	+	6.47285i	0.204258	+	0.214220i
$914$		0			0
$915$	0.225702	+	2.36366i	0.00746147	+	0.0781400i
$916$		0			0
$917$	−37.5423	+	34.1475i	−1.23976	+	1.12765i
$918$		0			0
$919$	25.1758	−	14.5353i	0.830474	−	0.479474i	−0.0235411	−	0.999723i	$-0.507494\pi$
$919$	25.1758	−	14.5353i	0.830474	−	0.479474i	0.854015	+	0.520249i	$0.174161\pi$
$920$		0			0
$921$	1.75849	−	3.04579i	0.0579441	−	0.100362i
$922$		0			0
$923$	−5.68571	+	8.84714i	−0.187147	+	0.291207i
$924$		0			0
$925$	−23.5080	−	10.7357i	−0.772938	−	0.352989i
$926$		0			0
$927$	4.72747	−	4.50763i	0.155270	−	0.148050i
$928$		0			0
$929$	0.933929	+	0.665048i	0.0306412	+	0.0218195i	0.595275	−	0.803522i	$-0.297043\pi$
$929$	0.933929	+	0.665048i	0.0306412	+	0.0218195i	−0.564634	+	0.825342i	$0.690983\pi$
$930$		0			0
$931$	−3.41442	+	17.7695i	−0.111903	+	0.582370i
$932$		0			0
$933$	35.4402	+	33.7922i	1.16026	+	1.10631i
$934$		0			0
$935$	−12.2204	+	0.582131i	−0.399651	+	0.0190377i
$936$		0			0
$937$	1.80041	+	12.5221i	0.0588168	+	0.409080i	0.997866	+	0.0652968i	$0.0207994\pi$
$937$	1.80041	+	12.5221i	0.0588168	+	0.409080i	−0.939049	+	0.343783i	$0.888292\pi$
$938$		0			0
$939$	−44.2961	−	6.36882i	−1.44555	−	0.207839i
$940$		0			0
$941$	33.1627	−	6.39159i	1.08107	−	0.208360i	0.382541	−	0.923938i	$-0.375049\pi$
$941$	33.1627	−	6.39159i	1.08107	−	0.208360i	0.698532	+	0.715579i	$0.253837\pi$
$942$		0			0
$943$	−23.2097	+	40.5083i	−0.755812	+	1.31913i
$944$		0			0
$945$	30.8323	−	14.9881i	1.00298	−	0.487564i
$946$		0			0
$947$	47.0882	−	18.8513i	1.53016	−	0.612584i	0.554562	−	0.832142i	$-0.312886\pi$
$947$	47.0882	−	18.8513i	1.53016	−	0.612584i	0.975599	+	0.219558i	$0.0704615\pi$
$948$		0			0
$949$	26.5692	+	10.6367i	0.862472	+	0.345282i
$950$		0			0
$951$	13.8460	+	21.5448i	0.448987	+	0.698637i
$952$		0			0
$953$	15.8415	+	53.9511i	0.513155	+	1.74765i	0.652885	+	0.757457i	$0.273558\pi$
$953$	15.8415	+	53.9511i	0.513155	+	1.74765i	−0.139730	+	0.990190i	$0.544624\pi$
$954$		0			0
$955$	−21.7220	+	7.51806i	−0.702908	+	0.243279i
$956$		0			0
$957$	−11.1238	+	15.6212i	−0.359582	+	0.504963i
$958$		0			0
$959$	−7.18745	−	0.169071i	−0.232095	−	0.00545959i
$960$		0			0
$961$	−8.98899	+	0.858344i	−0.289967	+	0.0276885i
$962$		0			0
$963$	−3.08382	−	5.98177i	−0.0993746	−	0.192760i
$964$		0			0
$965$	−58.7950			−1.89268
$966$		0			0
$967$	−20.4492			−0.657603			−0.328802	−	0.944399i	$-0.606645\pi$
$967$	−20.4492			−0.657603			−0.328802	+	0.944399i	$0.606645\pi$
$968$		0			0
$969$	−7.73531	−	15.0044i	−0.248494	−	0.482011i
$970$		0			0
$971$	13.5221	−	1.29120i	0.433945	−	0.0414367i	0.124202	−	0.992257i	$-0.460363\pi$
$971$	13.5221	−	1.29120i	0.433945	−	0.0414367i	0.309743	+	0.950820i	$0.399757\pi$
$972$		0			0
$973$	−15.1630	−	27.7505i	−0.486105	−	0.889640i
$974$		0			0
$975$	−11.6351	+	16.3392i	−0.372620	+	0.523272i
$976$		0			0
$977$	15.7612	−	5.45501i	0.504246	−	0.174521i	−0.0630896	−	0.998008i	$-0.520095\pi$
$977$	15.7612	−	5.45501i	0.504246	−	0.174521i	0.567336	+	0.823487i	$0.307974\pi$
$978$		0			0
$979$	4.51499	+	15.3766i	0.144300	+	0.491439i
$980$		0			0
$981$	−0.449084	−	0.698788i	−0.0143381	−	0.0223106i
$982$		0			0
$983$	−43.3434	−	17.3521i	−1.38244	−	0.553446i	−0.443113	−	0.896466i	$-0.646126\pi$
$983$	−43.3434	−	17.3521i	−1.38244	−	0.553446i	−0.939328	+	0.343020i	$0.888550\pi$
$984$		0			0
$985$	11.6310	−	4.65634i	0.370594	−	0.148363i
$986$		0			0
$987$	44.7932	+	3.19101i	1.42578	+	0.101571i
$988$		0			0
$989$	−5.31564	−	4.15197i	−0.169028	−	0.132025i
$990$		0			0
$991$	−50.5538	+	9.74345i	−1.60590	+	0.309511i	−0.911882	−	0.410452i	$-0.865371\pi$
$991$	−50.5538	+	9.74345i	−1.60590	+	0.309511i	−0.694013	+	0.719963i	$0.744159\pi$
$992$		0			0
$993$	−57.5123	−	8.26902i	−1.82510	−	0.262409i
$994$		0			0
$995$	−5.18138	−	36.0373i	−0.164261	−	1.14246i
$996$		0			0
$997$	20.4845	−	0.975797i	0.648751	−	0.0309038i	0.279372	−	0.960183i	$-0.409874\pi$
$997$	20.4845	−	0.975797i	0.648751	−	0.0309038i	0.369378	+	0.929279i	$0.379571\pi$
$998$		0			0
$999$	27.4873	+	26.2091i	0.869661	+	0.829220i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.5	yes	320
7.5	odd	6	inner	644.2.bc.a.33.5	✓	320
23.7	odd	22	inner	644.2.bc.a.605.5	yes	320
161.145	even	66	inner	644.2.bc.a.145.5	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.5	✓	320	7.5	odd	6	inner
644.2.bc.a.145.5	yes	320	161.145	even	66	inner
644.2.bc.a.493.5	yes	320	1.1	even	1	trivial
644.2.bc.a.605.5	yes	320	23.7	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.869461 - 1.68652i) q^{3} +(-2.83286 + 0.270506i) q^{5} +(2.32176 - 1.26863i) q^{7} +(-0.348215 + 0.489000i) q^{9} +O(q^{10})\)	\(q+(-0.869461 - 1.68652i) q^{3} +(-2.83286 + 0.270506i) q^{5} +(2.32176 - 1.26863i) q^{7} +(-0.348215 + 0.489000i) q^{9} +(-1.18042 + 0.408547i) q^{11} +(-0.961267 - 3.27377i) q^{13} +(2.91928 + 4.54248i) q^{15} +(-3.19520 - 1.27917i) q^{17} +(-2.39977 + 0.960722i) q^{19} +(-4.15825 - 2.81268i) q^{21} +(-0.440128 + 4.77559i) q^{23} +(3.04229 - 0.586354i) q^{25} +(-4.50694 - 0.648000i) q^{27} +(1.15149 + 8.00878i) q^{29} +(-4.68192 + 0.223027i) q^{31} +(1.71535 + 1.63558i) q^{33} +(-6.23407 + 4.22189i) q^{35} +(-6.79455 - 4.83838i) q^{37} +(-4.68550 + 4.46761i) q^{39} +(8.85506 + 4.04397i) q^{41} +(-0.760372 + 1.18316i) q^{43} +(0.854168 - 1.47946i) q^{45} +(-7.74681 + 4.47262i) q^{47} +(3.78117 - 5.89090i) q^{49} +(0.620766 + 6.50096i) q^{51} +(-3.31269 - 3.47425i) q^{53} +(3.23345 - 1.47667i) q^{55} +(3.70678 + 3.21194i) q^{57} +(0.486069 + 0.117919i) q^{59} +(0.390850 + 0.201497i) q^{61} +(-0.188115 + 1.57710i) q^{63} +(3.60871 + 9.01412i) q^{65} +(-1.50457 - 7.80643i) q^{67} +(8.43681 - 3.40991i) q^{69} +(-2.01845 - 2.32942i) q^{71} +(-5.18503 + 6.59330i) q^{73} +(-3.63405 - 4.62108i) q^{75} +(-2.22236 + 2.44606i) q^{77} +(8.06847 - 8.46197i) q^{79} +(3.41477 + 9.86634i) q^{81} +(-2.97437 - 6.51296i) q^{83} +(9.39759 + 2.75938i) q^{85} +(12.5058 - 8.90534i) q^{87} +(0.610460 - 12.8151i) q^{89} +(-6.38503 - 6.38144i) q^{91} +(4.44689 + 7.70224i) q^{93} +(6.53833 - 3.37074i) q^{95} +(6.62960 - 14.5168i) q^{97} +(0.211260 - 0.719487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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