LMFDB - Embedded newform 1120.2.bz.c.591.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(271,1120)] 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("1120.271"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6,0,2,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.c.271.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.275255 + 0.158919i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-1.44949 - 2.51059i) q^{9} +(2.44949 - 4.24264i) q^{11} +4.44949 q^{13} +0.317837i q^{15} +(-4.22474 - 2.43916i) q^{17} +(-3.67423 + 2.12132i) q^{19} +(-0.825765 - 0.158919i) q^{21} +(3.94949 - 2.28024i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.87492i q^{27} -7.24604i q^{29} +(-0.775255 + 1.34278i) q^{31} +(1.34847 - 0.778539i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(3.00000 - 1.73205i) q^{37} +(1.22474 + 0.707107i) q^{39} -8.02458i q^{41} +9.44949 q^{43} +(1.44949 - 2.51059i) q^{45} +(3.00000 + 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-0.775255 - 1.34278i) q^{51} +(1.77526 + 1.02494i) q^{53} +4.89898 q^{55} -1.34847 q^{57} +(-3.12372 - 1.80348i) q^{59} +(-0.174235 - 0.301783i) q^{61} +(5.79796 + 5.02118i) q^{63} +(2.22474 + 3.85337i) q^{65} +(6.17423 - 10.6941i) q^{67} +1.44949 q^{69} -1.41421i q^{71} +(-9.67423 - 5.58542i) q^{73} +(-0.275255 + 0.158919i) q^{75} +(-2.44949 + 12.7279i) q^{77} +(-6.67423 + 3.85337i) q^{79} +(-4.05051 + 7.01569i) q^{81} +1.87492i q^{83} -4.87832i q^{85} +(1.15153 - 1.99451i) q^{87} +(9.39898 - 5.42650i) q^{89} +(-11.1237 + 3.85337i) q^{91} +(-0.426786 + 0.246405i) q^{93} +(-3.67423 - 2.12132i) q^{95} +11.9494i q^{97} -14.2020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{5} - 10 q^{7} + 4 q^{9} + 8 q^{13} - 12 q^{17} - 18 q^{21} + 6 q^{23} - 2 q^{25} - 8 q^{31} - 24 q^{33} - 8 q^{35} + 12 q^{37} + 28 q^{43} - 4 q^{45} + 12 q^{47} + 22 q^{49} - 8 q^{51}+ \cdots - 96 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^5 - 10 * q^7 + 4 * q^9 + 8 * q^13 - 12 * q^17 - 18 * q^21 + 6 * q^23 - 2 * q^25 - 8 * q^31 - 24 * q^33 - 8 * q^35 + 12 * q^37 + 28 * q^43 - 4 * q^45 + 12 * q^47 + 22 * q^49 - 8 * q^51 + 12 * q^53 + 24 * q^57 + 12 * q^59 + 14 * q^61 - 16 * q^63 + 4 * q^65 + 10 * q^67 - 4 * q^69 - 24 * q^73 - 6 * q^75 - 12 * q^79 - 26 * q^81 + 34 * q^87 + 18 * q^89 - 20 * q^91 - 36 * q^93 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	0.275255	+	0.158919i	0.158919	+	0.0917517i	0.577350	−	0.816497i	$-0.304087\pi$
$3$	0.275255	+	0.158919i	0.158919	+	0.0917517i	−0.418432	+	0.908248i	$0.637420\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$	−1.44949	−	2.51059i	−0.483163	−	0.836863i
$10$		0			0
$11$	2.44949	−	4.24264i	0.738549	−	1.27920i	−0.214600	−	0.976702i	$-0.568845\pi$
$11$	2.44949	−	4.24264i	0.738549	−	1.27920i	0.953149	−	0.302502i	$-0.0978220\pi$
$12$		0			0
$13$	4.44949			1.23407			0.617033	−	0.786937i	$-0.288334\pi$
$13$	4.44949			1.23407			0.617033	+	0.786937i	$0.288334\pi$
$14$		0			0
$15$			0.317837i			0.0820652i
$16$		0			0
$17$	−4.22474	−	2.43916i	−1.02465	−	0.591583i	−0.109203	−	0.994019i	$-0.534830\pi$
$17$	−4.22474	−	2.43916i	−1.02465	−	0.591583i	−0.915448	+	0.402437i	$0.868163\pi$
$18$		0			0
$19$	−3.67423	+	2.12132i	−0.842927	+	0.486664i	−0.858258	−	0.513218i	$-0.828453\pi$
$19$	−3.67423	+	2.12132i	−0.842927	+	0.486664i	0.0153309	+	0.999882i	$0.495120\pi$
$20$		0			0
$21$	−0.825765	−	0.158919i	−0.180197	−	0.0346789i
$22$		0			0
$23$	3.94949	−	2.28024i	0.823526	−	0.475463i	−0.0281052	−	0.999605i	$-0.508947\pi$
$23$	3.94949	−	2.28024i	0.823526	−	0.475463i	0.851631	+	0.524142i	$0.175614\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	1.87492i		−	0.360828i
$28$		0			0
$29$		−	7.24604i		−	1.34556i	−0.739844	−	0.672778i	$-0.765101\pi$
$29$		−	7.24604i		−	1.34556i	0.739844	−	0.672778i	$-0.234899\pi$
$30$		0			0
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	−0.927209	−	0.374544i	$-0.877799\pi$
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	0.787969	+	0.615715i	$0.211133\pi$
$32$		0			0
$33$	1.34847	−	0.778539i	0.234738	−	0.135526i
$34$		0			0
$35$	−2.00000	−	1.73205i	−0.338062	−	0.292770i
$36$		0			0
$37$	3.00000	−	1.73205i	0.493197	−	0.284747i	−0.232703	−	0.972548i	$-0.574757\pi$
$37$	3.00000	−	1.73205i	0.493197	−	0.284747i	0.725900	+	0.687800i	$0.241424\pi$
$38$		0			0
$39$	1.22474	+	0.707107i	0.196116	+	0.113228i
$40$		0			0
$41$		−	8.02458i		−	1.25323i	−0.779329	−	0.626614i	$-0.784440\pi$
$41$		−	8.02458i		−	1.25323i	0.779329	−	0.626614i	$-0.215560\pi$
$42$		0			0
$43$	9.44949			1.44103			0.720517	−	0.693437i	$-0.243905\pi$
$43$	9.44949			1.44103			0.720517	+	0.693437i	$0.243905\pi$
$44$		0			0
$45$	1.44949	−	2.51059i	0.216077	−	0.374257i
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−0.775255	−	1.34278i	−0.108557	−	0.188027i
$52$		0			0
$53$	1.77526	+	1.02494i	0.243850	+	0.140787i	0.616945	−	0.787006i	$-0.288370\pi$
$53$	1.77526	+	1.02494i	0.243850	+	0.140787i	−0.373095	+	0.927793i	$0.621703\pi$
$54$		0			0
$55$	4.89898			0.660578
$56$		0			0
$57$	−1.34847			−0.178609
$58$		0			0
$59$	−3.12372	−	1.80348i	−0.406674	−	0.234794i	0.282686	−	0.959213i	$-0.408775\pi$
$59$	−3.12372	−	1.80348i	−0.406674	−	0.234794i	−0.689360	+	0.724419i	$0.742108\pi$
$60$		0			0
$61$	−0.174235	−	0.301783i	−0.0223085	−	0.0386394i	0.854656	−	0.519195i	$-0.173768\pi$
$61$	−0.174235	−	0.301783i	−0.0223085	−	0.0386394i	−0.876964	+	0.480556i	$0.840435\pi$
$62$		0			0
$63$	5.79796	+	5.02118i	0.730474	+	0.632609i
$64$		0			0
$65$	2.22474	+	3.85337i	0.275946	+	0.477952i
$66$		0			0
$67$	6.17423	−	10.6941i	0.754303	−	1.30649i	−0.191417	−	0.981509i	$-0.561308\pi$
$67$	6.17423	−	10.6941i	0.754303	−	1.30649i	0.945720	−	0.324982i	$-0.105358\pi$
$68$		0			0
$69$	1.44949			0.174498
$70$		0			0
$71$		−	1.41421i		−	0.167836i	−0.996473	−	0.0839181i	$-0.973257\pi$
$71$		−	1.41421i		−	0.167836i	0.996473	−	0.0839181i	$-0.0267434\pi$
$72$		0			0
$73$	−9.67423	−	5.58542i	−1.13228	−	0.653724i	−0.187775	−	0.982212i	$-0.560128\pi$
$73$	−9.67423	−	5.58542i	−1.13228	−	0.653724i	−0.944508	+	0.328488i	$0.893461\pi$
$74$		0			0
$75$	−0.275255	+	0.158919i	−0.0317837	+	0.0183503i
$76$		0			0
$77$	−2.44949	+	12.7279i	−0.279145	+	1.45048i
$78$		0			0
$79$	−6.67423	+	3.85337i	−0.750910	+	0.433538i	−0.826023	−	0.563637i	$-0.809402\pi$
$79$	−6.67423	+	3.85337i	−0.750910	+	0.433538i	0.0751126	+	0.997175i	$0.476068\pi$
$80$		0			0
$81$	−4.05051	+	7.01569i	−0.450057	+	0.779521i
$82$		0			0
$83$			1.87492i			0.205799i	0.994692	+	0.102899i	$0.0328120\pi$
$83$			1.87492i			0.205799i	−0.994692	+	0.102899i	$0.967188\pi$
$84$		0			0
$85$		−	4.87832i		−	0.529128i
$86$		0			0
$87$	1.15153	−	1.99451i	0.123457	−	0.213834i
$88$		0			0
$89$	9.39898	−	5.42650i	0.996290	−	0.575208i	0.0891414	−	0.996019i	$-0.471588\pi$
$89$	9.39898	−	5.42650i	0.996290	−	0.575208i	0.907148	+	0.420811i	$0.138254\pi$
$90$		0			0
$91$	−11.1237	+	3.85337i	−1.16608	+	0.403943i
$92$		0			0
$93$	−0.426786	+	0.246405i	−0.0442556	+	0.0255510i
$94$		0			0
$95$	−3.67423	−	2.12132i	−0.376969	−	0.217643i
$96$		0			0
$97$			11.9494i			1.21328i	0.794978	+	0.606638i	$0.207482\pi$
$97$			11.9494i			1.21328i	−0.794978	+	0.606638i	$0.792518\pi$
$98$		0			0
$99$	−14.2020			−1.42736
$100$		0			0
$101$	−7.62372	+	13.2047i	−0.758589	+	1.31391i	0.184981	+	0.982742i	$0.440778\pi$
$101$	−7.62372	+	13.2047i	−0.758589	+	1.31391i	−0.943570	+	0.331173i	$0.892556\pi$
$102$		0			0
$103$	−8.39898	−	14.5475i	−0.827576	−	1.43340i	−0.899935	−	0.436025i	$-0.856386\pi$
$103$	−8.39898	−	14.5475i	−0.827576	−	1.43340i	0.0723585	−	0.997379i	$-0.476947\pi$
$104$		0			0
$105$	−0.275255	−	0.794593i	−0.0268622	−	0.0775443i
$106$		0			0
$107$	−2.72474	−	4.71940i	−0.263411	−	0.456241i	0.703735	−	0.710462i	$-0.251514\pi$
$107$	−2.72474	−	4.71940i	−0.263411	−	0.456241i	−0.967146	+	0.254221i	$0.918181\pi$
$108$		0			0
$109$	6.82577	+	3.94086i	0.653790	+	0.377466i	0.789907	−	0.613227i	$-0.210129\pi$
$109$	6.82577	+	3.94086i	0.653790	+	0.377466i	−0.136117	+	0.990693i	$0.543462\pi$
$110$		0			0
$111$	1.10102			0.104504
$112$		0			0
$113$	8.44949			0.794861			0.397431	−	0.917632i	$-0.369902\pi$
$113$	8.44949			0.794861			0.397431	+	0.917632i	$0.369902\pi$
$114$		0			0
$115$	3.94949	+	2.28024i	0.368292	+	0.212633i
$116$		0			0
$117$	−6.44949	−	11.1708i	−0.596256	−	1.03274i
$118$		0			0
$119$	12.6742	+	2.43916i	1.16185	+	0.223597i
$120$		0			0
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$		0			0
$123$	1.27526	−	2.20881i	0.114986	−	0.199161i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	6.92820i		−	0.614779i	−0.951584	−	0.307389i	$-0.900545\pi$
$127$		−	6.92820i		−	0.614779i	0.951584	−	0.307389i	$-0.0994554\pi$
$128$		0			0
$129$	2.60102	+	1.50170i	0.229007	+	0.132217i
$130$		0			0
$131$	9.79796	−	5.65685i	0.856052	−	0.494242i	−0.00663646	−	0.999978i	$-0.502112\pi$
$131$	9.79796	−	5.65685i	0.856052	−	0.494242i	0.862688	+	0.505736i	$0.168779\pi$
$132$		0			0
$133$	7.34847	−	8.48528i	0.637193	−	0.735767i
$134$		0			0
$135$	1.62372	−	0.937458i	0.139748	−	0.0806835i
$136$		0			0
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	−0.577246	−	0.816571i	$-0.695872\pi$
$137$	4.89898	−	8.48528i	0.418548	−	0.724947i	0.995794	+	0.0916241i	$0.0292058\pi$
$138$		0			0
$139$			6.92820i			0.587643i	0.955860	+	0.293821i	$0.0949270\pi$
$139$			6.92820i			0.587643i	−0.955860	+	0.293821i	$0.905073\pi$
$140$		0			0
$141$			1.90702i			0.160600i
$142$		0			0
$143$	10.8990	−	18.8776i	0.911418	−	1.57862i
$144$		0			0
$145$	6.27526	−	3.62302i	0.521132	−	0.300875i
$146$		0			0
$147$	2.20204	−	0.317837i	0.181621	−	0.0262148i
$148$		0			0
$149$	−16.6237	+	9.59771i	−1.36187	+	0.786275i	−0.989873	−	0.141959i	$-0.954660\pi$
$149$	−16.6237	+	9.59771i	−1.36187	+	0.786275i	−0.371996	+	0.928234i	$0.621327\pi$
$150$		0			0
$151$	−6.67423	−	3.85337i	−0.543142	−	0.313583i	0.203210	−	0.979135i	$-0.434863\pi$
$151$	−6.67423	−	3.85337i	−0.543142	−	0.313583i	−0.746351	+	0.665552i	$0.768196\pi$
$152$		0			0
$153$			14.1421i			1.14332i
$154$		0			0
$155$	−1.55051			−0.124540
$156$		0			0
$157$	−5.34847	+	9.26382i	−0.426854	+	0.739333i	−0.996592	−	0.0824935i	$-0.973712\pi$
$157$	−5.34847	+	9.26382i	−0.426854	+	0.739333i	0.569737	+	0.821827i	$0.307045\pi$
$158$		0			0
$159$	0.325765	+	0.564242i	0.0258349	+	0.0447473i
$160$		0			0
$161$	−7.89898	+	9.12096i	−0.622527	+	0.718832i
$162$		0			0
$163$	2.89898	+	5.02118i	0.227066	+	0.393289i	0.956937	−	0.290295i	$-0.0937535\pi$
$163$	2.89898	+	5.02118i	0.227066	+	0.393289i	−0.729872	+	0.683584i	$0.760420\pi$
$164$		0			0
$165$	1.34847	+	0.778539i	0.104978	+	0.0606092i
$166$		0			0
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	6.79796			0.522920
$170$		0			0
$171$	10.6515	+	6.14966i	0.814543	+	0.470277i
$172$		0			0
$173$	5.44949	+	9.43879i	0.414317	+	0.717618i	0.995356	−	0.0962572i	$-0.0306871\pi$
$173$	5.44949	+	9.43879i	0.414317	+	0.717618i	−0.581039	+	0.813875i	$0.697354\pi$
$174$		0			0
$175$	0.500000	−	2.59808i	0.0377964	−	0.196396i
$176$		0			0
$177$	−0.573214	−	0.992836i	−0.0430854	−	0.0746261i
$178$		0			0
$179$	4.77526	−	8.27098i	0.356919	−	0.618202i	−0.630525	−	0.776169i	$-0.717160\pi$
$179$	4.77526	−	8.27098i	0.356919	−	0.618202i	0.987444	+	0.157966i	$0.0504938\pi$
$180$		0			0
$181$	12.3485			0.917854			0.458927	−	0.888474i	$-0.348234\pi$
$181$	12.3485			0.917854			0.458927	+	0.888474i	$0.348234\pi$
$182$		0			0
$183$		−	0.110756i		−	0.00818736i
$184$		0			0
$185$	3.00000	+	1.73205i	0.220564	+	0.127343i
$186$		0			0
$187$	−20.6969	+	11.9494i	−1.51351	+	0.873825i
$188$		0			0
$189$	1.62372	+	4.68729i	0.118109	+	0.340950i
$190$		0			0
$191$	−22.8990	+	13.2207i	−1.65691	+	0.956619i	−0.682784	+	0.730620i	$0.739231\pi$
$191$	−22.8990	+	13.2207i	−1.65691	+	0.956619i	−0.974128	+	0.225999i	$0.927435\pi$
$192$		0			0
$193$	−11.3485	+	19.6561i	−0.816881	+	1.41488i	0.0910889	+	0.995843i	$0.470965\pi$
$193$	−11.3485	+	19.6561i	−0.816881	+	1.41488i	−0.907970	+	0.419036i	$0.862368\pi$
$194$		0			0
$195$			1.41421i			0.101274i
$196$		0			0
$197$		−	0.921404i		−	0.0656473i	−0.999461	−	0.0328236i	$-0.989550\pi$
$197$		−	0.921404i		−	0.0656473i	0.999461	−	0.0328236i	$-0.0104500\pi$
$198$		0			0
$199$	−12.3485	+	21.3882i	−0.875360	+	1.51617i	−0.0189808	+	0.999820i	$0.506042\pi$
$199$	−12.3485	+	21.3882i	−0.875360	+	1.51617i	−0.856379	+	0.516348i	$0.827291\pi$
$200$		0			0
$201$	3.39898	−	1.96240i	0.239746	−	0.138417i
$202$		0			0
$203$	6.27526	+	18.1151i	0.440437	+	1.27143i
$204$		0			0
$205$	6.94949	−	4.01229i	0.485373	−	0.280230i
$206$		0			0
$207$	−11.4495	−	6.61037i	−0.795795	−	0.459452i
$208$		0			0
$209$			20.7846i			1.43770i
$210$		0			0
$211$	−8.24745			−0.567778			−0.283889	−	0.958857i	$-0.591625\pi$
$211$	−8.24745			−0.567778			−0.283889	+	0.958857i	$0.591625\pi$
$212$		0			0
$213$	0.224745	−	0.389270i	0.0153993	−	0.0266723i
$214$		0			0
$215$	4.72474	+	8.18350i	0.322225	+	0.558110i
$216$		0			0
$217$	0.775255	−	4.02834i	0.0526277	−	0.273462i
$218$		0			0
$219$	−1.77526	−	3.07483i	−0.119961	−	0.207778i
$220$		0			0
$221$	−18.7980	−	10.8530i	−1.26449	−	0.730052i
$222$		0			0
$223$	24.6969			1.65383			0.826915	−	0.562327i	$-0.190094\pi$
$223$	24.6969			1.65383			0.826915	+	0.562327i	$0.190094\pi$
$224$		0			0
$225$	2.89898			0.193265
$226$		0			0
$227$	9.24745	+	5.33902i	0.613775	+	0.354363i	0.774441	−	0.632646i	$-0.218031\pi$
$227$	9.24745	+	5.33902i	0.613775	+	0.354363i	−0.160667	+	0.987009i	$0.551364\pi$
$228$		0			0
$229$	−8.34847	−	14.4600i	−0.551682	−	0.955542i	−0.998153	−	0.0607438i	$-0.980653\pi$
$229$	−8.34847	−	14.4600i	−0.551682	−	0.955542i	0.446471	−	0.894798i	$-0.352681\pi$
$230$		0			0
$231$	−2.69694	+	3.11416i	−0.177446	+	0.204896i
$232$		0			0
$233$	0.123724	+	0.214297i	0.00810545	+	0.0140391i	0.870050	−	0.492964i	$-0.164087\pi$
$233$	0.123724	+	0.214297i	0.00810545	+	0.0140391i	−0.861944	+	0.507003i	$0.830753\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	−2.44949			−0.159111
$238$		0			0
$239$		−	3.32124i		−	0.214833i	−0.994214	−	0.107416i	$-0.965742\pi$
$239$		−	3.32124i		−	0.214833i	0.994214	−	0.107416i	$-0.0342578\pi$
$240$		0			0
$241$	−17.6969	−	10.2173i	−1.13996	−	0.658156i	−0.193539	−	0.981093i	$-0.561997\pi$
$241$	−17.6969	−	10.2173i	−1.13996	−	0.658156i	−0.946421	+	0.322936i	$0.895330\pi$
$242$		0			0
$243$	−7.10102	+	4.09978i	−0.455531	+	0.263001i
$244$		0			0
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$		0			0
$247$	−16.3485	+	9.43879i	−1.04023	+	0.600576i
$248$		0			0
$249$	−0.297959	+	0.516080i	−0.0188824	+	0.0327052i
$250$		0			0
$251$		−	13.7135i		−	0.865591i	−0.901492	−	0.432796i	$-0.857527\pi$
$251$		−	13.7135i		−	0.865591i	0.901492	−	0.432796i	$-0.142473\pi$
$252$		0			0
$253$		−	22.3417i		−	1.40461i
$254$		0			0
$255$	0.775255	−	1.34278i	0.0485484	−	0.0840882i
$256$		0			0
$257$	−11.4495	+	6.61037i	−0.714200	+	0.412343i	−0.812614	−	0.582802i	$-0.801956\pi$
$257$	−11.4495	+	6.61037i	−0.714200	+	0.412343i	0.0984145	+	0.995146i	$0.468623\pi$
$258$		0			0
$259$	−6.00000	+	6.92820i	−0.372822	+	0.430498i
$260$		0			0
$261$	−18.1918	+	10.5031i	−1.12605	+	0.650123i
$262$		0			0
$263$	4.74745	+	2.74094i	0.292740	+	0.169014i	0.639177	−	0.769060i	$-0.279275\pi$
$263$	4.74745	+	2.74094i	0.292740	+	0.169014i	−0.346437	+	0.938073i	$0.612608\pi$
$264$		0			0
$265$			2.04989i			0.125924i
$266$		0			0
$267$	3.44949			0.211105
$268$		0			0
$269$	8.17423	−	14.1582i	0.498392	−	0.863240i	−0.501606	−	0.865096i	$-0.667257\pi$
$269$	8.17423	−	14.1582i	0.498392	−	0.863240i	0.999998	+	0.00185590i	$0.000590752\pi$
$270$		0			0
$271$	1.67423	+	2.89986i	0.101703	+	0.176154i	0.912386	−	0.409330i	$-0.134238\pi$
$271$	1.67423	+	2.89986i	0.101703	+	0.176154i	−0.810684	+	0.585484i	$0.800904\pi$
$272$		0			0
$273$	−3.67423	−	0.707107i	−0.222375	−	0.0427960i
$274$		0			0
$275$	2.44949	+	4.24264i	0.147710	+	0.255841i
$276$		0			0
$277$	−5.02270	−	2.89986i	−0.301785	−	0.174236i	0.341459	−	0.939896i	$-0.389079\pi$
$277$	−5.02270	−	2.89986i	−0.301785	−	0.174236i	−0.643245	+	0.765661i	$0.722412\pi$
$278$		0			0
$279$	4.49490			0.269102
$280$		0			0
$281$	16.8990			1.00811			0.504054	−	0.863672i	$-0.331841\pi$
$281$	16.8990			1.00811			0.504054	+	0.863672i	$0.331841\pi$
$282$		0			0
$283$	7.34847	+	4.24264i	0.436821	+	0.252199i	0.702248	−	0.711932i	$-0.252180\pi$
$283$	7.34847	+	4.24264i	0.436821	+	0.252199i	−0.265427	+	0.964131i	$0.585513\pi$
$284$		0			0
$285$	−0.674235	−	1.16781i	−0.0399382	−	0.0691750i
$286$		0			0
$287$	6.94949	+	20.0614i	0.410215	+	1.18419i
$288$		0			0
$289$	3.39898	+	5.88721i	0.199940	+	0.346306i
$290$		0			0
$291$	−1.89898	+	3.28913i	−0.111320	+	0.192812i
$292$		0			0
$293$	24.4949			1.43101			0.715504	−	0.698609i	$-0.246197\pi$
$293$	24.4949			1.43101			0.715504	+	0.698609i	$0.246197\pi$
$294$		0			0
$295$		−	3.60697i		−	0.210006i
$296$		0			0
$297$	−7.95459	−	4.59259i	−0.461572	−	0.266489i
$298$		0			0
$299$	17.5732	−	10.1459i	1.01629	−	0.586753i
$300$		0			0
$301$	−23.6237	+	8.18350i	−1.36165	+	0.471689i
$302$		0			0
$303$	−4.19694	+	2.42310i	−0.241108	+	0.139204i
$304$		0			0
$305$	0.174235	−	0.301783i	0.00997664	−	0.0172801i
$306$		0			0
$307$			27.9664i			1.59613i	0.602572	+	0.798064i	$0.294143\pi$
$307$			27.9664i			1.59613i	−0.602572	+	0.798064i	$0.705857\pi$
$308$		0			0
$309$		−	5.33902i		−	0.303726i
$310$		0			0
$311$	−5.57321	+	9.65309i	−0.316028	+	0.547377i	−0.979655	−	0.200687i	$-0.935683\pi$
$311$	−5.57321	+	9.65309i	−0.316028	+	0.547377i	0.663628	+	0.748063i	$0.269016\pi$
$312$		0			0
$313$	−5.69694	+	3.28913i	−0.322010	+	0.185913i	−0.652288	−	0.757971i	$-0.726191\pi$
$313$	−5.69694	+	3.28913i	−0.322010	+	0.185913i	0.330278	+	0.943884i	$0.392857\pi$
$314$		0			0
$315$	−1.44949	+	7.53177i	−0.0816695	+	0.424367i
$316$		0			0
$317$	−0.426786	+	0.246405i	−0.0239707	+	0.0138395i	−0.511937	−	0.859023i	$-0.671072\pi$
$317$	−0.426786	+	0.246405i	−0.0239707	+	0.0138395i	0.487967	+	0.872862i	$0.337739\pi$
$318$		0			0
$319$	−30.7423	−	17.7491i	−1.72124	−	0.993759i
$320$		0			0
$321$		−	1.73205i		−	0.0966736i
$322$		0			0
$323$	20.6969			1.15161
$324$		0			0
$325$	−2.22474	+	3.85337i	−0.123407	+	0.213747i
$326$		0			0
$327$	1.25255	+	2.16948i	0.0692662	+	0.119973i
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	−1.57321	−	2.72489i	−0.0864717	−	0.149773i	0.819546	−	0.573014i	$-0.194226\pi$
$331$	−1.57321	−	2.72489i	−0.0864717	−	0.149773i	−0.906017	+	0.423240i	$0.860893\pi$
$332$		0			0
$333$	−8.69694	−	5.02118i	−0.476589	−	0.275159i
$334$		0			0
$335$	12.3485			0.674669
$336$		0			0
$337$	20.2474			1.10295			0.551474	−	0.834192i	$-0.314065\pi$
$337$	20.2474			1.10295			0.551474	+	0.834192i	$0.314065\pi$
$338$		0			0
$339$	2.32577	+	1.34278i	0.126318	+	0.0729299i
$340$		0			0
$341$	3.79796	+	6.57826i	0.205671	+	0.356233i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	0.724745	+	1.25529i	0.0390190	+	0.0675828i
$346$		0			0
$347$	−3.82577	+	6.62642i	−0.205378	+	0.355725i	−0.950253	−	0.311479i	$-0.899176\pi$
$347$	−3.82577	+	6.62642i	−0.205378	+	0.355725i	0.744875	+	0.667204i	$0.232509\pi$
$348$		0			0
$349$	−7.24745			−0.387947			−0.193974	−	0.981007i	$-0.562138\pi$
$349$	−7.24745			−0.387947			−0.193974	+	0.981007i	$0.562138\pi$
$350$		0			0
$351$		−	8.34242i		−	0.445285i
$352$		0			0
$353$	29.8207	+	17.2170i	1.58719	+	0.916367i	0.993767	+	0.111479i	$0.0355587\pi$
$353$	29.8207	+	17.2170i	1.58719	+	0.916367i	0.593427	+	0.804888i	$0.297775\pi$
$354$		0			0
$355$	1.22474	−	0.707107i	0.0650027	−	0.0375293i
$356$		0			0
$357$	3.10102	+	2.68556i	0.164123	+	0.142135i
$358$		0			0
$359$	19.7753	−	11.4172i	1.04370	−	0.602579i	0.122820	−	0.992429i	$-0.460806\pi$
$359$	19.7753	−	11.4172i	1.04370	−	0.602579i	0.920879	+	0.389850i	$0.127473\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$		−	4.13188i		−	0.216868i
$364$		0			0
$365$		−	11.1708i		−	0.584709i
$366$		0			0
$367$	−4.05051	+	7.01569i	−0.211435	+	0.366216i	−0.952164	−	0.305588i	$-0.901147\pi$
$367$	−4.05051	+	7.01569i	−0.211435	+	0.366216i	0.740729	+	0.671804i	$0.234480\pi$
$368$		0			0
$369$	−20.1464	+	11.6315i	−1.04878	+	0.605514i
$370$		0			0
$371$	−5.32577	−	1.02494i	−0.276500	−	0.0532124i
$372$		0			0
$373$	15.0000	−	8.66025i	0.776671	−	0.448411i	−0.0585785	−	0.998283i	$-0.518657\pi$
$373$	15.0000	−	8.66025i	0.776671	−	0.448411i	0.835249	+	0.549872i	$0.185323\pi$
$374$		0			0
$375$	−0.275255	−	0.158919i	−0.0142141	−	0.00820652i
$376$		0			0
$377$		−	32.2412i		−	1.66051i
$378$		0			0
$379$	17.3485			0.891131			0.445566	−	0.895249i	$-0.353003\pi$
$379$	17.3485			0.891131			0.445566	+	0.895249i	$0.353003\pi$
$380$		0			0
$381$	1.10102	−	1.90702i	0.0564070	−	0.0976998i
$382$		0			0
$383$	−2.60102	−	4.50510i	−0.132906	−	0.230200i	0.791890	−	0.610664i	$-0.209097\pi$
$383$	−2.60102	−	4.50510i	−0.132906	−	0.230200i	−0.924796	+	0.380464i	$0.875764\pi$
$384$		0			0
$385$	−12.2474	+	4.24264i	−0.624188	+	0.216225i
$386$		0			0
$387$	−13.6969	−	23.7238i	−0.696255	−	1.20595i
$388$		0			0
$389$	9.79796	+	5.65685i	0.496776	+	0.286814i	0.727381	−	0.686234i	$-0.240737\pi$
$389$	9.79796	+	5.65685i	0.496776	+	0.286814i	−0.230605	+	0.973047i	$0.574071\pi$
$390$		0			0
$391$	−22.2474			−1.12510
$392$		0			0
$393$	3.59592			0.181390
$394$		0			0
$395$	−6.67423	−	3.85337i	−0.335817	−	0.193884i
$396$		0			0
$397$	0.348469	+	0.603566i	0.0174892	+	0.0302921i	0.874638	−	0.484777i	$-0.161099\pi$
$397$	0.348469	+	0.603566i	0.0174892	+	0.0302921i	−0.857148	+	0.515070i	$0.827766\pi$
$398$		0			0
$399$	3.37117	−	1.16781i	0.168770	−	0.0584636i
$400$		0			0
$401$	15.3990	+	26.6718i	0.768988	+	1.33193i	0.938112	+	0.346332i	$0.112573\pi$
$401$	15.3990	+	26.6718i	0.768988	+	1.33193i	−0.169124	+	0.985595i	$0.554094\pi$
$402$		0			0
$403$	−3.44949	+	5.97469i	−0.171831	+	0.297621i
$404$		0			0
$405$	−8.10102			−0.402543
$406$		0			0
$407$		−	16.9706i		−	0.841200i
$408$		0			0
$409$	−10.1969	−	5.88721i	−0.504206	−	0.291104i	0.226243	−	0.974071i	$-0.427356\pi$
$409$	−10.1969	−	5.88721i	−0.504206	−	0.291104i	−0.730449	+	0.682967i	$0.760689\pi$
$410$		0			0
$411$	2.69694	−	1.55708i	0.133030	−	0.0768050i
$412$		0			0
$413$	9.37117	+	1.80348i	0.461125	+	0.0887436i
$414$		0			0
$415$	−1.62372	+	0.937458i	−0.0797055	+	0.0460180i
$416$		0			0
$417$	−1.10102	+	1.90702i	−0.0539172	+	0.0933873i
$418$		0			0
$419$			16.6848i			0.815107i	0.913181	+	0.407554i	$0.133618\pi$
$419$			16.6848i			0.815107i	−0.913181	+	0.407554i	$0.866382\pi$
$420$		0			0
$421$			4.06767i			0.198246i	0.995075	+	0.0991230i	$0.0316037\pi$
$421$			4.06767i			0.198246i	−0.995075	+	0.0991230i	$0.968396\pi$
$422$		0			0
$423$	8.69694	−	15.0635i	0.422860	−	0.732414i
$424$		0			0
$425$	4.22474	−	2.43916i	0.204930	−	0.118317i
$426$		0			0
$427$	0.696938	+	0.603566i	0.0337272	+	0.0292086i
$428$		0			0
$429$	6.00000	−	3.46410i	0.289683	−	0.167248i
$430$		0			0
$431$	8.20204	+	4.73545i	0.395078	+	0.228099i	0.684358	−	0.729146i	$-0.260082\pi$
$431$	8.20204	+	4.73545i	0.395078	+	0.228099i	−0.289280	+	0.957245i	$0.593416\pi$
$432$		0			0
$433$			7.70674i			0.370362i	0.982704	+	0.185181i	$0.0592872\pi$
$433$			7.70674i			0.370362i	−0.982704	+	0.185181i	$0.940713\pi$
$434$		0			0
$435$	2.30306			0.110423
$436$		0			0
$437$	−9.67423	+	16.7563i	−0.462781	+	0.801561i
$438$		0			0
$439$	−5.55051	−	9.61377i	−0.264911	−	0.458840i	0.702629	−	0.711556i	$-0.252009\pi$
$439$	−5.55051	−	9.61377i	−0.264911	−	0.458840i	−0.967540	+	0.252716i	$0.918676\pi$
$440$		0			0
$441$	−18.8434	−	7.53177i	−0.897303	−	0.358656i
$442$		0			0
$443$	−8.17423	−	14.1582i	−0.388370	−	0.672676i	0.603861	−	0.797090i	$-0.293628\pi$
$443$	−8.17423	−	14.1582i	−0.388370	−	0.672676i	−0.992230	+	0.124414i	$0.960295\pi$
$444$		0			0
$445$	9.39898	+	5.42650i	0.445554	+	0.257241i
$446$		0			0
$447$	−6.10102			−0.288568
$448$		0			0
$449$	−1.40408			−0.0662627			−0.0331314	−	0.999451i	$-0.510548\pi$
$449$	−1.40408			−0.0662627			−0.0331314	+	0.999451i	$0.510548\pi$
$450$		0			0
$451$	−34.0454	−	19.6561i	−1.60314	−	0.925571i
$452$		0			0
$453$	−1.22474	−	2.12132i	−0.0575435	−	0.0996683i
$454$		0			0
$455$	−8.89898	−	7.70674i	−0.417191	−	0.361298i
$456$		0			0
$457$	−4.79796	−	8.31031i	−0.224439	−	0.388740i	0.731712	−	0.681614i	$-0.238722\pi$
$457$	−4.79796	−	8.31031i	−0.224439	−	0.388740i	−0.956151	+	0.292874i	$0.905388\pi$
$458$		0			0
$459$	−4.57321	+	7.92104i	−0.213459	+	0.369722i
$460$		0			0
$461$	38.6969			1.80230			0.901148	−	0.433511i	$-0.142726\pi$
$461$	38.6969			1.80230			0.901148	+	0.433511i	$0.142726\pi$
$462$		0			0
$463$		−	12.1244i		−	0.563467i	−0.959493	−	0.281733i	$-0.909091\pi$
$463$		−	12.1244i		−	0.563467i	0.959493	−	0.281733i	$-0.0909093\pi$
$464$		0			0
$465$	−0.426786	−	0.246405i	−0.0197917	−	0.0114268i
$466$		0			0
$467$	19.6237	−	11.3298i	0.908078	−	0.524279i	0.0282655	−	0.999600i	$-0.491002\pi$
$467$	19.6237	−	11.3298i	0.908078	−	0.524279i	0.879812	+	0.475322i	$0.157668\pi$
$468$		0			0
$469$	−6.17423	+	32.0823i	−0.285100	+	1.48142i
$470$		0			0
$471$	−2.94439	+	1.69994i	−0.135670	+	0.0783292i
$472$		0			0
$473$	23.1464	−	40.0908i	1.06427	−	1.84338i
$474$		0			0
$475$		−	4.24264i		−	0.194666i
$476$		0			0
$477$		−	5.94258i		−	0.272092i
$478$		0			0
$479$	−4.22474	+	7.31747i	−0.193034	+	0.334344i	−0.946254	−	0.323424i	$-0.895166\pi$
$479$	−4.22474	+	7.31747i	−0.193034	+	0.334344i	0.753221	+	0.657768i	$0.228499\pi$
$480$		0			0
$481$	13.3485	−	7.70674i	0.608638	−	0.351397i
$482$		0			0
$483$	−3.62372	+	1.25529i	−0.164885	+	0.0571179i
$484$		0			0
$485$	−10.3485	+	5.97469i	−0.469900	+	0.271297i
$486$		0			0
$487$	26.3939	+	15.2385i	1.19602	+	0.690523i	0.959666	−	0.281144i	$-0.0907138\pi$
$487$	26.3939	+	15.2385i	1.19602	+	0.690523i	0.236355	+	0.971667i	$0.424047\pi$
$488$		0			0
$489$			1.84281i			0.0833346i
$490$		0			0
$491$	−0.853572			−0.0385212			−0.0192606	−	0.999814i	$-0.506131\pi$
$491$	−0.853572			−0.0385212			−0.0192606	+	0.999814i	$0.506131\pi$
$492$		0			0
$493$	−17.6742	+	30.6127i	−0.796007	+	1.37873i
$494$		0			0
$495$	−7.10102	−	12.2993i	−0.319167	−	0.552814i
$496$		0			0
$497$	1.22474	+	3.53553i	0.0549373	+	0.158590i
$498$		0			0
$499$	−13.6969	−	23.7238i	−0.613159	−	1.06202i	−0.990704	−	0.136032i	$-0.956565\pi$
$499$	−13.6969	−	23.7238i	−0.613159	−	1.06202i	0.377545	−	0.925991i	$-0.376768\pi$
$500$		0			0
$501$	−0.825765	−	0.476756i	−0.0368925	−	0.0212999i
$502$		0			0
$503$	23.6969			1.05659			0.528297	−	0.849060i	$-0.322831\pi$
$503$	23.6969			1.05659			0.528297	+	0.849060i	$0.322831\pi$
$504$		0			0
$505$	−15.2474			−0.678503
$506$		0			0
$507$	1.87117	+	1.08032i	0.0831017	+	0.0479788i
$508$		0			0
$509$	8.72474	+	15.1117i	0.386718	+	0.669814i	0.992006	−	0.126192i	$-0.0402755\pi$
$509$	8.72474	+	15.1117i	0.386718	+	0.669814i	−0.605288	+	0.796006i	$0.706942\pi$
$510$		0			0
$511$	29.0227	+	5.58542i	1.28389	+	0.247085i
$512$		0			0
$513$	3.97730	+	6.88888i	0.175602	+	0.304151i
$514$		0			0
$515$	8.39898	−	14.5475i	0.370103	−	0.641038i
$516$		0			0
$517$	29.3939			1.29274
$518$		0			0
$519$			3.46410i			0.152057i
$520$		0			0
$521$	−9.24745	−	5.33902i	−0.405138	−	0.233907i	0.283560	−	0.958954i	$-0.408484\pi$
$521$	−9.24745	−	5.33902i	−0.405138	−	0.233907i	−0.688699	+	0.725048i	$0.741818\pi$
$522$		0			0
$523$	10.3485	−	5.97469i	0.452507	−	0.261255i	−0.256381	−	0.966576i	$-0.582530\pi$
$523$	10.3485	−	5.97469i	0.452507	−	0.261255i	0.708888	+	0.705321i	$0.249197\pi$
$524$		0			0
$525$	0.550510	−	0.635674i	0.0240262	−	0.0277431i
$526$		0			0
$527$	6.55051	−	3.78194i	0.285345	−	0.164744i
$528$		0			0
$529$	−1.10102	+	1.90702i	−0.0478705	+	0.0829141i
$530$		0			0
$531$			10.4565i			0.453774i
$532$		0			0
$533$		−	35.7053i		−	1.54657i
$534$		0			0
$535$	2.72474	−	4.71940i	0.117801	−	0.204037i
$536$		0			0
$537$	2.62883	−	1.51775i	0.113442	−	0.0654959i
$538$		0			0
$539$	−4.89898	−	33.9411i	−0.211014	−	1.46195i
$540$		0			0
$541$	−24.5227	+	14.1582i	−1.05431	+	0.608708i	−0.923854	−	0.382746i	$-0.874979\pi$
$541$	−24.5227	+	14.1582i	−1.05431	+	0.608708i	−0.130460	+	0.991454i	$0.541645\pi$
$542$		0			0
$543$	3.39898	+	1.96240i	0.145864	+	0.0842147i
$544$		0			0
$545$			7.88171i			0.337616i
$546$		0			0
$547$	−9.04541			−0.386754			−0.193377	−	0.981125i	$-0.561944\pi$
$547$	−9.04541			−0.386754			−0.193377	+	0.981125i	$0.561944\pi$
$548$		0			0
$549$	−0.505103	+	0.874863i	−0.0215573	+	0.0373383i
$550$		0			0
$551$	15.3712	+	26.6237i	0.654834	+	1.13421i
$552$		0			0
$553$	13.3485	−	15.4135i	0.567635	−	0.655448i
$554$		0			0
$555$	0.550510	+	0.953512i	0.0233679	+	0.0404743i
$556$		0			0
$557$	−13.8990	−	8.02458i	−0.588919	−	0.340012i	0.175751	−	0.984435i	$-0.443765\pi$
$557$	−13.8990	−	8.02458i	−0.588919	−	0.340012i	−0.764670	+	0.644422i	$0.777098\pi$
$558$		0			0
$559$	42.0454			1.77833
$560$		0			0
$561$	−7.59592			−0.320700
$562$		0			0
$563$	−16.6237	−	9.59771i	−0.700606	−	0.404495i	0.106967	−	0.994263i	$-0.465886\pi$
$563$	−16.6237	−	9.59771i	−0.700606	−	0.404495i	−0.807573	+	0.589767i	$0.799219\pi$
$564$		0			0
$565$	4.22474	+	7.31747i	0.177736	+	0.307848i
$566$		0			0
$567$	4.05051	−	21.0471i	0.170105	−	0.883894i
$568$		0			0
$569$	−20.6969	−	35.8481i	−0.867661	−	1.50283i	−0.864381	−	0.502838i	$-0.832289\pi$
$569$	−20.6969	−	35.8481i	−0.867661	−	1.50283i	−0.00328010	−	0.999995i	$-0.501044\pi$
$570$		0			0
$571$	5.22474	−	9.04952i	0.218649	−	0.378711i	−0.735746	−	0.677257i	$-0.763168\pi$
$571$	5.22474	−	9.04952i	0.218649	−	0.378711i	0.954395	+	0.298546i	$0.0965018\pi$
$572$		0			0
$573$	−8.40408			−0.351086
$574$		0			0
$575$			4.56048i			0.190185i
$576$		0			0
$577$	25.3485	+	14.6349i	1.05527	+	0.609261i	0.924120	−	0.382102i	$-0.124800\pi$
$577$	25.3485	+	14.6349i	1.05527	+	0.609261i	0.131150	+	0.991362i	$0.458133\pi$
$578$		0			0
$579$	−6.24745	+	3.60697i	−0.259635	+	0.149900i
$580$		0			0
$581$	−1.62372	−	4.68729i	−0.0673634	−	0.194461i
$582$		0			0
$583$	8.69694	−	5.02118i	0.360190	−	0.207956i
$584$		0			0
$585$	6.44949	−	11.1708i	0.266654	−	0.461858i
$586$		0			0
$587$		−	5.30691i		−	0.219040i	−0.993985	−	0.109520i	$-0.965069\pi$
$587$		−	5.30691i		−	0.219040i	0.993985	−	0.109520i	$-0.0349313\pi$
$588$		0			0
$589$		−	6.57826i		−	0.271052i
$590$		0			0
$591$	0.146428	−	0.253621i	0.00602325	−	0.0104326i
$592$		0			0
$593$	8.57321	−	4.94975i	0.352060	−	0.203262i	−0.313532	−	0.949578i	$-0.601512\pi$
$593$	8.57321	−	4.94975i	0.352060	−	0.203262i	0.665592	+	0.746316i	$0.268179\pi$
$594$		0			0
$595$	4.22474	+	12.1958i	0.173198	+	0.499979i
$596$		0			0
$597$	−6.79796	+	3.92480i	−0.278222	+	0.160632i
$598$		0			0
$599$	−11.1464	−	6.43539i	−0.455431	−	0.262943i	0.254690	−	0.967023i	$-0.418026\pi$
$599$	−11.1464	−	6.43539i	−0.455431	−	0.262943i	−0.710121	+	0.704080i	$0.751360\pi$
$600$		0			0
$601$		−	25.8058i		−	1.05264i	−0.850287	−	0.526320i	$-0.823571\pi$
$601$		−	25.8058i		−	1.05264i	0.850287	−	0.526320i	$-0.176429\pi$
$602$		0			0
$603$	−35.7980			−1.45781
$604$		0			0
$605$	6.50000	−	11.2583i	0.264263	−	0.457716i
$606$		0			0
$607$	−10.8485	−	18.7901i	−0.440326	−	0.762667i	0.557388	−	0.830252i	$-0.311804\pi$
$607$	−10.8485	−	18.7901i	−0.440326	−	0.762667i	−0.997713	+	0.0675857i	$0.978470\pi$
$608$		0			0
$609$	−1.15153	+	5.98353i	−0.0466624	+	0.242465i
$610$		0			0
$611$	13.3485	+	23.1202i	0.540021	+	0.935344i
$612$		0			0
$613$	−0.674235	−	0.389270i	−0.0272321	−	0.0157224i	0.486322	−	0.873780i	$-0.338338\pi$
$613$	−0.674235	−	0.389270i	−0.0272321	−	0.0157224i	−0.513554	+	0.858057i	$0.671671\pi$
$614$		0			0
$615$	2.55051			0.102846
$616$		0			0
$617$	3.30306			0.132976			0.0664881	−	0.997787i	$-0.478821\pi$
$617$	3.30306			0.132976			0.0664881	+	0.997787i	$0.478821\pi$
$618$		0			0
$619$	13.3485	+	7.70674i	0.536520	+	0.309760i	0.743668	−	0.668550i	$-0.233085\pi$
$619$	13.3485	+	7.70674i	0.536520	+	0.309760i	−0.207147	+	0.978310i	$0.566418\pi$
$620$		0			0
$621$	−4.27526	−	7.40496i	−0.171560	−	0.297151i
$622$		0			0
$623$	−18.7980	+	21.7060i	−0.753124	+	0.869633i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.30306	+	5.72107i	−0.131912	+	0.228478i
$628$		0			0
$629$	−16.8990			−0.673806
$630$		0			0
$631$		−	39.3123i		−	1.56500i	−0.622653	−	0.782498i	$-0.713945\pi$
$631$		−	39.3123i		−	1.56500i	0.622653	−	0.782498i	$-0.286055\pi$
$632$		0			0
$633$	−2.27015	−	1.31067i	−0.0902305	−	0.0520946i
$634$		0			0
$635$	6.00000	−	3.46410i	0.238103	−	0.137469i
$636$		0			0
$637$	24.4722	−	19.2669i	0.969624	−	0.763381i
$638$		0			0
$639$	−3.55051	+	2.04989i	−0.140456	+	0.0810923i
$640$		0			0
$641$	21.6464	−	37.4927i	0.854983	−	1.48087i	−0.0216787	−	0.999765i	$-0.506901\pi$
$641$	21.6464	−	37.4927i	0.854983	−	1.48087i	0.876661	−	0.481108i	$-0.159766\pi$
$642$		0			0
$643$		−	6.57826i		−	0.259421i	−0.991552	−	0.129711i	$-0.958595\pi$
$643$		−	6.57826i		−	0.259421i	0.991552	−	0.129711i	$-0.0414048\pi$
$644$		0			0
$645$			3.00340i			0.118259i
$646$		0			0
$647$	−5.29796	+	9.17633i	−0.208284	+	0.360759i	−0.951174	−	0.308655i	$-0.900121\pi$
$647$	−5.29796	+	9.17633i	−0.208284	+	0.360759i	0.742890	+	0.669414i	$0.233455\pi$
$648$		0			0
$649$	−15.3031	+	8.83523i	−0.600698	+	0.346813i
$650$		0			0
$651$	0.853572	−	0.985620i	0.0334541	−	0.0386295i
$652$		0			0
$653$	−16.7753	+	9.68520i	−0.656466	+	0.379011i	−0.790929	−	0.611908i	$-0.790402\pi$
$653$	−16.7753	+	9.68520i	−0.656466	+	0.379011i	0.134463	+	0.990919i	$0.457069\pi$
$654$		0			0
$655$	9.79796	+	5.65685i	0.382838	+	0.221032i
$656$		0			0
$657$			32.3840i			1.26342i
$658$		0			0
$659$	36.7423			1.43128			0.715639	−	0.698470i	$-0.246135\pi$
$659$	36.7423			1.43128			0.715639	+	0.698470i	$0.246135\pi$
$660$		0			0
$661$	24.8712	−	43.0781i	0.967377	−	1.67555i	0.264287	−	0.964444i	$-0.414863\pi$
$661$	24.8712	−	43.0781i	0.967377	−	1.67555i	0.703090	−	0.711101i	$-0.251803\pi$
$662$		0			0
$663$	−3.44949	−	5.97469i	−0.133967	−	0.232038i
$664$		0			0
$665$	11.0227	+	2.12132i	0.427442	+	0.0822613i
$666$		0			0
$667$	−16.5227	−	28.6182i	−0.639762	−	1.10810i
$668$		0			0
$669$	6.79796	+	3.92480i	0.262824	+	0.151742i
$670$		0			0
$671$	−1.70714			−0.0659035
$672$		0			0
$673$	−26.8990			−1.03688			−0.518440	−	0.855114i	$-0.673487\pi$
$673$	−26.8990			−1.03688			−0.518440	+	0.855114i	$0.673487\pi$
$674$		0			0
$675$	1.62372	+	0.937458i	0.0624972	+	0.0360828i
$676$		0			0
$677$	−15.6742	−	27.1486i	−0.602410	−	1.04340i	−0.992455	−	0.122609i	$-0.960874\pi$
$677$	−15.6742	−	27.1486i	−0.602410	−	1.04340i	0.390045	−	0.920796i	$-0.372459\pi$
$678$		0			0
$679$	−10.3485	−	29.8735i	−0.397138	−	1.14644i
$680$		0			0
$681$	1.69694	+	2.93918i	0.0650268	+	0.112630i
$682$		0			0
$683$	−5.72474	+	9.91555i	−0.219051	+	0.379408i	−0.954518	−	0.298153i	$-0.903630\pi$
$683$	−5.72474	+	9.91555i	−0.219051	+	0.379408i	0.735467	+	0.677561i	$0.236963\pi$
$684$		0			0
$685$	9.79796			0.374361
$686$		0			0
$687$		−	5.30691i		−	0.202471i
$688$		0			0
$689$	7.89898	+	4.56048i	0.300927	+	0.173740i
$690$		0			0
$691$	27.0000	−	15.5885i	1.02713	−	0.593013i	0.110968	−	0.993824i	$-0.464605\pi$
$691$	27.0000	−	15.5885i	1.02713	−	0.593013i	0.916161	+	0.400811i	$0.131272\pi$
$692$		0			0
$693$	35.5051	−	12.2993i	1.34873	−	0.467213i
$694$		0			0
$695$	−6.00000	+	3.46410i	−0.227593	+	0.131401i
$696$		0			0
$697$	−19.5732	+	33.9018i	−0.741388	+	1.28412i
$698$		0			0
$699$			0.0786484i			0.00297476i
$700$		0			0
$701$			23.5809i			0.890639i	0.895372	+	0.445320i	$0.146910\pi$
$701$			23.5809i			0.890639i	−0.895372	+	0.445320i	$0.853090\pi$
$702$		0			0
$703$	−7.34847	+	12.7279i	−0.277153	+	0.480043i
$704$		0			0
$705$	−1.65153	+	0.953512i	−0.0622002	+	0.0359113i
$706$		0			0
$707$	7.62372	−	39.6140i	0.286720	−	1.48984i
$708$		0			0
$709$	−9.21964	+	5.32296i	−0.346251	+	0.199908i	−0.663033	−	0.748590i	$-0.730731\pi$
$709$	−9.21964	+	5.32296i	−0.346251	+	0.199908i	0.316782	+	0.948498i	$0.397398\pi$
$710$		0			0
$711$	19.3485	+	11.1708i	0.725624	+	0.418939i
$712$		0			0
$713$			7.07107i			0.264814i
$714$		0			0
$715$	21.7980			0.815197
$716$		0			0
$717$	0.527806	−	0.914188i	0.0197113	−	0.0341410i
$718$		0			0
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	0.956540	+	0.291602i	$0.0941882\pi$
$719$	19.5959	+	33.9411i	0.730804	+	1.26579i	−0.225735	+	0.974189i	$0.572478\pi$
$720$		0			0
$721$	33.5959	+	29.0949i	1.25118	+	1.08355i
$722$		0			0
$723$	−3.24745	−	5.62475i	−0.120774	−	0.209187i
$724$		0			0
$725$	6.27526	+	3.62302i	0.233057	+	0.134556i
$726$		0			0
$727$	14.5959			0.541333			0.270666	−	0.962673i	$-0.412756\pi$
$727$	14.5959			0.541333			0.270666	+	0.962673i	$0.412756\pi$
$728$		0			0
$729$	21.6969			0.803590
$730$		0			0
$731$	−39.9217	−	23.0488i	−1.47656	−	0.852490i
$732$		0			0
$733$	8.55051	+	14.8099i	0.315820	+	0.547017i	0.979612	−	0.200901i	$-0.0643870\pi$
$733$	8.55051	+	14.8099i	0.315820	+	0.547017i	−0.663791	+	0.747918i	$0.731054\pi$
$734$		0			0
$735$	1.37628	+	1.74810i	0.0507647	+	0.0644798i
$736$		0			0
$737$	−30.2474	−	52.3901i	−1.11418	−	1.92981i
$738$		0			0
$739$	−0.348469	+	0.603566i	−0.0128186	+	0.0222025i	−0.872364	−	0.488858i	$-0.837414\pi$
$739$	−0.348469	+	0.603566i	−0.0128186	+	0.0222025i	0.859545	+	0.511060i	$0.170747\pi$
$740$		0			0
$741$	−6.00000			−0.220416
$742$		0			0
$743$			51.1509i			1.87654i	0.345899	+	0.938272i	$0.387574\pi$
$743$			51.1509i			1.87654i	−0.345899	+	0.938272i	$0.612426\pi$
$744$		0			0
$745$	−16.6237	−	9.59771i	−0.609046	−	0.351633i
$746$		0			0
$747$	4.70714	−	2.71767i	0.172225	−	0.0994344i
$748$		0			0
$749$	10.8990	+	9.43879i	0.398240	+	0.344886i
$750$		0			0
$751$	−43.0454	+	24.8523i	−1.57075	+	0.906872i	−0.574672	+	0.818384i	$0.694870\pi$
$751$	−43.0454	+	24.8523i	−1.57075	+	0.906872i	−0.996077	+	0.0884887i	$0.971796\pi$
$752$		0			0
$753$	2.17934	−	3.77472i	0.0794195	−	0.137559i
$754$		0			0
$755$		−	7.70674i		−	0.280477i
$756$		0			0
$757$			33.5125i			1.21803i	0.793157	+	0.609017i	$0.208436\pi$
$757$			33.5125i			1.21803i	−0.793157	+	0.609017i	$0.791564\pi$
$758$		0			0
$759$	3.55051	−	6.14966i	0.128875	−	0.223219i
$760$		0			0
$761$	10.5959	−	6.11756i	0.384102	−	0.221761i	−0.295500	−	0.955343i	$-0.595486\pi$
$761$	10.5959	−	6.11756i	0.384102	−	0.221761i	0.679601	+	0.733582i	$0.262153\pi$
$762$		0			0
$763$	−20.4773	−	3.94086i	−0.741328	−	0.142669i
$764$		0			0
$765$	−12.2474	+	7.07107i	−0.442807	+	0.255655i
$766$		0			0
$767$	−13.8990	−	8.02458i	−0.501863	−	0.289751i
$768$		0			0
$769$		−	46.5904i		−	1.68009i	−0.542515	−	0.840046i	$-0.682528\pi$
$769$		−	46.5904i		−	1.68009i	0.542515	−	0.840046i	$-0.317472\pi$
$770$		0			0
$771$	−4.20204			−0.151333
$772$		0			0
$773$	5.87628	−	10.1780i	0.211355	−	0.366078i	−0.740784	−	0.671743i	$-0.765546\pi$
$773$	5.87628	−	10.1780i	0.211355	−	0.366078i	0.952139	+	0.305666i	$0.0988791\pi$
$774$		0			0
$775$	−0.775255	−	1.34278i	−0.0278480	−	0.0482341i
$776$		0			0
$777$	−2.75255	+	0.953512i	−0.0987472	+	0.0342070i
$778$		0			0
$779$	17.0227	+	29.4842i	0.609902	+	1.05638i
$780$		0			0
$781$	−6.00000	−	3.46410i	−0.214697	−	0.123955i
$782$		0			0
$783$	−13.5857			−0.485514
$784$		0			0
$785$	−10.6969			−0.381790
$786$		0			0
$787$	7.87117	+	4.54442i	0.280577	+	0.161991i	0.633685	−	0.773592i	$-0.281542\pi$
$787$	7.87117	+	4.54442i	0.280577	+	0.161991i	−0.353108	+	0.935583i	$0.614875\pi$
$788$		0			0
$789$	0.871173	+	1.50892i	0.0310146	+	0.0537188i
$790$		0			0
$791$	−21.1237	+	7.31747i	−0.751073	+	0.260179i
$792$		0			0
$793$	−0.775255	−	1.34278i	−0.0275301	−	0.0476836i
$794$		0			0
$795$	−0.325765	+	0.564242i	−0.0115537	+	0.0200116i
$796$		0			0
$797$	3.30306			0.117000			0.0585002	−	0.998287i	$-0.481368\pi$
$797$	3.30306			0.117000			0.0585002	+	0.998287i	$0.481368\pi$
$798$		0			0
$799$		−	29.2699i		−	1.03549i
$800$		0			0
$801$	−27.2474	−	15.7313i	−0.962741	−	0.555839i
$802$		0			0
$803$	−47.3939	+	27.3629i	−1.67249	+	0.965615i
$804$		0			0
$805$	−11.8485	−	2.28024i	−0.417604	−	0.0803679i
$806$		0			0
$807$	4.50000	−	2.59808i	0.158408	−	0.0914566i
$808$		0			0
$809$	6.39898	−	11.0834i	0.224976	−	0.389670i	−0.731336	−	0.682017i	$-0.761103\pi$
$809$	6.39898	−	11.0834i	0.224976	−	0.389670i	0.956312	+	0.292347i	$0.0944363\pi$
$810$		0			0
$811$			47.3689i			1.66335i	0.555264	+	0.831674i	$0.312617\pi$
$811$			47.3689i			1.66335i	−0.555264	+	0.831674i	$0.687383\pi$
$812$		0			0
$813$			1.06427i			0.0373255i
$814$		0			0
$815$	−2.89898	+	5.02118i	−0.101547	+	0.175884i
$816$		0			0
$817$	−34.7196	+	20.0454i	−1.21469	+	0.701300i
$818$		0			0
$819$	25.7980	+	22.3417i	0.901454	+	0.780682i
$820$		0			0
$821$	43.2929	−	24.9951i	1.51093	−	0.872336i	0.511013	−	0.859573i	$-0.329271\pi$
$821$	43.2929	−	24.9951i	1.51093	−	0.872336i	0.999919	−	0.0127632i	$-0.00406277\pi$
$822$		0			0
$823$	9.15153	+	5.28364i	0.319002	+	0.184176i	0.650948	−	0.759123i	$-0.274372\pi$
$823$	9.15153	+	5.28364i	0.319002	+	0.184176i	−0.331945	+	0.943299i	$0.607705\pi$
$824$		0			0
$825$			1.55708i			0.0542105i
$826$		0			0
$827$	13.0454			0.453633			0.226817	−	0.973937i	$-0.427168\pi$
$827$	13.0454			0.453633			0.226817	+	0.973937i	$0.427168\pi$
$828$		0			0
$829$	12.6515	−	21.9131i	0.439406	−	0.761073i	−0.558238	−	0.829681i	$-0.688522\pi$
$829$	12.6515	−	21.9131i	0.439406	−	0.761073i	0.997644	+	0.0686077i	$0.0218557\pi$
$830$		0			0
$831$	−0.921683	−	1.59640i	−0.0319728	−	0.0553786i
$832$		0			0
$833$	−33.7980	+	4.87832i	−1.17103	+	0.169024i
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$	2.51760	+	1.45354i	0.0870210	+	0.0502416i
$838$		0			0
$839$	−30.4949			−1.05280			−0.526400	−	0.850237i	$-0.676459\pi$
$839$	−30.4949			−1.05280			−0.526400	+	0.850237i	$0.676459\pi$
$840$		0			0
$841$	−23.5051			−0.810521
$842$		0			0
$843$	4.65153	+	2.68556i	0.160207	+	0.0924957i
$844$		0			0
$845$	3.39898	+	5.88721i	0.116928	+	0.202526i
$846$		0			0
$847$	26.0000	+	22.5167i	0.893371	+	0.773682i
$848$		0			0
$849$	1.34847	+	2.33562i	0.0462793	+	0.0801582i
$850$		0			0
$851$	7.89898	−	13.6814i	0.270774	−	0.468994i
$852$		0			0
$853$	−48.4495			−1.65888			−0.829439	−	0.558597i	$-0.811340\pi$
$853$	−48.4495			−1.65888			−0.829439	+	0.558597i	$0.811340\pi$
$854$		0			0
$855$			12.2993i			0.420628i
$856$		0			0
$857$	48.1918	+	27.8236i	1.64620	+	0.950435i	0.978562	+	0.205950i	$0.0660285\pi$
$857$	48.1918	+	27.8236i	1.64620	+	0.950435i	0.667639	+	0.744485i	$0.267305\pi$
$858$		0			0
$859$	−21.0000	+	12.1244i	−0.716511	+	0.413678i	−0.813467	−	0.581611i	$-0.802423\pi$
$859$	−21.0000	+	12.1244i	−0.716511	+	0.413678i	0.0969563	+	0.995289i	$0.469089\pi$
$860$		0			0
$861$	−1.27526	+	6.62642i	−0.0434606	+	0.225828i
$862$		0			0
$863$	−2.05051	+	1.18386i	−0.0698002	+	0.0402992i	−0.534494	−	0.845172i	$-0.679498\pi$
$863$	−2.05051	+	1.18386i	−0.0698002	+	0.0402992i	0.464694	+	0.885471i	$0.346164\pi$
$864$		0			0
$865$	−5.44949	+	9.43879i	−0.185288	+	0.320929i
$866$		0			0
$867$			2.16064i			0.0733793i
$868$		0			0
$869$			37.7552i			1.28076i
$870$		0			0
$871$	27.4722	−	47.5832i	0.930860	−	1.61230i
$872$		0			0
$873$	30.0000	−	17.3205i	1.01535	−	0.586210i
$874$		0			0
$875$	2.50000	−	0.866025i	0.0845154	−	0.0292770i
$876$		0			0
$877$	1.71964	−	0.992836i	0.0580682	−	0.0335257i	−0.470685	−	0.882301i	$-0.655993\pi$
$877$	1.71964	−	0.992836i	0.0580682	−	0.0335257i	0.528753	+	0.848776i	$0.322660\pi$
$878$		0			0
$879$	6.74235	+	3.89270i	0.227414	+	0.131297i
$880$		0			0
$881$			36.6588i			1.23507i	0.786545	+	0.617533i	$0.211868\pi$
$881$			36.6588i			1.23507i	−0.786545	+	0.617533i	$0.788132\pi$
$882$		0			0
$883$	40.4949			1.36276			0.681381	−	0.731929i	$-0.261380\pi$
$883$	40.4949			1.36276			0.681381	+	0.731929i	$0.261380\pi$
$884$		0			0
$885$	0.573214	−	0.992836i	0.0192684	−	0.0333738i
$886$		0			0
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$		0			0
$889$	6.00000	+	17.3205i	0.201234	+	0.580911i
$890$		0			0
$891$	19.8434	+	34.3697i	0.664778	+	1.15143i
$892$		0			0
$893$	−22.0454	−	12.7279i	−0.737721	−	0.425924i
$894$		0			0
$895$	9.55051			0.319238
$896$		0			0
$897$	6.44949			0.215342
$898$		0			0
$899$	9.72985	+	5.61753i	0.324509	+	0.187355i
$900$		0			0
$901$	−5.00000	−	8.66025i	−0.166574	−	0.288515i
$902$		0			0
$903$	−7.80306	−	1.50170i	−0.259670	−	0.0499734i
$904$		0			0
$905$	6.17423	+	10.6941i	0.205239	+	0.355484i
$906$		0			0
$907$	−4.17423	+	7.22999i	−0.138603	+	0.240068i	−0.926968	−	0.375140i	$-0.877595\pi$
$907$	−4.17423	+	7.22999i	−0.138603	+	0.240068i	0.788365	+	0.615208i	$0.210928\pi$
$908$		0			0
$909$	44.2020			1.46609
$910$		0			0
$911$		−	41.5050i		−	1.37512i	−0.726127	−	0.687561i	$-0.758681\pi$
$911$		−	41.5050i		−	1.37512i	0.726127	−	0.687561i	$-0.241319\pi$
$912$		0			0
$913$	7.95459	+	4.59259i	0.263259	+	0.151992i
$914$		0			0
$915$	0.0959179	−	0.0553782i	0.00317095	−	0.00183075i
$916$		0			0
$917$	−19.5959	+	22.6274i	−0.647114	+	0.747223i
$918$		0			0
$919$	−12.3712	+	7.14250i	−0.408087	+	0.235609i	−0.689968	−	0.723840i	$-0.742375\pi$
$919$	−12.3712	+	7.14250i	−0.408087	+	0.235609i	0.281880	+	0.959450i	$0.409042\pi$
$920$		0			0
$921$	−4.44439	+	7.69790i	−0.146448	+	0.253655i
$922$		0			0
$923$		−	6.29253i		−	0.207121i
$924$		0			0
$925$			3.46410i			0.113899i
$926$		0			0
$927$	−24.3485	+	42.1728i	−0.799709	+	1.38514i
$928$		0			0
$929$	−5.29796	+	3.05878i	−0.173820	+	0.100355i	−0.584386	−	0.811476i	$-0.698665\pi$
$929$	−5.29796	+	3.05878i	−0.173820	+	0.100355i	0.410566	+	0.911831i	$0.365331\pi$
$930$		0			0
$931$	−11.0227	+	27.5772i	−0.361255	+	0.903805i
$932$		0			0
$933$	−3.06811	+	1.77138i	−0.100445	+	0.0579922i
$934$		0			0
$935$	−20.6969	−	11.9494i	−0.676862	−	0.390787i
$936$		0			0
$937$			10.0424i			0.328070i	0.986455	+	0.164035i	$0.0524509\pi$
$937$			10.0424i			0.328070i	−0.986455	+	0.164035i	$0.947549\pi$
$938$		0			0
$939$	−2.09082			−0.0682312
$940$		0			0
$941$	7.89898	−	13.6814i	0.257499	−	0.446002i	−0.708072	−	0.706140i	$-0.750435\pi$
$941$	7.89898	−	13.6814i	0.257499	−	0.446002i	0.965571	+	0.260138i	$0.0837681\pi$
$942$		0			0
$943$	−18.2980	−	31.6930i	−0.595864	−	1.03207i
$944$		0			0
$945$	−3.24745	+	3.74983i	−0.105640	+	0.121982i
$946$		0			0
$947$	23.7247	+	41.0925i	0.770951	+	1.33533i	0.937042	+	0.349215i	$0.113552\pi$
$947$	23.7247	+	41.0925i	0.770951	+	1.33533i	−0.166092	+	0.986110i	$0.553115\pi$
$948$		0			0
$949$	−43.0454	−	24.8523i	−1.39731	−	0.806739i
$950$		0			0
$951$	−0.156633			−0.00507918
$952$		0			0
$953$	−10.8990			−0.353053			−0.176526	−	0.984296i	$-0.556486\pi$
$953$	−10.8990			−0.353053			−0.176526	+	0.984296i	$0.556486\pi$
$954$		0			0
$955$	−22.8990	−	13.2207i	−0.740994	−	0.427813i
$956$		0			0
$957$	−5.64133	−	9.77106i	−0.182358	−	0.315854i
$958$		0			0
$959$	−4.89898	+	25.4558i	−0.158196	+	0.822012i
$960$		0			0
$961$	14.2980	+	24.7648i	0.461224	+	0.798864i
$962$		0			0
$963$	−7.89898	+	13.6814i	−0.254541	+	0.440878i
$964$		0			0
$965$	−22.6969			−0.730640
$966$		0			0
$967$			52.6437i			1.69291i	0.532461	+	0.846454i	$0.321267\pi$
$967$			52.6437i			1.69291i	−0.532461	+	0.846454i	$0.678733\pi$
$968$		0			0
$969$	5.69694	+	3.28913i	0.183012	+	0.105662i
$970$		0			0
$971$	26.1464	−	15.0956i	0.839079	−	0.484442i	−0.0178722	−	0.999840i	$-0.505689\pi$
$971$	26.1464	−	15.0956i	0.839079	−	0.484442i	0.856951	+	0.515398i	$0.172356\pi$
$972$		0			0
$973$	−6.00000	−	17.3205i	−0.192351	−	0.555270i
$974$		0			0
$975$	−1.22474	+	0.707107i	−0.0392232	+	0.0226455i
$976$		0			0
$977$	14.6969	−	25.4558i	0.470197	−	0.814405i	−0.529222	−	0.848483i	$-0.677516\pi$
$977$	14.6969	−	25.4558i	0.470197	−	0.814405i	0.999419	+	0.0340785i	$0.0108496\pi$
$978$		0			0
$979$		−	53.1687i		−	1.69928i
$980$		0			0
$981$		−	22.8489i		−	0.729510i
$982$		0			0
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	−0.960489	−	0.278319i	$-0.910223\pi$
$983$	−7.50000	+	12.9904i	−0.239213	+	0.414329i	0.721276	+	0.692648i	$0.243556\pi$
$984$		0			0
$985$	0.797959	−	0.460702i	0.0254251	−	0.0146792i
$986$		0			0
$987$	−1.65153	−	4.76756i	−0.0525688	−	0.151753i
$988$		0			0
$989$	37.3207	−	21.5471i	1.18673	−	0.685158i
$990$		0			0
$991$	25.7196	+	14.8492i	0.817011	+	0.471702i	0.849385	−	0.527774i	$-0.176973\pi$
$991$	25.7196	+	14.8492i	0.817011	+	0.471702i	−0.0323734	+	0.999476i	$0.510307\pi$
$992$		0			0
$993$		−	1.00005i		−	0.0317357i
$994$		0			0
$995$	−24.6969			−0.782946
$996$		0			0
$997$	13.3258	−	23.0809i	0.422031	−	0.730980i	−0.574107	−	0.818780i	$-0.694651\pi$
$997$	13.3258	−	23.0809i	0.422031	−	0.730980i	0.996138	+	0.0878009i	$0.0279839\pi$
$998$		0			0
$999$	−3.24745	−	5.62475i	−0.102745	−	0.177959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.c.591.1		4
4.3	odd	2		280.2.bj.c.171.2	yes	4
7.5	odd	6		1120.2.bz.b.271.1		4
8.3	odd	2		1120.2.bz.b.591.1		4
8.5	even	2		280.2.bj.b.171.2	yes	4
28.19	even	6		280.2.bj.b.131.1	✓	4
56.5	odd	6		280.2.bj.c.131.2	yes	4
56.19	even	6	inner	1120.2.bz.c.271.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.b.131.1	✓	4	28.19	even	6
280.2.bj.b.171.2	yes	4	8.5	even	2
280.2.bj.c.131.2	yes	4	56.5	odd	6
280.2.bj.c.171.2	yes	4	4.3	odd	2
1120.2.bz.b.271.1		4	7.5	odd	6
1120.2.bz.b.591.1		4	8.3	odd	2
1120.2.bz.c.271.1		4	56.19	even	6	inner
1120.2.bz.c.591.1		4	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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.275255 + 0.158919i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-1.44949 - 2.51059i) q^{9} +(2.44949 - 4.24264i) q^{11} +4.44949 q^{13} +0.317837i q^{15} +(-4.22474 - 2.43916i) q^{17} +(-3.67423 + 2.12132i) q^{19} +(-0.825765 - 0.158919i) q^{21} +(3.94949 - 2.28024i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.87492i q^{27} -7.24604i q^{29} +(-0.775255 + 1.34278i) q^{31} +(1.34847 - 0.778539i) q^{33} +(-2.00000 - 1.73205i) q^{35} +(3.00000 - 1.73205i) q^{37} +(1.22474 + 0.707107i) q^{39} -8.02458i q^{41} +9.44949 q^{43} +(1.44949 - 2.51059i) q^{45} +(3.00000 + 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-0.775255 - 1.34278i) q^{51} +(1.77526 + 1.02494i) q^{53} +4.89898 q^{55} -1.34847 q^{57} +(-3.12372 - 1.80348i) q^{59} +(-0.174235 - 0.301783i) q^{61} +(5.79796 + 5.02118i) q^{63} +(2.22474 + 3.85337i) q^{65} +(6.17423 - 10.6941i) q^{67} +1.44949 q^{69} -1.41421i q^{71} +(-9.67423 - 5.58542i) q^{73} +(-0.275255 + 0.158919i) q^{75} +(-2.44949 + 12.7279i) q^{77} +(-6.67423 + 3.85337i) q^{79} +(-4.05051 + 7.01569i) q^{81} +1.87492i q^{83} -4.87832i q^{85} +(1.15153 - 1.99451i) q^{87} +(9.39898 - 5.42650i) q^{89} +(-11.1237 + 3.85337i) q^{91} +(-0.426786 + 0.246405i) q^{93} +(-3.67423 - 2.12132i) q^{95} +11.9494i q^{97} -14.2020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{5} - 10 q^{7} + 4 q^{9} + 8 q^{13} - 12 q^{17} - 18 q^{21} + 6 q^{23} - 2 q^{25} - 8 q^{31} - 24 q^{33} - 8 q^{35} + 12 q^{37} + 28 q^{43} - 4 q^{45} + 12 q^{47} + 22 q^{49} - 8 q^{51}+ \cdots - 96 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^5 - 10 * q^7 + 4 * q^9 + 8 * q^13 - 12 * q^17 - 18 * q^21 + 6 * q^23 - 2 * q^25 - 8 * q^31 - 24 * q^33 - 8 * q^35 + 12 * q^37 + 28 * q^43 - 4 * q^45 + 12 * q^47 + 22 * q^49 - 8 * q^51 + 12 * q^53 + 24 * q^57 + 12 * q^59 + 14 * q^61 - 16 * q^63 + 4 * q^65 + 10 * q^67 - 4 * q^69 - 24 * q^73 - 6 * q^75 - 12 * q^79 - 26 * q^81 + 34 * q^87 + 18 * q^89 - 20 * q^91 - 36 * q^93 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more