LMFDB - Embedded newform 640.2.q.e.609.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(289,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			609.5
Root			$-1.32661 + 0.490008i$ of defining polynomial
Character	$\chi$	$=$	640.609
Dual form			640.2.q.e.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.183790 + 0.183790i) q^{3} +(0.569800 + 2.16225i) q^{5} +3.84853 q^{7} -2.93244i q^{9} +(-1.60020 - 1.60020i) q^{11} +(1.80775 + 1.80775i) q^{13} +(-0.292677 + 0.502125i) q^{15} +4.93886i q^{17} +(4.77162 - 4.77162i) q^{19} +(0.707323 + 0.707323i) q^{21} +0.134544 q^{23} +(-4.35066 + 2.46410i) q^{25} +(1.09033 - 1.09033i) q^{27} +(-2.17142 + 2.17142i) q^{29} +2.26371 q^{31} -0.588201i q^{33} +(2.19289 + 8.32149i) q^{35} +(-4.35066 + 4.35066i) q^{37} +0.664493i q^{39} +3.34709i q^{41} +(2.70896 - 2.70896i) q^{43} +(6.34067 - 1.67091i) q^{45} +7.03343i q^{47} +7.81119 q^{49} +(-0.907714 + 0.907714i) q^{51} +(3.40020 - 3.40020i) q^{53} +(2.54823 - 4.37182i) q^{55} +1.75396 q^{57} +(0.107127 + 0.107127i) q^{59} +(3.46410 - 3.46410i) q^{61} -11.2856i q^{63} +(-2.87875 + 4.93886i) q^{65} +(1.91078 + 1.91078i) q^{67} +(0.0247279 + 0.0247279i) q^{69} -9.32899i q^{71} +9.82769 q^{73} +(-1.25249 - 0.346730i) q^{75} +(-6.15840 - 6.15840i) q^{77} -11.0073 q^{79} -8.39654 q^{81} +(-8.80967 - 8.80967i) q^{83} +(-10.6790 + 2.81416i) q^{85} -0.798174 q^{87} +1.12125i q^{89} +(6.95717 + 6.95717i) q^{91} +(0.416048 + 0.416048i) q^{93} +(13.0363 + 7.59857i) q^{95} -6.10461i q^{97} +(-4.69248 + 4.69248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 8 q^{11} + 8 q^{19} + 16 q^{21} + 16 q^{29} + 16 q^{31} + 24 q^{35} - 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} - 32 q^{69} - 48 q^{75} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) $ 16 * q + 8 * q^5 - 8 * q^11 + 8 * q^19 + 16 * q^21 + 16 * q^29 + 16 * q^31 + 24 * q^35 - 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 - 32 * q^69 - 48 * q^75 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 32 * q^95 - 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.183790	+	0.183790i	0.106111	+	0.106111i	0.758169	−	0.652058i	$-0.226094\pi$
$3$	0.183790	+	0.183790i	0.106111	+	0.106111i	−0.652058	+	0.758169i	$0.726094\pi$
$4$		0			0
$5$	0.569800	+	2.16225i	0.254822	+	0.966988i
$5$	0.569800	+	2.16225i	0.254822	+	0.966988i
$6$		0			0
$7$	3.84853			1.45461			0.727304	−	0.686315i	$-0.240773\pi$
$7$	3.84853			1.45461			0.727304	+	0.686315i	$0.240773\pi$
$8$		0			0
$9$		−	2.93244i		−	0.977481i
$10$		0			0
$11$	−1.60020	−	1.60020i	−0.482477	−	0.482477i	0.423445	−	0.905922i	$-0.360821\pi$
$11$	−1.60020	−	1.60020i	−0.482477	−	0.482477i	−0.905922	+	0.423445i	$0.860821\pi$
$12$		0			0
$13$	1.80775	+	1.80775i	0.501379	+	0.501379i	0.911866	−	0.410487i	$-0.134641\pi$
$13$	1.80775	+	1.80775i	0.501379	+	0.501379i	−0.410487	+	0.911866i	$0.634641\pi$
$14$		0			0
$15$	−0.292677	+	0.502125i	−0.0755689	+	0.129648i
$16$		0			0
$17$			4.93886i			1.19785i	0.800806	+	0.598924i	$0.204405\pi$
$17$			4.93886i			1.19785i	−0.800806	+	0.598924i	$0.795595\pi$
$18$		0			0
$19$	4.77162	−	4.77162i	1.09468	−	1.09468i	0.0996636	−	0.995021i	$-0.468223\pi$
$19$	4.77162	−	4.77162i	1.09468	−	1.09468i	0.995021	−	0.0996636i	$-0.0317767\pi$
$20$		0			0
$21$	0.707323	+	0.707323i	0.154351	+	0.154351i
$22$		0			0
$23$	0.134544			0.0280543			0.0140272	−	0.999902i	$-0.495535\pi$
$23$	0.134544			0.0280543			0.0140272	+	0.999902i	$0.495535\pi$
$24$		0			0
$25$	−4.35066	+	2.46410i	−0.870131	+	0.492820i
$26$		0			0
$27$	1.09033	−	1.09033i	0.209833	−	0.209833i
$28$		0			0
$29$	−2.17142	+	2.17142i	−0.403223	+	0.403223i	−0.879367	−	0.476144i	$-0.842034\pi$
$29$	−2.17142	+	2.17142i	−0.403223	+	0.403223i	0.476144	+	0.879367i	$0.342034\pi$
$30$		0			0
$31$	2.26371			0.406574			0.203287	−	0.979119i	$-0.434837\pi$
$31$	2.26371			0.406574			0.203287	+	0.979119i	$0.434837\pi$
$32$		0			0
$33$		−	0.588201i		−	0.102393i
$34$		0			0
$35$	2.19289	+	8.32149i	0.370667	+	1.40659i
$36$		0			0
$37$	−4.35066	+	4.35066i	−0.715243	+	0.715243i	−0.967627	−	0.252384i	$-0.918785\pi$
$37$	−4.35066	+	4.35066i	−0.715243	+	0.715243i	0.252384	+	0.967627i	$0.418785\pi$
$38$		0			0
$39$			0.664493i			0.106404i
$40$		0			0
$41$			3.34709i			0.522727i	0.965240	+	0.261364i	$0.0841722\pi$
$41$			3.34709i			0.522727i	−0.965240	+	0.261364i	$0.915828\pi$
$42$		0			0
$43$	2.70896	−	2.70896i	0.413112	−	0.413112i	−0.469709	−	0.882821i	$-0.655641\pi$
$43$	2.70896	−	2.70896i	0.413112	−	0.413112i	0.882821	+	0.469709i	$0.155641\pi$
$44$		0			0
$45$	6.34067	−	1.67091i	0.945212	−	0.249084i
$46$		0			0
$47$			7.03343i			1.02593i	0.858409	+	0.512966i	$0.171453\pi$
$47$			7.03343i			1.02593i	−0.858409	+	0.512966i	$0.828547\pi$
$48$		0			0
$49$	7.81119			1.11588
$50$		0			0
$51$	−0.907714	+	0.907714i	−0.127105	+	0.127105i
$52$		0			0
$53$	3.40020	−	3.40020i	0.467053	−	0.467053i	−0.433905	−	0.900958i	$-0.642865\pi$
$53$	3.40020	−	3.40020i	0.467053	−	0.467053i	0.900958	+	0.433905i	$0.142865\pi$
$54$		0			0
$55$	2.54823	−	4.37182i	0.343604	−	0.589496i
$56$		0			0
$57$	1.75396			0.232317
$58$		0			0
$59$	0.107127	+	0.107127i	0.0139468	+	0.0139468i	0.714046	−	0.700099i	$-0.246861\pi$
$59$	0.107127	+	0.107127i	0.0139468	+	0.0139468i	−0.700099	+	0.714046i	$0.746861\pi$
$60$		0			0
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	−0.449665	−	0.893197i	$-0.648457\pi$
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	0.893197	+	0.449665i	$0.148457\pi$
$62$		0			0
$63$		−	11.2856i		−	1.42185i
$64$		0			0
$65$	−2.87875	+	4.93886i	−0.357065	+	0.612590i
$66$		0			0
$67$	1.91078	+	1.91078i	0.233440	+	0.233440i	0.814127	−	0.580687i	$-0.197216\pi$
$67$	1.91078	+	1.91078i	0.233440	+	0.233440i	−0.580687	+	0.814127i	$0.697216\pi$
$68$		0			0
$69$	0.0247279	+	0.0247279i	0.00297689	+	0.00297689i
$70$		0			0
$71$		−	9.32899i		−	1.10715i	−0.832800	−	0.553573i	$-0.813264\pi$
$71$		−	9.32899i		−	1.10715i	0.832800	−	0.553573i	$-0.186736\pi$
$72$		0			0
$73$	9.82769			1.15024			0.575122	−	0.818068i	$-0.304955\pi$
$73$	9.82769			1.15024			0.575122	+	0.818068i	$0.304955\pi$
$74$		0			0
$75$	−1.25249	−	0.346730i	−0.144625	−	0.0400370i
$76$		0			0
$77$	−6.15840	−	6.15840i	−0.701815	−	0.701815i
$78$		0			0
$79$	−11.0073			−1.23842			−0.619211	−	0.785224i	$-0.712548\pi$
$79$	−11.0073			−1.23842			−0.619211	+	0.785224i	$0.712548\pi$
$80$		0			0
$81$	−8.39654			−0.932949
$82$		0			0
$83$	−8.80967	−	8.80967i	−0.966987	−	0.966987i	0.0324850	−	0.999472i	$-0.489658\pi$
$83$	−8.80967	−	8.80967i	−0.966987	−	0.966987i	−0.999472	+	0.0324850i	$0.989658\pi$
$84$		0			0
$85$	−10.6790	+	2.81416i	−1.15831	+	0.305239i
$86$		0			0
$87$	−0.798174			−0.0855732
$88$		0			0
$89$			1.12125i			0.118853i	0.998233	+	0.0594263i	$0.0189271\pi$
$89$			1.12125i			0.118853i	−0.998233	+	0.0594263i	$0.981073\pi$
$90$		0			0
$91$	6.95717	+	6.95717i	0.729310	+	0.729310i
$92$		0			0
$93$	0.416048	+	0.416048i	0.0431422	+	0.0431422i
$94$		0			0
$95$	13.0363	+	7.59857i	1.33750	+	0.779597i
$96$		0			0
$97$		−	6.10461i		−	0.619829i	−0.950764	−	0.309915i	$-0.899700\pi$
$97$		−	6.10461i		−	0.619829i	0.950764	−	0.309915i	$-0.100300\pi$
$98$		0			0
$99$	−4.69248	+	4.69248i	−0.471612	+	0.471612i
$100$		0			0
$101$	−2.17142	−	2.17142i	−0.216065	−	0.216065i	0.590773	−	0.806838i	$-0.298823\pi$
$101$	−2.17142	−	2.17142i	−0.216065	−	0.216065i	−0.806838	+	0.590773i	$0.798823\pi$
$102$		0			0
$103$	−15.3778			−1.51522			−0.757610	−	0.652707i	$-0.773633\pi$
$103$	−15.3778			−1.51522			−0.757610	+	0.652707i	$0.773633\pi$
$104$		0			0
$105$	−1.12638	+	1.93244i	−0.109923	+	0.188587i
$106$		0			0
$107$	−6.98419	+	6.98419i	−0.675187	+	0.675187i	−0.958907	−	0.283720i	$-0.908431\pi$
$107$	−6.98419	+	6.98419i	−0.675187	+	0.675187i	0.283720	+	0.958907i	$0.408431\pi$
$108$		0			0
$109$	−8.59694	+	8.59694i	−0.823437	+	0.823437i	−0.986599	−	0.163162i	$-0.947831\pi$
$109$	−8.59694	+	8.59694i	−0.823437	+	0.823437i	0.163162	+	0.986599i	$0.447831\pi$
$110$		0			0
$111$	−1.59922			−0.151791
$112$		0			0
$113$		−	14.5329i		−	1.36714i	−0.729883	−	0.683572i	$-0.760426\pi$
$113$		−	14.5329i		−	1.36714i	0.729883	−	0.683572i	$-0.239574\pi$
$114$		0			0
$115$	0.0766631	+	0.290918i	0.00714887	+	0.0271282i
$116$		0			0
$117$	5.30111	−	5.30111i	0.490088	−	0.490088i
$118$		0			0
$119$			19.0073i			1.74240i
$120$		0			0
$121$		−	5.87875i		−	0.534432i
$122$		0			0
$123$	−0.615163	+	0.615163i	−0.0554673	+	0.0554673i
$124$		0			0
$125$	−7.80701	−	8.00316i	−0.698280	−	0.715825i
$126$		0			0
$127$		−	5.96617i		−	0.529412i	−0.964329	−	0.264706i	$-0.914725\pi$
$127$		−	5.96617i		−	0.529412i	0.964329	−	0.264706i	$-0.0852749\pi$
$128$		0			0
$129$	0.995761			0.0876719
$130$		0			0
$131$	−2.37084	+	2.37084i	−0.207141	+	0.207141i	−0.803051	−	0.595910i	$-0.796791\pi$
$131$	−2.37084	+	2.37084i	−0.207141	+	0.207141i	0.595910	+	0.803051i	$0.296791\pi$
$132$		0			0
$133$	18.3637	−	18.3637i	1.59234	−	1.59234i
$134$		0			0
$135$	2.97883	+	1.73629i	0.256376	+	0.149436i
$136$		0			0
$137$	−18.2745			−1.56129			−0.780646	−	0.624973i	$-0.785110\pi$
$137$	−18.2745			−1.56129			−0.780646	+	0.624973i	$0.785110\pi$
$138$		0			0
$139$	0.136094	+	0.136094i	0.0115433	+	0.0115433i	0.712855	−	0.701312i	$-0.247402\pi$
$139$	0.136094	+	0.136094i	0.0115433	+	0.0115433i	−0.701312	+	0.712855i	$0.747402\pi$
$140$		0			0
$141$	−1.29268	+	1.29268i	−0.108863	+	0.108863i
$142$		0			0
$143$		−	5.78550i		−	0.483808i
$144$		0			0
$145$	−5.93244	−	3.45789i	−0.492663	−	0.287162i
$146$		0			0
$147$	1.43562	+	1.43562i	0.118408	+	0.118408i
$148$		0			0
$149$	2.40078	+	2.40078i	0.196680	+	0.196680i	0.798575	−	0.601895i	$-0.205588\pi$
$149$	2.40078	+	2.40078i	0.196680	+	0.196680i	−0.601895	+	0.798575i	$0.705588\pi$
$150$		0			0
$151$			17.9935i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$151$			17.9935i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$152$		0			0
$153$	14.4829			1.17087
$154$		0			0
$155$	1.28986	+	4.89471i	0.103604	+	0.393152i
$156$		0			0
$157$	12.6359	+	12.6359i	1.00846	+	1.00846i	0.999964	+	0.00849213i	$0.00270316\pi$
$157$	12.6359	+	12.6359i	1.00846	+	1.00846i	0.00849213	+	0.999964i	$0.497297\pi$
$158$		0			0
$159$	1.24985			0.0991193
$160$		0			0
$161$	0.517796			0.0408081
$162$		0			0
$163$	−15.8470	−	15.8470i	−1.24123	−	1.24123i	−0.959490	−	0.281743i	$-0.909087\pi$
$163$	−15.8470	−	15.8470i	−1.24123	−	1.24123i	−0.281743	−	0.959490i	$-0.590913\pi$
$164$		0			0
$165$	1.27184	−	0.335157i	0.0990125	−	0.0260919i
$166$		0			0
$167$	−12.7559			−0.987083			−0.493541	−	0.869722i	$-0.664298\pi$
$167$	−12.7559			−0.987083			−0.493541	+	0.869722i	$0.664298\pi$
$168$		0			0
$169$		−	6.46410i		−	0.497239i
$170$		0			0
$171$	−13.9925	−	13.9925i	−1.07003	−	1.07003i
$172$		0			0
$173$	−2.64673	−	2.64673i	−0.201227	−	0.201227i	0.599299	−	0.800525i	$-0.295446\pi$
$173$	−2.64673	−	2.64673i	−0.201227	−	0.201227i	−0.800525	+	0.599299i	$0.795446\pi$
$174$		0			0
$175$	−16.7436	+	9.48317i	−1.26570	+	0.716860i
$176$		0			0
$177$			0.0393779i			0.00295983i
$178$		0			0
$179$	11.6497	−	11.6497i	0.870736	−	0.870736i	−0.121817	−	0.992553i	$-0.538872\pi$
$179$	11.6497	−	11.6497i	0.870736	−	0.870736i	0.992553	+	0.121817i	$0.0388720\pi$
$180$		0			0
$181$	−1.24322	−	1.24322i	−0.0924079	−	0.0924079i	0.659392	−	0.751800i	$-0.270814\pi$
$181$	−1.24322	−	1.24322i	−0.0924079	−	0.0924079i	−0.751800	+	0.659392i	$0.770814\pi$
$182$		0			0
$183$	1.27334			0.0941278
$184$		0			0
$185$	−11.8862	−	6.92820i	−0.873892	−	0.509372i
$186$		0			0
$187$	7.90314	−	7.90314i	0.577935	−	0.577935i
$188$		0			0
$189$	4.19615	−	4.19615i	0.305225	−	0.305225i
$190$		0			0
$191$	5.07180			0.366982			0.183491	−	0.983021i	$-0.441260\pi$
$191$	5.07180			0.366982			0.183491	+	0.983021i	$0.441260\pi$
$192$		0			0
$193$		−	2.30278i		−	0.165758i	−0.996560	−	0.0828788i	$-0.973589\pi$
$193$		−	2.30278i		−	0.165758i	0.996560	−	0.0828788i	$-0.0264114\pi$
$194$		0			0
$195$	−1.43680	+	0.378628i	−0.102891	+	0.0271141i
$196$		0			0
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	−0.933511	−	0.358549i	$-0.883271\pi$
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	0.358549	+	0.933511i	$0.383271\pi$
$198$		0			0
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$		0			0
$201$			0.702368i			0.0495412i
$202$		0			0
$203$	−8.35679	+	8.35679i	−0.586532	+	0.586532i
$204$		0			0
$205$	−7.23724	+	1.90717i	−0.505471	+	0.133203i
$206$		0			0
$207$		−	0.394542i		−	0.0274226i
$208$		0			0
$209$	−15.2711			−1.05632
$210$		0			0
$211$	−0.478227	+	0.478227i	−0.0329225	+	0.0329225i	−0.723376	−	0.690454i	$-0.757411\pi$
$211$	−0.478227	+	0.478227i	−0.0329225	+	0.0329225i	0.690454	+	0.723376i	$0.257411\pi$
$212$		0			0
$213$	1.71458	−	1.71458i	0.117481	−	0.117481i
$214$		0			0
$215$	7.40101	+	4.31388i	0.504745	+	0.294204i
$216$		0			0
$217$	8.71196			0.591406
$218$		0			0
$219$	1.80623	+	1.80623i	0.122054	+	0.122054i
$220$		0			0
$221$	−8.92820	+	8.92820i	−0.600576	+	0.600576i
$222$		0			0
$223$		−	7.50859i		−	0.502813i	−0.967882	−	0.251406i	$-0.919107\pi$
$223$		−	7.50859i		−	0.502813i	0.967882	−	0.251406i	$-0.0808930\pi$
$224$		0			0
$225$	7.22584	+	12.7580i	0.481722	+	0.850536i
$226$		0			0
$227$	12.8788	+	12.8788i	0.854798	+	0.854798i	0.990720	−	0.135922i	$-0.0433997\pi$
$227$	12.8788	+	12.8788i	0.854798	+	0.854798i	−0.135922	+	0.990720i	$0.543400\pi$
$228$		0			0
$229$	−8.62166	−	8.62166i	−0.569736	−	0.569736i	0.362319	−	0.932054i	$-0.381985\pi$
$229$	−8.62166	−	8.62166i	−0.569736	−	0.569736i	−0.932054	+	0.362319i	$0.881985\pi$
$230$		0			0
$231$		−	2.26371i		−	0.148941i
$232$		0			0
$233$	4.63429			0.303602			0.151801	−	0.988411i	$-0.451493\pi$
$233$	4.63429			0.303602			0.151801	+	0.988411i	$0.451493\pi$
$234$		0			0
$235$	−15.2080	+	4.00765i	−0.992063	+	0.261430i
$236$		0			0
$237$	−2.02304	−	2.02304i	−0.131411	−	0.131411i
$238$		0			0
$239$	18.4220			1.19162			0.595810	−	0.803126i	$-0.296831\pi$
$239$	18.4220			1.19162			0.595810	+	0.803126i	$0.296831\pi$
$240$		0			0
$241$	18.3247			1.18040			0.590200	−	0.807257i	$-0.299049\pi$
$241$	18.3247			1.18040			0.590200	+	0.807257i	$0.299049\pi$
$242$		0			0
$243$	−4.81418	−	4.81418i	−0.308830	−	0.308830i
$244$		0			0
$245$	4.45082	+	16.8897i	0.284352	+	1.07905i
$246$		0			0
$247$	17.2518			1.09770
$248$		0			0
$249$		−	3.23827i		−	0.205217i
$250$		0			0
$251$	16.0222	+	16.0222i	1.01131	+	1.01131i	0.999935	+	0.0113760i	$0.00362116\pi$
$251$	16.0222	+	16.0222i	1.01131	+	1.01131i	0.0113760	+	0.999935i	$0.496379\pi$
$252$		0			0
$253$	−0.215297	−	0.215297i	−0.0135356	−	0.0135356i
$254$		0			0
$255$	−2.47992	−	1.44549i	−0.155299	−	0.0905201i
$256$		0			0
$257$		−	5.82098i		−	0.363103i	−0.983381	−	0.181551i	$-0.941888\pi$
$257$		−	5.82098i		−	0.363103i	0.983381	−	0.181551i	$-0.0581119\pi$
$258$		0			0
$259$	−16.7436	+	16.7436i	−1.04040	+	1.04040i
$260$		0			0
$261$	6.36758	+	6.36758i	0.394143	+	0.394143i
$262$		0			0
$263$	−0.806693			−0.0497428			−0.0248714	−	0.999691i	$-0.507918\pi$
$263$	−0.806693			−0.0497428			−0.0248714	+	0.999691i	$0.507918\pi$
$264$		0			0
$265$	9.28951	+	5.41465i	0.570650	+	0.332619i
$266$		0			0
$267$	−0.206075	+	0.206075i	−0.0126116	+	0.0126116i
$268$		0			0
$269$	15.1939	−	15.1939i	0.926387	−	0.926387i	−0.0710837	−	0.997470i	$-0.522646\pi$
$269$	15.1939	−	15.1939i	0.926387	−	0.926387i	0.997470	+	0.0710837i	$0.0226458\pi$
$270$		0			0
$271$	−10.8491			−0.659034			−0.329517	−	0.944150i	$-0.606886\pi$
$271$	−10.8491			−0.659034			−0.329517	+	0.944150i	$0.606886\pi$
$272$		0			0
$273$			2.55732i			0.154776i
$274$		0			0
$275$	10.9049	+	3.01886i	0.657593	+	0.182044i
$276$		0			0
$277$	−1.27334	+	1.27334i	−0.0765074	+	0.0765074i	−0.744325	−	0.667818i	$-0.767229\pi$
$277$	−1.27334	+	1.27334i	−0.0765074	+	0.0765074i	0.667818	+	0.744325i	$0.267229\pi$
$278$		0			0
$279$		−	6.63820i		−	0.397419i
$280$		0			0
$281$			20.2174i			1.20607i	0.797716	+	0.603033i	$0.206041\pi$
$281$			20.2174i			1.20607i	−0.797716	+	0.603033i	$0.793959\pi$
$282$		0			0
$283$	21.3741	−	21.3741i	1.27056	−	1.27056i	0.324759	−	0.945797i	$-0.394717\pi$
$283$	21.3741	−	21.3741i	1.27056	−	1.27056i	0.945797	−	0.324759i	$-0.105283\pi$
$284$		0			0
$285$	0.999404	+	3.79249i	0.0591996	+	0.224648i
$286$		0			0
$287$			12.8814i			0.760363i
$288$		0			0
$289$	−7.39230			−0.434841
$290$		0			0
$291$	1.12197	−	1.12197i	0.0657710	−	0.0657710i
$292$		0			0
$293$	−11.1656	+	11.1656i	−0.652301	+	0.652301i	−0.953547	−	0.301246i	$-0.902598\pi$
$293$	−11.1656	+	11.1656i	−0.652301	+	0.652301i	0.301246	+	0.953547i	$0.402598\pi$
$294$		0			0
$295$	−0.170595	+	0.292677i	−0.00993241	+	0.0170403i
$296$		0			0
$297$	−3.48947			−0.202480
$298$		0			0
$299$	0.243221	+	0.243221i	0.0140659	+	0.0140659i
$300$		0			0
$301$	10.4255	−	10.4255i	0.600916	−	0.600916i
$302$		0			0
$303$		−	0.798174i		−	0.0458539i
$304$		0			0
$305$	9.46410	+	5.51641i	0.541913	+	0.315869i
$306$		0			0
$307$	−2.18143	−	2.18143i	−0.124501	−	0.124501i	0.642111	−	0.766612i	$-0.278059\pi$
$307$	−2.18143	−	2.18143i	−0.124501	−	0.124501i	−0.766612	+	0.642111i	$0.778059\pi$
$308$		0			0
$309$	−2.82629	−	2.82629i	−0.160782	−	0.160782i
$310$		0			0
$311$		−	11.5517i		−	0.655038i	−0.944845	−	0.327519i	$-0.893787\pi$
$311$		−	11.5517i		−	0.655038i	0.944845	−	0.327519i	$-0.106213\pi$
$312$		0			0
$313$	−10.4265			−0.589343			−0.294671	−	0.955599i	$-0.595210\pi$
$313$	−10.4265			−0.589343			−0.294671	+	0.955599i	$0.595210\pi$
$314$		0			0
$315$	24.4023	−	6.43053i	1.37491	−	0.362320i
$316$		0			0
$317$	−10.0785	−	10.0785i	−0.566063	−	0.566063i	0.364960	−	0.931023i	$-0.381083\pi$
$317$	−10.0785	−	10.0785i	−0.566063	−	0.566063i	−0.931023	+	0.364960i	$0.881083\pi$
$318$		0			0
$319$	6.94941			0.389092
$320$		0			0
$321$	−2.56725			−0.143290
$322$		0			0
$323$	23.5663	+	23.5663i	1.31127	+	1.31127i
$324$		0			0
$325$	−12.3194	−	3.41041i	−0.683355	−	0.189176i
$326$		0			0
$327$	−3.16007			−0.174752
$328$		0			0
$329$			27.0684i			1.49233i
$330$		0			0
$331$	−8.77162	−	8.77162i	−0.482132	−	0.482132i	0.423680	−	0.905812i	$-0.360738\pi$
$331$	−8.77162	−	8.77162i	−0.482132	−	0.482132i	−0.905812	+	0.423680i	$0.860738\pi$
$332$		0			0
$333$	12.7580	+	12.7580i	0.699137	+	0.699137i
$334$		0			0
$335$	−3.04283	+	5.22036i	−0.166248	+	0.285219i
$336$		0			0
$337$			33.0226i			1.79885i	0.437072	+	0.899427i	$0.356016\pi$
$337$			33.0226i			1.79885i	−0.437072	+	0.899427i	$0.643984\pi$
$338$		0			0
$339$	2.67101	−	2.67101i	0.145070	−	0.145070i
$340$		0			0
$341$	−3.62238	−	3.62238i	−0.196163	−	0.196163i
$342$		0			0
$343$	3.12189			0.168566
$344$		0			0
$345$	−0.0393779	+	0.0675578i	−0.00212004	+	0.00363719i
$346$		0			0
$347$	−11.1412	+	11.1412i	−0.598090	+	0.598090i	−0.939804	−	0.341714i	$-0.888993\pi$
$347$	−11.1412	+	11.1412i	−0.598090	+	0.598090i	0.341714	+	0.939804i	$0.388993\pi$
$348$		0			0
$349$	10.8656	−	10.8656i	0.581622	−	0.581622i	−0.353727	−	0.935349i	$-0.615086\pi$
$349$	10.8656	−	10.8656i	0.581622	−	0.581622i	0.935349	+	0.353727i	$0.115086\pi$
$350$		0			0
$351$	3.94207			0.210412
$352$		0			0
$353$			11.3480i			0.603995i	0.953309	+	0.301998i	$0.0976534\pi$
$353$			11.3480i			0.603995i	−0.953309	+	0.301998i	$0.902347\pi$
$354$		0			0
$355$	20.1716	−	5.31566i	1.07060	−	0.282126i
$356$		0			0
$357$	−3.49337	+	3.49337i	−0.184889	+	0.184889i
$358$		0			0
$359$		−	26.5788i		−	1.40278i	−0.712779	−	0.701389i	$-0.752564\pi$
$359$		−	26.5788i		−	1.40278i	0.712779	−	0.701389i	$-0.247436\pi$
$360$		0			0
$361$		−	26.5367i		−	1.39667i
$362$		0			0
$363$	1.08046	−	1.08046i	0.0567093	−	0.0567093i
$364$		0			0
$365$	5.59982	+	21.2499i	0.293108	+	1.11227i
$366$		0			0
$367$		−	2.90729i		−	0.151760i	−0.997117	−	0.0758798i	$-0.975823\pi$
$367$		−	2.90729i		−	0.151760i	0.997117	−	0.0758798i	$-0.0241765\pi$
$368$		0			0
$369$	9.81514			0.510956
$370$		0			0
$371$	13.0858	−	13.0858i	0.679379	−	0.679379i
$372$		0			0
$373$	−4.65522	+	4.65522i	−0.241038	+	0.241038i	−0.817280	−	0.576241i	$-0.804519\pi$
$373$	−4.65522	+	4.65522i	−0.241038	+	0.241038i	0.576241	+	0.817280i	$0.304519\pi$
$374$		0			0
$375$	0.0360509	−	2.90576i	0.00186166	−	0.150053i
$376$		0			0
$377$	−7.85077			−0.404335
$378$		0			0
$379$	−9.52106	−	9.52106i	−0.489064	−	0.489064i	0.418947	−	0.908011i	$-0.362399\pi$
$379$	−9.52106	−	9.52106i	−0.489064	−	0.489064i	−0.908011	+	0.418947i	$0.862399\pi$
$380$		0			0
$381$	1.09652	−	1.09652i	0.0561767	−	0.0561767i
$382$		0			0
$383$			6.92429i			0.353815i	0.984228	+	0.176907i	$0.0566093\pi$
$383$			6.92429i			0.353815i	−0.984228	+	0.176907i	$0.943391\pi$
$384$		0			0
$385$	9.80695	−	16.8251i	0.499808	−	0.857485i
$386$		0			0
$387$	−7.94386	−	7.94386i	−0.403809	−	0.403809i
$388$		0			0
$389$	20.0232	+	20.0232i	1.01521	+	1.01521i	0.999882	+	0.0153322i	$0.00488057\pi$
$389$	20.0232	+	20.0232i	1.01521	+	1.01521i	0.0153322	+	0.999882i	$0.495119\pi$
$390$		0			0
$391$			0.664493i			0.0336049i
$392$		0			0
$393$	−0.871474			−0.0439601
$394$		0			0
$395$	−6.27199	−	23.8006i	−0.315578	−	1.19754i
$396$		0			0
$397$	3.81625	+	3.81625i	0.191532	+	0.191532i	0.796358	−	0.604826i	$-0.206757\pi$
$397$	3.81625	+	3.81625i	0.191532	+	0.191532i	−0.604826	+	0.796358i	$0.706757\pi$
$398$		0			0
$399$	6.75015			0.337930
$400$		0			0
$401$	1.68031			0.0839108			0.0419554	−	0.999119i	$-0.486641\pi$
$401$	1.68031			0.0839108			0.0419554	+	0.999119i	$0.486641\pi$
$402$		0			0
$403$	4.09222	+	4.09222i	0.203848	+	0.203848i
$404$		0			0
$405$	−4.78435	−	18.1554i	−0.237736	−	0.902151i
$406$		0			0
$407$	13.9238			0.690177
$408$		0			0
$409$			20.1317i			0.995448i	0.867335	+	0.497724i	$0.165831\pi$
$409$			20.1317i			0.995448i	−0.867335	+	0.497724i	$0.834169\pi$
$410$		0			0
$411$	−3.35867	−	3.35867i	−0.165671	−	0.165671i
$412$		0			0
$413$	0.412282	+	0.412282i	0.0202871	+	0.0202871i
$414$		0			0
$415$	14.0290	−	24.0685i	0.688655	−	1.18147i
$416$		0			0
$417$			0.0500256i			0.00244976i
$418$		0			0
$419$	−22.6570	+	22.6570i	−1.10687	+	1.10687i	−0.113306	+	0.993560i	$0.536144\pi$
$419$	−22.6570	+	22.6570i	−1.10687	+	1.10687i	−0.993560	+	0.113306i	$0.963856\pi$
$420$		0			0
$421$	10.1583	+	10.1583i	0.495084	+	0.495084i	0.909904	−	0.414820i	$-0.136155\pi$
$421$	10.1583	+	10.1583i	0.495084	+	0.495084i	−0.414820	+	0.909904i	$0.636155\pi$
$422$		0			0
$423$	20.6251			1.00283
$424$		0			0
$425$	−12.1698	−	21.4873i	−0.590324	−	1.04229i
$426$		0			0
$427$	13.3317	−	13.3317i	0.645166	−	0.645166i
$428$		0			0
$429$	1.06332	−	1.06332i	0.0513375	−	0.0513375i
$430$		0			0
$431$	−26.1518			−1.25969			−0.629843	−	0.776723i	$-0.716881\pi$
$431$	−26.1518			−1.25969			−0.629843	+	0.776723i	$0.716881\pi$
$432$		0			0
$433$			9.30795i			0.447312i	0.974668	+	0.223656i	$0.0717992\pi$
$433$			9.30795i			0.447312i	−0.974668	+	0.223656i	$0.928201\pi$
$434$		0			0
$435$	−0.454800	−	1.72585i	−0.0218060	−	0.0827483i
$436$		0			0
$437$	0.641992	−	0.641992i	0.0307107	−	0.0307107i
$438$		0			0
$439$			30.4799i			1.45473i	0.686252	+	0.727364i	$0.259255\pi$
$439$			30.4799i			1.45473i	−0.686252	+	0.727364i	$0.740745\pi$
$440$		0			0
$441$		−	22.9059i		−	1.09076i
$442$		0			0
$443$	−16.7437	+	16.7437i	−0.795516	+	0.795516i	−0.982385	−	0.186869i	$-0.940166\pi$
$443$	−16.7437	+	16.7437i	−0.795516	+	0.795516i	0.186869	+	0.982385i	$0.440166\pi$
$444$		0			0
$445$	−2.42443	+	0.638890i	−0.114929	+	0.0302863i
$446$		0			0
$447$			0.882482i			0.0417399i
$448$		0			0
$449$	5.40502			0.255079			0.127539	−	0.991834i	$-0.459292\pi$
$449$	5.40502			0.255079			0.127539	+	0.991834i	$0.459292\pi$
$450$		0			0
$451$	5.35600	−	5.35600i	0.252204	−	0.252204i
$452$		0			0
$453$	−3.30703	+	3.30703i	−0.155378	+	0.155378i
$454$		0			0
$455$	−11.0789	+	19.0073i	−0.519389	+	0.891078i
$456$		0			0
$457$	34.5929			1.61819			0.809095	−	0.587678i	$-0.199958\pi$
$457$	34.5929			1.61819			0.809095	+	0.587678i	$0.199958\pi$
$458$		0			0
$459$	5.38496	+	5.38496i	0.251349	+	0.251349i
$460$		0			0
$461$	−14.3876	+	14.3876i	−0.670099	+	0.670099i	−0.957739	−	0.287640i	$-0.907129\pi$
$461$	−14.3876	+	14.3876i	−0.670099	+	0.670099i	0.287640	+	0.957739i	$0.407129\pi$
$462$		0			0
$463$			20.6591i			0.960108i	0.877239	+	0.480054i	$0.159383\pi$
$463$			20.6591i			0.960108i	−0.877239	+	0.480054i	$0.840617\pi$
$464$		0			0
$465$	−0.662536	+	1.13666i	−0.0307244	+	0.0527116i
$466$		0			0
$467$	−16.3222	−	16.3222i	−0.755300	−	0.755300i	0.220163	−	0.975463i	$-0.429341\pi$
$467$	−16.3222	−	16.3222i	−0.755300	−	0.755300i	−0.975463	+	0.220163i	$0.929341\pi$
$468$		0			0
$469$	7.35371	+	7.35371i	0.339563	+	0.339563i
$470$		0			0
$471$			4.64472i			0.214017i
$472$		0			0
$473$	−8.66973			−0.398635
$474$		0			0
$475$	−9.00192	+	32.5174i	−0.413036	+	1.49200i
$476$		0			0
$477$	−9.97088	−	9.97088i	−0.456535	−	0.456535i
$478$		0			0
$479$	−19.5136			−0.891597			−0.445799	−	0.895133i	$-0.647080\pi$
$479$	−19.5136			−0.891597			−0.445799	+	0.895133i	$0.647080\pi$
$480$		0			0
$481$	−15.7298			−0.717216
$482$		0			0
$483$	0.0951660	+	0.0951660i	0.00433020	+	0.00433020i
$484$		0			0
$485$	13.1997	−	3.47841i	0.599367	−	0.157946i
$486$		0			0
$487$	15.6638			0.709794			0.354897	−	0.934905i	$-0.384516\pi$
$487$	15.6638			0.709794			0.354897	+	0.934905i	$0.384516\pi$
$488$		0			0
$489$		−	5.82505i		−	0.263418i
$490$		0			0
$491$	17.9076	+	17.9076i	0.808157	+	0.808157i	0.984355	−	0.176198i	$-0.0563799\pi$
$491$	17.9076	+	17.9076i	0.808157	+	0.808157i	−0.176198	+	0.984355i	$0.556380\pi$
$492$		0			0
$493$	−10.7244	−	10.7244i	−0.483001	−	0.483001i
$494$		0			0
$495$	−12.8201	−	7.47254i	−0.576221	−	0.335866i
$496$		0			0
$497$		−	35.9029i		−	1.61046i
$498$		0			0
$499$	2.32067	−	2.32067i	0.103887	−	0.103887i	−0.653253	−	0.757140i	$-0.726596\pi$
$499$	2.32067	−	2.32067i	0.103887	−	0.103887i	0.757140	+	0.653253i	$0.226596\pi$
$500$		0			0
$501$	−2.34441	−	2.34441i	−0.104741	−	0.104741i
$502$		0			0
$503$	−6.18913			−0.275960			−0.137980	−	0.990435i	$-0.544061\pi$
$503$	−6.18913			−0.275960			−0.137980	+	0.990435i	$0.544061\pi$
$504$		0			0
$505$	3.45789	−	5.93244i	0.153874	−	0.263990i
$506$		0			0
$507$	1.18804	−	1.18804i	0.0527627	−	0.0527627i
$508$		0			0
$509$	−18.6217	+	18.6217i	−0.825391	+	0.825391i	−0.986875	−	0.161485i	$-0.948372\pi$
$509$	−18.6217	+	18.6217i	−0.825391	+	0.825391i	0.161485	+	0.986875i	$0.448372\pi$
$510$		0			0
$511$	37.8222			1.67315
$512$		0			0
$513$		−	10.4052i		−	0.459403i
$514$		0			0
$515$	−8.76228	−	33.2507i	−0.386112	−	1.46520i
$516$		0			0
$517$	11.2549	−	11.2549i	0.494988	−	0.494988i
$518$		0			0
$519$		−	0.972885i		−	0.0427049i
$520$		0			0
$521$			24.0232i			1.05247i	0.850338	+	0.526237i	$0.176397\pi$
$521$			24.0232i			1.05247i	−0.850338	+	0.526237i	$0.823603\pi$
$522$		0			0
$523$	−16.1791	+	16.1791i	−0.707463	+	0.707463i	−0.966001	−	0.258538i	$-0.916759\pi$
$523$	−16.1791	+	16.1791i	−0.707463	+	0.707463i	0.258538	+	0.966001i	$0.416759\pi$
$524$		0			0
$525$	−4.82023	−	1.33440i	−0.210372	−	0.0582381i
$526$		0			0
$527$			11.1801i			0.487015i
$528$		0			0
$529$	−22.9819			−0.999213
$530$		0			0
$531$	0.314144	−	0.314144i	0.0136327	−	0.0136327i
$532$		0			0
$533$	−6.05069	+	6.05069i	−0.262084	+	0.262084i
$534$		0			0
$535$	−19.0811	−	11.1220i	−0.824950	−	0.480845i
$536$		0			0
$537$	4.28219			0.184790
$538$		0			0
$539$	−12.4994	−	12.4994i	−0.538389	−	0.538389i
$540$		0			0
$541$	−6.76526	+	6.76526i	−0.290861	+	0.290861i	−0.837420	−	0.546559i	$-0.815937\pi$
$541$	−6.76526	+	6.76526i	−0.290861	+	0.290861i	0.546559	+	0.837420i	$0.315937\pi$
$542$		0			0
$543$		−	0.456984i		−	0.0196111i
$544$		0			0
$545$	−23.4873	−	13.6902i	−1.00608	−	0.586423i
$546$		0			0
$547$	−4.38359	−	4.38359i	−0.187429	−	0.187429i	0.607155	−	0.794584i	$-0.292311\pi$
$547$	−4.38359	−	4.38359i	−0.187429	−	0.187429i	−0.794584	+	0.607155i	$0.792311\pi$
$548$		0			0
$549$	−10.1583	−	10.1583i	−0.433545	−	0.433545i
$550$		0			0
$551$			20.7224i			0.882805i
$552$		0			0
$553$	−42.3621			−1.80142
$554$		0			0
$555$	−0.911234	−	3.45791i	−0.0386797	−	0.146780i
$556$		0			0
$557$	3.92396	+	3.92396i	0.166264	+	0.166264i	0.785335	−	0.619071i	$-0.212491\pi$
$557$	3.92396	+	3.92396i	0.166264	+	0.166264i	−0.619071	+	0.785335i	$0.712491\pi$
$558$		0			0
$559$	9.79422			0.414252
$560$		0			0
$561$	2.90504			0.122651
$562$		0			0
$563$	6.61660	+	6.61660i	0.278857	+	0.278857i	0.832652	−	0.553796i	$-0.186821\pi$
$563$	6.61660	+	6.61660i	0.278857	+	0.278857i	−0.553796	+	0.832652i	$0.686821\pi$
$564$		0			0
$565$	31.4239	−	8.28087i	1.32201	−	0.348379i
$566$		0			0
$567$	−32.3144			−1.35708
$568$		0			0
$569$		−	40.2900i		−	1.68904i	−0.535521	−	0.844522i	$-0.679885\pi$
$569$		−	40.2900i		−	1.68904i	0.535521	−	0.844522i	$-0.320115\pi$
$570$		0			0
$571$	−22.6010	−	22.6010i	−0.945823	−	0.945823i	0.0527829	−	0.998606i	$-0.483191\pi$
$571$	−22.6010	−	22.6010i	−0.945823	−	0.945823i	−0.998606	+	0.0527829i	$0.983191\pi$
$572$		0			0
$573$	0.932147	+	0.932147i	0.0389410	+	0.0389410i
$574$		0			0
$575$	−0.585354	+	0.331530i	−0.0244110	+	0.0138257i
$576$		0			0
$577$			18.8020i			0.782737i	0.920234	+	0.391368i	$0.127998\pi$
$577$			18.8020i			0.782737i	−0.920234	+	0.391368i	$0.872002\pi$
$578$		0			0
$579$	0.423229	−	0.423229i	0.0175888	−	0.0175888i
$580$		0			0
$581$	−33.9043	−	33.9043i	−1.40659	−	1.40659i
$582$		0			0
$583$	−10.8820			−0.450685
$584$		0			0
$585$	14.4829	+	8.44176i	0.598795	+	0.349024i
$586$		0			0
$587$	−2.71961	+	2.71961i	−0.112250	+	0.112250i	−0.761001	−	0.648751i	$-0.775292\pi$
$587$	−2.71961	+	2.71961i	−0.112250	+	0.112250i	0.648751	+	0.761001i	$0.275292\pi$
$588$		0			0
$589$	10.8016	−	10.8016i	0.445071	−	0.445071i
$590$		0			0
$591$	−2.96636			−0.122020
$592$		0			0
$593$			4.04894i			0.166270i	0.996538	+	0.0831350i	$0.0264933\pi$
$593$			4.04894i			0.166270i	−0.996538	+	0.0831350i	$0.973507\pi$
$594$		0			0
$595$	−41.0986	+	10.8304i	−1.68488	+	0.444003i
$596$		0			0
$597$	4.01700	−	4.01700i	0.164405	−	0.164405i
$598$		0			0
$599$			19.0455i			0.778178i	0.921200	+	0.389089i	$0.127210\pi$
$599$			19.0455i			0.778178i	−0.921200	+	0.389089i	$0.872790\pi$
$600$		0			0
$601$			14.4406i			0.589045i	0.955645	+	0.294522i	$0.0951606\pi$
$601$			14.4406i			0.589045i	−0.955645	+	0.294522i	$0.904839\pi$
$602$		0			0
$603$	5.60327	−	5.60327i	0.228183	−	0.228183i
$604$		0			0
$605$	12.7113	−	3.34971i	0.516789	−	0.136185i
$606$		0			0
$607$		−	46.3473i		−	1.88118i	−0.339546	−	0.940589i	$-0.610273\pi$
$607$		−	46.3473i		−	1.88118i	0.339546	−	0.940589i	$-0.389727\pi$
$608$		0			0
$609$	−3.07180			−0.124475
$610$		0			0
$611$	−12.7147	+	12.7147i	−0.514380	+	0.514380i
$612$		0			0
$613$	−0.961106	+	0.961106i	−0.0388187	+	0.0388187i	−0.726250	−	0.687431i	$-0.758738\pi$
$613$	−0.961106	+	0.961106i	−0.0388187	+	0.0388187i	0.687431	+	0.726250i	$0.258738\pi$
$614$		0			0
$615$	−1.68066	−	0.979616i	−0.0677706	−	0.0395019i
$616$		0			0
$617$	3.44724			0.138781			0.0693903	−	0.997590i	$-0.477895\pi$
$617$	3.44724			0.138781			0.0693903	+	0.997590i	$0.477895\pi$
$618$		0			0
$619$	24.5574	+	24.5574i	0.987044	+	0.987044i	0.999917	−	0.0128733i	$-0.00409780\pi$
$619$	24.5574	+	24.5574i	0.987044	+	0.987044i	−0.0128733	+	0.999917i	$0.504098\pi$
$620$		0			0
$621$	0.146697	−	0.146697i	0.00588673	−	0.00588673i
$622$		0			0
$623$			4.31517i			0.172884i
$624$		0			0
$625$	12.8564	−	21.4409i	0.514256	−	0.857637i
$626$		0			0
$627$	−2.80667	−	2.80667i	−0.112088	−	0.112088i
$628$		0			0
$629$	−21.4873	−	21.4873i	−0.856753	−	0.856753i
$630$		0			0
$631$		−	22.7950i		−	0.907456i	−0.891140	−	0.453728i	$-0.850094\pi$
$631$		−	22.7950i		−	0.907456i	0.891140	−	0.453728i	$-0.149906\pi$
$632$		0			0
$633$	−0.175787			−0.00698691
$634$		0			0
$635$	12.9004	−	3.39952i	0.511935	−	0.134906i
$636$		0			0
$637$	14.1207	+	14.1207i	0.559481	+	0.559481i
$638$		0			0
$639$	−27.3567			−1.08221
$640$		0			0
$641$	30.4468			1.20258			0.601289	−	0.799032i	$-0.294654\pi$
$641$	30.4468			1.20258			0.601289	+	0.799032i	$0.294654\pi$
$642$		0			0
$643$	20.4452	+	20.4452i	0.806282	+	0.806282i	0.984069	−	0.177787i	$-0.0568939\pi$
$643$	20.4452	+	20.4452i	0.806282	+	0.806282i	−0.177787	+	0.984069i	$0.556894\pi$
$644$		0			0
$645$	0.567385	+	2.15308i	0.0223408	+	0.0847776i
$646$		0			0
$647$	−29.5876			−1.16321			−0.581604	−	0.813472i	$-0.697575\pi$
$647$	−29.5876			−1.16321			−0.581604	+	0.813472i	$0.697575\pi$
$648$		0			0
$649$		−	0.342849i		−	0.0134580i
$650$		0			0
$651$	1.60117	+	1.60117i	0.0627550	+	0.0627550i
$652$		0			0
$653$	−21.2334	−	21.2334i	−0.830928	−	0.830928i	0.156716	−	0.987644i	$-0.449909\pi$
$653$	−21.2334	−	21.2334i	−0.830928	−	0.830928i	−0.987644	+	0.156716i	$0.949909\pi$
$654$		0			0
$655$	−6.47725	−	3.77544i	−0.253087	−	0.147519i
$656$		0			0
$657$		−	28.8191i		−	1.12434i
$658$		0			0
$659$	20.0222	−	20.0222i	0.779954	−	0.779954i	−0.199869	−	0.979823i	$-0.564052\pi$
$659$	20.0222	−	20.0222i	0.779954	−	0.779954i	0.979823	+	0.199869i	$0.0640517\pi$
$660$		0			0
$661$	19.9536	+	19.9536i	0.776107	+	0.776107i	0.979166	−	0.203059i	$-0.0650885\pi$
$661$	19.9536	+	19.9536i	0.776107	+	0.776107i	−0.203059	+	0.979166i	$0.565088\pi$
$662$		0			0
$663$	−3.28184			−0.127456
$664$		0			0
$665$	50.1706	+	29.2433i	1.94553	+	1.13401i
$666$		0			0
$667$	−0.292152	+	0.292152i	−0.0113122	+	0.0113122i
$668$		0			0
$669$	1.38001	−	1.38001i	0.0533542	−	0.0533542i
$670$		0			0
$671$	−11.0865			−0.427989
$672$		0			0
$673$			2.91192i			0.112246i	0.998424	+	0.0561231i	$0.0178739\pi$
$673$			2.91192i			0.112246i	−0.998424	+	0.0561231i	$0.982126\pi$
$674$		0			0
$675$	−2.05696	+	7.43031i	−0.0791724	+	0.285993i
$676$		0			0
$677$	34.6045	−	34.6045i	1.32996	−	1.32996i	0.424558	−	0.905401i	$-0.360430\pi$
$677$	34.6045	−	34.6045i	1.32996	−	1.32996i	0.905401	−	0.424558i	$-0.139570\pi$
$678$		0			0
$679$		−	23.4938i		−	0.901609i
$680$		0			0
$681$			4.73401i			0.181408i
$682$		0			0
$683$	24.7435	−	24.7435i	0.946785	−	0.946785i	−0.0518690	−	0.998654i	$-0.516518\pi$
$683$	24.7435	−	24.7435i	0.946785	−	0.946785i	0.998654	+	0.0518690i	$0.0165178\pi$
$684$		0			0
$685$	−10.4128	−	39.5140i	−0.397852	−	1.50975i
$686$		0			0
$687$		−	3.16916i		−	0.120911i
$688$		0			0
$689$	12.2934			0.468341
$690$		0			0
$691$	−25.3782	+	25.3782i	−0.965431	+	0.965431i	−0.999422	−	0.0339907i	$-0.989178\pi$
$691$	−25.3782	+	25.3782i	−0.965431	+	0.965431i	0.0339907	+	0.999422i	$0.489178\pi$
$692$		0			0
$693$	−18.0592	+	18.0592i	−0.686011	+	0.686011i
$694$		0			0
$695$	−0.216723	+	0.371816i	−0.00822077	+	0.0141038i
$696$		0			0
$697$	−16.5308			−0.626148
$698$		0			0
$699$	0.851738	+	0.851738i	0.0322157	+	0.0322157i
$700$		0			0
$701$	32.3544	−	32.3544i	1.22201	−	1.22201i	0.255094	−	0.966916i	$-0.417894\pi$
$701$	32.3544	−	32.3544i	1.22201	−	1.22201i	0.966916	−	0.255094i	$-0.0821063\pi$
$702$		0			0
$703$			41.5194i			1.56593i
$704$		0			0
$705$	−3.53166	−	2.05852i	−0.133010	−	0.0775285i
$706$		0			0
$707$	−8.35679	−	8.35679i	−0.314290	−	0.314290i
$708$		0			0
$709$	−6.64939	−	6.64939i	−0.249723	−	0.249723i	0.571134	−	0.820857i	$-0.306504\pi$
$709$	−6.64939	−	6.64939i	−0.249723	−	0.249723i	−0.820857	+	0.571134i	$0.806504\pi$
$710$		0			0
$711$			32.2784i			1.21053i
$712$		0			0
$713$	0.304568			0.0114062
$714$		0			0
$715$	12.5097	−	3.29658i	0.467836	−	0.123285i
$716$		0			0
$717$	3.38578	+	3.38578i	0.126444	+	0.126444i
$718$		0			0
$719$	45.0785			1.68115			0.840573	−	0.541699i	$-0.182219\pi$
$719$	45.0785			1.68115			0.840573	+	0.541699i	$0.182219\pi$
$720$		0			0
$721$	−59.1820			−2.20405
$722$		0			0
$723$	3.36791	+	3.36791i	0.125254	+	0.125254i
$724$		0			0
$725$	4.09651	−	14.7977i	0.152141	−	0.549574i
$726$		0			0
$727$	−18.6075			−0.690116			−0.345058	−	0.938581i	$-0.612141\pi$
$727$	−18.6075			−0.690116			−0.345058	+	0.938581i	$0.612141\pi$
$728$		0			0
$729$			23.4200i			0.867409i
$730$		0			0
$731$	13.3792	+	13.3792i	0.494846	+	0.494846i
$732$		0			0
$733$	−7.95550	−	7.95550i	−0.293843	−	0.293843i	0.544753	−	0.838596i	$-0.316623\pi$
$733$	−7.95550	−	7.95550i	−0.293843	−	0.293843i	−0.838596	+	0.544753i	$0.816623\pi$
$734$		0			0
$735$	−2.28616	+	3.92219i	−0.0843261	+	0.144672i
$736$		0			0
$737$		−	6.11526i		−	0.225258i
$738$		0			0
$739$	15.2636	−	15.2636i	0.561479	−	0.561479i	−0.368249	−	0.929727i	$-0.620042\pi$
$739$	15.2636	−	15.2636i	0.561479	−	0.561479i	0.929727	+	0.368249i	$0.120042\pi$
$740$		0			0
$741$	3.17071	+	3.17071i	0.116479	+	0.116479i
$742$		0			0
$743$	33.3017			1.22172			0.610861	−	0.791738i	$-0.290823\pi$
$743$	33.3017			1.22172			0.610861	+	0.791738i	$0.290823\pi$
$744$		0			0
$745$	−3.82313	+	6.55906i	−0.140069	+	0.240305i
$746$		0			0
$747$	−25.8339	+	25.8339i	−0.945211	+	0.945211i
$748$		0			0
$749$	−26.8789	+	26.8789i	−0.982132	+	0.982132i
$750$		0			0
$751$	1.17214			0.0427720			0.0213860	−	0.999771i	$-0.493192\pi$
$751$	1.17214			0.0427720			0.0213860	+	0.999771i	$0.493192\pi$
$752$		0			0
$753$			5.88945i			0.214623i
$754$		0			0
$755$	−38.9064	+	10.2527i	−1.41595	+	0.373134i
$756$		0			0
$757$	−17.9408	+	17.9408i	−0.652069	+	0.652069i	−0.953491	−	0.301422i	$-0.902539\pi$
$757$	−17.9408	+	17.9408i	−0.652069	+	0.652069i	0.301422	+	0.953491i	$0.402539\pi$
$758$		0			0
$759$		−	0.0791389i		−	0.00287256i
$760$		0			0
$761$		−	15.4641i		−	0.560573i	−0.959916	−	0.280287i	$-0.909570\pi$
$761$		−	15.4641i		−	0.560573i	0.959916	−	0.280287i	$-0.0904295\pi$
$762$		0			0
$763$	−33.0856	+	33.0856i	−1.19778	+	1.19778i
$764$		0			0
$765$	8.25237	+	31.3157i	0.298365	+	1.13222i
$766$		0			0
$767$			0.387318i			0.0139852i
$768$		0			0
$769$	14.9777			0.540108			0.270054	−	0.962845i	$-0.412958\pi$
$769$	14.9777			0.540108			0.270054	+	0.962845i	$0.412958\pi$
$770$		0			0
$771$	1.06984	−	1.06984i	0.0385293	−	0.0385293i
$772$		0			0
$773$	−33.0120	+	33.0120i	−1.18736	+	1.18736i	−0.209566	+	0.977794i	$0.567205\pi$
$773$	−33.0120	+	33.0120i	−1.18736	+	1.18736i	−0.977794	+	0.209566i	$0.932795\pi$
$774$		0			0
$775$	−9.84862	+	5.57801i	−0.353773	+	0.200368i
$776$		0			0
$777$	−6.15464			−0.220796
$778$		0			0
$779$	15.9710	+	15.9710i	0.572222	+	0.572222i
$780$		0			0
$781$	−14.9282	+	14.9282i	−0.534173	+	0.534173i
$782$		0			0
$783$			4.73512i			0.169219i
$784$		0			0
$785$	−20.1221	+	34.5220i	−0.718188	+	1.23214i
$786$		0			0
$787$	28.8326	+	28.8326i	1.02777	+	1.02777i	0.999603	+	0.0281690i	$0.00896767\pi$
$787$	28.8326	+	28.8326i	1.02777	+	1.02777i	0.0281690	+	0.999603i	$0.491032\pi$
$788$		0			0
$789$	−0.148262	−	0.148262i	−0.00527828	−	0.00527828i
$790$		0			0
$791$		−	55.9305i		−	1.98866i
$792$		0			0
$793$	12.5244			0.444756
$794$		0			0
$795$	0.712163	+	2.70248i	0.0252578	+	0.0958472i
$796$		0			0
$797$	−23.1556	−	23.1556i	−0.820214	−	0.820214i	0.165924	−	0.986139i	$-0.446939\pi$
$797$	−23.1556	−	23.1556i	−0.820214	−	0.820214i	−0.986139	+	0.165924i	$0.946939\pi$
$798$		0			0
$799$	−34.7371			−1.22891
$800$		0			0
$801$	3.28801			0.116176
$802$		0			0
$803$	−15.7262	−	15.7262i	−0.554966	−	0.554966i
$804$		0			0
$805$	0.295040	+	1.11961i	0.0103988	+	0.0394609i
$806$		0			0
$807$	5.58497			0.196600
$808$		0			0
$809$		−	36.2210i		−	1.27346i	−0.771086	−	0.636731i	$-0.780286\pi$
$809$		−	36.2210i		−	1.27346i	0.771086	−	0.636731i	$-0.219714\pi$
$810$		0			0
$811$	−9.17312	−	9.17312i	−0.322112	−	0.322112i	0.527465	−	0.849577i	$-0.323143\pi$
$811$	−9.17312	−	9.17312i	−0.322112	−	0.322112i	−0.849577	+	0.527465i	$0.823143\pi$
$812$		0			0
$813$	−1.99395	−	1.99395i	−0.0699310	−	0.0699310i
$814$		0			0
$815$	25.2356	−	43.2948i	0.883963	−	1.51655i
$816$		0			0
$817$		−	25.8522i		−	0.904456i
$818$		0			0
$819$	20.4015	−	20.4015i	0.712886	−	0.712886i
$820$		0			0
$821$	−7.26795	−	7.26795i	−0.253653	−	0.253653i	0.568813	−	0.822467i	$-0.307403\pi$
$821$	−7.26795	−	7.26795i	−0.253653	−	0.253653i	−0.822467	+	0.568813i	$0.807403\pi$
$822$		0			0
$823$	28.2974			0.986384			0.493192	−	0.869920i	$-0.335830\pi$
$823$	28.2974			0.986384			0.493192	+	0.869920i	$0.335830\pi$
$824$		0			0
$825$	1.44939	+	2.55906i	0.0504612	+	0.0890951i
$826$		0			0
$827$	18.1661	−	18.1661i	0.631697	−	0.631697i	−0.316797	−	0.948494i	$-0.602607\pi$
$827$	18.1661	−	18.1661i	0.631697	−	0.631697i	0.948494	+	0.316797i	$0.102607\pi$
$828$		0			0
$829$	−11.0865	+	11.0865i	−0.385049	+	0.385049i	−0.872917	−	0.487868i	$-0.837775\pi$
$829$	−11.0865	+	11.0865i	−0.385049	+	0.385049i	0.487868	+	0.872917i	$0.337775\pi$
$830$		0			0
$831$	−0.468054			−0.0162366
$832$		0			0
$833$			38.5783i			1.33666i
$834$		0			0
$835$	−7.26832	−	27.5815i	−0.251531	−	0.954497i
$836$		0			0
$837$	2.46818	−	2.46818i	0.0853128	−	0.0853128i
$838$		0			0
$839$			11.9093i			0.411153i	0.978641	+	0.205577i	$0.0659069\pi$
$839$			11.9093i			0.411153i	−0.978641	+	0.205577i	$0.934093\pi$
$840$		0			0
$841$			19.5698i			0.674822i
$842$		0			0
$843$	−3.71576	+	3.71576i	−0.127977	+	0.127977i
$844$		0			0
$845$	13.9770	−	3.68325i	0.480824	−	0.126708i
$846$		0			0
$847$		−	22.6245i		−	0.777388i
$848$		0			0
$849$	7.85669			0.269641
$850$		0			0
$851$	−0.585354	+	0.585354i	−0.0200657	+	0.0200657i
$852$		0			0
$853$	−2.44597	+	2.44597i	−0.0837485	+	0.0837485i	−0.747740	−	0.663992i	$-0.768861\pi$
$853$	−2.44597	+	2.44597i	−0.0837485	+	0.0837485i	0.663992	+	0.747740i	$0.268861\pi$
$854$		0			0
$855$	22.2824	−	38.2282i	0.762041	−	1.30738i
$856$		0			0
$857$	2.57862			0.0880839			0.0440419	−	0.999030i	$-0.485976\pi$
$857$	2.57862			0.0880839			0.0440419	+	0.999030i	$0.485976\pi$
$858$		0			0
$859$	−33.0076	−	33.0076i	−1.12620	−	1.12620i	−0.990789	−	0.135416i	$-0.956763\pi$
$859$	−33.0076	−	33.0076i	−1.12620	−	1.12620i	−0.135416	−	0.990789i	$-0.543237\pi$
$860$		0			0
$861$	−2.36747	+	2.36747i	−0.0806832	+	0.0806832i
$862$		0			0
$863$			23.5500i			0.801652i	0.916154	+	0.400826i	$0.131277\pi$
$863$			23.5500i			0.801652i	−0.916154	+	0.400826i	$0.868723\pi$
$864$		0			0
$865$	4.21478	−	7.23099i	0.143307	−	0.245861i
$866$		0			0
$867$	−1.35863	−	1.35863i	−0.0461416	−	0.0461416i
$868$		0			0
$869$	17.6139	+	17.6139i	0.597511	+	0.597511i
$870$		0			0
$871$			6.90843i			0.234083i
$872$		0			0
$873$	−17.9014			−0.605871
$874$		0			0
$875$	−30.0455	−	30.8004i	−1.01572	−	1.04124i
$876$		0			0
$877$	34.2135	+	34.2135i	1.15531	+	1.15531i	0.985472	+	0.169836i	$0.0543237\pi$
$877$	34.2135	+	34.2135i	1.15531	+	1.15531i	0.169836	+	0.985472i	$0.445676\pi$
$878$		0			0
$879$	−4.10426			−0.138433
$880$		0			0
$881$	40.6823			1.37062			0.685310	−	0.728251i	$-0.259667\pi$
$881$	40.6823			1.37062			0.685310	+	0.728251i	$0.259667\pi$
$882$		0			0
$883$	35.8531	+	35.8531i	1.20655	+	1.20655i	0.972137	+	0.234415i	$0.0753176\pi$
$883$	35.8531	+	35.8531i	1.20655	+	1.20655i	0.234415	+	0.972137i	$0.424682\pi$
$884$		0			0
$885$	−0.0851449	+	0.0224375i	−0.00286211	+	0.000754230i
$886$		0			0
$887$	−9.33231			−0.313348			−0.156674	−	0.987650i	$-0.550077\pi$
$887$	−9.33231			−0.313348			−0.156674	+	0.987650i	$0.550077\pi$
$888$		0			0
$889$		−	22.9610i		−	0.770087i
$890$		0			0
$891$	13.4361	+	13.4361i	0.450127	+	0.450127i
$892$		0			0
$893$	33.5609	+	33.5609i	1.12307	+	1.12307i
$894$		0			0
$895$	31.8274	+	18.5515i	1.06387	+	0.620108i
$896$		0			0
$897$			0.0894035i			0.00298510i
$898$		0			0
$899$	−4.91548	+	4.91548i	−0.163940	+	0.163940i
$900$		0			0
$901$	16.7931	+	16.7931i	0.559459	+	0.559459i
$902$		0			0
$903$	3.83222			0.127528
$904$		0			0
$905$	1.97977	−	3.39654i	0.0658097	−	0.112905i
$906$		0			0
$907$	33.2170	−	33.2170i	1.10295	−	1.10295i	0.108899	−	0.994053i	$-0.465267\pi$
$907$	33.2170	−	33.2170i	1.10295	−	1.10295i	0.994053	−	0.108899i	$-0.0347327\pi$
$908$		0			0
$909$	−6.36758	+	6.36758i	−0.211199	+	0.211199i
$910$		0			0
$911$	5.77870			0.191457			0.0957284	−	0.995407i	$-0.469482\pi$
$911$	5.77870			0.191457			0.0957284	+	0.995407i	$0.469482\pi$
$912$		0			0
$913$			28.1944i			0.933098i
$914$		0			0
$915$	0.725548	+	2.75327i	0.0239859	+	0.0910204i
$916$		0			0
$917$	−9.12424	+	9.12424i	−0.301309	+	0.301309i
$918$		0			0
$919$			50.8572i			1.67763i	0.544420	+	0.838813i	$0.316750\pi$
$919$			50.8572i			1.67763i	−0.544420	+	0.838813i	$0.683250\pi$
$920$		0			0
$921$		−	0.801852i		−	0.0264219i
$922$		0			0
$923$	16.8644	−	16.8644i	0.555100	−	0.555100i
$924$		0			0
$925$	8.20775	−	29.6487i	0.269869	−	0.974842i
$926$		0			0
$927$			45.0945i			1.48110i
$928$		0			0
$929$	21.6815			0.711346			0.355673	−	0.934611i	$-0.384252\pi$
$929$	21.6815			0.711346			0.355673	+	0.934611i	$0.384252\pi$
$930$		0			0
$931$	37.2720	−	37.2720i	1.22154	−	1.22154i
$932$		0			0
$933$	2.12309	−	2.12309i	0.0695070	−	0.0695070i
$934$		0			0
$935$	21.5918	+	12.5854i	0.706126	+	0.411585i
$936$		0			0
$937$	19.7948			0.646668			0.323334	−	0.946285i	$-0.395196\pi$
$937$	19.7948			0.646668			0.323334	+	0.946285i	$0.395196\pi$
$938$		0			0
$939$	−1.91630	−	1.91630i	−0.0625360	−	0.0625360i
$940$		0			0
$941$	29.4510	−	29.4510i	0.960074	−	0.960074i	−0.0391593	−	0.999233i	$-0.512468\pi$
$941$	29.4510	−	29.4510i	0.960074	−	0.960074i	0.999233	+	0.0391593i	$0.0124680\pi$
$942$		0			0
$943$			0.450330i			0.0146648i
$944$		0			0
$945$	11.4641	+	6.68216i	0.372927	+	0.217371i
$946$		0			0
$947$	4.11783	+	4.11783i	0.133811	+	0.133811i	0.770840	−	0.637029i	$-0.219837\pi$
$947$	4.11783	+	4.11783i	0.133811	+	0.133811i	−0.637029	+	0.770840i	$0.719837\pi$
$948$		0			0
$949$	17.7660	+	17.7660i	0.576708	+	0.576708i
$950$		0			0
$951$		−	3.70465i		−	0.120131i
$952$		0			0
$953$	−40.3245			−1.30624			−0.653119	−	0.757255i	$-0.726540\pi$
$953$	−40.3245			−1.30624			−0.653119	+	0.757255i	$0.726540\pi$
$954$		0			0
$955$	2.88991	+	10.9665i	0.0935153	+	0.354867i
$956$		0			0
$957$	1.27723	+	1.27723i	0.0412871	+	0.0412871i
$958$		0			0
$959$	−70.3298			−2.27107
$960$		0			0
$961$	−25.8756			−0.834697
$962$		0			0
$963$	20.4807	+	20.4807i	0.659982	+	0.659982i
$964$		0			0
$965$	4.97919	−	1.31212i	0.160286	−	0.0422388i
$966$		0			0
$967$	58.1740			1.87075			0.935375	−	0.353656i	$-0.115062\pi$
$967$	58.1740			1.87075			0.935375	+	0.353656i	$0.115062\pi$
$968$		0			0
$969$			8.66254i			0.278281i
$970$		0			0
$971$	1.70830	+	1.70830i	0.0548220	+	0.0548220i	0.733986	−	0.679164i	$-0.237658\pi$
$971$	1.70830	+	1.70830i	0.0548220	+	0.0548220i	−0.679164	+	0.733986i	$0.737658\pi$
$972$		0			0
$973$	0.523762	+	0.523762i	0.0167910	+	0.0167910i
$974$		0			0
$975$	−1.63738	−	2.89098i	−0.0524381	−	0.0925855i
$976$		0			0
$977$			35.1811i			1.12554i	0.826612	+	0.562772i	$0.190265\pi$
$977$			35.1811i			1.12554i	−0.826612	+	0.562772i	$0.809735\pi$
$978$		0			0
$979$	1.79422	−	1.79422i	0.0573436	−	0.0573436i
$980$		0			0
$981$	25.2100	+	25.2100i	0.804894	+	0.804894i
$982$		0			0
$983$	27.7257			0.884312			0.442156	−	0.896938i	$-0.354214\pi$
$983$	27.7257			0.884312			0.442156	+	0.896938i	$0.354214\pi$
$984$		0			0
$985$	−22.0476	−	12.8510i	−0.702494	−	0.409468i
$986$		0			0
$987$	−4.97491	+	4.97491i	−0.158353	+	0.158353i
$988$		0			0
$989$	0.364474	−	0.364474i	0.0115896	−	0.0115896i
$990$		0			0
$991$	−7.02711			−0.223224			−0.111612	−	0.993752i	$-0.535601\pi$
$991$	−7.02711			−0.223224			−0.111612	+	0.993752i	$0.535601\pi$
$992$		0			0
$993$		−	3.22428i		−	0.102319i
$994$		0			0
$995$	47.2590	−	12.4538i	1.49821	−	0.394812i
$996$		0			0
$997$	−14.2467	+	14.2467i	−0.451197	+	0.451197i	−0.895752	−	0.444555i	$-0.853362\pi$
$997$	−14.2467	+	14.2467i	−0.451197	+	0.451197i	0.444555	+	0.895752i	$0.353362\pi$
$998$		0			0
$999$			9.48726i			0.300164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.q.e.609.5		16
4.3	odd	2		640.2.q.f.609.4		16
5.4	even	2	inner	640.2.q.e.609.4		16
8.3	odd	2		320.2.q.c.49.5		16
8.5	even	2		80.2.q.c.69.1	yes	16
16.3	odd	4		640.2.q.f.289.5		16
16.5	even	4		80.2.q.c.29.8	yes	16
16.11	odd	4		320.2.q.c.209.4		16
16.13	even	4	inner	640.2.q.e.289.4		16
20.19	odd	2		640.2.q.f.609.5		16
24.5	odd	2		720.2.bm.f.469.8		16
40.3	even	4		1600.2.l.h.1201.4		16
40.13	odd	4		400.2.l.i.101.4		16
40.19	odd	2		320.2.q.c.49.4		16
40.27	even	4		1600.2.l.h.1201.5		16
40.29	even	2		80.2.q.c.69.8	yes	16
40.37	odd	4		400.2.l.i.101.5		16
48.5	odd	4		720.2.bm.f.109.1		16
80.19	odd	4		640.2.q.f.289.4		16
80.27	even	4		1600.2.l.h.401.5		16
80.29	even	4	inner	640.2.q.e.289.5		16
80.37	odd	4		400.2.l.i.301.5		16
80.43	even	4		1600.2.l.h.401.4		16
80.53	odd	4		400.2.l.i.301.4		16
80.59	odd	4		320.2.q.c.209.5		16
80.69	even	4		80.2.q.c.29.1	✓	16
120.29	odd	2		720.2.bm.f.469.1		16
240.149	odd	4		720.2.bm.f.109.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.1	✓	16	80.69	even	4
80.2.q.c.29.8	yes	16	16.5	even	4
80.2.q.c.69.1	yes	16	8.5	even	2
80.2.q.c.69.8	yes	16	40.29	even	2
320.2.q.c.49.4		16	40.19	odd	2
320.2.q.c.49.5		16	8.3	odd	2
320.2.q.c.209.4		16	16.11	odd	4
320.2.q.c.209.5		16	80.59	odd	4
400.2.l.i.101.4		16	40.13	odd	4
400.2.l.i.101.5		16	40.37	odd	4
400.2.l.i.301.4		16	80.53	odd	4
400.2.l.i.301.5		16	80.37	odd	4
640.2.q.e.289.4		16	16.13	even	4	inner
640.2.q.e.289.5		16	80.29	even	4	inner
640.2.q.e.609.4		16	5.4	even	2	inner
640.2.q.e.609.5		16	1.1	even	1	trivial
640.2.q.f.289.4		16	80.19	odd	4
640.2.q.f.289.5		16	16.3	odd	4
640.2.q.f.609.4		16	4.3	odd	2
640.2.q.f.609.5		16	20.19	odd	2
720.2.bm.f.109.1		16	48.5	odd	4
720.2.bm.f.109.8		16	240.149	odd	4
720.2.bm.f.469.1		16	120.29	odd	2
720.2.bm.f.469.8		16	24.5	odd	2
1600.2.l.h.401.4		16	80.43	even	4
1600.2.l.h.401.5		16	80.27	even	4
1600.2.l.h.1201.4		16	40.3	even	4
1600.2.l.h.1201.5		16	40.27	even	4

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.183790 + 0.183790i) q^{3} +(0.569800 + 2.16225i) q^{5} +3.84853 q^{7} -2.93244i q^{9} +(-1.60020 - 1.60020i) q^{11} +(1.80775 + 1.80775i) q^{13} +(-0.292677 + 0.502125i) q^{15} +4.93886i q^{17} +(4.77162 - 4.77162i) q^{19} +(0.707323 + 0.707323i) q^{21} +0.134544 q^{23} +(-4.35066 + 2.46410i) q^{25} +(1.09033 - 1.09033i) q^{27} +(-2.17142 + 2.17142i) q^{29} +2.26371 q^{31} -0.588201i q^{33} +(2.19289 + 8.32149i) q^{35} +(-4.35066 + 4.35066i) q^{37} +0.664493i q^{39} +3.34709i q^{41} +(2.70896 - 2.70896i) q^{43} +(6.34067 - 1.67091i) q^{45} +7.03343i q^{47} +7.81119 q^{49} +(-0.907714 + 0.907714i) q^{51} +(3.40020 - 3.40020i) q^{53} +(2.54823 - 4.37182i) q^{55} +1.75396 q^{57} +(0.107127 + 0.107127i) q^{59} +(3.46410 - 3.46410i) q^{61} -11.2856i q^{63} +(-2.87875 + 4.93886i) q^{65} +(1.91078 + 1.91078i) q^{67} +(0.0247279 + 0.0247279i) q^{69} -9.32899i q^{71} +9.82769 q^{73} +(-1.25249 - 0.346730i) q^{75} +(-6.15840 - 6.15840i) q^{77} -11.0073 q^{79} -8.39654 q^{81} +(-8.80967 - 8.80967i) q^{83} +(-10.6790 + 2.81416i) q^{85} -0.798174 q^{87} +1.12125i q^{89} +(6.95717 + 6.95717i) q^{91} +(0.416048 + 0.416048i) q^{93} +(13.0363 + 7.59857i) q^{95} -6.10461i q^{97} +(-4.69248 + 4.69248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 8 q^{11} + 8 q^{19} + 16 q^{21} + 16 q^{29} + 16 q^{31} + 24 q^{35} - 8 q^{45} + 16 q^{49} + 16 q^{51} + 24 q^{59} - 32 q^{69} - 48 q^{75} + 16 q^{79} - 16 q^{81} + 16 q^{91} + 32 q^{95}+ \cdots - 88 q^{99}+O(q^{100}) \) 16 * q + 8 * q^5 - 8 * q^11 + 8 * q^19 + 16 * q^21 + 16 * q^29 + 16 * q^31 + 24 * q^35 - 8 * q^45 + 16 * q^49 + 16 * q^51 + 24 * q^59 - 32 * q^69 - 48 * q^75 + 16 * q^79 - 16 * q^81 + 16 * q^91 + 32 * q^95 - 88 * q^99

Introduction

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