LMFDB - Embedded newform 640.2.q.f.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.f.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.183790 + 0.183790i) q^{3} +(2.16225 + 0.569800i) q^{5} +3.84853 q^{7} -2.93244i q^{9} +(1.60020 + 1.60020i) q^{11} +(-1.80775 - 1.80775i) q^{13} +(0.292677 + 0.502125i) q^{15} -4.93886i q^{17} +(-4.77162 + 4.77162i) q^{19} +(0.707323 + 0.707323i) q^{21} +0.134544 q^{23} +(4.35066 + 2.46410i) q^{25} +(1.09033 - 1.09033i) q^{27} +(-2.17142 + 2.17142i) q^{29} -2.26371 q^{31} +0.588201i q^{33} +(8.32149 + 2.19289i) q^{35} +(4.35066 - 4.35066i) q^{37} -0.664493i q^{39} +3.34709i q^{41} +(2.70896 - 2.70896i) q^{43} +(1.67091 - 6.34067i) q^{45} +7.03343i q^{47} +7.81119 q^{49} +(0.907714 - 0.907714i) q^{51} +(-3.40020 + 3.40020i) q^{53} +(2.54823 + 4.37182i) q^{55} -1.75396 q^{57} +(-0.107127 - 0.107127i) q^{59} +(3.46410 - 3.46410i) q^{61} -11.2856i q^{63} +(-2.87875 - 4.93886i) q^{65} +(1.91078 + 1.91078i) q^{67} +(0.0247279 + 0.0247279i) q^{69} +9.32899i q^{71} -9.82769 q^{73} +(0.346730 + 1.25249i) q^{75} +(6.15840 + 6.15840i) q^{77} +11.0073 q^{79} -8.39654 q^{81} +(-8.80967 - 8.80967i) q^{83} +(2.81416 - 10.6790i) q^{85} -0.798174 q^{87} +1.12125i q^{89} +(-6.95717 - 6.95717i) q^{91} +(-0.416048 - 0.416048i) q^{93} +(-13.0363 + 7.59857i) q^{95} +6.10461i q^{97} +(4.69248 - 4.69248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.16225	+	0.569800i	0.966988	+	0.254822i
$5$	2.16225	+	0.569800i	0.966988	+	0.254822i
$6$		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	0.905922	−	0.423445i	$-0.139179\pi$
$11$	1.60020	+	1.60020i	0.482477	+	0.482477i	−0.423445	+	0.905922i	$0.639179\pi$
$12$		0			0
$13$	−1.80775	−	1.80775i	−0.501379	−	0.501379i	0.410487	−	0.911866i	$-0.365359\pi$
$13$	−1.80775	−	1.80775i	−0.501379	−	0.501379i	−0.911866	+	0.410487i	$0.865359\pi$
$14$		0			0
$15$	0.292677	+	0.502125i	0.0755689	+	0.129648i
$16$		0			0
$17$		−	4.93886i		−	1.19785i	−0.800806	−	0.598924i	$-0.795595\pi$
$17$		−	4.93886i		−	1.19785i	0.800806	−	0.598924i	$-0.204405\pi$
$18$		0			0
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.0996636	+	0.995021i	$0.531777\pi$
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.995021	+	0.0996636i	$0.968223\pi$
$20$		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	$-0.565163\pi$
$31$	−2.26371			−0.406574			−0.203287	+	0.979119i	$0.565163\pi$
$32$		0			0
$33$			0.588201i			0.102393i
$34$		0			0
$35$	8.32149	+	2.19289i	1.40659	+	0.370667i
$36$		0			0
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	−0.252384	−	0.967627i	$-0.581215\pi$
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	0.967627	+	0.252384i	$0.0812146\pi$
$38$		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
$45$	1.67091	−	6.34067i	0.249084	−	0.945212i
$46$		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	−0.900958	−	0.433905i	$-0.857135\pi$
$53$	−3.40020	+	3.40020i	−0.467053	+	0.467053i	0.433905	+	0.900958i	$0.357135\pi$
$54$		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	0.700099	−	0.714046i	$-0.253139\pi$
$59$	−0.107127	−	0.107127i	−0.0139468	−	0.0139468i	−0.714046	+	0.700099i	$0.753139\pi$
$60$		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	$0.186736\pi$
$71$			9.32899i			1.10715i	−0.832800	+	0.553573i	$0.813264\pi$
$72$		0			0
$73$	−9.82769			−1.15024			−0.575122	−	0.818068i	$-0.695045\pi$
$73$	−9.82769			−1.15024			−0.575122	+	0.818068i	$0.695045\pi$
$74$		0			0
$75$	0.346730	+	1.25249i	0.0400370	+	0.144625i
$76$		0			0
$77$	6.15840	+	6.15840i	0.701815	+	0.701815i
$78$		0			0
$79$	11.0073			1.23842			0.619211	−	0.785224i	$-0.287452\pi$
$79$	11.0073			1.23842			0.619211	+	0.785224i	$0.287452\pi$
$80$		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
$85$	2.81416	−	10.6790i	0.305239	−	1.15831i
$86$		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	$0.100300\pi$
$97$			6.10461i			0.619829i	−0.950764	+	0.309915i	$0.899700\pi$
$98$		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	$0.239574\pi$
$113$			14.5329i			1.36714i	−0.729883	+	0.683572i	$0.760426\pi$
$114$		0			0
$115$	0.290918	+	0.0766631i	0.0271282	+	0.00714887i
$116$		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
$125$	8.00316	+	7.80701i	0.715825	+	0.698280i
$126$		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	−0.595910	−	0.803051i	$-0.703209\pi$
$131$	2.37084	−	2.37084i	0.207141	−	0.207141i	0.803051	+	0.595910i	$0.203209\pi$
$132$		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	$-0.214890\pi$
$137$	18.2745			1.56129			0.780646	+	0.624973i	$0.214890\pi$
$138$		0			0
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	0.701312	−	0.712855i	$-0.252598\pi$
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	−0.712855	+	0.701312i	$0.752598\pi$
$140$		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	$-0.738520\pi$
$151$		−	17.9935i		−	1.46429i	0.681150	−	0.732144i	$-0.261480\pi$
$152$		0			0
$153$	−14.4829			−1.17087
$154$		0			0
$155$	−4.89471	−	1.28986i	−0.393152	−	0.103604i
$156$		0			0
$157$	−12.6359	−	12.6359i	−1.00846	−	1.00846i	−0.999964	−	0.00849213i	$-0.997297\pi$
$157$	−12.6359	−	12.6359i	−1.00846	−	1.00846i	−0.00849213	−	0.999964i	$-0.502703\pi$
$158$		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
$165$	−0.335157	+	1.27184i	−0.0260919	+	0.0990125i
$166$		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	0.800525	−	0.599299i	$-0.204554\pi$
$173$	2.64673	+	2.64673i	0.201227	+	0.201227i	−0.599299	+	0.800525i	$0.704554\pi$
$174$		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	−0.992553	−	0.121817i	$-0.961128\pi$
$179$	−11.6497	+	11.6497i	−0.870736	+	0.870736i	0.121817	+	0.992553i	$0.461128\pi$
$180$		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	$-0.558740\pi$
$191$	−5.07180			−0.366982			−0.183491	+	0.983021i	$0.558740\pi$
$192$		0			0
$193$			2.30278i			0.165758i	0.996560	+	0.0828788i	$0.0264114\pi$
$193$			2.30278i			0.165758i	−0.996560	+	0.0828788i	$0.973589\pi$
$194$		0			0
$195$	0.378628	−	1.43680i	0.0271141	−	0.102891i
$196$		0			0
$197$	8.06997	−	8.06997i	0.574961	−	0.574961i	−0.358549	−	0.933511i	$-0.616729\pi$
$197$	8.06997	−	8.06997i	0.574961	−	0.574961i	0.933511	+	0.358549i	$0.116729\pi$
$198$		0			0
$199$			21.8564i			1.54936i	0.632354	+	0.774680i	$0.282089\pi$
$199$			21.8564i			1.54936i	−0.632354	+	0.774680i	$0.717911\pi$
$200$		0			0
$201$			0.702368i			0.0495412i
$202$		0			0
$203$	−8.35679	+	8.35679i	−0.586532	+	0.586532i
$204$		0			0
$205$	−1.90717	+	7.23724i	−0.133203	+	0.505471i
$206$		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	−0.690454	−	0.723376i	$-0.742589\pi$
$211$	0.478227	−	0.478227i	0.0329225	−	0.0329225i	0.723376	+	0.690454i	$0.242589\pi$
$212$		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	$-0.548507\pi$
$233$	−4.63429			−0.303602			−0.151801	+	0.988411i	$0.548507\pi$
$234$		0			0
$235$	−4.00765	+	15.2080i	−0.261430	+	0.992063i
$236$		0			0
$237$	2.02304	+	2.02304i	0.131411	+	0.131411i
$238$		0			0
$239$	−18.4220			−1.19162			−0.595810	−	0.803126i	$-0.703169\pi$
$239$	−18.4220			−1.19162			−0.595810	+	0.803126i	$0.703169\pi$
$240$		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
$245$	16.8897	+	4.45082i	1.07905	+	0.284352i
$246$		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	$-0.996379\pi$
$251$	−16.0222	−	16.0222i	−1.01131	−	1.01131i	−0.0113760	−	0.999935i	$-0.503621\pi$
$252$		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	$0.0581119\pi$
$257$			5.82098i			0.363103i	−0.983381	+	0.181551i	$0.941888\pi$
$258$		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	$-0.393114\pi$
$271$	10.8491			0.659034			0.329517	+	0.944150i	$0.393114\pi$
$272$		0			0
$273$		−	2.55732i		−	0.154776i
$274$		0			0
$275$	3.01886	+	10.9049i	0.182044	+	0.657593i
$276$		0			0
$277$	1.27334	−	1.27334i	0.0765074	−	0.0765074i	−0.667818	−	0.744325i	$-0.732771\pi$
$277$	1.27334	−	1.27334i	0.0765074	−	0.0765074i	0.744325	+	0.667818i	$0.232771\pi$
$278$		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
$285$	−3.79249	−	0.999404i	−0.224648	−	0.0591996i
$286$		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	−0.301246	−	0.953547i	$-0.597402\pi$
$293$	11.1656	−	11.1656i	0.652301	−	0.652301i	0.953547	+	0.301246i	$0.0974024\pi$
$294$		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	$0.106213\pi$
$311$			11.5517i			0.655038i	−0.944845	+	0.327519i	$0.893787\pi$
$312$		0			0
$313$	10.4265			0.589343			0.294671	−	0.955599i	$-0.404790\pi$
$313$	10.4265			0.589343			0.294671	+	0.955599i	$0.404790\pi$
$314$		0			0
$315$	6.43053	−	24.4023i	0.362320	−	1.37491i
$316$		0			0
$317$	10.0785	+	10.0785i	0.566063	+	0.566063i	0.931023	−	0.364960i	$-0.118917\pi$
$317$	10.0785	+	10.0785i	0.566063	+	0.566063i	−0.364960	+	0.931023i	$0.618917\pi$
$318$		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
$325$	−3.41041	−	12.3194i	−0.189176	−	0.683355i
$326$		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	0.905812	−	0.423680i	$-0.139262\pi$
$331$	8.77162	+	8.77162i	0.482132	+	0.482132i	−0.423680	+	0.905812i	$0.639262\pi$
$332$		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	$-0.643984\pi$
$337$		−	33.0226i		−	1.79885i	0.437072	−	0.899427i	$-0.356016\pi$
$338$		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	$-0.902347\pi$
$353$		−	11.3480i		−	0.603995i	0.953309	−	0.301998i	$-0.0976534\pi$
$354$		0			0
$355$	−5.31566	+	20.1716i	−0.282126	+	1.07060i
$356$		0			0
$357$	3.49337	−	3.49337i	0.184889	−	0.184889i
$358$		0			0
$359$			26.5788i			1.40278i	0.712779	+	0.701389i	$0.247436\pi$
$359$			26.5788i			1.40278i	−0.712779	+	0.701389i	$0.752564\pi$
$360$		0			0
$361$		−	26.5367i		−	1.39667i
$362$		0			0
$363$	1.08046	−	1.08046i	0.0567093	−	0.0567093i
$364$		0			0
$365$	−21.2499	−	5.59982i	−1.11227	−	0.293108i
$366$		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	−0.576241	−	0.817280i	$-0.695481\pi$
$373$	4.65522	−	4.65522i	0.241038	−	0.241038i	0.817280	+	0.576241i	$0.195481\pi$
$374$		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	0.908011	−	0.418947i	$-0.137601\pi$
$379$	9.52106	+	9.52106i	0.489064	+	0.489064i	−0.418947	+	0.908011i	$0.637601\pi$
$380$		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
$395$	23.8006	+	6.27199i	1.19754	+	0.315578i
$396$		0			0
$397$	−3.81625	−	3.81625i	−0.191532	−	0.191532i	0.604826	−	0.796358i	$-0.293243\pi$
$397$	−3.81625	−	3.81625i	−0.191532	−	0.191532i	−0.796358	+	0.604826i	$0.793243\pi$
$398$		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
$405$	−18.1554	−	4.78435i	−0.902151	−	0.237736i
$406$		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	$-0.463856\pi$
$419$	22.6570	−	22.6570i	1.10687	−	1.10687i	0.993560	−	0.113306i	$-0.0361442\pi$
$420$		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	$-0.283119\pi$
$431$	26.1518			1.25969			0.629843	+	0.776723i	$0.283119\pi$
$432$		0			0
$433$		−	9.30795i		−	0.447312i	−0.974668	−	0.223656i	$-0.928201\pi$
$433$		−	9.30795i		−	0.447312i	0.974668	−	0.223656i	$-0.0717992\pi$
$434$		0			0
$435$	−1.72585	−	0.454800i	−0.0827483	−	0.0218060i
$436$		0			0
$437$	−0.641992	+	0.641992i	−0.0307107	+	0.0307107i
$438$		0			0
$439$		−	30.4799i		−	1.45473i	−0.686252	−	0.727364i	$-0.740745\pi$
$439$		−	30.4799i		−	1.45473i	0.686252	−	0.727364i	$-0.259255\pi$
$440$		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
$445$	−0.638890	+	2.42443i	−0.0302863	+	0.114929i
$446$		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	$-0.800042\pi$
$457$	−34.5929			−1.61819			−0.809095	+	0.587678i	$0.800042\pi$
$458$		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
$475$	−32.5174	+	9.00192i	−1.49200	+	0.413036i
$476$		0			0
$477$	9.97088	+	9.97088i	0.456535	+	0.456535i
$478$		0			0
$479$	19.5136			0.891597			0.445799	−	0.895133i	$-0.352920\pi$
$479$	19.5136			0.891597			0.445799	+	0.895133i	$0.352920\pi$
$480$		0			0
$481$	−15.7298			−0.717216
$482$		0			0
$483$	0.0951660	+	0.0951660i	0.00433020	+	0.00433020i
$484$		0			0
$485$	−3.47841	+	13.1997i	−0.157946	+	0.599367i
$486$		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	0.176198	−	0.984355i	$-0.443620\pi$
$491$	−17.9076	−	17.9076i	−0.808157	−	0.808157i	−0.984355	+	0.176198i	$0.943620\pi$
$492$		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	−0.757140	−	0.653253i	$-0.773404\pi$
$499$	−2.32067	+	2.32067i	−0.103887	+	0.103887i	0.653253	+	0.757140i	$0.273404\pi$
$500$		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
$515$	−33.2507	−	8.76228i	−1.46520	−	0.386112i
$516$		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
$525$	1.33440	+	4.82023i	0.0582381	+	0.210372i
$526$		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
$555$	3.45791	+	0.911234i	0.146780	+	0.0386797i
$556$		0			0
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	0.619071	−	0.785335i	$-0.287509\pi$
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	−0.785335	+	0.619071i	$0.787509\pi$
$558$		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
$565$	−8.28087	+	31.4239i	−0.348379	+	1.32201i
$566$		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	0.998606	−	0.0527829i	$-0.0168091\pi$
$571$	22.6010	+	22.6010i	0.945823	+	0.945823i	−0.0527829	+	0.998606i	$0.516809\pi$
$572$		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	$-0.872002\pi$
$577$		−	18.8020i		−	0.782737i	0.920234	−	0.391368i	$-0.127998\pi$
$578$		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	$-0.973507\pi$
$593$		−	4.04894i		−	0.166270i	0.996538	−	0.0831350i	$-0.0264933\pi$
$594$		0			0
$595$	10.8304	−	41.0986i	0.444003	−	1.68488i
$596$		0			0
$597$	−4.01700	+	4.01700i	−0.164405	+	0.164405i
$598$		0			0
$599$		−	19.0455i		−	0.778178i	−0.921200	−	0.389089i	$-0.872790\pi$
$599$		−	19.0455i		−	0.778178i	0.921200	−	0.389089i	$-0.127210\pi$
$600$		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
$605$	3.34971	−	12.7113i	0.136185	−	0.516789i
$606$		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	−0.687431	−	0.726250i	$-0.741262\pi$
$613$	0.961106	−	0.961106i	0.0388187	−	0.0388187i	0.726250	+	0.687431i	$0.241262\pi$
$614$		0			0
$615$	−1.68066	+	0.979616i	−0.0677706	+	0.0395019i
$616$		0			0
$617$	−3.44724			−0.138781			−0.0693903	−	0.997590i	$-0.522105\pi$
$617$	−3.44724			−0.138781			−0.0693903	+	0.997590i	$0.522105\pi$
$618$		0			0
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	0.0128733	−	0.999917i	$-0.495902\pi$
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	−0.999917	+	0.0128733i	$0.995902\pi$
$620$		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	$0.149906\pi$
$631$			22.7950i			0.907456i	−0.891140	+	0.453728i	$0.850094\pi$
$632$		0			0
$633$	0.175787			0.00698691
$634$		0			0
$635$	3.39952	−	12.9004i	0.134906	−	0.511935i
$636$		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
$645$	2.15308	+	0.567385i	0.0847776	+	0.0223408i
$646$		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	0.987644	−	0.156716i	$-0.0500908\pi$
$653$	21.2334	+	21.2334i	0.830928	+	0.830928i	−0.156716	+	0.987644i	$0.550091\pi$
$654$		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	−0.979823	−	0.199869i	$-0.935948\pi$
$659$	−20.0222	+	20.0222i	−0.779954	+	0.779954i	0.199869	+	0.979823i	$0.435948\pi$
$660$		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	$-0.982126\pi$
$673$		−	2.91192i		−	0.112246i	0.998424	−	0.0561231i	$-0.0178739\pi$
$674$		0			0
$675$	7.43031	−	2.05696i	0.285993	−	0.0791724i
$676$		0			0
$677$	−34.6045	+	34.6045i	−1.32996	+	1.32996i	−0.424558	+	0.905401i	$0.639570\pi$
$677$	−34.6045	+	34.6045i	−1.32996	+	1.32996i	−0.905401	+	0.424558i	$0.860430\pi$
$678$		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
$685$	39.5140	+	10.4128i	1.50975	+	0.397852i
$686$		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	−0.0339907	−	0.999422i	$-0.510822\pi$
$691$	25.3782	−	25.3782i	0.965431	−	0.965431i	0.999422	+	0.0339907i	$0.0108217\pi$
$692$		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
$715$	3.29658	−	12.5097i	0.123285	−	0.467836i
$716$		0			0
$717$	−3.38578	−	3.38578i	−0.126444	−	0.126444i
$718$		0			0
$719$	−45.0785			−1.68115			−0.840573	−	0.541699i	$-0.817781\pi$
$719$	−45.0785			−1.68115			−0.840573	+	0.541699i	$0.817781\pi$
$720$		0			0
$721$	−59.1820			−2.20405
$722$		0			0
$723$	3.36791	+	3.36791i	0.125254	+	0.125254i
$724$		0			0
$725$	−14.7977	+	4.09651i	−0.549574	+	0.152141i
$726$		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	0.838596	−	0.544753i	$-0.183377\pi$
$733$	7.95550	+	7.95550i	0.293843	+	0.293843i	−0.544753	+	0.838596i	$0.683377\pi$
$734$		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	−0.929727	−	0.368249i	$-0.879958\pi$
$739$	−15.2636	+	15.2636i	−0.561479	+	0.561479i	0.368249	+	0.929727i	$0.379958\pi$
$740$		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	$-0.506808\pi$
$751$	−1.17214			−0.0427720			−0.0213860	+	0.999771i	$0.506808\pi$
$752$		0			0
$753$		−	5.88945i		−	0.214623i
$754$		0			0
$755$	10.2527	−	38.9064i	0.373134	−	1.41595i
$756$		0			0
$757$	17.9408	−	17.9408i	0.652069	−	0.652069i	−0.301422	−	0.953491i	$-0.597461\pi$
$757$	17.9408	−	17.9408i	0.652069	−	0.652069i	0.953491	+	0.301422i	$0.0974612\pi$
$758$		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
$765$	−31.3157	−	8.25237i	−1.13222	−	0.298365i
$766$		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	$-0.432795\pi$
$773$	33.0120	−	33.0120i	1.18736	−	1.18736i	0.977794	−	0.209566i	$-0.0672052\pi$
$774$		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
$795$	−2.70248	−	0.712163i	−0.0958472	−	0.0252578i
$796$		0			0
$797$	23.1556	+	23.1556i	0.820214	+	0.820214i	0.986139	−	0.165924i	$-0.0530607\pi$
$797$	23.1556	+	23.1556i	0.820214	+	0.820214i	−0.165924	+	0.986139i	$0.553061\pi$
$798$		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
$805$	1.11961	+	0.295040i	0.0394609	+	0.0103988i
$806$		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	0.849577	−	0.527465i	$-0.176857\pi$
$811$	9.17312	+	9.17312i	0.322112	+	0.322112i	−0.527465	+	0.849577i	$0.676857\pi$
$812$		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
$835$	−27.5815	−	7.26832i	−0.954497	−	0.251531i
$836$		0			0
$837$	−2.46818	+	2.46818i	−0.0853128	+	0.0853128i
$838$		0			0
$839$		−	11.9093i		−	0.411153i	−0.978641	−	0.205577i	$-0.934093\pi$
$839$		−	11.9093i		−	0.411153i	0.978641	−	0.205577i	$-0.0659069\pi$
$840$		0			0
$841$			19.5698i			0.674822i
$842$		0			0
$843$	−3.71576	+	3.71576i	−0.127977	+	0.127977i
$844$		0			0
$845$	3.68325	−	13.9770i	0.126708	−	0.480824i
$846$		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	−0.663992	−	0.747740i	$-0.731139\pi$
$853$	2.44597	−	2.44597i	0.0837485	−	0.0837485i	0.747740	+	0.663992i	$0.231139\pi$
$854$		0			0
$855$	22.2824	+	38.2282i	0.762041	+	1.30738i
$856$		0			0
$857$	−2.57862			−0.0880839			−0.0440419	−	0.999030i	$-0.514024\pi$
$857$	−2.57862			−0.0880839			−0.0440419	+	0.999030i	$0.514024\pi$
$858$		0			0
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.990789	+	0.135416i	$0.0432371\pi$
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.135416	+	0.990789i	$0.456763\pi$
$860$		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
$875$	30.8004	+	30.0455i	1.04124	+	1.01572i
$876$		0			0
$877$	−34.2135	−	34.2135i	−1.15531	−	1.15531i	−0.985472	−	0.169836i	$-0.945676\pi$
$877$	−34.2135	−	34.2135i	−1.15531	−	1.15531i	−0.169836	−	0.985472i	$-0.554324\pi$
$878$		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
$885$	0.0224375	−	0.0851449i	0.000754230	−	0.00286211i
$886$		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	$-0.530518\pi$
$911$	−5.77870			−0.191457			−0.0957284	+	0.995407i	$0.530518\pi$
$912$		0			0
$913$		−	28.1944i		−	0.933098i
$914$		0			0
$915$	2.75327	+	0.725548i	0.0910204	+	0.0239859i
$916$		0			0
$917$	9.12424	−	9.12424i	0.301309	−	0.301309i
$918$		0			0
$919$		−	50.8572i		−	1.67763i	−0.544420	−	0.838813i	$-0.683250\pi$
$919$		−	50.8572i		−	1.67763i	0.544420	−	0.838813i	$-0.316750\pi$
$920$		0			0
$921$		−	0.801852i		−	0.0264219i
$922$		0			0
$923$	16.8644	−	16.8644i	0.555100	−	0.555100i
$924$		0			0
$925$	29.6487	−	8.20775i	0.974842	−	0.269869i
$926$		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	$-0.604804\pi$
$937$	−19.7948			−0.646668			−0.323334	+	0.946285i	$0.604804\pi$
$938$		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	$-0.273460\pi$
$953$	40.3245			1.30624			0.653119	+	0.757255i	$0.273460\pi$
$954$		0			0
$955$	−10.9665	−	2.88991i	−0.354867	−	0.0935153i
$956$		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
$965$	−1.31212	+	4.97919i	−0.0422388	+	0.160286i
$966$		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	0.679164	−	0.733986i	$-0.262342\pi$
$971$	−1.70830	−	1.70830i	−0.0548220	−	0.0548220i	−0.733986	+	0.679164i	$0.762342\pi$
$972$		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	$-0.809735\pi$
$977$		−	35.1811i		−	1.12554i	0.826612	−	0.562772i	$-0.190265\pi$
$978$		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	$-0.464399\pi$
$991$	7.02711			0.223224			0.111612	+	0.993752i	$0.464399\pi$
$992$		0			0
$993$			3.22428i			0.102319i
$994$		0			0
$995$	−12.4538	+	47.2590i	−0.394812	+	1.49821i
$996$		0			0
$997$	14.2467	−	14.2467i	0.451197	−	0.451197i	−0.444555	−	0.895752i	$-0.646638\pi$
$997$	14.2467	−	14.2467i	0.451197	−	0.451197i	0.895752	+	0.444555i	$0.146638\pi$
$998$		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.f.609.5		16
4.3	odd	2		640.2.q.e.609.4		16
5.4	even	2	inner	640.2.q.f.609.4		16
8.3	odd	2		80.2.q.c.69.8	yes	16
8.5	even	2		320.2.q.c.49.4		16
16.3	odd	4		640.2.q.e.289.5		16
16.5	even	4		320.2.q.c.209.5		16
16.11	odd	4		80.2.q.c.29.1	✓	16
16.13	even	4	inner	640.2.q.f.289.4		16
20.19	odd	2		640.2.q.e.609.5		16
24.11	even	2		720.2.bm.f.469.1		16
40.3	even	4		400.2.l.i.101.5		16
40.13	odd	4		1600.2.l.h.1201.5		16
40.19	odd	2		80.2.q.c.69.1	yes	16
40.27	even	4		400.2.l.i.101.4		16
40.29	even	2		320.2.q.c.49.5		16
40.37	odd	4		1600.2.l.h.1201.4		16
48.11	even	4		720.2.bm.f.109.8		16
80.19	odd	4		640.2.q.e.289.4		16
80.27	even	4		400.2.l.i.301.4		16
80.29	even	4	inner	640.2.q.f.289.5		16
80.37	odd	4		1600.2.l.h.401.4		16
80.43	even	4		400.2.l.i.301.5		16
80.53	odd	4		1600.2.l.h.401.5		16
80.59	odd	4		80.2.q.c.29.8	yes	16
80.69	even	4		320.2.q.c.209.4		16
120.59	even	2		720.2.bm.f.469.8		16
240.59	even	4		720.2.bm.f.109.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.1	✓	16	16.11	odd	4
80.2.q.c.29.8	yes	16	80.59	odd	4
80.2.q.c.69.1	yes	16	40.19	odd	2
80.2.q.c.69.8	yes	16	8.3	odd	2
320.2.q.c.49.4		16	8.5	even	2
320.2.q.c.49.5		16	40.29	even	2
320.2.q.c.209.4		16	80.69	even	4
320.2.q.c.209.5		16	16.5	even	4
400.2.l.i.101.4		16	40.27	even	4
400.2.l.i.101.5		16	40.3	even	4
400.2.l.i.301.4		16	80.27	even	4
400.2.l.i.301.5		16	80.43	even	4
640.2.q.e.289.4		16	80.19	odd	4
640.2.q.e.289.5		16	16.3	odd	4
640.2.q.e.609.4		16	4.3	odd	2
640.2.q.e.609.5		16	20.19	odd	2
640.2.q.f.289.4		16	16.13	even	4	inner
640.2.q.f.289.5		16	80.29	even	4	inner
640.2.q.f.609.4		16	5.4	even	2	inner
640.2.q.f.609.5		16	1.1	even	1	trivial
720.2.bm.f.109.1		16	240.59	even	4
720.2.bm.f.109.8		16	48.11	even	4
720.2.bm.f.469.1		16	24.11	even	2
720.2.bm.f.469.8		16	120.59	even	2
1600.2.l.h.401.4		16	80.37	odd	4
1600.2.l.h.401.5		16	80.53	odd	4
1600.2.l.h.1201.4		16	40.37	odd	4
1600.2.l.h.1201.5		16	40.13	odd	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)

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more