LMFDB - Embedded newform 512.2.k.a.497.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [512,2,Mod(17,512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(512, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			497.12
Character	$\chi$	$=$	512.497
Dual form			512.2.k.a.273.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.98130 - 1.05903i) q^{3} +(0.218926 + 0.266762i) q^{5} +(0.368096 - 0.245954i) q^{7} +(1.13730 - 1.70208i) q^{9} +(0.341220 - 0.103508i) q^{11} +(2.88278 + 2.36584i) q^{13} +(0.716264 + 0.296686i) q^{15} +(6.12855 - 2.53853i) q^{17} +(-0.500227 - 5.07889i) q^{19} +(0.468836 - 0.877130i) q^{21} +(-4.80482 + 0.955738i) q^{23} +(0.952218 - 4.78712i) q^{25} +(-0.209836 + 2.13050i) q^{27} +(-1.12675 + 3.71441i) q^{29} +(1.23628 + 1.23628i) q^{31} +(0.566441 - 0.566441i) q^{33} +(0.146197 + 0.0443482i) q^{35} +(-10.0376 - 0.988614i) q^{37} +(8.21714 + 1.63449i) q^{39} +(0.432861 + 2.17614i) q^{41} +(-4.05046 - 2.16502i) q^{43} +(0.703033 - 0.0692427i) q^{45} +(1.49454 + 3.60814i) q^{47} +(-2.60378 + 6.28609i) q^{49} +(9.45412 - 11.5199i) q^{51} +(-2.98330 - 9.83462i) q^{53} +(0.102314 + 0.0683639i) q^{55} +(-6.36977 - 9.53304i) q^{57} +(-9.60613 + 7.88354i) q^{59} +(0.312866 + 0.585330i) q^{61} -0.906251i q^{63} +1.28696i q^{65} +(1.69431 + 3.16984i) q^{67} +(-8.50763 + 6.98203i) q^{69} +(7.84873 + 11.7465i) q^{71} +(8.50764 + 5.68462i) q^{73} +(-3.18306 - 10.4931i) q^{75} +(0.100144 - 0.122025i) q^{77} +(5.13428 - 12.3952i) q^{79} +(4.19065 + 10.1171i) q^{81} +(-7.66719 + 0.755152i) q^{83} +(2.01888 + 1.07911i) q^{85} +(1.70122 + 8.55262i) q^{87} +(1.30486 + 0.259552i) q^{89} +(1.64303 + 0.161824i) q^{91} +(3.75869 + 1.14019i) q^{93} +(1.24534 - 1.24534i) q^{95} +(1.24876 + 1.24876i) q^{97} +(0.211889 - 0.698504i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

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
$3$	1.98130	−	1.05903i	1.14390	−	0.611429i	0.213129	−	0.977024i	$-0.431635\pi$
$3$	1.98130	−	1.05903i	1.14390	−	0.611429i	0.930774	+	0.365595i	$0.119135\pi$
$4$		0			0
$5$	0.218926	+	0.266762i	0.0979065	+	0.119299i	0.819659	−	0.572852i	$-0.194163\pi$
$5$	0.218926	+	0.266762i	0.0979065	+	0.119299i	−0.721752	+	0.692151i	$0.756663\pi$
$6$		0			0
$7$	0.368096	−	0.245954i	0.139127	−	0.0929618i	−0.484059	−	0.875035i	$-0.660838\pi$
$7$	0.368096	−	0.245954i	0.139127	−	0.0929618i	0.623186	+	0.782074i	$0.285838\pi$
$8$		0			0
$9$	1.13730	−	1.70208i	0.379098	−	0.567361i
$10$		0			0
$11$	0.341220	−	0.103508i	0.102882	−	0.0312088i	−0.238424	−	0.971161i	$-0.576631\pi$
$11$	0.341220	−	0.103508i	0.102882	−	0.0312088i	0.341306	+	0.939952i	$0.389131\pi$
$12$		0			0
$13$	2.88278	+	2.36584i	0.799541	+	0.656166i	0.942740	−	0.333528i	$-0.108239\pi$
$13$	2.88278	+	2.36584i	0.799541	+	0.656166i	−0.143200	+	0.989694i	$0.545739\pi$
$14$		0			0
$15$	0.716264	+	0.296686i	0.184939	+	0.0766041i
$16$		0			0
$17$	6.12855	−	2.53853i	1.48639	−	0.615684i	0.515864	−	0.856671i	$-0.327471\pi$
$17$	6.12855	−	2.53853i	1.48639	−	0.615684i	0.970528	+	0.240987i	$0.0774711\pi$
$18$		0			0
$19$	−0.500227	−	5.07889i	−0.114760	−	1.16518i	−0.864215	−	0.503122i	$-0.832185\pi$
$19$	−0.500227	−	5.07889i	−0.114760	−	1.16518i	0.749456	−	0.662055i	$-0.230315\pi$
$20$		0			0
$21$	0.468836	−	0.877130i	0.102308	−	0.191406i
$22$		0			0
$23$	−4.80482	+	0.955738i	−1.00187	+	0.199285i	−0.668662	−	0.743567i	$-0.733133\pi$
$23$	−4.80482	+	0.955738i	−1.00187	+	0.199285i	−0.333212	+	0.942852i	$0.608133\pi$
$24$		0			0
$25$	0.952218	−	4.78712i	0.190444	−	0.957425i
$26$		0			0
$27$	−0.209836	+	2.13050i	−0.0403829	+	0.410015i
$28$		0			0
$29$	−1.12675	+	3.71441i	−0.209233	+	0.689749i	0.788018	+	0.615652i	$0.211107\pi$
$29$	−1.12675	+	3.71441i	−0.209233	+	0.689749i	−0.997251	+	0.0740967i	$0.976393\pi$
$30$		0			0
$31$	1.23628	+	1.23628i	0.222042	+	0.222042i	0.809358	−	0.587316i	$-0.199815\pi$
$31$	1.23628	+	1.23628i	0.222042	+	0.222042i	−0.587316	+	0.809358i	$0.699815\pi$
$32$		0			0
$33$	0.566441	−	0.566441i	0.0986048	−	0.0986048i
$34$		0			0
$35$	0.146197	+	0.0443482i	0.0247117	+	0.00749622i
$36$		0			0
$37$	−10.0376	−	0.988614i	−1.65017	−	0.162527i	−0.770277	−	0.637709i	$-0.779882\pi$
$37$	−10.0376	−	0.988614i	−1.65017	−	0.162527i	−0.879888	+	0.475182i	$0.842382\pi$
$38$		0			0
$39$	8.21714	+	1.63449i	1.31580	+	0.261728i
$40$		0			0
$41$	0.432861	+	2.17614i	0.0676016	+	0.339856i	0.999753	−	0.0222118i	$-0.00707081\pi$
$41$	0.432861	+	2.17614i	0.0676016	+	0.339856i	−0.932152	+	0.362068i	$0.882071\pi$
$42$		0			0
$43$	−4.05046	−	2.16502i	−0.617690	−	0.330162i	0.132702	−	0.991156i	$-0.457635\pi$
$43$	−4.05046	−	2.16502i	−0.617690	−	0.330162i	−0.750391	+	0.660994i	$0.770135\pi$
$44$		0			0
$45$	0.703033	−	0.0692427i	0.104802	−	0.0103221i
$46$		0			0
$47$	1.49454	+	3.60814i	0.218001	+	0.526302i	0.994611	−	0.103681i	$-0.0330621\pi$
$47$	1.49454	+	3.60814i	0.218001	+	0.526302i	−0.776609	+	0.629982i	$0.783062\pi$
$48$		0			0
$49$	−2.60378	+	6.28609i	−0.371969	+	0.898013i
$50$		0			0
$51$	9.45412	−	11.5199i	1.32384	−	1.61311i
$52$		0			0
$53$	−2.98330	−	9.83462i	−0.409788	−	1.35089i	−0.882765	−	0.469815i	$-0.844321\pi$
$53$	−2.98330	−	9.83462i	−0.409788	−	1.35089i	0.472977	−	0.881075i	$-0.343179\pi$
$54$		0			0
$55$	0.102314	+	0.0683639i	0.0137960	+	0.00921819i
$56$		0			0
$57$	−6.36977	−	9.53304i	−0.843697	−	1.26268i
$58$		0			0
$59$	−9.60613	+	7.88354i	−1.25061	+	1.02635i	−0.252336	+	0.967640i	$0.581199\pi$
$59$	−9.60613	+	7.88354i	−1.25061	+	1.02635i	−0.998275	+	0.0587103i	$0.981301\pi$
$60$		0			0
$61$	0.312866	+	0.585330i	0.0400583	+	0.0749439i	0.901154	−	0.433499i	$-0.142721\pi$
$61$	0.312866	+	0.585330i	0.0400583	+	0.0749439i	−0.861096	+	0.508443i	$0.830221\pi$
$62$		0			0
$63$		−	0.906251i		−	0.114177i
$64$		0			0
$65$			1.28696i			0.159628i
$66$		0			0
$67$	1.69431	+	3.16984i	0.206993	+	0.387257i	0.963899	−	0.266266i	$-0.0857901\pi$
$67$	1.69431	+	3.16984i	0.206993	+	0.387257i	−0.756906	+	0.653523i	$0.773290\pi$
$68$		0			0
$69$	−8.50763	+	6.98203i	−1.02420	+	0.840538i
$70$		0			0
$71$	7.84873	+	11.7465i	0.931473	+	1.39405i	0.919057	+	0.394125i	$0.128952\pi$
$71$	7.84873	+	11.7465i	0.931473	+	1.39405i	0.0124161	+	0.999923i	$0.496048\pi$
$72$		0			0
$73$	8.50764	+	5.68462i	0.995744	+	0.665335i	0.942833	−	0.333264i	$-0.108150\pi$
$73$	8.50764	+	5.68462i	0.995744	+	0.665335i	0.0529105	+	0.998599i	$0.483150\pi$
$74$		0			0
$75$	−3.18306	−	10.4931i	−0.367548	−	1.21164i
$76$		0			0
$77$	0.100144	−	0.122025i	0.0114124	−	0.0139061i
$78$		0			0
$79$	5.13428	−	12.3952i	0.577651	−	1.39457i	−0.317264	−	0.948337i	$-0.602764\pi$
$79$	5.13428	−	12.3952i	0.577651	−	1.39457i	0.894915	−	0.446236i	$-0.147236\pi$
$80$		0			0
$81$	4.19065	+	10.1171i	0.465628	+	1.12413i
$82$		0			0
$83$	−7.66719	+	0.755152i	−0.841584	+	0.0828887i	−0.509616	−	0.860402i	$-0.670212\pi$
$83$	−7.66719	+	0.755152i	−0.841584	+	0.0828887i	−0.331968	+	0.943291i	$0.607712\pi$
$84$		0			0
$85$	2.01888	+	1.07911i	0.218978	+	0.117046i
$86$		0			0
$87$	1.70122	+	8.55262i	0.182390	+	0.916937i
$88$		0			0
$89$	1.30486	+	0.259552i	0.138314	+	0.0275124i	0.263762	−	0.964588i	$-0.415037\pi$
$89$	1.30486	+	0.259552i	0.138314	+	0.0275124i	−0.125448	+	0.992100i	$0.540037\pi$
$90$		0			0
$91$	1.64303	+	0.161824i	0.172236	+	0.0169638i
$92$		0			0
$93$	3.75869	+	1.14019i	0.389758	+	0.118232i
$94$		0			0
$95$	1.24534	−	1.24534i	0.127769	−	0.127769i
$96$		0			0
$97$	1.24876	+	1.24876i	0.126793	+	0.126793i	0.767655	−	0.640863i	$-0.221423\pi$
$97$	1.24876	+	1.24876i	0.126793	+	0.126793i	−0.640863	+	0.767655i	$0.721423\pi$
$98$		0			0
$99$	0.211889	−	0.698504i	0.0212956	−	0.0702023i
$100$		0			0
$101$	−0.851866	+	8.64914i	−0.0847639	+	0.860622i	0.854961	+	0.518692i	$0.173581\pi$
$101$	−0.851866	+	8.64914i	−0.0847639	+	0.860622i	−0.939725	+	0.341930i	$0.888919\pi$
$102$		0			0
$103$	1.04344	−	5.24573i	0.102813	−	0.516877i	−0.894717	−	0.446634i	$-0.852622\pi$
$103$	1.04344	−	5.24573i	0.102813	−	0.516877i	0.997530	−	0.0702431i	$-0.0223775\pi$
$104$		0			0
$105$	0.336625	−	0.0669589i	0.0328512	−	0.00653452i
$106$		0			0
$107$	−5.62301	+	10.5199i	−0.543596	+	1.01700i	0.448767	+	0.893649i	$0.351863\pi$
$107$	−5.62301	+	10.5199i	−0.543596	+	1.01700i	−0.992363	+	0.123349i	$0.960637\pi$
$108$		0			0
$109$	−1.60333	−	16.2789i	−0.153571	−	1.55923i	−0.695326	−	0.718695i	$-0.744740\pi$
$109$	−1.60333	−	16.2789i	−0.153571	−	1.55923i	0.541755	−	0.840537i	$-0.317760\pi$
$110$		0			0
$111$	−20.9344	+	8.67130i	−1.98700	+	0.823043i
$112$		0			0
$113$	−6.30665	−	2.61230i	−0.593279	−	0.245744i	0.0657814	−	0.997834i	$-0.479046\pi$
$113$	−6.30665	−	2.61230i	−0.593279	−	0.245744i	−0.659061	+	0.752090i	$0.729046\pi$
$114$		0			0
$115$	−1.30685	−	1.07251i	−0.121865	−	0.100012i
$116$		0			0
$117$	7.30543	−	2.21608i	0.675388	−	0.204877i
$118$		0			0
$119$	1.63153	−	2.44176i	0.149562	−	0.223836i
$120$		0			0
$121$	−9.04045	+	6.04063i	−0.821859	+	0.549149i
$122$		0			0
$123$	3.16222	+	3.85317i	0.285128	+	0.347429i
$124$		0			0
$125$	3.00722	−	1.60739i	0.268974	−	0.143769i
$126$		0			0
$127$	−9.99096			−0.886554			−0.443277	−	0.896385i	$-0.646184\pi$
$127$	−9.99096			−0.886554			−0.443277	+	0.896385i	$0.646184\pi$
$128$		0			0
$129$	−10.3180			−0.908448
$130$		0			0
$131$	−11.5172	+	6.15605i	−1.00626	+	0.537856i	−0.890289	−	0.455396i	$-0.849498\pi$
$131$	−11.5172	+	6.15605i	−1.00626	+	0.537856i	−0.115970	+	0.993253i	$0.536998\pi$
$132$		0			0
$133$	−1.43330	−	1.74648i	−0.124283	−	0.151439i
$134$		0			0
$135$	−0.614274	+	0.410445i	−0.0528683	+	0.0353254i
$136$		0			0
$137$	7.75191	−	11.6016i	0.662290	−	0.991188i	−0.336484	−	0.941689i	$-0.609238\pi$
$137$	7.75191	−	11.6016i	0.662290	−	0.991188i	0.998774	−	0.0494983i	$-0.0157622\pi$
$138$		0			0
$139$	7.83450	−	2.37657i	0.664513	−	0.201578i	0.0600311	−	0.998197i	$-0.480880\pi$
$139$	7.83450	−	2.37657i	0.664513	−	0.201578i	0.604482	+	0.796619i	$0.293380\pi$
$140$		0			0
$141$	6.78225	+	5.56605i	0.571168	+	0.468746i
$142$		0			0
$143$	1.22855	+	0.508881i	0.102736	+	0.0425548i
$144$		0			0
$145$	−1.23754	+	0.512605i	−0.102772	+	0.0425695i
$146$		0			0
$147$	1.49826	+	15.2121i	0.123574	+	1.25467i
$148$		0			0
$149$	−7.71742	+	14.4383i	−0.632236	+	1.18283i	0.338110	+	0.941107i	$0.390213\pi$
$149$	−7.71742	+	14.4383i	−0.632236	+	1.18283i	−0.970345	+	0.241723i	$0.922287\pi$
$150$		0			0
$151$	−20.1132	+	4.00077i	−1.63679	+	0.325578i	−0.925913	−	0.377736i	$-0.876703\pi$
$151$	−20.1132	+	4.00077i	−1.63679	+	0.325578i	−0.710879	+	0.703314i	$0.751703\pi$
$152$		0			0
$153$	2.64919	−	13.3184i	0.214174	−	1.07673i
$154$		0			0
$155$	−0.0591386	+	0.600445i	−0.00475013	+	0.0482289i
$156$		0			0
$157$	−2.17897	+	7.18310i	−0.173901	+	0.573274i	0.826052	+	0.563593i	$0.190581\pi$
$157$	−2.17897	+	7.18310i	−0.173901	+	0.573274i	−0.999953	+	0.00968062i	$0.996919\pi$
$158$		0			0
$159$	−16.3259	−	16.3259i	−1.29473	−	1.29473i
$160$		0			0
$161$	−1.53357	+	1.53357i	−0.120862	+	0.120862i
$162$		0			0
$163$	2.60805	+	0.791143i	0.204278	+	0.0619671i	0.390765	−	0.920490i	$-0.372210\pi$
$163$	2.60805	+	0.791143i	0.204278	+	0.0619671i	−0.186487	+	0.982457i	$0.559710\pi$
$164$		0			0
$165$	0.275113	+	0.0270963i	0.0214175	+	0.00210944i
$166$		0			0
$167$	13.9752	+	2.77985i	1.08144	+	0.215111i	0.703482	−	0.710713i	$-0.251628\pi$
$167$	13.9752	+	2.77985i	1.08144	+	0.215111i	0.377954	+	0.925824i	$0.376628\pi$
$168$		0			0
$169$	0.177073	+	0.890208i	0.0136210	+	0.0684775i
$170$		0			0
$171$	−9.21359	−	4.92477i	−0.704581	−	0.376606i
$172$		0			0
$173$	−2.28364	+	0.224919i	−0.173622	+	0.0171003i	−0.184455	−	0.982841i	$-0.559052\pi$
$173$	−2.28364	+	0.224919i	−0.173622	+	0.0171003i	0.0108325	+	0.999941i	$0.496552\pi$
$174$		0			0
$175$	−0.826903	−	1.99632i	−0.0625080	−	0.150908i
$176$		0			0
$177$	−10.6837	+	25.7928i	−0.803038	+	1.93870i
$178$		0			0
$179$	12.8160	−	15.6164i	0.957914	−	1.16722i	−0.0279388	−	0.999610i	$-0.508894\pi$
$179$	12.8160	−	15.6164i	0.957914	−	1.16722i	0.985853	−	0.167612i	$-0.0536056\pi$
$180$		0			0
$181$	−3.14930	−	10.3818i	−0.234085	−	0.771676i	−0.992750	−	0.120195i	$-0.961648\pi$
$181$	−3.14930	−	10.3818i	−0.234085	−	0.771676i	0.758665	−	0.651481i	$-0.225852\pi$
$182$		0			0
$183$	1.23976	+	0.828381i	0.0916457	+	0.0612357i
$184$		0			0
$185$	−1.93376	−	2.89407i	−0.142172	−	0.212776i
$186$		0			0
$187$	1.82843	−	1.50055i	0.133708	−	0.109731i
$188$		0			0
$189$	0.446764	+	0.835837i	0.0324973	+	0.0607982i
$190$		0			0
$191$		−	11.7107i		−	0.847356i	−0.905813	−	0.423678i	$-0.860739\pi$
$191$		−	11.7107i		−	0.847356i	0.905813	−	0.423678i	$-0.139261\pi$
$192$		0			0
$193$		−	13.0901i		−	0.942243i	−0.882068	−	0.471122i	$-0.843849\pi$
$193$		−	13.0901i		−	0.942243i	0.882068	−	0.471122i	$-0.156151\pi$
$194$		0			0
$195$	1.36292	+	2.54985i	0.0976009	+	0.182599i
$196$		0			0
$197$	−8.11859	+	6.66276i	−0.578426	+	0.474702i	−0.877532	−	0.479518i	$-0.840811\pi$
$197$	−8.11859	+	6.66276i	−0.578426	+	0.474702i	0.299106	+	0.954220i	$0.403311\pi$
$198$		0			0
$199$	−3.98946	−	5.97066i	−0.282806	−	0.423249i	0.662685	−	0.748898i	$-0.269417\pi$
$199$	−3.98946	−	5.97066i	−0.282806	−	0.423249i	−0.945490	+	0.325650i	$0.894417\pi$
$200$		0			0
$201$	6.71388	+	4.48607i	0.473560	+	0.316423i
$202$		0			0
$203$	0.498820	+	1.64439i	0.0350103	+	0.115413i
$204$		0			0
$205$	−0.485747	+	0.591884i	−0.0339260	+	0.0413390i
$206$		0			0
$207$	−3.83775	+	9.26516i	−0.266742	+	0.643973i
$208$		0			0
$209$	−0.696393	−	1.68124i	−0.0481705	−	0.116294i
$210$		0			0
$211$	10.8116	−	1.06485i	0.744303	−	0.0733074i	0.281246	−	0.959636i	$-0.409252\pi$
$211$	10.8116	−	1.06485i	0.744303	−	0.0733074i	0.463057	+	0.886328i	$0.346752\pi$
$212$		0			0
$213$	27.9905	+	14.9612i	1.91788	+	1.02513i
$214$		0			0
$215$	−0.309206	−	1.55449i	−0.0210877	−	0.106015i
$216$		0			0
$217$	0.759136	+	0.151002i	0.0515335	+	0.0102507i
$218$		0			0
$219$	22.8763	+	2.25312i	1.54584	+	0.152252i
$220$		0			0
$221$	23.6730	+	7.18114i	1.59242	+	0.483056i
$222$		0			0
$223$	18.3947	−	18.3947i	1.23180	−	1.23180i	0.268531	−	0.963271i	$-0.413462\pi$
$223$	18.3947	−	18.3947i	1.23180	−	1.23180i	0.963271	−	0.268531i	$-0.0865382\pi$
$224$		0			0
$225$	−7.06513	−	7.06513i	−0.471009	−	0.471009i
$226$		0			0
$227$	−3.92766	+	12.9478i	−0.260688	+	0.859374i	0.724702	+	0.689062i	$0.241977\pi$
$227$	−3.92766	+	12.9478i	−0.260688	+	0.859374i	−0.985390	+	0.170311i	$0.945523\pi$
$228$		0			0
$229$	2.49305	−	25.3124i	0.164745	−	1.67269i	−0.456998	−	0.889468i	$-0.651075\pi$
$229$	2.49305	−	25.3124i	0.164745	−	1.67269i	0.621744	−	0.783221i	$-0.286425\pi$
$230$		0			0
$231$	0.0691863	−	0.347823i	0.00455212	−	0.0228851i
$232$		0			0
$233$	−10.3183	+	2.05243i	−0.675971	+	0.134459i	−0.521126	−	0.853480i	$-0.674488\pi$
$233$	−10.3183	+	2.05243i	−0.675971	+	0.134459i	−0.154845	+	0.987939i	$0.549488\pi$
$234$		0			0
$235$	−0.635320	+	1.18860i	−0.0414437	+	0.0775358i
$236$		0			0
$237$	−2.95435	−	29.9960i	−0.191906	−	1.94845i
$238$		0			0
$239$	−1.35937	+	0.563069i	−0.0879303	+	0.0364219i	−0.426215	−	0.904622i	$-0.640153\pi$
$239$	−1.35937	+	0.563069i	−0.0879303	+	0.0364219i	0.338285	+	0.941044i	$0.390153\pi$
$240$		0			0
$241$	−19.8180	−	8.20887i	−1.27659	−	0.528780i	−0.361627	−	0.932323i	$-0.617779\pi$
$241$	−19.8180	−	8.20887i	−1.27659	−	0.528780i	−0.914961	+	0.403543i	$0.867779\pi$
$242$		0			0
$243$	14.0526	+	11.5327i	0.901477	+	0.739823i
$244$		0			0
$245$	−2.24692	+	0.681596i	−0.143551	+	0.0435456i
$246$		0			0
$247$	10.5738	−	15.8248i	0.672794	−	1.00691i
$248$		0			0
$249$	−14.3913	+	9.61594i	−0.912009	+	0.609385i
$250$		0			0
$251$	14.4786	+	17.6422i	0.913881	+	1.11357i	0.993165	+	0.116715i	$0.0372363\pi$
$251$	14.4786	+	17.6422i	0.913881	+	1.11357i	−0.0792849	+	0.996852i	$0.525264\pi$
$252$		0			0
$253$	−1.54058	+	0.823455i	−0.0968552	+	0.0517702i
$254$		0			0
$255$	5.14281			0.322055
$256$		0			0
$257$	28.7091			1.79082			0.895412	−	0.445238i	$-0.146881\pi$
$257$	28.7091			1.79082			0.895412	+	0.445238i	$0.146881\pi$
$258$		0			0
$259$	−3.93794	+	2.10487i	−0.244691	+	0.130790i
$260$		0			0
$261$	5.04078	+	6.14221i	0.312017	+	0.380193i
$262$		0			0
$263$	4.74324	−	3.16933i	0.292480	−	0.195429i	−0.400669	−	0.916223i	$-0.631222\pi$
$263$	4.74324	−	3.16933i	0.292480	−	0.195429i	0.693150	+	0.720794i	$0.256222\pi$
$264$		0			0
$265$	1.97038	−	2.94888i	0.121039	−	0.181148i
$266$		0			0
$267$	2.86018	−	0.867626i	0.175040	−	0.0530978i
$268$		0			0
$269$	−1.17292	−	0.962593i	−0.0715144	−	0.0586903i	0.597957	−	0.801528i	$-0.295979\pi$
$269$	−1.17292	−	0.962593i	−0.0715144	−	0.0586903i	−0.669471	+	0.742838i	$0.733479\pi$
$270$		0			0
$271$	24.3487	+	10.0856i	1.47908	+	0.612655i	0.968909	−	0.247418i	$-0.0795821\pi$
$271$	24.3487	+	10.0856i	1.47908	+	0.612655i	0.510171	+	0.860073i	$0.329582\pi$
$272$		0			0
$273$	3.42670	−	1.41939i	0.207394	−	0.0859052i
$274$		0			0
$275$	−0.170590	−	1.73203i	−0.0102869	−	0.104445i
$276$		0			0
$277$	9.12324	−	17.0684i	0.548162	−	1.02554i	−0.443451	−	0.896299i	$-0.646246\pi$
$277$	9.12324	−	17.0684i	0.548162	−	1.02554i	0.991613	−	0.129241i	$-0.0412540\pi$
$278$		0			0
$279$	3.51026	−	0.698234i	0.210154	−	0.0418022i
$280$		0			0
$281$	−1.77238	+	8.91038i	−0.105732	+	0.531548i	0.891223	+	0.453565i	$0.149848\pi$
$281$	−1.77238	+	8.91038i	−0.105732	+	0.531548i	−0.996955	+	0.0779833i	$0.975152\pi$
$282$		0			0
$283$	1.04971	−	10.6579i	0.0623989	−	0.633546i	−0.912224	−	0.409692i	$-0.865636\pi$
$283$	1.04971	−	10.6579i	0.0623989	−	0.633546i	0.974623	−	0.223854i	$-0.0718639\pi$
$284$		0			0
$285$	1.14854	−	3.78624i	0.0680338	−	0.224277i
$286$		0			0
$287$	0.694564	+	0.694564i	0.0409988	+	0.0409988i
$288$		0			0
$289$	19.0942	−	19.0942i	1.12319	−	1.12319i
$290$		0			0
$291$	3.79664	+	1.15170i	0.222563	+	0.0675137i
$292$		0			0
$293$	8.72926	+	0.859757i	0.509969	+	0.0502275i	0.349730	−	0.936851i	$-0.386273\pi$
$293$	8.72926	+	0.859757i	0.509969	+	0.0502275i	0.160239	+	0.987078i	$0.448773\pi$
$294$		0			0
$295$	−4.20605	−	0.836636i	−0.244886	−	0.0487108i
$296$		0			0
$297$	0.148924	+	0.748689i	0.00864142	+	0.0434433i
$298$		0			0
$299$	−16.1124	−	8.61225i	−0.931803	−	0.498059i
$300$		0			0
$301$	−2.02345	+	0.199293i	−0.116630	+	0.0114870i
$302$		0			0
$303$	7.47187	+	18.0387i	0.429248	+	1.03630i
$304$		0			0
$305$	−0.0876494	+	0.211604i	−0.00501879	+	0.0121164i
$306$		0			0
$307$	0.376887	−	0.459239i	0.0215101	−	0.0262101i	−0.762144	−	0.647407i	$-0.775853\pi$
$307$	0.376887	−	0.459239i	0.0215101	−	0.0262101i	0.783654	+	0.621197i	$0.213353\pi$
$308$		0			0
$309$	−3.48800	−	11.4984i	−0.198425	−	0.654121i
$310$		0			0
$311$	−6.08677	−	4.06705i	−0.345149	−	0.230621i	0.370897	−	0.928674i	$-0.379050\pi$
$311$	−6.08677	−	4.06705i	−0.345149	−	0.230621i	−0.716047	+	0.698053i	$0.754050\pi$
$312$		0			0
$313$	9.54440	+	14.2842i	0.539481	+	0.807391i	0.996632	−	0.0819983i	$-0.0261302\pi$
$313$	9.54440	+	14.2842i	0.539481	+	0.807391i	−0.457151	+	0.889389i	$0.651130\pi$
$314$		0			0
$315$	0.241753	−	0.198402i	0.0136212	−	0.0111787i
$316$		0			0
$317$	0.973065	+	1.82048i	0.0546528	+	0.102248i	0.907765	−	0.419480i	$-0.137788\pi$
$317$	0.973065	+	1.82048i	0.0546528	+	0.102248i	−0.853112	+	0.521728i	$0.825288\pi$
$318$		0			0
$319$			1.38406i			0.0774925i
$320$		0			0
$321$			26.7980i			1.49572i
$322$		0			0
$323$	−15.9586	−	29.8564i	−0.887958	−	1.66125i
$324$		0			0
$325$	14.0706	−	11.5475i	0.780497	−	0.640537i
$326$		0			0
$327$	−20.4164	−	30.5553i	−1.12903	−	1.68971i
$328$		0			0
$329$	1.43757	+	0.960554i	0.0792558	+	0.0529570i
$330$		0			0
$331$	−0.469599	−	1.54806i	−0.0258115	−	0.0850890i	0.943088	−	0.332542i	$-0.107906\pi$
$331$	−0.469599	−	1.54806i	−0.0258115	−	0.0850890i	−0.968900	+	0.247453i	$0.920406\pi$
$332$		0			0
$333$	−13.0984	+	15.9604i	−0.717787	+	0.874625i
$334$		0			0
$335$	−0.474662	+	1.14594i	−0.0259336	+	0.0626091i
$336$		0			0
$337$	−0.386968	−	0.934224i	−0.0210795	−	0.0508904i	0.912989	−	0.407983i	$-0.133768\pi$
$337$	−0.386968	−	0.934224i	−0.0210795	−	0.0508904i	−0.934069	+	0.357093i	$0.883768\pi$
$338$		0			0
$339$	−15.2618	+	1.50316i	−0.828909	+	0.0816404i
$340$		0			0
$341$	0.549808	+	0.293879i	0.0297738	+	0.0159144i
$342$		0			0
$343$	1.19222	+	5.99368i	0.0643737	+	0.323628i
$344$		0			0
$345$	−3.72508	−	0.740964i	−0.200551	−	0.0398921i
$346$		0			0
$347$	−7.79270	−	0.767514i	−0.418334	−	0.0412023i	−0.113339	−	0.993556i	$-0.536155\pi$
$347$	−7.79270	−	0.767514i	−0.418334	−	0.0412023i	−0.304995	+	0.952354i	$0.598655\pi$
$348$		0			0
$349$	15.6283	+	4.74079i	0.836564	+	0.253769i	0.679367	−	0.733798i	$-0.262254\pi$
$349$	15.6283	+	4.74079i	0.836564	+	0.253769i	0.157197	+	0.987567i	$0.449754\pi$
$350$		0			0
$351$	−5.64533	+	5.64533i	−0.301325	+	0.301325i
$352$		0			0
$353$	−6.39894	−	6.39894i	−0.340581	−	0.340581i	0.516005	−	0.856586i	$-0.327419\pi$
$353$	−6.39894	−	6.39894i	−0.340581	−	0.340581i	−0.856586	+	0.516005i	$0.827419\pi$
$354$		0			0
$355$	−1.41522	+	4.66534i	−0.0751118	+	0.247611i
$356$		0			0
$357$	0.646664	−	6.56569i	0.0342251	−	0.347493i
$358$		0			0
$359$	0.760488	−	3.82323i	0.0401370	−	0.201782i	−0.955514	−	0.294947i	$-0.904698\pi$
$359$	0.760488	−	3.82323i	0.0401370	−	0.201782i	0.995651	+	0.0931642i	$0.0296981\pi$
$360$		0			0
$361$	−6.90995	+	1.37447i	−0.363681	+	0.0723407i
$362$		0			0
$363$	−11.5146	+	21.5424i	−0.604362	+	1.13068i
$364$		0			0
$365$	0.346101	+	3.51402i	0.0181157	+	0.183932i
$366$		0			0
$367$	−7.53766	+	3.12220i	−0.393463	+	0.162978i	−0.570638	−	0.821202i	$-0.693304\pi$
$367$	−7.53766	+	3.12220i	−0.393463	+	0.162978i	0.177175	+	0.984179i	$0.443304\pi$
$368$		0			0
$369$	4.19626	+	1.73815i	0.218449	+	0.0904844i
$370$		0			0
$371$	−3.51700	−	2.88633i	−0.182594	−	0.149851i
$372$		0			0
$373$	−11.6759	+	3.54186i	−0.604557	+	0.183390i	−0.577701	−	0.816249i	$-0.696050\pi$
$373$	−11.6759	+	3.54186i	−0.604557	+	0.183390i	−0.0268569	+	0.999639i	$0.508550\pi$
$374$		0			0
$375$	4.25592	−	6.36944i	0.219775	−	0.328916i
$376$		0			0
$377$	−12.0359	+	8.04213i	−0.619880	+	0.414191i
$378$		0			0
$379$	4.86360	+	5.92631i	0.249826	+	0.304414i	0.882790	−	0.469767i	$-0.155662\pi$
$379$	4.86360	+	5.92631i	0.249826	+	0.304414i	−0.632964	+	0.774181i	$0.718162\pi$
$380$		0			0
$381$	−19.7951	+	10.5807i	−1.01413	+	0.542065i
$382$		0			0
$383$	29.8332			1.52440			0.762201	−	0.647340i	$-0.224119\pi$
$383$	29.8332			1.52440			0.762201	+	0.647340i	$0.224119\pi$
$384$		0			0
$385$	0.0544756			0.00277634
$386$		0			0
$387$	−8.29161	+	4.43196i	−0.421486	+	0.225289i
$388$		0			0
$389$	−9.37207	−	11.4199i	−0.475183	−	0.579012i	0.479159	−	0.877728i	$-0.340942\pi$
$389$	−9.37207	−	11.4199i	−0.475183	−	0.579012i	−0.954342	+	0.298716i	$0.903442\pi$
$390$		0			0
$391$	−27.0204	+	18.0545i	−1.36648	+	0.913054i
$392$		0			0
$393$	−16.2995	+	24.3939i	−0.822201	+	1.23051i
$394$		0			0
$395$	4.43060	−	1.34401i	0.222928	−	0.0676244i
$396$		0			0
$397$	−23.9087	−	19.6214i	−1.19994	−	0.984768i	−0.999988	−	0.00496308i	$-0.998420\pi$
$397$	−23.9087	−	19.6214i	−1.19994	−	0.984768i	−0.199956	−	0.979805i	$-0.564080\pi$
$398$		0			0
$399$	−4.68937	−	1.94240i	−0.234762	−	0.0972417i
$400$		0			0
$401$	9.71764	−	4.02518i	0.485276	−	0.201008i	−0.126612	−	0.991952i	$-0.540410\pi$
$401$	9.71764	−	4.02518i	0.485276	−	0.201008i	0.611888	+	0.790945i	$0.290410\pi$
$402$		0			0
$403$	0.639087	+	6.48876i	0.0318352	+	0.323228i
$404$		0			0
$405$	−1.78142	+	3.33280i	−0.0885195	+	0.165608i
$406$		0			0
$407$	−3.52735	+	0.701633i	−0.174844	+	0.0347787i
$408$		0			0
$409$	−1.47698	+	7.42528i	−0.0730320	+	0.367157i	−0.999967	−	0.00806414i	$-0.997433\pi$
$409$	−1.47698	+	7.42528i	−0.0730320	+	0.367157i	0.926936	+	0.375221i	$0.122433\pi$
$410$		0			0
$411$	3.07250	−	31.1956i	0.151555	−	1.53877i
$412$		0			0
$413$	−1.59699	+	5.26456i	−0.0785826	+	0.259052i
$414$		0			0
$415$	−1.87999	−	1.87999i	−0.0922851	−	0.0922851i
$416$		0			0
$417$	13.0056	−	13.0056i	0.636888	−	0.636888i
$418$		0			0
$419$	−6.18349	−	1.87574i	−0.302083	−	0.0916360i	0.135604	−	0.990763i	$-0.456702\pi$
$419$	−6.18349	−	1.87574i	−0.302083	−	0.0916360i	−0.437688	+	0.899127i	$0.644202\pi$
$420$		0			0
$421$	25.9282	+	2.55371i	1.26366	+	0.124460i	0.707560	−	0.706653i	$-0.249796\pi$
$421$	25.9282	+	2.55371i	1.26366	+	0.124460i	0.556104	+	0.831113i	$0.312296\pi$
$422$		0			0
$423$	7.84109	+	1.55969i	0.381247	+	0.0758347i
$424$		0			0
$425$	−6.31654	−	31.7554i	−0.306397	−	1.54036i
$426$		0			0
$427$	0.259129	+	0.138507i	0.0125401	+	0.00670283i
$428$		0			0
$429$	2.97304	−	0.292819i	0.143540	−	0.0141374i
$430$		0			0
$431$	7.24994	+	17.5029i	0.349217	+	0.843085i	0.996713	+	0.0810158i	$0.0258164\pi$
$431$	7.24994	+	17.5029i	0.349217	+	0.843085i	−0.647496	+	0.762069i	$0.724184\pi$
$432$		0			0
$433$	7.35319	−	17.7522i	0.353372	−	0.853115i	−0.642827	−	0.766011i	$-0.722239\pi$
$433$	7.35319	−	17.7522i	0.353372	−	0.853115i	0.996199	−	0.0871040i	$-0.0277612\pi$
$434$		0			0
$435$	−1.90907	+	2.32621i	−0.0915329	+	0.111533i
$436$		0			0
$437$	7.25759	+	23.9251i	0.347177	+	1.14449i
$438$		0			0
$439$	−27.3025	−	18.2430i	−1.30308	−	0.870689i	−0.306382	−	0.951909i	$-0.599118\pi$
$439$	−27.3025	−	18.2430i	−1.30308	−	0.870689i	−0.996696	+	0.0812198i	$0.974118\pi$
$440$		0			0
$441$	7.73817	+	11.5810i	0.368484	+	0.551476i
$442$		0			0
$443$	−0.878309	+	0.720809i	−0.0417297	+	0.0342467i	−0.655027	−	0.755605i	$-0.727343\pi$
$443$	−0.878309	+	0.720809i	−0.0417297	+	0.0342467i	0.613297	+	0.789852i	$0.289843\pi$
$444$		0			0
$445$	0.216428	+	0.404908i	0.0102597	+	0.0191945i
$446$		0			0
$447$			36.7795i			1.73961i
$448$		0			0
$449$		−	15.0354i		−	0.709565i	−0.934949	−	0.354783i	$-0.884555\pi$
$449$		−	15.0354i		−	0.709565i	0.934949	−	0.354783i	$-0.115445\pi$
$450$		0			0
$451$	0.372949	+	0.697739i	0.0175615	+	0.0328552i
$452$		0			0
$453$	−35.6134	+	29.2272i	−1.67326	+	1.37321i
$454$		0			0
$455$	0.316532	+	0.473724i	0.0148393	+	0.0222085i
$456$		0			0
$457$	28.3536	+	18.9453i	1.32633	+	0.886224i	0.998291	−	0.0584410i	$-0.0186130\pi$
$457$	28.3536	+	18.9453i	1.32633	+	0.886224i	0.328037	+	0.944665i	$0.393613\pi$
$458$		0			0
$459$	4.12234	+	13.5895i	0.192415	+	0.634306i
$460$		0			0
$461$	−9.62074	+	11.7229i	−0.448083	+	0.545990i	−0.947242	−	0.320520i	$-0.896142\pi$
$461$	−9.62074	+	11.7229i	−0.448083	+	0.545990i	0.499159	+	0.866510i	$0.333642\pi$
$462$		0			0
$463$	2.27451	−	5.49115i	0.105705	−	0.255196i	−0.862173	−	0.506614i	$-0.830897\pi$
$463$	2.27451	−	5.49115i	0.105705	−	0.255196i	0.967879	+	0.251418i	$0.0808970\pi$
$464$		0			0
$465$	0.518715	+	1.25229i	0.0240548	+	0.0580735i
$466$		0			0
$467$	−2.27610	+	0.224176i	−0.105325	+	0.0103736i	−0.150542	−	0.988604i	$-0.548102\pi$
$467$	−2.27610	+	0.224176i	−0.105325	+	0.0103736i	0.0452172	+	0.998977i	$0.485602\pi$
$468$		0			0
$469$	1.40330	+	0.750080i	0.0647985	+	0.0346355i
$470$		0			0
$471$	3.28990	+	16.5395i	0.151591	+	0.762098i
$472$		0			0
$473$	−1.60620	−	0.319492i	−0.0738530	−	0.0146903i
$474$		0			0
$475$	−24.7896	−	2.44156i	−1.13742	−	0.112027i
$476$		0			0
$477$	−20.1322	−	6.10705i	−0.921792	−	0.279622i
$478$		0			0
$479$	−3.76471	+	3.76471i	−0.172014	+	0.172014i	−0.787864	−	0.615850i	$-0.788813\pi$
$479$	−3.76471	+	3.76471i	−0.172014	+	0.172014i	0.615850	+	0.787864i	$0.288813\pi$
$480$		0			0
$481$	−26.5972	−	26.5972i	−1.21273	−	1.21273i
$482$		0			0
$483$	−1.41437	+	4.66254i	−0.0643559	+	0.212153i
$484$		0			0
$485$	−0.0597358	+	0.606507i	−0.00271246	+	0.0275401i
$486$		0			0
$487$	−3.17960	+	15.9849i	−0.144081	+	0.724347i	0.839425	+	0.543475i	$0.182892\pi$
$487$	−3.17960	+	15.9849i	−0.144081	+	0.724347i	−0.983507	+	0.180871i	$0.942108\pi$
$488$		0			0
$489$	6.00516	−	1.19450i	0.271563	−	0.0540172i
$490$		0			0
$491$	19.6364	−	36.7371i	0.886178	−	1.65792i	0.142077	−	0.989856i	$-0.454622\pi$
$491$	19.6364	−	36.7371i	0.886178	−	1.65792i	0.744101	−	0.668067i	$-0.232878\pi$
$492$		0			0
$493$	2.52377	+	25.6243i	0.113665	+	1.15406i
$494$		0			0
$495$	0.232722	−	0.0963966i	0.0104601	−	0.00433271i
$496$		0			0
$497$	5.77817	+	2.39340i	0.259186	+	0.107358i
$498$		0			0
$499$	−17.8372	−	14.6386i	−0.798502	−	0.655314i	0.143976	−	0.989581i	$-0.454011\pi$
$499$	−17.8372	−	14.6386i	−0.798502	−	0.655314i	−0.942478	+	0.334267i	$0.891511\pi$
$500$		0			0
$501$	30.6330	−	9.29243i	1.36858	−	0.415155i
$502$		0			0
$503$	1.37760	−	2.06172i	0.0614240	−	0.0919275i	−0.799486	−	0.600684i	$-0.794895\pi$
$503$	1.37760	−	2.06172i	0.0614240	−	0.0919275i	0.860910	+	0.508757i	$0.169895\pi$
$504$		0			0
$505$	−2.49375	+	1.66627i	−0.110971	+	0.0741482i
$506$		0			0
$507$	1.29359	+	1.57624i	0.0574503	+	0.0700033i
$508$		0			0
$509$	−23.2974	+	12.4527i	−1.03264	+	0.551956i	−0.898485	−	0.439005i	$-0.855331\pi$
$509$	−23.2974	+	12.4527i	−1.03264	+	0.551956i	−0.134152	+	0.990961i	$0.542831\pi$
$510$		0			0
$511$	4.52978			0.200386
$512$		0			0
$513$	10.9255			0.482374
$514$		0			0
$515$	1.62780	−	0.870075i	0.0717293	−	0.0383401i
$516$		0			0
$517$	0.883440	+	1.07647i	0.0388536	+	0.0473433i
$518$		0			0
$519$	−4.28638	+	2.86407i	−0.188151	+	0.125719i
$520$		0			0
$521$	−1.99218	+	2.98151i	−0.0872789	+	0.130622i	−0.872540	−	0.488543i	$-0.837529\pi$
$521$	−1.99218	+	2.98151i	−0.0872789	+	0.130622i	0.785261	+	0.619165i	$0.212529\pi$
$522$		0			0
$523$	18.7039	−	5.67376i	0.817864	−	0.248096i	0.146487	−	0.989213i	$-0.453203\pi$
$523$	18.7039	−	5.67376i	0.817864	−	0.248096i	0.671377	+	0.741116i	$0.265703\pi$
$524$		0			0
$525$	−3.75250	−	3.07960i	−0.163772	−	0.134405i
$526$		0			0
$527$	10.7149	+	4.43827i	0.466749	+	0.193334i
$528$		0			0
$529$	0.923635	−	0.382582i	0.0401580	−	0.0166340i
$530$		0			0
$531$	2.49344	+	25.3163i	0.108206	+	1.09864i
$532$		0			0
$533$	−3.90056	+	7.29743i	−0.168952	+	0.316087i
$534$		0			0
$535$	−4.03733	+	0.803074i	−0.174549	+	0.0347199i
$536$		0			0
$537$	8.85422	−	44.5132i	0.382088	−	1.92088i
$538$		0			0
$539$	−0.237803	+	2.41445i	−0.0102429	+	0.103998i
$540$		0			0
$541$	−1.70907	+	5.63405i	−0.0734787	+	0.242227i	−0.985984	−	0.166837i	$-0.946645\pi$
$541$	−1.70907	+	5.63405i	−0.0734787	+	0.242227i	0.912506	+	0.409064i	$0.134145\pi$
$542$		0			0
$543$	−17.2343	−	17.2343i	−0.739596	−	0.739596i
$544$		0			0
$545$	3.99156	−	3.99156i	0.170980	−	0.170980i
$546$		0			0
$547$	37.7107	+	11.4394i	1.61239	+	0.489114i	0.962584	−	0.270985i	$-0.0873493\pi$
$547$	37.7107	+	11.4394i	1.61239	+	0.489114i	0.649808	+	0.760098i	$0.274849\pi$
$548$		0			0
$549$	1.35210	+	0.133170i	0.0577063	+	0.00568357i
$550$		0			0
$551$	19.4287	+	3.86461i	0.827691	+	0.164638i
$552$		0			0
$553$	−1.15875	−	5.82543i	−0.0492751	−	0.247722i
$554$		0			0
$555$	−6.89624	−	3.68612i	−0.292729	−	0.156467i
$556$		0			0
$557$	−11.6561	+	1.14802i	−0.493883	+	0.0486433i	−0.341893	−	0.939739i	$-0.611068\pi$
$557$	−11.6561	+	1.14802i	−0.493883	+	0.0486433i	−0.151990	+	0.988382i	$0.548568\pi$
$558$		0			0
$559$	−6.55453	−	15.8240i	−0.277227	−	0.669285i
$560$		0			0
$561$	2.03354	−	4.90939i	0.0858560	−	0.207275i
$562$		0			0
$563$	−9.56861	+	11.6594i	−0.403269	+	0.491384i	−0.934560	−	0.355805i	$-0.884207\pi$
$563$	−9.56861	+	11.6594i	−0.403269	+	0.491384i	0.531292	+	0.847189i	$0.321707\pi$
$564$		0			0
$565$	−0.683825	−	2.25427i	−0.0287687	−	0.0948378i
$566$		0			0
$567$	4.03091	+	2.69337i	0.169282	+	0.113111i
$568$		0			0
$569$	11.2957	+	16.9052i	0.473541	+	0.708704i	0.988952	−	0.148239i	$-0.0473606\pi$
$569$	11.2957	+	16.9052i	0.473541	+	0.708704i	−0.515411	+	0.856943i	$0.672361\pi$
$570$		0			0
$571$	18.8129	−	15.4393i	0.787295	−	0.646116i	−0.152327	−	0.988330i	$-0.548677\pi$
$571$	18.8129	−	15.4393i	0.787295	−	0.646116i	0.939622	+	0.342214i	$0.111177\pi$
$572$		0			0
$573$	−12.4019	−	23.2024i	−0.518098	−	0.969293i
$574$		0			0
$575$			23.9113i			0.997172i
$576$		0			0
$577$			42.6044i			1.77364i	0.462112	+	0.886821i	$0.347092\pi$
$577$			42.6044i			1.77364i	−0.462112	+	0.886821i	$0.652908\pi$
$578$		0			0
$579$	−13.8627	−	25.9353i	−0.576115	−	1.07783i
$580$		0			0
$581$	−2.63653	+	2.16374i	−0.109382	+	0.0897672i
$582$		0			0
$583$	−2.03593	−	3.04698i	−0.0843194	−	0.126193i
$584$		0			0
$585$	2.19051	+	1.46365i	0.0905665	+	0.0605146i
$586$		0			0
$587$	4.33392	+	14.2870i	0.178880	+	0.589689i	0.999825	+	0.0186820i	$0.00594700\pi$
$587$	4.33392	+	14.2870i	0.178880	+	0.589689i	−0.820945	+	0.571007i	$0.806553\pi$
$588$		0			0
$589$	5.66050	−	6.89734i	0.233237	−	0.284200i
$590$		0			0
$591$	−9.02932	+	21.7987i	−0.371417	+	0.896679i
$592$		0			0
$593$	−6.02980	−	14.5572i	−0.247614	−	0.597794i	0.750386	−	0.661000i	$-0.229868\pi$
$593$	−6.02980	−	14.5572i	−0.247614	−	0.597794i	−0.998001	+	0.0632058i	$0.979868\pi$
$594$		0			0
$595$	1.00855	−	0.0993337i	0.0413466	−	0.00407229i
$596$		0			0
$597$	−14.2274	−	7.60470i	−0.582289	−	0.311240i
$598$		0			0
$599$	0.656841	+	3.30216i	0.0268378	+	0.134923i	0.991881	−	0.127167i	$-0.0405884\pi$
$599$	0.656841	+	3.30216i	0.0268378	+	0.134923i	−0.965044	+	0.262090i	$0.915588\pi$
$600$		0			0
$601$	7.04422	+	1.40118i	0.287340	+	0.0571554i	0.336656	−	0.941628i	$-0.390704\pi$
$601$	7.04422	+	1.40118i	0.287340	+	0.0571554i	−0.0493161	+	0.998783i	$0.515704\pi$
$602$		0			0
$603$	7.32226	+	0.721179i	0.298185	+	0.0293687i
$604$		0			0
$605$	−3.59059	−	1.08919i	−0.145978	−	0.0442821i
$606$		0			0
$607$	−11.7782	+	11.7782i	−0.478063	+	0.478063i	−0.904512	−	0.426449i	$-0.859764\pi$
$607$	−11.7782	+	11.7782i	−0.478063	+	0.478063i	0.426449	+	0.904512i	$0.359764\pi$
$608$		0			0
$609$	2.72976	+	2.72976i	0.110615	+	0.110615i
$610$		0			0
$611$	−4.22785	+	13.9373i	−0.171040	+	0.563845i
$612$		0			0
$613$	−2.92844	+	29.7330i	−0.118279	+	1.20090i	0.734492	+	0.678617i	$0.237421\pi$
$613$	−2.92844	+	29.7330i	−0.118279	+	1.20090i	−0.852771	+	0.522286i	$0.825079\pi$
$614$		0			0
$615$	−0.335588	+	1.68712i	−0.0135322	+	0.0680311i
$616$		0			0
$617$	−7.34064	+	1.46014i	−0.295523	+	0.0587832i	−0.340625	−	0.940199i	$-0.610639\pi$
$617$	−7.34064	+	1.46014i	−0.295523	+	0.0587832i	0.0451021	+	0.998982i	$0.485639\pi$
$618$		0			0
$619$	17.3810	−	32.5176i	0.698603	−	1.30699i	−0.242921	−	0.970046i	$-0.578105\pi$
$619$	17.3810	−	32.5176i	0.698603	−	1.30699i	0.941523	−	0.336948i	$-0.109395\pi$
$620$		0			0
$621$	−1.02798	−	10.4372i	−0.0412512	−	0.418831i
$622$		0			0
$623$	0.544149	−	0.225394i	0.0218009	−	0.00903022i
$624$		0			0
$625$	−21.4597	−	8.88891i	−0.858389	−	0.355556i
$626$		0			0
$627$	−3.16024	−	2.59354i	−0.126208	−	0.103576i
$628$		0			0
$629$	−64.0253	+	19.4219i	−2.55286	+	0.774401i
$630$		0			0
$631$	−15.3389	+	22.9563i	−0.610632	+	0.913876i	−0.999974	−	0.00721781i	$-0.997702\pi$
$631$	−15.3389	+	22.9563i	−0.610632	+	0.913876i	0.389342	+	0.921093i	$0.372702\pi$
$632$		0			0
$633$	20.2933	−	13.5596i	0.806588	−	0.538945i
$634$		0			0
$635$	−2.18728	−	2.66520i	−0.0867994	−	0.105765i
$636$		0			0
$637$	−22.3780	+	11.9613i	−0.886650	+	0.473924i
$638$		0			0
$639$	28.9198			1.14405
$640$		0			0
$641$	−45.6832			−1.80438			−0.902190	−	0.431339i	$-0.858041\pi$
$641$	−45.6832			−1.80438			−0.902190	+	0.431339i	$0.858041\pi$
$642$		0			0
$643$	−27.9453	+	14.9370i	−1.10205	+	0.589060i	−0.919085	−	0.394059i	$-0.871070\pi$
$643$	−27.9453	+	14.9370i	−1.10205	+	0.589060i	−0.182968	+	0.983119i	$0.558570\pi$
$644$		0			0
$645$	−2.25887	−	2.75244i	−0.0889429	−	0.108377i
$646$		0			0
$647$	23.9049	−	15.9728i	0.939801	−	0.627955i	0.0115592	−	0.999933i	$-0.496321\pi$
$647$	23.9049	−	15.9728i	0.939801	−	0.627955i	0.928241	+	0.371979i	$0.121321\pi$
$648$		0			0
$649$	−2.46179	+	3.68434i	−0.0966339	+	0.144623i
$650$		0			0
$651$	1.66399	−	0.504766i	0.0652169	−	0.0197833i
$652$		0			0
$653$	29.9234	+	24.5575i	1.17099	+	0.961010i	0.999707	−	0.0242106i	$-0.00770722\pi$
$653$	29.9234	+	24.5575i	1.17099	+	0.961010i	0.171288	+	0.985221i	$0.445207\pi$
$654$		0			0
$655$	−4.16360	−	1.72462i	−0.162685	−	0.0673864i
$656$		0			0
$657$	19.3514	−	8.01561i	0.754970	−	0.312719i
$658$		0			0
$659$	−4.60662	−	46.7718i	−0.179448	−	1.82197i	−0.490348	−	0.871527i	$-0.663130\pi$
$659$	−4.60662	−	46.7718i	−0.179448	−	1.82197i	0.310899	−	0.950443i	$-0.399370\pi$
$660$		0			0
$661$	2.95131	−	5.52151i	0.114793	−	0.214762i	−0.817963	−	0.575270i	$-0.804897\pi$
$661$	2.95131	−	5.52151i	0.114793	−	0.214762i	0.932756	+	0.360509i	$0.117397\pi$
$662$		0			0
$663$	54.5084	−	10.8424i	2.11693	−	0.421084i
$664$		0			0
$665$	0.152108	−	0.764700i	0.00589851	−	0.0296538i
$666$		0			0
$667$	1.86385	−	18.9240i	0.0721685	−	0.732739i
$668$		0			0
$669$	16.9649	−	55.9259i	0.655903	−	2.16222i
$670$		0			0
$671$	0.167342	+	0.167342i	0.00646018	+	0.00646018i
$672$		0			0
$673$	−28.4872	+	28.4872i	−1.09810	+	1.09810i	−0.103470	+	0.994633i	$0.532995\pi$
$673$	−28.4872	+	28.4872i	−1.09810	+	1.09810i	−0.994633	+	0.103470i	$0.967005\pi$
$674$		0			0
$675$	9.99915	+	3.03321i	0.384868	+	0.116748i
$676$		0			0
$677$	42.7509	+	4.21059i	1.64305	+	0.161826i	0.876846	−	0.480772i	$-0.159644\pi$
$677$	42.7509	+	4.21059i	1.64305	+	0.161826i	0.766203	+	0.642598i	$0.222144\pi$
$678$		0			0
$679$	0.766801	+	0.152526i	0.0294271	+	0.00585342i
$680$		0			0
$681$	5.93015	+	29.8129i	0.227244	+	1.14243i
$682$		0			0
$683$	−1.98890	−	1.06309i	−0.0761030	−	0.0406779i	0.432906	−	0.901439i	$-0.357488\pi$
$683$	−1.98890	−	1.06309i	−0.0761030	−	0.0406779i	−0.509009	+	0.860761i	$0.669988\pi$
$684$		0			0
$685$	4.79194	−	0.471965i	0.183091	−	0.0180329i
$686$		0			0
$687$	−21.8670	−	52.7916i	−0.834277	−	2.01412i
$688$		0			0
$689$	14.6669	−	35.4091i	0.558766	−	1.34898i
$690$		0			0
$691$	−13.5076	+	16.4591i	−0.513854	+	0.626133i	−0.963705	−	0.266971i	$-0.913977\pi$
$691$	−13.5076	+	16.4591i	−0.513854	+	0.626133i	0.449850	+	0.893104i	$0.351477\pi$
$692$		0			0
$693$	−0.0938043	−	0.309231i	−0.00356333	−	0.0117467i
$694$		0			0
$695$	2.34915	+	1.56965i	0.0891083	+	0.0595403i
$696$		0			0
$697$	8.17701	+	12.2378i	0.309726	+	0.463538i
$698$		0			0
$699$	−18.2700	+	14.9938i	−0.691033	+	0.567116i
$700$		0			0
$701$	−12.6018	−	23.5762i	−0.475962	−	0.890462i	−0.999266	−	0.0383160i	$-0.987801\pi$
$701$	−12.6018	−	23.5762i	−0.475962	−	0.890462i	0.523304	−	0.852146i	$-0.324699\pi$
$702$		0			0
$703$			51.4742i			1.94139i
$704$		0			0
$705$			3.02779i			0.114033i
$706$		0			0
$707$	1.81372	+	3.39323i	0.0682120	+	0.127616i
$708$		0			0
$709$	4.77831	−	3.92146i	0.179453	−	0.147273i	−0.540379	−	0.841422i	$-0.681719\pi$
$709$	4.77831	−	3.92146i	0.179453	−	0.147273i	0.719832	+	0.694149i	$0.244219\pi$
$710$		0			0
$711$	−15.2585	−	22.8360i	−0.572240	−	0.856418i
$712$		0			0
$713$	−7.12165	−	4.75854i	−0.266708	−	0.178209i
$714$		0			0
$715$	0.133211	+	0.439137i	0.00498179	+	0.0164228i
$716$		0			0
$717$	−2.09701	+	2.55521i	−0.0783143	+	0.0954262i
$718$		0			0
$719$	18.7107	−	45.1716i	0.697790	−	1.68461i	−0.0306728	−	0.999529i	$-0.509765\pi$
$719$	18.7107	−	45.1716i	0.697790	−	1.68461i	0.728463	−	0.685085i	$-0.240235\pi$
$720$		0			0
$721$	−0.906121	−	2.18757i	−0.0337457	−	0.0814694i
$722$		0			0
$723$	−47.9587	+	4.72352i	−1.78360	+	0.175670i
$724$		0			0
$725$	16.7084	+	8.93084i	0.620536	+	0.331683i
$726$		0			0
$727$	−1.96119	−	9.85958i	−0.0727366	−	0.365672i	0.927224	−	0.374506i	$-0.122188\pi$
$727$	−1.96119	−	9.85958i	−0.0727366	−	0.365672i	−0.999961	+	0.00883474i	$0.997188\pi$
$728$		0			0
$729$	7.83503	+	1.55848i	0.290186	+	0.0577216i
$730$		0			0
$731$	−30.3194	−	2.98620i	−1.12140	−	0.110449i
$732$		0			0
$733$	0.526225	+	0.159628i	0.0194365	+	0.00589601i	0.299988	−	0.953943i	$-0.403017\pi$
$733$	0.526225	+	0.159628i	0.0194365	+	0.00589601i	−0.280551	+	0.959839i	$0.590517\pi$
$734$		0			0
$735$	−3.72999	+	3.72999i	−0.137583	+	0.137583i
$736$		0			0
$737$	0.906237	+	0.906237i	0.0333817	+	0.0333817i
$738$		0			0
$739$	−6.71778	+	22.1456i	−0.247118	+	0.814638i	0.742366	+	0.669994i	$0.233703\pi$
$739$	−6.71778	+	22.1456i	−0.247118	+	0.814638i	−0.989484	+	0.144643i	$0.953797\pi$
$740$		0			0
$741$	4.19096	−	42.5515i	0.153959	−	1.56317i
$742$		0			0
$743$	−4.71157	+	23.6867i	−0.172851	+	0.868979i	0.792869	+	0.609392i	$0.208586\pi$
$743$	−4.71157	+	23.6867i	−0.172851	+	0.868979i	−0.965720	+	0.259587i	$0.916414\pi$
$744$		0			0
$745$	−5.54112	+	1.10220i	−0.203011	+	0.0403814i
$746$		0			0
$747$	−7.43453	+	13.9090i	−0.272015	+	0.508905i
$748$		0			0
$749$	0.517605	+	5.25533i	0.0189129	+	0.192026i
$750$		0			0
$751$	34.1473	−	14.1443i	1.24605	−	0.516132i	0.340452	−	0.940262i	$-0.389420\pi$
$751$	34.1473	−	14.1443i	1.24605	−	0.516132i	0.905602	+	0.424130i	$0.139420\pi$
$752$		0			0
$753$	47.3700	+	19.6213i	1.72626	+	0.715039i
$754$		0			0
$755$	−5.47056	−	4.48957i	−0.199094	−	0.163392i
$756$		0			0
$757$	31.5273	−	9.56371i	1.14588	−	0.347599i	0.340434	−	0.940268i	$-0.389426\pi$
$757$	31.5273	−	9.56371i	1.14588	−	0.347599i	0.805446	+	0.592669i	$0.201926\pi$
$758$		0			0
$759$	−2.18028	+	3.26302i	−0.0791391	+	0.118440i
$760$		0			0
$761$	24.4004	−	16.3038i	0.884514	−	0.591013i	−0.0282046	−	0.999602i	$-0.508979\pi$
$761$	24.4004	−	16.3038i	0.884514	−	0.591013i	0.912719	+	0.408589i	$0.133979\pi$
$762$		0			0
$763$	−4.59402	−	5.59783i	−0.166315	−	0.202655i
$764$		0			0
$765$	4.13280	−	2.20903i	0.149422	−	0.0798676i
$766$		0			0
$767$	−46.3436			−1.67337
$768$		0			0
$769$	41.5998			1.50013			0.750064	−	0.661366i	$-0.230023\pi$
$769$	41.5998			1.50013			0.750064	+	0.661366i	$0.230023\pi$
$770$		0			0
$771$	56.8813	−	30.4037i	2.04853	−	1.09496i
$772$		0			0
$773$	30.7928	+	37.5212i	1.10754	+	1.34954i	0.930903	+	0.365267i	$0.119022\pi$
$773$	30.7928	+	37.5212i	1.10754	+	1.34954i	0.176638	+	0.984276i	$0.443478\pi$
$774$		0			0
$775$	7.09543	−	4.74101i	0.254875	−	0.170302i
$776$		0			0
$777$	−5.57311	+	8.34075i	−0.199934	+	0.299223i
$778$		0			0
$779$	10.8358	−	3.28702i	0.388235	−	0.117770i
$780$		0			0
$781$	3.89400	+	3.19572i	0.139338	+	0.114352i
$782$		0			0
$783$	−7.67712	−	3.17997i	−0.274358	−	0.113643i
$784$		0			0
$785$	−2.39321	+	0.991299i	−0.0854173	+	0.0353810i
$786$		0			0
$787$	2.36961	+	24.0591i	0.0844676	+	0.857614i	0.940297	+	0.340355i	$0.110547\pi$
$787$	2.36961	+	24.0591i	0.0844676	+	0.857614i	−0.855829	+	0.517258i	$0.826953\pi$
$788$		0			0
$789$	6.04136	−	11.3026i	0.215078	−	0.402383i
$790$		0			0
$791$	−2.96395	+	0.589567i	−0.105386	+	0.0209626i
$792$		0			0
$793$	−0.482874	+	2.42757i	−0.0171474	+	0.0862056i
$794$		0			0
$795$	0.780967	−	7.92929i	0.0276981	−	0.281223i
$796$		0			0
$797$	14.0551	−	46.3336i	0.497858	−	1.64122i	−0.243346	−	0.969940i	$-0.578245\pi$
$797$	14.0551	−	46.3336i	0.497858	−	1.64122i	0.741204	−	0.671279i	$-0.234255\pi$
$798$		0			0
$799$	18.3187	+	18.3187i	0.648071	+	0.648071i
$800$		0			0
$801$	1.92578	−	1.92578i	0.0680442	−	0.0680442i
$802$		0			0
$803$	3.49138	+	1.05910i	0.123208	+	0.0373748i
$804$		0			0
$805$	−0.744834	−	0.0733597i	−0.0262519	−	0.00258559i
$806$		0			0
$807$	−3.34332	−	0.665028i	−0.117690	−	0.0234101i
$808$		0			0
$809$	−8.07476	−	40.5946i	−0.283894	−	1.42723i	−0.814772	−	0.579782i	$-0.803138\pi$
$809$	−8.07476	−	40.5946i	−0.283894	−	1.42723i	0.530878	−	0.847448i	$-0.321862\pi$
$810$		0			0
$811$	23.0513	+	12.3212i	0.809440	+	0.432655i	0.823549	−	0.567246i	$-0.191991\pi$
$811$	23.0513	+	12.3212i	0.809440	+	0.432655i	−0.0141085	+	0.999900i	$0.504491\pi$
$812$		0			0
$813$	58.9230	−	5.80341i	2.06652	−	0.203534i
$814$		0			0
$815$	0.359922	+	0.868928i	0.0126075	+	0.0304372i
$816$		0			0
$817$	−8.96973	+	21.6548i	−0.313811	+	0.757607i
$818$		0			0
$819$	2.14405	−	2.61253i	0.0749190	−	0.0912891i
$820$		0			0
$821$	−9.68297	−	31.9205i	−0.337938	−	1.11403i	−0.947087	−	0.320977i	$-0.895989\pi$
$821$	−9.68297	−	31.9205i	−0.337938	−	1.11403i	0.609149	−	0.793056i	$-0.291511\pi$
$822$		0			0
$823$	23.3392	+	15.5948i	0.813554	+	0.543599i	0.891321	−	0.453372i	$-0.149779\pi$
$823$	23.3392	+	15.5948i	0.813554	+	0.543599i	−0.0777674	+	0.996972i	$0.524779\pi$
$824$		0			0
$825$	−2.17225	−	3.25100i	−0.0756280	−	0.113185i
$826$		0			0
$827$	−8.73066	+	7.16507i	−0.303595	+	0.249154i	−0.773839	−	0.633383i	$-0.781666\pi$
$827$	−8.73066	+	7.16507i	−0.303595	+	0.249154i	0.470244	+	0.882536i	$0.344166\pi$
$828$		0			0
$829$	2.15888	+	4.03897i	0.0749809	+	0.140279i	0.916618	−	0.399764i	$-0.130908\pi$
$829$	2.15888	+	4.03897i	0.0749809	+	0.140279i	−0.841637	+	0.540043i	$0.818408\pi$
$830$		0			0
$831$		−	43.4793i		−	1.50828i
$832$		0			0
$833$			45.1344i			1.56381i
$834$		0			0
$835$	2.31798	+	4.33664i	0.0802170	+	0.150075i
$836$		0			0
$837$	−2.89331	+	2.37447i	−0.100007	+	0.0820738i
$838$		0			0
$839$	9.22350	+	13.8039i	0.318431	+	0.476565i	0.955810	−	0.293985i	$-0.0949816\pi$
$839$	9.22350	+	13.8039i	0.318431	+	0.476565i	−0.637379	+	0.770550i	$0.719982\pi$
$840$		0			0
$841$	11.5853	+	7.74108i	0.399495	+	0.266934i
$842$		0			0
$843$	5.92470	+	19.5311i	0.204057	+	0.672687i
$844$		0			0
$845$	−0.198707	+	0.242126i	−0.00683574	+	0.00832937i
$846$		0			0
$847$	−1.84203	+	4.44706i	−0.0632930	+	0.152803i
$848$		0			0
$849$	−9.20720	−	22.2281i	−0.315990	−	0.762868i
$850$		0			0
$851$	49.1735	−	4.84317i	1.68565	−	0.166022i
$852$		0			0
$853$	−6.96374	−	3.72220i	−0.238434	−	0.127446i	0.347853	−	0.937549i	$-0.386911\pi$
$853$	−6.96374	−	3.72220i	−0.238434	−	0.127446i	−0.586287	+	0.810103i	$0.699411\pi$
$854$		0			0
$855$	−0.703352	−	3.53599i	−0.0240541	−	0.120928i
$856$		0			0
$857$	−15.6791	−	3.11876i	−0.535586	−	0.106535i	−0.0801157	−	0.996786i	$-0.525529\pi$
$857$	−15.6791	−	3.11876i	−0.535586	−	0.106535i	−0.455471	+	0.890251i	$0.650529\pi$
$858$		0			0
$859$	−34.6074	−	3.40853i	−1.18079	−	0.116298i	−0.511489	−	0.859290i	$-0.670906\pi$
$859$	−34.6074	−	3.40853i	−1.18079	−	0.116298i	−0.669300	+	0.742992i	$0.733406\pi$
$860$		0			0
$861$	2.11170	+	0.640577i	0.0719666	+	0.0218308i
$862$		0			0
$863$	6.44788	−	6.44788i	0.219489	−	0.219489i	−0.588794	−	0.808283i	$-0.700397\pi$
$863$	6.44788	−	6.44788i	0.219489	−	0.219489i	0.808283	+	0.588794i	$0.200397\pi$
$864$		0			0
$865$	−0.559947	−	0.559947i	−0.0190388	−	0.0190388i
$866$		0			0
$867$	17.6100	−	58.0525i	0.598068	−	1.97157i
$868$		0			0
$869$	0.468912	−	4.76095i	0.0159068	−	0.161504i
$870$		0			0
$871$	−2.61499	+	13.1464i	−0.0886054	+	0.445450i
$872$		0			0
$873$	3.54571	−	0.705285i	0.120004	−	0.0238703i
$874$		0			0
$875$	0.711600	−	1.33131i	0.0240565	−	0.0450065i
$876$		0			0
$877$	3.95649	+	40.1710i	0.133601	+	1.35648i	0.795076	+	0.606510i	$0.207431\pi$
$877$	3.95649	+	40.1710i	0.133601	+	1.35648i	−0.661475	+	0.749967i	$0.730069\pi$
$878$		0			0
$879$	18.2058	−	7.54108i	0.614065	−	0.254354i
$880$		0			0
$881$	12.1498	+	5.03263i	0.409339	+	0.169554i	0.577844	−	0.816147i	$-0.303894\pi$
$881$	12.1498	+	5.03263i	0.409339	+	0.169554i	−0.168506	+	0.985701i	$0.553894\pi$
$882$		0			0
$883$	10.0211	+	8.22408i	0.337236	+	0.276762i	0.787735	−	0.616015i	$-0.211254\pi$
$883$	10.0211	+	8.22408i	0.337236	+	0.276762i	−0.450499	+	0.892777i	$0.648754\pi$
$884$		0			0
$885$	−9.21946	+	2.79669i	−0.309909	+	0.0940098i
$886$		0			0
$887$	26.2112	−	39.2278i	0.880085	−	1.31714i	−0.0675280	−	0.997717i	$-0.521511\pi$
$887$	26.2112	−	39.2278i	0.880085	−	1.31714i	0.947612	−	0.319422i	$-0.103489\pi$
$888$		0			0
$889$	−3.67763	+	2.45731i	−0.123344	+	0.0824157i
$890$		0			0
$891$	2.47714	+	3.01840i	0.0829873	+	0.101120i
$892$		0			0
$893$	17.5777	−	9.39550i	0.588216	−	0.314408i
$894$		0			0
$895$	6.97160			0.233035
$896$		0			0
$897$	−41.0440			−1.37042
$898$		0			0
$899$	−5.98503	+	3.19906i	−0.199612	+	0.106695i
$900$		0			0
$901$	−43.2488	−	52.6988i	−1.44083	−	1.75565i
$902$		0			0
$903$	−3.79800	+	2.53775i	−0.126390	+	0.0844509i
$904$		0			0
$905$	2.08002	−	3.11296i	0.0691421	−	0.103478i
$906$		0			0
$907$	−0.769492	+	0.233423i	−0.0255505	+	0.00775067i	−0.303034	−	0.952980i	$-0.598000\pi$
$907$	−0.769492	+	0.233423i	−0.0255505	+	0.00775067i	0.277484	+	0.960730i	$0.410500\pi$
$908$		0			0
$909$	13.7527	+	11.2866i	0.456149	+	0.374352i
$910$		0			0
$911$	−28.0619	−	11.6236i	−0.929733	−	0.385108i	−0.134156	−	0.990960i	$-0.542832\pi$
$911$	−28.0619	−	11.6236i	−0.929733	−	0.385108i	−0.795577	+	0.605852i	$0.792832\pi$
$912$		0			0
$913$	−2.53804	+	1.05129i	−0.0839968	+	0.0347926i
$914$		0			0
$915$	0.0504349	+	0.512074i	0.00166733	+	0.0169286i
$916$		0			0
$917$	−2.72531	+	5.09870i	−0.0899977	+	0.168374i
$918$		0			0
$919$	−46.5628	+	9.26192i	−1.53597	+	0.305523i	−0.889327	−	0.457273i	$-0.848826\pi$
$919$	−46.5628	+	9.26192i	−1.53597	+	0.305523i	−0.646640	+	0.762795i	$0.723826\pi$
$920$		0			0
$921$	0.260381	−	1.30902i	0.00857984	−	0.0431337i
$922$		0			0
$923$	−5.16404	+	52.4313i	−0.169976	+	1.72580i
$924$		0			0
$925$	−14.2906	+	47.1097i	−0.469871	+	1.54896i
$926$		0			0
$927$	−7.74197	−	7.74197i	−0.254280	−	0.254280i
$928$		0			0
$929$	−23.6982	+	23.6982i	−0.777514	+	0.777514i	−0.979408	−	0.201893i	$-0.935291\pi$
$929$	−23.6982	+	23.6982i	−0.777514	+	0.777514i	0.201893	+	0.979408i	$0.435291\pi$
$930$		0			0
$931$	33.2288	+	10.0798i	1.08903	+	0.330354i
$932$		0			0
$933$	−16.3668	−	1.61199i	−0.535826	−	0.0527742i
$934$		0			0
$935$	0.800579	+	0.159245i	0.0261817	+	0.00520787i
$936$		0			0
$937$	0.553058	+	2.78041i	0.0180676	+	0.0908320i	0.988767	−	0.149465i	$-0.0477551\pi$
$937$	0.553058	+	2.78041i	0.0180676	+	0.0908320i	−0.970699	+	0.240297i	$0.922755\pi$
$938$		0			0
$939$	34.0376	+	18.1935i	1.11078	+	0.593722i
$940$		0			0
$941$	19.8237	−	1.95246i	0.646233	−	0.0636484i	0.230409	−	0.973094i	$-0.425993\pi$
$941$	19.8237	−	1.95246i	0.646233	−	0.0636484i	0.415823	+	0.909445i	$0.363493\pi$
$942$		0			0
$943$	−4.15964	−	10.0423i	−0.135457	−	0.327021i
$944$		0			0
$945$	−0.125161	+	0.302166i	−0.00407149	+	0.00982945i
$946$		0			0
$947$	5.16522	−	6.29384i	0.167847	−	0.204522i	−0.682293	−	0.731079i	$-0.739017\pi$
$947$	5.16522	−	6.29384i	0.167847	−	0.204522i	0.850140	+	0.526557i	$0.176517\pi$
$948$		0			0
$949$	11.0768	+	36.5153i	0.359568	+	1.18534i
$950$		0			0
$951$	3.85586	+	2.57641i	0.125035	+	0.0835457i
$952$		0			0
$953$	−13.9965	−	20.9472i	−0.453391	−	0.678548i	0.532406	−	0.846489i	$-0.321288\pi$
$953$	−13.9965	−	20.9472i	−0.453391	−	0.678548i	−0.985797	+	0.167942i	$0.946288\pi$
$954$		0			0
$955$	3.12396	−	2.56377i	0.101089	−	0.0829617i
$956$		0			0
$957$	1.46576	+	2.74224i	0.0473812	+	0.0886439i
$958$		0			0
$959$		−	6.17709i		−	0.199469i
$960$		0			0
$961$		−	27.9432i		−	0.901395i
$962$		0			0
$963$	11.5107	+	21.5351i	0.370928	+	0.693958i
$964$		0			0
$965$	3.49193	−	2.86575i	0.112409	−	0.0922517i
$966$		0			0
$967$	−9.25371	−	13.8492i	−0.297579	−	0.445359i	0.652307	−	0.757955i	$-0.273801\pi$
$967$	−9.25371	−	13.8492i	−0.297579	−	0.445359i	−0.949886	+	0.312596i	$0.898801\pi$
$968$		0			0
$969$	−63.2373	−	42.2538i	−2.03148	−	1.35739i
$970$		0			0
$971$	−1.52465	−	5.02611i	−0.0489284	−	0.161295i	0.929072	−	0.369900i	$-0.120608\pi$
$971$	−1.52465	−	5.02611i	−0.0489284	−	0.161295i	−0.978000	+	0.208604i	$0.933108\pi$
$972$		0			0
$973$	2.29932	−	2.80173i	0.0737128	−	0.0898193i
$974$		0			0
$975$	15.6490	−	37.7801i	0.501170	−	1.20993i
$976$		0			0
$977$	16.0068	+	38.6438i	0.512102	+	1.23632i	0.942658	+	0.333760i	$0.108318\pi$
$977$	16.0068	+	38.6438i	0.512102	+	1.23632i	−0.430556	+	0.902564i	$0.641682\pi$
$978$		0			0
$979$	0.472109	−	0.0464987i	0.0150887	−	0.00148610i
$980$		0			0
$981$	−29.5314	−	15.7849i	−0.942866	−	0.503972i
$982$		0			0
$983$	0.961658	+	4.83458i	0.0306721	+	0.154199i	0.993086	−	0.117387i	$-0.0374518\pi$
$983$	0.961658	+	4.83458i	0.0306721	+	0.154199i	−0.962414	+	0.271586i	$0.912452\pi$
$984$		0			0
$985$	−3.55473	−	0.707081i	−0.113263	−	0.0225295i
$986$		0			0
$987$	3.86551	+	0.380719i	0.123040	+	0.0121184i
$988$		0			0
$989$	21.5309	+	6.53134i	0.684644	+	0.207684i
$990$		0			0
$991$	−7.41312	+	7.41312i	−0.235486	+	0.235486i	−0.814978	−	0.579492i	$-0.803251\pi$
$991$	−7.41312	+	7.41312i	−0.235486	+	0.235486i	0.579492	+	0.814978i	$0.303251\pi$
$992$		0			0
$993$	−2.56985	−	2.56985i	−0.0815517	−	0.0815517i
$994$		0			0
$995$	0.719346	−	2.37137i	0.0228048	−	0.0751773i
$996$		0			0
$997$	−1.91637	+	19.4573i	−0.0606921	+	0.616217i	0.915942	+	0.401310i	$0.131445\pi$
$997$	−1.91637	+	19.4573i	−0.0606921	+	0.616217i	−0.976634	+	0.214907i	$0.931055\pi$
$998$		0			0
$999$	4.21248	−	21.1776i	0.133277	−	0.670029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.497.12		240
4.3	odd	2		128.2.k.a.101.12	✓	240
128.19	odd	32		128.2.k.a.109.12	yes	240
128.109	even	32	inner	512.2.k.a.273.12		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.101.12	✓	240	4.3	odd	2
128.2.k.a.109.12	yes	240	128.19	odd	32
512.2.k.a.273.12		240	128.109	even	32	inner
512.2.k.a.497.12		240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.98130 - 1.05903i) q^{3} +(0.218926 + 0.266762i) q^{5} +(0.368096 - 0.245954i) q^{7} +(1.13730 - 1.70208i) q^{9} +(0.341220 - 0.103508i) q^{11} +(2.88278 + 2.36584i) q^{13} +(0.716264 + 0.296686i) q^{15} +(6.12855 - 2.53853i) q^{17} +(-0.500227 - 5.07889i) q^{19} +(0.468836 - 0.877130i) q^{21} +(-4.80482 + 0.955738i) q^{23} +(0.952218 - 4.78712i) q^{25} +(-0.209836 + 2.13050i) q^{27} +(-1.12675 + 3.71441i) q^{29} +(1.23628 + 1.23628i) q^{31} +(0.566441 - 0.566441i) q^{33} +(0.146197 + 0.0443482i) q^{35} +(-10.0376 - 0.988614i) q^{37} +(8.21714 + 1.63449i) q^{39} +(0.432861 + 2.17614i) q^{41} +(-4.05046 - 2.16502i) q^{43} +(0.703033 - 0.0692427i) q^{45} +(1.49454 + 3.60814i) q^{47} +(-2.60378 + 6.28609i) q^{49} +(9.45412 - 11.5199i) q^{51} +(-2.98330 - 9.83462i) q^{53} +(0.102314 + 0.0683639i) q^{55} +(-6.36977 - 9.53304i) q^{57} +(-9.60613 + 7.88354i) q^{59} +(0.312866 + 0.585330i) q^{61} -0.906251i q^{63} +1.28696i q^{65} +(1.69431 + 3.16984i) q^{67} +(-8.50763 + 6.98203i) q^{69} +(7.84873 + 11.7465i) q^{71} +(8.50764 + 5.68462i) q^{73} +(-3.18306 - 10.4931i) q^{75} +(0.100144 - 0.122025i) q^{77} +(5.13428 - 12.3952i) q^{79} +(4.19065 + 10.1171i) q^{81} +(-7.66719 + 0.755152i) q^{83} +(2.01888 + 1.07911i) q^{85} +(1.70122 + 8.55262i) q^{87} +(1.30486 + 0.259552i) q^{89} +(1.64303 + 0.161824i) q^{91} +(3.75869 + 1.14019i) q^{93} +(1.24534 - 1.24534i) q^{95} +(1.24876 + 1.24876i) q^{97} +(0.211889 - 0.698504i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35}+ \cdots + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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