LMFDB - Embedded newform 912.2.bh.f.239.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(239,912)] 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("912.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-2,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.12
Character	$\chi$	$=$	912.239
Dual form			912.2.bh.f.767.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63593 - 0.568988i) q^{3} +(0.164566 + 0.0950122i) q^{5} -0.883190i q^{7} +(2.35251 - 1.86164i) q^{9} +3.88483 q^{11} +(-2.04597 - 3.54372i) q^{13} +(0.323278 + 0.0617968i) q^{15} +(3.97390 + 2.29433i) q^{17} +(-3.03184 + 3.13176i) q^{19} +(-0.502525 - 1.44483i) q^{21} +(-1.39463 - 2.41558i) q^{23} +(-2.48195 - 4.29886i) q^{25} +(2.78927 - 4.38406i) q^{27} +(2.80681 - 1.62051i) q^{29} +4.38406i q^{31} +(6.35530 - 2.21042i) q^{33} +(0.0839138 - 0.145343i) q^{35} +0.128042 q^{37} +(-5.36338 - 4.63313i) q^{39} +(1.63972 + 0.946691i) q^{41} +(3.36531 + 1.94296i) q^{43} +(0.564021 - 0.0828466i) q^{45} +(-2.07366 - 3.59168i) q^{47} +6.21998 q^{49} +(7.80645 + 1.49225i) q^{51} +(11.2845 - 6.51511i) q^{53} +(0.639311 + 0.369107i) q^{55} +(-3.17793 + 6.84841i) q^{57} +(-4.94684 + 8.56818i) q^{59} +(-3.04597 - 5.27577i) q^{61} +(-1.64419 - 2.07771i) q^{63} -0.777567i q^{65} +(-12.7119 + 7.33924i) q^{67} +(-3.65595 - 3.15818i) q^{69} +(-4.43262 + 7.67752i) q^{71} +(2.37196 - 4.10835i) q^{73} +(-6.50628 - 5.62041i) q^{75} -3.43105i q^{77} +(0.305846 + 0.176580i) q^{79} +(2.06856 - 8.75906i) q^{81} -1.00091 q^{83} +(0.435979 + 0.755138i) q^{85} +(3.66968 - 4.24808i) q^{87} +(0.493698 - 0.285037i) q^{89} +(-3.12978 + 1.80698i) q^{91} +(2.49448 + 7.17199i) q^{93} +(-0.796493 + 0.227320i) q^{95} +(0.981945 - 1.70078i) q^{97} +(9.13909 - 7.23218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) $ 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$-1$

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
$3$	1.63593	−	0.568988i	0.944502	−	0.328505i
$3$	1.63593	−	0.568988i	0.944502	−	0.328505i
$4$		0			0
$5$	0.164566	+	0.0950122i	0.0735961	+	0.0424907i	0.536346	−	0.843998i	$-0.319804\pi$
$5$	0.164566	+	0.0950122i	0.0735961	+	0.0424907i	−0.462750	+	0.886489i	$0.653137\pi$
$6$		0			0
$7$		−	0.883190i		−	0.333814i	−0.985973	−	0.166907i	$-0.946622\pi$
$7$		−	0.883190i		−	0.333814i	0.985973	−	0.166907i	$-0.0533780\pi$
$8$		0			0
$9$	2.35251	−	1.86164i	0.784168	−	0.620548i
$10$		0			0
$11$	3.88483			1.17132			0.585661	−	0.810556i	$-0.300835\pi$
$11$	3.88483			1.17132			0.585661	+	0.810556i	$0.300835\pi$
$12$		0			0
$13$	−2.04597	−	3.54372i	−0.567449	−	0.982851i	−0.996817	−	0.0797210i	$-0.974597\pi$
$13$	−2.04597	−	3.54372i	−0.567449	−	0.982851i	0.429368	−	0.903130i	$-0.358736\pi$
$14$		0			0
$15$	0.323278	+	0.0617968i	0.0834701	+	0.0159559i
$16$		0			0
$17$	3.97390	+	2.29433i	0.963812	+	0.556457i	0.897344	−	0.441332i	$-0.145494\pi$
$17$	3.97390	+	2.29433i	0.963812	+	0.556457i	0.0664678	+	0.997789i	$0.478827\pi$
$18$		0			0
$19$	−3.03184	+	3.13176i	−0.695552	+	0.718476i
$19$	−3.03184	+	3.13176i	−0.695552	+	0.718476i
$20$		0			0
$21$	−0.502525	−	1.44483i	−0.109660	−	0.315288i
$22$		0			0
$23$	−1.39463	−	2.41558i	−0.290801	−	0.503683i	0.683198	−	0.730233i	$-0.260589\pi$
$23$	−1.39463	−	2.41558i	−0.290801	−	0.503683i	−0.973999	+	0.226550i	$0.927255\pi$
$24$		0			0
$25$	−2.48195	−	4.29886i	−0.496389	−	0.859771i
$26$		0			0
$27$	2.78927	−	4.38406i	0.536795	−	0.843713i
$28$		0			0
$29$	2.80681	−	1.62051i	0.521211	−	0.300921i	−0.216219	−	0.976345i	$-0.569372\pi$
$29$	2.80681	−	1.62051i	0.521211	−	0.300921i	0.737430	+	0.675424i	$0.236039\pi$
$30$		0			0
$31$			4.38406i			0.787400i	0.919239	+	0.393700i	$0.128805\pi$
$31$			4.38406i			0.787400i	−0.919239	+	0.393700i	$0.871195\pi$
$32$		0			0
$33$	6.35530	−	2.21042i	1.10632	−	0.384785i
$34$		0			0
$35$	0.0839138	−	0.145343i	0.0141840	−	0.0245675i
$36$		0			0
$37$	0.128042			0.0210500			0.0105250	−	0.999945i	$-0.496650\pi$
$37$	0.128042			0.0210500			0.0105250	+	0.999945i	$0.496650\pi$
$38$		0			0
$39$	−5.36338	−	4.63313i	−0.858829	−	0.741894i
$40$		0			0
$41$	1.63972	+	0.946691i	0.256081	+	0.147848i	0.622545	−	0.782584i	$-0.286099\pi$
$41$	1.63972	+	0.946691i	0.256081	+	0.147848i	−0.366465	+	0.930432i	$0.619432\pi$
$42$		0			0
$43$	3.36531	+	1.94296i	0.513204	+	0.296299i	0.734150	−	0.678987i	$-0.237581\pi$
$43$	3.36531	+	1.94296i	0.513204	+	0.296299i	−0.220945	+	0.975286i	$0.570914\pi$
$44$		0			0
$45$	0.564021	−	0.0828466i	0.0840793	−	0.0123500i
$46$		0			0
$47$	−2.07366	−	3.59168i	−0.302474	−	0.523901i	0.674221	−	0.738529i	$-0.264479\pi$
$47$	−2.07366	−	3.59168i	−0.302474	−	0.523901i	−0.976696	+	0.214628i	$0.931146\pi$
$48$		0			0
$49$	6.21998			0.888568
$50$		0			0
$51$	7.80645	+	1.49225i	1.09312	+	0.208957i
$52$		0			0
$53$	11.2845	−	6.51511i	1.55005	−	0.894919i	0.551909	−	0.833904i	$-0.313900\pi$
$53$	11.2845	−	6.51511i	1.55005	−	0.894919i	0.998137	−	0.0610148i	$-0.0194337\pi$
$54$		0			0
$55$	0.639311	+	0.369107i	0.0862047	+	0.0497703i
$56$		0			0
$57$	−3.17793	+	6.84841i	−0.420927	+	0.907094i
$58$		0			0
$59$	−4.94684	+	8.56818i	−0.644024	+	1.11548i	0.340502	+	0.940244i	$0.389403\pi$
$59$	−4.94684	+	8.56818i	−0.644024	+	1.11548i	−0.984526	+	0.175239i	$0.943930\pi$
$60$		0			0
$61$	−3.04597	−	5.27577i	−0.389996	−	0.675493i	0.602452	−	0.798155i	$-0.294190\pi$
$61$	−3.04597	−	5.27577i	−0.389996	−	0.675493i	−0.992449	+	0.122662i	$0.960857\pi$
$62$		0			0
$63$	−1.64419	−	2.07771i	−0.207148	−	0.261767i
$64$		0			0
$65$		−	0.777567i		−	0.0964453i
$66$		0			0
$67$	−12.7119	+	7.33924i	−1.55301	+	0.896631i	−0.555116	+	0.831773i	$0.687326\pi$
$67$	−12.7119	+	7.33924i	−1.55301	+	0.896631i	−0.997894	+	0.0648581i	$0.979341\pi$
$68$		0			0
$69$	−3.65595	−	3.15818i	−0.440125	−	0.380200i
$70$		0			0
$71$	−4.43262	+	7.67752i	−0.526055	+	0.911153i	0.473485	+	0.880802i	$0.342996\pi$
$71$	−4.43262	+	7.67752i	−0.526055	+	0.911153i	−0.999539	+	0.0303514i	$0.990337\pi$
$72$		0			0
$73$	2.37196	−	4.10835i	0.277617	−	0.480846i	−0.693175	−	0.720769i	$-0.743789\pi$
$73$	2.37196	−	4.10835i	0.277617	−	0.480846i	0.970792	+	0.239923i	$0.0771222\pi$
$74$		0			0
$75$	−6.50628	−	5.62041i	−0.751280	−	0.648989i
$76$		0			0
$77$		−	3.43105i		−	0.391004i
$78$		0			0
$79$	0.305846	+	0.176580i	0.0344104	+	0.0198669i	0.517107	−	0.855921i	$-0.327009\pi$
$79$	0.305846	+	0.176580i	0.0344104	+	0.0198669i	−0.482696	+	0.875788i	$0.660342\pi$
$80$		0			0
$81$	2.06856	−	8.75906i	0.229840	−	0.973228i
$82$		0			0
$83$	−1.00091			−0.109864			−0.0549318	−	0.998490i	$-0.517494\pi$
$83$	−1.00091			−0.109864			−0.0549318	+	0.998490i	$0.517494\pi$
$84$		0			0
$85$	0.435979	+	0.755138i	0.0472885	+	0.0819062i
$86$		0			0
$87$	3.66968	−	4.24808i	0.393431	−	0.455442i
$88$		0			0
$89$	0.493698	−	0.285037i	0.0523319	−	0.0302138i	−0.473606	−	0.880737i	$-0.657048\pi$
$89$	0.493698	−	0.285037i	0.0523319	−	0.0302138i	0.525938	+	0.850523i	$0.323715\pi$
$90$		0			0
$91$	−3.12978	+	1.80698i	−0.328090	+	0.189423i
$92$		0			0
$93$	2.49448	+	7.17199i	0.258665	+	0.743701i
$94$		0			0
$95$	−0.796493	+	0.227320i	−0.0817185	+	0.0233225i
$96$		0			0
$97$	0.981945	−	1.70078i	0.0997014	−	0.172688i	−0.811860	−	0.583853i	$-0.801545\pi$
$97$	0.981945	−	1.70078i	0.0997014	−	0.172688i	0.911561	+	0.411165i	$0.134878\pi$
$98$		0			0
$99$	9.13909	−	7.23218i	0.918513	−	0.726861i
$100$		0			0
$101$	−13.5976	+	7.85059i	−1.35301	+	0.781162i	−0.988670	−	0.150103i	$-0.952040\pi$
$101$	−13.5976	+	7.85059i	−1.35301	+	0.781162i	−0.364343	+	0.931265i	$0.618706\pi$
$102$		0			0
$103$			7.88493i			0.776925i	0.921465	+	0.388463i	$0.126994\pi$
$103$			7.88493i			0.776925i	−0.921465	+	0.388463i	$0.873006\pi$
$104$		0			0
$105$	0.0545783	−	0.285516i	0.00532630	−	0.0278635i
$106$		0			0
$107$	7.76967			0.751122			0.375561	−	0.926798i	$-0.377450\pi$
$107$	7.76967			0.751122			0.375561	+	0.926798i	$0.377450\pi$
$108$		0			0
$109$	−7.07388	+	12.2523i	−0.677555	+	1.17356i	0.298160	+	0.954516i	$0.403627\pi$
$109$	−7.07388	+	12.2523i	−0.677555	+	1.17356i	−0.975715	+	0.219043i	$0.929706\pi$
$110$		0			0
$111$	0.209468	−	0.0728545i	0.0198818	−	0.00691504i
$112$		0			0
$113$			16.6513i			1.56642i	0.621756	+	0.783211i	$0.286420\pi$
$113$			16.6513i			1.56642i	−0.621756	+	0.783211i	$0.713580\pi$
$114$		0			0
$115$		−	0.530029i		−	0.0494255i
$116$		0			0
$117$	−11.4103	−	4.52775i	−1.05488	−	0.418591i
$118$		0			0
$119$	2.02633	−	3.50971i	0.185753	−	0.321734i
$120$		0			0
$121$	4.09193			0.371994
$122$		0			0
$123$	3.22111	+	0.615737i	0.290438	+	0.0555191i
$124$		0			0
$125$		−	1.89338i		−	0.169349i
$126$		0			0
$127$	3.49086	−	2.01545i	0.309764	−	0.178842i	−0.337057	−	0.941484i	$-0.609432\pi$
$127$	3.49086	−	2.01545i	0.309764	−	0.178842i	0.646821	+	0.762642i	$0.276098\pi$
$128$		0			0
$129$	6.61091	+	1.26372i	0.582058	+	0.111264i
$130$		0			0
$131$	8.14962	−	14.1156i	0.712036	−	1.23328i	−0.252056	−	0.967713i	$-0.581107\pi$
$131$	8.14962	−	14.1156i	0.712036	−	1.23328i	0.964092	−	0.265569i	$-0.0855600\pi$
$132$		0			0
$133$	2.76594	+	2.67769i	0.239838	+	0.232185i
$134$		0			0
$135$	0.875558	−	0.456452i	0.0753560	−	0.0392852i
$136$		0			0
$137$	6.81691	−	3.93574i	0.582408	−	0.336253i	−0.179682	−	0.983725i	$-0.557507\pi$
$137$	6.81691	−	3.93574i	0.582408	−	0.336253i	0.762090	+	0.647472i	$0.224174\pi$
$138$		0			0
$139$	−14.2141	+	8.20649i	−1.20562	+	0.696065i	−0.961799	−	0.273755i	$-0.911734\pi$
$139$	−14.2141	+	8.20649i	−1.20562	+	0.696065i	−0.243821	+	0.969820i	$0.578401\pi$
$140$		0			0
$141$	−5.43598	−	4.69584i	−0.457792	−	0.395461i
$142$		0			0
$143$	−7.94824	−	13.7668i	−0.664665	−	1.15123i
$144$		0			0
$145$	0.615873			0.0511455
$146$		0			0
$147$	10.1754	−	3.53909i	0.839254	−	0.291899i
$148$		0			0
$149$	−17.8855	−	10.3262i	−1.46524	−	0.845956i	−0.465993	−	0.884789i	$-0.654303\pi$
$149$	−17.8855	−	10.3262i	−1.46524	−	0.845956i	−0.999246	+	0.0388328i	$0.987636\pi$
$150$		0			0
$151$			8.28797i			0.674465i	0.941421	+	0.337233i	$0.109491\pi$
$151$			8.28797i			0.674465i	−0.941421	+	0.337233i	$0.890509\pi$
$152$		0			0
$153$	13.6198	−	2.00056i	1.10110	−	0.161736i
$154$		0			0
$155$	−0.416539	+	0.721467i	−0.0334572	+	0.0579496i
$156$		0			0
$157$	−6.46389	+	11.1958i	−0.515875	+	0.893521i	0.483956	+	0.875093i	$0.339200\pi$
$157$	−6.46389	+	11.1958i	−0.515875	+	0.893521i	−0.999830	+	0.0184285i	$0.994134\pi$
$158$		0			0
$159$	14.7536	−	17.0790i	1.17004	−	1.35445i
$160$		0			0
$161$	−2.13341	+	1.23173i	−0.168137	+	0.0970737i
$162$		0			0
$163$		−	1.17314i		−	0.0918877i	−0.998944	−	0.0459439i	$-0.985370\pi$
$163$		−	1.17314i		−	0.0918877i	0.998944	−	0.0459439i	$-0.0146295\pi$
$164$		0			0
$165$	1.25588	+	0.240070i	0.0977704	+	0.0186894i
$166$		0			0
$167$	8.33122	+	14.4301i	0.644689	+	1.11663i	0.984373	+	0.176095i	$0.0563467\pi$
$167$	8.33122	+	14.4301i	0.644689	+	1.11663i	−0.339684	+	0.940540i	$0.610320\pi$
$168$		0			0
$169$	−1.87196	+	3.24233i	−0.143997	+	0.249410i
$170$		0			0
$171$	−1.30219	+	13.0117i	−0.0995813	+	0.995029i
$172$		0			0
$173$	−15.7521	−	9.09448i	−1.19761	−	0.691440i	−0.237588	−	0.971366i	$-0.576357\pi$
$173$	−15.7521	−	9.09448i	−1.19761	−	0.691440i	−0.960022	+	0.279926i	$0.909690\pi$
$174$		0			0
$175$	−3.79671	+	2.19203i	−0.287004	+	0.165702i
$176$		0			0
$177$	−3.21747	+	16.8316i	−0.241840	+	1.26514i
$178$		0			0
$179$	−0.833078			−0.0622672			−0.0311336	−	0.999515i	$-0.509912\pi$
$179$	−0.833078			−0.0622672			−0.0311336	+	0.999515i	$0.509912\pi$
$180$		0			0
$181$	5.07388	+	8.78822i	0.377138	+	0.653223i	0.990645	−	0.136467i	$-0.0435748\pi$
$181$	5.07388	+	8.78822i	0.377138	+	0.653223i	−0.613506	+	0.789690i	$0.710241\pi$
$182$		0			0
$183$	−7.98482	−	6.89765i	−0.590255	−	0.509889i
$184$		0			0
$185$	0.0210714	+	0.0121656i	0.00154920	+	0.000894431i
$186$		0			0
$187$	15.4379	+	8.91310i	1.12893	+	0.651790i
$188$		0			0
$189$	−3.87196	−	2.46346i	−0.281643	−	0.179190i
$190$		0			0
$191$	20.6144			1.49160			0.745802	−	0.666167i	$-0.232066\pi$
$191$	20.6144			1.49160			0.745802	+	0.666167i	$0.232066\pi$
$192$		0			0
$193$	−0.0820758	+	0.142159i	−0.00590794	+	0.0102329i	−0.868964	−	0.494875i	$-0.835214\pi$
$193$	−0.0820758	+	0.142159i	−0.00590794	+	0.0102329i	0.863056	+	0.505108i	$0.168547\pi$
$194$		0			0
$195$	−0.442426	−	1.27204i	−0.0316828	−	0.0910928i
$196$		0			0
$197$			16.4787i			1.17406i	0.809565	+	0.587031i	$0.199703\pi$
$197$			16.4787i			1.17406i	−0.809565	+	0.587031i	$0.800297\pi$
$198$		0			0
$199$	−13.6024	+	7.85332i	−0.964246	+	0.556707i	−0.897477	−	0.441061i	$-0.854602\pi$
$199$	−13.6024	+	7.85332i	−0.964246	+	0.556707i	−0.0667685	+	0.997768i	$0.521269\pi$
$200$		0			0
$201$	−16.6198	+	19.2394i	−1.17227	+	1.35704i
$202$		0			0
$203$	−1.43122	−	2.47894i	−0.100452	−	0.173988i
$204$		0			0
$205$	0.179894	+	0.311586i	0.0125644	+	0.0217621i
$206$		0			0
$207$	−7.77783	−	3.08635i	−0.540597	−	0.214516i
$208$		0			0
$209$	−11.7782	+	12.1664i	−0.814715	+	0.841566i
$210$		0			0
$211$	−5.09091	−	2.93924i	−0.350472	−	0.202345i	0.314421	−	0.949284i	$-0.398190\pi$
$211$	−5.09091	−	2.93924i	−0.350472	−	0.202345i	−0.664893	+	0.746938i	$0.731523\pi$
$212$		0			0
$213$	−2.88301	+	15.0820i	−0.197541	+	1.03340i
$214$		0			0
$215$	0.369210	+	0.639490i	0.0251799	+	0.0436129i
$216$		0			0
$217$	3.87196			0.262846
$218$		0			0
$219$	1.54274	−	8.07057i	0.104249	−	0.545359i
$220$		0			0
$221$		−	18.7765i		−	1.26304i
$222$		0			0
$223$	7.48344	+	4.32056i	0.501128	+	0.289326i	0.729179	−	0.684323i	$-0.239902\pi$
$223$	7.48344	+	4.32056i	0.501128	+	0.289326i	−0.228051	+	0.973649i	$0.573235\pi$
$224$		0			0
$225$	−13.8417	−	5.49258i	−0.922782	−	0.366172i
$226$		0			0
$227$	−15.5608			−1.03281			−0.516404	−	0.856345i	$-0.672730\pi$
$227$	−15.5608			−1.03281			−0.516404	+	0.856345i	$0.672730\pi$
$228$		0			0
$229$	−17.6599			−1.16700			−0.583500	−	0.812113i	$-0.698317\pi$
$229$	−17.6599			−1.16700			−0.583500	+	0.812113i	$0.698317\pi$
$230$		0			0
$231$	−1.95222	−	5.61294i	−0.128447	−	0.369304i
$232$		0			0
$233$	0.981453	+	0.566642i	0.0642971	+	0.0371220i	0.531804	−	0.846868i	$-0.321514\pi$
$233$	0.981453	+	0.566642i	0.0642971	+	0.0371220i	−0.467507	+	0.883989i	$0.654848\pi$
$234$		0			0
$235$		−	0.788092i		−	0.0514094i
$236$		0			0
$237$	0.600814	+	0.114850i	0.0390271	+	0.00746028i
$238$		0			0
$239$	−12.8508			−0.831248			−0.415624	−	0.909537i	$-0.636437\pi$
$239$	−12.8508			−0.831248			−0.415624	+	0.909537i	$0.636437\pi$
$240$		0			0
$241$	10.4639	+	18.1240i	0.674038	+	1.16747i	0.976749	+	0.214386i	$0.0687751\pi$
$241$	10.4639	+	18.1240i	0.674038	+	1.16747i	−0.302710	+	0.953083i	$0.597892\pi$
$242$		0			0
$243$	−1.59979	−	15.5061i	−0.102627	−	0.994720i
$244$		0			0
$245$	1.02360	+	0.590973i	0.0653952	+	0.0377559i
$246$		0			0
$247$	17.3011	+	4.33651i	1.10084	+	0.275926i
$248$		0			0
$249$	−1.63741	+	0.569504i	−0.103766	+	0.0360908i
$250$		0			0
$251$	5.19555	+	8.99896i	0.327941	+	0.568010i	0.982103	−	0.188344i	$-0.0603121\pi$
$251$	5.19555	+	8.99896i	0.327941	+	0.568010i	−0.654163	+	0.756354i	$0.726979\pi$
$252$		0			0
$253$	−5.41792	−	9.38412i	−0.340622	−	0.589975i
$254$		0			0
$255$	1.14289	+	0.987282i	0.0715708	+	0.0618260i
$256$		0			0
$257$	6.00002	−	3.46411i	0.374271	−	0.216085i	−0.301052	−	0.953608i	$-0.597338\pi$
$257$	6.00002	−	3.46411i	0.374271	−	0.216085i	0.675323	+	0.737522i	$0.264004\pi$
$258$		0			0
$259$		−	0.113086i		−	0.00702680i
$260$		0			0
$261$	3.58621	−	9.03754i	0.221981	−	0.559410i
$262$		0			0
$263$	−12.4648	+	21.5896i	−0.768611	+	1.33127i	0.169706	+	0.985495i	$0.445718\pi$
$263$	−12.4648	+	21.5896i	−0.768611	+	1.33127i	−0.938316	+	0.345778i	$0.887615\pi$
$264$		0			0
$265$	2.47606			0.152103
$266$		0			0
$267$	0.645470	−	0.747207i	0.0395022	−	0.0457283i
$268$		0			0
$269$	−22.5117	−	12.9972i	−1.37256	−	0.792451i	−0.381314	−	0.924445i	$-0.624528\pi$
$269$	−22.5117	−	12.9972i	−1.37256	−	0.792451i	−0.991250	+	0.131995i	$0.957862\pi$
$270$		0			0
$271$	5.02059	+	2.89864i	0.304979	+	0.176080i	0.644678	−	0.764455i	$-0.276992\pi$
$271$	5.02059	+	2.89864i	0.304979	+	0.176080i	−0.339698	+	0.940534i	$0.610325\pi$
$272$		0			0
$273$	−4.09193	+	4.73689i	−0.247655	+	0.286689i
$274$		0			0
$275$	−9.64195	−	16.7003i	−0.581431	−	1.00707i
$276$		0			0
$277$	11.0919			0.666450			0.333225	−	0.942847i	$-0.391863\pi$
$277$	11.0919			0.666450			0.333225	+	0.942847i	$0.391863\pi$
$278$		0			0
$279$	8.16156	+	10.3135i	0.488620	+	0.617454i
$280$		0			0
$281$	8.44149	−	4.87370i	0.503577	−	0.290741i	−0.226612	−	0.973985i	$-0.572765\pi$
$281$	8.44149	−	4.87370i	0.503577	−	0.290741i	0.730190	+	0.683245i	$0.239432\pi$
$282$		0			0
$283$	−26.1064	−	15.0725i	−1.55186	−	0.895969i	−0.997990	−	0.0633678i	$-0.979816\pi$
$283$	−26.1064	−	15.0725i	−1.55186	−	0.895969i	−0.553873	−	0.832601i	$-0.686851\pi$
$284$		0			0
$285$	−1.17366	+	0.825073i	−0.0695217	+	0.0488731i
$286$		0			0
$287$	0.836108	−	1.44818i	0.0493539	−	0.0854835i
$288$		0			0
$289$	2.02791	+	3.51245i	0.119289	+	0.206614i
$290$		0			0
$291$	0.638666	−	3.34106i	0.0374393	−	0.195857i
$292$		0			0
$293$			9.93742i			0.580550i	0.956943	+	0.290275i	$0.0937469\pi$
$293$			9.93742i			0.580550i	−0.956943	+	0.290275i	$0.906253\pi$
$294$		0			0
$295$	−1.62816	+	0.940021i	−0.0947954	+	0.0547301i
$296$		0			0
$297$	10.8358	−	17.0313i	0.628760	−	0.988259i
$298$		0			0
$299$	−5.70675	+	9.88438i	−0.330030	+	0.571629i
$300$		0			0
$301$	1.71600	−	2.97221i	0.0989088	−	0.171315i
$302$		0			0
$303$	−17.7778	+	20.5799i	−1.02131	+	1.18228i
$304$		0			0
$305$		−	1.15762i		−	0.0662849i
$306$		0			0
$307$	−21.0978	−	12.1808i	−1.20412	−	0.695197i	−0.242649	−	0.970114i	$-0.578016\pi$
$307$	−21.0978	−	12.1808i	−1.20412	−	0.695197i	−0.961468	+	0.274917i	$0.911350\pi$
$308$		0			0
$309$	4.48643	+	12.8992i	0.255224	+	0.733807i
$310$		0			0
$311$	24.1911			1.37175			0.685876	−	0.727718i	$-0.259419\pi$
$311$	24.1911			1.37175			0.685876	+	0.727718i	$0.259419\pi$
$312$		0			0
$313$	0.0180546	+	0.0312715i	0.00102051	+	0.00176757i	0.866535	−	0.499116i	$-0.166342\pi$
$313$	0.0180546	+	0.0312715i	0.00102051	+	0.00176757i	−0.865515	+	0.500884i	$0.833008\pi$
$314$		0			0
$315$	−0.0731693	−	0.498138i	−0.00412262	−	0.0280669i
$316$		0			0
$317$	19.2323	−	11.1038i	1.08019	−	0.623650i	0.149245	−	0.988800i	$-0.452316\pi$
$317$	19.2323	−	11.1038i	1.08019	−	0.623650i	0.930949	+	0.365150i	$0.118982\pi$
$318$		0			0
$319$	10.9040	−	6.29542i	0.610506	−	0.352476i
$320$		0			0
$321$	12.7106	−	4.42085i	0.709436	−	0.246748i
$322$		0			0
$323$	−19.2335	+	5.48926i	−1.07018	+	0.305430i
$324$		0			0
$325$	−10.1560	+	17.5906i	−0.563351	+	0.975753i
$326$		0			0
$327$	−4.60092	+	24.0688i	−0.254431	+	1.33101i
$328$		0			0
$329$	−3.17214	+	1.83144i	−0.174886	+	0.100970i
$330$		0			0
$331$		−	10.3895i		−	0.571060i	−0.958370	−	0.285530i	$-0.907830\pi$
$331$		−	10.3895i		−	0.571060i	0.958370	−	0.285530i	$-0.0921696\pi$
$332$		0			0
$333$	0.301220	−	0.238369i	0.0165068	−	0.0130625i
$334$		0			0
$335$	−2.78927			−0.152394
$336$		0			0
$337$	4.13790	−	7.16705i	0.225406	−	0.390414i	−0.731035	−	0.682340i	$-0.760963\pi$
$337$	4.13790	−	7.16705i	0.225406	−	0.390414i	0.956441	+	0.291925i	$0.0942959\pi$
$338$		0			0
$339$	9.47439	+	27.2403i	0.514578	+	1.47949i
$340$		0			0
$341$			17.0313i			0.922299i
$342$		0			0
$343$		−	11.6758i		−	0.630431i
$344$		0			0
$345$	−0.301580	−	0.867088i	−0.0162365	−	0.0466825i
$346$		0			0
$347$	−5.11467	+	8.85887i	−0.274570	+	0.475569i	−0.970027	−	0.242999i	$-0.921869\pi$
$347$	−5.11467	+	8.85887i	−0.274570	+	0.475569i	0.695457	+	0.718568i	$0.255202\pi$
$348$		0			0
$349$	−20.6356			−1.10460			−0.552299	−	0.833646i	$-0.686249\pi$
$349$	−20.6356			−1.10460			−0.552299	+	0.833646i	$0.686249\pi$
$350$		0			0
$351$	−21.2426	−	0.914746i	−1.13385	−	0.0488255i
$352$		0			0
$353$			25.4486i			1.35449i	0.735757	+	0.677245i	$0.236826\pi$
$353$			25.4486i			1.35449i	−0.735757	+	0.677245i	$0.763174\pi$
$354$		0			0
$355$	−1.45892	+	0.842305i	−0.0774312	+	0.0447049i
$356$		0			0
$357$	1.31794	−	6.89458i	0.0697530	−	0.364900i
$358$		0			0
$359$	8.07948	−	13.9941i	0.426419	−	0.738579i	−0.570133	−	0.821552i	$-0.693108\pi$
$359$	8.07948	−	13.9941i	0.426419	−	0.738579i	0.996552	+	0.0829734i	$0.0264417\pi$
$360$		0			0
$361$	−0.615873	−	18.9900i	−0.0324144	−	0.999475i
$362$		0			0
$363$	6.69410	−	2.32826i	0.351349	−	0.122202i
$364$		0			0
$365$	0.780687	−	0.450730i	0.0408630	−	0.0235923i
$366$		0			0
$367$	20.0266	−	11.5624i	1.04538	−	0.603551i	0.124029	−	0.992279i	$-0.460419\pi$
$367$	20.0266	−	11.5624i	1.04538	−	0.603551i	0.921353	+	0.388727i	$0.127085\pi$
$368$		0			0
$369$	5.61984	−	0.825475i	0.292557	−	0.0429725i
$370$		0			0
$371$	−5.75408	−	9.96636i	−0.298737	−	0.517428i
$372$		0			0
$373$	21.4597			1.11114			0.555570	−	0.831470i	$-0.312500\pi$
$373$	21.4597			1.11114			0.555570	+	0.831470i	$0.312500\pi$
$374$		0			0
$375$	−1.07731	−	3.09743i	−0.0556322	−	0.159951i
$376$		0			0
$377$	−11.4853	−	6.63102i	−0.591521	−	0.341515i
$378$		0			0
$379$			32.0384i			1.64570i	0.568256	+	0.822852i	$0.307618\pi$
$379$			32.0384i			1.64570i	−0.568256	+	0.822852i	$0.692382\pi$
$380$		0			0
$381$	4.56402	−	5.28338i	0.233822	−	0.270676i
$382$		0			0
$383$	8.82865	−	15.2917i	0.451123	−	0.781368i	−0.547333	−	0.836915i	$-0.684357\pi$
$383$	8.82865	−	15.2917i	0.451123	−	0.781368i	0.998456	+	0.0555472i	$0.0176903\pi$
$384$		0			0
$385$	0.325991	−	0.564633i	0.0166141	−	0.0287764i
$386$		0			0
$387$	11.5340	−	1.69418i	0.586306	−	0.0861200i
$388$		0			0
$389$	6.10731	−	3.52606i	0.309653	−	0.178778i	−0.337118	−	0.941462i	$-0.609452\pi$
$389$	6.10731	−	3.52606i	0.309653	−	0.178778i	0.646771	+	0.762684i	$0.276119\pi$
$390$		0			0
$391$		−	12.7990i		−	0.647274i
$392$		0			0
$393$	5.30059	−	27.7290i	0.267379	−	1.39875i
$394$		0			0
$395$	0.0335546	+	0.0581183i	0.00168831	+	0.00292425i
$396$		0			0
$397$	7.26594	−	12.5850i	0.364667	−	0.631622i	−0.624056	−	0.781380i	$-0.714516\pi$
$397$	7.26594	−	12.5850i	0.364667	−	0.631622i	0.988723	+	0.149758i	$0.0478494\pi$
$398$		0			0
$399$	6.04845	+	2.80672i	0.302801	+	0.140512i
$400$		0			0
$401$	16.7487	+	9.66986i	0.836389	+	0.482890i	0.856035	−	0.516917i	$-0.172921\pi$
$401$	16.7487	+	9.66986i	0.836389	+	0.482890i	−0.0196460	+	0.999807i	$0.506254\pi$
$402$		0			0
$403$	15.5359	−	8.96964i	0.773897	−	0.446810i
$404$		0			0
$405$	1.17263	−	1.24490i	0.0582685	−	0.0618598i
$406$		0			0
$407$	0.497423			0.0246563
$408$		0			0
$409$	−12.3300	−	21.3561i	−0.609677	−	1.05599i	−0.991293	−	0.131671i	$-0.957966\pi$
$409$	−12.3300	−	21.3561i	−0.609677	−	1.05599i	0.381616	−	0.924321i	$-0.375368\pi$
$410$		0			0
$411$	8.91256	−	10.3173i	0.439624	−	0.508916i
$412$		0			0
$413$	7.56734	+	4.36900i	0.372364	+	0.214985i
$414$		0			0
$415$	−0.164715	−	0.0950983i	−0.00808554	−	0.00466819i
$416$		0			0
$417$	−18.5837	+	21.5128i	−0.910049	+	1.05349i
$418$		0			0
$419$	27.0536			1.32165			0.660826	−	0.750539i	$-0.270206\pi$
$419$	27.0536			1.32165			0.660826	+	0.750539i	$0.270206\pi$
$420$		0			0
$421$	8.81779	−	15.2729i	0.429753	−	0.744354i	−0.567098	−	0.823650i	$-0.691934\pi$
$421$	8.81779	−	15.2729i	0.429753	−	0.744354i	0.996851	+	0.0792963i	$0.0252673\pi$
$422$		0			0
$423$	−11.5647	−	4.58904i	−0.562297	−	0.223127i
$424$		0			0
$425$		−	22.7776i		−	1.10488i
$426$		0			0
$427$	−4.65951	+	2.69017i	−0.225489	+	0.130186i
$428$		0			0
$429$	−20.8358	−	17.9989i	−1.00596	−	0.868997i
$430$		0			0
$431$	8.84242	+	15.3155i	0.425924	+	0.737723i	0.996506	−	0.0835180i	$-0.0266156\pi$
$431$	8.84242	+	15.3155i	0.425924	+	0.737723i	−0.570582	+	0.821241i	$0.693282\pi$
$432$		0			0
$433$	−4.00986	−	6.94528i	−0.192701	−	0.333769i	0.753443	−	0.657513i	$-0.228392\pi$
$433$	−4.00986	−	6.94528i	−0.192701	−	0.333769i	−0.946145	+	0.323744i	$0.895058\pi$
$434$		0			0
$435$	1.00752	−	0.350425i	0.0483070	−	0.0168016i
$436$		0			0
$437$	11.7933	+	2.95599i	0.564151	+	0.141404i
$438$		0			0
$439$	32.2680	+	18.6299i	1.54007	+	0.889159i	0.998834	+	0.0482867i	$0.0153761\pi$
$439$	32.2680	+	18.6299i	1.54007	+	0.889159i	0.541234	+	0.840872i	$0.317957\pi$
$440$		0			0
$441$	14.6325	−	11.5794i	0.696787	−	0.551399i
$442$		0			0
$443$	−10.1760	−	17.6253i	−0.483474	−	0.837402i	0.516346	−	0.856380i	$-0.327292\pi$
$443$	−10.1760	−	17.6253i	−0.483474	−	0.837402i	−0.999820	+	0.0189785i	$0.993959\pi$
$444$		0			0
$445$	0.108328			0.00513523
$446$		0			0
$447$	−35.1349	−	6.71626i	−1.66182	−	0.317668i
$448$		0			0
$449$		−	19.9098i		−	0.939601i	−0.882773	−	0.469800i	$-0.844326\pi$
$449$		−	19.9098i		−	0.939601i	0.882773	−	0.469800i	$-0.155674\pi$
$450$		0			0
$451$	6.37003	+	3.67774i	0.299953	+	0.173178i
$452$		0			0
$453$	4.71576	+	13.5585i	0.221566	+	0.637034i
$454$		0			0
$455$	−0.686740			−0.0321948
$456$		0			0
$457$	−6.52394			−0.305177			−0.152589	−	0.988290i	$-0.548761\pi$
$457$	−6.52394			−0.305177			−0.152589	+	0.988290i	$0.548761\pi$
$458$		0			0
$459$	21.1428	−	11.0223i	0.986859	−	0.514477i
$460$		0			0
$461$	31.5193	+	18.1977i	1.46800	+	0.847551i	0.999358	−	0.0358363i	$-0.0114095\pi$
$461$	31.5193	+	18.1977i	1.46800	+	0.847551i	0.468644	+	0.883387i	$0.344743\pi$
$462$		0			0
$463$		−	32.5227i		−	1.51146i	−0.654885	−	0.755728i	$-0.727283\pi$
$463$		−	32.5227i		−	1.51146i	0.654885	−	0.755728i	$-0.272717\pi$
$464$		0			0
$465$	−0.270921	+	1.41727i	−0.0125637	+	0.0657244i
$466$		0			0
$467$	36.7062			1.69856			0.849281	−	0.527941i	$-0.177036\pi$
$467$	36.7062			1.69856			0.849281	+	0.527941i	$0.177036\pi$
$468$		0			0
$469$	6.48195	+	11.2271i	0.299308	+	0.518417i
$470$		0			0
$471$	−4.20417	+	21.9934i	−0.193718	+	1.01340i
$472$		0			0
$473$	13.0737	+	7.54808i	0.601127	+	0.347061i
$474$		0			0
$475$	20.9879	+	5.26059i	0.962989	+	0.241372i
$476$		0			0
$477$	14.4180	−	36.3346i	0.660156	−	1.66365i
$478$		0			0
$479$	−2.90674	−	5.03462i	−0.132812	−	0.230038i	0.791947	−	0.610589i	$-0.209067\pi$
$479$	−2.90674	−	5.03462i	−0.132812	−	0.230038i	−0.924760	+	0.380552i	$0.875734\pi$
$480$		0			0
$481$	−0.261970	−	0.453746i	−0.0119448	−	0.0206890i
$482$		0			0
$483$	−2.78927	+	3.22890i	−0.126916	+	0.146920i
$484$		0			0
$485$	0.323190	−	0.186594i	0.0146753	−	0.00847278i
$486$		0			0
$487$		−	13.0072i		−	0.589413i	−0.955588	−	0.294706i	$-0.904778\pi$
$487$		−	13.0072i		−	0.589413i	0.955588	−	0.294706i	$-0.0952218\pi$
$488$		0			0
$489$	−0.667505	−	1.91918i	−0.0301856	−	0.0867882i
$490$		0			0
$491$	−11.2960	+	19.5653i	−0.509783	+	0.882970i	0.490153	+	0.871637i	$0.336941\pi$
$491$	−11.2960	+	19.5653i	−0.509783	+	0.882970i	−0.999936	+	0.0113335i	$0.996392\pi$
$492$		0			0
$493$	14.8720			0.669799
$494$		0			0
$495$	2.19113	−	0.321845i	0.0984839	−	0.0144659i
$496$		0			0
$497$	6.78071	+	3.91484i	0.304156	+	0.175605i
$498$		0			0
$499$	−30.9030	−	17.8418i	−1.38341	−	0.798711i	−0.390846	−	0.920456i	$-0.627818\pi$
$499$	−30.9030	−	17.8418i	−1.38341	−	0.798711i	−0.992561	+	0.121745i	$0.961151\pi$
$500$		0			0
$501$	21.8398	+	18.8662i	0.975731	+	0.842880i
$502$		0			0
$503$	−13.5573	−	23.4819i	−0.604490	−	1.04701i	−0.992132	−	0.125198i	$-0.960043\pi$
$503$	−13.5573	−	23.4819i	−0.604490	−	1.04701i	0.387642	−	0.921810i	$-0.373290\pi$
$504$		0			0
$505$	−2.98361			−0.132769
$506$		0			0
$507$	−1.21754	+	6.36933i	−0.0540728	+	0.282872i
$508$		0			0
$509$	14.7344	−	8.50694i	0.653093	−	0.377063i	−0.136547	−	0.990634i	$-0.543601\pi$
$509$	14.7344	−	8.50694i	0.653093	−	0.377063i	0.789640	+	0.613570i	$0.210267\pi$
$510$		0			0
$511$	−3.62846	−	2.09489i	−0.160513	−	0.0926725i
$512$		0			0
$513$	5.27321	+	22.0271i	0.232818	+	0.972520i
$514$		0			0
$515$	−0.749164	+	1.29759i	−0.0330121	+	0.0571787i
$516$		0			0
$517$	−8.05582	−	13.9531i	−0.354295	−	0.613656i
$518$		0			0
$519$	−30.9439	−	5.91513i	−1.35829	−	0.259646i
$520$		0			0
$521$		−	7.42530i		−	0.325309i	−0.986683	−	0.162654i	$-0.947994\pi$
$521$		−	7.42530i		−	0.325309i	0.986683	−	0.162654i	$-0.0520055\pi$
$522$		0			0
$523$	−28.4010	+	16.3973i	−1.24189	+	0.717004i	−0.969478	−	0.245177i	$-0.921154\pi$
$523$	−28.4010	+	16.3973i	−1.24189	+	0.717004i	−0.272410	+	0.962181i	$0.587821\pi$
$524$		0			0
$525$	−4.96389	+	5.74628i	−0.216642	+	0.250788i
$526$		0			0
$527$	−10.0585	+	17.4218i	−0.438154	+	0.758906i
$528$		0			0
$529$	7.60999	−	13.1809i	0.330869	−	0.573082i
$530$		0			0
$531$	4.31344	+	29.3660i	0.187187	+	1.27437i
$532$		0			0
$533$		−	7.74759i		−	0.335586i
$534$		0			0
$535$	1.27862	+	0.738213i	0.0552797	+	0.0319157i
$536$		0			0
$537$	−1.36285	+	0.474012i	−0.0588115	+	0.0204551i
$538$		0			0
$539$	24.1636			1.04080
$540$		0			0
$541$	−4.55582	−	7.89092i	−0.195870	−	0.339257i	0.751315	−	0.659943i	$-0.229420\pi$
$541$	−4.55582	−	7.89092i	−0.195870	−	0.339257i	−0.947185	+	0.320686i	$0.896086\pi$
$542$		0			0
$543$	13.3009	+	11.4899i	0.570795	+	0.493078i
$544$		0			0
$545$	−2.32824	+	1.34421i	−0.0997308	+	0.0575796i
$546$		0			0
$547$	19.6108	−	11.3223i	0.838497	−	0.484107i	−0.0182558	−	0.999833i	$-0.505811\pi$
$547$	19.6108	−	11.3223i	0.838497	−	0.484107i	0.856753	+	0.515727i	$0.172478\pi$
$548$		0			0
$549$	−16.9873	−	6.74077i	−0.724998	−	0.287689i
$550$		0			0
$551$	−3.43474	+	13.7034i	−0.146325	+	0.583784i
$552$		0			0
$553$	0.155954	−	0.270120i	0.00663184	−	0.0114867i
$554$		0			0
$555$	0.0413933	+	0.00791260i	0.00175705	+	0.000335871i
$556$		0			0
$557$	6.78665	−	3.91827i	0.287560	−	0.166023i	−0.349281	−	0.937018i	$-0.613574\pi$
$557$	6.78665	−	3.91827i	0.287560	−	0.166023i	0.636841	+	0.770995i	$0.280241\pi$
$558$		0			0
$559$		−	15.9009i		−	0.672538i
$560$		0			0
$561$	30.3268	+	5.79716i	1.28040	+	0.244756i
$562$		0			0
$563$	−8.10532			−0.341599			−0.170799	−	0.985306i	$-0.554635\pi$
$563$	−8.10532			−0.341599			−0.170799	+	0.985306i	$0.554635\pi$
$564$		0			0
$565$	−1.58208	+	2.74024i	−0.0665584	+	0.115283i
$566$		0			0
$567$	−7.73591	−	1.82693i	−0.324878	−	0.0767239i
$568$		0			0
$569$		−	28.8796i		−	1.21070i	−0.795961	−	0.605348i	$-0.793034\pi$
$569$		−	28.8796i		−	1.21070i	0.795961	−	0.605348i	$-0.206966\pi$
$570$		0			0
$571$		−	17.2330i		−	0.721177i	−0.932725	−	0.360588i	$-0.882576\pi$
$571$		−	17.2330i		−	0.721177i	0.932725	−	0.360588i	$-0.117424\pi$
$572$		0			0
$573$	33.7236	−	11.7293i	1.40882	−	0.490000i
$574$		0			0
$575$	−6.92281	+	11.9907i	−0.288701	+	0.500045i
$576$		0			0
$577$	2.32368			0.0967360			0.0483680	−	0.998830i	$-0.484598\pi$
$577$	2.32368			0.0967360			0.0483680	+	0.998830i	$0.484598\pi$
$578$		0			0
$579$	−0.0533828	+	0.279262i	−0.00221851	+	0.0116057i
$580$		0			0
$581$			0.883990i			0.0366741i
$582$		0			0
$583$	43.8384	−	25.3101i	1.81560	−	1.04824i
$584$		0			0
$585$	−1.44755	−	1.82923i	−0.0598490	−	0.0756294i
$586$		0			0
$587$	19.7447	−	34.1989i	0.814952	−	1.41154i	−0.0944101	−	0.995533i	$-0.530096\pi$
$587$	19.7447	−	34.1989i	0.814952	−	1.41154i	0.909362	−	0.416005i	$-0.136570\pi$
$588$		0			0
$589$	−13.7298	−	13.2918i	−0.565728	−	0.547678i
$590$		0			0
$591$	9.37621	+	26.9580i	0.385686	+	1.10890i
$592$		0			0
$593$	−8.44149	+	4.87370i	−0.346651	+	0.200139i	−0.663209	−	0.748434i	$-0.730806\pi$
$593$	−8.44149	+	4.87370i	−0.346651	+	0.200139i	0.316558	+	0.948573i	$0.397473\pi$
$594$		0			0
$595$	0.666930	−	0.385052i	0.0273415	−	0.0157856i
$596$		0			0
$597$	−17.7840	+	20.5870i	−0.727851	+	0.842571i
$598$		0			0
$599$	−17.1233	−	29.6584i	−0.699639	−	1.21181i	−0.968592	−	0.248656i	$-0.920011\pi$
$599$	−17.1233	−	29.6584i	−0.699639	−	1.21181i	0.268953	−	0.963153i	$-0.413322\pi$
$600$		0			0
$601$	−33.7716			−1.37757			−0.688786	−	0.724965i	$-0.741856\pi$
$601$	−33.7716			−1.37757			−0.688786	+	0.724965i	$0.741856\pi$
$602$		0			0
$603$	−16.2418	+	40.9307i	−0.661419	+	1.66683i
$604$		0			0
$605$	0.673393	+	0.388784i	0.0273773	+	0.0158063i
$606$		0			0
$607$			2.20131i			0.0893485i	0.999002	+	0.0446742i	$0.0142250\pi$
$607$			2.20131i			0.0893485i	−0.999002	+	0.0446742i	$0.985775\pi$
$608$		0			0
$609$	−3.75186	−	3.24102i	−0.152033	−	0.131333i
$610$		0			0
$611$	−8.48528	+	14.6969i	−0.343278	+	0.594574i
$612$		0			0
$613$	17.3497	−	30.0505i	0.700747	−	1.21373i	−0.267458	−	0.963570i	$-0.586184\pi$
$613$	17.3497	−	30.0505i	0.700747	−	1.21373i	0.968205	−	0.250160i	$-0.0804831\pi$
$614$		0			0
$615$	0.471583	+	0.407374i	0.0190160	+	0.0164269i
$616$		0			0
$617$	1.61865	−	0.934526i	0.0651642	−	0.0376226i	−0.467064	−	0.884224i	$-0.654688\pi$
$617$	1.61865	−	0.934526i	0.0651642	−	0.0376226i	0.532228	+	0.846601i	$0.321355\pi$
$618$		0			0
$619$		−	31.0103i		−	1.24641i	−0.782059	−	0.623204i	$-0.785831\pi$
$619$		−	31.0103i		−	1.24641i	0.782059	−	0.623204i	$-0.214169\pi$
$620$		0			0
$621$	−14.4801	−	0.623538i	−0.581064	−	0.0250217i
$622$		0			0
$623$	−0.251741	−	0.436029i	−0.0100858	−	0.0174691i
$624$		0			0
$625$	−12.2298	+	21.1827i	−0.489193	+	0.847308i
$626$		0			0
$627$	−12.3457	+	26.6049i	−0.493041	+	1.06250i
$628$		0			0
$629$	0.508827	+	0.293771i	0.0202883	+	0.0117134i
$630$		0			0
$631$	−1.86320	+	1.07572i	−0.0741726	+	0.0428236i	−0.536628	−	0.843819i	$-0.680302\pi$
$631$	−1.86320	+	1.07572i	−0.0741726	+	0.0428236i	0.462455	+	0.886643i	$0.346969\pi$
$632$		0			0
$633$	−10.0007	−	1.91171i	−0.397494	−	0.0759835i
$634$		0			0
$635$	0.765969			0.0303966
$636$		0			0
$637$	−12.7259	−	22.0418i	−0.504217	−	0.873329i
$638$		0			0
$639$	3.86505	+	26.3133i	0.152899	+	1.04094i
$640$		0			0
$641$	4.30303	+	2.48436i	0.169959	+	0.0981261i	0.582567	−	0.812783i	$-0.302048\pi$
$641$	4.30303	+	2.48436i	0.169959	+	0.0981261i	−0.412607	+	0.910909i	$0.635382\pi$
$642$		0			0
$643$	4.56207	+	2.63391i	0.179910	+	0.103871i	0.587251	−	0.809405i	$-0.300210\pi$
$643$	4.56207	+	2.63391i	0.179910	+	0.103871i	−0.407340	+	0.913277i	$0.633544\pi$
$644$		0			0
$645$	0.967862	+	0.836082i	0.0381095	+	0.0329207i
$646$		0			0
$647$	−34.8017			−1.36820			−0.684099	−	0.729389i	$-0.739804\pi$
$647$	−34.8017			−1.36820			−0.684099	+	0.729389i	$0.739804\pi$
$648$		0			0
$649$	−19.2177	+	33.2860i	−0.754359	+	1.30659i
$650$		0			0
$651$	6.33423	−	2.20310i	0.248258	−	0.0863462i
$652$		0			0
$653$			22.0175i			0.861612i	0.902445	+	0.430806i	$0.141771\pi$
$653$			22.0175i			0.861612i	−0.902445	+	0.430806i	$0.858229\pi$
$654$		0			0
$655$	2.68230	−	1.54863i	0.104806	−	0.0605099i
$656$		0			0
$657$	−2.06825	−	14.0807i	−0.0806900	−	0.549339i
$658$		0			0
$659$	23.1076	+	40.0236i	0.900145	+	1.55910i	0.827305	+	0.561753i	$0.189873\pi$
$659$	23.1076	+	40.0236i	0.900145	+	1.55910i	0.0728403	+	0.997344i	$0.476794\pi$
$660$		0			0
$661$	16.7118	+	28.9456i	0.650013	+	1.12586i	0.983119	+	0.182966i	$0.0585698\pi$
$661$	16.7118	+	28.9456i	0.650013	+	1.12586i	−0.333106	+	0.942889i	$0.608097\pi$
$662$		0			0
$663$	−10.6836	−	30.7170i	−0.414917	−	1.19295i
$664$		0			0
$665$	0.200766	+	0.703455i	0.00778539	+	0.0272788i
$666$		0			0
$667$	−7.82894	−	4.52004i	−0.303138	−	0.175017i
$668$		0			0
$669$	14.7007	+	2.81014i	0.568362	+	0.108646i
$670$		0			0
$671$	−11.8331	−	20.4955i	−0.456811	−	0.791219i
$672$		0			0
$673$	18.9639			0.731004			0.365502	−	0.930811i	$-0.380897\pi$
$673$	18.9639			0.731004			0.365502	+	0.930811i	$0.380897\pi$
$674$		0			0
$675$	−25.7693	−	1.10967i	−0.991859	−	0.0427113i
$676$		0			0
$677$			36.3779i			1.39812i	0.715065	+	0.699058i	$0.246397\pi$
$677$			36.3779i			1.39812i	−0.715065	+	0.699058i	$0.753603\pi$
$678$		0			0
$679$	−1.50211	−	0.867244i	−0.0576457	−	0.0332818i
$680$		0			0
$681$	−25.4563	+	8.85392i	−0.975489	+	0.339283i
$682$		0			0
$683$	−38.0643			−1.45649			−0.728245	−	0.685317i	$-0.759664\pi$
$683$	−38.0643			−1.45649			−0.728245	+	0.685317i	$0.759664\pi$
$684$		0			0
$685$	1.49577			0.0571506
$686$		0			0
$687$	−28.8903	+	10.0483i	−1.10223	+	0.383366i
$688$		0			0
$689$	−46.1754	−	26.6594i	−1.75914	−	1.01564i
$690$		0			0
$691$		−	22.2914i		−	0.848007i	−0.905661	−	0.424003i	$-0.860625\pi$
$691$		−	22.2914i		−	0.848007i	0.905661	−	0.424003i	$-0.139375\pi$
$692$		0			0
$693$	−6.38739	−	8.07155i	−0.242637	−	0.306613i
$694$		0			0
$695$	−3.11886			−0.118305
$696$		0			0
$697$	4.34405	+	7.52411i	0.164542	+	0.284996i
$698$		0			0
$699$	1.92800	+	0.368549i	0.0729236	+	0.0139398i
$700$		0			0
$701$	18.0231	+	10.4056i	0.680722	+	0.393015i	0.800127	−	0.599831i	$-0.204765\pi$
$701$	18.0231	+	10.4056i	0.680722	+	0.393015i	−0.119405	+	0.992846i	$0.538099\pi$
$702$		0			0
$703$	−0.388204	+	0.400998i	−0.0146414	+	0.0151239i
$704$		0			0
$705$	−0.448415	−	1.28926i	−0.0168883	−	0.0485563i
$706$		0			0
$707$	6.93356	+	12.0093i	0.260763	+	0.451655i
$708$		0			0
$709$	5.97375	+	10.3468i	0.224349	+	0.388584i	0.956124	−	0.292963i	$-0.0946412\pi$
$709$	5.97375	+	10.3468i	0.224349	+	0.388584i	−0.731775	+	0.681546i	$0.761308\pi$
$710$		0			0
$711$	1.04823	−	0.153971i	0.0393119	−	0.00577435i
$712$		0			0
$713$	10.5900	−	6.11416i	0.396600	−	0.228977i
$714$		0			0
$715$		−	3.02072i		−	0.112968i
$716$		0			0
$717$	−21.0229	+	7.31194i	−0.785116	+	0.273070i
$718$		0			0
$719$	−3.34780	+	5.79855i	−0.124852	+	0.216250i	−0.921675	−	0.387963i	$-0.873179\pi$
$719$	−3.34780	+	5.79855i	−0.124852	+	0.216250i	0.796823	+	0.604212i	$0.206512\pi$
$720$		0			0
$721$	6.96389			0.259349
$722$		0			0
$723$	27.4305	+	23.6957i	1.02015	+	0.881251i
$724$		0			0
$725$	−13.9327	−	8.04404i	−0.517447	−	0.298748i
$726$		0			0
$727$	39.8338	+	22.9981i	1.47735	+	0.852951i	0.999673	−	0.0255827i	$-0.00814412\pi$
$727$	39.8338	+	22.9981i	1.47735	+	0.852951i	0.477681	+	0.878533i	$0.341477\pi$
$728$		0			0
$729$	−11.4400	−	24.4566i	−0.423702	−	0.905802i
$730$		0			0
$731$	8.91559	+	15.4423i	0.329755	+	0.571152i
$732$		0			0
$733$	44.7636			1.65338			0.826691	−	0.562656i	$-0.190220\pi$
$733$	44.7636			1.65338			0.826691	+	0.562656i	$0.190220\pi$
$734$		0			0
$735$	2.01078	+	0.384375i	0.0741689	+	0.0141779i
$736$		0			0
$737$	−49.3838	+	28.5117i	−1.81907	+	1.05024i
$738$		0			0
$739$	−30.1266	−	17.3936i	−1.10822	−	0.639834i	−0.169855	−	0.985469i	$-0.554330\pi$
$739$	−30.1266	−	17.3936i	−1.10822	−	0.639834i	−0.938369	+	0.345635i	$0.887663\pi$
$740$		0			0
$741$	30.7708	−	2.74993i	1.13039	−	0.101021i
$742$		0			0
$743$	−20.4831	+	35.4779i	−0.751454	+	1.30156i	0.195664	+	0.980671i	$0.437314\pi$
$743$	−20.4831	+	35.4779i	−0.751454	+	1.30156i	−0.947118	+	0.320885i	$0.896020\pi$
$744$		0			0
$745$	−1.96223	−	3.39868i	−0.0718906	−	0.124518i
$746$		0			0
$747$	−2.35464	+	1.86333i	−0.0861516	+	0.0681757i
$748$		0			0
$749$		−	6.86209i		−	0.250735i
$750$		0			0
$751$	−27.5382	+	15.8992i	−1.00488	+	0.580169i	−0.909689	−	0.415290i	$-0.863680\pi$
$751$	−27.5382	+	15.8992i	−1.00488	+	0.580169i	−0.0951932	+	0.995459i	$0.530347\pi$
$752$		0			0
$753$	13.6198	+	11.7654i	0.496335	+	0.428756i
$754$		0			0
$755$	−0.787458	+	1.36392i	−0.0286585	+	0.0496380i
$756$		0			0
$757$	16.3579	−	28.3327i	0.594537	−	1.02977i	−0.399075	−	0.916918i	$-0.630669\pi$
$757$	16.3579	−	28.3327i	0.594537	−	1.02977i	0.993612	−	0.112850i	$-0.0359980\pi$
$758$		0			0
$759$	−14.2028	−	12.2690i	−0.515528	−	0.445336i
$760$		0			0
$761$			3.68720i			0.133661i	0.997764	+	0.0668305i	$0.0212887\pi$
$761$			3.68720i			0.133661i	−0.997764	+	0.0668305i	$0.978711\pi$
$762$		0			0
$763$	10.8211	+	6.24758i	0.391751	+	0.226178i
$764$		0			0
$765$	2.43144	+	0.964827i	0.0879089	+	0.0348834i
$766$		0			0
$767$	40.4843			1.46180
$768$		0			0
$769$	16.7397	+	28.9940i	0.603649	+	1.04555i	0.992263	+	0.124150i	$0.0396203\pi$
$769$	16.7397	+	28.9940i	0.603649	+	1.04555i	−0.388615	+	0.921400i	$0.627046\pi$
$770$		0			0
$771$	7.84455	−	9.08097i	0.282514	−	0.327043i
$772$		0			0
$773$	−18.1936	+	10.5041i	−0.654377	+	0.377805i	−0.790131	−	0.612938i	$-0.789988\pi$
$773$	−18.1936	+	10.5041i	−0.654377	+	0.377805i	0.135754	+	0.990743i	$0.456654\pi$
$774$		0			0
$775$	18.8464	−	10.8810i	0.676984	−	0.390857i
$776$		0			0
$777$	−0.0643444	−	0.185000i	−0.00230834	−	0.00663683i
$778$		0			0
$779$	−7.93617	+	2.26499i	−0.284343	+	0.0811516i
$780$		0			0
$781$	−17.2200	+	29.8259i	−0.616179	+	1.06725i
$782$		0			0
$783$	0.724526	−	16.8253i	0.0258925	−	0.601286i
$784$		0			0
$785$	−2.12747	+	1.22830i	−0.0759328	+	0.0438398i
$786$		0			0
$787$		−	4.64212i		−	0.165474i	−0.996571	−	0.0827369i	$-0.973634\pi$
$787$		−	4.64212i		−	0.165474i	0.996571	−	0.0827369i	$-0.0263661\pi$
$788$		0			0
$789$	−8.10720	+	42.4113i	−0.288624	+	1.50988i
$790$		0			0
$791$	14.7063			0.522894
$792$		0			0
$793$	−12.4639	+	21.5881i	−0.442606	+	0.766616i
$794$		0			0
$795$	4.05065	−	1.40885i	0.143662	−	0.0499667i
$796$		0			0
$797$		−	17.8020i		−	0.630581i	−0.948995	−	0.315290i	$-0.897898\pi$
$797$		−	17.8020i		−	0.630581i	0.948995	−	0.315290i	$-0.102102\pi$
$798$		0			0
$799$		−	19.0307i		−	0.673256i
$800$		0			0
$801$	0.630790	−	1.58964i	0.0222879	−	0.0561672i
$802$		0			0
$803$	9.21466	−	15.9603i	0.325178	−	0.563225i
$804$		0			0
$805$	−0.468117			−0.0164989
$806$		0			0
$807$	−44.2227	−	8.45347i	−1.55671	−	0.297576i
$808$		0			0
$809$		−	19.4705i		−	0.684545i	−0.939601	−	0.342273i	$-0.888803\pi$
$809$		−	19.4705i		−	0.684545i	0.939601	−	0.342273i	$-0.111197\pi$
$810$		0			0
$811$	30.4997	−	17.6090i	1.07099	−	0.618336i	0.142538	−	0.989789i	$-0.454474\pi$
$811$	30.4997	−	17.6090i	1.07099	−	0.618336i	0.928452	+	0.371453i	$0.121140\pi$
$812$		0			0
$813$	9.86260	+	1.88530i	0.345897	+	0.0661204i
$814$		0			0
$815$	0.111463	−	0.193060i	0.00390438	−	0.00676258i
$816$		0			0
$817$	−16.2880	+	4.64859i	−0.569844	+	0.162634i
$818$		0			0
$819$	−3.99887	+	10.0775i	−0.139732	+	0.352135i
$820$		0			0
$821$	−42.5458	+	24.5638i	−1.48486	+	0.857283i	−0.999852	−	0.0172271i	$-0.994516\pi$
$821$	−42.5458	+	24.5638i	−1.48486	+	0.857283i	−0.485007	+	0.874510i	$0.661183\pi$
$822$		0			0
$823$	−38.9007	+	22.4593i	−1.35599	+	0.782883i	−0.989081	−	0.147373i	$-0.952918\pi$
$823$	−38.9007	+	22.4593i	−1.35599	+	0.782883i	−0.366912	+	0.930256i	$0.619585\pi$
$824$		0			0
$825$	−25.2758	−	21.8344i	−0.879990	−	0.760175i
$826$		0			0
$827$	−26.0724	−	45.1588i	−0.906627	−	1.57032i	−0.818718	−	0.574196i	$-0.805315\pi$
$827$	−26.0724	−	45.1588i	−0.906627	−	1.57032i	−0.0879094	−	0.996128i	$-0.528019\pi$
$828$		0			0
$829$	−33.3316			−1.15766			−0.578828	−	0.815450i	$-0.696490\pi$
$829$	−33.3316			−1.15766			−0.578828	+	0.815450i	$0.696490\pi$
$830$		0			0
$831$	18.1456	−	6.31118i	0.629463	−	0.218932i
$832$		0			0
$833$	24.7175	+	14.2707i	0.856412	+	0.494450i
$834$		0			0
$835$			3.16627i			0.109573i
$836$		0			0
$837$	19.2200	+	12.2283i	0.664340	+	0.422673i
$838$		0			0
$839$	21.9144	−	37.9568i	0.756568	−	1.31041i	−0.188023	−	0.982165i	$-0.560208\pi$
$839$	21.9144	−	37.9568i	0.756568	−	1.31041i	0.944591	−	0.328250i	$-0.106459\pi$
$840$		0			0
$841$	−9.24789	+	16.0178i	−0.318893	+	0.552338i
$842$		0			0
$843$	11.0366	−	12.7761i	0.380120	−	0.440033i
$844$		0			0
$845$	−0.616121	+	0.355718i	−0.0211952	+	0.0122371i
$846$		0			0
$847$		−	3.61395i		−	0.124177i
$848$		0			0
$849$	−51.2842	−	9.80331i	−1.76007	−	0.336449i
$850$		0			0
$851$	−0.178572	−	0.309296i	−0.00612138	−	0.0106025i
$852$		0			0
$853$	−1.88413	+	3.26340i	−0.0645113	+	0.111737i	−0.896477	−	0.443090i	$-0.853882\pi$
$853$	−1.88413	+	3.26340i	−0.0645113	+	0.111737i	0.831966	+	0.554827i	$0.187216\pi$
$854$		0			0
$855$	−1.45057	+	2.01756i	−0.0496083	+	0.0689990i
$856$		0			0
$857$	−23.9869	−	13.8488i	−0.819376	−	0.473067i	0.0308250	−	0.999525i	$-0.490187\pi$
$857$	−23.9869	−	13.8488i	−0.819376	−	0.473067i	−0.850201	+	0.526458i	$0.823520\pi$
$858$		0			0
$859$	−10.8759	+	6.27918i	−0.371080	+	0.214243i	−0.673930	−	0.738795i	$-0.735395\pi$
$859$	−10.8759	+	6.27918i	−0.371080	+	0.214243i	0.302850	+	0.953038i	$0.402062\pi$
$860$		0			0
$861$	0.543813	−	2.84485i	0.0185331	−	0.0969523i
$862$		0			0
$863$	49.9994			1.70200			0.850999	−	0.525167i	$-0.175997\pi$
$863$	49.9994			1.70200			0.850999	+	0.525167i	$0.175997\pi$
$864$		0			0
$865$	−1.72817	−	2.99328i	−0.0587596	−	0.101775i
$866$		0			0
$867$	5.31605	+	4.59224i	0.180543	+	0.155961i
$868$		0			0
$869$	1.18816	+	0.685986i	0.0403056	+	0.0232705i
$870$		0			0
$871$	52.0164	+	30.0317i	1.76251	+	1.01758i
$872$		0			0
$873$	−0.856215	−	5.82912i	−0.0289785	−	0.197286i
$874$		0			0
$875$	−1.67222			−0.0565312
$876$		0			0
$877$	−21.7758	+	37.7168i	−0.735316	+	1.27361i	0.219268	+	0.975665i	$0.429633\pi$
$877$	−21.7758	+	37.7168i	−0.735316	+	1.27361i	−0.954584	+	0.297941i	$0.903700\pi$
$878$		0			0
$879$	5.65428	+	16.2569i	0.190714	+	0.548331i
$880$		0			0
$881$		−	34.8820i		−	1.17521i	−0.809149	−	0.587603i	$-0.800072\pi$
$881$		−	34.8820i		−	1.17521i	0.809149	−	0.587603i	$-0.199928\pi$
$882$		0			0
$883$	−11.1546	+	6.44011i	−0.375382	+	0.216727i	−0.675807	−	0.737079i	$-0.736205\pi$
$883$	−11.1546	+	6.44011i	−0.375382	+	0.216727i	0.300425	+	0.953805i	$0.402871\pi$
$884$		0			0
$885$	−2.12869	+	2.46421i	−0.0715553	+	0.0828335i
$886$		0			0
$887$	7.89788	+	13.6795i	0.265185	+	0.459314i	0.967612	−	0.252442i	$-0.0812337\pi$
$887$	7.89788	+	13.6795i	0.265185	+	0.459314i	−0.702427	+	0.711756i	$0.747900\pi$
$888$		0			0
$889$	−1.78002	−	3.08309i	−0.0597001	−	0.103404i
$890$		0			0
$891$	8.03601	−	34.0275i	0.269216	−	1.13996i
$892$		0			0
$893$	17.5353	+	4.39521i	0.586797	+	0.147080i
$894$		0			0
$895$	−0.137096	−	0.0791526i	−0.00458262	−	0.00264578i
$896$		0			0
$897$	−3.71172	+	19.4172i	−0.123931	+	0.648321i
$898$		0			0
$899$	7.10442	+	12.3052i	0.236946	+	0.410402i
$900$		0			0
$901$	59.7913			1.99194
$902$		0			0
$903$	1.11610	−	5.83869i	0.0371416	−	0.194300i
$904$		0			0
$905$			1.92832i			0.0640996i
$906$		0			0
$907$	33.8957	+	19.5697i	1.12549	+	0.649800i	0.942796	−	0.333370i	$-0.108186\pi$
$907$	33.8957	+	19.5697i	1.12549	+	0.649800i	0.182691	+	0.983170i	$0.441519\pi$
$908$		0			0
$909$	−17.3735	+	43.7825i	−0.576241	+	1.45217i
$910$		0			0
$911$	−49.1938			−1.62986			−0.814932	−	0.579556i	$-0.803226\pi$
$911$	−49.1938			−1.62986			−0.814932	+	0.579556i	$0.803226\pi$
$912$		0			0
$913$	−3.88835			−0.128686
$914$		0			0
$915$	−0.658670	−	1.89377i	−0.0217749	−	0.0626062i
$916$		0			0
$917$	−12.4667	−	7.19767i	−0.411687	−	0.237688i
$918$		0			0
$919$		−	44.1810i		−	1.45740i	−0.684835	−	0.728698i	$-0.740126\pi$
$919$		−	44.1810i		−	1.45740i	0.684835	−	0.728698i	$-0.259874\pi$
$920$		0			0
$921$	−41.4452	−	7.92253i	−1.36567	−	0.261056i
$922$		0			0
$923$	36.2759			1.19404
$924$		0			0
$925$	−0.317794	−	0.550435i	−0.0104490	−	0.0180982i
$926$		0			0
$927$	14.6789	+	18.5493i	0.482119	+	0.609240i
$928$		0			0
$929$	−50.5147	−	29.1647i	−1.65733	−	0.956861i	−0.973939	−	0.226811i	$-0.927170\pi$
$929$	−50.5147	−	29.1647i	−1.65733	−	0.956861i	−0.683393	−	0.730050i	$-0.739497\pi$
$930$		0			0
$931$	−18.8580	+	19.4795i	−0.618045	+	0.638414i
$932$		0			0
$933$	39.5749	−	13.7645i	1.29562	−	0.450628i
$934$		0			0
$935$	1.69371	+	2.93358i	0.0553901	+	0.0959385i
$936$		0			0
$937$	−8.26594	−	14.3170i	−0.270037	−	0.467717i	0.698834	−	0.715284i	$-0.253702\pi$
$937$	−8.26594	−	14.3170i	−0.270037	−	0.467717i	−0.968871	+	0.247567i	$0.920369\pi$
$938$		0			0
$939$	0.0473292	+	0.0408850i	0.00154453	+	0.00133423i
$940$		0			0
$941$	−52.1695	+	30.1201i	−1.70068	+	0.981886i	−0.755604	+	0.655029i	$0.772656\pi$
$941$	−52.1695	+	30.1201i	−1.70068	+	0.981886i	−0.945074	+	0.326857i	$0.894010\pi$
$942$		0			0
$943$		−	5.28115i		−	0.171978i
$944$		0			0
$945$	−0.403134	−	0.773284i	−0.0131140	−	0.0251549i
$946$		0			0
$947$	−4.95759	+	8.58679i	−0.161100	+	0.279033i	−0.935263	−	0.353952i	$-0.884837\pi$
$947$	−4.95759	+	8.58679i	−0.161100	+	0.279033i	0.774163	+	0.632986i	$0.218171\pi$
$948$		0			0
$949$	−19.4118			−0.630133
$950$		0			0
$951$	25.1447	−	29.1079i	0.815373	−	0.943888i
$952$		0			0
$953$	38.3422	+	22.1369i	1.24202	+	0.717083i	0.969506	−	0.245067i	$-0.0788100\pi$
$953$	38.3422	+	22.1369i	1.24202	+	0.717083i	0.272519	+	0.962150i	$0.412143\pi$
$954$		0			0
$955$	3.39243	+	1.95862i	0.109776	+	0.0633794i
$956$		0			0
$957$	14.2561	−	16.5031i	0.460834	−	0.533468i
$958$		0			0
$959$	−3.47601	−	6.02062i	−0.112246	−	0.194416i
$960$		0			0
$961$	11.7800			0.380001
$962$		0			0
$963$	18.2782	−	14.4644i	0.589006	−	0.466107i
$964$		0			0
$965$	−0.0270137	+	0.0155964i	−0.000869603	+	0.000502066i
$966$		0			0
$967$	9.17788	+	5.29885i	0.295141	+	0.170400i	0.640258	−	0.768160i	$-0.278827\pi$
$967$	9.17788	+	5.29885i	0.295141	+	0.170400i	−0.345117	+	0.938560i	$0.612161\pi$
$968$		0			0
$969$	−28.3413	+	19.9237i	−0.910454	+	0.640040i
$970$		0			0
$971$	20.0666	−	34.7564i	0.643968	−	1.11539i	−0.340571	−	0.940219i	$-0.610620\pi$
$971$	20.0666	−	34.7564i	0.643968	−	1.11539i	0.984539	−	0.175167i	$-0.0560464\pi$
$972$		0			0
$973$	7.24789	+	12.5537i	0.232357	+	0.402453i
$974$		0			0
$975$	−6.60553	+	34.5556i	−0.211546	+	1.10666i
$976$		0			0
$977$			5.89450i			0.188582i	0.995545	+	0.0942909i	$0.0300584\pi$
$977$			5.89450i			0.188582i	−0.995545	+	0.0942909i	$0.969942\pi$
$978$		0			0
$979$	1.91793	−	1.10732i	0.0612974	−	0.0353901i
$980$		0			0
$981$	6.16812	+	41.9927i	0.196933	+	1.34072i
$982$		0			0
$983$	12.2862	−	21.2803i	0.391869	−	0.678737i	−0.600827	−	0.799379i	$-0.705162\pi$
$983$	12.2862	−	21.2803i	0.391869	−	0.678737i	0.992696	+	0.120642i	$0.0384954\pi$
$984$		0			0
$985$	−1.56568	+	2.71184i	−0.0498867	+	0.0864064i
$986$		0			0
$987$	−4.14732	+	4.80100i	−0.132011	+	0.152818i
$988$		0			0
$989$		−	10.8389i		−	0.344656i
$990$		0			0
$991$	−24.3959	−	14.0850i	−0.774960	−	0.447423i	0.0596810	−	0.998217i	$-0.480992\pi$
$991$	−24.3959	−	14.0850i	−0.774960	−	0.447423i	−0.834641	+	0.550794i	$0.814325\pi$
$992$		0			0
$993$	−5.91151	−	16.9965i	−0.187596	−	0.539367i
$994$		0			0
$995$	−2.98465			−0.0946197
$996$		0			0
$997$	25.3917	+	43.9797i	0.804162	+	1.39285i	0.916855	+	0.399220i	$0.130719\pi$
$997$	25.3917	+	43.9797i	0.804162	+	1.39285i	−0.112693	+	0.993630i	$0.535948\pi$
$998$		0			0
$999$	0.357144	−	0.561345i	0.0112995	−	0.0177602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bh.f.239.12	yes	24
3.2	odd	2	inner	912.2.bh.f.239.7	yes	24
4.3	odd	2	inner	912.2.bh.f.239.1	✓	24
12.11	even	2	inner	912.2.bh.f.239.6	yes	24
19.7	even	3	inner	912.2.bh.f.767.6	yes	24
57.26	odd	6	inner	912.2.bh.f.767.1	yes	24
76.7	odd	6	inner	912.2.bh.f.767.7	yes	24
228.83	even	6	inner	912.2.bh.f.767.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bh.f.239.1	✓	24	4.3	odd	2	inner
912.2.bh.f.239.6	yes	24	12.11	even	2	inner
912.2.bh.f.239.7	yes	24	3.2	odd	2	inner
912.2.bh.f.239.12	yes	24	1.1	even	1	trivial
912.2.bh.f.767.1	yes	24	57.26	odd	6	inner
912.2.bh.f.767.6	yes	24	19.7	even	3	inner
912.2.bh.f.767.7	yes	24	76.7	odd	6	inner
912.2.bh.f.767.12	yes	24	228.83	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63593 - 0.568988i) q^{3} +(0.164566 + 0.0950122i) q^{5} -0.883190i q^{7} +(2.35251 - 1.86164i) q^{9} +3.88483 q^{11} +(-2.04597 - 3.54372i) q^{13} +(0.323278 + 0.0617968i) q^{15} +(3.97390 + 2.29433i) q^{17} +(-3.03184 + 3.13176i) q^{19} +(-0.502525 - 1.44483i) q^{21} +(-1.39463 - 2.41558i) q^{23} +(-2.48195 - 4.29886i) q^{25} +(2.78927 - 4.38406i) q^{27} +(2.80681 - 1.62051i) q^{29} +4.38406i q^{31} +(6.35530 - 2.21042i) q^{33} +(0.0839138 - 0.145343i) q^{35} +0.128042 q^{37} +(-5.36338 - 4.63313i) q^{39} +(1.63972 + 0.946691i) q^{41} +(3.36531 + 1.94296i) q^{43} +(0.564021 - 0.0828466i) q^{45} +(-2.07366 - 3.59168i) q^{47} +6.21998 q^{49} +(7.80645 + 1.49225i) q^{51} +(11.2845 - 6.51511i) q^{53} +(0.639311 + 0.369107i) q^{55} +(-3.17793 + 6.84841i) q^{57} +(-4.94684 + 8.56818i) q^{59} +(-3.04597 - 5.27577i) q^{61} +(-1.64419 - 2.07771i) q^{63} -0.777567i q^{65} +(-12.7119 + 7.33924i) q^{67} +(-3.65595 - 3.15818i) q^{69} +(-4.43262 + 7.67752i) q^{71} +(2.37196 - 4.10835i) q^{73} +(-6.50628 - 5.62041i) q^{75} -3.43105i q^{77} +(0.305846 + 0.176580i) q^{79} +(2.06856 - 8.75906i) q^{81} -1.00091 q^{83} +(0.435979 + 0.755138i) q^{85} +(3.66968 - 4.24808i) q^{87} +(0.493698 - 0.285037i) q^{89} +(-3.12978 + 1.80698i) q^{91} +(2.49448 + 7.17199i) q^{93} +(-0.796493 + 0.227320i) q^{95} +(0.981945 - 1.70078i) q^{97} +(9.13909 - 7.23218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) \) 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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