LMFDB - Embedded newform 1008.2.bf.i.31.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(31,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.i.943.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.624780 + 1.61544i) q^{3} +2.39618i q^{5} +(-2.35781 + 1.20030i) q^{7} +(-2.21930 + 2.01859i) q^{9} +1.17822i q^{11} +(3.94643 + 2.27847i) q^{13} +(-3.87088 + 1.49708i) q^{15} +(-3.59971 - 2.07829i) q^{17} +(-0.422526 - 0.731837i) q^{19} +(-3.41213 - 3.05898i) q^{21} -3.01797i q^{23} -0.741665 q^{25} +(-4.64749 - 2.32398i) q^{27} +(1.38403 + 2.39720i) q^{29} +(-3.47638 - 6.02126i) q^{31} +(-1.90334 + 0.736128i) q^{33} +(-2.87613 - 5.64973i) q^{35} +(4.62049 + 8.00292i) q^{37} +(-1.21509 + 7.79877i) q^{39} +(-2.48982 - 1.43750i) q^{41} +(-7.19863 + 4.15613i) q^{43} +(-4.83690 - 5.31784i) q^{45} +(-5.38111 + 9.32036i) q^{47} +(4.11855 - 5.66017i) q^{49} +(1.10834 - 7.11359i) q^{51} +(4.88791 - 8.46611i) q^{53} -2.82322 q^{55} +(0.918254 - 1.13980i) q^{57} +(-2.78034 - 4.81569i) q^{59} +(-0.597080 - 0.344724i) q^{61} +(2.80978 - 7.42328i) q^{63} +(-5.45962 + 9.45635i) q^{65} +(3.56340 - 2.05733i) q^{67} +(4.87535 - 1.88556i) q^{69} +9.65062i q^{71} +(6.02026 + 3.47580i) q^{73} +(-0.463377 - 1.19812i) q^{75} +(-1.41422 - 2.77802i) q^{77} +(11.7100 + 6.76075i) q^{79} +(0.850594 - 8.95971i) q^{81} +(-2.52663 - 4.37625i) q^{83} +(4.97996 - 8.62554i) q^{85} +(-3.00783 + 3.73354i) q^{87} +(-6.06236 + 3.50011i) q^{89} +(-12.0398 - 0.635304i) q^{91} +(7.55502 - 9.37784i) q^{93} +(1.75361 - 1.01245i) q^{95} +(-0.316523 + 0.182744i) q^{97} +(-2.37834 - 2.61482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.624780	+	1.61544i	0.360717	+	0.932675i
$3$	0.624780	+	1.61544i	0.360717	+	0.932675i
$4$		0			0
$5$			2.39618i			1.07160i	0.844344	+	0.535801i	$0.179990\pi$
$5$			2.39618i			1.07160i	−0.844344	+	0.535801i	$0.820010\pi$
$6$		0			0
$7$	−2.35781	+	1.20030i	−0.891169	+	0.453671i
$7$	−2.35781	+	1.20030i	−0.891169	+	0.453671i
$8$		0			0
$9$	−2.21930	+	2.01859i	−0.739767	+	0.672863i
$10$		0			0
$11$			1.17822i			0.355247i	0.984099	+	0.177623i	$0.0568409\pi$
$11$			1.17822i			0.355247i	−0.984099	+	0.177623i	$0.943159\pi$
$12$		0			0
$13$	3.94643	+	2.27847i	1.09454	+	0.631935i	0.934782	−	0.355221i	$-0.115594\pi$
$13$	3.94643	+	2.27847i	1.09454	+	0.631935i	0.159761	+	0.987156i	$0.448928\pi$
$14$		0			0
$15$	−3.87088	+	1.49708i	−0.999458	+	0.386545i
$16$		0			0
$17$	−3.59971	−	2.07829i	−0.873057	−	0.504060i	−0.00469432	−	0.999989i	$-0.501494\pi$
$17$	−3.59971	−	2.07829i	−0.873057	−	0.504060i	−0.868363	+	0.495929i	$0.834828\pi$
$18$		0			0
$19$	−0.422526	−	0.731837i	−0.0969342	−	0.167895i	0.813480	−	0.581593i	$-0.197570\pi$
$19$	−0.422526	−	0.731837i	−0.0969342	−	0.167895i	−0.910414	+	0.413698i	$0.864237\pi$
$20$		0			0
$21$	−3.41213	−	3.05898i	−0.744588	−	0.667525i
$22$		0			0
$23$		−	3.01797i		−	0.629289i	−0.949210	−	0.314645i	$-0.898115\pi$
$23$		−	3.01797i		−	0.629289i	0.949210	−	0.314645i	$-0.101885\pi$
$24$		0			0
$25$	−0.741665			−0.148333
$26$		0			0
$27$	−4.64749	−	2.32398i	−0.894409	−	0.447250i
$28$		0			0
$29$	1.38403	+	2.39720i	0.257007	+	0.445150i	0.965439	−	0.260630i	$-0.0839303\pi$
$29$	1.38403	+	2.39720i	0.257007	+	0.445150i	−0.708432	+	0.705780i	$0.750597\pi$
$30$		0			0
$31$	−3.47638	−	6.02126i	−0.624375	−	1.08145i	−0.988661	−	0.150163i	$-0.952020\pi$
$31$	−3.47638	−	6.02126i	−0.624375	−	1.08145i	0.364286	−	0.931287i	$-0.381313\pi$
$32$		0			0
$33$	−1.90334	+	0.736128i	−0.331330	+	0.128143i
$34$		0			0
$35$	−2.87613	−	5.64973i	−0.486156	−	0.954979i
$36$		0			0
$37$	4.62049	+	8.00292i	0.759603	+	1.31567i	0.943053	+	0.332643i	$0.107940\pi$
$37$	4.62049	+	8.00292i	0.759603	+	1.31567i	−0.183450	+	0.983029i	$0.558726\pi$
$38$		0			0
$39$	−1.21509	+	7.79877i	−0.194570	+	1.24880i
$40$		0			0
$41$	−2.48982	−	1.43750i	−0.388844	−	0.224499i	0.292815	−	0.956169i	$-0.405408\pi$
$41$	−2.48982	−	1.43750i	−0.388844	−	0.224499i	−0.681659	+	0.731670i	$0.738741\pi$
$42$		0			0
$43$	−7.19863	+	4.15613i	−1.09778	+	0.633804i	−0.935637	−	0.352963i	$-0.885174\pi$
$43$	−7.19863	+	4.15613i	−1.09778	+	0.633804i	−0.162144	+	0.986767i	$0.551841\pi$
$44$		0			0
$45$	−4.83690	−	5.31784i	−0.721042	−	0.792737i
$46$		0			0
$47$	−5.38111	+	9.32036i	−0.784916	+	1.35951i	0.144133	+	0.989558i	$0.453961\pi$
$47$	−5.38111	+	9.32036i	−0.784916	+	1.35951i	−0.929049	+	0.369956i	$0.879373\pi$
$48$		0			0
$49$	4.11855	−	5.66017i	0.588365	−	0.808596i
$50$		0			0
$51$	1.10834	−	7.11359i	0.155198	−	0.996102i
$52$		0			0
$53$	4.88791	−	8.46611i	0.671406	−	1.16291i	−0.306099	−	0.952000i	$-0.599024\pi$
$53$	4.88791	−	8.46611i	0.671406	−	1.16291i	0.977505	−	0.210910i	$-0.0676428\pi$
$54$		0			0
$55$	−2.82322			−0.380683
$56$		0			0
$57$	0.918254	−	1.13980i	0.121626	−	0.150971i
$58$		0			0
$59$	−2.78034	−	4.81569i	−0.361969	−	0.626949i	0.626316	−	0.779570i	$-0.284562\pi$
$59$	−2.78034	−	4.81569i	−0.361969	−	0.626949i	−0.988285	+	0.152621i	$0.951229\pi$
$60$		0			0
$61$	−0.597080	−	0.344724i	−0.0764482	−	0.0441374i	0.461289	−	0.887250i	$-0.347387\pi$
$61$	−0.597080	−	0.344724i	−0.0764482	−	0.0441374i	−0.537737	+	0.843113i	$0.680721\pi$
$62$		0			0
$63$	2.80978	−	7.42328i	0.353999	−	0.935246i
$64$		0			0
$65$	−5.45962	+	9.45635i	−0.677183	+	1.17292i
$66$		0			0
$67$	3.56340	−	2.05733i	0.435339	−	0.251343i	−0.266280	−	0.963896i	$-0.585794\pi$
$67$	3.56340	−	2.05733i	0.435339	−	0.251343i	0.701618	+	0.712553i	$0.252461\pi$
$68$		0			0
$69$	4.87535	−	1.88556i	0.586923	−	0.226995i
$70$		0			0
$71$			9.65062i			1.14532i	0.819794	+	0.572659i	$0.194088\pi$
$71$			9.65062i			1.14532i	−0.819794	+	0.572659i	$0.805912\pi$
$72$		0			0
$73$	6.02026	+	3.47580i	0.704618	+	0.406811i	0.809065	−	0.587719i	$-0.199974\pi$
$73$	6.02026	+	3.47580i	0.704618	+	0.406811i	−0.104447	+	0.994530i	$0.533307\pi$
$74$		0			0
$75$	−0.463377	−	1.19812i	−0.0535062	−	0.138347i
$76$		0			0
$77$	−1.41422	−	2.77802i	−0.161165	−	0.316585i
$78$		0			0
$79$	11.7100	+	6.76075i	1.31747	+	0.760643i	0.983321	−	0.181876i	$-0.0582170\pi$
$79$	11.7100	+	6.76075i	1.31747	+	0.760643i	0.334151	+	0.942519i	$0.391550\pi$
$80$		0			0
$81$	0.850594	−	8.95971i	0.0945104	−	0.995524i
$82$		0			0
$83$	−2.52663	−	4.37625i	−0.277333	−	0.480356i	0.693388	−	0.720565i	$-0.256117\pi$
$83$	−2.52663	−	4.37625i	−0.277333	−	0.480356i	−0.970721	+	0.240209i	$0.922784\pi$
$84$		0			0
$85$	4.97996	−	8.62554i	0.540152	−	0.935571i
$86$		0			0
$87$	−3.00783	+	3.73354i	−0.322473	+	0.400277i
$88$		0			0
$89$	−6.06236	+	3.50011i	−0.642609	+	0.371010i	−0.785619	−	0.618711i	$-0.787655\pi$
$89$	−6.06236	+	3.50011i	−0.642609	+	0.371010i	0.143010	+	0.989721i	$0.454322\pi$
$90$		0			0
$91$	−12.0398	−	0.635304i	−1.26211	−	0.0665979i
$92$		0			0
$93$	7.55502	−	9.37784i	0.783419	−	0.972437i
$94$		0			0
$95$	1.75361	−	1.01245i	0.179917	−	0.103875i
$96$		0			0
$97$	−0.316523	+	0.182744i	−0.0321380	+	0.0185549i	−0.515983	−	0.856599i	$-0.672573\pi$
$97$	−0.316523	+	0.182744i	−0.0321380	+	0.0185549i	0.483845	+	0.875154i	$0.339240\pi$
$98$		0			0
$99$	−2.37834	−	2.61482i	−0.239032	−	0.262800i
$100$		0			0
$101$			19.0574i			1.89628i	0.317855	+	0.948139i	$0.397037\pi$
$101$			19.0574i			1.89628i	−0.317855	+	0.948139i	$0.602963\pi$
$102$		0			0
$103$	3.79017			0.373456			0.186728	−	0.982412i	$-0.440212\pi$
$103$	3.79017			0.373456			0.186728	+	0.982412i	$0.440212\pi$
$104$		0			0
$105$	7.32986	−	8.17607i	0.715321	−	0.797902i
$106$		0			0
$107$	−11.6936	+	6.75131i	−1.13046	+	0.652673i	−0.944051	−	0.329798i	$-0.893019\pi$
$107$	−11.6936	+	6.75131i	−1.13046	+	0.652673i	−0.186412	+	0.982472i	$0.559686\pi$
$108$		0			0
$109$	8.13901	−	14.0972i	0.779576	−	1.35027i	−0.152610	−	0.988286i	$-0.548768\pi$
$109$	8.13901	−	14.0972i	0.779576	−	1.35027i	0.932186	−	0.361979i	$-0.117899\pi$
$110$		0			0
$111$	−10.0415	+	12.4642i	−0.953093	+	1.18305i
$112$		0			0
$113$	−9.03477	+	15.6487i	−0.849920	+	1.47210i	0.0313588	+	0.999508i	$0.490017\pi$
$113$	−9.03477	+	15.6487i	−0.849920	+	1.47210i	−0.881279	+	0.472597i	$0.843317\pi$
$114$		0			0
$115$	7.23158			0.674348
$116$		0			0
$117$	−13.3576	+	2.90961i	−1.23491	+	0.268993i
$118$		0			0
$119$	10.9820	+	0.579487i	1.00672	+	0.0531215i
$120$		0			0
$121$	9.61180			0.873800
$122$		0			0
$123$	0.766604	−	4.92027i	0.0691224	−	0.443646i
$124$		0			0
$125$			10.2037i			0.912649i
$126$		0			0
$127$			12.2396i			1.08609i	0.839703	+	0.543046i	$0.182729\pi$
$127$			12.2396i			1.08609i	−0.839703	+	0.543046i	$0.817271\pi$
$128$		0			0
$129$	−11.2115	−	9.03230i	−0.987122	−	0.795250i
$130$		0			0
$131$	−9.39696			−0.821016			−0.410508	−	0.911857i	$-0.634649\pi$
$131$	−9.39696			−0.821016			−0.410508	+	0.911857i	$0.634649\pi$
$132$		0			0
$133$	1.87466	+	1.21837i	0.162554	+	0.105646i
$134$		0			0
$135$	5.56866	−	11.1362i	0.479274	−	0.958452i
$136$		0			0
$137$	−8.51962			−0.727880			−0.363940	−	0.931422i	$-0.618569\pi$
$137$	−8.51962			−0.727880			−0.363940	+	0.931422i	$0.618569\pi$
$138$		0			0
$139$	−0.147974	+	0.256298i	−0.0125510	+	0.0217389i	−0.872233	−	0.489091i	$-0.837329\pi$
$139$	−0.147974	+	0.256298i	−0.0125510	+	0.0217389i	0.859682	+	0.510830i	$0.170662\pi$
$140$		0			0
$141$	−18.4185	−	2.86970i	−1.55112	−	0.241672i
$142$		0			0
$143$	−2.68454	+	4.64976i	−0.224493	+	0.388833i
$144$		0			0
$145$	−5.74412	+	3.31637i	−0.477024	+	0.275410i
$146$		0			0
$147$	11.7169	+	3.11692i	0.966390	+	0.257079i
$148$		0			0
$149$	−2.59649			−0.212713			−0.106356	−	0.994328i	$-0.533918\pi$
$149$	−2.59649			−0.212713			−0.106356	+	0.994328i	$0.533918\pi$
$150$		0			0
$151$		−	3.97811i		−	0.323734i	−0.986813	−	0.161867i	$-0.948248\pi$
$151$		−	3.97811i		−	0.323734i	0.986813	−	0.161867i	$-0.0517516\pi$
$152$		0			0
$153$	12.1841	−	2.65398i	0.985022	−	0.214561i
$154$		0			0
$155$	14.4280	−	8.33001i	1.15889	−	0.669083i
$156$		0			0
$157$	−7.91181	+	4.56789i	−0.631432	+	0.364557i	−0.781306	−	0.624148i	$-0.785446\pi$
$157$	−7.91181	+	4.56789i	−0.631432	+	0.364557i	0.149875	+	0.988705i	$0.452113\pi$
$158$		0			0
$159$	16.7304	+	2.60668i	1.32680	+	0.206723i
$160$		0			0
$161$	3.62247	+	7.11579i	0.285490	+	0.560803i
$162$		0			0
$163$	12.5316	−	7.23513i	0.981551	−	0.566699i	0.0788132	−	0.996889i	$-0.474887\pi$
$163$	12.5316	−	7.23513i	0.981551	−	0.566699i	0.902738	+	0.430190i	$0.141554\pi$
$164$		0			0
$165$	−1.76389	−	4.56075i	−0.137319	−	0.355054i
$166$		0			0
$167$	10.8613	−	18.8123i	0.840471	−	1.45574i	−0.0490255	−	0.998798i	$-0.515612\pi$
$167$	10.8613	−	18.8123i	0.840471	−	1.45574i	0.889497	−	0.456941i	$-0.151055\pi$
$168$		0			0
$169$	3.88288	+	6.72534i	0.298683	+	0.517334i
$170$		0			0
$171$	2.41499	+	0.771259i	0.184679	+	0.0589797i
$172$		0			0
$173$	7.12752	+	4.11508i	0.541895	+	0.312863i	0.745847	−	0.666118i	$-0.232045\pi$
$173$	7.12752	+	4.11508i	0.541895	+	0.312863i	−0.203951	+	0.978981i	$0.565378\pi$
$174$		0			0
$175$	1.74871	−	0.890221i	0.132190	−	0.0672944i
$176$		0			0
$177$	6.04236	−	7.50022i	0.454172	−	0.563751i
$178$		0			0
$179$	10.8750	+	6.27871i	0.812838	+	0.469292i	0.847941	−	0.530091i	$-0.177842\pi$
$179$	10.8750	+	6.27871i	0.812838	+	0.469292i	−0.0351022	+	0.999384i	$0.511176\pi$
$180$		0			0
$181$			18.4056i			1.36808i	0.729446	+	0.684039i	$0.239778\pi$
$181$			18.4056i			1.36808i	−0.729446	+	0.684039i	$0.760222\pi$
$182$		0			0
$183$	0.183838	−	1.17992i	0.0135897	−	0.0872225i
$184$		0			0
$185$	−19.1764	+	11.0715i	−1.40988	+	0.813993i
$186$		0			0
$187$	2.44868	−	4.24125i	0.179066	−	0.310151i
$188$		0			0
$189$	13.7474	−	0.0988847i	0.999974	−	0.00719280i
$190$		0			0
$191$	14.4283	+	8.33016i	1.04399	+	0.602750i	0.920962	−	0.389653i	$-0.127405\pi$
$191$	14.4283	+	8.33016i	1.04399	+	0.602750i	0.123031	+	0.992403i	$0.460738\pi$
$192$		0			0
$193$	1.17140	+	2.02893i	0.0843195	+	0.146046i	0.905101	−	0.425197i	$-0.139795\pi$
$193$	1.17140	+	2.02893i	0.0843195	+	0.146046i	−0.820782	+	0.571242i	$0.806462\pi$
$194$		0			0
$195$	−18.6872	−	2.91157i	−1.33822	−	0.208502i
$196$		0			0
$197$	12.9457			0.922345			0.461172	−	0.887311i	$-0.347429\pi$
$197$	12.9457			0.922345			0.461172	+	0.887311i	$0.347429\pi$
$198$		0			0
$199$	5.08704	−	8.81102i	0.360611	−	0.624597i	−0.627451	−	0.778656i	$-0.715902\pi$
$199$	5.08704	−	8.81102i	0.360611	−	0.624597i	0.988062	+	0.154060i	$0.0492349\pi$
$200$		0			0
$201$	5.54984	+	4.47109i	0.391455	+	0.315366i
$202$		0			0
$203$	−6.14064	−	3.99091i	−0.430988	−	0.280107i
$204$		0			0
$205$	3.44450	−	5.96604i	0.240574	−	0.416686i
$206$		0			0
$207$	6.09203	+	6.69777i	0.423426	+	0.465527i
$208$		0			0
$209$	0.862265	−	0.497829i	0.0596441	−	0.0344355i
$210$		0			0
$211$	2.61024	+	1.50702i	0.179696	+	0.103748i	0.587150	−	0.809478i	$-0.300250\pi$
$211$	2.61024	+	1.50702i	0.179696	+	0.103748i	−0.407454	+	0.913226i	$0.633583\pi$
$212$		0			0
$213$	−15.5900	+	6.02951i	−1.06821	+	0.413135i
$214$		0			0
$215$	−9.95883	−	17.2492i	−0.679187	−	1.17639i
$216$		0			0
$217$	15.4240	+	10.0243i	1.04705	+	0.680494i
$218$		0			0
$219$	−1.85361	+	11.8970i	−0.125256	+	0.803923i
$220$		0			0
$221$	−9.47066	−	16.4037i	−0.637066	−	1.10343i
$222$		0			0
$223$	1.46794	+	2.54255i	0.0983005	+	0.170262i	0.910981	−	0.412448i	$-0.135326\pi$
$223$	1.46794	+	2.54255i	0.0983005	+	0.170262i	−0.812681	+	0.582709i	$0.801993\pi$
$224$		0			0
$225$	1.64598	−	1.49712i	0.109732	−	0.0998078i
$226$		0			0
$227$	17.8584			1.18530			0.592652	−	0.805459i	$-0.298081\pi$
$227$	17.8584			1.18530			0.592652	+	0.805459i	$0.298081\pi$
$228$		0			0
$229$		−	15.8125i		−	1.04492i	−0.852663	−	0.522461i	$-0.825014\pi$
$229$		−	15.8125i		−	1.04492i	0.852663	−	0.522461i	$-0.174986\pi$
$230$		0			0
$231$	3.60415	−	4.02024i	0.237136	−	0.264512i
$232$		0			0
$233$	−2.60579	−	4.51336i	−0.170711	−	0.295680i	0.767958	−	0.640501i	$-0.221273\pi$
$233$	−2.60579	−	4.51336i	−0.170711	−	0.295680i	−0.938669	+	0.344820i	$0.887940\pi$
$234$		0			0
$235$	−22.3332	−	12.8941i	−1.45686	−	0.841118i
$236$		0			0
$237$	−3.60545	+	23.1407i	−0.234199	+	1.50315i
$238$		0			0
$239$	22.7367	+	13.1271i	1.47072	+	0.849118i	0.999459	−	0.0328775i	$-0.0104671\pi$
$239$	22.7367	+	13.1271i	1.47072	+	0.849118i	0.471257	+	0.881996i	$0.343800\pi$
$240$		0			0
$241$		−	11.3008i		−	0.727946i	−0.931409	−	0.363973i	$-0.881420\pi$
$241$		−	11.3008i		−	0.727946i	0.931409	−	0.363973i	$-0.118580\pi$
$242$		0			0
$243$	15.0053	−	4.22376i	0.962592	−	0.270955i
$244$		0			0
$245$	13.5628	+	9.86878i	0.866494	+	0.630493i
$246$		0			0
$247$		−	3.85086i		−	0.245024i
$248$		0			0
$249$	5.49098	−	6.81581i	0.347977	−	0.431934i
$250$		0			0
$251$	−22.5628			−1.42415			−0.712077	−	0.702102i	$-0.752245\pi$
$251$	−22.5628			−1.42415			−0.712077	+	0.702102i	$0.752245\pi$
$252$		0			0
$253$	3.55583			0.223553
$254$		0			0
$255$	17.0454	+	2.65577i	1.06743	+	0.166311i
$256$		0			0
$257$			9.27951i			0.578840i	0.957202	+	0.289420i	$0.0934624\pi$
$257$			9.27951i			0.578840i	−0.957202	+	0.289420i	$0.906538\pi$
$258$		0			0
$259$	−20.5002	−	13.3234i	−1.27382	−	0.827876i
$260$		0			0
$261$	−7.91054	−	2.52634i	−0.489650	−	0.156376i
$262$		0			0
$263$			14.3562i			0.885243i	0.896708	+	0.442622i	$0.145952\pi$
$263$			14.3562i			0.885243i	−0.896708	+	0.442622i	$0.854048\pi$
$264$		0			0
$265$	20.2863	+	11.7123i	1.24618	+	0.719481i
$266$		0			0
$267$	−9.44185	−	7.60659i	−0.577832	−	0.465516i
$268$		0			0
$269$	−17.6839	−	10.2098i	−1.07821	−	0.622503i	−0.147795	−	0.989018i	$-0.547218\pi$
$269$	−17.6839	−	10.2098i	−1.07821	−	0.622503i	−0.930412	+	0.366515i	$0.880551\pi$
$270$		0			0
$271$	8.40830	+	14.5636i	0.510768	+	0.884676i	0.999922	+	0.0124785i	$0.00397212\pi$
$271$	8.40830	+	14.5636i	0.510768	+	0.884676i	−0.489154	+	0.872197i	$0.662695\pi$
$272$		0			0
$273$	−6.49592	−	19.8465i	−0.393151	−	1.20117i
$274$		0			0
$275$		−	0.873844i		−	0.0526948i
$276$		0			0
$277$	−30.7831			−1.84958			−0.924790	−	0.380479i	$-0.875759\pi$
$277$	−30.7831			−1.84958			−0.924790	+	0.380479i	$0.875759\pi$
$278$		0			0
$279$	19.8696	+	6.34561i	1.18956	+	0.379902i
$280$		0			0
$281$	−9.98418	−	17.2931i	−0.595606	−	1.03162i	−0.993461	−	0.114172i	$-0.963579\pi$
$281$	−9.98418	−	17.2931i	−0.595606	−	1.03162i	0.397855	−	0.917448i	$-0.369755\pi$
$282$		0			0
$283$	15.4638	+	26.7841i	0.919226	+	1.59215i	0.800593	+	0.599209i	$0.204518\pi$
$283$	15.4638	+	26.7841i	0.919226	+	1.59215i	0.118634	+	0.992938i	$0.462149\pi$
$284$		0			0
$285$	2.73117	+	2.20030i	0.161781	+	0.130334i
$286$		0			0
$287$	7.59595	+	0.400815i	0.448375	+	0.0236594i
$288$		0			0
$289$	0.138597	+	0.240056i	0.00815275	+	0.0141210i
$290$		0			0
$291$	−0.492970	−	0.397149i	−0.0288984	−	0.0232813i
$292$		0			0
$293$	9.76019	+	5.63505i	0.570196	+	0.329203i	0.757228	−	0.653151i	$-0.226553\pi$
$293$	9.76019	+	5.63505i	0.570196	+	0.329203i	−0.187031	+	0.982354i	$0.559887\pi$
$294$		0			0
$295$	11.5392	−	6.66218i	0.671840	−	0.387887i
$296$		0			0
$297$	2.73816	−	5.47576i	0.158884	−	0.317736i
$298$		0			0
$299$	6.87635	−	11.9102i	0.397670	−	0.688784i
$300$		0			0
$301$	11.9844	−	18.4399i	0.690770	−	1.06286i
$302$		0			0
$303$	−30.7860	+	11.9067i	−1.76861	+	0.684019i
$304$		0			0
$305$	0.826020	−	1.43071i	0.0472978	−	0.0819222i
$306$		0			0
$307$	26.7888			1.52892			0.764459	−	0.644673i	$-0.223006\pi$
$307$	26.7888			1.52892			0.764459	+	0.644673i	$0.223006\pi$
$308$		0			0
$309$	2.36802	+	6.12280i	0.134712	+	0.348314i
$310$		0			0
$311$	−6.92838	−	12.0003i	−0.392872	−	0.680475i	0.599955	−	0.800034i	$-0.295185\pi$
$311$	−6.92838	−	12.0003i	−0.392872	−	0.680475i	−0.992827	+	0.119559i	$0.961852\pi$
$312$		0			0
$313$	27.2951	+	15.7588i	1.54281	+	0.890741i	0.998660	+	0.0517522i	$0.0164806\pi$
$313$	27.2951	+	15.7588i	1.54281	+	0.890741i	0.544149	+	0.838989i	$0.316853\pi$
$314$		0			0
$315$	17.7875	+	6.73273i	1.00221	+	0.379346i
$316$		0			0
$317$	2.85383	−	4.94298i	0.160287	−	0.277626i	−0.774684	−	0.632348i	$-0.782091\pi$
$317$	2.85383	−	4.94298i	0.160287	−	0.277626i	0.934972	+	0.354722i	$0.115425\pi$
$318$		0			0
$319$	−2.82443	+	1.63069i	−0.158138	+	0.0913009i
$320$		0			0
$321$	−18.2123	−	14.6723i	−1.01651	−	0.818925i
$322$		0			0
$323$			3.51253i			0.195442i
$324$		0			0
$325$	−2.92693	−	1.68986i	−0.162357	−	0.0937367i
$326$		0			0
$327$	27.8583	+	4.34047i	1.54057	+	0.240028i
$328$		0			0
$329$	1.50041	−	28.4346i	0.0827202	−	1.56765i
$330$		0			0
$331$	5.53172	+	3.19374i	0.304051	+	0.175544i	0.644261	−	0.764806i	$-0.277165\pi$
$331$	5.53172	+	3.19374i	0.304051	+	0.175544i	−0.340211	+	0.940349i	$0.610498\pi$
$332$		0			0
$333$	−26.4089	−	8.43402i	−1.44720	−	0.462181i
$334$		0			0
$335$	4.92973	+	8.53854i	0.269340	+	0.466510i
$336$		0			0
$337$	−3.37499	+	5.84566i	−0.183848	+	0.318433i	−0.943188	−	0.332261i	$-0.892189\pi$
$337$	−3.37499	+	5.84566i	−0.183848	+	0.318433i	0.759340	+	0.650694i	$0.225522\pi$
$338$		0			0
$339$	−30.9243	−	4.81817i	−1.67958	−	0.261687i
$340$		0			0
$341$	7.09437	−	4.09593i	0.384181	−	0.221807i
$342$		0			0
$343$	−2.91686	+	18.2891i	−0.157496	+	0.987520i
$344$		0			0
$345$	4.51814	+	11.6822i	0.243249	+	0.628948i
$346$		0			0
$347$	28.4215	−	16.4092i	1.52575	−	0.880891i	0.526214	−	0.850352i	$-0.323611\pi$
$347$	28.4215	−	16.4092i	1.52575	−	0.880891i	0.999534	−	0.0305390i	$-0.00972238\pi$
$348$		0			0
$349$	−0.798343	+	0.460924i	−0.0427343	+	0.0246727i	−0.521215	−	0.853425i	$-0.674521\pi$
$349$	−0.798343	+	0.460924i	−0.0427343	+	0.0246727i	0.478481	+	0.878098i	$0.341188\pi$
$350$		0			0
$351$	−13.0459	−	19.7606i	−0.696337	−	1.05474i
$352$		0			0
$353$		−	25.7242i		−	1.36916i	−0.728937	−	0.684581i	$-0.759985\pi$
$353$		−	25.7242i		−	1.36916i	0.728937	−	0.684581i	$-0.240015\pi$
$354$		0			0
$355$	−23.1246			−1.22733
$356$		0			0
$357$	5.92521	+	18.1028i	0.313595	+	0.958104i
$358$		0			0
$359$	−22.2113	+	12.8237i	−1.17227	+	0.676810i	−0.954213	−	0.299126i	$-0.903305\pi$
$359$	−22.2113	+	12.8237i	−1.17227	+	0.676810i	−0.218056	+	0.975936i	$0.569971\pi$
$360$		0			0
$361$	9.14294	−	15.8360i	0.481208	−	0.833476i
$362$		0			0
$363$	6.00526	+	15.5273i	0.315194	+	0.814972i
$364$		0			0
$365$	−8.32863	+	14.4256i	−0.435940	+	0.755071i
$366$		0			0
$367$	1.43115			0.0747053			0.0373527	−	0.999302i	$-0.488108\pi$
$367$	1.43115			0.0747053			0.0373527	+	0.999302i	$0.488108\pi$
$368$		0			0
$369$	8.42737	−	1.83568i	0.438711	−	0.0955617i
$370$		0			0
$371$	−1.36289	+	25.8285i	−0.0707577	+	1.34095i
$372$		0			0
$373$	9.20332			0.476530			0.238265	−	0.971200i	$-0.423421\pi$
$373$	9.20332			0.476530			0.238265	+	0.971200i	$0.423421\pi$
$374$		0			0
$375$	−16.4835	+	6.37508i	−0.851205	+	0.329208i
$376$		0			0
$377$			12.6139i			0.649647i
$378$		0			0
$379$		−	18.1804i		−	0.933863i	−0.884293	−	0.466932i	$-0.845359\pi$
$379$		−	18.1804i		−	0.933863i	0.884293	−	0.466932i	$-0.154641\pi$
$380$		0			0
$381$	−19.7724	+	7.64708i	−1.01297	+	0.391772i
$382$		0			0
$383$	−33.7806			−1.72611			−0.863055	−	0.505110i	$-0.831452\pi$
$383$	−33.7806			−1.72611			−0.863055	+	0.505110i	$0.831452\pi$
$384$		0			0
$385$	6.65663	−	3.38872i	0.339253	−	0.172705i
$386$		0			0
$387$	7.58641	−	23.7548i	0.385639	−	1.20752i
$388$		0			0
$389$	16.1526			0.818968			0.409484	−	0.912317i	$-0.365709\pi$
$389$	16.1526			0.818968			0.409484	+	0.912317i	$0.365709\pi$
$390$		0			0
$391$	−6.27221	+	10.8638i	−0.317199	+	0.549406i
$392$		0			0
$393$	−5.87103	−	15.1802i	−0.296154	−	0.765742i
$394$		0			0
$395$	−16.1999	+	28.0591i	−0.815108	+	1.41181i
$396$		0			0
$397$	−10.2662	+	5.92719i	−0.515246	+	0.297477i	−0.734987	−	0.678081i	$-0.762812\pi$
$397$	−10.2662	+	5.92719i	−0.515246	+	0.297477i	0.219742	+	0.975558i	$0.429479\pi$
$398$		0			0
$399$	−0.796962	+	3.78962i	−0.0398980	+	0.189718i
$400$		0			0
$401$	19.7416			0.985850			0.492925	−	0.870072i	$-0.335928\pi$
$401$	19.7416			0.985850			0.492925	+	0.870072i	$0.335928\pi$
$402$		0			0
$403$		−	31.6833i		−	1.57826i
$404$		0			0
$405$	21.4691	+	2.03817i	1.06681	+	0.101278i
$406$		0			0
$407$	−9.42920	+	5.44395i	−0.467388	+	0.269847i
$408$		0			0
$409$	−32.3307	+	18.6662i	−1.59865	+	0.922982i	−0.606905	+	0.794774i	$0.707589\pi$
$409$	−32.3307	+	18.6662i	−1.59865	+	0.922982i	−0.991747	+	0.128208i	$0.959077\pi$
$410$		0			0
$411$	−5.32288	−	13.7629i	−0.262558	−	0.678876i
$412$		0			0
$413$	12.3358	+	8.01724i	0.607005	+	0.394503i
$414$		0			0
$415$	10.4863	−	6.05425i	0.514750	−	0.297191i
$416$		0			0
$417$	−0.506485	−	0.0789130i	−0.0248027	−	0.00386439i
$418$		0			0
$419$	14.2178	−	24.6259i	0.694583	−	1.20305i	−0.275738	−	0.961233i	$-0.588922\pi$
$419$	14.2178	−	24.6259i	0.694583	−	1.20305i	0.970321	−	0.241820i	$-0.0777445\pi$
$420$		0			0
$421$	−4.05583	−	7.02490i	−0.197669	−	0.342373i	0.750103	−	0.661321i	$-0.230004\pi$
$421$	−4.05583	−	7.02490i	−0.197669	−	0.342373i	−0.947772	+	0.318948i	$0.896670\pi$
$422$		0			0
$423$	−6.87167	−	31.5469i	−0.334112	−	1.53387i
$424$		0			0
$425$	2.66978	+	1.54140i	0.129503	+	0.0747687i
$426$		0			0
$427$	1.82157	+	0.0961190i	0.0881522	+	0.00465152i
$428$		0			0
$429$	−9.18866	−	1.43164i	−0.443633	−	0.0691203i
$430$		0			0
$431$	−18.8674	−	10.8931i	−0.908809	−	0.524701i	−0.0287609	−	0.999586i	$-0.509156\pi$
$431$	−18.8674	−	10.8931i	−0.908809	−	0.524701i	−0.880048	+	0.474885i	$0.842489\pi$
$432$		0			0
$433$		−	12.3731i		−	0.594612i	−0.954782	−	0.297306i	$-0.903912\pi$
$433$		−	12.3731i		−	0.594612i	0.954782	−	0.297306i	$-0.0960881\pi$
$434$		0			0
$435$	−8.94622	−	7.20729i	−0.428938	−	0.345563i
$436$		0			0
$437$	−2.20866	+	1.27517i	−0.105654	+	0.0609996i
$438$		0			0
$439$	−18.6443	+	32.2929i	−0.889845	+	1.54126i	−0.0497864	+	0.998760i	$0.515854\pi$
$439$	−18.6443	+	32.2929i	−0.889845	+	1.54126i	−0.840058	+	0.542496i	$0.817479\pi$
$440$		0			0
$441$	2.28525	+	20.8753i	0.108821	+	0.994061i
$442$		0			0
$443$	0.922931	+	0.532854i	0.0438498	+	0.0253167i	0.521765	−	0.853089i	$-0.325274\pi$
$443$	0.922931	+	0.532854i	0.0438498	+	0.0253167i	−0.477915	+	0.878406i	$0.658607\pi$
$444$		0			0
$445$	−8.38687	−	14.5265i	−0.397576	−	0.688622i
$446$		0			0
$447$	−1.62223	−	4.19448i	−0.0767290	−	0.198392i
$448$		0			0
$449$	−0.713776			−0.0336852			−0.0168426	−	0.999858i	$-0.505361\pi$
$449$	−0.713776			−0.0336852			−0.0168426	+	0.999858i	$0.505361\pi$
$450$		0			0
$451$	1.69369	−	2.93355i	0.0797526	−	0.138136i
$452$		0			0
$453$	6.42640	−	2.48544i	0.301939	−	0.116776i
$454$		0			0
$455$	1.52230	−	28.8495i	0.0713665	−	1.35248i
$456$		0			0
$457$	−11.7455	+	20.3439i	−0.549433	+	0.951647i	0.448880	+	0.893592i	$0.351823\pi$
$457$	−11.7455	+	20.3439i	−0.549433	+	0.951647i	−0.998313	+	0.0580546i	$0.981510\pi$
$458$		0			0
$459$	11.8997	+	18.0245i	0.555430	+	0.841310i
$460$		0			0
$461$	−2.62177	+	1.51368i	−0.122108	+	0.0704991i	−0.559810	−	0.828621i	$-0.689126\pi$
$461$	−2.62177	+	1.51368i	−0.122108	+	0.0704991i	0.437702	+	0.899120i	$0.355793\pi$
$462$		0			0
$463$	−2.99321	−	1.72813i	−0.139106	−	0.0803129i	0.428832	−	0.903384i	$-0.358925\pi$
$463$	−2.99321	−	1.72813i	−0.139106	−	0.0803129i	−0.567938	+	0.823071i	$0.692259\pi$
$464$		0			0
$465$	22.4710	+	18.1032i	1.04207	+	0.839514i
$466$		0			0
$467$	−8.61849	−	14.9277i	−0.398816	−	0.690770i	0.594764	−	0.803900i	$-0.297245\pi$
$467$	−8.61849	−	14.9277i	−0.398816	−	0.690770i	−0.993580	+	0.113131i	$0.963912\pi$
$468$		0			0
$469$	−5.93241	+	9.12796i	−0.273933	+	0.421490i
$470$		0			0
$471$	−12.3223	−	9.92715i	−0.567781	−	0.457419i
$472$		0			0
$473$	−4.89684	−	8.48157i	−0.225157	−	0.389983i
$474$		0			0
$475$	0.313373	+	0.542778i	0.0143785	+	0.0249043i
$476$		0			0
$477$	6.24186	+	28.6555i	0.285795	+	1.31205i
$478$		0			0
$479$	−22.6565			−1.03520			−0.517601	−	0.855622i	$-0.673175\pi$
$479$	−22.6565			−1.03520			−0.517601	+	0.855622i	$0.673175\pi$
$480$		0			0
$481$			42.1106i			1.92008i
$482$		0			0
$483$	−9.23190	+	10.2977i	−0.420066	+	0.468561i
$484$		0			0
$485$	−0.437888	−	0.758444i	−0.0198835	−	0.0344392i
$486$		0			0
$487$	4.91789	+	2.83934i	0.222851	+	0.128663i	0.607270	−	0.794496i	$-0.292265\pi$
$487$	4.91789	+	2.83934i	0.222851	+	0.128663i	−0.384419	+	0.923159i	$0.625598\pi$
$488$		0			0
$489$	19.5174	+	15.7237i	0.882608	+	0.711051i
$490$		0			0
$491$	−24.6500	−	14.2317i	−1.11244	−	0.642266i	−0.172978	−	0.984926i	$-0.555339\pi$
$491$	−24.6500	−	14.2317i	−1.11244	−	0.642266i	−0.939460	+	0.342659i	$0.888672\pi$
$492$		0			0
$493$		−	11.5056i		−	0.518188i
$494$		0			0
$495$	6.26558	−	5.69893i	0.281617	−	0.256148i
$496$		0			0
$497$	−11.5837	−	22.7543i	−0.519598	−	1.02067i
$498$		0			0
$499$		−	5.52749i		−	0.247444i	−0.992317	−	0.123722i	$-0.960517\pi$
$499$		−	5.52749i		−	0.247444i	0.992317	−	0.123722i	$-0.0394831\pi$
$500$		0			0
$501$	37.1761	+	5.79223i	1.66090	+	0.258778i
$502$		0			0
$503$	24.3282			1.08474			0.542371	−	0.840139i	$-0.317527\pi$
$503$	24.3282			1.08474			0.542371	+	0.840139i	$0.317527\pi$
$504$		0			0
$505$	−45.6648			−2.03206
$506$		0			0
$507$	−8.43845	+	10.4744i	−0.374765	+	0.465185i
$508$		0			0
$509$		−	15.9895i		−	0.708722i	−0.935109	−	0.354361i	$-0.884698\pi$
$509$		−	15.9895i		−	0.708722i	0.935109	−	0.354361i	$-0.115302\pi$
$510$		0			0
$511$	−18.3666	−	0.969152i	−0.812492	−	0.0428728i
$512$		0			0
$513$	0.262913	+	4.38314i	0.0116079	+	0.193521i
$514$		0			0
$515$			9.08192i			0.400197i
$516$		0			0
$517$	−10.9814	−	6.34013i	−0.482963	−	0.278839i
$518$		0			0
$519$	−2.19453	+	14.0851i	−0.0963294	+	0.618268i
$520$		0			0
$521$	1.47503	+	0.851611i	0.0646224	+	0.0373098i	0.531963	−	0.846768i	$-0.321455\pi$
$521$	1.47503	+	0.851611i	0.0646224	+	0.0373098i	−0.467341	+	0.884077i	$0.654788\pi$
$522$		0			0
$523$	15.7605	+	27.2979i	0.689157	+	1.19366i	0.972111	+	0.234522i	$0.0753524\pi$
$523$	15.7605	+	27.2979i	0.689157	+	1.19366i	−0.282954	+	0.959134i	$0.591314\pi$
$524$		0			0
$525$	2.53066	+	2.26874i	0.110447	+	0.0990159i
$526$		0			0
$527$			28.8997i			1.25889i
$528$		0			0
$529$	13.8919			0.603995
$530$		0			0
$531$	15.8913	+	5.07510i	0.689624	+	0.220240i
$532$		0			0
$533$	−6.55059	−	11.3460i	−0.283738	−	0.491448i
$534$		0			0
$535$	−16.1773	−	28.0199i	−0.699407	−	1.21141i
$536$		0			0
$537$	−3.34838	+	21.4908i	−0.144493	+	0.927396i
$538$		0			0
$539$	6.66892	+	4.85256i	0.287251	+	0.209015i
$540$		0			0
$541$	−16.7934	−	29.0870i	−0.722004	−	1.25055i	−0.960195	−	0.279329i	$-0.909888\pi$
$541$	−16.7934	−	29.0870i	−0.722004	−	1.25055i	0.238192	−	0.971218i	$-0.423445\pi$
$542$		0			0
$543$	−29.7332	+	11.4994i	−1.27597	+	0.493488i
$544$		0			0
$545$	33.7794	+	19.5025i	1.44695	+	0.835396i
$546$		0			0
$547$	2.50860	−	1.44834i	0.107260	−	0.0619266i	−0.445410	−	0.895327i	$-0.646942\pi$
$547$	2.50860	−	1.44834i	0.107260	−	0.0619266i	0.552670	+	0.833400i	$0.313609\pi$
$548$		0			0
$549$	2.02096	−	0.440212i	0.0862523	−	0.0187878i
$550$		0			0
$551$	1.16957	−	2.02576i	0.0498256	−	0.0863004i
$552$		0			0
$553$	−35.7248	−	1.88509i	−1.51917	−	0.0801622i
$554$		0			0
$555$	−29.8664	−	24.0611i	−1.26776	−	1.02134i
$556$		0			0
$557$	−0.143138	+	0.247922i	−0.00606494	+	0.0105048i	−0.869042	−	0.494738i	$-0.835264\pi$
$557$	−0.143138	+	0.247922i	−0.00606494	+	0.0105048i	0.862977	+	0.505243i	$0.168597\pi$
$558$		0			0
$559$	−37.8785			−1.60209
$560$		0			0
$561$	8.38137	+	1.30586i	0.353862	+	0.0551335i
$562$		0			0
$563$	−1.15309	−	1.99720i	−0.0485968	−	0.0841721i	0.840704	−	0.541495i	$-0.182142\pi$
$563$	−1.15309	−	1.99720i	−0.0485968	−	0.0841721i	−0.889301	+	0.457323i	$0.848808\pi$
$564$		0			0
$565$	−37.4970	−	21.6489i	−1.57751	−	0.910777i
$566$		0			0
$567$	8.74882	+	22.1463i	0.367416	+	0.930057i
$568$		0			0
$569$	−4.19911	+	7.27307i	−0.176036	+	0.304903i	−0.940519	−	0.339740i	$-0.889661\pi$
$569$	−4.19911	+	7.27307i	−0.176036	+	0.304903i	0.764483	+	0.644643i	$0.222994\pi$
$570$		0			0
$571$	−25.6800	+	14.8264i	−1.07467	+	0.620464i	−0.929455	−	0.368936i	$-0.879722\pi$
$571$	−25.6800	+	14.8264i	−1.07467	+	0.620464i	−0.145220	+	0.989399i	$0.546389\pi$
$572$		0			0
$573$	−4.44240	+	28.5125i	−0.185584	+	1.19113i
$574$		0			0
$575$			2.23832i			0.0933443i
$576$		0			0
$577$	−15.9006	−	9.18021i	−0.661950	−	0.382177i	0.131070	−	0.991373i	$-0.458159\pi$
$577$	−15.9006	−	9.18021i	−0.661950	−	0.382177i	−0.793020	+	0.609196i	$0.791492\pi$
$578$		0			0
$579$	−2.54575	+	3.15997i	−0.105798	+	0.131324i
$580$		0			0
$581$	11.2101	+	7.28565i	0.465074	+	0.302260i
$582$		0			0
$583$	9.97494	+	5.75903i	0.413120	+	0.238515i
$584$		0			0
$585$	−6.97193	−	32.0072i	−0.288254	−	1.32334i
$586$		0			0
$587$	20.9740	+	36.3280i	0.865689	+	1.49942i	0.866362	+	0.499417i	$0.166453\pi$
$587$	20.9740	+	36.3280i	0.865689	+	1.49942i	−0.000672696		1.00000i	$0.500214\pi$
$588$		0			0
$589$	−2.93772	+	5.08828i	−0.121047	+	0.209659i
$590$		0			0
$591$	8.08822	+	20.9131i	0.332705	+	0.860248i
$592$		0			0
$593$	−32.7972	+	18.9355i	−1.34682	+	0.777587i	−0.987798	−	0.155742i	$-0.950223\pi$
$593$	−32.7972	+	18.9355i	−1.34682	+	0.777587i	−0.359023	+	0.933329i	$0.616890\pi$
$594$		0			0
$595$	−1.38855	+	26.3148i	−0.0569252	+	1.07880i
$596$		0			0
$597$	17.4120	+	2.71288i	0.712624	+	0.111031i
$598$		0			0
$599$	15.3685	−	8.87302i	0.627941	−	0.362542i	−0.152013	−	0.988378i	$-0.548576\pi$
$599$	15.3685	−	8.87302i	0.627941	−	0.362542i	0.779954	+	0.625837i	$0.215242\pi$
$600$		0			0
$601$	−3.17935	+	1.83560i	−0.129689	+	0.0748757i	−0.563441	−	0.826156i	$-0.690523\pi$
$601$	−3.17935	+	1.83560i	−0.129689	+	0.0748757i	0.433752	+	0.901032i	$0.357189\pi$
$602$		0			0
$603$	−3.75536	+	11.7589i	−0.152930	+	0.478859i
$604$		0			0
$605$			23.0316i			0.936367i
$606$		0			0
$607$	4.22770			0.171597			0.0857985	−	0.996313i	$-0.472656\pi$
$607$	4.22770			0.171597			0.0857985	+	0.996313i	$0.472656\pi$
$608$		0			0
$609$	2.61053	−	12.4133i	0.105784	−	0.503011i
$610$		0			0
$611$	−42.4724	+	24.5214i	−1.71825	+	0.992031i
$612$		0			0
$613$	10.8479	−	18.7891i	0.438141	−	0.758883i	−0.559405	−	0.828895i	$-0.688970\pi$
$613$	10.8479	−	18.7891i	0.438141	−	0.758883i	0.997546	+	0.0700114i	$0.0223036\pi$
$614$		0			0
$615$	11.7898	+	1.83692i	0.475412	+	0.0740718i
$616$		0			0
$617$	15.3743	−	26.6291i	0.618946	−	1.07205i	−0.370732	−	0.928740i	$-0.620893\pi$
$617$	15.3743	−	26.6291i	0.618946	−	1.07205i	0.989678	−	0.143307i	$-0.0457735\pi$
$618$		0			0
$619$	−18.1998			−0.731513			−0.365757	−	0.930711i	$-0.619190\pi$
$619$	−18.1998			−0.731513			−0.365757	+	0.930711i	$0.619190\pi$
$620$		0			0
$621$	−7.01368	+	14.0260i	−0.281449	+	0.562842i
$622$		0			0
$623$	10.0927	−	15.5293i	0.404356	−	0.622166i
$624$		0			0
$625$	−28.1583			−1.12633
$626$		0			0
$627$	1.34294	+	1.08190i	0.0536318	+	0.0432071i
$628$		0			0
$629$		−	38.4109i		−	1.53154i
$630$		0			0
$631$		−	33.2928i		−	1.32537i	−0.748900	−	0.662683i	$-0.769418\pi$
$631$		−	33.2928i		−	1.32537i	0.748900	−	0.662683i	$-0.230582\pi$
$632$		0			0
$633$	−0.803683	+	5.15825i	−0.0319435	+	0.205022i
$634$		0			0
$635$	−29.3284			−1.16386
$636$		0			0
$637$	29.1501	−	12.9535i	1.15497	−	0.513235i
$638$		0			0
$639$	−19.4806	−	21.4176i	−0.770642	−	0.847268i
$640$		0			0
$641$	−9.69328			−0.382862			−0.191431	−	0.981506i	$-0.561313\pi$
$641$	−9.69328			−0.382862			−0.191431	+	0.981506i	$0.561313\pi$
$642$		0			0
$643$	14.4563	−	25.0391i	0.570101	−	0.987444i	−0.426454	−	0.904509i	$-0.640237\pi$
$643$	14.4563	−	25.0391i	0.570101	−	0.987444i	0.996555	−	0.0829345i	$-0.0264292\pi$
$644$		0			0
$645$	21.6430	−	26.8649i	0.852192	−	1.05780i
$646$		0			0
$647$	−2.50961	+	4.34678i	−0.0986631	+	0.170889i	−0.911132	−	0.412116i	$-0.864790\pi$
$647$	−2.50961	+	4.34678i	−0.0986631	+	0.170889i	0.812468	+	0.583005i	$0.198123\pi$
$648$		0			0
$649$	5.67394	−	3.27585i	0.222721	−	0.128588i
$650$		0			0
$651$	−6.55708	+	31.1795i	−0.256992	+	1.22202i
$652$		0			0
$653$	40.9622			1.60298			0.801488	−	0.598011i	$-0.204042\pi$
$653$	40.9622			1.60298			0.801488	+	0.598011i	$0.204042\pi$
$654$		0			0
$655$		−	22.5168i		−	0.879804i
$656$		0			0
$657$	−20.3770	+	4.43859i	−0.794981	+	0.173166i
$658$		0			0
$659$	22.1113	−	12.7660i	0.861335	−	0.497292i	−0.00312417	−	0.999995i	$-0.500994\pi$
$659$	22.1113	−	12.7660i	0.861335	−	0.497292i	0.864459	+	0.502703i	$0.167661\pi$
$660$		0			0
$661$	−22.7131	+	13.1134i	−0.883437	+	0.510052i	−0.871790	−	0.489880i	$-0.837041\pi$
$661$	−22.7131	+	13.1134i	−0.883437	+	0.510052i	−0.0116467	+	0.999932i	$0.503707\pi$
$662$		0			0
$663$	20.5821	−	25.5480i	0.799342	−	0.992201i
$664$		0			0
$665$	−2.91944	+	4.49202i	−0.113211	+	0.174193i
$666$		0			0
$667$	7.23468	−	4.17694i	0.280128	−	0.161732i
$668$		0			0
$669$	−3.19020	+	3.95990i	−0.123340	+	0.153099i
$670$		0			0
$671$	0.406161	−	0.703491i	0.0156797	−	0.0271580i
$672$		0			0
$673$	22.4846	+	38.9445i	0.866719	+	1.50120i	0.865331	+	0.501202i	$0.167108\pi$
$673$	22.4846	+	38.9445i	0.866719	+	1.50120i	0.00138802	+	0.999999i	$0.499558\pi$
$674$		0			0
$675$	3.44688	+	1.72361i	0.132670	+	0.0663419i
$676$		0			0
$677$	−3.98363	−	2.29995i	−0.153103	−	0.0883943i	0.421491	−	0.906833i	$-0.361507\pi$
$677$	−3.98363	−	2.29995i	−0.153103	−	0.0883943i	−0.574595	+	0.818438i	$0.694840\pi$
$678$		0			0
$679$	0.526952	−	0.810799i	0.0202226	−	0.0311156i
$680$		0			0
$681$	11.1576	+	28.8492i	0.427559	+	1.10550i
$682$		0			0
$683$	32.7196	+	18.8906i	1.25198	+	0.722830i	0.971502	−	0.237030i	$-0.0761741\pi$
$683$	32.7196	+	18.8906i	1.25198	+	0.722830i	0.280477	+	0.959861i	$0.409507\pi$
$684$		0			0
$685$		−	20.4145i		−	0.779998i
$686$		0			0
$687$	25.5442	−	9.87935i	0.974572	−	0.376921i
$688$		0			0
$689$	38.5796	−	22.2739i	1.46977	−	0.848570i
$690$		0			0
$691$	−19.6202	+	33.9832i	−0.746388	+	1.29278i	0.203155	+	0.979147i	$0.434880\pi$
$691$	−19.6202	+	33.9832i	−0.746388	+	1.29278i	−0.949543	+	0.313636i	$0.898453\pi$
$692$		0			0
$693$	8.74626	+	3.31054i	0.332243	+	0.125757i
$694$		0			0
$695$	−0.614135	−	0.354571i	−0.0232955	−	0.0134496i
$696$		0			0
$697$	5.97508	+	10.3491i	0.226322	+	0.392001i
$698$		0			0
$699$	5.66303	−	7.02936i	0.214195	−	0.265875i
$700$		0			0
$701$	39.7725			1.50219			0.751093	−	0.660197i	$-0.229527\pi$
$701$	39.7725			1.50219			0.751093	+	0.660197i	$0.229527\pi$
$702$		0			0
$703$	3.90455	−	6.76289i	0.147263	−	0.255067i
$704$		0			0
$705$	6.87631	−	44.1340i	0.258977	−	1.66218i
$706$		0			0
$707$	−22.8746	−	44.9337i	−0.860287	−	1.68990i
$708$		0			0
$709$	2.01597	−	3.49177i	0.0757115	−	0.131136i	−0.825684	−	0.564133i	$-0.809211\pi$
$709$	2.01597	−	3.49177i	0.0757115	−	0.131136i	0.901395	+	0.432997i	$0.142544\pi$
$710$		0			0
$711$	−39.6351	+	8.63346i	−1.48643	+	0.323780i
$712$		0			0
$713$	−18.1720	+	10.4916i	−0.680545	+	0.392913i
$714$		0			0
$715$	−11.1417	−	6.43264i	−0.416674	−	0.240567i
$716$		0			0
$717$	−7.00054	+	44.9314i	−0.261440	+	1.67799i
$718$		0			0
$719$	−9.84247	−	17.0477i	−0.367062	−	0.635771i	0.622043	−	0.782983i	$-0.286303\pi$
$719$	−9.84247	−	17.0477i	−0.367062	−	0.635771i	−0.989105	+	0.147213i	$0.952970\pi$
$720$		0			0
$721$	−8.93650	+	4.54935i	−0.332813	+	0.169426i
$722$		0			0
$723$	18.2557	−	7.06049i	0.678937	−	0.262582i
$724$		0			0
$725$	−1.02648	−	1.77792i	−0.0381226	−	0.0660303i
$726$		0			0
$727$	−17.1082	−	29.6323i	−0.634508	−	1.09900i	−0.986619	−	0.163042i	$-0.947869\pi$
$727$	−17.1082	−	29.6323i	−0.634508	−	1.09900i	0.352111	−	0.935958i	$-0.385464\pi$
$728$		0			0
$729$	16.1983	+	21.6013i	0.599936	+	0.800048i
$730$		0			0
$731$	34.5506			1.27790
$732$		0			0
$733$		−	28.5601i		−	1.05489i	−0.849589	−	0.527446i	$-0.823150\pi$
$733$		−	28.5601i		−	1.05489i	0.849589	−	0.527446i	$-0.176850\pi$
$734$		0			0
$735$	−7.46870	+	28.0757i	−0.275487	+	1.03559i
$736$		0			0
$737$	2.42399	+	4.19847i	0.0892887	+	0.154653i
$738$		0			0
$739$	−4.57876	−	2.64355i	−0.168432	−	0.0972444i	0.413414	−	0.910543i	$-0.364336\pi$
$739$	−4.57876	−	2.64355i	−0.168432	−	0.0972444i	−0.581846	+	0.813299i	$0.697670\pi$
$740$		0			0
$741$	6.22084	−	2.40594i	0.228528	−	0.0883843i
$742$		0			0
$743$	−5.79804	−	3.34750i	−0.212709	−	0.122808i	0.389861	−	0.920874i	$-0.372523\pi$
$743$	−5.79804	−	3.34750i	−0.212709	−	0.122808i	−0.602570	+	0.798066i	$0.705857\pi$
$744$		0			0
$745$		−	6.22165i		−	0.227944i
$746$		0			0
$747$	14.4412	+	4.61199i	0.528376	+	0.168744i
$748$		0			0
$749$	19.4677	−	29.9542i	0.711335	−	1.09450i
$750$		0			0
$751$			19.3960i			0.707771i	0.935289	+	0.353885i	$0.115140\pi$
$751$			19.3960i			0.707771i	−0.935289	+	0.353885i	$0.884860\pi$
$752$		0			0
$753$	−14.0968	−	36.4489i	−0.513716	−	1.32827i
$754$		0			0
$755$	9.53226			0.346914
$756$		0			0
$757$	−8.20907			−0.298364			−0.149182	−	0.988810i	$-0.547664\pi$
$757$	−8.20907			−0.298364			−0.149182	+	0.988810i	$0.547664\pi$
$758$		0			0
$759$	2.22161	+	5.74423i	0.0806392	+	0.208502i
$760$		0			0
$761$		−	27.1871i		−	0.985530i	−0.870162	−	0.492765i	$-0.835986\pi$
$761$		−	27.1871i		−	0.985530i	0.870162	−	0.492765i	$-0.164014\pi$
$762$		0			0
$763$	−2.26939	+	43.0078i	−0.0821575	+	1.55699i
$764$		0			0
$765$	6.35940	+	29.1951i	0.229924	+	1.05555i
$766$		0			0
$767$		−	25.3397i		−	0.914963i
$768$		0			0
$769$	2.37389	+	1.37057i	0.0856047	+	0.0494239i	0.542191	−	0.840255i	$-0.317595\pi$
$769$	2.37389	+	1.37057i	0.0856047	+	0.0494239i	−0.456587	+	0.889679i	$0.650928\pi$
$770$		0			0
$771$	−14.9905	+	5.79765i	−0.539870	+	0.208797i
$772$		0			0
$773$	−16.2012	−	9.35376i	−0.582716	−	0.336431i	0.179496	−	0.983759i	$-0.442553\pi$
$773$	−16.2012	−	9.35376i	−0.582716	−	0.336431i	−0.762212	+	0.647327i	$0.775887\pi$
$774$		0			0
$775$	2.57831	+	4.46576i	0.0926155	+	0.160415i
$776$		0			0
$777$	8.71509	−	41.4410i	0.312652	−	1.48669i
$778$		0			0
$779$			2.42952i			0.0870466i
$780$		0			0
$781$	−11.3705			−0.406870
$782$		0			0
$783$	−0.861197	−	14.3574i	−0.0307767	−	0.513092i
$784$		0			0
$785$	−10.9455	−	18.9581i	−0.390661	−	0.676644i
$786$		0			0
$787$	1.95043	+	3.37825i	0.0695254	+	0.120421i	0.898692	−	0.438579i	$-0.144518\pi$
$787$	1.95043	+	3.37825i	0.0695254	+	0.120421i	−0.829167	+	0.559001i	$0.811185\pi$
$788$		0			0
$789$	−23.1917	+	8.96948i	−0.825645	+	0.319322i
$790$		0			0
$791$	2.51915	−	47.7411i	0.0895708	−	1.69748i
$792$		0			0
$793$	−1.57089	−	2.72086i	−0.0557839	−	0.0966206i
$794$		0			0
$795$	−6.24607	+	40.0889i	−0.221525	+	1.42181i
$796$		0			0
$797$	17.8952	+	10.3318i	0.633881	+	0.365971i	0.782253	−	0.622960i	$-0.214070\pi$
$797$	17.8952	+	10.3318i	0.633881	+	0.365971i	−0.148373	+	0.988932i	$0.547404\pi$
$798$		0			0
$799$	38.7409	−	22.3671i	1.37055	−	0.791289i
$800$		0			0
$801$	6.38893	−	20.0052i	0.225742	−	0.706849i
$802$		0			0
$803$	−4.09525	+	7.09319i	−0.144518	+	0.250313i
$804$		0			0
$805$	−17.0507	+	8.68008i	−0.600958	+	0.305932i
$806$		0			0
$807$	5.44480	−	34.9462i	0.191666	−	1.23016i
$808$		0			0
$809$	3.30713	−	5.72812i	0.116273	−	0.201390i	−0.802015	−	0.597304i	$-0.796239\pi$
$809$	3.30713	−	5.72812i	0.116273	−	0.201390i	0.918288	+	0.395914i	$0.129572\pi$
$810$		0			0
$811$	−9.08700			−0.319088			−0.159544	−	0.987191i	$-0.551002\pi$
$811$	−9.08700			−0.319088			−0.159544	+	0.987191i	$0.551002\pi$
$812$		0			0
$813$	−18.2733	+	22.6822i	−0.640873	+	0.795498i
$814$		0			0
$815$	17.3366	+	30.0280i	0.607276	+	1.05183i
$816$		0			0
$817$	6.08322	+	3.51215i	0.212825	+	0.122875i
$818$		0			0
$819$	28.0023	−	22.8935i	0.978481	−	0.799963i
$820$		0			0
$821$	23.9414	−	41.4676i	0.835559	−	1.44723i	−0.0580153	−	0.998316i	$-0.518477\pi$
$821$	23.9414	−	41.4676i	0.835559	−	1.44723i	0.893574	−	0.448915i	$-0.148189\pi$
$822$		0			0
$823$	40.0989	−	23.1511i	1.39776	−	0.806997i	0.403602	−	0.914935i	$-0.367758\pi$
$823$	40.0989	−	23.1511i	1.39776	−	0.806997i	0.994158	+	0.107938i	$0.0344248\pi$
$824$		0			0
$825$	1.41164	−	0.545960i	0.0491471	−	0.0190079i
$826$		0			0
$827$			50.1143i			1.74265i	0.490711	+	0.871323i	$0.336737\pi$
$827$			50.1143i			1.74265i	−0.490711	+	0.871323i	$0.663263\pi$
$828$		0			0
$829$	3.20662	+	1.85134i	0.111371	+	0.0642998i	0.554651	−	0.832083i	$-0.312852\pi$
$829$	3.20662	+	1.85134i	0.111371	+	0.0642998i	−0.443280	+	0.896383i	$0.646185\pi$
$830$		0			0
$831$	−19.2327	−	49.7283i	−0.667174	−	1.72506i
$832$		0			0
$833$	−26.5891	+	11.8154i	−0.921257	+	0.409379i
$834$		0			0
$835$	45.0776	+	26.0256i	1.55997	+	0.900652i
$836$		0			0
$837$	2.16314	+	36.0627i	0.0747691	+	1.24651i
$838$		0			0
$839$	3.48328	+	6.03321i	0.120256	+	0.208290i	0.919869	−	0.392227i	$-0.128295\pi$
$839$	3.48328	+	6.03321i	0.120256	+	0.208290i	−0.799613	+	0.600516i	$0.794962\pi$
$840$		0			0
$841$	10.6689	−	18.4792i	0.367895	−	0.637212i
$842$		0			0
$843$	21.6981	−	26.9332i	0.747322	−	0.927630i
$844$		0			0
$845$	−16.1151	+	9.30406i	−0.554376	+	0.320069i
$846$		0			0
$847$	−22.6628	+	11.5371i	−0.778703	+	0.396418i
$848$		0			0
$849$	−33.6066	+	41.7150i	−1.15338	+	1.43165i
$850$		0			0
$851$	24.1525	−	13.9445i	0.827938	−	0.478010i
$852$		0			0
$853$	−11.9559	+	6.90273i	−0.409361	+	0.236345i	−0.690515	−	0.723318i	$-0.742616\pi$
$853$	−11.9559	+	6.90273i	−0.409361	+	0.236345i	0.281154	+	0.959663i	$0.409283\pi$
$854$		0			0
$855$	−1.84807	+	5.78675i	−0.0632028	+	0.197903i
$856$		0			0
$857$		−	25.5523i		−	0.872848i	−0.899741	−	0.436424i	$-0.856245\pi$
$857$		−	25.5523i		−	0.872848i	0.899741	−	0.436424i	$-0.143755\pi$
$858$		0			0
$859$	54.4580			1.85808			0.929042	−	0.369974i	$-0.120633\pi$
$859$	54.4580			1.85808			0.929042	+	0.369974i	$0.120633\pi$
$860$		0			0
$861$	4.09830	+	12.5212i	0.139670	+	0.426722i
$862$		0			0
$863$	−31.3899	+	18.1230i	−1.06852	+	0.616913i	−0.927778	−	0.373133i	$-0.878283\pi$
$863$	−31.3899	+	18.1230i	−1.06852	+	0.616913i	−0.140746	+	0.990046i	$0.544950\pi$
$864$		0			0
$865$	−9.86045	+	17.0788i	−0.335265	+	0.580697i
$866$		0			0
$867$	−0.301205	+	0.373877i	−0.0102295	+	0.0126975i
$868$		0			0
$869$	−7.96564	+	13.7969i	−0.270216	+	0.468028i
$870$		0			0
$871$	18.7503			0.635329
$872$		0			0
$873$	0.333573	−	1.04449i	0.0112897	−	0.0353508i
$874$		0			0
$875$	−12.2475	−	24.0585i	−0.414043	−	0.813325i
$876$		0			0
$877$	31.2121			1.05396			0.526979	−	0.849878i	$-0.323325\pi$
$877$	31.2121			1.05396			0.526979	+	0.849878i	$0.323325\pi$
$878$		0			0
$879$	−3.00512	+	19.2877i	−0.101360	+	0.650557i
$880$		0			0
$881$		−	37.1488i		−	1.25157i	−0.779994	−	0.625787i	$-0.784778\pi$
$881$		−	37.1488i		−	1.25157i	0.779994	−	0.625787i	$-0.215222\pi$
$882$		0			0
$883$		−	42.8063i		−	1.44055i	−0.693690	−	0.720274i	$-0.744016\pi$
$883$		−	42.8063i		−	1.44055i	0.693690	−	0.720274i	$-0.255984\pi$
$884$		0			0
$885$	17.9718	+	14.4786i	0.604117	+	0.486692i
$886$		0			0
$887$	42.7659			1.43594			0.717970	−	0.696074i	$-0.245072\pi$
$887$	42.7659			1.43594			0.717970	+	0.696074i	$0.245072\pi$
$888$		0			0
$889$	−14.6913	−	28.8588i	−0.492729	−	0.967892i
$890$		0			0
$891$	10.5565	+	1.00219i	0.353656	+	0.0335745i
$892$		0			0
$893$	9.09465			0.304341
$894$		0			0
$895$	−15.0449	+	26.0585i	−0.502895	+	0.871040i
$896$		0			0
$897$	23.5364	+	3.66710i	0.785858	+	0.122441i
$898$		0			0
$899$	9.62279	−	16.6672i	0.320938	−	0.555881i
$900$		0			0
$901$	−35.1901	+	20.3170i	−1.17235	+	0.676858i
$902$		0			0
$903$	37.2762	+	7.83923i	1.24047	+	0.260873i
$904$		0			0
$905$	−44.1031			−1.46604
$906$		0			0
$907$		−	3.47172i		−	0.115277i	−0.998338	−	0.0576383i	$-0.981643\pi$
$907$		−	3.47172i		−	0.115277i	0.998338	−	0.0576383i	$-0.0183570\pi$
$908$		0			0
$909$	−38.4690	−	42.2940i	−1.27594	−	1.40280i
$910$		0			0
$911$	−30.2806	+	17.4825i	−1.00324	+	0.579222i	−0.909206	−	0.416347i	$-0.863310\pi$
$911$	−30.2806	+	17.4825i	−1.00324	+	0.579222i	−0.0940362	+	0.995569i	$0.529977\pi$
$912$		0			0
$913$	5.15618	−	2.97692i	0.170645	−	0.0985217i
$914$		0			0
$915$	2.82731	+	0.440509i	0.0934679	+	0.0145628i
$916$		0			0
$917$	22.1563	−	11.2792i	0.731664	−	0.372472i
$918$		0			0
$919$	37.8817	−	21.8710i	1.24960	−	0.721459i	0.278573	−	0.960415i	$-0.410139\pi$
$919$	37.8817	−	21.8710i	1.24960	−	0.721459i	0.971030	+	0.238956i	$0.0768052\pi$
$920$		0			0
$921$	16.7371	+	43.2757i	0.551506	+	1.42598i
$922$		0			0
$923$	−21.9887	+	38.0855i	−0.723766	+	1.25360i
$924$		0			0
$925$	−3.42685	−	5.93548i	−0.112674	−	0.195157i
$926$		0			0
$927$	−8.41153	+	7.65079i	−0.276271	+	0.251285i
$928$		0			0
$929$	17.0091	+	9.82023i	0.558051	+	0.322191i	0.752363	−	0.658749i	$-0.228914\pi$
$929$	17.0091	+	9.82023i	0.558051	+	0.322191i	−0.194312	+	0.980940i	$0.562247\pi$
$930$		0			0
$931$	−5.88252	−	0.622539i	−0.192792	−	0.0204029i
$932$		0			0
$933$	15.0571	−	18.6899i	0.492947	−	0.611881i
$934$		0			0
$935$	10.1628	+	5.86748i	0.332358	+	0.191887i
$936$		0			0
$937$			15.8778i			0.518705i	0.965783	+	0.259353i	$0.0835092\pi$
$937$			15.8778i			0.518705i	−0.965783	+	0.259353i	$0.916491\pi$
$938$		0			0
$939$	−8.40404	+	53.9394i	−0.274255	+	1.76024i
$940$		0			0
$941$	25.4073	−	14.6689i	0.828253	−	0.478192i	−0.0250008	−	0.999687i	$-0.507959\pi$
$941$	25.4073	−	14.6689i	0.828253	−	0.478192i	0.853254	+	0.521495i	$0.174626\pi$
$942$		0			0
$943$	−4.33831	+	7.51418i	−0.141275	+	0.244695i
$944$		0			0
$945$	0.236945	+	32.9411i	0.00770783	+	1.07158i
$946$		0			0
$947$	5.97633	+	3.45044i	0.194205	+	0.112124i	0.593949	−	0.804502i	$-0.297568\pi$
$947$	5.97633	+	3.45044i	0.194205	+	0.112124i	−0.399745	+	0.916627i	$0.630901\pi$
$948$		0			0
$949$	15.8390	+	27.4340i	0.514156	+	0.890545i
$950$		0			0
$951$	9.76812	+	1.52192i	0.316753	+	0.0493518i
$952$		0			0
$953$	−45.3915			−1.47037			−0.735187	−	0.677864i	$-0.762906\pi$
$953$	−45.3915			−1.47037			−0.735187	+	0.677864i	$0.762906\pi$
$954$		0			0
$955$	−19.9606	+	34.5727i	−0.645908	+	1.11875i
$956$		0			0
$957$	−4.39893	−	3.54388i	−0.142197	−	0.114558i
$958$		0			0
$959$	20.0877	−	10.2261i	0.648664	−	0.330218i
$960$		0			0
$961$	−8.67037	+	15.0175i	−0.279689	+	0.484436i
$962$		0			0
$963$	12.3235	−	38.5878i	0.397120	−	1.24347i
$964$		0			0
$965$	−4.86168	+	2.80689i	−0.156503	+	0.0903570i
$966$		0			0
$967$	32.6050	+	18.8245i	1.04851	+	0.605356i	0.922231	−	0.386639i	$-0.126364\pi$
$967$	32.6050	+	18.8245i	1.04851	+	0.605356i	0.126276	+	0.991995i	$0.459697\pi$
$968$		0			0
$969$	−5.67429	+	2.19456i	−0.182284	+	0.0704994i
$970$		0			0
$971$	−18.9496	−	32.8218i	−0.608123	−	1.05330i	−0.991550	−	0.129729i	$-0.958589\pi$
$971$	−18.9496	−	32.8218i	−0.608123	−	1.05330i	0.383426	−	0.923571i	$-0.374744\pi$
$972$		0			0
$973$	0.0412593	−	0.781915i	0.00132271	−	0.0250670i
$974$		0			0
$975$	0.901189	−	5.78407i	0.0288612	−	0.185239i
$976$		0			0
$977$	9.44571	+	16.3604i	0.302195	+	0.523417i	0.976633	−	0.214915i	$-0.0689473\pi$
$977$	9.44571	+	16.3604i	0.302195	+	0.523417i	−0.674438	+	0.738332i	$0.735614\pi$
$978$		0			0
$979$	−4.12389	−	7.14279i	−0.131800	−	0.228285i
$980$		0			0
$981$	10.3935	+	47.7152i	0.331839	+	1.52343i
$982$		0			0
$983$	15.9300			0.508088			0.254044	−	0.967193i	$-0.418239\pi$
$983$	15.9300			0.508088			0.254044	+	0.967193i	$0.418239\pi$
$984$		0			0
$985$			31.0202i			0.988387i
$986$		0			0
$987$	46.8719	−	15.3415i	1.49195	−	0.488327i
$988$		0			0
$989$	12.5431	+	21.7252i	0.398846	+	0.690822i
$990$		0			0
$991$	−49.5436	−	28.6040i	−1.57380	−	0.908636i	−0.995696	−	0.0926749i	$-0.970458\pi$
$991$	−49.5436	−	28.6040i	−1.57380	−	0.908636i	−0.578107	−	0.815961i	$-0.696208\pi$
$992$		0			0
$993$	−1.70319	+	10.9315i	−0.0540492	+	0.346902i
$994$		0			0
$995$	21.1128	+	12.1895i	0.669319	+	0.386432i
$996$		0			0
$997$			14.9085i			0.472157i	0.971734	+	0.236079i	$0.0758623\pi$
$997$			14.9085i			0.472157i	−0.971734	+	0.236079i	$0.924138\pi$
$998$		0			0
$999$	−2.87505	−	47.9314i	−0.0909627	−	1.51648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.i.31.10	yes	32
3.2	odd	2		3024.2.bf.i.1711.3		32
4.3	odd	2	inner	1008.2.bf.i.31.7	✓	32
7.5	odd	6		1008.2.cz.i.607.16	yes	32
9.2	odd	6		3024.2.cz.i.2719.13		32
9.7	even	3		1008.2.cz.i.367.1	yes	32
12.11	even	2		3024.2.bf.i.1711.4		32
21.5	even	6		3024.2.cz.i.1279.13		32
28.19	even	6		1008.2.cz.i.607.1	yes	32
36.7	odd	6		1008.2.cz.i.367.16	yes	32
36.11	even	6		3024.2.cz.i.2719.14		32
63.47	even	6		3024.2.bf.i.2287.13		32
63.61	odd	6	inner	1008.2.bf.i.943.7	yes	32
84.47	odd	6		3024.2.cz.i.1279.14		32
252.47	odd	6		3024.2.bf.i.2287.14		32
252.187	even	6	inner	1008.2.bf.i.943.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.7	✓	32	4.3	odd	2	inner
1008.2.bf.i.31.10	yes	32	1.1	even	1	trivial
1008.2.bf.i.943.7	yes	32	63.61	odd	6	inner
1008.2.bf.i.943.10	yes	32	252.187	even	6	inner
1008.2.cz.i.367.1	yes	32	9.7	even	3
1008.2.cz.i.367.16	yes	32	36.7	odd	6
1008.2.cz.i.607.1	yes	32	28.19	even	6
1008.2.cz.i.607.16	yes	32	7.5	odd	6
3024.2.bf.i.1711.3		32	3.2	odd	2
3024.2.bf.i.1711.4		32	12.11	even	2
3024.2.bf.i.2287.13		32	63.47	even	6
3024.2.bf.i.2287.14		32	252.47	odd	6
3024.2.cz.i.1279.13		32	21.5	even	6
3024.2.cz.i.1279.14		32	84.47	odd	6
3024.2.cz.i.2719.13		32	9.2	odd	6
3024.2.cz.i.2719.14		32	36.11	even	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.624780 + 1.61544i) q^{3} +2.39618i q^{5} +(-2.35781 + 1.20030i) q^{7} +(-2.21930 + 2.01859i) q^{9} +1.17822i q^{11} +(3.94643 + 2.27847i) q^{13} +(-3.87088 + 1.49708i) q^{15} +(-3.59971 - 2.07829i) q^{17} +(-0.422526 - 0.731837i) q^{19} +(-3.41213 - 3.05898i) q^{21} -3.01797i q^{23} -0.741665 q^{25} +(-4.64749 - 2.32398i) q^{27} +(1.38403 + 2.39720i) q^{29} +(-3.47638 - 6.02126i) q^{31} +(-1.90334 + 0.736128i) q^{33} +(-2.87613 - 5.64973i) q^{35} +(4.62049 + 8.00292i) q^{37} +(-1.21509 + 7.79877i) q^{39} +(-2.48982 - 1.43750i) q^{41} +(-7.19863 + 4.15613i) q^{43} +(-4.83690 - 5.31784i) q^{45} +(-5.38111 + 9.32036i) q^{47} +(4.11855 - 5.66017i) q^{49} +(1.10834 - 7.11359i) q^{51} +(4.88791 - 8.46611i) q^{53} -2.82322 q^{55} +(0.918254 - 1.13980i) q^{57} +(-2.78034 - 4.81569i) q^{59} +(-0.597080 - 0.344724i) q^{61} +(2.80978 - 7.42328i) q^{63} +(-5.45962 + 9.45635i) q^{65} +(3.56340 - 2.05733i) q^{67} +(4.87535 - 1.88556i) q^{69} +9.65062i q^{71} +(6.02026 + 3.47580i) q^{73} +(-0.463377 - 1.19812i) q^{75} +(-1.41422 - 2.77802i) q^{77} +(11.7100 + 6.76075i) q^{79} +(0.850594 - 8.95971i) q^{81} +(-2.52663 - 4.37625i) q^{83} +(4.97996 - 8.62554i) q^{85} +(-3.00783 + 3.73354i) q^{87} +(-6.06236 + 3.50011i) q^{89} +(-12.0398 - 0.635304i) q^{91} +(7.55502 - 9.37784i) q^{93} +(1.75361 - 1.01245i) q^{95} +(-0.316523 + 0.182744i) q^{97} +(-2.37834 - 2.61482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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