LMFDB - Embedded newform 1008.2.cz.i.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			607.1
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71140 - 0.266646i) q^{3} +(-2.07515 + 1.19809i) q^{5} +(2.21840 - 1.44177i) q^{7} +(2.85780 + 0.912676i) q^{9} +O(q^{10})$	\(q+(-1.71140 - 0.266646i) q^{3} +(-2.07515 + 1.19809i) q^{5} +(2.21840 - 1.44177i) q^{7} +(2.85780 + 0.912676i) q^{9} +(1.02037 + 0.589110i) q^{11} +(-3.94643 - 2.27847i) q^{13} +(3.87088 - 1.49708i) q^{15} +(-3.59971 + 2.07829i) q^{17} +(-0.422526 + 0.731837i) q^{19} +(-4.18101 + 1.87593i) q^{21} +(2.61363 - 1.50898i) q^{23} +(0.370832 - 0.642301i) q^{25} +(-4.64749 - 2.32398i) q^{27} +(1.38403 + 2.39720i) q^{29} +6.95275 q^{31} +(-1.58918 - 1.28028i) q^{33} +(-2.87613 + 5.64973i) q^{35} +(4.62049 - 8.00292i) q^{37} +(6.14639 + 4.95168i) q^{39} +(2.48982 + 1.43750i) q^{41} +(7.19863 - 4.15613i) q^{43} +(-7.02383 + 1.52996i) q^{45} +10.7622 q^{47} +(2.84257 - 6.39686i) q^{49} +(6.71472 - 2.59695i) q^{51} +(4.88791 + 8.46611i) q^{53} -2.82322 q^{55} +(0.918254 - 1.13980i) q^{57} +5.56068 q^{59} -0.689448i q^{61} +(7.65561 - 2.09562i) q^{63} +10.9192 q^{65} -4.11466i q^{67} +(-4.87535 + 1.88556i) q^{69} -9.65062i q^{71} +(6.02026 - 3.47580i) q^{73} +(-0.805910 + 1.00035i) q^{75} +(3.11295 - 0.164261i) q^{77} +13.5215i q^{79} +(7.33404 + 5.21649i) q^{81} +(-2.52663 - 4.37625i) q^{83} +(4.97996 - 8.62554i) q^{85} +(-1.72942 - 4.47163i) q^{87} +(-6.06236 - 3.50011i) q^{89} +(-12.0398 + 0.635304i) q^{91} +(-11.8990 - 1.85392i) q^{93} -2.02490i q^{95} +(0.316523 - 0.182744i) q^{97} +(2.37834 + 2.61482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9}+O(q^{10}) $ 32 * q - 4 * q^9	$ 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.71140	−	0.266646i	−0.988079	−	0.153948i
$3$	−1.71140	−	0.266646i	−0.988079	−	0.153948i
$4$		0			0
$5$	−2.07515	+	1.19809i	−0.928035	+	0.535801i	−0.886190	−	0.463323i	$-0.846657\pi$
$5$	−2.07515	+	1.19809i	−0.928035	+	0.535801i	−0.0418457	+	0.999124i	$0.513324\pi$
$6$		0			0
$7$	2.21840	−	1.44177i	0.838475	−	0.544939i
$7$	2.21840	−	1.44177i	0.838475	−	0.544939i
$8$		0			0
$9$	2.85780	+	0.912676i	0.952600	+	0.304225i
$10$		0			0
$11$	1.02037	+	0.589110i	0.307653	+	0.177623i	0.645876	−	0.763443i	$-0.276492\pi$
$11$	1.02037	+	0.589110i	0.307653	+	0.177623i	−0.338223	+	0.941066i	$0.609826\pi$
$12$		0			0
$13$	−3.94643	−	2.27847i	−1.09454	−	0.631935i	−0.159761	−	0.987156i	$-0.551072\pi$
$13$	−3.94643	−	2.27847i	−1.09454	−	0.631935i	−0.934782	+	0.355221i	$0.884406\pi$
$14$		0			0
$15$	3.87088	−	1.49708i	0.999458	−	0.386545i
$16$		0			0
$17$	−3.59971	+	2.07829i	−0.873057	+	0.504060i	−0.868363	−	0.495929i	$-0.834828\pi$
$17$	−3.59971	+	2.07829i	−0.873057	+	0.504060i	−0.00469432	+	0.999989i	$0.501494\pi$
$18$		0			0
$19$	−0.422526	+	0.731837i	−0.0969342	+	0.167895i	−0.910414	−	0.413698i	$-0.864237\pi$
$19$	−0.422526	+	0.731837i	−0.0969342	+	0.167895i	0.813480	+	0.581593i	$0.197570\pi$
$20$		0			0
$21$	−4.18101	+	1.87593i	−0.912372	+	0.409362i
$22$		0			0
$23$	2.61363	−	1.50898i	0.544981	−	0.314645i	−0.202115	−	0.979362i	$-0.564781\pi$
$23$	2.61363	−	1.50898i	0.544981	−	0.314645i	0.747095	+	0.664717i	$0.231448\pi$
$24$		0			0
$25$	0.370832	−	0.642301i	0.0741665	−	0.128460i
$26$		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
$31$	6.95275			1.24875			0.624375	−	0.781124i	$-0.285354\pi$
$31$	6.95275			1.24875			0.624375	+	0.781124i	$0.285354\pi$
$32$		0			0
$33$	−1.58918	−	1.28028i	−0.276640	−	0.222868i
$34$		0			0
$35$	−2.87613	+	5.64973i	−0.486156	+	0.954979i
$36$		0			0
$37$	4.62049	−	8.00292i	0.759603	−	1.31567i	−0.183450	−	0.983029i	$-0.558726\pi$
$37$	4.62049	−	8.00292i	0.759603	−	1.31567i	0.943053	−	0.332643i	$-0.107940\pi$
$38$		0			0
$39$	6.14639	+	4.95168i	0.984210	+	0.792904i
$40$		0			0
$41$	2.48982	+	1.43750i	0.388844	+	0.224499i	0.681659	−	0.731670i	$-0.261259\pi$
$41$	2.48982	+	1.43750i	0.388844	+	0.224499i	−0.292815	+	0.956169i	$0.594592\pi$
$42$		0			0
$43$	7.19863	−	4.15613i	1.09778	−	0.633804i	0.162144	−	0.986767i	$-0.448159\pi$
$43$	7.19863	−	4.15613i	1.09778	−	0.633804i	0.935637	+	0.352963i	$0.114826\pi$
$44$		0			0
$45$	−7.02383	+	1.52996i	−1.04705	+	0.228073i
$46$		0			0
$47$	10.7622			1.56983			0.784916	−	0.619602i	$-0.212706\pi$
$47$	10.7622			1.56983			0.784916	+	0.619602i	$0.212706\pi$
$48$		0			0
$49$	2.84257	−	6.39686i	0.406082	−	0.913837i
$50$		0			0
$51$	6.71472	−	2.59695i	0.940249	−	0.363646i
$52$		0			0
$53$	4.88791	+	8.46611i	0.671406	+	1.16291i	0.977505	+	0.210910i	$0.0676428\pi$
$53$	4.88791	+	8.46611i	0.671406	+	1.16291i	−0.306099	+	0.952000i	$0.599024\pi$
$54$		0			0
$55$	−2.82322			−0.380683
$56$		0			0
$57$	0.918254	−	1.13980i	0.121626	−	0.150971i
$58$		0			0
$59$	5.56068			0.723938			0.361969	−	0.932190i	$-0.382105\pi$
$59$	5.56068			0.723938			0.361969	+	0.932190i	$0.382105\pi$
$60$		0			0
$61$		−	0.689448i		−	0.0882748i	−0.999025	−	0.0441374i	$-0.985946\pi$
$61$		−	0.689448i		−	0.0882748i	0.999025	−	0.0441374i	$-0.0140539\pi$
$62$		0			0
$63$	7.65561	−	2.09562i	0.964516	−	0.264024i
$64$		0			0
$65$	10.9192			1.35437
$66$		0			0
$67$		−	4.11466i		−	0.502686i	−0.967898	−	0.251343i	$-0.919128\pi$
$67$		−	4.11466i		−	0.502686i	0.967898	−	0.251343i	$-0.0808722\pi$
$68$		0			0
$69$	−4.87535	+	1.88556i	−0.586923	+	0.226995i
$70$		0			0
$71$		−	9.65062i		−	1.14532i	−0.819794	−	0.572659i	$-0.805912\pi$
$71$		−	9.65062i		−	1.14532i	0.819794	−	0.572659i	$-0.194088\pi$
$72$		0			0
$73$	6.02026	−	3.47580i	0.704618	−	0.406811i	−0.104447	−	0.994530i	$-0.533307\pi$
$73$	6.02026	−	3.47580i	0.704618	−	0.406811i	0.809065	+	0.587719i	$0.199974\pi$
$74$		0			0
$75$	−0.805910	+	1.00035i	−0.0930585	+	0.115511i
$76$		0			0
$77$	3.11295	−	0.164261i	0.354753	−	0.0187192i
$78$		0			0
$79$			13.5215i			1.52129i	0.649170	+	0.760643i	$0.275116\pi$
$79$			13.5215i			1.52129i	−0.649170	+	0.760643i	$0.724884\pi$
$80$		0			0
$81$	7.33404	+	5.21649i	0.814894	+	0.579610i
$82$		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
$87$	−1.72942	−	4.47163i	−0.185414	−	0.479409i
$88$		0			0
$89$	−6.06236	−	3.50011i	−0.642609	−	0.371010i	0.143010	−	0.989721i	$-0.454322\pi$
$89$	−6.06236	−	3.50011i	−0.642609	−	0.371010i	−0.785619	+	0.618711i	$0.787655\pi$
$90$		0			0
$91$	−12.0398	+	0.635304i	−1.26211	+	0.0665979i
$92$		0			0
$93$	−11.8990	−	1.85392i	−1.23386	−	0.192243i
$94$		0			0
$95$		−	2.02490i		−	0.207750i
$96$		0			0
$97$	0.316523	−	0.182744i	0.0321380	−	0.0185549i	−0.483845	−	0.875154i	$-0.660760\pi$
$97$	0.316523	−	0.182744i	0.0321380	−	0.0185549i	0.515983	+	0.856599i	$0.327427\pi$
$98$		0			0
$99$	2.37834	+	2.61482i	0.239032	+	0.262800i
$100$		0			0
$101$	16.5042	+	9.52868i	1.64223	+	0.948139i	0.980040	+	0.198799i	$0.0637040\pi$
$101$	16.5042	+	9.52868i	1.64223	+	0.948139i	0.662185	+	0.749340i	$0.269629\pi$
$102$		0			0
$103$	−1.89508	−	3.28238i	−0.186728	−	0.323423i	0.757429	−	0.652917i	$-0.226455\pi$
$103$	−1.89508	−	3.28238i	−0.186728	−	0.323423i	−0.944158	+	0.329494i	$0.893122\pi$
$104$		0			0
$105$	6.42870	−	8.90206i	0.627377	−	0.868752i
$106$		0			0
$107$	−11.6936	−	6.75131i	−1.13046	−	0.652673i	−0.186412	−	0.982472i	$-0.559686\pi$
$107$	−11.6936	−	6.75131i	−1.13046	−	0.652673i	−0.944051	+	0.329798i	$0.893019\pi$
$108$		0			0
$109$	8.13901	+	14.0972i	0.779576	+	1.35027i	0.932186	+	0.361979i	$0.117899\pi$
$109$	8.13901	+	14.0972i	0.779576	+	1.35027i	−0.152610	+	0.988286i	$0.548768\pi$
$110$		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
$115$	−3.61579	+	6.26273i	−0.337174	+	0.584003i
$116$		0			0
$117$	−9.19860	−	10.1132i	−0.850411	−	0.934969i
$118$		0			0
$119$	−4.98915	+	9.80044i	−0.457355	+	0.898405i
$120$		0			0
$121$	−4.80590	−	8.32406i	−0.436900	−	0.756733i
$122$		0			0
$123$	−3.87778	−	3.12403i	−0.349647	−	0.281685i
$124$		0			0
$125$		−	10.2037i		−	0.912649i
$126$		0			0
$127$		−	12.2396i		−	1.08609i	−0.839703	−	0.543046i	$-0.817271\pi$
$127$		−	12.2396i		−	1.08609i	0.839703	−	0.543046i	$-0.182729\pi$
$128$		0			0
$129$	−13.4280	+	5.19333i	−1.18227	+	0.457248i
$130$		0			0
$131$	4.69848	+	8.13801i	0.410508	+	0.711021i	0.994945	−	0.100418i	$-0.0320180\pi$
$131$	4.69848	+	8.13801i	0.410508	+	0.711021i	−0.584437	+	0.811439i	$0.698685\pi$
$132$		0			0
$133$	0.117812	+	2.23269i	0.0102156	+	0.193599i
$134$		0			0
$135$	12.4286	−	0.745499i	1.06968	−	0.0641624i
$136$		0			0
$137$	4.25981	−	7.37820i	0.363940	−	0.630363i	−0.624665	−	0.780892i	$-0.714765\pi$
$137$	4.25981	−	7.37820i	0.363940	−	0.630363i	0.988605	+	0.150530i	$0.0480980\pi$
$138$		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
$147$	−6.57048	+	10.1896i	−0.541924	+	0.840427i
$148$		0			0
$149$	1.29824	+	2.24863i	0.106356	+	0.184215i	0.914292	−	0.405057i	$-0.132748\pi$
$149$	1.29824	+	2.24863i	0.106356	+	0.184215i	−0.807935	+	0.589271i	$0.799415\pi$
$150$		0			0
$151$	−3.44515	−	1.98906i	−0.280362	−	0.161867i	0.353225	−	0.935538i	$-0.385085\pi$
$151$	−3.44515	−	1.98906i	−0.280362	−	0.161867i	−0.633587	+	0.773671i	$0.718418\pi$
$152$		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
$157$			9.13578i			0.729114i	0.931181	+	0.364557i	$0.118780\pi$
$157$			9.13578i			0.729114i	−0.931181	+	0.364557i	$0.881220\pi$
$158$		0			0
$159$	−6.10773	−	15.7923i	−0.484375	−	1.25241i
$160$		0			0
$161$	3.62247	−	7.11579i	0.285490	−	0.560803i
$162$		0			0
$163$	12.5316	+	7.23513i	0.981551	+	0.566699i	0.902738	−	0.430190i	$-0.141554\pi$
$163$	12.5316	+	7.23513i	0.981551	+	0.566699i	0.0788132	+	0.996889i	$0.474887\pi$
$164$		0			0
$165$	4.83167	+	0.752800i	0.376145	+	0.0586054i
$166$		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
$171$	−1.87543	+	1.70581i	−0.143417	+	0.130447i
$172$		0			0
$173$			8.23015i			0.625727i	0.949798	+	0.312863i	$0.101288\pi$
$173$			8.23015i			0.625727i	−0.949798	+	0.312863i	$0.898712\pi$
$174$		0			0
$175$	−0.103399	−	1.95953i	−0.00781621	−	0.148127i
$176$		0			0
$177$	−9.51656	−	1.48273i	−0.715308	−	0.111449i
$178$		0			0
$179$	10.8750	−	6.27871i	0.812838	−	0.469292i	−0.0351022	−	0.999384i	$-0.511176\pi$
$179$	10.8750	−	6.27871i	0.812838	−	0.469292i	0.847941	+	0.530091i	$0.177842\pi$
$180$		0			0
$181$		−	18.4056i		−	1.36808i	−0.729446	−	0.684039i	$-0.760222\pi$
$181$		−	18.4056i		−	1.36808i	0.729446	−	0.684039i	$-0.239778\pi$
$182$		0			0
$183$	−0.183838	+	1.17992i	−0.0135897	+	0.0872225i
$184$		0			0
$185$			22.1430i			1.62799i
$186$		0			0
$187$	−4.89737			−0.358131
$188$		0			0
$189$	−13.6606	+	1.54512i	−0.993664	+	0.112391i
$190$		0			0
$191$			16.6603i			1.20550i	0.797930	+	0.602750i	$0.205928\pi$
$191$			16.6603i			1.20550i	−0.797930	+	0.602750i	$0.794072\pi$
$192$		0			0
$193$	−2.34281			−0.168639			−0.0843195	−	0.996439i	$-0.526872\pi$
$193$	−2.34281			−0.168639			−0.0843195	+	0.996439i	$0.526872\pi$
$194$		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	0.988062	−	0.154060i	$-0.0492349\pi$
$199$	5.08704	+	8.81102i	0.360611	+	0.624597i	−0.627451	+	0.778656i	$0.715902\pi$
$200$		0			0
$201$	−1.09716	+	7.04185i	−0.0773875	+	0.496693i
$202$		0			0
$203$	6.52655	+	3.32250i	0.458074	+	0.233194i
$204$		0			0
$205$	−6.88899			−0.481148
$206$		0			0
$207$	8.84646	−	1.92697i	0.614871	−	0.133934i
$208$		0			0
$209$	−0.862265	+	0.497829i	−0.0596441	+	0.0344355i
$210$		0			0
$211$	−2.61024	−	1.50702i	−0.179696	−	0.103748i	0.407454	−	0.913226i	$-0.366417\pi$
$211$	−2.61024	−	1.50702i	−0.179696	−	0.103748i	−0.587150	+	0.809478i	$0.699750\pi$
$212$		0			0
$213$	−2.57330	+	16.5161i	−0.176319	+	1.13166i
$214$		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
$219$	−11.2299	+	4.34321i	−0.758846	+	0.293487i
$220$		0			0
$221$	18.9413			1.27413
$222$		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
$227$	−8.92920	+	15.4658i	−0.592652	+	1.02650i	0.401222	+	0.915981i	$0.368586\pi$
$227$	−8.92920	+	15.4658i	−0.592652	+	1.02650i	−0.993874	+	0.110522i	$0.964748\pi$
$228$		0			0
$229$	13.6941	−	7.90626i	0.904928	−	0.522461i	0.0261325	−	0.999658i	$-0.491681\pi$
$229$	13.6941	−	7.90626i	0.904928	−	0.522461i	0.878796	+	0.477198i	$0.158347\pi$
$230$		0			0
$231$	−5.37130	−	0.548937i	−0.353406	−	0.0361174i
$232$		0			0
$233$	−2.60579	+	4.51336i	−0.170711	+	0.295680i	−0.938669	−	0.344820i	$-0.887940\pi$
$233$	−2.60579	+	4.51336i	−0.170711	+	0.295680i	0.767958	+	0.640501i	$0.221273\pi$
$234$		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	−0.471257	−	0.881996i	$-0.656200\pi$
$239$	−22.7367	−	13.1271i	−1.47072	−	0.849118i	−0.999459	+	0.0328775i	$0.989533\pi$
$240$		0			0
$241$	−9.78675	−	5.65038i	−0.630420	−	0.363973i	0.150495	−	0.988611i	$-0.451913\pi$
$241$	−9.78675	−	5.65038i	−0.630420	−	0.363973i	−0.780915	+	0.624638i	$0.785247\pi$
$242$		0			0
$243$	−11.1605	−	10.8831i	−0.715950	−	0.698152i
$244$		0			0
$245$	1.76523	+	16.6801i	0.112776	+	1.06565i
$246$		0			0
$247$	3.33494	−	1.92543i	0.212197	−	0.122512i
$248$		0			0
$249$	3.15717	+	8.16324i	0.200078	+	0.517324i
$250$		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
$255$	−10.8227	+	13.4339i	−0.677742	+	0.841263i
$256$		0			0
$257$	−8.03629	+	4.63976i	−0.501290	+	0.289420i	−0.729246	−	0.684251i	$-0.760129\pi$
$257$	−8.03629	+	4.63976i	−0.501290	+	0.289420i	0.227956	+	0.973671i	$0.426796\pi$
$258$		0			0
$259$	−1.28832	−	24.4154i	−0.0800526	−	1.51710i
$260$		0			0
$261$	1.76740	+	8.11390i	0.109399	+	0.502238i
$262$		0			0
$263$	12.4329	+	7.17812i	0.766643	+	0.442622i	0.831676	−	0.555261i	$-0.187382\pi$
$263$	12.4329	+	7.17812i	0.766643	+	0.442622i	−0.0650326	+	0.997883i	$0.520715\pi$
$264$		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	−0.930412	−	0.366515i	$-0.880551\pi$
$269$	−17.6839	+	10.2098i	−1.07821	+	0.622503i	−0.147795	+	0.989018i	$0.547218\pi$
$270$		0			0
$271$	8.40830	−	14.5636i	0.510768	−	0.884676i	−0.489154	−	0.872197i	$-0.662695\pi$
$271$	8.40830	−	14.5636i	0.510768	−	0.884676i	0.999922	−	0.0124785i	$-0.00397212\pi$
$272$		0			0
$273$	20.7743	+	2.12310i	1.25732	+	0.128496i
$274$		0			0
$275$	0.756771	−	0.436922i	0.0456350	−	0.0263474i
$276$		0			0
$277$	15.3916	−	26.6590i	0.924790	−	1.60178i	0.132891	−	0.991131i	$-0.457574\pi$
$277$	15.3916	−	26.6590i	0.924790	−	1.60178i	0.791899	−	0.610652i	$-0.209093\pi$
$278$		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
$283$	−30.9276			−1.83845			−0.919226	−	0.393729i	$-0.871185\pi$
$283$	−30.9276			−1.83845			−0.919226	+	0.393729i	$0.871185\pi$
$284$		0			0
$285$	−0.539930	+	3.46541i	−0.0319827	+	0.205273i
$286$		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
$291$	−0.590426	+	0.228350i	−0.0346114	+	0.0133861i
$292$		0			0
$293$	−9.76019	−	5.63505i	−0.570196	−	0.329203i	0.187031	−	0.982354i	$-0.440113\pi$
$293$	−9.76019	−	5.63505i	−0.570196	−	0.329203i	−0.757228	+	0.653151i	$0.773447\pi$
$294$		0			0
$295$	−11.5392	+	6.66218i	−0.671840	+	0.387887i
$296$		0			0
$297$	−3.37307	−	5.10919i	−0.195725	−	0.296465i
$298$		0			0
$299$	−13.7527			−0.795339
$300$		0			0
$301$	9.97722	−	19.5988i	0.575078	−	1.12965i
$302$		0			0
$303$	−25.7045	−	20.7082i	−1.47668	−	1.18965i
$304$		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
$311$	13.8568			0.785745			0.392872	−	0.919593i	$-0.371481\pi$
$311$	13.8568			0.785745			0.392872	+	0.919593i	$0.371481\pi$
$312$		0			0
$313$			31.5176i			1.78148i	0.454511	+	0.890741i	$0.349814\pi$
$313$			31.5176i			1.78148i	−0.454511	+	0.890741i	$0.650186\pi$
$314$		0			0
$315$	−13.3758	+	13.5208i	−0.753641	+	0.761813i
$316$		0			0
$317$	−5.70767			−0.320575			−0.160287	−	0.987070i	$-0.551242\pi$
$317$	−5.70767			−0.320575			−0.160287	+	0.987070i	$0.551242\pi$
$318$		0			0
$319$			3.26137i			0.182602i
$320$		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
$327$	−10.1702	−	26.2962i	−0.562412	−	1.45418i
$328$		0			0
$329$	23.8749	−	15.5167i	1.31627	−	0.855463i
$330$		0			0
$331$			6.38748i			0.351087i	0.984472	+	0.175544i	$0.0561683\pi$
$331$			6.38748i			0.351087i	−0.984472	+	0.175544i	$0.943832\pi$
$332$		0			0
$333$	20.5085	−	18.6537i	1.12386	−	1.02222i
$334$		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
$339$	19.6348	−	24.3721i	1.06642	−	1.32371i
$340$		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
$345$	7.85800	−	9.75392i	0.423061	−	0.525134i
$346$		0			0
$347$		−	32.8184i		−	1.76178i	−0.473319	−	0.880891i	$-0.656944\pi$
$347$		−	32.8184i		−	1.76178i	0.473319	−	0.880891i	$-0.343056\pi$
$348$		0			0
$349$	0.798343	−	0.460924i	0.0427343	−	0.0246727i	−0.478481	−	0.878098i	$-0.658812\pi$
$349$	0.798343	−	0.460924i	0.0427343	−	0.0246727i	0.521215	+	0.853425i	$0.325479\pi$
$350$		0			0
$351$	13.0459	+	19.7606i	0.696337	+	1.05474i
$352$		0			0
$353$	−22.2778	−	12.8621i	−1.18573	−	0.684581i	−0.228396	−	0.973568i	$-0.573348\pi$
$353$	−22.2778	−	12.8621i	−1.18573	−	0.684581i	−0.957333	+	0.288988i	$0.906681\pi$
$354$		0			0
$355$	11.5623	+	20.0265i	0.613663	+	1.06290i
$356$		0			0
$357$	11.1517	−	15.4422i	0.590210	−	0.817286i
$358$		0			0
$359$	−22.2113	−	12.8237i	−1.17227	−	0.676810i	−0.218056	−	0.975936i	$-0.569971\pi$
$359$	−22.2113	−	12.8237i	−1.17227	−	0.676810i	−0.954213	+	0.299126i	$0.903305\pi$
$360$		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
$367$	−0.715574	+	1.23941i	−0.0373527	+	0.0646967i	−0.884097	−	0.467303i	$-0.845226\pi$
$367$	−0.715574	+	1.23941i	−0.0373527	+	0.0646967i	0.846745	+	0.531999i	$0.178559\pi$
$368$		0			0
$369$	5.80343	+	6.38047i	0.302115	+	0.332154i
$370$		0			0
$371$	23.0496	+	11.7339i	1.19667	+	0.609196i
$372$		0			0
$373$	−4.60166	−	7.97031i	−0.238265	−	0.412687i	0.721952	−	0.691944i	$-0.243245\pi$
$373$	−4.60166	−	7.97031i	−0.238265	−	0.412687i	−0.960216	+	0.279257i	$0.909912\pi$
$374$		0			0
$375$	−2.72078	+	17.4627i	−0.140500	+	0.901769i
$376$		0			0
$377$		−	12.6139i		−	0.649647i
$378$		0			0
$379$			18.1804i			0.933863i	0.884293	+	0.466932i	$0.154641\pi$
$379$			18.1804i			0.933863i	−0.884293	+	0.466932i	$0.845359\pi$
$380$		0			0
$381$	−3.26365	+	20.9470i	−0.167202	+	1.07315i
$382$		0			0
$383$	16.8903	+	29.2549i	0.863055	+	1.49485i	0.868966	+	0.494872i	$0.164785\pi$
$383$	16.8903	+	29.2549i	0.863055	+	1.49485i	−0.00591108	+	0.999983i	$0.501882\pi$
$384$		0			0
$385$	−6.26303	+	4.07045i	−0.319194	+	0.207449i
$386$		0			0
$387$	24.3655	−	5.30738i	1.23857	−	0.269789i
$388$		0			0
$389$	−8.07629	+	13.9885i	−0.409484	+	0.709247i	−0.994832	−	0.101535i	$-0.967625\pi$
$389$	−8.07629	+	13.9885i	−0.409484	+	0.709247i	0.585348	+	0.810782i	$0.300958\pi$
$390$		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	0.219742	−	0.975558i	$-0.429479\pi$
$397$	−10.2662	−	5.92719i	−0.515246	−	0.297477i	−0.734987	+	0.678081i	$0.762812\pi$
$398$		0			0
$399$	0.393713	−	3.85245i	0.0197103	−	0.192864i
$400$		0			0
$401$	−9.87081	−	17.0968i	−0.492925	−	0.853771i	0.507042	−	0.861921i	$-0.330739\pi$
$401$	−9.87081	−	17.0968i	−0.492925	−	0.853771i	−0.999967	+	0.00815040i	$0.997406\pi$
$402$		0			0
$403$	−27.4385	−	15.8417i	−1.36681	−	0.789129i
$404$		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
$409$			37.3323i			1.84596i	0.384842	+	0.922982i	$0.374256\pi$
$409$			37.3323i			1.84596i	−0.384842	+	0.922982i	$0.625744\pi$
$410$		0			0
$411$	−9.25761	+	11.4912i	−0.456644	+	0.566820i
$412$		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
$417$	0.321583	−	0.399172i	0.0157480	−	0.0195475i
$418$		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
$423$	30.7563	+	9.82243i	1.49542	+	0.477583i
$424$		0			0
$425$			3.08279i			0.149537i
$426$		0			0
$427$	−0.994029	−	1.52947i	−0.0481044	−	0.0740163i
$428$		0			0
$429$	3.35449	+	8.67344i	0.161956	+	0.418757i
$430$		0			0
$431$	−18.8674	+	10.8931i	−0.908809	+	0.524701i	−0.880048	−	0.474885i	$-0.842489\pi$
$431$	−18.8674	+	10.8931i	−0.908809	+	0.524701i	−0.0287609	+	0.999586i	$0.509156\pi$
$432$		0			0
$433$			12.3731i			0.594612i	0.954782	+	0.297306i	$0.0960881\pi$
$433$			12.3731i			0.594612i	−0.954782	+	0.297306i	$0.903912\pi$
$434$		0			0
$435$	8.94622	+	7.20729i	0.428938	+	0.345563i
$436$		0			0
$437$			2.55034i			0.121999i
$438$		0			0
$439$	37.2886			1.77969			0.889845	−	0.456264i	$-0.150813\pi$
$439$	37.2886			1.77969			0.889845	+	0.456264i	$0.150813\pi$
$440$		0			0
$441$	13.9618	−	15.6866i	0.664846	−	0.746980i
$442$		0			0
$443$			1.06571i			0.0506333i	0.999679	+	0.0253167i	$0.00805941\pi$
$443$			1.06571i			0.0506333i	−0.999679	+	0.0253167i	$0.991941\pi$
$444$		0			0
$445$	16.7737			0.795152
$446$		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
$453$	5.36566	+	4.32271i	0.252101	+	0.203099i
$454$		0			0
$455$	24.2232	−	15.7431i	1.13560	−	0.738047i
$456$		0			0
$457$	23.4911			1.09887			0.549433	−	0.835538i	$-0.314844\pi$
$457$	23.4911			1.09887			0.549433	+	0.835538i	$0.314844\pi$
$458$		0			0
$459$	21.5595	−	1.29320i	1.00631	−	0.0603613i
$460$		0			0
$461$	2.62177	−	1.51368i	0.122108	−	0.0704991i	−0.437702	−	0.899120i	$-0.644207\pi$
$461$	2.62177	−	1.51368i	0.122108	−	0.0704991i	0.559810	+	0.828621i	$0.310874\pi$
$462$		0			0
$463$	2.99321	+	1.72813i	0.139106	+	0.0803129i	0.567938	−	0.823071i	$-0.307741\pi$
$463$	2.99321	+	1.72813i	0.139106	+	0.0803129i	−0.428832	+	0.903384i	$0.641075\pi$
$464$		0			0
$465$	26.9133	−	10.4088i	1.24807	−	0.482698i
$466$		0			0
$467$	−8.61849	+	14.9277i	−0.398816	+	0.690770i	−0.993580	−	0.113131i	$-0.963912\pi$
$467$	−8.61849	+	14.9277i	−0.398816	+	0.690770i	0.594764	+	0.803900i	$0.297245\pi$
$468$		0			0
$469$	−5.93241	−	9.12796i	−0.273933	−	0.421490i
$470$		0			0
$471$	2.43602	−	15.6350i	0.112246	−	0.720423i
$472$		0			0
$473$	9.79367			0.450314
$474$		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
$479$	11.3283	−	19.6211i	0.517601	−	0.896512i	−0.482190	−	0.876067i	$-0.660158\pi$
$479$	11.3283	−	19.6211i	0.517601	−	0.896512i	0.999791	−	0.0204450i	$-0.00650830\pi$
$480$		0			0
$481$	−36.4689	+	21.0553i	−1.66284	+	0.960039i
$482$		0			0
$483$	−8.09690	+	11.2121i	−0.368422	+	0.510167i
$484$		0			0
$485$	−0.437888	+	0.758444i	−0.0198835	+	0.0344392i
$486$		0			0
$487$	4.91789	−	2.83934i	0.222851	−	0.128663i	−0.384419	−	0.923159i	$-0.625598\pi$
$487$	4.91789	−	2.83934i	0.222851	−	0.128663i	0.607270	+	0.794496i	$0.292265\pi$
$488$		0			0
$489$	−19.5174	−	15.7237i	−0.882608	−	0.711051i
$490$		0			0
$491$	24.6500	+	14.2317i	1.11244	+	0.642266i	0.939460	−	0.342659i	$-0.111328\pi$
$491$	24.6500	+	14.2317i	1.11244	+	0.642266i	0.172978	+	0.984926i	$0.444661\pi$
$492$		0			0
$493$	−9.96418	−	5.75282i	−0.448764	−	0.259094i
$494$		0			0
$495$	−8.06821	−	2.57669i	−0.362639	−	0.115814i
$496$		0			0
$497$	−13.9140	−	21.4089i	−0.624129	−	0.960321i
$498$		0			0
$499$	4.78694	−	2.76374i	0.214293	−	0.123722i	−0.389012	−	0.921233i	$-0.627184\pi$
$499$	4.78694	−	2.76374i	0.214293	−	0.123722i	0.603305	+	0.797511i	$0.293850\pi$
$500$		0			0
$501$	−23.6042	+	29.2993i	−1.05456	+	1.30900i
$502$		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
$507$	−4.85188	−	12.5451i	−0.215480	−	0.557148i
$508$		0			0
$509$	13.8473	−	7.99474i	0.613771	−	0.354361i	−0.160669	−	0.987008i	$-0.551365\pi$
$509$	13.8473	−	7.99474i	0.613771	−	0.354361i	0.774440	+	0.632648i	$0.218032\pi$
$510$		0			0
$511$	8.34401	−	16.3906i	0.369117	−	0.725075i
$512$		0			0
$513$	3.66446	−	2.41926i	0.161790	−	0.106813i
$514$		0			0
$515$	7.86517	+	4.54096i	0.346581	+	0.200099i
$516$		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	−0.467341	−	0.884077i	$-0.654788\pi$
$521$	1.47503	−	0.851611i	0.0646224	−	0.0373098i	0.531963	+	0.846768i	$0.321455\pi$
$522$		0			0
$523$	15.7605	−	27.2979i	0.689157	−	1.19366i	−0.282954	−	0.959134i	$-0.591314\pi$
$523$	15.7605	−	27.2979i	0.689157	−	1.19366i	0.972111	−	0.234522i	$-0.0753524\pi$
$524$		0			0
$525$	−0.345544	+	3.38112i	−0.0150808	+	0.147564i
$526$		0			0
$527$	−25.0279	+	14.4498i	−1.09023	+	0.629445i
$528$		0			0
$529$	−6.94594	+	12.0307i	−0.301997	+	0.523075i
$530$		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
$535$	32.3546			1.39881
$536$		0			0
$537$	−20.2858	+	7.84561i	−0.875395	+	0.338563i
$538$		0			0
$539$	6.66892	−	4.85256i	0.287251	−	0.209015i
$540$		0			0
$541$	−16.7934	+	29.0870i	−0.722004	+	1.25055i	0.238192	+	0.971218i	$0.423445\pi$
$541$	−16.7934	+	29.0870i	−0.722004	+	1.25055i	−0.960195	+	0.279329i	$0.909888\pi$
$542$		0			0
$543$	−4.90777	+	31.4994i	−0.210613	+	1.35177i
$544$		0			0
$545$	−33.7794	−	19.5025i	−1.44695	−	0.835396i
$546$		0			0
$547$	−2.50860	+	1.44834i	−0.107260	+	0.0619266i	−0.552670	−	0.833400i	$-0.686391\pi$
$547$	−2.50860	+	1.44834i	−0.107260	+	0.0619266i	0.445410	+	0.895327i	$0.353058\pi$
$548$		0			0
$549$	0.629243	−	1.97031i	0.0268554	−	0.0840906i
$550$		0			0
$551$	−2.33915			−0.0996511
$552$		0			0
$553$	19.4949	+	29.9960i	0.829009	+	1.27556i
$554$		0			0
$555$	5.90434	−	37.8956i	0.250625	−	1.60858i
$556$		0			0
$557$	−0.143138	−	0.247922i	−0.00606494	−	0.0105048i	0.862977	−	0.505243i	$-0.168597\pi$
$557$	−0.143138	−	0.247922i	−0.00606494	−	0.0105048i	−0.869042	+	0.494738i	$0.835264\pi$
$558$		0			0
$559$	−37.8785			−1.60209
$560$		0			0
$561$	8.38137	+	1.30586i	0.353862	+	0.0551335i
$562$		0			0
$563$	2.30617			0.0971935			0.0485968	−	0.998818i	$-0.484525\pi$
$563$	2.30617			0.0971935			0.0485968	+	0.998818i	$0.484525\pi$
$564$		0			0
$565$		−	43.2978i		−	1.82155i
$566$		0			0
$567$	23.7908	+	0.998220i	0.999121	+	0.0419213i
$568$		0			0
$569$	8.39822			0.352072			0.176036	−	0.984384i	$-0.443673\pi$
$569$	8.39822			0.352072			0.176036	+	0.984384i	$0.443673\pi$
$570$		0			0
$571$			29.6527i			1.24093i	0.784235	+	0.620464i	$0.213056\pi$
$571$			29.6527i			1.24093i	−0.784235	+	0.620464i	$0.786944\pi$
$572$		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	−0.793020	−	0.609196i	$-0.791492\pi$
$577$	−15.9006	+	9.18021i	−0.661950	+	0.382177i	0.131070	+	0.991373i	$0.458159\pi$
$578$		0			0
$579$	4.00949	+	0.624700i	0.166629	+	0.0259616i
$580$		0			0
$581$	−11.9146	−	6.06543i	−0.494302	−	0.251636i
$582$		0			0
$583$			11.5181i			0.477030i
$584$		0			0
$585$	31.2050	+	9.96574i	1.29017	+	0.412033i
$586$		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
$591$	−22.1553	−	3.45192i	−0.911349	−	0.141993i
$592$		0			0
$593$	−32.7972	−	18.9355i	−1.34682	−	0.777587i	−0.359023	−	0.933329i	$-0.616890\pi$
$593$	−32.7972	−	18.9355i	−1.34682	−	0.777587i	−0.987798	+	0.155742i	$0.950223\pi$
$594$		0			0
$595$	−1.38855	−	26.3148i	−0.0569252	−	1.07880i
$596$		0			0
$597$	−6.35656	−	16.4356i	−0.260157	−	0.672666i
$598$		0			0
$599$		−	17.7460i		−	0.725083i	−0.931968	−	0.362542i	$-0.881909\pi$
$599$		−	17.7460i		−	0.725083i	0.931968	−	0.362542i	$-0.118091\pi$
$600$		0			0
$601$	3.17935	−	1.83560i	0.129689	−	0.0748757i	−0.433752	−	0.901032i	$-0.642811\pi$
$601$	3.17935	−	1.83560i	0.129689	−	0.0748757i	0.563441	+	0.826156i	$0.309477\pi$
$602$		0			0
$603$	3.75536	−	11.7589i	0.152930	−	0.478859i
$604$		0			0
$605$	19.9459	+	11.5158i	0.810917	+	0.468183i
$606$		0			0
$607$	−2.11385	−	3.66130i	−0.0857985	−	0.148607i	0.819933	−	0.572460i	$-0.194011\pi$
$607$	−2.11385	−	3.66130i	−0.0857985	−	0.148607i	−0.905731	+	0.423853i	$0.860677\pi$
$608$		0			0
$609$	−10.2836	−	7.42641i	−0.416713	−	0.300933i
$610$		0			0
$611$	−42.4724	−	24.5214i	−1.71825	−	0.992031i
$612$		0			0
$613$	10.8479	+	18.7891i	0.438141	+	0.758883i	0.997546	−	0.0700114i	$-0.0223036\pi$
$613$	10.8479	+	18.7891i	0.438141	+	0.758883i	−0.559405	+	0.828895i	$0.688970\pi$
$614$		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
$619$	9.09992	−	15.7615i	0.365757	−	0.633509i	−0.623141	−	0.782110i	$-0.714144\pi$
$619$	9.09992	−	15.7615i	0.365757	−	0.633509i	0.988897	+	0.148601i	$0.0474769\pi$
$620$		0			0
$621$	−15.6537	+	0.938950i	−0.628160	+	0.0376788i
$622$		0			0
$623$	−18.4951	+	0.975930i	−0.740990	+	0.0390998i
$624$		0			0
$625$	14.0791	+	24.3858i	0.563165	+	0.975431i
$626$		0			0
$627$	1.60843	−	0.622066i	0.0642343	−	0.0248429i
$628$		0			0
$629$			38.4109i			1.53154i
$630$		0			0
$631$			33.2928i			1.32537i	0.748900	+	0.662683i	$0.230582\pi$
$631$			33.2928i			1.32537i	−0.748900	+	0.662683i	$0.769418\pi$
$632$		0			0
$633$	4.06533	+	3.27514i	0.161583	+	0.130175i
$634$		0			0
$635$	14.6642	+	25.3991i	0.581930	+	1.00793i
$636$		0			0
$637$	−25.7931	+	18.7680i	−1.02196	+	0.743616i
$638$		0			0
$639$	8.80789	−	27.5795i	0.348435	−	1.09103i
$640$		0			0
$641$	4.84664	−	8.39463i	0.191431	−	0.331568i	−0.754294	−	0.656537i	$-0.772021\pi$
$641$	4.84664	−	8.39463i	0.191431	−	0.331568i	0.945725	+	0.324969i	$0.105354\pi$
$642$		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	0.812468	−	0.583005i	$-0.198123\pi$
$647$	−2.50961	−	4.34678i	−0.0986631	−	0.170889i	−0.911132	+	0.412116i	$0.864790\pi$
$648$		0			0
$649$	5.67394	+	3.27585i	0.222721	+	0.128588i
$650$		0			0
$651$	−29.0696	+	13.0429i	−1.13933	+	0.511191i
$652$		0			0
$653$	−20.4811	−	35.4743i	−0.801488	−	1.38822i	−0.918636	−	0.395104i	$-0.870709\pi$
$653$	−20.4811	−	35.4743i	−0.801488	−	1.38822i	0.117148	−	0.993114i	$-0.462625\pi$
$654$		0			0
$655$	−19.5001	−	11.2584i	−0.761932	−	0.439902i
$656$		0			0
$657$	20.3770	−	4.43859i	0.794981	−	0.173166i
$658$		0			0
$659$	−22.1113	+	12.7660i	−0.861335	+	0.497292i	−0.864459	−	0.502703i	$-0.832339\pi$
$659$	−22.1113	+	12.7660i	−0.861335	+	0.497292i	0.00312417	+	0.999995i	$0.499006\pi$
$660$		0			0
$661$			26.2268i			1.02010i	0.860143	+	0.510052i	$0.170374\pi$
$661$			26.2268i			1.02010i	−0.860143	+	0.510052i	$0.829626\pi$
$662$		0			0
$663$	−32.4162	−	5.05062i	−1.25894	−	0.196150i
$664$		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
$669$	−1.83428	−	4.74274i	−0.0709173	−	0.183365i
$670$		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
$675$	−3.21613	+	2.12328i	−0.123789	+	0.0817250i
$676$		0			0
$677$		−	4.59990i		−	0.176789i	−0.996086	−	0.0883943i	$-0.971826\pi$
$677$		−	4.59990i		−	0.176789i	0.996086	−	0.0883943i	$-0.0281736\pi$
$678$		0			0
$679$	0.438697	−	0.861754i	0.0168356	−	0.0330711i
$680$		0			0
$681$	19.4054	−	24.0873i	0.743615	−	0.923029i
$682$		0			0
$683$	32.7196	−	18.8906i	1.25198	−	0.722830i	0.280477	−	0.959861i	$-0.409507\pi$
$683$	32.7196	−	18.8906i	1.25198	−	0.722830i	0.971502	+	0.237030i	$0.0761741\pi$
$684$		0			0
$685$			20.4145i			0.779998i
$686$		0			0
$687$	−25.5442	+	9.87935i	−0.974572	+	0.376921i
$688$		0			0
$689$		−	44.5479i		−	1.69714i
$690$		0			0
$691$	39.2404			1.49278			0.746388	−	0.665511i	$-0.231786\pi$
$691$	39.2404			1.49278			0.746388	+	0.665511i	$0.231786\pi$
$692$		0			0
$693$	9.04609	+	2.37169i	0.343633	+	0.0900929i
$694$		0			0
$695$		−	0.709142i		−	0.0268993i
$696$		0			0
$697$	−11.9502			−0.452644
$698$		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
$705$	41.6593	−	16.1119i	1.56898	−	0.606811i
$706$		0			0
$707$	50.3510	−	2.65687i	1.89364	−	0.0999219i
$708$		0			0
$709$	−4.03195			−0.151423			−0.0757115	−	0.997130i	$-0.524123\pi$
$709$	−4.03195			−0.151423			−0.0757115	+	0.997130i	$0.524123\pi$
$710$		0			0
$711$	−12.3407	+	38.6417i	−0.462814	+	1.44918i
$712$		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
$717$	35.4114	+	28.5283i	1.32246	+	1.06541i
$718$		0			0
$719$	−9.84247	+	17.0477i	−0.367062	+	0.635771i	−0.989105	−	0.147213i	$-0.952970\pi$
$719$	−9.84247	+	17.0477i	−0.367062	+	0.635771i	0.622043	+	0.782983i	$0.286303\pi$
$720$		0			0
$721$	−8.93650	−	4.54935i	−0.332813	−	0.169426i
$722$		0			0
$723$	15.2424	+	12.2797i	0.566872	+	0.456686i
$724$		0			0
$725$	2.05297			0.0762453
$726$		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
$731$	−17.2753	+	29.9217i	−0.638951	+	1.10670i
$732$		0			0
$733$	24.7338	−	14.2801i	0.913563	−	0.527446i	0.0319871	−	0.999488i	$-0.489816\pi$
$733$	24.7338	−	14.2801i	0.913563	−	0.527446i	0.881576	+	0.472043i	$0.156483\pi$
$734$		0			0
$735$	1.42665	−	29.0171i	0.0526229	−	1.07031i
$736$		0			0
$737$	2.42399	−	4.19847i	0.0892887	−	0.154653i
$738$		0			0
$739$	−4.57876	+	2.64355i	−0.168432	+	0.0972444i	−0.581846	−	0.813299i	$-0.697670\pi$
$739$	−4.57876	+	2.64355i	−0.168432	+	0.0972444i	0.413414	+	0.910543i	$0.364336\pi$
$740$		0			0
$741$	−6.22084	+	2.40594i	−0.228528	+	0.0883843i
$742$		0			0
$743$	5.79804	+	3.34750i	0.212709	+	0.122808i	0.602570	−	0.798066i	$-0.294143\pi$
$743$	5.79804	+	3.34750i	0.212709	+	0.122808i	−0.389861	+	0.920874i	$0.627477\pi$
$744$		0			0
$745$	−5.38811	−	3.11082i	−0.197405	−	0.113972i
$746$		0			0
$747$	−3.22650	−	14.8124i	−0.118051	−	0.541959i
$748$		0			0
$749$	−35.6749	+	1.88246i	−1.30353	+	0.0687835i
$750$		0			0
$751$	−16.7974	+	9.69801i	−0.612947	+	0.353885i	−0.774118	−	0.633041i	$-0.781806\pi$
$751$	−16.7974	+	9.69801i	−0.612947	+	0.353885i	0.161171	+	0.986927i	$0.448473\pi$
$752$		0			0
$753$	38.6141	+	6.01628i	1.40718	+	0.219245i
$754$		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
$759$	−6.08545	−	0.948145i	−0.220888	−	0.0344155i
$760$		0			0
$761$	23.5447	−	13.5935i	0.853494	−	0.492765i	−0.00833421	−	0.999965i	$-0.502653\pi$
$761$	23.5447	−	13.5935i	0.853494	−	0.492765i	0.861828	+	0.507200i	$0.169320\pi$
$762$		0			0
$763$	38.3805	+	19.5385i	1.38947	+	0.707343i
$764$		0			0
$765$	22.1040	−	20.1050i	0.799173	−	0.726897i
$766$		0			0
$767$	−21.9448	−	12.6698i	−0.792382	−	0.457482i
$768$		0			0
$769$	−2.37389	−	1.37057i	−0.0856047	−	0.0494239i	0.456587	−	0.889679i	$-0.349072\pi$
$769$	−2.37389	−	1.37057i	−0.0856047	−	0.0494239i	−0.542191	+	0.840255i	$0.682405\pi$
$770$		0			0
$771$	14.9905	−	5.79765i	0.539870	−	0.208797i
$772$		0			0
$773$	−16.2012	+	9.35376i	−0.582716	+	0.336431i	−0.762212	−	0.647327i	$-0.775887\pi$
$773$	−16.2012	+	9.35376i	−0.582716	+	0.336431i	0.179496	+	0.983759i	$0.442553\pi$
$774$		0			0
$775$	2.57831	−	4.46576i	0.0926155	−	0.160415i
$776$		0			0
$777$	−4.30541	+	42.1280i	−0.154456	+	1.51133i
$778$		0			0
$779$	−2.10403	+	1.21476i	−0.0753845	+	0.0435233i
$780$		0			0
$781$	5.68527	−	9.84718i	0.203435	−	0.352360i
$782$		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
$787$	−3.90086			−0.139051			−0.0695254	−	0.997580i	$-0.522148\pi$
$787$	−3.90086			−0.139051			−0.0695254	+	0.997580i	$0.522148\pi$
$788$		0			0
$789$	−19.3636	−	15.5998i	−0.689363	−	0.555368i
$790$		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
$795$	31.5950	+	25.4537i	1.12056	+	0.902751i
$796$		0			0
$797$	−17.8952	−	10.3318i	−0.633881	−	0.365971i	0.148373	−	0.988932i	$-0.452596\pi$
$797$	−17.8952	−	10.3318i	−0.633881	−	0.365971i	−0.782253	+	0.622960i	$0.785930\pi$
$798$		0			0
$799$	−38.7409	+	22.3671i	−1.37055	+	0.791289i
$800$		0			0
$801$	−14.1306	−	15.5356i	−0.499279	−	0.548923i
$802$		0			0
$803$	8.19051			0.289037
$804$		0			0
$805$	1.00819	+	19.1064i	0.0355339	+	0.673411i
$806$		0			0
$807$	32.9867	−	12.7578i	1.16119	−	0.449094i
$808$		0			0
$809$	3.30713	+	5.72812i	0.116273	+	0.201390i	0.918288	−	0.395914i	$-0.129572\pi$
$809$	3.30713	+	5.72812i	0.116273	+	0.201390i	−0.802015	+	0.597304i	$0.796239\pi$
$810$		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
$815$	−34.6733			−1.21455
$816$		0			0
$817$			7.02430i			0.245749i
$818$		0			0
$819$	−34.9872	−	9.17286i	−1.22255	−	0.320526i
$820$		0			0
$821$	−47.8827			−1.67112			−0.835559	−	0.549401i	$-0.814856\pi$
$821$	−47.8827			−1.67112			−0.835559	+	0.549401i	$0.814856\pi$
$822$		0			0
$823$		−	46.3022i		−	1.61399i	−0.590556	−	0.806997i	$-0.701092\pi$
$823$		−	46.3022i		−	1.61399i	0.590556	−	0.806997i	$-0.298908\pi$
$824$		0			0
$825$	−1.41164	+	0.545960i	−0.0491471	+	0.0190079i
$826$		0			0
$827$		−	50.1143i		−	1.74265i	−0.490711	−	0.871323i	$-0.663263\pi$
$827$		−	50.1143i		−	1.74265i	0.490711	−	0.871323i	$-0.336737\pi$
$828$		0			0
$829$	3.20662	−	1.85134i	0.111371	−	0.0642998i	−0.443280	−	0.896383i	$-0.646185\pi$
$829$	3.20662	−	1.85134i	0.111371	−	0.0642998i	0.554651	+	0.832083i	$0.312852\pi$
$830$		0			0
$831$	−33.4497	+	41.5202i	−1.16036	+	1.44032i
$832$		0			0
$833$	3.06210	+	28.9345i	0.106095	+	1.00252i
$834$		0			0
$835$			52.0511i			1.80130i
$836$		0			0
$837$	−32.3128	−	16.1580i	−1.11689	−	0.558503i
$838$		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
$843$	12.4758	+	32.2577i	0.429690	+	1.11101i
$844$		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
$849$	52.9295	+	8.24670i	1.81654	+	0.283026i
$850$		0			0
$851$		−	27.8889i		−	0.956021i
$852$		0			0
$853$	11.9559	−	6.90273i	0.409361	−	0.236345i	−0.281154	−	0.959663i	$-0.590717\pi$
$853$	11.9559	−	6.90273i	0.409361	−	0.236345i	0.690515	+	0.723318i	$0.257384\pi$
$854$		0			0
$855$	1.84807	−	5.78675i	0.0632028	−	0.197903i
$856$		0			0
$857$	−22.1289	−	12.7761i	−0.755909	−	0.436424i	0.0719161	−	0.997411i	$-0.477089\pi$
$857$	−22.1289	−	12.7761i	−0.755909	−	0.436424i	−0.827825	+	0.560987i	$0.810422\pi$
$858$		0			0
$859$	−27.2290	−	47.1620i	−0.929042	−	1.60915i	−0.784928	−	0.619587i	$-0.787300\pi$
$859$	−27.2290	−	47.1620i	−0.929042	−	1.60915i	−0.144114	−	0.989561i	$-0.546033\pi$
$860$		0			0
$861$	−13.1066	−	1.33947i	−0.446672	−	0.0456490i
$862$		0			0
$863$	−31.3899	−	18.1230i	−1.06852	−	0.616913i	−0.140746	−	0.990046i	$-0.544950\pi$
$863$	−31.3899	−	18.1230i	−1.06852	−	0.616913i	−0.927778	+	0.373133i	$0.878283\pi$
$864$		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
$871$	−9.37515	+	16.2382i	−0.317665	+	0.550211i
$872$		0			0
$873$	1.07134	−	0.233364i	0.0362595	−	0.00789819i
$874$		0			0
$875$	−14.7115	−	22.6359i	−0.497338	−	0.765234i
$876$		0			0
$877$	−15.6061	−	27.0305i	−0.526979	−	0.912754i	−0.999506	−	0.0314380i	$-0.989991\pi$
$877$	−15.6061	−	27.0305i	−0.526979	−	0.912754i	0.472527	−	0.881316i	$-0.343342\pi$
$878$		0			0
$879$	15.2011	+	12.2464i	0.512719	+	0.413059i
$880$		0			0
$881$			37.1488i			1.25157i	0.779994	+	0.625787i	$0.215222\pi$
$881$			37.1488i			1.25157i	−0.779994	+	0.625787i	$0.784778\pi$
$882$		0			0
$883$			42.8063i			1.44055i	0.693690	+	0.720274i	$0.255984\pi$
$883$			42.8063i			1.44055i	−0.693690	+	0.720274i	$0.744016\pi$
$884$		0			0
$885$	21.5247	−	8.32479i	0.723546	−	0.279835i
$886$		0			0
$887$	−21.3830	−	37.0364i	−0.717970	−	1.24356i	−0.961803	−	0.273743i	$-0.911738\pi$
$887$	−21.3830	−	37.0364i	−0.717970	−	1.24356i	0.243833	−	0.969817i	$-0.421595\pi$
$888$		0			0
$889$	−17.6468	−	27.1524i	−0.591855	−	0.910662i
$890$		0			0
$891$	4.41034	+	9.64330i	0.147752	+	0.323063i
$892$		0			0
$893$	−4.54732	+	7.87620i	−0.152170	+	0.263567i
$894$		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
$903$	−22.3010	+	30.8810i	−0.742130	+	1.02765i
$904$		0			0
$905$	22.0515	+	38.1944i	0.733018	+	1.26962i
$906$		0			0
$907$	−3.00660	−	1.73586i	−0.0998324	−	0.0576383i	0.449253	−	0.893405i	$-0.351690\pi$
$907$	−3.00660	−	1.73586i	−0.0998324	−	0.0576383i	−0.549085	+	0.835767i	$0.685024\pi$
$908$		0			0
$909$	38.4690	+	42.2940i	1.27594	+	1.40280i
$910$		0			0
$911$	30.2806	−	17.4825i	1.00324	−	0.579222i	0.0940362	−	0.995569i	$-0.470023\pi$
$911$	30.2806	−	17.4825i	1.00324	−	0.579222i	0.909206	+	0.416347i	$0.136690\pi$
$912$		0			0
$913$		−	5.95384i		−	0.197043i
$914$		0			0
$915$	−1.03216	−	2.66877i	−0.0341222	−	0.0882270i
$916$		0			0
$917$	22.1563	+	11.2792i	0.731664	+	0.372472i
$918$		0			0
$919$	37.8817	+	21.8710i	1.24960	+	0.721459i	0.971030	−	0.238956i	$-0.0768052\pi$
$919$	37.8817	+	21.8710i	1.24960	+	0.721459i	0.278573	+	0.960415i	$0.410139\pi$
$920$		0			0
$921$	−45.8464	−	7.14312i	−1.51069	−	0.235374i
$922$		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
$927$	−2.42002	−	11.1100i	−0.0794839	−	0.364900i
$928$		0			0
$929$			19.6405i			0.644382i	0.946675	+	0.322191i	$0.104419\pi$
$929$			19.6405i			0.644382i	−0.946675	+	0.322191i	$0.895581\pi$
$930$		0			0
$931$	3.48039	+	4.78314i	0.114065	+	0.156761i
$932$		0			0
$933$	−23.7145	−	3.69485i	−0.776378	−	0.120964i
$934$		0			0
$935$	10.1628	−	5.86748i	0.332358	−	0.191887i
$936$		0			0
$937$		−	15.8778i		−	0.518705i	−0.965783	−	0.259353i	$-0.916491\pi$
$937$		−	15.8778i		−	0.518705i	0.965783	−	0.259353i	$-0.0835092\pi$
$938$		0			0
$939$	8.40404	−	53.9394i	0.274255	−	1.76024i
$940$		0			0
$941$		−	29.3378i		−	0.956385i	−0.878255	−	0.478192i	$-0.841292\pi$
$941$		−	29.3378i		−	0.956385i	0.878255	−	0.478192i	$-0.158708\pi$
$942$		0			0
$943$	8.67663			0.282550
$944$		0			0
$945$	26.4967	−	19.5730i	0.861936	−	0.636710i
$946$		0			0
$947$			6.90088i			0.224248i	0.993694	+	0.112124i	$0.0357654\pi$
$947$			6.90088i			0.224248i	−0.993694	+	0.112124i	$0.964235\pi$
$948$		0			0
$949$	−31.6780			−1.02831
$950$		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
$957$	0.869631	−	5.58152i	0.0281112	−	0.180425i
$958$		0			0
$959$	−1.18776	−	22.5095i	−0.0383547	−	0.726869i
$960$		0			0
$961$	17.3407			0.559379
$962$		0			0
$963$	−27.2562	−	29.9664i	−0.878320	−	0.965652i
$964$		0			0
$965$	4.86168	−	2.80689i	0.156503	−	0.0903570i
$966$		0			0
$967$	−32.6050	−	18.8245i	−1.04851	−	0.605356i	−0.126276	−	0.991995i	$-0.540303\pi$
$967$	−32.6050	−	18.8245i	−1.04851	−	0.605356i	−0.922231	+	0.386639i	$0.873636\pi$
$968$		0			0
$969$	−0.936601	+	6.01136i	−0.0300880	+	0.193113i
$970$		0			0
$971$	−18.9496	+	32.8218i	−0.608123	+	1.05330i	0.383426	+	0.923571i	$0.374744\pi$
$971$	−18.9496	+	32.8218i	−0.608123	+	1.05330i	−0.991550	+	0.129729i	$0.958589\pi$
$972$		0			0
$973$	0.0412593	+	0.781915i	0.00132271	+	0.0250670i
$974$		0			0
$975$	5.45975	−	2.11158i	0.174852	−	0.0676248i
$976$		0			0
$977$	−18.8914			−0.604390			−0.302195	−	0.953246i	$-0.597719\pi$
$977$	−18.8914			−0.604390			−0.302195	+	0.953246i	$0.597719\pi$
$978$		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
$983$	−7.96500	+	13.7958i	−0.254044	+	0.440017i	−0.964635	−	0.263588i	$-0.915094\pi$
$983$	−7.96500	+	13.7958i	−0.254044	+	0.440017i	0.710591	+	0.703605i	$0.248427\pi$
$984$		0			0
$985$	−26.8643	+	15.5101i	−0.855968	+	0.494194i
$986$		0			0
$987$	−44.9970	+	20.1892i	−1.43227	+	0.642629i
$988$		0			0
$989$	12.5431	−	21.7252i	0.398846	−	0.690822i
$990$		0			0
$991$	−49.5436	+	28.6040i	−1.57380	+	0.908636i	−0.578107	+	0.815961i	$0.696208\pi$
$991$	−49.5436	+	28.6040i	−1.57380	+	0.908636i	−0.995696	+	0.0926749i	$0.970458\pi$
$992$		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
$997$	12.9111	+	7.45425i	0.408900	+	0.236079i	0.690317	−	0.723507i	$-0.257471\pi$
$997$	12.9111	+	7.45425i	0.408900	+	0.236079i	−0.281417	+	0.959586i	$0.590804\pi$
$998$		0			0
$999$	−40.0723	+	26.4556i	−1.26783	+	0.837017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.1	yes	32
3.2	odd	2		3024.2.cz.i.1279.14		32
4.3	odd	2	inner	1008.2.cz.i.607.16	yes	32
7.3	odd	6		1008.2.bf.i.31.7	✓	32
9.2	odd	6		3024.2.bf.i.2287.14		32
9.7	even	3		1008.2.bf.i.943.10	yes	32
12.11	even	2		3024.2.cz.i.1279.13		32
21.17	even	6		3024.2.bf.i.1711.4		32
28.3	even	6		1008.2.bf.i.31.10	yes	32
36.7	odd	6		1008.2.bf.i.943.7	yes	32
36.11	even	6		3024.2.bf.i.2287.13		32
63.38	even	6		3024.2.cz.i.2719.14		32
63.52	odd	6	inner	1008.2.cz.i.367.16	yes	32
84.59	odd	6		3024.2.bf.i.1711.3		32
252.115	even	6	inner	1008.2.cz.i.367.1	yes	32
252.227	odd	6		3024.2.cz.i.2719.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.7	✓	32	7.3	odd	6
1008.2.bf.i.31.10	yes	32	28.3	even	6
1008.2.bf.i.943.7	yes	32	36.7	odd	6
1008.2.bf.i.943.10	yes	32	9.7	even	3
1008.2.cz.i.367.1	yes	32	252.115	even	6	inner
1008.2.cz.i.367.16	yes	32	63.52	odd	6	inner
1008.2.cz.i.607.1	yes	32	1.1	even	1	trivial
1008.2.cz.i.607.16	yes	32	4.3	odd	2	inner
3024.2.bf.i.1711.3		32	84.59	odd	6
3024.2.bf.i.1711.4		32	21.17	even	6
3024.2.bf.i.2287.13		32	36.11	even	6
3024.2.bf.i.2287.14		32	9.2	odd	6
3024.2.cz.i.1279.13		32	12.11	even	2
3024.2.cz.i.1279.14		32	3.2	odd	2
3024.2.cz.i.2719.13		32	252.227	odd	6
3024.2.cz.i.2719.14		32	63.38	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.71140 - 0.266646i) q^{3} +(-2.07515 + 1.19809i) q^{5} +(2.21840 - 1.44177i) q^{7} +(2.85780 + 0.912676i) q^{9} +O(q^{10})\)	\(q+(-1.71140 - 0.266646i) q^{3} +(-2.07515 + 1.19809i) q^{5} +(2.21840 - 1.44177i) q^{7} +(2.85780 + 0.912676i) q^{9} +(1.02037 + 0.589110i) q^{11} +(-3.94643 - 2.27847i) q^{13} +(3.87088 - 1.49708i) q^{15} +(-3.59971 + 2.07829i) q^{17} +(-0.422526 + 0.731837i) q^{19} +(-4.18101 + 1.87593i) q^{21} +(2.61363 - 1.50898i) q^{23} +(0.370832 - 0.642301i) q^{25} +(-4.64749 - 2.32398i) q^{27} +(1.38403 + 2.39720i) q^{29} +6.95275 q^{31} +(-1.58918 - 1.28028i) q^{33} +(-2.87613 + 5.64973i) q^{35} +(4.62049 - 8.00292i) q^{37} +(6.14639 + 4.95168i) q^{39} +(2.48982 + 1.43750i) q^{41} +(7.19863 - 4.15613i) q^{43} +(-7.02383 + 1.52996i) q^{45} +10.7622 q^{47} +(2.84257 - 6.39686i) q^{49} +(6.71472 - 2.59695i) q^{51} +(4.88791 + 8.46611i) q^{53} -2.82322 q^{55} +(0.918254 - 1.13980i) q^{57} +5.56068 q^{59} -0.689448i q^{61} +(7.65561 - 2.09562i) q^{63} +10.9192 q^{65} -4.11466i q^{67} +(-4.87535 + 1.88556i) q^{69} -9.65062i q^{71} +(6.02026 - 3.47580i) q^{73} +(-0.805910 + 1.00035i) q^{75} +(3.11295 - 0.164261i) q^{77} +13.5215i q^{79} +(7.33404 + 5.21649i) q^{81} +(-2.52663 - 4.37625i) q^{83} +(4.97996 - 8.62554i) q^{85} +(-1.72942 - 4.47163i) q^{87} +(-6.06236 - 3.50011i) q^{89} +(-12.0398 + 0.635304i) q^{91} +(-11.8990 - 1.85392i) q^{93} -2.02490i q^{95} +(0.316523 - 0.182744i) q^{97} +(2.37834 + 2.61482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 32 * q - 4 * q^9	\( 32 q - 4 q^{9} + 6 q^{13} - 18 q^{17} + 4 q^{21} + 16 q^{25} - 12 q^{29} + 2 q^{37} - 36 q^{41} + 12 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} - 36 q^{65} + 42 q^{69} + 42 q^{77} + 20 q^{81} - 12 q^{85} - 18 q^{89} - 38 q^{93} + 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 + 6 * q^13 - 18 * q^17 + 4 * q^21 + 16 * q^25 - 12 * q^29 + 2 * q^37 - 36 * q^41 + 12 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 - 36 * q^65 + 42 * q^69 + 42 * q^77 + 20 * q^81 - 12 * q^85 - 18 * q^89 - 38 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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