LMFDB - Embedded newform 1008.2.cz.i.607.5

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			607.5
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.i.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.958555 + 1.44263i) q^{3} +(0.377090 - 0.217713i) q^{5} +(0.473240 - 2.60308i) q^{7} +(-1.16234 - 2.76567i) q^{9} +O(q^{10})$	\(q+(-0.958555 + 1.44263i) q^{3} +(0.377090 - 0.217713i) q^{5} +(0.473240 - 2.60308i) q^{7} +(-1.16234 - 2.76567i) q^{9} +(-4.17467 - 2.41025i) q^{11} +(4.31639 + 2.49207i) q^{13} +(-0.0473830 + 0.752691i) q^{15} +(-4.92142 + 2.84139i) q^{17} +(-3.70969 + 6.42537i) q^{19} +(3.30165 + 3.17791i) q^{21} +(-2.73689 + 1.58014i) q^{23} +(-2.40520 + 4.16593i) q^{25} +(5.10401 + 0.974224i) q^{27} +(2.49630 + 4.32372i) q^{29} -2.65936 q^{31} +(7.47875 - 3.71214i) q^{33} +(-0.388272 - 1.08463i) q^{35} +(1.06500 - 1.84463i) q^{37} +(-7.73262 + 3.83815i) q^{39} +(-0.112731 - 0.0650855i) q^{41} +(-6.53530 + 3.77315i) q^{43} +(-1.04043 - 0.789852i) q^{45} -8.58674 q^{47} +(-6.55209 - 2.46377i) q^{49} +(0.618398 - 9.82340i) q^{51} +(-5.61000 - 9.71680i) q^{53} -2.09897 q^{55} +(-5.71347 - 11.5108i) q^{57} +12.4013 q^{59} +8.84273i q^{61} +(-7.74935 + 1.71685i) q^{63} +2.17023 q^{65} -0.936806i q^{67} +(0.343902 - 5.46297i) q^{69} +6.27328i q^{71} +(11.2357 - 6.48693i) q^{73} +(-3.70437 - 7.46308i) q^{75} +(-8.24970 + 9.72640i) q^{77} -3.44380i q^{79} +(-6.29791 + 6.42933i) q^{81} +(3.68712 + 6.38628i) q^{83} +(-1.23721 + 2.14292i) q^{85} +(-8.63036 - 0.543294i) q^{87} +(-13.2599 - 7.65563i) q^{89} +(8.52975 - 10.0566i) q^{91} +(2.54914 - 3.83646i) q^{93} +3.23059i q^{95} +(2.83887 - 1.63902i) q^{97} +(-1.81356 + 14.3473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.958555	+	1.44263i	−0.553422	+	0.832901i
$3$	−0.958555	+	1.44263i	−0.553422	+	0.832901i
$4$		0			0
$5$	0.377090	−	0.217713i	0.168640	−	0.0973643i	−0.413304	−	0.910593i	$-0.635625\pi$
$5$	0.377090	−	0.217713i	0.168640	−	0.0973643i	0.581944	+	0.813229i	$0.302292\pi$
$6$		0			0
$7$	0.473240	−	2.60308i	0.178868	−	0.983873i
$7$	0.473240	−	2.60308i	0.178868	−	0.983873i
$8$		0			0
$9$	−1.16234	−	2.76567i	−0.387448	−	0.921892i
$10$		0			0
$11$	−4.17467	−	2.41025i	−1.25871	−	0.726718i	−0.285888	−	0.958263i	$-0.592288\pi$
$11$	−4.17467	−	2.41025i	−1.25871	−	0.726718i	−0.972824	+	0.231546i	$0.925622\pi$
$12$		0			0
$13$	4.31639	+	2.49207i	1.19715	+	0.691176i	0.959919	−	0.280277i	$-0.0904264\pi$
$13$	4.31639	+	2.49207i	1.19715	+	0.691176i	0.237232	+	0.971453i	$0.423760\pi$
$14$		0			0
$15$	−0.0473830	+	0.752691i	−0.0122342	+	0.194344i
$16$		0			0
$17$	−4.92142	+	2.84139i	−1.19362	+	0.689137i	−0.959126	−	0.282980i	$-0.908677\pi$
$17$	−4.92142	+	2.84139i	−1.19362	+	0.689137i	−0.234495	+	0.972117i	$0.575344\pi$
$18$		0			0
$19$	−3.70969	+	6.42537i	−0.851061	+	1.47408i	0.0291916	+	0.999574i	$0.490707\pi$
$19$	−3.70969	+	6.42537i	−0.851061	+	1.47408i	−0.880252	+	0.474506i	$0.842627\pi$
$20$		0			0
$21$	3.30165	+	3.17791i	0.720479	+	0.693476i
$22$		0			0
$23$	−2.73689	+	1.58014i	−0.570681	+	0.329483i	−0.757421	−	0.652926i	$-0.773541\pi$
$23$	−2.73689	+	1.58014i	−0.570681	+	0.329483i	0.186740	+	0.982409i	$0.440208\pi$
$24$		0			0
$25$	−2.40520	+	4.16593i	−0.481040	+	0.833186i
$26$		0			0
$27$	5.10401	+	0.974224i	0.982267	+	0.187489i
$28$		0			0
$29$	2.49630	+	4.32372i	0.463552	+	0.802895i	0.999135	−	0.0415876i	$-0.0132416\pi$
$29$	2.49630	+	4.32372i	0.463552	+	0.802895i	−0.535583	+	0.844482i	$0.679908\pi$
$30$		0			0
$31$	−2.65936			−0.477635			−0.238817	−	0.971064i	$-0.576760\pi$
$31$	−2.65936			−0.477635			−0.238817	+	0.971064i	$0.576760\pi$
$32$		0			0
$33$	7.47875	−	3.71214i	1.30188	−	0.646201i
$34$		0			0
$35$	−0.388272	−	1.08463i	−0.0656299	−	0.183336i
$36$		0			0
$37$	1.06500	−	1.84463i	0.175085	−	0.303256i	−0.765106	−	0.643904i	$-0.777313\pi$
$37$	1.06500	−	1.84463i	0.175085	−	0.303256i	0.940191	+	0.340649i	$0.110647\pi$
$38$		0			0
$39$	−7.73262	+	3.83815i	−1.23821	+	0.614597i
$40$		0			0
$41$	−0.112731	−	0.0650855i	−0.0176057	−	0.0101646i	0.491171	−	0.871063i	$-0.336569\pi$
$41$	−0.112731	−	0.0650855i	−0.0176057	−	0.0101646i	−0.508777	+	0.860898i	$0.669902\pi$
$42$		0			0
$43$	−6.53530	+	3.77315i	−0.996623	+	0.575401i	−0.907247	−	0.420597i	$-0.861821\pi$
$43$	−6.53530	+	3.77315i	−0.996623	+	0.575401i	−0.0893758	+	0.995998i	$0.528487\pi$
$44$		0			0
$45$	−1.04043	−	0.789852i	−0.155099	−	0.117744i
$46$		0			0
$47$	−8.58674			−1.25250			−0.626252	−	0.779620i	$-0.715412\pi$
$47$	−8.58674			−1.25250			−0.626252	+	0.779620i	$0.715412\pi$
$48$		0			0
$49$	−6.55209	−	2.46377i	−0.936013	−	0.351967i
$50$		0			0
$51$	0.618398	−	9.82340i	0.0865930	−	1.37555i
$52$		0			0
$53$	−5.61000	−	9.71680i	−0.770593	−	1.33471i	−0.937239	−	0.348689i	$-0.886627\pi$
$53$	−5.61000	−	9.71680i	−0.770593	−	1.33471i	0.166646	−	0.986017i	$-0.446706\pi$
$54$		0			0
$55$	−2.09897			−0.283025
$56$		0			0
$57$	−5.71347	−	11.5108i	−0.756767	−	1.52464i
$58$		0			0
$59$	12.4013			1.61451			0.807255	−	0.590203i	$-0.200952\pi$
$59$	12.4013			1.61451			0.807255	+	0.590203i	$0.200952\pi$
$60$		0			0
$61$			8.84273i			1.13220i	0.824338	+	0.566098i	$0.191548\pi$
$61$			8.84273i			1.13220i	−0.824338	+	0.566098i	$0.808452\pi$
$62$		0			0
$63$	−7.74935	+	1.71685i	−0.976326	+	0.216303i
$64$		0			0
$65$	2.17023			0.269183
$66$		0			0
$67$		−	0.936806i		−	0.114449i	−0.998361	−	0.0572246i	$-0.981775\pi$
$67$		−	0.936806i		−	0.114449i	0.998361	−	0.0572246i	$-0.0182251\pi$
$68$		0			0
$69$	0.343902	−	5.46297i	0.0414009	−	0.657664i
$70$		0			0
$71$			6.27328i			0.744501i	0.928132	+	0.372251i	$0.121414\pi$
$71$			6.27328i			0.744501i	−0.928132	+	0.372251i	$0.878586\pi$
$72$		0			0
$73$	11.2357	−	6.48693i	1.31504	−	0.759238i	0.332112	−	0.943240i	$-0.392239\pi$
$73$	11.2357	−	6.48693i	1.31504	−	0.759238i	0.982926	+	0.184002i	$0.0589054\pi$
$74$		0			0
$75$	−3.70437	−	7.46308i	−0.427743	−	0.861763i
$76$		0			0
$77$	−8.24970	+	9.72640i	−0.940141	+	1.10843i
$78$		0			0
$79$		−	3.44380i		−	0.387458i	−0.981055	−	0.193729i	$-0.937942\pi$
$79$		−	3.44380i		−	0.387458i	0.981055	−	0.193729i	$-0.0620582\pi$
$80$		0			0
$81$	−6.29791	+	6.42933i	−0.699768	+	0.714370i
$82$		0			0
$83$	3.68712	+	6.38628i	0.404714	+	0.700985i	0.994288	−	0.106729i	$-0.0340377\pi$
$83$	3.68712	+	6.38628i	0.404714	+	0.700985i	−0.589574	+	0.807714i	$0.700704\pi$
$84$		0			0
$85$	−1.23721	+	2.14292i	−0.134195	+	0.232432i
$86$		0			0
$87$	−8.63036	−	0.543294i	−0.925271	−	0.0582472i
$88$		0			0
$89$	−13.2599	−	7.65563i	−1.40555	−	0.811495i	−0.410596	−	0.911817i	$-0.634679\pi$
$89$	−13.2599	−	7.65563i	−1.40555	−	0.811495i	−0.994955	+	0.100322i	$0.968013\pi$
$90$		0			0
$91$	8.52975	−	10.0566i	0.894161	−	1.05422i
$92$		0			0
$93$	2.54914	−	3.83646i	0.264334	−	0.397823i
$94$		0			0
$95$			3.23059i			0.331452i
$96$		0			0
$97$	2.83887	−	1.63902i	0.288244	−	0.166418i	−0.348906	−	0.937158i	$-0.613447\pi$
$97$	2.83887	−	1.63902i	0.288244	−	0.166418i	0.637150	+	0.770740i	$0.280113\pi$
$98$		0			0
$99$	−1.81356	+	14.3473i	−0.182269	+	1.44196i
$100$		0			0
$101$	−14.5973	−	8.42775i	−1.45249	−	0.838593i	−0.453863	−	0.891071i	$-0.649955\pi$
$101$	−14.5973	−	8.42775i	−1.45249	−	0.838593i	−0.998622	+	0.0524786i	$0.983288\pi$
$102$		0			0
$103$	1.64544	+	2.84999i	0.162130	+	0.280818i	0.935633	−	0.352976i	$-0.114830\pi$
$103$	1.64544	+	2.84999i	0.162130	+	0.280818i	−0.773502	+	0.633794i	$0.781497\pi$
$104$		0			0
$105$	1.93689	+	0.479546i	0.189021	+	0.0467988i
$106$		0			0
$107$	−10.1078	−	5.83572i	−0.977154	−	0.564160i	−0.0757442	−	0.997127i	$-0.524133\pi$
$107$	−10.1078	−	5.83572i	−0.977154	−	0.564160i	−0.901410	+	0.432967i	$0.857467\pi$
$108$		0			0
$109$	9.15538	+	15.8576i	0.876926	+	1.51888i	0.854697	+	0.519128i	$0.173743\pi$
$109$	9.15538	+	15.8576i	0.876926	+	1.51888i	0.0222293	+	0.999753i	$0.492924\pi$
$110$		0			0
$111$	1.64025	+	3.30458i	0.155686	+	0.313657i
$112$		0			0
$113$	−2.20802	+	3.82441i	−0.207713	+	0.359770i	−0.950994	−	0.309210i	$-0.899935\pi$
$113$	−2.20802	+	3.82441i	−0.207713	+	0.359770i	0.743281	+	0.668980i	$0.233269\pi$
$114$		0			0
$115$	−0.688037	+	1.19172i	−0.0641598	+	0.111128i
$116$		0			0
$117$	1.87512	−	14.8344i	0.173355	−	1.37144i
$118$		0			0
$119$	5.06735	+	14.1555i	0.464523	+	1.29764i
$120$		0			0
$121$	6.11860	+	10.5977i	0.556237	+	0.963430i
$122$		0			0
$123$	0.201953	−	0.100241i	0.0182095	−	0.00903845i
$124$		0			0
$125$			4.27171i			0.382073i
$126$		0			0
$127$			2.65009i			0.235158i	0.993064	+	0.117579i	$0.0375133\pi$
$127$			2.65009i			0.235158i	−0.993064	+	0.117579i	$0.962487\pi$
$128$		0			0
$129$	0.821188	−	13.0448i	0.0723015	−	1.14853i
$130$		0			0
$131$	−0.431746	−	0.747807i	−0.0377219	−	0.0653362i	0.846548	−	0.532312i	$-0.178677\pi$
$131$	−0.431746	−	0.747807i	−0.0377219	−	0.0653362i	−0.884270	+	0.466976i	$0.845343\pi$
$132$		0			0
$133$	14.9702	+	12.6974i	1.29808	+	1.10100i
$134$		0			0
$135$	2.13677	−	0.743840i	0.183904	−	0.0640195i
$136$		0			0
$137$	−3.43168	+	5.94385i	−0.293188	+	0.507817i	−0.974562	−	0.224119i	$-0.928050\pi$
$137$	−3.43168	+	5.94385i	−0.293188	+	0.507817i	0.681373	+	0.731936i	$0.261383\pi$
$138$		0			0
$139$	4.26364	−	7.38484i	0.361637	−	0.626374i	−0.626593	−	0.779346i	$-0.715551\pi$
$139$	4.26364	−	7.38484i	0.361637	−	0.626374i	0.988230	+	0.152972i	$0.0488846\pi$
$140$		0			0
$141$	8.23086	−	12.3875i	0.693164	−	1.04321i
$142$		0			0
$143$	−12.0130	−	20.8072i	−1.00458	−	1.73998i
$144$		0			0
$145$	1.88266	+	1.08696i	0.156347	+	0.0902668i
$146$		0			0
$147$	9.83483	−	7.09056i	0.811163	−	0.584820i
$148$		0			0
$149$	5.29476	+	9.17079i	0.433764	+	0.751300i	0.997194	−	0.0748632i	$-0.0238520\pi$
$149$	5.29476	+	9.17079i	0.433764	+	0.751300i	−0.563430	+	0.826164i	$0.690519\pi$
$150$		0			0
$151$	−7.25025	−	4.18594i	−0.590017	−	0.340647i	0.175087	−	0.984553i	$-0.443979\pi$
$151$	−7.25025	−	4.18594i	−0.590017	−	0.340647i	−0.765104	+	0.643906i	$0.777313\pi$
$152$		0			0
$153$	13.5787	+	10.3084i	1.09778	+	0.833384i
$154$		0			0
$155$	−1.00282	+	0.578978i	−0.0805483	+	0.0465046i
$156$		0			0
$157$		−	16.0542i		−	1.28127i	−0.767847	−	0.640634i	$-0.778672\pi$
$157$		−	16.0542i		−	1.28127i	0.767847	−	0.640634i	$-0.221328\pi$
$158$		0			0
$159$	19.3952	+	1.22096i	1.53814	+	0.0968282i
$160$		0			0
$161$	2.81804	+	7.87214i	0.222093	+	0.620412i
$162$		0			0
$163$	6.55417	+	3.78405i	0.513362	+	0.296390i	0.734215	−	0.678917i	$-0.237551\pi$
$163$	6.55417	+	3.78405i	0.513362	+	0.296390i	−0.220852	+	0.975307i	$0.570884\pi$
$164$		0			0
$165$	2.01198	−	3.02803i	0.156633	−	0.235732i
$166$		0			0
$167$	1.74172	−	3.01674i	0.134778	−	0.233443i	−0.790735	−	0.612159i	$-0.790301\pi$
$167$	1.74172	−	3.01674i	0.134778	−	0.233443i	0.925513	+	0.378717i	$0.123635\pi$
$168$		0			0
$169$	5.92082	+	10.2552i	0.455447	+	0.788858i
$170$		0			0
$171$	22.0824	+	2.79130i	1.68868	+	0.213456i
$172$		0			0
$173$			7.72540i			0.587351i	0.955905	+	0.293676i	$0.0948785\pi$
$173$			7.72540i			0.587351i	−0.955905	+	0.293676i	$0.905121\pi$
$174$		0			0
$175$	9.70603	+	8.23243i	0.733707	+	0.622313i
$176$		0			0
$177$	−11.8873	+	17.8904i	−0.893506	+	1.34473i
$178$		0			0
$179$	18.3972	−	10.6216i	1.37507	−	0.793899i	0.383511	−	0.923536i	$-0.374715\pi$
$179$	18.3972	−	10.6216i	1.37507	−	0.793899i	0.991561	+	0.129637i	$0.0413813\pi$
$180$		0			0
$181$			5.62129i			0.417827i	0.977934	+	0.208914i	$0.0669927\pi$
$181$			5.62129i			0.417827i	−0.977934	+	0.208914i	$0.933007\pi$
$182$		0			0
$183$	−12.7568	−	8.47625i	−0.943007	−	0.626582i
$184$		0			0
$185$		−	0.927457i		−	0.0681880i
$186$		0			0
$187$	27.3938			2.00323
$188$		0			0
$189$	4.95141	−	12.8251i	0.360162	−	0.932890i
$190$		0			0
$191$		−	12.5663i		−	0.909265i	−0.890679	−	0.454632i	$-0.849771\pi$
$191$		−	12.5663i		−	0.909265i	0.890679	−	0.454632i	$-0.150229\pi$
$192$		0			0
$193$	−21.0668			−1.51642			−0.758209	−	0.652012i	$-0.773925\pi$
$193$	−21.0668			−1.51642			−0.758209	+	0.652012i	$0.773925\pi$
$194$		0			0
$195$	−2.08028	+	3.13083i	−0.148972	+	0.224203i
$196$		0			0
$197$	−21.1720			−1.50844			−0.754222	−	0.656619i	$-0.771986\pi$
$197$	−21.1720			−1.50844			−0.754222	+	0.656619i	$0.771986\pi$
$198$		0			0
$199$	−5.87039	−	10.1678i	−0.416141	−	0.720778i	0.579406	−	0.815039i	$-0.303284\pi$
$199$	−5.87039	−	10.1678i	−0.416141	−	0.720778i	−0.995548	+	0.0942612i	$0.969951\pi$
$200$		0			0
$201$	1.35146	+	0.897981i	0.0953248	+	0.0633387i
$202$		0			0
$203$	12.4364	−	4.45192i	0.872861	−	0.312464i
$204$		0			0
$205$	−0.0566799			−0.00395870
$206$		0			0
$207$	7.55138	+	5.73268i	0.524857	+	0.398449i
$208$		0			0
$209$	30.9735	−	17.8825i	2.14248	−	1.23696i
$210$		0			0
$211$	−7.83611	−	4.52418i	−0.539460	−	0.311457i	0.205400	−	0.978678i	$-0.434150\pi$
$211$	−7.83611	−	4.52418i	−0.539460	−	0.311457i	−0.744860	+	0.667221i	$0.767484\pi$
$212$		0			0
$213$	−9.05000	−	6.01329i	−0.620096	−	0.412024i
$214$		0			0
$215$	−1.64293	+	2.84564i	−0.112047	+	0.194071i
$216$		0			0
$217$	−1.25852	+	6.92253i	−0.0854336	+	0.469932i
$218$		0			0
$219$	−1.41181	+	22.4270i	−0.0954014	+	1.51548i
$220$		0			0
$221$	−28.3237			−1.90526
$222$		0			0
$223$	6.74216	+	11.6778i	0.451488	+	0.782001i	0.998479	−	0.0551381i	$-0.0175599\pi$
$223$	6.74216	+	11.6778i	0.451488	+	0.782001i	−0.546990	+	0.837139i	$0.684227\pi$
$224$		0			0
$225$	14.3173	+	1.80976i	0.954486	+	0.120651i
$226$		0			0
$227$	−12.0358	+	20.8466i	−0.798845	+	1.38364i	0.121524	+	0.992589i	$0.461222\pi$
$227$	−12.0358	+	20.8466i	−0.798845	+	1.38364i	−0.920369	+	0.391052i	$0.872111\pi$
$228$		0			0
$229$	12.1965	−	7.04166i	0.805968	−	0.465326i	−0.0395859	−	0.999216i	$-0.512604\pi$
$229$	12.1965	−	7.04166i	0.805968	−	0.465326i	0.845554	+	0.533891i	$0.179271\pi$
$230$		0			0
$231$	−6.12377	−	21.2245i	−0.402914	−	1.39647i
$232$		0			0
$233$	1.10903	−	1.92090i	0.0726551	−	0.125842i	−0.827409	−	0.561600i	$-0.810186\pi$
$233$	1.10903	−	1.92090i	0.0726551	−	0.125842i	0.900064	+	0.435757i	$0.143519\pi$
$234$		0			0
$235$	−3.23798	+	1.86945i	−0.211222	+	0.121949i
$236$		0			0
$237$	4.96811	+	3.30107i	0.322714	+	0.214428i
$238$		0			0
$239$	10.5001	+	6.06225i	0.679197	+	0.392134i	0.799552	−	0.600596i	$-0.205070\pi$
$239$	10.5001	+	6.06225i	0.679197	+	0.392134i	−0.120356	+	0.992731i	$0.538403\pi$
$240$		0			0
$241$	−4.04515	−	2.33547i	−0.260571	−	0.150441i	0.364024	−	0.931390i	$-0.381403\pi$
$241$	−4.04515	−	2.33547i	−0.260571	−	0.150441i	−0.624595	+	0.780949i	$0.714736\pi$
$242$		0			0
$243$	−3.23823	−	15.2484i	−0.207732	−	0.978186i
$244$		0			0
$245$	−3.00712	+	0.497413i	−0.192118	+	0.0317786i
$246$		0			0
$247$	−32.0249	+	18.4896i	−2.03770	+	1.17646i
$248$		0			0
$249$	−12.7473	−	0.802463i	−0.807829	−	0.0508540i
$250$		0			0
$251$	10.4901			0.662132			0.331066	−	0.943608i	$-0.392592\pi$
$251$	10.4901			0.662132			0.331066	+	0.943608i	$0.392592\pi$
$252$		0			0
$253$	15.2342			0.957764
$254$		0			0
$255$	−1.90549	−	3.83894i	−0.119327	−	0.240404i
$256$		0			0
$257$	4.43629	−	2.56129i	0.276728	−	0.159769i	−0.355213	−	0.934785i	$-0.615592\pi$
$257$	4.43629	−	2.56129i	0.276728	−	0.159769i	0.631941	+	0.775016i	$0.282258\pi$
$258$		0			0
$259$	−4.29773	−	3.64523i	−0.267048	−	0.226504i
$260$		0			0
$261$	9.05644	−	11.9296i	0.560580	−	0.738424i
$262$		0			0
$263$	16.5367	+	9.54746i	1.01970	+	0.588722i	0.914016	−	0.405678i	$-0.132965\pi$
$263$	16.5367	+	9.54746i	1.01970	+	0.588722i	0.105680	+	0.994400i	$0.466298\pi$
$264$		0			0
$265$	−4.23095	−	2.44274i	−0.259905	−	0.150056i
$266$		0			0
$267$	23.7546	−	11.7908i	1.45376	−	0.721585i
$268$		0			0
$269$	6.02481	−	3.47842i	0.367339	−	0.212083i	−0.304956	−	0.952366i	$-0.598642\pi$
$269$	6.02481	−	3.47842i	0.367339	−	0.212083i	0.672295	+	0.740283i	$0.265309\pi$
$270$		0			0
$271$	1.40013	−	2.42510i	0.0850521	−	0.147315i	−0.820361	−	0.571846i	$-0.806228\pi$
$271$	1.40013	−	2.42510i	0.0850521	−	0.147315i	0.905413	+	0.424531i	$0.139561\pi$
$272$		0			0
$273$	6.33165	+	21.9450i	0.383209	+	1.32817i
$274$		0			0
$275$	20.0819	−	11.5943i	1.21098	−	0.699161i
$276$		0			0
$277$	−7.15055	+	12.3851i	−0.429635	+	0.744149i	−0.996841	−	0.0794266i	$-0.974691\pi$
$277$	−7.15055	+	12.3851i	−0.429635	+	0.744149i	0.567206	+	0.823576i	$0.308024\pi$
$278$		0			0
$279$	3.09109	+	7.35492i	0.185059	+	0.440328i
$280$		0			0
$281$	−9.38363	−	16.2529i	−0.559780	−	0.969568i	−0.997514	−	0.0704634i	$-0.977552\pi$
$281$	−9.38363	−	16.2529i	−0.559780	−	0.969568i	0.437734	−	0.899104i	$-0.355781\pi$
$282$		0			0
$283$	19.4723			1.15751			0.578755	−	0.815501i	$-0.303539\pi$
$283$	19.4723			1.15751			0.578755	+	0.815501i	$0.303539\pi$
$284$		0			0
$285$	−4.66054	−	3.09670i	−0.276067	−	0.183433i
$286$		0			0
$287$	−0.222772	+	0.262648i	−0.0131498	+	0.0155036i
$288$		0			0
$289$	7.64694	−	13.2449i	0.449820	−	0.779111i
$290$		0			0
$291$	−0.356716	+	5.66653i	−0.0209111	+	0.332178i
$292$		0			0
$293$	−8.77997	−	5.06912i	−0.512932	−	0.296141i	0.221106	−	0.975250i	$-0.429033\pi$
$293$	−8.77997	−	5.06912i	−0.512932	−	0.296141i	−0.734038	+	0.679109i	$0.762367\pi$
$294$		0			0
$295$	4.67641	−	2.69992i	0.272271	−	0.157196i
$296$		0			0
$297$	−18.9594	−	16.3690i	−1.10014	−	0.949825i
$298$		0			0
$299$	−15.7513			−0.910922
$300$		0			0
$301$	6.72907	+	18.7975i	0.387857	+	1.08347i
$302$		0			0
$303$	26.1504	−	12.9800i	1.50230	−	0.745681i
$304$		0			0
$305$	1.92518	+	3.33451i	0.110236	+	0.190933i
$306$		0			0
$307$	9.48057			0.541085			0.270542	−	0.962708i	$-0.412797\pi$
$307$	9.48057			0.541085			0.270542	+	0.962708i	$0.412797\pi$
$308$		0			0
$309$	−5.68872	−	0.358114i	−0.323620	−	0.0203724i
$310$		0			0
$311$	−0.940289			−0.0533189			−0.0266595	−	0.999645i	$-0.508487\pi$
$311$	−0.940289			−0.0533189			−0.0266595	+	0.999645i	$0.508487\pi$
$312$		0			0
$313$		−	13.4577i		−	0.760674i	−0.924848	−	0.380337i	$-0.875808\pi$
$313$		−	13.4577i		−	0.760674i	0.924848	−	0.380337i	$-0.124192\pi$
$314$		0			0
$315$	−2.54842	+	2.33454i	−0.143587	+	0.131537i
$316$		0			0
$317$	−4.38829			−0.246471			−0.123236	−	0.992377i	$-0.539327\pi$
$317$	−4.38829			−0.246471			−0.123236	+	0.992377i	$0.539327\pi$
$318$		0			0
$319$		−	24.0668i		−	1.34748i
$320$		0			0
$321$	18.1076	−	8.98787i	1.01067	−	0.501654i
$322$		0			0
$323$		−	42.1626i		−	2.34599i
$324$		0			0
$325$	−20.7636	+	11.9879i	−1.15176	+	0.664967i
$326$		0			0
$327$	−31.6525	−	1.99257i	−1.75039	−	0.110189i
$328$		0			0
$329$	−4.06359	+	22.3520i	−0.224033	+	1.23231i
$330$		0			0
$331$			4.22446i			0.232197i	0.993238	+	0.116099i	$0.0370388\pi$
$331$			4.22446i			0.232197i	−0.993238	+	0.116099i	$0.962961\pi$
$332$		0			0
$333$	−6.33955	−	0.801343i	−0.347405	−	0.0439133i
$334$		0			0
$335$	−0.203955	−	0.353261i	−0.0111433	−	0.0193007i
$336$		0			0
$337$	−0.959055	+	1.66113i	−0.0522431	+	0.0904876i	−0.890964	−	0.454073i	$-0.849970\pi$
$337$	−0.959055	+	1.66113i	−0.0522431	+	0.0904876i	0.838721	+	0.544561i	$0.183304\pi$
$338$		0			0
$339$	−3.40068	−	6.85126i	−0.184700	−	0.372109i
$340$		0			0
$341$	11.1020	+	6.40972i	0.601205	+	0.347106i
$342$		0			0
$343$	−9.51410	+	15.8897i	−0.513713	+	0.857962i
$344$		0			0
$345$	−1.05968	−	2.13491i	−0.0570512	−	0.114939i
$346$		0			0
$347$			26.9205i			1.44517i	0.691284	+	0.722583i	$0.257045\pi$
$347$			26.9205i			1.44517i	−0.691284	+	0.722583i	$0.742955\pi$
$348$		0			0
$349$	8.15394	−	4.70768i	0.436470	−	0.251996i	−0.265629	−	0.964075i	$-0.585580\pi$
$349$	8.15394	−	4.70768i	0.436470	−	0.251996i	0.702099	+	0.712079i	$0.252246\pi$
$350$		0			0
$351$	19.6031	+	16.9247i	1.04633	+	0.903372i
$352$		0			0
$353$	6.72279	+	3.88140i	0.357818	+	0.206586i	0.668123	−	0.744051i	$-0.267098\pi$
$353$	6.72279	+	3.88140i	0.357818	+	0.206586i	−0.310305	+	0.950637i	$0.600431\pi$
$354$		0			0
$355$	1.36578	+	2.36559i	0.0724879	+	0.125553i
$356$		0			0
$357$	−25.2785	−	6.25857i	−1.33788	−	0.331239i
$358$		0			0
$359$	−17.8936	−	10.3309i	−0.944387	−	0.545242i	−0.0530541	−	0.998592i	$-0.516896\pi$
$359$	−17.8936	−	10.3309i	−0.944387	−	0.545242i	−0.891333	+	0.453350i	$0.850229\pi$
$360$		0			0
$361$	−18.0236	−	31.2177i	−0.948608	−	1.64304i
$362$		0			0
$363$	−21.1536	−	1.33165i	−1.11028	−	0.0698935i
$364$		0			0
$365$	2.82458	−	4.89232i	0.147845	−	0.256076i
$366$		0			0
$367$	−8.57981	+	14.8607i	−0.447862	+	0.775720i	−0.998247	−	0.0591910i	$-0.981148\pi$
$367$	−8.57981	+	14.8607i	−0.447862	+	0.775720i	0.550384	+	0.834911i	$0.314481\pi$
$368$		0			0
$369$	−0.0489727	+	0.387430i	−0.00254941	+	0.0201688i
$370$		0			0
$371$	−27.9485	+	10.0049i	−1.45102	+	0.519429i
$372$		0			0
$373$	0.840146	+	1.45518i	0.0435011	+	0.0753461i	0.886956	−	0.461854i	$-0.152815\pi$
$373$	0.840146	+	1.45518i	0.0435011	+	0.0753461i	−0.843455	+	0.537200i	$0.819482\pi$
$374$		0			0
$375$	−6.16248	−	4.09467i	−0.318229	−	0.211448i
$376$		0			0
$377$			24.8838i			1.28158i
$378$		0			0
$379$		−	16.3442i		−	0.839543i	−0.907630	−	0.419771i	$-0.862110\pi$
$379$		−	16.3442i		−	0.839543i	0.907630	−	0.419771i	$-0.137890\pi$
$380$		0			0
$381$	−3.82309	−	2.54026i	−0.195863	−	0.130141i
$382$		0			0
$383$	8.49161	+	14.7079i	0.433901	+	0.751539i	0.997205	−	0.0747110i	$-0.0238034\pi$
$383$	8.49161	+	14.7079i	0.433901	+	0.751539i	−0.563304	+	0.826250i	$0.690470\pi$
$384$		0			0
$385$	−0.993318	+	5.46380i	−0.0506242	+	0.278461i
$386$		0			0
$387$	18.0316	+	13.6888i	0.916597	+	0.695841i
$388$		0			0
$389$	−19.4798	+	33.7400i	−0.987666	+	1.71069i	−0.358235	+	0.933631i	$0.616621\pi$
$389$	−19.4798	+	33.7400i	−0.987666	+	1.71069i	−0.629431	+	0.777056i	$0.716712\pi$
$390$		0			0
$391$	8.97960	−	15.5531i	0.454118	−	0.786555i
$392$		0			0
$393$	1.49266	+	0.0939651i	0.0752947	+	0.00473991i
$394$		0			0
$395$	−0.749760	−	1.29862i	−0.0377245	−	0.0653408i
$396$		0			0
$397$	8.84820	+	5.10851i	0.444078	+	0.256389i	0.705326	−	0.708883i	$-0.250801\pi$
$397$	8.84820	+	5.10851i	0.444078	+	0.256389i	−0.261248	+	0.965272i	$0.584134\pi$
$398$		0			0
$399$	−32.6673	+	9.42527i	−1.63541	+	0.471854i
$400$		0			0
$401$	1.86983	+	3.23864i	0.0933750	+	0.161730i	0.908929	−	0.416950i	$-0.136901\pi$
$401$	1.86983	+	3.23864i	0.0933750	+	0.161730i	−0.815554	+	0.578681i	$0.803568\pi$
$402$		0			0
$403$	−11.4788	−	6.62731i	−0.571801	−	0.330130i
$404$		0			0
$405$	−0.975133	+	3.79558i	−0.0484547	+	0.188604i
$406$		0			0
$407$	−8.89204	+	5.13382i	−0.440762	+	0.254474i
$408$		0			0
$409$		−	1.70503i		−	0.0843083i	−0.999111	−	0.0421541i	$-0.986578\pi$
$409$		−	1.70503i		−	0.0843083i	0.999111	−	0.0421541i	$-0.0134221\pi$
$410$		0			0
$411$	−5.28530	−	10.6481i	−0.260704	−	0.525234i
$412$		0			0
$413$	5.86879	−	32.2816i	0.288784	−	1.58847i
$414$		0			0
$415$	2.78076	+	1.60547i	0.136502	+	0.0788094i
$416$		0			0
$417$	6.56663	+	13.2296i	0.321569	+	0.647857i
$418$		0			0
$419$	−8.00198	+	13.8598i	−0.390922	+	0.677097i	−0.992571	−	0.121663i	$-0.961177\pi$
$419$	−8.00198	+	13.8598i	−0.390922	+	0.677097i	0.601649	+	0.798761i	$0.294511\pi$
$420$		0			0
$421$	−15.7342	−	27.2524i	−0.766837	−	1.32820i	−0.939270	−	0.343179i	$-0.888496\pi$
$421$	−15.7342	−	27.2524i	−0.766837	−	1.32820i	0.172433	−	0.985021i	$-0.444837\pi$
$422$		0			0
$423$	9.98074	+	23.7481i	0.485280	+	1.15467i
$424$		0			0
$425$		−	27.3364i		−	1.32601i
$426$		0			0
$427$	23.0184	+	4.18474i	1.11394	+	0.202514i
$428$		0			0
$429$	41.5321	+	2.61451i	2.00519	+	0.126230i
$430$		0			0
$431$	4.78381	−	2.76193i	0.230428	−	0.133038i	−0.380342	−	0.924846i	$-0.624194\pi$
$431$	4.78381	−	2.76193i	0.230428	−	0.133038i	0.610769	+	0.791809i	$0.290860\pi$
$432$		0			0
$433$		−	7.56302i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$433$		−	7.56302i		−	0.363456i	0.983349	−	0.181728i	$-0.0581690\pi$
$434$		0			0
$435$	−3.37271	+	1.67407i	−0.161709	+	0.0802656i
$436$		0			0
$437$		−	23.4474i		−	1.12164i
$438$		0			0
$439$	19.0091			0.907253			0.453627	−	0.891192i	$-0.350130\pi$
$439$	19.0091			0.907253			0.453627	+	0.891192i	$0.350130\pi$
$440$		0			0
$441$	0.801801	+	20.9847i	0.0381810	+	0.999271i
$442$		0			0
$443$		−	2.89634i		−	0.137609i	−0.997630	−	0.0688046i	$-0.978081\pi$
$443$		−	2.89634i		−	0.137609i	0.997630	−	0.0688046i	$-0.0219185\pi$
$444$		0			0
$445$	−6.66693			−0.316043
$446$		0			0
$447$	−18.3053	−	1.15235i	−0.865813	−	0.0545042i
$448$		0			0
$449$	31.1794			1.47145			0.735724	−	0.677281i	$-0.236842\pi$
$449$	31.1794			1.47145			0.735724	+	0.677281i	$0.236842\pi$
$450$		0			0
$451$	0.313744	+	0.543421i	0.0147736	+	0.0255887i
$452$		0			0
$453$	12.9885	−	6.44696i	0.610254	−	0.302905i
$454$		0			0
$455$	1.02704	−	5.64928i	0.0481483	−	0.264842i
$456$		0			0
$457$	−9.02824			−0.422323			−0.211162	−	0.977451i	$-0.567725\pi$
$457$	−9.02824			−0.422323			−0.211162	+	0.977451i	$0.567725\pi$
$458$		0			0
$459$	−27.8871	+	9.70788i	−1.30166	+	0.453125i
$460$		0			0
$461$	−1.19412	+	0.689428i	−0.0556159	+	0.0321099i	−0.527550	−	0.849524i	$-0.676889\pi$
$461$	−1.19412	+	0.689428i	−0.0556159	+	0.0321099i	0.471934	+	0.881634i	$0.343556\pi$
$462$		0			0
$463$	2.94275	+	1.69900i	0.136761	+	0.0789592i	0.566820	−	0.823842i	$-0.308174\pi$
$463$	2.94275	+	1.69900i	0.136761	+	0.0789592i	−0.430058	+	0.902801i	$0.641507\pi$
$464$		0			0
$465$	0.126008	−	2.00168i	0.00584350	−	0.0928255i
$466$		0			0
$467$	−8.37470	+	14.5054i	−0.387535	+	0.671230i	−0.992117	−	0.125312i	$-0.960007\pi$
$467$	−8.37470	+	14.5054i	−0.387535	+	0.671230i	0.604582	+	0.796543i	$0.293340\pi$
$468$		0			0
$469$	−2.43859	−	0.443334i	−0.112603	−	0.0204713i
$470$		0			0
$471$	23.1603	+	15.3889i	1.06717	+	0.709082i
$472$		0			0
$473$	36.3770			1.67262
$474$		0			0
$475$	−17.8451	−	30.9086i	−0.818789	−	1.41818i
$476$		0			0
$477$	−20.3528	+	26.8097i	−0.931889	+	1.22753i
$478$		0			0
$479$	−2.34006	+	4.05310i	−0.106920	+	0.185191i	−0.914521	−	0.404538i	$-0.867432\pi$
$479$	−2.34006	+	4.05310i	−0.106920	+	0.185191i	0.807601	+	0.589729i	$0.200766\pi$
$480$		0			0
$481$	9.19390	−	5.30810i	0.419206	−	0.242029i
$482$		0			0
$483$	−14.0578	−	3.48050i	−0.639653	−	0.158368i
$484$		0			0
$485$	0.713674	−	1.23612i	0.0324063	−	0.0561293i
$486$		0			0
$487$	14.9661	−	8.64071i	0.678181	−	0.391548i	−0.120988	−	0.992654i	$-0.538606\pi$
$487$	14.9661	−	8.64071i	0.678181	−	0.391548i	0.799169	+	0.601106i	$0.205273\pi$
$488$		0			0
$489$	−11.7415	+	5.82800i	−0.530969	+	0.263551i
$490$		0			0
$491$	15.7916	+	9.11730i	0.712666	+	0.411458i	0.812047	−	0.583591i	$-0.198353\pi$
$491$	15.7916	+	9.11730i	0.712666	+	0.411458i	−0.0993812	+	0.995049i	$0.531686\pi$
$492$		0			0
$493$	−24.5707	−	14.1859i	−1.10661	−	0.638901i
$494$		0			0
$495$	2.43973	+	5.80508i	0.109658	+	0.260919i
$496$		0			0
$497$	16.3299	+	2.96877i	0.732495	+	0.133167i
$498$		0			0
$499$	−27.4176	+	15.8295i	−1.22738	+	0.708627i	−0.966481	−	0.256739i	$-0.917352\pi$
$499$	−27.4176	+	15.8295i	−1.22738	+	0.708627i	−0.260898	+	0.965366i	$0.584018\pi$
$500$		0			0
$501$	2.68250	+	5.40436i	0.119845	+	0.241449i
$502$		0			0
$503$	−27.7607			−1.23779			−0.618894	−	0.785474i	$-0.712419\pi$
$503$	−27.7607			−1.23779			−0.618894	+	0.785474i	$0.712419\pi$
$504$		0			0
$505$	−7.33933			−0.326596
$506$		0			0
$507$	−20.4698	−	1.28860i	−0.909095	−	0.0572289i
$508$		0			0
$509$	21.2587	−	12.2737i	0.942275	−	0.544023i	0.0516025	−	0.998668i	$-0.483567\pi$
$509$	21.2587	−	12.2737i	0.942275	−	0.544023i	0.890673	+	0.454645i	$0.150234\pi$
$510$		0			0
$511$	−11.5688	−	32.3173i	−0.511775	−	1.42963i
$512$		0			0
$513$	−25.1940	+	29.1811i	−1.11234	+	1.28837i
$514$		0			0
$515$	1.24096	+	0.716470i	0.0546833	+	0.0315714i
$516$		0			0
$517$	35.8468	+	20.6962i	1.57654	+	0.910217i
$518$		0			0
$519$	−11.1449	−	7.40522i	−0.489205	−	0.325053i
$520$		0			0
$521$	10.9064	−	6.29680i	0.477817	−	0.275868i	−0.241689	−	0.970354i	$-0.577701\pi$
$521$	10.9064	−	6.29680i	0.477817	−	0.275868i	0.719506	+	0.694486i	$0.244368\pi$
$522$		0			0
$523$	−11.2363	+	19.4619i	−0.491330	+	0.851009i	−0.999950	−	0.00998216i	$-0.996823\pi$
$523$	−11.2363	+	19.4619i	−0.491330	+	0.851009i	0.508620	+	0.860991i	$0.330156\pi$
$524$		0			0
$525$	−21.1801	+	6.11094i	−0.924375	+	0.266703i
$526$		0			0
$527$	13.0878	−	7.55626i	0.570115	−	0.329156i
$528$		0			0
$529$	−6.50628	+	11.2692i	−0.282882	+	0.489966i
$530$		0			0
$531$	−14.4146	−	34.2979i	−0.625539	−	1.48840i
$532$		0			0
$533$	−0.324395	−	0.561869i	−0.0140511	−	0.0243372i
$534$		0			0
$535$	−5.08205			−0.219716
$536$		0			0
$537$	−2.31169	+	36.7218i	−0.0997567	+	1.58466i
$538$		0			0
$539$	21.4145	+	26.0776i	0.922389	+	1.12324i
$540$		0			0
$541$	−7.43945	+	12.8855i	−0.319847	+	0.553991i	−0.980456	−	0.196739i	$-0.936965\pi$
$541$	−7.43945	+	12.8855i	−0.319847	+	0.553991i	0.660609	+	0.750730i	$0.270298\pi$
$542$		0			0
$543$	−8.10942	−	5.38832i	−0.348009	−	0.231235i
$544$		0			0
$545$	6.90481	+	3.98649i	0.295770	+	0.170763i
$546$		0			0
$547$	−37.5042	+	21.6531i	−1.60356	+	0.925818i	−0.612797	+	0.790240i	$0.709956\pi$
$547$	−37.5042	+	21.6531i	−1.60356	+	0.925818i	−0.990767	+	0.135578i	$0.956711\pi$
$548$		0			0
$549$	24.4561	−	10.2783i	1.04376	−	0.438667i
$550$		0			0
$551$	−37.0420			−1.57804
$552$		0			0
$553$	−8.96449	−	1.62974i	−0.381209	−	0.0693037i
$554$		0			0
$555$	1.33797	+	0.889019i	0.0567939	+	0.0377368i
$556$		0			0
$557$	9.44755	+	16.3636i	0.400305	+	0.693349i	0.993763	−	0.111516i	$-0.0355707\pi$
$557$	9.44755	+	16.3636i	0.400305	+	0.693349i	−0.593457	+	0.804866i	$0.702237\pi$
$558$		0			0
$559$	−37.6118			−1.59081
$560$		0			0
$561$	−26.2585	+	39.5190i	−1.10863	+	1.66849i
$562$		0			0
$563$	19.2299			0.810445			0.405223	−	0.914218i	$-0.367194\pi$
$563$	19.2299			0.810445			0.405223	+	0.914218i	$0.367194\pi$
$564$		0			0
$565$			1.92286i			0.0808955i
$566$		0			0
$567$	13.7557	+	19.4366i	0.577683	+	0.816261i
$568$		0			0
$569$	−6.67301			−0.279747			−0.139874	−	0.990169i	$-0.544670\pi$
$569$	−6.67301			−0.279747			−0.139874	+	0.990169i	$0.544670\pi$
$570$		0			0
$571$		−	13.0933i		−	0.547938i	−0.961739	−	0.273969i	$-0.911663\pi$
$571$		−	13.0933i		−	0.547938i	0.961739	−	0.273969i	$-0.0883365\pi$
$572$		0			0
$573$	18.1285	+	12.0455i	0.757327	+	0.503207i
$574$		0			0
$575$		−	15.2023i		−	0.633978i
$576$		0			0
$577$	−7.59957	+	4.38761i	−0.316374	+	0.182659i	−0.649775	−	0.760126i	$-0.725137\pi$
$577$	−7.59957	+	4.38761i	−0.316374	+	0.182659i	0.333401	+	0.942785i	$0.391804\pi$
$578$		0			0
$579$	20.1936	−	30.3915i	0.839219	−	1.26303i
$580$		0			0
$581$	18.3689	−	6.57564i	0.762071	−	0.272803i
$582$		0			0
$583$			54.0860i			2.24001i
$584$		0			0
$585$	−2.52255	−	6.00214i	−0.104295	−	0.248158i
$586$		0			0
$587$	1.22575	+	2.12306i	0.0505920	+	0.0876279i	0.890212	−	0.455546i	$-0.150556\pi$
$587$	1.22575	+	2.12306i	0.0505920	+	0.0876279i	−0.839620	+	0.543174i	$0.817223\pi$
$588$		0			0
$589$	9.86539	−	17.0874i	0.406496	−	0.704072i
$590$		0			0
$591$	20.2946	−	30.5433i	0.834807	−	1.25638i
$592$		0			0
$593$	−7.67653	−	4.43205i	−0.315237	−	0.182002i	0.334030	−	0.942562i	$-0.391591\pi$
$593$	−7.67653	−	4.43205i	−0.315237	−	0.182002i	−0.649268	+	0.760560i	$0.724925\pi$
$594$		0			0
$595$	4.99270	+	4.23469i	0.204681	+	0.173605i
$596$		0			0
$597$	20.2955	+	1.27763i	0.830638	+	0.0522899i
$598$		0			0
$599$		−	48.3566i		−	1.97580i	−0.155097	−	0.987899i	$-0.549569\pi$
$599$		−	48.3566i		−	1.97580i	0.155097	−	0.987899i	$-0.450431\pi$
$600$		0			0
$601$	31.4198	−	18.1402i	1.28164	−	0.739955i	0.304492	−	0.952515i	$-0.401513\pi$
$601$	31.4198	−	18.1402i	1.28164	−	0.739955i	0.977148	+	0.212560i	$0.0681800\pi$
$602$		0			0
$603$	−2.59090	+	1.08889i	−0.105510	+	0.0443431i
$604$		0			0
$605$	4.61453	+	2.66420i	0.187607	+	0.108315i
$606$		0			0
$607$	16.4947	+	28.5696i	0.669499	+	1.15961i	0.978044	+	0.208396i	$0.0668244\pi$
$607$	16.4947	+	28.5696i	0.669499	+	1.15961i	−0.308546	+	0.951210i	$0.599842\pi$
$608$		0			0
$609$	−5.49847	+	22.2084i	−0.222809	+	0.899931i
$610$		0			0
$611$	−37.0637	−	21.3987i	−1.49944	−	0.865701i
$612$		0			0
$613$	−4.91100	−	8.50611i	−0.198354	−	0.343558i	0.749641	−	0.661844i	$-0.230226\pi$
$613$	−4.91100	−	8.50611i	−0.198354	−	0.343558i	−0.947995	+	0.318286i	$0.896893\pi$
$614$		0			0
$615$	0.0543308	−	0.0817679i	0.00219083	−	0.00329720i
$616$		0			0
$617$	3.68396	−	6.38080i	0.148311	−	0.256881i	−0.782293	−	0.622911i	$-0.785950\pi$
$617$	3.68396	−	6.38080i	0.148311	−	0.256881i	0.930603	+	0.366030i	$0.119283\pi$
$618$		0			0
$619$	−7.58588	+	13.1391i	−0.304902	+	0.528106i	−0.977240	−	0.212139i	$-0.931957\pi$
$619$	−7.58588	+	13.1391i	−0.304902	+	0.528106i	0.672337	+	0.740245i	$0.265290\pi$
$620$		0			0
$621$	−15.5085	+	5.39873i	−0.622336	+	0.216643i
$622$		0			0
$623$	−26.2034	+	30.8938i	−1.04982	+	1.23773i
$624$		0			0
$625$	−11.0960	−	19.2188i	−0.443840	−	0.768754i
$626$		0			0
$627$	−3.89195	+	61.8246i	−0.155429	+	2.46903i
$628$		0			0
$629$			12.1043i			0.482629i
$630$		0			0
$631$			6.33987i			0.252386i	0.992006	+	0.126193i	$0.0402759\pi$
$631$			6.33987i			0.252386i	−0.992006	+	0.126193i	$0.959724\pi$
$632$		0			0
$633$	14.0380	−	6.96790i	0.557962	−	0.276949i
$634$		0			0
$635$	0.576960	+	0.999325i	0.0228960	+	0.0396570i
$636$		0			0
$637$	−22.1415	−	26.9628i	−0.877278	−	1.06831i
$638$		0			0
$639$	17.3499	−	7.29171i	0.686350	−	0.288456i
$640$		0			0
$641$	−3.95669	+	6.85319i	−0.156280	+	0.270685i	−0.933524	−	0.358514i	$-0.883284\pi$
$641$	−3.95669	+	6.85319i	−0.156280	+	0.270685i	0.777244	+	0.629199i	$0.216617\pi$
$642$		0			0
$643$	−8.71529	+	15.0953i	−0.343697	+	0.595301i	−0.985116	−	0.171890i	$-0.945013\pi$
$643$	−8.71529	+	15.0953i	−0.343697	+	0.595301i	0.641419	+	0.767191i	$0.278346\pi$
$644$		0			0
$645$	−2.53036	−	5.09784i	−0.0996327	−	0.200727i
$646$		0			0
$647$	0.396991	+	0.687609i	0.0156073	+	0.0270327i	0.873724	−	0.486423i	$-0.161698\pi$
$647$	0.396991	+	0.687609i	0.0156073	+	0.0270327i	−0.858116	+	0.513455i	$0.828365\pi$
$648$		0			0
$649$	−51.7713	−	29.8902i	−2.03220	−	1.17329i
$650$		0			0
$651$	−8.78027	−	8.45120i	−0.344126	−	0.331229i
$652$		0			0
$653$	−6.17276	−	10.6915i	−0.241559	−	0.418392i	0.719600	−	0.694389i	$-0.244325\pi$
$653$	−6.17276	−	10.6915i	−0.241559	−	0.418392i	−0.961158	+	0.275997i	$0.910992\pi$
$654$		0			0
$655$	−0.325615	−	0.187994i	−0.0127228	−	0.00734553i
$656$		0			0
$657$	−31.0005	−	23.5342i	−1.20944	−	0.918157i
$658$		0			0
$659$	0.112430	−	0.0649117i	0.00437966	−	0.00252860i	−0.497809	−	0.867287i	$-0.665862\pi$
$659$	0.112430	−	0.0649117i	0.00437966	−	0.00252860i	0.502188	+	0.864758i	$0.332528\pi$
$660$		0			0
$661$			5.35244i			0.208186i	0.994568	+	0.104093i	$0.0331939\pi$
$661$			5.35244i			0.208186i	−0.994568	+	0.104093i	$0.966806\pi$
$662$		0			0
$663$	27.1498	−	40.8605i	1.05441	−	1.58689i
$664$		0			0
$665$	8.40950	+	1.52885i	0.326106	+	0.0592861i
$666$		0			0
$667$	−13.6642	−	7.88904i	−0.529080	−	0.305465i
$668$		0			0
$669$	−23.3094	−	1.46736i	−0.901193	−	0.0567314i
$670$		0			0
$671$	21.3132	−	36.9155i	0.822787	−	1.42511i
$672$		0			0
$673$	−10.1452	−	17.5720i	−0.391069	−	0.677351i	0.601522	−	0.798856i	$-0.294561\pi$
$673$	−10.1452	−	17.5720i	−0.391069	−	0.677351i	−0.992591	+	0.121505i	$0.961228\pi$
$674$		0			0
$675$	−16.3347	+	18.9197i	−0.628724	+	0.728221i
$676$		0			0
$677$			36.4252i			1.39993i	0.714175	+	0.699967i	$0.246802\pi$
$677$			36.4252i			1.39993i	−0.714175	+	0.699967i	$0.753198\pi$
$678$		0			0
$679$	−2.92305	−	8.16547i	−0.112176	−	0.313362i
$680$		0			0
$681$	−18.5369	−	37.3458i	−0.710337	−	1.43110i
$682$		0			0
$683$	14.6439	−	8.45468i	0.560334	−	0.323509i	−0.192945	−	0.981210i	$-0.561804\pi$
$683$	14.6439	−	8.45468i	0.560334	−	0.323509i	0.753280	+	0.657700i	$0.228471\pi$
$684$		0			0
$685$			2.98849i			0.114184i
$686$		0			0
$687$	−1.53254	+	24.3448i	−0.0584701	+	0.928813i
$688$		0			0
$689$		−	55.9220i		−	2.13046i
$690$		0			0
$691$	16.8747			0.641944			0.320972	−	0.947089i	$-0.395990\pi$
$691$	16.8747			0.641944			0.320972	+	0.947089i	$0.395990\pi$
$692$		0			0
$693$	36.4890	+	11.5106i	1.38610	+	0.437251i
$694$		0			0
$695$		−	3.71300i		−	0.140842i
$696$		0			0
$697$	0.739732			0.0280193
$698$		0			0
$699$	1.70807	+	3.44121i	0.0646053	+	0.130159i
$700$		0			0
$701$	40.8133			1.54150			0.770748	−	0.637140i	$-0.219883\pi$
$701$	40.8133			1.54150			0.770748	+	0.637140i	$0.219883\pi$
$702$		0			0
$703$	7.90162	+	13.6860i	0.298015	+	0.516178i
$704$		0			0
$705$	0.406866	−	6.46316i	0.0153234	−	0.243417i
$706$		0			0
$707$	−28.8462	+	34.0096i	−1.08487	+	1.27906i
$708$		0			0
$709$	42.7058			1.60385			0.801925	−	0.597424i	$-0.203809\pi$
$709$	42.7058			1.60385			0.801925	+	0.597424i	$0.203809\pi$
$710$		0			0
$711$	−9.52442	+	4.00288i	−0.357194	+	0.150120i
$712$		0			0
$713$	7.27838	−	4.20217i	0.272577	−	0.157373i
$714$		0			0
$715$	−9.05999	−	5.23079i	−0.338824	−	0.195620i
$716$		0			0
$717$	−18.8105	+	9.33676i	−0.702492	+	0.348688i
$718$		0			0
$719$	−9.82946	+	17.0251i	−0.366577	+	0.634930i	−0.989028	−	0.147729i	$-0.952804\pi$
$719$	−9.82946	+	17.0251i	−0.366577	+	0.634930i	0.622451	+	0.782659i	$0.286137\pi$
$720$		0			0
$721$	8.19746	−	2.93450i	0.305289	−	0.109286i
$722$		0			0
$723$	7.24671	−	3.59697i	0.269508	−	0.133773i
$724$		0			0
$725$	−24.0164			−0.891948
$726$		0			0
$727$	−17.8591	−	30.9329i	−0.662358	−	1.14724i	−0.979994	−	0.199026i	$-0.936222\pi$
$727$	−17.8591	−	30.9329i	−0.662358	−	1.14724i	0.317636	−	0.948213i	$-0.397111\pi$
$728$		0			0
$729$	25.1018	+	9.94489i	0.929695	+	0.368329i
$730$		0			0
$731$	21.4420	−	37.1386i	0.793060	−	1.37362i
$732$		0			0
$733$	−30.7034	+	17.7266i	−1.13406	+	0.654749i	−0.944952	−	0.327208i	$-0.893892\pi$
$733$	−30.7034	+	17.7266i	−1.13406	+	0.654749i	−0.189106	+	0.981957i	$0.560559\pi$
$734$		0			0
$735$	2.16491	−	4.81496i	0.0798540	−	0.177602i
$736$		0			0
$737$	−2.25794	+	3.91086i	−0.0831722	+	0.144058i
$738$		0			0
$739$	−18.6506	+	10.7679i	−0.686072	+	0.396104i	−0.802139	−	0.597137i	$-0.796305\pi$
$739$	−18.6506	+	10.7679i	−0.686072	+	0.396104i	0.116067	+	0.993241i	$0.462971\pi$
$740$		0			0
$741$	4.02407	−	63.9233i	0.147828	−	2.34828i
$742$		0			0
$743$	17.1882	+	9.92361i	0.630574	+	0.364062i	0.780974	−	0.624563i	$-0.214723\pi$
$743$	17.1882	+	9.92361i	0.630574	+	0.364062i	−0.150400	+	0.988625i	$0.548056\pi$
$744$		0			0
$745$	3.99321	+	2.30548i	0.146300	+	0.0844662i
$746$		0			0
$747$	13.3767	−	17.6204i	0.489427	−	0.644698i
$748$		0			0
$749$	−19.9743	+	23.5496i	−0.729843	+	0.860485i
$750$		0			0
$751$	29.5789	−	17.0774i	1.07935	−	0.623163i	0.148628	−	0.988893i	$-0.452514\pi$
$751$	29.5789	−	17.0774i	1.07935	−	0.623163i	0.930721	+	0.365731i	$0.119181\pi$
$752$		0			0
$753$	−10.0554	+	15.1334i	−0.366438	+	0.551490i
$754$		0			0
$755$	−3.64534			−0.132667
$756$		0			0
$757$	−20.3294			−0.738885			−0.369442	−	0.929254i	$-0.620451\pi$
$757$	−20.3294			−0.738885			−0.369442	+	0.929254i	$0.620451\pi$
$758$		0			0
$759$	−14.6028	+	21.9772i	−0.530048	+	0.797723i
$760$		0			0
$761$	31.8688	−	18.3995i	1.15524	−	0.666980i	0.205084	−	0.978744i	$-0.434253\pi$
$761$	31.8688	−	18.3995i	1.15524	−	0.666980i	0.950160	+	0.311764i	$0.100920\pi$
$762$		0			0
$763$	45.6113	−	16.3278i	1.65124	−	0.591105i
$764$		0			0
$765$	7.36469	+	0.930925i	0.266271	+	0.0336577i
$766$		0			0
$767$	53.5288	+	30.9049i	1.93281	+	1.11591i
$768$		0			0
$769$	−34.6942	−	20.0307i	−1.25111	−	0.722326i	−0.279777	−	0.960065i	$-0.590260\pi$
$769$	−34.6942	−	20.0307i	−1.25111	−	0.722326i	−0.971329	+	0.237739i	$0.923594\pi$
$770$		0			0
$771$	−0.557439	+	8.85505i	−0.0200757	+	0.318907i
$772$		0			0
$773$	−27.0859	+	15.6381i	−0.974213	+	0.562462i	−0.900518	−	0.434818i	$-0.856813\pi$
$773$	−27.0859	+	15.6381i	−0.974213	+	0.562462i	−0.0736952	+	0.997281i	$0.523479\pi$
$774$		0			0
$775$	6.39629	−	11.0787i	0.229762	−	0.397959i
$776$		0			0
$777$	9.37832	−	2.70586i	0.336445	−	0.0970723i
$778$		0			0
$779$	0.836396	−	0.482893i	0.0299670	−	0.0173015i
$780$		0			0
$781$	15.1202	−	26.1889i	0.541042	−	0.937113i
$782$		0			0
$783$	8.52887	+	24.5003i	0.304797	+	0.875568i
$784$		0			0
$785$	−3.49522	−	6.05390i	−0.124750	−	0.216073i
$786$		0			0
$787$	−40.7659			−1.45315			−0.726574	−	0.687088i	$-0.758888\pi$
$787$	−40.7659			−1.45315			−0.726574	+	0.687088i	$0.758888\pi$
$788$		0			0
$789$	−29.6248	+	14.7045i	−1.05467	+	0.523494i
$790$		0			0
$791$	8.91033	+	7.55753i	0.316815	+	0.268715i
$792$		0			0
$793$	−22.0367	+	38.1687i	−0.782546	+	1.35541i
$794$		0			0
$795$	7.57957	−	3.76218i	0.268820	−	0.133431i
$796$		0			0
$797$	−10.6301	−	6.13732i	−0.376539	−	0.217395i	0.299772	−	0.954011i	$-0.403089\pi$
$797$	−10.6301	−	6.13732i	−0.376539	−	0.217395i	−0.676311	+	0.736616i	$0.736423\pi$
$798$		0			0
$799$	42.2590	−	24.3982i	1.49502	−	0.863148i
$800$		0			0
$801$	−5.76037	+	45.5712i	−0.203533	+	1.61018i
$802$		0			0
$803$	−62.5405			−2.20700
$804$		0			0
$805$	2.77653	+	2.35499i	0.0978597	+	0.0830023i
$806$		0			0
$807$	−0.757042	+	12.0258i	−0.0266492	+	0.423328i
$808$		0			0
$809$	−14.5729	−	25.2410i	−0.512356	−	0.887427i	−0.999897	−	0.0143273i	$-0.995439\pi$
$809$	−14.5729	−	25.2410i	−0.512356	−	0.887427i	0.487541	−	0.873100i	$-0.337894\pi$
$810$		0			0
$811$	19.9170			0.699379			0.349690	−	0.936866i	$-0.386287\pi$
$811$	19.9170			0.699379			0.349690	+	0.936866i	$0.386287\pi$
$812$		0			0
$813$	2.15641	+	4.34447i	0.0756287	+	0.152367i
$814$		0			0
$815$	3.29535			0.115431
$816$		0			0
$817$		−	55.9889i		−	1.95880i
$818$		0			0
$819$	−37.7277	−	11.9013i	−1.31831	−	0.415866i
$820$		0			0
$821$	26.6617			0.930501			0.465250	−	0.885179i	$-0.345964\pi$
$821$	26.6617			0.930501			0.465250	+	0.885179i	$0.345964\pi$
$822$		0			0
$823$		−	31.7868i		−	1.10802i	−0.832511	−	0.554008i	$-0.813098\pi$
$823$		−	31.7868i		−	1.10802i	0.832511	−	0.554008i	$-0.186902\pi$
$824$		0			0
$825$	−2.52337	+	40.0844i	−0.0878525	+	1.39556i
$826$		0			0
$827$		−	43.7367i		−	1.52087i	−0.649413	−	0.760436i	$-0.724985\pi$
$827$		−	43.7367i		−	1.52087i	0.649413	−	0.760436i	$-0.275015\pi$
$828$		0			0
$829$	−6.03642	+	3.48513i	−0.209653	+	0.121043i	−0.601150	−	0.799136i	$-0.705291\pi$
$829$	−6.03642	+	3.48513i	−0.209653	+	0.121043i	0.391497	+	0.920179i	$0.371957\pi$
$830$		0			0
$831$	−11.0129	−	22.1874i	−0.382033	−	0.769672i
$832$		0			0
$833$	39.2461	−	6.49176i	1.35980	−	0.224926i
$834$		0			0
$835$		−	1.51678i		−	0.0524903i
$836$		0			0
$837$	−13.5734	−	2.59081i	−0.469165	−	0.0895515i
$838$		0			0
$839$	26.6379	+	46.1382i	0.919643	+	1.59287i	0.799958	+	0.600056i	$0.204855\pi$
$839$	26.6379	+	46.1382i	0.919643	+	1.59287i	0.119685	+	0.992812i	$0.461811\pi$
$840$		0			0
$841$	2.03696	−	3.52812i	0.0702400	−	0.121659i
$842$		0			0
$843$	32.4416	+	2.04225i	1.11735	+	0.0703388i
$844$		0			0
$845$	4.46537	+	2.57808i	0.153613	+	0.0886887i
$846$		0			0
$847$	30.4823	−	10.9120i	1.04739	−	0.374940i
$848$		0			0
$849$	−18.6653	+	28.0913i	−0.640592	+	0.964092i
$850$		0			0
$851$			6.73141i			0.230750i
$852$		0			0
$853$	−47.1872	+	27.2435i	−1.61566	+	0.932801i	−0.627632	+	0.778510i	$0.715976\pi$
$853$	−47.1872	+	27.2435i	−1.61566	+	0.932801i	−0.988025	+	0.154291i	$0.950691\pi$
$854$		0			0
$855$	8.93477	−	3.75506i	0.305563	−	0.128420i
$856$		0			0
$857$	23.1315	+	13.3550i	0.790157	+	0.456197i	0.840018	−	0.542559i	$-0.182545\pi$
$857$	23.1315	+	13.3550i	0.790157	+	0.456197i	−0.0498611	+	0.998756i	$0.515878\pi$
$858$		0			0
$859$	24.7463	+	42.8619i	0.844333	+	1.46243i	0.886199	+	0.463304i	$0.153336\pi$
$859$	24.7463	+	42.8619i	0.844333	+	1.46243i	−0.0418663	+	0.999123i	$0.513330\pi$
$860$		0			0
$861$	−0.165364	−	0.573139i	−0.00563559	−	0.0195325i
$862$		0			0
$863$	−20.7843	−	11.9998i	−0.707506	−	0.408479i	0.102631	−	0.994719i	$-0.467274\pi$
$863$	−20.7843	−	11.9998i	−0.707506	−	0.408479i	−0.810137	+	0.586241i	$0.800607\pi$
$864$		0			0
$865$	1.68192	+	2.91317i	0.0571870	+	0.0990509i
$866$		0			0
$867$	11.7774	+	23.7276i	0.399982	+	0.805833i
$868$		0			0
$869$	−8.30041	+	14.3767i	−0.281572	+	0.487697i
$870$		0			0
$871$	2.33459	−	4.04362i	0.0791044	−	0.137013i
$872$		0			0
$873$	−7.83275	−	5.94629i	−0.265098	−	0.201251i
$874$		0			0
$875$	11.1196	+	2.02154i	0.375912	+	0.0683407i
$876$		0			0
$877$	−3.24286	−	5.61681i	−0.109504	−	0.189666i	0.806066	−	0.591826i	$-0.201593\pi$
$877$	−3.24286	−	5.61681i	−0.109504	−	0.189666i	−0.915569	+	0.402160i	$0.868260\pi$
$878$		0			0
$879$	15.7289	−	7.80719i	0.530524	−	0.263330i
$880$		0			0
$881$		−	4.29737i		−	0.144782i	−0.997376	−	0.0723910i	$-0.976937\pi$
$881$		−	4.29737i		−	0.144782i	0.997376	−	0.0723910i	$-0.0230630\pi$
$882$		0			0
$883$		−	17.8931i		−	0.602150i	−0.953600	−	0.301075i	$-0.902654\pi$
$883$		−	17.8931i		−	0.602150i	0.953600	−	0.301075i	$-0.0973455\pi$
$884$		0			0
$885$	−0.587610	+	9.33434i	−0.0197523	+	0.313770i
$886$		0			0
$887$	−3.21055	−	5.56083i	−0.107800	−	0.186715i	0.807079	−	0.590444i	$-0.201047\pi$
$887$	−3.21055	−	5.56083i	−0.107800	−	0.186715i	−0.914879	+	0.403729i	$0.867714\pi$
$888$		0			0
$889$	6.89841	+	1.25413i	0.231365	+	0.0420622i
$890$		0			0
$891$	41.7880	−	11.6608i	1.39995	−	0.390652i
$892$		0			0
$893$	31.8541	−	55.1729i	1.06596	−	1.84629i
$894$		0			0
$895$	4.62494	−	8.01064i	0.154595	−	0.267766i
$896$		0			0
$897$	15.0985	−	22.7233i	0.504125	−	0.758708i
$898$		0			0
$899$	−6.63856	−	11.4983i	−0.221408	−	0.383491i
$900$		0			0
$901$	55.2184	+	31.8803i	1.83959	+	1.06209i
$902$		0			0
$903$	−33.5680	−	8.31093i	−1.11707	−	0.276570i
$904$		0			0
$905$	1.22383	+	2.11973i	0.0406815	+	0.0704624i
$906$		0			0
$907$	−10.3177	−	5.95693i	−0.342594	−	0.197797i	0.318825	−	0.947814i	$-0.396712\pi$
$907$	−10.3177	−	5.95693i	−0.342594	−	0.197797i	−0.661419	+	0.750017i	$0.730045\pi$
$908$		0			0
$909$	−6.34135	+	50.1673i	−0.210329	+	1.66394i
$910$		0			0
$911$	38.6598	−	22.3203i	1.28086	−	0.739504i	0.303853	−	0.952719i	$-0.401727\pi$
$911$	38.6598	−	22.3203i	1.28086	−	0.739504i	0.977005	+	0.213215i	$0.0683936\pi$
$912$		0			0
$913$		−	35.5475i		−	1.17645i
$914$		0			0
$915$	−6.65584	−	0.418995i	−0.220035	−	0.0138516i
$916$		0			0
$917$	−2.15092	+	0.769980i	−0.0710297	+	0.0254270i
$918$		0			0
$919$	28.4378	+	16.4185i	0.938075	+	0.541598i	0.889356	−	0.457215i	$-0.151153\pi$
$919$	28.4378	+	16.4185i	0.938075	+	0.541598i	0.0487187	+	0.998813i	$0.484486\pi$
$920$		0			0
$921$	−9.08765	+	13.6769i	−0.299448	+	0.450670i
$922$		0			0
$923$	−15.6334	+	27.0779i	−0.514581	+	0.891281i
$924$		0			0
$925$	5.12307	+	8.87342i	0.168446	+	0.291756i
$926$		0			0
$927$	5.96958	−	7.86343i	0.196067	−	0.258269i
$928$		0			0
$929$			15.0284i			0.493065i	0.969135	+	0.246533i	$0.0792912\pi$
$929$			15.0284i			0.493065i	−0.969135	+	0.246533i	$0.920709\pi$
$930$		0			0
$931$	40.1368	−	32.9598i	1.31543	−	1.08021i
$932$		0			0
$933$	0.901319	−	1.35649i	0.0295079	−	0.0444094i
$934$		0			0
$935$	10.3299	−	5.96399i	0.337825	−	0.195043i
$936$		0			0
$937$		−	14.0428i		−	0.458758i	−0.973337	−	0.229379i	$-0.926330\pi$
$937$		−	14.0428i		−	0.458758i	0.973337	−	0.229379i	$-0.0736695\pi$
$938$		0			0
$939$	19.4144	+	12.9000i	0.633566	+	0.420974i
$940$		0			0
$941$			34.5182i			1.12526i	0.826708	+	0.562631i	$0.190211\pi$
$941$			34.5182i			1.12526i	−0.826708	+	0.562631i	$0.809789\pi$
$942$		0			0
$943$	0.411378			0.0133963
$944$		0			0
$945$	−0.925070	−	5.91422i	−0.0300925	−	0.192389i
$946$		0			0
$947$		−	7.52673i		−	0.244586i	−0.992494	−	0.122293i	$-0.960975\pi$
$947$		−	7.52673i		−	0.244586i	0.992494	−	0.122293i	$-0.0390247\pi$
$948$		0			0
$949$	64.6635			2.09907
$950$		0			0
$951$	4.20642	−	6.33067i	0.136403	−	0.205286i
$952$		0			0
$953$	44.3406			1.43633			0.718166	−	0.695871i	$-0.244982\pi$
$953$	44.3406			1.43633			0.718166	+	0.695871i	$0.244982\pi$
$954$		0			0
$955$	−2.73585	−	4.73863i	−0.0885299	−	0.153338i
$956$		0			0
$957$	34.7195	+	23.0694i	1.12232	+	0.745727i
$958$		0			0
$959$	13.8483	+	11.7458i	0.447186	+	0.379292i
$960$		0			0
$961$	−23.9278			−0.771865
$962$		0			0
$963$	−4.39100	+	34.7379i	−0.141498	+	1.11941i
$964$		0			0
$965$	−7.94407	+	4.58651i	−0.255729	+	0.147645i
$966$		0			0
$967$	−42.3694	−	24.4620i	−1.36251	−	0.786644i	−0.372551	−	0.928012i	$-0.621517\pi$
$967$	−42.3694	−	24.4620i	−1.36251	−	0.786644i	−0.989957	+	0.141367i	$0.954850\pi$
$968$		0			0
$969$	60.8249	+	40.4152i	1.95398	+	1.29832i
$970$		0			0
$971$	2.57411	−	4.45849i	0.0826072	−	0.143080i	−0.821762	−	0.569831i	$-0.807009\pi$
$971$	2.57411	−	4.45849i	0.0826072	−	0.143080i	0.904369	+	0.426751i	$0.140342\pi$
$972$		0			0
$973$	−17.2056	−	14.5934i	−0.551587	−	0.467843i
$974$		0			0
$975$	2.60903	−	41.4451i	0.0835559	−	1.32731i
$976$		0			0
$977$	37.2686			1.19233			0.596165	−	0.802862i	$-0.296691\pi$
$977$	37.2686			1.19233			0.596165	+	0.802862i	$0.296691\pi$
$978$		0			0
$979$	36.9040	+	63.9195i	1.17946	+	2.04288i
$980$		0			0
$981$	33.2152	−	43.7528i	1.06048	−	1.39692i
$982$		0			0
$983$	4.79373	−	8.30299i	0.152896	−	0.264824i	−0.779395	−	0.626533i	$-0.784473\pi$
$983$	4.79373	−	8.30299i	0.152896	−	0.264824i	0.932291	+	0.361709i	$0.117807\pi$
$984$		0			0
$985$	−7.98377	+	4.60943i	−0.254384	+	0.146869i
$986$		0			0
$987$	−28.3504	−	27.2879i	−0.902404	−	0.868582i
$988$		0			0
$989$	11.9243	−	20.6534i	0.379169	−	0.656741i
$990$		0			0
$991$	9.50543	−	5.48797i	0.301950	−	0.174331i	−0.341369	−	0.939930i	$-0.610890\pi$
$991$	9.50543	−	5.48797i	0.301950	−	0.174331i	0.643319	+	0.765599i	$0.277557\pi$
$992$		0			0
$993$	−6.09431	−	4.04937i	−0.193397	−	0.128503i
$994$		0			0
$995$	−4.42734	−	2.55613i	−0.140356	−	0.0810346i
$996$		0			0
$997$	19.0817	+	11.0168i	0.604325	+	0.348907i	0.770741	−	0.637149i	$-0.219886\pi$
$997$	19.0817	+	11.0168i	0.604325	+	0.348907i	−0.166416	+	0.986056i	$0.553220\pi$
$998$		0			0
$999$	7.23284	−	8.37747i	0.228837	−	0.265051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.i.607.5	yes	32
3.2	odd	2		3024.2.cz.i.1279.7		32
4.3	odd	2	inner	1008.2.cz.i.607.12	yes	32
7.3	odd	6		1008.2.bf.i.31.1	✓	32
9.2	odd	6		3024.2.bf.i.2287.7		32
9.7	even	3		1008.2.bf.i.943.16	yes	32
12.11	even	2		3024.2.cz.i.1279.8		32
21.17	even	6		3024.2.bf.i.1711.9		32
28.3	even	6		1008.2.bf.i.31.16	yes	32
36.7	odd	6		1008.2.bf.i.943.1	yes	32
36.11	even	6		3024.2.bf.i.2287.8		32
63.38	even	6		3024.2.cz.i.2719.8		32
63.52	odd	6	inner	1008.2.cz.i.367.12	yes	32
84.59	odd	6		3024.2.bf.i.1711.10		32
252.115	even	6	inner	1008.2.cz.i.367.5	yes	32
252.227	odd	6		3024.2.cz.i.2719.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.1	✓	32	7.3	odd	6
1008.2.bf.i.31.16	yes	32	28.3	even	6
1008.2.bf.i.943.1	yes	32	36.7	odd	6
1008.2.bf.i.943.16	yes	32	9.7	even	3
1008.2.cz.i.367.5	yes	32	252.115	even	6	inner
1008.2.cz.i.367.12	yes	32	63.52	odd	6	inner
1008.2.cz.i.607.5	yes	32	1.1	even	1	trivial
1008.2.cz.i.607.12	yes	32	4.3	odd	2	inner
3024.2.bf.i.1711.9		32	21.17	even	6
3024.2.bf.i.1711.10		32	84.59	odd	6
3024.2.bf.i.2287.7		32	9.2	odd	6
3024.2.bf.i.2287.8		32	36.11	even	6
3024.2.cz.i.1279.7		32	3.2	odd	2
3024.2.cz.i.1279.8		32	12.11	even	2
3024.2.cz.i.2719.7		32	252.227	odd	6
3024.2.cz.i.2719.8		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)

\(f(q)\)	\(=\)	\(q+(-0.958555 + 1.44263i) q^{3} +(0.377090 - 0.217713i) q^{5} +(0.473240 - 2.60308i) q^{7} +(-1.16234 - 2.76567i) q^{9} +O(q^{10})\)	\(q+(-0.958555 + 1.44263i) q^{3} +(0.377090 - 0.217713i) q^{5} +(0.473240 - 2.60308i) q^{7} +(-1.16234 - 2.76567i) q^{9} +(-4.17467 - 2.41025i) q^{11} +(4.31639 + 2.49207i) q^{13} +(-0.0473830 + 0.752691i) q^{15} +(-4.92142 + 2.84139i) q^{17} +(-3.70969 + 6.42537i) q^{19} +(3.30165 + 3.17791i) q^{21} +(-2.73689 + 1.58014i) q^{23} +(-2.40520 + 4.16593i) q^{25} +(5.10401 + 0.974224i) q^{27} +(2.49630 + 4.32372i) q^{29} -2.65936 q^{31} +(7.47875 - 3.71214i) q^{33} +(-0.388272 - 1.08463i) q^{35} +(1.06500 - 1.84463i) q^{37} +(-7.73262 + 3.83815i) q^{39} +(-0.112731 - 0.0650855i) q^{41} +(-6.53530 + 3.77315i) q^{43} +(-1.04043 - 0.789852i) q^{45} -8.58674 q^{47} +(-6.55209 - 2.46377i) q^{49} +(0.618398 - 9.82340i) q^{51} +(-5.61000 - 9.71680i) q^{53} -2.09897 q^{55} +(-5.71347 - 11.5108i) q^{57} +12.4013 q^{59} +8.84273i q^{61} +(-7.74935 + 1.71685i) q^{63} +2.17023 q^{65} -0.936806i q^{67} +(0.343902 - 5.46297i) q^{69} +6.27328i q^{71} +(11.2357 - 6.48693i) q^{73} +(-3.70437 - 7.46308i) q^{75} +(-8.24970 + 9.72640i) q^{77} -3.44380i q^{79} +(-6.29791 + 6.42933i) q^{81} +(3.68712 + 6.38628i) q^{83} +(-1.23721 + 2.14292i) q^{85} +(-8.63036 - 0.543294i) q^{87} +(-13.2599 - 7.65563i) q^{89} +(8.52975 - 10.0566i) q^{91} +(2.54914 - 3.83646i) q^{93} +3.23059i q^{95} +(2.83887 - 1.63902i) q^{97} +(-1.81356 + 14.3473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9}+O(q^{10}) \) 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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