LMFDB - Embedded newform 1008.2.bf.i.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	1008.31
Dual form			1008.2.bf.i.943.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72863 - 0.108820i) q^{3} -0.435427i q^{5} +(2.49096 + 0.891704i) q^{7} +(2.97632 + 0.376218i) q^{9} +4.82050i q^{11} +(-4.31639 - 2.49207i) q^{13} +(-0.0473830 + 0.752691i) q^{15} +(-4.92142 - 2.84139i) q^{17} +(3.70969 + 6.42537i) q^{19} +(-4.20890 - 1.81249i) q^{21} -3.16029i q^{23} +4.81040 q^{25} +(-5.10401 - 0.974224i) q^{27} +(2.49630 + 4.32372i) q^{29} +(-1.32968 - 2.30307i) q^{31} +(0.524566 - 8.33285i) q^{33} +(0.388272 - 1.08463i) q^{35} +(1.06500 + 1.84463i) q^{37} +(7.19025 + 4.77757i) q^{39} +(0.112731 + 0.0650855i) q^{41} +(-6.53530 + 3.77315i) q^{43} +(0.163815 - 1.29597i) q^{45} +(-4.29337 + 7.43633i) q^{47} +(5.40973 + 4.44239i) q^{49} +(8.19812 + 5.44725i) q^{51} +(-5.61000 + 9.71680i) q^{53} +2.09897 q^{55} +(-5.71347 - 11.5108i) q^{57} +(6.20064 + 10.7398i) q^{59} +(7.65803 + 4.42137i) q^{61} +(7.07840 + 3.59114i) q^{63} +(-1.08511 + 1.87947i) q^{65} +(-0.811298 + 0.468403i) q^{67} +(-0.343902 + 5.46297i) q^{69} +6.27328i q^{71} +(11.2357 + 6.48693i) q^{73} +(-8.31540 - 0.523467i) q^{75} +(-4.29846 + 12.0077i) q^{77} +(2.98242 + 1.72190i) q^{79} +(8.71692 + 2.23949i) q^{81} +(-3.68712 - 6.38628i) q^{83} +(-1.23721 + 2.14292i) q^{85} +(-3.84467 - 7.74576i) q^{87} +(-13.2599 + 7.65563i) q^{89} +(-8.52975 - 10.0566i) q^{91} +(2.04790 + 4.12585i) q^{93} +(2.79778 - 1.61530i) q^{95} +(-2.83887 + 1.63902i) q^{97} +(-1.81356 + 14.3473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) $ 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72863	−	0.108820i	−0.998024	−	0.0628271i
$3$	−1.72863	−	0.108820i	−0.998024	−	0.0628271i
$4$		0			0
$5$		−	0.435427i		−	0.194729i	−0.995249	−	0.0973643i	$-0.968959\pi$
$5$		−	0.435427i		−	0.194729i	0.995249	−	0.0973643i	$-0.0310412\pi$
$6$		0			0
$7$	2.49096	+	0.891704i	0.941493	+	0.337032i
$7$	2.49096	+	0.891704i	0.941493	+	0.337032i
$8$		0			0
$9$	2.97632	+	0.376218i	0.992106	+	0.125406i
$10$		0			0
$11$			4.82050i			1.45344i	0.686936	+	0.726718i	$0.258955\pi$
$11$			4.82050i			1.45344i	−0.686936	+	0.726718i	$0.741045\pi$
$12$		0			0
$13$	−4.31639	−	2.49207i	−1.19715	−	0.691176i	−0.237232	−	0.971453i	$-0.576240\pi$
$13$	−4.31639	−	2.49207i	−1.19715	−	0.691176i	−0.959919	+	0.280277i	$0.909574\pi$
$14$		0			0
$15$	−0.0473830	+	0.752691i	−0.0122342	+	0.194344i
$16$		0			0
$17$	−4.92142	−	2.84139i	−1.19362	−	0.689137i	−0.234495	−	0.972117i	$-0.575344\pi$
$17$	−4.92142	−	2.84139i	−1.19362	−	0.689137i	−0.959126	+	0.282980i	$0.908677\pi$
$18$		0			0
$19$	3.70969	+	6.42537i	0.851061	+	1.47408i	0.880252	+	0.474506i	$0.157373\pi$
$19$	3.70969	+	6.42537i	0.851061	+	1.47408i	−0.0291916	+	0.999574i	$0.509293\pi$
$20$		0			0
$21$	−4.20890	−	1.81249i	−0.918458	−	0.395518i
$22$		0			0
$23$		−	3.16029i		−	0.658966i	−0.944162	−	0.329483i	$-0.893126\pi$
$23$		−	3.16029i		−	0.658966i	0.944162	−	0.329483i	$-0.106874\pi$
$24$		0			0
$25$	4.81040			0.962081
$26$		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
$31$	−1.32968	−	2.30307i	−0.238817	−	0.413644i	0.721558	−	0.692354i	$-0.243426\pi$
$31$	−1.32968	−	2.30307i	−0.238817	−	0.413644i	−0.960375	+	0.278710i	$0.910093\pi$
$32$		0			0
$33$	0.524566	−	8.33285i	0.0913151	−	1.45056i
$34$		0			0
$35$	0.388272	−	1.08463i	0.0656299	−	0.183336i
$36$		0			0
$37$	1.06500	+	1.84463i	0.175085	+	0.303256i	0.940191	−	0.340649i	$-0.110647\pi$
$37$	1.06500	+	1.84463i	0.175085	+	0.303256i	−0.765106	+	0.643904i	$0.777313\pi$
$38$		0			0
$39$	7.19025	+	4.77757i	1.15136	+	0.765024i
$40$		0			0
$41$	0.112731	+	0.0650855i	0.0176057	+	0.0101646i	0.508777	−	0.860898i	$-0.330098\pi$
$41$	0.112731	+	0.0650855i	0.0176057	+	0.0101646i	−0.491171	+	0.871063i	$0.663431\pi$
$42$		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
$45$	0.163815	−	1.29597i	0.0244201	−	0.193191i
$46$		0			0
$47$	−4.29337	+	7.43633i	−0.626252	+	1.08470i	0.362045	+	0.932161i	$0.382079\pi$
$47$	−4.29337	+	7.43633i	−0.626252	+	1.08470i	−0.988297	+	0.152540i	$0.951255\pi$
$48$		0			0
$49$	5.40973	+	4.44239i	0.772818	+	0.634627i
$50$		0			0
$51$	8.19812	+	5.44725i	1.14797	+	0.762768i
$52$		0			0
$53$	−5.61000	+	9.71680i	−0.770593	+	1.33471i	0.166646	+	0.986017i	$0.446706\pi$
$53$	−5.61000	+	9.71680i	−0.770593	+	1.33471i	−0.937239	+	0.348689i	$0.886627\pi$
$54$		0			0
$55$	2.09897			0.283025
$56$		0			0
$57$	−5.71347	−	11.5108i	−0.756767	−	1.52464i
$58$		0			0
$59$	6.20064	+	10.7398i	0.807255	+	1.39821i	0.914758	+	0.404002i	$0.132381\pi$
$59$	6.20064	+	10.7398i	0.807255	+	1.39821i	−0.107503	+	0.994205i	$0.534286\pi$
$60$		0			0
$61$	7.65803	+	4.42137i	0.980510	+	0.566098i	0.902424	−	0.430849i	$-0.141786\pi$
$61$	7.65803	+	4.42137i	0.980510	+	0.566098i	0.0780862	+	0.996947i	$0.475119\pi$
$62$		0			0
$63$	7.07840	+	3.59114i	0.891795	+	0.452441i
$64$		0			0
$65$	−1.08511	+	1.87947i	−0.134592	+	0.233120i
$66$		0			0
$67$	−0.811298	+	0.468403i	−0.0991158	+	0.0572246i	−0.548739	−	0.835994i	$-0.684892\pi$
$67$	−0.811298	+	0.468403i	−0.0991158	+	0.0572246i	0.449623	+	0.893219i	$0.351558\pi$
$68$		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	0.982926	−	0.184002i	$-0.0589054\pi$
$73$	11.2357	+	6.48693i	1.31504	+	0.759238i	0.332112	+	0.943240i	$0.392239\pi$
$74$		0			0
$75$	−8.31540	−	0.523467i	−0.960180	−	0.0604448i
$76$		0			0
$77$	−4.29846	+	12.0077i	−0.489855	+	1.36840i
$78$		0			0
$79$	2.98242	+	1.72190i	0.335548	+	0.193729i	0.658302	−	0.752754i	$-0.271275\pi$
$79$	2.98242	+	1.72190i	0.335548	+	0.193729i	−0.322754	+	0.946483i	$0.604608\pi$
$80$		0			0
$81$	8.71692	+	2.23949i	0.968547	+	0.248832i
$82$		0			0
$83$	−3.68712	−	6.38628i	−0.404714	−	0.700985i	0.589574	−	0.807714i	$-0.299296\pi$
$83$	−3.68712	−	6.38628i	−0.404714	−	0.700985i	−0.994288	+	0.106729i	$0.965962\pi$
$84$		0			0
$85$	−1.23721	+	2.14292i	−0.134195	+	0.232432i
$86$		0			0
$87$	−3.84467	−	7.74576i	−0.412192	−	0.830432i
$88$		0			0
$89$	−13.2599	+	7.65563i	−1.40555	+	0.811495i	−0.994955	−	0.100322i	$-0.968013\pi$
$89$	−13.2599	+	7.65563i	−1.40555	+	0.811495i	−0.410596	+	0.911817i	$0.634679\pi$
$90$		0			0
$91$	−8.52975	−	10.0566i	−0.894161	−	1.05422i
$92$		0			0
$93$	2.04790	+	4.12585i	0.212358	+	0.427831i
$94$		0			0
$95$	2.79778	−	1.61530i	0.287046	−	0.165726i
$96$		0			0
$97$	−2.83887	+	1.63902i	−0.288244	+	0.166418i	−0.637150	−	0.770740i	$-0.719887\pi$
$97$	−2.83887	+	1.63902i	−0.288244	+	0.166418i	0.348906	+	0.937158i	$0.386553\pi$
$98$		0			0
$99$	−1.81356	+	14.3473i	−0.182269	+	1.44196i
$100$		0			0
$101$		−	16.8555i		−	1.67719i	−0.544759	−	0.838593i	$-0.683379\pi$
$101$		−	16.8555i		−	1.67719i	0.544759	−	0.838593i	$-0.316621\pi$
$102$		0			0
$103$	3.29089			0.324261			0.162130	−	0.986769i	$-0.448163\pi$
$103$	3.29089			0.324261			0.162130	+	0.986769i	$0.448163\pi$
$104$		0			0
$105$	−0.789206	+	1.83267i	−0.0770187	+	0.178850i
$106$		0			0
$107$	10.1078	−	5.83572i	0.977154	−	0.564160i	0.0757442	−	0.997127i	$-0.475867\pi$
$107$	10.1078	−	5.83572i	0.977154	−	0.564160i	0.901410	+	0.432967i	$0.142533\pi$
$108$		0			0
$109$	9.15538	−	15.8576i	0.876926	−	1.51888i	0.0222293	−	0.999753i	$-0.492924\pi$
$109$	9.15538	−	15.8576i	0.876926	−	1.51888i	0.854697	−	0.519128i	$-0.173743\pi$
$110$		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
$115$	−1.37607			−0.128320
$116$		0			0
$117$	−11.9094	−	9.04109i	−1.10102	−	0.835849i
$118$		0			0
$119$	−9.72538	−	11.4662i	−0.891524	−	1.05111i
$120$		0			0
$121$	−12.2372			−1.11247
$122$		0			0
$123$	−0.187788	−	0.124776i	−0.0169323	−	0.0112507i
$124$		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
$129$	11.7077	−	5.81122i	1.03081	−	0.511649i
$130$		0			0
$131$	−0.863493			−0.0754437			−0.0377219	−	0.999288i	$-0.512010\pi$
$131$	−0.863493			−0.0754437			−0.0377219	+	0.999288i	$0.512010\pi$
$132$		0			0
$133$	3.51115	+	19.3132i	0.304455	+	1.67467i
$134$		0			0
$135$	−0.424203	+	2.22242i	−0.0365096	+	0.191275i
$136$		0			0
$137$	6.86336			0.586377			0.293188	−	0.956055i	$-0.405284\pi$
$137$	6.86336			0.586377			0.293188	+	0.956055i	$0.405284\pi$
$138$		0			0
$139$	−4.26364	+	7.38484i	−0.361637	+	0.626374i	−0.988230	−	0.152972i	$-0.951115\pi$
$139$	−4.26364	+	7.38484i	−0.361637	+	0.626374i	0.626593	+	0.779346i	$0.284449\pi$
$140$		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
$147$	−8.86799	−	8.26793i	−0.731420	−	0.681927i
$148$		0			0
$149$	−10.5895			−0.867527			−0.433764	−	0.901027i	$-0.642815\pi$
$149$	−10.5895			−0.867527			−0.433764	+	0.901027i	$0.642815\pi$
$150$		0			0
$151$			8.37187i			0.681293i	0.940191	+	0.340647i	$0.110646\pi$
$151$			8.37187i			0.681293i	−0.940191	+	0.340647i	$0.889354\pi$
$152$		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
$157$	13.9034	−	8.02712i	1.10961	−	0.640634i	0.170882	−	0.985292i	$-0.445338\pi$
$157$	13.9034	−	8.02712i	1.10961	−	0.640634i	0.938728	+	0.344658i	$0.112005\pi$
$158$		0			0
$159$	10.7550	−	16.1863i	0.852926	−	1.28365i
$160$		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	$-0.762449\pi$
$163$	−6.55417	+	3.78405i	−0.513362	+	0.296390i	0.220852	+	0.975307i	$0.429116\pi$
$164$		0			0
$165$	−3.62835	−	0.228410i	−0.282466	−	0.0177817i
$166$		0			0
$167$	−1.74172	+	3.01674i	−0.134778	+	0.233443i	−0.925513	−	0.378717i	$-0.876365\pi$
$167$	−1.74172	+	3.01674i	−0.134778	+	0.233443i	0.790735	+	0.612159i	$0.209699\pi$
$168$		0			0
$169$	5.92082	+	10.2552i	0.455447	+	0.788858i
$170$		0			0
$171$	8.62386	+	20.5196i	0.659483	+	1.56917i
$172$		0			0
$173$	6.69039	+	3.86270i	0.508661	+	0.293676i	0.732283	−	0.681000i	$-0.238455\pi$
$173$	6.69039	+	3.86270i	0.508661	+	0.293676i	−0.223622	+	0.974676i	$0.571788\pi$
$174$		0			0
$175$	11.9825	+	4.28946i	0.905792	+	0.324252i
$176$		0			0
$177$	−9.54991	−	19.2399i	−0.717815	−	1.44616i
$178$		0			0
$179$	−18.3972	−	10.6216i	−1.37507	−	0.793899i	−0.383511	−	0.923536i	$-0.625285\pi$
$179$	−18.3972	−	10.6216i	−1.37507	−	0.793899i	−0.991561	+	0.129637i	$0.958619\pi$
$180$		0			0
$181$		−	5.62129i		−	0.417827i	−0.977934	−	0.208914i	$-0.933007\pi$
$181$		−	5.62129i		−	0.417827i	0.977934	−	0.208914i	$-0.0669927\pi$
$182$		0			0
$183$	−12.7568	−	8.47625i	−0.943007	−	0.626582i
$184$		0			0
$185$	0.803202	−	0.463729i	0.0590525	−	0.0340940i
$186$		0			0
$187$	13.6969	−	23.7237i	1.00162	−	1.73485i
$188$		0			0
$189$	−11.8451	−	6.97801i	−0.861607	−	0.507576i
$190$		0			0
$191$	10.8827	+	6.28314i	0.787446	+	0.454632i	0.839063	−	0.544035i	$-0.183104\pi$
$191$	10.8827	+	6.28314i	0.787446	+	0.454632i	−0.0516165	+	0.998667i	$0.516437\pi$
$192$		0			0
$193$	10.5334	+	18.2443i	0.758209	+	1.31326i	0.943763	+	0.330622i	$0.107259\pi$
$193$	10.5334	+	18.2443i	0.758209	+	1.31326i	−0.185554	+	0.982634i	$0.559408\pi$
$194$		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	$-0.696716\pi$
$199$	5.87039	−	10.1678i	0.416141	−	0.720778i	0.995548	+	0.0942612i	$0.0300489\pi$
$200$		0			0
$201$	1.45341	−	0.721410i	0.102515	−	0.0508843i
$202$		0			0
$203$	2.36270	+	12.9962i	0.165829	+	0.912152i
$204$		0			0
$205$	0.0283399	−	0.0490862i	0.00197935	−	0.00342833i
$206$		0			0
$207$	1.18896	−	9.40602i	0.0826383	−	0.653764i
$208$		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
$213$	0.682657	−	10.8442i	0.0467749	−	0.743031i
$214$		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
$219$	−18.7164	−	12.4362i	−1.26474	−	0.840358i
$220$		0			0
$221$	14.1619	+	24.5291i	0.952630	+	1.65000i
$222$		0			0
$223$	−6.74216	−	11.6778i	−0.451488	−	0.782001i	0.546990	−	0.837139i	$-0.315773\pi$
$223$	−6.74216	−	11.6778i	−0.451488	−	0.782001i	−0.998479	+	0.0551381i	$0.982440\pi$
$224$		0			0
$225$	14.3173	+	1.80976i	0.954486	+	0.120651i
$226$		0			0
$227$	−24.0716			−1.59769			−0.798845	−	0.601537i	$-0.794555\pi$
$227$	−24.0716			−1.59769			−0.798845	+	0.601537i	$0.794555\pi$
$228$		0			0
$229$		−	14.0833i		−	0.930651i	−0.885140	−	0.465326i	$-0.845937\pi$
$229$		−	14.0833i		−	0.930651i	0.885140	−	0.465326i	$-0.154063\pi$
$230$		0			0
$231$	8.73711	−	20.2890i	0.574859	−	1.33492i
$232$		0			0
$233$	1.10903	+	1.92090i	0.0726551	+	0.125842i	0.900064	−	0.435757i	$-0.143519\pi$
$233$	1.10903	+	1.92090i	0.0726551	+	0.125842i	−0.827409	+	0.561600i	$0.810186\pi$
$234$		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
$241$		−	4.67094i		−	0.300881i	−0.988619	−	0.150441i	$-0.951931\pi$
$241$		−	4.67094i		−	0.300881i	0.988619	−	0.150441i	$-0.0480693\pi$
$242$		0			0
$243$	−14.8246	−	4.81982i	−0.951000	−	0.309191i
$244$		0			0
$245$	1.93433	−	2.35554i	0.123580	−	0.150490i
$246$		0			0
$247$		−	36.9792i		−	2.35293i
$248$		0			0
$249$	5.67871	+	11.4407i	0.359874	+	0.725028i
$250$		0			0
$251$	−10.4901			−0.662132			−0.331066	−	0.943608i	$-0.607408\pi$
$251$	−10.4901			−0.662132			−0.331066	+	0.943608i	$0.607408\pi$
$252$		0			0
$253$	15.2342			0.957764
$254$		0			0
$255$	2.37188	−	3.56968i	0.148533	−	0.223542i
$256$		0			0
$257$		−	5.12259i		−	0.319538i	−0.987154	−	0.159769i	$-0.948925\pi$
$257$		−	5.12259i		−	0.319538i	0.987154	−	0.159769i	$-0.0510750\pi$
$258$		0			0
$259$	1.00800	+	5.54456i	0.0626341	+	0.344522i
$260$		0			0
$261$	5.80312	+	13.8079i	0.359204	+	0.854688i
$262$		0			0
$263$		−	19.0949i		−	1.17744i	−0.808336	−	0.588722i	$-0.799631\pi$
$263$		−	19.0949i		−	1.17744i	0.808336	−	0.588722i	$-0.200369\pi$
$264$		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	0.672295	−	0.740283i	$-0.265309\pi$
$269$	6.02481	+	3.47842i	0.367339	+	0.212083i	−0.304956	+	0.952366i	$0.598642\pi$
$270$		0			0
$271$	−1.40013	−	2.42510i	−0.0850521	−	0.147315i	0.820361	−	0.571846i	$-0.193772\pi$
$271$	−1.40013	−	2.42510i	−0.0850521	−	0.147315i	−0.905413	+	0.424531i	$0.860439\pi$
$272$		0			0
$273$	13.6504	+	18.3123i	0.826161	+	1.10831i
$274$		0			0
$275$			23.1885i			1.39832i
$276$		0			0
$277$	14.3011			0.859270			0.429635	−	0.903003i	$-0.358642\pi$
$277$	14.3011			0.859270			0.429635	+	0.903003i	$0.358642\pi$
$278$		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
$283$	9.73617	+	16.8635i	0.578755	+	1.00243i	0.995622	+	0.0934662i	$0.0297947\pi$
$283$	9.73617	+	16.8635i	0.578755	+	1.00243i	−0.416867	+	0.908967i	$0.636872\pi$
$284$		0			0
$285$	−5.01209	+	2.48779i	−0.296891	+	0.147364i
$286$		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
$291$	5.08571	−	2.52434i	0.298130	−	0.147979i
$292$		0			0
$293$	8.77997	+	5.06912i	0.512932	+	0.296141i	0.734038	−	0.679109i	$-0.237633\pi$
$293$	8.77997	+	5.06912i	0.512932	+	0.296141i	−0.221106	+	0.975250i	$0.570967\pi$
$294$		0			0
$295$	4.67641	−	2.69992i	0.272271	−	0.157196i
$296$		0			0
$297$	4.69624	−	24.6039i	0.272504	−	1.42766i
$298$		0			0
$299$	−7.87566	+	13.6410i	−0.455461	+	0.788882i
$300$		0			0
$301$	−19.6437	+	3.57122i	−1.13224	+	0.205841i
$302$		0			0
$303$	−1.83421	+	29.1369i	−0.105373	+	1.67387i
$304$		0			0
$305$	1.92518	−	3.33451i	0.110236	−	0.190933i
$306$		0			0
$307$	−9.48057			−0.541085			−0.270542	−	0.962708i	$-0.587203\pi$
$307$	−9.48057			−0.541085			−0.270542	+	0.962708i	$0.587203\pi$
$308$		0			0
$309$	−5.68872	−	0.358114i	−0.323620	−	0.0203724i
$310$		0			0
$311$	−0.470145	−	0.814314i	−0.0266595	−	0.0461755i	0.852388	−	0.522910i	$-0.175154\pi$
$311$	−0.470145	−	0.814314i	−0.0266595	−	0.0461755i	−0.879047	+	0.476735i	$0.841820\pi$
$312$		0			0
$313$	−11.6547	−	6.72885i	−0.658763	−	0.380337i	0.133042	−	0.991110i	$-0.457525\pi$
$313$	−11.6547	−	6.72885i	−0.658763	−	0.380337i	−0.791806	+	0.610773i	$0.790859\pi$
$314$		0			0
$315$	1.56368	−	3.08212i	0.0881031	−	0.173658i
$316$		0			0
$317$	2.19415	−	3.80037i	0.123236	−	0.213450i	−0.797806	−	0.602914i	$-0.794006\pi$
$317$	2.19415	−	3.80037i	0.123236	−	0.213450i	0.921042	+	0.389464i	$0.127340\pi$
$318$		0			0
$319$	−20.8425	+	12.0334i	−1.16696	+	0.673742i
$320$		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
$327$	−17.5519	+	26.4156i	−0.970621	+	1.46079i
$328$		0			0
$329$	−17.3256	+	14.6952i	−0.955191	+	0.810171i
$330$		0			0
$331$	−3.65849	−	2.11223i	−0.201089	−	0.116099i	0.396075	−	0.918218i	$-0.370372\pi$
$331$	−3.65849	−	2.11223i	−0.201089	−	0.116099i	−0.597163	+	0.802120i	$0.703706\pi$
$332$		0			0
$333$	2.47579	+	5.89088i	0.135672	+	0.322818i
$334$		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
$339$	4.23302	−	6.37070i	0.229906	−	0.346009i
$340$		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
$345$	2.37872	+	0.149744i	0.128066	+	0.00806195i
$346$		0			0
$347$	23.3138	−	13.4602i	1.25155	−	0.722583i	0.280133	−	0.959961i	$-0.409621\pi$
$347$	23.3138	−	13.4602i	1.25155	−	0.722583i	0.971417	+	0.237378i	$0.0762881\pi$
$348$		0			0
$349$	−8.15394	+	4.70768i	−0.436470	+	0.251996i	−0.702099	−	0.712079i	$-0.747754\pi$
$349$	−8.15394	+	4.70768i	−0.436470	+	0.251996i	0.265629	+	0.964075i	$0.414420\pi$
$350$		0			0
$351$	19.6031	+	16.9247i	1.04633	+	0.903372i
$352$		0			0
$353$			7.76281i			0.413173i	0.978428	+	0.206586i	$0.0662354\pi$
$353$			7.76281i			0.413173i	−0.978428	+	0.206586i	$0.933765\pi$
$354$		0			0
$355$	2.73155			0.144976
$356$		0			0
$357$	15.5638	+	20.8792i	0.823725	+	1.10504i
$358$		0			0
$359$	17.8936	−	10.3309i	0.944387	−	0.545242i	0.0530541	−	0.998592i	$-0.483104\pi$
$359$	17.8936	−	10.3309i	0.944387	−	0.545242i	0.891333	+	0.453350i	$0.149771\pi$
$360$		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
$367$	−17.1596			−0.895725			−0.447862	−	0.894102i	$-0.647815\pi$
$367$	−17.1596			−0.895725			−0.447862	+	0.894102i	$0.647815\pi$
$368$		0			0
$369$	0.311038	+	0.236127i	0.0161920	+	0.0122923i
$370$		0			0
$371$	−22.6388	+	19.2017i	−1.17535	+	0.996901i
$372$		0			0
$373$	−1.68029			−0.0870022			−0.0435011	−	0.999053i	$-0.513851\pi$
$373$	−1.68029			−0.0870022			−0.0435011	+	0.999053i	$0.513851\pi$
$374$		0			0
$375$	−0.464847	+	7.38420i	−0.0240046	+	0.381319i
$376$		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
$381$	0.288382	−	4.58103i	0.0147743	−	0.234693i
$382$		0			0
$383$	16.9832			0.867802			0.433901	−	0.900961i	$-0.357137\pi$
$383$	16.9832			0.867802			0.433901	+	0.900961i	$0.357137\pi$
$384$		0			0
$385$	5.22845	+	1.87166i	0.266467	+	0.0953887i
$386$		0			0
$387$	−20.8706	+	8.77141i	−1.06091	+	0.445876i
$388$		0			0
$389$	38.9596			1.97533			0.987666	−	0.156575i	$-0.0500452\pi$
$389$	38.9596			1.97533			0.987666	+	0.156575i	$0.0500452\pi$
$390$		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	−0.261248	−	0.965272i	$-0.584134\pi$
$397$	8.84820	−	5.10851i	0.444078	−	0.256389i	0.705326	+	0.708883i	$0.250801\pi$
$398$		0			0
$399$	−3.96780	−	33.7675i	−0.198639	−	1.69049i
$400$		0			0
$401$	−3.73966			−0.186750			−0.0933750	−	0.995631i	$-0.529766\pi$
$401$	−3.73966			−0.186750			−0.0933750	+	0.995631i	$0.529766\pi$
$402$		0			0
$403$			13.2546i			0.660259i
$404$		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
$409$	1.47660	−	0.852515i	0.0730131	−	0.0421541i	−0.463049	−	0.886333i	$-0.653245\pi$
$409$	1.47660	−	0.852515i	0.0730131	−	0.0421541i	0.536062	+	0.844179i	$0.319911\pi$
$410$		0			0
$411$	−11.8642	−	0.746870i	−0.585218	−	0.0368404i
$412$		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
$417$	8.17387	−	12.3017i	0.400276	−	0.602416i
$418$		0			0
$419$	8.00198	−	13.8598i	0.390922	−	0.677097i	−0.601649	−	0.798761i	$-0.705489\pi$
$419$	8.00198	−	13.8598i	0.390922	−	0.677097i	0.992571	+	0.121663i	$0.0388228\pi$
$420$		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
$423$	−15.5761	+	20.5176i	−0.757336	+	0.997602i
$424$		0			0
$425$	−23.6740	−	13.6682i	−1.14836	−	0.663006i
$426$		0			0
$427$	15.1333	+	17.8421i	0.732350	+	0.863441i
$428$		0			0
$429$	−23.0303	+	34.6606i	−1.11191	+	1.67343i
$430$		0			0
$431$	−4.78381	−	2.76193i	−0.230428	−	0.133038i	0.380342	−	0.924846i	$-0.375806\pi$
$431$	−4.78381	−	2.76193i	−0.230428	−	0.133038i	−0.610769	+	0.791809i	$0.709140\pi$
$432$		0			0
$433$			7.56302i			0.363456i	0.983349	+	0.181728i	$0.0581690\pi$
$433$			7.56302i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$434$		0			0
$435$	−3.37271	+	1.67407i	−0.161709	+	0.0802656i
$436$		0			0
$437$	20.3060	−	11.7237i	0.971369	−	0.560820i
$438$		0			0
$439$	9.50453	−	16.4623i	0.453627	−	0.785704i	−0.544981	−	0.838448i	$-0.683463\pi$
$439$	9.50453	−	16.4623i	0.453627	−	0.785704i	0.998608	+	0.0527438i	$0.0167967\pi$
$440$		0			0
$441$	14.4298	+	15.2572i	0.687131	+	0.726533i
$442$		0			0
$443$	2.50830	+	1.44817i	0.119173	+	0.0688046i	0.558402	−	0.829571i	$-0.311415\pi$
$443$	2.50830	+	1.44817i	0.119173	+	0.0688046i	−0.439229	+	0.898375i	$0.644748\pi$
$444$		0			0
$445$	3.33346	+	5.77373i	0.158021	+	0.273701i
$446$		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
$453$	0.911025	−	14.4719i	0.0428037	−	0.679947i
$454$		0			0
$455$	−4.37890	+	3.71408i	−0.205286	+	0.174119i
$456$		0			0
$457$	4.51412	−	7.81868i	0.211162	−	0.365743i	−0.740917	−	0.671597i	$-0.765609\pi$
$457$	4.51412	−	7.81868i	0.211162	−	0.365743i	0.952078	+	0.305854i	$0.0989420\pi$
$458$		0			0
$459$	22.3508	+	19.2970i	1.04325	+	0.900708i
$460$		0			0
$461$	1.19412	−	0.689428i	0.0556159	−	0.0321099i	−0.471934	−	0.881634i	$-0.656444\pi$
$461$	1.19412	−	0.689428i	0.0556159	−	0.0321099i	0.527550	+	0.849524i	$0.323111\pi$
$462$		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
$465$	1.79651	−	0.891711i	0.0833110	−	0.0413521i
$466$		0			0
$467$	8.37470	+	14.5054i	0.387535	+	0.671230i	0.992117	−	0.125312i	$-0.0399933\pi$
$467$	8.37470	+	14.5054i	0.387535	+	0.671230i	−0.604582	+	0.796543i	$0.706660\pi$
$468$		0			0
$469$	−2.43859	+	0.443334i	−0.112603	+	0.0204713i
$470$		0			0
$471$	−24.9073	+	12.3629i	−1.14767	+	0.569655i
$472$		0			0
$473$	−18.1885	−	31.5034i	−0.836308	−	1.44853i
$474$		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
$479$	−4.68011			−0.213840			−0.106920	−	0.994268i	$-0.534099\pi$
$479$	−4.68011			−0.213840			−0.106920	+	0.994268i	$0.534099\pi$
$480$		0			0
$481$		−	10.6162i		−	0.484057i
$482$		0			0
$483$	−5.72799	+	13.3014i	−0.260633	+	0.605233i
$484$		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	$-0.461394\pi$
$487$	−14.9661	−	8.64071i	−0.678181	−	0.391548i	−0.799169	+	0.601106i	$0.794727\pi$
$488$		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
$493$		−	28.3718i		−	1.27780i
$494$		0			0
$495$	6.24721	+	0.789672i	0.280791	+	0.0354931i
$496$		0			0
$497$	−5.59391	+	15.6265i	−0.250921	+	0.700943i
$498$		0			0
$499$		−	31.6591i		−	1.41725i	−0.705583	−	0.708627i	$-0.749315\pi$
$499$		−	31.6591i		−	1.41725i	0.705583	−	0.708627i	$-0.250685\pi$
$500$		0			0
$501$	3.33906	−	5.02529i	0.149178	−	0.224514i
$502$		0			0
$503$	27.7607			1.23779			0.618894	−	0.785474i	$-0.287581\pi$
$503$	27.7607			1.23779			0.618894	+	0.785474i	$0.287581\pi$
$504$		0			0
$505$	−7.33933			−0.326596
$506$		0			0
$507$	−9.11893	−	18.3717i	−0.404986	−	0.815914i
$508$		0			0
$509$		−	24.5474i		−	1.08805i	−0.839070	−	0.544023i	$-0.816900\pi$
$509$		−	24.5474i		−	1.08805i	0.839070	−	0.544023i	$-0.183100\pi$
$510$		0			0
$511$	22.2032	+	26.1776i	0.982211	+	1.15803i
$512$		0			0
$513$	−12.6745	−	36.4092i	−0.559594	−	1.60750i
$514$		0			0
$515$		−	1.43294i		−	0.0631429i
$516$		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	0.719506	−	0.694486i	$-0.244368\pi$
$521$	10.9064	+	6.29680i	0.477817	+	0.275868i	−0.241689	+	0.970354i	$0.577701\pi$
$522$		0			0
$523$	11.2363	+	19.4619i	0.491330	+	0.851009i	0.999950	−	0.00998216i	$-0.00317747\pi$
$523$	11.2363	+	19.4619i	0.491330	+	0.851009i	−0.508620	+	0.860991i	$0.669844\pi$
$524$		0			0
$525$	−20.2465	−	8.71881i	−0.883631	−	0.380520i
$526$		0			0
$527$			15.1125i			0.658312i
$528$		0			0
$529$	13.0126			0.565764
$530$		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
$535$	−2.54103	−	4.40119i	−0.109858	−	0.190280i
$536$		0			0
$537$	30.6461	+	20.3629i	1.32248	+	0.878722i
$538$		0			0
$539$	−21.4145	+	26.0776i	−0.922389	+	1.12324i
$540$		0			0
$541$	−7.43945	−	12.8855i	−0.319847	−	0.553991i	0.660609	−	0.750730i	$-0.270298\pi$
$541$	−7.43945	−	12.8855i	−0.319847	−	0.553991i	−0.980456	+	0.196739i	$0.936965\pi$
$542$		0			0
$543$	−0.611708	+	9.71712i	−0.0262509	+	0.417002i
$544$		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
$549$	21.1293	+	16.0405i	0.901778	+	0.684591i
$550$		0			0
$551$	−18.5210	+	32.0793i	−0.789021	+	1.36662i
$552$		0			0
$553$	5.89365	+	6.94861i	0.250623	+	0.295485i
$554$		0			0
$555$	−1.43890	+	0.714211i	−0.0610779	+	0.0303165i
$556$		0			0
$557$	9.44755	−	16.3636i	0.400305	−	0.693349i	−0.593457	−	0.804866i	$-0.702237\pi$
$557$	9.44755	−	16.3636i	0.400305	−	0.693349i	0.993763	+	0.111516i	$0.0355707\pi$
$558$		0			0
$559$	37.6118			1.59081
$560$		0			0
$561$	−26.2585	+	39.5190i	−1.10863	+	1.66849i
$562$		0			0
$563$	9.61497	+	16.6536i	0.405223	+	0.701866i	0.994347	−	0.106176i	$-0.0338607\pi$
$563$	9.61497	+	16.6536i	0.405223	+	0.701866i	−0.589125	+	0.808042i	$0.700527\pi$
$564$		0			0
$565$	1.66525	+	0.961432i	0.0700575	+	0.0404477i
$566$		0			0
$567$	19.7165	+	13.3514i	0.828016	+	0.560705i
$568$		0			0
$569$	3.33650	−	5.77899i	0.139874	−	0.242268i	−0.787575	−	0.616219i	$-0.788664\pi$
$569$	3.33650	−	5.77899i	0.139874	−	0.242268i	0.927449	+	0.373951i	$0.121997\pi$
$570$		0			0
$571$	−11.3391	+	6.54665i	−0.474528	+	0.273969i	−0.718133	−	0.695906i	$-0.755003\pi$
$571$	−11.3391	+	6.54665i	−0.474528	+	0.273969i	0.243605	+	0.969874i	$0.421670\pi$
$572$		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	0.333401	−	0.942785i	$-0.391804\pi$
$577$	−7.59957	−	4.38761i	−0.316374	−	0.182659i	−0.649775	+	0.760126i	$0.725137\pi$
$578$		0			0
$579$	−16.2230	−	32.6839i	−0.674203	−	1.35830i
$580$		0			0
$581$	−3.48979	−	19.1958i	−0.144781	−	0.796375i
$582$		0			0
$583$	−46.8398	−	27.0430i	−1.93991	−	1.12001i
$584$		0			0
$585$	−3.93673	+	5.18566i	−0.162764	+	0.214401i
$586$		0			0
$587$	−1.22575	−	2.12306i	−0.0505920	−	0.0876279i	0.839620	−	0.543174i	$-0.182777\pi$
$587$	−1.22575	−	2.12306i	−0.0505920	−	0.0876279i	−0.890212	+	0.455546i	$0.849444\pi$
$588$		0			0
$589$	9.86539	−	17.0874i	0.406496	−	0.704072i
$590$		0			0
$591$	36.5986	+	2.30394i	1.50546	+	0.0947712i
$592$		0			0
$593$	−7.67653	+	4.43205i	−0.315237	+	0.182002i	−0.649268	−	0.760560i	$-0.724925\pi$
$593$	−7.67653	+	4.43205i	−0.315237	+	0.182002i	0.334030	+	0.942562i	$0.391591\pi$
$594$		0			0
$595$	−4.99270	+	4.23469i	−0.204681	+	0.173605i
$596$		0			0
$597$	−11.2542	+	16.9376i	−0.460603	+	0.693209i
$598$		0			0
$599$	−41.8781	+	24.1783i	−1.71109	+	0.987899i	−0.777998	+	0.628267i	$0.783764\pi$
$599$	−41.8781	+	24.1783i	−1.71109	+	0.987899i	−0.933094	+	0.359632i	$0.882902\pi$
$600$		0			0
$601$	−31.4198	+	18.1402i	−1.28164	+	0.739955i	−0.977148	−	0.212560i	$-0.931820\pi$
$601$	−31.4198	+	18.1402i	−1.28164	+	0.739955i	−0.304492	+	0.952515i	$0.598487\pi$
$602$		0			0
$603$	−2.59090	+	1.08889i	−0.105510	+	0.0443431i
$604$		0			0
$605$			5.32840i			0.216630i
$606$		0			0
$607$	32.9894			1.33900			0.669499	−	0.742813i	$-0.266509\pi$
$607$	32.9894			1.33900			0.669499	+	0.742813i	$0.266509\pi$
$608$		0			0
$609$	−2.66999	−	22.7227i	−0.108194	−	0.920768i
$610$		0			0
$611$	37.0637	−	21.3987i	1.49944	−	0.865701i
$612$		0			0
$613$	−4.91100	+	8.50611i	−0.198354	+	0.343558i	−0.947995	−	0.318286i	$-0.896893\pi$
$613$	−4.91100	+	8.50611i	−0.198354	+	0.343558i	0.749641	+	0.661844i	$0.230226\pi$
$614$		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
$619$	−15.1718			−0.609805			−0.304902	−	0.952384i	$-0.598624\pi$
$619$	−15.1718			−0.609805			−0.304902	+	0.952384i	$0.598624\pi$
$620$		0			0
$621$	−3.07883	+	16.1301i	−0.123549	+	0.647280i
$622$		0			0
$623$	−39.8565	+	7.24590i	−1.59682	+	0.290301i
$624$		0			0
$625$	22.1920			0.887680
$626$		0			0
$627$	55.4876	−	27.5418i	2.21596	−	1.09991i
$628$		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
$633$	13.0534	+	8.67335i	0.518826	+	0.344735i
$634$		0			0
$635$	1.15392			0.0457919
$636$		0			0
$637$	−12.2798	−	32.6565i	−0.486542	−	1.29390i
$638$		0			0
$639$	−2.36012	+	18.6713i	−0.0933650	+	0.738624i
$640$		0			0
$641$	7.91338			0.312560			0.156280	−	0.987713i	$-0.450050\pi$
$641$	7.91338			0.312560			0.156280	+	0.987713i	$0.450050\pi$
$642$		0			0
$643$	8.71529	−	15.0953i	0.343697	−	0.595301i	−0.641419	−	0.767191i	$-0.721654\pi$
$643$	8.71529	−	15.0953i	0.343697	−	0.595301i	0.985116	+	0.171890i	$0.0549872\pi$
$644$		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	$-0.838302\pi$
$647$	−0.396991	+	0.687609i	−0.0156073	+	0.0270327i	0.858116	+	0.513455i	$0.171635\pi$
$648$		0			0
$649$	−51.7713	+	29.8902i	−2.03220	+	1.17329i
$650$		0			0
$651$	1.42220	+	12.1034i	0.0557403	+	0.474371i
$652$		0			0
$653$	12.3455			0.483117			0.241559	−	0.970386i	$-0.422341\pi$
$653$	12.3455			0.483117			0.241559	+	0.970386i	$0.422341\pi$
$654$		0			0
$655$			0.375988i			0.0146911i
$656$		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
$661$	−4.63535	+	2.67622i	−0.180294	+	0.104093i	−0.587431	−	0.809274i	$-0.699861\pi$
$661$	−4.63535	+	2.67622i	−0.180294	+	0.104093i	0.407137	+	0.913367i	$0.366527\pi$
$662$		0			0
$663$	−21.8114	−	43.9427i	−0.847083	−	1.70659i
$664$		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
$669$	10.3839	+	20.9202i	0.401466	+	0.808822i
$670$		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
$675$	−24.5523	−	4.68641i	−0.945020	−	0.180380i
$676$		0			0
$677$	31.5452	+	18.2126i	1.21238	+	0.699967i	0.963277	−	0.268510i	$-0.0865312\pi$
$677$	31.5452	+	18.2126i	1.21238	+	0.699967i	0.249102	+	0.968477i	$0.419865\pi$
$678$		0			0
$679$	−8.53303	+	1.55130i	−0.327468	+	0.0595335i
$680$		0			0
$681$	41.6109	+	2.61947i	1.59453	+	0.100378i
$682$		0			0
$683$	−14.6439	−	8.45468i	−0.560334	−	0.323509i	0.192945	−	0.981210i	$-0.438196\pi$
$683$	−14.6439	−	8.45468i	−0.560334	−	0.323509i	−0.753280	+	0.657700i	$0.771529\pi$
$684$		0			0
$685$		−	2.98849i		−	0.114184i
$686$		0			0
$687$	−1.53254	+	24.3448i	−0.0584701	+	0.928813i
$688$		0			0
$689$	48.4299	−	27.9610i	1.84503	−	1.06523i
$690$		0			0
$691$	8.43736	−	14.6139i	0.320972	−	0.555940i	−0.659717	−	0.751514i	$-0.729324\pi$
$691$	8.43736	−	14.6139i	0.320972	−	0.555940i	0.980689	+	0.195574i	$0.0626571\pi$
$692$		0			0
$693$	−17.3111	+	34.1214i	−0.657593	+	1.29617i
$694$		0			0
$695$	3.21556	+	1.85650i	0.121973	+	0.0704211i
$696$		0			0
$697$	−0.369866	−	0.640626i	−0.0140097	−	0.0242655i
$698$		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
$705$	−5.39383	−	3.58394i	−0.203143	−	0.134979i
$706$		0			0
$707$	15.0301	−	41.9863i	0.565266	−	1.57906i
$708$		0			0
$709$	−21.3529	+	36.9843i	−0.801925	+	1.38898i	0.116422	+	0.993200i	$0.462858\pi$
$709$	−21.3529	+	36.9843i	−0.801925	+	1.38898i	−0.918347	+	0.395776i	$0.870476\pi$
$710$		0			0
$711$	8.22881	+	6.24695i	0.308604	+	0.234279i
$712$		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
$717$	−17.4911	−	11.6220i	−0.653218	−	0.434032i
$718$		0			0
$719$	9.82946	+	17.0251i	0.366577	+	0.634930i	0.989028	−	0.147729i	$-0.0471963\pi$
$719$	9.82946	+	17.0251i	0.366577	+	0.634930i	−0.622451	+	0.782659i	$0.713863\pi$
$720$		0			0
$721$	8.19746	+	2.93450i	0.305289	+	0.109286i
$722$		0			0
$723$	−0.508290	+	8.07432i	−0.0189035	+	0.300287i
$724$		0			0
$725$	12.0082	+	20.7988i	0.445974	+	0.772450i
$726$		0			0
$727$	17.8591	+	30.9329i	0.662358	+	1.14724i	0.979994	+	0.199026i	$0.0637777\pi$
$727$	17.8591	+	30.9329i	0.662358	+	1.14724i	−0.317636	+	0.948213i	$0.602889\pi$
$728$		0			0
$729$	25.1018	+	9.94489i	0.929695	+	0.368329i
$730$		0			0
$731$	42.8840			1.58612
$732$		0			0
$733$			35.4533i			1.30950i	0.755847	+	0.654749i	$0.227225\pi$
$733$			35.4533i			1.30950i	−0.755847	+	0.654749i	$0.772775\pi$
$734$		0			0
$735$	−3.60008	+	3.86136i	−0.132791	+	0.142428i
$736$		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	$-0.203695\pi$
$739$	18.6506	+	10.7679i	0.686072	+	0.396104i	−0.116067	+	0.993241i	$0.537029\pi$
$740$		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
$745$			4.61096i			0.168932i
$746$		0			0
$747$	−8.57140	−	20.3948i	−0.313611	−	0.746205i
$748$		0			0
$749$	30.3817	−	5.52339i	1.11012	−	0.201820i
$750$		0			0
$751$			34.1548i			1.24633i	0.782092	+	0.623163i	$0.214153\pi$
$751$			34.1548i			1.24633i	−0.782092	+	0.623163i	$0.785847\pi$
$752$		0			0
$753$	18.1336	+	1.14153i	0.660824	+	0.0415998i
$754$		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
$759$	−26.3342	−	1.65778i	−0.955872	−	0.0601736i
$760$		0			0
$761$		−	36.7989i		−	1.33396i	−0.745075	−	0.666980i	$-0.767587\pi$
$761$		−	36.7989i		−	1.33396i	0.745075	−	0.666980i	$-0.232413\pi$
$762$		0			0
$763$	36.9459	−	31.3367i	1.33753	−	1.13446i
$764$		0			0
$765$	−4.48855	+	5.91254i	−0.162284	+	0.213768i
$766$		0			0
$767$		−	61.8097i		−	2.23182i
$768$		0			0
$769$	34.6942	+	20.0307i	1.25111	+	0.722326i	0.971329	−	0.237739i	$-0.0764063\pi$
$769$	34.6942	+	20.0307i	1.25111	+	0.722326i	0.279777	+	0.960065i	$0.409740\pi$
$770$		0			0
$771$	−0.557439	+	8.85505i	−0.0200757	+	0.318907i
$772$		0			0
$773$	−27.0859	−	15.6381i	−0.974213	−	0.562462i	−0.0736952	−	0.997281i	$-0.523479\pi$
$773$	−27.0859	−	15.6381i	−0.974213	−	0.562462i	−0.900518	+	0.434818i	$0.856813\pi$
$774$		0			0
$775$	−6.39629	−	11.0787i	−0.229762	−	0.397959i
$776$		0			0
$777$	−1.13910	−	9.69418i	−0.0408650	−	0.347777i
$778$		0			0
$779$			0.965787i			0.0346029i
$780$		0			0
$781$	−30.2403			−1.08208
$782$		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
$787$	−20.3830	−	35.3043i	−0.726574	−	1.25846i	−0.958323	−	0.285687i	$-0.907778\pi$
$787$	−20.3830	−	35.3043i	−0.726574	−	1.25846i	0.231749	−	0.972776i	$-0.425555\pi$
$788$		0			0
$789$	−2.07791	+	33.0080i	−0.0739754	+	1.17512i
$790$		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
$795$	−7.04793	−	4.68301i	−0.249964	−	0.166089i
$796$		0			0
$797$	10.6301	+	6.13732i	0.376539	+	0.217395i	0.676311	−	0.736616i	$-0.263577\pi$
$797$	10.6301	+	6.13732i	0.376539	+	0.217395i	−0.299772	+	0.954011i	$0.596911\pi$
$798$		0			0
$799$	42.2590	−	24.3982i	1.49502	−	0.863148i
$800$		0			0
$801$	−42.3460	+	17.7969i	−1.49622	+	0.628824i
$802$		0			0
$803$	−31.2702	+	54.1616i	−1.10350	+	1.91132i
$804$		0			0
$805$	−3.42774	−	1.22705i	−0.120812	−	0.0432478i
$806$		0			0
$807$	−10.0361	−	6.66852i	−0.353289	−	0.234743i
$808$		0			0
$809$	−14.5729	+	25.2410i	−0.512356	+	0.887427i	0.487541	+	0.873100i	$0.337894\pi$
$809$	−14.5729	+	25.2410i	−0.512356	+	0.887427i	−0.999897	+	0.0143273i	$0.995439\pi$
$810$		0			0
$811$	−19.9170			−0.699379			−0.349690	−	0.936866i	$-0.613713\pi$
$811$	−19.9170			−0.699379			−0.349690	+	0.936866i	$0.613713\pi$
$812$		0			0
$813$	2.15641	+	4.34447i	0.0756287	+	0.152367i
$814$		0			0
$815$	1.64768	+	2.85386i	0.0577156	+	0.0999664i
$816$		0			0
$817$	−48.4878	−	27.9944i	−1.69637	−	0.979402i
$818$		0			0
$819$	−21.6038	−	33.1406i	−0.754897	−	1.15803i
$820$		0			0
$821$	−13.3309	+	23.0897i	−0.465250	+	0.805837i	−0.999213	−	0.0396708i	$-0.987369\pi$
$821$	−13.3309	+	23.0897i	−0.465250	+	0.805837i	0.533962	+	0.845508i	$0.320702\pi$
$822$		0			0
$823$	−27.5281	+	15.8934i	−0.959570	+	0.554008i	−0.896041	−	0.443972i	$-0.853569\pi$
$823$	−27.5281	+	15.8934i	−0.959570	+	0.554008i	−0.0635296	+	0.997980i	$0.520236\pi$
$824$		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	0.391497	−	0.920179i	$-0.371957\pi$
$829$	−6.03642	−	3.48513i	−0.209653	−	0.121043i	−0.601150	+	0.799136i	$0.705291\pi$
$830$		0			0
$831$	−24.7213	−	1.55624i	−0.857572	−	0.0539855i
$832$		0			0
$833$	−14.0010	−	37.2340i	−0.485107	−	1.29008i
$834$		0			0
$835$	1.31357	+	0.758390i	0.0454580	+	0.0262452i
$836$		0			0
$837$	4.54299	+	13.0503i	0.157029	+	0.451084i
$838$		0			0
$839$	−26.6379	−	46.1382i	−0.919643	−	1.59287i	−0.799958	−	0.600056i	$-0.795145\pi$
$839$	−26.6379	−	46.1382i	−0.919643	−	1.59287i	−0.119685	−	0.992812i	$-0.538189\pi$
$840$		0			0
$841$	2.03696	−	3.52812i	0.0702400	−	0.121659i
$842$		0			0
$843$	14.4522	+	29.1164i	0.497759	+	1.00282i
$844$		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
$849$	−14.9951	−	30.2103i	−0.514632	−	1.03681i
$850$		0			0
$851$	5.82957	−	3.36570i	0.199835	−	0.115375i
$852$		0			0
$853$	47.1872	−	27.2435i	1.61566	−	0.932801i	0.627632	−	0.778510i	$-0.284024\pi$
$853$	47.1872	−	27.2435i	1.61566	−	0.932801i	0.988025	−	0.154291i	$-0.0493093\pi$
$854$		0			0
$855$	8.93477	−	3.75506i	0.305563	−	0.128420i
$856$		0			0
$857$			26.7099i			0.912394i	0.889879	+	0.456197i	$0.150789\pi$
$857$			26.7099i			0.912394i	−0.889879	+	0.456197i	$0.849211\pi$
$858$		0			0
$859$	49.4926			1.68867			0.844333	−	0.535819i	$-0.179997\pi$
$859$	49.4926			1.68867			0.844333	+	0.535819i	$0.179997\pi$
$860$		0			0
$861$	−0.356509	−	0.478263i	−0.0121498	−	0.0162992i
$862$		0			0
$863$	20.7843	−	11.9998i	0.707506	−	0.408479i	−0.102631	−	0.994719i	$-0.532726\pi$
$863$	20.7843	−	11.9998i	0.707506	−	0.408479i	0.810137	+	0.586241i	$0.199393\pi$
$864$		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
$871$	4.66917			0.158209
$872$		0			0
$873$	−9.06601	+	3.81022i	−0.306838	+	0.128956i
$874$		0			0
$875$	3.80910	−	10.6406i	0.128771	−	0.359719i
$876$		0			0
$877$	6.48573			0.219008			0.109504	−	0.993986i	$-0.465074\pi$
$877$	6.48573			0.219008			0.109504	+	0.993986i	$0.465074\pi$
$878$		0			0
$879$	−14.6257	−	9.71806i	−0.493313	−	0.327782i
$880$		0			0
$881$			4.29737i			0.144782i	0.997376	+	0.0723910i	$0.0230630\pi$
$881$			4.29737i			0.144782i	−0.997376	+	0.0723910i	$0.976937\pi$
$882$		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
$885$	−8.37758	+	4.15828i	−0.281609	+	0.139779i
$886$		0			0
$887$	−6.42110			−0.215599			−0.107800	−	0.994173i	$-0.534381\pi$
$887$	−6.42110			−0.215599			−0.107800	+	0.994173i	$0.534381\pi$
$888$		0			0
$889$	−2.36310	+	6.60127i	−0.0792558	+	0.221399i
$890$		0			0
$891$	−10.7954	+	42.0199i	−0.361661	+	1.40772i
$892$		0			0
$893$	−63.7082			−2.13191
$894$		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
$903$	34.3452	−	4.03569i	1.14294	−	0.134299i
$904$		0			0
$905$	−2.44766			−0.0813629
$906$		0			0
$907$			11.9139i			0.395593i	0.980243	+	0.197797i	$0.0633786\pi$
$907$			11.9139i			0.395593i	−0.980243	+	0.197797i	$0.936621\pi$
$908$		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
$913$	30.7851	−	17.7738i	1.01884	−	0.588226i
$914$		0			0
$915$	−3.69078	+	5.55463i	−0.122014	+	0.183631i
$916$		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	$-0.848847\pi$
$919$	−28.4378	+	16.4185i	−0.938075	+	0.541598i	−0.0487187	+	0.998813i	$0.515514\pi$
$920$		0			0
$921$	16.3884	+	1.03167i	0.540016	+	0.0339948i
$922$		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
$927$	9.79472	+	1.23809i	0.321701	+	0.0406643i
$928$		0			0
$929$	13.0150	+	7.51419i	0.427007	+	0.246533i	0.698071	−	0.716029i	$-0.254042\pi$
$929$	13.0150	+	7.51419i	0.427007	+	0.246533i	−0.271064	+	0.962561i	$0.587375\pi$
$930$		0			0
$931$	−8.47559	+	51.2394i	−0.277776	+	1.67930i
$932$		0			0
$933$	0.724092	+	1.45881i	0.0237057	+	0.0477593i
$934$		0			0
$935$	−10.3299	−	5.96399i	−0.337825	−	0.195043i
$936$		0			0
$937$			14.0428i			0.458758i	0.973337	+	0.229379i	$0.0736695\pi$
$937$			14.0428i			0.458758i	−0.973337	+	0.229379i	$0.926330\pi$
$938$		0			0
$939$	19.4144	+	12.9000i	0.633566	+	0.420974i
$940$		0			0
$941$	−29.8936	+	17.2591i	−0.974505	+	0.562631i	−0.900607	−	0.434635i	$-0.856877\pi$
$941$	−29.8936	+	17.2591i	−0.974505	+	0.562631i	−0.0738984	+	0.997266i	$0.523544\pi$
$942$		0			0
$943$	0.205689	−	0.356264i	0.00669815	−	0.0116015i
$944$		0			0
$945$	−3.03841	+	5.15769i	−0.0988395	+	0.167780i
$946$		0			0
$947$	6.51834	+	3.76336i	0.211817	+	0.122293i	0.602156	−	0.798379i	$-0.294309\pi$
$947$	6.51834	+	3.76336i	0.211817	+	0.122293i	−0.390338	+	0.920672i	$0.627642\pi$
$948$		0			0
$949$	−32.3317	−	56.0002i	−1.04953	−	1.81784i
$950$		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
$957$	37.3384	−	18.5332i	1.20698	−	0.599095i
$958$		0			0
$959$	17.0963	+	6.12009i	0.552070	+	0.197628i
$960$		0			0
$961$	11.9639	−	20.7221i	0.385932	−	0.668455i
$962$		0			0
$963$	32.2794	−	13.5662i	1.04019	−	0.437165i
$964$		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
$969$	−4.58813	+	72.8835i	−0.147392	+	2.34136i
$970$		0			0
$971$	−2.57411	−	4.45849i	−0.0826072	−	0.143080i	0.821762	−	0.569831i	$-0.192991\pi$
$971$	−2.57411	−	4.45849i	−0.0826072	−	0.143080i	−0.904369	+	0.426751i	$0.859658\pi$
$972$		0			0
$973$	−17.2056	+	14.5934i	−0.551587	+	0.467843i
$974$		0			0
$975$	34.5880	+	22.9820i	1.10770	+	0.736015i
$976$		0			0
$977$	−18.6343	−	32.2756i	−0.596165	−	1.03259i	−0.993381	−	0.114863i	$-0.963357\pi$
$977$	−18.6343	−	32.2756i	−0.596165	−	1.03259i	0.397217	−	0.917725i	$-0.369976\pi$
$978$		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
$983$	9.58746			0.305793			0.152896	−	0.988242i	$-0.451140\pi$
$983$	9.58746			0.305793			0.152896	+	0.988242i	$0.451140\pi$
$984$		0			0
$985$			9.21886i			0.293737i
$986$		0			0
$987$	31.5487	−	23.5171i	1.00421	−	0.748559i
$988$		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	$-0.389110\pi$
$991$	−9.50543	−	5.48797i	−0.301950	−	0.174331i	−0.643319	+	0.765599i	$0.722443\pi$
$992$		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
$997$			22.0337i			0.697814i	0.937157	+	0.348907i	$0.113447\pi$
$997$			22.0337i			0.697814i	−0.937157	+	0.348907i	$0.886553\pi$
$998$		0			0
$999$	−3.63868	−	10.4526i	−0.115123	−	0.330704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.bf.i.31.1	✓	32
3.2	odd	2		3024.2.bf.i.1711.9		32
4.3	odd	2	inner	1008.2.bf.i.31.16	yes	32
7.5	odd	6		1008.2.cz.i.607.5	yes	32
9.2	odd	6		3024.2.cz.i.2719.8		32
9.7	even	3		1008.2.cz.i.367.12	yes	32
12.11	even	2		3024.2.bf.i.1711.10		32
21.5	even	6		3024.2.cz.i.1279.7		32
28.19	even	6		1008.2.cz.i.607.12	yes	32
36.7	odd	6		1008.2.cz.i.367.5	yes	32
36.11	even	6		3024.2.cz.i.2719.7		32
63.47	even	6		3024.2.bf.i.2287.7		32
63.61	odd	6	inner	1008.2.bf.i.943.16	yes	32
84.47	odd	6		3024.2.cz.i.1279.8		32
252.47	odd	6		3024.2.bf.i.2287.8		32
252.187	even	6	inner	1008.2.bf.i.943.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.1	✓	32	1.1	even	1	trivial
1008.2.bf.i.31.16	yes	32	4.3	odd	2	inner
1008.2.bf.i.943.1	yes	32	252.187	even	6	inner
1008.2.bf.i.943.16	yes	32	63.61	odd	6	inner
1008.2.cz.i.367.5	yes	32	36.7	odd	6
1008.2.cz.i.367.12	yes	32	9.7	even	3
1008.2.cz.i.607.5	yes	32	7.5	odd	6
1008.2.cz.i.607.12	yes	32	28.19	even	6
3024.2.bf.i.1711.9		32	3.2	odd	2
3024.2.bf.i.1711.10		32	12.11	even	2
3024.2.bf.i.2287.7		32	63.47	even	6
3024.2.bf.i.2287.8		32	252.47	odd	6
3024.2.cz.i.1279.7		32	21.5	even	6
3024.2.cz.i.1279.8		32	84.47	odd	6
3024.2.cz.i.2719.7		32	36.11	even	6
3024.2.cz.i.2719.8		32	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.72863 - 0.108820i) q^{3} -0.435427i q^{5} +(2.49096 + 0.891704i) q^{7} +(2.97632 + 0.376218i) q^{9} +4.82050i q^{11} +(-4.31639 - 2.49207i) q^{13} +(-0.0473830 + 0.752691i) q^{15} +(-4.92142 - 2.84139i) q^{17} +(3.70969 + 6.42537i) q^{19} +(-4.20890 - 1.81249i) q^{21} -3.16029i q^{23} +4.81040 q^{25} +(-5.10401 - 0.974224i) q^{27} +(2.49630 + 4.32372i) q^{29} +(-1.32968 - 2.30307i) q^{31} +(0.524566 - 8.33285i) q^{33} +(0.388272 - 1.08463i) q^{35} +(1.06500 + 1.84463i) q^{37} +(7.19025 + 4.77757i) q^{39} +(0.112731 + 0.0650855i) q^{41} +(-6.53530 + 3.77315i) q^{43} +(0.163815 - 1.29597i) q^{45} +(-4.29337 + 7.43633i) q^{47} +(5.40973 + 4.44239i) q^{49} +(8.19812 + 5.44725i) q^{51} +(-5.61000 + 9.71680i) q^{53} +2.09897 q^{55} +(-5.71347 - 11.5108i) q^{57} +(6.20064 + 10.7398i) q^{59} +(7.65803 + 4.42137i) q^{61} +(7.07840 + 3.59114i) q^{63} +(-1.08511 + 1.87947i) q^{65} +(-0.811298 + 0.468403i) q^{67} +(-0.343902 + 5.46297i) q^{69} +6.27328i q^{71} +(11.2357 + 6.48693i) q^{73} +(-8.31540 - 0.523467i) q^{75} +(-4.29846 + 12.0077i) q^{77} +(2.98242 + 1.72190i) q^{79} +(8.71692 + 2.23949i) q^{81} +(-3.68712 - 6.38628i) q^{83} +(-1.23721 + 2.14292i) q^{85} +(-3.84467 - 7.74576i) q^{87} +(-13.2599 + 7.65563i) q^{89} +(-8.52975 - 10.0566i) q^{91} +(2.04790 + 4.12585i) q^{93} +(2.79778 - 1.61530i) q^{95} +(-2.83887 + 1.63902i) q^{97} +(-1.81356 + 14.3473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{9} - 6 q^{13} - 18 q^{17} - 8 q^{21} - 32 q^{25} - 12 q^{29} + 30 q^{33} + 2 q^{37} + 36 q^{41} + 30 q^{45} + 2 q^{49} - 12 q^{53} - 46 q^{57} + 42 q^{61} + 18 q^{65} - 42 q^{69} - 66 q^{77}+ \cdots - 6 q^{97}+O(q^{100}) \) 32 * q - 4 * q^9 - 6 * q^13 - 18 * q^17 - 8 * q^21 - 32 * q^25 - 12 * q^29 + 30 * q^33 + 2 * q^37 + 36 * q^41 + 30 * q^45 + 2 * q^49 - 12 * q^53 - 46 * q^57 + 42 * q^61 + 18 * q^65 - 42 * q^69 - 66 * q^77 - 16 * q^81 - 12 * q^85 - 18 * q^89 + 58 * q^93 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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