LMFDB - Embedded newform 576.2.y.a.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819834 + 1.52574i) q^{3} +(-0.206232 + 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(-1.65574 - 2.50170i) q^{9} +O(q^{10})$	\(q+(-0.819834 + 1.52574i) q^{3} +(-0.206232 + 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(-1.65574 - 2.50170i) q^{9} +(-1.05570 - 3.93991i) q^{11} +(-0.454903 + 1.69772i) q^{13} +(-1.00524 - 0.945658i) q^{15} -6.68683i q^{17} +(0.708282 - 0.708282i) q^{19} +(3.96598 + 6.40914i) q^{21} +(-3.88191 + 2.24122i) q^{23} +(3.78027 + 2.18254i) q^{25} +(5.17437 - 0.475249i) q^{27} +(-1.06907 - 3.98981i) q^{29} +(4.94177 - 2.85313i) q^{31} +(6.87676 + 1.61936i) q^{33} +(2.45179 + 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-2.21733 - 2.08591i) q^{39} +(1.36389 + 2.36233i) q^{41} +(8.60436 - 2.30553i) q^{43} +(2.26695 - 0.758445i) q^{45} +(-1.23164 + 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(10.2023 + 5.48209i) q^{51} +(1.68291 + 1.68291i) q^{53} +3.25015 q^{55} +(0.499978 + 1.66133i) q^{57} +(1.00516 + 0.269331i) q^{59} +(1.97401 - 0.528935i) q^{61} +(-13.0301 + 0.796606i) q^{63} +(-1.21287 - 0.700250i) q^{65} +(-8.01120 - 2.14659i) q^{67} +(-0.236992 - 7.76019i) q^{69} +8.05218i q^{71} -9.73126i q^{73} +(-6.42917 + 3.97837i) q^{75} +(-17.1444 - 4.59383i) q^{77} +(-11.9835 - 6.91865i) q^{79} +(-3.51702 + 8.28436i) q^{81} +(-3.05012 + 0.817277i) q^{83} +(5.14666 + 1.37904i) q^{85} +(6.96385 + 1.63987i) q^{87} +1.71120 q^{89} +(5.40809 + 5.40809i) q^{91} +(0.301697 + 9.87893i) q^{93} +(0.399073 + 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +(-8.10851 + 9.16451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.819834	+	1.52574i	−0.473331	+	0.880884i
$3$	−0.819834	+	1.52574i	−0.473331	+	0.880884i
$4$		0			0
$5$	−0.206232	+	0.769670i	−0.0922300	+	0.344207i	−0.996585	−	0.0825742i	$-0.973686\pi$
$5$	−0.206232	+	0.769670i	−0.0922300	+	0.344207i	0.904355	+	0.426781i	$0.140353\pi$
$6$		0			0
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	−0.0815745	−	0.996667i	$-0.525995\pi$
$7$	2.17574	−	3.76849i	0.822352	−	1.42436i	0.903926	−	0.427688i	$-0.140672\pi$
$8$		0			0
$9$	−1.65574	−	2.50170i	−0.551915	−	0.833901i
$10$		0			0
$11$	−1.05570	−	3.93991i	−0.318304	−	1.18793i	−0.920874	−	0.389861i	$-0.872523\pi$
$11$	−1.05570	−	3.93991i	−0.318304	−	1.18793i	0.602570	−	0.798066i	$-0.294144\pi$
$12$		0			0
$13$	−0.454903	+	1.69772i	−0.126167	+	0.470863i	−0.999879	−	0.0155820i	$-0.995040\pi$
$13$	−0.454903	+	1.69772i	−0.126167	+	0.470863i	0.873711	+	0.486445i	$0.161707\pi$
$14$		0			0
$15$	−1.00524	−	0.945658i	−0.259551	−	0.244168i
$16$		0			0
$17$		−	6.68683i		−	1.62180i	−0.585188	−	0.810898i	$-0.698979\pi$
$17$		−	6.68683i		−	1.62180i	0.585188	−	0.810898i	$-0.301021\pi$
$18$		0			0
$19$	0.708282	−	0.708282i	0.162491	−	0.162491i	−0.621178	−	0.783669i	$-0.713346\pi$
$19$	0.708282	−	0.708282i	0.162491	−	0.162491i	0.783669	+	0.621178i	$0.213346\pi$
$20$		0			0
$21$	3.96598	+	6.40914i	0.865447	+	1.39859i
$22$		0			0
$23$	−3.88191	+	2.24122i	−0.809433	+	0.467327i	−0.846759	−	0.531977i	$-0.821449\pi$
$23$	−3.88191	+	2.24122i	−0.809433	+	0.467327i	0.0373258	+	0.999303i	$0.488116\pi$
$24$		0			0
$25$	3.78027	+	2.18254i	0.756053	+	0.436508i
$26$		0			0
$27$	5.17437	−	0.475249i	0.995809	−	0.0914618i
$28$		0			0
$29$	−1.06907	−	3.98981i	−0.198520	−	0.740888i	−0.991327	−	0.131415i	$-0.958048\pi$
$29$	−1.06907	−	3.98981i	−0.198520	−	0.740888i	0.792807	−	0.609473i	$-0.208619\pi$
$30$		0			0
$31$	4.94177	−	2.85313i	0.887568	−	0.512437i	0.0144215	−	0.999896i	$-0.495409\pi$
$31$	4.94177	−	2.85313i	0.887568	−	0.512437i	0.873146	+	0.487459i	$0.162076\pi$
$32$		0			0
$33$	6.87676	+	1.61936i	1.19709	+	0.281894i
$34$		0			0
$35$	2.45179	+	2.45179i	0.414427	+	0.414427i
$36$		0			0
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	−0.820698	−	0.571363i	$-0.806415\pi$
$37$	−1.51665	+	1.51665i	−0.249335	+	0.249335i	0.571363	+	0.820698i	$0.306415\pi$
$38$		0			0
$39$	−2.21733	−	2.08591i	−0.355057	−	0.334013i
$40$		0			0
$41$	1.36389	+	2.36233i	0.213005	+	0.368935i	0.952653	−	0.304058i	$-0.0983418\pi$
$41$	1.36389	+	2.36233i	0.213005	+	0.368935i	−0.739649	+	0.672993i	$0.765008\pi$
$42$		0			0
$43$	8.60436	−	2.30553i	1.31215	−	0.351590i	0.466120	−	0.884722i	$-0.345652\pi$
$43$	8.60436	−	2.30553i	1.31215	−	0.351590i	0.846033	+	0.533131i	$0.178985\pi$
$44$		0			0
$45$	2.26695	−	0.758445i	0.337937	−	0.113062i
$46$		0			0
$47$	−1.23164	+	2.13327i	−0.179654	+	0.311169i	−0.941762	−	0.336280i	$-0.890831\pi$
$47$	−1.23164	+	2.13327i	−0.179654	+	0.311169i	0.762108	+	0.647449i	$0.224164\pi$
$48$		0			0
$49$	−5.96768	−	10.3363i	−0.852525	−	1.47662i
$50$		0			0
$51$	10.2023	+	5.48209i	1.42861	+	0.767647i
$52$		0			0
$53$	1.68291	+	1.68291i	0.231165	+	0.231165i	0.813179	−	0.582014i	$-0.197735\pi$
$53$	1.68291	+	1.68291i	0.231165	+	0.231165i	−0.582014	+	0.813179i	$0.697735\pi$
$54$		0			0
$55$	3.25015			0.438250
$56$		0			0
$57$	0.499978	+	1.66133i	0.0662237	+	0.220048i
$58$		0			0
$59$	1.00516	+	0.269331i	0.130860	+	0.0350640i	0.323655	−	0.946175i	$-0.395088\pi$
$59$	1.00516	+	0.269331i	0.130860	+	0.0350640i	−0.192794	+	0.981239i	$0.561755\pi$
$60$		0			0
$61$	1.97401	−	0.528935i	0.252747	−	0.0677232i	−0.130221	−	0.991485i	$-0.541569\pi$
$61$	1.97401	−	0.528935i	0.252747	−	0.0677232i	0.382968	+	0.923762i	$0.374902\pi$
$62$		0			0
$63$	−13.0301	+	0.796606i	−1.64164	+	0.100363i
$64$		0			0
$65$	−1.21287	−	0.700250i	−0.150438	−	0.0868553i
$66$		0			0
$67$	−8.01120	−	2.14659i	−0.978723	−	0.262248i	−0.266217	−	0.963913i	$-0.585774\pi$
$67$	−8.01120	−	2.14659i	−0.978723	−	0.262248i	−0.712507	+	0.701665i	$0.752440\pi$
$68$		0			0
$69$	−0.236992	−	7.76019i	−0.0285305	−	0.934217i
$70$		0			0
$71$			8.05218i			0.955618i	0.878464	+	0.477809i	$0.158569\pi$
$71$			8.05218i			0.955618i	−0.878464	+	0.477809i	$0.841431\pi$
$72$		0			0
$73$		−	9.73126i		−	1.13896i	−0.822006	−	0.569479i	$-0.807145\pi$
$73$		−	9.73126i		−	1.13896i	0.822006	−	0.569479i	$-0.192855\pi$
$74$		0			0
$75$	−6.42917	+	3.97837i	−0.742377	+	0.459383i
$76$		0			0
$77$	−17.1444	−	4.59383i	−1.95379	−	0.523516i
$78$		0			0
$79$	−11.9835	−	6.91865i	−1.34824	−	0.778409i	−0.360243	−	0.932858i	$-0.617306\pi$
$79$	−11.9835	−	6.91865i	−1.34824	−	0.778409i	−0.988001	+	0.154449i	$0.950640\pi$
$80$		0			0
$81$	−3.51702	+	8.28436i	−0.390780	+	0.920484i
$82$		0			0
$83$	−3.05012	+	0.817277i	−0.334794	+	0.0897078i	−0.422300	−	0.906456i	$-0.638777\pi$
$83$	−3.05012	+	0.817277i	−0.334794	+	0.0897078i	0.0875058	+	0.996164i	$0.472110\pi$
$84$		0			0
$85$	5.14666	+	1.37904i	0.558233	+	0.149578i
$86$		0			0
$87$	6.96385	+	1.63987i	0.746603	+	0.175812i
$88$		0			0
$89$	1.71120			0.181386			0.0906932	−	0.995879i	$-0.471092\pi$
$89$	1.71120			0.181386			0.0906932	+	0.995879i	$0.471092\pi$
$90$		0			0
$91$	5.40809	+	5.40809i	0.566922	+	0.566922i
$92$		0			0
$93$	0.301697	+	9.87893i	0.0312845	+	1.02440i
$94$		0			0
$95$	0.399073	+	0.691214i	0.0409440	+	0.0709171i
$96$		0			0
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	−0.617715	−	0.786402i	$-0.711941\pi$
$97$	3.66561	−	6.34903i	0.372187	−	0.644646i	0.989902	+	0.141756i	$0.0452748\pi$
$98$		0			0
$99$	−8.10851	+	9.16451i	−0.814936	+	0.921068i
$100$		0			0
$101$	−14.0255	+	3.75813i	−1.39559	+	0.373948i	−0.876760	−	0.480928i	$-0.840300\pi$
$101$	−14.0255	+	3.75813i	−1.39559	+	0.373948i	−0.518833	+	0.854876i	$0.673633\pi$
$102$		0			0
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	0.955616	+	0.294616i	$0.0951917\pi$
$103$	7.43866	+	12.8841i	0.732953	+	1.26951i	−0.222663	+	0.974895i	$0.571475\pi$
$104$		0			0
$105$	−5.75084	+	1.73072i	−0.561224	+	0.168901i
$106$		0			0
$107$	0.0974799	−	0.0974799i	0.00942374	−	0.00942374i	−0.702379	−	0.711803i	$-0.747879\pi$
$107$	0.0974799	−	0.0974799i	0.00942374	−	0.00942374i	0.711803	+	0.702379i	$0.247879\pi$
$108$		0			0
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	0.989315	−	0.145791i	$-0.0465728\pi$
$109$	8.80665	+	8.80665i	0.843524	+	0.843524i	−0.145791	+	0.989315i	$0.546573\pi$
$110$		0			0
$111$	−1.07060	−	3.55740i	−0.101617	−	0.337654i
$112$		0			0
$113$	7.22037	−	4.16868i	0.679235	−	0.392157i	−0.120331	−	0.992734i	$-0.538396\pi$
$113$	7.22037	−	4.16868i	0.679235	−	0.392157i	0.799567	+	0.600577i	$0.205062\pi$
$114$		0			0
$115$	−0.924424	−	3.45000i	−0.0862030	−	0.321714i
$116$		0			0
$117$	5.00039	−	1.67296i	0.462286	−	0.154665i
$118$		0			0
$119$	−25.1993	−	14.5488i	−2.31001	−	1.33369i
$120$		0			0
$121$	−4.88210	+	2.81868i	−0.443827	+	0.256244i
$122$		0			0
$123$	−4.72247	+	0.144221i	−0.425811	+	0.0130040i
$124$		0			0
$125$	−5.27664	+	5.27664i	−0.471957	+	0.471957i
$126$		0			0
$127$			4.84829i			0.430216i	0.976590	+	0.215108i	$0.0690103\pi$
$127$			4.84829i			0.430216i	−0.976590	+	0.215108i	$0.930990\pi$
$128$		0			0
$129$	−3.53651	+	15.0181i	−0.311373	+	1.32227i
$130$		0			0
$131$	5.49193	−	20.4961i	0.479832	−	1.79076i	−0.122452	−	0.992474i	$-0.539076\pi$
$131$	5.49193	−	20.4961i	0.479832	−	1.79076i	0.602284	−	0.798282i	$-0.294258\pi$
$132$		0			0
$133$	−1.12812	−	4.21019i	−0.0978201	−	0.365070i
$134$		0			0
$135$	−0.701338	+	4.08057i	−0.0603616	+	0.351200i
$136$		0			0
$137$	−2.93860	+	5.08981i	−0.251062	+	0.434852i	−0.963818	−	0.266560i	$-0.914113\pi$
$137$	−2.93860	+	5.08981i	−0.251062	+	0.434852i	0.712757	+	0.701411i	$0.247446\pi$
$138$		0			0
$139$	1.86863	−	6.97384i	0.158496	−	0.591513i	−0.840285	−	0.542145i	$-0.817612\pi$
$139$	1.86863	−	6.97384i	0.158496	−	0.591513i	0.998781	−	0.0493686i	$-0.0157209\pi$
$140$		0			0
$141$	−2.24506	−	3.62809i	−0.189068	−	0.305540i
$142$		0			0
$143$	7.16910			0.599510
$144$		0			0
$145$	3.29131			0.273328
$146$		0			0
$147$	20.6630	−	0.631036i	1.70426	−	0.0520470i
$148$		0			0
$149$	1.16425	−	4.34504i	0.0953792	−	0.355960i	−0.901698	−	0.432367i	$-0.857678\pi$
$149$	1.16425	−	4.34504i	0.0953792	−	0.355960i	0.997077	+	0.0764076i	$0.0243450\pi$
$150$		0			0
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	−0.640650	−	0.767833i	$-0.721335\pi$
$151$	4.23499	−	7.33521i	0.344638	−	0.596931i	0.985288	+	0.170902i	$0.0546683\pi$
$152$		0			0
$153$	−16.7285	+	11.0717i	−1.35242	+	0.895093i
$154$		0			0
$155$	1.17682	+	4.39194i	0.0945241	+	0.352769i
$156$		0			0
$157$	−4.38117	+	16.3507i	−0.349655	+	1.30493i	0.537423	+	0.843313i	$0.319398\pi$
$157$	−4.38117	+	16.3507i	−0.349655	+	1.30493i	−0.887079	+	0.461618i	$0.847269\pi$
$158$		0			0
$159$	−3.94738	+	1.18797i	−0.313048	+	0.0942121i
$160$		0			0
$161$			19.5052i			1.53723i
$162$		0			0
$163$	−13.6982	+	13.6982i	−1.07293	+	1.07293i	−0.0758059	+	0.997123i	$0.524153\pi$
$163$	−13.6982	+	13.6982i	−1.07293	+	1.07293i	−0.997123	+	0.0758059i	$0.975847\pi$
$164$		0			0
$165$	−2.66458	+	4.95887i	−0.207437	+	0.386047i
$166$		0			0
$167$	7.11859	−	4.10992i	0.550853	−	0.318035i	−0.198613	−	0.980078i	$-0.563644\pi$
$167$	7.11859	−	4.10992i	0.550853	−	0.318035i	0.749466	+	0.662043i	$0.230310\pi$
$168$		0			0
$169$	8.58301	+	4.95540i	0.660232	+	0.381185i
$170$		0			0
$171$	−2.94464	−	0.599176i	−0.225183	−	0.0458202i
$172$		0			0
$173$	−2.52258	−	9.41440i	−0.191788	−	0.715764i	−0.993075	−	0.117483i	$-0.962517\pi$
$173$	−2.52258	−	9.41440i	−0.191788	−	0.715764i	0.801287	−	0.598281i	$-0.204149\pi$
$174$		0			0
$175$	16.4497	−	9.49727i	1.24348	−	0.717926i
$176$		0			0
$177$	−1.23499	+	1.31280i	−0.0928277	+	0.0986761i
$178$		0			0
$179$	−2.59887	−	2.59887i	−0.194248	−	0.194248i	0.603281	−	0.797529i	$-0.293860\pi$
$179$	−2.59887	−	2.59887i	−0.194248	−	0.194248i	−0.797529	+	0.603281i	$0.793860\pi$
$180$		0			0
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	−0.401021	−	0.916069i	$-0.631345\pi$
$181$	6.92926	−	6.92926i	0.515048	−	0.515048i	0.916069	+	0.401021i	$0.131345\pi$
$182$		0			0
$183$	−0.811348	+	3.44546i	−0.0599765	+	0.254696i
$184$		0			0
$185$	−0.854536	−	1.48010i	−0.0628267	−	0.108819i
$186$		0			0
$187$	−26.3455	+	7.05926i	−1.92657	+	0.516224i
$188$		0			0
$189$	9.46711	−	20.5336i	0.688631	−	1.49360i
$190$		0			0
$191$	−6.96728	+	12.0677i	−0.504135	+	0.873187i	0.495854	+	0.868406i	$0.334855\pi$
$191$	−6.96728	+	12.0677i	−0.504135	+	0.873187i	−0.999989	+	0.00478132i	$0.998478\pi$
$192$		0			0
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	0.813720	−	0.581256i	$-0.197439\pi$
$193$	−1.34094	−	2.32257i	−0.0965226	−	0.167182i	−0.910243	+	0.414074i	$0.864105\pi$
$194$		0			0
$195$	2.06275	−	1.27643i	0.147716	−	0.0914070i
$196$		0			0
$197$	14.2363	+	14.2363i	1.01430	+	1.01430i	0.999896	+	0.0144009i	$0.00458410\pi$
$197$	14.2363	+	14.2363i	1.01430	+	1.01430i	0.0144009	+	0.999896i	$0.495416\pi$
$198$		0			0
$199$	−7.90078			−0.560072			−0.280036	−	0.959990i	$-0.590346\pi$
$199$	−7.90078			−0.560072			−0.280036	+	0.959990i	$0.590346\pi$
$200$		0			0
$201$	9.84299	−	10.4631i	0.694271	−	0.738012i
$202$		0			0
$203$	−17.3615	−	4.65201i	−1.21854	−	0.326507i
$204$		0			0
$205$	−2.09950	+	0.562559i	−0.146635	+	0.0392908i
$206$		0			0
$207$	12.0343	+	6.00048i	0.836442	+	0.417062i
$208$		0			0
$209$	−3.53830	−	2.04284i	−0.244749	−	0.141306i
$210$		0			0
$211$	−13.2108	−	3.53982i	−0.909469	−	0.243691i	−0.226391	−	0.974037i	$-0.572693\pi$
$211$	−13.2108	−	3.53982i	−0.909469	−	0.243691i	−0.683078	+	0.730345i	$0.739359\pi$
$212$		0			0
$213$	−12.2855	−	6.60145i	−0.841789	−	0.452324i
$214$		0			0
$215$			7.09799i			0.484079i
$216$		0			0
$217$		−	24.8307i		−	1.68562i
$218$		0			0
$219$	14.8473	+	7.97802i	1.00329	+	0.539105i
$220$		0			0
$221$	11.3524	+	3.04186i	0.763643	+	0.204618i
$222$		0			0
$223$	24.3372	+	14.0511i	1.62974	+	0.940931i	0.984169	+	0.177230i	$0.0567136\pi$
$223$	24.3372	+	14.0511i	1.62974	+	0.940931i	0.645570	+	0.763701i	$0.276620\pi$
$224$		0			0
$225$	−0.799096	−	13.0708i	−0.0532731	−	0.871388i
$226$		0			0
$227$	−0.489998	+	0.131295i	−0.0325223	+	0.00871433i	−0.275044	−	0.961432i	$-0.588692\pi$
$227$	−0.489998	+	0.131295i	−0.0325223	+	0.00871433i	0.242521	+	0.970146i	$0.422026\pi$
$228$		0			0
$229$	−14.6181	−	3.91690i	−0.965988	−	0.258836i	−0.258855	−	0.965916i	$-0.583345\pi$
$229$	−14.6181	−	3.91690i	−0.965988	−	0.258836i	−0.707133	+	0.707080i	$0.750012\pi$
$230$		0			0
$231$	21.0646	−	22.3917i	1.38595	−	1.47326i
$232$		0			0
$233$	15.4968			1.01523			0.507614	−	0.861584i	$-0.330527\pi$
$233$	15.4968			1.01523			0.507614	+	0.861584i	$0.330527\pi$
$234$		0			0
$235$	−1.38791	−	1.38791i	−0.0905371	−	0.0905371i
$236$		0			0
$237$	20.3805	−	12.6114i	1.32385	−	0.819202i
$238$		0			0
$239$	7.61709	+	13.1932i	0.492709	+	0.853397i	0.999965	−	0.00839869i	$-0.00267342\pi$
$239$	7.61709	+	13.1932i	0.492709	+	0.853397i	−0.507256	+	0.861796i	$0.669340\pi$
$240$		0			0
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	0.408038	+	0.912965i	$0.366213\pi$
$241$	−9.10697	+	15.7737i	−0.586632	+	1.01608i	−0.994670	+	0.103111i	$0.967120\pi$
$242$		0			0
$243$	−9.75637	−	12.1578i	−0.625871	−	0.779926i
$244$		0			0
$245$	9.18628	−	2.46146i	0.586890	−	0.157257i
$246$		0			0
$247$	0.880265	+	1.52466i	0.0560099	+	0.0970121i
$248$		0			0
$249$	1.25364	−	5.32371i	0.0794463	−	0.337376i
$250$		0			0
$251$	−2.18418	+	2.18418i	−0.137864	+	0.137864i	−0.772671	−	0.634807i	$-0.781080\pi$
$251$	−2.18418	+	2.18418i	−0.137864	+	0.137864i	0.634807	+	0.772671i	$0.281080\pi$
$252$		0			0
$253$	12.9283	+	12.9283i	0.812796	+	0.812796i
$254$		0			0
$255$	−6.32346	+	6.72185i	−0.395990	+	0.420939i
$256$		0			0
$257$	16.6777	−	9.62887i	1.04033	−	0.600633i	0.120400	−	0.992725i	$-0.461582\pi$
$257$	16.6777	−	9.62887i	1.04033	−	0.600633i	0.919926	+	0.392093i	$0.128249\pi$
$258$		0			0
$259$	2.41564	+	9.01529i	0.150101	+	0.560183i
$260$		0			0
$261$	−8.21121	+	9.28058i	−0.508261	+	0.574453i
$262$		0			0
$263$	22.8254	+	13.1782i	1.40747	+	0.812605i	0.995144	−	0.0984300i	$-0.0313821\pi$
$263$	22.8254	+	13.1782i	1.40747	+	0.812605i	0.412329	+	0.911035i	$0.364715\pi$
$264$		0			0
$265$	−1.64235	+	0.948214i	−0.100889	+	0.0582483i
$266$		0			0
$267$	−1.40290	+	2.61083i	−0.0858559	+	0.159781i
$268$		0			0
$269$	−0.605506	+	0.605506i	−0.0369184	+	0.0369184i	−0.725325	−	0.688407i	$-0.758310\pi$
$269$	−0.605506	+	0.605506i	−0.0369184	+	0.0369184i	0.688407	+	0.725325i	$0.258310\pi$
$270$		0			0
$271$		−	19.1084i		−	1.16075i	−0.814349	−	0.580376i	$-0.802906\pi$
$271$		−	19.1084i		−	1.16075i	0.814349	−	0.580376i	$-0.197094\pi$
$272$		0			0
$273$	−12.6851	+	3.81759i	−0.767735	+	0.231051i
$274$		0			0
$275$	4.60819	−	17.1980i	0.277884	−	1.03708i
$276$		0			0
$277$	−1.82792	−	6.82191i	−0.109829	−	0.409889i	0.889019	−	0.457871i	$-0.151388\pi$
$277$	−1.82792	−	6.82191i	−0.109829	−	0.409889i	−0.998848	+	0.0479819i	$0.984721\pi$
$278$		0			0
$279$	−15.3200	−	7.63877i	−0.917183	−	0.457321i
$280$		0			0
$281$	−11.8490	+	20.5230i	−0.706849	+	1.22430i	0.259171	+	0.965831i	$0.416551\pi$
$281$	−11.8490	+	20.5230i	−0.706849	+	1.22430i	−0.966020	+	0.258467i	$0.916783\pi$
$282$		0			0
$283$	0.194826	−	0.727099i	0.0115812	−	0.0432215i	−0.959893	−	0.280365i	$-0.909544\pi$
$283$	0.194826	−	0.727099i	0.0115812	−	0.0432215i	0.971475	+	0.237143i	$0.0762112\pi$
$284$		0			0
$285$	−1.38178	+	0.0421989i	−0.0818498	+	0.00249965i
$286$		0			0
$287$	11.8699			0.700659
$288$		0			0
$289$	−27.7137			−1.63022
$290$		0			0
$291$	6.68175	+	10.7979i	0.391691	+	0.632985i
$292$		0			0
$293$	5.31070	−	19.8198i	0.310255	−	1.15789i	−0.618072	−	0.786121i	$-0.712086\pi$
$293$	5.31070	−	19.8198i	0.310255	−	1.15789i	0.928327	−	0.371765i	$-0.121247\pi$
$294$		0			0
$295$	−0.414592	+	0.718095i	−0.0241385	+	0.0418091i
$296$		0			0
$297$	−7.33500	−	19.8848i	−0.425620	−	1.15384i
$298$		0			0
$299$	−2.03907	−	7.60993i	−0.117923	−	0.440093i
$300$		0			0
$301$	10.0325	−	37.4417i	0.578262	−	2.15810i
$302$		0			0
$303$	5.76469	−	24.4803i	0.331173	−	1.40636i
$304$		0			0
$305$			1.62842i			0.0932432i
$306$		0			0
$307$	15.3450	−	15.3450i	0.875783	−	0.875783i	−0.117312	−	0.993095i	$-0.537428\pi$
$307$	15.3450	−	15.3450i	0.875783	−	0.875783i	0.993095	+	0.117312i	$0.0374277\pi$
$308$		0			0
$309$	−25.7563	+	0.786581i	−1.46522	+	0.0447470i
$310$		0			0
$311$	−0.576605	+	0.332903i	−0.0326963	+	0.0188772i	−0.516259	−	0.856432i	$-0.672676\pi$
$311$	−0.576605	+	0.332903i	−0.0326963	+	0.0188772i	0.483563	+	0.875310i	$0.339342\pi$
$312$		0			0
$313$	14.3283	+	8.27244i	0.809882	+	0.467586i	0.846915	−	0.531728i	$-0.178457\pi$
$313$	14.3283	+	8.27244i	0.809882	+	0.467586i	−0.0370327	+	0.999314i	$0.511791\pi$
$314$		0			0
$315$	2.07411	−	10.1932i	0.116863	−	0.574320i
$316$		0			0
$317$	−1.75927	−	6.56570i	−0.0988107	−	0.368767i	0.898759	−	0.438443i	$-0.144470\pi$
$317$	−1.75927	−	6.56570i	−0.0988107	−	0.368767i	−0.997570	+	0.0696766i	$0.977803\pi$
$318$		0			0
$319$	−14.5909	+	8.42404i	−0.816931	+	0.471656i
$320$		0			0
$321$	0.0688113	+	0.228646i	0.00384067	+	0.0127618i
$322$		0			0
$323$	−4.73616	−	4.73616i	−0.263527	−	0.263527i
$324$		0			0
$325$	−5.42499	+	5.42499i	−0.300924	+	0.300924i
$326$		0			0
$327$	−20.6566	+	6.21664i	−1.14231	+	0.343781i
$328$		0			0
$329$	5.35946	+	9.28286i	0.295477	+	0.511781i
$330$		0			0
$331$	−9.39568	+	2.51757i	−0.516434	+	0.138378i	−0.507616	−	0.861583i	$-0.669473\pi$
$331$	−9.39568	+	2.51757i	−0.516434	+	0.138378i	−0.00881711	+	0.999961i	$0.502807\pi$
$332$		0			0
$333$	6.30538	+	1.28302i	0.345532	+	0.0703090i
$334$		0			0
$335$	3.30434	−	5.72328i	0.180535	−	0.312696i
$336$		0			0
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	0.953147	+	0.302509i	$0.0978241\pi$
$337$	13.5580	+	23.4832i	0.738553	+	1.27921i	−0.214593	+	0.976704i	$0.568843\pi$
$338$		0			0
$339$	0.440806	+	14.4340i	0.0239413	+	0.783948i
$340$		0			0
$341$	−16.4581	−	16.4581i	−0.891254	−	0.891254i
$342$		0			0
$343$	−21.4761			−1.15960
$344$		0			0
$345$	6.02166	+	1.41800i	0.324195	+	0.0763425i
$346$		0			0
$347$	30.1679	+	8.08347i	1.61950	+	0.433944i	0.950854	−	0.309638i	$-0.100208\pi$
$347$	30.1679	+	8.08347i	1.61950	+	0.433944i	0.668645	+	0.743582i	$0.266875\pi$
$348$		0			0
$349$	−31.6714	+	8.48634i	−1.69533	+	0.454263i	−0.971757	−	0.235982i	$-0.924169\pi$
$349$	−31.6714	+	8.48634i	−1.69533	+	0.454263i	−0.723576	+	0.690245i	$0.757503\pi$
$350$		0			0
$351$	−1.54700	+	9.00083i	−0.0825726	+	0.480429i
$352$		0			0
$353$	−3.48989	−	2.01489i	−0.185748	−	0.107242i	0.404243	−	0.914652i	$-0.367535\pi$
$353$	−3.48989	−	2.01489i	−0.185748	−	0.107242i	−0.589990	+	0.807410i	$0.700869\pi$
$354$		0			0
$355$	−6.19752	−	1.66062i	−0.328930	−	0.0881366i
$356$		0			0
$357$	42.8569	−	26.5198i	2.26823	−	1.40358i
$358$		0			0
$359$		−	14.8043i		−	0.781342i	−0.920530	−	0.390671i	$-0.872243\pi$
$359$		−	14.8043i		−	0.781342i	0.920530	−	0.390671i	$-0.127757\pi$
$360$		0			0
$361$			17.9967i			0.947193i
$362$		0			0
$363$	−0.298054	−	9.75965i	−0.0156438	−	0.512249i
$364$		0			0
$365$	7.48986	+	2.00690i	0.392037	+	0.105046i
$366$		0			0
$367$	2.66934	+	1.54114i	0.139338	+	0.0804470i	0.568049	−	0.822995i	$-0.307699\pi$
$367$	2.66934	+	1.54114i	0.139338	+	0.0804470i	−0.428710	+	0.903442i	$0.641032\pi$
$368$		0			0
$369$	3.65160	−	7.32348i	0.190094	−	0.381245i
$370$		0			0
$371$	10.0036	−	2.68045i	0.519361	−	0.139162i
$372$		0			0
$373$	28.2816	+	7.57804i	1.46437	+	0.392376i	0.900996	−	0.433828i	$-0.142837\pi$
$373$	28.2816	+	7.57804i	1.46437	+	0.392376i	0.563372	+	0.826204i	$0.309504\pi$
$374$		0			0
$375$	−3.72479	−	12.3767i	−0.192347	−	0.639131i
$376$		0			0
$377$	7.25990			0.373904
$378$		0			0
$379$	13.0654	+	13.0654i	0.671124	+	0.671124i	0.957975	−	0.286851i	$-0.0926085\pi$
$379$	13.0654	+	13.0654i	0.671124	+	0.671124i	−0.286851	+	0.957975i	$0.592608\pi$
$380$		0			0
$381$	−7.39721	−	3.97479i	−0.378970	−	0.203635i
$382$		0			0
$383$	−1.66394	−	2.88203i	−0.0850235	−	0.147265i	0.820378	−	0.571822i	$-0.193763\pi$
$383$	−1.66394	−	2.88203i	−0.0850235	−	0.147265i	−0.905401	+	0.424557i	$0.860430\pi$
$384$		0			0
$385$	7.07147	−	12.2481i	0.360396	−	0.624223i
$386$		0			0
$387$	−20.0144	−	17.7082i	−1.01739	−	0.900157i
$388$		0			0
$389$	−6.62255	+	1.77451i	−0.335777	+	0.0899711i	−0.422768	−	0.906238i	$-0.638941\pi$
$389$	−6.62255	+	1.77451i	−0.335777	+	0.0899711i	0.0869912	+	0.996209i	$0.472275\pi$
$390$		0			0
$391$	14.9867	+	25.9577i	0.757908	+	1.31274i
$392$		0			0
$393$	26.7693	+	25.1827i	1.35033	+	1.27030i
$394$		0			0
$395$	7.79645	−	7.79645i	0.392282	−	0.392282i
$396$		0			0
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	0.763344	−	0.645993i	$-0.223556\pi$
$397$	2.33820	+	2.33820i	0.117351	+	0.117351i	−0.645993	+	0.763344i	$0.723556\pi$
$398$		0			0
$399$	7.34851	+	1.73045i	0.367886	+	0.0866307i
$400$		0			0
$401$	3.32787	−	1.92135i	0.166186	−	0.0959474i	−0.414600	−	0.910004i	$-0.636079\pi$
$401$	3.32787	−	1.92135i	0.166186	−	0.0959474i	0.580786	+	0.814056i	$0.302745\pi$
$402$		0			0
$403$	2.59579	+	9.68764i	0.129306	+	0.482575i
$404$		0			0
$405$	−5.65090	−	4.41545i	−0.280795	−	0.219405i
$406$		0			0
$407$	7.57656	+	4.37433i	0.375556	+	0.216828i
$408$		0			0
$409$	4.36888	−	2.52237i	0.216027	−	0.124723i	−0.388082	−	0.921625i	$-0.626862\pi$
$409$	4.36888	−	2.52237i	0.216027	−	0.124723i	0.604109	+	0.796901i	$0.293529\pi$
$410$		0			0
$411$	−5.35654	−	8.65634i	−0.264219	−	0.426986i
$412$		0			0
$413$	3.20193	−	3.20193i	0.157557	−	0.157557i
$414$		0			0
$415$		−	2.51613i		−	0.123512i
$416$		0			0
$417$	9.10827	+	8.56844i	0.446034	+	0.419598i
$418$		0			0
$419$	−5.72083	+	21.3504i	−0.279481	+	1.04304i	0.673298	+	0.739371i	$0.264877\pi$
$419$	−5.72083	+	21.3504i	−0.279481	+	1.04304i	−0.952779	+	0.303665i	$0.901790\pi$
$420$		0			0
$421$	2.13099	+	7.95298i	0.103858	+	0.387604i	0.998213	−	0.0597538i	$-0.0190316\pi$
$421$	2.13099	+	7.95298i	0.103858	+	0.387604i	−0.894355	+	0.447358i	$0.852365\pi$
$422$		0			0
$423$	7.37608	−	0.450943i	0.358637	−	0.0219256i
$424$		0			0
$425$	14.5943	−	25.2780i	0.707926	−	1.22616i
$426$		0			0
$427$	2.30165	−	8.58988i	0.111385	−	0.415693i
$428$		0			0
$429$	−5.87747	+	10.9382i	−0.283767	+	0.528099i
$430$		0			0
$431$	1.08094			0.0520671			0.0260336	−	0.999661i	$-0.491712\pi$
$431$	1.08094			0.0520671			0.0260336	+	0.999661i	$0.491712\pi$
$432$		0			0
$433$	−15.5307			−0.746359			−0.373179	−	0.927759i	$-0.621732\pi$
$433$	−15.5307			−0.746359			−0.373179	+	0.927759i	$0.621732\pi$
$434$		0			0
$435$	−2.69833	+	5.02167i	−0.129375	+	0.240771i
$436$		0			0
$437$	−1.16207	+	4.33690i	−0.0555893	+	0.207462i
$438$		0			0
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	−0.806950	−	0.590620i	$-0.798883\pi$
$439$	2.26321	−	3.91999i	0.108017	−	0.187091i	0.914967	+	0.403529i	$0.132217\pi$
$440$		0			0
$441$	−15.9774	+	32.0437i	−0.760831	+	1.52589i
$442$		0			0
$443$	6.82958	+	25.4883i	0.324483	+	1.21099i	0.914830	+	0.403838i	$0.132324\pi$
$443$	6.82958	+	25.4883i	0.324483	+	1.21099i	−0.590347	+	0.807149i	$0.701009\pi$
$444$		0			0
$445$	−0.352904	+	1.31706i	−0.0167293	+	0.0624345i
$446$		0			0
$447$	5.67490	+	5.33856i	0.268414	+	0.252505i
$448$		0			0
$449$			5.94688i			0.280650i	0.990105	+	0.140325i	$0.0448148\pi$
$449$			5.94688i			0.280650i	−0.990105	+	0.140325i	$0.955185\pi$
$450$		0			0
$451$	7.86752	−	7.86752i	0.370467	−	0.370467i
$452$		0			0
$453$	7.71961	+	12.4751i	0.362699	+	0.586133i
$454$		0			0
$455$	−5.27777	+	3.04712i	−0.247426	+	0.142851i
$456$		0			0
$457$	−18.2318	−	10.5261i	−0.852846	−	0.492391i	0.00876413	−	0.999962i	$-0.497210\pi$
$457$	−18.2318	−	10.5261i	−0.852846	−	0.492391i	−0.861610	+	0.507571i	$0.830544\pi$
$458$		0			0
$459$	−3.17791	−	34.6002i	−0.148332	−	1.61500i
$460$		0			0
$461$	10.2518	+	38.2603i	0.477475	+	1.78196i	0.611788	+	0.791021i	$0.290450\pi$
$461$	10.2518	+	38.2603i	0.477475	+	1.78196i	−0.134314	+	0.990939i	$0.542883\pi$
$462$		0			0
$463$	−9.98020	+	5.76207i	−0.463819	+	0.267786i	−0.713649	−	0.700504i	$-0.752959\pi$
$463$	−9.98020	+	5.76207i	−0.463819	+	0.267786i	0.249829	+	0.968290i	$0.419625\pi$
$464$		0			0
$465$	−7.66573	−	1.80515i	−0.355490	−	0.0837118i
$466$		0			0
$467$	25.1476	+	25.1476i	1.16369	+	1.16369i	0.983661	+	0.180032i	$0.0576202\pi$
$467$	25.1476	+	25.1476i	1.16369	+	1.16369i	0.180032	+	0.983661i	$0.442380\pi$
$468$		0			0
$469$	−25.5197	+	25.5197i	−1.17839	+	1.17839i
$470$		0			0
$471$	−21.3551	−	20.0894i	−0.983990	−	0.925671i
$472$		0			0
$473$	−18.1672	−	31.4664i	−0.835327	−	1.44683i
$474$		0			0
$475$	4.22335	−	1.13164i	0.193780	−	0.0519233i
$476$		0			0
$477$	1.42367	−	6.99660i	0.0651853	−	0.320352i
$478$		0			0
$479$	−2.64784	+	4.58619i	−0.120983	+	0.209548i	−0.920155	−	0.391553i	$-0.871938\pi$
$479$	−2.64784	+	4.58619i	−0.120983	+	0.209548i	0.799173	+	0.601101i	$0.205271\pi$
$480$		0			0
$481$	−1.88491	−	3.26477i	−0.0859447	−	0.148861i
$482$		0			0
$483$	−29.7598	−	15.9911i	−1.35412	−	0.727618i
$484$		0			0
$485$	4.13069	+	4.13069i	0.187565	+	0.187565i
$486$		0			0
$487$	−1.85543			−0.0840775			−0.0420387	−	0.999116i	$-0.513385\pi$
$487$	−1.85543			−0.0840775			−0.0420387	+	0.999116i	$0.513385\pi$
$488$		0			0
$489$	−9.66962	−	32.1302i	−0.437275	−	1.45298i
$490$		0			0
$491$	3.49505	+	0.936497i	0.157730	+	0.0422635i	0.336820	−	0.941569i	$-0.390649\pi$
$491$	3.49505	+	0.936497i	0.157730	+	0.0422635i	−0.179090	+	0.983833i	$0.557315\pi$
$492$		0			0
$493$	−26.6792	+	7.14866i	−1.20157	+	0.321960i
$494$		0			0
$495$	−5.38141	−	8.13090i	−0.241877	−	0.365457i
$496$		0			0
$497$	30.3446	+	17.5194i	1.36114	+	0.785854i
$498$		0			0
$499$	12.0253	+	3.22216i	0.538325	+	0.144244i	0.517730	−	0.855544i	$-0.326777\pi$
$499$	12.0253	+	3.22216i	0.538325	+	0.144244i	0.0205953	+	0.999788i	$0.493444\pi$
$500$		0			0
$501$	0.434592	+	14.2305i	0.0194162	+	0.635774i
$502$		0			0
$503$			16.6233i			0.741198i	0.928793	+	0.370599i	$0.120848\pi$
$503$			16.6233i			0.741198i	−0.928793	+	0.370599i	$0.879152\pi$
$504$		0			0
$505$		−	11.5701i		−	0.514862i
$506$		0			0
$507$	−14.5973	+	9.03281i	−0.648288	+	0.401161i
$508$		0			0
$509$	15.1091	+	4.04848i	0.669700	+	0.179446i	0.577620	−	0.816306i	$-0.303982\pi$
$509$	15.1091	+	4.04848i	0.669700	+	0.179446i	0.0920802	+	0.995752i	$0.470648\pi$
$510$		0			0
$511$	−36.6722	−	21.1727i	−1.62228	−	0.936624i
$512$		0			0
$513$	3.32830	−	4.00153i	0.146948	−	0.176672i
$514$		0			0
$515$	−11.4506	+	3.06819i	−0.504575	+	0.135200i
$516$		0			0
$517$	9.70511	+	2.60048i	0.426830	+	0.114369i
$518$		0			0
$519$	16.4320	+	3.86945i	0.721285	+	0.169850i
$520$		0			0
$521$	−40.4461			−1.77198			−0.885988	−	0.463709i	$-0.846518\pi$
$521$	−40.4461			−1.77198			−0.885988	+	0.463709i	$0.846518\pi$
$522$		0			0
$523$	−7.69126	−	7.69126i	−0.336315	−	0.336315i	0.518663	−	0.854979i	$-0.326430\pi$
$523$	−7.69126	−	7.69126i	−0.336315	−	0.336315i	−0.854979	+	0.518663i	$0.826430\pi$
$524$		0			0
$525$	1.00426	+	32.8842i	0.0438296	+	1.43518i
$526$		0			0
$527$	−19.0784	−	33.0448i	−0.831069	−	1.43945i
$528$		0			0
$529$	−1.45387	+	2.51818i	−0.0632119	+	0.109486i
$530$		0			0
$531$	−0.990498	−	2.96055i	−0.0429840	−	0.128477i
$532$		0			0
$533$	−4.63102	+	1.24088i	−0.200592	+	0.0537484i
$534$		0			0
$535$	0.0549239	+	0.0951309i	0.00237457	+	0.00411287i
$536$		0			0
$537$	6.09583	−	1.83455i	0.263054	−	0.0791666i
$538$		0			0
$539$	−34.4241	+	34.4241i	−1.48275	+	1.48275i
$540$		0			0
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	0.239302	−	0.970945i	$-0.423081\pi$
$541$	−17.0176	−	17.0176i	−0.731643	−	0.731643i	−0.970945	+	0.239302i	$0.923081\pi$
$542$		0			0
$543$	4.89138	+	16.2531i	0.209909	+	0.697486i
$544$		0			0
$545$	−8.59443	+	4.96200i	−0.368145	+	0.212549i
$546$		0			0
$547$	5.77510	+	21.5530i	0.246926	+	0.921539i	0.972406	+	0.233296i	$0.0749511\pi$
$547$	5.77510	+	21.5530i	0.246926	+	0.921539i	−0.725480	+	0.688243i	$0.758382\pi$
$548$		0			0
$549$	−4.59170	−	4.06261i	−0.195969	−	0.173388i
$550$		0			0
$551$	−3.58311	−	2.06871i	−0.152645	−	0.0881299i
$552$		0			0
$553$	−52.1457	+	30.1064i	−2.21746	+	1.28025i
$554$		0			0
$555$	2.95882	−	0.0903606i	0.125595	−	0.00383559i
$556$		0			0
$557$	−11.6516	+	11.6516i	−0.493695	+	0.493695i	−0.909468	−	0.415773i	$-0.863511\pi$
$557$	−11.6516	+	11.6516i	−0.493695	+	0.493695i	0.415773	+	0.909468i	$0.363511\pi$
$558$		0			0
$559$			15.6566i			0.662203i
$560$		0			0
$561$	10.8284	−	45.9837i	0.457174	−	1.94143i
$562$		0			0
$563$	1.30826	−	4.88249i	0.0551365	−	0.205772i	−0.932862	−	0.360233i	$-0.882697\pi$
$563$	1.30826	−	4.88249i	0.0551365	−	0.205772i	0.987999	+	0.154460i	$0.0493639\pi$
$564$		0			0
$565$	1.71944	+	6.41702i	0.0723372	+	0.269966i
$566$		0			0
$567$	23.5674	+	31.2785i	0.989737	+	1.31357i
$568$		0			0
$569$	2.79764	−	4.84565i	0.117283	−	0.203140i	−0.801407	−	0.598119i	$-0.795915\pi$
$569$	2.79764	−	4.84565i	0.117283	−	0.203140i	0.918690	+	0.394979i	$0.129248\pi$
$570$		0			0
$571$	2.31993	−	8.65808i	0.0970859	−	0.362329i	−0.900242	−	0.435391i	$-0.856610\pi$
$571$	2.31993	−	8.65808i	0.0970859	−	0.362329i	0.997327	+	0.0730613i	$0.0232769\pi$
$572$		0			0
$573$	−12.7001	−	20.5237i	−0.530554	−	0.857392i
$574$		0			0
$575$	−19.5662			−0.815966
$576$		0			0
$577$	16.6893			0.694785			0.347393	−	0.937720i	$-0.387067\pi$
$577$	16.6893			0.694785			0.347393	+	0.937720i	$0.387067\pi$
$578$		0			0
$579$	4.64297	−	0.141794i	0.192955	−	0.00589274i
$580$		0			0
$581$	−3.55636	+	13.2725i	−0.147543	+	0.550637i
$582$		0			0
$583$	4.85387	−	8.40714i	0.201027	−	0.348188i
$584$		0			0
$585$	0.256384	+	4.19367i	0.0106002	+	0.173387i
$586$		0			0
$587$	−1.34545	−	5.02128i	−0.0555325	−	0.207250i	0.932585	−	0.360950i	$-0.117548\pi$
$587$	−1.34545	−	5.02128i	−0.0555325	−	0.207250i	−0.988118	+	0.153700i	$0.950881\pi$
$588$		0			0
$589$	1.47934	−	5.52099i	0.0609553	−	0.227488i
$590$		0			0
$591$	−33.3923	+	10.0495i	−1.37358	+	0.413380i
$592$		0			0
$593$		−	44.7927i		−	1.83942i	−0.392602	−	0.919708i	$-0.628425\pi$
$593$		−	44.7927i		−	1.83942i	0.392602	−	0.919708i	$-0.371575\pi$
$594$		0			0
$595$	16.3947	−	16.3947i	0.672116	−	0.672116i
$596$		0			0
$597$	6.47733	−	12.0545i	0.265100	−	0.493358i
$598$		0			0
$599$	27.1165	−	15.6557i	1.10795	−	0.639674i	0.169651	−	0.985504i	$-0.445736\pi$
$599$	27.1165	−	15.6557i	1.10795	−	0.639674i	0.938297	+	0.345830i	$0.112403\pi$
$600$		0			0
$601$	15.4248	+	8.90549i	0.629189	+	0.363262i	0.780438	−	0.625233i	$-0.214996\pi$
$601$	15.4248	+	8.90549i	0.629189	+	0.363262i	−0.151249	+	0.988496i	$0.548330\pi$
$602$		0			0
$603$	7.89436	+	23.5958i	0.321483	+	0.960897i
$604$		0			0
$605$	−1.16261	−	4.33891i	−0.0472667	−	0.176402i
$606$		0			0
$607$	−29.3159	+	16.9255i	−1.18989	+	0.686986i	−0.958283	−	0.285823i	$-0.907733\pi$
$607$	−29.3159	+	16.9255i	−1.18989	+	0.686986i	−0.231612	+	0.972808i	$0.574400\pi$
$608$		0			0
$609$	21.3313	−	22.6753i	0.864389	−	0.918848i
$610$		0			0
$611$	−3.06141	−	3.06141i	−0.123852	−	0.123852i
$612$		0			0
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	−0.898448	−	0.439081i	$-0.855304\pi$
$613$	−11.3734	+	11.3734i	−0.459367	+	0.459367i	0.439081	+	0.898448i	$0.355304\pi$
$614$		0			0
$615$	0.862923	−	3.66448i	0.0347964	−	0.147766i
$616$		0			0
$617$	18.0269	+	31.2236i	0.725738	+	1.25701i	0.958670	+	0.284521i	$0.0918346\pi$
$617$	18.0269	+	31.2236i	0.725738	+	1.25701i	−0.232932	+	0.972493i	$0.574832\pi$
$618$		0			0
$619$	−16.0209	+	4.29280i	−0.643936	+	0.172542i	−0.565986	−	0.824415i	$-0.691504\pi$
$619$	−16.0209	+	4.29280i	−0.643936	+	0.172542i	−0.0779503	+	0.996957i	$0.524838\pi$
$620$		0			0
$621$	−19.0213	+	13.4418i	−0.763298	+	0.539400i
$622$		0			0
$623$	3.72312	−	6.44863i	0.149163	−	0.258359i
$624$		0			0
$625$	7.93964	+	13.7519i	0.317585	+	0.550074i
$626$		0			0
$627$	6.01764	−	3.72372i	0.240322	−	0.148711i
$628$		0			0
$629$	10.1416	+	10.1416i	0.404371	+	0.404371i
$630$		0			0
$631$	−24.4330			−0.972664			−0.486332	−	0.873774i	$-0.661665\pi$
$631$	−24.4330			−0.972664			−0.486332	+	0.873774i	$0.661665\pi$
$632$		0			0
$633$	16.2315	−	17.2541i	0.645144	−	0.685790i
$634$		0			0
$635$	−3.73158	−	0.999874i	−0.148083	−	0.0396788i
$636$		0			0
$637$	20.2629	−	5.42943i	0.802845	−	0.215122i
$638$		0			0
$639$	20.1441	−	13.3323i	0.796890	−	0.527420i
$640$		0			0
$641$	−40.0952	−	23.1490i	−1.58366	−	0.914329i	−0.994318	−	0.106448i	$-0.966052\pi$
$641$	−40.0952	−	23.1490i	−1.58366	−	0.914329i	−0.589346	−	0.807881i	$-0.700615\pi$
$642$		0			0
$643$	−10.5870	−	2.83678i	−0.417511	−	0.111872i	0.0439466	−	0.999034i	$-0.486007\pi$
$643$	−10.5870	−	2.83678i	−0.417511	−	0.111872i	−0.461458	+	0.887162i	$0.652674\pi$
$644$		0			0
$645$	−10.8297	−	5.81918i	−0.426418	−	0.229130i
$646$		0			0
$647$			10.0479i			0.395025i	0.980300	+	0.197512i	$0.0632863\pi$
$647$			10.0479i			0.395025i	−0.980300	+	0.197512i	$0.936714\pi$
$648$		0			0
$649$		−	4.24456i		−	0.166614i
$650$		0			0
$651$	37.8851	+	20.3570i	1.48483	+	0.797855i
$652$		0			0
$653$	−25.5935	−	6.85777i	−1.00155	−	0.268365i	−0.279457	−	0.960158i	$-0.590154\pi$
$653$	−25.5935	−	6.85777i	−1.00155	−	0.268365i	−0.722096	+	0.691793i	$0.756821\pi$
$654$		0			0
$655$	14.6427	+	8.45394i	0.572136	+	0.330323i
$656$		0			0
$657$	−24.3447	+	16.1125i	−0.949778	+	0.628608i
$658$		0			0
$659$	−6.76233	+	1.81196i	−0.263423	+	0.0705840i	−0.388113	−	0.921612i	$-0.626873\pi$
$659$	−6.76233	+	1.81196i	−0.263423	+	0.0705840i	0.124690	+	0.992196i	$0.460206\pi$
$660$		0			0
$661$	20.1902	+	5.40993i	0.785306	+	0.210422i	0.629123	−	0.777306i	$-0.283414\pi$
$661$	20.1902	+	5.40993i	0.785306	+	0.210422i	0.156183	+	0.987728i	$0.450081\pi$
$662$		0			0
$663$	−13.9481	+	14.8269i	−0.541701	+	0.575830i
$664$		0			0
$665$	3.47311			0.134681
$666$		0			0
$667$	13.0920	+	13.0920i	0.506926	+	0.506926i
$668$		0			0
$669$	−41.3907	+	25.6126i	−1.60026	+	0.990240i
$670$		0			0
$671$	−4.16791	−	7.21904i	−0.160901	−	0.278688i
$672$		0			0
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	−0.781941	−	0.623353i	$-0.785770\pi$
$673$	3.86200	−	6.68918i	0.148869	−	0.257849i	0.930810	+	0.365504i	$0.119103\pi$
$674$		0			0
$675$	20.5978	+	9.49670i	0.792808	+	0.365528i
$676$		0			0
$677$	7.62160	−	2.04220i	0.292922	−	0.0784882i	−0.109366	−	0.994002i	$-0.534882\pi$
$677$	7.62160	−	2.04220i	0.292922	−	0.0784882i	0.402287	+	0.915513i	$0.368215\pi$
$678$		0			0
$679$	−15.9508	−	27.6277i	−0.612137	−	1.06025i
$680$		0			0
$681$	0.201396	−	0.855248i	0.00771752	−	0.0327732i
$682$		0			0
$683$	23.0318	−	23.0318i	0.881288	−	0.881288i	−0.112378	−	0.993666i	$-0.535847\pi$
$683$	23.0318	−	23.0318i	0.881288	−	0.881288i	0.993666	+	0.112378i	$0.0358467\pi$
$684$		0			0
$685$	−3.31144	−	3.31144i	−0.126524	−	0.126524i
$686$		0			0
$687$	17.9605	−	19.0921i	0.685237	−	0.728409i
$688$		0			0
$689$	−3.62267	+	2.09155i	−0.138013	+	0.0796816i
$690$		0			0
$691$	6.66520	+	24.8749i	0.253556	+	0.946285i	0.968888	+	0.247500i	$0.0796089\pi$
$691$	6.66520	+	24.8749i	0.253556	+	0.946285i	−0.715332	+	0.698785i	$0.753724\pi$
$692$		0			0
$693$	16.8944	+	50.4964i	0.641764	+	1.91820i
$694$		0			0
$695$	4.98218	+	2.87646i	0.188985	+	0.109111i
$696$		0			0
$697$	15.7965	−	9.12014i	0.598337	−	0.345450i
$698$		0			0
$699$	−12.7048	+	23.6440i	−0.480540	+	0.894299i
$700$		0			0
$701$	35.0396	−	35.0396i	1.32343	−	1.32343i	0.412443	−	0.910983i	$-0.364675\pi$
$701$	35.0396	−	35.0396i	1.32343	−	1.32343i	0.910983	−	0.412443i	$-0.135325\pi$
$702$		0			0
$703$			2.14843i			0.0810295i
$704$		0			0
$705$	3.25543	−	0.979727i	0.122607	−	0.0368987i
$706$		0			0
$707$	−16.3534	+	61.0318i	−0.615034	+	2.29534i
$708$		0			0
$709$	−12.2110	−	45.5722i	−0.458595	−	1.71150i	−0.677297	−	0.735710i	$-0.736849\pi$
$709$	−12.2110	−	45.5722i	−0.458595	−	1.71150i	0.218702	−	0.975792i	$-0.429818\pi$
$710$		0			0
$711$	2.53314	+	41.4345i	0.0950000	+	1.55392i
$712$		0			0
$713$	−12.7890	+	22.1512i	−0.478951	+	0.829568i
$714$		0			0
$715$	−1.47850	+	5.51784i	−0.0552928	+	0.206356i
$716$		0			0
$717$	−26.3741	+	0.805449i	−0.984959	+	0.0300801i
$718$		0			0
$719$	−26.0582			−0.971806			−0.485903	−	0.874013i	$-0.661509\pi$
$719$	−26.0582			−0.971806			−0.485903	+	0.874013i	$0.661509\pi$
$720$		0			0
$721$	64.7383			2.41098
$722$		0			0
$723$	−16.6004	−	26.8267i	−0.617374	−	0.997695i
$724$		0			0
$725$	4.66655	−	17.4158i	0.173311	−	0.646807i
$726$		0			0
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	−0.759097	−	0.650978i	$-0.774359\pi$
$727$	4.96698	−	8.60307i	0.184215	−	0.319070i	0.943312	+	0.331908i	$0.107692\pi$
$728$		0			0
$729$	26.5483	−	4.91824i	0.983269	−	0.182157i
$730$		0			0
$731$	−15.4167	−	57.5359i	−0.570207	−	2.12804i
$732$		0			0
$733$	3.40512	−	12.7081i	0.125771	−	0.469384i	−0.874095	−	0.485755i	$-0.838545\pi$
$733$	3.40512	−	12.7081i	0.125771	−	0.469384i	0.999866	+	0.0163712i	$0.00521135\pi$
$734$		0			0
$735$	−3.77569	+	16.0338i	−0.139269	+	0.591417i
$736$		0			0
$737$			33.8295i			1.24613i
$738$		0			0
$739$	32.6637	−	32.6637i	1.20155	−	1.20155i	0.227861	−	0.973694i	$-0.426827\pi$
$739$	32.6637	−	32.6637i	1.20155	−	1.20155i	0.973694	−	0.227861i	$-0.0731732\pi$
$740$		0			0
$741$	−3.04791	+	0.0930813i	−0.111968	+	0.00341943i
$742$		0			0
$743$	8.76936	−	5.06299i	0.321717	−	0.185743i	−0.330441	−	0.943827i	$-0.607197\pi$
$743$	8.76936	−	5.06299i	0.321717	−	0.185743i	0.652157	+	0.758084i	$0.273864\pi$
$744$		0			0
$745$	3.10414	+	1.79218i	0.113727	+	0.0656603i
$746$		0			0
$747$	7.09480	+	6.27728i	0.259585	+	0.229674i
$748$		0			0
$749$	−0.155261	−	0.579443i	−0.00567312	−	0.0211724i
$750$		0			0
$751$	22.6187	−	13.0589i	0.825368	−	0.476526i	−0.0268964	−	0.999638i	$-0.508562\pi$
$751$	22.6187	−	13.0589i	0.825368	−	0.476526i	0.852264	+	0.523112i	$0.175229\pi$
$752$		0			0
$753$	−1.54182	−	5.12315i	−0.0561870	−	0.186698i
$754$		0			0
$755$	4.77230	+	4.77230i	0.173682	+	0.173682i
$756$		0			0
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	−0.662183	−	0.749342i	$-0.730370\pi$
$757$	2.39808	−	2.39808i	0.0871596	−	0.0871596i	0.749342	+	0.662183i	$0.230370\pi$
$758$		0			0
$759$	−30.3243	+	9.12612i	−1.10070	+	0.331257i
$760$		0			0
$761$	−23.1857	−	40.1589i	−0.840482	−	1.45576i	−0.889488	−	0.456959i	$-0.848939\pi$
$761$	−23.1857	−	40.1589i	−0.840482	−	1.45576i	0.0490055	−	0.998799i	$-0.484395\pi$
$762$		0			0
$763$	52.3487	−	14.0268i	1.89515	−	0.507804i
$764$		0			0
$765$	−5.07159	−	15.1587i	−0.183364	−	0.548065i
$766$		0			0
$767$	−0.914499	+	1.58396i	−0.0330206	+	0.0571934i
$768$		0			0
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	0.701661	−	0.712511i	$-0.252442\pi$
$769$	−7.38255	−	12.7870i	−0.266222	−	0.461109i	−0.967883	+	0.251401i	$0.919109\pi$
$770$		0			0
$771$	1.01818	+	33.3398i	0.0366688	+	1.20071i
$772$		0			0
$773$	22.1409	+	22.1409i	0.796353	+	0.796353i	0.982518	−	0.186165i	$-0.0596060\pi$
$773$	22.1409	+	22.1409i	0.796353	+	0.796353i	−0.186165	+	0.982518i	$0.559606\pi$
$774$		0			0
$775$	24.9083			0.894731
$776$		0			0
$777$	−15.7354	−	3.70541i	−0.564504	−	0.132931i
$778$		0			0
$779$	2.63922	+	0.707177i	0.0945599	+	0.0253372i
$780$		0			0
$781$	31.7248	−	8.50064i	1.13520	−	0.304177i
$782$		0			0
$783$	−7.42790	−	20.1367i	−0.265451	−	0.719626i
$784$		0			0
$785$	−11.6811	−	6.74410i	−0.416917	−	0.240707i
$786$		0			0
$787$	4.18136	+	1.12039i	0.149050	+	0.0399377i	0.332572	−	0.943078i	$-0.392083\pi$
$787$	4.18136	+	1.12039i	0.149050	+	0.0399377i	−0.183523	+	0.983015i	$0.558750\pi$
$788$		0			0
$789$	−38.8195	+	24.0215i	−1.38201	+	0.855190i
$790$		0			0
$791$		−	36.2799i		−	1.28996i
$792$		0			0
$793$			3.59194i			0.127553i
$794$		0			0
$795$	−0.100266	−	3.28318i	−0.00355608	−	0.116442i
$796$		0			0
$797$	51.5141	+	13.8032i	1.82472	+	0.488933i	0.997352	−	0.0727237i	$-0.0231691\pi$
$797$	51.5141	+	13.8032i	1.82472	+	0.488933i	0.827370	+	0.561657i	$0.189836\pi$
$798$		0			0
$799$	14.2648	+	8.23579i	0.504652	+	0.291361i
$800$		0			0
$801$	−2.83330	−	4.28090i	−0.100110	−	0.151258i
$802$		0			0
$803$	−38.3403	+	10.2732i	−1.35300	+	0.362535i
$804$		0			0
$805$	−15.0126	−	4.02261i	−0.529124	−	0.141778i
$806$		0			0
$807$	−0.427428	−	1.42026i	−0.0150462	−	0.0499954i
$808$		0			0
$809$	30.1140			1.05875			0.529375	−	0.848388i	$-0.322426\pi$
$809$	30.1140			1.05875			0.529375	+	0.848388i	$0.322426\pi$
$810$		0			0
$811$	−20.5672	−	20.5672i	−0.722214	−	0.722214i	0.246842	−	0.969056i	$-0.420607\pi$
$811$	−20.5672	−	20.5672i	−0.722214	−	0.722214i	−0.969056	+	0.246842i	$0.920607\pi$
$812$		0			0
$813$	29.1544	+	15.6657i	1.02249	+	0.549420i
$814$		0			0
$815$	−7.71810	−	13.3681i	−0.270353	−	0.468265i
$816$		0			0
$817$	4.46135	−	7.72728i	0.156083	−	0.270343i
$818$		0			0
$819$	4.57502	−	22.4839i	0.159864	−	0.785649i
$820$		0			0
$821$	31.8546	−	8.53541i	1.11173	−	0.297888i	0.344199	−	0.938897i	$-0.388151\pi$
$821$	31.8546	−	8.53541i	1.11173	−	0.297888i	0.767533	+	0.641009i	$0.221484\pi$
$822$		0			0
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	0.772134	−	0.635460i	$-0.219189\pi$
$823$	−4.71220	−	8.16178i	−0.164257	−	0.284502i	−0.936391	+	0.350958i	$0.885856\pi$
$824$		0			0
$825$	22.4617	+	21.1304i	0.782015	+	0.735666i
$826$		0			0
$827$	38.7468	−	38.7468i	1.34736	−	1.34736i	0.458841	−	0.888518i	$-0.348265\pi$
$827$	38.7468	−	38.7468i	1.34736	−	1.34736i	0.888518	−	0.458841i	$-0.151735\pi$
$828$		0			0
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	0.872548	−	0.488528i	$-0.162466\pi$
$829$	11.0569	+	11.0569i	0.384021	+	0.384021i	−0.488528	+	0.872548i	$0.662466\pi$
$830$		0			0
$831$	11.9070	+	2.80390i	0.413050	+	0.0972662i
$832$		0			0
$833$	−69.1173	+	39.9049i	−2.39477	+	1.38262i
$834$		0			0
$835$	1.69520	+	6.32656i	0.0586647	+	0.218940i
$836$		0			0
$837$	24.2146	−	17.1117i	0.836979	−	0.591468i
$838$		0			0
$839$	−25.3695	−	14.6471i	−0.875853	−	0.505674i	−0.00656388	−	0.999978i	$-0.502089\pi$
$839$	−25.3695	−	14.6471i	−0.875853	−	0.505674i	−0.869289	+	0.494305i	$0.835423\pi$
$840$		0			0
$841$	10.3391	−	5.96927i	0.356520	−	0.205837i
$842$		0			0
$843$	−21.5985	−	34.9038i	−0.743892	−	1.20215i
$844$		0			0
$845$	−5.58412	+	5.58412i	−0.192100	+	0.192100i
$846$		0			0
$847$			24.5309i			0.842891i
$848$		0			0
$849$	0.949637	+	0.893353i	0.0325914	+	0.0306598i
$850$		0			0
$851$	2.48834	−	9.28662i	0.0852992	−	0.318341i
$852$		0			0
$853$	−10.9035	−	40.6922i	−0.373327	−	1.39328i	−0.855774	−	0.517350i	$-0.826918\pi$
$853$	−10.9035	−	40.6922i	−0.373327	−	1.39328i	0.482447	−	0.875925i	$-0.339748\pi$
$854$		0			0
$855$	1.06845	−	2.14283i	0.0365402	−	0.0732834i
$856$		0			0
$857$	14.2207	−	24.6310i	0.485769	−	0.841377i	−0.514097	−	0.857732i	$-0.671873\pi$
$857$	14.2207	−	24.6310i	0.485769	−	0.841377i	0.999866	+	0.0163548i	$0.00520611\pi$
$858$		0			0
$859$	0.896437	−	3.34555i	0.0305860	−	0.114149i	−0.948945	−	0.315441i	$-0.897848\pi$
$859$	0.896437	−	3.34555i	0.0305860	−	0.114149i	0.979531	+	0.201293i	$0.0645142\pi$
$860$		0			0
$861$	−9.73136	+	18.1104i	−0.331644	+	0.617199i
$862$		0			0
$863$	11.1356			0.379062			0.189531	−	0.981875i	$-0.439303\pi$
$863$	11.1356			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$864$		0			0
$865$	7.76622			0.264059
$866$		0			0
$867$	22.7207	−	42.2839i	0.771635	−	1.43604i
$868$		0			0
$869$	−14.6080	+	54.5177i	−0.495541	+	1.84939i
$870$		0			0
$871$	7.28863	−	12.6243i	0.246966	−	0.427757i
$872$		0			0
$873$	−21.9527	+	1.34210i	−0.742986	+	0.0454231i
$874$		0			0
$875$	8.40437	+	31.3655i	0.284119	+	1.06035i
$876$		0			0
$877$	7.32539	−	27.3387i	0.247361	−	0.923163i	−0.724821	−	0.688937i	$-0.758078\pi$
$877$	7.32539	−	27.3387i	0.247361	−	0.923163i	0.972182	−	0.234226i	$-0.0752557\pi$
$878$		0			0
$879$	25.8859	+	24.3517i	0.873111	+	0.821362i
$880$		0			0
$881$			4.86363i			0.163860i	0.996638	+	0.0819299i	$0.0261084\pi$
$881$			4.86363i			0.163860i	−0.996638	+	0.0819299i	$0.973892\pi$
$882$		0			0
$883$	−8.56478	+	8.56478i	−0.288228	+	0.288228i	−0.836379	−	0.548151i	$-0.815332\pi$
$883$	−8.56478	+	8.56478i	−0.288228	+	0.288228i	0.548151	+	0.836379i	$0.315332\pi$
$884$		0			0
$885$	−0.755727	−	1.22128i	−0.0254035	−	0.0410528i
$886$		0			0
$887$	−3.99885	+	2.30874i	−0.134268	+	0.0775199i	−0.565630	−	0.824659i	$-0.691367\pi$
$887$	−3.99885	+	2.30874i	−0.134268	+	0.0775199i	0.431361	+	0.902179i	$0.358033\pi$
$888$		0			0
$889$	18.2707	+	10.5486i	0.612780	+	0.353789i
$890$		0			0
$891$	36.3525	+	5.11099i	1.21785	+	0.171225i
$892$		0			0
$893$	0.638605	+	2.38330i	0.0213701	+	0.0797543i
$894$		0			0
$895$	2.53624	−	1.46430i	0.0847772	−	0.0489461i
$896$		0			0
$897$	13.2824	+	3.12779i	0.443488	+	0.104434i
$898$		0			0
$899$	−16.6665	−	16.6665i	−0.555859	−	0.555859i
$900$		0			0
$901$	11.2533	−	11.2533i	0.374903	−	0.374903i
$902$		0			0
$903$	48.9012	+	46.0029i	1.62733	+	1.53088i
$904$		0			0
$905$	3.90421	+	6.76228i	0.129780	+	0.224786i
$906$		0			0
$907$	−8.35931	+	2.23987i	−0.277566	+	0.0743737i	−0.394917	−	0.918717i	$-0.629227\pi$
$907$	−8.35931	+	2.23987i	−0.277566	+	0.0743737i	0.117350	+	0.993091i	$0.462560\pi$
$908$		0			0
$909$	32.6244	+	28.8652i	1.08208	+	0.957398i
$910$		0			0
$911$	23.9969	−	41.5638i	0.795052	−	1.37707i	−0.127755	−	0.991806i	$-0.540777\pi$
$911$	23.9969	−	41.5638i	0.795052	−	1.37707i	0.922806	−	0.385264i	$-0.125890\pi$
$912$		0			0
$913$	6.43999	+	11.1544i	0.213133	+	0.369156i
$914$		0			0
$915$	−2.48454	−	1.33504i	−0.0821365	−	0.0441349i
$916$		0			0
$917$	−65.2905	−	65.2905i	−2.15608	−	2.15608i
$918$		0			0
$919$	−51.8939			−1.71182			−0.855910	−	0.517124i	$-0.827003\pi$
$919$	−51.8939			−1.71182			−0.855910	+	0.517124i	$0.827003\pi$
$920$		0			0
$921$	10.8320	+	35.9927i	0.356928	+	1.18600i
$922$		0			0
$923$	−13.6703	−	3.66296i	−0.449965	−	0.120568i
$924$		0			0
$925$	−9.04347	+	2.42319i	−0.297347	+	0.0796740i
$926$		0			0
$927$	19.9157	−	39.9421i	0.654119	−	1.31187i
$928$		0			0
$929$	8.80130	+	5.08143i	0.288761	+	0.166716i	0.637383	−	0.770547i	$-0.280017\pi$
$929$	8.80130	+	5.08143i	0.288761	+	0.166716i	−0.348622	+	0.937263i	$0.613350\pi$
$930$		0			0
$931$	−11.5478	−	3.09423i	−0.378465	−	0.101409i
$932$		0			0
$933$	−0.0352020	−	1.15267i	−0.00115246	−	0.0377368i
$934$		0			0
$935$		−	21.7332i		−	0.710751i
$936$		0			0
$937$			37.8157i			1.23539i	0.786420	+	0.617693i	$0.211932\pi$
$937$			37.8157i			1.23539i	−0.786420	+	0.617693i	$0.788068\pi$
$938$		0			0
$939$	−24.3684	+	15.0792i	−0.795232	+	0.492090i
$940$		0			0
$941$	−34.3731	−	9.21025i	−1.12053	−	0.300246i	−0.349433	−	0.936961i	$-0.613626\pi$
$941$	−34.3731	−	9.21025i	−1.12053	−	0.300246i	−0.771099	+	0.636716i	$0.780293\pi$
$942$		0			0
$943$	−10.5890	−	6.11357i	−0.344826	−	0.199085i
$944$		0			0
$945$	13.8517	+	11.5212i	0.450595	+	0.374786i
$946$		0			0
$947$	10.0399	−	2.69018i	0.326253	−	0.0874191i	−0.0919752	−	0.995761i	$-0.529318\pi$
$947$	10.0399	−	2.69018i	0.326253	−	0.0874191i	0.418228	+	0.908342i	$0.362651\pi$
$948$		0			0
$949$	16.5210	+	4.42678i	0.536293	+	0.143699i
$950$		0			0
$951$	11.4598	+	2.69860i	0.371611	+	0.0875080i
$952$		0			0
$953$	−24.6743			−0.799280			−0.399640	−	0.916672i	$-0.630865\pi$
$953$	−24.6743			−0.799280			−0.399640	+	0.916672i	$0.630865\pi$
$954$		0			0
$955$	−7.85126	−	7.85126i	−0.254061	−	0.254061i
$956$		0			0
$957$	−0.890777	−	29.1681i	−0.0287947	−	0.942871i
$958$		0			0
$959$	12.7873	+	22.1482i	0.412922	+	0.715203i
$960$		0			0
$961$	0.780708	−	1.35223i	0.0251841	−	0.0436202i
$962$		0			0
$963$	−0.405268	−	0.0824639i	−0.0130596	−	0.00265736i
$964$		0			0
$965$	2.06416	−	0.553089i	0.0664475	−	0.0178046i
$966$		0			0
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	0.590939	−	0.806716i	$-0.298757\pi$
$967$	−12.5371	−	21.7150i	−0.403167	−	0.698306i	−0.994106	+	0.108410i	$0.965424\pi$
$968$		0			0
$969$	11.1090	−	3.34327i	0.356873	−	0.107401i
$970$		0			0
$971$	−18.9203	+	18.9203i	−0.607180	+	0.607180i	−0.942208	−	0.335028i	$-0.891254\pi$
$971$	−18.9203	+	18.9203i	−0.607180	+	0.607180i	0.335028	+	0.942208i	$0.391254\pi$
$972$		0			0
$973$	−22.2152	−	22.2152i	−0.712186	−	0.712186i
$974$		0			0
$975$	−3.82952	−	12.7247i	−0.122643	−	0.407517i
$976$		0			0
$977$	−12.1897	+	7.03771i	−0.389982	+	0.225156i	−0.682152	−	0.731210i	$-0.738956\pi$
$977$	−12.1897	+	7.03771i	−0.389982	+	0.225156i	0.292170	+	0.956366i	$0.405623\pi$
$978$		0			0
$979$	−1.80650	−	6.74196i	−0.0577360	−	0.215474i
$980$		0			0
$981$	7.45005	−	36.6132i	0.237862	−	1.16897i
$982$		0			0
$983$	0.562149	+	0.324557i	0.0179298	+	0.0103518i	0.508938	−	0.860803i	$-0.330038\pi$
$983$	0.562149	+	0.324557i	0.0179298	+	0.0103518i	−0.491008	+	0.871155i	$0.663372\pi$
$984$		0			0
$985$	−13.8933	+	8.02129i	−0.442677	+	0.255579i
$986$		0			0
$987$	−18.5571	+	0.566722i	−0.590678	+	0.0180390i
$988$		0			0
$989$	−28.2341	+	28.2341i	−0.897792	+	0.897792i
$990$		0			0
$991$			36.5529i			1.16114i	0.814210	+	0.580571i	$0.197171\pi$
$991$			36.5529i			1.16114i	−0.814210	+	0.580571i	$0.802829\pi$
$992$		0			0
$993$	3.86176	−	16.3993i	0.122549	−	0.520417i
$994$		0			0
$995$	1.62940	−	6.08100i	0.0516554	−	0.192781i
$996$		0			0
$997$	−2.07498	−	7.74395i	−0.0657154	−	0.245253i	0.925253	−	0.379352i	$-0.123853\pi$
$997$	−2.07498	−	7.74395i	−0.0657154	−	0.245253i	−0.990968	+	0.134098i	$0.957186\pi$
$998$		0			0
$999$	−7.12691	+	8.56848i	−0.225485	+	0.271095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.8		88
3.2	odd	2		1728.2.z.a.1007.13		88
4.3	odd	2		144.2.u.a.83.20	yes	88
9.4	even	3		1728.2.z.a.1583.13		88
9.5	odd	6	inner	576.2.y.a.239.4		88
12.11	even	2		432.2.v.a.35.3		88
16.5	even	4		144.2.u.a.11.12	✓	88
16.11	odd	4	inner	576.2.y.a.335.4		88
36.23	even	6		144.2.u.a.131.12	yes	88
36.31	odd	6		432.2.v.a.179.11		88
48.5	odd	4		432.2.v.a.251.11		88
48.11	even	4		1728.2.z.a.143.13		88
144.5	odd	12		144.2.u.a.59.20	yes	88
144.59	even	12	inner	576.2.y.a.527.8		88
144.85	even	12		432.2.v.a.395.3		88
144.139	odd	12		1728.2.z.a.719.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.12	✓	88	16.5	even	4
144.2.u.a.59.20	yes	88	144.5	odd	12
144.2.u.a.83.20	yes	88	4.3	odd	2
144.2.u.a.131.12	yes	88	36.23	even	6
432.2.v.a.35.3		88	12.11	even	2
432.2.v.a.179.11		88	36.31	odd	6
432.2.v.a.251.11		88	48.5	odd	4
432.2.v.a.395.3		88	144.85	even	12
576.2.y.a.47.8		88	1.1	even	1	trivial
576.2.y.a.239.4		88	9.5	odd	6	inner
576.2.y.a.335.4		88	16.11	odd	4	inner
576.2.y.a.527.8		88	144.59	even	12	inner
1728.2.z.a.143.13		88	48.11	even	4
1728.2.z.a.719.13		88	144.139	odd	12
1728.2.z.a.1007.13		88	3.2	odd	2
1728.2.z.a.1583.13		88	9.4	even	3

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.819834 + 1.52574i) q^{3} +(-0.206232 + 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(-1.65574 - 2.50170i) q^{9} +O(q^{10})\)	\(q+(-0.819834 + 1.52574i) q^{3} +(-0.206232 + 0.769670i) q^{5} +(2.17574 - 3.76849i) q^{7} +(-1.65574 - 2.50170i) q^{9} +(-1.05570 - 3.93991i) q^{11} +(-0.454903 + 1.69772i) q^{13} +(-1.00524 - 0.945658i) q^{15} -6.68683i q^{17} +(0.708282 - 0.708282i) q^{19} +(3.96598 + 6.40914i) q^{21} +(-3.88191 + 2.24122i) q^{23} +(3.78027 + 2.18254i) q^{25} +(5.17437 - 0.475249i) q^{27} +(-1.06907 - 3.98981i) q^{29} +(4.94177 - 2.85313i) q^{31} +(6.87676 + 1.61936i) q^{33} +(2.45179 + 2.45179i) q^{35} +(-1.51665 + 1.51665i) q^{37} +(-2.21733 - 2.08591i) q^{39} +(1.36389 + 2.36233i) q^{41} +(8.60436 - 2.30553i) q^{43} +(2.26695 - 0.758445i) q^{45} +(-1.23164 + 2.13327i) q^{47} +(-5.96768 - 10.3363i) q^{49} +(10.2023 + 5.48209i) q^{51} +(1.68291 + 1.68291i) q^{53} +3.25015 q^{55} +(0.499978 + 1.66133i) q^{57} +(1.00516 + 0.269331i) q^{59} +(1.97401 - 0.528935i) q^{61} +(-13.0301 + 0.796606i) q^{63} +(-1.21287 - 0.700250i) q^{65} +(-8.01120 - 2.14659i) q^{67} +(-0.236992 - 7.76019i) q^{69} +8.05218i q^{71} -9.73126i q^{73} +(-6.42917 + 3.97837i) q^{75} +(-17.1444 - 4.59383i) q^{77} +(-11.9835 - 6.91865i) q^{79} +(-3.51702 + 8.28436i) q^{81} +(-3.05012 + 0.817277i) q^{83} +(5.14666 + 1.37904i) q^{85} +(6.96385 + 1.63987i) q^{87} +1.71120 q^{89} +(5.40809 + 5.40809i) q^{91} +(0.301697 + 9.87893i) q^{93} +(0.399073 + 0.691214i) q^{95} +(3.66561 - 6.34903i) q^{97} +(-8.10851 + 9.16451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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