LMFDB - Embedded newform 980.2.x.m.67.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.9
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.212826 - 1.39811i) q^{2} +(0.807254 - 0.216303i) q^{3} +(-1.90941 + 0.595107i) q^{4} +(0.780454 + 2.09545i) q^{5} +(-0.474220 - 1.08259i) q^{6} +(1.23840 + 2.54291i) q^{8} +(-1.99320 + 1.15078i) q^{9} +(2.76356 - 1.53712i) q^{10} +(-4.21811 - 2.43533i) q^{11} +(-1.41266 + 0.893414i) q^{12} +(-0.247904 + 0.247904i) q^{13} +(1.08328 + 1.52274i) q^{15} +(3.29169 - 2.27261i) q^{16} +(-5.83537 + 1.56358i) q^{17} +(2.03311 + 2.54180i) q^{18} +(-1.48858 - 2.57830i) q^{19} +(-2.73722 - 3.53661i) q^{20} +(-2.50713 + 6.41567i) q^{22} +(1.70618 - 6.36754i) q^{23} +(1.54974 + 1.78490i) q^{24} +(-3.78178 + 3.27080i) q^{25} +(0.399357 + 0.293836i) q^{26} +(-3.13296 + 3.13296i) q^{27} -4.67111i q^{29} +(1.89841 - 1.83862i) q^{30} +(-5.75848 - 3.32466i) q^{31} +(-3.87791 - 4.11847i) q^{32} +(-3.93186 - 1.05354i) q^{33} +(3.42797 + 7.82570i) q^{34} +(3.12101 - 3.38347i) q^{36} +(-0.641729 + 2.39496i) q^{37} +(-3.28794 + 2.62993i) q^{38} +(-0.146499 + 0.253744i) q^{39} +(-4.36201 + 4.57961i) q^{40} +1.15345 q^{41} +(-3.23212 - 3.23212i) q^{43} +(9.50338 + 2.13981i) q^{44} +(-3.96699 - 3.27852i) q^{45} +(-9.26562 - 1.03024i) q^{46} +(-4.74443 - 1.27127i) q^{47} +(2.16566 - 2.54658i) q^{48} +(5.37779 + 4.59123i) q^{50} +(-4.37242 + 2.52442i) q^{51} +(0.325821 - 0.620880i) q^{52} +(0.0828048 + 0.309032i) q^{53} +(5.04699 + 3.71344i) q^{54} +(1.81106 - 10.7395i) q^{55} +(-1.75936 - 1.75936i) q^{57} +(-6.53071 + 0.994133i) q^{58} +(0.423416 - 0.733378i) q^{59} +(-2.97461 - 2.26288i) q^{60} +(5.04573 + 8.73945i) q^{61} +(-3.42268 + 8.75855i) q^{62} +(-4.93275 + 6.29825i) q^{64} +(-0.712947 - 0.325992i) q^{65} +(-0.636158 + 5.72138i) q^{66} +(0.721946 + 2.69434i) q^{67} +(10.2116 - 6.45819i) q^{68} -5.50928i q^{69} +6.49911i q^{71} +(-5.39469 - 3.64341i) q^{72} +(0.321006 + 1.19801i) q^{73} +(3.48499 + 0.387495i) q^{74} +(-2.34538 + 3.45838i) q^{75} +(4.37668 + 4.03717i) q^{76} +(0.385940 + 0.150818i) q^{78} +(4.44724 + 7.70284i) q^{79} +(7.33114 + 5.12390i) q^{80} +(1.60090 - 2.77285i) q^{81} +(-0.245484 - 1.61264i) q^{82} +(10.8443 + 10.8443i) q^{83} +(-7.83063 - 11.0074i) q^{85} +(-3.83097 + 5.20673i) q^{86} +(-1.01038 - 3.77077i) q^{87} +(0.969119 - 13.7422i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-3.73945 + 6.24404i) q^{90} +(0.531576 + 13.1736i) q^{92} +(-5.36769 - 1.43827i) q^{93} +(-0.767630 + 6.90379i) q^{94} +(4.24092 - 5.13149i) q^{95} +(-4.02130 - 2.48585i) q^{96} +(2.35897 + 2.35897i) q^{97} +11.2101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.212826	−	1.39811i	−0.150491	−	0.988611i
$2$	−0.212826	−	1.39811i	−0.150491	−	0.988611i
$3$	0.807254	−	0.216303i	0.466069	−	0.124883i	−0.0181397	−	0.999835i	$-0.505774\pi$
$3$	0.807254	−	0.216303i	0.466069	−	0.124883i	0.484208	+	0.874953i	$0.339108\pi$
$4$	−1.90941	+	0.595107i	−0.954705	+	0.297554i
$5$	0.780454	+	2.09545i	0.349030	+	0.937112i
$5$	0.780454	+	2.09545i	0.349030	+	0.937112i
$6$	−0.474220	−	1.08259i	−0.193599	−	0.441967i
$7$		0			0
$7$		0			0
$8$	1.23840	+	2.54291i	0.437839	+	0.899053i
$9$	−1.99320	+	1.15078i	−0.664401	+	0.383592i
$10$	2.76356	−	1.53712i	0.873914	−	0.486081i
$11$	−4.21811	−	2.43533i	−1.27181	−	0.734279i	−0.296480	−	0.955039i	$-0.595813\pi$
$11$	−4.21811	−	2.43533i	−1.27181	−	0.734279i	−0.975328	+	0.220760i	$0.929146\pi$
$12$	−1.41266	+	0.893414i	−0.407799	+	0.257907i
$13$	−0.247904	+	0.247904i	−0.0687562	+	0.0687562i	−0.740649	−	0.671892i	$-0.765482\pi$
$13$	−0.247904	+	0.247904i	−0.0687562	+	0.0687562i	0.671892	+	0.740649i	$0.265482\pi$
$14$		0			0
$15$	1.08328	+	1.52274i	0.279701	+	0.393171i
$16$	3.29169	−	2.27261i	0.822924	−	0.568152i
$17$	−5.83537	+	1.56358i	−1.41528	+	0.379224i	−0.883808	−	0.467849i	$-0.845029\pi$
$17$	−5.83537	+	1.56358i	−1.41528	+	0.379224i	−0.531476	+	0.847073i	$0.678362\pi$
$18$	2.03311	+	2.54180i	0.479210	+	0.599108i
$19$	−1.48858	−	2.57830i	−0.341505	−	0.591503i	0.643208	−	0.765692i	$-0.277603\pi$
$19$	−1.48858	−	2.57830i	−0.341505	−	0.591503i	−0.984712	+	0.174188i	$0.944270\pi$
$20$	−2.73722	−	3.53661i	−0.612061	−	0.790810i
$21$		0			0
$22$	−2.50713	+	6.41567i	−0.534521	+	1.36783i
$23$	1.70618	−	6.36754i	0.355762	−	1.32772i	−0.523760	−	0.851866i	$-0.675471\pi$
$23$	1.70618	−	6.36754i	0.355762	−	1.32772i	0.879522	−	0.475858i	$-0.157862\pi$
$24$	1.54974	+	1.78490i	0.316339	+	0.364342i
$25$	−3.78178	+	3.27080i	−0.756357	+	0.654159i
$26$	0.399357	+	0.293836i	0.0783204	+	0.0576260i
$27$	−3.13296	+	3.13296i	−0.602938	+	0.602938i
$28$		0			0
$29$		−	4.67111i		−	0.867403i	−0.901057	−	0.433701i	$-0.857207\pi$
$29$		−	4.67111i		−	0.867403i	0.901057	−	0.433701i	$-0.142793\pi$
$30$	1.89841	−	1.83862i	0.346601	−	0.335684i
$31$	−5.75848	−	3.32466i	−1.03425	−	0.597127i	−0.116053	−	0.993243i	$-0.537024\pi$
$31$	−5.75848	−	3.32466i	−1.03425	−	0.597127i	−0.918200	+	0.396116i	$0.870358\pi$
$32$	−3.87791	−	4.11847i	−0.685524	−	0.728050i
$33$	−3.93186	−	1.05354i	−0.684448	−	0.183397i
$34$	3.42797	+	7.82570i	0.587892	+	1.34210i
$35$		0			0
$36$	3.12101	−	3.38347i	0.520168	−	0.563912i
$37$	−0.641729	+	2.39496i	−0.105500	+	0.393730i	−0.998401	−	0.0565217i	$-0.981999\pi$
$37$	−0.641729	+	2.39496i	−0.105500	+	0.393730i	0.892902	+	0.450251i	$0.148666\pi$
$38$	−3.28794	+	2.62993i	−0.533374	+	0.426631i
$39$	−0.146499	+	0.253744i	−0.0234587	+	0.0406316i
$40$	−4.36201	+	4.57961i	−0.689695	+	0.724100i
$41$	1.15345			0.180138			0.0900692	−	0.995936i	$-0.471291\pi$
$41$	1.15345			0.180138			0.0900692	+	0.995936i	$0.471291\pi$
$42$		0			0
$43$	−3.23212	−	3.23212i	−0.492894	−	0.492894i	0.416323	−	0.909217i	$-0.363318\pi$
$43$	−3.23212	−	3.23212i	−0.492894	−	0.492894i	−0.909217	+	0.416323i	$0.863318\pi$
$44$	9.50338	+	2.13981i	1.43269	+	0.322589i
$45$	−3.96699	−	3.27852i	−0.591364	−	0.488733i
$46$	−9.26562	−	1.03024i	−1.36614	−	0.151901i
$47$	−4.74443	−	1.27127i	−0.692047	−	0.185433i	−0.104381	−	0.994537i	$-0.533286\pi$
$47$	−4.74443	−	1.27127i	−0.692047	−	0.185433i	−0.587666	+	0.809104i	$0.699953\pi$
$48$	2.16566	−	2.54658i	0.312587	−	0.367567i
$49$		0			0
$50$	5.37779	+	4.59123i	0.760534	+	0.649298i
$51$	−4.37242	+	2.52442i	−0.612261	+	0.353489i
$52$	0.325821	−	0.620880i	0.0451833	−	0.0861006i
$53$	0.0828048	+	0.309032i	0.0113741	+	0.0424488i	0.971380	−	0.237532i	$-0.0763385\pi$
$53$	0.0828048	+	0.309032i	0.0113741	+	0.0424488i	−0.960006	+	0.279981i	$0.909672\pi$
$54$	5.04699	+	3.71344i	0.686808	+	0.505335i
$55$	1.81106	−	10.7395i	0.244203	−	1.44811i
$56$		0			0
$57$	−1.75936	−	1.75936i	−0.233033	−	0.233033i
$58$	−6.53071	+	0.994133i	−0.857524	+	0.130536i
$59$	0.423416	−	0.733378i	0.0551240	−	0.0954776i	−0.837147	−	0.546979i	$-0.815778\pi$
$59$	0.423416	−	0.733378i	0.0551240	−	0.0954776i	0.892271	+	0.451501i	$0.149111\pi$
$60$	−2.97461	−	2.26288i	−0.384021	−	0.292136i
$61$	5.04573	+	8.73945i	0.646039	+	1.11897i	0.984060	+	0.177834i	$0.0569090\pi$
$61$	5.04573	+	8.73945i	0.646039	+	1.11897i	−0.338021	+	0.941138i	$0.609758\pi$
$62$	−3.42268	+	8.75855i	−0.434681	+	1.11234i
$63$		0			0
$64$	−4.93275	+	6.29825i	−0.616594	+	0.787281i
$65$	−0.712947	−	0.325992i	−0.0884302	−	0.0404343i
$66$	−0.636158	+	5.72138i	−0.0783057	+	0.704253i
$67$	0.721946	+	2.69434i	0.0881998	+	0.329166i	0.995901	−	0.0904513i	$-0.0288309\pi$
$67$	0.721946	+	2.69434i	0.0881998	+	0.329166i	−0.907701	+	0.419617i	$0.862164\pi$
$68$	10.2116	−	6.45819i	1.23834	−	0.783170i
$69$		−	5.50928i		−	0.663239i
$70$		0			0
$71$			6.49911i			0.771303i	0.922645	+	0.385651i	$0.126023\pi$
$71$			6.49911i			0.771303i	−0.922645	+	0.385651i	$0.873977\pi$
$72$	−5.39469	−	3.64341i	−0.635771	−	0.429380i
$73$	0.321006	+	1.19801i	0.0375710	+	0.140217i	0.982164	−	0.188028i	$-0.0602096\pi$
$73$	0.321006	+	1.19801i	0.0375710	+	0.140217i	−0.944593	+	0.328245i	$0.893543\pi$
$74$	3.48499	+	0.387495i	0.405122	+	0.0450454i
$75$	−2.34538	+	3.45838i	−0.270821	+	0.399339i
$76$	4.37668	+	4.03717i	0.502040	+	0.463095i
$77$		0			0
$78$	0.385940	+	0.150818i	0.0436991	+	0.0170768i
$79$	4.44724	+	7.70284i	0.500353	+	0.866637i	1.00000		0.000408067i	$0.000129892\pi$
$79$	4.44724	+	7.70284i	0.500353	+	0.866637i	−0.499647	+	0.866229i	$0.666537\pi$
$80$	7.33114	+	5.12390i	0.819646	+	0.572870i
$81$	1.60090	−	2.77285i	0.177878	−	0.308094i
$82$	−0.245484	−	1.61264i	−0.0271091	−	0.178087i
$83$	10.8443	+	10.8443i	1.19032	+	1.19032i	0.976977	+	0.213343i	$0.0684351\pi$
$83$	10.8443	+	10.8443i	1.19032	+	1.19032i	0.213343	+	0.976977i	$0.431565\pi$
$84$		0			0
$85$	−7.83063	−	11.0074i	−0.849351	−	1.19392i
$86$	−3.83097	+	5.20673i	−0.413104	+	0.561456i
$87$	−1.01038	−	3.77077i	−0.108324	−	0.404269i
$88$	0.969119	−	13.7422i	0.103308	−	1.46492i
$89$	−8.26789	+	4.77347i	−0.876395	+	0.505987i	−0.869468	−	0.493989i	$-0.835538\pi$
$89$	−8.26789	+	4.77347i	−0.876395	+	0.505987i	−0.00692697	+	0.999976i	$0.502205\pi$
$90$	−3.73945	+	6.24404i	−0.394172	+	0.658179i
$91$		0			0
$92$	0.531576	+	13.1736i	0.0554207	+	1.37344i
$93$	−5.36769	−	1.43827i	−0.556604	−	0.149142i
$94$	−0.767630	+	6.90379i	−0.0791750	+	0.712071i
$95$	4.24092	−	5.13149i	0.435110	−	0.526480i
$96$	−4.02130	−	2.48585i	−0.410422	−	0.253711i
$97$	2.35897	+	2.35897i	0.239518	+	0.239518i	0.816650	−	0.577133i	$-0.195828\pi$
$97$	2.35897	+	2.35897i	0.239518	+	0.239518i	−0.577133	+	0.816650i	$0.695828\pi$
$98$		0			0
$99$	11.2101			1.12665
$100$	5.27450	−	8.49586i	0.527450	−	0.849586i
$101$	0.729492	−	1.26352i	0.0725872	−	0.125725i	−0.827447	−	0.561543i	$-0.810208\pi$
$101$	0.729492	−	1.26352i	0.0725872	−	0.125725i	0.900034	+	0.435819i	$0.143541\pi$
$102$	4.45997	+	5.57585i	0.441603	+	0.552091i
$103$	0.142820	−	0.533010i	0.0140724	−	0.0525190i	−0.958533	−	0.284983i	$-0.908012\pi$
$103$	0.142820	−	0.533010i	0.0140724	−	0.0525190i	0.972605	+	0.232464i	$0.0746787\pi$
$104$	−0.937400	−	0.323394i	−0.0919197	−	0.0317113i
$105$		0			0
$106$	0.414437	−	0.181540i	0.0402536	−	0.0176327i
$107$	−4.80344	−	1.28708i	−0.464366	−	0.124426i	0.0190477	−	0.999819i	$-0.493937\pi$
$107$	−4.80344	−	1.28708i	−0.464366	−	0.124426i	−0.483414	+	0.875392i	$0.660603\pi$
$108$	4.11766	−	7.84655i	0.396222	−	0.755035i
$109$	9.70303	+	5.60205i	0.929382	+	0.536579i	0.886616	−	0.462506i	$-0.153050\pi$
$109$	9.70303	+	5.60205i	0.929382	+	0.536579i	0.0427659	+	0.999085i	$0.486383\pi$
$110$	−15.4004	−	0.246411i	−1.46837	−	0.0234943i
$111$			2.07215i			0.196680i
$112$		0			0
$113$	5.88750	−	5.88750i	0.553850	−	0.553850i	−0.373700	−	0.927550i	$-0.621911\pi$
$113$	5.88750	−	5.88750i	0.553850	−	0.553850i	0.927550	+	0.373700i	$0.121911\pi$
$114$	−2.08534	+	2.83421i	−0.195310	+	0.265448i
$115$	14.6744	−	1.39437i	1.36840	−	0.130026i
$116$	2.77981	+	8.91906i	0.258099	+	0.828114i
$117$	0.208841	−	0.779405i	0.0193074	−	0.0720561i
$118$	−1.11545	−	0.435899i	−0.102686	−	0.0401278i
$119$		0			0
$120$	−2.53067	+	4.64043i	−0.231017	+	0.423611i
$121$	6.36163	+	11.0187i	0.578330	+	1.00170i
$122$	11.1448	−	8.91445i	1.00901	−	0.807076i
$123$	0.931126	−	0.249494i	0.0839568	−	0.0224962i
$124$	12.9738	+	2.92123i	1.16508	+	0.262334i
$125$	−9.80528	−	5.37182i	−0.877011	−	0.480470i
$126$		0			0
$127$	5.47059	−	5.47059i	0.485436	−	0.485436i	−0.421426	−	0.906863i	$-0.638470\pi$
$127$	5.47059	−	5.47059i	0.485436	−	0.485436i	0.906863	+	0.421426i	$0.138470\pi$
$128$	9.85545	+	5.55609i	0.871107	+	0.491093i
$129$	−3.30826	−	1.91002i	−0.291276	−	0.168168i
$130$	−0.304038	+	1.06616i	−0.0266659	+	0.0935081i
$131$	−4.93009	+	2.84639i	−0.430744	+	0.248690i	−0.699663	−	0.714473i	$-0.746667\pi$
$131$	−4.93009	+	2.84639i	−0.430744	+	0.248690i	0.268920	+	0.963163i	$0.413333\pi$
$132$	8.13450	−	0.328240i	0.708017	−	0.0285696i
$133$		0			0
$134$	3.61333	−	1.58278i	0.312144	−	0.136732i
$135$	−9.01008	−	4.11982i	−0.775464	−	0.354577i
$136$	−11.2025	−	12.9025i	−0.960610	−	1.10638i
$137$	−0.479505	+	0.128483i	−0.0409668	+	0.0109770i	−0.279244	−	0.960220i	$-0.590084\pi$
$137$	−0.479505	+	0.128483i	−0.0409668	+	0.0109770i	0.238277	+	0.971197i	$0.423417\pi$
$138$	−7.70256	+	1.17252i	−0.655685	+	0.0998112i
$139$	−6.37368			−0.540608			−0.270304	−	0.962775i	$-0.587124\pi$
$139$	−6.37368			−0.540608			−0.270304	+	0.962775i	$0.587124\pi$
$140$		0			0
$141$	−4.10494			−0.345699
$142$	9.08646	−	1.38318i	0.762519	−	0.116074i
$143$	1.64941	−	0.441959i	0.137931	−	0.0369585i
$144$	−3.94575	+	8.31777i	−0.328813	+	0.693148i
$145$	9.78805	−	3.64558i	0.812853	−	0.302749i
$146$	1.60663	−	0.703770i	0.132966	−	0.0582444i
$147$		0			0
$148$	−0.199937	−	4.95487i	−0.0164347	−	0.407288i
$149$	−5.05558	+	2.91884i	−0.414169	+	0.239121i	−0.692579	−	0.721342i	$-0.743526\pi$
$149$	−5.05558	+	2.91884i	−0.414169	+	0.239121i	0.278410	+	0.960462i	$0.410192\pi$
$150$	5.33434	+	2.54306i	0.435547	+	0.207640i
$151$	3.20930	+	1.85289i	0.261169	+	0.150786i	0.624868	−	0.780731i	$-0.285153\pi$
$151$	3.20930	+	1.85289i	0.261169	+	0.150786i	−0.363699	+	0.931517i	$0.618486\pi$
$152$	4.71293	−	6.97829i	0.382269	−	0.566014i
$153$	9.83174	−	9.83174i	0.794849	−	0.794849i
$154$		0			0
$155$	2.47242	−	14.6613i	0.198589	−	1.17763i
$156$	0.128722	−	0.571684i	0.0103060	−	0.0457714i
$157$	−10.6646	+	2.85757i	−0.851127	+	0.228059i	−0.657909	−	0.753097i	$-0.728559\pi$
$157$	−10.6646	+	2.85757i	−0.851127	+	0.228059i	−0.193218	+	0.981156i	$0.561892\pi$
$158$	9.82292	−	7.85708i	0.781469	−	0.625076i
$159$	0.133689	+	0.231556i	0.0106022	+	0.0183636i
$160$	5.60351	−	11.3402i	0.442996	−	0.896523i
$161$		0			0
$162$	−4.21745	−	1.64810i	−0.331354	−	0.129487i
$163$	0.187432	−	0.699506i	0.0146808	−	0.0547896i	−0.958197	−	0.286110i	$-0.907638\pi$
$163$	0.187432	−	0.699506i	0.0146808	−	0.0547896i	0.972878	+	0.231320i	$0.0743045\pi$
$164$	−2.20241	+	0.686425i	−0.171979	+	0.0536008i
$165$	−0.861001	−	9.06123i	−0.0670288	−	0.705416i
$166$	12.8536	−	17.4695i	0.997632	−	1.35590i
$167$	−2.79303	+	2.79303i	−0.216131	+	0.216131i	−0.806866	−	0.590735i	$-0.798838\pi$
$167$	−2.79303	+	2.79303i	−0.216131	+	0.216131i	0.590735	+	0.806866i	$0.298838\pi$
$168$		0			0
$169$			12.8771i			0.990545i
$170$	−13.7230	+	13.2907i	−1.05250	+	1.01935i
$171$	5.93410	+	3.42606i	0.453792	+	0.261997i
$172$	8.09490	+	4.24798i	0.617230	+	0.323906i
$173$	−21.8113	−	5.84433i	−1.65828	−	0.444336i	−0.696369	−	0.717684i	$-0.745202\pi$
$173$	−21.8113	−	5.84433i	−1.65828	−	0.444336i	−0.961915	+	0.273348i	$0.911869\pi$
$174$	−5.05691	+	2.21513i	−0.383363	+	0.167929i
$175$		0			0
$176$	−19.4193	+	1.56975i	−1.46378	+	0.118325i
$177$	0.183172	−	0.683609i	0.0137681	−	0.0513832i
$178$	8.43345	+	10.5435i	0.632114	+	0.790268i
$179$	−4.66406	+	8.07838i	−0.348608	+	0.603807i	−0.986002	−	0.166731i	$-0.946679\pi$
$179$	−4.66406	+	8.07838i	−0.348608	+	0.603807i	0.637394	+	0.770538i	$0.280012\pi$
$180$	9.52569	+	3.89926i	0.710003	+	0.290633i
$181$	−13.7888			−1.02492			−0.512458	−	0.858712i	$-0.671265\pi$
$181$	−13.7888			−1.02492			−0.512458	+	0.858712i	$0.671265\pi$
$182$		0			0
$183$	5.96356	+	5.96356i	0.440839	+	0.440839i
$184$	18.3050	−	3.54688i	1.34946	−	0.261480i
$185$	−5.51936	+	0.524451i	−0.405791	+	0.0385584i
$186$	−0.868471	+	7.81071i	−0.0636794	+	0.572709i
$187$	28.4220	+	7.61566i	2.07843	+	0.556913i
$188$	9.81561	−	0.396076i	0.715877	−	0.0288868i
$189$		0			0
$190$	−8.07696	−	4.83715i	−0.585964	−	0.350924i
$191$	−0.149824	+	0.0865011i	−0.0108409	+	0.00625900i	−0.505411	−	0.862879i	$-0.668659\pi$
$191$	−0.149824	+	0.0865011i	−0.0108409	+	0.00625900i	0.494570	+	0.869138i	$0.335326\pi$
$192$	−2.61965	+	6.15126i	−0.189057	+	0.443929i
$193$	−2.43607	−	9.09154i	−0.175352	−	0.654423i	−0.996491	−	0.0836952i	$-0.973328\pi$
$193$	−2.43607	−	9.09154i	−0.175352	−	0.654423i	0.821139	−	0.570728i	$-0.193339\pi$
$194$	2.79605	−	3.80015i	0.200745	−	0.272835i
$195$	−0.646043	−	0.108946i	−0.0462641	−	0.00780176i
$196$		0			0
$197$	−10.6666	−	10.6666i	−0.759966	−	0.759966i	0.216350	−	0.976316i	$-0.430585\pi$
$197$	−10.6666	−	10.6666i	−0.759966	−	0.759966i	−0.976316	+	0.216350i	$0.930585\pi$
$198$	−2.38579	−	15.6729i	−0.169551	−	1.11382i
$199$	−8.58014	+	14.8612i	−0.608230	+	1.05349i	0.383302	+	0.923623i	$0.374787\pi$
$199$	−8.58014	+	14.8612i	−0.608230	+	1.05349i	−0.991532	+	0.129862i	$0.958547\pi$
$200$	−13.0007	−	5.56618i	−0.919287	−	0.393589i
$201$	1.16559	+	2.01886i	0.0822143	+	0.142399i
$202$	−1.92179	−	0.750999i	−0.135217	−	0.0528401i
$203$		0			0
$204$	6.84644	−	7.42220i	0.479347	−	0.519658i
$205$	0.900213	+	2.41699i	0.0628736	+	0.168810i
$206$	−0.775601	−	0.0862388i	−0.0540387	−	0.00600854i
$207$	3.92686	+	14.6552i	0.272935	+	1.01861i
$208$	−0.252636	+	1.37941i	−0.0175172	+	0.0956451i
$209$			14.5008i			1.00304i
$210$		0			0
$211$		−	2.47386i		−	0.170307i	−0.996368	−	0.0851536i	$-0.972862\pi$
$211$		−	2.47386i		−	0.170307i	0.996368	−	0.0851536i	$-0.0271381\pi$
$212$	−0.342015	−	0.540791i	−0.0234897	−	0.0371416i
$213$	1.40578	+	5.24644i	0.0963224	+	0.359480i
$214$	−0.777176	+	6.98965i	−0.0531267	+	0.477802i
$215$	4.25021	−	9.29525i	0.289862	−	0.633931i
$216$	−11.8467	−	4.08698i	−0.806064	−	0.278084i
$217$		0			0
$218$	5.76721	−	14.7581i	0.390605	−	0.999548i
$219$	0.518268	+	0.897666i	0.0350213	+	0.0606587i
$220$	2.93309	+	21.5838i	0.197749	+	1.45518i
$221$	1.05899	−	1.83423i	0.0712356	−	0.123384i
$222$	2.89709	−	0.441008i	0.194440	−	0.0295985i
$223$	−7.05641	−	7.05641i	−0.472532	−	0.472532i	0.430201	−	0.902733i	$-0.358443\pi$
$223$	−7.05641	−	7.05641i	−0.472532	−	0.472532i	−0.902733	+	0.430201i	$0.858443\pi$
$224$		0			0
$225$	3.77391	−	10.8714i	0.251594	−	0.724757i
$226$	−9.48437	−	6.97835i	−0.630891	−	0.464193i
$227$	−5.27268	−	19.6779i	−0.349960	−	1.30607i	−0.886710	−	0.462327i	$-0.847015\pi$
$227$	−5.27268	−	19.6779i	−0.349960	−	1.30607i	0.536750	−	0.843742i	$-0.319652\pi$
$228$	4.40635	+	2.31233i	0.291818	+	0.153138i
$229$	8.26790	−	4.77347i	0.546358	−	0.315440i	−0.201294	−	0.979531i	$-0.564515\pi$
$229$	8.26790	−	4.77347i	0.546358	−	0.315440i	0.747652	+	0.664091i	$0.231181\pi$
$230$	−5.07257	−	20.2197i	−0.334476	−	1.33325i
$231$		0			0
$232$	11.8782	−	5.78468i	0.779841	−	0.379783i
$233$	−19.7757	−	5.29887i	−1.29555	−	0.347141i	−0.455782	−	0.890091i	$-0.650640\pi$
$233$	−19.7757	−	5.29887i	−1.29555	−	0.347141i	−0.839765	+	0.542951i	$0.817307\pi$
$234$	−1.13414	−	0.126105i	−0.0741410	−	0.00824372i
$235$	−1.03894	−	10.9339i	−0.0677730	−	0.713247i
$236$	−0.372036	+	1.65230i	−0.0242175	+	0.107555i
$237$	5.25620	+	5.25620i	0.341427	+	0.341427i
$238$		0			0
$239$	−25.5833			−1.65484			−0.827422	−	0.561581i	$-0.810193\pi$
$239$	−25.5833			−1.65484			−0.827422	+	0.561581i	$0.810193\pi$
$240$	7.02641	+	2.55054i	0.453553	+	0.164637i
$241$	8.01250	−	13.8781i	0.516131	−	0.893965i	−0.483694	−	0.875237i	$-0.660705\pi$
$241$	8.01250	−	13.8781i	0.516131	−	0.893965i	0.999825	−	0.0187274i	$-0.00596147\pi$
$242$	14.0514	−	11.2393i	0.903256	−	0.722490i
$243$	4.13279	−	15.4238i	0.265119	−	0.989436i
$244$	−14.8353	−	13.6845i	−0.949731	−	0.876057i
$245$		0			0
$246$	−0.546988	−	1.24872i	−0.0348747	−	0.0796152i
$247$	1.00820	+	0.270146i	0.0641501	+	0.0171890i
$248$	1.32302	−	18.7605i	0.0840120	−	1.19129i
$249$	11.0998	+	6.40847i	0.703421	+	0.406120i
$250$	−5.42356	+	14.8521i	−0.343016	+	0.939330i
$251$		−	28.9444i		−	1.82696i	−0.406889	−	0.913478i	$-0.633386\pi$
$251$		−	28.9444i		−	1.82696i	0.406889	−	0.913478i	$-0.366614\pi$
$252$		0			0
$253$	−22.7039	+	22.7039i	−1.42738	+	1.42738i
$254$	−8.81276	−	6.48419i	−0.552962	−	0.406854i
$255$	−8.70225	−	7.19197i	−0.544956	−	0.450379i
$256$	5.67051	−	14.9615i	0.354407	−	0.935091i
$257$	5.33306	−	19.9032i	0.332667	−	1.24153i	−0.573709	−	0.819059i	$-0.694496\pi$
$257$	5.33306	−	19.9032i	0.332667	−	1.24153i	0.906376	−	0.422471i	$-0.138837\pi$
$258$	−1.96634	+	5.03181i	−0.122419	+	0.313267i
$259$		0			0
$260$	1.55531	+	0.198172i	0.0964561	+	0.0122901i
$261$	5.37540	+	9.31047i	0.332729	+	0.576303i
$262$	5.02881	+	6.28701i	0.310681	+	0.388413i
$263$	12.2013	−	3.26932i	0.752362	−	0.201595i	0.137796	−	0.990461i	$-0.455998\pi$
$263$	12.2013	−	3.26932i	0.752362	−	0.201595i	0.614566	+	0.788866i	$0.289331\pi$
$264$	−2.19015	−	11.3030i	−0.134794	−	0.695654i
$265$	−0.582934	+	0.414698i	−0.0358093	+	0.0254747i
$266$		0			0
$267$	−5.64178	+	5.64178i	−0.345271	+	0.345271i
$268$	−2.98191	−	4.71497i	−0.182149	−	0.288012i
$269$	9.69903	+	5.59974i	0.591360	+	0.341422i	0.765635	−	0.643275i	$-0.222425\pi$
$269$	9.69903	+	5.59974i	0.591360	+	0.341422i	−0.174275	+	0.984697i	$0.555758\pi$
$270$	−3.84237	+	13.4739i	−0.233839	+	0.819993i
$271$	−20.6434	+	11.9184i	−1.25399	+	0.723994i	−0.971900	−	0.235392i	$-0.924362\pi$
$271$	−20.6434	+	11.9184i	−1.25399	+	0.723994i	−0.282094	+	0.959387i	$0.591029\pi$
$272$	−15.6548	+	18.4083i	−0.949214	+	1.11617i
$273$		0			0
$274$	0.281684	+	0.643054i	0.0170171	+	0.0388483i
$275$	23.9174	−	4.58670i	1.44228	−	0.276588i
$276$	3.27861	+	10.5195i	0.197349	+	0.633197i
$277$	5.30858	−	1.42243i	0.318962	−	0.0854656i	−0.0957860	−	0.995402i	$-0.530536\pi$
$277$	5.30858	−	1.42243i	0.318962	−	0.0854656i	0.414748	+	0.909936i	$0.363870\pi$
$278$	1.35648	+	8.91109i	0.0813565	+	0.534452i
$279$	15.3038			0.916212
$280$		0			0
$281$	29.7858			1.77687			0.888436	−	0.459001i	$-0.151793\pi$
$281$	29.7858			1.77687			0.888436	+	0.459001i	$0.151793\pi$
$282$	0.873639	+	5.73916i	0.0520244	+	0.341762i
$283$	−20.9364	+	5.60990i	−1.24454	+	0.333474i	−0.820225	−	0.572041i	$-0.806152\pi$
$283$	−20.9364	+	5.60990i	−1.24454	+	0.333474i	−0.424316	+	0.905514i	$0.639485\pi$
$284$	−3.86767	−	12.4095i	−0.229504	−	0.736367i
$285$	2.31355	−	5.05975i	0.137043	−	0.299713i
$286$	−0.968945	−	2.21200i	−0.0572949	−	0.130798i
$287$		0			0
$288$	12.4689	+	3.74635i	0.734737	+	0.220756i
$289$	16.8843	−	9.74814i	0.993193	−	0.573420i
$290$	−7.18007	−	12.9089i	−0.421628	−	0.758035i
$291$	2.41455	+	1.39404i	0.141543	+	0.0817200i
$292$	−1.32588	−	2.09646i	−0.0775912	−	0.122686i
$293$	2.85175	−	2.85175i	0.166601	−	0.166601i	−0.618883	−	0.785484i	$-0.712414\pi$
$293$	2.85175	−	2.85175i	0.166601	−	0.166601i	0.785484	+	0.618883i	$0.212414\pi$
$294$		0			0
$295$	1.86721	+	0.314877i	0.108713	+	0.0183329i
$296$	−6.88488	+	1.33406i	−0.400176	+	0.0775405i
$297$	20.8449	−	5.58539i	1.20955	−	0.324097i
$298$	5.15681	+	6.44704i	0.298726	+	0.373467i
$299$	1.15557	+	2.00151i	0.0668284	+	0.115750i
$300$	2.42018	−	7.99921i	0.139729	−	0.461835i
$301$		0			0
$302$	1.90752	−	4.88129i	0.109765	−	0.280887i
$303$	0.315583	−	1.17777i	0.0181298	−	0.0676612i
$304$	−10.7594	−	5.10402i	−0.617096	−	0.292736i
$305$	−14.3751	+	17.3938i	−0.823116	+	0.995965i
$306$	−15.8383	−	11.6534i	−0.905414	−	0.666179i
$307$	3.58241	−	3.58241i	0.204459	−	0.204459i	−0.597448	−	0.801907i	$-0.703819\pi$
$307$	3.58241	−	3.58241i	0.204459	−	0.204459i	0.801907	+	0.597448i	$0.203819\pi$
$308$		0			0
$309$		−	0.461167i		−	0.0262349i
$310$	−21.0243	−	0.336395i	−1.19410	−	0.0191059i
$311$	21.3073	+	12.3018i	1.20822	+	0.697569i	0.962371	−	0.271738i	$-0.0875984\pi$
$311$	21.3073	+	12.3018i	1.20822	+	0.697569i	0.245854	+	0.969307i	$0.420932\pi$
$312$	−0.826672	−	0.0582982i	−0.0468011	−	0.00330049i
$313$	−6.49513	−	1.74036i	−0.367126	−	0.0983712i	0.0705393	−	0.997509i	$-0.477528\pi$
$313$	−6.49513	−	1.74036i	−0.367126	−	0.0983712i	−0.437666	+	0.899138i	$0.644195\pi$
$314$	6.26489	+	14.3021i	0.353548	+	0.807113i
$315$		0			0
$316$	−13.0756	−	12.0613i	−0.735561	−	0.678501i
$317$	3.57664	−	13.3482i	0.200884	−	0.749709i	−0.789781	−	0.613389i	$-0.789806\pi$
$317$	3.57664	−	13.3482i	0.200884	−	0.749709i	0.990665	−	0.136320i	$-0.0435275\pi$
$318$	0.295288	−	0.236193i	0.0165589	−	0.0132450i
$319$	−11.3757	+	19.7032i	−0.636915	+	1.10317i
$320$	−17.0474	−	5.42082i	−0.952980	−	0.303033i
$321$	−4.15600			−0.231965
$322$		0			0
$323$	12.7178	+	12.7178i	0.707638	+	0.707638i
$324$	−1.40664	+	6.24721i	−0.0781467	+	0.347067i
$325$	0.126676	−	1.74836i	0.00702671	−	0.0969818i
$326$	−1.01788	−	0.113177i	−0.0563749	−	0.00626831i
$327$	9.04456	+	2.42348i	0.500165	+	0.134019i
$328$	1.42843	+	2.93311i	0.0788716	+	0.161954i
$329$		0			0
$330$	−12.4853	+	3.13224i	−0.687295	+	0.172424i
$331$	−1.62048	+	0.935587i	−0.0890699	+	0.0514245i	−0.543873	−	0.839167i	$-0.683043\pi$
$331$	−1.62048	+	0.935587i	−0.0890699	+	0.0514245i	0.454804	+	0.890592i	$0.349709\pi$
$332$	−27.1598	−	14.2527i	−1.49059	−	0.782221i
$333$	−1.47697	−	5.51214i	−0.0809376	−	0.302063i
$334$	4.49939	+	3.31053i	0.246196	+	0.181144i
$335$	−5.08240	+	3.61561i	−0.277681	+	0.197542i
$336$		0			0
$337$	15.5089	+	15.5089i	0.844825	+	0.844825i	0.989482	−	0.144657i	$-0.0462078\pi$
$337$	15.5089	+	15.5089i	0.844825	+	0.844825i	−0.144657	+	0.989482i	$0.546208\pi$
$338$	18.0036	−	2.74058i	0.979264	−	0.149068i
$339$	3.47923	−	6.02620i	0.188966	−	0.327298i
$340$	21.5025	+	16.3576i	1.16613	+	0.887113i
$341$	16.1933	+	28.0476i	0.876915	+	1.51886i
$342$	3.52706	−	9.02567i	0.190722	−	0.488052i
$343$		0			0
$344$	4.21633	−	12.2216i	0.227330	−	0.658946i
$345$	11.5444	−	4.29973i	0.621529	−	0.231490i
$346$	−3.52898	+	31.7384i	−0.189719	+	1.70627i
$347$	−2.72992	−	10.1882i	−0.146550	−	0.546931i	−0.999682	−	0.0252358i	$-0.991966\pi$
$347$	−2.72992	−	10.1882i	−0.146550	−	0.546931i	0.853132	−	0.521696i	$-0.174700\pi$
$348$	4.17323	+	6.59867i	0.223709	+	0.353726i
$349$			7.92462i			0.424195i	0.977249	+	0.212098i	$0.0680295\pi$
$349$			7.92462i			0.424195i	−0.977249	+	0.212098i	$0.931971\pi$
$350$		0			0
$351$		−	1.55335i		−	0.0829115i
$352$	6.32761	+	26.8161i	0.337263	+	1.42931i
$353$	2.32090	+	8.66171i	0.123529	+	0.461016i	0.999783	−	0.0208332i	$-0.00663188\pi$
$353$	2.32090	+	8.66171i	0.123529	+	0.461016i	−0.876254	+	0.481849i	$0.839965\pi$
$354$	−0.994742	−	0.110605i	−0.0528700	−	0.00587859i
$355$	−13.6185	+	5.07226i	−0.722797	+	0.269207i
$356$	12.9461	−	14.0348i	0.686141	−	0.743843i
$357$		0			0
$358$	12.2871	+	4.80156i	0.649392	+	0.253771i
$359$	−11.6112	−	20.1111i	−0.612814	−	1.06143i	−0.990764	−	0.135599i	$-0.956704\pi$
$359$	−11.6112	−	20.1111i	−0.612814	−	1.06143i	0.377950	−	0.925826i	$-0.376629\pi$
$360$	3.42427	−	14.1478i	0.180475	−	0.745655i
$361$	5.06824	−	8.77844i	0.266749	−	0.462023i
$362$	2.93462	+	19.2783i	0.154240	+	1.01324i
$363$	7.51883	+	7.51883i	0.394636	+	0.394636i
$364$		0			0
$365$	−2.25984	+	1.60764i	−0.118285	+	0.0841480i
$366$	7.06850	−	9.60689i	0.369476	−	0.502160i
$367$	8.07404	+	30.1327i	0.421462	+	1.57292i	0.771530	+	0.636192i	$0.219492\pi$
$367$	8.07404	+	30.1327i	0.421462	+	1.57292i	−0.350069	+	0.936724i	$0.613842\pi$
$368$	−8.85470	−	24.8375i	−0.461583	−	1.29474i
$369$	−2.29906	+	1.32736i	−0.119684	+	0.0690997i
$370$	1.90790	+	7.60504i	0.0991871	+	0.395367i
$371$		0			0
$372$	11.1051	−	0.448107i	0.575770	−	0.0232333i
$373$	17.9985	+	4.82267i	0.931925	+	0.249709i	0.692675	−	0.721250i	$-0.256432\pi$
$373$	17.9985	+	4.82267i	0.931925	+	0.249709i	0.239250	+	0.970958i	$0.423099\pi$
$374$	4.59857	−	41.3579i	0.237786	−	2.13857i
$375$	−9.07730	−	2.21551i	−0.468750	−	0.114408i
$376$	−2.64277	−	13.6390i	−0.136291	−	0.703377i
$377$	1.15799	+	1.15799i	0.0596393	+	0.0596393i
$378$		0			0
$379$	−18.6149			−0.956182			−0.478091	−	0.878310i	$-0.658671\pi$
$379$	−18.6149			−0.956182			−0.478091	+	0.878310i	$0.658671\pi$
$380$	−5.04387	+	12.3219i	−0.258745	+	0.632102i
$381$	3.23285	−	5.59946i	0.165624	−	0.286869i
$382$	0.152824	+	0.191061i	0.00781918	+	0.00977553i
$383$	8.07570	−	30.1389i	0.412649	−	1.54003i	−0.376849	−	0.926275i	$-0.622992\pi$
$383$	8.07570	−	30.1389i	0.412649	−	1.54003i	0.789498	−	0.613753i	$-0.210341\pi$
$384$	9.15766	+	2.35341i	0.467325	+	0.120097i
$385$		0			0
$386$	−12.1925	+	5.34080i	−0.620581	+	0.271840i
$387$	10.1617	+	2.72282i	0.516549	+	0.138409i
$388$	−5.90809	−	3.10041i	−0.299938	−	0.157399i
$389$	−3.21806	−	1.85795i	−0.163162	−	0.0942017i	0.416196	−	0.909275i	$-0.363363\pi$
$389$	−3.21806	−	1.85795i	−0.163162	−	0.0942017i	−0.579358	+	0.815073i	$0.696697\pi$
$390$	−0.0148230	+	0.926424i	−0.000750594	+	0.0469113i
$391$			39.8247i			2.01402i
$392$		0			0
$393$	−3.36415	+	3.36415i	−0.169699	+	0.169699i
$394$	−12.6430	+	17.1832i	−0.636944	+	0.865679i
$395$	−12.6700	+	15.3307i	−0.637498	+	0.771369i
$396$	−21.4046	+	6.67119i	−1.07562	+	0.335240i
$397$	1.15071	−	4.29450i	0.0577524	−	0.215535i	−0.931019	−	0.364971i	$-0.881079\pi$
$397$	1.15071	−	4.29450i	0.0577524	−	0.215535i	0.988771	+	0.149436i	$0.0477457\pi$
$398$	22.6037	+	8.83310i	1.13302	+	0.442763i
$399$		0			0
$400$	−5.01524	+	19.3610i	−0.250762	+	0.968049i
$401$	−17.5463	−	30.3911i	−0.876220	−	1.51766i	−0.855457	−	0.517873i	$-0.826724\pi$
$401$	−17.5463	−	30.3911i	−0.876220	−	1.51766i	−0.0207625	−	0.999784i	$-0.506609\pi$
$402$	2.57451	−	2.05928i	0.128405	−	0.102708i
$403$	2.25175	−	0.603354i	0.112168	−	0.0300552i
$404$	−0.640971	+	2.84670i	−0.0318895	+	0.141629i
$405$	7.05978	+	1.19053i	0.350803	+	0.0591578i
$406$		0			0
$407$	8.53940	−	8.53940i	0.423282	−	0.423282i
$408$	−11.8341	−	7.99242i	−0.585877	−	0.395684i
$409$	31.9026	+	18.4190i	1.57748	+	0.910759i	0.995210	+	0.0977650i	$0.0311693\pi$
$409$	31.9026	+	18.4190i	1.57748	+	0.910759i	0.582272	+	0.812994i	$0.302164\pi$
$410$	3.18762	−	1.77299i	0.157425	−	0.0875618i
$411$	−0.359291	+	0.207437i	−0.0177225	+	0.0102321i
$412$	0.0444969	+	1.10273i	0.00219220	+	0.0543275i
$413$		0			0
$414$	19.6538	−	8.60918i	0.965934	−	0.423118i
$415$	−14.2602	+	31.1872i	−0.700006	+	1.53092i
$416$	1.98234	+	0.0596373i	0.0971920	+	0.00292396i
$417$	−5.14518	+	1.37865i	−0.251961	+	0.0675126i
$418$	20.2736	−	3.08614i	0.991615	−	0.150948i
$419$	−31.8030			−1.55368			−0.776840	−	0.629699i	$-0.783178\pi$
$419$	−31.8030			−1.55368			−0.776840	+	0.629699i	$0.783178\pi$
$420$		0			0
$421$	13.1193			0.639396			0.319698	−	0.947519i	$-0.396418\pi$
$421$	13.1193			0.639396			0.319698	+	0.947519i	$0.396418\pi$
$422$	−3.45872	+	0.526501i	−0.168368	+	0.0256296i
$423$	10.9196	−	2.92589i	0.530928	−	0.142262i
$424$	−0.683294	+	0.593269i	−0.0331837	+	0.0288117i
$425$	16.9539	−	24.9994i	0.822387	−	1.21265i
$426$	7.03590	−	3.08201i	0.340890	−	0.149324i
$427$		0			0
$428$	9.93768	−	0.401002i	0.480356	−	0.0193831i
$429$	1.23590	−	0.713547i	0.0596698	−	0.0344504i
$430$	−13.9003	−	3.96398i	−0.670333	−	0.191160i
$431$	−17.0409	−	9.83859i	−0.820833	−	0.473908i	0.0298705	−	0.999554i	$-0.490491\pi$
$431$	−17.0409	−	9.83859i	−0.820833	−	0.473908i	−0.850704	+	0.525646i	$0.823824\pi$
$432$	−3.19276	+	17.4327i	−0.153612	+	0.838733i
$433$	12.6198	−	12.6198i	0.606466	−	0.606466i	−0.335554	−	0.942021i	$-0.608924\pi$
$433$	12.6198	−	12.6198i	0.606466	−	0.606466i	0.942021	+	0.335554i	$0.108924\pi$
$434$		0			0
$435$	7.11290	−	5.06010i	0.341037	−	0.242613i
$436$	−21.8609	−	4.92226i	−1.04695	−	0.235734i
$437$	−18.9572	+	5.07957i	−0.906847	+	0.242989i
$438$	1.14473	−	0.915641i	0.0546975	−	0.0437510i
$439$	2.34778	+	4.06648i	0.112054	+	0.194082i	0.916598	−	0.399810i	$-0.130924\pi$
$439$	2.34778	+	4.06648i	0.112054	+	0.194082i	−0.804545	+	0.593892i	$0.797591\pi$
$440$	29.5523	−	8.69438i	1.40885	−	0.414488i
$441$		0			0
$442$	−2.78983	−	1.09021i	−0.132699	−	0.0518562i
$443$	−1.07698	+	4.01934i	−0.0511688	+	0.190965i	−0.986779	−	0.162069i	$-0.948183\pi$
$443$	−1.07698	+	4.01934i	−0.0511688	+	0.190965i	0.935611	+	0.353034i	$0.114850\pi$
$444$	−1.23315	−	3.95659i	−0.0585229	−	0.187771i
$445$	−16.4553	−	13.5994i	−0.780054	−	0.644676i
$446$	−8.36383	+	11.3674i	−0.396039	+	0.538262i
$447$	−3.44978	+	3.44978i	−0.163169	+	0.163169i
$448$		0			0
$449$			41.3539i			1.95161i	0.218641	+	0.975805i	$0.429837\pi$
$449$			41.3539i			1.95161i	−0.218641	+	0.975805i	$0.570163\pi$
$450$	−16.0025	−	2.96263i	−0.754365	−	0.139660i
$451$	−4.86537	−	2.80902i	−0.229101	−	0.132272i
$452$	−7.73796	+	14.7454i	−0.363963	+	0.693563i
$453$	2.99151	+	0.801572i	0.140553	+	0.0376612i
$454$	−26.3897	+	11.5597i	−1.23853	+	0.542526i
$455$		0			0
$456$	2.29511	−	6.65268i	0.107478	−	0.311540i
$457$	5.99940	−	22.3901i	0.280640	−	1.04736i	−0.671326	−	0.741162i	$-0.734275\pi$
$457$	5.99940	−	22.3901i	0.280640	−	1.04736i	0.951967	−	0.306202i	$-0.0990582\pi$
$458$	−8.43345	−	10.5435i	−0.394069	−	0.492665i
$459$	13.3833	−	23.1806i	0.624680	−	1.08198i
$460$	−27.1897	+	11.3953i	−1.26773	+	0.531307i
$461$	−16.9131			−0.787723			−0.393861	−	0.919170i	$-0.628861\pi$
$461$	−16.9131			−0.787723			−0.393861	+	0.919170i	$0.628861\pi$
$462$		0			0
$463$	−22.3542	−	22.3542i	−1.03889	−	1.03889i	−0.999213	−	0.0396749i	$-0.987368\pi$
$463$	−22.3542	−	22.3542i	−1.03889	−	1.03889i	−0.0396749	−	0.999213i	$-0.512632\pi$
$464$	−10.6156	−	15.3759i	−0.492816	−	0.713806i
$465$	−1.17542	−	12.3702i	−0.0545089	−	0.573655i
$466$	−3.19962	+	28.7762i	−0.148220	+	1.33303i
$467$	−8.28849	−	2.22089i	−0.383546	−	0.102771i	0.0618940	−	0.998083i	$-0.480286\pi$
$467$	−8.28849	−	2.22089i	−0.383546	−	0.102771i	−0.445440	+	0.895312i	$0.646953\pi$
$468$	0.0650665	+	1.61249i	0.00300770	+	0.0745373i
$469$		0			0
$470$	−15.0656	+	3.77956i	−0.694925	+	0.174338i
$471$	−7.99094	+	4.61357i	−0.368203	+	0.212582i
$472$	2.38927	+	0.168495i	0.109975	+	0.00775561i
$473$	5.76217	+	21.5047i	0.264945	+	0.988787i
$474$	6.23008	−	8.46739i	0.286157	−	0.388920i
$475$	14.0626	+	4.88173i	0.645237	+	0.223989i
$476$		0			0
$477$	−0.520673	−	0.520673i	−0.0238400	−	0.0238400i
$478$	5.44478	+	35.7682i	0.249039	+	1.63600i
$479$	12.0963	−	20.9514i	0.552694	−	0.957294i	−0.445385	−	0.895339i	$-0.646933\pi$
$479$	12.0963	−	20.9514i	0.552694	−	0.957294i	0.998079	−	0.0619545i	$-0.0197334\pi$
$480$	2.07053	−	10.3665i	0.0945065	−	0.473164i
$481$	−0.434634	−	0.752808i	−0.0198176	−	0.0343251i
$482$	−21.1083	−	8.24873i	−0.961457	−	0.375719i
$483$		0			0
$484$	−18.7043	−	17.2533i	−0.850194	−	0.784241i
$485$	−3.10203	+	6.78417i	−0.140856	+	0.308053i
$486$	−22.4437	−	2.49550i	−1.01807	−	0.113198i
$487$	−4.79710	−	17.9030i	−0.217377	−	0.811263i	−0.985316	−	0.170740i	$-0.945384\pi$
$487$	−4.79710	−	17.9030i	−0.217377	−	0.811263i	0.767939	−	0.640523i	$-0.221282\pi$
$488$	−15.9750	+	23.6537i	−0.723155	+	1.07075i
$489$		−	0.605222i		−	0.0273691i
$490$		0			0
$491$			26.3306i			1.18828i	0.804360	+	0.594142i	$0.202508\pi$
$491$			26.3306i			1.18828i	−0.804360	+	0.594142i	$0.797492\pi$
$492$	−1.62943	+	1.03051i	−0.0734602	+	0.0464589i
$493$	7.30366	+	27.2576i	0.328940	+	1.22762i
$494$	0.163122	−	1.46706i	0.00733922	−	0.0660063i
$495$	8.74894	+	23.4901i	0.393236	+	1.05580i
$496$	−26.5108	+	2.14300i	−1.19037	+	0.0962235i
$497$		0			0
$498$	6.59741	−	16.8826i	0.295637	−	0.756528i
$499$	5.41316	+	9.37586i	0.242326	+	0.419721i	0.961376	−	0.275237i	$-0.0887562\pi$
$499$	5.41316	+	9.37586i	0.242326	+	0.419721i	−0.719050	+	0.694958i	$0.755423\pi$
$500$	21.9191	+	4.42181i	0.980253	+	0.197749i
$501$	−1.65055	+	2.85883i	−0.0737409	+	0.127723i
$502$	−40.4674	+	6.16012i	−1.80615	+	0.274940i
$503$	−1.75566	−	1.75566i	−0.0782809	−	0.0782809i	0.666882	−	0.745163i	$-0.267628\pi$
$503$	−1.75566	−	1.75566i	−0.0782809	−	0.0782809i	−0.745163	+	0.666882i	$0.767628\pi$
$504$		0			0
$505$	3.21697	+	0.542494i	0.143153	+	0.0241407i
$506$	36.5744	+	26.9105i	1.62593	+	1.19632i
$507$	2.78535	+	10.3951i	0.123702	+	0.461662i
$508$	−7.19001	+	13.7012i	−0.319005	+	0.607892i
$509$	−27.6605	+	15.9698i	−1.22603	+	0.707849i	−0.966197	−	0.257804i	$-0.917001\pi$
$509$	−27.6605	+	15.9698i	−1.22603	+	0.707849i	−0.259834	+	0.965653i	$0.583668\pi$
$510$	−8.20309	+	13.6973i	−0.363239	+	0.606527i
$511$		0			0
$512$	−22.1246	−	4.74380i	−0.977777	−	0.209648i
$513$	12.7414	+	3.41405i	0.562546	+	0.150734i
$514$	−28.9619	−	3.22026i	−1.27745	−	0.142040i
$515$	1.22836	−	0.116719i	0.0541279	−	0.00514325i
$516$	7.45350	+	1.67825i	0.328122	+	0.0738809i
$517$	16.9166	+	16.9166i	0.743991	+	0.743991i
$518$		0			0
$519$	−18.8714			−0.828364
$520$	−0.0539440	−	2.21667i	−0.00236560	−	0.0972072i
$521$	16.3491	−	28.3174i	0.716265	−	1.24061i	−0.246204	−	0.969218i	$-0.579183\pi$
$521$	16.3491	−	28.3174i	0.716265	−	1.24061i	0.962469	−	0.271390i	$-0.0874833\pi$
$522$	11.8730	−	9.49690i	0.519668	−	0.415668i
$523$	−9.21055	+	34.3742i	−0.402749	+	1.50308i	0.405421	+	0.914130i	$0.367125\pi$
$523$	−9.21055	+	34.3742i	−0.402749	+	1.50308i	−0.808170	+	0.588950i	$0.799542\pi$
$524$	7.71966	−	8.36885i	0.337235	−	0.365595i
$525$		0			0
$526$	−7.16760	−	16.3629i	−0.312522	−	0.713456i
$527$	38.8012	+	10.3968i	1.69021	+	0.452890i
$528$	−15.3368	+	5.46764i	−0.667446	+	0.237949i
$529$	−17.7159	−	10.2283i	−0.770257	−	0.444708i
$530$	0.703856	+	0.726746i	0.0305735	+	0.0315678i
$531$			1.94903i			0.0845806i
$532$		0			0
$533$	−0.285944	+	0.285944i	−0.0123856	+	0.0123856i
$534$	9.08853	+	6.68710i	0.393299	+	0.289379i
$535$	−1.05186	−	11.0698i	−0.0454759	−	0.478591i
$536$	−5.95740	+	5.17250i	−0.257321	+	0.223418i
$537$	−2.01770	+	7.53016i	−0.0870702	+	0.324950i
$538$	5.76483	−	14.7521i	0.248540	−	0.636006i
$539$		0			0
$540$	19.6557	+	2.50446i	0.845845	+	0.107775i
$541$	18.6970	+	32.3842i	0.803848	+	1.39231i	0.917066	+	0.398736i	$0.130551\pi$
$541$	18.6970	+	32.3842i	0.803848	+	1.39231i	−0.113218	+	0.993570i	$0.536116\pi$
$542$	21.0567	+	26.3251i	0.904463	+	1.13076i
$543$	−11.1311	+	2.98257i	−0.477681	+	0.127994i
$544$	29.0686	+	17.9694i	1.24631	+	0.770431i
$545$	−4.16602	+	24.7043i	−0.178453	+	1.05822i
$546$		0			0
$547$	−27.0715	+	27.0715i	−1.15749	+	1.15749i	−0.172480	+	0.985013i	$0.555178\pi$
$547$	−27.0715	+	27.0715i	−1.15749	+	1.15749i	−0.985013	+	0.172480i	$0.944822\pi$
$548$	0.839110	−	0.530683i	0.0358450	−	0.0226697i
$549$	−20.1143	−	11.6130i	−0.858458	−	0.495631i
$550$	−11.5030	−	32.4630i	−0.490487	−	1.38423i
$551$	−12.0435	+	6.95334i	−0.513072	+	0.296222i
$552$	14.0096	−	6.82266i	0.596287	−	0.290392i
$553$		0			0
$554$	−3.11852	−	7.11924i	−0.132493	−	0.302468i
$555$	−4.34208	+	1.61722i	−0.184311	+	0.0686472i
$556$	12.1700	−	3.79302i	0.516122	−	0.160860i
$557$	−15.8098	+	4.23623i	−0.669884	+	0.179495i	−0.577703	−	0.816247i	$-0.696051\pi$
$557$	−15.8098	+	4.23623i	−0.669884	+	0.179495i	−0.0921814	+	0.995742i	$0.529384\pi$
$558$	−3.25704	−	21.3963i	−0.137881	−	0.905778i
$559$	1.60251			0.0677790
$560$		0			0
$561$	24.5911			1.03824
$562$	−6.33919	−	41.6437i	−0.267403	−	1.75664i
$563$	−22.6700	+	6.07440i	−0.955425	+	0.256005i	−0.702663	−	0.711523i	$-0.748006\pi$
$563$	−22.6700	+	6.07440i	−0.955425	+	0.256005i	−0.252762	+	0.967528i	$0.581339\pi$
$564$	7.83802	−	2.44288i	0.330040	−	0.102864i
$565$	16.9319	+	7.74202i	0.712329	+	0.325709i
$566$	12.2991	+	28.0774i	0.516968	+	1.18018i
$567$		0			0
$568$	−16.5266	+	8.04848i	−0.693443	+	0.337707i
$569$	−16.8334	+	9.71879i	−0.705694	+	0.407433i	−0.809465	−	0.587168i	$-0.800243\pi$
$569$	−16.8334	+	9.71879i	−0.705694	+	0.407433i	0.103770	+	0.994601i	$0.466909\pi$
$570$	−7.56645	−	2.15774i	−0.316924	−	0.0903778i
$571$	40.3258	+	23.2821i	1.68758	+	0.974327i	0.956361	+	0.292189i	$0.0943835\pi$
$571$	40.3258	+	23.2821i	1.68758	+	0.974327i	0.731223	+	0.682138i	$0.238950\pi$
$572$	−2.88639	+	1.82546i	−0.120686	+	0.0763263i
$573$	−0.102236	+	0.102236i	−0.00427097	+	0.00427097i
$574$		0			0
$575$	14.3745	+	29.6612i	0.599459	+	1.23696i
$576$	2.58410	−	18.2302i	0.107671	−	0.759591i
$577$	23.5105	−	6.29961i	0.978754	−	0.262256i	0.266234	−	0.963908i	$-0.414221\pi$
$577$	23.5105	−	6.29961i	0.978754	−	0.262256i	0.712520	+	0.701652i	$0.247554\pi$
$578$	−17.2224	−	21.5314i	−0.716356	−	0.895587i
$579$	−3.93306	−	6.81225i	−0.163452	−	0.283108i
$580$	−16.5199	+	12.7859i	−0.685951	+	0.530904i
$581$		0			0
$582$	1.43514	−	3.67248i	0.0594884	−	0.152229i
$583$	0.403313	−	1.50519i	0.0167035	−	0.0623385i
$584$	−2.64890	+	2.29990i	−0.109612	+	0.0951707i
$585$	1.79619	−	0.170675i	0.0742634	−	0.00705653i
$586$	−4.59398	−	3.38013i	−0.189776	−	0.139632i
$587$	−0.195894	+	0.195894i	−0.00808542	+	0.00808542i	−0.711138	−	0.703053i	$-0.751820\pi$
$587$	−0.195894	+	0.195894i	−0.00808542	+	0.00808542i	0.703053	+	0.711138i	$0.251820\pi$
$588$		0			0
$589$			19.7961i			0.815686i
$590$	0.0428419	−	2.67757i	0.00176377	−	0.110234i
$591$	−10.9179	−	6.30346i	−0.449103	−	0.259290i
$592$	3.33044	+	9.34189i	0.136880	+	0.383949i
$593$	−4.03218	−	1.08042i	−0.165582	−	0.0443676i	0.175076	−	0.984555i	$-0.443983\pi$
$593$	−4.03218	−	1.08042i	−0.165582	−	0.0443676i	−0.340658	+	0.940187i	$0.610650\pi$
$594$	−12.2453	−	27.9548i	−0.502432	−	1.14700i
$595$		0			0
$596$	7.91615	−	8.58187i	0.324258	−	0.351527i
$597$	−3.71182	+	13.8527i	−0.151915	+	0.566954i
$598$	2.55239	−	2.04158i	0.104375	−	0.0834866i
$599$	8.35085	−	14.4641i	0.341206	−	0.590987i	−0.643451	−	0.765488i	$-0.722498\pi$
$599$	8.35085	−	14.4641i	0.341206	−	0.590987i	0.984657	+	0.174501i	$0.0558311\pi$
$600$	−11.6988	−	1.68124i	−0.477603	−	0.0686363i
$601$	38.4209			1.56722			0.783610	−	0.621253i	$-0.213376\pi$
$601$	38.4209			1.56722			0.783610	+	0.621253i	$0.213376\pi$
$602$		0			0
$603$	−4.53957	−	4.53957i	−0.184866	−	0.184866i
$604$	−7.23054	−	1.62805i	−0.294207	−	0.0662444i
$605$	−18.1241	+	21.9300i	−0.736848	+	0.891582i
$606$	−1.71382	−	0.190559i	−0.0696190	−	0.00774091i
$607$	−30.8579	−	8.26835i	−1.25248	−	0.335602i	−0.429188	−	0.903215i	$-0.641200\pi$
$607$	−30.8579	−	8.26835i	−1.25248	−	0.335602i	−0.823295	+	0.567613i	$0.807867\pi$
$608$	−4.84608	+	16.1291i	−0.196535	+	0.654122i
$609$		0			0
$610$	27.3778	+	16.3961i	1.10849	+	0.663858i
$611$	1.49132	−	0.861012i	0.0603322	−	0.0348328i
$612$	−12.9219	+	24.6238i	−0.522336	+	0.995357i
$613$	7.17171	+	26.7652i	0.289663	+	1.08104i	0.945364	+	0.326016i	$0.105706\pi$
$613$	7.17171	+	26.7652i	0.289663	+	1.08104i	−0.655702	+	0.755020i	$0.727627\pi$
$614$	−5.77103	−	4.24617i	−0.232900	−	0.171361i
$615$	1.24950	+	1.75641i	0.0503848	+	0.0708251i
$616$		0			0
$617$	10.6961	+	10.6961i	0.430610	+	0.430610i	0.888836	−	0.458226i	$-0.151515\pi$
$617$	10.6961	+	10.6961i	0.430610	+	0.430610i	−0.458226	+	0.888836i	$0.651515\pi$
$618$	−0.644761	+	0.0981483i	−0.0259361	+	0.00394810i
$619$	1.43357	−	2.48301i	0.0576199	−	0.0998006i	−0.835777	−	0.549070i	$-0.814982\pi$
$619$	1.43357	−	2.48301i	0.0576199	−	0.0998006i	0.893397	+	0.449269i	$0.148316\pi$
$620$	4.00420	+	29.4658i	0.160813	+	1.18338i
$621$	14.6039	+	25.2946i	0.586033	+	1.01504i
$622$	12.6644	−	32.4080i	0.507798	−	1.29944i
$623$		0			0
$624$	0.0944300	+	1.16818i	0.00378022	+	0.0467648i
$625$	3.60378	−	24.7389i	0.144151	−	0.989556i
$626$	−1.05089	+	9.45128i	−0.0420018	+	0.377749i
$627$	3.13656	+	11.7058i	0.125262	+	0.467485i
$628$	18.6625	−	11.8028i	0.744715	−	0.470985i
$629$		−	14.9789i		−	0.597247i
$630$		0			0
$631$		−	0.116828i		−	0.00465086i	−0.999997	−	0.00232543i	$-0.999260\pi$
$631$		−	0.116828i		−	0.00465086i	0.999997	−	0.00232543i	$-0.000740209\pi$
$632$	−14.0802	+	20.8481i	−0.560079	+	0.829292i
$633$	−0.535103	−	1.99703i	−0.0212684	−	0.0793748i
$634$	−19.4234	−	2.15968i	−0.771402	−	0.0857719i
$635$	15.7329	+	7.19378i	0.624340	+	0.285476i
$636$	−0.393068	−	0.362577i	−0.0155862	−	0.0143771i
$637$		0			0
$638$	29.9683	+	11.7111i	1.18646	+	0.463645i
$639$	−7.47903	−	12.9541i	−0.295866	−	0.512455i
$640$	−3.95075	+	24.9878i	−0.156167	+	0.987731i
$641$	−3.64503	+	6.31338i	−0.143970	+	0.249364i	−0.928988	−	0.370109i	$-0.879320\pi$
$641$	−3.64503	+	6.31338i	−0.143970	+	0.249364i	0.785018	+	0.619473i	$0.212654\pi$
$642$	0.884504	+	5.81053i	0.0349086	+	0.229323i
$643$	−2.55764	−	2.55764i	−0.100863	−	0.100863i	0.654874	−	0.755738i	$-0.272722\pi$
$643$	−2.55764	−	2.55764i	−0.100863	−	0.100863i	−0.755738	+	0.654874i	$0.772722\pi$
$644$		0			0
$645$	1.42041	−	8.42297i	0.0559286	−	0.331654i
$646$	15.0742	−	20.4876i	0.593086	−	0.806072i
$647$	−3.58712	−	13.3873i	−0.141024	−	0.526309i	−0.999900	−	0.0141258i	$-0.995503\pi$
$647$	−3.58712	−	13.3873i	−0.141024	−	0.526309i	0.858876	−	0.512183i	$-0.171163\pi$
$648$	9.03364	+	0.637067i	0.354875	+	0.0250264i
$649$	−3.57203	+	2.06231i	−0.140214	+	0.0809528i
$650$	−2.47136	+	0.194991i	−0.0969347	+	0.00764816i
$651$		0			0
$652$	0.0583963	+	1.44719i	0.00228698	+	0.0566762i
$653$	−28.5901	−	7.66070i	−1.11882	−	0.299786i	−0.348413	−	0.937341i	$-0.613279\pi$
$653$	−28.5901	−	7.66070i	−1.11882	−	0.299786i	−0.770405	+	0.637555i	$0.779946\pi$
$654$	1.46337	−	13.1610i	0.0572224	−	0.514638i
$655$	−9.81216	−	8.10926i	−0.383393	−	0.316855i
$656$	3.79680	−	2.62133i	0.148240	−	0.102346i
$657$	−2.01848	−	2.01848i	−0.0787482	−	0.0787482i
$658$		0			0
$659$	41.1139			1.60157			0.800784	−	0.598953i	$-0.204416\pi$
$659$	41.1139			1.60157			0.800784	+	0.598953i	$0.204416\pi$
$660$	7.03641	+	16.7892i	0.273892	+	0.653519i
$661$	−7.77799	+	13.4719i	−0.302529	+	0.523995i	−0.976708	−	0.214572i	$-0.931164\pi$
$661$	−7.77799	+	13.4719i	−0.302529	+	0.523995i	0.674179	+	0.738568i	$0.264498\pi$
$662$	1.65293	+	2.06649i	0.0642430	+	0.0803166i
$663$	0.458127	−	1.70975i	0.0177922	−	0.0664013i
$664$	−14.1466	+	41.0057i	−0.548993	+	1.59133i
$665$		0			0
$666$	−7.39222	+	3.23809i	−0.286443	+	0.125474i
$667$	−29.7435	−	7.96973i	−1.15167	−	0.308589i
$668$	3.67089	−	6.99520i	0.142031	−	0.270652i
$669$	−7.22264	−	4.16999i	−0.279243	−	0.161221i
$670$	6.13667	+	6.33624i	0.237080	+	0.244790i
$671$		−	49.1520i		−	1.89749i
$672$		0			0
$673$	2.25638	−	2.25638i	0.0869771	−	0.0869771i	−0.662280	−	0.749257i	$-0.730411\pi$
$673$	2.25638	−	2.25638i	0.0869771	−	0.0869771i	0.749257	+	0.662280i	$0.230411\pi$
$674$	18.3824	−	24.9838i	0.708065	−	0.962342i
$675$	1.60090	−	22.0955i	0.0616188	−	0.850454i
$676$	−7.66325	−	24.5876i	−0.294740	−	0.945679i
$677$	10.7790	−	40.2278i	0.414271	−	1.54608i	−0.372022	−	0.928224i	$-0.621335\pi$
$677$	10.7790	−	40.2278i	0.414271	−	1.54608i	0.786292	−	0.617855i	$-0.211998\pi$
$678$	−9.16574	−	3.58180i	−0.352008	−	0.137558i
$679$		0			0
$680$	18.2933	−	33.5441i	0.701518	−	1.28636i
$681$	−8.51279	−	14.7446i	−0.326211	−	0.565014i
$682$	35.7672	−	28.6092i	1.36960	−	1.09550i
$683$	−41.8335	+	11.2093i	−1.60072	+	0.428910i	−0.945259	−	0.326322i	$-0.894190\pi$
$683$	−41.8335	+	11.2093i	−1.60072	+	0.428910i	−0.655457	+	0.755233i	$0.727524\pi$
$684$	−13.3695	−	3.01032i	−0.511196	−	0.115102i
$685$	−0.643460	−	0.904501i	−0.0245853	−	0.0345592i
$686$		0			0
$687$	5.64178	−	5.64178i	0.215247	−	0.215247i
$688$	−17.9845	−	3.29381i	−0.685652	−	0.125575i
$689$	−0.0971379	−	0.0560826i	−0.00370066	−	0.00213658i
$690$	−8.46844	−	15.2252i	−0.322388	−	0.579613i
$691$	37.3091	−	21.5404i	1.41930	−	0.819436i	0.423067	−	0.906098i	$-0.360954\pi$
$691$	37.3091	−	21.5404i	1.41930	−	0.819436i	0.996238	+	0.0866626i	$0.0276202\pi$
$692$	45.1248	−	1.82086i	1.71539	−	0.0692186i
$693$		0			0
$694$	−13.6632	+	5.98504i	−0.518648	+	0.227189i
$695$	−4.97436	−	13.3557i	−0.188688	−	0.506610i
$696$	8.33748	−	7.23900i	0.316031	−	0.274394i
$697$	−6.73079	+	1.80351i	−0.254947	+	0.0683128i
$698$	11.0795	−	1.68656i	0.419364	−	0.0638374i
$699$	−17.1102			−0.647166
$700$		0			0
$701$	−13.3256			−0.503300			−0.251650	−	0.967818i	$-0.580973\pi$
$701$	−13.3256			−0.503300			−0.251650	+	0.967818i	$0.580973\pi$
$702$	−2.17175	+	0.330593i	−0.0819673	+	0.0124774i
$703$	7.13021	−	1.91053i	0.268921	−	0.0720572i
$704$	36.1452	−	14.5539i	1.36227	−	0.548519i
$705$	−3.20372	−	8.60169i	−0.120659	−	0.323958i
$706$	11.6161	−	5.08830i	0.437176	−	0.191501i
$707$		0			0
$708$	0.0570692	+	1.41430i	0.00214479	+	0.0531525i
$709$	−3.81245	+	2.20112i	−0.143180	+	0.0826648i	−0.569879	−	0.821729i	$-0.693010\pi$
$709$	−3.81245	+	2.20112i	−0.143180	+	0.0826648i	0.426699	+	0.904394i	$0.359676\pi$
$710$	9.98994	+	17.9607i	0.374916	+	0.674052i
$711$	−17.7285	−	10.2356i	−0.664871	−	0.383863i
$712$	−22.3774	−	15.1130i	−0.838629	−	0.566385i
$713$	−30.9949	+	30.9949i	−1.16077	+	1.16077i
$714$		0			0
$715$	2.21339	+	3.11133i	0.0827762	+	0.116357i
$716$	4.09809	−	18.2006i	0.153153	−	0.680187i
$717$	−20.6522	+	5.53374i	−0.771271	+	0.206661i
$718$	−25.6464	+	20.5138i	−0.957114	+	0.765570i
$719$	0.144472	+	0.250232i	0.00538788	+	0.00933208i	0.868707	−	0.495327i	$-0.164952\pi$
$719$	0.144472	+	0.250232i	0.00538788	+	0.00933208i	−0.863319	+	0.504659i	$0.831618\pi$
$720$	−20.5089	−	1.77648i	−0.764322	−	0.0662053i
$721$		0			0
$722$	−13.3519	−	5.21766i	−0.496905	−	0.194181i
$723$	3.46626	−	12.9363i	0.128912	−	0.481105i
$724$	26.3286	−	8.20584i	0.978493	−	0.304968i
$725$	15.2782	+	17.6651i	0.567420	+	0.656066i
$726$	8.91193	−	12.1123i	0.330753	−	0.449531i
$727$	−4.87969	+	4.87969i	−0.180978	+	0.180978i	−0.791782	−	0.610804i	$-0.790846\pi$
$727$	−4.87969	+	4.87969i	−0.180978	+	0.180978i	0.610804	+	0.791782i	$0.290846\pi$
$728$		0			0
$729$		−	3.73943i		−	0.138497i
$730$	2.72861	+	2.81735i	0.100991	+	0.104275i
$731$	23.9143	+	13.8069i	0.884502	+	0.510667i
$732$	−14.9358	−	7.83792i	−0.552044	−	0.289698i
$733$	−21.9180	−	5.87292i	−0.809561	−	0.216921i	−0.169783	−	0.985481i	$-0.554307\pi$
$733$	−21.9180	−	5.87292i	−0.809561	−	0.216921i	−0.639777	+	0.768560i	$0.720973\pi$
$734$	40.4105	−	17.7014i	1.49158	−	0.653371i
$735$		0			0
$736$	−32.8409	+	17.6659i	−1.21053	+	0.651173i
$737$	3.51635	−	13.1232i	0.129526	−	0.483399i
$738$	2.34509	+	2.93183i	0.0863241	+	0.107922i
$739$	−2.90840	+	5.03750i	−0.106987	+	0.185307i	−0.914548	−	0.404477i	$-0.867454\pi$
$739$	−2.90840	+	5.03750i	−0.106987	+	0.185307i	0.807561	+	0.589784i	$0.200787\pi$
$740$	10.2266	−	4.28600i	0.375938	−	0.157557i
$741$	0.872306			0.0320449
$742$		0			0
$743$	−5.70591	−	5.70591i	−0.209329	−	0.209329i	0.594653	−	0.803982i	$-0.297289\pi$
$743$	−5.70591	−	5.70591i	−0.209329	−	0.209329i	−0.803982	+	0.594653i	$0.797289\pi$
$744$	−2.98995	−	15.4307i	−0.109617	−	0.565717i
$745$	−10.0619	−	8.31567i	−0.368640	−	0.304663i
$746$	2.91208	−	26.1902i	0.106619	−	0.958890i
$747$	−34.0944	−	9.13556i	−1.24745	−	0.334253i
$748$	−58.8015	+	2.37274i	−2.15000	+	0.0867558i
$749$		0			0
$750$	−1.16564	+	13.1626i	−0.0425630	+	0.480629i
$751$	36.3916	−	21.0107i	1.32795	−	0.766690i	0.342965	−	0.939348i	$-0.388569\pi$
$751$	36.3916	−	21.0107i	1.32795	−	0.766690i	0.984982	+	0.172658i	$0.0552355\pi$
$752$	−18.5063	+	6.59761i	−0.674856	+	0.240590i
$753$	−6.26077	−	23.3655i	−0.228155	−	0.851486i
$754$	1.37254	−	1.86544i	0.0499850	−	0.0679353i
$755$	−1.37792	+	8.17101i	−0.0501477	+	0.297374i
$756$		0			0
$757$	−36.1581	−	36.1581i	−1.31419	−	1.31419i	−0.918298	−	0.395891i	$-0.870436\pi$
$757$	−36.1581	−	36.1581i	−1.31419	−	1.31419i	−0.395891	−	0.918298i	$-0.629564\pi$
$758$	3.96173	+	26.0256i	0.143896	+	0.945292i
$759$	−13.4169	+	23.2387i	−0.487002	+	0.843512i
$760$	18.3009	+	4.42945i	0.663842	+	0.160673i
$761$	0.178655	+	0.309439i	0.00647623	+	0.0112172i	0.869245	−	0.494381i	$-0.164605\pi$
$761$	0.178655	+	0.309439i	0.00647623	+	0.0112172i	−0.862769	+	0.505598i	$0.831272\pi$
$762$	−8.51669	−	3.32816i	−0.308527	−	0.120567i
$763$		0			0
$764$	0.234599	−	0.254328i	0.00848748	−	0.00920125i
$765$	28.2751	+	12.9287i	1.02229	+	0.467437i
$766$	−43.8562	−	4.87636i	−1.58459	−	0.176190i
$767$	0.0768408	+	0.286774i	0.00277456	+	0.0103548i
$768$	1.34133	−	13.3043i	0.0484012	−	0.480076i
$769$		−	23.4758i		−	0.846559i	−0.905999	−	0.423279i	$-0.860879\pi$
$769$		−	23.4758i		−	0.846559i	0.905999	−	0.423279i	$-0.139121\pi$
$770$		0			0
$771$		−	17.2205i		−	0.620183i
$772$	10.0619	+	15.9097i	0.362135	+	0.572604i
$773$	6.57570	+	24.5409i	0.236512	+	0.882673i	0.977462	+	0.211113i	$0.0677089\pi$
$773$	6.57570	+	24.5409i	0.236512	+	0.882673i	−0.740950	+	0.671560i	$0.765624\pi$
$774$	1.64412	−	14.7867i	0.0590968	−	0.531496i
$775$	32.6516	−	6.26167i	1.17288	−	0.224926i
$776$	−3.07731	+	8.92000i	−0.110469	+	0.320209i
$777$		0			0
$778$	−1.91272	+	4.89461i	−0.0685745	+	0.175480i
$779$	−1.71700	−	2.97394i	−0.0615181	−	0.106552i
$780$	1.29840	−	0.176443i	0.0464900	−	0.00631767i
$781$	15.8275	−	27.4140i	0.566351	−	0.980949i
$782$	55.6792	−	8.47572i	1.99108	−	0.303091i
$783$	14.6344	+	14.6344i	0.522990	+	0.522990i
$784$		0			0
$785$	−14.3111	−	20.1169i	−0.510785	−	0.718002i
$786$	5.41943	+	3.98747i	0.193305	+	0.142228i
$787$	−0.657725	−	2.45466i	−0.0234454	−	0.0874993i	0.953212	−	0.302303i	$-0.0977555\pi$
$787$	−0.657725	−	2.45466i	−0.0234454	−	0.0874993i	−0.976657	+	0.214804i	$0.931089\pi$
$788$	26.7148	+	14.0192i	0.951675	+	0.499413i
$789$	9.14236	−	5.27834i	0.325477	−	0.187914i
$790$	24.1304	+	14.4513i	0.858522	+	0.514154i
$791$		0			0
$792$	13.8825	+	28.5062i	0.493293	+	1.01292i
$793$	−3.41740	−	0.915690i	−0.121356	−	0.0325171i
$794$	−6.24908	−	0.694833i	−0.221771	−	0.0246587i
$795$	−0.380875	+	0.460857i	−0.0135083	+	0.0163449i
$796$	7.53898	−	33.4823i	0.267212	−	1.18675i
$797$	−31.6762	−	31.6762i	−1.12203	−	1.12203i	−0.991436	−	0.130593i	$-0.958312\pi$
$797$	−31.6762	−	31.6762i	−1.12203	−	1.12203i	−0.130593	−	0.991436i	$-0.541688\pi$
$798$		0			0
$799$	29.6732			1.04976
$800$	28.1361	+	2.89133i	0.994761	+	0.102224i
$801$	10.9864	−	19.0290i	0.388185	−	0.672357i
$802$	−38.7557	+	30.9996i	−1.36851	+	1.09463i
$803$	1.56351	−	5.83510i	0.0551751	−	0.205916i
$804$	−3.42702	−	3.16118i	−0.120862	−	0.111486i
$805$		0			0
$806$	−1.32278	−	3.01978i	−0.0465931	−	0.106367i
$807$	9.04083	+	2.42248i	0.318252	+	0.0852754i
$808$	4.11641	+	0.290296i	0.144815	+	0.0102126i
$809$	40.9623	+	23.6496i	1.44016	+	0.831475i	0.997860	−	0.0653930i	$-0.0208301\pi$
$809$	40.9623	+	23.6496i	1.44016	+	0.831475i	0.442298	+	0.896868i	$0.354163\pi$
$810$	0.161982	−	10.1237i	0.00569147	−	0.355711i
$811$		−	5.30651i		−	0.186337i	−0.995650	−	0.0931683i	$-0.970301\pi$
$811$		−	5.30651i		−	0.186337i	0.995650	−	0.0931683i	$-0.0296995\pi$
$812$		0			0
$813$	−14.0864	+	14.0864i	−0.494033	+	0.494033i
$814$	−13.7564	−	10.1216i	−0.482162	−	0.354762i
$815$	1.61206	−	0.153178i	0.0564680	−	0.00536561i
$816$	−8.65566	+	18.2464i	−0.303009	+	0.638752i
$817$	−3.52210	+	13.1447i	−0.123223	+	0.459874i
$818$	18.9620	−	48.5233i	0.662991	−	1.69658i
$819$		0			0
$820$	−3.15724	−	4.07930i	−0.110256	−	0.142455i
$821$	3.34048	+	5.78588i	0.116584	+	0.201929i	0.918412	−	0.395626i	$-0.129472\pi$
$821$	3.34048	+	5.78588i	0.116584	+	0.201929i	−0.801828	+	0.597555i	$0.796139\pi$
$822$	0.366485	+	0.458179i	0.0127826	+	0.0159808i
$823$	29.6750	−	7.95140i	1.03441	−	0.277168i	0.298613	−	0.954374i	$-0.403476\pi$
$823$	29.6750	−	7.95140i	1.03441	−	0.277168i	0.735794	+	0.677206i	$0.236809\pi$
$824$	1.53226	−	0.296900i	0.0533789	−	0.0103430i
$825$	18.3153	−	8.87605i	0.637658	−	0.309024i
$826$		0			0
$827$	34.0292	−	34.0292i	1.18331	−	1.18331i	0.204428	−	0.978882i	$-0.434467\pi$
$827$	34.0292	−	34.0292i	1.18331	−	1.18331i	0.978882	−	0.204428i	$-0.0655334\pi$
$828$	−16.2194	−	25.6459i	−0.563663	−	0.891258i
$829$	−3.90921	−	2.25698i	−0.135773	−	0.0783883i	0.430575	−	0.902555i	$-0.358311\pi$
$829$	−3.90921	−	2.25698i	−0.135773	−	0.0783883i	−0.566348	+	0.824166i	$0.691644\pi$
$830$	46.6380	+	13.2999i	1.61883	+	0.461645i
$831$	3.97770	−	2.29653i	0.137985	−	0.0796657i
$832$	−0.338513	−	2.78421i	−0.0117358	−	0.0965252i
$833$		0			0
$834$	3.02252	+	6.90010i	0.104661	+	0.238931i
$835$	−8.03248	−	3.67281i	−0.277975	−	0.127103i
$836$	−8.62950	−	27.6879i	−0.298458	−	0.957606i
$837$	28.4571	−	7.62506i	0.983622	−	0.263561i
$838$	6.76851	+	44.4640i	0.233814	+	1.53598i
$839$	28.1768			0.972772			0.486386	−	0.873744i	$-0.338315\pi$
$839$	28.1768			0.972772			0.486386	+	0.873744i	$0.338315\pi$
$840$		0			0
$841$	7.18076			0.247612
$842$	−2.79213	−	18.3422i	−0.0962232	−	0.632115i
$843$	24.0447	−	6.44276i	0.828144	−	0.221900i
$844$	1.47221	+	4.72360i	0.0506755	+	0.162593i
$845$	−26.9832	+	10.0500i	−0.928251	+	0.345729i
$846$	−6.41468	−	14.6440i	−0.220541	−	0.503472i
$847$		0			0
$848$	0.974876	+	0.829055i	0.0334774	+	0.0284699i
$849$	−15.6876	+	9.05723i	−0.538396	+	0.310843i
$850$	−38.5601	−	18.3829i	−1.32260	−	0.630528i
$851$	14.1551	+	8.17246i	0.485231	+	0.280148i
$852$	−5.80640	−	9.18102i	−0.198924	−	0.314536i
$853$	−7.11404	+	7.11404i	−0.243580	+	0.243580i	−0.818329	−	0.574749i	$-0.805100\pi$
$853$	−7.11404	+	7.11404i	−0.243580	+	0.243580i	0.574749	+	0.818329i	$0.305100\pi$
$854$		0			0
$855$	−2.54782	+	15.1085i	−0.0871336	+	0.516699i
$856$	−2.67564	−	13.8086i	−0.0914515	−	0.471968i
$857$	21.4508	−	5.74773i	0.732746	−	0.196339i	0.126894	−	0.991916i	$-0.459499\pi$
$857$	21.4508	−	5.74773i	0.732746	−	0.196339i	0.605852	+	0.795578i	$0.292832\pi$
$858$	−1.26065	−	1.57606i	−0.0430378	−	0.0538058i
$859$	−9.63913	−	16.6955i	−0.328883	−	0.569642i	0.653408	−	0.757006i	$-0.273339\pi$
$859$	−9.63913	−	16.6955i	−0.328883	−	0.569642i	−0.982290	+	0.187364i	$0.940005\pi$
$860$	−2.58373	+	20.2778i	−0.0881043	+	0.691466i
$861$		0			0
$862$	−10.1287	+	25.9190i	−0.344983	+	0.882804i
$863$	−4.28964	+	16.0091i	−0.146021	+	0.544958i	0.853687	+	0.520787i	$0.174361\pi$
$863$	−4.28964	+	16.0091i	−0.146021	+	0.544958i	−0.999708	+	0.0241711i	$0.992305\pi$
$864$	25.0523	+	0.753684i	0.852298	+	0.0256409i
$865$	−4.77626	−	50.2657i	−0.162398	−	1.70908i
$866$	−20.3296	−	14.9580i	−0.690827	−	0.508292i
$867$	11.5214	−	11.5214i	0.391286	−	0.391286i
$868$		0			0
$869$		−	43.3219i		−	1.46960i
$870$	−8.58837	−	8.86767i	−0.291173	−	0.300642i
$871$	−0.846911	−	0.488964i	−0.0286965	−	0.0165679i
$872$	−2.22929	+	31.6115i	−0.0754933	+	1.07050i
$873$	−7.41657	−	1.98726i	−0.251013	−	0.0672587i
$874$	11.1364	+	25.4232i	0.376694	+	0.859952i
$875$		0			0
$876$	−1.52379	−	1.40559i	−0.0514842	−	0.0474904i
$877$	−10.0222	+	37.4032i	−0.338424	+	1.26302i	0.561685	+	0.827351i	$0.310153\pi$
$877$	−10.0222	+	37.4032i	−0.338424	+	1.26302i	−0.900109	+	0.435665i	$0.856513\pi$
$878$	5.18571	−	4.14790i	0.175009	−	0.139985i
$879$	1.68525	−	2.91893i	0.0568419	−	0.0984531i
$880$	−18.4452	−	39.4669i	−0.621787	−	1.33043i
$881$	−34.3504			−1.15729			−0.578647	−	0.815578i	$-0.696419\pi$
$881$	−34.3504			−1.15729			−0.578647	+	0.815578i	$0.696419\pi$
$882$		0			0
$883$	−34.1114	−	34.1114i	−1.14794	−	1.14794i	−0.986957	−	0.160984i	$-0.948533\pi$
$883$	−34.1114	−	34.1114i	−1.14794	−	1.14794i	−0.160984	−	0.986957i	$-0.551467\pi$
$884$	−0.930489	+	4.13251i	−0.0312957	+	0.138991i
$885$	1.57542	−	0.149697i	0.0529572	−	0.00503201i
$886$	5.84868	+	0.650313i	0.196490	+	0.0218477i
$887$	40.4245	+	10.8317i	1.35732	+	0.363693i	0.862832	−	0.505490i	$-0.168688\pi$
$887$	40.4245	+	10.8317i	1.35732	+	0.363693i	0.494490	+	0.869184i	$0.335355\pi$
$888$	−5.26929	+	2.56615i	−0.176826	+	0.0861142i
$889$		0			0
$890$	−15.5114	+	25.9005i	−0.519943	+	0.868188i
$891$	−13.5056	+	7.79744i	−0.452454	+	0.261224i
$892$	17.6729	+	9.27425i	0.591732	+	0.310525i
$893$	3.78478	+	14.1250i	0.126653	+	0.472674i
$894$	5.55737	+	4.08897i	0.185866	+	0.136755i
$895$	−20.5679	−	3.46847i	−0.687509	−	0.115938i
$896$		0			0
$897$	1.36577	+	1.36577i	0.0456018	+	0.0456018i
$898$	57.8172	−	8.80118i	1.92938	−	0.293699i
$899$	−15.5298	+	26.8985i	−0.517949	+	0.897114i
$900$	−0.736321	+	23.0038i	−0.0245440	+	0.766792i
$901$	−0.966393	−	1.67384i	−0.0321952	−	0.0557637i
$902$	−2.89184	+	7.40015i	−0.0962877	+	0.246398i
$903$		0			0
$904$	22.2624	+	7.68031i	0.740437	+	0.255443i
$905$	−10.7616	−	28.8938i	−0.357726	−	0.960461i
$906$	0.484014	−	4.35305i	0.0160803	−	0.144620i
$907$	−7.45963	−	27.8397i	−0.247693	−	0.924403i	−0.972011	−	0.234936i	$-0.924512\pi$
$907$	−7.45963	−	27.8397i	−0.247693	−	0.924403i	0.724318	−	0.689466i	$-0.242155\pi$
$908$	21.7782	+	34.4354i	0.722734	+	1.14278i
$909$			3.35793i			0.111375i
$910$		0			0
$911$		−	19.1234i		−	0.633586i	−0.948495	−	0.316793i	$-0.897394\pi$
$911$		−	19.1234i		−	0.633586i	0.948495	−	0.316793i	$-0.102606\pi$
$912$	−9.78962	−	1.79294i	−0.324167	−	0.0593703i
$913$	−19.3331	−	72.1521i	−0.639832	−	2.38789i
$914$	−32.5806	−	3.62262i	−1.07767	−	0.119826i
$915$	−7.84203	+	17.1506i	−0.259249	+	0.566981i
$916$	−12.9461	+	14.0348i	−0.427751	+	0.463723i
$917$		0			0
$918$	−35.2573	−	13.7779i	−1.16366	−	0.454738i
$919$	13.6744	+	23.6848i	0.451077	+	0.781289i	0.998453	−	0.0555980i	$-0.0177065\pi$
$919$	13.6744	+	23.6848i	0.451077	+	0.781289i	−0.547376	+	0.836887i	$0.684373\pi$
$920$	21.7185	+	35.5889i	0.716037	+	1.17333i
$921$	2.11703	−	3.66680i	0.0697585	−	0.120825i
$922$	3.59955	+	23.6464i	0.118545	+	0.778752i
$923$	−1.61116	−	1.61116i	−0.0530319	−	0.0530319i
$924$		0			0
$925$	−5.40656	−	11.1562i	−0.177767	−	0.366814i
$926$	−26.4960	+	36.0111i	−0.870713	+	1.18340i
$927$	0.328707	+	1.22675i	0.0107962	+	0.0402918i
$928$	−19.2378	+	18.1141i	−0.631513	+	0.594625i
$929$	−12.9501	+	7.47676i	−0.424880	+	0.245305i	−0.697163	−	0.716913i	$-0.745555\pi$
$929$	−12.9501	+	7.47676i	−0.424880	+	0.245305i	0.272283	+	0.962217i	$0.412221\pi$
$930$	−17.0447	+	4.27607i	−0.558919	+	0.140218i
$931$		0			0
$932$	40.9133	−	1.65092i	1.34016	−	0.0540776i
$933$	19.8613	+	5.32182i	0.650230	+	0.174229i
$934$	−1.34104	+	12.0609i	−0.0438803	+	0.394644i
$935$	6.22388	+	65.5005i	0.203543	+	2.14210i
$936$	2.24058	−	0.434149i	0.0732358	−	0.0141906i
$937$	−22.4138	−	22.4138i	−0.732226	−	0.732226i	0.238835	−	0.971060i	$-0.423235\pi$
$937$	−22.4138	−	22.4138i	−0.732226	−	0.732226i	−0.971060	+	0.238835i	$0.923235\pi$
$938$		0			0
$939$	−5.61967			−0.183391
$940$	8.49059	+	20.2590i	0.276932	+	0.660774i
$941$	−12.6079	+	21.8376i	−0.411007	+	0.711884i	−0.995000	−	0.0998741i	$-0.968156\pi$
$941$	−12.6079	+	21.8376i	−0.411007	+	0.711884i	0.583994	+	0.811758i	$0.301489\pi$
$942$	8.15094	+	10.1903i	0.265572	+	0.332018i
$943$	1.96799	−	7.34462i	0.0640864	−	0.239174i
$944$	−0.272924	−	3.37631i	−0.00888292	−	0.109890i
$945$		0			0
$946$	28.8395	−	12.6329i	0.937655	−	0.410731i
$947$	−20.9252	−	5.60688i	−0.679976	−	0.182199i	−0.0977318	−	0.995213i	$-0.531159\pi$
$947$	−20.9252	−	5.60688i	−0.679976	−	0.182199i	−0.582245	+	0.813014i	$0.697825\pi$
$948$	−13.1642	−	6.90824i	−0.427555	−	0.224369i
$949$	−0.376571	−	0.217413i	−0.0122240	−	0.00705754i
$950$	3.83230	−	20.7000i	0.124336	−	0.671597i
$951$		−	11.5490i		−	0.374503i
$952$		0			0
$953$	22.8157	−	22.8157i	0.739074	−	0.739074i	−0.233325	−	0.972399i	$-0.574960\pi$
$953$	22.8157	−	22.8157i	0.739074	−	0.739074i	0.972399	+	0.233325i	$0.0749605\pi$
$954$	−0.617145	+	0.838770i	−0.0199808	+	0.0271562i
$955$	−0.298189	−	0.246439i	−0.00964918	−	0.00797457i
$956$	48.8490	−	15.2248i	1.57989	−	0.492405i
$957$	−4.92119	+	18.3661i	−0.159079	+	0.593692i
$958$	−31.8667	−	12.4529i	−1.02957	−	0.402336i
$959$		0			0
$960$	−14.9342	−	0.688567i	−0.481998	−	0.0222234i
$961$	6.60673	+	11.4432i	0.213120	+	0.369135i
$962$	−0.960006	+	0.767883i	−0.0309518	+	0.0247575i
$963$	11.0554	−	2.96228i	0.356254	−	0.0954580i
$964$	−7.04022	+	31.2672i	−0.226750	+	1.00705i
$965$	17.1496	−	12.2002i	0.552064	−	0.392737i
$966$		0			0
$967$	11.0053	−	11.0053i	0.353908	−	0.353908i	−0.507654	−	0.861561i	$-0.669487\pi$
$967$	11.0053	−	11.0053i	0.353908	−	0.353908i	0.861561	+	0.507654i	$0.169487\pi$
$968$	−20.1412	+	29.8225i	−0.647364	+	0.958532i
$969$	13.0174	+	7.51561i	0.418180	+	0.241436i
$970$	10.1452	+	2.89313i	0.325743	+	0.0928927i
$971$	−15.7328	+	9.08331i	−0.504888	+	0.291497i	−0.730730	−	0.682667i	$-0.760820\pi$
$971$	−15.7328	+	9.08331i	−0.504888	+	0.291497i	0.225842	+	0.974164i	$0.427487\pi$
$972$	1.28761	+	31.9098i	0.0413002	+	1.02351i
$973$		0			0
$974$	−24.0094	+	10.5171i	−0.769310	+	0.336989i
$975$	−0.275917	−	1.43877i	−0.00883641	−	0.0460777i
$976$	36.4703	+	17.3007i	1.16739	+	0.553781i
$977$	−0.733186	+	0.196456i	−0.0234567	+	0.00628520i	−0.270528	−	0.962712i	$-0.587198\pi$
$977$	−0.733186	+	0.196456i	−0.0234567	+	0.00628520i	0.247072	+	0.968997i	$0.420532\pi$
$978$	−0.846165	+	0.128807i	−0.0270574	+	0.00411879i
$979$	46.4999			1.48614
$980$		0			0
$981$	−25.7868			−0.823310
$982$	36.8130	−	5.60383i	1.17475	−	0.178826i
$983$	−32.5127	+	8.71176i	−1.03699	+	0.277862i	−0.736867	−	0.676037i	$-0.763696\pi$
$983$	−32.5127	+	8.71176i	−1.03699	+	0.277862i	−0.300127	+	0.953899i	$0.597029\pi$
$984$	1.78754	+	2.05879i	0.0569848	+	0.0656320i
$985$	14.0265	−	30.6762i	0.446923	−	0.977424i
$986$	36.5547	−	16.0124i	1.16414	−	0.509940i
$987$		0			0
$988$	−2.08583	+	0.0841666i	−0.0663591	+	0.00267770i
$989$	−26.0952	+	15.0661i	−0.829779	+	0.479073i
$990$	30.9797	−	17.2313i	0.984599	−	0.547645i
$991$	25.1531	+	14.5222i	0.799016	+	0.461312i	0.843127	−	0.537715i	$-0.180712\pi$
$991$	25.1531	+	14.5222i	0.799016	+	0.461312i	−0.0441111	+	0.999027i	$0.514046\pi$
$992$	8.63833	+	36.6089i	0.274267	+	1.16233i
$993$	−1.10577	+	1.10577i	−0.0350906	+	0.0350906i
$994$		0			0
$995$	−37.8373	−	6.38071i	−1.19952	−	0.202282i
$996$	−25.0078	−	5.63083i	−0.792402	−	0.178420i
$997$	−45.9271	+	12.3061i	−1.45453	+	0.389739i	−0.897596	−	0.440820i	$-0.854688\pi$
$997$	−45.9271	+	12.3061i	−1.45453	+	0.389739i	−0.556931	+	0.830559i	$0.688021\pi$
$998$	11.9564	−	9.56361i	0.378473	−	0.302731i
$999$	−5.49282	−	9.51384i	−0.173785	−	0.301004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.67.9		72
4.3	odd	2	inner	980.2.x.m.67.12		72
5.3	odd	4	inner	980.2.x.m.263.1		72
7.2	even	3	inner	980.2.x.m.667.4		72
7.3	odd	6		980.2.k.k.687.16		36
7.4	even	3		980.2.k.j.687.16		36
7.5	odd	6		140.2.w.b.107.4	yes	72
7.6	odd	2		140.2.w.b.67.9	yes	72
20.3	even	4	inner	980.2.x.m.263.4		72
28.3	even	6		980.2.k.k.687.12		36
28.11	odd	6		980.2.k.j.687.12		36
28.19	even	6		140.2.w.b.107.1	yes	72
28.23	odd	6	inner	980.2.x.m.667.1		72
28.27	even	2		140.2.w.b.67.12	yes	72
35.3	even	12		980.2.k.k.883.12		36
35.12	even	12		700.2.be.e.443.7		72
35.13	even	4		140.2.w.b.123.1	yes	72
35.18	odd	12		980.2.k.j.883.12		36
35.19	odd	6		700.2.be.e.107.15		72
35.23	odd	12	inner	980.2.x.m.863.12		72
35.27	even	4		700.2.be.e.543.18		72
35.33	even	12		140.2.w.b.23.12	yes	72
35.34	odd	2		700.2.be.e.207.10		72
140.3	odd	12		980.2.k.k.883.16		36
140.19	even	6		700.2.be.e.107.18		72
140.23	even	12	inner	980.2.x.m.863.9		72
140.27	odd	4		700.2.be.e.543.15		72
140.47	odd	12		700.2.be.e.443.10		72
140.83	odd	4		140.2.w.b.123.4	yes	72
140.103	odd	12		140.2.w.b.23.9	✓	72
140.123	even	12		980.2.k.j.883.16		36
140.139	even	2		700.2.be.e.207.7		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.9	✓	72	140.103	odd	12
140.2.w.b.23.12	yes	72	35.33	even	12
140.2.w.b.67.9	yes	72	7.6	odd	2
140.2.w.b.67.12	yes	72	28.27	even	2
140.2.w.b.107.1	yes	72	28.19	even	6
140.2.w.b.107.4	yes	72	7.5	odd	6
140.2.w.b.123.1	yes	72	35.13	even	4
140.2.w.b.123.4	yes	72	140.83	odd	4
700.2.be.e.107.15		72	35.19	odd	6
700.2.be.e.107.18		72	140.19	even	6
700.2.be.e.207.7		72	140.139	even	2
700.2.be.e.207.10		72	35.34	odd	2
700.2.be.e.443.7		72	35.12	even	12
700.2.be.e.443.10		72	140.47	odd	12
700.2.be.e.543.15		72	140.27	odd	4
700.2.be.e.543.18		72	35.27	even	4
980.2.k.j.687.12		36	28.11	odd	6
980.2.k.j.687.16		36	7.4	even	3
980.2.k.j.883.12		36	35.18	odd	12
980.2.k.j.883.16		36	140.123	even	12
980.2.k.k.687.12		36	28.3	even	6
980.2.k.k.687.16		36	7.3	odd	6
980.2.k.k.883.12		36	35.3	even	12
980.2.k.k.883.16		36	140.3	odd	12
980.2.x.m.67.9		72	1.1	even	1	trivial
980.2.x.m.67.12		72	4.3	odd	2	inner
980.2.x.m.263.1		72	5.3	odd	4	inner
980.2.x.m.263.4		72	20.3	even	4	inner
980.2.x.m.667.1		72	28.23	odd	6	inner
980.2.x.m.667.4		72	7.2	even	3	inner
980.2.x.m.863.9		72	140.23	even	12	inner
980.2.x.m.863.12		72	35.23	odd	12	inner

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.212826 - 1.39811i) q^{2} +(0.807254 - 0.216303i) q^{3} +(-1.90941 + 0.595107i) q^{4} +(0.780454 + 2.09545i) q^{5} +(-0.474220 - 1.08259i) q^{6} +(1.23840 + 2.54291i) q^{8} +(-1.99320 + 1.15078i) q^{9} +(2.76356 - 1.53712i) q^{10} +(-4.21811 - 2.43533i) q^{11} +(-1.41266 + 0.893414i) q^{12} +(-0.247904 + 0.247904i) q^{13} +(1.08328 + 1.52274i) q^{15} +(3.29169 - 2.27261i) q^{16} +(-5.83537 + 1.56358i) q^{17} +(2.03311 + 2.54180i) q^{18} +(-1.48858 - 2.57830i) q^{19} +(-2.73722 - 3.53661i) q^{20} +(-2.50713 + 6.41567i) q^{22} +(1.70618 - 6.36754i) q^{23} +(1.54974 + 1.78490i) q^{24} +(-3.78178 + 3.27080i) q^{25} +(0.399357 + 0.293836i) q^{26} +(-3.13296 + 3.13296i) q^{27} -4.67111i q^{29} +(1.89841 - 1.83862i) q^{30} +(-5.75848 - 3.32466i) q^{31} +(-3.87791 - 4.11847i) q^{32} +(-3.93186 - 1.05354i) q^{33} +(3.42797 + 7.82570i) q^{34} +(3.12101 - 3.38347i) q^{36} +(-0.641729 + 2.39496i) q^{37} +(-3.28794 + 2.62993i) q^{38} +(-0.146499 + 0.253744i) q^{39} +(-4.36201 + 4.57961i) q^{40} +1.15345 q^{41} +(-3.23212 - 3.23212i) q^{43} +(9.50338 + 2.13981i) q^{44} +(-3.96699 - 3.27852i) q^{45} +(-9.26562 - 1.03024i) q^{46} +(-4.74443 - 1.27127i) q^{47} +(2.16566 - 2.54658i) q^{48} +(5.37779 + 4.59123i) q^{50} +(-4.37242 + 2.52442i) q^{51} +(0.325821 - 0.620880i) q^{52} +(0.0828048 + 0.309032i) q^{53} +(5.04699 + 3.71344i) q^{54} +(1.81106 - 10.7395i) q^{55} +(-1.75936 - 1.75936i) q^{57} +(-6.53071 + 0.994133i) q^{58} +(0.423416 - 0.733378i) q^{59} +(-2.97461 - 2.26288i) q^{60} +(5.04573 + 8.73945i) q^{61} +(-3.42268 + 8.75855i) q^{62} +(-4.93275 + 6.29825i) q^{64} +(-0.712947 - 0.325992i) q^{65} +(-0.636158 + 5.72138i) q^{66} +(0.721946 + 2.69434i) q^{67} +(10.2116 - 6.45819i) q^{68} -5.50928i q^{69} +6.49911i q^{71} +(-5.39469 - 3.64341i) q^{72} +(0.321006 + 1.19801i) q^{73} +(3.48499 + 0.387495i) q^{74} +(-2.34538 + 3.45838i) q^{75} +(4.37668 + 4.03717i) q^{76} +(0.385940 + 0.150818i) q^{78} +(4.44724 + 7.70284i) q^{79} +(7.33114 + 5.12390i) q^{80} +(1.60090 - 2.77285i) q^{81} +(-0.245484 - 1.61264i) q^{82} +(10.8443 + 10.8443i) q^{83} +(-7.83063 - 11.0074i) q^{85} +(-3.83097 + 5.20673i) q^{86} +(-1.01038 - 3.77077i) q^{87} +(0.969119 - 13.7422i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-3.73945 + 6.24404i) q^{90} +(0.531576 + 13.1736i) q^{92} +(-5.36769 - 1.43827i) q^{93} +(-0.767630 + 6.90379i) q^{94} +(4.24092 - 5.13149i) q^{95} +(-4.02130 - 2.48585i) q^{96} +(2.35897 + 2.35897i) q^{97} +11.2101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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