LMFDB - Embedded newform 980.2.x.m.67.12

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)

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")

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);

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			67.12
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.883367 - 1.10438i) q^{2} +(-0.807254 + 0.216303i) q^{3} +(-0.439327 - 1.95115i) q^{4} +(0.780454 + 2.09545i) q^{5} +(-0.474220 + 1.08259i) q^{6} +(-2.54291 - 1.23840i) q^{8} +(-1.99320 + 1.15078i) q^{9} +(3.00360 + 0.989126i) q^{10} +(4.21811 + 2.43533i) q^{11} +(0.776689 + 1.48005i) q^{12} +(-0.247904 + 0.247904i) q^{13} +(-1.08328 - 1.52274i) q^{15} +(-3.61398 + 1.71439i) q^{16} +(-5.83537 + 1.56358i) q^{17} +(-0.489830 + 3.21782i) q^{18} +(1.48858 + 2.57830i) q^{19} +(3.74566 - 2.44337i) q^{20} +(6.41567 - 2.50713i) q^{22} +(-1.70618 + 6.36754i) q^{23} +(2.32064 + 0.449662i) q^{24} +(-3.78178 + 3.27080i) q^{25} +(0.0547911 + 0.492771i) q^{26} +(3.13296 - 3.13296i) q^{27} -4.67111i q^{29} +(-2.63862 - 0.148788i) q^{30} +(5.75848 + 3.32466i) q^{31} +(-1.29913 + 5.50566i) 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} +(4.16240 + 0.633619i) q^{38} +(0.146499 - 0.253744i) q^{39} +(0.610370 - 6.29503i) q^{40} +1.15345 q^{41} +(3.23212 + 3.23212i) q^{43} +(2.89856 - 9.30008i) q^{44} +(-3.96699 - 3.27852i) q^{45} +(5.52503 + 7.50914i) q^{46} +(4.74443 + 1.27127i) q^{47} +(2.54658 - 2.16566i) q^{48} +(0.271513 + 7.06585i) q^{50} +(4.37242 - 2.52442i) q^{51} +(0.592609 + 0.374787i) q^{52} +(0.0828048 + 0.309032i) q^{53} +(-0.692438 - 6.22754i) q^{54} +(-1.81106 + 10.7395i) q^{55} +(-1.75936 - 1.75936i) q^{57} +(-5.15869 - 4.12630i) q^{58} +(-0.423416 + 0.733378i) q^{59} +(-2.49519 + 2.78262i) q^{60} +(5.04573 + 8.73945i) q^{61} +(8.75855 - 3.42268i) q^{62} +(4.93275 + 6.29825i) q^{64} +(-0.712947 - 0.325992i) q^{65} +(-4.63678 + 3.41162i) q^{66} +(-0.721946 - 2.69434i) q^{67} +(5.61442 + 10.6988i) q^{68} -5.50928i q^{69} -6.49911i q^{71} +(6.49365 - 0.457943i) q^{72} +(0.321006 + 1.19801i) q^{73} +(2.07808 + 2.82435i) q^{74} +(2.34538 - 3.45838i) q^{75} +(4.37668 - 4.03717i) q^{76} +(-0.150818 - 0.385940i) q^{78} +(-4.44724 - 7.70284i) q^{79} +(-6.41295 - 6.23490i) q^{80} +(1.60090 - 2.77285i) q^{81} +(1.01892 - 1.27385i) q^{82} +(-10.8443 - 10.8443i) q^{83} +(-7.83063 - 11.0074i) q^{85} +(6.42465 - 0.714354i) q^{86} +(1.01038 + 3.77077i) q^{87} +(-7.71036 - 11.4165i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-7.12505 + 1.48495i) q^{90} +(13.1736 + 0.531576i) q^{92} +(-5.36769 - 1.43827i) q^{93} +(5.59504 - 4.11668i) q^{94} +(-4.24092 + 5.13149i) q^{95} +(-0.142163 - 4.72547i) 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 $

$2$	0.883367	−	1.10438i	0.624634	−	0.780917i
$2$	0.883367	−	1.10438i	0.624634	−	0.780917i
$3$	−0.807254	+	0.216303i	−0.466069	+	0.124883i	−0.484208	−	0.874953i	$-0.660892\pi$
$3$	−0.807254	+	0.216303i	−0.466069	+	0.124883i	0.0181397	+	0.999835i	$0.494226\pi$
$4$	−0.439327	−	1.95115i	−0.219664	−	0.975576i
$5$	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
$8$	−2.54291	−	1.23840i	−0.899053	−	0.437839i
$9$	−1.99320	+	1.15078i	−0.664401	+	0.383592i
$10$	3.00360	+	0.989126i	0.949823	+	0.312789i
$11$	4.21811	+	2.43533i	1.27181	+	0.734279i	0.975328	−	0.220760i	$-0.0708539\pi$
$11$	4.21811	+	2.43533i	1.27181	+	0.734279i	0.296480	+	0.955039i	$0.404187\pi$
$12$	0.776689	+	1.48005i	0.224211	+	0.427253i
$13$	−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
$16$	−3.61398	+	1.71439i	−0.903496	+	0.428597i
$17$	−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	$0.678362\pi$
$18$	−0.489830	+	3.21782i	−0.115454	+	0.758447i
$19$	1.48858	+	2.57830i	0.341505	+	0.591503i	0.984712	−	0.174188i	$-0.0557302\pi$
$19$	1.48858	+	2.57830i	0.341505	+	0.591503i	−0.643208	+	0.765692i	$0.722397\pi$
$20$	3.74566	−	2.44337i	0.837554	−	0.546354i
$21$		0			0
$22$	6.41567	−	2.50713i	1.36783	−	0.534521i
$23$	−1.70618	+	6.36754i	−0.355762	+	1.32772i	0.523760	+	0.851866i	$0.324529\pi$
$23$	−1.70618	+	6.36754i	−0.355762	+	1.32772i	−0.879522	+	0.475858i	$0.842138\pi$
$24$	2.32064	+	0.449662i	0.473699	+	0.0917868i
$25$	−3.78178	+	3.27080i	−0.756357	+	0.654159i
$26$	0.0547911	+	0.492771i	0.0107454	+	0.0966404i
$27$	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	$-0.142793\pi$
$30$	−2.63862	−	0.148788i	−0.481744	−	0.0271648i
$31$	5.75848	+	3.32466i	1.03425	+	0.597127i	0.918200	−	0.396116i	$-0.129642\pi$
$31$	5.75848	+	3.32466i	1.03425	+	0.597127i	0.116053	+	0.993243i	$0.462976\pi$
$32$	−1.29913	+	5.50566i	−0.229656	+	0.973272i
$33$	−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	$0.148666\pi$
$38$	4.16240	+	0.633619i	0.675231	+	0.102787i
$39$	0.146499	−	0.253744i	0.0234587	−	0.0406316i
$40$	0.610370	−	6.29503i	0.0965080	−	0.995332i
$41$	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	0.909217	−	0.416323i	$-0.136682\pi$
$43$	3.23212	+	3.23212i	0.492894	+	0.492894i	−0.416323	+	0.909217i	$0.636682\pi$
$44$	2.89856	−	9.30008i	0.436974	−	1.40204i
$45$	−3.96699	−	3.27852i	−0.591364	−	0.488733i
$46$	5.52503	+	7.50914i	0.814621	+	1.10716i
$47$	4.74443	+	1.27127i	0.692047	+	0.185433i	0.587666	−	0.809104i	$-0.300047\pi$
$47$	4.74443	+	1.27127i	0.692047	+	0.185433i	0.104381	+	0.994537i	$0.466714\pi$
$48$	2.54658	−	2.16566i	0.367567	−	0.312587i
$49$		0			0
$50$	0.271513	+	7.06585i	0.0383978	+	0.999263i
$51$	4.37242	−	2.52442i	0.612261	−	0.353489i
$52$	0.592609	+	0.374787i	0.0821801	+	0.0519737i
$53$	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	$0.909672\pi$
$54$	−0.692438	−	6.22754i	−0.0942289	−	0.847461i
$55$	−1.81106	+	10.7395i	−0.244203	+	1.44811i
$56$		0			0
$57$	−1.75936	−	1.75936i	−0.233033	−	0.233033i
$58$	−5.15869	−	4.12630i	−0.677370	−	0.541810i
$59$	−0.423416	+	0.733378i	−0.0551240	+	0.0954776i	−0.892271	−	0.451501i	$-0.850889\pi$
$59$	−0.423416	+	0.733378i	−0.0551240	+	0.0954776i	0.837147	+	0.546979i	$0.184222\pi$
$60$	−2.49519	+	2.78262i	−0.322128	+	0.359235i
$61$	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	$0.609758\pi$
$62$	8.75855	−	3.42268i	1.11234	−	0.434681i
$63$		0			0
$64$	4.93275	+	6.29825i	0.616594	+	0.787281i
$65$	−0.712947	−	0.325992i	−0.0884302	−	0.0404343i
$66$	−4.63678	+	3.41162i	−0.570748	+	0.419941i
$67$	−0.721946	−	2.69434i	−0.0881998	−	0.329166i	0.907701	−	0.419617i	$-0.137836\pi$
$67$	−0.721946	−	2.69434i	−0.0881998	−	0.329166i	−0.995901	+	0.0904513i	$0.971169\pi$
$68$	5.61442	+	10.6988i	0.680848	+	1.29742i
$69$		−	5.50928i		−	0.663239i
$70$		0			0
$71$		−	6.49911i		−	0.771303i	−0.922645	−	0.385651i	$-0.873977\pi$
$71$		−	6.49911i		−	0.771303i	0.922645	−	0.385651i	$-0.126023\pi$
$72$	6.49365	−	0.457943i	0.765284	−	0.0539691i
$73$	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	$0.893543\pi$
$74$	2.07808	+	2.82435i	0.241572	+	0.328324i
$75$	2.34538	−	3.45838i	0.270821	−	0.399339i
$76$	4.37668	−	4.03717i	0.502040	−	0.463095i
$77$		0			0
$78$	−0.150818	−	0.385940i	−0.0170768	−	0.0436991i
$79$	−4.44724	−	7.70284i	−0.500353	−	0.866637i	−1.00000		0.000408067i	$-0.999870\pi$
$79$	−4.44724	−	7.70284i	−0.500353	−	0.866637i	0.499647	−	0.866229i	$-0.333463\pi$
$80$	−6.41295	−	6.23490i	−0.716990	−	0.697084i
$81$	1.60090	−	2.77285i	0.177878	−	0.308094i
$82$	1.01892	−	1.27385i	0.112521	−	0.140673i
$83$	−10.8443	−	10.8443i	−1.19032	−	1.19032i	−0.976977	−	0.213343i	$-0.931565\pi$
$83$	−10.8443	−	10.8443i	−1.19032	−	1.19032i	−0.213343	−	0.976977i	$-0.568435\pi$
$84$		0			0
$85$	−7.83063	−	11.0074i	−0.849351	−	1.19392i
$86$	6.42465	−	0.714354i	0.692787	−	0.0770308i
$87$	1.01038	+	3.77077i	0.108324	+	0.404269i
$88$	−7.71036	−	11.4165i	−0.821927	−	1.21700i
$89$	−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	$0.502205\pi$
$90$	−7.12505	+	1.48495i	−0.751047	+	0.156527i
$91$		0			0
$92$	13.1736	+	0.531576i	1.37344	+	0.0554207i
$93$	−5.36769	−	1.43827i	−0.556604	−	0.149142i
$94$	5.59504	−	4.11668i	0.577084	−	0.424603i
$95$	−4.24092	+	5.13149i	−0.435110	+	0.526480i
$96$	−0.142163	−	4.72547i	−0.0145094	−	0.482292i
$97$	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
$100$	8.04326	+	5.94188i	0.804326	+	0.594188i
$101$	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	$0.143541\pi$
$102$	1.07452	−	7.05881i	0.106394	−	0.698927i
$103$	−0.142820	+	0.533010i	−0.0140724	+	0.0525190i	−0.972605	−	0.232464i	$-0.925321\pi$
$103$	−0.142820	+	0.533010i	−0.0140724	+	0.0525190i	0.958533	+	0.284983i	$0.0919879\pi$
$104$	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	0.483414	−	0.875392i	$-0.339397\pi$
$107$	4.80344	+	1.28708i	0.464366	+	0.124426i	−0.0190477	+	0.999819i	$0.506063\pi$
$108$	−7.48927	−	4.73648i	−0.720656	−	0.455768i
$109$	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	$0.486383\pi$
$110$	10.2607	+	11.4870i	0.978318	+	1.09524i
$111$		−	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	$0.121911\pi$
$114$	−3.49717	+	0.388849i	−0.327540	+	0.0364191i
$115$	−14.6744	+	1.39437i	−1.36840	+	0.130026i
$116$	−9.11404	+	2.05214i	−0.846217	+	0.190537i
$117$	0.208841	−	0.779405i	0.0193074	−	0.0720561i
$118$	0.435899	+	1.11545i	0.0401278	+	0.102686i
$119$		0			0
$120$	0.868912	+	5.21372i	0.0793204	+	0.475945i
$121$	6.36163	+	11.0187i	0.578330	+	1.00170i
$122$	14.1089	+	2.14772i	1.27736	+	0.194446i
$123$	−0.931126	+	0.249494i	−0.0839568	+	0.0224962i
$124$	3.95706	−	12.6963i	0.355354	−	1.14016i
$125$	−9.80528	−	5.37182i	−0.877011	−	0.480470i
$126$		0			0
$127$	−5.47059	+	5.47059i	−0.485436	+	0.485436i	−0.906863	−	0.421426i	$-0.861530\pi$
$127$	−5.47059	+	5.47059i	−0.485436	+	0.485436i	0.421426	+	0.906863i	$0.361530\pi$
$128$	11.3131	+	0.116014i	0.999947	+	0.0102543i
$129$	−3.30826	−	1.91002i	−0.291276	−	0.168168i
$130$	−0.989814	+	0.499397i	−0.0868124	+	0.0438000i
$131$	4.93009	−	2.84639i	0.430744	−	0.248690i	−0.268920	−	0.963163i	$-0.586667\pi$
$131$	4.93009	−	2.84639i	0.430744	−	0.248690i	0.699663	+	0.714473i	$0.253333\pi$
$132$	−0.328240	+	8.13450i	−0.0285696	+	0.708017i
$133$		0			0
$134$	−3.61333	−	1.58278i	−0.312144	−	0.136732i
$135$	9.01008	+	4.11982i	0.775464	+	0.354577i
$136$	16.7751	+	3.25045i	1.43846	+	0.278724i
$137$	−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	$0.423417\pi$
$138$	−6.08435	−	4.86671i	−0.517935	−	0.414282i
$139$	6.37368			0.540608			0.270304	−	0.962775i	$-0.412876\pi$
$139$	6.37368			0.540608			0.270304	+	0.962775i	$0.412876\pi$
$140$		0			0
$141$	−4.10494			−0.345699
$142$	−7.17752	−	5.74110i	−0.602324	−	0.481782i
$143$	−1.64941	+	0.441959i	−0.137931	+	0.0369585i
$144$	5.23053	−	7.57601i	0.435877	−	0.631334i
$145$	9.78805	−	3.64558i	0.812853	−	0.302749i
$146$	1.60663	+	0.703770i	0.132966	+	0.0582444i
$147$		0			0
$148$	4.95487	+	0.199937i	0.407288	+	0.0164347i
$149$	−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	$0.410192\pi$
$150$	−1.74755	−	5.64521i	−0.142687	−	0.460930i
$151$	−3.20930	−	1.85289i	−0.261169	−	0.150786i	0.363699	−	0.931517i	$-0.381514\pi$
$151$	−3.20930	−	1.85289i	−0.261169	−	0.150786i	−0.624868	+	0.780731i	$0.714847\pi$
$152$	−0.592370	−	8.39984i	−0.0480476	−	0.681317i
$153$	9.83174	−	9.83174i	0.794849	−	0.794849i
$154$		0			0
$155$	−2.47242	+	14.6613i	−0.198589	+	1.17763i
$156$	−0.559454	−	0.174365i	−0.0447922	−	0.0139604i
$157$	−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	$0.561892\pi$
$158$	−12.4354	−	1.89298i	−0.989310	−	0.150597i
$159$	−0.133689	−	0.231556i	−0.0106022	−	0.0183636i
$160$	−12.5507	+	1.57466i	−0.992221	+	0.124487i
$161$		0			0
$162$	−1.64810	−	4.21745i	−0.129487	−	0.331354i
$163$	−0.187432	+	0.699506i	−0.0146808	+	0.0547896i	−0.972878	−	0.231320i	$-0.925696\pi$
$163$	−0.187432	+	0.699506i	−0.0146808	+	0.0547896i	0.958197	+	0.286110i	$0.0923622\pi$
$164$	−0.506741	−	2.25055i	−0.0395698	−	0.175739i
$165$	−0.861001	−	9.06123i	−0.0670288	−	0.705416i
$166$	−21.5558	+	2.39679i	−1.67306	+	0.186027i
$167$	2.79303	−	2.79303i	0.216131	−	0.216131i	−0.590735	−	0.806866i	$-0.701162\pi$
$167$	2.79303	−	2.79303i	0.216131	−	0.216131i	0.806866	+	0.590735i	$0.201162\pi$
$168$		0			0
$169$			12.8771i			0.990545i
$170$	−19.0737	−	1.07553i	−1.46289	−	0.0824897i
$171$	−5.93410	−	3.42606i	−0.453792	−	0.261997i
$172$	4.88640	−	7.72631i	0.372584	−	0.589126i
$173$	−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
$178$	−2.03184	+	13.3477i	−0.152293	+	1.00045i
$179$	4.66406	−	8.07838i	0.348608	−	0.603807i	−0.637394	−	0.770538i	$-0.719988\pi$
$179$	4.66406	−	8.07838i	0.348608	−	0.603807i	0.986002	+	0.166731i	$0.0533211\pi$
$180$	−4.65408	+	9.18055i	−0.346895	+	0.684278i
$181$	−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
$184$	12.2242	−	14.0791i	0.901179	−	1.03793i
$185$	−5.51936	+	0.524451i	−0.405791	+	0.0385584i
$186$	−6.33004	+	4.65747i	−0.464141	+	0.341503i
$187$	−28.4220	−	7.61566i	−2.07843	−	0.556913i
$188$	0.396076	−	9.81561i	0.0288868	−	0.715877i
$189$		0			0
$190$	1.92085	+	9.21660i	0.139353	+	0.668642i
$191$	0.149824	−	0.0865011i	0.0108409	−	0.00625900i	−0.494570	−	0.869138i	$-0.664674\pi$
$191$	0.149824	−	0.0865011i	0.0108409	−	0.00625900i	0.505411	+	0.862879i	$0.331341\pi$
$192$	−5.34432	−	4.01732i	−0.385693	−	0.289925i
$193$	−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	$-0.193339\pi$
$194$	4.68905	−	0.521374i	0.336654	−	0.0374325i
$195$	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	$0.930585\pi$
$198$	−9.90260	+	12.3802i	−0.703747	+	0.879824i
$199$	8.58014	−	14.8612i	0.608230	−	1.05349i	−0.383302	−	0.923623i	$-0.625213\pi$
$199$	8.58014	−	14.8612i	0.608230	−	1.05349i	0.991532	−	0.129862i	$-0.0414535\pi$
$200$	13.6673	−	3.63399i	0.966422	−	0.256962i
$201$	1.16559	+	2.01886i	0.0822143	+	0.142399i
$202$	−0.750999	−	1.92179i	−0.0528401	−	0.135217i
$203$		0			0
$204$	−6.84644	−	7.42220i	−0.479347	−	0.519658i
$205$	0.900213	+	2.41699i	0.0628736	+	0.168810i
$206$	0.462486	+	0.628571i	0.0322229	+	0.0437946i
$207$	−3.92686	−	14.6552i	−0.272935	−	1.01861i
$208$	0.470917	−	1.32092i	0.0326523	−	0.0915897i
$209$			14.5008i			1.00304i
$210$		0			0
$211$			2.47386i			0.170307i	0.996368	+	0.0851536i	$0.0271381\pi$
$211$			2.47386i			0.170307i	−0.996368	+	0.0851536i	$0.972862\pi$
$212$	0.566589	−	0.297331i	0.0389135	−	0.0204208i
$213$	1.40578	+	5.24644i	0.0963224	+	0.359480i
$214$	5.66462	−	4.16788i	0.387226	−	0.284910i
$215$	−4.25021	+	9.29525i	−0.289862	+	0.633931i
$216$	−11.8467	+	4.08698i	−0.806064	+	0.278084i
$217$		0			0
$218$	14.7581	−	5.76721i	0.999548	−	0.390605i
$219$	−0.518268	−	0.897666i	−0.0350213	−	0.0606587i
$220$	21.7500	−	1.18450i	1.46638	−	0.0798591i
$221$	1.05899	−	1.83423i	0.0712356	−	0.123384i
$222$	−2.28845	−	1.83047i	−0.153591	−	0.122853i
$223$	7.05641	+	7.05641i	0.472532	+	0.472532i	0.902733	−	0.430201i	$-0.141557\pi$
$223$	7.05641	+	7.05641i	0.472532	+	0.472532i	−0.430201	+	0.902733i	$0.641557\pi$
$224$		0			0
$225$	3.77391	−	10.8714i	0.251594	−	0.724757i
$226$	−1.30124	−	11.7029i	−0.0865572	−	0.778464i
$227$	5.27268	+	19.6779i	0.349960	+	1.30607i	0.886710	+	0.462327i	$0.152985\pi$
$227$	5.27268	+	19.6779i	0.349960	+	1.30607i	−0.536750	+	0.843742i	$0.680348\pi$
$228$	−2.65984	+	4.20572i	−0.176153	+	0.278530i
$229$	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	$0.231181\pi$
$230$	−11.4230	+	17.4379i	−0.753209	+	1.14982i
$231$		0			0
$232$	−5.78468	+	11.8782i	−0.379783	+	0.779841i
$233$	−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	$0.817307\pi$
$234$	−0.676280	−	0.919141i	−0.0442098	−	0.0600861i
$235$	1.03894	+	10.9339i	0.0677730	+	0.713247i
$236$	1.61695	+	0.503956i	0.105254	+	0.0328047i
$237$	5.25620	+	5.25620i	0.341427	+	0.341427i
$238$		0			0
$239$	25.5833			1.65484			0.827422	−	0.561581i	$-0.189807\pi$
$239$	25.5833			1.65484			0.827422	+	0.561581i	$0.189807\pi$
$240$	6.52551	+	3.64601i	0.421220	+	0.235349i
$241$	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	$-0.00596147\pi$
$242$	17.7885	+	2.70784i	1.14349	+	0.174067i
$243$	−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
$248$	−10.5260	−	15.5856i	−0.668404	−	0.989685i
$249$	11.0998	+	6.40847i	0.703421	+	0.406120i
$250$	−14.5942	+	6.08351i	−0.923019	+	0.384755i
$251$			28.9444i			1.82696i	0.406889	+	0.913478i	$0.366614\pi$
$251$			28.9444i			1.82696i	−0.406889	+	0.913478i	$0.633386\pi$
$252$		0			0
$253$	−22.7039	+	22.7039i	−1.42738	+	1.42738i
$254$	1.20909	+	10.8742i	0.0758654	+	0.682306i
$255$	8.70225	+	7.19197i	0.544956	+	0.450379i
$256$	10.1217	−	12.3915i	0.632609	−	0.774471i
$257$	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	$-0.138837\pi$
$258$	−5.03181	+	1.96634i	−0.313267	+	0.122419i
$259$		0			0
$260$	−0.322842	+	1.53428i	−0.0200218	+	0.0951523i
$261$	5.37540	+	9.31047i	0.332729	+	0.576303i
$262$	1.21157	−	7.95911i	0.0748511	−	0.491716i
$263$	−12.2013	+	3.26932i	−0.752362	+	0.201595i	−0.614566	−	0.788866i	$-0.710669\pi$
$263$	−12.2013	+	3.26932i	−0.752362	+	0.201595i	−0.137796	+	0.990461i	$0.544002\pi$
$264$	8.69365	+	7.54824i	0.535057	+	0.464562i
$265$	−0.582934	+	0.414698i	−0.0358093	+	0.0254747i
$266$		0			0
$267$	5.64178	−	5.64178i	0.345271	−	0.345271i
$268$	−4.93989	+	2.59232i	−0.301752	+	0.158351i
$269$	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	$0.555758\pi$
$270$	12.5091	−	6.31127i	0.761277	−	0.384092i
$271$	20.6434	−	11.9184i	1.25399	−	0.723994i	0.282094	−	0.959387i	$-0.408971\pi$
$271$	20.6434	−	11.9184i	1.25399	−	0.723994i	0.971900	+	0.235392i	$0.0756375\pi$
$272$	18.4083	−	15.6548i	1.11617	−	0.949214i
$273$		0			0
$274$	−0.281684	+	0.643054i	−0.0170171	+	0.0388483i
$275$	−23.9174	+	4.58670i	−1.44228	+	0.276588i
$276$	−10.7494	+	2.42037i	−0.647040	+	0.145689i
$277$	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	$0.363870\pi$
$278$	5.63029	−	7.03899i	0.337683	−	0.422170i
$279$	−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	$0.151793\pi$
$282$	−3.62617	+	4.53343i	−0.215935	+	0.269962i
$283$	20.9364	−	5.60990i	1.24454	−	0.333474i	0.424316	−	0.905514i	$-0.360515\pi$
$283$	20.9364	−	5.60990i	1.24454	−	0.333474i	0.820225	+	0.572041i	$0.193848\pi$
$284$	−12.6808	+	2.85524i	−0.752464	+	0.169427i
$285$	2.31355	−	5.05975i	0.137043	−	0.299713i
$286$	−0.968945	+	2.21200i	−0.0572949	+	0.130798i
$287$		0			0
$288$	−3.74635	−	12.4689i	−0.220756	−	0.734737i
$289$	16.8843	−	9.74814i	0.993193	−	0.573420i
$290$	4.62031	−	14.0301i	0.271314	−	0.823879i
$291$	−2.41455	−	1.39404i	−0.141543	−	0.0817200i
$292$	2.19648	−	1.15265i	0.128539	−	0.0674538i
$293$	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
$296$	4.59777	−	5.29546i	0.267240	−	0.307792i
$297$	20.8449	−	5.58539i	1.20955	−	0.324097i
$298$	−1.24241	+	8.16170i	−0.0719709	+	0.472795i
$299$	−1.15557	−	2.00151i	−0.0668284	−	0.115750i
$300$	−7.77821	−	3.05683i	−0.449075	−	0.176486i
$301$		0			0
$302$	−4.88129	+	1.90752i	−0.280887	+	0.109765i
$303$	−0.315583	+	1.17777i	−0.0181298	+	0.0676612i
$304$	−9.79993	−	6.76593i	−0.562064	−	0.388053i
$305$	−14.3751	+	17.3938i	−0.823116	+	0.995965i
$306$	−2.17298	−	19.5430i	−0.124221	−	1.11720i
$307$	−3.58241	+	3.58241i	−0.204459	+	0.204459i	−0.801907	−	0.597448i	$-0.796181\pi$
$307$	−3.58241	+	3.58241i	−0.204459	+	0.204459i	0.597448	+	0.801907i	$0.296181\pi$
$308$		0			0
$309$		−	0.461167i		−	0.0262349i
$310$	14.0077	+	15.6818i	0.795583	+	0.890668i
$311$	−21.3073	−	12.3018i	−1.20822	−	0.697569i	−0.245854	−	0.969307i	$-0.579068\pi$
$311$	−21.3073	−	12.3018i	−1.20822	−	0.697569i	−0.962371	+	0.271738i	$0.912402\pi$
$312$	−0.686770	+	0.463824i	−0.0388807	+	0.0262588i
$313$	−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	$-0.0435275\pi$
$318$	−0.373823	−	0.0569050i	−0.0209630	−	0.00319107i
$319$	11.3757	−	19.7032i	0.636915	−	1.10317i
$320$	−9.34786	+	15.2518i	−0.522561	+	0.852602i
$321$	−4.15600			−0.231965
$322$		0			0
$323$	−12.7178	−	12.7178i	−0.707638	−	0.707638i
$324$	−6.11356	−	1.90542i	−0.339642	−	0.105857i
$325$	0.126676	−	1.74836i	0.00702671	−	0.0969818i
$326$	0.606952	+	0.824917i	0.0336160	+	0.0456879i
$327$	−9.04456	−	2.42348i	−0.500165	−	0.134019i
$328$	−2.93311	−	1.42843i	−0.161954	−	0.0788716i
$329$		0			0
$330$	−10.7677	−	7.05351i	−0.592740	−	0.388283i
$331$	1.62048	−	0.935587i	0.0890699	−	0.0514245i	−0.454804	−	0.890592i	$-0.650291\pi$
$331$	1.62048	−	0.935587i	0.0890699	−	0.0514245i	0.543873	+	0.839167i	$0.316957\pi$
$332$	−16.3947	+	25.9231i	−0.899777	+	1.42272i
$333$	−1.47697	−	5.51214i	−0.0809376	−	0.302063i
$334$	−0.617308	−	5.55185i	−0.0337776	−	0.303784i
$335$	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	$0.546208\pi$
$338$	14.2212	+	11.3752i	0.773534	+	0.618729i
$339$	−3.47923	+	6.02620i	−0.188966	+	0.327298i
$340$	−18.0369	+	20.1146i	−0.978187	+	1.09087i
$341$	16.1933	+	28.0476i	0.876915	+	1.51886i
$342$	−9.02567	+	3.52706i	−0.488052	+	0.190722i
$343$		0			0
$344$	−4.21633	−	12.2216i	−0.227330	−	0.658946i
$345$	11.5444	−	4.29973i	0.621529	−	0.231490i
$346$	−25.7218	+	18.9254i	−1.38281	+	1.01744i
$347$	2.72992	+	10.1882i	0.146550	+	0.546931i	0.999682	+	0.0252358i	$0.00803366\pi$
$347$	2.72992	+	10.1882i	0.146550	+	0.546931i	−0.853132	+	0.521696i	$0.825300\pi$
$348$	6.91346	−	3.62800i	0.370600	−	0.194481i
$349$			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
$352$	−18.8879	+	20.0597i	−1.00673	+	1.06918i
$353$	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	$0.839965\pi$
$354$	−0.593158	−	0.806170i	−0.0315260	−	0.0428474i
$355$	13.6185	−	5.07226i	0.722797	−	0.269207i
$356$	12.9461	+	14.0348i	0.686141	+	0.743843i
$357$		0			0
$358$	−4.80156	−	12.2871i	−0.253771	−	0.649392i
$359$	11.6112	+	20.1111i	0.612814	+	1.06143i	0.990764	+	0.135599i	$0.0432960\pi$
$359$	11.6112	+	20.1111i	0.612814	+	1.06143i	−0.377950	+	0.925826i	$0.623371\pi$
$360$	6.02759	+	13.2497i	0.317682	+	0.698320i
$361$	5.06824	−	8.77844i	0.266749	−	0.462023i
$362$	−12.1806	+	15.2282i	−0.640198	+	0.800375i
$363$	−7.51883	−	7.51883i	−0.394636	−	0.394636i
$364$		0			0
$365$	−2.25984	+	1.60764i	−0.118285	+	0.0841480i
$366$	−11.8541	+	1.31805i	−0.619622	+	0.0688955i
$367$	−8.07404	−	30.1327i	−0.421462	−	1.57292i	−0.771530	−	0.636192i	$-0.780508\pi$
$367$	−8.07404	−	30.1327i	−0.421462	−	1.57292i	0.350069	−	0.936724i	$-0.386158\pi$
$368$	−4.75034	−	25.9372i	−0.247628	−	1.35207i
$369$	−2.29906	+	1.32736i	−0.119684	+	0.0690997i
$370$	−4.29642	+	6.55877i	−0.223360	+	0.340974i
$371$		0			0
$372$	−0.448107	+	11.1051i	−0.0232333	+	0.575770i
$373$	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	$0.423099\pi$
$374$	−33.5177	+	24.6614i	−1.73316	+	1.27521i
$375$	9.07730	+	2.21551i	0.468750	+	0.114408i
$376$	−10.4903	−	9.10820i	−0.540997	−	0.469720i
$377$	1.15799	+	1.15799i	0.0596393	+	0.0596393i
$378$		0			0
$379$	18.6149			0.956182			0.478091	−	0.878310i	$-0.341329\pi$
$379$	18.6149			0.956182			0.478091	+	0.878310i	$0.341329\pi$
$380$	11.8755	+	6.02028i	0.609199	+	0.308834i
$381$	3.23285	−	5.59946i	0.165624	−	0.286869i
$382$	0.0368194	−	0.241876i	0.00188384	−	0.0123754i
$383$	−8.07570	+	30.1389i	−0.412649	+	1.54003i	0.376849	+	0.926275i	$0.377008\pi$
$383$	−8.07570	+	30.1389i	−0.412649	+	1.54003i	−0.789498	+	0.613753i	$0.789659\pi$
$384$	−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
$388$	3.56636	−	5.63908i	0.181054	−	0.286281i
$389$	−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	$0.696697\pi$
$390$	0.691010	−	0.617240i	0.0349907	−	0.0312552i
$391$		−	39.8247i		−	2.01402i
$392$		0			0
$393$	−3.36415	+	3.36415i	−0.169699	+	0.169699i
$394$	−21.2026	+	2.35751i	−1.06817	+	0.118770i
$395$	12.6700	−	15.3307i	0.637498	−	0.771369i
$396$	4.92489	+	21.8725i	0.247485	+	1.09914i
$397$	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	$0.0477457\pi$
$398$	−8.83310	−	22.6037i	−0.442763	−	1.13302i
$399$		0			0
$400$	8.05989	−	18.3040i	0.402995	−	0.915202i
$401$	−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	$-0.506609\pi$
$402$	3.25924	+	0.496135i	0.162556	+	0.0247450i
$403$	−2.25175	+	0.603354i	−0.112168	+	0.0300552i
$404$	−2.78580	−	0.868252i	−0.138599	−	0.0431971i
$405$	7.05978	+	1.19053i	0.350803	+	0.0591578i
$406$		0			0
$407$	−8.53940	+	8.53940i	−0.423282	+	0.423282i
$408$	−14.2449	+	1.00457i	−0.705227	+	0.0497337i
$409$	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	$0.302164\pi$
$410$	3.46450	+	1.14091i	0.171099	+	0.0563453i
$411$	0.359291	−	0.207437i	0.0177225	−	0.0102321i
$412$	1.10273	+	0.0444969i	0.0543275	+	0.00219220i
$413$		0			0
$414$	−19.6538	−	8.60918i	−0.965934	−	0.423118i
$415$	14.2602	−	31.1872i	0.700006	−	1.53092i
$416$	−1.04282	−	1.68693i	−0.0511282	−	0.0827088i
$417$	−5.14518	+	1.37865i	−0.251961	+	0.0675126i
$418$	16.0144	+	12.8095i	0.783290	+	0.626532i
$419$	31.8030			1.55368			0.776840	−	0.629699i	$-0.216822\pi$
$419$	31.8030			1.55368			0.776840	+	0.629699i	$0.216822\pi$
$420$		0			0
$421$	13.1193			0.639396			0.319698	−	0.947519i	$-0.396418\pi$
$421$	13.1193			0.639396			0.319698	+	0.947519i	$0.396418\pi$
$422$	2.73209	+	2.18532i	0.132996	+	0.106380i
$423$	−10.9196	+	2.92589i	−0.530928	+	0.142262i
$424$	0.172139	−	0.888384i	0.00835980	−	0.0431437i
$425$	16.9539	−	24.9994i	0.822387	−	1.21265i
$426$	7.03590	+	3.08201i	0.340890	+	0.149324i
$427$		0			0
$428$	0.401002	−	9.93768i	0.0193831	−	0.480356i
$429$	1.23590	−	0.713547i	0.0596698	−	0.0344504i
$430$	6.51103	+	12.9050i	0.313990	+	0.622333i
$431$	17.0409	+	9.83859i	0.820833	+	0.473908i	0.850704	−	0.525646i	$-0.176176\pi$
$431$	17.0409	+	9.83859i	0.820833	+	0.473908i	−0.0298705	+	0.999554i	$0.509509\pi$
$432$	−5.95136	+	16.6936i	−0.286335	+	0.803170i
$433$	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
$436$	6.66764	−	21.3932i	0.319322	−	1.02455i
$437$	−18.9572	+	5.07957i	−0.906847	+	0.242989i
$438$	−1.44919	−	0.220602i	−0.0692449	−	0.0105408i
$439$	−2.34778	−	4.06648i	−0.112054	−	0.194082i	0.804545	−	0.593892i	$-0.202409\pi$
$439$	−2.34778	−	4.06648i	−0.112054	−	0.194082i	−0.916598	+	0.399810i	$0.869076\pi$
$440$	17.9051	−	25.0667i	0.853591	−	1.19501i
$441$		0			0
$442$	−1.09021	−	2.78983i	−0.0518562	−	0.132699i
$443$	1.07698	−	4.01934i	0.0511688	−	0.190965i	−0.935611	−	0.353034i	$-0.885150\pi$
$443$	1.07698	−	4.01934i	0.0511688	−	0.190965i	0.986779	+	0.162069i	$0.0518168\pi$
$444$	−4.04309	+	0.910353i	−0.191876	+	0.0432035i
$445$	−16.4553	−	13.5994i	−0.780054	−	0.644676i
$446$	14.0264	−	1.55959i	0.664168	−	0.0738486i
$447$	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	$0.570163\pi$
$450$	−8.67240	−	13.7712i	−0.408821	−	0.649182i
$451$	4.86537	+	2.80902i	0.229101	+	0.132272i
$452$	−14.0739	−	8.90087i	−0.661983	−	0.418662i
$453$	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	$-0.0990582\pi$
$458$	2.03184	−	13.3477i	0.0949416	−	0.623695i
$459$	−13.3833	+	23.1806i	−0.624680	+	1.08198i
$460$	9.16750	+	28.0194i	0.427437	+	1.30641i
$461$	−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	$0.0126322\pi$
$463$	22.3542	+	22.3542i	1.03889	+	1.03889i	0.0396749	+	0.999213i	$0.487368\pi$
$464$	8.00809	+	16.8813i	0.371766	+	0.783695i
$465$	−1.17542	−	12.3702i	−0.0545089	−	0.573655i
$466$	−23.3212	+	17.1591i	−1.08033	+	0.794879i
$467$	8.28849	+	2.22089i	0.383546	+	0.102771i	0.445440	−	0.895312i	$-0.353047\pi$
$467$	8.28849	+	2.22089i	0.383546	+	0.102771i	−0.0618940	+	0.998083i	$0.519714\pi$
$468$	−1.61249	−	0.0650665i	−0.0745373	−	0.00300770i
$469$		0			0
$470$	12.9930	+	8.51123i	0.599320	+	0.392594i
$471$	7.99094	−	4.61357i	0.368203	−	0.212582i
$472$	1.98492	−	1.34055i	0.0913633	−	0.0617040i
$473$	5.76217	+	21.5047i	0.264945	+	0.988787i
$474$	10.4480	−	1.16171i	0.479893	−	0.0533592i
$475$	−14.0626	−	4.88173i	−0.645237	−	0.223989i
$476$		0			0
$477$	−0.520673	−	0.520673i	−0.0238400	−	0.0238400i
$478$	22.5994	−	28.2537i	1.03367	−	1.29230i
$479$	−12.0963	+	20.9514i	−0.552694	+	0.957294i	0.445385	+	0.895339i	$0.353067\pi$
$479$	−12.0963	+	20.9514i	−0.552694	+	0.957294i	−0.998079	+	0.0619545i	$0.980267\pi$
$480$	9.79102	−	3.98591i	0.446897	−	0.181931i
$481$	−0.434634	−	0.752808i	−0.0198176	−	0.0343251i
$482$	−8.24873	−	21.1083i	−0.375719	−	0.961457i
$483$		0			0
$484$	18.7043	−	17.2533i	0.850194	−	0.784241i
$485$	−3.10203	+	6.78417i	−0.140856	+	0.308053i
$486$	13.3830	+	18.1890i	0.607065	+	0.825071i
$487$	4.79710	+	17.9030i	0.217377	+	0.811263i	0.985316	+	0.170740i	$0.0546157\pi$
$487$	4.79710	+	17.9030i	0.217377	+	0.811263i	−0.767939	+	0.640523i	$0.778718\pi$
$488$	−2.00791	−	28.4722i	−0.0908937	−	1.28888i
$489$		−	0.605222i		−	0.0273691i
$490$		0			0
$491$		−	26.3306i		−	1.18828i	−0.804360	−	0.594142i	$-0.797492\pi$
$491$		−	26.3306i		−	1.18828i	0.804360	−	0.594142i	$-0.202508\pi$
$492$	0.895871	+	1.70716i	0.0403890	+	0.0769646i
$493$	7.30366	+	27.2576i	0.328940	+	1.22762i
$494$	−1.18895	+	0.874800i	−0.0534935	+	0.0393591i
$495$	−8.74894	−	23.4901i	−0.393236	−	1.05580i
$496$	−26.5108	−	2.14300i	−1.19037	−	0.0962235i
$497$		0			0
$498$	16.8826	−	6.59741i	0.756528	−	0.295637i
$499$	−5.41316	−	9.37586i	−0.242326	−	0.419721i	0.719050	−	0.694958i	$-0.244577\pi$
$499$	−5.41316	−	9.37586i	−0.242326	−	0.419721i	−0.961376	+	0.275237i	$0.911244\pi$
$500$	−6.17350	+	21.4916i	−0.276087	+	0.961133i
$501$	−1.65055	+	2.85883i	−0.0737409	+	0.127723i
$502$	31.9657	+	25.5685i	1.42670	+	1.14118i
$503$	1.75566	+	1.75566i	0.0782809	+	0.0782809i	0.745163	−	0.666882i	$-0.232372\pi$
$503$	1.75566	+	1.75566i	0.0782809	+	0.0782809i	−0.666882	+	0.745163i	$0.732372\pi$
$504$		0			0
$505$	3.21697	+	0.542494i	0.143153	+	0.0241407i
$506$	5.01795	+	45.1296i	0.223075	+	2.00626i
$507$	−2.78535	−	10.3951i	−0.123702	−	0.461662i
$508$	13.0773	+	8.27057i	0.580213	+	0.366947i
$509$	−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	$0.583668\pi$
$510$	15.6300	−	3.25747i	0.692107	−	0.144243i
$511$		0			0
$512$	−4.74380	−	22.1246i	−0.209648	−	0.977777i
$513$	12.7414	+	3.41405i	0.562546	+	0.150734i
$514$	−17.2698	−	23.4716i	−0.761737	−	1.03529i
$515$	−1.22836	+	0.116719i	−0.0541279	+	0.00514325i
$516$	−2.27334	+	7.29404i	−0.100078	+	0.321102i
$517$	16.9166	+	16.9166i	0.743991	+	0.743991i
$518$		0			0
$519$	18.8714			0.828364
$520$	1.40925	+	1.71188i	0.0617998	+	0.0750708i
$521$	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	$-0.0874833\pi$
$522$	15.0308	+	2.28805i	0.657879	+	0.100145i
$523$	9.21055	−	34.3742i	0.402749	−	1.50308i	−0.405421	−	0.914130i	$-0.632875\pi$
$523$	9.21055	−	34.3742i	0.402749	−	1.50308i	0.808170	−	0.588950i	$-0.200458\pi$
$524$	−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
$528$	16.0158	−	2.93326i	0.697000	−	0.127654i
$529$	−17.7159	−	10.2283i	−0.770257	−	0.444708i
$530$	−0.0569586	+	1.01011i	−0.00247412	+	0.0438765i
$531$		−	1.94903i		−	0.0845806i
$532$		0			0
$533$	−0.285944	+	0.285944i	−0.0123856	+	0.0123856i
$534$	−1.24693	−	11.2144i	−0.0539600	−	0.485297i
$535$	1.05186	+	11.0698i	0.0454759	+	0.478591i
$536$	−1.50082	+	7.74551i	−0.0648255	+	0.334555i
$537$	−2.01770	+	7.53016i	−0.0870702	+	0.324950i
$538$	14.7521	−	5.76483i	0.636006	−	0.248540i
$539$		0			0
$540$	4.08001	−	19.3900i	0.175576	−	0.834411i
$541$	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	$0.536116\pi$
$542$	5.07311	−	33.3266i	0.217909	−	1.43150i
$543$	11.1311	−	2.98257i	0.477681	−	0.127994i
$544$	−1.02765	−	34.1588i	−0.0440600	−	1.46455i
$545$	−4.16602	+	24.7043i	−0.178453	+	1.05822i
$546$		0			0
$547$	27.0715	−	27.0715i	1.15749	−	1.15749i	0.172480	−	0.985013i	$-0.444822\pi$
$547$	27.0715	−	27.0715i	1.15749	−	1.15749i	0.985013	−	0.172480i	$-0.0551781\pi$
$548$	0.461349	+	0.879140i	0.0197078	+	0.0375550i
$549$	−20.1143	−	11.6130i	−0.858458	−	0.495631i
$550$	−16.0624	+	30.4658i	−0.684903	+	1.29906i
$551$	12.0435	−	6.95334i	0.513072	−	0.296222i
$552$	−6.82266	+	14.0096i	−0.290392	+	0.596287i
$553$		0			0
$554$	3.11852	−	7.11924i	0.132493	−	0.302468i
$555$	4.34208	−	1.61722i	0.184311	−	0.0686472i
$556$	−2.80013	−	12.4360i	−0.118752	−	0.527404i
$557$	−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	$0.529384\pi$
$558$	−13.5188	+	16.9012i	−0.572298	+	0.715486i
$559$	−1.60251			−0.0677790
$560$		0			0
$561$	24.5911			1.03824
$562$	26.3118	−	32.8949i	1.10989	−	1.38759i
$563$	22.6700	−	6.07440i	0.955425	−	0.256005i	0.252762	−	0.967528i	$-0.418661\pi$
$563$	22.6700	−	6.07440i	0.955425	−	0.256005i	0.702663	+	0.711523i	$0.251994\pi$
$564$	1.80341	+	8.00937i	0.0759374	+	0.337255i
$565$	16.9319	+	7.74202i	0.712329	+	0.325709i
$566$	12.2991	−	28.0774i	0.516968	−	1.18018i
$567$		0			0
$568$	−8.04848	+	16.5266i	−0.337707	+	0.693443i
$569$	−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	$0.466909\pi$
$570$	−3.54419	−	7.02465i	−0.148450	−	0.294230i
$571$	−40.3258	−	23.2821i	−1.68758	−	0.974327i	−0.956361	−	0.292189i	$-0.905616\pi$
$571$	−40.3258	−	23.2821i	−1.68758	−	0.974327i	−0.731223	−	0.682138i	$-0.761050\pi$
$572$	1.58696	+	3.02409i	0.0663542	+	0.126444i
$573$	−0.102236	+	0.102236i	−0.00427097	+	0.00427097i
$574$		0			0
$575$	−14.3745	−	29.6612i	−0.599459	−	1.23696i
$576$	−17.0799	−	6.87720i	−0.711661	−	0.286550i
$577$	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	$0.247554\pi$
$578$	4.14931	−	27.2579i	0.172589	−	1.13378i
$579$	3.93306	+	6.81225i	0.163452	+	0.283108i
$580$	−11.4132	−	17.4964i	−0.473909	−	0.726497i
$581$		0			0
$582$	−3.67248	+	1.43514i	−0.152229	+	0.0594884i
$583$	−0.403313	+	1.50519i	−0.0167035	+	0.0623385i
$584$	0.667324	−	3.44397i	0.0276141	−	0.142512i
$585$	1.79619	−	0.170675i	0.0742634	−	0.00705653i
$586$	−0.630286	−	5.66857i	−0.0260369	−	0.234166i
$587$	0.195894	−	0.195894i	0.00808542	−	0.00808542i	−0.703053	−	0.711138i	$-0.748180\pi$
$587$	0.195894	−	0.195894i	0.00808542	−	0.00808542i	0.711138	+	0.703053i	$0.248180\pi$
$588$		0			0
$589$			19.7961i			0.815686i
$590$	−1.99718	+	1.78396i	−0.0822224	+	0.0734446i
$591$	10.9179	+	6.30346i	0.449103	+	0.259290i
$592$	−1.78670	−	9.75553i	−0.0734329	−	0.400950i
$593$	−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
$598$	−3.23122	−	0.491871i	−0.132135	−	0.0201141i
$599$	−8.35085	+	14.4641i	−0.341206	+	0.590987i	−0.984657	−	0.174501i	$-0.944169\pi$
$599$	−8.35085	+	14.4641i	−0.341206	+	0.590987i	0.643451	+	0.765488i	$0.277502\pi$
$600$	−10.2469	+	5.88982i	−0.418329	+	0.240451i
$601$	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
$604$	−2.20534	+	7.07586i	−0.0897339	+	0.287913i
$605$	−18.1241	+	21.9300i	−0.736848	+	0.891582i
$606$	1.02194	+	1.38893i	0.0415133	+	0.0564214i
$607$	30.8579	+	8.26835i	1.25248	+	0.335602i	0.823295	−	0.567613i	$-0.192133\pi$
$607$	30.8579	+	8.26835i	1.25248	+	0.335602i	0.429188	+	0.903215i	$0.358800\pi$
$608$	−16.1291	+	4.84608i	−0.654122	+	0.196535i
$609$		0			0
$610$	6.51094	+	31.2407i	0.263620	+	1.26490i
$611$	−1.49132	+	0.861012i	−0.0603322	+	0.0348328i
$612$	−23.5026	−	14.8639i	−0.950035	−	0.600836i
$613$	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	$0.727627\pi$
$614$	0.791775	+	7.12094i	0.0319534	+	0.287378i
$615$	−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	$0.651515\pi$
$618$	−0.509305	−	0.407380i	−0.0204873	−	0.0163872i
$619$	−1.43357	+	2.48301i	−0.0576199	+	0.0998006i	−0.893397	−	0.449269i	$-0.851684\pi$
$619$	−1.43357	+	2.48301i	−0.0576199	+	0.0998006i	0.835777	+	0.549070i	$0.185018\pi$
$620$	29.6927	−	1.61706i	1.19249	−	0.0649427i
$621$	14.6039	+	25.2946i	0.586033	+	1.01504i
$622$	−32.4080	+	12.6644i	−1.29944	+	0.507798i
$623$		0			0
$624$	−0.0944300	+	1.16818i	−0.00378022	+	0.0467648i
$625$	3.60378	−	24.7389i	0.144151	−	0.989556i
$626$	−7.65961	+	5.63573i	−0.306140	+	0.225249i
$627$	−3.13656	−	11.7058i	−0.125262	−	0.467485i
$628$	10.2608	+	19.5528i	0.409450	+	0.780242i
$629$		−	14.9789i		−	0.597247i
$630$		0			0
$631$			0.116828i			0.00465086i	0.999997	+	0.00232543i	$0.000740209\pi$
$631$			0.116828i			0.00465086i	−0.999997	+	0.00232543i	$0.999260\pi$
$632$	1.76974	+	25.0951i	0.0703966	+	0.998228i
$633$	−0.535103	−	1.99703i	−0.0212684	−	0.0793748i
$634$	−11.5820	−	15.7413i	−0.459982	−	0.625168i
$635$	−15.7329	−	7.19378i	−0.624340	−	0.285476i
$636$	−0.393068	+	0.362577i	−0.0155862	+	0.0143771i
$637$		0			0
$638$	−11.7111	−	29.9683i	−0.463645	−	1.18646i
$639$	7.47903	+	12.9541i	0.295866	+	0.512455i
$640$	8.58626	+	23.7966i	0.339402	+	0.940642i
$641$	−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	$0.212654\pi$
$642$	−3.67127	+	4.58981i	−0.144893	+	0.181146i
$643$	2.55764	+	2.55764i	0.100863	+	0.100863i	0.755738	−	0.654874i	$-0.227278\pi$
$643$	2.55764	+	2.55764i	0.100863	+	0.100863i	−0.654874	+	0.755738i	$0.727278\pi$
$644$		0			0
$645$	1.42041	−	8.42297i	0.0559286	−	0.331654i
$646$	−25.2799	+	2.81086i	−0.994622	+	0.110592i
$647$	3.58712	+	13.3873i	0.141024	+	0.526309i	0.999900	+	0.0141258i	$0.00449654\pi$
$647$	3.58712	+	13.3873i	0.141024	+	0.526309i	−0.858876	+	0.512183i	$0.828837\pi$
$648$	−7.50483	+	5.06854i	−0.294817	+	0.199111i
$649$	−3.57203	+	2.06231i	−0.140214	+	0.0809528i
$650$	−1.81896	−	1.68434i	−0.0713456	−	0.0660654i
$651$		0			0
$652$	1.44719	+	0.0583963i	0.0566762	+	0.00228698i
$653$	−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	$0.779946\pi$
$654$	−10.6661	+	7.84784i	−0.417078	+	0.306875i
$655$	9.81216	+	8.10926i	0.383393	+	0.316855i
$656$	−4.16854	+	1.97746i	−0.162754	+	0.0772067i
$657$	−2.01848	−	2.01848i	−0.0787482	−	0.0787482i
$658$		0			0
$659$	−41.1139			−1.60157			−0.800784	−	0.598953i	$-0.795584\pi$
$659$	−41.1139			−1.60157			−0.800784	+	0.598953i	$0.795584\pi$
$660$	−17.3016	+	5.66079i	−0.673463	+	0.220346i
$661$	−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	$0.264498\pi$
$662$	0.398234	−	2.61610i	0.0154778	−	0.101678i
$663$	−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
$668$	−6.67668	−	4.22257i	−0.258329	−	0.163376i
$669$	−7.22264	−	4.16999i	−0.279243	−	0.161221i
$670$	0.496602	−	8.80682i	0.0191854	−	0.340237i
$671$			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	$0.230411\pi$
$674$	30.8279	−	3.42774i	1.18745	−	0.132032i
$675$	−1.60090	+	22.0955i	−0.0616188	+	0.850454i
$676$	25.1251	−	5.65725i	0.966352	−	0.217587i
$677$	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	$-0.211998\pi$
$678$	3.58180	+	9.16574i	0.137558	+	0.352008i
$679$		0			0
$680$	6.28107	+	37.6882i	0.240868	+	1.44528i
$681$	−8.51279	−	14.7446i	−0.326211	−	0.565014i
$682$	45.2799	+	6.89269i	1.73386	+	0.263935i
$683$	41.8335	−	11.2093i	1.60072	−	0.428910i	0.655457	−	0.755233i	$-0.272476\pi$
$683$	41.8335	−	11.2093i	1.60072	−	0.428910i	0.945259	+	0.326322i	$0.105810\pi$
$684$	−4.07774	+	13.0835i	−0.155916	+	0.500260i
$685$	−0.643460	−	0.904501i	−0.0245853	−	0.0345592i
$686$		0			0
$687$	−5.64178	+	5.64178i	−0.215247	+	0.215247i
$688$	−17.2219	−	6.13972i	−0.656580	−	0.234075i
$689$	−0.0971379	−	0.0560826i	−0.00370066	−	0.00213658i
$690$	5.44937	−	16.5477i	0.207454	−	0.629959i
$691$	−37.3091	+	21.5404i	−1.41930	+	0.819436i	−0.996238	−	0.0866626i	$-0.972380\pi$
$691$	−37.3091	+	21.5404i	−1.41930	+	0.819436i	−0.423067	+	0.906098i	$0.639046\pi$
$692$	−1.82086	+	45.1248i	−0.0692186	+	1.71539i
$693$		0			0
$694$	13.6632	+	5.98504i	0.518648	+	0.227189i
$695$	4.97436	+	13.3557i	0.188688	+	0.506610i
$696$	2.10042	−	10.8400i	0.0796162	−	0.410888i
$697$	−6.73079	+	1.80351i	−0.254947	+	0.0683128i
$698$	8.75182	+	7.00034i	0.331261	+	0.264967i
$699$	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	$0.580973\pi$
$702$	1.71549	+	1.37217i	0.0647470	+	0.0517894i
$703$	−7.13021	+	1.91053i	−0.268921	+	0.0720572i
$704$	5.46859	+	38.5796i	0.206105	+	1.45402i
$705$	−3.20372	−	8.60169i	−0.120659	−	0.323958i
$706$	11.6161	+	5.08830i	0.437176	+	0.191501i
$707$		0			0
$708$	−1.41430	−	0.0570692i	−0.0531525	−	0.00214479i
$709$	−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	$0.359676\pi$
$710$	6.42844	−	19.5208i	0.241255	−	0.732601i
$711$	17.7285	+	10.2356i	0.664871	+	0.383863i
$712$	26.9359	−	1.89957i	1.00947	−	0.0711892i
$713$	−30.9949	+	30.9949i	−1.16077	+	1.16077i
$714$		0			0
$715$	−2.21339	−	3.11133i	−0.0827762	−	0.116357i
$716$	−17.8112	−	5.55123i	−0.665636	−	0.207459i
$717$	−20.6522	+	5.53374i	−0.771271	+	0.206661i
$718$	32.4673	+	4.94232i	1.21167	+	0.184446i
$719$	−0.144472	−	0.250232i	−0.00538788	−	0.00933208i	0.863319	−	0.504659i	$-0.168382\pi$
$719$	−0.144472	−	0.250232i	−0.00538788	−	0.00933208i	−0.868707	+	0.495327i	$0.835048\pi$
$720$	19.9573	+	5.04756i	0.743765	+	0.188111i
$721$		0			0
$722$	−5.21766	−	13.3519i	−0.194181	−	0.496905i
$723$	−3.46626	+	12.9363i	−0.128912	+	0.481105i
$724$	6.05781	+	26.9041i	0.225137	+	0.999884i
$725$	15.2782	+	17.6651i	0.567420	+	0.656066i
$726$	−14.9456	+	1.66179i	−0.554682	+	0.0616749i
$727$	4.87969	−	4.87969i	0.180978	−	0.180978i	−0.610804	−	0.791782i	$-0.709154\pi$
$727$	4.87969	−	4.87969i	0.180978	−	0.180978i	0.791782	+	0.610804i	$0.209154\pi$
$728$		0			0
$729$		−	3.73943i		−	0.138497i
$730$	−0.220809	+	3.91587i	−0.00817252	+	0.144933i
$731$	−23.9143	−	13.8069i	−0.884502	−	0.510667i
$732$	−9.01585	+	14.2558i	−0.333235	+	0.526908i
$733$	−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
$738$	−0.564994	+	3.71159i	−0.0207977	+	0.136625i
$739$	2.90840	−	5.03750i	0.106987	−	0.185307i	−0.807561	−	0.589784i	$-0.799213\pi$
$739$	2.90840	−	5.03750i	0.106987	−	0.185307i	0.914548	+	0.404477i	$0.132546\pi$
$740$	3.44809	+	10.5387i	0.126754	+	0.387410i
$741$	0.872306			0.0320449
$742$		0			0
$743$	5.70591	+	5.70591i	0.209329	+	0.209329i	0.803982	−	0.594653i	$-0.202711\pi$
$743$	5.70591	+	5.70591i	0.209329	+	0.209329i	−0.594653	+	0.803982i	$0.702711\pi$
$744$	11.8684	+	10.3047i	0.435117	+	0.377789i
$745$	−10.0619	−	8.31567i	−0.368640	−	0.304663i
$746$	21.2253	−	15.6170i	0.777114	−	0.571780i
$747$	34.0944	+	9.13556i	1.24745	+	0.334253i
$748$	−2.37274	+	58.8015i	−0.0867558	+	2.15000i
$749$		0			0
$750$	10.4654	−	8.06772i	0.382141	−	0.294591i
$751$	−36.3916	+	21.0107i	−1.32795	+	0.766690i	−0.984982	−	0.172658i	$-0.944764\pi$
$751$	−36.3916	+	21.0107i	−1.32795	+	0.766690i	−0.342965	+	0.939348i	$0.611431\pi$
$752$	−19.3258	+	3.53946i	−0.704738	+	0.129071i
$753$	−6.26077	−	23.3655i	−0.228155	−	0.851486i
$754$	2.30179	−	0.255935i	0.0838262	−	0.00932060i
$755$	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	$-0.629564\pi$
$758$	16.4438	−	20.5580i	0.597264	−	0.746699i
$759$	13.4169	−	23.2387i	0.487002	−	0.843512i
$760$	17.1391	−	7.79697i	0.621700	−	0.282826i
$761$	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	$0.831272\pi$
$762$	−3.32816	−	8.51669i	−0.120567	−	0.308527i
$763$		0			0
$764$	−0.234599	−	0.254328i	−0.00848748	−	0.00920125i
$765$	28.2751	+	12.9287i	1.02229	+	0.467437i
$766$	26.1511	+	35.5424i	0.944879	+	1.28420i
$767$	−0.0768408	−	0.286774i	−0.00277456	−	0.0103548i
$768$	−5.49050	+	12.1925i	−0.198121	+	0.439959i
$769$		−	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
$772$	−16.6687	+	8.74730i	−0.599921	+	0.314822i
$773$	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	$0.765624\pi$
$774$	−11.9836	+	8.81719i	−0.430740	+	0.316927i
$775$	−32.6516	+	6.26167i	−1.17288	+	0.224926i
$776$	−3.07731	−	8.92000i	−0.110469	−	0.320209i
$777$		0			0
$778$	−4.89461	+	1.91272i	−0.175480	+	0.0685745i
$779$	1.71700	+	2.97394i	0.0615181	+	0.106552i
$780$	−0.0712548	−	1.30839i	−0.00255133	−	0.0468479i
$781$	15.8275	−	27.4140i	0.566351	−	0.980949i
$782$	−43.9817	−	35.1798i	−1.57278	−	1.25803i
$783$	−14.6344	−	14.6344i	−0.522990	−	0.522990i
$784$		0			0
$785$	−14.3111	−	20.1169i	−0.510785	−	0.718002i
$786$	0.743536	+	6.68710i	0.0265211	+	0.238521i
$787$	0.657725	+	2.45466i	0.0234454	+	0.0874993i	0.976657	−	0.214804i	$-0.0689112\pi$
$787$	0.657725	+	2.45466i	0.0234454	+	0.0874993i	−0.953212	+	0.302303i	$0.902245\pi$
$788$	−16.1261	+	25.4984i	−0.574468	+	0.908342i
$789$	9.14236	−	5.27834i	0.325477	−	0.187914i
$790$	−5.73866	−	27.5352i	−0.204172	−	0.979657i
$791$		0			0
$792$	28.5062	+	13.8825i	1.01292	+	0.493293i
$793$	−3.41740	−	0.915690i	−0.121356	−	0.0325171i
$794$	−3.72628	−	5.06444i	−0.132241	−	0.179730i
$795$	0.380875	−	0.460857i	0.0135083	−	0.0163449i
$796$	−32.7660	−	10.2122i	−1.16136	−	0.361962i
$797$	−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
$800$	−13.0949	−	25.0704i	−0.462973	−	0.886372i
$801$	10.9864	−	19.0290i	0.388185	−	0.672357i
$802$	−49.0632	−	7.46861i	−1.73248	−	0.263726i
$803$	−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
$808$	−3.41977	+	2.30961i	−0.120307	+	0.0812517i
$809$	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	$0.354163\pi$
$810$	7.55117	−	6.74503i	0.265321	−	0.236996i
$811$			5.30651i			0.186337i	0.995650	+	0.0931683i	$0.0296995\pi$
$811$			5.30651i			0.186337i	−0.995650	+	0.0931683i	$0.970301\pi$
$812$		0			0
$813$	−14.0864	+	14.0864i	−0.494033	+	0.494033i
$814$	1.88736	+	16.9742i	0.0661518	+	0.594945i
$815$	−1.61206	+	0.153178i	−0.0564680	+	0.00536561i
$816$	−11.4740	+	16.6192i	−0.401671	+	0.581789i
$817$	−3.52210	+	13.1447i	−0.123223	+	0.459874i
$818$	48.5233	−	18.9620i	1.69658	−	0.662991i
$819$		0			0
$820$	4.32042	−	2.81830i	0.150876	−	0.0984193i
$821$	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	$0.796139\pi$
$822$	0.0882958	−	0.580038i	0.00307967	−	0.0202311i
$823$	−29.6750	+	7.95140i	−1.03441	+	0.277168i	−0.735794	−	0.677206i	$-0.763191\pi$
$823$	−29.6750	+	7.95140i	−1.03441	+	0.277168i	−0.298613	+	0.954374i	$0.596524\pi$
$824$	1.02325	−	1.17853i	0.0356468	−	0.0410560i
$825$	18.3153	−	8.87605i	0.637658	−	0.309024i
$826$		0			0
$827$	−34.0292	+	34.0292i	−1.18331	+	1.18331i	−0.204428	+	0.978882i	$0.565533\pi$
$827$	−34.0292	+	34.0292i	−1.18331	+	1.18331i	−0.978882	+	0.204428i	$0.934467\pi$
$828$	−26.8694	+	14.1003i	−0.933776	+	0.490020i
$829$	−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	$0.691644\pi$
$830$	−21.8457	−	43.2985i	−0.758274	−	1.50291i
$831$	−3.97770	+	2.29653i	−0.137985	+	0.0796657i
$832$	−2.78421	−	0.338513i	−0.0965252	−	0.0117358i
$833$		0			0
$834$	−3.02252	+	6.90010i	−0.104661	+	0.238931i
$835$	8.03248	+	3.67281i	0.277975	+	0.127103i
$836$	28.2932	−	6.37058i	0.978540	−	0.220331i
$837$	28.4571	−	7.62506i	0.983622	−	0.263561i
$838$	28.0937	−	35.1227i	0.970481	−	1.21329i
$839$	−28.1768			−0.972772			−0.486386	−	0.873744i	$-0.661685\pi$
$839$	−28.1768			−0.972772			−0.486386	+	0.873744i	$0.661685\pi$
$840$		0			0
$841$	7.18076			0.247612
$842$	11.5892	−	14.4888i	0.399389	−	0.499316i
$843$	−24.0447	+	6.44276i	−0.828144	+	0.221900i
$844$	4.82687	−	1.08683i	0.166148	−	0.0374103i
$845$	−26.9832	+	10.0500i	−0.928251	+	0.345729i
$846$	−6.41468	+	14.6440i	−0.220541	+	0.503472i
$847$		0			0
$848$	−0.829055	−	0.974876i	−0.0284699	−	0.0334774i
$849$	−15.6876	+	9.05723i	−0.538396	+	0.310843i
$850$	−12.6324	−	40.8073i	−0.433288	−	1.39968i
$851$	−14.1551	−	8.17246i	−0.485231	−	0.280148i
$852$	9.61900	−	5.04779i	0.329541	−	0.172934i
$853$	−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
$856$	−10.6208	−	9.22148i	−0.363011	−	0.315184i
$857$	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	$0.292832\pi$
$858$	0.303723	−	1.99523i	0.0103689	−	0.0681161i
$859$	9.63913	+	16.6955i	0.328883	+	0.569642i	0.982290	−	0.187364i	$-0.0599945\pi$
$859$	9.63913	+	16.6955i	0.328883	+	0.569642i	−0.653408	+	0.757006i	$0.726661\pi$
$860$	20.0037	+	4.20915i	0.682120	+	0.143531i
$861$		0			0
$862$	25.9190	−	10.1287i	0.882804	−	0.344983i
$863$	4.28964	−	16.0091i	0.146021	−	0.544958i	−0.853687	−	0.520787i	$-0.825639\pi$
$863$	4.28964	−	16.0091i	0.146021	−	0.544958i	0.999708	−	0.0241711i	$-0.00769465\pi$
$864$	13.1789	+	21.3191i	0.448355	+	0.725291i
$865$	−4.77626	−	50.2657i	−0.162398	−	1.70908i
$866$	−2.78918	−	25.0849i	−0.0947803	−	0.852420i
$867$	−11.5214	+	11.5214i	−0.391286	+	0.391286i
$868$		0			0
$869$		−	43.3219i		−	1.46960i
$870$	−0.695002	+	12.3253i	−0.0235628	+	0.417866i
$871$	0.846911	+	0.488964i	0.0286965	+	0.0165679i
$872$	−17.7364	−	26.2617i	−0.600629	−	0.889333i
$873$	−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	$0.856513\pi$
$878$	−6.56491	−	0.999338i	−0.221555	−	0.0337260i
$879$	−1.68525	+	2.91893i	−0.0568419	+	0.0984531i
$880$	−11.8665	−	41.9171i	−0.400020	−	1.41303i
$881$	−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	$0.0514666\pi$
$883$	34.1114	+	34.1114i	1.14794	+	1.14794i	0.160984	+	0.986957i	$0.448533\pi$
$884$	−4.04410	−	1.26043i	−0.136018	−	0.0423928i
$885$	1.57542	−	0.149697i	0.0529572	−	0.00503201i
$886$	−3.48753	−	4.73995i	−0.117166	−	0.159242i
$887$	−40.4245	−	10.8317i	−1.35732	−	0.363693i	−0.494490	−	0.869184i	$-0.664645\pi$
$887$	−40.4245	−	10.8317i	−1.35732	−	0.363693i	−0.862832	+	0.505490i	$0.831312\pi$
$888$	−2.56615	+	5.26929i	−0.0861142	+	0.176826i
$889$		0			0
$890$	−29.5550	+	6.15962i	−0.990687	+	0.206471i
$891$	13.5056	−	7.79744i	0.452454	−	0.261224i
$892$	10.6680	−	16.8682i	0.357193	−	0.564789i
$893$	3.78478	+	14.1250i	0.126653	+	0.472674i
$894$	−0.762462	−	6.85731i	−0.0255005	−	0.229343i
$895$	20.5679	+	3.46847i	0.687509	+	0.115938i
$896$		0			0
$897$	1.36577	+	1.36577i	0.0456018	+	0.0456018i
$898$	45.6706	+	36.5306i	1.52405	+	1.21904i
$899$	15.5298	−	26.8985i	0.517949	−	0.897114i
$900$	−22.8696	−	2.58739i	−0.762321	−	0.0862462i
$901$	−0.966393	−	1.67384i	−0.0321952	−	0.0557637i
$902$	7.40015	−	2.89184i	0.246398	−	0.0962877i
$903$		0			0
$904$	−22.2624	+	7.68031i	−0.740437	+	0.255443i
$905$	−10.7616	−	28.8938i	−0.357726	−	0.960461i
$906$	3.52784	−	2.59569i	0.117205	−	0.0862361i
$907$	7.45963	+	27.8397i	0.247693	+	0.924403i	0.972011	+	0.234936i	$0.0754882\pi$
$907$	7.45963	+	27.8397i	0.247693	+	0.924403i	−0.724318	+	0.689466i	$0.757845\pi$
$908$	36.0781	−	18.9328i	1.19730	−	0.628308i
$909$			3.35793i			0.111375i
$910$		0			0
$911$			19.1234i			0.633586i	0.948495	+	0.316793i	$0.102606\pi$
$911$			19.1234i			0.633586i	−0.948495	+	0.316793i	$0.897394\pi$
$912$	9.37453	+	3.34207i	0.310422	+	0.110667i
$913$	−19.3331	−	72.1521i	−0.639832	−	2.38789i
$914$	−19.4276	−	26.4043i	−0.642607	−	0.873376i
$915$	7.84203	−	17.1506i	0.259249	−	0.566981i
$916$	−12.9461	−	14.0348i	−0.427751	−	0.463723i
$917$		0			0
$918$	13.7779	+	35.2573i	0.454738	+	1.16366i
$919$	−13.6744	−	23.6848i	−0.451077	−	0.781289i	0.547376	−	0.836887i	$-0.315627\pi$
$919$	−13.6744	−	23.6848i	−0.451077	−	0.781289i	−0.998453	+	0.0555980i	$0.982293\pi$
$920$	39.0425	+	14.6270i	1.28719	+	0.482238i
$921$	2.11703	−	3.66680i	0.0697585	−	0.120825i
$922$	−14.9405	+	18.6786i	−0.492039	+	0.615146i
$923$	1.61116	+	1.61116i	0.0530319	+	0.0530319i
$924$		0			0
$925$	−5.40656	−	11.1562i	−0.177767	−	0.366814i
$926$	44.4346	−	4.94066i	1.46021	−	0.162360i
$927$	−0.328707	−	1.22675i	−0.0107962	−	0.0402918i
$928$	25.7175	+	6.06837i	0.844219	+	0.199204i
$929$	−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	$0.412221\pi$
$930$	−14.6998	−	9.62931i	−0.482025	−	0.315758i
$931$		0			0
$932$	−1.65092	+	40.9133i	−0.0540776	+	1.34016i
$933$	19.8613	+	5.32182i	0.650230	+	0.174229i
$934$	9.77450	−	7.19181i	0.319831	−	0.235323i
$935$	−6.22388	−	65.5005i	−0.203543	−	2.14210i
$936$	−1.49628	+	1.72333i	−0.0489073	+	0.0563287i
$937$	−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
$940$	20.8772	−	6.83067i	0.680939	−	0.222792i
$941$	−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	$0.301489\pi$
$942$	1.96377	−	12.9005i	0.0639832	−	0.420322i
$943$	−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	0.582245	−	0.813014i	$-0.302175\pi$
$947$	20.9252	+	5.60688i	0.679976	+	0.182199i	0.0977318	+	0.995213i	$0.468841\pi$
$948$	7.94645	−	12.5648i	0.258089	−	0.408087i
$949$	−0.376571	−	0.217413i	−0.0122240	−	0.00705754i
$950$	−17.8137	+	11.2182i	−0.577954	+	0.363965i
$951$			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	$0.0749605\pi$
$954$	−1.03497	+	0.115078i	−0.0335083	+	0.00372578i
$955$	0.298189	+	0.246439i	0.00964918	+	0.00797457i
$956$	−11.2394	−	49.9168i	−0.363509	−	1.61443i
$957$	−4.92119	+	18.3661i	−0.159079	+	0.593692i
$958$	12.4529	+	31.8667i	0.402336	+	1.02957i
$959$		0			0
$960$	4.24709	−	14.3341i	0.137074	−	0.462630i
$961$	6.60673	+	11.4432i	0.213120	+	0.369135i
$962$	−1.21533	−	0.185003i	−0.0391838	−	0.00596473i
$963$	−11.0554	+	2.96228i	−0.356254	+	0.0954580i
$964$	−30.5983	−	9.53660i	−0.985505	−	0.307153i
$965$	17.1496	−	12.2002i	0.552064	−	0.392737i
$966$		0			0
$967$	−11.0053	+	11.0053i	−0.353908	+	0.353908i	−0.861561	−	0.507654i	$-0.830513\pi$
$967$	−11.0053	+	11.0053i	−0.353908	+	0.353908i	0.507654	+	0.861561i	$0.330513\pi$
$968$	−2.53156	−	35.8977i	−0.0813675	−	1.15380i
$969$	13.0174	+	7.51561i	0.418180	+	0.241436i
$970$	4.75210	+	9.41875i	0.152581	+	0.302418i
$971$	15.7328	−	9.08331i	0.504888	−	0.291497i	−0.225842	−	0.974164i	$-0.572513\pi$
$971$	15.7328	−	9.08331i	0.504888	−	0.291497i	0.730730	+	0.682667i	$0.239180\pi$
$972$	31.9098	+	1.28761i	1.02351	+	0.0413002i
$973$		0			0
$974$	24.0094	+	10.5171i	0.769310	+	0.336989i
$975$	0.275917	+	1.43877i	0.00883641	+	0.0460777i
$976$	−33.2180	−	22.9339i	−1.06328	−	0.734097i
$977$	−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	$0.420532\pi$
$978$	−0.668397	−	0.534633i	−0.0213730	−	0.0170957i
$979$	−46.4999			−1.48614
$980$		0			0
$981$	−25.7868			−0.823310
$982$	−29.0791	−	23.2596i	−0.927951	−	0.742243i
$983$	32.5127	−	8.71176i	1.03699	−	0.277862i	0.300127	−	0.953899i	$-0.402971\pi$
$983$	32.5127	−	8.71176i	1.03699	−	0.277862i	0.736867	+	0.676037i	$0.236304\pi$
$984$	2.67674	+	0.518662i	0.0853314	+	0.0165343i
$985$	14.0265	−	30.6762i	0.446923	−	0.977424i
$986$	36.5547	+	16.0124i	1.16414	+	0.509940i
$987$		0			0
$988$	−0.0841666	+	2.08583i	−0.00267770	+	0.0663591i
$989$	−26.0952	+	15.0661i	−0.829779	+	0.479073i
$990$	−33.6706	−	11.0882i	−1.07012	−	0.352405i
$991$	−25.1531	−	14.5222i	−0.799016	−	0.461312i	0.0441111	−	0.999027i	$-0.485954\pi$
$991$	−25.1531	−	14.5222i	−0.799016	−	0.461312i	−0.843127	+	0.537715i	$0.819288\pi$
$992$	−25.7855	+	27.3851i	−0.818689	+	0.869476i
$993$	−1.10577	+	1.10577i	−0.0350906	+	0.0350906i
$994$		0			0
$995$	37.8373	+	6.38071i	1.19952	+	0.202282i
$996$	7.62746	−	24.4728i	0.241685	−	0.775451i
$997$	−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	$0.688021\pi$
$998$	−15.1364	−	2.30412i	−0.479133	−	0.0729357i
$999$	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.67.12		72
4.3	odd	2	inner	980.2.x.m.67.9		72
5.3	odd	4	inner	980.2.x.m.263.4		72
7.2	even	3	inner	980.2.x.m.667.1		72
7.3	odd	6		980.2.k.k.687.12		36
7.4	even	3		980.2.k.j.687.12		36
7.5	odd	6		140.2.w.b.107.1	yes	72
7.6	odd	2		140.2.w.b.67.12	yes	72
20.3	even	4	inner	980.2.x.m.263.1		72
28.3	even	6		980.2.k.k.687.16		36
28.11	odd	6		980.2.k.j.687.16		36
28.19	even	6		140.2.w.b.107.4	yes	72
28.23	odd	6	inner	980.2.x.m.667.4		72
28.27	even	2		140.2.w.b.67.9	yes	72
35.3	even	12		980.2.k.k.883.16		36
35.12	even	12		700.2.be.e.443.10		72
35.13	even	4		140.2.w.b.123.4	yes	72
35.18	odd	12		980.2.k.j.883.16		36
35.19	odd	6		700.2.be.e.107.18		72
35.23	odd	12	inner	980.2.x.m.863.9		72
35.27	even	4		700.2.be.e.543.15		72
35.33	even	12		140.2.w.b.23.9	✓	72
35.34	odd	2		700.2.be.e.207.7		72
140.3	odd	12		980.2.k.k.883.12		36
140.19	even	6		700.2.be.e.107.15		72
140.23	even	12	inner	980.2.x.m.863.12		72
140.27	odd	4		700.2.be.e.543.18		72
140.47	odd	12		700.2.be.e.443.7		72
140.83	odd	4		140.2.w.b.123.1	yes	72
140.103	odd	12		140.2.w.b.23.12	yes	72
140.123	even	12		980.2.k.j.883.12		36
140.139	even	2		700.2.be.e.207.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.9	✓	72	35.33	even	12
140.2.w.b.23.12	yes	72	140.103	odd	12
140.2.w.b.67.9	yes	72	28.27	even	2
140.2.w.b.67.12	yes	72	7.6	odd	2
140.2.w.b.107.1	yes	72	7.5	odd	6
140.2.w.b.107.4	yes	72	28.19	even	6
140.2.w.b.123.1	yes	72	140.83	odd	4
140.2.w.b.123.4	yes	72	35.13	even	4
700.2.be.e.107.15		72	140.19	even	6
700.2.be.e.107.18		72	35.19	odd	6
700.2.be.e.207.7		72	35.34	odd	2
700.2.be.e.207.10		72	140.139	even	2
700.2.be.e.443.7		72	140.47	odd	12
700.2.be.e.443.10		72	35.12	even	12
700.2.be.e.543.15		72	35.27	even	4
700.2.be.e.543.18		72	140.27	odd	4
980.2.k.j.687.12		36	7.4	even	3
980.2.k.j.687.16		36	28.11	odd	6
980.2.k.j.883.12		36	140.123	even	12
980.2.k.j.883.16		36	35.18	odd	12
980.2.k.k.687.12		36	7.3	odd	6
980.2.k.k.687.16		36	28.3	even	6
980.2.k.k.883.12		36	140.3	odd	12
980.2.k.k.883.16		36	35.3	even	12
980.2.x.m.67.9		72	4.3	odd	2	inner
980.2.x.m.67.12		72	1.1	even	1	trivial
980.2.x.m.263.1		72	20.3	even	4	inner
980.2.x.m.263.4		72	5.3	odd	4	inner
980.2.x.m.667.1		72	7.2	even	3	inner
980.2.x.m.667.4		72	28.23	odd	6	inner
980.2.x.m.863.9		72	35.23	odd	12	inner
980.2.x.m.863.12		72	140.23	even	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+(0.883367 - 1.10438i) q^{2} +(-0.807254 + 0.216303i) q^{3} +(-0.439327 - 1.95115i) q^{4} +(0.780454 + 2.09545i) q^{5} +(-0.474220 + 1.08259i) q^{6} +(-2.54291 - 1.23840i) q^{8} +(-1.99320 + 1.15078i) q^{9} +(3.00360 + 0.989126i) q^{10} +(4.21811 + 2.43533i) q^{11} +(0.776689 + 1.48005i) q^{12} +(-0.247904 + 0.247904i) q^{13} +(-1.08328 - 1.52274i) q^{15} +(-3.61398 + 1.71439i) q^{16} +(-5.83537 + 1.56358i) q^{17} +(-0.489830 + 3.21782i) q^{18} +(1.48858 + 2.57830i) q^{19} +(3.74566 - 2.44337i) q^{20} +(6.41567 - 2.50713i) q^{22} +(-1.70618 + 6.36754i) q^{23} +(2.32064 + 0.449662i) q^{24} +(-3.78178 + 3.27080i) q^{25} +(0.0547911 + 0.492771i) q^{26} +(3.13296 - 3.13296i) q^{27} -4.67111i q^{29} +(-2.63862 - 0.148788i) q^{30} +(5.75848 + 3.32466i) q^{31} +(-1.29913 + 5.50566i) 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} +(4.16240 + 0.633619i) q^{38} +(0.146499 - 0.253744i) q^{39} +(0.610370 - 6.29503i) q^{40} +1.15345 q^{41} +(3.23212 + 3.23212i) q^{43} +(2.89856 - 9.30008i) q^{44} +(-3.96699 - 3.27852i) q^{45} +(5.52503 + 7.50914i) q^{46} +(4.74443 + 1.27127i) q^{47} +(2.54658 - 2.16566i) q^{48} +(0.271513 + 7.06585i) q^{50} +(4.37242 - 2.52442i) q^{51} +(0.592609 + 0.374787i) q^{52} +(0.0828048 + 0.309032i) q^{53} +(-0.692438 - 6.22754i) q^{54} +(-1.81106 + 10.7395i) q^{55} +(-1.75936 - 1.75936i) q^{57} +(-5.15869 - 4.12630i) q^{58} +(-0.423416 + 0.733378i) q^{59} +(-2.49519 + 2.78262i) q^{60} +(5.04573 + 8.73945i) q^{61} +(8.75855 - 3.42268i) q^{62} +(4.93275 + 6.29825i) q^{64} +(-0.712947 - 0.325992i) q^{65} +(-4.63678 + 3.41162i) q^{66} +(-0.721946 - 2.69434i) q^{67} +(5.61442 + 10.6988i) q^{68} -5.50928i q^{69} -6.49911i q^{71} +(6.49365 - 0.457943i) q^{72} +(0.321006 + 1.19801i) q^{73} +(2.07808 + 2.82435i) q^{74} +(2.34538 - 3.45838i) q^{75} +(4.37668 - 4.03717i) q^{76} +(-0.150818 - 0.385940i) q^{78} +(-4.44724 - 7.70284i) q^{79} +(-6.41295 - 6.23490i) q^{80} +(1.60090 - 2.77285i) q^{81} +(1.01892 - 1.27385i) q^{82} +(-10.8443 - 10.8443i) q^{83} +(-7.83063 - 11.0074i) q^{85} +(6.42465 - 0.714354i) q^{86} +(1.01038 + 3.77077i) q^{87} +(-7.71036 - 11.4165i) q^{88} +(-8.26789 + 4.77347i) q^{89} +(-7.12505 + 1.48495i) q^{90} +(13.1736 + 0.531576i) q^{92} +(-5.36769 - 1.43827i) q^{93} +(5.59504 - 4.11668i) q^{94} +(-4.24092 + 5.13149i) q^{95} +(-0.142163 - 4.72547i) 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

Introduction

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