LMFDB - Embedded newform 980.2.s.e.619.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(19,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("980.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.10
Character	$\chi$	$=$	980.619
Dual form			980.2.s.e.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.444985 - 1.34238i) q^{2} +(-2.24836 - 1.29809i) q^{3} +(-1.60398 - 1.19468i) q^{4} +(-0.316513 + 2.21355i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(-2.31746 + 1.62154i) q^{8} +(1.87009 + 3.23909i) q^{9} +(2.83059 + 1.40988i) q^{10} +(3.12008 + 1.80138i) q^{11} +(2.05552 + 4.76818i) q^{12} -0.818282 q^{13} +(3.58504 - 4.56601i) q^{15} +(1.14549 + 3.83247i) q^{16} +(3.69814 - 6.40537i) q^{17} +(5.18026 - 1.06903i) q^{18} +(1.65329 + 2.86358i) q^{19} +(3.15217 - 3.17236i) q^{20} +(3.80652 - 3.38675i) q^{22} +(-1.26758 - 2.19550i) q^{23} +(7.31540 - 0.637523i) q^{24} +(-4.79964 - 1.40124i) q^{25} +(-0.364123 + 1.09845i) q^{26} -1.92166i q^{27} -2.04334 q^{29} +(-4.53404 - 6.84429i) q^{30} +(0.955727 - 1.65537i) q^{31} +(5.65437 + 0.167714i) q^{32} +(-4.67671 - 8.10030i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} +(6.20697 - 3.58360i) q^{37} +(4.57971 - 0.945096i) q^{38} +(1.83980 + 1.06221i) q^{39} +(-2.85585 - 5.64306i) q^{40} +2.65824i q^{41} +2.39696 q^{43} +(-2.85246 - 6.61686i) q^{44} +(-7.76182 + 3.11433i) q^{45} +(-3.51126 + 0.724604i) q^{46} +(1.15593 - 0.667376i) q^{47} +(2.39944 - 10.1037i) q^{48} +(-4.01676 + 5.81942i) q^{50} +(-16.6295 + 9.60106i) q^{51} +(1.31251 + 0.977584i) q^{52} +(-1.56838 - 0.905503i) q^{53} +(-2.57960 - 0.855108i) q^{54} +(-4.97499 + 6.33630i) q^{55} -8.58450i q^{57} +(-0.909256 + 2.74295i) q^{58} +(-0.955727 + 1.65537i) q^{59} +(-11.2052 + 3.04081i) q^{60} +(8.46625 - 4.88799i) q^{61} +(-1.79685 - 2.01956i) q^{62} +(2.74124 - 7.51569i) q^{64} +(0.258997 - 1.81131i) q^{65} +(-12.9548 + 2.67342i) q^{66} +(4.63112 - 8.02134i) q^{67} +(-13.5841 + 5.85597i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(-9.58617 - 4.47405i) q^{72} +(-3.69814 + 6.40537i) q^{73} +(-2.04855 - 9.92677i) q^{74} +(8.97240 + 9.38087i) q^{75} +(0.769222 - 6.56827i) q^{76} +(2.24457 - 1.99704i) q^{78} +(6.70979 - 3.87390i) q^{79} +(-8.84595 + 1.32257i) q^{80} +(3.11579 - 5.39670i) q^{81} +(3.56837 + 1.18287i) q^{82} -10.4973i q^{83} +(13.0081 + 10.2134i) q^{85} +(1.06661 - 3.21763i) q^{86} +(4.59418 + 2.65245i) q^{87} +(-10.1516 + 0.884696i) q^{88} +(9.19133 - 5.30662i) q^{89} +(0.726733 + 11.8052i) q^{90} +(-0.589761 + 5.03589i) q^{92} +(-4.29764 + 2.48125i) q^{93} +(-0.381503 - 1.84867i) q^{94} +(-6.86198 + 2.75329i) q^{95} +(-12.4954 - 7.71698i) q^{96} -7.32005 q^{97} +13.4750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) $ 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

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 $

$2$	0.444985	−	1.34238i	0.314652	−	0.949207i
$2$	0.444985	−	1.34238i	0.314652	−	0.949207i
$3$	−2.24836	−	1.29809i	−1.29809	−	0.749454i	−0.318019	−	0.948084i	$-0.603017\pi$
$3$	−2.24836	−	1.29809i	−1.29809	−	0.749454i	−0.980075	+	0.198630i	$0.936351\pi$
$4$	−1.60398	−	1.19468i	−0.801989	−	0.597339i
$5$	−0.316513	+	2.21355i	−0.141549	+	0.989931i
$5$	−0.316513	+	2.21355i	−0.141549	+	0.989931i
$6$	−2.74302	+	2.44053i	−1.11983	+	0.996342i
$7$		0			0
$7$		0			0
$8$	−2.31746	+	1.62154i	−0.819346	+	0.573300i
$9$	1.87009	+	3.23909i	0.623364	+	1.07970i
$10$	2.83059	+	1.40988i	0.895111	+	0.445843i
$11$	3.12008	+	1.80138i	0.940738	+	0.543136i	0.890192	−	0.455586i	$-0.150570\pi$
$11$	3.12008	+	1.80138i	0.940738	+	0.543136i	0.0505467	+	0.998722i	$0.483904\pi$
$12$	2.05552	+	4.76818i	0.593377	+	1.37646i
$13$	−0.818282			−0.226951			−0.113475	−	0.993541i	$-0.536198\pi$
$13$	−0.818282			−0.226951			−0.113475	+	0.993541i	$0.536198\pi$
$14$		0			0
$15$	3.58504	−	4.56601i	0.925652	−	1.17894i
$16$	1.14549	+	3.83247i	0.286371	+	0.958119i
$17$	3.69814	−	6.40537i	0.896931	−	1.55353i	0.0655347	−	0.997850i	$-0.479125\pi$
$17$	3.69814	−	6.40537i	0.896931	−	1.55353i	0.831396	−	0.555680i	$-0.187542\pi$
$18$	5.18026	−	1.06903i	1.22100	−	0.251973i
$19$	1.65329	+	2.86358i	0.379291	+	0.656951i	0.990959	−	0.134163i	$-0.0428346\pi$
$19$	1.65329	+	2.86358i	0.379291	+	0.656951i	−0.611668	+	0.791114i	$0.709501\pi$
$20$	3.15217	−	3.17236i	0.704846	−	0.709361i
$21$		0			0
$22$	3.80652	−	3.38675i	0.811553	−	0.722057i
$23$	−1.26758	−	2.19550i	−0.264308	−	0.457794i	0.703074	−	0.711116i	$-0.251810\pi$
$23$	−1.26758	−	2.19550i	−0.264308	−	0.457794i	−0.967382	+	0.253322i	$0.918477\pi$
$24$	7.31540	−	0.637523i	1.49325	−	0.130134i
$25$	−4.79964	−	1.40124i	−0.959928	−	0.280248i
$26$	−0.364123	+	1.09845i	−0.0714104	+	0.215423i
$27$		−	1.92166i		−	0.369823i
$28$		0			0
$29$	−2.04334			−0.379439			−0.189720	−	0.981838i	$-0.560758\pi$
$29$	−2.04334			−0.379439			−0.189720	+	0.981838i	$0.560758\pi$
$30$	−4.53404	−	6.84429i	−0.827799	−	1.24959i
$31$	0.955727	−	1.65537i	0.171654	−	0.297313i	−0.767345	−	0.641235i	$-0.778422\pi$
$31$	0.955727	−	1.65537i	0.171654	−	0.297313i	0.938998	+	0.343922i	$0.111756\pi$
$32$	5.65437	+	0.167714i	0.999560	+	0.0296479i
$33$	−4.67671	−	8.10030i	−0.814111	−	1.41008i
$34$	−6.95283	−	7.81461i	−1.19240	−	1.34019i
$35$		0			0
$36$	0.870092	−	7.42959i	0.145015	−	1.23827i
$37$	6.20697	−	3.58360i	1.02042	−	0.589140i	0.106195	−	0.994345i	$-0.466133\pi$
$37$	6.20697	−	3.58360i	1.02042	−	0.589140i	0.914226	+	0.405206i	$0.132800\pi$
$38$	4.57971	−	0.945096i	0.742927	−	0.153315i
$39$	1.83980	+	1.06221i	0.294603	+	0.170089i
$40$	−2.85585	−	5.64306i	−0.451550	−	0.892246i
$41$			2.65824i			0.415147i	0.978219	+	0.207573i	$0.0665566\pi$
$41$			2.65824i			0.415147i	−0.978219	+	0.207573i	$0.933443\pi$
$42$		0			0
$43$	2.39696			0.365533			0.182766	−	0.983156i	$-0.441495\pi$
$43$	2.39696			0.365533			0.182766	+	0.983156i	$0.441495\pi$
$44$	−2.85246	−	6.61686i	−0.430025	−	0.997529i
$45$	−7.76182	+	3.11433i	−1.15706	+	0.464257i
$46$	−3.51126	+	0.724604i	−0.517707	+	0.106837i
$47$	1.15593	−	0.667376i	0.168610	−	0.0973468i	−0.413320	−	0.910586i	$-0.635631\pi$
$47$	1.15593	−	0.667376i	0.168610	−	0.0973468i	0.581930	+	0.813239i	$0.302298\pi$
$48$	2.39944	−	10.1037i	0.346330	−	1.45835i
$49$		0			0
$50$	−4.01676	+	5.81942i	−0.568056	+	0.822990i
$51$	−16.6295	+	9.60106i	−2.32860	+	1.34442i
$52$	1.31251	+	0.977584i	0.182012	+	0.135567i
$53$	−1.56838	−	0.905503i	−0.215433	−	0.124380i	0.388401	−	0.921491i	$-0.373028\pi$
$53$	−1.56838	−	0.905503i	−0.215433	−	0.124380i	−0.603834	+	0.797110i	$0.706361\pi$
$54$	−2.57960	−	0.855108i	−0.351039	−	0.116365i
$55$	−4.97499	+	6.33630i	−0.670827	+	0.854386i
$56$		0			0
$57$		−	8.58450i		−	1.13705i
$58$	−0.909256	+	2.74295i	−0.119391	+	0.360166i
$59$	−0.955727	+	1.65537i	−0.124425	+	0.215510i	−0.921508	−	0.388359i	$-0.873042\pi$
$59$	−0.955727	+	1.65537i	−0.124425	+	0.215510i	0.797083	+	0.603870i	$0.206375\pi$
$60$	−11.2052	+	3.04081i	−1.44659	+	0.392567i
$61$	8.46625	−	4.88799i	1.08399	−	0.625843i	0.152021	−	0.988377i	$-0.451422\pi$
$61$	8.46625	−	4.88799i	1.08399	−	0.625843i	0.931970	+	0.362534i	$0.118088\pi$
$62$	−1.79685	−	2.01956i	−0.228200	−	0.256485i
$63$		0			0
$64$	2.74124	−	7.51569i	0.342655	−	0.939461i
$65$	0.258997	−	1.81131i	0.0321246	−	0.224666i
$66$	−12.9548	+	2.67342i	−1.59462	+	0.329075i
$67$	4.63112	−	8.02134i	0.565782	−	0.979963i	−0.431195	−	0.902259i	$-0.641908\pi$
$67$	4.63112	−	8.02134i	0.565782	−	0.979963i	0.996976	−	0.0777041i	$-0.0247589\pi$
$68$	−13.5841	+	5.85597i	−1.64731	+	0.710141i
$69$			6.58172i			0.792346i
$70$		0			0
$71$			1.38422i			0.164277i	0.996621	+	0.0821385i	$0.0261750\pi$
$71$			1.38422i			0.164277i	−0.996621	+	0.0821385i	$0.973825\pi$
$72$	−9.58617	−	4.47405i	−1.12974	−	0.527272i
$73$	−3.69814	+	6.40537i	−0.432835	+	0.749692i	−0.997116	−	0.0758908i	$-0.975820\pi$
$73$	−3.69814	+	6.40537i	−0.432835	+	0.749692i	0.564281	+	0.825583i	$0.309153\pi$
$74$	−2.04855	−	9.92677i	−0.238139	−	1.15396i
$75$	8.97240	+	9.38087i	1.03604	+	1.08321i
$76$	0.769222	−	6.56827i	0.0882358	−	0.753433i
$77$		0			0
$78$	2.24457	−	1.99704i	0.254147	−	0.226121i
$79$	6.70979	−	3.87390i	0.754910	−	0.435848i	−0.0725552	−	0.997364i	$-0.523115\pi$
$79$	6.70979	−	3.87390i	0.754910	−	0.435848i	0.827465	+	0.561517i	$0.189782\pi$
$80$	−8.84595	+	1.32257i	−0.989007	+	0.147867i
$81$	3.11579	−	5.39670i	0.346199	−	0.599634i
$82$	3.56837	+	1.18287i	0.394060	+	0.130627i
$83$		−	10.4973i		−	1.15223i	−0.817370	−	0.576113i	$-0.804569\pi$
$83$		−	10.4973i		−	1.15223i	0.817370	−	0.576113i	$-0.195431\pi$
$84$		0			0
$85$	13.0081	+	10.2134i	1.41093	+	1.10780i
$86$	1.06661	−	3.21763i	0.115015	−	0.346966i
$87$	4.59418	+	2.65245i	0.492547	+	0.284372i
$88$	−10.1516	+	0.884696i	−1.08217	+	0.0943090i
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.0737410	−	0.997277i	$-0.476506\pi$
$89$	9.19133	−	5.30662i	0.974279	−	0.562500i	0.900538	+	0.434777i	$0.143173\pi$
$90$	0.726733	+	11.8052i	0.0766044	+	1.24437i
$91$		0			0
$92$	−0.589761	+	5.03589i	−0.0614868	+	0.525027i
$93$	−4.29764	+	2.48125i	−0.445645	+	0.257293i
$94$	−0.381503	−	1.84867i	−0.0393490	−	0.190676i
$95$	−6.86198	+	2.75329i	−0.704025	+	0.282481i
$96$	−12.4954	−	7.71698i	−1.27530	−	0.787611i
$97$	−7.32005			−0.743239			−0.371619	−	0.928385i	$-0.621197\pi$
$97$	−7.32005			−0.743239			−0.371619	+	0.928385i	$0.621197\pi$
$98$		0			0
$99$			13.4750i			1.35428i
$100$	6.02448	+	7.98158i	0.602448	+	0.798158i
$101$	5.50608	+	3.17894i	0.547875	+	0.316316i	0.748265	−	0.663400i	$-0.230887\pi$
$101$	5.50608	+	3.17894i	0.547875	+	0.316316i	−0.200389	+	0.979716i	$0.564221\pi$
$102$	5.48841	+	26.5955i	0.543433	+	2.63335i
$103$	0.885144	−	0.511038i	0.0872158	−	0.0503541i	−0.455758	−	0.890104i	$-0.650632\pi$
$103$	0.885144	−	0.511038i	0.0872158	−	0.0503541i	0.542974	+	0.839750i	$0.317298\pi$
$104$	1.89634	−	1.32687i	0.185951	−	0.130111i
$105$		0			0
$106$	−1.91343	+	1.70243i	−0.185849	+	0.165354i
$107$	3.62578	+	6.28003i	0.350517	+	0.607114i	0.986340	−	0.164721i	$-0.0526724\pi$
$107$	3.62578	+	6.28003i	0.350517	+	0.607114i	−0.635823	+	0.771835i	$0.719339\pi$
$108$	−2.29576	+	3.08229i	−0.220910	+	0.296594i
$109$	3.98588	−	6.90375i	0.381778	−	0.661259i	−0.609538	−	0.792756i	$-0.708645\pi$
$109$	3.98588	−	6.90375i	0.381778	−	0.661259i	0.991316	+	0.131498i	$0.0419786\pi$
$110$	6.29193	+	9.49789i	0.599912	+	0.905588i
$111$	−18.6074			−1.76613
$112$		0			0
$113$		−	7.61610i		−	0.716462i	−0.933633	−	0.358231i	$-0.883380\pi$
$113$		−	7.61610i		−	0.716462i	0.933633	−	0.358231i	$-0.116620\pi$
$114$	−11.5237	−	3.81997i	−1.07929	−	0.357773i
$115$	5.26107	−	2.11094i	0.490597	−	0.196846i
$116$	3.27747	+	2.44114i	0.304306	+	0.226654i
$117$	−1.53026	−	2.65049i	−0.141473	−	0.245038i
$118$	1.79685	+	2.01956i	0.165414	+	0.185916i
$119$		0			0
$120$	−0.904229	+	16.3948i	−0.0825444	+	1.49663i
$121$	0.989917	+	1.71459i	0.0899925	+	0.155872i
$122$	−2.79420	−	13.5400i	−0.252975	−	1.22586i
$123$	3.45064	−	5.97668i	0.311134	−	0.538899i
$124$	−3.51060	+	1.51339i	−0.315261	+	0.135906i
$125$	4.62086	−	10.1807i	0.413303	−	0.910594i
$126$		0			0
$127$	8.78136			0.779220			0.389610	−	0.920980i	$-0.372610\pi$
$127$	8.78136			0.779220			0.389610	+	0.920980i	$0.372610\pi$
$128$	−8.86911	−	7.02416i	−0.783926	−	0.620854i
$129$	−5.38923	−	3.11147i	−0.474495	−	0.273950i
$130$	−2.31622	−	1.15368i	−0.203146	−	0.101184i
$131$	−6.69467	−	11.5955i	−0.584916	−	1.01310i	−0.994886	−	0.101005i	$-0.967794\pi$
$131$	−6.69467	−	11.5955i	−0.584916	−	1.01310i	0.409970	−	0.912099i	$-0.365539\pi$
$132$	−2.17592	+	18.5799i	−0.189389	+	1.61717i
$133$		0			0
$134$	−8.70692	−	9.78611i	−0.752164	−	0.845391i
$135$	4.25369	+	0.608229i	0.366099	+	0.0523481i
$136$	1.81624	+	20.8409i	0.155741	+	1.78709i
$137$	−4.52425	−	2.61208i	−0.386533	−	0.223165i	0.294124	−	0.955767i	$-0.404972\pi$
$137$	−4.52425	−	2.61208i	−0.386533	−	0.223165i	−0.680657	+	0.732602i	$0.738306\pi$
$138$	8.83519	+	2.92877i	0.752101	+	0.249313i
$139$	21.9442			1.86128			0.930641	−	0.365933i	$-0.119250\pi$
$139$	21.9442			1.86128			0.930641	+	0.365933i	$0.119250\pi$
$140$		0			0
$141$	−3.46527			−0.291828
$142$	1.85816	+	0.615958i	0.155933	+	0.0516901i
$143$	−2.55310	−	1.47403i	−0.213501	−	0.123265i
$144$	−10.2716	+	10.8774i	−0.855965	+	0.906451i
$145$	0.646745	−	4.52305i	0.0537092	−	0.375619i
$146$	6.95283	+	7.81461i	0.575421	+	0.646742i
$147$		0			0
$148$	−14.2371	−	1.66733i	−1.17028	−	0.137054i
$149$	11.9749	+	20.7411i	0.981019	+	1.69917i	0.658444	+	0.752630i	$0.271215\pi$
$149$	11.9749	+	20.7411i	0.981019	+	1.69917i	0.322575	+	0.946544i	$0.395452\pi$
$150$	16.5853	−	7.87004i	1.35418	−	0.642586i
$151$	−6.06876	−	3.50380i	−0.493869	−	0.285135i	0.232309	−	0.972642i	$-0.425372\pi$
$151$	−6.06876	−	3.50380i	−0.493869	−	0.285135i	−0.726178	+	0.687507i	$0.758705\pi$
$152$	−8.47484	−	3.95537i	−0.687400	−	0.320823i
$153$	27.6635			2.23646
$154$		0			0
$155$	3.36174	+	2.63950i	0.270022	+	0.212010i
$156$	−1.68200	−	3.90172i	−0.134667	−	0.312388i
$157$	3.21277	−	5.56468i	0.256407	−	0.444110i	−0.708870	−	0.705340i	$-0.750795\pi$
$157$	3.21277	−	5.56468i	0.256407	−	0.444110i	0.965277	+	0.261229i	$0.0841279\pi$
$158$	−2.21450	−	10.7309i	−0.176176	−	0.853706i
$159$	2.35085	+	4.07180i	0.186435	+	0.322915i
$160$	−2.16092	+	12.4632i	−0.170836	+	0.985299i
$161$		0			0
$162$	−5.85796	−	6.58403i	−0.460245	−	0.517290i
$163$	9.23950	+	16.0033i	0.723693	+	1.25347i	0.959510	+	0.281676i	$0.0908903\pi$
$163$	9.23950	+	16.0033i	0.723693	+	1.25347i	−0.235816	+	0.971798i	$0.575776\pi$
$164$	3.17574	−	4.26375i	0.247983	−	0.332943i
$165$	19.4107	−	7.78830i	1.51112	−	0.606318i
$166$	−14.0913	−	4.67113i	−1.09370	−	0.362550i
$167$		−	1.82894i		−	0.141527i	−0.997493	−	0.0707637i	$-0.977456\pi$
$167$		−	1.82894i		−	0.141527i	0.997493	−	0.0707637i	$-0.0225436\pi$
$168$		0			0
$169$	−12.3304			−0.948493
$170$	19.4987	−	12.9170i	1.49548	−	0.990692i
$171$	−6.18361	+	10.7103i	−0.472873	+	0.819039i
$172$	−3.84466	−	2.86359i	−0.293153	−	0.218347i
$173$	7.62476	+	13.2065i	0.579700	+	1.00407i	0.995514	+	0.0946193i	$0.0301634\pi$
$173$	7.62476	+	13.2065i	0.579700	+	1.00407i	−0.415814	+	0.909450i	$0.636503\pi$
$174$	5.60494	−	4.98684i	0.424909	−	0.378051i
$175$		0			0
$176$	−3.32973	+	14.0211i	−0.250988	+	1.05688i
$177$	4.29764	−	2.48125i	0.323031	−	0.186502i
$178$	−3.03350	−	14.6996i	−0.227371	−	1.10178i
$179$	10.8572	+	6.26844i	0.811509	+	0.468525i	0.847480	−	0.530828i	$-0.178119\pi$
$179$	10.8572	+	6.26844i	0.811509	+	0.468525i	−0.0359707	+	0.999353i	$0.511452\pi$
$180$	16.1704	+	4.27756i	1.20527	+	0.318830i
$181$		−	8.01839i		−	0.596002i	−0.954566	−	0.298001i	$-0.903680\pi$
$181$		−	8.01839i		−	0.596002i	0.954566	−	0.298001i	$-0.0963199\pi$
$182$		0			0
$183$	−25.3803			−1.87616
$184$	6.49765	+	3.03258i	0.479013	+	0.223564i
$185$	5.96790	+	14.8737i	0.438769	+	1.09354i
$186$	1.41839	+	6.87319i	0.104002	+	0.503967i
$187$	23.0770	−	13.3235i	1.68755	−	0.974310i
$188$	−2.65139	−	0.310508i	−0.193372	−	0.0226461i
$189$		0			0
$190$	0.642483	+	10.4366i	0.0466106	+	0.757148i
$191$	−5.85379	+	3.37969i	−0.423565	+	0.244546i	−0.696602	−	0.717458i	$-0.745305\pi$
$191$	−5.85379	+	3.37969i	−0.423565	+	0.244546i	0.273036	+	0.962004i	$0.411972\pi$
$192$	−15.9194	+	13.3396i	−1.14888	+	0.962704i
$193$	2.04384	+	1.18001i	0.147119	+	0.0849392i	0.571753	−	0.820426i	$-0.306264\pi$
$193$	2.04384	+	1.18001i	0.147119	+	0.0849392i	−0.424634	+	0.905365i	$0.639597\pi$
$194$	−3.25731	+	9.82631i	−0.233861	+	0.705488i
$195$	−2.93357	+	3.73628i	−0.210077	+	0.267561i
$196$		0			0
$197$			20.3205i			1.44777i	0.689918	+	0.723887i	$0.257647\pi$
$197$			20.3205i			1.44777i	−0.689918	+	0.723887i	$0.742353\pi$
$198$	18.0885	+	5.99615i	1.28550	+	0.426128i
$199$	5.72909	−	9.92308i	0.406125	−	0.703429i	−0.588327	−	0.808623i	$-0.700213\pi$
$199$	5.72909	−	9.92308i	0.406125	−	0.703429i	0.994452	+	0.105195i	$0.0335465\pi$
$200$	13.3951	−	4.53547i	0.947179	−	0.320706i
$201$	−20.8249	+	12.0233i	−1.46888	+	0.848056i
$202$	6.71746	−	5.97668i	0.472639	−	0.420518i
$203$		0			0
$204$	38.1436	+	4.46706i	2.67058	+	0.312757i
$205$	−5.88415	−	0.841366i	−0.410967	−	0.0587636i
$206$	−0.292133	−	1.41560i	−0.0203538	−	0.0986298i
$207$	4.74097	−	8.21159i	0.329520	−	0.570745i
$208$	−0.937331	−	3.13605i	−0.0649922	−	0.217446i
$209$			11.9128i			0.824026i
$210$		0			0
$211$		−	22.0647i		−	1.51900i	−0.650510	−	0.759498i	$-0.725445\pi$
$211$		−	22.0647i		−	1.51900i	0.650510	−	0.759498i	$-0.274555\pi$
$212$	1.43386	+	3.32611i	0.0984776	+	0.228438i
$213$	1.79685	−	3.11224i	0.123118	−	0.213247i
$214$	10.0436	−	2.07266i	0.686568	−	0.141684i
$215$	−0.758668	+	5.30579i	−0.0517408	+	0.361852i
$216$	3.11603	+	4.45336i	0.212019	+	0.303013i
$217$		0			0
$218$	−7.49381	−	8.42263i	−0.507545	−	0.570453i
$219$	16.6295	−	9.60106i	1.12372	−	0.648780i
$220$	15.5496	−	4.21976i	1.04835	−	0.284496i
$221$	−3.02612	+	5.24140i	−0.203559	+	0.352575i
$222$	−8.28000	+	24.9782i	−0.555717	+	1.67643i
$223$			23.5776i			1.57887i	0.613833	+	0.789436i	$0.289627\pi$
$223$			23.5776i			1.57887i	−0.613833	+	0.789436i	$0.710373\pi$
$224$		0			0
$225$	−4.43703	−	18.1669i	−0.295802	−	1.21113i
$226$	−10.2237	−	3.38905i	−0.680071	−	0.225436i
$227$	18.1231	+	10.4634i	1.20287	+	0.694478i	0.961192	−	0.275879i	$-0.0889689\pi$
$227$	18.1231	+	10.4634i	1.20287	+	0.694478i	0.241678	+	0.970356i	$0.422302\pi$
$228$	−10.2557	+	13.7693i	−0.679202	+	0.911897i
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	−0.640884	−	0.767638i	$-0.721432\pi$
$229$	−4.48735	+	2.59077i	−0.296533	+	0.171203i	0.344352	+	0.938841i	$0.388099\pi$
$230$	−0.492590	−	8.00170i	−0.0324804	−	0.527617i
$231$		0			0
$232$	4.73536	−	3.31335i	0.310892	−	0.217532i
$233$	17.9868	−	10.3847i	1.17836	−	0.680324i	0.222722	−	0.974882i	$-0.428506\pi$
$233$	17.9868	−	10.3847i	1.17836	−	0.680324i	0.955634	+	0.294558i	$0.0951724\pi$
$234$	−4.23892	+	0.874768i	−0.277107	+	0.0571854i
$235$	1.11141	+	2.76995i	0.0725002	+	0.180691i
$236$	3.51060	−	1.51339i	0.228520	−	0.0985130i
$237$	−20.1147			−1.30659
$238$		0			0
$239$			21.1286i			1.36670i	0.730092	+	0.683349i	$0.239477\pi$
$239$			21.1286i			1.36670i	−0.730092	+	0.683349i	$0.760523\pi$
$240$	21.6057	+	8.50926i	1.39464	+	0.549270i
$241$	−1.57448	−	0.909029i	−0.101421	−	0.0585557i	0.448431	−	0.893817i	$-0.351983\pi$
$241$	−1.57448	−	0.909029i	−0.101421	−	0.0585557i	−0.549853	+	0.835262i	$0.685316\pi$
$242$	2.74213	−	0.565882i	0.176271	−	0.0363763i
$243$	−19.0035	+	10.9716i	−1.21907	+	0.703832i
$244$	−19.4192	−	2.27422i	−1.24319	−	0.145592i
$245$		0			0
$246$	−6.48750	−	7.29160i	−0.413628	−	0.464896i
$247$	−1.35286	−	2.34322i	−0.0860803	−	0.149095i
$248$	0.469379	+	5.38599i	0.0298056	+	0.342011i
$249$	−13.6264	+	23.6017i	−0.863540	+	1.49570i
$250$	−11.6102	−	10.7332i	−0.734296	−	0.678830i
$251$	14.0187			0.884856			0.442428	−	0.896804i	$-0.354117\pi$
$251$	14.0187			0.884856			0.442428	+	0.896804i	$0.354117\pi$
$252$		0			0
$253$		−	9.13352i		−	0.574220i
$254$	3.90757	−	11.7879i	0.245183	−	0.739641i
$255$	−15.9890	−	39.8492i	−1.00127	−	2.49546i
$256$	−13.3757	+	8.78009i	−0.835983	+	0.548756i
$257$	−8.93624	−	15.4780i	−0.557427	−	0.965492i	−0.997710	−	0.0676333i	$-0.978455\pi$
$257$	−8.93624	−	15.4780i	−0.557427	−	0.965492i	0.440283	−	0.897859i	$-0.354878\pi$
$258$	−6.57491	+	5.84985i	−0.409336	+	0.364196i
$259$		0			0
$260$	−2.57936	+	2.59588i	−0.159965	+	0.160990i
$261$	−3.82124	−	6.61858i	−0.236529	−	0.409680i
$262$	−18.5446	+	3.82698i	−1.14569	+	0.236432i
$263$	−10.9482	+	18.9629i	−0.675097	+	1.16930i	0.301343	+	0.953516i	$0.402565\pi$
$263$	−10.9482	+	18.9629i	−0.675097	+	1.16930i	−0.976440	+	0.215787i	$0.930768\pi$
$264$	23.9730	+	11.1887i	1.47544	+	0.688615i
$265$	2.50079	−	3.18508i	0.153622	−	0.195658i
$266$		0			0
$267$	−27.5539			−1.68627
$268$	−17.0111	+	7.33335i	−1.03912	+	0.447955i
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	0.421955	−	0.906617i	$-0.361344\pi$
$269$	−2.49661	−	1.44142i	−0.152221	−	0.0878847i	−0.574176	+	0.818732i	$0.694677\pi$
$270$	2.70930	−	5.43942i	0.164883	−	0.331033i
$271$	−8.47793	−	14.6842i	−0.514997	−	0.892002i	−0.999849	−	0.0174049i	$-0.994460\pi$
$271$	−8.47793	−	14.6842i	−0.514997	−	0.892002i	0.484851	−	0.874597i	$-0.338874\pi$
$272$	28.7846	+	6.83578i	1.74532	+	0.414480i
$273$		0			0
$274$	−5.51963	+	4.91094i	−0.333453	+	0.296681i
$275$	−12.4511	−	13.0179i	−0.750829	−	0.785010i
$276$	7.86305	−	10.5569i	0.473300	−	0.635453i
$277$	−23.2541	−	13.4258i	−1.39720	−	0.806677i	−0.403106	−	0.915153i	$-0.632069\pi$
$277$	−23.2541	−	13.4258i	−1.39720	−	0.806677i	−0.994099	+	0.108477i	$0.965403\pi$
$278$	9.76483	−	29.4575i	0.585656	−	1.76674i
$279$	7.14919			0.428011
$280$		0			0
$281$	24.9497			1.48838			0.744188	−	0.667971i	$-0.232837\pi$
$281$	24.9497			1.48838			0.744188	+	0.667971i	$0.232837\pi$
$282$	−1.54199	+	4.65171i	−0.0918242	+	0.277005i
$283$	−8.52014	−	4.91910i	−0.506470	−	0.292410i	0.224912	−	0.974379i	$-0.427791\pi$
$283$	−8.52014	−	4.91910i	−0.506470	−	0.292410i	−0.731381	+	0.681969i	$0.761124\pi$
$284$	1.65370	−	2.22026i	0.0981292	−	0.131748i
$285$	19.0023	+	2.71711i	1.12560	+	0.160948i
$286$	−3.11481	+	2.77132i	−0.184183	+	0.163871i
$287$		0			0
$288$	10.0309	+	18.6287i	0.591079	+	1.09770i
$289$	−18.8525	−	32.6535i	−1.10897	−	1.92079i
$290$	−5.78387	−	2.88087i	−0.339640	−	0.169170i
$291$	16.4581	+	9.50211i	0.964793	+	0.557024i
$292$	13.5841	−	5.85597i	0.794949	−	0.342695i
$293$	−23.4039			−1.36727			−0.683636	−	0.729823i	$-0.739602\pi$
$293$	−23.4039			−1.36727			−0.683636	+	0.729823i	$0.739602\pi$
$294$		0			0
$295$	−3.36174	−	2.63950i	−0.195728	−	0.153678i
$296$	−8.57348	+	18.3697i	−0.498323	+	1.06772i
$297$	3.46163	−	5.99571i	0.200864	−	0.347907i
$298$	33.1710	−	6.84537i	1.92155	−	0.396542i
$299$	1.03723	+	1.79654i	0.0599848	+	0.103897i
$300$	−3.18439	−	25.7658i	−0.183851	−	1.48759i
$301$		0			0
$302$	−7.40395	+	6.58746i	−0.426049	+	0.379066i
$303$	−8.25311	−	14.2948i	−0.474129	−	0.821215i
$304$	−9.08079	+	9.61639i	−0.520819	+	0.551538i
$305$	8.14015	+	20.2876i	0.466104	+	1.16166i
$306$	12.3098	−	37.1349i	0.703705	−	2.12286i
$307$			2.18529i			0.124721i	0.998054	+	0.0623606i	$0.0198629\pi$
$307$			2.18529i			0.124721i	−0.998054	+	0.0623606i	$0.980137\pi$
$308$		0			0
$309$	−2.65350			−0.150952
$310$	5.03914	−	3.33821i	0.286204	−	0.189597i
$311$	−14.4501	+	25.0282i	−0.819388	+	1.41922i	0.0867457	+	0.996230i	$0.472353\pi$
$311$	−14.4501	+	25.0282i	−0.819388	+	1.41922i	−0.906134	+	0.422991i	$0.860980\pi$
$312$	−5.98606	+	0.521673i	−0.338894	+	0.0295339i
$313$	−3.17652	−	5.50189i	−0.179548	−	0.310985i	0.762178	−	0.647367i	$-0.224130\pi$
$313$	−3.17652	−	5.50189i	−0.179548	−	0.310985i	−0.941726	+	0.336382i	$0.890797\pi$
$314$	−6.04030	−	6.78897i	−0.340874	−	0.383124i
$315$		0			0
$316$	−15.3904	−	1.80240i	−0.865778	−	0.101393i
$317$	−16.2839	+	9.40153i	−0.914597	+	0.528043i	−0.881907	−	0.471423i	$-0.843741\pi$
$317$	−16.2839	+	9.40153i	−0.914597	+	0.528043i	−0.0326894	+	0.999466i	$0.510407\pi$
$318$	6.51200	−	1.34386i	0.365175	−	0.0753597i
$319$	−6.37538	−	3.68083i	−0.356953	−	0.206087i
$320$	15.7687	+	8.44670i	0.881499	+	0.472185i
$321$		−	18.8264i		−	1.05079i
$322$		0			0
$323$	24.4564			1.36079
$324$	−11.4450	+	4.93382i	−0.635832	+	0.274101i
$325$	3.92746	+	1.14661i	0.217856	+	0.0636024i
$326$	25.5939	−	5.28172i	1.41752	−	0.292527i
$327$	−17.9234	+	10.3481i	−0.991167	+	0.572250i
$328$	−4.31042	−	6.16035i	−0.238003	−	0.340149i
$329$		0			0
$330$	−1.81741	−	29.5222i	−0.100045	−	1.62514i
$331$	11.3353	−	6.54441i	0.623042	−	0.359713i	−0.155010	−	0.987913i	$-0.549541\pi$
$331$	11.3353	−	6.54441i	0.623042	−	0.359713i	0.778052	+	0.628199i	$0.216208\pi$
$332$	−12.5409	+	16.8374i	−0.688269	+	0.924071i
$333$	23.2152	+	13.4033i	1.27219	+	0.734497i
$334$	−2.45513	−	0.813849i	−0.134339	−	0.0445318i
$335$	16.2899	+	12.7901i	0.890010	+	0.698798i
$336$		0			0
$337$			11.7319i			0.639079i	0.947573	+	0.319539i	$0.103528\pi$
$337$			11.7319i			0.639079i	−0.947573	+	0.319539i	$0.896472\pi$
$338$	−5.48685	+	16.5521i	−0.298445	+	0.900317i
$339$	−9.88640	+	17.1238i	−0.536956	+	0.930035i
$340$	−8.66297	−	31.9226i	−0.469816	−	1.73125i
$341$	5.96388	−	3.44325i	0.322962	−	0.186462i
$342$	11.6257	+	13.0667i	0.628648	+	0.706566i
$343$		0			0
$344$	−5.55485	+	3.88675i	−0.299498	+	0.209560i
$345$	−14.5690	−	2.08320i	−0.784369	−	0.112156i
$346$	21.1210	−	4.35866i	1.13547	−	0.234323i
$347$	−2.20585	+	3.82065i	−0.118416	+	0.205103i	−0.919140	−	0.393930i	$-0.871115\pi$
$347$	−2.20585	+	3.82065i	−0.118416	+	0.205103i	0.800724	+	0.599034i	$0.204448\pi$
$348$	−4.20013	−	9.74303i	−0.225151	−	0.522281i
$349$			18.3479i			0.982142i	0.871120	+	0.491071i	$0.163394\pi$
$349$			18.3479i			0.982142i	−0.871120	+	0.491071i	$0.836606\pi$
$350$		0			0
$351$			1.57246i			0.0839316i
$352$	17.3399	+	10.7089i	0.924222	+	0.570788i
$353$	5.87406	−	10.1742i	0.312645	−	0.541516i	−0.666289	−	0.745693i	$-0.732118\pi$
$353$	5.87406	−	10.1742i	0.312645	−	0.541516i	0.978934	+	0.204177i	$0.0654518\pi$
$354$	−1.41839	−	6.87319i	−0.0753867	−	0.365306i
$355$	−3.06405	−	0.438125i	−0.162623	−	0.0232533i
$356$	−21.0824	−	2.46899i	−1.11736	−	0.130856i
$357$		0			0
$358$	13.2459	−	11.7852i	0.700070	−	0.622868i
$359$	0.171388	−	0.0989510i	0.00904552	−	0.00522243i	−0.495470	−	0.868625i	$-0.665004\pi$
$359$	0.171388	−	0.0989510i	0.00904552	−	0.00522243i	0.504516	+	0.863402i	$0.331671\pi$
$360$	12.9377	−	19.8034i	0.681877	−	1.04373i
$361$	4.03326	−	6.98581i	0.212277	−	0.367674i
$362$	−10.7637	−	3.56806i	−0.565730	−	0.187533i
$363$		−	5.14002i		−	0.269781i
$364$		0			0
$365$	−13.0081	−	10.2134i	−0.680876	−	0.534595i
$366$	−11.2938	+	34.0700i	−0.590338	+	1.78087i
$367$	−6.51964	−	3.76412i	−0.340323	−	0.196485i	0.320092	−	0.947386i	$-0.396286\pi$
$367$	−6.51964	−	3.76412i	−0.340323	−	0.196485i	−0.660415	+	0.750901i	$0.729619\pi$
$368$	6.96223	−	7.37287i	0.362931	−	0.384337i
$369$	−8.61028	+	4.97115i	−0.448233	+	0.258787i
$370$	22.6218	−	1.39262i	1.17605	−	0.0723987i
$371$		0			0
$372$	9.85761	+	1.15444i	0.511093	+	0.0598550i
$373$	−26.9674	+	15.5696i	−1.39632	+	0.806164i	−0.994005	−	0.109339i	$-0.965127\pi$
$373$	−26.9674	+	15.5696i	−1.39632	+	0.806164i	−0.402312	+	0.915503i	$0.631793\pi$
$374$	−7.61632	−	36.9068i	−0.393830	−	1.90841i
$375$	−23.6049	+	16.8917i	−1.21895	+	0.872284i
$376$	−1.59665	+	3.42100i	−0.0823408	+	0.176425i
$377$	1.67203			0.0861140
$378$		0			0
$379$		−	16.3396i		−	0.839307i	−0.907684	−	0.419654i	$-0.862152\pi$
$379$		−	16.3396i		−	0.839307i	0.907684	−	0.419654i	$-0.137848\pi$
$380$	14.2958	+	3.78166i	0.733357	+	0.193995i
$381$	−19.7437	−	11.3990i	−1.01150	−	0.583990i
$382$	1.93198	+	9.36193i	0.0988489	+	0.478998i
$383$	7.66318	−	4.42434i	0.391570	−	0.226073i	−0.291270	−	0.956641i	$-0.594078\pi$
$383$	7.66318	−	4.42434i	0.391570	−	0.226073i	0.682840	+	0.730568i	$0.260744\pi$
$384$	10.8230	+	27.3058i	0.552307	+	1.39344i
$385$		0			0
$386$	2.49351	−	2.21853i	0.126916	−	0.112920i
$387$	4.48253	+	7.76397i	0.227860	+	0.394665i
$388$	11.7412	+	8.74511i	0.596069	+	0.443966i
$389$	−4.67264	+	8.09325i	−0.236912	+	0.410344i	−0.959827	−	0.280594i	$-0.909469\pi$
$389$	−4.67264	+	8.09325i	−0.236912	+	0.410344i	0.722915	+	0.690937i	$0.242802\pi$
$390$	3.71013	+	5.60056i	0.187870	+	0.283595i
$391$	−18.7507			−0.948263
$392$		0			0
$393$			34.7612i			1.75347i
$394$	27.2779	+	9.04231i	1.37424	+	0.455545i
$395$	6.45134	+	16.0786i	0.324602	+	0.809003i
$396$	16.0983	−	21.6135i	0.808968	−	1.08612i
$397$	10.1513	+	17.5826i	0.509480	+	0.882446i	0.999940	+	0.0109817i	$0.00349564\pi$
$397$	10.1513	+	17.5826i	0.509480	+	0.882446i	−0.490459	+	0.871464i	$0.663171\pi$
$398$	−10.7712	−	12.1063i	−0.539912	−	0.606831i
$399$		0			0
$400$	−0.127710	−	19.9996i	−0.00638551	−	0.999980i
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	0.970593	−	0.240726i	$-0.0773857\pi$
$401$	5.54334	+	9.60135i	0.276821	+	0.479469i	−0.693772	+	0.720195i	$0.744052\pi$
$402$	6.87304	+	33.3051i	0.342796	+	1.66111i
$403$	−0.782054	+	1.35456i	−0.0389569	+	0.0674753i
$404$	−5.03382	−	11.6769i	−0.250442	−	0.580949i
$405$	10.9597	+	8.60509i	0.544592	+	0.427590i
$406$		0			0
$407$	25.8216			1.27993
$408$	22.9698	−	49.2155i	1.13717	−	2.43653i
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	0.368633	−	0.929575i	$-0.379826\pi$
$409$	−5.09812	−	2.94340i	−0.252086	−	0.145542i	−0.620719	+	0.784033i	$0.713159\pi$
$410$	−3.74779	+	7.52438i	−0.185090	+	0.371602i
$411$	6.78145	+	11.7458i	0.334504	+	0.579378i
$412$	−2.03028	−	0.237769i	−0.100025	−	0.0117140i
$413$		0			0
$414$	−8.91343	−	10.0182i	−0.438071	−	0.492369i
$415$	23.2363	+	3.32252i	1.14062	+	0.163096i
$416$	−4.62687	−	0.137237i	−0.226851	−	0.00672860i
$417$	−49.3385	−	28.4856i	−2.41612	−	1.39495i
$418$	15.9915	+	5.30101i	0.782171	+	0.259281i
$419$	−16.7262			−0.817126			−0.408563	−	0.912730i	$-0.633970\pi$
$419$	−16.7262			−0.817126			−0.408563	+	0.912730i	$0.633970\pi$
$420$		0			0
$421$	−1.18823			−0.0579109			−0.0289555	−	0.999581i	$-0.509218\pi$
$421$	−1.18823			−0.0579109			−0.0289555	+	0.999581i	$0.509218\pi$
$422$	−29.6192	−	9.81845i	−1.44184	−	0.477955i
$423$	4.32339	+	2.49611i	0.210210	+	0.121365i
$424$	5.10296	−	0.444713i	0.247822	−	0.0215972i
$425$	−26.7252	+	25.5615i	−1.29636	+	1.23991i
$426$	−3.37824	−	3.79696i	−0.163676	−	0.183963i
$427$		0			0
$428$	1.68696	−	14.4047i	0.0815421	−	0.696276i
$429$	3.82687	+	6.62833i	0.184763	+	0.320019i
$430$	6.78480	+	3.37942i	0.327192	+	0.162970i
$431$	−20.8669	−	12.0475i	−1.00512	−	0.580307i	−0.0953622	−	0.995443i	$-0.530401\pi$
$431$	−20.8669	−	12.0475i	−1.00512	−	0.580307i	−0.909760	+	0.415135i	$0.863734\pi$
$432$	7.36470	−	2.20123i	0.354334	−	0.105907i
$433$	−14.9805			−0.719916			−0.359958	−	0.932968i	$-0.617209\pi$
$433$	−14.9805			−0.719916			−0.359958	+	0.932968i	$0.617209\pi$
$434$		0			0
$435$	−7.32546	+	9.32992i	−0.351229	+	0.447335i
$436$	−14.6410	+	6.31161i	−0.701178	+	0.302271i
$437$	4.19134	−	7.25962i	0.200499	−	0.347275i
$438$	−5.48841	−	26.5955i	−0.262246	−	1.27078i
$439$	−8.66266	−	15.0042i	−0.413446	−	0.716110i	0.581818	−	0.813319i	$-0.302342\pi$
$439$	−8.66266	−	15.0042i	−0.413446	−	0.716110i	−0.995264	+	0.0972091i	$0.969008\pi$
$440$	1.25481	−	22.7512i	0.0598206	−	1.08462i
$441$		0			0
$442$	5.68938	+	6.39456i	0.270616	+	0.304158i
$443$	−12.6162	−	21.8520i	−0.599416	−	1.03822i	−0.992907	−	0.118890i	$-0.962066\pi$
$443$	−12.6162	−	21.8520i	−0.599416	−	1.03822i	0.393492	−	0.919328i	$-0.371267\pi$
$444$	29.8458	+	22.2298i	1.41642	+	1.05498i
$445$	8.83730	+	22.0251i	0.418928	+	1.04409i
$446$	31.6501	+	10.4917i	1.49868	+	0.496795i
$447$		−	62.1779i		−	2.94091i
$448$		0			0
$449$	7.06145			0.333251			0.166625	−	0.986020i	$-0.446713\pi$
$449$	7.06145			0.333251			0.166625	+	0.986020i	$0.446713\pi$
$450$	−26.3614	−	2.12782i	−1.24269	−	0.100307i
$451$	−4.78848	+	8.29390i	−0.225481	+	0.390544i
$452$	−9.09879	+	12.2160i	−0.427971	+	0.574594i
$453$	9.09653	+	15.7556i	0.427392	+	0.740265i
$454$	22.1103	−	19.6720i	1.03769	−	0.923255i
$455$		0			0
$456$	13.9201	+	19.8942i	0.651867	+	0.931633i
$457$	16.3519	−	9.44078i	0.764910	−	0.441621i	−0.0661459	−	0.997810i	$-0.521070\pi$
$457$	16.3519	−	9.44078i	0.764910	−	0.441621i	0.831056	+	0.556189i	$0.187737\pi$
$458$	1.48100	+	7.17660i	0.0692028	+	0.335340i
$459$	−12.3089	−	7.10656i	−0.574531	−	0.331706i
$460$	−10.9605	−	2.89939i	−0.511038	−	0.135185i
$461$			34.6087i			1.61189i	0.591992	+	0.805944i	$0.298342\pi$
$461$			34.6087i			1.61189i	−0.591992	+	0.805944i	$0.701658\pi$
$462$		0			0
$463$	15.0235			0.698202			0.349101	−	0.937085i	$-0.386487\pi$
$463$	15.0235			0.698202			0.349101	+	0.937085i	$0.386487\pi$
$464$	−2.34062	−	7.83106i	−0.108661	−	0.363548i
$465$	−4.13211	−	10.2984i	−0.191622	−	0.477577i
$466$	−5.93636	−	28.7662i	−0.274997	−	1.33257i
$467$	−22.0309	+	12.7195i	−1.01947	+	0.588590i	−0.913950	−	0.405828i	$-0.866983\pi$
$467$	−22.0309	+	12.7195i	−1.01947	+	0.588590i	−0.105518	+	0.994417i	$0.533650\pi$
$468$	−0.711981	+	6.07950i	−0.0329113	+	0.281025i
$469$		0			0
$470$	4.21288	−	0.259348i	0.194326	−	0.0119628i
$471$	−14.4470	+	8.34096i	−0.665681	+	0.384331i
$472$	−0.469379	−	5.38599i	−0.0216049	−	0.247910i
$473$	7.47869	+	4.31782i	0.343871	+	0.198534i
$474$	−8.95074	+	27.0016i	−0.411121	+	1.24023i
$475$	−3.92264	−	16.0608i	−0.179983	−	0.736921i
$476$		0			0
$477$		−	6.77350i		−	0.310137i
$478$	28.3627	+	9.40192i	1.29728	+	0.430034i
$479$	10.2844	−	17.8131i	0.469905	−	0.813900i	−0.529502	−	0.848308i	$-0.677621\pi$
$479$	10.2844	−	17.8131i	0.469905	−	0.813900i	0.999408	+	0.0344084i	$0.0109547\pi$
$480$	21.0369	−	25.2166i	0.960198	−	1.15098i
$481$	−5.07906	+	2.93239i	−0.231585	+	0.133706i
$482$	−1.92089	+	1.70906i	−0.0874939	+	0.0778453i
$483$		0			0
$484$	0.460576	−	3.93279i	0.0209353	−	0.178763i
$485$	2.31689	−	16.2033i	0.105205	−	0.735755i
$486$	6.27189	+	30.3921i	0.284499	+	1.37861i
$487$	14.5295	−	25.1658i	0.658394	−	1.14037i	−0.322638	−	0.946522i	$-0.604570\pi$
$487$	14.5295	−	25.1658i	0.658394	−	1.14037i	0.981031	−	0.193849i	$-0.0620971\pi$
$488$	−11.6941	+	25.0560i	−0.529369	+	1.13423i
$489$		−	47.9749i		−	2.16950i
$490$		0			0
$491$		−	9.51815i		−	0.429548i	−0.976664	−	0.214774i	$-0.931098\pi$
$491$		−	9.51815i		−	0.429548i	0.976664	−	0.214774i	$-0.0689015\pi$
$492$	−12.6750	+	5.46405i	−0.571431	+	0.246339i
$493$	−7.55657	+	13.0884i	−0.340331	+	0.589470i
$494$	−3.74750	+	0.773356i	−0.168608	+	0.0347949i
$495$	−29.8276	−	4.26500i	−1.34065	−	0.191698i
$496$	7.43893	+	1.76660i	0.334018	+	0.0793226i
$497$		0			0
$498$	25.6189	+	28.7943i	1.14801	+	1.29030i
$499$	−17.4855	+	10.0953i	−0.782760	+	0.451927i	−0.837407	−	0.546579i	$-0.815930\pi$
$499$	−17.4855	+	10.0953i	−0.782760	+	0.451927i	0.0546477	+	0.998506i	$0.482596\pi$
$500$	−19.5745	+	10.8092i	−0.875397	+	0.483404i
$501$	−2.37413	+	4.11211i	−0.106068	+	0.183716i
$502$	6.23813	−	18.8185i	0.278421	−	0.839911i
$503$			13.3134i			0.593616i	0.954937	+	0.296808i	$0.0959221\pi$
$503$			13.3134i			0.593616i	−0.954937	+	0.296808i	$0.904078\pi$
$504$		0			0
$505$	−8.77949	+	11.1818i	−0.390682	+	0.497585i
$506$	−12.2607	−	4.06428i	−0.545053	−	0.180679i
$507$	27.7233	+	16.0060i	1.23123	+	0.710853i
$508$	−14.0851	−	10.4909i	−0.624926	−	0.465459i
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	−0.749495	−	0.662010i	$-0.769704\pi$
$509$	−12.4294	+	7.17613i	−0.550925	+	0.318077i	0.198570	+	0.980087i	$0.436370\pi$
$510$	−60.6077	+	3.73105i	−2.68376	+	0.165214i
$511$		0			0
$512$	5.83424	+	21.8623i	0.257839	+	0.966188i
$513$	5.50282	−	3.17706i	0.242956	−	0.140270i
$514$	−24.7539	+	5.10836i	−1.09185	+	0.225320i
$515$	0.851050	+	2.12106i	0.0375018	+	0.0934652i
$516$	4.92699	+	11.4291i	0.216899	+	0.503140i
$517$	4.80879			0.211490
$518$		0			0
$519$		−	39.5906i		−	1.73783i
$520$	2.33689	+	4.61762i	0.102479	+	0.202496i
$521$	31.9571	+	18.4505i	1.40007	+	0.808330i	0.994399	−	0.105690i	$-0.0337053\pi$
$521$	31.9571	+	18.4505i	1.40007	+	0.808330i	0.405669	+	0.914020i	$0.367039\pi$
$522$	−10.5851	+	2.18439i	−0.463295	+	0.0956083i
$523$	15.7185	−	9.07509i	0.687323	−	0.396826i	−0.115285	−	0.993332i	$-0.536778\pi$
$523$	15.7185	−	9.07509i	0.687323	−	0.396826i	0.802608	+	0.596506i	$0.203445\pi$
$524$	−3.11481	+	26.5969i	−0.136071	+	1.16189i
$525$		0			0
$526$	20.5837	+	23.1349i	0.897490	+	1.00873i
$527$	−7.06883	−	12.2436i	−0.307923	−	0.533338i
$528$	25.6871	−	27.2022i	1.11789	−	1.18382i
$529$	8.28651	−	14.3526i	0.360283	−	0.624028i
$530$	−3.16278	−	4.77433i	−0.137383	−	0.207384i
$531$	−7.14919			−0.310248
$532$		0			0
$533$		−	2.17519i		−	0.0942178i
$534$	−12.2611	+	36.9879i	−0.530589	+	1.60062i
$535$	−15.0488	+	6.03814i	−0.650616	+	0.261052i
$536$	2.27445	+	26.0987i	0.0982412	+	1.12729i
$537$	−16.2740	−	28.1874i	−0.702276	−	1.21638i
$538$	−3.04588	+	2.70999i	−0.131317	+	0.116836i
$539$		0			0
$540$	−6.09618	−	6.05738i	−0.262338	−	0.260668i
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	0.994100	−	0.108463i	$-0.0345930\pi$
$541$	9.37629	+	16.2402i	0.403118	+	0.698221i	−0.590982	+	0.806685i	$0.701260\pi$
$542$	−23.4843	+	4.84637i	−1.00874	+	0.208169i
$543$	−10.4086	+	18.0283i	−0.446677	+	0.773667i
$544$	21.9849	−	35.5981i	0.942596	−	1.52626i
$545$	14.0202	+	11.0081i	0.600561	+	0.471535i
$546$		0			0
$547$	−34.1580			−1.46049			−0.730246	−	0.683185i	$-0.760594\pi$
$547$	−34.1580			−1.46049			−0.730246	+	0.683185i	$0.760594\pi$
$548$	4.13621	+	9.59475i	0.176690	+	0.409867i
$549$	31.6653	+	18.2820i	1.35144	+	0.780256i
$550$	−23.0156	+	10.9213i	−0.981387	+	0.465687i
$551$	−3.37824	−	5.85128i	−0.143918	−	0.249273i
$552$	−10.6725	−	15.2529i	−0.454252	−	0.649206i
$553$		0			0
$554$	−28.3702	+	25.2416i	−1.20534	+	1.07241i
$555$	5.88948	−	41.1884i	0.249994	−	1.74835i
$556$	−35.1980	−	26.2163i	−1.49273	−	1.11182i
$557$	35.0192	+	20.2183i	1.48381	+	0.856679i	0.999831	−	0.0184005i	$-0.00585738\pi$
$557$	35.0192	+	20.2183i	1.48381	+	0.856679i	0.483980	+	0.875079i	$0.339191\pi$
$558$	3.18128	−	9.59694i	0.134674	−	0.406271i
$559$	−1.96139			−0.0829579
$560$		0			0
$561$	−69.1805			−2.92080
$562$	11.1022	−	33.4920i	0.468320	−	1.41278i
$563$	−0.276201	−	0.159465i	−0.0116405	−	0.00672065i	0.494168	−	0.869366i	$-0.335473\pi$
$563$	−0.276201	−	0.159465i	−0.0116405	−	0.00672065i	−0.505809	+	0.862646i	$0.668806\pi$
$564$	5.55821	+	4.13988i	0.234043	+	0.174320i
$565$	16.8586	+	2.41059i	0.709248	+	0.101414i
$566$	−10.3946	+	9.24835i	−0.436920	+	0.388737i
$567$		0			0
$568$	−2.24457	−	3.20788i	−0.0941800	−	0.134600i
$569$	−15.3058	−	26.5104i	−0.641651	−	1.11137i	−0.985064	−	0.172188i	$-0.944916\pi$
$569$	−15.3058	−	26.5104i	−0.641651	−	1.11137i	0.343413	−	0.939184i	$-0.388417\pi$
$570$	12.1031	−	24.2992i	0.506943	−	1.01778i
$571$	−7.35081	−	4.24399i	−0.307622	−	0.177606i	0.338240	−	0.941060i	$-0.390168\pi$
$571$	−7.35081	−	4.24399i	−0.307622	−	0.177606i	−0.645862	+	0.763454i	$0.723502\pi$
$572$	2.33412	+	5.41446i	0.0975945	+	0.226390i
$573$	17.5486			0.733103
$574$		0			0
$575$	3.00748	+	12.3138i	0.125421	+	0.513521i
$576$	29.4704	−	5.17589i	1.22793	−	0.215662i
$577$	1.68251	−	2.91419i	0.0700438	−	0.121319i	−0.828876	−	0.559432i	$-0.811019\pi$
$577$	1.68251	−	2.91419i	0.0700438	−	0.121319i	0.898920	+	0.438112i	$0.144353\pi$
$578$	−52.2225	+	10.7769i	−2.17217	+	0.448262i
$579$	−3.06354	−	5.30620i	−0.127316	−	0.220518i
$580$	−6.44095	+	6.48221i	−0.267446	+	0.269159i
$581$		0			0
$582$	20.0791	−	17.8648i	0.832305	−	0.740520i
$583$	−3.26230	−	5.65048i	−0.135111	−	0.234019i
$584$	−1.81624	−	20.8409i	−0.0751565	−	0.862401i
$585$	6.35136	−	2.54840i	0.262596	−	0.105364i
$586$	−10.4144	+	31.4170i	−0.430215	+	1.29782i
$587$			2.02359i			0.0835225i	0.999128	+	0.0417613i	$0.0132969\pi$
$587$			2.02359i			0.0835225i	−0.999128	+	0.0417613i	$0.986703\pi$
$588$		0			0
$589$	6.32038			0.260427
$590$	−5.03914	+	3.33821i	−0.207458	+	0.137432i
$591$	26.3779	−	45.6878i	1.08504	−	1.87935i
$592$	20.8440	+	19.6831i	0.856685	+	0.808971i
$593$	13.4129	+	23.2318i	0.550802	+	0.954016i	0.998217	+	0.0596901i	$0.0190113\pi$
$593$	13.4129	+	23.2318i	0.550802	+	0.954016i	−0.447415	+	0.894326i	$0.647655\pi$
$594$	−6.50817	−	7.31483i	−0.267033	−	0.300131i
$595$		0			0
$596$	5.57151	−	47.5743i	0.228218	−	1.94872i
$597$	−25.7622	+	14.8738i	−1.05438	+	0.608744i
$598$	2.87320	−	0.592930i	0.117494	−	0.0242467i
$599$	−32.0964	−	18.5309i	−1.31143	−	0.757152i	−0.329093	−	0.944297i	$-0.606743\pi$
$599$	−32.0964	−	18.5309i	−1.31143	−	0.757152i	−0.982332	+	0.187146i	$0.940076\pi$
$600$	−36.0046	−	7.19073i	−1.46988	−	0.293560i
$601$			1.27911i			0.0521761i	0.999660	+	0.0260880i	$0.00830503\pi$
$601$			1.27911i			0.0521761i	−0.999660	+	0.0260880i	$0.991695\pi$
$602$		0			0
$603$	34.6425			1.41075
$604$	5.54824	+	12.8702i	0.225755	+	0.523683i
$605$	−4.10865	+	1.64855i	−0.167040	+	0.0670229i
$606$	−22.8616	+	4.71785i	−0.928689	+	0.191650i
$607$	19.5800	−	11.3045i	0.794727	−	0.458836i	−0.0468970	−	0.998900i	$-0.514933\pi$
$607$	19.5800	−	11.3045i	0.794727	−	0.458836i	0.841624	+	0.540064i	$0.181600\pi$
$608$	8.86805	+	16.4690i	0.359647	+	0.667907i
$609$		0			0
$610$	30.8560	−	1.89951i	1.24932	−	0.0769091i
$611$	−0.945877	+	0.546102i	−0.0382661	+	0.0220929i
$612$	−44.3716	−	33.0489i	−1.79361	−	1.33592i
$613$	2.61492	+	1.50973i	0.105616	+	0.0609773i	0.551877	−	0.833925i	$-0.313912\pi$
$613$	2.61492	+	1.50973i	0.105616	+	0.0609773i	−0.446262	+	0.894903i	$0.647245\pi$
$614$	2.93350	+	0.972422i	0.118386	+	0.0392437i
$615$	12.1375	+	9.52987i	0.489432	+	0.384281i
$616$		0			0
$617$		−	14.3344i		−	0.577081i	−0.957468	−	0.288540i	$-0.906830\pi$
$617$		−	14.3344i		−	0.577081i	0.957468	−	0.288540i	$-0.0931700\pi$
$618$	−1.18077	+	3.56201i	−0.0474974	+	0.143285i
$619$	10.8987	−	18.8771i	0.438055	−	0.758733i	−0.559485	−	0.828841i	$-0.689001\pi$
$619$	10.8987	−	18.8771i	0.438055	−	0.758733i	0.997539	+	0.0701078i	$0.0223343\pi$
$620$	−2.23881	−	8.24990i	−0.0899127	−	0.331324i
$621$	−4.21901	+	2.43584i	−0.169303	+	0.0977471i
$622$	27.1674	+	30.5347i	1.08931	+	1.22433i
$623$		0			0
$624$	−1.96342	+	8.26771i	−0.0785997	+	0.330973i
$625$	21.0731	+	13.4509i	0.842923	+	0.538035i
$626$	−8.79915	+	1.81584i	−0.351685	+	0.0725757i
$627$	15.4639	−	26.7843i	0.617570	−	1.06966i
$628$	−11.8012	+	5.08740i	−0.470920	+	0.203009i
$629$		−	53.0106i		−	2.11367i
$630$		0			0
$631$			15.1512i			0.603160i	0.953441	+	0.301580i	$0.0975140\pi$
$631$			15.1512i			0.603160i	−0.953441	+	0.301580i	$0.902486\pi$
$632$	−9.26800	+	19.8578i	−0.368661	+	0.789899i
$633$	−28.6420	+	49.6094i	−1.13842	+	1.97180i
$634$	5.37434	+	26.0428i	0.213442	+	1.03429i
$635$	−2.77942	+	19.4380i	−0.110298	+	0.771374i
$636$	1.09378	−	9.33959i	0.0433710	−	0.370339i
$637$		0			0
$638$	−7.77803	+	6.92029i	−0.307935	+	0.273977i
$639$	−4.48363	+	2.58863i	−0.177370	+	0.102404i
$640$	18.3555	−	17.4090i	0.725567	−	0.688152i
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	0.401613	+	0.915809i	$0.368450\pi$
$641$	−14.9960	+	25.9739i	−0.592308	+	1.02591i	−0.993921	+	0.110098i	$0.964884\pi$
$642$	−25.2722	−	8.37746i	−0.997415	−	0.330632i
$643$			1.63196i			0.0643583i	0.999482	+	0.0321792i	$0.0102447\pi$
$643$			1.63196i			0.0643583i	−0.999482	+	0.0321792i	$0.989755\pi$
$644$		0			0
$645$	8.59318	−	10.9445i	0.338356	−	0.430940i
$646$	10.8827	−	32.8298i	0.428175	−	1.29167i
$647$	28.3765	+	16.3832i	1.11560	+	0.644090i	0.940273	−	0.340421i	$-0.110570\pi$
$647$	28.3765	+	16.3832i	1.11560	+	0.644090i	0.175323	+	0.984511i	$0.443903\pi$
$648$	1.53023	+	17.5590i	0.0601132	+	0.689783i
$649$	−5.96388	+	3.44325i	−0.234103	+	0.135159i
$650$	3.28684	−	4.76193i	0.128921	−	0.186778i
$651$		0			0
$652$	4.29883	−	36.7071i	0.168355	−	1.43756i
$653$	−19.5109	+	11.2646i	−0.763521	+	0.440819i	−0.830558	−	0.556932i	$-0.811979\pi$
$653$	−19.5109	+	11.2646i	−0.763521	+	0.440819i	0.0670377	+	0.997750i	$0.478645\pi$
$654$	5.91544	+	28.6648i	0.231312	+	1.12088i
$655$	27.7862	−	11.1489i	1.08570	−	0.435623i
$656$	−10.1876	+	3.04497i	−0.397760	+	0.118886i
$657$	−27.6635			−1.07925
$658$		0			0
$659$		−	19.2525i		−	0.749969i	−0.927031	−	0.374985i	$-0.877648\pi$
$659$		−	19.2525i		−	0.749969i	0.927031	−	0.374985i	$-0.122352\pi$
$660$	−40.4388	−	10.6973i	−1.57408	−	0.416391i
$661$	−30.1079	−	17.3828i	−1.17106	−	0.676113i	−0.217132	−	0.976142i	$-0.569670\pi$
$661$	−30.1079	−	17.3828i	−1.17106	−	0.676113i	−0.953930	+	0.300030i	$0.903003\pi$
$662$	−3.74108	−	18.1284i	−0.145401	−	0.704580i
$663$	13.6077	−	7.85638i	0.528477	−	0.305117i
$664$	17.0217	+	24.3270i	0.660570	+	0.944071i
$665$		0			0
$666$	28.3228	−	25.1994i	1.09749	−	0.976458i
$667$	2.59009	+	4.48617i	0.100289	+	0.173705i
$668$	−2.18499	+	2.93357i	−0.0845398	+	0.113503i
$669$	30.6059	−	53.0110i	1.18329	−	2.04952i
$670$	24.4179	−	16.1758i	0.943347	−	0.624926i
$671$	35.2205			1.35967
$672$		0			0
$673$		−	42.6368i		−	1.64353i	−0.569827	−	0.821764i	$-0.692990\pi$
$673$		−	42.6368i		−	1.64353i	0.569827	−	0.821764i	$-0.307010\pi$
$674$	15.7487	+	5.22053i	0.606618	+	0.201087i
$675$	−2.69270	+	9.22326i	−0.103642	+	0.355003i
$676$	19.7777	+	14.7309i	0.760681	+	0.566572i
$677$	−0.892648	−	1.54611i	−0.0343073	−	0.0594219i	0.848362	−	0.529417i	$-0.177589\pi$
$677$	−0.892648	−	1.54611i	−0.0343073	−	0.0594219i	−0.882669	+	0.469995i	$0.844256\pi$
$678$	18.5873	+	20.8911i	0.713842	+	0.802319i
$679$		0			0
$680$	−46.7072	−	2.57606i	−1.79114	−	0.0987874i
$681$	−27.1648	−	47.0509i	−1.04096	−	1.80299i
$682$	−1.96832	−	9.53800i	−0.0753708	−	0.365229i
$683$	4.30263	−	7.45237i	0.164636	−	0.285157i	−0.771890	−	0.635756i	$-0.780689\pi$
$683$	4.30263	−	7.45237i	0.164636	−	0.285157i	0.936526	+	0.350599i	$0.114022\pi$
$684$	22.7138	−	9.79170i	0.868483	−	0.374395i
$685$	7.21396	−	9.18792i	0.275631	−	0.351052i
$686$		0			0
$687$	13.4523			0.513236
$688$	2.74568	+	9.18628i	0.104678	+	0.350224i
$689$	1.28338	+	0.740957i	0.0488927	+	0.0282282i
$690$	−9.27943	+	18.6302i	−0.353262	+	0.709238i
$691$	−20.1511	−	34.9027i	−0.766583	−	1.32776i	−0.939405	−	0.342808i	$-0.888622\pi$
$691$	−20.1511	−	34.9027i	−0.766583	−	1.32776i	0.172822	−	0.984953i	$-0.444711\pi$
$692$	3.54755	−	30.2920i	0.134858	−	1.15153i
$693$		0			0
$694$	4.14720	+	4.66123i	0.157426	+	0.176938i
$695$	−6.94562	+	48.5746i	−0.263463	+	1.84254i
$696$	−14.9479	+	1.30268i	−0.566597	+	0.0493778i
$697$	17.0270	+	9.83053i	0.644943	+	0.372358i
$698$	24.6299	+	8.16454i	0.932256	+	0.309033i
$699$	−53.9212			−2.03949
$700$		0			0
$701$	37.3051			1.40899			0.704497	−	0.709707i	$-0.251172\pi$
$701$	37.3051			1.40899			0.704497	+	0.709707i	$0.251172\pi$
$702$	2.11084	+	0.699719i	0.0796684	+	0.0264092i
$703$	20.5239	+	11.8495i	0.774072	+	0.446911i
$704$	22.0915	−	18.5115i	0.832604	−	0.697679i
$705$	1.09680	−	7.67055i	0.0413080	−	0.288890i
$706$	−11.0438	−	12.4126i	−0.415637	−	0.467154i
$707$		0			0
$708$	−9.85761	−	1.15444i	−0.370472	−	0.0433866i
$709$	4.02866	+	6.97784i	0.151299	+	0.262058i	0.931705	−	0.363215i	$-0.118321\pi$
$709$	4.02866	+	6.97784i	0.151299	+	0.262058i	−0.780406	+	0.625273i	$0.784988\pi$
$710$	−1.95159	+	3.91817i	−0.0732418	+	0.147046i
$711$	25.0958	+	14.4891i	0.941168	+	0.543383i
$712$	−12.6957	+	27.2019i	−0.475790	+	1.01944i
$713$	−4.84582			−0.181477
$714$		0			0
$715$	4.07095	−	5.18488i	0.152245	−	0.193903i
$716$	−9.92601	−	23.0254i	−0.370953	−	0.860498i
$717$	27.4269	−	47.5049i	1.02428	−	1.77410i
$718$	−0.0565649	−	0.274100i	−0.00211098	−	0.0102293i
$719$	5.87241	+	10.1713i	0.219004	+	0.379326i	0.954504	−	0.298199i	$-0.0963859\pi$
$719$	5.87241	+	10.1713i	0.219004	+	0.379326i	−0.735500	+	0.677525i	$0.763053\pi$
$720$	−20.8267	−	26.1795i	−0.776164	−	0.975654i
$721$		0			0
$722$	−7.58289	−	8.52275i	−0.282206	−	0.317184i
$723$	2.36001	+	4.08766i	0.0877697	+	0.152022i
$724$	−9.57940	+	12.8613i	−0.356016	+	0.477987i
$725$	9.80731	+	2.86321i	0.364234	+	0.106337i
$726$	−6.89987	−	2.28723i	−0.256078	−	0.0848871i
$727$		−	33.3549i		−	1.23706i	−0.785760	−	0.618532i	$-0.787728\pi$
$727$		−	33.3549i		−	1.23706i	0.785760	−	0.618532i	$-0.212272\pi$
$728$		0			0
$729$	38.2742			1.41756
$730$	−19.4987	+	12.9170i	−0.721680	+	0.478081i
$731$	8.86429	−	15.3534i	0.327857	−	0.567866i
$732$	40.7094	+	30.3213i	1.50466	+	1.12071i
$733$	−5.75003	−	9.95934i	−0.212382	−	0.367856i	0.740077	−	0.672522i	$-0.234789\pi$
$733$	−5.75003	−	9.95934i	−0.212382	−	0.367856i	−0.952460	+	0.304665i	$0.901455\pi$
$734$	−7.95403	+	7.07688i	−0.293588	+	0.261212i
$735$		0			0
$736$	−6.79912	−	12.6268i	−0.250619	−	0.465429i
$737$	28.8989	−	16.6848i	1.06451	−	0.614593i
$738$	2.84173	+	13.7704i	0.104606	+	0.506894i
$739$	9.70301	+	5.60203i	0.356931	+	0.206074i	0.667734	−	0.744400i	$-0.267265\pi$
$739$	9.70301	+	5.60203i	0.356931	+	0.206074i	−0.310803	+	0.950474i	$0.600598\pi$
$740$	8.19695	−	30.9868i	0.301326	−	1.13910i
$741$			7.02455i			0.258053i
$742$		0			0
$743$	−43.7950			−1.60668			−0.803341	−	0.595520i	$-0.796946\pi$
$743$	−43.7950			−1.60668			−0.803341	+	0.595520i	$0.796946\pi$
$744$	5.93619	−	12.7190i	0.217631	−	0.466300i
$745$	−49.7016	+	19.9422i	−1.82093	+	0.730625i
$746$	8.90030	+	43.1287i	0.325863	+	1.57905i
$747$	34.0017	−	19.6309i	1.24406	−	0.718256i
$748$	−52.9322	−	6.19898i	−1.93539	−	0.226657i
$749$		0			0
$750$	12.1713	+	39.2034i	0.444432	+	1.43151i
$751$	44.5322	−	25.7107i	1.62500	−	0.938196i	0.639450	−	0.768832i	$-0.279162\pi$
$751$	44.5322	−	25.7107i	1.62500	−	0.938196i	0.985554	−	0.169364i	$-0.0541714\pi$
$752$	3.88180	+	3.66560i	0.141555	+	0.133671i
$753$	−31.5192	−	18.1976i	−1.14862	−	0.663159i
$754$	0.744028	−	2.24450i	0.0270959	−	0.0817400i
$755$	9.67670	−	12.3245i	0.352171	−	0.448536i
$756$		0			0
$757$			18.1453i			0.659502i	0.944068	+	0.329751i	$0.106965\pi$
$757$			18.1453i			0.659502i	−0.944068	+	0.329751i	$0.893035\pi$
$758$	−21.9339	−	7.27086i	−0.796676	−	0.264089i
$759$	−11.8562	+	20.5355i	−0.430352	+	0.745391i
$760$	11.4378	−	17.5076i	0.414893	−	0.635067i
$761$	28.4860	−	16.4464i	1.03262	−	0.596181i	0.114883	−	0.993379i	$-0.463351\pi$
$761$	28.4860	−	16.4464i	1.03262	−	0.596181i	0.917733	+	0.397198i	$0.130017\pi$
$762$	−24.0875	+	21.4312i	−0.872598	+	0.776370i
$763$		0			0
$764$	13.4270	+	1.57246i	0.485771	+	0.0568895i
$765$	−8.75585	+	61.2346i	−0.316568	+	2.21394i
$766$	−2.52915	−	12.2557i	−0.0913821	−	0.442816i
$767$	0.782054	−	1.35456i	0.0282383	−	0.0489102i
$768$	41.4709	−	2.37790i	1.49645	−	0.0858049i
$769$			20.8502i			0.751876i	0.926645	+	0.375938i	$0.122679\pi$
$769$			20.8502i			0.751876i	−0.926645	+	0.375938i	$0.877321\pi$
$770$		0			0
$771$			46.4003i			1.67107i
$772$	−1.86854	−	4.33445i	−0.0672503	−	0.156000i
$773$	4.34380	−	7.52368i	0.156236	−	0.270608i	−0.777273	−	0.629164i	$-0.783397\pi$
$773$	4.34380	−	7.52368i	0.156236	−	0.270608i	0.933508	+	0.358556i	$0.116731\pi$
$774$	12.4169	−	2.56242i	0.446315	−	0.0921042i
$775$	−6.90671	+	6.60597i	−0.248096	+	0.237293i
$776$	16.9639	−	11.8697i	0.608970	−	0.426099i
$777$		0			0
$778$	8.78497	+	9.87384i	0.314957	+	0.353994i
$779$	−7.61208	+	4.39484i	−0.272731	+	0.157461i
$780$	9.16904	−	2.48824i	0.328304	−	0.0890933i
$781$	−2.49351	+	4.31888i	−0.0892247	+	0.154542i
$782$	−8.34377	+	25.1706i	−0.298373	+	0.900098i
$783$			3.92660i			0.140325i
$784$		0			0
$785$	11.3008	+	8.87294i	0.403344	+	0.316689i
$786$	46.6628	+	15.4682i	1.66441	+	0.551733i
$787$	−32.2270	−	18.6062i	−1.14877	−	0.663241i	−0.200180	−	0.979759i	$-0.564153\pi$
$787$	−32.2270	−	18.6062i	−1.14877	−	0.663241i	−0.948586	+	0.316518i	$0.897486\pi$
$788$	24.2765	−	32.5936i	0.864813	−	1.16110i
$789$	49.2312	−	28.4237i	1.75268	−	1.01191i
$790$	24.4544	−	1.50543i	0.870048	−	0.0535608i
$791$		0			0
$792$	−21.8501	−	31.2277i	−0.776411	−	1.10963i
$793$	−6.92778	+	3.99976i	−0.246013	+	0.142036i
$794$	28.1198	−	5.80296i	0.997933	−	0.205939i
$795$	−9.75722	+	3.91496i	−0.346053	+	0.138849i
$796$	−21.0442	+	9.07197i	−0.745893	+	0.321547i
$797$	−21.3900			−0.757671			−0.378835	−	0.925464i	$-0.623675\pi$
$797$	−21.3900			−0.757671			−0.378835	+	0.925464i	$0.623675\pi$
$798$		0			0
$799$		−	9.87221i		−	0.349254i
$800$	−26.9039	−	8.72808i	−0.951197	−	0.308584i
$801$	34.3773	+	19.8477i	1.21466	+	0.701285i
$802$	15.3554	−	3.16883i	0.542217	−	0.111895i
$803$	−23.0770	+	13.3235i	−0.814368	+	0.470176i
$804$	47.7666	+	5.59403i	1.68460	+	0.197286i
$805$		0			0
$806$	1.47033	+	1.65257i	0.0517902	+	0.0582094i
$807$	3.74219	+	6.48166i	0.131731	+	0.228165i
$808$	−17.9149	+	1.56125i	−0.630243	+	0.0549244i
$809$	−12.1707	+	21.0803i	−0.427900	+	0.741144i	−0.996686	−	0.0813411i	$-0.974080\pi$
$809$	−12.1707	+	21.0803i	−0.427900	+	0.741144i	0.568787	+	0.822485i	$0.307413\pi$
$810$	16.4282	−	10.8830i	0.577229	−	0.382389i
$811$	31.3778			1.10183			0.550913	−	0.834563i	$-0.314280\pi$
$811$	31.3778			1.10183			0.550913	+	0.834563i	$0.314280\pi$
$812$		0			0
$813$			44.0206i			1.54387i
$814$	11.4902	−	34.6625i	0.402733	−	1.21492i
$815$	−38.3485	+	15.3869i	−1.34329	+	0.538979i
$816$	−55.8447	−	52.7344i	−1.95496	−	1.84607i
$817$	3.96287	+	6.86389i	0.138643	+	0.240137i
$818$	−6.21976	+	5.53386i	−0.217469	+	0.193487i
$819$		0			0
$820$	8.43287	+	8.37920i	0.294489	+	0.292614i
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	0.864651	−	0.502373i	$-0.167539\pi$
$821$	−0.0785681	−	0.136084i	−0.00274204	−	0.00474936i	−0.867393	+	0.497623i	$0.834206\pi$
$822$	18.7850	−	3.87658i	0.655202	−	0.135211i
$823$	9.34753	−	16.1904i	0.325835	−	0.564362i	−0.655846	−	0.754894i	$-0.727688\pi$
$823$	9.34753	−	16.1904i	0.325835	−	0.564362i	0.981681	+	0.190532i	$0.0610214\pi$
$824$	−1.22262	+	2.61960i	−0.0425919	+	0.0912582i
$825$	11.0961	+	45.4317i	0.386316	+	1.58173i
$826$		0			0
$827$	−35.2960			−1.22736			−0.613681	−	0.789554i	$-0.710312\pi$
$827$	−35.2960			−1.22736			−0.613681	+	0.789554i	$0.710312\pi$
$828$	−17.4146	+	7.50728i	−0.605200	+	0.260896i
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	0.726744	−	0.686908i	$-0.241033\pi$
$829$	14.2590	+	8.23245i	0.495237	+	0.285925i	−0.231508	+	0.972833i	$0.574366\pi$
$830$	14.7999	−	29.7135i	0.513711	−	1.03137i
$831$	34.8558	+	60.3720i	1.20913	+	2.09428i
$832$	−2.24311	+	6.14996i	−0.0777659	+	0.213211i
$833$		0			0
$834$	−60.1934	+	53.5555i	−2.08433	+	1.85447i
$835$	4.04845	+	0.578882i	0.140102	+	0.0200330i
$836$	14.2320	−	19.1079i	0.492223	−	0.660859i
$837$	−3.18105	−	1.83658i	−0.109953	−	0.0634814i
$838$	−7.44288	+	22.4529i	−0.257110	+	0.775622i
$839$	−54.8000			−1.89191			−0.945953	−	0.324303i	$-0.894870\pi$
$839$	−54.8000			−1.89191			−0.945953	+	0.324303i	$0.894870\pi$
$840$		0			0
$841$	−24.8248			−0.856026
$842$	−0.528745	+	1.59506i	−0.0182218	+	0.0549694i
$843$	−56.0960	−	32.3871i	−1.93205	−	1.11547i
$844$	−26.3602	+	35.3913i	−0.907356	+	1.21822i
$845$	3.90274	−	27.2940i	0.134258	−	0.938943i
$846$	5.27458	−	4.69291i	0.181344	−	0.161346i
$847$		0			0
$848$	1.67376	−	7.04801i	0.0574773	−	0.242030i
$849$	12.7709	+	22.1199i	0.438297	+	0.759152i
$850$	22.4210	+	47.2499i	0.769033	+	1.62066i
$851$	−15.7356	−	9.08496i	−0.539410	−	0.311428i
$852$	−6.60023	+	2.84530i	−0.226120	+	0.0974783i
$853$	38.9225			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$853$	38.9225			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$854$		0			0
$855$	−21.7507	−	17.0777i	−0.743858	−	0.584046i
$856$	−18.5859	−	8.67440i	−0.635253	−	0.296485i
$857$	14.6766	−	25.4206i	0.501342	−	0.868350i	−0.498657	−	0.866800i	$-0.666173\pi$
$857$	14.6766	−	25.4206i	0.501342	−	0.868350i	0.999999	−	0.00155047i	$-0.000493529\pi$
$858$	10.6006	−	2.18761i	0.361900	−	0.0746839i
$859$	23.6874	+	41.0277i	0.808202	+	1.39985i	0.914108	+	0.405471i	$0.132893\pi$
$859$	23.6874	+	41.0277i	0.808202	+	1.39985i	−0.105905	+	0.994376i	$0.533774\pi$
$860$	7.55561	−	7.60401i	0.257644	−	0.259294i
$861$		0			0
$862$	−25.4578	+	22.6504i	−0.867095	+	0.771474i
$863$	11.8505	+	20.5257i	0.403397	+	0.698704i	0.994133	−	0.108161i	$-0.0344961\pi$
$863$	11.8505	+	20.5257i	0.403397	+	0.698704i	−0.590737	+	0.806865i	$0.701163\pi$
$864$	0.322288	−	10.8658i	0.0109645	−	0.369660i
$865$	−31.6466	+	12.6978i	−1.07602	+	0.431738i
$866$	−6.66609	+	20.1095i	−0.226523	+	0.683350i
$867$			97.8892i			3.32449i
$868$		0			0
$869$	27.9134			0.946897
$870$	9.26460	+	13.9852i	0.314099	+	0.474144i
$871$	−3.78957	+	6.56372i	−0.128405	+	0.222403i
$872$	1.95755	+	22.4624i	0.0662912	+	0.760673i
$873$	−13.6892	−	23.7103i	−0.463308	−	0.802474i
$874$	−7.88009	−	8.85680i	−0.266548	−	0.299586i
$875$		0			0
$876$	−38.1436	−	4.46706i	−1.28875	−	0.150928i
$877$	28.7555	−	16.6020i	0.971004	−	0.560610i	0.0714621	−	0.997443i	$-0.477234\pi$
$877$	28.7555	−	16.6020i	0.971004	−	0.560610i	0.899542	+	0.436834i	$0.143900\pi$
$878$	−23.9961	+	4.95197i	−0.809829	+	0.167121i
$879$	52.6205	+	30.3805i	1.77485	+	1.02471i
$880$	−29.9825	−	11.8084i	−1.01071	−	0.398061i
$881$		−	19.2043i		−	0.647008i	−0.946227	−	0.323504i	$-0.895139\pi$
$881$		−	19.2043i		−	0.647008i	0.946227	−	0.323504i	$-0.104861\pi$
$882$		0			0
$883$	8.57526			0.288581			0.144290	−	0.989535i	$-0.453910\pi$
$883$	8.57526			0.288581			0.144290	+	0.989535i	$0.453910\pi$
$884$	11.1156	−	4.79184i	0.373859	−	0.161167i
$885$	4.13211	+	10.2984i	0.138899	+	0.346177i
$886$	−34.9477	+	7.21202i	−1.17409	+	0.242292i
$887$	−12.7746	+	7.37543i	−0.428930	+	0.247643i	−0.698891	−	0.715229i	$-0.746323\pi$
$887$	−12.7746	+	7.37543i	−0.428930	+	0.247643i	0.269961	+	0.962871i	$0.412989\pi$
$888$	43.1219	−	30.1725i	1.44707	−	1.01252i
$889$		0			0
$890$	33.4986	−	2.06220i	1.12287	−	0.0691250i
$891$	19.4430	−	11.2254i	0.651365	−	0.376066i
$892$	28.1676	−	37.8179i	0.943122	−	1.26624i
$893$	3.82218	+	2.20673i	0.127904	+	0.0738455i
$894$	−83.4665	−	27.6682i	−2.79154	−	0.925364i
$895$	−17.3120	+	22.0491i	−0.578676	+	0.737019i
$896$		0			0
$897$		−	5.38571i		−	0.179824i
$898$	3.14224	−	9.47917i	0.104858	−	0.316324i
$899$	−1.95288	+	3.38248i	−0.0651321	+	0.112812i
$900$	−14.5868	+	34.4402i	−0.486225	+	1.14801i
$901$	−11.6002	+	6.69736i	−0.386457	+	0.223121i
$902$	9.00277	+	10.1186i	0.299760	+	0.336914i
$903$		0			0
$904$	12.3498	+	17.6500i	0.410747	+	0.587030i
$905$	17.7491	+	2.53793i	0.590001	+	0.0843635i
$906$	25.1979	−	5.19999i	0.837144	−	0.172758i
$907$	−23.7946	+	41.2134i	−0.790085	+	1.36847i	0.135828	+	0.990732i	$0.456631\pi$
$907$	−23.7946	+	41.2134i	−0.790085	+	1.36847i	−0.925914	+	0.377736i	$0.876703\pi$
$908$	−16.5686	−	38.4342i	−0.549850	−	1.27548i
$909$			23.7796i			0.788720i
$910$		0			0
$911$			34.7074i			1.14991i	0.818186	+	0.574954i	$0.194980\pi$
$911$			34.7074i			1.14991i	−0.818186	+	0.574954i	$0.805020\pi$
$912$	32.8999	−	9.83342i	1.08942	−	0.325617i
$913$	18.9095	−	32.7523i	0.625814	−	1.08394i
$914$	−5.39678	−	26.1515i	−0.178510	−	0.865015i
$915$	8.03319	−	56.1806i	0.265569	−	1.85727i
$916$	10.2928	+	1.20540i	0.340082	+	0.0398276i
$917$		0			0
$918$	−15.0170	+	13.3610i	−0.495635	+	0.440977i
$919$	−44.9270	+	25.9386i	−1.48200	+	0.855635i	−0.999792	−	0.0204194i	$-0.993500\pi$
$919$	−44.9270	+	25.9386i	−1.48200	+	0.855635i	−0.482212	+	0.876055i	$0.660167\pi$
$920$	−8.76936	+	13.4230i	−0.289117	+	0.442544i
$921$	2.83671	−	4.91333i	0.0934729	−	0.161900i
$922$	46.4581	+	15.4003i	1.53001	+	0.507183i
$923$		−	1.13269i		−	0.0372828i
$924$		0			0
$925$	−34.8127	+	8.50253i	−1.14463	+	0.279562i
$926$	6.68524	−	20.1673i	0.219690	−	0.662738i
$927$	3.31060	+	1.91138i	0.108734	+	0.0627778i
$928$	−11.5538	−	0.342696i	−0.379272	−	0.0112496i
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.969928	−	0.243393i	$-0.921740\pi$
$929$	−37.9198	+	21.8930i	−1.24411	+	0.718286i	−0.274180	+	0.961678i	$0.588406\pi$
$930$	−15.6631	+	0.964232i	−0.513614	+	0.0316184i
$931$		0			0
$932$	−41.2568	−	4.83166i	−1.35141	−	0.158266i
$933$	64.9780	−	37.5151i	2.12728	−	1.22819i
$934$	7.27106	+	35.2338i	0.237916	+	1.15289i
$935$	22.1881	+	55.2992i	0.725629	+	1.80848i
$936$	7.84419	+	3.66104i	0.256396	+	0.119665i
$937$	14.2224			0.464624			0.232312	−	0.972641i	$-0.425371\pi$
$937$	14.2224			0.464624			0.232312	+	0.972641i	$0.425371\pi$
$938$		0			0
$939$			16.4937i			0.538251i
$940$	1.52652	−	5.77070i	0.0497897	−	0.188220i
$941$	−4.80070	−	2.77169i	−0.156498	−	0.0903544i	0.419706	−	0.907660i	$-0.362133\pi$
$941$	−4.80070	−	2.77169i	−0.156498	−	0.0903544i	−0.576204	+	0.817306i	$0.695467\pi$
$942$	4.76807	+	23.1049i	0.155352	+	0.752799i
$943$	5.83617	−	3.36951i	0.190052	−	0.109726i
$944$	−7.43893	−	1.76660i	−0.242116	−	0.0574979i
$945$		0			0
$946$	9.12407	−	8.11789i	0.296649	−	0.263935i
$947$	29.7881	+	51.5945i	0.967983	+	1.67660i	0.701377	+	0.712791i	$0.252569\pi$
$947$	29.7881	+	51.5945i	0.967983	+	1.67660i	0.266607	+	0.963805i	$0.414098\pi$
$948$	32.2636	+	24.0306i	1.04787	+	0.780479i
$949$	3.02612	−	5.24140i	0.0982321	−	0.170143i
$950$	−23.3053	−	1.88114i	−0.756123	−	0.0610323i
$951$	48.8163			1.58298
$952$		0			0
$953$		−	12.2577i		−	0.397065i	−0.980094	−	0.198532i	$-0.936383\pi$
$953$		−	12.2577i		−	0.397065i	0.980094	−	0.198532i	$-0.0636175\pi$
$954$	−9.09262	−	3.01410i	−0.294384	−	0.0975852i
$955$	−5.62832	−	14.0274i	−0.182128	−	0.453916i
$956$	25.2419	−	33.8899i	0.816383	−	1.09608i
$957$	9.55612	+	16.5517i	0.308906	+	0.535040i
$958$	−19.3355	−	21.7321i	−0.624703	−	0.702133i
$959$		0			0
$960$	−24.4893	−	39.4606i	−0.790387	−	1.27358i
$961$	13.6732	+	23.6826i	0.441070	+	0.763956i
$962$	1.67629	+	8.12290i	0.0540458	+	0.261893i
$963$	−13.5611	+	23.4885i	−0.437000	+	0.756906i
$964$	1.43944	+	3.33907i	0.0463612	+	0.107544i
$965$	−3.25893	+	4.15067i	−0.104909	+	0.133615i
$966$		0			0
$967$	53.4551			1.71900			0.859499	−	0.511137i	$-0.170775\pi$
$967$	53.4551			1.71900			0.859499	+	0.511137i	$0.170775\pi$
$968$	−5.07436	−	2.36830i	−0.163096	−	0.0761201i
$969$	−54.9869	−	31.7467i	−1.76643	−	1.01985i
$970$	−20.7201	−	10.3204i	−0.665282	−	0.331368i
$971$	11.1284	+	19.2749i	0.357126	+	0.618561i	0.987479	−	0.157748i	$-0.0504232\pi$
$971$	11.1284	+	19.2749i	0.357126	+	0.618561i	−0.630353	+	0.776308i	$0.717090\pi$
$972$	43.5887	+	5.10475i	1.39811	+	0.163735i
$973$		0			0
$974$	−27.3167	−	30.7025i	−0.875284	−	0.983772i
$975$	−7.34195	−	7.67620i	−0.235131	−	0.245835i
$976$	28.4311	+	26.8476i	0.910056	+	0.859369i
$977$	−27.5351	−	15.8974i	−0.880926	−	0.508603i	−0.00996251	−	0.999950i	$-0.503171\pi$
$977$	−27.5351	−	15.8974i	−0.880926	−	0.508603i	−0.870964	+	0.491347i	$0.836505\pi$
$978$	−64.4006	−	21.3481i	−2.05931	−	0.682637i
$979$	38.2369			1.22206
$980$		0			0
$981$	29.8158			0.951947
$982$	−12.7770	−	4.23543i	−0.407730	−	0.135158i
$983$	17.8275	+	10.2927i	0.568609	+	0.328287i	0.756594	−	0.653885i	$-0.226862\pi$
$983$	17.8275	+	10.2927i	0.568609	+	0.328287i	−0.187985	+	0.982172i	$0.560195\pi$
$984$	1.69469	+	19.4460i	0.0540246	+	0.619917i
$985$	−44.9805	−	6.43170i	−1.43320	−	0.204931i
$986$	14.2070	+	15.9679i	0.452444	+	0.508522i
$987$		0			0
$988$	−0.629440	+	5.37470i	−0.0200252	+	0.170992i
$989$	−3.03832	−	5.26253i	−0.0966131	−	0.167339i
$990$	−18.9981	+	38.1421i	−0.603798	+	1.21224i
$991$	32.2836	+	18.6390i	1.02552	+	0.592086i	0.915699	−	0.401865i	$-0.131638\pi$
$991$	32.2836	+	18.6390i	1.02552	+	0.592086i	0.109824	+	0.993951i	$0.464971\pi$
$992$	5.68166	−	9.19977i	0.180393	−	0.292093i
$993$	−33.9810			−1.07836
$994$		0			0
$995$	20.1519	+	15.8224i	0.638859	+	0.501605i
$996$	50.0529	−	21.5773i	1.58599	−	0.683704i
$997$	−6.32111	+	10.9485i	−0.200191	+	0.346742i	−0.948590	−	0.316508i	$-0.897490\pi$
$997$	−6.32111	+	10.9485i	−0.200191	+	0.346742i	0.748399	+	0.663249i	$0.230823\pi$
$998$	5.77092	+	27.9645i	0.182675	+	0.885201i
$999$	−6.88644	−	11.9277i	−0.217877	−	0.377375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.e.619.10		32
4.3	odd	2	inner	980.2.s.e.619.15		32
5.4	even	2	inner	980.2.s.e.619.7		32
7.2	even	3		140.2.s.b.19.2	✓	32
7.3	odd	6		980.2.c.d.979.27		32
7.4	even	3		980.2.c.d.979.28		32
7.5	odd	6	inner	980.2.s.e.19.2		32
7.6	odd	2		140.2.s.b.59.10	yes	32
20.19	odd	2	inner	980.2.s.e.619.2		32
28.3	even	6		980.2.c.d.979.8		32
28.11	odd	6		980.2.c.d.979.7		32
28.19	even	6	inner	980.2.s.e.19.7		32
28.23	odd	6		140.2.s.b.19.7	yes	32
28.27	even	2		140.2.s.b.59.15	yes	32
35.2	odd	12		700.2.p.e.551.7		32
35.4	even	6		980.2.c.d.979.5		32
35.9	even	6		140.2.s.b.19.15	yes	32
35.13	even	4		700.2.p.e.451.2		32
35.19	odd	6	inner	980.2.s.e.19.15		32
35.23	odd	12		700.2.p.e.551.10		32
35.24	odd	6		980.2.c.d.979.6		32
35.27	even	4		700.2.p.e.451.15		32
35.34	odd	2		140.2.s.b.59.7	yes	32
140.19	even	6	inner	980.2.s.e.19.10		32
140.23	even	12		700.2.p.e.551.2		32
140.27	odd	4		700.2.p.e.451.7		32
140.39	odd	6		980.2.c.d.979.26		32
140.59	even	6		980.2.c.d.979.25		32
140.79	odd	6		140.2.s.b.19.10	yes	32
140.83	odd	4		700.2.p.e.451.10		32
140.107	even	12		700.2.p.e.551.15		32
140.139	even	2		140.2.s.b.59.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.2	✓	32	7.2	even	3
140.2.s.b.19.7	yes	32	28.23	odd	6
140.2.s.b.19.10	yes	32	140.79	odd	6
140.2.s.b.19.15	yes	32	35.9	even	6
140.2.s.b.59.2	yes	32	140.139	even	2
140.2.s.b.59.7	yes	32	35.34	odd	2
140.2.s.b.59.10	yes	32	7.6	odd	2
140.2.s.b.59.15	yes	32	28.27	even	2
700.2.p.e.451.2		32	35.13	even	4
700.2.p.e.451.7		32	140.27	odd	4
700.2.p.e.451.10		32	140.83	odd	4
700.2.p.e.451.15		32	35.27	even	4
700.2.p.e.551.2		32	140.23	even	12
700.2.p.e.551.7		32	35.2	odd	12
700.2.p.e.551.10		32	35.23	odd	12
700.2.p.e.551.15		32	140.107	even	12
980.2.c.d.979.5		32	35.4	even	6
980.2.c.d.979.6		32	35.24	odd	6
980.2.c.d.979.7		32	28.11	odd	6
980.2.c.d.979.8		32	28.3	even	6
980.2.c.d.979.25		32	140.59	even	6
980.2.c.d.979.26		32	140.39	odd	6
980.2.c.d.979.27		32	7.3	odd	6
980.2.c.d.979.28		32	7.4	even	3
980.2.s.e.19.2		32	7.5	odd	6	inner
980.2.s.e.19.7		32	28.19	even	6	inner
980.2.s.e.19.10		32	140.19	even	6	inner
980.2.s.e.19.15		32	35.19	odd	6	inner
980.2.s.e.619.2		32	20.19	odd	2	inner
980.2.s.e.619.7		32	5.4	even	2	inner
980.2.s.e.619.10		32	1.1	even	1	trivial
980.2.s.e.619.15		32	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.444985 - 1.34238i) q^{2} +(-2.24836 - 1.29809i) q^{3} +(-1.60398 - 1.19468i) q^{4} +(-0.316513 + 2.21355i) q^{5} +(-2.74302 + 2.44053i) q^{6} +(-2.31746 + 1.62154i) q^{8} +(1.87009 + 3.23909i) q^{9} +(2.83059 + 1.40988i) q^{10} +(3.12008 + 1.80138i) q^{11} +(2.05552 + 4.76818i) q^{12} -0.818282 q^{13} +(3.58504 - 4.56601i) q^{15} +(1.14549 + 3.83247i) q^{16} +(3.69814 - 6.40537i) q^{17} +(5.18026 - 1.06903i) q^{18} +(1.65329 + 2.86358i) q^{19} +(3.15217 - 3.17236i) q^{20} +(3.80652 - 3.38675i) q^{22} +(-1.26758 - 2.19550i) q^{23} +(7.31540 - 0.637523i) q^{24} +(-4.79964 - 1.40124i) q^{25} +(-0.364123 + 1.09845i) q^{26} -1.92166i q^{27} -2.04334 q^{29} +(-4.53404 - 6.84429i) q^{30} +(0.955727 - 1.65537i) q^{31} +(5.65437 + 0.167714i) q^{32} +(-4.67671 - 8.10030i) q^{33} +(-6.95283 - 7.81461i) q^{34} +(0.870092 - 7.42959i) q^{36} +(6.20697 - 3.58360i) q^{37} +(4.57971 - 0.945096i) q^{38} +(1.83980 + 1.06221i) q^{39} +(-2.85585 - 5.64306i) q^{40} +2.65824i q^{41} +2.39696 q^{43} +(-2.85246 - 6.61686i) q^{44} +(-7.76182 + 3.11433i) q^{45} +(-3.51126 + 0.724604i) q^{46} +(1.15593 - 0.667376i) q^{47} +(2.39944 - 10.1037i) q^{48} +(-4.01676 + 5.81942i) q^{50} +(-16.6295 + 9.60106i) q^{51} +(1.31251 + 0.977584i) q^{52} +(-1.56838 - 0.905503i) q^{53} +(-2.57960 - 0.855108i) q^{54} +(-4.97499 + 6.33630i) q^{55} -8.58450i q^{57} +(-0.909256 + 2.74295i) q^{58} +(-0.955727 + 1.65537i) q^{59} +(-11.2052 + 3.04081i) q^{60} +(8.46625 - 4.88799i) q^{61} +(-1.79685 - 2.01956i) q^{62} +(2.74124 - 7.51569i) q^{64} +(0.258997 - 1.81131i) q^{65} +(-12.9548 + 2.67342i) q^{66} +(4.63112 - 8.02134i) q^{67} +(-13.5841 + 5.85597i) q^{68} +6.58172i q^{69} +1.38422i q^{71} +(-9.58617 - 4.47405i) q^{72} +(-3.69814 + 6.40537i) q^{73} +(-2.04855 - 9.92677i) q^{74} +(8.97240 + 9.38087i) q^{75} +(0.769222 - 6.56827i) q^{76} +(2.24457 - 1.99704i) q^{78} +(6.70979 - 3.87390i) q^{79} +(-8.84595 + 1.32257i) q^{80} +(3.11579 - 5.39670i) q^{81} +(3.56837 + 1.18287i) q^{82} -10.4973i q^{83} +(13.0081 + 10.2134i) q^{85} +(1.06661 - 3.21763i) q^{86} +(4.59418 + 2.65245i) q^{87} +(-10.1516 + 0.884696i) q^{88} +(9.19133 - 5.30662i) q^{89} +(0.726733 + 11.8052i) q^{90} +(-0.589761 + 5.03589i) q^{92} +(-4.29764 + 2.48125i) q^{93} +(-0.381503 - 1.84867i) q^{94} +(-6.86198 + 2.75329i) q^{95} +(-12.4954 - 7.71698i) q^{96} -7.32005 q^{97} +13.4750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) \) 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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