LMFDB - Embedded newform 968.2.o.h.269.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(245,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.7
Character	$\chi$	$=$	968.269
Dual form			968.2.o.h.493.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.918304 - 1.07551i) q^{2} +(1.38306 - 1.90362i) q^{3} +(-0.313437 - 1.97529i) q^{4} +(-3.96394 - 1.28796i) q^{5} +(-0.777288 - 3.23559i) q^{6} +(0.754993 - 0.548534i) q^{7} +(-2.41227 - 1.47681i) q^{8} +(-0.783857 - 2.41246i) q^{9} +(-5.02532 + 3.08051i) q^{10} +(-4.19369 - 2.13527i) q^{12} +(2.78966 - 0.906416i) q^{13} +(0.103359 - 1.31572i) q^{14} +(-7.93416 + 5.76451i) q^{15} +(-3.80351 + 1.23825i) q^{16} +(-0.755937 + 2.32653i) q^{17} +(-3.31444 - 1.37233i) q^{18} +(1.57693 - 2.17046i) q^{19} +(-1.30165 + 8.23362i) q^{20} -2.19587i q^{21} -3.47129 q^{23} +(-6.14759 + 2.54952i) q^{24} +(10.0089 + 7.27191i) q^{25} +(1.58690 - 3.83267i) q^{26} +(1.03698 + 0.336937i) q^{27} +(-1.32016 - 1.31940i) q^{28} +(-2.68762 - 3.69919i) q^{29} +(-1.08620 + 13.8268i) q^{30} +(-1.13033 - 3.47878i) q^{31} +(-2.16103 + 5.22781i) q^{32} +(1.80803 + 2.94948i) q^{34} +(-3.69924 + 1.20196i) q^{35} +(-4.51962 + 2.30450i) q^{36} +(2.66741 + 3.67137i) q^{37} +(-0.886245 - 3.68914i) q^{38} +(2.13280 - 6.56407i) q^{39} +(7.66002 + 8.96090i) q^{40} +(3.33815 + 2.42531i) q^{41} +(-2.36168 - 2.01648i) q^{42} -11.4650i q^{43} +10.5724i q^{45} +(-3.18769 + 3.73340i) q^{46} +(-2.63954 - 1.91774i) q^{47} +(-2.90332 + 8.95302i) q^{48} +(-1.89399 + 5.82912i) q^{49} +(17.0122 - 4.08686i) q^{50} +(3.38333 + 4.65675i) q^{51} +(-2.66481 - 5.22628i) q^{52} +(-0.618312 + 0.200902i) q^{53} +(1.31464 - 0.805875i) q^{54} +(-2.63133 + 0.208231i) q^{56} +(-1.95073 - 6.00374i) q^{57} +(-6.44656 - 0.506423i) q^{58} +(-1.71025 - 2.35396i) q^{59} +(13.8734 + 13.8654i) q^{60} +(-10.1820 - 3.30834i) q^{61} +(-4.77944 - 1.97891i) q^{62} +(-1.91512 - 1.39142i) q^{63} +(3.63807 + 7.12492i) q^{64} -12.2255 q^{65} -5.42623i q^{67} +(4.83251 + 0.763971i) q^{68} +(-4.80099 + 6.60800i) q^{69} +(-2.10431 + 5.08233i) q^{70} +(-2.39528 + 7.37192i) q^{71} +(-1.67188 + 6.97711i) q^{72} +(10.5698 - 7.67944i) q^{73} +(6.39808 + 0.502615i) q^{74} +(27.6859 - 8.99568i) q^{75} +(-4.78154 - 2.43459i) q^{76} +(-5.10116 - 8.32165i) q^{78} +(-1.49461 - 4.59993i) q^{79} +(16.6718 - 0.00958362i) q^{80} +(8.23210 - 5.98097i) q^{81} +(5.67388 - 1.36304i) q^{82} +(-0.627378 - 0.203847i) q^{83} +(-4.33748 + 0.688267i) q^{84} +(5.99298 - 8.24863i) q^{85} +(-12.3307 - 10.5283i) q^{86} -10.7590 q^{87} -2.74629 q^{89} +(11.3708 + 9.70872i) q^{90} +(1.60897 - 2.21456i) q^{91} +(1.08803 + 6.85678i) q^{92} +(-8.18558 - 2.65966i) q^{93} +(-4.48644 + 1.07778i) q^{94} +(-9.04633 + 6.57255i) q^{95} +(6.96291 + 11.3441i) q^{96} +(0.565208 + 1.73953i) q^{97} +(4.53000 + 7.38991i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) $ 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.918304	−	1.07551i	0.649339	−	0.760499i
$2$	0.918304	−	1.07551i	0.649339	−	0.760499i
$3$	1.38306	−	1.90362i	0.798510	−	1.09905i	−0.194486	−	0.980905i	$-0.562304\pi$
$3$	1.38306	−	1.90362i	0.798510	−	1.09905i	0.992996	−	0.118149i	$-0.0376960\pi$
$4$	−0.313437	−	1.97529i	−0.156718	−	0.987643i
$5$	−3.96394	−	1.28796i	−1.77273	−	0.575995i	−0.774343	−	0.632766i	$-0.781919\pi$
$5$	−3.96394	−	1.28796i	−1.77273	−	0.575995i	−0.998387	+	0.0567713i	$0.981919\pi$
$6$	−0.777288	−	3.23559i	−0.317327	−	1.32092i
$7$	0.754993	−	0.548534i	0.285360	−	0.207327i	−0.435892	−	0.899999i	$-0.643567\pi$
$7$	0.754993	−	0.548534i	0.285360	−	0.207327i	0.721252	+	0.692673i	$0.243567\pi$
$8$	−2.41227	−	1.47681i	−0.852865	−	0.522131i
$9$	−0.783857	−	2.41246i	−0.261286	−	0.804154i
$10$	−5.02532	+	3.08051i	−1.58915	+	0.974144i
$11$		0			0
$11$		0			0
$12$	−4.19369	−	2.13527i	−1.21061	−	0.616401i
$13$	2.78966	−	0.906416i	0.773713	−	0.251394i	0.104559	−	0.994519i	$-0.466657\pi$
$13$	2.78966	−	0.906416i	0.773713	−	0.251394i	0.669153	+	0.743124i	$0.266657\pi$
$14$	0.103359	−	1.31572i	0.0276239	−	0.351642i
$15$	−7.93416	+	5.76451i	−2.04859	+	1.48839i
$16$	−3.80351	+	1.23825i	−0.950879	+	0.309564i
$17$	−0.755937	+	2.32653i	−0.183342	+	0.564267i	−0.999916	−	0.0129730i	$-0.995870\pi$
$17$	−0.755937	+	2.32653i	−0.183342	+	0.564267i	0.816574	+	0.577240i	$0.195870\pi$
$18$	−3.31444	−	1.37233i	−0.781221	−	0.323461i
$19$	1.57693	−	2.17046i	0.361772	−	0.497937i	−0.588869	−	0.808228i	$-0.700427\pi$
$19$	1.57693	−	2.17046i	0.361772	−	0.497937i	0.950641	+	0.310291i	$0.100427\pi$
$20$	−1.30165	+	8.23362i	−0.291058	+	1.84109i
$21$		−	2.19587i		−	0.479179i
$22$		0			0
$23$	−3.47129			−0.723813			−0.361907	−	0.932214i	$-0.617874\pi$
$23$	−3.47129			−0.723813			−0.361907	+	0.932214i	$0.617874\pi$
$24$	−6.14759	+	2.54952i	−1.25487	+	0.520419i
$25$	10.0089	+	7.27191i	2.00178	+	1.45438i
$26$	1.58690	−	3.83267i	0.311216	−	0.751648i
$27$	1.03698	+	0.336937i	0.199568	+	0.0648435i
$28$	−1.32016	−	1.31940i	−0.249486	−	0.249343i
$29$	−2.68762	−	3.69919i	−0.499078	−	0.686922i	0.482952	−	0.875647i	$-0.339565\pi$
$29$	−2.68762	−	3.69919i	−0.499078	−	0.686922i	−0.982030	+	0.188725i	$0.939565\pi$
$30$	−1.08620	+	13.8268i	−0.198311	+	2.52442i
$31$	−1.13033	−	3.47878i	−0.203012	−	0.624808i	−0.999789	−	0.0205342i	$-0.993463\pi$
$31$	−1.13033	−	3.47878i	−0.203012	−	0.624808i	0.796777	−	0.604274i	$-0.206537\pi$
$32$	−2.16103	+	5.22781i	−0.382019	+	0.924154i
$33$		0			0
$34$	1.80803	+	2.94948i	0.310074	+	0.505832i
$35$	−3.69924	+	1.20196i	−0.625286	+	0.203168i
$36$	−4.51962	+	2.30450i	−0.753269	+	0.384083i
$37$	2.66741	+	3.67137i	0.438519	+	0.603570i	0.969882	−	0.243575i	$-0.0783200\pi$
$37$	2.66741	+	3.67137i	0.438519	+	0.603570i	−0.531363	+	0.847144i	$0.678320\pi$
$38$	−0.886245	−	3.68914i	−0.143768	−	0.598458i
$39$	2.13280	−	6.56407i	0.341521	−	1.05109i
$40$	7.66002	+	8.96090i	1.21116	+	1.41684i
$41$	3.33815	+	2.42531i	0.521332	+	0.378770i	0.817105	−	0.576488i	$-0.195577\pi$
$41$	3.33815	+	2.42531i	0.521332	+	0.378770i	−0.295774	+	0.955258i	$0.595577\pi$
$42$	−2.36168	−	2.01648i	−0.364415	−	0.311149i
$43$		−	11.4650i		−	1.74839i	−0.485573	−	0.874196i	$-0.661389\pi$
$43$		−	11.4650i		−	1.74839i	0.485573	−	0.874196i	$-0.338611\pi$
$44$		0			0
$45$			10.5724i			1.57605i
$46$	−3.18769	+	3.73340i	−0.470000	+	0.550459i
$47$	−2.63954	−	1.91774i	−0.385016	−	0.279731i	0.378394	−	0.925645i	$-0.376477\pi$
$47$	−2.63954	−	1.91774i	−0.385016	−	0.279731i	−0.763410	+	0.645914i	$0.776477\pi$
$48$	−2.90332	+	8.95302i	−0.419059	+	1.29226i
$49$	−1.89399	+	5.82912i	−0.270571	+	0.832731i
$50$	17.0122	−	4.08686i	2.40589	−	0.577969i
$51$	3.38333	+	4.65675i	0.473760	+	0.652075i
$52$	−2.66481	−	5.22628i	−0.369543	−	0.724754i
$53$	−0.618312	+	0.200902i	−0.0849317	+	0.0275960i	−0.351175	−	0.936310i	$-0.614218\pi$
$53$	−0.618312	+	0.200902i	−0.0849317	+	0.0275960i	0.266243	+	0.963906i	$0.414218\pi$
$54$	1.31464	−	0.805875i	0.178901	−	0.109666i
$55$		0			0
$56$	−2.63133	+	0.208231i	−0.351626	+	0.0278261i
$57$	−1.95073	−	6.00374i	−0.258381	−	0.795215i
$58$	−6.44656	−	0.506423i	−0.846474	−	0.0664966i
$59$	−1.71025	−	2.35396i	−0.222655	−	0.306459i	0.683046	−	0.730376i	$-0.260655\pi$
$59$	−1.71025	−	2.35396i	−0.222655	−	0.306459i	−0.905701	+	0.423917i	$0.860655\pi$
$60$	13.8734	+	13.8654i	1.79105	+	1.79002i
$61$	−10.1820	−	3.30834i	−1.30367	−	0.423589i	−0.426815	−	0.904339i	$-0.640365\pi$
$61$	−10.1820	−	3.30834i	−1.30367	−	0.423589i	−0.876858	+	0.480750i	$0.840365\pi$
$62$	−4.77944	−	1.97891i	−0.606990	−	0.251321i
$63$	−1.91512	−	1.39142i	−0.241283	−	0.175302i
$64$	3.63807	+	7.12492i	0.454759	+	0.890615i
$65$	−12.2255			−1.51639
$66$		0			0
$67$		−	5.42623i		−	0.662919i	−0.943469	−	0.331460i	$-0.892459\pi$
$67$		−	5.42623i		−	0.662919i	0.943469	−	0.331460i	$-0.107541\pi$
$68$	4.83251	+	0.763971i	0.586028	+	0.0926451i
$69$	−4.80099	+	6.60800i	−0.577972	+	0.795510i
$70$	−2.10431	+	5.08233i	−0.251514	+	0.607454i
$71$	−2.39528	+	7.37192i	−0.284268	+	0.874886i	0.702350	+	0.711832i	$0.252134\pi$
$71$	−2.39528	+	7.37192i	−0.284268	+	0.874886i	−0.986617	+	0.163054i	$0.947866\pi$
$72$	−1.67188	+	6.97711i	−0.197032	+	0.822260i
$73$	10.5698	−	7.67944i	1.23711	−	0.898811i	0.239705	−	0.970846i	$-0.422949\pi$
$73$	10.5698	−	7.67944i	1.23711	−	0.898811i	0.997402	+	0.0720351i	$0.0229494\pi$
$74$	6.39808	+	0.502615i	0.743762	+	0.0584278i
$75$	27.6859	−	8.99568i	3.19689	−	1.03873i
$76$	−4.78154	−	2.43459i	−0.548481	−	0.279266i
$77$		0			0
$78$	−5.10116	−	8.32165i	−0.577593	−	0.942242i
$79$	−1.49461	−	4.59993i	−0.168157	−	0.517533i	0.831098	−	0.556125i	$-0.187713\pi$
$79$	−1.49461	−	4.59993i	−0.168157	−	0.517533i	−0.999255	+	0.0385925i	$0.987713\pi$
$80$	16.6718	−	0.00958362i	1.86396	−	0.00107148i
$81$	8.23210	−	5.98097i	0.914678	−	0.664552i
$82$	5.67388	−	1.36304i	0.626575	−	0.150523i
$83$	−0.627378	−	0.203847i	−0.0688637	−	0.0223752i	0.274383	−	0.961621i	$-0.411527\pi$
$83$	−0.627378	−	0.203847i	−0.0688637	−	0.0223752i	−0.343246	+	0.939245i	$0.611527\pi$
$84$	−4.33748	+	0.688267i	−0.473258	+	0.0750961i
$85$	5.99298	−	8.24863i	0.650030	−	0.894690i
$86$	−12.3307	−	10.5283i	−1.32965	−	1.13530i
$87$	−10.7590			−1.15348
$88$		0			0
$89$	−2.74629			−0.291107			−0.145553	−	0.989350i	$-0.546496\pi$
$89$	−2.74629			−0.291107			−0.145553	+	0.989350i	$0.546496\pi$
$90$	11.3708	+	9.70872i	1.19858	+	1.02339i
$91$	1.60897	−	2.21456i	0.168666	−	0.232149i
$92$	1.08803	+	6.85678i	0.113435	+	0.714869i
$93$	−8.18558	−	2.65966i	−0.848805	−	0.275794i
$94$	−4.48644	+	1.07778i	−0.462741	+	0.111165i
$95$	−9.04633	+	6.57255i	−0.928134	+	0.674329i
$96$	6.96291	+	11.3441i	0.710649	+	1.15781i
$97$	0.565208	+	1.73953i	0.0573882	+	0.176623i	0.975642	−	0.219371i	$-0.0704004\pi$
$97$	0.565208	+	1.73953i	0.0573882	+	0.176623i	−0.918253	+	0.395993i	$0.870400\pi$
$98$	4.53000	+	7.38991i	0.457599	+	0.746493i
$99$		0			0
$100$	11.2269	−	22.0498i	1.12269	−	2.20498i
$101$	12.0604	−	3.91868i	1.20006	−	0.389923i	0.360276	−	0.932846i	$-0.382682\pi$
$101$	12.0604	−	3.91868i	1.20006	−	0.389923i	0.839783	+	0.542923i	$0.182682\pi$
$102$	8.11529	+	0.637514i	0.803534	+	0.0631233i
$103$	3.12802	−	2.27264i	0.308213	−	0.223930i	−0.422916	−	0.906169i	$-0.638994\pi$
$103$	3.12802	−	2.27264i	0.308213	−	0.223930i	0.731129	+	0.682239i	$0.238994\pi$
$104$	−8.06801	−	1.93328i	−0.791133	−	0.189574i
$105$	−2.82821	+	8.70432i	−0.276005	+	0.849455i
$106$	−0.351727	+	0.849489i	−0.0341627	+	0.0825096i
$107$	7.51315	−	10.3410i	0.726324	−	0.999699i	−0.272966	−	0.962024i	$-0.588005\pi$
$107$	7.51315	−	10.3410i	0.726324	−	0.999699i	0.999290	−	0.0376755i	$-0.0119953\pi$
$108$	0.340518	−	2.15395i	0.0327663	−	0.207264i
$109$		−	1.85065i		−	0.177260i	−0.996065	−	0.0886299i	$-0.971751\pi$
$109$		−	1.85065i		−	0.177260i	0.996065	−	0.0886299i	$-0.0282489\pi$
$110$		0			0
$111$	10.6781			1.01352
$112$	−2.19240	+	3.02123i	−0.207162	+	0.285480i
$113$	−13.4956	−	9.80514i	−1.26956	−	0.922390i	−0.270376	−	0.962755i	$-0.587148\pi$
$113$	−13.4956	−	9.80514i	−1.26956	−	0.922390i	−0.999185	+	0.0403644i	$0.987148\pi$
$114$	−8.24844	−	3.41523i	−0.772537	−	0.319865i
$115$	13.7600	+	4.47089i	1.28313	+	0.416913i
$116$	−6.46456	+	6.46827i	−0.600219	+	0.600564i
$117$	−4.37339	−	6.01945i	−0.404320	−	0.556498i
$118$	−4.10223	−	0.322259i	−0.377641	−	0.0296664i
$119$	0.705457	+	2.17117i	0.0646692	+	0.199031i
$120$	27.6524	−	2.18829i	2.52431	−	0.199762i
$121$		0			0
$122$	−12.9083	+	7.91278i	−1.16866	+	0.716390i
$123$	9.23373	−	3.00022i	0.832577	−	0.270521i
$124$	−6.51731	+	3.32310i	−0.585272	+	0.298423i
$125$	−18.0596	−	24.8569i	−1.61530	−	2.22327i
$126$	−3.25515	+	0.781987i	−0.289992	+	0.0696649i
$127$	2.01174	−	6.19150i	0.178513	−	0.549407i	−0.821263	−	0.570549i	$-0.806730\pi$
$127$	2.01174	−	6.19150i	0.178513	−	0.549407i	0.999776	+	0.0211425i	$0.00673036\pi$
$128$	11.0038	+	2.63006i	0.972604	+	0.232467i
$129$	−21.8249	−	15.8567i	−1.92158	−	1.39611i
$130$	−11.2267	+	13.1486i	−0.984648	+	1.15321i
$131$			6.91569i			0.604227i	0.953272	+	0.302114i	$0.0976922\pi$
$131$			6.91569i			0.604227i	−0.953272	+	0.302114i	$0.902308\pi$
$132$		0			0
$133$		−	2.50368i		−	0.217097i
$134$	−5.83595	−	4.98292i	−0.504150	−	0.430459i
$135$	−3.67659	−	2.67120i	−0.316430	−	0.229900i
$136$	5.25937	−	4.49585i	0.450987	−	0.385516i
$137$	1.79833	−	5.53469i	0.153642	−	0.472861i	−0.844379	−	0.535746i	$-0.820030\pi$
$137$	1.79833	−	5.53469i	0.153642	−	0.472861i	0.998021	+	0.0628856i	$0.0200303\pi$
$138$	2.69819	+	11.2317i	0.229685	+	0.956102i
$139$	5.60470	+	7.71421i	0.475385	+	0.654311i	0.977610	−	0.210426i	$-0.0674852\pi$
$139$	5.60470	+	7.71421i	0.475385	+	0.654311i	−0.502225	+	0.864737i	$0.667485\pi$
$140$	3.53369	+	6.93033i	0.298651	+	0.585720i
$141$	−7.30128	+	2.37233i	−0.614879	+	0.199786i
$142$	5.72896	+	9.34580i	0.480764	+	0.784282i
$143$		0			0
$144$	5.96865	+	8.20522i	0.497388	+	0.683769i
$145$	5.88915	+	18.1249i	0.489067	+	1.50519i
$146$	1.44702	−	18.4200i	0.119757	−	1.52445i
$147$	8.47690	+	11.6675i	0.699163	+	0.962315i
$148$	6.41595	−	6.41964i	0.527387	−	0.527691i
$149$	13.2407	+	4.30218i	1.08472	+	0.352448i	0.796205	−	0.605027i	$-0.206838\pi$
$149$	13.2407	+	4.30218i	1.08472	+	0.352448i	0.288518	+	0.957474i	$0.406838\pi$
$150$	15.7491	−	38.0372i	1.28591	−	3.10572i
$151$	12.3153	+	8.94761i	1.00221	+	0.728146i	0.962560	−	0.271068i	$-0.0873768\pi$
$151$	12.3153	+	8.94761i	1.00221	+	0.728146i	0.0396467	+	0.999214i	$0.487377\pi$
$152$	−7.00933	+	2.90690i	−0.568532	+	0.235781i
$153$	6.20522			0.501662
$154$		0			0
$155$			15.2455i			1.22455i
$156$	−13.6344	−	2.15546i	−1.09163	−	0.172575i
$157$	−0.513689	+	0.707032i	−0.0409969	+	0.0564273i	−0.829023	−	0.559214i	$-0.811103\pi$
$157$	−0.513689	+	0.707032i	−0.0409969	+	0.0564273i	0.788026	+	0.615641i	$0.211103\pi$
$158$	−6.31977	−	2.61667i	−0.502774	−	0.208171i
$159$	−0.472722	+	1.45489i	−0.0374893	+	0.115380i
$160$	15.2994	−	17.9394i	1.20953	−	1.41823i
$161$	−2.62080	+	1.90412i	−0.206548	+	0.150066i
$162$	1.12698	−	14.3460i	0.0885442	−	1.12713i
$163$	−7.15847	+	2.32593i	−0.560695	+	0.182181i	−0.575634	−	0.817708i	$-0.695245\pi$
$163$	−7.15847	+	2.32593i	−0.560695	+	0.182181i	0.0149391	+	0.999888i	$0.495245\pi$
$164$	3.74438	−	7.35399i	0.292387	−	0.574250i
$165$		0			0
$166$	−0.795363	+	0.487556i	−0.0617321	+	0.0378417i
$167$	−0.0441598	−	0.135910i	−0.00341719	−	0.0105170i	0.949333	−	0.314271i	$-0.101760\pi$
$167$	−0.0441598	−	0.135910i	−0.00341719	−	0.0105170i	−0.952751	+	0.303754i	$0.901760\pi$
$168$	−3.24289	+	5.29703i	−0.250194	+	0.408675i
$169$	−3.55661	+	2.58402i	−0.273585	+	0.198771i
$170$	−3.36810	−	14.0203i	−0.258321	−	1.07530i
$171$	−6.47223	−	2.10296i	−0.494944	−	0.160817i
$172$	−22.6466	+	3.59354i	−1.72679	+	0.274005i
$173$	0.663666	−	0.913458i	0.0504576	−	0.0694489i	−0.783043	−	0.621968i	$-0.786333\pi$
$173$	0.663666	−	0.913458i	0.0504576	−	0.0694489i	0.833500	+	0.552519i	$0.186333\pi$
$174$	−9.88000	+	11.5714i	−0.749001	+	0.877223i
$175$	11.5456			0.872762
$176$		0			0
$177$	−6.84641			−0.514608
$178$	−2.52193	+	2.95366i	−0.189027	+	0.221386i
$179$	−8.91201	+	12.2663i	−0.666115	+	0.916829i	−0.999664	−	0.0259041i	$-0.991754\pi$
$179$	−8.91201	+	12.2663i	−0.666115	+	0.916829i	0.333550	+	0.942733i	$0.391754\pi$
$180$	20.8836	−	3.31379i	1.55657	−	0.246996i
$181$	−16.0929	−	5.22890i	−1.19618	−	0.388661i	−0.357824	−	0.933789i	$-0.616481\pi$
$181$	−16.0929	−	5.22890i	−1.19618	−	0.388661i	−0.838353	+	0.545128i	$0.816481\pi$
$182$	−0.904254	−	3.76410i	−0.0670278	−	0.279014i
$183$	−20.3801	+	14.8070i	−1.50654	+	1.09457i
$184$	8.37367	+	5.12643i	0.617315	+	0.377925i
$185$	−5.84486	−	17.9886i	−0.429723	−	1.32255i
$186$	−10.3773	+	6.36129i	−0.760903	+	0.466432i
$187$		0			0
$188$	−2.96075	+	5.81494i	−0.215935	+	0.424098i
$189$	0.967737	−	0.314437i	0.0703925	−	0.0228719i
$190$	−1.23845	+	15.7650i	−0.0898468	+	1.14371i
$191$	13.4880	−	9.79958i	0.975955	−	0.709073i	0.0191543	−	0.999817i	$-0.493903\pi$
$191$	13.4880	−	9.79958i	0.975955	−	0.709073i	0.956801	+	0.290743i	$0.0939026\pi$
$192$	18.5948	+	2.92869i	1.34196	+	0.211360i
$193$	−0.0558394	+	0.171856i	−0.00401941	+	0.0123705i	−0.953046	−	0.302825i	$-0.902070\pi$
$193$	−0.0558394	+	0.171856i	−0.00401941	+	0.0123705i	0.949027	+	0.315196i	$0.102070\pi$
$194$	2.38991	+	0.989533i	0.171586	+	0.0710443i
$195$	−16.9086	+	23.2727i	−1.21085	+	1.66659i
$196$	12.1078	+	1.91412i	0.864845	+	0.136723i
$197$			8.38885i			0.597681i	0.954303	+	0.298840i	$0.0965998\pi$
$197$			8.38885i			0.597681i	−0.954303	+	0.298840i	$0.903400\pi$
$198$		0			0
$199$	22.0996			1.56660			0.783298	−	0.621646i	$-0.213536\pi$
$199$	22.0996			1.56660			0.783298	+	0.621646i	$0.213536\pi$
$200$	−13.4050	−	32.3231i	−0.947875	−	2.28559i
$201$	−10.3295	−	7.50479i	−0.728584	−	0.529347i
$202$	6.86058	−	16.5696i	0.482709	−	1.16584i
$203$	−4.05826	−	1.31861i	−0.284834	−	0.0925482i
$204$	8.13796	−	8.14264i	0.569771	−	0.570099i
$205$	−10.1085	−	13.9132i	−0.706011	−	0.971741i
$206$	0.428229	−	5.45118i	0.0298361	−	0.379802i
$207$	2.72099	+	8.37435i	0.189122	+	0.582057i
$208$	−9.48814	+	6.90187i	−0.657884	+	0.478559i
$209$		0			0
$210$	6.76442	+	11.0350i	0.466789	+	0.761485i
$211$	−14.3029	+	4.64730i	−0.984653	+	0.319933i	−0.756717	−	0.653743i	$-0.773198\pi$
$211$	−14.3029	+	4.64730i	−0.984653	+	0.319933i	−0.227937	+	0.973676i	$0.573198\pi$
$212$	0.590640	+	1.15837i	0.0405653	+	0.0795574i
$213$	10.7205	+	14.7555i	0.734556	+	1.01103i
$214$	−4.22244	−	17.5766i	−0.288640	−	1.20151i
$215$	−14.7665	+	45.4465i	−1.00706	+	3.09943i
$216$	−2.00389	−	2.34421i	−0.136348	−	0.159503i
$217$	−2.76162	−	2.00643i	−0.187471	−	0.136206i
$218$	−1.99039	−	1.69946i	−0.134806	−	0.115102i
$219$		−	30.7421i		−	2.07736i
$220$		0			0
$221$			7.17543i			0.482672i
$222$	9.80571	−	11.4844i	0.658116	−	0.770779i
$223$	8.31394	+	6.04043i	0.556743	+	0.404497i	0.830265	−	0.557368i	$-0.188189\pi$
$223$	8.31394	+	6.04043i	0.556743	+	0.404497i	−0.273523	+	0.961866i	$0.588189\pi$
$224$	1.23607	+	5.13235i	0.0825884	+	0.342920i
$225$	9.69765	−	29.8463i	0.646510	−	1.98975i
$226$	−22.9386	+	5.51056i	−1.52585	+	0.366557i
$227$	9.20991	+	12.6764i	0.611283	+	0.841360i	0.996682	−	0.0813906i	$-0.0259361\pi$
$227$	9.20991	+	12.6764i	0.611283	+	0.841360i	−0.385399	+	0.922750i	$0.625936\pi$
$228$	−11.2477	+	5.73505i	−0.744896	+	0.379813i
$229$	−13.3858	+	4.34932i	−0.884561	+	0.287411i	−0.715850	−	0.698254i	$-0.753961\pi$
$229$	−13.3858	+	4.34932i	−0.884561	+	0.287411i	−0.168711	+	0.985666i	$0.553961\pi$
$230$	17.4443	−	10.6933i	1.15024	−	0.705098i
$231$		0			0
$232$	1.02026	+	12.8925i	0.0669831	+	0.846436i
$233$	3.73889	+	11.5071i	0.244943	+	0.753857i	0.995646	+	0.0932169i	$0.0297150\pi$
$233$	3.73889	+	11.5071i	0.244943	+	0.753857i	−0.750703	+	0.660640i	$0.770285\pi$
$234$	−10.4901	−	0.824069i	−0.685757	−	0.0538711i
$235$	7.99301	+	11.0014i	0.521407	+	0.717655i
$236$	−4.11368	+	4.11605i	−0.267778	+	0.267932i
$237$	−10.8236	−	3.51682i	−0.703071	−	0.228442i
$238$	2.98294	+	1.23507i	0.193355	+	0.0800578i
$239$	−17.5944	−	12.7831i	−1.13809	−	0.826869i	−0.151236	−	0.988498i	$-0.548325\pi$
$239$	−17.5944	−	12.7831i	−1.13809	−	0.826869i	−0.986852	+	0.161629i	$0.948325\pi$
$240$	23.0398	−	31.7499i	1.48721	−	2.04945i
$241$	6.93967			0.447024			0.223512	−	0.974701i	$-0.428248\pi$
$241$	6.93967			0.447024			0.223512	+	0.974701i	$0.428248\pi$
$242$		0			0
$243$		−	20.6718i		−	1.32609i
$244$	−3.34350	+	21.1493i	−0.214045	+	1.35395i
$245$	15.0154	−	20.6669i	0.959298	−	1.32036i
$246$	5.25260	−	12.6861i	0.334894	−	0.808834i
$247$	2.43176	−	7.48419i	0.154729	−	0.476208i
$248$	−2.41085	+	10.0610i	−0.153089	+	0.638876i
$249$	−1.25575	+	0.912354i	−0.0795798	+	0.0578181i
$250$	−43.3180	−	3.40294i	−2.73967	−	0.215221i
$251$	16.8602	−	5.47821i	1.06421	−	0.345781i	0.275977	−	0.961164i	$-0.410999\pi$
$251$	16.8602	−	5.47821i	1.06421	−	0.345781i	0.788229	+	0.615383i	$0.210999\pi$
$252$	−2.14818	+	4.21904i	−0.135323	+	0.265775i
$253$		0			0
$254$	−4.81162	−	7.84932i	−0.301908	−	0.492510i
$255$	−7.41360	−	22.8167i	−0.464257	−	1.42884i
$256$	12.9335	−	9.41944i	0.808341	−	0.588715i
$257$	−14.3637	+	10.4358i	−0.895983	+	0.650970i	−0.937431	−	0.348171i	$-0.886803\pi$
$257$	−14.3637	+	10.4358i	−0.895983	+	0.650970i	0.0414480	+	0.999141i	$0.486803\pi$
$258$	−37.0960	+	8.91159i	−2.30949	+	0.554811i
$259$	4.02775	+	1.30869i	0.250272	+	0.0813183i
$260$	3.83192	+	24.1488i	0.237645	+	1.49765i
$261$	−6.81744	+	9.38341i	−0.421989	+	0.580818i
$262$	7.43789	+	6.35071i	0.459514	+	0.392348i
$263$	27.6424			1.70450			0.852252	−	0.523132i	$-0.175237\pi$
$263$	27.6424			1.70450			0.852252	+	0.523132i	$0.175237\pi$
$264$		0			0
$265$	2.70971			0.166456
$266$	−2.69273	−	2.29914i	−0.165102	−	0.140969i
$267$	−3.79829	+	5.22789i	−0.232451	+	0.319942i
$268$	−10.7184	+	1.70078i	−0.654728	+	0.103892i
$269$	10.1081	+	3.28433i	0.616304	+	0.200249i	0.600498	−	0.799626i	$-0.294969\pi$
$269$	10.1081	+	3.28433i	0.616304	+	0.200249i	0.0158051	+	0.999875i	$0.494969\pi$
$270$	−6.24912	+	1.50123i	−0.380309	+	0.0913620i
$271$	15.9765	−	11.6076i	0.970504	−	0.705113i	0.0149379	−	0.999888i	$-0.495245\pi$
$271$	15.9765	−	11.6076i	0.970504	−	0.705113i	0.955566	+	0.294776i	$0.0952449\pi$
$272$	−0.00562486	−	9.78505i	−0.000341057	−	0.593306i
$273$	−1.99037	−	6.12574i	−0.120463	−	0.370747i
$274$	−4.30120	−	7.01665i	−0.259845	−	0.423891i
$275$		0			0
$276$	14.5575	+	7.41215i	0.876259	+	0.446159i
$277$	11.9218	−	3.87361i	0.716309	−	0.232743i	0.0718867	−	0.997413i	$-0.477098\pi$
$277$	11.9218	−	3.87361i	0.716309	−	0.232743i	0.644422	+	0.764670i	$0.277098\pi$
$278$	13.4435	+	1.05608i	0.806288	+	0.0633397i
$279$	−7.50642	+	5.45374i	−0.449398	+	0.326507i
$280$	10.6986	+	2.56363i	0.639365	+	0.153206i
$281$	7.35576	−	22.6387i	0.438808	−	1.35051i	−0.450325	−	0.892864i	$-0.648692\pi$
$281$	7.35576	−	22.6387i	0.438808	−	1.35051i	0.889134	−	0.457648i	$-0.151308\pi$
$282$	−4.15333	+	10.0311i	−0.247327	+	0.597344i
$283$	16.2989	−	22.4336i	0.968872	−	1.33354i	0.0262574	−	0.999655i	$-0.491641\pi$
$283$	16.2989	−	22.4336i	0.968872	−	1.33354i	0.942615	−	0.333883i	$-0.108359\pi$
$284$	15.3124	+	2.42074i	0.908625	+	0.143644i
$285$			26.3110i			1.55853i
$286$		0			0
$287$	3.85065			0.227297
$288$	14.3058	+	1.11555i	0.842979	+	0.0657344i
$289$	8.91197	+	6.47492i	0.524233	+	0.380878i
$290$	24.9015	+	10.3104i	1.46227	+	0.605445i
$291$	4.09312	+	1.32994i	0.239943	+	0.0779622i
$292$	−18.4821	−	18.4715i	−1.08158	−	1.08096i
$293$	3.29976	+	4.54174i	0.192774	+	0.265331i	0.894453	−	0.447163i	$-0.147566\pi$
$293$	3.29976	+	4.54174i	0.192774	+	0.265331i	−0.701678	+	0.712494i	$0.747566\pi$
$294$	20.3328	+	1.59729i	1.18583	+	0.0931557i
$295$	3.74752	+	11.5337i	0.218189	+	0.671518i
$296$	−1.01258	−	12.7956i	−0.0588553	−	0.743728i
$297$		0			0
$298$	16.7860	−	10.2898i	0.972389	−	0.596073i
$299$	−9.68371	+	3.14643i	−0.560023	+	0.181963i
$300$	−26.4468	−	51.8680i	−1.52691	−	2.99460i
$301$	−6.28893	−	8.65597i	−0.362488	−	0.498922i
$302$	20.9324	−	5.02861i	1.20453	−	0.289364i
$303$	9.22065	−	28.3782i	0.529712	−	1.63029i
$304$	−3.31030	+	10.2080i	−0.189859	+	0.585469i
$305$	36.0999	+	26.2281i	2.06708	+	1.50182i
$306$	5.69828	−	6.67377i	0.325749	−	0.381514i
$307$			27.8554i			1.58979i	0.606747	+	0.794895i	$0.292474\pi$
$307$			27.8554i			1.58979i	−0.606747	+	0.794895i	$0.707526\pi$
$308$		0			0
$309$		−	9.09775i		−	0.517553i
$310$	16.3967	+	14.0000i	0.931270	+	0.795148i
$311$	19.7461	+	14.3464i	1.11970	+	0.813509i	0.984164	−	0.177263i	$-0.0567243\pi$
$311$	19.7461	+	14.3464i	1.11970	+	0.813509i	0.135536	+	0.990772i	$0.456724\pi$
$312$	−14.8388	+	12.6846i	−0.840079	+	0.718122i
$313$	2.82291	−	8.68803i	0.159561	−	0.491077i	−0.839034	−	0.544079i	$-0.816879\pi$
$313$	2.82291	−	8.68803i	0.159561	−	0.491077i	0.998594	+	0.0530024i	$0.0168791\pi$
$314$	0.288697	+	1.20175i	0.0162921	+	0.0678185i
$315$	5.79935	+	7.98212i	0.326756	+	0.449742i
$316$	−8.61772	+	4.39407i	−0.484785	+	0.247186i
$317$	17.0715	−	5.54688i	0.958833	−	0.311544i	0.212533	−	0.977154i	$-0.431829\pi$
$317$	17.0715	−	5.54688i	0.958833	−	0.311544i	0.746299	+	0.665610i	$0.231829\pi$
$318$	1.13064	+	1.84445i	0.0634033	+	0.103431i
$319$		0			0
$320$	−5.24447	−	32.9285i	−0.293175	−	1.84076i
$321$	−9.29411	−	28.6043i	−0.518747	−	1.59654i
$322$	−0.358790	+	4.56725i	−0.0199946	+	0.254523i
$323$	3.85758	+	5.30951i	0.214642	+	0.295429i
$324$	−14.3944	−	14.3861i	−0.799687	−	0.799228i
$325$	34.5129	+	11.2139i	1.91443	+	0.622036i
$326$	−4.07209	+	9.83490i	−0.225532	+	0.544705i
$327$	−3.52293	−	2.55955i	−0.194818	−	0.141544i
$328$	−4.47080	−	10.7803i	−0.246858	−	0.595243i
$329$	−3.04478			−0.167864
$330$		0			0
$331$		−	13.1934i		−	0.725173i	−0.931950	−	0.362586i	$-0.881894\pi$
$331$		−	13.1934i		−	0.725173i	0.931950	−	0.362586i	$-0.118106\pi$
$332$	−0.206014	+	1.30314i	−0.0113065	+	0.0715193i
$333$	6.76618	−	9.31285i	0.370784	−	0.510341i
$334$	−0.186724	−	0.0773123i	−0.0102171	−	0.00423034i
$335$	−6.98878	+	21.5093i	−0.381838	+	1.17518i
$336$	2.71905	+	8.35204i	0.148336	+	0.455641i
$337$	19.3122	−	14.0311i	1.05200	−	0.764324i	0.0794093	−	0.996842i	$-0.474697\pi$
$337$	19.3122	−	14.0311i	1.05200	−	0.764324i	0.972592	+	0.232518i	$0.0746966\pi$
$338$	−0.486903	+	6.19808i	−0.0264840	+	0.337131i
$339$	−37.3305	+	12.1294i	−2.02751	+	0.658779i
$340$	−18.1718	−	9.25244i	−0.985506	−	0.501784i
$341$		0			0
$342$	−8.20522	+	5.02979i	−0.443688	+	0.271980i
$343$	3.78619	+	11.6527i	0.204435	+	0.629186i
$344$	−16.9316	+	27.6566i	−0.912889	+	1.49114i
$345$	27.5417	−	20.0102i	1.48280	−	1.07732i
$346$	−0.372985	−	1.55261i	−0.0200518	−	0.0834688i
$347$	−35.3993	−	11.5019i	−1.90033	−	0.617456i	−0.963528	−	0.267607i	$-0.913767\pi$
$347$	−35.3993	−	11.5019i	−1.90033	−	0.617456i	−0.936806	−	0.349849i	$-0.886233\pi$
$348$	3.37226	+	21.2521i	0.180772	+	1.13923i
$349$	−16.7013	+	22.9874i	−0.894001	+	1.23049i	0.0783407	+	0.996927i	$0.475038\pi$
$349$	−16.7013	+	22.9874i	−0.894001	+	1.23049i	−0.972342	+	0.233561i	$0.924962\pi$
$350$	10.6023	−	12.4173i	0.566718	−	0.663735i
$351$	3.19824			0.170709
$352$		0			0
$353$	−6.72158			−0.357754			−0.178877	−	0.983871i	$-0.557246\pi$
$353$	−6.72158			−0.357754			−0.178877	+	0.983871i	$0.557246\pi$
$354$	−6.28708	+	7.36337i	−0.334155	+	0.391359i
$355$	18.9895	−	26.1368i	1.00786	−	1.38720i
$356$	0.860789	+	5.42472i	0.0456218	+	0.287510i
$357$	5.10877	+	1.65994i	0.270385	+	0.0878534i
$358$	5.00861	+	20.8492i	0.264713	+	1.10191i
$359$	16.0396	−	11.6534i	0.846536	−	0.615044i	−0.0776527	−	0.996980i	$-0.524743\pi$
$359$	16.0396	−	11.6534i	0.846536	−	0.615044i	0.924189	+	0.381936i	$0.124743\pi$
$360$	15.6135	−	25.5036i	0.822903	−	1.34416i
$361$	3.64714	+	11.2248i	0.191955	+	0.590777i
$362$	−20.4019	+	12.5063i	−1.07230	+	0.657319i
$363$		0			0
$364$	−4.87871	−	2.48406i	−0.255714	−	0.130200i
$365$	−51.7891	+	16.8273i	−2.71077	+	0.880782i
$366$	−2.79006	+	35.5164i	−0.145839	+	1.85647i
$367$	−3.67959	+	2.67338i	−0.192073	+	0.139549i	−0.679666	−	0.733522i	$-0.737875\pi$
$367$	−3.67959	+	2.67338i	−0.192073	+	0.139549i	0.487593	+	0.873071i	$0.337875\pi$
$368$	13.2031	−	4.29834i	0.688258	−	0.224066i
$369$	3.23434	−	9.95426i	0.168373	−	0.518198i
$370$	−24.7143	−	10.2328i	−1.28483	−	0.531980i
$371$	−0.356620	+	0.490845i	−0.0185148	+	0.0254834i
$372$	−2.68792	+	17.0025i	−0.139362	+	0.881539i
$373$		−	33.3992i		−	1.72934i	−0.502336	−	0.864672i	$-0.667526\pi$
$373$		−	33.3992i		−	1.72934i	0.502336	−	0.864672i	$-0.332474\pi$
$374$		0			0
$375$	−72.2956			−3.73333
$376$	3.53514	+	8.52419i	0.182311	+	0.439602i
$377$	−10.8505	−	7.88338i	−0.558831	−	0.406015i
$378$	0.550497	−	1.32956i	0.0283145	−	0.0683851i
$379$	8.79578	+	2.85792i	0.451809	+	0.146802i	0.526077	−	0.850437i	$-0.323662\pi$
$379$	8.79578	+	2.85792i	0.451809	+	0.146802i	−0.0742686	+	0.997238i	$0.523662\pi$
$380$	15.8181	+	15.8090i	0.811452	+	0.810986i
$381$	−9.00389	−	12.3928i	−0.461283	−	0.634902i
$382$	1.84652	−	23.5054i	0.0944761	−	1.20264i
$383$	9.76741	+	30.0610i	0.499091	+	1.53605i	0.810482	+	0.585764i	$0.199205\pi$
$383$	9.76741	+	30.0610i	0.499091	+	1.53605i	−0.311390	+	0.950282i	$0.600795\pi$
$384$	20.2255	−	17.3094i	1.03213	−	0.883318i
$385$		0			0
$386$	0.133555	+	0.217872i	0.00679777	+	0.0110894i
$387$	−27.6588	+	8.98689i	−1.40598	+	0.456829i
$388$	3.25892	−	1.66168i	0.165447	−	0.0843591i
$389$	−2.93624	−	4.04139i	−0.148873	−	0.204906i	0.728067	−	0.685506i	$-0.240419\pi$
$389$	−2.93624	−	4.04139i	−0.148873	−	0.204906i	−0.876940	+	0.480600i	$0.840419\pi$
$390$	9.50273	+	39.5567i	0.481190	+	2.00303i
$391$	2.62407	−	8.07607i	0.132705	−	0.408424i
$392$	13.1773	−	11.2643i	0.665555	−	0.568934i
$393$	13.1648	+	9.56482i	0.664078	+	0.482481i
$394$	9.02227	+	7.70351i	0.454536	+	0.388097i
$395$			20.1589i			1.01430i
$396$		0			0
$397$			17.7950i			0.893107i	0.894757	+	0.446553i	$0.147349\pi$
$397$			17.7950i			0.893107i	−0.894757	+	0.446553i	$0.852651\pi$
$398$	20.2941	−	23.7683i	1.01725	−	1.19140i
$399$	−4.76605	−	3.46274i	−0.238601	−	0.173354i
$400$	−47.0736	−	15.2652i	−2.35368	−	0.763261i
$401$	−3.76193	+	11.5780i	−0.187862	+	0.578180i	−0.999986	−	0.00530515i	$-0.998311\pi$
$401$	−3.76193	+	11.5780i	−0.187862	+	0.578180i	0.812124	+	0.583485i	$0.198311\pi$
$402$	−17.5571	+	4.21774i	−0.875666	+	0.210362i
$403$	−6.30645	−	8.68008i	−0.314147	−	0.432386i
$404$	−11.5207	−	22.5946i	−0.573176	−	1.12412i
$405$	−40.3349	+	13.1056i	−2.00426	+	0.651222i
$406$	−5.14489	+	3.15381i	−0.255337	+	0.156521i
$407$		0			0
$408$	−1.28436	−	16.2299i	−0.0635852	−	0.803497i
$409$	−0.181701	−	0.559218i	−0.00898453	−	0.0276516i	0.946464	−	0.322810i	$-0.104628\pi$
$409$	−0.181701	−	0.559218i	−0.00898453	−	0.0276516i	−0.955448	+	0.295159i	$0.904628\pi$
$410$	−24.2465	−	1.90473i	−1.19745	−	0.0940681i
$411$	−8.04874	−	11.0781i	−0.397015	−	0.546444i
$412$	−5.46955	−	5.46641i	−0.269465	−	0.269311i
$413$	−2.58245	−	0.839090i	−0.127074	−	0.0412889i
$414$	11.5054	+	4.76375i	0.565458	+	0.234125i
$415$	2.22434	+	1.61608i	0.109189	+	0.0793302i
$416$	−1.28997	+	16.5426i	−0.0632460	+	0.811067i
$417$	22.4365			1.09872
$418$		0			0
$419$		−	11.1507i		−	0.544748i	−0.962191	−	0.272374i	$-0.912191\pi$
$419$		−	11.1507i		−	0.544748i	0.962191	−	0.272374i	$-0.0878088\pi$
$420$	18.0800	+	2.85826i	0.882213	+	0.139469i
$421$	−20.4783	+	28.1860i	−0.998053	+	1.37370i	−0.0715408	+	0.997438i	$0.522792\pi$
$421$	−20.4783	+	28.1860i	−0.998053	+	1.37370i	−0.926512	+	0.376265i	$0.877208\pi$
$422$	−8.13621	+	19.6505i	−0.396065	+	0.956573i
$423$	−2.55745	+	7.87102i	−0.124347	+	0.382702i
$424$	1.78823	+	0.428500i	0.0868440	+	0.0208098i
$425$	−24.4845	+	17.7890i	−1.18767	+	0.862893i
$426$	25.7143	+	2.02004i	1.24586	+	0.0978714i
$427$	−9.50208	+	3.08741i	−0.459838	+	0.149410i
$428$	−22.7813	−	11.5994i	−1.10117	−	0.560678i
$429$		0			0
$430$	35.3180	+	57.6152i	1.70319	+	2.77845i
$431$	7.68362	+	23.6478i	0.370107	+	1.13907i	0.946721	+	0.322056i	$0.104374\pi$
$431$	7.68362	+	23.6478i	0.370107	+	1.13907i	−0.576614	+	0.817017i	$0.695626\pi$
$432$	−4.36140	+	0.00250711i	−0.209838	+	0.000120624i
$433$	0.443102	−	0.321932i	0.0212941	−	0.0154711i	−0.577087	−	0.816682i	$-0.695811\pi$
$433$	0.443102	−	0.321932i	0.0212941	−	0.0154711i	0.598381	+	0.801211i	$0.295811\pi$
$434$	−4.69394	+	1.12763i	−0.225317	+	0.0541280i
$435$	42.6480	+	13.8572i	2.04481	+	0.664400i
$436$	−3.65556	+	0.580061i	−0.175070	+	0.0277799i
$437$	−5.47397	+	7.53428i	−0.261856	+	0.360413i
$438$	−33.0634	−	28.2306i	−1.57983	−	1.34891i
$439$	−27.5308			−1.31397			−0.656987	−	0.753902i	$-0.728169\pi$
$439$	−27.5308			−1.31397			−0.656987	+	0.753902i	$0.728169\pi$
$440$		0			0
$441$	15.5471			0.740340
$442$	7.71724	+	6.58923i	0.367072	+	0.313418i
$443$	−4.73434	+	6.51626i	−0.224935	+	0.309597i	−0.906537	−	0.422127i	$-0.861284\pi$
$443$	−4.73434	+	6.51626i	−0.224935	+	0.309597i	0.681602	+	0.731724i	$0.261284\pi$
$444$	−3.34690	−	21.0922i	−0.158837	−	1.00099i
$445$	10.8862	+	3.53713i	0.516054	+	0.167676i
$446$	14.1313	−	3.39476i	0.669134	−	0.160747i
$447$	26.5024	−	19.2551i	1.25352	−	0.910737i
$448$	6.65498	+	3.38366i	0.314418	+	0.159863i
$449$	−10.4357	−	32.1177i	−0.492490	−	1.51573i	−0.820833	−	0.571169i	$-0.806490\pi$
$449$	−10.4357	−	32.1177i	−0.492490	−	1.51573i	0.328343	−	0.944559i	$-0.393510\pi$
$450$	−23.1945	−	37.8379i	−1.09340	−	1.78369i
$451$		0			0
$452$	−15.1379	+	29.7310i	−0.712029	+	1.39843i
$453$	34.0656	−	11.0686i	1.60054	−	0.520048i
$454$	22.0910	+	1.73541i	1.03678	+	0.0814467i
$455$	−9.23016	+	6.70610i	−0.432716	+	0.314387i
$456$	−4.16069	+	17.3635i	−0.194842	+	0.813120i
$457$	1.18421	−	3.64464i	0.0553952	−	0.170489i	−0.919531	−	0.393018i	$-0.871431\pi$
$457$	1.18421	−	3.64464i	0.0553952	−	0.170489i	0.974926	+	0.222529i	$0.0714311\pi$
$458$	−7.61453	+	18.3906i	−0.355804	+	0.859335i
$459$	−1.56779	+	2.15788i	−0.0731781	+	0.100721i
$460$	4.51841	−	28.5813i	0.210672	−	1.33261i
$461$			15.8380i			0.737649i	0.929499	+	0.368825i	$0.120240\pi$
$461$			15.8380i			0.737649i	−0.929499	+	0.368825i	$0.879760\pi$
$462$		0			0
$463$	30.4131			1.41341			0.706707	−	0.707506i	$-0.250180\pi$
$463$	30.4131			1.41341			0.706707	+	0.707506i	$0.250180\pi$
$464$	14.8029	+	10.7420i	0.687209	+	0.498683i
$465$	29.0217	+	21.0855i	1.34585	+	0.977815i
$466$	15.8094	+	6.54583i	0.732358	+	0.303230i
$467$	19.1937	+	6.23642i	0.888179	+	0.288587i	0.717349	−	0.696714i	$-0.245355\pi$
$467$	19.1937	+	6.23642i	0.888179	+	0.288587i	0.170830	+	0.985301i	$0.445355\pi$
$468$	−10.5194	+	10.5254i	−0.486258	+	0.486537i
$469$	−2.97647	−	4.09676i	−0.137441	−	0.189171i
$470$	19.1722	+	1.50611i	0.884346	+	0.0694716i
$471$	0.635457	+	1.95574i	0.0292803	+	0.0901155i
$472$	0.649234	+	8.20408i	0.0298834	+	0.377624i
$473$		0			0
$474$	−13.7218	+	8.41142i	−0.630261	+	0.386349i
$475$	31.5667	−	10.2567i	1.44838	−	0.470608i
$476$	4.06758	−	2.07401i	0.186437	−	0.0950619i
$477$	0.969336	+	1.33418i	0.0443828	+	0.0610878i
$478$	−29.9053	+	7.18418i	−1.36784	+	0.328597i
$479$	−3.88139	+	11.9457i	−0.177345	+	0.545813i	−0.999733	−	0.0231151i	$-0.992642\pi$
$479$	−3.88139	+	11.9457i	−0.177345	+	0.545813i	0.822388	+	0.568928i	$0.192642\pi$
$480$	−12.9898	−	53.9355i	−0.592899	−	2.46181i
$481$	10.7689	+	7.82410i	0.491022	+	0.356748i
$482$	6.37273	−	7.46367i	0.290270	−	0.339961i
$483$			7.62250i			0.346836i
$484$		0			0
$485$		−	7.62338i		−	0.346160i
$486$	−22.2326	−	18.9829i	−1.00849	−	0.861084i
$487$	−11.5300	−	8.37704i	−0.522475	−	0.379600i	0.295061	−	0.955479i	$-0.404660\pi$
$487$	−11.5300	−	8.37704i	−0.522475	−	0.379600i	−0.817535	+	0.575878i	$0.804660\pi$
$488$	19.6760	+	23.0175i	0.890689	+	1.04195i
$489$	−5.47291	+	16.8439i	−0.247494	+	0.761707i
$490$	−8.43874	−	35.1277i	−0.381224	−	1.58691i
$491$	−11.9935	−	16.5077i	−0.541261	−	0.744982i	0.447533	−	0.894267i	$-0.352303\pi$
$491$	−11.9935	−	16.5077i	−0.541261	−	0.744982i	−0.988794	+	0.149285i	$0.952303\pi$
$492$	−8.82048	−	17.2989i	−0.397658	−	0.779894i
$493$	10.6380	−	3.45648i	0.479109	−	0.155672i
$494$	−5.81622	−	9.48814i	−0.261684	−	0.426892i
$495$		0			0
$496$	8.60683	+	11.8320i	0.386458	+	0.531271i
$497$	2.23533	+	6.87964i	0.100268	+	0.308594i
$498$	−0.171913	+	2.18839i	−0.00770362	+	0.0980639i
$499$	−19.6174	−	27.0010i	−0.878195	−	1.20873i	−0.976918	−	0.213617i	$-0.931476\pi$
$499$	−19.6174	−	27.0010i	−0.878195	−	1.20873i	0.0987224	−	0.995115i	$-0.468524\pi$
$500$	−43.4390	+	43.4640i	−1.94265	+	1.94377i
$501$	−0.319796	−	0.103908i	−0.0142874	−	0.00464227i
$502$	9.59092	−	23.1639i	0.428064	−	1.03386i
$503$	11.9855	+	8.70794i	0.534405	+	0.388268i	0.822003	−	0.569483i	$-0.192857\pi$
$503$	11.9855	+	8.70794i	0.534405	+	0.388268i	−0.287598	+	0.957751i	$0.592857\pi$
$504$	2.56493	+	6.18475i	0.114251	+	0.275491i
$505$	−52.8541			−2.35197
$506$		0			0
$507$			10.3443i			0.459405i
$508$	−12.8605	−	2.03312i	−0.570594	−	0.0902051i
$509$	−14.0753	+	19.3730i	−0.623877	+	0.858694i	−0.997628	−	0.0688356i	$-0.978072\pi$
$509$	−14.0753	+	19.3730i	−0.623877	+	0.858694i	0.373751	+	0.927529i	$0.378072\pi$
$510$	−31.3475	−	12.9793i	−1.38809	−	0.574732i
$511$	3.76772	−	11.5958i	0.166674	−	0.512970i
$512$	1.74615	−	22.5599i	0.0771696	−	0.997018i
$513$	2.36656	−	1.71941i	0.104486	−	0.0759136i
$514$	−1.96641	+	25.0316i	−0.0867345	+	1.10409i
$515$	−15.3264	+	4.97984i	−0.675361	+	0.219438i
$516$	−24.4809	+	48.0806i	−1.07771	+	2.11663i
$517$		0			0
$518$	5.10621	−	3.13010i	0.224354	−	0.137529i
$519$	−0.820985	−	2.52673i	−0.0360372	−	0.110911i
$520$	29.4912	+	18.0547i	1.29327	+	0.791752i
$521$	−16.6784	+	12.1176i	−0.730695	+	0.530881i	−0.889783	−	0.456383i	$-0.849145\pi$
$521$	−16.6784	+	12.1176i	−0.730695	+	0.530881i	0.159088	+	0.987264i	$0.449145\pi$
$522$	3.83145	+	15.9490i	0.167698	+	0.698070i
$523$	21.4952	+	6.98423i	0.939922	+	0.305399i	0.738614	−	0.674129i	$-0.235481\pi$
$523$	21.4952	+	6.98423i	0.939922	+	0.305399i	0.201308	+	0.979528i	$0.435481\pi$
$524$	13.6605	−	2.16763i	0.596761	−	0.0946935i
$525$	15.9682	−	21.9783i	0.696909	−	0.959213i
$526$	25.3841	−	29.7296i	1.10680	−	1.29627i
$527$	8.94797			0.389779
$528$		0			0
$529$	−10.9502			−0.476095
$530$	2.48834	−	2.91432i	0.108086	−	0.126590i
$531$	−4.33824	+	5.97108i	−0.188264	+	0.259123i
$532$	−4.94549	+	0.784745i	−0.214414	+	0.0340230i
$533$	11.5107	+	3.74004i	0.498582	+	0.161999i
$534$	2.13466	+	8.88589i	0.0923759	+	0.384530i
$535$	−43.1005	+	31.3144i	−1.86340	+	1.35384i
$536$	−8.01350	+	13.0895i	−0.346131	+	0.565381i
$537$	11.0246	+	33.9301i	0.475745	+	1.46419i
$538$	12.8147	−	7.85537i	0.552479	−	0.338669i
$539$		0			0
$540$	−4.12400	+	8.09956i	−0.177469	+	0.348550i
$541$	4.99695	−	1.62361i	0.214836	−	0.0698044i	−0.199622	−	0.979873i	$-0.563971\pi$
$541$	4.99695	−	1.62361i	0.214836	−	0.0698044i	0.414458	+	0.910069i	$0.363971\pi$
$542$	2.18720	−	27.8422i	0.0939484	−	1.19592i
$543$	−32.2113	+	23.4029i	−1.38232	+	1.00431i
$544$	−10.5291	−	8.97960i	−0.451430	−	0.384997i
$545$	−2.38357	+	7.33586i	−0.102101	+	0.314234i
$546$	−8.41605	−	3.48463i	−0.360174	−	0.149128i
$547$	−18.4779	+	25.4327i	−0.790059	+	1.08742i	0.204042	+	0.978962i	$0.434592\pi$
$547$	−18.4779	+	25.4327i	−0.790059	+	1.08742i	−0.994101	+	0.108461i	$0.965408\pi$
$548$	−11.4963	−	1.81744i	−0.491096	−	0.0776373i
$549$			27.1570i			1.15903i
$550$		0			0
$551$	−12.2671			−0.522596
$552$	21.3400	−	8.85011i	0.908292	−	0.376686i
$553$	−3.65164	−	2.65307i	−0.155284	−	0.112820i
$554$	6.78169	−	16.3791i	0.288126	−	0.695881i
$555$	−42.3273	−	13.7530i	−1.79669	−	0.583781i
$556$	13.4811	−	13.4888i	0.571724	−	0.572053i
$557$	−8.16465	−	11.2377i	−0.345947	−	0.476156i	0.600219	−	0.799835i	$-0.295080\pi$
$557$	−8.16465	−	11.2377i	−0.345947	−	0.476156i	−0.946167	+	0.323680i	$0.895080\pi$
$558$	−1.02764	+	13.0814i	−0.0435034	+	0.553780i
$559$	−10.3920	−	31.9834i	−0.439536	−	1.35275i
$560$	12.5818	−	9.15226i	0.531678	−	0.386754i
$561$		0			0
$562$	−17.5933	−	28.7004i	−0.742129	−	1.21065i
$563$	19.5119	−	6.33980i	0.822328	−	0.267191i	0.132518	−	0.991181i	$-0.457694\pi$
$563$	19.5119	−	6.33980i	0.822328	−	0.267191i	0.689810	+	0.723990i	$0.257694\pi$
$564$	6.97452	+	13.6785i	0.293680	+	0.575971i
$565$	40.8672	+	56.2489i	1.71930	+	2.36641i
$566$	−9.16012	−	38.1305i	−0.385028	−	1.60274i
$567$	2.93441	−	9.03118i	0.123234	−	0.379274i
$568$	16.6650	−	14.2457i	0.699247	−	0.597735i
$569$	−16.9333	−	12.3028i	−0.709882	−	0.515760i	0.173253	−	0.984877i	$-0.444572\pi$
$569$	−16.9333	−	12.3028i	−0.709882	−	0.515760i	−0.883136	+	0.469118i	$0.844572\pi$
$570$	28.2977	+	24.1615i	1.18526	+	1.01201i
$571$		−	6.00582i		−	0.251336i	−0.992072	−	0.125668i	$-0.959893\pi$
$571$		−	6.00582i		−	0.251336i	0.992072	−	0.125668i	$-0.0401074\pi$
$572$		0			0
$573$		−	39.2293i		−	1.63883i
$574$	3.53606	−	4.14140i	0.147592	−	0.172859i
$575$	−34.7438	−	25.2429i	−1.44892	−	1.05270i
$576$	14.3369	−	14.3616i	0.597370	−	0.598401i
$577$	−14.0359	+	43.1981i	−0.584323	+	1.79836i	0.0176474	+	0.999844i	$0.494382\pi$
$577$	−14.0359	+	43.1981i	−0.584323	+	1.79836i	−0.601971	+	0.798518i	$0.705618\pi$
$578$	15.1477	−	3.63895i	0.630062	−	0.151360i
$579$	0.249919	+	0.343984i	0.0103863	+	0.0142955i
$580$	33.9561	−	17.3138i	1.40995	−	0.718915i
$581$	−0.585483	+	0.190235i	−0.0242899	+	0.00789228i
$582$	5.18909	−	3.18090i	0.215095	−	0.131853i
$583$		0			0
$584$	−36.8384	+	2.91522i	−1.52438	+	0.120633i
$585$	9.58303	+	29.4935i	0.396210	+	1.21941i
$586$	7.91486	+	0.621769i	0.326960	+	0.0256850i
$587$	2.91089	+	4.00649i	0.120145	+	0.165366i	0.864853	−	0.502025i	$-0.167411\pi$
$587$	2.91089	+	4.00649i	0.120145	+	0.165366i	−0.744708	+	0.667390i	$0.767411\pi$
$588$	20.3896	−	20.4013i	0.840853	−	0.841336i
$589$	−9.33300	−	3.03247i	−0.384559	−	0.124951i
$590$	15.8459	+	6.56094i	0.652367	+	0.270110i
$591$	15.9692	+	11.6023i	0.656883	+	0.477254i
$592$	−14.6916	−	10.6612i	−0.603822	−	0.438172i
$593$	17.6332			0.724110			0.362055	−	0.932157i	$-0.382075\pi$
$593$	17.6332			0.724110			0.362055	+	0.932157i	$0.382075\pi$
$594$		0			0
$595$		−	9.51502i		−	0.390078i
$596$	4.34790	−	27.5027i	0.178097	−	1.12655i
$597$	30.5650	−	42.0691i	1.25094	−	1.72177i
$598$	−5.50858	+	13.3043i	−0.225262	+	0.544053i
$599$	13.9531	−	42.9433i	0.570109	−	1.75462i	−0.0821494	−	0.996620i	$-0.526178\pi$
$599$	13.9531	−	42.9433i	0.570109	−	1.75462i	0.652259	−	0.757996i	$-0.273822\pi$
$600$	−80.0706	−	19.1868i	−3.26887	−	0.783296i
$601$	−12.6510	+	9.19149i	−0.516045	+	0.374929i	−0.815112	−	0.579304i	$-0.803325\pi$
$601$	−12.6510	+	9.19149i	−0.516045	+	0.374929i	0.299067	+	0.954232i	$0.403325\pi$
$602$	−15.0847	−	1.18501i	−0.614807	−	0.0482975i
$603$	−13.0906	+	4.25338i	−0.533089	+	0.173211i
$604$	13.8140	−	27.1308i	0.562084	−	1.10394i
$605$		0			0
$606$	−22.0537	−	35.9767i	−0.895869	−	1.46145i
$607$	12.9576	+	39.8795i	0.525934	+	1.61866i	0.762462	+	0.647033i	$0.223990\pi$
$607$	12.9576	+	39.8795i	0.525934	+	1.61866i	−0.236528	+	0.971625i	$0.576010\pi$
$608$	7.93894	+	12.9343i	0.321967	+	0.524555i
$609$	−8.12295	+	5.90167i	−0.329158	+	0.239148i
$610$	61.3593	−	14.7404i	2.48436	−	0.596821i
$611$	−9.10169	−	2.95732i	−0.368215	−	0.119640i
$612$	−1.94494	−	12.2571i	−0.0786197	−	0.495464i
$613$	−16.3942	+	22.5646i	−0.662154	+	0.911377i	−0.999550	−	0.0299855i	$-0.990454\pi$
$613$	−16.3942	+	22.5646i	−0.662154	+	0.911377i	0.337396	+	0.941363i	$0.390454\pi$
$614$	29.9587	+	25.5797i	1.20903	+	1.03231i
$615$	−40.4662			−1.63175
$616$		0			0
$617$	−14.7471			−0.593697			−0.296849	−	0.954925i	$-0.595936\pi$
$617$	−14.7471			−0.593697			−0.296849	+	0.954925i	$0.595936\pi$
$618$	−9.78470	−	8.35450i	−0.393599	−	0.336067i
$619$	−3.01034	+	4.14338i	−0.120996	+	0.166537i	−0.865218	−	0.501395i	$-0.832820\pi$
$619$	−3.01034	+	4.14338i	−0.120996	+	0.166537i	0.744222	+	0.667932i	$0.232820\pi$
$620$	30.1143	−	4.77851i	1.20942	−	0.191909i
$621$	−3.59967	−	1.16960i	−0.144450	−	0.0469346i
$622$	33.5626	−	8.06277i	1.34574	−	0.323288i
$623$	−2.07343	+	1.50644i	−0.0830703	+	0.0603541i
$624$	0.0158699	+	27.6075i	0.000635306	+	1.10518i
$625$	20.4571	+	62.9606i	0.818285	+	2.51842i
$626$	−6.75176	−	11.0143i	−0.269855	−	0.440221i
$627$		0			0
$628$	1.55760	+	0.793073i	0.0621550	+	0.0316471i
$629$	−10.5580	+	3.43049i	−0.420973	+	0.136783i
$630$	13.9104	+	1.09276i	0.554204	+	0.0435366i
$631$	39.2452	−	28.5133i	1.56233	−	1.13510i	0.628255	−	0.778007i	$-0.283769\pi$
$631$	39.2452	−	28.5133i	1.56233	−	1.13510i	0.934070	−	0.357089i	$-0.116231\pi$
$632$	−3.18783	+	13.3035i	−0.126805	+	0.529186i
$633$	−10.9351	+	33.6548i	−0.434631	+	1.33766i
$634$	9.71114	−	23.4543i	0.385678	−	0.931489i
$635$	−15.9489	+	21.9517i	−0.632911	+	0.871127i
$636$	3.02199	+	0.477746i	0.119830	+	0.0189439i
$637$			17.9780i			0.712314i
$638$		0			0
$639$	19.6620			0.777818
$640$	−40.2309	−	24.5979i	−1.59026	−	0.972316i
$641$	5.84236	+	4.24472i	0.230759	+	0.167656i	0.697156	−	0.716919i	$-0.254448\pi$
$641$	5.84236	+	4.24472i	0.230759	+	0.167656i	−0.466397	+	0.884575i	$0.654448\pi$
$642$	−39.2990	−	16.2716i	−1.55101	−	0.642188i
$643$	−11.3753	−	3.69606i	−0.448598	−	0.145758i	0.0760011	−	0.997108i	$-0.475785\pi$
$643$	−11.3753	−	3.69606i	−0.448598	−	0.145758i	−0.524599	+	0.851349i	$0.675785\pi$
$644$	4.58264	+	4.58000i	0.180581	+	0.180477i
$645$	66.0899	+	90.9649i	2.60229	+	3.58174i
$646$	9.25286	+	0.726878i	0.364049	+	0.0285986i
$647$	−8.09476	−	24.9131i	−0.318238	−	0.979436i	−0.974401	−	0.224817i	$-0.927822\pi$
$647$	−8.09476	−	24.9131i	−0.318238	−	0.979436i	0.656163	−	0.754619i	$-0.272178\pi$
$648$	−28.6908	+	2.27046i	−1.12708	+	0.0891921i
$649$		0			0
$650$	43.7540	−	26.8211i	1.71617	−	1.05201i
$651$	−7.63897	+	2.48205i	−0.299395	+	0.0972793i
$652$	6.83810	+	13.4110i	0.267801	+	0.525215i
$653$	−20.1129	−	27.6830i	−0.787077	−	1.08332i	−0.994466	−	0.105060i	$-0.966497\pi$
$653$	−20.1129	−	27.6830i	−0.787077	−	1.08332i	0.207389	−	0.978259i	$-0.433503\pi$
$654$	−5.98794	+	1.43849i	−0.234147	+	0.0562493i
$655$	8.90716	−	27.4134i	0.348032	−	1.07113i
$656$	−15.6999	−	5.09122i	−0.612977	−	0.198779i
$657$	−26.8116	−	19.4798i	−1.04602	−	0.759978i
$658$	−2.79603	+	3.27469i	−0.109001	+	0.127661i
$659$			2.73052i			0.106366i	0.998585	+	0.0531831i	$0.0169367\pi$
$659$			2.73052i			0.106366i	−0.998585	+	0.0531831i	$0.983063\pi$
$660$		0			0
$661$		−	11.2478i		−	0.437488i	−0.975782	−	0.218744i	$-0.929804\pi$
$661$		−	11.2478i		−	0.437488i	0.975782	−	0.218744i	$-0.0701959\pi$
$662$	−14.1896	−	12.1155i	−0.551493	−	0.470883i
$663$	13.6593	+	9.92405i	0.530483	+	0.385418i
$664$	1.21236	+	1.41825i	0.0470487	+	0.0550388i
$665$	−3.22465	+	9.92445i	−0.125047	+	0.384854i
$666$	−3.80264	−	15.8291i	−0.147349	−	0.613365i
$667$	9.32949	+	12.8409i	0.361239	+	0.497203i
$668$	−0.254620	+	0.129827i	−0.00985153	+	0.00502317i
$669$	22.9973	−	7.47229i	0.889129	−	0.288895i
$670$	16.7156	+	27.2685i	0.645779	+	1.05348i
$671$		0			0
$672$	11.4796	+	4.74534i	0.442835	+	0.183056i
$673$	6.19370	+	19.0622i	0.238749	+	0.734795i	0.996602	+	0.0823692i	$0.0262487\pi$
$673$	6.19370	+	19.0622i	0.238749	+	0.734795i	−0.757852	+	0.652426i	$0.773751\pi$
$674$	2.64386	−	33.6552i	0.101838	−	1.29635i
$675$	7.92893	+	10.9132i	0.305185	+	0.420050i
$676$	6.21896	+	6.21539i	0.239191	+	0.239053i
$677$	−25.8130	−	8.38714i	−0.992073	−	0.322344i	−0.232380	−	0.972625i	$-0.574651\pi$
$677$	−25.8130	−	8.38714i	−0.992073	−	0.322344i	−0.759694	+	0.650281i	$0.774651\pi$
$678$	−21.2354	+	51.2877i	−0.815542	+	1.96969i
$679$	1.38092	+	1.00330i	0.0529949	+	0.0385031i
$680$	−26.6383	+	11.0474i	−1.02153	+	0.423649i
$681$	36.8688			1.41282
$682$		0			0
$683$			41.8019i			1.59951i	0.600330	+	0.799753i	$0.295036\pi$
$683$			41.8019i			1.59951i	−0.600330	+	0.799753i	$0.704964\pi$
$684$	−2.12531	+	13.4437i	−0.0812631	+	0.514031i
$685$	−14.2570	+	19.6230i	−0.544731	+	0.749758i
$686$	16.0094	+	6.62863i	0.611243	+	0.253082i
$687$	−10.2340	+	31.4969i	−0.390450	+	1.20168i
$688$	14.1966	+	43.6072i	0.541239	+	1.66251i
$689$	−1.54278	+	1.12090i	−0.0587753	+	0.0427027i
$690$	3.77049	−	47.9969i	0.143540	−	1.82721i
$691$	27.3669	−	8.89205i	1.04109	−	0.338270i	0.261922	−	0.965089i	$-0.415644\pi$
$691$	27.3669	−	8.89205i	1.04109	−	0.338270i	0.779165	+	0.626819i	$0.215644\pi$
$692$	−2.01236	−	1.02462i	−0.0764984	−	0.0389502i
$693$		0			0
$694$	−44.8777	+	27.5100i	−1.70354	+	1.04426i
$695$	−12.2811	−	37.7974i	−0.465849	−	1.43374i
$696$	25.9535	+	15.8889i	0.983765	+	0.602269i
$697$	−8.16600	+	5.93295i	−0.309309	+	0.224726i
$698$	9.38626	+	39.0718i	0.355275	+	1.47889i
$699$	27.0763	+	8.79761i	1.02412	+	0.332756i
$700$	−3.61880	−	22.8058i	−0.136778	−	0.861978i
$701$	13.2737	−	18.2697i	0.501342	−	0.690037i	−0.481088	−	0.876672i	$-0.659758\pi$
$701$	13.2737	−	18.2697i	0.501342	−	0.690037i	0.982429	+	0.186635i	$0.0597582\pi$
$702$	2.93695	−	3.43973i	0.110848	−	0.129824i
$703$	12.1749			0.459184
$704$		0			0
$705$	31.9973			1.20509
$706$	−6.17245	+	7.22911i	−0.232303	+	0.272071i
$707$	6.95602	−	9.57414i	0.261608	−	0.360073i
$708$	2.14592	+	13.5236i	0.0806484	+	0.508249i
$709$	13.8303	+	4.49374i	0.519408	+	0.168766i	0.556977	−	0.830528i	$-0.311961\pi$
$709$	13.8303	+	4.49374i	0.519408	+	0.168766i	−0.0375687	+	0.999294i	$0.511961\pi$
$710$	−10.6722	−	44.4250i	−0.400522	−	1.66724i
$711$	−9.92561	+	7.21138i	−0.372239	+	0.270448i
$712$	6.62480	+	4.05575i	0.248275	+	0.151996i
$713$	3.92368	+	12.0759i	0.146943	+	0.452244i
$714$	6.47669	−	3.97020i	0.242384	−	0.148581i
$715$		0			0
$716$	27.0229	+	13.7591i	1.00989	+	0.514200i
$717$	−48.6682	+	15.8133i	−1.81755	+	0.590557i
$718$	2.19583	−	27.9521i	0.0819478	−	1.04316i
$719$	4.84126	−	3.51738i	0.180549	−	0.131176i	−0.493840	−	0.869553i	$-0.664407\pi$
$719$	4.84126	−	3.51738i	0.180549	−	0.131176i	0.674389	+	0.738376i	$0.264407\pi$
$720$	−13.0914	−	40.2125i	−0.487887	−	1.49863i
$721$	1.11501	−	3.43165i	0.0415252	−	0.127801i
$722$	15.4215	+	6.38520i	0.573929	+	0.237633i
$723$	9.59798	−	13.2105i	0.356953	−	0.491303i
$724$	−5.28447	+	33.4270i	−0.196396	+	1.24231i
$725$		−	56.5690i		−	2.10092i
$726$		0			0
$727$	−13.7234			−0.508973			−0.254486	−	0.967076i	$-0.581906\pi$
$727$	−13.7234			−0.508973			−0.254486	+	0.967076i	$0.581906\pi$
$728$	−7.15176	+	2.96597i	−0.265062	+	0.109926i
$729$	−14.6548	−	10.6473i	−0.542771	−	0.394346i
$730$	−29.4602	+	71.1522i	−1.09037	+	2.63346i
$731$	26.6737	+	8.66679i	0.986561	+	0.320553i
$732$	35.6360	+	35.6155i	1.31715	+	1.31639i
$733$	27.3103	+	37.5894i	1.00873	+	1.38840i	0.919813	+	0.392358i	$0.128340\pi$
$733$	27.3103	+	37.5894i	1.00873	+	1.38840i	0.0889165	+	0.996039i	$0.471660\pi$
$734$	−0.503739	+	6.41240i	−0.0185934	+	0.236686i
$735$	−18.5747	−	57.1671i	−0.685139	−	2.10864i
$736$	7.50155	−	18.1472i	0.276511	−	0.668915i
$737$		0			0
$738$	−7.73579	−	12.6196i	−0.284758	−	0.464534i
$739$	−11.9623	+	3.88679i	−0.440040	+	0.142978i	−0.520654	−	0.853768i	$-0.674312\pi$
$739$	−11.9623	+	3.88679i	−0.440040	+	0.142978i	0.0806139	+	0.996745i	$0.474312\pi$
$740$	−33.7007	+	17.1836i	−1.23886	+	0.631681i
$741$	−10.8838	−	14.9802i	−0.399825	−	0.550312i
$742$	0.200423	+	0.834292i	0.00735775	+	0.0306278i
$743$	2.89308	−	8.90399i	0.106137	−	0.326656i	−0.883859	−	0.467754i	$-0.845063\pi$
$743$	2.89308	−	8.90399i	0.106137	−	0.326656i	0.989996	+	0.141098i	$0.0450634\pi$
$744$	15.8180	+	18.5043i	0.579916	+	0.678402i
$745$	−46.9445	−	34.1072i	−1.71991	−	1.24959i
$746$	−35.9211	−	30.6706i	−1.31517	−	1.12293i
$747$			1.67331i			0.0612233i
$748$		0			0
$749$		−	11.9286i		−	0.435861i
$750$	−66.3893	+	77.7545i	−2.42419	+	2.83919i
$751$	−3.20540	−	2.32886i	−0.116967	−	0.0849813i	0.527764	−	0.849391i	$-0.323031\pi$
$751$	−3.20540	−	2.32886i	−0.116967	−	0.0849813i	−0.644731	+	0.764410i	$0.723031\pi$
$752$	12.4142	+	4.02572i	0.452698	+	0.146803i
$753$	12.8902	−	39.6720i	0.469746	−	1.44573i
$754$	−18.4427	+	4.43051i	−0.671645	+	0.161350i
$755$	−37.2931	−	51.3295i	−1.35723	−	1.86807i
$756$	−0.924427	−	1.81300i	−0.0336211	−	0.0659383i
$757$	3.39413	−	1.10282i	0.123362	−	0.0400826i	−0.246686	−	0.969096i	$-0.579342\pi$
$757$	3.39413	−	1.10282i	0.123362	−	0.0400826i	0.370047	+	0.929013i	$0.379342\pi$
$758$	11.1509	−	6.83549i	0.405019	−	0.248276i
$759$		0			0
$760$	31.5286	−	2.49503i	1.14366	−	0.0905042i
$761$	−15.3896	−	47.3644i	−0.557873	−	1.71696i	−0.688233	−	0.725490i	$-0.741613\pi$
$761$	−15.3896	−	47.3644i	−0.557873	−	1.71696i	0.130360	−	0.991467i	$-0.458387\pi$
$762$	−21.5969	−	1.69659i	−0.782372	−	0.0614609i
$763$	−1.01514	−	1.39723i	−0.0367507	−	0.0505830i
$764$	−23.5846	−	23.5711i	−0.853261	−	0.852771i
$765$	−24.5972	−	7.99210i	−0.889312	−	0.288955i
$766$	41.3003	+	17.1002i	1.49224	+	0.617855i
$767$	−6.90468	−	5.01654i	−0.249313	−	0.181137i
$768$	−0.0432833	−	37.6480i	−0.00156185	−	1.35850i
$769$	−30.5772			−1.10264			−0.551321	−	0.834293i	$-0.685876\pi$
$769$	−30.5772			−1.10264			−0.551321	+	0.834293i	$0.685876\pi$
$770$		0			0
$771$			41.7764i			1.50454i
$772$	0.356967	+	0.0564328i	0.0128475	+	0.00203106i
$773$	−14.0666	+	19.3610i	−0.505940	+	0.696367i	−0.983228	−	0.182380i	$-0.941620\pi$
$773$	−14.0666	+	19.3610i	−0.505940	+	0.696367i	0.477288	+	0.878747i	$0.341620\pi$
$774$	−15.7337	+	38.0000i	−0.565537	+	1.36588i
$775$	13.9841	−	43.0385i	0.502322	−	1.54599i
$776$	1.20552	−	5.03092i	0.0432758	−	0.180600i
$777$	8.06186	−	5.85729i	0.289218	−	0.210129i
$778$	−7.04290	−	0.553270i	−0.252500	−	0.0198357i
$779$	10.5281	−	3.42078i	0.377207	−	0.122562i
$780$	51.2699	+	26.1048i	1.83576	+	0.934701i
$781$		0			0
$782$	−6.27618	−	10.2385i	−0.224436	−	0.366128i
$783$	−1.54063	−	4.74156i	−0.0550574	−	0.169449i
$784$	−0.0140930	−	24.5164i	−0.000503323	−	0.875585i
$785$	2.94687	−	2.14102i	0.105178	−	0.0764164i
$786$	22.3764	−	5.37549i	0.798138	−	0.191737i
$787$	−12.8385	−	4.17150i	−0.457645	−	0.148698i	0.0711172	−	0.997468i	$-0.477344\pi$
$787$	−12.8385	−	4.17150i	−0.457645	−	0.148698i	−0.528762	+	0.848770i	$0.677344\pi$
$788$	16.5704	−	2.62937i	0.590295	−	0.0936675i
$789$	38.2311	−	52.6206i	1.36106	−	1.87334i
$790$	21.6811	+	18.5120i	0.771377	+	0.658627i
$791$	−15.5676			−0.553519
$792$		0			0
$793$	−31.4031			−1.11516
$794$	19.1387	+	16.3412i	0.679207	+	0.579929i
$795$	3.74769	−	5.15825i	0.132917	−	0.182944i
$796$	−6.92681	−	43.6530i	−0.245514	−	1.54724i
$797$	−22.7188	−	7.38178i	−0.804740	−	0.261476i	−0.122372	−	0.992484i	$-0.539050\pi$
$797$	−22.7188	−	7.38178i	−0.804740	−	0.261476i	−0.682368	+	0.731008i	$0.739050\pi$
$798$	−8.10088	+	1.94608i	−0.286768	+	0.0688905i
$799$	6.45701	−	4.69129i	0.228433	−	0.165966i
$800$	−59.6457	+	36.6099i	−2.10879	+	1.29436i
$801$	2.15270	+	6.62533i	0.0760619	+	0.234095i
$802$	8.99768	+	14.6782i	0.317719	+	0.518304i
$803$		0			0
$804$	−11.5865	+	22.7559i	−0.408624	+	0.802540i
$805$	12.8411	−	4.17234i	0.452590	−	0.147056i
$806$	−15.1267	−	1.18831i	−0.532817	−	0.0418565i
$807$	20.2323	−	14.6996i	0.712209	−	0.517450i
$808$	−34.8802	−	8.35808i	−1.22708	−	0.294036i
$809$	−6.23775	+	19.1978i	−0.219308	+	0.674959i	0.779512	+	0.626387i	$0.215467\pi$
$809$	−6.23775	+	19.1978i	−0.219308	+	0.674959i	−0.998820	+	0.0485722i	$0.984533\pi$
$810$	−22.9445	+	55.4154i	−0.806187	+	1.94710i
$811$	2.22185	−	3.05811i	0.0780197	−	0.107385i	−0.768223	−	0.640182i	$-0.778859\pi$
$811$	2.22185	−	3.05811i	0.0780197	−	0.107385i	0.846243	+	0.532797i	$0.178859\pi$
$812$	−1.33262	+	8.42953i	−0.0467659	+	0.295819i
$813$		−	46.4672i		−	1.62968i
$814$		0			0
$815$	31.3715			1.09890
$816$	−18.6348	−	13.5226i	−0.652348	−	0.473386i
$817$	−24.8842	−	18.0795i	−0.870589	−	0.632520i
$818$	−0.768300	−	0.318111i	−0.0268630	−	0.0111225i
$819$	−6.60375	−	2.14569i	−0.230754	−	0.0749764i
$820$	−24.3142	+	24.3282i	−0.849089	+	0.849577i
$821$	−19.1100	−	26.3027i	−0.666943	−	0.917969i	0.332743	−	0.943018i	$-0.392026\pi$
$821$	−19.1100	−	26.3027i	−0.666943	−	0.917969i	−0.999686	+	0.0250487i	$0.992026\pi$
$822$	−19.3058	−	1.51661i	−0.673368	−	0.0528978i
$823$	6.41677	+	19.7488i	0.223674	+	0.688399i	0.998423	+	0.0561302i	$0.0178762\pi$
$823$	6.41677	+	19.7488i	0.223674	+	0.688399i	−0.774749	+	0.632269i	$0.782124\pi$
$824$	−10.9019	+	0.862726i	−0.379785	+	0.0300545i
$825$		0			0
$826$	−3.27392	+	2.00691i	−0.113914	+	0.0698293i
$827$	−10.6651	+	3.46530i	−0.370862	+	0.120500i	−0.488518	−	0.872554i	$-0.662462\pi$
$827$	−10.6651	+	3.46530i	−0.370862	+	0.120500i	0.117655	+	0.993054i	$0.462462\pi$
$828$	15.6889	−	7.99956i	0.545226	−	0.278004i
$829$	4.00990	+	5.51915i	0.139270	+	0.191688i	0.872954	−	0.487802i	$-0.162201\pi$
$829$	4.00990	+	5.51915i	0.139270	+	0.191688i	−0.733685	+	0.679490i	$0.762201\pi$
$830$	3.78073	−	0.908247i	0.131231	−	0.0315257i
$831$	9.11461	−	28.0519i	0.316182	−	0.973110i
$832$	16.6071	+	16.5785i	0.575748	+	0.574756i
$833$	−12.1299	−	8.81289i	−0.420276	−	0.305348i
$834$	20.6036	−	24.1307i	0.713443	−	0.835577i
$835$			0.595616i			0.0206121i
$836$		0			0
$837$		−	3.98829i		−	0.137856i
$838$	−11.9927	−	10.2397i	−0.414281	−	0.353726i
$839$	15.6723	+	11.3866i	0.541067	+	0.393108i	0.824481	−	0.565889i	$-0.191467\pi$
$839$	15.6723	+	11.3866i	0.541067	+	0.393108i	−0.283414	+	0.958998i	$0.591467\pi$
$840$	19.6770	−	16.8204i	0.678921	−	0.580360i
$841$	2.50079	−	7.69664i	0.0862342	−	0.265402i
$842$	11.5090	+	47.9079i	0.396625	+	1.65102i
$843$	−32.9220	−	45.3132i	−1.13389	−	1.56067i
$844$	13.6628	+	26.7957i	0.470293	+	0.922347i
$845$	17.4263	−	5.66215i	0.599484	−	0.194784i
$846$	6.11683	+	9.97855i	0.210301	+	0.343070i
$847$		0			0
$848$	2.10299	−	1.52976i	0.0722170	−	0.0525322i
$849$	−20.1625	−	62.0539i	−0.691977	−	2.12969i
$850$	−3.35195	+	42.6689i	−0.114971	+	1.46353i
$851$	−9.25933	−	12.7444i	−0.317406	−	0.436872i
$852$	25.7861	−	25.8010i	0.883419	−	0.883927i
$853$	10.6051	+	3.44582i	0.363113	+	0.117983i	0.484891	−	0.874575i	$-0.338859\pi$
$853$	10.6051	+	3.44582i	0.363113	+	0.117983i	−0.121777	+	0.992557i	$0.538859\pi$
$854$	−5.40526	+	13.0548i	−0.184964	+	0.446724i
$855$	22.9470	+	16.6720i	0.784772	+	0.570171i
$856$	−33.3954	+	13.8497i	−1.14143	+	0.473373i
$857$	30.4078			1.03871			0.519355	−	0.854558i	$-0.326172\pi$
$857$	30.4078			1.03871			0.519355	+	0.854558i	$0.326172\pi$
$858$		0			0
$859$		−	27.7908i		−	0.948210i	−0.880468	−	0.474105i	$-0.842772\pi$
$859$		−	27.7908i		−	0.948210i	0.880468	−	0.474105i	$-0.157228\pi$
$860$	94.3983	+	14.9234i	3.21895	+	0.508884i
$861$	5.32567	−	7.33016i	0.181498	−	0.249811i
$862$	32.4893	+	13.4520i	1.10659	+	0.458178i
$863$	0.0685484	−	0.210970i	0.00233341	−	0.00718151i	−0.949883	−	0.312606i	$-0.898798\pi$
$863$	0.0685484	−	0.210970i	0.00233341	−	0.00718151i	0.952216	+	0.305424i	$0.0987982\pi$
$864$	−4.00239	+	4.69302i	−0.136164	+	0.159660i
$865$	−3.80724	+	2.76612i	−0.129450	+	0.0940508i
$866$	0.0606611	−	0.772191i	0.00206135	−	0.0262401i
$867$	24.6516	−	8.00978i	0.837211	−	0.272026i
$868$	−3.09769	+	6.08388i	−0.105142	+	0.206500i
$869$		0			0
$870$	54.0673	−	33.1432i	1.83305	−	1.12366i
$871$	−4.91842	−	15.1373i	−0.166654	−	0.512909i
$872$	−2.73305	+	4.46426i	−0.0925529	+	0.151179i
$873$	3.75351	−	2.72709i	0.127037	−	0.0922979i
$874$	3.07641	+	12.8061i	0.104061	+	0.433171i
$875$	−27.2697	−	8.86048i	−0.921886	−	0.299539i
$876$	−60.7244	+	9.63569i	−2.05169	+	0.325560i
$877$	−9.13829	+	12.5778i	−0.308578	+	0.424721i	−0.934937	−	0.354813i	$-0.884544\pi$
$877$	−9.13829	+	12.5778i	−0.308578	+	0.424721i	0.626359	+	0.779535i	$0.284544\pi$
$878$	−25.2816	+	29.6096i	−0.853214	+	0.999276i
$879$	13.2095			0.445545
$880$		0			0
$881$	21.4338			0.722125			0.361062	−	0.932542i	$-0.382414\pi$
$881$	21.4338			0.722125			0.361062	+	0.932542i	$0.382414\pi$
$882$	14.2770	−	16.7211i	0.480732	−	0.563028i
$883$	−8.38770	+	11.5447i	−0.282269	+	0.388509i	−0.926484	−	0.376335i	$-0.877184\pi$
$883$	−8.38770	+	11.5447i	−0.282269	+	0.388509i	0.644215	+	0.764844i	$0.277184\pi$
$884$	14.1735	−	2.24904i	0.476708	−	0.0756435i
$885$	27.1388	+	8.81793i	0.912260	+	0.296411i
$886$	2.66073	+	11.0757i	0.0893890	+	0.372096i
$887$	19.1016	−	13.8781i	0.641369	−	0.465982i	−0.218951	−	0.975736i	$-0.570264\pi$
$887$	19.1016	−	13.8781i	0.641369	−	0.465982i	0.860320	+	0.509754i	$0.170264\pi$
$888$	−25.7584	−	15.7695i	−0.864394	−	0.529189i
$889$	−1.87740	−	5.77805i	−0.0629660	−	0.193789i
$890$	13.8010	−	8.46000i	0.462611	−	0.283580i
$891$		0			0
$892$	9.32569	−	18.3157i	0.312247	−	0.613255i
$893$	−8.32474	+	2.70487i	−0.278577	+	0.0905151i
$894$	3.62821	−	46.1856i	0.121345	−	1.54468i
$895$	51.1253	−	37.1447i	1.70893	−	1.24161i
$896$	9.75044	−	4.05026i	0.325739	−	0.135310i
$897$	−7.40355	+	22.7858i	−0.247197	+	0.760795i
$898$	−44.1259	−	18.2701i	−1.47250	−	0.609682i
$899$	−9.83079	+	13.5309i	−0.327875	+	0.451282i
$900$	−61.9946	−	9.80071i	−2.06649	−	0.326690i
$901$		−	1.59039i		−	0.0529837i
$902$		0			0
$903$	−25.1756			−0.837792
$904$	18.0747	+	43.5831i	0.601156	+	1.44955i
$905$	57.0568	+	41.4542i	1.89663	+	1.37798i
$906$	19.3782	−	46.8022i	0.643799	−	1.55490i
$907$	−43.0717	−	13.9948i	−1.43017	−	0.464691i	−0.511353	−	0.859371i	$-0.670855\pi$
$907$	−43.0717	−	13.9948i	−1.43017	−	0.464691i	−0.918819	+	0.394680i	$0.870855\pi$
$908$	22.1527	−	22.1655i	0.735164	−	0.735587i
$909$	−18.9073	−	26.0237i	−0.627116	−	0.863151i
$910$	−1.26362	+	16.0854i	−0.0418886	+	0.533224i
$911$	−6.93864	−	21.3549i	−0.229887	−	0.707520i	−0.997759	−	0.0669163i	$-0.978684\pi$
$911$	−6.93864	−	21.3549i	−0.229887	−	0.707520i	0.767871	−	0.640604i	$-0.221316\pi$
$912$	14.8538	+	20.4198i	0.491859	+	0.676168i
$913$		0			0
$914$	−2.83237	−	4.62051i	−0.0936864	−	0.152833i
$915$	99.8567	−	32.4454i	3.30116	−	1.07261i
$916$	12.7868	+	25.0776i	0.422487	+	0.828588i
$917$	3.79350	+	5.22130i	0.125272	+	0.172423i
$918$	0.881108	+	3.66776i	0.0290809	+	0.121054i
$919$	−12.8344	+	39.5001i	−0.423367	+	1.30299i	0.481182	+	0.876621i	$0.340207\pi$
$919$	−12.8344	+	39.5001i	−0.423367	+	1.30299i	−0.904549	+	0.426369i	$0.859793\pi$
$920$	−26.5901	−	31.1059i	−0.876650	−	1.02553i
$921$	53.0260	+	38.5256i	1.74727	+	1.26946i
$922$	17.0339	+	14.5441i	0.560982	+	0.478984i
$923$			22.7363i			0.748373i
$924$		0			0
$925$			56.1436i			1.84599i
$926$	27.9284	−	32.7095i	0.917785	−	1.07490i
$927$	−7.93458	−	5.76481i	−0.260606	−	0.189341i
$928$	25.1466	−	6.05629i	0.825479	−	0.198807i
$929$	−11.5262	+	35.4741i	−0.378164	+	1.16387i	0.563156	+	0.826351i	$0.309587\pi$
$929$	−11.5262	+	35.4741i	−0.378164	+	1.16387i	−0.941319	+	0.337517i	$0.890413\pi$
$930$	49.3283	−	11.8502i	1.61754	−	0.388582i
$931$	9.66515	+	13.3029i	0.316763	+	0.435986i
$932$	21.5580	−	10.9921i	0.706155	−	0.360059i
$933$	54.6201	−	17.7471i	1.78818	−	0.581015i
$934$	24.3330	−	14.9161i	0.796199	−	0.488069i
$935$		0			0
$936$	1.66020	+	20.9792i	0.0542653	+	0.685726i
$937$	−4.07584	−	12.5441i	−0.133152	−	0.409799i	0.862146	−	0.506660i	$-0.169120\pi$
$937$	−4.07584	−	12.5441i	−0.133152	−	0.409799i	−0.995298	+	0.0968606i	$0.969120\pi$
$938$	−7.13941	−	0.560851i	−0.233110	−	0.0183124i
$939$	−12.6344	−	17.3898i	−0.412309	−	0.567495i
$940$	19.2257	−	19.2367i	0.627073	−	0.627434i
$941$	−23.4640	−	7.62393i	−0.764906	−	0.248533i	−0.0995231	−	0.995035i	$-0.531732\pi$
$941$	−23.4640	−	7.62393i	−0.764906	−	0.248533i	−0.665383	+	0.746502i	$0.731732\pi$
$942$	2.68695	+	1.11252i	0.0875456	+	0.0362478i
$943$	−11.5877	−	8.41894i	−0.377347	−	0.274159i
$944$	9.41976	+	6.83558i	0.306587	+	0.222479i
$945$	−4.24104			−0.137961
$946$		0			0
$947$			38.8667i			1.26300i	0.775376	+	0.631500i	$0.217560\pi$
$947$			38.8667i			1.26300i	−0.775376	+	0.631500i	$0.782440\pi$
$948$	−3.55419	+	22.4821i	−0.115435	+	0.730185i
$949$	22.5255	−	31.0037i	0.731209	−	1.00642i
$950$	17.9567	−	43.3690i	0.582593	−	1.40708i
$951$	13.0518	−	40.1693i	0.423234	−	1.30258i
$952$	1.50466	−	6.27928i	0.0487663	−	0.203513i
$953$	42.5387	−	30.9061i	1.37796	−	1.00115i	0.380895	−	0.924618i	$-0.375616\pi$
$953$	42.5387	−	30.9061i	1.37796	−	1.00115i	0.997067	−	0.0765301i	$-0.0243841\pi$
$954$	2.32506	+	0.182650i	0.0752767	+	0.00591352i
$955$	−66.0871	+	21.4730i	−2.13853	+	0.694850i
$956$	−19.7355	+	38.7607i	−0.638292	+	1.25361i
$957$		0			0
$958$	9.28340	+	15.1442i	0.299933	+	0.489288i
$959$	−1.67824	−	5.16510i	−0.0541933	−	0.166790i
$960$	−69.9367	−	35.5586i	−2.25720	−	1.14765i
$961$	14.2552	−	10.3570i	0.459846	−	0.334098i
$962$	18.3040	−	4.39719i	0.590146	−	0.141771i
$963$	−30.8364	−	10.0194i	−0.993690	−	0.322869i
$964$	−2.17515	−	13.7078i	−0.0700568	−	0.441500i
$965$	0.442689	−	0.609309i	0.0142506	−	0.0196143i
$966$	8.19807	+	6.99977i	0.263768	+	0.225214i
$967$	2.98370			0.0959493			0.0479746	−	0.998849i	$-0.484723\pi$
$967$	2.98370			0.0959493			0.0479746	+	0.998849i	$0.484723\pi$
$968$		0			0
$969$	15.4425			0.496086
$970$	−8.19901	−	7.00058i	−0.263254	−	0.224775i
$971$	8.84279	−	12.1711i	0.283779	−	0.390588i	−0.643202	−	0.765696i	$-0.722395\pi$
$971$	8.84279	−	12.1711i	0.283779	−	0.390588i	0.926981	+	0.375108i	$0.122395\pi$
$972$	−40.8326	+	6.47929i	−1.30971	+	0.207823i
$973$	8.46302	+	2.74980i	0.271312	+	0.0881546i
$974$	−19.5976	+	4.70795i	−0.627949	+	0.150853i
$975$	69.0803	−	50.1898i	2.21234	−	1.60736i
$976$	42.8240	−	0.0246170i	1.37076	−	0.000787972i
$977$	−3.53247	−	10.8718i	−0.113014	−	0.347820i	0.878514	−	0.477717i	$-0.158536\pi$
$977$	−3.53247	−	10.8718i	−0.113014	−	0.347820i	−0.991528	+	0.129896i	$0.958536\pi$
$978$	13.0899	+	21.3540i	0.418570	+	0.682824i
$979$		0			0
$980$	−45.5294	−	23.1819i	−1.45438	−	0.740519i
$981$	−4.46462	+	1.45064i	−0.142544	+	0.0463154i
$982$	−28.7679	−	2.25992i	−0.918020	−	0.0721170i
$983$	−47.0065	+	34.1522i	−1.49927	+	1.08929i	−0.528606	+	0.848868i	$0.677285\pi$
$983$	−47.0065	+	34.1522i	−1.49927	+	1.08929i	−0.970669	+	0.240419i	$0.922715\pi$
$984$	−26.7050	−	6.39912i	−0.851323	−	0.203996i
$985$	10.8045	−	33.2529i	0.344261	−	1.05953i
$986$	6.05140	−	14.6153i	0.192716	−	0.465446i
$987$	−4.21111	+	5.79610i	−0.134041	+	0.184492i
$988$	−15.5456	−	2.45761i	−0.494572	−	0.0781869i
$989$			39.7982i			1.26551i
$990$		0			0
$991$	30.2307			0.960311			0.480156	−	0.877183i	$-0.340580\pi$
$991$	30.2307			0.960311			0.480156	+	0.877183i	$0.340580\pi$
$992$	20.6291	+	1.60863i	0.654974	+	0.0510740i
$993$	−25.1151	−	18.2472i	−0.797004	−	0.579058i
$994$	9.45182	+	3.91348i	0.299794	+	0.124128i
$995$	−87.6014	−	28.4634i	−2.77715	−	0.902351i
$996$	2.19576	+	2.19450i	0.0695753	+	0.0695353i
$997$	7.87606	+	10.8405i	0.249437	+	0.343321i	0.915314	−	0.402741i	$-0.131942\pi$
$997$	7.87606	+	10.8405i	0.249437	+	0.343321i	−0.665877	+	0.746062i	$0.731942\pi$
$998$	−47.0546	−	3.69647i	−1.48949	−	0.117010i
$999$	1.52904	+	4.70590i	0.0483767	+	0.148888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.h.269.7		40
8.5	even	2	inner	968.2.o.h.269.1		40
11.2	odd	10		968.2.o.g.493.10		40
11.3	even	5		968.2.c.d.485.3		10
11.4	even	5	inner	968.2.o.h.245.9		40
11.5	even	5	inner	968.2.o.h.565.5		40
11.6	odd	10		968.2.o.g.565.6		40
11.7	odd	10		968.2.o.g.245.2		40
11.8	odd	10		88.2.c.a.45.8	yes	10
11.9	even	5	inner	968.2.o.h.493.1		40
11.10	odd	2		968.2.o.g.269.4		40
33.8	even	10		792.2.f.g.397.3		10
44.3	odd	10		3872.2.c.f.1937.2		10
44.19	even	10		352.2.c.a.177.2		10
88.3	odd	10		3872.2.c.f.1937.9		10
88.5	even	10	inner	968.2.o.h.565.9		40
88.13	odd	10		968.2.o.g.493.4		40
88.19	even	10		352.2.c.a.177.9		10
88.21	odd	2		968.2.o.g.269.10		40
88.29	odd	10		968.2.o.g.245.6		40
88.37	even	10	inner	968.2.o.h.245.5		40
88.53	even	10	inner	968.2.o.h.493.7		40
88.61	odd	10		968.2.o.g.565.2		40
88.69	even	10		968.2.c.d.485.4		10
88.85	odd	10		88.2.c.a.45.7	✓	10
132.107	odd	10		3168.2.f.g.1585.10		10
176.19	even	20		2816.2.a.p.1.5		5
176.85	odd	20		2816.2.a.r.1.5		5
176.107	even	20		2816.2.a.q.1.1		5
176.173	odd	20		2816.2.a.o.1.1		5
264.107	odd	10		3168.2.f.g.1585.1		10
264.173	even	10		792.2.f.g.397.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.7	✓	10	88.85	odd	10
88.2.c.a.45.8	yes	10	11.8	odd	10
352.2.c.a.177.2		10	44.19	even	10
352.2.c.a.177.9		10	88.19	even	10
792.2.f.g.397.3		10	33.8	even	10
792.2.f.g.397.4		10	264.173	even	10
968.2.c.d.485.3		10	11.3	even	5
968.2.c.d.485.4		10	88.69	even	10
968.2.o.g.245.2		40	11.7	odd	10
968.2.o.g.245.6		40	88.29	odd	10
968.2.o.g.269.4		40	11.10	odd	2
968.2.o.g.269.10		40	88.21	odd	2
968.2.o.g.493.4		40	88.13	odd	10
968.2.o.g.493.10		40	11.2	odd	10
968.2.o.g.565.2		40	88.61	odd	10
968.2.o.g.565.6		40	11.6	odd	10
968.2.o.h.245.5		40	88.37	even	10	inner
968.2.o.h.245.9		40	11.4	even	5	inner
968.2.o.h.269.1		40	8.5	even	2	inner
968.2.o.h.269.7		40	1.1	even	1	trivial
968.2.o.h.493.1		40	11.9	even	5	inner
968.2.o.h.493.7		40	88.53	even	10	inner
968.2.o.h.565.5		40	11.5	even	5	inner
968.2.o.h.565.9		40	88.5	even	10	inner
2816.2.a.o.1.1		5	176.173	odd	20
2816.2.a.p.1.5		5	176.19	even	20
2816.2.a.q.1.1		5	176.107	even	20
2816.2.a.r.1.5		5	176.85	odd	20
3168.2.f.g.1585.1		10	264.107	odd	10
3168.2.f.g.1585.10		10	132.107	odd	10
3872.2.c.f.1937.2		10	44.3	odd	10
3872.2.c.f.1937.9		10	88.3	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.918304 - 1.07551i) q^{2} +(1.38306 - 1.90362i) q^{3} +(-0.313437 - 1.97529i) q^{4} +(-3.96394 - 1.28796i) q^{5} +(-0.777288 - 3.23559i) q^{6} +(0.754993 - 0.548534i) q^{7} +(-2.41227 - 1.47681i) q^{8} +(-0.783857 - 2.41246i) q^{9} +(-5.02532 + 3.08051i) q^{10} +(-4.19369 - 2.13527i) q^{12} +(2.78966 - 0.906416i) q^{13} +(0.103359 - 1.31572i) q^{14} +(-7.93416 + 5.76451i) q^{15} +(-3.80351 + 1.23825i) q^{16} +(-0.755937 + 2.32653i) q^{17} +(-3.31444 - 1.37233i) q^{18} +(1.57693 - 2.17046i) q^{19} +(-1.30165 + 8.23362i) q^{20} -2.19587i q^{21} -3.47129 q^{23} +(-6.14759 + 2.54952i) q^{24} +(10.0089 + 7.27191i) q^{25} +(1.58690 - 3.83267i) q^{26} +(1.03698 + 0.336937i) q^{27} +(-1.32016 - 1.31940i) q^{28} +(-2.68762 - 3.69919i) q^{29} +(-1.08620 + 13.8268i) q^{30} +(-1.13033 - 3.47878i) q^{31} +(-2.16103 + 5.22781i) q^{32} +(1.80803 + 2.94948i) q^{34} +(-3.69924 + 1.20196i) q^{35} +(-4.51962 + 2.30450i) q^{36} +(2.66741 + 3.67137i) q^{37} +(-0.886245 - 3.68914i) q^{38} +(2.13280 - 6.56407i) q^{39} +(7.66002 + 8.96090i) q^{40} +(3.33815 + 2.42531i) q^{41} +(-2.36168 - 2.01648i) q^{42} -11.4650i q^{43} +10.5724i q^{45} +(-3.18769 + 3.73340i) q^{46} +(-2.63954 - 1.91774i) q^{47} +(-2.90332 + 8.95302i) q^{48} +(-1.89399 + 5.82912i) q^{49} +(17.0122 - 4.08686i) q^{50} +(3.38333 + 4.65675i) q^{51} +(-2.66481 - 5.22628i) q^{52} +(-0.618312 + 0.200902i) q^{53} +(1.31464 - 0.805875i) q^{54} +(-2.63133 + 0.208231i) q^{56} +(-1.95073 - 6.00374i) q^{57} +(-6.44656 - 0.506423i) q^{58} +(-1.71025 - 2.35396i) q^{59} +(13.8734 + 13.8654i) q^{60} +(-10.1820 - 3.30834i) q^{61} +(-4.77944 - 1.97891i) q^{62} +(-1.91512 - 1.39142i) q^{63} +(3.63807 + 7.12492i) q^{64} -12.2255 q^{65} -5.42623i q^{67} +(4.83251 + 0.763971i) q^{68} +(-4.80099 + 6.60800i) q^{69} +(-2.10431 + 5.08233i) q^{70} +(-2.39528 + 7.37192i) q^{71} +(-1.67188 + 6.97711i) q^{72} +(10.5698 - 7.67944i) q^{73} +(6.39808 + 0.502615i) q^{74} +(27.6859 - 8.99568i) q^{75} +(-4.78154 - 2.43459i) q^{76} +(-5.10116 - 8.32165i) q^{78} +(-1.49461 - 4.59993i) q^{79} +(16.6718 - 0.00958362i) q^{80} +(8.23210 - 5.98097i) q^{81} +(5.67388 - 1.36304i) q^{82} +(-0.627378 - 0.203847i) q^{83} +(-4.33748 + 0.688267i) q^{84} +(5.99298 - 8.24863i) q^{85} +(-12.3307 - 10.5283i) q^{86} -10.7590 q^{87} -2.74629 q^{89} +(11.3708 + 9.70872i) q^{90} +(1.60897 - 2.21456i) q^{91} +(1.08803 + 6.85678i) q^{92} +(-8.18558 - 2.65966i) q^{93} +(-4.48644 + 1.07778i) q^{94} +(-9.04633 + 6.57255i) q^{95} +(6.96291 + 11.3441i) q^{96} +(0.565208 + 1.73953i) q^{97} +(4.53000 + 7.38991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100}) \) 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

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