LMFDB - Embedded newform 961.2.d.s.374.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] 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("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			374.13
Character	$\chi$	$=$	961.374
Dual form			961.2.d.s.388.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.52867 + 1.11064i) q^{2} +(-1.51240 + 1.09883i) q^{3} +(0.485270 + 1.49351i) q^{4} +2.49142 q^{5} -3.53237 q^{6} +(-1.20568 - 3.71070i) q^{7} +(0.250863 - 0.772076i) q^{8} +(0.152897 - 0.470567i) q^{9} +(3.80856 + 2.76708i) q^{10} +(0.0141253 + 0.0434731i) q^{11} +(-2.37503 - 1.72556i) q^{12} +(4.08371 - 2.96699i) q^{13} +(2.27818 - 7.01152i) q^{14} +(-3.76803 + 2.73763i) q^{15} +(3.78190 - 2.74771i) q^{16} +(0.125212 - 0.385364i) q^{17} +(0.756362 - 0.549529i) q^{18} +(4.57684 + 3.32527i) q^{19} +(1.20901 + 3.72095i) q^{20} +(5.90089 + 4.28724i) q^{21} +(-0.0266903 + 0.0821442i) q^{22} +(-0.219651 + 0.676016i) q^{23} +(0.468972 + 1.44335i) q^{24} +1.20716 q^{25} +9.53793 q^{26} +(-1.44723 - 4.45412i) q^{27} +(4.95688 - 3.60138i) q^{28} +(4.62825 + 3.36262i) q^{29} -8.80062 q^{30} +7.20939 q^{32} +(-0.0691324 - 0.0502277i) q^{33} +(0.619411 - 0.450028i) q^{34} +(-3.00385 - 9.24490i) q^{35} +0.776992 q^{36} -5.89948 q^{37} +(3.30329 + 10.1665i) q^{38} +(-2.91602 + 8.97458i) q^{39} +(0.625004 - 1.92356i) q^{40} +(0.714048 + 0.518786i) q^{41} +(4.25891 + 13.1076i) q^{42} +(-2.41999 - 1.75823i) q^{43} +(-0.0580728 + 0.0421924i) q^{44} +(0.380929 - 1.17238i) q^{45} +(-1.08659 + 0.789452i) q^{46} +(-2.58894 + 1.88097i) q^{47} +(-2.70050 + 8.31129i) q^{48} +(-6.65251 + 4.83333i) q^{49} +(1.84535 + 1.34073i) q^{50} +(0.234076 + 0.720412i) q^{51} +(6.41293 + 4.65927i) q^{52} +(1.60313 - 4.93392i) q^{53} +(2.73460 - 8.41624i) q^{54} +(0.0351919 + 0.108310i) q^{55} -3.16740 q^{56} -10.5759 q^{57} +(3.34040 + 10.2807i) q^{58} +(-1.16487 + 0.846324i) q^{59} +(-5.91719 - 4.29909i) q^{60} +13.4661 q^{61} -1.93048 q^{63} +(3.45699 + 2.51165i) q^{64} +(10.1742 - 7.39201i) q^{65} +(-0.0498957 - 0.153563i) q^{66} -2.20378 q^{67} +0.636306 q^{68} +(-0.410623 - 1.26377i) q^{69} +(5.67590 - 17.4686i) q^{70} +(-2.78550 + 8.57288i) q^{71} +(-0.324958 - 0.236096i) q^{72} +(0.688450 + 2.11883i) q^{73} +(-9.01836 - 6.55223i) q^{74} +(-1.82571 + 1.32646i) q^{75} +(-2.74531 + 8.44919i) q^{76} +(0.144285 - 0.104829i) q^{77} +(-14.4252 + 10.4805i) q^{78} +(-0.968314 + 2.98016i) q^{79} +(9.42228 - 6.84569i) q^{80} +(8.28396 + 6.01865i) q^{81} +(0.515357 + 1.58611i) q^{82} +(-12.2082 - 8.86980i) q^{83} +(-3.53951 + 10.8935i) q^{84} +(0.311956 - 0.960102i) q^{85} +(-1.74661 - 5.37550i) q^{86} -10.6947 q^{87} +0.0371080 q^{88} +(2.44465 + 7.52387i) q^{89} +(1.88441 - 1.36911i) q^{90} +(-15.9333 - 11.5762i) q^{91} -1.11623 q^{92} -6.04673 q^{94} +(11.4028 + 8.28463i) q^{95} +(-10.9035 + 7.92186i) q^{96} +(0.767803 + 2.36305i) q^{97} -15.5376 q^{98} +0.0226167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) $ 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.52867	+	1.11064i	1.08093	+	0.785344i	0.977846	−	0.209328i	$-0.0671276\pi$
$2$	1.52867	+	1.11064i	1.08093	+	0.785344i	0.103088	+	0.994672i	$0.467128\pi$
$3$	−1.51240	+	1.09883i	−0.873187	+	0.634407i	−0.931440	−	0.363894i	$-0.881447\pi$
$3$	−1.51240	+	1.09883i	−0.873187	+	0.634407i	0.0582534	+	0.998302i	$0.481447\pi$
$4$	0.485270	+	1.49351i	0.242635	+	0.746754i
$5$	2.49142			1.11420			0.557098	−	0.830447i	$-0.311915\pi$
$5$	2.49142			1.11420			0.557098	+	0.830447i	$0.311915\pi$
$6$	−3.53237			−1.44209
$7$	−1.20568	−	3.71070i	−0.455704	−	1.40251i	−0.870307	−	0.492510i	$-0.836079\pi$
$7$	−1.20568	−	3.71070i	−0.455704	−	1.40251i	0.414603	−	0.910002i	$-0.363921\pi$
$8$	0.250863	−	0.772076i	0.0886934	−	0.272970i
$9$	0.152897	−	0.470567i	0.0509655	−	0.156856i
$10$	3.80856	+	2.76708i	1.20437	+	0.875027i
$11$	0.0141253	+	0.0434731i	0.00425893	+	0.0131076i	0.953163	−	0.302456i	$-0.0978065\pi$
$11$	0.0141253	+	0.0434731i	0.00425893	+	0.0131076i	−0.948904	+	0.315563i	$0.897806\pi$
$12$	−2.37503	−	1.72556i	−0.685612	−	0.498126i
$13$	4.08371	−	2.96699i	1.13262	−	0.822895i	0.146545	−	0.989204i	$-0.453185\pi$
$13$	4.08371	−	2.96699i	1.13262	−	0.822895i	0.986074	+	0.166309i	$0.0531848\pi$
$14$	2.27818	−	7.01152i	0.608869	−	1.87391i
$15$	−3.76803	+	2.73763i	−0.972901	+	0.706854i
$16$	3.78190	−	2.74771i	0.945474	−	0.686927i
$17$	0.125212	−	0.385364i	0.0303684	−	0.0934644i	−0.934723	−	0.355376i	$-0.884353\pi$
$17$	0.125212	−	0.385364i	0.0303684	−	0.0934644i	0.965092	+	0.261911i	$0.0843529\pi$
$18$	0.756362	−	0.549529i	0.178276	−	0.129525i
$19$	4.57684	+	3.32527i	1.05000	+	0.762869i	0.972212	−	0.234102i	$-0.0752148\pi$
$19$	4.57684	+	3.32527i	1.05000	+	0.762869i	0.0777863	+	0.996970i	$0.475215\pi$
$20$	1.20901	+	3.72095i	0.270343	+	0.832030i
$21$	5.90089	+	4.28724i	1.28768	+	0.935553i
$22$	−0.0266903	+	0.0821442i	−0.00569038	+	0.0175132i
$23$	−0.219651	+	0.676016i	−0.0458004	+	0.140959i	−0.971342	−	0.237688i	$-0.923611\pi$
$23$	−0.219651	+	0.676016i	−0.0458004	+	0.140959i	0.925541	+	0.378647i	$0.123611\pi$
$24$	0.468972	+	1.44335i	0.0957284	+	0.294622i
$25$	1.20716			0.241432
$26$	9.53793			1.87054
$27$	−1.44723	−	4.45412i	−0.278520	−	0.857195i
$28$	4.95688	−	3.60138i	0.936762	−	0.680597i
$29$	4.62825	+	3.36262i	0.859445	+	0.624424i	0.927734	−	0.373242i	$-0.121754\pi$
$29$	4.62825	+	3.36262i	0.859445	+	0.624424i	−0.0682887	+	0.997666i	$0.521754\pi$
$30$	−8.80062			−1.60677
$31$		0			0
$31$		0			0
$32$	7.20939			1.27445
$33$	−0.0691324	−	0.0502277i	−0.0120344	−	0.00874351i
$34$	0.619411	−	0.450028i	0.106228	−	0.0771792i
$35$	−3.00385	−	9.24490i	−0.507743	−	1.56267i
$36$	0.776992			0.129499
$37$	−5.89948			−0.969868			−0.484934	−	0.874551i	$-0.661156\pi$
$37$	−5.89948			−0.969868			−0.484934	+	0.874551i	$0.661156\pi$
$38$	3.30329	+	10.1665i	0.535864	+	1.64922i
$39$	−2.91602	+	8.97458i	−0.466936	+	1.43708i
$40$	0.625004	−	1.92356i	0.0988218	−	0.304142i
$41$	0.714048	+	0.518786i	0.111515	+	0.0810207i	0.642145	−	0.766583i	$-0.278045\pi$
$41$	0.714048	+	0.518786i	0.111515	+	0.0810207i	−0.530630	+	0.847604i	$0.678045\pi$
$42$	4.25891	+	13.1076i	0.657164	+	2.02254i
$43$	−2.41999	−	1.75823i	−0.369045	−	0.268127i	0.387770	−	0.921756i	$-0.373246\pi$
$43$	−2.41999	−	1.75823i	−0.369045	−	0.268127i	−0.756815	+	0.653629i	$0.773246\pi$
$44$	−0.0580728	+	0.0421924i	−0.00875481	+	0.00636074i
$45$	0.380929	−	1.17238i	0.0567856	−	0.174768i
$46$	−1.08659	+	0.789452i	−0.160209	+	0.116398i
$47$	−2.58894	+	1.88097i	−0.377635	+	0.274368i	−0.760370	−	0.649490i	$-0.774982\pi$
$47$	−2.58894	+	1.88097i	−0.377635	+	0.274368i	0.382735	+	0.923858i	$0.374982\pi$
$48$	−2.70050	+	8.31129i	−0.389784	+	1.19963i
$49$	−6.65251	+	4.83333i	−0.950358	+	0.690476i
$50$	1.84535	+	1.34073i	0.260972	+	0.189607i
$51$	0.234076	+	0.720412i	0.0327772	+	0.100878i
$52$	6.41293	+	4.65927i	0.889313	+	0.646124i
$53$	1.60313	−	4.93392i	0.220207	−	0.677726i	−0.778536	−	0.627600i	$-0.784038\pi$
$53$	1.60313	−	4.93392i	0.220207	−	0.677726i	0.998743	−	0.0501265i	$-0.0159624\pi$
$54$	2.73460	−	8.41624i	0.372132	−	1.14531i
$55$	0.0351919	+	0.108310i	0.00474528	+	0.0146045i
$56$	−3.16740			−0.423262
$57$	−10.5759			−1.40081
$58$	3.34040	+	10.2807i	0.438616	+	1.34992i
$59$	−1.16487	+	0.846324i	−0.151653	+	0.110182i	−0.661024	−	0.750365i	$-0.729878\pi$
$59$	−1.16487	+	0.846324i	−0.151653	+	0.110182i	0.509372	+	0.860547i	$0.329878\pi$
$60$	−5.91719	−	4.29909i	−0.763906	−	0.555010i
$61$	13.4661			1.72416			0.862080	−	0.506772i	$-0.169161\pi$
$61$	13.4661			1.72416			0.862080	+	0.506772i	$0.169161\pi$
$62$		0			0
$63$	−1.93048			−0.243217
$64$	3.45699	+	2.51165i	0.432123	+	0.313956i
$65$	10.1742	−	7.39201i	1.26196	−	0.916866i
$66$	−0.0498957	−	0.153563i	−0.00614173	−	0.0189023i
$67$	−2.20378			−0.269234			−0.134617	−	0.990898i	$-0.542980\pi$
$67$	−2.20378			−0.269234			−0.134617	+	0.990898i	$0.542980\pi$
$68$	0.636306			0.0771634
$69$	−0.410623	−	1.26377i	−0.0494332	−	0.152140i
$70$	5.67590	−	17.4686i	0.678400	−	2.08790i
$71$	−2.78550	+	8.57288i	−0.330578	+	1.01741i	0.638282	+	0.769803i	$0.279645\pi$
$71$	−2.78550	+	8.57288i	−0.330578	+	1.01741i	−0.968860	+	0.247611i	$0.920355\pi$
$72$	−0.324958	−	0.236096i	−0.0382967	−	0.0278242i
$73$	0.688450	+	2.11883i	0.0805770	+	0.247990i	0.983227	−	0.182384i	$-0.0583815\pi$
$73$	0.688450	+	2.11883i	0.0805770	+	0.247990i	−0.902650	+	0.430375i	$0.858381\pi$
$74$	−9.01836	−	6.55223i	−1.04836	−	0.761681i
$75$	−1.82571	+	1.32646i	−0.210815	+	0.153166i
$76$	−2.74531	+	8.44919i	−0.314909	+	0.969189i
$77$	0.144285	−	0.104829i	0.0164428	−	0.0119464i
$78$	−14.4252	+	10.4805i	−1.63333	+	1.18669i
$79$	−0.968314	+	2.98016i	−0.108944	+	0.335295i	−0.990636	−	0.136531i	$-0.956405\pi$
$79$	−0.968314	+	2.98016i	−0.108944	+	0.335295i	0.881692	+	0.471825i	$0.156405\pi$
$80$	9.42228	−	6.84569i	1.05344	−	0.765371i
$81$	8.28396	+	6.01865i	0.920440	+	0.668739i
$82$	0.515357	+	1.58611i	0.0569117	+	0.175156i
$83$	−12.2082	−	8.86980i	−1.34003	−	0.973587i	−0.999443	−	0.0333732i	$-0.989375\pi$
$83$	−12.2082	−	8.86980i	−1.34003	−	0.973587i	−0.340585	−	0.940214i	$-0.610625\pi$
$84$	−3.53951	+	10.8935i	−0.386192	+	1.18858i
$85$	0.311956	−	0.960102i	0.0338364	−	0.104138i
$86$	−1.74661	−	5.37550i	−0.188341	−	0.579655i
$87$	−10.6947			−1.14660
$88$	0.0371080			0.00395573
$89$	2.44465	+	7.52387i	0.259133	+	0.797528i	0.992987	+	0.118222i	$0.0377194\pi$
$89$	2.44465	+	7.52387i	0.259133	+	0.797528i	−0.733855	+	0.679307i	$0.762281\pi$
$90$	1.88441	−	1.36911i	0.198635	−	0.144316i
$91$	−15.9333	−	11.5762i	−1.67026	−	1.21351i
$92$	−1.11623			−0.116375
$93$		0			0
$94$	−6.04673			−0.623672
$95$	11.4028	+	8.28463i	1.16990	+	0.849985i
$96$	−10.9035	+	7.92186i	−1.11283	+	0.808521i
$97$	0.767803	+	2.36305i	0.0779585	+	0.239932i	0.982439	−	0.186583i	$-0.0597413\pi$
$97$	0.767803	+	2.36305i	0.0779585	+	0.239932i	−0.904481	+	0.426515i	$0.859741\pi$
$98$	−15.5376			−1.56954
$99$	0.0226167			0.00227307
$100$	0.585799	+	1.80290i	0.0585799	+	0.180290i
$101$	−4.22444	+	13.0015i	−0.420347	+	1.29370i	0.487033	+	0.873384i	$0.338079\pi$
$101$	−4.22444	+	13.0015i	−0.420347	+	1.29370i	−0.907380	+	0.420312i	$0.861921\pi$
$102$	−0.442296	+	1.36125i	−0.0437939	+	0.134784i
$103$	−4.01460	−	2.91678i	−0.395570	−	0.287399i	0.372164	−	0.928167i	$-0.378616\pi$
$103$	−4.01460	−	2.91678i	−0.395570	−	0.287399i	−0.767734	+	0.640768i	$0.778616\pi$
$104$	−1.26629	−	3.89725i	−0.124170	−	0.382156i
$105$	14.7016	+	10.6813i	1.43473	+	1.04239i
$106$	7.93049	−	5.76184i	0.770277	−	0.559639i
$107$	−4.72500	+	14.5421i	−0.456783	+	1.40583i	0.412245	+	0.911073i	$0.364745\pi$
$107$	−4.72500	+	14.5421i	−0.456783	+	1.40583i	−0.869029	+	0.494762i	$0.835255\pi$
$108$	5.94996	−	4.32290i	0.572535	−	0.415971i
$109$	10.4172	−	7.56853i	0.997786	−	0.724934i	0.0361738	−	0.999346i	$-0.488483\pi$
$109$	10.4172	−	7.56853i	0.997786	−	0.724934i	0.961612	+	0.274411i	$0.0884830\pi$
$110$	−0.0664966	+	0.204655i	−0.00634020	+	0.0195131i
$111$	8.92240	−	6.48250i	0.846876	−	0.615292i
$112$	−14.7557	−	10.7206i	−1.39428	−	1.01300i
$113$	−0.500690	−	1.54097i	−0.0471010	−	0.144962i	0.924740	−	0.380599i	$-0.124282\pi$
$113$	−0.500690	−	1.54097i	−0.0471010	−	0.144962i	−0.971841	+	0.235637i	$0.924282\pi$
$114$	−16.1671	−	11.7461i	−1.51419	−	1.10012i
$115$	−0.547242	+	1.68424i	−0.0510306	+	0.157056i
$116$	−2.77615	+	8.54412i	−0.257759	+	0.793301i
$117$	−0.771783	−	2.37531i	−0.0713514	−	0.219597i
$118$	−2.72066			−0.250457
$119$	−1.58093			−0.144924
$120$	1.16840	+	3.59598i	0.106660	+	0.328266i
$121$	8.89750	−	6.46441i	0.808863	−	0.587674i
$122$	20.5853	+	14.9561i	1.86370	+	1.35406i
$123$	−1.64998			−0.148774
$124$		0			0
$125$	−9.44955			−0.845193
$126$	−2.95107	−	2.14408i	−0.262902	−	0.191009i
$127$	14.8572	−	10.7944i	1.31836	−	0.957846i	0.318411	−	0.947953i	$-0.396851\pi$
$127$	14.8572	−	10.7944i	1.31836	−	0.957846i	0.999951	−	0.00989324i	$-0.00314917\pi$
$128$	−1.96060	−	6.03410i	−0.173294	−	0.533344i
$129$	5.59199			0.492347
$130$	23.7630			2.08415
$131$	−4.51519	−	13.8963i	−0.394494	−	1.21413i	−0.929355	−	0.369187i	$-0.879636\pi$
$131$	−4.51519	−	13.8963i	−0.394494	−	1.21413i	0.534861	−	0.844940i	$-0.320364\pi$
$132$	0.0414675	−	0.127624i	0.00360928	−	0.0111082i
$133$	6.82087	−	20.9925i	0.591444	−	1.82028i
$134$	−3.36885	−	2.44762i	−0.291025	−	0.211442i
$135$	−3.60566	−	11.0971i	−0.310325	−	0.955083i
$136$	−0.266119	−	0.193347i	−0.0228195	−	0.0165794i
$137$	−17.5042	+	12.7175i	−1.49548	+	1.08653i	−0.523343	+	0.852122i	$0.675315\pi$
$137$	−17.5042	+	12.7175i	−1.49548	+	1.08653i	−0.972138	+	0.234408i	$0.924685\pi$
$138$	0.775889	−	2.38794i	0.0660481	−	0.203275i
$139$	−0.111579	+	0.0810666i	−0.00946398	+	0.00687598i	−0.592507	−	0.805565i	$-0.701862\pi$
$139$	−0.111579	+	0.0810666i	−0.00946398	+	0.00687598i	0.583043	+	0.812441i	$0.301862\pi$
$140$	12.3497	−	8.97255i	1.04374	−	0.758319i
$141$	1.84866	−	5.68958i	0.155685	−	0.479149i
$142$	−13.7795	+	10.0114i	−1.15635	+	0.840140i
$143$	0.186668	+	0.135622i	0.0156099	+	0.0113413i
$144$	−0.714743	−	2.19975i	−0.0595619	−	0.183313i
$145$	11.5309	+	8.37770i	0.957590	+	0.695730i
$146$	−1.30085	+	4.00362i	−0.107659	+	0.331342i
$147$	4.75029	−	14.6199i	0.391797	−	1.20583i
$148$	−2.86284	−	8.81092i	−0.235324	−	0.724253i
$149$	15.0189			1.23039			0.615196	−	0.788374i	$-0.289077\pi$
$149$	15.0189			1.23039			0.615196	+	0.788374i	$0.289077\pi$
$150$	−4.26414			−0.348166
$151$	−0.810084	−	2.49318i	−0.0659237	−	0.202892i	0.912669	−	0.408700i	$-0.134018\pi$
$151$	−0.810084	−	2.49318i	−0.0659237	−	0.202892i	−0.978592	+	0.205808i	$0.934018\pi$
$152$	3.71552	−	2.69948i	0.301368	−	0.218957i
$153$	−0.162195	−	0.117842i	−0.0131127	−	0.00952693i
$154$	0.336992			0.0271556
$155$		0			0
$156$	−14.8187			−1.18644
$157$	−15.1916	−	11.0373i	−1.21242	−	0.880874i	−0.216971	−	0.976178i	$-0.569618\pi$
$157$	−15.1916	−	11.0373i	−1.21242	−	0.880874i	−0.995448	+	0.0953037i	$0.969618\pi$
$158$	−4.79013	+	3.48024i	−0.381083	+	0.276873i
$159$	2.99694	+	9.22364i	0.237673	+	0.731482i
$160$	17.9616			1.41999
$161$	2.77332			0.218568
$162$	5.97887	+	18.4011i	0.469745	+	1.44573i
$163$	1.39104	−	4.28119i	0.108955	−	0.335328i	−0.881684	−	0.471841i	$-0.843590\pi$
$163$	1.39104	−	4.28119i	0.108955	−	0.335328i	0.990638	+	0.136513i	$0.0435895\pi$
$164$	−0.428305	+	1.31819i	−0.0334450	+	0.102933i
$165$	−0.172238	−	0.125138i	−0.0134087	−	0.00974198i
$166$	−8.81118	−	27.1180i	−0.683880	−	2.10477i
$167$	14.2117	+	10.3254i	1.09973	+	0.799004i	0.981017	−	0.193924i	$-0.0621215\pi$
$167$	14.2117	+	10.3254i	1.09973	+	0.799004i	0.118718	+	0.992928i	$0.462121\pi$
$168$	4.79039	−	3.48042i	0.369587	−	0.268521i
$169$	3.85645	−	11.8689i	0.296650	−	0.912996i
$170$	1.54321	−	1.12121i	0.118359	−	0.0859927i
$171$	2.26455	−	1.64529i	0.173174	−	0.125818i
$172$	1.45158	−	4.46749i	0.110682	−	0.340643i
$173$	−9.21880	+	6.69785i	−0.700893	+	0.509228i	−0.880223	−	0.474561i	$-0.842607\pi$
$173$	−9.21880	+	6.69785i	−0.700893	+	0.509228i	0.179330	+	0.983789i	$0.442607\pi$
$174$	−16.3487	−	11.8780i	−1.23939	−	0.900472i
$175$	−1.45545	−	4.47941i	−0.110022	−	0.338612i
$176$	0.172872	+	0.125599i	0.0130307	+	0.00946735i
$177$	0.831784	−	2.55997i	0.0625207	−	0.192419i
$178$	−4.61927	+	14.2167i	−0.346229	+	1.06558i
$179$	−1.54491	−	4.75475i	−0.115472	−	0.355387i	0.876573	−	0.481269i	$-0.159824\pi$
$179$	−1.54491	−	4.75475i	−0.115472	−	0.355387i	−0.992045	+	0.125882i	$0.959824\pi$
$180$	1.93581			0.144287
$181$	4.73492			0.351944			0.175972	−	0.984395i	$-0.443693\pi$
$181$	4.73492			0.351944			0.175972	+	0.984395i	$0.443693\pi$
$182$	−11.4997	−	35.3924i	−0.852413	−	2.62346i
$183$	−20.3662	+	14.7969i	−1.50551	+	1.09382i
$184$	0.466834	+	0.339175i	0.0344154	+	0.0250043i
$185$	−14.6981			−1.08062
$186$		0			0
$187$	0.0185216			0.00135443
$188$	−4.06558	−	2.95382i	−0.296513	−	0.215429i
$189$	−14.7830	+	10.7405i	−1.07530	+	0.781255i
$190$	8.22987	+	25.3289i	0.597058	+	1.83755i
$191$	−14.6223			−1.05803			−0.529017	−	0.848611i	$-0.677439\pi$
$191$	−14.6223			−1.05803			−0.529017	+	0.848611i	$0.677439\pi$
$192$	−7.98823			−0.576501
$193$	−2.23624	−	6.88243i	−0.160968	−	0.495408i	0.837749	−	0.546056i	$-0.183871\pi$
$193$	−2.23624	−	6.88243i	−0.160968	−	0.495408i	−0.998717	+	0.0506477i	$0.983871\pi$
$194$	−1.45079	+	4.46509i	−0.104161	+	0.320575i
$195$	−7.26502	+	22.3594i	−0.520259	+	1.60119i
$196$	−10.4469	−	7.59010i	−0.746206	−	0.542150i
$197$	2.57351	+	7.92044i	0.183355	+	0.564308i	0.999916	−	0.0129506i	$-0.00412243\pi$
$197$	2.57351	+	7.92044i	0.183355	+	0.564308i	−0.816561	+	0.577259i	$0.804122\pi$
$198$	0.0345735	+	0.0251191i	0.00245703	+	0.00178514i
$199$	−6.50207	+	4.72403i	−0.460920	+	0.334878i	−0.793892	−	0.608059i	$-0.791948\pi$
$199$	−6.50207	+	4.72403i	−0.460920	+	0.334878i	0.332972	+	0.942937i	$0.391948\pi$
$200$	0.302832	−	0.932020i	0.0214134	−	0.0659038i
$201$	3.33300	−	2.42157i	0.235092	−	0.170804i
$202$	−20.8978	+	15.1831i	−1.47036	+	1.06828i
$203$	6.89750	−	21.2283i	0.484109	−	1.48994i
$204$	−0.962351	+	0.699189i	−0.0673781	+	0.0489530i
$205$	1.77899	+	1.29251i	0.124250	+	0.0902730i
$206$	−2.89750	−	8.91759i	−0.201878	−	0.621318i
$207$	0.284527	+	0.206721i	0.0197760	+	0.0143681i
$208$	7.29175	−	22.4417i	0.505592	−	1.55605i
$209$	−0.0799106	+	0.245939i	−0.00552753	+	0.0170120i
$210$	10.6107	+	32.6564i	0.732209	+	2.25351i
$211$	−15.9134			−1.09552			−0.547762	−	0.836634i	$-0.684520\pi$
$211$	−15.9134			−1.09552			−0.547762	+	0.836634i	$0.684520\pi$
$212$	8.14680			0.559524
$213$	−5.20731	−	16.0264i	−0.356799	−	1.09811i
$214$	−23.3741	+	16.9822i	−1.59782	+	1.16088i
$215$	−6.02921	−	4.38048i	−0.411189	−	0.298746i
$216$	−3.80198			−0.258692
$217$		0			0
$218$	24.3304			1.64786
$219$	−3.36944	−	2.44804i	−0.227686	−	0.165423i
$220$	−0.144684	+	0.105119i	−0.00975457	+	0.00708711i
$221$	−0.632040	−	1.94522i	−0.0425156	−	0.130850i
$222$	20.8392			1.39863
$223$	−16.4962			−1.10467			−0.552334	−	0.833623i	$-0.686263\pi$
$223$	−16.4962			−1.10467			−0.552334	+	0.833623i	$0.686263\pi$
$224$	−8.69221	−	26.7519i	−0.580773	−	1.78743i
$225$	0.184571	−	0.568051i	0.0123047	−	0.0378700i
$226$	0.946074	−	2.91172i	0.0629319	−	0.193685i
$227$	0.322652	+	0.234420i	0.0214152	+	0.0155590i	0.598441	−	0.801167i	$-0.295787\pi$
$227$	0.322652	+	0.234420i	0.0214152	+	0.0155590i	−0.577026	+	0.816726i	$0.695787\pi$
$228$	−5.13218	−	15.7952i	−0.339887	−	1.04606i
$229$	−20.8353	−	15.1377i	−1.37684	−	1.00033i	−0.997168	−	0.0752068i	$-0.976038\pi$
$229$	−20.8353	−	15.1377i	−1.37684	−	1.00033i	−0.379668	−	0.925123i	$-0.623962\pi$
$230$	−2.70714	+	1.96685i	−0.178504	+	0.129691i
$231$	−0.103028	+	0.317088i	−0.00677876	+	0.0208629i
$232$	3.75726	−	2.72981i	0.246676	−	0.179221i
$233$	8.59181	−	6.24232i	0.562868	−	0.408948i	−0.269639	−	0.962961i	$-0.586904\pi$
$233$	8.59181	−	6.24232i	0.562868	−	0.408948i	0.832508	+	0.554014i	$0.186904\pi$
$234$	1.45832	−	4.48824i	0.0953332	−	0.293405i
$235$	−6.45012	+	4.68629i	−0.420760	+	0.305700i
$236$	−1.82927	−	1.32904i	−0.119075	−	0.0865131i
$237$	−1.81020	−	5.57122i	−0.117585	−	0.361889i
$238$	−2.41673	−	1.75586i	−0.156653	−	0.113815i
$239$	−3.46866	+	10.6754i	−0.224369	+	0.690536i	0.773986	+	0.633202i	$0.218260\pi$
$239$	−3.46866	+	10.6754i	−0.224369	+	0.690536i	−0.998355	+	0.0573336i	$0.981740\pi$
$240$	−6.72808	+	20.7069i	−0.434296	+	1.33662i
$241$	4.20632	+	12.9457i	0.270953	+	0.833907i	0.990262	+	0.139217i	$0.0444585\pi$
$241$	4.20632	+	12.9457i	0.270953	+	0.833907i	−0.719309	+	0.694690i	$0.755542\pi$
$242$	20.7810			1.33585
$243$	−5.09214			−0.326661
$244$	6.53471	+	20.1118i	0.418342	+	1.28752i
$245$	−16.5742	+	12.0418i	−1.05889	+	0.769325i
$246$	−2.52228	−	1.83255i	−0.160815	−	0.116839i
$247$	28.5565			1.81701
$248$		0			0
$249$	28.2101			1.78775
$250$	−14.4452	−	10.4951i	−0.913598	−	0.663768i
$251$	−11.5465	+	8.38900i	−0.728807	+	0.529509i	−0.889186	−	0.457546i	$-0.848728\pi$
$251$	−11.5465	+	8.38900i	−0.728807	+	0.529509i	0.160379	+	0.987056i	$0.448728\pi$
$252$	−0.936804	−	2.88318i	−0.0590131	−	0.181624i
$253$	−0.0324911			−0.00204270
$254$	34.7005			2.17730
$255$	0.583181	+	1.79485i	0.0365202	+	0.112398i
$256$	6.34553	−	19.5295i	0.396596	−	1.22060i
$257$	2.12795	−	6.54916i	0.132738	−	0.408525i	−0.862493	−	0.506068i	$-0.831098\pi$
$257$	2.12795	−	6.54916i	0.132738	−	0.408525i	0.995231	+	0.0975429i	$0.0310983\pi$
$258$	8.54831	+	6.21071i	0.532195	+	0.386662i
$259$	7.11288	+	21.8912i	0.441973	+	1.36025i
$260$	15.9773	+	11.6082i	0.990869	+	0.719908i
$261$	2.28999	−	1.66377i	0.141747	−	0.102985i
$262$	8.53163	−	26.2577i	0.527086	−	1.62220i
$263$	−15.7794	+	11.4644i	−0.972997	+	0.706924i	−0.956133	−	0.292934i	$-0.905368\pi$
$263$	−15.7794	+	11.4644i	−0.972997	+	0.706924i	−0.0168647	+	0.999858i	$0.505368\pi$
$264$	−0.0561223	+	0.0407753i	−0.00345409	+	0.00250954i
$265$	3.99406	−	12.2925i	0.245353	−	0.755119i
$266$	33.7420	−	24.5150i	2.06886	−	1.50311i
$267$	−11.9647	−	8.69288i	−0.732229	−	0.531996i
$268$	−1.06943	−	3.29136i	−0.0653257	−	0.201052i
$269$	4.22803	+	3.07184i	0.257788	+	0.187294i	0.709171	−	0.705036i	$-0.249069\pi$
$269$	4.22803	+	3.07184i	0.257788	+	0.187294i	−0.451384	+	0.892330i	$0.649069\pi$
$270$	6.81304	−	20.9684i	0.414628	−	1.27609i
$271$	−6.52376	+	20.0781i	−0.396290	+	1.21966i	0.531662	+	0.846957i	$0.321568\pi$
$271$	−6.52376	+	20.0781i	−0.396290	+	1.21966i	−0.927952	+	0.372700i	$0.878432\pi$
$272$	−0.585327	−	1.80145i	−0.0354907	−	0.109229i
$273$	36.8177			2.22831
$274$	−40.8827			−2.46982
$275$	0.0170515	+	0.0524790i	0.00102824	+	0.00316460i
$276$	1.68818	−	1.22654i	0.101617	−	0.0738289i
$277$	23.9990	+	17.4363i	1.44196	+	1.04765i	0.987628	+	0.156813i	$0.0501219\pi$
$277$	23.9990	+	17.4363i	1.44196	+	1.04765i	0.454332	+	0.890833i	$0.349878\pi$
$278$	−0.260603			−0.0156299
$279$		0			0
$280$	−7.89132			−0.471597
$281$	−19.7573	−	14.3545i	−1.17862	−	0.856317i	−0.186604	−	0.982435i	$-0.559748\pi$
$281$	−19.7573	−	14.3545i	−1.17862	−	0.856317i	−0.992015	+	0.126118i	$0.959748\pi$
$282$	9.14509	−	6.64430i	0.544582	−	0.395662i
$283$	5.50453	+	16.9412i	0.327210	+	1.00705i	0.970433	+	0.241371i	$0.0775970\pi$
$283$	5.50453	+	16.9412i	0.327210	+	1.00705i	−0.643223	+	0.765679i	$0.722403\pi$
$284$	−14.1554			−0.839968
$285$	−26.3490			−1.56078
$286$	0.134726	+	0.414643i	0.00796650	+	0.0245184i
$287$	1.06415	−	3.27511i	0.0628146	−	0.193323i
$288$	1.10229	−	3.39250i	0.0649531	−	0.199905i
$289$	13.6205	+	9.89584i	0.801204	+	0.582109i
$290$	8.32233	+	25.6135i	0.488704	+	1.50408i
$291$	−3.75781	−	2.73021i	−0.220287	−	0.160048i
$292$	−2.83041	+	2.05641i	−0.165637	+	0.120342i
$293$	−6.42404	+	19.7712i	−0.375296	+	1.15504i	0.567982	+	0.823041i	$0.307724\pi$
$293$	−6.42404	+	19.7712i	−0.375296	+	1.15504i	−0.943279	+	0.332002i	$0.892276\pi$
$294$	23.4991	−	17.0731i	1.37050	−	0.995725i
$295$	−2.90217	+	2.10855i	−0.168971	+	0.122764i
$296$	−1.47996	+	4.55485i	−0.0860209	+	0.264745i
$297$	0.173192	−	0.125831i	0.0100496	−	0.00730146i
$298$	22.9589	+	16.6806i	1.32997	+	0.966282i
$299$	1.10874	+	3.41236i	0.0641202	+	0.197342i
$300$	−2.86704	−	2.08303i	−0.165529	−	0.120264i
$301$	−3.60652	+	11.0997i	−0.207876	+	0.639777i
$302$	1.53069	−	4.71097i	0.0880811	−	0.271086i
$303$	−7.89730	−	24.3054i	−0.453688	−	1.39631i
$304$	26.4460			1.51678
$305$	33.5497			1.92105
$306$	−0.117063	−	0.360282i	−0.00669203	−	0.0205960i
$307$	9.73056	−	7.06966i	0.555352	−	0.403487i	−0.274403	−	0.961615i	$-0.588480\pi$
$307$	9.73056	−	7.06966i	0.555352	−	0.403487i	0.829755	+	0.558128i	$0.188480\pi$
$308$	0.226580	+	0.164620i	0.0129106	+	0.00938011i
$309$	9.27673			0.527734
$310$		0			0
$311$	−4.84477			−0.274722			−0.137361	−	0.990521i	$-0.543862\pi$
$311$	−4.84477			−0.274722			−0.137361	+	0.990521i	$0.543862\pi$
$312$	6.19754	+	4.50278i	0.350867	+	0.254920i
$313$	−22.0043	+	15.9871i	−1.24376	+	0.903642i	−0.997843	−	0.0656502i	$-0.979088\pi$
$313$	−22.0043	+	15.9871i	−1.24376	+	0.903642i	−0.245913	+	0.969292i	$0.579088\pi$
$314$	−10.9644	−	33.7449i	−0.618755	−	1.90433i
$315$	−4.80963			−0.270992
$316$	−4.92079			−0.276816
$317$	6.68805	+	20.5837i	0.375639	+	1.15610i	0.943047	+	0.332660i	$0.107946\pi$
$317$	6.68805	+	20.5837i	0.375639	+	1.15610i	−0.567408	+	0.823437i	$0.692054\pi$
$318$	−5.66285	+	17.4284i	−0.317557	+	0.977339i
$319$	−0.0808083	+	0.248702i	−0.00452440	+	0.0139247i
$320$	8.61280	+	6.25756i	0.481470	+	0.349808i
$321$	−8.83309	−	27.1854i	−0.493015	−	1.51734i
$322$	4.23950	+	3.08017i	0.236258	+	0.171651i
$323$	1.85451	−	1.34738i	0.103188	−	0.0749704i
$324$	−4.96894	+	15.2928i	−0.276052	+	0.849602i
$325$	4.92970	−	3.58164i	0.273450	−	0.198673i
$326$	6.88132	−	4.99957i	0.381121	−	0.276901i
$327$	−7.43850	+	22.8934i	−0.411350	+	1.26601i
$328$	0.579670	−	0.421155i	0.0320069	−	0.0232544i
$329$	10.1012	+	7.33892i	0.556895	+	0.404608i
$330$	−0.124311	−	0.382590i	−0.00684309	−	0.0210609i
$331$	2.97733	+	2.16315i	0.163649	+	0.118898i	0.666596	−	0.745420i	$-0.267751\pi$
$331$	2.97733	+	2.16315i	0.163649	+	0.118898i	−0.502947	+	0.864317i	$0.667751\pi$
$332$	7.32283	−	22.5373i	0.401892	−	1.23690i
$333$	−0.902011	+	2.77610i	−0.0494299	+	0.152130i
$334$	10.2572	+	31.5683i	0.561247	+	1.72734i
$335$	−5.49053			−0.299980
$336$	34.0966			1.86012
$337$	3.60271	+	11.0880i	0.196252	+	0.604002i	0.999960	+	0.00897723i	$0.00285758\pi$
$337$	3.60271	+	11.0880i	0.196252	+	0.604002i	−0.803708	+	0.595024i	$0.797142\pi$
$338$	19.0774	−	13.8606i	1.03768	−	0.753915i
$339$	2.45050	+	1.78039i	0.133093	+	0.0966976i
$340$	1.58530			0.0859751
$341$		0			0
$342$	5.28908			0.286000
$343$	3.86026	+	2.80464i	0.208434	+	0.151436i
$344$	−1.96457	+	1.42734i	−0.105923	+	0.0769573i
$345$	−1.02303	−	3.14857i	−0.0550783	−	0.169513i
$346$	−21.5315			−1.15754
$347$	33.4325			1.79475			0.897375	−	0.441268i	$-0.145471\pi$
$347$	33.4325			1.79475			0.897375	+	0.441268i	$0.145471\pi$
$348$	−5.18983	−	15.9727i	−0.278204	−	0.856225i
$349$	−2.32092	+	7.14305i	−0.124236	+	0.382359i	−0.993761	−	0.111530i	$-0.964425\pi$
$349$	−2.32092	+	7.14305i	−0.124236	+	0.382359i	0.869525	+	0.493889i	$0.164425\pi$
$350$	2.75013	−	8.46403i	0.147001	−	0.452422i
$351$	−19.1254	−	13.8954i	−1.02084	−	0.741683i
$352$	0.101834	+	0.313414i	0.00542779	+	0.0167050i
$353$	13.0167	+	9.45720i	0.692810	+	0.503356i	0.877583	−	0.479425i	$-0.159155\pi$
$353$	13.0167	+	9.45720i	0.692810	+	0.503356i	−0.184773	+	0.982781i	$0.559155\pi$
$354$	4.11474	−	2.98953i	0.218696	−	0.158892i
$355$	−6.93984	+	21.3586i	−0.368328	+	1.13360i
$356$	−10.0506	+	7.30222i	−0.532683	+	0.387017i
$357$	2.39101	−	1.73717i	0.126546	−	0.0919409i
$358$	2.91918	−	8.98430i	0.154283	−	0.474835i
$359$	10.8683	−	7.89628i	0.573607	−	0.416750i	−0.262807	−	0.964848i	$-0.584648\pi$
$359$	10.8683	−	7.89628i	0.573607	−	0.416750i	0.836414	+	0.548099i	$0.184648\pi$
$360$	−0.809606	−	0.588213i	−0.0426700	−	0.0310016i
$361$	4.01872	+	12.3683i	0.211511	+	0.650965i
$362$	7.23813	+	5.25881i	0.380428	+	0.276397i
$363$	−6.35335	+	19.5536i	−0.333464	+	1.02630i
$364$	9.55720	−	29.4140i	0.500933	−	1.54171i
$365$	1.71522	+	5.27889i	0.0897785	+	0.276310i
$366$	−47.5674			−2.48639
$367$	−8.54411			−0.445999			−0.222999	−	0.974819i	$-0.571585\pi$
$367$	−8.54411			−0.445999			−0.222999	+	0.974819i	$0.571585\pi$
$368$	1.02680	+	3.16016i	0.0535256	+	0.164735i
$369$	0.353299	−	0.256687i	0.0183920	−	0.0133626i
$370$	−22.4685	−	16.3243i	−1.16808	−	0.848661i
$371$	−20.2412			−1.05087
$372$		0			0
$373$	−21.0750			−1.09122			−0.545612	−	0.838038i	$-0.683703\pi$
$373$	−21.0750			−1.09122			−0.545612	+	0.838038i	$0.683703\pi$
$374$	0.0283134	+	0.0205709i	0.00146405	+	0.00106370i
$375$	14.2915	−	10.3834i	0.738011	−	0.536197i
$376$	0.802787	+	2.47072i	0.0414006	+	0.127418i
$377$	28.8773			1.48726
$378$	−34.5272			−1.77589
$379$	5.28270	+	16.2585i	0.271354	+	0.835143i	0.990161	+	0.139933i	$0.0446886\pi$
$379$	5.28270	+	16.2585i	0.271354	+	0.835143i	−0.718807	+	0.695210i	$0.755311\pi$
$380$	−6.83971	+	21.0505i	−0.350870	+	1.07987i
$381$	−10.6089	+	32.6509i	−0.543512	+	1.67276i
$382$	−22.3527	−	16.2402i	−1.14367	−	0.830921i
$383$	−0.429605	−	1.32219i	−0.0219518	−	0.0675607i	0.939481	−	0.342602i	$-0.111308\pi$
$383$	−0.429605	−	1.32219i	−0.0219518	−	0.0675607i	−0.961432	+	0.275042i	$0.911308\pi$
$384$	9.59564	+	6.97164i	0.489675	+	0.355770i
$385$	0.359474	−	0.261173i	0.0183205	−	0.0133106i
$386$	4.22546	−	13.0046i	0.215070	−	0.661919i
$387$	−1.19737	+	0.869942i	−0.0608659	+	0.0442217i
$388$	−3.15665	+	2.29344i	−0.160254	+	0.116432i
$389$	−4.95640	+	15.2542i	−0.251300	+	0.773420i	0.743237	+	0.669029i	$0.233290\pi$
$389$	−4.95640	+	15.2542i	−0.251300	+	0.773420i	−0.994536	+	0.104392i	$0.966710\pi$
$390$	−35.9392	+	26.1114i	−1.81985	+	1.32220i
$391$	0.233009	+	0.169291i	0.0117838	+	0.00856141i
$392$	2.06283	+	6.34875i	0.104189	+	0.320660i
$393$	22.0984	+	16.0554i	1.11472	+	0.809890i
$394$	−4.86275	+	14.9660i	−0.244982	+	0.753976i
$395$	−2.41247	+	7.42483i	−0.121385	+	0.373584i
$396$	0.0109752	+	0.0337782i	0.000551525	+	0.00169742i
$397$	−18.4943			−0.928203			−0.464102	−	0.885782i	$-0.653623\pi$
$397$	−18.4943			−0.928203			−0.464102	+	0.885782i	$0.653623\pi$
$398$	−15.1863			−0.761218
$399$	12.7512	+	39.2440i	0.638357	+	1.96466i
$400$	4.56536	−	3.31693i	0.228268	−	0.165846i
$401$	−12.1165	−	8.80318i	−0.605071	−	0.439610i	0.242604	−	0.970125i	$-0.421998\pi$
$401$	−12.1165	−	8.80318i	−0.605071	−	0.439610i	−0.847675	+	0.530515i	$0.821998\pi$
$402$	7.78457			0.388259
$403$		0			0
$404$	−21.4678			−1.06806
$405$	20.6388	+	14.9950i	1.02555	+	0.745106i
$406$	34.1211	−	24.7904i	1.69340	−	1.23033i
$407$	−0.0833317	−	0.256469i	−0.00413060	−	0.0127127i
$408$	0.614934			0.0304438
$409$	−8.02650			−0.396885			−0.198442	−	0.980113i	$-0.563588\pi$
$409$	−8.02650			−0.396885			−0.198442	+	0.980113i	$0.563588\pi$
$410$	1.28397	+	3.95165i	0.0634107	+	0.195158i
$411$	12.4990	−	38.4680i	0.616531	−	1.89749i
$412$	2.40806	−	7.41126i	0.118637	−	0.365127i
$413$	4.54491	+	3.30207i	0.223640	+	0.162484i
$414$	0.205355	+	0.632017i	0.0100926	+	0.0310620i
$415$	−30.4158	−	22.0984i	−1.49305	−	1.08477i
$416$	29.4411	−	21.3902i	1.44347	−	1.04874i
$417$	0.0796739	−	0.245211i	0.00390165	−	0.0120080i
$418$	−0.395308	+	0.287208i	−0.0193352	+	0.0140478i
$419$	−1.18027	+	0.857519i	−0.0576601	+	0.0418925i	−0.616242	−	0.787557i	$-0.711346\pi$
$419$	−1.18027	+	0.857519i	−0.0576601	+	0.0418925i	0.558582	+	0.829449i	$0.311346\pi$
$420$	−8.81840	+	27.1402i	−0.430294	+	1.32431i
$421$	−10.3040	+	7.48630i	−0.502186	+	0.364860i	−0.809851	−	0.586635i	$-0.800452\pi$
$421$	−10.3040	+	7.48630i	−0.502186	+	0.364860i	0.307665	+	0.951495i	$0.400452\pi$
$422$	−24.3264	−	17.6741i	−1.18419	−	0.860364i
$423$	0.489285	+	1.50586i	0.0237898	+	0.0732176i
$424$	−3.40720	−	2.47547i	−0.165468	−	0.120220i
$425$	0.151151	−	0.465196i	0.00733192	−	0.0225653i
$426$	9.83942	−	30.2826i	0.476721	−	1.46720i
$427$	−16.2358	−	49.9687i	−0.785707	−	2.41816i
$428$	−24.0116			−1.16064
$429$	−0.431342			−0.0208254
$430$	−4.35153	−	13.3926i	−0.209849	−	0.645849i
$431$	28.4410	−	20.6636i	1.36996	−	0.995331i	0.372215	−	0.928146i	$-0.378598\pi$
$431$	28.4410	−	20.6636i	1.36996	−	0.995331i	0.997741	−	0.0671848i	$-0.0214017\pi$
$432$	−17.7119	−	12.8684i	−0.852164	−	0.619133i
$433$	−29.5616			−1.42064			−0.710319	−	0.703880i	$-0.751449\pi$
$433$	−29.5616			−1.42064			−0.710319	+	0.703880i	$0.751449\pi$
$434$		0			0
$435$	−26.6450			−1.27753
$436$	16.3588	+	11.8854i	0.783445	+	0.569206i
$437$	−3.25324	+	2.36362i	−0.155624	+	0.113067i
$438$	−2.43186	−	7.48450i	−0.116199	−	0.357623i
$439$	18.5627			0.885948			0.442974	−	0.896535i	$-0.353923\pi$
$439$	18.5627			0.885948			0.442974	+	0.896535i	$0.353923\pi$
$440$	0.0924516			0.00440746
$441$	1.25726	+	3.86945i	0.0598696	+	0.184260i
$442$	1.19427	−	3.67557i	0.0568054	−	0.174829i
$443$	7.67156	−	23.6106i	0.364487	−	1.12178i	−0.585815	−	0.810445i	$-0.699225\pi$
$443$	7.67156	−	23.6106i	0.364487	−	1.12178i	0.950302	−	0.311330i	$-0.100775\pi$
$444$	14.0114	+	10.1799i	0.664953	+	0.483117i
$445$	6.09065	+	18.7451i	0.288725	+	0.888603i
$446$	−25.2173	−	18.3214i	−1.19407	−	0.867544i
$447$	−22.7146	+	16.5031i	−1.07436	+	0.780570i
$448$	5.15195	−	15.8561i	0.243407	−	0.749129i
$449$	−10.2071	+	7.41588i	−0.481702	+	0.349977i	−0.801984	−	0.597345i	$-0.796222\pi$
$449$	−10.2071	+	7.41588i	−0.481702	+	0.349977i	0.320282	+	0.947322i	$0.396222\pi$
$450$	0.913050	−	0.663370i	0.0430416	−	0.0312716i
$451$	−0.0124671	+	0.0383698i	−0.000587053	+	0.00180676i
$452$	2.05847	−	1.49557i	0.0968225	−	0.0703456i
$453$	3.96475	+	2.88056i	0.186280	+	0.135340i
$454$	0.232871	+	0.716703i	0.0109292	+	0.0336366i
$455$	−39.6964	−	28.8411i	−1.86100	−	1.35209i
$456$	−2.65310	+	8.16542i	−0.124243	+	0.382381i
$457$	6.00706	−	18.4878i	0.280998	−	0.864824i	−0.706571	−	0.707642i	$-0.749759\pi$
$457$	6.00706	−	18.4878i	0.280998	−	0.864824i	0.987570	−	0.157182i	$-0.0502409\pi$
$458$	−15.0377	−	46.2812i	−0.702665	−	2.16258i
$459$	−1.89767			−0.0885755
$460$	−2.78098			−0.129664
$461$	−10.7173	−	32.9843i	−0.499152	−	1.53623i	−0.810385	−	0.585898i	$-0.800742\pi$
$461$	−10.7173	−	32.9843i	−0.499152	−	1.53623i	0.311232	−	0.950334i	$-0.399258\pi$
$462$	−0.509668	+	0.370296i	−0.0237119	+	0.0172277i
$463$	−9.94344	−	7.22433i	−0.462111	−	0.335743i	0.332248	−	0.943192i	$-0.392193\pi$
$463$	−9.94344	−	7.22433i	−0.462111	−	0.335743i	−0.794359	+	0.607449i	$0.792193\pi$
$464$	26.7431			1.24152
$465$		0			0
$466$	20.0671			0.929588
$467$	30.5674	+	22.2085i	1.41449	+	1.02769i	0.992650	+	0.121019i	$0.0386163\pi$
$467$	30.5674	+	22.2085i	1.41449	+	1.02769i	0.421842	+	0.906669i	$0.361384\pi$
$468$	3.17301	−	2.30533i	0.146673	−	0.106564i
$469$	2.65705	+	8.17756i	0.122691	+	0.377605i
$470$	−15.0649			−0.694893
$471$	35.1039			1.61750
$472$	0.361205	+	1.11168i	0.0166258	+	0.0511690i
$473$	0.0422525	−	0.130040i	0.00194277	−	0.00597924i
$474$	3.42045	−	10.5270i	0.157106	−	0.483523i
$475$	5.52498	+	4.01413i	0.253503	+	0.184181i
$476$	−0.767180	−	2.36114i	−0.0351637	−	0.108223i
$477$	−2.07663	−	1.50876i	−0.0950823	−	0.0690813i
$478$	−17.1590	+	12.4668i	−0.784836	+	0.570217i
$479$	1.97776	−	6.08693i	0.0903663	−	0.278119i	−0.895652	−	0.444755i	$-0.853291\pi$
$479$	1.97776	−	6.08693i	0.0903663	−	0.278119i	0.986018	+	0.166636i	$0.0532906\pi$
$480$	−27.1652	+	19.7367i	−1.23992	+	0.900851i
$481$	−24.0918	+	17.5037i	−1.09849	+	0.798100i
$482$	−7.94801	+	24.4615i	−0.362022	+	1.11419i
$483$	−4.19438	+	3.04740i	−0.190851	+	0.138661i
$484$	13.9723	+	10.1515i	0.635106	+	0.461432i
$485$	1.91292	+	5.88735i	0.0868611	+	0.267331i
$486$	−7.78420	−	5.65555i	−0.353099	−	0.256541i
$487$	−0.0140005	+	0.0430891i	−0.000634424	+	0.00195256i	−0.951373	−	0.308041i	$-0.900327\pi$
$487$	−0.0140005	+	0.0430891i	−0.000634424	+	0.00195256i	0.950739	+	0.309993i	$0.100327\pi$
$488$	3.37815	−	10.3969i	0.152922	−	0.470644i
$489$	2.60046	+	8.00339i	0.117597	+	0.361926i
$490$	−38.7107			−1.74877
$491$	−26.0723			−1.17663			−0.588314	−	0.808633i	$-0.700208\pi$
$491$	−26.0723			−1.17663			−0.588314	+	0.808633i	$0.700208\pi$
$492$	−0.800688	−	2.46426i	−0.0360978	−	0.111098i
$493$	1.87535	−	1.36252i	0.0844614	−	0.0613648i
$494$	43.6535	+	31.7162i	1.96407	+	1.42698i
$495$	0.0563477			0.00253264
$496$		0			0
$497$	35.1698			1.57758
$498$	43.1240	+	31.3314i	1.93243	+	1.40400i
$499$	12.7797	−	9.28496i	0.572096	−	0.415652i	−0.263770	−	0.964586i	$-0.584966\pi$
$499$	12.7797	−	9.28496i	0.572096	−	0.415652i	0.835866	+	0.548934i	$0.184966\pi$
$500$	−4.58558	−	14.1130i	−0.205073	−	0.631151i
$501$	−32.8397			−1.46717
$502$	−26.9680			−1.20364
$503$	6.64957	+	20.4653i	0.296490	+	0.912502i	0.982717	+	0.185114i	$0.0592656\pi$
$503$	6.64957	+	20.4653i	0.296490	+	0.912502i	−0.686227	+	0.727387i	$0.740734\pi$
$504$	−0.484285	+	1.49048i	−0.0215718	+	0.0663911i
$505$	−10.5248	+	32.3921i	−0.468349	+	1.44143i
$506$	−0.0496682	−	0.0360861i	−0.00220802	−	0.00160422i
$507$	7.20939	+	22.1882i	0.320180	+	0.985413i
$508$	23.3312	+	16.9511i	1.03516	+	0.752085i
$509$	13.3461	−	9.69654i	0.591557	−	0.429791i	−0.251315	−	0.967905i	$-0.580863\pi$
$509$	13.3461	−	9.69654i	0.591557	−	0.429791i	0.842872	+	0.538114i	$0.180863\pi$
$510$	−1.10195	+	3.39144i	−0.0487950	+	0.150175i
$511$	7.03229	−	5.10926i	0.311090	−	0.226020i
$512$	21.1248	−	15.3481i	0.933593	−	0.678295i
$513$	8.18739	−	25.1982i	0.361482	−	1.11253i
$514$	10.5267	−	7.64812i	0.464314	−	0.337344i
$515$	−10.0020	−	7.26691i	−0.440743	−	0.320218i
$516$	2.71363	+	8.35168i	0.119461	+	0.367662i
$517$	−0.118341	−	0.0859798i	−0.00520464	−	0.00378139i
$518$	−13.4401	+	41.3643i	−0.590523	+	1.81744i
$519$	6.58278	−	20.2597i	0.288952	−	0.889303i
$520$	−3.15486	−	9.70967i	−0.138350	−	0.425797i
$521$	−0.178355			−0.00781387			−0.00390693	−	0.999992i	$-0.501244\pi$
$521$	−0.178355			−0.00781387			−0.00390693	+	0.999992i	$0.501244\pi$
$522$	5.34849			0.234097
$523$	−0.394523	−	1.21422i	−0.0172513	−	0.0530940i	0.942060	−	0.335444i	$-0.108886\pi$
$523$	−0.394523	−	1.21422i	−0.0172513	−	0.0530940i	−0.959312	+	0.282350i	$0.908886\pi$
$524$	18.5632	−	13.4869i	0.810936	−	0.589180i
$525$	7.12332	+	5.17539i	0.310887	+	0.225873i
$526$	−36.8543			−1.60692
$527$		0			0
$528$	−0.399463			−0.0173844
$529$	18.1986	+	13.2221i	0.791245	+	0.574873i
$530$	19.7582	−	14.3551i	0.858239	−	0.623547i
$531$	0.220149	+	0.677548i	0.00955363	+	0.0294031i
$532$	34.6624			1.50280
$533$	4.45520			0.192976
$534$	−8.63543	−	26.5771i	−0.373691	−	1.15010i
$535$	−11.7720	+	36.2304i	−0.508946	+	1.56638i
$536$	−0.552846	+	1.70149i	−0.0238793	+	0.0734930i
$537$	7.56118	+	5.49352i	0.326289	+	0.237063i
$538$	3.05154	+	9.39168i	0.131561	+	0.404904i
$539$	−0.304088	−	0.220933i	−0.0130980	−	0.00951625i
$540$	14.8238	−	10.7701i	0.637916	−	0.463473i
$541$	5.78003	−	17.7891i	0.248503	−	0.764813i	−0.746538	−	0.665343i	$-0.768285\pi$
$541$	5.78003	−	17.7891i	0.248503	−	0.764813i	0.995041	−	0.0994700i	$-0.0317147\pi$
$542$	−32.2723	+	23.4472i	−1.38621	+	1.00714i
$543$	−7.16111	+	5.20285i	−0.307313	+	0.223276i
$544$	0.902704	−	2.77824i	0.0387031	−	0.119116i
$545$	25.9536	−	18.8564i	1.11173	−	0.807719i
$546$	56.2822	+	40.8914i	2.40866	+	1.74999i
$547$	−7.14984	−	22.0050i	−0.305705	−	0.940864i	−0.979413	−	0.201866i	$-0.935299\pi$
$547$	−7.14984	−	22.0050i	−0.305705	−	0.940864i	0.673708	−	0.738998i	$-0.264701\pi$
$548$	−27.4879	−	19.9712i	−1.17423	−	0.853126i
$549$	2.05892	−	6.33672i	0.0878728	−	0.270445i
$550$	−0.0322194	+	0.0991612i	−0.00137384	+	0.00422825i
$551$	10.0011	+	30.7804i	0.426063	+	1.31129i
$552$	−1.07874			−0.0459140
$553$	12.2260			0.519901
$554$	17.3211	+	53.3087i	0.735901	+	2.26487i
$555$	22.2294	−	16.1506i	0.943586	−	0.685555i
$556$	−0.175219	−	0.127304i	−0.00743096	−	0.00539891i
$557$	−26.2162			−1.11082			−0.555408	−	0.831578i	$-0.687438\pi$
$557$	−26.2162			−1.11082			−0.555408	+	0.831578i	$0.687438\pi$
$558$		0			0
$559$	−15.0992			−0.638628
$560$	−36.7625	−	26.7096i	−1.55350	−	1.12868i
$561$	−0.0280121	+	0.0203520i	−0.00118267	+	0.000859263i
$562$	−14.2596	−	43.8866i	−0.601506	−	1.85124i
$563$	−27.0430			−1.13972			−0.569862	−	0.821740i	$-0.693003\pi$
$563$	−27.0430			−1.13972			−0.569862	+	0.821740i	$0.693003\pi$
$564$	9.39453			0.395581
$565$	−1.24743	−	3.83919i	−0.0524797	−	0.161516i
$566$	−10.4010	+	32.0111i	−0.437188	+	1.34553i
$567$	12.3456	−	37.9959i	0.518467	−	1.59568i
$568$	5.92014	+	4.30123i	0.248404	+	0.180476i
$569$	3.87789	+	11.9349i	0.162570	+	0.500338i	0.998849	−	0.0479657i	$-0.0152738\pi$
$569$	3.87789	+	11.9349i	0.162570	+	0.500338i	−0.836279	+	0.548304i	$0.815274\pi$
$570$	−40.2790	−	29.2644i	−1.68710	−	1.22575i
$571$	20.9857	−	15.2470i	0.878225	−	0.638068i	−0.0545560	−	0.998511i	$-0.517374\pi$
$571$	20.9857	−	15.2470i	0.878225	−	0.638068i	0.932781	+	0.360443i	$0.117374\pi$
$572$	−0.111968	+	0.344603i	−0.00468163	+	0.0144086i
$573$	22.1149	−	16.0674i	0.923862	−	0.671225i
$574$	5.26421	−	3.82467i	0.219724	−	0.159639i
$575$	−0.265154	+	0.816060i	−0.0110577	+	0.0340321i
$576$	1.71046	−	1.24272i	0.0712692	−	0.0517801i
$577$	−21.5373	−	15.6478i	−0.896610	−	0.651425i	0.0409831	−	0.999160i	$-0.486951\pi$
$577$	−21.5373	−	15.6478i	−0.896610	−	0.651425i	−0.937593	+	0.347735i	$0.886951\pi$
$578$	9.83044	+	30.2550i	0.408892	+	1.25844i
$579$	10.9447	+	7.95178i	0.454846	+	0.330465i
$580$	−6.91655	+	21.2870i	−0.287194	+	0.883893i
$581$	−18.1939	+	55.9952i	−0.754812	+	2.32307i
$582$	−2.71217	−	8.34719i	−0.112423	−	0.346002i
$583$	0.237137			0.00982122
$584$	1.80861			0.0748406
$585$	−1.92283	−	5.91788i	−0.0794994	−	0.244674i
$586$	−31.7790	+	23.0888i	−1.31278	+	0.953788i
$587$	−18.6750	−	13.5682i	−0.770801	−	0.560019i	0.131403	−	0.991329i	$-0.458052\pi$
$587$	−18.6750	−	13.5682i	−0.770801	−	0.560019i	−0.902204	+	0.431310i	$0.858052\pi$
$588$	24.1401			0.995521
$589$		0			0
$590$	−6.77830			−0.279058
$591$	−12.5954	−	9.15107i	−0.518104	−	0.376425i
$592$	−22.3112	+	16.2101i	−0.916986	+	0.666229i
$593$	6.70571	+	20.6380i	0.275370	+	0.847503i	0.989121	+	0.147103i	$0.0469949\pi$
$593$	6.70571	+	20.6380i	0.275370	+	0.847503i	−0.713751	+	0.700400i	$0.753005\pi$
$594$	0.404507			0.0165971
$595$	−3.93877			−0.161474
$596$	7.28820	+	22.4308i	0.298536	+	0.918801i
$597$	4.64287	−	14.2893i	0.190020	−	0.584822i
$598$	−2.09501	+	6.44779i	−0.0856715	+	0.263670i
$599$	19.7187	+	14.3265i	0.805685	+	0.585364i	0.912576	−	0.408906i	$-0.134090\pi$
$599$	19.7187	+	14.3265i	0.805685	+	0.585364i	−0.106891	+	0.994271i	$0.534090\pi$
$600$	0.566124	+	1.74235i	0.0231119	+	0.0711312i
$601$	−6.85477	−	4.98028i	−0.279612	−	0.203150i	0.439136	−	0.898420i	$-0.355285\pi$
$601$	−6.85477	−	4.98028i	−0.279612	−	0.203150i	−0.718748	+	0.695271i	$0.755285\pi$
$602$	−17.8410	+	12.9623i	−0.727146	+	0.528302i
$603$	−0.336950	+	1.03703i	−0.0137217	+	0.0422310i
$604$	3.33048	−	2.41973i	0.135515	−	0.0984576i
$605$	22.1674	−	16.1055i	0.901232	−	0.654783i
$606$	14.9223	−	45.9261i	0.606176	−	1.86562i
$607$	−33.6673	+	24.4608i	−1.36652	+	0.992832i	−0.368515	+	0.929622i	$0.620134\pi$
$607$	−33.6673	+	24.4608i	−1.36652	+	0.992832i	−0.998000	+	0.0632099i	$0.979866\pi$
$608$	32.9962	+	23.9731i	1.33817	+	0.972239i
$609$	12.8944	+	39.6849i	0.522508	+	1.60811i
$610$	51.2865	+	37.2618i	2.07653	+	1.50869i
$611$	−4.99165	+	15.3627i	−0.201940	+	0.621509i
$612$	0.0972890	−	0.299425i	0.00393267	−	0.0121035i
$613$	12.3349	+	37.9628i	0.498201	+	1.53330i	0.811908	+	0.583785i	$0.198429\pi$
$613$	12.3349	+	37.9628i	0.498201	+	1.53330i	−0.313708	+	0.949520i	$0.601571\pi$
$614$	22.7267			0.917175
$615$	−4.11080			−0.165763
$616$	−0.0447404	−	0.137697i	−0.00180264	−	0.00554796i
$617$	7.37563	−	5.35871i	0.296932	−	0.215734i	−0.429337	−	0.903144i	$-0.641253\pi$
$617$	7.37563	−	5.35871i	0.296932	−	0.215734i	0.726269	+	0.687411i	$0.241253\pi$
$618$	14.1811	+	10.3031i	0.570446	+	0.414453i
$619$	13.4807			0.541834			0.270917	−	0.962603i	$-0.412673\pi$
$619$	13.4807			0.541834			0.270917	+	0.962603i	$0.412673\pi$
$620$		0			0
$621$	3.32894			0.133586
$622$	−7.40606	−	5.38082i	−0.296956	−	0.215751i
$623$	24.9713	−	18.1427i	1.00046	−	0.726874i
$624$	13.6315	+	41.9533i	0.545695	+	1.67948i
$625$	−29.5786			−1.18314
$626$	−51.3933			−2.05409
$627$	−0.149388	−	0.459768i	−0.00596596	−	0.0183613i
$628$	9.11231	−	28.0448i	0.363621	−	1.11911i
$629$	−0.738687	+	2.27345i	−0.0294534	+	0.0906482i
$630$	−7.35234	−	5.34179i	−0.292924	−	0.212822i
$631$	−7.99720	−	24.6128i	−0.318363	−	0.979822i	−0.974348	−	0.225047i	$-0.927746\pi$
$631$	−7.99720	−	24.6128i	−0.318363	−	0.979822i	0.655984	−	0.754774i	$-0.272254\pi$
$632$	2.05800	+	1.49522i	0.0818628	+	0.0594768i
$633$	24.0675	−	17.4861i	0.956597	−	0.695009i
$634$	−12.6374	+	38.8938i	−0.501894	+	1.54467i
$635$	37.0154	−	26.8933i	1.46891	−	1.06723i
$636$	−12.3212	+	8.95191i	−0.488569	+	0.354966i
$637$	−12.8265	+	39.4759i	−0.508204	+	1.56409i
$638$	−0.399749	+	0.290435i	−0.0158262	+	0.0114984i
$639$	3.60823	+	2.62153i	0.142739	+	0.103706i
$640$	−4.88467	−	15.0335i	−0.193083	−	0.594250i
$641$	29.5053	+	21.4369i	1.16539	+	0.846706i	0.990450	−	0.137873i	$-0.0440266\pi$
$641$	29.5053	+	21.4369i	1.16539	+	0.846706i	0.174941	+	0.984579i	$0.444027\pi$
$642$	16.6905	−	51.3680i	0.658721	−	2.02733i
$643$	11.1602	−	34.3474i	0.440114	−	1.35453i	−0.447641	−	0.894213i	$-0.647736\pi$
$643$	11.1602	−	34.3474i	0.440114	−	1.35453i	0.887754	−	0.460317i	$-0.152264\pi$
$644$	1.34581	+	4.14198i	0.0530323	+	0.163217i
$645$	13.9320			0.548571
$646$	4.33140			0.170417
$647$	1.11928	+	3.44480i	0.0440036	+	0.135429i	0.970645	−	0.240518i	$-0.0773174\pi$
$647$	1.11928	+	3.44480i	0.0440036	+	0.135429i	−0.926641	+	0.375947i	$0.877317\pi$
$648$	6.72500	−	4.88600i	0.264183	−	0.191940i
$649$	−0.0532463	−	0.0386857i	−0.00209010	−	0.00151855i
$650$	11.5138			0.451609
$651$		0			0
$652$	7.06902			0.276844
$653$	−21.4112	−	15.5562i	−0.837886	−	0.608760i	0.0838930	−	0.996475i	$-0.473265\pi$
$653$	−21.4112	−	15.5562i	−0.837886	−	0.608760i	−0.921779	+	0.387715i	$0.873265\pi$
$654$	−36.7974	+	26.7349i	−1.43889	+	1.04542i
$655$	−11.2492	−	34.6215i	−0.439543	−	1.35278i
$656$	4.12593			0.161090
$657$	1.10231			0.0430054
$658$	7.29041	+	22.4376i	0.284210	+	0.874708i
$659$	7.30662	−	22.4875i	0.284625	−	0.875987i	−0.701885	−	0.712290i	$-0.747658\pi$
$659$	7.30662	−	22.4875i	0.284625	−	0.875987i	0.986511	−	0.163697i	$-0.0523419\pi$
$660$	0.103313	−	0.317964i	0.00402145	−	0.0123767i
$661$	9.05352	+	6.57777i	0.352141	+	0.255846i	0.749767	−	0.661702i	$-0.230166\pi$
$661$	9.05352	+	6.57777i	0.352141	+	0.255846i	−0.397626	+	0.917548i	$0.630166\pi$
$662$	2.14886	+	6.61350i	0.0835177	+	0.257041i
$663$	3.09336	+	2.24745i	0.120136	+	0.0872839i
$664$	−9.91076	+	7.20059i	−0.384612	+	0.279437i
$665$	16.9936	−	52.3010i	0.658985	−	2.02815i
$666$	−4.46214	+	3.24194i	−0.172904	+	0.125622i
$667$	−3.28979	+	2.39017i	−0.127381	+	0.0925478i
$668$	−8.52456	+	26.2359i	−0.329825	+	1.01510i
$669$	24.9489	−	18.1264i	0.964581	−	0.700809i
$670$	−8.39322	−	6.09803i	−0.324258	−	0.235588i
$671$	0.190212	+	0.585414i	0.00734307	+	0.0225997i
$672$	42.5418	+	30.9084i	1.64108	+	1.19232i
$673$	15.9108	−	48.9684i	0.613317	−	1.88760i	0.189378	−	0.981904i	$-0.439353\pi$
$673$	15.9108	−	48.9684i	0.613317	−	1.88760i	0.423939	−	0.905691i	$-0.360647\pi$
$674$	−6.80747	+	20.9512i	−0.262214	+	0.807011i
$675$	−1.74704	−	5.37684i	−0.0672436	−	0.206955i
$676$	19.5978			0.753761
$677$	29.7254			1.14244			0.571221	−	0.820796i	$-0.306470\pi$
$677$	29.7254			1.14244			0.571221	+	0.820796i	$0.306470\pi$
$678$	1.76862	+	5.44326i	0.0679236	+	0.209047i
$679$	7.84286	−	5.69817i	0.300981	−	0.218676i
$680$	−0.663014	−	0.481708i	−0.0254254	−	0.0184727i
$681$	−0.745567			−0.0285702
$682$		0			0
$683$	23.6925			0.906569			0.453285	−	0.891366i	$-0.350252\pi$
$683$	23.6925			0.906569			0.453285	+	0.891366i	$0.350252\pi$
$684$	3.55617	+	2.58371i	0.135973	+	0.0987905i
$685$	−43.6102	+	31.6846i	−1.66626	+	1.21061i
$686$	2.78610	+	8.57475i	0.106374	+	0.327385i
$687$	48.1451			1.83685
$688$	−13.9833			−0.533107
$689$	−8.09218	−	24.9052i	−0.308288	−	0.948812i
$690$	1.93306	−	5.94936i	0.0735905	−	0.226488i
$691$	−5.21667	+	16.0553i	−0.198452	+	0.610771i	0.801467	+	0.598039i	$0.204053\pi$
$691$	−5.21667	+	16.0553i	−0.198452	+	0.610771i	−0.999919	+	0.0127326i	$0.995947\pi$
$692$	−14.4769	−	10.5181i	−0.550329	−	0.399838i
$693$	−0.0272685	−	0.0839238i	−0.00103584	−	0.00318800i
$694$	51.1073	+	37.1316i	1.94001	+	1.40950i
$695$	−0.277989	+	0.201971i	−0.0105447	+	0.00766119i
$696$	−2.68291	+	8.25715i	−0.101695	+	0.312986i
$697$	0.289329	−	0.210210i	0.0109591	−	0.00796226i
$698$	−11.4813	+	8.34166i	−0.434574	+	0.315736i
$699$	−6.13507	+	18.8818i	−0.232050	+	0.714176i
$700$	5.98375	−	4.34745i	0.226164	−	0.164318i
$701$	17.7479	+	12.8946i	0.670329	+	0.487022i	0.870135	−	0.492813i	$-0.164031\pi$
$701$	17.7479	+	12.8946i	0.670329	+	0.487022i	−0.199806	+	0.979835i	$0.564031\pi$
$702$	−13.8036	−	42.4831i	−0.520983	−	1.60342i
$703$	−27.0010	−	19.6173i	−1.01836	−	0.739882i
$704$	−0.0603582	+	0.185764i	−0.00227484	+	0.00700123i
$705$	4.60578	−	14.1751i	0.173464	−	0.533866i
$706$	9.39469	+	28.9139i	0.353574	+	1.08819i
$707$	53.3379			2.00598
$708$	4.22697			0.158859
$709$	−6.72394	−	20.6942i	−0.252523	−	0.777185i	−0.994308	−	0.106547i	$-0.966020\pi$
$709$	−6.72394	−	20.6942i	−0.252523	−	0.777185i	0.741785	−	0.670638i	$-0.233980\pi$
$710$	−34.3306	+	24.9426i	−1.28840	+	0.936080i
$711$	1.25432	+	0.911314i	0.0470405	+	0.0341769i
$712$	6.42227			0.240685
$713$		0			0
$714$	5.58445			0.208993
$715$	0.465067	+	0.337891i	0.0173925	+	0.0126364i
$716$	6.35156	−	4.61468i	0.237369	−	0.172459i
$717$	−6.48442	−	19.9570i	−0.242165	−	0.745308i
$718$	25.3840			0.947323
$719$	−32.2135			−1.20136			−0.600681	−	0.799489i	$-0.705104\pi$
$719$	−32.2135			−1.20136			−0.600681	+	0.799489i	$0.705104\pi$
$720$	−1.78072	−	5.48050i	−0.0663636	−	0.204246i
$721$	−5.98296	+	18.4137i	−0.222817	+	0.685761i
$722$	−7.59353	+	23.3705i	−0.282602	+	0.869759i
$723$	−20.5867	−	14.9571i	−0.765629	−	0.556262i
$724$	2.29771	+	7.07164i	0.0853939	+	0.262815i
$725$	5.58705	+	4.05923i	0.207498	+	0.150756i
$726$	−31.4293	+	22.8347i	−1.16645	+	0.847476i
$727$	−0.520765	+	1.60275i	−0.0193141	+	0.0594426i	−0.960249	−	0.279145i	$-0.909949\pi$
$727$	−0.520765	+	1.60275i	−0.0193141	+	0.0594426i	0.940935	+	0.338587i	$0.109949\pi$
$728$	−12.9348	+	9.39766i	−0.479394	+	0.348300i
$729$	−17.1505	+	12.4606i	−0.635204	+	0.461503i
$730$	−3.24097	+	9.97469i	−0.119954	+	0.369180i
$731$	−0.980570	+	0.712425i	−0.0362677	+	0.0263500i
$732$	−31.9824	−	23.2366i	−1.18210	−	0.858850i
$733$	−3.67519	−	11.3111i	−0.135746	−	0.417784i	0.859959	−	0.510363i	$-0.170489\pi$
$733$	−3.67519	−	11.3111i	−0.135746	−	0.417784i	−0.995705	+	0.0925789i	$0.970489\pi$
$734$	−13.0611	−	9.48947i	−0.482095	−	0.350263i
$735$	11.8350	−	36.4243i	0.436539	−	1.34353i
$736$	−1.58355	+	4.87366i	−0.0583704	+	0.179646i
$737$	−0.0311289	−	0.0958051i	−0.00114665	−	0.00352902i
$738$	0.825166			0.0303748
$739$	22.7613			0.837287			0.418643	−	0.908151i	$-0.362506\pi$
$739$	22.7613			0.837287			0.418643	+	0.908151i	$0.362506\pi$
$740$	−7.13253	−	21.9517i	−0.262197	−	0.806960i
$741$	−43.1890	+	31.3786i	−1.58659	+	1.15272i
$742$	−30.9421	−	22.4807i	−1.13592	−	0.825293i
$743$	30.8079			1.13023			0.565116	−	0.825011i	$-0.308831\pi$
$743$	30.8079			1.13023			0.565116	+	0.825011i	$0.308831\pi$
$744$		0			0
$745$	37.4182			1.37090
$746$	−32.2168	−	23.4069i	−1.17954	−	0.856987i
$747$	−6.04044	+	4.38863i	−0.221008	+	0.160572i
$748$	0.00898798	+	0.0276622i	0.000328633	+	0.00101143i
$749$	59.6581			2.17986
$750$	33.3793			1.21884
$751$	−5.04688	−	15.5327i	−0.184163	−	0.566796i	0.815770	−	0.578377i	$-0.196314\pi$
$751$	−5.04688	−	15.5327i	−0.184163	−	0.566796i	−0.999933	+	0.0115805i	$0.996314\pi$
$752$	−4.62273	+	14.2273i	−0.168574	+	0.518816i
$753$	8.24488	−	25.3751i	0.300460	−	0.924721i
$754$	44.1440	+	32.0725i	1.60763	+	1.16801i
$755$	−2.01826	−	6.21156i	−0.0734519	−	0.226062i
$756$	−23.2147	−	16.8665i	−0.844312	−	0.613428i
$757$	33.3019	−	24.1953i	1.21038	−	0.879392i	0.215115	−	0.976589i	$-0.430988\pi$
$757$	33.3019	−	24.1953i	1.21038	−	0.879392i	0.995265	+	0.0971964i	$0.0309875\pi$
$758$	−9.98189	+	30.7211i	−0.362558	+	1.11584i
$759$	0.0491397	−	0.0357021i	0.00178366	−	0.00129590i
$760$	9.25691	−	6.72554i	0.335783	−	0.243961i
$761$	13.8773	−	42.7098i	0.503050	−	1.54823i	−0.300975	−	0.953632i	$-0.597312\pi$
$761$	13.8773	−	42.7098i	0.503050	−	1.54823i	0.804024	−	0.594596i	$-0.202688\pi$
$762$	−52.4811	+	38.1298i	−1.90119	+	1.38130i
$763$	−40.6443	−	29.5298i	−1.47142	−	1.06905i
$764$	−7.09578	−	21.8386i	−0.256716	−	0.790091i
$765$	−0.404096	−	0.293593i	−0.0146101	−	0.0106149i
$766$	0.811756	−	2.49833i	0.0293300	−	0.0902683i
$767$	−2.24594	+	6.91229i	−0.0810961	+	0.249588i
$768$	11.8626	+	36.5092i	0.428053	+	1.31741i
$769$	9.25261			0.333658			0.166829	−	0.985986i	$-0.446647\pi$
$769$	9.25261			0.333658			0.166829	+	0.985986i	$0.446647\pi$
$770$	0.839588			0.0302567
$771$	3.97806	+	12.2432i	0.143267	+	0.440929i
$772$	9.19379	−	6.67968i	0.330892	−	0.240407i
$773$	5.12225	+	3.72153i	0.184234	+	0.133854i	0.676080	−	0.736828i	$-0.263677\pi$
$773$	5.12225	+	3.72153i	0.184234	+	0.133854i	−0.491845	+	0.870683i	$0.663677\pi$
$774$	−2.79659			−0.100521
$775$		0			0
$776$	2.01707			0.0724086
$777$	−34.8122	−	25.2925i	−1.24888	−	0.907364i
$778$	−24.5187	+	17.8139i	−0.879039	+	0.638660i
$779$	1.54298	+	4.74880i	0.0552829	+	0.170143i
$780$	−36.9195			−1.32193
$781$	−0.412035			−0.0147438
$782$	0.168172	+	0.517581i	0.00601382	+	0.0185086i
$783$	8.27937	−	25.4813i	0.295881	−	0.910627i
$784$	−11.8785	+	36.5583i	−0.424233	+	1.30565i
$785$	−37.8485	−	27.4986i	−1.35087	−	0.981466i
$786$	15.9493	+	49.0870i	0.568894	+	1.75087i
$787$	15.2075	+	11.0489i	0.542087	+	0.393850i	0.824860	−	0.565338i	$-0.191254\pi$
$787$	15.2075	+	11.0489i	0.542087	+	0.393850i	−0.282772	+	0.959187i	$0.591254\pi$
$788$	−10.5804	+	7.68711i	−0.376911	+	0.273842i
$789$	11.2674	−	34.6775i	0.401131	−	1.23455i
$790$	−11.9342	+	8.67072i	−0.424601	+	0.308490i
$791$	−5.11439	+	3.71582i	−0.181847	+	0.132119i
$792$	0.00567369	−	0.0174618i	0.000201606	−	0.000620479i
$793$	54.9918	−	39.9539i	1.95282	−	1.41880i
$794$	−28.2717	−	20.5406i	−1.00333	−	0.728959i
$795$	7.46663	+	22.9799i	0.264814	+	0.815014i
$796$	−10.2106	−	7.41847i	−0.361907	−	0.262941i
$797$	5.32030	−	16.3742i	0.188455	−	0.580003i	−0.811536	−	0.584302i	$-0.801368\pi$
$797$	5.32030	−	16.3742i	0.188455	−	0.580003i	0.999991	+	0.00429869i	$0.00136832\pi$
$798$	−24.0938	+	74.1532i	−0.852913	+	2.62500i
$799$	0.400692	+	1.23320i	0.0141755	+	0.0436276i
$800$	8.70289			0.307694
$801$	3.91427			0.138304
$802$	−8.74500	−	26.9143i	−0.308797	−	0.950379i
$803$	−0.0823876	+	0.0598581i	−0.00290739	+	0.00211235i
$804$	5.23404	+	3.80275i	0.184590	+	0.134113i
$805$	6.90950			0.243528
$806$		0			0
$807$	−9.76991			−0.343917
$808$	8.97838	+	6.52317i	0.315858	+	0.229484i
$809$	35.1526	−	25.5398i	1.23590	−	0.897933i	0.238581	−	0.971123i	$-0.423318\pi$
$809$	35.1526	−	25.5398i	1.23590	−	0.897933i	0.997318	+	0.0731898i	$0.0233179\pi$
$810$	14.8959	+	45.8448i	0.523387	+	1.61082i
$811$	−32.0197			−1.12436			−0.562182	−	0.827014i	$-0.690038\pi$
$811$	−32.0197			−1.12436			−0.562182	+	0.827014i	$0.690038\pi$
$812$	35.0518			1.23008
$813$	−12.1957	−	37.5346i	−0.427724	−	1.31640i
$814$	0.157459	−	0.484608i	0.00551892	−	0.0169855i
$815$	3.46567	−	10.6662i	0.121397	−	0.373621i
$816$	2.86473	+	2.08135i	0.100286	+	0.0728619i
$817$	−5.22933	−	16.0942i	−0.182951	−	0.563066i
$818$	−12.2699	−	8.91459i	−0.429006	−	0.311691i
$819$	−7.88352	+	5.72771i	−0.275472	+	0.200142i
$820$	−1.06709	+	3.28415i	−0.0372643	+	0.114688i
$821$	−38.6331	+	28.0686i	−1.34830	+	0.979599i	−0.349209	+	0.937045i	$0.613550\pi$
$821$	−38.6331	+	28.0686i	−1.34830	+	0.979599i	−0.999094	+	0.0425545i	$0.986450\pi$
$822$	61.8312	−	44.9230i	2.15661	−	1.56687i
$823$	−4.59190	+	14.1324i	−0.160063	+	0.492625i	−0.998639	−	0.0521611i	$-0.983389\pi$
$823$	−4.59190	+	14.1324i	−0.160063	+	0.492625i	0.838575	+	0.544786i	$0.183389\pi$
$824$	−3.25909	+	2.36787i	−0.113536	+	0.0824885i
$825$	−0.0834540	−	0.0606329i	−0.00290549	−	0.00211097i
$826$	3.28024	+	10.0956i	0.114134	+	0.351269i
$827$	16.2029	+	11.7721i	0.563429	+	0.409355i	0.832712	−	0.553706i	$-0.186787\pi$
$827$	16.2029	+	11.7721i	0.563429	+	0.409355i	−0.269283	+	0.963061i	$0.586787\pi$
$828$	−0.170667	+	0.525259i	−0.00593109	+	0.0182540i
$829$	−17.2234	+	53.0082i	−0.598194	+	1.84105i	−0.0600548	+	0.998195i	$0.519128\pi$
$829$	−17.2234	+	53.0082i	−0.598194	+	1.84105i	−0.538139	+	0.842856i	$0.680872\pi$
$830$	−21.9523	−	67.5623i	−0.761976	−	2.34512i
$831$	−55.4556			−1.92373
$832$	21.5694			0.747784
$833$	1.02961	+	3.16883i	0.0356740	+	0.109793i
$834$	0.394137	−	0.286358i	0.0136479	−	0.00991575i
$835$	35.4073	+	25.7249i	1.22532	+	0.890247i
$836$	−0.406091			−0.0140449
$837$		0			0
$838$	−2.75665			−0.0952268
$839$	10.2524	+	7.44881i	0.353952	+	0.257161i	0.750525	−	0.660842i	$-0.229801\pi$
$839$	10.2524	+	7.44881i	0.353952	+	0.257161i	−0.396573	+	0.918003i	$0.629801\pi$
$840$	11.9349	−	8.67119i	0.411792	−	0.299185i
$841$	1.15201	+	3.54552i	0.0397245	+	0.122259i
$842$	−24.0660			−0.829371
$843$	45.6541			1.57241
$844$	−7.72230	−	23.7668i	−0.265813	−	0.818087i
$845$	9.60804	−	29.5705i	0.330527	−	1.01726i
$846$	−0.924524	+	2.84539i	−0.0317858	+	0.0978266i
$847$	−34.7150	−	25.2219i	−1.19282	−	0.866636i
$848$	−7.49411	−	23.0645i	−0.257349	−	0.792038i
$849$	−26.9405	−	19.5734i	−0.924596	−	0.671758i
$850$	0.747728	−	0.543256i	0.0256469	−	0.0186335i
$851$	1.29583	−	3.98814i	0.0444203	−	0.136712i
$852$	21.4087	−	15.5543i	0.733449	−	0.532882i
$853$	−4.57334	+	3.32273i	−0.156588	+	0.113768i	−0.663320	−	0.748336i	$-0.730853\pi$
$853$	−4.57334	+	3.32273i	−0.156588	+	0.113768i	0.506732	+	0.862104i	$0.330853\pi$
$854$	30.6783	−	94.4180i	1.04979	−	3.23092i
$855$	5.64193	−	4.09910i	0.192950	−	0.140186i
$856$	10.0423	+	7.29613i	0.343237	+	0.249377i
$857$	−16.6553	−	51.2598i	−0.568935	−	1.75100i	−0.655961	−	0.754794i	$-0.727737\pi$
$857$	−16.6553	−	51.2598i	−0.568935	−	1.75100i	0.0870269	−	0.996206i	$-0.472263\pi$
$858$	−0.659380	−	0.479068i	−0.0225109	−	0.0163551i
$859$	−11.1945	+	34.4531i	−0.381951	+	1.17552i	0.556718	+	0.830702i	$0.312060\pi$
$859$	−11.1945	+	34.4531i	−0.381951	+	1.17552i	−0.938668	+	0.344821i	$0.887940\pi$
$860$	3.61648	−	11.1304i	0.123321	−	0.379543i
$861$	1.98935	+	6.12259i	0.0677969	+	0.208657i
$862$	66.4269			2.26251
$863$	−42.4456			−1.44486			−0.722432	−	0.691442i	$-0.756976\pi$
$863$	−42.4456			−1.44486			−0.722432	+	0.691442i	$0.756976\pi$
$864$	−10.4336	−	32.1115i	−0.354960	−	1.09245i
$865$	−22.9679	+	16.6871i	−0.780932	+	0.567380i
$866$	−45.1899	−	32.8324i	−1.53562	−	1.11569i
$867$	−31.4734			−1.06889
$868$		0			0
$869$	−0.143235			−0.00485890
$870$	−40.7315	−	29.5932i	−1.38093	−	1.00330i
$871$	−8.99960	+	6.53859i	−0.304940	+	0.221552i
$872$	−3.23020	−	9.94153i	−0.109388	−	0.336663i
$873$	1.22937			0.0416079
$874$	−7.59827			−0.257015
$875$	11.3931	+	35.0644i	0.385158	+	1.18539i
$876$	2.02108	−	6.22025i	0.0682860	−	0.210163i
$877$	4.29810	−	13.2282i	0.145136	−	0.446684i	−0.851892	−	0.523717i	$-0.824545\pi$
$877$	4.29810	−	13.2282i	0.145136	−	0.446684i	0.997029	+	0.0770333i	$0.0245448\pi$
$878$	28.3762	+	20.6165i	0.957651	+	0.695774i
$879$	−12.0093	−	36.9609i	−0.405064	−	1.24666i
$880$	0.430695	+	0.312919i	0.0145187	+	0.0105485i
$881$	−9.84833	+	7.15523i	−0.331799	+	0.241066i	−0.741193	−	0.671292i	$-0.765740\pi$
$881$	−9.84833	+	7.15523i	−0.331799	+	0.241066i	0.409395	+	0.912357i	$0.365740\pi$
$882$	−2.37565	+	7.31149i	−0.0799922	+	0.246191i
$883$	30.5610	−	22.2038i	1.02846	−	0.747219i	0.0604589	−	0.998171i	$-0.480744\pi$
$883$	30.5610	−	22.2038i	1.02846	−	0.747219i	0.968000	+	0.250952i	$0.0807436\pi$
$884$	2.59849	−	1.88791i	0.0873967	−	0.0634974i
$885$	2.07232	−	6.37795i	0.0696603	−	0.214392i
$886$	37.9503	−	27.5725i	1.27497	−	0.926317i
$887$	14.2437	+	10.3487i	0.478257	+	0.347474i	0.800650	−	0.599132i	$-0.204487\pi$
$887$	14.2437	+	10.3487i	0.478257	+	0.347474i	−0.322394	+	0.946606i	$0.604487\pi$
$888$	−2.76669	−	8.51499i	−0.0928440	−	0.285744i
$889$	−57.9677	−	42.1160i	−1.94417	−	1.41252i
$890$	−11.5085	+	35.4196i	−0.385767	+	1.18727i
$891$	−0.144636	+	0.445144i	−0.00484549	+	0.0149129i
$892$	−8.00511	−	24.6372i	−0.268031	−	0.824915i
$893$	−18.1039			−0.605823
$894$	−53.0522			−1.77433
$895$	−3.84902	−	11.8461i	−0.128659	−	0.395971i
$896$	−20.0269	+	14.5504i	−0.669051	+	0.486094i
$897$	−5.42645	−	3.94255i	−0.181184	−	0.131638i
$898$	−23.8397			−0.795541
$899$		0			0
$900$	0.937955			0.0312652
$901$	−1.70062	−	1.23557i	−0.0566560	−	0.0411630i
$902$	−0.0616734	+	0.0448083i	−0.00205350	+	0.00149195i
$903$	−6.74215	−	20.7502i	−0.224365	−	0.690523i
$904$	−1.31535			−0.0437478
$905$	11.7967			0.392134
$906$	2.86152	+	8.80685i	0.0950676	+	0.292588i
$907$	−14.9326	+	45.9579i	−0.495830	+	1.52601i	0.319830	+	0.947475i	$0.396374\pi$
$907$	−14.9326	+	45.9579i	−0.495830	+	1.52601i	−0.815660	+	0.578532i	$0.803626\pi$
$908$	−0.193535	+	0.595641i	−0.00642270	+	0.0197670i
$909$	5.47217	+	3.97576i	0.181500	+	0.131868i
$910$	−28.6505	−	88.1772i	−0.949755	−	2.92305i
$911$	45.6489	+	33.1659i	1.51242	+	1.09883i	0.965091	+	0.261915i	$0.0843540\pi$
$911$	45.6489	+	33.1659i	1.51242	+	1.09883i	0.547325	+	0.836920i	$0.315646\pi$
$912$	−39.9970	+	29.0595i	−1.32443	+	0.962257i
$913$	0.213153	−	0.656018i	0.00705434	−	0.0217110i
$914$	29.7162	−	21.5901i	0.982925	−	0.714137i
$915$	−50.7408	+	36.8653i	−1.67744	+	1.21873i
$916$	12.4976	−	38.4636i	0.412932	−	1.27087i
$917$	−46.1212	+	33.5090i	−1.52306	+	1.10656i
$918$	−2.90091	−	2.10763i	−0.0957442	−	0.0695623i
$919$	11.7240	+	36.0827i	0.386739	+	1.19026i	0.935211	+	0.354090i	$0.115209\pi$
$919$	11.7240	+	36.0827i	0.386739	+	1.19026i	−0.548473	+	0.836168i	$0.684791\pi$
$920$	1.16308	+	0.845026i	0.0383455	+	0.0278597i
$921$	−6.94820	+	21.3844i	−0.228951	+	0.704639i
$922$	20.2507	−	62.3252i	0.666921	−	2.05257i
$923$	14.0605	+	43.2737i	0.462807	+	1.42437i
$924$	−0.523570			−0.0172242
$925$	−7.12162			−0.234157
$926$	−7.17658	−	22.0873i	−0.235837	−	0.725832i
$927$	−1.98636	+	1.44317i	−0.0652406	+	0.0474001i
$928$	33.3669	+	24.2425i	1.09532	+	0.795798i
$929$	18.3179			0.600990			0.300495	−	0.953783i	$-0.402848\pi$
$929$	18.3179			0.600990			0.300495	+	0.953783i	$0.402848\pi$
$930$		0			0
$931$	−46.5196			−1.52462
$932$	13.4923	+	9.80273i	0.441955	+	0.321099i
$933$	7.32725	−	5.32356i	0.239883	−	0.174285i
$934$	22.0618	+	67.8991i	0.721883	+	2.22173i
$935$	0.0461450			0.00150910
$936$	−2.02753			−0.0662719
$937$	0.262421	+	0.807650i	0.00857293	+	0.0263848i	0.955251	−	0.295795i	$-0.0955845\pi$
$937$	0.262421	+	0.807650i	0.00857293	+	0.0263848i	−0.946679	+	0.322180i	$0.895584\pi$
$938$	−5.02061	+	15.4518i	−0.163929	+	0.504521i
$939$	15.7124	−	48.3578i	0.512754	−	1.57810i
$940$	−10.1291	−	7.35919i	−0.330374	−	0.240030i
$941$	1.34917	+	4.15233i	0.0439818	+	0.135362i	0.970636	−	0.240553i	$-0.0773286\pi$
$941$	1.34917	+	4.15233i	0.0439818	+	0.135362i	−0.926654	+	0.375915i	$0.877329\pi$
$942$	53.6623	+	38.9879i	1.74841	+	1.27030i
$943$	−0.507549	+	0.368756i	−0.0165281	+	0.0120083i
$944$	−2.07995	+	6.40142i	−0.0676965	+	0.208348i
$945$	−36.8306	+	26.7590i	−1.19810	+	0.870471i
$946$	0.209018	−	0.151861i	0.00679577	−	0.00493742i
$947$	−8.13419	+	25.0345i	−0.264326	+	0.813511i	0.727522	+	0.686084i	$0.240672\pi$
$947$	−8.13419	+	25.0345i	−0.264326	+	0.813511i	−0.991848	+	0.127427i	$0.959328\pi$
$948$	7.44222	−	5.40709i	0.241712	−	0.175614i
$949$	9.09798	+	6.61007i	0.295333	+	0.214572i
$950$	3.98760	+	12.2726i	0.129375	+	0.398175i
$951$	−32.7330	−	23.7819i	−1.06144	−	0.771180i
$952$	−0.396598	+	1.22060i	−0.0128538	+	0.0395600i
$953$	7.43162	−	22.8722i	0.240734	−	0.740903i	−0.755575	−	0.655062i	$-0.772642\pi$
$953$	7.43162	−	22.8722i	0.240734	−	0.740903i	0.996309	−	0.0858404i	$-0.0273575\pi$
$954$	−1.49879	−	4.61279i	−0.0485250	−	0.149345i
$955$	−36.4303			−1.17886
$956$	−17.6271			−0.570100
$957$	−0.151066	−	0.464933i	−0.00488326	−	0.0150291i
$958$	9.78377	−	7.10832i	0.316099	−	0.229660i
$959$	68.2953	+	49.6194i	2.20537	+	1.60229i
$960$	−19.9020			−0.642334
$961$		0			0
$962$	−56.2688			−1.81418
$963$	6.12059	+	4.44687i	0.197233	+	0.143298i
$964$	−17.2933	+	12.5643i	−0.556981	+	0.404670i
$965$	−5.57140	−	17.1470i	−0.179350	−	0.551982i
$966$	−9.79640			−0.315194
$967$	9.14301			0.294019			0.147010	−	0.989135i	$-0.453035\pi$
$967$	9.14301			0.294019			0.147010	+	0.989135i	$0.453035\pi$
$968$	−2.75897	−	8.49123i	−0.0886766	−	0.272918i
$969$	−1.32423	+	4.07557i	−0.0425405	+	0.130926i
$970$	−3.61454	+	11.1244i	−0.116056	+	0.357183i
$971$	13.9132	+	10.1085i	0.446494	+	0.324397i	0.788210	−	0.615406i	$-0.211008\pi$
$971$	13.9132	+	10.1085i	0.446494	+	0.324397i	−0.341716	+	0.939803i	$0.611008\pi$
$972$	−2.47106	−	7.60515i	−0.0792593	−	0.243935i
$973$	0.435342	+	0.316294i	0.0139564	+	0.0101399i
$974$	−0.0692589	+	0.0503195i	−0.00221920	+	0.00161234i
$975$	−3.52010	+	10.8338i	−0.112733	+	0.346958i
$976$	50.9275	−	37.0010i	1.63015	−	1.18437i
$977$	13.1169	−	9.52998i	0.419647	−	0.304891i	−0.357849	−	0.933779i	$-0.616490\pi$
$977$	13.1169	−	9.52998i	0.419647	−	0.304891i	0.777496	+	0.628888i	$0.216490\pi$
$978$	−4.91368	+	15.1227i	−0.157122	+	0.483572i
$979$	−0.292554	+	0.212553i	−0.00935008	+	0.00679323i
$980$	−26.0275	−	18.9101i	−0.831419	−	0.604061i
$981$	−1.96875	−	6.05920i	−0.0628574	−	0.193455i
$982$	−39.8560	−	28.9571i	−1.27186	−	0.924058i
$983$	5.34146	−	16.4393i	0.170366	−	0.524333i	−0.829025	−	0.559211i	$-0.811104\pi$
$983$	5.34146	−	16.4393i	0.170366	−	0.524333i	0.999392	+	0.0348777i	$0.0111042\pi$
$984$	−0.413920	+	1.27391i	−0.0131953	+	0.0406109i
$985$	6.41168	+	19.7331i	0.204293	+	0.628750i
$986$	4.38007			0.139490
$987$	−23.3412			−0.742959
$988$	13.8576	+	42.6494i	0.440870	+	1.35686i
$989$	1.72014	−	1.24976i	0.0546974	−	0.0397400i
$990$	0.0861371	+	0.0625823i	0.00273762	+	0.00198899i
$991$	−6.17867			−0.196272			−0.0981359	−	0.995173i	$-0.531288\pi$
$991$	−6.17867			−0.196272			−0.0981359	+	0.995173i	$0.531288\pi$
$992$		0			0
$993$	−6.87985			−0.218325
$994$	53.7631	+	39.0612i	1.70526	+	1.23894i
$995$	−16.1994	+	11.7695i	−0.513555	+	0.373119i
$996$	13.6895	+	42.1321i	0.433770	+	1.33501i
$997$	−7.14278			−0.226214			−0.113107	−	0.993583i	$-0.536080\pi$
$997$	−7.14278			−0.226214			−0.113107	+	0.993583i	$0.536080\pi$
$998$	29.8482			0.944828
$999$	8.53791	+	26.2770i	0.270127	+	0.831367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.s.374.13		64
31.2	even	5	inner	961.2.d.s.628.4		64
31.3	odd	30		961.2.g.w.235.13		128
31.4	even	5		961.2.a.l.1.4	yes	16
31.5	even	3		961.2.g.w.732.14		128
31.6	odd	6		961.2.g.w.816.14		128
31.7	even	15		961.2.c.l.439.3		32
31.8	even	5	inner	961.2.d.s.531.4		64
31.9	even	15		961.2.g.w.844.3		128
31.10	even	15		961.2.g.w.448.4		128
31.11	odd	30		961.2.c.l.521.4		32
31.12	odd	30		961.2.g.w.846.4		128
31.13	odd	30		961.2.g.w.338.14		128
31.14	even	15		961.2.g.w.547.4		128
31.15	odd	10	inner	961.2.d.s.388.14		64
31.16	even	5	inner	961.2.d.s.388.13		64
31.17	odd	30		961.2.g.w.547.3		128
31.18	even	15		961.2.g.w.338.13		128
31.19	even	15		961.2.g.w.846.3		128
31.20	even	15		961.2.c.l.521.3		32
31.21	odd	30		961.2.g.w.448.3		128
31.22	odd	30		961.2.g.w.844.4		128
31.23	odd	10	inner	961.2.d.s.531.3		64
31.24	odd	30		961.2.c.l.439.4		32
31.25	even	3		961.2.g.w.816.13		128
31.26	odd	6		961.2.g.w.732.13		128
31.27	odd	10		961.2.a.l.1.3	✓	16
31.28	even	15		961.2.g.w.235.14		128
31.29	odd	10	inner	961.2.d.s.628.3		64
31.30	odd	2	inner	961.2.d.s.374.14		64
93.35	odd	10		8649.2.a.bs.1.13		16
93.89	even	10		8649.2.a.bs.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.3	✓	16	31.27	odd	10
961.2.a.l.1.4	yes	16	31.4	even	5
961.2.c.l.439.3		32	31.7	even	15
961.2.c.l.439.4		32	31.24	odd	30
961.2.c.l.521.3		32	31.20	even	15
961.2.c.l.521.4		32	31.11	odd	30
961.2.d.s.374.13		64	1.1	even	1	trivial
961.2.d.s.374.14		64	31.30	odd	2	inner
961.2.d.s.388.13		64	31.16	even	5	inner
961.2.d.s.388.14		64	31.15	odd	10	inner
961.2.d.s.531.3		64	31.23	odd	10	inner
961.2.d.s.531.4		64	31.8	even	5	inner
961.2.d.s.628.3		64	31.29	odd	10	inner
961.2.d.s.628.4		64	31.2	even	5	inner
961.2.g.w.235.13		128	31.3	odd	30
961.2.g.w.235.14		128	31.28	even	15
961.2.g.w.338.13		128	31.18	even	15
961.2.g.w.338.14		128	31.13	odd	30
961.2.g.w.448.3		128	31.21	odd	30
961.2.g.w.448.4		128	31.10	even	15
961.2.g.w.547.3		128	31.17	odd	30
961.2.g.w.547.4		128	31.14	even	15
961.2.g.w.732.13		128	31.26	odd	6
961.2.g.w.732.14		128	31.5	even	3
961.2.g.w.816.13		128	31.25	even	3
961.2.g.w.816.14		128	31.6	odd	6
961.2.g.w.844.3		128	31.9	even	15
961.2.g.w.844.4		128	31.22	odd	30
961.2.g.w.846.3		128	31.19	even	15
961.2.g.w.846.4		128	31.12	odd	30
8649.2.a.bs.1.13		16	93.35	odd	10
8649.2.a.bs.1.14		16	93.89	even	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.52867 + 1.11064i) q^{2} +(-1.51240 + 1.09883i) q^{3} +(0.485270 + 1.49351i) q^{4} +2.49142 q^{5} -3.53237 q^{6} +(-1.20568 - 3.71070i) q^{7} +(0.250863 - 0.772076i) q^{8} +(0.152897 - 0.470567i) q^{9} +(3.80856 + 2.76708i) q^{10} +(0.0141253 + 0.0434731i) q^{11} +(-2.37503 - 1.72556i) q^{12} +(4.08371 - 2.96699i) q^{13} +(2.27818 - 7.01152i) q^{14} +(-3.76803 + 2.73763i) q^{15} +(3.78190 - 2.74771i) q^{16} +(0.125212 - 0.385364i) q^{17} +(0.756362 - 0.549529i) q^{18} +(4.57684 + 3.32527i) q^{19} +(1.20901 + 3.72095i) q^{20} +(5.90089 + 4.28724i) q^{21} +(-0.0266903 + 0.0821442i) q^{22} +(-0.219651 + 0.676016i) q^{23} +(0.468972 + 1.44335i) q^{24} +1.20716 q^{25} +9.53793 q^{26} +(-1.44723 - 4.45412i) q^{27} +(4.95688 - 3.60138i) q^{28} +(4.62825 + 3.36262i) q^{29} -8.80062 q^{30} +7.20939 q^{32} +(-0.0691324 - 0.0502277i) q^{33} +(0.619411 - 0.450028i) q^{34} +(-3.00385 - 9.24490i) q^{35} +0.776992 q^{36} -5.89948 q^{37} +(3.30329 + 10.1665i) q^{38} +(-2.91602 + 8.97458i) q^{39} +(0.625004 - 1.92356i) q^{40} +(0.714048 + 0.518786i) q^{41} +(4.25891 + 13.1076i) q^{42} +(-2.41999 - 1.75823i) q^{43} +(-0.0580728 + 0.0421924i) q^{44} +(0.380929 - 1.17238i) q^{45} +(-1.08659 + 0.789452i) q^{46} +(-2.58894 + 1.88097i) q^{47} +(-2.70050 + 8.31129i) q^{48} +(-6.65251 + 4.83333i) q^{49} +(1.84535 + 1.34073i) q^{50} +(0.234076 + 0.720412i) q^{51} +(6.41293 + 4.65927i) q^{52} +(1.60313 - 4.93392i) q^{53} +(2.73460 - 8.41624i) q^{54} +(0.0351919 + 0.108310i) q^{55} -3.16740 q^{56} -10.5759 q^{57} +(3.34040 + 10.2807i) q^{58} +(-1.16487 + 0.846324i) q^{59} +(-5.91719 - 4.29909i) q^{60} +13.4661 q^{61} -1.93048 q^{63} +(3.45699 + 2.51165i) q^{64} +(10.1742 - 7.39201i) q^{65} +(-0.0498957 - 0.153563i) q^{66} -2.20378 q^{67} +0.636306 q^{68} +(-0.410623 - 1.26377i) q^{69} +(5.67590 - 17.4686i) q^{70} +(-2.78550 + 8.57288i) q^{71} +(-0.324958 - 0.236096i) q^{72} +(0.688450 + 2.11883i) q^{73} +(-9.01836 - 6.55223i) q^{74} +(-1.82571 + 1.32646i) q^{75} +(-2.74531 + 8.44919i) q^{76} +(0.144285 - 0.104829i) q^{77} +(-14.4252 + 10.4805i) q^{78} +(-0.968314 + 2.98016i) q^{79} +(9.42228 - 6.84569i) q^{80} +(8.28396 + 6.01865i) q^{81} +(0.515357 + 1.58611i) q^{82} +(-12.2082 - 8.86980i) q^{83} +(-3.53951 + 10.8935i) q^{84} +(0.311956 - 0.960102i) q^{85} +(-1.74661 - 5.37550i) q^{86} -10.6947 q^{87} +0.0371080 q^{88} +(2.44465 + 7.52387i) q^{89} +(1.88441 - 1.36911i) q^{90} +(-15.9333 - 11.5762i) q^{91} -1.11623 q^{92} -6.04673 q^{94} +(11.4028 + 8.28463i) q^{95} +(-10.9035 + 7.92186i) q^{96} +(0.767803 + 2.36305i) q^{97} -15.5376 q^{98} +0.0226167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) \) 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more