LMFDB - Embedded newform 210.2.x.a.137.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(23,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("210.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.7
Character	$\chi$	$=$	210.137
Dual form			210.2.x.a.23.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.03943 - 1.38549i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.22506 + 0.221605i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-0.736347 - 2.54122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.839170 - 2.88024i) q^{9} +(2.20660 + 0.361834i) q^{10} +(-1.83587 - 1.05994i) q^{11} +(1.59292 - 0.680155i) q^{12} +(3.28206 - 3.28206i) q^{13} +(0.0535403 + 2.64521i) q^{14} +(-2.00576 + 3.31314i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.375258 + 1.40048i) q^{17} +(0.0651145 + 2.99929i) q^{18} +(-4.72549 + 2.72826i) q^{19} +(-2.03776 - 0.920615i) q^{20} +(-4.28622 - 1.62122i) q^{21} +(1.49898 + 1.49898i) q^{22} +(1.47375 - 5.50010i) q^{23} +(-1.71468 + 0.244702i) q^{24} +(4.90178 - 0.986167i) q^{25} +(-4.01969 + 2.32077i) q^{26} +(-4.86281 - 1.83115i) q^{27} +(0.632915 - 2.56893i) q^{28} +7.20525 q^{29} +(2.79492 - 2.68112i) q^{30} +(-0.528063 + 0.914632i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.37679 + 1.44185i) q^{33} -1.44989i q^{34} +(2.20156 + 5.49119i) q^{35} +(0.713378 - 2.91395i) q^{36} +(-1.66812 + 6.22550i) q^{37} +(5.27060 - 1.41225i) q^{38} +(-1.13579 - 7.95874i) q^{39} +(1.73005 + 1.41666i) q^{40} -1.86758i q^{41} +(3.72057 + 2.67533i) q^{42} +(1.79293 - 1.79293i) q^{43} +(-1.05994 - 1.83587i) q^{44} +(2.50548 + 6.22275i) q^{45} +(-2.84706 + 4.93126i) q^{46} +(10.7419 + 2.87830i) q^{47} +(1.71959 + 0.207427i) q^{48} +(-5.91559 + 3.74244i) q^{49} +(-4.99000 - 0.316111i) q^{50} +(2.33041 + 0.935787i) q^{51} +(4.48338 - 1.20132i) q^{52} +(6.47741 - 1.73562i) q^{53} +(4.22318 + 3.02734i) q^{54} +(4.31980 + 1.95159i) q^{55} +(-1.27624 + 2.31759i) q^{56} +(-1.13183 + 9.38296i) q^{57} +(-6.95973 - 1.86485i) q^{58} +(-2.63659 + 4.56671i) q^{59} +(-3.39361 + 1.86638i) q^{60} +(4.11857 + 7.13357i) q^{61} +(0.746794 - 0.746794i) q^{62} +(-6.70141 + 4.25337i) q^{63} +1.00000i q^{64} +(-6.57547 + 8.03011i) q^{65} +(3.63491 - 0.518738i) q^{66} +(9.10412 - 2.43944i) q^{67} +(-0.375258 + 1.40048i) q^{68} +(-6.08848 - 7.75883i) q^{69} +(-0.705321 - 5.87388i) q^{70} -1.75938i q^{71} +(-1.44326 + 2.63002i) q^{72} +(0.323412 + 1.20699i) q^{73} +(3.22256 - 5.58163i) q^{74} +(3.72874 - 7.81643i) q^{75} -5.45653 q^{76} +(-1.34170 + 5.44582i) q^{77} +(-0.962782 + 7.98152i) q^{78} +(13.8415 - 7.99137i) q^{79} +(-1.30445 - 1.81616i) q^{80} +(-7.59159 + 4.83403i) q^{81} +(-0.483365 + 1.80394i) q^{82} +(-9.47707 - 9.47707i) q^{83} +(-2.90136 - 3.54712i) q^{84} +(-1.14532 - 3.03300i) q^{85} +(-2.19589 + 1.26779i) q^{86} +(7.48935 - 9.98280i) q^{87} +(0.548664 + 2.04764i) q^{88} +(0.199936 + 0.346299i) q^{89} +(-0.809541 - 6.65918i) q^{90} +(-10.7572 - 5.92370i) q^{91} +(4.02635 - 4.02635i) q^{92} +(0.718330 + 1.68232i) q^{93} +(-9.63096 - 5.56044i) q^{94} +(9.90990 - 7.11774i) q^{95} +(-1.60731 - 0.645421i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(6.68263 - 2.08385i) q^{98} +(-1.51227 + 6.17721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43}+ \cdots + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.03943	−	1.38549i	0.600115	−	0.799914i
$3$	1.03943	−	1.38549i	0.600115	−	0.799914i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.22506	+	0.221605i	−0.995077	+	0.0991046i
$5$	−2.22506	+	0.221605i	−0.995077	+	0.0991046i
$6$	−1.36260	+	1.06926i	−0.556281	+	0.436522i
$7$	−0.736347	−	2.54122i	−0.278313	−	0.960490i
$7$	−0.736347	−	2.54122i	−0.278313	−	0.960490i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.839170	−	2.88024i	−0.279723	−	0.960081i
$10$	2.20660	+	0.361834i	0.697788	+	0.114422i
$11$	−1.83587	−	1.05994i	−0.553535	−	0.319583i	0.197012	−	0.980401i	$-0.436876\pi$
$11$	−1.83587	−	1.05994i	−0.553535	−	0.319583i	−0.750546	+	0.660818i	$0.770210\pi$
$12$	1.59292	−	0.680155i	0.459836	−	0.196344i
$13$	3.28206	−	3.28206i	0.910280	−	0.910280i	−0.0860135	−	0.996294i	$-0.527413\pi$
$13$	3.28206	−	3.28206i	0.910280	−	0.910280i	0.996294	+	0.0860135i	$0.0274128\pi$
$14$	0.0535403	+	2.64521i	0.0143092	+	0.706962i
$15$	−2.00576	+	3.31314i	−0.517886	+	0.855450i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.375258	+	1.40048i	0.0910134	+	0.339667i	0.996385	−	0.0849537i	$-0.0270742\pi$
$17$	0.375258	+	1.40048i	0.0910134	+	0.339667i	−0.905371	+	0.424620i	$0.860408\pi$
$18$	0.0651145	+	2.99929i	0.0153476	+	0.706940i
$19$	−4.72549	+	2.72826i	−1.08410	+	0.625906i	−0.932000	−	0.362458i	$-0.881937\pi$
$19$	−4.72549	+	2.72826i	−1.08410	+	0.625906i	−0.152102	+	0.988365i	$0.548604\pi$
$20$	−2.03776	−	0.920615i	−0.455657	−	0.205856i
$21$	−4.28622	−	1.62122i	−0.935329	−	0.353779i
$22$	1.49898	+	1.49898i	0.319583	+	0.319583i
$23$	1.47375	−	5.50010i	0.307298	−	1.14685i	−0.623652	−	0.781702i	$-0.714352\pi$
$23$	1.47375	−	5.50010i	0.307298	−	1.14685i	0.930949	−	0.365148i	$-0.118982\pi$
$24$	−1.71468	+	0.244702i	−0.350007	+	0.0499496i
$25$	4.90178	−	0.986167i	0.980357	−	0.197233i
$26$	−4.01969	+	2.32077i	−0.788326	+	0.455140i
$27$	−4.86281	−	1.83115i	−0.935848	−	0.352405i
$28$	0.632915	−	2.56893i	0.119610	−	0.485483i
$29$	7.20525			1.33798			0.668990	−	0.743271i	$-0.266727\pi$
$29$	7.20525			1.33798			0.668990	+	0.743271i	$0.266727\pi$
$30$	2.79492	−	2.68112i	0.510281	−	0.489503i
$31$	−0.528063	+	0.914632i	−0.0948429	+	0.164273i	−0.909543	−	0.415610i	$-0.863568\pi$
$31$	−0.528063	+	0.914632i	−0.0948429	+	0.164273i	0.814700	+	0.579882i	$0.196902\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−3.37679	+	1.44185i	−0.587824	+	0.250993i
$34$		−	1.44989i		−	0.248653i
$35$	2.20156	+	5.49119i	0.372132	+	0.928180i
$36$	0.713378	−	2.91395i	0.118896	−	0.485658i
$37$	−1.66812	+	6.22550i	−0.274237	+	1.02347i	0.682114	+	0.731246i	$0.261061\pi$
$37$	−1.66812	+	6.22550i	−0.274237	+	1.02347i	−0.956351	+	0.292221i	$0.905606\pi$
$38$	5.27060	−	1.41225i	0.855004	−	0.229098i
$39$	−1.13579	−	7.95874i	−0.181872	−	1.27442i
$40$	1.73005	+	1.41666i	0.273545	+	0.223993i
$41$		−	1.86758i		−	0.291667i	−0.989309	−	0.145833i	$-0.953414\pi$
$41$		−	1.86758i		−	0.291667i	0.989309	−	0.145833i	$-0.0465863\pi$
$42$	3.72057	+	2.67533i	0.574096	+	0.412813i
$43$	1.79293	−	1.79293i	0.273420	−	0.273420i	−0.557056	−	0.830475i	$-0.688069\pi$
$43$	1.79293	−	1.79293i	0.273420	−	0.273420i	0.830475	+	0.557056i	$0.188069\pi$
$44$	−1.05994	−	1.83587i	−0.159792	−	0.276767i
$45$	2.50548	+	6.22275i	0.373495	+	0.927632i
$46$	−2.84706	+	4.93126i	−0.419776	+	0.727074i
$47$	10.7419	+	2.87830i	1.56687	+	0.419843i	0.934832	−	0.355091i	$-0.115550\pi$
$47$	10.7419	+	2.87830i	1.56687	+	0.419843i	0.632042	+	0.774934i	$0.282217\pi$
$48$	1.71959	+	0.207427i	0.248201	+	0.0299396i
$49$	−5.91559	+	3.74244i	−0.845084	+	0.534634i
$50$	−4.99000	−	0.316111i	−0.705692	−	0.0447048i
$51$	2.33041	+	0.935787i	0.326323	+	0.131036i
$52$	4.48338	−	1.20132i	0.621733	−	0.166593i
$53$	6.47741	−	1.73562i	0.889741	−	0.238405i	0.215136	−	0.976584i	$-0.430981\pi$
$53$	6.47741	−	1.73562i	0.889741	−	0.238405i	0.674605	+	0.738179i	$0.264314\pi$
$54$	4.22318	+	3.02734i	0.574701	+	0.411969i
$55$	4.31980	+	1.95159i	0.582482	+	0.263152i
$56$	−1.27624	+	2.31759i	−0.170544	+	0.309701i
$57$	−1.13183	+	9.38296i	−0.149915	+	1.24280i
$58$	−6.95973	−	1.86485i	−0.913858	−	0.244867i
$59$	−2.63659	+	4.56671i	−0.343255	+	0.594535i	−0.985035	−	0.172354i	$-0.944863\pi$
$59$	−2.63659	+	4.56671i	−0.343255	+	0.594535i	0.641780	+	0.766889i	$0.278196\pi$
$60$	−3.39361	+	1.86638i	−0.438114	+	0.240949i
$61$	4.11857	+	7.13357i	0.527328	+	0.913360i	0.999493	+	0.0318490i	$0.0101396\pi$
$61$	4.11857	+	7.13357i	0.527328	+	0.913360i	−0.472164	+	0.881511i	$0.656527\pi$
$62$	0.746794	−	0.746794i	0.0948429	−	0.0948429i
$63$	−6.70141	+	4.25337i	−0.844298	+	0.535874i
$64$			1.00000i			0.125000i
$65$	−6.57547	+	8.03011i	−0.815586	+	0.996012i
$66$	3.63491	−	0.518738i	0.447426	−	0.0638522i
$67$	9.10412	−	2.43944i	1.11225	−	0.298025i	0.344504	−	0.938785i	$-0.388047\pi$
$67$	9.10412	−	2.43944i	1.11225	−	0.298025i	0.767742	+	0.640760i	$0.221380\pi$
$68$	−0.375258	+	1.40048i	−0.0455067	+	0.169833i
$69$	−6.08848	−	7.75883i	−0.732967	−	0.934054i
$70$	−0.705321	−	5.87388i	−0.0843020	−	0.702064i
$71$		−	1.75938i		−	0.208800i	−0.994535	−	0.104400i	$-0.966708\pi$
$71$		−	1.75938i		−	0.208800i	0.994535	−	0.104400i	$-0.0332922\pi$
$72$	−1.44326	+	2.63002i	−0.170089	+	0.309951i
$73$	0.323412	+	1.20699i	0.0378525	+	0.141268i	0.982266	−	0.187492i	$-0.0600360\pi$
$73$	0.323412	+	1.20699i	0.0378525	+	0.141268i	−0.944414	+	0.328760i	$0.893369\pi$
$74$	3.22256	−	5.58163i	0.374615	−	0.648852i
$75$	3.72874	−	7.81643i	0.430557	−	0.902563i
$76$	−5.45653			−0.625906
$77$	−1.34170	+	5.44582i	−0.152901	+	0.620609i
$78$	−0.962782	+	7.98152i	−0.109014	+	0.903729i
$79$	13.8415	−	7.99137i	1.55728	−	0.899099i	0.559770	−	0.828648i	$-0.310890\pi$
$79$	13.8415	−	7.99137i	1.55728	−	0.899099i	0.997515	−	0.0704506i	$-0.0224437\pi$
$80$	−1.30445	−	1.81616i	−0.145841	−	0.203052i
$81$	−7.59159	+	4.83403i	−0.843510	+	0.537114i
$82$	−0.483365	+	1.80394i	−0.0533787	+	0.199212i
$83$	−9.47707	−	9.47707i	−1.04024	−	1.04024i	−0.999156	−	0.0410882i	$-0.986918\pi$
$83$	−9.47707	−	9.47707i	−1.04024	−	1.04024i	−0.0410882	−	0.999156i	$-0.513082\pi$
$84$	−2.90136	−	3.54712i	−0.316565	−	0.387023i
$85$	−1.14532	−	3.03300i	−0.124228	−	0.328975i
$86$	−2.19589	+	1.26779i	−0.236788	+	0.136710i
$87$	7.48935	−	9.98280i	0.802943	−	1.07027i
$88$	0.548664	+	2.04764i	0.0584878	+	0.218280i
$89$	0.199936	+	0.346299i	0.0211931	+	0.0367076i	0.876427	−	0.481534i	$-0.159920\pi$
$89$	0.199936	+	0.346299i	0.0211931	+	0.0367076i	−0.855234	+	0.518242i	$0.826587\pi$
$90$	−0.809541	−	6.65918i	−0.0853331	−	0.701939i
$91$	−10.7572	−	5.92370i	−1.12766	−	0.620973i
$92$	4.02635	−	4.02635i	0.419776	−	0.419776i
$93$	0.718330	+	1.68232i	0.0744873	+	0.174449i
$94$	−9.63096	−	5.56044i	−0.993358	−	0.573516i
$95$	9.90990	−	7.11774i	1.01673	−	0.730264i
$96$	−1.60731	−	0.645421i	−0.164045	−	0.0658730i
$97$	−8.63390	−	8.63390i	−0.876640	−	0.876640i	0.116546	−	0.993185i	$-0.462818\pi$
$97$	−8.63390	−	8.63390i	−0.876640	−	0.876640i	−0.993185	+	0.116546i	$0.962818\pi$
$98$	6.68263	−	2.08385i	0.675048	−	0.210500i
$99$	−1.51227	+	6.17721i	−0.151989	+	0.620833i
$100$	4.73815	+	1.59685i	0.473815	+	0.159685i
$101$	−3.82984	−	2.21116i	−0.381084	−	0.220019i	0.297206	−	0.954813i	$-0.403945\pi$
$101$	−3.82984	−	2.21116i	−0.381084	−	0.220019i	−0.678290	+	0.734795i	$0.737279\pi$
$102$	−2.00880	−	1.50705i	−0.198901	−	0.149221i
$103$	−10.3424	−	2.77123i	−1.01906	−	0.273057i	−0.289652	−	0.957132i	$-0.593539\pi$
$103$	−10.3424	−	2.77123i	−1.01906	−	0.273057i	−0.729412	+	0.684075i	$0.760206\pi$
$104$	−4.64154			−0.455140
$105$	9.89636	+	2.65746i	0.965786	+	0.259342i
$106$	−6.70591			−0.651335
$107$	−10.3122	−	2.76314i	−0.996917	−	0.267123i	−0.276763	−	0.960938i	$-0.589262\pi$
$107$	−10.3122	−	2.76314i	−0.996917	−	0.267123i	−0.720153	+	0.693815i	$0.755928\pi$
$108$	−3.29574	−	4.01722i	−0.317133	−	0.386558i
$109$	7.42120	+	4.28463i	0.710822	+	0.410393i	0.811365	−	0.584539i	$-0.198725\pi$
$109$	7.42120	+	4.28463i	0.710822	+	0.410393i	−0.100543	+	0.994933i	$0.532058\pi$
$110$	−3.66750	−	3.00314i	−0.349682	−	0.286338i
$111$	6.89149	+	8.78214i	0.654111	+	0.833564i
$112$	1.83259	−	1.90830i	0.173163	−	0.180318i
$113$	7.12484	+	7.12484i	0.670249	+	0.670249i	0.957773	−	0.287524i	$-0.0928322\pi$
$113$	7.12484	+	7.12484i	0.670249	+	0.670249i	−0.287524	+	0.957773i	$0.592832\pi$
$114$	3.52176	−	8.77030i	0.329843	−	0.821414i
$115$	−2.06033	+	12.5646i	−0.192127	+	1.17166i
$116$	6.23993	+	3.60262i	0.579363	+	0.334495i
$117$	−12.2073	−	6.69893i	−1.12857	−	0.619316i
$118$	3.72870	−	3.72870i	0.343255	−	0.343255i
$119$	3.28261	−	1.98485i	0.300916	−	0.181951i
$120$	3.76103	−	0.924457i	0.343334	−	0.0843910i
$121$	−3.25306	−	5.63447i	−0.295733	−	0.512224i
$122$	−2.13193	−	7.95646i	−0.193016	−	0.720344i
$123$	−2.58751	−	1.94122i	−0.233308	−	0.175034i
$124$	−0.914632	+	0.528063i	−0.0821364	+	0.0474215i
$125$	−10.6882	+	3.28054i	−0.955984	+	0.293420i
$126$	7.57391	−	2.37399i	0.674738	−	0.211492i
$127$	−11.2870	−	11.2870i	−1.00156	−	1.00156i	−0.999999	−	0.00155629i	$-0.999505\pi$
$127$	−11.2870	−	11.2870i	−1.00156	−	1.00156i	−0.00155629	−	0.999999i	$-0.500495\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−0.620464	−	4.34772i	−0.0546288	−	0.382795i
$130$	8.42976	−	6.05463i	0.739339	−	0.531026i
$131$	5.01434	−	2.89503i	0.438105	−	0.252940i	−0.264689	−	0.964334i	$-0.585269\pi$
$131$	5.01434	−	2.89503i	0.438105	−	0.252940i	0.702793	+	0.711394i	$0.251936\pi$
$132$	−3.64531	−	0.439721i	−0.317283	−	0.0382728i
$133$	10.4127	+	9.99956i	0.902897	+	0.867072i
$134$	−9.42528			−0.814220
$135$	11.2258	+	2.99679i	0.966166	+	0.257923i
$136$	0.724943	−	1.25564i	0.0621633	−	0.107670i
$137$	2.90062	+	10.8253i	0.247816	+	0.924864i	0.971947	+	0.235201i	$0.0755747\pi$
$137$	2.90062	+	10.8253i	0.247816	+	0.924864i	−0.724130	+	0.689663i	$0.757759\pi$
$138$	3.87289	+	9.07027i	0.329682	+	0.772113i
$139$			20.1333i			1.70768i	0.520535	+	0.853841i	$0.325733\pi$
$139$			20.1333i			1.70768i	−0.520535	+	0.853841i	$0.674267\pi$
$140$	−0.838986	+	5.85629i	−0.0709072	+	0.494947i
$141$	15.1534	−	11.8911i	1.27614	−	1.00141i
$142$	−0.455361	+	1.69943i	−0.0382131	+	0.142613i
$143$	−9.50422	+	2.54665i	−0.794782	+	0.212961i
$144$	2.07478	−	2.16686i	0.172898	−	0.180572i
$145$	−16.0321	+	1.59672i	−1.33139	+	0.132600i
$146$		−	1.24957i		−	0.103415i
$147$	−0.963730	+	12.0860i	−0.0794871	+	0.996836i
$148$	−4.55738	+	4.55738i	−0.374615	+	0.374615i
$149$	5.90510	+	10.2279i	0.483765	+	0.837905i	0.999826	−	0.0186464i	$-0.00593567\pi$
$149$	5.90510	+	10.2279i	0.483765	+	0.837905i	−0.516061	+	0.856552i	$0.672602\pi$
$150$	−5.62472	+	6.58502i	−0.459257	+	0.537665i
$151$	4.33354	−	7.50591i	0.352658	−	0.610822i	−0.634056	−	0.773287i	$-0.718611\pi$
$151$	4.33354	−	7.50591i	0.352658	−	0.610822i	0.986714	+	0.162465i	$0.0519445\pi$
$152$	5.27060	+	1.41225i	0.427502	+	0.114549i
$153$	3.71882	−	2.25608i	0.300649	−	0.182393i
$154$	2.70547	−	4.91300i	0.218013	−	0.395901i
$155$	0.972285	−	2.15213i	0.0780958	−	0.172863i
$156$	2.99575	−	7.46037i	0.239852	−	0.597308i
$157$	−16.8625	+	4.51828i	−1.34577	+	0.360598i	−0.858572	−	0.512693i	$-0.828648\pi$
$157$	−16.8625	+	4.51828i	−1.34577	+	0.360598i	−0.487198	+	0.873291i	$0.661981\pi$
$158$	−15.4381	+	4.13664i	−1.22819	+	0.329093i
$159$	4.32813	−	10.7784i	0.343243	−	0.854786i
$160$	0.789941	+	2.09189i	0.0624504	+	0.165378i
$161$	−15.0621	+	0.304865i	−1.18706	+	0.0240267i
$162$	8.58405	−	2.70446i	0.674427	−	0.212483i
$163$	−5.03620	−	1.34945i	−0.394466	−	0.105697i	0.0561330	−	0.998423i	$-0.482123\pi$
$163$	−5.03620	−	1.34945i	−0.394466	−	0.105697i	−0.450599	+	0.892726i	$0.648790\pi$
$164$	0.933789	−	1.61737i	0.0729167	−	0.126295i
$165$	7.19404	−	3.95650i	0.560055	−	0.308013i
$166$	6.70130	+	11.6070i	0.520122	+	0.900877i
$167$	5.99458	−	5.99458i	0.463874	−	0.463874i	−0.436049	−	0.899923i	$-0.643623\pi$
$167$	5.99458	−	5.99458i	0.463874	−	0.463874i	0.899923	+	0.436049i	$0.143623\pi$
$168$	1.88444	+	4.17719i	0.145388	+	0.322277i
$169$		−	8.54387i		−	0.657221i
$170$	0.321301	+	3.22608i	0.0246427	+	0.247429i
$171$	11.8235	+	11.3211i	0.904169	+	0.865744i
$172$	2.44919	−	0.656259i	0.186749	−	0.0500393i
$173$	1.29750	−	4.84235i	0.0986474	−	0.368157i	−0.898900	−	0.438154i	$-0.855632\pi$
$173$	1.29750	−	4.84235i	0.0986474	−	0.368157i	0.997547	+	0.0699972i	$0.0222991\pi$
$174$	−9.81790	+	7.70426i	−0.744293	+	0.584059i
$175$	−6.11548	−	11.7303i	−0.462287	−	0.886731i
$176$		−	2.11988i		−	0.159792i
$177$	3.58658	+	8.39975i	0.269584	+	0.631364i
$178$	−0.103494	−	0.386246i	−0.00775723	−	0.0289504i
$179$	−4.04588	+	7.00767i	−0.302403	+	0.523778i	−0.976680	−	0.214701i	$-0.931122\pi$
$179$	−4.04588	+	7.00767i	−0.302403	+	0.523778i	0.674277	+	0.738479i	$0.264456\pi$
$180$	−0.941565	+	6.64180i	−0.0701801	+	0.495050i
$181$	10.6946			0.794924			0.397462	−	0.917619i	$-0.369891\pi$
$181$	10.6946			0.794924			0.397462	+	0.917619i	$0.369891\pi$
$182$	8.85747	+	8.50602i	0.656559	+	0.630508i
$183$	14.1645	+	1.70861i	1.04707	+	0.126304i
$184$	−4.93126	+	2.84706i	−0.363537	+	0.209888i
$185$	2.33206	−	14.2218i	0.171457	−	1.04561i
$186$	−0.258436	−	1.81092i	−0.0189495	−	0.132783i
$187$	0.795501	−	2.96885i	0.0581728	−	0.217104i
$188$	7.86365	+	7.86365i	0.573516	+	0.573516i
$189$	−1.07264	+	13.7058i	−0.0780228	+	0.996952i
$190$	−11.4144	+	4.31034i	−0.828090	+	0.312705i
$191$	0.647671	−	0.373933i	0.0468638	−	0.0270569i	−0.476385	−	0.879237i	$-0.658053\pi$
$191$	0.647671	−	0.373933i	0.0468638	−	0.0270569i	0.523249	+	0.852180i	$0.324720\pi$
$192$	1.38549	+	1.03943i	0.0999892	+	0.0750144i
$193$	2.39615	+	8.94254i	0.172478	+	0.643698i	0.996967	+	0.0778200i	$0.0247960\pi$
$193$	2.39615	+	8.94254i	0.172478	+	0.643698i	−0.824489	+	0.565878i	$0.808537\pi$
$194$	6.10509	+	10.5743i	0.438320	+	0.759192i
$195$	4.29090	+	17.4570i	0.307278	+	1.25012i
$196$	−6.99427	+	0.283250i	−0.499590	+	0.0202322i
$197$	−2.71376	+	2.71376i	−0.193348	+	0.193348i	−0.797141	−	0.603793i	$-0.793655\pi$
$197$	−2.71376	+	2.71376i	−0.193348	+	0.193348i	0.603793	+	0.797141i	$0.293655\pi$
$198$	3.05952	−	5.57532i	0.217431	−	0.396221i
$199$	−4.85488	−	2.80297i	−0.344153	−	0.198697i	0.317954	−	0.948106i	$-0.397004\pi$
$199$	−4.85488	−	2.80297i	−0.344153	−	0.198697i	−0.662107	+	0.749409i	$0.730338\pi$
$200$	−4.16341	−	2.76876i	−0.294397	−	0.195781i
$201$	6.08327	−	15.1493i	0.429081	−	1.06855i
$202$	3.12705	+	3.12705i	0.220019	+	0.220019i
$203$	−5.30556	−	18.3101i	−0.372377	−	1.28512i
$204$	1.55030	+	1.97562i	0.108543	+	0.138321i
$205$	0.413864	+	4.15547i	0.0289055	+	0.290231i
$206$	9.27271	+	5.35360i	0.646060	+	0.373003i
$207$	−17.0783	+	0.370770i	−1.18703	+	0.0257703i
$208$	4.48338	+	1.20132i	0.310867	+	0.0832964i
$209$	11.5672			0.800117
$210$	−8.87135	−	5.12828i	−0.612181	−	0.353885i
$211$	14.8448			1.02196			0.510978	−	0.859594i	$-0.329283\pi$
$211$	14.8448			1.02196			0.510978	+	0.859594i	$0.329283\pi$
$212$	6.47741	+	1.73562i	0.444870	+	0.119203i
$213$	−2.43761	−	1.82875i	−0.167022	−	0.125304i
$214$	9.24565	+	5.33798i	0.632020	+	0.364897i
$215$	−3.59206	+	4.38670i	−0.244976	+	0.299171i
$216$	2.14371	+	4.73334i	0.145861	+	0.322063i
$217$	2.71312	+	0.668438i	0.184178	+	0.0453765i
$218$	−6.05939	−	6.05939i	−0.410393	−	0.410393i
$219$	2.00844	+	0.806498i	0.135718	+	0.0544981i
$220$	2.76526	+	3.85003i	0.186434	+	0.259569i
$221$	5.82809	+	3.36485i	0.392040	+	0.226344i
$222$	−4.38368	−	10.2665i	−0.294213	−	0.689045i
$223$	5.02812	−	5.02812i	0.336708	−	0.336708i	−0.518419	−	0.855127i	$-0.673479\pi$
$223$	5.02812	−	5.02812i	0.336708	−	0.336708i	0.855127	+	0.518419i	$0.173479\pi$
$224$	−2.26405	+	1.36897i	−0.151273	+	0.0914683i
$225$	−6.95383	−	13.2908i	−0.463589	−	0.886051i
$226$	−5.03803	−	8.72612i	−0.335124	−	0.580453i
$227$	−3.01201	−	11.2410i	−0.199914	−	0.746089i	−0.990940	−	0.134307i	$-0.957119\pi$
$227$	−3.01201	−	11.2410i	−0.199914	−	0.746089i	0.791026	−	0.611783i	$-0.209547\pi$
$228$	−5.67168	+	7.55997i	−0.375616	+	0.500671i
$229$	−3.58186	+	2.06799i	−0.236696	+	0.136657i	−0.613657	−	0.789572i	$-0.710302\pi$
$229$	−3.58186	+	2.06799i	−0.236696	+	0.136657i	0.376961	+	0.926229i	$0.376969\pi$
$230$	5.24209	−	11.6033i	0.345653	−	0.765096i
$231$	6.15053	+	7.51947i	0.404675	+	0.494745i
$232$	−5.09488	−	5.09488i	−0.334495	−	0.334495i
$233$	5.87626	−	21.9305i	0.384967	−	1.43671i	−0.453253	−	0.891382i	$-0.649737\pi$
$233$	5.87626	−	21.9305i	0.384967	−	1.43671i	0.838220	−	0.545333i	$-0.183597\pi$
$234$	10.0576	+	9.63016i	0.657485	+	0.629543i
$235$	−24.5393	−	4.02392i	−1.60077	−	0.262491i
$236$	−4.56671	+	2.63659i	−0.297267	+	0.171627i
$237$	3.31526	−	27.4837i	0.215349	−	1.78526i
$238$	−3.68448	+	1.06762i	−0.238829	+	0.0692034i
$239$	10.6159			0.686682			0.343341	−	0.939211i	$-0.388441\pi$
$239$	10.6159			0.686682			0.343341	+	0.939211i	$0.388441\pi$
$240$	−3.87215	−	0.0804705i	−0.249946	−	0.00519435i
$241$	10.0635	−	17.4304i	0.648245	−	1.12279i	−0.335297	−	0.942112i	$-0.608837\pi$
$241$	10.0635	−	17.4304i	0.648245	−	1.12279i	0.983542	−	0.180680i	$-0.0578300\pi$
$242$	1.68391	+	6.28443i	0.108246	+	0.403979i
$243$	−1.19343	+	15.5427i	−0.0765583	+	0.997065i
$244$			8.23713i			0.527328i
$245$	12.3332	−	9.63806i	0.787939	−	0.615753i
$246$	1.99692	+	2.54477i	0.127319	+	0.162249i
$247$	−6.55502	+	24.4637i	−0.417086	+	1.55659i
$248$	1.02014	−	0.273346i	0.0647789	−	0.0173575i
$249$	−22.9811	+	3.27964i	−1.45637	+	0.207839i
$250$	11.1731	−	0.402441i	0.706649	−	0.0254526i
$251$			17.8395i			1.12602i	0.826450	+	0.563010i	$0.190357\pi$
$251$			17.8395i			1.12602i	−0.826450	+	0.563010i	$0.809643\pi$
$252$	−7.93027	+	0.332825i	−0.499560	+	0.0209660i
$253$	−8.53537	+	8.53537i	−0.536614	+	0.536614i
$254$	7.98108	+	13.8236i	0.500778	+	0.867372i
$255$	−5.39268	−	1.56575i	−0.337702	−	0.0980512i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.963390	−	0.258140i	−0.0600946	−	0.0161023i	0.228646	−	0.973510i	$-0.426570\pi$
$257$	−0.963390	−	0.258140i	−0.0600946	−	0.0161023i	−0.288741	+	0.957407i	$0.593237\pi$
$258$	−0.525951	+	4.36016i	−0.0327443	+	0.271452i
$259$	17.0487	−	0.345073i	1.05935	−	0.0214418i
$260$	−9.70957	+	3.66654i	−0.602162	+	0.227389i
$261$	−6.04643	−	20.7529i	−0.374264	−	1.28457i
$262$	−5.59277	+	1.49858i	−0.345522	+	0.0925824i
$263$	−16.6722	+	4.46730i	−1.02805	+	0.275466i	−0.733153	−	0.680063i	$-0.761952\pi$
$263$	−16.6722	+	4.46730i	−1.02805	+	0.275466i	−0.294898	+	0.955529i	$0.595286\pi$
$264$	3.40729	+	1.36821i	0.209704	+	0.0842077i
$265$	−14.0280	+	5.29728i	−0.861733	+	0.325409i
$266$	−7.46983	−	12.3538i	−0.458005	−	0.757462i
$267$	0.687613	+	0.0829443i	0.0420812	+	0.00507611i
$268$	9.10412	+	2.43944i	0.556123	+	0.149013i
$269$	−13.8205	+	23.9379i	−0.842653	+	1.45952i	0.0449907	+	0.998987i	$0.485674\pi$
$269$	−13.8205	+	23.9379i	−0.842653	+	1.45952i	−0.887644	+	0.460531i	$0.847659\pi$
$270$	−10.0677	−	5.80014i	−0.612700	−	0.352985i
$271$	−2.56520	−	4.44305i	−0.155825	−	0.269896i	0.777534	−	0.628840i	$-0.216470\pi$
$271$	−2.56520	−	4.44305i	−0.155825	−	0.269896i	−0.933359	+	0.358944i	$0.883137\pi$
$272$	−1.02522	+	1.02522i	−0.0621633	+	0.0621633i
$273$	−19.3886	+	8.74669i	−1.17345	+	0.529374i
$274$		−	11.2071i		−	0.677047i
$275$	−10.0443	−	3.38512i	−0.605694	−	0.204130i
$276$	−1.39336	−	9.76359i	−0.0838706	−	0.587699i
$277$	26.6082	−	7.12965i	1.59873	−	0.428379i	0.654073	−	0.756432i	$-0.273059\pi$
$277$	26.6082	−	7.12965i	1.59873	−	0.428379i	0.944659	+	0.328053i	$0.106392\pi$
$278$	5.21087	−	19.4472i	0.312527	−	1.16637i
$279$	3.07750	+	0.753417i	0.184245	+	0.0451059i
$280$	2.32612	−	5.43959i	0.139012	−	0.325078i
$281$			19.8830i			1.18612i	0.805157	+	0.593062i	$0.202081\pi$
$281$			19.8830i			1.18612i	−0.805157	+	0.593062i	$0.797919\pi$
$282$	−17.7147	+	7.56392i	−1.05489	+	0.450425i
$283$	1.36944	+	5.11082i	0.0814048	+	0.303807i	0.994609	−	0.103695i	$-0.0330666\pi$
$283$	1.36944	+	5.11082i	0.0814048	+	0.303807i	−0.913204	+	0.407502i	$0.866400\pi$
$284$	0.879690	−	1.52367i	0.0522000	−	0.0904131i
$285$	0.439089	−	21.1285i	0.0260094	−	1.25154i
$286$	9.83949			0.581821
$287$	−4.74593	+	1.37518i	−0.280143	+	0.0811746i
$288$	−2.56491	+	1.55604i	−0.151139	+	0.0916904i
$289$	12.9019	−	7.44892i	0.758935	−	0.438172i
$290$	15.8991	+	2.60711i	0.933626	+	0.153094i
$291$	−20.9365	+	2.98785i	−1.22732	+	0.175151i
$292$	−0.323412	+	1.20699i	−0.0189263	+	0.0706338i
$293$	21.3392	+	21.3392i	1.24665	+	1.24665i	0.957191	+	0.289456i	$0.0934744\pi$
$293$	21.3392	+	21.3392i	1.24665	+	1.24665i	0.289456	+	0.957191i	$0.406526\pi$
$294$	4.05898	−	11.4247i	0.236724	−	0.666304i
$295$	4.85457	−	10.7455i	0.282644	−	0.625626i
$296$	5.58163	−	3.22256i	0.324426	−	0.187307i
$297$	6.98656	+	8.51602i	0.405402	+	0.494150i
$298$	−3.05671	−	11.4078i	−0.177070	−	0.660835i
$299$	−13.2147	−	22.8886i	−0.764228	−	1.32368i
$300$	7.13739	−	4.90486i	0.412078	−	0.283182i
$301$	−5.87645	−	3.23601i	−0.338713	−	0.186521i
$302$	−6.12855	+	6.12855i	−0.352658	+	0.352658i
$303$	−7.04440	+	3.00787i	−0.404690	+	0.172797i
$304$	−4.72549	−	2.72826i	−0.271025	−	0.156477i
$305$	−10.7449	−	14.9599i	−0.615251	−	0.856603i
$306$	−4.17602	+	1.21670i	−0.238727	+	0.0695541i
$307$	17.8595	+	17.8595i	1.01929	+	1.01929i	0.999810	+	0.0194830i	$0.00620203\pi$
$307$	17.8595	+	17.8595i	1.01929	+	1.01929i	0.0194830	+	0.999810i	$0.493798\pi$
$308$	−3.88486	+	4.04537i	−0.221360	+	0.230506i
$309$	−14.5897	+	11.4488i	−0.829978	+	0.651297i
$310$	−1.49617	+	1.82715i	−0.0849766	+	0.103775i
$311$	13.1923	+	7.61659i	0.748068	+	0.431897i	0.824996	−	0.565139i	$-0.191178\pi$
$311$	13.1923	+	7.61659i	0.748068	+	0.431897i	−0.0769272	+	0.997037i	$0.524511\pi$
$312$	−4.82455	+	6.43081i	−0.273137	+	0.364073i
$313$	22.0349	+	5.90424i	1.24549	+	0.333727i	0.820591	−	0.571515i	$-0.193644\pi$
$313$	22.0349	+	5.90424i	1.24549	+	0.333727i	0.424895	+	0.905243i	$0.360311\pi$
$314$	17.4573			0.985172
$315$	13.9685	−	10.9491i	0.787034	−	0.616910i
$316$	15.9827			0.899099
$317$	−4.77643	−	1.27984i	−0.268271	−	0.0718830i	0.122176	−	0.992508i	$-0.461013\pi$
$317$	−4.77643	−	1.27984i	−0.268271	−	0.0718830i	−0.390447	+	0.920625i	$0.627679\pi$
$318$	−6.97032	+	9.29097i	−0.390876	+	0.521012i
$319$	−13.2279	−	7.63712i	−0.740619	−	0.427596i
$320$	−0.221605	−	2.22506i	−0.0123881	−	0.124385i
$321$	−14.5471	+	11.4153i	−0.811940	+	0.637142i
$322$	14.6278	+	3.60389i	0.815177	+	0.200837i
$323$	−5.59416	−	5.59416i	−0.311267	−	0.311267i
$324$	−8.99152	+	0.390595i	−0.499529	+	0.0216997i
$325$	12.8513	−	19.3246i	0.712862	−	1.07194i
$326$	4.51534	+	2.60693i	0.250081	+	0.144385i
$327$	13.6501	−	5.82843i	0.754854	−	0.322313i
$328$	−1.32058	+	1.32058i	−0.0729167	+	0.0729167i
$329$	−0.595415	−	29.4171i	−0.0328263	−	1.62181i
$330$	−7.97293	+	1.95973i	−0.438895	+	0.107880i
$331$	0.118156	+	0.204653i	0.00649446	+	0.0112487i	0.869254	−	0.494365i	$-0.164599\pi$
$331$	0.118156	+	0.204653i	0.00649446	+	0.0112487i	−0.862760	+	0.505614i	$0.831266\pi$
$332$	−3.46885	−	12.9459i	−0.190378	−	0.710500i
$333$	19.3308	−	0.419671i	1.05932	−	0.0229978i
$334$	−7.34183	+	4.23880i	−0.401727	+	0.231937i
$335$	−19.7166	+	7.44542i	−1.07723	+	0.406787i
$336$	−0.739092	−	4.52258i	−0.0403208	−	0.246727i
$337$	−0.442376	−	0.442376i	−0.0240977	−	0.0240977i	0.694955	−	0.719053i	$-0.255424\pi$
$337$	−0.442376	−	0.442376i	−0.0240977	−	0.0240977i	−0.719053	+	0.694955i	$0.755424\pi$
$338$	−2.21132	+	8.25275i	−0.120280	+	0.448890i
$339$	17.2772	−	2.46563i	0.938368	−	0.133915i
$340$	0.524618	−	3.19932i	0.0284514	−	0.173507i
$341$	1.93891	−	1.11943i	0.104998	−	0.0606204i
$342$	−8.49056	−	13.9955i	−0.459117	−	0.756789i
$343$	13.8663	+	12.2771i	0.748708	+	0.662900i
$344$	−2.53559			−0.136710
$345$	15.2666	+	15.9146i	0.821928	+	0.856815i
$346$	−2.50658	+	4.34153i	−0.134755	+	0.233402i
$347$	−1.05651	−	3.94296i	−0.0567166	−	0.211669i	0.931752	−	0.363095i	$-0.118280\pi$
$347$	−1.05651	−	3.94296i	−0.0567166	−	0.211669i	−0.988469	+	0.151426i	$0.951613\pi$
$348$	11.4774	−	4.90069i	0.615252	−	0.262704i
$349$		−	11.9140i		−	0.637743i	−0.947798	−	0.318871i	$-0.896696\pi$
$349$		−	11.9140i		−	0.637743i	0.947798	−	0.318871i	$-0.103304\pi$
$350$	2.87106	+	12.9134i	0.153465	+	0.690253i
$351$	−21.9700	+	9.95010i	−1.17267	+	0.531097i
$352$	−0.548664	+	2.04764i	−0.0292439	+	0.109140i
$353$	6.82920	−	1.82988i	0.363482	−	0.0973946i	−0.0724557	−	0.997372i	$-0.523084\pi$
$353$	6.82920	−	1.82988i	0.363482	−	0.0973946i	0.435937	+	0.899977i	$0.356417\pi$
$354$	−1.29036	−	9.04181i	−0.0685817	−	0.480567i
$355$	0.389887	+	3.91473i	0.0206930	+	0.207772i
$356$			0.399872i			0.0211931i
$357$	0.662050	−	6.61114i	0.0350394	−	0.349899i
$358$	5.72174	−	5.72174i	0.302403	−	0.302403i
$359$	−4.55001	−	7.88085i	−0.240140	−	0.415935i	0.720614	−	0.693337i	$-0.243860\pi$
$359$	−4.55001	−	7.88085i	−0.240140	−	0.415935i	−0.960754	+	0.277401i	$0.910527\pi$
$360$	2.62851	−	6.17179i	0.138534	−	0.325282i
$361$	5.38683	−	9.33027i	0.283518	−	0.491067i
$362$	−10.3302	−	2.76797i	−0.542943	−	0.145481i
$363$	−11.1878	−	1.34955i	−0.587209	−	0.0708329i
$364$	−6.35414	−	10.5087i	−0.333047	−	0.550804i
$365$	−0.987086	−	2.61396i	−0.0516665	−	0.136821i
$366$	−13.2396	−	5.31642i	−0.692045	−	0.277894i
$367$	−10.6737	+	2.86001i	−0.557163	+	0.149291i	−0.526403	−	0.850235i	$-0.676460\pi$
$367$	−10.6737	+	2.86001i	−0.557163	+	0.149291i	−0.0307603	+	0.999527i	$0.509793\pi$
$368$	5.50010	−	1.47375i	0.286713	−	0.0768244i
$369$	−5.37908	+	1.56722i	−0.280024	+	0.0815860i
$370$	−5.93347	+	13.1336i	−0.308466	+	0.682784i
$371$	−9.18020	−	15.1825i	−0.476612	−	0.788236i
$372$	−0.219070	+	1.81610i	−0.0113582	+	0.0941603i
$373$	−33.1354	−	8.87861i	−1.71569	−	0.459717i	−0.738880	−	0.673837i	$-0.764645\pi$
$373$	−33.1354	−	8.87861i	−1.71569	−	0.459717i	−0.976807	+	0.214120i	$0.931312\pi$
$374$	−1.53679	+	2.66180i	−0.0794655	+	0.137638i
$375$	−6.56450	+	18.2183i	−0.338989	+	0.940790i
$376$	−5.56044	−	9.63096i	−0.286758	−	0.496679i
$377$	23.6481	−	23.6481i	1.21794	−	1.21794i
$378$	4.58341	−	12.9612i	0.235745	−	0.666651i
$379$			17.2109i			0.884063i	0.897000	+	0.442031i	$0.145742\pi$
$379$			17.2109i			0.884063i	−0.897000	+	0.442031i	$0.854258\pi$
$380$	12.1411	−	1.20919i	0.622825	−	0.0620302i
$381$	−27.3700	+	3.90597i	−1.40221	+	0.200109i
$382$	−0.722383	+	0.193562i	−0.0369604	+	0.00990350i
$383$	−4.92466	+	18.3791i	−0.251639	+	0.939128i	0.718291	+	0.695743i	$0.244925\pi$
$383$	−4.92466	+	18.3791i	−0.251639	+	0.939128i	−0.969930	+	0.243385i	$0.921742\pi$
$384$	−1.06926	−	1.36260i	−0.0545653	−	0.0695351i
$385$	1.77855	−	12.4146i	0.0906431	−	0.632707i
$386$		−	9.25799i		−	0.471220i
$387$	−6.66866	−	3.65950i	−0.338987	−	0.186023i
$388$	−3.16023	−	11.7941i	−0.160436	−	0.598756i
$389$	−18.4175	+	31.9000i	−0.933804	+	1.61740i	−0.157052	+	0.987590i	$0.550199\pi$
$389$	−18.4175	+	31.9000i	−0.933804	+	1.61740i	−0.776752	+	0.629806i	$0.783134\pi$
$390$	0.373507	−	17.9727i	0.0189132	−	0.910084i
$391$	8.25583			0.417515
$392$	6.82925	+	1.53665i	0.344929	+	0.0776126i
$393$	1.20102	−	9.95650i	0.0605833	−	0.502239i
$394$	3.32367	−	1.91892i	0.167444	−	0.0966739i
$395$	−29.0271	+	20.8486i	−1.46051	+	1.04901i
$396$	−4.39827	+	4.59348i	−0.221022	+	0.230831i
$397$	−5.18227	+	19.3405i	−0.260091	+	0.970672i	0.705096	+	0.709112i	$0.250904\pi$
$397$	−5.18227	+	19.3405i	−0.260091	+	0.970672i	−0.965187	+	0.261561i	$0.915763\pi$
$398$	3.96399	+	3.96399i	0.198697	+	0.198697i
$399$	24.6776	−	4.03288i	1.23542	−	0.201896i
$400$	3.30494	+	3.75198i	0.165247	+	0.187599i
$401$	9.00824	−	5.20091i	0.449850	−	0.259721i	−0.257917	−	0.966167i	$-0.583036\pi$
$401$	9.00824	−	5.20091i	0.449850	−	0.259721i	0.707767	+	0.706446i	$0.249703\pi$
$402$	−9.79692	+	13.0586i	−0.488626	+	0.651306i
$403$	1.26874	+	4.73502i	0.0632006	+	0.235868i
$404$	−2.21116	−	3.82984i	−0.110009	−	0.190542i
$405$	15.8205	−	12.4383i	0.786127	−	0.618065i
$406$	0.385771	+	19.0594i	0.0191455	+	0.945901i
$407$	9.66109	−	9.66109i	0.478883	−	0.478883i
$408$	−0.986147	−	2.30955i	−0.0488216	−	0.114340i
$409$	13.4035	+	7.73849i	0.662758	+	0.382644i	0.793327	−	0.608796i	$-0.208347\pi$
$409$	13.4035	+	7.73849i	0.662758	+	0.382644i	−0.130569	+	0.991439i	$0.541680\pi$
$410$	0.675754	−	4.12099i	0.0333731	−	0.203521i
$411$	18.0133	+	7.23331i	0.888529	+	0.356793i
$412$	−7.57114	−	7.57114i	−0.373003	−	0.373003i
$413$	13.5465	+	3.33747i	0.666577	+	0.164226i
$414$	16.5924	+	4.06206i	0.815471	+	0.199640i
$415$	23.1872	+	18.9869i	1.13822	+	0.932030i
$416$	−4.01969	−	2.32077i	−0.197082	−	0.113785i
$417$	27.8945	+	20.9271i	1.36600	+	1.02481i
$418$	−11.1730	−	2.99380i	−0.546490	−	0.146432i
$419$	−14.9110			−0.728451			−0.364225	−	0.931311i	$-0.618666\pi$
$419$	−14.9110			−0.728451			−0.364225	+	0.931311i	$0.618666\pi$
$420$	7.24177	+	7.24961i	0.353362	+	0.353745i
$421$	−16.5292			−0.805586			−0.402793	−	0.915291i	$-0.631960\pi$
$421$	−16.5292			−0.805586			−0.402793	+	0.915291i	$0.631960\pi$
$422$	−14.3389	−	3.84211i	−0.698009	−	0.187031i
$423$	−0.724131	−	33.3548i	−0.0352085	−	1.62176i
$424$	−5.80749	−	3.35295i	−0.282036	−	0.162834i
$425$	3.22054	+	6.49479i	0.156219	+	0.315044i
$426$	1.88123	+	2.39734i	0.0911459	+	0.116151i
$427$	15.0953	−	15.7190i	0.730511	−	0.760694i
$428$	−7.54904	−	7.54904i	−0.364897	−	0.364897i
$429$	−6.35061	+	15.8151i	−0.306610	+	0.763559i
$430$	4.60503	−	3.30754i	0.222074	−	0.159504i
$431$	−6.60065	−	3.81089i	−0.317942	−	0.183564i	0.332533	−	0.943092i	$-0.392097\pi$
$431$	−6.60065	−	3.81089i	−0.317942	−	0.183564i	−0.650475	+	0.759528i	$0.725430\pi$
$432$	−0.845583	−	5.12689i	−0.0406831	−	0.246668i
$433$	−7.94117	+	7.94117i	−0.381628	+	0.381628i	−0.871689	−	0.490060i	$-0.836975\pi$
$433$	−7.94117	+	7.94117i	−0.381628	+	0.381628i	0.490060	+	0.871689i	$0.336975\pi$
$434$	−2.44767	−	1.34787i	−0.117492	−	0.0646997i
$435$	−14.4520	+	23.8720i	−0.692921	+	1.14458i
$436$	4.28463	+	7.42120i	0.205197	+	0.355411i
$437$	8.04154	+	30.0114i	0.384679	+	1.43564i
$438$	−1.73127	−	1.29884i	−0.0827231	−	0.0620610i
$439$	11.5080	−	6.64413i	0.549245	−	0.317107i	−0.199572	−	0.979883i	$-0.563955\pi$
$439$	11.5080	−	6.64413i	0.549245	−	0.317107i	0.748818	+	0.662776i	$0.230622\pi$
$440$	−1.67458	−	4.43454i	−0.0798324	−	0.211409i
$441$	15.7433	+	13.8978i	0.749681	+	0.661799i
$442$	−4.75862	−	4.75862i	−0.226344	−	0.226344i
$443$	−6.35418	+	23.7141i	−0.301896	+	1.12669i	0.633688	+	0.773589i	$0.281540\pi$
$443$	−6.35418	+	23.7141i	−0.301896	+	1.12669i	−0.935584	+	0.353104i	$0.885126\pi$
$444$	1.57713	+	11.0513i	0.0748474	+	0.524471i
$445$	−0.521610	−	0.726229i	−0.0247267	−	0.0344266i
$446$	−6.15816	+	3.55542i	−0.291597	+	0.168354i
$447$	20.3087	+	2.44976i	0.960566	+	0.115870i
$448$	2.54122	−	0.736347i	0.120061	−	0.0347891i
$449$	5.93549			0.280113			0.140056	−	0.990144i	$-0.455272\pi$
$449$	5.93549			0.280113			0.140056	+	0.990144i	$0.455272\pi$
$450$	3.27698	+	14.6377i	0.154478	+	0.690026i
$451$	−1.97952	+	3.42863i	−0.0932119	+	0.161448i
$452$	2.60787	+	9.73272i	0.122664	+	0.457789i
$453$	−5.89496	−	13.8059i	−0.276969	−	0.648660i
$454$			11.6375i			0.546175i
$455$	25.2481	+	10.7968i	1.18365	+	0.506160i
$456$	7.43508	−	5.83443i	0.348180	−	0.273222i
$457$	−2.69512	+	10.0583i	−0.126072	+	0.470508i	−0.999876	−	0.0157712i	$-0.994980\pi$
$457$	−2.69512	+	10.0583i	−0.126072	+	0.470508i	0.873803	+	0.486280i	$0.161646\pi$
$458$	3.99505	−	1.07047i	0.186676	−	0.0500198i
$459$	0.739682	−	7.49743i	0.0345254	−	0.349950i
$460$	−8.06662	+	9.85113i	−0.376108	+	0.459312i
$461$		−	32.7232i		−	1.52407i	−0.647535	−	0.762035i	$-0.724200\pi$
$461$		−	32.7232i		−	1.52407i	0.647535	−	0.762035i	$-0.275800\pi$
$462$	−3.99478	−	8.85512i	−0.185854	−	0.411978i
$463$	6.59995	−	6.59995i	0.306726	−	0.306726i	−0.536912	−	0.843638i	$-0.680409\pi$
$463$	6.59995	−	6.59995i	0.306726	−	0.306726i	0.843638	+	0.536912i	$0.180409\pi$
$464$	3.60262	+	6.23993i	0.167248	+	0.289681i
$465$	−1.97114	−	3.58408i	−0.0914093	−	0.166208i
$466$	−11.3521	+	19.6623i	−0.525874	+	0.910841i
$467$	−0.776556	−	0.208078i	−0.0359347	−	0.00962868i	0.240807	−	0.970573i	$-0.422588\pi$
$467$	−0.776556	−	0.208078i	−0.0359347	−	0.00962868i	−0.276742	+	0.960944i	$0.589255\pi$
$468$	−7.22241	−	11.9051i	−0.333856	−	0.550314i
$469$	−12.9029	−	21.3393i	−0.595803	−	0.985357i
$470$	22.6617	+	10.2380i	1.04531	+	0.472246i
$471$	−11.2673	+	28.0592i	−0.519170	+	1.29290i
$472$	5.09350	−	1.36480i	0.234447	−	0.0628200i
$473$	−5.19198	+	1.39119i	−0.238728	+	0.0639669i
$474$	−10.3156	+	25.6891i	−0.473811	+	1.17994i
$475$	−20.4728	+	18.0335i	−0.939357	+	0.827432i
$476$	3.83525	−	0.0776272i	0.175788	−	0.00355804i
$477$	−10.4346	−	17.2000i	−0.477770	−	0.787535i
$478$	−10.2541	−	2.74758i	−0.469013	−	0.125672i
$479$	8.48718	−	14.7002i	0.387789	−	0.671670i	−0.604363	−	0.796709i	$-0.706572\pi$
$479$	8.48718	−	14.7002i	0.387789	−	0.671670i	0.992152	+	0.125039i	$0.0399056\pi$
$480$	3.71938	+	1.07991i	0.169766	+	0.0492911i
$481$	14.9576	+	25.9074i	0.682009	+	1.18127i
$482$	−14.2319	+	14.2319i	−0.648245	+	0.648245i
$483$	−15.2337	+	21.1854i	−0.693156	+	0.963967i
$484$		−	6.50612i		−	0.295733i
$485$	21.1243	+	17.2976i	0.959203	+	0.785445i
$486$	5.17551	−	14.7042i	0.234766	−	0.666997i
$487$	15.4471	−	4.13903i	0.699974	−	0.187557i	0.108755	−	0.994069i	$-0.465314\pi$
$487$	15.4471	−	4.13903i	0.699974	−	0.187557i	0.591219	+	0.806511i	$0.298647\pi$
$488$	2.13193	−	7.95646i	0.0965078	−	0.360172i
$489$	−7.10443	+	5.57496i	−0.321273	+	0.252108i
$490$	−14.4075	+	6.11759i	−0.650863	+	0.276365i
$491$		−	6.87591i		−	0.310305i	−0.987891	−	0.155153i	$-0.950413\pi$
$491$		−	6.87591i		−	0.310305i	0.987891	−	0.155153i	$-0.0495869\pi$
$492$	−1.27024	−	2.97490i	−0.0572670	−	0.134119i
$493$	2.70383	+	10.0908i	0.121774	+	0.454468i
$494$	12.6633	−	21.9335i	0.569750	−	0.986837i
$495$	1.99600	−	14.0798i	0.0897136	−	0.632839i
$496$	−1.05613			−0.0474215
$497$	−4.47097	+	1.29551i	−0.200550	+	0.0581117i
$498$	23.0469	+	2.78007i	1.03276	+	0.124578i
$499$	−26.8381	+	15.4950i	−1.20144	+	0.693651i	−0.960875	−	0.276982i	$-0.910666\pi$
$499$	−26.8381	+	15.4950i	−1.20144	+	0.693651i	−0.240564	+	0.970633i	$0.577332\pi$
$500$	−10.8965	−	2.50308i	−0.487308	−	0.111941i
$501$	−2.07449	−	14.5364i	−0.0926813	−	0.649437i
$502$	4.61720	−	17.2316i	0.206076	−	0.769085i
$503$	19.3755	+	19.3755i	0.863913	+	0.863913i	0.991790	−	0.127877i	$-0.0408164\pi$
$503$	19.3755	+	19.3755i	0.863913	+	0.863913i	−0.127877	+	0.991790i	$0.540816\pi$
$504$	7.74620	+	1.73102i	0.345043	+	0.0771058i
$505$	9.01164	+	4.07126i	0.401013	+	0.181168i
$506$	10.4537	−	6.03542i	0.464722	−	0.268307i
$507$	−11.8375	−	8.88076i	−0.525720	−	0.394408i
$508$	−4.13131	−	15.4183i	−0.183297	−	0.684075i
$509$	−10.4397	−	18.0821i	−0.462733	−	0.801477i	0.536363	−	0.843987i	$-0.319798\pi$
$509$	−10.4397	−	18.0821i	−0.462733	−	0.801477i	−0.999096	+	0.0425105i	$0.986464\pi$
$510$	4.80368	+	2.90813i	0.212710	+	0.128774i
$511$	2.82909	−	1.71063i	0.125151	−	0.0756736i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	27.9750	−	4.61395i	1.23513	−	0.203711i
$514$	0.863752	+	0.498688i	0.0380985	+	0.0219962i
$515$	23.6265	+	3.87423i	1.04111	+	0.170719i
$516$	1.63652	−	4.07547i	0.0720439	−	0.179412i
$517$	−16.6700	−	16.6700i	−0.733144	−	0.733144i
$518$	−16.5571	−	4.07921i	−0.727476	−	0.179230i
$519$	−5.36037	−	6.83096i	−0.235294	−	0.299846i
$520$	10.3277	−	1.02859i	0.452900	−	0.0451065i
$521$	18.9520	+	10.9419i	0.830300	+	0.479374i	0.853956	−	0.520346i	$-0.174197\pi$
$521$	18.9520	+	10.9419i	0.830300	+	0.479374i	−0.0236551	+	0.999720i	$0.507530\pi$
$522$	0.469166	+	21.6106i	0.0205349	+	0.945872i
$523$	12.6632	+	3.39310i	0.553724	+	0.148370i	0.524822	−	0.851212i	$-0.324132\pi$
$523$	12.6632	+	3.39310i	0.553724	+	0.148370i	0.0289028	+	0.999582i	$0.490799\pi$
$524$	5.79006			0.252940
$525$	−22.6089	−	3.71993i	−0.986733	−	0.162351i
$526$	17.2603			0.752586
$527$	−1.47909	−	0.396320i	−0.0644300	−	0.0172640i
$528$	−2.93707	−	2.20346i	−0.127820	−	0.0958934i
$529$	−8.16059	−	4.71152i	−0.354808	−	0.204849i
$530$	14.9210	−	1.48606i	0.648129	−	0.0645503i
$531$	15.3658	+	3.76177i	0.666818	+	0.163247i
$532$	4.01789	+	13.8662i	0.174198	+	0.601177i
$533$	−6.12951	−	6.12951i	−0.265499	−	0.265499i
$534$	−0.642716	−	0.258085i	−0.0278130	−	0.0111685i
$535$	23.5576	+	3.86293i	1.01848	+	0.167009i
$536$	−8.16253	−	4.71264i	−0.352568	−	0.203555i
$537$	5.50365	+	12.8895i	0.237500	+	0.556224i
$538$	19.5452	−	19.5452i	0.842653	−	0.842653i
$539$	14.8270	−	0.600456i	0.638643	−	0.0258635i
$540$	8.22346	+	8.20821i	0.353881	+	0.353225i
$541$	−11.6807	−	20.2316i	−0.502194	−	0.869826i	−0.999997	−	0.00253553i	$-0.999193\pi$
$541$	−11.6807	−	20.2316i	−0.502194	−	0.869826i	0.497803	−	0.867290i	$-0.334140\pi$
$542$	1.32784	+	4.95558i	0.0570358	+	0.212860i
$543$	11.1163	−	14.8173i	0.477046	−	0.635870i
$544$	1.25564	−	0.724943i	0.0538350	−	0.0310817i
$545$	−17.4621	−	7.88899i	−0.747995	−	0.337927i
$546$	20.9917	−	3.43052i	0.898363	−	0.146813i
$547$	−2.60152	−	2.60152i	−0.111233	−	0.111233i	0.649300	−	0.760533i	$-0.275062\pi$
$547$	−2.60152	−	2.60152i	−0.111233	−	0.111233i	−0.760533	+	0.649300i	$0.775062\pi$
$548$	−2.90062	+	10.8253i	−0.123908	+	0.462432i
$549$	17.0902	−	17.8487i	0.729393	−	0.761766i
$550$	8.82591	+	5.86943i	0.376338	+	0.250273i
$551$	−34.0483	+	19.6578i	−1.45051	+	0.837451i
$552$	−1.18112	+	9.79153i	−0.0502717	+	0.416755i
$553$	−30.4999	−	29.2897i	−1.29699	−	1.24553i
$554$	−27.5468			−1.17035
$555$	−17.2801	−	18.0136i	−0.733501	−	0.764635i
$556$	−10.0666	+	17.4359i	−0.426920	+	0.739448i
$557$	−9.87848	−	36.8670i	−0.418565	−	1.56211i	−0.777587	−	0.628776i	$-0.783556\pi$
$557$	−9.87848	−	36.8670i	−0.418565	−	1.56211i	0.359022	−	0.933329i	$-0.383110\pi$
$558$	−2.77763	−	1.52426i	−0.117587	−	0.0645271i
$559$		−	11.7690i		−	0.497777i
$560$	−3.65473	+	4.65220i	−0.154440	+	0.196591i
$561$	−3.28645	−	4.18807i	−0.138754	−	0.176820i
$562$	5.14611	−	19.2055i	0.217076	−	0.810137i
$563$	3.84263	−	1.02963i	0.161948	−	0.0433937i	−0.176934	−	0.984223i	$-0.556618\pi$
$563$	3.84263	−	1.02963i	0.161948	−	0.0433937i	0.338882	+	0.940829i	$0.389951\pi$
$564$	19.0687	−	2.72130i	0.802938	−	0.114587i
$565$	−17.4321	−	14.2743i	−0.733374	−	0.600525i
$566$		−	5.29112i		−	0.222402i
$567$	17.8744	+	15.7324i	0.750652	+	0.660697i
$568$	−1.24407	+	1.24407i	−0.0522000	+	0.0522000i
$569$	−2.50482	−	4.33847i	−0.105007	−	0.181878i	0.808734	−	0.588175i	$-0.200153\pi$
$569$	−2.50482	−	4.33847i	−0.105007	−	0.181878i	−0.913741	+	0.406297i	$0.866820\pi$
$570$	−5.89258	+	20.2949i	−0.246813	+	0.850059i
$571$	−16.4609	+	28.5111i	−0.688867	+	1.19315i	0.283338	+	0.959020i	$0.408558\pi$
$571$	−16.4609	+	28.5111i	−0.688867	+	1.19315i	−0.972205	+	0.234132i	$0.924775\pi$
$572$	−9.50422	−	2.54665i	−0.397391	−	0.106481i
$573$	0.155128	−	1.28602i	0.00648057	−	0.0537243i
$574$	4.94014	−	0.0999906i	0.206197	−	0.00417353i
$575$	1.79997	−	28.4137i	0.0750641	−	1.18493i
$576$	2.88024	−	0.839170i	0.120010	−	0.0349654i
$577$	−22.0443	+	5.90675i	−0.917716	+	0.245901i	−0.686609	−	0.727027i	$-0.740901\pi$
$577$	−22.0443	+	5.90675i	−0.917716	+	0.245901i	−0.231107	+	0.972928i	$0.574235\pi$
$578$	−14.3902	+	3.85584i	−0.598553	+	0.160382i
$579$	14.8804	+	5.97530i	0.618410	+	0.248325i
$580$	−14.6826	−	6.63326i	−0.609660	−	0.275431i
$581$	−17.1049	+	31.0617i	−0.709631	+	1.28866i
$582$	20.9964	+	2.53273i	0.870330	+	0.104985i
$583$	−13.7313	−	3.67929i	−0.568693	−	0.152381i
$584$	0.624785	−	1.08216i	0.0258538	−	0.0447800i
$585$	28.6466	+	12.2003i	1.18439	+	0.504421i
$586$	−15.0891	−	26.1350i	−0.623324	−	1.07963i
$587$	−29.3071	+	29.3071i	−1.20963	+	1.20963i	−0.238489	+	0.971145i	$0.576652\pi$
$587$	−29.3071	+	29.3071i	−1.20963	+	1.20963i	−0.971145	+	0.238489i	$0.923348\pi$
$588$	−6.87761	+	9.98491i	−0.283628	+	0.411771i
$589$		−	5.76278i		−	0.237451i
$590$	−7.47029	+	9.12288i	−0.307547	+	0.375583i
$591$	0.939127	+	6.58066i	0.0386305	+	0.270692i
$592$	−6.22550	+	1.66812i	−0.255867	+	0.0685593i
$593$	−5.64362	+	21.0623i	−0.231756	+	0.864925i	0.747829	+	0.663892i	$0.231096\pi$
$593$	−5.64362	+	21.0623i	−0.231756	+	0.864925i	−0.979584	+	0.201033i	$0.935570\pi$
$594$	−4.54439	−	10.0341i	−0.186459	−	0.411704i
$595$	−6.86415	+	5.14386i	−0.281403	+	0.210878i
$596$			11.8102i			0.483765i
$597$	−8.92979	+	3.81290i	−0.365472	+	0.156052i
$598$	6.84045	+	25.5289i	0.279727	+	1.04396i
$599$	6.91835	−	11.9829i	0.282676	−	0.489610i	−0.689367	−	0.724413i	$-0.742111\pi$
$599$	6.91835	−	11.9829i	0.282676	−	0.489610i	0.972043	+	0.234803i	$0.0754445\pi$
$600$	−8.16366	+	2.89043i	−0.333280	+	0.118001i
$601$	7.92094			0.323102			0.161551	−	0.986864i	$-0.448350\pi$
$601$	7.92094			0.323102			0.161551	+	0.986864i	$0.448350\pi$
$602$	4.83868	+	4.64669i	0.197210	+	0.189385i
$603$	−14.6661	−	24.1750i	−0.597249	−	0.984481i
$604$	7.50591	−	4.33354i	0.305411	−	0.176329i
$605$	8.48688	+	11.8161i	0.345041	+	0.480394i
$606$	7.58286	−	1.08215i	0.308033	−	0.0439594i
$607$	8.55795	−	31.9387i	0.347356	−	1.29635i	−0.542479	−	0.840070i	$-0.682514\pi$
$607$	8.55795	−	31.9387i	0.347356	−	1.29635i	0.889835	−	0.456282i	$-0.150819\pi$
$608$	3.85835	+	3.85835i	0.156477	+	0.156477i
$609$	−30.8832	−	11.6813i	−1.25145	−	0.473349i
$610$	6.50685	+	17.2312i	0.263455	+	0.697669i
$611$	44.7025	−	25.8090i	1.80847	−	1.04412i
$612$	4.34863	−	0.0944086i	0.175783	−	0.00381624i
$613$	2.45744	+	9.17128i	0.0992549	+	0.370424i	0.997630	−	0.0688043i	$-0.0219184\pi$
$613$	2.45744	+	9.17128i	0.0992549	+	0.370424i	−0.898375	+	0.439229i	$0.855252\pi$
$614$	−12.6285	−	21.8733i	−0.509647	−	0.882734i
$615$	6.18755	+	3.74592i	0.249506	+	0.151050i
$616$	4.79950	−	2.90205i	0.193378	−	0.116927i
$617$	−13.7827	+	13.7827i	−0.554873	+	0.554873i	−0.927843	−	0.372971i	$-0.878339\pi$
$617$	−13.7827	+	13.7827i	−0.554873	+	0.554873i	0.372971	+	0.927843i	$0.378339\pi$
$618$	17.0557	−	7.28256i	0.686081	−	0.292948i
$619$	−6.45537	−	3.72701i	−0.259463	−	0.149801i	0.364626	−	0.931154i	$-0.381197\pi$
$619$	−6.45537	−	3.72701i	−0.259463	−	0.149801i	−0.624090	+	0.781353i	$0.714530\pi$
$620$	1.91809	−	1.37766i	0.0770323	−	0.0553281i
$621$	−17.2380	+	24.0473i	−0.691739	+	0.964984i
$622$	−10.7715	−	10.7715i	−0.431897	−	0.431897i
$623$	0.732799	−	0.763077i	0.0293590	−	0.0305720i
$624$	6.32458	−	4.96300i	0.253186	−	0.198679i
$625$	23.0549	−	9.66795i	0.922198	−	0.386718i
$626$	−19.7560	−	11.4061i	−0.789607	−	0.455880i
$627$	12.0233	−	16.0262i	0.480163	−	0.640025i
$628$	−16.8625	−	4.51828i	−0.672885	−	0.180299i
$629$	−9.34468			−0.372597
$630$	−16.3263	+	6.96068i	−0.650456	+	0.277320i
$631$	−49.0067			−1.95093			−0.975463	−	0.220162i	$-0.929342\pi$
$631$	−49.0067			−1.95093			−0.975463	+	0.220162i	$0.929342\pi$
$632$	−15.4381	−	4.13664i	−0.614096	−	0.164547i
$633$	15.4301	−	20.5673i	0.613292	−	0.817477i
$634$	4.28243	+	2.47246i	0.170077	+	0.0981940i
$635$	27.6154	+	22.6129i	1.09588	+	0.897366i
$636$	9.13750	−	7.17034i	0.362325	−	0.284322i
$637$	−7.13242	+	31.6982i	−0.282597	+	1.25593i
$638$	10.8005	+	10.8005i	0.427596	+	0.427596i
$639$	−5.06744	+	1.47642i	−0.200465	+	0.0584062i
$640$	−0.361834	+	2.20660i	−0.0143028	+	0.0872235i
$641$	−20.1256	−	11.6195i	−0.794915	−	0.458944i	0.0467751	−	0.998905i	$-0.485106\pi$
$641$	−20.1256	−	11.6195i	−0.794915	−	0.458944i	−0.841690	+	0.539961i	$0.818439\pi$
$642$	17.0059	−	7.26131i	0.671171	−	0.286581i
$643$	15.5301	−	15.5301i	0.612445	−	0.612445i	−0.331137	−	0.943583i	$-0.607432\pi$
$643$	15.5301	−	15.5301i	0.612445	−	0.612445i	0.943583	+	0.331137i	$0.107432\pi$
$644$	−13.1966	−	7.26705i	−0.520020	−	0.286362i
$645$	2.34404	+	9.53644i	0.0922966	+	0.375497i
$646$	3.95567	+	6.85142i	0.155634	+	0.269565i
$647$	−11.1785	−	41.7186i	−0.439471	−	1.64013i	−0.730135	−	0.683303i	$-0.760543\pi$
$647$	−11.1785	−	41.7186i	−0.439471	−	1.64013i	0.290663	−	0.956825i	$-0.406124\pi$
$648$	8.78624	+	1.94989i	0.345156	+	0.0765989i
$649$	9.68086	−	5.58925i	0.380007	−	0.219397i
$650$	−17.4150	+	15.3400i	−0.683072	+	0.601684i
$651$	3.74621	−	3.06421i	0.146826	−	0.120096i
$652$	−3.68676	−	3.68676i	−0.144385	−	0.144385i
$653$	6.47076	−	24.1492i	0.253220	−	0.945031i	−0.715852	−	0.698252i	$-0.753961\pi$
$653$	6.47076	−	24.1492i	0.253220	−	0.945031i	0.969072	−	0.246778i	$-0.0793720\pi$
$654$	−14.6935	+	2.09692i	−0.574563	+	0.0819959i
$655$	−10.5156	+	7.55281i	−0.410880	+	0.295113i
$656$	1.61737	−	0.933789i	0.0631477	−	0.0364583i
$657$	3.20503	−	1.94438i	0.125040	−	0.0758573i
$658$	−7.03857	+	28.5688i	−0.274392	+	1.11373i
$659$	20.0343			0.780425			0.390213	−	0.920725i	$-0.372401\pi$
$659$	20.0343			0.780425			0.390213	+	0.920725i	$0.372401\pi$
$660$	8.20847	+	0.170587i	0.319514	+	0.00664011i
$661$	−6.62569	+	11.4760i	−0.257709	+	0.446366i	−0.965628	−	0.259928i	$-0.916301\pi$
$661$	−6.62569	+	11.4760i	−0.257709	+	0.446366i	0.707918	+	0.706294i	$0.249634\pi$
$662$	−0.0611622	−	0.228261i	−0.00237714	−	0.00887160i
$663$	10.7199	−	4.57724i	0.416325	−	0.177765i
$664$			13.4026i			0.520122i
$665$	−25.3849	−	19.9421i	−0.984382	−	0.773322i
$666$	−18.7807	−	4.59781i	−0.727739	−	0.178161i
$667$	10.6187	−	39.6296i	0.411158	−	1.53446i
$668$	8.18874	−	2.19417i	0.316832	−	0.0848949i
$669$	−1.74003	−	12.1928i	−0.0672736	−	0.471401i
$670$	20.9718	−	2.08869i	0.810212	−	0.0806930i
$671$		−	17.4617i		−	0.674102i
$672$	−0.456622	+	4.55977i	−0.0176146	+	0.175897i
$673$	−18.6445	+	18.6445i	−0.718692	+	0.718692i	−0.968337	−	0.249645i	$-0.919686\pi$
$673$	−18.6445	+	18.6445i	−0.718692	+	0.718692i	0.249645	+	0.968337i	$0.419686\pi$
$674$	0.312807	+	0.541798i	0.0120489	+	0.0208693i
$675$	−25.6422	−	4.18035i	−0.986970	−	0.160902i
$676$	4.27194	−	7.39921i	0.164305	−	0.284585i
$677$	47.8038	+	12.8090i	1.83725	+	0.492290i	0.998625	−	0.0524196i	$-0.0166933\pi$
$677$	47.8038	+	12.8090i	1.83725	+	0.492290i	0.838625	+	0.544709i	$0.183360\pi$
$678$	−17.3266	−	2.09005i	−0.665425	−	0.0802679i
$679$	−15.5831	+	28.2982i	−0.598024	+	1.08598i
$680$	−1.33479	+	2.95452i	−0.0511867	+	0.113301i
$681$	−18.7050	−	7.51109i	−0.716779	−	0.287826i
$682$	−2.16257	+	0.579459i	−0.0828091	+	0.0221886i
$683$	9.58678	−	2.56877i	0.366828	−	0.0982913i	−0.0706962	−	0.997498i	$-0.522522\pi$
$683$	9.58678	−	2.56877i	0.366828	−	0.0982913i	0.437524	+	0.899207i	$0.355855\pi$
$684$	4.57895	+	15.7161i	0.175081	+	0.600921i
$685$	−8.85297	−	23.4440i	−0.338255	−	0.895751i
$686$	−10.2162	−	15.4476i	−0.390058	−	0.589792i
$687$	−0.857916	+	7.11217i	−0.0327315	+	0.271346i
$688$	2.44919	+	0.656259i	0.0933746	+	0.0250196i
$689$	15.5629	−	26.9557i	0.592898	−	1.02693i
$690$	−10.6274	−	19.3237i	−0.404579	−	0.735639i
$691$	−3.42873	−	5.93874i	−0.130435	−	0.225920i	0.793409	−	0.608689i	$-0.208304\pi$
$691$	−3.42873	−	5.93874i	−0.130435	−	0.225920i	−0.923844	+	0.382768i	$0.874971\pi$
$692$	3.54485	−	3.54485i	0.134755	−	0.134755i
$693$	16.8112	−	0.705547i	0.638605	−	0.0268015i
$694$			4.08205i			0.154953i
$695$	−4.46162	−	44.7977i	−0.169239	−	1.69927i
$696$	−12.3547	+	1.76314i	−0.468303	+	0.0668316i
$697$	2.61551	−	0.700824i	0.0990695	−	0.0265456i
$698$	−3.08358	+	11.5081i	−0.116715	+	0.435587i
$699$	−24.2765	−	30.9367i	−0.918223	−	1.17013i
$700$	0.569013	−	13.2165i	0.0215067	−	0.499537i
$701$			28.8845i			1.09095i	0.838127	+	0.545476i	$0.183651\pi$
$701$			28.8845i			1.09095i	−0.838127	+	0.545476i	$0.816349\pi$
$702$	23.7966	−	3.92481i	0.898147	−	0.148132i
$703$	−9.10213	−	33.9696i	−0.343293	−	1.28119i
$704$	1.05994	−	1.83587i	0.0399479	−	0.0691918i
$705$	−31.0820	+	29.8164i	−1.17062	+	1.12295i
$706$	−7.07011			−0.266087
$707$	−2.79895	+	11.3607i	−0.105265	+	0.427261i
$708$	−1.09380	+	9.06769i	−0.0411076	+	0.340785i
$709$	21.3823	−	12.3450i	0.803027	−	0.463628i	−0.0415013	−	0.999138i	$-0.513214\pi$
$709$	21.3823	−	12.3450i	0.803027	−	0.463628i	0.844529	+	0.535510i	$0.179881\pi$
$710$	0.636604	−	3.88225i	0.0238913	−	0.145698i
$711$	−34.6324	−	33.1606i	−1.29882	−	1.24362i
$712$	0.103494	−	0.386246i	0.00387862	−	0.0144752i
$713$	4.25234	+	4.25234i	0.159251	+	0.159251i
$714$	−2.35058	+	6.21452i	−0.0879683	+	0.232573i
$715$	20.5831	−	7.77262i	0.769764	−	0.290679i
$716$	−7.00767	+	4.04588i	−0.261889	+	0.151202i
$717$	11.0344	−	14.7082i	0.412089	−	0.549287i
$718$	2.35526	+	8.78994i	0.0878975	+	0.328038i
$719$	11.2630	+	19.5080i	0.420038	+	0.727527i	0.995943	−	0.0899900i	$-0.0286835\pi$
$719$	11.2630	+	19.5080i	0.420038	+	0.727527i	−0.575905	+	0.817517i	$0.695350\pi$
$720$	−4.13632	+	5.28118i	−0.154151	+	0.196818i
$721$	0.573266	+	28.3228i	0.0213496	+	1.05480i
$722$	−7.61813	+	7.61813i	−0.283518	+	0.283518i
$723$	−13.6894	−	32.0606i	−0.509116	−	1.19234i
$724$	9.26180	+	5.34730i	0.344212	+	0.198731i
$725$	35.3186	−	7.10558i	1.31170	−	0.263894i
$726$	10.4573	+	4.19919i	0.388108	+	0.155846i
$727$	6.61815	+	6.61815i	0.245454	+	0.245454i	0.819102	−	0.573648i	$-0.194472\pi$
$727$	6.61815	+	6.61815i	0.245454	+	0.245454i	−0.573648	+	0.819102i	$0.694472\pi$
$728$	3.41778	+	11.7952i	0.126671	+	0.437158i
$729$	20.2938	+	17.8090i	0.751622	+	0.659594i
$730$	0.276910	+	2.78037i	0.0102489	+	0.102906i
$731$	3.18378	+	1.83816i	0.117756	+	0.0679867i
$732$	11.4125	+	8.56192i	0.421817	+	0.316458i
$733$	−1.86630	−	0.500074i	−0.0689334	−	0.0184707i	0.224188	−	0.974546i	$-0.428027\pi$
$733$	−1.86630	−	0.500074i	−0.0689334	−	0.0184707i	−0.293121	+	0.956075i	$0.594694\pi$
$734$	11.0502			0.407872
$735$	−0.533955	−	27.1056i	−0.0196952	−	0.999806i
$736$	−5.69412			−0.209888
$737$	−19.2996	−	5.17132i	−0.710911	−	0.190488i
$738$	5.60141	−	0.121607i	0.206191	−	0.00447640i
$739$	−9.70996	−	5.60605i	−0.357187	−	0.206222i	0.310659	−	0.950521i	$-0.399450\pi$
$739$	−9.70996	−	5.60605i	−0.357187	−	0.206222i	−0.667846	+	0.744299i	$0.732784\pi$
$740$	9.13052	−	11.1504i	0.335644	−	0.409897i
$741$	27.0807	+	34.5102i	0.994835	+	1.26776i
$742$	4.93787	+	17.0412i	0.181275	+	0.625601i
$743$	11.6014	+	11.6014i	0.425613	+	0.425613i	0.887131	−	0.461518i	$-0.152695\pi$
$743$	11.6014	+	11.6014i	0.425613	+	0.425613i	−0.461518	+	0.887131i	$0.652695\pi$
$744$	0.681646	−	1.69752i	0.0249904	−	0.0622340i
$745$	−15.4058	−	21.4492i	−0.564424	−	0.785837i
$746$	29.7084	+	17.1522i	1.08770	+	0.627985i
$747$	−19.3434	+	35.2491i	−0.707737	+	1.28970i
$748$	2.17335	−	2.17335i	0.0794655	−	0.0794655i
$749$	0.571594	+	28.2401i	0.0208856	+	1.03187i
$750$	11.0561	−	15.8985i	0.403711	−	0.580532i
$751$	−6.85013	−	11.8648i	−0.249965	−	0.432952i	0.713551	−	0.700603i	$-0.247086\pi$
$751$	−6.85013	−	11.8648i	−0.249965	−	0.432952i	−0.963516	+	0.267652i	$0.913752\pi$
$752$	2.87830	+	10.7419i	0.104961	+	0.391718i
$753$	24.7165	+	18.5429i	0.900718	+	0.675741i
$754$	−28.9629	+	16.7217i	−1.05476	+	0.608969i
$755$	−7.97904	+	17.6614i	−0.290387	+	0.642765i
$756$	−7.78184	+	11.3333i	−0.283023	+	0.412187i
$757$	28.3749	+	28.3749i	1.03130	+	1.03130i	0.999494	+	0.0318111i	$0.0101275\pi$
$757$	28.3749	+	28.3749i	1.03130	+	1.03130i	0.0318111	+	0.999494i	$0.489873\pi$
$758$	4.45450	−	16.6244i	0.161795	−	0.603826i
$759$	2.95376	+	20.6976i	0.107215	+	0.751275i
$760$	−12.0404	−	1.97436i	−0.436750	−	0.0716175i
$761$	−4.58035	+	2.64447i	−0.166038	+	0.0958618i	−0.580716	−	0.814106i	$-0.697227\pi$
$761$	−4.58035	+	2.64447i	−0.166038	+	0.0958618i	0.414679	+	0.909968i	$0.363894\pi$
$762$	27.4483	+	3.31099i	0.994347	+	0.119945i
$763$	5.42361	−	22.0139i	0.196348	−	0.796956i
$764$	0.747866			0.0270569
$765$	−7.77464	+	5.84401i	−0.281093	+	0.211291i
$766$	9.51372	−	16.4782i	0.343745	−	0.595383i
$767$	6.33477	+	23.6417i	0.228735	+	0.853652i
$768$	0.680155	+	1.59292i	0.0245430	+	0.0574795i
$769$			0.931143i			0.0335779i	0.999859	+	0.0167889i	$0.00534434\pi$
$769$			0.931143i			0.0335779i	−0.999859	+	0.0167889i	$0.994656\pi$
$770$	−4.93108	+	11.5313i	−0.177704	+	0.415558i
$771$	−1.35903	+	1.06645i	−0.0489442	+	0.0384073i
$772$	−2.39615	+	8.94254i	−0.0862392	+	0.321849i
$773$	−11.1376	+	2.98432i	−0.400593	+	0.107339i	−0.453490	−	0.891261i	$-0.649821\pi$
$773$	−11.1376	+	2.98432i	−0.400593	+	0.107339i	0.0528969	+	0.998600i	$0.483155\pi$
$774$	5.49428	+	5.26078i	0.197488	+	0.189095i
$775$	−1.68647	+	5.00409i	−0.0605798	+	0.179752i
$776$			12.2102i			0.438320i
$777$	17.2428	−	23.9795i	0.618583	−	0.860259i
$778$	26.0463	−	26.0463i	0.933804	−	0.933804i
$779$	5.09524	+	8.82522i	0.182556	+	0.316196i
$780$	−5.01246	+	17.2636i	−0.179475	+	0.618138i
$781$	−1.86483	+	3.22999i	−0.0667290	+	0.115578i
$782$	−7.97452	−	2.13677i	−0.285168	−	0.0764106i
$783$	−35.0377	−	13.1939i	−1.25215	−	0.471510i
$784$	−6.19884	−	3.25183i	−0.221387	−	0.116137i
$785$	36.5187	−	13.7902i	1.30341	−	0.492195i
$786$	−3.73703	+	9.30639i	−0.133295	+	0.331948i
$787$	−19.0519	+	5.10495i	−0.679129	+	0.181972i	−0.581863	−	0.813287i	$-0.697676\pi$
$787$	−19.0519	+	5.10495i	−0.679129	+	0.181972i	−0.0972652	+	0.995258i	$0.531010\pi$
$788$	−3.70707	+	0.993307i	−0.132059	+	0.0353851i
$789$	−11.1402	+	27.7426i	−0.396601	+	0.987663i
$790$	33.4341	−	12.6254i	1.18953	−	0.449192i
$791$	12.8594	−	23.3521i	0.457229	−	0.830307i
$792$	5.43729	−	3.29861i	0.193206	−	0.117211i
$793$	36.9302	+	9.89542i	1.31143	+	0.351397i
$794$	10.0114	−	17.3402i	0.355291	−	0.615382i
$795$	−7.24180	+	24.9418i	−0.256840	+	0.884595i
$796$	−2.80297	−	4.85488i	−0.0993485	−	0.172077i
$797$	−13.9935	+	13.9935i	−0.495674	+	0.495674i	−0.910088	−	0.414414i	$-0.863986\pi$
$797$	−13.9935	+	13.9935i	−0.495674	+	0.495674i	0.414414	+	0.910088i	$0.363986\pi$
$798$	−24.8805	−	2.49157i	−0.880760	−	0.0882006i
$799$			16.1240i			0.570426i
$800$	−2.22124	−	4.47952i	−0.0785327	−	0.158375i
$801$	0.829645	−	0.866467i	0.0293140	−	0.0306151i
$802$	−10.0474	+	2.69219i	−0.354786	+	0.0950645i
$803$	0.685594	−	2.55867i	0.0241941	−	0.0902936i
$804$	12.8429	−	10.0780i	0.452935	−	0.355425i
$805$	33.4466	−	4.01618i	1.17884	−	0.141552i
$806$		−	4.90205i		−	0.172667i
$807$	18.8002	+	44.0300i	0.661799	+	1.54993i
$808$	1.14458	+	4.27164i	0.0402662	+	0.150276i
$809$	−12.8197	+	22.2044i	−0.450717	+	0.780666i	−0.998431	−	0.0560005i	$-0.982165\pi$
$809$	−12.8197	+	22.2044i	−0.450717	+	0.780666i	0.547713	+	0.836666i	$0.315498\pi$
$810$	−18.5007	+	7.91986i	−0.650048	+	0.278275i
$811$	−11.0170			−0.386858			−0.193429	−	0.981114i	$-0.561961\pi$
$811$	−11.0170			−0.386858			−0.193429	+	0.981114i	$0.561961\pi$
$812$	4.56031	−	18.5098i	0.160035	−	0.649567i
$813$	−8.82215	−	1.06418i	−0.309406	−	0.0373226i
$814$	−11.8324	+	6.83143i	−0.414725	+	0.239441i
$815$	11.5049	+	1.88655i	0.402999	+	0.0660831i
$816$	0.354790	+	2.48609i	0.0124201	+	0.0870305i
$817$	−3.58089	+	13.3641i	−0.125280	+	0.467550i
$818$	−10.9439	−	10.9439i	−0.382644	−	0.382644i
$819$	−8.03460	+	35.9543i	−0.280752	+	1.25634i
$820$	−1.71932	+	3.80568i	−0.0600413	+	0.132900i
$821$	13.0985	−	7.56242i	0.457141	−	0.263930i	−0.253700	−	0.967283i	$-0.581648\pi$
$821$	13.0985	−	7.56242i	0.457141	−	0.263930i	0.710841	+	0.703352i	$0.248314\pi$
$822$	−15.5274	−	11.6490i	−0.541579	−	0.406306i
$823$	10.6131	+	39.6086i	0.369949	+	1.38067i	0.860586	+	0.509305i	$0.170097\pi$
$823$	10.6131	+	39.6086i	0.369949	+	1.38067i	−0.490637	+	0.871364i	$0.663236\pi$
$824$	5.35360	+	9.27271i	0.186502	+	0.323030i
$825$	−15.1304	+	10.3977i	−0.526773	+	0.362001i
$826$	−12.2211	−	6.72983i	−0.425225	−	0.234161i
$827$	25.1800	−	25.1800i	0.875596	−	0.875596i	−0.117480	−	0.993075i	$-0.537482\pi$
$827$	25.1800	−	25.1800i	0.875596	−	0.875596i	0.993075	+	0.117480i	$0.0374815\pi$
$828$	−14.9757	−	8.21808i	−0.520440	−	0.285598i
$829$	25.3933	+	14.6608i	0.881944	+	0.509191i	0.871299	−	0.490752i	$-0.163278\pi$
$829$	25.3933	+	14.6608i	0.881944	+	0.509191i	0.0106454	+	0.999943i	$0.496611\pi$
$830$	−17.4830	−	24.3412i	−0.606842	−	0.844896i
$831$	17.7793	−	44.2762i	0.616757	−	1.53592i
$832$	3.28206	+	3.28206i	0.113785	+	0.113785i
$833$	−7.46108	−	6.88029i	−0.258511	−	0.238388i
$834$	−21.5276	−	27.4337i	−0.745441	−	0.949950i
$835$	−12.0099	+	14.6667i	−0.415618	+	0.507563i
$836$	10.0175	+	5.78358i	0.346461	+	0.200029i
$837$	4.24270	−	3.48072i	0.146649	−	0.120311i
$838$	14.4029	+	3.85925i	0.497541	+	0.133316i
$839$	−20.2876			−0.700407			−0.350203	−	0.936674i	$-0.613888\pi$
$839$	−20.2876			−0.700407			−0.350203	+	0.936674i	$0.613888\pi$
$840$	−5.11867	−	8.87689i	−0.176611	−	0.306282i
$841$	22.9156			0.790192
$842$	15.9660	+	4.27808i	0.550225	+	0.147432i
$843$	27.5478	+	20.6670i	0.948796	+	0.711811i
$844$	12.8559	+	7.42239i	0.442520	+	0.255489i
$845$	1.89336	+	19.0106i	0.0651336	+	0.653986i
$846$	−7.93340	+	32.4057i	−0.272756	+	1.11413i
$847$	−11.9230	+	12.4157i	−0.409680	+	0.426607i
$848$	4.74179	+	4.74179i	0.162834	+	0.162834i
$849$	8.50444	+	3.41500i	0.291872	+	0.117202i
$850$	−1.42983	−	7.10702i	−0.0490427	−	0.243769i
$851$	31.7825	+	18.3496i	1.08949	+	0.629018i
$852$	−1.19665	−	2.80255i	−0.0409966	−	0.0960138i
$853$	−7.01032	+	7.01032i	−0.240029	+	0.240029i	−0.816862	−	0.576833i	$-0.804288\pi$
$853$	−7.01032	+	7.01032i	−0.240029	+	0.240029i	0.576833	+	0.816862i	$0.304288\pi$
$854$	−18.6493	+	11.2764i	−0.638165	+	0.385871i
$855$	−28.8169	−	22.5699i	−0.985517	−	0.771875i
$856$	5.33798	+	9.24565i	0.182448	+	0.316010i
$857$	5.41712	+	20.2170i	0.185045	+	0.690599i	0.994621	+	0.103583i	$0.0330307\pi$
$857$	5.41712	+	20.2170i	0.185045	+	0.690599i	−0.809575	+	0.587016i	$0.800303\pi$
$858$	10.2275	−	13.6325i	0.349160	−	0.465407i
$859$	11.7809	−	6.80172i	0.401960	−	0.232072i	−0.285369	−	0.958418i	$-0.592116\pi$
$859$	11.7809	−	6.80172i	0.401960	−	0.232072i	0.687329	+	0.726346i	$0.258783\pi$
$860$	−5.30417	+	2.00297i	−0.180871	+	0.0683006i
$861$	−3.02775	+	8.00484i	−0.103186	+	0.272804i
$862$	5.38941	+	5.38941i	0.183564	+	0.183564i
$863$	−12.1635	+	45.3947i	−0.414050	+	1.54525i	0.372681	+	0.927959i	$0.378438\pi$
$863$	−12.1635	+	45.3947i	−0.414050	+	1.54525i	−0.786731	+	0.617296i	$0.788228\pi$
$864$	−0.510166	+	5.17105i	−0.0173562	+	0.175923i
$865$	−1.81394	+	11.0620i	−0.0616757	+	0.376121i
$866$	9.72591	−	5.61526i	0.330500	−	0.190814i
$867$	3.09022	−	25.6181i	0.104949	−	0.870036i
$868$	2.01541	+	1.93544i	0.0684075	+	0.0656932i
$869$	−33.8814			−1.14935
$870$	20.1381	−	19.3181i	0.682746	−	0.654946i
$871$	21.8739	−	37.8867i	0.741169	−	1.28374i
$872$	−2.21789	−	8.27727i	−0.0751072	−	0.280304i
$873$	−17.6224	+	32.1130i	−0.596428	+	1.08686i
$874$		−	31.0701i		−	1.05096i
$875$	16.2068	+	24.7455i	0.547890	+	0.836550i
$876$	1.33611	+	1.70267i	0.0451430	+	0.0575278i
$877$	5.73970	−	21.4208i	0.193816	−	0.723330i	−0.798754	−	0.601657i	$-0.794507\pi$
$877$	5.73970	−	21.4208i	0.193816	−	0.723330i	0.992570	−	0.121673i	$-0.0388260\pi$
$878$	−12.8355	+	3.43925i	−0.433176	+	0.116069i
$879$	51.7458	−	7.38465i	1.74534	−	0.249078i
$880$	0.469774	+	4.71685i	0.0158361	+	0.159005i
$881$		−	44.7263i		−	1.50687i	−0.657525	−	0.753433i	$-0.728396\pi$
$881$		−	44.7263i		−	1.50687i	0.657525	−	0.753433i	$-0.271604\pi$
$882$	−11.6099	−	17.4989i	−0.390924	−	0.589218i
$883$	−3.98957	+	3.98957i	−0.134260	+	0.134260i	−0.771043	−	0.636783i	$-0.780265\pi$
$883$	−3.98957	+	3.98957i	−0.134260	+	0.134260i	0.636783	+	0.771043i	$0.280265\pi$
$884$	3.36485	+	5.82809i	0.113172	+	0.196020i
$885$	−9.84178	−	17.8951i	−0.330828	−	0.601539i
$886$	12.2753	−	21.2615i	0.412398	−	0.714295i
$887$	29.7508	+	7.97169i	0.998933	+	0.267663i	0.720998	−	0.692937i	$-0.243683\pi$
$887$	29.7508	+	7.97169i	0.998933	+	0.267663i	0.277935	+	0.960600i	$0.410350\pi$
$888$	1.33689	−	11.0829i	0.0448632	−	0.371919i
$889$	−20.3715	+	36.9937i	−0.683239	+	1.24073i
$890$	0.315875	+	0.836486i	0.0105882	+	0.0280391i
$891$	19.0609	−	0.828014i	0.638565	−	0.0277395i
$892$	6.86854	−	1.84042i	0.229976	−	0.0616218i
$893$	−58.6137	+	15.7055i	−1.96143	+	0.525564i
$894$	−18.9826	−	7.62255i	−0.634873	−	0.254936i
$895$	7.44939	−	16.4891i	0.249006	−	0.551169i
$896$	−2.64521	+	0.0535403i	−0.0883702	+	0.00178865i
$897$	−45.4478	−	5.48220i	−1.51746	−	0.183045i
$898$	−5.73324	−	1.53622i	−0.191321	−	0.0512642i
$899$	−3.80482	+	6.59015i	−0.126898	+	0.219794i
$900$	0.623187	−	14.9870i	0.0207729	−	0.499568i
$901$	4.86140	+	8.42019i	0.161957	+	0.280517i
$902$	2.79946	−	2.79946i	0.0932119	−	0.0932119i
$903$	−10.5916	+	4.77816i	−0.352467	+	0.159007i
$904$		−	10.0761i		−	0.335124i
$905$	−23.7961	+	2.36997i	−0.791010	+	0.0787806i
$906$	2.12085	+	14.8612i	0.0704605	+	0.493732i
$907$	−23.0840	+	6.18534i	−0.766491	+	0.205381i	−0.620821	−	0.783952i	$-0.713201\pi$
$907$	−23.0840	+	6.18534i	−0.766491	+	0.205381i	−0.145670	+	0.989333i	$0.546534\pi$
$908$	3.01201	−	11.2410i	0.0999570	−	0.373045i
$909$	−3.15479	+	12.8864i	−0.104638	+	0.427415i
$910$	−21.5934	−	16.9636i	−0.715813	−	0.562336i
$911$			27.2518i			0.902892i	0.892298	+	0.451446i	$0.149092\pi$
$911$			27.2518i			0.902892i	−0.892298	+	0.451446i	$0.850908\pi$
$912$	−8.69180	+	3.71128i	−0.287814	+	0.122893i
$913$	7.35353	+	27.4438i	0.243366	+	0.908256i
$914$	5.20657	−	9.01804i	0.172218	−	0.298290i
$915$	−31.8954	−	0.662846i	−1.05443	−	0.0219130i
$916$	−4.13598			−0.136657
$917$	−11.0492	−	10.6108i	−0.364876	−	0.350399i
$918$	−2.65495	+	7.05051i	−0.0876266	+	0.232702i
$919$	−8.37600	+	4.83589i	−0.276299	+	0.159521i	−0.631747	−	0.775175i	$-0.717662\pi$
$919$	−8.37600	+	4.83589i	−0.276299	+	0.159521i	0.355448	+	0.934696i	$0.384328\pi$
$920$	10.3414	−	7.42767i	0.340946	−	0.244883i
$921$	43.3078	−	6.18046i	1.42704	−	0.203653i
$922$	−8.46938	+	31.6082i	−0.278924	+	1.04096i
$923$	−5.77440	−	5.77440i	−0.190067	−	0.190067i
$924$	1.56678	+	9.58731i	0.0515434	+	0.315400i
$925$	−2.03737	+	32.1611i	−0.0669883	+	1.05745i
$926$	−8.08325	+	4.66687i	−0.265632	+	0.153363i
$927$	0.697195	+	32.1140i	0.0228989	+	1.05476i
$928$	−1.86485	−	6.95973i	−0.0612169	−	0.228464i
$929$	−15.3159	−	26.5279i	−0.502499	−	0.870353i	−0.999996	−	0.00288755i	$-0.999081\pi$
$929$	−15.3159	−	26.5279i	−0.502499	−	0.870353i	0.497497	−	0.867466i	$-0.334252\pi$
$930$	0.976343	+	3.97213i	0.0320155	+	0.130251i
$931$	17.7437	−	33.8241i	0.581526	−	1.10854i
$932$	16.0542	−	16.0542i	0.525874	−	0.525874i
$933$	24.2652	−	10.3609i	0.794408	−	0.339202i
$934$	0.696241	+	0.401975i	0.0227817	+	0.0131530i
$935$	−1.11213	+	6.78215i	−0.0363704	+	0.221800i
$936$	3.89504	+	13.3688i	0.127313	+	0.436971i
$937$	−0.818219	−	0.818219i	−0.0267300	−	0.0267300i	0.693615	−	0.720345i	$-0.256017\pi$
$937$	−0.818219	−	0.818219i	−0.0267300	−	0.0267300i	−0.720345	+	0.693615i	$0.756017\pi$
$938$	6.94027	+	23.9517i	0.226608	+	0.782051i
$939$	31.0840	−	24.3921i	1.01439	−	0.796007i
$940$	−19.2397	−	15.7545i	−0.627530	−	0.513854i
$941$	−39.7684	−	22.9603i	−1.29641	−	0.748484i	−0.316630	−	0.948549i	$-0.602551\pi$
$941$	−39.7684	−	22.9603i	−1.29641	−	0.748484i	−0.979783	+	0.200065i	$0.935885\pi$
$942$	18.1456	−	24.1869i	0.591217	−	0.788053i
$943$	−10.2719	−	2.75234i	−0.334498	−	0.0896285i
$944$	−5.27318			−0.171627
$945$	−0.650593	−	30.7340i	−0.0211638	−	0.999776i
$946$	5.37514			0.174761
$947$	−30.6129	−	8.20271i	−0.994787	−	0.266552i	−0.275527	−	0.961293i	$-0.588852\pi$
$947$	−30.6129	−	8.20271i	−0.994787	−	0.266552i	−0.719260	+	0.694741i	$0.755519\pi$
$948$	16.6129	−	22.1439i	0.539563	−	0.719201i
$949$	5.02288	+	2.89996i	0.163050	+	0.0941367i
$950$	24.4426	−	12.1202i	0.793023	−	0.393233i
$951$	−6.73797	+	5.28739i	−0.218494	+	0.171456i
$952$	−3.72466	−	0.917654i	−0.120717	−	0.0297413i
$953$	−12.7159	−	12.7159i	−0.411908	−	0.411908i	0.470495	−	0.882403i	$-0.344076\pi$
$953$	−12.7159	−	12.7159i	−0.411908	−	0.411908i	−0.882403	+	0.470495i	$0.844076\pi$
$954$	5.62740	+	19.3146i	0.182194	+	0.625335i
$955$	−1.35824	+	0.975551i	−0.0439517	+	0.0315681i
$956$	9.19360	+	5.30793i	0.297342	+	0.171671i
$957$	−24.3306	+	10.3889i	−0.786497	+	0.335824i
$958$	−12.0027	+	12.0027i	−0.387789	+	0.387789i
$959$	25.3735	−	15.3422i	0.819352	−	0.495427i
$960$	−3.31314	−	2.00576i	−0.106931	−	0.0647357i
$961$	14.9423	+	25.8808i	0.482010	+	0.834865i
$962$	−7.74264	−	28.8959i	−0.249633	−	0.931642i
$963$	0.695160	+	32.0203i	0.0224012	+	1.03184i
$964$	17.4304	−	10.0635i	0.561396	−	0.324122i
$965$	−7.31327	−	19.3667i	−0.235423	−	0.623436i
$966$	20.1978	−	16.5207i	0.649852	−	0.531545i
$967$	−3.87679	−	3.87679i	−0.124669	−	0.124669i	0.642019	−	0.766688i	$-0.278097\pi$
$967$	−3.87679	−	3.87679i	−0.124669	−	0.124669i	−0.766688	+	0.642019i	$0.778097\pi$
$968$	−1.68391	+	6.28443i	−0.0541229	+	0.201989i
$969$	−13.5654	+	1.93592i	−0.435783	+	0.0621907i
$970$	−15.9275	−	22.1756i	−0.511401	−	0.712015i
$971$	−9.52298	+	5.49809i	−0.305607	+	0.176442i	−0.644959	−	0.764217i	$-0.723126\pi$
$971$	−9.52298	+	5.49809i	−0.305607	+	0.176442i	0.339352	+	0.940659i	$0.389792\pi$
$972$	−8.80489	+	12.8637i	−0.282417	+	0.412602i
$973$	51.1630	−	14.8251i	1.64021	−	0.475270i
$974$	−15.9920			−0.512416
$975$	−13.4161	−	37.8919i	−0.429658	−	1.21351i
$976$	−4.11857	+	7.13357i	−0.131832	+	0.228340i
$977$	−12.2836	−	45.8432i	−0.392988	−	1.46665i	−0.825180	−	0.564870i	$-0.808926\pi$
$977$	−12.2836	−	45.8432i	−0.392988	−	1.46665i	0.432191	−	0.901782i	$-0.357741\pi$
$978$	8.30526	−	3.54624i	0.265573	−	0.113396i
$979$		−	0.847678i		−	0.0270919i
$980$	15.4999	−	2.18021i	0.495126	−	0.0696443i
$981$	6.11313	−	24.9704i	0.195177	−	0.797243i
$982$	−1.77962	+	6.64162i	−0.0567898	+	0.211942i
$983$	−29.4055	+	7.87919i	−0.937891	+	0.251307i	−0.695216	−	0.718801i	$-0.744691\pi$
$983$	−29.4055	+	7.87919i	−0.937891	+	0.251307i	−0.242675	+	0.970108i	$0.578025\pi$
$984$	0.457000	+	3.20230i	0.0145686	+	0.102085i
$985$	5.43691	−	6.63967i	0.173234	−	0.211557i
$986$		−	10.4468i		−	0.332693i
$987$	−41.3760	−	29.7520i	−1.31701	−	0.947018i
$988$	−17.9087	+	17.9087i	−0.569750	+	0.569750i
$989$	−7.21898	−	12.5036i	−0.229550	−	0.397593i
$990$	−5.57211	+	13.0834i	−0.177093	+	0.415819i
$991$	7.93677	−	13.7469i	0.252120	−	0.436684i	−0.711989	−	0.702190i	$-0.752206\pi$
$991$	7.93677	−	13.7469i	0.252120	−	0.436684i	0.964109	+	0.265506i	$0.0855389\pi$
$992$	1.02014	+	0.273346i	0.0323895	+	0.00867873i
$993$	0.406360	+	0.0490178i	0.0128954	+	0.00155553i
$994$	4.65393	−	0.0941977i	0.147614	−	0.00298777i
$995$	11.4236	+	5.16090i	0.362151	+	0.163612i
$996$	−21.5421	−	8.65032i	−0.682587	−	0.274096i
$997$	27.0051	−	7.23598i	0.855259	−	0.229166i	0.195556	−	0.980693i	$-0.437349\pi$
$997$	27.0051	−	7.23598i	0.855259	−	0.229166i	0.659703	+	0.751527i	$0.270682\pi$
$998$	29.9340	−	8.02080i	0.947545	−	0.253894i
$999$	19.5116	−	27.2189i	0.617318	−	0.861166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.137.7	yes	64
3.2	odd	2	inner	210.2.x.a.137.10	yes	64
5.3	odd	4	inner	210.2.x.a.53.7	yes	64
7.2	even	3	inner	210.2.x.a.107.14	yes	64
15.8	even	4	inner	210.2.x.a.53.14	yes	64
21.2	odd	6	inner	210.2.x.a.107.7	yes	64
35.23	odd	12	inner	210.2.x.a.23.10	yes	64
105.23	even	12	inner	210.2.x.a.23.7	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.7	✓	64	105.23	even	12	inner
210.2.x.a.23.10	yes	64	35.23	odd	12	inner
210.2.x.a.53.7	yes	64	5.3	odd	4	inner
210.2.x.a.53.14	yes	64	15.8	even	4	inner
210.2.x.a.107.7	yes	64	21.2	odd	6	inner
210.2.x.a.107.14	yes	64	7.2	even	3	inner
210.2.x.a.137.7	yes	64	1.1	even	1	trivial
210.2.x.a.137.10	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.03943 - 1.38549i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.22506 + 0.221605i) q^{5} +(-1.36260 + 1.06926i) q^{6} +(-0.736347 - 2.54122i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.839170 - 2.88024i) q^{9} +(2.20660 + 0.361834i) q^{10} +(-1.83587 - 1.05994i) q^{11} +(1.59292 - 0.680155i) q^{12} +(3.28206 - 3.28206i) q^{13} +(0.0535403 + 2.64521i) q^{14} +(-2.00576 + 3.31314i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.375258 + 1.40048i) q^{17} +(0.0651145 + 2.99929i) q^{18} +(-4.72549 + 2.72826i) q^{19} +(-2.03776 - 0.920615i) q^{20} +(-4.28622 - 1.62122i) q^{21} +(1.49898 + 1.49898i) q^{22} +(1.47375 - 5.50010i) q^{23} +(-1.71468 + 0.244702i) q^{24} +(4.90178 - 0.986167i) q^{25} +(-4.01969 + 2.32077i) q^{26} +(-4.86281 - 1.83115i) q^{27} +(0.632915 - 2.56893i) q^{28} +7.20525 q^{29} +(2.79492 - 2.68112i) q^{30} +(-0.528063 + 0.914632i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.37679 + 1.44185i) q^{33} -1.44989i q^{34} +(2.20156 + 5.49119i) q^{35} +(0.713378 - 2.91395i) q^{36} +(-1.66812 + 6.22550i) q^{37} +(5.27060 - 1.41225i) q^{38} +(-1.13579 - 7.95874i) q^{39} +(1.73005 + 1.41666i) q^{40} -1.86758i q^{41} +(3.72057 + 2.67533i) q^{42} +(1.79293 - 1.79293i) q^{43} +(-1.05994 - 1.83587i) q^{44} +(2.50548 + 6.22275i) q^{45} +(-2.84706 + 4.93126i) q^{46} +(10.7419 + 2.87830i) q^{47} +(1.71959 + 0.207427i) q^{48} +(-5.91559 + 3.74244i) q^{49} +(-4.99000 - 0.316111i) q^{50} +(2.33041 + 0.935787i) q^{51} +(4.48338 - 1.20132i) q^{52} +(6.47741 - 1.73562i) q^{53} +(4.22318 + 3.02734i) q^{54} +(4.31980 + 1.95159i) q^{55} +(-1.27624 + 2.31759i) q^{56} +(-1.13183 + 9.38296i) q^{57} +(-6.95973 - 1.86485i) q^{58} +(-2.63659 + 4.56671i) q^{59} +(-3.39361 + 1.86638i) q^{60} +(4.11857 + 7.13357i) q^{61} +(0.746794 - 0.746794i) q^{62} +(-6.70141 + 4.25337i) q^{63} +1.00000i q^{64} +(-6.57547 + 8.03011i) q^{65} +(3.63491 - 0.518738i) q^{66} +(9.10412 - 2.43944i) q^{67} +(-0.375258 + 1.40048i) q^{68} +(-6.08848 - 7.75883i) q^{69} +(-0.705321 - 5.87388i) q^{70} -1.75938i q^{71} +(-1.44326 + 2.63002i) q^{72} +(0.323412 + 1.20699i) q^{73} +(3.22256 - 5.58163i) q^{74} +(3.72874 - 7.81643i) q^{75} -5.45653 q^{76} +(-1.34170 + 5.44582i) q^{77} +(-0.962782 + 7.98152i) q^{78} +(13.8415 - 7.99137i) q^{79} +(-1.30445 - 1.81616i) q^{80} +(-7.59159 + 4.83403i) q^{81} +(-0.483365 + 1.80394i) q^{82} +(-9.47707 - 9.47707i) q^{83} +(-2.90136 - 3.54712i) q^{84} +(-1.14532 - 3.03300i) q^{85} +(-2.19589 + 1.26779i) q^{86} +(7.48935 - 9.98280i) q^{87} +(0.548664 + 2.04764i) q^{88} +(0.199936 + 0.346299i) q^{89} +(-0.809541 - 6.65918i) q^{90} +(-10.7572 - 5.92370i) q^{91} +(4.02635 - 4.02635i) q^{92} +(0.718330 + 1.68232i) q^{93} +(-9.63096 - 5.56044i) q^{94} +(9.90990 - 7.11774i) q^{95} +(-1.60731 - 0.645421i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(6.68263 - 2.08385i) q^{98} +(-1.51227 + 6.17721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43}+ \cdots + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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