LMFDB - Embedded newform 210.2.x.a.107.7

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			107.7
Character	$\chi$	$=$	210.107
Dual form			210.2.x.a.53.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.38549 - 1.03943i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.30445 - 1.81616i) q^{5} +(-1.36260 - 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.839170 - 2.88024i) q^{9} +(-1.41666 + 1.73005i) q^{10} +(-1.83587 + 1.05994i) q^{11} +(-0.680155 + 1.59292i) q^{12} +(3.28206 - 3.28206i) q^{13} +(-0.0535403 + 2.64521i) q^{14} +(-3.69506 - 1.16039i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.40048 + 0.375258i) q^{17} +(-2.99929 - 0.0651145i) 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} +(5.50010 - 1.47375i) q^{23} +(1.71468 + 0.244702i) q^{24} +(-1.59685 + 4.73815i) q^{25} +(-4.01969 - 2.32077i) q^{26} +(-1.83115 - 4.86281i) q^{27} +(2.56893 - 0.632915i) q^{28} -7.20525 q^{29} +(-0.164496 + 3.86949i) q^{30} +(-0.528063 - 0.914632i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.44185 + 3.37679i) q^{33} -1.44989i q^{34} +(1.97756 + 5.57577i) q^{35} +(0.713378 + 2.91395i) q^{36} +(6.22550 - 1.66812i) q^{37} +(1.41225 - 5.27060i) q^{38} +(1.13579 - 7.95874i) q^{39} +(0.361834 - 2.20660i) q^{40} +1.86758i q^{41} +(2.67533 + 3.72057i) q^{42} +(1.79293 - 1.79293i) q^{43} +(1.05994 - 1.83587i) q^{44} +(-6.32562 + 2.23305i) q^{45} +(-2.84706 - 4.93126i) q^{46} +(2.87830 + 10.7419i) q^{47} +(-0.207427 - 1.71959i) q^{48} +(5.91559 + 3.74244i) q^{49} +(4.99000 + 0.316111i) q^{50} +(2.33041 - 0.935787i) q^{51} +(-1.20132 + 4.48338i) q^{52} +(1.73562 - 6.47741i) q^{53} +(-4.22318 + 3.02734i) q^{54} +(4.31980 + 1.95159i) q^{55} +(-1.27624 - 2.31759i) q^{56} +(9.38296 - 1.13183i) q^{57} +(1.86485 + 6.95973i) q^{58} +(2.63659 + 4.56671i) q^{59} +(3.78021 - 0.842606i) q^{60} +(4.11857 - 7.13357i) q^{61} +(-0.746794 + 0.746794i) q^{62} +(-4.25337 + 6.70141i) q^{63} +1.00000i q^{64} +(-10.2420 - 1.67947i) q^{65} +(3.63491 + 0.518738i) q^{66} +(-2.43944 + 9.10412i) q^{67} +(-1.40048 + 0.375258i) q^{68} +(6.08848 - 7.75883i) q^{69} +(4.87395 - 3.35329i) q^{70} +1.75938i q^{71} +(2.63002 - 1.44326i) q^{72} +(-1.20699 - 0.323412i) q^{73} +(-3.22256 - 5.58163i) q^{74} +(2.71256 + 8.22448i) q^{75} -5.45653 q^{76} +(5.44582 - 1.34170i) q^{77} +(-7.98152 + 0.962782i) q^{78} +(-13.8415 - 7.99137i) q^{79} +(-2.22506 + 0.221605i) q^{80} +(-7.59159 - 4.83403i) q^{81} +(1.80394 - 0.483365i) 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} +(-9.98280 + 7.48935i) q^{87} +(-2.04764 - 0.548664i) q^{88} +(-0.199936 + 0.346299i) q^{89} +(3.79416 + 5.53212i) q^{90} +(-10.7572 + 5.92370i) q^{91} +(-4.02635 + 4.02635i) q^{92} +(-1.68232 - 0.718330i) q^{93} +(9.63096 - 5.56044i) q^{94} +(-1.20919 - 12.1411i) q^{95} +(-1.60731 + 0.645421i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(2.08385 - 6.68263i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.38549	−	1.03943i	0.799914	−	0.600115i
$3$	1.38549	−	1.03943i	0.799914	−	0.600115i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.30445	−	1.81616i	−0.583366	−	0.812210i
$5$	−1.30445	−	1.81616i	−0.583366	−	0.812210i
$6$	−1.36260	−	1.06926i	−0.556281	−	0.436522i
$7$	−2.54122	−	0.736347i	−0.960490	−	0.278313i
$7$	−2.54122	−	0.736347i	−0.960490	−	0.278313i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.839170	−	2.88024i	0.279723	−	0.960081i
$10$	−1.41666	+	1.73005i	−0.447986	+	0.547091i
$11$	−1.83587	+	1.05994i	−0.553535	+	0.319583i	−0.750546	−	0.660818i	$-0.770210\pi$
$11$	−1.83587	+	1.05994i	−0.553535	+	0.319583i	0.197012	+	0.980401i	$0.436876\pi$
$12$	−0.680155	+	1.59292i	−0.196344	+	0.459836i
$13$	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
$15$	−3.69506	−	1.16039i	−0.954061	−	0.299611i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.40048	+	0.375258i	0.339667	+	0.0910134i	0.424620	−	0.905371i	$-0.360408\pi$
$17$	1.40048	+	0.375258i	0.339667	+	0.0910134i	−0.0849537	+	0.996385i	$0.527074\pi$
$18$	−2.99929	−	0.0651145i	−0.706940	−	0.0153476i
$19$	4.72549	+	2.72826i	1.08410	+	0.625906i	0.932000	−	0.362458i	$-0.118063\pi$
$19$	4.72549	+	2.72826i	1.08410	+	0.625906i	0.152102	+	0.988365i	$0.451396\pi$
$20$	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
$23$	5.50010	−	1.47375i	1.14685	−	0.307298i	0.365148	−	0.930949i	$-0.381018\pi$
$23$	5.50010	−	1.47375i	1.14685	−	0.307298i	0.781702	+	0.623652i	$0.214352\pi$
$24$	1.71468	+	0.244702i	0.350007	+	0.0499496i
$25$	−1.59685	+	4.73815i	−0.319369	+	0.947630i
$26$	−4.01969	−	2.32077i	−0.788326	−	0.455140i
$27$	−1.83115	−	4.86281i	−0.352405	−	0.935848i
$28$	2.56893	−	0.632915i	0.485483	−	0.119610i
$29$	−7.20525			−1.33798			−0.668990	−	0.743271i	$-0.733273\pi$
$29$	−7.20525			−1.33798			−0.668990	+	0.743271i	$0.733273\pi$
$30$	−0.164496	+	3.86949i	−0.0300327	+	0.706469i
$31$	−0.528063	−	0.914632i	−0.0948429	−	0.164273i	0.814700	−	0.579882i	$-0.196902\pi$
$31$	−0.528063	−	0.914632i	−0.0948429	−	0.164273i	−0.909543	+	0.415610i	$0.863568\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−1.44185	+	3.37679i	−0.250993	+	0.587824i
$34$		−	1.44989i		−	0.248653i
$35$	1.97756	+	5.57577i	0.334269	+	0.942478i
$36$	0.713378	+	2.91395i	0.118896	+	0.485658i
$37$	6.22550	−	1.66812i	1.02347	−	0.274237i	0.292221	−	0.956351i	$-0.405606\pi$
$37$	6.22550	−	1.66812i	1.02347	−	0.274237i	0.731246	+	0.682114i	$0.238939\pi$
$38$	1.41225	−	5.27060i	0.229098	−	0.855004i
$39$	1.13579	−	7.95874i	0.181872	−	1.27442i
$40$	0.361834	−	2.20660i	0.0572110	−	0.348894i
$41$			1.86758i			0.291667i	0.989309	+	0.145833i	$0.0465863\pi$
$41$			1.86758i			0.291667i	−0.989309	+	0.145833i	$0.953414\pi$
$42$	2.67533	+	3.72057i	0.412813	+	0.574096i
$43$	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
$45$	−6.32562	+	2.23305i	−0.942968	+	0.332884i
$46$	−2.84706	−	4.93126i	−0.419776	−	0.727074i
$47$	2.87830	+	10.7419i	0.419843	+	1.56687i	0.774934	+	0.632042i	$0.217783\pi$
$47$	2.87830	+	10.7419i	0.419843	+	1.56687i	−0.355091	+	0.934832i	$0.615550\pi$
$48$	−0.207427	−	1.71959i	−0.0299396	−	0.248201i
$49$	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
$52$	−1.20132	+	4.48338i	−0.166593	+	0.621733i
$53$	1.73562	−	6.47741i	0.238405	−	0.889741i	−0.738179	−	0.674605i	$-0.764314\pi$
$53$	1.73562	−	6.47741i	0.238405	−	0.889741i	0.976584	−	0.215136i	$-0.0690194\pi$
$54$	−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
$57$	9.38296	−	1.13183i	1.24280	−	0.149915i
$58$	1.86485	+	6.95973i	0.244867	+	0.913858i
$59$	2.63659	+	4.56671i	0.343255	+	0.594535i	0.985035	−	0.172354i	$-0.0551372\pi$
$59$	2.63659	+	4.56671i	0.343255	+	0.594535i	−0.641780	+	0.766889i	$0.721804\pi$
$60$	3.78021	−	0.842606i	0.488023	−	0.108780i
$61$	4.11857	−	7.13357i	0.527328	−	0.913360i	−0.472164	−	0.881511i	$-0.656527\pi$
$61$	4.11857	−	7.13357i	0.527328	−	0.913360i	0.999493	−	0.0318490i	$-0.0101396\pi$
$62$	−0.746794	+	0.746794i	−0.0948429	+	0.0948429i
$63$	−4.25337	+	6.70141i	−0.535874	+	0.844298i
$64$			1.00000i			0.125000i
$65$	−10.2420	−	1.67947i	−1.27036	−	0.208312i
$66$	3.63491	+	0.518738i	0.447426	+	0.0638522i
$67$	−2.43944	+	9.10412i	−0.298025	+	1.11225i	0.640760	+	0.767742i	$0.278620\pi$
$67$	−2.43944	+	9.10412i	−0.298025	+	1.11225i	−0.938785	+	0.344504i	$0.888047\pi$
$68$	−1.40048	+	0.375258i	−0.169833	+	0.0455067i
$69$	6.08848	−	7.75883i	0.732967	−	0.934054i
$70$	4.87395	−	3.35329i	0.582549	−	0.400795i
$71$			1.75938i			0.208800i	0.994535	+	0.104400i	$0.0332922\pi$
$71$			1.75938i			0.208800i	−0.994535	+	0.104400i	$0.966708\pi$
$72$	2.63002	−	1.44326i	0.309951	−	0.170089i
$73$	−1.20699	−	0.323412i	−0.141268	−	0.0378525i	0.187492	−	0.982266i	$-0.439964\pi$
$73$	−1.20699	−	0.323412i	−0.141268	−	0.0378525i	−0.328760	+	0.944414i	$0.606631\pi$
$74$	−3.22256	−	5.58163i	−0.374615	−	0.648852i
$75$	2.71256	+	8.22448i	0.313220	+	0.949681i
$76$	−5.45653			−0.625906
$77$	5.44582	−	1.34170i	0.620609	−	0.152901i
$78$	−7.98152	+	0.962782i	−0.903729	+	0.109014i
$79$	−13.8415	−	7.99137i	−1.55728	−	0.899099i	−0.997515	−	0.0704506i	$-0.977556\pi$
$79$	−13.8415	−	7.99137i	−1.55728	−	0.899099i	−0.559770	−	0.828648i	$-0.689110\pi$
$80$	−2.22506	+	0.221605i	−0.248769	+	0.0247761i
$81$	−7.59159	−	4.83403i	−0.843510	−	0.537114i
$82$	1.80394	−	0.483365i	0.199212	−	0.0533787i
$83$	9.47707	+	9.47707i	1.04024	+	1.04024i	0.999156	+	0.0410882i	$0.0130825\pi$
$83$	9.47707	+	9.47707i	1.04024	+	1.04024i	0.0410882	+	0.999156i	$0.486918\pi$
$84$	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
$87$	−9.98280	+	7.48935i	−1.07027	+	0.802943i
$88$	−2.04764	−	0.548664i	−0.218280	−	0.0584878i
$89$	−0.199936	+	0.346299i	−0.0211931	+	0.0367076i	−0.876427	−	0.481534i	$-0.840080\pi$
$89$	−0.199936	+	0.346299i	−0.0211931	+	0.0367076i	0.855234	+	0.518242i	$0.173413\pi$
$90$	3.79416	+	5.53212i	0.399939	+	0.583137i
$91$	−10.7572	+	5.92370i	−1.12766	+	0.620973i
$92$	−4.02635	+	4.02635i	−0.419776	+	0.419776i
$93$	−1.68232	−	0.718330i	−0.174449	−	0.0744873i
$94$	9.63096	−	5.56044i	0.993358	−	0.573516i
$95$	−1.20919	−	12.1411i	−0.124060	−	1.24565i
$96$	−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	$0.962818\pi$
$98$	2.08385	−	6.68263i	0.210500	−	0.675048i
$99$	1.51227	+	6.17721i	0.151989	+	0.620833i
$100$	−0.986167	−	4.90178i	−0.0986167	−	0.490178i
$101$	−3.82984	+	2.21116i	−0.381084	+	0.220019i	−0.678290	−	0.734795i	$-0.737279\pi$
$101$	−3.82984	+	2.21116i	−0.381084	+	0.220019i	0.297206	+	0.954813i	$0.403945\pi$
$102$	−1.50705	−	2.00880i	−0.149221	−	0.198901i
$103$	2.77123	+	10.3424i	0.273057	+	1.01906i	0.957132	+	0.289652i	$0.0935395\pi$
$103$	2.77123	+	10.3424i	0.273057	+	1.01906i	−0.684075	+	0.729412i	$0.739794\pi$
$104$	4.64154			0.455140
$105$	8.53552	+	5.66965i	0.832981	+	0.553301i
$106$	−6.70591			−0.651335
$107$	−2.76314	−	10.3122i	−0.267123	−	0.996917i	−0.960938	−	0.276763i	$-0.910738\pi$
$107$	−2.76314	−	10.3122i	−0.267123	−	0.996917i	0.693815	−	0.720153i	$-0.255928\pi$
$108$	4.01722	+	3.29574i	0.386558	+	0.317133i
$109$	−7.42120	+	4.28463i	−0.710822	+	0.410393i	−0.811365	−	0.584539i	$-0.801275\pi$
$109$	−7.42120	+	4.28463i	−0.710822	+	0.410393i	0.100543	+	0.994933i	$0.467942\pi$
$110$	0.767044	−	4.67772i	0.0731348	−	0.446003i
$111$	6.89149	−	8.78214i	0.654111	−	0.833564i
$112$	−1.90830	+	1.83259i	−0.180318	+	0.173163i
$113$	−7.12484	−	7.12484i	−0.670249	−	0.670249i	0.287524	−	0.957773i	$-0.407168\pi$
$113$	−7.12484	−	7.12484i	−0.670249	−	0.670249i	−0.957773	+	0.287524i	$0.907168\pi$
$114$	−3.52176	−	8.77030i	−0.329843	−	0.821414i
$115$	−9.85113	−	8.06662i	−0.918623	−	0.752216i
$116$	6.23993	−	3.60262i	0.579363	−	0.334495i
$117$	−6.69893	−	12.2073i	−0.619316	−	1.12857i
$118$	3.72870	−	3.72870i	0.343255	−	0.343255i
$119$	−3.28261	−	1.98485i	−0.300916	−	0.181951i
$120$	−1.79229	−	3.43332i	−0.163613	−	0.313418i
$121$	−3.25306	+	5.63447i	−0.295733	+	0.512224i
$122$	−7.95646	−	2.13193i	−0.720344	−	0.193016i
$123$	1.94122	+	2.58751i	0.175034	+	0.233308i
$124$	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	$-0.500495\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	0.620464	−	4.34772i	0.0546288	−	0.382795i
$130$	1.02859	+	10.3277i	0.0902130	+	0.905799i
$131$	5.01434	+	2.89503i	0.438105	+	0.252940i	0.702793	−	0.711394i	$-0.251936\pi$
$131$	5.01434	+	2.89503i	0.438105	+	0.252940i	−0.264689	+	0.964334i	$0.585269\pi$
$132$	−0.439721	−	3.64531i	−0.0382728	−	0.317283i
$133$	−9.99956	−	10.4127i	−0.867072	−	0.902897i
$134$	9.42528			0.814220
$135$	−6.44299	+	9.66892i	−0.554524	+	0.832168i
$136$	0.724943	+	1.25564i	0.0621633	+	0.107670i
$137$	10.8253	+	2.90062i	0.924864	+	0.247816i	0.689663	−	0.724130i	$-0.257759\pi$
$137$	10.8253	+	2.90062i	0.924864	+	0.247816i	0.235201	+	0.971947i	$0.424425\pi$
$138$	−9.07027	−	3.87289i	−0.772113	−	0.329682i
$139$			20.1333i			1.70768i	0.520535	+	0.853841i	$0.325733\pi$
$139$			20.1333i			1.70768i	−0.520535	+	0.853841i	$0.674267\pi$
$140$	−4.50050	−	3.83998i	−0.380362	−	0.324538i
$141$	15.1534	+	11.8911i	1.27614	+	1.00141i
$142$	1.69943	−	0.455361i	0.142613	−	0.0382131i
$143$	−2.54665	+	9.50422i	−0.212961	+	0.794782i
$144$	−2.07478	−	2.16686i	−0.172898	−	0.180572i
$145$	9.39885	+	13.0859i	0.780532	+	1.08672i
$146$			1.24957i			0.103415i
$147$	12.0860	−	0.963730i	0.996836	−	0.0794871i
$148$	−4.55738	+	4.55738i	−0.374615	+	0.374615i
$149$	−5.90510	+	10.2279i	−0.483765	+	0.837905i	−0.999826	−	0.0186464i	$-0.994064\pi$
$149$	−5.90510	+	10.2279i	−0.483765	+	0.837905i	0.516061	+	0.856552i	$0.327398\pi$
$150$	7.24217	−	4.74879i	0.591321	−	0.387737i
$151$	4.33354	+	7.50591i	0.352658	+	0.610822i	0.986714	−	0.162465i	$-0.0519445\pi$
$151$	4.33354	+	7.50591i	0.352658	+	0.610822i	−0.634056	+	0.773287i	$0.718611\pi$
$152$	1.41225	+	5.27060i	0.114549	+	0.427502i
$153$	2.25608	−	3.71882i	0.182393	−	0.300649i
$154$	−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
$157$	4.51828	−	16.8625i	0.360598	−	1.34577i	−0.512693	−	0.858572i	$-0.671352\pi$
$157$	4.51828	−	16.8625i	0.360598	−	1.34577i	0.873291	−	0.487198i	$-0.161981\pi$
$158$	−4.13664	+	15.4381i	−0.329093	+	1.22819i
$159$	−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
$162$	−2.70446	+	8.58405i	−0.212483	+	0.674427i
$163$	1.34945	+	5.03620i	0.105697	+	0.394466i	0.998423	−	0.0561330i	$-0.0178771\pi$
$163$	1.34945	+	5.03620i	0.105697	+	0.394466i	−0.892726	+	0.450599i	$0.851210\pi$
$164$	−0.933789	−	1.61737i	−0.0729167	−	0.126295i
$165$	8.01359	−	1.78622i	0.623857	−	0.139057i
$166$	6.70130	−	11.6070i	0.520122	−	0.900877i
$167$	−5.99458	+	5.99458i	−0.463874	+	0.463874i	−0.899923	−	0.436049i	$-0.856377\pi$
$167$	−5.99458	+	5.99458i	−0.463874	+	0.463874i	0.436049	+	0.899923i	$0.356377\pi$
$168$	−4.17719	−	1.88444i	−0.322277	−	0.145388i
$169$		−	8.54387i		−	0.657221i
$170$	−2.63322	+	1.89130i	−0.201959	+	0.145056i
$171$	11.8235	−	11.3211i	0.904169	−	0.865744i
$172$	−0.656259	+	2.44919i	−0.0500393	+	0.186749i
$173$	4.84235	−	1.29750i	0.368157	−	0.0986474i	−0.0699972	−	0.997547i	$-0.522299\pi$
$173$	4.84235	−	1.29750i	0.368157	−	0.0986474i	0.438154	+	0.898900i	$0.355632\pi$
$174$	9.81790	+	7.70426i	0.744293	+	0.584059i
$175$	7.54686	−	10.8648i	0.570489	−	0.821305i
$176$			2.11988i			0.159792i
$177$	8.39975	+	3.58658i	0.631364	+	0.269584i
$178$	0.386246	+	0.103494i	0.0289504	+	0.00775723i
$179$	4.04588	+	7.00767i	0.302403	+	0.523778i	0.976680	−	0.214701i	$-0.0688777\pi$
$179$	4.04588	+	7.00767i	0.302403	+	0.523778i	−0.674277	+	0.738479i	$0.735544\pi$
$180$	4.36162	−	5.09669i	0.325096	−	0.379885i
$181$	10.6946			0.794924			0.397462	−	0.917619i	$-0.369891\pi$
$181$	10.6946			0.794924			0.397462	+	0.917619i	$0.369891\pi$
$182$	8.50602	+	8.85747i	0.630508	+	0.656559i
$183$	−1.70861	−	14.1645i	−0.126304	−	1.04707i
$184$	4.93126	+	2.84706i	0.363537	+	0.209888i
$185$	−11.1504	−	9.13052i	−0.819793	−	0.671289i
$186$	−0.258436	+	1.81092i	−0.0189495	+	0.132783i
$187$	−2.96885	+	0.795501i	−0.217104	+	0.0581728i
$188$	−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	0.523249	−	0.852180i	$-0.324720\pi$
$191$	0.647671	+	0.373933i	0.0468638	+	0.0270569i	−0.476385	+	0.879237i	$0.658053\pi$
$192$	1.03943	+	1.38549i	0.0750144	+	0.0999892i
$193$	−8.94254	−	2.39615i	−0.643698	−	0.172478i	−0.0778200	−	0.996967i	$-0.524796\pi$
$193$	−8.94254	−	2.39615i	−0.643698	−	0.172478i	−0.565878	+	0.824489i	$0.691463\pi$
$194$	−6.10509	+	10.5743i	−0.438320	+	0.759192i
$195$	−15.9359	+	8.31897i	−1.14119	+	0.595734i
$196$	−6.99427	−	0.283250i	−0.499590	−	0.0202322i
$197$	2.71376	−	2.71376i	0.193348	−	0.193348i	−0.603793	−	0.797141i	$-0.706345\pi$
$197$	2.71376	−	2.71376i	0.193348	−	0.193348i	0.797141	+	0.603793i	$0.206345\pi$
$198$	5.57532	−	3.05952i	0.396221	−	0.217431i
$199$	4.85488	−	2.80297i	0.344153	−	0.198697i	−0.317954	−	0.948106i	$-0.602996\pi$
$199$	4.85488	−	2.80297i	0.344153	−	0.198697i	0.662107	+	0.749409i	$0.269662\pi$
$200$	−4.47952	+	2.22124i	−0.316750	+	0.157065i
$201$	6.08327	+	15.1493i	0.429081	+	1.06855i
$202$	3.12705	+	3.12705i	0.220019	+	0.220019i
$203$	18.3101	+	5.30556i	1.28512	+	0.372377i
$204$	−1.55030	+	1.97562i	−0.108543	+	0.138321i
$205$	3.39181	−	2.43615i	0.236895	−	0.170148i
$206$	9.27271	−	5.35360i	0.646060	−	0.373003i
$207$	0.370770	−	17.0783i	0.0257703	−	1.18703i
$208$	−1.20132	−	4.48338i	−0.0832964	−	0.310867i
$209$	−11.5672			−0.800117
$210$	3.26730	−	9.71209i	0.225465	−	0.670198i
$211$	14.8448			1.02196			0.510978	−	0.859594i	$-0.329283\pi$
$211$	14.8448			1.02196			0.510978	+	0.859594i	$0.329283\pi$
$212$	1.73562	+	6.47741i	0.119203	+	0.444870i
$213$	1.82875	+	2.43761i	0.125304	+	0.167022i
$214$	−9.24565	+	5.33798i	−0.632020	+	0.364897i
$215$	−5.59503	−	0.917463i	−0.381578	−	0.0625705i
$216$	2.14371	−	4.73334i	0.145861	−	0.322063i
$217$	0.668438	+	2.71312i	0.0453765	+	0.184178i
$218$	6.05939	+	6.05939i	0.410393	+	0.410393i
$219$	−2.00844	+	0.806498i	−0.135718	+	0.0544981i
$220$	−4.71685	+	0.469774i	−0.318010	+	0.0316722i
$221$	5.82809	−	3.36485i	0.392040	−	0.226344i
$222$	−10.2665	−	4.38368i	−0.689045	−	0.294213i
$223$	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
$225$	12.3070	+	8.57542i	0.820467	+	0.571694i
$226$	−5.03803	+	8.72612i	−0.335124	+	0.580453i
$227$	−11.2410	−	3.01201i	−0.746089	−	0.199914i	−0.134307	−	0.990940i	$-0.542881\pi$
$227$	−11.2410	−	3.01201i	−0.746089	−	0.199914i	−0.611783	+	0.791026i	$0.709547\pi$
$228$	−7.55997	+	5.67168i	−0.500671	+	0.375616i
$229$	3.58186	+	2.06799i	0.236696	+	0.136657i	0.613657	−	0.789572i	$-0.289698\pi$
$229$	3.58186	+	2.06799i	0.236696	+	0.136657i	−0.376961	+	0.926229i	$0.623031\pi$
$230$	−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
$233$	21.9305	−	5.87626i	1.43671	−	0.384967i	0.545333	−	0.838220i	$-0.316403\pi$
$233$	21.9305	−	5.87626i	1.43671	−	0.384967i	0.891382	+	0.453253i	$0.149737\pi$
$234$	−10.0576	+	9.63016i	−0.657485	+	0.629543i
$235$	15.7545	−	19.2397i	1.02771	−	1.25506i
$236$	−4.56671	−	2.63659i	−0.297267	−	0.171627i
$237$	−27.4837	+	3.31526i	−1.78526	+	0.215349i
$238$	−1.06762	+	3.68448i	−0.0692034	+	0.238829i
$239$	−10.6159			−0.686682			−0.343341	−	0.939211i	$-0.611559\pi$
$239$	−10.6159			−0.686682			−0.343341	+	0.939211i	$0.611559\pi$
$240$	−2.85246	+	2.61983i	−0.184125	+	0.169109i
$241$	10.0635	+	17.4304i	0.648245	+	1.12279i	0.983542	+	0.180680i	$0.0578300\pi$
$241$	10.0635	+	17.4304i	0.648245	+	1.12279i	−0.335297	+	0.942112i	$0.608837\pi$
$242$	6.28443	+	1.68391i	0.403979	+	0.108246i
$243$	−15.5427	+	1.19343i	−0.997065	+	0.0765583i
$244$			8.23713i			0.527328i
$245$	−0.919713	−	15.6254i	−0.0587583	−	0.998272i
$246$	1.99692	−	2.54477i	0.127319	−	0.162249i
$247$	24.4637	−	6.55502i	1.55659	−	0.417086i
$248$	0.273346	−	1.02014i	0.0173575	−	0.0647789i
$249$	22.9811	+	3.27964i	1.45637	+	0.207839i
$250$	−5.93507	−	9.47496i	−0.375367	−	0.599249i
$251$		−	17.8395i		−	1.12602i	−0.826450	−	0.563010i	$-0.809643\pi$
$251$		−	17.8395i		−	1.12602i	0.826450	−	0.563010i	$-0.190357\pi$
$252$	0.332825	−	7.93027i	0.0209660	−	0.499560i
$253$	−8.53537	+	8.53537i	−0.536614	+	0.536614i
$254$	−7.98108	+	13.8236i	−0.500778	+	0.867372i
$255$	−4.73943	−	3.01171i	−0.296794	−	0.188600i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.258140	−	0.963390i	−0.0161023	−	0.0600946i	0.957407	−	0.288741i	$-0.0932367\pi$
$257$	−0.258140	−	0.963390i	−0.0161023	−	0.0600946i	−0.973510	+	0.228646i	$0.926570\pi$
$258$	−4.36016	+	0.525951i	−0.271452	+	0.0327443i
$259$	−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
$262$	1.49858	−	5.59277i	0.0925824	−	0.345522i
$263$	−4.46730	+	16.6722i	−0.275466	+	1.02805i	0.680063	+	0.733153i	$0.261952\pi$
$263$	−4.46730	+	16.6722i	−0.275466	+	1.02805i	−0.955529	+	0.294898i	$0.904714\pi$
$264$	−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
$267$	0.0829443	+	0.687613i	0.00507611	+	0.0420812i
$268$	−2.43944	−	9.10412i	−0.149013	−	0.556123i
$269$	13.8205	+	23.9379i	0.842653	+	1.45952i	0.887644	+	0.460531i	$0.152341\pi$
$269$	13.8205	+	23.9379i	0.842653	+	1.45952i	−0.0449907	+	0.998987i	$0.514326\pi$
$270$	11.0070	+	3.72095i	0.669866	+	0.226450i
$271$	−2.56520	+	4.44305i	−0.155825	+	0.269896i	−0.933359	−	0.358944i	$-0.883137\pi$
$271$	−2.56520	+	4.44305i	−0.155825	+	0.269896i	0.777534	+	0.628840i	$0.216470\pi$
$272$	1.02522	−	1.02522i	0.0621633	−	0.0621633i
$273$	−8.74669	+	19.3886i	−0.529374	+	1.17345i
$274$		−	11.2071i		−	0.677047i
$275$	−2.09055	−	10.3912i	−0.126065	−	0.626611i
$276$	−1.39336	+	9.76359i	−0.0838706	+	0.587699i
$277$	−7.12965	+	26.6082i	−0.428379	+	1.59873i	0.328053	+	0.944659i	$0.393608\pi$
$277$	−7.12965	+	26.6082i	−0.428379	+	1.59873i	−0.756432	+	0.654073i	$0.773059\pi$
$278$	19.4472	−	5.21087i	1.16637	−	0.312527i
$279$	−3.07750	+	0.753417i	−0.184245	+	0.0451059i
$280$	−2.54432	+	5.34101i	−0.152052	+	0.319187i
$281$		−	19.8830i		−	1.18612i	−0.805157	−	0.593062i	$-0.797919\pi$
$281$		−	19.8830i		−	1.18612i	0.805157	−	0.593062i	$-0.202081\pi$
$282$	7.56392	−	17.7147i	0.450425	−	1.05489i
$283$	−5.11082	−	1.36944i	−0.303807	−	0.0814048i	0.103695	−	0.994609i	$-0.466933\pi$
$283$	−5.11082	−	1.36944i	−0.303807	−	0.0814048i	−0.407502	+	0.913204i	$0.633600\pi$
$284$	−0.879690	−	1.52367i	−0.0522000	−	0.0904131i
$285$	−14.2951	−	15.5645i	−0.846771	−	0.921962i
$286$	9.83949			0.581821
$287$	1.37518	−	4.74593i	0.0811746	−	0.280143i
$288$	−1.55604	+	2.56491i	−0.0916904	+	0.151139i
$289$	−12.9019	−	7.44892i	−0.758935	−	0.438172i
$290$	10.2074	−	12.4655i	0.599397	−	0.731997i
$291$	−20.9365	−	2.98785i	−1.22732	−	0.175151i
$292$	1.20699	−	0.323412i	0.0706338	−	0.0189263i
$293$	−21.3392	−	21.3392i	−1.24665	−	1.24665i	−0.957191	−	0.289456i	$-0.906526\pi$
$293$	−21.3392	−	21.3392i	−1.24665	−	1.24665i	−0.289456	−	0.957191i	$-0.593474\pi$
$294$	−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
$297$	8.51602	+	6.98656i	0.494150	+	0.405402i
$298$	11.4078	+	3.05671i	0.660835	+	0.177070i
$299$	13.2147	−	22.8886i	0.764228	−	1.32368i
$300$	−6.46139	−	5.76632i	−0.373048	−	0.332919i
$301$	−5.87645	+	3.23601i	−0.338713	+	0.186521i
$302$	6.12855	−	6.12855i	0.352658	−	0.352658i
$303$	−3.00787	+	7.04440i	−0.172797	+	0.404690i
$304$	4.72549	−	2.72826i	0.271025	−	0.156477i
$305$	−18.3281	+	1.82539i	−1.04946	+	0.104521i
$306$	−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	$0.493798\pi$
$308$	−4.04537	+	3.88486i	−0.230506	+	0.221360i
$309$	14.5897	+	11.4488i	0.829978	+	0.651297i
$310$	2.33045	+	0.382143i	0.132360	+	0.0217042i
$311$	13.1923	−	7.61659i	0.748068	−	0.431897i	−0.0769272	−	0.997037i	$-0.524511\pi$
$311$	13.1923	−	7.61659i	0.748068	−	0.431897i	0.824996	+	0.565139i	$0.191178\pi$
$312$	6.43081	−	4.82455i	0.364073	−	0.273137i
$313$	−5.90424	−	22.0349i	−0.333727	−	1.24549i	−0.905243	−	0.424895i	$-0.860311\pi$
$313$	−5.90424	−	22.0349i	−0.333727	−	1.24549i	0.571515	−	0.820591i	$-0.306356\pi$
$314$	−17.4573			−0.985172
$315$	17.7191	−	1.01683i	0.998357	−	0.0572919i
$316$	15.9827			0.899099
$317$	−1.27984	−	4.77643i	−0.0718830	−	0.268271i	0.920625	−	0.390447i	$-0.127679\pi$
$317$	−1.27984	−	4.77643i	−0.0718830	−	0.268271i	−0.992508	+	0.122176i	$0.961013\pi$
$318$	−9.29097	+	6.97032i	−0.521012	+	0.390876i
$319$	13.2279	−	7.63712i	0.740619	−	0.427596i
$320$	1.81616	−	1.30445i	0.101526	−	0.0729207i
$321$	−14.5471	−	11.4153i	−0.811940	−	0.637142i
$322$	3.60389	+	14.6278i	0.200837	+	0.815177i
$323$	5.59416	+	5.59416i	0.311267	+	0.311267i
$324$	8.99152	+	0.390595i	0.499529	+	0.0216997i
$325$	10.3100	+	20.7919i	0.571894	+	1.15332i
$326$	4.51534	−	2.60693i	0.250081	−	0.144385i
$327$	−5.82843	+	13.6501i	−0.322313	+	0.754854i
$328$	−1.32058	+	1.32058i	−0.0729167	+	0.0729167i
$329$	0.595415	−	29.4171i	0.0328263	−	1.62181i
$330$	−3.79943	−	7.27822i	−0.209152	−	0.400653i
$331$	0.118156	−	0.204653i	0.00649446	−	0.0112487i	−0.862760	−	0.505614i	$-0.831266\pi$
$331$	0.118156	−	0.204653i	0.00649446	−	0.0112487i	0.869254	+	0.494365i	$0.164599\pi$
$332$	−12.9459	−	3.46885i	−0.710500	−	0.190378i
$333$	0.419671	−	19.3308i	0.0229978	−	1.05932i
$334$	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	$0.755424\pi$
$338$	−8.25275	+	2.21132i	−0.448890	+	0.120280i
$339$	−17.2772	−	2.46563i	−0.938368	−	0.133915i
$340$	2.50838	+	2.05399i	0.136036	+	0.111393i
$341$	1.93891	+	1.11943i	0.104998	+	0.0606204i
$342$	−13.9955	−	8.49056i	−0.756789	−	0.459117i
$343$	−12.2771	−	13.8663i	−0.662900	−	0.748708i
$344$	2.53559			0.136710
$345$	−22.0333	−	0.936660i	−1.18624	−	0.0504281i
$346$	−2.50658	−	4.34153i	−0.134755	−	0.233402i
$347$	−3.94296	−	1.05651i	−0.211669	−	0.0567166i	0.151426	−	0.988469i	$-0.451613\pi$
$347$	−3.94296	−	1.05651i	−0.211669	−	0.0567166i	−0.363095	+	0.931752i	$0.618280\pi$
$348$	4.90069	−	11.4774i	0.262704	−	0.615252i
$349$		−	11.9140i		−	0.637743i	−0.947798	−	0.318871i	$-0.896696\pi$
$349$		−	11.9140i		−	0.637743i	0.947798	−	0.318871i	$-0.103304\pi$
$350$	−12.4479	−	4.47767i	−0.665369	−	0.239342i
$351$	−21.9700	−	9.95010i	−1.17267	−	0.531097i
$352$	2.04764	−	0.548664i	0.109140	−	0.0292439i
$353$	1.82988	−	6.82920i	0.0973946	−	0.363482i	−0.899977	−	0.435937i	$-0.856417\pi$
$353$	1.82988	−	6.82920i	0.0973946	−	0.363482i	0.997372	+	0.0724557i	$0.0230836\pi$
$354$	1.29036	−	9.04181i	0.0685817	−	0.480567i
$355$	3.19531	−	2.29502i	0.169589	−	0.121807i
$356$		−	0.399872i		−	0.0211931i
$357$	−6.61114	+	0.662050i	−0.349899	+	0.0350394i
$358$	5.72174	−	5.72174i	0.302403	−	0.302403i
$359$	4.55001	−	7.88085i	0.240140	−	0.415935i	−0.720614	−	0.693337i	$-0.756140\pi$
$359$	4.55001	−	7.88085i	0.240140	−	0.415935i	0.960754	+	0.277401i	$0.0894732\pi$
$360$	−6.05190	−	2.89388i	−0.318963	−	0.152521i
$361$	5.38683	+	9.33027i	0.283518	+	0.491067i
$362$	−2.76797	−	10.3302i	−0.145481	−	0.542943i
$363$	1.34955	+	11.1878i	0.0708329	+	0.587209i
$364$	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
$367$	2.86001	−	10.6737i	0.149291	−	0.557163i	−0.850235	−	0.526403i	$-0.823540\pi$
$367$	2.86001	−	10.6737i	0.149291	−	0.557163i	0.999527	−	0.0307603i	$-0.00979286\pi$
$368$	1.47375	−	5.50010i	0.0768244	−	0.286713i
$369$	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
$372$	1.81610	−	0.219070i	0.0941603	−	0.0113582i
$373$	8.87861	+	33.1354i	0.459717	+	1.71569i	0.673837	+	0.738880i	$0.264645\pi$
$373$	8.87861	+	33.1354i	0.459717	+	1.71569i	−0.214120	+	0.976807i	$0.568688\pi$
$374$	1.53679	+	2.66180i	0.0794655	+	0.137638i
$375$	11.3985	−	15.6548i	0.588618	−	0.808411i
$376$	−5.56044	+	9.63096i	−0.286758	+	0.496679i
$377$	−23.6481	+	23.6481i	−1.21794	+	1.21794i
$378$	12.9612	−	4.58341i	0.666651	−	0.235745i
$379$			17.2109i			0.884063i	0.897000	+	0.442031i	$0.145742\pi$
$379$			17.2109i			0.884063i	−0.897000	+	0.442031i	$0.854258\pi$
$380$	7.11774	+	9.90990i	0.365132	+	0.508367i
$381$	−27.3700	−	3.90597i	−1.40221	−	0.200109i
$382$	0.193562	−	0.722383i	0.00990350	−	0.0369604i
$383$	−18.3791	+	4.92466i	−0.939128	+	0.251639i	−0.695743	−	0.718291i	$-0.744925\pi$
$383$	−18.3791	+	4.92466i	−0.939128	+	0.251639i	−0.243385	+	0.969930i	$0.578258\pi$
$384$	1.06926	−	1.36260i	0.0545653	−	0.0695351i
$385$	−9.54051	−	8.14029i	−0.486230	−	0.414867i
$386$			9.25799i			0.471220i
$387$	−3.65950	−	6.66866i	−0.186023	−	0.338987i
$388$	11.7941	+	3.16023i	0.598756	+	0.160436i
$389$	18.4175	+	31.9000i	0.933804	+	1.61740i	0.776752	+	0.629806i	$0.216866\pi$
$389$	18.4175	+	31.9000i	0.933804	+	1.61740i	0.157052	+	0.987590i	$0.449801\pi$
$390$	12.1600	+	13.2398i	0.615746	+	0.670423i
$391$	8.25583			0.417515
$392$	1.53665	+	6.82925i	0.0776126	+	0.344929i
$393$	9.95650	−	1.20102i	0.502239	−	0.0605833i
$394$	−3.32367	−	1.91892i	−0.167444	−	0.0966739i
$395$	3.54185	+	35.5625i	0.178210	+	1.78935i
$396$	−4.39827	−	4.59348i	−0.221022	−	0.230831i
$397$	19.3405	−	5.18227i	0.970672	−	0.260091i	0.261561	−	0.965187i	$-0.415763\pi$
$397$	19.3405	−	5.18227i	0.970672	−	0.260091i	0.709112	+	0.705096i	$0.249096\pi$
$398$	−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	0.707767	−	0.706446i	$-0.249703\pi$
$401$	9.00824	+	5.20091i	0.449850	+	0.259721i	−0.257917	+	0.966167i	$0.583036\pi$
$402$	13.0586	−	9.79692i	0.651306	−	0.488626i
$403$	−4.73502	−	1.26874i	−0.235868	−	0.0632006i
$404$	2.21116	−	3.82984i	0.110009	−	0.190542i
$405$	1.12346	+	20.0932i	0.0558254	+	0.998441i
$406$	0.385771	−	19.0594i	0.0191455	−	0.945901i
$407$	−9.66109	+	9.66109i	−0.478883	+	0.478883i
$408$	2.30955	+	0.986147i	0.114340	+	0.0488216i
$409$	−13.4035	+	7.73849i	−0.662758	+	0.382644i	−0.793327	−	0.608796i	$-0.791653\pi$
$409$	−13.4035	+	7.73849i	−0.662758	+	0.382644i	0.130569	+	0.991439i	$0.458320\pi$
$410$	−3.23101	−	2.64572i	−0.159568	−	0.130663i
$411$	18.0133	−	7.23331i	0.888529	−	0.356793i
$412$	−7.57114	−	7.57114i	−0.373003	−	0.373003i
$413$	−3.33747	−	13.5465i	−0.164226	−	0.666577i
$414$	−16.5924	+	4.06206i	−0.815471	+	0.199640i
$415$	4.84952	−	29.5742i	0.238054	−	1.45174i
$416$	−4.01969	+	2.32077i	−0.197082	+	0.113785i
$417$	20.9271	+	27.8945i	1.02481	+	1.36600i
$418$	2.99380	+	11.1730i	0.146432	+	0.546490i
$419$	14.9110			0.728451			0.364225	−	0.931311i	$-0.381334\pi$
$419$	14.9110			0.728451			0.364225	+	0.931311i	$0.381334\pi$
$420$	−10.2268	−	0.642299i	−0.499017	−	0.0313410i
$421$	−16.5292			−0.805586			−0.402793	−	0.915291i	$-0.631960\pi$
$421$	−16.5292			−0.805586			−0.402793	+	0.915291i	$0.631960\pi$
$422$	−3.84211	−	14.3389i	−0.187031	−	0.698009i
$423$	33.3548	+	0.724131i	1.62176	+	0.0352085i
$424$	5.80749	−	3.35295i	0.282036	−	0.162834i
$425$	−4.01438	+	6.03647i	−0.194726	+	0.292812i
$426$	1.88123	−	2.39734i	0.0911459	−	0.116151i
$427$	−15.7190	+	15.0953i	−0.760694	+	0.730511i
$428$	7.54904	+	7.54904i	0.364897	+	0.364897i
$429$	6.35061	+	15.8151i	0.306610	+	0.763559i
$430$	0.561898	+	5.64184i	0.0270971	+	0.272074i
$431$	−6.60065	+	3.81089i	−0.317942	+	0.183564i	−0.650475	−	0.759528i	$-0.725430\pi$
$431$	−6.60065	+	3.81089i	−0.317942	+	0.183564i	0.332533	+	0.943092i	$0.392097\pi$
$432$	−5.12689	−	0.845583i	−0.246668	−	0.0406831i
$433$	−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
$435$	26.6238	+	8.36088i	1.27652	+	0.400874i
$436$	4.28463	−	7.42120i	0.205197	−	0.355411i
$437$	30.0114	+	8.04154i	1.43564	+	0.384679i
$438$	1.29884	+	1.73127i	0.0620610	+	0.0827231i
$439$	−11.5080	−	6.64413i	−0.549245	−	0.317107i	0.199572	−	0.979883i	$-0.436045\pi$
$439$	−11.5080	−	6.64413i	−0.549245	−	0.317107i	−0.748818	+	0.662776i	$0.769378\pi$
$440$	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
$443$	−23.7141	+	6.35418i	−1.12669	+	0.301896i	−0.773589	−	0.633688i	$-0.781540\pi$
$443$	−23.7141	+	6.35418i	−1.12669	+	0.301896i	−0.353104	+	0.935584i	$0.614874\pi$
$444$	−1.57713	+	11.0513i	−0.0748474	+	0.524471i
$445$	0.889738	−	0.0886134i	0.0421776	−	0.00420068i
$446$	−6.15816	−	3.55542i	−0.291597	−	0.168354i
$447$	2.44976	+	20.3087i	0.115870	+	0.960566i
$448$	0.736347	−	2.54122i	0.0347891	−	0.120061i
$449$	−5.93549			−0.280113			−0.140056	−	0.990144i	$-0.544728\pi$
$449$	−5.93549			−0.280113			−0.140056	+	0.990144i	$0.544728\pi$
$450$	5.09793	−	14.1071i	0.240319	−	0.665016i
$451$	−1.97952	−	3.42863i	−0.0932119	−	0.161448i
$452$	9.73272	+	2.60787i	0.457789	+	0.122664i
$453$	13.8059	+	5.89496i	0.648660	+	0.276969i
$454$			11.6375i			0.546175i
$455$	24.7905	+	11.8096i	1.16220	+	0.553641i
$456$	7.43508	+	5.83443i	0.348180	+	0.273222i
$457$	10.0583	−	2.69512i	0.470508	−	0.126072i	−0.0157712	−	0.999876i	$-0.505020\pi$
$457$	10.0583	−	2.69512i	0.470508	−	0.126072i	0.486280	+	0.873803i	$0.338354\pi$
$458$	1.07047	−	3.99505i	0.0500198	−	0.186676i
$459$	−0.739682	−	7.49743i	−0.0345254	−	0.349950i
$460$	12.5646	+	2.06033i	0.585829	+	0.0960633i
$461$			32.7232i			1.52407i	0.647535	+	0.762035i	$0.275800\pi$
$461$			32.7232i			1.52407i	−0.647535	+	0.762035i	$0.724200\pi$
$462$	−8.85512	−	3.99478i	−0.411978	−	0.185854i
$463$	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
$465$	0.889899	+	3.99238i	0.0412681	+	0.185142i
$466$	−11.3521	−	19.6623i	−0.525874	−	0.910841i
$467$	−0.208078	−	0.776556i	−0.00962868	−	0.0359347i	0.960944	−	0.276742i	$-0.0892546\pi$
$467$	−0.208078	−	0.776556i	−0.00962868	−	0.0359347i	−0.970573	+	0.240807i	$0.922588\pi$
$468$	11.9051	+	7.22241i	0.550314	+	0.333856i
$469$	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
$472$	−1.36480	+	5.09350i	−0.0628200	+	0.234447i
$473$	−1.39119	+	5.19198i	−0.0639669	+	0.238728i
$474$	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
$477$	−17.2000	−	10.4346i	−0.787535	−	0.477770i
$478$	2.74758	+	10.2541i	0.125672	+	0.469013i
$479$	−8.48718	−	14.7002i	−0.387789	−	0.671670i	0.604363	−	0.796709i	$-0.293428\pi$
$479$	−8.48718	−	14.7002i	−0.387789	−	0.671670i	−0.992152	+	0.125039i	$0.960094\pi$
$480$	3.26883	+	2.07720i	0.149201	+	0.0948109i
$481$	14.9576	−	25.9074i	0.682009	−	1.18127i
$482$	14.2319	−	14.2319i	0.648245	−	0.648245i
$483$	−21.1854	+	15.2337i	−0.963967	+	0.693156i
$484$		−	6.50612i		−	0.295733i
$485$	−4.41806	+	26.9430i	−0.200614	+	1.22342i
$486$	5.17551	+	14.7042i	0.234766	+	0.666997i
$487$	−4.13903	+	15.4471i	−0.187557	+	0.699974i	0.806511	+	0.591219i	$0.201353\pi$
$487$	−4.13903	+	15.4471i	−0.187557	+	0.699974i	−0.994069	+	0.108755i	$0.965314\pi$
$488$	7.95646	−	2.13193i	0.360172	−	0.0965078i
$489$	7.10443	+	5.57496i	0.321273	+	0.252108i
$490$	−14.8550	+	4.93253i	−0.671079	+	0.222829i
$491$			6.87591i			0.310305i	0.987891	+	0.155153i	$0.0495869\pi$
$491$			6.87591i			0.310305i	−0.987891	+	0.155153i	$0.950413\pi$
$492$	−2.97490	−	1.27024i	−0.134119	−	0.0572670i
$493$	−10.0908	−	2.70383i	−0.454468	−	0.121774i
$494$	−12.6633	−	21.9335i	−0.569750	−	0.986837i
$495$	9.24610	−	10.8044i	0.415581	−	0.485620i
$496$	−1.05613			−0.0474215
$497$	1.29551	−	4.47097i	0.0581117	−	0.200550i
$498$	−2.78007	−	23.0469i	−0.124578	−	1.03276i
$499$	26.8381	+	15.4950i	1.20144	+	0.693651i	0.960875	−	0.276982i	$-0.0893343\pi$
$499$	26.8381	+	15.4950i	1.20144	+	0.693651i	0.240564	+	0.970633i	$0.422668\pi$
$500$	−7.61600	+	8.18514i	−0.340598	+	0.366051i
$501$	−2.07449	+	14.5364i	−0.0926813	+	0.649437i
$502$	−17.2316	+	4.61720i	−0.769085	+	0.206076i
$503$	−19.3755	−	19.3755i	−0.863913	−	0.863913i	0.127877	−	0.991790i	$-0.459184\pi$
$503$	−19.3755	−	19.3755i	−0.863913	−	0.863913i	−0.991790	+	0.127877i	$0.959184\pi$
$504$	−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
$507$	−8.88076	−	11.8375i	−0.394408	−	0.525720i
$508$	15.4183	+	4.13131i	0.684075	+	0.183297i
$509$	10.4397	−	18.0821i	0.462733	−	0.801477i	−0.536363	−	0.843987i	$-0.680202\pi$
$509$	10.4397	−	18.0821i	0.462733	−	0.801477i	0.999096	+	0.0425105i	$0.0135356\pi$
$510$	−1.68243	+	5.35742i	−0.0744993	+	0.237231i
$511$	2.82909	+	1.71063i	0.125151	+	0.0756736i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.61395	−	27.9750i	0.203711	−	1.23513i
$514$	−0.863752	+	0.498688i	−0.0380985	+	0.0219962i
$515$	15.1684	−	18.5240i	0.668401	−	0.816266i
$516$	1.63652	+	4.07547i	0.0720439	+	0.179412i
$517$	−16.6700	−	16.6700i	−0.733144	−	0.733144i
$518$	4.07921	+	16.5571i	0.179230	+	0.727476i
$519$	5.36037	−	6.83096i	0.235294	−	0.299846i
$520$	−6.05463	−	8.42976i	−0.265513	−	0.369669i
$521$	18.9520	−	10.9419i	0.830300	−	0.479374i	−0.0236551	−	0.999720i	$-0.507530\pi$
$521$	18.9520	−	10.9419i	0.830300	−	0.479374i	0.853956	+	0.520346i	$0.174197\pi$
$522$	21.6106	+	0.469166i	0.945872	+	0.0205349i
$523$	−3.39310	−	12.6632i	−0.148370	−	0.553724i	−0.999582	−	0.0289028i	$-0.990799\pi$
$523$	−3.39310	−	12.6632i	−0.148370	−	0.553724i	0.851212	−	0.524822i	$-0.175868\pi$
$524$	−5.79006			−0.252940
$525$	−0.837151	−	22.8976i	−0.0365363	−	0.999332i
$526$	17.2603			0.752586
$527$	−0.396320	−	1.47909i	−0.0172640	−	0.0644300i
$528$	2.20346	+	2.93707i	0.0958934	+	0.127820i
$529$	8.16059	−	4.71152i	0.354808	−	0.204849i
$530$	8.74749	+	12.1790i	0.379967	+	0.529021i
$531$	15.3658	−	3.76177i	0.666818	−	0.163247i
$532$	13.8662	+	4.01789i	0.601177	+	0.174198i
$533$	6.12951	+	6.12951i	0.265499	+	0.265499i
$534$	0.642716	−	0.258085i	0.0278130	−	0.0111685i
$535$	−15.1242	+	18.4700i	−0.653875	+	0.798527i
$536$	−8.16253	+	4.71264i	−0.352568	+	0.203555i
$537$	12.8895	+	5.50365i	0.556224	+	0.237500i
$538$	19.5452	−	19.5452i	0.842653	−	0.842653i
$539$	−14.8270	−	0.600456i	−0.638643	−	0.0258635i
$540$	0.745331	−	11.5950i	0.0320740	−	0.498970i
$541$	−11.6807	+	20.2316i	−0.502194	+	0.869826i	0.497803	+	0.867290i	$0.334140\pi$
$541$	−11.6807	+	20.2316i	−0.502194	+	0.869826i	−0.999997	+	0.00253553i	$0.999193\pi$
$542$	4.95558	+	1.32784i	0.212860	+	0.0570358i
$543$	14.8173	−	11.1163i	0.635870	−	0.477046i
$544$	−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	$0.775062\pi$
$548$	−10.8253	+	2.90062i	−0.462432	+	0.123908i
$549$	−17.0902	−	17.8487i	−0.729393	−	0.761766i
$550$	−9.49603	+	4.70875i	−0.404912	+	0.200782i
$551$	−34.0483	−	19.6578i	−1.45051	−	0.837451i
$552$	9.79153	−	1.18112i	0.416755	−	0.0502717i
$553$	29.2897	+	30.4999i	1.24553	+	1.29699i
$554$	27.5468			1.17035
$555$	−24.9393	−	1.06020i	−1.05861	−	0.0450028i
$556$	−10.0666	−	17.4359i	−0.426920	−	0.739448i
$557$	−36.8670	−	9.87848i	−1.56211	−	0.418565i	−0.628776	−	0.777587i	$-0.716444\pi$
$557$	−36.8670	−	9.87848i	−1.56211	−	0.418565i	−0.933329	+	0.359022i	$0.883110\pi$
$558$	1.52426	+	2.77763i	0.0645271	+	0.117587i
$559$		−	11.7690i		−	0.497777i
$560$	5.81754	+	1.07527i	0.245836	+	0.0454384i
$561$	−3.28645	+	4.18807i	−0.138754	+	0.176820i
$562$	−19.2055	+	5.14611i	−0.810137	+	0.217076i
$563$	1.02963	−	3.84263i	0.0433937	−	0.161948i	−0.940829	−	0.338882i	$-0.889951\pi$
$563$	1.02963	−	3.84263i	0.0433937	−	0.161948i	0.984223	+	0.176934i	$0.0566180\pi$
$564$	−19.0687	−	2.72130i	−0.802938	−	0.114587i
$565$	−3.64586	+	22.2338i	−0.153383	+	0.935383i
$566$			5.29112i			0.222402i
$567$	15.7324	+	17.8744i	0.660697	+	0.750652i
$568$	−1.24407	+	1.24407i	−0.0522000	+	0.0522000i
$569$	2.50482	−	4.33847i	0.105007	−	0.181878i	−0.808734	−	0.588175i	$-0.799847\pi$
$569$	2.50482	−	4.33847i	0.105007	−	0.181878i	0.913741	+	0.406297i	$0.133180\pi$
$570$	−11.3343	+	17.8364i	−0.474742	+	0.747086i
$571$	−16.4609	−	28.5111i	−0.688867	−	1.19315i	−0.972205	−	0.234132i	$-0.924775\pi$
$571$	−16.4609	−	28.5111i	−0.688867	−	1.19315i	0.283338	−	0.959020i	$-0.408558\pi$
$572$	−2.54665	−	9.50422i	−0.106481	−	0.397391i
$573$	1.28602	−	0.155128i	0.0537243	−	0.00648057i
$574$	−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
$577$	5.90675	−	22.0443i	0.245901	−	0.917716i	−0.727027	−	0.686609i	$-0.759099\pi$
$577$	5.90675	−	22.0443i	0.245901	−	0.917716i	0.972928	−	0.231107i	$-0.0742347\pi$
$578$	−3.85584	+	14.3902i	−0.160382	+	0.598553i
$579$	−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
$582$	2.53273	+	20.9964i	0.104985	+	0.870330i
$583$	3.67929	+	13.7313i	0.152381	+	0.568693i
$584$	−0.624785	−	1.08216i	−0.0258538	−	0.0447800i
$585$	−13.4321	+	28.0901i	−0.555347	+	1.16138i
$586$	−15.0891	+	26.1350i	−0.623324	+	1.07963i
$587$	29.3071	−	29.3071i	1.20963	−	1.20963i	0.238489	−	0.971145i	$-0.423348\pi$
$587$	29.3071	−	29.3071i	1.20963	−	1.20963i	0.971145	−	0.238489i	$-0.0766522\pi$
$588$	−9.98491	+	6.87761i	−0.411771	+	0.283628i
$589$		−	5.76278i		−	0.237451i
$590$	−11.6358	−	1.90802i	−0.479038	−	0.0785519i
$591$	0.939127	−	6.58066i	0.0386305	−	0.270692i
$592$	1.66812	−	6.22550i	0.0685593	−	0.255867i
$593$	−21.0623	+	5.64362i	−0.864925	+	0.231756i	−0.663892	−	0.747829i	$-0.731096\pi$
$593$	−21.0623	+	5.64362i	−0.864925	+	0.231756i	−0.201033	+	0.979584i	$0.564430\pi$
$594$	4.54439	−	10.0341i	0.186459	−	0.411704i
$595$	0.677184	+	8.55087i	0.0277618	+	0.350551i
$596$		−	11.8102i		−	0.483765i
$597$	3.81290	−	8.92979i	0.156052	−	0.365472i
$598$	−25.5289	−	6.84045i	−1.04396	−	0.279727i
$599$	−6.91835	−	11.9829i	−0.282676	−	0.489610i	0.689367	−	0.724413i	$-0.257889\pi$
$599$	−6.91835	−	11.9829i	−0.282676	−	0.489610i	−0.972043	+	0.234803i	$0.924556\pi$
$600$	−3.89751	+	7.73365i	−0.159115	+	0.315725i
$601$	7.92094			0.323102			0.161551	−	0.986864i	$-0.448350\pi$
$601$	7.92094			0.323102			0.161551	+	0.986864i	$0.448350\pi$
$602$	4.64669	+	4.83868i	0.189385	+	0.197210i
$603$	24.1750	+	14.6661i	0.984481	+	0.597249i
$604$	−7.50591	−	4.33354i	−0.305411	−	0.176329i
$605$	14.4765	−	1.44179i	0.588554	−	0.0586170i
$606$	7.58286	+	1.08215i	0.308033	+	0.0439594i
$607$	−31.9387	+	8.55795i	−1.29635	+	0.347356i	−0.840070	−	0.542479i	$-0.817486\pi$
$607$	−31.9387	+	8.55795i	−1.29635	+	0.347356i	−0.456282	+	0.889835i	$0.650819\pi$
$608$	−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
$612$	−0.0944086	+	4.34863i	−0.00381624	+	0.175783i
$613$	−9.17128	−	2.45744i	−0.370424	−	0.0992549i	0.0688043	−	0.997630i	$-0.478082\pi$
$613$	−9.17128	−	2.45744i	−0.370424	−	0.0992549i	−0.439229	+	0.898375i	$0.644748\pi$
$614$	12.6285	−	21.8733i	0.509647	−	0.882734i
$615$	2.16712	−	6.90082i	0.0873865	−	0.278268i
$616$	4.79950	+	2.90205i	0.193378	+	0.116927i
$617$	13.7827	−	13.7827i	0.554873	−	0.554873i	−0.372971	−	0.927843i	$-0.621661\pi$
$617$	13.7827	−	13.7827i	0.554873	−	0.554873i	0.927843	+	0.372971i	$0.121661\pi$
$618$	7.28256	−	17.0557i	0.292948	−	0.686081i
$619$	6.45537	−	3.72701i	0.259463	−	0.149801i	−0.364626	−	0.931154i	$-0.618803\pi$
$619$	6.45537	−	3.72701i	0.259463	−	0.149801i	0.624090	+	0.781353i	$0.285470\pi$
$620$	−0.234042	−	2.34994i	−0.00939937	−	0.0943760i
$621$	−17.2380	−	24.0473i	−0.691739	−	0.964984i
$622$	−10.7715	−	10.7715i	−0.431897	−	0.431897i
$623$	0.763077	−	0.732799i	0.0305720	−	0.0293590i
$624$	−6.32458	−	4.96300i	−0.253186	−	0.198679i
$625$	−19.9002	−	15.1322i	−0.796007	−	0.605288i
$626$	−19.7560	+	11.4061i	−0.789607	+	0.455880i
$627$	−16.0262	+	12.0233i	−0.640025	+	0.480163i
$628$	4.51828	+	16.8625i	0.180299	+	0.672885i
$629$	9.34468			0.372597
$630$	−5.56822	−	16.8521i	−0.221843	−	0.671406i
$631$	−49.0067			−1.95093			−0.975463	−	0.220162i	$-0.929342\pi$
$631$	−49.0067			−1.95093			−0.975463	+	0.220162i	$0.929342\pi$
$632$	−4.13664	−	15.4381i	−0.164547	−	0.614096i
$633$	20.5673	−	15.4301i	0.817477	−	0.613292i
$634$	−4.28243	+	2.47246i	−0.170077	+	0.0981940i
$635$	−5.77566	+	35.2221i	−0.229200	+	1.39775i
$636$	9.13750	+	7.17034i	0.362325	+	0.284322i
$637$	31.6982	−	7.13242i	1.25593	−	0.282597i
$638$	−10.8005	−	10.8005i	−0.427596	−	0.427596i
$639$	5.06744	+	1.47642i	0.200465	+	0.0584062i
$640$	−1.73005	−	1.41666i	−0.0683864	−	0.0559983i
$641$	−20.1256	+	11.6195i	−0.794915	+	0.458944i	−0.841690	−	0.539961i	$-0.818439\pi$
$641$	−20.1256	+	11.6195i	−0.794915	+	0.458944i	0.0467751	+	0.998905i	$0.485106\pi$
$642$	−7.26131	+	17.0059i	−0.286581	+	0.671171i
$643$	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
$645$	−8.70550	+	4.54450i	−0.342779	+	0.178940i
$646$	3.95567	−	6.85142i	0.155634	−	0.269565i
$647$	−41.7186	−	11.1785i	−1.64013	−	0.439471i	−0.683303	−	0.730135i	$-0.739457\pi$
$647$	−41.7186	−	11.1785i	−1.64013	−	0.439471i	−0.956825	+	0.290663i	$0.906124\pi$
$648$	−1.94989	−	8.78624i	−0.0765989	−	0.345156i
$649$	−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
$653$	24.1492	−	6.47076i	0.945031	−	0.253220i	0.246778	−	0.969072i	$-0.420628\pi$
$653$	24.1492	−	6.47076i	0.945031	−	0.253220i	0.698252	+	0.715852i	$0.253961\pi$
$654$	14.6935	+	2.09692i	0.574563	+	0.0819959i
$655$	−1.28310	−	12.8832i	−0.0501350	−	0.503389i
$656$	1.61737	+	0.933789i	0.0631477	+	0.0364583i
$657$	−1.94438	+	3.20503i	−0.0758573	+	0.125040i
$658$	−28.5688	+	7.03857i	−1.11373	+	0.274392i
$659$	−20.0343			−0.780425			−0.390213	−	0.920725i	$-0.627599\pi$
$659$	−20.0343			−0.780425			−0.390213	+	0.920725i	$0.627599\pi$
$660$	−6.04686	+	5.55371i	−0.235374	+	0.216178i
$661$	−6.62569	−	11.4760i	−0.257709	−	0.446366i	0.707918	−	0.706294i	$-0.249634\pi$
$661$	−6.62569	−	11.4760i	−0.257709	−	0.446366i	−0.965628	+	0.259928i	$0.916301\pi$
$662$	−0.228261	−	0.0611622i	−0.00887160	−	0.00237714i
$663$	4.57724	−	10.7199i	0.177765	−	0.416325i
$664$			13.4026i			0.520122i
$665$	−5.86723	+	31.7436i	−0.227522	+	1.23096i
$666$	−18.7807	+	4.59781i	−0.727739	+	0.178161i
$667$	−39.6296	+	10.6187i	−1.53446	+	0.411158i
$668$	2.19417	−	8.18874i	0.0848949	−	0.316832i
$669$	1.74003	−	12.1928i	0.0672736	−	0.471401i
$670$	−12.2948	−	17.1178i	−0.474988	−	0.661318i
$671$			17.4617i			0.674102i
$672$	4.55977	−	0.456622i	0.175897	−	0.0176146i
$673$	−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
$675$	25.9648	−	0.911103i	0.999385	−	0.0350684i
$676$	4.27194	+	7.39921i	0.164305	+	0.284585i
$677$	12.8090	+	47.8038i	0.492290	+	1.83725i	0.544709	+	0.838625i	$0.316640\pi$
$677$	12.8090	+	47.8038i	0.492290	+	1.83725i	−0.0524196	+	0.998625i	$0.516693\pi$
$678$	2.09005	+	17.3266i	0.0802679	+	0.665425i
$679$	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
$682$	0.579459	−	2.16257i	0.0221886	−	0.0828091i
$683$	2.56877	−	9.58678i	0.0982913	−	0.366828i	−0.899207	−	0.437524i	$-0.855855\pi$
$683$	2.56877	−	9.58678i	0.0982913	−	0.366828i	0.997498	+	0.0706962i	$0.0225221\pi$
$684$	−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
$687$	7.11217	−	0.857916i	0.271346	−	0.0327315i
$688$	−0.656259	−	2.44919i	−0.0250196	−	0.0933746i
$689$	−15.5629	−	26.9557i	−0.592898	−	1.02693i
$690$	4.79791	+	21.5250i	0.182653	+	0.819443i
$691$	−3.42873	+	5.93874i	−0.130435	+	0.225920i	−0.923844	−	0.382768i	$-0.874971\pi$
$691$	−3.42873	+	5.93874i	−0.130435	+	0.225920i	0.793409	+	0.608689i	$0.208304\pi$
$692$	−3.54485	+	3.54485i	−0.134755	+	0.134755i
$693$	0.705547	−	16.8112i	0.0268015	−	0.638605i
$694$			4.08205i			0.154953i
$695$	36.5651	−	26.2627i	1.38700	−	0.996202i
$696$	−12.3547	−	1.76314i	−0.468303	−	0.0668316i
$697$	−0.700824	+	2.61551i	−0.0265456	+	0.0990695i
$698$	−11.5081	+	3.08358i	−0.435587	+	0.116715i
$699$	24.2765	−	30.9367i	0.918223	−	1.17013i
$700$	−1.10334	+	13.1827i	−0.0417025	+	0.498258i
$701$		−	28.8845i		−	1.09095i	−0.838127	−	0.545476i	$-0.816349\pi$
$701$		−	28.8845i		−	1.09095i	0.838127	−	0.545476i	$-0.183651\pi$
$702$	−3.92481	+	23.7966i	−0.148132	+	0.898147i
$703$	33.9696	+	9.10213i	1.28119	+	0.343293i
$704$	−1.05994	−	1.83587i	−0.0399479	−	0.0691918i
$705$	1.82934	−	43.0321i	0.0688969	−	1.62068i
$706$	−7.07011			−0.266087
$707$	11.3607	−	2.79895i	0.427261	−	0.105265i
$708$	−9.06769	+	1.09380i	−0.340785	+	0.0411076i
$709$	−21.3823	−	12.3450i	−0.803027	−	0.463628i	0.0415013	−	0.999138i	$-0.486786\pi$
$709$	−21.3823	−	12.3450i	−0.803027	−	0.463628i	−0.844529	+	0.535510i	$0.820119\pi$
$710$	−3.04382	−	2.49244i	−0.114233	−	0.0935395i
$711$	−34.6324	+	33.1606i	−1.29882	+	1.24362i
$712$	−0.386246	+	0.103494i	−0.0144752	+	0.00387862i
$713$	−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
$717$	−14.7082	+	11.0344i	−0.549287	+	0.412089i
$718$	−8.78994	−	2.35526i	−0.328038	−	0.0878975i
$719$	−11.2630	+	19.5080i	−0.420038	+	0.727527i	−0.995943	−	0.0899900i	$-0.971316\pi$
$719$	−11.2630	+	19.5080i	−0.420038	+	0.727527i	0.575905	+	0.817517i	$0.304650\pi$
$720$	−1.22893	+	6.59467i	−0.0457995	+	0.245769i
$721$	0.573266	−	28.3228i	0.0213496	−	1.05480i
$722$	7.61813	−	7.61813i	0.283518	−	0.283518i
$723$	32.0606	+	13.6894i	1.19234	+	0.509116i
$724$	−9.26180	+	5.34730i	−0.344212	+	0.198731i
$725$	11.5057	−	34.1396i	0.427310	−	1.26791i
$726$	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	$0.694472\pi$
$728$	−11.7952	−	3.41778i	−0.437158	−	0.126671i
$729$	−20.2938	+	17.8090i	−0.751622	+	0.659594i
$730$	2.26941	−	1.62999i	0.0839947	−	0.0603288i
$731$	3.18378	−	1.83816i	0.117756	−	0.0679867i
$732$	8.56192	+	11.4125i	0.316458	+	0.421817i
$733$	0.500074	+	1.86630i	0.0184707	+	0.0689334i	0.974546	−	0.224188i	$-0.0719728\pi$
$733$	0.500074	+	1.86630i	0.0184707	+	0.0689334i	−0.956075	+	0.293121i	$0.905306\pi$
$734$	−11.0502			−0.407872
$735$	−17.5158	−	20.6929i	−0.646080	−	0.763270i
$736$	−5.69412			−0.209888
$737$	−5.17132	−	19.2996i	−0.190488	−	0.710911i
$738$	0.121607	−	5.60141i	0.00447640	−	0.206191i
$739$	9.70996	−	5.60605i	0.357187	−	0.206222i	−0.310659	−	0.950521i	$-0.600550\pi$
$739$	9.70996	−	5.60605i	0.357187	−	0.206222i	0.667846	+	0.744299i	$0.267216\pi$
$740$	14.2218	+	2.33206i	0.522803	+	0.0857284i
$741$	27.0807	−	34.5102i	0.994835	−	1.26776i
$742$	17.0412	+	4.93787i	0.625601	+	0.181275i
$743$	−11.6014	−	11.6014i	−0.425613	−	0.425613i	0.461518	−	0.887131i	$-0.347305\pi$
$743$	−11.6014	−	11.6014i	−0.425613	−	0.425613i	−0.887131	+	0.461518i	$0.847305\pi$
$744$	−0.681646	−	1.69752i	−0.0249904	−	0.0622340i
$745$	26.2784	−	2.61720i	0.962767	−	0.0958866i
$746$	29.7084	−	17.1522i	1.08770	−	0.627985i
$747$	35.2491	−	19.3434i	1.28970	−	0.707737i
$748$	2.17335	−	2.17335i	0.0794655	−	0.0794655i
$749$	−0.571594	+	28.2401i	−0.0208856	+	1.03187i
$750$	−18.0715	−	6.95838i	−0.659880	−	0.254084i
$751$	−6.85013	+	11.8648i	−0.249965	+	0.432952i	−0.963516	−	0.267652i	$-0.913752\pi$
$751$	−6.85013	+	11.8648i	−0.249965	+	0.432952i	0.713551	+	0.700603i	$0.247086\pi$
$752$	10.7419	+	2.87830i	0.391718	+	0.104961i
$753$	−18.5429	−	24.7165i	−0.675741	−	0.900718i
$754$	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	$0.489873\pi$
$758$	16.6244	−	4.45450i	0.603826	−	0.161795i
$759$	−2.95376	+	20.6976i	−0.107215	+	0.751275i
$760$	7.73002	−	9.44008i	0.280397	−	0.342428i
$761$	−4.58035	−	2.64447i	−0.166038	−	0.0958618i	0.414679	−	0.909968i	$-0.363894\pi$
$761$	−4.58035	−	2.64447i	−0.166038	−	0.0958618i	−0.580716	+	0.814106i	$0.697227\pi$
$762$	3.31099	+	27.4483i	0.119945	+	0.994347i
$763$	22.0139	−	5.42361i	0.796956	−	0.196348i
$764$	−0.747866			−0.0270569
$765$	−9.69689	+	0.753612i	−0.350592	+	0.0272469i
$766$	9.51372	+	16.4782i	0.343745	+	0.595383i
$767$	23.6417	+	6.33477i	0.853652	+	0.228735i
$768$	−1.59292	−	0.680155i	−0.0574795	−	0.0245430i
$769$			0.931143i			0.0335779i	0.999859	+	0.0167889i	$0.00534434\pi$
$769$			0.931143i			0.0335779i	−0.999859	+	0.0167889i	$0.994656\pi$
$770$	−5.39365	+	11.3223i	−0.194374	+	0.408027i
$771$	−1.35903	−	1.06645i	−0.0489442	−	0.0384073i
$772$	8.94254	−	2.39615i	0.321849	−	0.0862392i
$773$	−2.98432	+	11.1376i	−0.107339	+	0.400593i	−0.998600	−	0.0528969i	$-0.983155\pi$
$773$	−2.98432	+	11.1376i	−0.107339	+	0.400593i	0.891261	+	0.453490i	$0.149821\pi$
$774$	−5.49428	+	5.26078i	−0.197488	+	0.189095i
$775$	5.17690	−	1.04152i	0.185960	−	0.0374124i
$776$		−	12.2102i		−	0.438320i
$777$	−23.9795	+	17.2428i	−0.860259	+	0.618583i
$778$	26.0463	−	26.0463i	0.933804	−	0.933804i
$779$	−5.09524	+	8.82522i	−0.182556	+	0.316196i
$780$	9.64141	−	15.1724i	0.345218	−	0.543259i
$781$	−1.86483	−	3.22999i	−0.0667290	−	0.115578i
$782$	−2.13677	−	7.97452i	−0.0764106	−	0.285168i
$783$	13.1939	+	35.0377i	0.471510	+	1.25215i
$784$	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
$787$	5.10495	−	19.0519i	0.181972	−	0.679129i	−0.813287	−	0.581863i	$-0.802324\pi$
$787$	5.10495	−	19.0519i	0.181972	−	0.679129i	0.995258	−	0.0972652i	$-0.0310095\pi$
$788$	−0.993307	+	3.70707i	−0.0353851	+	0.132059i
$789$	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
$792$	−3.29861	+	5.43729i	−0.117211	+	0.193206i
$793$	−9.89542	−	36.9302i	−0.351397	−	1.31143i
$794$	−10.0114	−	17.3402i	−0.355291	−	0.615382i
$795$	−13.9295	+	21.9205i	−0.494029	+	0.777438i
$796$	−2.80297	+	4.85488i	−0.0993485	+	0.172077i
$797$	13.9935	−	13.9935i	0.495674	−	0.495674i	−0.414414	−	0.910088i	$-0.636014\pi$
$797$	13.9935	−	13.9935i	0.495674	−	0.495674i	0.910088	+	0.414414i	$0.136014\pi$
$798$	2.49157	+	24.8805i	0.0882006	+	0.880760i
$799$			16.1240i			0.570426i
$800$	2.76876	−	4.16341i	0.0978904	−	0.147199i
$801$	0.829645	+	0.866467i	0.0293140	+	0.0306151i
$802$	2.69219	−	10.0474i	0.0950645	−	0.354786i
$803$	2.55867	−	0.685594i	0.0902936	−	0.0241941i
$804$	−12.8429	−	10.0780i	−0.452935	−	0.355425i
$805$	19.0941	+	27.7529i	0.672977	+	0.978161i
$806$			4.90205i			0.172667i
$807$	44.0300	+	18.8002i	1.54993	+	0.661799i
$808$	−4.27164	−	1.14458i	−0.150276	−	0.0402662i
$809$	12.8197	+	22.2044i	0.450717	+	0.780666i	0.998431	−	0.0560005i	$-0.0178349\pi$
$809$	12.8197	+	22.2044i	0.450717	+	0.780666i	−0.547713	+	0.836666i	$0.684502\pi$
$810$	19.1178	−	6.28569i	0.671731	−	0.220857i
$811$	−11.0170			−0.386858			−0.193429	−	0.981114i	$-0.561961\pi$
$811$	−11.0170			−0.386858			−0.193429	+	0.981114i	$0.561961\pi$
$812$	−18.5098	+	4.56031i	−0.649567	+	0.160035i
$813$	1.06418	+	8.82215i	0.0373226	+	0.309406i
$814$	11.8324	+	6.83143i	0.414725	+	0.239441i
$815$	7.38625	−	9.02026i	0.258729	−	0.315966i
$816$	0.354790	−	2.48609i	0.0124201	−	0.0870305i
$817$	13.3641	−	3.58089i	0.467550	−	0.125280i
$818$	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	0.710841	−	0.703352i	$-0.248314\pi$
$821$	13.0985	+	7.56242i	0.457141	+	0.263930i	−0.253700	+	0.967283i	$0.581648\pi$
$822$	−11.6490	−	15.5274i	−0.406306	−	0.541579i
$823$	−39.6086	−	10.6131i	−1.38067	−	0.369949i	−0.509305	−	0.860586i	$-0.670097\pi$
$823$	−39.6086	−	10.6131i	−1.38067	−	0.369949i	−0.871364	+	0.490637i	$0.836764\pi$
$824$	−5.35360	+	9.27271i	−0.186502	+	0.323030i
$825$	−13.6973	−	12.2239i	−0.476880	−	0.425581i
$826$	−12.2211	+	6.72983i	−0.425225	+	0.234161i
$827$	−25.1800	+	25.1800i	−0.875596	+	0.875596i	−0.993075	−	0.117480i	$-0.962518\pi$
$827$	−25.1800	+	25.1800i	−0.875596	+	0.875596i	0.117480	+	0.993075i	$0.462518\pi$
$828$	8.21808	+	14.9757i	0.285598	+	0.520440i
$829$	−25.3933	+	14.6608i	−0.881944	+	0.509191i	−0.871299	−	0.490752i	$-0.836722\pi$
$829$	−25.3933	+	14.6608i	−0.881944	+	0.509191i	−0.0106454	+	0.999943i	$0.503389\pi$
$830$	−29.8216	+	2.97008i	−1.03512	+	0.103093i
$831$	17.7793	+	44.2762i	0.616757	+	1.53592i
$832$	3.28206	+	3.28206i	0.113785	+	0.113785i
$833$	6.88029	+	7.46108i	0.238388	+	0.258511i
$834$	21.5276	−	27.4337i	0.745441	−	0.949950i
$835$	18.7067	+	3.06749i	0.647371	+	0.106155i
$836$	10.0175	−	5.78358i	0.346461	−	0.200029i
$837$	−3.48072	+	4.24270i	−0.120311	+	0.146649i
$838$	−3.85925	−	14.4029i	−0.133316	−	0.497541i
$839$	20.2876			0.700407			0.350203	−	0.936674i	$-0.386112\pi$
$839$	20.2876			0.700407			0.350203	+	0.936674i	$0.386112\pi$
$840$	2.02648	+	10.0446i	0.0699201	+	0.346571i
$841$	22.9156			0.790192
$842$	4.27808	+	15.9660i	0.147432	+	0.550225i
$843$	−20.6670	−	27.5478i	−0.711811	−	0.948796i
$844$	−12.8559	+	7.42239i	−0.442520	+	0.255489i
$845$	−15.5170	+	11.1450i	−0.533801	+	0.383400i
$846$	−7.93340	−	32.4057i	−0.272756	−	1.11413i
$847$	12.4157	−	11.9230i	0.426607	−	0.409680i
$848$	−4.74179	−	4.74179i	−0.162834	−	0.162834i
$849$	−8.50444	+	3.41500i	−0.291872	+	0.117202i
$850$	6.86978	+	2.31524i	0.235631	+	0.0794122i
$851$	31.7825	−	18.3496i	1.08949	−	0.629018i
$852$	−2.80255	−	1.19665i	−0.0960138	−	0.0409966i
$853$	−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
$855$	−35.9840	−	6.70568i	−1.23063	−	0.229329i
$856$	5.33798	−	9.24565i	0.182448	−	0.316010i
$857$	20.2170	+	5.41712i	0.690599	+	0.185045i	0.587016	−	0.809575i	$-0.300303\pi$
$857$	20.2170	+	5.41712i	0.690599	+	0.185045i	0.103583	+	0.994621i	$0.466969\pi$
$858$	13.6325	−	10.2275i	0.465407	−	0.349160i
$859$	−11.7809	−	6.80172i	−0.401960	−	0.232072i	0.285369	−	0.958418i	$-0.407884\pi$
$859$	−11.7809	−	6.80172i	−0.401960	−	0.232072i	−0.687329	+	0.726346i	$0.741217\pi$
$860$	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
$863$	−45.3947	+	12.1635i	−1.54525	+	0.414050i	−0.927959	−	0.372681i	$-0.878438\pi$
$863$	−45.3947	+	12.1635i	−1.54525	+	0.414050i	−0.617296	+	0.786731i	$0.711772\pi$
$864$	0.510166	+	5.17105i	0.0173562	+	0.175923i
$865$	−8.67305	−	7.10194i	−0.294892	−	0.241473i
$866$	9.72591	+	5.61526i	0.330500	+	0.190814i
$867$	−25.6181	+	3.09022i	−0.870036	+	0.104949i
$868$	−1.93544	−	2.01541i	−0.0656932	−	0.0684075i
$869$	33.8814			1.14935
$870$	1.18523	−	27.8806i	0.0401832	−	0.945241i
$871$	21.8739	+	37.8867i	0.741169	+	1.28374i
$872$	−8.27727	−	2.21789i	−0.280304	−	0.0751072i
$873$	−32.1130	+	17.6224i	−1.08686	+	0.596428i
$874$		−	31.0701i		−	1.05096i
$875$	−29.5767	+	0.466331i	−0.999876	+	0.0157649i
$876$	1.33611	−	1.70267i	0.0451430	−	0.0575278i
$877$	−21.4208	+	5.73970i	−0.723330	+	0.193816i	−0.601657	−	0.798754i	$-0.705493\pi$
$877$	−21.4208	+	5.73970i	−0.723330	+	0.193816i	−0.121673	+	0.992570i	$0.538826\pi$
$878$	−3.43925	+	12.8355i	−0.116069	+	0.433176i
$879$	−51.7458	−	7.38465i	−1.74534	−	0.249078i
$880$	3.85003	−	2.76526i	0.129784	−	0.0932170i
$881$			44.7263i			1.50687i	0.657525	+	0.753433i	$0.271604\pi$
$881$			44.7263i			1.50687i	−0.657525	+	0.753433i	$0.728396\pi$
$882$	−17.4989	−	11.6099i	−0.589218	−	0.390924i
$883$	−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
$885$	−4.44322	−	19.9338i	−0.149357	−	0.670066i
$886$	12.2753	+	21.2615i	0.412398	+	0.714295i
$887$	7.97169	+	29.7508i	0.267663	+	0.998933i	0.960600	+	0.277935i	$0.0896499\pi$
$887$	7.97169	+	29.7508i	0.267663	+	0.998933i	−0.692937	+	0.720998i	$0.743683\pi$
$888$	11.0829	−	1.33689i	0.371919	−	0.0448632i
$889$	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
$892$	−1.84042	+	6.86854i	−0.0616218	+	0.229976i
$893$	−15.7055	+	58.6137i	−0.525564	+	1.96143i
$894$	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
$897$	−5.48220	−	45.4478i	−0.183045	−	1.51746i
$898$	1.53622	+	5.73324i	0.0512642	+	0.191321i
$899$	3.80482	+	6.59015i	0.126898	+	0.219794i
$900$	−14.9459	−	1.27303i	−0.498196	−	0.0424343i
$901$	4.86140	−	8.42019i	0.161957	−	0.280517i
$902$	−2.79946	+	2.79946i	−0.0932119	+	0.0932119i
$903$	−4.77816	+	10.5916i	−0.159007	+	0.352467i
$904$		−	10.0761i		−	0.335124i
$905$	−13.9505	−	19.4231i	−0.463731	−	0.645645i
$906$	2.12085	−	14.8612i	0.0704605	−	0.493732i
$907$	6.18534	−	23.0840i	0.205381	−	0.766491i	−0.783952	−	0.620821i	$-0.786799\pi$
$907$	6.18534	−	23.0840i	0.205381	−	0.766491i	0.989333	−	0.145670i	$-0.0465339\pi$
$908$	11.2410	−	3.01201i	0.373045	−	0.0999570i
$909$	3.15479	+	12.8864i	0.104638	+	0.427415i
$910$	4.99090	−	27.0023i	0.165447	−	0.895119i
$911$		−	27.2518i		−	0.902892i	−0.892298	−	0.451446i	$-0.850908\pi$
$911$		−	27.2518i		−	0.902892i	0.892298	−	0.451446i	$-0.149092\pi$
$912$	3.71128	−	8.69180i	0.122893	−	0.287814i
$913$	−27.4438	−	7.35353i	−0.908256	−	0.243366i
$914$	−5.20657	−	9.01804i	−0.172218	−	0.298290i
$915$	−23.4961	+	21.5799i	−0.776756	+	0.713408i
$916$	−4.13598			−0.136657
$917$	−10.6108	−	11.0492i	−0.350399	−	0.364876i
$918$	−7.05051	+	2.65495i	−0.232702	+	0.0876266i
$919$	8.37600	+	4.83589i	0.276299	+	0.159521i	0.631747	−	0.775175i	$-0.282338\pi$
$919$	8.37600	+	4.83589i	0.276299	+	0.159521i	−0.355448	+	0.934696i	$0.615672\pi$
$920$	−1.26184	−	12.6698i	−0.0416018	−	0.417710i
$921$	43.3078	+	6.18046i	1.42704	+	0.203653i
$922$	31.6082	−	8.46938i	1.04096	−	0.278924i
$923$	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
$927$	32.1140	+	0.697195i	1.05476	+	0.0228989i
$928$	6.95973	+	1.86485i	0.228464	+	0.0612169i
$929$	15.3159	−	26.5279i	0.502499	−	0.870353i	−0.497497	−	0.867466i	$-0.665748\pi$
$929$	15.3159	−	26.5279i	0.502499	−	0.870353i	0.999996	−	0.00288755i	$-0.000919138\pi$
$930$	3.62602	−	1.89288i	0.118902	−	0.0620700i
$931$	17.7437	+	33.8241i	0.581526	+	1.10854i
$932$	−16.0542	+	16.0542i	−0.525874	+	0.525874i
$933$	10.3609	−	24.2652i	0.339202	−	0.794408i
$934$	−0.696241	+	0.401975i	−0.0227817	+	0.0131530i
$935$	5.31745	+	4.35421i	0.173899	+	0.142398i
$936$	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	$0.756017\pi$
$938$	−23.9517	−	6.94027i	−0.782051	−	0.226608i
$939$	−31.0840	−	24.3921i	−1.01439	−	0.796007i
$940$	−4.02392	+	24.5393i	−0.131246	+	0.800384i
$941$	−39.7684	+	22.9603i	−1.29641	+	0.748484i	−0.979783	−	0.200065i	$-0.935885\pi$
$941$	−39.7684	+	22.9603i	−1.29641	+	0.748484i	−0.316630	+	0.948549i	$0.602551\pi$
$942$	−24.1869	+	18.1456i	−0.788053	+	0.591217i
$943$	2.75234	+	10.2719i	0.0896285	+	0.334498i
$944$	5.27318			0.171627
$945$	23.4927	−	19.8266i	0.764218	−	0.644958i
$946$	5.37514			0.174761
$947$	−8.20271	−	30.6129i	−0.266552	−	0.994787i	−0.961293	−	0.275527i	$-0.911148\pi$
$947$	−8.20271	−	30.6129i	−0.266552	−	0.994787i	0.694741	−	0.719260i	$-0.255519\pi$
$948$	22.1439	−	16.6129i	0.719201	−	0.539563i
$949$	−5.02288	+	2.89996i	−0.163050	+	0.0941367i
$950$	22.7177	+	15.1078i	0.737061	+	0.490162i
$951$	−6.73797	−	5.28739i	−0.218494	−	0.171456i
$952$	−0.917654	−	3.72466i	−0.0297413	−	0.120717i
$953$	12.7159	+	12.7159i	0.411908	+	0.411908i	0.882403	−	0.470495i	$-0.155924\pi$
$953$	12.7159	+	12.7159i	0.411908	+	0.411908i	−0.470495	+	0.882403i	$0.655924\pi$
$954$	−5.62740	+	19.3146i	−0.182194	+	0.625335i
$955$	−0.165731	−	1.66405i	−0.00536292	−	0.0538473i
$956$	9.19360	−	5.30793i	0.297342	−	0.171671i
$957$	10.3889	−	24.3306i	0.335824	−	0.786497i
$958$	−12.0027	+	12.0027i	−0.387789	+	0.387789i
$959$	−25.3735	−	15.3422i	−0.819352	−	0.495427i
$960$	1.16039	−	3.69506i	0.0374514	−	0.119258i
$961$	14.9423	−	25.8808i	0.482010	−	0.834865i
$962$	−28.8959	−	7.74264i	−0.931642	−	0.249633i
$963$	−32.0203	−	0.695160i	−1.03184	−	0.0224012i
$964$	−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	$0.778097\pi$
$968$	−6.28443	+	1.68391i	−0.201989	+	0.0541229i
$969$	13.5654	+	1.93592i	0.435783	+	0.0621907i
$970$	27.1684	−	2.70583i	0.872324	−	0.0868790i
$971$	−9.52298	−	5.49809i	−0.305607	−	0.176442i	0.339352	−	0.940659i	$-0.389792\pi$
$971$	−9.52298	−	5.49809i	−0.305607	−	0.176442i	−0.644959	+	0.764217i	$0.723126\pi$
$972$	12.8637	−	8.80489i	0.412602	−	0.282417i
$973$	14.8251	−	51.1630i	0.475270	−	1.64021i
$974$	15.9920			0.512416
$975$	35.8960	+	18.0904i	1.14959	+	0.579358i
$976$	−4.11857	−	7.13357i	−0.131832	−	0.228340i
$977$	−45.8432	−	12.2836i	−1.46665	−	0.392988i	−0.564870	−	0.825180i	$-0.691074\pi$
$977$	−45.8432	−	12.2836i	−1.46665	−	0.392988i	−0.901782	+	0.432191i	$0.857741\pi$
$978$	3.54624	−	8.30526i	0.113396	−	0.265573i
$979$		−	0.847678i		−	0.0270919i
$980$	8.60921	+	13.0722i	0.275011	+	0.417575i
$981$	6.11313	+	24.9704i	0.195177	+	0.797243i
$982$	6.64162	−	1.77962i	0.211942	−	0.0567898i
$983$	−7.87919	+	29.4055i	−0.251307	+	0.937891i	0.718801	+	0.695216i	$0.244691\pi$
$983$	−7.87919	+	29.4055i	−0.251307	+	0.937891i	−0.970108	+	0.242675i	$0.921975\pi$
$984$	−0.457000	+	3.20230i	−0.0145686	+	0.102085i
$985$	−8.46858	−	1.38866i	−0.269831	−	0.0442465i
$986$			10.4468i			0.332693i
$987$	−29.7520	−	41.3760i	−0.947018	−	1.31701i
$988$	−17.9087	+	17.9087i	−0.569750	+	0.569750i
$989$	7.21898	−	12.5036i	0.229550	−	0.397593i
$990$	−12.8293	−	6.13467i	−0.407741	−	0.194973i
$991$	7.93677	+	13.7469i	0.252120	+	0.436684i	0.964109	−	0.265506i	$-0.0855389\pi$
$991$	7.93677	+	13.7469i	0.252120	+	0.436684i	−0.711989	+	0.702190i	$0.752206\pi$
$992$	0.273346	+	1.02014i	0.00867873	+	0.0323895i
$993$	−0.0490178	−	0.406360i	−0.00155553	−	0.0128954i
$994$	−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
$997$	−7.23598	+	27.0051i	−0.229166	+	0.855259i	0.751527	+	0.659703i	$0.229318\pi$
$997$	−7.23598	+	27.0051i	−0.229166	+	0.855259i	−0.980693	+	0.195556i	$0.937349\pi$
$998$	8.02080	−	29.9340i	0.253894	−	0.947545i
$999$	−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.107.7	yes	64
3.2	odd	2	inner	210.2.x.a.107.14	yes	64
5.3	odd	4	inner	210.2.x.a.23.7	✓	64
7.4	even	3	inner	210.2.x.a.137.10	yes	64
15.8	even	4	inner	210.2.x.a.23.10	yes	64
21.11	odd	6	inner	210.2.x.a.137.7	yes	64
35.18	odd	12	inner	210.2.x.a.53.14	yes	64
105.53	even	12	inner	210.2.x.a.53.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.7	✓	64	5.3	odd	4	inner
210.2.x.a.23.10	yes	64	15.8	even	4	inner
210.2.x.a.53.7	yes	64	105.53	even	12	inner
210.2.x.a.53.14	yes	64	35.18	odd	12	inner
210.2.x.a.107.7	yes	64	1.1	even	1	trivial
210.2.x.a.107.14	yes	64	3.2	odd	2	inner
210.2.x.a.137.7	yes	64	21.11	odd	6	inner
210.2.x.a.137.10	yes	64	7.4	even	3	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+(-0.258819 - 0.965926i) q^{2} +(1.38549 - 1.03943i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.30445 - 1.81616i) q^{5} +(-1.36260 - 1.06926i) q^{6} +(-2.54122 - 0.736347i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.839170 - 2.88024i) q^{9} +(-1.41666 + 1.73005i) q^{10} +(-1.83587 + 1.05994i) q^{11} +(-0.680155 + 1.59292i) q^{12} +(3.28206 - 3.28206i) q^{13} +(-0.0535403 + 2.64521i) q^{14} +(-3.69506 - 1.16039i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.40048 + 0.375258i) q^{17} +(-2.99929 - 0.0651145i) 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} +(5.50010 - 1.47375i) q^{23} +(1.71468 + 0.244702i) q^{24} +(-1.59685 + 4.73815i) q^{25} +(-4.01969 - 2.32077i) q^{26} +(-1.83115 - 4.86281i) q^{27} +(2.56893 - 0.632915i) q^{28} -7.20525 q^{29} +(-0.164496 + 3.86949i) q^{30} +(-0.528063 - 0.914632i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.44185 + 3.37679i) q^{33} -1.44989i q^{34} +(1.97756 + 5.57577i) q^{35} +(0.713378 + 2.91395i) q^{36} +(6.22550 - 1.66812i) q^{37} +(1.41225 - 5.27060i) q^{38} +(1.13579 - 7.95874i) q^{39} +(0.361834 - 2.20660i) q^{40} +1.86758i q^{41} +(2.67533 + 3.72057i) q^{42} +(1.79293 - 1.79293i) q^{43} +(1.05994 - 1.83587i) q^{44} +(-6.32562 + 2.23305i) q^{45} +(-2.84706 - 4.93126i) q^{46} +(2.87830 + 10.7419i) q^{47} +(-0.207427 - 1.71959i) q^{48} +(5.91559 + 3.74244i) q^{49} +(4.99000 + 0.316111i) q^{50} +(2.33041 - 0.935787i) q^{51} +(-1.20132 + 4.48338i) q^{52} +(1.73562 - 6.47741i) q^{53} +(-4.22318 + 3.02734i) q^{54} +(4.31980 + 1.95159i) q^{55} +(-1.27624 - 2.31759i) q^{56} +(9.38296 - 1.13183i) q^{57} +(1.86485 + 6.95973i) q^{58} +(2.63659 + 4.56671i) q^{59} +(3.78021 - 0.842606i) q^{60} +(4.11857 - 7.13357i) q^{61} +(-0.746794 + 0.746794i) q^{62} +(-4.25337 + 6.70141i) q^{63} +1.00000i q^{64} +(-10.2420 - 1.67947i) q^{65} +(3.63491 + 0.518738i) q^{66} +(-2.43944 + 9.10412i) q^{67} +(-1.40048 + 0.375258i) q^{68} +(6.08848 - 7.75883i) q^{69} +(4.87395 - 3.35329i) q^{70} +1.75938i q^{71} +(2.63002 - 1.44326i) q^{72} +(-1.20699 - 0.323412i) q^{73} +(-3.22256 - 5.58163i) q^{74} +(2.71256 + 8.22448i) q^{75} -5.45653 q^{76} +(5.44582 - 1.34170i) q^{77} +(-7.98152 + 0.962782i) q^{78} +(-13.8415 - 7.99137i) q^{79} +(-2.22506 + 0.221605i) q^{80} +(-7.59159 - 4.83403i) q^{81} +(1.80394 - 0.483365i) 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} +(-9.98280 + 7.48935i) q^{87} +(-2.04764 - 0.548664i) q^{88} +(-0.199936 + 0.346299i) q^{89} +(3.79416 + 5.53212i) q^{90} +(-10.7572 + 5.92370i) q^{91} +(-4.02635 + 4.02635i) q^{92} +(-1.68232 - 0.718330i) q^{93} +(9.63096 - 5.56044i) q^{94} +(-1.20919 - 12.1411i) q^{95} +(-1.60731 + 0.645421i) q^{96} +(-8.63390 - 8.63390i) q^{97} +(2.08385 - 6.68263i) 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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Database

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