LMFDB - Embedded newform 210.2.x.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

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")

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

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			23.7
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.03943 + 1.38549i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.22506 - 0.221605i) q^{5} +(-1.36260 - 1.06926i) q^{6} +(-0.736347 + 2.54122i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.839170 + 2.88024i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.750546	−	0.660818i	$-0.770210\pi$
$11$	−1.83587	+	1.05994i	−0.553535	+	0.319583i	0.197012	+	0.980401i	$0.436876\pi$
$12$	1.59292	+	0.680155i	0.459836	+	0.196344i
$13$	3.28206	+	3.28206i	0.910280	+	0.910280i	0.996294	−	0.0860135i	$-0.0274128\pi$
$13$	3.28206	+	3.28206i	0.910280	+	0.910280i	−0.0860135	+	0.996294i	$0.527413\pi$
$14$	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	−0.905371	−	0.424620i	$-0.860408\pi$
$17$	0.375258	−	1.40048i	0.0910134	−	0.339667i	0.996385	+	0.0849537i	$0.0270742\pi$
$18$	0.0651145	−	2.99929i	0.0153476	−	0.706940i
$19$	−4.72549	−	2.72826i	−1.08410	−	0.625906i	−0.152102	−	0.988365i	$-0.548604\pi$
$19$	−4.72549	−	2.72826i	−1.08410	−	0.625906i	−0.932000	+	0.362458i	$0.881937\pi$
$20$	−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	0.930949	+	0.365148i	$0.118982\pi$
$23$	1.47375	+	5.50010i	0.307298	+	1.14685i	−0.623652	+	0.781702i	$0.714352\pi$
$24$	−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	0.814700	−	0.579882i	$-0.196902\pi$
$31$	−0.528063	−	0.914632i	−0.0948429	−	0.164273i	−0.909543	+	0.415610i	$0.863568\pi$
$32$	−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	−0.956351	−	0.292221i	$-0.905606\pi$
$37$	−1.66812	−	6.22550i	−0.274237	−	1.02347i	0.682114	−	0.731246i	$-0.261061\pi$
$38$	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	$0.0465863\pi$
$41$			1.86758i			0.291667i	−0.989309	+	0.145833i	$0.953414\pi$
$42$	3.72057	−	2.67533i	0.574096	−	0.412813i
$43$	1.79293	+	1.79293i	0.273420	+	0.273420i	0.830475	−	0.557056i	$-0.188069\pi$
$43$	1.79293	+	1.79293i	0.273420	+	0.273420i	−0.557056	+	0.830475i	$0.688069\pi$
$44$	−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	0.632042	−	0.774934i	$-0.282217\pi$
$47$	10.7419	−	2.87830i	1.56687	−	0.419843i	0.934832	+	0.355091i	$0.115550\pi$
$48$	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	0.674605	−	0.738179i	$-0.264314\pi$
$53$	6.47741	+	1.73562i	0.889741	+	0.238405i	0.215136	+	0.976584i	$0.430981\pi$
$54$	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	0.641780	−	0.766889i	$-0.278196\pi$
$59$	−2.63659	−	4.56671i	−0.343255	−	0.594535i	−0.985035	+	0.172354i	$0.944863\pi$
$60$	−3.39361	−	1.86638i	−0.438114	−	0.240949i
$61$	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
$63$	−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	0.767742	−	0.640760i	$-0.221380\pi$
$67$	9.10412	+	2.43944i	1.11225	+	0.298025i	0.344504	+	0.938785i	$0.388047\pi$
$68$	−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	$0.0332922\pi$
$71$			1.75938i			0.208800i	−0.994535	+	0.104400i	$0.966708\pi$
$72$	−1.44326	−	2.63002i	−0.170089	−	0.309951i
$73$	0.323412	−	1.20699i	0.0378525	−	0.141268i	−0.944414	−	0.328760i	$-0.893369\pi$
$73$	0.323412	−	1.20699i	0.0378525	−	0.141268i	0.982266	+	0.187492i	$0.0600360\pi$
$74$	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	0.997515	+	0.0704506i	$0.0224437\pi$
$79$	13.8415	+	7.99137i	1.55728	+	0.899099i	0.559770	+	0.828648i	$0.310890\pi$
$80$	−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	−0.0410882	+	0.999156i	$0.513082\pi$
$83$	−9.47707	+	9.47707i	−1.04024	+	1.04024i	−0.999156	+	0.0410882i	$0.986918\pi$
$84$	−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	−0.855234	−	0.518242i	$-0.826587\pi$
$89$	0.199936	−	0.346299i	0.0211931	−	0.0367076i	0.876427	+	0.481534i	$0.159920\pi$
$90$	−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	−0.993185	−	0.116546i	$-0.962818\pi$
$97$	−8.63390	+	8.63390i	−0.876640	+	0.876640i	0.116546	+	0.993185i	$0.462818\pi$
$98$	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	−0.678290	−	0.734795i	$-0.737279\pi$
$101$	−3.82984	+	2.21116i	−0.381084	+	0.220019i	0.297206	+	0.954813i	$0.403945\pi$
$102$	−2.00880	+	1.50705i	−0.198901	+	0.149221i
$103$	−10.3424	+	2.77123i	−1.01906	+	0.273057i	−0.729412	−	0.684075i	$-0.760206\pi$
$103$	−10.3424	+	2.77123i	−1.01906	+	0.273057i	−0.289652	+	0.957132i	$0.593539\pi$
$104$	−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	−0.720153	−	0.693815i	$-0.755928\pi$
$107$	−10.3122	+	2.76314i	−0.996917	+	0.267123i	−0.276763	+	0.960938i	$0.589262\pi$
$108$	−3.29574	+	4.01722i	−0.317133	+	0.386558i
$109$	7.42120	−	4.28463i	0.710822	−	0.410393i	−0.100543	−	0.994933i	$-0.532058\pi$
$109$	7.42120	−	4.28463i	0.710822	−	0.410393i	0.811365	+	0.584539i	$0.198725\pi$
$110$	−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	−0.287524	−	0.957773i	$-0.592832\pi$
$113$	7.12484	−	7.12484i	0.670249	−	0.670249i	0.957773	+	0.287524i	$0.0928322\pi$
$114$	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	−0.00155629	+	0.999999i	$0.500495\pi$
$127$	−11.2870	+	11.2870i	−1.00156	+	1.00156i	−0.999999	+	0.00155629i	$0.999505\pi$
$128$	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	0.702793	−	0.711394i	$-0.251936\pi$
$131$	5.01434	+	2.89503i	0.438105	+	0.252940i	−0.264689	+	0.964334i	$0.585269\pi$
$132$	−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	−0.724130	−	0.689663i	$-0.757759\pi$
$137$	2.90062	−	10.8253i	0.247816	−	0.924864i	0.971947	−	0.235201i	$-0.0755747\pi$
$138$	3.87289	−	9.07027i	0.329682	−	0.772113i
$139$		−	20.1333i		−	1.70768i	−0.520535	−	0.853841i	$-0.674267\pi$
$139$		−	20.1333i		−	1.70768i	0.520535	−	0.853841i	$-0.325733\pi$
$140$	−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	−0.516061	−	0.856552i	$-0.672602\pi$
$149$	5.90510	−	10.2279i	0.483765	−	0.837905i	0.999826	+	0.0186464i	$0.00593567\pi$
$150$	−5.62472	−	6.58502i	−0.459257	−	0.537665i
$151$	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	$0.718611\pi$
$152$	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	−0.487198	−	0.873291i	$-0.661981\pi$
$157$	−16.8625	−	4.51828i	−1.34577	−	0.360598i	−0.858572	+	0.512693i	$0.828648\pi$
$158$	−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	−0.450599	−	0.892726i	$-0.648790\pi$
$163$	−5.03620	+	1.34945i	−0.394466	+	0.105697i	0.0561330	+	0.998423i	$0.482123\pi$
$164$	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	0.899923	−	0.436049i	$-0.143623\pi$
$167$	5.99458	+	5.99458i	0.463874	+	0.463874i	−0.436049	+	0.899923i	$0.643623\pi$
$168$	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	0.997547	−	0.0699972i	$-0.0222991\pi$
$173$	1.29750	+	4.84235i	0.0986474	+	0.368157i	−0.898900	+	0.438154i	$0.855632\pi$
$174$	−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	0.674277	−	0.738479i	$-0.264456\pi$
$179$	−4.04588	−	7.00767i	−0.302403	−	0.523778i	−0.976680	+	0.214701i	$0.931122\pi$
$180$	−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	0.523249	−	0.852180i	$-0.324720\pi$
$191$	0.647671	+	0.373933i	0.0468638	+	0.0270569i	−0.476385	+	0.879237i	$0.658053\pi$
$192$	1.38549	−	1.03943i	0.0999892	−	0.0750144i
$193$	2.39615	−	8.94254i	0.172478	−	0.643698i	−0.824489	−	0.565878i	$-0.808537\pi$
$193$	2.39615	−	8.94254i	0.172478	−	0.643698i	0.996967	−	0.0778200i	$-0.0247960\pi$
$194$	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	0.603793	−	0.797141i	$-0.293655\pi$
$197$	−2.71376	−	2.71376i	−0.193348	−	0.193348i	−0.797141	+	0.603793i	$0.793655\pi$
$198$	3.05952	+	5.57532i	0.217431	+	0.396221i
$199$	−4.85488	+	2.80297i	−0.344153	+	0.198697i	−0.662107	−	0.749409i	$-0.730338\pi$
$199$	−4.85488	+	2.80297i	−0.344153	+	0.198697i	0.317954	+	0.948106i	$0.397004\pi$
$200$	−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	0.855127	−	0.518419i	$-0.173479\pi$
$223$	5.02812	+	5.02812i	0.336708	+	0.336708i	−0.518419	+	0.855127i	$0.673479\pi$
$224$	−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	0.791026	+	0.611783i	$0.209547\pi$
$227$	−3.01201	+	11.2410i	−0.199914	+	0.746089i	−0.990940	+	0.134307i	$0.957119\pi$
$228$	−5.67168	−	7.55997i	−0.375616	−	0.500671i
$229$	−3.58186	−	2.06799i	−0.236696	−	0.136657i	0.376961	−	0.926229i	$-0.376969\pi$
$229$	−3.58186	−	2.06799i	−0.236696	−	0.136657i	−0.613657	+	0.789572i	$0.710302\pi$
$230$	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	0.838220	+	0.545333i	$0.183597\pi$
$233$	5.87626	+	21.9305i	0.384967	+	1.43671i	−0.453253	+	0.891382i	$0.649737\pi$
$234$	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	0.983542	+	0.180680i	$0.0578300\pi$
$241$	10.0635	+	17.4304i	0.648245	+	1.12279i	−0.335297	+	0.942112i	$0.608837\pi$
$242$	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	$-0.809643\pi$
$251$		−	17.8395i		−	1.12602i	0.826450	−	0.563010i	$-0.190357\pi$
$252$	−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	−0.288741	−	0.957407i	$-0.593237\pi$
$257$	−0.963390	+	0.258140i	−0.0600946	+	0.0161023i	0.228646	+	0.973510i	$0.426570\pi$
$258$	−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	−0.294898	−	0.955529i	$-0.595286\pi$
$263$	−16.6722	−	4.46730i	−1.02805	−	0.275466i	−0.733153	+	0.680063i	$0.761952\pi$
$264$	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	−0.887644	−	0.460531i	$-0.847659\pi$
$269$	−13.8205	−	23.9379i	−0.842653	−	1.45952i	0.0449907	−	0.998987i	$-0.485674\pi$
$270$	−10.0677	+	5.80014i	−0.612700	+	0.352985i
$271$	−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
$273$	−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	0.944659	−	0.328053i	$-0.106392\pi$
$277$	26.6082	+	7.12965i	1.59873	+	0.428379i	0.654073	+	0.756432i	$0.273059\pi$
$278$	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	$-0.797919\pi$
$281$		−	19.8830i		−	1.18612i	0.805157	−	0.593062i	$-0.202081\pi$
$282$	−17.7147	−	7.56392i	−1.05489	−	0.450425i
$283$	1.36944	−	5.11082i	0.0814048	−	0.303807i	−0.913204	−	0.407502i	$-0.866400\pi$
$283$	1.36944	−	5.11082i	0.0814048	−	0.303807i	0.994609	+	0.103695i	$0.0330666\pi$
$284$	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	0.289456	−	0.957191i	$-0.406526\pi$
$293$	21.3392	−	21.3392i	1.24665	−	1.24665i	0.957191	−	0.289456i	$-0.0934744\pi$
$294$	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	0.0194830	−	0.999810i	$-0.493798\pi$
$307$	17.8595	−	17.8595i	1.01929	−	1.01929i	0.999810	−	0.0194830i	$-0.00620203\pi$
$308$	−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	−0.0769272	−	0.997037i	$-0.524511\pi$
$311$	13.1923	−	7.61659i	0.748068	−	0.431897i	0.824996	+	0.565139i	$0.191178\pi$
$312$	−4.82455	−	6.43081i	−0.273137	−	0.364073i
$313$	22.0349	−	5.90424i	1.24549	−	0.333727i	0.424895	−	0.905243i	$-0.360311\pi$
$313$	22.0349	−	5.90424i	1.24549	−	0.333727i	0.820591	+	0.571515i	$0.193644\pi$
$314$	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	−0.390447	−	0.920625i	$-0.627679\pi$
$317$	−4.77643	+	1.27984i	−0.268271	+	0.0718830i	0.122176	+	0.992508i	$0.461013\pi$
$318$	−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	−0.862760	−	0.505614i	$-0.831266\pi$
$331$	0.118156	−	0.204653i	0.00649446	−	0.0112487i	0.869254	+	0.494365i	$0.164599\pi$
$332$	−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	−0.719053	−	0.694955i	$-0.755424\pi$
$337$	−0.442376	+	0.442376i	−0.0240977	+	0.0240977i	0.694955	+	0.719053i	$0.255424\pi$
$338$	−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	−0.988469	−	0.151426i	$-0.951613\pi$
$347$	−1.05651	+	3.94296i	−0.0567166	+	0.211669i	0.931752	+	0.363095i	$0.118280\pi$
$348$	11.4774	+	4.90069i	0.615252	+	0.262704i
$349$			11.9140i			0.637743i	0.947798	+	0.318871i	$0.103304\pi$
$349$			11.9140i			0.637743i	−0.947798	+	0.318871i	$0.896696\pi$
$350$	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	0.435937	−	0.899977i	$-0.356417\pi$
$353$	6.82920	+	1.82988i	0.363482	+	0.0973946i	−0.0724557	+	0.997372i	$0.523084\pi$
$354$	−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	−0.960754	−	0.277401i	$-0.910527\pi$
$359$	−4.55001	+	7.88085i	−0.240140	+	0.415935i	0.720614	+	0.693337i	$0.243860\pi$
$360$	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	−0.0307603	−	0.999527i	$-0.509793\pi$
$367$	−10.6737	−	2.86001i	−0.557163	−	0.149291i	−0.526403	+	0.850235i	$0.676460\pi$
$368$	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	−0.976807	−	0.214120i	$-0.931312\pi$
$373$	−33.1354	+	8.87861i	−1.71569	+	0.459717i	−0.738880	+	0.673837i	$0.764645\pi$
$374$	−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	$-0.854258\pi$
$379$		−	17.2109i		−	0.884063i	0.897000	−	0.442031i	$-0.145742\pi$
$380$	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	−0.969930	−	0.243385i	$-0.921742\pi$
$383$	−4.92466	−	18.3791i	−0.251639	−	0.939128i	0.718291	−	0.695743i	$-0.244925\pi$
$384$	−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	−0.776752	−	0.629806i	$-0.783134\pi$
$389$	−18.4175	−	31.9000i	−0.933804	−	1.61740i	−0.157052	−	0.987590i	$-0.550199\pi$
$390$	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	−0.965187	−	0.261561i	$-0.915763\pi$
$397$	−5.18227	−	19.3405i	−0.260091	−	0.970672i	0.705096	−	0.709112i	$-0.250904\pi$
$398$	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	$0.583036\pi$
$402$	−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	−0.130569	−	0.991439i	$-0.541680\pi$
$409$	13.4035	−	7.73849i	0.662758	−	0.382644i	0.793327	+	0.608796i	$0.208347\pi$
$410$	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	−0.650475	−	0.759528i	$-0.725430\pi$
$431$	−6.60065	+	3.81089i	−0.317942	+	0.183564i	0.332533	+	0.943092i	$0.392097\pi$
$432$	−0.845583	+	5.12689i	−0.0406831	+	0.246668i
$433$	−7.94117	−	7.94117i	−0.381628	−	0.381628i	0.490060	−	0.871689i	$-0.336975\pi$
$433$	−7.94117	−	7.94117i	−0.381628	−	0.381628i	−0.871689	+	0.490060i	$0.836975\pi$
$434$	−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	0.748818	−	0.662776i	$-0.230622\pi$
$439$	11.5080	+	6.64413i	0.549245	+	0.317107i	−0.199572	+	0.979883i	$0.563955\pi$
$440$	−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	−0.935584	−	0.353104i	$-0.885126\pi$
$443$	−6.35418	−	23.7141i	−0.301896	−	1.12669i	0.633688	−	0.773589i	$-0.281540\pi$
$444$	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	0.873803	−	0.486280i	$-0.161646\pi$
$457$	−2.69512	−	10.0583i	−0.126072	−	0.470508i	−0.999876	+	0.0157712i	$0.994980\pi$
$458$	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	$0.275800\pi$
$461$			32.7232i			1.52407i	−0.647535	+	0.762035i	$0.724200\pi$
$462$	−3.99478	+	8.85512i	−0.185854	+	0.411978i
$463$	6.59995	+	6.59995i	0.306726	+	0.306726i	0.843638	−	0.536912i	$-0.180409\pi$
$463$	6.59995	+	6.59995i	0.306726	+	0.306726i	−0.536912	+	0.843638i	$0.680409\pi$
$464$	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	−0.276742	−	0.960944i	$-0.589255\pi$
$467$	−0.776556	+	0.208078i	−0.0359347	+	0.00962868i	0.240807	+	0.970573i	$0.422588\pi$
$468$	−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	0.992152	−	0.125039i	$-0.0399056\pi$
$479$	8.48718	+	14.7002i	0.387789	+	0.671670i	−0.604363	+	0.796709i	$0.706572\pi$
$480$	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	0.591219	−	0.806511i	$-0.298647\pi$
$487$	15.4471	+	4.13903i	0.699974	+	0.187557i	0.108755	+	0.994069i	$0.465314\pi$
$488$	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	$0.0495869\pi$
$491$			6.87591i			0.310305i	−0.987891	+	0.155153i	$0.950413\pi$
$492$	−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	−0.240564	−	0.970633i	$-0.577332\pi$
$499$	−26.8381	−	15.4950i	−1.20144	−	0.693651i	−0.960875	+	0.276982i	$0.910666\pi$
$500$	−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	−0.127877	−	0.991790i	$-0.540816\pi$
$503$	19.3755	−	19.3755i	0.863913	−	0.863913i	0.991790	+	0.127877i	$0.0408164\pi$
$504$	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	−0.999096	−	0.0425105i	$-0.986464\pi$
$509$	−10.4397	+	18.0821i	−0.462733	+	0.801477i	0.536363	+	0.843987i	$0.319798\pi$
$510$	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	−0.0236551	−	0.999720i	$-0.507530\pi$
$521$	18.9520	−	10.9419i	0.830300	−	0.479374i	0.853956	+	0.520346i	$0.174197\pi$
$522$	0.469166	−	21.6106i	0.0205349	−	0.945872i
$523$	12.6632	−	3.39310i	0.553724	−	0.148370i	0.0289028	−	0.999582i	$-0.490799\pi$
$523$	12.6632	−	3.39310i	0.553724	−	0.148370i	0.524822	+	0.851212i	$0.324132\pi$
$524$	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	0.497803	+	0.867290i	$0.334140\pi$
$541$	−11.6807	+	20.2316i	−0.502194	+	0.869826i	−0.999997	+	0.00253553i	$0.999193\pi$
$542$	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	−0.760533	−	0.649300i	$-0.775062\pi$
$547$	−2.60152	+	2.60152i	−0.111233	+	0.111233i	0.649300	+	0.760533i	$0.275062\pi$
$548$	−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	0.359022	+	0.933329i	$0.383110\pi$
$557$	−9.87848	+	36.8670i	−0.418565	+	1.56211i	−0.777587	+	0.628776i	$0.783556\pi$
$558$	−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	0.338882	−	0.940829i	$-0.389951\pi$
$563$	3.84263	+	1.02963i	0.161948	+	0.0433937i	−0.176934	+	0.984223i	$0.556618\pi$
$564$	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	−0.913741	−	0.406297i	$-0.866820\pi$
$569$	−2.50482	+	4.33847i	−0.105007	+	0.181878i	0.808734	+	0.588175i	$0.200153\pi$
$570$	−5.89258	−	20.2949i	−0.246813	−	0.850059i
$571$	−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	$-0.408558\pi$
$572$	−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	−0.231107	−	0.972928i	$-0.574235\pi$
$577$	−22.0443	−	5.90675i	−0.917716	−	0.245901i	−0.686609	+	0.727027i	$0.740901\pi$
$578$	−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	−0.971145	−	0.238489i	$-0.923348\pi$
$587$	−29.3071	−	29.3071i	−1.20963	−	1.20963i	−0.238489	−	0.971145i	$-0.576652\pi$
$588$	−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	−0.979584	−	0.201033i	$-0.935570\pi$
$593$	−5.64362	−	21.0623i	−0.231756	−	0.864925i	0.747829	−	0.663892i	$-0.231096\pi$
$594$	−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	0.972043	−	0.234803i	$-0.0754445\pi$
$599$	6.91835	+	11.9829i	0.282676	+	0.489610i	−0.689367	+	0.724413i	$0.742111\pi$
$600$	−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	0.889835	+	0.456282i	$0.150819\pi$
$607$	8.55795	+	31.9387i	0.347356	+	1.29635i	−0.542479	+	0.840070i	$0.682514\pi$
$608$	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	−0.898375	−	0.439229i	$-0.855252\pi$
$613$	2.45744	−	9.17128i	0.0992549	−	0.370424i	0.997630	+	0.0688043i	$0.0219184\pi$
$614$	−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	0.372971	−	0.927843i	$-0.378339\pi$
$617$	−13.7827	−	13.7827i	−0.554873	−	0.554873i	−0.927843	+	0.372971i	$0.878339\pi$
$618$	17.0557	+	7.28256i	0.686081	+	0.292948i
$619$	−6.45537	+	3.72701i	−0.259463	+	0.149801i	−0.624090	−	0.781353i	$-0.714530\pi$
$619$	−6.45537	+	3.72701i	−0.259463	+	0.149801i	0.364626	+	0.931154i	$0.381197\pi$
$620$	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	−0.841690	−	0.539961i	$-0.818439\pi$
$641$	−20.1256	+	11.6195i	−0.794915	+	0.458944i	0.0467751	+	0.998905i	$0.485106\pi$
$642$	17.0059	+	7.26131i	0.671171	+	0.286581i
$643$	15.5301	+	15.5301i	0.612445	+	0.612445i	0.943583	−	0.331137i	$-0.107432\pi$
$643$	15.5301	+	15.5301i	0.612445	+	0.612445i	−0.331137	+	0.943583i	$0.607432\pi$
$644$	−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	0.290663	+	0.956825i	$0.406124\pi$
$647$	−11.1785	+	41.7186i	−0.439471	+	1.64013i	−0.730135	+	0.683303i	$0.760543\pi$
$648$	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	0.969072	+	0.246778i	$0.0793720\pi$
$653$	6.47076	+	24.1492i	0.253220	+	0.945031i	−0.715852	+	0.698252i	$0.753961\pi$
$654$	−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	0.707918	−	0.706294i	$-0.249634\pi$
$661$	−6.62569	−	11.4760i	−0.257709	−	0.446366i	−0.965628	+	0.259928i	$0.916301\pi$
$662$	−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	0.249645	−	0.968337i	$-0.419686\pi$
$673$	−18.6445	−	18.6445i	−0.718692	−	0.718692i	−0.968337	+	0.249645i	$0.919686\pi$
$674$	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	0.838625	−	0.544709i	$-0.183360\pi$
$677$	47.8038	−	12.8090i	1.83725	−	0.492290i	0.998625	+	0.0524196i	$0.0166933\pi$
$678$	−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	0.437524	−	0.899207i	$-0.355855\pi$
$683$	9.58678	+	2.56877i	0.366828	+	0.0982913i	−0.0706962	+	0.997498i	$0.522522\pi$
$684$	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	−0.923844	−	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
$693$	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	$-0.816349\pi$
$701$		−	28.8845i		−	1.09095i	0.838127	−	0.545476i	$-0.183651\pi$
$702$	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	0.844529	−	0.535510i	$-0.179881\pi$
$709$	21.3823	+	12.3450i	0.803027	+	0.463628i	−0.0415013	+	0.999138i	$0.513214\pi$
$710$	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	−0.575905	−	0.817517i	$-0.695350\pi$
$719$	11.2630	−	19.5080i	0.420038	−	0.727527i	0.995943	+	0.0899900i	$0.0286835\pi$
$720$	−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	−0.573648	−	0.819102i	$-0.694472\pi$
$727$	6.61815	−	6.61815i	0.245454	−	0.245454i	0.819102	+	0.573648i	$0.194472\pi$
$728$	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	−0.293121	−	0.956075i	$-0.594694\pi$
$733$	−1.86630	+	0.500074i	−0.0689334	+	0.0184707i	0.224188	+	0.974546i	$0.428027\pi$
$734$	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	−0.667846	−	0.744299i	$-0.732784\pi$
$739$	−9.70996	+	5.60605i	−0.357187	+	0.206222i	0.310659	+	0.950521i	$0.399450\pi$
$740$	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	−0.461518	−	0.887131i	$-0.652695\pi$
$743$	11.6014	−	11.6014i	0.425613	−	0.425613i	0.887131	+	0.461518i	$0.152695\pi$
$744$	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	−0.963516	−	0.267652i	$-0.913752\pi$
$751$	−6.85013	+	11.8648i	−0.249965	+	0.432952i	0.713551	+	0.700603i	$0.247086\pi$
$752$	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	0.0318111	−	0.999494i	$-0.489873\pi$
$757$	28.3749	−	28.3749i	1.03130	−	1.03130i	0.999494	−	0.0318111i	$-0.0101275\pi$
$758$	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	0.414679	−	0.909968i	$-0.363894\pi$
$761$	−4.58035	−	2.64447i	−0.166038	−	0.0958618i	−0.580716	+	0.814106i	$0.697227\pi$
$762$	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	$-0.994656\pi$
$769$		−	0.931143i		−	0.0335779i	0.999859	−	0.0167889i	$-0.00534434\pi$
$770$	−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	0.0528969	−	0.998600i	$-0.483155\pi$
$773$	−11.1376	−	2.98432i	−0.400593	−	0.107339i	−0.453490	+	0.891261i	$0.649821\pi$
$774$	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	−0.0972652	−	0.995258i	$-0.531010\pi$
$787$	−19.0519	−	5.10495i	−0.679129	−	0.181972i	−0.581863	+	0.813287i	$0.697676\pi$
$788$	−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	0.414414	−	0.910088i	$-0.363986\pi$
$797$	−13.9935	−	13.9935i	−0.495674	−	0.495674i	−0.910088	+	0.414414i	$0.863986\pi$
$798$	−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	0.547713	−	0.836666i	$-0.315498\pi$
$809$	−12.8197	−	22.2044i	−0.450717	−	0.780666i	−0.998431	+	0.0560005i	$0.982165\pi$
$810$	−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	0.710841	−	0.703352i	$-0.248314\pi$
$821$	13.0985	+	7.56242i	0.457141	+	0.263930i	−0.253700	+	0.967283i	$0.581648\pi$
$822$	−15.5274	+	11.6490i	−0.541579	+	0.406306i
$823$	10.6131	−	39.6086i	0.369949	−	1.38067i	−0.490637	−	0.871364i	$-0.663236\pi$
$823$	10.6131	−	39.6086i	0.369949	−	1.38067i	0.860586	−	0.509305i	$-0.170097\pi$
$824$	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	0.993075	−	0.117480i	$-0.0374815\pi$
$827$	25.1800	+	25.1800i	0.875596	+	0.875596i	−0.117480	+	0.993075i	$0.537482\pi$
$828$	−14.9757	+	8.21808i	−0.520440	+	0.285598i
$829$	25.3933	−	14.6608i	0.881944	−	0.509191i	0.0106454	−	0.999943i	$-0.496611\pi$
$829$	25.3933	−	14.6608i	0.881944	−	0.509191i	0.871299	+	0.490752i	$0.163278\pi$
$830$	−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	0.576833	−	0.816862i	$-0.304288\pi$
$853$	−7.01032	−	7.01032i	−0.240029	−	0.240029i	−0.816862	+	0.576833i	$0.804288\pi$
$854$	−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	−0.809575	−	0.587016i	$-0.800303\pi$
$857$	5.41712	−	20.2170i	0.185045	−	0.690599i	0.994621	−	0.103583i	$-0.0330307\pi$
$858$	10.2275	+	13.6325i	0.349160	+	0.465407i
$859$	11.7809	+	6.80172i	0.401960	+	0.232072i	0.687329	−	0.726346i	$-0.258783\pi$
$859$	11.7809	+	6.80172i	0.401960	+	0.232072i	−0.285369	+	0.958418i	$0.592116\pi$
$860$	−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	−0.786731	−	0.617296i	$-0.788228\pi$
$863$	−12.1635	−	45.3947i	−0.414050	−	1.54525i	0.372681	−	0.927959i	$-0.378438\pi$
$864$	−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	0.992570	+	0.121673i	$0.0388260\pi$
$877$	5.73970	+	21.4208i	0.193816	+	0.723330i	−0.798754	+	0.601657i	$0.794507\pi$
$878$	−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	$0.271604\pi$
$881$			44.7263i			1.50687i	−0.657525	+	0.753433i	$0.728396\pi$
$882$	−11.6099	+	17.4989i	−0.390924	+	0.589218i
$883$	−3.98957	−	3.98957i	−0.134260	−	0.134260i	0.636783	−	0.771043i	$-0.280265\pi$
$883$	−3.98957	−	3.98957i	−0.134260	−	0.134260i	−0.771043	+	0.636783i	$0.780265\pi$
$884$	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	0.277935	−	0.960600i	$-0.410350\pi$
$887$	29.7508	−	7.97169i	0.998933	−	0.267663i	0.720998	+	0.692937i	$0.243683\pi$
$888$	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	−0.145670	−	0.989333i	$-0.546534\pi$
$907$	−23.0840	−	6.18534i	−0.766491	−	0.205381i	−0.620821	+	0.783952i	$0.713201\pi$
$908$	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	$-0.850908\pi$
$911$		−	27.2518i		−	0.902892i	0.892298	−	0.451446i	$-0.149092\pi$
$912$	−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	0.355448	−	0.934696i	$-0.384328\pi$
$919$	−8.37600	−	4.83589i	−0.276299	−	0.159521i	−0.631747	+	0.775175i	$0.717662\pi$
$920$	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	0.497497	+	0.867466i	$0.334252\pi$
$929$	−15.3159	+	26.5279i	−0.502499	+	0.870353i	−0.999996	+	0.00288755i	$0.999081\pi$
$930$	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	−0.720345	−	0.693615i	$-0.756017\pi$
$937$	−0.818219	+	0.818219i	−0.0267300	+	0.0267300i	0.693615	+	0.720345i	$0.256017\pi$
$938$	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	−0.979783	−	0.200065i	$-0.935885\pi$
$941$	−39.7684	+	22.9603i	−1.29641	+	0.748484i	−0.316630	+	0.948549i	$0.602551\pi$
$942$	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	−0.719260	−	0.694741i	$-0.755519\pi$
$947$	−30.6129	+	8.20271i	−0.994787	+	0.266552i	−0.275527	+	0.961293i	$0.588852\pi$
$948$	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	−0.882403	−	0.470495i	$-0.844076\pi$
$953$	−12.7159	+	12.7159i	−0.411908	+	0.411908i	0.470495	+	0.882403i	$0.344076\pi$
$954$	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	−0.766688	−	0.642019i	$-0.778097\pi$
$967$	−3.87679	+	3.87679i	−0.124669	+	0.124669i	0.642019	+	0.766688i	$0.278097\pi$
$968$	−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	0.339352	−	0.940659i	$-0.389792\pi$
$971$	−9.52298	−	5.49809i	−0.305607	−	0.176442i	−0.644959	+	0.764217i	$0.723126\pi$
$972$	−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	0.432191	+	0.901782i	$0.357741\pi$
$977$	−12.2836	+	45.8432i	−0.392988	+	1.46665i	−0.825180	+	0.564870i	$0.808926\pi$
$978$	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	−0.242675	−	0.970108i	$-0.578025\pi$
$983$	−29.4055	−	7.87919i	−0.937891	−	0.251307i	−0.695216	+	0.718801i	$0.744691\pi$
$984$	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	0.964109	−	0.265506i	$-0.0855389\pi$
$991$	7.93677	+	13.7469i	0.252120	+	0.436684i	−0.711989	+	0.702190i	$0.752206\pi$
$992$	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	0.659703	−	0.751527i	$-0.270682\pi$
$997$	27.0051	+	7.23598i	0.855259	+	0.229166i	0.195556	+	0.980693i	$0.437349\pi$
$998$	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.23.7	✓	64
3.2	odd	2	inner	210.2.x.a.23.10	yes	64
5.2	odd	4	inner	210.2.x.a.107.7	yes	64
7.4	even	3	inner	210.2.x.a.53.14	yes	64
15.2	even	4	inner	210.2.x.a.107.14	yes	64
21.11	odd	6	inner	210.2.x.a.53.7	yes	64
35.32	odd	12	inner	210.2.x.a.137.10	yes	64
105.32	even	12	inner	210.2.x.a.137.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.7	✓	64	1.1	even	1	trivial
210.2.x.a.23.10	yes	64	3.2	odd	2	inner
210.2.x.a.53.7	yes	64	21.11	odd	6	inner
210.2.x.a.53.14	yes	64	7.4	even	3	inner
210.2.x.a.107.7	yes	64	5.2	odd	4	inner
210.2.x.a.107.14	yes	64	15.2	even	4	inner
210.2.x.a.137.7	yes	64	105.32	even	12	inner
210.2.x.a.137.10	yes	64	35.32	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.03943 + 1.38549i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.22506 - 0.221605i) q^{5} +(-1.36260 - 1.06926i) q^{6} +(-0.736347 + 2.54122i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.839170 + 2.88024i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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