LMFDB - Embedded newform 546.2.ch.a.137.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.3
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.47304 - 0.911131i) q^{3} -1.00000i q^{4} +(1.94682 + 0.521648i) q^{5} +(1.68586 - 0.397328i) q^{6} +(-2.63140 - 0.275187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33968 + 2.68426i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47304 - 0.911131i) q^{3} -1.00000i q^{4} +(1.94682 + 0.521648i) q^{5} +(1.68586 - 0.397328i) q^{6} +(-2.63140 - 0.275187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33968 + 2.68426i) q^{9} +(-1.74547 + 1.00775i) q^{10} +(0.0824122 - 0.307566i) q^{11} +(-0.911131 + 1.47304i) q^{12} +(3.50443 + 0.847906i) q^{13} +(2.05527 - 1.66609i) q^{14} +(-2.39245 - 2.54222i) q^{15} -1.00000 q^{16} -1.73518 q^{17} +(-2.84536 - 0.950764i) q^{18} +(-3.08534 + 0.826715i) q^{19} +(0.521648 - 1.94682i) q^{20} +(3.62542 + 2.80291i) q^{21} +(0.159208 + 0.275756i) q^{22} +8.17145 q^{23} +(-0.397328 - 1.68586i) q^{24} +(-0.812142 - 0.468891i) q^{25} +(-3.07757 + 1.87845i) q^{26} +(0.472318 - 5.17464i) q^{27} +(-0.275187 + 2.63140i) q^{28} +(4.90662 + 2.83284i) q^{29} +(3.48933 + 0.105903i) q^{30} +(9.15825 - 2.45395i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.401630 + 0.377969i) q^{33} +(1.22696 - 1.22696i) q^{34} +(-4.97931 - 1.90841i) q^{35} +(2.68426 - 1.33968i) q^{36} +(6.57940 - 6.57940i) q^{37} +(1.59709 - 2.76624i) q^{38} +(-4.38961 - 4.44200i) q^{39} +(1.00775 + 1.74547i) q^{40} +(2.95324 + 11.0217i) q^{41} +(-4.54552 + 0.581600i) q^{42} +(-4.91216 + 2.83604i) q^{43} +(-0.307566 - 0.0824122i) q^{44} +(1.20787 + 5.92461i) q^{45} +(-5.77809 + 5.77809i) q^{46} +(0.692489 - 2.58440i) q^{47} +(1.47304 + 0.911131i) q^{48} +(6.84854 + 1.44826i) q^{49} +(0.905827 - 0.242716i) q^{50} +(2.55598 + 1.58098i) q^{51} +(0.847906 - 3.50443i) q^{52} +(8.76242 + 5.05898i) q^{53} +(3.32504 + 3.99300i) q^{54} +(0.320883 - 0.555786i) q^{55} +(-1.66609 - 2.05527i) q^{56} +(5.29807 + 1.59337i) q^{57} +(-5.47262 + 1.46639i) q^{58} +(0.870720 + 0.870720i) q^{59} +(-2.54222 + 2.39245i) q^{60} +(-2.23949 + 3.87891i) q^{61} +(-4.74066 + 8.21107i) q^{62} +(-2.78656 - 7.43203i) q^{63} +1.00000i q^{64} +(6.38019 + 3.47880i) q^{65} +(0.0167309 - 0.551259i) q^{66} +(1.77232 - 6.61438i) q^{67} +1.73518i q^{68} +(-12.0369 - 7.44527i) q^{69} +(4.87035 - 2.17146i) q^{70} +(8.58837 + 2.30125i) q^{71} +(-0.950764 + 2.84536i) q^{72} +(-2.17455 - 8.11552i) q^{73} +9.30468i q^{74} +(0.769095 + 1.43066i) q^{75} +(0.826715 + 3.08534i) q^{76} +(-0.301498 + 0.786652i) q^{77} +(6.24489 + 0.0370439i) q^{78} +(4.25965 + 7.37793i) q^{79} +(-1.94682 - 0.521648i) q^{80} +(-5.41052 + 7.19210i) q^{81} +(-9.88175 - 5.70523i) q^{82} +(-5.00416 + 5.00416i) q^{83} +(2.80291 - 3.62542i) q^{84} +(-3.37808 - 0.905154i) q^{85} +(1.46804 - 5.47880i) q^{86} +(-4.64655 - 8.64345i) q^{87} +(0.275756 - 0.159208i) q^{88} +(-7.74170 - 7.74170i) q^{89} +(-5.04343 - 3.33524i) q^{90} +(-8.98824 - 3.19556i) q^{91} -8.17145i q^{92} +(-15.7263 - 4.72962i) q^{93} +(1.33779 + 2.31711i) q^{94} -6.43786 q^{95} +(-1.68586 + 0.397328i) q^{96} +(4.69524 - 17.5229i) q^{97} +(-5.86672 + 3.81858i) q^{98} +(0.935995 - 0.190824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.47304	−	0.911131i	−0.850459	−	0.526042i
$3$	−1.47304	−	0.911131i	−0.850459	−	0.526042i
$4$		−	1.00000i		−	0.500000i
$5$	1.94682	+	0.521648i	0.870644	+	0.233288i	0.666366	−	0.745625i	$-0.267849\pi$
$5$	1.94682	+	0.521648i	0.870644	+	0.233288i	0.204278	+	0.978913i	$0.434515\pi$
$6$	1.68586	−	0.397328i	0.688250	−	0.162208i
$7$	−2.63140	−	0.275187i	−0.994576	−	0.104011i
$7$	−2.63140	−	0.275187i	−0.994576	−	0.104011i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.33968	+	2.68426i	0.446560	+	0.894754i
$10$	−1.74547	+	1.00775i	−0.551966	+	0.318678i
$11$	0.0824122	−	0.307566i	0.0248482	−	0.0927348i	−0.952388	−	0.304888i	$-0.901381\pi$
$11$	0.0824122	−	0.307566i	0.0248482	−	0.0927348i	0.977236	+	0.212153i	$0.0680476\pi$
$12$	−0.911131	+	1.47304i	−0.263021	+	0.425229i
$13$	3.50443	+	0.847906i	0.971955	+	0.235167i
$13$	3.50443	+	0.847906i	0.971955	+	0.235167i
$14$	2.05527	−	1.66609i	0.549294	−	0.445283i
$15$	−2.39245	−	2.54222i	−0.617727	−	0.656397i
$16$	−1.00000			−0.250000
$17$	−1.73518			−0.420843			−0.210421	−	0.977611i	$-0.567484\pi$
$17$	−1.73518			−0.420843			−0.210421	+	0.977611i	$0.567484\pi$
$18$	−2.84536	−	0.950764i	−0.670657	−	0.224097i
$19$	−3.08534	+	0.826715i	−0.707826	+	0.189662i	−0.594734	−	0.803923i	$-0.702742\pi$
$19$	−3.08534	+	0.826715i	−0.707826	+	0.189662i	−0.113093	+	0.993584i	$0.536076\pi$
$20$	0.521648	−	1.94682i	0.116644	−	0.435322i
$21$	3.62542	+	2.80291i	0.791132	+	0.611646i
$22$	0.159208	+	0.275756i	0.0339433	+	0.0587915i
$23$	8.17145			1.70387			0.851933	−	0.523651i	$-0.175430\pi$
$23$	8.17145			1.70387			0.851933	+	0.523651i	$0.175430\pi$
$24$	−0.397328	−	1.68586i	−0.0811041	−	0.344125i
$25$	−0.812142	−	0.468891i	−0.162428	−	0.0937781i
$26$	−3.07757	+	1.87845i	−0.603561	+	0.368394i
$27$	0.472318	−	5.17464i	0.0908977	−	0.995860i
$28$	−0.275187	+	2.63140i	−0.0520055	+	0.497288i
$29$	4.90662	+	2.83284i	0.911137	+	0.526045i	0.880797	−	0.473495i	$-0.157008\pi$
$29$	4.90662	+	2.83284i	0.911137	+	0.526045i	0.0303399	+	0.999540i	$0.490341\pi$
$30$	3.48933	+	0.105903i	0.637062	+	0.0193351i
$31$	9.15825	−	2.45395i	1.64487	−	0.440742i	0.686701	−	0.726940i	$-0.259058\pi$
$31$	9.15825	−	2.45395i	1.64487	−	0.440742i	0.958170	+	0.286198i	$0.0923916\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.401630	+	0.377969i	−0.0699147	+	0.0657959i
$34$	1.22696	−	1.22696i	0.210421	−	0.210421i
$35$	−4.97931	−	1.90841i	−0.841657	−	0.322579i
$36$	2.68426	−	1.33968i	0.447377	−	0.223280i
$37$	6.57940	−	6.57940i	1.08165	−	1.08165i	0.0852907	−	0.996356i	$-0.472818\pi$
$37$	6.57940	−	6.57940i	1.08165	−	1.08165i	0.996356	−	0.0852907i	$-0.0271819\pi$
$38$	1.59709	−	2.76624i	0.259082	−	0.448744i
$39$	−4.38961	−	4.44200i	−0.702900	−	0.711289i
$40$	1.00775	+	1.74547i	0.159339	+	0.275983i
$41$	2.95324	+	11.0217i	0.461219	+	1.72129i	0.669129	+	0.743146i	$0.266667\pi$
$41$	2.95324	+	11.0217i	0.461219	+	1.72129i	−0.207910	+	0.978148i	$0.566666\pi$
$42$	−4.54552	+	0.581600i	−0.701389	+	0.0897429i
$43$	−4.91216	+	2.83604i	−0.749098	+	0.432492i	−0.825368	−	0.564595i	$-0.809032\pi$
$43$	−4.91216	+	2.83604i	−0.749098	+	0.432492i	0.0762701	+	0.997087i	$0.475699\pi$
$44$	−0.307566	−	0.0824122i	−0.0463674	−	0.0124241i
$45$	1.20787	+	5.92461i	0.180059	+	0.883189i
$46$	−5.77809	+	5.77809i	−0.851933	+	0.851933i
$47$	0.692489	−	2.58440i	0.101010	−	0.376974i	−0.896852	−	0.442331i	$-0.854152\pi$
$47$	0.692489	−	2.58440i	0.101010	−	0.376974i	0.997862	+	0.0653565i	$0.0208184\pi$
$48$	1.47304	+	0.911131i	0.212615	+	0.131511i
$49$	6.84854	+	1.44826i	0.978363	+	0.206894i
$50$	0.905827	−	0.242716i	0.128103	−	0.0343252i
$51$	2.55598	+	1.58098i	0.357909	+	0.221381i
$52$	0.847906	−	3.50443i	0.117583	−	0.485978i
$53$	8.76242	+	5.05898i	1.20361	+	0.694905i	0.961356	−	0.275308i	$-0.0887798\pi$
$53$	8.76242	+	5.05898i	1.20361	+	0.694905i	0.242254	+	0.970213i	$0.422113\pi$
$54$	3.32504	+	3.99300i	0.452481	+	0.543379i
$55$	0.320883	−	0.555786i	0.0432679	−	0.0749421i
$56$	−1.66609	−	2.05527i	−0.222641	−	0.274647i
$57$	5.29807	+	1.59337i	0.701747	+	0.211047i
$58$	−5.47262	+	1.46639i	−0.718591	+	0.192546i
$59$	0.870720	+	0.870720i	0.113358	+	0.113358i	0.761511	−	0.648152i	$-0.224458\pi$
$59$	0.870720	+	0.870720i	0.113358	+	0.113358i	−0.648152	+	0.761511i	$0.724458\pi$
$60$	−2.54222	+	2.39245i	−0.328199	+	0.308863i
$61$	−2.23949	+	3.87891i	−0.286737	+	0.496644i	−0.973029	−	0.230683i	$-0.925904\pi$
$61$	−2.23949	+	3.87891i	−0.286737	+	0.496644i	0.686292	+	0.727326i	$0.259237\pi$
$62$	−4.74066	+	8.21107i	−0.602065	+	1.04281i
$63$	−2.78656	−	7.43203i	−0.351073	−	0.936348i
$64$			1.00000i			0.125000i
$65$	6.38019	+	3.47880i	0.791365	+	0.431492i
$66$	0.0167309	−	0.551259i	0.00205944	−	0.0678553i
$67$	1.77232	−	6.61438i	0.216523	−	0.808076i	−0.769102	−	0.639127i	$-0.779296\pi$
$67$	1.77232	−	6.61438i	0.216523	−	0.808076i	0.985625	−	0.168949i	$-0.0540373\pi$
$68$			1.73518i			0.210421i
$69$	−12.0369	−	7.44527i	−1.44907	−	0.896305i
$70$	4.87035	−	2.17146i	0.582118	−	0.259539i
$71$	8.58837	+	2.30125i	1.01925	+	0.273108i	0.729490	−	0.683991i	$-0.239757\pi$
$71$	8.58837	+	2.30125i	1.01925	+	0.273108i	0.289762	+	0.957099i	$0.406424\pi$
$72$	−0.950764	+	2.84536i	−0.112049	+	0.335328i
$73$	−2.17455	−	8.11552i	−0.254511	−	0.949850i	−0.968362	−	0.249551i	$-0.919717\pi$
$73$	−2.17455	−	8.11552i	−0.254511	−	0.949850i	0.713850	−	0.700298i	$-0.246950\pi$
$74$			9.30468i			1.08165i
$75$	0.769095	+	1.43066i	0.0888075	+	0.165199i
$76$	0.826715	+	3.08534i	0.0948308	+	0.353913i
$77$	−0.301498	+	0.786652i	−0.0343589	+	0.0896473i
$78$	6.24489	+	0.0370439i	0.707094	+	0.00419439i
$79$	4.25965	+	7.37793i	0.479248	+	0.830082i	0.999717	−	0.0237989i	$-0.00757616\pi$
$79$	4.25965	+	7.37793i	0.479248	+	0.830082i	−0.520469	+	0.853881i	$0.674243\pi$
$80$	−1.94682	−	0.521648i	−0.217661	−	0.0583221i
$81$	−5.41052	+	7.19210i	−0.601169	+	0.799122i
$82$	−9.88175	−	5.70523i	−1.09126	−	0.630037i
$83$	−5.00416	+	5.00416i	−0.549278	+	0.549278i	−0.926232	−	0.376954i	$-0.876971\pi$
$83$	−5.00416	+	5.00416i	−0.549278	+	0.549278i	0.376954	+	0.926232i	$0.376971\pi$
$84$	2.80291	−	3.62542i	0.305823	−	0.395566i
$85$	−3.37808	−	0.905154i	−0.366404	−	0.0981777i
$86$	1.46804	−	5.47880i	0.158303	−	0.590795i
$87$	−4.64655	−	8.64345i	−0.498162	−	0.926676i
$88$	0.275756	−	0.159208i	0.0293957	−	0.0169716i
$89$	−7.74170	−	7.74170i	−0.820618	−	0.820618i	0.165578	−	0.986197i	$-0.447051\pi$
$89$	−7.74170	−	7.74170i	−0.820618	−	0.820618i	−0.986197	+	0.165578i	$0.947051\pi$
$90$	−5.04343	−	3.33524i	−0.531624	−	0.351565i
$91$	−8.98824	−	3.19556i	−0.942223	−	0.334985i
$92$		−	8.17145i		−	0.851933i
$93$	−15.7263	−	4.72962i	−1.63074	−	0.490439i
$94$	1.33779	+	2.31711i	0.137982	+	0.238992i
$95$	−6.43786			−0.660510
$96$	−1.68586	+	0.397328i	−0.172063	+	0.0405521i
$97$	4.69524	−	17.5229i	0.476729	−	1.77918i	−0.137991	−	0.990433i	$-0.544065\pi$
$97$	4.69524	−	17.5229i	0.476729	−	1.77918i	0.614721	−	0.788745i	$-0.289269\pi$
$98$	−5.86672	+	3.81858i	−0.592629	+	0.385735i
$99$	0.935995	−	0.190824i	0.0940710	−	0.0191786i
$100$	−0.468891	+	0.812142i	−0.0468891	+	0.0812142i
$101$	−1.51198	−	2.61883i	−0.150448	−	0.260583i	0.780944	−	0.624600i	$-0.214738\pi$
$101$	−1.51198	−	2.61883i	−0.150448	−	0.260583i	−0.931392	+	0.364018i	$0.881405\pi$
$102$	−2.92527	+	0.689435i	−0.289645	+	0.0682642i
$103$	−8.34991	+	4.82082i	−0.822741	+	0.475010i	−0.851361	−	0.524580i	$-0.824222\pi$
$103$	−8.34991	+	4.82082i	−0.822741	+	0.475010i	0.0286195	+	0.999590i	$0.490889\pi$
$104$	1.87845	+	3.07757i	0.184197	+	0.301780i
$105$	5.59590	+	7.34796i	0.546104	+	0.717087i
$106$	−9.77321	+	2.61872i	−0.949258	+	0.254353i
$107$		−	1.99482i		−	0.192846i	−0.995340	−	0.0964231i	$-0.969260\pi$
$107$		−	1.99482i		−	0.192846i	0.995340	−	0.0964231i	$-0.0307402\pi$
$108$	−5.17464	−	0.472318i	−0.497930	−	0.0454488i
$109$	−1.63998	+	0.439432i	−0.157082	+	0.0420899i	−0.336503	−	0.941682i	$-0.609244\pi$
$109$	−1.63998	+	0.439432i	−0.157082	+	0.0420899i	0.179421	+	0.983772i	$0.442578\pi$
$110$	0.166101	+	0.619898i	0.0158371	+	0.0591050i
$111$	−15.6864	+	3.69700i	−1.48889	+	0.350904i
$112$	2.63140	+	0.275187i	0.248644	+	0.0260028i
$113$	−11.8425	+	6.83728i	−1.11405	+	0.643197i	−0.939875	−	0.341518i	$-0.889059\pi$
$113$	−11.8425	+	6.83728i	−1.11405	+	0.643197i	−0.174175	+	0.984715i	$0.555726\pi$
$114$	−4.87299	+	2.61962i	−0.456397	+	0.245350i
$115$	15.9083	+	4.26262i	1.48346	+	0.397492i
$116$	2.83284	−	4.90662i	0.263022	−	0.455568i
$117$	2.41882	+	10.5427i	0.223620	+	0.974677i
$118$	−1.23138			−0.113358
$119$	4.56595	+	0.477499i	0.418560	+	0.0437723i
$120$	0.105903	−	3.48933i	0.00966755	−	0.318531i
$121$	9.43847	+	5.44931i	0.858043	+	0.495391i
$122$	−1.15925	−	4.32636i	−0.104953	−	0.391690i
$123$	5.69194	−	18.9261i	0.513225	−	1.70651i
$124$	−2.45395	−	9.15825i	−0.220371	−	0.822436i
$125$	−8.46235	−	8.46235i	−0.756895	−	0.756895i
$126$	7.22563	+	3.28485i	0.643711	+	0.292637i
$127$	−7.05537	−	4.07342i	−0.626063	−	0.361457i	0.153163	−	0.988201i	$-0.451054\pi$
$127$	−7.05537	−	4.07342i	−0.626063	−	0.361457i	−0.779226	+	0.626744i	$0.784387\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	9.81980	+	0.298035i	0.864585	+	0.0262405i
$130$	−6.97136	+	2.05159i	−0.611428	+	0.179936i
$131$	−3.37282	+	1.94730i	−0.294685	+	0.170136i	−0.640053	−	0.768331i	$-0.721088\pi$
$131$	−3.37282	+	1.94730i	−0.294685	+	0.170136i	0.345368	+	0.938467i	$0.387754\pi$
$132$	0.377969	+	0.401630i	0.0328979	+	0.0349574i
$133$	8.34628	−	1.32637i	0.723714	−	0.115011i
$134$	3.42386	+	5.93029i	0.295776	+	0.512299i
$135$	3.61886	−	9.82770i	0.311462	−	0.845834i
$136$	−1.22696	−	1.22696i	−0.105211	−	0.105211i
$137$	−6.55117	−	6.55117i	−0.559704	−	0.559704i	0.369519	−	0.929223i	$-0.379522\pi$
$137$	−6.55117	−	6.55117i	−0.559704	−	0.559704i	−0.929223	+	0.369519i	$0.879522\pi$
$138$	13.7759	−	3.24674i	1.17269	−	0.276381i
$139$	−6.24961	−	10.8246i	−0.530085	−	0.918134i	−0.999384	−	0.0350950i	$-0.988827\pi$
$139$	−6.24961	−	10.8246i	−0.530085	−	0.918134i	0.469299	−	0.883039i	$-0.344507\pi$
$140$	−1.90841	+	4.97931i	−0.161290	+	0.420828i
$141$	−3.37480	+	3.17598i	−0.284209	+	0.267465i
$142$	−7.70012	+	4.44567i	−0.646180	+	0.373072i
$143$	0.549595	−	1.00797i	0.0459595	−	0.0842905i
$144$	−1.33968	−	2.68426i	−0.111640	−	0.223688i
$145$	8.07455	+	8.07455i	0.670555	+	0.670555i
$146$	7.27617	+	4.20090i	0.602181	+	0.347669i
$147$	−8.76861	−	8.37326i	−0.723223	−	0.690615i
$148$	−6.57940	−	6.57940i	−0.540823	−	0.540823i
$149$	1.81241	+	6.76401i	0.148478	+	0.554129i	0.999576	+	0.0291212i	$0.00927089\pi$
$149$	1.81241	+	6.76401i	0.148478	+	0.554129i	−0.851097	+	0.525008i	$0.824062\pi$
$150$	−1.55546	−	0.467798i	−0.127003	−	0.0381956i
$151$	2.10118	+	7.84172i	0.170992	+	0.638150i	0.997200	+	0.0747849i	$0.0238270\pi$
$151$	2.10118	+	7.84172i	0.170992	+	0.638150i	−0.826208	+	0.563365i	$0.809506\pi$
$152$	−2.76624	−	1.59709i	−0.224372	−	0.129541i
$153$	−2.32458	−	4.65768i	−0.187931	−	0.376551i
$154$	−0.343056	−	0.769438i	−0.0276442	−	0.0620031i
$155$	19.1096			1.53492
$156$	−4.44200	+	4.38961i	−0.355644	+	0.351450i
$157$	0.394972	−	0.684111i	0.0315222	−	0.0545980i	−0.849834	−	0.527051i	$-0.823298\pi$
$157$	0.394972	−	0.684111i	0.0315222	−	0.0545980i	0.881356	+	0.472453i	$0.156631\pi$
$158$	−8.22901	−	2.20496i	−0.654665	−	0.175417i
$159$	−8.29797	−	15.4358i	−0.658072	−	1.22414i
$160$	1.74547	−	1.00775i	0.137991	−	0.0796694i
$161$	−21.5024	−	2.24868i	−1.69462	−	0.177221i
$162$	−1.25976	−	8.91140i	−0.0989764	−	0.700145i
$163$	1.26971	+	4.73861i	0.0994511	+	0.371157i	0.997657	−	0.0684191i	$-0.0217955\pi$
$163$	1.26971	+	4.73861i	0.0994511	+	0.371157i	−0.898206	+	0.439576i	$0.855129\pi$
$164$	11.0217	−	2.95324i	0.860647	−	0.230610i
$165$	−0.979067	+	0.526327i	−0.0762202	+	0.0409745i
$166$		−	7.07695i		−	0.549278i
$167$	−13.4875	+	3.61395i	−1.04369	+	0.279656i	−0.739642	−	0.673000i	$-0.765005\pi$
$167$	−13.4875	+	3.61395i	−1.04369	+	0.279656i	−0.304049	+	0.952657i	$0.598339\pi$
$168$	0.581600	+	4.54552i	0.0448714	+	0.350694i
$169$	11.5621	+	5.94286i	0.889393	+	0.457143i
$170$	3.02870	−	1.74862i	0.232291	−	0.134113i
$171$	−6.35249	−	7.17434i	−0.485787	−	0.548635i
$172$	2.83604	+	4.91216i	0.216246	+	0.374549i
$173$	0.852828	−	1.47714i	0.0648393	−	0.112305i	−0.831783	−	0.555100i	$-0.812680\pi$
$173$	0.852828	−	1.47714i	0.0648393	−	0.112305i	0.896623	+	0.442795i	$0.146013\pi$
$174$	9.39745	+	2.82624i	0.712419	+	0.214257i
$175$	2.00804	+	1.45733i	0.151794	+	0.110164i
$176$	−0.0824122	+	0.307566i	−0.00621205	+	0.0231837i
$177$	−0.489263	−	2.07594i	−0.0367753	−	0.156038i
$178$	10.9484			0.820618
$179$	9.00676	+	15.6002i	0.673197	+	1.16601i	0.976992	+	0.213274i	$0.0684126\pi$
$179$	9.00676	+	15.6002i	0.673197	+	1.16601i	−0.303796	+	0.952737i	$0.598254\pi$
$180$	5.92461	−	1.20787i	0.441594	−	0.0900293i
$181$			1.58696i			0.117957i	0.998259	+	0.0589787i	$0.0187844\pi$
$181$			1.58696i			0.117957i	−0.998259	+	0.0589787i	$0.981216\pi$
$182$	8.61524	−	4.09605i	0.638604	−	0.303619i
$183$	6.83305	−	3.67331i	0.505114	−	0.271539i
$184$	5.77809	+	5.77809i	0.425966	+	0.425966i
$185$	16.2410	−	9.37676i	1.19406	−	0.689393i
$186$	14.4645	−	7.77584i	1.06059	−	0.570152i
$187$	−0.143000	+	0.533683i	−0.0104572	+	0.0390268i
$188$	−2.58440	−	0.692489i	−0.188487	−	0.0505050i
$189$	−2.66685	+	13.4866i	−0.193985	+	0.981004i
$190$	4.55225	−	4.55225i	0.330255	−	0.330255i
$191$	5.05275	+	2.91721i	0.365604	+	0.211082i	0.671536	−	0.740972i	$-0.265635\pi$
$191$	5.05275	+	2.91721i	0.365604	+	0.211082i	−0.305932	+	0.952053i	$0.598968\pi$
$192$	0.911131	−	1.47304i	0.0657553	−	0.106307i
$193$	7.25495	+	1.94396i	0.522223	+	0.139929i	0.510295	−	0.860000i	$-0.329536\pi$
$193$	7.25495	+	1.94396i	0.522223	+	0.139929i	0.0119283	+	0.999929i	$0.496203\pi$
$194$	9.07051	+	15.7106i	0.651225	+	1.12795i
$195$	−6.22861	−	10.9376i	−0.446040	−	0.783257i
$196$	1.44826	−	6.84854i	0.103447	−	0.489182i
$197$	−1.76322	−	6.58042i	−0.125624	−	0.468836i	0.874237	−	0.485499i	$-0.161362\pi$
$197$	−1.76322	−	6.58042i	−0.125624	−	0.468836i	−0.999861	+	0.0166638i	$0.994696\pi$
$198$	−0.526915	+	0.796781i	−0.0374462	+	0.0566248i
$199$			20.1607i			1.42916i	0.699555	+	0.714579i	$0.253382\pi$
$199$			20.1607i			1.42916i	−0.699555	+	0.714579i	$0.746618\pi$
$200$	−0.242716	−	0.905827i	−0.0171626	−	0.0640517i
$201$	−8.63727	+	8.12842i	−0.609226	+	0.573335i
$202$	2.92092	+	0.782658i	0.205515	+	0.0550676i
$203$	−12.1317	−	8.80457i	−0.851480	−	0.617960i
$204$	1.58098	−	2.55598i	0.110691	−	0.178955i
$205$			22.9977i			1.60623i
$206$	2.49544	−	9.31312i	0.173866	−	0.648876i
$207$	10.9471	+	21.9343i	0.760878	+	1.52454i
$208$	−3.50443	−	0.847906i	−0.242989	−	0.0587917i
$209$			1.01708i			0.0703529i
$210$	−9.15269	−	1.23889i	−0.631596	−	0.0854917i
$211$	4.69434	−	8.13083i	0.323171	−	0.559749i	−0.657969	−	0.753045i	$-0.728584\pi$
$211$	4.69434	−	8.13083i	0.323171	−	0.559749i	0.981141	+	0.193296i	$0.0619176\pi$
$212$	5.05898	−	8.76242i	0.347452	−	0.601805i
$213$	−10.5543	−	11.2150i	−0.723166	−	0.768436i
$214$	1.41055	+	1.41055i	0.0964231	+	0.0964231i
$215$	−11.0425	+	2.95883i	−0.753092	+	0.201790i
$216$	3.99300	−	3.32504i	0.271689	−	0.226241i
$217$	−24.7743	+	3.93708i	−1.68179	+	0.267267i
$218$	0.848917	−	1.47037i	0.0574959	−	0.0995858i
$219$	−4.19112	+	13.9358i	−0.283209	+	0.941691i
$220$	−0.555786	−	0.320883i	−0.0374711	−	0.0216339i
$221$	−6.08082	−	1.47127i	−0.409040	−	0.0989682i
$222$	8.47779	−	13.7061i	0.568992	−	0.919896i
$223$	−26.1665	+	7.01130i	−1.75224	+	0.469512i	−0.985102	−	0.171969i	$-0.944987\pi$
$223$	−26.1665	+	7.01130i	−1.75224	+	0.469512i	−0.767139	+	0.641481i	$0.778320\pi$
$224$	−2.05527	+	1.66609i	−0.137323	+	0.111321i
$225$	0.170615	−	2.80817i	0.0113743	−	0.187211i
$226$	3.53924	−	13.2086i	0.235426	−	0.878624i
$227$	−3.69556	+	3.69556i	−0.245283	+	0.245283i	−0.819031	−	0.573749i	$-0.805489\pi$
$227$	−3.69556	+	3.69556i	−0.245283	+	0.245283i	0.573749	+	0.819031i	$0.305489\pi$
$228$	1.59337	−	5.29807i	0.105524	−	0.350873i
$229$	−1.74739	−	0.468212i	−0.115471	−	0.0309403i	0.200621	−	0.979669i	$-0.435704\pi$
$229$	−1.74739	−	0.468212i	−0.115471	−	0.0309403i	−0.316092	+	0.948729i	$0.602371\pi$
$230$	−14.2630	+	8.23476i	−0.940476	+	0.542984i
$231$	1.16086	−	0.884063i	0.0763790	−	0.0581671i
$232$	1.46639	+	5.47262i	0.0962729	+	0.359295i
$233$	13.7779	+	23.8640i	0.902620	+	1.56338i	0.824081	+	0.566472i	$0.191692\pi$
$233$	13.7779	+	23.8640i	0.902620	+	1.56338i	0.0785387	+	0.996911i	$0.474975\pi$
$234$	−9.16520	−	5.74448i	−0.599148	−	0.375528i
$235$	2.69630	−	4.67013i	0.175887	−	0.304646i
$236$	0.870720	−	0.870720i	0.0566791	−	0.0566791i
$237$	0.447640	−	14.7491i	0.0290774	−	0.958055i
$238$	−3.56626	+	2.89097i	−0.231166	+	0.187394i
$239$	4.03167	−	4.03167i	0.260787	−	0.260787i	−0.564587	−	0.825374i	$-0.690964\pi$
$239$	4.03167	−	4.03167i	0.260787	−	0.260787i	0.825374	+	0.564587i	$0.190964\pi$
$240$	2.39245	+	2.54222i	0.154432	+	0.164099i
$241$	−8.47353	+	8.47353i	−0.545828	+	0.545828i	−0.925231	−	0.379403i	$-0.876129\pi$
$241$	−8.47353	+	8.47353i	−0.545828	+	0.545828i	0.379403	+	0.925231i	$0.376129\pi$
$242$	−10.5272	+	2.82077i	−0.676717	+	0.181326i
$243$	14.5228	−	5.66453i	0.931641	−	0.363380i
$244$	3.87891	+	2.23949i	0.248322	+	0.143369i
$245$	12.5774	+	6.39202i	0.803540	+	0.408371i
$246$	9.35797	+	17.4076i	0.596642	+	1.10987i
$247$	−11.5134	+	0.281089i	−0.732578	+	0.0178853i
$248$	8.21107	+	4.74066i	0.521403	+	0.301032i
$249$	11.9308	−	2.81187i	0.756081	−	0.178195i
$250$	11.9676			0.756895
$251$	−0.221280	−	0.383269i	−0.0139671	−	0.0241917i	0.858957	−	0.512047i	$-0.171113\pi$
$251$	−0.221280	−	0.383269i	−0.0139671	−	0.0241917i	−0.872924	+	0.487855i	$0.837779\pi$
$252$	−7.43203	+	2.78656i	−0.468174	+	0.175537i
$253$	0.673427	−	2.51326i	0.0423380	−	0.158008i
$254$	7.86924	−	2.10856i	0.493760	−	0.132303i
$255$	4.15132	+	4.41120i	0.259966	+	0.276240i
$256$	1.00000			0.0625000
$257$	−23.5776			−1.47073			−0.735366	−	0.677671i	$-0.762990\pi$
$257$	−23.5776			−1.47073			−0.735366	+	0.677671i	$0.762990\pi$
$258$	−7.15439	+	6.73291i	−0.445413	+	0.419172i
$259$	−19.1236	+	15.5025i	−1.18828	+	0.963277i
$260$	3.47880	−	6.38019i	0.215746	−	0.395682i
$261$	−1.03078	+	16.9657i	−0.0638040	+	1.05015i
$262$	1.00800	−	3.76190i	0.0622743	−	0.232411i
$263$	3.43408	−	1.98267i	0.211754	−	0.122256i	−0.390372	−	0.920657i	$-0.627654\pi$
$263$	3.43408	−	1.98267i	0.211754	−	0.122256i	0.602126	+	0.798401i	$0.294320\pi$
$264$	−0.551259	−	0.0167309i	−0.0339277	−	0.00102972i
$265$	14.4198	+	14.4198i	0.885803	+	0.885803i
$266$	−4.96382	+	6.83960i	−0.304352	+	0.419363i
$267$	4.35011	+	18.4575i	0.266222	+	1.12958i
$268$	−6.61438	−	1.77232i	−0.404038	−	0.108262i
$269$		−	32.7706i		−	1.99806i	−0.0440238	−	0.999030i	$-0.514018\pi$
$269$		−	32.7706i		−	1.99806i	0.0440238	−	0.999030i	$-0.485982\pi$
$270$	4.39031	+	9.50816i	0.267186	+	0.578648i
$271$	5.03012	−	5.03012i	0.305558	−	0.305558i	−0.537626	−	0.843184i	$-0.680679\pi$
$271$	5.03012	−	5.03012i	0.305558	−	0.305558i	0.843184	+	0.537626i	$0.180679\pi$
$272$	1.73518			0.105211
$273$	10.3284	+	12.8966i	0.625106	+	0.780540i
$274$	9.26475			0.559704
$275$	−0.211145	+	0.211145i	−0.0127325	+	0.0127325i
$276$	−7.44527	+	12.0369i	−0.448152	+	0.724534i
$277$		−	15.2521i		−	0.916411i	−0.888846	−	0.458206i	$-0.848492\pi$
$277$		−	15.2521i		−	0.916411i	0.888846	−	0.458206i	$-0.151508\pi$
$278$	12.0733	+	3.23504i	0.724110	+	0.194025i
$279$	18.8562	+	21.2957i	1.12889	+	1.27494i
$280$	−2.17146	−	4.87035i	−0.129769	−	0.291059i
$281$	−16.5961	−	16.5961i	−0.990043	−	0.990043i	0.00990785	−	0.999951i	$-0.496846\pi$
$281$	−16.5961	−	16.5961i	−0.990043	−	0.990043i	−0.999951	+	0.00990785i	$0.996846\pi$
$282$	0.140586	−	4.63210i	0.00837178	−	0.275837i
$283$	20.2573	−	11.6956i	1.20417	−	0.695230i	0.242693	−	0.970103i	$-0.421969\pi$
$283$	20.2573	−	11.6956i	1.20417	−	0.695230i	0.961481	+	0.274873i	$0.0886358\pi$
$284$	2.30125	−	8.58837i	0.136554	−	0.509626i
$285$	9.48321	+	5.86574i	0.561737	+	0.347456i
$286$	0.324119	+	1.10136i	0.0191655	+	0.0651250i
$287$	−4.73815	−	29.8151i	−0.279684	−	1.75993i
$288$	2.84536	+	0.950764i	0.167664	+	0.0560243i
$289$	−13.9892			−0.822891
$290$	−11.4191			−0.670555
$291$	−22.8819	+	21.5339i	−1.34136	+	1.26234i
$292$	−8.11552	+	2.17455i	−0.474925	+	0.127256i
$293$	−1.88395	+	7.03100i	−0.110062	+	0.410755i	−0.998870	−	0.0475233i	$-0.984867\pi$
$293$	−1.88395	+	7.03100i	−0.110062	+	0.410755i	0.888809	+	0.458279i	$0.151534\pi$
$294$	12.1211	−	0.279554i	0.706919	−	0.0163039i
$295$	1.24092	+	2.14934i	0.0722494	+	0.125140i
$296$	9.30468			0.540823
$297$	−1.55262	−	0.571723i	−0.0900922	−	0.0331747i
$298$	−6.06444	−	3.50131i	−0.351304	−	0.202825i
$299$	28.6363	+	6.92862i	1.65608	+	0.400692i
$300$	1.43066	−	0.769095i	0.0825993	−	0.0444037i
$301$	13.7063	−	6.11099i	0.790019	−	0.352232i
$302$	−7.03070	−	4.05917i	−0.404571	−	0.233579i
$303$	−0.158892	+	5.23524i	−0.00912809	+	0.300757i
$304$	3.08534	−	0.826715i	0.176957	−	0.0474154i
$305$	−6.38331	+	6.38331i	−0.365507	+	0.365507i
$306$	4.93720	+	1.64975i	0.282241	+	0.0943097i
$307$	14.4331	−	14.4331i	0.823738	−	0.823738i	−0.162904	−	0.986642i	$-0.552086\pi$
$307$	14.4331	−	14.4331i	0.823738	−	0.823738i	0.986642	+	0.162904i	$0.0520859\pi$
$308$	0.786652	+	0.301498i	0.0448236	+	0.0171794i
$309$	16.6921	+	0.506614i	0.949583	+	0.0288202i
$310$	−13.5125	+	13.5125i	−0.767458	+	0.767458i
$311$	−1.83957	+	3.18622i	−0.104312	+	0.180674i	−0.913457	−	0.406935i	$-0.866597\pi$
$311$	−1.83957	+	3.18622i	−0.104312	+	0.180674i	0.809145	+	0.587609i	$0.199931\pi$
$312$	0.0370439	−	6.24489i	0.00209720	−	0.353547i
$313$	10.8024	+	18.7103i	0.610587	+	1.05757i	0.991142	+	0.132809i	$0.0423997\pi$
$313$	10.8024	+	18.7103i	0.610587	+	1.05757i	−0.380555	+	0.924758i	$0.624267\pi$
$314$	0.204452	+	0.763027i	0.0115379	+	0.0430601i
$315$	−1.54801	−	15.9224i	−0.0872207	−	0.897127i
$316$	7.37793	−	4.25965i	0.415041	−	0.239624i
$317$	29.9394	+	8.02225i	1.68157	+	0.450574i	0.968192	−	0.250209i	$-0.0804992\pi$
$317$	29.9394	+	8.02225i	1.68157	+	0.450574i	0.713375	+	0.700783i	$0.247166\pi$
$318$	16.7823	+	5.04720i	0.941105	+	0.283033i
$319$	1.27565	−	1.27565i	0.0714228	−	0.0714228i
$320$	−0.521648	+	1.94682i	−0.0291610	+	0.108830i
$321$	−1.81754	+	2.93844i	−0.101445	+	0.164008i
$322$	16.7945	−	13.6144i	0.935922	−	0.758702i
$323$	5.35363	−	1.43450i	0.297884	−	0.0798177i
$324$	7.19210	+	5.41052i	0.399561	+	0.300585i
$325$	−2.44852	−	2.33182i	−0.135820	−	0.129346i
$326$	−4.24852	−	2.45288i	−0.235304	−	0.135853i
$327$	2.81613	+	0.846939i	0.155733	+	0.0468359i
$328$	−5.70523	+	9.88175i	−0.315019	+	0.545628i
$329$	−2.53341	+	6.61004i	−0.139672	+	0.364423i
$330$	0.320136	−	1.06447i	0.0176229	−	0.0585974i
$331$	−3.74604	+	1.00375i	−0.205901	+	0.0551709i	−0.360295	−	0.932838i	$-0.617324\pi$
$331$	−3.74604	+	1.00375i	−0.205901	+	0.0551709i	0.154394	+	0.988009i	$0.450657\pi$
$332$	5.00416	+	5.00416i	0.274639	+	0.274639i
$333$	26.4751	+	8.84655i	1.45083	+	0.484788i
$334$	6.98162	−	12.0925i	0.382017	−	0.661673i
$335$	6.90077	−	11.9525i	0.377029	−	0.653034i
$336$	−3.62542	−	2.80291i	−0.197783	−	0.152911i
$337$			11.4662i			0.624601i	0.949983	+	0.312301i	$0.101100\pi$
$337$			11.4662i			0.624601i	−0.949983	+	0.312301i	$0.898900\pi$
$338$	−12.3779	+	3.97341i	−0.673268	+	0.216125i
$339$	23.6741	+	0.718520i	1.28580	+	0.0390246i
$340$	−0.905154	+	3.37808i	−0.0490888	+	0.183202i
$341$		−	3.01901i		−	0.163488i
$342$	9.56491	+	0.581134i	0.517211	+	0.0314241i
$343$	−17.6227	−	5.69558i	−0.951538	−	0.307532i
$344$	−5.47880	−	1.46804i	−0.295397	−	0.0791515i
$345$	−19.5498	−	20.7736i	−1.05252	−	1.11841i
$346$	0.441456	+	1.64754i	0.0237328	+	0.0885721i
$347$		−	11.3853i		−	0.611193i	−0.952161	−	0.305596i	$-0.901144\pi$
$347$		−	11.3853i		−	0.611193i	0.952161	−	0.305596i	$-0.0988558\pi$
$348$	−8.64345	+	4.64655i	−0.463338	+	0.249081i
$349$	−3.55915	−	13.2829i	−0.190517	−	0.711018i	−0.993382	−	0.114858i	$-0.963359\pi$
$349$	−3.55915	−	13.2829i	−0.190517	−	0.711018i	0.802865	−	0.596161i	$-0.203308\pi$
$350$	−2.45039	+	0.389410i	−0.130979	+	0.0208148i
$351$	6.04282	−	17.7337i	0.322542	−	0.946555i
$352$	−0.159208	−	0.275756i	−0.00848582	−	0.0146979i
$353$	4.77588	+	1.27969i	0.254194	+	0.0681111i	0.383666	−	0.923472i	$-0.374661\pi$
$353$	4.77588	+	1.27969i	0.254194	+	0.0681111i	−0.129472	+	0.991583i	$0.541328\pi$
$354$	1.81388	+	1.12195i	0.0964064	+	0.0596311i
$355$	15.5196	+	8.96022i	0.823693	+	0.475559i
$356$	−7.74170	+	7.74170i	−0.410309	+	0.410309i
$357$	−6.29076	−	4.86356i	−0.332942	−	0.257407i
$358$	−17.3997	−	4.66224i	−0.919604	−	0.246407i
$359$	9.13440	−	34.0901i	0.482095	−	1.79920i	−0.110703	−	0.993854i	$-0.535310\pi$
$359$	9.13440	−	34.0901i	0.482095	−	1.79920i	0.592799	−	0.805351i	$-0.298023\pi$
$360$	−3.33524	+	5.04343i	−0.175783	+	0.265812i
$361$	−7.61859	+	4.39860i	−0.400979	+	0.231505i
$362$	−1.12215	−	1.12215i	−0.0589787	−	0.0589787i
$363$	−8.93819	−	16.6267i	−0.469133	−	0.872677i
$364$	−3.19556	+	8.98824i	−0.167493	+	0.471112i
$365$		−	16.9338i		−	0.886355i
$366$	−2.23427	+	7.42912i	−0.116787	+	0.388326i
$367$	−2.94215	−	5.09596i	−0.153579	−	0.266007i	0.778962	−	0.627072i	$-0.215747\pi$
$367$	−2.94215	−	5.09596i	−0.153579	−	0.266007i	−0.932541	+	0.361065i	$0.882413\pi$
$368$	−8.17145			−0.425966
$369$	−25.6286	+	22.6928i	−1.33417	+	1.18134i
$370$	−4.85377	+	18.1145i	−0.252336	+	0.941729i
$371$	−21.6653	−	15.7235i	−1.12480	−	0.816325i
$372$	−4.72962	+	15.7263i	−0.245219	+	0.815372i
$373$	12.6706	−	21.9461i	0.656058	−	1.13633i	−0.325570	−	0.945518i	$-0.605556\pi$
$373$	12.6706	−	21.9461i	0.656058	−	1.13633i	0.981627	−	0.190807i	$-0.0611106\pi$
$374$	−0.276255	−	0.478487i	−0.0142848	−	0.0247420i
$375$	4.75504	+	20.1757i	0.245549	+	1.04187i
$376$	2.31711	−	1.33779i	0.119496	−	0.0689911i
$377$	14.7929	+	14.0878i	0.761876	+	0.725561i
$378$	−7.65070	−	11.4222i	−0.393510	−	0.587495i
$379$	−15.5730	+	4.17276i	−0.799930	+	0.214341i	−0.635553	−	0.772057i	$-0.719228\pi$
$379$	−15.5730	+	4.17276i	−0.799930	+	0.214341i	−0.164377	+	0.986398i	$0.552561\pi$
$380$			6.43786i			0.330255i
$381$	6.68140	+	12.4287i	0.342298	+	0.636740i
$382$	−5.63561	+	1.51006i	−0.288343	+	0.0772613i
$383$	0.851532	+	3.17796i	0.0435112	+	0.162386i	0.984263	−	0.176710i	$-0.0565455\pi$
$383$	0.851532	+	3.17796i	0.0435112	+	0.162386i	−0.940752	+	0.339096i	$0.889879\pi$
$384$	0.397328	+	1.68586i	0.0202760	+	0.0860313i
$385$	−0.997317	+	1.37419i	−0.0508280	+	0.0700353i
$386$	−6.50461	+	3.75544i	−0.331076	+	0.191147i
$387$	−14.1934	−	9.38615i	−0.721490	−	0.477125i
$388$	−17.5229	−	4.69524i	−0.889589	−	0.238365i
$389$	6.54932	−	11.3437i	0.332064	−	0.575151i	−0.650853	−	0.759204i	$-0.725588\pi$
$389$	6.54932	−	11.3437i	0.332064	−	0.575151i	0.982916	+	0.184053i	$0.0589218\pi$
$390$	12.1383	+	3.32975i	0.614649	+	0.168609i
$391$	−14.1789			−0.717060
$392$	3.81858	+	5.86672i	0.192867	+	0.296314i
$393$	6.74254	+	0.204639i	0.340116	+	0.0103227i
$394$	5.89984	+	3.40628i	0.297230	+	0.171606i
$395$	4.44408	+	16.5855i	0.223606	+	0.834508i
$396$	−0.190824	−	0.935995i	−0.00958928	−	0.0470355i
$397$	−2.29439	−	8.56279i	−0.115152	−	0.429754i	0.884146	−	0.467211i	$-0.154741\pi$
$397$	−2.29439	−	8.56279i	−0.115152	−	0.429754i	−0.999298	+	0.0374568i	$0.988074\pi$
$398$	−14.2558	−	14.2558i	−0.714579	−	0.714579i
$399$	−13.5029	−	5.65076i	−0.675990	−	0.282892i
$400$	0.812142	+	0.468891i	0.0406071	+	0.0234445i
$401$	−14.2366	−	14.2366i	−0.710941	−	0.710941i	0.255791	−	0.966732i	$-0.417664\pi$
$401$	−14.2366	−	14.2366i	−0.710941	−	0.710941i	−0.966732	+	0.255791i	$0.917664\pi$
$402$	0.359808	−	11.8551i	0.0179456	−	0.591280i
$403$	34.1752	−	0.834359i	1.70239	−	0.0415624i
$404$	−2.61883	+	1.51198i	−0.130291	+	0.0752238i
$405$	−14.2850	+	11.1793i	−0.709830	+	0.555505i
$406$	14.8042	−	2.35265i	0.734720	−	0.116760i
$407$	−1.48138	−	2.56583i	−0.0734293	−	0.127183i
$408$	0.689435	+	2.92527i	0.0341321	+	0.144823i
$409$	−2.21509	−	2.21509i	−0.109529	−	0.109529i	0.650218	−	0.759747i	$-0.274677\pi$
$409$	−2.21509	−	2.21509i	−0.109529	−	0.109529i	−0.759747	+	0.650218i	$0.774677\pi$
$410$	−16.2618	−	16.2618i	−0.803115	−	0.803115i
$411$	3.68114	+	15.6191i	0.181577	+	0.770433i
$412$	4.82082	+	8.34991i	0.237505	+	0.411371i
$413$	−2.05160	−	2.53083i	−0.100953	−	0.124534i
$414$	−23.2507	−	7.76912i	−1.14271	−	0.381831i
$415$	−12.3526	+	7.13177i	−0.606365	+	0.350085i
$416$	3.07757	−	1.87845i	0.150890	−	0.0920985i
$417$	−0.656763	+	21.6393i	−0.0321618	+	1.05968i
$418$	−0.719184	−	0.719184i	−0.0351764	−	0.0351764i
$419$	19.8536	+	11.4625i	0.969914	+	0.559980i	0.899210	−	0.437517i	$-0.144142\pi$
$419$	19.8536	+	11.4625i	0.969914	+	0.559980i	0.0707039	+	0.997497i	$0.477475\pi$
$420$	7.34796	−	5.59590i	0.358544	−	0.273052i
$421$	−4.64444	−	4.64444i	−0.226356	−	0.226356i	0.584812	−	0.811169i	$-0.301168\pi$
$421$	−4.64444	−	4.64444i	−0.226356	−	0.226356i	−0.811169	+	0.584812i	$0.801168\pi$
$422$	2.42997	+	9.06876i	0.118289	+	0.441460i
$423$	7.86493	−	1.60345i	0.382406	−	0.0779624i
$424$	2.61872	+	9.77321i	0.127176	+	0.474629i
$425$	1.40921	+	0.813609i	0.0683569	+	0.0394659i
$426$	15.3932	+	0.467189i	0.745801	+	0.0226354i
$427$	6.96042	−	9.59069i	0.336838	−	0.464126i
$428$	−1.99482			−0.0964231
$429$	−1.72797	+	0.984022i	−0.0834270	+	0.0475090i
$430$	5.71602	−	9.90044i	0.275651	−	0.477441i
$431$	−22.0913	−	5.91933i	−1.06410	−	0.285124i	−0.316032	−	0.948748i	$-0.602351\pi$
$431$	−22.0913	−	5.91933i	−1.06410	−	0.285124i	−0.748066	+	0.663624i	$0.769017\pi$
$432$	−0.472318	+	5.17464i	−0.0227244	+	0.248965i
$433$	19.5686	−	11.2980i	0.940408	−	0.542945i	0.0503199	−	0.998733i	$-0.483976\pi$
$433$	19.5686	−	11.2980i	0.940408	−	0.542945i	0.890088	+	0.455788i	$0.150643\pi$
$434$	14.7342	−	20.3020i	0.707262	−	0.974529i
$435$	−4.53714	−	19.2511i	−0.217539	−	0.923020i
$436$	0.439432	+	1.63998i	0.0210450	+	0.0785409i
$437$	−25.2117	+	6.75546i	−1.20604	+	0.323158i
$438$	−6.89050	−	12.8176i	−0.329241	−	0.612450i
$439$		−	13.5362i		−	0.646046i	−0.946391	−	0.323023i	$-0.895301\pi$
$439$		−	13.5362i		−	0.646046i	0.946391	−	0.323023i	$-0.104699\pi$
$440$	0.619898	−	0.166101i	0.0295525	−	0.00791857i
$441$	5.28735	+	20.3235i	0.251779	+	0.967785i
$442$	5.34013	−	3.25945i	0.254004	−	0.155036i
$443$	9.12553	−	5.26863i	0.433567	−	0.250320i	−0.267298	−	0.963614i	$-0.586131\pi$
$443$	9.12553	−	5.26863i	0.433567	−	0.250320i	0.700865	+	0.713294i	$0.252797\pi$
$444$	3.69700	+	15.6864i	0.175452	+	0.744444i
$445$	−11.0332	−	19.1101i	−0.523025	−	0.905907i
$446$	13.5448	−	23.4603i	0.641365	−	1.11088i
$447$	3.49315	−	11.6150i	0.165220	−	0.549370i
$448$	0.275187	−	2.63140i	0.0130014	−	0.124322i
$449$	−4.82222	+	17.9968i	−0.227575	+	0.849321i	0.753782	+	0.657125i	$0.228228\pi$
$449$	−4.82222	+	17.9968i	−0.227575	+	0.849321i	−0.981357	+	0.192196i	$0.938439\pi$
$450$	1.86503	+	2.10632i	0.0879183	+	0.0992927i
$451$	3.63328			0.171084
$452$	6.83728	+	11.8425i	0.321599	+	0.557025i
$453$	4.04972	−	13.4656i	0.190272	−	0.632669i
$454$		−	5.22631i		−	0.245283i
$455$	−15.8315	−	10.9099i	−0.742193	−	0.511462i
$456$	2.61962	+	4.87299i	0.122675	+	0.228199i
$457$	−15.4102	−	15.4102i	−0.720860	−	0.720860i	0.247921	−	0.968780i	$-0.420253\pi$
$457$	−15.4102	−	15.4102i	−0.720860	−	0.720860i	−0.968780	+	0.247921i	$0.920253\pi$
$458$	1.56667	−	0.904516i	0.0732056	−	0.0422653i
$459$	−0.819557	+	8.97893i	−0.0382536	+	0.419101i
$460$	4.26262	−	15.9083i	0.198746	−	0.741730i
$461$	15.6286	+	4.18767i	0.727897	+	0.195039i	0.603693	−	0.797217i	$-0.293695\pi$
$461$	15.6286	+	4.18767i	0.727897	+	0.195039i	0.124205	+	0.992257i	$0.460362\pi$
$462$	−0.195725	+	1.44598i	−0.00910597	+	0.0672731i
$463$	−17.0921	+	17.0921i	−0.794339	+	0.794339i	−0.982196	−	0.187857i	$-0.939846\pi$
$463$	−17.0921	+	17.0921i	−0.794339	+	0.794339i	0.187857	+	0.982196i	$0.439846\pi$
$464$	−4.90662	−	2.83284i	−0.227784	−	0.131511i
$465$	−28.1491	−	17.4113i	−1.30538	−	0.807431i
$466$	−26.6168	−	7.13196i	−1.23300	−	0.330382i
$467$	4.41723	+	7.65086i	0.204405	+	0.354040i	0.949943	−	0.312423i	$-0.101141\pi$
$467$	4.41723	+	7.65086i	0.204405	+	0.354040i	−0.745538	+	0.666463i	$0.767807\pi$
$468$	10.5427	−	2.41882i	0.487338	−	0.111810i
$469$	−6.48388	+	16.9174i	−0.299398	+	0.781172i
$470$	1.39571	+	5.20885i	0.0643792	+	0.240267i
$471$	−1.20512	+	0.647850i	−0.0555292	+	0.0298514i
$472$			1.23138i			0.0566791i
$473$	0.467448	+	1.74454i	0.0214933	+	0.0802140i
$474$	10.1126	+	10.7457i	0.464489	+	0.493566i
$475$	2.89338	+	0.775278i	0.132757	+	0.0355722i
$476$	0.477499	−	4.56595i	0.0218861	−	0.209280i
$477$	−1.84081	+	30.2980i	−0.0842850	+	1.38725i
$478$			5.70164i			0.260787i
$479$	−1.73886	+	6.48952i	−0.0794507	+	0.296514i	−0.994206	−	0.107495i	$-0.965717\pi$
$479$	−1.73886	+	6.48952i	−0.0794507	+	0.296514i	0.914755	+	0.404009i	$0.132384\pi$
$480$	−3.48933	−	0.105903i	−0.159266	−	0.00483378i
$481$	28.6358	−	17.4784i	1.30568	−	0.796945i
$482$		−	11.9834i		−	0.545828i
$483$	29.6250	+	22.9039i	1.34798	+	1.04216i
$484$	5.44931	−	9.43847i	0.247696	−	0.429022i
$485$	18.2816	−	31.6646i	0.830123	−	1.43782i
$486$	−6.26377	+	14.2746i	−0.284131	+	0.647510i
$487$	−4.12826	−	4.12826i	−0.187069	−	0.187069i	0.607359	−	0.794428i	$-0.292229\pi$
$487$	−4.12826	−	4.12826i	−0.187069	−	0.187069i	−0.794428	+	0.607359i	$0.792229\pi$
$488$	−4.32636	+	1.15925i	−0.195845	+	0.0524766i
$489$	2.44717	−	8.13702i	0.110665	−	0.367969i
$490$	−13.4134	+	4.37371i	−0.605956	+	0.197584i
$491$	−17.0153	+	29.4714i	−0.767891	+	1.33003i	0.170813	+	0.985303i	$0.445360\pi$
$491$	−17.0153	+	29.4714i	−0.767891	+	1.33003i	−0.938704	+	0.344723i	$0.887973\pi$
$492$	−18.9261	−	5.69194i	−0.853255	−	0.256613i
$493$	−8.51387	−	4.91548i	−0.383445	−	0.221382i
$494$	7.94241	−	8.33993i	0.357346	−	0.375231i
$495$	1.92175	+	0.116760i	0.0863764	+	0.00524796i
$496$	−9.15825	+	2.45395i	−0.411218	+	0.110185i
$497$	−21.9662	−	8.41892i	−0.985318	−	0.377640i
$498$	−6.44803	+	10.4246i	−0.288943	+	0.467138i
$499$	4.68152	−	17.4717i	0.209574	−	0.782140i	−0.778433	−	0.627728i	$-0.783985\pi$
$499$	4.68152	−	17.4717i	0.209574	−	0.782140i	0.988007	−	0.154412i	$-0.0493483\pi$
$500$	−8.46235	+	8.46235i	−0.378448	+	0.378448i
$501$	23.1603	+	6.96536i	1.03473	+	0.311189i
$502$	0.427481	+	0.114543i	0.0190794	+	0.00511231i
$503$	−16.3897	+	9.46263i	−0.730783	+	0.421918i	−0.818708	−	0.574209i	$-0.805310\pi$
$503$	−16.3897	+	9.46263i	−0.730783	+	0.421918i	0.0879257	+	0.996127i	$0.471976\pi$
$504$	3.28485	−	7.22563i	0.146319	−	0.321855i
$505$	−1.57744	−	5.88710i	−0.0701953	−	0.261972i
$506$	1.30096	+	2.25333i	0.0578348	+	0.100173i
$507$	−11.6167	−	19.2887i	−0.515916	−	0.856639i
$508$	−4.07342	+	7.05537i	−0.180729	+	0.313031i
$509$	−10.1520	+	10.1520i	−0.449980	+	0.449980i	−0.895348	−	0.445368i	$-0.853073\pi$
$509$	−10.1520	+	10.1520i	−0.449980	+	0.449980i	0.445368	+	0.895348i	$0.353073\pi$
$510$	−6.05462	−	0.183760i	−0.268103	−	0.00813704i
$511$	3.48882	+	21.9536i	0.154336	+	0.971170i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.82069	+	16.3560i	0.124537	+	0.722136i
$514$	16.6719	−	16.6719i	0.735366	−	0.735366i
$515$	−18.7705	+	5.02955i	−0.827129	+	0.221628i
$516$	0.298035	−	9.81980i	0.0131203	−	0.432293i
$517$	−0.737807	−	0.425973i	−0.0324487	−	0.0187343i
$518$	2.56053	−	24.4843i	0.112503	−	1.07578i
$519$	−2.60212	+	1.39885i	−0.114220	+	0.0614025i
$520$	2.05159	+	6.97136i	0.0899682	+	0.305714i
$521$	−20.3889	−	11.7715i	−0.893253	−	0.515720i	−0.0182476	−	0.999833i	$-0.505809\pi$
$521$	−20.3889	−	11.7715i	−0.893253	−	0.515720i	−0.875005	+	0.484114i	$0.839142\pi$
$522$	−11.2677	−	12.7255i	−0.493175	−	0.556979i
$523$	−16.3944			−0.716875			−0.358438	−	0.933554i	$-0.616690\pi$
$523$	−16.3944			−0.716875			−0.358438	+	0.933554i	$0.616690\pi$
$524$	1.94730	+	3.37282i	0.0850682	+	0.147343i
$525$	−1.63010	−	3.97629i	−0.0711433	−	0.173540i
$526$	−1.02630	+	3.83022i	−0.0447490	+	0.167005i
$527$	−15.8912	+	4.25804i	−0.692232	+	0.185483i
$528$	0.401630	−	0.377969i	0.0174787	−	0.0164490i
$529$	43.7726			1.90316
$530$	−20.3927			−0.885803
$531$	−1.17076	+	3.50373i	−0.0508065	+	0.152049i
$532$	−1.32637	−	8.34628i	−0.0575055	−	0.361857i
$533$	1.00412	+	41.1287i	0.0434934	+	1.78148i
$534$	−16.1274	−	9.97544i	−0.697902	−	0.431680i
$535$	1.04059	−	3.88354i	0.0449887	−	0.167900i
$536$	5.93029	−	3.42386i	0.256150	−	0.147888i
$537$	0.946507	−	31.1860i	0.0408448	−	1.34577i
$538$	23.1723	+	23.1723i	0.999030	+	0.999030i
$539$	1.00984	−	1.98703i	0.0434968	−	0.0855874i
$540$	−9.82770	−	3.61886i	−0.422917	−	0.155731i
$541$	0.258251	+	0.0691982i	0.0111031	+	0.00297506i	0.264366	−	0.964422i	$-0.414837\pi$
$541$	0.258251	+	0.0691982i	0.0111031	+	0.00297506i	−0.253263	+	0.967397i	$0.581504\pi$
$542$			7.11366i			0.305558i
$543$	1.44592	−	2.33764i	0.0620506	−	0.100318i
$544$	−1.22696	+	1.22696i	−0.0526054	+	0.0526054i
$545$	−3.42197			−0.146581
$546$	−16.4226	−	1.81599i	−0.702823	−	0.0777173i
$547$	20.0364			0.856695			0.428348	−	0.903614i	$-0.359096\pi$
$547$	20.0364			0.856695			0.428348	+	0.903614i	$0.359096\pi$
$548$	−6.55117	+	6.55117i	−0.279852	+	0.279852i
$549$	−13.4122	−	0.814883i	−0.572419	−	0.0347784i
$550$		−	0.298605i		−	0.0127325i
$551$	−17.4806	−	4.68390i	−0.744697	−	0.199541i
$552$	−3.24674	−	13.7759i	−0.138191	−	0.586343i
$553$	−9.17853	−	20.5865i	−0.390311	−	0.875427i
$554$	10.7849	+	10.7849i	0.458206	+	0.458206i
$555$	−32.4671	−	0.985391i	−1.37815	−	0.0418275i
$556$	−10.8246	+	6.24961i	−0.459067	+	0.265043i
$557$	−10.6843	+	39.8743i	−0.452708	+	1.68953i	0.242034	+	0.970268i	$0.422186\pi$
$557$	−10.6843	+	39.8743i	−0.452708	+	1.68953i	−0.694741	+	0.719260i	$0.744481\pi$
$558$	−28.3916	−	1.72498i	−1.20191	−	0.0730244i
$559$	−19.6190	+	5.77366i	−0.829797	+	0.244200i
$560$	4.97931	+	1.90841i	0.210414	+	0.0806449i
$561$	0.696900	−	0.655843i	0.0294231	−	0.0276897i
$562$	23.4705			0.990043
$563$	28.4329			1.19831			0.599153	−	0.800635i	$-0.295504\pi$
$563$	28.4329			1.19831			0.599153	+	0.800635i	$0.295504\pi$
$564$	3.17598	+	3.37480i	0.133733	+	0.142105i
$565$	−26.6219	+	7.13331i	−1.11999	+	0.300101i
$566$	−6.05408	+	22.5941i	−0.254472	+	0.949702i
$567$	16.2164	−	17.4364i	0.681026	−	0.732259i
$568$	4.44567	+	7.70012i	0.186536	+	0.323090i
$569$	2.67609			0.112187			0.0560937	−	0.998426i	$-0.482135\pi$
$569$	2.67609			0.112187			0.0560937	+	0.998426i	$0.482135\pi$
$570$	−10.8533	+	2.55794i	−0.454596	+	0.107140i
$571$	12.5618	+	7.25258i	0.525696	+	0.303511i	0.739262	−	0.673418i	$-0.235174\pi$
$571$	12.5618	+	7.25258i	0.525696	+	0.303511i	−0.213566	+	0.976929i	$0.568508\pi$
$572$	−1.00797	−	0.549595i	−0.0421453	−	0.0229797i
$573$	−4.78493	−	8.90088i	−0.199894	−	0.371840i
$574$	24.4328	+	17.7321i	1.01981	+	0.740123i
$575$	−6.63638	−	3.83152i	−0.276756	−	0.159785i
$576$	−2.68426	+	1.33968i	−0.111844	+	0.0558199i
$577$	7.06609	−	1.89335i	0.294165	−	0.0788213i	−0.108718	−	0.994073i	$-0.534675\pi$
$577$	7.06609	−	1.89335i	0.294165	−	0.0788213i	0.402883	+	0.915251i	$0.368008\pi$
$578$	9.89182	−	9.89182i	0.411446	−	0.411446i
$579$	−8.91562	−	9.47374i	−0.370520	−	0.393715i
$580$	8.07455	−	8.07455i	0.335278	−	0.335278i
$581$	14.5450	−	11.7909i	0.603429	−	0.489168i
$582$	0.953207	−	31.4067i	0.0395117	−	1.30185i
$583$	2.27810	−	2.27810i	0.0943494	−	0.0943494i
$584$	4.20090	−	7.27617i	0.173835	−	0.301090i
$585$	−0.790609	+	21.7866i	−0.0326877	+	0.900764i
$586$	−3.63951	−	6.30382i	−0.150347	−	0.260409i
$587$	0.226259	+	0.844409i	0.00933869	+	0.0348525i	0.970438	−	0.241351i	$-0.0775904\pi$
$587$	0.226259	+	0.844409i	0.00933869	+	0.0348525i	−0.961099	+	0.276203i	$0.910924\pi$
$588$	−8.37326	+	8.76861i	−0.345307	+	0.361611i
$589$	−26.2276	+	15.1425i	−1.08069	+	0.623937i
$590$	−2.39728	−	0.642350i	−0.0986945	−	0.0264451i
$591$	−3.39834	+	11.2997i	−0.139789	+	0.464809i
$592$	−6.57940	+	6.57940i	−0.270412	+	0.270412i
$593$	5.06518	−	18.9035i	0.208002	−	0.776274i	−0.780512	−	0.625141i	$-0.785041\pi$
$593$	5.06518	−	18.9035i	0.208002	−	0.776274i	0.988514	−	0.151132i	$-0.0482920\pi$
$594$	1.50214	−	0.693600i	0.0616335	−	0.0284587i
$595$	8.63999	+	3.31143i	0.354205	+	0.135755i
$596$	6.76401	−	1.81241i	0.277064	−	0.0742392i
$597$	18.3691	−	29.6975i	0.751797	−	1.21544i
$598$	−25.1482	+	15.3497i	−1.02839	+	0.627694i
$599$	−9.45870	−	5.46098i	−0.386472	−	0.223130i	0.294158	−	0.955757i	$-0.404961\pi$
$599$	−9.45870	−	5.46098i	−0.386472	−	0.223130i	−0.680630	+	0.732627i	$0.738294\pi$
$600$	−0.467798	+	1.55546i	−0.0190978	+	0.0635015i
$601$	−11.6415	+	20.1636i	−0.474865	+	0.822490i	−0.999586	−	0.0287844i	$-0.990836\pi$
$601$	−11.6415	+	20.1636i	−0.474865	+	0.822490i	0.524721	+	0.851274i	$0.324170\pi$
$602$	−5.37070	+	14.0129i	−0.218894	+	0.571125i
$603$	20.1291	−	4.10378i	0.819719	−	0.167119i
$604$	7.84172	−	2.10118i	0.319075	−	0.0854959i
$605$	15.5324	+	15.5324i	0.631481	+	0.631481i
$606$	−3.58952	−	3.81423i	−0.145814	−	0.154942i
$607$	3.74159	−	6.48062i	0.151866	−	0.263040i	−0.780047	−	0.625721i	$-0.784805\pi$
$607$	3.74159	−	6.48062i	0.151866	−	0.263040i	0.931914	+	0.362680i	$0.118138\pi$
$608$	−1.59709	+	2.76624i	−0.0647706	+	0.112186i
$609$	9.84836	+	24.0231i	0.399076	+	0.973464i
$610$		−	9.02736i		−	0.365507i
$611$	4.61811	−	8.46971i	0.186829	−	0.342648i
$612$	−4.65768	+	2.32458i	−0.188275	+	0.0939657i
$613$	10.5787	−	39.4804i	0.427272	−	1.59460i	−0.331640	−	0.943406i	$-0.607602\pi$
$613$	10.5787	−	39.4804i	0.427272	−	1.59460i	0.758912	−	0.651194i	$-0.225731\pi$
$614$			20.4114i			0.823738i
$615$	20.9540	−	33.8765i	0.844945	−	1.36603i
$616$	−0.769438	+	0.343056i	−0.0310015	+	0.0138221i
$617$	−44.0674	−	11.8078i	−1.77409	−	0.475365i	−0.784602	−	0.620000i	$-0.787133\pi$
$617$	−44.0674	−	11.8078i	−1.77409	−	0.475365i	−0.989485	+	0.144635i	$0.953799\pi$
$618$	−12.1614	+	11.4449i	−0.489201	+	0.460381i
$619$	−10.4246	−	38.9050i	−0.418999	−	1.56372i	−0.776689	−	0.629884i	$-0.783102\pi$
$619$	−10.4246	−	38.9050i	−0.418999	−	1.56372i	0.357690	−	0.933840i	$-0.383564\pi$
$620$		−	19.1096i		−	0.767458i
$621$	3.85953	−	42.2843i	0.154877	−	1.69681i
$622$	−0.952230	−	3.55377i	−0.0381809	−	0.142493i
$623$	18.2411	+	22.5019i	0.730814	+	0.901521i
$624$	4.38961	+	4.44200i	0.175725	+	0.177822i
$625$	−9.71583	−	16.8283i	−0.388633	−	0.673132i
$626$	−20.8686	−	5.59173i	−0.834077	−	0.223490i
$627$	0.926693	−	1.49820i	0.0370086	−	0.0598322i
$628$	−0.684111	−	0.394972i	−0.0272990	−	0.0157611i
$629$	−11.4164	+	11.4164i	−0.455203	+	0.455203i
$630$	12.3535	+	10.1642i	0.492174	+	0.404953i
$631$	28.5404	+	7.64739i	1.13618	+	0.304438i	0.777413	−	0.628991i	$-0.216532\pi$
$631$	28.5404	+	7.64739i	1.13618	+	0.304438i	0.358764	+	0.933428i	$0.383198\pi$
$632$	−2.20496	+	8.22901i	−0.0877085	+	0.327332i
$633$	−14.3232	+	7.69986i	−0.569295	+	0.306042i
$634$	−26.8430	+	15.4978i	−1.06607	+	0.615496i
$635$	−11.6106	−	11.6106i	−0.460754	−	0.460754i
$636$	−15.4358	+	8.29797i	−0.612069	+	0.329036i
$637$	22.7723	+	10.8822i	0.902271	+	0.431170i
$638$			1.80404i			0.0714228i
$639$	5.32851	+	26.1364i	0.210793	+	1.03394i
$640$	−1.00775	−	1.74547i	−0.0398347	−	0.0689957i
$641$	−11.5450			−0.456000			−0.228000	−	0.973661i	$-0.573219\pi$
$641$	−11.5450			−0.456000			−0.228000	+	0.973661i	$0.573219\pi$
$642$	−0.792595	−	3.36298i	−0.0312812	−	0.132726i
$643$	−4.78185	+	17.8461i	−0.188578	+	0.703782i	0.805258	+	0.592924i	$0.202027\pi$
$643$	−4.78185	+	17.8461i	−0.188578	+	0.703782i	−0.993836	+	0.110858i	$0.964640\pi$
$644$	−2.24868	+	21.5024i	−0.0886104	+	0.847312i
$645$	18.9619	+	5.70270i	0.746624	+	0.224544i
$646$	−2.77124	+	4.79993i	−0.109033	+	0.188851i
$647$	16.7693	+	29.0453i	0.659269	+	1.14189i	0.980805	+	0.194990i	$0.0624675\pi$
$647$	16.7693	+	29.0453i	0.659269	+	1.14189i	−0.321536	+	0.946897i	$0.604199\pi$
$648$	−8.91140	+	1.25976i	−0.350073	+	0.0494882i
$649$	0.339562	−	0.196046i	0.0133290	−	0.00769549i
$650$	3.38021	−	0.0825250i	0.132583	−	0.00323690i
$651$	40.0807	+	16.7732i	1.57089	+	0.657394i
$652$	4.73861	−	1.26971i	0.185578	−	0.0497255i
$653$			2.66969i			0.104473i	0.998635	+	0.0522365i	$0.0166350\pi$
$653$			2.66969i			0.104473i	−0.998635	+	0.0522365i	$0.983365\pi$
$654$	−2.59018	+	1.39243i	−0.101284	+	0.0544484i
$655$	−7.58208	+	2.03161i	−0.296256	+	0.0793817i
$656$	−2.95324	−	11.0217i	−0.115305	−	0.430323i
$657$	18.8710	−	16.7092i	0.736227	−	0.651890i
$658$	−2.88261	−	6.46540i	−0.112376	−	0.252047i
$659$	9.41494	−	5.43572i	0.366754	−	0.211746i	−0.305285	−	0.952261i	$-0.598752\pi$
$659$	9.41494	−	5.43572i	0.366754	−	0.211746i	0.672039	+	0.740515i	$0.265419\pi$
$660$	0.526327	+	0.979067i	0.0204872	+	0.0381101i
$661$	−17.2437	−	4.62045i	−0.670704	−	0.179715i	−0.0926320	−	0.995700i	$-0.529528\pi$
$661$	−17.2437	−	4.62045i	−0.670704	−	0.179715i	−0.578072	+	0.815986i	$0.696195\pi$
$662$	1.93909	−	3.35860i	0.0753649	−	0.130536i
$663$	7.61676	+	7.70766i	0.295810	+	0.299341i
$664$	−7.07695			−0.274639
$665$	16.9406	+	1.77162i	0.656928	+	0.0687004i
$666$	−24.9762	+	12.4653i	−0.967808	+	0.483020i
$667$	40.0942	+	23.1484i	1.55245	+	0.896310i
$668$	3.61395	+	13.4875i	0.139828	+	0.521845i
$669$	44.9325	+	13.5132i	1.73719	+	0.522452i
$670$	3.57210	+	13.3313i	0.138002	+	0.515031i
$671$	1.00846	+	1.00846i	0.0389312	+	0.0389312i
$672$	4.54552	−	0.581600i	0.175347	−	0.0224357i
$673$	−34.4898	−	19.9127i	−1.32948	−	0.767577i	−0.344263	−	0.938873i	$-0.611871\pi$
$673$	−34.4898	−	19.9127i	−1.32948	−	0.767577i	−0.985220	+	0.171296i	$0.945205\pi$
$674$	−8.10780	−	8.10780i	−0.312301	−	0.312301i
$675$	−2.80993	+	3.98108i	−0.108154	+	0.153232i
$676$	5.94286	−	11.5621i	0.228571	−	0.444697i
$677$	6.28708	−	3.62985i	0.241632	−	0.139506i	−0.374295	−	0.927310i	$-0.622115\pi$
$677$	6.28708	−	3.62985i	0.241632	−	0.139506i	0.615927	+	0.787804i	$0.288782\pi$
$678$	−17.2482	+	16.2321i	−0.662413	+	0.623389i
$679$	−17.1771	+	44.8176i	−0.659198	+	1.71994i
$680$	−1.74862	−	3.02870i	−0.0670566	−	0.116145i
$681$	8.81083	−	2.07656i	0.337632	−	0.0795738i
$682$	2.13476	+	2.13476i	0.0817442	+	0.0817442i
$683$	−27.5520	−	27.5520i	−1.05425	−	1.05425i	−0.998442	−	0.0558055i	$-0.982227\pi$
$683$	−27.5520	−	27.5520i	−1.05425	−	1.05425i	−0.0558055	−	0.998442i	$-0.517773\pi$
$684$	−7.17434	+	6.35249i	−0.274318	+	0.242894i
$685$	−9.33653	−	16.1713i	−0.356730	−	0.617875i
$686$	16.4885	−	8.43377i	0.629535	−	0.322003i
$687$	2.14737	+	2.28180i	0.0819273	+	0.0870560i
$688$	4.91216	−	2.83604i	0.187274	−	0.108123i
$689$	26.4178	+	25.1586i	1.00644	+	0.958465i
$690$	28.5129	+	0.865379i	1.08547	+	0.0329444i
$691$	14.8468	+	14.8468i	0.564797	+	0.564797i	0.930666	−	0.365869i	$-0.119228\pi$
$691$	14.8468	+	14.8468i	0.564797	+	0.564797i	−0.365869	+	0.930666i	$0.619228\pi$
$692$	−1.47714	−	0.852828i	−0.0561525	−	0.0324197i
$693$	−2.51549	+	0.244562i	−0.0955555	+	0.00929013i
$694$	8.05059	+	8.05059i	0.305596	+	0.305596i
$695$	−6.52020	−	24.3337i	−0.247325	−	0.923031i
$696$	2.82624	−	9.39745i	0.107128	−	0.356209i
$697$	−5.12441	−	19.1246i	−0.194101	−	0.724394i
$698$	11.9091	+	6.87574i	0.450768	+	0.260251i
$699$	1.44790	−	47.7060i	0.0547646	−	1.80441i
$700$	1.45733	−	2.00804i	0.0550819	−	0.0758968i
$701$	44.5628			1.68311			0.841557	−	0.540169i	$-0.181640\pi$
$701$	44.5628			1.68311			0.841557	+	0.540169i	$0.181640\pi$
$702$	8.26671	+	16.8125i	0.312007	+	0.634548i
$703$	−14.8604	+	25.7390i	−0.560471	+	0.970765i
$704$	0.307566	+	0.0824122i	0.0115918	+	0.00310603i
$705$	−8.22686	+	4.42259i	−0.309841	+	0.166564i
$706$	−4.28193	+	2.47218i	−0.161153	+	0.0930415i
$707$	3.25796	+	7.30726i	0.122528	+	0.274818i
$708$	−2.07594	+	0.489263i	−0.0780188	+	0.0183876i
$709$	−5.82399	−	21.7354i	−0.218725	−	0.816291i	−0.984822	−	0.173567i	$-0.944471\pi$
$709$	−5.82399	−	21.7354i	−0.218725	−	0.816291i	0.766097	−	0.642724i	$-0.222196\pi$
$710$	−17.3098	+	4.63815i	−0.649626	+	0.174067i
$711$	−14.0977	+	21.3181i	−0.528706	+	0.799490i
$712$		−	10.9484i		−	0.410309i
$713$	74.8362	−	20.0523i	2.80264	−	0.750965i
$714$	7.88729	−	1.00918i	0.295174	−	0.0377676i
$715$	1.59577	−	1.67564i	0.0596783	−	0.0626652i
$716$	15.6002	−	9.00676i	0.583005	−	0.336598i
$717$	−9.61218	+	2.26542i	−0.358974	+	0.0846036i
$718$	17.6463	+	30.5643i	0.658554	+	1.14065i
$719$	−18.4516	+	31.9591i	−0.688129	+	1.19187i	0.284314	+	0.958731i	$0.408234\pi$
$719$	−18.4516	+	31.9591i	−0.688129	+	1.19187i	−0.972442	+	0.233143i	$0.925099\pi$
$720$	−1.20787	−	5.92461i	−0.0450147	−	0.220797i
$721$	23.2986	−	10.3877i	0.867685	−	0.386859i
$722$	2.27688	−	8.49744i	0.0847368	−	0.316242i
$723$	20.2023	−	4.76133i	0.751333	−	0.177076i
$724$	1.58696			0.0589787
$725$	−2.65658	−	4.60134i	−0.0986630	−	0.170889i
$726$	18.0771	+	5.43661i	0.670905	+	0.201772i
$727$		−	0.374079i		−	0.0138738i	−0.999976	−	0.00693690i	$-0.997792\pi$
$727$		−	0.374079i		−	0.0138738i	0.999976	−	0.00693690i	$-0.00220810\pi$
$728$	−4.09605	−	8.61524i	−0.151810	−	0.319302i
$729$	−26.5538	−	4.88816i	−0.983475	−	0.181043i
$730$	11.9740	+	11.9740i	0.443178	+	0.443178i
$731$	8.52348	−	4.92103i	0.315252	−	0.182011i
$732$	−3.67331	−	6.83305i	−0.135769	−	0.252557i
$733$	−8.62755	+	32.1984i	−0.318666	+	1.18928i	0.601862	+	0.798600i	$0.294426\pi$
$733$	−8.62755	+	32.1984i	−0.318666	+	1.18928i	−0.920528	+	0.390677i	$0.872241\pi$
$734$	5.68380	+	1.52297i	0.209793	+	0.0562138i
$735$	−12.7030	−	20.8753i	−0.468557	−	0.769999i
$736$	5.77809	−	5.77809i	0.212983	−	0.212983i
$737$	−1.88830	−	1.09021i	−0.0695565	−	0.0401585i
$738$	2.07596	−	34.1684i	0.0764172	−	1.25776i
$739$	−16.7621	−	4.49138i	−0.616603	−	0.165218i	−0.0630197	−	0.998012i	$-0.520073\pi$
$739$	−16.7621	−	4.49138i	−0.616603	−	0.165218i	−0.553583	+	0.832794i	$0.686740\pi$
$740$	−9.37676	−	16.2410i	−0.344697	−	0.597032i
$741$	17.2157	+	10.0761i	0.632435	+	0.370156i
$742$	26.4379	−	4.20145i	0.970565	−	0.154240i
$743$	7.77656	+	29.0225i	0.285294	+	1.06473i	0.948624	+	0.316406i	$0.102476\pi$
$743$	7.77656	+	29.0225i	0.285294	+	1.06473i	−0.663329	+	0.748328i	$0.730857\pi$
$744$	−7.77584	−	14.4645i	−0.285076	−	0.530296i
$745$			14.1137i			0.517087i
$746$	6.55877	+	24.4777i	0.240134	+	0.896192i
$747$	−20.1364	−	6.72850i	−0.736754	−	0.246183i
$748$	0.533683	+	0.143000i	0.0195134	+	0.00522859i
$749$	−0.548948	+	5.24916i	−0.0200581	+	0.191800i
$750$	−17.6287	−	10.9040i	−0.643708	−	0.398159i
$751$			12.3592i			0.450993i	0.974244	+	0.225497i	$0.0724004\pi$
$751$			12.3592i			0.450993i	−0.974244	+	0.225497i	$0.927600\pi$
$752$	−0.692489	+	2.58440i	−0.0252525	+	0.0942435i
$753$	−0.0232540	+	0.766185i	−0.000847424	+	0.0279213i
$754$	−20.4218	+	0.498581i	−0.743718	+	0.0181573i
$755$			16.3625i			0.595492i
$756$	13.4866	+	2.66685i	0.490502	+	0.0969926i
$757$	−1.59168	+	2.75688i	−0.0578508	+	0.100200i	−0.893500	−	0.449062i	$-0.851758\pi$
$757$	−1.59168	+	2.75688i	−0.0578508	+	0.100200i	0.835650	+	0.549263i	$0.185091\pi$
$758$	8.06116	−	13.9623i	0.292795	−	0.507135i
$759$	−3.28190	+	3.08855i	−0.119125	+	0.112107i
$760$	−4.55225	−	4.55225i	−0.165128	−	0.165128i
$761$	34.2868	−	9.18712i	1.24290	−	0.333033i	0.423308	−	0.905986i	$-0.360869\pi$
$761$	34.2868	−	9.18712i	1.24290	−	0.333033i	0.819588	+	0.572953i	$0.194202\pi$
$762$	−13.5129	−	4.06393i	−0.489519	−	0.147221i
$763$	4.43637	−	0.705019i	0.160608	−	0.0255234i
$764$	2.91721	−	5.05275i	0.105541	−	0.182802i
$765$	−2.09587	−	10.2803i	−0.0757764	−	0.371684i
$766$	−2.84928	−	1.64503i	−0.102949	−	0.0594374i
$767$	2.31309	+	3.78967i	0.0835209	+	0.136837i
$768$	−1.47304	−	0.911131i	−0.0531537	−	0.0328776i
$769$	−6.58832	+	1.76533i	−0.237581	+	0.0636596i	−0.375645	−	0.926764i	$-0.622579\pi$
$769$	−6.58832	+	1.76533i	−0.237581	+	0.0636596i	0.138064	+	0.990423i	$0.455912\pi$
$770$	−0.266491	−	1.67691i	−0.00960367	−	0.0604317i
$771$	34.7307	+	21.4823i	1.25080	+	0.773666i
$772$	1.94396	−	7.25495i	0.0699646	−	0.261111i
$773$	−35.0716	+	35.0716i	−1.26144	+	1.26144i	−0.311042	+	0.950396i	$0.600678\pi$
$773$	−35.0716	+	35.0716i	−1.26144	+	1.26144i	−0.950396	+	0.311042i	$0.899322\pi$
$774$	16.6732	−	3.39923i	0.599308	−	0.122183i
$775$	−8.58844	−	2.30127i	−0.308506	−	0.0826639i
$776$	15.7106	−	9.07051i	0.563977	−	0.325612i
$777$	42.2946	−	5.41160i	1.51731	−	0.194140i
$778$	3.39018	+	12.6523i	0.121544	+	0.453607i
$779$	−18.2235	−	31.5641i	−0.652926	−	1.13090i
$780$	−10.9376	+	6.22861i	−0.391629	+	0.223020i
$781$	1.41557	−	2.45184i	0.0506532	−	0.0877339i
$782$	10.0260	−	10.0260i	0.358530	−	0.358530i
$783$	16.9764	−	24.0520i	0.606687	−	0.859548i
$784$	−6.84854	−	1.44826i	−0.244591	−	0.0517234i
$785$	1.12580	−	1.12580i	0.0401817	−	0.0401817i
$786$	−4.91240	+	4.62300i	−0.175220	+	0.164897i
$787$	−7.77263	+	7.77263i	−0.277064	+	0.277064i	−0.831936	−	0.554872i	$-0.812767\pi$
$787$	−7.77263	+	7.77263i	−0.277064	+	0.277064i	0.554872	+	0.831936i	$0.312767\pi$
$788$	−6.58042	+	1.76322i	−0.234418	+	0.0628121i
$789$	−6.86500	−	0.208356i	−0.244400	−	0.00741765i
$790$	−14.8702	−	8.58530i	−0.529057	−	0.305451i
$791$	33.0439	−	14.7327i	1.17491	−	0.523835i
$792$	0.796781	+	0.526915i	0.0283124	+	0.0187231i
$793$	−11.1371	+	11.6945i	−0.395490	+	0.415284i
$794$	7.67718	+	4.43242i	0.272453	+	0.157301i
$795$	−8.10258	−	34.3793i	−0.287369	−	1.21931i
$796$	20.1607			0.714579
$797$	−14.1455	−	24.5007i	−0.501059	−	0.867859i	−0.999999	−	0.00122281i	$-0.999611\pi$
$797$	−14.1455	−	24.5007i	−0.501059	−	0.867859i	0.498941	−	0.866636i	$-0.333723\pi$
$798$	13.5437	−	5.55229i	0.479441	−	0.196549i
$799$	−1.20159	+	4.48441i	−0.0425093	+	0.158647i
$800$	−0.905827	+	0.242716i	−0.0320258	+	0.00858129i
$801$	10.4094	−	31.1521i	0.367796	−	1.10071i
$802$	20.1336			0.710941
$803$	−2.67527			−0.0944082
$804$	8.12842	+	8.63727i	0.286667	+	0.304613i
$805$	−40.6882	−	15.5944i	−1.43407	−	0.549632i
$806$	−23.5755	+	24.7555i	−0.830413	+	0.871975i
$807$	−29.8584	+	48.2724i	−1.05106	+	1.69927i
$808$	0.782658	−	2.92092i	0.0275338	−	0.102758i
$809$	23.8736	−	13.7834i	0.839350	−	0.484599i	−0.0176930	−	0.999843i	$-0.505632\pi$
$809$	23.8736	−	13.7834i	0.839350	−	0.484599i	0.857043	+	0.515244i	$0.172299\pi$
$810$	2.19608	−	18.0060i	0.0771625	−	0.632667i
$811$	5.14696	+	5.14696i	0.180734	+	0.180734i	0.791676	−	0.610942i	$-0.209209\pi$
$811$	5.14696	+	5.14696i	0.180734	+	0.180734i	−0.610942	+	0.791676i	$0.709209\pi$
$812$	−8.80457	+	12.1317i	−0.308980	+	0.425740i
$813$	−11.9927	+	2.82645i	−0.420601	+	0.0991281i
$814$	2.86181	+	0.766819i	0.100306	+	0.0268770i
$815$			9.88755i			0.346346i
$816$	−2.55598	−	1.58098i	−0.0894774	−	0.0553453i
$817$	12.8111	−	12.8111i	0.448204	−	0.448204i
$818$	3.13261			0.109529
$819$	−3.46364	−	28.4078i	−0.121030	−	0.992649i
$820$	22.9977			0.803115
$821$	20.7097	−	20.7097i	0.722772	−	0.722772i	−0.246397	−	0.969169i	$-0.579247\pi$
$821$	20.7097	−	20.7097i	0.722772	−	0.722772i	0.969169	+	0.246397i	$0.0792467\pi$
$822$	−13.6473	−	8.44141i	−0.476005	−	0.294428i
$823$			7.75667i			0.270381i	0.990820	+	0.135190i	$0.0431646\pi$
$823$			7.75667i			0.270381i	−0.990820	+	0.135190i	$0.956835\pi$
$824$	−9.31312	−	2.49544i	−0.324438	−	0.0869329i
$825$	0.503406	−	0.118644i	0.0175264	−	0.00413065i
$826$	3.24027	+	0.338861i	0.112743	+	0.0117905i
$827$	−0.310218	−	0.310218i	−0.0107874	−	0.0107874i	0.701693	−	0.712480i	$-0.252428\pi$
$827$	−0.310218	−	0.310218i	−0.0107874	−	0.0107874i	−0.712480	+	0.701693i	$0.752428\pi$
$828$	21.9343	−	10.9471i	0.762270	−	0.380439i
$829$	−45.6094	+	26.3326i	−1.58408	+	0.914568i	−0.589824	+	0.807532i	$0.700803\pi$
$829$	−45.6094	+	26.3326i	−1.58408	+	0.914568i	−0.994255	+	0.107036i	$0.965864\pi$
$830$	3.69168	−	13.7775i	0.128140	−	0.478225i
$831$	−13.8967	+	22.4670i	−0.482071	+	0.779370i
$832$	−0.847906	+	3.50443i	−0.0293958	+	0.121494i
$833$	−11.8835	−	2.51298i	−0.411737	−	0.0870698i
$834$	−14.8369	−	15.7657i	−0.513760	−	0.545922i
$835$	−28.1428			−0.973923
$836$	1.01708			0.0351764
$837$	−8.37268	−	48.5497i	−0.289402	−	1.67812i
$838$	−22.1439	+	5.93343i	−0.764947	+	0.204967i
$839$	6.92710	−	25.8523i	0.239150	−	0.892520i	−0.737084	−	0.675801i	$-0.763798\pi$
$839$	6.92710	−	25.8523i	0.239150	−	0.892520i	0.976234	−	0.216719i	$-0.0695354\pi$
$840$	−1.23889	+	9.15269i	−0.0427459	+	0.315798i
$841$	1.54995	+	2.68459i	0.0534466	+	0.0925722i
$842$	6.56823			0.226356
$843$	9.32547	+	39.5680i	0.321186	+	1.36279i
$844$	−8.13083	−	4.69434i	−0.279875	−	0.161586i
$845$	19.4092	+	17.6010i	0.667698	+	0.605494i
$846$	−4.42754	+	6.69516i	−0.152222	+	0.230184i
$847$	−23.3368	−	16.9367i	−0.801863	−	0.581950i
$848$	−8.76242	−	5.05898i	−0.300903	−	0.173726i
$849$	−40.4960	−	1.22907i	−1.38982	−	0.0421816i
$850$	−1.57177	+	0.421155i	−0.0539114	+	0.0144455i
$851$	53.7633	−	53.7633i	1.84298	−	1.84298i
$852$	−11.2150	+	10.5543i	−0.384218	+	0.361583i
$853$	32.9511	−	32.9511i	1.12822	−	1.12822i	0.137757	−	0.990466i	$-0.456011\pi$
$853$	32.9511	−	32.9511i	1.12822	−	1.12822i	0.990466	−	0.137757i	$-0.0439892\pi$
$854$	1.85988	+	11.7034i	0.0636438	+	0.400482i
$855$	−8.62466	−	17.2809i	−0.294957	−	0.590994i
$856$	1.41055	−	1.41055i	0.0482115	−	0.0482115i
$857$	−7.37534	+	12.7745i	−0.251937	+	0.436368i	−0.964059	−	0.265688i	$-0.914401\pi$
$857$	−7.37534	+	12.7745i	−0.251937	+	0.436368i	0.712122	+	0.702056i	$0.247734\pi$
$858$	0.526048	−	1.91766i	0.0179590	−	0.0654680i
$859$	−2.50434	−	4.33765i	−0.0854471	−	0.147999i	0.820135	−	0.572171i	$-0.193899\pi$
$859$	−2.50434	−	4.33765i	−0.0854471	−	0.147999i	−0.905582	+	0.424172i	$0.860565\pi$
$860$	2.95883	+	11.0425i	0.100895	+	0.376546i
$861$	−20.1860	+	48.2358i	−0.687937	+	1.64387i
$862$	19.8065	−	11.4353i	0.674611	−	0.389487i
$863$	−21.4726	−	5.75357i	−0.730936	−	0.195854i	−0.125890	−	0.992044i	$-0.540179\pi$
$863$	−21.4726	−	5.75357i	−0.730936	−	0.195854i	−0.605046	+	0.796190i	$0.706845\pi$
$864$	−3.32504	−	3.99300i	−0.113120	−	0.135845i
$865$	2.43085	−	2.43085i	0.0826514	−	0.0826514i
$866$	−5.84825	+	21.8260i	−0.198732	+	0.741677i
$867$	20.6065	+	12.7460i	0.699835	+	0.432875i
$868$	3.93708	+	24.7743i	0.133633	+	0.840896i
$869$	2.62025	−	0.702094i	0.0888859	−	0.0238169i
$870$	16.8208	+	10.4043i	0.570279	+	0.352740i
$871$	11.8193	−	21.6769i	0.400483	−	0.734494i
$872$	−1.47037	−	0.848917i	−0.0497929	−	0.0287480i
$873$	53.3261	−	10.8718i	1.80481	−	0.367954i
$874$	13.0506	−	22.6042i	0.441442	−	0.764599i
$875$	19.9391	+	24.5966i	0.674065	+	0.831516i
$876$	13.9358	+	4.19112i	0.470846	+	0.141605i
$877$	31.7350	−	8.50337i	1.07161	−	0.287138i	0.320458	−	0.947263i	$-0.396163\pi$
$877$	31.7350	−	8.50337i	1.07161	−	0.287138i	0.751156	+	0.660124i	$0.229496\pi$
$878$	9.57152	+	9.57152i	0.323023	+	0.323023i
$879$	9.18130	−	8.64040i	0.309677	−	0.291433i
$880$	−0.320883	+	0.555786i	−0.0108170	+	0.0187355i
$881$	−16.7038	+	28.9319i	−0.562766	+	0.974740i	0.434487	+	0.900678i	$0.356930\pi$
$881$	−16.7038	+	28.9319i	−0.562766	+	0.974740i	−0.997254	+	0.0740619i	$0.976404\pi$
$882$	−18.1096	−	10.6322i	−0.609782	−	0.358003i
$883$		−	8.36445i		−	0.281486i	−0.990046	−	0.140743i	$-0.955051\pi$
$883$		−	8.36445i		−	0.281486i	0.990046	−	0.140743i	$-0.0449491\pi$
$884$	−1.47127	+	6.08082i	−0.0494841	+	0.204520i
$885$	0.130407	−	4.29671i	0.00438358	−	0.144432i
$886$	−2.72724	+	10.1782i	−0.0916235	+	0.341944i
$887$			34.6995i			1.16509i	0.812797	+	0.582547i	$0.197944\pi$
$887$			34.6995i			1.16509i	−0.812797	+	0.582547i	$0.802056\pi$
$888$	−13.7061	−	8.47779i	−0.459948	−	0.284496i
$889$	17.4445	+	12.6603i	0.585071	+	0.424614i
$890$	21.3146	+	5.71122i	0.714466	+	0.191441i
$891$	1.76615	+	2.25681i	0.0591684	+	0.0756060i
$892$	7.01130	+	26.1665i	0.234756	+	0.876121i
$893$			8.54627i			0.285990i
$894$	5.74300	+	10.6831i	0.192075	+	0.357295i
$895$	9.39672	+	35.0690i	0.314098	+	1.17223i
$896$	1.66609	+	2.05527i	0.0556603	+	0.0686617i
$897$	−35.8695	−	36.2976i	−1.19765	−	1.21194i
$898$	−9.31582	−	16.1355i	−0.310873	−	0.538448i
$899$	51.8877	+	13.9033i	1.73055	+	0.463700i
$900$	−2.80817	−	0.170615i	−0.0936055	−	0.00568717i
$901$	−15.2044	−	8.77824i	−0.506531	−	0.292446i
$902$	−2.56911	+	2.56911i	−0.0855421	+	0.0855421i
$903$	−25.7578	−	3.48654i	−0.857167	−	0.116025i
$904$	−13.2086	−	3.53924i	−0.439312	−	0.117713i
$905$	−0.827833	+	3.08951i	−0.0275181	+	0.102699i
$906$	6.65804	+	12.3852i	0.221199	+	0.411471i
$907$	−42.7978	+	24.7093i	−1.42108	+	0.820460i	−0.996391	−	0.0848810i	$-0.972949\pi$
$907$	−42.7978	+	24.7093i	−1.42108	+	0.820460i	−0.424686	+	0.905340i	$0.639616\pi$
$908$	3.69556	+	3.69556i	0.122641	+	0.122641i
$909$	5.00405	−	7.56693i	0.165974	−	0.250979i
$910$	18.9090	−	3.48013i	0.626828	−	0.115365i
$911$		−	45.2150i		−	1.49804i	−0.662547	−	0.749020i	$-0.730525\pi$
$911$		−	45.2150i		−	1.49804i	0.662547	−	0.749020i	$-0.269475\pi$
$912$	−5.29807	−	1.59337i	−0.175437	−	0.0527618i
$913$	1.12671	+	1.95151i	0.0372886	+	0.0645857i
$914$	21.7933			0.720860
$915$	15.2189	−	3.58682i	0.503121	−	0.118577i
$916$	−0.468212	+	1.74739i	−0.0154702	+	0.0577354i
$917$	9.41113	−	4.19597i	0.310783	−	0.138563i
$918$	−5.76955	−	6.92858i	−0.190424	−	0.228677i
$919$	−10.9831	+	19.0234i	−0.362300	+	0.627522i	−0.988339	−	0.152269i	$-0.951342\pi$
$919$	−10.9831	+	19.0234i	−0.362300	+	0.627522i	0.626039	+	0.779792i	$0.284675\pi$
$920$	8.23476	+	14.2630i	0.271492	+	0.470238i
$921$	−34.4109	+	8.11002i	−1.13388	+	0.267234i
$922$	−14.0122	+	8.08997i	−0.461468	+	0.266429i
$923$	28.1461	+	15.3467i	0.926442	+	0.505143i
$924$	−0.884063	−	1.16086i	−0.0290835	−	0.0381895i
$925$	−8.42843	+	2.25839i	−0.277125	+	0.0742554i
$926$		−	24.1719i		−	0.794339i
$927$	−24.1266	−	15.9550i	−0.792420	−	0.524031i
$928$	5.47262	−	1.46639i	0.179648	−	0.0481365i
$929$	11.5511	+	43.1094i	0.378980	+	1.41437i	0.847441	+	0.530889i	$0.178142\pi$
$929$	11.5511	+	43.1094i	0.378980	+	1.41437i	−0.468461	+	0.883484i	$0.655191\pi$
$930$	32.2161	−	7.59275i	1.05641	−	0.248976i
$931$	−22.3274	+	1.19343i	−0.731751	+	0.0391130i
$932$	23.8640	−	13.7779i	0.781692	−	0.451310i
$933$	5.61282	−	3.01734i	0.183755	−	0.0987832i
$934$	−8.53343	−	2.28653i	−0.279222	−	0.0748174i
$935$	−0.556790	+	0.964388i	−0.0182090	+	0.0315389i
$936$	−5.74448	+	9.16520i	−0.187764	+	0.299574i
$937$	−29.5886			−0.966618			−0.483309	−	0.875450i	$-0.660565\pi$
$937$	−29.5886			−0.966618			−0.483309	+	0.875450i	$0.660565\pi$
$938$	−7.37760	−	16.5472i	−0.240887	−	0.540285i
$939$	1.13521	−	37.4033i	0.0370461	−	1.22061i
$940$	−4.67013	−	2.69630i	−0.152323	−	0.0879437i
$941$	0.262735	+	0.980539i	0.00856490	+	0.0319647i	0.970076	−	0.242801i	$-0.0780663\pi$
$941$	0.262735	+	0.980539i	0.00856490	+	0.0319647i	−0.961511	+	0.274766i	$0.911400\pi$
$942$	0.394052	−	1.31025i	0.0128389	−	0.0426903i
$943$	24.1323	+	90.0630i	0.785856	+	2.93285i
$944$	−0.870720	−	0.870720i	−0.0283395	−	0.0283395i
$945$	−12.2271	+	24.8648i	−0.397749	+	0.808851i
$946$	−1.56411	−	0.903040i	−0.0508537	−	0.0293604i
$947$	35.5521	+	35.5521i	1.15529	+	1.15529i	0.985476	+	0.169813i	$0.0543165\pi$
$947$	35.5521	+	35.5521i	1.15529	+	1.15529i	0.169813	+	0.985476i	$0.445684\pi$
$948$	−14.7491	−	0.447640i	−0.479027	−	0.0145387i
$949$	−0.739361	−	30.2841i	−0.0240007	−	0.983064i
$950$	−2.59413	+	1.49772i	−0.0841647	+	0.0485925i
$951$	−36.7926	−	39.0958i	−1.19308	−	1.26777i
$952$	2.89097	+	3.56626i	0.0936970	+	0.115583i
$953$	7.74649	+	13.4173i	0.250933	+	0.434629i	0.963783	−	0.266688i	$-0.0859292\pi$
$953$	7.74649	+	13.4173i	0.250933	+	0.434629i	−0.712850	+	0.701317i	$0.752596\pi$
$954$	−20.1223	−	22.7256i	−0.651483	−	0.735768i
$955$	8.31504	+	8.31504i	0.269068	+	0.269068i
$956$	−4.03167	−	4.03167i	−0.130394	−	0.130394i
$957$	−3.04137	+	0.716796i	−0.0983135	+	0.0231707i
$958$	−3.35922	−	5.81835i	−0.108532	−	0.187982i
$959$	15.4360	+	19.0415i	0.498453	+	0.614884i
$960$	2.54222	−	2.39245i	0.0820496	−	0.0772159i
$961$	51.0050	−	29.4477i	1.64532	−	0.949927i
$962$	−7.88949	+	32.6076i	−0.254367	+	1.05131i
$963$	5.35461	−	2.67241i	0.172550	−	0.0861173i
$964$	8.47353	+	8.47353i	0.272914	+	0.272914i
$965$	13.1100	+	7.56907i	0.422026	+	0.243657i
$966$	−37.1435	+	4.75252i	−1.19507	+	0.152910i
$967$	−38.0208	−	38.0208i	−1.22267	−	1.22267i	−0.966680	−	0.255986i	$-0.917600\pi$
$967$	−38.0208	−	38.0208i	−1.22267	−	1.22267i	−0.255986	−	0.966680i	$-0.582400\pi$
$968$	2.82077	+	10.5272i	0.0906629	+	0.338359i
$969$	−9.19311	−	2.76478i	−0.295325	−	0.0888177i
$970$	9.46323	+	35.3173i	0.303846	+	1.13397i
$971$	−27.0163	−	15.5978i	−0.866993	−	0.500559i	−0.000645091	−	1.00000i	$-0.500205\pi$
$971$	−27.0163	−	15.5978i	−0.866993	−	0.500559i	−0.866348	+	0.499441i	$0.833539\pi$
$972$	−5.66453	−	14.5228i	−0.181690	−	0.465821i
$973$	13.4664	+	30.2038i	0.431714	+	0.968289i
$974$	5.83824			0.187069
$975$	1.48218	+	5.66578i	0.0474676	+	0.181450i
$976$	2.23949	−	3.87891i	0.0716843	−	0.124161i
$977$	−29.7767	−	7.97863i	−0.952640	−	0.255259i	−0.251158	−	0.967946i	$-0.580811\pi$
$977$	−29.7767	−	7.97863i	−0.952640	−	0.255259i	−0.701482	+	0.712687i	$0.747478\pi$
$978$	4.02333	+	7.48415i	0.128652	+	0.239317i
$979$	−3.01910	+	1.74308i	−0.0964907	+	0.0557089i
$980$	6.39202	−	12.5774i	0.204186	−	0.401770i
$981$	−3.37660	−	3.81344i	−0.107806	−	0.121754i
$982$	−8.80778	−	32.8711i	−0.281068	−	1.04896i
$983$	−10.7079	+	2.86918i	−0.341530	+	0.0915128i	−0.425507	−	0.904955i	$-0.639904\pi$
$983$	−10.7079	+	2.86918i	−0.341530	+	0.0915128i	0.0839772	+	0.996468i	$0.473238\pi$
$984$	17.4076	−	9.35797i	0.554934	−	0.298321i
$985$		−	13.7307i		−	0.437495i
$986$	9.49599	−	2.54444i	0.302414	−	0.0810315i
$987$	9.75443	−	7.42857i	0.310487	−	0.236454i
$988$	0.281089	+	11.5134i	0.00894263	+	0.366289i
$989$	−40.1395	+	23.1745i	−1.27636	+	0.736908i
$990$	−1.44145	+	1.27632i	−0.0458122	+	0.0405642i
$991$	19.1688	+	33.2013i	0.608917	+	1.05467i	0.991419	+	0.130720i	$0.0417289\pi$
$991$	19.1688	+	33.2013i	0.608917	+	1.05467i	−0.382503	+	0.923954i	$0.624938\pi$
$992$	4.74066	−	8.21107i	0.150516	−	0.260702i
$993$	6.43260	+	1.93457i	0.204132	+	0.0613919i
$994$	21.4855	−	9.57936i	0.681479	−	0.303839i
$995$	−10.5168	+	39.2493i	−0.333406	+	1.24429i
$996$	−2.81187	−	11.9308i	−0.0890974	−	0.378041i
$997$	−32.9386			−1.04318			−0.521588	−	0.853198i	$-0.674660\pi$
$997$	−32.9386			−1.04318			−0.521588	+	0.853198i	$0.674660\pi$
$998$	9.04401	+	15.6647i	0.286283	+	0.495857i
$999$	−30.9385	−	37.1536i	−0.978850	−	1.17549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.3	yes	152
3.2	odd	2	inner	546.2.ch.a.137.29	yes	152
7.2	even	3		546.2.bw.a.527.35	yes	152
13.2	odd	12		546.2.bw.a.431.16	✓	152
21.2	odd	6		546.2.bw.a.527.16	yes	152
39.2	even	12		546.2.bw.a.431.35	yes	152
91.2	odd	12	inner	546.2.ch.a.275.29	yes	152
273.2	even	12	inner	546.2.ch.a.275.3	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.16	✓	152	13.2	odd	12
546.2.bw.a.431.35	yes	152	39.2	even	12
546.2.bw.a.527.16	yes	152	21.2	odd	6
546.2.bw.a.527.35	yes	152	7.2	even	3
546.2.ch.a.137.3	yes	152	1.1	even	1	trivial
546.2.ch.a.137.29	yes	152	3.2	odd	2	inner
546.2.ch.a.275.3	yes	152	273.2	even	12	inner
546.2.ch.a.275.29	yes	152	91.2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47304 - 0.911131i) q^{3} -1.00000i q^{4} +(1.94682 + 0.521648i) q^{5} +(1.68586 - 0.397328i) q^{6} +(-2.63140 - 0.275187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33968 + 2.68426i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47304 - 0.911131i) q^{3} -1.00000i q^{4} +(1.94682 + 0.521648i) q^{5} +(1.68586 - 0.397328i) q^{6} +(-2.63140 - 0.275187i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.33968 + 2.68426i) q^{9} +(-1.74547 + 1.00775i) q^{10} +(0.0824122 - 0.307566i) q^{11} +(-0.911131 + 1.47304i) q^{12} +(3.50443 + 0.847906i) q^{13} +(2.05527 - 1.66609i) q^{14} +(-2.39245 - 2.54222i) q^{15} -1.00000 q^{16} -1.73518 q^{17} +(-2.84536 - 0.950764i) q^{18} +(-3.08534 + 0.826715i) q^{19} +(0.521648 - 1.94682i) q^{20} +(3.62542 + 2.80291i) q^{21} +(0.159208 + 0.275756i) q^{22} +8.17145 q^{23} +(-0.397328 - 1.68586i) q^{24} +(-0.812142 - 0.468891i) q^{25} +(-3.07757 + 1.87845i) q^{26} +(0.472318 - 5.17464i) q^{27} +(-0.275187 + 2.63140i) q^{28} +(4.90662 + 2.83284i) q^{29} +(3.48933 + 0.105903i) q^{30} +(9.15825 - 2.45395i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.401630 + 0.377969i) q^{33} +(1.22696 - 1.22696i) q^{34} +(-4.97931 - 1.90841i) q^{35} +(2.68426 - 1.33968i) q^{36} +(6.57940 - 6.57940i) q^{37} +(1.59709 - 2.76624i) q^{38} +(-4.38961 - 4.44200i) q^{39} +(1.00775 + 1.74547i) q^{40} +(2.95324 + 11.0217i) q^{41} +(-4.54552 + 0.581600i) q^{42} +(-4.91216 + 2.83604i) q^{43} +(-0.307566 - 0.0824122i) q^{44} +(1.20787 + 5.92461i) q^{45} +(-5.77809 + 5.77809i) q^{46} +(0.692489 - 2.58440i) q^{47} +(1.47304 + 0.911131i) q^{48} +(6.84854 + 1.44826i) q^{49} +(0.905827 - 0.242716i) q^{50} +(2.55598 + 1.58098i) q^{51} +(0.847906 - 3.50443i) q^{52} +(8.76242 + 5.05898i) q^{53} +(3.32504 + 3.99300i) q^{54} +(0.320883 - 0.555786i) q^{55} +(-1.66609 - 2.05527i) q^{56} +(5.29807 + 1.59337i) q^{57} +(-5.47262 + 1.46639i) q^{58} +(0.870720 + 0.870720i) q^{59} +(-2.54222 + 2.39245i) q^{60} +(-2.23949 + 3.87891i) q^{61} +(-4.74066 + 8.21107i) q^{62} +(-2.78656 - 7.43203i) q^{63} +1.00000i q^{64} +(6.38019 + 3.47880i) q^{65} +(0.0167309 - 0.551259i) q^{66} +(1.77232 - 6.61438i) q^{67} +1.73518i q^{68} +(-12.0369 - 7.44527i) q^{69} +(4.87035 - 2.17146i) q^{70} +(8.58837 + 2.30125i) q^{71} +(-0.950764 + 2.84536i) q^{72} +(-2.17455 - 8.11552i) q^{73} +9.30468i q^{74} +(0.769095 + 1.43066i) q^{75} +(0.826715 + 3.08534i) q^{76} +(-0.301498 + 0.786652i) q^{77} +(6.24489 + 0.0370439i) q^{78} +(4.25965 + 7.37793i) q^{79} +(-1.94682 - 0.521648i) q^{80} +(-5.41052 + 7.19210i) q^{81} +(-9.88175 - 5.70523i) q^{82} +(-5.00416 + 5.00416i) q^{83} +(2.80291 - 3.62542i) q^{84} +(-3.37808 - 0.905154i) q^{85} +(1.46804 - 5.47880i) q^{86} +(-4.64655 - 8.64345i) q^{87} +(0.275756 - 0.159208i) q^{88} +(-7.74170 - 7.74170i) q^{89} +(-5.04343 - 3.33524i) q^{90} +(-8.98824 - 3.19556i) q^{91} -8.17145i q^{92} +(-15.7263 - 4.72962i) q^{93} +(1.33779 + 2.31711i) q^{94} -6.43786 q^{95} +(-1.68586 + 0.397328i) q^{96} +(4.69524 - 17.5229i) q^{97} +(-5.86672 + 3.81858i) q^{98} +(0.935995 - 0.190824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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