LMFDB - Embedded newform 252.2.bi.c.139.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.20
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.161186 - 1.40500i) q^{2} +(1.59413 + 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.694651 - 2.34893i) q^{6} +(2.30627 + 1.29658i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +O(q^{10})$	\(q+(-0.161186 - 1.40500i) q^{2} +(1.59413 + 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.694651 - 2.34893i) q^{6} +(2.30627 + 1.29658i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +(0.931077 - 2.14589i) q^{10} +(-4.24842 + 2.45282i) q^{11} +(-3.41221 - 0.597369i) q^{12} +(-0.876334 - 0.505952i) q^{13} +(1.44996 - 3.44929i) q^{14} +(1.72337 + 2.28859i) q^{15} +(3.58970 - 1.76466i) q^{16} -7.66107i q^{17} +(2.69829 - 3.27402i) q^{18} +2.85119 q^{19} +(-3.16505 - 0.962273i) q^{20} +(2.79833 + 3.62896i) q^{21} +(4.13100 + 5.57365i) q^{22} +(-1.98118 - 1.14384i) q^{23} +(-0.289302 + 4.89043i) q^{24} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 + 1.31280i) q^{26} +(1.85727 + 4.85289i) q^{27} +(-5.07996 - 1.48121i) q^{28} +(-4.19857 - 7.27213i) q^{29} +(2.93767 - 2.79022i) q^{30} +(-0.348784 + 0.604112i) q^{31} +(-3.05795 - 4.75909i) q^{32} +(-8.43384 + 1.03268i) q^{33} +(-10.7638 + 1.23486i) q^{34} +(2.23130 + 3.76463i) q^{35} +(-5.03492 - 3.26337i) q^{36} +3.97490 q^{37} +(-0.459573 - 4.00592i) q^{38} +(-1.05431 - 1.40010i) q^{39} +(-0.841829 + 4.60200i) q^{40} +(6.69947 + 3.86794i) q^{41} +(4.64763 - 4.51658i) q^{42} +(-6.70811 + 3.87293i) q^{43} +(7.16511 - 6.70244i) q^{44} +(1.19723 + 4.81555i) q^{45} +(-1.28775 + 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(6.91767 - 0.381802i) q^{48} +(3.63774 + 5.98054i) q^{49} +(-2.57243 + 1.90659i) q^{50} +(5.18884 - 12.2128i) q^{51} +(1.93629 + 0.588693i) q^{52} -8.61878 q^{53} +(6.51894 - 3.39168i) q^{54} -8.11418 q^{55} +(-1.26228 + 7.37609i) q^{56} +(4.54518 + 1.93111i) q^{57} +(-9.54058 + 7.07115i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(-4.39377 - 3.67768i) q^{60} +(5.12759 - 2.96042i) q^{61} +(0.904996 + 0.392667i) q^{62} +(2.00301 + 7.68036i) q^{63} +(-6.19361 + 5.06352i) q^{64} +(-0.836869 - 1.44950i) q^{65} +(2.81034 + 11.6831i) q^{66} +(2.18590 + 1.26203i) q^{67} +(3.46995 + 14.9241i) q^{68} +(-2.38355 - 3.16528i) q^{69} +(4.92964 - 3.74178i) q^{70} +1.00362i q^{71} +(-3.77347 + 7.60006i) q^{72} +5.89658i q^{73} +(-0.640700 - 5.58473i) q^{74} +(-0.476618 - 3.89250i) q^{75} +(-5.55423 + 1.29140i) q^{76} +(-12.9783 + 0.148439i) q^{77} +(-1.79719 + 1.70698i) q^{78} +(4.90752 - 2.83336i) q^{79} +(6.60149 + 0.440989i) q^{80} +(-0.326126 + 8.99409i) q^{81} +(4.35458 - 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(-7.09492 - 5.80191i) q^{84} +(6.33589 - 10.9741i) q^{85} +(6.52272 + 8.80062i) q^{86} +(-1.76767 - 14.4364i) q^{87} +(-10.5718 - 8.98662i) q^{88} +8.19734i q^{89} +(6.57286 - 2.45831i) q^{90} +(-1.36505 - 2.30310i) q^{91} +(4.37750 + 1.33089i) q^{92} +(-0.965174 + 0.726805i) q^{93} +(-8.42407 + 6.24363i) q^{94} +(4.08418 + 2.35800i) q^{95} +(-1.65146 - 9.65778i) q^{96} +(-8.82136 + 5.09301i) q^{97} +(7.81629 - 6.07500i) q^{98} +(-14.1441 - 4.06600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.161186	−	1.40500i	−0.113976	−	0.993484i
$2$	−0.161186	−	1.40500i	−0.113976	−	0.993484i
$3$	1.59413	+	0.677299i	0.920374	+	0.391039i
$3$	1.59413	+	0.677299i	0.920374	+	0.391039i
$4$	−1.94804	+	0.452933i	−0.974019	+	0.226466i
$5$	1.43245	+	0.827025i	0.640611	+	0.369857i	0.784850	−	0.619686i	$-0.212740\pi$
$5$	1.43245	+	0.827025i	0.640611	+	0.369857i	−0.144239	+	0.989543i	$0.546073\pi$
$6$	0.694651	−	2.34893i	0.283590	−	0.958946i
$7$	2.30627	+	1.29658i	0.871687	+	0.490063i
$7$	2.30627	+	1.29658i	0.871687	+	0.490063i
$8$	0.950366	+	2.66398i	0.336005	+	0.941860i
$9$	2.08253	+	2.15941i	0.694177	+	0.719804i
$10$	0.931077	−	2.14589i	0.294432	−	0.678591i
$11$	−4.24842	+	2.45282i	−1.28095	+	0.739554i	−0.977021	−	0.213142i	$-0.931630\pi$
$11$	−4.24842	+	2.45282i	−1.28095	+	0.739554i	−0.303924	+	0.952696i	$0.598297\pi$
$12$	−3.41221	−	0.597369i	−0.985019	−	0.172446i
$13$	−0.876334	−	0.505952i	−0.243051	−	0.140326i	0.373527	−	0.927619i	$-0.378148\pi$
$13$	−0.876334	−	0.505952i	−0.243051	−	0.140326i	−0.616578	+	0.787294i	$0.711482\pi$
$14$	1.44996	−	3.44929i	0.387518	−	0.921862i
$15$	1.72337	+	2.28859i	0.444973	+	0.590910i
$16$	3.58970	−	1.76466i	0.897426	−	0.441165i
$17$		−	7.66107i		−	1.85808i	−0.369976	−	0.929041i	$-0.620634\pi$
$17$		−	7.66107i		−	1.85808i	0.369976	−	0.929041i	$-0.379366\pi$
$18$	2.69829	−	3.27402i	0.635994	−	0.771694i
$19$	2.85119			0.654108			0.327054	−	0.945006i	$-0.393944\pi$
$19$	2.85119			0.654108			0.327054	+	0.945006i	$0.393944\pi$
$20$	−3.16505	−	0.962273i	−0.707727	−	0.215171i
$21$	2.79833	+	3.62896i	0.610645	+	0.791905i
$22$	4.13100	+	5.57365i	0.880732	+	1.18831i
$23$	−1.98118	−	1.14384i	−0.413105	−	0.238506i	0.279018	−	0.960286i	$-0.409991\pi$
$23$	−1.98118	−	1.14384i	−0.413105	−	0.238506i	−0.692123	+	0.721780i	$0.743324\pi$
$24$	−0.289302	+	4.89043i	−0.0590534	+	0.998255i
$25$	−1.13206	−	1.96079i	−0.226412	−	0.392157i
$26$	−0.569608	+	1.31280i	−0.111709	+	0.257461i
$27$	1.85727	+	4.85289i	0.357431	+	0.933939i
$28$	−5.07996	−	1.48121i	−0.960023	−	0.279923i
$29$	−4.19857	−	7.27213i	−0.779654	−	1.35040i	−0.932141	−	0.362096i	$-0.882061\pi$
$29$	−4.19857	−	7.27213i	−0.779654	−	1.35040i	0.152486	−	0.988306i	$-0.451272\pi$
$30$	2.93767	−	2.79022i	0.536343	−	0.509423i
$31$	−0.348784	+	0.604112i	−0.0626435	+	0.108502i	−0.895646	−	0.444767i	$-0.853286\pi$
$31$	−0.348784	+	0.604112i	−0.0626435	+	0.108502i	0.833003	+	0.553269i	$0.186620\pi$
$32$	−3.05795	−	4.75909i	−0.540575	−	0.841296i
$33$	−8.43384	+	1.03268i	−1.46814	+	0.179767i
$34$	−10.7638	+	1.23486i	−1.84597	+	0.211777i
$35$	2.23130	+	3.76463i	0.377159	+	0.636339i
$36$	−5.03492	−	3.26337i	−0.839153	−	0.543895i
$37$	3.97490			0.653470			0.326735	−	0.945116i	$-0.394051\pi$
$37$	3.97490			0.653470			0.326735	+	0.945116i	$0.394051\pi$
$38$	−0.459573	−	4.00592i	−0.0745525	−	0.649845i
$39$	−1.05431	−	1.40010i	−0.168825	−	0.224195i
$40$	−0.841829	+	4.60200i	−0.133105	+	0.727639i
$41$	6.69947	+	3.86794i	1.04628	+	0.604071i	0.921606	−	0.388127i	$-0.126878\pi$
$41$	6.69947	+	3.86794i	1.04628	+	0.604071i	0.124675	+	0.992198i	$0.460211\pi$
$42$	4.64763	−	4.51658i	0.717145	−	0.696923i
$43$	−6.70811	+	3.87293i	−1.02298	+	0.590617i	−0.914965	−	0.403533i	$-0.867782\pi$
$43$	−6.70811	+	3.87293i	−1.02298	+	0.590617i	−0.108013	+	0.994150i	$0.534449\pi$
$44$	7.16511	−	6.70244i	1.08018	−	1.01043i
$45$	1.19723	+	4.81555i	0.178473	+	0.717860i
$46$	−1.28775	+	2.96793i	−0.189868	+	0.437597i
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	−0.998861	−	0.0477158i	$-0.984806\pi$
$47$	−3.70722	−	6.42109i	−0.540754	−	0.936613i	0.458107	−	0.888897i	$-0.348528\pi$
$48$	6.91767	−	0.381802i	0.998480	−	0.0551084i
$49$	3.63774	+	5.98054i	0.519677	+	0.854363i
$50$	−2.57243	+	1.90659i	−0.363796	+	0.269633i
$51$	5.18884	−	12.2128i	0.726582	−	1.71013i
$52$	1.93629	+	0.588693i	0.268516	+	0.0816370i
$53$	−8.61878			−1.18388			−0.591940	−	0.805982i	$-0.701638\pi$
$53$	−8.61878			−1.18388			−0.591940	+	0.805982i	$0.701638\pi$
$54$	6.51894	−	3.39168i	0.887115	−	0.461549i
$55$	−8.11418			−1.09412
$56$	−1.26228	+	7.37609i	−0.168679	+	0.985671i
$57$	4.54518	+	1.93111i	0.602024	+	0.255782i
$58$	−9.54058	+	7.07115i	−1.25274	+	0.928487i
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	−0.982742	−	0.184981i	$-0.940778\pi$
$59$	−2.54378	+	4.40596i	−0.331172	+	0.573607i	0.651570	+	0.758589i	$0.274111\pi$
$60$	−4.39377	−	3.67768i	−0.567234	−	0.474786i
$61$	5.12759	−	2.96042i	0.656521	−	0.379042i	−0.134429	−	0.990923i	$-0.542920\pi$
$61$	5.12759	−	2.96042i	0.656521	−	0.379042i	0.790950	+	0.611881i	$0.209587\pi$
$62$	0.904996	+	0.392667i	0.114935	+	0.0498687i
$63$	2.00301	+	7.68036i	0.252356	+	0.967634i
$64$	−6.19361	+	5.06352i	−0.774201	+	0.632940i
$65$	−0.836869	−	1.44950i	−0.103801	−	0.179788i
$66$	2.81034	+	11.6831i	0.345929	+	1.43809i
$67$	2.18590	+	1.26203i	0.267051	+	0.154182i	0.627547	−	0.778579i	$-0.284059\pi$
$67$	2.18590	+	1.26203i	0.267051	+	0.154182i	−0.360496	+	0.932761i	$0.617393\pi$
$68$	3.46995	+	14.9241i	0.420793	+	1.80981i
$69$	−2.38355	−	3.16528i	−0.286946	−	0.381055i
$70$	4.92964	−	3.74178i	0.589205	−	0.447229i
$71$			1.00362i			0.119108i	0.998225	+	0.0595539i	$0.0189678\pi$
$71$			1.00362i			0.119108i	−0.998225	+	0.0595539i	$0.981032\pi$
$72$	−3.77347	+	7.60006i	−0.444708	+	0.895676i
$73$			5.89658i			0.690142i	0.938577	+	0.345071i	$0.112145\pi$
$73$			5.89658i			0.690142i	−0.938577	+	0.345071i	$0.887855\pi$
$74$	−0.640700	−	5.58473i	−0.0744799	−	0.649212i
$75$	−0.476618	−	3.89250i	−0.0550351	−	0.449467i
$76$	−5.55423	+	1.29140i	−0.637113	+	0.148133i
$77$	−12.9783	+	0.148439i	−1.47901	+	0.0169162i
$78$	−1.79719	+	1.70698i	−0.203492	+	0.193278i
$79$	4.90752	−	2.83336i	0.552139	−	0.318778i	−0.197845	−	0.980233i	$-0.563394\pi$
$79$	4.90752	−	2.83336i	0.552139	−	0.318778i	0.749984	+	0.661456i	$0.230061\pi$
$80$	6.60149	+	0.440989i	0.738069	+	0.0493041i
$81$	−0.326126	+	8.99409i	−0.0362362	+	0.999343i
$82$	4.35458	−	10.0362i	0.480883	−	1.10831i
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	0.924649	−	0.380820i	$-0.124358\pi$
$83$	1.20736	+	2.09120i	0.132525	+	0.229539i	−0.792125	+	0.610359i	$0.791025\pi$
$84$	−7.09492	−	5.80191i	−0.774119	−	0.633040i
$85$	6.33589	−	10.9741i	0.687224	−	1.19031i
$86$	6.52272	+	8.80062i	0.703363	+	0.948996i
$87$	−1.76767	−	14.4364i	−0.189514	−	1.54775i
$88$	−10.5718	−	8.98662i	−1.12696	−	0.957977i
$89$			8.19734i			0.868916i	0.900692	+	0.434458i	$0.143060\pi$
$89$			8.19734i			0.868916i	−0.900692	+	0.434458i	$0.856940\pi$
$90$	6.57286	−	2.45831i	0.692841	−	0.259129i
$91$	−1.36505	−	2.30310i	−0.143096	−	0.241431i
$92$	4.37750	+	1.33089i	0.456386	+	0.138755i
$93$	−0.965174	+	0.726805i	−0.100084	+	0.0753662i
$94$	−8.42407	+	6.24363i	−0.868876	+	0.643981i
$95$	4.08418	+	2.35800i	0.419028	+	0.241926i
$96$	−1.65146	−	9.65778i	−0.168552	−	0.985693i
$97$	−8.82136	+	5.09301i	−0.895673	+	0.517117i	−0.875794	−	0.482685i	$-0.839662\pi$
$97$	−8.82136	+	5.09301i	−0.895673	+	0.517117i	−0.0198794	+	0.999802i	$0.506328\pi$
$98$	7.81629	−	6.07500i	0.789565	−	0.613667i
$99$	−14.1441	−	4.06600i	−1.42154	−	0.408648i
$100$	3.09340	+	3.30694i	0.309340	+	0.330694i
$101$	0.846450	−	0.488698i	0.0842249	−	0.0486273i	−0.457296	−	0.889315i	$-0.651182\pi$
$101$	0.846450	−	0.488698i	0.0842249	−	0.0486273i	0.541521	+	0.840687i	$0.317849\pi$
$102$	−17.9953	−	5.32177i	−1.78180	−	0.526934i
$103$	6.53514	−	11.3192i	0.643926	−	1.11531i	−0.340622	−	0.940200i	$-0.610638\pi$
$103$	6.53514	−	11.3192i	0.643926	−	1.11531i	0.984548	−	0.175113i	$-0.0560290\pi$
$104$	0.515008	−	2.81538i	0.0505007	−	0.276071i
$105$	1.00722	+	7.51259i	0.0982942	+	0.733154i
$106$	1.38923	+	12.1094i	0.134934	+	1.17617i
$107$			1.03143i			0.0997116i	0.998756	+	0.0498558i	$0.0158762\pi$
$107$			1.03143i			0.0997116i	−0.998756	+	0.0498558i	$0.984124\pi$
$108$	−5.81606	−	8.61240i	−0.559651	−	0.828729i
$109$	−0.842410			−0.0806882			−0.0403441	−	0.999186i	$-0.512845\pi$
$109$	−0.842410			−0.0806882			−0.0403441	+	0.999186i	$0.512845\pi$
$110$	1.30789	+	11.4004i	0.124703	+	1.08699i
$111$	6.33653	+	2.69220i	0.601437	+	0.255532i
$112$	10.5668	+	0.584576i	0.998473	+	0.0552372i
$113$	3.19162	−	5.52804i	0.300242	−	0.520035i	−0.675949	−	0.736949i	$-0.736266\pi$
$113$	3.19162	−	5.52804i	0.300242	−	0.520035i	0.976191	+	0.216914i	$0.0695992\pi$
$114$	1.98058	−	6.69724i	0.185499	−	0.627254i
$115$	−1.89196	−	3.27697i	−0.176426	−	0.305579i
$116$	11.4728	+	12.2647i	1.06522	+	1.13875i
$117$	−0.732435	−	2.94603i	−0.0677136	−	0.272360i
$118$	6.60039	+	2.86383i	0.607615	+	0.263637i
$119$	9.93322	−	17.6685i	0.910577	−	1.61967i
$120$	−4.45892	+	6.76603i	−0.407042	+	0.617651i
$121$	6.53269	−	11.3149i	0.593881	−	1.02863i
$122$	−4.98587	−	6.72707i	−0.451400	−	0.609041i
$123$	8.06010	+	10.7036i	0.726755	+	0.965108i
$124$	0.405823	−	1.33481i	0.0364440	−	0.119869i
$125$		−	12.0152i		−	1.07467i
$126$	10.4680	−	4.05220i	0.932566	−	0.360999i
$127$		−	17.9070i		−	1.58899i	−0.607272	−	0.794494i	$-0.707736\pi$
$127$		−	17.9070i		−	1.58899i	0.607272	−	0.794494i	$-0.292264\pi$
$128$	8.11256	+	7.88584i	0.717056	+	0.697016i
$129$	−13.3168	+	1.63057i	−1.17248	+	0.143564i
$130$	−1.90165	+	1.40944i	−0.166786	+	0.123616i
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	−0.997605	−	0.0691675i	$-0.977966\pi$
$131$	−5.02346	+	8.70089i	−0.438902	+	0.760200i	0.558703	+	0.829368i	$0.311299\pi$
$132$	15.9617	−	5.83167i	1.38929	−	0.507582i
$133$	6.57561	+	3.69681i	0.570177	+	0.320554i
$134$	1.42081	−	3.27461i	0.122740	−	0.282883i
$135$	−1.35302	+	8.48753i	−0.116450	+	0.730490i
$136$	20.4090	−	7.28082i	1.75005	−	0.624325i
$137$	1.97707	+	3.42439i	0.168913	+	0.292566i	0.938038	−	0.346533i	$-0.112641\pi$
$137$	1.97707	+	3.42439i	0.168913	+	0.292566i	−0.769125	+	0.639098i	$0.779308\pi$
$138$	−4.06302	+	3.85909i	−0.345867	+	0.328507i
$139$	4.85060	−	8.40148i	0.411422	−	0.712605i	−0.583623	−	0.812025i	$-0.698365\pi$
$139$	4.85060	−	8.40148i	0.411422	−	0.712605i	0.995046	+	0.0994201i	$0.0316988\pi$
$140$	−6.05179	−	6.32301i	−0.511469	−	0.534392i
$141$	−1.56081	−	12.7470i	−0.131444	−	1.07349i
$142$	1.41008	−	0.161770i	0.118332	−	0.0135754i
$143$	4.96404			0.415114
$144$	11.2863	+	4.07669i	0.940525	+	0.339724i
$145$		−	13.8893i		−	1.15344i
$146$	8.28468	−	0.950447i	0.685645	−	0.0786596i
$147$	1.74843	+	11.9976i	0.144208	+	0.989547i
$148$	−7.74327	+	1.80036i	−0.636493	+	0.147989i
$149$	−3.46856	+	6.00773i	−0.284156	+	0.492172i	−0.972404	−	0.233303i	$-0.925047\pi$
$149$	−3.46856	+	6.00773i	−0.284156	+	0.492172i	0.688248	+	0.725475i	$0.258380\pi$
$150$	−5.39213	+	1.29706i	−0.440266	+	0.105905i
$151$	−10.8500	+	6.26427i	−0.882964	+	0.509779i	−0.871635	−	0.490156i	$-0.836940\pi$
$151$	−10.8500	+	6.26427i	−0.882964	+	0.509779i	−0.0113294	+	0.999936i	$0.503606\pi$
$152$	2.70967	+	7.59552i	0.219784	+	0.616078i
$153$	16.5434	−	15.9544i	1.33746	−	1.28984i
$154$	2.30048	+	18.2105i	0.185378	+	1.46745i
$155$	−0.999232	+	0.576907i	−0.0802602	+	0.0463383i
$156$	2.68799	+	2.24991i	0.215212	+	0.180137i
$157$	1.44619	+	0.834956i	0.115418	+	0.0666367i	0.556598	−	0.830782i	$-0.312106\pi$
$157$	1.44619	+	0.834956i	0.115418	+	0.0666367i	−0.441180	+	0.897419i	$0.645440\pi$
$158$	−4.77189	−	6.43836i	−0.379631	−	0.512208i
$159$	−13.7395	−	5.83749i	−1.08961	−	0.462943i
$160$	−0.444480	−	9.34615i	−0.0351392	−	0.738878i
$161$	−3.08606	−	5.20676i	−0.243215	−	0.410350i
$162$	12.6892	−	0.991517i	0.996961	−	0.0779010i
$163$			7.06914i			0.553698i	0.960913	+	0.276849i	$0.0892901\pi$
$163$			7.06914i			0.553698i	−0.960913	+	0.276849i	$0.910710\pi$
$164$	−14.8027	−	4.50048i	−1.15590	−	0.351429i
$165$	−12.9351	−	5.49573i	−1.00700	−	0.427842i
$166$	2.74352	−	2.03341i	0.212939	−	0.157823i
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	−0.842770	−	0.538274i	$-0.819076\pi$
$167$	0.578614	−	1.00219i	0.0447745	−	0.0775518i	0.887544	+	0.460723i	$0.152410\pi$
$168$	−7.00806	+	10.9035i	−0.540684	+	0.841226i
$169$	−5.98803	−	10.3716i	−0.460617	−	0.797813i
$170$	−16.4398	−	7.13305i	−1.26088	−	0.547080i
$171$	5.93769	+	6.15689i	0.454067	+	0.470830i
$172$	11.3135	−	10.5829i	0.862645	−	0.806942i
$173$	−1.30347	+	0.752561i	−0.0991013	+	0.0572162i	−0.548732	−	0.835999i	$-0.684889\pi$
$173$	−1.30347	+	0.752561i	−0.0991013	+	0.0572162i	0.449630	+	0.893215i	$0.351556\pi$
$174$	−19.9983	+	4.81053i	−1.51606	+	0.364686i
$175$	−0.0685097	−	5.98991i	−0.00517884	−	0.452794i
$176$	−10.9222	+	16.3019i	−0.823288	+	1.22880i
$177$	−7.03929	+	5.30080i	−0.529105	+	0.398432i
$178$	11.5172	−	1.32130i	0.863254	−	0.0990355i
$179$			1.28088i			0.0957374i	0.998854	+	0.0478687i	$0.0152429\pi$
$179$			1.28088i			0.0957374i	−0.998854	+	0.0478687i	$0.984757\pi$
$180$	−4.51338	−	8.83862i	−0.336407	−	0.658792i
$181$			26.6202i			1.97866i	0.145683	+	0.989331i	$0.453462\pi$
$181$			26.6202i			1.97866i	−0.145683	+	0.989331i	$0.546538\pi$
$182$	−3.01582	+	2.28912i	−0.223548	+	0.169681i
$183$	10.1792	−	1.24639i	0.752465	−	0.0921357i
$184$	1.16431	−	6.36490i	0.0858341	−	0.469227i
$185$	5.69385	+	3.28734i	0.418620	+	0.241690i
$186$	1.17673	+	1.23892i	0.0862822	+	0.0908418i
$187$	18.7913	+	32.5474i	1.37415	+	2.38010i
$188$	10.1301	+	10.8294i	0.738815	+	0.789816i
$189$	−2.00883	+	13.6002i	−0.146121	+	0.989267i
$190$	2.65468	−	6.11835i	0.192591	−	0.443872i
$191$	−7.44229	+	4.29681i	−0.538506	+	0.310906i	−0.744473	−	0.667653i	$-0.767299\pi$
$191$	−7.44229	+	4.29681i	−0.538506	+	0.310906i	0.205968	+	0.978559i	$0.433966\pi$
$192$	−13.3030	+	3.87701i	−0.960059	+	0.279799i
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	−0.969882	−	0.243573i	$-0.921680\pi$
$193$	−3.80654	+	6.59312i	−0.274001	+	0.474583i	0.695882	+	0.718156i	$0.255014\pi$
$194$	8.57756	+	11.5731i	0.615833	+	0.830898i
$195$	−0.352337	−	2.87751i	−0.0252314	−	0.206063i
$196$	−9.79524	−	10.0027i	−0.699660	−	0.714476i
$197$	14.3946			1.02557			0.512786	−	0.858517i	$-0.328614\pi$
$197$	14.3946			1.02557			0.512786	+	0.858517i	$0.328614\pi$
$198$	−3.43288	+	20.5278i	−0.243964	+	1.45885i
$199$	−21.9194			−1.55382			−0.776911	−	0.629610i	$-0.783215\pi$
$199$	−21.9194			−1.55382			−0.776911	+	0.629610i	$0.783215\pi$
$200$	4.14763	−	4.87925i	0.293282	−	0.345015i
$201$	2.62985	+	3.49236i	0.185495	+	0.246332i
$202$	−0.823056	−	1.11049i	−0.0579100	−	0.0781337i
$203$	−0.254088	−	22.2153i	−0.0178335	−	1.55921i
$204$	−4.57649	+	26.1411i	−0.320418	+	1.83025i
$205$	6.39776	+	11.0813i	0.446839	+	0.773948i
$206$	−16.9568	−	7.35736i	−1.18144	−	0.512611i
$207$	−1.65586	−	6.66026i	−0.115090	−	0.462920i
$208$	−4.03861	−	0.269785i	−0.280027	−	0.0187062i
$209$	−12.1130	+	6.99347i	−0.837876	+	0.483748i
$210$	10.3928	−	2.62606i	0.717173	−	0.181216i
$211$	1.45464	+	0.839838i	0.100142	+	0.0578168i	0.549234	−	0.835668i	$-0.314919\pi$
$211$	1.45464	+	0.839838i	0.100142	+	0.0578168i	−0.449093	+	0.893485i	$0.648253\pi$
$212$	16.7897	−	3.90373i	1.15312	−	0.268109i
$213$	−0.679751	+	1.59991i	−0.0465758	+	0.109624i
$214$	1.44915	−	0.166252i	0.0990619	−	0.0113647i
$215$	−12.8120			−0.873774
$216$	−11.1629	+	9.55975i	−0.759542	+	0.650459i
$217$	−1.58767	+	0.941016i	−0.107778	+	0.0638803i
$218$	0.135785	+	1.18358i	0.00919651	+	0.0801624i
$219$	−3.99375	+	9.39994i	−0.269873	+	0.635189i
$220$	15.8067	−	3.67518i	1.06569	−	0.247780i
$221$	−3.87613	+	6.71366i	−0.260737	+	0.451609i
$222$	2.76117	−	9.33676i	0.185318	−	0.626642i
$223$	−4.09002	−	7.08413i	−0.273888	−	0.474388i	0.695966	−	0.718075i	$-0.254977\pi$
$223$	−4.09002	−	7.08413i	−0.273888	−	0.474388i	−0.969854	+	0.243687i	$0.921643\pi$
$224$	−0.881903	−	14.9406i	−0.0589246	−	0.998262i
$225$	1.87659	−	6.52798i	0.125106	−	0.435199i
$226$	−8.28133	−	3.59317i	−0.550866	−	0.239014i
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.832000	+	0.554776i	$0.187196\pi$
$227$	13.5064	+	23.3937i	0.896450	+	1.55270i	0.0644498	+	0.997921i	$0.479471\pi$
$228$	−9.72885	−	1.70321i	−0.644309	−	0.112798i
$229$	−10.4216	−	6.01689i	−0.688677	−	0.397608i	0.114439	−	0.993430i	$-0.463493\pi$
$229$	−10.4216	−	6.01689i	−0.688677	−	0.397608i	−0.803116	+	0.595823i	$0.796826\pi$
$230$	−4.29918	+	3.18640i	−0.283480	+	0.210105i
$231$	−20.7897	−	8.55354i	−1.36786	−	0.562782i
$232$	15.3827	−	18.0961i	1.00992	−	1.18807i
$233$	12.9746			0.849992			0.424996	−	0.905195i	$-0.360276\pi$
$233$	12.9746			0.849992			0.424996	+	0.905195i	$0.360276\pi$
$234$	−4.02110	+	1.50393i	−0.262868	+	0.0983148i
$235$		−	12.2639i		−	0.800005i
$236$	2.95978	−	9.73514i	0.192665	−	0.633704i
$237$	9.74228	−	1.19290i	0.632829	−	0.0774869i
$238$	−26.4253	−	11.1082i	−1.71290	−	0.720040i
$239$	−5.65067	−	3.26242i	−0.365512	−	0.211028i	0.305984	−	0.952037i	$-0.401015\pi$
$239$	−5.65067	−	3.26242i	−0.365512	−	0.211028i	−0.671496	+	0.741008i	$0.734348\pi$
$240$	10.2250	+	5.17418i	0.660019	+	0.333992i
$241$	20.0162	−	11.5564i	1.28936	−	0.744410i	0.310817	−	0.950470i	$-0.399397\pi$
$241$	20.0162	−	11.5564i	1.28936	−	0.744410i	0.978539	+	0.206059i	$0.0660640\pi$
$242$	−16.9505	−	7.35460i	−1.08962	−	0.472772i
$243$	−6.61158	+	14.1169i	−0.424133	+	0.905600i
$244$	−8.64787	+	8.08945i	−0.553623	+	0.517874i
$245$	0.264820	+	11.5753i	0.0169188	+	0.739520i
$246$	13.7393	−	13.0497i	0.875986	−	0.832018i
$247$	−2.49859	−	1.44256i	−0.158982	−	0.0917881i
$248$	−1.94082	−	0.355028i	−0.123242	−	0.0225443i
$249$	0.508319	+	4.15140i	0.0322134	+	0.263084i
$250$	−16.8814	+	1.93669i	−1.06767	+	0.122487i
$251$	5.55147			0.350406			0.175203	−	0.984532i	$-0.443942\pi$
$251$	5.55147			0.350406			0.175203	+	0.984532i	$0.443942\pi$
$252$	−7.38063	−	14.0544i	−0.464936	−	0.885344i
$253$	11.2225			0.705553
$254$	−25.1593	+	2.88636i	−1.57863	+	0.181106i
$255$	17.5330	−	13.2029i	1.09796	−	0.826797i
$256$	9.77195	−	12.6692i	0.610747	−	0.791826i
$257$	16.9652	+	9.79486i	1.05826	+	0.610987i	0.924950	−	0.380088i	$-0.124106\pi$
$257$	16.9652	+	9.79486i	1.05826	+	0.610987i	0.133309	+	0.991074i	$0.457440\pi$
$258$	4.43743	+	18.4472i	0.276263	+	1.14847i
$259$	9.16719	+	5.15380i	0.569622	+	0.320241i
$260$	2.28678	+	2.44464i	0.141820	+	0.151610i
$261$	6.95989	−	24.2109i	0.430806	−	1.49862i
$262$	13.0344	+	5.65549i	0.805270	+	0.349397i
$263$	11.4745	−	6.62480i	0.707548	−	0.408503i	−0.102605	−	0.994722i	$-0.532718\pi$
$263$	11.4745	−	6.62480i	0.707548	−	0.408503i	0.810152	+	0.586219i	$0.199384\pi$
$264$	−10.7663	−	21.4862i	−0.662619	−	1.32238i
$265$	−12.3460	−	7.12794i	−0.758406	−	0.437866i
$266$	4.13411	−	9.83459i	0.253479	−	0.602997i
$267$	−5.55205	+	13.0677i	−0.339780	+	0.799728i
$268$	−4.82984	−	1.46842i	−0.295029	−	0.0896980i
$269$			23.5318i			1.43476i	0.696683	+	0.717379i	$0.254658\pi$
$269$			23.5318i			1.43476i	−0.696683	+	0.717379i	$0.745342\pi$
$270$	12.1430	+	0.532920i	0.739002	+	0.0324325i
$271$	20.2947			1.23281			0.616406	−	0.787428i	$-0.288588\pi$
$271$	20.2947			1.23281			0.616406	+	0.787428i	$0.288588\pi$
$272$	−13.5192	−	27.5010i	−0.819721	−	1.66749i
$273$	−0.616188	−	4.59600i	−0.0372934	−	0.278163i
$274$	4.49259	−	3.32975i	0.271407	−	0.201157i
$275$	9.61892	+	5.55349i	0.580043	+	0.334888i
$276$	6.07691	+	5.08650i	0.365787	+	0.306171i
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	0.996789	+	0.0800689i	$0.0255140\pi$
$277$	9.44902	+	16.3662i	0.567736	+	0.983348i	−0.429053	+	0.903279i	$0.641153\pi$
$278$	−12.5859	−	5.46088i	−0.754853	−	0.327522i
$279$	−2.03088	+	0.504913i	−0.121586	+	0.0302284i
$280$	−7.90836	+	9.52193i	−0.472615	+	0.569044i
$281$	−1.06714	−	1.84834i	−0.0636602	−	0.110263i	0.832439	−	0.554117i	$-0.186944\pi$
$281$	−1.06714	−	1.84834i	−0.0636602	−	0.110263i	−0.896099	+	0.443854i	$0.853611\pi$
$282$	−17.6579	+	4.24757i	−1.05151	+	0.252939i
$283$	0.122715	−	0.212549i	0.00729468	−	0.0126347i	−0.862355	−	0.506304i	$-0.831011\pi$
$283$	0.122715	−	0.212549i	0.00729468	−	0.0126347i	0.869650	+	0.493669i	$0.164345\pi$
$284$	−0.454572	−	1.95509i	−0.0269739	−	0.116013i
$285$	4.91366	+	6.52519i	0.291060	+	0.386519i
$286$	−0.800135	−	6.97447i	−0.0473130	−	0.412409i
$287$	10.4357	+	17.6069i	0.615997	+	1.03930i
$288$	3.90855	−	16.5143i	0.230313	−	0.973117i
$289$	−41.6920			−2.45247
$290$	−19.5144	+	2.23876i	−1.14593	+	0.131465i
$291$	−17.5119	+	2.14425i	−1.02657	+	0.125698i
$292$	−2.67075	−	11.4868i	−0.156294	−	0.672212i
$293$	−9.64296	−	5.56736i	−0.563347	−	0.325249i	0.191141	−	0.981563i	$-0.438781\pi$
$293$	−9.64296	−	5.56736i	−0.563347	−	0.325249i	−0.754488	+	0.656314i	$0.772115\pi$
$294$	16.5748	−	4.39039i	0.966663	−	0.256053i
$295$	−7.28768	+	4.20754i	−0.424305	+	0.244973i
$296$	3.77762	+	10.5891i	0.219569	+	0.615478i
$297$	−19.7937	−	16.0616i	−1.14855	−	0.931986i
$298$	8.99993	+	3.90496i	0.521352	+	0.226208i
$299$	1.15745	+	2.00476i	0.0669371	+	0.115939i
$300$	2.69151	+	7.36686i	0.155394	+	0.425326i
$301$	−20.4923	+	0.234381i	−1.18116	+	0.0135095i
$302$	10.5502	+	14.2346i	0.607094	+	0.819108i
$303$	1.68035	−	0.205751i	0.0965336	−	0.0118201i
$304$	10.2349	−	5.03138i	0.587013	−	0.288569i
$305$	9.79335			0.560765
$306$	−25.0825	−	20.6718i	−1.43387	−	1.18173i
$307$	−23.3864			−1.33473			−0.667366	−	0.744730i	$-0.732578\pi$
$307$	−23.3864			−1.33473			−0.667366	+	0.744730i	$0.732578\pi$
$308$	25.2149	−	6.16745i	1.43675	−	0.351423i
$309$	18.0844	−	13.6181i	1.02878	−	0.774705i
$310$	0.971615	+	1.31093i	0.0551840	+	0.0744558i
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.00684678	+	0.999977i	$0.502179\pi$
$311$	−15.3325	+	26.5567i	−0.869428	+	1.50589i	−0.862582	+	0.505918i	$0.831154\pi$
$312$	2.72785	−	4.13928i	0.154434	−	0.234340i
$313$	13.6566	−	7.88467i	0.771919	−	0.445668i	−0.0616396	−	0.998098i	$-0.519633\pi$
$313$	13.6566	−	7.88467i	0.771919	−	0.445668i	0.833559	+	0.552431i	$0.186300\pi$
$314$	0.940006	−	2.16647i	0.0530476	−	0.122261i
$315$	−3.48263	+	12.6583i	−0.196224	+	0.713213i
$316$	−8.27672	+	7.74227i	−0.465602	+	0.435537i
$317$	−3.31354	−	5.73923i	−0.186107	−	0.322347i	0.757842	−	0.652438i	$-0.226254\pi$
$317$	−3.31354	−	5.73923i	−0.186107	−	0.322347i	−0.943949	+	0.330091i	$0.892920\pi$
$318$	−5.98705	+	20.2449i	−0.335737	+	1.13528i
$319$	35.6745	+	20.5967i	1.99739	+	1.15319i
$320$	−13.0597	+	2.13096i	−0.730058	+	0.119125i
$321$	−0.698583	+	1.64423i	−0.0389911	+	0.0917720i
$322$	−6.81806	+	5.17516i	−0.379956	+	0.288400i
$323$		−	21.8432i		−	1.21539i
$324$	−3.43841	−	17.6685i	−0.191023	−	0.981586i
$325$			2.29107i			0.127086i
$326$	9.93212	−	1.13945i	0.550089	−	0.0631082i
$327$	−1.34291	−	0.570563i	−0.0742633	−	0.0315522i
$328$	−3.93718	+	21.5232i	−0.217394	+	1.18842i
$329$	−0.224352	−	19.6155i	−0.0123689	−	1.08144i
$330$	−5.63653	+	19.0596i	−0.310281	+	1.04920i
$331$	−6.89178	+	3.97897i	−0.378807	+	0.218704i	−0.677299	−	0.735708i	$-0.736850\pi$
$331$	−6.89178	+	3.97897i	−0.378807	+	0.218704i	0.298492	+	0.954412i	$0.403516\pi$
$332$	−3.29915	−	3.52689i	−0.181064	−	0.193563i
$333$	8.27786	+	8.58346i	0.453624	+	0.470371i
$334$	−1.50134	−	0.651413i	−0.0821496	−	0.0356437i
$335$	2.08746	+	3.61559i	0.114050	+	0.197541i
$336$	16.4490	+	8.08881i	0.897369	+	0.441281i
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.0139542	+	0.999903i	$0.504442\pi$
$337$	−16.0246	+	27.7555i	−0.872918	+	1.51194i	−0.858964	+	0.512036i	$0.828891\pi$
$338$	−13.6068	+	10.0849i	−0.740114	+	0.548547i
$339$	8.83201	−	6.65077i	0.479689	−	0.361220i
$340$	−7.37204	+	24.2477i	−0.399805	+	1.31502i
$341$		−	3.42203i		−	0.185313i
$342$	7.69335	−	9.33485i	0.416009	−	0.504771i
$343$	0.635325	+	18.5094i	0.0343043	+	0.999411i
$344$	−16.6926	−	14.1896i	−0.900004	−	0.765052i
$345$	−0.796550	−	6.50536i	−0.0428848	−	0.350237i
$346$	1.26745	+	1.71008i	0.0681385	+	0.0919343i
$347$	−2.35072	−	1.35719i	−0.126193	−	0.0728576i	0.435575	−	0.900153i	$-0.356545\pi$
$347$	−2.35072	−	1.35719i	−0.126193	−	0.0728576i	−0.561768	+	0.827295i	$0.689879\pi$
$348$	9.98223	+	27.3221i	0.535104	+	1.46462i
$349$	0.192902	−	0.111372i	0.0103258	−	0.00596160i	−0.494828	−	0.868991i	$-0.664769\pi$
$349$	0.192902	−	0.111372i	0.0103258	−	0.00596160i	0.505154	+	0.863029i	$0.331436\pi$
$350$	−8.40476	+	1.06175i	−0.449253	+	0.0567527i
$351$	0.827742	−	5.19244i	0.0441816	−	0.277152i
$352$	24.6647	+	12.7180i	1.31463	+	0.677869i
$353$	24.5385	−	14.1673i	1.30605	−	0.754049i	0.324617	−	0.945846i	$-0.394765\pi$
$353$	24.5385	−	14.1673i	1.30605	−	0.754049i	0.981435	+	0.191796i	$0.0614312\pi$
$354$	8.58224	+	9.03577i	0.456141	+	0.480246i
$355$	−0.830019	+	1.43763i	−0.0440528	+	0.0763017i
$356$	−3.71284	−	15.9687i	−0.196780	−	0.846341i
$357$	27.8017	−	21.4382i	1.47142	−	1.13463i
$358$	1.79963	−	0.206460i	0.0951135	−	0.0109117i
$359$		−	21.8680i		−	1.15415i	−0.816691	−	0.577075i	$-0.804194\pi$
$359$		−	21.8680i		−	1.15415i	0.816691	−	0.577075i	$-0.195806\pi$
$360$	−11.6907	+	7.76595i	−0.616156	+	0.409301i
$361$	−10.8707			−0.572143
$362$	37.4013	−	4.29081i	1.96577	−	0.225520i
$363$	18.0776	−	13.6130i	0.948827	−	0.714495i
$364$	3.70232	+	3.86825i	0.194054	+	0.202751i
$365$	−4.87662	+	8.44655i	−0.255254	+	0.442113i
$366$	−3.39191	−	14.1008i	−0.177298	−	0.737060i
$367$	−3.75833	−	6.50962i	−0.196183	−	0.339800i	0.751104	−	0.660183i	$-0.229521\pi$
$367$	−3.75833	−	6.50962i	−0.196183	−	0.339800i	−0.947288	+	0.320384i	$0.896188\pi$
$368$	−9.13034	−	0.609920i	−0.475952	−	0.0317943i
$369$	5.59937	+	22.5220i	0.291492	+	1.17245i
$370$	3.70094	−	8.52972i	0.192403	−	0.443439i
$371$	−19.8772	−	11.1750i	−1.03197	−	0.580176i
$372$	1.55100	−	1.85300i	0.0804157	−	0.0960737i
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	−0.705393	−	0.708816i	$-0.749230\pi$
$373$	5.04377	−	8.73606i	0.261156	−	0.452336i	0.966549	+	0.256480i	$0.0825629\pi$
$374$	42.7001	−	31.6479i	2.20797	−	1.63647i
$375$	8.13790	−	19.1539i	0.420239	−	0.989102i
$376$	13.5825	−	15.9784i	0.700462	−	0.824021i
$377$			8.49709i			0.437622i
$378$	19.4320	+	0.630239i	0.999474	+	0.0324160i
$379$			20.7129i			1.06395i	0.846761	+	0.531974i	$0.178550\pi$
$379$			20.7129i			1.06395i	−0.846761	+	0.531974i	$0.821450\pi$
$380$	−9.02416	−	2.74362i	−0.462930	−	0.140745i
$381$	12.1284	−	28.5462i	0.621356	−	1.46246i
$382$	7.23661	+	9.76382i	0.370257	+	0.499561i
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	−0.334926	−	0.942245i	$-0.608711\pi$
$383$	12.6923	−	21.9837i	0.648545	−	1.12331i	0.983471	−	0.181068i	$-0.0579555\pi$
$384$	7.59144	+	18.0657i	0.387399	+	0.921912i
$385$	−18.7135	−	10.5207i	−0.953727	−	0.536186i
$386$	9.87688	+	4.28546i	0.502720	+	0.218124i
$387$	−22.3331	−	6.42009i	−1.13526	−	0.326351i
$388$	14.8776	−	13.9169i	0.755293	−	0.706522i
$389$	15.9336	+	27.5978i	0.807865	+	1.39926i	0.914340	+	0.404947i	$0.132710\pi$
$389$	15.9336	+	27.5978i	0.807865	+	1.39926i	−0.106475	+	0.994315i	$0.533957\pi$
$390$	−3.98610	+	0.958848i	−0.201844	+	0.0485531i
$391$	−8.76301	+	15.1780i	−0.443164	+	0.767583i
$392$	−12.4749	+	15.3746i	−0.630076	+	0.776533i
$393$	−13.9012	+	10.4680i	−0.701222	+	0.528041i
$394$	−2.32021	−	20.2244i	−0.116890	−	1.01889i
$395$	9.37303			0.471608
$396$	29.3949	+	1.51439i	1.47715	+	0.0761009i
$397$		−	10.3571i		−	0.519806i	−0.965635	−	0.259903i	$-0.916309\pi$
$397$		−	10.3571i		−	0.519806i	0.965635	−	0.259903i	$-0.0836906\pi$
$398$	3.53310	+	30.7967i	0.177098	+	1.54370i
$399$	7.97856	+	10.3469i	0.399427	+	0.517991i
$400$	−7.52388	−	5.04094i	−0.376194	−	0.252047i
$401$	9.69923	−	16.7996i	0.484356	−	0.838930i	−0.515482	−	0.856900i	$-0.672387\pi$
$401$	9.69923	−	16.7996i	0.484356	−	0.838930i	0.999839	+	0.0179704i	$0.00572046\pi$
$402$	4.48286	−	4.25785i	0.223585	−	0.212362i
$403$	0.611303	−	0.352936i	0.0304512	−	0.0175810i
$404$	−1.42757	+	1.33539i	−0.0710242	+	0.0664380i
$405$	−7.90549	+	12.6139i	−0.392827	+	0.626788i
$406$	−31.1715	+	3.93779i	−1.54701	+	0.195429i
$407$	−16.8870	+	9.74974i	−0.837060	+	0.483277i
$408$	37.4659	+	2.21636i	1.85484	+	0.109726i
$409$	−14.1825	−	8.18830i	−0.701282	−	0.404885i	0.106543	−	0.994308i	$-0.466022\pi$
$409$	−14.1825	−	8.18830i	−0.701282	−	0.404885i	−0.807825	+	0.589423i	$0.799355\pi$
$410$	14.5379	−	10.7750i	0.717976	−	0.532139i
$411$	0.832384	+	6.79801i	0.0410585	+	0.335321i
$412$	−7.60387	+	25.0102i	−0.374616	+	1.23216i
$413$	−11.5793	+	6.86310i	−0.569782	+	0.337711i
$414$	−9.09076	+	3.40002i	−0.446786	+	0.167102i
$415$			3.99405i			0.196060i
$416$	0.271921	+	5.71773i	0.0133320	+	0.280335i
$417$	13.4228	−	10.1078i	0.657319	−	0.494981i
$418$	11.7783	+	15.8915i	0.576093	+	0.777281i
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	−0.489722	−	0.871879i	$-0.662902\pi$
$419$	10.4437	−	18.0890i	0.510209	−	0.883707i	0.999930	−	0.0118282i	$-0.00376511\pi$
$420$	−5.36479	−	14.1786i	−0.261775	−	0.691845i
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	0.793061	−	0.609143i	$-0.208486\pi$
$421$	−2.68795	−	4.65567i	−0.131003	−	0.226904i	−0.924063	+	0.382239i	$0.875153\pi$
$422$	0.945502	−	2.17914i	0.0460263	−	0.106079i
$423$	6.14539	−	21.3775i	0.298799	−	1.03941i
$424$	−8.19100	−	22.9603i	−0.397790	−	1.11505i
$425$	−15.0217	+	8.67279i	−0.728660	+	0.420692i
$426$	2.35743	+	0.697166i	0.114218	+	0.0337778i
$427$	15.6640	−	0.179157i	0.758035	−	0.00867004i
$428$	−0.467166	−	2.00926i	−0.0225813	−	0.0971210i
$429$	7.91335	+	3.36214i	0.382060	+	0.162326i
$430$	2.06512	+	18.0009i	0.0995892	+	0.868080i
$431$		−	0.569062i		−	0.0274108i	−0.999906	−	0.0137054i	$-0.995637\pi$
$431$		−	0.569062i		−	0.0274108i	0.999906	−	0.0137054i	$-0.00436270\pi$
$432$	15.2307	+	14.1430i	0.732789	+	0.680455i
$433$		−	29.1119i		−	1.39903i	−0.714619	−	0.699514i	$-0.753400\pi$
$433$		−	29.1119i		−	1.39903i	0.714619	−	0.699514i	$-0.246600\pi$
$434$	1.57804	+	2.07900i	0.0757482	+	0.0997951i
$435$	9.40720	−	22.1414i	0.451041	−	1.06160i
$436$	1.64105	−	0.381555i	0.0785919	−	0.0182732i
$437$	−5.64873	−	3.26129i	−0.270215	−	0.156009i
$438$	13.8506	+	4.09607i	0.661809	+	0.195718i
$439$	−0.679870	−	1.17757i	−0.0324484	−	0.0562023i	0.849345	−	0.527838i	$-0.176997\pi$
$439$	−0.679870	−	1.17757i	−0.0324484	−	0.0562023i	−0.881794	+	0.471636i	$0.843664\pi$
$440$	−7.71145	−	21.6160i	−0.367629	−	1.03050i
$441$	−5.33875	+	20.3100i	−0.254226	+	0.967145i
$442$	10.0575	+	4.36381i	0.478384	+	0.207565i
$443$	−3.04716	+	1.75928i	−0.144775	+	0.0835858i	−0.570638	−	0.821202i	$-0.693304\pi$
$443$	−3.04716	+	1.75928i	−0.144775	+	0.0835858i	0.425863	+	0.904788i	$0.359971\pi$
$444$	−13.5632	−	2.37449i	−0.643681	−	0.112688i
$445$	−6.77940	+	11.7423i	−0.321374	+	0.556637i
$446$	−9.29393	+	6.88834i	−0.440080	+	0.326172i
$447$	−9.59839	+	7.22787i	−0.453988	+	0.341867i
$448$	−20.8494	+	3.64729i	−0.985041	+	0.172318i
$449$	13.2772			0.626591			0.313295	−	0.949656i	$-0.398567\pi$
$449$	13.2772			0.626591			0.313295	+	0.949656i	$0.398567\pi$
$450$	−9.47428	−	1.58439i	−0.446622	−	0.0746889i
$451$	−37.9495			−1.78697
$452$	−3.71356	+	12.2144i	−0.174671	+	0.574518i
$453$	−21.5392	+	2.63737i	−1.01200	+	0.123915i
$454$	30.6911	−	22.7472i	1.44040	−	1.06758i
$455$	−0.0506454	−	4.42801i	−0.00237429	−	0.207588i
$456$	−0.824854	+	13.9435i	−0.0386273	+	0.652966i
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	0.998301	+	0.0582701i	$0.0185584\pi$
$457$	11.7494	+	20.3506i	0.549614	+	0.951959i	−0.448687	+	0.893689i	$0.648108\pi$
$458$	−6.77391	+	15.6121i	−0.316524	+	0.729507i
$459$	37.1783	−	14.2287i	1.73534	−	0.664137i
$460$	5.16986	+	5.52674i	0.241046	+	0.257685i
$461$	13.3984	−	7.73555i	0.624024	−	0.360280i	−0.154410	−	0.988007i	$-0.549348\pi$
$461$	13.3984	−	7.73555i	0.624024	−	0.360280i	0.778434	+	0.627726i	$0.216014\pi$
$462$	−8.66670	+	30.5881i	−0.403212	+	1.42309i
$463$	18.2044	+	10.5103i	0.846031	+	0.488456i	0.859310	−	0.511456i	$-0.170894\pi$
$463$	18.2044	+	10.5103i	0.846031	+	0.488456i	−0.0132786	+	0.999912i	$0.504227\pi$
$464$	−27.9045	−	18.6958i	−1.29543	−	0.867929i
$465$	−1.98365	+	0.242888i	−0.0919895	+	0.0112637i
$466$	−2.09132	−	18.2292i	−0.0968786	−	0.844453i
$467$	−29.6578			−1.37240			−0.686199	−	0.727414i	$-0.740722\pi$
$467$	−29.6578			−1.37240			−0.686199	+	0.727414i	$0.740722\pi$
$468$	2.76116	+	5.40723i	0.127635	+	0.249949i
$469$	3.40495	+	5.74479i	0.157226	+	0.265270i
$470$	−17.2307	+	1.97676i	−0.794792	+	0.0911813i
$471$	1.73990	+	2.31053i	0.0801703	+	0.106464i
$472$	−14.1549	−	2.58932i	−0.651534	−	0.119183i
$473$	18.9992	−	32.9076i	0.873586	−	1.51310i
$474$	−3.24634	−	13.4956i	−0.149109	−	0.619874i
$475$	−3.22772	−	5.59057i	−0.148098	−	0.256513i
$476$	−11.3477	+	38.9179i	−0.520119	+	1.78380i
$477$	−17.9489	−	18.6115i	−0.821823	−	0.852162i
$478$	−3.67288	+	8.46504i	−0.167994	+	0.387182i
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	0.911246	−	0.411863i	$-0.135122\pi$
$479$	2.16539	+	3.75057i	0.0989393	+	0.171368i	−0.812307	+	0.583231i	$0.801788\pi$
$480$	5.62158	−	15.2001i	0.256589	−	0.693785i
$481$	−3.48334	−	2.01111i	−0.158827	−	0.0916987i
$482$	−19.4630	−	26.2600i	−0.886515	−	1.19611i
$483$	−1.39305	−	10.3905i	−0.0633861	−	0.472782i
$484$	−7.60102	+	25.0008i	−0.345501	+	1.13640i
$485$	−16.8482			−0.765037
$486$	20.8999	+	7.01380i	0.948040	+	0.318153i
$487$		−	33.3117i		−	1.50950i	−0.656015	−	0.754748i	$-0.727759\pi$
$487$		−	33.3117i		−	1.50950i	0.656015	−	0.754748i	$-0.272241\pi$
$488$	12.7596	+	10.8463i	0.577599	+	0.490990i
$489$	−4.78792	+	11.2692i	−0.216517	+	0.509609i
$490$	16.2206	−	2.23785i	0.732773	−	0.101096i
$491$	27.8604	+	16.0852i	1.25732	+	0.725916i	0.972553	−	0.232680i	$-0.0747495\pi$
$491$	27.8604	+	16.0852i	1.25732	+	0.725916i	0.284770	+	0.958596i	$0.408083\pi$
$492$	−20.5494	−	17.2003i	−0.926437	−	0.775448i
$493$	−55.7123	+	32.1655i	−2.50916	+	1.44866i
$494$	−1.62406	+	3.74304i	−0.0730699	+	0.168407i
$495$	−16.8980	−	17.5219i	−0.759511	−	0.787550i
$496$	−0.185980	+	2.78407i	−0.00835075	+	0.125008i
$497$	−1.30128	+	2.31462i	−0.0583703	+	0.103825i
$498$	5.75077	−	1.38333i	0.257698	−	0.0619887i
$499$	−29.5577	−	17.0652i	−1.32319	−	0.763941i	−0.338950	−	0.940805i	$-0.610072\pi$
$499$	−29.5577	−	17.0652i	−1.32319	−	0.763941i	−0.984235	+	0.176863i	$0.943405\pi$
$500$	5.44208	+	23.4061i	0.243377	+	1.04675i
$501$	1.60117	−	1.20573i	0.0715351	−	0.0538681i
$502$	−0.894821	−	7.79980i	−0.0399378	−	0.348122i
$503$	9.76180			0.435257			0.217629	−	0.976032i	$-0.430168\pi$
$503$	9.76180			0.435257			0.217629	+	0.976032i	$0.430168\pi$
$504$	−18.5568	+	12.6352i	−0.826583	+	0.562814i
$505$	1.61666			0.0719405
$506$	−1.80891	−	15.7676i	−0.0804161	−	0.700956i
$507$	−2.52107	−	20.5894i	−0.111965	−	0.914405i
$508$	8.11066	+	34.8835i	0.359852	+	1.54770i
$509$	−12.0256	−	6.94300i	−0.533027	−	0.307743i	0.209221	−	0.977868i	$-0.432907\pi$
$509$	−12.0256	−	6.94300i	−0.533027	−	0.307743i	−0.742248	+	0.670125i	$0.766240\pi$
$510$	−21.3761	−	22.5057i	−0.946550	−	0.996570i
$511$	−7.64541	+	13.5991i	−0.338213	+	0.601588i
$512$	−19.3753	−	11.6875i	−0.856276	−	0.516518i
$513$	5.29542	+	13.8365i	0.233799	+	0.610897i
$514$	11.0272	−	25.4149i	0.486389	−	1.12100i
$515$	18.7225	−	10.8094i	0.825012	−	0.476321i
$516$	25.2030	−	9.20802i	1.10950	−	0.405361i
$517$	31.4996	+	18.1863i	1.38535	+	0.799833i
$518$	5.76345	−	13.7106i	0.253231	−	0.602410i
$519$	−2.58762	+	0.316842i	−0.113584	+	0.0139078i
$520$	3.06611	−	3.60696i	0.134458	−	0.158176i
$521$			15.9160i			0.697291i	0.937255	+	0.348646i	$0.113358\pi$
$521$			15.9160i			0.697291i	−0.937255	+	0.348646i	$0.886642\pi$
$522$	−35.1381	−	5.87616i	−1.53795	−	0.257193i
$523$	28.0511			1.22659			0.613294	−	0.789855i	$-0.289844\pi$
$523$	28.0511			1.22659			0.613294	+	0.789855i	$0.289844\pi$
$524$	5.84497	−	19.2249i	0.255339	−	0.839846i
$525$	3.94775	−	9.59512i	0.172294	−	0.418765i
$526$	−11.1574	−	15.0538i	−0.486484	−	0.656378i
$527$	4.62815	+	2.67206i	0.201605	+	0.116397i
$528$	−28.4527	+	18.5899i	−1.23824	+	0.809021i
$529$	−8.88328	−	15.3863i	−0.386229	−	0.668969i
$530$	−8.02475	+	18.4950i	−0.348573	+	0.803370i
$531$	−14.8118	+	3.68248i	−0.642777	+	0.159806i
$532$	−14.4839	−	4.22321i	−0.627958	−	0.183100i
$533$	−3.91398	−	6.77921i	−0.169533	−	0.293640i
$534$	19.2549	+	5.69429i	0.833243	+	0.246416i
$535$	−0.853014	+	1.47746i	−0.0368790	+	0.0638763i
$536$	−1.28462	+	7.02260i	−0.0554872	+	0.303330i
$537$	−0.867538	+	2.04189i	−0.0374370	+	0.0881142i
$538$	33.0621	−	3.79300i	1.42541	−	0.163528i
$539$	−30.1238	−	16.4851i	−1.29753	−	0.710063i
$540$	−1.20854	−	17.1469i	−0.0520073	−	0.737883i
$541$	4.98478			0.214313			0.107156	−	0.994242i	$-0.465825\pi$
$541$	4.98478			0.214313			0.107156	+	0.994242i	$0.465825\pi$
$542$	−3.27122	−	28.5140i	−0.140511	−	1.22478i
$543$	−18.0298	+	42.4362i	−0.773734	+	1.82111i
$544$	−36.4597	+	23.4272i	−1.56320	+	1.00443i
$545$	−1.20671	−	0.696694i	−0.0516897	−	0.0298431i
$546$	−6.35805	+	1.60655i	−0.272099	+	0.0687542i
$547$	24.9146	−	14.3844i	1.06527	−	0.615034i	0.138384	−	0.990379i	$-0.455809\pi$
$547$	24.9146	−	14.3844i	1.06527	−	0.615034i	0.926885	+	0.375345i	$0.122476\pi$
$548$	−5.40243	−	5.77536i	−0.230780	−	0.246711i
$549$	17.0711	+	4.90742i	0.728578	+	0.209444i
$550$	6.25220	−	14.4097i	0.266595	−	0.614432i
$551$	−11.9709	−	20.7342i	−0.509978	−	0.883308i
$552$	6.16701	−	9.35792i	0.262485	−	0.398299i
$553$	14.9917	−	0.171468i	0.637514	−	0.00729157i
$554$	21.4714	−	15.9139i	0.912232	−	0.676115i
$555$	6.85025	+	9.09691i	0.290777	+	0.386142i
$556$	−5.64384	+	18.5634i	−0.239352	+	0.787264i
$557$	−24.8923			−1.05472			−0.527360	−	0.849642i	$-0.676818\pi$
$557$	−24.8923			−1.05472			−0.527360	+	0.849642i	$0.676818\pi$
$558$	1.03675	+	2.77200i	0.0438892	+	0.117348i
$559$	7.83806			0.331515
$560$	14.6530	+	9.57642i	0.619203	+	0.404678i
$561$	7.91146	+	64.6123i	0.334022	+	2.72793i
$562$	−2.42491	+	1.79726i	−0.102289	+	0.0758127i
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	−0.963687	−	0.267036i	$-0.913956\pi$
$563$	−5.94575	+	10.2983i	−0.250584	+	0.434024i	0.713103	+	0.701059i	$0.247289\pi$
$564$	8.81404	+	24.1247i	0.371138	+	1.01583i
$565$	9.14366	−	5.27909i	0.384677	−	0.222093i
$566$	−0.318411	−	0.138155i	−0.0133838	−	0.00580708i
$567$	−12.4137	+	20.3199i	−0.521328	+	0.853357i
$568$	−2.67363	+	0.953807i	−0.112183	+	0.0400208i
$569$	2.96159	+	5.12962i	0.124156	+	0.215045i	0.921403	−	0.388609i	$-0.127044\pi$
$569$	2.96159	+	5.12962i	0.124156	+	0.215045i	−0.797247	+	0.603654i	$0.793711\pi$
$570$	8.37586	−	7.95546i	0.350826	−	0.333218i
$571$	−28.8922	−	16.6809i	−1.20910	−	0.698074i	−0.246537	−	0.969133i	$-0.579293\pi$
$571$	−28.8922	−	16.6809i	−1.20910	−	0.698074i	−0.962563	+	0.271059i	$0.912626\pi$
$572$	−9.67014	+	2.24838i	−0.404329	+	0.0940093i
$573$	−14.7742	+	1.80903i	−0.617203	+	0.0755735i
$574$	23.0556	−	17.5001i	0.962322	−	0.730439i
$575$			5.17956i			0.216003i
$576$	−23.8326	−	2.82962i	−0.993025	−	0.117901i
$577$			29.0803i			1.21063i	0.795987	+	0.605314i	$0.206952\pi$
$577$			29.0803i			1.21063i	−0.795987	+	0.605314i	$0.793048\pi$
$578$	6.72017	+	58.5772i	0.279522	+	2.43649i
$579$	−10.5336	+	7.93215i	−0.437763	+	0.329649i
$580$	6.29091	+	27.0568i	0.261216	+	1.12347i
$581$	0.0730664	+	6.38831i	0.00303130	+	0.265032i
$582$	5.83535	+	24.2586i	0.241883	+	1.00555i
$583$	36.6162	−	21.1403i	1.51649	−	0.875544i
$584$	−15.7084	+	5.60391i	−0.650018	+	0.231891i
$585$	1.38726	−	4.82577i	0.0573562	−	0.199521i
$586$	−6.26782	+	14.4457i	−0.258921	+	0.596747i
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	0.978066	−	0.208297i	$-0.0667921\pi$
$587$	7.47781	+	12.9519i	0.308642	+	0.534584i	−0.669423	+	0.742881i	$0.733459\pi$
$588$	−8.84013	−	22.5799i	−0.364561	−	0.931180i
$589$	−0.994450	+	1.72244i	−0.0409756	+	0.0709718i
$590$	7.08626	+	9.56098i	0.291737	+	0.393619i
$591$	22.9469	+	9.74944i	0.943910	+	0.401038i
$592$	14.2687	−	7.01436i	0.586441	−	0.288288i
$593$			15.6604i			0.643096i	0.946893	+	0.321548i	$0.104203\pi$
$593$			15.6604i			0.643096i	−0.946893	+	0.321548i	$0.895797\pi$
$594$	−19.3760	+	30.3990i	−0.795006	+	1.24729i
$595$	28.8411	−	17.0942i	1.18237	−	0.700793i
$596$	4.03580	−	13.2743i	0.165313	−	0.543737i
$597$	−34.9424	−	14.8460i	−1.43010	−	0.607605i
$598$	2.63012	−	1.94936i	0.107554	−	0.0797151i
$599$	−33.5225	−	19.3542i	−1.36969	−	0.790791i	−0.378803	−	0.925477i	$-0.623664\pi$
$599$	−33.5225	−	19.3542i	−1.36969	−	0.790791i	−0.990888	+	0.134686i	$0.956997\pi$
$600$	9.91659	−	4.96900i	0.404843	−	0.202859i
$601$	22.3109	−	12.8812i	0.910081	−	0.525435i	0.0296235	−	0.999561i	$-0.490569\pi$
$601$	22.3109	−	12.8812i	0.910081	−	0.525435i	0.880457	+	0.474126i	$0.157236\pi$
$602$	3.63238	+	28.7538i	0.148045	+	1.17192i
$603$	1.82696	+	7.34849i	0.0743997	+	0.299254i
$604$	18.2990	−	17.1174i	0.744576	−	0.696496i
$605$	18.7155	−	10.8054i	0.760893	−	0.439302i
$606$	−0.559928	−	2.32772i	−0.0227455	−	0.0945573i
$607$	3.14595	−	5.44895i	0.127690	−	0.221166i	−0.795091	−	0.606490i	$-0.792577\pi$
$607$	3.14595	−	5.44895i	0.127690	−	0.221166i	0.922781	+	0.385324i	$0.125910\pi$
$608$	−8.71881	−	13.5691i	−0.353594	−	0.550298i
$609$	14.6413	−	35.5862i	0.593297	−	1.44203i
$610$	−1.57855	−	13.7596i	−0.0639137	−	0.557111i
$611$			7.50270i			0.303527i
$612$	−25.0009	+	38.5729i	−1.01060	+	1.55922i
$613$	22.1645			0.895217			0.447608	−	0.894230i	$-0.352276\pi$
$613$	22.1645			0.895217			0.447608	+	0.894230i	$0.352276\pi$
$614$	3.76957	+	32.8579i	0.152127	+	1.32604i
$615$	2.69357	+	21.9982i	0.108615	+	0.887053i
$616$	−12.7296	−	34.4328i	−0.512888	−	1.38734i
$617$	−20.1769	+	34.9474i	−0.812291	+	1.40693i	0.0989666	+	0.995091i	$0.468446\pi$
$617$	−20.1769	+	34.9474i	−0.812291	+	1.40693i	−0.911257	+	0.411838i	$0.864887\pi$
$618$	−22.0483	−	23.2135i	−0.886913	−	0.933782i
$619$	−19.4800	−	33.7403i	−0.782966	−	1.35614i	−0.930207	−	0.367035i	$-0.880373\pi$
$619$	−19.4800	−	33.7403i	−0.782966	−	1.35614i	0.147241	−	0.989101i	$-0.452961\pi$
$620$	1.68524	−	1.57642i	0.0676809	−	0.0633106i
$621$	1.87133	−	11.7389i	0.0750938	−	0.471065i
$622$	39.7836	+	17.2616i	1.59518	+	0.692127i
$623$	−10.6285	+	18.9053i	−0.425823	+	0.757423i
$624$	−6.25537	−	3.16542i	−0.250415	−	0.126718i
$625$	4.27658	−	7.40725i	0.171063	−	0.296290i
$626$	−13.2792	−	17.9167i	−0.530744	−	0.716094i
$627$	−24.0465	+	2.94438i	−0.960324	+	0.117587i
$628$	−3.19540	−	0.971501i	−0.127510	−	0.0387671i
$629$		−	30.4520i		−	1.21420i
$630$	18.3462	+	2.85275i	0.730930	+	0.113656i
$631$		−	1.06032i		−	0.0422108i	−0.999777	−	0.0211054i	$-0.993281\pi$
$631$		−	1.06032i		−	0.0422108i	0.999777	−	0.0211054i	$-0.00671856\pi$
$632$	12.2120	+	10.3808i	0.485766	+	0.412927i
$633$	1.75007	+	2.32404i	0.0695592	+	0.0923724i
$634$	−7.52950	+	5.58061i	−0.299035	+	0.221634i
$635$	14.8095	−	25.6508i	0.587698	−	1.01792i
$636$	29.4091	+	5.14859i	1.16614	+	0.204155i
$637$	−0.162010	−	7.08147i	−0.00641907	−	0.280578i
$638$	23.1881	−	53.4425i	0.918024	−	2.11581i
$639$	−2.16723	+	2.09007i	−0.0857343	+	0.0826819i
$640$	5.09904	+	18.0053i	0.201557	+	0.711724i
$641$	−13.7294	−	23.7800i	−0.542278	−	0.939253i	−0.998773	−	0.0495272i	$-0.984229\pi$
$641$	−13.7294	−	23.7800i	−0.542278	−	0.939253i	0.456495	−	0.889726i	$-0.349105\pi$
$642$	2.42274	+	0.716481i	0.0956180	+	0.0282772i
$643$	−0.0203966	+	0.0353280i	−0.000804364	+	0.00139320i	−0.866427	−	0.499303i	$-0.833589\pi$
$643$	−0.0203966	+	0.0353280i	−0.000804364	+	0.00139320i	0.865623	+	0.500696i	$0.166923\pi$
$644$	8.37007	+	8.74519i	0.329827	+	0.344609i
$645$	−20.4241	−	8.67759i	−0.804199	−	0.341680i
$646$	−30.6896	+	3.52082i	−1.20747	+	0.138525i
$647$	−12.6901			−0.498899			−0.249449	−	0.968388i	$-0.580250\pi$
$647$	−12.6901			−0.498899			−0.249449	+	0.968388i	$0.580250\pi$
$648$	−24.2700	+	7.67889i	−0.953417	+	0.301655i
$649$		−	24.9578i		−	0.979680i
$650$	3.21895	−	0.369289i	0.126258	−	0.0144847i
$651$	−3.16831	+	0.424777i	−0.124176	+	0.0166483i
$652$	−3.20184	−	13.7709i	−0.125394	−	0.539312i
$653$	−3.40787	+	5.90260i	−0.133360	+	0.230987i	−0.924970	−	0.380041i	$-0.875910\pi$
$653$	−3.40787	+	5.90260i	−0.133360	+	0.230987i	0.791610	+	0.611027i	$0.209243\pi$
$654$	−0.585181	+	1.97876i	−0.0228824	+	0.0773756i
$655$	−14.3917	+	8.30905i	−0.562330	+	0.324661i
$656$	30.8747	+	2.06248i	1.20545	+	0.0805261i
$657$	−12.7331	+	12.2798i	−0.496767	+	0.479081i
$658$	−27.5235	+	3.47696i	−1.07298	+	0.135546i
$659$	−21.9583	+	12.6776i	−0.855375	+	0.493851i	−0.862461	−	0.506124i	$-0.831078\pi$
$659$	−21.9583	+	12.6776i	−0.855375	+	0.493851i	0.00708581	+	0.999975i	$0.497744\pi$
$660$	27.6873	+	4.84716i	1.07773	+	0.188676i
$661$	27.4120	+	15.8263i	1.06620	+	0.615572i	0.927141	−	0.374712i	$-0.122258\pi$
$661$	27.4120	+	15.8263i	1.06620	+	0.615572i	0.139061	+	0.990284i	$0.455592\pi$
$662$	6.70131	+	9.04158i	0.260454	+	0.351411i
$663$	−10.7262	+	8.07717i	−0.416572	+	0.313691i
$664$	−4.42349	+	5.20378i	−0.171665	+	0.201946i
$665$	6.36187	+	10.7337i	0.246703	+	0.416234i
$666$	10.7255	−	13.0139i	0.415603	−	0.504279i
$667$			19.2099i			0.743810i
$668$	−0.673239	+	2.21438i	−0.0260484	+	0.0856768i
$669$	−1.72197	−	14.0632i	−0.0665754	−	0.543716i
$670$	4.74343	−	3.51566i	0.183255	−	0.135822i
$671$	−14.5228	+	25.1541i	−0.560645	+	0.971065i
$672$	8.71340	−	24.4147i	0.336127	−	0.941817i
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	0.820047	−	0.572297i	$-0.193947\pi$
$673$	−2.22066	−	3.84630i	−0.0856002	−	0.148264i	−0.905647	+	0.424033i	$0.860614\pi$
$674$	41.5794	+	18.0408i	1.60158	+	0.694905i
$675$	7.41294	−	9.13547i	0.285324	−	0.351624i
$676$	16.3625	+	17.4920i	0.629328	+	0.672770i
$677$	−5.61421	+	3.24137i	−0.215772	+	0.124576i	−0.603991	−	0.796991i	$-0.706424\pi$
$677$	−5.61421	+	3.24137i	−0.215772	+	0.124576i	0.388219	+	0.921567i	$0.373090\pi$
$678$	−10.7679	−	11.3369i	−0.413539	−	0.435393i
$679$	−26.9479	+	0.308217i	−1.03417	+	0.0118283i
$680$	35.2562	+	6.44931i	1.35201	+	0.247320i
$681$	5.68643	+	46.4406i	0.217904	+	1.77961i
$682$	−4.80794	+	0.551583i	−0.184106	+	0.0211212i
$683$			28.5921i			1.09405i	0.837117	+	0.547024i	$0.184239\pi$
$683$			28.5921i			1.09405i	−0.837117	+	0.547024i	$0.815761\pi$
$684$	−14.3555	−	9.30449i	−0.548897	−	0.355766i
$685$			6.54035i			0.249894i
$686$	25.9032	−	3.87608i	0.988989	−	0.147990i
$687$	−12.5381	−	16.6503i	−0.478360	−	0.635247i
$688$	−17.2457	+	25.7402i	−0.657488	+	0.981337i
$689$	7.55293	+	4.36069i	0.287744	+	0.166129i
$690$	−9.01163	+	2.16773i	−0.343067	+	0.0825239i
$691$	−4.98156	−	8.62831i	−0.189507	−	0.328236i	0.755579	−	0.655058i	$-0.227356\pi$
$691$	−4.98156	−	8.62831i	−0.189507	−	0.328236i	−0.945086	+	0.326822i	$0.894022\pi$
$692$	2.19836	−	2.05640i	0.0835690	−	0.0781728i
$693$	−27.3482	−	27.7163i	−1.03887	−	1.05286i
$694$	−1.52794	+	3.52151i	−0.0579999	+	0.133675i
$695$	13.8965	−	8.02313i	0.527123	−	0.304335i
$696$	36.7785	−	18.4290i	1.39409	−	0.698548i
$697$	29.6326	−	51.3251i	1.12241	−	1.94408i
$698$	−0.187570	−	0.253075i	−0.00709964	−	0.00957902i
$699$	20.6832	+	8.78766i	0.782311	+	0.332380i
$700$	2.84648	+	11.6375i	0.107587	+	0.439857i
$701$	−13.0365			−0.492382			−0.246191	−	0.969221i	$-0.579179\pi$
$701$	−13.0365			−0.492382			−0.246191	+	0.969221i	$0.579179\pi$
$702$	−7.42879	−	0.326026i	−0.280382	−	0.0123051i
$703$	11.3332			0.427440
$704$	13.8931	−	36.7038i	0.523616	−	1.38332i
$705$	8.30630	−	19.5502i	0.312833	−	0.736304i
$706$	−23.8603	−	32.1929i	−0.897994	−	1.21160i
$707$	2.58578	−	0.0295749i	0.0972482	−	0.00111228i
$708$	11.3119	−	13.5145i	0.425127	−	0.507905i
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	0.837113	−	0.547031i	$-0.184242\pi$
$709$	−1.46945	−	2.54516i	−0.0551862	−	0.0955853i	−0.892299	+	0.451445i	$0.850909\pi$
$710$	2.15366	+	0.934447i	0.0808254	+	0.0350692i
$711$	16.3385	+	4.69680i	0.612740	+	0.176144i
$712$	−21.8376	+	7.79047i	−0.818397	+	0.291960i
$713$	1.38201	−	0.797904i	0.0517567	−	0.0298817i
$714$	−34.6018	−	35.6058i	−1.29494	−	1.33252i
$715$	7.11073	+	4.10538i	0.265926	+	0.153533i
$716$	−0.580152	−	2.49520i	−0.0216813	−	0.0932500i
$717$	−6.79830	−	9.02793i	−0.253887	−	0.337154i
$718$	−30.7245	+	3.52482i	−1.14663	+	0.131545i
$719$	52.8108			1.96951			0.984754	−	0.173951i	$-0.0556534\pi$
$719$	52.8108			1.96951			0.984754	+	0.173951i	$0.0556534\pi$
$720$	12.7955	+	15.1737i	0.476861	+	0.565491i
$721$	29.7481	−	17.6317i	1.10788	−	0.656640i
$722$	1.75221	+	15.2733i	0.0652105	+	0.568415i
$723$	39.7356	−	4.86543i	1.47778	−	0.180947i
$724$	−12.0571	−	51.8571i	−0.448100	−	1.92726i
$725$	−9.50606	+	16.4650i	−0.353046	+	0.611494i
$726$	−22.0400	−	23.2048i	−0.817983	−	0.861209i
$727$	13.3309	+	23.0897i	0.494414	+	0.856351i	0.999979	−	0.00643778i	$-0.00204922\pi$
$727$	13.3309	+	23.0897i	0.494414	+	0.856351i	−0.505565	+	0.862789i	$0.668716\pi$
$728$	4.83812	−	5.82526i	0.179313	−	0.215899i
$729$	−20.1011	+	18.0262i	−0.744486	+	0.667638i
$730$	12.6534	+	5.49017i	0.468324	+	0.203200i
$731$	29.6708	+	51.3913i	1.09741	+	1.90078i
$732$	−19.2649	+	7.03848i	−0.712049	+	0.260150i
$733$	23.6033	+	13.6274i	0.871807	+	0.503338i	0.867948	−	0.496654i	$-0.165438\pi$
$733$	23.6033	+	13.6274i	0.871807	+	0.503338i	0.00385894	+	0.999993i	$0.498772\pi$
$734$	−8.54021	+	6.32971i	−0.315225	+	0.233634i
$735$	−7.41780	+	18.6320i	−0.273609	+	0.687251i
$736$	0.614749	+	12.9264i	0.0226599	+	0.476474i
$737$	−12.3822			−0.456103
$738$	30.7408	−	11.4973i	1.13159	−	0.423223i
$739$			42.7029i			1.57085i	0.618957	+	0.785425i	$0.287556\pi$
$739$			42.7029i			1.57085i	−0.618957	+	0.785425i	$0.712444\pi$
$740$	−12.5808	−	3.82494i	−0.462479	−	0.140608i
$741$	−3.00605	−	3.99194i	−0.110430	−	0.146647i
$742$	−12.4969	+	29.7287i	−0.458775	+	1.09137i
$743$	31.9011	+	18.4181i	1.17034	+	0.675695i	0.953760	−	0.300571i	$-0.0971772\pi$
$743$	31.9011	+	18.4181i	1.17034	+	0.675695i	0.216578	+	0.976265i	$0.430510\pi$
$744$	−2.85346	−	1.88048i	−0.104613	−	0.0689416i
$745$	−9.93708	+	5.73718i	−0.364067	+	0.210194i
$746$	−13.0871	−	5.67835i	−0.479154	−	0.207899i
$747$	−2.00141	+	6.96217i	−0.0732278	+	0.254733i
$748$	−51.3479	−	54.8924i	−1.87746	−	2.00707i
$749$	−1.33733	+	2.37874i	−0.0488650	+	0.0869173i
$750$	−28.2229	−	8.34639i	−1.03055	−	0.304767i
$751$	−20.8062	−	12.0125i	−0.759228	−	0.438341i	0.0697904	−	0.997562i	$-0.477767\pi$
$751$	−20.8062	−	12.0125i	−0.759228	−	0.438341i	−0.829019	+	0.559221i	$0.811100\pi$
$752$	−24.6389	−	16.5078i	−0.898487	−	0.601979i
$753$	8.84979	+	3.76001i	0.322504	+	0.137022i
$754$	11.9384	−	1.36961i	0.434771	−	0.0498784i
$755$	−20.7228			−0.754181
$756$	−2.24669	−	27.4035i	−0.0817112	−	0.996656i
$757$	45.4741			1.65279			0.826393	−	0.563094i	$-0.190389\pi$
$757$	45.4741			1.65279			0.826393	+	0.563094i	$0.190389\pi$
$758$	29.1015	−	3.33863i	1.05701	−	0.121264i
$759$	17.8902	+	7.60100i	0.649373	+	0.275899i
$760$	−2.40021	+	13.1212i	−0.0870649	+	0.475955i
$761$	−33.8844	−	19.5632i	−1.22831	−	0.709164i	−0.261633	−	0.965167i	$-0.584261\pi$
$761$	−33.8844	−	19.5632i	−1.22831	−	0.709164i	−0.966676	+	0.256003i	$0.917594\pi$
$762$	−42.0622	−	12.4391i	−1.52375	−	0.450622i
$763$	−1.94282	−	1.09226i	−0.0703349	−	0.0395423i
$764$	12.5517	−	11.7412i	0.454105	−	0.424782i
$765$	36.8923	−	9.17208i	1.33384	−	0.331617i
$766$	−32.9328	−	14.2892i	−1.18991	−	0.516288i
$767$	4.45841	−	2.57406i	0.160984	−	0.0929440i
$768$	24.1587	−	13.5779i	0.871750	−	0.489950i
$769$	14.2130	+	8.20587i	0.512534	+	0.295911i	0.733874	−	0.679285i	$-0.237710\pi$
$769$	14.2130	+	8.20587i	0.512534	+	0.295911i	−0.221341	+	0.975196i	$0.571043\pi$
$770$	−11.7652	+	27.9882i	−0.423990	+	1.00862i
$771$	20.4108	+	27.1048i	0.735075	+	0.976157i
$772$	4.42904	−	14.5677i	0.159405	−	0.524305i
$773$		−	43.6024i		−	1.56827i	−0.620591	−	0.784134i	$-0.713107\pi$
$773$		−	43.6024i		−	1.56827i	0.620591	−	0.784134i	$-0.286893\pi$
$774$	−5.42042	+	32.4128i	−0.194833	+	1.16505i
$775$	1.57938			0.0567330
$776$	−21.9512	−	18.6597i	−0.788003	−	0.669845i
$777$	11.1231	+	14.4248i	0.399038	+	0.517486i
$778$	36.2065	−	26.8350i	1.29807	−	0.962082i
$779$	19.1015	+	11.0282i	0.684380	+	0.395127i
$780$	1.98968	+	5.44591i	0.0712421	+	0.194995i
$781$	−2.46170	−	4.26379i	−0.0880866	−	0.152571i
$782$	22.7375	+	9.86553i	0.813091	+	0.352790i
$783$	27.4930	−	33.8815i	0.982520	−	1.21083i
$784$	23.6120	+	15.0490i	0.843287	+	0.537464i
$785$	1.38106	+	2.39206i	0.0492921	+	0.0853764i
$786$	16.9482	+	17.8438i	0.604522	+	0.636468i
$787$	2.89125	−	5.00779i	0.103062	−	0.178508i	−0.809883	−	0.586592i	$-0.800469\pi$
$787$	2.89125	−	5.00779i	0.103062	−	0.178508i	0.912945	+	0.408083i	$0.133803\pi$
$788$	−28.0412	+	6.51978i	−0.998926	+	0.232257i
$789$	22.7789	−	2.78916i	0.810949	−	0.0992968i
$790$	−1.51080	−	13.1691i	−0.0537520	−	0.468535i
$791$	14.5283	−	8.61095i	0.516567	−	0.306170i
$792$	−2.61034	−	41.5439i	−0.0927544	−	1.47620i
$793$	−5.99131			−0.212758
$794$	−14.5517	+	1.66942i	−0.516419	+	0.0592454i
$795$	−14.8534	−	19.7248i	−0.526795	−	0.699567i
$796$	42.6997	−	9.92799i	1.51345	−	0.351888i
$797$	−11.1404	−	6.43191i	−0.394613	−	0.227830i	0.289544	−	0.957165i	$-0.406496\pi$
$797$	−11.1404	−	6.43191i	−0.394613	−	0.227830i	−0.684157	+	0.729335i	$0.739830\pi$
$798$	13.2513	−	12.8776i	0.469090	−	0.455863i
$799$	−49.1924	+	28.4013i	−1.74030	+	1.00476i
$800$	−5.86976	+	11.3836i	−0.207527	+	0.402470i
$801$	−17.7014	+	17.0712i	−0.625449	+	0.603182i
$802$	−25.1667	−	10.9195i	−0.888668	−	0.385582i
$803$	−14.4633	−	25.0511i	−0.510398	−	0.884035i
$804$	−6.70485	−	5.61210i	−0.236462	−	0.197924i
$805$	−0.114497	−	10.0107i	−0.00403549	−	0.352830i
$806$	−0.594408	−	0.801991i	−0.0209371	−	0.0282489i
$807$	−15.9381	+	37.5128i	−0.561046	+	1.32051i
$808$	2.10632	+	1.79049i	0.0741001	+	0.0629890i
$809$	11.6895			0.410980			0.205490	−	0.978659i	$-0.434121\pi$
$809$	11.6895			0.410980			0.205490	+	0.978659i	$0.434121\pi$
$810$	18.9967	+	9.07402i	0.667476	+	0.318829i
$811$	23.0355			0.808885			0.404443	−	0.914563i	$-0.367466\pi$
$811$	23.0355			0.808885			0.404443	+	0.914563i	$0.367466\pi$
$812$	10.5570	+	43.1611i	0.370478	+	1.51466i
$813$	32.3524	+	13.7456i	1.13465	+	0.482078i
$814$	16.4203	+	22.1547i	0.575532	+	0.776523i
$815$	−5.84635	+	10.1262i	−0.204789	+	0.354705i
$816$	−2.92501	−	52.9968i	−0.102396	−	1.85526i
$817$	−19.1261	+	11.0425i	−0.669138	+	0.386327i
$818$	−9.21851	+	21.2463i	−0.322318	+	0.742859i
$819$	2.13058	−	7.74399i	0.0744485	−	0.270597i
$820$	−17.4821	−	18.6889i	−0.610503	−	0.652646i
$821$	5.85488	+	10.1410i	0.204337	+	0.353922i	0.949921	−	0.312489i	$-0.101163\pi$
$821$	5.85488	+	10.1410i	0.204337	+	0.353922i	−0.745584	+	0.666411i	$0.767830\pi$
$822$	9.41702	−	2.26524i	0.328456	−	0.0790094i
$823$	−30.7319	−	17.7431i	−1.07125	−	0.618484i	−0.142724	−	0.989763i	$-0.545586\pi$
$823$	−30.7319	−	17.7431i	−1.07125	−	0.618484i	−0.928521	+	0.371279i	$0.878919\pi$
$824$	36.3649	+	6.65212i	1.26683	+	0.231737i
$825$	11.5725	+	15.3679i	0.402902	+	0.535041i
$826$	11.5091	+	15.1627i	0.400452	+	0.527578i
$827$		−	28.8739i		−	1.00405i	−0.864854	−	0.502023i	$-0.832589\pi$
$827$		−	28.8739i		−	1.00405i	0.864854	−	0.502023i	$-0.167411\pi$
$828$	6.24233	+	12.2245i	0.216936	+	0.424829i
$829$		−	31.4981i		−	1.09397i	−0.837141	−	0.546987i	$-0.815775\pi$
$829$		−	31.4981i		−	1.09397i	0.837141	−	0.546987i	$-0.184225\pi$
$830$	5.61164	−	0.643786i	0.194783	−	0.0223461i
$831$	3.97821	+	32.4897i	0.138002	+	1.12706i
$832$	7.98956	−	1.30367i	0.276988	−	0.0451965i
$833$	45.8173	−	27.8690i	1.58748	−	0.965603i
$834$	−16.3650	−	17.2298i	−0.566674	−	0.596619i
$835$	1.65767	−	0.957057i	0.0573661	−	0.0331203i
$836$	20.4291	−	19.1099i	0.706555	−	0.660931i
$837$	−3.57948	−	0.570615i	−0.123725	−	0.0197233i
$838$	−27.0984	−	11.7577i	−0.936100	−	0.406162i
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	0.967868	−	0.251458i	$-0.0809102\pi$
$839$	7.70959	+	13.3534i	0.266165	+	0.461011i	−0.701703	+	0.712469i	$0.747577\pi$
$840$	−19.0562	+	9.82292i	−0.657501	+	0.338923i
$841$	−20.7559	+	35.9503i	−0.715722	+	1.23967i
$842$	−6.10795	+	4.52700i	−0.210494	+	0.156011i
$843$	−0.449285	−	3.66928i	−0.0154742	−	0.126377i
$844$	−3.21409	−	0.977182i	−0.110633	−	0.0336360i
$845$		−	19.8090i		−	0.681450i
$846$	−31.0260	−	5.18849i	−1.06669	−	0.178384i
$847$	29.7369	−	17.6251i	1.02177	−	0.605606i
$848$	−30.9389	+	15.2092i	−1.06245	+	0.522287i
$849$	0.339584	−	0.255717i	0.0116545	−	0.00877619i
$850$	14.6065	+	19.7075i	0.501000	+	0.675963i
$851$	−7.87501	−	4.54664i	−0.269952	−	0.155857i
$852$	0.599531	−	3.42456i	0.0205396	−	0.117323i
$853$	−9.82218	+	5.67084i	−0.336305	+	0.194166i	−0.658637	−	0.752461i	$-0.728867\pi$
$853$	−9.82218	+	5.67084i	−0.336305	+	0.194166i	0.322332	+	0.946627i	$0.395533\pi$
$854$	−2.77654	−	21.9790i	−0.0950112	−	0.752107i
$855$	3.41354	+	13.7301i	0.116740	+	0.469558i
$856$	−2.74770	+	0.980232i	−0.0939144	+	0.0335036i
$857$	0.268417	−	0.154971i	0.00916895	−	0.00529370i	−0.495409	−	0.868660i	$-0.664982\pi$
$857$	0.268417	−	0.154971i	0.00916895	−	0.00529370i	0.504577	+	0.863366i	$0.331648\pi$
$858$	3.44828	−	11.6602i	0.117722	−	0.398072i
$859$	−9.88124	+	17.1148i	−0.337144	+	0.583950i	−0.983894	−	0.178752i	$-0.942794\pi$
$859$	−9.88124	+	17.1148i	−0.337144	+	0.583950i	0.646751	+	0.762702i	$0.276127\pi$
$860$	24.9583	−	5.80299i	0.851073	−	0.197880i
$861$	4.71068	+	35.1359i	0.160540	+	1.19743i
$862$	−0.799531	+	0.0917250i	−0.0272321	+	0.00312417i
$863$			23.9730i			0.816051i	0.912970	+	0.408026i	$0.133783\pi$
$863$			23.9730i			0.816051i	−0.912970	+	0.408026i	$0.866217\pi$
$864$	17.4159	−	23.6788i	0.592501	−	0.805570i
$865$	−2.48955			−0.0846472
$866$	−40.9021	+	4.69244i	−1.38991	+	0.159455i
$867$	−66.4626	−	28.2380i	−2.25719	−	0.959011i
$868$	2.66663	−	2.55224i	0.0905113	−	0.0866288i
$869$	−13.8995	+	24.0746i	−0.471507	+	0.816674i
$870$	−32.6249	−	9.64821i	−1.10609	−	0.327105i
$871$	−1.27705	−	2.21192i	−0.0432713	−	0.0749481i
$872$	−0.800598	−	2.24416i	−0.0271117	−	0.0759970i
$873$	−29.3687	−	8.44259i	−0.993979	−	0.285738i
$874$	−3.67161	+	8.46212i	−0.124194	+	0.286236i
$875$	15.5787	−	27.7103i	0.526657	−	0.936779i
$876$	3.52243	−	20.1203i	0.119012	−	0.679803i
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	−0.469524	−	0.882919i	$-0.655575\pi$
$877$	15.6916	−	27.1787i	0.529868	−	0.917759i	0.999393	−	0.0348396i	$-0.0110920\pi$
$878$	−1.54490	+	1.14502i	−0.0521377	+	0.0386427i
$879$	−11.6014	−	15.4063i	−0.391305	−	0.519641i
$880$	−29.1275	+	14.3188i	−0.981888	+	0.482686i
$881$		−	2.85106i		−	0.0960548i	−0.998846	−	0.0480274i	$-0.984707\pi$
$881$		−	2.85106i		−	0.0960548i	0.998846	−	0.0480274i	$-0.0152935\pi$
$882$	29.3961	+	4.22723i	0.989818	+	0.142338i
$883$		−	58.5844i		−	1.97152i	−0.168153	−	0.985761i	$-0.553780\pi$
$883$		−	58.5844i		−	1.97152i	0.168153	−	0.985761i	$-0.446220\pi$
$884$	4.51002	−	14.8341i	0.151688	−	0.498924i
$885$	−14.4673	+	1.77145i	−0.486313	+	0.0595467i
$886$	2.96294	+	3.99768i	0.0995419	+	0.134305i
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	−0.993133	−	0.116987i	$-0.962676\pi$
$887$	−11.7716	+	20.3891i	−0.395253	+	0.684598i	0.597881	+	0.801585i	$0.296010\pi$
$888$	−1.14995	+	19.4390i	−0.0385897	+	0.652330i
$889$	23.2179	−	41.2983i	0.778704	−	1.38510i
$890$	17.5906	+	7.63235i	0.589638	+	0.255837i
$891$	−20.6754	−	39.0106i	−0.692652	−	1.30690i
$892$	11.1762	+	11.9476i	0.374205	+	0.400037i
$893$	−10.5700	−	18.3078i	−0.353711	−	0.612646i
$894$	11.7023	+	12.3207i	0.391383	+	0.412065i
$895$	−1.05932	+	1.83479i	−0.0354091	+	0.0613304i
$896$	8.48508	+	28.7055i	0.283466	+	0.958982i
$897$	0.487308	+	3.97981i	0.0162707	+	0.132882i
$898$	−2.14010	−	18.6545i	−0.0714162	−	0.622508i
$899$	5.85758			0.195361
$900$	−0.698941	+	13.5667i	−0.0232980	+	0.452224i
$901$			66.0291i			2.19975i
$902$	6.11694	+	53.3190i	0.203672	+	1.77533i
$903$	−32.8262	−	13.5058i	−1.09239	−	0.449444i
$904$	17.7598	+	3.24875i	0.590683	+	0.108052i
$905$	−22.0156	+	38.1321i	−0.731822	+	1.26755i
$906$	7.17733	+	29.8374i	0.238451	+	0.991283i
$907$	16.2312	−	9.37107i	0.538947	−	0.311161i	−0.205705	−	0.978614i	$-0.565949\pi$
$907$	16.2312	−	9.37107i	0.538947	−	0.311161i	0.744652	+	0.667453i	$0.232615\pi$
$908$	−36.9067	−	39.4544i	−1.22479	−	1.30934i
$909$	2.81806	+	0.810105i	0.0934691	+	0.0268695i
$910$	−6.21317	+	0.784890i	−0.205965	+	0.0260189i
$911$	27.7633	−	16.0291i	0.919838	−	0.531069i	0.0362544	−	0.999343i	$-0.488457\pi$
$911$	27.7633	−	16.0291i	0.919838	−	0.531069i	0.883583	+	0.468274i	$0.155124\pi$
$912$	19.7236	−	1.08859i	0.653114	−	0.0360468i
$913$	−10.2587	−	5.92286i	−0.339513	−	0.196018i
$914$	26.6987	−	19.7881i	0.883113	−	0.654533i
$915$	15.6119	+	6.63303i	0.516114	+	0.219281i
$916$	23.0269	+	7.00087i	0.760829	+	0.231315i
$917$	−22.8669	+	13.5532i	−0.755131	+	0.447567i
$918$	−25.9839	−	49.9420i	−0.857595	−	1.64833i
$919$			40.9560i			1.35101i	0.737354	+	0.675507i	$0.236075\pi$
$919$			40.9560i			1.35101i	−0.737354	+	0.675507i	$0.763925\pi$
$920$	6.93174	−	8.15448i	0.228533	−	0.268845i
$921$	−37.2811	−	15.8396i	−1.22845	−	0.521932i
$922$	−13.0281	−	17.5778i	−0.429056	−	0.578894i
$923$	0.507783	−	0.879506i	0.0167139	−	0.0289493i
$924$	44.3732	+	7.24631i	1.45977	+	0.238386i
$925$	−4.49983	−	7.79394i	−0.147954	−	0.256263i
$926$	11.8327	−	27.2713i	0.388846	−	0.896190i
$927$	38.0524	−	9.46051i	1.24981	−	0.310724i
$928$	−21.7697	+	42.2192i	−0.714625	+	1.38591i
$929$	20.6442	−	11.9189i	0.677314	−	0.391047i	−0.121528	−	0.992588i	$-0.538779\pi$
$929$	20.6442	−	11.9189i	0.677314	−	0.391047i	0.798842	+	0.601540i	$0.205446\pi$
$930$	0.660994	+	2.74787i	0.0216748	+	0.0901062i
$931$	10.3719	+	17.0517i	0.339925	+	0.558845i
$932$	−25.2749	+	5.87660i	−0.827908	+	0.192495i
$933$	−42.4290	+	31.9503i	−1.38906	+	1.04601i
$934$	4.78042	+	41.6691i	0.156420	+	1.36345i
$935$			62.1633i			2.03296i
$936$	7.15208	−	4.75100i	0.233773	−	0.155291i
$937$			28.7675i			0.939794i	0.882721	+	0.469897i	$0.155709\pi$
$937$			28.7675i			0.939794i	−0.882721	+	0.469897i	$0.844291\pi$
$938$	7.52259	−	5.70992i	0.245621	−	0.186436i
$939$	27.1108	−	3.31959i	0.884728	−	0.108331i
$940$	5.55470	+	23.8904i	0.181174	+	0.779220i
$941$	35.9743	+	20.7698i	1.17273	+	0.677075i	0.954321	−	0.298783i	$-0.0965807\pi$
$941$	35.9743	+	20.7698i	1.17273	+	0.677075i	0.218407	+	0.975858i	$0.429914\pi$
$942$	2.96584	−	2.81698i	0.0966324	−	0.0917822i
$943$	−8.84858	−	15.3262i	−0.288149	−	0.499089i
$944$	−1.35640	+	20.3050i	−0.0441472	+	0.660872i
$945$	−14.1252	+	17.8202i	−0.459493	+	0.579691i
$946$	−49.2976	−	21.3896i	−1.60280	−	0.695437i
$947$	−11.5666	+	6.67800i	−0.375865	+	0.217006i	−0.676018	−	0.736885i	$-0.736296\pi$
$947$	−11.5666	+	6.67800i	−0.375865	+	0.217006i	0.300152	+	0.953891i	$0.402962\pi$
$948$	−18.4380	+	6.73640i	−0.598840	+	0.218788i
$949$	2.98338	−	5.16737i	0.0968447	−	0.167740i
$950$	−7.33448	+	5.43606i	−0.237962	+	0.176369i
$951$	−1.39506	−	11.3934i	−0.0452380	−	0.369455i
$952$	56.5087	+	9.67041i	1.83146	+	0.313420i
$953$	−6.70188			−0.217095			−0.108548	−	0.994091i	$-0.534620\pi$
$953$	−6.70188			−0.217095			−0.108548	+	0.994091i	$0.534620\pi$
$954$	−23.2560	+	28.2181i	−0.752941	+	0.913593i
$955$	−14.2143			−0.459963
$956$	12.4854	+	3.79594i	0.403806	+	0.122769i
$957$	42.9199	+	56.9962i	1.38740	+	1.84243i
$958$	4.92051	−	3.64691i	0.158975	−	0.117826i
$959$	0.119648	+	10.4610i	0.00386363	+	0.337803i
$960$	−22.2622	−	5.44827i	−0.718509	−	0.175842i
$961$	15.2567	+	26.4254i	0.492152	+	0.852432i
$962$	−2.26414	+	5.21825i	−0.0729987	+	0.168243i
$963$	−2.22727	+	2.14798i	−0.0717729	+	0.0692175i
$964$	−33.7581	+	31.5782i	−1.08727	+	1.01707i
$965$	−10.9053	+	6.29620i	−0.351055	+	0.202682i
$966$	−14.3740	+	3.63204i	−0.462477	+	0.116859i
$967$	−18.7298	−	10.8137i	−0.602311	−	0.347744i	0.167639	−	0.985848i	$-0.446386\pi$
$967$	−18.7298	−	10.8137i	−0.602311	−	0.347744i	−0.769950	+	0.638104i	$0.779719\pi$
$968$	36.3513	+	6.64962i	1.16837	+	0.213727i
$969$	14.7944	−	34.8209i	0.475263	−	1.11861i
$970$	2.71570	+	23.6717i	0.0871958	+	0.760052i
$971$	−25.7885			−0.827592			−0.413796	−	0.910370i	$-0.635797\pi$
$971$	−25.7885			−0.827592			−0.413796	+	0.910370i	$0.635797\pi$
$972$	6.48560	−	30.4949i	0.208026	−	0.978123i
$973$	22.0800	−	13.0869i	0.707853	−	0.419545i
$974$	−46.8028	+	5.36938i	−1.49966	+	0.172046i
$975$	−1.55174	+	3.65228i	−0.0496955	+	0.116966i
$976$	13.1824	−	19.6755i	0.421958	−	0.629796i
$977$	18.8498	−	32.6488i	0.603058	−	1.04453i	−0.389298	−	0.921112i	$-0.627282\pi$
$977$	18.8498	−	32.6488i	0.603058	−	1.04453i	0.992355	−	0.123414i	$-0.0393844\pi$
$978$	16.6049	+	4.91059i	0.530966	+	0.157023i
$979$	−20.1066	−	34.8257i	−0.642610	−	1.11303i
$980$	−5.75872	−	22.4292i	−0.183956	−	0.716475i
$981$	−1.75434	−	1.81911i	−0.0560119	−	0.0580797i
$982$	18.1090	−	41.7365i	0.577881	−	1.33187i
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	−0.953240	−	0.302214i	$-0.902274\pi$
$983$	−23.1492	−	40.0956i	−0.738345	−	1.27885i	0.214895	−	0.976637i	$-0.431059\pi$
$984$	−20.8541	+	31.6443i	−0.664803	+	1.00878i
$985$	20.6195	+	11.9047i	0.656992	+	0.379315i
$986$	54.1725	+	73.0910i	1.72521	+	2.32769i
$987$	12.9279	−	31.4217i	0.411500	−	1.00016i
$988$	5.52074	+	1.67847i	0.175638	+	0.0533994i
$989$	17.7200			0.563463
$990$	−21.8945	+	26.5660i	−0.695852	+	0.844323i
$991$			12.6519i			0.401900i	0.979602	+	0.200950i	$0.0644028\pi$
$991$			12.6519i			0.401900i	−0.979602	+	0.200950i	$0.935597\pi$
$992$	3.94159	−	0.187452i	0.125146	−	0.00595162i
$993$	−13.6814	+	1.67522i	−0.434166	+	0.0531615i
$994$	3.46178	+	1.45521i	0.109801	+	0.0461564i
$995$	−31.3984	−	18.1279i	−0.995395	−	0.574692i
$996$	−2.87053	−	7.85685i	−0.0909561	−	0.248954i
$997$	12.9778	−	7.49276i	0.411012	−	0.237298i	−0.280212	−	0.959938i	$-0.590405\pi$
$997$	12.9778	−	7.49276i	0.411012	−	0.237298i	0.691225	+	0.722640i	$0.257072\pi$
$998$	−19.2122	+	44.2792i	−0.608152	+	1.40163i
$999$	7.38246	+	19.2898i	0.233571	+	0.610302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.20	yes	80
3.2	odd	2		756.2.bi.c.307.21		80
4.3	odd	2	inner	252.2.bi.c.139.9	✓	80
7.6	odd	2	inner	252.2.bi.c.139.19	yes	80
9.2	odd	6		756.2.bi.c.559.32		80
9.7	even	3	inner	252.2.bi.c.223.10	yes	80
12.11	even	2		756.2.bi.c.307.31		80
21.20	even	2		756.2.bi.c.307.22		80
28.27	even	2	inner	252.2.bi.c.139.10	yes	80
36.7	odd	6	inner	252.2.bi.c.223.19	yes	80
36.11	even	6		756.2.bi.c.559.22		80
63.20	even	6		756.2.bi.c.559.31		80
63.34	odd	6	inner	252.2.bi.c.223.9	yes	80
84.83	odd	2		756.2.bi.c.307.32		80
252.83	odd	6		756.2.bi.c.559.21		80
252.223	even	6	inner	252.2.bi.c.223.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.9	✓	80	4.3	odd	2	inner
252.2.bi.c.139.10	yes	80	28.27	even	2	inner
252.2.bi.c.139.19	yes	80	7.6	odd	2	inner
252.2.bi.c.139.20	yes	80	1.1	even	1	trivial
252.2.bi.c.223.9	yes	80	63.34	odd	6	inner
252.2.bi.c.223.10	yes	80	9.7	even	3	inner
252.2.bi.c.223.19	yes	80	36.7	odd	6	inner
252.2.bi.c.223.20	yes	80	252.223	even	6	inner
756.2.bi.c.307.21		80	3.2	odd	2
756.2.bi.c.307.22		80	21.20	even	2
756.2.bi.c.307.31		80	12.11	even	2
756.2.bi.c.307.32		80	84.83	odd	2
756.2.bi.c.559.21		80	252.83	odd	6
756.2.bi.c.559.22		80	36.11	even	6
756.2.bi.c.559.31		80	63.20	even	6
756.2.bi.c.559.32		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.161186 - 1.40500i) q^{2} +(1.59413 + 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.694651 - 2.34893i) q^{6} +(2.30627 + 1.29658i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +O(q^{10})\)	\(q+(-0.161186 - 1.40500i) q^{2} +(1.59413 + 0.677299i) q^{3} +(-1.94804 + 0.452933i) q^{4} +(1.43245 + 0.827025i) q^{5} +(0.694651 - 2.34893i) q^{6} +(2.30627 + 1.29658i) q^{7} +(0.950366 + 2.66398i) q^{8} +(2.08253 + 2.15941i) q^{9} +(0.931077 - 2.14589i) q^{10} +(-4.24842 + 2.45282i) q^{11} +(-3.41221 - 0.597369i) q^{12} +(-0.876334 - 0.505952i) q^{13} +(1.44996 - 3.44929i) q^{14} +(1.72337 + 2.28859i) q^{15} +(3.58970 - 1.76466i) q^{16} -7.66107i q^{17} +(2.69829 - 3.27402i) q^{18} +2.85119 q^{19} +(-3.16505 - 0.962273i) q^{20} +(2.79833 + 3.62896i) q^{21} +(4.13100 + 5.57365i) q^{22} +(-1.98118 - 1.14384i) q^{23} +(-0.289302 + 4.89043i) q^{24} +(-1.13206 - 1.96079i) q^{25} +(-0.569608 + 1.31280i) q^{26} +(1.85727 + 4.85289i) q^{27} +(-5.07996 - 1.48121i) q^{28} +(-4.19857 - 7.27213i) q^{29} +(2.93767 - 2.79022i) q^{30} +(-0.348784 + 0.604112i) q^{31} +(-3.05795 - 4.75909i) q^{32} +(-8.43384 + 1.03268i) q^{33} +(-10.7638 + 1.23486i) q^{34} +(2.23130 + 3.76463i) q^{35} +(-5.03492 - 3.26337i) q^{36} +3.97490 q^{37} +(-0.459573 - 4.00592i) q^{38} +(-1.05431 - 1.40010i) q^{39} +(-0.841829 + 4.60200i) q^{40} +(6.69947 + 3.86794i) q^{41} +(4.64763 - 4.51658i) q^{42} +(-6.70811 + 3.87293i) q^{43} +(7.16511 - 6.70244i) q^{44} +(1.19723 + 4.81555i) q^{45} +(-1.28775 + 2.96793i) q^{46} +(-3.70722 - 6.42109i) q^{47} +(6.91767 - 0.381802i) q^{48} +(3.63774 + 5.98054i) q^{49} +(-2.57243 + 1.90659i) q^{50} +(5.18884 - 12.2128i) q^{51} +(1.93629 + 0.588693i) q^{52} -8.61878 q^{53} +(6.51894 - 3.39168i) q^{54} -8.11418 q^{55} +(-1.26228 + 7.37609i) q^{56} +(4.54518 + 1.93111i) q^{57} +(-9.54058 + 7.07115i) q^{58} +(-2.54378 + 4.40596i) q^{59} +(-4.39377 - 3.67768i) q^{60} +(5.12759 - 2.96042i) q^{61} +(0.904996 + 0.392667i) q^{62} +(2.00301 + 7.68036i) q^{63} +(-6.19361 + 5.06352i) q^{64} +(-0.836869 - 1.44950i) q^{65} +(2.81034 + 11.6831i) q^{66} +(2.18590 + 1.26203i) q^{67} +(3.46995 + 14.9241i) q^{68} +(-2.38355 - 3.16528i) q^{69} +(4.92964 - 3.74178i) q^{70} +1.00362i q^{71} +(-3.77347 + 7.60006i) q^{72} +5.89658i q^{73} +(-0.640700 - 5.58473i) q^{74} +(-0.476618 - 3.89250i) q^{75} +(-5.55423 + 1.29140i) q^{76} +(-12.9783 + 0.148439i) q^{77} +(-1.79719 + 1.70698i) q^{78} +(4.90752 - 2.83336i) q^{79} +(6.60149 + 0.440989i) q^{80} +(-0.326126 + 8.99409i) q^{81} +(4.35458 - 10.0362i) q^{82} +(1.20736 + 2.09120i) q^{83} +(-7.09492 - 5.80191i) q^{84} +(6.33589 - 10.9741i) q^{85} +(6.52272 + 8.80062i) q^{86} +(-1.76767 - 14.4364i) q^{87} +(-10.5718 - 8.98662i) q^{88} +8.19734i q^{89} +(6.57286 - 2.45831i) q^{90} +(-1.36505 - 2.30310i) q^{91} +(4.37750 + 1.33089i) q^{92} +(-0.965174 + 0.726805i) q^{93} +(-8.42407 + 6.24363i) q^{94} +(4.08418 + 2.35800i) q^{95} +(-1.65146 - 9.65778i) q^{96} +(-8.82136 + 5.09301i) q^{97} +(7.81629 - 6.07500i) q^{98} +(-14.1441 - 4.06600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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