LMFDB - Embedded newform 841.2.e.l.196.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			196.7
Character	$\chi$	$=$	841.196
Dual form			841.2.e.l.236.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.498437 - 0.113765i) q^{2} +(1.16826 - 2.42591i) q^{3} +(-1.56644 + 0.754358i) q^{4} +(0.490395 + 2.14856i) q^{5} +(0.306319 - 1.34207i) q^{6} +(1.17312 + 0.564943i) q^{7} +(-1.49438 + 1.19173i) q^{8} +(-2.64975 - 3.32268i) q^{9} +(0.488862 + 1.01513i) q^{10} +(3.91583 + 3.12277i) q^{11} +4.68133i q^{12} +(-1.95640 + 2.45325i) q^{13} +(0.648996 + 0.148129i) q^{14} +(5.78512 + 1.32042i) q^{15} +(1.55874 - 1.95460i) q^{16} -1.37659i q^{17} +(-1.69874 - 1.35470i) q^{18} +(2.58255 + 5.36272i) q^{19} +(-2.38896 - 2.99566i) q^{20} +(2.74100 - 2.18588i) q^{21} +(2.30706 + 1.11102i) q^{22} +(-0.192554 + 0.843634i) q^{23} +(1.14521 + 5.01749i) q^{24} +(0.129021 - 0.0621331i) q^{25} +(-0.696049 + 1.44536i) q^{26} +(-3.28098 + 0.748862i) q^{27} -2.26379 q^{28} +3.03374 q^{30} +(2.67520 - 0.610597i) q^{31} +(2.21321 - 4.59578i) q^{32} +(12.1503 - 5.85126i) q^{33} +(-0.156607 - 0.686142i) q^{34} +(-0.638524 + 2.79756i) q^{35} +(6.65717 + 3.20593i) q^{36} +(4.61280 - 3.67858i) q^{37} +(1.89733 + 2.37918i) q^{38} +(3.66578 + 7.61208i) q^{39} +(-3.29335 - 2.62636i) q^{40} +1.90869i q^{41} +(1.11754 - 1.40135i) q^{42} +(-10.7381 - 2.45090i) q^{43} +(-8.48960 - 1.93770i) q^{44} +(5.83956 - 7.32258i) q^{45} +0.442405i q^{46} +(2.24903 + 1.79354i) q^{47} +(-2.92068 - 6.06485i) q^{48} +(-3.30739 - 4.14733i) q^{49} +(0.0572401 - 0.0456475i) q^{50} +(-3.33948 - 1.60821i) q^{51} +(1.21396 - 5.31869i) q^{52} +(1.29129 + 5.65752i) q^{53} +(-1.55017 + 0.746522i) q^{54} +(-4.78915 + 9.94478i) q^{55} +(-2.42635 + 0.553798i) q^{56} +16.0266 q^{57} -4.35304 q^{59} +(-10.0581 + 2.29570i) q^{60} +(-2.35836 + 4.89717i) q^{61} +(1.26396 - 0.608689i) q^{62} +(-1.23134 - 5.39485i) q^{63} +(-0.532309 + 2.33220i) q^{64} +(-6.23036 - 3.00038i) q^{65} +(5.39047 - 4.29876i) q^{66} +(1.47317 + 1.84730i) q^{67} +(1.03844 + 2.15634i) q^{68} +(1.82163 + 1.45270i) q^{69} +1.46705i q^{70} +(9.72005 - 12.1886i) q^{71} +(7.91950 + 1.80757i) q^{72} +(3.31130 + 0.755782i) q^{73} +(1.88070 - 2.35832i) q^{74} -0.385580i q^{75} +(-8.09083 - 6.45222i) q^{76} +(2.82954 + 5.87559i) q^{77} +(2.69315 + 3.37711i) q^{78} +(-1.65445 + 1.31938i) q^{79} +(4.96397 + 2.39052i) q^{80} +(0.820701 - 3.59573i) q^{81} +(0.217143 + 0.951364i) q^{82} +(-5.72931 + 2.75909i) q^{83} +(-2.64468 + 5.49174i) q^{84} +(2.95768 - 0.675070i) q^{85} -5.63110 q^{86} -9.57325 q^{88} +(11.6336 - 2.65530i) q^{89} +(2.07760 - 4.31419i) q^{90} +(-3.68103 + 1.77269i) q^{91} +(-0.334778 - 1.46676i) q^{92} +(1.64407 - 7.20313i) q^{93} +(1.32504 + 0.638106i) q^{94} +(-10.2557 + 8.17862i) q^{95} +(-8.56336 - 10.7381i) q^{96} +(-4.95650 - 10.2923i) q^{97} +(-2.12035 - 1.69092i) q^{98} -21.2856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 16 q^{4} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 12 q^{9} - 12 q^{13} - 8 q^{16} + 10 q^{20} - 8 q^{22} + 10 q^{23} + 20 q^{24} - 12 q^{25} + 60 q^{28} + 312 q^{30} + 54 q^{33} - 8 q^{35} + 42 q^{36} + 82 q^{38}+ \cdots - 74 q^{96}+O(q^{100}) $ 72 * q + 16 * q^4 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 12 * q^9 - 12 * q^13 - 8 * q^16 + 10 * q^20 - 8 * q^22 + 10 * q^23 + 20 * q^24 - 12 * q^25 + 60 * q^28 + 312 * q^30 + 54 * q^33 - 8 * q^35 + 42 * q^36 + 82 * q^38 - 42 * q^42 - 32 * q^45 + 24 * q^49 - 46 * q^51 + 26 * q^53 - 38 * q^54 + 192 * q^57 - 204 * q^59 - 18 * q^63 + 2 * q^64 - 64 * q^65 - 18 * q^67 + 72 * q^74 + 10 * q^80 + 44 * q^81 - 38 * q^82 + 48 * q^83 - 204 * q^86 + 252 * q^88 + 32 * q^91 - 46 * q^92 - 24 * q^93 + 74 * q^94 - 74 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

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 $

$2$	0.498437	−	0.113765i	0.352448	−	0.0804440i	−0.0426314	−	0.999091i	$-0.513574\pi$
$2$	0.498437	−	0.113765i	0.352448	−	0.0804440i	0.395080	+	0.918647i	$0.370717\pi$
$3$	1.16826	−	2.42591i	0.674494	−	1.40060i	−0.229608	−	0.973283i	$-0.573744\pi$
$3$	1.16826	−	2.42591i	0.674494	−	1.40060i	0.904102	−	0.427318i	$-0.140541\pi$
$4$	−1.56644	+	0.754358i	−0.783220	+	0.377179i
$5$	0.490395	+	2.14856i	0.219311	+	0.960865i	0.957989	+	0.286806i	$0.0925936\pi$
$5$	0.490395	+	2.14856i	0.219311	+	0.960865i	−0.738677	+	0.674059i	$0.764549\pi$
$6$	0.306319	−	1.34207i	0.125054	−	0.547898i
$7$	1.17312	+	0.564943i	0.443396	+	0.213528i	0.642241	−	0.766503i	$-0.278005\pi$
$7$	1.17312	+	0.564943i	0.443396	+	0.213528i	−0.198845	+	0.980031i	$0.563719\pi$
$8$	−1.49438	+	1.19173i	−0.528345	+	0.421341i
$9$	−2.64975	−	3.32268i	−0.883251	−	1.10756i
$10$	0.488862	+	1.01513i	0.154592	+	0.321013i
$11$	3.91583	+	3.12277i	1.18067	+	0.941550i	0.999125	−	0.0418330i	$-0.0133197\pi$
$11$	3.91583	+	3.12277i	1.18067	+	0.941550i	0.181542	+	0.983383i	$0.441891\pi$
$12$			4.68133i			1.35138i
$13$	−1.95640	+	2.45325i	−0.542608	+	0.680409i	−0.975237	−	0.221164i	$-0.929015\pi$
$13$	−1.95640	+	2.45325i	−0.542608	+	0.680409i	0.432629	+	0.901572i	$0.357586\pi$
$14$	0.648996	+	0.148129i	0.173451	+	0.0395891i
$15$	5.78512	+	1.32042i	1.49371	+	0.340930i
$16$	1.55874	−	1.95460i	0.389685	−	0.488650i
$17$		−	1.37659i		−	0.333871i	−0.985968	−	0.166936i	$-0.946613\pi$
$17$		−	1.37659i		−	0.333871i	0.985968	−	0.166936i	$-0.0533872\pi$
$18$	−1.69874	−	1.35470i	−0.400397	−	0.319306i
$19$	2.58255	+	5.36272i	0.592478	+	1.23029i	0.954524	+	0.298133i	$0.0963640\pi$
$19$	2.58255	+	5.36272i	0.592478	+	1.23029i	−0.362046	+	0.932160i	$0.617922\pi$
$20$	−2.38896	−	2.99566i	−0.534187	−	0.669850i
$21$	2.74100	−	2.18588i	0.598136	−	0.476998i
$22$	2.30706	+	1.11102i	0.491866	+	0.236870i
$23$	−0.192554	+	0.843634i	−0.0401503	+	0.175910i	−0.991027	−	0.133659i	$-0.957327\pi$
$23$	−0.192554	+	0.843634i	−0.0401503	+	0.175910i	0.950877	+	0.309568i	$0.100185\pi$
$24$	1.14521	+	5.01749i	0.233765	+	1.02419i
$25$	0.129021	−	0.0621331i	0.0258041	−	0.0124266i
$26$	−0.696049	+	1.44536i	−0.136506	+	0.283458i
$27$	−3.28098	+	0.748862i	−0.631425	+	0.144119i
$28$	−2.26379			−0.427815
$29$		0			0
$29$		0			0
$30$	3.03374			0.553882
$31$	2.67520	−	0.610597i	0.480480	−	0.109666i	0.0245809	−	0.999698i	$-0.492175\pi$
$31$	2.67520	−	0.610597i	0.480480	−	0.109666i	0.455899	+	0.890031i	$0.349318\pi$
$32$	2.21321	−	4.59578i	0.391244	−	0.812427i
$33$	12.1503	−	5.85126i	2.11509	−	1.01857i
$34$	−0.156607	−	0.686142i	−0.0268579	−	0.117672i
$35$	−0.638524	+	2.79756i	−0.107930	+	0.472873i
$36$	6.65717	+	3.20593i	1.10953	+	0.534321i
$37$	4.61280	−	3.67858i	0.758339	−	0.604755i	−0.166089	−	0.986111i	$-0.553114\pi$
$37$	4.61280	−	3.67858i	0.758339	−	0.604755i	0.924428	+	0.381356i	$0.124543\pi$
$38$	1.89733	+	2.37918i	0.307788	+	0.385954i
$39$	3.66578	+	7.61208i	0.586995	+	1.21891i
$40$	−3.29335	−	2.62636i	−0.520724	−	0.415263i
$41$			1.90869i			0.298088i	0.988831	+	0.149044i	$0.0476196\pi$
$41$			1.90869i			0.298088i	−0.988831	+	0.149044i	$0.952380\pi$
$42$	1.11754	−	1.40135i	0.172440	−	0.216233i
$43$	−10.7381	−	2.45090i	−1.63755	−	0.373759i	−0.697978	−	0.716119i	$-0.745917\pi$
$43$	−10.7381	−	2.45090i	−1.63755	−	0.373759i	−0.939569	+	0.342360i	$0.888774\pi$
$44$	−8.48960	−	1.93770i	−1.27985	−	0.292119i
$45$	5.83956	−	7.32258i	0.870511	−	1.09159i
$46$			0.442405i			0.0652290i
$47$	2.24903	+	1.79354i	0.328054	+	0.261615i	0.773641	−	0.633624i	$-0.218433\pi$
$47$	2.24903	+	1.79354i	0.328054	+	0.261615i	−0.445587	+	0.895239i	$0.647005\pi$
$48$	−2.92068	−	6.06485i	−0.421563	−	0.875385i
$49$	−3.30739	−	4.14733i	−0.472484	−	0.592476i
$50$	0.0572401	−	0.0456475i	0.00809498	−	0.00645553i
$51$	−3.33948	−	1.60821i	−0.467620	−	0.225194i
$52$	1.21396	−	5.31869i	0.168346	−	0.737570i
$53$	1.29129	+	5.65752i	0.177373	+	0.777121i	0.982837	+	0.184476i	$0.0590589\pi$
$53$	1.29129	+	5.65752i	0.177373	+	0.777121i	−0.805464	+	0.592644i	$0.798084\pi$
$54$	−1.55017	+	0.746522i	−0.210951	+	0.101589i
$55$	−4.78915	+	9.94478i	−0.645769	+	1.34095i
$56$	−2.42635	+	0.553798i	−0.324234	+	0.0740043i
$57$	16.0266			2.12277
$58$		0			0
$59$	−4.35304			−0.566717			−0.283359	−	0.959014i	$-0.591449\pi$
$59$	−4.35304			−0.566717			−0.283359	+	0.959014i	$0.591449\pi$
$60$	−10.0581	+	2.29570i	−1.29850	+	0.296374i
$61$	−2.35836	+	4.89717i	−0.301956	+	0.627019i	−0.995642	−	0.0932591i	$-0.970272\pi$
$61$	−2.35836	+	4.89717i	−0.301956	+	0.627019i	0.693685	+	0.720278i	$0.255986\pi$
$62$	1.26396	−	0.608689i	0.160522	−	0.0773035i
$63$	−1.23134	−	5.39485i	−0.155134	−	0.679688i
$64$	−0.532309	+	2.33220i	−0.0665386	+	0.291525i
$65$	−6.23036	−	3.00038i	−0.772781	−	0.372152i
$66$	5.39047	−	4.29876i	0.663521	−	0.529141i
$67$	1.47317	+	1.84730i	0.179976	+	0.225683i	0.863634	−	0.504120i	$-0.168183\pi$
$67$	1.47317	+	1.84730i	0.179976	+	0.225683i	−0.683657	+	0.729803i	$0.739612\pi$
$68$	1.03844	+	2.15634i	0.125929	+	0.261495i
$69$	1.82163	+	1.45270i	0.219298	+	0.174885i
$70$			1.46705i			0.175346i
$71$	9.72005	−	12.1886i	1.15356	−	1.44651i	0.279863	−	0.960040i	$-0.409711\pi$
$71$	9.72005	−	12.1886i	1.15356	−	1.44651i	0.873695	−	0.486475i	$-0.161718\pi$
$72$	7.91950	+	1.80757i	0.933322	+	0.213025i
$73$	3.31130	+	0.755782i	0.387558	+	0.0884576i	0.411860	−	0.911247i	$-0.364879\pi$
$73$	3.31130	+	0.755782i	0.387558	+	0.0884576i	−0.0243021	+	0.999705i	$0.507736\pi$
$74$	1.88070	−	2.35832i	0.218626	−	0.274149i
$75$		−	0.385580i		−	0.0445230i
$76$	−8.09083	−	6.45222i	−0.928082	−	0.740120i
$77$	2.82954	+	5.87559i	0.322455	+	0.669586i
$78$	2.69315	+	3.37711i	0.304939	+	0.382382i
$79$	−1.65445	+	1.31938i	−0.186141	+	0.148442i	−0.712127	−	0.702051i	$-0.752268\pi$
$79$	−1.65445	+	1.31938i	−0.186141	+	0.148442i	0.525986	+	0.850493i	$0.323696\pi$
$80$	4.96397	+	2.39052i	0.554989	+	0.267269i
$81$	0.820701	−	3.59573i	0.0911890	−	0.399525i
$82$	0.217143	+	0.951364i	0.0239794	+	0.105061i
$83$	−5.72931	+	2.75909i	−0.628874	+	0.302850i	−0.721039	−	0.692894i	$-0.756335\pi$
$83$	−5.72931	+	2.75909i	−0.628874	+	0.302850i	0.0921658	+	0.995744i	$0.470621\pi$
$84$	−2.64468	+	5.49174i	−0.288559	+	0.599198i
$85$	2.95768	−	0.675070i	0.320805	−	0.0732217i
$86$	−5.63110			−0.607217
$87$		0			0
$88$	−9.57325			−1.02051
$89$	11.6336	−	2.65530i	1.23316	−	0.281461i	0.444214	−	0.895921i	$-0.353483\pi$
$89$	11.6336	−	2.65530i	1.23316	−	0.281461i	0.788949	+	0.614459i	$0.210626\pi$
$90$	2.07760	−	4.31419i	0.218998	−	0.454755i
$91$	−3.68103	+	1.77269i	−0.385877	+	0.185828i
$92$	−0.334778	−	1.46676i	−0.0349030	−	0.152920i
$93$	1.64407	−	7.20313i	0.170482	−	0.746930i
$94$	1.32504	+	0.638106i	0.136668	+	0.0658156i
$95$	−10.2557	+	8.17862i	−1.05221	+	0.839109i
$96$	−8.56336	−	10.7381i	−0.873994	−	1.09595i
$97$	−4.95650	−	10.2923i	−0.503256	−	1.04502i	−0.985608	−	0.169045i	$-0.945932\pi$
$97$	−4.95650	−	10.2923i	−0.503256	−	1.04502i	0.482352	−	0.875977i	$-0.339783\pi$
$98$	−2.12035	−	1.69092i	−0.214187	−	0.170809i
$99$		−	21.2856i		−	2.13929i
$100$	−0.155233	+	0.194655i	−0.0155233	+	0.0194655i
$101$	0.950079	+	0.216849i	0.0945364	+	0.0215773i	0.269527	−	0.962993i	$-0.413133\pi$
$101$	0.950079	+	0.216849i	0.0945364	+	0.0215773i	−0.174991	+	0.984570i	$0.555990\pi$
$102$	−1.84748	−	0.421674i	−0.182927	−	0.0417520i
$103$	−4.84899	+	6.08044i	−0.477785	+	0.599124i	−0.961058	−	0.276346i	$-0.910876\pi$
$103$	−4.84899	+	6.08044i	−0.477785	+	0.599124i	0.483273	+	0.875470i	$0.339448\pi$
$104$		−	5.99760i		−	0.588113i
$105$	6.04066	+	4.81727i	0.589508	+	0.470117i
$106$	1.28726	+	2.67302i	0.125029	+	0.259626i
$107$	−3.39760	−	4.26045i	−0.328458	−	0.411874i	0.589993	−	0.807409i	$-0.299131\pi$
$107$	−3.39760	−	4.26045i	−0.328458	−	0.411874i	−0.918451	+	0.395535i	$0.870559\pi$
$108$	4.57455	−	3.64808i	0.440186	−	0.351037i
$109$	−7.11000	−	3.42400i	−0.681015	−	0.327960i	0.0611961	−	0.998126i	$-0.480509\pi$
$109$	−7.11000	−	3.42400i	−0.681015	−	0.327960i	−0.742211	+	0.670166i	$0.766223\pi$
$110$	−1.25572	+	5.50169i	−0.119729	+	0.524565i
$111$	−3.53498	−	15.4878i	−0.335526	−	1.47003i
$112$	2.93282	−	1.41237i	0.277126	−	0.133457i
$113$	7.50659	−	15.5876i	0.706161	−	1.46636i	−0.170555	−	0.985348i	$-0.554556\pi$
$113$	7.50659	−	15.5876i	0.706161	−	1.46636i	0.876715	−	0.481009i	$-0.159730\pi$
$114$	7.98825	−	1.82326i	0.748168	−	0.170764i
$115$	−1.90703			−0.177831
$116$		0			0
$117$	13.3353			1.23285
$118$	−2.16972	+	0.495224i	−0.199739	+	0.0455890i
$119$	0.777692	−	1.61489i	0.0712909	−	0.148037i
$120$	−10.2188	+	4.92111i	−0.932843	+	0.449233i
$121$	3.13430	+	13.7322i	0.284936	+	1.24839i
$122$	−0.618365	+	2.70923i	−0.0559841	+	0.245282i
$123$	4.63032	+	2.22984i	0.417502	+	0.201058i
$124$	−3.72993	+	2.97452i	−0.334958	+	0.267120i
$125$	7.06705	+	8.86180i	0.632096	+	0.792623i
$126$	−1.22749	−	2.54891i	−0.109354	−	0.227075i
$127$	4.31272	+	3.43928i	0.382692	+	0.305187i	0.795875	−	0.605462i	$-0.207011\pi$
$127$	4.31272	+	3.43928i	0.382692	+	0.305187i	−0.413183	+	0.910648i	$0.635583\pi$
$128$			11.4249i			1.00983i
$129$	−18.4906	+	23.1864i	−1.62800	+	2.04145i
$130$	−3.44678	−	0.786705i	−0.302303	−	0.0689986i
$131$	−0.0275831	−	0.00629566i	−0.00240995	−	0.000550054i	0.221316	−	0.975202i	$-0.428965\pi$
$131$	−0.0275831	−	0.00629566i	−0.00240995	−	0.000550054i	−0.223726	+	0.974652i	$0.571822\pi$
$132$	−14.6187	+	18.3313i	−1.27240	+	1.59553i
$133$			7.75009i			0.672018i
$134$	0.944440	+	0.753166i	0.0815872	+	0.0650636i
$135$	−3.21795	−	6.68215i	−0.276957	−	0.575108i
$136$	1.64052	+	2.05715i	0.140673	+	0.176399i
$137$	−4.81191	+	3.83737i	−0.411109	+	0.327849i	−0.807110	−	0.590402i	$-0.798969\pi$
$137$	−4.81191	+	3.83737i	−0.411109	+	0.327849i	0.396000	+	0.918250i	$0.370398\pi$
$138$	1.07323	+	0.516843i	0.0913598	+	0.0439966i
$139$	−2.76107	+	12.0971i	−0.234191	+	1.02606i	0.711931	+	0.702249i	$0.247821\pi$
$139$	−2.76107	+	12.0971i	−0.234191	+	1.02606i	−0.946122	+	0.323809i	$0.895036\pi$
$140$	−1.11015	−	4.86388i	−0.0938247	−	0.411073i
$141$	6.97841	−	3.36062i	0.587688	−	0.283016i
$142$	3.45820	−	7.18103i	0.290206	−	0.602619i
$143$	−15.3219	+	3.49711i	−1.28128	+	0.292443i
$144$	−10.6248			−0.885400
$145$		0			0
$146$	1.73646			0.143710
$147$	−13.9249	+	3.17828i	−1.14851	+	0.262140i
$148$	−4.45070	+	9.24198i	−0.365845	+	0.759686i
$149$	−18.7471	+	9.02813i	−1.53582	+	0.739614i	−0.994844	−	0.101422i	$-0.967661\pi$
$149$	−18.7471	+	9.02813i	−1.53582	+	0.739614i	−0.540980	+	0.841035i	$0.681947\pi$
$150$	−0.0438655	−	0.192187i	−0.00358161	−	0.0156920i
$151$	4.45672	−	19.5262i	0.362683	−	1.58902i	−0.383672	−	0.923469i	$-0.625341\pi$
$151$	4.45672	−	19.5262i	0.362683	−	1.58902i	0.746355	−	0.665548i	$-0.231802\pi$
$152$	−10.2503	−	4.93626i	−0.831405	−	0.400384i
$153$	−4.57396	+	3.64761i	−0.369783	+	0.294892i
$154$	2.07878	+	2.60671i	0.167513	+	0.210055i
$155$	2.62381	+	5.44840i	0.210749	+	0.437626i
$156$	−11.4845	−	9.15855i	−0.919493	−	0.733271i
$157$			11.7893i			0.940890i	0.882429	+	0.470445i	$0.155907\pi$
$157$			11.7893i			0.940890i	−0.882429	+	0.470445i	$0.844093\pi$
$158$	−0.674542	+	0.845848i	−0.0536636	+	0.0672921i
$159$	15.2332	+	3.47688i	1.20807	+	0.275735i
$160$	10.9597	+	2.50147i	0.866437	+	0.197759i
$161$	−0.702494	+	0.880899i	−0.0553643	+	0.0694246i
$162$		−	1.88561i		−	0.148148i
$163$	1.95975	+	1.56285i	0.153500	+	0.122412i	0.697228	−	0.716849i	$-0.254416\pi$
$163$	1.95975	+	1.56285i	0.153500	+	0.122412i	−0.543728	+	0.839261i	$0.682988\pi$
$164$	−1.43984	−	2.98985i	−0.112432	−	0.233468i
$165$	18.5302	+	23.2361i	1.44257	+	1.80893i
$166$	−2.54181	+	2.02703i	−0.197283	+	0.157328i
$167$	−2.40640	−	1.15886i	−0.186213	−	0.0896754i	0.338454	−	0.940983i	$-0.390096\pi$
$167$	−2.40640	−	1.15886i	−0.186213	−	0.0896754i	−0.524667	+	0.851307i	$0.675810\pi$
$168$	−1.49113	+	6.53308i	−0.115043	+	0.504038i
$169$	0.701848	+	3.07500i	0.0539883	+	0.236538i
$170$	1.39742	−	0.672961i	0.107177	−	0.0516137i
$171$	10.9755	−	22.7909i	0.839319	−	1.74286i
$172$	18.6695	−	4.26118i	1.42353	−	0.324912i
$173$	−23.5982			−1.79414			−0.897071	−	0.441887i	$-0.854309\pi$
$173$	−23.5982			−1.79414			−0.897071	+	0.441887i	$0.854309\pi$
$174$		0			0
$175$	0.186458			0.0140949
$176$	12.2075	−	2.78629i	0.920177	−	0.210024i
$177$	−5.08547	+	10.5601i	−0.382247	+	0.793745i
$178$	5.49656	−	2.64700i	0.411984	−	0.198401i
$179$	−4.66369	−	20.4329i	−0.348580	−	1.52723i	−0.780406	−	0.625273i	$-0.784988\pi$
$179$	−4.66369	−	20.4329i	−0.348580	−	1.52723i	0.431826	−	0.901957i	$-0.357869\pi$
$180$	−3.62348	+	15.8755i	−0.270078	+	1.18329i
$181$	−8.19331	−	3.94569i	−0.609004	−	0.293281i	0.103850	−	0.994593i	$-0.466884\pi$
$181$	−8.19331	−	3.94569i	−0.609004	−	0.293281i	−0.712854	+	0.701312i	$0.752598\pi$
$182$	−1.63309	+	1.30235i	−0.121053	+	0.0965364i
$183$	9.12495	+	11.4423i	0.674536	+	0.845841i
$184$	−0.717636	−	1.49019i	−0.0529048	−	0.109858i
$185$	10.1657	+	8.10691i	0.747401	+	0.596032i
$186$		−	3.77735i		−	0.276969i
$187$	4.29876	−	5.39047i	0.314356	−	0.394190i
$188$	−4.87594	−	1.11290i	−0.355614	−	0.0811666i
$189$	−4.27204	−	0.975064i	−0.310745	−	0.0709255i
$190$	−4.18136	+	5.24327i	−0.303348	+	0.380386i
$191$			19.2700i			1.39433i	0.716912	+	0.697163i	$0.245555\pi$
$191$			19.2700i			1.39433i	−0.716912	+	0.697163i	$0.754445\pi$
$192$	5.03583	+	4.01594i	0.363430	+	0.289826i
$193$	−2.30742	−	4.79140i	−0.166092	−	0.344893i	0.801266	−	0.598308i	$-0.204160\pi$
$193$	−2.30742	−	4.79140i	−0.166092	−	0.344893i	−0.967357	+	0.253416i	$0.918446\pi$
$194$	−3.64140	−	4.56618i	−0.261438	−	0.327832i
$195$	−14.5573	+	11.6091i	−1.04247	+	0.831344i
$196$	8.30940	+	4.00160i	0.593529	+	0.285828i
$197$	2.21912	−	9.72260i	0.158106	−	0.692706i	−0.832278	−	0.554358i	$-0.812964\pi$
$197$	2.21912	−	9.72260i	0.158106	−	0.692706i	0.990384	−	0.138348i	$-0.0441792\pi$
$198$	−2.42156	−	10.6096i	−0.172093	−	0.753988i
$199$	19.9927	−	9.62796i	1.41724	−	0.682508i	0.440664	−	0.897672i	$-0.354743\pi$
$199$	19.9927	−	9.62796i	1.41724	−	0.682508i	0.976578	+	0.215165i	$0.0690288\pi$
$200$	−0.118760	+	0.246609i	−0.00839763	+	0.0174379i
$201$	6.20242	−	1.41566i	0.437485	−	0.0998531i
$202$	0.498225			0.0350550
$203$		0			0
$204$	6.44425			0.451188
$205$	−4.10094	+	0.936013i	−0.286422	+	0.0653740i
$206$	−1.72518	+	3.58236i	−0.120199	+	0.249595i
$207$	3.31335	−	1.59563i	0.230294	−	0.110904i
$208$	1.74560	+	7.64796i	0.121035	+	0.530291i
$209$	−6.63372	+	29.0642i	−0.458864	+	2.01041i
$210$	3.55893	+	1.71389i	0.245589	+	0.118270i
$211$	5.71545	−	4.55792i	0.393468	−	0.313780i	−0.406694	−	0.913565i	$-0.633318\pi$
$211$	5.71545	−	4.55792i	0.393468	−	0.313780i	0.800162	+	0.599784i	$0.204747\pi$
$212$	−6.29053	−	7.88808i	−0.432036	−	0.541755i
$213$	−18.2128	−	37.8193i	−1.24792	−	2.59134i
$214$	−2.17818	−	1.73704i	−0.148897	−	0.118742i
$215$		−	24.2734i		−	1.65543i
$216$	4.01060	−	5.02914i	0.272887	−	0.342189i
$217$	3.48327	+	0.795034i	0.236460	+	0.0539705i
$218$	−3.93342	−	0.897778i	−0.266405	−	0.0608052i
$219$	5.70191	−	7.14997i	0.385299	−	0.483150i
$220$		−	19.1906i		−	1.29383i
$221$	3.37711	+	2.69315i	0.227169	+	0.181161i
$222$	−3.52393	−	7.31752i	−0.236511	−	0.491120i
$223$	3.42929	+	4.30020i	0.229642	+	0.287962i	0.883281	−	0.468845i	$-0.155330\pi$
$223$	3.42929	+	4.30020i	0.229642	+	0.287962i	−0.653638	+	0.756807i	$0.726758\pi$
$224$	5.19271	−	4.14105i	0.346952	−	0.276685i
$225$	−0.548321	−	0.264058i	−0.0365548	−	0.0176038i
$226$	1.96824	−	8.62343i	0.130925	−	0.573622i
$227$	−3.50493	−	15.3561i	−0.232630	−	1.01922i	−0.947448	−	0.319910i	$-0.896347\pi$
$227$	−3.50493	−	15.3561i	−0.232630	−	1.01922i	0.714818	−	0.699311i	$-0.246510\pi$
$228$	−25.1047	+	12.0898i	−1.66260	+	0.800665i
$229$	−6.43545	+	13.3634i	−0.425267	+	0.883076i	0.572726	+	0.819747i	$0.305886\pi$
$229$	−6.43545	+	13.3634i	−0.425267	+	0.883076i	−0.997993	+	0.0633287i	$0.979828\pi$
$230$	−0.950533	+	0.216953i	−0.0626763	+	0.0143055i
$231$	17.5593			1.15532
$232$		0			0
$233$	−15.8867			−1.04078			−0.520388	−	0.853930i	$-0.674213\pi$
$233$	−15.8867			−1.04078			−0.520388	+	0.853930i	$0.674213\pi$
$234$	6.64683	−	1.51710i	0.434517	−	0.0991757i
$235$	−2.75062	+	5.71171i	−0.179430	+	0.372591i
$236$	6.81877	−	3.28375i	0.443864	−	0.213754i
$237$	1.26788	+	5.55494i	0.0823575	+	0.360832i
$238$	0.203912	−	0.893398i	0.0132177	−	0.0579104i
$239$	−8.46905	−	4.07848i	−0.547818	−	0.263815i	0.139438	−	0.990231i	$-0.455470\pi$
$239$	−8.46905	−	4.07848i	−0.547818	−	0.263815i	−0.687256	+	0.726416i	$0.741185\pi$
$240$	11.5984	−	9.24942i	0.748674	−	0.597047i
$241$	6.50942	+	8.16255i	0.419308	+	0.525796i	0.945959	−	0.324286i	$-0.105124\pi$
$241$	6.50942	+	8.16255i	0.419308	+	0.525796i	−0.526651	+	0.850082i	$0.676552\pi$
$242$	3.12450	+	6.48809i	0.200850	+	0.417070i
$243$	−15.6576	−	12.4865i	−1.00443	−	0.801008i
$244$		−	9.45018i		−	0.604986i
$245$	7.28887	−	9.13995i	0.465669	−	0.583930i
$246$	2.56160	+	0.584669i	0.163322	+	0.0372771i
$247$	−18.2086	−	4.15599i	−1.15859	−	0.264440i
$248$	−3.27011	+	4.10059i	−0.207652	+	0.260388i
$249$			17.1221i			1.08507i
$250$	4.53064	+	3.61307i	0.286543	+	0.228510i
$251$	−6.41374	−	13.3183i	−0.404832	−	0.840642i	−0.999332	−	0.0365464i	$-0.988364\pi$
$251$	−6.41374	−	13.3183i	−0.404832	−	0.840642i	0.594500	−	0.804095i	$-0.297350\pi$
$252$	5.99847	+	7.52185i	0.377868	+	0.473832i
$253$	−3.38848	+	2.70223i	−0.213032	+	0.169887i
$254$	2.54089	+	1.22363i	0.159430	+	0.0767772i
$255$	1.81767	−	7.96372i	0.113827	−	0.498707i
$256$	0.235133	+	1.03019i	0.0146958	+	0.0643866i
$257$	−1.55916	+	0.750850i	−0.0972575	+	0.0468368i	−0.481880	−	0.876237i	$-0.660046\pi$
$257$	−1.55916	+	0.750850i	−0.0972575	+	0.0468368i	0.384623	+	0.923074i	$0.374332\pi$
$258$	−6.57858	+	13.6606i	−0.409564	+	0.850469i
$259$	7.48953	−	1.70944i	0.465377	−	0.106219i
$260$	12.0228			0.745625
$261$		0			0
$262$	−0.0144647			−0.000893630
$263$	13.1918	−	3.01095i	0.813442	−	0.185663i	0.204489	−	0.978869i	$-0.434447\pi$
$263$	13.1918	−	3.01095i	0.813442	−	0.185663i	0.608953	+	0.793206i	$0.291590\pi$
$264$	−11.1840	+	23.2239i	−0.688329	+	1.42933i
$265$	−11.5223	+	5.54884i	−0.707808	+	0.340863i
$266$	0.881690	+	3.86294i	0.0540599	+	0.236852i
$267$	7.14955	−	31.3242i	0.437546	−	1.91701i
$268$	−3.70115	−	1.78238i	−0.226084	−	0.108876i
$269$	23.3684	−	18.6357i	1.42480	−	1.13624i	0.455534	−	0.890218i	$-0.349448\pi$
$269$	23.3684	−	18.6357i	1.42480	−	1.13624i	0.969265	−	0.246021i	$-0.0791231\pi$
$270$	−2.36414	−	2.96454i	−0.143877	−	0.180416i
$271$	4.06287	+	8.43664i	0.246802	+	0.512490i	0.987162	−	0.159721i	$-0.0510594\pi$
$271$	4.06287	+	8.43664i	0.246802	+	0.512490i	−0.740360	+	0.672210i	$0.765345\pi$
$272$	−2.69067	−	2.14574i	−0.163146	−	0.130105i
$273$			11.0008i			0.665799i
$274$	−1.96188	+	2.46012i	−0.118521	+	0.148621i
$275$	0.699250	+	0.159599i	0.0421663	+	0.00962419i
$276$	−3.94933	−	0.901409i	−0.237722	−	0.0542585i
$277$	13.9800	−	17.5304i	0.839978	−	1.05330i	−0.157852	−	0.987463i	$-0.550457\pi$
$277$	13.9800	−	17.5304i	0.839978	−	1.05330i	0.997830	−	0.0658364i	$-0.0209715\pi$
$278$			6.34374i			0.380472i
$279$	−9.11744	−	7.27092i	−0.545847	−	0.435298i
$280$	−2.37974	−	4.94157i	−0.142216	−	0.295315i
$281$	−5.43187	−	6.81135i	−0.324038	−	0.406331i	0.592954	−	0.805237i	$-0.297962\pi$
$281$	−5.43187	−	6.81135i	−0.324038	−	0.406331i	−0.916992	+	0.398905i	$0.869390\pi$
$282$	3.09598	−	2.46896i	0.184363	−	0.147024i
$283$	−13.0263	−	6.27313i	−0.774332	−	0.372899i	0.00461408	−	0.999989i	$-0.498531\pi$
$283$	−13.0263	−	6.27313i	−0.774332	−	0.372899i	−0.778946	+	0.627091i	$0.784246\pi$
$284$	−6.03134	+	26.4250i	−0.357894	+	1.56804i
$285$	7.85935	+	34.4341i	0.465548	+	2.03970i
$286$	−7.23913	+	3.48618i	−0.428059	+	0.206142i
$287$	−1.07830	+	2.23912i	−0.0636502	+	0.132171i
$288$	−21.1348	+	4.82388i	−1.24538	+	0.284250i
$289$	15.1050			0.888530
$290$		0			0
$291$	−30.7586			−1.80310
$292$	−5.75708	+	1.31402i	−0.336908	+	0.0768970i
$293$	14.2123	−	29.5121i	0.830291	−	1.72412i	0.153229	−	0.988191i	$-0.451033\pi$
$293$	14.2123	−	29.5121i	0.830291	−	1.72412i	0.677062	−	0.735926i	$-0.263253\pi$
$294$	−6.57913	+	3.16834i	−0.383703	+	0.184782i
$295$	−2.13471	−	9.35276i	−0.124287	−	0.544539i
$296$	−2.50941	+	10.9944i	−0.145856	+	0.639038i
$297$	−15.1863	−	7.31333i	−0.881197	−	0.424362i
$298$	−8.31717	+	6.63273i	−0.481801	+	0.384223i
$299$	−1.69293	−	2.12287i	−0.0979048	−	0.122769i
$300$	0.290865	+	0.603988i	0.0167931	+	0.0348713i
$301$	−11.2124	−	8.94161i	−0.646274	−	0.515386i
$302$		−	10.2396i		−	0.589222i
$303$	1.63599	−	2.05147i	0.0939854	−	0.117854i
$304$	14.5075	+	3.31125i	0.832063	+	0.189913i
$305$	−11.6784	−	2.66552i	−0.668703	−	0.152627i
$306$	−1.86486	+	2.33846i	−0.106607	+	0.133681i
$307$		−	28.4921i		−	1.62613i	−0.582173	−	0.813065i	$-0.697798\pi$
$307$		−	28.4921i		−	1.62613i	0.582173	−	0.813065i	$-0.302202\pi$
$308$	−8.86460	−	7.06928i	−0.505107	−	0.402810i
$309$	9.08574	+	18.8667i	0.516870	+	1.07329i
$310$	1.92764	+	2.41719i	0.109483	+	0.137287i
$311$	17.0499	−	13.5968i	0.966810	−	0.771005i	−0.00662321	−	0.999978i	$-0.502108\pi$
$311$	17.0499	−	13.5968i	0.966810	−	0.771005i	0.973433	+	0.228973i	$0.0735368\pi$
$312$	−14.5496	−	7.00674i	−0.823711	−	0.396678i
$313$	5.32440	−	23.3277i	0.300953	−	1.31856i	−0.567740	−	0.823208i	$-0.692182\pi$
$313$	5.32440	−	23.3277i	0.300953	−	1.31856i	0.868693	−	0.495352i	$-0.164961\pi$
$314$	1.34121	+	5.87623i	0.0756890	+	0.331615i
$315$	10.9873	−	5.29122i	0.619066	−	0.298126i
$316$	1.59632	−	3.31478i	0.0897998	−	0.186471i
$317$	−9.11805	+	2.08114i	−0.512121	+	0.116888i	−0.470769	−	0.882256i	$-0.656024\pi$
$317$	−9.11805	+	2.08114i	−0.512121	+	0.116888i	−0.0413517	+	0.999145i	$0.513166\pi$
$318$	7.98835			0.447964
$319$		0			0
$320$	−5.27191			−0.294709
$321$	−14.3048	+	3.26497i	−0.798414	+	0.182233i
$322$	−0.249933	+	0.518992i	−0.0139282	+	0.0289223i
$323$	7.38225	−	3.55510i	0.410759	−	0.197811i
$324$	1.42689	+	6.25159i	0.0792714	+	0.347311i
$325$	−0.0999881	+	0.438077i	−0.00554634	+	0.0243001i
$326$	1.15461	+	0.556032i	0.0639480	+	0.0307957i
$327$	−16.6126	+	13.2481i	−0.918681	+	0.732623i
$328$	−2.27465	−	2.85232i	−0.125597	−	0.157493i
$329$	1.62512	+	3.37460i	0.0895959	+	0.186048i
$330$	11.8796	+	9.47367i	0.653951	+	0.521508i
$331$			10.2474i			0.563247i	0.959525	+	0.281623i	$0.0908729\pi$
$331$			10.2474i			0.563247i	−0.959525	+	0.281623i	$0.909127\pi$
$332$	6.89328	−	8.64390i	0.378318	−	0.474396i
$333$	−24.4455	−	5.57953i	−1.33961	−	0.305757i
$334$	−1.33128	−	0.303855i	−0.0728443	−	0.0166262i
$335$	−3.24659	+	4.07110i	−0.177380	+	0.222428i
$336$		−	8.76478i		−	0.478158i
$337$	12.4652	+	9.94065i	0.679022	+	0.541502i	0.901146	−	0.433517i	$-0.142727\pi$
$337$	12.4652	+	9.94065i	0.679022	+	0.541502i	−0.222124	+	0.975019i	$0.571299\pi$
$338$	0.699654	+	1.45285i	0.0380562	+	0.0790244i
$339$	−29.0445	−	36.4206i	−1.57748	−	1.97810i
$340$	−4.12378	+	3.28860i	−0.223643	+	0.178350i
$341$	12.3824	+	5.96304i	0.670543	+	0.322917i
$342$	2.87780	−	12.6085i	0.155614	−	0.681788i
$343$	−3.56509	−	15.6197i	−0.192497	−	0.843384i
$344$	18.9677	−	9.13435i	1.02267	−	0.492491i
$345$	−2.22790	+	4.62628i	−0.119946	+	0.249070i
$346$	−11.7622	+	2.68466i	−0.632342	+	0.144328i
$347$	−36.7925			−1.97513			−0.987563	−	0.157224i	$-0.949746\pi$
$347$	−36.7925			−1.97513			−0.987563	+	0.157224i	$0.949746\pi$
$348$		0			0
$349$	32.4894			1.73912			0.869558	−	0.493831i	$-0.164404\pi$
$349$	32.4894			1.73912			0.869558	+	0.493831i	$0.164404\pi$
$350$	0.0929375	−	0.0212124i	0.00496772	−	0.00113385i
$351$	4.58177	−	9.51413i	0.244557	−	0.507827i
$352$	23.0181	−	11.0849i	1.22687	−	0.590829i
$353$	−2.67405	−	11.7158i	−0.142325	−	0.623568i	−0.994892	−	0.100949i	$-0.967812\pi$
$353$	−2.67405	−	11.7158i	−0.142325	−	0.623568i	0.852566	−	0.522619i	$-0.175045\pi$
$354$	−1.33342	+	5.84209i	−0.0708704	+	0.310504i
$355$	30.9545	+	14.9069i	1.64289	+	0.791176i
$356$	−16.2203	+	12.9353i	−0.859677	+	0.685569i
$357$	−3.00905	−	3.77323i	−0.159256	−	0.199700i
$358$	−4.64911	−	9.65397i	−0.245713	−	0.510228i
$359$	3.05587	+	2.43698i	0.161283	+	0.128619i	0.700806	−	0.713352i	$-0.252824\pi$
$359$	3.05587	+	2.43698i	0.161283	+	0.128619i	−0.539523	+	0.841971i	$0.681395\pi$
$360$			17.9019i			0.943515i
$361$	−10.2429	+	12.8442i	−0.539102	+	0.676012i
$362$	−4.53273	−	1.03457i	−0.238235	−	0.0543756i
$363$	36.9749	+	8.43927i	1.94068	+	0.442947i
$364$	4.42887	−	5.55363i	0.232136	−	0.291089i
$365$			7.48515i			0.391791i
$366$	5.84995	+	4.66518i	0.305782	+	0.243853i
$367$	5.54823	+	11.5210i	0.289615	+	0.601392i	0.994117	−	0.108310i	$-0.0345439\pi$
$367$	5.54823	+	11.5210i	0.289615	+	0.601392i	−0.704502	+	0.709702i	$0.748830\pi$
$368$	1.34883	+	1.69137i	0.0703124	+	0.0881690i
$369$	6.34199	−	5.05756i	0.330151	−	0.263286i
$370$	5.98927	+	2.88428i	0.311367	+	0.149947i
$371$	−1.68134	+	7.36644i	−0.0872909	+	0.382446i
$372$	2.85841	+	12.5235i	0.148201	+	0.649313i
$373$	−22.5120	+	10.8412i	−1.16563	+	0.561338i	−0.913693	−	0.406406i	$-0.866782\pi$
$373$	−22.5120	+	10.8412i	−1.16563	+	0.561338i	−0.251937	+	0.967744i	$0.581068\pi$
$374$	1.52941	−	3.17586i	0.0790841	−	0.164220i
$375$	29.7541	−	6.79117i	1.53649	−	0.350695i
$376$	−5.49833			−0.283555
$377$		0			0
$378$	−2.24027			−0.115227
$379$	−12.7084	+	2.90061i	−0.652786	+	0.148994i	−0.536073	−	0.844172i	$-0.680093\pi$
$379$	−12.7084	+	2.90061i	−0.652786	+	0.148994i	−0.116713	+	0.993166i	$0.537236\pi$
$380$	9.89528	−	20.5478i	0.507617	−	1.05408i
$381$	13.3818	−	6.44431i	0.685568	−	0.330152i
$382$	2.19225	+	9.60488i	0.112165	+	0.491428i
$383$	5.34830	−	23.4324i	0.273285	−	1.19734i	−0.632824	−	0.774296i	$-0.718104\pi$
$383$	5.34830	−	23.4324i	0.273285	−	1.19734i	0.906109	−	0.423045i	$-0.139039\pi$
$384$	27.7157	+	13.3472i	1.41436	+	0.681121i
$385$	−11.2365	+	8.96079i	−0.572664	+	0.456684i
$386$	−1.69520	−	2.12571i	−0.0862833	−	0.108196i
$387$	20.3098	+	42.1736i	1.03240	+	2.14381i
$388$	15.5281	+	12.3833i	0.788321	+	0.628665i
$389$		−	17.6717i		−	0.895991i	−0.894036	−	0.447995i	$-0.852138\pi$
$389$		−	17.6717i		−	0.895991i	0.894036	−	0.447995i	$-0.147862\pi$
$390$	−5.93521	+	7.44251i	−0.300541	+	0.376866i
$391$	1.16134	+	0.265067i	0.0587312	+	0.0134050i
$392$	9.88501	+	2.25619i	0.499269	+	0.113955i
$393$	−0.0474969	+	0.0595592i	−0.00239590	+	0.00300436i
$394$		−	5.09856i		−	0.256862i
$395$	−3.64611	−	2.90767i	−0.183456	−	0.146301i
$396$	16.0570	+	33.3427i	0.806894	+	1.67553i
$397$	18.8622	+	23.6524i	0.946665	+	1.18708i	0.982224	+	0.187713i	$0.0601076\pi$
$397$	18.8622	+	23.6524i	0.946665	+	1.18708i	−0.0355584	+	0.999368i	$0.511321\pi$
$398$	8.86976	−	7.07340i	0.444601	−	0.354557i
$399$	18.8010	+	9.05410i	0.941229	+	0.453272i
$400$	0.0796645	−	0.349033i	0.00398323	−	0.0174517i
$401$	2.74975	+	12.0474i	0.137316	+	0.601620i	0.996019	+	0.0891461i	$0.0284138\pi$
$401$	2.74975	+	12.0474i	0.137316	+	0.601620i	−0.858703	+	0.512474i	$0.828729\pi$
$402$	2.93046	−	1.41124i	0.146158	−	0.0703861i
$403$	−3.73582	+	7.75750i	−0.186094	+	0.386429i
$404$	−1.65182	+	0.377018i	−0.0821813	+	0.0187574i
$405$	8.12810			0.403889
$406$		0			0
$407$	29.5503			1.46475
$408$	6.90701	−	1.57648i	0.341948	−	0.0780474i
$409$	2.64972	−	5.50220i	0.131020	−	0.272066i	−0.825130	−	0.564943i	$-0.808898\pi$
$409$	2.64972	−	5.50220i	0.131020	−	0.272066i	0.956150	+	0.292877i	$0.0946125\pi$
$410$	−1.93758	+	0.933088i	−0.0956901	+	0.0460819i
$411$	3.68757	+	16.1563i	0.181895	+	0.796932i
$412$	3.00882	−	13.1825i	0.148234	−	0.649456i
$413$	−5.10662	−	2.45922i	−0.251280	−	0.121010i
$414$	1.46997	−	1.17226i	0.0722452	−	0.0576136i
$415$	−8.73770	−	10.9567i	−0.428917	−	0.537845i
$416$	6.94466	+	14.4207i	0.340490	+	0.707035i
$417$	26.1207	+	20.8306i	1.27914	+	1.02008i
$418$			15.2414i			0.745480i
$419$	−7.23714	+	9.07508i	−0.353557	+	0.443347i	−0.926526	−	0.376230i	$-0.877220\pi$
$419$	−7.23714	+	9.07508i	−0.353557	+	0.443347i	0.572969	+	0.819577i	$0.305792\pi$
$420$	−13.0963	−	2.98914i	−0.639033	−	0.145855i
$421$	19.7781	+	4.51422i	0.963925	+	0.220010i	0.675391	−	0.737460i	$-0.263975\pi$
$421$	19.7781	+	4.51422i	0.963925	+	0.220010i	0.288534	+	0.957470i	$0.406832\pi$
$422$	2.33026	−	2.92206i	0.113435	−	0.142243i
$423$		−	12.2252i		−	0.594412i
$424$	−8.67194	−	6.91564i	−0.421147	−	0.335853i
$425$	−0.0855315	−	0.177608i	−0.00414889	−	0.00861525i
$426$	−13.3805	−	16.7786i	−0.648286	−	0.812925i
$427$	−5.53325	+	4.41262i	−0.267773	+	0.213542i
$428$	8.53604	+	4.11074i	0.412605	+	0.198700i
$429$	−9.41618	+	41.2550i	−0.454618	+	1.99181i
$430$	−2.76146	−	12.0988i	−0.133170	−	0.583454i
$431$	−15.3018	+	7.36896i	−0.737062	+	0.354950i	−0.764457	−	0.644674i	$-0.776993\pi$
$431$	−15.3018	+	7.36896i	−0.737062	+	0.354950i	0.0273954	+	0.999625i	$0.491279\pi$
$432$	−3.65047	+	7.58029i	−0.175634	+	0.364707i
$433$	−15.5357	+	3.54593i	−0.746600	+	0.170407i	−0.578862	−	0.815425i	$-0.696503\pi$
$433$	−15.5357	+	3.54593i	−0.746600	+	0.170407i	−0.167737	+	0.985832i	$0.553646\pi$
$434$	1.82664			0.0876815
$435$		0			0
$436$	13.7203			0.657084
$437$	−5.02146	+	1.14612i	−0.240209	+	0.0548261i
$438$	2.02863	−	4.21249i	0.0969316	−	0.201280i
$439$	−4.86840	+	2.34450i	−0.232356	+	0.111897i	−0.546440	−	0.837499i	$-0.684017\pi$
$439$	−4.86840	+	2.34450i	−0.232356	+	0.111897i	0.314083	+	0.949395i	$0.398303\pi$
$440$	−4.69467	−	20.5687i	−0.223810	−	0.980575i
$441$	−5.01652	+	21.9788i	−0.238882	+	1.04661i
$442$	1.98966	+	0.958171i	0.0946386	+	0.0455755i
$443$	14.8950	−	11.8783i	0.707682	−	0.564357i	−0.202140	−	0.979357i	$-0.564790\pi$
$443$	14.8950	−	11.8783i	0.707682	−	0.564357i	0.909822	+	0.414999i	$0.136218\pi$
$444$	17.2207	+	21.5940i	0.817256	+	1.02481i
$445$	11.4101	+	23.6934i	0.540893	+	1.12318i
$446$	2.19850	+	1.75324i	0.104102	+	0.0830185i
$447$			56.0260i			2.64994i
$448$	−1.94202	+	2.43522i	−0.0917518	+	0.115053i
$449$	−17.2440	−	3.93582i	−0.813793	−	0.185743i	−0.204682	−	0.978828i	$-0.565616\pi$
$449$	−17.2440	−	3.93582i	−0.813793	−	0.185743i	−0.609110	+	0.793086i	$0.708473\pi$
$450$	−0.303344	−	0.0692364i	−0.0142998	−	0.00326383i
$451$	−5.96041	+	7.47411i	−0.280665	+	0.351942i
$452$			30.0797i			1.41483i
$453$	−42.1622	−	33.6232i	−1.98095	−	1.57976i
$454$	−3.49398	−	7.25532i	−0.163980	−	0.340509i
$455$	−5.61389	−	7.03959i	−0.263183	−	0.330021i
$456$	−23.9499	+	19.0994i	−1.12156	+	0.894411i
$457$	−13.6028	−	6.55078i	−0.636314	−	0.306433i	0.0877740	−	0.996140i	$-0.472025\pi$
$457$	−13.6028	−	6.55078i	−0.636314	−	0.306433i	−0.724088	+	0.689708i	$0.757739\pi$
$458$	−1.68739	+	7.39293i	−0.0788464	+	0.345449i
$459$	1.03087	+	4.51655i	0.0481170	+	0.210815i
$460$	2.98724	−	1.43858i	0.139281	−	0.0670742i
$461$	9.67638	−	20.0932i	0.450674	−	0.935834i	−0.544597	−	0.838698i	$-0.683317\pi$
$461$	9.67638	−	20.0932i	0.450674	−	0.935834i	0.995271	−	0.0971364i	$-0.0309683\pi$
$462$	8.75220	−	1.99763i	0.407189	−	0.0929383i
$463$	26.7391			1.24267			0.621335	−	0.783545i	$-0.286591\pi$
$463$	26.7391			1.24267			0.621335	+	0.783545i	$0.286591\pi$
$464$		0			0
$465$	16.2826			0.755088
$466$	−7.91855	+	1.80736i	−0.366820	+	0.0837242i
$467$	5.01624	−	10.4163i	0.232124	−	0.482010i	−0.752075	−	0.659078i	$-0.770947\pi$
$467$	5.01624	−	10.4163i	0.232124	−	0.482010i	0.984199	+	0.177067i	$0.0566611\pi$
$468$	−20.8890	+	10.0596i	−0.965595	+	0.465006i
$469$	0.684582	+	2.99935i	0.0316111	+	0.138497i
$470$	−0.721216	+	3.15985i	−0.0332672	+	0.145753i
$471$	28.5998	+	13.7730i	1.31781	+	0.634624i
$472$	6.50511	−	5.18765i	0.299422	−	0.238781i
$473$	−34.3950	−	43.1300i	−1.58148	−	1.98312i
$474$	1.26392	+	2.62455i	0.0580535	+	0.120549i
$475$	0.666405	+	0.531440i	0.0305768	+	0.0243841i
$476$			3.11630i			0.142835i
$477$	15.3766	−	19.2816i	0.704044	−	0.882844i
$478$	−4.68528	−	1.06938i	−0.214300	−	0.0489125i
$479$	23.7181	+	5.41349i	1.08371	+	0.247349i	0.726840	−	0.686807i	$-0.240988\pi$
$479$	23.7181	+	5.41349i	1.08371	+	0.247349i	0.356866	+	0.934156i	$0.383845\pi$
$480$	18.8720	−	23.6648i	0.861387	−	1.08015i
$481$			18.5131i			0.844125i
$482$	4.17315	+	3.32797i	0.190082	+	0.151585i
$483$	1.31629	+	2.73330i	0.0598933	+	0.124370i
$484$	−15.2687	−	19.1464i	−0.694032	−	0.870289i
$485$	19.6829	−	15.6966i	0.893756	−	0.712746i
$486$	−9.22483	−	4.44245i	−0.418447	−	0.201513i
$487$	−0.286359	+	1.25462i	−0.0129762	+	0.0568523i	−0.981001	−	0.194000i	$-0.937854\pi$
$487$	−0.286359	+	1.25462i	−0.0129762	+	0.0568523i	0.968025	+	0.250852i	$0.0807109\pi$
$488$	−2.31183	−	10.1288i	−0.104652	−	0.458509i
$489$	6.08083	−	2.92838i	0.274985	−	0.132426i
$490$	2.59324	−	5.38491i	0.117150	−	0.243265i
$491$	−31.8396	+	7.26719i	−1.43690	+	0.327963i	−0.868869	−	0.495042i	$-0.835153\pi$
$491$	−31.8396	+	7.26719i	−1.43690	+	0.327963i	−0.568033	+	0.823006i	$0.692295\pi$
$492$	−8.93522			−0.402831
$493$		0			0
$494$	−9.54865			−0.429614
$495$	45.7335	−	10.4384i	2.05557	−	0.469169i
$496$	2.97647	−	6.18071i	0.133648	−	0.277522i
$497$	18.2886	−	8.80732i	0.820355	−	0.395062i
$498$	1.94790	+	8.53431i	0.0872875	+	0.382432i
$499$	−2.33273	+	10.2203i	−0.104427	+	0.457525i	0.895495	+	0.445071i	$0.146822\pi$
$499$	−2.33273	+	10.2203i	−0.104427	+	0.457525i	−0.999922	+	0.0124542i	$0.996036\pi$
$500$	−17.7551	−	8.55039i	−0.794031	−	0.382385i
$501$	−5.62259	+	4.48387i	−0.251199	+	0.200324i
$502$	−4.71200	−	5.90866i	−0.210307	−	0.263717i
$503$	−1.64458	−	3.41500i	−0.0733280	−	0.152267i	0.861082	−	0.508465i	$-0.169787\pi$
$503$	−1.64458	−	3.41500i	−0.0733280	−	0.152267i	−0.934410	+	0.356198i	$0.884073\pi$
$504$	8.26931	+	6.59456i	0.368344	+	0.293745i
$505$			2.14764i			0.0955689i
$506$	−1.38153	+	1.73238i	−0.0614164	+	0.0770137i
$507$	8.27961	+	1.88977i	0.367710	+	0.0839275i
$508$	−9.35006	−	2.13409i	−0.414842	−	0.0946850i
$509$	−4.99932	+	6.26895i	−0.221591	+	0.277866i	−0.880184	−	0.474633i	$-0.842581\pi$
$509$	−4.99932	+	6.26895i	−0.221591	+	0.277866i	0.658593	+	0.752500i	$0.271152\pi$
$510$		−	4.17620i		−	0.184925i
$511$	3.45756	+	2.75731i	0.152954	+	0.121976i
$512$	−9.67974	−	20.1002i	−0.427788	−	0.888311i
$513$	−12.4892	−	15.6610i	−0.551414	−	0.691451i
$514$	−0.691721	+	0.551629i	−0.0305105	+	0.0243313i
$515$	−15.4421	−	7.43653i	−0.680461	−	0.327693i
$516$	11.4735	−	50.2686i	0.505092	−	2.21295i
$517$	3.20599	+	14.0464i	0.140999	+	0.617759i
$518$	3.53859	−	1.70409i	0.155477	−	0.0748736i
$519$	−27.5688	+	57.2473i	−1.21014	+	2.51288i
$520$	12.8862	−	2.94119i	0.565097	−	0.128980i
$521$	6.39024			0.279962			0.139981	−	0.990154i	$-0.455296\pi$
$521$	6.39024			0.279962			0.139981	+	0.990154i	$0.455296\pi$
$522$		0			0
$523$	−16.3261			−0.713891			−0.356946	−	0.934125i	$-0.616182\pi$
$523$	−16.3261			−0.713891			−0.356946	+	0.934125i	$0.616182\pi$
$524$	0.0479564	−	0.0109457i	0.00209499	−	0.000478167i
$525$	0.217831	−	0.452330i	0.00950691	−	0.0197413i
$526$	6.23275	−	3.00154i	0.271761	−	0.130873i
$527$	−0.840539	−	3.68264i	−0.0366145	−	0.160418i
$528$	7.50225	−	32.8695i	0.326493	−	1.43046i
$529$	20.0476	+	9.65444i	0.871637	+	0.419758i
$530$	−5.11187	+	4.07658i	−0.222046	+	0.177075i
$531$	11.5345	+	14.4638i	0.500554	+	0.627674i
$532$	−5.84634	−	12.1401i	−0.253471	−	0.526338i
$533$	−4.68250	−	3.73417i	−0.202821	−	0.161745i
$534$		−	16.4265i		−	0.710846i
$535$	7.48768	−	9.38925i	0.323721	−	0.405933i
$536$	−4.40296	−	1.00495i	−0.190179	−	0.0434071i
$537$	−55.0169	−	12.5572i	−2.37415	−	0.541885i
$538$	9.52761	−	11.9472i	0.410764	−	0.515082i
$539$		−	26.5684i		−	1.14438i
$540$	10.0815	+	8.03970i	0.433837	+	0.345973i
$541$	9.52857	+	19.7863i	0.409665	+	0.850678i	0.999082	+	0.0428490i	$0.0136434\pi$
$541$	9.52857	+	19.7863i	0.409665	+	0.850678i	−0.589416	+	0.807829i	$0.700642\pi$
$542$	2.98488	+	3.74292i	0.128212	+	0.160772i
$543$	−19.1438	+	15.2667i	−0.821539	+	0.655156i
$544$	−6.32648	−	3.04667i	−0.271246	−	0.130625i
$545$	3.86996	−	16.9554i	0.165771	−	0.726289i
$546$	1.25151	+	5.48321i	0.0535596	+	0.234660i
$547$	−3.69865	+	1.78117i	−0.158143	+	0.0761575i	−0.511281	−	0.859414i	$-0.670829\pi$
$547$	−3.69865	+	1.78117i	−0.158143	+	0.0761575i	0.353138	+	0.935571i	$0.385115\pi$
$548$	4.64282	−	9.64092i	0.198332	−	0.411840i
$549$	22.5208	−	5.14023i	0.961165	−	0.219380i
$550$	0.366689			0.0156357
$551$		0			0
$552$	−4.45344			−0.189551
$553$	−2.68624	+	0.613117i	−0.114231	+	0.0260724i
$554$	4.97382	−	10.3282i	0.211317	−	0.438805i
$555$	31.5429	−	15.1902i	1.33892	−	0.644790i
$556$	−4.80045	−	21.0322i	−0.203584	−	0.891962i
$557$	−5.53882	+	24.2671i	−0.234687	+	1.02823i	0.711010	+	0.703182i	$0.248238\pi$
$557$	−5.53882	+	24.2671i	−0.234687	+	1.02823i	−0.945697	+	0.325050i	$0.894619\pi$
$558$	−5.37165	−	2.58685i	−0.227400	−	0.109510i
$559$	27.0207	−	21.5483i	1.14285	−	0.911396i
$560$	4.47281	+	5.60873i	0.189011	+	0.237012i
$561$	−8.05475	−	16.7259i	−0.340072	−	0.706167i
$562$	−3.48234	−	2.77708i	−0.146894	−	0.117144i
$563$		−	22.6338i		−	0.953902i	−0.878930	−	0.476951i	$-0.841742\pi$
$563$		−	22.6338i		−	0.953902i	0.878930	−	0.476951i	$-0.158258\pi$
$564$	−8.39615	+	10.5284i	−0.353542	+	0.443327i
$565$	37.1721	+	8.48428i	1.56384	+	0.356936i
$566$	−7.20645	−	1.64482i	−0.302910	−	0.0691371i
$567$	2.99416	−	3.75455i	0.125743	−	0.157676i
$568$			29.7981i			1.25030i
$569$	−8.12929	−	6.48290i	−0.340798	−	0.271777i	0.438102	−	0.898925i	$-0.355651\pi$
$569$	−8.12929	−	6.48290i	−0.340798	−	0.271777i	−0.778900	+	0.627148i	$0.784222\pi$
$570$	7.83479	+	16.2691i	0.328163	+	0.681438i
$571$	22.2441	+	27.8932i	0.930887	+	1.16730i	0.985651	+	0.168796i	$0.0539880\pi$
$571$	22.2441	+	27.8932i	0.930887	+	1.16730i	−0.0547638	+	0.998499i	$0.517441\pi$
$572$	21.3627	−	17.0362i	0.893219	−	0.712318i
$573$	46.7473	+	22.5123i	1.95290	+	0.940465i
$574$	−0.282733	+	1.23873i	−0.0118010	+	0.0517037i
$575$	0.0275741	+	0.120810i	0.00114992	+	0.00503813i
$576$	9.15965	−	4.41105i	0.381652	−	0.183794i
$577$	−0.698030	+	1.44947i	−0.0290594	+	0.0603424i	−0.914993	−	0.403469i	$-0.867804\pi$
$577$	−0.698030	+	1.44947i	−0.0290594	+	0.0603424i	0.885934	+	0.463812i	$0.153519\pi$
$578$	7.52890	−	1.71842i	0.313161	−	0.0714770i
$579$	−14.3192			−0.595085
$580$		0			0
$581$	−8.27988			−0.343507
$582$	−15.3312	+	3.49926i	−0.635500	+	0.145049i
$583$	−12.6107	+	26.1863i	−0.522280	+	1.08453i
$584$	−5.84904	+	2.81675i	−0.242035	+	0.116558i
$585$	6.53958	+	28.6518i	0.270379	+	1.18461i
$586$	3.72649	−	16.3268i	0.153940	−	0.674454i
$587$	−22.3028	−	10.7405i	−0.920536	−	0.443307i	−0.0872738	−	0.996184i	$-0.527815\pi$
$587$	−22.3028	−	10.7405i	−0.920536	−	0.443307i	−0.833263	+	0.552877i	$0.813530\pi$
$588$	19.4150	−	15.4830i	0.800663	−	0.638507i
$589$	10.1833	+	12.7695i	0.419596	+	0.526157i
$590$	−2.12804	−	4.41891i	−0.0876098	−	0.181924i
$591$	−20.9937	−	16.7419i	−0.863564	−	0.688669i
$592$		−	14.7501i		−	0.606227i
$593$	6.36426	−	7.98053i	0.261349	−	0.327721i	−0.633793	−	0.773503i	$-0.718503\pi$
$593$	6.36426	−	7.98053i	0.261349	−	0.327721i	0.895142	+	0.445782i	$0.147074\pi$
$594$	−8.40141	−	1.91757i	−0.344714	−	0.0786787i
$595$	3.85107	+	0.878983i	0.157879	+	0.0360348i
$596$	22.5558	−	28.2841i	0.923921	−	1.15856i
$597$		−	59.7483i		−	2.44534i
$598$	−1.08533	−	0.865521i	−0.0443824	−	0.0353938i
$599$	−8.14582	−	16.9150i	−0.332829	−	0.691127i	0.665650	−	0.746264i	$-0.268155\pi$
$599$	−8.14582	−	16.9150i	−0.332829	−	0.691127i	−0.998479	+	0.0551377i	$0.982440\pi$
$600$	0.459508	+	0.576205i	0.0187593	+	0.0235235i
$601$	31.9072	−	25.4451i	1.30152	−	1.03793i	0.305196	−	0.952290i	$-0.401278\pi$
$601$	31.9072	−	25.4451i	1.30152	−	1.03793i	0.996326	−	0.0856397i	$-0.0272934\pi$
$602$	−6.60594	−	3.18125i	−0.269238	−	0.129658i
$603$	2.23445	−	9.78975i	0.0909937	−	0.398670i
$604$	7.74854	+	33.9486i	0.315283	+	1.38135i
$605$	−27.9675	+	13.4684i	−1.13704	+	0.547570i
$606$	0.582055	−	1.20865i	0.0236444	−	0.0490980i
$607$	−11.4104	+	2.60434i	−0.463133	+	0.105707i	−0.447719	−	0.894174i	$-0.647764\pi$
$607$	−11.4104	+	2.60434i	−0.463133	+	0.105707i	−0.0154135	+	0.999881i	$0.504906\pi$
$608$	30.3616			1.23133
$609$		0			0
$610$	−6.12419			−0.247961
$611$	−8.79999	+	2.00854i	−0.356010	+	0.0812568i
$612$	4.41323	−	9.16417i	0.178394	−	0.370440i
$613$	12.4961	−	6.01779i	0.504711	−	0.243056i	−0.164161	−	0.986434i	$-0.552492\pi$
$613$	12.4961	−	6.01779i	0.504711	−	0.243056i	0.668872	+	0.743377i	$0.266777\pi$
$614$	−3.24140	−	14.2015i	−0.130812	−	0.573127i
$615$	−2.52027	+	11.0420i	−0.101627	+	0.445258i
$616$	−11.2305	−	5.40834i	−0.452491	−	0.217908i
$617$	−19.7258	+	15.7308i	−0.794131	+	0.633298i	−0.934162	−	0.356849i	$-0.883851\pi$
$617$	−19.7258	+	15.7308i	−0.794131	+	0.633298i	0.140031	+	0.990147i	$0.455280\pi$
$618$	6.67505	+	8.37025i	0.268510	+	0.336701i
$619$	−12.5407	−	26.0411i	−0.504054	−	1.04668i	−0.985417	−	0.170158i	$-0.945572\pi$
$619$	−12.5407	−	26.0411i	−0.504054	−	1.04668i	0.481362	−	0.876522i	$-0.340142\pi$
$620$	−8.22008	−	6.55530i	−0.330126	−	0.263267i
$621$		−	2.91215i		−	0.116860i
$622$	6.95145	−	8.71684i	0.278728	−	0.349513i
$623$	15.1477	+	3.45736i	0.606880	+	0.138516i
$624$	20.5926	+	4.70012i	0.824363	+	0.188155i
$625$	−15.1280	+	18.9700i	−0.605121	+	0.758798i
$626$		−	12.2331i		−	0.488934i
$627$	62.7573	+	50.0473i	2.50629	+	1.99870i
$628$	−8.89336	−	18.4673i	−0.354884	−	0.736924i
$629$	−5.06388	−	6.34991i	−0.201910	−	0.253187i
$630$	4.87454	−	3.88731i	0.194206	−	0.154874i
$631$	14.1425	+	6.81069i	0.563006	+	0.271129i	0.693665	−	0.720298i	$-0.255995\pi$
$631$	14.1425	+	6.81069i	0.563006	+	0.271129i	−0.130659	+	0.991427i	$0.541709\pi$
$632$	0.900039	−	3.94333i	0.0358016	−	0.156857i
$633$	−4.37999	−	19.1900i	−0.174089	−	0.762734i
$634$	−4.30802	+	2.07463i	−0.171093	+	0.0823942i
$635$	−5.27456	+	10.9527i	−0.209315	+	0.434646i
$636$	−26.4847	+	6.04497i	−1.05019	+	0.239699i
$637$	16.6450			0.659499
$638$		0			0
$639$	−66.2544			−2.62098
$640$	−24.5470	+	5.60270i	−0.970307	+	0.221466i
$641$	−14.1210	+	29.3226i	−0.557746	+	1.15817i	0.411348	+	0.911479i	$0.365058\pi$
$641$	−14.1210	+	29.3226i	−0.557746	+	1.15817i	−0.969094	+	0.246693i	$0.920656\pi$
$642$	−6.75858	+	3.25476i	−0.266740	+	0.128455i
$643$	5.46633	+	23.9496i	0.215571	+	0.944479i	0.960707	+	0.277566i	$0.0895276\pi$
$643$	5.46633	+	23.9496i	0.215571	+	0.944479i	−0.745135	+	0.666913i	$0.767615\pi$
$644$	0.435901	−	1.90981i	0.0171769	−	0.0752570i
$645$	−58.8851	−	28.3576i	−2.31860	−	1.11658i
$646$	3.27514	−	2.61184i	0.128859	−	0.102761i
$647$	−8.11895	−	10.1808i	−0.319189	−	0.400250i	0.596190	−	0.802843i	$-0.296680\pi$
$647$	−8.11895	−	10.1808i	−0.319189	−	0.400250i	−0.915379	+	0.402593i	$0.868109\pi$
$648$	3.05870	+	6.35145i	0.120157	+	0.249509i
$649$	−17.0457	−	13.5935i	−0.669104	−	0.533593i
$650$			0.229729i			0.00901071i
$651$	5.99804	−	7.52131i	0.235082	−	0.294783i
$652$	−4.24879	−	0.969758i	−0.166395	−	0.0379786i
$653$	−29.2080	−	6.66653i	−1.14300	−	0.260882i	−0.391219	−	0.920298i	$-0.627946\pi$
$653$	−29.2080	−	6.66653i	−1.14300	−	0.260882i	−0.751778	+	0.659416i	$0.770804\pi$
$654$	−6.77318	+	8.49330i	−0.264852	+	0.332114i
$655$		−	0.0623513i		−	0.00243627i
$656$	3.73073	+	2.97516i	0.145661	+	0.116160i
$657$	−6.26289	−	13.0050i	−0.244339	−	0.507375i
$658$	1.19393	+	1.49714i	0.0465444	+	0.0583648i
$659$	−11.1031	+	8.85440i	−0.432514	+	0.344918i	−0.815421	−	0.578869i	$-0.803494\pi$
$659$	−11.1031	+	8.85440i	−0.432514	+	0.344918i	0.382907	+	0.923787i	$0.374923\pi$
$660$	−46.5548	−	22.4196i	−1.81214	−	0.872682i
$661$	−8.98572	+	39.3690i	−0.349504	+	1.53128i	0.428806	+	0.903396i	$0.358934\pi$
$661$	−8.98572	+	39.3690i	−0.349504	+	1.53128i	−0.778310	+	0.627880i	$0.783923\pi$
$662$	1.16579	+	5.10768i	0.0453099	+	0.198515i
$663$	10.4787	−	5.04627i	0.406958	−	0.195981i
$664$	5.27370	−	10.9509i	0.204659	−	0.424979i
$665$	−16.6515	+	3.80061i	−0.645719	+	0.147381i
$666$	−12.8193			−0.496739
$667$		0			0
$668$	4.64368			0.179669
$669$	14.4382	−	3.29542i	0.558213	−	0.127408i
$670$	−1.15507	+	2.39854i	−0.0446244	+	0.0926635i
$671$	−24.5277	+	11.8119i	−0.946880	+	0.455993i
$672$	−3.97939	−	17.4349i	−0.153508	−	0.672564i
$673$	−9.07755	+	39.7713i	−0.349914	+	1.53307i	0.427461	+	0.904034i	$0.359408\pi$
$673$	−9.07755	+	39.7713i	−0.349914	+	1.53307i	−0.777374	+	0.629038i	$0.783449\pi$
$674$	7.34401	+	3.53669i	0.282881	+	0.136228i
$675$	−0.376785	+	0.300476i	−0.0145025	+	0.0115653i
$676$	−3.41905	−	4.28735i	−0.131502	−	0.164898i
$677$	8.93310	+	18.5498i	0.343327	+	0.712926i	0.999117	−	0.0420177i	$-0.0133786\pi$
$677$	8.93310	+	18.5498i	0.343327	+	0.712926i	−0.655790	+	0.754943i	$0.727664\pi$
$678$	−18.6203	−	14.8492i	−0.715107	−	0.570279i
$679$		−	14.8742i		−	0.570818i
$680$	−3.61540	+	4.53357i	−0.138644	+	0.173855i
$681$	−41.3472	−	9.43723i	−1.58443	−	0.361636i
$682$	6.85022	+	1.56352i	0.262309	+	0.0598702i
$683$	7.87927	−	9.88029i	0.301492	−	0.378059i	−0.607890	−	0.794021i	$-0.707984\pi$
$683$	7.87927	−	9.88029i	0.301492	−	0.378059i	0.909382	+	0.415963i	$0.136555\pi$
$684$			43.9801i			1.68162i
$685$	−10.6046	−	8.45686i	−0.405179	−	0.323120i
$686$	−3.55395	−	7.37986i	−0.135690	−	0.281764i
$687$	24.9001	+	31.2237i	0.949997	+	1.19126i
$688$	−21.5285	+	17.1684i	−0.820765	+	0.654539i
$689$	−16.4056	−	7.90052i	−0.625003	−	0.300986i
$690$	−0.584159	+	2.55937i	−0.0222385	+	0.0974334i
$691$	4.92158	+	21.5628i	0.187226	+	0.820289i	0.978071	+	0.208273i	$0.0667842\pi$
$691$	4.92158	+	21.5628i	0.187226	+	0.820289i	−0.790845	+	0.612016i	$0.790359\pi$
$692$	36.9652	−	17.8015i	1.40521	−	0.676712i
$693$	12.0252	−	24.9705i	0.456798	−	0.948551i
$694$	−18.3388	+	4.18570i	−0.696130	+	0.158887i
$695$	−27.3453			−1.03726
$696$		0			0
$697$	2.62748			0.0995229
$698$	16.1939	−	3.69615i	0.612948	−	0.139901i
$699$	−18.5598	+	38.5398i	−0.701996	+	1.45771i
$700$	−0.292075	+	0.140656i	−0.0110394	+	0.00531630i
$701$	0.486817	+	2.13288i	0.0183868	+	0.0805579i	0.983289	−	0.182052i	$-0.0582739\pi$
$701$	0.486817	+	2.13288i	0.0183868	+	0.0805579i	−0.964902	+	0.262610i	$0.915417\pi$
$702$	1.20135	−	5.26344i	0.0453419	−	0.198656i
$703$	31.6400	+	15.2370i	1.19333	+	0.574675i
$704$	−9.36735	+	7.47021i	−0.353045	+	0.281544i
$705$	10.6427	+	13.3455i	0.400827	+	0.502621i
$706$	−2.66569	−	5.53537i	−0.100325	−	0.208326i
$707$	0.992046	+	0.791130i	0.0373097	+	0.0297535i
$708$		−	20.3780i		−	0.765852i
$709$	−18.5787	+	23.2969i	−0.697736	+	0.874934i	−0.996852	−	0.0792830i	$-0.974737\pi$
$709$	−18.5787	+	23.2969i	−0.697736	+	0.874934i	0.299116	+	0.954217i	$0.403308\pi$
$710$	17.1248	+	3.90861i	0.642681	+	0.146688i
$711$	8.76778	+	2.00119i	0.328818	+	0.0750505i
$712$	−14.2207	+	17.8322i	−0.532944	+	0.668290i
$713$			2.37446i			0.0889244i
$714$	−1.92908	−	1.53839i	−0.0721941	−	0.0575729i
$715$	−15.0275	−	31.2050i	−0.561997	−	1.16700i
$716$	22.7191	+	28.4889i	0.849054	+	1.06468i
$717$	−19.7881	+	15.7805i	−0.738999	+	0.589332i
$718$	1.80040	+	0.867029i	0.0671905	+	0.0323572i
$719$	−1.80941	+	7.92753i	−0.0674795	+	0.295647i	−0.997396	−	0.0721247i	$-0.977022\pi$
$719$	−1.80941	+	7.92753i	−0.0674795	+	0.295647i	0.929916	+	0.367772i	$0.119879\pi$
$720$	−5.21035	−	22.8280i	−0.194178	−	0.850750i
$721$	−9.12353	+	4.39366i	−0.339778	+	0.163628i
$722$	−3.64423	+	7.56733i	−0.135624	+	0.281627i
$723$	27.4063	−	6.25531i	1.01925	−	0.232637i
$724$	15.8108			0.587604
$725$		0			0
$726$	19.3898			0.719621
$727$	9.94820	−	2.27061i	0.368958	−	0.0842123i	−0.0340217	−	0.999421i	$-0.510832\pi$
$727$	9.94820	−	2.27061i	0.368958	−	0.0842123i	0.402980	+	0.915209i	$0.367974\pi$
$728$	3.38830	−	7.03588i	0.125579	−	0.260767i
$729$	−38.6143	+	18.5957i	−1.43016	+	0.688728i
$730$	0.851549	+	3.73088i	0.0315172	+	0.138086i
$731$	−3.37388	+	14.7819i	−0.124787	+	0.546729i
$732$	−22.9253	−	11.0402i	−0.847343	−	0.408059i
$733$	−19.2798	+	15.3751i	−0.712115	+	0.567893i	−0.911138	−	0.412102i	$-0.864795\pi$
$733$	−19.2798	+	15.3751i	−0.712115	+	0.567893i	0.199023	+	0.979995i	$0.436223\pi$
$734$	4.07613	+	5.11131i	0.150453	+	0.188662i
$735$	−13.6574	−	28.3600i	−0.503762	−	1.04607i
$736$	3.45100	+	2.75208i	0.127205	+	0.101443i
$737$			11.8341i			0.435913i
$738$	2.58571	−	3.24237i	0.0951812	−	0.119353i
$739$	4.06706	+	0.928279i	0.149609	+	0.0341473i	0.296670	−	0.954980i	$-0.404124\pi$
$739$	4.06706	+	0.928279i	0.149609	+	0.0341473i	−0.147060	+	0.989128i	$0.546981\pi$
$740$	−22.0395	−	5.03038i	−0.810190	−	0.184921i
$741$	−31.3544	+	39.3172i	−1.15183	+	1.44435i
$742$			3.86299i			0.141815i
$743$	2.18799	+	1.74486i	0.0802694	+	0.0640127i	0.662802	−	0.748794i	$-0.269367\pi$
$743$	2.18799	+	1.74486i	0.0802694	+	0.0640127i	−0.582533	+	0.812807i	$0.697938\pi$
$744$	6.12733	+	12.7235i	0.224639	+	0.466468i
$745$	−28.5910	−	35.8520i	−1.04749	−	1.31351i
$746$	−9.98749	+	7.96476i	−0.365668	+	0.291610i
$747$	24.3488	+	11.7258i	0.890878	+	0.429024i
$748$	−2.66740	+	11.6867i	−0.0975299	+	0.427307i
$749$	−1.57886	−	6.91746i	−0.0576905	−	0.252758i
$750$	14.0579	−	6.76995i	0.513323	−	0.247203i
$751$	6.37845	−	13.2450i	0.232753	−	0.483316i	−0.751579	−	0.659643i	$-0.770707\pi$
$751$	6.37845	−	13.2450i	0.232753	−	0.483316i	0.984332	+	0.176327i	$0.0564216\pi$
$752$	7.01130	−	1.60028i	0.255676	−	0.0583564i
$753$	−39.8019			−1.45046
$754$		0			0
$755$	44.1387			1.60637
$756$	7.42744	−	1.69526i	0.270133	−	0.0616562i
$757$	9.95155	−	20.6646i	0.361695	−	0.751068i	−0.638127	−	0.769931i	$-0.720290\pi$
$757$	9.95155	−	20.6646i	0.361695	−	0.751068i	0.999822	+	0.0188632i	$0.00600469\pi$
$758$	−6.00435	+	2.89154i	−0.218088	+	0.105026i
$759$	2.59674	+	11.3771i	0.0942557	+	0.412961i
$760$	5.57918	−	24.4440i	0.202378	−	0.886677i
$761$	11.3722	+	5.47655i	0.412241	+	0.198525i	0.628497	−	0.777812i	$-0.283670\pi$
$761$	11.3722	+	5.47655i	0.412241	+	0.198525i	−0.216256	+	0.976337i	$0.569385\pi$
$762$	5.93683	−	4.73446i	0.215069	−	0.171511i
$763$	−6.40650	−	8.03349i	−0.231931	−	0.290832i
$764$	−14.5365	−	30.1853i	−0.525911	−	1.09207i
$765$	−10.0802	−	8.03866i	−0.364449	−	0.290638i
$766$		−	12.2880i		−	0.443985i
$767$	8.51628	−	10.6791i	0.307505	−	0.385599i
$768$	2.77384	+	0.633110i	0.100092	+	0.0228454i
$769$	3.43897	+	0.784923i	0.124013	+	0.0283050i	0.284077	−	0.958802i	$-0.408313\pi$
$769$	3.43897	+	0.784923i	0.124013	+	0.0283050i	−0.160064	+	0.987107i	$0.551170\pi$
$770$	−4.58125	+	5.74471i	−0.165097	+	0.207025i
$771$			4.65956i			0.167810i
$772$	7.22887	+	5.76483i	0.260173	+	0.207481i
$773$	11.3711	+	23.6123i	0.408989	+	0.849274i	0.999119	+	0.0419657i	$0.0133620\pi$
$773$	11.3711	+	23.6123i	0.408989	+	0.849274i	−0.590130	+	0.807308i	$0.700924\pi$
$774$	14.9210	+	18.7104i	0.536325	+	0.672531i
$775$	0.307218	−	0.244998i	0.0110356	−	0.00880059i
$776$	19.6725	+	9.47380i	0.706203	+	0.340089i
$777$	4.60276	−	20.1660i	0.165123	−	0.723452i
$778$	−2.01042	−	8.80824i	−0.0720771	−	0.315791i
$779$	−10.2358	+	4.92930i	−0.366735	+	0.176610i
$780$	14.0458	−	29.1664i	0.502920	−	1.04432i
$781$	76.1241	−	17.3748i	2.72393	−	0.621720i
$782$	0.609008			0.0217781
$783$		0			0
$784$	−13.2617			−0.473634
$785$	−25.3301	+	5.78142i	−0.904068	+	0.206348i
$786$	−0.0168985	+	0.0350900i	−0.000602748	+	0.00125162i
$787$	−16.2283	+	7.81515i	−0.578477	+	0.278580i	−0.700156	−	0.713989i	$-0.746886\pi$
$787$	−16.2283	+	7.81515i	−0.578477	+	0.278580i	0.121679	+	0.992569i	$0.461172\pi$
$788$	3.85820	+	16.9039i	0.137443	+	0.602176i
$789$	8.10715	−	35.5197i	0.288622	−	1.26454i
$790$	−2.14815	−	1.03449i	−0.0764277	−	0.0368056i
$791$	17.6122	−	14.0453i	0.626218	−	0.499392i
$792$	25.3668	+	31.8089i	0.901368	+	1.13028i
$793$	−7.40010	−	15.3665i	−0.262785	−	0.545679i
$794$	12.0924	+	9.64339i	0.429144	+	0.342231i
$795$			34.4345i			1.22127i
$796$	−24.0544	+	30.1632i	−0.852585	+	1.06911i
$797$	34.0970	+	7.78241i	1.20778	+	0.275667i	0.778581	−	0.627544i	$-0.215940\pi$
$797$	34.0970	+	7.78241i	1.20778	+	0.275667i	0.429196	+	0.903211i	$0.358797\pi$
$798$	10.4012	+	2.37400i	0.368198	+	0.0840387i
$799$	2.46896	−	3.09598i	0.0873455	−	0.109528i
$800$		−	0.730464i		−	0.0258258i
$801$	−39.6490	−	31.6190i	−1.40093	−	1.11720i
$802$	2.74115	+	5.69207i	0.0967935	+	0.200994i
$803$	10.6063	+	13.2999i	0.374290	+	0.469344i
$804$	−8.64780	+	6.89639i	−0.304985	+	0.243217i
$805$	−2.23716	−	1.07736i	−0.0788497	−	0.0379720i
$806$	−0.979537	+	4.29163i	−0.0345027	+	0.151166i
$807$	−17.9082	−	78.4611i	−0.630399	−	2.76196i
$808$	−1.67821	+	0.808183i	−0.0590392	+	0.0284318i
$809$	16.6011	−	34.4725i	0.583663	−	1.21199i	−0.374888	−	0.927070i	$-0.622319\pi$
$809$	16.6011	−	34.4725i	0.583663	−	1.21199i	0.958551	−	0.284919i	$-0.0919668\pi$
$810$	4.05135	−	0.924694i	0.142350	−	0.0324904i
$811$	−31.7116			−1.11354			−0.556772	−	0.830665i	$-0.687960\pi$
$811$	−31.7116			−1.11354			−0.556772	+	0.830665i	$0.687960\pi$
$812$		0			0
$813$	25.2130			0.884260
$814$	14.7290	−	3.36179i	0.516250	−	0.117831i
$815$	−2.39683	+	4.97706i	−0.0839572	+	0.174339i
$816$	−8.34878	+	4.02056i	−0.292266	+	0.140748i
$817$	−14.5882	−	63.9151i	−0.510377	−	2.23611i
$818$	0.694761	−	3.04395i	0.0242917	−	0.106429i
$819$	15.6439	+	7.53371i	0.546642	+	0.263249i
$820$	5.71779	−	4.55979i	0.199674	−	0.159235i
$821$	13.3976	+	16.8000i	0.467579	+	0.586325i	0.958576	−	0.284836i	$-0.0919391\pi$
$821$	13.3976	+	16.8000i	0.467579	+	0.586325i	−0.490998	+	0.871161i	$0.663368\pi$
$822$	3.67605	+	7.63339i	0.128217	+	0.266245i
$823$	6.96053	+	5.55083i	0.242629	+	0.193490i	0.737253	−	0.675617i	$-0.236123\pi$
$823$	6.96053	+	5.55083i	0.242629	+	0.193490i	−0.494624	+	0.869107i	$0.664694\pi$
$824$		−	14.8652i		−	0.517854i
$825$	1.20408	−	1.50987i	0.0419206	−	0.0525668i
$826$	−2.82510	−	0.644811i	−0.0982979	−	0.0224358i
$827$	26.7462	+	6.10465i	0.930058	+	0.212280i	0.660605	−	0.750734i	$-0.270300\pi$
$827$	26.7462	+	6.10465i	0.930058	+	0.212280i	0.269453	+	0.963014i	$0.413157\pi$
$828$	−3.98650	+	4.99891i	−0.138540	+	0.173724i
$829$			40.4211i			1.40388i	0.712234	+	0.701942i	$0.247683\pi$
$829$			40.4211i			1.40388i	−0.712234	+	0.701942i	$0.752317\pi$
$830$	−5.60169	−	4.46720i	−0.194437	−	0.155059i
$831$	−26.1949	−	54.3943i	−0.908692	−	1.88692i
$832$	−4.68005	−	5.86860i	−0.162252	−	0.203457i
$833$	−5.70916	+	4.55290i	−0.197811	+	0.157749i
$834$	15.3893	+	7.41112i	0.532889	+	0.256626i
$835$	1.30980	−	5.73860i	0.0453274	−	0.198592i
$836$	−11.5335	−	50.5316i	−0.398894	−	1.74767i
$837$	−8.32003	+	4.00671i	−0.287582	+	0.138492i
$838$	−2.57483	+	5.34669i	−0.0889461	+	0.184698i
$839$	7.90216	−	1.80362i	0.272813	−	0.0622677i	−0.0839258	−	0.996472i	$-0.526746\pi$
$839$	7.90216	−	1.80362i	0.272813	−	0.0622677i	0.356738	+	0.934204i	$0.383889\pi$
$840$	−14.7680			−0.509543
$841$		0			0
$842$	10.3717			0.357432
$843$	−22.8696	+	5.21983i	−0.787670	+	0.179781i
$844$	−5.51461	+	11.4512i	−0.189821	+	0.394167i
$845$	−6.26263	+	3.01592i	−0.215441	+	0.103751i
$846$	−1.39081	−	6.09352i	−0.0478169	−	0.209499i
$847$	−4.08104	+	17.8802i	−0.140226	+	0.614371i
$848$	13.0710	+	6.29466i	0.448860	+	0.216159i
$849$	−30.4361	+	24.2720i	−1.04456	+	0.833012i
$850$	−0.0628377	−	0.0787959i	−0.00215531	−	0.00270268i
$851$	2.21517	+	4.59984i	0.0759349	+	0.157680i
$852$	57.0586	+	45.5027i	1.95480	+	1.55890i
$853$		−	12.7043i		−	0.434988i	−0.976062	−	0.217494i	$-0.930212\pi$
$853$		−	12.7043i		−	0.434988i	0.976062	−	0.217494i	$-0.0697883\pi$
$854$	−2.25598	+	2.82890i	−0.0771979	+	0.0968031i
$855$	54.3500	+	12.4050i	1.85873	+	0.424243i
$856$	10.1546	+	2.31773i	0.347078	+	0.0792184i
$857$	−28.8170	+	36.1353i	−0.984369	+	1.23436i	−0.0122372	+	0.999925i	$0.503895\pi$
$857$	−28.8170	+	36.1353i	−0.984369	+	1.23436i	−0.972132	+	0.234435i	$0.924676\pi$
$858$			21.6343i			0.738581i
$859$	−4.73186	−	3.77354i	−0.161449	−	0.128751i	0.539433	−	0.842029i	$-0.318639\pi$
$859$	−4.73186	−	3.77354i	−0.161449	−	0.128751i	−0.700882	+	0.713277i	$0.747210\pi$
$860$	18.3108	+	38.0228i	0.624394	+	1.29657i
$861$	4.17217	+	5.23173i	0.142187	+	0.178297i
$862$	−6.78866	+	5.41377i	−0.231223	+	0.184394i
$863$	−11.8311	−	5.69757i	−0.402736	−	0.193948i	0.221540	−	0.975151i	$-0.428892\pi$
$863$	−11.8311	−	5.69757i	−0.402736	−	0.193948i	−0.624276	+	0.781204i	$0.714606\pi$
$864$	−3.81990	+	16.7361i	−0.129955	+	0.569372i
$865$	−11.5725	−	50.7022i	−0.393475	−	1.72393i
$866$	−7.34019	+	3.53485i	−0.249430	+	0.120119i
$867$	17.6465	−	36.6434i	0.599308	−	1.24448i
$868$	−6.05608	+	1.38226i	−0.205557	+	0.0469170i
$869$	−10.5987			−0.359536
$870$		0			0
$871$	−7.41398			−0.251213
$872$	14.7056	−	3.35645i	0.497993	−	0.113664i
$873$	−21.0645	+	43.7409i	−0.712925	+	1.48040i
$874$	−2.37249	+	1.14253i	−0.0802508	+	0.0386468i
$875$	3.28406	+	14.3884i	0.111021	+	0.486417i
$876$	−3.53807	+	15.5013i	−0.119540	+	0.523740i
$877$	−27.7280	−	13.3531i	−0.936309	−	0.450903i	−0.0974436	−	0.995241i	$-0.531067\pi$
$877$	−27.7280	−	13.3531i	−0.936309	−	0.450903i	−0.838866	+	0.544338i	$0.816781\pi$
$878$	−2.15987	+	1.72244i	−0.0728921	+	0.0581295i
$879$	−54.9902	−	68.9555i	−1.85477	−	2.32581i
$880$	11.9730	+	24.8622i	0.403610	+	0.838106i
$881$	23.0801	+	18.4058i	0.777589	+	0.620107i	0.929726	−	0.368253i	$-0.120044\pi$
$881$	23.0801	+	18.4058i	0.777589	+	0.620107i	−0.152136	+	0.988360i	$0.548615\pi$
$882$			11.5258i			0.388093i
$883$	−22.4589	+	28.1626i	−0.755803	+	0.947747i	−0.999757	−	0.0220394i	$-0.992984\pi$
$883$	−22.4589	+	28.1626i	−0.755803	+	0.947747i	0.243954	+	0.969787i	$0.421555\pi$
$884$	−7.32164	−	1.67112i	−0.246253	−	0.0562057i
$885$	−25.1829	−	5.74782i	−0.846513	−	0.193211i
$886$	6.07287	−	7.61514i	0.204022	−	0.255836i
$887$		−	14.2942i		−	0.479952i	−0.970779	−	0.239976i	$-0.922860\pi$
$887$		−	14.2942i		−	0.479952i	0.970779	−	0.239976i	$-0.0771396\pi$
$888$	23.7399	+	18.9319i	0.796658	+	0.635314i
$889$	3.11632	+	6.47111i	0.104518	+	0.217034i
$890$	8.38273	+	10.5116i	0.280990	+	0.352350i
$891$	14.4423	−	11.5174i	0.483837	−	0.385847i
$892$	−8.61567	−	4.14909i	−0.288474	−	0.138922i
$893$	−3.81003	+	16.6928i	−0.127498	+	0.558604i
$894$	6.37380	+	27.9255i	0.213172	+	0.933967i
$895$	41.6144	−	20.0404i	1.39101	−	0.669877i
$896$	−6.45440	+	13.4027i	−0.215626	+	0.447753i
$897$	−7.12767	+	1.62684i	−0.237986	+	0.0543188i
$898$	−9.04279			−0.301762
$899$		0			0
$900$	1.05811			0.0352702
$901$	7.78807	−	1.77758i	0.259458	−	0.0592196i
$902$	−2.12060	+	4.40346i	−0.0706081	+	0.146619i
$903$	−34.7906	+	16.7543i	−1.15776	+	0.557547i
$904$	7.35850	+	32.2397i	0.244740	+	1.07228i
$905$	4.45960	−	19.5388i	0.148242	−	0.649491i
$906$	−24.8403	−	11.9625i	−0.825265	−	0.397427i
$907$	−15.7536	+	12.5631i	−0.523089	+	0.417149i	−0.849112	−	0.528212i	$-0.822863\pi$
$907$	−15.7536	+	12.5631i	−0.523089	+	0.417149i	0.326024	+	0.945362i	$0.394291\pi$
$908$	17.0743	+	21.4105i	0.566629	+	0.710531i
$909$	−1.79695	−	3.73141i	−0.0596012	−	0.123763i
$910$	−3.59903	−	2.87013i	−0.119307	−	0.0951439i
$911$			18.4045i			0.609769i	0.952389	+	0.304885i	$0.0986179\pi$
$911$			18.4045i			0.609769i	−0.952389	+	0.304885i	$0.901382\pi$
$912$	24.9813	−	31.3256i	0.827213	−	1.03729i
$913$	−31.0510	−	7.08719i	−1.02764	−	0.234552i
$914$	−7.52541	−	1.71763i	−0.248918	−	0.0568140i
$915$	−20.1097	+	25.2168i	−0.664806	+	0.833640i
$916$		−	25.7875i		−	0.852044i
$917$	−0.0288015	−	0.0229684i	−0.000951109	−	0.000758484i
$918$	1.02765	+	2.13394i	0.0339175	+	0.0704305i
$919$	3.31549	+	4.15749i	0.109368	+	0.137143i	0.833503	−	0.552516i	$-0.186332\pi$
$919$	3.31549	+	4.15749i	0.109368	+	0.137143i	−0.724135	+	0.689659i	$0.757761\pi$
$920$	2.84983	−	2.27266i	0.0939561	−	0.0749275i
$921$	−69.1193	−	33.2861i	−2.27756	−	1.09681i
$922$	2.53716	−	11.1160i	0.0835570	−	0.366087i
$923$	10.8852	+	47.6914i	0.358292	+	1.56978i
$924$	−27.5056	+	13.2460i	−0.904867	+	0.435761i
$925$	0.366584	−	0.761220i	0.0120532	−	0.0250288i
$926$	13.3277	−	3.04197i	0.437977	−	0.0999653i
$927$	33.0520			1.08557
$928$		0			0
$929$	−1.90689			−0.0625630			−0.0312815	−	0.999511i	$-0.509959\pi$
$929$	−1.90689			−0.0625630			−0.0312815	+	0.999511i	$0.509959\pi$
$930$	8.11586	−	1.85239i	0.266130	−	0.0607423i
$931$	13.6995	−	28.4473i	0.448983	−	0.932323i
$932$	24.8856	−	11.9843i	0.815156	−	0.392559i
$933$	−13.0660	−	57.2461i	−0.427763	−	1.87415i
$934$	1.31527	−	5.76256i	0.0430368	−	0.188557i
$935$	13.6898	+	6.59268i	0.447706	+	0.215604i
$936$	−19.9281	+	15.8922i	−0.651371	+	0.519451i
$937$	2.10308	+	2.63718i	0.0687047	+	0.0861530i	0.814996	−	0.579466i	$-0.196739\pi$
$937$	2.10308	+	2.63718i	0.0687047	+	0.0861530i	−0.746292	+	0.665619i	$0.768168\pi$
$938$	0.682442	+	1.41711i	0.0222825	+	0.0462702i
$939$	−50.3707	−	40.1693i	−1.64378	−	1.31087i
$940$		−	11.0220i		−	0.359498i
$941$	12.3641	−	15.5041i	0.403059	−	0.505420i	−0.538334	−	0.842731i	$-0.680946\pi$
$941$	12.3641	−	15.5041i	0.403059	−	0.505420i	0.941393	+	0.337312i	$0.109518\pi$
$942$	15.8221	+	3.61129i	0.515512	+	0.117662i
$943$	−1.61024	−	0.367527i	−0.0524366	−	0.0119683i
$944$	−6.78526	+	8.50845i	−0.220841	+	0.276926i
$945$		−	9.65689i		−	0.314139i
$946$	−22.0504	−	17.5846i	−0.716921	−	0.571726i
$947$	−17.5787	−	36.5025i	−0.571230	−	1.18617i	−0.963844	−	0.266467i	$-0.914144\pi$
$947$	−17.5787	−	36.5025i	−0.571230	−	1.18617i	0.392614	−	0.919703i	$-0.371571\pi$
$948$	−6.17647	−	7.74504i	−0.200602	−	0.251547i
$949$	−8.33234	+	6.64482i	−0.270479	+	0.215700i
$950$	0.392620	+	0.189076i	0.0127383	+	0.00613444i
$951$	−5.60358	+	24.5509i	−0.181709	+	0.796117i
$952$	0.762350	+	3.34007i	0.0247079	+	0.108252i
$953$	2.11000	−	1.01612i	0.0683497	−	0.0329155i	−0.399397	−	0.916778i	$-0.630780\pi$
$953$	2.11000	−	1.01612i	0.0683497	−	0.0329155i	0.467746	+	0.883863i	$0.345066\pi$
$954$	5.47068	−	11.3600i	0.177120	−	0.367793i
$955$	−41.4027	+	9.44990i	−1.33976	+	0.305792i
$956$	16.3429			0.528567
$957$		0			0
$958$	12.4378			0.401848
$959$	−7.81283	+	1.78323i	−0.252289	+	0.0575834i
$960$	−6.15895	+	12.7892i	−0.198779	+	0.412769i
$961$	−21.1462	+	10.1835i	−0.682134	+	0.328499i
$962$	2.10614	+	9.22762i	0.0679048	+	0.297511i
$963$	−5.15335	+	22.5783i	−0.166064	+	0.727576i
$964$	−16.3541	−	7.87572i	−0.526730	−	0.253660i
$965$	9.16307	−	7.30730i	0.294970	−	0.235230i
$966$	0.967043	+	1.21263i	0.0311141	+	0.0390158i
$967$	5.73972	+	11.9187i	0.184577	+	0.383278i	0.972640	−	0.232316i	$-0.0746303\pi$
$967$	5.73972	+	11.9187i	0.184577	+	0.383278i	−0.788063	+	0.615594i	$0.788916\pi$
$968$	−21.0490	−	16.7860i	−0.676540	−	0.539523i
$969$		−	22.0620i		−	0.708732i
$970$	8.02498	−	10.0630i	0.257667	−	0.323104i
$971$	−20.1227	−	4.59287i	−0.645767	−	0.147392i	−0.112920	−	0.993604i	$-0.536021\pi$
$971$	−20.1227	−	4.59287i	−0.645767	−	0.147392i	−0.532846	+	0.846212i	$0.678878\pi$
$972$	33.9459	+	7.74793i	1.08882	+	0.248515i
$973$	−10.0732	+	12.6314i	−0.322932	+	0.404944i
$974$			0.657928i			0.0210814i
$975$	0.945923	+	0.754349i	0.0302938	+	0.0241585i
$976$	5.89595	+	12.2431i	0.188725	+	0.391891i
$977$	−1.68503	−	2.11296i	−0.0539088	−	0.0675995i	0.754146	−	0.656707i	$-0.228051\pi$
$977$	−1.68503	−	2.11296i	−0.0539088	−	0.0675995i	−0.808055	+	0.589107i	$0.799480\pi$
$978$	2.69777	−	2.15140i	0.0862651	−	0.0687941i
$979$	53.8472	+	25.9314i	1.72096	+	0.828773i
$980$	−4.52278	+	19.8156i	−0.144475	+	0.632986i
$981$	7.46289	+	32.6971i	0.238272	+	1.04394i
$982$	−15.0433	+	7.24447i	−0.480051	+	0.231180i
$983$	−6.32843	+	13.1411i	−0.201846	+	0.419137i	−0.977180	−	0.212415i	$-0.931867\pi$
$983$	−6.32843	+	13.1411i	−0.201846	+	0.419137i	0.775334	+	0.631551i	$0.217582\pi$
$984$	−9.57685	+	2.18585i	−0.305299	+	0.0696825i
$985$	21.9778			0.700272
$986$		0			0
$987$	10.0850			0.321011
$988$	31.6578	−	7.22568i	1.00717	−	0.229880i
$989$	4.13533	−	8.58711i	0.131496	−	0.273054i
$990$	21.6077	−	10.4057i	0.686739	−	0.330716i
$991$	4.97316	+	21.7888i	0.157978	+	0.692146i	0.990426	+	0.138043i	$0.0440813\pi$
$991$	4.97316	+	21.7888i	0.157978	+	0.692146i	−0.832449	+	0.554102i	$0.813062\pi$
$992$	3.11461	−	13.6460i	0.0988891	−	0.433261i
$993$	24.8592	+	11.9716i	0.788884	+	0.379907i
$994$	8.11374	−	6.47050i	0.257352	−	0.205232i
$995$	30.4905	+	38.2339i	0.966615	+	1.21210i
$996$	−12.9162	−	26.8208i	−0.409266	−	0.849850i
$997$	−42.5456	−	33.9290i	−1.34743	−	1.07454i	−0.990070	−	0.140575i	$-0.955105\pi$
$997$	−42.5456	−	33.9290i	−1.34743	−	1.07454i	−0.357362	−	0.933966i	$-0.616324\pi$
$998$			5.35958i			0.169655i
$999$	−12.3797	+	15.5237i	−0.391678	+	0.491148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.l.196.7		72
29.2	odd	28		841.2.a.h.1.3	yes	6
29.3	odd	28		841.2.d.n.778.3		36
29.4	even	14	inner	841.2.e.l.236.7		72
29.5	even	14		841.2.b.d.840.6		12
29.6	even	14	inner	841.2.e.l.270.7		72
29.7	even	7	inner	841.2.e.l.63.6		72
29.8	odd	28		841.2.d.o.190.3		36
29.9	even	14	inner	841.2.e.l.651.6		72
29.10	odd	28		841.2.d.o.605.3		36
29.11	odd	28		841.2.d.n.574.3		36
29.12	odd	4		841.2.d.o.645.3		36
29.13	even	14	inner	841.2.e.l.267.6		72
29.14	odd	28		841.2.d.n.571.4		36
29.15	odd	28		841.2.d.o.571.3		36
29.16	even	7	inner	841.2.e.l.267.7		72
29.17	odd	4		841.2.d.n.645.4		36
29.18	odd	28		841.2.d.o.574.4		36
29.19	odd	28		841.2.d.n.605.4		36
29.20	even	7	inner	841.2.e.l.651.7		72
29.21	odd	28		841.2.d.n.190.4		36
29.22	even	14	inner	841.2.e.l.63.7		72
29.23	even	7	inner	841.2.e.l.270.6		72
29.24	even	7		841.2.b.d.840.7		12
29.25	even	7	inner	841.2.e.l.236.6		72
29.26	odd	28		841.2.d.o.778.4		36
29.27	odd	28		841.2.a.g.1.4	✓	6
29.28	even	2	inner	841.2.e.l.196.6		72
87.2	even	28		7569.2.a.y.1.4		6
87.56	even	28		7569.2.a.bc.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.4	✓	6	29.27	odd	28
841.2.a.h.1.3	yes	6	29.2	odd	28
841.2.b.d.840.6		12	29.5	even	14
841.2.b.d.840.7		12	29.24	even	7
841.2.d.n.190.4		36	29.21	odd	28
841.2.d.n.571.4		36	29.14	odd	28
841.2.d.n.574.3		36	29.11	odd	28
841.2.d.n.605.4		36	29.19	odd	28
841.2.d.n.645.4		36	29.17	odd	4
841.2.d.n.778.3		36	29.3	odd	28
841.2.d.o.190.3		36	29.8	odd	28
841.2.d.o.571.3		36	29.15	odd	28
841.2.d.o.574.4		36	29.18	odd	28
841.2.d.o.605.3		36	29.10	odd	28
841.2.d.o.645.3		36	29.12	odd	4
841.2.d.o.778.4		36	29.26	odd	28
841.2.e.l.63.6		72	29.7	even	7	inner
841.2.e.l.63.7		72	29.22	even	14	inner
841.2.e.l.196.6		72	29.28	even	2	inner
841.2.e.l.196.7		72	1.1	even	1	trivial
841.2.e.l.236.6		72	29.25	even	7	inner
841.2.e.l.236.7		72	29.4	even	14	inner
841.2.e.l.267.6		72	29.13	even	14	inner
841.2.e.l.267.7		72	29.16	even	7	inner
841.2.e.l.270.6		72	29.23	even	7	inner
841.2.e.l.270.7		72	29.6	even	14	inner
841.2.e.l.651.6		72	29.9	even	14	inner
841.2.e.l.651.7		72	29.20	even	7	inner
7569.2.a.y.1.4		6	87.2	even	28
7569.2.a.bc.1.3		6	87.56	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.498437 - 0.113765i) q^{2} +(1.16826 - 2.42591i) q^{3} +(-1.56644 + 0.754358i) q^{4} +(0.490395 + 2.14856i) q^{5} +(0.306319 - 1.34207i) q^{6} +(1.17312 + 0.564943i) q^{7} +(-1.49438 + 1.19173i) q^{8} +(-2.64975 - 3.32268i) q^{9} +(0.488862 + 1.01513i) q^{10} +(3.91583 + 3.12277i) q^{11} +4.68133i q^{12} +(-1.95640 + 2.45325i) q^{13} +(0.648996 + 0.148129i) q^{14} +(5.78512 + 1.32042i) q^{15} +(1.55874 - 1.95460i) q^{16} -1.37659i q^{17} +(-1.69874 - 1.35470i) q^{18} +(2.58255 + 5.36272i) q^{19} +(-2.38896 - 2.99566i) q^{20} +(2.74100 - 2.18588i) q^{21} +(2.30706 + 1.11102i) q^{22} +(-0.192554 + 0.843634i) q^{23} +(1.14521 + 5.01749i) q^{24} +(0.129021 - 0.0621331i) q^{25} +(-0.696049 + 1.44536i) q^{26} +(-3.28098 + 0.748862i) q^{27} -2.26379 q^{28} +3.03374 q^{30} +(2.67520 - 0.610597i) q^{31} +(2.21321 - 4.59578i) q^{32} +(12.1503 - 5.85126i) q^{33} +(-0.156607 - 0.686142i) q^{34} +(-0.638524 + 2.79756i) q^{35} +(6.65717 + 3.20593i) q^{36} +(4.61280 - 3.67858i) q^{37} +(1.89733 + 2.37918i) q^{38} +(3.66578 + 7.61208i) q^{39} +(-3.29335 - 2.62636i) q^{40} +1.90869i q^{41} +(1.11754 - 1.40135i) q^{42} +(-10.7381 - 2.45090i) q^{43} +(-8.48960 - 1.93770i) q^{44} +(5.83956 - 7.32258i) q^{45} +0.442405i q^{46} +(2.24903 + 1.79354i) q^{47} +(-2.92068 - 6.06485i) q^{48} +(-3.30739 - 4.14733i) q^{49} +(0.0572401 - 0.0456475i) q^{50} +(-3.33948 - 1.60821i) q^{51} +(1.21396 - 5.31869i) q^{52} +(1.29129 + 5.65752i) q^{53} +(-1.55017 + 0.746522i) q^{54} +(-4.78915 + 9.94478i) q^{55} +(-2.42635 + 0.553798i) q^{56} +16.0266 q^{57} -4.35304 q^{59} +(-10.0581 + 2.29570i) q^{60} +(-2.35836 + 4.89717i) q^{61} +(1.26396 - 0.608689i) q^{62} +(-1.23134 - 5.39485i) q^{63} +(-0.532309 + 2.33220i) q^{64} +(-6.23036 - 3.00038i) q^{65} +(5.39047 - 4.29876i) q^{66} +(1.47317 + 1.84730i) q^{67} +(1.03844 + 2.15634i) q^{68} +(1.82163 + 1.45270i) q^{69} +1.46705i q^{70} +(9.72005 - 12.1886i) q^{71} +(7.91950 + 1.80757i) q^{72} +(3.31130 + 0.755782i) q^{73} +(1.88070 - 2.35832i) q^{74} -0.385580i q^{75} +(-8.09083 - 6.45222i) q^{76} +(2.82954 + 5.87559i) q^{77} +(2.69315 + 3.37711i) q^{78} +(-1.65445 + 1.31938i) q^{79} +(4.96397 + 2.39052i) q^{80} +(0.820701 - 3.59573i) q^{81} +(0.217143 + 0.951364i) q^{82} +(-5.72931 + 2.75909i) q^{83} +(-2.64468 + 5.49174i) q^{84} +(2.95768 - 0.675070i) q^{85} -5.63110 q^{86} -9.57325 q^{88} +(11.6336 - 2.65530i) q^{89} +(2.07760 - 4.31419i) q^{90} +(-3.68103 + 1.77269i) q^{91} +(-0.334778 - 1.46676i) q^{92} +(1.64407 - 7.20313i) q^{93} +(1.32504 + 0.638106i) q^{94} +(-10.2557 + 8.17862i) q^{95} +(-8.56336 - 10.7381i) q^{96} +(-4.95650 - 10.2923i) q^{97} +(-2.12035 - 1.69092i) q^{98} -21.2856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 16 q^{4} - 4 q^{5} - 6 q^{6} + 8 q^{7} + 12 q^{9} - 12 q^{13} - 8 q^{16} + 10 q^{20} - 8 q^{22} + 10 q^{23} + 20 q^{24} - 12 q^{25} + 60 q^{28} + 312 q^{30} + 54 q^{33} - 8 q^{35} + 42 q^{36} + 82 q^{38}+ \cdots - 74 q^{96}+O(q^{100}) \) 72 * q + 16 * q^4 - 4 * q^5 - 6 * q^6 + 8 * q^7 + 12 * q^9 - 12 * q^13 - 8 * q^16 + 10 * q^20 - 8 * q^22 + 10 * q^23 + 20 * q^24 - 12 * q^25 + 60 * q^28 + 312 * q^30 + 54 * q^33 - 8 * q^35 + 42 * q^36 + 82 * q^38 - 42 * q^42 - 32 * q^45 + 24 * q^49 - 46 * q^51 + 26 * q^53 - 38 * q^54 + 192 * q^57 - 204 * q^59 - 18 * q^63 + 2 * q^64 - 64 * q^65 - 18 * q^67 + 72 * q^74 + 10 * q^80 + 44 * q^81 - 38 * q^82 + 48 * q^83 - 204 * q^86 + 252 * q^88 + 32 * q^91 - 46 * q^92 - 24 * q^93 + 74 * q^94 - 74 * q^96

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