LMFDB - Embedded newform 200.2.o.a.189.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.24
Character	$\chi$	$=$	200.189
Dual form			200.2.o.a.109.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22823 + 0.701037i) q^{2} +(0.970606 - 2.98722i) q^{3} +(1.01709 + 1.72207i) q^{4} +(0.762120 + 2.10218i) q^{5} +(3.28628 - 2.98856i) q^{6} +1.71800i q^{7} +(0.0419895 + 2.82812i) q^{8} +(-5.55435 - 4.03547i) q^{9} +(-0.537651 + 3.11624i) q^{10} +(-1.35234 - 1.86134i) q^{11} +(6.13139 - 1.36683i) q^{12} +(-4.80828 - 3.49342i) q^{13} +(-1.20438 + 2.11009i) q^{14} +(7.01940 - 0.236226i) q^{15} +(-1.93104 + 3.50301i) q^{16} +(-2.53693 + 0.824300i) q^{17} +(-3.99300 - 8.85029i) q^{18} +(5.48112 - 1.78092i) q^{19} +(-2.84496 + 3.45054i) q^{20} +(5.13203 + 1.66750i) q^{21} +(-0.356118 - 3.23419i) q^{22} +(-0.393834 - 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.83835 + 3.20423i) q^{25} +(-3.45665 - 7.66150i) q^{26} +(-9.82268 + 7.13660i) q^{27} +(-2.95851 + 1.74736i) q^{28} +(1.22579 + 0.398283i) q^{29} +(8.78703 + 4.63072i) q^{30} +(0.362926 + 1.11697i) q^{31} +(-4.82750 + 2.94877i) q^{32} +(-6.87282 + 2.23312i) q^{33} +(-3.69380 - 0.766057i) q^{34} +(-3.61155 + 1.30932i) q^{35} +(1.30007 - 13.6694i) q^{36} +(-2.95345 - 2.14581i) q^{37} +(7.98057 + 1.65509i) q^{38} +(-15.1026 + 10.9726i) q^{39} +(-5.91322 + 2.24363i) q^{40} +(6.21636 + 4.51645i) q^{41} +(5.13434 + 5.64582i) q^{42} +3.75396 q^{43} +(1.82990 - 4.22198i) q^{44} +(4.25022 - 14.7518i) q^{45} +(-0.103710 - 0.941873i) q^{46} +(8.51974 + 2.76823i) q^{47} +(8.58998 + 9.16849i) q^{48} +4.04848 q^{49} +(-6.96065 + 1.24470i) q^{50} +8.37845i q^{51} +(1.12544 - 11.8333i) q^{52} +(-1.09116 + 3.35825i) q^{53} +(-17.0675 + 1.87931i) q^{54} +(2.88223 - 4.26144i) q^{55} +(-4.85870 + 0.0721379i) q^{56} -18.1019i q^{57} +(1.22634 + 1.34851i) q^{58} +(-3.58141 + 4.92938i) q^{59} +(7.54618 + 11.8476i) q^{60} +(-0.542140 - 0.746192i) q^{61} +(-0.337282 + 1.62632i) q^{62} +(6.93293 - 9.54236i) q^{63} +(-7.99647 + 0.237503i) q^{64} +(3.67932 - 12.7703i) q^{65} +(-10.0069 - 2.07533i) q^{66} +(-4.74089 - 14.5910i) q^{67} +(-3.99980 - 3.53039i) q^{68} +(-2.00153 + 0.650336i) q^{69} +(-5.35369 - 0.923683i) q^{70} +(1.92683 - 5.93017i) q^{71} +(11.1796 - 15.8778i) q^{72} +(3.14398 + 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(5.84621 + 14.5760i) q^{75} +(8.64169 + 7.62750i) q^{76} +(3.19778 - 2.32332i) q^{77} +(-26.2416 + 2.88947i) q^{78} +(-0.125628 + 0.386644i) q^{79} +(-8.83565 - 1.38969i) q^{80} +(5.41990 + 16.6807i) q^{81} +(4.46891 + 9.90513i) q^{82} +(0.356893 + 1.09840i) q^{83} +(2.34821 + 10.5337i) q^{84} +(-3.66628 - 4.70489i) q^{85} +(4.61072 + 2.63166i) q^{86} +(2.37952 - 3.27513i) q^{87} +(5.20730 - 3.90274i) q^{88} +(3.34918 - 2.43332i) q^{89} +(15.5618 - 15.1390i) q^{90} +(6.00168 - 8.26061i) q^{91} +(0.532909 - 1.22954i) q^{92} +3.68890 q^{93} +(8.52356 + 9.37268i) q^{94} +(7.92110 + 10.1650i) q^{95} +(4.12301 + 17.2829i) q^{96} +(-14.4383 - 4.69127i) q^{97} +(4.97247 + 2.83814i) q^{98} +15.7959i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.22823	+	0.701037i	0.868489	+	0.495708i
$2$	1.22823	+	0.701037i	0.868489	+	0.495708i
$3$	0.970606	−	2.98722i	0.560380	−	1.72467i	−0.120915	−	0.992663i	$-0.538583\pi$
$3$	0.970606	−	2.98722i	0.560380	−	1.72467i	0.681295	−	0.732009i	$-0.261417\pi$
$4$	1.01709	+	1.72207i	0.508547	+	0.861034i
$5$	0.762120	+	2.10218i	0.340830	+	0.940125i
$5$	0.762120	+	2.10218i	0.340830	+	0.940125i
$6$	3.28628	−	2.98856i	1.34162	−	1.22007i
$7$			1.71800i			0.649342i	0.945827	+	0.324671i	$0.105254\pi$
$7$			1.71800i			0.649342i	−0.945827	+	0.324671i	$0.894746\pi$
$8$	0.0419895	+	2.82812i	0.0148455	+	0.999890i
$9$	−5.55435	−	4.03547i	−1.85145	−	1.34516i
$10$	−0.537651	+	3.11624i	−0.170020	+	0.985441i
$11$	−1.35234	−	1.86134i	−0.407747	−	0.561215i	0.554920	−	0.831903i	$-0.312749\pi$
$11$	−1.35234	−	1.86134i	−0.407747	−	0.561215i	−0.962667	+	0.270688i	$0.912749\pi$
$12$	6.13139	−	1.36683i	1.76998	−	0.394570i
$13$	−4.80828	−	3.49342i	−1.33358	−	0.968900i	−0.999654	−	0.0262994i	$-0.991628\pi$
$13$	−4.80828	−	3.49342i	−1.33358	−	0.968900i	−0.333922	−	0.942601i	$-0.608372\pi$
$14$	−1.20438	+	2.11009i	−0.321884	+	0.563947i
$15$	7.01940	−	0.236226i	1.81240	−	0.0609934i
$16$	−1.93104	+	3.50301i	−0.482760	+	0.875752i
$17$	−2.53693	+	0.824300i	−0.615297	+	0.199922i	−0.600051	−	0.799962i	$-0.704853\pi$
$17$	−2.53693	+	0.824300i	−0.615297	+	0.199922i	−0.0152459	+	0.999884i	$0.504853\pi$
$18$	−3.99300	−	8.85029i	−0.941159	−	2.08603i
$19$	5.48112	−	1.78092i	1.25746	−	0.408572i	0.396868	−	0.917876i	$-0.370097\pi$
$19$	5.48112	−	1.78092i	1.25746	−	0.408572i	0.860587	+	0.509304i	$0.170097\pi$
$20$	−2.84496	+	3.45054i	−0.636152	+	0.771564i
$21$	5.13203	+	1.66750i	1.11990	+	0.363878i
$22$	−0.356118	−	3.23419i	−0.0759246	−	0.689533i
$23$	−0.393834	−	0.542066i	−0.0821200	−	0.113029i	0.765981	−	0.642864i	$-0.222254\pi$
$23$	−0.393834	−	0.542066i	−0.0821200	−	0.113029i	−0.848101	+	0.529835i	$0.822254\pi$
$24$	8.48896	+	2.61955i	1.73280	+	0.534714i
$25$	−3.83835	+	3.20423i	−0.767669	+	0.640846i
$26$	−3.45665	−	7.66150i	−0.677905	−	1.50254i
$27$	−9.82268	+	7.13660i	−1.89038	+	1.37344i
$28$	−2.95851	+	1.74736i	−0.559106	+	0.330221i
$29$	1.22579	+	0.398283i	0.227624	+	0.0739594i	0.420608	−	0.907242i	$-0.361817\pi$
$29$	1.22579	+	0.398283i	0.227624	+	0.0739594i	−0.192985	+	0.981202i	$0.561817\pi$
$30$	8.78703	+	4.63072i	1.60429	+	0.845450i
$31$	0.362926	+	1.11697i	0.0651834	+	0.200614i	0.978344	−	0.206986i	$-0.0663656\pi$
$31$	0.362926	+	1.11697i	0.0651834	+	0.200614i	−0.913160	+	0.407600i	$0.866366\pi$
$32$	−4.82750	+	2.94877i	−0.853390	+	0.521273i
$33$	−6.87282	+	2.23312i	−1.19640	+	0.388735i
$34$	−3.69380	−	0.766057i	−0.633482	−	0.131378i
$35$	−3.61155	+	1.30932i	−0.610463	+	0.221315i
$36$	1.30007	−	13.6694i	0.216678	−	2.27824i
$37$	−2.95345	−	2.14581i	−0.485545	−	0.352769i	0.317924	−	0.948116i	$-0.397014\pi$
$37$	−2.95345	−	2.14581i	−0.485545	−	0.352769i	−0.803468	+	0.595347i	$0.797014\pi$
$38$	7.98057	+	1.65509i	1.29462	+	0.268491i
$39$	−15.1026	+	10.9726i	−2.41834	+	1.75703i
$40$	−5.91322	+	2.24363i	−0.934961	+	0.354749i
$41$	6.21636	+	4.51645i	0.970832	+	0.705351i	0.955641	−	0.294534i	$-0.0951643\pi$
$41$	6.21636	+	4.51645i	0.970832	+	0.705351i	0.0151912	+	0.999885i	$0.495164\pi$
$42$	5.13434	+	5.64582i	0.792245	+	0.871169i
$43$	3.75396			0.572473			0.286236	−	0.958159i	$-0.407596\pi$
$43$	3.75396			0.572473			0.286236	+	0.958159i	$0.407596\pi$
$44$	1.82990	−	4.22198i	0.275867	−	0.636488i
$45$	4.25022	−	14.7518i	0.633585	−	2.19906i
$46$	−0.103710	−	0.941873i	−0.0152912	−	0.138872i
$47$	8.51974	+	2.76823i	1.24273	+	0.403788i	0.855311	−	0.518115i	$-0.173366\pi$
$47$	8.51974	+	2.76823i	1.24273	+	0.403788i	0.387421	+	0.921903i	$0.373366\pi$
$48$	8.58998	+	9.16849i	1.23986	+	1.32336i
$49$	4.04848			0.578355
$50$	−6.96065	+	1.24470i	−0.984385	+	0.176028i
$51$			8.37845i			1.17322i
$52$	1.12544	−	11.8333i	0.156070	−	1.64099i
$53$	−1.09116	+	3.35825i	−0.149882	+	0.461291i	−0.997607	−	0.0691467i	$-0.977972\pi$
$53$	−1.09116	+	3.35825i	−0.149882	+	0.461291i	0.847724	+	0.530438i	$0.177972\pi$
$54$	−17.0675	+	1.87931i	−2.32260	+	0.255742i
$55$	2.88223	−	4.26144i	0.388640	−	0.574612i
$56$	−4.85870	+	0.0721379i	−0.649270	+	0.00963984i
$57$		−	18.1019i		−	2.39765i
$58$	1.22634	+	1.34851i	0.161026	+	0.177068i
$59$	−3.58141	+	4.92938i	−0.466259	+	0.641751i	−0.975792	−	0.218700i	$-0.929818\pi$
$59$	−3.58141	+	4.92938i	−0.466259	+	0.641751i	0.509533	+	0.860451i	$0.329818\pi$
$60$	7.54618	+	11.8476i	0.974208	+	1.52952i
$61$	−0.542140	−	0.746192i	−0.0694139	−	0.0955401i	0.772898	−	0.634530i	$-0.218806\pi$
$61$	−0.542140	−	0.746192i	−0.0694139	−	0.0955401i	−0.842312	+	0.538990i	$0.818806\pi$
$62$	−0.337282	+	1.62632i	−0.0428349	+	0.206543i
$63$	6.93293	−	9.54236i	0.873467	−	1.20222i
$64$	−7.99647	+	0.237503i	−0.999559	+	0.0296878i
$65$	3.67932	−	12.7703i	0.456364	−	1.58396i
$66$	−10.0069	−	2.07533i	−1.23176	−	0.255455i
$67$	−4.74089	−	14.5910i	−0.579192	−	1.78257i	−0.621440	−	0.783462i	$-0.713452\pi$
$67$	−4.74089	−	14.5910i	−0.579192	−	1.78257i	0.0422481	−	0.999107i	$-0.486548\pi$
$68$	−3.99980	−	3.53039i	−0.485047	−	0.428122i
$69$	−2.00153	+	0.650336i	−0.240956	+	0.0782912i
$70$	−5.35369	−	0.923683i	−0.639888	−	0.110401i
$71$	1.92683	−	5.93017i	0.228673	−	0.703782i	−0.769225	−	0.638978i	$-0.779358\pi$
$71$	1.92683	−	5.93017i	0.228673	−	0.703782i	0.997898	−	0.0648044i	$-0.0206424\pi$
$72$	11.1796	−	15.8778i	1.31752	−	1.87122i
$73$	3.14398	+	4.32732i	0.367975	+	0.506475i	0.952349	−	0.305010i	$-0.0986598\pi$
$73$	3.14398	+	4.32732i	0.367975	+	0.506475i	−0.584374	+	0.811485i	$0.698660\pi$
$74$	−2.12322	−	4.70603i	−0.246820	−	0.547064i
$75$	5.84621	+	14.5760i	0.675063	+	1.68309i
$76$	8.64169	+	7.62750i	0.991269	+	0.874934i
$77$	3.19778	−	2.32332i	0.364421	−	0.264767i
$78$	−26.2416	+	2.88947i	−2.97128	+	0.327168i
$79$	−0.125628	+	0.386644i	−0.0141343	+	0.0435008i	−0.957875	−	0.287186i	$-0.907280\pi$
$79$	−0.125628	+	0.386644i	−0.0141343	+	0.0435008i	0.943741	+	0.330687i	$0.107280\pi$
$80$	−8.83565	−	1.38969i	−0.987856	−	0.155372i
$81$	5.41990	+	16.6807i	0.602211	+	1.85342i
$82$	4.46891	+	9.90513i	0.493509	+	1.09384i
$83$	0.356893	+	1.09840i	0.0391741	+	0.120565i	0.968731	−	0.248113i	$-0.0798104\pi$
$83$	0.356893	+	1.09840i	0.0391741	+	0.120565i	−0.929557	+	0.368678i	$0.879810\pi$
$84$	2.34821	+	10.5337i	0.256211	+	1.14932i
$85$	−3.66628	−	4.70489i	−0.397664	−	0.510317i
$86$	4.61072	+	2.63166i	0.497186	+	0.283779i
$87$	2.37952	−	3.27513i	0.255111	−	0.351131i
$88$	5.20730	−	3.90274i	0.555100	−	0.416033i
$89$	3.34918	−	2.43332i	0.355013	−	0.257932i	−0.395956	−	0.918269i	$-0.629587\pi$
$89$	3.34918	−	2.43332i	0.355013	−	0.257932i	0.750969	+	0.660338i	$0.229587\pi$
$90$	15.5618	−	15.1390i	1.64036	−	1.59579i
$91$	6.00168	−	8.26061i	0.629148	−	0.865947i
$92$	0.532909	−	1.22954i	0.0555596	−	0.128188i
$93$	3.68890			0.382521
$94$	8.52356	+	9.37268i	0.879138	+	0.966718i
$95$	7.92110	+	10.1650i	0.812688	+	1.04291i
$96$	4.12301	+	17.2829i	0.420803	+	1.76393i
$97$	−14.4383	−	4.69127i	−1.46598	−	0.476327i	−0.536091	−	0.844160i	$-0.680100\pi$
$97$	−14.4383	−	4.69127i	−1.46598	−	0.476327i	−0.929892	+	0.367833i	$0.880100\pi$
$98$	4.97247	+	2.83814i	0.502295	+	0.286695i
$99$			15.7959i			1.58754i
$100$	−9.42186	−	3.35090i	−0.942186	−	0.335090i
$101$			13.7524i			1.36842i	0.729286	+	0.684209i	$0.239852\pi$
$101$			13.7524i			1.36842i	−0.729286	+	0.684209i	$0.760148\pi$
$102$	−5.87361	+	10.2907i	−0.581574	+	1.01893i
$103$	8.32817	+	2.70599i	0.820599	+	0.266629i	0.689081	−	0.724685i	$-0.258015\pi$
$103$	8.32817	+	2.70599i	0.820599	+	0.266629i	0.131519	+	0.991314i	$0.458015\pi$
$104$	9.67789	−	13.7451i	0.948996	−	1.34781i
$105$	0.405836	+	12.0593i	0.0396056	+	1.17687i
$106$	−3.69445	+	3.35975i	−0.358837	+	0.326328i
$107$	3.49350			0.337729			0.168865	−	0.985639i	$-0.445990\pi$
$107$	3.49350			0.337729			0.168865	+	0.985639i	$0.445990\pi$
$108$	−22.2803	−	9.65675i	−2.14392	−	0.929221i
$109$	−2.56568	+	3.53135i	−0.245747	+	0.338242i	−0.914016	−	0.405678i	$-0.867036\pi$
$109$	−2.56568	+	3.53135i	−0.245747	+	0.338242i	0.668269	+	0.743920i	$0.267036\pi$
$110$	6.52746	−	3.21347i	0.622369	−	0.306392i
$111$	−9.27664	+	6.73988i	−0.880500	+	0.639721i
$112$	−6.01816	−	3.31752i	−0.568663	−	0.313477i
$113$	−0.895884	+	1.23308i	−0.0842776	+	0.115998i	−0.849074	−	0.528274i	$-0.822839\pi$
$113$	−0.895884	+	1.23308i	−0.0842776	+	0.115998i	0.764796	+	0.644272i	$0.222839\pi$
$114$	12.6901	−	22.2333i	1.18854	−	2.08234i
$115$	0.839373	−	1.24103i	0.0782719	−	0.115727i
$116$	0.560872	+	2.51599i	0.0520757	+	0.233604i
$117$	12.6093	+	38.8073i	1.16573	+	3.58774i
$118$	−7.85447	+	3.54371i	−0.723062	+	0.326225i
$119$	−1.41615	−	4.35845i	−0.129818	−	0.399538i
$120$	0.962817	+	19.8418i	0.0878928	+	1.81130i
$121$	1.76343	−	5.42728i	0.160312	−	0.493389i
$122$	−0.142764	−	1.29656i	−0.0129252	−	0.117385i
$123$	19.5253	−	14.1859i	1.76053	−	1.27910i
$124$	−1.55437	+	1.76105i	−0.139587	+	0.158147i
$125$	−9.66116	−	5.62690i	−0.864120	−	0.503285i
$126$	15.2048	−	6.85996i	1.35455	−	0.611134i
$127$	−9.99210	−	13.7529i	−0.886655	−	1.22038i	−0.974533	−	0.224245i	$-0.928008\pi$
$127$	−9.99210	−	13.7529i	−0.886655	−	1.22038i	0.0878777	−	0.996131i	$-0.471992\pi$
$128$	−9.98800	−	5.31412i	−0.882823	−	0.469706i
$129$	3.64361	−	11.2139i	0.320802	−	0.987328i
$130$	13.4715	−	13.1055i	1.18153	−	1.14943i
$131$	5.71604	−	1.85725i	0.499413	−	0.162269i	−0.0484693	−	0.998825i	$-0.515434\pi$
$131$	5.71604	−	1.85725i	0.499413	−	0.162269i	0.547882	+	0.836556i	$0.315434\pi$
$132$	−10.8359	−	9.56419i	−0.943142	−	0.832455i
$133$	3.05962	+	9.41655i	0.265303	+	0.816519i
$134$	4.40591	−	21.2446i	0.380612	−	1.83525i
$135$	−22.4885	−	15.2101i	−1.93550	−	1.30908i
$136$	−2.43774	−	7.14013i	−0.209035	−	0.612261i
$137$	−2.43382	+	3.34986i	−0.207935	+	0.286198i	−0.900228	−	0.435418i	$-0.856600\pi$
$137$	−2.43382	+	3.34986i	−0.207935	+	0.286198i	0.692293	+	0.721616i	$0.256600\pi$
$138$	−2.91424	−	0.604384i	−0.248077	−	0.0514486i
$139$	−5.91784	−	8.14520i	−0.501944	−	0.690867i	0.480591	−	0.876945i	$-0.340422\pi$
$139$	−5.91784	−	8.14520i	−0.501944	−	0.690867i	−0.982535	+	0.186078i	$0.940422\pi$
$140$	−5.92802	−	4.88763i	−0.501009	−	0.413080i
$141$	16.5386	−	22.7635i	1.39280	−	1.91703i
$142$	6.52386	−	5.93283i	0.547470	−	0.497872i
$143$			13.6741i			1.14349i
$144$	24.8620	−	11.6643i	2.07183	−	0.972023i
$145$	0.0969343	+	2.88038i	0.00804996	+	0.239202i
$146$	0.827918	+	7.51899i	0.0685190	+	0.622276i
$147$	3.92948	−	12.0937i	0.324098	−	0.997472i
$148$	0.691293	−	7.26854i	0.0568239	−	0.597470i
$149$			13.6951i			1.12195i	0.827834	+	0.560973i	$0.189573\pi$
$149$			13.6951i			1.12195i	−0.827834	+	0.560973i	$0.810427\pi$
$150$	−3.03785	+	22.0011i	−0.248039	+	1.79638i
$151$	−12.0927			−0.984088			−0.492044	−	0.870570i	$-0.663750\pi$
$151$	−12.0927			−0.984088			−0.492044	+	0.870570i	$0.663750\pi$
$152$	5.26681	+	15.4265i	0.427195	+	1.25125i
$153$	17.4175	+	5.65928i	1.40812	+	0.457525i
$154$	5.55634	−	0.611810i	0.447742	−	0.0493010i
$155$	−2.07149	+	1.61420i	−0.166386	+	0.129656i
$156$	−34.2564	−	14.8474i	−2.74270	−	1.18875i
$157$	−12.6051			−1.00599			−0.502997	−	0.864288i	$-0.667769\pi$
$157$	−12.6051			−1.00599			−0.502997	+	0.864288i	$0.667769\pi$
$158$	−0.425352	+	0.386817i	−0.0338392	+	0.0307735i
$159$	8.97273	+	6.51907i	0.711584	+	0.516996i
$160$	−9.87798	−	7.90098i	−0.780923	−	0.624627i
$161$	0.931268	−	0.676606i	0.0733942	−	0.0533240i
$162$	−5.03694	+	24.2873i	−0.395739	+	1.90819i
$163$	−9.55541	−	6.94241i	−0.748438	−	0.543772i	0.146904	−	0.989151i	$-0.453069\pi$
$163$	−9.55541	−	6.94241i	−0.748438	−	0.543772i	−0.895342	+	0.445379i	$0.853069\pi$
$164$	−1.45502	+	15.2987i	−0.113618	+	1.19462i
$165$	−9.93233	−	12.7460i	−0.773231	−	0.992277i
$166$	−0.331676	+	1.59929i	−0.0257430	+	0.124129i
$167$	10.4420	−	3.39280i	0.808023	−	0.262543i	0.124263	−	0.992249i	$-0.460343\pi$
$167$	10.4420	−	3.39280i	0.808023	−	0.262543i	0.683760	+	0.729707i	$0.260343\pi$
$168$	−4.50039	+	14.5840i	−0.347213	+	1.12518i
$169$	6.89835	+	21.2309i	0.530642	+	1.63315i
$170$	−1.20473	−	8.34888i	−0.0923985	−	0.640330i
$171$	−37.6309	−	12.2270i	−2.87771	−	0.935024i
$172$	3.81812	+	6.46457i	0.291129	+	0.492919i
$173$	−12.2681	+	8.91328i	−0.932725	+	0.677664i	−0.946659	−	0.322238i	$-0.895565\pi$
$173$	−12.2681	+	8.91328i	−0.932725	+	0.677664i	0.0139334	+	0.999903i	$0.495565\pi$
$174$	5.21858	−	2.35448i	0.395620	−	0.178492i
$175$	−5.50486	−	6.59427i	−0.416128	−	0.498480i
$176$	9.13172	−	1.14294i	0.688329	−	0.0861527i
$177$	11.2490	+	15.4829i	0.845527	+	1.16377i
$178$	5.81941	−	0.640777i	0.436183	−	0.0480283i
$179$	20.5530	+	6.67808i	1.53620	+	0.499143i	0.950326	−	0.311256i	$-0.100750\pi$
$179$	20.5530	+	6.67808i	1.53620	+	0.499143i	0.585878	+	0.810399i	$0.300750\pi$
$180$	29.7264	−	7.68476i	2.21568	−	0.572788i
$181$	8.26366	−	2.68502i	0.614233	−	0.199576i	0.0146547	−	0.999893i	$-0.495335\pi$
$181$	8.26366	−	2.68502i	0.614233	−	0.199576i	0.599578	+	0.800316i	$0.295335\pi$
$182$	13.1624	−	5.93852i	0.975665	−	0.440192i
$183$	−2.75524	+	0.895233i	−0.203673	+	0.0661775i
$184$	1.51649	−	1.13657i	0.111797	−	0.0837890i
$185$	2.26000	−	7.84406i	0.166158	−	0.576707i
$186$	4.53081	+	2.58605i	0.332215	+	0.189619i
$187$	4.96511	+	3.60736i	0.363085	+	0.263796i
$188$	3.89829	+	17.4871i	0.284312	+	1.27538i
$189$	−12.2607	−	16.8753i	−0.891831	−	1.22750i
$190$	2.60285	+	18.0380i	0.188831	+	1.30861i
$191$	0.689197	+	0.500731i	0.0498686	+	0.0362316i	0.612440	−	0.790517i	$-0.290188\pi$
$191$	0.689197	+	0.500731i	0.0498686	+	0.0362316i	−0.562572	+	0.826748i	$0.690188\pi$
$192$	−7.05196	+	24.1177i	−0.508931	+	1.74055i
$193$		−	10.7404i		−	0.773113i	−0.922266	−	0.386557i	$-0.873664\pi$
$193$		−	10.7404i		−	0.773113i	0.922266	−	0.386557i	$-0.126336\pi$
$194$	−14.4447	−	15.8837i	−1.03707	−	1.14038i
$195$	−34.5765	−	23.3859i	−2.47607	−	1.67470i
$196$	4.11769	+	6.97177i	0.294121	+	0.497983i
$197$	6.98882	−	21.5094i	0.497933	−	1.53248i	−0.314403	−	0.949290i	$-0.601804\pi$
$197$	6.98882	−	21.5094i	0.497933	−	1.53248i	0.812336	−	0.583190i	$-0.198196\pi$
$198$	−11.0735	+	19.4010i	−0.786959	+	1.37877i
$199$	0.706769			0.0501015			0.0250508	−	0.999686i	$-0.492025\pi$
$199$	0.706769			0.0501015			0.0250508	+	0.999686i	$0.492025\pi$
$200$	−9.22310	−	10.7207i	−0.652172	−	0.758071i
$201$	−48.1879			−3.39891
$202$	−9.64096	+	16.8911i	−0.678336	+	1.18846i
$203$	−0.684250	+	2.10590i	−0.0480249	+	0.147806i
$204$	−14.4283	+	8.52167i	−1.01018	+	0.596636i
$205$	−4.75679	+	16.5100i	−0.332229	+	1.15311i
$206$	8.33191	+	9.16193i	0.580511	+	0.638342i
$207$			4.60013i			0.319731i
$208$	21.5225	−	10.0975i	1.49231	−	0.700136i
$209$	−10.7273	−	7.79381i	−0.742020	−	0.539109i
$210$	−7.95557	+	15.0961i	−0.548986	+	1.04173i
$211$	10.7903	+	14.8516i	0.742834	+	1.02242i	0.998451	+	0.0556452i	$0.0177216\pi$
$211$	10.7903	+	14.8516i	0.742834	+	1.02242i	−0.255616	+	0.966778i	$0.582278\pi$
$212$	−6.89295	+	1.53660i	−0.473409	+	0.105534i
$213$	−15.8445	−	11.5117i	−1.08565	−	0.788770i
$214$	4.29082	+	2.44907i	0.293314	+	0.167415i
$215$	2.86096	+	7.89150i	0.195116	+	0.538196i
$216$	−20.5956	−	27.4800i	−1.40135	−	1.86978i
$217$	−1.91895	+	0.623506i	−0.130267	+	0.0423263i
$218$	−5.62685	+	2.53868i	−0.381098	+	0.171941i
$219$	15.9782	−	5.19164i	1.07971	−	0.350818i
$220$	10.2700	+	0.629120i	0.692402	+	0.0424153i
$221$	15.0779	+	4.89911i	1.01425	+	0.329550i
$222$	−16.1187	+	1.77484i	−1.08182	+	0.119119i
$223$	−4.51123	−	6.20918i	−0.302094	−	0.415797i	0.630801	−	0.775945i	$-0.282726\pi$
$223$	−4.51123	−	6.20918i	−0.302094	−	0.415797i	−0.932895	+	0.360147i	$0.882726\pi$
$224$	−5.06597	−	8.29364i	−0.338485	−	0.554142i
$225$	34.2501	−	2.30788i	2.28334	−	0.153858i
$226$	−1.96478	+	0.886455i	−0.130695	+	0.0589661i
$227$	−9.47829	+	6.88638i	−0.629096	+	0.457065i	−0.856087	−	0.516832i	$-0.827111\pi$
$227$	−9.47829	+	6.88638i	−0.629096	+	0.457065i	0.226991	+	0.973897i	$0.427111\pi$
$228$	31.1727	−	18.4113i	2.06446	−	1.21932i
$229$	−25.6372	−	8.33003i	−1.69415	−	0.550464i	−0.706582	−	0.707631i	$-0.749764\pi$
$229$	−25.6372	−	8.33003i	−1.69415	−	0.550464i	−0.987572	+	0.157167i	$0.949764\pi$
$230$	1.90095	−	0.935837i	0.125345	−	0.0617073i
$231$	−3.83649	−	11.8075i	−0.252422	−	0.776876i
$232$	−1.07492	+	3.48340i	−0.0705720	+	0.228696i
$233$	13.2560	−	4.30712i	0.868426	−	0.282169i	0.159283	−	0.987233i	$-0.449082\pi$
$233$	13.2560	−	4.30712i	0.868426	−	0.282169i	0.709144	+	0.705064i	$0.249082\pi$
$234$	−11.7183	+	56.5039i	−0.766050	+	3.69377i
$235$	0.673733	+	20.0198i	0.0439495	+	1.30595i
$236$	−12.1314	−	1.15378i	−0.789684	−	0.0751049i
$237$	1.03305	+	0.750558i	0.0671041	+	0.0487540i
$238$	1.31608	−	6.34594i	0.0853090	−	0.411346i
$239$	7.73830	−	5.62220i	0.500549	−	0.363670i	−0.308678	−	0.951167i	$-0.599886\pi$
$239$	7.73830	−	5.62220i	0.500549	−	0.363670i	0.809227	+	0.587497i	$0.199886\pi$
$240$	−12.7272	+	25.0452i	−0.821540	+	1.61666i
$241$	20.3460	+	14.7823i	1.31060	+	0.952210i	0.999999	+	0.00167085i	$0.000531849\pi$
$241$	20.3460	+	14.7823i	1.31060	+	0.952210i	0.310606	+	0.950539i	$0.399468\pi$
$242$	5.97063	−	5.42972i	0.383806	−	0.349035i
$243$	18.6651			1.19737
$244$	0.733587	−	1.69255i	0.0469631	−	0.108354i
$245$	3.08543	+	8.51066i	0.197121	+	0.543726i
$246$	33.9264	−	3.73564i	2.16307	−	0.238176i
$247$	−32.5763	−	10.5847i	−2.07278	−	0.673486i
$248$	−3.14369	+	1.07330i	−0.199624	+	0.0681545i
$249$	3.62757			0.229888
$250$	−7.92145	−	13.6840i	−0.500996	−	0.865449i
$251$		−	6.91776i		−	0.436645i	−0.975877	−	0.218323i	$-0.929941\pi$
$251$		−	6.91776i		−	0.436645i	0.975877	−	0.218323i	$-0.0700585\pi$
$252$	23.4840	+	2.23351i	1.47936	+	0.140698i
$253$	−0.476370	+	1.46612i	−0.0299492	+	0.0921740i
$254$	−2.63126	−	23.8966i	−0.165100	−	1.49941i
$255$	−17.6130	+	6.38538i	−1.10297	+	0.399868i
$256$	−8.54216	−	13.5289i	−0.533885	−	0.845557i
$257$			29.8090i			1.85943i	0.368277	+	0.929716i	$0.379948\pi$
$257$			29.8090i			1.85943i	−0.368277	+	0.929716i	$0.620052\pi$
$258$	12.3365	−	11.2189i	0.768040	−	0.698459i
$259$	3.68650	−	5.07403i	0.229068	−	0.315285i
$260$	25.7335	−	6.65253i	1.59593	−	0.412572i
$261$	−5.20121	−	7.15885i	−0.321947	−	0.443122i
$262$	8.32261	+	1.72602i	0.514173	+	0.106634i
$263$	−15.5573	+	21.4128i	−0.959304	+	1.32037i	−0.0120353	+	0.999928i	$0.503831\pi$
$263$	−15.5573	+	21.4128i	−0.959304	+	1.32037i	−0.947269	+	0.320441i	$0.896169\pi$
$264$	−6.60409	−	19.3434i	−0.406454	−	1.19050i
$265$	−7.89125	+	0.265567i	−0.484755	+	0.0163137i
$266$	−2.84344	+	13.7106i	−0.174342	+	0.840650i
$267$	−4.01813	−	12.3665i	−0.245906	−	0.756820i
$268$	20.3047	−	23.0045i	1.24031	−	1.40522i
$269$	−7.64014	+	2.48243i	−0.465827	+	0.151357i	−0.532521	−	0.846417i	$-0.678755\pi$
$269$	−7.64014	+	2.48243i	−0.465827	+	0.151357i	0.0666932	+	0.997774i	$0.478755\pi$
$270$	−16.9581	−	34.4468i	−1.03204	−	2.09637i
$271$	2.87827	−	8.85842i	0.174843	−	0.538111i	−0.824784	−	0.565449i	$-0.808703\pi$
$271$	2.87827	−	8.85842i	0.174843	−	0.538111i	0.999626	+	0.0273381i	$0.00870306\pi$
$272$	2.01140	−	10.4787i	0.121959	−	0.635362i
$273$	−18.8510	−	25.9461i	−1.14091	−	1.57033i
$274$	−5.33766	+	2.40820i	−0.322460	+	0.145485i
$275$	11.1549	+	2.81125i	0.672667	+	0.169525i
$276$	−3.15566	−	2.78531i	−0.189949	−	0.167656i
$277$	3.05174	−	2.21722i	0.183361	−	0.133220i	−0.492318	−	0.870415i	$-0.663850\pi$
$277$	3.05174	−	2.21722i	0.183361	−	0.133220i	0.675679	+	0.737196i	$0.263850\pi$
$278$	−1.55837	−	14.1528i	−0.0934647	−	0.848829i
$279$	2.49169	−	7.66863i	0.149173	−	0.459109i
$280$	−3.85455	−	10.1589i	−0.230354	−	0.607110i
$281$	−6.62409	−	20.3869i	−0.395160	−	1.21618i	−0.928837	−	0.370489i	$-0.879190\pi$
$281$	−6.62409	−	20.3869i	−0.395160	−	1.21618i	0.533676	−	0.845689i	$-0.320810\pi$
$282$	36.2713	−	16.3646i	2.15992	−	0.974495i
$283$	−0.286114	−	0.880568i	−0.0170077	−	0.0523443i	0.942192	−	0.335072i	$-0.108761\pi$
$283$	−0.286114	−	0.880568i	−0.0170077	−	0.0523443i	−0.959200	+	0.282728i	$0.908761\pi$
$284$	12.1719	−	2.71341i	0.722271	−	0.161011i
$285$	38.0535	−	13.7958i	2.25409	−	0.817193i
$286$	−9.58608	+	16.7950i	−0.566837	+	0.993108i
$287$	−7.75925	+	10.6797i	−0.458014	+	0.630402i
$288$	38.7133	+	3.10276i	2.28120	+	0.182832i
$289$	−7.99672	+	5.80996i	−0.470395	+	0.341762i
$290$	−1.90019	+	3.60572i	−0.111583	+	0.211735i
$291$	−28.0277	+	38.5769i	−1.64301	+	2.26142i
$292$	−4.25422	+	9.81544i	−0.248959	+	0.574405i
$293$	13.3571			0.780332			0.390166	−	0.920744i	$-0.372418\pi$
$293$	13.3571			0.780332			0.390166	+	0.920744i	$0.372418\pi$
$294$	13.3044	−	12.0991i	0.775931	−	0.705636i
$295$	−13.0919	−	3.77199i	−0.762241	−	0.219614i
$296$	5.94458	−	8.44281i	0.345522	−	0.490728i
$297$	26.5673	+	8.63223i	1.54159	+	0.500893i
$298$	−9.60077	+	16.8207i	−0.556157	+	0.974397i
$299$			3.98223i			0.230298i
$300$	−19.1548	+	24.8928i	−1.10590	+	1.43718i
$301$			6.44929i			0.371731i
$302$	−14.8526	−	8.47742i	−0.854670	−	0.487821i
$303$	41.0815	+	13.3482i	2.36007	+	0.766833i
$304$	−4.34568	+	22.6395i	−0.249242	+	1.29846i
$305$	1.15546	−	1.70837i	0.0661612	−	0.0978207i
$306$	17.4253	+	19.1612i	0.996137	+	1.09537i
$307$	14.1781			0.809186			0.404593	−	0.914497i	$-0.367413\pi$
$307$	14.1781			0.809186			0.404593	+	0.914497i	$0.367413\pi$
$308$	7.25336	+	3.14376i	0.413298	+	0.179132i
$309$	16.1668	−	22.2516i	0.919695	−	1.26585i
$310$	−3.67588	+	0.530423i	−0.208776	+	0.0301260i
$311$	0.386936	−	0.281125i	0.0219411	−	0.0159412i	−0.576761	−	0.816913i	$-0.695683\pi$
$311$	0.386936	−	0.281125i	0.0219411	−	0.0159412i	0.598702	+	0.800972i	$0.295683\pi$
$312$	−31.6661	−	42.2510i	−1.79274	−	2.39199i
$313$	−6.67701	+	9.19012i	−0.377407	+	0.519456i	−0.954895	−	0.296943i	$-0.904033\pi$
$313$	−6.67701	+	9.19012i	−0.377407	+	0.519456i	0.577488	+	0.816399i	$0.304033\pi$
$314$	−15.4819	−	8.83662i	−0.873695	−	0.498679i
$315$	25.3435	+	7.30187i	1.42794	+	0.411414i
$316$	−0.793603	+	0.176913i	−0.0446436	+	0.00995211i
$317$	4.27173	+	13.1470i	0.239924	+	0.738411i	0.996430	+	0.0844241i	$0.0269051\pi$
$317$	4.27173	+	13.1470i	0.239924	+	0.738411i	−0.756505	+	0.653987i	$0.773095\pi$
$318$	6.45046	+	14.2971i	0.361724	+	0.801744i
$319$	−0.916348	−	2.82023i	−0.0513056	−	0.157902i
$320$	−6.59354	−	16.6290i	−0.368590	−	0.929592i
$321$	3.39081	−	10.4358i	0.189257	−	0.582472i
$322$	1.61814	−	0.178173i	0.0901752	−	0.00992921i
$323$	−12.4372	+	9.03618i	−0.692026	+	0.502786i
$324$	−23.2128	+	26.2993i	−1.28960	+	1.46107i
$325$	29.6496	−	1.99788i	1.64466	−	0.110822i
$326$	−6.86935	−	15.2256i	−0.380458	−	0.843267i
$327$	8.05866	+	11.0918i	0.445645	+	0.613378i
$328$	−12.5120	+	17.7702i	−0.690861	+	0.981197i
$329$	−4.75581	+	14.6369i	−0.262197	+	0.806958i
$330$	−3.26374	−	22.6180i	−0.179663	−	1.24508i
$331$	6.42804	−	2.08860i	0.353317	−	0.114800i	−0.126981	−	0.991905i	$-0.540529\pi$
$331$	6.42804	−	2.08860i	0.353317	−	0.114800i	0.480298	+	0.877105i	$0.340529\pi$
$332$	−1.52853	+	1.73177i	−0.0838891	+	0.0950434i
$333$	7.74516	+	23.8372i	0.424432	+	1.30627i
$334$	15.2036	+	3.15307i	0.831904	+	0.172528i
$335$	27.0597	−	21.0863i	1.47843	−	1.15207i
$336$	−15.7514	+	14.7576i	−0.859311	+	0.805091i
$337$	−9.77379	+	13.4525i	−0.532412	+	0.732803i	−0.987496	−	0.157646i	$-0.949609\pi$
$337$	−9.77379	+	13.4525i	−0.532412	+	0.732803i	0.455083	+	0.890449i	$0.349609\pi$
$338$	−6.41092	+	30.9124i	−0.348708	+	1.68141i
$339$	2.81392	+	3.87303i	0.152831	+	0.210354i
$340$	4.37319	−	11.0989i	0.237170	−	0.601922i
$341$	1.58826	−	2.18606i	0.0860093	−	0.118382i
$342$	−37.6478	−	41.3983i	−2.03576	−	2.23856i
$343$			18.9813i			1.02489i
$344$	0.157627	+	10.6166i	0.00849867	+	0.572410i
$345$	−2.89253	−	3.71194i	−0.155728	−	0.199844i
$346$	−21.3166	+	2.34717i	−1.14599	+	0.126185i
$347$	−0.155098	+	0.477342i	−0.00832608	+	0.0256250i	−0.955133	−	0.296176i	$-0.904288\pi$
$347$	−0.155098	+	0.477342i	−0.00832608	+	0.0256250i	0.946807	+	0.321801i	$0.104288\pi$
$348$	8.06019	+	0.766585i	0.432072	+	0.0410933i
$349$			1.38740i			0.0742660i	0.999310	+	0.0371330i	$0.0118225\pi$
$349$			1.38740i			0.0742660i	−0.999310	+	0.0371330i	$0.988177\pi$
$350$	−2.13840	−	11.9584i	−0.114302	−	0.639203i
$351$	72.1613			3.85169
$352$	12.0171	+	4.99788i	0.640513	+	0.266388i
$353$	−27.1323	−	8.81582i	−1.44411	−	0.469218i	−0.520931	−	0.853599i	$-0.674415\pi$
$353$	−27.1323	−	8.81582i	−1.44411	−	0.469218i	−0.923175	+	0.384380i	$0.874415\pi$
$354$	2.96225	+	26.9026i	0.157442	+	1.42985i
$355$	13.9348	−	0.468952i	0.739582	−	0.0248894i
$356$	7.59678	+	3.29260i	0.402629	+	0.174508i
$357$	−14.3942			−0.761820
$358$	20.5622	+	22.6106i	1.08675	+	1.19501i
$359$	−18.7073	−	13.5917i	−0.987336	−	0.717342i	−0.0279998	−	0.999608i	$-0.508914\pi$
$359$	−18.7073	−	13.5917i	−0.987336	−	0.717342i	−0.959336	+	0.282266i	$0.908914\pi$
$360$	41.8982	+	11.4007i	2.20823	+	0.600869i
$361$	11.4997	−	8.35500i	0.605246	−	0.439737i
$362$	12.0320	+	2.49531i	0.632386	+	0.131150i
$363$	−14.5009	−	10.5355i	−0.761099	−	0.552971i
$364$	20.3296	+	1.93350i	1.06556	+	0.101343i
$365$	−6.70073	+	9.90716i	−0.350732	+	0.518565i
$366$	−4.01166	−	0.831977i	−0.209693	−	0.0434881i
$367$	26.8195	−	8.71417i	1.39996	−	0.454876i	0.490785	−	0.871281i	$-0.336710\pi$
$367$	26.8195	−	8.71417i	1.39996	−	0.454876i	0.909179	+	0.416405i	$0.136710\pi$
$368$	2.65937	−	0.332852i	0.138629	−	0.0173511i
$369$	−16.3018	−	50.1719i	−0.848640	−	2.61184i
$370$	8.27478	−	8.04996i	0.430185	−	0.418498i
$371$	−5.76946	−	1.87461i	−0.299535	−	0.0973250i
$372$	3.75195	+	6.35253i	0.194530	+	0.329364i
$373$	14.5528	−	10.5732i	0.753515	−	0.547461i	−0.143399	−	0.989665i	$-0.545803\pi$
$373$	14.5528	−	10.5732i	0.753515	−	0.547461i	0.896914	+	0.442204i	$0.145803\pi$
$374$	3.56939	+	7.91139i	0.184569	+	0.409088i
$375$	−26.1860	+	23.3985i	−1.35224	+	1.20829i
$376$	−7.47114	+	24.2110i	−0.385295	+	1.24859i
$377$	−4.50257	−	6.19726i	−0.231894	−	0.319175i
$378$	−3.22865	−	29.3220i	−0.166064	−	1.50816i
$379$	−5.18753	−	1.68553i	−0.266466	−	0.0865799i	0.172737	−	0.984968i	$-0.444739\pi$
$379$	−5.18753	−	1.68553i	−0.266466	−	0.0865799i	−0.439203	+	0.898388i	$0.644739\pi$
$380$	−9.44840	+	23.9795i	−0.484693	+	1.23012i
$381$	−50.7814	+	16.4999i	−2.60161	+	0.845315i
$382$	0.495461	+	1.09817i	0.0253500	+	0.0561870i
$383$	−13.2382	+	4.30135i	−0.676440	+	0.219789i	−0.627036	−	0.778990i	$-0.715732\pi$
$383$	−13.2382	+	4.30135i	−0.676440	+	0.219789i	−0.0494042	+	0.998779i	$0.515732\pi$
$384$	−25.5689	+	24.6784i	−1.30480	+	1.25937i
$385$	7.32114	+	4.95166i	0.373120	+	0.252360i
$386$	7.52944	−	13.1917i	0.383239	−	0.671441i
$387$	−20.8508	−	15.1490i	−1.05990	−	0.770066i
$388$	−6.60636	−	29.6351i	−0.335387	−	1.50450i
$389$	−21.7230	−	29.8991i	−1.10140	−	1.51594i	−0.833518	−	0.552492i	$-0.813677\pi$
$389$	−21.7230	−	29.8991i	−1.10140	−	1.51594i	−0.267880	−	0.963452i	$-0.586323\pi$
$390$	−26.0735	−	52.9626i	−1.32028	−	2.68186i
$391$	1.44596	+	1.05055i	0.0731251	+	0.0531285i
$392$	0.169994	+	11.4496i	0.00858599	+	0.578291i
$393$		−	18.8777i		−	0.952255i
$394$	23.6627	−	21.5190i	1.19211	−	1.08411i
$395$	−0.908540	+	0.0305754i	−0.0457136	+	0.00153842i
$396$	−27.2016	+	16.0659i	−1.36693	+	0.807341i
$397$	−7.32490	+	22.5437i	−0.367626	+	1.13144i	0.580694	+	0.814122i	$0.302781\pi$
$397$	−7.32490	+	22.5437i	−0.367626	+	1.13144i	−0.948320	+	0.317315i	$0.897219\pi$
$398$	0.868074	+	0.495471i	0.0435126	+	0.0248357i
$399$	31.0990			1.55690
$400$	−3.81244	−	19.6333i	−0.190622	−	0.981663i
$401$	−0.881338			−0.0440119			−0.0220060	−	0.999758i	$-0.507005\pi$
$401$	−0.881338			−0.0440119			−0.0220060	+	0.999758i	$0.507005\pi$
$402$	−59.1858	−	33.7815i	−2.95192	−	1.68487i
$403$	2.15700	−	6.63856i	0.107448	−	0.330690i
$404$	−23.6826	+	13.9875i	−1.17825	+	0.695904i
$405$	−30.9354	+	24.1063i	−1.53719	+	1.19785i
$406$	−2.31673	+	2.10685i	−0.114978	+	0.104561i
$407$			8.39925i			0.416335i
$408$	−23.6952	+	0.351807i	−1.17309	+	0.0174171i
$409$	28.9714	+	21.0489i	1.43254	+	1.04080i	0.989536	+	0.144283i	$0.0460876\pi$
$409$	28.9714	+	21.0489i	1.43254	+	1.04080i	0.443005	+	0.896519i	$0.353912\pi$
$410$	−17.4166	+	16.9434i	−0.860143	+	0.836774i
$411$	7.64449	+	10.5217i	0.377075	+	0.518999i
$412$	3.81063	+	17.0939i	0.187737	+	0.842158i
$413$	−8.46866	−	6.15285i	−0.416716	−	0.302762i
$414$	−3.22486	+	5.65001i	−0.158493	+	0.277683i
$415$	−2.03705	+	1.58737i	−0.0999949	+	0.0779209i
$416$	33.5132	+	2.68599i	1.64312	+	0.131692i
$417$	−30.0754	+	9.77209i	−1.47280	+	0.478541i
$418$	−7.71178	−	17.0928i	−0.377196	−	0.836036i
$419$	−18.1069	+	5.88329i	−0.884581	+	0.287418i	−0.715858	−	0.698246i	$-0.753964\pi$
$419$	−18.1069	+	5.88329i	−0.884581	+	0.287418i	−0.168723	+	0.985664i	$0.553964\pi$
$420$	−20.3542	+	12.9643i	−0.993183	+	0.632594i
$421$	8.42477	+	2.73737i	0.410598	+	0.133411i	0.507031	−	0.861928i	$-0.330743\pi$
$421$	8.42477	+	2.73737i	0.410598	+	0.133411i	−0.0964323	+	0.995340i	$0.530743\pi$
$422$	2.84145	+	25.8055i	0.138320	+	1.25619i
$423$	−36.1505	−	49.7569i	−1.75770	−	2.41926i
$424$	−9.54333	−	2.94492i	−0.463465	−	0.143018i
$425$	7.09639	−	11.2929i	0.344225	−	0.547785i
$426$	−11.3906	−	25.2466i	−0.551875	−	1.22320i
$427$	1.28196	−	0.931395i	0.0620382	−	0.0450734i
$428$	3.55322	+	6.01605i	0.171751	+	0.290797i
$429$	40.8476	+	13.2722i	1.97214	+	0.640788i
$430$	−2.01832	+	11.6982i	−0.0973319	+	0.564138i
$431$	0.956566	+	2.94401i	0.0460762	+	0.141808i	0.971448	−	0.237253i	$-0.0762471\pi$
$431$	0.956566	+	2.94401i	0.0460762	+	0.141808i	−0.925372	+	0.379061i	$0.876247\pi$
$432$	−6.03156	−	48.1900i	−0.290194	−	2.31854i
$433$	8.67407	−	2.81837i	0.416849	−	0.135442i	−0.0930806	−	0.995659i	$-0.529671\pi$
$433$	8.67407	−	2.81837i	0.416849	−	0.135442i	0.509930	+	0.860216i	$0.329671\pi$
$434$	−2.79402	−	0.579450i	−0.134117	−	0.0278145i
$435$	8.69840	+	2.50615i	0.417056	+	0.120161i
$436$	−8.69077	−	0.826558i	−0.416212	−	0.0395849i
$437$	−3.12403	−	2.26974i	−0.149443	−	0.108576i
$438$	23.2645	+	4.82481i	1.11162	+	0.230538i
$439$	31.0958	−	22.5924i	1.48412	−	1.07828i	0.507920	−	0.861404i	$-0.330415\pi$
$439$	31.0958	−	22.5924i	1.48412	−	1.07828i	0.976200	−	0.216872i	$-0.0695854\pi$
$440$	12.1729	+	7.97234i	0.580318	+	0.380067i
$441$	−22.4867	−	16.3375i	−1.07080	−	0.777978i
$442$	15.0847	+	16.5874i	0.717505	+	0.788983i
$443$	−33.8214			−1.60690			−0.803451	−	0.595371i	$-0.797005\pi$
$443$	−33.8214			−1.60690			−0.803451	+	0.595371i	$0.797005\pi$
$444$	−21.0417	−	9.11993i	−0.998597	−	0.432813i
$445$	7.66777	+	5.18611i	0.363487	+	0.245845i
$446$	−1.18796	−	10.7888i	−0.0562516	−	0.510866i
$447$	40.9102	+	13.2925i	1.93499	+	0.628715i
$448$	−0.408029	−	13.7379i	−0.0192775	−	0.649056i
$449$	11.7494			0.554489			0.277245	−	0.960799i	$-0.410579\pi$
$449$	11.7494			0.554489			0.277245	+	0.960799i	$0.410579\pi$
$450$	43.6849	+	21.1760i	2.05932	+	0.998246i
$451$		−	17.6785i		−	0.832450i
$452$	−3.03464	−	0.288618i	−0.142738	−	0.0135754i
$453$	−11.7372	+	36.1235i	−0.551463	+	1.69723i
$454$	−16.4691	+	1.81342i	−0.772934	+	0.0851080i
$455$	21.9393	+	6.32107i	1.02853	+	0.296336i
$456$	51.1942	−	0.760090i	2.39739	−	0.0355945i
$457$		−	12.5132i		−	0.585342i	−0.956213	−	0.292671i	$-0.905456\pi$
$457$		−	12.5132i		−	0.585342i	0.956213	−	0.292671i	$-0.0945441\pi$
$458$	−25.6487	−	28.2038i	−1.19848	−	1.31788i
$459$	19.0368	−	26.2019i	0.888562	−	1.22300i
$460$	2.99086	+	0.183215i	0.139450	+	0.00854242i
$461$	7.24736	+	9.97513i	0.337543	+	0.464588i	0.943722	−	0.330740i	$-0.107298\pi$
$461$	7.24736	+	9.97513i	0.337543	+	0.464588i	−0.606179	+	0.795328i	$0.707298\pi$
$462$	3.56541	−	17.1918i	0.165878	−	0.799836i
$463$	−9.71829	+	13.3761i	−0.451647	+	0.621639i	−0.972751	−	0.231854i	$-0.925521\pi$
$463$	−9.71829	+	13.3761i	−0.451647	+	0.621639i	0.521103	+	0.853494i	$0.325521\pi$
$464$	−3.76224	+	3.52485i	−0.174658	+	0.163637i
$465$	2.81138	+	7.75474i	0.130375	+	0.359617i
$466$	19.3008	+	4.00279i	0.894092	+	0.185426i
$467$	−4.96826	−	15.2907i	−0.229904	−	0.707571i	−0.997757	−	0.0669450i	$-0.978675\pi$
$467$	−4.96826	−	15.2907i	−0.229904	−	0.707571i	0.767853	−	0.640626i	$-0.221325\pi$
$468$	−54.0041	+	61.1847i	−2.49634	+	2.82826i
$469$	25.0672	−	8.14484i	1.15750	−	0.376094i
$470$	−13.2071	+	25.0612i	−0.609199	+	1.15599i
$471$	−12.2346	+	37.6541i	−0.563739	+	1.73501i
$472$	−14.0912	−	9.92164i	−0.648602	−	0.456681i
$473$	−5.07663	−	6.98739i	−0.233424	−	0.321280i
$474$	0.742658	+	1.64607i	0.0341114	+	0.0756063i
$475$	−15.3320	+	24.3986i	−0.703478	+	1.11948i
$476$	6.06519	−	6.87165i	0.277998	−	0.314962i
$477$	19.6128	−	14.2495i	0.898008	−	0.652441i
$478$	13.4458	−	1.48052i	0.614995	−	0.0677173i
$479$	−6.65413	+	20.4793i	−0.304035	+	0.935723i	0.676001	+	0.736901i	$0.263712\pi$
$479$	−6.65413	+	20.4793i	−0.304035	+	0.935723i	−0.980036	+	0.198822i	$0.936288\pi$
$480$	−33.1896	+	21.8390i	−1.51489	+	0.996807i
$481$	6.70481	+	20.6353i	0.305713	+	0.940889i
$482$	14.6267	+	32.4194i	0.666227	+	1.47666i
$483$	−1.11727	−	3.43862i	−0.0508378	−	0.156463i
$484$	11.1397	−	2.48330i	0.506351	−	0.112877i
$485$	−1.14176	−	33.9272i	−0.0518448	−	1.54055i
$486$	22.9250	+	13.0849i	1.03990	+	0.593545i
$487$	15.7256	−	21.6444i	0.712593	−	0.980800i	−0.287144	−	0.957887i	$-0.592706\pi$
$487$	15.7256	−	21.6444i	0.712593	−	0.980800i	0.999737	−	0.0229129i	$-0.00729405\pi$
$488$	2.08755	−	1.56457i	0.0944991	−	0.0708246i
$489$	−30.0131	+	21.8058i	−1.35724	+	0.986091i
$490$	−2.17667	+	12.6160i	−0.0983320	+	0.569934i
$491$	−0.191575	+	0.263680i	−0.00864564	+	0.0118997i	−0.813318	−	0.581820i	$-0.802341\pi$
$491$	−0.191575	+	0.263680i	−0.00864564	+	0.0118997i	0.804672	+	0.593719i	$0.202341\pi$
$492$	44.2882	+	19.1954i	1.99666	+	0.865397i
$493$	−3.43806			−0.154842
$494$	−32.5909	−	35.8376i	−1.46633	−	1.61241i
$495$	−33.2058	+	12.0383i	−1.49249	+	0.541083i
$496$	−4.61359	−	0.885585i	−0.207156	−	0.0397639i
$497$	10.1880	+	3.31029i	0.456995	+	0.148487i
$498$	4.45549	+	2.54306i	0.199655	+	0.113957i
$499$			23.2206i			1.03950i	0.854320	+	0.519748i	$0.173974\pi$
$499$			23.2206i			1.03950i	−0.854320	+	0.519748i	$0.826026\pi$
$500$	−0.136391	−	22.3603i	−0.00609961	−	0.999981i
$501$		−	34.4855i		−	1.54070i
$502$	4.84961	−	8.49660i	0.216449	−	0.379222i
$503$	−8.85545	−	2.87731i	−0.394845	−	0.128293i	0.104863	−	0.994487i	$-0.466559\pi$
$503$	−8.85545	−	2.87731i	−0.394845	−	0.128293i	−0.499708	+	0.866194i	$0.666559\pi$
$504$	27.2780	+	19.2064i	1.21506	+	0.855523i
$505$	−28.9101	+	10.4810i	−1.28648	+	0.466398i
$506$	−1.61289	+	1.46677i	−0.0717019	+	0.0652061i
$507$	70.1170			3.11401
$508$	13.5206	−	31.1951i	0.599880	−	1.38406i
$509$	−11.8276	+	16.2793i	−0.524249	+	0.721567i	−0.986240	−	0.165318i	$-0.947135\pi$
$509$	−11.8276	+	16.2793i	−0.524249	+	0.721567i	0.461992	+	0.886884i	$0.347135\pi$
$510$	−26.1092	−	4.50468i	−1.15614	−	0.199471i
$511$	−7.43433	+	5.40135i	−0.328875	+	0.238942i
$512$	−1.00745	−	22.6050i	−0.0445236	−	0.999008i
$513$	−41.1296	+	56.6100i	−1.81592	+	2.49939i
$514$	−20.8972	+	36.6122i	−0.921736	+	1.61490i
$515$	0.658584	+	19.5696i	0.0290207	+	0.862341i
$516$	23.0170	−	5.13102i	1.01327	−	0.225881i
$517$	−6.36899	−	19.6017i	−0.280108	−	0.862083i
$518$	8.08494	−	3.64770i	0.355232	−	0.160271i
$519$	14.7185	+	45.2987i	0.646068	+	1.98839i
$520$	36.2703	+	9.86933i	1.59056	+	0.432799i
$521$	5.18227	−	15.9494i	0.227039	−	0.698755i	−0.771039	−	0.636788i	$-0.780263\pi$
$521$	5.18227	−	15.9494i	0.227039	−	0.698755i	0.998078	−	0.0619670i	$-0.0197373\pi$
$522$	−1.36966	−	12.4389i	−0.0599482	−	0.544438i
$523$	−0.0366350	+	0.0266169i	−0.00160194	+	0.00116388i	−0.588586	−	0.808435i	$-0.700315\pi$
$523$	−0.0366350	+	0.0266169i	−0.00160194	+	0.00116388i	0.586984	+	0.809599i	$0.300315\pi$
$524$	9.01207	+	7.95441i	0.393694	+	0.347490i
$525$	−25.0416	+	10.0438i	−1.09290	+	0.438347i
$526$	−34.1191	+	15.3936i	−1.48766	+	0.671191i
$527$	−1.84144	−	2.53452i	−0.0802144	−	0.110406i
$528$	5.44908	−	28.3878i	0.237141	−	1.23542i
$529$	6.96866	−	21.4473i	0.302985	−	0.932493i
$530$	−9.87843	−	5.20588i	−0.429092	−	0.226129i
$531$	39.7848	−	12.9268i	1.72651	−	0.560978i
$532$	−13.1040	+	14.8464i	−0.568132	+	0.643673i
$533$	−14.1121	−	43.4327i	−0.611265	−	1.88128i
$534$	3.73422	−	18.0058i	0.161595	−	0.779187i
$535$	2.66246	+	7.34397i	0.115108	+	0.317508i
$536$	41.0658	−	14.0204i	1.77377	−	0.605591i
$537$	39.8978	−	54.9146i	1.72172	−	2.36974i
$538$	−11.1241	−	2.30703i	−0.479595	−	0.0994630i
$539$	−5.47494	−	7.53561i	−0.235822	−	0.324582i
$540$	3.32000	−	54.1969i	0.142870	−	2.33226i
$541$	10.3777	−	14.2837i	0.446173	−	0.614104i	−0.525397	−	0.850857i	$-0.676083\pi$
$541$	10.3777	−	14.2837i	0.446173	−	0.614104i	0.971570	+	0.236753i	$0.0760832\pi$
$542$	9.74526	−	8.86239i	0.418595	−	0.380672i
$543$		−	27.2915i		−	1.17119i
$544$	9.81639	−	11.4601i	0.420874	−	0.491349i
$545$	−9.37891	−	2.70221i	−0.401748	−	0.115750i
$546$	−4.96411	−	45.0831i	−0.212444	−	1.92938i
$547$	−10.9369	+	33.6604i	−0.467630	+	1.43922i	0.388015	+	0.921653i	$0.373161\pi$
$547$	−10.9369	+	33.6604i	−0.467630	+	1.43922i	−0.855645	+	0.517563i	$0.826839\pi$
$548$	−8.24411	−	0.784077i	−0.352171	−	0.0334941i
$549$			6.33240i			0.270260i
$550$	11.7300	+	11.2729i	0.500169	+	0.480677i
$551$	7.42802			0.316444
$552$	−1.92327	−	5.63324i	−0.0818597	−	0.239767i
$553$	−0.664253	−	0.215829i	−0.0282469	−	0.00917798i
$554$	5.30259	−	0.583869i	0.225285	−	0.0248062i
$555$	−21.2384	−	14.3646i	−0.901518	−	0.609744i
$556$	8.00761	−	18.4754i	0.339598	−	0.783530i
$557$	27.7529			1.17593			0.587964	−	0.808887i	$-0.299930\pi$
$557$	27.7529			1.17593			0.587964	+	0.808887i	$0.299930\pi$
$558$	8.43636	−	7.67207i	0.357140	−	0.324784i
$559$	−18.0501	−	13.1141i	−0.763436	−	0.554669i
$560$	2.38748	−	15.1796i	0.100890	−	0.641456i
$561$	15.5951	−	11.3305i	0.658428	−	0.478376i
$562$	6.15605	−	29.6835i	0.259677	−	1.25212i
$563$	23.5565	+	17.1148i	0.992788	+	0.721303i	0.960530	−	0.278177i	$-0.0897302\pi$
$563$	23.5565	+	17.1148i	0.992788	+	0.721303i	0.0322580	+	0.999480i	$0.489730\pi$
$564$	56.0216	+	5.32808i	2.35893	+	0.224353i
$565$	−3.27493	−	0.943558i	−0.137777	−	0.0396958i
$566$	0.265897	−	1.28212i	0.0111765	−	0.0538913i
$567$	−28.6575	+	9.31138i	−1.20350	+	0.391041i
$568$	16.8521	+	5.20029i	0.707099	+	0.218199i
$569$	5.68191	+	17.4871i	0.238198	+	0.733098i	0.996681	+	0.0814052i	$0.0259408\pi$
$569$	5.68191	+	17.4871i	0.238198	+	0.733098i	−0.758483	+	0.651693i	$0.774059\pi$
$570$	56.4098	+	9.73250i	2.36274	+	0.407649i
$571$	−20.4740	−	6.65241i	−0.856811	−	0.278395i	−0.152515	−	0.988301i	$-0.548737\pi$
$571$	−20.4740	−	6.65241i	−0.856811	−	0.278395i	−0.704296	+	0.709906i	$0.748737\pi$
$572$	−23.5478	+	13.9079i	−0.984583	+	0.581518i
$573$	2.16473	−	1.57277i	0.0904330	−	0.0657034i
$574$	−17.0170	+	7.67758i	−0.710276	+	0.320456i
$575$	3.24857	+	0.818702i	0.135475	+	0.0341422i
$576$	45.3736	+	30.9504i	1.89057	+	1.28960i
$577$	1.65018	+	2.27128i	0.0686978	+	0.0945545i	0.841983	−	0.539504i	$-0.181388\pi$
$577$	1.65018	+	2.27128i	0.0686978	+	0.0945545i	−0.773285	+	0.634058i	$0.781388\pi$
$578$	−13.8948	+	1.52996i	−0.577948	+	0.0636379i
$579$	−32.0840	−	10.4247i	−1.33337	−	0.433237i
$580$	−4.86161	+	3.09654i	−0.201868	+	0.128577i
$581$	−1.88705	+	0.613141i	−0.0782882	+	0.0254374i
$582$	−61.4683	+	27.7327i	−2.54794	+	1.14956i
$583$	7.72646	−	2.51048i	0.319997	−	0.103973i
$584$	−12.1061	+	9.07325i	−0.500956	+	0.375454i
$585$	−71.9704	+	56.0828i	−2.97561	+	2.31874i
$586$	16.4056	+	9.36385i	0.677710	+	0.386817i
$587$	9.41724	+	6.84202i	0.388691	+	0.282401i	0.764919	−	0.644127i	$-0.222779\pi$
$587$	9.41724	+	6.84202i	0.388691	+	0.282401i	−0.376228	+	0.926527i	$0.622779\pi$
$588$	24.8229	−	5.53359i	1.02368	−	0.228201i
$589$	3.97848	+	5.47591i	0.163931	+	0.225631i
$590$	−13.4356	−	13.8108i	−0.553134	−	0.568581i
$591$	−57.4698	−	41.7543i	−2.36399	−	1.71754i
$592$	13.2200	−	6.20233i	0.543340	−	0.254914i
$593$		−	12.6560i		−	0.519720i	−0.965646	−	0.259860i	$-0.916324\pi$
$593$		−	12.6560i		−	0.519720i	0.965646	−	0.259860i	$-0.0836765\pi$
$594$	26.5792	+	29.2270i	1.09056	+	1.19920i
$595$	8.08298	−	6.29866i	0.331370	−	0.258220i
$596$	−23.5839	+	13.9292i	−0.966033	+	0.570562i
$597$	0.685994	−	2.11127i	0.0280759	−	0.0864087i
$598$	−2.79169	+	4.89109i	−0.114161	+	0.200012i
$599$	−20.9771			−0.857101			−0.428550	−	0.903518i	$-0.640976\pi$
$599$	−20.9771			−0.857101			−0.428550	+	0.903518i	$0.640976\pi$
$600$	−40.9772	+	17.1458i	−1.67289	+	0.699975i
$601$	23.0207			0.939032			0.469516	−	0.882924i	$-0.344428\pi$
$601$	23.0207			0.939032			0.469516	+	0.882924i	$0.344428\pi$
$602$	−4.52119	+	7.92120i	−0.184270	+	0.322844i
$603$	−32.5488	+	100.175i	−1.32549	+	4.07944i
$604$	−12.2994	−	20.8244i	−0.500455	−	0.847334i
$605$	12.7531	−	0.429184i	0.518487	−	0.0174488i
$606$	41.0999	+	45.1943i	1.66957	+	1.83589i
$607$		−	26.0419i		−	1.05701i	−0.848931	−	0.528504i	$-0.822753\pi$
$607$		−	26.0419i		−	1.05701i	0.848931	−	0.528504i	$-0.177247\pi$
$608$	−21.2086	+	24.7600i	−0.860122	+	1.00415i
$609$	5.62666	+	4.08801i	0.228004	+	0.165654i
$610$	2.61679	−	1.28825i	0.105951	−	0.0521596i
$611$	−31.2947	−	43.0734i	−1.26605	−	1.74257i
$612$	7.96953	+	35.7501i	0.322149	+	1.44511i
$613$	13.6825	+	9.94089i	0.552629	+	0.401509i	0.828754	−	0.559613i	$-0.189050\pi$
$613$	13.6825	+	9.94089i	0.552629	+	0.401509i	−0.276125	+	0.961122i	$0.589050\pi$
$614$	17.4139	+	9.93937i	0.702770	+	0.401120i
$615$	44.7020	+	30.2343i	1.80256	+	1.21916i
$616$	6.70489	+	8.94613i	0.270148	+	0.360450i
$617$	5.20768	−	1.69208i	0.209653	−	0.0681205i	−0.202308	−	0.979322i	$-0.564844\pi$
$617$	5.20768	−	1.69208i	0.209653	−	0.0681205i	0.411961	+	0.911202i	$0.364844\pi$
$618$	35.4557	−	15.9966i	1.42624	−	0.643478i
$619$	−15.1429	+	4.92021i	−0.608643	+	0.197760i	−0.597091	−	0.802173i	$-0.703677\pi$
$619$	−15.1429	+	4.92021i	−0.608643	+	0.197760i	−0.0115514	+	0.999933i	$0.503677\pi$
$620$	−4.88666	−	1.92544i	−0.196253	−	0.0773277i
$621$	7.73701	+	2.51391i	0.310476	+	0.100880i
$622$	0.672325	−	0.0740299i	0.0269578	−	0.00296833i
$623$	4.18044	+	5.75389i	0.167486	+	0.230525i
$624$	−9.27363	−	74.0930i	−0.371242	−	2.96609i
$625$	4.46582	−	24.5979i	0.178633	−	0.983916i
$626$	−14.6435	+	6.60673i	−0.585272	+	0.264058i
$627$	−33.6938	+	24.4799i	−1.34560	+	0.977635i
$628$	−12.8205	−	21.7068i	−0.511595	−	0.866195i
$629$	9.26151	+	3.00925i	0.369281	+	0.119987i
$630$	26.0088	+	26.7351i	1.03621	+	1.06515i
$631$	−15.0147	−	46.2106i	−0.597727	−	1.83961i	−0.540654	−	0.841245i	$-0.681823\pi$
$631$	−15.0147	−	46.2106i	−0.597727	−	1.83961i	−0.0570726	−	0.998370i	$-0.518177\pi$
$632$	−1.09875	−	0.339056i	−0.0437059	−	0.0134869i
$633$	54.8380	−	17.8179i	2.17961	−	0.708200i
$634$	−3.96990	+	19.1422i	−0.157665	+	0.760235i
$635$	21.2960	−	31.4866i	0.845107	−	1.24951i
$636$	−2.10018	+	22.0822i	−0.0832776	+	0.875615i
$637$	−19.4662	−	14.1431i	−0.771280	−	0.560368i
$638$	0.851600	−	4.10628i	0.0337152	−	0.162569i
$639$	−34.6333	+	25.1626i	−1.37007	+	0.995417i
$640$	3.55920	−	25.0466i	0.140690	−	0.990054i
$641$	15.1755	+	11.0256i	0.599396	+	0.435486i	0.845664	−	0.533715i	$-0.179205\pi$
$641$	15.1755	+	11.0256i	0.599396	+	0.435486i	−0.246269	+	0.969202i	$0.579205\pi$
$642$	11.4806	−	10.4405i	0.453104	−	0.412055i
$643$	37.8673			1.49334			0.746669	−	0.665195i	$-0.231652\pi$
$643$	37.8673			1.49334			0.746669	+	0.665195i	$0.231652\pi$
$644$	2.11235	+	0.915536i	0.0832382	+	0.0360772i
$645$	26.3505	−	0.886783i	1.03755	−	0.0349171i
$646$	−21.6105	+	2.37953i	−0.850252	+	0.0936215i
$647$	−37.5073	−	12.1869i	−1.47456	−	0.479115i	−0.542080	−	0.840327i	$-0.682363\pi$
$647$	−37.5073	−	12.1869i	−1.47456	−	0.479115i	−0.932484	+	0.361212i	$0.882363\pi$
$648$	−46.9475	+	16.0285i	−1.84427	+	0.629660i
$649$	14.0185			0.550276
$650$	37.8170	+	18.3316i	1.48331	+	0.719024i
$651$			6.33752i			0.248387i
$652$	2.23657	−	23.5162i	0.0875907	−	0.920964i
$653$	6.71891	−	20.6787i	0.262931	−	0.809219i	−0.729232	−	0.684267i	$-0.760122\pi$
$653$	6.71891	−	20.6787i	0.262931	−	0.809219i	0.992163	−	0.124952i	$-0.0398776\pi$
$654$	2.12212	+	19.2727i	0.0829815	+	0.753622i
$655$	8.26059	+	10.6007i	0.322768	+	0.414204i
$656$	−27.8252	+	13.0545i	−1.08639	+	0.509693i
$657$		−	36.7229i		−	1.43270i
$658$	−16.1022	+	14.6435i	−0.627731	+	0.570861i
$659$	−3.19947	+	4.40369i	−0.124634	+	0.171543i	−0.866774	−	0.498701i	$-0.833811\pi$
$659$	−3.19947	+	4.40369i	−0.124634	+	0.171543i	0.742141	+	0.670244i	$0.233811\pi$
$660$	11.8474	−	30.0681i	0.461161	−	1.17040i
$661$	−26.8362	−	36.9368i	−1.04381	−	1.43668i	−0.894058	−	0.447951i	$-0.852154\pi$
$661$	−26.8362	−	36.9368i	−1.04381	−	1.43668i	−0.149747	−	0.988724i	$-0.547846\pi$
$662$	9.35929	+	1.94102i	0.363759	+	0.0754399i
$663$	29.2694	−	40.2859i	1.13673	−	1.56458i
$664$	−3.09143	+	1.05546i	−0.119971	+	0.0409596i
$665$	−17.4635	+	13.6084i	−0.677206	+	0.527712i
$666$	−7.19790	+	34.7071i	−0.278913	+	1.34487i
$667$	−0.266862	−	0.821317i	−0.0103329	−	0.0318015i
$668$	16.4631	+	14.5310i	0.636976	+	0.562221i
$669$	−22.9268	+	7.44937i	−0.886402	+	0.288009i
$670$	48.0178	−	6.92889i	1.85509	−	0.267686i
$671$	−0.655758	+	2.01821i	−0.0253152	+	0.0779123i
$672$	−29.6920	+	7.08332i	−1.14539	+	0.273245i
$673$	25.2847	+	34.8014i	0.974654	+	1.34150i	0.939661	+	0.342108i	$0.111141\pi$
$673$	25.2847	+	34.8014i	0.974654	+	1.34150i	0.0349929	+	0.999388i	$0.488859\pi$
$674$	−21.4351	+	9.67092i	−0.825651	+	0.372510i
$675$	14.8356	−	58.8669i	0.571021	−	2.26579i
$676$	−29.5448	+	33.4733i	−1.13634	+	1.28743i
$677$	37.8808	−	27.5220i	1.45588	−	1.05776i	0.471466	−	0.881884i	$-0.343725\pi$
$677$	37.8808	−	27.5220i	1.45588	−	1.05776i	0.984413	−	0.175873i	$-0.0562749\pi$
$678$	0.741002	+	6.72964i	0.0284580	+	0.258450i
$679$	8.05960	−	24.8049i	0.309299	−	0.951924i
$680$	13.1520	−	10.5662i	0.504357	−	0.405196i
$681$	11.3714	+	34.9977i	0.435755	+	1.34111i
$682$	3.48326	−	1.57155i	0.133381	−	0.0601776i
$683$	0.331130	+	1.01911i	0.0126703	+	0.0389953i	0.957192	−	0.289454i	$-0.0934739\pi$
$683$	0.331130	+	1.01911i	0.0126703	+	0.0389953i	−0.944521	+	0.328450i	$0.893474\pi$
$684$	−17.2184	−	77.2391i	−0.658362	−	2.95331i
$685$	−8.89688	−	2.56333i	−0.339932	−	0.0979399i
$686$	−13.3066	+	23.3133i	−0.508047	+	0.890108i
$687$	−49.7673	+	68.4988i	−1.89874	+	2.61339i
$688$	−7.24904	+	13.1501i	−0.276367	+	0.501345i
$689$	16.9784	−	12.3355i	0.646824	−	0.469945i
$690$	−0.950476	−	6.58689i	−0.0361840	−	0.250758i
$691$	8.71658	−	11.9973i	0.331595	−	0.456401i	−0.610368	−	0.792118i	$-0.708979\pi$
$691$	8.71658	−	11.9973i	0.331595	−	0.456401i	0.941963	+	0.335717i	$0.108979\pi$
$692$	−27.8271	−	12.0608i	−1.05783	−	0.458484i
$693$	−27.1373			−1.03086
$694$	−0.525130	+	0.477556i	−0.0199337	+	0.0181278i
$695$	12.6126	−	18.6480i	0.478424	−	0.707359i
$696$	9.36235	+	6.59204i	0.354879	+	0.249870i
$697$	−19.4934	−	6.33379i	−0.738366	−	0.239910i
$698$	−0.972622	+	1.70405i	−0.0368143	+	0.0644992i
$699$		−	43.7790i		−	1.65587i
$700$	5.75683	−	16.1867i	0.217588	−	0.611801i
$701$		−	6.33651i		−	0.239327i	−0.992815	−	0.119663i	$-0.961818\pi$
$701$		−	6.33651i		−	0.239327i	0.992815	−	0.119663i	$-0.0381815\pi$
$702$	88.6306	+	50.5878i	3.34515	+	1.90931i
$703$	−20.0098	−	6.50156i	−0.754682	−	0.245211i
$704$	11.2560	+	14.5630i	0.424228	+	0.548863i
$705$	60.4574	+	17.4187i	2.27696	+	0.656027i
$706$	−27.1445	−	29.8486i	−1.02159	−	1.12337i
$707$	−23.6266			−0.888571
$708$	−15.2214	+	35.1192i	−0.572054	+	1.31986i
$709$	−25.4810	+	35.0716i	−0.956960	+	1.31714i	−0.00859395	+	0.999963i	$0.502736\pi$
$709$	−25.4810	+	35.0716i	−0.956960	+	1.31714i	−0.948366	+	0.317179i	$0.897264\pi$
$710$	17.4439	+	9.19282i	0.654656	+	0.345000i
$711$	2.25807	−	1.64059i	0.0846843	−	0.0615268i
$712$	7.02235	+	9.36970i	0.263174	+	0.351144i
$713$	0.462540	−	0.636631i	0.0173222	−	0.0238420i
$714$	−17.6793	−	10.0908i	−0.661632	−	0.377640i
$715$	−28.7455	+	10.4213i	−1.07502	+	0.389736i
$716$	9.40423	+	42.1859i	0.351452	+	1.57656i
$717$	−9.28391	−	28.5729i	−0.346714	−	1.06708i
$718$	−13.4486	−	29.8082i	−0.501898	−	1.11243i
$719$	2.82195	+	8.68507i	0.105241	+	0.323898i	0.989787	−	0.142555i	$-0.0455316\pi$
$719$	2.82195	+	8.68507i	0.105241	+	0.323898i	−0.884546	+	0.466453i	$0.845532\pi$
$720$	43.4683	+	43.3748i	1.61997	+	1.61649i
$721$	−4.64888	+	14.3078i	−0.173133	+	0.532850i
$722$	19.9814	−	2.20016i	0.743631	−	0.0818814i
$723$	63.9059	−	46.4303i	2.37669	−	1.72676i
$724$	13.0287	+	11.4997i	0.484208	+	0.427382i
$725$	−5.98120	+	2.39896i	−0.222136	+	0.0890953i
$726$	−10.4246	−	23.1057i	−0.386894	−	0.857532i
$727$	24.3866	+	33.5653i	0.904449	+	1.24487i	0.969027	+	0.246955i	$0.0794300\pi$
$727$	24.3866	+	33.5653i	0.904449	+	1.24487i	−0.0645777	+	0.997913i	$0.520570\pi$
$728$	23.6140	+	16.6266i	0.875192	+	0.616223i
$729$	1.85677	−	5.71454i	0.0687691	−	0.211649i
$730$	−15.1753	+	7.47080i	−0.561664	+	0.276507i
$731$	−9.52354	+	3.09439i	−0.352241	+	0.114450i
$732$	−4.34399	−	3.83418i	−0.160559	−	0.141715i
$733$	11.2254	+	34.5481i	0.414619	+	1.27606i	0.912592	+	0.408872i	$0.134078\pi$
$733$	11.2254	+	34.5481i	0.414619	+	1.27606i	−0.497973	+	0.867193i	$0.665922\pi$
$734$	39.0494	+	8.09844i	1.44134	+	0.298919i
$735$	28.4179	−	0.956359i	1.04821	−	0.0352758i
$736$	3.49966	+	1.45550i	0.128999	+	0.0536504i
$737$	−20.7474	+	28.5564i	−0.764241	+	1.05189i
$738$	15.1500	−	73.0508i	0.557678	−	2.68904i
$739$	−27.2866	−	37.5567i	−1.00375	−	1.38155i	−0.922995	−	0.384813i	$-0.874266\pi$
$739$	−27.2866	−	37.5567i	−1.00375	−	1.38155i	−0.0807577	−	0.996734i	$-0.525734\pi$
$740$	15.8066	−	4.08627i	0.581064	−	0.150214i
$741$	−63.2375	+	87.0389i	−2.32309	+	3.19745i
$742$	−5.77205	−	6.34706i	−0.211899	−	0.233008i
$743$		−	43.8156i		−	1.60744i	−0.595008	−	0.803720i	$-0.702851\pi$
$743$		−	43.8156i		−	1.60744i	0.595008	−	0.803720i	$-0.297149\pi$
$744$	0.154895	+	10.4326i	0.00567873	+	0.382479i
$745$	−28.7896	+	10.4373i	−1.05477	+	0.382393i
$746$	25.2864	−	2.78429i	0.925801	−	0.101940i
$747$	2.45027	−	7.54115i	0.0896506	−	0.275916i
$748$	−1.16215	+	12.2193i	−0.0424923	+	0.446781i
$749$			6.00182i			0.219302i
$750$	−48.5656	+	10.3814i	−1.77336	+	0.379074i
$751$	0.0692442			0.00252676			0.00126338	−	0.999999i	$-0.499598\pi$
$751$	0.0692442			0.00252676			0.00126338	+	0.999999i	$0.499598\pi$
$752$	−26.1491	+	24.4992i	−0.953560	+	0.893393i
$753$	−20.6649	−	6.71442i	−0.753070	−	0.244687i
$754$	−1.18568	−	10.7681i	−0.0431799	−	0.392152i
$755$	−9.21607	−	25.4210i	−0.335407	−	0.925166i
$756$	16.5903	−	38.2775i	0.603382	−	1.39214i
$757$	−17.1602			−0.623700			−0.311850	−	0.950131i	$-0.600949\pi$
$757$	−17.1602			−0.623700			−0.311850	+	0.950131i	$0.600949\pi$
$758$	−5.18986	−	5.70687i	−0.188504	−	0.207283i
$759$	3.91725	+	2.84605i	0.142187	+	0.103305i
$760$	−28.4153	+	22.8286i	−1.03073	+	0.828081i
$761$	8.77922	−	6.37847i	0.318246	−	0.231220i	−0.417180	−	0.908824i	$-0.636982\pi$
$761$	8.77922	−	6.37847i	0.318246	−	0.231220i	0.735427	+	0.677604i	$0.236982\pi$
$762$	−73.9383	−	15.3340i	−2.67850	−	0.555493i
$763$	−6.06686	−	4.40783i	−0.219635	−	0.159574i
$764$	−0.161315	+	1.69614i	−0.00583618	+	0.0613640i
$765$	1.37736	+	40.9277i	0.0497984	+	1.47975i
$766$	−19.2750	−	3.99743i	−0.696432	−	0.144433i
$767$	34.4408	−	11.1905i	1.24358	−	0.404065i
$768$	−48.7049	+	12.3860i	−1.75749	+	0.446943i
$769$	5.30296	+	16.3208i	0.191230	+	0.588545i	1.00000		0.000419828i	$0.000133635\pi$
$769$	5.30296	+	16.3208i	0.191230	+	0.588545i	−0.808770	+	0.588125i	$0.799866\pi$
$770$	5.52073	+	11.2142i	0.198953	+	0.404131i
$771$	89.0459	+	28.9328i	3.20691	+	1.04199i
$772$	18.4958	−	10.9240i	0.665677	−	0.393164i
$773$	29.9036	−	21.7262i	1.07556	−	0.781437i	0.0986535	−	0.995122i	$-0.468546\pi$
$773$	29.9036	−	21.7262i	1.07556	−	0.781437i	0.976903	+	0.213685i	$0.0685465\pi$
$774$	−14.9895	−	33.2236i	−0.538788	−	1.19420i
$775$	−4.97207	−	3.12443i	−0.178602	−	0.112233i
$776$	12.6612	−	41.0300i	0.454511	−	1.47289i
$777$	−11.5791	−	15.9372i	−0.415398	−	0.571746i
$778$	−5.72040	−	51.9516i	−0.205086	−	1.86255i
$779$	42.1161	+	13.6843i	1.50896	+	0.490292i
$780$	5.10456	−	83.3287i	0.182773	−	2.98364i
$781$	−13.6438	+	4.43314i	−0.488214	+	0.158630i
$782$	1.03949	+	2.30398i	0.0371721	+	0.0823903i
$783$	−14.8829	+	4.83576i	−0.531873	+	0.172816i
$784$	−7.81779	+	14.1819i	−0.279207	+	0.506496i
$785$	−9.60657	−	26.4982i	−0.342873	−	0.945760i
$786$	13.2340	−	23.1862i	0.472041	−	0.827023i
$787$	19.5842	+	14.2288i	0.698102	+	0.507201i	0.879313	−	0.476244i	$-0.158002\pi$
$787$	19.5842	+	14.2288i	0.698102	+	0.507201i	−0.181212	+	0.983444i	$0.558002\pi$
$788$	44.1489	−	9.84182i	1.57274	−	0.350600i
$789$	48.8646	+	67.2564i	1.73963	+	2.39439i
$790$	−1.13733	−	0.599367i	−0.0404644	−	0.0213245i
$791$	−2.11843	−	1.53913i	−0.0753225	−	0.0547250i
$792$	−44.6726	+	0.663261i	−1.58737	+	0.0235680i
$793$			5.48182i			0.194665i
$794$	−24.8006	+	22.5538i	−0.880142	+	0.800405i
$795$	−6.86599	+	23.8306i	−0.243511	+	0.845186i
$796$	0.718850	+	1.21710i	0.0254790	+	0.0431391i
$797$	0.311905	−	0.959946i	0.0110483	−	0.0340030i	−0.945380	−	0.325969i	$-0.894309\pi$
$797$	0.311905	−	0.959946i	0.0110483	−	0.0340030i	0.956429	+	0.291966i	$0.0943094\pi$
$798$	38.1967	+	21.8016i	1.35215	+	0.771767i
$799$	−23.8959			−0.845375
$800$	9.08110	−	26.7868i	0.321065	−	0.947057i
$801$	−28.4221			−1.00425
$802$	−1.08249	−	0.617851i	−0.0382239	−	0.0218171i
$803$	3.80287	−	11.7040i	0.134200	−	0.413027i
$804$	−49.0116	−	82.9829i	−1.72851	−	2.92658i
$805$	2.13209	+	1.44204i	0.0751462	+	0.0508253i
$806$	7.30317	−	6.64154i	0.257243	−	0.233938i
$807$			25.2322i			0.888217i
$808$	−38.8934	+	0.577458i	−1.36827	+	0.0203149i
$809$	−14.0834	−	10.2322i	−0.495147	−	0.359745i	0.312013	−	0.950078i	$-0.398997\pi$
$809$	−14.0834	−	10.2322i	−0.495147	−	0.359745i	−0.807160	+	0.590332i	$0.798997\pi$
$810$	−54.8952	+	7.92128i	−1.92882	+	0.278325i
$811$	4.13632	+	5.69316i	0.145246	+	0.199914i	0.875441	−	0.483325i	$-0.160571\pi$
$811$	4.13632	+	5.69316i	0.145246	+	0.199914i	−0.730195	+	0.683238i	$0.760571\pi$
$812$	−4.32246	+	0.963577i	−0.151689	+	0.0338149i
$813$	−23.6684	−	17.1961i	−0.830086	−	0.603093i
$814$	−5.88819	+	10.3162i	−0.206381	+	0.361583i
$815$	7.31186	−	25.3782i	0.256123	−	0.888959i
$816$	−29.3498	−	16.1791i	−1.02745	−	0.566383i
$817$	20.5759	−	6.68551i	0.719859	−	0.233896i
$818$	20.8274	+	46.1629i	0.728212	+	1.61405i
$819$	−66.6709	+	21.6627i	−2.32967	+	0.756956i
$820$	−33.2695	+	8.60069i	−1.16182	+	0.300349i
$821$	24.4826	+	7.95489i	0.854450	+	0.277628i	0.703309	−	0.710884i	$-0.251705\pi$
$821$	24.4826	+	7.95489i	0.854450	+	0.277628i	0.151141	+	0.988512i	$0.451705\pi$
$822$	2.01305	+	18.2822i	0.0702134	+	0.637664i
$823$	24.5580	+	33.8012i	0.856038	+	1.17823i	0.982500	+	0.186264i	$0.0596378\pi$
$823$	24.5580	+	33.8012i	0.856038	+	1.17823i	−0.126462	+	0.991971i	$0.540362\pi$
$824$	−7.30315	+	23.6667i	−0.254417	+	0.824467i
$825$	19.2249	−	30.5936i	0.669324	−	1.06513i
$826$	−6.08809	−	13.4940i	−0.211832	−	0.469515i
$827$	21.0719	−	15.3096i	0.732741	−	0.532368i	−0.157688	−	0.987489i	$-0.550404\pi$
$827$	21.0719	−	15.3096i	0.732741	−	0.532368i	0.890429	+	0.455121i	$0.150404\pi$
$828$	−7.92174	+	4.67876i	−0.275299	+	0.162598i
$829$	−3.94736	−	1.28257i	−0.137097	−	0.0445457i	0.239665	−	0.970856i	$-0.422963\pi$
$829$	−3.94736	−	1.28257i	−0.137097	−	0.0445457i	−0.376762	+	0.926310i	$0.622963\pi$
$830$	−3.61477	+	0.521605i	−0.125470	+	0.0181052i
$831$	−3.66128	−	11.2683i	−0.127008	−	0.390892i
$832$	39.2790	+	26.7931i	1.36175	+	0.928882i
$833$	−10.2707	+	3.33717i	−0.355860	+	0.115626i
$834$	−43.7901	−	9.08161i	−1.51633	−	0.314470i
$835$	15.0903	+	19.3652i	0.522222	+	0.670160i
$836$	2.51085	−	26.4001i	0.0868396	−	0.913067i
$837$	−11.5363	−	8.38160i	−0.398752	−	0.289710i
$838$	−26.3639	−	5.46759i	−0.910724	−	0.188875i
$839$	−31.5974	+	22.9568i	−1.09086	+	0.792557i	−0.979545	−	0.201227i	$-0.935507\pi$
$839$	−31.5974	+	22.9568i	−1.09086	+	0.792557i	−0.111317	+	0.993785i	$0.535507\pi$
$840$	−34.0881	+	1.65412i	−1.17615	+	0.0570725i
$841$	−22.1176	−	16.0693i	−0.762674	−	0.554115i
$842$	8.42855	+	9.26820i	0.290467	+	0.319403i
$843$	−67.3294			−2.31895
$844$	−14.6007	+	33.6870i	−0.502576	+	1.15956i
$845$	−39.3739	+	30.6821i	−1.35450	+	1.05550i
$846$	−9.51966	−	86.4557i	−0.327293	−	2.97241i
$847$	9.32406	+	3.02957i	0.320378	+	0.104097i
$848$	−9.65690	−	10.3073i	−0.331619	−	0.353953i
$849$	−2.90815			−0.0998075
$850$	16.6327	−	8.89540i	0.570498	−	0.305110i
$851$			2.44606i			0.0838498i
$852$	3.70861	−	38.9939i	0.127055	−	1.33591i
$853$	−3.09392	+	9.52211i	−0.105934	+	0.326031i	−0.989948	−	0.141428i	$-0.954831\pi$
$853$	−3.09392	+	9.52211i	−0.105934	+	0.326031i	0.884015	+	0.467459i	$0.154831\pi$
$854$	2.22748	−	0.245268i	0.0762227	−	0.00839290i
$855$	−2.97582	−	88.4256i	−0.101771	−	3.02409i
$856$	0.146690	+	9.88002i	0.00501378	+	0.337692i
$857$			31.6591i			1.08146i	0.841198	+	0.540728i	$0.181851\pi$
$857$			31.6591i			1.08146i	−0.841198	+	0.540728i	$0.818149\pi$
$858$	40.8660	+	44.9370i	1.39514	+	1.53412i
$859$	10.6822	−	14.7028i	0.364473	−	0.501654i	−0.586915	−	0.809649i	$-0.699658\pi$
$859$	10.6822	−	14.7028i	0.364473	−	0.501654i	0.951388	+	0.307994i	$0.0996577\pi$
$860$	−10.6798	+	12.9532i	−0.364180	+	0.441699i
$861$	24.3714	+	33.5444i	0.830575	+	1.14319i
$862$	−0.888977	+	4.28651i	−0.0302787	+	0.145999i
$863$	1.06034	−	1.45943i	0.0360944	−	0.0496797i	−0.790588	−	0.612348i	$-0.790225\pi$
$863$	1.06034	−	1.45943i	0.0360944	−	0.0496797i	0.826683	+	0.562668i	$0.190225\pi$
$864$	26.3749	−	63.4167i	0.897291	−	2.15748i
$865$	−28.0871	−	18.9968i	−0.954990	−	0.645909i
$866$	12.6295	+	2.61923i	0.429169	+	0.0890052i
$867$	9.59395	+	29.5271i	0.325828	+	1.00279i
$868$	−3.02548	−	2.67041i	−0.102691	−	0.0906395i
$869$	0.889568	−	0.289038i	0.0301765	−	0.00980495i
$870$	8.92672	+	9.17602i	0.302644	+	0.311096i
$871$	−28.1768	+	86.7193i	−0.954735	+	2.93837i
$872$	−10.0948	−	7.10776i	−0.341853	−	0.240699i
$873$	61.2636	+	84.3221i	2.07346	+	2.85387i
$874$	−2.24585	−	4.97782i	−0.0759671	−	0.168377i
$875$	9.66700	−	16.5978i	0.326804	−	0.561110i
$876$	25.1917	+	22.2352i	0.851149	+	0.751258i
$877$	−25.8054	+	18.7487i	−0.871387	+	0.633100i	−0.930959	−	0.365124i	$-0.881026\pi$
$877$	−25.8054	+	18.7487i	−0.871387	+	0.633100i	0.0595719	+	0.998224i	$0.481026\pi$
$878$	54.0308	−	5.94935i	1.82345	−	0.200781i
$879$	12.9645	−	39.9007i	0.437282	−	1.34582i
$880$	9.36214	+	18.3255i	0.315598	+	0.617752i
$881$	5.46376	+	16.8157i	0.184079	+	0.566536i	0.999931	−	0.0117237i	$-0.00373186\pi$
$881$	5.46376	+	16.8157i	0.184079	+	0.566536i	−0.815852	+	0.578260i	$0.803732\pi$
$882$	−16.1656	−	35.8303i	−0.544324	−	1.20647i
$883$	−3.19347	−	9.82850i	−0.107469	−	0.330755i	0.882833	−	0.469687i	$-0.155633\pi$
$883$	−3.19347	−	9.82850i	−0.107469	−	0.330755i	−0.990302	+	0.138932i	$0.955633\pi$
$884$	6.89904	+	30.9481i	0.232040	+	1.04090i
$885$	−23.9749	+	35.4473i	−0.805906	+	1.19155i
$886$	−41.5404	−	23.7101i	−1.39558	−	0.796555i
$887$	18.9891	−	26.1362i	0.637591	−	0.877568i	−0.360894	−	0.932607i	$-0.617528\pi$
$887$	18.9891	−	26.1362i	0.637591	−	0.877568i	0.998484	+	0.0550388i	$0.0175282\pi$
$888$	−19.4507	−	25.9524i	−0.652722	−	0.870906i
$889$	23.6275	−	17.1664i	0.792442	−	0.575742i
$890$	5.78212	+	11.7451i	0.193817	+	0.393697i
$891$	23.7190	−	32.6464i	0.794615	−	1.09369i
$892$	6.10429	−	14.0840i	0.204387	−	0.471566i
$893$	51.6277			1.72766
$894$	40.9286	+	45.0059i	1.36886	+	1.50522i
$895$	1.62531	+	48.2957i	0.0543282	+	1.61435i
$896$	9.12964	−	17.1594i	0.305000	−	0.573254i
$897$	11.8958	+	3.86518i	0.397189	+	0.129055i
$898$	14.4310	+	8.23678i	0.481568	+	0.274865i
$899$			1.51372i			0.0504854i
$900$	38.8099	+	56.6337i	1.29366	+	1.88779i
$901$		−	9.41910i		−	0.313796i
$902$	12.3933	−	21.7133i	0.412652	−	0.722974i
$903$	19.2654	+	6.25972i	0.641113	+	0.208310i
$904$	−3.52490	−	2.48189i	−0.117237	−	0.0825463i
$905$	11.9423	+	15.3254i	0.396976	+	0.509434i
$906$	−39.7399	+	36.1397i	−1.32027	+	1.20066i
$907$	−38.2694			−1.27071			−0.635357	−	0.772219i	$-0.719147\pi$
$907$	−38.2694			−1.27071			−0.635357	+	0.772219i	$0.719147\pi$
$908$	−21.4991	−	9.31817i	−0.713474	−	0.309234i
$909$	55.4975	−	76.3858i	1.84074	−	2.53356i
$910$	22.5152	+	23.1440i	0.746372	+	0.767216i
$911$	−39.1122	+	28.4167i	−1.29584	+	0.941486i	−0.999906	−	0.0137212i	$-0.995632\pi$
$911$	−39.1122	+	28.4167i	−1.29584	+	0.941486i	−0.295938	+	0.955207i	$0.595632\pi$
$912$	63.4111	+	34.9555i	2.09975	+	1.15749i
$913$	1.56186	−	2.14972i	0.0516901	−	0.0711453i
$914$	8.77221	−	15.3691i	0.290159	−	0.508363i
$915$	−3.98177	−	5.10975i	−0.131633	−	0.168923i
$916$	−11.7305	−	52.6214i	−0.387588	−	1.73866i
$917$	3.19076	+	9.82014i	0.105368	+	0.324290i
$918$	41.7501	−	18.8364i	1.37796	−	0.621695i
$919$	−2.97260	−	9.14872i	−0.0980570	−	0.301788i	0.889981	−	0.455997i	$-0.150717\pi$
$919$	−2.97260	−	9.14872i	−0.0980570	−	0.301788i	−0.988038	+	0.154209i	$0.950717\pi$
$920$	3.54502	+	2.32173i	0.116876	+	0.0765453i
$921$	13.7613	−	42.3531i	0.453452	−	1.39558i
$922$	1.90848	+	17.3324i	0.0628523	+	0.570813i
$923$	−29.9813	+	21.7827i	−0.986847	+	0.716986i
$924$	16.4312	−	18.6160i	0.540548	−	0.612422i
$925$	18.2120	−	1.22718i	0.598808	−	0.0403495i
$926$	−21.3134	+	9.61601i	−0.700403	+	0.316002i
$927$	−35.3377	−	48.6381i	−1.16064	−	1.59749i
$928$	−7.09195	+	1.69186i	−0.232805	+	0.0555379i
$929$	5.02685	−	15.4710i	0.164926	−	0.507589i	−0.834105	−	0.551605i	$-0.814015\pi$
$929$	5.02685	−	15.4710i	0.164926	−	0.507589i	0.999031	+	0.0440168i	$0.0140155\pi$
$930$	−1.98334	+	11.4955i	−0.0650363	+	0.376952i
$931$	22.1902	−	7.21004i	0.727255	−	0.236300i
$932$	20.8997	+	18.4469i	0.684593	+	0.604249i
$933$	−0.464221	−	1.42872i	−0.0151979	−	0.0467743i
$934$	4.61722	−	22.2635i	0.151080	−	0.728483i
$935$	−3.79933	+	13.1868i	−0.124251	+	0.431255i
$936$	−109.222	+	37.2900i	−3.57004	+	1.21886i
$937$	2.13418	−	2.93745i	0.0697207	−	0.0959623i	−0.772733	−	0.634732i	$-0.781111\pi$
$937$	2.13418	−	2.93745i	0.0697207	−	0.0959623i	0.842453	+	0.538769i	$0.181111\pi$
$938$	36.4981	+	7.56934i	1.19171	+	0.247148i
$939$	20.9721	+	28.8657i	0.684400	+	0.941996i
$940$	−33.7902	+	21.5222i	−1.10211	+	0.701977i
$941$	−23.9722	+	32.9948i	−0.781470	+	1.07560i	0.213648	+	0.976911i	$0.431465\pi$
$941$	−23.9722	+	32.9948i	−0.781470	+	1.07560i	−0.995118	+	0.0986904i	$0.968535\pi$
$942$	−41.4238	+	37.6710i	−1.34966	+	1.22739i
$943$		−	5.14841i		−	0.167655i
$944$	−10.3518	−	22.0645i	−0.336923	−	0.718140i
$945$	26.1310	−	38.6352i	0.850041	−	1.25680i
$946$	−1.33685	−	12.1410i	−0.0434648	−	0.394739i
$947$	−7.79156	+	23.9800i	−0.253192	+	0.779244i	0.740989	+	0.671517i	$0.234357\pi$
$947$	−7.79156	+	23.9800i	−0.253192	+	0.779244i	−0.994181	+	0.107727i	$0.965643\pi$
$948$	−0.241799	+	2.54238i	−0.00785328	+	0.0825726i
$949$		−	31.7902i		−	1.03195i
$950$	−35.9355	+	19.2188i	−1.16590	+	0.623539i
$951$	43.4193			1.40797
$952$	12.2667	−	4.18803i	0.397567	−	0.135735i
$953$	22.2071	+	7.21551i	0.719357	+	0.233733i	0.645745	−	0.763554i	$-0.276547\pi$
$953$	22.2071	+	7.21551i	0.719357	+	0.233733i	0.0736128	+	0.997287i	$0.476547\pi$
$954$	34.0785	−	3.75239i	1.10333	−	0.121488i
$955$	−0.527378	+	1.83044i	−0.0170655	+	0.0592315i
$956$	17.5524	+	7.60757i	0.567685	+	0.246047i
$957$	−9.31405			−0.301081
$958$	−22.5295	+	20.4885i	−0.727897	+	0.661953i
$959$	−5.75505	−	4.18129i	−0.185840	−	0.135021i
$960$	−56.0743	+	3.55610i	−1.80979	+	0.114773i
$961$	23.9636	−	17.4106i	0.773020	−	0.561632i
$962$	−6.23106	+	30.0452i	−0.200898	+	0.968696i
$963$	−19.4041	−	14.0979i	−0.625289	−	0.454299i
$964$	−4.76225	+	50.0722i	−0.153382	+	1.61272i
$965$	22.5784	−	8.18550i	0.726823	−	0.263500i
$966$	1.03833	−	5.00666i	0.0334077	−	0.161087i
$967$	−23.8786	+	7.75862i	−0.767883	+	0.249500i	−0.666659	−	0.745363i	$-0.732276\pi$
$967$	−23.8786	+	7.75862i	−0.767883	+	0.249500i	−0.101225	+	0.994864i	$0.532276\pi$
$968$	15.4230	+	4.75930i	0.495715	+	0.152970i
$969$	14.9214	+	45.9233i	0.479344	+	1.47527i
$970$	22.3819	−	42.4708i	0.718638	−	1.36365i
$971$	9.54087	+	3.10002i	0.306181	+	0.0994843i	0.458078	−	0.888912i	$-0.348538\pi$
$971$	9.54087	+	3.10002i	0.306181	+	0.0994843i	−0.151897	+	0.988396i	$0.548538\pi$
$972$	18.9842	+	32.1426i	0.608917	+	1.03097i
$973$	13.9934	−	10.1668i	0.448609	−	0.325934i
$974$	34.4881	−	15.5600i	1.10507	−	0.498576i
$975$	22.8100	−	90.5089i	0.730503	−	2.89860i
$976$	3.66081	−	0.458195i	0.117180	−	0.0146665i
$977$	12.8529	+	17.6906i	0.411202	+	0.565971i	0.963511	−	0.267668i	$-0.0862531\pi$
$977$	12.8529	+	17.6906i	0.411202	+	0.565971i	−0.552309	+	0.833640i	$0.686253\pi$
$978$	−52.1496	+	5.74220i	−1.66756	+	0.183615i
$979$	−9.05848	−	2.94328i	−0.289510	−	0.0940676i
$980$	−11.5178	+	13.9695i	−0.367921	+	0.446238i
$981$	28.5014	−	9.26065i	0.909978	−	0.295670i
$982$	−0.420147	+	0.189558i	−0.0134074	+	0.00604905i
$983$	−17.7241	+	5.75890i	−0.565311	+	0.183681i	−0.577709	−	0.816243i	$-0.696053\pi$
$983$	−17.7241	+	5.75890i	−0.565311	+	0.183681i	0.0123987	+	0.999923i	$0.496053\pi$
$984$	40.9393	+	54.6240i	1.30510	+	1.74135i
$985$	50.5430	−	1.70094i	1.61043	−	0.0541965i
$986$	−4.22272	−	2.41021i	−0.134479	−	0.0767566i
$987$	39.1076	+	28.4133i	1.24481	+	0.904406i
$988$	−14.9056	−	66.8642i	−0.474210	−	2.12723i
$989$	−1.47843	−	2.03489i	−0.0470115	−	0.0647058i
$990$	−49.2237	−	8.49267i	−1.56443	−	0.269915i
$991$	29.3074	+	21.2931i	0.930981	+	0.676398i	0.946233	−	0.323486i	$-0.104855\pi$
$991$	29.3074	+	21.2931i	0.930981	+	0.676398i	−0.0152515	+	0.999884i	$0.504855\pi$
$992$	−5.04571	−	4.32200i	−0.160202	−	0.137224i
$993$		−	21.2292i		−	0.673688i
$994$	10.1926	+	11.2080i	0.323289	+	0.355495i
$995$	0.538643	+	1.48576i	0.0170761	+	0.0471017i
$996$	3.68958	+	6.24693i	0.116909	+	0.197942i
$997$	−5.62136	+	17.3008i	−0.178030	+	0.547921i	−0.999759	−	0.0219581i	$-0.993010\pi$
$997$	−5.62136	+	17.3008i	−0.178030	+	0.547921i	0.821729	+	0.569879i	$0.193010\pi$
$998$	−16.2785	+	28.5202i	−0.515286	+	0.902791i
$999$	44.3246			1.40237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.189.24	yes	112
4.3	odd	2		800.2.be.a.689.1		112
5.2	odd	4		1000.2.t.b.301.19		224
5.3	odd	4		1000.2.t.b.301.38		224
5.4	even	2		1000.2.o.a.949.5		112
8.3	odd	2		800.2.be.a.689.28		112
8.5	even	2	inner	200.2.o.a.189.17	yes	112
25.9	even	10	inner	200.2.o.a.109.17	✓	112
25.12	odd	20		1000.2.t.b.701.4		224
25.13	odd	20		1000.2.t.b.701.53		224
25.16	even	5		1000.2.o.a.549.12		112
40.13	odd	4		1000.2.t.b.301.53		224
40.29	even	2		1000.2.o.a.949.12		112
40.37	odd	4		1000.2.t.b.301.4		224
100.59	odd	10		800.2.be.a.209.28		112
200.13	odd	20		1000.2.t.b.701.38		224
200.37	odd	20		1000.2.t.b.701.19		224
200.59	odd	10		800.2.be.a.209.1		112
200.109	even	10	inner	200.2.o.a.109.24	yes	112
200.141	even	10		1000.2.o.a.549.5		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.17	✓	112	25.9	even	10	inner
200.2.o.a.109.24	yes	112	200.109	even	10	inner
200.2.o.a.189.17	yes	112	8.5	even	2	inner
200.2.o.a.189.24	yes	112	1.1	even	1	trivial
800.2.be.a.209.1		112	200.59	odd	10
800.2.be.a.209.28		112	100.59	odd	10
800.2.be.a.689.1		112	4.3	odd	2
800.2.be.a.689.28		112	8.3	odd	2
1000.2.o.a.549.5		112	200.141	even	10
1000.2.o.a.549.12		112	25.16	even	5
1000.2.o.a.949.5		112	5.4	even	2
1000.2.o.a.949.12		112	40.29	even	2
1000.2.t.b.301.4		224	40.37	odd	4
1000.2.t.b.301.19		224	5.2	odd	4
1000.2.t.b.301.38		224	5.3	odd	4
1000.2.t.b.301.53		224	40.13	odd	4
1000.2.t.b.701.4		224	25.12	odd	20
1000.2.t.b.701.19		224	200.37	odd	20
1000.2.t.b.701.38		224	200.13	odd	20
1000.2.t.b.701.53		224	25.13	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22823 + 0.701037i) q^{2} +(0.970606 - 2.98722i) q^{3} +(1.01709 + 1.72207i) q^{4} +(0.762120 + 2.10218i) q^{5} +(3.28628 - 2.98856i) q^{6} +1.71800i q^{7} +(0.0419895 + 2.82812i) q^{8} +(-5.55435 - 4.03547i) q^{9} +(-0.537651 + 3.11624i) q^{10} +(-1.35234 - 1.86134i) q^{11} +(6.13139 - 1.36683i) q^{12} +(-4.80828 - 3.49342i) q^{13} +(-1.20438 + 2.11009i) q^{14} +(7.01940 - 0.236226i) q^{15} +(-1.93104 + 3.50301i) q^{16} +(-2.53693 + 0.824300i) q^{17} +(-3.99300 - 8.85029i) q^{18} +(5.48112 - 1.78092i) q^{19} +(-2.84496 + 3.45054i) q^{20} +(5.13203 + 1.66750i) q^{21} +(-0.356118 - 3.23419i) q^{22} +(-0.393834 - 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.83835 + 3.20423i) q^{25} +(-3.45665 - 7.66150i) q^{26} +(-9.82268 + 7.13660i) q^{27} +(-2.95851 + 1.74736i) q^{28} +(1.22579 + 0.398283i) q^{29} +(8.78703 + 4.63072i) q^{30} +(0.362926 + 1.11697i) q^{31} +(-4.82750 + 2.94877i) q^{32} +(-6.87282 + 2.23312i) q^{33} +(-3.69380 - 0.766057i) q^{34} +(-3.61155 + 1.30932i) q^{35} +(1.30007 - 13.6694i) q^{36} +(-2.95345 - 2.14581i) q^{37} +(7.98057 + 1.65509i) q^{38} +(-15.1026 + 10.9726i) q^{39} +(-5.91322 + 2.24363i) q^{40} +(6.21636 + 4.51645i) q^{41} +(5.13434 + 5.64582i) q^{42} +3.75396 q^{43} +(1.82990 - 4.22198i) q^{44} +(4.25022 - 14.7518i) q^{45} +(-0.103710 - 0.941873i) q^{46} +(8.51974 + 2.76823i) q^{47} +(8.58998 + 9.16849i) q^{48} +4.04848 q^{49} +(-6.96065 + 1.24470i) q^{50} +8.37845i q^{51} +(1.12544 - 11.8333i) q^{52} +(-1.09116 + 3.35825i) q^{53} +(-17.0675 + 1.87931i) q^{54} +(2.88223 - 4.26144i) q^{55} +(-4.85870 + 0.0721379i) q^{56} -18.1019i q^{57} +(1.22634 + 1.34851i) q^{58} +(-3.58141 + 4.92938i) q^{59} +(7.54618 + 11.8476i) q^{60} +(-0.542140 - 0.746192i) q^{61} +(-0.337282 + 1.62632i) q^{62} +(6.93293 - 9.54236i) q^{63} +(-7.99647 + 0.237503i) q^{64} +(3.67932 - 12.7703i) q^{65} +(-10.0069 - 2.07533i) q^{66} +(-4.74089 - 14.5910i) q^{67} +(-3.99980 - 3.53039i) q^{68} +(-2.00153 + 0.650336i) q^{69} +(-5.35369 - 0.923683i) q^{70} +(1.92683 - 5.93017i) q^{71} +(11.1796 - 15.8778i) q^{72} +(3.14398 + 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(5.84621 + 14.5760i) q^{75} +(8.64169 + 7.62750i) q^{76} +(3.19778 - 2.32332i) q^{77} +(-26.2416 + 2.88947i) q^{78} +(-0.125628 + 0.386644i) q^{79} +(-8.83565 - 1.38969i) q^{80} +(5.41990 + 16.6807i) q^{81} +(4.46891 + 9.90513i) q^{82} +(0.356893 + 1.09840i) q^{83} +(2.34821 + 10.5337i) q^{84} +(-3.66628 - 4.70489i) q^{85} +(4.61072 + 2.63166i) q^{86} +(2.37952 - 3.27513i) q^{87} +(5.20730 - 3.90274i) q^{88} +(3.34918 - 2.43332i) q^{89} +(15.5618 - 15.1390i) q^{90} +(6.00168 - 8.26061i) q^{91} +(0.532909 - 1.22954i) q^{92} +3.68890 q^{93} +(8.52356 + 9.37268i) q^{94} +(7.92110 + 10.1650i) q^{95} +(4.12301 + 17.2829i) q^{96} +(-14.4383 - 4.69127i) q^{97} +(4.97247 + 2.83814i) q^{98} +15.7959i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

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