LMFDB - Embedded newform 261.2.e.a.88.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(88,261)] 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("261.88"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			88.10
Character	$\chi$	$=$	261.88
Dual form			261.2.e.a.175.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.942480 - 1.63242i) q^{2} +(1.71821 - 0.218551i) q^{3} +(-0.776536 - 1.34500i) q^{4} +(-0.325626 - 0.564001i) q^{5} +(1.26261 - 3.01082i) q^{6} +(-0.0750596 + 0.130007i) q^{7} +0.842439 q^{8} +(2.90447 - 0.751031i) q^{9} -1.22758 q^{10} +(-3.11160 + 5.38944i) q^{11} +(-1.62820 - 2.14128i) q^{12} +(-1.52292 - 2.63778i) q^{13} +(0.141484 + 0.245058i) q^{14} +(-0.682756 - 0.897905i) q^{15} +(2.34706 - 4.06522i) q^{16} -3.36094 q^{17} +(1.51140 - 5.44916i) q^{18} -7.32089 q^{19} +(-0.505721 + 0.875935i) q^{20} +(-0.100555 + 0.239783i) q^{21} +(5.86524 + 10.1589i) q^{22} +(4.09451 + 7.09190i) q^{23} +(1.44749 - 0.184116i) q^{24} +(2.28794 - 3.96282i) q^{25} -5.74130 q^{26} +(4.82634 - 1.92520i) q^{27} +0.233146 q^{28} +(0.500000 - 0.866025i) q^{29} +(-2.10924 + 0.268290i) q^{30} +(2.00387 + 3.47080i) q^{31} +(-3.58166 - 6.20363i) q^{32} +(-4.16850 + 9.94022i) q^{33} +(-3.16762 + 5.48647i) q^{34} +0.0977654 q^{35} +(-3.26557 - 3.32331i) q^{36} -4.97458 q^{37} +(-6.89979 + 11.9508i) q^{38} +(-3.19319 - 4.19942i) q^{39} +(-0.274320 - 0.475137i) q^{40} +(-0.631601 - 1.09397i) q^{41} +(0.296657 + 0.390139i) q^{42} +(4.21514 - 7.30084i) q^{43} +9.66508 q^{44} +(-1.36935 - 1.39357i) q^{45} +15.4360 q^{46} +(-4.42882 + 7.67093i) q^{47} +(3.14427 - 7.49784i) q^{48} +(3.48873 + 6.04266i) q^{49} +(-4.31267 - 7.46976i) q^{50} +(-5.77479 + 0.734536i) q^{51} +(-2.36521 + 4.09666i) q^{52} +7.56487 q^{53} +(1.40599 - 9.69310i) q^{54} +4.05287 q^{55} +(-0.0632332 + 0.109523i) q^{56} +(-12.5788 + 1.59999i) q^{57} +(-0.942480 - 1.63242i) q^{58} +(-1.68776 - 2.92329i) q^{59} +(-0.677497 + 1.61556i) q^{60} +(0.864726 - 1.49775i) q^{61} +7.55442 q^{62} +(-0.120369 + 0.433974i) q^{63} -4.11437 q^{64} +(-0.991807 + 1.71786i) q^{65} +(12.2979 + 16.1732i) q^{66} +(-1.22333 - 2.11887i) q^{67} +(2.60989 + 4.52046i) q^{68} +(8.58516 + 11.2905i) q^{69} +(0.0921420 - 0.159595i) q^{70} -5.16416 q^{71} +(2.44684 - 0.632698i) q^{72} +4.79821 q^{73} +(-4.68845 + 8.12063i) q^{74} +(3.06507 - 7.30898i) q^{75} +(5.68494 + 9.84660i) q^{76} +(-0.467110 - 0.809059i) q^{77} +(-9.86473 + 1.25476i) q^{78} +(2.16455 - 3.74910i) q^{79} -3.05705 q^{80} +(7.87190 - 4.36270i) q^{81} -2.38109 q^{82} +(6.47530 - 11.2155i) q^{83} +(0.400593 - 0.0509543i) q^{84} +(1.09441 + 1.89557i) q^{85} +(-7.94537 - 13.7618i) q^{86} +(0.669833 - 1.59729i) q^{87} +(-2.62133 + 4.54028i) q^{88} -18.3266 q^{89} +(-3.56548 + 0.921954i) q^{90} +0.457240 q^{91} +(6.35908 - 11.0142i) q^{92} +(4.20161 + 5.52561i) q^{93} +(8.34814 + 14.4594i) q^{94} +(2.38387 + 4.12899i) q^{95} +(-7.50985 - 9.87634i) q^{96} +(-2.04388 + 3.54010i) q^{97} +13.1522 q^{98} +(-4.98990 + 17.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) $ 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.942480	−	1.63242i	0.666434	−	1.15430i	−0.312461	−	0.949931i	$-0.601153\pi$
$2$	0.942480	−	1.63242i	0.666434	−	1.15430i	0.978894	−	0.204367i	$-0.0655135\pi$
$3$	1.71821	−	0.218551i	0.992007	−	0.126180i
$3$	1.71821	−	0.218551i	0.992007	−	0.126180i
$4$	−0.776536	−	1.34500i	−0.388268	−	0.672500i
$5$	−0.325626	−	0.564001i	−0.145624	−	0.252229i	0.783981	−	0.620784i	$-0.213186\pi$
$5$	−0.325626	−	0.564001i	−0.145624	−	0.252229i	−0.929606	+	0.368556i	$0.879852\pi$
$6$	1.26261	−	3.01082i	0.515458	−	1.22916i
$7$	−0.0750596	+	0.130007i	−0.0283699	+	0.0491380i	−0.879862	−	0.475230i	$-0.842365\pi$
$7$	−0.0750596	+	0.130007i	−0.0283699	+	0.0491380i	0.851492	+	0.524368i	$0.175698\pi$
$8$	0.842439			0.297847
$9$	2.90447	−	0.751031i	0.968157	−	0.250344i
$10$	−1.22758			−0.388196
$11$	−3.11160	+	5.38944i	−0.938182	+	1.62498i	−0.169323	+	0.985561i	$0.554158\pi$
$11$	−3.11160	+	5.38944i	−0.938182	+	1.62498i	−0.768859	+	0.639418i	$0.779175\pi$
$12$	−1.62820	−	2.14128i	−0.470021	−	0.618133i
$13$	−1.52292	−	2.63778i	−0.422383	−	0.731588i	0.573789	−	0.819003i	$-0.305473\pi$
$13$	−1.52292	−	2.63778i	−0.422383	−	0.731588i	−0.996172	+	0.0874146i	$0.972140\pi$
$14$	0.141484	+	0.245058i	0.0378133	+	0.0654945i
$15$	−0.682756	−	0.897905i	−0.176287	−	0.231838i
$16$	2.34706	−	4.06522i	0.586764	−	1.01630i
$17$	−3.36094			−0.815147			−0.407574	−	0.913172i	$-0.633625\pi$
$17$	−3.36094			−0.815147			−0.407574	+	0.913172i	$0.633625\pi$
$18$	1.51140	−	5.44916i	0.356242	−	1.28438i
$19$	−7.32089			−1.67953			−0.839764	−	0.542952i	$-0.817306\pi$
$19$	−7.32089			−1.67953			−0.839764	+	0.542952i	$0.817306\pi$
$20$	−0.505721	+	0.875935i	−0.113083	+	0.195865i
$21$	−0.100555	+	0.239783i	−0.0219428	+	0.0523250i
$22$	5.86524	+	10.1589i	1.25047	+	2.16588i
$23$	4.09451	+	7.09190i	0.853765	+	1.47876i	0.877786	+	0.479053i	$0.159020\pi$
$23$	4.09451	+	7.09190i	0.853765	+	1.47876i	−0.0240213	+	0.999711i	$0.507647\pi$
$24$	1.44749	−	0.184116i	0.295467	−	0.0375825i
$25$	2.28794	−	3.96282i	0.457587	−	0.792564i
$26$	−5.74130			−1.12596
$27$	4.82634	−	1.92520i	0.928830	−	0.370505i
$28$	0.233146			0.0440605
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i
$30$	−2.10924	+	0.268290i	−0.385093	+	0.0489827i
$31$	2.00387	+	3.47080i	0.359905	+	0.623374i	0.987945	−	0.154807i	$-0.0494757\pi$
$31$	2.00387	+	3.47080i	0.359905	+	0.623374i	−0.628039	+	0.778182i	$0.716142\pi$
$32$	−3.58166	−	6.20363i	−0.633155	−	1.09666i
$33$	−4.16850	+	9.94022i	−0.725643	+	1.73037i
$34$	−3.16762	+	5.48647i	−0.543242	+	0.940922i
$35$	0.0977654			0.0165254
$36$	−3.26557	−	3.32331i	−0.544261	−	0.553885i
$37$	−4.97458			−0.817817			−0.408908	−	0.912575i	$-0.634090\pi$
$37$	−4.97458			−0.817817			−0.408908	+	0.912575i	$0.634090\pi$
$38$	−6.89979	+	11.9508i	−1.11929	+	1.93867i
$39$	−3.19319	−	4.19942i	−0.511319	−	0.672445i
$40$	−0.274320	−	0.475137i	−0.0433738	−	0.0751257i
$41$	−0.631601	−	1.09397i	−0.0986395	−	0.170849i	0.812482	−	0.582986i	$-0.198116\pi$
$41$	−0.631601	−	1.09397i	−0.0986395	−	0.170849i	−0.911122	+	0.412137i	$0.864782\pi$
$42$	0.296657	+	0.390139i	0.0457752	+	0.0601997i
$43$	4.21514	−	7.30084i	0.642803	−	1.11337i	−0.342001	−	0.939700i	$-0.611105\pi$
$43$	4.21514	−	7.30084i	0.642803	−	1.11337i	0.984804	−	0.173668i	$-0.0555620\pi$
$44$	9.66508			1.45706
$45$	−1.36935	−	1.39357i	−0.204131	−	0.207741i
$46$	15.4360			2.27591
$47$	−4.42882	+	7.67093i	−0.646009	+	1.11892i	0.338058	+	0.941125i	$0.390230\pi$
$47$	−4.42882	+	7.67093i	−0.646009	+	1.11892i	−0.984067	+	0.177796i	$0.943103\pi$
$48$	3.14427	−	7.49784i	0.453836	−	1.08222i
$49$	3.48873	+	6.04266i	0.498390	+	0.863237i
$50$	−4.31267	−	7.46976i	−0.609903	−	1.05638i
$51$	−5.77479	+	0.734536i	−0.808632	+	0.102856i
$52$	−2.36521	+	4.09666i	−0.327996	+	0.568105i
$53$	7.56487			1.03912			0.519558	−	0.854435i	$-0.326097\pi$
$53$	7.56487			1.03912			0.519558	+	0.854435i	$0.326097\pi$
$54$	1.40599	−	9.69310i	0.191331	−	1.31906i
$55$	4.05287			0.546489
$56$	−0.0632332	+	0.109523i	−0.00844989	+	0.0146356i
$57$	−12.5788	+	1.59999i	−1.66610	+	0.211923i
$58$	−0.942480	−	1.63242i	−0.123754	−	0.214348i
$59$	−1.68776	−	2.92329i	−0.219728	−	0.380580i	0.734997	−	0.678070i	$-0.237184\pi$
$59$	−1.68776	−	2.92329i	−0.219728	−	0.380580i	−0.954725	+	0.297491i	$0.903850\pi$
$60$	−0.677497	+	1.61556i	−0.0874645	+	0.208568i
$61$	0.864726	−	1.49775i	0.110717	−	0.191767i	−0.805343	−	0.592810i	$-0.798019\pi$
$61$	0.864726	−	1.49775i	0.110717	−	0.191767i	0.916059	+	0.401042i	$0.131352\pi$
$62$	7.55442			0.959412
$63$	−0.120369	+	0.433974i	−0.0151651	+	0.0546755i
$64$	−4.11437			−0.514296
$65$	−0.991807	+	1.71786i	−0.123018	+	0.213074i
$66$	12.2979	+	16.1732i	1.51377	+	1.99079i
$67$	−1.22333	−	2.11887i	−0.149453	−	0.258861i	0.781572	−	0.623815i	$-0.214418\pi$
$67$	−1.22333	−	2.11887i	−0.149453	−	0.258861i	−0.931026	+	0.364954i	$0.881085\pi$
$68$	2.60989	+	4.52046i	0.316496	+	0.548187i
$69$	8.58516	+	11.2905i	1.03353	+	1.35922i
$70$	0.0921420	−	0.159595i	0.0110131	−	0.0190752i
$71$	−5.16416			−0.612873			−0.306437	−	0.951891i	$-0.599137\pi$
$71$	−5.16416			−0.612873			−0.306437	+	0.951891i	$0.599137\pi$
$72$	2.44684	−	0.632698i	0.288363	−	0.0745642i
$73$	4.79821			0.561587			0.280794	−	0.959768i	$-0.409402\pi$
$73$	4.79821			0.561587			0.280794	+	0.959768i	$0.409402\pi$
$74$	−4.68845	+	8.12063i	−0.545021	+	0.944004i
$75$	3.06507	−	7.30898i	0.353924	−	0.843968i
$76$	5.68494	+	9.84660i	0.652107	+	1.12948i
$77$	−0.467110	−	0.809059i	−0.0532322	−	0.0922008i
$78$	−9.86473	+	1.25476i	−1.11696	+	0.142074i
$79$	2.16455	−	3.74910i	0.243530	−	0.421807i	−0.718187	−	0.695850i	$-0.755028\pi$
$79$	2.16455	−	3.74910i	0.243530	−	0.421807i	0.961717	+	0.274043i	$0.0883611\pi$
$80$	−3.05705			−0.341789
$81$	7.87190	−	4.36270i	0.874656	−	0.484744i
$82$	−2.38109			−0.262947
$83$	6.47530	−	11.2155i	0.710757	−	1.23107i	−0.253817	−	0.967252i	$-0.581686\pi$
$83$	6.47530	−	11.2155i	0.710757	−	1.23107i	0.964574	−	0.263814i	$-0.0849806\pi$
$84$	0.400593	−	0.0509543i	0.0437083	−	0.00555956i
$85$	1.09441	+	1.89557i	0.118705	+	0.205604i
$86$	−7.94537	−	13.7618i	−0.856771	−	1.48397i
$87$	0.669833	−	1.59729i	0.0718136	−	0.171247i
$88$	−2.62133	+	4.54028i	−0.279435	+	0.483996i
$89$	−18.3266			−1.94261			−0.971307	−	0.237831i	$-0.923564\pi$
$89$	−18.3266			−1.94261			−0.971307	+	0.237831i	$0.923564\pi$
$90$	−3.56548	+	0.921954i	−0.375835	+	0.0971825i
$91$	0.457240			0.0479318
$92$	6.35908	−	11.0142i	0.662980	−	1.14831i
$93$	4.20161	+	5.52561i	0.435686	+	0.572979i
$94$	8.34814	+	14.4594i	0.861045	+	1.49137i
$95$	2.38387	+	4.12899i	0.244580	+	0.423625i
$96$	−7.50985	−	9.87634i	−0.766471	−	1.00800i
$97$	−2.04388	+	3.54010i	−0.207524	+	0.359442i	−0.950934	−	0.309394i	$-0.899874\pi$
$97$	−2.04388	+	3.54010i	−0.207524	+	0.359442i	0.743410	+	0.668836i	$0.233207\pi$
$98$	13.1522			1.32858
$99$	−4.98990	+	17.9904i	−0.501504	+	1.80810i
$100$	−7.10666			−0.710666
$101$	4.62241	−	8.00625i	0.459947	−	0.796652i	−0.539010	−	0.842299i	$-0.681202\pi$
$101$	4.62241	−	8.00625i	0.459947	−	0.796652i	0.998958	+	0.0456471i	$0.0145350\pi$
$102$	−4.24355	+	10.1192i	−0.420174	+	1.00195i
$103$	2.52895	+	4.38028i	0.249185	+	0.431601i	0.963300	−	0.268427i	$-0.0865039\pi$
$103$	2.52895	+	4.38028i	0.249185	+	0.431601i	−0.714115	+	0.700029i	$0.753171\pi$
$104$	−1.28297	−	2.22217i	−0.125806	−	0.217902i
$105$	0.167981	−	0.0213667i	0.0163933	−	0.00208518i
$106$	7.12974	−	12.3491i	0.692502	−	1.19945i
$107$	7.20552			0.696584			0.348292	−	0.937386i	$-0.386762\pi$
$107$	7.20552			0.696584			0.348292	+	0.937386i	$0.386762\pi$
$108$	−6.33723	−	4.99645i	−0.609800	−	0.480783i
$109$	−1.74654			−0.167289			−0.0836443	−	0.996496i	$-0.526656\pi$
$109$	−1.74654			−0.167289			−0.0836443	+	0.996496i	$0.526656\pi$
$110$	3.81975	−	6.61600i	0.364199	−	0.630811i
$111$	−8.54737	+	1.08720i	−0.811280	+	0.103192i
$112$	0.352338	+	0.610267i	0.0332928	+	0.0576648i
$113$	2.18091	+	3.77745i	0.205163	+	0.355353i	0.950185	−	0.311688i	$-0.100894\pi$
$113$	2.18091	+	3.77745i	0.205163	+	0.355353i	−0.745022	+	0.667040i	$0.767561\pi$
$114$	−9.24341	+	22.0419i	−0.865725	+	2.06441i
$115$	2.66656	−	4.61862i	0.248658	−	0.430688i
$116$	−1.55307			−0.144199
$117$	−6.40434	−	6.51759i	−0.592081	−	0.602552i
$118$	−6.36272			−0.585736
$119$	0.252271	−	0.436946i	0.0231256	−	0.0400547i
$120$	−0.575181	−	0.756430i	−0.0525066	−	0.0690523i
$121$	−13.8641	−	24.0133i	−1.26037	−	2.18303i
$122$	−1.62997	−	2.82320i	−0.147571	−	0.255600i
$123$	−1.32431	−	1.74162i	−0.119409	−	0.157037i
$124$	3.11215	−	5.39041i	0.279480	−	0.484073i
$125$	−6.23631			−0.557792
$126$	0.594983	+	0.605505i	0.0530053	+	0.0539426i
$127$	−17.3725			−1.54156			−0.770779	−	0.637102i	$-0.780133\pi$
$127$	−17.3725			−1.54156			−0.770779	+	0.637102i	$0.780133\pi$
$128$	3.28562	−	5.69086i	0.290411	−	0.503006i
$129$	5.64688	−	13.4656i	0.497180	−	1.18558i
$130$	1.86952	+	3.23810i	0.163967	+	0.284000i
$131$	−6.29669	−	10.9062i	−0.550145	−	0.952879i	−0.998264	−	0.0589046i	$-0.981239\pi$
$131$	−6.29669	−	10.9062i	−0.550145	−	0.952879i	0.448119	−	0.893974i	$-0.352094\pi$
$132$	16.6066	−	2.11231i	1.44542	−	0.183853i
$133$	0.549503	−	0.951767i	0.0476479	−	0.0825287i
$134$	−4.61185			−0.398403
$135$	−2.65740	−	2.09517i	−0.228713	−	0.180323i
$136$	−2.83139			−0.242789
$137$	−1.23113	+	2.13238i	−0.105183	+	0.182182i	−0.913813	−	0.406136i	$-0.866876\pi$
$137$	−1.23113	+	2.13238i	−0.105183	+	0.182182i	0.808630	+	0.588317i	$0.200209\pi$
$138$	26.5222	−	3.37355i	2.25772	−	0.287175i
$139$	−4.22918	−	7.32515i	−0.358714	−	0.621311i	0.629032	−	0.777379i	$-0.283451\pi$
$139$	−4.22918	−	7.32515i	−0.358714	−	0.621311i	−0.987746	+	0.156068i	$0.950118\pi$
$140$	−0.0759184	−	0.131495i	−0.00641628	−	0.0111133i
$141$	−5.93313	+	14.1482i	−0.499660	+	1.19149i
$142$	−4.86712	+	8.43010i	−0.408440	+	0.707438i
$143$	18.9549			1.58509
$144$	3.76385	−	13.5700i	0.313654	−	1.13084i
$145$	−0.651252			−0.0540836
$146$	4.52221	−	7.83270i	0.374261	−	0.648239i
$147$	7.31499	+	9.62008i	0.603330	+	0.793451i
$148$	3.86295	+	6.69082i	0.317532	+	0.549982i
$149$	1.23212	+	2.13409i	0.100939	+	0.174832i	0.912072	−	0.410031i	$-0.134482\pi$
$149$	1.23212	+	2.13409i	0.100939	+	0.174832i	−0.811133	+	0.584862i	$0.801149\pi$
$150$	−9.04257	−	11.8921i	−0.738323	−	0.970982i
$151$	2.76220	−	4.78427i	0.224785	−	0.389339i	−0.731470	−	0.681873i	$-0.761165\pi$
$151$	2.76220	−	4.78427i	0.224785	−	0.389339i	0.956255	+	0.292535i	$0.0944988\pi$
$152$	−6.16741			−0.500243
$153$	−9.76175	+	2.52417i	−0.789191	+	0.204067i
$154$	−1.76097			−0.141903
$155$	1.30502	−	2.26037i	0.104822	−	0.181557i
$156$	−3.16859	+	7.55584i	−0.253690	+	0.604951i
$157$	−8.57650	−	14.8549i	−0.684479	−	1.18555i	−0.973600	−	0.228260i	$-0.926696\pi$
$157$	−8.57650	−	14.8549i	−0.684479	−	1.18555i	0.289121	−	0.957292i	$-0.406637\pi$
$158$	−4.08008	−	7.06691i	−0.324594	−	0.562213i
$159$	12.9980	−	1.65331i	1.03081	−	0.131116i
$160$	−2.33257	+	4.04012i	−0.184406	+	0.319400i
$161$	−1.22933			−0.0968847
$162$	0.297346	−	16.9620i	0.0233617	−	1.33266i
$163$	11.9666			0.937300			0.468650	−	0.883384i	$-0.344741\pi$
$163$	11.9666			0.937300			0.468650	+	0.883384i	$0.344741\pi$
$164$	−0.980923	+	1.69901i	−0.0765972	+	0.132670i
$165$	6.96367	−	0.885758i	0.542121	−	0.0689562i
$166$	−12.2057	−	21.1409i	−0.947344	−	1.64085i
$167$	10.8962	+	18.8728i	0.843175	+	1.46042i	0.887197	+	0.461391i	$0.152649\pi$
$167$	10.8962	+	18.8728i	0.843175	+	1.46042i	−0.0440224	+	0.999031i	$0.514017\pi$
$168$	−0.0847113	+	0.202003i	−0.00653562	+	0.0155849i
$169$	1.86141	−	3.22406i	0.143186	−	0.248005i
$170$	4.12583			0.316437
$171$	−21.2633	+	5.49822i	−1.62605	+	0.420459i
$172$	−13.0928			−0.998320
$173$	−7.67695	+	13.2969i	−0.583668	+	1.01094i	0.411372	+	0.911467i	$0.365050\pi$
$173$	−7.67695	+	13.2969i	−0.583668	+	1.01094i	−0.995040	+	0.0994750i	$0.968284\pi$
$174$	−1.97614	−	2.59886i	−0.149811	−	0.197019i
$175$	0.343463	+	0.594895i	0.0259634	+	0.0449699i
$176$	14.6062	+	25.2986i	1.10098	+	1.90696i
$177$	−3.53881	−	4.65395i	−0.265993	−	0.349812i
$178$	−17.2724	+	29.9167i	−1.29462	+	2.24235i
$179$	2.66166			0.198942			0.0994711	−	0.995040i	$-0.468285\pi$
$179$	2.66166			0.198942			0.0994711	+	0.995040i	$0.468285\pi$
$180$	−0.810998	+	2.92394i	−0.0604482	+	0.217938i
$181$	−0.388292			−0.0288615			−0.0144307	−	0.999896i	$-0.504594\pi$
$181$	−0.388292			−0.0288615			−0.0144307	+	0.999896i	$0.504594\pi$
$182$	0.430939	−	0.746409i	0.0319433	−	0.0553275i
$183$	1.15844	−	2.76243i	0.0856346	−	0.204205i
$184$	3.44938	+	5.97450i	0.254292	+	0.440446i
$185$	1.61985	+	2.80567i	0.119094	+	0.206277i
$186$	12.9801	−	1.65102i	0.951744	−	0.121059i
$187$	10.4579	−	18.1136i	0.764756	−	1.32460i
$188$	13.7565			1.00330
$189$	−0.111974	+	0.771963i	−0.00814489	+	0.0561521i
$190$	8.98701			0.651986
$191$	−7.24508	+	12.5489i	−0.524236	+	0.908003i	0.475366	+	0.879788i	$0.342316\pi$
$191$	−7.24508	+	12.5489i	−0.524236	+	0.908003i	−0.999602	+	0.0282149i	$0.991018\pi$
$192$	−7.06933	+	0.899198i	−0.510185	+	0.0648940i
$193$	−0.897884	−	1.55518i	−0.0646311	−	0.111944i	0.831899	−	0.554927i	$-0.187254\pi$
$193$	−0.897884	−	1.55518i	−0.0646311	−	0.111944i	−0.896530	+	0.442982i	$0.853920\pi$
$194$	3.85262	+	6.67294i	0.276602	+	0.479089i
$195$	−1.32869	+	3.16840i	−0.0951495	+	0.226894i
$196$	5.41826	−	9.38469i	0.387018	−	0.670335i
$197$	0.412253			0.0293718			0.0146859	−	0.999892i	$-0.495325\pi$
$197$	0.412253			0.0293718			0.0146859	+	0.999892i	$0.495325\pi$
$198$	24.6650	+	25.1012i	1.75287	+	1.78387i
$199$	−8.19784			−0.581129			−0.290565	−	0.956855i	$-0.593843\pi$
$199$	−8.19784			−0.581129			−0.290565	+	0.956855i	$0.593843\pi$
$200$	1.92745	−	3.33844i	0.136291	−	0.236063i
$201$	−2.56501	−	3.37329i	−0.180922	−	0.237934i
$202$	−8.71306	−	15.0915i	−0.613049	−	1.06183i
$203$	0.0750596	+	0.130007i	0.00526815	+	0.00912470i
$204$	5.47228	+	7.19670i	0.383137	+	0.503870i
$205$	−0.411332	+	0.712447i	−0.0287287	+	0.0497595i
$206$	9.53395			0.664262
$207$	17.2186	+	17.5231i	1.19678	+	1.21794i
$208$	−14.2975			−0.991356
$209$	22.7797	−	39.4555i	1.57570	−	2.72920i
$210$	0.123439	−	0.294354i	0.00851813	−	0.0203124i
$211$	6.05308	+	10.4842i	0.416711	+	0.721764i	0.995606	−	0.0936373i	$-0.0298494\pi$
$211$	6.05308	+	10.4842i	0.416711	+	0.721764i	−0.578895	+	0.815402i	$0.696516\pi$
$212$	−5.87440	−	10.1748i	−0.403455	−	0.698805i
$213$	−8.87310	+	1.12863i	−0.607975	+	0.0773326i
$214$	6.79106	−	11.7625i	0.464227	−	0.804065i
$215$	−5.49024			−0.374431
$216$	4.06590	−	1.62187i	0.276650	−	0.110354i
$217$	−0.601638			−0.0408418
$218$	−1.64608	+	2.85110i	−0.111487	+	0.193101i
$219$	8.24431	−	1.04865i	0.557099	−	0.0708613i
$220$	−3.14720	−	5.45111i	−0.212184	−	0.367514i
$221$	5.11845	+	8.86541i	0.344304	+	0.596352i
$222$	−6.28095	+	14.9776i	−0.421550	+	1.00523i
$223$	3.72052	−	6.44412i	0.249144	−	0.431530i	−0.714144	−	0.699998i	$-0.753184\pi$
$223$	3.72052	−	6.44412i	0.249144	−	0.431530i	0.963289	+	0.268468i	$0.0865174\pi$
$224$	1.07535			0.0718501
$225$	3.66904	−	13.2282i	0.244603	−	0.881880i
$226$	8.22186			0.546910
$227$	−2.40680	+	4.16871i	−0.159745	+	0.276687i	−0.934777	−	0.355236i	$-0.884401\pi$
$227$	−2.40680	+	4.16871i	−0.159745	+	0.276687i	0.775032	+	0.631923i	$0.217734\pi$
$228$	11.9199	+	15.6761i	0.789413	+	1.03817i
$229$	10.7389	+	18.6002i	0.709644	+	1.22914i	0.964989	+	0.262289i	$0.0844773\pi$
$229$	10.7389	+	18.6002i	0.709644	+	1.22914i	−0.255346	+	0.966850i	$0.582189\pi$
$230$	−5.02636	−	8.70591i	−0.331428	−	0.574051i
$231$	−0.979413	−	1.28804i	−0.0644406	−	0.0847470i
$232$	0.421220	−	0.729574i	0.0276544	−	0.0478989i
$233$	2.70699			0.177341			0.0886706	−	0.996061i	$-0.471738\pi$
$233$	2.70699			0.177341			0.0886706	+	0.996061i	$0.471738\pi$
$234$	−16.6754	+	4.31189i	−1.09011	+	0.281877i
$235$	5.76855			0.376299
$236$	−2.62122	+	4.54008i	−0.170627	+	0.295534i
$237$	2.89977	−	6.91480i	0.188360	−	0.449164i
$238$	−0.475520	−	0.823625i	−0.0308234	−	0.0533877i
$239$	11.1027	+	19.2304i	0.718173	+	1.24391i	0.961723	+	0.274024i	$0.0883549\pi$
$239$	11.1027	+	19.2304i	0.718173	+	1.24391i	−0.243549	+	0.969888i	$0.578312\pi$
$240$	−5.25264	+	0.668121i	−0.339057	+	0.0431270i
$241$	−1.70779	+	2.95798i	−0.110008	+	0.190540i	−0.915773	−	0.401695i	$-0.868421\pi$
$241$	−1.70779	+	2.95798i	−0.110008	+	0.190540i	0.805765	+	0.592235i	$0.201754\pi$
$242$	−52.2664			−3.35981
$243$	12.5721	−	9.21643i	0.806500	−	0.591234i
$244$	−2.68596			−0.171951
$245$	2.27204	−	3.93530i	0.145156	−	0.251417i
$246$	−4.09120	+	0.520388i	−0.260845	+	0.0331787i
$247$	11.1491	+	19.3109i	0.709403	+	1.22872i
$248$	1.68814	+	2.92394i	0.107197	+	0.185670i
$249$	8.67474	−	20.6858i	0.549739	−	1.31091i
$250$	−5.87759	+	10.1803i	−0.371732	+	0.643858i
$251$	3.54213			0.223577			0.111789	−	0.993732i	$-0.464342\pi$
$251$	3.54213			0.223577			0.111789	+	0.993732i	$0.464342\pi$
$252$	0.677166	−	0.175100i	0.0426574	−	0.0110303i
$253$	−50.9619			−3.20395
$254$	−16.3732	+	28.3592i	−1.02735	+	1.77942i
$255$	2.29470	+	3.01780i	0.143700	+	0.188982i
$256$	−10.3076	−	17.8533i	−0.644227	−	1.11583i
$257$	−1.76320	−	3.05395i	−0.109985	−	0.190500i	0.805779	−	0.592217i	$-0.201747\pi$
$257$	−1.76320	−	3.05395i	−0.109985	−	0.190500i	−0.915764	+	0.401716i	$0.868414\pi$
$258$	−16.6594	−	21.9091i	−1.03717	−	1.36400i
$259$	0.373390	−	0.646731i	0.0232013	−	0.0401859i
$260$	3.08070			0.191057
$261$	0.801824	−	2.89086i	0.0496316	−	0.178940i
$262$	−23.7380			−1.46654
$263$	−5.17371	+	8.96113i	−0.319025	+	0.552567i	−0.980285	−	0.197590i	$-0.936689\pi$
$263$	−5.17371	+	8.96113i	−0.319025	+	0.552567i	0.661260	+	0.750157i	$0.270022\pi$
$264$	−3.51171	+	8.37404i	−0.216131	+	0.515386i
$265$	−2.46332	−	4.26660i	−0.151321	−	0.262095i
$266$	−1.03579	−	1.79404i	−0.0635084	−	0.110000i
$267$	−31.4889	+	4.00529i	−1.92709	+	0.245120i
$268$	−1.89992	+	3.29075i	−0.116056	+	0.201015i
$269$	18.8710			1.15058			0.575291	−	0.817949i	$-0.304889\pi$
$269$	18.8710			1.15058			0.575291	+	0.817949i	$0.304889\pi$
$270$	−5.92474	+	2.36335i	−0.360568	+	0.143829i
$271$	23.3585			1.41893			0.709464	−	0.704742i	$-0.248937\pi$
$271$	23.3585			1.41893			0.709464	+	0.704742i	$0.248937\pi$
$272$	−7.88831	+	13.6629i	−0.478299	+	0.828438i
$273$	0.785633	−	0.0999301i	0.0475486	−	0.00604805i
$274$	2.32063	+	4.01946i	0.140195	+	0.242824i
$275$	14.2383	+	24.6614i	0.858600	+	1.48714i
$276$	8.51904	−	20.3145i	0.512786	−	1.22279i
$277$	−10.7518	+	18.6226i	−0.646011	+	1.11892i	0.338056	+	0.941126i	$0.390231\pi$
$277$	−10.7518	+	18.6226i	−0.646011	+	1.11892i	−0.984067	+	0.177798i	$0.943103\pi$
$278$	−15.9437			−0.956238
$279$	8.42686	+	8.57587i	0.504503	+	0.513424i
$280$	0.0823615			0.00492204
$281$	15.1241	−	26.1957i	0.902226	−	1.56270i	0.0776285	−	0.996982i	$-0.475265\pi$
$281$	15.1241	−	26.1957i	0.902226	−	1.56270i	0.824598	−	0.565719i	$-0.191401\pi$
$282$	17.5039	+	23.0198i	1.04234	+	1.37081i
$283$	6.89101	+	11.9356i	0.409628	+	0.709497i	0.994848	−	0.101378i	$-0.0323251\pi$
$283$	6.89101	+	11.9356i	0.409628	+	0.709497i	−0.585220	+	0.810875i	$0.698992\pi$
$284$	4.01016	+	6.94580i	0.237959	+	0.412158i
$285$	4.99838	+	6.57346i	0.296079	+	0.389378i
$286$	17.8646	−	30.9424i	1.05636	−	1.82966i
$287$	0.189631			0.0111936
$288$	−15.0620	−	15.3283i	−0.887534	−	0.903229i
$289$	−5.70409			−0.335535
$290$	−0.613792	+	1.06312i	−0.0360431	+	0.0624285i
$291$	−2.73811	+	6.52931i	−0.160511	+	0.382755i
$292$	−3.72598	−	6.45359i	−0.218047	−	0.377668i
$293$	−11.1585	−	19.3271i	−0.651887	−	1.12910i	−0.982665	−	0.185393i	$-0.940644\pi$
$293$	−11.1585	−	19.3271i	−0.651887	−	1.12910i	0.330778	−	0.943709i	$-0.392689\pi$
$294$	22.5983	−	2.87443i	1.31796	−	0.167640i
$295$	−1.09916	+	1.90380i	−0.0639955	+	0.110843i
$296$	−4.19079			−0.243584
$297$	−4.64187	+	32.0018i	−0.269349	+	1.85693i
$298$	4.64499			0.269077
$299$	12.4713	−	21.6008i	0.721231	−	1.24921i
$300$	−12.2107	+	1.55317i	−0.704986	+	0.0896721i
$301$	0.632774	+	1.09600i	0.0364725	+	0.0631722i
$302$	−5.20664	−	9.01816i	−0.299608	−	0.518937i
$303$	6.19249	−	14.7666i	0.355749	−	0.848321i
$304$	−17.1825	+	29.7610i	−0.985486	+	1.70691i
$305$	−1.12631			−0.0644923
$306$	−5.07974	+	18.3143i	−0.290389	+	1.04696i
$307$	19.1156			1.09098			0.545491	−	0.838116i	$-0.316343\pi$
$307$	19.1156			1.09098			0.545491	+	0.838116i	$0.316343\pi$
$308$	−0.725457	+	1.25653i	−0.0413367	+	0.0715973i
$309$	5.30258	+	6.97352i	0.301653	+	0.396710i
$310$	−2.45992	−	4.26070i	−0.139714	−	0.241992i
$311$	3.13421	+	5.42862i	0.177725	+	0.307829i	0.941101	−	0.338126i	$-0.109793\pi$
$311$	3.13421	+	5.42862i	0.177725	+	0.307829i	−0.763376	+	0.645954i	$0.776460\pi$
$312$	−2.69007	−	3.53775i	−0.152295	−	0.200286i
$313$	−9.17060	+	15.8839i	−0.518353	+	0.897814i	0.481420	+	0.876490i	$0.340121\pi$
$313$	−9.17060	+	15.8839i	−0.518353	+	0.897814i	−0.999773	+	0.0213234i	$0.993212\pi$
$314$	−32.3327			−1.82464
$315$	0.283957	−	0.0734249i	0.0159992	−	0.00413702i
$316$	−6.72340			−0.378221
$317$	4.25841	−	7.37578i	0.239176	−	0.414265i	−0.721302	−	0.692621i	$-0.756456\pi$
$317$	4.25841	−	7.37578i	0.239176	−	0.414265i	0.960478	+	0.278356i	$0.0897893\pi$
$318$	9.55147	−	22.7765i	0.535620	−	1.27724i
$319$	3.11160	+	5.38944i	0.174216	+	0.301751i
$320$	1.33975	+	2.32051i	0.0748940	+	0.129720i
$321$	12.3806	−	1.57477i	0.691016	−	0.0878952i
$322$	−1.15862	+	2.00679i	−0.0645673	+	0.111834i
$323$	24.6051			1.36906
$324$	−11.9807	−	7.19992i	−0.665592	−	0.399996i
$325$	−13.9374			−0.773108
$326$	11.2783	−	19.5346i	0.624648	−	1.08192i
$327$	−3.00092	+	0.381708i	−0.165951	+	0.0211085i
$328$	−0.532086	−	0.921600i	−0.0293795	−	0.0508868i
$329$	−0.664850	−	1.15155i	−0.0366544	−	0.0634872i
$330$	5.11719	−	12.2025i	0.281692	−	0.671723i
$331$	3.30929	−	5.73186i	0.181895	−	0.315051i	−0.760631	−	0.649185i	$-0.775110\pi$
$331$	3.30929	−	5.73186i	0.181895	−	0.315051i	0.942526	+	0.334133i	$0.108444\pi$
$332$	−20.1132			−1.10386
$333$	−14.4485	+	3.73607i	−0.791775	+	0.204735i
$334$	41.0779			2.24768
$335$	−0.796695	+	1.37992i	−0.0435281	+	0.0753929i
$336$	0.738764	+	0.971562i	0.0403029	+	0.0530030i
$337$	6.21218	+	10.7598i	0.338399	+	0.586124i	0.984132	−	0.177439i	$-0.0567813\pi$
$337$	6.21218	+	10.7598i	0.338399	+	0.586124i	−0.645733	+	0.763563i	$0.723448\pi$
$338$	−3.50869	−	6.07723i	−0.190847	−	0.330558i
$339$	4.57282	+	6.01380i	0.248362	+	0.326625i
$340$	1.69970	−	2.94396i	0.0921790	−	0.159659i
$341$	−24.9409			−1.35063
$342$	−11.0648	+	39.8927i	−0.598317	+	2.15715i
$343$	−2.09829			−0.113297
$344$	3.55100	−	6.15051i	0.191457	−	0.331614i
$345$	3.57230	−	8.51852i	0.192326	−	0.458622i
$346$	14.4707	+	25.0641i	0.777952	+	1.34745i
$347$	−6.20061	−	10.7398i	−0.332866	−	0.576541i	0.650207	−	0.759757i	$-0.274682\pi$
$347$	−6.20061	−	10.7398i	−0.332866	−	0.576541i	−0.983073	+	0.183217i	$0.941349\pi$
$348$	−2.66850	+	0.339425i	−0.143047	+	0.0181951i
$349$	3.25795	−	5.64294i	0.174394	−	0.302060i	−0.765557	−	0.643368i	$-0.777537\pi$
$349$	3.25795	−	5.64294i	0.174394	−	0.302060i	0.939951	+	0.341308i	$0.110870\pi$
$350$	1.29483			0.0692114
$351$	−12.4284	−	9.79890i	−0.663379	−	0.523027i
$352$	44.5788			2.37606
$353$	0.175322	−	0.303666i	0.00933144	−	0.0161625i	−0.861322	−	0.508059i	$-0.830363\pi$
$353$	0.175322	−	0.303666i	0.00933144	−	0.0161625i	0.870653	+	0.491897i	$0.163696\pi$
$354$	−10.9325	+	1.39058i	−0.581054	+	0.0739084i
$355$	1.68159	+	2.91259i	0.0892493	+	0.154584i
$356$	14.2313	+	24.6493i	0.754255	+	1.30641i
$357$	0.337958	−	0.805897i	0.0178867	−	0.0426526i
$358$	2.50856	−	4.34496i	0.132582	−	0.229638i
$359$	−26.3424			−1.39030			−0.695148	−	0.718867i	$-0.744661\pi$
$359$	−26.3424			−1.39030			−0.695148	+	0.718867i	$0.744661\pi$
$360$	−1.15360	−	1.17400i	−0.0607999	−	0.0618751i
$361$	34.5954			1.82081
$362$	−0.365957	+	0.633856i	−0.0192343	+	0.0333147i
$363$	−29.0695	−	38.2298i	−1.52575	−	2.00654i
$364$	−0.355063	−	0.614988i	−0.0186104	−	0.0322341i
$365$	−1.56242	−	2.70619i	−0.0817809	−	0.141649i
$366$	−3.41764	−	4.49460i	−0.178643	−	0.234937i
$367$	10.1812	−	17.6344i	0.531455	−	0.920506i	−0.467871	−	0.883797i	$-0.654979\pi$
$367$	10.1812	−	17.6344i	0.531455	−	0.920506i	0.999326	−	0.0367097i	$-0.0116877\pi$
$368$	38.4402			2.00383
$369$	−2.65607	−	2.70304i	−0.138269	−	0.140715i
$370$	6.10672			0.317473
$371$	−0.567816	+	0.983487i	−0.0294795	+	0.0510601i
$372$	4.16925	−	9.94200i	0.216165	−	0.515469i
$373$	11.3795	+	19.7099i	0.589210	+	1.02054i	0.994336	+	0.106280i	$0.0338941\pi$
$373$	11.3795	+	19.7099i	0.589210	+	1.02054i	−0.405127	+	0.914261i	$0.632773\pi$
$374$	−19.7127	−	34.1434i	−1.01932	−	1.76551i
$375$	−10.7153	+	1.36295i	−0.553334	+	0.0703824i
$376$	−3.73101	+	6.46230i	−0.192412	+	0.333268i
$377$	−3.04585			−0.156869
$378$	1.15464	+	0.910348i	0.0593882	+	0.0468233i
$379$	31.7657			1.63170			0.815848	−	0.578266i	$-0.196271\pi$
$379$	31.7657			1.63170			0.815848	+	0.578266i	$0.196271\pi$
$380$	3.70233	−	6.41262i	0.189925	−	0.328960i
$381$	−29.8495	+	3.79677i	−1.52924	+	0.194514i
$382$	13.6567	+	23.6541i	0.698737	+	1.21025i
$383$	−0.342922	−	0.593959i	−0.0175225	−	0.0303499i	0.857131	−	0.515098i	$-0.172245\pi$
$383$	−0.342922	−	0.593959i	−0.0175225	−	0.0303499i	−0.874654	+	0.484748i	$0.838911\pi$
$384$	4.40164	−	10.4962i	0.224620	−	0.535630i
$385$	−0.304207	+	0.526901i	−0.0155038	+	0.0268534i
$386$	−3.38495			−0.172289
$387$	6.75960	−	24.3708i	0.343610	−	1.23884i
$388$	6.34858			0.322300
$389$	6.43760	−	11.1503i	0.326399	−	0.565340i	−0.655395	−	0.755286i	$-0.727498\pi$
$389$	6.43760	−	11.1503i	0.326399	−	0.565340i	0.981795	+	0.189946i	$0.0608313\pi$
$390$	3.91990	+	5.15514i	0.198492	+	0.261040i
$391$	−13.7614	−	23.8355i	−0.695944	−	1.20541i
$392$	2.93905	+	5.09058i	0.148444	+	0.257113i
$393$	−13.2026	−	17.3630i	−0.665982	−	0.875845i
$394$	0.388540	−	0.672972i	0.0195744	−	0.0339038i
$395$	−2.81933			−0.141856
$396$	28.0719	−	7.25877i	1.41067	−	0.364767i
$397$	−1.55840			−0.0782140			−0.0391070	−	0.999235i	$-0.512451\pi$
$397$	−1.55840			−0.0782140			−0.0391070	+	0.999235i	$0.512451\pi$
$398$	−7.72629	+	13.3823i	−0.387284	+	0.670796i
$399$	0.736150	−	1.75543i	0.0368536	−	0.0878813i
$400$	−10.7398	−	18.6019i	−0.536991	−	0.930096i
$401$	−0.503982	−	0.872923i	−0.0251677	−	0.0435917i	0.853167	−	0.521637i	$-0.174679\pi$
$401$	−0.503982	−	0.872923i	−0.0251677	−	0.0435917i	−0.878335	+	0.478046i	$0.841345\pi$
$402$	−7.92411	+	1.00792i	−0.395219	+	0.0502706i
$403$	6.10347	−	10.5715i	0.304036	−	0.526605i
$404$	−14.3579			−0.714332
$405$	−5.02386	−	3.01915i	−0.249638	−	0.150023i
$406$	0.282969			0.0140435
$407$	15.4789	−	26.8102i	0.767261	−	1.32893i
$408$	−4.86491	+	0.618802i	−0.240849	+	0.0306353i
$409$	3.14762	+	5.45184i	0.155640	+	0.269576i	0.933292	−	0.359119i	$-0.116923\pi$
$409$	3.14762	+	5.45184i	0.155640	+	0.269576i	−0.777652	+	0.628695i	$0.783589\pi$
$410$	0.775344	+	1.34293i	0.0382915	+	0.0663228i
$411$	−1.64931	+	3.93294i	−0.0813542	+	0.193998i
$412$	3.92765	−	6.80289i	0.193501	−	0.335154i
$413$	0.506731			0.0249346
$414$	44.8334	−	11.5929i	2.20344	−	0.569760i
$415$	−8.43411			−0.414014
$416$	−10.9092	+	18.8953i	−0.534867	+	0.926418i
$417$	−8.86752	−	11.6618i	−0.434245	−	0.571083i
$418$	−42.9387	−	74.3721i	−2.10020	−	3.63766i
$419$	7.69813	+	13.3335i	0.376078	+	0.651386i	0.990488	−	0.137601i	$-0.0439391\pi$
$419$	7.69813	+	13.3335i	0.376078	+	0.651386i	−0.614410	+	0.788987i	$0.710606\pi$
$420$	−0.159182	−	0.209343i	−0.00776728	−	0.0102149i
$421$	−8.44555	+	14.6281i	−0.411611	+	0.712931i	−0.995066	−	0.0992142i	$-0.968367\pi$
$421$	−8.44555	+	14.6281i	−0.411611	+	0.712931i	0.583455	+	0.812145i	$0.301700\pi$
$422$	22.8196			1.11084
$423$	−7.10226	+	25.6062i	−0.345324	+	1.24502i
$424$	6.37295			0.309498
$425$	−7.68961	+	13.3188i	−0.373001	+	0.646056i
$426$	−6.52031	+	15.5484i	−0.315910	+	0.753321i
$427$	0.129812	+	0.224841i	0.00628204	+	0.0108808i
$428$	−5.59535	−	9.69143i	−0.270461	−	0.468453i
$429$	32.5684	−	4.14261i	1.57242	−	0.200007i
$430$	−5.17444	+	8.96239i	−0.249534	+	0.432205i
$431$	2.48270			0.119588			0.0597938	−	0.998211i	$-0.480956\pi$
$431$	2.48270			0.119588			0.0597938	+	0.998211i	$0.480956\pi$
$432$	3.50133	−	24.1387i	0.168458	−	1.16137i
$433$	−4.55419			−0.218861			−0.109430	−	0.993994i	$-0.534903\pi$
$433$	−4.55419			−0.218861			−0.109430	+	0.993994i	$0.534903\pi$
$434$	−0.567032	+	0.982128i	−0.0272184	+	0.0471436i
$435$	−1.11899	+	0.142332i	−0.0536513	+	0.00682428i
$436$	1.35625	+	2.34910i	0.0649528	+	0.112502i
$437$	−29.9755	−	51.9190i	−1.43392	−	2.48362i
$438$	6.05825	−	14.4465i	0.289475	−	0.690282i
$439$	6.31584	−	10.9394i	0.301439	−	0.522107i	−0.675023	−	0.737796i	$-0.735866\pi$
$439$	6.31584	−	10.9394i	0.301439	−	0.522107i	0.976462	+	0.215689i	$0.0691998\pi$
$440$	3.41430			0.162770
$441$	14.6711	+	14.9306i	0.698626	+	0.710980i
$442$	19.2961			0.917824
$443$	−19.8477	+	34.3773i	−0.942994	+	1.63331i	−0.183274	+	0.983062i	$0.558670\pi$
$443$	−19.8477	+	34.3773i	−0.942994	+	1.63331i	−0.759720	+	0.650251i	$0.774664\pi$
$444$	8.09963	+	10.6520i	0.384391	+	0.505520i
$445$	5.96761	+	10.3362i	0.282892	+	0.489983i
$446$	−7.01302	−	12.1469i	−0.332076	−	0.575173i
$447$	2.58344	+	3.39753i	0.122193	+	0.160698i
$448$	0.308823	−	0.534897i	0.0145905	−	0.0252715i
$449$	−8.24509			−0.389110			−0.194555	−	0.980892i	$-0.562326\pi$
$449$	−8.24509			−0.389110			−0.194555	+	0.980892i	$0.562326\pi$
$450$	−18.1360	−	18.4567i	−0.854941	−	0.870059i
$451$	7.86116			0.370167
$452$	3.38712	−	5.86666i	0.159317	−	0.275944i
$453$	3.70043	−	8.82405i	0.173861	−	0.414590i
$454$	4.53673	+	7.85784i	0.212919	+	0.368787i
$455$	−0.148889	−	0.257884i	−0.00698003	−	0.0120898i
$456$	−10.5969	+	1.34789i	−0.496244	+	0.0631208i
$457$	12.7303	−	22.0496i	0.595500	−	1.03144i	−0.397976	−	0.917396i	$-0.630287\pi$
$457$	12.7303	−	22.0496i	0.595500	−	1.03144i	0.993476	−	0.114041i	$-0.0363794\pi$
$458$	40.4846			1.89172
$459$	−16.2210	+	6.47048i	−0.757134	+	0.302016i
$460$	−8.28273			−0.386184
$461$	−10.0807	+	17.4603i	−0.469506	+	0.813208i	−0.999392	−	0.0348608i	$-0.988901\pi$
$461$	−10.0807	+	17.4603i	−0.469506	+	0.813208i	0.529886	+	0.848069i	$0.322235\pi$
$462$	−3.02571	+	0.384861i	−0.140769	+	0.0179054i
$463$	16.4781	+	28.5410i	0.765804	+	1.32641i	0.939820	+	0.341669i	$0.110992\pi$
$463$	16.4781	+	28.5410i	0.765804	+	1.32641i	−0.174016	+	0.984743i	$0.555675\pi$
$464$	−2.34706	−	4.06522i	−0.108959	−	0.188723i
$465$	1.74830	−	4.16899i	0.0810753	−	0.193332i
$466$	2.55129	−	4.41896i	0.118186	−	0.204704i
$467$	−10.5923			−0.490151			−0.245076	−	0.969504i	$-0.578813\pi$
$467$	−10.5923			−0.490151			−0.245076	+	0.969504i	$0.578813\pi$
$468$	−3.79296	+	13.6750i	−0.175330	+	0.632127i
$469$	0.367290			0.0169599
$470$	5.43674	−	9.41672i	0.250778	−	0.434361i
$471$	−17.9828	−	23.6494i	−0.828602	−	1.08971i
$472$	−1.42184	−	2.46269i	−0.0654453	−	0.113355i
$473$	26.2316	+	45.4345i	1.20613	+	2.08908i
$474$	−8.55490	−	11.2507i	−0.392940	−	0.516762i
$475$	−16.7497	+	29.0114i	−0.768530	+	1.33113i
$476$	−0.783589			−0.0359158
$477$	21.9720	−	5.68145i	1.00603	−	0.260136i
$478$	41.8562			1.91446
$479$	−15.6489	+	27.1047i	−0.715017	+	1.23845i	0.247936	+	0.968776i	$0.420248\pi$
$479$	−15.6489	+	27.1047i	−0.715017	+	1.23845i	−0.962953	+	0.269669i	$0.913086\pi$
$480$	−3.12486	+	7.45156i	−0.142630	+	0.340115i
$481$	7.57591	+	13.1219i	0.345432	+	0.598305i
$482$	3.21911	+	5.57567i	0.146627	+	0.253965i
$483$	−2.11224	+	0.268671i	−0.0961104	+	0.0122250i
$484$	−21.5319	+	37.2944i	−0.978724	+	1.69520i
$485$	2.66216			0.120882
$486$	−3.19616	−	29.2093i	−0.144981	−	1.32496i
$487$	−22.2489			−1.00820			−0.504098	−	0.863646i	$-0.668175\pi$
$487$	−22.2489			−1.00820			−0.504098	+	0.863646i	$0.668175\pi$
$488$	0.728479	−	1.26176i	0.0329767	−	0.0571173i
$489$	20.5612	−	2.61532i	0.929808	−	0.118269i
$490$	−4.28271	−	7.41788i	−0.193473	−	0.335105i
$491$	−14.7597	−	25.5646i	−0.666096	−	1.15371i	−0.978987	−	0.203923i	$-0.934631\pi$
$491$	−14.7597	−	25.5646i	−0.666096	−	1.15371i	0.312891	−	0.949789i	$-0.398703\pi$
$492$	−1.31411	+	3.13363i	−0.0592446	+	0.141275i
$493$	−1.68047	+	2.91066i	−0.0756845	+	0.131089i
$494$	42.0314			1.89108
$495$	11.7714	−	3.04383i	0.529087	−	0.136810i
$496$	18.8128			0.844718
$497$	0.387620	−	0.671377i	0.0173871	−	0.0301154i
$498$	−25.5922	−	33.6568i	−1.14682	−	1.50820i
$499$	−9.84970	−	17.0602i	−0.440933	−	0.763718i	0.556826	−	0.830629i	$-0.312019\pi$
$499$	−9.84970	−	17.0602i	−0.440933	−	0.763718i	−0.997759	+	0.0669108i	$0.978686\pi$
$500$	4.84272	+	8.38784i	0.216573	+	0.375115i
$501$	22.8466	+	30.0460i	1.02071	+	1.34236i
$502$	3.33838	−	5.78225i	0.148999	−	0.258074i
$503$	−11.3600			−0.506516			−0.253258	−	0.967399i	$-0.581502\pi$
$503$	−11.3600			−0.506516			−0.253258	+	0.967399i	$0.581502\pi$
$504$	−0.101404	+	0.365597i	−0.00451688	+	0.0162850i
$505$	−6.02071			−0.267918
$506$	−48.0306	+	83.1914i	−2.13522	+	3.69831i
$507$	2.49367	−	5.94642i	0.110748	−	0.264090i
$508$	13.4904	+	23.3660i	0.598538	+	1.03670i
$509$	3.69501	+	6.39995i	0.163779	+	0.283673i	0.936221	−	0.351412i	$-0.114298\pi$
$509$	3.69501	+	6.39995i	0.163779	+	0.283673i	−0.772442	+	0.635085i	$0.780965\pi$
$510$	7.08904	−	0.901704i	0.313908	−	0.0399281i
$511$	−0.360151	+	0.623800i	−0.0159322	+	0.0275953i
$512$	−25.7165			−1.13652
$513$	−35.3331	+	14.0942i	−1.56000	+	0.622274i
$514$	−6.64713			−0.293192
$515$	1.64699	−	2.85266i	0.0725749	−	0.125703i
$516$	−22.4962	+	2.86145i	−0.990341	+	0.125968i
$517$	−27.5614	−	47.7377i	−1.21215	−	2.09950i
$518$	−0.703826	−	1.21906i	−0.0309243	−	0.0535625i
$519$	−10.2846	+	24.5246i	−0.451442	+	1.07651i
$520$	−0.835537	+	1.44719i	−0.0366407	+	0.0634636i
$521$	−35.2381			−1.54381			−0.771904	−	0.635740i	$-0.780695\pi$
$521$	−35.2381			−1.54381			−0.771904	+	0.635740i	$0.780695\pi$
$522$	−3.96341	−	4.03349i	−0.173474	−	0.176541i
$523$	−40.4775			−1.76996			−0.884978	−	0.465633i	$-0.845827\pi$
$523$	−40.4775			−1.76996			−0.884978	+	0.465633i	$0.845827\pi$
$524$	−9.77922	+	16.9381i	−0.427207	+	0.739945i
$525$	0.720155	+	0.947089i	0.0314302	+	0.0413344i
$526$	9.75223	+	16.8914i	0.425218	+	0.736499i
$527$	−6.73488	−	11.6651i	−0.293376	−	0.508142i
$528$	30.6255	+	40.2761i	1.33280	+	1.75279i
$529$	−22.0301	+	38.1572i	−0.957829	+	1.65901i
$530$	−9.28652			−0.403381
$531$	−7.09753	−	7.22304i	−0.308007	−	0.313453i
$532$	−1.70684			−0.0740007
$533$	−1.92376	+	3.33205i	−0.0833273	+	0.144327i
$534$	−23.1393	+	55.1780i	−1.00133	+	2.38779i
$535$	−2.34631	−	4.06392i	−0.101440	−	0.175699i
$536$	−1.03058	−	1.78502i	−0.0445143	−	0.0771010i
$537$	4.57329	−	0.581709i	0.197352	−	0.0251026i
$538$	17.7855	−	30.8054i	0.766787	−	1.32811i
$539$	−43.4221			−1.87032
$540$	−0.754433	+	5.20118i	−0.0324656	+	0.223823i
$541$	0.0307893			0.00132374			0.000661869	−	1.00000i	$-0.499789\pi$
$541$	0.0307893			0.00132374			0.000661869		1.00000i	$0.499789\pi$
$542$	22.0149	−	38.1310i	0.945622	−	1.63786i
$543$	−0.667165	+	0.0848614i	−0.0286308	+	0.00364175i
$544$	12.0378	+	20.8500i	0.516114	+	0.893936i
$545$	0.568720	+	0.985052i	0.0243613	+	0.0421950i
$546$	0.577315	−	1.37667i	0.0247068	−	0.0589159i
$547$	−17.8729	+	30.9567i	−0.764189	+	1.32361i	0.176485	+	0.984303i	$0.443527\pi$
$547$	−17.8729	+	30.9567i	−0.764189	+	1.32361i	−0.940674	+	0.339311i	$0.889806\pi$
$548$	3.82408			0.163356
$549$	1.38671	−	4.99960i	0.0591835	−	0.213378i
$550$	53.6771			2.28880
$551$	−3.66044	+	6.34008i	−0.155940	+	0.270096i
$552$	7.23248	+	9.51156i	0.307835	+	0.404839i
$553$	0.324940	+	0.562812i	0.0138178	+	0.0239332i
$554$	20.2666	+	35.1028i	0.861047	+	1.49138i
$555$	3.39643	+	4.46670i	0.144170	+	0.189601i
$556$	−6.56822	+	11.3765i	−0.278555	+	0.482471i
$557$	34.9173			1.47949			0.739747	−	0.672885i	$-0.234945\pi$
$557$	34.9173			1.47949			0.739747	+	0.672885i	$0.234945\pi$
$558$	21.9416	−	5.67360i	0.928862	−	0.240183i
$559$	−25.6773			−1.08604
$560$	0.229461	−	0.397438i	0.00969649	−	0.0167948i
$561$	14.0101	−	33.4085i	0.591506	−	1.41051i
$562$	−28.5083	−	49.3778i	−1.20255	−	2.08287i
$563$	−3.95239	−	6.84574i	−0.166573	−	0.288513i	0.770640	−	0.637271i	$-0.219937\pi$
$563$	−3.95239	−	6.84574i	−0.166573	−	0.288513i	−0.937213	+	0.348758i	$0.886604\pi$
$564$	23.6366	−	3.00650i	0.995280	−	0.126597i
$565$	1.42032	−	2.46007i	0.0597535	−	0.103496i
$566$	25.9786			1.09196
$567$	−0.0236808	+	1.35086i	−0.000994499	+	0.0567310i
$568$	−4.35049			−0.182543
$569$	8.57122	−	14.8458i	0.359324	−	0.622368i	−0.628524	−	0.777790i	$-0.716341\pi$
$569$	8.57122	−	14.8458i	0.359324	−	0.622368i	0.987848	+	0.155423i	$0.0496739\pi$
$570$	15.4415	−	1.96412i	0.646775	−	0.0822678i
$571$	22.3224	+	38.6635i	0.934162	+	1.61802i	0.776121	+	0.630584i	$0.217184\pi$
$571$	22.3224	+	38.6635i	0.934162	+	1.61802i	0.158041	+	0.987433i	$0.449482\pi$
$572$	−14.7192	−	25.4943i	−0.615439	−	1.06597i
$573$	−9.70599	+	23.1449i	−0.405474	+	0.966894i
$574$	0.178723	−	0.309558i	0.00745977	−	0.0129207i
$575$	37.4719			1.56269
$576$	−11.9501	+	3.09002i	−0.497919	+	0.128751i
$577$	−38.5978			−1.60685			−0.803423	−	0.595409i	$-0.796990\pi$
$577$	−38.5978			−1.60685			−0.803423	+	0.595409i	$0.796990\pi$
$578$	−5.37599	+	9.31149i	−0.223612	+	0.387307i
$579$	−1.88264	−	2.47589i	−0.0782397	−	0.102894i
$580$	0.505721	+	0.875935i	0.0209989	+	0.0363712i
$581$	0.972067	+	1.68367i	0.0403281	+	0.0698504i
$582$	8.07798	+	10.6235i	0.334843	+	0.440358i
$583$	−23.5388	+	40.7705i	−0.974879	+	1.68854i
$584$	4.04220			0.167267
$585$	−1.59051	+	5.73435i	−0.0657594	+	0.237086i
$586$	−42.0667			−1.73776
$587$	4.94062	−	8.55741i	0.203921	−	0.353202i	−0.745867	−	0.666095i	$-0.767965\pi$
$587$	4.94062	−	8.55741i	0.203921	−	0.353202i	0.949788	+	0.312893i	$0.101298\pi$
$588$	7.25865	−	17.3090i	0.299342	−	0.713812i
$589$	−14.6701	−	25.4093i	−0.604471	−	1.04697i
$590$	2.07187	+	3.58858i	0.0852975	+	0.147740i
$591$	0.708336	−	0.0900983i	0.0291371	−	0.00370615i
$592$	−11.6756	+	20.2228i	−0.479865	+	0.831151i
$593$	3.33898			0.137116			0.0685578	−	0.997647i	$-0.478160\pi$
$593$	3.33898			0.137116			0.0685578	+	0.997647i	$0.478160\pi$
$594$	47.8655	+	37.7385i	1.96395	+	1.54843i
$595$	−0.328584			−0.0134706
$596$	1.91357	−	3.31440i	0.0783829	−	0.135763i
$597$	−14.0856	+	1.79164i	−0.576484	+	0.0733271i
$598$	−23.5078	−	40.7167i	−0.961306	−	1.66503i
$599$	10.7721	+	18.6579i	0.440138	+	0.762341i	0.997699	−	0.0677945i	$-0.0215962\pi$
$599$	10.7721	+	18.6579i	0.440138	+	0.762341i	−0.557561	+	0.830136i	$0.688263\pi$
$600$	2.58214	−	6.15737i	0.105415	−	0.251374i
$601$	8.78418	−	15.2146i	0.358314	−	0.620618i	−0.629365	−	0.777110i	$-0.716685\pi$
$601$	8.78418	−	15.2146i	0.358314	−	0.620618i	0.987679	+	0.156491i	$0.0500184\pi$
$602$	2.38551			0.0972259
$603$	−5.14446	−	5.23543i	−0.209498	−	0.213203i
$604$	−8.57980			−0.349107
$605$	−9.02901	+	15.6387i	−0.367081	+	0.635804i
$606$	−18.2691	−	24.0260i	−0.742131	−	0.975990i
$607$	−7.91038	−	13.7012i	−0.321073	−	0.556114i	0.659637	−	0.751584i	$-0.270710\pi$
$607$	−7.91038	−	13.7012i	−0.321073	−	0.556114i	−0.980710	+	0.195470i	$0.937377\pi$
$608$	26.2210	+	45.4161i	1.06340	+	1.84186i
$609$	0.157381	+	0.206975i	0.00637740	+	0.00838704i
$610$	−1.06152	+	1.83861i	−0.0429798	+	0.0744432i
$611$	26.9790			1.09145
$612$	10.9754	+	11.1694i	0.443653	+	0.451498i
$613$	14.6371			0.591188			0.295594	−	0.955314i	$-0.404482\pi$
$613$	14.6371			0.591188			0.295594	+	0.955314i	$0.404482\pi$
$614$	18.0160	−	31.2047i	0.727068	−	1.25932i
$615$	−0.551047	+	1.31403i	−0.0222204	+	0.0529868i
$616$	−0.393512	−	0.681583i	−0.0158551	−	0.0274618i
$617$	−20.9972	−	36.3682i	−0.845315	−	1.46413i	−0.885347	−	0.464931i	$-0.846079\pi$
$617$	−20.9972	−	36.3682i	−0.845315	−	1.46413i	0.0400319	−	0.999198i	$-0.487254\pi$
$618$	16.3813	−	2.08365i	0.658953	−	0.0838168i
$619$	15.8383	−	27.4328i	0.636595	−	1.10262i	−0.349579	−	0.936907i	$-0.613675\pi$
$619$	15.8383	−	27.4328i	0.636595	−	1.10262i	0.986175	−	0.165709i	$-0.0529912\pi$
$620$	−4.05359			−0.162796
$621$	33.4149	+	26.3452i	1.34089	+	1.05720i
$622$	11.8157			0.473768
$623$	1.37559	−	2.38258i	0.0551117	−	0.0954562i
$624$	−24.5661	+	3.12474i	−0.983432	+	0.125090i
$625$	−9.40897	−	16.2968i	−0.376359	−	0.651873i
$626$	17.2862	+	29.9406i	0.690896	+	1.19667i
$627$	30.5171	−	72.7713i	1.21874	−	2.90620i
$628$	−13.3199	+	23.0708i	−0.531523	+	0.920625i
$629$	16.7193			0.666641
$630$	0.147763	−	0.532739i	0.00588703	−	0.0212248i
$631$	13.5591			0.539780			0.269890	−	0.962891i	$-0.413013\pi$
$631$	13.5591			0.539780			0.269890	+	0.962891i	$0.413013\pi$
$632$	1.82350	−	3.15839i	0.0725349	−	0.125634i
$633$	12.6918	+	16.6912i	0.504453	+	0.663415i
$634$	−8.02693	−	13.9030i	−0.318790	−	0.552161i
$635$	5.65693	+	9.79810i	0.224489	+	0.388826i
$636$	−12.3171	−	16.1985i	−0.488406	−	0.642312i
$637$	10.6261	−	18.4050i	0.421023	−	0.729233i
$638$	11.7305			0.464414
$639$	−14.9992	+	3.87845i	−0.593358	+	0.153429i
$640$	−4.27954			−0.169164
$641$	−11.4631	+	19.8547i	−0.452765	+	0.784212i	−0.998557	−	0.0537090i	$-0.982896\pi$
$641$	−11.4631	+	19.8547i	−0.452765	+	0.784212i	0.545792	+	0.837921i	$0.316229\pi$
$642$	9.09775	−	21.6945i	0.359060	−	0.856215i
$643$	−1.11698	−	1.93467i	−0.0440494	−	0.0762958i	0.843160	−	0.537663i	$-0.180693\pi$
$643$	−1.11698	−	1.93467i	−0.0440494	−	0.0762958i	−0.887210	+	0.461367i	$0.847359\pi$
$644$	0.954619	+	1.65345i	0.0376173	+	0.0651550i
$645$	−9.43337	+	1.19990i	−0.371439	+	0.0472459i
$646$	23.1898	−	40.1659i	0.912389	−	1.58030i
$647$	−33.6056			−1.32117			−0.660587	−	0.750749i	$-0.729693\pi$
$647$	−33.6056			−1.32117			−0.660587	+	0.750749i	$0.729693\pi$
$648$	6.63160	−	3.67531i	0.260514	−	0.144380i
$649$	21.0065			0.824578
$650$	−13.1357	+	22.7517i	−0.515225	+	0.892396i
$651$	−1.03374	+	0.131488i	−0.0405154	+	0.00515344i
$652$	−9.29253	−	16.0951i	−0.363924	−	0.630334i
$653$	−16.3604	−	28.3371i	−0.640233	−	1.10892i	−0.985381	−	0.170368i	$-0.945504\pi$
$653$	−16.3604	−	28.3371i	−0.640233	−	1.10892i	0.345147	−	0.938549i	$-0.387829\pi$
$654$	−2.20520	+	5.25853i	−0.0862301	+	0.205625i
$655$	−4.10074	+	7.10268i	−0.160229	+	0.277525i
$656$	−5.92961			−0.231512
$657$	13.9362	−	3.60360i	0.543705	−	0.140590i
$658$	−2.50643			−0.0977109
$659$	17.5766	−	30.4435i	0.684686	−	1.18591i	−0.288849	−	0.957375i	$-0.593273\pi$
$659$	17.5766	−	30.4435i	0.684686	−	1.18591i	0.973535	−	0.228536i	$-0.0733939\pi$
$660$	−6.59889	−	8.67832i	−0.256861	−	0.337803i
$661$	16.6995	+	28.9243i	0.649534	+	1.12503i	0.983234	+	0.182347i	$0.0583693\pi$
$661$	16.6995	+	28.9243i	0.649534	+	1.12503i	−0.333700	+	0.942679i	$0.608297\pi$
$662$	−6.23788	−	10.8043i	−0.242442	−	0.419922i
$663$	10.7321	+	14.1140i	0.416800	+	0.548141i
$664$	5.45505	−	9.44842i	0.211697	−	0.366670i
$665$	−0.715730			−0.0277548
$666$	−7.51861	+	27.1073i	−0.291340	+	1.05039i
$667$	8.18903			0.317080
$668$	16.9226	−	29.3108i	0.654756	−	1.13407i
$669$	4.98425	−	11.8855i	0.192702	−	0.459518i
$670$	1.50174	+	2.60109i	0.0580172	+	0.100489i
$671$	5.38136	+	9.32078i	0.207745	+	0.359825i
$672$	1.84768	−	0.235019i	0.0712758	−	0.00906607i
$673$	−8.64980	+	14.9819i	−0.333425	+	0.577509i	−0.983181	−	0.182634i	$-0.941538\pi$
$673$	−8.64980	+	14.9819i	−0.333425	+	0.577509i	0.649756	+	0.760143i	$0.274871\pi$
$674$	23.4194			0.902082
$675$	3.41314	−	23.5307i	0.131372	−	0.905696i
$676$	−5.78182			−0.222378
$677$	−16.6439	+	28.8281i	−0.639678	+	1.10795i	0.345826	+	0.938299i	$0.387599\pi$
$677$	−16.6439	+	28.8281i	−0.639678	+	1.10795i	−0.985503	+	0.169655i	$0.945735\pi$
$678$	14.1269	−	1.79689i	0.542539	−	0.0690093i
$679$	−0.306825	−	0.531436i	−0.0117749	−	0.0203947i
$680$	0.921973	+	1.59690i	0.0353561	+	0.0612385i
$681$	−3.22431	+	7.68871i	−0.123556	+	0.294632i
$682$	−23.5063	+	40.7141i	−0.900103	+	1.55902i
$683$	−48.6379			−1.86108			−0.930538	−	0.366196i	$-0.880660\pi$
$683$	−48.6379			−1.86108			−0.930538	+	0.366196i	$0.880660\pi$
$684$	23.9068	+	24.3296i	0.914101	+	0.930266i
$685$	1.60355			0.0612687
$686$	−1.97759	+	3.42529i	−0.0755048	+	0.130778i
$687$	22.5167	+	29.6121i	0.859065	+	1.12977i
$688$	−19.7863	−	34.2709i	−0.754347	−	1.30657i
$689$	−11.5207	−	19.9545i	−0.438904	−	0.760205i
$690$	−10.5390	−	13.8600i	−0.401213	−	0.527643i
$691$	14.5808	−	25.2547i	0.554680	−	0.960734i	−0.443248	−	0.896399i	$-0.646174\pi$
$691$	14.5808	−	25.2547i	0.554680	−	0.960734i	0.997928	−	0.0643353i	$-0.0204927\pi$
$692$	23.8457			0.906479
$693$	−1.96434	−	1.99907i	−0.0746190	−	0.0759385i
$694$	−23.3758			−0.887333
$695$	−2.75426	+	4.77052i	−0.104475	+	0.180956i
$696$	0.564294	−	1.34562i	0.0213895	−	0.0510055i
$697$	2.12277	+	3.67675i	0.0804058	+	0.139267i
$698$	−6.14111	−	10.6367i	−0.232444	−	0.402605i
$699$	4.65118	−	0.591616i	0.175924	−	0.0223770i
$700$	0.533423	−	0.923916i	0.0201615	−	0.0349207i
$701$	23.7323			0.896355			0.448178	−	0.893944i	$-0.352073\pi$
$701$	23.7323			0.896355			0.448178	+	0.893944i	$0.352073\pi$
$702$	−27.7095	+	11.0532i	−1.04583	+	0.417174i
$703$	36.4184			1.37355
$704$	12.8023	−	22.1742i	0.482503	−	0.835720i
$705$	9.91157	−	1.26072i	0.373291	−	0.0474815i
$706$	−0.330475	−	0.572399i	−0.0124376	−	0.0215425i
$707$	0.693913	+	1.20189i	0.0260973	+	0.0452018i
$708$	−3.51155	+	8.37366i	−0.131972	+	0.314702i
$709$	−7.84966	+	13.5960i	−0.294800	+	0.510609i	−0.974938	−	0.222475i	$-0.928586\pi$
$709$	−7.84966	+	13.5960i	−0.294800	+	0.510609i	0.680138	+	0.733084i	$0.261920\pi$
$710$	6.33944			0.237915
$711$	3.47117	−	12.5148i	0.130179	−	0.469342i
$712$	−15.4390			−0.578602
$713$	−16.4097	+	28.4225i	−0.614549	+	1.06443i
$714$	−0.997046	−	1.31123i	−0.0373135	−	0.0490716i
$715$	−6.17221	−	10.6906i	−0.230827	−	0.399805i
$716$	−2.06688	−	3.57994i	−0.0772429	−	0.133789i
$717$	23.2795	+	30.6153i	0.869391	+	1.14335i
$718$	−24.8271	+	43.0019i	−0.926540	+	1.60482i
$719$	29.9724			1.11778			0.558890	−	0.829242i	$-0.311227\pi$
$719$	29.9724			1.11778			0.558890	+	0.829242i	$0.311227\pi$
$720$	−8.87911	+	2.29594i	−0.330905	+	0.0855646i
$721$	−0.759289			−0.0282774
$722$	32.6055	−	56.4744i	1.21345	−	2.10176i
$723$	−2.28787	+	5.45566i	−0.0850867	+	0.202898i
$724$	0.301523	+	0.522252i	0.0112060	+	0.0194094i
$725$	−2.28794	−	3.96282i	−0.0849718	−	0.147175i
$726$	−89.8046	+	11.4229i	−3.33296	+	0.423943i
$727$	9.88240	−	17.1168i	0.366518	−	0.634827i	−0.622501	−	0.782619i	$-0.713883\pi$
$727$	9.88240	−	17.1168i	0.366518	−	0.634827i	0.989018	+	0.147792i	$0.0472166\pi$
$728$	0.385197			0.0142763
$729$	19.5872	−	18.5834i	0.725452	−	0.688273i
$730$	−5.89020			−0.218006
$731$	−14.1668	+	24.5377i	−0.523979	+	0.907558i
$732$	−4.61504	+	0.587020i	−0.170577	+	0.0216969i
$733$	5.55085	+	9.61436i	0.205025	+	0.355114i	0.950141	−	0.311821i	$-0.100939\pi$
$733$	5.55085	+	9.61436i	0.205025	+	0.355114i	−0.745115	+	0.666936i	$0.767606\pi$
$734$	−19.1912	−	33.2401i	−0.708359	−	1.22691i
$735$	3.04378	−	7.25821i	0.112272	−	0.267723i
$736$	29.3303	−	50.8016i	1.08113	−	1.87257i
$737$	15.2260			0.560858
$738$	−6.91580	+	1.78827i	−0.254574	+	0.0658271i
$739$	−17.1570			−0.631131			−0.315566	−	0.948904i	$-0.602194\pi$
$739$	−17.1570			−0.631131			−0.315566	+	0.948904i	$0.602194\pi$
$740$	2.51575	−	4.35741i	0.0924809	−	0.160182i
$741$	23.3770	+	30.7435i	0.858774	+	1.12939i
$742$	1.07031	+	1.85383i	0.0392923	+	0.0680563i
$743$	−9.80104	−	16.9759i	−0.359565	−	0.622786i	0.628323	−	0.777953i	$-0.283742\pi$
$743$	−9.80104	−	16.9759i	−0.359565	−	0.622786i	−0.987888	+	0.155167i	$0.950408\pi$
$744$	3.53960	+	4.65499i	0.129768	+	0.170660i
$745$	0.802420	−	1.38983i	0.0293984	−	0.0509195i
$746$	42.8999			1.57068
$747$	10.3841	−	37.4384i	0.379934	−	1.36980i
$748$	−32.4837			−1.18772
$749$	−0.540843	+	0.936768i	−0.0197620	+	0.0342288i
$750$	−7.87401	+	18.7764i	−0.287518	+	0.685617i
$751$	3.53623	+	6.12493i	0.129039	+	0.223502i	0.923304	−	0.384069i	$-0.125477\pi$
$751$	3.53623	+	6.12493i	0.129039	+	0.223502i	−0.794266	+	0.607571i	$0.792144\pi$
$752$	20.7893	+	36.0082i	0.758110	+	1.31308i
$753$	6.08611	−	0.774134i	0.221790	−	0.0282110i
$754$	−2.87065	+	4.97211i	−0.104543	+	0.181073i
$755$	−3.59778			−0.130937
$756$	1.12524	−	0.448853i	0.0409247	−	0.0163246i
$757$	23.9606			0.870862			0.435431	−	0.900222i	$-0.356596\pi$
$757$	23.9606			0.870862			0.435431	+	0.900222i	$0.356596\pi$
$758$	29.9386	−	51.8551i	1.08742	−	1.88346i
$759$	−87.5631	+	11.1378i	−3.17834	+	0.404275i
$760$	2.00827	+	3.47842i	0.0728475	+	0.126176i
$761$	−5.34343	−	9.25509i	−0.193699	−	0.335497i	0.752774	−	0.658279i	$-0.228715\pi$
$761$	−5.34343	−	9.25509i	−0.193699	−	0.335497i	−0.946473	+	0.322782i	$0.895382\pi$
$762$	−21.9346	+	52.3054i	−0.794608	+	1.89483i
$763$	0.131095	−	0.227063i	0.00474595	−	0.00822023i
$764$	22.5043			0.814176
$765$	4.60231	+	4.68370i	0.166397	+	0.169340i
$766$	−1.29279			−0.0467104
$767$	−5.14066	+	8.90388i	−0.185618	+	0.321501i
$768$	−21.6125	−	28.4230i	−0.779874	−	1.02563i
$769$	15.0032	+	25.9863i	0.541029	+	0.937089i	0.998845	+	0.0480425i	$0.0152983\pi$
$769$	15.0032	+	25.9863i	0.541029	+	0.937089i	−0.457817	+	0.889047i	$0.651368\pi$
$770$	0.573417	+	0.993188i	0.0206645	+	0.0357920i
$771$	−3.69699	−	4.86198i	−0.133144	−	0.175100i
$772$	−1.39448	+	2.41531i	−0.0501884	+	0.0869289i
$773$	42.0161			1.51121			0.755607	−	0.655025i	$-0.227342\pi$
$773$	42.0161			1.51121			0.755607	+	0.655025i	$0.227342\pi$
$774$	−33.4126	−	34.0035i	−1.20099	−	1.22223i
$775$	18.3389			0.658752
$776$	−1.72184	+	2.98232i	−0.0618105	+	0.107059i
$777$	0.500218	−	1.19282i	0.0179452	−	0.0427923i
$778$	−12.1346	−	21.0178i	−0.435047	−	0.753524i
$779$	4.62388	+	8.00880i	0.165668	+	0.286945i
$780$	5.29327	−	0.673289i	0.189530	−	0.0241076i
$781$	16.0688	−	27.8320i	0.574987	−	0.995906i
$782$	−51.8794			−1.85520
$783$	0.745899	−	5.14234i	0.0266562	−	0.183772i
$784$	32.7530			1.16975
$785$	−5.58546	+	9.67430i	−0.199354	+	0.345291i
$786$	−40.7868	+	5.18797i	−1.45482	+	0.185049i
$787$	−20.2553	−	35.0832i	−0.722024	−	1.25058i	−0.960187	−	0.279357i	$-0.909879\pi$
$787$	−20.2553	−	35.0832i	−0.722024	−	1.25058i	0.238163	−	0.971225i	$-0.423455\pi$
$788$	−0.320130	−	0.554481i	−0.0114041	−	0.0197526i
$789$	−6.93104	+	16.5278i	−0.246752	+	0.588405i
$790$	−2.65716	+	4.60234i	−0.0945376	+	0.163744i
$791$	−0.654793			−0.0232818
$792$	−4.20369	+	15.1558i	−0.149372	+	0.538538i
$793$	−5.26764			−0.187059
$794$	−1.46876	+	2.54397i	−0.0521245	+	0.0902823i
$795$	−5.16496	−	6.79253i	−0.183182	−	0.240906i
$796$	6.36592	+	11.0261i	0.225634	+	0.390810i
$797$	−16.2984	−	28.2297i	−0.577320	−	0.999948i	−0.995785	−	0.0917150i	$-0.970765\pi$
$797$	−16.2984	−	28.2297i	−0.577320	−	0.999948i	0.418465	−	0.908233i	$-0.362568\pi$
$798$	−2.17179	−	2.85616i	−0.0768806	−	0.101107i
$799$	14.8850	−	25.7815i	0.526593	−	0.912085i
$800$	−32.7785			−1.15889
$801$	−53.2290	+	13.7638i	−1.88075	+	0.486321i
$802$	−1.89997			−0.0670903
$803$	−14.9301	+	25.8597i	−0.526871	+	0.912568i
$804$	−2.54526	+	6.06943i	−0.0897642	+	0.214052i
$805$	0.400302	+	0.693343i	0.0141088	+	0.0244371i
$806$	−11.5048	−	19.9269i	−0.405239	−	0.701895i
$807$	32.4242	−	4.12426i	1.14139	−	0.145181i
$808$	3.89410	−	6.74478i	0.136994	−	0.237281i
$809$	−25.5711			−0.899033			−0.449517	−	0.893272i	$-0.648404\pi$
$809$	−25.5711			−0.899033			−0.449517	+	0.893272i	$0.648404\pi$
$810$	−9.66343	+	5.35558i	−0.339538	+	0.188176i
$811$	−41.3219			−1.45101			−0.725503	−	0.688219i	$-0.758393\pi$
$811$	−41.3219			−1.45101			−0.725503	+	0.688219i	$0.758393\pi$
$812$	0.116573	−	0.201910i	0.00409091	−	0.00708567i
$813$	40.1347	−	5.10502i	1.40759	−	0.179041i
$814$	−29.1771	−	50.5362i	−1.02266	−	1.77129i
$815$	−3.89665	−	6.74920i	−0.136494	−	0.236414i
$816$	−10.5677	+	25.1998i	−0.369943	+	0.882168i
$817$	−30.8586	+	53.4486i	−1.07961	+	1.86993i
$818$	11.8663			0.414895
$819$	1.32804	−	0.343401i	0.0464055	−	0.0119994i
$820$	1.27766			0.0446177
$821$	−0.00980586	+	0.0169843i	−0.000342227	+	0.000592755i	−0.866196	−	0.499704i	$-0.833442\pi$
$821$	−0.00980586	+	0.0169843i	−0.000342227	+	0.000592755i	0.865854	+	0.500296i	$0.166776\pi$
$822$	4.86579	+	6.39908i	0.169714	+	0.223194i
$823$	−1.60265	−	2.77587i	−0.0558649	−	0.0967608i	0.836741	−	0.547600i	$-0.184458\pi$
$823$	−1.60265	−	2.77587i	−0.0558649	−	0.0967608i	−0.892605	+	0.450839i	$0.851125\pi$
$824$	2.13049	+	3.69012i	0.0742191	+	0.128551i
$825$	29.8541	+	39.2616i	1.03938	+	1.36691i
$826$	0.477583	−	0.827199i	0.0166172	−	0.0287819i
$827$	35.6068			1.23817			0.619086	−	0.785323i	$-0.287503\pi$
$827$	35.6068			1.23817			0.619086	+	0.785323i	$0.287503\pi$
$828$	10.1977	−	36.7664i	0.354395	−	1.27772i
$829$	27.4849			0.954592			0.477296	−	0.878743i	$-0.341617\pi$
$829$	27.4849			0.954592			0.477296	+	0.878743i	$0.341617\pi$
$830$	−7.94898	+	13.7680i	−0.275913	+	0.477895i
$831$	−14.4038	+	34.3473i	−0.499661	+	1.19149i
$832$	6.26586	+	10.8528i	0.217230	+	0.376253i
$833$	−11.7254	−	20.3090i	−0.406261	−	0.703666i
$834$	−27.3945	+	3.48450i	−0.948595	+	0.120658i
$835$	7.09619	−	12.2910i	0.245574	−	0.425346i
$836$	−70.7569			−2.44718
$837$	16.3533	+	12.8934i	0.565254	+	0.445662i
$838$	29.0213			1.00252
$839$	24.4908	−	42.4193i	0.845516	−	1.46448i	−0.0396569	−	0.999213i	$-0.512626\pi$
$839$	24.4908	−	42.4193i	0.845516	−	1.46448i	0.885173	−	0.465263i	$-0.154040\pi$
$840$	0.141514	−	0.0180002i	0.00488270	−	0.000621065i
$841$	−0.500000	−	0.866025i	−0.0172414	−	0.0298629i
$842$	15.9195	+	27.5734i	0.548623	+	0.950243i
$843$	20.2612	−	48.3149i	0.697833	−	1.66405i
$844$	9.40087	−	16.2828i	0.323591	−	0.560476i
$845$	−2.42450			−0.0834053
$846$	35.1064	+	35.7272i	1.20698	+	1.22833i
$847$	4.16253			0.143026
$848$	17.7552	−	30.7529i	0.609715	−	1.05606i
$849$	14.4487	+	19.0018i	0.495879	+	0.652139i
$850$	14.4946	+	25.1054i	0.497161	+	0.861108i
$851$	−20.3685	−	35.2793i	−0.698223	−	1.20936i
$852$	8.40830	+	11.0579i	0.288064	+	0.378837i
$853$	−1.96536	+	3.40410i	−0.0672926	+	0.116554i	−0.897709	−	0.440590i	$-0.854769\pi$
$853$	−1.96536	+	3.40410i	−0.0672926	+	0.116554i	0.830416	+	0.557144i	$0.188103\pi$
$854$	0.489380			0.0167462
$855$	10.0249	+	10.2022i	0.342844	+	0.348907i
$856$	6.07022			0.207476
$857$	−4.52729	+	7.84150i	−0.154649	+	0.267861i	−0.932931	−	0.360054i	$-0.882758\pi$
$857$	−4.52729	+	7.84150i	−0.154649	+	0.267861i	0.778282	+	0.627915i	$0.216091\pi$
$858$	23.9326	−	57.0698i	0.817045	−	1.94833i
$859$	13.6275	+	23.6035i	0.464964	+	0.805342i	0.999200	−	0.0399938i	$-0.0127338\pi$
$859$	13.6275	+	23.6035i	0.464964	+	0.805342i	−0.534236	+	0.845336i	$0.679400\pi$
$860$	4.26337	+	7.38438i	0.145380	+	0.251805i
$861$	0.325825	−	0.0414440i	0.0111041	−	0.00141241i
$862$	2.33990	−	4.05282i	0.0796973	−	0.138040i
$863$	−26.7758			−0.911458			−0.455729	−	0.890118i	$-0.650621\pi$
$863$	−26.7758			−0.911458			−0.455729	+	0.890118i	$0.650621\pi$
$864$	−29.2296	−	23.0454i	−0.994410	−	0.784021i
$865$	9.99927			0.339985
$866$	−4.29224	+	7.43437i	−0.145856	+	0.252630i
$867$	−9.80082	+	1.24663i	−0.332853	+	0.0423379i
$868$	0.467194	+	0.809203i	0.0158576	+	0.0274662i
$869$	13.4704	+	23.3314i	0.456952	+	0.791463i
$870$	−0.822276	+	1.96080i	−0.0278778	+	0.0664775i
$871$	−3.72607	+	6.45374i	−0.126253	+	0.218677i
$872$	−1.47136			−0.0498264
$873$	−3.27766	+	11.8171i	−0.110932	+	0.399949i
$874$	−113.005			−3.82245
$875$	0.468095	−	0.810764i	0.0158245	−	0.0274088i
$876$	−7.81245	−	10.2743i	−0.263958	−	0.347136i
$877$	−9.93348	−	17.2053i	−0.335430	−	0.580981i	0.648137	−	0.761523i	$-0.275548\pi$
$877$	−9.93348	−	17.2053i	−0.335430	−	0.580981i	−0.983567	+	0.180542i	$0.942215\pi$
$878$	−11.9051	−	20.6203i	−0.401778	−	0.695900i
$879$	−23.3966	−	30.7693i	−0.789147	−	1.03782i
$880$	9.51231	−	16.4758i	0.320660	−	0.555399i
$881$	−7.32226			−0.246693			−0.123347	−	0.992364i	$-0.539363\pi$
$881$	−7.32226			−0.246693			−0.123347	+	0.992364i	$0.539363\pi$
$882$	38.2003	−	9.87774i	1.28627	−	0.332601i
$883$	−23.7755			−0.800110			−0.400055	−	0.916491i	$-0.631009\pi$
$883$	−23.7755			−0.800110			−0.400055	+	0.916491i	$0.631009\pi$
$884$	7.94932	−	13.7686i	0.267365	−	0.463089i
$885$	−1.47250	+	3.51134i	−0.0494977	+	0.118032i
$886$	37.4121	+	64.7997i	1.25689	+	2.17699i
$887$	15.7516	+	27.2826i	0.528887	+	0.916059i	0.999433	+	0.0336835i	$0.0107238\pi$
$887$	15.7516	+	27.2826i	0.528887	+	0.916059i	−0.470546	+	0.882376i	$0.655943\pi$
$888$	−7.20064	+	0.915900i	−0.241638	+	0.0307356i
$889$	1.30397	−	2.25854i	0.0437338	−	0.0757492i
$890$	22.4974			0.754115
$891$	−0.981687	+	56.0001i	−0.0328877	+	1.87608i
$892$	−11.5565			−0.386939
$893$	32.4229	−	56.1581i	1.08499	−	1.87926i
$894$	7.98105	−	1.01517i	0.266926	−	0.0339522i
$895$	−0.866707	−	1.50118i	−0.0289708	−	0.0501789i
$896$	0.493235	+	0.854308i	0.0164778	+	0.0285404i
$897$	16.7073	−	39.8403i	0.557841	−	1.33023i
$898$	−7.77084	+	13.4595i	−0.259316	+	0.449149i
$899$	4.00774			0.133665
$900$	−20.6411	+	5.33732i	−0.688036	+	0.177911i
$901$	−25.4251			−0.847032
$902$	7.40898	−	12.8327i	0.246692	−	0.427283i
$903$	1.32677	+	1.74485i	0.0441520	+	0.0580651i
$904$	1.83729	+	3.18227i	0.0611072	+	0.105841i
$905$	0.126438	+	0.218997i	0.00420294	+	0.00727970i
$906$	−10.9170	−	14.3572i	−0.362693	−	0.476984i
$907$	22.4195	−	38.8316i	0.744426	−	1.28938i	−0.206037	−	0.978544i	$-0.566057\pi$
$907$	22.4195	−	38.8316i	0.744426	−	1.28938i	0.950462	−	0.310839i	$-0.100610\pi$
$908$	7.47588			0.248096
$909$	7.41272	−	26.7255i	0.245864	−	0.886429i
$910$	−0.561300			−0.0186069
$911$	−8.15573	+	14.1261i	−0.270211	+	0.468020i	−0.968916	−	0.247391i	$-0.920427\pi$
$911$	−8.15573	+	14.1261i	−0.270211	+	0.468020i	0.698704	+	0.715410i	$0.253760\pi$
$912$	−23.0189	+	54.8908i	−0.762230	+	1.81762i
$913$	40.2971	+	69.7965i	1.33364	+	2.30993i
$914$	−23.9962	−	41.5626i	−0.793723	−	1.37477i
$915$	−1.93523	+	0.246156i	−0.0639768	+	0.00813766i
$916$	16.6782	−	28.8875i	0.551064	−	0.954471i
$917$	1.89051			0.0624301
$918$	−4.72544	+	32.5779i	−0.155963	+	1.07523i
$919$	−45.1973			−1.49092			−0.745461	−	0.666550i	$-0.767770\pi$
$919$	−45.1973			−1.49092			−0.745461	+	0.666550i	$0.767770\pi$
$920$	2.24642	−	3.89091i	0.0740621	−	0.128279i
$921$	32.8445	−	4.17772i	1.08226	−	0.137661i
$922$	19.0017	+	32.9120i	0.625789	+	1.08390i
$923$	7.86462	+	13.6219i	0.258867	+	0.448371i
$924$	−0.971869	+	2.31752i	−0.0319722	+	0.0762409i
$925$	−11.3815	+	19.7134i	−0.374222	+	0.648172i
$926$	62.1213			2.04143
$927$	10.6350	+	10.8231i	0.349299	+	0.355476i
$928$	−7.16333			−0.235148
$929$	6.78776	−	11.7568i	0.222699	−	0.385727i	−0.732927	−	0.680307i	$-0.761847\pi$
$929$	6.78776	−	11.7568i	0.222699	−	0.385727i	0.955627	+	0.294580i	$0.0951799\pi$
$930$	−5.15783	−	6.78315i	−0.169132	−	0.222428i
$931$	−25.5406	−	44.2377i	−0.837060	−	1.44983i
$932$	−2.10208	−	3.64091i	−0.0688559	−	0.119262i
$933$	6.57166	+	8.64251i	0.215146	+	0.282943i
$934$	−9.98299	+	17.2910i	−0.326653	+	0.565780i
$935$	−13.6214			−0.445469
$936$	−5.39527	−	5.49068i	−0.176350	−	0.179468i
$937$	29.9370			0.977998			0.488999	−	0.872284i	$-0.337362\pi$
$937$	29.9370			0.977998			0.488999	+	0.872284i	$0.337362\pi$
$938$	0.346163	−	0.599573i	0.0113026	−	0.0195767i
$939$	−12.2855	+	29.2961i	−0.400923	+	0.956044i
$940$	−4.47949	−	7.75871i	−0.146105	−	0.253061i
$941$	−6.69835	−	11.6019i	−0.218360	−	0.378211i	0.735947	−	0.677040i	$-0.236737\pi$
$941$	−6.69835	−	11.6019i	−0.218360	−	0.378211i	−0.954307	+	0.298829i	$0.903404\pi$
$942$	−55.5543	+	7.06634i	−1.81006	+	0.230234i
$943$	5.17220	−	8.95851i	0.168430	−	0.291729i
$944$	−15.8451			−0.515713
$945$	0.471850	−	0.188218i	0.0153493	−	0.00612274i
$946$	98.8912			3.21523
$947$	−5.77705	+	10.0061i	−0.187729	+	0.325156i	−0.944493	−	0.328533i	$-0.893446\pi$
$947$	−5.77705	+	10.0061i	−0.187729	+	0.325156i	0.756764	+	0.653688i	$0.226779\pi$
$948$	−11.5522	+	1.46940i	−0.375198	+	0.0477240i
$949$	−7.30730	−	12.6566i	−0.237205	−	0.410851i
$950$	31.5725	+	54.6853i	1.02435	+	1.77422i
$951$	5.70485	−	13.6038i	0.184992	−	0.441133i
$952$	0.212523	−	0.368100i	0.00688790	−	0.0119302i
$953$	7.74102			0.250756			0.125378	−	0.992109i	$-0.459986\pi$
$953$	7.74102			0.250756			0.125378	+	0.992109i	$0.459986\pi$
$954$	11.4336	−	41.2222i	0.370176	−	1.33462i
$955$	9.43675			0.305366
$956$	17.2433	−	29.8663i	0.557688	−	0.965944i
$957$	6.52424	+	8.58014i	0.210899	+	0.277357i
$958$	29.4976	+	51.0913i	0.953023	+	1.65068i
$959$	−0.184817	−	0.320112i	−0.00596804	−	0.0103369i
$960$	2.80911	+	3.69431i	0.0906636	+	0.119233i
$961$	7.46903	−	12.9367i	0.240936	−	0.417314i
$962$	28.5606			0.920829
$963$	20.9282	−	5.41157i	0.674403	−	0.174385i
$964$	5.30464			0.170851
$965$	−0.584749	+	1.01281i	−0.0188237	+	0.0326037i
$966$	−1.55216	+	3.70129i	−0.0499400	+	0.119087i
$967$	18.9876	+	32.8875i	0.610600	+	1.05759i	0.991139	+	0.132825i	$0.0424049\pi$
$967$	18.9876	+	32.8875i	0.610600	+	1.05759i	−0.380540	+	0.924765i	$0.624262\pi$
$968$	−11.6796	−	20.2297i	−0.375398	−	0.650208i
$969$	42.2766	−	5.37745i	1.35812	−	0.172749i
$970$	2.50903	−	4.34577i	0.0805601	−	0.139534i
$971$	−12.2056			−0.391697			−0.195848	−	0.980634i	$-0.562746\pi$
$971$	−12.2056			−0.391697			−0.195848	+	0.980634i	$0.562746\pi$
$972$	−22.1588	−	9.75258i	−0.710743	−	0.312814i
$973$	1.26976			0.0407067
$974$	−20.9692	+	36.3197i	−0.671896	+	1.16376i
$975$	−23.9473	+	3.04603i	−0.766928	+	0.0975510i
$976$	−4.05912	−	7.03060i	−0.129929	−	0.225044i
$977$	8.69015	+	15.0518i	0.278022	+	0.481549i	0.970893	−	0.239513i	$-0.0769877\pi$
$977$	8.69015	+	15.0518i	0.278022	+	0.481549i	−0.692871	+	0.721062i	$0.743654\pi$
$978$	15.1092	−	36.0294i	0.483138	−	1.15209i
$979$	57.0249	−	98.7701i	1.82252	−	3.15670i
$980$	−7.05730			−0.225437
$981$	−5.07278	+	1.31171i	−0.161962	+	0.0418796i
$982$	−55.6429			−1.77564
$983$	0.662240	−	1.14703i	0.0211222	−	0.0365847i	−0.855271	−	0.518181i	$-0.826609\pi$
$983$	0.662240	−	1.14703i	0.0211222	−	0.0365847i	0.876393	+	0.481596i	$0.159943\pi$
$984$	−1.11565	−	1.46721i	−0.0355656	−	0.0467730i
$985$	−0.134240	−	0.232511i	−0.00427725	−	0.00740842i
$986$	3.16762	+	5.48647i	0.100877	+	0.174725i
$987$	−1.39402	−	1.83331i	−0.0443722	−	0.0583547i
$988$	17.3154	−	29.9912i	0.550878	−	0.954148i
$989$	69.0358			2.19521
$990$	6.12553	−	22.0847i	0.194682	−	0.701898i
$991$	50.5456			1.60563			0.802816	−	0.596227i	$-0.203334\pi$
$991$	50.5456			1.60563			0.802816	+	0.596227i	$0.203334\pi$
$992$	14.3544	−	24.8625i	0.455752	−	0.789385i
$993$	4.43334	−	10.5718i	0.140688	−	0.335485i
$994$	−0.730648	−	1.26552i	−0.0231747	−	0.0401398i
$995$	2.66943	+	4.62359i	0.0846266	+	0.146578i
$996$	−34.5587	+	4.39576i	−1.09503	+	0.139285i
$997$	−24.6313	+	42.6627i	−0.780082	+	1.35114i	0.151811	+	0.988410i	$0.451490\pi$
$997$	−24.6313	+	42.6627i	−0.780082	+	1.35114i	−0.931893	+	0.362733i	$0.881844\pi$
$998$	−37.1326			−1.17541
$999$	−24.0091	+	9.57708i	−0.759613	+	0.303005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.e.a.88.10	✓	22
3.2	odd	2		783.2.e.a.262.2		22
9.2	odd	6		2349.2.a.e.1.10		11
9.4	even	3	inner	261.2.e.a.175.10	yes	22
9.5	odd	6		783.2.e.a.523.2		22
9.7	even	3		2349.2.a.f.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.e.a.88.10	✓	22	1.1	even	1	trivial
261.2.e.a.175.10	yes	22	9.4	even	3	inner
783.2.e.a.262.2		22	3.2	odd	2
783.2.e.a.523.2		22	9.5	odd	6
2349.2.a.e.1.10		11	9.2	odd	6
2349.2.a.f.1.2		11	9.7	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.942480 - 1.63242i) q^{2} +(1.71821 - 0.218551i) q^{3} +(-0.776536 - 1.34500i) q^{4} +(-0.325626 - 0.564001i) q^{5} +(1.26261 - 3.01082i) q^{6} +(-0.0750596 + 0.130007i) q^{7} +0.842439 q^{8} +(2.90447 - 0.751031i) q^{9} -1.22758 q^{10} +(-3.11160 + 5.38944i) q^{11} +(-1.62820 - 2.14128i) q^{12} +(-1.52292 - 2.63778i) q^{13} +(0.141484 + 0.245058i) q^{14} +(-0.682756 - 0.897905i) q^{15} +(2.34706 - 4.06522i) q^{16} -3.36094 q^{17} +(1.51140 - 5.44916i) q^{18} -7.32089 q^{19} +(-0.505721 + 0.875935i) q^{20} +(-0.100555 + 0.239783i) q^{21} +(5.86524 + 10.1589i) q^{22} +(4.09451 + 7.09190i) q^{23} +(1.44749 - 0.184116i) q^{24} +(2.28794 - 3.96282i) q^{25} -5.74130 q^{26} +(4.82634 - 1.92520i) q^{27} +0.233146 q^{28} +(0.500000 - 0.866025i) q^{29} +(-2.10924 + 0.268290i) q^{30} +(2.00387 + 3.47080i) q^{31} +(-3.58166 - 6.20363i) q^{32} +(-4.16850 + 9.94022i) q^{33} +(-3.16762 + 5.48647i) q^{34} +0.0977654 q^{35} +(-3.26557 - 3.32331i) q^{36} -4.97458 q^{37} +(-6.89979 + 11.9508i) q^{38} +(-3.19319 - 4.19942i) q^{39} +(-0.274320 - 0.475137i) q^{40} +(-0.631601 - 1.09397i) q^{41} +(0.296657 + 0.390139i) q^{42} +(4.21514 - 7.30084i) q^{43} +9.66508 q^{44} +(-1.36935 - 1.39357i) q^{45} +15.4360 q^{46} +(-4.42882 + 7.67093i) q^{47} +(3.14427 - 7.49784i) q^{48} +(3.48873 + 6.04266i) q^{49} +(-4.31267 - 7.46976i) q^{50} +(-5.77479 + 0.734536i) q^{51} +(-2.36521 + 4.09666i) q^{52} +7.56487 q^{53} +(1.40599 - 9.69310i) q^{54} +4.05287 q^{55} +(-0.0632332 + 0.109523i) q^{56} +(-12.5788 + 1.59999i) q^{57} +(-0.942480 - 1.63242i) q^{58} +(-1.68776 - 2.92329i) q^{59} +(-0.677497 + 1.61556i) q^{60} +(0.864726 - 1.49775i) q^{61} +7.55442 q^{62} +(-0.120369 + 0.433974i) q^{63} -4.11437 q^{64} +(-0.991807 + 1.71786i) q^{65} +(12.2979 + 16.1732i) q^{66} +(-1.22333 - 2.11887i) q^{67} +(2.60989 + 4.52046i) q^{68} +(8.58516 + 11.2905i) q^{69} +(0.0921420 - 0.159595i) q^{70} -5.16416 q^{71} +(2.44684 - 0.632698i) q^{72} +4.79821 q^{73} +(-4.68845 + 8.12063i) q^{74} +(3.06507 - 7.30898i) q^{75} +(5.68494 + 9.84660i) q^{76} +(-0.467110 - 0.809059i) q^{77} +(-9.86473 + 1.25476i) q^{78} +(2.16455 - 3.74910i) q^{79} -3.05705 q^{80} +(7.87190 - 4.36270i) q^{81} -2.38109 q^{82} +(6.47530 - 11.2155i) q^{83} +(0.400593 - 0.0509543i) q^{84} +(1.09441 + 1.89557i) q^{85} +(-7.94537 - 13.7618i) q^{86} +(0.669833 - 1.59729i) q^{87} +(-2.62133 + 4.54028i) q^{88} -18.3266 q^{89} +(-3.56548 + 0.921954i) q^{90} +0.457240 q^{91} +(6.35908 - 11.0142i) q^{92} +(4.20161 + 5.52561i) q^{93} +(8.34814 + 14.4594i) q^{94} +(2.38387 + 4.12899i) q^{95} +(-7.50985 - 9.87634i) q^{96} +(-2.04388 + 3.54010i) q^{97} +13.1522 q^{98} +(-4.98990 + 17.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} - 2 q^{3} - 5 q^{4} + q^{5} - q^{6} + 7 q^{7} + 6 q^{8} - 2 q^{9} - 20 q^{10} - 3 q^{11} + 10 q^{12} + 7 q^{13} + 10 q^{14} - 8 q^{15} + 7 q^{16} + 2 q^{17} + 2 q^{18} - 56 q^{19} + 4 q^{20}+ \cdots - 40 q^{99}+O(q^{100}) \) 22 * q - q^2 - 2 * q^3 - 5 * q^4 + q^5 - q^6 + 7 * q^7 + 6 * q^8 - 2 * q^9 - 20 * q^10 - 3 * q^11 + 10 * q^12 + 7 * q^13 + 10 * q^14 - 8 * q^15 + 7 * q^16 + 2 * q^17 + 2 * q^18 - 56 * q^19 + 4 * q^20 + 16 * q^21 + 13 * q^22 - 4 * q^23 - 33 * q^24 + 4 * q^25 - 12 * q^26 + 13 * q^27 - 32 * q^28 + 11 * q^29 + 46 * q^30 + 27 * q^31 - 7 * q^32 - 10 * q^33 + 19 * q^34 - 22 * q^35 + 19 * q^36 - 28 * q^37 + 5 * q^38 + 17 * q^39 + 24 * q^40 + 9 * q^41 - 50 * q^42 + 25 * q^43 + 46 * q^44 - 56 * q^45 - 20 * q^46 - 6 * q^47 + 33 * q^48 + 12 * q^49 - 41 * q^50 - 15 * q^51 + 20 * q^52 - 12 * q^53 + 5 * q^54 - 70 * q^55 + 10 * q^56 + 25 * q^57 + q^58 - 48 * q^60 + 25 * q^61 - 12 * q^62 - 11 * q^63 - 50 * q^64 - 5 * q^65 + 29 * q^66 + 29 * q^67 + 50 * q^68 + 20 * q^69 + 7 * q^70 - 2 * q^71 + 30 * q^72 - 26 * q^73 - 14 * q^74 + 46 * q^75 + 38 * q^76 - 9 * q^77 - 39 * q^78 + 27 * q^79 - 74 * q^80 - 38 * q^81 - 34 * q^82 + 12 * q^83 + 60 * q^84 + 7 * q^85 - q^86 - q^87 - 5 * q^88 + 46 * q^89 - 35 * q^90 - 86 * q^91 - 19 * q^92 + 78 * q^93 - 10 * q^94 - 8 * q^95 - 75 * q^96 + 36 * q^97 + 86 * q^98 - 40 * q^99

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