LMFDB - Embedded newform 171.2.h.c.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(7,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("171.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	171.49
Dual form			171.2.h.c.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.370889 q^{2} +(1.73173 + 0.0335006i) q^{3} -1.86244 q^{4} +(1.77761 + 3.07890i) q^{5} +(0.642278 + 0.0124250i) q^{6} +(-0.124876 - 0.216291i) q^{7} -1.43254 q^{8} +(2.99776 + 0.116028i) q^{9} +(0.659294 + 1.14193i) q^{10} +(-0.815815 - 1.41303i) q^{11} +(-3.22524 - 0.0623929i) q^{12} -1.32541 q^{13} +(-0.0463150 - 0.0802199i) q^{14} +(2.97518 + 5.39137i) q^{15} +3.19357 q^{16} +(3.73000 - 6.46055i) q^{17} +(1.11183 + 0.0430334i) q^{18} +(-4.07660 - 1.54315i) q^{19} +(-3.31069 - 5.73428i) q^{20} +(-0.209005 - 0.378740i) q^{21} +(-0.302577 - 0.524078i) q^{22} -4.49143 q^{23} +(-2.48076 - 0.0479909i) q^{24} +(-3.81976 + 6.61602i) q^{25} -0.491582 q^{26} +(5.18741 + 0.301355i) q^{27} +(0.232573 + 0.402829i) q^{28} +(2.06363 - 3.57430i) q^{29} +(1.10346 + 1.99960i) q^{30} +(-4.32871 + 7.49755i) q^{31} +4.04953 q^{32} +(-1.36543 - 2.47432i) q^{33} +(1.38342 - 2.39615i) q^{34} +(0.443959 - 0.768960i) q^{35} +(-5.58314 - 0.216095i) q^{36} +3.10599 q^{37} +(-1.51197 - 0.572336i) q^{38} +(-2.29526 - 0.0444022i) q^{39} +(-2.54649 - 4.41064i) q^{40} +(-2.77461 - 4.80577i) q^{41} +(-0.0775175 - 0.140471i) q^{42} -10.0406 q^{43} +(1.51941 + 2.63169i) q^{44} +(4.97159 + 9.43605i) q^{45} -1.66582 q^{46} +(-1.68288 + 2.91483i) q^{47} +(5.53039 + 0.106987i) q^{48} +(3.46881 - 6.00816i) q^{49} +(-1.41671 + 2.45381i) q^{50} +(6.67577 - 11.0629i) q^{51} +2.46851 q^{52} +(0.254182 + 0.440256i) q^{53} +(1.92395 + 0.111769i) q^{54} +(2.90039 - 5.02363i) q^{55} +(0.178889 + 0.309845i) q^{56} +(-7.00787 - 2.80888i) q^{57} +(0.765376 - 1.32567i) q^{58} +(5.23121 + 9.06071i) q^{59} +(-5.54110 - 10.0411i) q^{60} +(-2.07050 + 3.58621i) q^{61} +(-1.60547 + 2.78076i) q^{62} +(-0.349251 - 0.662876i) q^{63} -4.88521 q^{64} +(-2.35606 - 4.08082i) q^{65} +(-0.506423 - 0.917697i) q^{66} -0.799350 q^{67} +(-6.94690 + 12.0324i) q^{68} +(-7.77793 - 0.150466i) q^{69} +(0.164660 - 0.285199i) q^{70} +(5.60051 - 9.70037i) q^{71} +(-4.29440 - 0.166214i) q^{72} +(-1.84754 + 3.20004i) q^{73} +1.15198 q^{74} +(-6.83642 + 11.3292i) q^{75} +(7.59244 + 2.87402i) q^{76} +(-0.203751 + 0.352907i) q^{77} +(-0.851285 - 0.0164683i) q^{78} +9.85529 q^{79} +(5.67691 + 9.83269i) q^{80} +(8.97308 + 0.695646i) q^{81} +(-1.02907 - 1.78241i) q^{82} +(0.185251 + 0.320865i) q^{83} +(0.389259 + 0.705381i) q^{84} +26.5219 q^{85} -3.72396 q^{86} +(3.69338 - 6.12059i) q^{87} +(1.16868 + 2.02422i) q^{88} +(4.01034 + 6.94611i) q^{89} +(1.84391 + 3.49973i) q^{90} +(0.165512 + 0.286675i) q^{91} +8.36503 q^{92} +(-7.74732 + 12.8387i) q^{93} +(-0.624161 + 1.08108i) q^{94} +(-2.49539 - 15.2946i) q^{95} +(7.01269 + 0.135662i) q^{96} +6.43155 q^{97} +(1.28654 - 2.22836i) q^{98} +(-2.28166 - 4.33058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.370889			0.262258			0.131129	−	0.991365i	$-0.458140\pi$
$2$	0.370889			0.262258			0.131129	+	0.991365i	$0.458140\pi$
$3$	1.73173	+	0.0335006i	0.999813	+	0.0193416i
$3$	1.73173	+	0.0335006i	0.999813	+	0.0193416i
$4$	−1.86244			−0.931221
$5$	1.77761	+	3.07890i	0.794969	+	1.37693i	0.922859	+	0.385139i	$0.125846\pi$
$5$	1.77761	+	3.07890i	0.794969	+	1.37693i	−0.127889	+	0.991788i	$0.540820\pi$
$6$	0.642278	+	0.0124250i	0.262209	+	0.00507249i
$7$	−0.124876	−	0.216291i	−0.0471985	−	0.0817503i	0.841461	−	0.540318i	$-0.181696\pi$
$7$	−0.124876	−	0.216291i	−0.0471985	−	0.0817503i	−0.888660	+	0.458568i	$0.848363\pi$
$8$	−1.43254			−0.506478
$9$	2.99776	+	0.116028i	0.999252	+	0.0386759i
$10$	0.659294	+	1.14193i	0.208487	+	0.361110i
$11$	−0.815815	−	1.41303i	−0.245977	−	0.426045i	0.716429	−	0.697660i	$-0.245776\pi$
$11$	−0.815815	−	1.41303i	−0.245977	−	0.426045i	−0.962406	+	0.271615i	$0.912442\pi$
$12$	−3.22524	−	0.0623929i	−0.931046	−	0.0180113i
$13$	−1.32541			−0.367604			−0.183802	−	0.982963i	$-0.558841\pi$
$13$	−1.32541			−0.367604			−0.183802	+	0.982963i	$0.558841\pi$
$14$	−0.0463150	−	0.0802199i	−0.0123782	−	0.0214397i
$15$	2.97518	+	5.39137i	0.768189	+	1.39205i
$16$	3.19357			0.798393
$17$	3.73000	−	6.46055i	0.904658	−	1.56691i	0.0832816	−	0.996526i	$-0.473460\pi$
$17$	3.73000	−	6.46055i	0.904658	−	1.56691i	0.821376	−	0.570387i	$-0.193207\pi$
$18$	1.11183	+	0.0430334i	0.262062	+	0.0101431i
$19$	−4.07660	−	1.54315i	−0.935237	−	0.354022i
$19$	−4.07660	−	1.54315i	−0.935237	−	0.354022i
$20$	−3.31069	−	5.73428i	−0.740292	−	1.28222i
$21$	−0.209005	−	0.378740i	−0.0456085	−	0.0826479i
$22$	−0.302577	−	0.524078i	−0.0645096	−	0.111734i
$23$	−4.49143			−0.936528			−0.468264	−	0.883589i	$-0.655120\pi$
$23$	−4.49143			−0.936528			−0.468264	+	0.883589i	$0.655120\pi$
$24$	−2.48076	−	0.0479909i	−0.506384	−	0.00979609i
$25$	−3.81976	+	6.61602i	−0.763952	+	1.32320i
$26$	−0.491582			−0.0964071
$27$	5.18741	+	0.301355i	0.998317	+	0.0579958i
$28$	0.232573	+	0.402829i	0.0439522	+	0.0761275i
$29$	2.06363	−	3.57430i	0.383206	−	0.663732i	−0.608313	−	0.793697i	$-0.708153\pi$
$29$	2.06363	−	3.57430i	0.383206	−	0.663732i	0.991518	+	0.129966i	$0.0414867\pi$
$30$	1.10346	+	1.99960i	0.201464	+	0.365075i
$31$	−4.32871	+	7.49755i	−0.777460	+	1.34660i	0.155941	+	0.987766i	$0.450159\pi$
$31$	−4.32871	+	7.49755i	−0.777460	+	1.34660i	−0.933401	+	0.358834i	$0.883174\pi$
$32$	4.04953			0.715863
$33$	−1.36543	−	2.47432i	−0.237691	−	0.430723i
$34$	1.38342	−	2.39615i	0.237254	−	0.410936i
$35$	0.443959	−	0.768960i	0.0750428	−	0.129978i
$36$	−5.58314	−	0.216095i	−0.930524	−	0.0360158i
$37$	3.10599			0.510622			0.255311	−	0.966859i	$-0.417822\pi$
$37$	3.10599			0.510622			0.255311	+	0.966859i	$0.417822\pi$
$38$	−1.51197	−	0.572336i	−0.245274	−	0.0928452i
$39$	−2.29526	−	0.0444022i	−0.367535	−	0.00711004i
$40$	−2.54649	−	4.41064i	−0.402635	−	0.697384i
$41$	−2.77461	−	4.80577i	−0.433322	−	0.750535i	0.563835	−	0.825887i	$-0.309325\pi$
$41$	−2.77461	−	4.80577i	−0.433322	−	0.750535i	−0.997157	+	0.0753521i	$0.975992\pi$
$42$	−0.0775175	−	0.140471i	−0.0119612	−	0.0216751i
$43$	−10.0406			−1.53118			−0.765591	−	0.643328i	$-0.777553\pi$
$43$	−10.0406			−1.53118			−0.765591	+	0.643328i	$0.777553\pi$
$44$	1.51941	+	2.63169i	0.229059	+	0.396742i
$45$	4.97159	+	9.43605i	0.741121	+	1.40664i
$46$	−1.66582			−0.245612
$47$	−1.68288	+	2.91483i	−0.245473	+	0.425171i	−0.962264	−	0.272116i	$-0.912277\pi$
$47$	−1.68288	+	2.91483i	−0.245473	+	0.425171i	0.716792	+	0.697287i	$0.245610\pi$
$48$	5.53039	+	0.106987i	0.798243	+	0.0154422i
$49$	3.46881	−	6.00816i	0.495545	−	0.858308i
$50$	−1.41671	+	2.45381i	−0.200353	+	0.347021i
$51$	6.67577	−	11.0629i	0.934795	−	1.54912i
$52$	2.46851			0.342320
$53$	0.254182	+	0.440256i	0.0349146	+	0.0604739i	0.882955	−	0.469458i	$-0.155551\pi$
$53$	0.254182	+	0.440256i	0.0349146	+	0.0604739i	−0.848040	+	0.529932i	$0.822217\pi$
$54$	1.92395	+	0.111769i	0.261817	+	0.0152099i
$55$	2.90039	−	5.02363i	0.391089	−	0.677386i
$56$	0.178889	+	0.309845i	0.0239050	+	0.0414047i
$57$	−7.00787	−	2.80888i	−0.928215	−	0.372045i
$58$	0.765376	−	1.32567i	0.100499	−	0.174069i
$59$	5.23121	+	9.06071i	0.681045	+	1.17960i	0.974662	+	0.223681i	$0.0718075\pi$
$59$	5.23121	+	9.06071i	0.681045	+	1.17960i	−0.293617	+	0.955923i	$0.594859\pi$
$60$	−5.54110	−	10.0411i	−0.715353	−	1.29630i
$61$	−2.07050	+	3.58621i	−0.265100	+	0.459168i	−0.967590	−	0.252527i	$-0.918738\pi$
$61$	−2.07050	+	3.58621i	−0.265100	+	0.459168i	0.702489	+	0.711694i	$0.252072\pi$
$62$	−1.60547	+	2.78076i	−0.203895	+	0.353157i
$63$	−0.349251	−	0.662876i	−0.0440015	−	0.0835145i
$64$	−4.88521			−0.610652
$65$	−2.35606	−	4.08082i	−0.292234	−	0.506164i
$66$	−0.506423	−	0.917697i	−0.0623364	−	0.112961i
$67$	−0.799350			−0.0976561			−0.0488281	−	0.998807i	$-0.515549\pi$
$67$	−0.799350			−0.0976561			−0.0488281	+	0.998807i	$0.515549\pi$
$68$	−6.94690	+	12.0324i	−0.842436	+	1.45914i
$69$	−7.77793	−	0.150466i	−0.936353	−	0.0181139i
$70$	0.164660	−	0.285199i	0.0196806	−	0.0340878i
$71$	5.60051	−	9.70037i	0.664658	−	1.15122i	−0.314719	−	0.949185i	$-0.601910\pi$
$71$	5.60051	−	9.70037i	0.664658	−	1.15122i	0.979378	−	0.202037i	$-0.0647563\pi$
$72$	−4.29440	−	0.166214i	−0.506099	−	0.0195885i
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	−0.953655	−	0.300902i	$-0.902712\pi$
$73$	−1.84754	+	3.20004i	−0.216239	+	0.374537i	0.737416	+	0.675439i	$0.236046\pi$
$74$	1.15198			0.133915
$75$	−6.83642	+	11.3292i	−0.789402	+	1.30818i
$76$	7.59244	+	2.87402i	0.870912	+	0.329673i
$77$	−0.203751	+	0.352907i	−0.0232195	+	0.0402174i
$78$	−0.851285	−	0.0164683i	−0.0963891	−	0.00186467i
$79$	9.85529			1.10881			0.554403	−	0.832248i	$-0.312947\pi$
$79$	9.85529			1.10881			0.554403	+	0.832248i	$0.312947\pi$
$80$	5.67691	+	9.83269i	0.634698	+	1.09933i
$81$	8.97308	+	0.695646i	0.997008	+	0.0772940i
$82$	−1.02907	−	1.78241i	−0.113642	−	0.196834i
$83$	0.185251	+	0.320865i	0.0203340	+	0.0352195i	0.876013	−	0.482287i	$-0.160194\pi$
$83$	0.185251	+	0.320865i	0.0203340	+	0.0352195i	−0.855679	+	0.517506i	$0.826860\pi$
$84$	0.389259	+	0.705381i	0.0424716	+	0.0769634i
$85$	26.5219			2.87670
$86$	−3.72396			−0.401565
$87$	3.69338	−	6.12059i	0.395972	−	0.656196i
$88$	1.16868	+	2.02422i	0.124582	+	0.215783i
$89$	4.01034	+	6.94611i	0.425095	+	0.736286i	0.996429	−	0.0844315i	$-0.0269074\pi$
$89$	4.01034	+	6.94611i	0.425095	+	0.736286i	−0.571334	+	0.820717i	$0.693574\pi$
$90$	1.84391	+	3.49973i	0.194365	+	0.368904i
$91$	0.165512	+	0.286675i	0.0173504	+	0.0300517i
$92$	8.36503			0.872115
$93$	−7.74732	+	12.8387i	−0.803360	+	1.33131i
$94$	−0.624161	+	1.08108i	−0.0643772	+	0.111505i
$95$	−2.49539	−	15.2946i	−0.256022	−	1.56919i
$96$	7.01269	+	0.135662i	0.715729	+	0.0138459i
$97$	6.43155			0.653024			0.326512	−	0.945193i	$-0.394127\pi$
$97$	6.43155			0.653024			0.326512	+	0.945193i	$0.394127\pi$
$98$	1.28654	−	2.22836i	0.129961	−	0.225098i
$99$	−2.28166	−	4.33058i	−0.229316	−	0.435240i
$100$	7.11408	−	12.3220i	0.711408	−	1.23220i
$101$	−3.78177	+	6.55021i	−0.376300	+	0.651771i	−0.990521	−	0.137364i	$-0.956137\pi$
$101$	−3.78177	+	6.55021i	−0.376300	+	0.651771i	0.614221	+	0.789134i	$0.289470\pi$
$102$	2.47597	−	4.10313i	0.245158	−	0.406270i
$103$	−6.90927	+	11.9672i	−0.680791	+	1.17916i	0.293949	+	0.955821i	$0.405030\pi$
$103$	−6.90927	+	11.9672i	−0.680791	+	1.17916i	−0.974740	+	0.223343i	$0.928303\pi$
$104$	1.89871			0.186183
$105$	0.794576	−	1.31675i	0.0775427	−	0.128502i
$106$	0.0942734	+	0.163286i	0.00915664	+	0.0158598i
$107$	12.0119			1.16123			0.580616	−	0.814177i	$-0.302812\pi$
$107$	12.0119			1.16123			0.580616	+	0.814177i	$0.302812\pi$
$108$	−9.66124	−	0.561256i	−0.929653	−	0.0540069i
$109$	−7.62598	+	13.2086i	−0.730436	+	1.26515i	0.226261	+	0.974067i	$0.427350\pi$
$109$	−7.62598	+	13.2086i	−0.730436	+	1.26515i	−0.956697	+	0.291086i	$0.905984\pi$
$110$	1.07572	−	1.86321i	0.102566	−	0.177650i
$111$	5.37873	+	0.104053i	0.510526	+	0.00987623i
$112$	−0.398799	−	0.690740i	−0.0376830	−	0.0652688i
$113$	−1.46481	+	2.53713i	−0.137798	+	0.238673i	−0.926663	−	0.375894i	$-0.877336\pi$
$113$	−1.46481	+	2.53713i	−0.137798	+	0.238673i	0.788865	+	0.614567i	$0.210669\pi$
$114$	−2.59914	−	1.04178i	−0.243432	−	0.0975718i
$115$	−7.98399	−	13.8287i	−0.744511	−	1.28953i
$116$	−3.84338	+	6.65693i	−0.356849	+	0.618081i
$117$	−3.97327	−	0.153785i	−0.367329	−	0.0142174i
$118$	1.94020	+	3.36052i	0.178610	+	0.309361i
$119$	−1.86314			−0.170794
$120$	−4.26206	−	7.72334i	−0.389071	−	0.705041i
$121$	4.16889	−	7.22073i	0.378990	−	0.656430i
$122$	−0.767926	+	1.33009i	−0.0695248	+	0.120420i
$123$	−4.64387	−	8.41523i	−0.418724	−	0.758776i
$124$	8.06198	−	13.9638i	0.723987	−	1.25398i
$125$	−9.38406			−0.839336
$126$	−0.129533	−	0.245853i	−0.0115397	−	0.0219024i
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	0.820835	−	0.571165i	$-0.193509\pi$
$127$	−0.949181	−	1.64403i	−0.0842262	−	0.145884i	−0.905061	+	0.425281i	$0.860175\pi$
$128$	−9.91094			−0.876012
$129$	−17.3876	−	0.336367i	−1.53090	−	0.0296155i
$130$	−0.873838	−	1.51353i	−0.0766407	−	0.132746i
$131$	1.51445	+	2.62310i	0.132318	+	0.229181i	0.924570	−	0.381013i	$-0.124425\pi$
$131$	1.51445	+	2.62310i	0.132318	+	0.229181i	−0.792252	+	0.610194i	$0.791091\pi$
$132$	2.54304	+	4.60827i	0.221343	+	0.401098i
$133$	0.175300	+	1.07443i	0.0152004	+	0.0931652i
$134$	−0.296470			−0.0256111
$135$	8.29332	+	16.5072i	0.713775	+	1.42071i
$136$	−5.34336	+	9.25497i	−0.458190	+	0.793608i
$137$	−2.12874	+	3.68708i	−0.181870	+	0.315009i	−0.942517	−	0.334157i	$-0.891548\pi$
$137$	−2.12874	+	3.68708i	−0.181870	+	0.315009i	0.760647	+	0.649166i	$0.224882\pi$
$138$	−2.88475	−	0.0558061i	−0.245566	−	0.00475053i
$139$	−17.2721			−1.46500			−0.732502	−	0.680765i	$-0.761648\pi$
$139$	−17.2721			−1.46500			−0.732502	+	0.680765i	$0.761648\pi$
$140$	−0.826848	+	1.43214i	−0.0698814	+	0.121038i
$141$	−3.01193	+	4.99131i	−0.253650	+	0.420344i
$142$	2.07717	−	3.59776i	0.174312	−	0.301917i
$143$	1.08129	+	1.87285i	0.0904222	+	0.156616i
$144$	9.57354	+	0.370543i	0.797795	+	0.0308786i
$145$	14.6732			1.21855
$146$	−0.685234	+	1.18686i	−0.0567104	+	0.0982253i
$147$	6.20831	−	10.2883i	0.512053	−	0.848563i
$148$	−5.78473			−0.475501
$149$	−0.923073	−	1.59881i	−0.0756211	−	0.130980i	0.825735	−	0.564058i	$-0.190761\pi$
$149$	−0.923073	−	1.59881i	−0.0756211	−	0.130980i	−0.901356	+	0.433079i	$0.857427\pi$
$150$	−2.53555	+	4.20187i	−0.207027	+	0.343081i
$151$	−5.59926	−	9.69820i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$151$	−5.59926	−	9.69820i	−0.455661	−	0.789228i	−0.998726	+	0.0504626i	$0.983930\pi$
$152$	5.83989	+	2.21061i	0.473677	+	0.179305i
$153$	11.9312	−	18.9344i	0.964583	−	1.53075i
$154$	−0.0755689	+	0.130889i	−0.00608952	+	0.0105473i
$155$	−30.7790			−2.47223
$156$	4.27478	+	0.0826965i	0.342256	+	0.00662102i
$157$	−10.3856	−	17.9883i	−0.828858	−	1.43562i	−0.898935	−	0.438083i	$-0.855658\pi$
$157$	−10.3856	−	17.9883i	−0.828858	−	1.43562i	0.0700766	−	0.997542i	$-0.477676\pi$
$158$	3.65522			0.290794
$159$	0.425425	+	0.770919i	0.0337384	+	0.0611379i
$160$	7.19847	+	12.4681i	0.569089	+	0.985692i
$161$	0.560870	+	0.971456i	0.0442028	+	0.0765614i
$162$	3.32801	+	0.258007i	0.261474	+	0.0202710i
$163$	−5.41671			−0.424269			−0.212135	−	0.977240i	$-0.568042\pi$
$163$	−5.41671			−0.424269			−0.212135	+	0.977240i	$0.568042\pi$
$164$	5.16755	+	8.95046i	0.403518	+	0.698914i
$165$	5.19098	−	8.60239i	0.404118	−	0.669695i
$166$	0.0687077	+	0.119005i	0.00533275	+	0.00923660i
$167$	−1.50006			−0.116078			−0.0580392	−	0.998314i	$-0.518485\pi$
$167$	−1.50006			−0.116078			−0.0580392	+	0.998314i	$0.518485\pi$
$168$	0.299407	+	0.542559i	0.0230997	+	0.0418594i
$169$	−11.2433			−0.864867
$170$	9.83667			0.754438
$171$	−12.0416	−	5.09898i	−0.920845	−	0.389928i
$172$	18.7001			1.42587
$173$	22.4134			1.70406			0.852031	−	0.523491i	$-0.175371\pi$
$173$	22.4134			1.70406			0.852031	+	0.523491i	$0.175371\pi$
$174$	1.36983	−	2.27006i	0.103847	−	0.172093i
$175$	1.90798			0.144230
$176$	−2.60536	−	4.51262i	−0.196387	−	0.340151i
$177$	8.75548	+	15.8659i	0.658102	+	1.19256i
$178$	1.48739	+	2.57623i	0.111485	+	0.193097i
$179$	−12.7134			−0.950242			−0.475121	−	0.879920i	$-0.657596\pi$
$179$	−12.7134			−0.950242			−0.475121	+	0.879920i	$0.657596\pi$
$180$	−9.25929	−	17.5741i	−0.690147	−	1.30990i
$181$	1.31157	+	2.27170i	0.0974880	+	0.168854i	0.910644	−	0.413191i	$-0.135586\pi$
$181$	1.31157	+	2.27170i	0.0974880	+	0.168854i	−0.813156	+	0.582045i	$0.802253\pi$
$182$	0.0613866	+	0.106325i	0.00455027	+	0.00788131i
$183$	−3.70568	+	6.14098i	−0.273932	+	0.453954i
$184$	6.43414			0.474331
$185$	5.52123	+	9.56304i	0.405929	+	0.703089i
$186$	−2.87340	+	4.76173i	−0.210688	+	0.349147i
$187$	−12.1720			−0.890101
$188$	3.13426	−	5.42870i	0.228589	−	0.395928i
$189$	−0.582600	−	1.15962i	−0.0423779	−	0.0843500i
$190$	−0.925514	−	5.67259i	−0.0671439	−	0.411533i
$191$	−1.70417	−	2.95170i	−0.123309	−	0.213578i	0.797762	−	0.602973i	$-0.206017\pi$
$191$	−1.70417	−	2.95170i	−0.123309	−	0.213578i	−0.921071	+	0.389395i	$0.872684\pi$
$192$	−8.45985	−	0.163658i	−0.610537	−	0.0118110i
$193$	−0.248883	−	0.431077i	−0.0179150	−	0.0310296i	0.856929	−	0.515435i	$-0.172369\pi$
$193$	−0.248883	−	0.431077i	−0.0179150	−	0.0310296i	−0.874844	+	0.484405i	$0.839036\pi$
$194$	2.38539			0.171261
$195$	−3.94335	−	7.14580i	−0.282389	−	0.511721i
$196$	−6.46046	+	11.1898i	−0.461461	+	0.799275i
$197$	−2.64398			−0.188376			−0.0941880	−	0.995554i	$-0.530025\pi$
$197$	−2.64398			−0.188376			−0.0941880	+	0.995554i	$0.530025\pi$
$198$	−0.846243	−	1.60617i	−0.0601399	−	0.114145i
$199$	0.106311	+	0.184136i	0.00753617	+	0.0130530i	0.869769	−	0.493459i	$-0.164268\pi$
$199$	0.106311	+	0.184136i	0.00753617	+	0.0130530i	−0.862233	+	0.506512i	$0.830934\pi$
$200$	5.47195	−	9.47770i	0.386925	−	0.670174i
$201$	−1.38426	−	0.0267787i	−0.0976379	−	0.00188882i
$202$	−1.40262	+	2.42940i	−0.0986877	+	0.170932i
$203$	−1.03079			−0.0723470
$204$	−12.4332	+	20.6041i	−0.870500	+	1.44257i
$205$	9.86433	−	17.0855i	0.688955	−	1.19330i
$206$	−2.56257	+	4.43851i	−0.178543	+	0.309245i
$207$	−13.4642	−	0.521131i	−0.935828	−	0.0362211i
$208$	−4.23280			−0.293492
$209$	1.14524	+	7.01930i	0.0792177	+	0.485535i
$210$	0.294700	−	0.488370i	0.0203362	−	0.0337007i
$211$	4.26187	+	7.38178i	0.293400	+	0.508183i	0.974611	−	0.223903i	$-0.0718800\pi$
$211$	4.26187	+	7.38178i	0.293400	+	0.508183i	−0.681212	+	0.732086i	$0.738547\pi$
$212$	−0.473399	−	0.819952i	−0.0325132	−	0.0563145i
$213$	10.0235	−	16.6108i	0.686801	−	1.13815i
$214$	4.45508			0.304543
$215$	−17.8483	−	30.9141i	−1.21724	−	2.10833i
$216$	−7.43115	−	0.431702i	−0.505626	−	0.0293736i
$217$	2.16220			0.146780
$218$	−2.82839	+	4.89892i	−0.191563	+	0.331797i
$219$	−3.30665	+	5.47970i	−0.223442	+	0.370284i
$220$	−5.40181	+	9.35621i	−0.364190	+	0.630796i
$221$	−4.94380	+	8.56290i	−0.332556	+	0.576003i
$222$	1.99491	+	0.0385920i	0.133890	+	0.00259012i
$223$	15.6032			1.04487			0.522433	−	0.852680i	$-0.325025\pi$
$223$	15.6032			1.04487			0.522433	+	0.852680i	$0.325025\pi$
$224$	−0.505688	−	0.875877i	−0.0337877	−	0.0585220i
$225$	−12.2184	+	19.3900i	−0.814557	+	1.29267i
$226$	−0.543283	+	0.940994i	−0.0361386	+	0.0625940i
$227$	−0.595426	−	1.03131i	−0.0395198	−	0.0684503i	0.845589	−	0.533835i	$-0.179249\pi$
$227$	−0.595426	−	1.03131i	−0.0395198	−	0.0684503i	−0.885109	+	0.465384i	$0.845916\pi$
$228$	13.0517	+	5.23137i	0.864373	+	0.346456i
$229$	−9.98443	+	17.2935i	−0.659790	+	1.14279i	0.320880	+	0.947120i	$0.396021\pi$
$229$	−9.98443	+	17.2935i	−0.659790	+	1.14279i	−0.980670	+	0.195669i	$0.937312\pi$
$230$	−2.96118	−	5.12891i	−0.195254	−	0.338190i
$231$	−0.364663	+	0.604312i	−0.0239931	+	0.0397608i
$232$	−2.95622	+	5.12032i	−0.194085	+	0.336166i
$233$	6.18432	−	10.7115i	0.405148	−	0.701737i	−0.589191	−	0.807994i	$-0.700553\pi$
$233$	6.18432	−	10.7115i	0.405148	−	0.701737i	0.994339	+	0.106257i	$0.0338867\pi$
$234$	−1.47364	−	0.0570371i	−0.0963350	−	0.00372863i
$235$	−11.9660			−0.780573
$236$	−9.74281	−	16.8750i	−0.634203	−	1.09847i
$237$	17.0667	+	0.330158i	1.10860	+	0.0214461i
$238$	−0.691019			−0.0447921
$239$	8.11631	−	14.0579i	0.525000	−	0.909327i	−0.474576	−	0.880215i	$-0.657398\pi$
$239$	8.11631	−	14.0579i	0.525000	−	0.909327i	0.999576	−	0.0291128i	$-0.00926819\pi$
$240$	9.50145	+	17.2177i	0.613316	+	1.11140i
$241$	−5.24347	+	9.08196i	−0.337762	+	0.585020i	−0.984011	−	0.178106i	$-0.943003\pi$
$241$	−5.24347	+	9.08196i	−0.337762	+	0.585020i	0.646250	+	0.763126i	$0.276336\pi$
$242$	1.54620	−	2.67809i	0.0993933	−	0.172154i
$243$	15.5156	+	1.50527i	0.995327	+	0.0965633i
$244$	3.85619	−	6.67911i	0.246867	−	0.427586i
$245$	24.6647			1.57577
$246$	−1.72236	−	3.12112i	−0.109814	−	0.198995i
$247$	5.40319	+	2.04531i	0.343797	+	0.130140i
$248$	6.20104	−	10.7405i	0.393767	−	0.682024i
$249$	0.310056	+	0.561856i	0.0196490	+	0.0356062i
$250$	−3.48044			−0.220123
$251$	−7.02198	−	12.1624i	−0.443223	−	0.767685i	0.554703	−	0.832048i	$-0.312832\pi$
$251$	−7.02198	−	12.1624i	−0.443223	−	0.767685i	−0.997927	+	0.0643630i	$0.979498\pi$
$252$	0.650459	+	1.23457i	0.0409751	+	0.0777705i
$253$	3.66418	+	6.34654i	0.230365	+	0.399004i
$254$	−0.352041	−	0.609753i	−0.0220890	−	0.0382593i
$255$	45.9286	+	0.888499i	2.87616	+	0.0556399i
$256$	6.09457			0.380910
$257$	17.1607			1.07045			0.535227	−	0.844709i	$-0.320226\pi$
$257$	17.1607			1.07045			0.535227	+	0.844709i	$0.320226\pi$
$258$	−6.44888	−	0.124755i	−0.401490	−	0.00776690i
$259$	−0.387862	−	0.671797i	−0.0241006	−	0.0417435i
$260$	4.38803	+	7.60029i	0.272134	+	0.471350i
$261$	6.60096	−	10.4755i	0.408589	−	0.648414i
$262$	0.561691	+	0.972878i	0.0347014	+	0.0601046i
$263$	19.4995			1.20239			0.601194	−	0.799103i	$-0.294692\pi$
$263$	19.4995			1.20239			0.601194	+	0.799103i	$0.294692\pi$
$264$	1.95603	+	3.54455i	0.120385	+	0.218152i
$265$	−0.903671	+	1.56520i	−0.0555121	+	0.0961498i
$266$	0.0650167	+	0.398496i	0.00398643	+	0.0244333i
$267$	6.71211	+	12.1631i	0.410774	+	0.744370i
$268$	1.48874			0.0909394
$269$	−11.5796	+	20.0564i	−0.706020	+	1.22286i	0.260303	+	0.965527i	$0.416178\pi$
$269$	−11.5796	+	20.0564i	−0.706020	+	1.22286i	−0.966322	+	0.257335i	$0.917156\pi$
$270$	3.07590	+	6.12234i	0.187193	+	0.372594i
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	0.307190	+	0.951648i	$0.400611\pi$
$271$	−11.0388	+	19.1197i	−0.670557	+	1.16144i	−0.977746	+	0.209790i	$0.932722\pi$
$272$	11.9120	−	20.6322i	0.722272	−	1.25101i
$273$	0.277018	+	0.501988i	0.0167659	+	0.0303817i
$274$	−0.789525	+	1.36750i	−0.0476970	+	0.0826136i
$275$	12.4649			0.751660
$276$	14.4859	+	0.280234i	0.871951	+	0.0168681i
$277$	14.7992	+	25.6330i	0.889199	+	1.54014i	0.840824	+	0.541309i	$0.182071\pi$
$277$	14.7992	+	25.6330i	0.889199	+	1.54014i	0.0483752	+	0.998829i	$0.484596\pi$
$278$	−6.40605			−0.384209
$279$	−13.8464	+	21.9736i	−0.828959	+	1.31552i
$280$	−0.635988	+	1.10156i	−0.0380075	+	0.0658310i
$281$	−14.4042	+	24.9487i	−0.859280	+	1.48832i	0.0133368	+	0.999911i	$0.495755\pi$
$281$	−14.4042	+	24.9487i	−0.859280	+	1.48832i	−0.872617	+	0.488406i	$0.837579\pi$
$282$	−1.11709	+	1.85122i	−0.0665219	+	0.110239i
$283$	−8.01020	−	13.8741i	−0.476157	−	0.824728i	0.523470	−	0.852044i	$-0.324637\pi$
$283$	−8.01020	−	13.8741i	−0.476157	−	0.824728i	−0.999627	+	0.0273162i	$0.991304\pi$
$284$	−10.4306	+	18.0664i	−0.618944	+	1.07204i
$285$	−3.80896	−	26.5696i	−0.225623	−	1.57385i
$286$	0.401040	+	0.694621i	0.0237140	+	0.0410738i
$287$	−0.692963	+	1.20025i	−0.0409043	+	0.0708483i
$288$	12.1395	+	0.469859i	0.715328	+	0.0276867i
$289$	−19.3258	−	33.4732i	−1.13681	−	1.96901i
$290$	5.44215			0.319574
$291$	11.1377	+	0.215461i	0.652902	+	0.0126305i
$292$	3.44094	−	5.95989i	0.201366	−	0.348776i
$293$	−0.400378	+	0.693475i	−0.0233903	+	0.0405132i	−0.877484	−	0.479607i	$-0.840779\pi$
$293$	−0.400378	+	0.693475i	−0.0233903	+	0.0405132i	0.854093	+	0.520120i	$0.174113\pi$
$294$	2.30259	−	3.81581i	0.134290	−	0.222543i
$295$	−18.5980	+	32.2127i	−1.08282	+	1.87550i
$296$	−4.44945			−0.258619
$297$	−3.80614	−	7.57582i	−0.220855	−	0.439594i
$298$	−0.342358	−	0.592981i	−0.0198322	−	0.0343504i
$299$	5.95301			0.344271
$300$	12.7324	−	21.0999i	0.735108	−	1.21820i
$301$	1.25383	+	2.17170i	0.0722696	+	0.125175i
$302$	−2.07670	−	3.59696i	−0.119501	−	0.206982i
$303$	−6.76842	+	11.2165i	−0.388836	+	0.644370i
$304$	−13.0189	−	4.92815i	−0.746686	−	0.282649i
$305$	−14.7221			−0.842987
$306$	4.42516	−	7.02255i	0.252970	−	0.401452i
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	−0.792902	−	0.609349i	$-0.791431\pi$
$307$	2.29987	−	3.98349i	0.131260	−	0.227350i	0.924163	+	0.381999i	$0.124764\pi$
$308$	0.379474	−	0.657268i	0.0216225	−	0.0374513i
$309$	−12.3659	+	20.4925i	−0.703470	+	1.16578i
$310$	−11.4156			−0.648362
$311$	16.4116	−	28.4257i	0.930615	−	1.61187i	0.148342	−	0.988936i	$-0.452606\pi$
$311$	16.4116	−	28.4257i	0.930615	−	1.61187i	0.782273	−	0.622936i	$-0.214060\pi$
$312$	3.28804	+	0.0636078i	0.186149	+	0.00360108i
$313$	9.19380	−	15.9241i	0.519664	−	0.900085i	−0.480074	−	0.877228i	$-0.659390\pi$
$313$	9.19380	−	15.9241i	0.519664	−	0.900085i	0.999739	−	0.0228573i	$-0.00727633\pi$
$314$	−3.85189	−	6.67167i	−0.217375	−	0.376504i
$315$	1.42010	−	2.25364i	0.0800136	−	0.126978i
$316$	−18.3549			−1.03254
$317$	−0.679102	+	1.17624i	−0.0381422	+	0.0660642i	−0.884466	−	0.466604i	$-0.845477\pi$
$317$	−0.679102	+	1.17624i	−0.0381422	+	0.0660642i	0.846324	+	0.532668i	$0.178811\pi$
$318$	0.157786	+	0.285925i	0.00884817	+	0.0160339i
$319$	−6.73415			−0.377040
$320$	−8.68398	−	15.0411i	−0.485449	−	0.840823i
$321$	20.8013	+	0.402405i	1.16102	+	0.0224601i
$322$	0.208021	+	0.360302i	0.0115925	+	0.0200789i
$323$	−25.1753	+	20.5812i	−1.40079	+	1.14517i
$324$	−16.7118	−	1.29560i	−0.928435	−	0.0719778i
$325$	5.06277	−	8.76897i	0.280832	−	0.486415i
$326$	−2.00900			−0.111268
$327$	−13.6486	+	22.6182i	−0.754770	+	1.25079i
$328$	3.97473	+	6.88444i	0.219468	+	0.380130i
$329$	0.840601			0.0463438
$330$	1.92528	−	3.19053i	0.105983	−	0.175633i
$331$	8.39869	+	14.5470i	0.461634	+	0.799573i	0.999043	−	0.0437490i	$-0.0139302\pi$
$331$	8.39869	+	14.5470i	0.461634	+	0.799573i	−0.537409	+	0.843322i	$0.680597\pi$
$332$	−0.345020	−	0.597592i	−0.0189354	−	0.0327971i
$333$	9.31100	+	0.360381i	0.510240	+	0.0197488i
$334$	−0.556357			−0.0304425
$335$	−1.42093	−	2.46112i	−0.0776336	−	0.134465i
$336$	−0.667471	−	1.20953i	−0.0364135	−	0.0659854i
$337$	−18.2612	−	31.6293i	−0.994750	−	1.72296i	−0.585999	−	0.810312i	$-0.699298\pi$
$337$	−18.2612	−	31.6293i	−0.994750	−	1.72296i	−0.408751	−	0.912646i	$-0.634035\pi$
$338$	−4.17001			−0.226819
$339$	−2.62165	+	4.34454i	−0.142389	+	0.235963i
$340$	−49.3954			−2.67884
$341$	14.1257			0.764951
$342$	−4.46610	−	1.89115i	−0.241499	−	0.102262i
$343$	−3.48094			−0.187953
$344$	14.3836			0.775511
$345$	−13.3628	−	24.2150i	−0.719430	−	1.30369i
$346$	8.31290			0.446904
$347$	5.07542	+	8.79089i	0.272463	+	0.471920i	0.969492	−	0.245123i	$-0.0788284\pi$
$347$	5.07542	+	8.79089i	0.272463	+	0.471920i	−0.697029	+	0.717043i	$0.745495\pi$
$348$	−6.87870	+	11.3992i	−0.368737	+	0.611063i
$349$	8.63614	+	14.9582i	0.462282	+	0.800696i	0.999074	−	0.0430183i	$-0.0136974\pi$
$349$	8.63614	+	14.9582i	0.462282	+	0.800696i	−0.536792	+	0.843715i	$0.680364\pi$
$350$	0.707649			0.0378254
$351$	−6.87546	−	0.399420i	−0.366985	−	0.0213195i
$352$	−3.30367	−	5.72212i	−0.176086	−	0.304990i
$353$	−8.45158	−	14.6386i	−0.449832	−	0.779132i	0.548543	−	0.836123i	$-0.315183\pi$
$353$	−8.45158	−	14.6386i	−0.449832	−	0.779132i	−0.998375	+	0.0569905i	$0.981850\pi$
$354$	3.24731	+	5.88450i	0.172593	+	0.312758i
$355$	39.8220			2.11353
$356$	−7.46902	−	12.9367i	−0.395857	−	0.685645i
$357$	−3.22646	−	0.0624164i	−0.170762	−	0.00330343i
$358$	−4.71525			−0.249209
$359$	3.82747	−	6.62938i	0.202006	−	0.349885i	−0.747168	−	0.664635i	$-0.768587\pi$
$359$	3.82747	−	6.62938i	0.202006	−	0.349885i	0.949175	+	0.314750i	$0.101921\pi$
$360$	−7.12198	−	13.5175i	−0.375361	−	0.712434i
$361$	14.2374	+	12.5816i	0.749337	+	0.662189i
$362$	0.486446	+	0.842549i	0.0255670	+	0.0442834i
$363$	7.46128	−	12.3647i	0.391616	−	0.648977i
$364$	−0.308256	−	0.533915i	−0.0161570	−	0.0279848i
$365$	−13.1368			−0.687613
$366$	−1.37440	+	2.27762i	−0.0718409	+	0.119053i
$367$	12.3888	−	21.4579i	0.646688	−	1.12010i	−0.337221	−	0.941425i	$-0.609487\pi$
$367$	12.3888	−	21.4579i	0.646688	−	1.12010i	0.983909	−	0.178670i	$-0.0571796\pi$
$368$	−14.3437			−0.747717
$369$	−7.76001	−	14.7285i	−0.403970	−	0.766733i
$370$	2.04776	+	3.54683i	0.106458	+	0.184391i
$371$	0.0634823	−	0.109955i	0.00329584	−	0.00570856i
$372$	14.4289	−	23.9113i	0.748105	−	1.23974i
$373$	11.5863	−	20.0681i	0.599917	−	1.03909i	−0.392916	−	0.919574i	$-0.628534\pi$
$373$	11.5863	−	20.0681i	0.599917	−	1.03909i	0.992833	−	0.119512i	$-0.0381330\pi$
$374$	−4.51444			−0.233436
$375$	−16.2506	−	0.314372i	−0.839179	−	0.0162341i
$376$	2.41078	−	4.17560i	0.124327	−	0.215340i
$377$	−2.73516	+	4.73744i	−0.140868	+	0.243990i
$378$	−0.216080	−	0.430090i	−0.0111140	−	0.0221215i
$379$	29.0801			1.49374			0.746871	−	0.664969i	$-0.231555\pi$
$379$	29.0801			1.49374			0.746871	+	0.664969i	$0.231555\pi$
$380$	4.64752	+	28.4852i	0.238413	+	1.46126i
$381$	−1.58865	−	2.87881i	−0.0813888	−	0.147486i
$382$	−0.632057	−	1.09475i	−0.0323388	−	0.0560125i
$383$	1.41428	+	2.44960i	0.0722662	+	0.125169i	0.899894	−	0.436108i	$-0.143644\pi$
$383$	1.41428	+	2.44960i	0.0722662	+	0.125169i	−0.827628	+	0.561277i	$0.810310\pi$
$384$	−17.1630	−	0.332023i	−0.875848	−	0.0169435i
$385$	−1.44875			−0.0738353
$386$	−0.0923078	−	0.159882i	−0.00469834	−	0.00813777i
$387$	−30.0994	−	1.16499i	−1.53004	−	0.0592199i
$388$	−11.9784			−0.608110
$389$	−9.58295	+	16.5982i	−0.485875	+	0.841560i	−0.999868	−	0.0162341i	$-0.994832\pi$
$389$	−9.58295	+	16.5982i	−0.485875	+	0.841560i	0.513993	+	0.857794i	$0.328166\pi$
$390$	−1.46254	−	2.65030i	−0.0740588	−	0.134203i
$391$	−16.7530	+	29.0171i	−0.847238	+	1.46746i
$392$	−4.96920	+	8.60691i	−0.250983	+	0.434715i
$393$	2.53473	+	4.59322i	0.127860	+	0.231697i
$394$	−0.980624			−0.0494031
$395$	17.5188	+	30.3435i	0.881467	+	1.52675i
$396$	4.24946	+	8.06546i	0.213544	+	0.405305i
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	−0.118029	−	0.993010i	$-0.537658\pi$
$397$	15.9590	−	27.6417i	0.800958	−	1.38730i	0.918986	−	0.394289i	$-0.129009\pi$
$398$	0.0394295	+	0.0682939i	0.00197642	+	0.00342326i
$399$	0.267577	+	1.86650i	0.0133956	+	0.0934418i
$400$	−12.1987	+	21.1287i	−0.609934	+	1.05644i
$401$	−19.1703	−	33.2040i	−0.957320	−	1.65813i	−0.728967	−	0.684548i	$-0.759999\pi$
$401$	−19.1703	−	33.2040i	−0.957320	−	1.65813i	−0.228353	−	0.973578i	$-0.573334\pi$
$402$	−0.513405	−	0.00993193i	−0.0256063	−	0.000495360i
$403$	5.73734	−	9.93737i	0.285797	−	0.495015i
$404$	7.04332	−	12.1994i	0.350418	−	0.606942i
$405$	13.8088	+	28.8638i	0.686163	+	1.43425i
$406$	−0.382307			−0.0189736
$407$	−2.53391	−	4.38887i	−0.125601	−	0.217548i
$408$	−9.56329	+	15.8481i	−0.473453	+	0.784597i
$409$	2.29288			0.113375			0.0566877	−	0.998392i	$-0.481946\pi$
$409$	2.29288			0.113375			0.0566877	+	0.998392i	$0.481946\pi$
$410$	3.65857	−	6.33683i	0.180684	−	0.312954i
$411$	−3.80991	+	6.31370i	−0.187929	+	0.311432i
$412$	12.8681	−	22.2882i	0.633966	−	1.09806i
$413$	1.30650	−	2.26292i	0.0642886	−	0.111351i
$414$	−4.99373	−	0.193282i	−0.245428	−	0.00949928i
$415$	−0.658608	+	1.14074i	−0.0323298	+	0.0559968i
$416$	−5.36731			−0.263154
$417$	−29.9106	−	0.578627i	−1.46473	−	0.0283355i
$418$	0.424756	+	2.60338i	0.0207755	+	0.127335i
$419$	5.32211	−	9.21817i	0.260002	−	0.450337i	−0.706240	−	0.707972i	$-0.749610\pi$
$419$	5.32211	−	9.21817i	0.260002	−	0.450337i	0.966242	+	0.257636i	$0.0829434\pi$
$420$	−1.47985	+	2.45238i	−0.0722094	+	0.119664i
$421$	25.8645			1.26056			0.630280	−	0.776367i	$-0.282940\pi$
$421$	25.8645			1.26056			0.630280	+	0.776367i	$0.282940\pi$
$422$	1.58068	+	2.73782i	0.0769464	+	0.133275i
$423$	−5.38305	+	8.54268i	−0.261733	+	0.415359i
$424$	−0.364125	−	0.630684i	−0.0176835	−	0.0306287i
$425$	28.4954	+	49.3555i	1.38223	+	2.39409i
$426$	3.71762	−	6.16075i	0.180119	−	0.298489i
$427$	1.03422			0.0500494
$428$	−22.3714			−1.08136
$429$	1.80976	+	3.27950i	0.0873761	+	0.158336i
$430$	−6.61973	−	11.4657i	−0.319232	−	0.552926i
$431$	−9.52984	−	16.5062i	−0.459036	−	0.795074i	0.539874	−	0.841746i	$-0.318472\pi$
$431$	−9.52984	−	16.5062i	−0.459036	−	0.795074i	−0.998910	+	0.0466716i	$0.985139\pi$
$432$	16.5663	+	0.962399i	0.797049	+	0.0463034i
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	0.985312	+	0.170761i	$0.0546226\pi$
$433$	13.3288	+	23.0861i	0.640540	+	1.10945i	−0.344773	+	0.938686i	$0.612044\pi$
$434$	0.801937			0.0384942
$435$	25.4101	+	0.491563i	1.21832	+	0.0235686i
$436$	14.2029	−	24.6002i	0.680197	−	1.17814i
$437$	18.3098	+	6.93094i	0.875876	+	0.331552i
$438$	−1.22640	+	2.03236i	−0.0585996	+	0.0971100i
$439$	−1.94705			−0.0929274			−0.0464637	−	0.998920i	$-0.514795\pi$
$439$	−1.94705			−0.0929274			−0.0464637	+	0.998920i	$0.514795\pi$
$440$	−4.15492	+	7.19653i	−0.198078	+	0.343081i
$441$	11.0958	−	17.6085i	0.528370	−	0.838501i
$442$	−1.83360	+	3.17589i	−0.0872154	+	0.151062i
$443$	−3.28115	+	5.68312i	−0.155892	+	0.270013i	−0.933384	−	0.358880i	$-0.883159\pi$
$443$	−3.28115	+	5.68312i	−0.155892	+	0.270013i	0.777491	+	0.628894i	$0.216492\pi$
$444$	−10.0176	−	0.193792i	−0.475413	−	0.00919695i
$445$	−14.2576	+	24.6949i	−0.675875	+	1.17065i
$446$	5.78704			0.274024
$447$	−1.54495	−	2.79962i	−0.0730736	−	0.132418i
$448$	0.610044	+	1.05663i	0.0288219	+	0.0499209i
$449$	−35.5348			−1.67699			−0.838495	−	0.544910i	$-0.816564\pi$
$449$	−35.5348			−1.67699			−0.838495	+	0.544910i	$0.816564\pi$
$450$	−4.53165	+	7.19154i	−0.213624	+	0.339013i
$451$	−4.52714	+	7.84124i	−0.213175	+	0.369229i
$452$	2.72813	−	4.72526i	0.128320	−	0.222257i
$453$	−9.37149	−	16.9822i	−0.440311	−	0.797894i
$454$	−0.220837	−	0.382501i	−0.0103644	−	0.0179516i
$455$	−0.588430	+	1.01919i	−0.0275860	+	0.0477804i
$456$	10.0390	+	4.02382i	0.470121	+	0.188433i
$457$	−3.32444	−	5.75809i	−0.155511	−	0.269352i	0.777734	−	0.628593i	$-0.216369\pi$
$457$	−3.32444	−	5.75809i	−0.155511	−	0.269352i	−0.933245	+	0.359241i	$0.883036\pi$
$458$	−3.70311	+	6.41398i	−0.173035	+	0.299706i
$459$	21.2959	−	32.3894i	0.994009	−	1.51181i
$460$	14.8697	+	25.7551i	0.693304	+	1.20084i
$461$	−6.97181			−0.324709			−0.162355	−	0.986732i	$-0.551909\pi$
$461$	−6.97181			−0.324709			−0.162355	+	0.986732i	$0.551909\pi$
$462$	−0.135250	+	0.224133i	−0.00629238	+	0.0104276i
$463$	8.59691	−	14.8903i	0.399532	−	0.692010i	−0.594136	−	0.804365i	$-0.702506\pi$
$463$	8.59691	−	14.8903i	0.399532	−	0.692010i	0.993668	+	0.112354i	$0.0358392\pi$
$464$	6.59033	−	11.4148i	0.305949	−	0.529919i
$465$	−53.3008	−	1.03111i	−2.47177	−	0.0478168i
$466$	2.29369	−	3.97280i	0.106253	−	0.184036i
$467$	36.5485			1.69126			0.845632	−	0.533766i	$-0.179224\pi$
$467$	36.5485			1.69126			0.845632	+	0.533766i	$0.179224\pi$
$468$	7.39998	+	0.286415i	0.342064	+	0.0132396i
$469$	0.0998193	+	0.172892i	0.00460923	+	0.00798341i
$470$	−4.43804			−0.204712
$471$	−17.3823	−	31.4988i	−0.800936	−	1.45139i
$472$	−7.49390	−	12.9798i	−0.344935	−	0.597444i
$473$	8.19130	+	14.1877i	0.376636	+	0.652353i
$474$	6.32984	+	0.122452i	0.290739	+	0.00562441i
$475$	25.7811	−	21.0764i	1.18292	−	0.967054i
$476$	3.47000			0.159047
$477$	0.710894	+	1.34927i	0.0325496	+	0.0617790i
$478$	3.01025	−	5.21391i	0.137686	−	0.238479i
$479$	9.98270	−	17.2905i	0.456121	−	0.790025i	−0.542631	−	0.839971i	$-0.682572\pi$
$479$	9.98270	−	17.2905i	0.456121	−	0.790025i	0.998752	+	0.0499464i	$0.0159050\pi$
$480$	12.0481	+	21.8325i	0.549918	+	0.996514i
$481$	−4.11673			−0.187707
$482$	−1.94475	+	3.36840i	−0.0885807	+	0.153426i
$483$	0.938730	+	1.70109i	0.0427137	+	0.0774021i
$484$	−7.76432	+	13.4482i	−0.352924	+	0.611281i
$485$	11.4327	+	19.8021i	0.519134	+	0.899167i
$486$	5.75457	+	0.558289i	0.261033	+	0.0253245i
$487$	0.541412			0.0245337			0.0122669	−	0.999925i	$-0.496095\pi$
$487$	0.541412			0.0245337			0.0122669	+	0.999925i	$0.496095\pi$
$488$	2.96607	−	5.13738i	0.134268	−	0.232558i
$489$	−9.38026	−	0.181463i	−0.424190	−	0.00820604i
$490$	9.14787			0.413259
$491$	3.67184	+	6.35982i	0.165708	+	0.287015i	0.936906	−	0.349580i	$-0.113676\pi$
$491$	3.67184	+	6.35982i	0.165708	+	0.287015i	−0.771199	+	0.636595i	$0.780342\pi$
$492$	8.64894	+	15.6729i	0.389924	+	0.706588i
$493$	−15.3946	−	26.6643i	−0.693340	−	1.20090i
$494$	2.00398	+	0.758583i	0.0901635	+	0.0341302i
$495$	9.27755	−	14.7231i	0.416995	−	0.661753i
$496$	−13.8241	+	23.9440i	−0.620718	+	1.07512i
$497$	−2.79747			−0.125484
$498$	0.114996	+	0.208386i	0.00515310	+	0.00933801i
$499$	5.97373	+	10.3468i	0.267421	+	0.463187i	0.968195	−	0.250197i	$-0.0804952\pi$
$499$	5.97373	+	10.3468i	0.267421	+	0.463187i	−0.700774	+	0.713383i	$0.747162\pi$
$500$	17.4773			0.781607
$501$	−2.59770	−	0.0502530i	−0.116057	−	0.00224514i
$502$	−2.60437	−	4.51091i	−0.116239	−	0.201332i
$503$	14.7358	+	25.5232i	0.657038	+	1.13802i	0.981379	+	0.192083i	$0.0615242\pi$
$503$	14.7358	+	25.5232i	0.657038	+	1.13802i	−0.324341	+	0.945940i	$0.605142\pi$
$504$	0.500315	+	0.949595i	0.0222858	+	0.0422983i
$505$	−26.8900			−1.19659
$506$	1.35900	+	2.35386i	0.0604151	+	0.104642i
$507$	−19.4703	−	0.376657i	−0.864706	−	0.0167279i
$508$	1.76779	+	3.06191i	0.0784332	+	0.135850i
$509$	17.9044			0.793600			0.396800	−	0.917905i	$-0.370121\pi$
$509$	17.9044			0.793600			0.396800	+	0.917905i	$0.370121\pi$
$510$	17.0344	+	0.329534i	0.754297	+	0.0145920i
$511$	0.922853			0.0408246
$512$	22.0823			0.975909
$513$	−20.6820	−	9.23343i	−0.913131	−	0.407666i
$514$	6.36470			0.280735
$515$	−49.1278			−2.16483
$516$	32.3834	+	0.626464i	1.42560	+	0.0275786i
$517$	5.49166			0.241523
$518$	−0.143854	−	0.249162i	−0.00632058	−	0.0109476i
$519$	38.8139	+	0.750864i	1.70374	+	0.0329593i
$520$	3.37515	+	5.84593i	0.148010	+	0.256361i
$521$	−27.8411			−1.21974			−0.609871	−	0.792501i	$-0.708779\pi$
$521$	−27.8411			−1.21974			−0.609871	+	0.792501i	$0.708779\pi$
$522$	2.44823	−	3.88523i	0.107156	−	0.170052i
$523$	−12.9624	−	22.4515i	−0.566805	−	0.981735i	−0.996879	−	0.0789417i	$-0.974846\pi$
$523$	−12.9624	−	22.4515i	−0.566805	−	0.981735i	0.430074	−	0.902794i	$-0.358487\pi$
$524$	−2.82057	−	4.88537i	−0.123217	−	0.213418i
$525$	3.30410	+	0.0639185i	0.144203	+	0.00278963i
$526$	7.23214			0.315336
$527$	32.2922	+	55.9317i	1.40667	+	2.43642i
$528$	−4.36060	−	7.90191i	−0.189771	−	0.343886i
$529$	−2.82704			−0.122915
$530$	−0.335162	+	0.580517i	−0.0145585	+	0.0252161i
$531$	14.6306	+	27.7688i	0.634913	+	1.20506i
$532$	−0.326485	−	2.00107i	−0.0141549	−	0.0867574i
$533$	3.67751	+	6.36964i	0.159291	+	0.275900i
$534$	2.48945	+	4.51116i	0.107729	+	0.195217i
$535$	21.3524	+	36.9834i	0.923144	+	1.59893i
$536$	1.14510			0.0494607
$537$	−22.0161	−	0.425906i	−0.950064	−	0.0183792i
$538$	−4.29474	+	7.43871i	−0.185159	+	0.320705i
$539$	−11.3196			−0.487571
$540$	−15.4458	−	30.7437i	−0.664682	−	1.32300i
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	−0.999428	−	0.0338181i	$-0.989233\pi$
$541$	−12.3043	−	21.3116i	−0.529001	−	0.916257i	0.470427	−	0.882439i	$-0.344100\pi$
$542$	−4.09415	+	7.09128i	−0.175859	+	0.304597i
$543$	2.19517	+	3.97790i	0.0942038	+	0.170708i
$544$	15.1048	−	26.1622i	0.647611	−	1.12170i
$545$	−54.2239			−2.32270
$546$	0.102743	+	0.186182i	0.00439699	+	0.00796784i
$547$	−6.44357	+	11.1606i	−0.275507	+	0.477192i	−0.970263	−	0.242054i	$-0.922179\pi$
$547$	−6.44357	+	11.1606i	−0.275507	+	0.477192i	0.694756	+	0.719246i	$0.255512\pi$
$548$	3.96465	−	6.86697i	0.169361	−	0.293343i
$549$	−6.62296	+	10.5104i	−0.282661	+	0.448571i
$550$	4.62308			0.197129
$551$	−13.9283	+	11.3865i	−0.593364	+	0.485083i
$552$	11.1422	+	0.215548i	0.474243	+	0.00917432i
$553$	−1.23068	−	2.13161i	−0.0523340	−	0.0906452i
$554$	5.48887	+	9.50700i	0.233200	+	0.403914i
$555$	9.24089	+	16.7455i	0.392254	+	0.710809i
$556$	32.1684			1.36424
$557$	−11.8767	−	20.5710i	−0.503231	−	0.871622i	−0.999993	−	0.00373498i	$-0.998811\pi$
$557$	−11.8767	−	20.5710i	−0.503231	−	0.871622i	0.496762	−	0.867887i	$-0.334522\pi$
$558$	−5.13546	+	8.14976i	−0.217401	+	0.345007i
$559$	13.3080			0.562868
$560$	1.41781	−	2.45573i	0.0599136	−	0.103773i
$561$	−21.0785	−	0.407768i	−0.889935	−	0.0172160i
$562$	−5.34234	+	9.25321i	−0.225353	+	0.390323i
$563$	13.3440	−	23.1125i	0.562383	−	0.974077i	−0.434904	−	0.900477i	$-0.643218\pi$
$563$	13.3440	−	23.1125i	0.562383	−	0.974077i	0.997288	−	0.0735999i	$-0.0234488\pi$
$564$	5.60955	−	9.29602i	0.236204	−	0.391433i
$565$	−10.4154			−0.438181
$566$	−2.97090	−	5.14574i	−0.124876	−	0.216292i
$567$	−0.970056	−	2.02766i	−0.0407385	−	0.0851539i
$568$	−8.02294	+	13.8961i	−0.336635	+	0.583069i
$569$	6.57047	+	11.3804i	0.275448	+	0.477090i	0.970248	−	0.242113i	$-0.0778404\pi$
$569$	6.57047	+	11.3804i	0.275448	+	0.477090i	−0.694800	+	0.719203i	$0.744507\pi$
$570$	−1.41270	−	9.85438i	−0.0591716	−	0.412755i
$571$	−1.08070	+	1.87182i	−0.0452258	+	0.0783333i	−0.887752	−	0.460322i	$-0.847734\pi$
$571$	−1.08070	+	1.87182i	−0.0452258	+	0.0783333i	0.842526	+	0.538655i	$0.181067\pi$
$572$	−2.01384	−	3.48808i	−0.0842031	−	0.145844i
$573$	−2.85227	−	5.16863i	−0.119155	−	0.215923i
$574$	−0.257012	+	0.445158i	−0.0107275	+	0.0185805i
$575$	17.1562	−	29.7154i	0.715463	−	1.23922i
$576$	−14.6447	−	0.566821i	−0.610195	−	0.0236175i
$577$	4.53956			0.188985			0.0944923	−	0.995526i	$-0.469877\pi$
$577$	4.53956			0.188985			0.0944923	+	0.995526i	$0.469877\pi$
$578$	−7.16772	−	12.4149i	−0.298138	−	0.516390i
$579$	−0.416555	−	0.754846i	−0.0173114	−	0.0313703i
$580$	−27.3281			−1.13474
$581$	0.0462667	−	0.0801364i	0.00191947	−	0.00332462i
$582$	4.13084	+	0.0799120i	0.171229	+	0.00331246i
$583$	0.414731	−	0.718336i	0.0171764	−	0.0297504i
$584$	2.64668	−	4.58418i	0.109520	−	0.189695i
$585$	−6.58941	−	12.5067i	−0.272439	−	0.517087i
$586$	−0.148496	+	0.257202i	−0.00613430	+	0.0106249i
$587$	24.2678			1.00164			0.500819	−	0.865552i	$-0.333032\pi$
$587$	24.2678			1.00164			0.500819	+	0.865552i	$0.333032\pi$
$588$	−11.5626	+	19.1613i	−0.476834	+	0.790200i
$589$	29.2163	−	23.8847i	1.20384	−	0.984152i
$590$	−6.89781	+	11.9474i	−0.283978	+	0.491865i
$591$	−4.57866	−	0.0885750i	−0.188341	−	0.00364349i
$592$	9.91920			0.407677
$593$	16.5350	+	28.6395i	0.679013	+	1.17608i	0.975279	+	0.220979i	$0.0709252\pi$
$593$	16.5350	+	28.6395i	0.679013	+	1.17608i	−0.296266	+	0.955106i	$0.595741\pi$
$594$	−1.41165	−	2.80979i	−0.0579209	−	0.115287i
$595$	−3.31193	−	5.73644i	−0.135776	−	0.235171i
$596$	1.71917	+	2.97769i	0.0704199	+	0.121971i
$597$	0.177932	+	0.322434i	0.00728229	+	0.0131963i
$598$	2.20791			0.0902880
$599$	−13.2848			−0.542803			−0.271401	−	0.962466i	$-0.587487\pi$
$599$	−13.2848			−0.542803			−0.271401	+	0.962466i	$0.587487\pi$
$600$	9.79343	−	16.2295i	0.399815	−	0.662565i
$601$	−7.35146	−	12.7331i	−0.299872	−	0.519394i	0.676234	−	0.736687i	$-0.263611\pi$
$601$	−7.35146	−	12.7331i	−0.299872	−	0.519394i	−0.976106	+	0.217293i	$0.930277\pi$
$602$	0.465032	+	0.805459i	0.0189533	+	0.0328280i
$603$	−2.39626	−	0.0927468i	−0.0975831	−	0.00377694i
$604$	10.4283	+	18.0623i	0.424321	+	0.734946i
$605$	29.6426			1.20514
$606$	−2.51033	+	4.16007i	−0.101975	+	0.168991i
$607$	−1.19304	+	2.06641i	−0.0484241	+	0.0838729i	−0.889221	−	0.457477i	$-0.848753\pi$
$607$	−1.19304	+	2.06641i	−0.0484241	+	0.0838729i	0.840797	+	0.541350i	$0.182087\pi$
$608$	−16.5083	−	6.24903i	−0.669502	−	0.253431i
$609$	−1.78504	−	0.0345320i	−0.0723335	−	0.00139931i
$610$	−5.46028			−0.221080
$611$	2.23051	−	3.86336i	0.0902368	−	0.156295i
$612$	−22.2212	+	35.2641i	−0.898239	+	1.42547i
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	−0.819084	−	0.573673i	$-0.805518\pi$
$613$	2.16079	−	3.74260i	0.0872736	−	0.151162i	0.906358	+	0.422511i	$0.138851\pi$
$614$	0.852996	−	1.47743i	0.0344241	−	0.0596243i
$615$	17.6547	−	29.2570i	0.711906	−	1.17976i
$616$	0.291880	−	0.505552i	0.0117602	−	0.0203693i
$617$	−9.61045			−0.386902			−0.193451	−	0.981110i	$-0.561968\pi$
$617$	−9.61045			−0.386902			−0.193451	+	0.981110i	$0.561968\pi$
$618$	−4.58637	+	7.60043i	−0.184491	+	0.305734i
$619$	−1.79677	−	3.11209i	−0.0722182	−	0.125086i	0.827655	−	0.561237i	$-0.189674\pi$
$619$	−1.79677	−	3.11209i	−0.0722182	−	0.125086i	−0.899873	+	0.436152i	$0.856341\pi$
$620$	57.3241			2.30219
$621$	−23.2989	−	1.35352i	−0.934952	−	0.0543147i
$622$	6.08687	−	10.5428i	0.244061	−	0.422727i
$623$	1.00159	−	1.73480i	0.0401277	−	0.0695032i
$624$	−7.33006	−	0.141802i	−0.293437	−	0.00567660i
$625$	2.41765	+	4.18750i	0.0967061	+	0.167500i
$626$	3.40988	−	5.90608i	0.136286	−	0.236055i
$627$	1.74809	+	12.1939i	0.0698119	+	0.486976i
$628$	19.3425	+	33.5022i	0.771850	+	1.33688i
$629$	11.5853	−	20.0664i	0.461938	−	0.800100i
$630$	0.526700	−	0.835851i	0.0209842	−	0.0333011i
$631$	12.6319	+	21.8792i	0.502870	+	0.870996i	0.999994	+	0.00331669i	$0.00105574\pi$
$631$	12.6319	+	21.8792i	0.502870	+	0.870996i	−0.497125	+	0.867679i	$0.665611\pi$
$632$	−14.1181			−0.561586
$633$	7.13311	+	12.9260i	0.283516	+	0.513763i
$634$	−0.251872	+	0.436254i	−0.0100031	+	0.0173259i
$635$	3.37454	−	5.84487i	0.133915	−	0.231947i
$636$	−0.792330	−	1.43579i	−0.0314179	−	0.0569328i
$637$	−4.59761	+	7.96330i	−0.182164	+	0.315517i
$638$	−2.49762			−0.0988818
$639$	17.9145	−	28.4295i	0.708686	−	1.12465i
$640$	−17.6177	−	30.5148i	−0.696402	−	1.20620i
$641$	−23.3043			−0.920463			−0.460231	−	0.887799i	$-0.652234\pi$
$641$	−23.3043			−0.920463			−0.460231	+	0.887799i	$0.652234\pi$
$642$	7.71498	+	0.149248i	0.304486	+	0.00589034i
$643$	−8.62978	−	14.9472i	−0.340325	−	0.589461i	0.644168	−	0.764884i	$-0.277204\pi$
$643$	−8.62978	−	14.9472i	−0.340325	−	0.589461i	−0.984493	+	0.175423i	$0.943871\pi$
$644$	−1.04459	−	1.80928i	−0.0411625	−	0.0712956i
$645$	−29.8727	−	54.1328i	−1.17624	−	2.13148i
$646$	−9.33724	+	7.63333i	−0.367369	+	0.300329i
$647$	−35.6673			−1.40223			−0.701114	−	0.713049i	$-0.747314\pi$
$647$	−35.6673			−1.40223			−0.701114	+	0.713049i	$0.747314\pi$
$648$	−12.8543	−	0.996539i	−0.504963	−	0.0391477i
$649$	8.53539	−	14.7837i	0.335043	−	0.580312i
$650$	1.87772	−	3.25231i	0.0736504	−	0.127566i
$651$	3.74434	+	0.0724351i	0.146752	+	0.00283896i
$652$	10.0883			0.395088
$653$	−8.46548	+	14.6626i	−0.331280	+	0.573794i	−0.982763	−	0.184869i	$-0.940814\pi$
$653$	−8.46548	+	14.6626i	−0.331280	+	0.573794i	0.651483	+	0.758663i	$0.274147\pi$
$654$	−5.06212	+	8.38883i	−0.197944	+	0.328029i
$655$	−5.38418	+	9.32566i	−0.210377	+	0.364384i
$656$	−8.86092	−	15.3476i	−0.345961	−	0.599222i
$657$	−5.90978	+	9.37858i	−0.230563	+	0.365893i
$658$	0.311770			0.0121540
$659$	2.26182	−	3.91760i	0.0881082	−	0.152608i	−0.818603	−	0.574359i	$-0.805251\pi$
$659$	2.26182	−	3.91760i	0.0881082	−	0.152608i	0.906711	+	0.421752i	$0.138585\pi$
$660$	−9.66790	+	16.0214i	−0.376323	+	0.623634i
$661$	20.0800			0.781021			0.390510	−	0.920599i	$-0.372299\pi$
$661$	20.0800			0.781021			0.390510	+	0.920599i	$0.372299\pi$
$662$	3.11498	+	5.39530i	0.121067	+	0.209694i
$663$	−8.84817	+	14.6630i	−0.343634	+	0.569463i
$664$	−0.265379	−	0.459651i	−0.0102987	−	0.0178379i
$665$	−2.99646	+	2.44965i	−0.116198	+	0.0949933i
$666$	3.45335	+	0.133661i	0.133815	+	0.00517928i
$667$	−9.26864	+	16.0537i	−0.358883	+	0.621604i
$668$	2.79378			0.108095
$669$	27.0204	+	0.522716i	1.04467	+	0.0202094i
$670$	−0.527007	−	0.912803i	−0.0203600	−	0.0352646i
$671$	6.75658			0.260835
$672$	−0.846371	−	1.53372i	−0.0326495	−	0.0591646i
$673$	8.72911	+	15.1193i	0.336482	+	0.582805i	0.983768	−	0.179443i	$-0.0574294\pi$
$673$	8.72911	+	15.1193i	0.336482	+	0.582805i	−0.647286	+	0.762247i	$0.724096\pi$
$674$	−6.77287	−	11.7310i	−0.260881	−	0.451860i
$675$	−21.8084	+	33.1689i	−0.839407	+	1.27667i
$676$	20.9399			0.805382
$677$	−20.4904	−	35.4905i	−0.787511	−	1.36401i	−0.927487	−	0.373854i	$-0.878036\pi$
$677$	−20.4904	−	35.4905i	−0.787511	−	1.36401i	0.139976	−	0.990155i	$-0.455297\pi$
$678$	−0.972341	+	1.61134i	−0.0373425	+	0.0618833i
$679$	−0.803143	−	1.39108i	−0.0308218	−	0.0533849i
$680$	−37.9936			−1.45699
$681$	−0.996565	−	1.80589i	−0.0381885	−	0.0692018i
$682$	5.23907			0.200614
$683$	20.9461			0.801480			0.400740	−	0.916192i	$-0.368753\pi$
$683$	20.9461			0.801480			0.400740	+	0.916192i	$0.368753\pi$
$684$	22.4268	+	9.49654i	0.857510	+	0.363109i
$685$	−15.1362			−0.578325
$686$	−1.29104			−0.0492922
$687$	−17.8696	+	29.6132i	−0.681769	+	1.12981i
$688$	−32.0655			−1.22248
$689$	−0.336897	−	0.583522i	−0.0128347	−	0.0222304i
$690$	−4.95613	−	8.98107i	−0.188676	−	0.341903i
$691$	−10.5768	−	18.3195i	−0.402359	−	0.696907i	0.591651	−	0.806194i	$-0.298476\pi$
$691$	−10.5768	−	18.3195i	−0.402359	−	0.696907i	−0.994010	+	0.109288i	$0.965143\pi$
$692$	−41.7437			−1.58686
$693$	−0.651742	+	1.03429i	−0.0247576	+	0.0392893i
$694$	1.88242	+	3.26044i	0.0714556	+	0.123765i
$695$	−30.7031	−	53.1793i	−1.16463	−	2.01720i
$696$	−5.29090	+	8.76797i	−0.200551	+	0.332349i
$697$	−41.3972			−1.56803
$698$	3.20305	+	5.54785i	0.121237	+	0.209989i
$699$	11.0684	−	18.3423i	0.418645	−	0.693769i
$700$	−3.55350			−0.134310
$701$	−1.32346	+	2.29231i	−0.0499865	+	0.0865792i	−0.889936	−	0.456085i	$-0.849251\pi$
$701$	−1.32346	+	2.29231i	−0.0499865	+	0.0865792i	0.839950	+	0.542665i	$0.182585\pi$
$702$	−2.55003	−	0.148141i	−0.0962448	−	0.00559121i
$703$	−12.6619	−	4.79300i	−0.477552	−	0.180771i
$704$	3.98543	+	6.90297i	0.150207	+	0.260165i
$705$	−20.7218	−	0.400867i	−0.780427	−	0.0150975i
$706$	−3.13460	−	5.42928i	−0.117972	−	0.204334i
$707$	1.88900			0.0710432
$708$	−16.3066	−	29.5494i	−0.612838	−	1.11053i
$709$	−13.4226	+	23.2486i	−0.504097	+	0.873121i	0.495892	+	0.868384i	$0.334841\pi$
$709$	−13.4226	+	23.2486i	−0.504097	+	0.873121i	−0.999989	+	0.00473700i	$0.998492\pi$
$710$	14.7695			0.554291
$711$	29.5437	+	1.14349i	1.10798	+	0.0428841i
$712$	−5.74496	−	9.95056i	−0.215301	−	0.372913i
$713$	19.4421	−	33.6748i	0.728113	−	1.26113i
$714$	−1.19666	−	0.0231496i	−0.0447838	−	0.000866351i
$715$	−3.84422	+	6.65839i	−0.143766	+	0.249010i
$716$	23.6779			0.884885
$717$	14.5262	−	24.0725i	0.542490	−	0.899003i
$718$	1.41957	−	2.45876i	0.0529778	−	0.0917602i
$719$	1.94193	−	3.36352i	0.0724217	−	0.125438i	−0.827540	−	0.561406i	$-0.810261\pi$
$719$	1.94193	−	3.36352i	0.0724217	−	0.125438i	0.899962	+	0.435968i	$0.143594\pi$
$720$	15.8771	+	30.1347i	0.591705	+	1.12305i
$721$	3.45120			0.128529
$722$	5.28049	+	4.66638i	0.196520	+	0.173665i
$723$	−9.38451	+	15.5518i	−0.349014	+	0.578378i
$724$	−2.44272	−	4.23091i	−0.0907828	−	0.157240i
$725$	15.7651	+	27.3060i	0.585502	+	1.01412i
$726$	2.76731	−	4.58592i	0.102704	−	0.170200i
$727$	−52.3039			−1.93984			−0.969922	−	0.243417i	$-0.921732\pi$
$727$	−52.3039			−1.93984			−0.969922	+	0.243417i	$0.921732\pi$
$728$	−0.237102	−	0.410673i	−0.00878758	−	0.0152205i
$729$	26.8184	+	3.12650i	0.993273	+	0.115796i
$730$	−4.87230			−0.180332
$731$	−37.4516	+	64.8680i	−1.38520	+	2.39923i
$732$	6.90162	−	11.4372i	0.255091	−	0.422731i
$733$	3.06517	−	5.30902i	0.113215	−	0.196093i	−0.803850	−	0.594832i	$-0.797219\pi$
$733$	3.06517	−	5.30902i	0.113215	−	0.196093i	0.917065	+	0.398739i	$0.130552\pi$
$734$	4.59485	−	7.95852i	0.169599	−	0.293754i
$735$	42.7125	+	0.826283i	1.57548	+	0.0304779i
$736$	−18.1882			−0.670426
$737$	0.652121	+	1.12951i	0.0240212	+	0.0416059i
$738$	−2.87810	−	5.46262i	−0.105944	−	0.201082i
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	−0.962410	−	0.271602i	$-0.912447\pi$
$739$	−6.68714	+	11.5825i	−0.245990	+	0.426068i	0.716419	+	0.697670i	$0.245780\pi$
$740$	−10.2830	−	17.8106i	−0.378009	−	0.654731i
$741$	9.28833	+	3.72293i	0.341215	+	0.136765i
$742$	0.0235449	−	0.0407809i	0.000864360	−	0.00149712i
$743$	1.37195	+	2.37629i	0.0503321	+	0.0871778i	0.890094	−	0.455777i	$-0.150639\pi$
$743$	1.37195	+	2.37629i	0.0503321	+	0.0871778i	−0.839762	+	0.542955i	$0.817305\pi$
$744$	11.0983	−	18.3919i	0.406884	−	0.674280i
$745$	3.28172	−	5.68410i	0.120233	−	0.208249i
$746$	4.29724	−	7.44304i	0.157333	−	0.272509i
$747$	0.518109	+	0.983368i	0.0189566	+	0.0359796i
$748$	22.6696			0.828881
$749$	−1.49999	−	2.59806i	−0.0548085	−	0.0949311i
$750$	−6.02718	−	0.116597i	−0.220081	−	0.00425752i
$751$	−20.9472			−0.764374			−0.382187	−	0.924085i	$-0.624829\pi$
$751$	−20.9472			−0.764374			−0.382187	+	0.924085i	$0.624829\pi$
$752$	−5.37439	+	9.30871i	−0.195984	+	0.339454i
$753$	−11.7527	−	21.2972i	−0.428292	−	0.776114i
$754$	−1.01444	+	1.75706i	−0.0369438	+	0.0639885i
$755$	19.9065	−	34.4791i	0.724473	−	1.25482i
$756$	1.08506	+	2.15973i	0.0394632	+	0.0785484i
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	−0.791819	−	0.610756i	$-0.790865\pi$
$757$	3.65990	−	6.33913i	0.133021	−	0.230400i	0.924840	+	0.380357i	$0.124199\pi$
$758$	10.7855			0.391746
$759$	6.13274	+	11.1132i	0.222604	+	0.403385i
$760$	3.57474	+	21.9100i	0.129670	+	0.794761i
$761$	6.05266	−	10.4835i	0.219409	−	0.380027i	−0.735219	−	0.677830i	$-0.762921\pi$
$761$	6.05266	−	10.4835i	0.219409	−	0.380027i	0.954627	+	0.297803i	$0.0962539\pi$
$762$	−0.589212	−	1.06772i	−0.0213449	−	0.0386794i
$763$	3.80919			0.137902
$764$	3.17391	+	5.49737i	0.114828	+	0.198888i
$765$	79.5061	+	3.07727i	2.87455	+	0.111259i
$766$	0.524540	+	0.908530i	0.0189524	+	0.0328265i
$767$	−6.93352	−	12.0092i	−0.250355	−	0.433627i
$768$	10.5541	+	0.204172i	0.380839	+	0.00736741i
$769$	−28.9659			−1.04454			−0.522269	−	0.852781i	$-0.674914\pi$
$769$	−28.9659			−1.04454			−0.522269	+	0.852781i	$0.674914\pi$
$770$	−0.537327			−0.0193639
$771$	29.7176	+	0.574893i	1.07025	+	0.0207043i
$772$	0.463529	+	0.802856i	0.0166828	+	0.0288954i
$773$	21.7876	+	37.7372i	0.783645	+	1.35731i	0.929805	+	0.368052i	$0.119975\pi$
$773$	21.7876	+	37.7372i	0.783645	+	1.35731i	−0.146160	+	0.989261i	$0.546691\pi$
$774$	−11.1635	−	0.432083i	−0.401265	−	0.0155309i
$775$	−33.0693	−	57.2777i	−1.18788	−	2.05748i
$776$	−9.21343			−0.330743
$777$	−0.649166	−	1.17636i	−0.0232887	−	0.0422018i
$778$	−3.55421	+	6.15608i	−0.127425	+	0.220706i
$779$	3.89499	+	23.8729i	0.139552	+	0.855334i
$780$	7.34426	+	13.3086i	0.262967	+	0.476525i
$781$	−18.2759			−0.653964
$782$	−6.21352	+	10.7621i	−0.222195	+	0.384853i
$783$	11.7820	−	17.9195i	0.421054	−	0.640390i
$784$	11.0779	−	19.1875i	0.395639	−	0.685267i
$785$	36.9229	−	63.9523i	1.31783	−	2.28255i
$786$	0.940104	+	1.70358i	0.0335324	+	0.0607645i
$787$	3.10060	−	5.37040i	0.110525	−	0.191434i	−0.805457	−	0.592654i	$-0.798080\pi$
$787$	3.10060	−	5.37040i	0.110525	−	0.191434i	0.915982	+	0.401220i	$0.131414\pi$
$788$	4.92426			0.175420
$789$	33.7677	+	0.653244i	1.20216	+	0.0232561i
$790$	6.49754	+	11.2541i	0.231172	+	0.400402i
$791$	0.731677			0.0260155
$792$	3.26857	+	6.20372i	0.116143	+	0.220440i
$793$	2.74427	−	4.75322i	0.0974520	−	0.168792i
$794$	5.91901	−	10.2520i	0.210058	−	0.363831i
$795$	−1.61735	+	2.68023i	−0.0573614	+	0.0950581i
$796$	−0.197997	−	0.342942i	−0.00701784	−	0.0121552i
$797$	−19.1606	+	33.1871i	−0.678702	+	1.17555i	0.296671	+	0.954980i	$0.404124\pi$
$797$	−19.1606	+	33.1871i	−0.678702	+	1.17555i	−0.975372	+	0.220566i	$0.929210\pi$
$798$	0.0992414	+	0.692264i	0.00351311	+	0.0245059i
$799$	12.5543	+	21.7446i	0.444138	+	0.769269i
$800$	−15.4683	+	26.7918i	−0.546885	+	0.947233i
$801$	11.2161	+	21.2880i	0.396300	+	0.752176i
$802$	−7.11006	−	12.3150i	−0.251065	−	0.434857i
$803$	6.02902			0.212759
$804$	2.57809	+	0.0498738i	0.0909224	+	0.00175891i
$805$	−1.99401	+	3.45373i	−0.0702797	+	0.121728i
$806$	2.12792	−	3.68566i	0.0749527	−	0.129822i
$807$	−20.7246	+	34.3443i	−0.729540	+	1.20898i
$808$	5.41752	−	9.38342i	0.190588	−	0.330108i
$809$	−36.9557			−1.29929			−0.649647	−	0.760236i	$-0.725083\pi$
$809$	−36.9557			−1.29929			−0.649647	+	0.760236i	$0.725083\pi$
$810$	5.12152	+	10.7053i	0.179952	+	0.376145i
$811$	21.0016	+	36.3759i	0.737467	+	1.27733i	0.953632	+	0.300974i	$0.0973118\pi$
$811$	21.0016	+	36.3759i	0.737467	+	1.27733i	−0.216165	+	0.976357i	$0.569355\pi$
$812$	1.91978			0.0673710
$813$	−19.7566	+	32.7403i	−0.692895	+	1.14825i
$814$	−0.939801	−	1.62778i	−0.0329400	−	0.0570537i
$815$	−9.62877	−	16.6775i	−0.337281	−	0.584188i
$816$	21.3195	−	35.3303i	0.746333	−	1.23681i
$817$	40.9317	+	15.4942i	1.43202	+	0.542072i
$818$	0.850402			0.0297336
$819$	0.462902	+	0.878586i	0.0161751	+	0.0307003i
$820$	−18.3717	+	31.8208i	−0.641569	+	1.11123i
$821$	8.86017	−	15.3463i	0.309222	−	0.535588i	−0.668970	−	0.743289i	$-0.733265\pi$
$821$	8.86017	−	15.3463i	0.309222	−	0.535588i	0.978192	+	0.207701i	$0.0665981\pi$
$822$	−1.41305	+	2.34168i	−0.0492859	+	0.0816756i
$823$	−29.2027			−1.01794			−0.508971	−	0.860784i	$-0.669974\pi$
$823$	−29.2027			−1.01794			−0.508971	+	0.860784i	$0.669974\pi$
$824$	9.89779	−	17.1435i	0.344806	−	0.597221i
$825$	21.5858	+	0.417581i	0.751519	+	0.0145383i
$826$	0.484566	−	0.839294i	0.0168602	−	0.0292028i
$827$	7.34515	+	12.7222i	0.255416	+	0.442393i	0.965008	−	0.262219i	$-0.0844543\pi$
$827$	7.34515	+	12.7222i	0.255416	+	0.442393i	−0.709593	+	0.704612i	$0.751121\pi$
$828$	25.0763	+	0.970576i	0.871462	+	0.0337298i
$829$	−2.88680			−0.100263			−0.0501314	−	0.998743i	$-0.515964\pi$
$829$	−2.88680			−0.100263			−0.0501314	+	0.998743i	$0.515964\pi$
$830$	−0.244270	+	0.423089i	−0.00847875	+	0.0146856i
$831$	24.7695	+	44.8851i	0.859244	+	1.55705i
$832$	6.47493			0.224478
$833$	−25.8773	−	44.8209i	−0.896596	−	1.55295i
$834$	−11.0935	−	0.214607i	−0.384137	−	0.00743122i
$835$	−2.66652	−	4.61855i	−0.0922788	−	0.159831i
$836$	−2.13294	−	13.0730i	−0.0737692	−	0.452140i
$837$	−24.7142	+	37.5884i	−0.854249	+	1.29924i
$838$	1.97391	−	3.41892i	0.0681877	−	0.118105i
$839$	−15.1184			−0.521946			−0.260973	−	0.965346i	$-0.584043\pi$
$839$	−15.1184			−0.521946			−0.260973	+	0.965346i	$0.584043\pi$
$840$	−1.13826	+	1.88630i	−0.0392737	+	0.0650835i
$841$	5.98290	+	10.3627i	0.206307	+	0.357334i
$842$	9.59288			0.330592
$843$	−25.7799	+	42.7218i	−0.887906	+	1.47142i
$844$	−7.93749	−	13.7481i	−0.273220	−	0.473230i
$845$	−19.9861	−	34.6170i	−0.687543	−	1.19086i
$846$	−1.99652	+	3.16839i	−0.0686416	+	0.108931i
$847$	−2.08237			−0.0715511
$848$	0.811749	+	1.40599i	0.0278756	+	0.0482819i
$849$	−13.4067	−	24.2945i	−0.460116	−	0.833783i
$850$	10.5686	+	18.3054i	0.362501	+	0.627871i
$851$	−13.9503			−0.478212
$852$	−18.6682	+	30.9366i	−0.639563	+	1.05987i
$853$	26.1014			0.893696			0.446848	−	0.894610i	$-0.352546\pi$
$853$	26.1014			0.893696			0.446848	+	0.894610i	$0.352546\pi$
$854$	0.383581			0.0131259
$855$	−5.70598	−	46.1389i	−0.195141	−	1.57792i
$856$	−17.2075			−0.588139
$857$	41.6454			1.42258			0.711291	−	0.702898i	$-0.248111\pi$
$857$	41.6454			1.42258			0.711291	+	0.702898i	$0.248111\pi$
$858$	0.671221	+	1.21633i	0.0229151	+	0.0415248i
$859$	9.44030			0.322099			0.161049	−	0.986946i	$-0.448512\pi$
$859$	9.44030			0.322099			0.161049	+	0.986946i	$0.448512\pi$
$860$	33.2414	+	57.5758i	1.13352	+	1.96332i
$861$	−1.24023	+	2.05528i	−0.0422670	+	0.0700439i
$862$	−3.53451	−	6.12196i	−0.120386	−	0.208515i
$863$	31.0403			1.05662			0.528311	−	0.849051i	$-0.322825\pi$
$863$	31.0403			1.05662			0.528311	+	0.849051i	$0.322825\pi$
$864$	21.0066	+	1.22035i	0.714658	+	0.0415171i
$865$	39.8422	+	69.0088i	1.35468	+	2.34637i
$866$	4.94349	+	8.56238i	0.167987	+	0.290962i
$867$	−32.3456	−	58.6139i	−1.09851	−	1.99063i
$868$	−4.02698			−0.136684
$869$	−8.04009	−	13.9258i	−0.272741	−	0.472402i
$870$	9.42431	+	0.182315i	0.319514	+	0.00618107i
$871$	1.05947			0.0358988
$872$	10.9245	−	18.9218i	0.369950	−	0.640772i
$873$	19.2802	+	0.746238i	0.652536	+	0.0252563i
$874$	6.79090	+	2.57061i	0.229706	+	0.0869522i
$875$	1.17184	+	2.02969i	0.0396154	+	0.0686159i
$876$	6.15843	−	10.2056i	0.208074	−	0.344816i
$877$	20.7277	+	35.9014i	0.699924	+	1.21230i	0.968492	+	0.249044i	$0.0801163\pi$
$877$	20.7277	+	35.9014i	0.699924	+	1.21230i	−0.268568	+	0.963261i	$0.586550\pi$
$878$	−0.722138			−0.0243710
$879$	−0.716577	+	1.18750i	−0.0241695	+	0.0400532i
$880$	9.26261	−	16.0433i	0.312243	−	0.540820i
$881$	15.2233			0.512886			0.256443	−	0.966559i	$-0.417449\pi$
$881$	15.2233			0.512886			0.256443	+	0.966559i	$0.417449\pi$
$882$	4.11530	−	6.53080i	0.138569	−	0.219904i
$883$	−0.314882	−	0.545392i	−0.0105966	−	0.0183539i	0.860678	−	0.509149i	$-0.170040\pi$
$883$	−0.314882	−	0.545392i	−0.0105966	−	0.0183539i	−0.871275	+	0.490795i	$0.836706\pi$
$884$	9.20753	−	15.9479i	0.309683	−	0.536386i
$885$	−33.2859	+	55.1606i	−1.11889	+	1.85420i
$886$	−1.21694	+	2.10781i	−0.0408840	+	0.0708132i
$887$	−1.12719			−0.0378474			−0.0189237	−	0.999821i	$-0.506024\pi$
$887$	−1.12719			−0.0378474			−0.0189237	+	0.999821i	$0.506024\pi$
$888$	−7.70523	−	0.149059i	−0.258570	−	0.00500210i
$889$	−0.237059	+	0.410599i	−0.00795071	+	0.0137710i
$890$	−5.28798	+	9.15906i	−0.177254	+	0.307012i
$891$	−6.33740	−	13.2468i	−0.212311	−	0.443783i
$892$	−29.0600			−0.973000
$893$	11.3584	−	9.28567i	0.380095	−	0.310733i
$894$	−0.573004	−	1.03835i	−0.0191641	−	0.0347276i
$895$	−22.5994	−	39.1432i	−0.755413	−	1.30841i
$896$	1.23763	+	2.14365i	0.0413465	+	0.0716142i
$897$	10.3090	+	0.199429i	0.344207	+	0.00665876i
$898$	−13.1795			−0.439804
$899$	17.8657	+	30.9443i	0.595854	+	1.03205i
$900$	22.7560	−	36.1128i	0.758532	−	1.20376i
$901$	3.79240			0.126343
$902$	−1.67907	+	2.90823i	−0.0559068	+	0.0968334i
$903$	2.09854	+	3.80279i	0.0698350	+	0.126549i
$904$	2.09840	−	3.63453i	0.0697917	−	0.120883i
$905$	−4.66290	+	8.07637i	−0.155000	+	0.268468i
$906$	−3.47578	−	6.29851i	−0.115475	−	0.209254i
$907$	28.7319			0.954028			0.477014	−	0.878896i	$-0.341719\pi$
$907$	28.7319			0.954028			0.477014	+	0.878896i	$0.341719\pi$
$908$	1.10895	+	1.92075i	0.0368016	+	0.0637423i
$909$	−12.0968	+	19.1971i	−0.401226	+	0.636729i
$910$	−0.218242	+	0.378006i	−0.00723466	+	0.0125308i
$911$	−19.6724	−	34.0735i	−0.651774	−	1.12891i	−0.982692	−	0.185246i	$-0.940692\pi$
$911$	−19.6724	−	34.0735i	−0.651774	−	1.12891i	0.330918	−	0.943660i	$-0.392642\pi$
$912$	−22.3801	−	8.97035i	−0.741080	−	0.297038i
$913$	0.302262	−	0.523532i	0.0100034	−	0.0173264i
$914$	−1.23300	−	2.13561i	−0.0407839	−	0.0706398i
$915$	−25.4947	−	0.493200i	−0.842829	−	0.0163047i
$916$	18.5954	−	32.2082i	0.614410	−	1.06419i
$917$	0.378235	−	0.655122i	0.0124904	−	0.0216340i
$918$	7.89843	−	12.0129i	0.260687	−	0.396484i
$919$	14.3218			0.472433			0.236217	−	0.971700i	$-0.424093\pi$
$919$	14.3218			0.472433			0.236217	+	0.971700i	$0.424093\pi$
$920$	11.4374	+	19.8101i	0.377079	+	0.653120i
$921$	4.11619	−	6.82127i	0.135633	−	0.224768i
$922$	−2.58577			−0.0851577
$923$	−7.42300	+	12.8570i	−0.244331	+	0.423194i
$924$	0.679164	−	1.12550i	0.0223428	−	0.0370261i
$925$	−11.8641	+	20.5493i	−0.390091	+	0.675657i
$926$	3.18850	−	5.52264i	0.104781	−	0.181485i
$927$	−22.1008	+	35.0731i	−0.725887	+	1.15195i
$928$	8.35672	−	14.4743i	0.274323	−	0.475141i
$929$	1.78788			0.0586586			0.0293293	−	0.999570i	$-0.490663\pi$
$929$	1.78788			0.0586586			0.0293293	+	0.999570i	$0.490663\pi$
$930$	−19.7687	−	0.382429i	−0.648240	−	0.0125403i
$931$	−23.4124	+	19.1400i	−0.767312	+	0.627288i
$932$	−11.5179	+	19.9496i	−0.377282	+	0.653472i
$933$	29.3726	−	48.6757i	0.961617	−	1.59357i
$934$	13.5555			0.443548
$935$	−21.6369	−	37.4763i	−0.707603	−	1.22560i
$936$	5.69185	+	0.220303i	0.186044	+	0.00720082i
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	0.957099	−	0.289761i	$-0.0935759\pi$
$937$	6.96721	+	12.0676i	0.227609	+	0.394230i	−0.729490	+	0.683991i	$0.760243\pi$
$938$	0.0370219	+	0.0641238i	0.00120881	+	0.00209372i
$939$	16.4546	−	27.2682i	0.536976	−	0.889866i
$940$	22.2859			0.726886
$941$	−45.4329			−1.48107			−0.740535	−	0.672017i	$-0.765428\pi$
$941$	−45.4329			−1.48107			−0.740535	+	0.672017i	$0.765428\pi$
$942$	−6.44692	−	11.6826i	−0.210052	−	0.380638i
$943$	12.4620	+	21.5848i	0.405818	+	0.702897i
$944$	16.7062	+	28.9360i	0.543741	+	0.941787i
$945$	2.53473	−	3.85512i	0.0824546	−	0.125407i
$946$	3.03806	+	5.26208i	0.0987759	+	0.171085i
$947$	−5.17499			−0.168165			−0.0840823	−	0.996459i	$-0.526796\pi$
$947$	−5.17499			−0.168165			−0.0840823	+	0.996459i	$0.526796\pi$
$948$	−31.7857	−	0.614900i	−1.03235	−	0.0199710i
$949$	2.44876	−	4.24138i	0.0794902	−	0.137681i
$950$	9.56194	−	7.81702i	0.310230	−	0.253618i
$951$	−1.21542	+	2.01418i	−0.0394128	+	0.0653141i
$952$	2.66902			0.0865035
$953$	12.9234	−	22.3840i	0.418630	−	0.725088i	−0.577172	−	0.816622i	$-0.695844\pi$
$953$	12.9234	−	22.3840i	0.418630	−	0.725088i	0.995802	+	0.0915347i	$0.0291772\pi$
$954$	0.263663	+	0.500431i	0.00853640	+	0.0162020i
$955$	6.05867	−	10.4939i	0.196054	−	0.339575i
$956$	−15.1162	+	26.1819i	−0.488891	+	0.846785i
$957$	−11.6617	−	0.225598i	−0.376969	−	0.00729255i
$958$	3.70247	−	6.41287i	0.119621	−	0.207190i
$959$	1.06331			0.0343360
$960$	−14.5344	−	26.3380i	−0.469096	−	0.850055i
$961$	−21.9755	−	38.0628i	−0.708888	−	1.22783i
$962$	−1.52685			−0.0492276
$963$	36.0087	+	1.39371i	1.16036	+	0.0449118i
$964$	9.76565	−	16.9146i	0.314531	−	0.544783i
$965$	0.884830	−	1.53257i	0.0284837	−	0.0493352i
$966$	0.348165	+	0.630914i	0.0112020	+	0.0202993i
$967$	−13.0699	−	22.6377i	−0.420299	−	0.727979i	0.575670	−	0.817682i	$-0.304741\pi$
$967$	−13.0699	−	22.6377i	−0.420299	−	0.727979i	−0.995969	+	0.0897035i	$0.971408\pi$
$968$	−5.97209	+	10.3440i	−0.191950	+	0.332468i
$969$	−44.2862	+	34.7976i	−1.42268	+	1.11786i
$970$	4.24028	+	7.34438i	0.136147	+	0.235814i
$971$	6.28902	−	10.8929i	0.201824	−	0.349570i	−0.747292	−	0.664496i	$-0.768646\pi$
$971$	6.28902	−	10.8929i	0.201824	−	0.349570i	0.949116	+	0.314926i	$0.101980\pi$
$972$	−28.8969	−	2.80348i	−0.926869	−	0.0899217i
$973$	2.15687	+	3.73581i	0.0691461	+	0.119764i
$974$	0.200804			0.00643417
$975$	9.06110	−	15.0159i	0.290187	−	0.480892i
$976$	−6.61229	+	11.4528i	−0.211654	+	0.366596i
$977$	18.8495	−	32.6483i	0.603050	−	1.04451i	−0.389307	−	0.921108i	$-0.627285\pi$
$977$	18.8495	−	32.6483i	0.603050	−	1.04451i	0.992356	−	0.123405i	$-0.0393813\pi$
$978$	−3.47904	−	0.0673027i	−0.111247	−	0.00215210i
$979$	6.54338	−	11.3335i	0.209127	−	0.362219i
$980$	−45.9366			−1.46739
$981$	−24.3934	+	38.7113i	−0.778821	+	1.23596i
$982$	1.36185	+	2.35879i	0.0434583	+	0.0752719i
$983$	−23.2447			−0.741390			−0.370695	−	0.928755i	$-0.620881\pi$
$983$	−23.2447			−0.741390			−0.370695	+	0.928755i	$0.620881\pi$
$984$	6.65252	+	12.0551i	0.212075	+	0.384304i
$985$	−4.69996	−	8.14056i	−0.149753	−	0.259380i
$986$	−5.70970	−	9.88950i	−0.181834	−	0.314946i
$987$	1.45569	+	0.0281606i	0.0463352	+	0.000896363i
$988$	−10.0631	−	3.80927i	−0.320151	−	0.121189i
$989$	45.0968			1.43400
$990$	3.44094	−	5.46063i	0.109360	−	0.173550i
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	−0.990532	−	0.137282i	$-0.956163\pi$
$991$	−11.8484	+	20.5220i	−0.376376	+	0.651903i	0.614156	+	0.789185i	$0.289497\pi$
$992$	−17.5293	+	30.3616i	−0.556555	+	0.963982i
$993$	14.0569	+	25.4727i	0.446082	+	0.808352i
$994$	−1.03755			−0.0329091
$995$	−0.377957	+	0.654641i	−0.0119820	+	0.0207535i
$996$	−0.577460	−	1.04642i	−0.0182975	−	0.0331572i
$997$	9.46564	−	16.3950i	0.299780	−	0.519234i	−0.676306	−	0.736621i	$-0.736420\pi$
$997$	9.46564	−	16.3950i	0.299780	−	0.519234i	0.976085	+	0.217387i	$0.0697535\pi$
$998$	2.21559	+	3.83752i	0.0701333	+	0.121475i
$999$	16.1120	+	0.936006i	0.509762	+	0.0296139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.h.c.49.9	yes	32
3.2	odd	2		513.2.h.c.334.8		32
9.2	odd	6		513.2.g.c.505.9		32
9.7	even	3		171.2.g.c.106.8	✓	32
19.7	even	3		171.2.g.c.121.8	yes	32
57.26	odd	6		513.2.g.c.64.9		32
171.7	even	3	inner	171.2.h.c.7.9	yes	32
171.83	odd	6		513.2.h.c.235.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.8	✓	32	9.7	even	3
171.2.g.c.121.8	yes	32	19.7	even	3
171.2.h.c.7.9	yes	32	171.7	even	3	inner
171.2.h.c.49.9	yes	32	1.1	even	1	trivial
513.2.g.c.64.9		32	57.26	odd	6
513.2.g.c.505.9		32	9.2	odd	6
513.2.h.c.235.8		32	171.83	odd	6
513.2.h.c.334.8		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.370889 q^{2} +(1.73173 + 0.0335006i) q^{3} -1.86244 q^{4} +(1.77761 + 3.07890i) q^{5} +(0.642278 + 0.0124250i) q^{6} +(-0.124876 - 0.216291i) q^{7} -1.43254 q^{8} +(2.99776 + 0.116028i) q^{9} +(0.659294 + 1.14193i) q^{10} +(-0.815815 - 1.41303i) q^{11} +(-3.22524 - 0.0623929i) q^{12} -1.32541 q^{13} +(-0.0463150 - 0.0802199i) q^{14} +(2.97518 + 5.39137i) q^{15} +3.19357 q^{16} +(3.73000 - 6.46055i) q^{17} +(1.11183 + 0.0430334i) q^{18} +(-4.07660 - 1.54315i) q^{19} +(-3.31069 - 5.73428i) q^{20} +(-0.209005 - 0.378740i) q^{21} +(-0.302577 - 0.524078i) q^{22} -4.49143 q^{23} +(-2.48076 - 0.0479909i) q^{24} +(-3.81976 + 6.61602i) q^{25} -0.491582 q^{26} +(5.18741 + 0.301355i) q^{27} +(0.232573 + 0.402829i) q^{28} +(2.06363 - 3.57430i) q^{29} +(1.10346 + 1.99960i) q^{30} +(-4.32871 + 7.49755i) q^{31} +4.04953 q^{32} +(-1.36543 - 2.47432i) q^{33} +(1.38342 - 2.39615i) q^{34} +(0.443959 - 0.768960i) q^{35} +(-5.58314 - 0.216095i) q^{36} +3.10599 q^{37} +(-1.51197 - 0.572336i) q^{38} +(-2.29526 - 0.0444022i) q^{39} +(-2.54649 - 4.41064i) q^{40} +(-2.77461 - 4.80577i) q^{41} +(-0.0775175 - 0.140471i) q^{42} -10.0406 q^{43} +(1.51941 + 2.63169i) q^{44} +(4.97159 + 9.43605i) q^{45} -1.66582 q^{46} +(-1.68288 + 2.91483i) q^{47} +(5.53039 + 0.106987i) q^{48} +(3.46881 - 6.00816i) q^{49} +(-1.41671 + 2.45381i) q^{50} +(6.67577 - 11.0629i) q^{51} +2.46851 q^{52} +(0.254182 + 0.440256i) q^{53} +(1.92395 + 0.111769i) q^{54} +(2.90039 - 5.02363i) q^{55} +(0.178889 + 0.309845i) q^{56} +(-7.00787 - 2.80888i) q^{57} +(0.765376 - 1.32567i) q^{58} +(5.23121 + 9.06071i) q^{59} +(-5.54110 - 10.0411i) q^{60} +(-2.07050 + 3.58621i) q^{61} +(-1.60547 + 2.78076i) q^{62} +(-0.349251 - 0.662876i) q^{63} -4.88521 q^{64} +(-2.35606 - 4.08082i) q^{65} +(-0.506423 - 0.917697i) q^{66} -0.799350 q^{67} +(-6.94690 + 12.0324i) q^{68} +(-7.77793 - 0.150466i) q^{69} +(0.164660 - 0.285199i) q^{70} +(5.60051 - 9.70037i) q^{71} +(-4.29440 - 0.166214i) q^{72} +(-1.84754 + 3.20004i) q^{73} +1.15198 q^{74} +(-6.83642 + 11.3292i) q^{75} +(7.59244 + 2.87402i) q^{76} +(-0.203751 + 0.352907i) q^{77} +(-0.851285 - 0.0164683i) q^{78} +9.85529 q^{79} +(5.67691 + 9.83269i) q^{80} +(8.97308 + 0.695646i) q^{81} +(-1.02907 - 1.78241i) q^{82} +(0.185251 + 0.320865i) q^{83} +(0.389259 + 0.705381i) q^{84} +26.5219 q^{85} -3.72396 q^{86} +(3.69338 - 6.12059i) q^{87} +(1.16868 + 2.02422i) q^{88} +(4.01034 + 6.94611i) q^{89} +(1.84391 + 3.49973i) q^{90} +(0.165512 + 0.286675i) q^{91} +8.36503 q^{92} +(-7.74732 + 12.8387i) q^{93} +(-0.624161 + 1.08108i) q^{94} +(-2.49539 - 15.2946i) q^{95} +(7.01269 + 0.135662i) q^{96} +6.43155 q^{97} +(1.28654 - 2.22836i) q^{98} +(-2.28166 - 4.33058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + q^{3} + 34 q^{4} + 3 q^{5} - 7 q^{6} + q^{7} - 36 q^{8} + 17 q^{9} - 8 q^{10} + 7 q^{11} - 3 q^{12} + 8 q^{13} + q^{14} - 14 q^{15} + 22 q^{16} - 7 q^{17} + 6 q^{18} + 7 q^{19} - 3 q^{20}+ \cdots - 49 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + q^3 + 34 * q^4 + 3 * q^5 - 7 * q^6 + q^7 - 36 * q^8 + 17 * q^9 - 8 * q^10 + 7 * q^11 - 3 * q^12 + 8 * q^13 + q^14 - 14 * q^15 + 22 * q^16 - 7 * q^17 + 6 * q^18 + 7 * q^19 - 3 * q^20 + 8 * q^21 - 8 * q^22 - 10 * q^23 - 39 * q^24 - 9 * q^25 - 4 * q^26 - 5 * q^27 - 10 * q^28 + 10 * q^29 - 5 * q^30 - 10 * q^31 - 34 * q^32 + q^33 - 13 * q^34 - 3 * q^35 - 19 * q^36 + 2 * q^37 - 46 * q^38 + 12 * q^40 + 6 * q^41 + 16 * q^42 - 14 * q^43 + 20 * q^44 - 35 * q^45 - 9 * q^47 - 15 * q^48 - 13 * q^49 + q^50 - 10 * q^51 - 38 * q^52 + 16 * q^53 - 40 * q^54 + 15 * q^55 - 6 * q^56 + 69 * q^57 + 37 * q^59 - 19 * q^60 - 12 * q^61 + 54 * q^62 + 21 * q^63 - 64 * q^64 + 54 * q^65 + 37 * q^66 + 22 * q^67 - 2 * q^68 + 3 * q^69 + 24 * q^70 + 9 * q^71 + 15 * q^72 - 10 * q^73 - 12 * q^74 - 76 * q^75 - 40 * q^76 + 46 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 + 17 * q^81 + 7 * q^82 + 3 * q^83 + 12 * q^84 + 54 * q^85 - 34 * q^86 - 9 * q^87 + 9 * q^88 + 30 * q^89 + 133 * q^90 - q^91 + 34 * q^92 + 27 * q^93 - 18 * q^94 + 3 * q^95 - 5 * q^96 + 18 * q^98 - 49 * q^99

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