LMFDB - Embedded newform 544.2.x.a.77.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(77,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.8
Character	$\chi$	$=$	544.77
Dual form			544.2.x.a.325.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34415 + 0.439614i) q^{2} +(-1.74308 + 1.74308i) q^{3} +(1.61348 - 1.18181i) q^{4} -1.54170i q^{5} +(1.57668 - 3.10924i) q^{6} +(-3.72407 - 1.54256i) q^{7} +(-1.64922 + 2.29784i) q^{8} -3.07663i q^{9} +(0.677751 + 2.07227i) q^{10} +(-0.535610 - 0.535610i) q^{11} +(-0.752426 + 4.87241i) q^{12} +(-0.319703 + 0.771831i) q^{13} +(5.68385 + 0.436280i) q^{14} +(2.68730 + 2.68730i) q^{15} +(1.20663 - 3.81367i) q^{16} +(3.91800 + 1.28423i) q^{17} +(1.35253 + 4.13546i) q^{18} +(-0.708395 + 0.293427i) q^{19} +(-1.82200 - 2.48750i) q^{20} +(9.18015 - 3.80254i) q^{21} +(0.955403 + 0.484479i) q^{22} +(1.67085 + 0.692089i) q^{23} +(-1.13061 - 6.88003i) q^{24} +2.62317 q^{25} +(0.0904211 - 1.17800i) q^{26} +(0.133576 + 0.133576i) q^{27} +(-7.83174 + 1.91227i) q^{28} +(1.99044 + 1.99044i) q^{29} +(-4.79350 - 2.43076i) q^{30} +(3.87550 + 1.60528i) q^{31} +(0.0546467 + 5.65659i) q^{32} +1.86722 q^{33} +(-5.83095 - 0.00378999i) q^{34} +(-2.37816 + 5.74139i) q^{35} +(-3.63601 - 4.96408i) q^{36} +0.0754085 q^{37} +(0.823195 - 0.705830i) q^{38} +(-0.788094 - 1.90263i) q^{39} +(3.54258 + 2.54259i) q^{40} +(0.242343 - 0.585068i) q^{41} +(-10.6678 + 9.14691i) q^{42} +(-3.78287 + 9.13266i) q^{43} +(-1.49719 - 0.231204i) q^{44} -4.74323 q^{45} +(-2.55013 - 0.195742i) q^{46} +5.14829 q^{47} +(4.54426 + 8.75076i) q^{48} +(6.53948 + 6.53948i) q^{49} +(-3.52594 + 1.15318i) q^{50} +(-9.06789 + 4.59087i) q^{51} +(0.396327 + 1.62316i) q^{52} +(6.42881 + 2.66290i) q^{53} +(-0.238269 - 0.120825i) q^{54} +(-0.825749 + 0.825749i) q^{55} +(9.68637 - 6.01332i) q^{56} +(0.723321 - 1.74625i) q^{57} +(-3.55048 - 1.80043i) q^{58} +(4.36411 + 1.80767i) q^{59} +(7.51178 + 1.16001i) q^{60} -0.758472 q^{61} +(-5.91496 - 0.454020i) q^{62} +(-4.74590 + 11.4576i) q^{63} +(-2.56017 - 7.57928i) q^{64} +(1.18993 + 0.492885i) q^{65} +(-2.50982 + 0.820856i) q^{66} +(-6.16484 + 14.8832i) q^{67} +(7.83934 - 2.55827i) q^{68} +(-4.11878 + 1.70606i) q^{69} +(0.672612 - 8.76276i) q^{70} +(12.4854 - 5.17163i) q^{71} +(7.06962 + 5.07403i) q^{72} +(-11.8380 + 4.90345i) q^{73} +(-0.101360 + 0.0331506i) q^{74} +(-4.57239 + 4.57239i) q^{75} +(-0.796205 + 1.31063i) q^{76} +(1.16844 + 2.82086i) q^{77} +(1.89574 + 2.21096i) q^{78} +(-4.98470 - 12.0341i) q^{79} +(-5.87951 - 1.86026i) q^{80} +8.76423 q^{81} +(-0.0685415 + 0.892956i) q^{82} +(13.8395 - 5.73250i) q^{83} +(10.3181 - 16.9846i) q^{84} +(1.97989 - 6.04037i) q^{85} +(1.06990 - 13.9387i) q^{86} -6.93899 q^{87} +(2.11409 - 0.347411i) q^{88} +(-0.612092 - 0.612092i) q^{89} +(6.37562 - 2.08519i) q^{90} +(2.38119 - 2.38119i) q^{91} +(3.51380 - 0.857963i) q^{92} +(-9.55343 + 3.95716i) q^{93} +(-6.92007 + 2.26326i) q^{94} +(0.452375 + 1.09213i) q^{95} +(-9.95512 - 9.76462i) q^{96} +(0.671568 - 1.62131i) q^{97} +(-11.6649 - 5.91520i) q^{98} +(-1.64788 + 1.64788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.34415	+	0.439614i	−0.950458	+	0.310854i
$2$	−1.34415	+	0.439614i	−0.950458	+	0.310854i
$3$	−1.74308	+	1.74308i	−1.00637	+	1.00637i	−0.00638618	+	0.999980i	$0.502033\pi$
$3$	−1.74308	+	1.74308i	−1.00637	+	1.00637i	−0.999980	+	0.00638618i	$0.997967\pi$
$4$	1.61348	−	1.18181i	0.806740	−	0.590907i
$5$		−	1.54170i		−	0.689468i	−0.938700	−	0.344734i	$-0.887969\pi$
$5$		−	1.54170i		−	0.689468i	0.938700	−	0.344734i	$-0.112031\pi$
$6$	1.57668	−	3.10924i	0.643675	−	1.26934i
$7$	−3.72407	−	1.54256i	−1.40757	−	0.583034i	−0.455863	−	0.890050i	$-0.650669\pi$
$7$	−3.72407	−	1.54256i	−1.40757	−	0.583034i	−0.951704	+	0.307016i	$0.900669\pi$
$8$	−1.64922	+	2.29784i	−0.583086	+	0.812410i
$9$		−	3.07663i		−	1.02554i
$10$	0.677751	+	2.07227i	0.214324	+	0.655310i
$11$	−0.535610	−	0.535610i	−0.161493	−	0.161493i	0.621735	−	0.783228i	$-0.286428\pi$
$11$	−0.535610	−	0.535610i	−0.161493	−	0.161493i	−0.783228	+	0.621735i	$0.786428\pi$
$12$	−0.752426	+	4.87241i	−0.217207	+	1.40654i
$13$	−0.319703	+	0.771831i	−0.0886696	+	0.214067i	−0.961993	−	0.273073i	$-0.911960\pi$
$13$	−0.319703	+	0.771831i	−0.0886696	+	0.214067i	0.873324	+	0.487140i	$0.161960\pi$
$14$	5.68385	+	0.436280i	1.51907	+	0.116601i
$15$	2.68730	+	2.68730i	0.693857	+	0.693857i
$16$	1.20663	−	3.81367i	0.301658	−	0.953416i
$17$	3.91800	+	1.28423i	0.950255	+	0.311472i
$17$	3.91800	+	1.28423i	0.950255	+	0.311472i
$18$	1.35253	+	4.13546i	0.318794	+	0.974736i
$19$	−0.708395	+	0.293427i	−0.162517	+	0.0673167i	−0.462459	−	0.886641i	$-0.653033\pi$
$19$	−0.708395	+	0.293427i	−0.162517	+	0.0673167i	0.299942	+	0.953957i	$0.403033\pi$
$20$	−1.82200	−	2.48750i	−0.407411	−	0.556221i
$21$	9.18015	−	3.80254i	2.00327	−	0.829783i
$22$	0.955403	+	0.484479i	0.203693	+	0.103291i
$23$	1.67085	+	0.692089i	0.348396	+	0.144311i	0.550018	−	0.835153i	$-0.314621\pi$
$23$	1.67085	+	0.692089i	0.348396	+	0.144311i	−0.201621	+	0.979464i	$0.564621\pi$
$24$	−1.13061	−	6.88003i	−0.230784	−	1.40438i
$25$	2.62317			0.524634
$26$	0.0904211	−	1.17800i	0.0177330	−	0.231025i
$27$	0.133576	+	0.133576i	0.0257068	+	0.0257068i
$28$	−7.83174	+	1.91227i	−1.48006	+	0.361385i
$29$	1.99044	+	1.99044i	0.369616	+	0.369616i	0.867337	−	0.497721i	$-0.165830\pi$
$29$	1.99044	+	1.99044i	0.369616	+	0.369616i	−0.497721	+	0.867337i	$0.665830\pi$
$30$	−4.79350	−	2.43076i	−0.875169	−	0.443793i
$31$	3.87550	+	1.60528i	0.696060	+	0.288318i	0.702523	−	0.711662i	$-0.252057\pi$
$31$	3.87550	+	1.60528i	0.696060	+	0.288318i	−0.00646224	+	0.999979i	$0.502057\pi$
$32$	0.0546467	+	5.65659i	0.00966027	+	0.999953i
$33$	1.86722			0.325041
$34$	−5.83095	−	0.00378999i	−1.00000	−	0.000649978i
$35$	−2.37816	+	5.74139i	−0.401983	+	0.970472i
$36$	−3.63601	−	4.96408i	−0.606001	−	0.827347i
$37$	0.0754085			0.0123971			0.00619854	−	0.999981i	$-0.498027\pi$
$37$	0.0754085			0.0123971			0.00619854	+	0.999981i	$0.498027\pi$
$38$	0.823195	−	0.705830i	0.133540	−	0.114501i
$39$	−0.788094	−	1.90263i	−0.126196	−	0.304664i
$40$	3.54258	+	2.54259i	0.560131	+	0.402019i
$41$	0.242343	−	0.585068i	0.0378476	−	0.0913722i	−0.903825	−	0.427901i	$-0.859253\pi$
$41$	0.242343	−	0.585068i	0.0378476	−	0.0913722i	0.941673	+	0.336529i	$0.109253\pi$
$42$	−10.6678	+	9.14691i	−1.64608	+	1.41140i
$43$	−3.78287	+	9.13266i	−0.576882	+	1.39272i	0.318715	+	0.947851i	$0.396749\pi$
$43$	−3.78287	+	9.13266i	−0.576882	+	1.39272i	−0.895597	+	0.444866i	$0.853251\pi$
$44$	−1.49719	−	0.231204i	−0.225710	−	0.0348554i
$45$	−4.74323			−0.707080
$46$	−2.55013	−	0.195742i	−0.375996	−	0.0288606i
$47$	5.14829			0.750955			0.375477	−	0.926832i	$-0.377479\pi$
$47$	5.14829			0.750955			0.375477	+	0.926832i	$0.377479\pi$
$48$	4.54426	+	8.75076i	0.655907	+	1.26306i
$49$	6.53948	+	6.53948i	0.934211	+	0.934211i
$50$	−3.52594	+	1.15318i	−0.498643	+	0.163085i
$51$	−9.06789	+	4.59087i	−1.26976	+	0.642850i
$52$	0.396327	+	1.62316i	0.0549606	+	0.225092i
$53$	6.42881	+	2.66290i	0.883065	+	0.365777i	0.777685	−	0.628655i	$-0.216394\pi$
$53$	6.42881	+	2.66290i	0.883065	+	0.365777i	0.105380	+	0.994432i	$0.466394\pi$
$54$	−0.238269	−	0.120825i	−0.0324243	−	0.0164422i
$55$	−0.825749	+	0.825749i	−0.111344	+	0.111344i
$56$	9.68637	−	6.01332i	1.29440	−	0.803564i
$57$	0.723321	−	1.74625i	0.0958062	−	0.231297i
$58$	−3.55048	−	1.80043i	−0.466201	−	0.236408i
$59$	4.36411	+	1.80767i	0.568159	+	0.235339i	0.648223	−	0.761451i	$-0.275513\pi$
$59$	4.36411	+	1.80767i	0.568159	+	0.235339i	−0.0800643	+	0.996790i	$0.525513\pi$
$60$	7.51178	+	1.16001i	0.969766	+	0.149757i
$61$	−0.758472			−0.0971124			−0.0485562	−	0.998820i	$-0.515462\pi$
$61$	−0.758472			−0.0971124			−0.0485562	+	0.998820i	$0.515462\pi$
$62$	−5.91496	−	0.454020i	−0.751201	−	0.0576606i
$63$	−4.74590	+	11.4576i	−0.597927	+	1.44352i
$64$	−2.56017	−	7.57928i	−0.320021	−	0.947410i
$65$	1.18993	+	0.492885i	0.147593	+	0.0611348i
$66$	−2.50982	+	0.820856i	−0.308938	+	0.101040i
$67$	−6.16484	+	14.8832i	−0.753155	+	1.81828i	−0.212196	+	0.977227i	$0.568061\pi$
$67$	−6.16484	+	14.8832i	−0.753155	+	1.81828i	−0.540959	+	0.841049i	$0.681939\pi$
$68$	7.83934	−	2.55827i	0.950660	−	0.310236i
$69$	−4.11878	+	1.70606i	−0.495843	+	0.205385i
$70$	0.672612	−	8.76276i	0.0803925	−	1.04735i
$71$	12.4854	−	5.17163i	1.48175	−	0.613759i	0.512243	−	0.858841i	$-0.328815\pi$
$71$	12.4854	−	5.17163i	1.48175	−	0.613759i	0.969502	+	0.245081i	$0.0788147\pi$
$72$	7.06962	+	5.07403i	0.833163	+	0.597981i
$73$	−11.8380	+	4.90345i	−1.38553	+	0.573906i	−0.945954	−	0.324300i	$-0.894871\pi$
$73$	−11.8380	+	4.90345i	−1.38553	+	0.573906i	−0.439576	+	0.898205i	$0.644871\pi$
$74$	−0.101360	+	0.0331506i	−0.0117829	+	0.00385368i
$75$	−4.57239	+	4.57239i	−0.527974	+	0.527974i
$76$	−0.796205	+	1.31063i	−0.0913309	+	0.150339i
$77$	1.16844	+	2.82086i	0.133156	+	0.321467i
$78$	1.89574	+	2.21096i	0.214650	+	0.250342i
$79$	−4.98470	−	12.0341i	−0.560822	−	1.35395i	−0.909110	−	0.416557i	$-0.863237\pi$
$79$	−4.98470	−	12.0341i	−0.560822	−	1.35395i	0.348287	−	0.937388i	$-0.386763\pi$
$80$	−5.87951	−	1.86026i	−0.657350	−	0.207983i
$81$	8.76423			0.973803
$82$	−0.0685415	+	0.892956i	−0.00756914	+	0.0986105i
$83$	13.8395	−	5.73250i	1.51908	−	0.629223i	0.541673	−	0.840589i	$-0.317791\pi$
$83$	13.8395	−	5.73250i	1.51908	−	0.629223i	0.977407	+	0.211366i	$0.0677912\pi$
$84$	10.3181	−	16.9846i	1.12580	−	1.85317i
$85$	1.97989	−	6.04037i	0.214750	−	0.655170i
$86$	1.06990	−	13.9387i	0.115371	−	1.50304i
$87$	−6.93899			−0.743938
$88$	2.11409	−	0.347411i	0.225362	−	0.0370342i
$89$	−0.612092	−	0.612092i	−0.0648816	−	0.0648816i	0.673921	−	0.738803i	$-0.264609\pi$
$89$	−0.612092	−	0.612092i	−0.0648816	−	0.0648816i	−0.738803	+	0.673921i	$0.764609\pi$
$90$	6.37562	−	2.08519i	0.672049	−	0.219798i
$91$	2.38119	−	2.38119i	0.249617	−	0.249617i
$92$	3.51380	−	0.857963i	0.366339	−	0.0894489i
$93$	−9.55343	+	3.95716i	−0.990644	+	0.410338i
$94$	−6.92007	+	2.26326i	−0.713751	+	0.233437i
$95$	0.452375	+	1.09213i	0.0464127	+	0.112050i
$96$	−9.95512	−	9.76462i	−1.01604	−	0.996597i
$97$	0.671568	−	1.62131i	0.0681874	−	0.164619i	−0.886112	−	0.463471i	$-0.846604\pi$
$97$	0.671568	−	1.62131i	0.0681874	−	0.164619i	0.954299	+	0.298852i	$0.0966037\pi$
$98$	−11.6649	−	5.91520i	−1.17833	−	0.597525i
$99$	−1.64788	+	1.64788i	−0.165618	+	0.165618i
$100$	4.23243	−	3.10010i	0.423243	−	0.310010i
$101$	3.30528	−	1.36909i	0.328888	−	0.136230i	−0.212129	−	0.977242i	$-0.568040\pi$
$101$	3.30528	−	1.36909i	0.328888	−	0.136230i	0.541017	+	0.841012i	$0.318040\pi$
$102$	10.1704	−	10.1572i	1.00702	−	1.00571i
$103$	9.63847	−	9.63847i	0.949707	−	0.949707i	−0.0490877	−	0.998794i	$-0.515631\pi$
$103$	9.63847	−	9.63847i	0.949707	−	0.949707i	0.998794	+	0.0490877i	$0.0156314\pi$
$104$	−1.24629	−	2.00754i	−0.122209	−	0.196856i
$105$	−5.86237	−	14.1530i	−0.572108	−	1.38119i
$106$	−9.81193	−	0.753144i	−0.953019	−	0.0731518i
$107$	2.17698			0.210456			0.105228	−	0.994448i	$-0.466443\pi$
$107$	2.17698			0.210456			0.105228	+	0.994448i	$0.466443\pi$
$108$	0.373385	+	0.0576603i	0.0359290	+	0.00554837i
$109$		−	1.51399i		−	0.145014i	−0.997368	−	0.0725070i	$-0.976900\pi$
$109$		−	1.51399i		−	0.145014i	0.997368	−	0.0725070i	$-0.0231000\pi$
$110$	0.746920	−	1.47294i	0.0712160	−	0.140439i
$111$	−0.131443	+	0.131443i	−0.0124760	+	0.0124760i
$112$	−10.3764	+	12.3411i	−0.980477	+	1.16612i
$113$	3.29017	+	7.94317i	0.309513	+	0.747231i	0.999721	+	0.0236195i	$0.00751903\pi$
$113$	3.29017	+	7.94317i	0.309513	+	0.747231i	−0.690208	+	0.723611i	$0.742481\pi$
$114$	−0.204576	+	2.66521i	−0.0191603	+	0.249619i
$115$	1.06699	−	2.57594i	0.0994974	−	0.240208i
$116$	5.56388	+	0.859206i	0.516593	+	0.0797753i
$117$	2.37464	+	0.983608i	0.219536	+	0.0909346i
$118$	−6.66070	−	0.511261i	−0.613167	−	0.0470654i
$119$	−12.6099	−	10.8263i	−1.15595	−	0.992448i
$120$	−10.6069	+	1.74305i	−0.968275	+	0.159118i
$121$		−	10.4262i		−	0.947840i
$122$	1.01950	−	0.333435i	0.0923012	−	0.0301878i
$123$	0.597395	+	1.44224i	0.0538653	+	0.130042i
$124$	8.15019	−	1.99003i	0.731908	−	0.178710i
$125$		−	11.7526i		−	1.05119i
$126$	1.34227	−	17.4871i	0.119579	−	1.55787i
$127$	−2.45313	−	2.45313i	−0.217680	−	0.217680i	0.589840	−	0.807520i	$-0.299191\pi$
$127$	−2.45313	−	2.45313i	−0.217680	−	0.217680i	−0.807520	+	0.589840i	$0.799191\pi$
$128$	6.77321	+	9.06221i	0.598673	+	0.800994i
$129$	−9.32509	−	22.5128i	−0.821028	−	1.98214i
$130$	−1.81612	−	0.139402i	−0.159284	−	0.0122263i
$131$	15.3397	+	15.3397i	1.34024	+	1.34024i	0.895821	+	0.444416i	$0.146589\pi$
$131$	15.3397	+	15.3397i	1.34024	+	1.34024i	0.444416	+	0.895821i	$0.353411\pi$
$132$	3.01272	−	2.20671i	0.262224	−	0.192069i
$133$	3.09074			0.268001
$134$	1.74359	−	22.7154i	0.150623	−	1.96232i
$135$	0.205934	−	0.205934i	0.0177240	−	0.0177240i
$136$	−9.41260	+	6.88498i	−0.807124	+	0.590383i
$137$	−5.91472	−	5.91472i	−0.505329	−	0.505329i	0.407760	−	0.913089i	$-0.366310\pi$
$137$	−5.91472	−	5.91472i	−0.505329	−	0.505329i	−0.913089	+	0.407760i	$0.866310\pi$
$138$	4.78626	−	4.10387i	0.407433	−	0.349345i
$139$			8.17829i			0.693673i	0.937926	+	0.346837i	$0.112744\pi$
$139$			8.17829i			0.693673i	−0.937926	+	0.346837i	$0.887256\pi$
$140$	2.94814	+	12.0742i	0.249163	+	1.02045i
$141$	−8.97386	+	8.97386i	−0.755735	+	0.755735i
$142$	−14.5087	+	12.4402i	−1.21755	+	1.04396i
$143$	0.584637	−	0.242165i	0.0488898	−	0.0202508i
$144$	−11.7332	−	3.71236i	−0.977771	−	0.309363i
$145$	3.06866	−	3.06866i	0.254838	−	0.254838i
$146$	13.7564	−	11.7951i	1.13849	−	0.976171i
$147$	−22.7976			−1.88032
$148$	0.121670	−	0.0891188i	0.0100012	−	0.00732552i
$149$	−13.0046	+	5.38667i	−1.06538	+	0.441293i	−0.845357	−	0.534203i	$-0.820612\pi$
$149$	−13.0046	+	5.38667i	−1.06538	+	0.441293i	−0.220019	+	0.975496i	$0.570612\pi$
$150$	4.13589	−	8.15606i	0.337694	−	0.665940i
$151$	15.3560			1.24966			0.624828	−	0.780762i	$-0.285169\pi$
$151$	15.3560			1.24966			0.624828	+	0.780762i	$0.285169\pi$
$152$	0.494048	−	2.11170i	0.0400726	−	0.171282i
$153$	3.95111	−	12.0543i	0.319428	−	0.974529i
$154$	−2.81065	−	3.27800i	−0.226489	−	0.264149i
$155$	2.47486	−	5.97484i	0.198786	−	0.479911i
$156$	−3.52012	−	2.13847i	−0.281836	−	0.171215i
$157$	16.7994	+	6.95853i	1.34074	+	0.555351i	0.933698	−	0.358061i	$-0.116562\pi$
$157$	16.7994	+	6.95853i	1.34074	+	0.555351i	0.407037	+	0.913412i	$0.366562\pi$
$158$	11.9906	+	13.9843i	0.953917	+	1.11253i
$159$	−15.8475	+	6.56427i	−1.25679	+	0.520580i
$160$	8.72075	−	0.0842487i	0.689435	−	0.00666044i
$161$	−5.15478	−	5.15478i	−0.406254	−	0.406254i
$162$	−11.7804	+	3.85288i	−0.925559	+	0.302711i
$163$	−22.2964			−1.74639			−0.873196	−	0.487369i	$-0.837957\pi$
$163$	−22.2964			−1.74639			−0.873196	+	0.487369i	$0.837957\pi$
$164$	−0.300426	−	1.23040i	−0.0234593	−	0.0960780i
$165$		−	2.87869i		−	0.224105i
$166$	−16.0822	+	13.7894i	−1.24822	+	1.07026i
$167$	20.4171	−	8.45706i	1.57993	−	0.654427i	0.591524	−	0.806288i	$-0.298527\pi$
$167$	20.4171	−	8.45706i	1.57993	−	0.654427i	0.988402	+	0.151861i	$0.0485266\pi$
$168$	−6.40241	+	27.3658i	−0.493956	+	2.11131i
$169$	8.69888	+	8.69888i	0.669144	+	0.669144i
$170$	−0.00584302	+	8.98956i	−0.000448139	+	0.689468i
$171$	0.902766	+	2.17947i	0.0690363	+	0.166668i
$172$	4.68952	+	19.2060i	0.357572	+	1.46444i
$173$	1.76653	+	1.76653i	0.134307	+	0.134307i	0.771064	−	0.636757i	$-0.219725\pi$
$173$	1.76653	+	1.76653i	0.134307	+	0.134307i	−0.636757	+	0.771064i	$0.719725\pi$
$174$	9.32705	−	3.05048i	0.707082	−	0.231256i
$175$	−9.76888	−	4.04640i	−0.738458	−	0.305879i
$176$	−2.68892	+	1.39635i	−0.202685	+	0.105254i
$177$	−10.7579	+	4.45606i	−0.808612	+	0.334938i
$178$	1.09183	+	0.553659i	0.0818359	+	0.0414985i
$179$	5.00746	+	12.0891i	0.374275	+	0.903580i	0.993015	+	0.117985i	$0.0376433\pi$
$179$	5.00746	+	12.0891i	0.374275	+	0.903580i	−0.618740	+	0.785596i	$0.712357\pi$
$180$	−7.65311	+	5.60562i	−0.570429	+	0.417818i
$181$	−0.523618	−	0.523618i	−0.0389202	−	0.0389202i	0.687379	−	0.726299i	$-0.258761\pi$
$181$	−0.523618	−	0.523618i	−0.0389202	−	0.0389202i	−0.726299	+	0.687379i	$0.758761\pi$
$182$	−2.15388	+	4.24749i	−0.159656	+	0.314845i
$183$	1.32208	−	1.32208i	0.0977306	−	0.0977306i
$184$	−4.34591	+	2.69795i	−0.320384	+	0.198895i
$185$		−	0.116257i		−	0.00854739i
$186$	11.1016	−	9.51883i	0.814010	−	0.697955i
$187$	−1.41068	−	2.78637i	−0.103159	−	0.203760i
$188$	8.30665	−	6.08432i	0.605825	−	0.443744i
$189$	−0.291399	−	0.703498i	−0.0211961	−	0.0511720i
$190$	−1.08818	−	1.26912i	−0.0789445	−	0.0920714i
$191$			18.0796i			1.30819i	0.756412	+	0.654096i	$0.226951\pi$
$191$			18.0796i			1.30819i	−0.756412	+	0.654096i	$0.773049\pi$
$192$	17.6738	+	8.74870i	1.27550	+	0.631383i
$193$	14.9358	−	6.18659i	1.07510	−	0.445321i	0.226312	−	0.974055i	$-0.427333\pi$
$193$	14.9358	−	6.18659i	1.07510	−	0.445321i	0.848788	+	0.528734i	$0.177333\pi$
$194$	−0.189939	+	2.47451i	−0.0136368	+	0.177660i
$195$	−2.93327	+	1.21500i	−0.210056	+	0.0870081i
$196$	18.2798	+	2.82287i	1.30570	+	0.201633i
$197$	−9.88663	−	9.88663i	−0.704393	−	0.704393i	0.260957	−	0.965350i	$-0.415962\pi$
$197$	−9.88663	−	9.88663i	−0.704393	−	0.704393i	−0.965350	+	0.260957i	$0.915962\pi$
$198$	1.49056	−	2.93942i	0.105930	−	0.208896i
$199$	1.07858	+	2.60391i	0.0764582	+	0.184587i	0.957487	−	0.288476i	$-0.0931485\pi$
$199$	1.07858	+	2.60391i	0.0764582	+	0.184587i	−0.881029	+	0.473062i	$0.843149\pi$
$200$	−4.32618	+	6.02764i	−0.305907	+	0.426218i
$201$	−15.1968	−	36.6884i	−1.07190	−	2.58780i
$202$	−3.84092	+	3.29331i	−0.270246	+	0.231717i
$203$	−4.34218	−	10.4829i	−0.304761	−	0.735759i
$204$	−9.20530	+	18.1238i	−0.644500	+	1.26892i
$205$	−0.901997	−	0.373619i	−0.0629982	−	0.0260947i
$206$	−8.71835	+	17.1928i	−0.607436	+	1.19788i
$207$	2.12930	−	5.14059i	0.147997	−	0.357296i
$208$	2.55774	+	2.15055i	0.177347	+	0.149114i
$209$	0.536586	+	0.222261i	0.0371164	+	0.0153741i
$210$	14.1018	+	16.4466i	0.973114	+	1.13492i
$211$		−	4.22538i		−	0.290887i	−0.989367	−	0.145444i	$-0.953539\pi$
$211$		−	4.22538i		−	0.290887i	0.989367	−	0.145444i	$-0.0464610\pi$
$212$	13.5198	−	3.30112i	0.928544	−	0.226722i
$213$	−12.7485	+	30.7776i	−0.873512	+	2.10884i
$214$	−2.92618	+	0.957029i	−0.200030	+	0.0654211i
$215$	14.0798	+	5.83204i	0.960233	+	0.397742i
$216$	−0.527234	+	0.0866413i	−0.0358737	+	0.00589519i
$217$	−11.9564	−	11.9564i	−0.811653	−	0.811653i
$218$	0.665571	+	2.03503i	0.0450782	+	0.137830i
$219$	12.0874	−	29.1816i	0.816792	−	1.97191i
$220$	−0.356447	+	2.30821i	−0.0240317	+	0.155619i
$221$	−2.24381	+	2.61346i	−0.150935	+	0.175801i
$222$	0.118895	−	0.234463i	0.00797970	−	0.0157361i
$223$	16.9102	−	16.9102i	1.13239	−	1.13239i	0.142610	−	0.989779i	$-0.454450\pi$
$223$	16.9102	−	16.9102i	1.13239	−	1.13239i	0.989779	−	0.142610i	$-0.0455495\pi$
$224$	8.52213	−	21.1499i	0.569409	−	1.41313i
$225$		−	8.07054i		−	0.538036i
$226$	−7.91441	−	9.23041i	−0.526459	−	0.613998i
$227$		−	21.1864i		−	1.40619i	−0.711097	−	0.703094i	$-0.751801\pi$
$227$		−	21.1864i		−	1.40619i	0.711097	−	0.703094i	$-0.248199\pi$
$228$	−0.896681	−	3.67237i	−0.0593842	−	0.243209i
$229$	−5.10600	−	2.11498i	−0.337414	−	0.139761i	0.207542	−	0.978226i	$-0.433454\pi$
$229$	−5.10600	−	2.11498i	−0.337414	−	0.139761i	−0.544956	+	0.838465i	$0.683454\pi$
$230$	−0.301775	+	3.93152i	−0.0198985	+	0.259237i
$231$	−6.95366	−	2.88030i	−0.457517	−	0.189510i
$232$	−7.85640	+	1.29106i	−0.515798	+	0.0847620i
$233$	−3.07294	+	1.27285i	−0.201315	+	0.0833873i	−0.481063	−	0.876686i	$-0.659749\pi$
$233$	−3.07294	+	1.27285i	−0.201315	+	0.0833873i	0.279748	+	0.960073i	$0.409749\pi$
$234$	−3.62428	−	0.278192i	−0.236927	−	0.0181860i
$235$		−	7.93709i		−	0.517759i
$236$	9.17773	−	2.24092i	0.597419	−	0.145872i
$237$	29.6651	+	12.2877i	1.92696	+	0.798172i
$238$	21.7090	+	9.00872i	1.40719	+	0.583948i
$239$			12.6246i			0.816619i	0.912844	+	0.408309i	$0.133882\pi$
$239$			12.6246i			0.816619i	−0.912844	+	0.408309i	$0.866118\pi$
$240$	13.4910	−	7.00587i	0.870841	−	0.452227i
$241$	−1.25258	+	3.02399i	−0.0806855	+	0.194792i	−0.959074	−	0.283155i	$-0.908619\pi$
$241$	−1.25258	+	3.02399i	−0.0806855	+	0.194792i	0.878389	+	0.477947i	$0.158619\pi$
$242$	4.58352	+	14.0144i	0.294640	+	0.900882i
$243$	−15.6775	+	15.6775i	−1.00571	+	1.00571i
$244$	−1.22378	+	0.896373i	−0.0783444	+	0.0573844i
$245$	10.0819	−	10.0819i	0.644108	−	0.644108i
$246$	−1.43702	−	1.67596i	−0.0916209	−	0.106856i
$247$		−	0.640570i		−	0.0407585i
$248$	−10.0802	+	6.25783i	−0.640095	+	0.397373i
$249$	−14.1311	+	34.1154i	−0.895521	+	2.16198i
$250$	5.16661	+	15.7973i	0.326765	+	0.999108i
$251$	−9.70676	−	23.4342i	−0.612685	−	1.47915i	−0.860039	−	0.510228i	$-0.829561\pi$
$251$	−9.70676	−	23.4342i	−0.612685	−	1.47915i	0.247354	−	0.968925i	$-0.420439\pi$
$252$	5.88335	+	24.0954i	0.370617	+	1.51787i
$253$	−0.524235	−	1.26561i	−0.0329584	−	0.0795685i
$254$	4.37581	+	2.21895i	0.274562	+	0.139229i
$255$	7.07773	+	13.9799i	0.443224	+	0.875458i
$256$	−13.0881	−	9.20337i	−0.818005	−	0.575211i
$257$	−12.9627	+	12.9627i	−0.808590	+	0.808590i	−0.984421	−	0.175830i	$-0.943739\pi$
$257$	−12.9627	+	12.9627i	−0.808590	+	0.808590i	0.175830	+	0.984421i	$0.443739\pi$
$258$	22.4312	+	26.1611i	1.39651	+	1.62872i
$259$	−0.280827	−	0.116322i	−0.0174497	−	0.00722791i
$260$	2.50242	−	0.611016i	0.155194	−	0.0378936i
$261$	6.12387	−	6.12387i	0.379058	−	0.379058i
$262$	−27.3624	−	13.8753i	−1.69046	−	0.857220i
$263$	−7.17476			−0.442415			−0.221207	−	0.975227i	$-0.571000\pi$
$263$	−7.17476			−0.442415			−0.221207	+	0.975227i	$0.571000\pi$
$264$	−3.07945	+	4.29058i	−0.189527	+	0.264067i
$265$	4.10538	−	9.91127i	0.252192	−	0.608845i
$266$	−4.15442	+	1.35873i	−0.254724	+	0.0833093i
$267$	2.13385			0.130589
$268$	7.64238	+	31.2995i	0.466832	+	1.91192i
$269$	6.67026	+	6.67026i	0.406693	+	0.406693i	0.880584	−	0.473891i	$-0.157151\pi$
$269$	6.67026	+	6.67026i	0.406693	+	0.406693i	−0.473891	+	0.880584i	$0.657151\pi$
$270$	−0.186275	+	0.367338i	−0.0113363	+	0.0223555i
$271$			9.65410i			0.586445i	0.956044	+	0.293222i	$0.0947276\pi$
$271$			9.65410i			0.586445i	−0.956044	+	0.293222i	$0.905272\pi$
$272$	9.62521	−	13.3924i	0.583614	−	0.812031i
$273$			8.30121i			0.502412i
$274$	10.5505	+	5.35008i	0.637377	+	0.323210i
$275$	−1.40500	−	1.40500i	−0.0847246	−	0.0847246i
$276$	−4.62933	+	7.62032i	−0.278653	+	0.458690i
$277$	−25.6337			−1.54018			−0.770089	−	0.637937i	$-0.779788\pi$
$277$	−25.6337			−1.54018			−0.770089	+	0.637937i	$0.779788\pi$
$278$	−3.59529	−	10.9928i	−0.215631	−	0.659307i
$279$	4.93887	−	11.9235i	0.295682	−	0.713841i
$280$	−9.27071	−	14.9334i	−0.554031	−	0.892444i
$281$	−8.74072			−0.521428			−0.260714	−	0.965416i	$-0.583958\pi$
$281$	−8.74072			−0.521428			−0.260714	+	0.965416i	$0.583958\pi$
$282$	8.11718	−	16.0072i	0.483371	−	0.953217i
$283$	−12.9721	+	12.9721i	−0.771109	+	0.771109i	−0.978300	−	0.207191i	$-0.933568\pi$
$283$	−12.9721	+	12.9721i	−0.771109	+	0.771109i	0.207191	+	0.978300i	$0.433568\pi$
$284$	14.0330	−	23.0997i	0.832708	−	1.37072i
$285$	−2.69219	−	1.11514i	−0.159472	−	0.0660553i
$286$	−0.679381	+	0.582520i	−0.0401726	+	0.0344451i
$287$	−1.80501	+	1.80501i	−0.106546	+	0.106546i
$288$	17.4032	−	0.168128i	1.02550	−	0.00990703i
$289$	13.7015	+	10.0632i	0.805971	+	0.591955i
$290$	−2.77572	+	5.47377i	−0.162996	+	0.321431i
$291$	1.65547	+	3.99666i	0.0970455	+	0.234288i
$292$	−13.3054	+	21.9019i	−0.778638	+	1.28171i
$293$	8.20759	+	19.8149i	0.479493	+	1.15760i	0.959847	+	0.280523i	$0.0905080\pi$
$293$	8.20759	+	19.8149i	0.479493	+	1.15760i	−0.480355	+	0.877074i	$0.659492\pi$
$294$	30.6434	−	10.0222i	1.78716	−	0.584504i
$295$	2.78688	−	6.72813i	0.162259	−	0.391727i
$296$	−0.124365	+	0.173277i	−0.00722857	+	0.0100715i
$297$		−	0.143090i		−	0.00830292i
$298$	15.1120	−	12.9575i	0.875417	−	0.750607i
$299$	−1.06835	+	1.06835i	−0.0617843	+	0.0617843i
$300$	−1.97374	+	12.7812i	−0.113954	+	0.737921i
$301$	28.1754	−	28.1754i	1.62400	−	1.62400i
$302$	−20.6408	+	6.75073i	−1.18775	+	0.388461i
$303$	−3.37493	+	8.14779i	−0.193884	+	0.468079i
$304$	0.264260	+	3.05564i	0.0151564	+	0.175253i
$305$			1.16933i			0.0669559i
$306$	−0.0116604	+	17.9397i	−0.000666581	+	1.02554i
$307$	−10.7137	−	4.43775i	−0.611462	−	0.253276i	0.0553912	−	0.998465i	$-0.482359\pi$
$307$	−10.7137	−	4.43775i	−0.611462	−	0.253276i	−0.666854	+	0.745189i	$0.732359\pi$
$308$	5.21899	+	3.17053i	0.297380	+	0.180658i
$309$			33.6012i			1.91150i
$310$	−0.699961	+	9.11907i	−0.0397551	+	0.517928i
$311$	−12.1016	+	5.01263i	−0.686217	+	0.284240i	−0.698423	−	0.715685i	$-0.746115\pi$
$311$	−12.1016	+	5.01263i	−0.686217	+	0.284240i	0.0122061	+	0.999926i	$0.496115\pi$
$312$	5.67168	+	1.32693i	0.321095	+	0.0751225i
$313$	21.1504	+	8.76080i	1.19549	+	0.495190i	0.889540	−	0.456857i	$-0.151025\pi$
$313$	21.1504	+	8.76080i	1.19549	+	0.495190i	0.305954	+	0.952046i	$0.401025\pi$
$314$	−25.6399	−	1.96807i	−1.44695	−	0.111065i
$315$	17.6642	+	7.31673i	0.995262	+	0.412251i
$316$	−22.2648	−	13.5258i	−1.25249	−	0.760887i
$317$		−	26.0699i		−	1.46423i	−0.681181	−	0.732115i	$-0.738534\pi$
$317$		−	26.0699i		−	1.46423i	0.681181	−	0.732115i	$-0.261466\pi$
$318$	18.4157	−	15.7902i	1.03270	−	0.885468i
$319$		−	2.13221i		−	0.119381i
$320$	−11.6850	+	3.94700i	−0.653209	+	0.220644i
$321$	−3.79464	+	3.79464i	−0.211796	+	0.211796i
$322$	9.19491	+	4.66269i	0.512412	+	0.259841i
$323$	−3.15232	+	0.239905i	−0.175400	+	0.0133487i
$324$	14.1409	−	10.3577i	0.785606	−	0.575427i
$325$	−0.838635	+	2.02465i	−0.0465191	+	0.112307i
$326$	29.9698	−	9.80183i	1.65987	−	0.542873i
$327$	2.63900	+	2.63900i	0.145937	+	0.145937i
$328$	0.944718	+	1.52177i	0.0521633	+	0.0840257i
$329$	−19.1726	−	7.94155i	−1.05702	−	0.437832i
$330$	1.26551	+	3.86939i	0.0696641	+	0.213003i
$331$	−1.19213	+	2.87805i	−0.0655251	+	0.158192i	−0.953250	−	0.302183i	$-0.902285\pi$
$331$	−1.19213	+	2.87805i	−0.0655251	+	0.158192i	0.887725	+	0.460374i	$0.152285\pi$
$332$	15.5550	−	25.6050i	0.853689	−	1.40525i
$333$		−	0.232004i		−	0.0127138i
$334$	−23.7259	+	20.3432i	−1.29822	+	1.11313i
$335$	22.9454	+	9.50431i	1.25364	+	0.519276i
$336$	−3.42457	−	39.5983i	−0.186826	−	2.16026i
$337$	−6.29759	+	15.2037i	−0.343051	+	0.828200i	0.654352	+	0.756190i	$0.272941\pi$
$337$	−6.29759	+	15.2037i	−0.343051	+	0.828200i	−0.997404	+	0.0720098i	$0.977059\pi$
$338$	−15.5167	−	7.86845i	−0.843999	−	0.427987i
$339$	−19.5806	−	8.11054i	−1.06347	−	0.440504i
$340$	−3.94408	−	12.0859i	−0.213898	−	0.655449i
$341$	−1.21595	−	2.93556i	−0.0658474	−	0.158970i
$342$	−2.17158	−	2.53267i	−0.117426	−	0.136951i
$343$	−3.46802	−	8.37253i	−0.187255	−	0.452074i
$344$	−14.7466	−	23.7542i	−0.795086	−	1.28074i
$345$	2.63022	+	6.34992i	0.141606	+	0.341868i
$346$	−3.15107	−	1.59789i	−0.169403	−	0.0859031i
$347$	−2.91386	−	2.91386i	−0.156424	−	0.156424i	0.624556	−	0.780980i	$-0.285280\pi$
$347$	−2.91386	−	2.91386i	−0.156424	−	0.156424i	−0.780980	+	0.624556i	$0.785280\pi$
$348$	−11.1959	+	8.20060i	−0.600165	+	0.439598i
$349$	19.0235	−	7.87980i	1.01831	−	0.421796i	0.189827	−	0.981817i	$-0.439207\pi$
$349$	19.0235	−	7.87980i	1.01831	−	0.421796i	0.828478	+	0.560022i	$0.189207\pi$
$350$	14.9097	+	1.14444i	0.796957	+	0.0611728i
$351$	−0.145803	+	0.0603937i	−0.00778240	+	0.00322358i
$352$	3.00046	−	3.05900i	0.159925	−	0.163045i
$353$			12.3795i			0.658895i	0.944174	+	0.329447i	$0.106862\pi$
$353$			12.3795i			0.658895i	−0.944174	+	0.329447i	$0.893138\pi$
$354$	12.5013	−	10.7189i	0.664435	−	0.569705i
$355$	−7.97308	−	19.2487i	−0.423167	−	1.02162i
$356$	−1.71098	−	0.264219i	−0.0906815	−	0.0140036i
$357$	40.8512	−	3.10895i	2.16207	−	0.164543i
$358$	−12.0453	−	14.0482i	−0.636614	−	0.742470i
$359$			21.2267i			1.12030i	0.828390	+	0.560151i	$0.189257\pi$
$359$			21.2267i			1.12030i	−0.828390	+	0.560151i	$0.810743\pi$
$360$	7.82262	−	10.8992i	0.412288	−	0.574439i
$361$	−13.0193	+	13.0193i	−0.685227	+	0.685227i
$362$	0.934010	+	0.473631i	0.0490905	+	0.0248935i
$363$	18.1737	+	18.1737i	0.953874	+	0.953874i
$364$	1.02788	−	6.65614i	0.0538755	−	0.348876i
$365$	7.55963	+	18.2506i	0.395689	+	0.955279i
$366$	−1.19586	+	2.35827i	−0.0625089	+	0.123269i
$367$	−17.0273	+	7.05292i	−0.888816	+	0.368159i	−0.779909	−	0.625893i	$-0.784735\pi$
$367$	−17.0273	+	7.05292i	−0.888816	+	0.368159i	−0.108906	+	0.994052i	$0.534735\pi$
$368$	4.65550	−	5.53697i	0.242684	−	0.288634i
$369$	−1.80004	−	0.745600i	−0.0937063	−	0.0388144i
$370$	0.0511082	+	0.156267i	0.00265699	+	0.00812393i
$371$	−19.8337	−	19.8337i	−1.02971	−	1.02971i
$372$	−10.7376	+	17.6752i	−0.556720	+	0.916415i
$373$	4.65148	+	11.2297i	0.240845	+	0.581450i	0.997367	−	0.0725174i	$-0.0231033\pi$
$373$	4.65148	+	11.2297i	0.240845	+	0.581450i	−0.756523	+	0.653968i	$0.773103\pi$
$374$	3.12109	+	3.12515i	0.161388	+	0.161598i
$375$	20.4857	+	20.4857i	1.05788	+	1.05788i
$376$	−8.49064	+	11.8300i	−0.437871	+	0.610083i
$377$	−2.17264	+	0.899936i	−0.111897	+	0.0463491i
$378$	0.700951	+	0.817505i	0.0360530	+	0.0420479i
$379$		−	11.7139i		−	0.601704i	−0.953671	−	0.300852i	$-0.902729\pi$
$379$		−	11.7139i		−	0.601704i	0.953671	−	0.300852i	$-0.0972710\pi$
$380$	2.02059	+	1.22751i	0.103654	+	0.0629697i
$381$	8.55199			0.438132
$382$	−7.94803	−	24.3016i	−0.406656	−	1.24338i
$383$	−19.0219	−	19.0219i	−0.971971	−	0.971971i	0.0276463	−	0.999618i	$-0.491199\pi$
$383$	−19.0219	−	19.0219i	−0.971971	−	0.971971i	−0.999618	+	0.0276463i	$0.991199\pi$
$384$	−27.6023	−	3.98990i	−1.40858	−	0.203609i
$385$	4.34892	−	1.80138i	0.221641	−	0.0918068i
$386$	−17.3562	+	14.8817i	−0.883407	+	0.757458i
$387$	28.0978	+	11.6385i	1.42829	+	0.591618i
$388$	−0.832525	−	3.40962i	−0.0422650	−	0.173097i
$389$	−10.7635	+	25.9855i	−0.545732	+	1.31751i	0.374893	+	0.927068i	$0.377679\pi$
$389$	−10.7635	+	25.9855i	−0.545732	+	1.31751i	−0.920626	+	0.390447i	$0.872321\pi$
$390$	3.40863	−	2.92265i	0.172603	−	0.147994i
$391$	5.65760	+	4.85736i	0.286117	+	0.245647i
$392$	−25.8117	+	4.24168i	−1.30369	+	0.214237i
$393$	−53.4766			−2.69754
$394$	17.6354	+	8.94281i	0.888459	+	0.450532i
$395$	−18.5530	+	7.68489i	−0.933501	+	0.386669i
$396$	−0.711331	+	4.60630i	−0.0357457	+	0.231475i
$397$	0.349589			0.0175454			0.00877269	−	0.999962i	$-0.497208\pi$
$397$	0.349589			0.0175454			0.00877269	+	0.999962i	$0.497208\pi$
$398$	−2.59448	−	3.02589i	−0.130050	−	0.151674i
$399$	−5.38740	+	5.38740i	−0.269707	+	0.269707i
$400$	3.16520	−	10.0039i	0.158260	−	0.500195i
$401$	15.9901	−	6.62333i	0.798509	−	0.330753i	0.0541502	−	0.998533i	$-0.482755\pi$
$401$	15.9901	−	6.62333i	0.798509	−	0.330753i	0.744359	+	0.667779i	$0.232755\pi$
$402$	36.5556	+	42.6340i	1.82323	+	2.12639i
$403$	−2.47802	+	2.47802i	−0.123439	+	0.123439i
$404$	3.71499	−	6.11523i	0.184828	−	0.304244i
$405$		−	13.5118i		−	0.671406i
$406$	10.4450	+	12.1818i	0.518376	+	0.604571i
$407$	−0.0403896	−	0.0403896i	−0.00200204	−	0.00200204i
$408$	4.40582	−	28.4079i	0.218121	−	1.40640i
$409$	−17.7984	+	17.7984i	−0.880075	+	0.880075i	−0.993542	−	0.113467i	$-0.963804\pi$
$409$	−17.7984	+	17.7984i	−0.880075	+	0.880075i	0.113467	+	0.993542i	$0.463804\pi$
$410$	1.37667	+	0.105670i	0.0679888	+	0.00521868i
$411$	20.6196			1.01709
$412$	4.16059	−	26.9424i	0.204978	−	1.32735i
$413$	−13.4638	−	13.4638i	−0.662511	−	0.662511i
$414$	−0.602227	+	7.84580i	−0.0295979	+	0.385600i
$415$	−8.83777	−	21.3363i	−0.433829	−	1.04736i
$416$	−4.38340	−	1.76625i	−0.214914	−	0.0865975i
$417$	−14.2554	−	14.2554i	−0.698089	−	0.698089i
$418$	−0.818961	−	0.0628618i	−0.0400567	−	0.00307467i
$419$			19.3830i			0.946923i	0.880815	+	0.473461i	$0.156996\pi$
$419$			19.3830i			0.946923i	−0.880815	+	0.473461i	$0.843004\pi$
$420$	−26.1850	−	15.9074i	−1.27770	−	0.776199i
$421$	3.44678	+	8.32125i	0.167986	+	0.405553i	0.985345	−	0.170576i	$-0.0545627\pi$
$421$	3.44678	+	8.32125i	0.167986	+	0.405553i	−0.817359	+	0.576129i	$0.804563\pi$
$422$	1.85754	+	5.67955i	0.0904235	+	0.276476i
$423$		−	15.8394i		−	0.770137i
$424$	−16.7214	+	10.3807i	−0.812064	+	0.504131i
$425$	10.2776	+	3.36876i	0.498537	+	0.163409i
$426$	3.60563	−	46.9741i	0.174694	−	2.27590i
$427$	2.82461	+	1.16999i	0.136692	+	0.0566198i
$428$	3.51251	−	2.57278i	0.169783	−	0.124360i
$429$	−0.596956	+	1.44118i	−0.0288213	+	0.0695807i
$430$	−21.4892	−	1.64947i	−1.03630	−	0.0795443i
$431$	10.4675	+	25.2707i	0.504200	+	1.21725i	0.947176	+	0.320714i	$0.103923\pi$
$431$	10.4675	+	25.2707i	0.504200	+	1.21725i	−0.442976	+	0.896534i	$0.646077\pi$
$432$	0.670593	−	0.348238i	0.0322639	−	0.0167546i
$433$	23.4390	−	23.4390i	1.12641	−	1.12641i	0.135648	−	0.990757i	$-0.456688\pi$
$433$	23.4390	−	23.4390i	1.12641	−	1.12641i	0.990757	−	0.135648i	$-0.0433116\pi$
$434$	21.3274	+	10.8150i	1.02375	+	0.519136i
$435$			10.6978i			0.512921i
$436$	−1.78926	−	2.44279i	−0.0856898	−	0.116989i
$437$	−1.38670			−0.0663348
$438$	−3.41866	+	44.5382i	−0.163350	+	2.12812i
$439$	−12.4237	−	29.9935i	−0.592951	−	1.43151i	−0.880640	−	0.473787i	$-0.842887\pi$
$439$	−12.4237	−	29.9935i	−0.592951	−	1.43151i	0.287689	−	0.957724i	$-0.407113\pi$
$440$	−0.535603	−	3.25928i	−0.0255339	−	0.155380i
$441$	20.1196	−	20.1196i	0.958075	−	0.958075i
$442$	1.86710	−	4.49930i	0.0888087	−	0.214010i
$443$	−10.8087	+	4.47710i	−0.513535	+	0.212713i	−0.624375	−	0.781125i	$-0.714646\pi$
$443$	−10.8087	+	4.47710i	−0.513535	+	0.212713i	0.110839	+	0.993838i	$0.464646\pi$
$444$	−0.0567393	+	0.367421i	−0.00269273	+	0.0174370i
$445$	−0.943660	+	0.943660i	−0.0447338	+	0.0447338i
$446$	−15.2959	+	30.1638i	−0.724280	+	1.42830i
$447$	13.2786	−	32.0573i	0.628055	−	1.51626i
$448$	−2.15726	+	32.1750i	−0.101921	+	1.52013i
$449$	1.26838	+	3.06213i	0.0598584	+	0.144511i	0.950979	−	0.309256i	$-0.100080\pi$
$449$	1.26838	+	3.06213i	0.0598584	+	0.144511i	−0.891120	+	0.453767i	$0.850080\pi$
$450$	3.54792	+	10.8480i	0.167251	+	0.511380i
$451$	−0.443170	+	0.183567i	−0.0208680	+	0.00864383i
$452$	14.6960	+	8.92777i	0.691240	+	0.419927i
$453$	−26.7667	+	26.7667i	−1.25761	+	1.25761i
$454$	9.31381	+	28.4776i	0.437119	+	1.33652i
$455$	−3.67108	−	3.67108i	−0.172103	−	0.172103i
$456$	2.81970	+	4.54203i	0.132045	+	0.212700i
$457$	−23.3251			−1.09110			−0.545550	−	0.838078i	$-0.683679\pi$
$457$	−23.3251			−1.09110			−0.545550	+	0.838078i	$0.683679\pi$
$458$	7.79301	+	0.598175i	0.364143	+	0.0279509i
$459$	0.351810	+	0.694896i	0.0164211	+	0.0324350i
$460$	−1.32272	−	5.41722i	−0.0616721	−	0.252579i
$461$	−27.1256	+	11.2358i	−1.26337	+	0.523303i	−0.910941	−	0.412536i	$-0.864643\pi$
$461$	−27.1256	+	11.2358i	−1.26337	+	0.523303i	−0.352425	+	0.935840i	$0.614643\pi$
$462$	10.6130	+	0.814631i	0.493761	+	0.0379001i
$463$	18.7476			0.871276			0.435638	−	0.900122i	$-0.356523\pi$
$463$	18.7476			0.871276			0.435638	+	0.900122i	$0.356523\pi$
$464$	9.99262	−	5.18916i	0.463896	−	0.240901i
$465$	6.10074	+	14.7285i	0.282915	+	0.683017i
$466$	3.57092	−	3.06181i	0.165420	−	0.141836i
$467$	−8.03474	−	19.3976i	−0.371803	−	0.897613i	−0.993445	−	0.114311i	$-0.963534\pi$
$467$	−8.03474	−	19.3976i	−0.371803	−	0.897613i	0.621642	−	0.783302i	$-0.286466\pi$
$468$	4.99387	−	1.21935i	0.230842	−	0.0563646i
$469$	45.9166	−	45.9166i	2.12023	−	2.12023i
$470$	3.48926	+	10.6686i	0.160947	+	0.492108i
$471$	−41.4118	+	17.1533i	−1.90816	+	0.790384i
$472$	−11.3511	+	7.04679i	−0.522477	+	0.324355i
$473$	6.91769	−	2.86540i	0.318076	−	0.131751i
$474$	−45.2762	−	3.47531i	−2.07961	−	0.159626i
$475$	−1.85824	+	0.769709i	−0.0852620	+	0.0353167i
$476$	−33.1406	−	2.56547i	−1.51900	−	0.117588i
$477$	8.19276	−	19.7791i	0.375121	−	0.905622i
$478$	−5.54996	−	16.9694i	−0.253849	−	0.776162i
$479$	−25.5205	−	10.5710i	−1.16606	−	0.482999i	−0.286174	−	0.958178i	$-0.592383\pi$
$479$	−25.5205	−	10.5710i	−1.16606	−	0.482999i	−0.879889	+	0.475179i	$0.842383\pi$
$480$	−15.0541	+	15.3478i	−0.687121	+	0.700527i
$481$	−0.0241083	+	0.0582026i	−0.00109924	+	0.00265381i
$482$	0.354264	−	4.61534i	0.0161363	−	0.210223i
$483$	17.9704			0.817679
$484$	−12.3219	−	16.8225i	−0.560085	−	0.764660i
$485$	−2.49957	−	1.03535i	−0.113499	−	0.0470130i
$486$	14.1808	−	27.9649i	0.643255	−	1.26851i
$487$	9.74037	−	23.5153i	0.441378	−	1.06558i	−0.534087	−	0.845429i	$-0.679345\pi$
$487$	9.74037	−	23.5153i	0.441378	−	1.06558i	0.975466	−	0.220152i	$-0.0706553\pi$
$488$	1.25088	−	1.74285i	0.0566249	−	0.0788951i
$489$	38.8644	−	38.8644i	1.75751	−	1.75751i
$490$	−9.11944	+	17.9837i	−0.411974	+	0.812421i
$491$	27.8616	+	11.5407i	1.25738	+	0.520822i	0.909103	−	0.416571i	$-0.136768\pi$
$491$	27.8616	+	11.5407i	1.25738	+	0.520822i	0.348273	+	0.937393i	$0.386768\pi$
$492$	2.66835	+	1.62101i	0.120298	+	0.0730810i
$493$	5.24238	+	10.3548i	0.236105	+	0.466355i
$494$	0.281604	+	0.861023i	0.0126699	+	0.0387393i
$495$	2.54053	+	2.54053i	0.114188	+	0.114188i
$496$	10.7983	−	12.8429i	0.484859	−	0.576662i
$497$	−54.4741			−2.44350
$498$	3.99667	−	52.0685i	0.179095	−	2.33325i
$499$	30.6467			1.37194			0.685968	−	0.727632i	$-0.259379\pi$
$499$	30.6467			1.37194			0.685968	+	0.727632i	$0.259379\pi$
$500$	−13.8894	−	18.9626i	−0.621153	−	0.848033i
$501$	−20.8473	+	50.3299i	−0.931391	+	2.24858i
$502$	23.3493	+	27.2319i	1.04213	+	1.21542i
$503$	4.09172	−	9.87829i	0.182441	−	0.440451i	−0.806028	−	0.591878i	$-0.798387\pi$
$503$	4.09172	−	9.87829i	0.182441	−	0.440451i	0.988468	+	0.151427i	$0.0483867\pi$
$504$	−18.5008	−	29.8014i	−0.824090	−	1.32746i
$505$	−2.11073	−	5.09574i	−0.0939261	−	0.226758i
$506$	1.26103	+	1.47072i	0.0560597	+	0.0653813i
$507$	−30.3256			−1.34681
$508$	−6.85722	−	1.05893i	−0.304240	−	0.0469825i
$509$	10.7563	−	25.9679i	0.476763	−	1.15101i	−0.484355	−	0.874871i	$-0.660946\pi$
$509$	10.7563	−	25.9679i	0.476763	−	1.15101i	0.961118	−	0.276136i	$-0.0890542\pi$
$510$	−15.6593	−	15.6797i	−0.693406	−	0.694308i
$511$	51.6494			2.28483
$512$	21.6383	+	6.61701i	0.956286	+	0.292433i
$513$	−0.133820	−	0.0554300i	−0.00590829	−	0.00244729i
$514$	11.7252	−	23.1224i	0.517177	−	1.01988i
$515$	−14.8596	−	14.8596i	−0.654792	−	0.654792i
$516$	−41.6517	−	25.3033i	−1.83361	−	1.11392i
$517$	−2.75748	−	2.75748i	−0.121274	−	0.121274i
$518$	0.428610	+	0.0328992i	0.0188321	+	0.00144551i
$519$	−6.15839			−0.270324
$520$	−3.09502	+	1.92140i	−0.135726	+	0.0842588i
$521$	22.7217	+	9.41163i	0.995455	+	0.412331i	0.820129	−	0.572179i	$-0.193902\pi$
$521$	22.7217	+	9.41163i	0.995455	+	0.412331i	0.175327	+	0.984510i	$0.443902\pi$
$522$	−5.53926	+	10.9235i	−0.242447	+	0.478110i
$523$	24.6520	−	10.2112i	1.07796	−	0.446504i	0.228164	−	0.973623i	$-0.426728\pi$
$523$	24.6520	−	10.2112i	1.07796	−	0.446504i	0.849792	+	0.527119i	$0.176728\pi$
$524$	42.8790	+	6.62162i	1.87318	+	0.289267i
$525$	24.0811	−	9.97472i	1.05099	−	0.435333i
$526$	9.64396	−	3.15413i	0.420497	−	0.137526i
$527$	13.1227	+	11.2665i	0.571632	+	0.490778i
$528$	2.25305	−	7.12095i	0.0980512	−	0.309900i
$529$	−13.9507	−	13.9507i	−0.606552	−	0.606552i
$530$	−1.16112	+	15.1270i	−0.0504358	+	0.657076i
$531$	5.56155	−	13.4268i	0.241351	−	0.582672i
$532$	4.98685	−	3.65268i	0.216207	−	0.158364i
$533$	0.374096	+	0.374096i	0.0162039	+	0.0162039i
$534$	−2.86821	+	0.938068i	−0.124120	+	0.0405942i
$535$		−	3.35624i		−	0.145103i
$536$	−24.0322	−	38.7115i	−1.03803	−	1.67208i
$537$	−29.8006	−	12.3438i	−1.28599	−	0.532674i
$538$	−11.8982	−	6.03349i	−0.512967	−	0.260122i
$539$		−	7.00522i		−	0.301736i
$540$	0.0888947	−	0.575647i	0.00382542	−	0.0247719i
$541$	0.191058	−	0.191058i	0.00821422	−	0.00821422i	−0.702988	−	0.711202i	$-0.748151\pi$
$541$	0.191058	−	0.191058i	0.00821422	−	0.00821422i	0.711202	+	0.702988i	$0.248151\pi$
$542$	−4.24408	−	12.9766i	−0.182299	−	0.557391i
$543$	1.82541			0.0783359
$544$	−7.05026	+	22.2327i	−0.302277	+	0.953220i
$545$	−2.33411			−0.0999824
$546$	−3.64933	−	11.1581i	−0.156177	−	0.477521i
$547$	26.2001	−	26.2001i	1.12024	−	1.12024i	0.128531	−	0.991706i	$-0.458974\pi$
$547$	26.2001	−	26.2001i	1.12024	−	1.12024i	0.991706	−	0.128531i	$-0.0410260\pi$
$548$	−16.5334	−	2.55318i	−0.706271	−	0.109066i
$549$			2.33354i			0.0995931i
$550$	2.50618	+	1.27087i	0.106864	+	0.0541902i
$551$	−1.99407	−	0.825971i	−0.0849503	−	0.0351875i
$552$	2.87252	−	12.2780i	0.122262	−	0.522585i
$553$			52.5052i			2.23275i
$554$	34.4555	−	11.2689i	1.46387	−	0.478770i
$555$	0.202645	+	0.202645i	0.00860180	+	0.00860180i
$556$	9.66521	+	13.1955i	0.409896	+	0.559614i
$557$	8.04413	−	19.4202i	0.340841	−	0.822862i	−0.656791	−	0.754073i	$-0.728086\pi$
$557$	8.04413	−	19.4202i	0.340841	−	0.822862i	0.997631	−	0.0687891i	$-0.0219135\pi$
$558$	−1.39685	+	18.1982i	−0.0591335	+	0.770389i
$559$	−5.83947	−	5.83947i	−0.246983	−	0.246983i
$560$	19.0262	+	15.9973i	0.804003	+	0.676007i
$561$	7.31577	+	2.39794i	0.308872	+	0.101241i
$562$	11.7488	−	3.84254i	0.495595	−	0.162088i
$563$	25.8690	−	10.7153i	1.09025	−	0.451595i	0.236154	−	0.971716i	$-0.424113\pi$
$563$	25.8690	−	10.7153i	1.09025	−	0.451595i	0.854093	+	0.520120i	$0.174113\pi$
$564$	−3.87370	+	25.0846i	−0.163112	+	1.05625i
$565$	12.2460	−	5.07244i	0.515191	−	0.213399i
$566$	11.7337	−	23.1391i	0.493204	−	0.972609i
$567$	−32.6386	−	13.5194i	−1.37069	−	0.567760i
$568$	−8.70756	+	37.2186i	−0.365361	+	1.56166i
$569$	37.1670			1.55812			0.779061	−	0.626948i	$-0.215696\pi$
$569$	37.1670			1.55812			0.779061	+	0.626948i	$0.215696\pi$
$570$	4.10894	+	0.315394i	0.172105	+	0.0132104i
$571$	7.99531	+	7.99531i	0.334593	+	0.334593i	0.854328	−	0.519735i	$-0.173969\pi$
$571$	7.99531	+	7.99531i	0.334593	+	0.334593i	−0.519735	+	0.854328i	$0.673969\pi$
$572$	0.657106	−	1.08166i	0.0274750	−	0.0452265i
$573$	−31.5141	−	31.5141i	−1.31652	−	1.31652i
$574$	1.63269	−	3.21970i	0.0681473	−	0.134388i
$575$	4.38293	+	1.81547i	0.182781	+	0.0757102i
$576$	−23.3187	+	7.87670i	−0.971611	+	0.328196i
$577$	37.3310			1.55411			0.777055	−	0.629433i	$-0.216713\pi$
$577$	37.3310			1.55411			0.777055	+	0.629433i	$0.216713\pi$
$578$	−22.8408	−	7.50313i	−0.950053	−	0.312089i
$579$	−15.2505	+	36.8179i	−0.633788	+	1.53010i
$580$	1.32463	−	8.57781i	0.0550025	−	0.356174i
$581$	−60.3819			−2.50507
$582$	−3.98219	−	4.64435i	−0.165067	−	0.192514i
$583$	−2.01706	−	4.86961i	−0.0835381	−	0.201679i
$584$	8.25603	−	35.2887i	0.341637	−	1.46026i
$585$	1.51643	−	3.66097i	0.0626965	−	0.151363i
$586$	−19.7431	−	23.0260i	−0.815581	−	0.951195i
$587$	9.90700	−	23.9176i	0.408906	−	0.987186i	−0.576521	−	0.817083i	$-0.695590\pi$
$587$	9.90700	−	23.9176i	0.408906	−	0.987186i	0.985426	−	0.170103i	$-0.0544101\pi$
$588$	−36.7835	+	26.9426i	−1.51693	+	1.11109i
$589$	−3.21642			−0.132530
$590$	−0.788210	+	10.2688i	−0.0324501	+	0.422759i
$591$	34.4663			1.41775
$592$	0.0909902	−	0.287583i	0.00373968	−	0.0118196i
$593$	−5.57966	−	5.57966i	−0.229129	−	0.229129i	0.583200	−	0.812329i	$-0.301801\pi$
$593$	−5.57966	−	5.57966i	−0.229129	−	0.229129i	−0.812329	+	0.583200i	$0.801801\pi$
$594$	0.0629043	+	0.192334i	0.00258099	+	0.00789157i
$595$	−16.6909	+	19.4407i	−0.684261	+	0.796990i
$596$	−14.6166	+	24.0603i	−0.598718	+	0.985547i
$597$	−6.41886	−	2.65878i	−0.262707	−	0.108817i
$598$	0.966362	−	1.90569i	0.0395175	−	0.0779293i
$599$	−16.8441	+	16.8441i	−0.688231	+	0.688231i	−0.961841	−	0.273610i	$-0.911782\pi$
$599$	−16.8441	+	16.8441i	−0.688231	+	0.688231i	0.273610	+	0.961841i	$0.411782\pi$
$600$	−2.96577	−	18.0475i	−0.121077	−	0.736786i
$601$	−14.0123	+	33.8288i	−0.571575	+	1.37990i	0.328639	+	0.944456i	$0.393410\pi$
$601$	−14.0123	+	33.8288i	−0.571575	+	1.37990i	−0.900214	+	0.435448i	$0.856590\pi$
$602$	−25.4856	+	50.2582i	−1.03872	+	2.04837i
$603$	45.7902	+	18.9669i	1.86472	+	0.772393i
$604$	24.7766	−	18.1480i	1.00815	−	0.738431i
$605$	−16.0741			−0.653505
$606$	0.954525	−	12.4355i	0.0387749	−	0.505159i
$607$	−16.1315	+	38.9449i	−0.654758	+	1.58073i	0.151035	+	0.988528i	$0.451739\pi$
$607$	−16.1315	+	38.9449i	−0.654758	+	1.58073i	−0.805793	+	0.592197i	$0.798261\pi$
$608$	−1.69851	−	3.99106i	−0.0688835	−	0.161859i
$609$	25.8413	+	10.7038i	1.04714	+	0.433741i
$610$	−0.514055	−	1.57176i	−0.0208135	−	0.0636387i
$611$	−1.64592	+	3.97361i	−0.0665869	+	0.160755i
$612$	−7.87086	−	24.1188i	−0.318161	−	0.974943i
$613$	−27.9781	+	11.5889i	−1.13002	+	0.468071i	−0.867789	−	0.496933i	$-0.834459\pi$
$613$	−27.9781	+	11.5889i	−1.13002	+	0.468071i	−0.262234	+	0.965004i	$0.584459\pi$
$614$	16.3517	+	1.25512i	0.659901	+	0.0506527i
$615$	2.22350	−	0.921003i	0.0896600	−	0.0371384i
$616$	−8.40892	−	1.96732i	−0.338805	−	0.0792657i
$617$	13.9895	−	5.79463i	0.563195	−	0.233283i	−0.0828765	−	0.996560i	$-0.526411\pi$
$617$	13.9895	−	5.79463i	0.563195	−	0.233283i	0.646072	+	0.763277i	$0.276411\pi$
$618$	−14.7715	−	45.1650i	−0.594199	−	1.81680i
$619$	−8.47216	+	8.47216i	−0.340525	+	0.340525i	−0.856565	−	0.516040i	$-0.827406\pi$
$619$	−8.47216	+	8.47216i	−0.340525	+	0.340525i	0.516040	+	0.856565i	$0.327406\pi$
$620$	−3.06802	−	12.5651i	−0.123215	−	0.504627i
$621$	0.130739	+	0.315633i	0.00524639	+	0.0126659i
$622$	14.0627	−	12.0577i	0.563863	−	0.483472i
$623$	1.33529	+	3.22366i	0.0534971	+	0.129153i
$624$	−8.20692	+	0.709758i	−0.328540	+	0.0284130i
$625$	−5.00311			−0.200124
$626$	−32.2807	−	2.47780i	−1.29020	−	0.0990330i
$627$	−1.32273	+	0.547892i	−0.0528247	+	0.0218807i
$628$	35.3291	−	8.62629i	1.40979	−	0.344227i
$629$	0.295451	+	0.0968419i	0.0117804	+	0.00386134i
$630$	−26.9598	−	2.06938i	−1.07410	−	0.0824461i
$631$	−44.7395			−1.78105			−0.890527	−	0.454931i	$-0.849664\pi$
$631$	−44.7395			−1.78105			−0.890527	+	0.454931i	$0.849664\pi$
$632$	35.8734	+	8.39283i	1.42697	+	0.333849i
$633$	7.36517	+	7.36517i	0.292739	+	0.292739i
$634$	11.4607	+	35.0418i	0.455161	+	1.39169i
$635$	−3.78198	+	3.78198i	−0.150083	+	0.150083i
$636$	−17.8119	+	29.3202i	−0.706289	+	1.16262i
$637$	−7.13806	+	2.95668i	−0.282820	+	0.117148i
$638$	0.937347	+	2.86600i	0.0371099	+	0.113466i
$639$	−15.9112	−	38.4130i	−0.629437	−	1.51960i
$640$	13.9712	−	10.4422i	0.552259	−	0.412766i
$641$	−7.35376	+	17.7535i	−0.290456	+	0.701223i	−0.999994	−	0.00344420i	$-0.998904\pi$
$641$	−7.35376	+	17.7535i	−0.290456	+	0.701223i	0.709538	+	0.704667i	$0.248904\pi$
$642$	3.43239	−	6.76874i	0.135465	−	0.267141i
$643$	16.1882	−	16.1882i	0.638401	−	0.638401i	−0.311760	−	0.950161i	$-0.600918\pi$
$643$	16.1882	−	16.1882i	0.638401	−	0.638401i	0.950161	+	0.311760i	$0.100918\pi$
$644$	−14.4091	−	2.22514i	−0.567799	−	0.0876828i
$645$	−34.7078	+	14.3765i	−1.36662	+	0.566072i
$646$	4.13173	−	1.70827i	0.162561	−	0.0672111i
$647$	29.5524	−	29.5524i	1.16182	−	1.16182i	0.177748	−	0.984076i	$-0.443119\pi$
$647$	29.5524	−	29.5524i	1.16182	−	1.16182i	0.984076	−	0.177748i	$-0.0568812\pi$
$648$	−14.4541	+	20.1388i	−0.567811	+	0.791128i
$649$	−1.36925	−	3.30567i	−0.0537479	−	0.129759i
$650$	0.237190	−	3.09010i	0.00930336	−	0.121204i
$651$	41.6818			1.63364
$652$	−35.9749	+	26.3503i	−1.40888	+	1.03196i
$653$			38.1636i			1.49346i	0.665128	+	0.746729i	$0.268377\pi$
$653$			38.1636i			1.49346i	−0.665128	+	0.746729i	$0.731623\pi$
$654$	−4.70736	−	2.38707i	−0.184072	−	0.0933419i
$655$	23.6492	−	23.6492i	0.924050	−	0.924050i
$656$	−1.93883	−	1.63018i	−0.0756987	−	0.0636477i
$657$	15.0861	+	36.4211i	0.588566	+	1.42092i
$658$	29.2621	+	2.24610i	1.14075	+	0.0875619i
$659$	3.06585	−	7.40161i	0.119428	−	0.288326i	−0.852848	−	0.522159i	$-0.825127\pi$
$659$	3.06585	−	7.40161i	0.119428	−	0.288326i	0.972277	+	0.233833i	$0.0751269\pi$
$660$	−3.40207	−	4.64470i	−0.132425	−	0.180795i
$661$	4.46230	+	1.84834i	0.173563	+	0.0718922i	0.467773	−	0.883849i	$-0.345056\pi$
$661$	4.46230	+	1.84834i	0.173563	+	0.0718922i	−0.294210	+	0.955741i	$0.595056\pi$
$662$	0.337167	−	4.39260i	0.0131044	−	0.170723i
$663$	−0.644343	−	8.46659i	−0.0250242	−	0.328815i
$664$	−9.65191	+	41.2551i	−0.374567	+	1.60101i
$665$		−	4.76499i		−	0.184778i
$666$	0.101992	+	0.311849i	0.00395212	+	0.0120839i
$667$	1.94817	+	4.70330i	0.0754335	+	0.182112i
$668$	22.9480	−	37.7745i	0.887883	−	1.46154i
$669$			58.9515i			2.27920i
$670$	−35.0203	−	2.68809i	−1.35295	−	0.103850i
$671$	0.406246	+	0.406246i	0.0156829	+	0.0156829i
$672$	22.0111	+	51.7205i	0.849096	+	1.99516i
$673$	7.59891	+	18.3454i	0.292917	+	0.707163i	1.00000		3.29429e-5i	$1.04860e-5\pi$
$673$	7.59891	+	18.3454i	0.292917	+	0.707163i	−0.707083	+	0.707130i	$0.749990\pi$
$674$	1.78114	−	23.2046i	0.0686068	−	0.893808i
$675$	0.350394	+	0.350394i	0.0134867	+	0.0134867i
$676$	24.3159	+	3.75500i	0.935227	+	0.144423i
$677$	1.72849			0.0664311			0.0332156	−	0.999448i	$-0.489425\pi$
$677$	1.72849			0.0664311			0.0332156	+	0.999448i	$0.489425\pi$
$678$	29.8847	+	2.29389i	1.14772	+	0.0880963i
$679$	−5.00194	+	5.00194i	−0.191957	+	0.191957i
$680$	10.6146	+	14.5114i	0.407050	+	0.556486i
$681$	36.9294	+	36.9294i	1.41514	+	1.41514i
$682$	2.92494	+	3.41129i	0.112002	+	0.130625i
$683$			34.3723i			1.31522i	0.753358	+	0.657610i	$0.228433\pi$
$683$			34.3723i			1.31522i	−0.753358	+	0.657610i	$0.771567\pi$
$684$	4.03232	+	2.44963i	0.154180	+	0.0936639i
$685$	−9.11871	+	9.11871i	−0.348408	+	0.348408i
$686$	8.34222	+	9.72935i	0.318507	+	0.371468i
$687$	12.5867	−	5.21359i	0.480213	−	0.198911i
$688$	30.2644	+	25.4463i	1.15382	+	0.970133i
$689$	−4.11062	+	4.11062i	−0.156602	+	0.156602i
$690$	−6.32692	−	7.37896i	−0.240862	−	0.280912i
$691$	−6.08935			−0.231650			−0.115825	−	0.993270i	$-0.536951\pi$
$691$	−6.08935			−0.231650			−0.115825	+	0.993270i	$0.536951\pi$
$692$	4.93797	+	0.762550i	0.187713	+	0.0289878i
$693$	8.67876	−	3.59486i	0.329679	−	0.136557i
$694$	5.19763	+	2.63569i	0.197299	+	0.100049i
$695$	12.6084			0.478265
$696$	11.4439	−	15.9447i	0.433780	−	0.604383i
$697$	1.70086	−	1.98107i	0.0644248	−	0.0750385i
$698$	−22.1064	+	18.9546i	−0.836739	+	0.717443i
$699$	3.13768	−	7.57504i	0.118678	−	0.286514i
$700$	−20.5440	+	5.01621i	−0.776490	+	0.189595i
$701$	22.9794	+	9.51837i	0.867919	+	0.359504i	0.771800	−	0.635866i	$-0.219357\pi$
$701$	22.9794	+	9.51837i	0.867919	+	0.359504i	0.0961195	+	0.995370i	$0.469357\pi$
$702$	0.169432	−	0.145275i	0.00639478	−	0.00548306i
$703$	−0.0534190	+	0.0221269i	−0.00201474	+	0.000834531i
$704$	−2.68829	+	5.43080i	−0.101319	+	0.204681i
$705$	13.8350	+	13.8350i	0.521055	+	0.521055i
$706$	−5.44220	−	16.6399i	−0.204820	−	0.626252i
$707$	−14.4210			−0.542358
$708$	−12.0914	+	19.9036i	−0.454422	+	0.748023i
$709$			31.7728i			1.19325i	0.802519	+	0.596626i	$0.203492\pi$
$709$			31.7728i			1.19325i	−0.802519	+	0.596626i	$0.796508\pi$
$710$	19.1790	+	22.3681i	0.719776	+	0.839459i
$711$	−37.0246	+	15.3361i	−1.38853	+	0.575148i
$712$	2.41596	−	0.397019i	0.0905420	−	0.0148789i
$713$	5.36438	+	5.36438i	0.200898	+	0.200898i
$714$	−53.5434	+	22.1376i	−2.00381	+	0.828480i
$715$	−0.373344	−	0.901333i	−0.0139623	−	0.0337079i
$716$	22.3665	+	13.5876i	0.835874	+	0.507792i
$717$	−22.0057	−	22.0057i	−0.821817	−	0.821817i
$718$	−9.33155	−	28.5319i	−0.348250	−	1.06480i
$719$	19.6046	+	8.12049i	0.731128	+	0.302843i	0.717016	−	0.697057i	$-0.245508\pi$
$719$	19.6046	+	8.12049i	0.731128	+	0.302843i	0.0141128	+	0.999900i	$0.495508\pi$
$720$	−5.72333	+	18.0891i	−0.213296	+	0.674141i
$721$	−50.7623	+	21.0264i	−1.89049	+	0.783065i
$722$	11.7764	−	23.2234i	0.438273	−	0.864284i
$723$	−3.08770	−	7.45438i	−0.114833	−	0.277231i
$724$	−1.46367	−	0.226028i	−0.0543967	−	0.00840025i
$725$	5.22128	+	5.22128i	0.193913	+	0.193913i
$726$	−32.4177	−	16.4388i	−1.20313	−	0.610101i
$727$	4.33309	−	4.33309i	0.160706	−	0.160706i	−0.622174	−	0.782879i	$-0.713750\pi$
$727$	4.33309	−	4.33309i	0.160706	−	0.160706i	0.782879	+	0.622174i	$0.213750\pi$
$728$	1.54451	+	9.39871i	0.0572432	+	0.348340i
$729$		−	28.3613i		−	1.05042i
$730$	−18.1845	−	21.2082i	−0.673038	−	0.784950i
$731$	−26.5497	+	30.9237i	−0.981977	+	1.14375i
$732$	0.570694	−	3.69559i	0.0210935	−	0.136593i
$733$	4.36551	+	10.5393i	0.161244	+	0.389277i	0.983766	−	0.179456i	$-0.0574338\pi$
$733$	4.36551	+	10.5393i	0.161244	+	0.389277i	−0.822522	+	0.568733i	$0.807434\pi$
$734$	19.7866	−	16.9656i	0.730338	−	0.626212i
$735$			35.1470i			1.29642i
$736$	−3.82356	+	9.48914i	−0.140938	+	0.349774i
$737$	11.2736	−	4.66966i	0.415267	−	0.172009i
$738$	2.74730	+	0.210877i	0.101129	+	0.00776249i
$739$	−2.10988	+	0.873939i	−0.0776130	+	0.0321484i	−0.421152	−	0.906990i	$-0.638374\pi$
$739$	−2.10988	+	0.873939i	−0.0776130	+	0.0321484i	0.343539	+	0.939138i	$0.388374\pi$
$740$	−0.137394	−	0.187578i	−0.00505071	−	0.00689552i
$741$	1.11656	+	1.11656i	0.0410180	+	0.0410180i
$742$	35.3786	+	17.9403i	1.29879	+	0.658608i
$743$	5.59365	+	13.5043i	0.205211	+	0.495423i	0.992657	−	0.120960i	$-0.0385972\pi$
$743$	5.59365	+	13.5043i	0.205211	+	0.495423i	−0.787446	+	0.616383i	$0.788597\pi$
$744$	6.66274	−	28.4785i	0.244268	−	1.04407i
$745$	8.30461	+	20.0491i	0.304257	+	0.734542i
$746$	−11.1890	−	13.0495i	−0.409659	−	0.477776i
$747$	−17.6368	−	42.5790i	−0.645296	−	1.55788i
$748$	−5.56907	−	2.82859i	−0.203625	−	0.103424i
$749$	−8.10722	−	3.35812i	−0.296231	−	0.122703i
$750$	−36.5417	−	18.5301i	−1.33431	−	0.676623i
$751$	−4.84182	+	11.6892i	−0.176681	+	0.426545i	−0.987267	−	0.159075i	$-0.949149\pi$
$751$	−4.84182	+	11.6892i	−0.176681	+	0.426545i	0.810586	+	0.585620i	$0.199149\pi$
$752$	6.21208	−	19.6338i	0.226531	−	0.715972i
$753$	57.7672	+	23.9280i	2.10516	+	0.871984i
$754$	2.52473	−	2.16477i	0.0919451	−	0.0788363i
$755$		−	23.6743i		−	0.861598i
$756$	−1.30157	−	0.790701i	−0.0473376	−	0.0287575i
$757$	5.55091	−	13.4011i	0.201751	−	0.487071i	−0.790328	−	0.612684i	$-0.790090\pi$
$757$	5.55091	−	13.4011i	0.201751	−	0.487071i	0.992079	+	0.125613i	$0.0400898\pi$
$758$	5.14961	+	15.7453i	0.187042	+	0.571894i
$759$	3.11985	+	1.29228i	0.113243	+	0.0469069i
$760$	−3.25561	−	0.761672i	−0.118093	−	0.0276287i
$761$	−28.7851	−	28.7851i	−1.04346	−	1.04346i	−0.999012	−	0.0444475i	$-0.985847\pi$
$761$	−28.7851	−	28.7851i	−1.04346	−	1.04346i	−0.0444475	−	0.999012i	$-0.514153\pi$
$762$	−11.4952	+	3.75957i	−0.416426	+	0.136195i
$763$	−2.33542	+	5.63821i	−0.0845480	+	0.204117i
$764$	21.3667	+	29.1710i	0.773019	+	1.05537i
$765$	−18.5840	−	6.09141i	−0.671906	−	0.220235i
$766$	33.9305	+	17.2060i	1.22596	+	0.621677i
$767$	−2.79044	+	2.79044i	−0.100757	+	0.100757i
$768$	38.8557	−	6.77135i	1.40208	−	0.244340i
$769$		−	22.5206i		−	0.812113i	−0.913848	−	0.406056i	$-0.866904\pi$
$769$		−	22.5206i		−	0.812113i	0.913848	−	0.406056i	$-0.133096\pi$
$770$	−5.05369	+	4.33317i	−0.182122	+	0.156157i
$771$		−	45.1899i		−	1.62748i
$772$	16.7871	−	27.6332i	0.604182	−	0.994542i
$773$	−14.5916	−	6.04405i	−0.524824	−	0.217389i	0.104510	−	0.994524i	$-0.466672\pi$
$773$	−14.5916	−	6.04405i	−0.524824	−	0.217389i	−0.629335	+	0.777135i	$0.716672\pi$
$774$	−42.8841	−	3.29170i	−1.54144	−	0.118318i
$775$	10.1661	+	4.21094i	0.365177	+	0.151261i
$776$	2.61795	+	4.21705i	0.0939790	+	0.151383i
$777$	0.692261	−	0.286744i	0.0248347	−	0.0102869i
$778$	3.04423	−	39.6601i	0.109141	−	1.42189i
$779$			0.485569i			0.0173973i
$780$	−3.29687	+	5.42696i	−0.118047	+	0.194316i
$781$	−9.45729	−	3.91734i	−0.338408	−	0.140173i
$782$	−9.74002	−	4.04187i	−0.348303	−	0.144537i
$783$			0.531753i			0.0190033i
$784$	32.8301	−	17.0486i	1.17250	−	0.608880i
$785$	10.7279	−	25.8995i	0.382896	−	0.924394i
$786$	71.8805	−	23.5090i	2.56389	−	0.838540i
$787$	−26.1703	+	26.1703i	−0.932871	+	0.932871i	−0.997884	−	0.0650139i	$-0.979291\pi$
$787$	−26.1703	+	26.1703i	−0.932871	+	0.932871i	0.0650139	+	0.997884i	$0.479291\pi$
$788$	−27.6360	−	4.26771i	−0.984493	−	0.152031i
$789$	12.5062	−	12.5062i	0.445231	−	0.445231i
$790$	21.5596	−	18.4858i	0.767056	−	0.657695i
$791$		−	34.6562i		−	1.23223i
$792$	−1.06886	−	6.50427i	−0.0379802	−	0.231119i
$793$	0.242486	−	0.585412i	0.00861092	−	0.0207886i
$794$	−0.469901	+	0.153684i	−0.0166761	+	0.00545405i
$795$	10.1201	+	24.4321i	0.358923	+	0.866517i
$796$	4.81760	+	2.92668i	0.170755	+	0.103734i
$797$	−8.05787	−	19.4534i	−0.285425	−	0.689076i	0.714520	−	0.699615i	$-0.246645\pi$
$797$	−8.05787	−	19.4534i	−0.285425	−	0.689076i	−0.999944	+	0.0105393i	$0.996645\pi$
$798$	4.87310	−	9.60986i	0.172506	−	0.340185i
$799$	20.1710	+	6.61159i	0.713599	+	0.233901i
$800$	0.143348	+	14.8382i	0.00506811	+	0.524610i
$801$	−1.88318	+	1.88318i	−0.0665389	+	0.0665389i
$802$	−18.5814	+	15.9322i	−0.656133	+	0.562587i
$803$	8.96688	+	3.71420i	0.316434	+	0.131071i
$804$	−67.8786	−	41.2361i	−2.39389	−	1.45429i
$805$	−7.94711	+	7.94711i	−0.280099	+	0.280099i
$806$	2.24146	−	4.42020i	0.0789519	−	0.155695i
$807$	−23.2536			−0.818564
$808$	−2.30517	+	9.85295i	−0.0810955	+	0.346626i
$809$	−2.55333	+	6.16429i	−0.0897704	+	0.216725i	−0.962388	−	0.271680i	$-0.912421\pi$
$809$	−2.55333	+	6.16429i	−0.0897704	+	0.216725i	0.872617	+	0.488404i	$0.162421\pi$
$810$	5.93997	+	18.1619i	0.208709	+	0.638143i
$811$	0.0944107			0.00331521			0.00165760	−	0.999999i	$-0.499472\pi$
$811$	0.0944107			0.00331521			0.00165760	+	0.999999i	$0.499472\pi$
$812$	−19.3949	−	11.7824i	−0.680628	−	0.413480i
$813$	−16.8278	−	16.8278i	−0.590178	−	0.590178i
$814$	0.0720455	+	0.0365338i	0.00252519	+	0.00128051i
$815$			34.3744i			1.20408i
$816$	6.56643	+	40.1214i	0.229871	+	1.40453i
$817$		−	7.57952i		−	0.265174i
$818$	16.0993	−	31.7482i	0.562899	−	1.11005i
$819$	−7.32606	−	7.32606i	−0.255993	−	0.255993i
$820$	−1.89690	+	0.463166i	−0.0662427	+	0.0161744i
$821$	−30.6579			−1.06997			−0.534984	−	0.844862i	$-0.679682\pi$
$821$	−30.6579			−1.06997			−0.534984	+	0.844862i	$0.679682\pi$
$822$	−27.7159	+	9.06468i	−0.966703	+	0.316167i
$823$	7.67500	−	18.5291i	0.267534	−	0.645884i	−0.731832	−	0.681485i	$-0.761335\pi$
$823$	7.67500	−	18.5291i	0.267534	−	0.645884i	0.999366	+	0.0356010i	$0.0113345\pi$
$824$	6.25177	+	38.0436i	0.217791	+	1.32531i
$825$	4.89804			0.170528
$826$	24.0163	+	12.1785i	0.835633	+	0.423744i
$827$	−1.56174	+	1.56174i	−0.0543069	+	0.0543069i	−0.733739	−	0.679432i	$-0.762226\pi$
$827$	−1.56174	+	1.56174i	−0.0543069	+	0.0543069i	0.679432	+	0.733739i	$0.262226\pi$
$828$	−2.63964	−	10.8107i	−0.0917338	−	0.375697i
$829$	−19.8861	−	8.23710i	−0.690673	−	0.286086i	0.00960737	−	0.999954i	$-0.496942\pi$
$829$	−19.8861	−	8.23710i	−0.690673	−	0.286086i	−0.700281	+	0.713868i	$0.746942\pi$
$830$	21.2590	+	24.7939i	0.737911	+	0.860610i
$831$	44.6814	−	44.6814i	1.54998	−	1.54998i
$832$	6.66842	+	0.447101i	0.231186	+	0.0155004i
$833$	17.2235	+	34.0199i	0.596759	+	1.17872i
$834$	25.4282	+	12.8945i	0.880508	+	0.446500i
$835$	−13.0382	−	31.4770i	−0.451206	−	1.08931i
$836$	1.12844	−	0.275531i	0.0390280	−	0.00952944i
$837$	0.303247	+	0.732104i	0.0104818	+	0.0253052i
$838$	−8.52105	−	26.0537i	−0.294355	−	0.900010i
$839$	15.2367	−	36.7847i	0.526030	−	1.26995i	−0.408075	−	0.912948i	$-0.633800\pi$
$839$	15.2367	−	36.7847i	0.526030	−	1.26995i	0.934105	−	0.356999i	$-0.116200\pi$
$840$	42.1897	+	9.87057i	1.45568	+	0.340567i
$841$		−	21.0763i		−	0.726768i
$842$	−8.29112	−	9.66976i	−0.285731	−	0.333242i
$843$	15.2357	−	15.2357i	0.524747	−	0.524747i
$844$	−4.99362	−	6.81757i	−0.171887	−	0.234670i
$845$	13.4110	−	13.4110i	0.461353	−	0.461353i
$846$	6.96321	+	21.2905i	0.239400	+	0.731983i
$847$	−16.0831	+	38.8281i	−0.552623	+	1.33415i
$848$	17.9126	−	21.3042i	0.615121	−	0.731589i
$849$		−	45.2226i		−	1.55204i
$850$	−15.2956	−	0.00994180i	−0.524634	−	0.000341001i
$851$	0.125996	+	0.0521894i	0.00431910	+	0.00178903i
$852$	15.8039	+	64.7253i	0.541434	+	2.21745i
$853$		−	20.6627i		−	0.707478i	−0.935344	−	0.353739i	$-0.884910\pi$
$853$		−	20.6627i		−	0.707478i	0.935344	−	0.353739i	$-0.115090\pi$
$854$	−4.31104	−	0.330906i	−0.147521	−	0.0113234i
$855$	3.36008	−	1.39179i	0.114912	−	0.0475983i
$856$	−3.59031	+	5.00235i	−0.122714	+	0.170977i
$857$	1.56952	+	0.650118i	0.0536139	+	0.0222076i	0.409329	−	0.912387i	$-0.365763\pi$
$857$	1.56952	+	0.650118i	0.0536139	+	0.0222076i	−0.355715	+	0.934594i	$0.615763\pi$
$858$	0.168836	−	2.19959i	0.00576397	−	0.0750928i
$859$	39.1221	+	16.2049i	1.33483	+	0.552904i	0.932029	−	0.362384i	$-0.118037\pi$
$859$	39.1221	+	16.2049i	1.33483	+	0.552904i	0.402800	+	0.915288i	$0.368037\pi$
$860$	29.6098	−	7.22981i	1.00969	−	0.246535i
$861$		−	6.29253i		−	0.214449i
$862$	−25.1792	−	29.3660i	−0.857607	−	1.00021i
$863$			55.3625i			1.88456i	0.334826	+	0.942280i	$0.391322\pi$
$863$			55.3625i			1.88456i	−0.334826	+	0.942280i	$0.608678\pi$
$864$	−0.748288	+	0.762887i	−0.0254573	+	0.0259539i
$865$	2.72345	−	2.72345i	0.0926002	−	0.0926002i
$866$	−21.2014	+	41.8096i	−0.720453	+	1.42075i
$867$	−41.4238	+	6.34177i	−1.40682	+	0.215378i
$868$	−33.4216	−	5.16116i	−1.13440	−	0.175181i
$869$	−3.77575	+	9.11546i	−0.128083	+	0.309221i
$870$	−4.70291	−	14.3795i	−0.159444	−	0.487510i
$871$	−9.51642	−	9.51642i	−0.322452	−	0.322452i
$872$	3.47891	+	2.49690i	0.117811	+	0.0845556i
$873$	−4.98817	−	2.06617i	−0.168824	−	0.0699292i
$874$	1.86393	−	0.609612i	0.0630484	−	0.0206204i
$875$	−18.1291	+	43.7676i	−0.612877	+	1.47962i
$876$	−14.9844	−	61.3690i	−0.506277	−	2.07347i
$877$		−	26.3069i		−	0.888320i	−0.895947	−	0.444160i	$-0.853502\pi$
$877$		−	26.3069i		−	0.888320i	0.895947	−	0.444160i	$-0.146498\pi$
$878$	29.8849	+	34.8541i	1.00857	+	1.17627i
$879$	−48.8453	−	20.2324i	−1.64751	−	0.682422i
$880$	2.15275	+	4.14550i	0.0725694	+	0.139745i
$881$	−8.67119	+	20.9341i	−0.292140	+	0.705288i	−0.999999	−	0.00106541i	$-0.999661\pi$
$881$	−8.67119	+	20.9341i	−0.292140	+	0.705288i	0.707860	+	0.706353i	$0.249661\pi$
$882$	−18.1989	+	35.8886i	−0.612788	+	1.20843i
$883$	50.0747	+	20.7416i	1.68515	+	0.698011i	0.999551	−	0.0299694i	$-0.00954098\pi$
$883$	50.0747	+	20.7416i	1.68515	+	0.698011i	0.685598	+	0.727981i	$0.259541\pi$
$884$	−0.531705	+	6.86853i	−0.0178832	+	0.231014i
$885$	6.86990	+	16.5854i	0.230929	+	0.557512i
$886$	12.5603	−	10.7695i	0.421971	−	0.361810i
$887$	0.100945	+	0.243703i	0.00338941	+	0.00818275i	0.925565	−	0.378588i	$-0.123590\pi$
$887$	0.100945	+	0.243703i	0.00338941	+	0.00818275i	−0.922176	+	0.386771i	$0.873590\pi$
$888$	−0.0852573	−	0.518813i	−0.00286105	−	0.0174102i
$889$	5.35153	+	12.9197i	0.179485	+	0.433314i
$890$	0.853574	−	1.68327i	0.0286119	−	0.0564232i
$891$	−4.69421	−	4.69421i	−0.157262	−	0.157262i
$892$	7.29954	−	47.2689i	0.244407	−	1.58268i
$893$	−3.64702	+	1.51064i	−0.122043	+	0.0505518i
$894$	−3.75556	+	48.9273i	−0.125605	+	1.63637i
$895$	18.6377	−	7.71998i	0.622989	−	0.258051i
$896$	−11.2449	−	44.1964i	−0.375666	−	1.47650i
$897$		−	3.72444i		−	0.124355i
$898$	−3.05104	−	3.55837i	−0.101815	−	0.118744i
$899$	4.51874	+	10.9092i	0.150708	+	0.363842i
$900$	−9.53787	−	13.0216i	−0.317929	−	0.434055i
$901$	21.7683	+	18.6893i	0.725208	+	0.622632i
$902$	0.514988	−	0.441565i	0.0171472	−	0.0147025i
$903$			98.2237i			3.26868i
$904$	−23.6784	−	5.53972i	−0.787531	−	0.184248i
$905$	−0.807260	+	0.807260i	−0.0268342	+	0.0268342i
$906$	24.2115	−	47.7456i	0.804373	−	1.58624i
$907$	−5.74752	−	5.74752i	−0.190843	−	0.190843i	0.605217	−	0.796060i	$-0.293086\pi$
$907$	−5.74752	−	5.74752i	−0.190843	−	0.190843i	−0.796060	+	0.605217i	$0.793086\pi$
$908$	−25.0383	−	34.1837i	−0.830926	−	1.13443i
$909$	−4.21220	−	10.1691i	−0.139710	−	0.337289i
$910$	6.54834	+	3.32062i	0.217075	+	0.110078i
$911$	−29.4719	+	12.2077i	−0.976447	+	0.404458i	−0.813108	−	0.582113i	$-0.802226\pi$
$911$	−29.4719	+	12.2077i	−0.976447	+	0.404458i	−0.163339	+	0.986570i	$0.552226\pi$
$912$	−5.78684	−	4.86559i	−0.191621	−	0.161116i
$913$	−10.4830	−	4.34218i	−0.346935	−	0.143705i
$914$	31.3524	−	10.2540i	1.03704	−	0.339173i
$915$	−2.03824	−	2.03824i	−0.0673821	−	0.0673821i
$916$	−10.7379	+	2.62188i	−0.354791	+	0.0866292i
$917$	−33.4637	−	80.7886i	−1.10507	−	2.66788i
$918$	−0.778371	−	0.779384i	−0.0256901	−	0.0257235i
$919$	12.2501	+	12.2501i	0.404093	+	0.404093i	0.879673	−	0.475580i	$-0.157762\pi$
$919$	12.2501	+	12.2501i	0.404093	+	0.404093i	−0.475580	+	0.879673i	$0.657762\pi$
$920$	4.15942	+	6.70007i	0.137132	+	0.220895i
$921$	26.4101	−	10.9394i	0.870243	−	0.360467i
$922$	31.5215	−	27.0274i	1.03811	−	0.890100i
$923$			11.2900i			0.371615i
$924$	−14.6236	+	3.57063i	−0.481080	+	0.117465i
$925$	0.197809			0.00650393
$926$	−25.1996	+	8.24172i	−0.828111	+	0.270840i
$927$	−29.6540	−	29.6540i	−0.973966	−	0.973966i
$928$	−11.1504	+	11.3679i	−0.366028	+	0.373170i
$929$	8.55235	−	3.54250i	0.280593	−	0.116226i	−0.237949	−	0.971278i	$-0.576475\pi$
$929$	8.55235	−	3.54250i	0.280593	−	0.116226i	0.518542	+	0.855052i	$0.326475\pi$
$930$	−14.6752	−	17.1153i	−0.481217	−	0.561234i
$931$	−6.55139	−	2.71367i	−0.214713	−	0.0889371i
$932$	−3.45384	+	5.68536i	−0.113134	+	0.186230i
$933$	12.3566	−	29.8314i	0.404535	−	0.976635i
$934$	19.3273	+	22.5411i	0.632410	+	0.737566i
$935$	−4.29574	+	2.17483i	−0.140486	+	0.0711247i
$936$	−6.17647	+	3.83437i	−0.201884	+	0.125330i
$937$	15.4257			0.503936			0.251968	−	0.967736i	$-0.418922\pi$
$937$	15.4257			0.503936			0.251968	+	0.967736i	$0.418922\pi$
$938$	−41.5332	+	81.9044i	−1.35611	+	2.67427i
$939$	−52.1376	+	21.5961i	−1.70145	+	0.704762i
$940$	−9.38017	−	12.8063i	−0.305947	−	0.417697i
$941$	43.4486			1.41639			0.708193	−	0.706019i	$-0.249511\pi$
$941$	43.4486			1.41639			0.708193	+	0.706019i	$0.249511\pi$
$942$	48.1229	−	41.2619i	1.56793	−	1.34438i
$943$	0.809838	−	0.809838i	0.0263719	−	0.0263719i
$944$	12.1597	−	14.4621i	0.395765	−	0.470700i
$945$	−1.08458	+	0.449248i	−0.0352814	+	0.0146140i
$946$	−8.03874	+	6.89264i	−0.261362	+	0.224099i
$947$	−2.36771	+	2.36771i	−0.0769402	+	0.0769402i	−0.744530	−	0.667589i	$-0.767326\pi$
$947$	−2.36771	+	2.36771i	−0.0769402	+	0.0769402i	0.667589	+	0.744530i	$0.267326\pi$
$948$	62.3858	−	15.2327i	2.02620	−	0.494736i
$949$		−	10.7046i		−	0.347485i
$950$	2.15938	−	1.85151i	0.0700596	−	0.0600710i
$951$	45.4418	+	45.4418i	1.47355	+	1.47355i
$952$	45.6737	−	11.1207i	1.48029	−	0.360423i
$953$	−4.07644	+	4.07644i	−0.132049	+	0.132049i	−0.770042	−	0.637993i	$-0.779765\pi$
$953$	−4.07644	+	4.07644i	−0.132049	+	0.132049i	0.637993	+	0.770042i	$0.279765\pi$
$954$	−2.31715	+	30.1877i	−0.0750204	+	0.977363i
$955$	27.8732			0.901956
$956$	14.9200	+	20.3696i	0.482546	+	0.658799i
$957$	3.71660	+	3.71660i	0.120141	+	0.120141i
$958$	38.9506	+	2.98977i	1.25844	+	0.0965950i
$959$	12.9030	+	31.1507i	0.416661	+	1.00591i
$960$	13.4878	−	27.2477i	0.435318	−	0.879416i
$961$	−9.47775	−	9.47775i	−0.305734	−	0.305734i
$962$	0.00681852	−	0.0888314i	0.000219838	−	0.00286404i
$963$		−	6.69776i		−	0.215832i
$964$	1.55278	+	6.35945i	0.0500118	+	0.204824i
$965$	−9.53785	−	23.0264i	−0.307034	−	0.741246i
$966$	−24.1549	+	7.90002i	−0.777170	+	0.254179i
$967$		−	23.2499i		−	0.747666i	−0.927496	−	0.373833i	$-0.878043\pi$
$967$		−	23.2499i		−	0.747666i	0.927496	−	0.373833i	$-0.121957\pi$
$968$	23.9579	+	17.1951i	0.770035	+	0.552673i
$969$	5.07657	−	5.91291i	0.163083	−	0.189950i
$970$	3.81495	+	0.292828i	0.122491	+	0.00940213i
$971$	37.6582	+	15.5985i	1.20851	+	0.500580i	0.893739	−	0.448588i	$-0.148073\pi$
$971$	37.6582	+	15.5985i	1.20851	+	0.500580i	0.314769	+	0.949168i	$0.398073\pi$
$972$	−6.76741	+	43.8231i	−0.217065	+	1.40563i
$973$	12.6155	−	30.4565i	0.404435	−	0.976392i
$974$	−2.75485	+	35.8901i	−0.0882712	+	1.14999i
$975$	−2.06731	−	4.99092i	−0.0662068	−	0.159837i
$976$	−0.915196	+	2.89256i	−0.0292947	+	0.0925885i
$977$	11.1512	−	11.1512i	0.356759	−	0.356759i	−0.505858	−	0.862617i	$-0.668824\pi$
$977$	11.1512	−	11.1512i	0.356759	−	0.356759i	0.862617	+	0.505858i	$0.168824\pi$
$978$	−35.1543	+	69.3249i	−1.12411	+	2.21677i
$979$			0.655685i			0.0209558i
$980$	4.35200	−	28.1818i	0.139020	−	0.900236i
$981$	−4.65799			−0.148718
$982$	−42.5236	−	3.26402i	−1.35698	−	0.104159i
$983$	−9.86935	−	23.8267i	−0.314783	−	0.759954i	−0.999514	−	0.0311583i	$-0.990080\pi$
$983$	−9.86935	−	23.8267i	−0.314783	−	0.759954i	0.684731	−	0.728796i	$-0.259920\pi$
$984$	−4.29928	−	1.00585i	−0.137056	−	0.0320652i
$985$	−15.2422	+	15.2422i	−0.485656	+	0.485656i
$986$	−11.5986	−	11.6137i	−0.369376	−	0.369856i
$987$	47.2620	−	19.5766i	1.50437	−	0.623129i
$988$	−0.757035	−	1.03355i	−0.0240845	−	0.0328815i
$989$	−12.6412	+	12.6412i	−0.401967	+	0.401967i
$990$	−4.53170	−	2.29800i	−0.144027	−	0.0730351i
$991$	−0.746650	+	1.80257i	−0.0237181	+	0.0572606i	−0.935295	−	0.353869i	$-0.884866\pi$
$991$	−0.746650	+	1.80257i	−0.0237181	+	0.0572606i	0.911577	+	0.411130i	$0.134866\pi$
$992$	−8.86865	+	22.0098i	−0.281580	+	0.698813i
$993$	−2.93869	−	7.09462i	−0.0932564	−	0.225141i
$994$	73.2214	−	23.9476i	2.32244	−	0.759571i
$995$	4.01444	−	1.66284i	0.127266	−	0.0527155i
$996$	17.5179	+	71.7449i	0.555076	+	2.27332i
$997$	35.7941	−	35.7941i	1.13361	−	1.13361i	0.144039	−	0.989572i	$-0.453991\pi$
$997$	35.7941	−	35.7941i	1.13361	−	1.13361i	0.989572	−	0.144039i	$-0.0460092\pi$
$998$	−41.1938	+	13.4727i	−1.30397	+	0.426472i
$999$	0.0100728	+	0.0100728i	0.000318689	+	0.000318689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.x.a.77.8	yes	280
17.2	even	8		544.2.v.a.461.29	✓	280
32.5	even	8		544.2.v.a.485.29	yes	280
544.325	even	8	inner	544.2.x.a.325.8	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.v.a.461.29	✓	280	17.2	even	8
544.2.v.a.485.29	yes	280	32.5	even	8
544.2.x.a.77.8	yes	280	1.1	even	1	trivial
544.2.x.a.325.8	yes	280	544.325	even	8	inner

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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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34415 + 0.439614i) q^{2} +(-1.74308 + 1.74308i) q^{3} +(1.61348 - 1.18181i) q^{4} -1.54170i q^{5} +(1.57668 - 3.10924i) q^{6} +(-3.72407 - 1.54256i) q^{7} +(-1.64922 + 2.29784i) q^{8} -3.07663i q^{9} +(0.677751 + 2.07227i) q^{10} +(-0.535610 - 0.535610i) q^{11} +(-0.752426 + 4.87241i) q^{12} +(-0.319703 + 0.771831i) q^{13} +(5.68385 + 0.436280i) q^{14} +(2.68730 + 2.68730i) q^{15} +(1.20663 - 3.81367i) q^{16} +(3.91800 + 1.28423i) q^{17} +(1.35253 + 4.13546i) q^{18} +(-0.708395 + 0.293427i) q^{19} +(-1.82200 - 2.48750i) q^{20} +(9.18015 - 3.80254i) q^{21} +(0.955403 + 0.484479i) q^{22} +(1.67085 + 0.692089i) q^{23} +(-1.13061 - 6.88003i) q^{24} +2.62317 q^{25} +(0.0904211 - 1.17800i) q^{26} +(0.133576 + 0.133576i) q^{27} +(-7.83174 + 1.91227i) q^{28} +(1.99044 + 1.99044i) q^{29} +(-4.79350 - 2.43076i) q^{30} +(3.87550 + 1.60528i) q^{31} +(0.0546467 + 5.65659i) q^{32} +1.86722 q^{33} +(-5.83095 - 0.00378999i) q^{34} +(-2.37816 + 5.74139i) q^{35} +(-3.63601 - 4.96408i) q^{36} +0.0754085 q^{37} +(0.823195 - 0.705830i) q^{38} +(-0.788094 - 1.90263i) q^{39} +(3.54258 + 2.54259i) q^{40} +(0.242343 - 0.585068i) q^{41} +(-10.6678 + 9.14691i) q^{42} +(-3.78287 + 9.13266i) q^{43} +(-1.49719 - 0.231204i) q^{44} -4.74323 q^{45} +(-2.55013 - 0.195742i) q^{46} +5.14829 q^{47} +(4.54426 + 8.75076i) q^{48} +(6.53948 + 6.53948i) q^{49} +(-3.52594 + 1.15318i) q^{50} +(-9.06789 + 4.59087i) q^{51} +(0.396327 + 1.62316i) q^{52} +(6.42881 + 2.66290i) q^{53} +(-0.238269 - 0.120825i) q^{54} +(-0.825749 + 0.825749i) q^{55} +(9.68637 - 6.01332i) q^{56} +(0.723321 - 1.74625i) q^{57} +(-3.55048 - 1.80043i) q^{58} +(4.36411 + 1.80767i) q^{59} +(7.51178 + 1.16001i) q^{60} -0.758472 q^{61} +(-5.91496 - 0.454020i) q^{62} +(-4.74590 + 11.4576i) q^{63} +(-2.56017 - 7.57928i) q^{64} +(1.18993 + 0.492885i) q^{65} +(-2.50982 + 0.820856i) q^{66} +(-6.16484 + 14.8832i) q^{67} +(7.83934 - 2.55827i) q^{68} +(-4.11878 + 1.70606i) q^{69} +(0.672612 - 8.76276i) q^{70} +(12.4854 - 5.17163i) q^{71} +(7.06962 + 5.07403i) q^{72} +(-11.8380 + 4.90345i) q^{73} +(-0.101360 + 0.0331506i) q^{74} +(-4.57239 + 4.57239i) q^{75} +(-0.796205 + 1.31063i) q^{76} +(1.16844 + 2.82086i) q^{77} +(1.89574 + 2.21096i) q^{78} +(-4.98470 - 12.0341i) q^{79} +(-5.87951 - 1.86026i) q^{80} +8.76423 q^{81} +(-0.0685415 + 0.892956i) q^{82} +(13.8395 - 5.73250i) q^{83} +(10.3181 - 16.9846i) q^{84} +(1.97989 - 6.04037i) q^{85} +(1.06990 - 13.9387i) q^{86} -6.93899 q^{87} +(2.11409 - 0.347411i) q^{88} +(-0.612092 - 0.612092i) q^{89} +(6.37562 - 2.08519i) q^{90} +(2.38119 - 2.38119i) q^{91} +(3.51380 - 0.857963i) q^{92} +(-9.55343 + 3.95716i) q^{93} +(-6.92007 + 2.26326i) q^{94} +(0.452375 + 1.09213i) q^{95} +(-9.95512 - 9.76462i) q^{96} +(0.671568 - 1.62131i) q^{97} +(-11.6649 - 5.91520i) q^{98} +(-1.64788 + 1.64788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 8 q^{4} - 4 q^{6} - 4 q^{7} - 4 q^{8} + 4 q^{10} - 4 q^{11} - 4 q^{12} + 8 q^{14} - 24 q^{16} + 4 q^{18} + 12 q^{19} + 12 q^{20} - 12 q^{21} - 4 q^{22} - 4 q^{23} + 48 q^{24}+ \cdots + 20 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 8 * q^4 - 4 * q^6 - 4 * q^7 - 4 * q^8 + 4 * q^10 - 4 * q^11 - 4 * q^12 + 8 * q^14 - 24 * q^16 + 4 * q^18 + 12 * q^19 + 12 * q^20 - 12 * q^21 - 4 * q^22 - 4 * q^23 + 48 * q^24 - 256 * q^25 - 4 * q^26 + 8 * q^27 + 28 * q^28 - 4 * q^29 + 8 * q^30 - 24 * q^31 - 64 * q^32 + 8 * q^33 - 28 * q^34 + 12 * q^35 + 44 * q^36 - 8 * q^37 - 4 * q^39 + 48 * q^40 - 4 * q^41 + 56 * q^42 - 4 * q^43 - 32 * q^44 + 32 * q^45 + 8 * q^46 - 80 * q^47 - 56 * q^48 + 12 * q^50 - 4 * q^51 - 28 * q^52 - 4 * q^53 + 124 * q^54 - 32 * q^56 - 4 * q^57 + 24 * q^58 - 4 * q^59 + 20 * q^60 - 72 * q^61 - 4 * q^62 - 36 * q^63 - 8 * q^64 + 12 * q^65 + 48 * q^66 - 8 * q^67 - 20 * q^68 + 4 * q^69 + 44 * q^70 + 28 * q^71 + 52 * q^72 - 4 * q^73 - 32 * q^74 + 4 * q^75 - 20 * q^76 - 4 * q^77 - 104 * q^78 + 76 * q^80 - 240 * q^81 - 104 * q^82 - 44 * q^83 + 36 * q^84 + 48 * q^85 + 32 * q^86 + 88 * q^87 + 12 * q^88 + 84 * q^90 - 56 * q^91 - 124 * q^92 - 4 * q^93 - 136 * q^94 + 12 * q^95 - 4 * q^96 - 8 * q^97 + 20 * q^99

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