LMFDB - Embedded newform 168.2.t.a.115.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.7
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.647418 - 1.25732i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.16170 + 1.62802i) q^{4} +(-1.61398 - 2.79550i) q^{5} +(-0.0679787 + 1.41258i) q^{6} +(-1.82725 + 1.91341i) q^{7} +(2.79905 + 0.406616i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.46991 + 3.83914i) q^{10} +(-1.10660 + 1.91668i) q^{11} +(1.82007 - 0.829058i) q^{12} -5.08369 q^{13} +(3.58876 + 1.05866i) q^{14} +3.22796i q^{15} +(-1.30091 - 3.78254i) q^{16} +(-2.73597 - 1.57961i) q^{17} +(0.765161 - 1.18934i) q^{18} +(2.93566 - 1.69490i) q^{19} +(6.42609 + 0.619932i) q^{20} +(2.53915 - 0.743436i) q^{21} +(3.12631 + 0.150450i) q^{22} +(-2.65351 + 1.53200i) q^{23} +(-2.22074 - 1.75166i) q^{24} +(-2.70987 + 4.69363i) q^{25} +(3.29127 + 6.39182i) q^{26} -1.00000i q^{27} +(-0.992355 - 5.19762i) q^{28} -9.88340i q^{29} +(4.05858 - 2.08984i) q^{30} +(1.01402 - 1.75634i) q^{31} +(-3.91363 + 4.08454i) q^{32} +(1.91668 - 1.10660i) q^{33} +(-0.214760 + 4.46266i) q^{34} +(8.29809 + 2.01987i) q^{35} +(-1.99076 - 0.192050i) q^{36} +(0.798374 - 0.460941i) q^{37} +(-4.03163 - 2.59375i) q^{38} +(4.40261 + 2.54185i) q^{39} +(-3.38092 - 8.48100i) q^{40} -5.96303i q^{41} +(-2.57863 - 2.71121i) q^{42} -6.68790 q^{43} +(-1.83487 - 4.02817i) q^{44} +(1.61398 - 2.79550i) q^{45} +(3.64414 + 2.34446i) q^{46} +(-1.06113 - 1.83793i) q^{47} +(-0.764652 + 3.92623i) q^{48} +(-0.322287 - 6.99258i) q^{49} +(7.65581 + 0.368427i) q^{50} +(1.57961 + 2.73597i) q^{51} +(5.90572 - 8.27636i) q^{52} +(3.12560 + 1.80457i) q^{53} +(-1.25732 + 0.647418i) q^{54} +7.14411 q^{55} +(-5.89259 + 4.61274i) q^{56} -3.38981 q^{57} +(-12.4266 + 6.39869i) q^{58} +(-10.6351 - 6.14015i) q^{59} +(-5.25519 - 3.74992i) q^{60} +(6.34115 + 10.9832i) q^{61} +(-2.86477 - 0.137864i) q^{62} +(-2.57069 - 0.625743i) q^{63} +(7.66933 + 2.27627i) q^{64} +(8.20498 + 14.2114i) q^{65} +(-2.63224 - 1.69345i) q^{66} +(-4.40720 + 7.63350i) q^{67} +(5.75002 - 2.61918i) q^{68} +3.06401 q^{69} +(-2.83271 - 11.7410i) q^{70} +11.7036i q^{71} +(1.04738 + 2.62735i) q^{72} +(7.82068 + 4.51527i) q^{73} +(-1.09643 - 0.705388i) q^{74} +(4.69363 - 2.70987i) q^{75} +(-0.651014 + 6.74828i) q^{76} +(-1.64537 - 5.61964i) q^{77} +(0.345583 - 7.18112i) q^{78} +(9.60105 - 5.54317i) q^{79} +(-8.47445 + 9.74164i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.49743 + 3.86057i) q^{82} -3.57322i q^{83} +(-1.73940 + 4.99745i) q^{84} +10.1979i q^{85} +(4.32987 + 8.40882i) q^{86} +(-4.94170 + 8.55928i) q^{87} +(-3.87677 + 4.91493i) q^{88} +(-6.32253 + 3.65032i) q^{89} +(-4.55975 - 0.219433i) q^{90} +(9.28920 - 9.72719i) q^{91} +(0.588444 - 6.09969i) q^{92} +(-1.75634 + 1.01402i) q^{93} +(-1.62387 + 2.52409i) q^{94} +(-9.47619 - 5.47108i) q^{95} +(5.43158 - 1.58050i) q^{96} -15.2238i q^{97} +(-8.58324 + 4.93234i) q^{98} -2.21319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−0.647418	−	1.25732i	−0.457794	−	0.889058i
$2$	−0.647418	−	1.25732i	−0.457794	−	0.889058i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.16170	+	1.62802i	−0.580850	+	0.814011i
$5$	−1.61398	−	2.79550i	−0.721794	−	1.25018i	−0.960280	−	0.279038i	$-0.909984\pi$
$5$	−1.61398	−	2.79550i	−0.721794	−	1.25018i	0.238486	−	0.971146i	$-0.423349\pi$
$6$	−0.0679787	+	1.41258i	−0.0277522	+	0.576683i
$7$	−1.82725	+	1.91341i	−0.690637	+	0.723202i
$7$	−1.82725	+	1.91341i	−0.690637	+	0.723202i
$8$	2.79905	+	0.406616i	0.989613	+	0.143760i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.46991	+	3.83914i	−0.781054	+	1.21404i
$11$	−1.10660	+	1.91668i	−0.333652	+	0.577902i	−0.983225	−	0.182397i	$-0.941614\pi$
$11$	−1.10660	+	1.91668i	−0.333652	+	0.577902i	0.649573	+	0.760299i	$0.274948\pi$
$12$	1.82007	−	0.829058i	0.525410	−	0.239329i
$13$	−5.08369			−1.40996			−0.704981	−	0.709226i	$-0.749045\pi$
$13$	−5.08369			−1.40996			−0.704981	+	0.709226i	$0.749045\pi$
$14$	3.58876	+	1.05866i	0.959138	+	0.282940i
$15$			3.22796i			0.833456i
$16$	−1.30091	−	3.78254i	−0.325227	−	0.945636i
$17$	−2.73597	−	1.57961i	−0.663571	−	0.383113i	0.130065	−	0.991505i	$-0.458481\pi$
$17$	−2.73597	−	1.57961i	−0.663571	−	0.383113i	−0.793636	+	0.608393i	$0.791815\pi$
$18$	0.765161	−	1.18934i	0.180350	−	0.280330i
$19$	2.93566	−	1.69490i	0.673486	−	0.388838i	−0.123910	−	0.992293i	$-0.539543\pi$
$19$	2.93566	−	1.69490i	0.673486	−	0.388838i	0.797396	+	0.603456i	$0.206210\pi$
$20$	6.42609	+	0.619932i	1.43692	+	0.138621i
$21$	2.53915	−	0.743436i	0.554089	−	0.162231i
$22$	3.12631	+	0.150450i	0.666532	+	0.0320761i
$23$	−2.65351	+	1.53200i	−0.553294	+	0.319445i	−0.750450	−	0.660928i	$-0.770163\pi$
$23$	−2.65351	+	1.53200i	−0.553294	+	0.319445i	0.197155	+	0.980372i	$0.436830\pi$
$24$	−2.22074	−	1.75166i	−0.453306	−	0.357557i
$25$	−2.70987	+	4.69363i	−0.541974	+	0.938726i
$26$	3.29127	+	6.39182i	0.645472	+	1.25354i
$27$		−	1.00000i		−	0.192450i
$28$	−0.992355	−	5.19762i	−0.187538	−	0.982257i
$29$		−	9.88340i		−	1.83530i	−0.397387	−	0.917651i	$-0.630083\pi$
$29$		−	9.88340i		−	1.83530i	0.397387	−	0.917651i	$-0.369917\pi$
$30$	4.05858	−	2.08984i	0.740991	−	0.381551i
$31$	1.01402	−	1.75634i	0.182124	−	0.315448i	−0.760480	−	0.649362i	$-0.775036\pi$
$31$	1.01402	−	1.75634i	0.182124	−	0.315448i	0.942604	+	0.333914i	$0.108369\pi$
$32$	−3.91363	+	4.08454i	−0.691839	+	0.722052i
$33$	1.91668	−	1.10660i	0.333652	−	0.192634i
$34$	−0.214760	+	4.46266i	−0.0368311	+	0.765340i
$35$	8.29809	+	2.01987i	1.40263	+	0.341421i
$36$	−1.99076	−	0.192050i	−0.331793	−	0.0320084i
$37$	0.798374	−	0.460941i	0.131252	−	0.0757783i	−0.432936	−	0.901424i	$-0.642523\pi$
$37$	0.798374	−	0.460941i	0.131252	−	0.0757783i	0.564188	+	0.825646i	$0.309189\pi$
$38$	−4.03163	−	2.59375i	−0.654017	−	0.420761i
$39$	4.40261	+	2.54185i	0.704981	+	0.407021i
$40$	−3.38092	−	8.48100i	−0.534570	−	1.34096i
$41$		−	5.96303i		−	0.931269i	−0.884977	−	0.465635i	$-0.845826\pi$
$41$		−	5.96303i		−	0.931269i	0.884977	−	0.465635i	$-0.154174\pi$
$42$	−2.57863	−	2.71121i	−0.397891	−	0.418349i
$43$	−6.68790			−1.01990			−0.509948	−	0.860205i	$-0.670335\pi$
$43$	−6.68790			−1.01990			−0.509948	+	0.860205i	$0.670335\pi$
$44$	−1.83487	−	4.02817i	−0.276617	−	0.607270i
$45$	1.61398	−	2.79550i	0.240598	−	0.416728i
$46$	3.64414	+	2.34446i	0.537300	+	0.345671i
$47$	−1.06113	−	1.83793i	−0.154782	−	0.268090i	0.778198	−	0.628019i	$-0.216134\pi$
$47$	−1.06113	−	1.83793i	−0.154782	−	0.268090i	−0.932980	+	0.359929i	$0.882801\pi$
$48$	−0.764652	+	3.92623i	−0.110368	+	0.566703i
$49$	−0.322287	−	6.99258i	−0.0460410	−	0.998940i
$50$	7.65581	+	0.368427i	1.08269	+	0.0521034i
$51$	1.57961	+	2.73597i	0.221190	+	0.383113i
$52$	5.90572	−	8.27636i	0.818976	−	1.14772i
$53$	3.12560	+	1.80457i	0.429334	+	0.247876i	0.699063	−	0.715060i	$-0.253601\pi$
$53$	3.12560	+	1.80457i	0.429334	+	0.247876i	−0.269729	+	0.962936i	$0.586934\pi$
$54$	−1.25732	+	0.647418i	−0.171099	+	0.0881024i
$55$	7.14411			0.963311
$56$	−5.89259	+	4.61274i	−0.787431	+	0.616403i
$57$	−3.38981			−0.448991
$58$	−12.4266	+	6.39869i	−1.63169	+	0.840190i
$59$	−10.6351	−	6.14015i	−1.38457	−	0.799379i	−0.391869	−	0.920021i	$-0.628172\pi$
$59$	−10.6351	−	6.14015i	−1.38457	−	0.799379i	−0.992696	+	0.120642i	$0.961505\pi$
$60$	−5.25519	−	3.74992i	−0.678442	−	0.484113i
$61$	6.34115	+	10.9832i	0.811901	+	1.40625i	0.911532	+	0.411230i	$0.134901\pi$
$61$	6.34115	+	10.9832i	0.811901	+	1.40625i	−0.0996301	+	0.995025i	$0.531766\pi$
$62$	−2.86477	−	0.137864i	−0.363827	−	0.0175087i
$63$	−2.57069	−	0.625743i	−0.323876	−	0.0788361i
$64$	7.66933	+	2.27627i	0.958666	+	0.284534i
$65$	8.20498	+	14.2114i	1.01770	+	1.76271i
$66$	−2.63224	−	1.69345i	−0.324006	−	0.208449i
$67$	−4.40720	+	7.63350i	−0.538425	+	0.932580i	0.460564	+	0.887627i	$0.347647\pi$
$67$	−4.40720	+	7.63350i	−0.538425	+	0.932580i	−0.998989	+	0.0449534i	$0.985686\pi$
$68$	5.75002	−	2.61918i	0.697293	−	0.317623i
$69$	3.06401			0.368863
$70$	−2.83271	−	11.7410i	−0.338574	−	1.40332i
$71$			11.7036i			1.38896i	0.719512	+	0.694480i	$0.244366\pi$
$71$			11.7036i			1.38896i	−0.719512	+	0.694480i	$0.755634\pi$
$72$	1.04738	+	2.62735i	0.123435	+	0.309637i
$73$	7.82068	+	4.51527i	0.915342	+	0.528473i	0.882146	−	0.470976i	$-0.156098\pi$
$73$	7.82068	+	4.51527i	0.915342	+	0.528473i	0.0331957	+	0.999449i	$0.489432\pi$
$74$	−1.09643	−	0.705388i	−0.127458	−	0.0819997i
$75$	4.69363	−	2.70987i	0.541974	−	0.312909i
$76$	−0.651014	+	6.74828i	−0.0746764	+	0.774081i
$77$	−1.64537	−	5.61964i	−0.187507	−	0.640418i
$78$	0.345583	−	7.18112i	0.0391295	−	0.813101i
$79$	9.60105	−	5.54317i	1.08020	−	0.623655i	0.149252	−	0.988799i	$-0.452313\pi$
$79$	9.60105	−	5.54317i	1.08020	−	0.623655i	0.930951	+	0.365144i	$0.118980\pi$
$80$	−8.47445	+	9.74164i	−0.947472	+	1.08915i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.49743	+	3.86057i	−0.827953	+	0.426329i
$83$		−	3.57322i		−	0.392212i	−0.980583	−	0.196106i	$-0.937170\pi$
$83$		−	3.57322i		−	0.392212i	0.980583	−	0.196106i	$-0.0628297\pi$
$84$	−1.73940	+	4.99745i	−0.189785	+	0.545266i
$85$			10.1979i			1.10611i
$86$	4.32987	+	8.40882i	0.466902	+	0.906746i
$87$	−4.94170	+	8.55928i	−0.529806	+	0.917651i
$88$	−3.87677	+	4.91493i	−0.413265	+	0.523933i
$89$	−6.32253	+	3.65032i	−0.670187	+	0.386933i	−0.796147	−	0.605103i	$-0.793132\pi$
$89$	−6.32253	+	3.65032i	−0.670187	+	0.386933i	0.125960	+	0.992035i	$0.459799\pi$
$90$	−4.55975	−	0.219433i	−0.480640	−	0.0231302i
$91$	9.28920	−	9.72719i	0.973772	−	1.01969i
$92$	0.588444	−	6.09969i	0.0613495	−	0.635937i
$93$	−1.75634	+	1.01402i	−0.182124	+	0.105149i
$94$	−1.62387	+	2.52409i	−0.167489	+	0.260340i
$95$	−9.47619	−	5.47108i	−0.972237	−	0.561321i
$96$	5.43158	−	1.58050i	0.554358	−	0.161309i
$97$		−	15.2238i		−	1.54574i	−0.634566	−	0.772869i	$-0.718821\pi$
$97$		−	15.2238i		−	1.54574i	0.634566	−	0.772869i	$-0.281179\pi$
$98$	−8.58324	+	4.93234i	−0.867038	+	0.498241i
$99$	−2.21319			−0.222434
$100$	−4.49328	−	9.86431i	−0.449328	−	0.986431i
$101$	−4.92124	+	8.52383i	−0.489681	+	0.848153i	−0.999929	−	0.0118744i	$-0.996220\pi$
$101$	−4.92124	+	8.52383i	−0.489681	+	0.848153i	0.510248	+	0.860027i	$0.329554\pi$
$102$	2.41732	−	3.75740i	0.239350	−	0.372038i
$103$	−0.992258	−	1.71864i	−0.0977701	−	0.169343i	0.812991	−	0.582276i	$-0.197838\pi$
$103$	−0.992258	−	1.71864i	−0.0977701	−	0.169343i	−0.910761	+	0.412933i	$0.864504\pi$
$104$	−14.2295	−	2.06711i	−1.39532	−	0.202697i
$105$	−6.17642	−	5.89831i	−0.602757	−	0.575616i
$106$	0.245344	−	5.09818i	0.0238299	−	0.495179i
$107$	1.61805	+	2.80255i	0.156423	+	0.270933i	0.933576	−	0.358379i	$-0.116670\pi$
$107$	1.61805	+	2.80255i	0.156423	+	0.270933i	−0.777153	+	0.629311i	$0.783337\pi$
$108$	1.62802	+	1.16170i	0.156656	+	0.111785i
$109$	−3.62997	−	2.09576i	−0.347688	−	0.200738i	0.315979	−	0.948766i	$-0.397667\pi$
$109$	−3.62997	−	2.09576i	−0.347688	−	0.200738i	−0.663666	+	0.748029i	$0.731001\pi$
$110$	−4.62523	−	8.98242i	−0.440998	−	0.856440i
$111$	−0.921883			−0.0875012
$112$	9.61465	+	4.42249i	0.908499	+	0.417886i
$113$	−2.84651			−0.267777			−0.133889	−	0.990996i	$-0.542746\pi$
$113$	−2.84651			−0.267777			−0.133889	+	0.990996i	$0.542746\pi$
$114$	2.19462	+	4.26207i	0.205545	+	0.399179i
$115$	8.56542	+	4.94525i	0.798729	+	0.461147i
$116$	16.0904	+	11.4815i	1.49396	+	1.06603i
$117$	−2.54185	−	4.40261i	−0.234994	−	0.407021i
$118$	−0.834798	+	17.3469i	−0.0768494	+	1.59691i
$119$	8.02177	−	2.34868i	0.735354	−	0.215304i
$120$	−1.31254	+	9.03522i	−0.119818	+	0.824799i
$121$	3.05088	+	5.28429i	0.277353	+	0.480390i
$122$	9.70400	−	15.0836i	0.878559	−	1.36560i
$123$	−2.98152	+	5.16414i	−0.268834	+	0.465635i
$124$	1.68137	+	3.69119i	0.150991	+	0.331479i
$125$	1.35490			0.121186
$126$	0.877554	+	3.63729i	0.0781787	+	0.324036i
$127$		−	21.0058i		−	1.86396i	−0.362506	−	0.931981i	$-0.618079\pi$
$127$		−	21.0058i		−	1.86396i	0.362506	−	0.931981i	$-0.381921\pi$
$128$	−2.10326	−	11.1165i	−0.185904	−	0.982568i
$129$	5.79189	+	3.34395i	0.509948	+	0.294418i
$130$	12.5563	−	19.5170i	1.10126	−	1.71176i
$131$	−0.494446	+	0.285468i	−0.0431999	+	0.0249415i	−0.521444	−	0.853285i	$-0.674607\pi$
$131$	−0.494446	+	0.285468i	−0.0431999	+	0.0249415i	0.478245	+	0.878227i	$0.341273\pi$
$132$	−0.425045	+	4.40593i	−0.0369954	+	0.383487i
$133$	−2.12115	+	8.71414i	−0.183927	+	0.755612i
$134$	12.4510	+	0.599191i	1.07561	+	0.0517623i
$135$	−2.79550	+	1.61398i	−0.240598	+	0.138909i
$136$	−7.01582	−	5.53390i	−0.601602	−	0.474528i
$137$	6.57813	−	11.3937i	0.562008	−	0.973426i	−0.435313	−	0.900279i	$-0.643362\pi$
$137$	6.57813	−	11.3937i	0.562008	−	0.973426i	0.997321	−	0.0731470i	$-0.0233042\pi$
$138$	−1.98369	−	3.85243i	−0.168863	−	0.327941i
$139$			9.54821i			0.809869i	0.914346	+	0.404934i	$0.132706\pi$
$139$			9.54821i			0.809869i	−0.914346	+	0.404934i	$0.867294\pi$
$140$	−12.9283	+	11.1630i	−1.09264	+	0.943444i
$141$			2.12226i			0.178727i
$142$	14.7151	−	7.57711i	1.23487	−	0.635857i
$143$	5.62560	−	9.74383i	0.470436	−	0.814820i
$144$	2.62532	−	3.01789i	0.218777	−	0.251491i
$145$	−27.6290	+	15.9516i	−2.29447	+	1.32471i
$146$	0.613885	−	12.7564i	0.0508055	−	1.05572i
$147$	−3.21718	+	6.21689i	−0.265349	+	0.512761i
$148$	−0.177048	+	1.83524i	−0.0145533	+	0.150856i
$149$	9.17651	−	5.29806i	0.751769	−	0.434034i	−0.0745636	−	0.997216i	$-0.523756\pi$
$149$	9.17651	−	5.29806i	0.751769	−	0.434034i	0.826333	+	0.563182i	$0.190423\pi$
$150$	−6.44591	−	4.14697i	−0.526306	−	0.338599i
$151$	1.05318	+	0.608052i	0.0857063	+	0.0494826i	0.542241	−	0.840223i	$-0.317576\pi$
$151$	1.05318	+	0.608052i	0.0857063	+	0.0494826i	−0.456534	+	0.889706i	$0.650909\pi$
$152$	8.90622	−	3.55043i	0.722390	−	0.287978i
$153$		−	3.15923i		−	0.255409i
$154$	−6.00044	+	5.70701i	−0.483529	+	0.459884i
$155$	−6.54645			−0.525824
$156$	−9.25269	+	4.21468i	−0.740808	+	0.337444i
$157$	−1.81252	+	3.13938i	−0.144655	+	0.250550i	−0.929244	−	0.369466i	$-0.879541\pi$
$157$	−1.81252	+	3.13938i	−0.144655	+	0.250550i	0.784589	+	0.620016i	$0.212874\pi$
$158$	−13.1854	−	8.48283i	−1.04898	−	0.674858i
$159$	−1.80457	−	3.12560i	−0.143111	−	0.247876i
$160$	17.7349	+	4.34817i	1.40206	+	0.343753i
$161$	1.91728	−	7.87661i	0.151103	−	0.620764i
$162$	1.41258	+	0.0679787i	0.110983	+	0.00534091i
$163$	−9.91572	−	17.1745i	−0.776659	−	1.34521i	−0.933857	−	0.357646i	$-0.883580\pi$
$163$	−9.91572	−	17.1745i	−0.776659	−	1.34521i	0.157198	−	0.987567i	$-0.449754\pi$
$164$	9.70794	+	6.92725i	0.758063	+	0.540927i
$165$	−6.18698	−	3.57205i	−0.481656	−	0.278084i
$166$	−4.49268	+	2.31337i	−0.348700	+	0.179552i
$167$	−12.3971			−0.959317			−0.479659	−	0.877455i	$-0.659240\pi$
$167$	−12.3971			−0.959317			−0.479659	+	0.877455i	$0.659240\pi$
$168$	7.40950	−	1.04845i	0.571656	−	0.0808899i
$169$	12.8439			0.987994
$170$	12.8220	−	6.60229i	0.983400	−	0.506372i
$171$	2.93566	+	1.69490i	0.224495	+	0.129613i
$172$	7.76933	−	10.8880i	0.592406	−	0.830206i
$173$	0.519326	+	0.899499i	0.0394836	+	0.0683876i	0.885092	−	0.465416i	$-0.154095\pi$
$173$	0.519326	+	0.899499i	0.0394836	+	0.0683876i	−0.845608	+	0.533804i	$0.820762\pi$
$174$	13.9611	+	0.671861i	1.05839	+	0.0509336i
$175$	−4.02923	−	13.7615i	−0.304581	−	1.04028i
$176$	8.68952	+	1.69232i	0.654997	+	0.127564i
$177$	6.14015	+	10.6351i	0.461522	+	0.799379i
$178$	8.68293	+	5.58616i	0.650813	+	0.418700i
$179$	1.26304	−	2.18764i	0.0944038	−	0.163512i	−0.814956	−	0.579523i	$-0.803239\pi$
$179$	1.26304	−	2.18764i	0.0944038	−	0.163512i	0.909360	+	0.416011i	$0.136572\pi$
$180$	2.67617	+	5.87512i	0.199470	+	0.437906i
$181$	8.29867			0.616835			0.308418	−	0.951251i	$-0.400201\pi$
$181$	8.29867			0.616835			0.308418	+	0.951251i	$0.400201\pi$
$182$	−18.2442	−	5.38192i	−1.35235	−	0.398934i
$183$		−	12.6823i		−	0.937503i
$184$	−8.05022	+	3.20919i	−0.593470	+	0.236585i
$185$	−2.57712	−	1.48790i	−0.189474	−	0.109393i
$186$	2.41204	+	1.55178i	0.176859	+	0.113782i
$187$	6.05524	−	3.49599i	0.442803	−	0.255652i
$188$	4.22491	+	0.407581i	0.308133	+	0.0297259i
$189$	1.91341	+	1.82725i	0.139180	+	0.132913i
$190$	−0.743834	+	15.4567i	−0.0539634	+	1.12134i
$191$	−5.26146	+	3.03771i	−0.380706	+	0.219801i	−0.678125	−	0.734946i	$-0.737207\pi$
$191$	−5.26146	+	3.03771i	−0.380706	+	0.219801i	0.297419	+	0.954747i	$0.403874\pi$
$192$	−5.50370	−	5.80597i	−0.397195	−	0.419010i
$193$	4.59340	−	7.95599i	0.330640	−	0.572685i	−0.651998	−	0.758221i	$-0.726069\pi$
$193$	4.59340	−	7.95599i	0.330640	−	0.572685i	0.982637	+	0.185536i	$0.0594021\pi$
$194$	−19.1411	+	9.85613i	−1.37425	+	0.707629i
$195$		−	16.4100i		−	1.17514i
$196$	11.7585	+	7.59858i	0.839890	+	0.542756i
$197$			20.2764i			1.44463i	0.691563	+	0.722316i	$0.256922\pi$
$197$			20.2764i			1.44463i	−0.691563	+	0.722316i	$0.743078\pi$
$198$	1.43286	+	2.78269i	0.101829	+	0.197757i
$199$	1.64355	−	2.84672i	0.116508	−	0.201799i	−0.801873	−	0.597494i	$-0.796163\pi$
$199$	1.64355	−	2.84672i	0.116508	−	0.201799i	0.918382	+	0.395696i	$0.129496\pi$
$200$	−9.49355	+	12.0358i	−0.671296	+	0.851061i
$201$	7.63350	−	4.40720i	0.538425	−	0.310860i
$202$	13.9033	+	0.669078i	0.978230	+	0.0470762i
$203$	18.9110	+	18.0595i	1.32729	+	1.26753i
$204$	−6.28926	−	0.606731i	−0.440336	−	0.0424797i
$205$	−16.6696	+	9.62422i	−1.16426	+	0.672185i
$206$	−1.51847	+	2.36026i	−0.105797	+	0.164447i
$207$	−2.65351	−	1.53200i	−0.184431	−	0.106482i
$208$	6.61342	+	19.2293i	0.458558	+	1.33331i
$209$			7.50230i			0.518945i
$210$	−3.41732	+	11.5844i	−0.235818	+	0.799399i
$211$	−21.6901			−1.49320			−0.746602	−	0.665271i	$-0.768316\pi$
$211$	−21.6901			−1.49320			−0.746602	+	0.665271i	$0.768316\pi$
$212$	−6.56888	+	2.99218i	−0.451153	+	0.205504i
$213$	5.85179	−	10.1356i	0.400958	−	0.694480i
$214$	2.47614	−	3.84883i	0.169265	−	0.263101i
$215$	10.7941	+	18.6960i	0.736154	+	1.27506i
$216$	0.406616	−	2.79905i	0.0276667	−	0.190451i
$217$	1.50772	+	5.14952i	0.102351	+	0.349572i
$218$	−0.284934	+	5.92086i	−0.0192982	+	0.401011i
$219$	−4.51527	−	7.82068i	−0.305114	−	0.528473i
$220$	−8.29931	+	11.6308i	−0.559539	+	0.784146i
$221$	13.9088	+	8.03027i	0.935610	+	0.540175i
$222$	0.596844	+	1.15910i	0.0400575	+	0.0777937i
$223$	−19.3266			−1.29420			−0.647102	−	0.762404i	$-0.724019\pi$
$223$	−19.3266			−1.29420			−0.647102	+	0.762404i	$0.724019\pi$
$224$	−0.664217	−	14.9519i	−0.0443799	−	0.999015i
$225$	−5.41974			−0.361316
$226$	1.84288	+	3.57897i	0.122587	+	0.238070i
$227$	−0.466841	−	0.269531i	−0.0309853	−	0.0178894i	0.484427	−	0.874832i	$-0.339028\pi$
$227$	−0.466841	−	0.269531i	−0.0309853	−	0.0178894i	−0.515413	+	0.856942i	$0.672361\pi$
$228$	3.93794	−	5.51868i	0.260796	−	0.365483i
$229$	−11.4311	−	19.7993i	−0.755392	−	1.30838i	−0.945179	−	0.326551i	$-0.894113\pi$
$229$	−11.4311	−	19.7993i	−0.755392	−	1.30838i	0.189788	−	0.981825i	$-0.439220\pi$
$230$	0.672343	−	13.9711i	0.0443330	−	0.921227i
$231$	−1.38489	+	5.68944i	−0.0911191	+	0.374337i
$232$	4.01875	−	27.6641i	0.263844	−	1.81624i
$233$	1.50245	+	2.60232i	0.0984287	+	0.170484i	0.911034	−	0.412330i	$-0.135285\pi$
$233$	1.50245	+	2.60232i	0.0984287	+	0.170484i	−0.812606	+	0.582814i	$0.801952\pi$
$234$	−3.88984	+	6.04624i	−0.254287	+	0.395255i
$235$	−3.42529	+	5.93277i	−0.223441	+	0.387011i
$236$	22.3510	−	10.1811i	1.45493	−	0.662732i
$237$	−11.0863			−0.720135
$238$	−8.14648	−	8.56534i	−0.528058	−	0.555208i
$239$		−	11.2699i		−	0.728988i	−0.931206	−	0.364494i	$-0.881242\pi$
$239$		−	11.2699i		−	0.728988i	0.931206	−	0.364494i	$-0.118758\pi$
$240$	12.2099	−	4.19928i	0.788146	−	0.271063i
$241$	9.76276	+	5.63653i	0.628875	+	0.363081i	0.780316	−	0.625385i	$-0.215058\pi$
$241$	9.76276	+	5.63653i	0.628875	+	0.363081i	−0.151441	+	0.988466i	$0.548392\pi$
$242$	4.66883	−	7.25708i	0.300124	−	0.466503i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−25.2474	−	2.43564i	−1.61630	−	0.155926i
$245$	−19.0276	+	12.1868i	−1.21563	+	0.778588i
$246$	8.42325	+	0.405359i	0.537047	+	0.0258447i
$247$	−14.9240	+	8.61637i	−0.949590	+	0.548246i
$248$	3.55245	−	4.50376i	0.225581	−	0.285989i
$249$	−1.78661	+	3.09450i	−0.113222	+	0.196106i
$250$	−0.877184	−	1.70353i	−0.0554780	−	0.107741i
$251$			3.26625i			0.206164i	0.994673	+	0.103082i	$0.0328704\pi$
$251$			3.26625i			0.206164i	−0.994673	+	0.103082i	$0.967130\pi$
$252$	4.00509	−	3.45821i	0.252297	−	0.217847i
$253$		−	6.78124i		−	0.426333i
$254$	−26.4110	+	13.5995i	−1.65717	+	0.853311i
$255$	5.09893	−	8.83161i	0.319308	−	0.553057i
$256$	−12.6153	+	9.84149i	−0.788455	+	0.615093i
$257$	−10.4533	+	6.03522i	−0.652059	+	0.376467i	−0.789245	−	0.614079i	$-0.789528\pi$
$257$	−10.4533	+	6.03522i	−0.652059	+	0.376467i	0.137185	+	0.990545i	$0.456194\pi$
$258$	0.454635	−	9.44719i	0.0283043	−	0.588156i
$259$	−0.576861	+	2.36987i	−0.0358444	+	0.147257i
$260$	−32.6683	−	3.15154i	−2.02600	−	0.195450i
$261$	8.55928	−	4.94170i	0.529806	−	0.305884i
$262$	0.679038	+	0.436858i	0.0419511	+	0.0269892i
$263$	14.1861	+	8.19034i	0.874752	+	0.505038i	0.868924	−	0.494945i	$-0.164812\pi$
$263$	14.1861	+	8.19034i	0.874752	+	0.505038i	0.00582745	+	0.999983i	$0.498145\pi$
$264$	5.81485	−	2.31807i	0.357879	−	0.142667i
$265$		−	11.6501i		−	0.715663i
$266$	12.3297	−	2.97474i	0.755984	−	0.182393i
$267$	7.30063			0.446791
$268$	−7.30765	−	16.0428i	−0.446386	−	0.979973i
$269$	3.73572	−	6.47046i	0.227771	−	0.394511i	−0.729376	−	0.684113i	$-0.760190\pi$
$269$	3.73572	−	6.47046i	0.227771	−	0.394511i	0.957147	+	0.289602i	$0.0935229\pi$
$270$	3.83914	+	2.46991i	0.233643	+	0.150314i
$271$	−4.48617	−	7.77027i	−0.272515	−	0.472011i	0.696990	−	0.717081i	$-0.254522\pi$
$271$	−4.48617	−	7.77027i	−0.272515	−	0.472011i	−0.969505	+	0.245070i	$0.921189\pi$
$272$	−2.41571	+	12.4039i	−0.146474	+	0.752095i
$273$	−12.9083	+	3.77940i	−0.781244	+	0.228740i
$274$	−18.5843	−	0.894345i	−1.12272	−	0.0540294i
$275$	−5.99747	−	10.3879i	−0.361661	−	0.626415i
$276$	−3.55945	+	4.98827i	−0.214254	+	0.300258i
$277$	−5.31638	−	3.06942i	−0.319430	−	0.184423i	0.331708	−	0.943382i	$-0.392375\pi$
$277$	−5.31638	−	3.06942i	−0.319430	−	0.184423i	−0.651139	+	0.758959i	$0.725708\pi$
$278$	12.0051	−	6.18169i	0.720021	−	0.370753i
$279$	2.02805			0.121416
$280$	22.4054	+	9.02785i	1.33898	+	0.539517i
$281$	−19.2936			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$281$	−19.2936			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$282$	2.66836	−	1.37399i	0.158898	−	0.0818199i
$283$	19.3500	+	11.1718i	1.15024	+	0.664092i	0.948946	−	0.315439i	$-0.102152\pi$
$283$	19.3500	+	11.1718i	1.15024	+	0.664092i	0.201295	+	0.979531i	$0.435485\pi$
$284$	−19.0537	−	13.5960i	−1.13063	−	0.806777i
$285$	5.47108	+	9.47619i	0.324079	+	0.561321i
$286$	−15.8932	−	0.764842i	−0.939785	−	0.0452260i
$287$	11.4097	+	10.8960i	0.673495	+	0.643169i
$288$	−5.49413	−	1.34703i	−0.323745	−	0.0793746i
$289$	−3.50964	−	6.07887i	−0.206449	−	0.357581i
$290$	37.9438	+	24.4111i	2.22814	+	1.43347i
$291$	−7.61188	+	13.1842i	−0.446216	+	0.772869i
$292$	−16.4362	+	7.48685i	−0.961859	+	0.438135i
$293$	14.0707			0.822018			0.411009	−	0.911631i	$-0.365176\pi$
$293$	14.0707			0.822018			0.411009	+	0.911631i	$0.365176\pi$
$294$	9.89947	+	0.0200906i	0.577349	+	0.00117170i
$295$			39.6403i			2.30795i
$296$	2.42211	−	0.965565i	0.140782	−	0.0561223i
$297$	1.91668	+	1.10660i	0.111217	+	0.0642113i
$298$	−12.6024	−	8.10774i	−0.730037	−	0.469669i
$299$	13.4896	−	7.78823i	0.780124	−	0.450405i
$300$	−1.04086	+	10.7894i	−0.0600943	+	0.622925i
$301$	12.2205	−	12.7967i	0.704377	−	0.737590i
$302$	0.0826691	−	1.71784i	0.00475707	−	0.0988507i
$303$	8.52383	−	4.92124i	0.489681	−	0.282718i
$304$	−10.2301	−	8.89934i	−0.586735	−	0.510412i
$305$	20.4690	−	35.4533i	1.17205	−	2.03005i
$306$	−3.97216	+	2.04534i	−0.227073	+	0.116924i
$307$			9.61787i			0.548921i	0.961598	+	0.274460i	$0.0884992\pi$
$307$			9.61787i			0.548921i	−0.961598	+	0.274460i	$0.911501\pi$
$308$	11.0603	+	3.84964i	0.630220	+	0.219354i
$309$			1.98452i			0.112895i
$310$	4.23829	+	8.23098i	0.240719	+	0.467488i
$311$	−10.8485	+	18.7902i	−0.615162	+	1.06549i	0.375194	+	0.926946i	$0.377576\pi$
$311$	−10.8485	+	18.7902i	−0.615162	+	1.06549i	−0.990356	+	0.138546i	$0.955757\pi$
$312$	11.2895	+	8.90491i	0.639145	+	0.504142i
$313$	−9.46514	+	5.46470i	−0.535001	+	0.308883i	−0.743051	−	0.669235i	$-0.766622\pi$
$313$	−9.46514	+	5.46470i	−0.535001	+	0.308883i	0.208049	+	0.978118i	$0.433289\pi$
$314$	5.12065	+	0.246425i	0.288975	+	0.0139066i
$315$	2.39978	+	8.19629i	0.135212	+	0.461809i
$316$	−2.12914	+	22.0702i	−0.119773	+	1.24155i
$317$	6.14253	−	3.54639i	0.344999	−	0.199185i	−0.317482	−	0.948264i	$-0.602837\pi$
$317$	6.14253	−	3.54639i	0.344999	−	0.199185i	0.662480	+	0.749079i	$0.269504\pi$
$318$	−2.76157	+	4.29249i	−0.154861	+	0.240711i
$319$	18.9433	+	10.9369i	1.06062	+	0.612352i
$320$	−6.01484	−	25.1134i	−0.336240	−	1.40388i
$321$		−	3.23611i		−	0.180622i
$322$	−11.1447	+	2.68883i	−0.621069	+	0.149843i
$323$	−10.7092			−0.595874
$324$	−0.829058	−	1.82007i	−0.0460588	−	0.101115i
$325$	13.7761	−	23.8610i	0.764163	−	1.32357i
$326$	−15.1742	+	23.5863i	−0.840423	+	1.30633i
$327$	2.09576	+	3.62997i	0.115896	+	0.200738i
$328$	2.42466	−	16.6908i	0.133880	−	0.921595i
$329$	5.45567	+	1.32799i	0.300781	+	0.0732144i
$330$	−0.485647	+	10.0916i	−0.0267340	+	0.555525i
$331$	−5.86202	−	10.1533i	−0.322206	−	0.558077i	0.658737	−	0.752373i	$-0.271091\pi$
$331$	−5.86202	−	10.1533i	−0.322206	−	0.558077i	−0.980943	+	0.194297i	$0.937758\pi$
$332$	5.81729	+	4.15101i	0.319265	+	0.227816i
$333$	0.798374	+	0.460941i	0.0437506	+	0.0252594i
$334$	8.02611	+	15.5871i	0.439169	+	0.852889i
$335$	28.4526			1.55453
$336$	−6.11529	−	8.63732i	−0.333616	−	0.471204i
$337$	23.5287			1.28169			0.640846	−	0.767670i	$-0.278584\pi$
$337$	23.5287			1.28169			0.640846	+	0.767670i	$0.278584\pi$
$338$	−8.31539	−	16.1489i	−0.452298	−	0.878385i
$339$	2.46515	+	1.42326i	0.133889	+	0.0773007i
$340$	−16.6024	−	11.8469i	−0.900389	−	0.642486i
$341$	2.24423	+	3.88712i	0.121532	+	0.210499i
$342$	0.230435	−	4.78837i	0.0124605	−	0.258925i
$343$	13.9686	+	12.1605i	0.754232	+	0.656608i
$344$	−18.7197	−	2.71940i	−1.00930	−	0.146620i
$345$	−4.94525	−	8.56542i	−0.266243	−	0.461147i
$346$	0.794735	−	1.23531i	0.0427252	−	0.0664107i
$347$	5.17132	−	8.95699i	0.277611	−	0.480837i	−0.693179	−	0.720765i	$-0.743791\pi$
$347$	5.17132	−	8.95699i	0.277611	−	0.480837i	0.970791	+	0.239928i	$0.0771240\pi$
$348$	−8.19392	−	17.9885i	−0.439240	−	0.964285i
$349$	−0.830301			−0.0444450			−0.0222225	−	0.999753i	$-0.507074\pi$
$349$	−0.830301			−0.0444450			−0.0222225	+	0.999753i	$0.507074\pi$
$350$	−14.6941	+	13.9755i	−0.785430	+	0.747022i
$351$			5.08369i			0.271347i
$352$	−3.49796	−	12.0211i	−0.186442	−	0.640729i
$353$	−4.21179	−	2.43168i	−0.224171	−	0.129425i	0.383709	−	0.923454i	$-0.374647\pi$
$353$	−4.21179	−	2.43168i	−0.224171	−	0.129425i	−0.607880	+	0.794029i	$0.707980\pi$
$354$	9.39640	−	14.6054i	0.499413	−	0.776271i
$355$	32.7173	−	18.8894i	1.73646	−	1.00254i
$356$	1.40209	−	14.5338i	0.0743106	−	0.770289i
$357$	−8.12140	−	1.97686i	−0.429830	−	0.104627i
$358$	−3.56828	−	0.171719i	−0.188589	−	0.00907564i
$359$	16.3080	−	9.41543i	0.860704	−	0.496928i	−0.00354407	−	0.999994i	$-0.501128\pi$
$359$	16.3080	−	9.41543i	0.860704	−	0.496928i	0.864248	+	0.503066i	$0.167795\pi$
$360$	5.65430	−	7.16846i	0.298008	−	0.377811i
$361$	−3.75460	+	6.50317i	−0.197611	+	0.342272i
$362$	−5.37271	−	10.4341i	−0.282383	−	0.548403i
$363$		−	6.10177i		−	0.320260i
$364$	5.04483	+	26.4231i	0.264421	+	1.38495i
$365$		−	29.1503i		−	1.52579i
$366$	−15.9457	+	8.21076i	−0.833495	+	0.429183i
$367$	−10.7270	+	18.5796i	−0.559943	+	0.969850i	0.437557	+	0.899190i	$0.355844\pi$
$367$	−10.7270	+	18.5796i	−0.559943	+	0.969850i	−0.997501	+	0.0706593i	$0.977490\pi$
$368$	9.24684	+	8.04401i	0.482025	+	0.419323i
$369$	5.16414	−	2.98152i	0.268834	−	0.155212i
$370$	−0.202291	+	4.20355i	−0.0105166	+	0.218532i
$371$	−9.16414	+	2.68316i	−0.475779	+	0.139303i
$372$	0.389487	−	4.03735i	0.0201940	−	0.209327i
$373$	14.1525	−	8.17098i	0.732791	−	0.423077i	−0.0866513	−	0.996239i	$-0.527617\pi$
$373$	14.1525	−	8.17098i	0.732791	−	0.423077i	0.819442	+	0.573162i	$0.194283\pi$
$374$	−8.31585	−	5.34999i	−0.430002	−	0.276642i
$375$	−1.17337	−	0.677448i	−0.0605928	−	0.0349832i
$376$	−2.22282	−	5.57593i	−0.114633	−	0.287557i
$377$			50.2442i			2.58771i
$378$	1.05866	−	3.58876i	0.0544517	−	0.184586i
$379$	−4.31636			−0.221717			−0.110858	−	0.993836i	$-0.535360\pi$
$379$	−4.31636			−0.221717			−0.110858	+	0.993836i	$0.535360\pi$
$380$	19.9155	−	9.07169i	1.02165	−	0.465368i
$381$	−10.5029	+	18.1916i	−0.538080	+	0.931981i
$382$	7.22573	+	4.64867i	0.369700	+	0.237846i
$383$	−10.0948	−	17.4848i	−0.515823	−	0.893431i	−0.999831	−	0.0183677i	$-0.994153\pi$
$383$	−10.0948	−	17.4848i	−0.515823	−	0.893431i	0.484009	−	0.875063i	$-0.339180\pi$
$384$	−3.73676	+	10.6788i	−0.190691	+	0.544950i
$385$	−13.0541	+	13.6696i	−0.665298	+	0.696668i
$386$	−12.9771	−	0.624506i	−0.660515	−	0.0317865i
$387$	−3.34395	−	5.79189i	−0.169983	−	0.294418i
$388$	24.7846	+	17.6854i	1.25825	+	0.897842i
$389$	−29.2383	−	16.8807i	−1.48244	−	0.855886i	−0.482637	−	0.875820i	$-0.660321\pi$
$389$	−29.2383	−	16.8807i	−1.48244	−	0.855886i	−0.999801	+	0.0199339i	$0.993654\pi$
$390$	−20.6326	+	10.6241i	−1.04477	+	0.537973i
$391$	9.67989			0.489533
$392$	1.94119	−	19.7036i	0.0980451	−	0.995182i
$393$	0.570937			0.0287999
$394$	25.4939	−	13.1273i	1.28436	−	0.661343i
$395$	−30.9918	−	17.8931i	−1.55937	−	0.900302i
$396$	2.57107	−	3.60313i	0.129201	−	0.181064i
$397$	−0.0441158	−	0.0764109i	−0.00221411	−	0.00383495i	0.864916	−	0.501916i	$-0.167371\pi$
$397$	−0.0441158	−	0.0764109i	−0.00221411	−	0.00383495i	−0.867130	+	0.498081i	$0.834038\pi$
$398$	−4.64330	−	0.223453i	−0.232748	−	0.0112007i
$399$	6.19404	−	6.48610i	0.310090	−	0.324711i
$400$	21.2792	+	4.14421i	1.06396	+	0.207211i
$401$	12.6037	+	21.8303i	0.629400	+	1.09015i	0.987672	+	0.156536i	$0.0500327\pi$
$401$	12.6037	+	21.8303i	0.629400	+	1.09015i	−0.358272	+	0.933617i	$0.616634\pi$
$402$	−10.4833	−	6.74443i	−0.522860	−	0.336382i
$403$	−5.15498	+	8.92869i	−0.256788	+	0.444770i
$404$	−8.15998	−	17.9140i	−0.405974	−	0.891255i
$405$	3.22796			0.160399
$406$	10.4632	−	35.4692i	0.519279	−	1.76031i
$407$			2.04031i			0.101134i
$408$	3.30893	+	8.30041i	0.163816	+	0.410932i
$409$	−26.9181	−	15.5412i	−1.33102	−	0.768462i	−0.345560	−	0.938397i	$-0.612311\pi$
$409$	−26.9181	−	15.5412i	−1.33102	−	0.768462i	−0.985455	+	0.169935i	$0.945644\pi$
$410$	22.8929	+	14.7281i	1.13060	+	0.727371i
$411$	−11.3937	+	6.57813i	−0.562008	+	0.324475i
$412$	3.95069	+	0.381127i	0.194637	+	0.0187768i
$413$	31.1816	−	9.12962i	1.53434	−	0.449239i
$414$	−0.208287	+	4.32815i	−0.0102367	+	0.212717i
$415$	−9.98894	+	5.76712i	−0.490338	+	0.283097i
$416$	19.8957	−	20.7646i	0.975467	−	1.01807i
$417$	4.77411	−	8.26899i	0.233789	−	0.404934i
$418$	9.43278	−	4.85713i	0.461373	−	0.237570i
$419$			22.7655i			1.11217i	0.831126	+	0.556085i	$0.187697\pi$
$419$			22.7655i			1.11217i	−0.831126	+	0.556085i	$0.812303\pi$
$420$	16.7777	−	3.20328i	0.818668	−	0.156304i
$421$		−	24.0207i		−	1.17070i	−0.810781	−	0.585349i	$-0.800958\pi$
$421$		−	24.0207i		−	1.17070i	0.810781	−	0.585349i	$-0.199042\pi$
$422$	14.0425	+	27.2713i	0.683580	+	1.32755i
$423$	1.06113	−	1.83793i	0.0515939	−	0.0893633i
$424$	8.01494	+	6.32198i	0.389240	+	0.307023i
$425$	14.8283	−	8.56109i	0.719276	−	0.415274i
$426$	−16.5322	−	0.795594i	−0.800989	−	0.0385467i
$427$	−32.6023	−	7.93586i	−1.57773	−	0.384043i
$428$	−6.44230	−	0.621496i	−0.311400	−	0.0300411i
$429$	−9.74383	+	5.62560i	−0.470436	+	0.271607i
$430$	16.5185	−	25.6758i	0.796593	−	1.23820i
$431$	−28.2391	−	16.3039i	−1.36023	−	0.785330i	−0.370577	−	0.928802i	$-0.620840\pi$
$431$	−28.2391	−	16.3039i	−1.36023	−	0.785330i	−0.989654	+	0.143471i	$0.954174\pi$
$432$	−3.78254	+	1.30091i	−0.181988	+	0.0625900i
$433$		−	18.4752i		−	0.887861i	−0.896061	−	0.443931i	$-0.853584\pi$
$433$		−	18.4752i		−	0.887861i	0.896061	−	0.443931i	$-0.146416\pi$
$434$	5.49846	−	5.22958i	0.263935	−	0.251028i
$435$	31.9032			1.52964
$436$	7.62888	−	3.47502i	0.365357	−	0.166423i
$437$	−5.19319	+	8.99487i	−0.248424	+	0.430283i
$438$	−6.90982	+	10.7404i	−0.330164	+	0.513196i
$439$	11.2138	+	19.4229i	0.535206	+	0.927004i	0.999153	+	0.0411413i	$0.0130994\pi$
$439$	11.2138	+	19.4229i	0.535206	+	0.927004i	−0.463947	+	0.885863i	$0.653567\pi$
$440$	19.9967	+	2.90491i	0.953305	+	0.138486i
$441$	5.89461	−	3.77540i	0.280696	−	0.179781i
$442$	1.09177	−	22.6868i	0.0519304	−	1.07910i
$443$	−4.52168	−	7.83178i	−0.214832	−	0.372099i	0.738389	−	0.674375i	$-0.235587\pi$
$443$	−4.52168	−	7.83178i	−0.214832	−	0.372099i	−0.953220	+	0.302276i	$0.902254\pi$
$444$	1.07095	−	1.50084i	0.0508251	−	0.0712269i
$445$	20.4089	+	11.7831i	0.967474	+	0.558571i
$446$	12.5124	+	24.2997i	0.592478	+	1.15062i
$447$	−10.5961			−0.501179
$448$	−18.3693	+	10.5153i	−0.867866	+	0.496799i
$449$	5.65664			0.266954			0.133477	−	0.991052i	$-0.457386\pi$
$449$	5.65664			0.266954			0.133477	+	0.991052i	$0.457386\pi$
$450$	3.50884	+	6.81434i	0.165408	+	0.321231i
$451$	11.4292	+	6.59867i	0.538182	+	0.310719i
$452$	3.30679	−	4.63418i	0.155538	−	0.217974i
$453$	−0.608052	−	1.05318i	−0.0285688	−	0.0494826i
$454$	−0.0366447	+	0.761467i	−0.00171982	+	0.0357374i
$455$	−42.1849	−	10.2684i	−1.97766	−	0.481391i
$456$	−9.48823	−	1.37835i	−0.444327	−	0.0645471i
$457$	−4.68971	−	8.12282i	−0.219376	−	0.379970i	0.735242	−	0.677805i	$-0.237069\pi$
$457$	−4.68971	−	8.12282i	−0.219376	−	0.379970i	−0.954617	+	0.297835i	$0.903735\pi$
$458$	−17.4933	+	27.1910i	−0.817410	+	1.27055i
$459$	−1.57961	+	2.73597i	−0.0737301	+	0.127704i
$460$	−18.0014	+	8.19979i	−0.839320	+	0.382317i
$461$	−31.7960			−1.48089			−0.740444	−	0.672118i	$-0.765385\pi$
$461$	−31.7960			−1.48089			−0.740444	+	0.672118i	$0.765385\pi$
$462$	8.05004	−	1.94220i	0.374522	−	0.0903592i
$463$			8.87505i			0.412458i	0.978504	+	0.206229i	$0.0661193\pi$
$463$			8.87505i			0.412458i	−0.978504	+	0.206229i	$0.933881\pi$
$464$	−37.3844	+	12.8574i	−1.73553	+	0.596890i
$465$	5.66939	+	3.27323i	0.262912	+	0.151792i
$466$	2.29923	−	3.57384i	0.106510	−	0.165555i
$467$	2.70998	−	1.56461i	0.125403	−	0.0724015i	−0.435986	−	0.899953i	$-0.643600\pi$
$467$	2.70998	−	1.56461i	0.125403	−	0.0724015i	0.561389	+	0.827552i	$0.310267\pi$
$468$	10.1204	+	0.976326i	0.467816	+	0.0451307i
$469$	−6.55294	−	22.3811i	−0.302587	−	1.03346i
$470$	9.67698	+	0.465693i	0.446366	+	0.0214808i
$471$	3.13938	−	1.81252i	0.144655	−	0.0835165i
$472$	−27.2713	−	21.5109i	−1.25526	−	0.990121i
$473$	7.40081	−	12.8186i	0.340290	−	0.589399i
$474$	7.17750	+	13.9391i	0.329673	+	0.640242i
$475$			18.3719i			0.842959i
$476$	−5.49518	+	15.7881i	−0.251871	+	0.723645i
$477$			3.60913i			0.165251i
$478$	−14.1698	+	7.29632i	−0.648113	+	0.333726i
$479$	8.19517	−	14.1945i	0.374447	−	0.648561i	−0.615797	−	0.787905i	$-0.711166\pi$
$479$	8.19517	−	14.1945i	0.374447	−	0.648561i	0.990244	+	0.139344i	$0.0444993\pi$
$480$	−13.1848	−	12.6330i	−0.601799	−	0.576617i
$481$	−4.05869	+	2.34328i	−0.185060	+	0.106845i
$482$	0.766328	−	15.9241i	0.0349053	−	0.725323i
$483$	−5.59872	+	5.86270i	−0.254750	+	0.266762i
$484$	−12.1471	−	1.17185i	−0.552143	−	0.0532658i
$485$	−42.5580	+	24.5708i	−1.93246	+	1.11570i
$486$	−1.18934	−	0.765161i	−0.0539495	−	0.0347084i
$487$	−25.4297	−	14.6819i	−1.15233	−	0.665299i	−0.202877	−	0.979204i	$-0.565029\pi$
$487$	−25.4297	−	14.6819i	−1.15233	−	0.665299i	−0.949454	+	0.313905i	$0.898363\pi$
$488$	13.2832	+	33.3209i	0.601304	+	1.50837i
$489$			19.8314i			0.896808i
$490$	27.6415	+	16.0337i	1.24872	+	0.724330i
$491$	33.8967			1.52974			0.764869	−	0.644186i	$-0.222804\pi$
$491$	33.8967			1.52974			0.764869	+	0.644186i	$0.222804\pi$
$492$	−4.94370	−	10.8531i	−0.222879	−	0.489298i
$493$	−15.6120	+	27.0407i	−0.703128	+	1.21785i
$494$	20.4956	+	13.1858i	0.922140	+	0.593258i
$495$	3.57205	+	6.18698i	0.160552	+	0.278084i
$496$	−7.96258	−	1.55075i	−0.357530	−	0.0696307i
$497$	−22.3938	−	21.3854i	−1.00450	−	0.959267i
$498$	5.04746	+	0.242903i	0.226182	+	0.0108847i
$499$	4.44527	+	7.69943i	0.198997	+	0.344674i	0.948204	−	0.317663i	$-0.102898\pi$
$499$	4.44527	+	7.69943i	0.198997	+	0.344674i	−0.749206	+	0.662337i	$0.769565\pi$
$500$	−1.57398	+	2.20580i	−0.0703906	+	0.0986463i
$501$	10.7362	+	6.19856i	0.479659	+	0.276931i
$502$	4.10672	−	2.11463i	0.183292	−	0.0943805i
$503$	−1.51626			−0.0676065			−0.0338032	−	0.999429i	$-0.510762\pi$
$503$	−1.51626			−0.0676065			−0.0338032	+	0.999429i	$0.510762\pi$
$504$	−6.94104	−	2.79677i	−0.309179	−	0.124578i
$505$	31.7711			1.41380
$506$	−8.52618	+	4.39030i	−0.379035	+	0.195173i
$507$	−11.1232	−	6.42196i	−0.493997	−	0.285209i
$508$	34.1979	+	24.4024i	1.51729	+	1.08268i
$509$	3.71720	+	6.43837i	0.164762	+	0.285376i	0.936571	−	0.350479i	$-0.113981\pi$
$509$	3.71720	+	6.43837i	0.164762	+	0.285376i	−0.771809	+	0.635855i	$0.780648\pi$
$510$	−14.4053	−	0.693238i	−0.637877	−	0.0306971i
$511$	−22.9299	+	6.71363i	−1.01436	+	0.296994i
$512$	20.5412	+	9.48986i	0.907803	+	0.419397i
$513$	−1.69490	−	2.93566i	−0.0748318	−	0.129613i
$514$	14.3559	+	9.23582i	0.633210	+	0.407375i
$515$	−3.20297	+	5.54771i	−0.141140	+	0.244461i
$516$	−12.1725	+	5.54466i	−0.535863	+	0.244090i
$517$	4.69698			0.206573
$518$	3.35316	−	0.809001i	0.147329	−	0.0355455i
$519$		−	1.03865i		−	0.0455917i
$520$	17.1875	+	43.1148i	0.753723	+	1.89071i
$521$	−11.7724	−	6.79678i	−0.515757	−	0.297772i	0.219440	−	0.975626i	$-0.429577\pi$
$521$	−11.7724	−	6.79678i	−0.515757	−	0.297772i	−0.735197	+	0.677854i	$0.762910\pi$
$522$	−11.7547	−	7.56239i	−0.514490	−	0.330997i
$523$	3.38679	−	1.95536i	0.148094	−	0.0855020i	−0.424122	−	0.905605i	$-0.639417\pi$
$523$	3.38679	−	1.95536i	0.148094	−	0.0855020i	0.572216	+	0.820103i	$0.306084\pi$
$524$	0.109649	−	1.13660i	0.00479002	−	0.0496524i
$525$	−3.39136	+	13.9325i	−0.148011	+	0.608063i
$526$	1.11354	−	23.1390i	0.0485525	−	1.00891i
$527$	−5.54868	+	3.20353i	−0.241704	+	0.139548i
$528$	−6.67918	−	5.81035i	−0.290674	−	0.252863i
$529$	−6.80594	+	11.7882i	−0.295910	+	0.512532i
$530$	−14.6479	+	7.54251i	−0.636266	+	0.327626i
$531$		−	12.2803i		−	0.532920i
$532$	−11.7227	−	13.5765i	−0.508243	−	0.588615i
$533$			30.3142i			1.31305i
$534$	−4.72656	−	9.17922i	−0.204538	−	0.397224i
$535$	5.22301	−	9.04652i	0.225811	−	0.391115i
$536$	−15.4399	+	19.5745i	−0.666900	+	0.845489i
$537$	−2.18764	+	1.26304i	−0.0944038	+	0.0545041i
$538$	−10.5540	−	0.507899i	−0.455015	−	0.0218971i
$539$	13.7592	+	7.12025i	0.592650	+	0.306691i
$540$	0.619932	−	6.42609i	0.0266776	−	0.276535i
$541$	29.3866	−	16.9663i	1.26343	−	0.729440i	0.289691	−	0.957120i	$-0.406447\pi$
$541$	29.3866	−	16.9663i	1.26343	−	0.729440i	0.973736	+	0.227680i	$0.0731140\pi$
$542$	−6.86528	+	10.6712i	−0.294889	+	0.458366i
$543$	−7.18686	−	4.14933i	−0.308418	−	0.178065i
$544$	17.1596	−	4.99317i	0.735711	−	0.214080i
$545$			13.5301i			0.579565i
$546$	13.1090	+	13.7830i	0.561012	+	0.589856i
$547$	19.9416			0.852640			0.426320	−	0.904572i	$-0.359810\pi$
$547$	19.9416			0.852640			0.426320	+	0.904572i	$0.359810\pi$
$548$	10.9073	+	23.9453i	0.465937	+	1.02289i
$549$	−6.34115	+	10.9832i	−0.270634	+	0.468752i
$550$	−9.17805	+	14.2661i	−0.391353	+	0.608307i
$551$	−16.7514	−	29.0143i	−0.713634	−	1.23605i
$552$	8.57629	+	1.24587i	0.365031	+	0.0530278i
$553$	−6.93720	+	28.4995i	−0.295000	+	1.21192i
$554$	−0.417310	+	8.67158i	−0.0177298	+	0.368420i
$555$	1.48790	+	2.57712i	0.0631579	+	0.109393i
$556$	−15.5447	−	11.0922i	−0.659242	−	0.470412i
$557$	−29.5999	−	17.0895i	−1.25419	−	0.724107i	−0.282251	−	0.959341i	$-0.591081\pi$
$557$	−29.5999	−	17.0895i	−1.25419	−	0.724107i	−0.971939	+	0.235234i	$0.924414\pi$
$558$	−1.31299	−	2.54990i	−0.0555834	−	0.107946i
$559$	33.9992			1.43801
$560$	−3.15480	−	34.0156i	−0.133314	−	1.43742i
$561$	−6.99199			−0.295202
$562$	12.4910	+	24.2582i	0.526902	+	1.02327i
$563$	1.95583	+	1.12920i	0.0824283	+	0.0475900i	0.540648	−	0.841249i	$-0.318179\pi$
$563$	1.95583	+	1.12920i	0.0824283	+	0.0475900i	−0.458219	+	0.888839i	$0.651513\pi$
$564$	−3.45509	−	2.46543i	−0.145485	−	0.103813i
$565$	4.59422	+	7.95742i	0.193280	+	0.334771i
$566$	1.51888	−	31.5620i	0.0638434	−	1.32665i
$567$	−0.743436	−	2.53915i	−0.0312214	−	0.106634i
$568$	−4.75886	+	32.7589i	−0.199677	+	1.37453i
$569$	−14.5803	−	25.2538i	−0.611236	−	1.05869i	−0.991032	−	0.133622i	$-0.957339\pi$
$569$	−14.5803	−	25.2538i	−0.611236	−	1.05869i	0.379796	−	0.925070i	$-0.375994\pi$
$570$	8.37252	−	13.0140i	0.350686	−	0.545095i
$571$	13.1289	−	22.7399i	0.549427	−	0.951636i	−0.448886	−	0.893589i	$-0.648179\pi$
$571$	13.1289	−	22.7399i	0.549427	−	0.951636i	0.998314	−	0.0580474i	$-0.0184874\pi$
$572$	9.32790	+	20.4780i	0.390019	+	0.856228i
$573$	6.07541			0.253804
$574$	6.31284	−	21.3999i	0.263493	−	0.893215i
$575$		−	16.6061i		−	0.692522i
$576$	1.86335	+	7.77997i	0.0776398	+	0.324165i
$577$	0.0467698	+	0.0270026i	0.00194705	+	0.00112413i	0.500973	−	0.865463i	$-0.332976\pi$
$577$	0.0467698	+	0.0270026i	0.00194705	+	0.00112413i	−0.499026	+	0.866587i	$0.666309\pi$
$578$	−5.37087	+	8.34830i	−0.223399	+	0.347244i
$579$	−7.95599	+	4.59340i	−0.330640	+	0.190895i
$580$	6.12703	−	63.5116i	0.254411	−	2.63718i
$581$	6.83705	+	6.52919i	0.283649	+	0.270876i
$582$	21.5048	+	1.03489i	0.891401	+	0.0428976i
$583$	−6.91756	+	3.99386i	−0.286496	+	0.165409i
$584$	20.0545	+	15.8185i	0.829860	+	0.654573i
$585$	−8.20498	+	14.2114i	−0.339234	+	0.587571i
$586$	−9.10962	−	17.6913i	−0.376315	−	0.730822i
$587$			4.75946i			0.196444i	0.995165	+	0.0982219i	$0.0313155\pi$
$587$			4.75946i			0.196444i	−0.995165	+	0.0982219i	$0.968685\pi$
$588$	−6.38384	−	12.4598i	−0.263265	−	0.513833i
$589$		−	6.87468i		−	0.283266i
$590$	49.8405	−	25.6639i	2.05190	−	1.05656i
$591$	10.1382	−	17.5599i	0.417029	−	0.722316i
$592$	−2.78214	−	2.42024i	−0.114345	−	0.0994713i
$593$	−10.2802	+	5.93527i	−0.422157	+	0.243732i	−0.696000	−	0.718042i	$-0.745038\pi$
$593$	−10.2802	+	5.93527i	−0.422157	+	0.243732i	0.273843	+	0.961774i	$0.411705\pi$
$594$	0.150450	−	3.12631i	0.00617304	−	0.128274i
$595$	−19.5127	−	18.6341i	−0.799944	−	0.763923i
$596$	−2.03499	+	21.0943i	−0.0833565	+	0.864057i
$597$	−2.84672	+	1.64355i	−0.116508	+	0.0672662i
$598$	−18.5257	−	11.9185i	−0.757572	−	0.487383i
$599$	25.6580	+	14.8136i	1.04836	+	0.605269i	0.922189	−	0.386740i	$-0.126399\pi$
$599$	25.6580	+	14.8136i	1.04836	+	0.605269i	0.126167	+	0.992009i	$0.459732\pi$
$600$	14.2396	−	5.67655i	0.581328	−	0.231744i
$601$		−	26.4608i		−	1.07936i	−0.841870	−	0.539680i	$-0.818545\pi$
$601$		−	26.4608i		−	1.07936i	0.841870	−	0.539680i	$-0.181455\pi$
$602$	−24.0013	−	7.08023i	−0.978220	−	0.288569i
$603$	−8.81440			−0.358950
$604$	−2.21340	+	1.00822i	−0.0900618	+	0.0410239i
$605$	9.84814	−	17.0575i	0.400384	−	0.693485i
$606$	−11.7060	−	7.53107i	−0.475525	−	0.305929i
$607$	−7.69208	−	13.3231i	−0.312212	−	0.540767i	0.666629	−	0.745390i	$-0.267737\pi$
$607$	−7.69208	−	13.3231i	−0.312212	−	0.540767i	−0.978841	+	0.204623i	$0.934403\pi$
$608$	−4.56618	+	18.6241i	−0.185183	+	0.755305i
$609$	−7.34768	−	25.0955i	−0.297743	−	1.01692i
$610$	−57.8282	−	2.78291i	−2.34139	−	0.112677i
$611$	5.39446	+	9.34348i	0.218237	+	0.377997i
$612$	5.14329	+	3.67007i	0.207905	+	0.148354i
$613$	16.8302	+	9.71692i	0.679765	+	0.392463i	0.799767	−	0.600311i	$-0.204957\pi$
$613$	16.8302	+	9.71692i	0.679765	+	0.392463i	−0.120001	+	0.992774i	$0.538290\pi$
$614$	12.0927	−	6.22678i	0.488023	−	0.251292i
$615$	19.2484			0.776172
$616$	−2.32043	−	16.3987i	−0.0934928	−	0.660721i
$617$	−0.173969			−0.00700371			−0.00350186	−	0.999994i	$-0.501115\pi$
$617$	−0.173969			−0.00700371			−0.00350186	+	0.999994i	$0.501115\pi$
$618$	2.49517	−	1.28481i	0.100370	−	0.0516827i
$619$	−32.8798	−	18.9832i	−1.32155	−	0.762998i	−0.337575	−	0.941299i	$-0.609607\pi$
$619$	−32.8798	−	18.9832i	−1.32155	−	0.762998i	−0.983976	+	0.178300i	$0.942940\pi$
$620$	7.60501	−	10.6578i	0.305425	−	0.428026i
$621$	1.53200	+	2.65351i	0.0614771	+	0.106482i
$622$	30.6487	+	1.47493i	1.22890	+	0.0591394i
$623$	4.56831	−	18.7677i	0.183026	−	0.751910i
$624$	3.88726	−	19.9598i	0.155615	−	0.799030i
$625$	11.3626	+	19.6805i	0.454503	+	0.787222i
$626$	12.9988	+	8.36275i	0.519535	+	0.334243i
$627$	3.75115	−	6.49718i	0.149807	−	0.259473i
$628$	−3.00537	−	6.59783i	−0.119927	−	0.263282i
$629$	−2.91244			−0.116127
$630$	8.75169	−	8.32372i	0.348676	−	0.331625i
$631$		−	26.0140i		−	1.03560i	−0.855501	−	0.517801i	$-0.826751\pi$
$631$		−	26.0140i		−	1.03560i	0.855501	−	0.517801i	$-0.173249\pi$
$632$	29.1277	−	11.6117i	1.15864	−	0.461887i
$633$	18.7841	+	10.8450i	0.746602	+	0.431051i
$634$	−8.43572	−	5.42711i	−0.335025	−	0.215538i
$635$	−58.7216	+	33.9030i	−2.33030	+	1.34540i
$636$	7.18491	+	0.693136i	0.284900	+	0.0274846i
$637$	1.63841	+	35.5481i	0.0649161	+	1.40847i
$638$	1.48696	−	30.8986i	0.0588693	−	1.22329i
$639$	−10.1356	+	5.85179i	−0.400958	+	0.231493i
$640$	−27.6815	+	23.8215i	−1.09421	+	0.941626i
$641$	−12.4573	+	21.5767i	−0.492035	+	0.852230i	−0.999958	−	0.00917289i	$-0.997080\pi$
$641$	−12.4573	+	21.5767i	−0.492035	+	0.852230i	0.507923	+	0.861403i	$0.330413\pi$
$642$	−4.06882	+	2.09511i	−0.160583	+	0.0826875i
$643$			4.80941i			0.189665i	0.995493	+	0.0948323i	$0.0302315\pi$
$643$			4.80941i			0.189665i	−0.995493	+	0.0948323i	$0.969769\pi$
$644$	10.5960	+	12.2716i	0.417540	+	0.483570i
$645$		−	21.5883i		−	0.850038i
$646$	6.93331	+	13.4648i	0.272788	+	0.529767i
$647$	4.27034	−	7.39644i	0.167884	−	0.290784i	−0.769792	−	0.638295i	$-0.779640\pi$
$647$	4.27034	−	7.39644i	0.167884	−	0.290784i	0.937676	+	0.347511i	$0.112973\pi$
$648$	−1.75166	+	2.22074i	−0.0688118	+	0.0872388i
$649$	23.5374	−	13.5893i	0.923925	−	0.533428i
$650$	−38.9198	−	1.87297i	−1.52656	−	0.0734638i
$651$	1.26903	−	5.21348i	0.0497374	−	0.204332i
$652$	39.4796	+	3.80864i	1.54614	+	0.149158i
$653$	24.1955	−	13.9693i	0.946845	−	0.546661i	0.0547454	−	0.998500i	$-0.482565\pi$
$653$	24.1955	−	13.9693i	0.946845	−	0.546661i	0.892099	+	0.451839i	$0.149232\pi$
$654$	3.20719	−	4.98515i	0.125411	−	0.194935i
$655$	1.59605	+	0.921481i	0.0623629	+	0.0360052i
$656$	−22.5554	+	7.75736i	−0.880641	+	0.302874i
$657$			9.03055i			0.352315i
$658$	−1.86240	−	7.71928i	−0.0726038	−	0.300929i
$659$	28.0553			1.09288			0.546439	−	0.837499i	$-0.315983\pi$
$659$	28.0553			1.09288			0.546439	+	0.837499i	$0.315983\pi$
$660$	13.0028	−	5.92288i	0.506133	−	0.230548i
$661$	4.47127	−	7.74447i	0.173912	−	0.301225i	−0.765872	−	0.642993i	$-0.777692\pi$
$661$	4.47127	−	7.74447i	0.173912	−	0.301225i	0.939784	+	0.341768i	$0.111026\pi$
$662$	−8.97077	+	13.9439i	−0.348659	+	0.541944i
$663$	−8.03027	−	13.9088i	−0.311870	−	0.540175i
$664$	1.45293	−	10.0016i	0.0563846	−	0.388138i
$665$	27.7838	−	8.13480i	1.07741	−	0.315454i
$666$	0.0626684	−	1.30223i	0.00242835	−	0.0504605i
$667$	15.1414	+	26.2257i	0.586277	+	1.01546i
$668$	14.4017	−	20.1828i	0.557219	−	0.780895i
$669$	16.7373	+	9.66329i	0.647102	+	0.373604i
$670$	−18.4207	−	35.7739i	−0.711654	−	1.38207i
$671$	−28.0684			−1.08357
$672$	−6.90071	+	13.2808i	−0.266201	+	0.512319i
$673$	45.4881			1.75344			0.876720	−	0.481002i	$-0.159727\pi$
$673$	45.4881			1.75344			0.876720	+	0.481002i	$0.159727\pi$
$674$	−15.2329	−	29.5831i	−0.586750	−	1.13950i
$675$	4.69363	+	2.70987i	0.180658	+	0.104303i
$676$	−14.9208	+	20.9102i	−0.573876	+	0.804238i
$677$	5.48447	+	9.49939i	0.210785	+	0.365091i	0.951961	−	0.306221i	$-0.0990645\pi$
$677$	5.48447	+	9.49939i	0.210785	+	0.365091i	−0.741175	+	0.671312i	$0.765731\pi$
$678$	0.193502	−	4.02092i	0.00743141	−	0.154423i
$679$	29.1293	+	27.8177i	1.11788	+	1.06754i
$680$	−4.14661	+	28.5443i	−0.159015	+	1.09462i
$681$	0.269531	+	0.466841i	0.0103284	+	0.0178894i
$682$	3.43439	−	5.33830i	0.131510	−	0.204414i
$683$	14.1037	−	24.4283i	0.539663	−	0.934723i	−0.459259	−	0.888302i	$-0.651885\pi$
$683$	14.1037	−	24.4283i	0.539663	−	0.934723i	0.998922	−	0.0464211i	$-0.0147816\pi$
$684$	−6.16969	+	2.81035i	−0.235904	+	0.107456i
$685$	−42.4679			−1.62262
$686$	6.24617	−	25.4359i	0.238480	−	0.971147i
$687$			22.8623i			0.872251i
$688$	8.70035	+	25.2973i	0.331698	+	0.964450i
$689$	−15.8896	−	9.17386i	−0.605345	−	0.349496i
$690$	−7.56781	+	11.7632i	−0.288102	+	0.447816i
$691$	8.22050	−	4.74611i	0.312723	−	0.180550i	−0.335422	−	0.942068i	$-0.608879\pi$
$691$	8.22050	−	4.74611i	0.312723	−	0.180550i	0.648144	+	0.761518i	$0.275545\pi$
$692$	−2.06770	−	0.199474i	−0.0786023	−	0.00758285i
$693$	4.04407	−	4.23475i	0.153621	−	0.160865i
$694$	−14.6098	−	0.703079i	−0.554581	−	0.0266885i
$695$	26.6920	−	15.4106i	1.01249	−	0.584559i
$696$	−17.3124	+	21.9484i	−0.656224	+	0.831954i
$697$	−9.41929	+	16.3147i	−0.356781	+	0.617963i
$698$	0.537552	+	1.04395i	0.0203466	+	0.0395142i
$699$		−	3.00490i		−	0.113656i
$700$	27.0848	+	9.42711i	1.02371	+	0.356311i
$701$			14.3589i			0.542328i	0.962533	+	0.271164i	$0.0874085\pi$
$701$			14.3589i			0.542328i	−0.962533	+	0.271164i	$0.912591\pi$
$702$	6.39182	−	3.29127i	0.241244	−	0.124221i
$703$	1.56250	−	2.70633i	0.0589309	−	0.102071i
$704$	−12.8497	+	12.1808i	−0.484293	+	0.459079i
$705$	5.93277	−	3.42529i	0.223441	−	0.129004i
$706$	−0.330605	+	6.86988i	−0.0124425	+	0.258551i
$707$	−7.31725	−	24.9915i	−0.275193	−	0.939904i
$708$	−24.4471	−	2.35844i	−0.918778	−	0.0886355i
$709$	−8.90161	+	5.13935i	−0.334307	+	0.193012i	−0.657752	−	0.753235i	$-0.728492\pi$
$709$	−8.90161	+	5.13935i	−0.334307	+	0.193012i	0.323445	+	0.946247i	$0.395159\pi$
$710$	−44.9317	−	28.9068i	−1.68626	−	1.08485i
$711$	9.60105	+	5.54317i	0.360068	+	0.207885i
$712$	−19.1813	+	7.64656i	−0.718851	+	0.286567i
$713$			6.21394i			0.232714i
$714$	2.77239	+	11.4910i	0.103754	+	0.430041i
$715$	−36.3184			−1.35823
$716$	2.09426	+	4.59764i	0.0782662	+	0.171822i
$717$	−5.63494	+	9.76000i	−0.210441	+	0.364494i
$718$	−22.3963	−	14.4086i	−0.835823	−	0.537726i
$719$	7.39467	+	12.8079i	0.275775	+	0.477656i	0.970330	−	0.241783i	$-0.0777324\pi$
$719$	7.39467	+	12.8079i	0.275775	+	0.477656i	−0.694556	+	0.719439i	$0.744399\pi$
$720$	−12.6737	−	2.46827i	−0.472322	−	0.0919869i
$721$	5.10158	+	1.24180i	0.189993	+	0.0462469i
$722$	10.6074	+	0.510466i	0.394765	+	0.0189976i
$723$	−5.63653	−	9.76276i	−0.209625	−	0.363081i
$724$	−9.64056	+	13.5104i	−0.358289	+	0.502111i
$725$	46.3890	+	26.7827i	1.72285	+	0.994685i
$726$	−7.67187	+	3.95040i	−0.284730	+	0.146613i
$727$	−43.5679			−1.61585			−0.807923	−	0.589289i	$-0.799408\pi$
$727$	−43.5679			−1.61585			−0.807923	+	0.589289i	$0.799408\pi$
$728$	29.9561	−	23.4497i	1.11025	−	0.869105i
$729$	−1.00000			−0.0370370
$730$	−36.6512	+	18.8724i	−1.35652	+	0.698499i
$731$	18.2979	+	10.5643i	0.676773	+	0.390735i
$732$	20.6471	+	14.7330i	0.763138	+	0.544548i
$733$	11.3412	+	19.6435i	0.418896	+	0.725549i	0.995829	−	0.0912424i	$-0.0290838\pi$
$733$	11.3412	+	19.6435i	0.418896	+	0.725549i	−0.576933	+	0.816792i	$0.695750\pi$
$734$	30.3054	+	1.45841i	1.11859	+	0.0538309i
$735$	22.5718	−	1.04033i	0.832572	−	0.0383731i
$736$	4.12731	−	16.8341i	0.152135	−	0.620511i
$737$	−9.75399	−	16.8944i	−0.359293	−	0.622314i
$738$	−7.09207	−	4.56268i	−0.261063	−	0.167954i
$739$	−2.32595	+	4.02866i	−0.0855615	+	0.148197i	−0.905630	−	0.424068i	$-0.860602\pi$
$739$	−2.32595	+	4.02866i	−0.0855615	+	0.148197i	0.820069	+	0.572265i	$0.193935\pi$
$740$	5.41617	−	2.46711i	0.199103	−	0.0906929i
$741$	17.2327			0.633060
$742$	9.30662	+	9.78512i	0.341657	+	0.359223i
$743$		−	28.3209i		−	1.03899i	−0.854473	−	0.519496i	$-0.826120\pi$
$743$		−	28.3209i		−	1.03899i	0.854473	−	0.519496i	$-0.173880\pi$
$744$	−5.32839	+	2.12414i	−0.195348	+	0.0778748i
$745$	−29.6214	−	17.1019i	−1.08525	−	0.626567i
$746$	−19.4361	−	12.5042i	−0.711607	−	0.457812i
$747$	3.09450	−	1.78661i	0.113222	−	0.0653687i
$748$	−1.34281	+	13.9194i	−0.0490982	+	0.508942i
$749$	−8.31902	−	2.02497i	−0.303971	−	0.0739908i
$750$	−0.0921040	+	1.91390i	−0.00336316	+	0.0698856i
$751$	28.5823	−	16.5020i	1.04298	−	0.602166i	0.122306	−	0.992492i	$-0.460971\pi$
$751$	28.5823	−	16.5020i	1.04298	−	0.602166i	0.920677	+	0.390326i	$0.127638\pi$
$752$	−5.57162	+	6.40475i	−0.203176	+	0.233557i
$753$	1.63312	−	2.82866i	0.0595144	−	0.103082i
$754$	63.1729	−	32.5290i	2.30062	−	1.18464i
$755$		−	3.92554i		−	0.142865i
$756$	−5.19762	+	0.992355i	−0.189036	+	0.0360916i
$757$			19.0350i			0.691838i	0.938264	+	0.345919i	$0.112433\pi$
$757$			19.0350i			0.691838i	−0.938264	+	0.345919i	$0.887567\pi$
$758$	2.79449	+	5.42704i	0.101500	+	0.197119i
$759$	−3.39062	+	5.87273i	−0.123072	+	0.213166i
$760$	−24.2997	−	19.1670i	−0.881442	−	0.695260i
$761$	43.2756	−	24.9852i	1.56874	−	0.905712i	0.572424	−	0.819958i	$-0.306003\pi$
$761$	43.2756	−	24.9852i	1.56874	−	0.905712i	0.996316	−	0.0857544i	$-0.0273301\pi$
$762$	29.6723	+	1.42795i	1.07492	+	0.0517290i
$763$	10.6429	−	3.11613i	0.385300	−	0.112811i
$764$	1.16679	−	12.0947i	0.0422128	−	0.437570i
$765$	−8.83161	+	5.09893i	−0.319308	+	0.184352i
$766$	−15.4484	+	24.0124i	−0.558172	+	0.867603i
$767$	54.0653	+	31.2146i	1.95219	+	1.12709i
$768$	15.8459	−	2.21534i	0.571789	−	0.0799392i
$769$			24.2908i			0.875949i	0.898987	+	0.437974i	$0.144304\pi$
$769$			24.2908i			0.875949i	−0.898987	+	0.437974i	$0.855696\pi$
$770$	25.6385	+	7.56320i	0.923948	+	0.272559i
$771$	12.0704			0.434706
$772$	7.61639	+	16.7206i	0.274120	+	0.601788i
$773$	8.01612	−	13.8843i	0.288320	−	0.499385i	−0.685089	−	0.728459i	$-0.740237\pi$
$773$	8.01612	−	13.8843i	0.288320	−	0.499385i	0.973409	+	0.229075i	$0.0735700\pi$
$774$	−5.11732	+	7.95419i	−0.183938	+	0.285907i
$775$	5.49574	+	9.51890i	0.197413	+	0.341929i
$776$	6.19021	−	42.6120i	0.222216	−	1.52968i
$777$	1.68451	−	1.76394i	0.0604316	−	0.0632810i
$778$	−2.29506	+	47.6907i	−0.0822818	+	1.70979i
$779$	−10.1068	−	17.5054i	−0.362112	−	0.627197i
$780$	26.7158	+	19.0634i	0.956578	+	0.682581i
$781$	−22.4321	−	12.9512i	−0.802682	−	0.463429i
$782$	−6.26694	−	12.1707i	−0.224105	−	0.435224i
$783$	−9.88340			−0.353204
$784$	−26.0305	+	10.3158i	−0.929659	+	0.368420i
$785$	11.7015			0.417644
$786$	−0.369635	−	0.717849i	−0.0131844	−	0.0256048i
$787$	−8.71618	−	5.03229i	−0.310698	−	0.179382i	0.336541	−	0.941669i	$-0.390743\pi$
$787$	−8.71618	−	5.03229i	−0.310698	−	0.179382i	−0.647239	+	0.762287i	$0.724076\pi$
$788$	−33.0104	−	23.5551i	−1.17595	−	0.839114i
$789$	−8.19034	−	14.1861i	−0.291584	−	0.505038i
$790$	−2.43270	+	50.5510i	−0.0865517	+	1.79852i
$791$	5.20130	−	5.44655i	0.184937	−	0.193657i
$792$	−6.19484	−	0.899919i	−0.220124	−	0.0319772i
$793$	−32.2365	−	55.8352i	−1.14475	−	1.98277i
$794$	−0.0675114	+	0.104937i	−0.00239589	+	0.00372409i
$795$	−5.82507	+	10.0893i	−0.206594	+	0.357831i
$796$	2.72520	+	5.98277i	0.0965923	+	0.212054i
$797$	53.0872			1.88045			0.940223	−	0.340560i	$-0.110617\pi$
$797$	53.0872			1.88045			0.940223	+	0.340560i	$0.110617\pi$
$798$	−12.1652	−	3.58866i	−0.430644	−	0.127037i
$799$			6.70471i			0.237196i
$800$	−8.56591	−	29.4377i	−0.302851	−	1.04078i
$801$	−6.32253	−	3.65032i	−0.223396	−	0.128978i
$802$	19.2878	−	29.9802i	0.681074	−	1.05864i
$803$	−17.3087	+	9.99318i	−0.610811	+	0.352652i
$804$	−1.69281	+	17.5473i	−0.0597008	+	0.618847i
$805$	−25.1135	+	7.35295i	−0.885134	+	0.259157i
$806$	14.5636	+	0.700857i	0.512982	+	0.0246866i
$807$	−6.47046	+	3.73572i	−0.227771	+	0.131504i
$808$	−17.2407	+	21.8575i	−0.606525	+	0.768946i
$809$	−26.9529	+	46.6838i	−0.947614	+	1.64132i	−0.197183	+	0.980367i	$0.563179\pi$
$809$	−26.9529	+	46.6838i	−0.947614	+	1.64132i	−0.750431	+	0.660949i	$0.770154\pi$
$810$	−2.08984	−	4.05858i	−0.0734295	−	0.142604i
$811$			48.2050i			1.69271i	0.532621	+	0.846354i	$0.321207\pi$
$811$			48.2050i			1.69271i	−0.532621	+	0.846354i	$0.678793\pi$
$812$	−51.3702	+	9.80785i	−1.80274	+	0.344188i
$813$			8.97234i			0.314674i
$814$	2.56531	−	1.32093i	0.0899142	−	0.0462986i
$815$	−32.0076	+	55.4387i	−1.12118	+	1.94193i
$816$	8.29400	−	9.53421i	0.290348	−	0.333764i
$817$	−19.6334	+	11.3353i	−0.686885	+	0.396574i
$818$	−2.11294	+	43.9063i	−0.0738771	+	1.53515i
$819$	13.0686	+	3.18108i	0.456654	+	0.111156i
$820$	3.69667	−	38.3190i	0.129093	−	1.33816i
$821$	−22.4271	+	12.9483i	−0.782712	+	0.451899i	−0.837390	−	0.546605i	$-0.815920\pi$
$821$	−22.4271	+	12.9483i	−0.782712	+	0.451899i	0.0546787	+	0.998504i	$0.482587\pi$
$822$	15.6473	+	10.0667i	0.545761	+	0.351115i
$823$	−48.1100	−	27.7763i	−1.67701	−	0.968221i	−0.963552	−	0.267522i	$-0.913795\pi$
$823$	−48.1100	−	27.7763i	−1.67701	−	0.968221i	−0.713457	−	0.700699i	$-0.752871\pi$
$824$	−2.07855	−	5.21403i	−0.0724098	−	0.181639i
$825$			11.9949i			0.417610i
$826$	−31.6663	−	33.2945i	−1.10181	−	1.15846i
$827$	23.2870			0.809770			0.404885	−	0.914368i	$-0.367312\pi$
$827$	23.2870			0.809770			0.404885	+	0.914368i	$0.367312\pi$
$828$	5.57671	−	2.54024i	0.193804	−	0.0882794i
$829$	−2.58838	+	4.48320i	−0.0898980	+	0.155708i	−0.907468	−	0.420122i	$-0.861987\pi$
$829$	−2.58838	+	4.48320i	−0.0898980	+	0.155708i	0.817570	+	0.575829i	$0.195321\pi$
$830$	13.7181	+	8.82554i	0.476163	+	0.306339i
$831$	3.06942	+	5.31638i	0.106477	+	0.184423i
$832$	−38.9885	−	11.5719i	−1.35168	−	0.401182i
$833$	−10.1638	+	19.6406i	−0.352155	+	0.680506i
$834$	−13.4876	−	0.649075i	−0.467037	−	0.0224756i
$835$	20.0087	+	34.6561i	0.692430	+	1.19932i
$836$	−12.2139	−	8.71542i	−0.422427	−	0.301429i
$837$	−1.75634	−	1.01402i	−0.0607080	−	0.0350498i
$838$	28.6235	−	14.7388i	0.988783	−	0.509144i
$839$	12.7298			0.439480			0.219740	−	0.975558i	$-0.429479\pi$
$839$	12.7298			0.439480			0.219740	+	0.975558i	$0.429479\pi$
$840$	−14.8897	−	19.0211i	−0.513745	−	0.656289i
$841$	−68.6816			−2.36833
$842$	−30.2017	+	15.5514i	−1.04082	+	0.535938i
$843$	16.7087	+	9.64680i	0.575480	+	0.332253i
$844$	25.1973	−	35.3119i	0.867328	−	1.21548i
$845$	−20.7298	−	35.9052i	−0.713128	−	1.23517i
$846$	−2.99786	−	0.144268i	−0.103069	−	0.00496005i
$847$	−15.6858	−	3.81814i	−0.538969	−	0.131193i
$848$	2.75973	−	14.1703i	0.0947695	−	0.486610i
$849$	−11.1718	−	19.3500i	−0.383414	−	0.664092i
$850$	−20.3641	−	13.1012i	−0.698483	−	0.449368i
$851$	−1.41233	+	2.44622i	−0.0484139	+	0.0838554i
$852$	9.70295	+	21.3014i	0.332418	+	0.729773i
$853$	47.2928			1.61927			0.809637	−	0.586930i	$-0.199664\pi$
$853$	47.2928			1.61927			0.809637	+	0.586930i	$0.199664\pi$
$854$	11.1294	+	46.1293i	0.380840	+	1.57851i
$855$		−	10.9422i		−	0.374214i
$856$	3.38945	+	8.50239i	0.115849	+	0.290606i
$857$	45.2524	+	26.1265i	1.54579	+	0.892463i	0.998456	+	0.0555505i	$0.0176914\pi$
$857$	45.2524	+	26.1265i	1.54579	+	0.892463i	0.547336	+	0.836913i	$0.315642\pi$
$858$	13.3815	+	8.60898i	0.456837	+	0.293906i
$859$	43.7066	−	25.2340i	1.49125	−	0.860973i	0.491299	−	0.870991i	$-0.336522\pi$
$859$	43.7066	−	25.2340i	1.49125	−	0.860973i	0.999950	+	0.0100178i	$0.00318880\pi$
$860$	−42.9770	−	4.14604i	−1.46551	−	0.141379i
$861$	−4.43313	−	15.1411i	−0.151081	−	0.516006i
$862$	−2.21663	+	46.0610i	−0.0754988	+	1.56884i
$863$	−23.1918	+	13.3898i	−0.789457	+	0.455793i	−0.839771	−	0.542940i	$-0.817311\pi$
$863$	−23.1918	+	13.3898i	−0.789457	+	0.455793i	0.0503147	+	0.998733i	$0.483978\pi$
$864$	4.08454	+	3.91363i	0.138959	+	0.133144i
$865$	1.67636	−	2.90355i	0.0569981	−	0.0987236i
$866$	−23.2292	+	11.9612i	−0.789360	+	0.406457i
$867$			7.01927i			0.238387i
$868$	−10.1350	−	3.52759i	−0.344006	−	0.119734i
$869$			24.5362i			0.832335i
$870$	−20.6547	−	40.1125i	−0.700261	−	1.35994i
$871$	22.4049	−	38.8063i	0.759160	−	1.31490i
$872$	−9.30828	−	7.34214i	−0.315218	−	0.248636i
$873$	13.1842	−	7.61188i	0.446216	−	0.257623i
$874$	14.6716	+	0.706053i	0.496274	+	0.0238826i
$875$	−2.47574	+	2.59247i	−0.0836952	+	0.0876416i
$876$	17.9776	+	1.73432i	0.607408	+	0.0585973i
$877$	−22.4411	+	12.9564i	−0.757783	+	0.437506i	−0.828499	−	0.559990i	$-0.810805\pi$
$877$	−22.4411	+	12.9564i	−0.757783	+	0.437506i	0.0707159	+	0.997496i	$0.477472\pi$
$878$	17.1607	−	26.6741i	0.579147	−	0.900206i
$879$	−12.1856	−	7.03534i	−0.411009	−	0.237296i
$880$	−9.29383	−	27.0229i	−0.313295	−	0.910942i
$881$		−	10.0120i		−	0.337313i	−0.985675	−	0.168657i	$-0.946057\pi$
$881$		−	10.0120i		−	0.337313i	0.985675	−	0.168657i	$-0.0539429\pi$
$882$	−8.56315	−	4.96714i	−0.288336	−	0.167252i
$883$	−23.6231			−0.794981			−0.397491	−	0.917606i	$-0.630119\pi$
$883$	−23.6231			−0.794981			−0.397491	+	0.917606i	$0.630119\pi$
$884$	−29.2314	+	13.3151i	−0.983157	+	0.447836i
$885$	19.8202	−	34.3295i	0.666248	−	1.15397i
$886$	−6.91962	+	10.7556i	−0.232469	+	0.361342i
$887$	9.08123	+	15.7291i	0.304918	+	0.528133i	0.977243	−	0.212123i	$-0.0680377\pi$
$887$	9.08123	+	15.7291i	0.304918	+	0.528133i	−0.672325	+	0.740256i	$0.734704\pi$
$888$	−2.58039	−	0.374852i	−0.0865923	−	0.0125792i
$889$	40.1927	+	38.3829i	1.34802	+	1.28732i
$890$	1.60200	−	33.2891i	0.0536990	−	1.11585i
$891$	−1.10660	−	1.91668i	−0.0370724	−	0.0642113i
$892$	22.4517	−	31.4641i	0.751738	−	1.05350i
$893$	−6.23023	−	3.59703i	−0.208487	−	0.120370i
$894$	6.86012	+	13.3227i	0.229437	+	0.445578i
$895$	−8.15407			−0.272560
$896$	25.1136	+	16.2882i	0.838987	+	0.544152i
$897$	−15.5765			−0.520083
$898$	−3.66221	−	7.11220i	−0.122210	−	0.237337i
$899$	−17.3586	−	10.0220i	−0.578942	−	0.334252i
$900$	6.29611	−	8.82345i	0.209870	−	0.294115i
$901$	−5.70104	−	9.87449i	−0.189929	−	0.328967i
$902$	0.897138	−	18.6423i	0.0298714	−	0.620721i
$903$	−16.9816	+	4.97203i	−0.565113	+	0.165459i
$904$	−7.96752	−	1.15744i	−0.264996	−	0.0384958i
$905$	−13.3939	−	23.1989i	−0.445228	−	0.771158i
$906$	−0.930515	+	1.44636i	−0.0309143	+	0.0480521i
$907$	27.7185	−	48.0098i	0.920377	−	1.59414i	0.121546	−	0.992586i	$-0.461215\pi$
$907$	27.7185	−	48.0098i	0.920377	−	1.59414i	0.798832	−	0.601554i	$-0.205452\pi$
$908$	0.981131	−	0.446913i	0.0325600	−	0.0148313i
$909$	−9.84247			−0.326454
$910$	14.4006	+	59.6878i	0.477376	+	1.97863i
$911$			18.4722i			0.612012i	0.952030	+	0.306006i	$0.0989928\pi$
$911$			18.4722i			0.612012i	−0.952030	+	0.306006i	$0.901007\pi$
$912$	4.40983	+	12.8221i	0.146024	+	0.424582i
$913$	6.84874	+	3.95412i	0.226660	+	0.130862i
$914$	−7.17677	+	11.1553i	−0.237386	+	0.368985i
$915$	−35.4533	+	20.4690i	−1.17205	+	0.676684i
$916$	45.5133	+	4.39071i	1.50380	+	0.145073i
$917$	0.357259	−	1.46770i	0.0117977	−	0.0484678i
$918$	4.46266	+	0.214760i	0.147290	+	0.00708814i
$919$	−0.144308	+	0.0833164i	−0.00476029	+	0.00274835i	−0.502378	−	0.864648i	$-0.667541\pi$
$919$	−0.144308	+	0.0833164i	−0.00476029	+	0.00274835i	0.497618	+	0.867396i	$0.334208\pi$
$920$	21.9642	+	17.3248i	0.724138	+	0.571182i
$921$	4.80893	−	8.32932i	0.158460	−	0.274460i
$922$	20.5853	+	39.9777i	0.677941	+	1.31660i
$923$		−	59.4974i		−	1.95838i
$924$	−7.65370	−	8.86405i	−0.251788	−	0.291606i
$925$			4.99636i			0.164279i
$926$	11.1588	−	5.74587i	0.366700	−	0.188821i
$927$	0.992258	−	1.71864i	0.0325900	−	0.0564476i
$928$	40.3692	+	38.6800i	1.32518	+	1.26973i
$929$	14.0194	−	8.09409i	0.459961	−	0.265559i	−0.252067	−	0.967710i	$-0.581110\pi$
$929$	14.0194	−	8.09409i	0.459961	−	0.265559i	0.712028	+	0.702151i	$0.247777\pi$
$930$	0.445019	−	9.24738i	0.0145928	−	0.303234i
$931$	−12.7979	−	19.9816i	−0.419433	−	0.654870i
$932$	−5.98202	−	0.577092i	−0.195948	−	0.0189033i
$933$	18.7902	−	10.8485i	0.615162	−	0.355164i
$934$	−3.72170	−	2.39435i	−0.121778	−	0.0783457i
$935$	−19.5461	−	11.2849i	−0.639225	−	0.369057i
$936$	−5.32458	−	13.3567i	−0.174039	−	0.436576i
$937$		−	19.5153i		−	0.637538i	−0.947832	−	0.318769i	$-0.896730\pi$
$937$		−	19.5153i		−	0.637538i	0.947832	−	0.318769i	$-0.103270\pi$
$938$	−23.8977	+	22.7291i	−0.780288	+	0.742131i
$939$	10.9294			0.356668
$940$	−5.67953	−	12.4685i	−0.185246	−	0.406679i
$941$	12.3201	−	21.3390i	0.401624	−	0.695633i	−0.592298	−	0.805719i	$-0.701779\pi$
$941$	12.3201	−	21.3390i	0.401624	−	0.695633i	0.993922	+	0.110086i	$0.0351126\pi$
$942$	−4.31140	−	2.77374i	−0.140473	−	0.0903733i
$943$	9.13538	+	15.8229i	0.297489	+	0.515266i
$944$	−9.39015	+	48.2153i	−0.305623	+	1.56927i
$945$	2.01987	−	8.29809i	0.0657065	−	0.269937i
$946$	−20.9085	−	1.00619i	−0.679793	−	0.0327142i
$947$	4.30769	+	7.46115i	0.139981	+	0.242455i	0.927489	−	0.373850i	$-0.121962\pi$
$947$	4.30769	+	7.46115i	0.139981	+	0.242455i	−0.787508	+	0.616304i	$0.788629\pi$
$948$	12.8790	−	18.0488i	0.418290	−	0.586198i
$949$	−39.7579	−	22.9543i	−1.29060	−	0.745127i
$950$	23.0993	−	11.8943i	0.749440	−	0.385901i
$951$	−7.09278			−0.229999
$952$	23.4083	−	3.31230i	0.758668	−	0.107352i
$953$	−27.4982			−0.890755			−0.445378	−	0.895343i	$-0.646931\pi$
$953$	−27.4982			−0.890755			−0.445378	+	0.895343i	$0.646931\pi$
$954$	4.53783	−	2.33662i	0.146918	−	0.0756508i
$955$	16.9838	+	9.80560i	0.549583	+	0.317302i
$956$	18.3476	+	13.0922i	0.593404	+	0.423432i
$957$	−10.9369	−	18.9433i	−0.353541	−	0.612352i
$958$	−23.1526	−	1.11419i	−0.748028	−	0.0359980i
$959$	9.78084	+	33.4058i	0.315840	+	1.07873i
$960$	−7.34772	+	24.7563i	−0.237147	+	0.799006i
$961$	13.4435	+	23.2849i	0.433662	+	0.751124i
$962$	5.57392	+	3.58598i	0.179710	+	0.115617i
$963$	−1.61805	+	2.80255i	−0.0521410	+	0.0903109i
$964$	−20.5178	+	9.34603i	−0.660834	+	0.301015i
$965$	−29.6546			−0.954616
$966$	10.9960	+	3.24375i	0.353790	+	0.104366i
$967$		−	21.2591i		−	0.683647i	−0.939764	−	0.341823i	$-0.888956\pi$
$967$		−	21.2591i		−	0.683647i	0.939764	−	0.341823i	$-0.111044\pi$
$968$	6.39090	+	16.0315i	0.205411	+	0.515272i
$969$	9.27442	+	5.35459i	0.297937	+	0.172014i
$970$	58.4462	+	37.6013i	1.87659	+	1.20730i
$971$	−27.3347	+	15.7817i	−0.877213	+	0.506459i	−0.869738	−	0.493513i	$-0.835713\pi$
$971$	−27.3347	+	15.7817i	−0.877213	+	0.506459i	−0.00747434	+	0.999972i	$0.502379\pi$
$972$	−0.192050	+	1.99076i	−0.00616002	+	0.0638536i
$973$	−18.2697	−	17.4470i	−0.585698	−	0.559325i
$974$	−1.99611	+	41.4786i	−0.0639594	+	1.32906i
$975$	−23.8610	+	13.7761i	−0.764163	+	0.441189i
$976$	33.2952	−	38.2738i	1.06575	−	1.22512i
$977$	9.75712	−	16.8998i	0.312158	−	0.540673i	−0.666671	−	0.745352i	$-0.732282\pi$
$977$	9.75712	−	16.8998i	0.312158	−	0.540673i	0.978829	+	0.204678i	$0.0656149\pi$
$978$	24.9344	−	12.8392i	0.797315	−	0.410553i
$979$		−	16.1577i		−	0.516403i
$980$	2.26388	−	45.1347i	0.0723168	−	1.44178i
$981$		−	4.19152i		−	0.133825i
$982$	−21.9454	−	42.6190i	−0.700305	−	1.36003i
$983$	−11.2401	+	19.4684i	−0.358503	+	0.620946i	−0.987711	−	0.156291i	$-0.950046\pi$
$983$	−11.2401	+	19.4684i	−0.358503	+	0.620946i	0.629208	+	0.777237i	$0.283380\pi$
$984$	−10.4452	+	13.2423i	−0.332981	+	0.422150i
$985$	56.6825	−	32.7257i	1.80606	−	1.04273i
$986$	44.1063	+	2.12256i	1.40463	+	0.0675961i
$987$	−4.06076	−	3.87791i	−0.129255	−	0.123435i
$988$	3.30955	−	34.3062i	0.105291	−	1.09143i
$989$	17.7464	−	10.2459i	0.564302	−	0.325800i
$990$	5.46639	−	8.49677i	0.173733	−	0.270045i
$991$	38.9073	+	22.4631i	1.23593	+	0.713565i	0.968260	−	0.249945i	$-0.0804125\pi$
$991$	38.9073	+	22.4631i	1.23593	+	0.713565i	0.267671	+	0.963510i	$0.413746\pi$
$992$	3.20533	+	11.0155i	0.101769	+	0.349742i
$993$			11.7240i			0.372051i
$994$	−12.3901	+	42.0014i	−0.392992	+	1.33220i
$995$	−10.6107			−0.336381
$996$	−2.96241	−	6.50353i	−0.0938676	−	0.206072i
$997$	−14.5890	+	25.2688i	−0.462037	+	0.800272i	−0.999062	−	0.0432942i	$-0.986215\pi$
$997$	−14.5890	+	25.2688i	−0.462037	+	0.800272i	0.537025	+	0.843566i	$0.319548\pi$
$998$	6.80268	−	10.5739i	0.215335	−	0.334710i
$999$	−0.460941	−	0.798374i	−0.0145835	−	0.0252594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.115.7	yes	32
3.2	odd	2		504.2.bk.c.451.10		32
4.3	odd	2		672.2.bb.a.367.9		32
7.3	odd	6		1176.2.p.a.979.31		32
7.4	even	3		1176.2.p.a.979.32		32
7.5	odd	6	inner	168.2.t.a.19.5	✓	32
8.3	odd	2	inner	168.2.t.a.115.5	yes	32
8.5	even	2		672.2.bb.a.367.16		32
12.11	even	2		2016.2.bs.c.1711.15		32
21.5	even	6		504.2.bk.c.19.12		32
24.5	odd	2		2016.2.bs.c.1711.2		32
24.11	even	2		504.2.bk.c.451.12		32
28.3	even	6		4704.2.p.a.3919.20		32
28.11	odd	6		4704.2.p.a.3919.9		32
28.19	even	6		672.2.bb.a.271.16		32
56.3	even	6		1176.2.p.a.979.30		32
56.5	odd	6		672.2.bb.a.271.9		32
56.11	odd	6		1176.2.p.a.979.29		32
56.19	even	6	inner	168.2.t.a.19.7	yes	32
56.45	odd	6		4704.2.p.a.3919.10		32
56.53	even	6		4704.2.p.a.3919.19		32
84.47	odd	6		2016.2.bs.c.271.2		32
168.5	even	6		2016.2.bs.c.271.15		32
168.131	odd	6		504.2.bk.c.19.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.5	✓	32	7.5	odd	6	inner
168.2.t.a.19.7	yes	32	56.19	even	6	inner
168.2.t.a.115.5	yes	32	8.3	odd	2	inner
168.2.t.a.115.7	yes	32	1.1	even	1	trivial
504.2.bk.c.19.10		32	168.131	odd	6
504.2.bk.c.19.12		32	21.5	even	6
504.2.bk.c.451.10		32	3.2	odd	2
504.2.bk.c.451.12		32	24.11	even	2
672.2.bb.a.271.9		32	56.5	odd	6
672.2.bb.a.271.16		32	28.19	even	6
672.2.bb.a.367.9		32	4.3	odd	2
672.2.bb.a.367.16		32	8.5	even	2
1176.2.p.a.979.29		32	56.11	odd	6
1176.2.p.a.979.30		32	56.3	even	6
1176.2.p.a.979.31		32	7.3	odd	6
1176.2.p.a.979.32		32	7.4	even	3
2016.2.bs.c.271.2		32	84.47	odd	6
2016.2.bs.c.271.15		32	168.5	even	6
2016.2.bs.c.1711.2		32	24.5	odd	2
2016.2.bs.c.1711.15		32	12.11	even	2
4704.2.p.a.3919.9		32	28.11	odd	6
4704.2.p.a.3919.10		32	56.45	odd	6
4704.2.p.a.3919.19		32	56.53	even	6
4704.2.p.a.3919.20		32	28.3	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647418 - 1.25732i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.16170 + 1.62802i) q^{4} +(-1.61398 - 2.79550i) q^{5} +(-0.0679787 + 1.41258i) q^{6} +(-1.82725 + 1.91341i) q^{7} +(2.79905 + 0.406616i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.46991 + 3.83914i) q^{10} +(-1.10660 + 1.91668i) q^{11} +(1.82007 - 0.829058i) q^{12} -5.08369 q^{13} +(3.58876 + 1.05866i) q^{14} +3.22796i q^{15} +(-1.30091 - 3.78254i) q^{16} +(-2.73597 - 1.57961i) q^{17} +(0.765161 - 1.18934i) q^{18} +(2.93566 - 1.69490i) q^{19} +(6.42609 + 0.619932i) q^{20} +(2.53915 - 0.743436i) q^{21} +(3.12631 + 0.150450i) q^{22} +(-2.65351 + 1.53200i) q^{23} +(-2.22074 - 1.75166i) q^{24} +(-2.70987 + 4.69363i) q^{25} +(3.29127 + 6.39182i) q^{26} -1.00000i q^{27} +(-0.992355 - 5.19762i) q^{28} -9.88340i q^{29} +(4.05858 - 2.08984i) q^{30} +(1.01402 - 1.75634i) q^{31} +(-3.91363 + 4.08454i) q^{32} +(1.91668 - 1.10660i) q^{33} +(-0.214760 + 4.46266i) q^{34} +(8.29809 + 2.01987i) q^{35} +(-1.99076 - 0.192050i) q^{36} +(0.798374 - 0.460941i) q^{37} +(-4.03163 - 2.59375i) q^{38} +(4.40261 + 2.54185i) q^{39} +(-3.38092 - 8.48100i) q^{40} -5.96303i q^{41} +(-2.57863 - 2.71121i) q^{42} -6.68790 q^{43} +(-1.83487 - 4.02817i) q^{44} +(1.61398 - 2.79550i) q^{45} +(3.64414 + 2.34446i) q^{46} +(-1.06113 - 1.83793i) q^{47} +(-0.764652 + 3.92623i) q^{48} +(-0.322287 - 6.99258i) q^{49} +(7.65581 + 0.368427i) q^{50} +(1.57961 + 2.73597i) q^{51} +(5.90572 - 8.27636i) q^{52} +(3.12560 + 1.80457i) q^{53} +(-1.25732 + 0.647418i) q^{54} +7.14411 q^{55} +(-5.89259 + 4.61274i) q^{56} -3.38981 q^{57} +(-12.4266 + 6.39869i) q^{58} +(-10.6351 - 6.14015i) q^{59} +(-5.25519 - 3.74992i) q^{60} +(6.34115 + 10.9832i) q^{61} +(-2.86477 - 0.137864i) q^{62} +(-2.57069 - 0.625743i) q^{63} +(7.66933 + 2.27627i) q^{64} +(8.20498 + 14.2114i) q^{65} +(-2.63224 - 1.69345i) q^{66} +(-4.40720 + 7.63350i) q^{67} +(5.75002 - 2.61918i) q^{68} +3.06401 q^{69} +(-2.83271 - 11.7410i) q^{70} +11.7036i q^{71} +(1.04738 + 2.62735i) q^{72} +(7.82068 + 4.51527i) q^{73} +(-1.09643 - 0.705388i) q^{74} +(4.69363 - 2.70987i) q^{75} +(-0.651014 + 6.74828i) q^{76} +(-1.64537 - 5.61964i) q^{77} +(0.345583 - 7.18112i) q^{78} +(9.60105 - 5.54317i) q^{79} +(-8.47445 + 9.74164i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.49743 + 3.86057i) q^{82} -3.57322i q^{83} +(-1.73940 + 4.99745i) q^{84} +10.1979i q^{85} +(4.32987 + 8.40882i) q^{86} +(-4.94170 + 8.55928i) q^{87} +(-3.87677 + 4.91493i) q^{88} +(-6.32253 + 3.65032i) q^{89} +(-4.55975 - 0.219433i) q^{90} +(9.28920 - 9.72719i) q^{91} +(0.588444 - 6.09969i) q^{92} +(-1.75634 + 1.01402i) q^{93} +(-1.62387 + 2.52409i) q^{94} +(-9.47619 - 5.47108i) q^{95} +(5.43158 - 1.58050i) q^{96} -15.2238i q^{97} +(-8.58324 + 4.93234i) q^{98} -2.21319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

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