LMFDB - Embedded newform 168.2.t.a.115.5

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			115.5
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.765161 - 1.18934i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.829058 + 1.82007i) 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} +(2.08984 - 4.05858i) q^{10} +(-1.10660 + 1.91668i) q^{11} +(1.62802 - 1.16170i) q^{12} +5.08369 q^{13} +(-3.67384 - 0.709159i) q^{14} -3.22796i q^{15} +(-2.62532 - 3.01789i) q^{16} +(-2.73597 - 1.57961i) q^{17} +(0.647418 - 1.25732i) 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} +(-2.62735 - 1.04738i) q^{24} +(-2.70987 + 4.69363i) q^{25} +(-3.88984 - 6.04624i) q^{26} -1.00000i q^{27} +(1.96765 + 4.91206i) q^{28} +9.88340i q^{29} +(-3.83914 + 2.46991i) q^{30} +(-1.01402 + 1.75634i) q^{31} +(-1.58050 + 5.43158i) 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} +(-4.26207 - 2.19462i) q^{38} +(-4.40261 - 2.54185i) q^{39} +(5.65430 + 7.16846i) q^{40} -5.96303i q^{41} +(2.82706 + 2.45107i) q^{42} -6.68790 q^{43} +(-2.57107 - 3.60313i) q^{44} +(-1.61398 + 2.79550i) q^{45} +(-3.85243 - 1.98369i) 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} +(-4.21468 + 9.25269i) q^{52} +(-3.12560 - 1.80457i) q^{53} +(-1.18934 + 0.765161i) q^{54} -7.14411 q^{55} +(4.33655 - 6.09872i) q^{56} -3.38981 q^{57} +(11.7547 - 7.56239i) q^{58} +(-10.6351 - 6.14015i) q^{59} +(5.87512 + 2.67617i) 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} +(-2.78269 - 1.43286i) q^{66} +(-4.40720 + 7.63350i) q^{67} +(5.14329 - 3.67007i) q^{68} -3.06401 q^{69} +(-3.94706 - 11.4148i) q^{70} -11.7036i q^{71} +(1.75166 + 2.22074i) q^{72} +(7.82068 + 4.51527i) q^{73} +(1.15910 + 0.596844i) 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} +(4.19928 - 12.2099i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.09207 + 4.56268i) q^{82} -3.57322i q^{83} +(0.752000 - 5.23780i) q^{84} -10.1979i q^{85} +(5.11732 + 7.95419i) q^{86} +(4.94170 - 8.55928i) q^{87} +(-2.31807 + 5.81485i) 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} +(1.37399 - 2.66836i) q^{94} +(9.47619 + 5.47108i) q^{95} +(4.08454 - 3.91363i) q^{96} -15.2238i q^{97} +(-8.06995 + 5.73375i) 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 $

$2$	−0.765161	−	1.18934i	−0.541050	−	0.840990i
$2$	−0.765161	−	1.18934i	−0.541050	−	0.840990i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.829058	+	1.82007i	−0.414529	+	0.910036i
$5$	1.61398	+	2.79550i	0.721794	+	1.25018i	0.960280	+	0.279038i	$0.0900156\pi$
$5$	1.61398	+	2.79550i	0.721794	+	1.25018i	−0.238486	+	0.971146i	$0.576651\pi$
$6$	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
$10$	2.08984	−	4.05858i	0.660866	−	1.28343i
$11$	−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	$0.274948\pi$
$12$	1.62802	−	1.16170i	0.469969	−	0.335354i
$13$	5.08369			1.40996			0.704981	−	0.709226i	$-0.250955\pi$
$13$	5.08369			1.40996			0.704981	+	0.709226i	$0.250955\pi$
$14$	−3.67384	−	0.709159i	−0.981875	−	0.189531i
$15$		−	3.22796i		−	0.833456i
$16$	−2.62532	−	3.01789i	−0.656331	−	0.754473i
$17$	−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	$0.791815\pi$
$18$	0.647418	−	1.25732i	0.152598	−	0.296353i
$19$	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	−0.197155	−	0.980372i	$-0.563170\pi$
$23$	2.65351	−	1.53200i	0.553294	−	0.319445i	0.750450	+	0.660928i	$0.229837\pi$
$24$	−2.62735	−	1.04738i	−0.536306	−	0.213796i
$25$	−2.70987	+	4.69363i	−0.541974	+	0.938726i
$26$	−3.88984	−	6.04624i	−0.762861	−	1.18576i
$27$		−	1.00000i		−	0.192450i
$28$	1.96765	+	4.91206i	0.371850	+	0.928293i
$29$			9.88340i			1.83530i	0.397387	+	0.917651i	$0.369917\pi$
$29$			9.88340i			1.83530i	−0.397387	+	0.917651i	$0.630083\pi$
$30$	−3.83914	+	2.46991i	−0.700928	+	0.450942i
$31$	−1.01402	+	1.75634i	−0.182124	+	0.315448i	−0.942604	−	0.333914i	$-0.891631\pi$
$31$	−1.01402	+	1.75634i	−0.182124	+	0.315448i	0.760480	+	0.649362i	$0.224964\pi$
$32$	−1.58050	+	5.43158i	−0.279396	+	0.960176i
$33$	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	−0.564188	−	0.825646i	$-0.690811\pi$
$37$	−0.798374	+	0.460941i	−0.131252	+	0.0757783i	0.432936	+	0.901424i	$0.357477\pi$
$38$	−4.26207	−	2.19462i	−0.691399	−	0.356015i
$39$	−4.40261	−	2.54185i	−0.704981	−	0.407021i
$40$	5.65430	+	7.16846i	0.894023	+	1.13343i
$41$		−	5.96303i		−	0.931269i	−0.884977	−	0.465635i	$-0.845826\pi$
$41$		−	5.96303i		−	0.931269i	0.884977	−	0.465635i	$-0.154174\pi$
$42$	2.82706	+	2.45107i	0.436225	+	0.378208i
$43$	−6.68790			−1.01990			−0.509948	−	0.860205i	$-0.670335\pi$
$43$	−6.68790			−1.01990			−0.509948	+	0.860205i	$0.670335\pi$
$44$	−2.57107	−	3.60313i	−0.387603	−	0.543192i
$45$	−1.61398	+	2.79550i	−0.240598	+	0.416728i
$46$	−3.85243	−	1.98369i	−0.568010	−	0.292479i
$47$	1.06113	+	1.83793i	0.154782	+	0.268090i	0.932980	−	0.359929i	$-0.117199\pi$
$47$	1.06113	+	1.83793i	0.154782	+	0.268090i	−0.778198	+	0.628019i	$0.783866\pi$
$48$	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
$52$	−4.21468	+	9.25269i	−0.584471	+	1.28312i
$53$	−3.12560	−	1.80457i	−0.429334	−	0.247876i	0.269729	−	0.962936i	$-0.413066\pi$
$53$	−3.12560	−	1.80457i	−0.429334	−	0.247876i	−0.699063	+	0.715060i	$0.746399\pi$
$54$	−1.18934	+	0.765161i	−0.161849	+	0.104125i
$55$	−7.14411			−0.963311
$56$	4.33655	−	6.09872i	0.579495	−	0.814976i
$57$	−3.38981			−0.448991
$58$	11.7547	−	7.56239i	1.54347	−	0.992991i
$59$	−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	$0.961505\pi$
$60$	5.87512	+	2.67617i	0.758475	+	0.345492i
$61$	−6.34115	−	10.9832i	−0.811901	−	1.40625i	−0.911532	−	0.411230i	$-0.865099\pi$
$61$	−6.34115	−	10.9832i	−0.811901	−	1.40625i	0.0996301	−	0.995025i	$-0.468234\pi$
$62$	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
$66$	−2.78269	−	1.43286i	−0.342526	−	0.176373i
$67$	−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	$0.985686\pi$
$68$	5.14329	−	3.67007i	0.623716	−	0.445062i
$69$	−3.06401			−0.368863
$70$	−3.94706	−	11.4148i	−0.471763	−	1.36433i
$71$		−	11.7036i		−	1.38896i	−0.719512	−	0.694480i	$-0.755634\pi$
$71$		−	11.7036i		−	1.38896i	0.719512	−	0.694480i	$-0.244366\pi$
$72$	1.75166	+	2.22074i	0.206435	+	0.261716i
$73$	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	$0.489432\pi$
$74$	1.15910	+	0.596844i	0.134743	+	0.0693817i
$75$	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	−0.930951	−	0.365144i	$-0.881020\pi$
$79$	−9.60105	+	5.54317i	−1.08020	+	0.623655i	−0.149252	+	0.988799i	$0.547687\pi$
$80$	4.19928	−	12.2099i	0.469494	−	1.36511i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.09207	+	4.56268i	−0.783188	+	0.503863i
$83$		−	3.57322i		−	0.392212i	−0.980583	−	0.196106i	$-0.937170\pi$
$83$		−	3.57322i		−	0.392212i	0.980583	−	0.196106i	$-0.0628297\pi$
$84$	0.752000	−	5.23780i	0.0820499	−	0.571490i
$85$		−	10.1979i		−	1.10611i
$86$	5.11732	+	7.95419i	0.551815	+	0.857722i
$87$	4.94170	−	8.55928i	0.529806	−	0.917651i
$88$	−2.31807	+	5.81485i	−0.247107	+	0.619865i
$89$	−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
$94$	1.37399	−	2.66836i	0.141716	−	0.275220i
$95$	9.47619	+	5.47108i	0.972237	+	0.561321i
$96$	4.08454	−	3.91363i	0.416877	−	0.399433i
$97$		−	15.2238i		−	1.54574i	−0.634566	−	0.772869i	$-0.718821\pi$
$97$		−	15.2238i		−	1.54574i	0.634566	−	0.772869i	$-0.281179\pi$
$98$	−8.06995	+	5.73375i	−0.815188	+	0.579197i
$99$	−2.21319			−0.222434
$100$	−6.29611	−	8.82345i	−0.629611	−	0.882345i
$101$	4.92124	−	8.52383i	0.489681	−	0.848153i	−0.510248	−	0.860027i	$-0.670446\pi$
$101$	4.92124	−	8.52383i	0.489681	−	0.848153i	0.999929	+	0.0118744i	$0.00377982\pi$
$102$	2.04534	−	3.97216i	0.202519	−	0.393302i
$103$	0.992258	+	1.71864i	0.0977701	+	0.169343i	0.910761	−	0.412933i	$-0.135496\pi$
$103$	0.992258	+	1.71864i	0.0977701	+	0.169343i	−0.812991	+	0.582276i	$0.802162\pi$
$104$	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	$0.783337\pi$
$108$	1.82007	+	0.829058i	0.175137	+	0.0797762i
$109$	3.62997	+	2.09576i	0.347688	+	0.200738i	0.663666	−	0.748029i	$-0.268999\pi$
$109$	3.62997	+	2.09576i	0.347688	+	0.200738i	−0.315979	+	0.948766i	$0.602333\pi$
$110$	5.46639	+	8.49677i	0.521200	+	0.810135i
$111$	0.921883			0.0875012
$112$	−10.5716	−	0.491128i	−0.998923	−	0.0464072i
$113$	−2.84651			−0.267777			−0.133889	−	0.990996i	$-0.542746\pi$
$113$	−2.84651			−0.267777			−0.133889	+	0.990996i	$0.542746\pi$
$114$	2.59375	+	4.03163i	0.242927	+	0.377597i
$115$	8.56542	+	4.94525i	0.798729	+	0.461147i
$116$	−17.9885	−	8.19392i	−1.67019	−	0.760786i
$117$	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
$122$	−8.21076	+	15.9457i	−0.743367	+	1.44366i
$123$	−2.98152	+	5.16414i	−0.268834	+	0.465635i
$124$	−2.35598	−	3.30170i	−0.211573	−	0.296502i
$125$	−1.35490			−0.121186
$126$	−1.22277	−	3.53622i	−0.108933	−	0.315031i
$127$			21.0058i			1.86396i	0.362506	+	0.931981i	$0.381921\pi$
$127$			21.0058i			1.86396i	−0.362506	+	0.931981i	$0.618079\pi$
$128$	−8.57553	−	7.37972i	−0.757977	−	0.652282i
$129$	5.79189	+	3.34395i	0.509948	+	0.294418i
$130$	10.6241	−	20.6326i	0.931796	−	1.80959i
$131$	−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
$136$	−8.30041	−	3.30893i	−0.711754	−	0.283738i
$137$	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	$-0.0233042\pi$
$138$	2.34446	+	3.64414i	0.199573	+	0.310210i
$139$			9.54821i			0.809869i	0.914346	+	0.404934i	$0.132706\pi$
$139$			9.54821i			0.809869i	−0.914346	+	0.404934i	$0.867294\pi$
$140$	−10.5559	+	13.4285i	−0.892138	+	1.13492i
$141$		−	2.12226i		−	0.178727i
$142$	−13.9195	+	8.95512i	−1.16810	+	0.751497i
$143$	−5.62560	+	9.74383i	−0.470436	+	0.814820i
$144$	1.30091	−	3.78254i	0.108409	−	0.315212i
$145$	−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	−0.826333	−	0.563182i	$-0.809577\pi$
$149$	−9.17651	+	5.29806i	−0.751769	+	0.434034i	0.0745636	+	0.997216i	$0.476244\pi$
$150$	−6.81434	−	3.50884i	−0.556388	−	0.286495i
$151$	−1.05318	−	0.608052i	−0.0857063	−	0.0494826i	0.456534	−	0.889706i	$-0.349091\pi$
$151$	−1.05318	−	0.608052i	−0.0857063	−	0.0494826i	−0.542241	+	0.840223i	$0.682424\pi$
$152$	7.52787	−	5.93780i	0.610591	−	0.481619i
$153$		−	3.15923i		−	0.255409i
$154$	5.42469	−	6.25683i	0.437134	−	0.504190i
$155$	−6.54645			−0.525824
$156$	8.27636	−	5.90572i	0.662639	−	0.472836i
$157$	1.81252	−	3.13938i	0.144655	−	0.250550i	−0.784589	−	0.620016i	$-0.787126\pi$
$157$	1.81252	−	3.13938i	0.144655	−	0.250550i	0.929244	+	0.369466i	$0.120459\pi$
$158$	13.9391	+	7.17750i	1.10893	+	0.571011i
$159$	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	$-0.449754\pi$
$164$	10.8531	+	4.94370i	0.847488	+	0.386038i
$165$	6.18698	+	3.57205i	0.481656	+	0.278084i
$166$	−4.24978	+	2.73409i	−0.329847	+	0.212207i
$167$	12.3971			0.959317			0.479659	−	0.877455i	$-0.340760\pi$
$167$	12.3971			0.959317			0.479659	+	0.877455i	$0.340760\pi$
$168$	−6.80492	+	3.11337i	−0.525011	+	0.240202i
$169$	12.8439			0.987994
$170$	−12.1287	+	7.80301i	−0.930231	+	0.598463i
$171$	2.93566	+	1.69490i	0.224495	+	0.129613i
$172$	5.54466	−	12.1725i	0.422776	−	0.928141i
$173$	−0.519326	−	0.899499i	−0.0394836	−	0.0683876i	0.845608	−	0.533804i	$-0.179238\pi$
$173$	−0.519326	−	0.899499i	−0.0394836	−	0.0683876i	−0.885092	+	0.465416i	$0.845905\pi$
$174$	−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
$178$	9.17922	+	4.72656i	0.688011	+	0.354271i
$179$	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	$0.136572\pi$
$180$	−3.74992	−	5.25519i	−0.279503	−	0.391699i
$181$	−8.29867			−0.616835			−0.308418	−	0.951251i	$-0.599799\pi$
$181$	−8.29867			−0.616835			−0.308418	+	0.951251i	$0.599799\pi$
$182$	−18.6767	−	3.60514i	−1.38441	−	0.267231i
$183$			12.6823i			0.937503i
$184$	6.80435	−	5.36710i	0.501624	−	0.395668i
$185$	−2.57712	−	1.48790i	−0.189474	−	0.109393i
$186$	−2.54990	−	1.31299i	−0.186968	−	0.0962734i
$187$	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	−0.297419	−	0.954747i	$-0.596126\pi$
$191$	5.26146	−	3.03771i	0.380706	−	0.219801i	0.678125	+	0.734946i	$0.262793\pi$
$192$	−7.77997	−	1.86335i	−0.561471	−	0.134476i
$193$	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	$0.0594021\pi$
$194$	−18.1062	+	11.6486i	−1.29995	+	0.836322i
$195$		−	16.4100i		−	1.17514i
$196$	12.9942	+	5.21067i	0.928156	+	0.372191i
$197$		−	20.2764i		−	1.44463i	−0.691563	−	0.722316i	$-0.743078\pi$
$197$		−	20.2764i		−	1.44463i	0.691563	−	0.722316i	$-0.256922\pi$
$198$	1.69345	+	2.63224i	0.120348	+	0.187065i
$199$	−1.64355	+	2.84672i	−0.116508	+	0.201799i	−0.918382	−	0.395696i	$-0.870504\pi$
$199$	−1.64355	+	2.84672i	−0.116508	+	0.201799i	0.801873	+	0.597494i	$0.203837\pi$
$200$	−5.67655	+	14.2396i	−0.401392	+	1.00689i
$201$	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
$206$	1.28481	−	2.49517i	0.0895171	−	0.173847i
$207$	2.65351	+	1.53200i	0.184431	+	0.106482i
$208$	−13.3463	−	15.3420i	−0.925402	−	1.06378i
$209$			7.50230i			0.518945i
$210$	−2.28914	+	11.8590i	−0.157965	+	0.818350i
$211$	−21.6901			−1.49320			−0.746602	−	0.665271i	$-0.768316\pi$
$211$	−21.6901			−1.49320			−0.746602	+	0.665271i	$0.768316\pi$
$212$	5.87575	−	4.19273i	0.403548	−	0.287958i
$213$	−5.85179	+	10.1356i	−0.400958	+	0.694480i
$214$	2.09511	−	4.06882i	0.143219	−	0.278138i
$215$	−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
$220$	5.92288	−	13.0028i	0.399321	−	0.876648i
$221$	−13.9088	−	8.03027i	−0.935610	−	0.540175i
$222$	−0.705388	−	1.09643i	−0.0473426	−	0.0735877i
$223$	19.3266			1.29420			0.647102	−	0.762404i	$-0.275981\pi$
$223$	19.3266			1.29420			0.647102	+	0.762404i	$0.275981\pi$
$224$	7.50486	+	12.9490i	0.501439	+	0.865193i
$225$	−5.41974			−0.361316
$226$	2.17804	+	3.38547i	0.144881	+	0.225198i
$227$	−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	$0.672361\pi$
$228$	2.81035	−	6.16969i	0.186120	−	0.408598i
$229$	11.4311	+	19.7993i	0.755392	+	1.30838i	0.945179	+	0.326551i	$0.105887\pi$
$229$	11.4311	+	19.7993i	0.755392	+	1.30838i	−0.189788	+	0.981825i	$0.560780\pi$
$230$	−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	$0.801952\pi$
$234$	3.29127	−	6.39182i	0.215157	−	0.417846i
$235$	−3.42529	+	5.93277i	−0.223441	+	0.387011i
$236$	19.9926	−	14.2660i	1.30141	−	0.928639i
$237$	11.0863			0.720135
$238$	8.93133	+	7.74349i	0.578932	+	0.501936i
$239$			11.2699i			0.728988i	0.931206	+	0.364494i	$0.118758\pi$
$239$			11.2699i			0.728988i	−0.931206	+	0.364494i	$0.881242\pi$
$240$	−9.74164	+	8.47445i	−0.628820	+	0.547023i
$241$	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	$0.548392\pi$
$242$	3.95040	−	7.67187i	0.253941	−	0.493166i
$243$	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
$248$	−2.12414	+	5.32839i	−0.134883	+	0.338353i
$249$	−1.78661	+	3.09450i	−0.113222	+	0.196106i
$250$	1.03671	+	1.61143i	0.0655675	+	0.101916i
$251$			3.26625i			0.206164i	0.994673	+	0.103082i	$0.0328704\pi$
$251$			3.26625i			0.206164i	−0.994673	+	0.103082i	$0.967130\pi$
$252$	−3.27015	+	4.16006i	−0.206000	+	0.262059i
$253$			6.78124i			0.426333i
$254$	24.9830	−	16.0728i	1.56757	−	1.00850i
$255$	−5.09893	+	8.83161i	−0.319308	+	0.553057i
$256$	−2.21534	+	15.8459i	−0.138459	+	0.990368i
$257$	−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
$262$	0.717849	+	0.369635i	0.0443489	+	0.0228361i
$263$	−14.1861	−	8.19034i	−0.874752	−	0.505038i	−0.00582745	−	0.999983i	$-0.501855\pi$
$263$	−14.1861	−	8.19034i	−0.874752	−	0.505038i	−0.868924	+	0.494945i	$0.835188\pi$
$264$	4.91493	−	3.87677i	0.302493	−	0.238599i
$265$		−	11.6501i		−	0.715663i
$266$	−11.9871	+	4.14496i	−0.734976	+	0.254144i
$267$	7.30063			0.446791
$268$	−10.2397	−	14.3500i	−0.625488	−	0.876568i
$269$	−3.73572	+	6.47046i	−0.227771	+	0.394511i	−0.957147	−	0.289602i	$-0.906477\pi$
$269$	−3.73572	+	6.47046i	−0.227771	+	0.394511i	0.729376	+	0.684113i	$0.239810\pi$
$270$	−4.05858	−	2.08984i	−0.246997	−	0.127184i
$271$	4.48617	+	7.77027i	0.272515	+	0.472011i	0.969505	−	0.245070i	$-0.0788111\pi$
$271$	4.48617	+	7.77027i	0.272515	+	0.472011i	−0.696990	+	0.717081i	$0.745478\pi$
$272$	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
$276$	2.54024	−	5.57671i	0.152904	−	0.335678i
$277$	5.31638	+	3.06942i	0.319430	+	0.184423i	0.651139	−	0.758959i	$-0.274292\pi$
$277$	5.31638	+	3.06942i	0.319430	+	0.184423i	−0.331708	+	0.943382i	$0.607625\pi$
$278$	11.3561	−	7.30592i	0.681092	−	0.438180i
$279$	−2.02805			−0.121416
$280$	24.0481	+	2.27959i	1.43715	+	0.136231i
$281$	−19.2936			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$281$	−19.2936			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$282$	−2.52409	+	1.62387i	−0.150307	+	0.0967001i
$283$	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	$0.435485\pi$
$284$	21.3014	+	9.70295i	1.26400	+	0.575764i
$285$	−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
$290$	40.1125	+	20.6547i	2.35549	+	1.21289i
$291$	−7.61188	+	13.1842i	−0.446216	+	0.772869i
$292$	−14.7019	+	10.4908i	−0.860365	+	0.613927i
$293$	−14.0707			−0.822018			−0.411009	−	0.911631i	$-0.634824\pi$
$293$	−14.0707			−0.822018			−0.411009	+	0.911631i	$0.634824\pi$
$294$	9.85566	−	0.930602i	0.574794	−	0.0542738i
$295$		−	39.6403i		−	2.30795i
$296$	−2.04726	+	1.61483i	−0.118995	+	0.0938599i
$297$	1.91668	+	1.10660i	0.111217	+	0.0642113i
$298$	13.3227	+	6.86012i	0.771763	+	0.397396i
$299$	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
$304$	−12.8221	−	4.40983i	−0.735397	−	0.252921i
$305$	20.4690	−	35.4533i	1.17205	−	2.03005i
$306$	−3.75740	+	2.41732i	−0.214796	+	0.138189i
$307$			9.61787i			0.548921i	0.961598	+	0.274460i	$0.0884992\pi$
$307$			9.61787i			0.548921i	−0.961598	+	0.274460i	$0.911501\pi$
$308$	−11.5923	−	1.66432i	−0.660530	−	0.0948335i
$309$		−	1.98452i		−	0.112895i
$310$	5.00909	+	7.78596i	0.284497	+	0.442213i
$311$	10.8485	−	18.7902i	0.615162	−	1.06549i	−0.375194	−	0.926946i	$-0.622424\pi$
$311$	10.8485	−	18.7902i	0.615162	−	1.06549i	0.990356	−	0.138546i	$-0.0442428\pi$
$312$	−13.3567	−	5.32458i	−0.756172	−	0.301445i
$313$	−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	−0.662480	−	0.749079i	$-0.730496\pi$
$317$	−6.14253	+	3.54639i	−0.344999	+	0.199185i	0.317482	+	0.948264i	$0.397163\pi$
$318$	2.33662	−	4.53783i	0.131031	−	0.254469i
$319$	−18.9433	−	10.9369i	−1.06062	−	0.612352i
$320$	18.7415	+	17.7657i	1.04768	+	0.993134i
$321$		−	3.23611i		−	0.180622i
$322$	−10.8350	+	3.74657i	−0.603810	+	0.208788i
$323$	−10.7092			−0.595874
$324$	−1.16170	−	1.62802i	−0.0645389	−	0.0904456i
$325$	−13.7761	+	23.8610i	−0.764163	+	1.32357i
$326$	−12.8392	+	24.9344i	−0.711099	+	1.38099i
$327$	−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	$0.937758\pi$
$332$	6.50353	+	2.96241i	0.356927	+	0.162583i
$333$	−0.798374	−	0.460941i	−0.0437506	−	0.0252594i
$334$	−9.48578	−	14.7444i	−0.519039	−	0.806776i
$335$	−28.4526			−1.55453
$336$	8.90971	+	5.71113i	0.486065	+	0.311568i
$337$	23.5287			1.28169			0.640846	−	0.767670i	$-0.278584\pi$
$337$	23.5287			1.28169			0.640846	+	0.767670i	$0.278584\pi$
$338$	−9.82767	−	15.2758i	−0.534555	−	0.830893i
$339$	2.46515	+	1.42326i	0.133889	+	0.0773007i
$340$	18.5609	+	8.45463i	1.00660	+	0.458517i
$341$	−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
$346$	−0.672442	+	1.30592i	−0.0361507	+	0.0702065i
$347$	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	$0.0771240\pi$
$348$	11.4815	+	16.0904i	0.615475	+	0.862536i
$349$	0.830301			0.0444450			0.0222225	−	0.999753i	$-0.492926\pi$
$349$	0.830301			0.0444450			0.0222225	+	0.999753i	$0.492926\pi$
$350$	13.2841	−	15.3219i	0.710068	−	0.818991i
$351$		−	5.08369i		−	0.271347i
$352$	−8.66163	−	9.03989i	−0.461666	−	0.481828i
$353$	−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	$0.707980\pi$
$354$	7.95049	−	15.4402i	0.422564	−	0.820640i
$355$	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	−0.864248	−	0.503066i	$-0.832205\pi$
$359$	−16.3080	+	9.41543i	−0.860704	+	0.496928i	0.00354407	+	0.999994i	$0.498872\pi$
$360$	−3.38092	+	8.48100i	−0.178190	+	0.446988i
$361$	−3.75460	+	6.50317i	−0.197611	+	0.342272i
$362$	6.34982	+	9.86994i	0.333739	+	0.518752i
$363$		−	6.10177i		−	0.320260i
$364$	10.0029	+	24.9714i	0.524295	+	1.30886i
$365$			29.1503i			1.52579i
$366$	15.0836	−	9.70400i	0.788431	−	0.507236i
$367$	10.7270	−	18.5796i	0.559943	−	0.969850i	−0.437557	−	0.899190i	$-0.644156\pi$
$367$	10.7270	−	18.5796i	0.559943	−	0.969850i	0.997501	−	0.0706593i	$-0.0225103\pi$
$368$	−11.5897	−	3.98599i	−0.604157	−	0.207784i
$369$	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	−0.819442	−	0.573162i	$-0.805717\pi$
$373$	−14.1525	+	8.17098i	−0.732791	+	0.423077i	0.0866513	+	0.996239i	$0.472383\pi$
$374$	−8.79116	−	4.52674i	−0.454580	−	0.234072i
$375$	1.17337	+	0.677448i	0.0605928	+	0.0349832i
$376$	3.71749	+	4.71299i	0.191715	+	0.243054i
$377$			50.2442i			2.58771i
$378$	−0.709159	+	3.67384i	−0.0364752	+	0.188962i
$379$	−4.31636			−0.221717			−0.110858	−	0.993836i	$-0.535360\pi$
$379$	−4.31636			−0.221717			−0.110858	+	0.993836i	$0.535360\pi$
$380$	−17.8141	+	12.7115i	−0.913843	+	0.652087i
$381$	10.5029	−	18.1916i	0.538080	−	0.931981i
$382$	−7.63873	−	3.93333i	−0.390831	−	0.201247i
$383$	10.0948	+	17.4848i	0.515823	+	0.893431i	0.999831	+	0.0183677i	$0.00584695\pi$
$383$	10.0948	+	17.4848i	0.515823	+	0.893431i	−0.484009	+	0.875063i	$0.660820\pi$
$384$	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
$388$	27.7083	+	12.6214i	1.40668	+	0.640753i
$389$	29.2383	+	16.8807i	1.48244	+	0.855886i	0.999801	−	0.0199339i	$-0.00634559\pi$
$389$	29.2383	+	16.8807i	1.48244	+	0.855886i	0.482637	+	0.875820i	$0.339679\pi$
$390$	−19.5170	+	12.5563i	−0.988283	+	0.635811i
$391$	−9.67989			−0.489533
$392$	−3.74539	−	19.4415i	−0.189171	−	0.981944i
$393$	0.570937			0.0287999
$394$	−24.1155	+	15.5147i	−1.21492	+	0.781618i
$395$	−30.9918	−	17.8931i	−1.55937	−	0.900302i
$396$	1.83487	−	4.02817i	0.0922056	−	0.202423i
$397$	0.0441158	+	0.0764109i	0.00221411	+	0.00383495i	0.867130	−	0.498081i	$-0.165962\pi$
$397$	0.0441158	+	0.0764109i	0.00221411	+	0.00383495i	−0.864916	+	0.501916i	$0.832629\pi$
$398$	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	$0.616634\pi$
$402$	−11.0825	−	5.70660i	−0.552745	−	0.284620i
$403$	−5.15498	+	8.92869i	−0.256788	+	0.444770i
$404$	11.4340	+	16.0238i	0.568862	+	0.797212i
$405$	−3.22796			−0.160399
$406$	7.00890	−	36.3100i	0.347846	−	1.80204i
$407$		−	2.04031i		−	0.101134i
$408$	5.53390	+	7.01582i	0.273969	+	0.347335i
$409$	−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	$0.945644\pi$
$410$	−24.2014	−	12.4618i	−1.19522	−	0.615444i
$411$	−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
$416$	−8.03479	+	27.6125i	−0.393938	+	1.35381i
$417$	4.77411	−	8.26899i	0.233789	−	0.404934i
$418$	8.92279	−	5.74047i	0.436428	−	0.280775i
$419$			22.7655i			1.11217i	0.831126	+	0.556085i	$0.187697\pi$
$419$			22.7655i			1.11217i	−0.831126	+	0.556085i	$0.812303\pi$
$420$	15.8560	−	6.35149i	0.773691	−	0.309921i
$421$			24.0207i			1.17070i	0.810781	+	0.585349i	$0.199042\pi$
$421$			24.0207i			1.17070i	−0.810781	+	0.585349i	$0.800958\pi$
$422$	16.5964	+	25.7968i	0.807899	+	1.25577i
$423$	−1.06113	+	1.83793i	−0.0515939	+	0.0893633i
$424$	−9.48247	−	3.78015i	−0.460509	−	0.183580i
$425$	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
$430$	−13.9766	+	27.1434i	−0.674014	+	1.30897i
$431$	28.2391	+	16.3039i	1.36023	+	0.785330i	0.989654	−	0.143471i	$-0.0458265\pi$
$431$	28.2391	+	16.3039i	1.36023	+	0.785330i	0.370577	+	0.928802i	$0.379160\pi$
$432$	−3.01789	+	2.62532i	−0.145198	+	0.126311i
$433$		−	18.4752i		−	0.887861i	−0.896061	−	0.443931i	$-0.853584\pi$
$433$		−	18.4752i		−	0.887861i	0.896061	−	0.443931i	$-0.146416\pi$
$434$	4.97088	−	5.73340i	0.238610	−	0.275212i
$435$	31.9032			1.52964
$436$	−6.82389	+	4.86929i	−0.326805	+	0.233197i
$437$	5.19319	−	8.99487i	0.248424	−	0.430283i
$438$	−5.84654	+	11.3543i	−0.279358	+	0.542528i
$439$	−11.2138	−	19.4229i	−0.535206	−	0.927004i	−0.999153	−	0.0411413i	$-0.986901\pi$
$439$	−11.2138	−	19.4229i	−0.535206	−	0.927004i	0.463947	−	0.885863i	$-0.346433\pi$
$440$	−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	$0.902254\pi$
$444$	−0.764294	+	1.67789i	−0.0362718	+	0.0796293i
$445$	−20.4089	−	11.7831i	−0.967474	−	0.558571i
$446$	−14.7879	−	22.9859i	−0.700229	−	1.08841i
$447$	10.5961			0.501179
$448$	9.65836	−	18.8339i	0.456315	−	0.889818i
$449$	5.65664			0.266954			0.133477	−	0.991052i	$-0.457386\pi$
$449$	5.65664			0.266954			0.133477	+	0.991052i	$0.457386\pi$
$450$	4.14697	+	6.44591i	0.195490	+	0.303863i
$451$	11.4292	+	6.59867i	0.538182	+	0.310719i
$452$	2.35993	−	5.18086i	0.111002	−	0.243687i
$453$	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	$0.903735\pi$
$458$	14.8015	−	28.7452i	0.691627	−	1.34317i
$459$	−1.57961	+	2.73597i	−0.0737301	+	0.127704i
$460$	−16.1019	+	11.4898i	−0.750757	+	0.535714i
$461$	31.7960			1.48089			0.740444	−	0.672118i	$-0.234615\pi$
$461$	31.7960			1.48089			0.740444	+	0.672118i	$0.234615\pi$
$462$	−7.82634	+	2.70623i	−0.364114	+	0.125905i
$463$		−	8.87505i		−	0.412458i	−0.978504	−	0.206229i	$-0.933881\pi$
$463$		−	8.87505i		−	0.412458i	0.978504	−	0.206229i	$-0.0661193\pi$
$464$	29.8270	−	25.9471i	1.38469	−	1.20457i
$465$	5.66939	+	3.27323i	0.262912	+	0.151792i
$466$	1.94543	−	3.77811i	0.0901201	−	0.175018i
$467$	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
$472$	−32.2647	−	12.8622i	−1.48510	−	0.592030i
$473$	7.40081	−	12.8186i	0.340290	−	0.589399i
$474$	−8.48283	−	13.1854i	−0.389629	−	0.605627i
$475$			18.3719i			0.842959i
$476$	2.37574	−	16.5474i	0.108892	−	0.758448i
$477$		−	3.60913i		−	0.165251i
$478$	13.4037	−	8.62327i	0.613072	−	0.394419i
$479$	−8.19517	+	14.1945i	−0.374447	+	0.648561i	−0.990244	−	0.139344i	$-0.955501\pi$
$479$	−8.19517	+	14.1945i	−0.374447	+	0.648561i	0.615797	+	0.787905i	$0.288834\pi$
$480$	17.5329	+	5.10180i	0.800265	+	0.232864i
$481$	−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
$486$	−1.25732	−	0.647418i	−0.0570331	−	0.0293675i
$487$	25.4297	+	14.6819i	1.15233	+	0.665299i	0.949454	−	0.313905i	$-0.101637\pi$
$487$	25.4297	+	14.6819i	1.15233	+	0.665299i	0.202877	+	0.979204i	$0.434971\pi$
$488$	−22.2151	−	28.1641i	−1.00563	−	1.27493i
$489$			19.8314i			0.896808i
$490$	−29.0534	−	13.3053i	−1.31250	−	0.601074i
$491$	33.8967			1.52974			0.764869	−	0.644186i	$-0.222804\pi$
$491$	33.8967			1.52974			0.764869	+	0.644186i	$0.222804\pi$
$492$	−6.92725	−	9.70794i	−0.312305	−	0.437668i
$493$	15.6120	−	27.0407i	0.703128	−	1.21785i
$494$	−21.6670	−	11.1568i	−0.974846	−	0.501967i
$495$	−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	$0.769565\pi$
$500$	1.12329	−	2.46601i	0.0502349	−	0.110283i
$501$	−10.7362	−	6.19856i	−0.479659	−	0.276931i
$502$	3.88468	−	2.49921i	0.173382	−	0.111545i
$503$	1.51626			0.0676065			0.0338032	−	0.999429i	$-0.489238\pi$
$503$	1.51626			0.0676065			0.0338032	+	0.999429i	$0.489238\pi$
$504$	7.44992	+	0.706200i	0.331846	+	0.0314567i
$505$	31.7711			1.41380
$506$	8.06520	−	5.18874i	0.358542	−	0.230668i
$507$	−11.1232	−	6.42196i	−0.493997	−	0.285209i
$508$	−38.2321	−	17.4150i	−1.69627	−	0.772667i
$509$	−3.71720	−	6.43837i	−0.164762	−	0.285376i	0.771809	−	0.635855i	$-0.219352\pi$
$509$	−3.71720	−	6.43837i	−0.164762	−	0.285376i	−0.936571	+	0.350479i	$0.886019\pi$
$510$	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
$514$	15.1764	+	7.81462i	0.669402	+	0.344688i
$515$	−3.20297	+	5.54771i	−0.141140	+	0.244461i
$516$	−10.8880	+	7.76933i	−0.479319	+	0.342026i
$517$	−4.69698			−0.206573
$518$	3.25998	−	1.12725i	0.143235	−	0.0495286i
$519$			1.03865i			0.0455917i
$520$	28.7447	+	36.4422i	1.26054	+	1.59810i
$521$	−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	$0.762910\pi$
$522$	12.4266	+	6.39869i	0.543897	+	0.280063i
$523$	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
$528$	−8.37151	−	2.87916i	−0.364323	−	0.125300i
$529$	−6.80594	+	11.7882i	−0.295910	+	0.512532i
$530$	−13.8560	+	8.91423i	−0.601865	+	0.387209i
$531$		−	12.2803i		−	0.532920i
$532$	14.1018	+	11.0852i	0.611391	+	0.480603i
$533$		−	30.3142i		−	1.31305i
$534$	−5.58616	−	8.68293i	−0.241737	−	0.375747i
$535$	−5.22301	+	9.04652i	−0.225811	+	0.391115i
$536$	−9.23207	+	23.1586i	−0.398764	+	1.00030i
$537$	−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	−0.973736	−	0.227680i	$-0.926886\pi$
$541$	−29.3866	+	16.9663i	−1.26343	+	0.729440i	−0.289691	+	0.957120i	$0.593553\pi$
$542$	5.80886	−	11.2811i	0.249512	−	0.484564i
$543$	7.18686	+	4.14933i	0.308418	+	0.178065i
$544$	12.9040	−	12.3641i	0.553255	−	0.530104i
$545$			13.5301i			0.579565i
$546$	14.3719	+	12.4605i	0.615060	+	0.533259i
$547$	19.9416			0.852640			0.426320	−	0.904572i	$-0.359810\pi$
$547$	19.9416			0.852640			0.426320	+	0.904572i	$0.359810\pi$
$548$	15.2836	+	21.4187i	0.652884	+	0.914961i
$549$	6.34115	−	10.9832i	0.270634	−	0.468752i
$550$	−7.76574	+	15.0815i	−0.331132	+	0.643075i
$551$	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
$556$	−17.3784	−	7.91602i	−0.737010	−	0.335714i
$557$	29.5999	+	17.0895i	1.25419	+	0.724107i	0.971939	−	0.235234i	$-0.0755857\pi$
$557$	29.5999	+	17.0895i	1.25419	+	0.724107i	0.282251	+	0.959341i	$0.408919\pi$
$558$	1.55178	+	2.41204i	0.0656921	+	0.102110i
$559$	−33.9992			−1.43801
$560$	−15.6894	−	30.3456i	−0.662999	−	1.28233i
$561$	−6.99199			−0.295202
$562$	14.7627	+	22.9466i	0.622727	+	0.967945i
$563$	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	$0.651513\pi$
$564$	3.86267	+	1.75948i	0.162648	+	0.0740874i
$565$	−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	$-0.375994\pi$
$570$	−7.08416	+	13.7578i	−0.296723	+	0.576250i
$571$	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	$-0.0184874\pi$
$572$	−13.0705	−	18.3172i	−0.546506	−	0.765881i
$573$	−6.07541			−0.253804
$574$	−4.22873	+	21.9072i	−0.176504	+	0.914390i
$575$			16.6061i			0.692522i
$576$	5.80597	+	5.50370i	0.241916	+	0.229321i
$577$	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	$0.666309\pi$
$578$	−4.54441	+	8.82546i	−0.189022	+	0.367091i
$579$	−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
$584$	23.7264	+	9.45845i	0.981807	+	0.391393i
$585$	−8.20498	+	14.2114i	−0.339234	+	0.587571i
$586$	10.7663	+	16.7348i	0.444753	+	0.691310i
$587$			4.75946i			0.196444i	0.995165	+	0.0982219i	$0.0313155\pi$
$587$			4.75946i			0.196444i	−0.995165	+	0.0982219i	$0.968685\pi$
$588$	−8.64796	−	11.0097i	−0.356636	−	0.454031i
$589$			6.87468i			0.283266i
$590$	−47.1458	+	30.3312i	−1.94096	+	1.24872i
$591$	−10.1382	+	17.5599i	−0.417029	+	0.722316i
$592$	3.48706	+	1.19928i	0.143317	+	0.0492903i
$593$	−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
$598$	−19.5846	−	10.0845i	−0.800873	−	0.412385i
$599$	−25.6580	−	14.8136i	−1.04836	−	0.605269i	−0.126167	−	0.992009i	$-0.540268\pi$
$599$	−25.6580	−	14.8136i	−1.04836	−	0.605269i	−0.922189	+	0.386740i	$0.873601\pi$
$600$	12.0358	−	9.49355i	0.491360	−	0.387573i
$601$		−	26.4608i		−	1.07936i	−0.841870	−	0.539680i	$-0.818545\pi$
$601$		−	26.4608i		−	1.07936i	0.841870	−	0.539680i	$-0.181455\pi$
$602$	24.5703	+	4.74278i	1.00141	+	0.193301i
$603$	−8.81440			−0.358950
$604$	1.97984	−	1.41275i	0.0805587	−	0.0574839i
$605$	−9.84814	+	17.0575i	−0.400384	+	0.693485i
$606$	12.3751	+	6.37219i	0.502705	+	0.258853i
$607$	7.69208	+	13.3231i	0.312212	+	0.540767i	0.978841	−	0.204623i	$-0.0655967\pi$
$607$	7.69208	+	13.3231i	0.312212	+	0.540767i	−0.666629	+	0.745390i	$0.732263\pi$
$608$	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
$612$	5.75002	+	2.61918i	0.232431	+	0.105874i
$613$	−16.8302	−	9.71692i	−0.679765	−	0.392463i	0.120001	−	0.992774i	$-0.461710\pi$
$613$	−16.8302	−	9.71692i	−0.679765	−	0.392463i	−0.799767	+	0.600311i	$0.795043\pi$
$614$	11.4389	−	7.35921i	0.461637	−	0.296994i
$615$	−19.2484			−0.776172
$616$	6.89050	+	15.0606i	0.277626	+	0.606809i
$617$	−0.173969			−0.00700371			−0.00350186	−	0.999994i	$-0.501115\pi$
$617$	−0.173969			−0.00700371			−0.00350186	+	0.999994i	$0.501115\pi$
$618$	−2.36026	+	1.51847i	−0.0949438	+	0.0610820i
$619$	−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	$0.942940\pi$
$620$	5.42739	−	11.9150i	0.217969	−	0.478519i
$621$	−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
$626$	13.7417	+	7.07589i	0.549230	+	0.282810i
$627$	3.75115	−	6.49718i	0.149807	−	0.259473i
$628$	4.21121	+	5.90164i	0.168045	+	0.235501i
$629$	2.91244			0.116127
$630$	7.91196	−	9.12564i	0.315220	−	0.363574i
$631$			26.0140i			1.03560i	0.855501	+	0.517801i	$0.173249\pi$
$631$			26.0140i			1.03560i	−0.855501	+	0.517801i	$0.826751\pi$
$632$	−24.6199	+	19.4195i	−0.979326	+	0.772468i
$633$	18.7841	+	10.8450i	0.746602	+	0.431051i
$634$	8.91788	+	4.59199i	0.354174	+	0.182371i
$635$	−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
$640$	6.78925	−	35.8836i	0.268369	−	1.41842i
$641$	−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	$0.330413\pi$
$642$	−3.84883	+	2.47614i	−0.151901	+	0.0977255i
$643$			4.80941i			0.189665i	0.995493	+	0.0948323i	$0.0302315\pi$
$643$			4.80941i			0.189665i	−0.995493	+	0.0948323i	$0.969769\pi$
$644$	12.7465	+	10.0198i	0.502281	+	0.394833i
$645$			21.5883i			0.850038i
$646$	8.19424	+	12.7368i	0.322398	+	0.501125i
$647$	−4.27034	+	7.39644i	−0.167884	+	0.290784i	−0.937676	−	0.347511i	$-0.887027\pi$
$647$	−4.27034	+	7.39644i	−0.167884	+	0.290784i	0.769792	+	0.638295i	$0.220360\pi$
$648$	−1.04738	+	2.62735i	−0.0411451	+	0.103212i
$649$	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	−0.892099	−	0.451839i	$-0.850768\pi$
$653$	−24.1955	+	13.9693i	−0.946845	+	0.546661i	−0.0547454	+	0.998500i	$0.517435\pi$
$654$	−2.71367	+	5.27008i	−0.106113	+	0.206076i
$655$	−1.59605	−	0.921481i	−0.0623629	−	0.0360052i
$656$	−17.9958	+	15.6549i	−0.702617	+	0.611221i
$657$			9.03055i			0.352315i
$658$	−2.59504	−	7.50478i	−0.101165	−	0.292567i
$659$	28.0553			1.09288			0.546439	−	0.837499i	$-0.315983\pi$
$659$	28.0553			1.09288			0.546439	+	0.837499i	$0.315983\pi$
$660$	−11.6308	+	8.29931i	−0.452727	+	0.323050i
$661$	−4.47127	+	7.74447i	−0.173912	+	0.301225i	−0.939784	−	0.341768i	$-0.888974\pi$
$661$	−4.47127	+	7.74447i	−0.173912	+	0.301225i	0.765872	+	0.642993i	$0.222308\pi$
$662$	−7.59035	+	14.7408i	−0.295007	+	0.572919i
$663$	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
$668$	−10.2779	+	22.5636i	−0.397665	+	0.873013i
$669$	−16.7373	−	9.66329i	−0.647102	−	0.373604i
$670$	21.7708	+	33.8398i	0.841078	+	1.30734i
$671$	28.0684			1.08357
$672$	−0.0248868	−	14.9666i	−0.000960030	−	0.577349i
$673$	45.4881			1.75344			0.876720	−	0.481002i	$-0.159727\pi$
$673$	45.4881			1.75344			0.876720	+	0.481002i	$0.159727\pi$
$674$	−18.0033	−	27.9836i	−0.693459	−	1.07789i
$675$	4.69363	+	2.70987i	0.180658	+	0.104303i
$676$	−10.6484	+	23.3769i	−0.409552	+	0.899110i
$677$	−5.48447	−	9.49939i	−0.210785	−	0.365091i	0.741175	−	0.671312i	$-0.234269\pi$
$677$	−5.48447	−	9.49939i	−0.210785	−	0.365091i	−0.951961	+	0.306221i	$0.900935\pi$
$678$	−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
$682$	−2.90591	+	5.64342i	−0.111273	+	0.216098i
$683$	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	$-0.0147816\pi$
$684$	−5.51868	+	3.93794i	−0.211012	+	0.150571i
$685$	42.4679			1.62262
$686$	−3.77482	+	25.9182i	−0.144123	+	0.989560i
$687$		−	22.8623i		−	0.872251i
$688$	17.5579	+	20.1834i	0.669389	+	0.769483i
$689$	−15.8896	−	9.17386i	−0.605345	−	0.349496i
$690$	−6.40328	+	12.4355i	−0.243769	+	0.473411i
$691$	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
$696$	10.3517	−	25.9672i	0.392381	−	0.984284i
$697$	−9.41929	+	16.3147i	−0.356781	+	0.617963i
$698$	−0.635313	−	0.987510i	−0.0240470	−	0.0373778i
$699$		−	3.00490i		−	0.113656i
$700$	−28.3875	−	4.07564i	−1.07295	−	0.154045i
$701$		−	14.3589i		−	0.542328i	−0.962533	−	0.271164i	$-0.912591\pi$
$701$		−	14.3589i		−	0.542328i	0.962533	−	0.271164i	$-0.0874085\pi$
$702$	−6.04624	+	3.88984i	−0.228201	+	0.146813i
$703$	−1.56250	+	2.70633i	−0.0589309	+	0.102071i
$704$	−4.12397	+	17.2186i	−0.155428	+	0.648950i
$705$	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	−0.323445	−	0.946247i	$-0.604841\pi$
$709$	8.90161	−	5.13935i	0.334307	−	0.193012i	0.657752	+	0.753235i	$0.271508\pi$
$710$	−47.4999	−	24.4586i	−1.78264	−	0.917916i
$711$	−9.60105	−	5.54317i	−0.360068	−	0.207885i
$712$	−16.2128	+	12.7882i	−0.607600	+	0.479260i
$713$			6.21394i			0.232714i
$714$	−3.86301	−	11.1717i	−0.144570	−	0.418091i
$715$	−36.3184			−1.35823
$716$	2.93454	+	4.11250i	0.109669	+	0.153691i
$717$	5.63494	−	9.76000i	0.210441	−	0.364494i
$718$	23.6764	+	12.1914i	0.883595	+	0.454981i
$719$	−7.39467	−	12.8079i	−0.275775	−	0.477656i	0.694556	−	0.719439i	$-0.255601\pi$
$719$	−7.39467	−	12.8079i	−0.275775	−	0.477656i	−0.970330	+	0.241783i	$0.922268\pi$
$720$	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
$724$	6.88008	−	15.1042i	0.255696	−	0.561342i
$725$	−46.3890	−	26.7827i	−1.72285	−	0.994685i
$726$	−7.25708	+	4.66883i	−0.269335	+	0.173277i
$727$	43.5679			1.61585			0.807923	−	0.589289i	$-0.200592\pi$
$727$	43.5679			1.61585			0.807923	+	0.589289i	$0.200592\pi$
$728$	22.0457	−	31.0040i	0.817067	−	1.14908i
$729$	−1.00000			−0.0370370
$730$	34.6696	−	22.3046i	1.28318	−	0.825531i
$731$	18.2979	+	10.5643i	0.676773	+	0.390735i
$732$	−23.0827	−	10.5144i	−0.853162	−	0.388622i
$733$	−11.3412	−	19.6435i	−0.418896	−	0.725549i	0.576933	−	0.816792i	$-0.304250\pi$
$733$	−11.3412	−	19.6435i	−0.418896	−	0.725549i	−0.995829	+	0.0912424i	$0.970916\pi$
$734$	−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
$738$	−7.49743	−	3.86057i	−0.275984	−	0.142110i
$739$	−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	$0.193935\pi$
$740$	4.84467	−	3.45699i	0.178094	−	0.127081i
$741$	−17.2327			−0.633060
$742$	10.2032	+	8.84623i	0.374572	+	0.324755i
$743$			28.3209i			1.03899i	0.854473	+	0.519496i	$0.173880\pi$
$743$			28.3209i			1.03899i	−0.854473	+	0.519496i	$0.826120\pi$
$744$	4.50376	−	3.55245i	0.165116	−	0.130239i
$745$	−29.6214	−	17.1019i	−1.08525	−	0.626567i
$746$	20.5470	+	10.5801i	0.752281	+	0.387364i
$747$	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	−0.920677	−	0.390326i	$-0.872362\pi$
$751$	−28.5823	+	16.5020i	−1.04298	+	0.602166i	−0.122306	+	0.992492i	$0.539029\pi$
$752$	2.76087	−	8.02754i	0.100678	−	0.292734i
$753$	1.63312	−	2.82866i	0.0595144	−	0.103082i
$754$	59.7574	−	38.4449i	2.17624	−	1.40008i
$755$		−	3.92554i		−	0.142865i
$756$	4.91206	−	1.96765i	0.178650	−	0.0715626i
$757$		−	19.0350i		−	0.691838i	−0.938264	−	0.345919i	$-0.887567\pi$
$757$		−	19.0350i		−	0.691838i	0.938264	−	0.345919i	$-0.112433\pi$
$758$	3.30271	+	5.13362i	0.119960	+	0.186461i
$759$	3.39062	−	5.87273i	0.123072	−	0.213166i
$760$	28.7489	+	11.4607i	1.04283	+	0.415722i
$761$	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
$766$	13.0712	−	25.3849i	0.472281	−	0.917193i
$767$	−54.0653	−	31.2146i	−1.95219	−	1.12709i
$768$	9.84149	−	12.6153i	0.355124	−	0.455214i
$769$			24.2908i			0.875949i	0.898987	+	0.437974i	$0.144304\pi$
$769$			24.2908i			0.875949i	−0.898987	+	0.437974i	$0.855696\pi$
$770$	26.2463	+	5.06631i	0.945851	+	0.182577i
$771$	12.0704			0.434706
$772$	10.6723	+	14.9563i	0.384104	+	0.538289i
$773$	−8.01612	+	13.8843i	−0.288320	+	0.499385i	−0.973409	−	0.229075i	$-0.926430\pi$
$773$	−8.01612	+	13.8843i	−0.288320	+	0.499385i	0.685089	+	0.728459i	$0.259763\pi$
$774$	−4.32987	+	8.40882i	−0.155634	+	0.302249i
$775$	−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
$780$	29.8673	+	13.6048i	1.06942	+	0.487131i
$781$	22.4321	+	12.9512i	0.802682	+	0.463429i
$782$	7.40667	+	11.5127i	0.264862	+	0.411693i
$783$	9.88340			0.353204
$784$	−20.2567	+	19.3304i	−0.723455	+	0.690372i
$785$	11.7015			0.417644
$786$	−0.436858	−	0.679038i	−0.0155822	−	0.0242205i
$787$	−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	$0.724076\pi$
$788$	36.9045	+	16.8103i	1.31467	+	0.598842i
$789$	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
$794$	0.0571228	−	0.110935i	0.00202721	−	0.00393695i
$795$	−5.82507	+	10.0893i	−0.206594	+	0.357831i
$796$	−3.81863	−	5.35148i	−0.135348	−	0.189678i
$797$	−53.0872			−1.88045			−0.940223	−	0.340560i	$-0.889383\pi$
$797$	−53.0872			−1.88045			−0.940223	+	0.340560i	$0.889383\pi$
$798$	12.4536	+	2.40391i	0.440853	+	0.0850975i
$799$		−	6.70471i		−	0.237196i
$800$	−21.2108	−	22.1372i	−0.749917	−	0.782667i
$801$	−6.32253	−	3.65032i	−0.223396	−	0.128978i
$802$	16.3198	−	31.6938i	0.576271	−	1.11915i
$803$	−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
$808$	10.3088	−	25.8597i	0.362664	−	0.909739i
$809$	−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	$0.770154\pi$
$810$	2.46991	+	3.83914i	0.0867838	+	0.134894i
$811$			48.2050i			1.69271i	0.532621	+	0.846354i	$0.321207\pi$
$811$			48.2050i			1.69271i	−0.532621	+	0.846354i	$0.678793\pi$
$812$	−48.5479	+	19.4470i	−1.70370	+	0.682458i
$813$		−	8.97234i		−	0.314674i
$814$	−2.42662	+	1.56116i	−0.0850529	+	0.0547187i
$815$	32.0076	−	55.4387i	1.12118	−	1.94193i
$816$	4.10987	−	11.9499i	0.143874	−	0.418331i
$817$	−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	−0.0546787	−	0.998504i	$-0.517413\pi$
$821$	22.4271	−	12.9483i	0.782712	−	0.451899i	0.837390	+	0.546605i	$0.184080\pi$
$822$	16.5416	+	8.51760i	0.576955	+	0.297086i
$823$	48.1100	+	27.7763i	1.67701	+	0.968221i	0.963552	+	0.267522i	$0.0862048\pi$
$823$	48.1100	+	27.7763i	1.67701	+	0.968221i	0.713457	+	0.700699i	$0.247129\pi$
$824$	3.47620	+	4.40709i	0.121099	+	0.153528i
$825$			11.9949i			0.417610i
$826$	34.7171	+	30.0999i	1.20796	+	1.04731i
$827$	23.2870			0.809770			0.404885	−	0.914368i	$-0.367312\pi$
$827$	23.2870			0.809770			0.404885	+	0.914368i	$0.367312\pi$
$828$	−4.98827	+	3.55945i	−0.173354	+	0.123700i
$829$	2.58838	−	4.48320i	0.0898980	−	0.155708i	−0.817570	−	0.575829i	$-0.804679\pi$
$829$	2.58838	−	4.48320i	0.0898980	−	0.155708i	0.907468	+	0.420122i	$0.138013\pi$
$830$	−14.5022	−	7.46747i	−0.503379	−	0.259200i
$831$	−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
$836$	−13.6547	−	6.21985i	−0.472259	−	0.215118i
$837$	1.75634	+	1.01402i	0.0607080	+	0.0350498i
$838$	27.0760	−	17.4193i	0.935323	−	0.601739i
$839$	−12.7298			−0.439480			−0.219740	−	0.975558i	$-0.570521\pi$
$839$	−12.7298			−0.439480			−0.219740	+	0.975558i	$0.570521\pi$
$840$	−19.6864	−	13.9982i	−0.679246	−	0.482984i
$841$	−68.6816			−2.36833
$842$	28.5688	−	18.3797i	0.984546	−	0.633407i
$843$	16.7087	+	9.64680i	0.575480	+	0.332253i
$844$	17.9823	−	39.4775i	0.618977	−	1.35887i
$845$	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
$850$	−21.5280	−	11.0852i	−0.738406	−	0.380220i
$851$	−1.41233	+	2.44622i	−0.0484139	+	0.0838554i
$852$	−13.5960	−	19.0537i	−0.465793	−	0.652769i
$853$	−47.2928			−1.61927			−0.809637	−	0.586930i	$-0.800336\pi$
$853$	−47.2928			−1.61927			−0.809637	+	0.586930i	$0.800336\pi$
$854$	15.5075	+	44.8474i	0.530657	+	1.53465i
$855$			10.9422i			0.374214i
$856$	5.66857	+	7.18654i	0.193748	+	0.245631i
$857$	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	$0.315642\pi$
$858$	−14.1463	−	7.28423i	−0.482948	−	0.248680i
$859$	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	−0.0503147	−	0.998733i	$-0.516022\pi$
$863$	23.1918	−	13.3898i	0.789457	−	0.455793i	0.839771	+	0.542940i	$0.182689\pi$
$864$	5.43158	+	1.58050i	0.184786	+	0.0537698i
$865$	1.67636	−	2.90355i	0.0569981	−	0.0987236i
$866$	−21.9733	+	14.1365i	−0.746682	+	0.480377i
$867$			7.01927i			0.238387i
$868$	−10.6225	−	1.52509i	−0.360551	−	0.0517649i
$869$		−	24.5362i		−	0.832335i
$870$	−24.4111	−	37.9438i	−0.827614	−	1.28642i
$871$	−22.4049	+	38.8063i	−0.759160	+	1.31490i
$872$	11.0126	+	4.39014i	0.372934	+	0.148669i
$873$	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	−0.0707159	−	0.997496i	$-0.522528\pi$
$877$	22.4411	−	12.9564i	0.757783	−	0.437506i	0.828499	+	0.559990i	$0.189195\pi$
$878$	−14.5201	+	28.1987i	−0.490028	+	0.951659i
$879$	12.1856	+	7.03534i	0.411009	+	0.237296i
$880$	18.7556	+	21.5601i	0.632251	+	0.726792i
$881$		−	10.0120i		−	0.337313i	−0.985675	−	0.168657i	$-0.946057\pi$
$881$		−	10.0120i		−	0.337313i	0.985675	−	0.168657i	$-0.0539429\pi$
$882$	−9.00055	−	4.12190i	−0.303064	−	0.138792i
$883$	−23.6231			−0.794981			−0.397491	−	0.917606i	$-0.630119\pi$
$883$	−23.6231			−0.794981			−0.397491	+	0.917606i	$0.630119\pi$
$884$	26.1469	−	18.6575i	0.879416	−	0.627521i
$885$	−19.8202	+	34.3295i	−0.666248	+	1.15397i
$886$	−5.85484	+	11.3704i	−0.196697	+	0.381996i
$887$	−9.08123	−	15.7291i	−0.304918	−	0.528133i	0.672325	−	0.740256i	$-0.265296\pi$
$887$	−9.08123	−	15.7291i	−0.304918	−	0.528133i	−0.977243	+	0.212123i	$0.931962\pi$
$888$	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
$892$	−16.0229	+	35.1758i	−0.536485	+	1.17777i
$893$	6.23023	+	3.59703i	0.208487	+	0.120370i
$894$	−8.10774	−	12.6024i	−0.271163	−	0.421487i
$895$	8.15407			0.272560
$896$	−29.7901	+	2.92389i	−0.995218	+	0.0976802i
$897$	−15.5765			−0.520083
$898$	−4.32824	−	6.72767i	−0.144435	−	0.224505i
$899$	−17.3586	−	10.0220i	−0.578942	−	0.334252i
$900$	4.49328	−	9.86431i	0.149776	−	0.328810i
$901$	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
$906$	0.787328	−	1.52903i	0.0261572	−	0.0507986i
$907$	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	$-0.205452\pi$
$908$	0.877604	−	0.626227i	0.0291243	−	0.0207821i
$909$	9.84247			0.326454
$910$	−20.0656	−	58.0292i	−0.665169	−	1.92365i
$911$		−	18.4722i		−	0.612012i	−0.952030	−	0.306006i	$-0.901007\pi$
$911$		−	18.4722i		−	0.612012i	0.952030	−	0.306006i	$-0.0989928\pi$
$912$	8.89934	+	10.2301i	0.294687	+	0.338751i
$913$	6.84874	+	3.95412i	0.226660	+	0.130862i
$914$	−6.07241	+	11.7929i	−0.200858	+	0.390075i
$915$	−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	−0.497618	−	0.867396i	$-0.665792\pi$
$919$	0.144308	−	0.0833164i	0.00476029	−	0.00274835i	0.502378	+	0.864648i	$0.332459\pi$
$920$	25.9858	+	10.3591i	0.856727	+	0.341531i
$921$	4.80893	−	8.32932i	0.158460	−	0.274460i
$922$	−24.3290	−	37.8162i	−0.801235	−	1.24541i
$923$		−	59.4974i		−	1.95838i
$924$	9.20703	+	7.23747i	0.302889	+	0.238095i
$925$		−	4.99636i		−	0.164279i
$926$	−10.5554	+	6.79084i	−0.346874	+	0.223161i
$927$	−0.992258	+	1.71864i	−0.0325900	+	0.0564476i
$928$	−53.6824	−	15.6208i	−1.76221	−	0.512776i
$929$	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
$934$	−3.93442	−	2.02591i	−0.128738	−	0.0662899i
$935$	19.5461	+	11.2849i	0.639225	+	0.369057i
$936$	8.90491	+	11.2895i	0.291066	+	0.369010i
$937$		−	19.5153i		−	0.637538i	−0.947832	−	0.318769i	$-0.896730\pi$
$937$		−	19.5153i		−	0.637538i	0.947832	−	0.318769i	$-0.103270\pi$
$938$	21.6047	−	24.9188i	0.705419	−	0.813629i
$939$	10.9294			0.356668
$940$	−7.95831	−	11.1529i	−0.259572	−	0.363767i
$941$	−12.3201	+	21.3390i	−0.401624	+	0.695633i	−0.993922	−	0.110086i	$-0.964887\pi$
$941$	−12.3201	+	21.3390i	−0.401624	+	0.695633i	0.592298	+	0.805719i	$0.298221\pi$
$942$	4.55783	+	2.34692i	0.148502	+	0.0764667i
$943$	−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	$0.788629\pi$
$948$	−9.19122	+	20.1779i	−0.298517	+	0.655349i
$949$	39.7579	+	22.9543i	1.29060	+	0.745127i
$950$	21.8504	−	14.0574i	0.708920	−	0.456083i
$951$	7.09278			0.229999
$952$	−21.4983	+	9.83585i	−0.696764	+	0.318782i
$953$	−27.4982			−0.890755			−0.445378	−	0.895343i	$-0.646931\pi$
$953$	−27.4982			−0.890755			−0.445378	+	0.895343i	$0.646931\pi$
$954$	−4.29249	+	2.76157i	−0.138974	+	0.0894090i
$955$	16.9838	+	9.80560i	0.549583	+	0.317302i
$956$	−20.5120	−	9.34339i	−0.663405	−	0.302187i
$957$	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
$962$	5.89251	+	3.03417i	0.189982	+	0.0978255i
$963$	−1.61805	+	2.80255i	−0.0521410	+	0.0903109i
$964$	−18.3528	+	13.0959i	−0.591104	+	0.421791i
$965$	29.6546			0.954616
$966$	11.2567	+	2.17287i	0.362177	+	0.0699108i
$967$			21.2591i			0.683647i	0.939764	+	0.341823i	$0.111044\pi$
$967$			21.2591i			0.683647i	−0.939764	+	0.341823i	$0.888956\pi$
$968$	10.6882	+	13.5504i	0.343533	+	0.435527i
$969$	9.27442	+	5.35459i	0.297937	+	0.172014i
$970$	−61.7868	−	31.8152i	−1.98385	−	1.02153i
$971$	−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
$976$	−16.4985	+	47.9714i	−0.528105	+	1.53553i
$977$	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	$0.0656149\pi$
$978$	23.5863	−	15.1742i	0.754207	−	0.485219i
$979$		−	16.1577i		−	0.516403i
$980$	6.40596	+	44.7351i	0.204631	+	1.42901i
$981$			4.19152i			0.133825i
$982$	−25.9365	−	40.3147i	−0.827666	−	1.28650i
$983$	11.2401	−	19.4684i	0.358503	−	0.620946i	−0.629208	−	0.777237i	$-0.716620\pi$
$983$	11.2401	−	19.4684i	0.358503	−	0.620946i	0.987711	+	0.156291i	$0.0499538\pi$
$984$	−6.24558	+	15.6670i	−0.199102	+	0.499445i
$985$	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
$990$	−4.62523	+	8.98242i	−0.146999	+	0.285480i
$991$	−38.9073	−	22.4631i	−1.23593	−	0.713565i	−0.267671	−	0.963510i	$-0.586254\pi$
$991$	−38.9073	−	22.4631i	−1.23593	−	0.713565i	−0.968260	+	0.249945i	$0.919588\pi$
$992$	−7.93702	−	8.28364i	−0.252001	−	0.263006i
$993$			11.7240i			0.372051i
$994$	−8.29970	+	42.9971i	−0.263250	+	1.36378i
$995$	−10.6107			−0.336381
$996$	−4.15101	−	5.81729i	−0.131530	−	0.184328i
$997$	14.5890	−	25.2688i	0.462037	−	0.800272i	−0.537025	−	0.843566i	$-0.680452\pi$
$997$	14.5890	−	25.2688i	0.462037	−	0.800272i	0.999062	+	0.0432942i	$0.0137853\pi$
$998$	5.75589	−	11.1782i	0.182200	−	0.353841i
$999$	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.115.5	yes	32
3.2	odd	2		504.2.bk.c.451.12		32
4.3	odd	2		672.2.bb.a.367.16		32
7.3	odd	6		1176.2.p.a.979.30		32
7.4	even	3		1176.2.p.a.979.29		32
7.5	odd	6	inner	168.2.t.a.19.7	yes	32
8.3	odd	2	inner	168.2.t.a.115.7	yes	32
8.5	even	2		672.2.bb.a.367.9		32
12.11	even	2		2016.2.bs.c.1711.2		32
21.5	even	6		504.2.bk.c.19.10		32
24.5	odd	2		2016.2.bs.c.1711.15		32
24.11	even	2		504.2.bk.c.451.10		32
28.3	even	6		4704.2.p.a.3919.10		32
28.11	odd	6		4704.2.p.a.3919.19		32
28.19	even	6		672.2.bb.a.271.9		32
56.3	even	6		1176.2.p.a.979.31		32
56.5	odd	6		672.2.bb.a.271.16		32
56.11	odd	6		1176.2.p.a.979.32		32
56.19	even	6	inner	168.2.t.a.19.5	✓	32
56.45	odd	6		4704.2.p.a.3919.20		32
56.53	even	6		4704.2.p.a.3919.9		32
84.47	odd	6		2016.2.bs.c.271.15		32
168.5	even	6		2016.2.bs.c.271.2		32
168.131	odd	6		504.2.bk.c.19.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.5	✓	32	56.19	even	6	inner
168.2.t.a.19.7	yes	32	7.5	odd	6	inner
168.2.t.a.115.5	yes	32	1.1	even	1	trivial
168.2.t.a.115.7	yes	32	8.3	odd	2	inner
504.2.bk.c.19.10		32	21.5	even	6
504.2.bk.c.19.12		32	168.131	odd	6
504.2.bk.c.451.10		32	24.11	even	2
504.2.bk.c.451.12		32	3.2	odd	2
672.2.bb.a.271.9		32	28.19	even	6
672.2.bb.a.271.16		32	56.5	odd	6
672.2.bb.a.367.9		32	8.5	even	2
672.2.bb.a.367.16		32	4.3	odd	2
1176.2.p.a.979.29		32	7.4	even	3
1176.2.p.a.979.30		32	7.3	odd	6
1176.2.p.a.979.31		32	56.3	even	6
1176.2.p.a.979.32		32	56.11	odd	6
2016.2.bs.c.271.2		32	168.5	even	6
2016.2.bs.c.271.15		32	84.47	odd	6
2016.2.bs.c.1711.2		32	12.11	even	2
2016.2.bs.c.1711.15		32	24.5	odd	2
4704.2.p.a.3919.9		32	56.53	even	6
4704.2.p.a.3919.10		32	28.3	even	6
4704.2.p.a.3919.19		32	28.11	odd	6
4704.2.p.a.3919.20		32	56.45	odd	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+(-0.765161 - 1.18934i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.829058 + 1.82007i) 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} +(2.08984 - 4.05858i) q^{10} +(-1.10660 + 1.91668i) q^{11} +(1.62802 - 1.16170i) q^{12} +5.08369 q^{13} +(-3.67384 - 0.709159i) q^{14} -3.22796i q^{15} +(-2.62532 - 3.01789i) q^{16} +(-2.73597 - 1.57961i) q^{17} +(0.647418 - 1.25732i) 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} +(-2.62735 - 1.04738i) q^{24} +(-2.70987 + 4.69363i) q^{25} +(-3.88984 - 6.04624i) q^{26} -1.00000i q^{27} +(1.96765 + 4.91206i) q^{28} +9.88340i q^{29} +(-3.83914 + 2.46991i) q^{30} +(-1.01402 + 1.75634i) q^{31} +(-1.58050 + 5.43158i) 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} +(-4.26207 - 2.19462i) q^{38} +(-4.40261 - 2.54185i) q^{39} +(5.65430 + 7.16846i) q^{40} -5.96303i q^{41} +(2.82706 + 2.45107i) q^{42} -6.68790 q^{43} +(-2.57107 - 3.60313i) q^{44} +(-1.61398 + 2.79550i) q^{45} +(-3.85243 - 1.98369i) 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} +(-4.21468 + 9.25269i) q^{52} +(-3.12560 - 1.80457i) q^{53} +(-1.18934 + 0.765161i) q^{54} -7.14411 q^{55} +(4.33655 - 6.09872i) q^{56} -3.38981 q^{57} +(11.7547 - 7.56239i) q^{58} +(-10.6351 - 6.14015i) q^{59} +(5.87512 + 2.67617i) 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} +(-2.78269 - 1.43286i) q^{66} +(-4.40720 + 7.63350i) q^{67} +(5.14329 - 3.67007i) q^{68} -3.06401 q^{69} +(-3.94706 - 11.4148i) q^{70} -11.7036i q^{71} +(1.75166 + 2.22074i) q^{72} +(7.82068 + 4.51527i) q^{73} +(1.15910 + 0.596844i) 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} +(4.19928 - 12.2099i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.09207 + 4.56268i) q^{82} -3.57322i q^{83} +(0.752000 - 5.23780i) q^{84} -10.1979i q^{85} +(5.11732 + 7.95419i) q^{86} +(4.94170 - 8.55928i) q^{87} +(-2.31807 + 5.81485i) 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} +(1.37399 - 2.66836i) q^{94} +(9.47619 + 5.47108i) q^{95} +(4.08454 - 3.91363i) q^{96} -15.2238i q^{97} +(-8.06995 + 5.73375i) 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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