LMFDB - Embedded newform 456.2.bk.a.253.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.9
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.05611 - 0.940554i) q^{2} +(0.342020 - 0.939693i) q^{3} +(0.230718 + 1.98665i) q^{4} +(0.947207 - 0.167018i) q^{5} +(-1.24504 + 0.670726i) q^{6} +(-2.07120 + 3.58743i) q^{7} +(1.62489 - 2.31511i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.15744 - 0.714510i) q^{10} +(-3.48297 + 2.01090i) q^{11} +(1.94575 + 0.462670i) q^{12} +(0.968388 + 2.66062i) q^{13} +(5.56157 - 1.84062i) q^{14} +(0.167018 - 0.947207i) q^{15} +(-3.89354 + 0.916709i) q^{16} +(-4.03497 + 3.38574i) q^{17} +(0.204448 + 1.39936i) q^{18} +(-4.29473 + 0.745167i) q^{19} +(0.550344 + 1.84323i) q^{20} +(2.66269 + 3.17327i) q^{21} +(5.56974 + 1.15221i) q^{22} +(0.454571 - 2.57800i) q^{23} +(-1.61975 - 2.31871i) q^{24} +(-3.82916 + 1.39370i) q^{25} +(1.47974 - 3.72072i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-7.60482 - 3.28707i) q^{28} +(3.68646 - 4.39335i) q^{29} +(-1.06729 + 0.843261i) q^{30} +(-3.91628 + 6.78320i) q^{31} +(4.97420 + 2.69394i) q^{32} +(0.698377 + 3.96069i) q^{33} +(7.44582 + 0.219405i) q^{34} +(-1.36269 + 3.74396i) q^{35} +(1.10025 - 1.67016i) q^{36} -7.05889i q^{37} +(5.23656 + 3.25245i) q^{38} +2.83138 q^{39} +(1.15244 - 2.46428i) q^{40} +(8.37393 + 3.04786i) q^{41} +(0.172549 - 5.85570i) q^{42} +(5.33840 - 0.941305i) q^{43} +(-4.79852 - 6.45549i) q^{44} +(-0.832960 - 0.480910i) q^{45} +(-2.90482 + 2.29509i) q^{46} +(8.68801 + 7.29011i) q^{47} +(-0.470244 + 3.97226i) q^{48} +(-5.07975 - 8.79839i) q^{49} +(5.35484 + 2.12963i) q^{50} +(1.80151 + 4.94962i) q^{51} +(-5.06230 + 2.53770i) q^{52} +(-7.06214 - 1.24524i) q^{53} +(1.38489 + 0.286491i) q^{54} +(-2.96324 + 2.48645i) q^{55} +(4.93983 + 10.6242i) q^{56} +(-0.768657 + 4.29059i) q^{57} +(-8.02546 + 1.17253i) q^{58} +(0.737198 + 0.878558i) q^{59} +(1.92030 + 0.113269i) q^{60} +(10.6744 + 1.88219i) q^{61} +(10.5160 - 3.48030i) q^{62} +(3.89259 - 1.41679i) q^{63} +(-2.71949 - 7.52359i) q^{64} +(1.36164 + 2.35842i) q^{65} +(2.98768 - 4.83977i) q^{66} +(-4.33950 + 5.17162i) q^{67} +(-7.65721 - 7.23491i) q^{68} +(-2.26706 - 1.30889i) q^{69} +(4.96054 - 2.67234i) q^{70} +(-0.902366 - 5.11757i) q^{71} +(-2.73286 + 0.729022i) q^{72} +(6.42957 + 2.34017i) q^{73} +(-6.63927 + 7.45494i) q^{74} +4.07490i q^{75} +(-2.47126 - 8.36020i) q^{76} -16.6599i q^{77} +(-2.99023 - 2.66306i) q^{78} +(-2.05326 - 0.747324i) q^{79} +(-3.53488 + 1.51860i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-5.97708 - 11.0950i) q^{82} +(-10.3608 - 5.98184i) q^{83} +(-5.68983 + 6.02195i) q^{84} +(-3.25647 + 3.88091i) q^{85} +(-6.52327 - 4.02694i) q^{86} +(-2.86755 - 4.96675i) q^{87} +(-1.00399 + 11.3310i) q^{88} +(11.2624 - 4.09919i) q^{89} +(0.427372 + 1.29133i) q^{90} +(-11.5505 - 2.03667i) q^{91} +(5.22646 + 0.308282i) q^{92} +(5.03468 + 6.00010i) q^{93} +(-2.31872 - 15.8707i) q^{94} +(-3.94354 + 1.42313i) q^{95} +(4.23275 - 3.75284i) q^{96} +(-9.89030 + 8.29895i) q^{97} +(-2.91060 + 14.0698i) q^{98} +(3.96069 + 0.698377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.05611	−	0.940554i	−0.746779	−	0.665072i
$2$	−1.05611	−	0.940554i	−0.746779	−	0.665072i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	0.230718	+	1.98665i	0.115359	+	0.993324i
$5$	0.947207	−	0.167018i	0.423604	−	0.0746928i	0.0422173	−	0.999108i	$-0.486558\pi$
$5$	0.947207	−	0.167018i	0.423604	−	0.0746928i	0.381386	+	0.924416i	$0.375447\pi$
$6$	−1.24504	+	0.670726i	−0.508286	+	0.273823i
$7$	−2.07120	+	3.58743i	−0.782841	+	1.35592i	0.147440	+	0.989071i	$0.452897\pi$
$7$	−2.07120	+	3.58743i	−0.782841	+	1.35592i	−0.930281	+	0.366849i	$0.880437\pi$
$8$	1.62489	−	2.31511i	0.574484	−	0.818516i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−1.15744	−	0.714510i	−0.366015	−	0.225948i
$11$	−3.48297	+	2.01090i	−1.05016	+	0.606308i	−0.922693	−	0.385536i	$-0.874017\pi$
$11$	−3.48297	+	2.01090i	−1.05016	+	0.606308i	−0.127463	+	0.991843i	$0.540683\pi$
$12$	1.94575	+	0.462670i	0.561689	+	0.133561i
$13$	0.968388	+	2.66062i	0.268582	+	0.737924i	0.998519	+	0.0544090i	$0.0173275\pi$
$13$	0.968388	+	2.66062i	0.268582	+	0.737924i	−0.729936	+	0.683515i	$0.760450\pi$
$14$	5.56157	−	1.84062i	1.48639	−	0.491928i
$15$	0.167018	−	0.947207i	0.0431239	−	0.244568i
$16$	−3.89354	+	0.916709i	−0.973385	+	0.229177i
$17$	−4.03497	+	3.38574i	−0.978623	+	0.821162i	−0.983881	−	0.178824i	$-0.942771\pi$
$17$	−4.03497	+	3.38574i	−0.978623	+	0.821162i	0.00525786	+	0.999986i	$0.498326\pi$
$18$	0.204448	+	1.39936i	0.0481887	+	0.329832i
$19$	−4.29473	+	0.745167i	−0.985279	+	0.170953i
$19$	−4.29473	+	0.745167i	−0.985279	+	0.170953i
$20$	0.550344	+	1.84323i	0.123061	+	0.412159i
$21$	2.66269	+	3.17327i	0.581046	+	0.692463i
$22$	5.56974	+	1.15221i	1.18747	+	0.245651i
$23$	0.454571	−	2.57800i	0.0947847	−	0.537550i	−0.900028	−	0.435831i	$-0.856455\pi$
$23$	0.454571	−	2.57800i	0.0947847	−	0.537550i	0.994813	−	0.101719i	$-0.0324344\pi$
$24$	−1.61975	−	2.31871i	−0.330630	−	0.473304i
$25$	−3.82916	+	1.39370i	−0.765831	+	0.278740i
$26$	1.47974	−	3.72072i	0.290201	−	0.729693i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−7.60482	−	3.28707i	−1.43718	−	0.621197i
$29$	3.68646	−	4.39335i	0.684558	−	0.815824i	−0.306128	−	0.951990i	$-0.599034\pi$
$29$	3.68646	−	4.39335i	0.684558	−	0.815824i	0.990686	+	0.136166i	$0.0434781\pi$
$30$	−1.06729	+	0.843261i	−0.194859	+	0.153958i
$31$	−3.91628	+	6.78320i	−0.703386	+	1.21830i	0.263885	+	0.964554i	$0.414996\pi$
$31$	−3.91628	+	6.78320i	−0.703386	+	1.21830i	−0.967271	+	0.253745i	$0.918337\pi$
$32$	4.97420	+	2.69394i	0.879323	+	0.476226i
$33$	0.698377	+	3.96069i	0.121572	+	0.689468i
$34$	7.44582	+	0.219405i	1.27695	+	0.0376277i
$35$	−1.36269	+	3.74396i	−0.230337	+	0.632845i
$36$	1.10025	−	1.67016i	0.183375	−	0.278360i
$37$		−	7.05889i		−	1.16048i	−0.814447	−	0.580238i	$-0.802960\pi$
$37$		−	7.05889i		−	1.16048i	0.814447	−	0.580238i	$-0.197040\pi$
$38$	5.23656	+	3.25245i	0.849482	+	0.527617i
$39$	2.83138			0.453383
$40$	1.15244	−	2.46428i	0.182216	−	0.389636i
$41$	8.37393	+	3.04786i	1.30779	+	0.475996i	0.899525	−	0.436869i	$-0.143913\pi$
$41$	8.37393	+	3.04786i	1.30779	+	0.475996i	0.408263	+	0.912864i	$0.366135\pi$
$42$	0.172549	−	5.85570i	0.0266249	−	0.903554i
$43$	5.33840	−	0.941305i	0.814099	−	0.143548i	0.248929	−	0.968522i	$-0.419922\pi$
$43$	5.33840	−	0.941305i	0.814099	−	0.143548i	0.565170	+	0.824974i	$0.308810\pi$
$44$	−4.79852	−	6.45549i	−0.723405	−	0.973202i
$45$	−0.832960	−	0.480910i	−0.124170	−	0.0716898i
$46$	−2.90482	+	2.29509i	−0.428293	+	0.338393i
$47$	8.68801	+	7.29011i	1.26728	+	1.06337i	0.994867	+	0.101190i	$0.0322650\pi$
$47$	8.68801	+	7.29011i	1.26728	+	1.06337i	0.272410	+	0.962181i	$0.412179\pi$
$48$	−0.470244	+	3.97226i	−0.0678738	+	0.573347i
$49$	−5.07975	−	8.79839i	−0.725679	−	1.25691i
$50$	5.35484	+	2.12963i	0.757289	+	0.301176i
$51$	1.80151	+	4.94962i	0.252262	+	0.693085i
$52$	−5.06230	+	2.53770i	−0.702014	+	0.351915i
$53$	−7.06214	−	1.24524i	−0.970059	−	0.171048i	−0.333902	−	0.942608i	$-0.608366\pi$
$53$	−7.06214	−	1.24524i	−0.970059	−	0.171048i	−0.636156	+	0.771560i	$0.719477\pi$
$54$	1.38489	+	0.286491i	0.188460	+	0.0389864i
$55$	−2.96324	+	2.48645i	−0.399563	+	0.335273i
$56$	4.93983	+	10.6242i	0.660112	+	1.41972i
$57$	−0.768657	+	4.29059i	−0.101811	+	0.568303i
$58$	−8.02546	+	1.17253i	−1.05380	+	0.153961i
$59$	0.737198	+	0.878558i	0.0959750	+	0.114379i	0.811894	−	0.583805i	$-0.198437\pi$
$59$	0.737198	+	0.878558i	0.0959750	+	0.114379i	−0.715919	+	0.698183i	$0.753992\pi$
$60$	1.92030	+	0.113269i	0.247910	+	0.0146229i
$61$	10.6744	+	1.88219i	1.36672	+	0.240990i	0.808400	−	0.588634i	$-0.200334\pi$
$61$	10.6744	+	1.88219i	1.36672	+	0.240990i	0.558322	+	0.829624i	$0.311445\pi$
$62$	10.5160	−	3.48030i	1.33553	−	0.441999i
$63$	3.89259	−	1.41679i	0.490420	−	0.178498i
$64$	−2.71949	−	7.52359i	−0.339936	−	0.940449i
$65$	1.36164	+	2.35842i	0.168890	+	0.292526i
$66$	2.98768	−	4.83977i	0.367758	−	0.595734i
$67$	−4.33950	+	5.17162i	−0.530155	+	0.631814i	−0.962951	−	0.269678i	$-0.913083\pi$
$67$	−4.33950	+	5.17162i	−0.530155	+	0.631814i	0.432796	+	0.901492i	$0.357527\pi$
$68$	−7.65721	−	7.23491i	−0.928573	−	0.877362i
$69$	−2.26706	−	1.30889i	−0.272922	−	0.157571i
$70$	4.96054	−	2.67234i	0.592898	−	0.319405i
$71$	−0.902366	−	5.11757i	−0.107091	−	0.607344i	−0.990364	−	0.138486i	$-0.955777\pi$
$71$	−0.902366	−	5.11757i	−0.107091	−	0.607344i	0.883273	−	0.468859i	$-0.155335\pi$
$72$	−2.73286	+	0.729022i	−0.322071	+	0.0859160i
$73$	6.42957	+	2.34017i	0.752524	+	0.273896i	0.689668	−	0.724126i	$-0.257757\pi$
$73$	6.42957	+	2.34017i	0.752524	+	0.273896i	0.0628568	+	0.998023i	$0.479979\pi$
$74$	−6.63927	+	7.45494i	−0.771799	+	0.866619i
$75$			4.07490i			0.470529i
$76$	−2.47126	−	8.36020i	−0.283472	−	0.958980i
$77$		−	16.6599i		−	1.89857i
$78$	−2.99023	−	2.66306i	−0.338577	−	0.301532i
$79$	−2.05326	−	0.747324i	−0.231009	−	0.0840805i	0.223922	−	0.974607i	$-0.428114\pi$
$79$	−2.05326	−	0.747324i	−0.231009	−	0.0840805i	−0.454931	+	0.890527i	$0.650336\pi$
$80$	−3.53488	+	1.51860i	−0.395212	+	0.169785i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−5.97708	−	11.0950i	−0.660058	−	1.22524i
$83$	−10.3608	−	5.98184i	−1.13725	−	0.656592i	−0.191502	−	0.981492i	$-0.561336\pi$
$83$	−10.3608	−	5.98184i	−1.13725	−	0.656592i	−0.945748	+	0.324900i	$0.894669\pi$
$84$	−5.68983	+	6.02195i	−0.620812	+	0.657048i
$85$	−3.25647	+	3.88091i	−0.353214	+	0.420944i
$86$	−6.52327	−	4.02694i	−0.703422	−	0.434236i
$87$	−2.86755	−	4.96675i	−0.307434	−	0.532491i
$88$	−1.00399	+	11.3310i	−0.107026	+	1.20788i
$89$	11.2624	−	4.09919i	1.19382	−	0.434513i	0.332754	−	0.943014i	$-0.392022\pi$
$89$	11.2624	−	4.09919i	1.19382	−	0.434513i	0.861062	+	0.508501i	$0.169800\pi$
$90$	0.427372	+	1.29133i	0.0450490	+	0.136119i
$91$	−11.5505	−	2.03667i	−1.21082	−	0.213501i
$92$	5.22646	+	0.308282i	0.544896	+	0.0321407i
$93$	5.03468	+	6.00010i	0.522072	+	0.622181i
$94$	−2.31872	−	15.8707i	−0.239158	−	1.63693i
$95$	−3.94354	+	1.42313i	−0.404599	+	0.146010i
$96$	4.23275	−	3.75284i	0.432004	−	0.383023i
$97$	−9.89030	+	8.29895i	−1.00421	+	0.842631i	−0.987562	−	0.157231i	$-0.949743\pi$
$97$	−9.89030	+	8.29895i	−1.00421	+	0.842631i	−0.0166463	+	0.999861i	$0.505299\pi$
$98$	−2.91060	+	14.0698i	−0.294015	+	1.42127i
$99$	3.96069	+	0.698377i	0.398064	+	0.0701895i
$100$	−3.65224	−	7.28564i	−0.365224	−	0.728564i
$101$	0.744611	+	2.04580i	0.0740915	+	0.203565i	0.971210	−	0.238225i	$-0.0765657\pi$
$101$	0.744611	+	2.04580i	0.0740915	+	0.203565i	−0.897118	+	0.441790i	$0.854344\pi$
$102$	2.75279	−	6.92174i	0.272567	−	0.685355i
$103$	4.43516	+	7.68192i	0.437009	+	0.756922i	0.997457	−	0.0712673i	$-0.0227043\pi$
$103$	4.43516	+	7.68192i	0.437009	+	0.756922i	−0.560448	+	0.828190i	$0.689371\pi$
$104$	7.73316	+	2.08129i	0.758299	+	0.204087i
$105$	3.05211	+	2.56102i	0.297855	+	0.249930i
$106$	6.28714	+	7.95743i	0.610661	+	0.772894i
$107$	−10.4902	−	6.05651i	−1.01413	−	0.585505i	−0.101728	−	0.994812i	$-0.532437\pi$
$107$	−10.4902	−	6.05651i	−1.01413	−	0.585505i	−0.912397	+	0.409307i	$0.865771\pi$
$108$	−1.19313	−	1.60513i	−0.114809	−	0.154454i
$109$	12.5111	−	2.20605i	1.19835	−	0.211301i	0.461363	−	0.887211i	$-0.347360\pi$
$109$	12.5111	−	2.20605i	1.19835	−	0.211301i	0.736984	+	0.675910i	$0.236249\pi$
$110$	5.46814	+	0.161129i	0.521366	+	0.0153630i
$111$	−6.63319	−	2.41428i	−0.629595	−	0.229154i
$112$	4.77568	−	15.8665i	0.451259	−	1.49924i
$113$	−18.1535			−1.70774			−0.853871	−	0.520485i	$-0.825751\pi$
$113$	−18.1535			−1.70774			−0.853871	+	0.520485i	$0.825751\pi$
$114$	4.84731	−	3.80835i	0.453992	−	0.356685i
$115$		−	2.51782i		−	0.234788i
$116$	9.57856	+	6.31007i	0.889347	+	0.585875i
$117$	0.968388	−	2.66062i	0.0895275	−	0.245975i
$118$	0.0477724	−	1.62122i	0.00439781	−	0.149246i
$119$	−3.78886	−	21.4877i	−0.347324	−	1.96977i
$120$	−1.92150	−	1.92577i	−0.175409	−	0.175798i
$121$	2.58740	−	4.48151i	0.235218	−	0.407410i
$122$	−9.50303	−	12.0277i	−0.860364	−	1.08893i
$123$	5.72811	−	6.82649i	0.516486	−	0.615524i
$124$	−14.3794	−	6.21527i	−1.29131	−	0.558148i
$125$	−7.55903	+	4.36421i	−0.676100	+	0.390347i
$126$	−5.44354	−	2.16491i	−0.484949	−	0.192866i
$127$	−5.41950	+	1.97254i	−0.480903	+	0.175034i	−0.571085	−	0.820891i	$-0.693477\pi$
$127$	−5.41950	+	1.97254i	−0.480903	+	0.175034i	0.0901820	+	0.995925i	$0.471255\pi$
$128$	−4.20427	+	10.5035i	−0.371609	+	0.928389i
$129$	0.941305	−	5.33840i	0.0828773	−	0.470020i
$130$	0.780192	−	3.77143i	0.0684274	−	0.330777i
$131$	−7.69042	−	9.16509i	−0.671915	−	0.800758i	0.317128	−	0.948383i	$-0.397282\pi$
$131$	−7.69042	−	9.16509i	−0.671915	−	0.800758i	−0.989043	+	0.147625i	$0.952837\pi$
$132$	−7.70737	+	2.30123i	−0.670840	+	0.200296i
$133$	6.22202	−	16.9504i	0.539518	−	1.46979i
$134$	9.44716	−	1.38024i	0.816110	−	0.119235i
$135$	−0.736796	+	0.618245i	−0.0634133	+	0.0532101i
$136$	1.28200	+	14.8428i	0.109931	+	1.27276i
$137$	0.569412	−	3.22930i	0.0486482	−	0.275897i	−0.950774	−	0.309885i	$-0.899709\pi$
$137$	0.569412	−	3.22930i	0.0486482	−	0.275897i	0.999422	+	0.0339874i	$0.0108206\pi$
$138$	1.16317	+	3.51461i	0.0990159	+	0.299183i
$139$	3.98947	+	10.9610i	0.338382	+	0.929698i	0.985854	+	0.167608i	$0.0536044\pi$
$139$	3.98947	+	10.9610i	0.338382	+	0.929698i	−0.647471	+	0.762090i	$0.724173\pi$
$140$	−7.75233	−	1.84339i	−0.655192	−	0.155795i
$141$	9.82194	−	5.67070i	0.827156	−	0.477559i
$142$	−3.86036	+	6.25342i	−0.323954	+	0.524775i
$143$	−8.72311	−	7.31955i	−0.729463	−	0.612092i
$144$	3.57187	+	1.80048i	0.297656	+	0.150040i
$145$	2.75807	−	4.77711i	0.229045	−	0.396718i
$146$	−4.58925	−	8.51883i	−0.379809	−	0.705023i
$147$	−10.0052	+	1.76418i	−0.825212	+	0.145507i
$148$	14.0235	−	1.62861i	1.15273	−	0.133871i
$149$	−3.70030	+	10.1665i	−0.303140	+	0.832871i	0.690810	+	0.723036i	$0.257254\pi$
$149$	−3.70030	+	10.1665i	−0.303140	+	0.832871i	−0.993950	+	0.109834i	$0.964968\pi$
$150$	3.83267	−	4.30353i	0.312936	−	0.351382i
$151$	18.4866			1.50441			0.752207	−	0.658927i	$-0.228989\pi$
$151$	18.4866			1.50441			0.752207	+	0.658927i	$0.228989\pi$
$152$	−5.25331	+	11.1536i	−0.426100	+	0.904676i
$153$	5.26728			0.425834
$154$	−15.6695	+	17.5946i	−1.26269	+	1.41781i
$155$	−2.57661	+	7.07919i	−0.206959	+	0.568614i
$156$	0.653249	+	5.62495i	0.0523017	+	0.450356i
$157$	−7.53247	+	1.32818i	−0.601157	+	0.106000i	−0.465941	−	0.884816i	$-0.654284\pi$
$157$	−7.53247	+	1.32818i	−0.601157	+	0.106000i	−0.135216	+	0.990816i	$0.543173\pi$
$158$	1.46556	+	2.72045i	0.116593	+	0.216427i
$159$	−3.58554	+	6.21034i	−0.284352	+	0.492512i
$160$	5.16154	+	1.72094i	0.408055	+	0.136052i
$161$	8.30688	+	6.97030i	0.654674	+	0.549337i
$162$	0.742874	−	1.20339i	0.0583657	−	0.0945470i
$163$	−10.6354	+	6.14036i	−0.833030	+	0.480950i	−0.854889	−	0.518811i	$-0.826375\pi$
$163$	−10.6354	+	6.14036i	−0.833030	+	0.480950i	0.0218590	+	0.999761i	$0.493042\pi$
$164$	−4.12301	+	17.3392i	−0.321953	+	1.35397i
$165$	1.32301	+	3.63495i	0.102997	+	0.282981i
$166$	5.31591	+	16.0624i	0.412595	+	1.24668i
$167$	0.560539	−	3.17898i	0.0433758	−	0.245997i	−0.955409	−	0.295287i	$-0.904585\pi$
$167$	0.560539	−	3.17898i	0.0433758	−	0.245997i	0.998785	+	0.0492902i	$0.0156959\pi$
$168$	11.6730	−	1.00822i	0.900594	−	0.0777858i
$169$	3.81743	−	3.20321i	0.293649	−	0.246401i
$170$	7.08938	−	1.03576i	0.543730	−	0.0794395i
$171$	3.76894	+	2.18977i	0.288218	+	0.167456i
$172$	3.10171	+	10.3884i	0.236503	+	0.792105i
$173$	5.98517	+	7.13284i	0.455044	+	0.542300i	0.943973	−	0.330024i	$-0.107057\pi$
$173$	5.98517	+	7.13284i	0.455044	+	0.542300i	−0.488929	+	0.872324i	$0.662612\pi$
$174$	−1.64305	+	7.94250i	−0.124560	+	0.602119i
$175$	2.93116	−	16.6235i	0.221575	−	1.25661i
$176$	11.7177	−	11.0224i	0.883254	−	0.830843i
$177$	1.07771	−	0.392255i	0.0810057	−	0.0294837i
$178$	−15.7498	−	6.26374i	−1.18050	−	0.469487i
$179$	9.55011	−	5.51376i	0.713809	−	0.412118i	−0.0986610	−	0.995121i	$-0.531456\pi$
$179$	9.55011	−	5.51376i	0.713809	−	0.412118i	0.812470	+	0.583003i	$0.198123\pi$
$180$	0.763219	−	1.76575i	0.0568870	−	0.131611i
$181$	−1.95404	+	2.32873i	−0.145242	+	0.173093i	−0.833761	−	0.552125i	$-0.813817\pi$
$181$	−1.95404	+	2.32873i	−0.145242	+	0.173093i	0.688519	+	0.725219i	$0.258261\pi$
$182$	10.2830	+	13.0148i	0.762225	+	0.964723i
$183$	5.41956	−	9.38695i	0.400625	−	0.693903i
$184$	−5.22974	−	5.24134i	−0.385541	−	0.386397i
$185$	−1.17896	−	6.68623i	−0.0866791	−	0.491582i
$186$	0.326261	−	11.0721i	0.0239226	−	0.811847i
$187$	7.24531	−	19.9063i	0.529830	−	1.45570i
$188$	−12.4784	+	18.9420i	−0.910081	+	1.38149i
$189$		−	4.14240i		−	0.301316i
$190$	5.50332	+	2.20614i	0.399253	+	0.160050i
$191$	0.743436			0.0537932			0.0268966	−	0.999638i	$-0.491438\pi$
$191$	0.743436			0.0537932			0.0268966	+	0.999638i	$0.491438\pi$
$192$	−7.99998	−	0.0177374i	−0.577349	−	0.00128009i
$193$	−4.33421	−	1.57752i	−0.311983	−	0.113553i	0.181283	−	0.983431i	$-0.441975\pi$
$193$	−4.33421	−	1.57752i	−0.311983	−	0.113553i	−0.493266	+	0.869878i	$0.664197\pi$
$194$	18.2508	+	0.537794i	1.31033	+	0.0386114i
$195$	2.68190	−	0.472891i	0.192055	−	0.0338644i
$196$	16.3073	−	12.1216i	1.16481	−	0.865830i
$197$	10.4177	+	6.01464i	0.742228	+	0.428525i	0.822879	−	0.568217i	$-0.192367\pi$
$197$	10.4177	+	6.01464i	0.742228	+	0.428525i	−0.0806511	+	0.996742i	$0.525700\pi$
$198$	−3.52605	−	4.46280i	−0.250585	−	0.317158i
$199$	6.45154	+	5.41348i	0.457337	+	0.383751i	0.842150	−	0.539243i	$-0.181290\pi$
$199$	6.45154	+	5.41348i	0.457337	+	0.383751i	−0.384813	+	0.922995i	$0.625734\pi$
$200$	−2.99538	+	11.1295i	−0.211805	+	0.786977i
$201$	3.37553	+	5.84660i	0.238092	+	0.412387i
$202$	1.13780	−	2.86093i	0.0800552	−	0.201294i
$203$	8.12542	+	22.3244i	0.570292	+	1.56687i
$204$	−9.41751	+	4.72094i	−0.659358	+	0.330532i
$205$	8.44089	+	1.48836i	0.589537	+	0.103951i
$206$	2.54126	−	12.2844i	0.177058	−	0.855897i
$207$	−2.00533	+	1.68267i	−0.139380	+	0.116954i
$208$	−6.20947	−	9.47151i	−0.430550	−	0.656731i
$209$	13.4600	−	11.2317i	0.931047	−	0.776910i
$210$	−0.814568	−	5.57538i	−0.0562106	−	0.384738i
$211$	11.7472	+	13.9998i	0.808714	+	0.963788i	0.999842	−	0.0177774i	$-0.00565903\pi$
$211$	11.7472	+	13.9998i	0.808714	+	0.963788i	−0.191128	+	0.981565i	$0.561215\pi$
$212$	0.844504	−	14.3173i	0.0580008	−	0.983314i
$213$	−5.11757	−	0.902366i	−0.350650	−	0.0618291i
$214$	5.38227	+	16.2629i	0.367925	+	1.11171i
$215$	4.89936	−	1.78322i	0.334133	−	0.121615i
$216$	−0.249637	+	2.81739i	−0.0169857	+	0.191699i
$217$	−16.2228	−	28.0988i	−1.10128	−	1.90747i
$218$	−15.2880	−	9.43756i	−1.03543	−	0.639192i
$219$	4.39809	−	5.24143i	0.297195	−	0.354183i
$220$	−5.62338	−	5.31325i	−0.379128	−	0.358219i
$221$	−12.9156	−	7.45682i	−0.868797	−	0.501600i
$222$	4.73459	+	8.78861i	0.317765	+	0.589853i
$223$	4.50296	+	25.5376i	0.301541	+	1.71012i	0.639357	+	0.768910i	$0.279201\pi$
$223$	4.50296	+	25.5376i	0.301541	+	1.71012i	−0.337816	+	0.941212i	$0.609688\pi$
$224$	−19.9669	+	12.2649i	−1.33409	+	0.819482i
$225$	3.82916	+	1.39370i	0.255277	+	0.0929133i
$226$	19.1721	+	17.0744i	1.27531	+	1.13577i
$227$			9.42625i			0.625642i	0.949812	+	0.312821i	$0.101274\pi$
$227$			9.42625i			0.625642i	−0.949812	+	0.312821i	$0.898726\pi$
$228$	−8.70123	−	0.537136i	−0.576253	−	0.0355727i
$229$			6.97155i			0.460693i	0.973109	+	0.230346i	$0.0739859\pi$
$229$			6.97155i			0.460693i	−0.973109	+	0.230346i	$0.926014\pi$
$230$	−2.36815	+	2.65909i	−0.156151	+	0.175335i
$231$	−15.6552	−	5.69801i	−1.03003	−	0.374902i
$232$	−4.18102	−	15.6732i	−0.274497	−	1.02900i
$233$	3.90671	+	22.1561i	0.255937	+	1.45149i	0.793655	+	0.608368i	$0.208176\pi$
$233$	3.90671	+	22.1561i	0.255937	+	1.45149i	−0.537718	+	0.843125i	$0.680713\pi$
$234$	−3.52518	+	1.89908i	−0.230448	+	0.124147i
$235$	9.44692	+	5.45418i	0.616249	+	0.355792i
$236$	−1.57530	+	1.66725i	−0.102543	+	0.108529i
$237$	−1.40451	+	1.67383i	−0.0912327	+	0.108727i
$238$	−16.2089	+	26.2569i	−1.05067	+	1.70198i
$239$	−2.04736	−	3.54613i	−0.132432	−	0.229380i	0.792181	−	0.610286i	$-0.208945\pi$
$239$	−2.04736	−	3.54613i	−0.132432	−	0.229380i	−0.924614	+	0.380906i	$0.875612\pi$
$240$	0.218022	+	3.84109i	0.0140733	+	0.247942i
$241$	23.8557	−	8.68276i	1.53668	−	0.559306i	0.571434	−	0.820648i	$-0.306387\pi$
$241$	23.8557	−	8.68276i	1.53668	−	0.559306i	0.965246	+	0.261342i	$0.0841650\pi$
$242$	−6.94767	+	2.29936i	−0.446613	+	0.147808i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	−1.27647	+	21.6406i	−0.0817177	+	1.38540i
$245$	−6.28107	−	7.48548i	−0.401283	−	0.478230i
$246$	−12.4702	+	1.82190i	−0.795069	+	0.116160i
$247$	−6.14158	−	10.7051i	−0.390779	−	0.681146i
$248$	9.34036	+	20.0886i	0.593113	+	1.27563i
$249$	−9.16471	+	7.69010i	−0.580790	+	0.487340i
$250$	12.0879	+	2.50061i	0.764506	+	0.158152i
$251$	−13.2527	−	2.33681i	−0.836505	−	0.147498i	−0.261043	−	0.965327i	$-0.584067\pi$
$251$	−13.2527	−	2.33681i	−0.836505	−	0.147498i	−0.575462	+	0.817829i	$0.695178\pi$
$252$	3.71274	+	7.40632i	0.233881	+	0.466554i
$253$	3.60083	+	9.89321i	0.226382	+	0.621980i
$254$	7.57884	+	3.01412i	0.475539	+	0.189123i
$255$	2.53308	+	4.38743i	0.158628	+	0.274751i
$256$	14.3193	−	7.13849i	0.894955	−	0.446155i
$257$	−13.8912	−	11.6561i	−0.866511	−	0.727089i	0.0968491	−	0.995299i	$-0.469124\pi$
$257$	−13.8912	−	11.6561i	−0.866511	−	0.727089i	−0.963361	+	0.268210i	$0.913568\pi$
$258$	−6.01517	+	4.75257i	−0.374488	+	0.295882i
$259$	25.3233	+	14.6204i	1.57351	+	0.908467i
$260$	−4.37120	+	3.24922i	−0.271090	+	0.201508i
$261$	−5.64798	+	0.995891i	−0.349601	+	0.0616441i
$262$	−0.498360	+	16.9126i	−0.0307888	+	1.04486i
$263$	−0.0960277	−	0.0349512i	−0.00592132	−	0.00215518i	0.339058	−	0.940766i	$-0.389892\pi$
$263$	−0.0960277	−	0.0349512i	−0.00592132	−	0.00215518i	−0.344979	+	0.938610i	$0.612114\pi$
$264$	10.3042	+	4.81885i	0.634181	+	0.296580i
$265$	−6.89728			−0.423697
$266$	−22.5139	+	12.0493i	−1.38042	+	0.738790i
$267$		−	11.9852i		−	0.733484i
$268$	−11.2754	−	7.42788i	−0.688754	−	0.453730i
$269$	−3.12301	+	8.58041i	−0.190413	+	0.523157i	−0.997758	−	0.0669235i	$-0.978682\pi$
$269$	−3.12301	+	8.58041i	−0.190413	+	0.523157i	0.807345	+	0.590080i	$0.200904\pi$
$270$	1.35963	+	0.0400640i	0.0827443	+	0.00243822i
$271$	−0.0244133	−	0.138455i	−0.00148300	−	0.00841053i	0.984057	−	0.177852i	$-0.0569148\pi$
$271$	−0.0244133	−	0.138455i	−0.00148300	−	0.00841053i	−0.985540	+	0.169441i	$0.945804\pi$
$272$	12.6066	−	16.8814i	0.764385	−	1.02359i
$273$	−5.86435	+	10.1574i	−0.354927	+	0.614751i
$274$	−3.63869	+	2.87492i	−0.219821	+	0.173680i
$275$	10.5343	−	12.5543i	0.635240	−	0.757050i
$276$	2.07724	−	4.80583i	0.125035	−	0.289277i
$277$	−8.02721	+	4.63451i	−0.482308	+	0.278461i	−0.721378	−	0.692542i	$-0.756491\pi$
$277$	−8.02721	+	4.63451i	−0.482308	+	0.278461i	0.239070	+	0.971002i	$0.423158\pi$
$278$	6.09609	−	15.3283i	0.365619	−	0.919328i
$279$	7.36021	−	2.67890i	0.440644	−	0.160381i
$280$	6.45348	+	9.23830i	0.385669	+	0.552094i
$281$	0.264790	−	1.50170i	0.0157961	−	0.0895839i	−0.975891	−	0.218260i	$-0.929962\pi$
$281$	0.264790	−	1.50170i	0.0157961	−	0.0895839i	0.991687	+	0.128677i	$0.0410729\pi$
$282$	−15.7066	−	3.24920i	−0.935314	−	0.193487i
$283$	−10.4250	−	12.4241i	−0.619704	−	0.738535i	0.361315	−	0.932444i	$-0.382328\pi$
$283$	−10.4250	−	12.4241i	−0.619704	−	0.738535i	−0.981020	+	0.193909i	$0.937883\pi$
$284$	9.95862	−	2.97340i	0.590936	−	0.176439i
$285$	−0.0114707	+	4.19246i	−0.000679467	+	0.248340i
$286$	2.32809	+	15.9348i	0.137663	+	0.942243i
$287$	−28.2781	+	23.7281i	−1.66920	+	1.40063i
$288$	−2.07883	−	5.26103i	−0.122496	−	0.310009i
$289$	1.86571	−	10.5810i	0.109748	−	0.622410i
$290$	−7.40594	+	2.45102i	−0.434892	+	0.143929i
$291$	4.41578	+	12.1323i	0.258858	+	0.711205i
$292$	−3.16568	+	13.3132i	−0.185258	+	0.779097i
$293$	5.58070	−	3.22202i	0.326028	−	0.188232i	−0.328048	−	0.944661i	$-0.606391\pi$
$293$	5.58070	−	3.22202i	0.326028	−	0.188232i	0.654076	+	0.756429i	$0.273058\pi$
$294$	12.2258	+	7.54723i	0.713024	+	0.440163i
$295$	0.845014	+	0.709051i	0.0491986	+	0.0412825i
$296$	−16.3421	−	11.4699i	−0.949867	−	0.666675i
$297$	2.01090	−	3.48297i	0.116684	−	0.202103i
$298$	13.4700	−	7.25655i	0.780297	−	0.420361i
$299$	7.29929	−	1.28706i	0.422129	−	0.0744327i
$300$	−8.09540	+	0.940152i	−0.467388	+	0.0542797i
$301$	−7.68005	+	21.1008i	−0.442671	+	1.21623i
$302$	−19.5237	−	17.3876i	−1.12347	−	1.00054i
$303$	2.17710			0.125071
$304$	16.0386	−	6.83836i	0.919877	−	0.392207i
$305$	10.4253			0.596949
$306$	−5.56280	−	4.95416i	−0.318004	−	0.283210i
$307$	2.30853	−	6.34264i	0.131755	−	0.361993i	−0.856219	−	0.516612i	$-0.827193\pi$
$307$	2.30853	−	6.34264i	0.131755	−	0.361993i	0.987974	+	0.154619i	$0.0494150\pi$
$308$	33.0973	−	3.84373i	1.88589	−	0.219017i
$309$	8.73556	−	1.54031i	0.496949	−	0.0876255i
$310$	9.37953	−	5.05293i	0.532722	−	0.286987i
$311$	11.4531	−	19.8373i	0.649443	−	1.12487i	−0.333813	−	0.942639i	$-0.608335\pi$
$311$	11.4531	−	19.8373i	0.649443	−	1.12487i	0.983256	−	0.182229i	$-0.0583312\pi$
$312$	4.60067	−	6.55495i	0.260461	−	0.371101i
$313$	−16.6680	−	13.9862i	−0.942134	−	0.790544i	0.0358215	−	0.999358i	$-0.488595\pi$
$313$	−16.6680	−	13.9862i	−0.942134	−	0.790544i	−0.977955	+	0.208814i	$0.933040\pi$
$314$	9.20430	+	5.68200i	0.519429	+	0.320654i
$315$	3.45046	−	1.99212i	0.194411	−	0.112243i
$316$	1.01095	−	4.25152i	0.0568702	−	0.239167i
$317$	0.124158	+	0.341122i	0.00697343	+	0.0191593i	0.943131	−	0.332423i	$-0.107866\pi$
$317$	0.124158	+	0.341122i	0.00697343	+	0.0191593i	−0.936157	+	0.351582i	$0.885644\pi$
$318$	9.62786	−	3.18638i	0.539904	−	0.178683i
$319$	−4.00527	+	22.7150i	−0.224252	+	1.27180i
$320$	−3.83249	−	6.67219i	−0.214243	−	0.372987i
$321$	−9.27912	+	7.78611i	−0.517910	+	0.434578i
$322$	−2.21700	−	15.1744i	−0.123549	−	0.845639i
$323$	14.8062	−	17.5476i	0.823837	−	0.976373i
$324$	−1.91640	+	0.572190i	−0.106467	+	0.0317883i
$325$	−7.41622	−	8.83831i	−0.411378	−	0.490261i
$326$	17.0075	+	3.51831i	0.941956	+	0.194861i
$327$	2.20605	−	12.5111i	0.121995	−	0.691866i
$328$	20.6628	−	14.4342i	1.14091	−	0.796993i
$329$	−44.1474	+	16.0683i	−2.43392	+	0.885875i
$330$	2.02162	−	5.08326i	0.111287	−	0.279824i
$331$	7.74117	−	4.46936i	0.425493	−	0.245658i	−0.271932	−	0.962317i	$-0.587662\pi$
$331$	7.74117	−	4.46936i	0.425493	−	0.245658i	0.697425	+	0.716658i	$0.254329\pi$
$332$	9.49338	−	21.9635i	0.521017	−	1.20540i
$333$	−4.53737	+	5.40743i	−0.248646	+	0.296325i
$334$	−3.58199	+	2.83012i	−0.195998	+	0.154857i
$335$	−3.24665	+	5.62337i	−0.177384	+	0.307237i
$336$	−13.2762	−	9.91432i	−0.724278	−	0.540871i
$337$	2.65148	+	15.0373i	0.144435	+	0.819134i	0.967819	+	0.251648i	$0.0809727\pi$
$337$	2.65148	+	15.0373i	0.144435	+	0.819134i	−0.823383	+	0.567486i	$0.807916\pi$
$338$	−7.04440	−	0.207576i	−0.383165	−	0.0112907i
$339$	−6.20888	+	17.0587i	−0.337220	+	0.926504i
$340$	−8.46132	−	5.57406i	−0.458880	−	0.302296i
$341$		−	31.5010i		−	1.70587i
$342$	−1.92080	−	5.85752i	−0.103865	−	0.316738i
$343$	13.0879			0.706683
$344$	6.49508	−	13.8885i	0.350191	−	0.748819i
$345$	−2.36598	−	0.861146i	−0.127380	−	0.0463625i
$346$	0.387855	−	13.1624i	0.0208512	−	0.707615i
$347$	2.56077	−	0.451533i	0.137470	−	0.0242396i	−0.104490	−	0.994526i	$-0.533321\pi$
$347$	2.56077	−	0.451533i	0.137470	−	0.0242396i	0.241959	+	0.970286i	$0.422210\pi$
$348$	9.20558	−	6.84274i	0.493471	−	0.366809i
$349$	−12.6478	−	7.30220i	−0.677020	−	0.390878i	0.121711	−	0.992566i	$-0.461162\pi$
$349$	−12.6478	−	7.30220i	−0.677020	−	0.390878i	−0.798731	+	0.601688i	$0.794495\pi$
$350$	−18.7309	+	14.7992i	−1.00121	+	0.791051i
$351$	−2.16896	−	1.81997i	−0.115771	−	0.0971430i
$352$	−22.7422	+	0.619679i	−1.21217	+	0.0330290i
$353$	5.77123	+	9.99607i	0.307172	+	0.532037i	0.977742	−	0.209809i	$-0.0672841\pi$
$353$	5.77123	+	9.99607i	0.307172	+	0.532037i	−0.670571	+	0.741845i	$0.733951\pi$
$354$	−1.50711	−	0.599383i	−0.0801022	−	0.0318568i
$355$	−1.70945	−	4.69669i	−0.0907284	−	0.249274i
$356$	10.7421	+	21.4287i	0.569329	+	1.13572i
$357$	−21.4877	−	3.78886i	−1.13725	−	0.200528i
$358$	−15.2719	−	3.15928i	−0.807145	−	0.166973i
$359$	16.4999	−	13.8451i	0.870831	−	0.730714i	−0.0934415	−	0.995625i	$-0.529787\pi$
$359$	16.4999	−	13.8451i	0.870831	−	0.730714i	0.964273	+	0.264910i	$0.0853424\pi$
$360$	−2.46682	+	1.14697i	−0.130013	+	0.0604507i
$361$	17.8895	−	6.40059i	0.941550	−	0.336873i
$362$	4.25397	−	0.621509i	0.223584	−	0.0326658i
$363$	−3.32630	−	3.96413i	−0.174585	−	0.208063i
$364$	1.38123	−	23.4167i	0.0723963	−	1.22737i
$365$	6.48098	+	1.14277i	0.339230	+	0.0598154i
$366$	−14.5525	+	4.81622i	−0.760674	+	0.251748i
$367$	20.7335	−	7.54639i	1.08228	−	0.393919i	0.261526	−	0.965197i	$-0.415774\pi$
$367$	20.7335	−	7.54639i	1.08228	−	0.393919i	0.820757	+	0.571278i	$0.193552\pi$
$368$	0.593387	+	10.4543i	0.0309325	+	0.544966i
$369$	−4.45567	−	7.71746i	−0.231953	−	0.401755i
$370$	−5.04365	+	8.17025i	−0.262207	+	0.424751i
$371$	19.0943	−	22.7557i	0.991328	−	1.18142i
$372$	−10.7585	+	11.3865i	−0.557802	+	0.590361i
$373$	31.2992	+	18.0706i	1.62061	+	0.935659i	0.986757	+	0.162206i	$0.0518608\pi$
$373$	31.2992	+	18.0706i	1.62061	+	0.935659i	0.633853	+	0.773454i	$0.281473\pi$
$374$	−26.3748	+	14.2086i	−1.36381	+	0.734708i
$375$	1.51567	+	8.59581i	0.0782690	+	0.443886i
$376$	30.9945	−	8.26812i	1.59842	−	0.426396i
$377$	15.2590	+	5.55381i	0.785877	+	0.286036i
$378$	−3.89615	+	4.37482i	−0.200396	+	0.225016i
$379$		−	20.4329i		−	1.04957i	−0.851235	−	0.524784i	$-0.824146\pi$
$379$		−	20.4329i		−	1.04957i	0.851235	−	0.524784i	$-0.175854\pi$
$380$	−3.73709	−	7.50609i	−0.191709	−	0.385054i
$381$			5.76731i			0.295468i
$382$	−0.785147	−	0.699242i	−0.0401716	−	0.0357763i
$383$	32.1947	+	11.7179i	1.64507	+	0.598757i	0.987915	−	0.154997i	$-0.0495369\pi$
$383$	32.1947	+	11.7179i	1.64507	+	0.598757i	0.657156	+	0.753754i	$0.271759\pi$
$384$	8.43214	+	7.54314i	0.430301	+	0.384934i
$385$	−2.78250	−	15.7804i	−0.141809	−	0.804241i
$386$	3.09364	+	5.74259i	0.157462	+	0.292290i
$387$	−4.69451	−	2.71038i	−0.238636	−	0.137776i
$388$	−18.7690	−	17.7338i	−0.952850	−	0.900299i
$389$	−18.6599	+	22.2381i	−0.946097	+	1.12751i	0.0456059	+	0.998960i	$0.485478\pi$
$389$	−18.6599	+	22.2381i	−0.946097	+	1.12751i	−0.991702	+	0.128554i	$0.958966\pi$
$390$	−3.27715	−	2.02305i	−0.165945	−	0.102441i
$391$	6.89426	+	11.9412i	0.348658	+	0.603893i
$392$	−28.6233	−	2.53619i	−1.44569	−	0.128097i
$393$	−11.2426	+	4.09199i	−0.567117	+	0.206414i
$394$	−5.34506	−	16.1505i	−0.269280	−	0.813648i
$395$	−2.06968	−	0.364940i	−0.104137	−	0.0183621i
$396$	−0.473627	+	8.02963i	−0.0238007	+	0.403504i
$397$	−17.8995	−	21.3318i	−0.898352	−	1.07061i	−0.997145	−	0.0755068i	$-0.975943\pi$
$397$	−17.8995	−	21.3318i	−0.898352	−	1.07061i	0.0987928	−	0.995108i	$-0.468502\pi$
$398$	−1.72183	−	11.7852i	−0.0863077	−	0.590740i
$399$	−13.8001	−	11.6442i	−0.690871	−	0.582938i
$400$	13.6314	−	8.93665i	0.681568	−	0.446832i
$401$	−7.44595	+	6.24789i	−0.371833	+	0.312005i	−0.809486	−	0.587139i	$-0.800254\pi$
$401$	−7.44595	+	6.24789i	−0.371833	+	0.312005i	0.437653	+	0.899144i	$0.355810\pi$
$402$	1.93412	−	9.34950i	0.0964650	−	0.466310i
$403$	−21.8400	−	3.85099i	−1.08793	−	0.191831i
$404$	−3.89249	+	1.95128i	−0.193659	+	0.0970799i
$405$	0.328961	+	0.903814i	0.0163462	+	0.0449109i
$406$	12.4160	−	31.2193i	0.616196	−	1.54939i
$407$	14.1947	+	24.5859i	0.703605	+	1.21868i
$408$	14.3862	+	3.87186i	0.712222	+	0.191686i
$409$	−10.6064	−	8.89985i	−0.524454	−	0.440069i	0.341727	−	0.939799i	$-0.388988\pi$
$409$	−10.6064	−	8.89985i	−0.524454	−	0.440069i	−0.866181	+	0.499730i	$0.833433\pi$
$410$	−7.51459	−	9.51097i	−0.371119	−	0.469713i
$411$	−2.83980	−	1.63956i	−0.140077	−	0.0808734i
$412$	−14.2380	+	10.5835i	−0.701456	+	0.521409i
$413$	−4.67865	+	0.824972i	−0.230221	+	0.0405942i
$414$	3.70048	+	0.109042i	0.181869	+	0.00535910i
$415$	−10.8129	−	3.93559i	−0.530786	−	0.193190i
$416$	−2.35060	+	15.8433i	−0.115248	+	0.776780i
$417$	11.6644			0.571210
$418$	−24.7791	−	0.798025i	−1.21199	−	0.0390327i
$419$		−	19.5671i		−	0.955915i	−0.878383	−	0.477958i	$-0.841377\pi$
$419$		−	19.5671i		−	0.955915i	0.878383	−	0.477958i	$-0.158623\pi$
$420$	−4.38367	+	6.65433i	−0.213901	+	0.324698i
$421$	−5.46872	+	15.0252i	−0.266529	+	0.732283i	0.732162	+	0.681131i	$0.238512\pi$
$421$	−5.46872	+	15.0252i	−0.266529	+	0.732283i	−0.998691	+	0.0511522i	$0.983711\pi$
$422$	0.761253	−	25.8342i	0.0370572	−	1.25759i
$423$	−1.96941	−	11.1691i	−0.0957561	−	0.543060i
$424$	−14.3581	+	14.3263i	−0.697289	+	0.695744i
$425$	10.7318	−	18.5881i	0.520570	−	0.901653i
$426$	4.55597	+	5.76635i	0.220738	+	0.279380i
$427$	−28.8611	+	34.3954i	−1.39669	+	1.66451i
$428$	9.61189	−	22.2377i	0.464608	−	1.07490i
$429$	−9.86161	+	5.69360i	−0.476123	+	0.274890i
$430$	−6.85145	−	2.72484i	−0.330406	−	0.131403i
$431$	−8.22921	+	2.99519i	−0.396387	+	0.144273i	−0.532520	−	0.846417i	$-0.678755\pi$
$431$	−8.22921	+	2.99519i	−0.396387	+	0.144273i	0.136133	+	0.990691i	$0.456533\pi$
$432$	2.91355	−	2.74066i	0.140178	−	0.131860i
$433$	−0.805420	+	4.56776i	−0.0387060	+	0.219513i	−0.998025	−	0.0628101i	$-0.979994\pi$
$433$	−0.805420	+	4.56776i	−0.0387060	+	0.219513i	0.959320	+	0.282323i	$0.0911049\pi$
$434$	−9.29538	+	44.9337i	−0.446192	+	2.15689i
$435$	−3.54570	−	4.22560i	−0.170003	−	0.202602i
$436$	7.26917	+	24.3462i	0.348130	+	1.16597i
$437$	−0.0312197	+	11.4106i	−0.00149344	+	0.545841i
$438$	−9.57469	+	1.39887i	−0.457496	+	0.0668407i
$439$	−19.4739	+	16.3405i	−0.929438	+	0.779891i	−0.975716	−	0.219037i	$-0.929708\pi$
$439$	−19.4739	+	16.3405i	−0.929438	+	0.779891i	0.0462783	+	0.998929i	$0.485264\pi$
$440$	0.941489	+	10.9004i	0.0448837	+	0.519658i
$441$	−1.76418	+	10.0052i	−0.0840086	+	0.476436i
$442$	6.62669	+	20.0230i	0.315199	+	0.952397i
$443$	−2.69015	−	7.39112i	−0.127813	−	0.351163i	0.859237	−	0.511578i	$-0.170939\pi$
$443$	−2.69015	−	7.39112i	−0.127813	−	0.351163i	−0.987050	+	0.160415i	$0.948717\pi$
$444$	3.26594	−	13.7348i	0.154995	−	0.651826i
$445$	9.98321	−	5.76381i	0.473250	−	0.273231i
$446$	19.2639	−	31.2057i	0.912170	−	1.47763i
$447$	8.28779	+	6.95428i	0.391999	+	0.328926i
$448$	32.6229	+	5.82691i	1.54129	+	0.275296i
$449$	−9.59860	+	16.6253i	−0.452986	+	0.784595i	−0.998570	−	0.0534615i	$-0.982975\pi$
$449$	−9.59860	+	16.6253i	−0.452986	+	0.784595i	0.545584	+	0.838056i	$0.316308\pi$
$450$	−2.73315	−	5.07342i	−0.128842	−	0.239163i
$451$	−35.2951	+	6.22348i	−1.66198	+	0.293052i
$452$	−4.18834	−	36.0647i	−0.197003	−	1.69634i
$453$	6.32277	−	17.3717i	0.297070	−	0.816193i
$454$	8.86590	−	9.95512i	0.416097	−	0.467217i
$455$	−11.2809			−0.528856
$456$	8.68422	+	8.75125i	0.406676	+	0.409815i
$457$	17.1450			0.802008			0.401004	−	0.916076i	$-0.368661\pi$
$457$	17.1450			0.802008			0.401004	+	0.916076i	$0.368661\pi$
$458$	6.55712	−	7.36269i	0.306394	−	0.344036i
$459$	1.80151	−	4.94962i	0.0840875	−	0.231028i
$460$	5.00203	−	0.580906i	0.233221	−	0.0270849i
$461$	−4.38372	+	0.772967i	−0.204170	+	0.0360007i	−0.274798	−	0.961502i	$-0.588611\pi$
$461$	−4.38372	+	0.772967i	−0.204170	+	0.0360007i	0.0706277	+	0.997503i	$0.477500\pi$
$462$	11.1742	+	20.7422i	0.519872	+	0.965016i
$463$	−19.5732	+	33.9018i	−0.909643	+	1.57555i	−0.0950829	+	0.995469i	$0.530312\pi$
$463$	−19.5732	+	33.9018i	−0.909643	+	1.57555i	−0.814560	+	0.580079i	$0.803022\pi$
$464$	−10.3259	+	20.4851i	−0.479370	+	0.950996i
$465$	5.77101	+	4.84245i	0.267624	+	0.224563i
$466$	16.7131	−	27.0736i	0.774218	−	1.25416i
$467$	−12.8480	+	7.41781i	−0.594536	+	0.343255i	−0.766889	−	0.641780i	$-0.778196\pi$
$467$	−12.8480	+	7.41781i	−0.594536	+	0.343255i	0.172353	+	0.985035i	$0.444863\pi$
$468$	5.50915	+	1.30999i	0.254660	+	0.0605544i
$469$	−9.56482	−	26.2791i	−0.441662	−	1.21346i
$470$	−4.84700	−	14.6455i	−0.223575	−	0.675548i
$471$	−1.32818	+	7.53247i	−0.0611992	+	0.347078i
$472$	3.23182	−	0.279138i	0.148757	−	0.0128484i
$473$	−16.7007	+	14.0135i	−0.767897	+	0.644342i
$474$	3.05764	−	0.446724i	0.140442	−	0.0205187i
$475$	15.4067	−	8.83893i	0.706906	−	0.405558i
$476$	41.8143	−	12.4847i	1.91656	−	0.572236i
$477$	4.60948	+	5.49337i	0.211054	+	0.251524i
$478$	−1.17310	+	5.67073i	−0.0536562	+	0.259373i
$479$	1.78524	−	10.1246i	0.0815698	−	0.462605i	−0.916474	−	0.400093i	$-0.868978\pi$
$479$	1.78524	−	10.1246i	0.0815698	−	0.462605i	0.998044	−	0.0625119i	$-0.0199111\pi$
$480$	3.38250	−	4.26166i	0.154389	−	0.194517i
$481$	18.7811	−	6.83575i	0.856343	−	0.311683i
$482$	−33.3607	−	13.2676i	−1.51954	−	0.604325i
$483$	9.39106	−	5.42193i	0.427308	−	0.246706i
$484$	9.50014	+	4.10629i	0.431825	+	0.186650i
$485$	−7.98209	+	9.51268i	−0.362448	+	0.431949i
$486$	−0.876735	−	1.10966i	−0.0397695	−	0.0503350i
$487$	1.70943	−	2.96082i	0.0774617	−	0.134168i	−0.824692	−	0.565581i	$-0.808652\pi$
$487$	1.70943	−	2.96082i	0.0774617	−	0.134168i	0.902154	+	0.431414i	$0.141985\pi$
$488$	21.7022	−	21.6542i	0.982414	−	0.980238i
$489$	2.13252	+	12.0941i	0.0964361	+	0.546916i
$490$	−0.407030	+	13.8131i	−0.0183877	+	0.624014i
$491$	0.0996970	−	0.273915i	0.00449926	−	0.0123616i	−0.937423	−	0.348194i	$-0.886795\pi$
$491$	0.0996970	−	0.273915i	0.00449926	−	0.0123616i	0.941922	+	0.335832i	$0.109017\pi$
$492$	14.8834	+	9.80474i	0.670996	+	0.442032i
$493$			30.2084i			1.36052i
$494$	−3.58253	+	17.0822i	−0.161186	+	0.768562i
$495$	3.86824			0.173864
$496$	9.02998	−	30.0008i	0.405458	−	1.34707i
$497$	20.2279	+	7.36235i	0.907345	+	0.330247i
$498$	16.9119	+	0.498339i	0.757838	+	0.0223311i
$499$	40.7329	−	7.18230i	1.82345	−	0.321524i	0.846081	−	0.533054i	$-0.178956\pi$
$499$	40.7329	−	7.18230i	1.82345	−	0.321524i	0.977372	+	0.211530i	$0.0678445\pi$
$500$	−10.4141	−	14.0102i	−0.465735	−	0.626557i
$501$	−2.79555	−	1.61401i	−0.124896	−	0.0721086i
$502$	11.7984	+	14.9328i	0.526588	+	0.666485i
$503$	−20.6441	−	17.3225i	−0.920475	−	0.772370i	0.0536076	−	0.998562i	$-0.482928\pi$
$503$	−20.6441	−	17.3225i	−0.920475	−	0.772370i	−0.974083	+	0.226192i	$0.927372\pi$
$504$	3.04499	−	11.3139i	0.135635	−	0.503961i
$505$	1.04699	+	1.81343i	0.0465903	+	0.0806967i
$506$	5.50223	−	13.8350i	0.244604	−	0.615043i
$507$	−1.70439	−	4.68278i	−0.0756947	−	0.207969i
$508$	−5.16911	−	10.3115i	−0.229342	−	0.457501i
$509$	−27.1029	−	4.77897i	−1.20131	−	0.211824i	−0.463048	−	0.886333i	$-0.653244\pi$
$509$	−27.1029	−	4.77897i	−1.20131	−	0.211824i	−0.738267	+	0.674509i	$0.764355\pi$
$510$	1.45141	−	7.01609i	0.0642695	−	0.310678i
$511$	−21.7121	+	18.2186i	−0.960488	+	0.805945i
$512$	−21.8368	−	5.92906i	−0.965060	−	0.262030i
$513$	3.34676	−	2.79270i	0.147763	−	0.123301i
$514$	3.70739	+	25.3756i	0.163526	+	1.11927i
$515$	5.48403	+	6.53562i	0.241655	+	0.287994i
$516$	10.8227	+	0.638377i	0.476443	+	0.0281030i
$517$	−44.9198	−	7.92057i	−1.97557	−	0.348346i
$518$	−12.9928	−	39.2586i	−0.570870	−	1.72492i
$519$	8.74973	−	3.18464i	0.384070	−	0.139790i
$520$	7.67252	+	0.679830i	0.336462	+	0.0298125i
$521$	10.9770	+	19.0128i	0.480912	+	0.832964i	0.999760	−	0.0219022i	$-0.00697225\pi$
$521$	10.9770	+	19.0128i	0.480912	+	0.832964i	−0.518848	+	0.854867i	$0.673639\pi$
$522$	6.90155	+	4.26046i	0.302073	+	0.186475i
$523$	24.8753	−	29.6453i	1.08772	−	1.29630i	0.135539	−	0.990772i	$-0.456724\pi$
$523$	24.8753	−	29.6453i	1.08772	−	1.29630i	0.952184	−	0.305525i	$-0.0988321\pi$
$524$	16.4335	−	17.3927i	0.717900	−	0.759804i
$525$	−14.6184	−	8.43995i	−0.638000	−	0.368350i
$526$	0.0685419	+	0.127231i	0.00298857	+	0.00554755i
$527$	−7.16408	−	40.6295i	−0.312072	−	1.76985i
$528$	−6.34996	−	14.7809i	−0.276347	−	0.643256i
$529$	15.1735	+	5.52269i	0.659716	+	0.240117i
$530$	7.28426	+	6.48726i	0.316408	+	0.281789i
$531$		−	1.14688i		−	0.0497702i
$532$	35.1101	+	8.45021i	1.52221	+	0.366363i
$533$			25.2314i			1.09289i
$534$	−11.2728	+	12.6577i	−0.487820	+	0.547751i
$535$	−10.9479	−	3.98472i	−0.473320	−	0.172274i
$536$	4.92168	+	18.4497i	0.212584	+	0.796907i
$537$	−1.91491	−	10.8600i	−0.0826344	−	0.468643i
$538$	11.3686	−	6.12445i	0.490134	−	0.264044i
$539$	35.3853	+	20.4297i	1.52415	+	0.879970i
$540$	−1.39823	−	1.32111i	−0.0601701	−	0.0568517i
$541$	−11.1255	+	13.2589i	−0.478324	+	0.570045i	−0.950208	−	0.311616i	$-0.899130\pi$
$541$	−11.1255	+	13.2589i	−0.478324	+	0.570045i	0.471884	+	0.881661i	$0.343574\pi$
$542$	−0.104441	+	0.169185i	−0.00448613	+	0.00726712i
$543$	1.51997	+	2.63267i	0.0652282	+	0.112979i
$544$	−29.1917	+	5.97139i	−1.25158	+	0.256021i
$545$	11.4822	−	4.17917i	0.491842	−	0.179016i
$546$	15.7469	−	5.21150i	0.673906	−	0.223032i
$547$	−24.7443	−	4.36309i	−1.05799	−	0.186552i	−0.382527	−	0.923945i	$-0.624946\pi$
$547$	−24.7443	−	4.36309i	−1.05799	−	0.186552i	−0.675465	+	0.737392i	$0.736057\pi$
$548$	6.54685	+	0.386166i	0.279668	+	0.0164962i
$549$	−6.96725	−	8.30324i	−0.297355	−	0.354374i
$550$	−22.9332	+	3.35057i	−0.977877	+	0.142869i
$551$	−12.5586	+	21.6153i	−0.535013	+	0.920842i
$552$	−6.71393	+	3.12170i	−0.285764	+	0.132868i
$553$	6.93368	−	5.81805i	0.294850	−	0.247409i
$554$	12.8366	+	2.65549i	0.545374	+	0.112821i
$555$	−6.68623	−	1.17896i	−0.283815	−	0.0500442i
$556$	−20.8552	+	10.4546i	−0.884456	+	0.443372i
$557$	5.48597	+	15.0726i	0.232448	+	0.638645i	0.999997	−	0.00234448i	$-0.000746273\pi$
$557$	5.48597	+	15.0726i	0.232448	+	0.638645i	−0.767549	+	0.640990i	$0.778524\pi$
$558$	−10.2928	−	4.09347i	−0.435729	−	0.173291i
$559$	7.67410	+	13.2919i	0.324580	+	0.562189i
$560$	1.87356	−	15.8265i	0.0791726	−	0.668790i
$561$	−16.2278	−	13.6167i	−0.685138	−	0.574899i
$562$	−1.69208	+	1.33690i	−0.0713759	+	0.0563939i
$563$	29.9572	+	17.2958i	1.26254	+	0.728930i	0.973566	−	0.228406i	$-0.0733513\pi$
$563$	29.9572	+	17.2958i	1.26254	+	0.728930i	0.288978	+	0.957336i	$0.406685\pi$
$564$	13.5318	+	18.2044i	0.569790	+	0.766543i
$565$	−17.1952	+	3.03197i	−0.723406	+	0.127556i
$566$	−0.675571	+	22.9264i	−0.0283964	+	0.963670i
$567$	−3.89259	−	1.41679i	−0.163473	−	0.0594994i
$568$	−13.3140	−	6.22640i	−0.558643	−	0.261254i
$569$	−26.9520			−1.12989			−0.564944	−	0.825129i	$-0.691102\pi$
$569$	−26.9520			−1.12989			−0.564944	+	0.825129i	$0.691102\pi$
$570$	3.95534	−	4.41689i	0.165671	−	0.185003i
$571$			36.1833i			1.51423i	0.653284	+	0.757113i	$0.273391\pi$
$571$			36.1833i			1.51423i	−0.653284	+	0.757113i	$0.726609\pi$
$572$	12.5288	−	19.0185i	0.523856	−	0.795203i
$573$	0.254270	−	0.698602i	0.0106223	−	0.0291845i
$574$	52.1822	+	1.53765i	2.17804	+	0.0641801i
$575$	1.85233	+	10.5051i	0.0772477	+	0.438093i
$576$	−2.75282	+	7.51146i	−0.114701	+	0.312977i
$577$	−18.4073	+	31.8824i	−0.766307	+	1.32728i	0.173246	+	0.984879i	$0.444575\pi$
$577$	−18.4073	+	31.8824i	−0.766307	+	1.32728i	−0.939553	+	0.342404i	$0.888759\pi$
$578$	−11.9223	+	9.41981i	−0.495904	+	0.391813i
$579$	−2.96478	+	3.53328i	−0.123212	+	0.146838i
$580$	10.1268	+	4.37714i	0.420491	+	0.181751i
$581$	42.9188	−	24.7792i	1.78057	−	1.02801i
$582$	6.74751	−	16.9662i	0.279693	−	0.703272i
$583$	27.1013	−	9.86406i	1.12242	−	0.408528i
$584$	15.8651	−	11.0827i	0.656502	−	0.458604i
$585$	0.472891	−	2.68190i	0.0195516	−	0.110883i
$586$	−8.92429	−	1.84616i	−0.368659	−	0.0762640i
$587$	19.8256	+	23.6273i	0.818292	+	0.975202i	0.999967	−	0.00815666i	$-0.00259637\pi$
$587$	19.8256	+	23.6273i	0.818292	+	0.975202i	−0.181675	+	0.983359i	$0.558152\pi$
$588$	−5.81317	−	19.4697i	−0.239731	−	0.802917i
$589$	11.7648	−	32.0503i	0.484759	−	1.32061i
$590$	−0.225523	−	1.54361i	−0.00928465	−	0.0635496i
$591$	9.21496	−	7.73227i	0.379053	−	0.318063i
$592$	6.47096	+	27.4841i	0.265955	+	1.12959i
$593$	0.378880	−	2.14874i	0.0155587	−	0.0882380i	−0.976040	−	0.217593i	$-0.930180\pi$
$593$	0.378880	−	2.14874i	0.0155587	−	0.0882380i	0.991598	+	0.129355i	$0.0412906\pi$
$594$	−5.39964	+	1.78703i	−0.221550	+	0.0733228i
$595$	−7.17767	−	19.7205i	−0.294256	−	0.808461i
$596$	−21.0509	−	5.00560i	−0.862280	−	0.205037i
$597$	7.29356	−	4.21094i	0.298506	−	0.172342i
$598$	−8.91937	−	5.50610i	−0.364740	−	0.225161i
$599$	−2.59665	−	2.17885i	−0.106096	−	0.0890254i	0.588196	−	0.808718i	$-0.299838\pi$
$599$	−2.59665	−	2.17885i	−0.106096	−	0.0890254i	−0.694293	+	0.719693i	$0.744283\pi$
$600$	9.43386	+	6.62126i	0.385136	+	0.270312i
$601$	−16.4249	+	28.4487i	−0.669984	+	1.16045i	0.307924	+	0.951411i	$0.400366\pi$
$601$	−16.4249	+	28.4487i	−0.669984	+	1.16045i	−0.977908	+	0.209036i	$0.932967\pi$
$602$	27.9573	−	15.0611i	1.13946	−	0.613846i
$603$	6.64851	−	1.17231i	0.270748	−	0.0477402i
$604$	4.26517	+	36.7263i	0.173547	+	1.49437i
$605$	1.70231	−	4.67706i	0.0692088	−	0.190150i
$606$	−2.29924	−	2.04768i	−0.0934004	−	0.0831812i
$607$	21.5824			0.876003			0.438001	−	0.898974i	$-0.355686\pi$
$607$	21.5824			0.876003			0.438001	+	0.898974i	$0.355686\pi$
$608$	−23.3703	−	7.86314i	−0.947791	−	0.318892i
$609$	23.7571			0.962687
$610$	−11.0102	−	9.80552i	−0.445789	−	0.397014i
$611$	−10.9829	+	30.1752i	−0.444319	+	1.22076i
$612$	1.21525	+	10.4642i	0.0491237	+	0.422991i
$613$	−34.5284	+	6.08829i	−1.39459	+	0.245904i	−0.819918	−	0.572481i	$-0.805981\pi$
$613$	−34.5284	+	6.08829i	−1.39459	+	0.245904i	−0.574671	+	0.818384i	$0.694870\pi$
$614$	−8.40364	+	4.52720i	−0.339143	+	0.182703i
$615$	4.28555	−	7.42280i	0.172810	−	0.299316i
$616$	−38.5695	−	27.0704i	−1.55401	−	1.09070i
$617$	−3.58547	−	3.00857i	−0.144346	−	0.121120i	0.567756	−	0.823197i	$-0.307812\pi$
$617$	−3.58547	−	3.00857i	−0.144346	−	0.121120i	−0.712101	+	0.702077i	$0.752256\pi$
$618$	−10.6744	−	6.58953i	−0.429388	−	0.265070i
$619$	12.2153	−	7.05248i	0.490972	−	0.283463i	−0.234005	−	0.972235i	$-0.575183\pi$
$619$	12.2153	−	7.05248i	0.490972	−	0.283463i	0.724978	+	0.688772i	$0.241850\pi$
$620$	−14.6583	−	3.48553i	−0.588692	−	0.139982i
$621$	0.895331	+	2.45990i	0.0359284	+	0.0987124i
$622$	−30.7536	+	10.1780i	−1.23311	+	0.408102i
$623$	−8.62122	+	48.8934i	−0.345402	+	1.95887i
$624$	−11.0241	+	2.59555i	−0.441316	+	0.103905i
$625$	9.17673	−	7.70019i	0.367069	−	0.308007i
$626$	4.44849	+	30.4480i	0.177797	+	1.21695i
$627$	−5.95072	−	16.4897i	−0.237649	−	0.658535i
$628$	−4.37649	−	14.6579i	−0.174641	−	0.584915i
$629$	23.8996	+	28.4824i	0.952939	+	1.13567i
$630$	−5.51774	−	1.14145i	−0.219832	−	0.0454764i
$631$	6.17186	−	35.0024i	0.245698	−	1.39342i	−0.573168	−	0.819438i	$-0.694286\pi$
$631$	6.17186	−	35.0024i	0.245698	−	1.39342i	0.818866	−	0.573984i	$-0.194603\pi$
$632$	−5.06645	+	3.53920i	−0.201532	+	0.140782i
$633$	17.1733	−	6.25058i	0.682578	−	0.248438i
$634$	0.189719	−	0.477039i	0.00753472	−	0.0189456i
$635$	−4.80394	+	2.77356i	−0.190639	+	0.110065i
$636$	−13.1650	−	5.69037i	−0.522026	−	0.225638i
$637$	18.4900	−	22.0356i	0.732602	−	0.873081i
$638$	25.5946	−	20.2223i	1.01330	−	0.800607i
$639$	−2.59826	+	4.50032i	−0.102786	+	0.178030i
$640$	−2.22804	+	10.6512i	−0.0880709	+	0.421026i
$641$	−0.414784	−	2.35236i	−0.0163830	−	0.0929125i	0.975520	−	0.219911i	$-0.0705767\pi$
$641$	−0.414784	−	2.35236i	−0.0163830	−	0.0929125i	−0.991903	+	0.126999i	$0.959466\pi$
$642$	17.1230	+	0.504561i	0.675790	+	0.0199134i
$643$	14.6414	−	40.2270i	0.577401	−	1.58640i	−0.215144	−	0.976582i	$-0.569022\pi$
$643$	14.6414	−	40.2270i	0.577401	−	1.58640i	0.792545	−	0.609814i	$-0.208756\pi$
$644$	−11.9310	+	18.1110i	−0.470147	+	0.713674i
$645$		−	5.21379i		−	0.205293i
$646$	−32.1413	+	4.60609i	−1.26458	+	0.181224i
$647$	15.9617			0.627517			0.313759	−	0.949503i	$-0.398412\pi$
$647$	15.9617			0.627517			0.313759	+	0.949503i	$0.398412\pi$
$648$	2.56210	+	1.19819i	0.100649	+	0.0470692i
$649$	−4.33433	−	1.57757i	−0.170137	−	0.0619249i
$650$	−0.480591	+	16.3095i	−0.0188503	+	0.639713i
$651$	−31.9527	+	5.63413i	−1.25233	+	0.220819i
$652$	−14.6525	−	19.7121i	−0.573837	−	0.771987i
$653$	16.2884	+	9.40413i	0.637415	+	0.368012i	0.783618	−	0.621243i	$-0.213372\pi$
$653$	16.2884	+	9.40413i	0.637415	+	0.368012i	−0.146203	+	0.989255i	$0.546705\pi$
$654$	−14.0972	+	11.1382i	−0.551244	+	0.435536i
$655$	−8.81516	−	7.39680i	−0.344437	−	0.289017i
$656$	−35.3982	−	4.19051i	−1.38207	−	0.163612i
$657$	−3.42110	−	5.92552i	−0.133470	−	0.231177i
$658$	61.7374	+	24.5531i	2.40677	+	0.957180i
$659$	−0.593555	−	1.63078i	−0.0231216	−	0.0635261i	0.927595	−	0.373588i	$-0.121873\pi$
$659$	−0.593555	−	1.63078i	−0.0231216	−	0.0635261i	−0.950716	+	0.310062i	$0.899650\pi$
$660$	−6.91613	+	3.46701i	−0.269210	+	0.134953i
$661$	28.9214	+	5.09963i	1.12491	+	0.198352i	0.704997	−	0.709210i	$-0.250948\pi$
$661$	28.9214	+	5.09963i	1.12491	+	0.198352i	0.419916	+	0.907563i	$0.362060\pi$
$662$	−12.3792	−	2.56086i	−0.481130	−	0.0995307i
$663$	−11.4245	+	9.58630i	−0.443691	+	0.372301i
$664$	−30.6838	+	14.2667i	−1.19076	+	0.553656i
$665$	3.06252	−	17.0948i	0.118759	−	0.662906i
$666$	9.87792	−	1.44317i	0.382762	−	0.0559218i
$667$	−9.65030	−	11.5008i	−0.373661	−	0.445312i
$668$	6.44483	+	0.380148i	0.249358	+	0.0147084i
$669$	25.5376	+	4.50296i	0.987340	+	0.174095i
$670$	8.71789	−	2.88522i	0.336801	−	0.111466i
$671$	−40.9637	+	14.9096i	−1.58139	+	0.575577i
$672$	4.69615	+	22.9576i	0.181158	+	0.885608i
$673$	3.56320	+	6.17165i	0.137351	+	0.237899i	0.926493	−	0.376311i	$-0.122808\pi$
$673$	3.56320	+	6.17165i	0.137351	+	0.237899i	−0.789142	+	0.614211i	$0.789474\pi$
$674$	11.3431	−	18.3748i	0.436922	−	0.707772i
$675$	2.61930	−	3.12156i	0.100817	−	0.120149i
$676$	7.24439	+	6.84486i	0.278631	+	0.263264i
$677$	19.5805	+	11.3048i	0.752541	+	0.434480i	0.826611	−	0.562773i	$-0.190266\pi$
$677$	19.5805	+	11.3048i	0.752541	+	0.434480i	−0.0740703	+	0.997253i	$0.523599\pi$
$678$	22.6019	−	12.1761i	0.868021	−	0.467619i
$679$	−9.28706	−	52.6695i	−0.356405	−	2.02127i
$680$	3.69334	+	13.8451i	0.141633	+	0.530936i
$681$	8.85778	+	3.22397i	0.339431	+	0.123543i
$682$	−29.6283	+	33.2683i	−1.13453	+	1.27391i
$683$			20.3260i			0.777751i	0.921290	+	0.388876i	$0.127136\pi$
$683$			20.3260i			0.777751i	−0.921290	+	0.388876i	$0.872864\pi$
$684$	−3.48074	+	7.99277i	−0.133089	+	0.305611i
$685$		−	3.15391i		−	0.120505i
$686$	−13.8223	−	12.3099i	−0.527736	−	0.469995i
$687$	6.55111	+	2.38441i	0.249941	+	0.0909709i
$688$	−19.9224	+	8.55877i	−0.759534	+	0.326300i
$689$	−3.52576	−	19.9956i	−0.134321	−	0.761770i
$690$	1.68877	+	3.13479i	0.0642904	+	0.119339i
$691$	5.30897	+	3.06514i	0.201963	+	0.116603i	0.597571	−	0.801816i	$-0.296133\pi$
$691$	5.30897	+	3.06514i	0.201963	+	0.116603i	−0.395608	+	0.918420i	$0.629466\pi$
$692$	−12.7896	+	13.5361i	−0.486186	+	0.514565i
$693$	−10.7088	+	12.7622i	−0.406792	+	0.484796i
$694$	−3.12914	−	1.93168i	−0.118780	−	0.0733255i
$695$	5.60954	+	9.71600i	0.212782	+	0.368549i
$696$	−16.1580	−	1.43170i	−0.612468	−	0.0542683i
$697$	−44.1078	+	16.0539i	−1.67070	+	0.608086i
$698$	6.48928	+	19.6078i	0.245623	+	0.742167i
$699$	22.1561	+	3.90671i	0.838020	+	0.147766i
$700$	33.7012	+	1.98787i	1.27379	+	0.0751342i
$701$	−15.2584	−	18.1842i	−0.576300	−	0.686808i	0.396611	−	0.917987i	$-0.370186\pi$
$701$	−15.2584	−	18.1842i	−0.576300	−	0.686808i	−0.972911	+	0.231179i	$0.925742\pi$
$702$	0.578868	+	3.96211i	0.0218480	+	0.149540i
$703$	5.26006	+	30.3161i	0.198387	+	1.14339i
$704$	24.6011	+	20.7359i	0.927187	+	0.781512i
$705$	8.35630	−	7.01176i	0.314716	−	0.264078i
$706$	3.30681	−	15.9851i	0.124453	−	0.601605i
$707$	−8.88140	−	1.56603i	−0.334019	−	0.0588966i
$708$	1.02792	+	2.05053i	0.0386316	+	0.0770637i
$709$	6.34485	+	17.4323i	0.238286	+	0.654685i	0.999977	+	0.00674484i	$0.00214696\pi$
$709$	6.34485	+	17.4323i	0.238286	+	0.654685i	−0.761692	+	0.647940i	$0.775631\pi$
$710$	−2.61212	+	6.56803i	−0.0980312	+	0.246494i
$711$	1.09251	+	1.89229i	0.0409725	+	0.0709665i
$712$	8.81009	−	32.7345i	0.330172	−	1.22678i
$713$	15.7069	+	13.1796i	0.588227	+	0.493581i
$714$	19.1296	+	24.2118i	0.715909	+	0.906103i
$715$	−9.48508	−	5.47622i	−0.354722	−	0.204799i
$716$	13.1573	+	17.7006i	0.491710	+	0.661502i
$717$	−4.03251	+	0.711039i	−0.150597	+	0.0265543i
$718$	−30.4477	−	0.897197i	−1.13630	−	0.0334831i
$719$	4.65149	+	1.69300i	0.173471	+	0.0631384i	0.427296	−	0.904112i	$-0.359466\pi$
$719$	4.65149	+	1.69300i	0.173471	+	0.0631384i	−0.253824	+	0.967250i	$0.581689\pi$
$720$	3.68402	+	1.10886i	0.137295	+	0.0413247i
$721$	−36.7444			−1.36843
$722$	−24.9132	−	10.0663i	−0.927175	−	0.374629i
$723$		−	25.3867i		−	0.944142i
$724$	−5.07720	−	3.34471i	−0.188693	−	0.124305i
$725$	−7.99301	+	21.9606i	−0.296853	+	0.815597i
$726$	−0.215553	+	7.31510i	−0.00799993	+	0.271489i
$727$	−4.52770	−	25.6779i	−0.167923	−	0.952340i	−0.945999	−	0.324169i	$-0.894915\pi$
$727$	−4.52770	−	25.6779i	−0.167923	−	0.952340i	0.778076	−	0.628170i	$-0.216196\pi$
$728$	−23.4834	+	23.4314i	−0.870353	+	0.868425i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−5.76976	−	7.30260i	−0.213549	−	0.270281i
$731$	−18.3533	+	21.8726i	−0.678820	+	0.808987i
$732$	19.8989	+	8.60101i	0.735486	+	0.317903i
$733$	21.4897	−	12.4071i	0.793742	−	0.458267i	−0.0475363	−	0.998870i	$-0.515137\pi$
$733$	21.4897	−	12.4071i	0.793742	−	0.458267i	0.841278	+	0.540602i	$0.181804\pi$
$734$	−28.9946	−	11.5312i	−1.07021	−	0.425625i
$735$	−9.18231	+	3.34209i	−0.338694	+	0.123275i
$736$	9.20611	−	11.5989i	0.339342	−	0.427542i
$737$	4.71479	−	26.7389i	0.173672	−	0.984940i
$738$	−2.55302	+	12.3412i	−0.0939779	+	0.454288i
$739$	6.51644	+	7.76599i	0.239711	+	0.285677i	0.872465	−	0.488676i	$-0.162520\pi$
$739$	6.51644	+	7.76599i	0.239711	+	0.285677i	−0.632754	+	0.774353i	$0.718076\pi$
$740$	13.0112	−	3.88482i	0.478301	−	0.142809i
$741$	−12.1600	+	2.10985i	−0.446709	+	0.0775072i
$742$	−41.5686	+	6.07322i	−1.52603	+	0.222955i
$743$	−7.64190	+	6.41231i	−0.280354	+	0.235245i	−0.772111	−	0.635487i	$-0.780799\pi$
$743$	−7.64190	+	6.41231i	−0.280354	+	0.235245i	0.491757	+	0.870732i	$0.336355\pi$
$744$	22.0717	−	1.90637i	0.809187	−	0.0698909i
$745$	−1.80696	+	10.2478i	−0.0662019	+	0.375449i
$746$	−16.0589	−	48.5230i	−0.587957	−	1.77655i
$747$	4.09182	+	11.2422i	0.149712	+	0.411330i
$748$	41.2185	+	9.80114i	1.50710	+	0.358365i
$749$	43.4546	−	25.0885i	1.58780	−	0.916715i
$750$	6.48411	−	10.5037i	0.236766	−	0.383539i
$751$	−3.11617	−	2.61478i	−0.113711	−	0.0954145i	0.584159	−	0.811639i	$-0.301424\pi$
$751$	−3.11617	−	2.61478i	−0.113711	−	0.0954145i	−0.697870	+	0.716224i	$0.745869\pi$
$752$	−40.5100	−	20.4199i	−1.47725	−	0.744638i
$753$	−6.72859	+	11.6543i	−0.245203	+	0.424705i
$754$	−10.8914	−	20.2173i	−0.396642	−	0.736270i
$755$	17.5106	−	3.08759i	0.637276	−	0.112369i
$756$	8.22950	−	0.955726i	0.299304	−	0.0347594i
$757$	5.95690	−	16.3664i	0.216507	−	0.594848i	−0.783128	−	0.621861i	$-0.786377\pi$
$757$	5.95690	−	16.3664i	0.216507	−	0.594848i	0.999635	+	0.0270122i	$0.00859929\pi$
$758$	−19.2183	+	21.5793i	−0.698038	+	0.783796i
$759$	10.5281			0.382147
$760$	−3.11312	+	11.4422i	−0.112925	+	0.415051i
$761$	−4.56662			−0.165540			−0.0827700	−	0.996569i	$-0.526377\pi$
$761$	−4.56662			−0.165540			−0.0827700	+	0.996569i	$0.526377\pi$
$762$	5.42447	−	6.09089i	0.196508	−	0.220650i
$763$	−17.9990	+	49.4519i	−0.651608	+	1.79028i
$764$	0.171524	+	1.47695i	0.00620552	+	0.0534340i
$765$	4.98920	−	0.879730i	0.180385	−	0.0318067i
$766$	−22.9797	−	42.6562i	−0.830289	−	1.54123i
$767$	−1.62362	+	2.81219i	−0.0586255	+	0.101542i
$768$	−1.81050	−	15.8972i	−0.0653307	−	0.573642i
$769$	−12.3124	−	10.3314i	−0.443998	−	0.372559i	0.393205	−	0.919451i	$-0.371366\pi$
$769$	−12.3124	−	10.3314i	−0.443998	−	0.372559i	−0.837203	+	0.546892i	$0.815811\pi$
$770$	−11.9037	+	19.2828i	−0.428978	+	0.694904i
$771$	−15.7043	+	9.06686i	−0.565575	+	0.326535i
$772$	2.13401	−	8.97452i	0.0768046	−	0.323000i
$773$	3.94599	+	10.8415i	0.141927	+	0.389942i	0.990207	−	0.139606i	$-0.0445836\pi$
$773$	3.94599	+	10.8415i	0.141927	+	0.389942i	−0.848280	+	0.529548i	$0.822361\pi$
$774$	2.40865	+	7.27789i	0.0865770	+	0.261598i
$775$	5.54232	−	31.4321i	0.199086	−	1.12907i
$776$	3.14238	+	36.3820i	0.112805	+	1.30604i
$777$	22.3997	−	18.7956i	0.803586	−	0.674289i
$778$	40.6229	−	5.93505i	1.45640	−	0.212782i
$779$	−38.2350	−	6.84977i	−1.36991	−	0.245419i
$780$	1.55823	+	5.21889i	0.0557936	+	0.186866i
$781$	13.4338	+	16.0098i	0.480700	+	0.572876i
$782$	3.95028	−	19.0956i	0.141262	−	0.682857i
$783$	−0.995891	+	5.64798i	−0.0355902	+	0.201842i
$784$	27.8438	+	29.6002i	0.994421	+	1.05715i
$785$	−6.91298	+	2.51612i	−0.246735	+	0.0898041i
$786$	15.7222	+	6.25274i	0.560791	+	0.223028i
$787$	2.24008	−	1.29331i	0.0798502	−	0.0461015i	−0.459543	−	0.888155i	$-0.651987\pi$
$787$	2.24008	−	1.29331i	0.0798502	−	0.0461015i	0.539393	+	0.842054i	$0.318654\pi$
$788$	−9.54543	+	22.0839i	−0.340042	+	0.786707i
$789$	−0.0656868	+	0.0782825i	−0.00233851	+	0.00278693i
$790$	1.84255	+	2.33206i	0.0655550	+	0.0829708i
$791$	37.5996	−	65.1245i	1.33689	−	2.31556i
$792$	8.05249	−	8.03466i	0.286133	−	0.285499i
$793$	5.32919	+	30.2234i	0.189245	+	1.07326i
$794$	−1.15994	+	39.3642i	−0.0411647	+	1.39698i
$795$	−2.35901	+	6.48132i	−0.0836654	+	0.229869i
$796$	−9.26620	+	14.0659i	−0.328432	+	0.498553i
$797$		−	27.4536i		−	0.972458i	−0.873831	−	0.486229i	$-0.838372\pi$
$797$		−	27.4536i		−	0.972458i	0.873831	−	0.486229i	$-0.161628\pi$
$798$	3.62242	+	25.2772i	0.128232	+	0.894805i
$799$	−59.7382			−2.11339
$800$	−22.8015	−	3.38298i	−0.806156	−	0.119606i
$801$	−11.2624	−	4.09919i	−0.397938	−	0.144838i
$802$	13.7402	+	0.404880i	0.485183	+	0.0142968i
$803$	−27.0999	+	4.77844i	−0.956333	+	0.168627i
$804$	−10.8363	+	8.05491i	−0.382168	+	0.284075i
$805$	9.03250	+	5.21492i	0.318354	+	0.183802i
$806$	19.4433	+	24.6088i	0.684862	+	0.866807i
$807$	6.99481	+	5.86934i	0.246229	+	0.206611i
$808$	5.94617	+	1.60034i	0.209185	+	0.0562997i
$809$	−18.4028	−	31.8746i	−0.647009	−	1.12065i	−0.983834	−	0.179084i	$-0.942686\pi$
$809$	−18.4028	−	31.8746i	−0.647009	−	1.12065i	0.336825	−	0.941567i	$-0.390647\pi$
$810$	0.502668	−	1.26393i	0.0176619	−	0.0444099i
$811$	0.607873	+	1.67012i	0.0213453	+	0.0586457i	0.949908	−	0.312531i	$-0.101177\pi$
$811$	0.607873	+	1.67012i	0.0213453	+	0.0586457i	−0.928562	+	0.371176i	$0.878955\pi$
$812$	−42.4760	+	21.2930i	−1.49062	+	0.747237i
$813$	−0.138455	−	0.0244133i	−0.00485582	−	0.000856213i
$814$	8.13330	−	39.3162i	0.285072	−	1.37803i
$815$	−9.04839	+	7.59250i	−0.316951	+	0.265954i
$816$	−11.5516	−	17.6201i	−0.404388	−	0.616826i
$817$	−22.2256	+	8.02066i	−0.777575	+	0.280607i
$818$	2.83072	+	19.3751i	0.0989739	+	0.677435i
$819$	7.53907	+	8.98471i	0.263436	+	0.313951i
$820$	−1.00938	+	17.1125i	−0.0352490	+	0.597593i
$821$	11.0014	+	1.93985i	0.383953	+	0.0677013i	0.362293	−	0.932064i	$-0.381994\pi$
$821$	11.0014	+	1.93985i	0.383953	+	0.0677013i	0.0216596	+	0.999765i	$0.493105\pi$
$822$	1.45703	+	4.40253i	0.0508199	+	0.153556i
$823$	10.7919	−	3.92793i	0.376182	−	0.136919i	−0.147008	−	0.989135i	$-0.546964\pi$
$823$	10.7919	−	3.92793i	0.376182	−	0.136919i	0.523189	+	0.852216i	$0.324742\pi$
$824$	24.9911	+	2.21436i	0.870608	+	0.0771409i
$825$	−8.19421	−	14.1928i	−0.285286	−	0.494129i
$826$	5.71708	+	3.52926i	0.198922	+	0.122799i
$827$	27.3080	−	32.5444i	0.949593	−	1.13168i	−0.0415844	−	0.999135i	$-0.513241\pi$
$827$	27.3080	−	32.5444i	0.949593	−	1.13168i	0.991177	−	0.132545i	$-0.0423150\pi$
$828$	−3.80554	−	3.59566i	−0.132252	−	0.124958i
$829$	2.32127	+	1.34019i	0.0806212	+	0.0465466i	0.539769	−	0.841813i	$-0.318512\pi$
$829$	2.32127	+	1.34019i	0.0806212	+	0.0465466i	−0.459147	+	0.888360i	$0.651845\pi$
$830$	7.71797	+	14.3265i	0.267895	+	0.497282i
$831$	1.60955	+	9.12821i	0.0558346	+	0.316654i
$832$	17.3839	−	14.5213i	0.602679	−	0.503435i
$833$	50.2857	+	18.3025i	1.74230	+	0.634144i
$834$	−12.3189	−	10.9710i	−0.426568	−	0.379895i
$835$		−	3.10477i		−	0.107445i
$836$	25.4188	+	24.1489i	0.879128	+	0.835207i
$837$		−	7.83257i		−	0.270733i
$838$	−18.4039	+	20.6649i	−0.635752	+	0.713858i
$839$	37.0551	+	13.4869i	1.27928	+	0.465621i	0.890195	−	0.455580i	$-0.150568\pi$
$839$	37.0551	+	13.4869i	1.27928	+	0.465621i	0.389088	+	0.921201i	$0.372790\pi$
$840$	10.8884	−	2.90460i	0.375685	−	0.100218i
$841$	−0.675744	−	3.83233i	−0.0233015	−	0.132149i
$842$	19.9076	−	10.7246i	0.686060	−	0.369593i
$843$	−1.32057	−	0.762433i	−0.0454830	−	0.0262596i
$844$	−25.1024	+	26.5676i	−0.864061	+	0.914496i
$845$	3.08091	−	3.67168i	0.105986	−	0.126310i
$846$	−8.42522	+	13.6481i	−0.289665	+	0.469231i
$847$	10.7181	+	18.5642i	0.368277	+	0.637874i
$848$	28.6382	−	1.62552i	0.983441	−	0.0558204i
$849$	−15.2404	+	5.54705i	−0.523049	+	0.190374i
$850$	−28.8170	+	9.53710i	−0.988415	+	0.327120i
$851$	−18.1978	−	3.20877i	−0.623814	−	0.109995i
$852$	0.611969	−	10.3750i	0.0209657	−	0.355442i
$853$	−22.4736	−	26.7829i	−0.769480	−	0.917030i	0.228928	−	0.973443i	$-0.426478\pi$
$853$	−22.4736	−	26.7829i	−0.769480	−	0.917030i	−0.998408	+	0.0564130i	$0.982034\pi$
$854$	62.8311	−	9.17969i	2.15004	−	0.314122i
$855$	3.93570	+	1.44468i	0.134598	+	0.0494071i
$856$	−31.0669	+	14.4448i	−1.06184	+	0.493714i
$857$	42.8537	−	35.9585i	1.46386	−	1.22832i	0.542235	−	0.840227i	$-0.317578\pi$
$857$	42.8537	−	35.9585i	1.46386	−	1.22832i	0.921620	−	0.388093i	$-0.126866\pi$
$858$	15.7700	+	3.26233i	0.538380	+	0.111374i
$859$	−46.0269	−	8.11579i	−1.57042	−	0.276907i	−0.680404	−	0.732838i	$-0.738196\pi$
$859$	−46.0269	−	8.11579i	−1.57042	−	0.276907i	−0.890015	+	0.455930i	$0.849307\pi$
$860$	4.67300	+	9.32188i	0.159348	+	0.317873i
$861$	12.6255	+	34.6882i	0.430275	+	1.18217i
$862$	11.5080	+	4.57678i	0.391966	+	0.155886i
$863$	−13.0436	−	22.5921i	−0.444008	−	0.769044i	0.553975	−	0.832533i	$-0.313110\pi$
$863$	−13.0436	−	22.5921i	−0.444008	−	0.769044i	−0.997983	+	0.0634895i	$0.979777\pi$
$864$	−5.65476	+	0.154080i	−0.192379	+	0.00524192i
$865$	6.86050	+	5.75665i	0.233264	+	0.195732i
$866$	5.14683	−	4.06650i	0.174896	−	0.138185i
$867$	−9.30474	−	5.37210i	−0.316006	−	0.182446i
$868$	52.0795	−	38.7119i	1.76769	−	1.31397i
$869$	8.65423	−	1.52597i	0.293575	−	0.0517651i
$870$	−0.229771	+	7.79761i	−0.00778997	+	0.264364i
$871$	−17.9621	−	6.53765i	−0.608621	−	0.221520i
$872$	15.2219	−	32.5492i	0.515478	−	1.10226i
$873$	12.9109			0.436967
$874$	10.7652	−	12.0214i	0.364139	−	0.406630i
$875$		−	36.1566i		−	1.22232i
$876$	11.4276	+	7.52816i	0.386103	+	0.254353i
$877$	6.86073	−	18.8497i	0.231670	−	0.636509i	−0.768323	−	0.640062i	$-0.778909\pi$
$877$	6.86073	−	18.8497i	0.231670	−	0.636509i	0.999994	+	0.00355269i	$0.00113086\pi$
$878$	35.9356	+	1.05891i	1.21277	+	0.0357365i
$879$	−1.11900	−	6.34614i	−0.0377428	−	0.214050i
$880$	9.25813	−	12.3975i	0.312092	−	0.417921i
$881$	−25.3134	+	43.8441i	−0.852830	+	1.47714i	0.0258146	+	0.999667i	$0.491782\pi$
$881$	−25.3134	+	43.8441i	−0.852830	+	1.47714i	−0.878644	+	0.477477i	$0.841551\pi$
$882$	11.2736	−	8.90720i	0.379600	−	0.299921i
$883$	4.12136	−	4.91164i	0.138695	−	0.165290i	−0.692226	−	0.721681i	$-0.743370\pi$
$883$	4.12136	−	4.91164i	0.138695	−	0.165290i	0.830921	+	0.556391i	$0.187814\pi$
$884$	11.8342	−	27.3792i	0.398028	−	0.920861i
$885$	0.955302	−	0.551544i	0.0321121	−	0.0185399i
$886$	−4.11067	+	10.3360i	−0.138101	+	0.347246i
$887$	4.46844	−	1.62638i	0.150036	−	0.0546085i	−0.265911	−	0.963998i	$-0.585673\pi$
$887$	4.46844	−	1.62638i	0.150036	−	0.0546085i	0.415946	+	0.909389i	$0.363450\pi$
$888$	−16.3675	+	11.4336i	−0.549258	+	0.383688i
$889$	4.14855	−	23.5276i	0.139138	−	0.789090i
$890$	−15.9645	−	3.30256i	−0.535131	−	0.110702i
$891$	−2.58516	−	3.08087i	−0.0866060	−	0.103213i
$892$	−49.6953	+	14.8378i	−1.66392	+	0.496805i
$893$	−42.7450	−	24.8350i	−1.43041	−	0.831073i
$894$	−2.21191	−	15.1396i	−0.0739772	−	0.506343i
$895$	8.12503	−	6.81771i	0.271590	−	0.227891i
$896$	−28.9727	−	36.8374i	−0.967911	−	1.23065i
$897$	1.28706	−	7.29929i	0.0429738	−	0.243716i
$898$	25.7741	−	8.53003i	0.860092	−	0.284651i
$899$	15.3638	+	42.2116i	0.512410	+	1.40784i
$900$	−1.88534	+	7.92874i	−0.0628445	+	0.264291i
$901$	32.7116	−	18.8860i	1.08978	−	0.629185i
$902$	43.1289	+	26.6243i	1.43603	+	0.886492i
$903$	17.2015	+	14.4338i	0.572430	+	0.480326i
$904$	−29.4974	+	42.0275i	−0.981070	+	1.39781i
$905$	−1.46194	+	2.53215i	−0.0485964	+	0.0841715i
$906$	−23.0165	+	12.3994i	−0.764672	+	0.411943i
$907$	−25.4895	+	4.49448i	−0.846364	+	0.149237i	−0.579981	−	0.814630i	$-0.696940\pi$
$907$	−25.4895	+	4.49448i	−0.846364	+	0.149237i	−0.266384	+	0.963867i	$0.585829\pi$
$908$	−18.7266	+	2.17480i	−0.621466	+	0.0721734i
$909$	0.744611	−	2.04580i	0.0246972	−	0.0678550i
$910$	11.9138	+	10.6103i	0.394939	+	0.351727i
$911$	4.32447			0.143276			0.0716380	−	0.997431i	$-0.477177\pi$
$911$	4.32447			0.143276			0.0716380	+	0.997431i	$0.477177\pi$
$912$	−0.940429	−	17.4102i	−0.0311407	−	0.576510i
$913$	48.1154			1.59239
$914$	−18.1069	−	16.1258i	−0.598923	−	0.533393i
$915$	3.56565	−	9.79654i	0.117877	−	0.323864i
$916$	−13.8500	+	1.60846i	−0.457617	+	0.0531450i
$917$	48.8075	−	8.60608i	1.61177	−	0.284198i
$918$	−6.55797	+	3.53290i	−0.216445	+	0.116603i
$919$	23.0145	−	39.8623i	0.759180	−	1.31494i	−0.184090	−	0.982909i	$-0.558934\pi$
$919$	23.0145	−	39.8623i	0.759180	−	1.31494i	0.943269	−	0.332028i	$-0.107733\pi$
$920$	−5.82904	−	4.09118i	−0.192178	−	0.134882i
$921$	−5.17056	−	4.33862i	−0.170376	−	0.142962i
$922$	5.35668	+	3.30679i	0.176413	+	0.108903i
$923$	12.7421	−	7.35665i	0.419411	−	0.242147i
$924$	7.70803	−	32.4159i	0.253575	−	1.06641i
$925$	9.83798	+	27.0296i	0.323471	+	0.888728i
$926$	52.5578	−	17.3942i	1.72716	−	0.571609i
$927$	1.54031	−	8.73556i	0.0505906	−	0.286913i
$928$	30.1726	−	11.9223i	0.990464	−	0.391369i
$929$	16.5511	−	13.8880i	0.543024	−	0.455651i	−0.329547	−	0.944139i	$-0.606896\pi$
$929$	16.5511	−	13.8880i	0.543024	−	0.455651i	0.872571	+	0.488488i	$0.162451\pi$
$930$	−1.54021	−	10.5421i	−0.0505054	−	0.345688i
$931$	28.3725	+	34.0015i	0.929870	+	1.11435i
$932$	−43.1150	+	12.8731i	−1.41228	+	0.421671i
$933$	−14.7238	−	17.5471i	−0.482034	−	0.574466i
$934$	20.5457	+	4.25027i	0.672277	+	0.139073i
$935$	3.53809	−	20.0655i	0.115708	−	0.656213i
$936$	−4.58612	−	6.56514i	−0.149902	−	0.214588i
$937$	32.0210	−	11.6547i	1.04608	−	0.380743i	0.238899	−	0.971044i	$-0.423214\pi$
$937$	32.0210	−	11.6547i	1.04608	−	0.380743i	0.807183	+	0.590302i	$0.200991\pi$
$938$	−14.6155	+	36.7497i	−0.477212	+	1.19992i
$939$	−18.8435	+	10.8793i	−0.614934	+	0.355032i
$940$	−8.65597	+	20.0261i	−0.282327	+	0.653179i
$941$	8.41151	−	10.0244i	0.274207	−	0.326788i	−0.611312	−	0.791389i	$-0.709358\pi$
$941$	8.41151	−	10.0244i	0.274207	−	0.326788i	0.885520	+	0.464602i	$0.153803\pi$
$942$	8.48739	−	6.70586i	0.276534	−	0.218489i
$943$	11.6639	−	20.2025i	0.379830	−	0.657885i
$944$	−3.67569	−	2.74490i	−0.119634	−	0.0893390i
$945$	−0.691856	−	3.92371i	−0.0225061	−	0.127638i
$946$	30.8181	+	0.908114i	1.00198	+	0.0295253i
$947$	−17.1326	+	47.0715i	−0.556735	+	1.52962i	0.267608	+	0.963528i	$0.413767\pi$
$947$	−17.1326	+	47.0715i	−0.556735	+	1.52962i	−0.824343	+	0.566090i	$0.808455\pi$
$948$	−3.64936	−	2.40408i	−0.118526	−	0.0780810i
$949$			19.3729i			0.628870i
$950$	−24.5846	−	5.15596i	−0.797628	−	0.167281i
$951$	0.363015			0.0117716
$952$	−55.9029	−	26.1434i	−1.81182	−	0.847314i
$953$	−28.2577	−	10.2849i	−0.915356	−	0.333162i	−0.158966	−	0.987284i	$-0.550816\pi$
$953$	−28.2577	−	10.2849i	−0.915356	−	0.333162i	−0.756389	+	0.654122i	$0.773038\pi$
$954$	0.298707	−	10.1370i	0.00967099	−	0.328199i
$955$	0.704188	−	0.124167i	0.0227870	−	0.00401796i
$956$	6.57254	−	4.88553i	0.212571	−	0.158009i
$957$	19.9752	+	11.5327i	0.645707	+	0.372799i
$958$	−11.4081	+	9.01354i	−0.368580	+	0.291214i
$959$	10.4055	+	8.73125i	0.336011	+	0.281947i
$960$	−7.58060	+	1.31934i	−0.244663	+	0.0425815i
$961$	−15.1746	−	26.2831i	−0.489502	−	0.847843i
$962$	−26.2642	−	10.4453i	−0.846791	−	0.336771i
$963$	4.14290	+	11.3825i	0.133503	+	0.366797i
$964$	22.7535	+	45.3896i	0.732842	+	1.46190i
$965$	−4.36887	−	0.770350i	−0.140639	−	0.0247984i
$966$	−15.0176	−	3.10667i	−0.483182	−	0.0999553i
$967$	32.3802	−	27.1702i	1.04128	−	0.873734i	0.0491264	−	0.998793i	$-0.484356\pi$
$967$	32.3802	−	27.1702i	1.04128	−	0.873734i	0.992149	+	0.125058i	$0.0399118\pi$
$968$	−6.17097	−	13.2721i	−0.198342	−	0.426581i
$969$	−11.4253	−	19.9149i	−0.367034	−	0.639758i
$970$	17.3771	−	2.53881i	0.557946	−	0.0815164i
$971$	−17.0139	−	20.2764i	−0.546003	−	0.650701i	0.420520	−	0.907283i	$-0.361848\pi$
$971$	−17.0139	−	20.2764i	−0.546003	−	0.650701i	−0.966522	+	0.256583i	$0.917403\pi$
$972$	−0.117765	+	1.99653i	−0.00377732	+	0.0640387i
$973$	−47.5847	−	8.39047i	−1.52550	−	0.268986i
$974$	−4.59015	+	1.51913i	−0.147078	+	0.0486760i
$975$	−10.8418	+	3.94609i	−0.347215	+	0.126376i
$976$	−43.2868	+	2.45697i	−1.38558	+	0.0786458i
$977$	−28.9883	−	50.2093i	−0.927419	−	1.60634i	−0.787624	−	0.616157i	$-0.788689\pi$
$977$	−28.9883	−	50.2093i	−0.927419	−	1.60634i	−0.139796	−	0.990180i	$-0.544645\pi$
$978$	9.12302	−	14.7784i	0.291722	−	0.472563i
$979$	−30.9837	+	36.9249i	−0.990243	+	1.18013i
$980$	13.4219	−	14.2053i	0.428746	−	0.453772i
$981$	−11.0021	−	6.35206i	−0.351270	−	0.202806i
$982$	−0.362923	+	0.195513i	−0.0115813	+	0.00623907i
$983$	0.716053	+	4.06094i	0.0228385	+	0.129524i	0.994095	−	0.108510i	$-0.0346081\pi$
$983$	0.716053	+	4.06094i	0.0228385	+	0.129524i	−0.971257	+	0.238034i	$0.923497\pi$
$984$	−6.49657	−	24.3535i	−0.207103	−	0.776361i
$985$	10.8722	+	3.95717i	0.346418	+	0.126086i
$986$	28.4126	−	31.9032i	0.904842	−	1.01601i
$987$			46.9806i			1.49541i
$988$	19.8502	−	14.6710i	0.631519	−	0.466746i
$989$		−	14.1903i		−	0.451225i
$990$	−4.08526	−	3.63828i	−0.129838	−	0.115632i
$991$	15.8028	+	5.75174i	0.501991	+	0.182710i	0.580589	−	0.814196i	$-0.302822\pi$
$991$	15.8028	+	5.75174i	0.501991	+	0.182710i	−0.0785981	+	0.996906i	$0.525044\pi$
$992$	−37.7539	+	23.1908i	−1.19869	+	0.736308i
$993$	−1.55219	−	8.80293i	−0.0492574	−	0.279353i
$994$	−14.4381	−	26.8008i	−0.457949	−	0.850071i
$995$	7.01509	+	4.05016i	0.222393	+	0.128399i
$996$	−17.3920	−	16.4328i	−0.551086	−	0.520693i
$997$	−3.77624	+	4.50034i	−0.119595	+	0.142527i	−0.822520	−	0.568737i	$-0.807432\pi$
$997$	−3.77624	+	4.50034i	−0.119595	+	0.142527i	0.702925	+	0.711264i	$0.251877\pi$
$998$	−49.7735	−	30.7262i	−1.57555	−	0.972620i
$999$	3.52945	+	6.11318i	0.111667	+	0.193413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.9	✓	240
8.5	even	2	inner	456.2.bk.a.253.27	yes	240
19.16	even	9	inner	456.2.bk.a.301.27	yes	240
152.149	even	18	inner	456.2.bk.a.301.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.9	✓	240	1.1	even	1	trivial
456.2.bk.a.253.27	yes	240	8.5	even	2	inner
456.2.bk.a.301.9	yes	240	152.149	even	18	inner
456.2.bk.a.301.27	yes	240	19.16	even	9	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05611 - 0.940554i) q^{2} +(0.342020 - 0.939693i) q^{3} +(0.230718 + 1.98665i) q^{4} +(0.947207 - 0.167018i) q^{5} +(-1.24504 + 0.670726i) q^{6} +(-2.07120 + 3.58743i) q^{7} +(1.62489 - 2.31511i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.15744 - 0.714510i) q^{10} +(-3.48297 + 2.01090i) q^{11} +(1.94575 + 0.462670i) q^{12} +(0.968388 + 2.66062i) q^{13} +(5.56157 - 1.84062i) q^{14} +(0.167018 - 0.947207i) q^{15} +(-3.89354 + 0.916709i) q^{16} +(-4.03497 + 3.38574i) q^{17} +(0.204448 + 1.39936i) q^{18} +(-4.29473 + 0.745167i) q^{19} +(0.550344 + 1.84323i) q^{20} +(2.66269 + 3.17327i) q^{21} +(5.56974 + 1.15221i) q^{22} +(0.454571 - 2.57800i) q^{23} +(-1.61975 - 2.31871i) q^{24} +(-3.82916 + 1.39370i) q^{25} +(1.47974 - 3.72072i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-7.60482 - 3.28707i) q^{28} +(3.68646 - 4.39335i) q^{29} +(-1.06729 + 0.843261i) q^{30} +(-3.91628 + 6.78320i) q^{31} +(4.97420 + 2.69394i) q^{32} +(0.698377 + 3.96069i) q^{33} +(7.44582 + 0.219405i) q^{34} +(-1.36269 + 3.74396i) q^{35} +(1.10025 - 1.67016i) q^{36} -7.05889i q^{37} +(5.23656 + 3.25245i) q^{38} +2.83138 q^{39} +(1.15244 - 2.46428i) q^{40} +(8.37393 + 3.04786i) q^{41} +(0.172549 - 5.85570i) q^{42} +(5.33840 - 0.941305i) q^{43} +(-4.79852 - 6.45549i) q^{44} +(-0.832960 - 0.480910i) q^{45} +(-2.90482 + 2.29509i) q^{46} +(8.68801 + 7.29011i) q^{47} +(-0.470244 + 3.97226i) q^{48} +(-5.07975 - 8.79839i) q^{49} +(5.35484 + 2.12963i) q^{50} +(1.80151 + 4.94962i) q^{51} +(-5.06230 + 2.53770i) q^{52} +(-7.06214 - 1.24524i) q^{53} +(1.38489 + 0.286491i) q^{54} +(-2.96324 + 2.48645i) q^{55} +(4.93983 + 10.6242i) q^{56} +(-0.768657 + 4.29059i) q^{57} +(-8.02546 + 1.17253i) q^{58} +(0.737198 + 0.878558i) q^{59} +(1.92030 + 0.113269i) q^{60} +(10.6744 + 1.88219i) q^{61} +(10.5160 - 3.48030i) q^{62} +(3.89259 - 1.41679i) q^{63} +(-2.71949 - 7.52359i) q^{64} +(1.36164 + 2.35842i) q^{65} +(2.98768 - 4.83977i) q^{66} +(-4.33950 + 5.17162i) q^{67} +(-7.65721 - 7.23491i) q^{68} +(-2.26706 - 1.30889i) q^{69} +(4.96054 - 2.67234i) q^{70} +(-0.902366 - 5.11757i) q^{71} +(-2.73286 + 0.729022i) q^{72} +(6.42957 + 2.34017i) q^{73} +(-6.63927 + 7.45494i) q^{74} +4.07490i q^{75} +(-2.47126 - 8.36020i) q^{76} -16.6599i q^{77} +(-2.99023 - 2.66306i) q^{78} +(-2.05326 - 0.747324i) q^{79} +(-3.53488 + 1.51860i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-5.97708 - 11.0950i) q^{82} +(-10.3608 - 5.98184i) q^{83} +(-5.68983 + 6.02195i) q^{84} +(-3.25647 + 3.88091i) q^{85} +(-6.52327 - 4.02694i) q^{86} +(-2.86755 - 4.96675i) q^{87} +(-1.00399 + 11.3310i) q^{88} +(11.2624 - 4.09919i) q^{89} +(0.427372 + 1.29133i) q^{90} +(-11.5505 - 2.03667i) q^{91} +(5.22646 + 0.308282i) q^{92} +(5.03468 + 6.00010i) q^{93} +(-2.31872 - 15.8707i) q^{94} +(-3.94354 + 1.42313i) q^{95} +(4.23275 - 3.75284i) q^{96} +(-9.89030 + 8.29895i) q^{97} +(-2.91060 + 14.0698i) q^{98} +(3.96069 + 0.698377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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