LMFDB - Embedded newform 588.2.n.d.275.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.10
Character	$\chi$	$=$	588.275
Dual form			588.2.n.d.263.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.938613 + 1.05783i) q^{2} +(1.62729 + 0.593231i) q^{3} +(-0.238012 + 1.98579i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(0.899858 + 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(2.29615 + 1.93072i) q^{9} +(-0.228045 - 1.11266i) q^{10} +(1.17273 + 2.03122i) q^{11} +(-1.56535 + 3.09026i) q^{12} +5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(-3.88670 - 0.945282i) q^{16} +(1.02661 - 0.592715i) q^{17} +(0.112823 + 4.24114i) q^{18} +(-6.16982 - 3.56215i) q^{19} +(0.962960 - 1.28559i) q^{20} +(-1.04795 + 3.14708i) q^{22} +(-3.94356 + 6.83044i) q^{23} +(-4.73822 + 1.24468i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(4.94516 + 5.57327i) q^{26} +(2.59115 + 4.50399i) q^{27} +4.23132i q^{29} +(0.288969 - 1.94590i) q^{30} +(4.24264 - 2.44949i) q^{31} +(-2.64816 - 4.99872i) q^{32} +(0.703383 + 4.00109i) q^{33} +(1.59058 + 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(-2.02292 - 9.87011i) q^{38} +(8.57351 + 3.12549i) q^{39} +(2.26378 - 0.188022i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(-4.31270 + 1.84533i) q^{44} +(-0.821730 - 2.26491i) q^{45} +(-10.9269 + 2.23952i) q^{46} +(3.04954 - 5.28195i) q^{47} +(-5.76402 - 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(2.02221 - 0.355501i) q^{51} +(-1.25398 + 10.4623i) q^{52} +(7.55175 - 4.36001i) q^{53} +(-2.33238 + 6.96850i) q^{54} -1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-4.47602 + 3.97157i) q^{58} +(0.331087 + 0.573459i) q^{59} +(2.32967 - 1.52077i) q^{60} +(-0.479062 + 0.829760i) q^{61} +(6.57334 + 2.18887i) q^{62} +(2.80221 - 7.49317i) q^{64} +(-3.66443 - 2.11566i) q^{65} +(-3.57227 + 4.49953i) q^{66} +(7.29738 - 4.21314i) q^{67} +(0.932660 + 2.17971i) q^{68} +(-10.4693 + 8.77567i) q^{69} +9.67432 q^{71} +(-8.44885 - 0.785398i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-1.45185 + 0.297563i) q^{74} +(-1.30603 - 7.42914i) q^{75} +(8.54216 - 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(6.00000 + 3.46410i) q^{79} +(2.32371 + 2.21822i) q^{80} +(1.54464 + 8.86646i) q^{81} +(7.58404 - 6.72931i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(8.40251 - 7.45554i) q^{86} +(-2.51015 + 6.88559i) q^{87} +(-6.00000 - 2.83005i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(1.62461 - 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(8.35713 - 1.46917i) q^{93} +(8.44975 - 1.73182i) q^{94} +(2.86085 + 4.95513i) q^{95} +(-1.34393 - 9.70535i) q^{96} -4.37827 q^{97} +(-1.22896 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.938613	+	1.05783i	0.663700	+	0.747999i
$2$	0.938613	+	1.05783i	0.663700	+	0.747999i
$3$	1.62729	+	0.593231i	0.939517	+	0.342502i
$3$	1.62729	+	0.593231i	0.939517	+	0.342502i
$4$	−0.238012	+	1.98579i	−0.119006	+	0.992894i
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	0.336347	−	0.941738i	$-0.390808\pi$
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	−0.647396	+	0.762154i	$0.724142\pi$
$6$	0.899858	+	2.27821i	0.367365	+	0.930077i
$7$		0			0
$7$		0			0
$8$	−2.32403	+	1.61211i	−0.821668	+	0.569967i
$9$	2.29615	+	1.93072i	0.765384	+	0.643573i
$10$	−0.228045	−	1.11266i	−0.0721141	−	0.351854i
$11$	1.17273	+	2.03122i	0.353590	+	0.612436i	0.986876	−	0.161482i	$-0.0516274\pi$
$11$	1.17273	+	2.03122i	0.353590	+	0.612436i	−0.633285	+	0.773918i	$0.718294\pi$
$12$	−1.56535	+	3.09026i	−0.451876	+	0.892081i
$13$	5.26858			1.46124			0.730621	−	0.682784i	$-0.239231\pi$
$13$	5.26858			1.46124			0.730621	+	0.682784i	$0.239231\pi$
$14$		0			0
$15$	−0.893604	−	1.06607i	−0.230727	−	0.275257i
$16$	−3.88670	−	0.945282i	−0.971675	−	0.236320i
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	−0.370312	−	0.928908i	$-0.620749\pi$
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	0.619302	+	0.785153i	$0.287416\pi$
$18$	0.112823	+	4.24114i	0.0265927	+	0.999646i
$19$	−6.16982	−	3.56215i	−1.41545	−	0.817213i	−0.419560	−	0.907728i	$-0.637815\pi$
$19$	−6.16982	−	3.56215i	−1.41545	−	0.817213i	−0.995895	+	0.0905147i	$0.971149\pi$
$20$	0.962960	−	1.28559i	0.215324	−	0.287467i
$21$		0			0
$22$	−1.04795	+	3.14708i	−0.223424	+	0.670959i
$23$	−3.94356	+	6.83044i	−0.822288	+	1.42425i	0.0816860	+	0.996658i	$0.473970\pi$
$23$	−3.94356	+	6.83044i	−0.822288	+	1.42425i	−0.903974	+	0.427587i	$0.859364\pi$
$24$	−4.73822	+	1.24468i	−0.967186	+	0.254070i
$25$	−2.17750	−	3.77153i	−0.435499	−	0.754307i
$26$	4.94516	+	5.57327i	0.969825	+	1.09301i
$27$	2.59115	+	4.50399i	0.498666	+	0.866794i
$28$		0			0
$29$			4.23132i			0.785737i	0.919595	+	0.392868i	$0.128517\pi$
$29$			4.23132i			0.785737i	−0.919595	+	0.392868i	$0.871483\pi$
$30$	0.288969	−	1.94590i	0.0527584	−	0.355272i
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	−0.0680129	−	0.997684i	$-0.521666\pi$
$31$	4.24264	−	2.44949i	0.762001	−	0.439941i	0.830014	+	0.557743i	$0.188333\pi$
$32$	−2.64816	−	4.99872i	−0.468133	−	0.883658i
$33$	0.703383	+	4.00109i	0.122443	+	0.696500i
$34$	1.59058	+	0.529652i	0.272783	+	0.0908346i
$35$		0			0
$36$	−4.38051	+	4.10014i	−0.730085	+	0.683356i
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	−0.905877	−	0.423541i	$-0.860787\pi$
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	0.819736	+	0.572742i	$0.194120\pi$
$38$	−2.02292	−	9.87011i	−0.328162	−	1.60114i
$39$	8.57351	+	3.12549i	1.37286	+	0.500478i
$40$	2.26378	−	0.188022i	0.357935	−	0.0297289i
$41$		−	7.16942i		−	1.11968i	−0.828602	−	0.559838i	$-0.810863\pi$
$41$		−	7.16942i		−	1.11968i	0.828602	−	0.559838i	$-0.189137\pi$
$42$		0			0
$43$		−	7.94315i		−	1.21132i	−0.795724	−	0.605659i	$-0.792909\pi$
$43$		−	7.94315i		−	1.21132i	0.795724	−	0.605659i	$-0.207091\pi$
$44$	−4.31270	+	1.84533i	−0.650164	+	0.278194i
$45$	−0.821730	−	2.26491i	−0.122496	−	0.337633i
$46$	−10.9269	+	2.23952i	−1.61109	+	0.330200i
$47$	3.04954	−	5.28195i	0.444821	−	0.770452i	−0.553219	−	0.833036i	$-0.686601\pi$
$47$	3.04954	−	5.28195i	0.444821	−	0.770452i	0.998040	+	0.0625838i	$0.0199341\pi$
$48$	−5.76402	−	3.84396i	−0.831965	−	0.554828i
$49$		0			0
$50$	1.94582	−	5.84343i	0.275180	−	0.826386i
$51$	2.02221	−	0.355501i	0.283167	−	0.0497801i
$52$	−1.25398	+	10.4623i	−0.173896	+	1.45086i
$53$	7.55175	−	4.36001i	1.03731	−	0.598893i	0.118242	−	0.992985i	$-0.462274\pi$
$53$	7.55175	−	4.36001i	1.03731	−	0.598893i	0.919071	+	0.394092i	$0.128941\pi$
$54$	−2.33238	+	6.96850i	−0.317397	+	0.948293i
$55$		−	1.88369i		−	0.253997i
$56$		0			0
$57$	−7.92692	−	9.45679i	−1.04995	−	1.25258i
$58$	−4.47602	+	3.97157i	−0.587731	+	0.521493i
$59$	0.331087	+	0.573459i	0.0431038	+	0.0746580i	0.886772	−	0.462206i	$-0.152942\pi$
$59$	0.331087	+	0.573459i	0.0431038	+	0.0746580i	−0.843669	+	0.536864i	$0.819609\pi$
$60$	2.32967	−	1.52077i	0.300759	−	0.196331i
$61$	−0.479062	+	0.829760i	−0.0613376	+	0.106240i	−0.895064	−	0.445939i	$-0.852870\pi$
$61$	−0.479062	+	0.829760i	−0.0613376	+	0.106240i	0.833726	+	0.552178i	$0.186203\pi$
$62$	6.57334	+	2.18887i	0.834815	+	0.277987i
$63$		0			0
$64$	2.80221	−	7.49317i	0.350276	−	0.936647i
$65$	−3.66443	−	2.11566i	−0.454517	−	0.262416i
$66$	−3.57227	+	4.49953i	−0.439716	+	0.553854i
$67$	7.29738	−	4.21314i	0.891517	−	0.514717i	0.0170783	−	0.999854i	$-0.494564\pi$
$67$	7.29738	−	4.21314i	0.891517	−	0.514717i	0.874438	+	0.485137i	$0.161230\pi$
$68$	0.932660	+	2.17971i	0.113102	+	0.264328i
$69$	−10.4693	+	8.77567i	−1.26036	+	1.05647i
$70$		0			0
$71$	9.67432			1.14813			0.574065	−	0.818810i	$-0.305366\pi$
$71$	9.67432			1.14813			0.574065	+	0.818810i	$0.305366\pi$
$72$	−8.44885	−	0.785398i	−0.995707	−	0.0925601i
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	−1.45185	+	0.297563i	−0.168774	+	0.0345910i
$75$	−1.30603	−	7.42914i	−0.150807	−	0.857843i
$76$	8.54216	−	11.4041i	0.979853	−	1.30814i
$77$		0			0
$78$	4.74097	+	12.0029i	0.536810	+	1.35907i
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	0.797988	−	0.602673i	$-0.205898\pi$
$79$	6.00000	+	3.46410i	0.675053	+	0.389742i	−0.122936	+	0.992415i	$0.539231\pi$
$80$	2.32371	+	2.21822i	0.259799	+	0.248004i
$81$	1.54464	+	8.86646i	0.171626	+	0.985162i
$82$	7.58404	−	6.72931i	0.837517	−	0.743128i
$83$	−5.18229			−0.568830			−0.284415	−	0.958701i	$-0.591799\pi$
$83$	−5.18229			−0.568830			−0.284415	+	0.958701i	$0.591799\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	8.40251	−	7.45554i	0.906066	−	0.803952i
$87$	−2.51015	+	6.88559i	−0.269117	+	0.738213i
$88$	−6.00000	−	2.83005i	−0.639602	−	0.301685i
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.999996	−	0.00273917i	$-0.999128\pi$
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.502370	−	0.864653i	$-0.667539\pi$
$90$	1.62461	−	2.99513i	0.171249	−	0.315714i
$91$		0			0
$92$	−12.6252	−	9.45679i	−1.31627	−	0.985938i
$93$	8.35713	−	1.46917i	0.866594	−	0.152345i
$94$	8.44975	−	1.73182i	0.871525	−	0.178623i
$95$	2.86085	+	4.95513i	0.293517	+	0.508386i
$96$	−1.34393	−	9.70535i	−0.137164	−	0.990548i
$97$	−4.37827			−0.444546			−0.222273	−	0.974984i	$-0.571348\pi$
$97$	−4.37827			−0.444546			−0.222273	+	0.974984i	$0.571348\pi$
$98$		0			0
$99$	−1.22896	+	6.92820i	−0.123515	+	0.696311i
$100$	8.00773	−	3.42637i	0.800773	−	0.342637i
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	−0.815959	−	0.578110i	$-0.803790\pi$
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	0.0926791	+	0.995696i	$0.470457\pi$
$102$	2.27414	+	1.80548i	0.225173	+	0.178769i
$103$	2.22304	+	1.28347i	0.219043	+	0.126465i	0.605507	−	0.795840i	$-0.292970\pi$
$103$	2.22304	+	1.28347i	0.219043	+	0.126465i	−0.386464	+	0.922304i	$0.626304\pi$
$104$	−12.2443	+	8.49353i	−1.20065	+	0.832859i
$105$		0			0
$106$	11.7003	+	3.89612i	1.13644	+	0.378424i
$107$	3.04995	−	5.28267i	0.294850	−	0.510695i	−0.680100	−	0.733119i	$-0.738064\pi$
$107$	3.04995	−	5.28267i	0.294850	−	0.510695i	0.974950	+	0.222424i	$0.0713970\pi$
$108$	−9.56070	+	4.07346i	−0.919978	+	0.391969i
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	0.705471	−	0.708739i	$-0.250736\pi$
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	−0.966521	+	0.256586i	$0.917402\pi$
$110$	1.99262	−	1.76806i	0.189989	−	0.168577i
$111$	−1.39105	+	1.16601i	−0.132033	+	0.110673i
$112$		0			0
$113$			7.09803i			0.667726i	0.942622	+	0.333863i	$0.108352\pi$
$113$			7.09803i			0.667726i	−0.942622	+	0.333863i	$0.891648\pi$
$114$	2.56337	−	17.2616i	0.240082	−	1.61670i
$115$	5.48569	−	3.16716i	0.511543	−	0.295340i
$116$	−8.40251	−	1.00710i	−0.780153	−	0.0935073i
$117$	12.0975	+	10.1722i	1.11841	+	0.940416i
$118$	−0.295860	+	0.888490i	−0.0272361	+	0.0817921i
$119$		0			0
$120$	3.79537	+	1.03698i	0.346469	+	0.0946629i
$121$	2.74943	−	4.76214i	0.249948	−	0.432922i
$122$	−1.32740	+	0.272057i	−0.120177	+	0.0246308i
$123$	4.25313	−	11.6667i	0.383492	−	1.05195i
$124$	3.85437	+	9.00799i	0.346132	+	0.808941i
$125$			7.51322i			0.672003i
$126$		0			0
$127$			4.16202i			0.369320i	0.982802	+	0.184660i	$0.0591184\pi$
$127$			4.16202i			0.369320i	−0.982802	+	0.184660i	$0.940882\pi$
$128$	10.5567	−	4.06893i	0.933089	−	0.359646i
$129$	4.71212	−	12.9258i	0.414879	−	1.13805i
$130$	−1.20147	−	5.86214i	−0.105376	−	0.514143i
$131$	−5.24594	+	9.08624i	−0.458340	+	0.793869i	−0.998873	−	0.0474541i	$-0.984889\pi$
$131$	−5.24594	+	9.08624i	−0.458340	+	0.793869i	0.540533	+	0.841323i	$0.318223\pi$
$132$	−8.11272	+	0.444463i	−0.706122	+	0.0386855i
$133$		0			0
$134$	11.3062	+	3.76488i	0.976707	+	0.325236i
$135$	0.00642439	−	4.17315i	0.000552924	−	0.359168i
$136$	−1.43035	+	3.03250i	−0.122652	+	0.260034i
$137$	−11.6844	+	6.74600i	−0.998267	+	0.576350i	−0.907735	−	0.419544i	$-0.862190\pi$
$137$	−11.6844	+	6.74600i	−0.998267	+	0.576350i	−0.0905318	+	0.995894i	$0.528857\pi$
$138$	−19.1098	−	2.83784i	−1.62674	−	0.241573i
$139$		−	7.57264i		−	0.642303i	−0.947028	−	0.321151i	$-0.895930\pi$
$139$		−	7.57264i		−	0.642303i	0.947028	−	0.321151i	$-0.104070\pi$
$140$		0			0
$141$	8.09591	−	6.78619i	0.681798	−	0.571501i
$142$	9.08044	+	10.2338i	0.762014	+	0.858801i
$143$	6.17860	+	10.7017i	0.516681	+	0.894917i
$144$	−7.09939	−	9.67464i	−0.591615	−	0.806220i
$145$	1.69914	−	2.94299i	0.141106	−	0.244402i
$146$	−0.631873	+	1.89756i	−0.0522942	+	0.157043i
$147$		0			0
$148$	−1.67750	−	1.25651i	−0.137889	−	0.103285i
$149$	−13.9442	−	8.05067i	−1.14235	−	0.659536i	−0.195339	−	0.980736i	$-0.562581\pi$
$149$	−13.9442	−	8.05067i	−1.14235	−	0.659536i	−0.947012	+	0.321199i	$0.895914\pi$
$150$	6.63292	−	8.35464i	0.541576	−	0.682154i
$151$	−15.0553	+	8.69219i	−1.22518	+	0.707360i	−0.966019	−	0.258473i	$-0.916781\pi$
$151$	−15.0553	+	8.69219i	−1.22518	+	0.707360i	−0.259166	+	0.965833i	$0.583448\pi$
$152$	20.0814	−	1.66790i	1.62882	−	0.135284i
$153$	3.50163	+	0.621137i	0.283090	+	0.0502160i
$154$		0			0
$155$	−3.93449			−0.316026
$156$	−8.24715	+	16.2813i	−0.660300	+	1.30354i
$157$	1.96109	+	3.39671i	0.156512	+	0.271087i	0.933609	−	0.358295i	$-0.116642\pi$
$157$	1.96109	+	3.39671i	0.156512	+	0.271087i	−0.777096	+	0.629381i	$0.783308\pi$
$158$	1.96724	+	9.59843i	0.156506	+	0.763610i
$159$	14.8754	−	2.61506i	1.17970	−	0.207388i
$160$	−0.165435	+	4.54014i	−0.0130788	+	0.358930i
$161$		0			0
$162$	−7.92940	+	9.95614i	−0.622992	+	0.782228i
$163$	6.32987	+	3.65455i	0.495793	+	0.286246i	0.726975	−	0.686664i	$-0.240926\pi$
$163$	6.32987	+	3.65455i	0.495793	+	0.286246i	−0.231181	+	0.972911i	$0.574259\pi$
$164$	14.2370	+	1.70641i	1.11172	+	0.133248i
$165$	1.11746	−	3.06531i	0.0869944	−	0.238634i
$166$	−4.86417	−	5.48199i	−0.377532	−	0.425485i
$167$	−8.37196			−0.647842			−0.323921	−	0.946084i	$-0.605001\pi$
$167$	−8.37196			−0.647842			−0.323921	+	0.946084i	$0.605001\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	−0.893604	−	1.00710i	−0.0685363	−	0.0772414i
$171$	−7.28935	−	20.0914i	−0.557430	−	1.53643i
$172$	15.7734	+	1.89056i	1.20271	+	0.144154i
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	0.0166803	−	0.999861i	$-0.494690\pi$
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	−0.857565	+	0.514376i	$0.828024\pi$
$174$	−9.63986	+	3.80759i	−0.730796	+	0.288653i
$175$		0			0
$176$	−2.63796	−	9.00331i	−0.198844	−	0.678650i
$177$	0.198581	+	1.12960i	0.0149262	+	0.0849056i
$178$	−4.64706	−	22.6736i	−0.348312	−	1.69946i
$179$	−10.5589	−	18.2885i	−0.789206	−	1.36694i	−0.926454	−	0.376408i	$-0.877159\pi$
$179$	−10.5589	−	18.2885i	−0.789206	−	1.36694i	0.137248	−	0.990537i	$-0.456174\pi$
$180$	4.69322	−	1.09270i	0.349812	−	0.0814453i
$181$	12.4075			0.922239			0.461120	−	0.887338i	$-0.347448\pi$
$181$	12.4075			0.922239			0.461120	+	0.887338i	$0.347448\pi$
$182$		0			0
$183$	−1.27181	+	1.06607i	−0.0940151	+	0.0788059i
$184$	−1.84648	−	22.2316i	−0.136124	−	1.63893i
$185$	0.728878	−	0.420818i	0.0535882	−	0.0309392i
$186$	9.39823	+	7.46145i	0.689112	+	0.547100i
$187$	2.40787	+	1.39019i	0.176081	+	0.101660i
$188$	9.76301	+	7.31290i	0.712041	+	0.533348i
$189$		0			0
$190$	−2.55646	+	7.67724i	−0.185465	+	0.556966i
$191$	3.04995	−	5.28267i	0.220687	−	0.382241i	−0.734330	−	0.678793i	$-0.762503\pi$
$191$	3.04995	−	5.28267i	0.220687	−	0.382241i	0.955017	+	0.296552i	$0.0958368\pi$
$192$	9.00519	−	10.5312i	0.649894	−	0.760025i
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	0.854185	−	0.519969i	$-0.174057\pi$
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	−0.877399	+	0.479761i	$0.840723\pi$
$194$	−4.10950	−	4.63147i	−0.295045	−	0.332520i
$195$	−4.70802	−	5.61665i	−0.337149	−	0.402217i
$196$		0			0
$197$			14.9111i			1.06237i	0.847256	+	0.531185i	$0.178253\pi$
$197$			14.9111i			1.06237i	−0.847256	+	0.531185i	$0.821747\pi$
$198$	−8.48239	+	5.20287i	−0.602817	+	0.369752i
$199$	−16.1940	+	9.34962i	−1.14796	+	0.662777i	−0.948390	−	0.317106i	$-0.897289\pi$
$199$	−16.1940	+	9.34962i	−1.14796	+	0.662777i	−0.199573	+	0.979883i	$0.563956\pi$
$200$	11.1407	+	5.25479i	0.787765	+	0.371570i
$201$	14.3743	−	2.52698i	1.01389	−	0.178239i
$202$	−11.2620	−	3.75017i	−0.792394	−	0.263861i
$203$		0			0
$204$	0.224639	+	4.10030i	0.0157278	+	0.287078i
$205$	−2.87897	+	4.98652i	−0.201076	+	0.348274i
$206$	0.728878	+	3.55629i	0.0507833	+	0.247778i
$207$	−22.2427	+	8.06983i	−1.54597	+	0.560892i
$208$	−20.4774	−	4.98029i	−1.41985	−	0.345321i
$209$		−	16.7097i		−	1.15583i
$210$		0			0
$211$			11.7243i			0.807132i	0.914950	+	0.403566i	$0.132229\pi$
$211$			11.7243i			0.807132i	−0.914950	+	0.403566i	$0.867771\pi$
$212$	6.86064	+	16.0339i	0.471191	+	1.10121i
$213$	15.7429	+	5.73911i	1.07869	+	0.393237i
$214$	8.45090	−	1.73205i	0.577691	−	0.118401i
$215$	−3.18967	+	5.52466i	−0.217533	+	0.376779i
$216$	−13.2828	−	6.29020i	−0.903782	−	0.427994i
$217$		0			0
$218$	2.43547	−	7.31389i	0.164951	−	0.495359i
$219$	0.424112	+	2.41249i	0.0286588	+	0.163021i
$220$	3.74061	+	0.448340i	0.252192	+	0.0302271i
$221$	5.40879	−	3.12277i	0.363835	−	0.210060i
$222$	−2.53911	−	0.377060i	−0.170414	−	0.0253066i
$223$		−	0.683260i		−	0.0457545i	−0.999738	−	0.0228772i	$-0.992717\pi$
$223$		−	0.683260i		−	0.0457545i	0.999738	−	0.0228772i	$-0.00728269\pi$
$224$		0			0
$225$	2.28191	−	12.8642i	0.152128	−	0.857610i
$226$	−7.50851	+	6.66230i	−0.499459	+	0.443170i
$227$	−4.37694	−	7.58108i	−0.290507	−	0.503174i	0.683422	−	0.730023i	$-0.260491\pi$
$227$	−4.37694	−	7.58108i	−0.290507	−	0.503174i	−0.973930	+	0.226850i	$0.927157\pi$
$228$	20.6659	−	13.4904i	1.36863	−	0.893420i
$229$	9.24927	−	16.0202i	0.611209	−	1.05864i	−0.379828	−	0.925057i	$-0.624017\pi$
$229$	9.24927	−	16.0202i	0.611209	−	1.05864i	0.991037	−	0.133588i	$-0.0426498\pi$
$230$	8.49926	+	2.83019i	0.560425	+	0.186617i
$231$		0			0
$232$	−6.82135	−	9.83371i	−0.447844	−	0.645615i
$233$	8.78072	+	5.06955i	0.575244	+	0.332117i	0.759241	−	0.650810i	$-0.225570\pi$
$233$	8.78072	+	5.06955i	0.575244	+	0.332117i	−0.183997	+	0.982927i	$0.558904\pi$
$234$	0.594419	+	22.3448i	0.0388584	+	1.46072i
$235$	−4.24206	+	2.44916i	−0.276722	+	0.159765i
$236$	−1.21757	+	0.520978i	−0.0792571	+	0.0339128i
$237$	7.70873	+	9.19649i	0.500736	+	0.597376i
$238$		0			0
$239$	−1.49470			−0.0966841			−0.0483421	−	0.998831i	$-0.515394\pi$
$239$	−1.49470			−0.0966841			−0.0483421	+	0.998831i	$0.515394\pi$
$240$	2.46544	+	4.98819i	0.159143	+	0.321986i
$241$	5.16686	+	8.94926i	0.332827	+	0.576472i	0.983065	−	0.183258i	$-0.0586643\pi$
$241$	5.16686	+	8.94926i	0.332827	+	0.576472i	−0.650238	+	0.759730i	$0.725331\pi$
$242$	7.61819	−	1.56138i	0.489716	−	0.100370i
$243$	−2.74629	+	15.3446i	−0.176174	+	0.984359i
$244$	−1.53370	−	1.14881i	−0.0981853	−	0.0735449i
$245$		0			0
$246$	16.3335	−	6.45146i	1.04138	−	0.411330i
$247$	−32.5062	−	18.7675i	−2.06832	−	1.19415i
$248$	−5.91117	+	12.5323i	−0.375360	+	0.795801i
$249$	−8.43310	−	3.07430i	−0.534426	−	0.194826i
$250$	−7.94771	+	7.05200i	−0.502658	+	0.446008i
$251$	26.9555			1.70142			0.850709	−	0.525636i	$-0.176173\pi$
$251$	26.9555			1.70142			0.850709	+	0.525636i	$0.176173\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	−4.40272	+	3.90653i	−0.276251	+	0.245117i
$255$	−1.54926	−	0.564784i	−0.0970183	−	0.0353682i
$256$	14.2129	+	7.34805i	0.888305	+	0.459253i
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	0.573506	−	0.819201i	$-0.305583\pi$
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	−0.422696	+	0.906271i	$0.638916\pi$
$258$	18.0962	−	7.14771i	1.12662	−	0.444997i
$259$		0			0
$260$	5.07343	−	6.77323i	0.314641	−	0.420058i
$261$	−8.16950	+	9.71577i	−0.505679	+	0.601391i
$262$	−14.5356	+	2.97914i	−0.898013	+	0.184052i
$263$	7.65516	+	13.2591i	0.472037	+	0.817592i	0.999488	−	0.0319931i	$-0.0101855\pi$
$263$	7.65516	+	13.2591i	0.472037	+	0.817592i	−0.527451	+	0.849586i	$0.676852\pi$
$264$	−8.08487	−	8.16471i	−0.497589	−	0.502503i
$265$	−7.00325			−0.430206
$266$		0			0
$267$	−18.2097	−	21.7241i	−1.11442	−	1.32949i
$268$	6.62954	+	15.4938i	0.404964	+	0.946435i
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.633487	+	0.773754i	$0.718377\pi$
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.986834	+	0.161739i	$0.948290\pi$
$270$	4.42052	−	3.91018i	0.269024	−	0.237966i
$271$	17.0488	+	9.84312i	1.03564	+	0.597927i	0.918595	−	0.395199i	$-0.129325\pi$
$271$	17.0488	+	9.84312i	1.03564	+	0.597927i	0.117045	+	0.993127i	$0.462658\pi$
$272$	−4.55042	+	1.33327i	−0.275910	+	0.0808412i
$273$		0			0
$274$	−18.1033	−	6.02825i	−1.09366	−	0.364180i
$275$	5.10721	−	8.84595i	0.307977	−	0.533431i
$276$	−14.9348	−	22.8786i	−0.898969	−	1.37713i
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	0.992965	−	0.118406i	$-0.0377785\pi$
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	−0.599025	+	0.800730i	$0.704445\pi$
$278$	8.01057	−	7.10778i	0.480442	−	0.426296i
$279$	14.4710	+	2.56695i	0.866358	+	0.153679i
$280$		0			0
$281$			2.86670i			0.171013i	0.996338	+	0.0855066i	$0.0272509\pi$
$281$			2.86670i			0.171013i	−0.996338	+	0.0855066i	$0.972749\pi$
$282$	14.7776	+	2.19449i	0.879991	+	0.130680i
$283$	−1.72374	+	0.995200i	−0.102466	+	0.0591585i	−0.550357	−	0.834929i	$-0.685508\pi$
$283$	−1.72374	+	0.995200i	−0.102466	+	0.0591585i	0.447892	+	0.894088i	$0.352175\pi$
$284$	−2.30260	+	19.2111i	−0.136634	+	1.13997i
$285$	1.71589	+	9.76059i	0.101641	+	0.578167i
$286$	−5.52122	+	16.5806i	−0.326477	+	0.980433i
$287$		0			0
$288$	3.57056	−	16.5907i	0.210397	−	0.977616i
$289$	−7.79738	+	13.5055i	−0.458669	+	0.794439i
$290$	4.70802	−	0.964931i	0.276465	−	0.0566627i
$291$	−7.12472	−	2.59733i	−0.417659	−	0.152258i
$292$	−2.60038	+	1.11266i	−0.152176	+	0.0651135i
$293$		−	16.7482i		−	0.978441i	−0.872160	−	0.489221i	$-0.837281\pi$
$293$		−	16.7482i		−	0.978441i	0.872160	−	0.489221i	$-0.162719\pi$
$294$		0			0
$295$		−	0.531807i		−	0.0309630i
$296$	−0.245340	−	2.95389i	−0.0142601	−	0.171691i
$297$	−6.10991	+	10.5451i	−0.354533	+	0.611891i
$298$	−4.57193	−	22.3070i	−0.264845	−	1.29221i
$299$	−20.7769	+	35.9867i	−1.20156	+	2.08117i
$300$	15.0635	−	0.825270i	0.869694	−	0.0476470i
$301$		0			0
$302$	−23.3260	−	7.76737i	−1.34226	−	0.446962i
$303$	−14.3182	+	2.51710i	−0.822557	+	0.144604i
$304$	20.6130	+	19.6772i	1.18224	+	1.12857i
$305$	0.666400	−	0.384746i	0.0381579	−	0.0220305i
$306$	2.62961	+	4.28714i	0.150325	+	0.245079i
$307$			15.4869i			0.883885i	0.897043	+	0.441942i	$0.145710\pi$
$307$			15.4869i			0.883885i	−0.897043	+	0.441942i	$0.854290\pi$
$308$		0			0
$309$	2.85614	+	3.40737i	0.162480	+	0.193838i
$310$	−3.69296	−	4.16202i	−0.209746	−	0.236387i
$311$	−5.44973	−	9.43920i	−0.309026	−	0.535248i	0.669124	−	0.743151i	$-0.266670\pi$
$311$	−5.44973	−	9.43920i	−0.309026	−	0.535248i	−0.978149	+	0.207903i	$0.933336\pi$
$312$	−24.9637	+	6.55772i	−1.41329	+	0.371258i
$313$	−16.9011	+	29.2736i	−0.955308	+	1.65464i	−0.221646	+	0.975127i	$0.571143\pi$
$313$	−16.9011	+	29.2736i	−0.955308	+	1.65464i	−0.733662	+	0.679514i	$0.762190\pi$
$314$	−1.75244	+	5.26270i	−0.0988958	+	0.296991i
$315$		0			0
$316$	−8.30704	+	11.0902i	−0.467307	+	0.623874i
$317$	8.04243	+	4.64330i	0.451708	+	0.260794i	0.708551	−	0.705659i	$-0.249349\pi$
$317$	8.04243	+	4.64330i	0.451708	+	0.260794i	−0.256843	+	0.966453i	$0.582682\pi$
$318$	16.7285	+	13.2811i	0.938089	+	0.744768i
$319$	−8.59476	+	4.96218i	−0.481214	+	0.277829i
$320$	−4.95798	+	4.08643i	−0.277160	+	0.228439i
$321$	8.09701	−	6.78712i	0.451931	−	0.378820i
$322$		0			0
$323$	−8.44536			−0.469912
$324$	−17.9745	+	0.956999i	−0.998586	+	0.0531666i
$325$	−11.4723	−	19.8706i	−0.636369	−	1.10222i
$326$	2.07540	+	10.1261i	0.114946	+	0.560835i
$327$	−1.63468	−	9.29864i	−0.0903981	−	0.514216i
$328$	11.5579	+	16.6619i	0.638178	+	0.920002i
$329$		0			0
$330$	4.29145	−	1.69505i	0.236236	−	0.0933096i
$331$	−0.878968	−	0.507473i	−0.0483125	−	0.0278932i	0.475649	−	0.879635i	$-0.342213\pi$
$331$	−0.878968	−	0.507473i	−0.0483125	−	0.0278932i	−0.523962	+	0.851742i	$0.675547\pi$
$332$	1.23345	−	10.2909i	0.0676942	−	0.564788i
$333$	−2.95536	+	1.07223i	−0.161953	+	0.0587579i
$334$	−7.85803	−	8.85611i	−0.429972	−	0.484585i
$335$	−6.76735			−0.369740
$336$		0			0
$337$	−12.6597			−0.689620			−0.344810	−	0.938673i	$-0.612057\pi$
$337$	−12.6597			−0.689620			−0.344810	+	0.938673i	$0.612057\pi$
$338$	13.8520	+	15.6114i	0.753449	+	0.849148i
$339$	−4.21077	+	11.5506i	−0.228698	+	0.627340i
$340$	0.226598	−	1.89056i	0.0122890	−	0.102530i
$341$	9.95091	+	5.74516i	0.538872	+	0.311118i
$342$	14.4115	−	26.5690i	0.779283	−	1.43669i
$343$		0			0
$344$	12.8052	+	18.4601i	0.690411	+	0.995302i
$345$	10.8057	−	1.89962i	0.581758	−	0.102272i
$346$	−3.62632	−	17.6933i	−0.194952	−	0.951197i
$347$	−12.8143	−	22.1950i	−0.687907	−	1.19149i	−0.972514	−	0.232846i	$-0.925196\pi$
$347$	−12.8143	−	22.1950i	−0.687907	−	1.19149i	0.284607	−	0.958644i	$-0.408137\pi$
$348$	−13.0759	−	6.62348i	−0.700941	−	0.355056i
$349$	−28.1235			−1.50542			−0.752709	−	0.658354i	$-0.771253\pi$
$349$	−28.1235			−1.50542			−0.752709	+	0.658354i	$0.771253\pi$
$350$		0			0
$351$	13.6517	+	23.7297i	0.728672	+	1.26660i
$352$	7.04795	−	11.2411i	0.375657	−	0.599155i
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	−0.243335	−	0.969942i	$-0.578241\pi$
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	0.718327	+	0.695705i	$0.244908\pi$
$354$	−1.00853	+	1.27032i	−0.0536028	+	0.0675166i
$355$	−6.72874	−	3.88484i	−0.357124	−	0.206186i
$356$	19.6230	−	26.1975i	1.04002	−	1.38847i
$357$		0			0
$358$	9.43543	−	28.3353i	0.498678	−	1.49757i
$359$	−13.4197	+	23.2436i	−0.708265	+	1.22675i	0.257235	+	0.966349i	$0.417188\pi$
$359$	−13.4197	+	23.2436i	−0.708265	+	1.22675i	−0.965500	+	0.260402i	$0.916145\pi$
$360$	5.56101	+	3.93900i	0.293091	+	0.207604i
$361$	15.8778	+	27.5012i	0.835675	+	1.44743i
$362$	11.6458	+	13.1250i	0.612090	+	0.689834i
$363$	7.29917	−	6.11835i	0.383107	−	0.321130i
$364$		0			0
$365$		−	1.13579i		−	0.0594499i
$366$	−2.32146	−	0.344739i	−0.121345	−	0.0180198i
$367$	−11.5631	+	6.67596i	−0.603589	+	0.348482i	−0.770452	−	0.637498i	$-0.779969\pi$
$367$	−11.5631	+	6.67596i	−0.603589	+	0.348482i	0.166863	+	0.985980i	$0.446636\pi$
$368$	21.7841	−	22.8201i	1.13558	−	1.18958i
$369$	13.8422	−	16.4621i	0.720594	−	0.856982i
$370$	1.12929	+	0.376045i	0.0587089	+	0.0195496i
$371$		0			0
$372$	0.928355	+	16.9452i	0.0481330	+	0.878565i
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	−0.403753	−	0.914868i	$-0.632295\pi$
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	0.994176	−	0.107773i	$-0.0343720\pi$
$374$	0.789478	+	3.85197i	0.0408230	+	0.199180i
$375$	−4.45708	+	12.2262i	−0.230162	+	0.631358i
$376$	1.42788	+	17.1916i	0.0736371	+	0.886589i
$377$			22.2931i			1.14815i
$378$		0			0
$379$		−	1.98122i		−	0.101768i	−0.998705	−	0.0508842i	$-0.983796\pi$
$379$		−	1.98122i		−	0.101768i	0.998705	−	0.0508842i	$-0.0162040\pi$
$380$	−10.5208	+	4.50165i	−0.539703	+	0.230930i
$381$	−2.46904	+	6.77282i	−0.126493	+	0.346982i
$382$	8.45090	−	1.73205i	0.432386	−	0.0886194i
$383$	14.4104	−	24.9596i	0.736339	−	1.27538i	−0.217795	−	0.975995i	$-0.569886\pi$
$383$	14.4104	−	24.9596i	0.736339	−	1.27538i	0.954134	−	0.299381i	$-0.0967803\pi$
$384$	19.5926	−	0.358762i	0.999832	−	0.0183080i
$385$		0			0
$386$	0.288191	−	0.865458i	0.0146685	−	0.0440506i
$387$	15.3360	−	18.2387i	0.779573	−	0.927124i
$388$	1.04208	−	8.69432i	0.0529036	−	0.441387i
$389$	−1.69719	+	0.979873i	−0.0860509	+	0.0496815i	−0.542408	−	0.840115i	$-0.682487\pi$
$389$	−1.69719	+	0.979873i	−0.0860509	+	0.0496815i	0.456357	+	0.889797i	$0.349154\pi$
$390$	1.52246	−	10.2522i	0.0770927	−	0.519138i
$391$			9.34962i			0.472831i
$392$		0			0
$393$	−13.9269	+	11.6739i	−0.702520	+	0.588870i
$394$	−15.7734	+	13.9957i	−0.794652	+	0.705095i
$395$	−2.78210	−	4.81874i	−0.139983	−	0.242457i
$396$	−13.4654	−	4.08945i	−0.676663	−	0.205503i
$397$	2.28155	−	3.95176i	0.114508	−	0.198333i	−0.803075	−	0.595878i	$-0.796804\pi$
$397$	2.28155	−	3.95176i	0.114508	−	0.198333i	0.917583	+	0.397545i	$0.130138\pi$
$398$	−25.0902	−	8.35485i	−1.25766	−	0.418791i
$399$		0			0
$400$	4.89811	+	16.7172i	0.244906	+	0.835858i
$401$	−23.1931	−	13.3905i	−1.15821	−	0.668692i	−0.207335	−	0.978270i	$-0.566479\pi$
$401$	−23.1931	−	13.3905i	−1.15821	−	0.668692i	−0.950874	+	0.309578i	$0.899812\pi$
$402$	16.1650	+	12.8338i	0.806239	+	0.640089i
$403$	22.3527	−	12.9053i	1.11347	−	0.642860i
$404$	−6.60364	−	15.4333i	−0.328544	−	0.767835i
$405$	2.48610	−	6.78712i	0.123535	−	0.337255i
$406$		0			0
$407$	−2.45792			−0.121835
$408$	−4.12658	+	4.08622i	−0.204296	+	0.202298i
$409$	−9.02122	−	15.6252i	−0.446071	−	0.772617i	0.552055	−	0.833807i	$-0.313844\pi$
$409$	−9.02122	−	15.6252i	−0.446071	−	0.772617i	−0.998126	+	0.0611902i	$0.980510\pi$
$410$	−7.97713	+	1.63495i	−0.393962	+	0.0807444i
$411$	−23.0159	+	4.04614i	−1.13529	+	0.199582i
$412$	−3.07782	+	4.10901i	−0.151633	+	0.202436i
$413$		0			0
$414$	−29.4138	−	15.9545i	−1.44561	−	0.784123i
$415$	3.60442	+	2.08101i	0.176934	+	0.102153i
$416$	−13.9520	−	26.3362i	−0.684055	−	1.29124i
$417$	4.49233	−	12.3229i	0.219990	−	0.603454i
$418$	17.6760	−	15.6839i	0.864564	−	0.767127i
$419$	−17.5395			−0.856861			−0.428430	−	0.903575i	$-0.640933\pi$
$419$	−17.5395			−0.856861			−0.428430	+	0.903575i	$0.640933\pi$
$420$		0			0
$421$	15.4006			0.750582			0.375291	−	0.926907i	$-0.377543\pi$
$421$	15.4006			0.750582			0.375291	+	0.926907i	$0.377543\pi$
$422$	−12.4023	+	11.0046i	−0.603734	+	0.535693i
$423$	17.2002	−	6.24037i	0.836301	−	0.303417i
$424$	−10.5217	+	22.3070i	−0.510978	+	1.08333i
$425$	−4.47089	−	2.58127i	−0.216870	−	0.125210i
$426$	8.70551	+	22.0402i	0.421784	+	1.06785i
$427$		0			0
$428$	9.76434	+	7.31389i	0.471977	+	0.353530i
$429$	3.70583	+	21.0801i	0.178919	+	1.01775i
$430$	−8.83802	+	1.81139i	−0.426207	+	0.0873532i
$431$	4.50180	+	7.79735i	0.216844	+	0.375585i	0.953841	−	0.300311i	$-0.0970903\pi$
$431$	4.50180	+	7.79735i	0.216844	+	0.375585i	−0.736997	+	0.675896i	$0.763757\pi$
$432$	−5.81346	−	19.9550i	−0.279700	−	0.960087i
$433$	−6.15889			−0.295977			−0.147989	−	0.988989i	$-0.547280\pi$
$433$	−6.15889			−0.295977			−0.147989	+	0.988989i	$0.547280\pi$
$434$		0			0
$435$	4.51087	−	3.78113i	0.216280	−	0.181291i
$436$	10.0228	−	4.28860i	0.480006	−	0.205387i
$437$	48.6621	−	28.0951i	2.32782	−	1.34397i
$438$	−2.15393	+	2.71304i	−0.102919	+	0.129634i
$439$	25.3306	+	14.6246i	1.20896	+	0.697996i	0.962533	−	0.271164i	$-0.0874086\pi$
$439$	25.3306	+	14.6246i	1.20896	+	0.697996i	0.246432	+	0.969160i	$0.420742\pi$
$440$	3.03671	+	4.37775i	0.144770	+	0.208701i
$441$		0			0
$442$	8.38012	+	2.79052i	0.398602	+	0.132731i
$443$	−3.60820	+	6.24958i	−0.171431	+	0.296927i	−0.938920	−	0.344135i	$-0.888172\pi$
$443$	−3.60820	+	6.24958i	−0.171431	+	0.296927i	0.767490	+	0.641061i	$0.221506\pi$
$444$	−1.98437	−	3.03986i	−0.0941741	−	0.144265i
$445$	6.57193	+	11.3829i	0.311539	+	0.539602i
$446$	0.722774	−	0.641317i	0.0342243	−	0.0303672i
$447$	−17.9153	−	21.3729i	−0.847365	−	1.01090i
$448$		0			0
$449$			4.43423i			0.209264i	0.994511	+	0.104632i	$0.0333665\pi$
$449$			4.43423i			0.209264i	−0.994511	+	0.104632i	$0.966634\pi$
$450$	15.7499	−	9.66058i	0.742459	−	0.455404i
$451$	14.5627	−	8.40777i	0.685730	−	0.395907i
$452$	−14.0952	−	1.68941i	−0.662981	−	0.0794634i
$453$	−29.6559	+	5.21344i	−1.39335	+	0.244949i
$454$	3.91125	−	11.7458i	0.183564	−	0.551256i
$455$		0			0
$456$	33.6678	+	9.19877i	1.57664	+	0.430772i
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	−0.980392	−	0.197055i	$-0.936862\pi$
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	0.660851	+	0.750517i	$0.270196\pi$
$458$	25.6281	−	5.25261i	1.19752	−	0.245438i
$459$	5.32969	+	3.08805i	0.248768	+	0.144138i
$460$	4.98366	+	11.6472i	0.232364	+	0.543055i
$461$			5.25789i			0.244885i	0.992476	+	0.122442i	$0.0390726\pi$
$461$			5.25789i			0.244885i	−0.992476	+	0.122442i	$0.960927\pi$
$462$		0			0
$463$			15.8863i			0.738299i	0.929370	+	0.369149i	$0.120351\pi$
$463$			15.8863i			0.738299i	−0.929370	+	0.369149i	$0.879649\pi$
$464$	3.99979	−	16.4459i	0.185686	−	0.763481i
$465$	−6.40256	−	2.33406i	−0.296911	−	0.108240i
$466$	2.87897	+	14.0469i	0.133366	+	0.650708i
$467$	13.5384	−	23.4491i	0.626481	−	1.08510i	−0.361771	−	0.932267i	$-0.617828\pi$
$467$	13.5384	−	23.4491i	0.626481	−	1.08510i	0.988252	−	0.152830i	$-0.0488388\pi$
$468$	−23.0791	+	21.6019i	−1.06683	+	0.998548i
$469$		0			0
$470$	−6.57245	−	2.18858i	−0.303164	−	0.100951i
$471$	1.17623	+	6.69082i	0.0541979	+	0.308297i
$472$	−1.69393	−	0.798987i	−0.0779696	−	0.0367763i
$473$	16.1343	−	9.31514i	0.741856	−	0.428311i
$474$	−2.49281	+	16.7865i	−0.114499	+	0.771029i
$475$			31.0263i			1.42358i
$476$		0			0
$477$	25.7579	+	4.56908i	1.17937	+	0.209204i
$478$	−1.40294	−	1.58114i	−0.0641692	−	0.0723196i
$479$	7.63026	+	13.2160i	0.348635	+	0.603854i	0.986007	−	0.166702i	$-0.0533119\pi$
$479$	7.63026	+	13.2160i	0.348635	+	0.603854i	−0.637372	+	0.770556i	$0.719979\pi$
$480$	−2.96257	+	7.28999i	−0.135222	+	0.332741i
$481$	−2.76061	+	4.78152i	−0.125873	+	0.218019i
$482$	−4.61712	+	13.8655i	−0.210304	+	0.631558i
$483$		0			0
$484$	8.80221	+	6.59322i	0.400100	+	0.299692i
$485$	3.04520	+	1.75815i	0.138275	+	0.0798334i
$486$	−18.8097	+	11.4976i	−0.853227	+	0.521540i
$487$	5.25172	−	3.03208i	0.237978	−	0.137397i	−0.376269	−	0.926511i	$-0.622793\pi$
$487$	5.25172	−	3.03208i	0.237978	−	0.137397i	0.614247	+	0.789114i	$0.289460\pi$
$488$	−0.224310	−	2.70068i	−0.0101540	−	0.122254i
$489$	8.13254	+	9.70209i	0.367766	+	0.438744i
$490$		0			0
$491$	4.03833			0.182247			0.0911235	−	0.995840i	$-0.470954\pi$
$491$	4.03833			0.182247			0.0911235	+	0.995840i	$0.470954\pi$
$492$	22.1554	+	11.2226i	0.998841	+	0.505955i
$493$	2.50797	+	4.34393i	0.112953	+	0.195641i
$494$	−10.6579	−	52.0015i	−0.479523	−	2.33966i
$495$	3.63688	−	4.32524i	0.163466	−	0.194405i
$496$	−18.8053	+	5.50994i	−0.844384	+	0.247404i
$497$		0			0
$498$	−4.66333	−	11.8064i	−0.208969	−	0.529056i
$499$	33.3430	+	19.2506i	1.49264	+	0.861776i	0.999964	−	0.00843800i	$-0.00268593\pi$
$499$	33.3430	+	19.2506i	1.49264	+	0.861776i	0.492675	+	0.870214i	$0.336019\pi$
$500$	−14.9197	−	1.78823i	−0.667227	−	0.0799723i
$501$	−13.6236	−	4.96651i	−0.608658	−	0.221887i
$502$	25.3008	+	28.5144i	1.12923	+	1.27266i
$503$	14.3498			0.639827			0.319914	−	0.947447i	$-0.396346\pi$
$503$	14.3498			0.639827			0.319914	+	0.947447i	$0.396346\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	−17.3633	−	19.5687i	−0.771891	−	0.869933i
$507$	24.0155	+	8.75487i	1.06656	+	0.388817i
$508$	−8.26489	−	0.990610i	−0.366695	−	0.0439512i
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	0.713656	−	0.700496i	$-0.247038\pi$
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	−0.249819	+	0.968292i	$0.580371\pi$
$510$	−0.856707	−	2.16897i	−0.0379356	−	0.0960435i
$511$		0			0
$512$	5.56740	+	21.9318i	0.246047	+	0.969258i
$513$	0.0569891	−	37.0189i	0.00251613	−	1.63442i
$514$	0.792689	+	3.86763i	0.0349640	+	0.170594i
$515$	−1.03079	−	1.78538i	−0.0454220	−	0.0786732i
$516$	24.5464	+	12.4338i	1.08059	+	0.547366i
$517$	14.3051			0.629137
$518$		0			0
$519$	−14.2099	−	16.9524i	−0.623746	−	0.744126i
$520$	11.9269	−	0.990610i	0.523030	−	0.0434411i
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.962582	−	0.270990i	$-0.912649\pi$
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.246606	+	0.969116i	$0.579316\pi$
$522$	−17.9456	+	0.477392i	−0.785459	+	0.0208949i
$523$	−31.7039	−	18.3043i	−1.38631	−	0.800389i	−0.393417	−	0.919360i	$-0.628707\pi$
$523$	−31.7039	−	18.3043i	−1.38631	−	0.800389i	−0.992898	+	0.118971i	$0.962040\pi$
$524$	−16.7947	−	12.5800i	−0.733682	−	0.549558i
$525$		0			0
$526$	−6.84068	+	20.5430i	−0.298268	+	0.895719i
$527$	2.90370	−	5.02935i	0.126487	−	0.219082i
$528$	1.04832	−	16.2159i	0.0456221	−	0.705708i
$529$	−19.6033	−	33.9539i	−0.852316	−	1.47625i
$530$	−6.57334	−	7.40826i	−0.285528	−	0.321794i
$531$	−0.346963	+	1.95599i	−0.0150569	+	0.0848825i
$532$		0			0
$533$		−	37.7727i		−	1.63612i
$534$	5.88857	−	39.6533i	0.254823	−	1.71597i
$535$	−4.24264	+	2.44949i	−0.183425	+	0.105901i
$536$	−10.1673	+	21.5556i	−0.439159	+	0.931061i
$537$	−6.33303	−	36.0245i	−0.273291	−	1.55457i
$538$	−41.1744	−	13.7108i	−1.77515	−	0.591113i
$539$		0			0
$540$	8.28546	+	1.00602i	0.356549	+	0.0432921i
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	−0.154589	−	0.987979i	$-0.549405\pi$
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	0.932909	−	0.360111i	$-0.117261\pi$
$542$	5.58985	+	27.2736i	0.240105	+	1.17150i
$543$	20.1906	+	7.36050i	0.866460	+	0.315869i
$544$	−5.68145	−	3.56215i	−0.243590	−	0.152726i
$545$			4.37775i			0.187522i
$546$		0			0
$547$		−	31.3917i		−	1.34221i	−0.741361	−	0.671106i	$-0.765820\pi$
$547$		−	31.3917i		−	1.34221i	0.741361	−	0.671106i	$-0.234180\pi$
$548$	−10.6151	−	24.8084i	−0.453454	−	1.05976i
$549$	−2.70203	+	0.980320i	−0.115320	+	0.0418391i
$550$	14.1512	−	2.90036i	0.603410	−	0.123672i
$551$	15.0726	−	26.1065i	0.642115	−	1.11218i
$552$	10.1837	−	37.2726i	0.433447	−	1.58643i
$553$		0			0
$554$	−5.85888	+	17.5946i	−0.248920	+	0.747525i
$555$	1.43574	−	0.252400i	0.0609437	−	0.0107138i
$556$	15.0376	+	1.80238i	0.637738	+	0.0764378i
$557$	−30.5691	+	17.6491i	−1.29526	+	0.747816i	−0.979581	−	0.201051i	$-0.935564\pi$
$557$	−30.5691	+	17.6491i	−1.29526	+	0.747816i	−0.315675	+	0.948867i	$0.602231\pi$
$558$	10.8673	+	17.7173i	0.460049	+	0.750032i
$559$		−	41.8491i		−	1.77003i
$560$		0			0
$561$	3.09361	+	3.69066i	0.130612	+	0.155820i
$562$	−3.03249	+	2.69073i	−0.127918	+	0.113501i
$563$	−13.2232	−	22.9032i	−0.557290	−	0.965254i	−0.997721	−	0.0674681i	$-0.978508\pi$
$563$	−13.2232	−	22.9032i	−0.557290	−	0.965254i	0.440432	−	0.897786i	$-0.354825\pi$
$564$	11.5490	+	17.6919i	0.486301	+	0.744965i
$565$	2.85030	−	4.93686i	0.119913	−	0.207695i
$566$	−2.67067	−	0.889314i	−0.112257	−	0.0373807i
$567$		0			0
$568$	−22.4834	+	15.5961i	−0.943382	+	0.654396i
$569$	23.7332	+	13.7024i	0.994948	+	0.574434i	0.906750	−	0.421669i	$-0.138556\pi$
$569$	23.7332	+	13.7024i	0.994948	+	0.574434i	0.0881985	+	0.996103i	$0.471889\pi$
$570$	−8.71449	+	10.9765i	−0.365010	+	0.459757i
$571$	24.3299	−	14.0469i	1.01817	−	0.587843i	0.104599	−	0.994514i	$-0.466644\pi$
$571$	24.3299	−	14.0469i	1.01817	−	0.587843i	0.913574	+	0.406672i	$0.133311\pi$
$572$	−22.7218	+	9.72227i	−0.950046	+	0.406509i
$573$	8.09701	−	6.78712i	0.338257	−	0.283536i
$574$		0			0
$575$	34.3483			1.43242
$576$	20.9015	−	11.7952i	0.870897	−	0.491466i
$577$	11.4154	+	19.7721i	0.475231	+	0.823124i	0.999598	−	0.0283688i	$-0.00903129\pi$
$577$	11.4154	+	19.7721i	0.475231	+	0.823124i	−0.524367	+	0.851492i	$0.675698\pi$
$578$	−21.6052	+	4.42809i	−0.898658	+	0.184184i
$579$	−0.193433	−	1.10031i	−0.00803880	−	0.0457275i
$580$	5.43974	+	4.07459i	0.225873	+	0.169188i
$581$		0			0
$582$	−3.93982	−	9.97464i	−0.163311	−	0.413462i
$583$	17.7123	+	10.2262i	0.733568	+	0.423526i
$584$	−3.61776	−	1.70641i	−0.149704	−	0.0706116i
$585$	−4.32935	−	11.9329i	−0.178997	−	0.493364i
$586$	17.7168	−	15.7201i	0.731874	−	0.649391i
$587$	−28.4011			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$587$	−28.4011			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	0.562562	−	0.499161i	0.0231603	−	0.0205501i
$591$	−8.84572	+	24.2647i	−0.363864	+	0.998115i
$592$	2.89443	−	3.03208i	0.118960	−	0.124618i
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	0.860389	−	0.509638i	$-0.170221\pi$
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	−0.0111655	+	0.999938i	$0.503554\pi$
$594$	−16.8898	+	3.43456i	−0.692998	+	0.140922i
$595$		0			0
$596$	19.3058	−	25.7740i	0.790796	−	1.05574i
$597$	−31.8989	+	5.60775i	−1.30553	+	0.229510i
$598$	−57.5694	+	11.7991i	−2.35419	+	0.482501i
$599$	19.5625	+	33.8832i	0.799300	+	1.38443i	0.920072	+	0.391749i	$0.128130\pi$
$599$	19.5625	+	33.8832i	0.799300	+	1.38443i	−0.120772	+	0.992680i	$0.538537\pi$
$600$	15.0118	+	15.1601i	0.612855	+	0.618907i
$601$	−4.88356			−0.199204			−0.0996022	−	0.995027i	$-0.531757\pi$
$601$	−4.88356			−0.199204			−0.0996022	+	0.995027i	$0.531757\pi$
$602$		0			0
$603$	24.8903	+	4.41518i	1.01361	+	0.179800i
$604$	−13.6775	−	31.9655i	−0.556529	−	1.30066i
$605$	−3.82459	+	2.20813i	−0.155492	+	0.0897732i
$606$	−16.1019	−	12.7836i	−0.654095	−	0.519299i
$607$	−27.4754	−	15.8630i	−1.11519	−	0.643857i	−0.175024	−	0.984564i	$-0.556000\pi$
$607$	−27.4754	−	15.8630i	−1.11519	−	0.643857i	−0.940170	+	0.340707i	$0.889334\pi$
$608$	−1.46753	+	40.2744i	−0.0595161	+	1.63334i
$609$		0			0
$610$	1.03249	+	0.343811i	0.0418042	+	0.0139205i
$611$	16.0667	−	27.8284i	0.649990	−	1.12582i
$612$	−2.06687	+	6.80565i	−0.0835485	+	0.275102i
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	−0.979079	−	0.203479i	$-0.934775\pi$
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	0.313322	−	0.949647i	$-0.398558\pi$
$614$	−16.3825	+	14.5362i	−0.661145	+	0.586634i
$615$	−7.64308	+	6.40662i	−0.308199	+	0.258340i
$616$		0			0
$617$		−	14.3990i		−	0.579680i	−0.957075	−	0.289840i	$-0.906398\pi$
$617$		−	14.3990i		−	0.579680i	0.957075	−	0.289840i	$-0.0936021\pi$
$618$	−0.923606	+	6.21951i	−0.0371529	+	0.250185i
$619$	21.3838	−	12.3460i	0.859489	−	0.496226i	−0.00435197	−	0.999991i	$-0.501385\pi$
$619$	21.3838	−	12.3460i	0.859489	−	0.496226i	0.863841	+	0.503764i	$0.168052\pi$
$620$	0.936455	−	7.81306i	0.0376089	−	0.313780i
$621$	−40.9826	−	0.0630910i	−1.64457	−	0.00253175i
$622$	4.86990	−	14.6246i	0.195265	−	0.586395i
$623$		0			0
$624$	−30.3682	−	20.2522i	−1.21570	−	0.810738i
$625$	−7.87046	+	13.6320i	−0.314818	+	0.545281i
$626$	−46.8301	+	9.59805i	−1.87171	+	0.383615i
$627$	9.91272	−	27.1916i	0.395876	−	1.08593i
$628$	−7.21190	+	3.08585i	−0.287786	+	0.123139i
$629$			1.24227i			0.0495327i
$630$		0			0
$631$			15.8863i			0.632423i	0.948689	+	0.316212i	$0.102411\pi$
$631$			15.8863i			0.632423i	−0.948689	+	0.316212i	$0.897589\pi$
$632$	−19.5287	+	1.62199i	−0.776809	+	0.0645192i
$633$	−6.95521	+	19.0788i	−0.276445	+	0.758315i
$634$	2.63690	+	12.8658i	0.104725	+	0.510966i
$635$	1.67131	−	2.89479i	0.0663239	−	0.114876i
$636$	1.65244	+	30.1618i	0.0655235	+	1.19599i
$637$		0			0
$638$	−13.3163	−	4.43423i	−0.527197	−	0.175553i
$639$	22.2137	+	18.6784i	0.878761	+	0.738906i
$640$	−8.97638	−	1.40913i	−0.354823	−	0.0557006i
$641$	16.8007	−	9.69989i	0.663588	−	0.383122i	−0.130055	−	0.991507i	$-0.541515\pi$
$641$	16.8007	−	9.69989i	0.663588	−	0.383122i	0.793643	+	0.608384i	$0.208182\pi$
$642$	14.7796	+	2.19479i	0.583303	+	0.0866213i
$643$		−	37.0568i		−	1.46138i	−0.682710	−	0.730690i	$-0.739199\pi$
$643$		−	37.0568i		−	1.46138i	0.682710	−	0.730690i	$-0.260801\pi$
$644$		0			0
$645$	−8.46792	+	7.09803i	−0.333424	+	0.279485i
$646$	−7.92692	−	8.93376i	−0.311881	−	0.351494i
$647$	22.7029	+	39.3225i	0.892542	+	1.54593i	0.836818	+	0.547481i	$0.184413\pi$
$647$	22.7029	+	39.3225i	0.892542	+	1.54593i	0.0557235	+	0.998446i	$0.482253\pi$
$648$	−17.8835	−	18.1158i	−0.702529	−	0.711655i
$649$	−0.776548	+	1.34502i	−0.0304822	+	0.0527967i
$650$	10.2517	−	30.7866i	0.402105	−	1.20755i
$651$		0			0
$652$	−8.76374	+	11.6999i	−0.343215	+	0.458205i
$653$	−0.855070	−	0.493675i	−0.0334615	−	0.0193190i	0.483176	−	0.875523i	$-0.339483\pi$
$653$	−0.855070	−	0.493675i	−0.0334615	−	0.0193190i	−0.516637	+	0.856204i	$0.672816\pi$
$654$	8.30205	−	10.4570i	0.324636	−	0.408903i
$655$	7.29738	−	4.21314i	0.285132	−	0.164621i
$656$	−6.77712	+	27.8654i	−0.264602	+	1.08796i
$657$	−0.741015	+	4.17743i	−0.0289097	+	0.162977i
$658$		0			0
$659$	−6.67629			−0.260071			−0.130036	−	0.991509i	$-0.541509\pi$
$659$	−6.67629			−0.260071			−0.130036	+	0.991509i	$0.541509\pi$
$660$	5.82109	+	2.94863i	0.226585	+	0.114775i
$661$	−1.35571	−	2.34815i	−0.0527309	−	0.0913326i	0.838455	−	0.544971i	$-0.183459\pi$
$661$	−1.35571	−	2.34815i	−0.0527309	−	0.0913326i	−0.891186	+	0.453638i	$0.850126\pi$
$662$	−0.288191	−	1.40612i	−0.0112009	−	0.0546504i
$663$	10.6542	−	1.87299i	0.413775	−	0.0727408i
$664$	12.0438	−	8.35442i	0.467390	−	0.324214i
$665$		0			0
$666$	−3.90818	−	2.11986i	−0.151439	−	0.0821431i
$667$	−28.9018	−	16.6865i	−1.11908	−	0.646102i
$668$	1.99262	−	16.6249i	0.0770970	−	0.643238i
$669$	0.405331	−	1.11186i	0.0156710	−	0.0429871i
$670$	−6.35192	−	7.15871i	−0.245396	−	0.276565i
$671$	−2.24723			−0.0867535
$672$		0			0
$673$	37.2088			1.43430			0.717148	−	0.696921i	$-0.245447\pi$
$673$	37.2088			1.43430			0.717148	+	0.696921i	$0.245447\pi$
$674$	−11.8826	−	13.3919i	−0.457700	−	0.515835i
$675$	11.3448	−	19.5800i	0.436660	−	0.753635i
$676$	−3.51256	+	29.3061i	−0.135099	+	1.12716i
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	0.303238	−	0.952915i	$-0.401932\pi$
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	−0.673630	+	0.739069i	$0.735266\pi$
$678$	−16.1708	+	6.38722i	−0.621037	+	0.245300i
$679$		0			0
$680$	2.21258	−	1.53480i	0.0848487	−	0.0588570i
$681$	−2.62522	−	14.9332i	−0.100599	−	0.572240i
$682$	3.26265	+	15.9189i	0.124933	+	0.609565i
$683$	4.83716	+	8.37821i	0.185089	+	0.320583i	0.943606	−	0.331069i	$-0.107409\pi$
$683$	4.83716	+	8.37821i	0.185089	+	0.320583i	−0.758518	+	0.651652i	$0.774076\pi$
$684$	41.6323	−	9.69309i	1.59185	−	0.370624i
$685$	10.8357			0.414013
$686$		0			0
$687$	24.5549	−	20.5826i	0.936829	−	0.785274i
$688$	−7.50851	+	30.8726i	−0.286259	+	1.17701i
$689$	39.7870	−	22.9710i	1.51576	−	0.875127i
$690$	12.1518	+	9.64757i	0.462612	+	0.367277i
$691$	7.20943	+	4.16236i	0.274260	+	0.158344i	0.630822	−	0.775928i	$-0.282718\pi$
$691$	7.20943	+	4.16236i	0.274260	+	0.158344i	−0.356562	+	0.934272i	$0.616051\pi$
$692$	15.3128	−	20.4432i	0.582105	−	0.777133i
$693$		0			0
$694$	11.4509	−	34.3879i	0.434670	−	1.30535i
$695$	−3.04088	+	5.26697i	−0.115347	+	0.199787i
$696$	−5.26666	−	20.0490i	−0.199632	−	0.759954i
$697$	−4.24943	−	7.36022i	−0.160958	−	0.278788i
$698$	−26.3971	−	29.7499i	−0.999145	−	1.12605i
$699$	11.2814	+	13.4586i	0.426700	+	0.509052i
$700$		0			0
$701$		−	34.0535i		−	1.28618i	−0.765790	−	0.643091i	$-0.777652\pi$
$701$		−	34.0535i		−	1.28618i	0.765790	−	0.643091i	$-0.222348\pi$
$702$	−12.2883	+	36.7141i	−0.463793	+	1.38568i
$703$	6.46568	−	3.73296i	0.243858	−	0.140791i
$704$	18.5065	−	3.09553i	0.697491	−	0.116667i
$705$	−8.35599	+	1.46897i	−0.314705	+	0.0553244i
$706$	13.8269	+	4.60425i	0.520382	+	0.173283i
$707$		0			0
$708$	−2.29040	+	0.125482i	−0.0860785	+	0.00471589i
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	−0.942245	−	0.334924i	$-0.891289\pi$
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	0.761175	+	0.648546i	$0.224623\pi$
$710$	−2.20618	−	10.7642i	−0.0827964	−	0.403974i
$711$	7.08871	+	19.5384i	0.265847	+	0.732748i
$712$	46.1310	−	3.83148i	1.72883	−	0.143591i
$713$			38.6388i			1.44703i
$714$		0			0
$715$		−	9.92437i		−	0.371150i
$716$	38.8301	−	16.6148i	1.45115	−	0.620923i
$717$	−2.43231	−	0.886703i	−0.0908364	−	0.0331145i
$718$	−37.1837	+	7.62097i	−1.38768	+	0.284412i
$719$	4.04585	−	7.00762i	0.150885	−	0.261340i	−0.780668	−	0.624946i	$-0.785121\pi$
$719$	4.04585	−	7.00762i	0.150885	−	0.261340i	0.931553	+	0.363606i	$0.118454\pi$
$720$	1.05284	+	9.57981i	0.0392369	+	0.357018i
$721$		0			0
$722$	−14.1885	+	42.6090i	−0.528040	+	1.58574i
$723$	3.09900	+	17.6282i	0.115253	+	0.655599i
$724$	−2.95312	+	24.6386i	−0.109752	+	0.915686i
$725$	15.9586	−	9.21369i	0.592687	−	0.342188i
$726$	13.3233	+	1.97852i	0.494473	+	0.0734299i
$727$			36.9501i			1.37040i	0.728353	+	0.685202i	$0.240286\pi$
$727$			36.9501i			1.37040i	−0.728353	+	0.685202i	$0.759714\pi$
$728$		0			0
$729$	−13.5719	+	23.3410i	−0.502664	+	0.864482i
$730$	1.20147	−	1.06607i	0.0444685	−	0.0394569i
$731$	−4.70802	−	8.15453i	−0.174133	−	0.301606i
$732$	−1.81427	−	2.77929i	−0.0670575	−	0.102725i
$733$	18.9776	−	32.8702i	0.700954	−	1.21409i	−0.267178	−	0.963647i	$-0.586091\pi$
$733$	18.9776	−	32.8702i	0.700954	−	1.21409i	0.968132	−	0.250440i	$-0.0805753\pi$
$734$	−17.9153	−	5.96566i	−0.661266	−	0.220197i
$735$		0			0
$736$	44.5867	+	1.62466i	1.64349	+	0.0598857i
$737$	17.1157	+	9.88173i	0.630463	+	0.363998i
$738$	30.4065	−	0.808878i	1.11928	−	0.0297752i
$739$	19.1667	−	11.0659i	0.705058	−	0.407065i	−0.104171	−	0.994559i	$-0.533219\pi$
$739$	19.1667	−	11.0659i	0.705058	−	0.407065i	0.809228	+	0.587494i	$0.199885\pi$
$740$	0.662173	+	1.54756i	0.0243420	+	0.0568893i
$741$	−41.7636	−	49.8238i	−1.53422	−	1.83032i
$742$		0			0
$743$	−21.7884			−0.799340			−0.399670	−	0.916659i	$-0.630875\pi$
$743$	−21.7884			−0.799340			−0.399670	+	0.916659i	$0.630875\pi$
$744$	−17.0537	+	16.8870i	−0.625220	+	0.619107i
$745$	6.46568	+	11.1989i	0.236884	+	0.410296i
$746$	31.5956	−	6.47567i	1.15680	−	0.237091i
$747$	−11.8993	−	10.0056i	−0.435374	−	0.366084i
$748$	−3.33371	+	4.45064i	−0.121893	+	0.162731i
$749$		0			0
$750$	−17.1167	+	6.76083i	−0.625014	+	0.246871i
$751$	4.44124	+	2.56415i	0.162063	+	0.0935671i	0.578838	−	0.815443i	$-0.303506\pi$
$751$	4.44124	+	2.56415i	0.162063	+	0.0935671i	−0.416775	+	0.909010i	$0.636840\pi$
$752$	−16.8456	+	17.6467i	−0.614295	+	0.643509i
$753$	43.8645	+	15.9909i	1.59851	+	0.582740i
$754$	−23.5823	+	20.9246i	−0.858816	+	0.762027i
$755$	13.9618			0.508122
$756$		0			0
$757$	−30.4486			−1.10667			−0.553337	−	0.832958i	$-0.686646\pi$
$757$	−30.4486			−1.10667			−0.553337	+	0.832958i	$0.686646\pi$
$758$	2.09580	−	1.85960i	0.0761228	−	0.0675437i
$759$	−30.1030	−	10.9741i	−1.09267	−	0.398335i
$760$	−14.6369	−	6.90387i	−0.530936	−	0.250430i
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.987110	−	0.160046i	$-0.0511642\pi$
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.354951	+	0.934885i	$0.384498\pi$
$762$	−9.48197	+	3.74523i	−0.343496	+	0.135675i
$763$		0			0
$764$	9.76434	+	7.31389i	0.353261	+	0.264607i
$765$	−2.18605	−	1.83814i	−0.0790367	−	0.0664580i
$766$	39.9288	−	8.18360i	1.44269	−	0.295686i
$767$	1.74436	+	3.02131i	0.0629851	+	0.109093i
$768$	18.7694	+	20.3890i	0.677283	+	0.735723i
$769$	7.77655			0.280430			0.140215	−	0.990121i	$-0.455221\pi$
$769$	7.77655			0.280430			0.140215	+	0.990121i	$0.455221\pi$
$770$		0			0
$771$	3.10619	+	3.70567i	0.111867	+	0.133456i
$772$	1.18601	−	0.507473i	0.0426853	−	0.0182643i
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	−0.518631	−	0.854998i	$-0.673558\pi$
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	0.481135	+	0.876647i	$0.340225\pi$
$774$	33.6880	−	0.896173i	1.21089	−	0.0322123i
$775$	−18.4767	−	10.6675i	−0.663701	−	0.383188i
$776$	10.1752	−	7.05825i	0.365269	−	0.253376i
$777$		0			0
$778$	−2.62954	−	0.875618i	−0.0942737	−	0.0313924i
$779$	−25.5386	+	44.2341i	−0.915014	+	1.58485i
$780$	12.2740	−	8.01230i	0.439481	−	0.286886i
$781$	11.3453	+	19.6507i	0.405968	+	0.703157i
$782$	−9.89031	+	8.77567i	−0.353677	+	0.313817i
$783$	−19.0579	+	10.9640i	−0.681072	+	0.391820i
$784$		0			0
$785$		−	3.15000i		−	0.112428i
$786$	−25.4210	−	3.77505i	−0.906737	−	0.134652i
$787$	−19.4895	+	11.2522i	−0.694724	+	0.401099i	−0.805380	−	0.592760i	$-0.798038\pi$
$787$	−19.4895	+	11.2522i	−0.694724	+	0.401099i	0.110655	+	0.993859i	$0.464705\pi$
$788$	−29.6102	−	3.54901i	−1.05482	−	0.126428i
$789$	4.59144	+	26.1177i	0.163460	+	0.929816i
$790$	2.48610	−	7.46593i	0.0884514	−	0.265626i
$791$		0			0
$792$	−8.31288	−	18.0826i	−0.295385	−	0.642536i
$793$	−2.52398	+	4.37166i	−0.0896290	+	0.155242i
$794$	6.32179	−	1.29568i	0.224352	−	0.0459819i
$795$	−11.3963	−	4.15455i	−0.404186	−	0.147347i
$796$	−14.7120	−	34.3832i	−0.521452	−	1.21868i
$797$		−	18.3911i		−	0.651447i	−0.945465	−	0.325724i	$-0.894392\pi$
$797$		−	18.3911i		−	0.651447i	0.945465	−	0.325724i	$-0.105608\pi$
$798$		0			0
$799$		−	7.23003i		−	0.255780i
$800$	−13.0865	+	20.8723i	−0.462678	+	0.737948i
$801$	−16.7451	−	46.1540i	−0.591658	−	1.63077i
$802$	−7.60442	−	37.1029i	−0.268521	−	1.31015i
$803$	−1.65849	+	2.87258i	−0.0585267	+	0.101371i
$804$	1.59678	+	29.1458i	0.0563140	+	1.02789i
$805$		0			0
$806$	34.6322	+	11.5323i	1.21987	+	0.406206i
$807$	−52.3477	+	9.20262i	−1.84273	+	0.323948i
$808$	10.1275	−	21.4714i	0.356286	−	0.755362i
$809$	−11.5087	+	6.64455i	−0.404624	+	0.233610i	−0.688477	−	0.725258i	$-0.741721\pi$
$809$	−11.5087	+	6.64455i	−0.404624	+	0.233610i	0.283853	+	0.958868i	$0.408387\pi$
$810$	9.51311	−	3.74061i	0.334256	−	0.131431i
$811$			6.46254i			0.226930i	0.993542	+	0.113465i	$0.0361950\pi$
$811$			6.46254i			0.226930i	−0.993542	+	0.113465i	$0.963805\pi$
$812$		0			0
$813$	21.9041	+	26.1315i	0.768210	+	0.916472i
$814$	−2.30704	−	2.60007i	−0.0808617	−	0.0911323i
$815$	−2.93506	−	5.08367i	−0.102811	−	0.178073i
$816$	−8.19579	−	0.529836i	−0.286910	−	0.0185480i
$817$	−28.2947	+	49.0078i	−0.989906	+	1.71457i
$818$	8.06140	−	24.2090i	0.281860	−	0.846446i
$819$		0			0
$820$	−9.21694	−	6.90387i	−0.321869	−	0.241094i
$821$	24.1767	+	13.9584i	0.843774	+	0.487153i	0.858545	−	0.512738i	$-0.171369\pi$
$821$	24.1767	+	13.9584i	0.843774	+	0.487153i	−0.0147715	+	0.999891i	$0.504702\pi$
$822$	−25.8831	−	20.5491i	−0.902778	−	0.716734i
$823$	−38.9668	+	22.4975i	−1.35830	+	0.784213i	−0.989394	−	0.145256i	$-0.953600\pi$
$823$	−38.9668	+	22.4975i	−1.35830	+	0.784213i	−0.368902	+	0.929468i	$0.620266\pi$
$824$	−7.23552	+	0.600958i	−0.252061	+	0.0209354i
$825$	13.5586	−	11.3652i	0.472051	−	0.395685i
$826$		0			0
$827$	−34.2989			−1.19269			−0.596344	−	0.802729i	$-0.703381\pi$
$827$	−34.2989			−1.19269			−0.596344	+	0.802729i	$0.703381\pi$
$828$	−10.7309	−	46.0899i	−0.372926	−	1.60174i
$829$	−11.5078	−	19.9322i	−0.399684	−	0.692273i	0.594003	−	0.804463i	$-0.297547\pi$
$829$	−11.5078	−	19.9322i	−0.399684	−	0.692273i	−0.993687	+	0.112190i	$0.964213\pi$
$830$	1.18179	+	5.76613i	0.0410207	+	0.200145i
$831$	3.93246	+	22.3692i	0.136416	+	0.775980i
$832$	14.7637	−	39.4784i	0.511838	−	1.36867i
$833$		0			0
$834$	17.2521	−	6.81430i	0.597391	−	0.235960i
$835$	5.82291	+	3.36186i	0.201510	+	0.116342i
$836$	33.1819	+	3.97711i	1.14762	+	0.137551i
$837$	22.0258	+	12.7618i	0.761323	+	0.441114i
$838$	−16.4628	−	18.5538i	−0.568698	−	0.640931i
$839$	46.9847			1.62209			0.811046	−	0.584983i	$-0.198899\pi$
$839$	46.9847			1.62209			0.811046	+	0.584983i	$0.198899\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	14.4552	+	16.2913i	0.498161	+	0.561434i
$843$	−1.70062	+	4.66496i	−0.0585724	+	0.160670i
$844$	−23.2819	−	2.79052i	−0.801396	−	0.0960535i
$845$	−10.2645	−	5.92623i	−0.353110	−	0.203868i
$846$	22.7456	+	12.3376i	0.782009	+	0.424175i
$847$		0			0
$848$	−33.4728	+	9.80751i	−1.14946	+	0.336791i
$849$	−3.39541	+	0.596905i	−0.116530	+	0.0204857i
$850$	−1.46589	−	7.15226i	−0.0502795	−	0.245320i
$851$	−4.13266	−	7.15798i	−0.141666	−	0.245372i
$852$	−15.1437	+	29.8961i	−0.518813	+	1.02422i
$853$	12.7498			0.436545			0.218272	−	0.975888i	$-0.429958\pi$
$853$	12.7498			0.436545			0.218272	+	0.975888i	$0.429958\pi$
$854$		0			0
$855$	−2.99803	+	16.9012i	−0.102531	+	0.578010i
$856$	1.42807	+	17.1939i	0.0488105	+	0.587676i
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.875315	−	0.483553i	$-0.839346\pi$
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.0188889	+	0.999822i	$0.506013\pi$
$858$	−18.8208	+	23.7061i	−0.642531	+	0.809314i
$859$	−15.8982	−	9.17880i	−0.542438	−	0.313177i	0.203628	−	0.979048i	$-0.434727\pi$
$859$	−15.8982	−	9.17880i	−0.542438	−	0.313177i	−0.746066	+	0.665872i	$0.768060\pi$
$860$	−10.2116	−	7.64893i	−0.348214	−	0.260826i
$861$		0			0
$862$	−4.02283	+	12.0808i	−0.137018	+	0.411475i
$863$	13.1968	−	22.8576i	0.449225	−	0.778080i	−0.549111	−	0.835749i	$-0.685034\pi$
$863$	13.1968	−	22.8576i	0.449225	−	0.778080i	0.998336	+	0.0576693i	$0.0183669\pi$
$864$	15.6525	−	24.8797i	0.532508	−	0.846425i
$865$	5.12839	+	8.88264i	0.174371	+	0.302019i
$866$	−5.78081	−	6.51506i	−0.196440	−	0.221391i
$867$	−20.7005	+	17.3517i	−0.703025	+	0.589293i
$868$		0			0
$869$			16.2498i			0.551236i
$870$	8.23375	+	1.22272i	0.279150	+	0.0414542i
$871$	38.4468	−	22.1973i	1.30272	−	0.752126i
$872$	13.9442	+	6.57712i	0.472209	+	0.222729i
$873$	−10.0532	−	8.45322i	−0.340249	−	0.286098i
$874$	75.3947	+	25.1059i	2.55026	+	0.849218i
$875$		0			0
$876$	−4.89164	+	0.267993i	−0.165273	+	0.00905464i
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	−0.858004	−	0.513643i	$-0.828296\pi$
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	0.873830	+	0.486232i	$0.161629\pi$
$878$	8.30525	+	40.5224i	0.280289	+	1.36756i
$879$	9.93557	−	27.2542i	0.335118	−	0.919262i
$880$	−1.78062	+	7.32134i	−0.0600246	+	0.246802i
$881$			37.1298i			1.25093i	0.780251	+	0.625467i	$0.215091\pi$
$881$			37.1298i			1.25093i	−0.780251	+	0.625467i	$0.784909\pi$
$882$		0			0
$883$			5.76235i			0.193918i	0.995288	+	0.0969592i	$0.0309116\pi$
$883$			5.76235i			0.193918i	−0.995288	+	0.0969592i	$0.969088\pi$
$884$	4.91379	+	11.4840i	0.165269	+	0.386247i
$885$	0.315485	−	0.865405i	0.0106049	−	0.0290903i
$886$	−9.99770	+	2.04908i	−0.335879	+	0.0688400i
$887$	−13.0672	+	22.6330i	−0.438752	+	0.759941i	−0.997594	−	0.0693335i	$-0.977913\pi$
$887$	−13.0672	+	22.6330i	−0.438752	+	0.759941i	0.558841	+	0.829275i	$0.311246\pi$
$888$	1.35310	−	4.95238i	0.0454070	−	0.166191i
$889$		0			0
$890$	−5.87270	+	17.6361i	−0.196853	+	0.591165i
$891$	−16.1983	+	13.5354i	−0.542664	+	0.453454i
$892$	1.35681	+	0.162624i	0.0454293	+	0.00544505i
$893$	−37.6302	+	21.7258i	−1.25925	+	0.727027i
$894$	5.79337	−	39.0122i	0.193759	−	1.30476i
$895$			16.9601i			0.566915i
$896$		0			0
$897$	−55.1586	+	46.2353i	−1.84169	+	1.54375i
$898$	−4.69066	+	4.16202i	−0.156529	+	0.138888i
$899$	10.3646	+	17.9520i	0.345678	+	0.598732i
$900$	25.0023	+	7.59321i	0.833412	+	0.253107i
$901$	5.16848	−	8.95207i	0.172187	−	0.298237i
$902$	22.5627	+	7.51322i	0.751257	+	0.250163i
$903$		0			0
$904$	−11.4428	−	16.4960i	−0.380582	−	0.548649i
$905$	−8.62971	−	4.98237i	−0.286861	−	0.165619i
$906$	−33.3503	−	26.4775i	−1.10799	−	0.879655i
$907$	−35.3624	+	20.4165i	−1.17419	+	0.677918i	−0.954663	−	0.297689i	$-0.903784\pi$
$907$	−35.3624	+	20.4165i	−1.17419	+	0.677918i	−0.219525	+	0.975607i	$0.570451\pi$
$908$	16.0962	−	6.88728i	0.534170	−	0.228562i
$909$	−24.7931	−	4.39793i	−0.822334	−	0.145870i
$910$		0			0
$911$	−4.31270			−0.142886			−0.0714430	−	0.997445i	$-0.522760\pi$
$911$	−4.31270			−0.142886			−0.0714430	+	0.997445i	$0.522760\pi$
$912$	21.8702	+	44.2489i	0.724196	+	1.46523i
$913$	−6.07741	−	10.5264i	−0.201133	−	0.348372i
$914$	−18.9276	+	3.87930i	−0.626069	+	0.128316i
$915$	1.31267	−	0.230765i	0.0433955	−	0.00762885i
$916$	29.6113	+	22.1801i	0.978384	+	0.732850i
$917$		0			0
$918$	1.73588	+	8.53639i	0.0572927	+	0.281743i
$919$	−14.9668	−	8.64107i	−0.493708	−	0.285043i	0.232403	−	0.972620i	$-0.425341\pi$
$919$	−14.9668	−	8.64107i	−0.493708	−	0.285043i	−0.726112	+	0.687577i	$0.758674\pi$
$920$	−7.64308	+	16.2041i	−0.251985	+	0.534234i
$921$	−9.18732	+	25.2017i	−0.302733	+	0.830425i
$922$	−5.56196	+	4.93513i	−0.183173	+	0.162530i
$923$	50.9699			1.67770
$924$		0			0
$925$	4.56383			0.150058
$926$	−16.8050	+	14.9111i	−0.552247	+	0.490009i
$927$	2.62642	+	7.23913i	0.0862629	+	0.237764i
$928$	21.1512	−	11.2052i	0.694323	−	0.367829i
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	0.791479	−	0.611196i	$-0.209311\pi$
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	−0.133571	+	0.991039i	$0.542645\pi$
$930$	−3.54048	−	8.96360i	−0.116097	−	0.293928i
$931$		0			0
$932$	−12.1570	+	16.2300i	−0.398214	+	0.531632i
$933$	−3.26866	−	18.5933i	−0.107011	−	0.608717i
$934$	37.5125	−	7.68837i	1.22745	−	0.251571i
$935$	−1.11649	−	1.93382i	−0.0365132	−	0.0632426i
$936$	−44.5135	−	4.13793i	−1.45497	−	0.135253i
$937$	−3.10294			−0.101369			−0.0506843	−	0.998715i	$-0.516140\pi$
$937$	−3.10294			−0.101369			−0.0506843	+	0.998715i	$0.516140\pi$
$938$		0			0
$939$	−44.8691	+	37.6104i	−1.46425	+	1.22737i
$940$	−3.85384	−	9.00676i	−0.125698	−	0.293768i
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	−0.127503	−	0.991838i	$-0.540696\pi$
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	0.795206	+	0.606340i	$0.207363\pi$
$942$	−5.97372	+	7.52434i	−0.194634	+	0.245156i
$943$	48.9703	+	28.2730i	1.59469	+	0.920696i
$944$	−0.744755	−	2.54183i	−0.0242397	−	0.0827296i
$945$		0			0
$946$	24.9977	+	8.32404i	0.812745	+	0.270638i
$947$	28.7686	−	49.8286i	0.934852	−	1.61921i	0.159955	−	0.987124i	$-0.448865\pi$
$947$	28.7686	−	49.8286i	0.934852	−	1.61921i	0.774897	−	0.632087i	$-0.217802\pi$
$948$	−20.0970	+	13.1190i	−0.652722	+	0.426086i
$949$	3.72545	+	6.45267i	0.120933	+	0.209462i
$950$	−32.8205	+	29.1217i	−1.06484	+	0.944831i
$951$	10.3328	+	12.3270i	0.335065	+	0.399731i
$952$		0			0
$953$		−	14.1961i		−	0.459855i	−0.973208	−	0.229928i	$-0.926151\pi$
$953$		−	14.1961i		−	0.459855i	0.973208	−	0.229928i	$-0.0738490\pi$
$954$	19.3434	+	31.5361i	0.626266	+	1.02102i
$955$	−4.24264	+	2.44949i	−0.137289	+	0.0792636i
$956$	0.355756	−	2.96816i	0.0115060	−	0.0959970i
$957$	−16.9299	+	2.97624i	−0.547266	+	0.0962082i
$958$	−6.81842	+	20.4762i	−0.220293	+	0.661557i
$959$		0			0
$960$	−10.4923	+	3.70859i	−0.338637	+	0.119694i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	−7.64918	+	1.56774i	−0.246620	+	0.0505458i
$963$	17.2025	−	6.24122i	0.554343	−	0.201120i
$964$	−19.0011	+	8.13025i	−0.611984	+	0.261858i
$965$			0.518021i			0.0166757i
$966$		0			0
$967$		−	31.5730i		−	1.01532i	−0.861558	−	0.507660i	$-0.830511\pi$
$967$		−	31.5730i		−	1.01532i	0.861558	−	0.507660i	$-0.169489\pi$
$968$	1.28736	+	15.4997i	0.0413772	+	0.498180i
$969$	−13.7431	−	5.01005i	−0.441491	−	0.160946i
$970$	0.998442	+	4.87153i	0.0320580	+	0.156415i
$971$	−14.6620	+	25.3953i	−0.470526	+	0.814974i	−0.999432	−	0.0337060i	$-0.989269\pi$
$971$	−14.6620	+	25.3953i	−0.470526	+	0.814974i	0.528906	+	0.848680i	$0.322602\pi$
$972$	−29.8175	−	9.10575i	−0.956398	−	0.292067i
$973$		0			0
$974$	8.13677	+	2.70948i	0.260719	+	0.0868174i
$975$	−6.88091	−	39.1410i	−0.220366	−	1.25352i
$976$	2.64633	−	2.77218i	0.0847069	−	0.0887353i
$977$	10.3022	−	5.94797i	0.329596	−	0.190292i	−0.326066	−	0.945347i	$-0.605723\pi$
$977$	10.3022	−	5.94797i	0.329596	−	0.190292i	0.655662	+	0.755055i	$0.272390\pi$
$978$	−2.62986	+	17.7094i	−0.0840938	+	0.566283i
$979$		−	38.3855i		−	1.22681i
$980$		0			0
$981$	2.85614	−	16.1013i	0.0911896	−	0.514076i
$982$	3.79042	+	4.27187i	0.120957	+	0.136321i
$983$	−7.49013	−	12.9733i	−0.238898	−	0.413783i	0.721500	−	0.692414i	$-0.243453\pi$
$983$	−7.49013	−	12.9733i	−0.238898	−	0.413783i	−0.960398	+	0.278631i	$0.910119\pi$
$984$	8.92367	+	33.9703i	0.284476	+	1.08293i
$985$	5.98772	−	10.3710i	0.190785	−	0.330449i
$986$	−2.24113	+	6.73027i	−0.0713721	+	0.214336i
$987$		0			0
$988$	45.0051	−	60.0835i	1.43180	−	1.91151i
$989$	54.2552	+	31.3243i	1.72521	+	0.996053i
$990$	7.98899	−	0.212524i	0.253907	−	0.00675446i
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$	−23.4795	−	14.7212i	−0.745475	−	0.467397i
$993$	−1.12929	−	1.34724i	−0.0358369	−	0.0427533i
$994$		0			0
$995$	15.0178			0.476096
$996$	8.11208	−	16.0146i	0.257041	−	0.507443i
$997$	9.81912	+	17.0072i	0.310975	+	0.538624i	0.978574	−	0.205897i	$-0.0660113\pi$
$997$	9.81912	+	17.0072i	0.310975	+	0.538624i	−0.667599	+	0.744521i	$0.732678\pi$
$998$	10.9323	+	53.3402i	0.346056	+	1.68845i
$999$	−5.44532	−	0.00838284i	−0.172282	−	0.000265221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.d.275.10		24
3.2	odd	2	inner	588.2.n.d.275.4		24
4.3	odd	2		588.2.n.h.275.11		24
7.2	even	3		588.2.e.f.491.13	yes	24
7.3	odd	6		588.2.n.h.263.2		24
7.4	even	3		588.2.n.h.263.1		24
7.5	odd	6		588.2.e.f.491.14	yes	24
7.6	odd	2	inner	588.2.n.d.275.9		24
12.11	even	2		588.2.n.h.275.1		24
21.2	odd	6		588.2.e.f.491.12	yes	24
21.5	even	6		588.2.e.f.491.11	yes	24
21.11	odd	6		588.2.n.h.263.11		24
21.17	even	6		588.2.n.h.263.12		24
21.20	even	2	inner	588.2.n.d.275.3		24
28.3	even	6	inner	588.2.n.d.263.3		24
28.11	odd	6	inner	588.2.n.d.263.4		24
28.19	even	6		588.2.e.f.491.9	✓	24
28.23	odd	6		588.2.e.f.491.10	yes	24
28.27	even	2		588.2.n.h.275.12		24
84.11	even	6	inner	588.2.n.d.263.10		24
84.23	even	6		588.2.e.f.491.15	yes	24
84.47	odd	6		588.2.e.f.491.16	yes	24
84.59	odd	6	inner	588.2.n.d.263.9		24
84.83	odd	2		588.2.n.h.275.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.9	✓	24	28.19	even	6
588.2.e.f.491.10	yes	24	28.23	odd	6
588.2.e.f.491.11	yes	24	21.5	even	6
588.2.e.f.491.12	yes	24	21.2	odd	6
588.2.e.f.491.13	yes	24	7.2	even	3
588.2.e.f.491.14	yes	24	7.5	odd	6
588.2.e.f.491.15	yes	24	84.23	even	6
588.2.e.f.491.16	yes	24	84.47	odd	6
588.2.n.d.263.3		24	28.3	even	6	inner
588.2.n.d.263.4		24	28.11	odd	6	inner
588.2.n.d.263.9		24	84.59	odd	6	inner
588.2.n.d.263.10		24	84.11	even	6	inner
588.2.n.d.275.3		24	21.20	even	2	inner
588.2.n.d.275.4		24	3.2	odd	2	inner
588.2.n.d.275.9		24	7.6	odd	2	inner
588.2.n.d.275.10		24	1.1	even	1	trivial
588.2.n.h.263.1		24	7.4	even	3
588.2.n.h.263.2		24	7.3	odd	6
588.2.n.h.263.11		24	21.11	odd	6
588.2.n.h.263.12		24	21.17	even	6
588.2.n.h.275.1		24	12.11	even	2
588.2.n.h.275.2		24	84.83	odd	2
588.2.n.h.275.11		24	4.3	odd	2
588.2.n.h.275.12		24	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.938613 + 1.05783i) q^{2} +(1.62729 + 0.593231i) q^{3} +(-0.238012 + 1.98579i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(0.899858 + 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(2.29615 + 1.93072i) q^{9} +(-0.228045 - 1.11266i) q^{10} +(1.17273 + 2.03122i) q^{11} +(-1.56535 + 3.09026i) q^{12} +5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(-3.88670 - 0.945282i) q^{16} +(1.02661 - 0.592715i) q^{17} +(0.112823 + 4.24114i) q^{18} +(-6.16982 - 3.56215i) q^{19} +(0.962960 - 1.28559i) q^{20} +(-1.04795 + 3.14708i) q^{22} +(-3.94356 + 6.83044i) q^{23} +(-4.73822 + 1.24468i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(4.94516 + 5.57327i) q^{26} +(2.59115 + 4.50399i) q^{27} +4.23132i q^{29} +(0.288969 - 1.94590i) q^{30} +(4.24264 - 2.44949i) q^{31} +(-2.64816 - 4.99872i) q^{32} +(0.703383 + 4.00109i) q^{33} +(1.59058 + 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(-2.02292 - 9.87011i) q^{38} +(8.57351 + 3.12549i) q^{39} +(2.26378 - 0.188022i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(-4.31270 + 1.84533i) q^{44} +(-0.821730 - 2.26491i) q^{45} +(-10.9269 + 2.23952i) q^{46} +(3.04954 - 5.28195i) q^{47} +(-5.76402 - 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(2.02221 - 0.355501i) q^{51} +(-1.25398 + 10.4623i) q^{52} +(7.55175 - 4.36001i) q^{53} +(-2.33238 + 6.96850i) q^{54} -1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-4.47602 + 3.97157i) q^{58} +(0.331087 + 0.573459i) q^{59} +(2.32967 - 1.52077i) q^{60} +(-0.479062 + 0.829760i) q^{61} +(6.57334 + 2.18887i) q^{62} +(2.80221 - 7.49317i) q^{64} +(-3.66443 - 2.11566i) q^{65} +(-3.57227 + 4.49953i) q^{66} +(7.29738 - 4.21314i) q^{67} +(0.932660 + 2.17971i) q^{68} +(-10.4693 + 8.77567i) q^{69} +9.67432 q^{71} +(-8.44885 - 0.785398i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-1.45185 + 0.297563i) q^{74} +(-1.30603 - 7.42914i) q^{75} +(8.54216 - 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(6.00000 + 3.46410i) q^{79} +(2.32371 + 2.21822i) q^{80} +(1.54464 + 8.86646i) q^{81} +(7.58404 - 6.72931i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(8.40251 - 7.45554i) q^{86} +(-2.51015 + 6.88559i) q^{87} +(-6.00000 - 2.83005i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(1.62461 - 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(8.35713 - 1.46917i) q^{93} +(8.44975 - 1.73182i) q^{94} +(2.86085 + 4.95513i) q^{95} +(-1.34393 - 9.70535i) q^{96} -4.37827 q^{97} +(-1.22896 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 36 q^{16} - 12 q^{18} + 12 q^{25} + 12 q^{30} + 12 q^{36} + 96 q^{39} - 96 q^{46} - 12 q^{51} - 24 q^{57} - 120 q^{58} - 84 q^{60} - 48 q^{64} + 48 q^{67} - 72 q^{72} - 24 q^{78} + 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q - 12 * q^4 - 36 * q^16 - 12 * q^18 + 12 * q^25 + 12 * q^30 + 12 * q^36 + 96 * q^39 - 96 * q^46 - 12 * q^51 - 24 * q^57 - 120 * q^58 - 84 * q^60 - 48 * q^64 + 48 * q^67 - 72 * q^72 - 24 * q^78 + 144 * q^79 + 12 * q^81 - 48 * q^85 - 144 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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