LMFDB - Embedded newform 637.2.bc.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	637.31
Dual form			637.2.bc.b.411.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84208 - 0.493585i) q^{2} +(-2.29307 - 1.32391i) q^{3} +(1.41759 + 0.818448i) q^{4} +(0.885596 - 3.30509i) q^{5} +(3.57057 + 3.57057i) q^{6} +(0.489646 + 0.489646i) q^{8} +(2.00545 + 3.47355i) q^{9} +O(q^{10})$	\(q+(-1.84208 - 0.493585i) q^{2} +(-2.29307 - 1.32391i) q^{3} +(1.41759 + 0.818448i) q^{4} +(0.885596 - 3.30509i) q^{5} +(3.57057 + 3.57057i) q^{6} +(0.489646 + 0.489646i) q^{8} +(2.00545 + 3.47355i) q^{9} +(-3.26268 + 5.65113i) q^{10} +(1.66384 - 0.445825i) q^{11} +(-2.16710 - 3.75352i) q^{12} +(-3.57057 - 0.501030i) q^{13} +(-6.40637 + 6.40637i) q^{15} +(-2.29718 - 3.97884i) q^{16} +(-1.22596 + 2.12343i) q^{17} +(-1.97972 - 7.38842i) q^{18} +(-1.34794 + 5.03057i) q^{19} +(3.96046 - 3.96046i) q^{20} -3.28498 q^{22} +(-3.97172 + 2.29307i) q^{23} +(-0.474548 - 1.77104i) q^{24} +(-5.80922 - 3.35395i) q^{25} +(6.32999 + 2.68532i) q^{26} -2.67669i q^{27} +0.184063 q^{29} +(14.9631 - 8.63897i) q^{30} +(-2.46060 + 0.659317i) q^{31} +(1.90926 + 7.12546i) q^{32} +(-4.40553 - 1.18046i) q^{33} +(3.30641 - 3.30641i) q^{34} +6.56544i q^{36} +(0.0563202 - 0.210190i) q^{37} +(4.96603 - 8.60141i) q^{38} +(7.52426 + 5.87600i) q^{39} +(2.05195 - 1.18470i) q^{40} +(4.63239 + 4.63239i) q^{41} -0.562412i q^{43} +(2.72353 + 0.729768i) q^{44} +(13.2564 - 3.55205i) q^{45} +(8.44806 - 2.26365i) q^{46} +(-3.72492 - 0.998090i) q^{47} +12.1650i q^{48} +(9.04560 + 9.04560i) q^{50} +(5.62243 - 3.24611i) q^{51} +(-4.65155 - 3.63258i) q^{52} +(-2.67755 + 4.63764i) q^{53} +(-1.32117 + 4.93069i) q^{54} -5.89396i q^{55} +(9.75092 - 9.75092i) q^{57} +(-0.339059 - 0.0908505i) q^{58} +(3.73550 + 13.9411i) q^{59} +(-14.3249 + 3.83834i) q^{60} +(1.30750 - 0.754885i) q^{61} +4.85807 q^{62} -4.87935i q^{64} +(-4.81803 + 11.3573i) q^{65} +(7.53270 + 4.34901i) q^{66} +(1.78754 + 6.67118i) q^{67} +(-3.47583 + 2.00677i) q^{68} +12.1432 q^{69} +(1.70926 - 1.70926i) q^{71} +(-0.718846 + 2.68277i) q^{72} +(-3.15770 - 11.7847i) q^{73} +(-0.207493 + 0.359389i) q^{74} +(8.88063 + 15.3817i) q^{75} +(-6.02809 + 6.02809i) q^{76} +(-10.9600 - 14.5379i) q^{78} +(-1.48398 - 2.57034i) q^{79} +(-15.1848 + 4.06875i) q^{80} +(2.47267 - 4.28279i) q^{81} +(-6.24677 - 10.8197i) q^{82} +(0.504742 + 0.504742i) q^{83} +(5.93241 + 5.93241i) q^{85} +(-0.277598 + 1.03601i) q^{86} +(-0.422069 - 0.243682i) q^{87} +(1.03299 + 0.596396i) q^{88} +(7.20177 + 1.92971i) q^{89} -26.1726 q^{90} -7.50704 q^{92} +(6.51522 + 1.74575i) q^{93} +(6.36898 + 3.67713i) q^{94} +(15.4328 + 8.91011i) q^{95} +(5.05537 - 18.8669i) q^{96} +(-12.0949 - 12.0949i) q^{97} +(4.88535 + 4.88535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9	$ 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37} - 6 q^{39} + 132 q^{40} - 42 q^{44} + 24 q^{45} + 12 q^{46} - 30 q^{47} + 88 q^{50} - 36 q^{52} - 12 q^{53} - 78 q^{54} + 40 q^{57} + 26 q^{58} + 54 q^{59} + 16 q^{60} + 48 q^{61} - 8 q^{65} - 12 q^{66} + 16 q^{67} + 48 q^{68} - 36 q^{71} + 22 q^{72} - 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} - 138 q^{80} + 16 q^{81} - 84 q^{85} + 42 q^{86} + 24 q^{87} + 60 q^{89} + 48 q^{92} + 6 q^{93} + 72 q^{94} + 42 q^{96} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.84208	−	0.493585i	−1.30255	−	0.349017i	−0.460136	−	0.887849i	$-0.652199\pi$
$2$	−1.84208	−	0.493585i	−1.30255	−	0.349017i	−0.842414	+	0.538832i	$0.818866\pi$
$3$	−2.29307	−	1.32391i	−1.32391	−	0.764357i	−0.339557	−	0.940586i	$-0.610277\pi$
$3$	−2.29307	−	1.32391i	−1.32391	−	0.764357i	−0.984349	+	0.176228i	$0.943610\pi$
$4$	1.41759	+	0.818448i	0.708797	+	0.409224i
$5$	0.885596	−	3.30509i	0.396051	−	1.47808i	−0.423932	−	0.905694i	$-0.639351\pi$
$5$	0.885596	−	3.30509i	0.396051	−	1.47808i	0.819983	−	0.572388i	$-0.193983\pi$
$6$	3.57057	+	3.57057i	1.45768	+	1.45768i
$7$		0			0
$7$		0			0
$8$	0.489646	+	0.489646i	0.173116	+	0.173116i
$9$	2.00545	+	3.47355i	0.668485	+	1.15785i
$10$	−3.26268	+	5.65113i	−1.03175	+	1.78705i
$11$	1.66384	−	0.445825i	0.501667	−	0.134421i	0.000893225	−	1.00000i	$-0.499716\pi$
$11$	1.66384	−	0.445825i	0.501667	−	0.134421i	0.500773	+	0.865578i	$0.333049\pi$
$12$	−2.16710	−	3.75352i	−0.625587	−	1.08355i
$13$	−3.57057	−	0.501030i	−0.990298	−	0.138961i
$13$	−3.57057	−	0.501030i	−0.990298	−	0.138961i
$14$		0			0
$15$	−6.40637	+	6.40637i	−1.65412	+	1.65412i
$16$	−2.29718	−	3.97884i	−0.574296	−	0.994709i
$17$	−1.22596	+	2.12343i	−0.297339	+	0.515006i	−0.975526	−	0.219883i	$-0.929433\pi$
$17$	−1.22596	+	2.12343i	−0.297339	+	0.515006i	0.678187	+	0.734889i	$0.262766\pi$
$18$	−1.97972	−	7.38842i	−0.466625	−	1.74147i
$19$	−1.34794	+	5.03057i	−0.309238	+	1.15409i	0.619997	+	0.784604i	$0.287134\pi$
$19$	−1.34794	+	5.03057i	−0.309238	+	1.15409i	−0.929235	+	0.369488i	$0.879533\pi$
$20$	3.96046	−	3.96046i	0.885586	−	0.885586i
$21$		0			0
$22$	−3.28498			−0.700361
$23$	−3.97172	+	2.29307i	−0.828160	+	0.478139i	−0.853222	−	0.521547i	$-0.825355\pi$
$23$	−3.97172	+	2.29307i	−0.828160	+	0.478139i	0.0250620	+	0.999686i	$0.492022\pi$
$24$	−0.474548	−	1.77104i	−0.0968668	−	0.361512i
$25$	−5.80922	−	3.35395i	−1.16184	−	0.670790i
$26$	6.32999	+	2.68532i	1.24141	+	0.526634i
$27$		−	2.67669i		−	0.515130i
$28$		0			0
$29$	0.184063			0.0341796			0.0170898	−	0.999854i	$-0.494560\pi$
$29$	0.184063			0.0341796			0.0170898	+	0.999854i	$0.494560\pi$
$30$	14.9631	−	8.63897i	2.73188	−	1.57725i
$31$	−2.46060	+	0.659317i	−0.441938	+	0.118417i	−0.472924	−	0.881103i	$-0.656802\pi$
$31$	−2.46060	+	0.659317i	−0.441938	+	0.118417i	0.0309869	+	0.999520i	$0.490135\pi$
$32$	1.90926	+	7.12546i	0.337513	+	1.25962i
$33$	−4.40553	−	1.18046i	−0.766905	−	0.205492i
$34$	3.30641	−	3.30641i	0.567045	−	0.567045i
$35$		0			0
$36$			6.56544i			1.09424i
$37$	0.0563202	−	0.210190i	0.00925899	−	0.0345550i	−0.961142	−	0.276055i	$-0.910973\pi$
$37$	0.0563202	−	0.210190i	0.00925899	−	0.0345550i	0.970401	+	0.241500i	$0.0776394\pi$
$38$	4.96603	−	8.60141i	0.805596	−	1.39533i
$39$	7.52426	+	5.87600i	1.20485	+	0.940912i
$40$	2.05195	−	1.18470i	0.324442	−	0.187317i
$41$	4.63239	+	4.63239i	0.723458	+	0.723458i	0.969308	−	0.245850i	$-0.0790671\pi$
$41$	4.63239	+	4.63239i	0.723458	+	0.723458i	−0.245850	+	0.969308i	$0.579067\pi$
$42$		0			0
$43$		−	0.562412i		−	0.0857671i	−0.999080	−	0.0428835i	$-0.986346\pi$
$43$		−	0.562412i		−	0.0857671i	0.999080	−	0.0428835i	$-0.0136544\pi$
$44$	2.72353	+	0.729768i	0.410588	+	0.110017i
$45$	13.2564	−	3.55205i	1.97615	−	0.529508i
$46$	8.44806	−	2.26365i	1.24560	−	0.333757i
$47$	−3.72492	−	0.998090i	−0.543336	−	0.145586i	−0.0232964	−	0.999729i	$-0.507416\pi$
$47$	−3.72492	−	0.998090i	−0.543336	−	0.145586i	−0.520040	+	0.854142i	$0.674083\pi$
$48$			12.1650i			1.75587i
$49$		0			0
$50$	9.04560	+	9.04560i	1.27924	+	1.27924i
$51$	5.62243	−	3.24611i	0.787298	−	0.454547i
$52$	−4.65155	−	3.63258i	−0.645054	−	0.503748i
$53$	−2.67755	+	4.63764i	−0.367789	+	0.637029i	−0.989220	−	0.146440i	$-0.953219\pi$
$53$	−2.67755	+	4.63764i	−0.367789	+	0.637029i	0.621430	+	0.783469i	$0.286552\pi$
$54$	−1.32117	+	4.93069i	−0.179789	+	0.670982i
$55$		−	5.89396i		−	0.794742i
$56$		0			0
$57$	9.75092	−	9.75092i	1.29154	−	1.29154i
$58$	−0.339059	−	0.0908505i	−0.0445206	−	0.0119293i
$59$	3.73550	+	13.9411i	0.486320	+	1.81497i	0.574041	+	0.818827i	$0.305375\pi$
$59$	3.73550	+	13.9411i	0.486320	+	1.81497i	−0.0877205	+	0.996145i	$0.527958\pi$
$60$	−14.3249	+	3.83834i	−1.84934	+	0.495528i
$61$	1.30750	−	0.754885i	0.167408	−	0.0966531i	−0.413955	−	0.910297i	$-0.635853\pi$
$61$	1.30750	−	0.754885i	0.167408	−	0.0966531i	0.581363	+	0.813644i	$0.302520\pi$
$62$	4.85807			0.616975
$63$		0			0
$64$		−	4.87935i		−	0.609918i
$65$	−4.81803	+	11.3573i	−0.597603	+	1.40871i
$66$	7.53270	+	4.34901i	0.927212	+	0.535326i
$67$	1.78754	+	6.67118i	0.218382	+	0.815014i	0.984948	+	0.172848i	$0.0552971\pi$
$67$	1.78754	+	6.67118i	0.218382	+	0.815014i	−0.766566	+	0.642165i	$0.778036\pi$
$68$	−3.47583	+	2.00677i	−0.421506	+	0.243357i
$69$	12.1432			1.46188
$70$		0			0
$71$	1.70926	−	1.70926i	0.202852	−	0.202852i	−0.598369	−	0.801221i	$-0.704184\pi$
$71$	1.70926	−	1.70926i	0.202852	−	0.202852i	0.801221	+	0.598369i	$0.204184\pi$
$72$	−0.718846	+	2.68277i	−0.0847168	+	0.316168i
$73$	−3.15770	−	11.7847i	−0.369581	−	1.37929i	−0.861104	−	0.508429i	$-0.830226\pi$
$73$	−3.15770	−	11.7847i	−0.369581	−	1.37929i	0.491523	−	0.870864i	$-0.336440\pi$
$74$	−0.207493	+	0.359389i	−0.0241206	+	0.0417781i
$75$	8.88063	+	15.3817i	1.02545	+	1.77613i
$76$	−6.02809	+	6.02809i	−0.691469	+	0.691469i
$77$		0			0
$78$	−10.9600	−	14.5379i	−1.24098	−	1.64610i
$79$	−1.48398	−	2.57034i	−0.166961	−	0.289185i	0.770389	−	0.637574i	$-0.220062\pi$
$79$	−1.48398	−	2.57034i	−0.166961	−	0.289185i	−0.937350	+	0.348389i	$0.886729\pi$
$80$	−15.1848	+	4.06875i	−1.69771	+	0.454900i
$81$	2.47267	−	4.28279i	0.274741	−	0.475866i
$82$	−6.24677	−	10.8197i	−0.689840	−	1.19484i
$83$	0.504742	+	0.504742i	0.0554026	+	0.0554026i	0.734265	−	0.678863i	$-0.237527\pi$
$83$	0.504742	+	0.504742i	0.0554026	+	0.0554026i	−0.678863	+	0.734265i	$0.737527\pi$
$84$		0			0
$85$	5.93241	+	5.93241i	0.643460	+	0.643460i
$86$	−0.277598	+	1.03601i	−0.0299342	+	0.111716i
$87$	−0.422069	−	0.243682i	−0.0452505	−	0.0261254i
$88$	1.03299	+	0.596396i	0.110117	+	0.0635760i
$89$	7.20177	+	1.92971i	0.763386	+	0.204549i	0.619447	−	0.785038i	$-0.287357\pi$
$89$	7.20177	+	1.92971i	0.763386	+	0.204549i	0.143938	+	0.989587i	$0.454023\pi$
$90$	−26.1726			−2.75884
$91$		0			0
$92$	−7.50704			−0.782663
$93$	6.51522	+	1.74575i	0.675597	+	0.181026i
$94$	6.36898	+	3.67713i	0.656910	+	0.379267i
$95$	15.4328	+	8.91011i	1.58337	+	0.914158i
$96$	5.05537	−	18.8669i	0.515961	−	1.92559i
$97$	−12.0949	−	12.0949i	−1.22805	−	1.22805i	−0.964699	−	0.263356i	$-0.915171\pi$
$97$	−12.0949	−	12.0949i	−1.22805	−	1.22805i	−0.263356	−	0.964699i	$-0.584829\pi$
$98$		0			0
$99$	4.88535	+	4.88535i	0.490996	+	0.490996i
$100$	−5.49007	−	9.50908i	−0.549007	−	0.950908i
$101$	4.11357	−	7.12491i	0.409316	−	0.708955i	−0.585498	−	0.810674i	$-0.699101\pi$
$101$	4.11357	−	7.12491i	0.409316	−	0.708955i	0.994813	+	0.101719i	$0.0324342\pi$
$102$	−11.9592	+	3.20446i	−1.18414	+	0.317289i
$103$	3.74883	+	6.49316i	0.369383	+	0.639790i	0.989469	−	0.144743i	$-0.0462357\pi$
$103$	3.74883	+	6.49316i	0.369383	+	0.639790i	−0.620086	+	0.784534i	$0.712902\pi$
$104$	−1.50299	−	1.99364i	−0.147380	−	0.195493i
$105$		0			0
$106$	7.22133	−	7.22133i	0.701398	−	0.701398i
$107$	1.99457	+	3.45470i	0.192823	+	0.333978i	0.946185	−	0.323628i	$-0.104902\pi$
$107$	1.99457	+	3.45470i	0.192823	+	0.333978i	−0.753362	+	0.657606i	$0.771569\pi$
$108$	2.19073	−	3.79446i	0.210803	−	0.365122i
$109$	−3.02188	−	11.2778i	−0.289443	−	1.08022i	−0.945531	−	0.325532i	$-0.894456\pi$
$109$	−3.02188	−	11.2778i	−0.289443	−	1.08022i	0.656088	−	0.754685i	$-0.272210\pi$
$110$	−2.90917	+	10.8572i	−0.277378	+	1.03519i
$111$	−0.407418	+	0.407418i	−0.0386704	+	0.0386704i
$112$		0			0
$113$	−8.36429			−0.786846			−0.393423	−	0.919358i	$-0.628709\pi$
$113$	−8.36429			−0.786846			−0.393423	+	0.919358i	$0.628709\pi$
$114$	−22.7749	+	13.1491i	−2.13307	+	1.23153i
$115$	4.06147	+	15.1576i	0.378734	+	1.41346i
$116$	0.260926	+	0.150646i	0.0242264	+	0.0139871i
$117$	−5.42026	−	13.4073i	−0.501103	−	1.23951i
$118$		−	27.5244i		−	2.53382i
$119$		0			0
$120$	−6.27370			−0.572708
$121$	−6.95668	+	4.01644i	−0.632425	+	0.365131i
$122$	−2.78112	+	0.745199i	−0.251791	+	0.0674671i
$123$	−4.48956	−	16.7553i	−0.404810	−	1.51077i
$124$	−4.02775	−	1.07923i	−0.361703	−	0.0969180i
$125$	−4.13226	+	4.13226i	−0.369601	+	0.369601i
$126$		0			0
$127$		−	12.0998i		−	1.07368i	−0.843684	−	0.536840i	$-0.819618\pi$
$127$		−	12.0998i		−	1.07368i	0.843684	−	0.536840i	$-0.180382\pi$
$128$	1.41015	−	5.26276i	0.124641	−	0.465167i
$129$	−0.744581	+	1.28965i	−0.0655567	+	0.113548i
$130$	14.4810	−	18.5431i	1.27007	−	1.62633i
$131$	−1.54544	+	0.892262i	−0.135026	+	0.0779573i	−0.565991	−	0.824411i	$-0.691506\pi$
$131$	−1.54544	+	0.892262i	−0.135026	+	0.0779573i	0.430965	+	0.902368i	$0.358173\pi$
$132$	−5.27911	−	5.27911i	−0.459488	−	0.459488i
$133$		0			0
$134$		−	13.1712i		−	1.13781i
$135$	−8.84671	−	2.37047i	−0.761404	−	0.204018i
$136$	−1.64001	+	0.439440i	−0.140630	+	0.0376817i
$137$	−18.7562	+	5.02570i	−1.60245	+	0.429374i	−0.945780	−	0.324807i	$-0.894701\pi$
$137$	−18.7562	+	5.02570i	−1.60245	+	0.429374i	−0.656666	+	0.754181i	$0.728034\pi$
$138$	−22.3689	−	5.99372i	−1.90416	−	0.510219i
$139$			13.5866i			1.15240i	0.817310	+	0.576198i	$0.195464\pi$
$139$			13.5866i			1.15240i	−0.817310	+	0.576198i	$0.804536\pi$
$140$		0			0
$141$	7.22014	+	7.22014i	0.608046	+	0.608046i
$142$	−3.99226	+	2.30493i	−0.335023	+	0.193426i
$143$	−6.16423	+	0.758214i	−0.515479	+	0.0634050i
$144$	9.21379	−	15.9587i	0.767815	−	1.32990i
$145$	0.163005	−	0.608344i	0.0135368	−	0.0505202i
$146$			23.2670i			1.92559i
$147$		0			0
$148$	0.251869	−	0.251869i	0.0207035	−	0.0207035i
$149$	−3.54964	−	0.951123i	−0.290798	−	0.0779190i	0.110471	−	0.993879i	$-0.464764\pi$
$149$	−3.54964	−	0.951123i	−0.290798	−	0.0779190i	−0.401269	+	0.915960i	$0.631431\pi$
$150$	−8.76669	−	32.7177i	−0.715797	−	2.67139i
$151$	−17.3905	+	4.65978i	−1.41522	+	0.379207i	−0.883786	−	0.467892i	$-0.845014\pi$
$151$	−17.3905	+	4.65978i	−1.41522	+	0.379207i	−0.531435	+	0.847099i	$0.678347\pi$
$152$	−3.12321	+	1.80319i	−0.253326	+	0.146258i
$153$	−9.83443			−0.795066
$154$		0			0
$155$			8.71641i			0.700119i
$156$	5.85714	+	14.4880i	0.468947	+	1.15997i
$157$	15.8740	+	9.16488i	1.26689	+	0.731437i	0.974398	−	0.224832i	$-0.0721833\pi$
$157$	15.8740	+	9.16488i	1.26689	+	0.731437i	0.292489	+	0.956269i	$0.405517\pi$
$158$	1.46494	+	5.46724i	0.116545	+	0.434951i
$159$	12.2796	−	7.08964i	0.973836	−	0.562245i
$160$	25.2411			1.99549
$161$		0			0
$162$	−6.66879	+	6.66879i	−0.523949	+	0.523949i
$163$	−3.34454	+	12.4820i	−0.261964	+	0.977665i	0.702118	+	0.712061i	$0.252238\pi$
$163$	−3.34454	+	12.4820i	−0.261964	+	0.977665i	−0.964082	+	0.265604i	$0.914429\pi$
$164$	2.77547	+	10.3582i	0.216728	+	0.808840i
$165$	−7.80305	+	13.5153i	−0.607467	+	1.05216i
$166$	−0.680643	−	1.17891i	−0.0528282	−	0.0915011i
$167$	−10.6807	+	10.6807i	−0.826494	+	0.826494i	−0.987030	−	0.160536i	$-0.948678\pi$
$167$	−10.6807	+	10.6807i	−0.826494	+	0.826494i	0.160536	+	0.987030i	$0.448678\pi$
$168$		0			0
$169$	12.4979	+	3.57793i	0.961380	+	0.275225i
$170$	−7.99984	−	13.8561i	−0.613560	−	1.06272i
$171$	−20.1772	+	5.40645i	−1.54299	+	0.413442i
$172$	0.460305	−	0.797272i	0.0350979	−	0.0607914i
$173$	1.31009	+	2.26914i	0.0996041	+	0.172519i	0.911521	−	0.411254i	$-0.134909\pi$
$173$	1.31009	+	2.26914i	0.0996041	+	0.172519i	−0.811917	+	0.583773i	$0.801576\pi$
$174$	0.657209	+	0.657209i	0.0498229	+	0.0498229i
$175$		0			0
$176$	−5.59601	−	5.59601i	−0.421815	−	0.421815i
$177$	9.89089	−	36.9133i	0.743445	−	2.77457i
$178$	−12.3138	−	7.10936i	−0.922957	−	0.532869i
$179$	21.9610	+	12.6792i	1.64144	+	0.947687i	0.980322	+	0.197406i	$0.0632517\pi$
$179$	21.9610	+	12.6792i	1.64144	+	0.947687i	0.661119	+	0.750281i	$0.270082\pi$
$180$	21.6994	+	5.81433i	1.61737	+	0.433374i
$181$	−1.00365			−0.0746008			−0.0373004	−	0.999304i	$-0.511876\pi$
$181$	−1.00365			−0.0746008			−0.0373004	+	0.999304i	$0.511876\pi$
$182$		0			0
$183$	−3.99758			−0.295510
$184$	−3.06753	−	0.821942i	−0.226141	−	0.0605944i
$185$	−0.644820	−	0.372287i	−0.0474081	−	0.0273711i
$186$	−11.1399	−	6.43162i	−0.816817	−	0.471589i
$187$	−1.09313	+	4.07960i	−0.0799373	+	0.298330i
$188$	−4.46354	−	4.46354i	−0.325537	−	0.325537i
$189$		0			0
$190$	−24.0305	−	24.0305i	−1.74336	−	1.74336i
$191$	0.525192	+	0.909659i	0.0380016	+	0.0658206i	0.884401	−	0.466729i	$-0.154567\pi$
$191$	0.525192	+	0.909659i	0.0380016	+	0.0658206i	−0.846399	+	0.532549i	$0.821234\pi$
$192$	−6.45980	+	11.1887i	−0.466196	+	0.807475i
$193$	−1.90975	+	0.511716i	−0.137467	+	0.0368341i	−0.326896	−	0.945060i	$-0.606003\pi$
$193$	−1.90975	+	0.511716i	−0.137467	+	0.0368341i	0.189430	+	0.981894i	$0.439336\pi$
$194$	16.3100	+	28.2497i	1.17099	+	2.02821i
$195$	26.0842	−	19.6646i	1.86793	−	1.40821i
$196$		0			0
$197$	−3.36094	+	3.36094i	−0.239457	+	0.239457i	−0.816625	−	0.577168i	$-0.804158\pi$
$197$	−3.36094	+	3.36094i	−0.239457	+	0.239457i	0.577168	+	0.816625i	$0.304158\pi$
$198$	−6.58788	−	11.4105i	−0.468180	−	0.810912i
$199$	5.10311	−	8.83885i	0.361750	−	0.626569i	−0.626499	−	0.779422i	$-0.715513\pi$
$199$	5.10311	−	8.83885i	0.361750	−	0.626569i	0.988249	+	0.152853i	$0.0488461\pi$
$200$	−1.20221	−	4.48671i	−0.0850091	−	0.317258i
$201$	4.73306	−	17.6640i	0.333844	−	1.24592i
$202$	−11.0943	+	11.0943i	−0.780591	+	0.780591i
$203$		0			0
$204$	10.6271			0.744045
$205$	19.4129	−	11.2080i	1.35586	−	0.782803i
$206$	−3.70073	−	13.8113i	−0.257842	−	0.962280i
$207$	−15.9302	−	9.19730i	−1.10722	−	0.639257i
$208$	6.20873	+	15.3577i	0.430498	+	1.06486i
$209$			8.97101i			0.620538i
$210$		0			0
$211$	16.1396			1.11109			0.555547	−	0.831485i	$-0.312509\pi$
$211$	16.1396			1.11109			0.555547	+	0.831485i	$0.312509\pi$
$212$	−7.59134	+	4.38286i	−0.521375	+	0.301016i
$213$	−6.18236	+	1.65656i	−0.423608	+	0.113505i
$214$	−1.96898	−	7.34833i	−0.134597	−	0.502322i
$215$	−1.85882	−	0.498070i	−0.126771	−	0.0339681i
$216$	1.31063	−	1.31063i	0.0891772	−	0.0891772i
$217$		0			0
$218$			22.2662i			1.50806i
$219$	−8.36099	+	31.2036i	−0.564983	+	2.10855i
$220$	4.82390	−	8.35524i	0.325227	−	0.563310i
$221$	5.44128	−	6.96760i	0.366020	−	0.468691i
$222$	0.951593	−	0.549403i	0.0638668	−	0.0368735i
$223$	−0.0939482	−	0.0939482i	−0.00629124	−	0.00629124i	0.703954	−	0.710245i	$-0.251416\pi$
$223$	−0.0939482	−	0.0939482i	−0.00629124	−	0.00629124i	−0.710245	+	0.703954i	$0.751416\pi$
$224$		0			0
$225$		−	26.9048i		−	1.79365i
$226$	15.4077	+	4.12848i	1.02491	+	0.274623i
$227$	25.6086	−	6.86181i	1.69970	−	0.455434i	0.726839	−	0.686808i	$-0.240989\pi$
$227$	25.6086	−	6.86181i	1.69970	−	0.455434i	0.972865	+	0.231374i	$0.0743221\pi$
$228$	21.8035	−	5.84222i	1.44397	−	0.386910i
$229$	−17.0148	−	4.55909i	−1.12437	−	0.301273i	−0.351718	−	0.936106i	$-0.614402\pi$
$229$	−17.0148	−	4.55909i	−1.12437	−	0.301273i	−0.772650	+	0.634833i	$0.781069\pi$
$230$		−	29.9263i		−	1.97328i
$231$		0			0
$232$	0.0901255	+	0.0901255i	0.00591703	+	0.00591703i
$233$	4.40536	−	2.54344i	0.288605	−	0.166626i	−0.348708	−	0.937232i	$-0.613379\pi$
$233$	4.40536	−	2.54344i	0.288605	−	0.166626i	0.637313	+	0.770605i	$0.280046\pi$
$234$	3.36691	+	27.3728i	0.220102	+	1.78942i
$235$	−6.59756	+	11.4273i	−0.430377	+	0.745435i
$236$	−6.11462	+	22.8201i	−0.398028	+	1.48546i
$237$			7.85862i			0.510472i
$238$		0			0
$239$	−13.0182	+	13.0182i	−0.842079	+	0.842079i	−0.989129	−	0.147050i	$-0.953022\pi$
$239$	−13.0182	+	13.0182i	−0.842079	+	0.842079i	0.147050	+	0.989129i	$0.453022\pi$
$240$	40.2065	+	10.7733i	2.59532	+	0.695413i
$241$	0.705731	+	2.63382i	0.0454601	+	0.169659i	0.984924	−	0.172989i	$-0.0553426\pi$
$241$	0.705731	+	2.63382i	0.0454601	+	0.169659i	−0.939464	+	0.342649i	$0.888676\pi$
$242$	14.7972	−	3.96490i	0.951202	−	0.254874i
$243$	−18.2943	+	10.5622i	−1.17358	+	0.677566i
$244$	2.47133			0.158211
$245$		0			0
$246$			33.0805i			2.10914i
$247$	7.33337	−	17.2867i	0.466611	−	1.09992i
$248$	−1.52766	−	0.881993i	−0.0970063	−	0.0560066i
$249$	−0.489179	−	1.82564i	−0.0310004	−	0.115695i
$250$	9.65160	−	5.57235i	0.610421	−	0.352426i
$251$	−21.4230			−1.35221			−0.676105	−	0.736805i	$-0.736334\pi$
$251$	−21.4230			−1.35221			−0.676105	+	0.736805i	$0.736334\pi$
$252$		0			0
$253$	−5.58599	+	5.58599i	−0.351188	+	0.351188i
$254$	−5.97226	+	22.2888i	−0.374733	+	1.39852i
$255$	−5.74949	−	21.4574i	−0.360047	−	1.34371i
$256$	−10.0746	+	17.4497i	−0.629662	+	1.09061i
$257$	4.80460	+	8.32182i	0.299703	+	0.519101i	0.976068	−	0.217466i	$-0.0697791\pi$
$257$	4.80460	+	8.32182i	0.299703	+	0.519101i	−0.676365	+	0.736567i	$0.736446\pi$
$258$	2.00813	−	2.00813i	0.125021	−	0.125021i
$259$		0			0
$260$	−16.1254	+	12.1568i	−1.00006	+	0.753932i
$261$	0.369129	+	0.639350i	0.0228485	+	0.0395748i
$262$	3.28724	−	0.880814i	0.203086	−	0.0544168i
$263$	3.93499	−	6.81560i	0.242642	−	0.420268i	−0.718824	−	0.695192i	$-0.755319\pi$
$263$	3.93499	−	6.81560i	0.242642	−	0.420268i	0.961466	+	0.274924i	$0.0886527\pi$
$264$	−1.57914	−	2.73516i	−0.0971896	−	0.168337i
$265$	12.9566	+	12.9566i	0.795918	+	0.795918i
$266$		0			0
$267$	−13.9594	−	13.9594i	−0.854303	−	0.854303i
$268$	−2.92601	+	10.9200i	−0.178734	+	0.667046i
$269$	3.44131	+	1.98684i	0.209820	+	0.121140i	0.601228	−	0.799078i	$-0.294678\pi$
$269$	3.44131	+	1.98684i	0.209820	+	0.121140i	−0.391408	+	0.920217i	$0.628012\pi$
$270$	15.1264	+	8.73320i	0.920560	+	0.531486i
$271$	−16.5133	−	4.42472i	−1.00311	−	0.268782i	−0.280362	−	0.959894i	$-0.590454\pi$
$271$	−16.5133	−	4.42472i	−1.00311	−	0.268782i	−0.722748	+	0.691112i	$0.757121\pi$
$272$	11.2650			0.683042
$273$		0			0
$274$	37.0310			2.23712
$275$	−11.1609	−	2.99055i	−0.673026	−	0.180337i
$276$	17.2142	+	9.93861i	1.03617	+	0.598234i
$277$	−21.7301	−	12.5459i	−1.30564	−	0.753811i	−0.324273	−	0.945963i	$-0.605120\pi$
$277$	−21.7301	−	12.5459i	−1.30564	−	0.753811i	−0.981365	+	0.192153i	$0.938453\pi$
$278$	6.70611	−	25.0276i	0.402206	−	1.50105i
$279$	−7.22480	−	7.22480i	−0.432537	−	0.432537i
$280$		0			0
$281$	−2.15639	−	2.15639i	−0.128639	−	0.128639i	0.639856	−	0.768495i	$-0.278994\pi$
$281$	−2.15639	−	2.15639i	−0.128639	−	0.128639i	−0.768495	+	0.639856i	$0.778994\pi$
$282$	−9.73635	−	16.8639i	−0.579791	−	1.00423i
$283$	−5.67952	+	9.83723i	−0.337613	+	0.584762i	−0.983983	−	0.178261i	$-0.942953\pi$
$283$	−5.67952	+	9.83723i	−0.337613	+	0.584762i	0.646370	+	0.763024i	$0.276286\pi$
$284$	3.82198	−	1.02410i	0.226793	−	0.0607689i
$285$	−23.5923	−	40.8631i	−1.39749	−	2.42052i
$286$	11.7293	+	1.64588i	0.693566	+	0.0973226i
$287$		0			0
$288$	−20.9217	+	20.9217i	−1.23282	+	1.23282i
$289$	5.49404	+	9.51596i	0.323179	+	0.559762i
$290$	−0.600538	+	1.04016i	−0.0352648	+	0.0610805i
$291$	11.7220	+	43.7471i	0.687156	+	2.56450i
$292$	5.16882	−	19.2903i	0.302482	−	1.12888i
$293$	10.2833	−	10.2833i	0.600758	−	0.600758i	−0.339756	−	0.940514i	$-0.610344\pi$
$293$	10.2833	−	10.2833i	0.600758	−	0.600758i	0.940514	+	0.339756i	$0.110344\pi$
$294$		0			0
$295$	49.3846			2.87528
$296$	0.130496	−	0.0753417i	0.00758490	−	0.00437915i
$297$	−1.19334	−	4.45359i	−0.0692443	−	0.258423i
$298$	6.06927	+	3.50410i	0.351583	+	0.202987i
$299$	15.3302	−	6.19763i	0.886568	−	0.358418i
$300$			29.0733i			1.67855i
$301$		0			0
$302$	34.3348			1.97575
$303$	−18.8654	+	10.8920i	−1.08379	+	0.625727i
$304$	23.1123	−	6.19292i	1.32558	−	0.355188i
$305$	−1.33705	−	4.98992i	−0.0765590	−	0.285722i
$306$	18.1158	+	4.85412i	1.03561	+	0.277492i
$307$	−7.01794	+	7.01794i	−0.400535	+	0.400535i	−0.878422	−	0.477886i	$-0.841403\pi$
$307$	−7.01794	+	7.01794i	−0.400535	+	0.400535i	0.477886	+	0.878422i	$0.341403\pi$
$308$		0			0
$309$		−	19.8524i		−	1.12936i
$310$	4.30229	−	16.0563i	0.244353	−	0.911939i
$311$	−1.26356	+	2.18855i	−0.0716498	+	0.124101i	−0.899625	−	0.436664i	$-0.856160\pi$
$311$	−1.26356	+	2.18855i	−0.0716498	+	0.124101i	0.827975	+	0.560766i	$0.189493\pi$
$312$	0.807065	+	6.56138i	0.0456910	+	0.371465i
$313$	2.98609	−	1.72402i	0.168784	−	0.0974473i	−0.413229	−	0.910627i	$-0.635599\pi$
$313$	2.98609	−	1.72402i	0.168784	−	0.0974473i	0.582012	+	0.813180i	$0.302266\pi$
$314$	−24.7177	−	24.7177i	−1.39490	−	1.39490i
$315$		0			0
$316$		−	4.85825i		−	0.273298i
$317$	30.5805	+	8.19402i	1.71757	+	0.460222i	0.977261	−	0.212041i	$-0.0680112\pi$
$317$	30.5805	+	8.19402i	1.71757	+	0.460222i	0.740312	+	0.672264i	$0.234678\pi$
$318$	−26.1194	+	6.99867i	−1.46470	+	0.392466i
$319$	0.306251	−	0.0820597i	0.0171468	−	0.00459446i
$320$	−16.1267	−	4.32113i	−0.901509	−	0.241559i
$321$		−	10.5625i		−	0.589541i
$322$		0			0
$323$	−9.02953	−	9.02953i	−0.502416	−	0.502416i
$324$	7.01048	−	4.04750i	0.389471	−	0.224861i
$325$	19.0618	+	14.8861i	1.05736	+	0.825733i
$326$	12.3218	−	21.3420i	0.682443	−	1.18203i
$327$	−8.00136	+	29.8615i	−0.442476	+	1.65134i
$328$			4.53646i			0.250484i
$329$		0			0
$330$	21.0448	−	21.0448i	1.15848	−	1.15848i
$331$	−31.4996	−	8.44029i	−1.73137	−	0.463920i	−0.750874	−	0.660445i	$-0.770368\pi$
$331$	−31.4996	−	8.44029i	−1.73137	−	0.463920i	−0.980499	+	0.196525i	$0.937034\pi$
$332$	0.302414	+	1.12862i	0.0165971	+	0.0619412i
$333$	0.843053	−	0.225895i	0.0461990	−	0.0123790i
$334$	24.9465	−	14.4029i	1.36501	−	0.788089i
$335$	23.6319			1.29115
$336$		0			0
$337$			8.54695i			0.465582i	0.972527	+	0.232791i	$0.0747858\pi$
$337$			8.54695i			0.465582i	−0.972527	+	0.232791i	$0.925214\pi$
$338$	−21.2562	−	12.7596i	−1.15619	−	0.694032i
$339$	19.1799	+	11.0735i	1.04171	+	0.601432i
$340$	3.55437	+	13.2651i	0.192763	+	0.719401i
$341$	−3.80011	+	2.19400i	−0.205788	+	0.118812i
$342$	39.8365			2.15411
$343$		0			0
$344$	0.275383	−	0.275383i	0.0148476	−	0.0148476i
$345$	10.7540	−	40.1345i	0.578977	−	2.16077i
$346$	−1.29328	−	4.82658i	−0.0695270	−	0.259478i
$347$	−1.36789	+	2.36925i	−0.0734321	+	0.127188i	−0.900403	−	0.435056i	$-0.856729\pi$
$347$	−1.36789	+	2.36925i	−0.0734321	+	0.127188i	0.826971	+	0.562244i	$0.190062\pi$
$348$	−0.398881	−	0.690883i	−0.0213823	−	0.0370352i
$349$	−8.57575	+	8.57575i	−0.459049	+	0.459049i	−0.898343	−	0.439294i	$-0.855229\pi$
$349$	−8.57575	+	8.57575i	−0.459049	+	0.459049i	0.439294	+	0.898343i	$0.355229\pi$
$350$		0			0
$351$	−1.34110	+	9.55732i	−0.0715828	+	0.510132i
$352$	6.35341	+	11.0044i	0.338638	+	0.586538i
$353$	−10.5982	+	2.83977i	−0.564083	+	0.151146i	−0.529581	−	0.848259i	$-0.677651\pi$
$353$	−10.5982	+	2.83977i	−0.564083	+	0.151146i	−0.0345014	+	0.999405i	$0.510984\pi$
$354$	−36.4397	+	63.1154i	−1.93675	+	3.35455i
$355$	−4.13555	−	7.16298i	−0.219492	−	0.380171i
$356$	8.62981	+	8.62981i	0.457379	+	0.457379i
$357$		0			0
$358$	−34.1957	−	34.1957i	−1.80730	−	1.80730i
$359$	−0.277147	+	1.03433i	−0.0146273	+	0.0545897i	−0.972854	−	0.231421i	$-0.925663\pi$
$359$	−0.277147	+	1.03433i	−0.0146273	+	0.0545897i	0.958226	+	0.286011i	$0.0923292\pi$
$360$	8.23019	+	4.75170i	0.433769	+	0.250437i
$361$	−7.03523	−	4.06179i	−0.370275	−	0.213779i
$362$	1.84881	+	0.495387i	0.0971712	+	0.0260370i
$363$	21.2695			1.11636
$364$		0			0
$365$	−41.7459			−2.18508
$366$	7.36388	+	1.97315i	0.384916	+	0.103138i
$367$	−6.72705	−	3.88386i	−0.351149	−	0.202736i	0.314042	−	0.949409i	$-0.398317\pi$
$367$	−6.72705	−	3.88386i	−0.351149	−	0.202736i	−0.665191	+	0.746673i	$0.731650\pi$
$368$	18.2475	+	10.5352i	0.951218	+	0.549186i
$369$	−6.80078	+	25.3809i	−0.354035	+	1.32128i
$370$	1.00406	+	1.00406i	0.0521984	+	0.0521984i
$371$		0			0
$372$	7.80712	+	7.80712i	0.404781	+	0.404781i
$373$	8.89119	+	15.4000i	0.460368	+	0.797382i	0.998979	−	0.0451732i	$-0.0143840\pi$
$373$	8.89119	+	15.4000i	0.460368	+	0.797382i	−0.538611	+	0.842555i	$0.681051\pi$
$374$	4.02726	−	6.97542i	0.208245	−	0.360690i
$375$	14.9463	−	4.00485i	0.771824	−	0.206810i
$376$	−1.33518	−	2.31260i	−0.0688568	−	0.119263i
$377$	−0.657209	−	0.0922209i	−0.0338480	−	0.00474962i
$378$		0			0
$379$	−25.3241	+	25.3241i	−1.30081	+	1.30081i	−0.372964	+	0.927846i	$0.621659\pi$
$379$	−25.3241	+	25.3241i	−1.30081	+	1.30081i	−0.927846	+	0.372964i	$0.878341\pi$
$380$	14.5849	+	25.2618i	0.748191	+	1.29590i
$381$	−16.0189	+	27.7456i	−0.820675	+	1.42145i
$382$	−0.518453	−	1.93489i	−0.0265264	−	0.0989978i
$383$	−5.37524	+	20.0607i	−0.274662	+	1.02505i	0.681405	+	0.731906i	$0.261369\pi$
$383$	−5.37524	+	20.0607i	−0.274662	+	1.02505i	−0.956068	+	0.293147i	$0.905298\pi$
$384$	−10.2010	+	10.2010i	−0.520567	+	0.520567i
$385$		0			0
$386$	3.77049			0.191913
$387$	1.95357	−	1.12789i	0.0993053	−	0.0573340i
$388$	−7.24662	−	27.0448i	−0.367892	−	1.37299i
$389$	6.90083	+	3.98420i	0.349886	+	0.202007i	0.664635	−	0.747168i	$-0.268587\pi$
$389$	6.90083	+	3.98420i	0.349886	+	0.202007i	−0.314749	+	0.949175i	$0.601920\pi$
$390$	−57.7553	+	23.3491i	−2.92455	+	1.18233i
$391$		−	11.2449i		−	0.568677i
$392$		0			0
$393$	4.72508			0.238349
$394$	7.85005	−	4.53223i	0.395480	−	0.228330i
$395$	−9.80941	+	2.62842i	−0.493565	+	0.132250i
$396$	2.92703	+	10.9238i	0.147089	+	0.548943i
$397$	−29.6791	−	7.95249i	−1.48955	−	0.399124i	−0.579966	−	0.814641i	$-0.696934\pi$
$397$	−29.6791	−	7.95249i	−1.48955	−	0.399124i	−0.909586	+	0.415516i	$0.863601\pi$
$398$	−13.7631	+	13.7631i	−0.689880	+	0.689880i
$399$		0			0
$400$			30.8186i			1.54093i
$401$	5.83228	−	21.7664i	0.291250	−	1.08696i	−0.652900	−	0.757444i	$-0.726448\pi$
$401$	5.83228	−	21.7664i	0.291250	−	1.08696i	0.944150	−	0.329516i	$-0.106885\pi$
$402$	−17.4374	+	30.2024i	−0.869697	+	1.50636i
$403$	9.11610	−	1.12130i	0.454105	−	0.0558560i
$404$	11.6627	−	6.73348i	0.580243	−	0.335003i
$405$	−11.9652	−	11.9652i	−0.594557	−	0.594557i
$406$		0			0
$407$		−	0.374831i		−	0.0185797i
$408$	4.34245	+	1.16356i	0.214983	+	0.0576046i
$409$	−38.1167	+	10.2133i	−1.88475	+	0.505016i	−0.885568	+	0.464510i	$0.846230\pi$
$409$	−38.1167	+	10.2133i	−1.88475	+	0.505016i	−0.999179	+	0.0405065i	$0.987103\pi$
$410$	−41.2923	+	11.0642i	−2.03928	+	0.546423i
$411$	49.6628	+	13.3071i	2.44968	+	0.656391i
$412$			12.2729i			0.604642i
$413$		0			0
$414$	24.8051	+	24.8051i	1.21910	+	1.21910i
$415$	2.11521	−	1.22122i	0.103832	−	0.0599473i
$416$	−3.24708	−	26.3986i	−0.159201	−	1.29430i
$417$	17.9873	−	31.1549i	0.880843	−	1.52566i
$418$	4.42795	−	16.5253i	0.216578	−	0.808281i
$419$		−	6.86945i		−	0.335595i	−0.985821	−	0.167797i	$-0.946335\pi$
$419$		−	6.86945i		−	0.335595i	0.985821	−	0.167797i	$-0.0536654\pi$
$420$		0			0
$421$	−16.8752	+	16.8752i	−0.822445	+	0.822445i	−0.986458	−	0.164013i	$-0.947556\pi$
$421$	−16.8752	+	16.8752i	−0.822445	+	0.822445i	0.164013	+	0.986458i	$0.447556\pi$
$422$	−29.7304	−	7.96624i	−1.44725	−	0.387790i
$423$	−4.00325	−	14.9403i	−0.194645	−	0.726424i
$424$	−3.58185	+	0.959754i	−0.173950	+	0.0466098i
$425$	14.2437	−	8.22363i	0.690923	−	0.398904i
$426$	12.2061			0.591386
$427$		0			0
$428$			6.52981i			0.315630i
$429$	15.1388	+	6.42222i	0.730909	+	0.310068i
$430$	3.17827	+	1.83497i	0.153270	+	0.0884903i
$431$	−9.20095	−	34.3384i	−0.443194	−	1.65402i	−0.720661	−	0.693288i	$-0.756161\pi$
$431$	−9.20095	−	34.3384i	−0.443194	−	1.65402i	0.277467	−	0.960735i	$-0.410505\pi$
$432$	−10.6501	+	6.14885i	−0.512404	+	0.295837i
$433$	6.53945			0.314266			0.157133	−	0.987577i	$-0.449775\pi$
$433$	6.53945			0.314266			0.157133	+	0.987577i	$0.449775\pi$
$434$		0			0
$435$	−1.17917	+	1.17917i	−0.0565370	+	0.0565370i
$436$	4.94650	−	18.4606i	0.236894	−	0.884101i
$437$	−6.18184	−	23.0709i	−0.295717	−	1.10363i
$438$	30.8033	−	53.3528i	1.47184	−	2.54930i
$439$	−12.2931	−	21.2923i	−0.586719	−	1.01623i	−0.994659	−	0.103218i	$-0.967086\pi$
$439$	−12.2931	−	21.2923i	−0.586719	−	1.01623i	0.407940	−	0.913009i	$-0.366247\pi$
$440$	2.88595	−	2.88595i	0.137582	−	0.137582i
$441$		0			0
$442$	−13.4624	+	10.1492i	−0.640340	+	0.482746i
$443$	7.79952	+	13.5092i	0.370566	+	0.641840i	0.989653	−	0.143483i	$-0.0458303\pi$
$443$	7.79952	+	13.5092i	0.370566	+	0.641840i	−0.619086	+	0.785323i	$0.712497\pi$
$444$	−0.911004	+	0.244103i	−0.0432343	+	0.0115846i
$445$	12.7557	−	22.0935i	0.604679	−	1.04733i
$446$	0.126689	+	0.219432i	0.00599890	+	0.0103904i
$447$	6.88038	+	6.88038i	0.325431	+	0.325431i
$448$		0			0
$449$	28.6271	+	28.6271i	1.35100	+	1.35100i	0.884550	+	0.466445i	$0.154465\pi$
$449$	28.6271	+	28.6271i	1.35100	+	1.35100i	0.466445	+	0.884550i	$0.345535\pi$
$450$	−13.2798	+	49.5608i	−0.626015	+	2.33632i
$451$	9.77279	+	5.64232i	0.460183	+	0.265686i
$452$	−11.8572	−	6.84573i	−0.557714	−	0.321996i
$453$	46.0468	+	12.3382i	2.16347	+	0.579700i
$454$	−50.5601			−2.37290
$455$		0			0
$456$	9.54900			0.447173
$457$	12.6236	+	3.38248i	0.590507	+	0.158226i	0.541685	−	0.840582i	$-0.317787\pi$
$457$	12.6236	+	3.38248i	0.590507	+	0.158226i	0.0488218	+	0.998808i	$0.484453\pi$
$458$	29.0923	+	16.7965i	1.35939	+	0.784847i
$459$	5.68376	+	3.28152i	0.265295	+	0.153168i
$460$	−6.64821	+	24.8114i	−0.309974	+	1.15684i
$461$	3.55813	+	3.55813i	0.165719	+	0.165719i	0.785095	−	0.619376i	$-0.212614\pi$
$461$	3.55813	+	3.55813i	0.165719	+	0.165719i	−0.619376	+	0.785095i	$0.712614\pi$
$462$		0			0
$463$	−11.6246	−	11.6246i	−0.540241	−	0.540241i	0.383359	−	0.923600i	$-0.374767\pi$
$463$	−11.6246	−	11.6246i	−0.540241	−	0.540241i	−0.923600	+	0.383359i	$0.874767\pi$
$464$	−0.422825	−	0.732355i	−0.0196292	−	0.0339987i
$465$	11.5397	−	19.9874i	0.535141	−	0.926891i
$466$	−9.37044	+	2.51080i	−0.434077	+	0.116311i
$467$	2.86541	+	4.96304i	0.132595	+	0.229662i	0.924676	−	0.380754i	$-0.124336\pi$
$467$	2.86541	+	4.96304i	0.132595	+	0.229662i	−0.792081	+	0.610416i	$0.791002\pi$
$468$	3.28948	−	23.4423i	0.152056	−	1.08362i
$469$		0			0
$470$	17.7936	−	17.7936i	0.820757	−	0.820757i
$471$	−24.2669	−	42.0315i	−1.11816	−	1.93671i
$472$	−4.99711	+	8.65525i	−0.230011	+	0.398390i
$473$	−0.250737	−	0.935764i	−0.0115289	−	0.0430265i
$474$	3.87890	−	14.4762i	0.178164	−	0.664915i
$475$	24.7028	−	24.7028i	1.13344	−	1.13344i
$476$		0			0
$477$	−21.4788			−0.983445
$478$	30.4062	−	17.5550i	1.39075	−	0.802949i
$479$	−5.24001	−	19.5560i	−0.239422	−	0.893536i	−0.976105	−	0.217298i	$-0.930276\pi$
$479$	−5.24001	−	19.5560i	−0.239422	−	0.893536i	0.736683	−	0.676238i	$-0.236391\pi$
$480$	−57.8797	−	33.4169i	−2.64184	−	1.52527i
$481$	−0.306407	+	0.722280i	−0.0139709	+	0.0329331i
$482$		−	5.20006i		−	0.236856i
$483$		0			0
$484$	−13.1490			−0.597681
$485$	−50.6861	+	29.2636i	−2.30154	+	1.32879i
$486$	38.9129	−	10.4267i	1.76513	−	0.472964i
$487$	−0.409978	−	1.53006i	−0.0185779	−	0.0693336i	0.956015	−	0.293319i	$-0.0947598\pi$
$487$	−0.409978	−	1.53006i	−0.0185779	−	0.0693336i	−0.974592	+	0.223986i	$0.928093\pi$
$488$	1.00984	+	0.270585i	0.0457132	+	0.0122488i
$489$	24.1942	−	24.1942i	1.09410	−	1.09410i
$490$		0			0
$491$		−	22.7308i		−	1.02583i	−0.858440	−	0.512913i	$-0.828566\pi$
$491$		−	22.7308i		−	1.02583i	0.858440	−	0.512913i	$-0.171434\pi$
$492$	7.34893	−	27.4266i	0.331316	−	1.23649i
$493$	−0.225654	+	0.390843i	−0.0101629	+	0.0176027i
$494$	−22.0411	+	28.2238i	−0.991676	+	1.26985i
$495$	20.4730	−	11.8201i	0.920191	−	0.531273i
$496$	8.27577	+	8.27577i	0.371593	+	0.371593i
$497$		0			0
$498$			3.60443i			0.161518i
$499$	5.69314	+	1.52547i	0.254860	+	0.0682895i	0.383987	−	0.923339i	$-0.374551\pi$
$499$	5.69314	+	1.52547i	0.254860	+	0.0682895i	−0.129127	+	0.991628i	$0.541217\pi$
$500$	−9.23991	+	2.47583i	−0.413221	+	0.110722i
$501$	38.6317	−	10.3513i	1.72594	−	0.462464i
$502$	39.4630	+	10.5741i	1.76132	+	0.471945i
$503$			11.3499i			0.506069i	0.967457	+	0.253035i	$0.0814286\pi$
$503$			11.3499i			0.506069i	−0.967457	+	0.253035i	$0.918571\pi$
$504$		0			0
$505$	−19.9055	−	19.9055i	−0.885784	−	0.885784i
$506$	13.0470	−	7.53270i	0.580011	−	0.334870i
$507$	−23.9218	−	24.7505i	−1.06241	−	1.09921i
$508$	9.90302	−	17.1525i	0.439376	−	0.761021i
$509$	−7.67573	+	28.6462i	−0.340221	+	1.26972i	0.557876	+	0.829924i	$0.311616\pi$
$509$	−7.67573	+	28.6462i	−0.340221	+	1.26972i	−0.898097	+	0.439797i	$0.855050\pi$
$510$			42.3642i			1.87592i
$511$		0			0
$512$	19.4659	−	19.4659i	0.860279	−	0.860279i
$513$	13.4653	+	3.60802i	0.594507	+	0.159298i
$514$	−4.74296	−	17.7010i	−0.209203	−	0.780756i
$515$	24.7804	−	6.63990i	1.09196	−	0.292589i
$516$	−2.11103	+	1.21880i	−0.0929327	+	0.0536547i
$517$	−6.64265			−0.292143
$518$		0			0
$519$		−	6.93773i		−	0.304532i
$520$	−7.92021	+	3.20195i	−0.347324	+	0.140415i
$521$	−35.0486	−	20.2353i	−1.53551	−	0.886524i	−0.999094	−	0.0425681i	$-0.986446\pi$
$521$	−35.0486	−	20.2353i	−1.53551	−	0.886524i	−0.536412	−	0.843956i	$-0.680221\pi$
$522$	−0.364393	−	1.35993i	−0.0159490	−	0.0595227i
$523$	29.2572	−	16.8917i	1.27933	−	0.738621i	0.302604	−	0.953116i	$-0.402144\pi$
$523$	29.2572	−	16.8917i	1.27933	−	0.738621i	0.976725	+	0.214495i	$0.0688107\pi$
$524$	−2.92108			−0.127608
$525$		0			0
$526$	−10.6127	+	10.6127i	−0.462734	+	0.462734i
$527$	1.61659	−	6.03321i	0.0704199	−	0.262811i
$528$	5.42346	+	20.2406i	0.236026	+	0.880860i
$529$	−0.983639	+	1.70371i	−0.0427669	+	0.0740744i
$530$	−17.4720	−	30.2623i	−0.758934	−	1.31451i
$531$	−40.9336	+	40.9336i	−1.77637	+	1.77637i
$532$		0			0
$533$	−14.2193	−	18.8612i	−0.615906	−	0.816971i
$534$	18.8243	+	32.6046i	0.814605	+	1.41094i
$535$	13.1845	−	3.53277i	0.570015	−	0.152735i
$536$	−2.39125	+	4.14177i	−0.103286	+	0.178897i
$537$	−33.5721	−	58.1486i	−1.44874	−	2.50930i
$538$	−5.35850	−	5.35850i	−0.231021	−	0.231021i
$539$		0			0
$540$	−10.6009	−	10.6009i	−0.456192	−	0.456192i
$541$	−4.16337	+	15.5379i	−0.178997	+	0.668026i	0.816839	+	0.576866i	$0.195724\pi$
$541$	−4.16337	+	15.5379i	−0.178997	+	0.668026i	−0.995836	+	0.0911607i	$0.970942\pi$
$542$	28.2348	+	16.3014i	1.21279	+	0.700205i
$543$	2.30145	+	1.32874i	0.0987645	+	0.0570217i
$544$	−17.4711	−	4.68136i	−0.749066	−	0.200712i
$545$	−39.9503			−1.71128
$546$		0			0
$547$	4.19513			0.179371			0.0896853	−	0.995970i	$-0.471414\pi$
$547$	4.19513			0.179371			0.0896853	+	0.995970i	$0.471414\pi$
$548$	−30.7019	−	8.22654i	−1.31152	−	0.351420i
$549$	5.24426	+	3.02777i	0.223819	+	0.129222i
$550$	19.0832	+	11.0177i	0.813709	+	0.469795i
$551$	−0.248105	+	0.925940i	−0.0105696	+	0.0394464i
$552$	5.94589	+	5.94589i	0.253074	+	0.253074i
$553$		0			0
$554$	33.8363	+	33.8363i	1.43757	+	1.43757i
$555$	0.985746	+	1.70736i	0.0418426	+	0.0724735i
$556$	−11.1199	+	19.2602i	−0.471588	+	0.816814i
$557$	−32.8478	+	8.80155i	−1.39181	+	0.372934i	−0.875396	−	0.483407i	$-0.839399\pi$
$557$	−32.8478	+	8.80155i	−1.39181	+	0.372934i	−0.516412	+	0.856340i	$0.672733\pi$
$558$	9.74263	+	16.8747i	0.412438	+	0.714364i
$559$	−0.281785	+	2.00813i	−0.0119183	+	0.0849349i
$560$		0			0
$561$	7.90763	−	7.90763i	0.333860	−	0.333860i
$562$	2.90789	+	5.03661i	0.122662	+	0.212457i
$563$	14.8890	−	25.7886i	0.627498	−	1.08686i	−0.360554	−	0.932738i	$-0.617412\pi$
$563$	14.8890	−	25.7886i	0.627498	−	1.08686i	0.988052	−	0.154120i	$-0.0492542\pi$
$564$	4.32591	+	16.1445i	0.182154	+	0.679807i
$565$	−7.40738	+	27.6447i	−0.311631	+	1.16302i
$566$	15.3177	−	15.3177i	0.643849	−	0.643849i
$567$		0			0
$568$	1.67386			0.0702338
$569$	10.9152	−	6.30190i	0.457589	−	0.264189i	−0.253441	−	0.967351i	$-0.581562\pi$
$569$	10.9152	−	6.30190i	0.457589	−	0.264189i	0.711030	+	0.703162i	$0.248229\pi$
$570$	23.2896	+	86.9179i	0.975494	+	3.64059i
$571$	−4.31551	−	2.49156i	−0.180598	−	0.104269i	0.406975	−	0.913439i	$-0.366583\pi$
$571$	−4.31551	−	2.49156i	−0.180598	−	0.104269i	−0.587574	+	0.809171i	$0.699917\pi$
$572$	−9.35892	−	3.97026i	−0.391316	−	0.166005i
$573$		−	2.78122i		−	0.116187i
$574$		0			0
$575$	30.7634			1.28292
$576$	16.9486	−	9.78531i	0.706194	−	0.407721i
$577$	−0.563527	+	0.150997i	−0.0234599	+	0.00628607i	−0.270530	−	0.962712i	$-0.587199\pi$
$577$	−0.563527	+	0.150997i	−0.0234599	+	0.00628607i	0.247070	+	0.968998i	$0.420532\pi$
$578$	−5.42355	−	20.2410i	−0.225590	−	0.841913i
$579$	5.05666	+	1.35493i	0.210148	+	0.0563089i
$580$	0.728973	−	0.728973i	0.0302689	−	0.0302689i
$581$		0			0
$582$		−	86.3716i		−	3.58022i
$583$	−2.38743	+	8.91001i	−0.0988773	+	0.369015i
$584$	4.22417	−	7.31648i	0.174797	−	0.302758i
$585$	−49.1126	+	6.04096i	−2.03056	+	0.249763i
$586$	−24.0184	+	13.8670i	−0.992191	+	0.572842i
$587$	2.10756	+	2.10756i	0.0869883	+	0.0869883i	0.749262	−	0.662274i	$-0.230408\pi$
$587$	2.10756	+	2.10756i	0.0869883	+	0.0869883i	−0.662274	+	0.749262i	$0.730408\pi$
$588$		0			0
$589$		−	13.2670i		−	0.546656i
$590$	−90.9706	−	24.3755i	−3.74520	−	1.00352i
$591$	12.1565	−	3.25731i	0.500050	−	0.133988i
$592$	−0.965689	+	0.258756i	−0.0396896	+	0.0106348i
$593$	−1.35537	−	0.363170i	−0.0556584	−	0.0149136i	0.230882	−	0.972982i	$-0.425839\pi$
$593$	−1.35537	−	0.363170i	−0.0556584	−	0.0149136i	−0.286541	+	0.958068i	$0.592505\pi$
$594$			8.79289i			0.360777i
$595$		0			0
$596$	−4.25350	−	4.25350i	−0.174230	−	0.174230i
$597$	−23.4036	+	13.5121i	−0.957846	+	0.553012i
$598$	−31.2985	+	3.84979i	−1.27989	+	0.157430i
$599$	−23.1607	+	40.1154i	−0.946319	+	1.63907i	−0.193230	+	0.981153i	$0.561896\pi$
$599$	−23.1607	+	40.1154i	−0.946319	+	1.63907i	−0.753089	+	0.657919i	$0.771437\pi$
$600$	−3.18322	+	11.8800i	−0.129955	+	0.484997i
$601$		−	41.2270i		−	1.68169i	−0.541279	−	0.840843i	$-0.682060\pi$
$601$		−	41.2270i		−	1.68169i	0.541279	−	0.840843i	$-0.317940\pi$
$602$		0			0
$603$	−19.5878	+	19.5878i	−0.797678	+	0.797678i
$604$	−28.4665	−	7.62757i	−1.15828	−	0.310361i
$605$	7.11389	+	26.5494i	0.289221	+	1.07939i
$606$	40.1278	−	10.7522i	1.63008	−	0.436779i
$607$	7.17511	−	4.14255i	0.291229	−	0.168141i	−0.347267	−	0.937766i	$-0.612890\pi$
$607$	7.17511	−	4.14255i	0.291229	−	0.168141i	0.638496	+	0.769625i	$0.279557\pi$
$608$	−38.4187			−1.55808
$609$		0			0
$610$			9.85180i			0.398888i
$611$	12.8000	+	5.43005i	0.517834	+	0.219676i
$612$	−13.9412	−	8.04897i	−0.563540	−	0.325360i
$613$	4.61049	+	17.2066i	0.186216	+	0.694967i	0.994367	+	0.105992i	$0.0338018\pi$
$613$	4.61049	+	17.2066i	0.186216	+	0.694967i	−0.808151	+	0.588975i	$0.799532\pi$
$614$	16.3916	−	9.46369i	0.661511	−	0.381923i
$615$	−59.3536			−2.39337
$616$		0			0
$617$	−1.41807	+	1.41807i	−0.0570895	+	0.0570895i	−0.735075	−	0.677986i	$-0.762853\pi$
$617$	−1.41807	+	1.41807i	−0.0570895	+	0.0570895i	0.677986	+	0.735075i	$0.262853\pi$
$618$	−9.79884	+	36.5698i	−0.394167	+	1.47105i
$619$	−2.63864	−	9.84753i	−0.106056	−	0.395806i	0.892407	−	0.451231i	$-0.149015\pi$
$619$	−2.63864	−	9.84753i	−0.106056	−	0.395806i	−0.998463	+	0.0554256i	$0.982348\pi$
$620$	−7.13392	+	12.3563i	−0.286505	+	0.496242i
$621$	6.13785	+	10.6311i	0.246303	+	0.426610i
$622$	3.40781	−	3.40781i	0.136641	−	0.136641i
$623$		0			0
$624$	6.09504	−	43.4360i	0.243997	−	1.73883i
$625$	−6.77177	−	11.7291i	−0.270871	−	0.469162i
$626$	−6.35157	+	1.70190i	−0.253860	+	0.0680215i
$627$	11.8768	−	20.5712i	0.474313	−	0.821533i
$628$	15.0020	+	25.9841i	0.598643	+	1.03688i
$629$	0.377276	+	0.377276i	0.0150430	+	0.0150430i
$630$		0			0
$631$	−4.32633	−	4.32633i	−0.172228	−	0.172228i	0.615729	−	0.787958i	$-0.288861\pi$
$631$	−4.32633	−	4.32633i	−0.172228	−	0.172228i	−0.787958	+	0.615729i	$0.788861\pi$
$632$	0.531928	−	1.98518i	0.0211589	−	0.0789663i
$633$	−37.0092	−	21.3673i	−1.47098	−	0.849272i
$634$	−52.2874	−	30.1881i	−2.07660	−	1.19892i
$635$	−39.9908	−	10.7155i	−1.58699	−	0.425232i
$636$	23.2100			0.920336
$637$		0			0
$638$	−0.604643			−0.0239380
$639$	9.36504	+	2.50936i	0.370475	+	0.0992686i
$640$	−16.1451	−	9.32137i	−0.638190	−	0.368459i
$641$	25.2944	+	14.6037i	0.999068	+	0.576812i	0.907972	−	0.419030i	$-0.137630\pi$
$641$	25.2944	+	14.6037i	0.999068	+	0.576812i	0.0910953	+	0.995842i	$0.470963\pi$
$642$	−5.21349	+	19.4570i	−0.205760	+	0.767907i
$643$	14.6743	+	14.6743i	0.578699	+	0.578699i	0.934545	−	0.355846i	$-0.115807\pi$
$643$	14.6743	+	14.6743i	0.578699	+	0.578699i	−0.355846	+	0.934545i	$0.615807\pi$
$644$		0			0
$645$	3.60302	+	3.60302i	0.141869	+	0.141869i
$646$	12.1763	+	21.0900i	0.479070	+	0.829774i
$647$	−4.85993	+	8.41764i	−0.191064	+	0.330932i	−0.945603	−	0.325323i	$-0.894527\pi$
$647$	−4.85993	+	8.41764i	−0.191064	+	0.330932i	0.754539	+	0.656255i	$0.227860\pi$
$648$	3.30779	−	0.886318i	0.129942	−	0.0348179i
$649$	12.4305	+	21.5303i	0.487941	+	0.845139i
$650$	−27.7658	−	36.8301i	−1.08907	−	1.44459i
$651$		0			0
$652$	−14.9570	+	14.9570i	−0.585763	+	0.585763i
$653$	−7.16248	−	12.4058i	−0.280289	−	0.485475i	0.691167	−	0.722695i	$-0.257097\pi$
$653$	−7.16248	−	12.4058i	−0.280289	−	0.485475i	−0.971456	+	0.237220i	$0.923764\pi$
$654$	29.4783	−	51.0580i	1.15269	−	1.99653i
$655$	1.58037	+	5.89801i	0.0617501	+	0.230454i
$656$	7.79008	−	29.0730i	0.304151	−	1.13511i
$657$	34.6021	−	34.6021i	1.34995	−	1.34995i
$658$		0			0
$659$	−19.4182			−0.756424			−0.378212	−	0.925719i	$-0.623461\pi$
$659$	−19.4182			−0.756424			−0.378212	+	0.925719i	$0.623461\pi$
$660$	−22.1231	+	12.7728i	−0.861141	+	0.497180i
$661$	6.53565	+	24.3914i	0.254207	+	0.948715i	0.968530	+	0.248898i	$0.0800684\pi$
$661$	6.53565	+	24.3914i	0.254207	+	0.948715i	−0.714322	+	0.699817i	$0.753265\pi$
$662$	53.8588	+	31.0954i	2.09328	+	1.20856i
$663$	−21.7017	+	8.77347i	−0.842824	+	0.340733i
$664$			0.494289i			0.0191821i
$665$		0			0
$666$	−1.66447			−0.0644970
$667$	−0.731045	+	0.422069i	−0.0283062	+	0.0163426i
$668$	−23.8824	+	6.39927i	−0.924038	+	0.247595i
$669$	0.0910515	+	0.339809i	0.00352025	+	0.0131378i
$670$	−43.5319	−	11.6643i	−1.68178	−	0.450632i
$671$	1.83892	−	1.83892i	0.0709908	−	0.0709908i
$672$		0			0
$673$			39.3180i			1.51560i	0.652488	+	0.757799i	$0.273725\pi$
$673$			39.3180i			1.51560i	−0.652488	+	0.757799i	$0.726275\pi$
$674$	4.21864	−	15.7442i	0.162496	−	0.606443i
$675$	−8.97750	+	15.5495i	−0.345544	+	0.598500i
$676$	14.7886	+	15.3010i	0.568794	+	0.588498i
$677$	−12.1361	+	7.00677i	−0.466428	+	0.269292i	−0.714743	−	0.699387i	$-0.753456\pi$
$677$	−12.1361	+	7.00677i	−0.466428	+	0.269292i	0.248315	+	0.968679i	$0.420123\pi$
$678$	−29.8653	−	29.8653i	−1.14697	−	1.14697i
$679$		0			0
$680$			5.80956i			0.222786i
$681$	−67.8068	−	18.1688i	−2.59836	−	0.696229i
$682$	8.08304	−	2.16584i	0.309516	−	0.0829345i
$683$	5.76967	−	1.54598i	0.220770	−	0.0591552i	−0.146738	−	0.989175i	$-0.546878\pi$
$683$	5.76967	−	1.54598i	0.220770	−	0.0591552i	0.367509	+	0.930020i	$0.380211\pi$
$684$	−33.0279	−	8.84980i	−1.26285	−	0.338381i
$685$			66.4415i			2.53860i
$686$		0			0
$687$	32.9803	+	32.9803i	1.25828	+	1.25828i
$688$	−2.23775	+	1.29196i	−0.0853133	+	0.0492556i
$689$	11.8840	−	15.2175i	0.452743	−	0.579741i
$690$	−39.6196	+	68.6231i	−1.50829	+	2.61244i
$691$	6.43667	−	24.0220i	0.244862	−	0.913839i	−0.728590	−	0.684950i	$-0.759824\pi$
$691$	6.43667	−	24.0220i	0.244862	−	0.913839i	0.973453	−	0.228889i	$-0.0735093\pi$
$692$			4.28895i			0.163041i
$693$		0			0
$694$	3.68919	−	3.68919i	0.140040	−	0.140040i
$695$	44.9048	+	12.0322i	1.70334	+	0.456407i
$696$	−0.0873466	−	0.325982i	−0.00331087	−	0.0123563i
$697$	−15.5157	+	4.15741i	−0.587698	+	0.157473i
$698$	20.0301	−	11.5644i	0.758150	−	0.437718i
$699$	−13.4691			−0.509448
$700$		0			0
$701$		−	50.8136i		−	1.91920i	−0.281364	−	0.959601i	$-0.590787\pi$
$701$		−	50.8136i		−	1.91920i	0.281364	−	0.959601i	$-0.409213\pi$
$702$	7.18777	−	16.9434i	0.271285	−	0.639488i
$703$	0.981460	+	0.566646i	0.0370165	+	0.0213715i
$704$	−2.17533	−	8.11845i	−0.0819859	−	0.305976i
$705$	30.2574	−	17.4691i	1.13956	−	0.657924i
$706$	20.9243			0.787498
$707$		0			0
$708$	44.2329	−	44.2329i	1.66237	−	1.66237i
$709$	4.23445	−	15.8032i	0.159028	−	0.593501i	−0.839699	−	0.543053i	$-0.817268\pi$
$709$	4.23445	−	15.8032i	0.159028	−	0.593501i	0.998727	−	0.0504483i	$-0.0160650\pi$
$710$	4.08248	+	15.2360i	0.153213	+	0.571798i
$711$	5.95212	−	10.3094i	0.223222	−	0.386632i
$712$	2.58144	+	4.47119i	0.0967436	+	0.167565i
$713$	8.26096	−	8.26096i	0.309376	−	0.309376i
$714$		0			0
$715$	−2.95305	+	21.0448i	−0.110438	+	0.787031i
$716$	20.7545	+	35.9478i	0.775632	+	1.34343i
$717$	47.0866	−	12.6168i	1.75848	−	0.471184i
$718$	1.02106	−	1.76852i	0.0381055	−	0.0660007i
$719$	13.2682	+	22.9812i	0.494821	+	0.857055i	0.999982	−	0.00597015i	$-0.00190037\pi$
$719$	13.2682	+	22.9812i	0.494821	+	0.857055i	−0.505161	+	0.863025i	$0.668567\pi$
$720$	−44.5854	−	44.5854i	−1.66160	−	1.66160i
$721$		0			0
$722$	10.9546	+	10.9546i	0.407690	+	0.407690i
$723$	1.86864	−	6.97387i	0.0694955	−	0.259361i
$724$	−1.42277	−	0.821436i	−0.0528768	−	0.0305284i
$725$	−1.06926	−	0.617337i	−0.0397113	−	0.0229273i
$726$	−39.1803	−	10.4983i	−1.45412	−	0.389629i
$727$	−30.2407			−1.12157			−0.560783	−	0.827963i	$-0.689500\pi$
$727$	−30.2407			−1.12157			−0.560783	+	0.827963i	$0.689500\pi$
$728$		0			0
$729$	41.0975			1.52213
$730$	76.8994	+	20.6051i	2.84618	+	0.762630i
$731$	1.19424	+	0.689495i	0.0441706	+	0.0255019i
$732$	−5.66695	−	3.27181i	−0.209456	−	0.120930i
$733$	−3.45279	+	12.8860i	−0.127532	+	0.475955i	−0.999917	−	0.0128637i	$-0.995905\pi$
$733$	−3.45279	+	12.8860i	−0.127532	+	0.475955i	0.872386	+	0.488818i	$0.162572\pi$
$734$	10.4748	+	10.4748i	0.386631	+	0.386631i
$735$		0			0
$736$	−23.9223	−	23.9223i	−0.881786	−	0.881786i
$737$	5.94835	+	10.3028i	0.219110	+	0.379510i
$738$	25.0552	−	43.3969i	0.922295	−	1.59746i
$739$	8.49643	−	2.27661i	0.312546	−	0.0837466i	−0.0991361	−	0.995074i	$-0.531608\pi$
$739$	8.49643	−	2.27661i	0.312546	−	0.0837466i	0.411683	+	0.911327i	$0.364941\pi$
$740$	−0.609395	−	1.05550i	−0.0224018	−	0.0388011i
$741$	−39.7019	+	29.9308i	−1.45848	+	1.09954i
$742$		0			0
$743$	−7.57023	+	7.57023i	−0.277725	+	0.277725i	−0.832200	−	0.554475i	$-0.812919\pi$
$743$	−7.57023	+	7.57023i	−0.277725	+	0.277725i	0.554475	+	0.832200i	$0.312919\pi$
$744$	2.33535	+	4.04495i	0.0856181	+	0.148295i
$745$	−6.28710	+	10.8896i	−0.230341	+	0.398963i
$746$	−8.77711	−	32.7566i	−0.321353	−	1.19931i
$747$	−0.741008	+	2.76548i	−0.0271121	+	0.101184i
$748$	−4.88855	+	4.88855i	−0.178743	+	0.178743i
$749$		0			0
$750$	−29.5091			−1.07752
$751$	−31.9329	+	18.4365i	−1.16525	+	0.672756i	−0.952556	−	0.304363i	$-0.901556\pi$
$751$	−31.9329	+	18.4365i	−1.16525	+	0.672756i	−0.212692	+	0.977119i	$0.568223\pi$
$752$	4.58559	+	17.1137i	0.167219	+	0.624071i
$753$	49.1246	+	28.3621i	1.79020	+	1.03357i
$754$	1.16511	+	0.494267i	0.0424309	+	0.0180001i
$755$			61.6040i			2.24200i
$756$		0			0
$757$	4.46764			0.162379			0.0811896	−	0.996699i	$-0.474128\pi$
$757$	4.46764			0.162379			0.0811896	+	0.996699i	$0.474128\pi$
$758$	59.1486	−	34.1495i	2.14837	−	1.24036i
$759$	20.2044	−	5.41376i	0.733374	−	0.196507i
$760$	3.19379	+	11.9194i	0.115851	+	0.432362i
$761$	43.2252	+	11.5822i	1.56691	+	0.419853i	0.934844	−	0.355059i	$-0.115539\pi$
$761$	43.2252	+	11.5822i	1.56691	+	0.419853i	0.632069	+	0.774912i	$0.282206\pi$
$762$	43.2030	−	43.2030i	1.56508	−	1.56508i
$763$		0			0
$764$			1.71937i			0.0622046i
$765$	−8.70933	+	32.5037i	−0.314887	+	1.17517i
$766$	19.8033	−	34.3003i	0.715522	−	1.23932i
$767$	−6.35296	−	51.6491i	−0.229392	−	1.86494i
$768$	46.2035	−	26.6756i	1.66723	−	0.962573i
$769$	19.6232	+	19.6232i	0.707631	+	0.707631i	0.966036	−	0.258406i	$-0.0831971\pi$
$769$	19.6232	+	19.6232i	0.707631	+	0.707631i	−0.258406	+	0.966036i	$0.583197\pi$
$770$		0			0
$771$		−	25.4434i		−	0.916321i
$772$	−3.12606	−	0.837625i	−0.112509	−	0.0301468i
$773$	10.1019	−	2.70681i	0.363342	−	0.0973571i	−0.0725293	−	0.997366i	$-0.523107\pi$
$773$	10.1019	−	2.70681i	0.363342	−	0.0973571i	0.435871	+	0.900009i	$0.356440\pi$
$774$	−4.15534	+	1.11342i	−0.149361	+	0.0400211i
$775$	16.5055	+	4.42263i	0.592895	+	0.158866i
$776$		−	11.8445i		−	0.425192i
$777$		0			0
$778$	−10.7454	−	10.7454i	−0.385240	−	0.385240i
$779$	−29.5477	+	17.0594i	−1.05866	+	0.611216i
$780$	53.0712	−	6.52787i	1.90025	−	0.233735i
$781$	2.08191	−	3.60597i	0.0744964	−	0.129032i
$782$	−5.55029	+	20.7140i	−0.198478	+	0.740730i
$783$		−	0.492679i		−	0.0176069i
$784$		0			0
$785$	44.3488	−	44.3488i	1.58287	−	1.58287i
$786$	−8.70400	−	2.33223i	−0.310461	−	0.0831878i
$787$	−1.71942	−	6.41695i	−0.0612906	−	0.228740i	0.928486	−	0.371368i	$-0.121111\pi$
$787$	−1.71942	−	6.41695i	−0.0612906	−	0.228740i	−0.989776	+	0.142629i	$0.954445\pi$
$788$	−7.51521	+	2.01369i	−0.267718	+	0.0717349i
$789$	−18.0464	+	10.4191i	−0.642470	+	0.370930i
$790$	19.3671			0.689050
$791$		0			0
$792$			4.78418i			0.169998i
$793$	−5.04673	+	2.04027i	−0.179215	+	0.0724522i
$794$	50.7462	+	29.2983i	1.80091	+	1.03976i
$795$	−12.5571	−	46.8638i	−0.445355	−	1.66209i
$796$	14.4683	−	8.35326i	0.512814	−	0.296073i
$797$	21.9115			0.776146			0.388073	−	0.921629i	$-0.373141\pi$
$797$	21.9115			0.776146			0.388073	+	0.921629i	$0.373141\pi$
$798$		0			0
$799$	6.68598	−	6.68598i	0.236533	−	0.236533i
$800$	12.8071	−	47.7969i	0.452801	−	1.68988i
$801$	7.73988	+	28.8856i	0.273475	+	1.02062i
$802$	−21.4871	+	37.2167i	−0.758735	+	1.31417i
$803$	−10.5078	−	18.2001i	−0.370812	−	0.642266i
$804$	21.1666	−	21.1666i	0.746489	−	0.746489i
$805$		0			0
$806$	−17.3461	−	2.43404i	−0.610989	−	0.0857353i
$807$	−5.26078	−	9.11193i	−0.185188	−	0.320755i
$808$	5.50288	−	1.47449i	0.193591	−	0.0518724i
$809$	11.2486	−	19.4832i	0.395480	−	0.684992i	−0.597682	−	0.801733i	$-0.703912\pi$
$809$	11.2486	−	19.4832i	0.395480	−	0.684992i	0.993162	+	0.116741i	$0.0372449\pi$
$810$	16.1351	+	27.9468i	0.566929	+	0.981950i
$811$	−12.3587	−	12.3587i	−0.433973	−	0.433973i	0.456004	−	0.889978i	$-0.349280\pi$
$811$	−12.3587	−	12.3587i	−0.433973	−	0.433973i	−0.889978	+	0.456004i	$0.849280\pi$
$812$		0			0
$813$	32.0082	+	32.0082i	1.12258	+	1.12258i
$814$	−0.185011	+	0.690471i	−0.00648463	+	0.0242010i
$815$	38.2922	+	22.1080i	1.34132	+	0.774410i
$816$	−25.8315	−	14.9138i	−0.904283	−	0.522088i
$817$	2.82926	+	0.758097i	0.0989831	+	0.0265224i
$818$	75.2552			2.63124
$819$		0			0
$820$	36.6928			1.28137
$821$	24.3445	+	6.52308i	0.849628	+	0.227657i	0.657258	−	0.753665i	$-0.271716\pi$
$821$	24.3445	+	6.52308i	0.849628	+	0.227657i	0.192370	+	0.981323i	$0.438383\pi$
$822$	−84.9148	−	49.0256i	−2.96174	−	1.70996i
$823$	35.2081	+	20.3274i	1.22728	+	0.708568i	0.966459	−	0.256820i	$-0.0826749\pi$
$823$	35.2081	+	20.3274i	1.22728	+	0.708568i	0.260817	+	0.965388i	$0.416008\pi$
$824$	−1.34375	+	5.01495i	−0.0468118	+	0.174704i
$825$	21.6335	+	21.6335i	0.753182	+	0.753182i
$826$		0			0
$827$	−21.0284	−	21.0284i	−0.731228	−	0.731228i	0.239635	−	0.970863i	$-0.422972\pi$
$827$	−21.0284	−	21.0284i	−0.731228	−	0.731228i	−0.970863	+	0.239635i	$0.922972\pi$
$828$	−15.0550	−	26.0761i	−0.523198	−	0.906206i
$829$	−8.91208	+	15.4362i	−0.309530	+	0.536121i	−0.978260	−	0.207385i	$-0.933505\pi$
$829$	−8.91208	+	15.4362i	−0.309530	+	0.536121i	0.668730	+	0.743505i	$0.266838\pi$
$830$	−4.49918	+	1.20555i	−0.156169	+	0.0418453i
$831$	33.2192	+	57.5373i	1.15236	+	1.99595i
$832$	−2.44470	+	17.4221i	−0.0847547	+	0.604001i
$833$		0			0
$834$	−48.5117	+	48.5117i	−1.67982	+	1.67982i
$835$	25.8418	+	44.7593i	0.894292	+	1.54896i
$836$	−7.34230	+	12.7172i	−0.253939	+	0.439835i
$837$	1.76479	+	6.58628i	0.0610000	+	0.227655i
$838$	−3.39066	+	12.6541i	−0.117128	+	0.437129i
$839$	−19.0512	+	19.0512i	−0.657721	+	0.657721i	−0.954840	−	0.297119i	$-0.903974\pi$
$839$	−19.0512	+	19.0512i	−0.657721	+	0.657721i	0.297119	+	0.954840i	$0.403974\pi$
$840$		0			0
$841$	−28.9661			−0.998832
$842$	39.4147	−	22.7561i	1.35832	−	0.784228i
$843$	2.08990	+	7.79961i	0.0719800	+	0.268633i
$844$	22.8793	+	13.2094i	0.787539	+	0.454686i
$845$	22.8935	−	38.1382i	0.787560	−	1.31199i
$846$			29.4973i			1.01414i
$847$		0			0
$848$	24.6032			0.844879
$849$	26.0471	−	15.0383i	0.893935	−	0.516114i
$850$	−30.2972	+	8.11811i	−1.03919	+	0.278449i
$851$	0.258293	+	0.963962i	0.00885416	+	0.0330442i
$852$	−10.1199	−	2.71161i	−0.346701	−	0.0928983i
$853$	9.31374	−	9.31374i	0.318896	−	0.318896i	−0.529447	−	0.848343i	$-0.677600\pi$
$853$	9.31374	−	9.31374i	0.318896	−	0.318896i	0.848343	+	0.529447i	$0.177600\pi$
$854$		0			0
$855$			71.4753i			2.44440i
$856$	−0.714946	+	2.66821i	−0.0244363	+	0.0911977i
$857$	−17.9524	+	31.0945i	−0.613242	+	1.06217i	0.377448	+	0.926031i	$0.376802\pi$
$857$	−17.9524	+	31.0945i	−0.613242	+	1.06217i	−0.990690	+	0.136136i	$0.956532\pi$
$858$	−24.7171	−	19.3025i	−0.843827	−	0.658978i
$859$	17.6264	−	10.1766i	0.601406	−	0.347222i	−0.168189	−	0.985755i	$-0.553792\pi$
$859$	17.6264	−	10.1766i	0.601406	−	0.347222i	0.769594	+	0.638533i	$0.220458\pi$
$860$	−2.22741	−	2.22741i	−0.0759541	−	0.0759541i
$861$		0			0
$862$			67.7957i			2.30913i
$863$	7.87746	+	2.11076i	0.268152	+	0.0718511i	0.390390	−	0.920650i	$-0.372340\pi$
$863$	7.87746	+	2.11076i	0.268152	+	0.0718511i	−0.122238	+	0.992501i	$0.539007\pi$
$864$	19.0727	−	5.11051i	0.648866	−	0.173863i
$865$	8.65991	−	2.32042i	0.294446	−	0.0788965i
$866$	−12.0462	−	3.22777i	−0.409347	−	0.109684i
$867$		−	29.0944i		−	0.988097i
$868$		0			0
$869$	−3.61503	−	3.61503i	−0.122632	−	0.122632i
$870$	2.75416	−	1.59011i	0.0933746	−	0.0539099i
$871$	−3.04006	−	24.7155i	−0.103009	−	0.837453i
$872$	4.04248	−	7.00178i	0.136896	−	0.237110i
$873$	17.7565	−	66.2682i	0.600967	−	2.24284i
$874$			45.5498i			1.54075i
$875$		0			0
$876$	−37.3910	+	37.3910i	−1.26333	+	1.26333i
$877$	43.1175	+	11.5533i	1.45597	+	0.390127i	0.898097	−	0.439797i	$-0.144949\pi$
$877$	43.1175	+	11.5533i	1.45597	+	0.390127i	0.557877	+	0.829924i	$0.311616\pi$
$878$	12.1354	+	45.2899i	0.409550	+	1.52846i
$879$	−37.1945	+	9.96625i	−1.25454	+	0.336153i
$880$	−23.4511	+	13.5395i	−0.790537	+	0.456417i
$881$	0.616060			0.0207556			0.0103778	−	0.999946i	$-0.496697\pi$
$881$	0.616060			0.0207556			0.0103778	+	0.999946i	$0.496697\pi$
$882$		0			0
$883$		−	16.5050i		−	0.555437i	−0.960662	−	0.277719i	$-0.910422\pi$
$883$		−	16.5050i		−	0.555437i	0.960662	−	0.277719i	$-0.0895783\pi$
$884$	13.4161	−	5.42382i	0.451233	−	0.182423i
$885$	−113.243	−	65.3806i	−3.80661	−	2.19774i
$886$	−7.69945	−	28.7347i	−0.258668	−	0.965362i
$887$	−16.0290	+	9.25435i	−0.538201	+	0.310731i	−0.744350	−	0.667790i	$-0.767240\pi$
$887$	−16.0290	+	9.25435i	−0.538201	+	0.310731i	0.206148	+	0.978521i	$0.433907\pi$
$888$	−0.398981			−0.0133889
$889$		0			0
$890$	−34.4021	+	34.4021i	−1.15316	+	1.15316i
$891$	2.20476	−	8.22826i	0.0738621	−	0.275657i
$892$	−0.0562886	−	0.210072i	−0.00188468	−	0.00703373i
$893$	10.0419	−	17.3931i	0.336040	−	0.582039i
$894$	−9.27819	−	16.0703i	−0.310309	−	0.537471i
$895$	61.3544	−	61.3544i	2.05085	−	2.05085i
$896$		0			0
$897$	−43.3583	−	6.08413i	−1.44769	−	0.203143i
$898$	−38.6036	−	66.8633i	−1.28822	−	2.23126i
$899$	−0.452905	+	0.121356i	−0.0151052	+	0.00404744i
$900$	22.0202	−	38.1400i	0.734005	−	1.27133i
$901$	−6.56513	−	11.3711i	−0.218716	−	0.378828i
$902$	−15.2173	−	15.2173i	−0.506681	−	0.506681i
$903$		0			0
$904$	−4.09554	−	4.09554i	−0.136216	−	0.136216i
$905$	−0.888830	+	3.31716i	−0.0295457	+	0.110266i
$906$	−78.7322	−	45.4560i	−2.61570	−	1.51018i
$907$	−23.9675	−	13.8377i	−0.795829	−	0.459472i	0.0461819	−	0.998933i	$-0.485295\pi$
$907$	−23.9675	−	13.8377i	−0.795829	−	0.459472i	−0.842010	+	0.539461i	$0.818628\pi$
$908$	41.9186	+	11.2321i	1.39112	+	0.372749i
$909$	32.9983			1.09448
$910$		0			0
$911$	23.1900			0.768320			0.384160	−	0.923267i	$-0.374491\pi$
$911$	23.1900			0.768320			0.384160	+	0.923267i	$0.374491\pi$
$912$	−61.1970	−	16.3977i	−2.02643	−	0.542981i
$913$	1.06484	+	0.614783i	0.0352409	+	0.0203464i
$914$	−21.5842	−	12.4616i	−0.713940	−	0.412194i
$915$	−3.54025	+	13.2124i	−0.117037	+	0.436788i
$916$	−20.3886	−	20.3886i	−0.673659	−	0.673659i
$917$		0			0
$918$	−8.85025	−	8.85025i	−0.292102	−	0.292102i
$919$	−11.1083	−	19.2401i	−0.366428	−	0.634672i	0.622576	−	0.782559i	$-0.286086\pi$
$919$	−11.1083	−	19.2401i	−0.366428	−	0.634672i	−0.989004	+	0.147887i	$0.952753\pi$
$920$	−5.43318	+	9.41055i	−0.179127	+	0.310257i
$921$	25.3838	−	6.80156i	0.836423	−	0.224119i
$922$	−4.79814	−	8.31062i	−0.158018	−	0.273696i
$923$	−6.95942	+	5.24664i	−0.229072	+	0.172695i
$924$		0			0
$925$	−1.03214	+	1.03214i	−0.0339367	+	0.0339367i
$926$	15.6757	+	27.1512i	0.515137	+	0.892243i
$927$	−15.0362	+	26.0435i	−0.493854	+	0.855380i
$928$	0.351424	+	1.31153i	0.0115361	+	0.0430531i
$929$	−5.16075	+	19.2602i	−0.169319	+	0.631907i	0.828131	+	0.560535i	$0.189404\pi$
$929$	−5.16075	+	19.2602i	−0.169319	+	0.631907i	−0.997450	+	0.0713719i	$0.977262\pi$
$930$	−31.1225	+	31.1225i	−1.02055	+	1.02055i
$931$		0			0
$932$	8.32668			0.272750
$933$	5.79486	−	3.34567i	0.189715	−	0.109532i
$934$	−2.82865	−	10.5567i	−0.0925561	−	0.345424i
$935$	12.5154	+	7.22576i	0.409297	+	0.236308i
$936$	3.91084	−	9.21886i	0.127830	−	0.301328i
$937$			32.0817i			1.04806i	0.851699	+	0.524031i	$0.175572\pi$
$937$			32.0817i			1.04806i	−0.851699	+	0.524031i	$0.824428\pi$
$938$		0			0
$939$	−9.12975			−0.297938
$940$	−18.7053	+	10.7995i	−0.610100	+	0.352241i
$941$	7.75209	−	2.07717i	0.252711	−	0.0677137i	−0.130240	−	0.991483i	$-0.541575\pi$
$941$	7.75209	−	2.07717i	0.252711	−	0.0677137i	0.382950	+	0.923769i	$0.374908\pi$
$942$	23.9555	+	89.4032i	0.780513	+	2.91291i
$943$	−29.0209	−	7.77614i	−0.945052	−	0.253226i
$944$	46.8881	−	46.8881i	1.52608	−	1.52608i
$945$		0			0
$946$			1.84751i			0.0600679i
$947$	4.28837	−	16.0044i	0.139353	−	0.520074i	−0.860589	−	0.509301i	$-0.829904\pi$
$947$	4.28837	−	16.0044i	0.139353	−	0.520074i	0.999942	−	0.0107733i	$-0.00342930\pi$
$948$	−6.43187	+	11.1403i	−0.208897	+	0.361821i
$949$	5.37030	+	43.6601i	0.174327	+	1.41727i
$950$	−57.6974	+	33.3116i	−1.87195	+	1.08077i
$951$	−59.2752	−	59.2752i	−1.92213	−	1.92213i
$952$		0			0
$953$			37.7682i			1.22343i	0.791077	+	0.611717i	$0.209521\pi$
$953$			37.7682i			1.22343i	−0.791077	+	0.611717i	$0.790479\pi$
$954$	39.5657	+	10.6016i	1.28099	+	0.343239i
$955$	3.47161	−	0.930216i	0.112339	−	0.0301011i
$956$	−29.1093	+	7.79981i	−0.941461	+	0.252264i
$957$	−0.810894	−	0.217279i	−0.0262125	−	0.00702362i
$958$			38.6101i			1.24744i
$959$		0			0
$960$	31.2589	+	31.2589i	1.00888	+	1.00888i
$961$	−21.2269	+	12.2554i	−0.684739	+	0.395334i
$962$	0.920933	−	1.17926i	0.0296921	−	0.0380209i
$963$	−8.00004	+	13.8565i	−0.257798	+	0.446519i
$964$	−1.15521	+	4.31129i	−0.0372067	+	0.138857i
$965$			6.76507i			0.217775i
$966$		0			0
$967$	−33.4886	+	33.4886i	−1.07692	+	1.07692i	−0.0801380	+	0.996784i	$0.525536\pi$
$967$	−33.4886	+	33.4886i	−1.07692	+	1.07692i	−0.996784	+	0.0801380i	$0.974464\pi$
$968$	−5.37294	−	1.43968i	−0.172693	−	0.0462729i
$969$	8.75112	+	32.6596i	0.281126	+	1.04918i
$970$	107.812	−	28.8882i	3.46164	−	0.927543i
$971$	−51.9221	+	29.9772i	−1.66626	+	0.962015i	−0.696631	+	0.717430i	$0.745318\pi$
$971$	−51.9221	+	29.9772i	−1.66626	+	0.962015i	−0.969628	+	0.244585i	$0.921348\pi$
$972$	−34.5785			−1.10910
$973$		0			0
$974$			3.02085i			0.0967944i
$975$	−24.0022	−	59.3709i	−0.768686	−	1.90139i
$976$	−6.00712	−	3.46821i	−0.192283	−	0.111015i
$977$	7.79257	+	29.0823i	0.249306	+	0.930424i	0.971170	+	0.238389i	$0.0766192\pi$
$977$	7.79257	+	29.0823i	0.249306	+	0.930424i	−0.721864	+	0.692035i	$0.756714\pi$
$978$	−56.5097	+	32.6259i	−1.80698	+	1.04326i
$979$	12.8429			0.410461
$980$		0			0
$981$	33.1137	−	33.1137i	1.05724	−	1.05724i
$982$	−11.2196	+	41.8720i	−0.358031	+	1.33619i
$983$	4.08428	+	15.2428i	0.130268	+	0.486168i	0.999973	−	0.00740505i	$-0.00235712\pi$
$983$	4.08428	+	15.2428i	0.130268	+	0.486168i	−0.869704	+	0.493573i	$0.835690\pi$
$984$	6.00585	−	10.4024i	0.191459	−	0.331617i
$985$	8.13178	+	14.0847i	0.259100	+	0.448775i
$986$	0.608587	−	0.608587i	0.0193814	−	0.0193814i
$987$		0			0
$988$	24.5440	−	18.5035i	0.780847	−	0.588673i
$989$	1.28965	+	2.23374i	0.0410085	+	0.0710289i
$990$	−43.5471	+	11.6684i	−1.38402	+	0.370846i
$991$	−15.1135	+	26.1773i	−0.480096	+	0.831550i	−0.999739	−	0.0228331i	$-0.992731\pi$
$991$	−15.1135	+	26.1773i	−0.480096	+	0.831550i	0.519644	+	0.854383i	$0.326065\pi$
$992$	−9.39588	−	16.2741i	−0.298319	−	0.516704i
$993$	61.0567	+	61.0567i	1.93757	+	1.93757i
$994$		0			0
$995$	−24.6939	−	24.6939i	−0.782849	−	0.782849i
$996$	0.800734	−	2.98838i	0.0253722	−	0.0946905i
$997$	40.0442	+	23.1195i	1.26821	+	0.732203i	0.974650	−	0.223737i	$-0.0718257\pi$
$997$	40.0442	+	23.1195i	1.26821	+	0.732203i	0.293563	+	0.955940i	$0.405159\pi$
$998$	−9.73428	−	5.62009i	−0.308133	−	0.177901i
$999$	−0.562614	−	0.150752i	−0.0178003	−	0.00476958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.b.31.2		32
7.2	even	3		91.2.bb.a.5.7	✓	32
7.3	odd	6		637.2.i.a.538.13		32
7.4	even	3		637.2.i.a.538.14		32
7.5	odd	6	inner	637.2.bc.b.460.7		32
7.6	odd	2		91.2.bb.a.31.2	yes	32
13.8	odd	4	inner	637.2.bc.b.619.7		32
21.2	odd	6		819.2.fn.e.460.2		32
21.20	even	2		819.2.fn.e.577.7		32
91.34	even	4		91.2.bb.a.73.7	yes	32
91.47	even	12	inner	637.2.bc.b.411.2		32
91.60	odd	12		637.2.i.a.489.14		32
91.73	even	12		637.2.i.a.489.13		32
91.86	odd	12		91.2.bb.a.47.2	yes	32
273.86	even	12		819.2.fn.e.775.7		32
273.125	odd	4		819.2.fn.e.73.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.7	✓	32	7.2	even	3
91.2.bb.a.31.2	yes	32	7.6	odd	2
91.2.bb.a.47.2	yes	32	91.86	odd	12
91.2.bb.a.73.7	yes	32	91.34	even	4
637.2.i.a.489.13		32	91.73	even	12
637.2.i.a.489.14		32	91.60	odd	12
637.2.i.a.538.13		32	7.3	odd	6
637.2.i.a.538.14		32	7.4	even	3
637.2.bc.b.31.2		32	1.1	even	1	trivial
637.2.bc.b.411.2		32	91.47	even	12	inner
637.2.bc.b.460.7		32	7.5	odd	6	inner
637.2.bc.b.619.7		32	13.8	odd	4	inner
819.2.fn.e.73.2		32	273.125	odd	4
819.2.fn.e.460.2		32	21.2	odd	6
819.2.fn.e.577.7		32	21.20	even	2
819.2.fn.e.775.7		32	273.86	even	12

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.84208 - 0.493585i) q^{2} +(-2.29307 - 1.32391i) q^{3} +(1.41759 + 0.818448i) q^{4} +(0.885596 - 3.30509i) q^{5} +(3.57057 + 3.57057i) q^{6} +(0.489646 + 0.489646i) q^{8} +(2.00545 + 3.47355i) q^{9} +O(q^{10})\)	\(q+(-1.84208 - 0.493585i) q^{2} +(-2.29307 - 1.32391i) q^{3} +(1.41759 + 0.818448i) q^{4} +(0.885596 - 3.30509i) q^{5} +(3.57057 + 3.57057i) q^{6} +(0.489646 + 0.489646i) q^{8} +(2.00545 + 3.47355i) q^{9} +(-3.26268 + 5.65113i) q^{10} +(1.66384 - 0.445825i) q^{11} +(-2.16710 - 3.75352i) q^{12} +(-3.57057 - 0.501030i) q^{13} +(-6.40637 + 6.40637i) q^{15} +(-2.29718 - 3.97884i) q^{16} +(-1.22596 + 2.12343i) q^{17} +(-1.97972 - 7.38842i) q^{18} +(-1.34794 + 5.03057i) q^{19} +(3.96046 - 3.96046i) q^{20} -3.28498 q^{22} +(-3.97172 + 2.29307i) q^{23} +(-0.474548 - 1.77104i) q^{24} +(-5.80922 - 3.35395i) q^{25} +(6.32999 + 2.68532i) q^{26} -2.67669i q^{27} +0.184063 q^{29} +(14.9631 - 8.63897i) q^{30} +(-2.46060 + 0.659317i) q^{31} +(1.90926 + 7.12546i) q^{32} +(-4.40553 - 1.18046i) q^{33} +(3.30641 - 3.30641i) q^{34} +6.56544i q^{36} +(0.0563202 - 0.210190i) q^{37} +(4.96603 - 8.60141i) q^{38} +(7.52426 + 5.87600i) q^{39} +(2.05195 - 1.18470i) q^{40} +(4.63239 + 4.63239i) q^{41} -0.562412i q^{43} +(2.72353 + 0.729768i) q^{44} +(13.2564 - 3.55205i) q^{45} +(8.44806 - 2.26365i) q^{46} +(-3.72492 - 0.998090i) q^{47} +12.1650i q^{48} +(9.04560 + 9.04560i) q^{50} +(5.62243 - 3.24611i) q^{51} +(-4.65155 - 3.63258i) q^{52} +(-2.67755 + 4.63764i) q^{53} +(-1.32117 + 4.93069i) q^{54} -5.89396i q^{55} +(9.75092 - 9.75092i) q^{57} +(-0.339059 - 0.0908505i) q^{58} +(3.73550 + 13.9411i) q^{59} +(-14.3249 + 3.83834i) q^{60} +(1.30750 - 0.754885i) q^{61} +4.85807 q^{62} -4.87935i q^{64} +(-4.81803 + 11.3573i) q^{65} +(7.53270 + 4.34901i) q^{66} +(1.78754 + 6.67118i) q^{67} +(-3.47583 + 2.00677i) q^{68} +12.1432 q^{69} +(1.70926 - 1.70926i) q^{71} +(-0.718846 + 2.68277i) q^{72} +(-3.15770 - 11.7847i) q^{73} +(-0.207493 + 0.359389i) q^{74} +(8.88063 + 15.3817i) q^{75} +(-6.02809 + 6.02809i) q^{76} +(-10.9600 - 14.5379i) q^{78} +(-1.48398 - 2.57034i) q^{79} +(-15.1848 + 4.06875i) q^{80} +(2.47267 - 4.28279i) q^{81} +(-6.24677 - 10.8197i) q^{82} +(0.504742 + 0.504742i) q^{83} +(5.93241 + 5.93241i) q^{85} +(-0.277598 + 1.03601i) q^{86} +(-0.422069 - 0.243682i) q^{87} +(1.03299 + 0.596396i) q^{88} +(7.20177 + 1.92971i) q^{89} -26.1726 q^{90} -7.50704 q^{92} +(6.51522 + 1.74575i) q^{93} +(6.36898 + 3.67713i) q^{94} +(15.4328 + 8.91011i) q^{95} +(5.05537 - 18.8669i) q^{96} +(-12.0949 - 12.0949i) q^{97} +(4.88535 + 4.88535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9	\( 32 q - 2 q^{2} + 12 q^{3} + 6 q^{5} - 16 q^{8} + 8 q^{9} - 10 q^{11} - 44 q^{15} + 12 q^{16} - 4 q^{18} - 12 q^{19} - 8 q^{22} + 12 q^{24} - 24 q^{26} + 16 q^{29} - 24 q^{31} + 4 q^{32} - 48 q^{33} - 8 q^{37} - 6 q^{39} + 132 q^{40} - 42 q^{44} + 24 q^{45} + 12 q^{46} - 30 q^{47} + 88 q^{50} - 36 q^{52} - 12 q^{53} - 78 q^{54} + 40 q^{57} + 26 q^{58} + 54 q^{59} + 16 q^{60} + 48 q^{61} - 8 q^{65} - 12 q^{66} + 16 q^{67} + 48 q^{68} - 36 q^{71} + 22 q^{72} - 66 q^{73} + 12 q^{74} - 176 q^{78} - 32 q^{79} - 138 q^{80} + 16 q^{81} - 84 q^{85} + 42 q^{86} + 24 q^{87} + 60 q^{89} + 48 q^{92} + 6 q^{93} + 72 q^{94} + 42 q^{96} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 12 * q^3 + 6 * q^5 - 16 * q^8 + 8 * q^9 - 10 * q^11 - 44 * q^15 + 12 * q^16 - 4 * q^18 - 12 * q^19 - 8 * q^22 + 12 * q^24 - 24 * q^26 + 16 * q^29 - 24 * q^31 + 4 * q^32 - 48 * q^33 - 8 * q^37 - 6 * q^39 + 132 * q^40 - 42 * q^44 + 24 * q^45 + 12 * q^46 - 30 * q^47 + 88 * q^50 - 36 * q^52 - 12 * q^53 - 78 * q^54 + 40 * q^57 + 26 * q^58 + 54 * q^59 + 16 * q^60 + 48 * q^61 - 8 * q^65 - 12 * q^66 + 16 * q^67 + 48 * q^68 - 36 * q^71 + 22 * q^72 - 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 - 138 * q^80 + 16 * q^81 - 84 * q^85 + 42 * q^86 + 24 * q^87 + 60 * q^89 + 48 * q^92 + 6 * q^93 + 72 * q^94 + 42 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more