LMFDB - Embedded newform 833.2.t.b.48.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(48,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.48"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.t (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,0,0,0,0,0,0,-24,0,-8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			48.1
Character	$\chi$	$=$	833.48
Dual form			833.2.t.b.538.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14596 + 0.888885i) q^{2} +(-0.289938 - 0.0576723i) q^{3} +(2.40081 - 2.40081i) q^{4} +(0.677905 + 1.01456i) q^{5} +(0.673459 - 0.133959i) q^{6} +(-1.24022 + 2.99415i) q^{8} +(-2.69090 - 1.11461i) q^{9} +(-2.35658 - 1.57462i) q^{10} +(2.84210 - 0.565328i) q^{11} +(-0.834545 + 0.557625i) q^{12} +(-0.992715 + 0.992715i) q^{13} +(-0.138039 - 0.333255i) q^{15} -0.737233i q^{16} +(1.27351 - 3.92150i) q^{17} +6.76532 q^{18} +(1.25391 + 3.02722i) q^{19} +(4.06327 + 0.808235i) q^{20} +(-5.59651 + 3.73947i) q^{22} +(0.353504 + 1.77718i) q^{23} +(0.532266 - 0.796593i) q^{24} +(1.34365 - 3.24385i) q^{25} +(1.24792 - 3.01274i) q^{26} +(1.45331 + 0.971068i) q^{27} +(-1.94103 - 2.90495i) q^{29} +(0.592451 + 0.592451i) q^{30} +(-0.338656 + 1.70254i) q^{31} +(-1.82512 - 4.40623i) q^{32} -0.856636 q^{33} +(0.752866 + 9.54738i) q^{34} +(-9.13629 + 3.78437i) q^{36} +(0.119959 - 0.603075i) q^{37} +(-5.38170 - 5.38170i) q^{38} +(0.345078 - 0.230574i) q^{39} +(-3.87849 + 0.771479i) q^{40} +(4.22160 - 6.31807i) q^{41} +(-2.34069 - 0.969547i) q^{43} +(5.46608 - 8.18057i) q^{44} +(-0.693343 - 3.48567i) q^{45} +(-2.33832 - 3.49954i) q^{46} +(8.15868 - 8.15868i) q^{47} +(-0.0425179 + 0.213752i) q^{48} +8.15551i q^{50} +(-0.595401 + 1.06355i) q^{51} +4.76663i q^{52} +(-7.36524 + 3.05078i) q^{53} +(-3.98190 - 0.792049i) q^{54} +(2.50023 + 2.50023i) q^{55} +(-0.188971 - 0.950022i) q^{57} +(6.74753 + 4.50855i) q^{58} +(7.82317 + 3.24046i) q^{59} +(-1.13148 - 0.468676i) q^{60} +(8.05173 + 5.37999i) q^{61} +(-0.786620 - 3.95460i) q^{62} +(8.87587 + 8.87587i) q^{64} +(-1.68013 - 0.334199i) q^{65} +(1.83830 - 0.761451i) q^{66} -4.17201i q^{67} +(-6.35732 - 12.4722i) q^{68} -0.535661i q^{69} +(3.14489 - 15.8104i) q^{71} +(6.67461 - 6.67461i) q^{72} +(7.64134 + 11.4361i) q^{73} +(0.278637 + 1.40080i) q^{74} +(-0.576655 + 0.863025i) q^{75} +(10.2782 + 4.25736i) q^{76} +(-0.535570 + 0.801536i) q^{78} +(11.7027 - 2.32781i) q^{79} +(0.747965 - 0.499774i) q^{80} +(5.81321 + 5.81321i) q^{81} +(-3.44334 + 17.3108i) q^{82} +(-7.64634 + 3.16722i) q^{83} +(4.84191 - 1.36636i) q^{85} +5.88485 q^{86} +(0.395242 + 0.954199i) q^{87} +(-1.83214 + 9.21080i) q^{88} +(6.08671 + 6.08671i) q^{89} +(4.58624 + 6.86380i) q^{90} +(5.11537 + 3.41798i) q^{92} +(0.196379 - 0.474100i) q^{93} +(-10.2561 + 24.7603i) q^{94} +(-2.22125 + 3.32433i) q^{95} +(0.275055 + 1.38279i) q^{96} +(-3.34327 + 2.23390i) q^{97} +(-8.27792 - 1.64658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 24 q^{9} - 8 q^{11} - 24 q^{12} - 32 q^{13} + 32 q^{17} + 40 q^{18} - 40 q^{19} + 40 q^{20} - 24 q^{22} - 8 q^{23} + 16 q^{24} - 8 q^{25} - 24 q^{27} + 8 q^{31} + 40 q^{32} - 24 q^{34} - 120 q^{36}+ \cdots - 40 q^{99}+O(q^{100}) $ 72 * q - 24 * q^9 - 8 * q^11 - 24 * q^12 - 32 * q^13 + 32 * q^17 + 40 * q^18 - 40 * q^19 + 40 * q^20 - 24 * q^22 - 8 * q^23 + 16 * q^24 - 8 * q^25 - 24 * q^27 + 8 * q^31 + 40 * q^32 - 24 * q^34 - 120 * q^36 - 48 * q^37 - 56 * q^38 - 16 * q^39 - 48 * q^40 + 56 * q^41 - 24 * q^43 + 96 * q^44 + 40 * q^45 - 64 * q^46 + 24 * q^47 - 224 * q^48 + 104 * q^51 - 40 * q^53 + 48 * q^54 + 48 * q^57 + 32 * q^58 + 8 * q^59 - 48 * q^60 - 128 * q^61 + 48 * q^62 + 56 * q^65 + 120 * q^66 + 32 * q^68 - 120 * q^73 + 48 * q^74 + 32 * q^75 + 8 * q^76 + 48 * q^78 + 32 * q^79 - 32 * q^80 + 80 * q^81 + 64 * q^82 - 32 * q^83 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 136 * q^88 - 16 * q^89 + 32 * q^90 - 8 * q^92 - 96 * q^93 + 32 * q^94 + 32 * q^95 + 40 * q^96 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−2.14596	+	0.888885i	−1.51742	+	0.628537i	−0.977073	−	0.212905i	$-0.931708\pi$
$2$	−2.14596	+	0.888885i	−1.51742	+	0.628537i	−0.540349	+	0.841441i	$0.681708\pi$
$3$	−0.289938	−	0.0576723i	−0.167396	−	0.0332971i	0.110681	−	0.993856i	$-0.464697\pi$
$3$	−0.289938	−	0.0576723i	−0.167396	−	0.0332971i	−0.278077	+	0.960559i	$0.589697\pi$
$4$	2.40081	−	2.40081i	1.20040	−	1.20040i
$5$	0.677905	+	1.01456i	0.303168	+	0.453724i	0.951506	−	0.307629i	$-0.0995356\pi$
$5$	0.677905	+	1.01456i	0.303168	+	0.453724i	−0.648338	+	0.761353i	$0.724536\pi$
$6$	0.673459	−	0.133959i	0.274938	−	0.0546887i
$7$		0			0
$7$		0			0
$8$	−1.24022	+	2.99415i	−0.438484	+	1.05859i
$9$	−2.69090	−	1.11461i	−0.896967	−	0.371536i
$10$	−2.35658	−	1.57462i	−0.745216	−	0.497938i
$11$	2.84210	−	0.565328i	0.856925	−	0.170453i	0.252972	−	0.967473i	$-0.418592\pi$
$11$	2.84210	−	0.565328i	0.856925	−	0.170453i	0.603952	+	0.797021i	$0.293592\pi$
$12$	−0.834545	+	0.557625i	−0.240912	+	0.160972i
$13$	−0.992715	+	0.992715i	−0.275330	+	0.275330i	−0.831241	−	0.555912i	$-0.812369\pi$
$13$	−0.992715	+	0.992715i	−0.275330	+	0.275330i	0.555912	+	0.831241i	$0.312369\pi$
$14$		0			0
$15$	−0.138039	−	0.333255i	−0.0356414	−	0.0860461i
$16$		−	0.737233i		−	0.184308i
$17$	1.27351	−	3.92150i	0.308871	−	0.951104i
$17$	1.27351	−	3.92150i	0.308871	−	0.951104i
$18$	6.76532			1.59460
$19$	1.25391	+	3.02722i	0.287668	+	0.694491i	0.999973	−	0.00737872i	$-0.00234874\pi$
$19$	1.25391	+	3.02722i	0.287668	+	0.694491i	−0.712305	+	0.701870i	$0.752349\pi$
$20$	4.06327	+	0.808235i	0.908576	+	0.180727i
$21$		0			0
$22$	−5.59651	+	3.73947i	−1.19318	+	0.797257i
$23$	0.353504	+	1.77718i	0.0737107	+	0.370569i	0.999980	−	0.00629315i	$-0.00200319\pi$
$23$	0.353504	+	1.77718i	0.0737107	+	0.370569i	−0.926270	+	0.376862i	$0.877003\pi$
$24$	0.532266	−	0.796593i	0.108648	−	0.162604i
$25$	1.34365	−	3.24385i	0.268729	−	0.648770i
$26$	1.24792	−	3.01274i	0.244736	−	0.590846i
$27$	1.45331	+	0.971068i	0.279689	+	0.186882i
$28$		0			0
$29$	−1.94103	−	2.90495i	−0.360440	−	0.539436i	0.606288	−	0.795245i	$-0.292658\pi$
$29$	−1.94103	−	2.90495i	−0.360440	−	0.539436i	−0.966727	+	0.255809i	$0.917658\pi$
$30$	0.592451	+	0.592451i	0.108166	+	0.108166i
$31$	−0.338656	+	1.70254i	−0.0608244	+	0.305785i	−0.999207	−	0.0398128i	$-0.987324\pi$
$31$	−0.338656	+	1.70254i	−0.0608244	+	0.305785i	0.938383	+	0.345598i	$0.112324\pi$
$32$	−1.82512	−	4.40623i	−0.322639	−	0.778919i
$33$	−0.856636			−0.149121
$34$	0.752866	+	9.54738i	0.129115	+	1.63736i
$35$		0			0
$36$	−9.13629	+	3.78437i	−1.52271	+	0.630729i
$37$	0.119959	−	0.603075i	0.0197211	−	0.0991449i	−0.969671	−	0.244413i	$-0.921405\pi$
$37$	0.119959	−	0.603075i	0.0197211	−	0.0991449i	0.989392	+	0.145269i	$0.0464046\pi$
$38$	−5.38170	−	5.38170i	−0.873026	−	0.873026i
$39$	0.345078	−	0.230574i	0.0552567	−	0.0369214i
$40$	−3.87849	+	0.771479i	−0.613243	+	0.121982i
$41$	4.22160	−	6.31807i	0.659303	−	0.986717i	−0.339631	−	0.940559i	$-0.610302\pi$
$41$	4.22160	−	6.31807i	0.659303	−	0.986717i	0.998934	−	0.0461582i	$-0.0146978\pi$
$42$		0			0
$43$	−2.34069	−	0.969547i	−0.356952	−	0.147855i	0.196999	−	0.980404i	$-0.436881\pi$
$43$	−2.34069	−	0.969547i	−0.356952	−	0.147855i	−0.553951	+	0.832549i	$0.686881\pi$
$44$	5.46608	−	8.18057i	0.824043	−	1.23327i
$45$	−0.693343	−	3.48567i	−0.103357	−	0.519613i
$46$	−2.33832	−	3.49954i	−0.344766	−	0.515979i
$47$	8.15868	−	8.15868i	1.19007	−	1.19007i	0.213018	−	0.977048i	$-0.431671\pi$
$47$	8.15868	−	8.15868i	1.19007	−	1.19007i	0.977048	−	0.213018i	$-0.0683294\pi$
$48$	−0.0425179	+	0.213752i	−0.00613693	+	0.0308524i
$49$		0			0
$50$			8.15551i			1.15336i
$51$	−0.595401	+	1.06355i	−0.0833728	+	0.148926i
$52$			4.76663i			0.661013i
$53$	−7.36524	+	3.05078i	−1.01169	+	0.419057i	−0.826072	−	0.563564i	$-0.809430\pi$
$53$	−7.36524	+	3.05078i	−1.01169	+	0.419057i	−0.185621	+	0.982621i	$0.559430\pi$
$54$	−3.98190	−	0.792049i	−0.541868	−	0.107784i
$55$	2.50023	+	2.50023i	0.337131	+	0.337131i
$56$		0			0
$57$	−0.188971	−	0.950022i	−0.0250298	−	0.125833i
$58$	6.74753	+	4.50855i	0.885994	+	0.592002i
$59$	7.82317	+	3.24046i	1.01849	+	0.421872i	0.828545	−	0.559923i	$-0.189169\pi$
$59$	7.82317	+	3.24046i	1.01849	+	0.421872i	0.189945	+	0.981795i	$0.439169\pi$
$60$	−1.13148	−	0.468676i	−0.146074	−	0.0605059i
$61$	8.05173	+	5.37999i	1.03092	+	0.688837i	0.951388	−	0.307995i	$-0.0996581\pi$
$61$	8.05173	+	5.37999i	1.03092	+	0.688837i	0.0795299	+	0.996832i	$0.474658\pi$
$62$	−0.786620	−	3.95460i	−0.0999008	−	0.502235i
$63$		0			0
$64$	8.87587	+	8.87587i	1.10948	+	1.10948i
$65$	−1.68013	−	0.334199i	−0.208395	−	0.0414523i
$66$	1.83830	−	0.761451i	0.226280	−	0.0937281i
$67$		−	4.17201i		−	0.509692i	−0.966982	−	0.254846i	$-0.917975\pi$
$67$		−	4.17201i		−	0.509692i	0.966982	−	0.254846i	$-0.0820247\pi$
$68$	−6.35732	−	12.4722i	−0.770938	−	1.51248i
$69$		−	0.535661i		−	0.0644860i
$70$		0			0
$71$	3.14489	−	15.8104i	0.373230	−	1.87635i	−0.0993292	−	0.995055i	$-0.531670\pi$
$71$	3.14489	−	15.8104i	0.373230	−	1.87635i	0.472559	−	0.881299i	$-0.343330\pi$
$72$	6.67461	−	6.67461i	0.786610	−	0.786610i
$73$	7.64134	+	11.4361i	0.894351	+	1.33849i	0.940584	+	0.339561i	$0.110278\pi$
$73$	7.64134	+	11.4361i	0.894351	+	1.33849i	−0.0462327	+	0.998931i	$0.514722\pi$
$74$	0.278637	+	1.40080i	0.0323909	+	0.162840i
$75$	−0.576655	+	0.863025i	−0.0665863	+	0.0996535i
$76$	10.2782	+	4.25736i	1.17899	+	0.488352i
$77$		0			0
$78$	−0.535570	+	0.801536i	−0.0606413	+	0.0907561i
$79$	11.7027	−	2.32781i	1.31665	−	0.261899i	0.513715	−	0.857961i	$-0.328269\pi$
$79$	11.7027	−	2.32781i	1.31665	−	0.261899i	0.802938	+	0.596062i	$0.203269\pi$
$80$	0.747965	−	0.499774i	0.0836251	−	0.0558765i
$81$	5.81321	+	5.81321i	0.645913	+	0.645913i
$82$	−3.44334	+	17.3108i	−0.380253	+	1.91166i
$83$	−7.64634	+	3.16722i	−0.839295	+	0.347647i	−0.760575	−	0.649250i	$-0.775083\pi$
$83$	−7.64634	+	3.16722i	−0.839295	+	0.347647i	−0.0787193	+	0.996897i	$0.525083\pi$
$84$		0			0
$85$	4.84191	−	1.36636i	0.525178	−	0.148202i
$86$	5.88485			0.634579
$87$	0.395242	+	0.954199i	0.0423744	+	0.102301i
$88$	−1.83214	+	9.21080i	−0.195307	+	0.981875i
$89$	6.08671	+	6.08671i	0.645190	+	0.645190i	0.951827	−	0.306637i	$-0.0992037\pi$
$89$	6.08671	+	6.08671i	0.645190	+	0.645190i	−0.306637	+	0.951827i	$0.599204\pi$
$90$	4.58624	+	6.86380i	0.483433	+	0.723508i
$91$		0			0
$92$	5.11537	+	3.41798i	0.533314	+	0.356349i
$93$	0.196379	−	0.474100i	0.0203635	−	0.0491619i
$94$	−10.2561	+	24.7603i	−1.05783	+	2.55383i
$95$	−2.22125	+	3.32433i	−0.227895	+	0.341069i
$96$	0.275055	+	1.38279i	0.0280727	+	0.141131i
$97$	−3.34327	+	2.23390i	−0.339458	+	0.226818i	−0.713601	−	0.700553i	$-0.752937\pi$
$97$	−3.34327	+	2.23390i	−0.339458	+	0.226818i	0.374143	+	0.927371i	$0.377937\pi$
$98$		0			0
$99$	−8.27792	−	1.64658i	−0.831962	−	0.165488i
$100$	−4.56202	−	11.0137i	−0.456202	−	1.10137i
$101$	18.8006			1.87073			0.935367	−	0.353678i	$-0.115069\pi$
$101$	18.8006			1.87073			0.935367	+	0.353678i	$0.115069\pi$
$102$	0.332335	−	2.81157i	0.0329060	−	0.278387i
$103$			7.75081i			0.763710i	0.924222	+	0.381855i	$0.124715\pi$
$103$			7.75081i			0.763710i	−0.924222	+	0.381855i	$0.875285\pi$
$104$	−1.74116	−	4.20353i	−0.170735	−	0.412190i
$105$		0			0
$106$	13.0937	−	13.0937i	1.27177	−	1.27177i
$107$	−9.68110	+	6.46870i	−0.935907	+	0.625353i	−0.927183	−	0.374609i	$-0.877777\pi$
$107$	−9.68110	+	6.46870i	−0.935907	+	0.625353i	−0.00872397	+	0.999962i	$0.502777\pi$
$108$	5.82045	−	1.15776i	0.560073	−	0.111405i
$109$	4.13458	+	2.76264i	0.396021	+	0.264613i	0.737597	−	0.675242i	$-0.235961\pi$
$109$	4.13458	+	2.76264i	0.396021	+	0.264613i	−0.341576	+	0.939854i	$0.610961\pi$
$110$	−7.58781	−	3.14297i	−0.723469	−	0.299671i
$111$	−0.0695614	+	0.167936i	−0.00660248	+	0.0159398i
$112$		0			0
$113$	17.7143	−	3.52360i	1.66643	−	0.331473i	0.730297	−	0.683130i	$-0.239382\pi$
$113$	17.7143	−	3.52360i	1.66643	−	0.331473i	0.936129	+	0.351657i	$0.114382\pi$
$114$	1.24998	+	1.87073i	0.117072	+	0.175210i
$115$	−1.56341	+	1.56341i	−0.145789	+	0.145789i
$116$	−11.6343	−	2.31420i	−1.08021	−	0.214868i
$117$	3.77779	−	1.56481i	0.349256	−	0.144667i
$118$	−19.6686			−1.81064
$119$		0			0
$120$	1.16901			0.106716
$121$	−2.40476	+	0.996082i	−0.218614	+	0.0905529i
$122$	−22.0609	−	4.38818i	−1.99730	−	0.397287i
$123$	−1.58838	+	1.58838i	−0.143219	+	0.143219i
$124$	3.27442	+	4.90051i	0.294051	+	0.440079i
$125$	10.1857	−	2.02606i	0.911036	−	0.181216i
$126$		0			0
$127$	3.10433	−	7.49451i	0.275465	−	0.665030i	−0.724235	−	0.689554i	$-0.757807\pi$
$127$	3.10433	−	7.49451i	0.275465	−	0.665030i	0.999699	+	0.0245232i	$0.00780675\pi$
$128$	−18.1244	−	7.50738i	−1.60199	−	0.663565i
$129$	0.622740	+	0.416102i	0.0548292	+	0.0366357i
$130$	3.90256	−	0.776267i	0.342277	−	0.0680832i
$131$	0.919082	−	0.614111i	0.0803006	−	0.0536551i	−0.514772	−	0.857327i	$-0.672123\pi$
$131$	0.919082	−	0.614111i	0.0803006	−	0.0536551i	0.595072	+	0.803672i	$0.297123\pi$
$132$	−2.05662	+	2.05662i	−0.179005	+	0.179005i
$133$		0			0
$134$	3.70843	+	8.95295i	0.320360	+	0.773417i
$135$			2.13275i			0.183558i
$136$	10.1621	+	8.67660i	0.871397	+	0.744012i
$137$	2.26065			0.193140			0.0965701	−	0.995326i	$-0.469213\pi$
$137$	2.26065			0.193140			0.0965701	+	0.995326i	$0.469213\pi$
$138$	0.476141	+	1.14951i	0.0405318	+	0.0978524i
$139$	17.9220	+	3.56491i	1.52012	+	0.302372i	0.883363	−	0.468689i	$-0.155274\pi$
$139$	17.9220	+	3.56491i	1.52012	+	0.302372i	0.636762	+	0.771061i	$0.280274\pi$
$140$		0			0
$141$	−2.83604	+	1.89498i	−0.238838	+	0.159586i
$142$	7.30485	+	36.7240i	0.613010	+	3.08181i
$143$	−2.26018	+	3.38260i	−0.189006	+	0.282868i
$144$	−0.821726	+	1.98382i	−0.0684772	+	0.165318i
$145$	1.63141	−	3.93856i	0.135481	−	0.327080i
$146$	−26.5634	−	17.7491i	−2.19840	−	1.46892i
$147$		0			0
$148$	−1.15987	−	1.73586i	−0.0953405	−	0.142687i
$149$	−10.6110	−	10.6110i	−0.869286	−	0.869286i	0.123108	−	0.992393i	$-0.460714\pi$
$149$	−10.6110	−	10.6110i	−0.869286	−	0.869286i	−0.992393	+	0.123108i	$0.960714\pi$
$150$	0.470347	−	2.36459i	0.0384037	−	0.193068i
$151$	−2.28297	−	5.51157i	−0.185785	−	0.448525i	0.803355	−	0.595501i	$-0.203046\pi$
$151$	−2.28297	−	5.51157i	−0.185785	−	0.448525i	−0.989140	+	0.146975i	$0.953046\pi$
$152$	−10.6191			−0.861321
$153$	−7.79782	+	9.13291i	−0.630417	+	0.738352i
$154$		0			0
$155$	−1.95690	+	0.810574i	−0.157182	+	0.0651069i
$156$	0.274903	−	1.38203i	0.0220098	−	0.110651i
$157$	−7.19105	−	7.19105i	−0.573908	−	0.573908i	0.359310	−	0.933218i	$-0.383012\pi$
$157$	−7.19105	−	7.19105i	−0.573908	−	0.573908i	−0.933218	+	0.359310i	$0.883012\pi$
$158$	−23.0443	+	15.3977i	−1.83331	+	1.22498i
$159$	2.31141	−	0.459768i	0.183307	−	0.0364619i
$160$	3.23312	−	4.83870i	0.255600	−	0.382533i
$161$		0			0
$162$	−17.6422	−	7.30763i	−1.38610	−	0.574142i
$163$	2.94622	−	4.40933i	0.230766	−	0.345365i	−0.697958	−	0.716139i	$-0.745908\pi$
$163$	2.94622	−	4.40933i	0.230766	−	0.345365i	0.928723	+	0.370774i	$0.120908\pi$
$164$	−5.03322	−	25.3037i	−0.393028	−	1.97589i
$165$	−0.580718	−	0.869106i	−0.0452088	−	0.0676598i
$166$	13.5934	−	13.5934i	1.05505	−	1.05505i
$167$	4.01155	−	20.1674i	0.310423	−	1.56060i	−0.438987	−	0.898494i	$-0.644663\pi$
$167$	4.01155	−	20.1674i	0.310423	−	1.56060i	0.749409	−	0.662107i	$-0.230337\pi$
$168$		0			0
$169$			11.0290i			0.848387i
$170$	−9.17599	+	7.23605i	−0.703766	+	0.554979i
$171$		−	9.54356i		−	0.729815i
$172$	−7.94724	+	3.29186i	−0.605972	+	0.251002i
$173$	−21.5211	−	4.28082i	−1.63622	−	0.325465i	−0.710507	−	0.703690i	$-0.751534\pi$
$173$	−21.5211	−	4.28082i	−1.63622	−	0.325465i	−0.925713	+	0.378226i	$0.876534\pi$
$174$	−1.69635	−	1.69635i	−0.128600	−	0.128600i
$175$		0			0
$176$	−0.416779	−	2.09529i	−0.0314159	−	0.157938i
$177$	−2.08135	−	1.39071i	−0.156444	−	0.104532i
$178$	−18.4722	−	7.65144i	−1.38455	−	0.573500i
$179$	−5.61690	−	2.32660i	−0.419827	−	0.173898i	0.162761	−	0.986665i	$-0.447960\pi$
$179$	−5.61690	−	2.32660i	−0.419827	−	0.173898i	−0.582588	+	0.812768i	$0.697960\pi$
$180$	−10.0330	−	6.70384i	−0.747816	−	0.499674i
$181$	0.178749	+	0.898634i	0.0132863	+	0.0667949i	0.986860	−	0.161580i	$-0.0516589\pi$
$181$	0.178749	+	0.898634i	0.0132863	+	0.0667949i	−0.973573	+	0.228375i	$0.926659\pi$
$182$		0			0
$183$	−2.02423	−	2.02423i	−0.149635	−	0.149635i
$184$	−5.75958	−	1.14565i	−0.424602	−	0.0844586i
$185$	0.693175	−	0.287122i	0.0509632	−	0.0211097i
$186$			1.19196i			0.0873985i
$187$	1.40250	−	11.8652i	0.102561	−	0.867672i
$188$		−	39.1748i		−	2.85712i
$189$		0			0
$190$	1.81176	−	9.10832i	0.131439	−	0.660787i
$191$	5.74974	−	5.74974i	0.416037	−	0.416037i	−0.467798	−	0.883835i	$-0.654953\pi$
$191$	5.74974	−	5.74974i	0.416037	−	0.416037i	0.883835	+	0.467798i	$0.154953\pi$
$192$	−2.06156	−	3.08535i	−0.148780	−	0.222666i
$193$	2.66520	+	13.3989i	0.191845	+	0.964470i	0.949965	+	0.312356i	$0.101118\pi$
$193$	2.66520	+	13.3989i	0.191845	+	0.964470i	−0.758120	+	0.652115i	$0.773882\pi$
$194$	5.18883	−	7.76564i	0.372537	−	0.557540i
$195$	0.467861	+	0.193794i	0.0335042	+	0.0138779i
$196$		0			0
$197$	−1.91933	+	2.87248i	−0.136747	+	0.204656i	−0.893522	−	0.449019i	$-0.851774\pi$
$197$	−1.91933	+	2.87248i	−0.136747	+	0.204656i	0.756775	+	0.653675i	$0.226774\pi$
$198$	19.2277	−	3.82463i	1.36645	−	0.271804i
$199$	17.9984	−	12.0261i	1.27587	−	0.852511i	0.281615	−	0.959527i	$-0.409130\pi$
$199$	17.9984	−	12.0261i	1.27587	−	0.852511i	0.994257	+	0.107017i	$0.0341298\pi$
$200$	8.04617	+	8.04617i	0.568950	+	0.568950i
$201$	−0.240609	+	1.20962i	−0.0169713	+	0.0853203i
$202$	−40.3454	+	16.7116i	−2.83869	+	1.17582i
$203$		0			0
$204$	1.12393	+	3.98281i	0.0786906	+	0.278852i
$205$	9.27189			0.647577
$206$	−6.88957	−	16.6329i	−0.480019	−	1.15887i
$207$	1.02962	−	5.17625i	0.0715635	−	0.359774i
$208$	0.731863	+	0.731863i	0.0507456	+	0.0507456i
$209$	5.27512	+	7.89477i	0.364888	+	0.546093i
$210$		0			0
$211$	−19.6995	−	13.1628i	−1.35617	−	0.906165i	−0.356566	−	0.934270i	$-0.616053\pi$
$211$	−19.6995	−	13.1628i	−1.35617	−	0.906165i	−0.999605	+	0.0281055i	$0.991053\pi$
$212$	−10.3582	+	25.0068i	−0.711402	+	1.71748i
$213$	−1.82365	+	4.40267i	−0.124954	+	0.301666i
$214$	15.0253	−	22.4869i	1.02711	−	1.53718i
$215$	−0.603108	−	3.03203i	−0.0411316	−	0.206783i
$216$	−4.70994	+	3.14708i	−0.320471	+	0.214132i
$217$		0			0
$218$	−11.3283	−	2.25334i	−0.767249	−	0.152615i
$219$	−1.55597	−	3.75645i	−0.105143	−	0.253837i
$220$	12.0051			0.809386
$221$	2.62870	+	5.15717i	0.176826	+	0.346909i
$222$		−	0.422216i		−	0.0283373i
$223$	−1.69064	−	4.08158i	−0.113214	−	0.273323i	0.857109	−	0.515135i	$-0.172258\pi$
$223$	−1.69064	−	4.08158i	−0.113214	−	0.273323i	−0.970323	+	0.241812i	$0.922258\pi$
$224$		0			0
$225$	−7.23124	+	7.23124i	−0.482083	+	0.482083i
$226$	−34.8822	+	23.3075i	−2.32033	+	1.55039i
$227$	6.60020	−	1.31286i	0.438070	−	0.0871376i	0.0288721	−	0.999583i	$-0.490808\pi$
$227$	6.60020	−	1.31286i	0.438070	−	0.0871376i	0.409198	+	0.912445i	$0.365808\pi$
$228$	−2.73450	−	1.82713i	−0.181097	−	0.121005i
$229$	−5.49313	−	2.27533i	−0.362997	−	0.150358i	0.193728	−	0.981055i	$-0.437942\pi$
$229$	−5.49313	−	2.27533i	−0.362997	−	0.150358i	−0.556724	+	0.830697i	$0.687942\pi$
$230$	1.96532	−	4.74471i	0.129590	−	0.312857i
$231$		0			0
$232$	11.1052	−	2.20895i	0.729090	−	0.145025i
$233$	−3.59561	−	5.38121i	−0.235556	−	0.352535i	0.694793	−	0.719210i	$-0.255496\pi$
$233$	−3.59561	−	5.38121i	−0.235556	−	0.352535i	−0.930349	+	0.366675i	$0.880496\pi$
$234$	−6.71603	+	6.71603i	−0.439041	+	0.439041i
$235$	13.8083	+	2.74663i	0.900752	+	0.179171i
$236$	26.5616	−	11.0022i	1.72901	−	0.716181i
$237$	−3.52730			−0.229123
$238$		0			0
$239$	9.05783			0.585902			0.292951	−	0.956127i	$-0.405363\pi$
$239$	9.05783			0.585902			0.292951	+	0.956127i	$0.405363\pi$
$240$	−0.245687	+	0.101767i	−0.0158590	+	0.00656902i
$241$	−20.4093	−	4.05966i	−1.31468	−	0.261506i	−0.512550	−	0.858657i	$-0.671299\pi$
$241$	−20.4093	−	4.05966i	−1.31468	−	0.261506i	−0.802129	+	0.597151i	$0.796299\pi$
$242$	4.27510	−	4.27510i	0.274814	−	0.274814i
$243$	−4.26341	−	6.38065i	−0.273498	−	0.409319i
$244$	32.2469	−	6.41432i	2.06440	−	0.410635i
$245$		0			0
$246$	1.99671	−	4.82048i	0.127306	−	0.307343i
$247$	−4.24995	−	1.76038i	−0.270418	−	0.112011i
$248$	−4.67766	−	3.12551i	−0.297031	−	0.198470i
$249$	2.39963	−	0.477315i	0.152070	−	0.0302486i
$250$	−20.0571	+	13.4018i	−1.26852	+	0.847601i
$251$	−14.0153	+	14.0153i	−0.884635	+	0.884635i	−0.994001	−	0.109367i	$-0.965118\pi$
$251$	−14.0153	+	14.0153i	−0.884635	+	0.884635i	0.109367	+	0.994001i	$0.465118\pi$
$252$		0			0
$253$	2.00939	+	4.85109i	0.126329	+	0.304985i
$254$			18.8423i			1.18227i
$255$	−1.48265	+	0.116916i	−0.0928474	+	0.00732155i
$256$	20.4627			1.27892
$257$	3.61998	+	8.73940i	0.225808	+	0.545149i	0.995659	−	0.0930748i	$-0.0296696\pi$
$257$	3.61998	+	8.73940i	0.225808	+	0.545149i	−0.769851	+	0.638224i	$0.779670\pi$
$258$	−1.70624	−	0.339392i	−0.106226	−	0.0211296i
$259$		0			0
$260$	−4.83602	+	3.23133i	−0.299917	+	0.200398i
$261$	1.98523	+	9.98042i	0.122883	+	0.617772i
$262$	−1.42644	+	2.13482i	−0.0881256	+	0.131889i
$263$	−11.0673	+	26.7188i	−0.682438	+	1.64755i	0.0770484	+	0.997027i	$0.475450\pi$
$263$	−11.0673	+	26.7188i	−0.682438	+	1.64755i	−0.759486	+	0.650523i	$0.774550\pi$
$264$	1.06242	−	2.56490i	0.0653872	−	0.157859i
$265$	−8.08812	−	5.40431i	−0.496849	−	0.331984i
$266$		0			0
$267$	−1.41373	−	2.11580i	−0.0865191	−	0.129485i
$268$	−10.0162	−	10.0162i	−0.611835	−	0.611835i
$269$	−1.46193	+	7.34963i	−0.0891356	+	0.448115i	0.910282	+	0.413989i	$0.135865\pi$
$269$	−1.46193	+	7.34963i	−0.0891356	+	0.448115i	−0.999418	+	0.0341260i	$0.989135\pi$
$270$	−1.89577	−	4.57680i	−0.115373	−	0.278535i
$271$	−1.21904			−0.0740511			−0.0370256	−	0.999314i	$-0.511788\pi$
$271$	−1.21904			−0.0740511			−0.0370256	+	0.999314i	$0.511788\pi$
$272$	−2.89106	−	0.938874i	−0.175296	−	0.0569276i
$273$		0			0
$274$	−4.85126	+	2.00946i	−0.293075	+	0.121396i
$275$	1.98493	−	9.97894i	0.119696	−	0.601753i
$276$	−1.28602	−	1.28602i	−0.0774092	−	0.0774092i
$277$	0.777746	−	0.519673i	0.0467302	−	0.0312241i	−0.531986	−	0.846753i	$-0.678554\pi$
$277$	0.777746	−	0.519673i	0.0467302	−	0.0312241i	0.578716	+	0.815529i	$0.303554\pi$
$278$	−41.6287	+	8.28046i	−2.49672	+	0.496629i
$279$	2.80895	−	4.20390i	0.168168	−	0.251681i
$280$		0			0
$281$	5.59849	+	2.31897i	0.333978	+	0.138338i	0.543369	−	0.839494i	$-0.317148\pi$
$281$	5.59849	+	2.31897i	0.333978	+	0.138338i	−0.209391	+	0.977832i	$0.567148\pi$
$282$	4.40161	−	6.58747i	0.262112	−	0.392278i
$283$	−4.38208	−	22.0302i	−0.260488	−	1.30956i	−0.860451	−	0.509533i	$-0.829818\pi$
$283$	−4.38208	−	22.0302i	−0.260488	−	1.30956i	0.599964	−	0.800027i	$-0.295182\pi$
$284$	−30.4075	−	45.5081i	−1.80435	−	2.70041i
$285$	0.835747	−	0.835747i	0.0495054	−	0.0495054i
$286$	1.84351	−	9.26797i	0.109009	−	0.548026i
$287$		0			0
$288$			13.8910i			0.818537i
$289$	−13.7563	−	9.98814i	−0.809197	−	0.587537i
$290$			9.90213i			0.581473i
$291$	1.09818	−	0.454879i	0.0643762	−	0.0266655i
$292$	45.8012	+	9.11042i	2.68031	+	0.533147i
$293$	−11.6686	−	11.6686i	−0.681688	−	0.681688i	0.278692	−	0.960380i	$-0.410099\pi$
$293$	−11.6686	−	11.6686i	−0.681688	−	0.681688i	−0.960380	+	0.278692i	$0.910099\pi$
$294$		0			0
$295$	2.01573	+	10.1338i	0.117360	+	0.590011i
$296$	1.65692	+	1.10712i	0.0963067	+	0.0643501i
$297$	4.67941	+	1.93827i	0.271527	+	0.112470i
$298$	32.2027	+	13.3388i	1.86545	+	0.772695i
$299$	−2.11517	−	1.41331i	−0.122323	−	0.0817338i
$300$	0.687519	+	3.45639i	0.0396939	+	0.199555i
$301$		0			0
$302$	9.79831	+	9.79831i	0.563829	+	0.563829i
$303$	−5.45102	−	1.08428i	−0.313153	−	0.0622900i
$304$	2.23177	−	0.924428i	0.128001	−	0.0530196i
$305$			11.8161i			0.676586i
$306$	8.61569	−	26.5302i	0.492526	−	1.51663i
$307$		−	11.4234i		−	0.651969i	−0.945375	−	0.325985i	$-0.894304\pi$
$307$		−	11.4234i		−	0.651969i	0.945375	−	0.325985i	$-0.105696\pi$
$308$		0			0
$309$	0.447007	−	2.24725i	0.0254293	−	0.127842i
$310$	3.47892	−	3.47892i	0.197589	−	0.197589i
$311$	6.26058	+	9.36962i	0.355005	+	0.531303i	0.965393	−	0.260800i	$-0.0839864\pi$
$311$	6.26058	+	9.36962i	0.355005	+	0.531303i	−0.610388	+	0.792103i	$0.708986\pi$
$312$	0.262401	+	1.31918i	0.0148555	+	0.0746838i
$313$	−15.5367	+	23.2524i	−0.878189	+	1.31430i	0.0703115	+	0.997525i	$0.477601\pi$
$313$	−15.5367	+	23.2524i	−0.878189	+	1.31430i	−0.948500	+	0.316777i	$0.897399\pi$
$314$	21.8237	+	9.03967i	1.23158	+	0.510138i
$315$		0			0
$316$	22.5072	−	33.6845i	1.26613	−	1.89490i
$317$	8.39290	−	1.66945i	0.471392	−	0.0937657i	0.0463227	−	0.998927i	$-0.485250\pi$
$317$	8.39290	−	1.66945i	0.471392	−	0.0937657i	0.425069	+	0.905161i	$0.360250\pi$
$318$	−4.55150	+	3.04122i	−0.255236	+	0.170543i
$319$	−7.15884	−	7.15884i	−0.400818	−	0.400818i
$320$	−2.98808	+	15.0221i	−0.167039	+	0.839760i
$321$	3.17998	−	1.31719i	0.177489	−	0.0735185i
$322$		0			0
$323$	13.4681	−	1.06204i	0.749386	−	0.0590934i
$324$	27.9128			1.55071
$325$	1.88636	+	4.55408i	0.104637	+	0.252615i
$326$	−2.40308	+	12.0811i	−0.133094	+	0.669109i
$327$	−1.03944	−	1.03944i	−0.0574814	−	0.0574814i
$328$	13.6816	+	20.4759i	0.755438	+	1.13059i
$329$		0			0
$330$	2.01873	+	1.34887i	0.111128	+	0.0742530i
$331$	−6.22403	+	15.0261i	−0.342104	+	0.825911i	0.655399	+	0.755283i	$0.272500\pi$
$331$	−6.22403	+	15.0261i	−0.342104	+	0.825911i	−0.997503	+	0.0706284i	$0.977500\pi$
$332$	−10.7535	+	25.9613i	−0.590175	+	1.42481i
$333$	−0.994990	+	1.48911i	−0.0545251	+	0.0816026i
$334$	9.31789	+	46.8442i	0.509852	+	2.56320i
$335$	4.23274	−	2.82823i	0.231259	−	0.154522i
$336$		0			0
$337$	5.14392	+	1.02319i	0.280207	+	0.0557366i	0.333193	−	0.942859i	$-0.391874\pi$
$337$	5.14392	+	1.02319i	0.280207	+	0.0557366i	−0.0529861	+	0.998595i	$0.516874\pi$
$338$	−9.80354	−	23.6678i	−0.533242	−	1.28736i
$339$	−5.33928			−0.289990
$340$	8.34411	−	14.9048i	0.452523	−	0.808328i
$341$			5.03023i			0.272402i
$342$	8.48313	+	20.4801i	0.458715	+	1.10744i
$343$		0			0
$344$	5.80594	−	5.80594i	0.313035	−	0.313035i
$345$	0.543458	−	0.363127i	0.0292588	−	0.0195501i
$346$	49.9886	−	9.94335i	2.68740	−	0.534558i
$347$	−16.5465	−	11.0560i	−0.888263	−	0.593519i	0.0255407	−	0.999674i	$-0.491869\pi$
$347$	−16.5465	−	11.0560i	−0.888263	−	0.593519i	−0.913804	+	0.406155i	$0.866869\pi$
$348$	3.23975	+	1.34195i	0.173669	+	0.0719359i
$349$	−9.16782	+	22.1331i	−0.490742	+	1.18476i	0.463601	+	0.886044i	$0.346557\pi$
$349$	−9.16782	+	22.1331i	−0.490742	+	1.18476i	−0.954343	+	0.298712i	$0.903443\pi$
$350$		0			0
$351$	−2.40671	+	0.478725i	−0.128461	+	0.0255524i
$352$	−7.67814	−	11.4912i	−0.409246	−	0.612480i
$353$	−10.1371	+	10.1371i	−0.539543	+	0.539543i	−0.923395	−	0.383852i	$-0.874597\pi$
$353$	−10.1371	+	10.1371i	−0.539543	+	0.539543i	0.383852	+	0.923395i	$0.374597\pi$
$354$	5.70267	+	1.13433i	0.303094	+	0.0602890i
$355$	18.1725	−	7.52731i	0.964498	−	0.399508i
$356$	29.2260			1.54898
$357$		0			0
$358$	14.1217			0.746355
$359$	29.6521	−	12.2823i	1.56498	−	0.648236i	0.579035	−	0.815303i	$-0.303430\pi$
$359$	29.6521	−	12.2823i	1.56498	−	0.648236i	0.985946	+	0.167067i	$0.0534296\pi$
$360$	11.2965	+	2.24702i	0.595379	+	0.118428i
$361$	5.84329	−	5.84329i	0.307541	−	0.307541i
$362$	−1.18237	−	1.76954i	−0.0621440	−	0.0930051i
$363$	0.754676	−	0.150114i	0.0396102	−	0.00787897i
$364$		0			0
$365$	−6.42244	+	15.5052i	−0.336166	+	0.811577i
$366$	6.14321	+	2.54460i	0.321111	+	0.133008i
$367$	17.6578	+	11.7985i	0.921728	+	0.615879i	0.923283	−	0.384120i	$-0.125495\pi$
$367$	17.6578	+	11.7985i	0.921728	+	0.615879i	−0.00155517	+	0.999999i	$0.500495\pi$
$368$	1.31020	−	0.260615i	0.0682989	−	0.0135855i
$369$	−18.4021	+	12.2959i	−0.957974	+	0.640098i
$370$	−1.23231	+	1.23231i	−0.0640645	+	0.0640645i
$371$		0			0
$372$	−0.666755	−	1.60969i	−0.0345696	−	0.0834585i
$373$		−	9.90478i		−	0.512850i	−0.966564	−	0.256425i	$-0.917455\pi$
$373$		−	9.90478i		−	0.512850i	0.966564	−	0.256425i	$-0.0825446\pi$
$374$	7.53712	+	26.7090i	0.389735	+	1.38109i
$375$	−3.07007			−0.158538
$376$	14.3098	+	34.5469i	0.737971	+	1.78162i
$377$	4.81068	+	0.956903i	0.247762	+	0.0492830i
$378$		0			0
$379$	−22.3558	+	14.9376i	−1.14834	+	0.767295i	−0.976006	−	0.217744i	$-0.930130\pi$
$379$	−22.3558	+	14.9376i	−1.14834	+	0.767295i	−0.172332	+	0.985039i	$0.555130\pi$
$380$	2.64829	+	13.3139i	0.135855	+	0.682987i
$381$	−1.33229	+	1.99391i	−0.0682552	+	0.102151i
$382$	−7.22784	+	17.4496i	−0.369809	+	0.892797i
$383$	8.68998	−	20.9795i	0.444037	−	1.07200i	−0.530482	−	0.847696i	$-0.677989\pi$
$383$	8.68998	−	20.9795i	0.444037	−	1.07200i	0.974519	−	0.224305i	$-0.0720111\pi$
$384$	4.82199	+	3.22195i	0.246071	+	0.164420i
$385$		0			0
$386$	−17.6294	−	26.3843i	−0.897315	−	1.34293i
$387$	5.21791	+	5.21791i	0.265241	+	0.265241i
$388$	−2.66338	+	13.3897i	−0.135213	+	0.679759i
$389$	1.85773	+	4.48496i	0.0941908	+	0.227397i	0.963952	−	0.266076i	$-0.0857272\pi$
$389$	1.85773	+	4.48496i	0.0941908	+	0.227397i	−0.869761	+	0.493473i	$0.835727\pi$
$390$	−1.17627			−0.0595627
$391$	7.41942	+	0.876995i	0.375216	+	0.0443515i
$392$		0			0
$393$	−0.301894	+	0.125049i	−0.0152285	+	0.00630787i
$394$	1.56550	−	7.87030i	0.0788687	−	0.396500i
$395$	10.2950	+	10.2950i	0.517998	+	0.517998i
$396$	−23.8268	+	15.9206i	−1.19734	+	0.800038i
$397$	−20.1076	+	3.99966i	−1.00917	+	0.200737i	−0.671878	−	0.740662i	$-0.734512\pi$
$397$	−20.1076	+	3.99966i	−1.00917	+	0.200737i	−0.337295	+	0.941399i	$0.609512\pi$
$398$	−27.9339	+	41.8061i	−1.40020	+	2.09555i
$399$		0			0
$400$	−2.39148	−	0.990581i	−0.119574	−	0.0495291i
$401$	17.1277	−	25.6335i	0.855318	−	1.28007i	−0.103090	−	0.994672i	$-0.532873\pi$
$401$	17.1277	−	25.6335i	0.855318	−	1.28007i	0.958408	−	0.285402i	$-0.0921270\pi$
$402$	−0.558879	−	2.80967i	−0.0278744	−	0.140134i
$403$	−1.35395	−	2.02633i	−0.0674449	−	0.100938i
$404$	45.1367	−	45.1367i	2.24563	−	2.24563i
$405$	−1.95703	+	9.83864i	−0.0972455	+	0.488886i
$406$		0			0
$407$		−	1.78181i		−	0.0883212i
$408$	−2.44599	−	3.10175i	−0.121095	−	0.153560i
$409$		−	20.5229i		−	1.01479i	−0.861712	−	0.507397i	$-0.830608\pi$
$409$		−	20.5229i		−	1.01479i	0.861712	−	0.507397i	$-0.169392\pi$
$410$	−19.8971	+	8.24164i	−0.982647	+	0.407026i
$411$	−0.655448	−	0.130377i	−0.0323309	−	0.00643101i
$412$	18.6082	+	18.6082i	0.916759	+	0.916759i
$413$		0			0
$414$	2.39157	+	12.0232i	0.117539	+	0.590909i
$415$	−8.39682	−	5.61057i	−0.412184	−	0.275412i
$416$	6.18596	+	2.56231i	0.303292	+	0.125628i
$417$	−4.99068	−	2.06721i	−0.244394	−	0.101231i
$418$	−18.3377	−	12.2529i	−0.896927	−	0.599308i
$419$	−0.549943	−	2.76475i	−0.0268665	−	0.135067i	0.965024	−	0.262161i	$-0.0844351\pi$
$419$	−0.549943	−	2.76475i	−0.0268665	−	0.135067i	−0.991891	+	0.127094i	$0.959435\pi$
$420$		0			0
$421$	−1.40311	−	1.40311i	−0.0683836	−	0.0683836i	0.672088	−	0.740471i	$-0.265398\pi$
$421$	−1.40311	−	1.40311i	−0.0683836	−	0.0683836i	−0.740471	+	0.672088i	$0.765398\pi$
$422$	53.9746	+	10.7362i	2.62744	+	0.522630i
$423$	−31.0479	+	12.8605i	−1.50960	+	0.625298i
$424$		−	25.8363i		−	1.25472i
$425$	−11.0096	−	9.40019i	−0.534045	−	0.455976i
$426$		−	11.0690i		−	0.536293i
$427$		0			0
$428$	−7.71234	+	38.7725i	−0.372790	+	1.87414i
$429$	0.850396	−	0.850396i	0.0410575	−	0.0410575i
$430$	3.98937	+	5.97051i	0.192384	+	0.287924i
$431$	−0.553010	−	2.78017i	−0.0266376	−	0.133916i	0.965178	−	0.261593i	$-0.0842479\pi$
$431$	−0.553010	−	2.78017i	−0.0266376	−	0.133916i	−0.991816	+	0.127677i	$0.959248\pi$
$432$	0.715904	−	1.07143i	0.0344439	−	0.0515490i
$433$	14.5043	+	6.00788i	0.697032	+	0.288720i	0.702926	−	0.711262i	$-0.251876\pi$
$433$	14.5043	+	6.00788i	0.697032	+	0.288720i	−0.00589445	+	0.999983i	$0.501876\pi$
$434$		0			0
$435$	−0.700153	+	1.04785i	−0.0335698	+	0.0502407i
$436$	16.5589	−	3.29377i	0.793027	−	0.157743i
$437$	−4.93666	+	3.29857i	−0.236152	+	0.157792i
$438$	6.67810	+	6.67810i	0.319092	+	0.319092i
$439$	6.52863	−	32.8217i	0.311595	−	1.56649i	−0.434512	−	0.900666i	$-0.643079\pi$
$439$	6.52863	−	32.8217i	0.311595	−	1.56649i	0.746107	−	0.665826i	$-0.231921\pi$
$440$	−10.5869	+	4.38524i	−0.504711	+	0.209058i
$441$		0			0
$442$	−10.2252	−	8.73045i	−0.486364	−	0.415265i
$443$	33.0936			1.57232			0.786162	−	0.618021i	$-0.212065\pi$
$443$	33.0936			1.57232			0.786162	+	0.618021i	$0.212065\pi$
$444$	0.236178	+	0.570185i	0.0112085	+	0.0270598i
$445$	−2.04910	+	10.3015i	−0.0971367	+	0.488339i
$446$	7.25610	+	7.25610i	0.343586	+	0.343586i
$447$	2.46457	+	3.68849i	0.116570	+	0.174459i
$448$		0			0
$449$	−9.67076	−	6.46180i	−0.456392	−	0.304951i	0.306042	−	0.952018i	$-0.400995\pi$
$449$	−9.67076	−	6.46180i	−0.456392	−	0.304951i	−0.762433	+	0.647067i	$0.775995\pi$
$450$	9.09020	−	21.9457i	0.428516	−	1.03453i
$451$	8.42641	−	20.3432i	0.396784	−	0.957922i
$452$	34.0692	−	50.9882i	1.60248	−	2.39828i
$453$	0.344054	+	1.72968i	0.0161651	+	0.0812674i
$454$	−12.9968	+	8.68416i	−0.609968	+	0.407568i
$455$		0			0
$456$	3.07888	+	0.612426i	0.144182	+	0.0286795i
$457$	−6.30871	−	15.2306i	−0.295109	−	0.712456i	−0.999995	−	0.00313553i	$-0.999002\pi$
$457$	−6.30871	−	15.2306i	−0.295109	−	0.712456i	0.704886	−	0.709320i	$-0.250998\pi$
$458$	13.8105			0.645324
$459$	5.65884	−	4.46248i	0.264132	−	0.208291i
$460$			7.50690i			0.350011i
$461$	3.58512	+	8.65524i	0.166976	+	0.403115i	0.985113	−	0.171908i	$-0.0549932\pi$
$461$	3.58512	+	8.65524i	0.166976	+	0.403115i	−0.818137	+	0.575023i	$0.804993\pi$
$462$		0			0
$463$	−16.4176	+	16.4176i	−0.762990	+	0.762990i	−0.976862	−	0.213872i	$-0.931392\pi$
$463$	−16.4176	+	16.4176i	−0.762990	+	0.762990i	0.213872	+	0.976862i	$0.431392\pi$
$464$	−2.14163	+	1.43099i	−0.0994226	+	0.0664320i
$465$	0.614127	−	0.122158i	0.0284795	−	0.00566492i
$466$	12.4993	+	8.35177i	0.579019	+	0.386888i
$467$	3.49736	+	1.44866i	0.161839	+	0.0670358i	0.462132	−	0.886811i	$-0.347085\pi$
$467$	3.49736	+	1.44866i	0.161839	+	0.0670358i	−0.300293	+	0.953847i	$0.597085\pi$
$468$	5.31293	−	12.8265i	0.245590	−	0.592907i
$469$		0			0
$470$	−32.0734	+	6.37980i	−1.47944	+	0.294278i
$471$	1.67023	+	2.49968i	0.0769603	+	0.115179i
$472$	−19.4049	+	19.4049i	−0.893182	+	0.893182i
$473$	−7.20059	−	1.43229i	−0.331083	−	0.0658566i
$474$	7.56944	−	3.13536i	0.347676	−	0.144012i
$475$	11.5047			0.527870
$476$		0			0
$477$	23.2195			1.06315
$478$	−19.4377	+	8.05137i	−0.889061	+	0.368261i
$479$	−2.21730	−	0.441048i	−0.101311	−	0.0201520i	0.144175	−	0.989552i	$-0.453947\pi$
$479$	−2.21730	−	0.441048i	−0.101311	−	0.0201520i	−0.245485	+	0.969400i	$0.578947\pi$
$480$	−1.21646	+	1.21646i	−0.0555236	+	0.0555236i
$481$	0.479597	+	0.717767i	0.0218677	+	0.0327274i
$482$	47.4061	−	9.42966i	2.15929	−	0.429509i
$483$		0			0
$484$	−3.38195	+	8.16475i	−0.153725	+	0.371125i
$485$	−4.53284	−	1.87756i	−0.205826	−	0.0852558i
$486$	14.8208	+	9.90292i	0.672284	+	0.449206i
$487$	−16.6652	+	3.31492i	−0.755173	+	0.150213i	−0.557640	−	0.830083i	$-0.688293\pi$
$487$	−16.6652	+	3.31492i	−0.755173	+	0.150213i	−0.197533	+	0.980296i	$0.563293\pi$
$488$	−26.0944	+	17.4357i	−1.18124	+	0.789278i
$489$	−1.10852	+	1.10852i	−0.0501288	+	0.0501288i
$490$		0			0
$491$	−8.10418	−	19.5652i	−0.365737	−	0.882966i	−0.994438	−	0.105320i	$-0.966413\pi$
$491$	−8.10418	−	19.5652i	−0.365737	−	0.882966i	0.628702	−	0.777647i	$-0.283587\pi$
$492$			7.62678i			0.343842i
$493$	−13.8637	+	3.91226i	−0.624389	+	0.176199i
$494$	10.6850			0.480740
$495$	−3.94110	−	9.51465i	−0.177139	−	0.427652i
$496$	1.25517	+	0.249669i	0.0563587	+	0.0112105i
$497$		0			0
$498$	−4.72522	+	3.15729i	−0.211742	+	0.141482i
$499$	3.84766	+	19.3435i	0.172245	+	0.865933i	0.966168	+	0.257915i	$0.0830354\pi$
$499$	3.84766	+	19.3435i	0.172245	+	0.865933i	−0.793923	+	0.608019i	$0.791965\pi$
$500$	19.5897	−	29.3181i	0.876078	−	1.31114i
$501$	−2.32620	+	5.61594i	−0.103927	+	0.250902i
$502$	17.6182	−	42.5341i	0.786339	−	1.89839i
$503$	−26.9483	−	18.0063i	−1.20157	−	0.802862i	−0.216711	−	0.976236i	$-0.569533\pi$
$503$	−26.9483	−	18.0063i	−1.20157	−	0.802862i	−0.984856	+	0.173374i	$0.944533\pi$
$504$		0			0
$505$	12.7451	+	19.0743i	0.567148	+	0.848796i
$506$	−8.62411	−	8.62411i	−0.383389	−	0.383389i
$507$	0.636069	−	3.19774i	0.0282488	−	0.142016i
$508$	−10.5400	−	25.4458i	−0.467636	−	1.12897i
$509$	−11.2289			−0.497712			−0.248856	−	0.968541i	$-0.580055\pi$
$509$	−11.2289			−0.497712			−0.248856	+	0.968541i	$0.580055\pi$
$510$	3.07779	−	1.56880i	0.136287	−	0.0694678i
$511$		0			0
$512$	−7.66320	+	3.17420i	−0.338669	+	0.140281i
$513$	−1.11731	+	5.61711i	−0.0493305	+	0.248001i
$514$	−15.5366	−	15.5366i	−0.685292	−	0.685292i
$515$	−7.86363	+	5.25431i	−0.346513	+	0.231533i
$516$	2.49406	−	0.496099i	0.109795	−	0.0218395i
$517$	18.5754	−	27.8001i	0.816947	−	1.22265i
$518$		0			0
$519$	5.99291	+	2.48234i	0.263059	+	0.108963i
$520$	3.08438	−	4.61610i	0.135259	−	0.202429i
$521$	6.25235	+	31.4327i	0.273920	+	1.37709i	0.835419	+	0.549613i	$0.185225\pi$
$521$	6.25235	+	31.4327i	0.273920	+	1.37709i	−0.561499	+	0.827478i	$0.689775\pi$
$522$	−13.1317	−	19.6529i	−0.574757	−	0.860185i
$523$	−21.7968	+	21.7968i	−0.953108	+	0.953108i	−0.998949	−	0.0458406i	$-0.985403\pi$
$523$	−21.7968	+	21.7968i	−0.953108	+	0.953108i	0.0458406	+	0.998949i	$0.485403\pi$
$524$	0.732177	−	3.68090i	0.0319853	−	0.160801i
$525$		0			0
$526$		−	67.1749i		−	2.92897i
$527$	6.24523	+	3.49624i	0.272046	+	0.152299i
$528$			0.631541i			0.0274843i
$529$	18.2158	−	7.54524i	0.791992	−	0.328054i
$530$	22.1606	+	4.40801i	0.962594	+	0.191472i
$531$	−17.4395	−	17.4395i	−0.756811	−	0.756811i
$532$		0			0
$533$	2.08120	+	10.4629i	0.0901467	+	0.453198i
$534$	4.91452	+	3.28378i	0.212672	+	0.142103i
$535$	−13.1257	−	5.43686i	−0.567475	−	0.235056i
$536$	12.4916	+	5.17420i	0.539556	+	0.223491i
$537$	1.49437	+	0.998508i	0.0644870	+	0.0430888i
$538$	−3.39573	−	17.0715i	−0.146400	−	0.736004i
$539$		0			0
$540$	5.12033	+	5.12033i	0.220344	+	0.220344i
$541$	−25.2901	−	5.03052i	−1.08731	−	0.216279i	−0.381277	−	0.924461i	$-0.624516\pi$
$541$	−25.2901	−	5.03052i	−1.08731	−	0.216279i	−0.706030	+	0.708182i	$0.749516\pi$
$542$	2.61600	−	1.08358i	0.112367	−	0.0465439i
$543$		−	0.270857i		−	0.0116236i
$544$	−19.6034	+	1.54584i	−0.840487	+	0.0662773i
$545$			6.06757i			0.259906i
$546$		0			0
$547$	−4.11814	+	20.7033i	−0.176079	+	0.885208i	0.787198	+	0.616700i	$0.211531\pi$
$547$	−4.11814	+	20.7033i	−0.176079	+	0.885208i	−0.963277	+	0.268509i	$0.913469\pi$
$548$	5.42738	−	5.42738i	0.231846	−	0.231846i
$549$	−15.6698	−	23.4515i	−0.668771	−	1.00089i
$550$	4.61054	+	23.1788i	0.196594	+	0.988346i
$551$	6.36004	−	9.51847i	0.270947	−	0.405500i
$552$	1.60385	+	0.664337i	0.0682644	+	0.0282760i
$553$		0			0
$554$	−1.20708	+	1.80652i	−0.0512839	+	0.0767518i
$555$	−0.217537	+	0.0432707i	−0.00923392	+	0.00183674i
$556$	51.5859	−	34.4686i	2.18773	−	1.46179i
$557$	−0.907608	−	0.907608i	−0.0384566	−	0.0384566i	0.687617	−	0.726074i	$-0.258657\pi$
$557$	−0.907608	−	0.907608i	−0.0384566	−	0.0384566i	−0.726074	+	0.687617i	$0.758657\pi$
$558$	−2.29112	+	11.5182i	−0.0969907	+	0.487605i
$559$	3.28613	−	1.36116i	0.138988	−	0.0575709i
$560$		0			0
$561$	−1.09093	+	3.35930i	−0.0460593	+	0.141830i
$562$	−14.0754			−0.593736
$563$	−8.88866	−	21.4591i	−0.374612	−	0.904394i	−0.992956	−	0.118486i	$-0.962196\pi$
$563$	−8.88866	−	21.4591i	−0.374612	−	0.904394i	0.618343	−	0.785908i	$-0.287804\pi$
$564$	−2.25930	+	11.3583i	−0.0951338	+	0.478270i
$565$	15.5835	+	15.5835i	0.655605	+	0.655605i
$566$	28.9861	+	43.3807i	1.21838	+	1.82343i
$567$		0			0
$568$	43.4385	+	29.0247i	1.82264	+	1.21785i
$569$	−13.0817	+	31.5819i	−0.548412	+	1.32398i	0.370248	+	0.928933i	$0.379273\pi$
$569$	−13.0817	+	31.5819i	−0.548412	+	1.32398i	−0.918660	+	0.395050i	$0.870727\pi$
$570$	−1.05059	+	2.53636i	−0.0440046	+	0.106236i
$571$	16.3847	−	24.5214i	0.685679	−	1.02619i	−0.311435	−	0.950267i	$-0.600810\pi$
$571$	16.3847	−	24.5214i	0.685679	−	1.02619i	0.997114	−	0.0759232i	$-0.0241904\pi$
$572$	2.69471	+	13.5472i	0.112672	+	0.566438i
$573$	−1.99867	+	1.33547i	−0.0834956	+	0.0557900i
$574$		0			0
$575$	6.23991	+	1.24119i	0.260222	+	0.0517614i
$576$	−13.9910	−	33.7772i	−0.582957	−	1.40738i
$577$	−7.41197			−0.308564			−0.154282	−	0.988027i	$-0.549307\pi$
$577$	−7.41197			−0.308564			−0.154282	+	0.988027i	$0.549307\pi$
$578$	38.3989	+	9.20631i	1.59718	+	0.382932i
$579$		−	4.03854i		−	0.167836i
$580$	−5.53904	−	13.3724i	−0.229996	−	0.555259i
$581$		0			0
$582$	−1.95230	+	1.95230i	−0.0809255	+	0.0809255i
$583$	−19.2080	+	12.8344i	−0.795515	+	0.531546i
$584$	−43.7183	+	8.69611i	−1.80908	+	0.359848i
$585$	4.14857	+	2.77199i	0.171522	+	0.114608i
$586$	35.4124	+	14.6683i	1.46287	+	0.605942i
$587$	−13.7594	+	33.2180i	−0.567909	+	1.37105i	0.335405	+	0.942074i	$0.391127\pi$
$587$	−13.7594	+	33.2180i	−0.567909	+	1.37105i	−0.903314	+	0.428980i	$0.858873\pi$
$588$		0			0
$589$	−5.57860	+	1.10965i	−0.229862	+	0.0457225i
$590$	−13.3334	−	19.9549i	−0.548929	−	0.821530i
$591$	0.722150	−	0.722150i	0.0297053	−	0.0297053i
$592$	−0.444607	−	0.0884378i	−0.0182732	−	0.00363477i
$593$	−39.9556	+	16.5501i	−1.64078	+	0.679632i	−0.996376	−	0.0850549i	$-0.972893\pi$
$593$	−39.9556	+	16.5501i	−1.64078	+	0.679632i	−0.644402	+	0.764687i	$0.722893\pi$
$594$	−11.7647			−0.482712
$595$		0			0
$596$	−50.9498			−2.08699
$597$	−5.91200	+	2.44883i	−0.241962	+	0.100224i
$598$	5.79533	+	1.15276i	0.236989	+	0.0471400i
$599$	14.3654	−	14.3654i	0.586954	−	0.586954i	−0.349851	−	0.936805i	$-0.613768\pi$
$599$	14.3654	−	14.3654i	0.586954	−	0.586954i	0.936805	+	0.349851i	$0.113768\pi$
$600$	−1.86885	−	2.79693i	−0.0762955	−	0.114184i
$601$	−23.9093	+	4.75585i	−0.975280	+	0.193995i	−0.656908	−	0.753971i	$-0.728136\pi$
$601$	−23.9093	+	4.75585i	−0.975280	+	0.193995i	−0.318372	+	0.947966i	$0.603136\pi$
$602$		0			0
$603$	−4.65015	+	11.2265i	−0.189369	+	0.457177i
$604$	−18.7132	−	7.75125i	−0.761428	−	0.315394i
$605$	−2.64078	−	1.76451i	−0.107363	−	0.0717376i
$606$	12.6615	−	2.51852i	0.514337	−	0.102308i
$607$	13.7331	−	9.17615i	0.557409	−	0.372449i	−0.244726	−	0.969592i	$-0.578698\pi$
$607$	13.7331	−	9.17615i	0.557409	−	0.372449i	0.802134	+	0.597144i	$0.203698\pi$
$608$	11.0501	−	11.0501i	0.448140	−	0.448140i
$609$		0			0
$610$	−10.5031	−	25.3568i	−0.425259	−	1.02667i
$611$			16.1985i			0.655321i
$612$	3.20528	+	40.6474i	0.129566	+	1.64307i
$613$	48.1133			1.94328			0.971639	−	0.236468i	$-0.0759897\pi$
$613$	48.1133			1.94328			0.971639	+	0.236468i	$0.0759897\pi$
$614$	10.1541	+	24.5142i	0.409787	+	0.989312i
$615$	−2.68827	−	0.534731i	−0.108402	−	0.0215624i
$616$		0			0
$617$	22.3116	−	14.9081i	0.898230	−	0.600178i	−0.0184371	−	0.999830i	$-0.505869\pi$
$617$	22.3116	−	14.9081i	0.898230	−	0.600178i	0.916667	+	0.399652i	$0.130869\pi$
$618$	1.03829	+	5.21985i	0.0417663	+	0.209973i
$619$	−18.2881	+	27.3701i	−0.735063	+	1.10010i	0.255997	+	0.966678i	$0.417596\pi$
$619$	−18.2881	+	27.3701i	−0.735063	+	1.10010i	−0.991059	+	0.133421i	$0.957404\pi$
$620$	−2.75210	+	6.64417i	−0.110527	+	0.266836i
$621$	−1.21202	+	2.92607i	−0.0486366	+	0.117419i
$622$	−21.7635	−	14.5419i	−0.872635	−	0.583076i
$623$		0			0
$624$	−0.169987	−	0.254403i	−0.00680491	−	0.0101843i
$625$	−3.45319	−	3.45319i	−0.138128	−	0.138128i
$626$	12.6725	−	63.7090i	0.506495	−	2.54632i
$627$	−1.07415	−	2.59322i	−0.0428973	−	0.103563i
$628$	−34.5286			−1.37784
$629$	−2.21219	−	1.23844i	−0.0882058	−	0.0493799i
$630$		0			0
$631$	24.2265	−	10.0349i	0.964441	−	0.399485i	0.155801	−	0.987788i	$-0.450204\pi$
$631$	24.2265	−	10.0349i	0.964441	−	0.399485i	0.808640	+	0.588304i	$0.200204\pi$
$632$	−7.54407	+	37.9266i	−0.300087	+	1.50864i
$633$	4.95251	+	4.95251i	0.196845	+	0.196845i
$634$	−16.5269	+	11.0429i	−0.656365	+	0.438569i
$635$	9.70805	−	1.93105i	0.385252	−	0.0766314i
$636$	4.44543	−	6.65305i	0.176273	−	0.263811i
$637$		0			0
$638$	21.7259	+	8.99918i	0.860138	+	0.356281i
$639$	−26.0850	+	39.0390i	−1.03191	+	1.54436i
$640$	−4.66997	−	23.4775i	−0.184597	−	0.928032i
$641$	6.94300	+	10.3909i	0.274232	+	0.410417i	0.942865	−	0.333176i	$-0.108120\pi$
$641$	6.94300	+	10.3909i	0.274232	+	0.410417i	−0.668633	+	0.743593i	$0.733120\pi$
$642$	−5.65328	+	5.65328i	−0.223117	+	0.223117i
$643$	−7.45861	+	37.4970i	−0.294139	+	1.47874i	0.497349	+	0.867551i	$0.334307\pi$
$643$	−7.45861	+	37.4970i	−0.294139	+	1.47874i	−0.791488	+	0.611185i	$0.790693\pi$
$644$		0			0
$645$			0.913883i			0.0359841i
$646$	−27.9580	+	14.2507i	−1.09999	+	0.560686i
$647$		−	5.94824i		−	0.233849i	−0.993141	−	0.116925i	$-0.962696\pi$
$647$		−	5.94824i		−	0.233849i	0.993141	−	0.116925i	$-0.0373036\pi$
$648$	−24.6153	+	10.1960i	−0.966981	+	0.400536i
$649$	24.0661	+	4.78705i	0.944678	+	0.187908i
$650$	−8.09610	−	8.09610i	−0.317555	−	0.317555i
$651$		0			0
$652$	−3.51264	−	17.6592i	−0.137566	−	0.691589i
$653$	−18.9706	−	12.6757i	−0.742376	−	0.496040i	0.125948	−	0.992037i	$-0.459803\pi$
$653$	−18.9706	−	12.6757i	−0.742376	−	0.496040i	−0.868324	+	0.495997i	$0.834803\pi$
$654$	3.15455	+	1.30666i	0.123353	+	0.0510944i
$655$	1.24610	+	0.516152i	0.0486892	+	0.0201677i
$656$	−4.65789	−	3.11230i	−0.181860	−	0.121515i
$657$	−7.81535	−	39.2904i	−0.304906	−	1.53287i
$658$		0			0
$659$	−32.6310	−	32.6310i	−1.27112	−	1.27112i	−0.945500	−	0.325623i	$-0.894426\pi$
$659$	−32.6310	−	32.6310i	−1.27112	−	1.27112i	−0.325623	−	0.945500i	$-0.605574\pi$
$660$	−3.48075	−	0.692363i	−0.135488	−	0.0269502i
$661$	−10.9507	+	4.53594i	−0.425934	+	0.176428i	−0.585345	−	0.810785i	$-0.699041\pi$
$661$	−10.9507	+	4.53594i	−0.425934	+	0.176428i	0.159410	+	0.987212i	$0.449041\pi$
$662$		−	37.7779i		−	1.46828i
$663$	−0.464735	−	1.64686i	−0.0180488	−	0.0639588i
$664$		−	26.8224i		−	1.04091i
$665$		0			0
$666$	0.811561	−	4.07999i	0.0314474	−	0.158097i
$667$	4.47647	−	4.47647i	0.173330	−	0.173330i
$668$	−38.7871	−	58.0490i	−1.50072	−	2.24598i
$669$	0.254788	+	1.28091i	0.00985069	+	0.0495227i
$670$	−6.56931	+	9.83167i	−0.253795	+	0.379831i
$671$	25.9252	+	10.7386i	1.00083	+	0.414559i
$672$		0			0
$673$	−15.4252	+	23.0854i	−0.594596	+	0.889876i	−0.999702	−	0.0243938i	$-0.992234\pi$
$673$	−15.4252	+	23.0854i	−0.594596	+	0.889876i	0.405106	+	0.914270i	$0.367234\pi$
$674$	−11.9481	+	2.37663i	−0.460225	+	0.0915444i
$675$	5.10273	−	3.40953i	0.196404	−	0.131233i
$676$	26.4786	+	26.4786i	1.01841	+	1.01841i
$677$	−4.40555	+	22.1482i	−0.169319	+	0.851225i	0.798966	+	0.601376i	$0.205381\pi$
$677$	−4.40555	+	22.1482i	−0.169319	+	0.851225i	−0.968285	+	0.249848i	$0.919619\pi$
$678$	11.4579	−	4.74600i	0.440037	−	0.182269i
$679$		0			0
$680$	−1.91393	+	16.1920i	−0.0733960	+	0.620934i
$681$	−1.98936			−0.0762326
$682$	−4.47130	−	10.7947i	−0.171215	−	0.413349i
$683$	1.82942	−	9.19713i	0.0700009	−	0.351918i	−0.929872	−	0.367884i	$-0.880082\pi$
$683$	1.82942	−	9.19713i	0.0700009	−	0.351918i	0.999873	+	0.0159658i	$0.00508229\pi$
$684$	−22.9122	−	22.9122i	−0.876072	−	0.876072i
$685$	1.53251	+	2.29356i	0.0585540	+	0.0876323i
$686$		0			0
$687$	1.46145	+	0.976506i	0.0557576	+	0.0372560i
$688$	−0.714782	+	1.72564i	−0.0272508	+	0.0657893i
$689$	4.28303	−	10.3401i	0.163170	−	0.393928i
$690$	−0.843461	+	1.26233i	−0.0321100	+	0.0480560i
$691$	3.06384	+	15.4030i	0.116554	+	0.585957i	0.994281	+	0.106796i	$0.0340590\pi$
$691$	3.06384	+	15.4030i	0.116554	+	0.585957i	−0.877727	+	0.479161i	$0.840941\pi$
$692$	−61.9454	+	41.3906i	−2.35481	+	1.57344i
$693$		0			0
$694$	45.3357	+	9.01782i	1.72092	+	0.342312i
$695$	8.53262	+	20.5996i	0.323661	+	0.781386i
$696$	−3.34721			−0.126876
$697$	−19.4001	−	24.6011i	−0.734830	−	0.931834i
$698$		−	55.6458i		−	2.10622i
$699$	0.732158	+	1.76759i	0.0276928	+	0.0668562i
$700$		0			0
$701$	−15.0328	+	15.0328i	−0.567780	+	0.567780i	−0.931506	−	0.363726i	$-0.881505\pi$
$701$	−15.0328	+	15.0328i	−0.567780	+	0.567780i	0.363726	+	0.931506i	$0.381505\pi$
$702$	4.73917	−	3.16661i	0.178869	−	0.119516i
$703$	1.97606	−	0.393062i	0.0745284	−	0.0148246i
$704$	30.2439	+	20.2083i	1.13986	+	0.761630i
$705$	−3.84514	−	1.59271i	−0.144816	−	0.0599848i
$706$	12.7431	−	30.7645i	0.479591	−	1.15784i
$707$		0			0
$708$	−8.33575	+	1.65808i	−0.313277	+	0.0623146i
$709$	21.2886	+	31.8606i	0.799510	+	1.19655i	0.977170	+	0.212459i	$0.0681473\pi$
$709$	21.2886	+	31.8606i	0.799510	+	1.19655i	−0.177660	+	0.984092i	$0.556853\pi$
$710$	−32.3066	+	32.3066i	−1.21244	+	1.21244i
$711$	−34.0853	−	6.77999i	−1.27830	−	0.254270i
$712$	−25.7734	+	10.6757i	−0.965899	+	0.400088i
$713$	−3.14544			−0.117798
$714$		0			0
$715$	−4.96403			−0.185644
$716$	−19.0708	+	7.89938i	−0.712709	+	0.295214i
$717$	−2.62621	−	0.522386i	−0.0980776	−	0.0195088i
$718$	−52.7147	+	52.7147i	−1.96729	+	1.96729i
$719$	3.77982	+	5.65690i	0.140964	+	0.210967i	0.895233	−	0.445598i	$-0.147009\pi$
$719$	3.77982	+	5.65690i	0.140964	+	0.210967i	−0.754270	+	0.656565i	$0.772009\pi$
$720$	−2.56975	+	0.511156i	−0.0957690	+	0.0190496i
$721$		0			0
$722$	−7.34544	+	17.7335i	−0.273369	+	0.659971i
$723$	5.68331	+	2.35410i	0.211364	+	0.0875500i
$724$	2.58659	+	1.72830i	0.0961298	+	0.0642319i
$725$	−12.0313	+	2.39317i	−0.446831	+	0.0888801i
$726$	−1.48607	+	0.992960i	−0.0551532	+	0.0368522i
$727$	24.9994	−	24.9994i	0.927178	−	0.927178i	−0.0703449	−	0.997523i	$-0.522410\pi$
$727$	24.9994	−	24.9994i	0.927178	−	0.927178i	0.997523	+	0.0703449i	$0.0224100\pi$
$728$		0			0
$729$	−8.57013	−	20.6901i	−0.317412	−	0.766301i
$730$		−	38.9822i		−	1.44280i
$731$	−6.78297	+	7.94431i	−0.250877	+	0.293831i
$732$	−9.71954			−0.359245
$733$	−10.2741	−	24.8039i	−0.379482	−	0.916152i	−0.992063	−	0.125743i	$-0.959868\pi$
$733$	−10.2741	−	24.8039i	−0.379482	−	0.916152i	0.612580	−	0.790408i	$-0.290132\pi$
$734$	−48.3804	−	9.62346i	−1.78575	−	0.355208i
$735$		0			0
$736$	7.18550	−	4.80120i	0.264861	−	0.176975i
$737$	−2.35855	−	11.8572i	−0.0868784	−	0.436767i
$738$	28.5605	−	42.7438i	1.05133	−	1.57342i
$739$	4.92429	−	11.8883i	0.181143	−	0.437318i	−0.807060	−	0.590470i	$-0.798942\pi$
$739$	4.92429	−	11.8883i	0.181143	−	0.437318i	0.988203	+	0.153152i	$0.0489424\pi$
$740$	0.974853	−	2.35350i	0.0358363	−	0.0865165i
$741$	1.13070	+	0.755507i	0.0415371	+	0.0277542i
$742$		0			0
$743$	4.99320	+	7.47285i	0.183183	+	0.274152i	0.911684	−	0.410892i	$-0.134783\pi$
$743$	4.99320	+	7.47285i	0.183183	+	0.274152i	−0.728501	+	0.685044i	$0.759783\pi$
$744$	1.17598	+	1.17598i	0.0431133	+	0.0431133i
$745$	3.57220	−	17.9587i	0.130875	−	0.657955i
$746$	8.80421	+	21.2552i	0.322345	+	0.778209i
$747$	24.1057			0.881983
$748$	−25.1190	−	31.8533i	−0.918442	−	1.16467i
$749$		0			0
$750$	6.58824	−	2.72894i	0.240568	−	0.0996467i
$751$	−6.34892	+	31.9182i	−0.231675	+	1.16471i	0.673341	+	0.739332i	$0.264859\pi$
$751$	−6.34892	+	31.9182i	−0.231675	+	1.16471i	−0.905016	+	0.425378i	$0.860141\pi$
$752$	−6.01486	−	6.01486i	−0.219339	−	0.219339i
$753$	4.87185	−	3.25526i	0.177540	−	0.118628i
$754$	−11.1741	+	2.22266i	−0.406936	+	0.0809447i
$755$	4.04417	−	6.05252i	0.147182	−	0.220274i
$756$		0			0
$757$	48.4770	+	20.0798i	1.76193	+	0.729815i	0.996243	+	0.0865985i	$0.0275997\pi$
$757$	48.4770	+	20.0798i	1.76193	+	0.729815i	0.765685	+	0.643216i	$0.222400\pi$
$758$	34.6967	−	51.9273i	1.26024	−	1.88608i
$759$	−0.302824	−	1.52240i	−0.0109918	−	0.0552596i
$760$	−7.19873	−	10.7737i	−0.261125	−	0.390802i
$761$	19.7026	−	19.7026i	0.714217	−	0.714217i	−0.253198	−	0.967415i	$-0.581482\pi$
$761$	19.7026	−	19.7026i	0.714217	−	0.714217i	0.967415	+	0.253198i	$0.0814823\pi$
$762$	1.08668	−	5.46310i	0.0393662	−	0.197907i
$763$		0			0
$764$		−	27.6080i		−	0.998823i
$765$	−14.5520	−	1.72009i	−0.526130	−	0.0621899i
$766$			52.7455i			1.90577i
$767$	−10.9830	+	4.54932i	−0.396574	+	0.164266i
$768$	−5.93291	−	1.18013i	−0.214085	−	0.0425842i
$769$	−15.7390	−	15.7390i	−0.567562	−	0.567562i	0.363883	−	0.931445i	$-0.381451\pi$
$769$	−15.7390	−	15.7390i	−0.567562	−	0.567562i	−0.931445	+	0.363883i	$0.881451\pi$
$770$		0			0
$771$	−0.545548	−	2.74266i	−0.0196474	−	0.0987744i
$772$	38.5667	+	25.7694i	1.38804	+	0.927462i
$773$	31.0066	+	12.8434i	1.11523	+	0.461944i	0.862736	−	0.505654i	$-0.168749\pi$
$773$	31.0066	+	12.8434i	1.11523	+	0.461944i	0.252495	+	0.967598i	$0.418749\pi$
$774$	−15.8355	−	6.55929i	−0.569197	−	0.235769i
$775$	5.06775	+	3.38616i	0.182039	+	0.121635i
$776$	−2.54226	−	12.7808i	−0.0912617	−	0.458803i
$777$		0			0
$778$	−7.97324	−	7.97324i	−0.285854	−	0.285854i
$779$	24.4197	+	4.85738i	0.874927	+	0.174034i
$780$	1.58850	−	0.657980i	0.0568776	−	0.0235595i
$781$		−	46.7127i		−	1.67151i
$782$	−16.7013	+	4.71302i	−0.597238	+	0.168537i
$783$		−	6.10665i		−	0.218234i
$784$		0			0
$785$	2.42088	−	12.1706i	0.0864049	−	0.434387i
$786$	0.536698	−	0.536698i	0.0191434	−	0.0191434i
$787$	6.65136	+	9.95446i	0.237095	+	0.354838i	0.930868	−	0.365356i	$-0.119053\pi$
$787$	6.65136	+	9.95446i	0.237095	+	0.354838i	−0.693773	+	0.720194i	$0.744053\pi$
$788$	2.28833	+	11.5042i	0.0815185	+	0.409821i
$789$	4.74976	−	7.10852i	0.169096	−	0.253070i
$790$	−31.2437	−	12.9416i	−1.11160	−	0.460440i
$791$		0			0
$792$	15.1965	−	22.7432i	0.539986	−	0.808146i
$793$	−13.3339	+	2.65227i	−0.473500	+	0.0941849i
$794$	39.5949	−	26.4565i	1.40517	−	0.938905i
$795$	2.03338	+	2.03338i	0.0721164	+	0.0721164i
$796$	14.3382	−	72.0831i	0.508205	−	2.55492i
$797$	39.2612	−	16.2625i	1.39070	−	0.576049i	0.443383	−	0.896332i	$-0.353778\pi$
$797$	39.2612	−	16.2625i	1.39070	−	0.576049i	0.947322	+	0.320284i	$0.103778\pi$
$798$		0			0
$799$	−21.6041	−	42.3845i	−0.764299	−	1.49945i
$800$	−16.7455			−0.592042
$801$	−9.59444	−	23.1630i	−0.339003	−	0.818425i
$802$	−13.9702	+	70.2329i	−0.493305	+	2.48001i
$803$	28.1826	+	28.1826i	0.994541	+	0.994541i
$804$	2.32642	+	3.48173i	0.0820463	+	0.122791i
$805$		0			0
$806$	4.70669	+	3.14491i	0.165786	+	0.110775i
$807$	0.847740	−	2.04662i	0.0298419	−	0.0720446i
$808$	−23.3169	+	56.2920i	−0.820286	+	1.98035i
$809$	−19.4969	+	29.1792i	−0.685474	+	1.02588i	0.311657	+	0.950195i	$0.399116\pi$
$809$	−19.4969	+	29.1792i	−0.685474	+	1.02588i	−0.997131	+	0.0756902i	$0.975884\pi$
$810$	−4.54572	−	22.8529i	−0.159720	−	0.802969i
$811$	−9.53464	+	6.37084i	−0.334806	+	0.223711i	−0.711597	−	0.702588i	$-0.752028\pi$
$811$	−9.53464	+	6.37084i	−0.334806	+	0.223711i	0.376790	+	0.926299i	$0.377028\pi$
$812$		0			0
$813$	0.353445	+	0.0703045i	0.0123959	+	0.00246569i
$814$	1.58383	+	3.82370i	0.0555131	+	0.134021i
$815$	6.47077			0.226661
$816$	0.784082	+	0.438949i	0.0274484	+	0.0153663i
$817$		−	8.30152i		−	0.290433i
$818$	18.2425	+	44.0414i	0.637835	+	1.53987i
$819$		0			0
$820$	22.2600	−	22.2600i	0.777353	−	0.777353i
$821$	17.2687	−	11.5386i	0.602682	−	0.402699i	−0.216459	−	0.976292i	$-0.569451\pi$
$821$	17.2687	−	11.5386i	0.602682	−	0.402699i	0.819141	+	0.573593i	$0.194451\pi$
$822$	1.52245	−	0.302835i	0.0531017	−	0.0105626i
$823$	−28.9171	−	19.3218i	−1.00799	−	0.673516i	−0.0621201	−	0.998069i	$-0.519786\pi$
$823$	−28.9171	−	19.3218i	−1.00799	−	0.673516i	−0.945868	+	0.324553i	$0.894786\pi$
$824$	−23.2071	−	9.61269i	−0.808458	−	0.334874i
$825$	−1.15102	+	2.77880i	−0.0400732	+	0.0967454i
$826$		0			0
$827$	−36.3331	+	7.22711i	−1.26343	+	0.251311i	−0.780948	−	0.624596i	$-0.785264\pi$
$827$	−36.3331	+	7.22711i	−1.26343	+	0.251311i	−0.482479	+	0.875907i	$0.660264\pi$
$828$	−9.95524	−	14.8991i	−0.345969	−	0.517779i
$829$	−26.3926	+	26.3926i	−0.916653	+	0.916653i	−0.996784	−	0.0801309i	$-0.974466\pi$
$829$	−26.3926	+	26.3926i	−0.916653	+	0.916653i	0.0801309	+	0.996784i	$0.474466\pi$
$830$	23.0064	+	4.57625i	0.798563	+	0.158844i
$831$	−0.255469	+	0.105819i	−0.00886211	+	0.00367081i
$832$	−17.6224			−0.610948
$833$		0			0
$834$	12.5473			0.434477
$835$	23.1804	−	9.60165i	0.802192	−	0.332279i
$836$	31.6183	+	6.28928i	1.09354	+	0.217519i
$837$	−2.14545	+	2.14545i	−0.0741577	+	0.0741577i
$838$	3.63770	+	5.44420i	0.125662	+	0.188067i
$839$	−50.8081	+	10.1064i	−1.75409	+	0.348910i	−0.964370	−	0.264557i	$-0.914774\pi$
$839$	−50.8081	+	10.1064i	−1.75409	+	0.348910i	−0.789720	+	0.613468i	$0.789774\pi$
$840$		0			0
$841$	6.42666	−	15.5153i	0.221609	−	0.535011i
$842$	4.25823	+	1.76382i	0.146748	+	0.0607851i
$843$	−1.48948	−	0.995236i	−0.0513003	−	0.0342777i
$844$	−78.8961	+	15.6934i	−2.71571	+	0.540189i
$845$	−11.1896	+	7.47664i	−0.384933	+	0.257204i
$846$	55.1961	−	55.1961i	1.89768	−	1.89768i
$847$		0			0
$848$	2.24914	+	5.42990i	0.0772357	+	0.186463i
$849$			6.64012i			0.227888i
$850$	31.9819	+	10.3861i	1.09697	+	0.356241i
$851$	1.11418			0.0381936
$852$	6.19174	+	14.9482i	0.212126	+	0.512117i
$853$	26.6210	+	5.29524i	0.911484	+	0.181305i	0.628491	−	0.777817i	$-0.283673\pi$
$853$	26.6210	+	5.29524i	0.911484	+	0.181305i	0.282993	+	0.959122i	$0.408673\pi$
$854$		0			0
$855$	9.68249	−	6.46963i	0.331134	−	0.221257i
$856$	−7.36160	−	37.0093i	−0.251614	−	1.26495i
$857$	−20.4457	+	30.5991i	−0.698411	+	1.04525i	0.297484	+	0.954727i	$0.403853\pi$
$857$	−20.4457	+	30.5991i	−0.698411	+	1.04525i	−0.995895	+	0.0905188i	$0.971147\pi$
$858$	−1.06901	+	2.58082i	−0.0364954	+	0.0881076i
$859$	18.5544	−	44.7942i	0.633066	−	1.52836i	−0.202682	−	0.979245i	$-0.564966\pi$
$859$	18.5544	−	44.7942i	0.633066	−	1.52836i	0.835748	−	0.549113i	$-0.185034\pi$
$860$	−8.72725	−	5.83137i	−0.297597	−	0.198848i
$861$		0			0
$862$	3.65799	+	5.47457i	0.124592	+	0.186464i
$863$	−1.94989	−	1.94989i	−0.0663750	−	0.0663750i	0.673140	−	0.739515i	$-0.264945\pi$
$863$	−1.94989	−	1.94989i	−0.0663750	−	0.0663750i	−0.739515	+	0.673140i	$0.764945\pi$
$864$	1.62629	−	8.17592i	0.0553276	−	0.278150i
$865$	−10.2461	−	24.7364i	−0.348380	−	0.841063i
$866$	−36.4659			−1.23916
$867$	3.41245	+	3.68930i	0.115893	+	0.125295i
$868$		0			0
$869$	31.9442	−	13.2317i	1.08363	−	0.448855i
$870$	0.571078	−	2.87100i	0.0193614	−	0.0973361i
$871$	4.14161	+	4.14161i	0.140333	+	0.140333i
$872$	−13.3995	+	8.95329i	−0.453766	+	0.303197i
$873$	11.4863	−	2.28477i	0.388753	−	0.0773278i
$874$	7.66182	−	11.4667i	0.259165	−	0.387867i
$875$		0			0
$876$	−12.7541	−	5.28292i	−0.430921	−	0.178493i
$877$	−19.8245	+	29.6695i	−0.669426	+	1.00187i	0.328919	+	0.944358i	$0.393316\pi$
$877$	−19.8245	+	29.6695i	−0.669426	+	1.00187i	−0.998345	+	0.0575087i	$0.981684\pi$
$878$	15.1645	+	76.2371i	0.511777	+	2.57288i
$879$	2.71022	+	4.05613i	0.0914135	+	0.136810i
$880$	1.84325	−	1.84325i	0.0621361	−	0.0621361i
$881$	−6.27071	+	31.5250i	−0.211266	+	1.06210i	0.718942	+	0.695070i	$0.244627\pi$
$881$	−6.27071	+	31.5250i	−0.211266	+	1.06210i	−0.930208	+	0.367034i	$0.880373\pi$
$882$		0			0
$883$		−	21.3713i		−	0.719203i	−0.933106	−	0.359601i	$-0.882913\pi$
$883$		−	21.3713i		−	0.719203i	0.933106	−	0.359601i	$-0.117087\pi$
$884$	18.6924	+	6.07035i	0.628692	+	0.204168i
$885$		−	3.05442i		−	0.102673i
$886$	−71.0175	+	29.4164i	−2.38588	+	0.988263i
$887$	−10.9115	−	2.17044i	−0.366373	−	0.0728762i	0.00847067	−	0.999964i	$-0.497304\pi$
$887$	−10.9115	−	2.17044i	−0.366373	−	0.0728762i	−0.374844	+	0.927088i	$0.622304\pi$
$888$	−0.416555	−	0.416555i	−0.0139787	−	0.0139787i
$889$		0			0
$890$	−4.75959	−	23.9281i	−0.159542	−	0.802070i
$891$	19.8081	+	13.2353i	0.663596	+	0.443401i
$892$	−13.8580	−	5.74016i	−0.464000	−	0.192195i
$893$	34.9284	+	14.4678i	1.16883	+	0.484147i
$894$	−8.56750	−	5.72462i	−0.286540	−	0.191460i
$895$	−1.44726	−	7.27588i	−0.0483766	−	0.243206i
$896$		0			0
$897$	0.531759	+	0.531759i	0.0177549	+	0.0177549i
$898$	26.4968	+	5.27055i	0.884211	+	0.175881i
$899$	5.60313	−	2.32089i	0.186875	−	0.0774062i
$900$			34.7216i			1.15739i
$901$	2.58394	+	32.7680i	0.0860837	+	1.09166i
$902$			51.1457i			1.70296i
$903$		0			0
$904$	−11.4195	+	57.4095i	−0.379806	+	1.90941i
$905$	−0.790540	+	0.790540i	−0.0262784	+	0.0262784i
$906$	−2.27581	−	3.40599i	−0.0756088	−	0.113157i
$907$	−4.96213	−	24.9463i	−0.164765	−	0.828328i	−0.971431	−	0.237321i	$-0.923731\pi$
$907$	−4.96213	−	24.9463i	−0.164765	−	0.828328i	0.806666	−	0.591007i	$-0.201269\pi$
$908$	12.6939	−	18.9977i	0.421261	−	0.630461i
$909$	−50.5907	−	20.9553i	−1.67799	−	0.695045i
$910$		0			0
$911$	−6.83991	+	10.2367i	−0.226616	+	0.339155i	−0.927302	−	0.374315i	$-0.877878\pi$
$911$	−6.83991	+	10.2367i	−0.226616	+	0.339155i	0.700685	+	0.713471i	$0.252878\pi$
$912$	−0.700388	+	0.139316i	−0.0231922	+	0.00461321i
$913$	−19.9411	+	13.3242i	−0.659955	+	0.440968i
$914$	27.0764	+	27.0764i	0.895609	+	0.895609i
$915$	0.681459	−	3.42592i	0.0225283	−	0.113258i
$916$	−18.6506	+	7.72532i	−0.616232	+	0.255252i
$917$		0			0
$918$	−8.17701	+	14.6063i	−0.269881	+	0.482081i
$919$	13.4651			0.444174			0.222087	−	0.975027i	$-0.428713\pi$
$919$	13.4651			0.444174			0.222087	+	0.975027i	$0.428713\pi$
$920$	−2.74212	−	6.62007i	−0.0904051	−	0.218257i
$921$	−0.658815	+	3.31209i	−0.0217087	+	0.109137i
$922$	−15.3870	−	15.3870i	−0.506745	−	0.506745i
$923$	12.5733	+	18.8172i	0.413855	+	0.619377i
$924$		0			0
$925$	−1.79510	−	1.19945i	−0.0590226	−	0.0394376i
$926$	20.6381	−	49.8248i	0.678210	−	1.63734i
$927$	8.63911	−	20.8566i	0.283745	−	0.685022i
$928$	−9.25729	+	13.8545i	−0.303885	+	0.454796i
$929$	1.83455	+	9.22292i	0.0601898	+	0.302594i	0.999140	−	0.0414580i	$-0.0132003\pi$
$929$	1.83455	+	9.22292i	0.0601898	+	0.302594i	−0.938950	+	0.344052i	$0.888200\pi$
$930$	−1.20931	+	0.808033i	−0.0396548	+	0.0264965i
$931$		0			0
$932$	−21.5516	−	4.28688i	−0.705947	−	0.140422i
$933$	−1.27481	−	3.07767i	−0.0417355	−	0.100758i
$934$	−8.79288			−0.287712
$935$	12.9887	−	6.62059i	0.424777	−	0.216516i
$936$			13.2520i			0.433154i
$937$	16.1388	+	38.9625i	0.527232	+	1.27285i	0.933330	+	0.359021i	$0.116889\pi$
$937$	16.1388	+	38.9625i	0.527232	+	1.27285i	−0.406098	+	0.913830i	$0.633111\pi$
$938$		0			0
$939$	5.84571	−	5.84571i	0.190768	−	0.190768i
$940$	39.7451	−	26.5568i	1.29634	−	0.866188i
$941$	13.4355	−	2.67249i	0.437985	−	0.0871206i	0.0288273	−	0.999584i	$-0.490823\pi$
$941$	13.4355	−	2.67249i	0.437985	−	0.0871206i	0.409157	+	0.912464i	$0.365823\pi$
$942$	−5.80618	−	3.87957i	−0.189176	−	0.126403i
$943$	12.7207	+	5.26910i	0.414244	+	0.171585i
$944$	2.38898	−	5.76750i	0.0777546	−	0.187716i
$945$		0			0
$946$	16.7253	−	3.32687i	0.543786	−	0.108166i
$947$	11.3367	+	16.9665i	0.368393	+	0.551339i	0.968638	−	0.248478i	$-0.0799303\pi$
$947$	11.3367	+	16.9665i	0.368393	+	0.551339i	−0.600245	+	0.799816i	$0.704930\pi$
$948$	−8.46836	+	8.46836i	−0.275040	+	0.275040i
$949$	−18.9384	−	3.76709i	−0.614768	−	0.122285i
$950$	−24.6885	+	10.2263i	−0.801001	+	0.331786i
$951$	−2.52970			−0.0820312
$952$		0			0
$953$	32.5616			1.05477			0.527387	−	0.849625i	$-0.323172\pi$
$953$	32.5616			1.05477			0.527387	+	0.849625i	$0.323172\pi$
$954$	−49.8282	+	20.6395i	−1.61325	+	0.668228i
$955$	9.73122	+	1.93566i	0.314895	+	0.0626365i
$956$	21.7461	−	21.7461i	0.703319	−	0.703319i
$957$	1.66275	+	2.48849i	0.0537492	+	0.0804413i
$958$	5.15027	−	1.02445i	0.166398	−	0.0330985i
$959$		0			0
$960$	1.73272	−	4.18314i	0.0559231	−	0.135010i
$961$	25.8563	+	10.7100i	0.834075	+	0.345485i
$962$	−1.66721	−	1.11399i	−0.0537529	−	0.0359165i
$963$	33.2609	−	6.61601i	1.07182	−	0.213198i
$964$	−58.7453	+	39.2523i	−1.89206	+	1.26423i
$965$	−11.7871	+	11.7871i	−0.379442	+	0.379442i
$966$		0			0
$967$	0.545323	+	1.31653i	0.0175364	+	0.0423366i	0.932405	−	0.361415i	$-0.117706\pi$
$967$	0.545323	+	1.31653i	0.0175364	+	0.0423366i	−0.914869	+	0.403751i	$0.867706\pi$
$968$		−	8.43556i		−	0.271129i
$969$	−3.96617	−	0.468811i	−0.127412	−	0.0150604i
$970$	11.3962			0.365911
$971$	10.2573	+	24.7633i	0.329172	+	0.794692i	0.998654	+	0.0518637i	$0.0165161\pi$
$971$	10.2573	+	24.7633i	0.329172	+	0.794692i	−0.669482	+	0.742828i	$0.733484\pi$
$972$	−25.5543	−	5.08307i	−0.819655	−	0.163040i
$973$		0			0
$974$	32.8163	−	21.9271i	1.05150	−	0.702591i
$975$	−0.284284	−	1.42919i	−0.00910437	−	0.0457708i
$976$	3.96631	−	5.93600i	0.126958	−	0.190007i
$977$	7.59246	−	18.3298i	0.242904	−	0.586423i	−0.754664	−	0.656111i	$-0.772200\pi$
$977$	7.59246	−	18.3298i	0.242904	−	0.586423i	0.997569	+	0.0696879i	$0.0222003\pi$
$978$	1.39349	−	3.36417i	0.0445588	−	0.107574i
$979$	20.7400	+	13.8580i	0.662853	+	0.442905i
$980$		0			0
$981$	−8.04649	−	12.0424i	−0.256905	−	0.384485i
$982$	34.7825	+	34.7825i	1.10995	+	1.10995i
$983$	0.936352	−	4.70736i	0.0298650	−	0.150141i	−0.962976	−	0.269589i	$-0.913112\pi$
$983$	0.936352	−	4.70736i	0.0298650	−	0.150141i	0.992841	+	0.119447i	$0.0381123\pi$
$984$	−2.78591	−	6.72579i	−0.0888117	−	0.214410i
$985$	−4.21542			−0.134315
$986$	26.2733	−	20.7188i	0.836714	−	0.659820i
$987$		0			0
$988$	−14.4296	+	5.97695i	−0.459068	+	0.190152i
$989$	0.895619	−	4.50258i	0.0284790	−	0.143174i
$990$	16.9149	+	16.9149i	0.537589	+	0.537589i
$991$	3.64457	−	2.43522i	0.115774	−	0.0773574i	−0.496335	−	0.868131i	$-0.665321\pi$
$991$	3.64457	−	2.43522i	0.115774	−	0.0773574i	0.612109	+	0.790773i	$0.290321\pi$
$992$	8.11987	−	1.61514i	0.257806	−	0.0512809i
$993$	2.67117	−	3.99769i	0.0847672	−	0.126863i
$994$		0			0
$995$	24.4024	+	10.1078i	0.773609	+	0.320439i
$996$	4.61509	−	6.90698i	0.146235	−	0.218856i
$997$	4.29460	+	21.5904i	0.136011	+	0.683775i	0.987273	+	0.159034i	$0.0508379\pi$
$997$	4.29460	+	21.5904i	0.136011	+	0.683775i	−0.851262	+	0.524741i	$0.824162\pi$
$998$	−25.4510	−	38.0902i	−0.805639	−	1.20572i
$999$	0.759964	−	0.759964i	0.0240442	−	0.0240442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.t.b.48.1	✓	72
7.2	even	3		833.2.bc.c.31.9		144
7.3	odd	6		833.2.bc.b.558.9		144
7.4	even	3		833.2.bc.c.558.9		144
7.5	odd	6		833.2.bc.b.31.9		144
7.6	odd	2		833.2.t.c.48.1	yes	72
17.11	odd	16		833.2.t.c.538.1	yes	72
119.11	odd	48		833.2.bc.b.215.9		144
119.45	even	48		833.2.bc.c.215.9		144
119.62	even	16	inner	833.2.t.b.538.1	yes	72
119.79	odd	48		833.2.bc.b.521.9		144
119.96	even	48		833.2.bc.c.521.9		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.b.48.1	✓	72	1.1	even	1	trivial
833.2.t.b.538.1	yes	72	119.62	even	16	inner
833.2.t.c.48.1	yes	72	7.6	odd	2
833.2.t.c.538.1	yes	72	17.11	odd	16
833.2.bc.b.31.9		144	7.5	odd	6
833.2.bc.b.215.9		144	119.11	odd	48
833.2.bc.b.521.9		144	119.79	odd	48
833.2.bc.b.558.9		144	7.3	odd	6
833.2.bc.c.31.9		144	7.2	even	3
833.2.bc.c.215.9		144	119.45	even	48
833.2.bc.c.521.9		144	119.96	even	48
833.2.bc.c.558.9		144	7.4	even	3

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14596 + 0.888885i) q^{2} +(-0.289938 - 0.0576723i) q^{3} +(2.40081 - 2.40081i) q^{4} +(0.677905 + 1.01456i) q^{5} +(0.673459 - 0.133959i) q^{6} +(-1.24022 + 2.99415i) q^{8} +(-2.69090 - 1.11461i) q^{9} +(-2.35658 - 1.57462i) q^{10} +(2.84210 - 0.565328i) q^{11} +(-0.834545 + 0.557625i) q^{12} +(-0.992715 + 0.992715i) q^{13} +(-0.138039 - 0.333255i) q^{15} -0.737233i q^{16} +(1.27351 - 3.92150i) q^{17} +6.76532 q^{18} +(1.25391 + 3.02722i) q^{19} +(4.06327 + 0.808235i) q^{20} +(-5.59651 + 3.73947i) q^{22} +(0.353504 + 1.77718i) q^{23} +(0.532266 - 0.796593i) q^{24} +(1.34365 - 3.24385i) q^{25} +(1.24792 - 3.01274i) q^{26} +(1.45331 + 0.971068i) q^{27} +(-1.94103 - 2.90495i) q^{29} +(0.592451 + 0.592451i) q^{30} +(-0.338656 + 1.70254i) q^{31} +(-1.82512 - 4.40623i) q^{32} -0.856636 q^{33} +(0.752866 + 9.54738i) q^{34} +(-9.13629 + 3.78437i) q^{36} +(0.119959 - 0.603075i) q^{37} +(-5.38170 - 5.38170i) q^{38} +(0.345078 - 0.230574i) q^{39} +(-3.87849 + 0.771479i) q^{40} +(4.22160 - 6.31807i) q^{41} +(-2.34069 - 0.969547i) q^{43} +(5.46608 - 8.18057i) q^{44} +(-0.693343 - 3.48567i) q^{45} +(-2.33832 - 3.49954i) q^{46} +(8.15868 - 8.15868i) q^{47} +(-0.0425179 + 0.213752i) q^{48} +8.15551i q^{50} +(-0.595401 + 1.06355i) q^{51} +4.76663i q^{52} +(-7.36524 + 3.05078i) q^{53} +(-3.98190 - 0.792049i) q^{54} +(2.50023 + 2.50023i) q^{55} +(-0.188971 - 0.950022i) q^{57} +(6.74753 + 4.50855i) q^{58} +(7.82317 + 3.24046i) q^{59} +(-1.13148 - 0.468676i) q^{60} +(8.05173 + 5.37999i) q^{61} +(-0.786620 - 3.95460i) q^{62} +(8.87587 + 8.87587i) q^{64} +(-1.68013 - 0.334199i) q^{65} +(1.83830 - 0.761451i) q^{66} -4.17201i q^{67} +(-6.35732 - 12.4722i) q^{68} -0.535661i q^{69} +(3.14489 - 15.8104i) q^{71} +(6.67461 - 6.67461i) q^{72} +(7.64134 + 11.4361i) q^{73} +(0.278637 + 1.40080i) q^{74} +(-0.576655 + 0.863025i) q^{75} +(10.2782 + 4.25736i) q^{76} +(-0.535570 + 0.801536i) q^{78} +(11.7027 - 2.32781i) q^{79} +(0.747965 - 0.499774i) q^{80} +(5.81321 + 5.81321i) q^{81} +(-3.44334 + 17.3108i) q^{82} +(-7.64634 + 3.16722i) q^{83} +(4.84191 - 1.36636i) q^{85} +5.88485 q^{86} +(0.395242 + 0.954199i) q^{87} +(-1.83214 + 9.21080i) q^{88} +(6.08671 + 6.08671i) q^{89} +(4.58624 + 6.86380i) q^{90} +(5.11537 + 3.41798i) q^{92} +(0.196379 - 0.474100i) q^{93} +(-10.2561 + 24.7603i) q^{94} +(-2.22125 + 3.32433i) q^{95} +(0.275055 + 1.38279i) q^{96} +(-3.34327 + 2.23390i) q^{97} +(-8.27792 - 1.64658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 24 q^{9} - 8 q^{11} - 24 q^{12} - 32 q^{13} + 32 q^{17} + 40 q^{18} - 40 q^{19} + 40 q^{20} - 24 q^{22} - 8 q^{23} + 16 q^{24} - 8 q^{25} - 24 q^{27} + 8 q^{31} + 40 q^{32} - 24 q^{34} - 120 q^{36}+ \cdots - 40 q^{99}+O(q^{100}) \) 72 * q - 24 * q^9 - 8 * q^11 - 24 * q^12 - 32 * q^13 + 32 * q^17 + 40 * q^18 - 40 * q^19 + 40 * q^20 - 24 * q^22 - 8 * q^23 + 16 * q^24 - 8 * q^25 - 24 * q^27 + 8 * q^31 + 40 * q^32 - 24 * q^34 - 120 * q^36 - 48 * q^37 - 56 * q^38 - 16 * q^39 - 48 * q^40 + 56 * q^41 - 24 * q^43 + 96 * q^44 + 40 * q^45 - 64 * q^46 + 24 * q^47 - 224 * q^48 + 104 * q^51 - 40 * q^53 + 48 * q^54 + 48 * q^57 + 32 * q^58 + 8 * q^59 - 48 * q^60 - 128 * q^61 + 48 * q^62 + 56 * q^65 + 120 * q^66 + 32 * q^68 - 120 * q^73 + 48 * q^74 + 32 * q^75 + 8 * q^76 + 48 * q^78 + 32 * q^79 - 32 * q^80 + 80 * q^81 + 64 * q^82 - 32 * q^83 - 32 * q^85 - 80 * q^86 - 64 * q^87 + 136 * q^88 - 16 * q^89 + 32 * q^90 - 8 * q^92 - 96 * q^93 + 32 * q^94 + 32 * q^95 + 40 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more