LMFDB - Embedded newform 735.2.p.g.374.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(374,735)] 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("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.8
Character	$\chi$	$=$	735.374
Dual form			735.2.p.g.509.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02274 - 1.77144i) q^{2} +(1.72810 - 0.116943i) q^{3} +(-1.09199 + 1.89138i) q^{4} +(0.990993 + 2.00448i) q^{5} +(-1.97455 - 2.94161i) q^{6} +0.376326 q^{8} +(2.97265 - 0.404178i) q^{9} +(2.53728 - 3.80554i) q^{10} +(4.46847 + 2.57987i) q^{11} +(-1.66588 + 3.39619i) q^{12} -2.98151 q^{13} +(1.94694 + 3.34805i) q^{15} +(1.79910 + 3.11613i) q^{16} +(1.17568 + 0.678781i) q^{17} +(-3.75622 - 4.85249i) q^{18} +(-2.67938 + 1.54694i) q^{19} +(-4.87339 - 0.314523i) q^{20} -10.5542i q^{22} +(3.61476 + 6.26095i) q^{23} +(0.650328 - 0.0440086i) q^{24} +(-3.03586 + 3.97285i) q^{25} +(3.04931 + 5.28156i) q^{26} +(5.08976 - 1.04609i) q^{27} -2.69332i q^{29} +(3.93963 - 6.87306i) q^{30} +(-3.76937 - 2.17625i) q^{31} +(4.05634 - 7.02578i) q^{32} +(8.02366 + 3.93572i) q^{33} -2.77686i q^{34} +(-2.48165 + 6.06377i) q^{36} +(6.58079 - 3.79942i) q^{37} +(5.48062 + 3.16424i) q^{38} +(-5.15235 + 0.348667i) q^{39} +(0.372936 + 0.754337i) q^{40} +7.68540 q^{41} -7.79107i q^{43} +(-9.75905 + 5.63439i) q^{44} +(3.75604 + 5.55807i) q^{45} +(7.39391 - 12.8066i) q^{46} +(-5.25990 + 3.03680i) q^{47} +(3.47342 + 5.17458i) q^{48} +(10.1425 + 1.31465i) q^{50} +(2.11107 + 1.03551i) q^{51} +(3.25578 - 5.63918i) q^{52} +(-3.14616 + 5.44930i) q^{53} +(-7.05858 - 7.94631i) q^{54} +(-0.743074 + 11.5136i) q^{55} +(-4.44934 + 2.98661i) q^{57} +(-4.77104 + 2.75456i) q^{58} +(-2.12502 + 3.68065i) q^{59} +(-8.45847 + 0.0263817i) q^{60} +(4.51526 - 2.60689i) q^{61} +8.90293i q^{62} -9.39791 q^{64} +(-2.95466 - 5.97638i) q^{65} +(-1.23423 - 18.2386i) q^{66} +(4.89919 + 2.82855i) q^{67} +(-2.56767 + 1.48244i) q^{68} +(6.97884 + 10.3968i) q^{69} -11.2688i q^{71} +(1.11868 - 0.152102i) q^{72} +(2.45608 - 4.25406i) q^{73} +(-13.4609 - 7.77163i) q^{74} +(-4.78168 + 7.22050i) q^{75} -6.75699i q^{76} +(5.88715 + 8.77046i) q^{78} +(-5.96472 - 10.3312i) q^{79} +(-4.46331 + 6.69431i) q^{80} +(8.67328 - 2.40296i) q^{81} +(-7.86016 - 13.6142i) q^{82} -12.1558i q^{83} +(-0.195507 + 3.02930i) q^{85} +(-13.8014 + 7.96823i) q^{86} +(-0.314964 - 4.65432i) q^{87} +(1.68160 + 0.970873i) q^{88} +(-4.66058 - 8.07237i) q^{89} +(6.00432 - 12.3380i) q^{90} -15.7891 q^{92} +(-6.76834 - 3.31997i) q^{93} +(10.7590 + 6.21171i) q^{94} +(-5.75607 - 3.83776i) q^{95} +(6.18814 - 12.6156i) q^{96} -19.2504 q^{97} +(14.3259 + 5.86300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) $ 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.02274	−	1.77144i	−0.723186	−	1.25259i	−0.959716	−	0.280970i	$-0.909344\pi$
$2$	−1.02274	−	1.77144i	−0.723186	−	1.25259i	0.236531	−	0.971624i	$-0.423990\pi$
$3$	1.72810	−	0.116943i	0.997718	−	0.0675170i
$3$	1.72810	−	0.116943i	0.997718	−	0.0675170i
$4$	−1.09199	+	1.89138i	−0.545995	+	0.945691i
$5$	0.990993	+	2.00448i	0.443186	+	0.896430i
$5$	0.990993	+	2.00448i	0.443186	+	0.896430i
$6$	−1.97455	−	2.94161i	−0.806107	−	1.20091i
$7$		0			0
$7$		0			0
$8$	0.376326			0.133051
$9$	2.97265	−	0.404178i	0.990883	−	0.134726i
$10$	2.53728	−	3.80554i	0.802357	−	1.20342i
$11$	4.46847	+	2.57987i	1.34730	+	0.777861i	0.987866	−	0.155311i	$-0.0496379\pi$
$11$	4.46847	+	2.57987i	1.34730	+	0.777861i	0.359430	+	0.933172i	$0.382971\pi$
$12$	−1.66588	+	3.39619i	−0.480899	+	0.980397i
$13$	−2.98151			−0.826923			−0.413462	−	0.910522i	$-0.635680\pi$
$13$	−2.98151			−0.826923			−0.413462	+	0.910522i	$0.635680\pi$
$14$		0			0
$15$	1.94694	+	3.34805i	0.502699	+	0.864462i
$16$	1.79910	+	3.11613i	0.449774	+	0.779032i
$17$	1.17568	+	0.678781i	0.285145	+	0.164629i	0.635750	−	0.771895i	$-0.280691\pi$
$17$	1.17568	+	0.678781i	0.285145	+	0.164629i	−0.350605	+	0.936523i	$0.614024\pi$
$18$	−3.75622	−	4.85249i	−0.885349	−	1.14374i
$19$	−2.67938	+	1.54694i	−0.614693	+	0.354893i	−0.774800	−	0.632206i	$-0.782149\pi$
$19$	−2.67938	+	1.54694i	−0.614693	+	0.354893i	0.160107	+	0.987100i	$0.448816\pi$
$20$	−4.87339	−	0.314523i	−1.08972	−	0.0703294i
$21$		0			0
$22$		−	10.5542i		−	2.25015i
$23$	3.61476	+	6.26095i	0.753730	+	1.30550i	0.946003	+	0.324157i	$0.105081\pi$
$23$	3.61476	+	6.26095i	0.753730	+	1.30550i	−0.192274	+	0.981341i	$0.561586\pi$
$24$	0.650328	−	0.0440086i	0.132748	−	0.00898322i
$25$	−3.03586	+	3.97285i	−0.607173	+	0.794570i
$26$	3.04931	+	5.28156i	0.598019	+	1.03580i
$27$	5.08976	−	1.04609i	0.979526	−	0.201320i
$28$		0			0
$29$		−	2.69332i		−	0.500136i	−0.968228	−	0.250068i	$-0.919547\pi$
$29$		−	2.69332i		−	0.500136i	0.968228	−	0.250068i	$-0.0804531\pi$
$30$	3.93963	−	6.87306i	0.719275	−	1.25484i
$31$	−3.76937	−	2.17625i	−0.676999	−	0.390865i	0.121725	−	0.992564i	$-0.461158\pi$
$31$	−3.76937	−	2.17625i	−0.676999	−	0.390865i	−0.798723	+	0.601699i	$0.794491\pi$
$32$	4.05634	−	7.02578i	0.717066	−	1.24199i
$33$	8.02366	+	3.93572i	1.39674	+	0.685121i
$34$		−	2.77686i		−	0.476228i
$35$		0			0
$36$	−2.48165	+	6.06377i	−0.413608	+	1.01063i
$37$	6.58079	−	3.79942i	1.08188	−	0.624621i	0.150473	−	0.988614i	$-0.451920\pi$
$37$	6.58079	−	3.79942i	1.08188	−	0.624621i	0.931402	+	0.363993i	$0.118587\pi$
$38$	5.48062	+	3.16424i	0.889074	+	0.513307i
$39$	−5.15235	+	0.348667i	−0.825036	+	0.0558314i
$40$	0.372936	+	0.754337i	0.0589664	+	0.119271i
$41$	7.68540			1.20026			0.600129	−	0.799903i	$-0.295116\pi$
$41$	7.68540			1.20026			0.600129	+	0.799903i	$0.295116\pi$
$42$		0			0
$43$		−	7.79107i		−	1.18813i	−0.804418	−	0.594064i	$-0.797523\pi$
$43$		−	7.79107i		−	1.18813i	0.804418	−	0.594064i	$-0.202477\pi$
$44$	−9.75905	+	5.63439i	−1.47123	+	0.849417i
$45$	3.75604	+	5.55807i	0.559917	+	0.828548i
$46$	7.39391	−	12.8066i	1.09017	−	1.88823i
$47$	−5.25990	+	3.03680i	−0.767235	+	0.442963i	−0.831887	−	0.554945i	$-0.812739\pi$
$47$	−5.25990	+	3.03680i	−0.767235	+	0.442963i	0.0646524	+	0.997908i	$0.479406\pi$
$48$	3.47342	+	5.17458i	0.501346	+	0.746887i
$49$		0			0
$50$	10.1425	+	1.31465i	1.43437	+	0.185920i
$51$	2.11107	+	1.03551i	0.295609	+	0.145001i
$52$	3.25578	−	5.63918i	0.451496	−	0.782014i
$53$	−3.14616	+	5.44930i	−0.432158	+	0.748519i	−0.997059	−	0.0766394i	$-0.975581\pi$
$53$	−3.14616	+	5.44930i	−0.432158	+	0.748519i	0.564901	+	0.825159i	$0.308914\pi$
$54$	−7.05858	−	7.94631i	−0.960551	−	1.08136i
$55$	−0.743074	+	11.5136i	−0.100196	+	1.55249i
$56$		0			0
$57$	−4.44934	+	2.98661i	−0.589329	+	0.395586i
$58$	−4.77104	+	2.75456i	−0.626468	+	0.361692i
$59$	−2.12502	+	3.68065i	−0.276655	+	0.479180i	−0.970551	−	0.240895i	$-0.922559\pi$
$59$	−2.12502	+	3.68065i	−0.276655	+	0.479180i	0.693897	+	0.720075i	$0.255892\pi$
$60$	−8.45847	+	0.0263817i	−1.09198	+	0.00340586i
$61$	4.51526	−	2.60689i	0.578120	−	0.333778i	−0.182266	−	0.983249i	$-0.558343\pi$
$61$	4.51526	−	2.60689i	0.578120	−	0.333778i	0.760386	+	0.649472i	$0.225010\pi$
$62$			8.90293i			1.13067i
$63$		0			0
$64$	−9.39791			−1.17474
$65$	−2.95466	−	5.97638i	−0.366481	−	0.741279i
$66$	−1.23423	−	18.2386i	−0.151924	−	2.24502i
$67$	4.89919	+	2.82855i	0.598531	+	0.345562i	0.768463	−	0.639894i	$-0.221022\pi$
$67$	4.89919	+	2.82855i	0.598531	+	0.345562i	−0.169932	+	0.985456i	$0.554355\pi$
$68$	−2.56767	+	1.48244i	−0.311375	+	0.179773i
$69$	6.97884	+	10.3968i	0.840153	+	1.25163i
$70$		0			0
$71$		−	11.2688i		−	1.33736i	−0.743551	−	0.668679i	$-0.766860\pi$
$71$		−	11.2688i		−	1.33736i	0.743551	−	0.668679i	$-0.233140\pi$
$72$	1.11868	−	0.152102i	0.131838	−	0.0179254i
$73$	2.45608	−	4.25406i	0.287463	−	0.497900i	−0.685741	−	0.727846i	$-0.740522\pi$
$73$	2.45608	−	4.25406i	0.287463	−	0.497900i	0.973203	+	0.229946i	$0.0738549\pi$
$74$	−13.4609	−	7.77163i	−1.56479	−	0.903434i
$75$	−4.78168	+	7.22050i	−0.552140	+	0.833751i
$76$		−	6.75699i		−	0.775079i
$77$		0			0
$78$	5.88715	+	8.77046i	0.666589	+	0.993059i
$79$	−5.96472	−	10.3312i	−0.671084	−	1.16235i	−0.977597	−	0.210485i	$-0.932496\pi$
$79$	−5.96472	−	10.3312i	−0.671084	−	1.16235i	0.306513	−	0.951866i	$-0.400838\pi$
$80$	−4.46331	+	6.69431i	−0.499014	+	0.748447i
$81$	8.67328	−	2.40296i	0.963698	−	0.266995i
$82$	−7.86016	−	13.6142i	−0.868009	−	1.50344i
$83$		−	12.1558i		−	1.33428i	−0.744934	−	0.667138i	$-0.767519\pi$
$83$		−	12.1558i		−	1.33428i	0.744934	−	0.667138i	$-0.232481\pi$
$84$		0			0
$85$	−0.195507	+	3.02930i	−0.0212057	+	0.328573i
$86$	−13.8014	+	7.96823i	−1.48824	+	0.859237i
$87$	−0.314964	−	4.65432i	−0.0337677	−	0.498995i
$88$	1.68160	+	0.970873i	0.179259	+	0.103495i
$89$	−4.66058	−	8.07237i	−0.494021	−	0.855669i	0.505955	−	0.862560i	$-0.331140\pi$
$89$	−4.66058	−	8.07237i	−0.494021	−	0.855669i	−0.999976	+	0.00689023i	$0.997807\pi$
$90$	6.00432	−	12.3380i	0.632911	−	1.30054i
$91$		0			0
$92$	−15.7891			−1.64613
$93$	−6.76834	−	3.31997i	−0.701844	−	0.344265i
$94$	10.7590	+	6.21171i	1.10971	+	0.640689i
$95$	−5.75607	−	3.83776i	−0.590560	−	0.393746i
$96$	6.18814	−	12.6156i	0.631574	−	1.28757i
$97$	−19.2504			−1.95458			−0.977289	−	0.211910i	$-0.932032\pi$
$97$	−19.2504			−1.95458			−0.977289	+	0.211910i	$0.932032\pi$
$98$		0			0
$99$	14.3259	+	5.86300i	1.43981	+	0.589254i
$100$	−4.19904	−	10.0803i	−0.419904	−	1.00803i
$101$	−2.59470	+	4.49416i	−0.258183	+	0.447185i	−0.965755	−	0.259455i	$-0.916457\pi$
$101$	−2.59470	+	4.49416i	−0.258183	+	0.447185i	0.707573	+	0.706641i	$0.249790\pi$
$102$	−0.324734	−	4.79869i	−0.0321535	−	0.475141i
$103$	2.33050	+	4.03654i	0.229631	+	0.397733i	0.957699	−	0.287773i	$-0.0929147\pi$
$103$	2.33050	+	4.03654i	0.229631	+	0.397733i	−0.728068	+	0.685505i	$0.759581\pi$
$104$	−1.12202			−0.110023
$105$		0			0
$106$	12.8708			1.25012
$107$	0.439926	+	0.761974i	0.0425293	+	0.0736628i	0.886506	−	0.462716i	$-0.153125\pi$
$107$	0.439926	+	0.761974i	0.0425293	+	0.0736628i	−0.843977	+	0.536379i	$0.819792\pi$
$108$	−3.57942	+	10.7690i	−0.344430	+	1.03625i
$109$	−2.93877	+	5.09010i	−0.281483	+	0.487543i	−0.971750	−	0.236012i	$-0.924160\pi$
$109$	−2.93877	+	5.09010i	−0.281483	+	0.487543i	0.690267	+	0.723555i	$0.257493\pi$
$110$	21.1556	−	10.4591i	2.01710	−	0.997235i
$111$	10.9279	−	7.33535i	1.03723	−	0.696241i
$112$		0			0
$113$	−3.00476			−0.282664			−0.141332	−	0.989962i	$-0.545139\pi$
$113$	−3.00476			−0.282664			−0.141332	+	0.989962i	$0.545139\pi$
$114$	9.84109	+	4.82720i	0.921703	+	0.452108i
$115$	−8.96773	+	13.4503i	−0.836245	+	1.25424i
$116$	5.09409	+	2.94107i	0.472974	+	0.273072i
$117$	−8.86300	+	1.20506i	−0.819384	+	0.111408i
$118$	8.69338			0.800291
$119$		0			0
$120$	0.732685	+	1.25996i	0.0668847	+	0.115018i
$121$	7.81150	+	13.5299i	0.710137	+	1.22999i
$122$	−9.23587	−	5.33233i	−0.836176	−	0.482766i
$123$	13.2811	−	0.898753i	1.19752	−	0.0810378i
$124$	8.23223	−	4.75288i	0.739276	−	0.426821i
$125$	−10.9720	−	2.14826i	−0.981366	−	0.192146i
$126$		0			0
$127$			4.49556i			0.398916i	0.979906	+	0.199458i	$0.0639182\pi$
$127$			4.49556i			0.398916i	−0.979906	+	0.199458i	$0.936082\pi$
$128$	1.49893	+	2.59623i	0.132488	+	0.229476i
$129$	−0.911111	−	13.4637i	−0.0802188	−	1.18542i
$130$	−7.56493	+	11.3463i	−0.663488	+	0.995134i
$131$	3.82312	+	6.62184i	0.334028	+	0.578553i	0.983298	−	0.182005i	$-0.0582587\pi$
$131$	3.82312	+	6.62184i	0.334028	+	0.578553i	−0.649270	+	0.760558i	$0.724925\pi$
$132$	−16.2057	+	10.8780i	−1.41053	+	0.946812i
$133$		0			0
$134$		−	11.5715i		−	0.999622i
$135$	7.14078	+	9.16565i	0.614581	+	0.788854i
$136$	0.442440	+	0.255443i	0.0379389	+	0.0219040i
$137$	1.60555	−	2.78090i	0.137172	−	0.237588i	−0.789253	−	0.614068i	$-0.789532\pi$
$137$	1.60555	−	2.78090i	0.137172	−	0.237588i	0.926425	+	0.376480i	$0.122866\pi$
$138$	11.2798	−	22.9958i	0.960197	−	1.95753i
$139$		−	10.1096i		−	0.857483i	−0.903427	−	0.428741i	$-0.858957\pi$
$139$		−	10.1096i		−	0.857483i	0.903427	−	0.428741i	$-0.141043\pi$
$140$		0			0
$141$	−8.73449	+	5.86300i	−0.735577	+	0.493754i
$142$	−19.9619	+	11.5250i	−1.67517	+	0.967159i
$143$	−13.3228	−	7.69193i	−1.11411	−	0.643232i
$144$	6.60755	+	8.53599i	0.550629	+	0.711333i
$145$	5.39870	−	2.66906i	0.448337	−	0.221653i
$146$	−10.0477			−0.831555
$147$		0			0
$148$			16.5957i			1.36416i
$149$	5.63832	−	3.25529i	0.461909	−	0.266683i	−0.250938	−	0.968003i	$-0.580739\pi$
$149$	5.63832	−	3.25529i	0.461909	−	0.266683i	0.712847	+	0.701320i	$0.247406\pi$
$150$	17.6811	+	1.08575i	1.44365	+	0.0886511i
$151$	5.87611	−	10.1777i	0.478191	−	0.828251i	−0.521496	−	0.853254i	$-0.674626\pi$
$151$	5.87611	−	10.1777i	0.478191	−	0.828251i	0.999687	+	0.0250023i	$0.00795931\pi$
$152$	−1.00832	+	0.582155i	−0.0817857	+	0.0472190i
$153$	3.76924	+	1.54259i	0.304725	+	0.124711i
$154$		0			0
$155$	0.626818	−	9.71226i	0.0503472	−	0.780108i
$156$	4.96685	−	10.1258i	0.397666	−	0.810713i
$157$	−6.00307	+	10.3976i	−0.479097	+	0.829821i	−0.999713	−	0.0239706i	$-0.992369\pi$
$157$	−6.00307	+	10.3976i	−0.479097	+	0.829821i	0.520615	+	0.853791i	$0.325703\pi$
$158$	−12.2007	+	21.1322i	−0.970636	+	1.68119i
$159$	−4.79961	+	9.78485i	−0.380634	+	0.775989i
$160$	18.1028	+	1.16834i	1.43115	+	0.0923650i
$161$		0			0
$162$	−13.1272	−	12.9066i	−1.03137	−	1.01404i
$163$	15.7593	−	9.09863i	1.23436	−	0.712659i	0.266426	−	0.963855i	$-0.414157\pi$
$163$	15.7593	−	9.09863i	1.23436	−	0.712659i	0.967936	+	0.251196i	$0.0808239\pi$
$164$	−8.39238	+	14.5360i	−0.655334	+	1.13507i
$165$	0.0623280	+	19.9835i	0.00485222	+	1.55572i
$166$	−21.5333	+	12.4323i	−1.67131	+	0.964930i
$167$			20.6432i			1.59742i	0.601716	+	0.798710i	$0.294484\pi$
$167$			20.6432i			1.59742i	−0.601716	+	0.798710i	$0.705516\pi$
$168$		0			0
$169$	−4.11057			−0.316198
$170$	5.56616	−	2.75185i	0.426905	−	0.211057i
$171$	−7.33963	+	5.68147i	−0.561276	+	0.434473i
$172$	14.7359	+	8.50777i	1.12360	+	0.648712i
$173$	−15.9654	+	9.21766i	−1.21383	+	0.700805i	−0.963592	−	0.267379i	$-0.913843\pi$
$173$	−15.9654	+	9.21766i	−1.21383	+	0.700805i	−0.250239	+	0.968184i	$0.580509\pi$
$174$	−7.92270	+	5.31809i	−0.600618	+	0.403163i
$175$		0			0
$176$			18.5658i			1.39945i
$177$	−3.24183	+	6.60903i	−0.243671	+	0.496765i
$178$	−9.53312	+	16.5119i	−0.714538	+	1.23762i
$179$	14.1419	+	8.16484i	1.05702	+	0.610269i	0.924605	−	0.380926i	$-0.124395\pi$
$179$	14.1419	+	8.16484i	1.05702	+	0.610269i	0.132411	+	0.991195i	$0.457728\pi$
$180$	−14.6140	+	1.03475i	−1.08926	+	0.0771256i
$181$		−	3.55998i		−	0.264612i	−0.991209	−	0.132306i	$-0.957762\pi$
$181$		−	3.55998i		−	0.264612i	0.991209	−	0.132306i	$-0.0422381\pi$
$182$		0			0
$183$	7.49796	−	5.03299i	0.554265	−	0.372049i
$184$	1.36033	+	2.35616i	0.100285	+	0.173698i
$185$	14.1374	+	9.42585i	1.03940	+	0.693002i
$186$	1.04113	+	15.3851i	0.0763396	+	1.12809i
$187$	3.50234	+	6.06623i	0.256116	+	0.443606i
$188$		−	13.2646i		−	0.967423i
$189$		0			0
$190$	−0.911387	+	14.1215i	−0.0661189	+	1.02448i
$191$	−0.285090	+	0.164597i	−0.0206284	+	0.0119098i	−0.510279	−	0.860009i	$-0.670458\pi$
$191$	−0.285090	+	0.164597i	−0.0206284	+	0.0119098i	0.489650	+	0.871919i	$0.337124\pi$
$192$	−16.2405	+	1.09902i	−1.17206	+	0.0793148i
$193$	−6.98270	−	4.03147i	−0.502626	−	0.290191i	0.227171	−	0.973855i	$-0.427052\pi$
$193$	−6.98270	−	4.03147i	−0.502626	−	0.290191i	−0.729797	+	0.683664i	$0.760386\pi$
$194$	19.6881	+	34.1008i	1.41352	+	2.44829i
$195$	−5.80484	−	9.98225i	−0.415693	−	0.714844i
$196$		0			0
$197$	−9.61468			−0.685017			−0.342509	−	0.939515i	$-0.611277\pi$
$197$	−9.61468			−0.685017			−0.342509	+	0.939515i	$0.611277\pi$
$198$	−4.26575	−	31.3738i	−0.303154	−	2.22964i
$199$	−9.66445	−	5.57977i	−0.685095	−	0.395540i	0.116677	−	0.993170i	$-0.462776\pi$
$199$	−9.66445	−	5.57977i	−0.685095	−	0.395540i	−0.801772	+	0.597630i	$0.796109\pi$
$200$	−1.14247	+	1.49508i	−0.0807851	+	0.105718i
$201$	8.79706	+	4.31508i	0.620497	+	0.304363i
$202$	10.6148			0.746855
$203$		0			0
$204$	−4.26382	+	2.86208i	−0.298527	+	0.200386i
$205$	7.61618	+	15.4052i	0.531937	+	1.07595i
$206$	4.76699	−	8.25666i	0.332132	−	0.575269i
$207$	13.2759	+	17.1506i	0.922742	+	1.19205i
$208$	−5.36403	−	9.29078i	−0.371929	−	0.644199i
$209$	−15.9637			−1.10423
$210$		0			0
$211$	1.20704			0.0830957			0.0415479	−	0.999137i	$-0.486771\pi$
$211$	1.20704			0.0830957			0.0415479	+	0.999137i	$0.486771\pi$
$212$	−6.87114	−	11.9012i	−0.471912	−	0.817375i
$213$	−1.31780	−	19.4736i	−0.0902944	−	1.33431i
$214$	0.899859	−	1.55860i	0.0615131	−	0.106544i
$215$	15.6170	−	7.72090i	1.06507	−	0.526561i
$216$	1.91541	−	0.393670i	0.130327	−	0.0267859i
$217$		0			0
$218$	12.0224			0.814258
$219$	3.74687	−	7.63865i	0.253190	−	0.516172i
$220$	−20.9652	−	13.9782i	−1.41347	−	0.942408i
$221$	−3.50532	−	2.02379i	−0.235793	−	0.136135i
$222$	−24.1705	−	11.8560i	−1.62222	−	0.795722i
$223$	4.30580			0.288338			0.144169	−	0.989553i	$-0.453949\pi$
$223$	4.30580			0.288338			0.144169	+	0.989553i	$0.453949\pi$
$224$		0			0
$225$	−7.41882	+	13.0369i	−0.494588	+	0.869127i
$226$	3.07309	+	5.32274i	0.204419	+	0.354064i
$227$	−3.50545	−	2.02387i	−0.232665	−	0.134329i	0.379136	−	0.925341i	$-0.376221\pi$
$227$	−3.50545	−	2.02387i	−0.232665	−	0.134329i	−0.611801	+	0.791012i	$0.709555\pi$
$228$	−0.790181	−	11.6767i	−0.0523310	−	0.773311i
$229$	−7.42385	+	4.28616i	−0.490582	+	0.283238i	−0.724816	−	0.688943i	$-0.758075\pi$
$229$	−7.42385	+	4.28616i	−0.490582	+	0.283238i	0.234234	+	0.972180i	$0.424742\pi$
$230$	32.9979	+	2.12965i	2.17582	+	0.140425i
$231$		0			0
$232$		−	1.01356i		−	0.0665438i
$233$	4.55956	+	7.89739i	0.298707	+	0.517375i	0.975840	−	0.218485i	$-0.0701114\pi$
$233$	4.55956	+	7.89739i	0.298707	+	0.517375i	−0.677134	+	0.735860i	$0.736778\pi$
$234$	11.1992	+	14.4678i	0.732116	+	0.945787i
$235$	−11.2997	−	7.53390i	−0.737113	−	0.491457i
$236$	−4.64101	−	8.03846i	−0.302104	−	0.523259i
$237$	−11.5158	−	17.1558i	−0.748031	−	1.11439i
$238$		0			0
$239$			17.7528i			1.14834i	0.818738	+	0.574168i	$0.194674\pi$
$239$			17.7528i			1.14834i	−0.818738	+	0.574168i	$0.805326\pi$
$240$	−6.93019	+	12.0904i	−0.447342	+	0.780431i
$241$	20.7990	+	12.0083i	1.33978	+	0.773524i	0.986775	−	0.162096i	$-0.0518254\pi$
$241$	20.7990	+	12.0083i	1.33978	+	0.773524i	0.353008	+	0.935620i	$0.385159\pi$
$242$	15.9783	−	27.6752i	1.02712	−	1.77903i
$243$	14.7073	−	5.16682i	0.943472	−	0.331452i
$244$			11.3868i			0.728964i
$245$		0			0
$246$	−15.1752	−	22.6075i	−0.967536	−	1.44140i
$247$	7.98863	−	4.61224i	0.508304	−	0.293469i
$248$	−1.41851	−	0.818977i	−0.0900755	−	0.0520051i
$249$	−1.42154	−	21.0065i	−0.0900864	−	1.33123i
$250$	7.41600	+	21.6333i	0.469029	+	1.36821i
$251$	−8.80742			−0.555919			−0.277960	−	0.960593i	$-0.589658\pi$
$251$	−8.80742			−0.555919			−0.277960	+	0.960593i	$0.589658\pi$
$252$		0			0
$253$			37.3025i			2.34519i
$254$	7.96359	−	4.59778i	0.499680	−	0.288490i
$255$	0.0163989	+	5.25779i	0.00102694	+	0.329255i
$256$	−6.33188	+	10.9671i	−0.395742	+	0.685446i
$257$	10.0743	−	5.81639i	0.628416	−	0.362816i	−0.151722	−	0.988423i	$-0.548482\pi$
$257$	10.0743	−	5.81639i	0.628416	−	0.362816i	0.780139	+	0.625607i	$0.215149\pi$
$258$	−22.9183	+	15.3839i	−1.42683	+	0.957758i
$259$		0			0
$260$	14.5301	+	0.937754i	0.901117	+	0.0581570i
$261$	−1.08858	−	8.00629i	−0.0673813	−	0.495577i
$262$	7.82011	−	13.5448i	0.483128	−	0.836803i
$263$	−0.489850	+	0.848446i	−0.0302055	+	0.0523174i	−0.880733	−	0.473613i	$-0.842949\pi$
$263$	−0.489850	+	0.848446i	−0.0302055	+	0.0523174i	0.850528	+	0.525931i	$0.176283\pi$
$264$	3.01951	+	1.48111i	0.185838	+	0.0911562i
$265$	−14.0408	−	0.906179i	−0.862521	−	0.0556661i
$266$		0			0
$267$	−8.99796	−	13.4048i	−0.550666	−	0.820362i
$268$	−10.6997	+	6.17749i	−0.653590	+	0.377350i
$269$	10.3046	−	17.8481i	0.628282	−	1.08822i	−0.359614	−	0.933101i	$-0.617092\pi$
$269$	10.3046	−	17.8481i	0.628282	−	1.08822i	0.987896	−	0.155116i	$-0.0495751\pi$
$270$	8.93321	−	22.0235i	0.543658	−	1.34031i
$271$	−2.25140	+	1.29985i	−0.136763	+	0.0789602i	−0.566820	−	0.823841i	$-0.691827\pi$
$271$	−2.25140	+	1.29985i	−0.136763	+	0.0789602i	0.430057	+	0.902802i	$0.358493\pi$
$272$			4.88477i			0.296183i
$273$		0			0
$274$	−6.56824			−0.396802
$275$	−23.8151	+	9.92042i	−1.43611	+	0.598224i
$276$	−27.2852	+	1.84643i	−1.64237	+	0.111142i
$277$	−16.5840	−	9.57476i	−0.996434	−	0.575292i	−0.0892430	−	0.996010i	$-0.528445\pi$
$277$	−16.5840	−	9.57476i	−0.996434	−	0.575292i	−0.907191	+	0.420718i	$0.861778\pi$
$278$	−17.9085	+	10.3395i	−1.07408	+	0.620119i
$279$	−12.0846	−	4.94572i	−0.723486	−	0.296093i
$280$		0			0
$281$		−	14.8209i		−	0.884138i	−0.896981	−	0.442069i	$-0.854245\pi$
$281$		−	14.8209i		−	0.884138i	0.896981	−	0.442069i	$-0.145755\pi$
$282$	19.3190	+	9.47626i	1.15043	+	0.564303i
$283$	−1.14292	+	1.97960i	−0.0679398	+	0.117675i	−0.897994	−	0.440007i	$-0.854976\pi$
$283$	−1.14292	+	1.97960i	−0.0679398	+	0.117675i	0.830054	+	0.557682i	$0.188309\pi$
$284$	21.3136	+	12.3054i	1.26473	+	0.730191i
$285$	−10.3958	−	5.95889i	−0.615797	−	0.352974i
$286$			31.4674i			1.86070i
$287$		0			0
$288$	9.21840	−	22.5247i	0.543200	−	1.32728i
$289$	−7.57851	−	13.1264i	−0.445795	−	0.772139i
$290$	−10.2495	−	6.83369i	−0.601873	−	0.401288i
$291$	−33.2665	+	2.25119i	−1.95012	+	0.131967i
$292$	5.36403	+	9.29078i	0.313906	+	0.543702i
$293$		−	29.4268i		−	1.71913i	−0.511023	−	0.859567i	$-0.670733\pi$
$293$		−	29.4268i		−	1.71913i	0.511023	−	0.859567i	$-0.329267\pi$
$294$		0			0
$295$	−9.48367	−	0.612065i	−0.552160	−	0.0356358i
$296$	2.47652	−	1.42982i	0.143945	−	0.0831066i
$297$	25.4423	+	8.45653i	1.47631	+	0.490698i
$298$	−11.5331	−	6.65861i	−0.668092	−	0.385723i
$299$	−10.7775	−	18.6671i	−0.623277	−	1.07955i
$300$	−8.43517	−	16.9287i	−0.487005	−	0.977378i
$301$		0			0
$302$	−24.0389			−1.38328
$303$	−3.95834	+	8.06978i	−0.227401	+	0.463597i
$304$	−9.64094	−	5.56620i	−0.552946	−	0.319244i
$305$	9.70004	+	6.46733i	0.555423	+	0.370318i
$306$	−1.12235	−	8.25463i	−0.0641602	−	0.471886i
$307$	19.6726			1.12278			0.561388	−	0.827553i	$-0.310268\pi$
$307$	19.6726			1.12278			0.561388	+	0.827553i	$0.310268\pi$
$308$		0			0
$309$	4.49938	+	6.70301i	0.255961	+	0.381321i
$310$	−17.8457	+	8.82274i	−1.01357	+	0.501098i
$311$	3.88227	−	6.72428i	0.220143	−	0.381299i	−0.734708	−	0.678383i	$-0.762681\pi$
$311$	3.88227	−	6.72428i	0.220143	−	0.381299i	0.954851	+	0.297084i	$0.0960142\pi$
$312$	−1.93896	+	0.131212i	−0.109772	+	0.00742843i
$313$	7.69453	+	13.3273i	0.434921	+	0.753305i	0.997289	−	0.0735820i	$-0.0234431\pi$
$313$	7.69453	+	13.3273i	0.434921	+	0.753305i	−0.562368	+	0.826887i	$0.690110\pi$
$314$	24.5583			1.38590
$315$		0			0
$316$	26.0537			1.46563
$317$	0.807245	+	1.39819i	0.0453394	+	0.0785301i	0.887805	−	0.460221i	$-0.152230\pi$
$317$	0.807245	+	1.39819i	0.0453394	+	0.0785301i	−0.842465	+	0.538751i	$0.818896\pi$
$318$	22.2420	−	1.50515i	1.24727	−	0.0844044i
$319$	6.94842	−	12.0350i	0.389037	−	0.673832i
$320$	−9.31327	−	18.8379i	−0.520627	−	1.05307i
$321$	0.849343	+	1.26532i	0.0474057	+	0.0706233i
$322$		0			0
$323$	−4.20014			−0.233702
$324$	−4.92623	+	19.0285i	−0.273679	+	1.05714i
$325$	9.05147	−	11.8451i	0.502085	−	0.657048i
$326$	−32.2353	−	18.6110i	−1.78535	−	1.03077i
$327$	−4.48323	+	9.13986i	−0.247923	+	0.505435i
$328$	2.89221			0.159696
$329$		0			0
$330$	35.3358	−	20.5483i	1.94517	−	1.13115i
$331$	−15.2284	−	26.3763i	−0.837026	−	1.44977i	−0.892370	−	0.451305i	$-0.850959\pi$
$331$	−15.2284	−	26.3763i	−0.837026	−	1.44977i	0.0553437	−	0.998467i	$-0.482375\pi$
$332$	22.9913	+	13.2741i	1.26181	+	0.728508i
$333$	18.0267	−	13.9542i	0.987859	−	0.764683i
$334$	36.5681	−	21.1126i	2.00092	−	1.15523i
$335$	−0.814699	+	12.6234i	−0.0445117	+	0.689689i
$336$		0			0
$337$		−	22.5247i		−	1.22700i	−0.789696	−	0.613498i	$-0.789762\pi$
$337$		−	22.5247i		−	1.22700i	0.789696	−	0.613498i	$-0.210238\pi$
$338$	4.20404	+	7.28161i	0.228670	+	0.396067i
$339$	−5.19253	+	0.351386i	−0.282019	+	0.0190846i
$340$	−5.51607	−	3.67774i	−0.299151	−	0.199453i
$341$	−11.2289	−	19.4490i	−0.608078	−	1.05322i
$342$	17.5709	+	7.19103i	0.950124	+	0.388846i
$343$		0			0
$344$		−	2.93198i		−	0.158082i
$345$	−13.9242	+	24.2921i	−0.749654	+	1.30784i
$346$	32.6570	+	18.8545i	1.75565	+	1.01362i
$347$	−6.22579	+	10.7834i	−0.334218	+	0.578882i	−0.983334	−	0.181807i	$-0.941805\pi$
$347$	−6.22579	+	10.7834i	−0.334218	+	0.578882i	0.649116	+	0.760689i	$0.275139\pi$
$348$	9.14703	+	4.48675i	0.490332	+	0.240515i
$349$		−	17.9519i		−	0.960945i	−0.877010	−	0.480472i	$-0.840465\pi$
$349$		−	17.9519i		−	0.960945i	0.877010	−	0.480472i	$-0.159535\pi$
$350$		0			0
$351$	−15.1752	+	3.11893i	−0.809993	+	0.166476i
$352$	36.2513	−	20.9297i	1.93220	−	1.11556i
$353$	10.9825	+	6.34074i	0.584539	+	0.337484i	0.762935	−	0.646475i	$-0.223758\pi$
$353$	10.9825	+	6.34074i	0.584539	+	0.337484i	−0.178396	+	0.983959i	$0.557091\pi$
$354$	15.0230	−	1.01663i	0.798464	−	0.0540332i
$355$	22.5880	−	11.1673i	1.19885	−	0.592698i
$356$	20.3572			1.07893
$357$		0			0
$358$		−	33.4020i		−	1.76535i
$359$	−0.0626501	+	0.0361710i	−0.00330654	+	0.00190903i	−0.501652	−	0.865069i	$-0.667274\pi$
$359$	−0.0626501	+	0.0361710i	−0.00330654	+	0.00190903i	0.498346	+	0.866978i	$0.333941\pi$
$360$	1.41349	+	2.09165i	0.0744977	+	0.110239i
$361$	−4.71393	+	8.16477i	−0.248102	+	0.429725i
$362$	−6.30628	+	3.64093i	−0.331451	+	0.191363i
$363$	15.0813	+	22.4675i	0.791562	+	1.17924i
$364$		0			0
$365$	10.9611	+	0.707418i	0.573732	+	0.0370280i
$366$	−16.5841	−	8.13472i	−0.866863	−	0.425209i
$367$	−5.35942	+	9.28279i	−0.279760	+	0.484558i	−0.971325	−	0.237756i	$-0.923588\pi$
$367$	−5.35942	+	9.28279i	−0.279760	+	0.484558i	0.691565	+	0.722314i	$0.256921\pi$
$368$	−13.0066	+	22.5281i	−0.678016	+	1.17436i
$369$	22.8460	−	3.10627i	1.18931	−	0.161706i
$370$	2.23844	−	34.6836i	0.116371	−	1.80312i
$371$		0			0
$372$	13.6703	−	9.17614i	0.708771	−	0.475761i
$373$	−18.5158	+	10.6901i	−0.958710	+	0.553511i	−0.895776	−	0.444506i	$-0.853379\pi$
$373$	−18.5158	+	10.6901i	−0.958710	+	0.553511i	−0.0629341	+	0.998018i	$0.520046\pi$
$374$	7.16395	−	12.4083i	0.370439	−	0.641620i
$375$	−19.2119	−	2.42930i	−0.992100	−	0.125449i
$376$	−1.97943	+	1.14283i	−0.102082	+	0.0589368i
$377$			8.03017i			0.413575i
$378$		0			0
$379$	24.3043			1.24843			0.624214	−	0.781253i	$-0.285419\pi$
$379$	24.3043			1.24843			0.624214	+	0.781253i	$0.285419\pi$
$380$	13.5442	−	6.69613i	0.694804	−	0.343504i
$381$	0.525723	+	7.76876i	0.0269336	+	0.398006i
$382$	0.583145	+	0.336679i	0.0298363	+	0.0172260i
$383$	−6.39716	+	3.69340i	−0.326880	+	0.188724i	−0.654455	−	0.756101i	$-0.727102\pi$
$383$	−6.39716	+	3.69340i	−0.326880	+	0.188724i	0.327575	+	0.944825i	$0.393768\pi$
$384$	2.89392	+	4.31125i	0.147680	+	0.220008i
$385$		0			0
$386$			16.4925i			0.839449i
$387$	−3.14898	−	23.1601i	−0.160072	−	1.17730i
$388$	21.0212	−	36.4098i	1.06719	−	1.84843i
$389$	−11.1441	−	6.43407i	−0.565030	−	0.326220i	0.190132	−	0.981759i	$-0.439108\pi$
$389$	−11.1441	−	6.43407i	−0.565030	−	0.326220i	−0.755162	+	0.655538i	$0.772442\pi$
$390$	−11.7461	+	20.4921i	−0.594786	+	1.03766i
$391$			9.81452i			0.496342i
$392$		0			0
$393$	7.38111	+	10.9961i	0.372328	+	0.554681i
$394$	9.83330	+	17.0318i	0.495395	+	0.858049i
$395$	14.7977	−	22.1943i	0.744552	−	1.11672i
$396$	−26.7329	+	20.6935i	−1.34338	+	1.03989i
$397$	−8.12330	−	14.0700i	−0.407697	−	0.706151i	0.586935	−	0.809634i	$-0.300335\pi$
$397$	−8.12330	−	14.0700i	−0.407697	−	0.706151i	−0.994631	+	0.103483i	$0.967001\pi$
$398$			22.8266i			1.14419i
$399$		0			0
$400$	−17.8417	−	2.31260i	−0.892086	−	0.115630i
$401$	8.85133	−	5.11032i	0.442015	−	0.255197i	−0.262437	−	0.964949i	$-0.584526\pi$
$401$	8.85133	−	5.11032i	0.442015	−	0.255197i	0.704452	+	0.709752i	$0.251193\pi$
$402$	−1.35320	−	19.9966i	−0.0674915	−	0.997341i
$403$	11.2384	+	6.48851i	0.559826	+	0.323216i
$404$	−5.66678	−	9.81514i	−0.281933	−	0.488322i
$405$	13.4118	+	15.0041i	0.666440	+	0.745559i
$406$		0			0
$407$	39.2081			1.94347
$408$	0.794451	+	0.389690i	0.0393312	+	0.0192925i
$409$	−15.7321	−	9.08292i	−0.777901	−	0.449122i	0.0577846	−	0.998329i	$-0.481596\pi$
$409$	−15.7321	−	9.08292i	−0.777901	−	0.449122i	−0.835686	+	0.549208i	$0.814930\pi$
$410$	19.5000	−	29.2471i	0.963035	−	1.44441i
$411$	2.44935	−	4.99342i	0.120817	−	0.246307i
$412$	−10.1795			−0.501509
$413$		0			0
$414$	16.8034	−	41.0581i	0.825840	−	2.01789i
$415$	24.3661	−	12.0464i	1.19609	−	0.591332i
$416$	−12.0940	+	20.9475i	−0.592959	+	1.02703i
$417$	−1.18224	−	17.4703i	−0.0578947	−	0.855526i
$418$	16.3267	+	28.2786i	0.798564	+	1.38315i
$419$	3.38983			0.165604			0.0828019	−	0.996566i	$-0.473613\pi$
$419$	3.38983			0.165604			0.0828019	+	0.996566i	$0.473613\pi$
$420$		0			0
$421$	−5.12428			−0.249742			−0.124871	−	0.992173i	$-0.539852\pi$
$421$	−5.12428			−0.249742			−0.124871	+	0.992173i	$0.539852\pi$
$422$	−1.23448	−	2.13819i	−0.0600936	−	0.104085i
$423$	−14.4084	+	11.1533i	−0.700561	+	0.542291i
$424$	−1.18398	+	2.05071i	−0.0574991	+	0.0995914i
$425$	−6.26591	+	2.61012i	−0.303941	+	0.126610i
$426$	−33.1484	+	22.2508i	−1.60605	+	1.07805i
$427$		0			0
$428$	−1.92158			−0.0928830
$429$	−23.9227	−	11.7344i	−1.15500	−	0.566543i
$430$	−29.6492	−	19.7681i	−1.42981	−	0.953303i
$431$	11.3803	+	6.57042i	0.548170	+	0.316486i	0.748384	−	0.663266i	$-0.230830\pi$
$431$	11.3803	+	6.57042i	0.548170	+	0.316486i	−0.200214	+	0.979752i	$0.564164\pi$
$432$	12.4167	+	13.9783i	0.597400	+	0.672533i
$433$	4.76504			0.228993			0.114497	−	0.993424i	$-0.463475\pi$
$433$	4.76504			0.228993			0.114497	+	0.993424i	$0.463475\pi$
$434$		0			0
$435$	9.01735	−	5.24374i	0.432349	−	0.251418i
$436$	−6.41821	−	11.1167i	−0.307377	−	0.532392i
$437$	−19.3707	−	11.1837i	−0.926625	−	0.534987i
$438$	−17.3635	+	1.17501i	−0.829658	+	0.0561441i
$439$	−24.7933	+	14.3144i	−1.18332	+	0.683189i	−0.956780	−	0.290813i	$-0.906074\pi$
$439$	−24.7933	+	14.3144i	−1.18332	+	0.683189i	−0.226538	+	0.974002i	$0.572741\pi$
$440$	−0.279638	+	4.33286i	−0.0133312	+	0.206561i
$441$		0			0
$442$			8.27925i			0.393804i
$443$	14.2368	+	24.6589i	0.676411	+	1.17158i	0.976054	+	0.217527i	$0.0697989\pi$
$443$	14.2368	+	24.6589i	0.676411	+	1.17158i	−0.299644	+	0.954051i	$0.596868\pi$
$444$	1.94075	+	28.6790i	0.0921039	+	1.36105i
$445$	11.5623	−	17.3417i	0.548105	−	0.822076i
$446$	−4.40371	−	7.62745i	−0.208522	−	0.361170i
$447$	9.36289	−	6.28482i	0.442849	−	0.297262i
$448$		0			0
$449$			3.55207i			0.167633i	0.996481	+	0.0838164i	$0.0267109\pi$
$449$			3.55207i			0.167633i	−0.996481	+	0.0838164i	$0.973289\pi$
$450$	30.6816	−	0.191391i	1.44634	−	0.00902228i
$451$	34.3420	+	19.8274i	1.61710	+	0.933634i
$452$	3.28117	−	5.68315i	0.154333	−	0.267313i
$453$	8.96429	−	18.2753i	0.421179	−	0.858647i
$454$			8.27957i			0.388579i
$455$		0			0
$456$	−1.67440	+	1.12394i	−0.0784109	+	0.0526331i
$457$	−25.3222	+	14.6198i	−1.18452	+	0.683885i	−0.957057	−	0.289901i	$-0.906378\pi$
$457$	−25.3222	+	14.6198i	−1.18452	+	0.683885i	−0.227467	+	0.973786i	$0.573044\pi$
$458$	15.1853	+	8.76725i	0.709564	+	0.409667i
$459$	6.69401	+	2.22497i	0.312450	+	0.103852i
$460$	−15.6469	−	31.6490i	−0.729541	−	1.47564i
$461$	−28.3247			−1.31921			−0.659607	−	0.751611i	$-0.729277\pi$
$461$	−28.3247			−1.31921			−0.659607	+	0.751611i	$0.729277\pi$
$462$		0			0
$463$		−	39.6458i		−	1.84249i	−0.388977	−	0.921247i	$-0.627172\pi$
$463$		−	39.6458i		−	1.84249i	0.388977	−	0.921247i	$-0.372828\pi$
$464$	8.39272	−	4.84554i	0.389622	−	0.224948i
$465$	−0.0525766	−	16.8571i	−0.00243818	−	0.781727i
$466$	9.32648	−	16.1539i	0.432041	−	0.748317i
$467$	−17.7695	+	10.2592i	−0.822272	+	0.474739i	−0.851199	−	0.524842i	$-0.824124\pi$
$467$	−17.7695	+	10.2592i	−0.822272	+	0.474739i	0.0289272	+	0.999582i	$0.490791\pi$
$468$	7.39907	−	18.0792i	0.342022	−	0.835712i
$469$		0			0
$470$	−1.78914	+	27.7220i	−0.0825270	+	1.27872i
$471$	−9.15797	+	18.6701i	−0.421977	+	0.860274i
$472$	−0.799701	+	1.38512i	−0.0368092	+	0.0637555i
$473$	20.1000	−	34.8142i	0.924199	−	1.60076i
$474$	−18.6128	+	37.9454i	−0.854912	+	1.74289i
$475$	1.98848	−	15.3411i	0.0912375	−	0.703898i
$476$		0			0
$477$	−7.14993	+	17.4705i	−0.327373	+	0.799918i
$478$	31.4480	−	18.1565i	1.43840	−	0.830460i
$479$	3.30937	−	5.73200i	0.151209	−	0.261902i	−0.780463	−	0.625202i	$-0.785017\pi$
$479$	3.30937	−	5.73200i	0.151209	−	0.261902i	0.931672	+	0.363300i	$0.118350\pi$
$480$	31.4201	−	0.0979983i	1.43412	−	0.00447299i
$481$	−19.6207	+	11.3280i	−0.894628	+	0.516514i
$482$		−	49.1255i		−	2.23761i
$483$		0			0
$484$	−34.1203			−1.55092
$485$	−19.0770	−	38.5869i	−0.866241	−	1.75214i
$486$	−24.1944	−	20.7687i	−1.09748	−	0.942087i
$487$	−17.1819	−	9.91996i	−0.778585	−	0.449516i	0.0573437	−	0.998354i	$-0.481737\pi$
$487$	−17.1819	−	9.91996i	−0.778585	−	0.449516i	−0.835929	+	0.548838i	$0.815070\pi$
$488$	1.69921	−	0.981038i	0.0769196	−	0.0444095i
$489$	26.1696	−	17.5663i	1.18343	−	0.794374i
$490$		0			0
$491$		−	11.6654i		−	0.526454i	−0.964734	−	0.263227i	$-0.915213\pi$
$491$		−	11.6654i		−	0.526454i	0.964734	−	0.263227i	$-0.0847868\pi$
$492$	−12.8030	+	26.1011i	−0.577202	+	1.17673i
$493$	1.82817	−	3.16649i	0.0823367	−	0.142611i
$494$	−16.3406	−	9.43422i	−0.735196	−	0.424466i
$495$	2.44464	+	34.5262i	0.109878	+	1.55184i
$496$		−	15.6611i		−	0.703205i
$497$		0			0
$498$	−35.7578	+	24.0023i	−1.60234	+	1.07557i
$499$	7.47555	+	12.9480i	0.334651	+	0.579633i	0.983418	−	0.181354i	$-0.0580481\pi$
$499$	7.47555	+	12.9480i	0.334651	+	0.579633i	−0.648766	+	0.760988i	$0.724715\pi$
$500$	16.0445	−	18.4064i	0.717532	−	0.823158i
$501$	2.41408	+	35.6735i	0.107853	+	1.59378i
$502$	9.00769	+	15.6018i	0.402033	+	0.696341i
$503$		−	2.45361i		−	0.109401i	−0.998503	−	0.0547006i	$-0.982580\pi$
$503$		−	2.45361i		−	0.109401i	0.998503	−	0.0547006i	$-0.0174204\pi$
$504$		0			0
$505$	−11.5798	−	0.747345i	−0.515293	−	0.0332564i
$506$	66.0790	−	38.1507i	2.93757	−	1.69601i
$507$	−7.10347	+	0.480702i	−0.315476	+	0.0213487i
$508$	−8.50281	−	4.90910i	−0.377251	−	0.217806i
$509$	4.51330	+	7.81726i	0.200048	+	0.346494i	0.948544	−	0.316646i	$-0.102557\pi$
$509$	4.51330	+	7.81726i	0.200048	+	0.346494i	−0.748495	+	0.663140i	$0.769223\pi$
$510$	9.29706	−	5.40639i	0.411681	−	0.239399i
$511$		0			0
$512$	31.8992			1.40976
$513$	−12.0192	+	10.6765i	−0.530660	+	0.471377i
$514$	−20.6067	−	11.8973i	−0.908923	−	0.524767i
$515$	−5.78165	+	8.67163i	−0.254770	+	0.382117i
$516$	26.4600	+	12.9790i	1.16484	+	0.571369i
$517$	−31.3383			−1.37826
$518$		0			0
$519$	−26.5119	+	17.7961i	−1.16374	+	0.781160i
$520$	−1.11191	−	2.24907i	−0.0487607	−	0.0986280i
$521$	−10.7379	+	18.5986i	−0.470436	+	0.814819i	−0.999428	−	0.0338078i	$-0.989237\pi$
$521$	−10.7379	+	18.5986i	−0.470436	+	0.814819i	0.528993	+	0.848626i	$0.322570\pi$
$522$	−13.0693	+	10.1167i	−0.572027	+	0.442795i
$523$	−16.7146	−	28.9505i	−0.730876	−	1.26591i	−0.956509	−	0.291702i	$-0.905778\pi$
$523$	−16.7146	−	28.9505i	−0.730876	−	1.26591i	0.225633	−	0.974212i	$-0.427555\pi$
$524$	−16.6992			−0.729510
$525$		0			0
$526$	2.00396			0.0873766
$527$	−2.95439	−	5.11715i	−0.128695	−	0.222907i
$528$	2.17113	+	32.0835i	0.0944865	+	1.39625i
$529$	−14.6330	+	25.3451i	−0.636217	+	1.10196i
$530$	12.7549	+	25.7992i	0.554036	+	1.12065i
$531$	−4.82931	+	11.8002i	−0.209574	+	0.512084i
$532$		0			0
$533$	−22.9141			−0.992521
$534$	−14.5432	+	29.6489i	−0.629347	+	1.28304i
$535$	−1.09140	+	1.63693i	−0.0471852	+	0.0707708i
$536$	1.84369	+	1.06446i	0.0796353	+	0.0459775i
$537$	25.3934	+	12.4558i	1.09581	+	0.537509i
$538$	−42.1557			−1.81746
$539$		0			0
$540$	−25.1334	+	3.49715i	−1.08157	+	0.150493i
$541$	2.35776	+	4.08376i	0.101368	+	0.175574i	0.912248	−	0.409637i	$-0.134345\pi$
$541$	2.35776	+	4.08376i	0.101368	+	0.175574i	−0.810881	+	0.585212i	$0.801011\pi$
$542$	4.60520	+	2.65881i	0.197810	+	0.114206i
$543$	−0.416315	−	6.15200i	−0.0178658	−	0.264008i
$544$	9.53793	−	5.50673i	0.408935	−	0.236099i
$545$	−13.1153	−	0.846445i	−0.561797	−	0.0362577i
$546$		0			0
$547$		−	1.20004i		−	0.0513100i	−0.999671	−	0.0256550i	$-0.991833\pi$
$547$		−	1.20004i		−	0.0513100i	0.999671	−	0.0256550i	$-0.00816713\pi$
$548$	3.50649	+	6.07342i	0.149790	+	0.259444i
$549$	12.3686	−	9.57433i	0.527881	−	0.408622i
$550$	41.9300	+	32.0410i	1.78790	+	1.36623i
$551$	4.16641	+	7.21643i	0.177495	+	0.307430i
$552$	2.62632	+	3.91259i	0.111783	+	0.166531i
$553$		0			0
$554$			39.1699i			1.66417i
$555$	25.5331	+	14.6355i	1.08382	+	0.621244i
$556$	19.1211	+	11.0395i	0.810913	+	0.468181i
$557$	−5.53829	+	9.59261i	−0.234665	+	0.406452i	−0.959175	−	0.282812i	$-0.908733\pi$
$557$	−5.53829	+	9.59261i	−0.234665	+	0.406452i	0.724510	+	0.689264i	$0.242066\pi$
$558$	3.59836	+	26.4653i	0.152331	+	1.12036i
$559$			23.2292i			0.982491i
$560$		0			0
$561$	6.76179	+	10.0735i	0.285483	+	0.425302i
$562$	−26.2542	+	15.1579i	−1.10747	+	0.639396i
$563$	3.89342	+	2.24787i	0.164088	+	0.0947364i	0.579795	−	0.814762i	$-0.303133\pi$
$563$	3.89342	+	2.24787i	0.164088	+	0.0947364i	−0.415707	+	0.909499i	$0.636466\pi$
$564$	−1.55120	−	22.9226i	−0.0653175	−	0.965215i
$565$	−2.97770	−	6.02298i	−0.125273	−	0.253389i
$566$	4.67565			0.196532
$567$		0			0
$568$		−	4.24073i		−	0.177937i
$569$	22.3092	−	12.8802i	0.935250	−	0.539967i	0.0467822	−	0.998905i	$-0.485103\pi$
$569$	22.3092	−	12.8802i	0.935250	−	0.539967i	0.888468	+	0.458938i	$0.151770\pi$
$570$	0.0764458	+	24.5100i	0.00320196	+	1.02661i
$571$	−6.15890	+	10.6675i	−0.257742	+	0.446422i	−0.965637	−	0.259896i	$-0.916312\pi$
$571$	−6.15890	+	10.6675i	−0.257742	+	0.446422i	0.707895	+	0.706318i	$0.249645\pi$
$572$	29.0968	−	16.7990i	1.21660	−	0.702402i
$573$	−0.473415	+	0.317778i	−0.0197772	+	0.0132754i
$574$		0			0
$575$	−35.8477	−	4.64649i	−1.49495	−	0.193772i
$576$	−27.9367	+	3.79843i	−1.16403	+	0.158268i
$577$	19.3036	−	33.4348i	0.803619	−	1.39191i	−0.113601	−	0.993526i	$-0.536239\pi$
$577$	19.3036	−	33.4348i	0.803619	−	1.39191i	0.917220	−	0.398382i	$-0.130428\pi$
$578$	−15.5017	+	26.8497i	−0.644785	+	1.11680i
$579$	−12.5383	−	6.15019i	−0.521072	−	0.255593i
$580$	−0.847110	+	13.1256i	−0.0351743	+	0.545010i
$581$		0			0
$582$	38.0108	+	56.6271i	1.57560	+	2.34727i
$583$	−28.1170	+	16.2334i	−1.16449	+	0.672318i
$584$	0.924287	−	1.60091i	0.0382473	−	0.0662462i
$585$	−11.1987	−	16.5715i	−0.463009	−	0.685146i
$586$	−52.1278	+	30.0960i	−2.15338	+	1.24325i
$587$			36.4813i			1.50574i	0.658166	+	0.752872i	$0.271332\pi$
$587$			36.4813i			1.50574i	−0.658166	+	0.752872i	$0.728668\pi$
$588$		0			0
$589$	13.4661			0.554862
$590$	8.61508	+	17.4257i	0.354677	+	0.717404i
$591$	−16.6151	+	1.12437i	−0.683454	+	0.0462503i
$592$	23.6789	+	13.6710i	0.973199	+	0.561877i
$593$	25.5462	−	14.7491i	1.04906	−	0.605673i	0.126672	−	0.991945i	$-0.459571\pi$
$593$	25.5462	−	14.7491i	1.04906	−	0.605673i	0.922385	+	0.386272i	$0.126237\pi$
$594$	−11.0406	−	53.7181i	−0.453000	−	2.20408i
$595$		0			0
$596$			14.2190i			0.582431i
$597$	−17.3536	−	8.51221i	−0.710237	−	0.348381i
$598$	−22.0451	+	38.1832i	−0.901490	+	1.56143i
$599$	29.5321	+	17.0504i	1.20665	+	0.696658i	0.962025	−	0.272960i	$-0.0880026\pi$
$599$	29.5321	+	17.0504i	1.20665	+	0.696658i	0.244622	+	0.969618i	$0.421336\pi$
$600$	−1.79947	+	2.71726i	−0.0734630	+	0.110932i
$601$			26.3724i			1.07575i	0.843023	+	0.537877i	$0.180773\pi$
$601$			26.3724i			1.07575i	−0.843023	+	0.537877i	$0.819227\pi$
$602$		0			0
$603$	15.7068	+	6.42814i	0.639630	+	0.261774i
$604$	12.8333	+	22.2279i	0.522180	+	0.904442i
$605$	−19.3793	+	29.0660i	−0.787880	+	1.18170i
$606$	18.3434	−	1.24133i	0.745151	−	0.0504254i
$607$	−13.0019	−	22.5200i	−0.527732	−	0.914059i	−0.999477	−	0.0323243i	$-0.989709\pi$
$607$	−13.0019	−	22.5200i	−0.527732	−	0.914059i	0.471745	−	0.881735i	$-0.343624\pi$
$608$			25.0997i			1.01793i
$609$		0			0
$610$	1.53586	−	23.7974i	0.0621850	−	0.963528i
$611$	15.6825	−	9.05427i	0.634445	−	0.366297i
$612$	−7.03360	+	5.44458i	−0.284316	+	0.220084i
$613$	32.9089	+	19.0000i	1.32918	+	0.767402i	0.985173	−	0.171565i	$-0.0548824\pi$
$613$	32.9089	+	19.0000i	1.32918	+	0.767402i	0.344007	+	0.938967i	$0.388216\pi$
$614$	−20.1199	−	34.8488i	−0.811975	−	1.40638i
$615$	14.9630	+	25.7311i	0.603368	+	1.03758i
$616$		0			0
$617$	−11.9931			−0.482824			−0.241412	−	0.970423i	$-0.577610\pi$
$617$	−11.9931			−0.482824			−0.241412	+	0.970423i	$0.577610\pi$
$618$	7.27226	−	14.8258i	0.292533	−	0.596381i
$619$	−4.69663	−	2.71160i	−0.188774	−	0.108988i	0.402635	−	0.915361i	$-0.368094\pi$
$619$	−4.69663	−	2.71160i	−0.188774	−	0.108988i	−0.591408	+	0.806372i	$0.701428\pi$
$620$	17.6851	+	11.7912i	0.710251	+	0.473548i
$621$	24.9478	+	28.0854i	1.00112	+	1.12703i
$622$	−15.8822			−0.636817
$623$		0			0
$624$	−10.3561	−	15.4281i	−0.414574	−	0.617618i
$625$	−6.56706	−	24.1221i	−0.262682	−	0.964882i
$626$	15.7390	−	27.2607i	0.629057	−	1.08956i
$627$	−27.5868	+	1.86684i	−1.10171	+	0.0745544i
$628$	−13.1106	−	22.7082i	−0.523169	−	0.906156i
$629$	10.3159			0.411322
$630$		0			0
$631$	−8.33250			−0.331711			−0.165856	−	0.986150i	$-0.553039\pi$
$631$	−8.33250			−0.331711			−0.165856	+	0.986150i	$0.553039\pi$
$632$	−2.24468	−	3.88790i	−0.0892885	−	0.154652i
$633$	2.08588	−	0.141154i	0.0829061	−	0.00561037i
$634$	1.65120	−	2.85996i	0.0655776	−	0.113584i
$635$	−9.01124	+	4.45507i	−0.357600	+	0.176794i
$636$	−13.2658	−	19.7629i	−0.526022	−	0.783648i
$637$		0			0
$638$	−28.4257			−1.12538
$639$	−4.55459	−	33.4981i	−0.180177	−	1.32517i
$640$	−3.71865	+	5.57743i	−0.146993	+	0.220467i
$641$	−17.5189	−	10.1146i	−0.691957	−	0.399501i	0.112388	−	0.993664i	$-0.464150\pi$
$641$	−17.5189	−	10.1146i	−0.691957	−	0.399501i	−0.804345	+	0.594163i	$0.797483\pi$
$642$	1.37278	−	2.79865i	0.0541792	−	0.110454i
$643$	15.2611			0.601838			0.300919	−	0.953650i	$-0.402707\pi$
$643$	15.2611			0.601838			0.300919	+	0.953650i	$0.402707\pi$
$644$		0			0
$645$	26.0849	−	15.1688i	1.02709	−	0.597270i
$646$	4.29565	+	7.44028i	0.169010	+	0.292734i
$647$	1.15882	+	0.669043i	0.0455577	+	0.0263028i	0.522606	−	0.852574i	$-0.324960\pi$
$647$	1.15882	+	0.669043i	0.0455577	+	0.0263028i	−0.477048	+	0.878877i	$0.658293\pi$
$648$	3.26398	−	0.904294i	0.128221	−	0.0355240i
$649$	−18.9912	+	10.9646i	−0.745471	+	0.430398i
$650$	−30.2401	−	3.91965i	−1.18612	−	0.153741i
$651$		0			0
$652$			39.7424i			1.55643i
$653$	−12.3467	−	21.3850i	−0.483162	−	0.836862i	0.516651	−	0.856196i	$-0.327179\pi$
$653$	−12.3467	−	21.3850i	−0.483162	−	0.836862i	−0.999813	+	0.0193346i	$0.993845\pi$
$654$	20.7758	−	1.40593i	0.812400	−	0.0549763i
$655$	−9.48465	+	14.2256i	−0.370596	+	0.555839i
$656$	13.8268	+	23.9487i	0.539845	+	0.935039i
$657$	5.58167	−	13.6385i	0.217762	−	0.532089i
$658$		0			0
$659$		−	26.9484i		−	1.04976i	−0.851176	−	0.524880i	$-0.824110\pi$
$659$		−	26.9484i		−	1.04976i	0.851176	−	0.524880i	$-0.175890\pi$
$660$	−37.8645	−	21.7039i	−1.47387	−	0.844824i
$661$	−20.6311	−	11.9114i	−0.802458	−	0.463300i	0.0418717	−	0.999123i	$-0.486668\pi$
$661$	−20.6311	−	11.9114i	−0.802458	−	0.463300i	−0.844330	+	0.535823i	$0.820001\pi$
$662$	−31.1493	+	53.9521i	−1.21065	+	2.09691i
$663$	−6.29420	−	3.08739i	−0.244446	−	0.119904i
$664$		−	4.57455i		−	0.177527i
$665$		0			0
$666$	−43.1555	−	17.6617i	−1.67224	−	0.684379i
$667$	16.8627	−	9.73570i	0.652927	−	0.376968i
$668$	−39.0442	−	22.5422i	−1.51067	−	0.872183i
$669$	7.44085	−	0.503533i	0.287680	−	0.0194677i
$670$	23.1947	−	11.4672i	0.896091	−	0.443018i
$671$	26.9018			1.03853
$672$		0			0
$673$		−	6.03450i		−	0.232613i	−0.993213	−	0.116307i	$-0.962895\pi$
$673$		−	6.03450i		−	0.232613i	0.993213	−	0.116307i	$-0.0371055\pi$
$674$	−39.9010	+	23.0369i	−1.53693	+	0.887346i
$675$	−11.2959	+	23.3966i	−0.434779	+	0.900537i
$676$	4.48870	−	7.77466i	0.172642	−	0.299025i
$677$	31.8105	−	18.3658i	1.22258	−	0.705854i	0.257109	−	0.966382i	$-0.417230\pi$
$677$	31.8105	−	18.3658i	1.22258	−	0.705854i	0.965466	+	0.260528i	$0.0838967\pi$
$678$	5.93305	+	8.83885i	0.227858	+	0.339454i
$679$		0			0
$680$	−0.0735744	+	1.14000i	−0.00282145	+	0.0437171i
$681$	−6.29444	−	3.08751i	−0.241203	−	0.118314i
$682$	−22.9684	+	39.7825i	−0.879507	+	1.52335i
$683$	10.8878	−	18.8582i	0.416609	−	0.721587i	−0.578987	−	0.815337i	$-0.696552\pi$
$683$	10.8878	−	18.8582i	0.416609	−	0.721587i	0.995596	+	0.0937493i	$0.0298852\pi$
$684$	−2.73102	−	20.0861i	−0.104423	−	0.768013i
$685$	7.16534	+	0.462443i	0.273774	+	0.0176690i
$686$		0			0
$687$	−12.3279	+	8.27508i	−0.470339	+	0.315714i
$688$	24.2780	−	14.0169i	0.925589	−	0.534389i
$689$	9.38031	−	16.2472i	0.357361	−	0.618968i
$690$	57.2727	−	0.178632i	2.18034	−	0.00680039i
$691$	37.6212	−	21.7206i	1.43118	−	0.826292i	0.433968	−	0.900928i	$-0.357113\pi$
$691$	37.6212	−	21.7206i	1.43118	−	0.826292i	0.997211	+	0.0746366i	$0.0237797\pi$
$692$		−	40.2623i		−	1.53054i
$693$		0			0
$694$	25.4694			0.966806
$695$	20.2644	−	10.0185i	0.768673	−	0.380024i
$696$	−0.118529	−	1.75154i	−0.00449284	−	0.0663919i
$697$	9.03559	+	5.21670i	0.342247	+	0.197597i
$698$	−31.8007	+	18.3601i	−1.20367	+	0.694942i
$699$	8.80291	+	13.1143i	0.332957	+	0.496027i
$700$		0			0
$701$			8.07995i			0.305176i	0.988290	+	0.152588i	$0.0487607\pi$
$701$			8.07995i			0.305176i	−0.988290	+	0.152588i	$0.951239\pi$
$702$	21.0453	+	23.6921i	0.794302	+	0.894199i
$703$	−11.7550	+	20.3602i	−0.443347	+	0.767900i
$704$	−41.9943	−	24.2454i	−1.58272	−	0.913784i
$705$	−20.4081	−	11.6979i	−0.768613	−	0.440568i
$706$		−	25.9397i		−	0.976253i
$707$		0			0
$708$	−8.96016	−	13.3485i	−0.336744	−	0.501668i
$709$	10.1372	+	17.5581i	0.380710	+	0.659408i	0.991164	−	0.132643i	$-0.0423464\pi$
$709$	10.1372	+	17.5581i	0.380710	+	0.659408i	−0.610454	+	0.792052i	$0.709013\pi$
$710$	−42.8838	−	28.5920i	−1.60940	−	1.07304i
$711$	−21.9067	−	28.3002i	−0.821564	−	1.06134i
$712$	−1.75390	−	3.03784i	−0.0657301	−	0.113848i
$713$		−	31.4664i		−	1.17843i
$714$		0			0
$715$	2.21549	−	34.3280i	0.0828545	−	1.28379i
$716$	−30.8856	+	17.8318i	−1.15425	+	0.666407i
$717$	2.07607	+	30.6787i	0.0775322	+	1.14572i
$718$	0.128149	+	0.0739871i	0.00478249	+	0.00276117i
$719$	−15.2126	−	26.3490i	−0.567335	−	0.982654i	−0.996828	−	0.0795834i	$-0.974641\pi$
$719$	−15.2126	−	26.3490i	−0.567335	−	0.982654i	0.429493	−	0.903070i	$-0.358692\pi$
$720$	−10.5622	+	21.7038i	−0.393629	+	0.808853i
$721$		0			0
$722$	19.2845			0.717694
$723$	37.3471	+	18.3193i	1.38895	+	0.681301i
$724$	6.73329	+	3.88747i	0.250241	+	0.144477i
$725$	10.7001	+	8.17655i	0.397393	+	0.303669i
$726$	24.3756	−	49.6939i	0.904663	−	1.84431i
$727$	51.1502			1.89706			0.948528	−	0.316692i	$-0.102572\pi$
$727$	51.1502			1.89706			0.948528	+	0.316692i	$0.102572\pi$
$728$		0			0
$729$	24.8114	−	10.6487i	0.918941	−	0.394396i
$730$	−9.95723	−	20.1404i	−0.368533	−	0.745431i
$731$	5.28843	−	9.15983i	0.195600	−	0.338789i
$732$	1.33160	+	19.6775i	0.0492174	+	0.727300i
$733$	−18.2685	−	31.6419i	−0.674761	−	1.16872i	−0.976539	−	0.215342i	$-0.930913\pi$
$733$	−18.2685	−	31.6419i	−0.674761	−	1.16872i	0.301778	−	0.953378i	$-0.402420\pi$
$734$	21.9252			0.809272
$735$		0			0
$736$	58.6508			2.16190
$737$	14.5946	+	25.2786i	0.537599	+	0.931148i
$738$	−28.8680	−	37.2933i	−1.06265	−	1.37279i
$739$	−8.04332	+	13.9314i	−0.295878	+	0.512476i	−0.975189	−	0.221375i	$-0.928946\pi$
$739$	−8.04332	+	13.9314i	−0.295878	+	0.512476i	0.679310	+	0.733851i	$0.262279\pi$
$740$	−33.2657	+	16.4462i	−1.22287	+	0.604576i
$741$	13.2658	−	8.90461i	0.487330	−	0.327119i
$742$		0			0
$743$	27.5407			1.01037			0.505186	−	0.863011i	$-0.331424\pi$
$743$	27.5407			1.01037			0.505186	+	0.863011i	$0.331424\pi$
$744$	−2.54710	−	1.24939i	−0.0933812	−	0.0458048i
$745$	12.1127	+	8.07592i	0.443774	+	0.295879i
$746$	37.8736	+	21.8663i	1.38665	+	0.800583i
$747$	−4.91312	−	36.1350i	−0.179762	−	1.32211i
$748$	−15.2981			−0.559353
$749$		0			0
$750$	15.3454	+	36.5173i	0.560336	+	1.33342i
$751$	19.1381	+	33.1481i	0.698357	+	1.20959i	0.969036	+	0.246921i	$0.0794187\pi$
$751$	19.1381	+	33.1481i	0.698357	+	1.20959i	−0.270678	+	0.962670i	$0.587248\pi$
$752$	−18.9261	−	10.9270i	−0.690165	−	0.398467i
$753$	−15.2201	+	1.02996i	−0.554651	+	0.0375340i
$754$	14.2249	−	8.21276i	0.518041	−	0.299091i
$755$	26.2242	+	1.69248i	0.954397	+	0.0615956i
$756$		0			0
$757$			36.0954i			1.31191i	0.754800	+	0.655955i	$0.227734\pi$
$757$			36.0954i			1.31191i	−0.754800	+	0.655955i	$0.772266\pi$
$758$	−24.8570	−	43.0535i	−0.902845	−	1.56377i
$759$	4.36226	+	64.4624i	0.158340	+	2.33984i
$760$	−2.16616	−	1.44425i	−0.0785747	−	0.0523883i
$761$	−15.1094	−	26.1703i	−0.547716	−	0.948672i	−0.998431	−	0.0560037i	$-0.982164\pi$
$761$	−15.1094	−	26.1703i	−0.547716	−	0.948672i	0.450715	−	0.892668i	$-0.351169\pi$
$762$	13.2242	−	8.87670i	0.479062	−	0.321569i
$763$		0			0
$764$		−	0.718951i		−	0.0260108i
$765$	0.643200	+	9.08406i	0.0232549	+	0.328435i
$766$	13.0852	+	7.55477i	0.472789	+	0.272965i
$767$	6.33579	−	10.9739i	0.228772	−	0.396245i
$768$	−9.65958	+	19.6927i	−0.348560	+	0.710601i
$769$			16.8667i			0.608228i	0.952636	+	0.304114i	$0.0983603\pi$
$769$			16.8667i			0.608228i	−0.952636	+	0.304114i	$0.901640\pi$
$770$		0			0
$771$	16.7292	−	11.2294i	0.602486	−	0.404417i
$772$	15.2501	−	8.80464i	0.548862	−	0.316886i
$773$	−30.8665	−	17.8208i	−1.11019	−	0.640968i	−0.171311	−	0.985217i	$-0.554800\pi$
$773$	−30.8665	−	17.8208i	−1.11019	−	0.640968i	−0.938879	+	0.344248i	$0.888134\pi$
$774$	−37.8061	+	29.2650i	−1.35891	+	1.05191i
$775$	20.0892	−	8.36835i	0.721625	−	0.300600i
$776$	−7.24441			−0.260059
$777$		0			0
$778$			26.3215i			0.943671i
$779$	−20.5921	+	11.8889i	−0.737790	+	0.425963i
$780$	25.2191	−	0.0786574i	0.902987	−	0.00281639i
$781$	29.0720	−	50.3543i	1.04028	−	1.80182i
$782$	17.3858	−	10.0377i	0.621715	−	0.358947i
$783$	−2.81745	−	13.7084i	−0.100687	−	0.489896i
$784$		0			0
$785$	−26.7908	−	1.72905i	−0.956205	−	0.0617124i
$786$	11.9300	−	24.3213i	0.425527	−	0.867513i
$787$	−0.818196	+	1.41716i	−0.0291655	+	0.0505162i	−0.880240	−	0.474529i	$-0.842618\pi$
$787$	−0.818196	+	1.41716i	−0.0291655	+	0.0505162i	0.851074	+	0.525045i	$0.175952\pi$
$788$	10.4991	−	18.1850i	0.374016	−	0.647815i
$789$	−0.747290	+	1.52348i	−0.0266042	+	0.0542374i
$790$	−54.4499	−	3.51414i	−1.93724	−	0.125027i
$791$		0			0
$792$	5.39121	+	2.20640i	0.191568	+	0.0784010i
$793$	−13.4623	+	7.77247i	−0.478061	+	0.276009i
$794$	−16.6160	+	28.7798i	−0.589681	+	1.02136i
$795$	−24.3699	+	0.0760089i	−0.864311	+	0.00269576i
$796$	21.1070	−	12.1861i	0.748116	−	0.431925i
$797$			13.2950i			0.470934i	0.971882	+	0.235467i	$0.0756620\pi$
$797$			13.2950i			0.470934i	−0.971882	+	0.235467i	$0.924338\pi$
$798$		0			0
$799$	−8.24529			−0.291698
$800$	15.5979	+	37.4445i	0.551468	+	1.32386i
$801$	−17.1170	−	22.1126i	−0.604798	−	0.781311i
$802$	−18.1052	−	10.4530i	−0.639317	−	0.369110i
$803$	21.9499	−	12.6728i	0.774594	−	0.447212i
$804$	−17.7678	+	11.9266i	−0.626621	+	0.420618i
$805$		0			0
$806$		−	26.5442i		−	0.934980i
$807$	15.7202	−	32.0483i	0.553376	−	1.12815i
$808$	−0.976453	+	1.69127i	−0.0343515	+	0.0594985i
$809$	−30.7676	−	17.7637i	−1.08173	−	0.624537i	−0.150367	−	0.988630i	$-0.548046\pi$
$809$	−30.7676	−	17.7637i	−1.08173	−	0.624537i	−0.931363	+	0.364093i	$0.881379\pi$
$810$	12.8620	−	39.1035i	0.451924	−	1.37396i
$811$		−	31.4512i		−	1.10440i	−0.833711	−	0.552201i	$-0.813788\pi$
$811$		−	31.4512i		−	1.10440i	0.833711	−	0.552201i	$-0.186212\pi$
$812$		0			0
$813$	−3.73864	+	2.50955i	−0.131120	+	0.0880138i
$814$	−40.0997	−	69.4546i	−1.40549	−	2.43438i
$815$	33.8553	+	22.5725i	1.18590	+	0.790679i
$816$	0.571239	+	8.44136i	0.0199974	+	0.295507i
$817$	12.0524	+	20.8753i	0.421658	+	0.730334i
$818$			37.1578i			1.29919i
$819$		0			0
$820$	−37.4539	−	2.41723i	−1.30795	−	0.0844134i
$821$	−42.4107	+	24.4858i	−1.48014	+	0.854561i	−0.999747	−	0.0224909i	$-0.992840\pi$
$821$	−42.4107	+	24.4858i	−1.48014	+	0.854561i	−0.480396	+	0.877052i	$0.659507\pi$
$822$	−11.3506	+	0.768109i	−0.395896	+	0.0267909i
$823$	33.6438	+	19.4243i	1.17275	+	0.677087i	0.954326	−	0.298767i	$-0.0965754\pi$
$823$	33.6438	+	19.4243i	1.17275	+	0.677087i	0.218423	+	0.975854i	$0.429909\pi$
$824$	0.877027	+	1.51906i	0.0305527	+	0.0529188i
$825$	−39.9948	+	19.9285i	−1.39244	+	0.693820i
$826$		0			0
$827$	44.6506			1.55265			0.776327	−	0.630330i	$-0.217081\pi$
$827$	44.6506			1.55265			0.776327	+	0.630330i	$0.217081\pi$
$828$	−46.9355	+	6.38161i	−1.63112	+	0.221776i
$829$	−36.4907	−	21.0679i	−1.26737	−	0.731719i	−0.292884	−	0.956148i	$-0.594615\pi$
$829$	−36.4907	−	21.0679i	−1.26737	−	0.731719i	−0.974491	+	0.224429i	$0.927948\pi$
$830$	−46.2595	−	30.8427i	−1.60569	−	1.07057i
$831$	−29.7784	−	14.6068i	−1.03300	−	0.506703i
$832$	28.0200			0.971419
$833$		0			0
$834$	−29.7385	+	19.9619i	−1.02976	+	0.691223i
$835$	−41.3789	+	20.4573i	−1.43198	+	0.707954i
$836$	17.4322	−	30.1934i	0.602904	−	1.04426i
$837$	−21.4617	−	7.13349i	−0.741827	−	0.246569i
$838$	−3.46691	−	6.00486i	−0.119762	−	0.207434i
$839$	25.5067			0.880588			0.440294	−	0.897854i	$-0.354874\pi$
$839$	25.5067			0.880588			0.440294	+	0.897854i	$0.354874\pi$
$840$		0			0
$841$	21.7460			0.749863
$842$	5.24080	+	9.07733i	0.180610	+	0.312825i
$843$	−1.73319	−	25.6119i	−0.0596944	−	0.882121i
$844$	−1.31807	+	2.28296i	−0.0453698	+	0.0785829i
$845$	−4.07355	−	8.23955i	−0.140134	−	0.283449i
$846$	34.4934	+	14.1167i	1.18591	+	0.485342i
$847$		0			0
$848$	−22.6410			−0.777494
$849$	−1.74359	+	3.55461i	−0.0598397	+	0.121994i
$850$	11.0321	+	8.43018i	0.378396	+	0.289153i
$851$	47.5760	+	27.4680i	1.63088	+	0.941591i
$852$	38.2710	+	18.7725i	1.31114	+	0.643134i
$853$	6.38527			0.218628			0.109314	−	0.994007i	$-0.465135\pi$
$853$	6.38527			0.218628			0.109314	+	0.994007i	$0.465135\pi$
$854$		0			0
$855$	−18.6619	−	9.08183i	−0.638224	−	0.310592i
$856$	0.165555	+	0.286750i	0.00565857	+	0.00980093i
$857$	48.2820	+	27.8756i	1.64928	+	0.952212i	0.977359	+	0.211590i	$0.0678641\pi$
$857$	48.2820	+	27.8756i	1.64928	+	0.952212i	0.671922	+	0.740622i	$0.265469\pi$
$858$	3.67988	+	54.3787i	0.125629	+	1.85646i
$859$	23.6086	−	13.6304i	0.805514	−	0.465064i	−0.0398813	−	0.999204i	$-0.512698\pi$
$859$	23.6086	−	13.6304i	0.805514	−	0.465064i	0.845396	+	0.534140i	$0.179365\pi$
$860$	−2.45047	+	37.9689i	−0.0835603	+	1.29473i
$861$		0			0
$862$		−	26.8793i		−	0.915513i
$863$	−11.0986	−	19.2234i	−0.377801	−	0.654371i	0.612941	−	0.790129i	$-0.289986\pi$
$863$	−11.0986	−	19.2234i	−0.377801	−	0.654371i	−0.990742	+	0.135758i	$0.956653\pi$
$864$	13.2962	−	40.0029i	0.452346	−	1.36093i
$865$	−34.2982	−	22.8678i	−1.16618	−	0.777527i
$866$	−4.87339	−	8.44095i	−0.165604	−	0.286835i
$867$	−14.6315	−	21.7974i	−0.496910	−	0.740279i
$868$		0			0
$869$		−	61.5529i		−	2.08804i
$870$	−18.5113	−	10.6107i	−0.627593	−	0.359736i
$871$	−14.6070	−	8.43336i	−0.494939	−	0.285753i
$872$	−1.10593	+	1.91553i	−0.0374517	+	0.0648682i
$873$	−57.2246	+	7.78057i	−1.93676	+	0.263332i
$874$			45.7519i			1.54758i
$875$		0			0
$876$	10.3561	+	15.4281i	0.349899	+	0.521267i
$877$	−24.5874	+	14.1955i	−0.830256	+	0.479348i	−0.853940	−	0.520371i	$-0.825794\pi$
$877$	−24.5874	+	14.1955i	−0.830256	+	0.479348i	0.0236844	+	0.999719i	$0.492460\pi$
$878$	50.7141	+	29.2798i	1.71152	+	0.988145i
$879$	−3.44126	−	50.8525i	−0.116071	−	1.71521i
$880$	−37.2147	+	18.3986i	−1.25451	+	0.620215i
$881$	20.0653			0.676017			0.338009	−	0.941143i	$-0.390247\pi$
$881$	20.0653			0.676017			0.338009	+	0.941143i	$0.390247\pi$
$882$		0			0
$883$			31.1643i			1.04876i	0.851484	+	0.524381i	$0.175703\pi$
$883$			31.1643i			1.04876i	−0.851484	+	0.524381i	$0.824297\pi$
$884$	7.65554	−	4.41993i	0.257484	−	0.148658i
$885$	−16.4603	+	0.0513391i	−0.553307	+	0.00172574i
$886$	29.1211	−	50.4392i	0.978341	−	1.69454i
$887$	11.0655	−	6.38865i	0.371542	−	0.214510i	−0.302590	−	0.953121i	$-0.597851\pi$
$887$	11.0655	−	6.38865i	0.371542	−	0.214510i	0.674132	+	0.738611i	$0.264518\pi$
$888$	4.11246	−	2.76048i	0.138005	−	0.0926356i
$889$		0			0
$890$	−42.5449	−	2.74580i	−1.42611	−	0.0920394i
$891$	44.9556	+	11.6384i	1.50607	+	0.389902i
$892$	−4.70189	+	8.14391i	−0.157431	+	0.272678i
$893$	9.39553	−	16.2735i	0.314409	−	0.544573i
$894$	−20.7089	−	10.1580i	−0.692611	−	0.339735i
$895$	−2.35170	+	36.4385i	−0.0786085	+	1.21800i
$896$		0			0
$897$	−20.8075	−	30.9983i	−0.694742	−	1.03500i
$898$	6.29227	−	3.63284i	0.209976	−	0.121230i
$899$	−5.86132	+	10.1521i	−0.195486	+	0.338592i
$900$	−16.5565	−	28.2680i	−0.551883	−	0.942267i
$901$	−7.39776	+	4.27110i	−0.246455	+	0.142291i
$902$		−	81.1129i		−	2.70076i
$903$		0			0
$904$	−1.13077			−0.0376088
$905$	7.13591	−	3.52792i	0.237206	−	0.117272i
$906$	−41.5416	+	2.81118i	−1.38013	+	0.0933952i
$907$	−0.294628	−	0.170103i	−0.00978295	−	0.00564819i	0.495101	−	0.868836i	$-0.335131\pi$
$907$	−0.294628	−	0.170103i	−0.00978295	−	0.00564819i	−0.504884	+	0.863187i	$0.668465\pi$
$908$	7.65583	−	4.42009i	0.254068	−	0.146686i
$909$	−5.89670	+	14.4083i	−0.195581	+	0.477892i
$910$		0			0
$911$			34.4235i			1.14050i	0.821471	+	0.570250i	$0.193154\pi$
$911$			34.4235i			1.14050i	−0.821471	+	0.570250i	$0.806846\pi$
$912$	−17.3114	−	8.49150i	−0.573239	−	0.281182i
$913$	31.3605	−	54.3181i	1.03788	−	1.79767i
$914$	51.7960	+	29.9045i	1.71326	+	0.989152i
$915$	17.5189	+	10.0418i	0.579158	+	0.331973i
$916$		−	18.7218i		−	0.618585i
$917$		0			0
$918$	−2.90484	−	14.1336i	−0.0958741	−	0.466477i
$919$	19.6862	+	34.0974i	0.649386	+	1.12477i	0.983270	+	0.182156i	$0.0583075\pi$
$919$	19.6862	+	34.0974i	0.649386	+	1.12477i	−0.333883	+	0.942614i	$0.608359\pi$
$920$	−3.37479	+	5.06168i	−0.111263	+	0.166879i
$921$	33.9962	−	2.30057i	1.12021	−	0.0758064i
$922$	28.9688	+	50.1754i	0.954037	+	1.65244i
$923$			33.5980i			1.10589i
$924$		0			0
$925$	−4.88386	+	37.6790i	−0.160580	+	1.23888i
$926$	−70.2299	+	40.5473i	−2.30790	+	1.33247i
$927$	8.55924	+	11.0573i	0.281122	+	0.363169i
$928$	−18.9227	−	10.9250i	−0.621167	−	0.358631i
$929$	22.4875	+	38.9495i	0.737791	+	1.27789i	0.953488	+	0.301431i	$0.0974642\pi$
$929$	22.4875	+	38.9495i	0.737791	+	1.27789i	−0.215697	+	0.976460i	$0.569202\pi$
$930$	−29.8074	+	17.3335i	−0.977423	+	0.568388i
$931$		0			0
$932$	−19.9160			−0.652369
$933$	5.92258	−	12.0742i	0.193897	−	0.395292i
$934$	36.3470	+	20.9850i	1.18931	+	0.686649i
$935$	−8.68883	+	13.0320i	−0.284155	+	0.426190i
$936$	−3.33537	+	0.453496i	−0.109020	+	0.0148230i
$937$	30.0270			0.980941			0.490470	−	0.871458i	$-0.336825\pi$
$937$	30.0270			0.980941			0.490470	+	0.871458i	$0.336825\pi$
$938$		0			0
$939$	14.8554	+	22.1311i	0.484789	+	0.722221i
$940$	26.5887	−	13.1452i	0.867227	−	0.428748i
$941$	2.04631	−	3.54431i	0.0667077	−	0.115541i	−0.830743	−	0.556657i	$-0.812084\pi$
$941$	2.04631	−	3.54431i	0.0667077	−	0.115541i	0.897450	+	0.441116i	$0.145417\pi$
$942$	42.4392	−	2.87192i	1.38274	−	0.0935721i
$943$	27.7809	+	48.1179i	0.904670	+	1.56693i
$944$	−15.2925			−0.497728
$945$		0			0
$946$	−82.2282			−2.67347
$947$	−0.875134	−	1.51578i	−0.0284380	−	0.0492561i	0.851456	−	0.524426i	$-0.175720\pi$
$947$	−0.875134	−	1.51578i	−0.0284380	−	0.0492561i	−0.879894	+	0.475170i	$0.842387\pi$
$948$	45.0233	−	3.04679i	1.46229	−	0.0989552i
$949$	−7.32285	+	12.6835i	−0.237710	+	0.411725i
$950$	−29.2095	+	12.1675i	−0.947680	+	0.394765i
$951$	1.55851	+	2.32181i	0.0505380	+	0.0752897i
$952$		0			0
$953$	33.2268			1.07632			0.538161	−	0.842842i	$-0.319119\pi$
$953$	33.2268			1.07632			0.538161	+	0.842842i	$0.319119\pi$
$954$	38.2603	−	5.20208i	1.23872	−	0.168424i
$955$	−0.612453	−	0.408342i	−0.0198185	−	0.0132136i
$956$	−33.5774	−	19.3859i	−1.08597	−	0.626985i
$957$	10.6001	−	21.6103i	0.342654	−	0.698561i
$958$	−13.5385			−0.437409
$959$		0			0
$960$	−18.2972	−	31.4646i	−0.590540	−	1.01552i
$961$	−6.02790	−	10.4406i	−0.194448	−	0.336795i
$962$	40.1337	+	23.1712i	1.29396	+	0.747070i
$963$	1.61572	+	2.08727i	0.0520658	+	0.0672614i
$964$	−45.4247	+	26.2259i	−1.46303	+	0.844680i
$965$	1.16117	−	17.9918i	0.0373794	−	0.579178i
$966$		0			0
$967$			4.20353i			0.135176i	0.997713	+	0.0675882i	$0.0215304\pi$
$967$			4.20353i			0.135176i	−0.997713	+	0.0675882i	$0.978470\pi$
$968$	2.93967	+	5.09166i	0.0944845	+	0.163652i
$969$	−7.25826	+	0.491177i	−0.233169	+	0.0157789i
$970$	−48.8435	+	73.2580i	−1.56827	+	2.35217i
$971$	25.7671	+	44.6300i	0.826907	+	1.43224i	0.900453	+	0.434953i	$0.143235\pi$
$971$	25.7671	+	44.6300i	0.826907	+	1.43224i	−0.0735462	+	0.997292i	$0.523432\pi$
$972$	−6.28776	+	33.4592i	−0.201680	+	1.07320i
$973$		0			0
$974$			40.5821i			1.30033i
$975$	14.2566	−	21.5280i	0.456578	−	0.689448i
$976$	16.2468	+	9.38008i	0.520047	+	0.300249i
$977$	−24.8093	+	42.9710i	−0.793720	+	1.37476i	0.129929	+	0.991523i	$0.458525\pi$
$977$	−24.8093	+	42.9710i	−0.793720	+	1.37476i	−0.923649	+	0.383240i	$0.874808\pi$
$978$	−57.8821	−	28.3920i	−1.85087	−	0.907877i
$979$		−	48.0949i		−	1.53712i
$980$		0			0
$981$	−6.67862	+	16.3189i	−0.213232	+	0.521021i
$982$	−20.6646	+	11.9307i	−0.659433	+	0.380724i
$983$	−18.8016	−	10.8551i	−0.599677	−	0.346224i	0.169238	−	0.985575i	$-0.445869\pi$
$983$	−18.8016	−	10.8551i	−0.599677	−	0.346224i	−0.768914	+	0.639352i	$0.779203\pi$
$984$	4.99803	−	0.338224i	0.159331	−	0.0107822i
$985$	−9.52808	−	19.2724i	−0.303590	−	0.614070i
$986$	−7.47897			−0.238179
$987$		0			0
$988$			20.1461i			0.640931i
$989$	48.7795	−	28.1629i	1.55110	−	0.895527i
$990$	58.6607	−	39.6418i	1.86436	−	1.25990i
$991$	8.17396	−	14.1577i	0.259655	−	0.449735i	−0.706495	−	0.707718i	$-0.749725\pi$
$991$	8.17396	−	14.1577i	0.259655	−	0.449735i	0.966149	+	0.257983i	$0.0830580\pi$
$992$	−30.5797	+	17.6552i	−0.970905	+	0.560553i
$993$	−29.4006	−	43.8000i	−0.933000	−	1.38995i
$994$		0			0
$995$	1.60713	−	24.9017i	0.0509493	−	0.789437i
$996$	41.2836	+	20.2502i	1.30812	+	0.641652i
$997$	−16.4511	+	28.4941i	−0.521010	+	0.902416i	0.478691	+	0.877983i	$0.341111\pi$
$997$	−16.4511	+	28.4941i	−0.521010	+	0.902416i	−0.999701	+	0.0244329i	$0.992222\pi$
$998$	15.2911	−	26.4849i	0.484030	−	0.838365i
$999$	29.5201	−	26.2222i	0.933976	−	0.829635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.g.374.8		64
3.2	odd	2	inner	735.2.p.g.374.26		64
5.4	even	2	inner	735.2.p.g.374.25		64
7.2	even	3	inner	735.2.p.g.509.6		64
7.3	odd	6		735.2.g.c.734.28	yes	32
7.4	even	3		735.2.g.c.734.25	yes	32
7.5	odd	6	inner	735.2.p.g.509.7		64
7.6	odd	2	inner	735.2.p.g.374.5		64
15.14	odd	2	inner	735.2.p.g.374.7		64
21.2	odd	6	inner	735.2.p.g.509.28		64
21.5	even	6	inner	735.2.p.g.509.25		64
21.11	odd	6		735.2.g.c.734.6	yes	32
21.17	even	6		735.2.g.c.734.7	yes	32
21.20	even	2	inner	735.2.p.g.374.27		64
35.4	even	6		735.2.g.c.734.8	yes	32
35.9	even	6	inner	735.2.p.g.509.27		64
35.19	odd	6	inner	735.2.p.g.509.26		64
35.24	odd	6		735.2.g.c.734.5	✓	32
35.34	odd	2	inner	735.2.p.g.374.28		64
105.44	odd	6	inner	735.2.p.g.509.5		64
105.59	even	6		735.2.g.c.734.26	yes	32
105.74	odd	6		735.2.g.c.734.27	yes	32
105.89	even	6	inner	735.2.p.g.509.8		64
105.104	even	2	inner	735.2.p.g.374.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.5	✓	32	35.24	odd	6
735.2.g.c.734.6	yes	32	21.11	odd	6
735.2.g.c.734.7	yes	32	21.17	even	6
735.2.g.c.734.8	yes	32	35.4	even	6
735.2.g.c.734.25	yes	32	7.4	even	3
735.2.g.c.734.26	yes	32	105.59	even	6
735.2.g.c.734.27	yes	32	105.74	odd	6
735.2.g.c.734.28	yes	32	7.3	odd	6
735.2.p.g.374.5		64	7.6	odd	2	inner
735.2.p.g.374.6		64	105.104	even	2	inner
735.2.p.g.374.7		64	15.14	odd	2	inner
735.2.p.g.374.8		64	1.1	even	1	trivial
735.2.p.g.374.25		64	5.4	even	2	inner
735.2.p.g.374.26		64	3.2	odd	2	inner
735.2.p.g.374.27		64	21.20	even	2	inner
735.2.p.g.374.28		64	35.34	odd	2	inner
735.2.p.g.509.5		64	105.44	odd	6	inner
735.2.p.g.509.6		64	7.2	even	3	inner
735.2.p.g.509.7		64	7.5	odd	6	inner
735.2.p.g.509.8		64	105.89	even	6	inner
735.2.p.g.509.25		64	21.5	even	6	inner
735.2.p.g.509.26		64	35.19	odd	6	inner
735.2.p.g.509.27		64	35.9	even	6	inner
735.2.p.g.509.28		64	21.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02274 - 1.77144i) q^{2} +(1.72810 - 0.116943i) q^{3} +(-1.09199 + 1.89138i) q^{4} +(0.990993 + 2.00448i) q^{5} +(-1.97455 - 2.94161i) q^{6} +0.376326 q^{8} +(2.97265 - 0.404178i) q^{9} +(2.53728 - 3.80554i) q^{10} +(4.46847 + 2.57987i) q^{11} +(-1.66588 + 3.39619i) q^{12} -2.98151 q^{13} +(1.94694 + 3.34805i) q^{15} +(1.79910 + 3.11613i) q^{16} +(1.17568 + 0.678781i) q^{17} +(-3.75622 - 4.85249i) q^{18} +(-2.67938 + 1.54694i) q^{19} +(-4.87339 - 0.314523i) q^{20} -10.5542i q^{22} +(3.61476 + 6.26095i) q^{23} +(0.650328 - 0.0440086i) q^{24} +(-3.03586 + 3.97285i) q^{25} +(3.04931 + 5.28156i) q^{26} +(5.08976 - 1.04609i) q^{27} -2.69332i q^{29} +(3.93963 - 6.87306i) q^{30} +(-3.76937 - 2.17625i) q^{31} +(4.05634 - 7.02578i) q^{32} +(8.02366 + 3.93572i) q^{33} -2.77686i q^{34} +(-2.48165 + 6.06377i) q^{36} +(6.58079 - 3.79942i) q^{37} +(5.48062 + 3.16424i) q^{38} +(-5.15235 + 0.348667i) q^{39} +(0.372936 + 0.754337i) q^{40} +7.68540 q^{41} -7.79107i q^{43} +(-9.75905 + 5.63439i) q^{44} +(3.75604 + 5.55807i) q^{45} +(7.39391 - 12.8066i) q^{46} +(-5.25990 + 3.03680i) q^{47} +(3.47342 + 5.17458i) q^{48} +(10.1425 + 1.31465i) q^{50} +(2.11107 + 1.03551i) q^{51} +(3.25578 - 5.63918i) q^{52} +(-3.14616 + 5.44930i) q^{53} +(-7.05858 - 7.94631i) q^{54} +(-0.743074 + 11.5136i) q^{55} +(-4.44934 + 2.98661i) q^{57} +(-4.77104 + 2.75456i) q^{58} +(-2.12502 + 3.68065i) q^{59} +(-8.45847 + 0.0263817i) q^{60} +(4.51526 - 2.60689i) q^{61} +8.90293i q^{62} -9.39791 q^{64} +(-2.95466 - 5.97638i) q^{65} +(-1.23423 - 18.2386i) q^{66} +(4.89919 + 2.82855i) q^{67} +(-2.56767 + 1.48244i) q^{68} +(6.97884 + 10.3968i) q^{69} -11.2688i q^{71} +(1.11868 - 0.152102i) q^{72} +(2.45608 - 4.25406i) q^{73} +(-13.4609 - 7.77163i) q^{74} +(-4.78168 + 7.22050i) q^{75} -6.75699i q^{76} +(5.88715 + 8.77046i) q^{78} +(-5.96472 - 10.3312i) q^{79} +(-4.46331 + 6.69431i) q^{80} +(8.67328 - 2.40296i) q^{81} +(-7.86016 - 13.6142i) q^{82} -12.1558i q^{83} +(-0.195507 + 3.02930i) q^{85} +(-13.8014 + 7.96823i) q^{86} +(-0.314964 - 4.65432i) q^{87} +(1.68160 + 0.970873i) q^{88} +(-4.66058 - 8.07237i) q^{89} +(6.00432 - 12.3380i) q^{90} -15.7891 q^{92} +(-6.76834 - 3.31997i) q^{93} +(10.7590 + 6.21171i) q^{94} +(-5.75607 - 3.83776i) q^{95} +(6.18814 - 12.6156i) q^{96} -19.2504 q^{97} +(14.3259 + 5.86300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) \) 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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