LMFDB - Embedded newform 1040.2.df.a.849.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(49,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.1
Root			$-3.07108i$ of defining polynomial
Character	$\chi$	$=$	1040.849
Dual form			1040.2.df.a.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.65963 - 1.53554i) q^{3} +(-1.36822 + 1.76861i) q^{5} +(1.84755 + 3.20005i) q^{7} +(3.21577 + 5.56988i) q^{9} +(0.924355 + 0.533677i) q^{11} +(-3.15963 - 1.73687i) q^{13} +(6.35473 - 2.60289i) q^{15} +(2.42435 - 1.39970i) q^{17} +(-1.90368 + 1.09909i) q^{19} -11.3479i q^{21} +(-0.979330 - 0.565416i) q^{23} +(-1.25595 - 4.83969i) q^{25} -10.5385i q^{27} +(-1.36822 + 2.36983i) q^{29} -4.20191i q^{31} +(-1.63896 - 2.83877i) q^{33} +(-8.18749 - 1.11078i) q^{35} +(-5.15963 + 8.93675i) q^{37} +(5.73644 + 9.47118i) q^{39} +(4.27662 + 2.46911i) q^{41} +(3.80737 - 2.19819i) q^{43} +(-14.2508 - 1.93338i) q^{45} -10.5582 q^{47} +(-3.32688 + 5.76232i) q^{49} -8.59720 q^{51} +3.81853i q^{53} +(-2.20859 + 0.904635i) q^{55} +6.75081 q^{57} +(3.12664 - 1.80517i) q^{59} +(-7.61068 - 13.1821i) q^{61} +(-11.8826 + 20.5812i) q^{63} +(7.39491 - 3.21174i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.73644 + 3.00760i) q^{69} +(-10.6385 + 6.14216i) q^{71} -1.23397 q^{73} +(-4.09117 + 14.8004i) q^{75} +3.94398i q^{77} -14.2237 q^{79} +(-6.53504 + 11.3190i) q^{81} +8.18235 q^{83} +(-0.841526 + 6.20283i) q^{85} +(7.27793 - 4.20191i) q^{87} +(-7.62533 - 4.40249i) q^{89} +(-0.279516 - 13.3199i) q^{91} +(-6.45221 + 11.1756i) q^{93} +(0.660795 - 4.87067i) q^{95} +(-4.37540 - 7.57842i) q^{97} +6.86472i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{5} + 5 q^{7} + 8 q^{9} + 3 q^{11} - 4 q^{13} + 10 q^{15} + 15 q^{17} - 9 q^{19} - 6 q^{23} + 5 q^{25} - 3 q^{29} + 10 q^{33} - 15 q^{35} - 20 q^{37} + 30 q^{39} + 21 q^{41} + 18 q^{43} - 36 q^{45}+ \cdots + 4 q^{97}+O(q^{100}) $ 8 * q - 3 * q^5 + 5 * q^7 + 8 * q^9 + 3 * q^11 - 4 * q^13 + 10 * q^15 + 15 * q^17 - 9 * q^19 - 6 * q^23 + 5 * q^25 - 3 * q^29 + 10 * q^33 - 15 * q^35 - 20 * q^37 + 30 * q^39 + 21 * q^41 + 18 * q^43 - 36 * q^45 + 6 * q^47 - 15 * q^49 + 20 * q^51 - 31 * q^55 - 24 * q^57 - 30 * q^59 - 5 * q^61 - 25 * q^63 + 21 * q^65 - 16 * q^67 - 2 * q^69 - 26 * q^73 + 24 * q^75 - 4 * q^79 + 8 * q^81 - 48 * q^83 - 29 * q^85 + 12 * q^87 - 39 * q^89 - 19 * q^91 - 18 * q^93 - 15 * q^95 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.65963	−	1.53554i	−1.53554	−	0.886545i	−0.999092	−	0.0426119i	$-0.986432\pi$
$3$	−2.65963	−	1.53554i	−1.53554	−	0.886545i	−0.536449	−	0.843933i	$-0.680235\pi$
$4$		0			0
$5$	−1.36822	+	1.76861i	−0.611886	+	0.790946i
$5$	−1.36822	+	1.76861i	−0.611886	+	0.790946i
$6$		0			0
$7$	1.84755	+	3.20005i	0.698308	+	1.20951i	0.969053	+	0.246854i	$0.0793968\pi$
$7$	1.84755	+	3.20005i	0.698308	+	1.20951i	−0.270745	+	0.962651i	$0.587270\pi$
$8$		0			0
$9$	3.21577	+	5.56988i	1.07192	+	1.85663i
$10$		0			0
$11$	0.924355	+	0.533677i	0.278704	+	0.160910i	0.632836	−	0.774286i	$-0.281891\pi$
$11$	0.924355	+	0.533677i	0.278704	+	0.160910i	−0.354133	+	0.935195i	$0.615224\pi$
$12$		0			0
$13$	−3.15963	−	1.73687i	−0.876325	−	0.481721i
$13$	−3.15963	−	1.73687i	−0.876325	−	0.481721i
$14$		0			0
$15$	6.35473	−	2.60289i	1.64079	−	0.672064i
$16$		0			0
$17$	2.42435	−	1.39970i	0.587992	−	0.339478i	−0.176311	−	0.984335i	$-0.556416\pi$
$17$	2.42435	−	1.39970i	0.587992	−	0.339478i	0.764303	+	0.644857i	$0.223083\pi$
$18$		0			0
$19$	−1.90368	+	1.09909i	−0.436735	+	0.252149i	−0.702212	−	0.711968i	$-0.747804\pi$
$19$	−1.90368	+	1.09909i	−0.436735	+	0.252149i	0.265477	+	0.964117i	$0.414471\pi$
$20$		0			0
$21$		−	11.3479i		−	2.47633i
$22$		0			0
$23$	−0.979330	−	0.565416i	−0.204204	−	0.117897i	0.394411	−	0.918934i	$-0.370949\pi$
$23$	−0.979330	−	0.565416i	−0.204204	−	0.117897i	−0.598615	+	0.801037i	$0.704282\pi$
$24$		0			0
$25$	−1.25595	−	4.83969i	−0.251190	−	0.967938i
$26$		0			0
$27$		−	10.5385i		−	2.02814i
$28$		0			0
$29$	−1.36822	+	2.36983i	−0.254072	+	0.440066i	−0.964643	−	0.263560i	$-0.915103\pi$
$29$	−1.36822	+	2.36983i	−0.254072	+	0.440066i	0.710571	+	0.703625i	$0.248437\pi$
$30$		0			0
$31$		−	4.20191i		−	0.754686i	−0.926074	−	0.377343i	$-0.876838\pi$
$31$		−	4.20191i		−	0.754686i	0.926074	−	0.377343i	$-0.123162\pi$
$32$		0			0
$33$	−1.63896	−	2.83877i	−0.285307	−	0.494166i
$34$		0			0
$35$	−8.18749	−	1.11078i	−1.38394	−	0.187756i
$36$		0			0
$37$	−5.15963	+	8.93675i	−0.848239	+	1.46919i	0.0345400	+	0.999403i	$0.489003\pi$
$37$	−5.15963	+	8.93675i	−0.848239	+	1.46919i	−0.882779	+	0.469789i	$0.844330\pi$
$38$		0			0
$39$	5.73644	+	9.47118i	0.918565	+	1.51660i
$40$		0			0
$41$	4.27662	+	2.46911i	0.667896	+	0.385610i	0.795279	−	0.606244i	$-0.207324\pi$
$41$	4.27662	+	2.46911i	0.667896	+	0.385610i	−0.127383	+	0.991854i	$0.540658\pi$
$42$		0			0
$43$	3.80737	−	2.19819i	0.580618	−	0.335220i	−0.180761	−	0.983527i	$-0.557856\pi$
$43$	3.80737	−	2.19819i	0.580618	−	0.335220i	0.761379	+	0.648307i	$0.224523\pi$
$44$		0			0
$45$	−14.2508	−	1.93338i	−2.12438	−	0.288211i
$46$		0			0
$47$	−10.5582			−1.54007			−0.770034	−	0.638003i	$-0.779761\pi$
$47$	−10.5582			−1.54007			−0.770034	+	0.638003i	$0.779761\pi$
$48$		0			0
$49$	−3.32688	+	5.76232i	−0.475269	+	0.823189i
$50$		0			0
$51$	−8.59720			−1.20385
$52$		0			0
$53$			3.81853i			0.524515i	0.964998	+	0.262258i	$0.0844670\pi$
$53$			3.81853i			0.524515i	−0.964998	+	0.262258i	$0.915533\pi$
$54$		0			0
$55$	−2.20859	+	0.904635i	−0.297806	+	0.121981i
$56$		0			0
$57$	6.75081			0.894166
$58$		0			0
$59$	3.12664	−	1.80517i	0.407054	−	0.235013i	−0.282469	−	0.959276i	$-0.591154\pi$
$59$	3.12664	−	1.80517i	0.407054	−	0.235013i	0.689523	+	0.724264i	$0.257820\pi$
$60$		0			0
$61$	−7.61068	−	13.1821i	−0.974448	−	1.68779i	−0.681744	−	0.731590i	$-0.738778\pi$
$61$	−7.61068	−	13.1821i	−0.974448	−	1.68779i	−0.292704	−	0.956203i	$-0.594555\pi$
$62$		0			0
$63$	−11.8826	+	20.5812i	−1.49707	+	2.59299i
$64$		0			0
$65$	7.39491	−	3.21174i	0.917226	−	0.398367i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$	1.73644	+	3.00760i	0.209043	+	0.362073i
$70$		0			0
$71$	−10.6385	+	6.14216i	−1.26256	+	0.728941i	−0.973570	−	0.228391i	$-0.926654\pi$
$71$	−10.6385	+	6.14216i	−1.26256	+	0.728941i	−0.288993	+	0.957331i	$0.593320\pi$
$72$		0			0
$73$	−1.23397			−0.144425			−0.0722127	−	0.997389i	$-0.523006\pi$
$73$	−1.23397			−0.144425			−0.0722127	+	0.997389i	$0.523006\pi$
$74$		0			0
$75$	−4.09117	+	14.8004i	−0.472408	+	1.70900i
$76$		0			0
$77$			3.94398i			0.449458i
$78$		0			0
$79$	−14.2237			−1.60029			−0.800145	−	0.599807i	$-0.795244\pi$
$79$	−14.2237			−1.60029			−0.800145	+	0.599807i	$0.795244\pi$
$80$		0			0
$81$	−6.53504	+	11.3190i	−0.726115	+	1.25767i
$82$		0			0
$83$	8.18235			0.898129			0.449065	−	0.893499i	$-0.351757\pi$
$83$	8.18235			0.898129			0.449065	+	0.893499i	$0.351757\pi$
$84$		0			0
$85$	−0.841526	+	6.20283i	−0.0912763	+	0.672792i
$86$		0			0
$87$	7.27793	−	4.20191i	0.780276	−	0.450492i
$88$		0			0
$89$	−7.62533	−	4.40249i	−0.808283	−	0.466663i	0.0380761	−	0.999275i	$-0.487877\pi$
$89$	−7.62533	−	4.40249i	−0.808283	−	0.466663i	−0.846359	+	0.532612i	$0.821210\pi$
$90$		0			0
$91$	−0.279516	−	13.3199i	−0.0293012	−	1.39631i
$92$		0			0
$93$	−6.45221	+	11.1756i	−0.669063	+	1.15885i
$94$		0			0
$95$	0.660795	−	4.87067i	0.0677961	−	0.499721i
$96$		0			0
$97$	−4.37540	−	7.57842i	−0.444255	−	0.769472i	0.553745	−	0.832686i	$-0.313198\pi$
$97$	−4.37540	−	7.57842i	−0.444255	−	0.769472i	−0.998000	+	0.0632142i	$0.979865\pi$
$98$		0			0
$99$			6.86472i			0.689931i
$100$		0			0
$101$	−1.29141	+	2.23680i	−0.128501	+	0.222569i	−0.923096	−	0.384570i	$-0.874350\pi$
$101$	−1.29141	+	2.23680i	−0.128501	+	0.222569i	0.794595	+	0.607139i	$0.207683\pi$
$102$		0			0
$103$			3.00760i			0.296348i	0.988961	+	0.148174i	$0.0473395\pi$
$103$			3.00760i			0.296348i	−0.988961	+	0.148174i	$0.952660\pi$
$104$		0			0
$105$	20.0701	+	15.5265i	1.95864	+	1.51523i
$106$		0			0
$107$	−4.74231	−	2.73798i	−0.458457	−	0.264690i	0.252938	−	0.967482i	$-0.418603\pi$
$107$	−4.74231	−	2.73798i	−0.458457	−	0.264690i	−0.711395	+	0.702792i	$0.751936\pi$
$108$		0			0
$109$		−	11.8872i		−	1.13859i	−0.822134	−	0.569294i	$-0.807217\pi$
$109$		−	11.8872i		−	1.13859i	0.822134	−	0.569294i	$-0.192783\pi$
$110$		0			0
$111$	27.4455	−	15.8457i	2.60501	−	1.50400i
$112$		0			0
$113$	−8.02198	+	4.63149i	−0.754644	+	0.435694i	−0.827370	−	0.561658i	$-0.810164\pi$
$113$	−8.02198	+	4.63149i	−0.754644	+	0.435694i	0.0727253	+	0.997352i	$0.476830\pi$
$114$		0			0
$115$	2.33994	−	0.958437i	0.218200	−	0.0893747i
$116$		0			0
$117$	−0.486514	−	23.1841i	−0.0449782	−	2.14337i
$118$		0			0
$119$	8.95823	+	5.17204i	0.821200	+	0.474120i
$120$		0			0
$121$	−4.93038	−	8.53967i	−0.448216	−	0.776333i
$122$		0			0
$123$	−7.58283	−	13.1338i	−0.683721	−	1.18424i
$124$		0			0
$125$	10.2779	+	4.40048i	0.919286	+	0.393591i
$126$		0			0
$127$	−6.41203	−	3.70199i	−0.568976	−	0.328498i	0.187765	−	0.982214i	$-0.439876\pi$
$127$	−6.41203	−	3.70199i	−0.568976	−	0.328498i	−0.756740	+	0.653716i	$0.773209\pi$
$128$		0			0
$129$	−13.5016			−1.18875
$130$		0			0
$131$	7.35829			0.642897			0.321448	−	0.946927i	$-0.395830\pi$
$131$	7.35829			0.642897			0.321448	+	0.946927i	$0.395830\pi$
$132$		0			0
$133$	−7.03430	−	4.06126i	−0.609952	−	0.352156i
$134$		0			0
$135$	18.6385	+	14.4190i	1.60415	+	1.24099i
$136$		0			0
$137$	6.70228	+	11.6087i	0.572615	+	0.991798i	0.996296	+	0.0859866i	$0.0274042\pi$
$137$	6.70228	+	11.6087i	0.572615	+	0.991798i	−0.423682	+	0.905811i	$0.639262\pi$
$138$		0			0
$139$	−5.67914	−	9.83657i	−0.481699	−	0.834327i	0.518081	−	0.855332i	$-0.326647\pi$
$139$	−5.67914	−	9.83657i	−0.481699	−	0.834327i	−0.999779	+	0.0210051i	$0.993313\pi$
$140$		0			0
$141$	28.0809	+	16.2125i	2.36484	+	1.36534i
$142$		0			0
$143$	−1.99370	−	3.29171i	−0.166721	−	0.275266i
$144$		0			0
$145$	−2.31927	−	5.66229i	−0.192605	−	0.470227i
$146$		0			0
$147$	17.6966	−	10.2171i	1.45959	−	0.842694i
$148$		0			0
$149$	6.06332	−	3.50066i	0.496726	−	0.286785i	−0.230634	−	0.973041i	$-0.574080\pi$
$149$	6.06332	−	3.50066i	0.496726	−	0.286785i	0.727361	+	0.686255i	$0.240747\pi$
$150$		0			0
$151$		−	0.194458i		−	0.0158248i	−0.999969	−	0.00791239i	$-0.997481\pi$
$151$		−	0.194458i		−	0.0158248i	0.999969	−	0.00791239i	$-0.00251862\pi$
$152$		0			0
$153$	15.5923	+	9.00224i	1.26057	+	0.727788i
$154$		0			0
$155$	7.43154	+	5.74914i	0.596916	+	0.461782i
$156$		0			0
$157$		−	16.8889i		−	1.34788i	−0.738786	−	0.673940i	$-0.764601\pi$
$157$		−	16.8889i		−	1.34788i	0.738786	−	0.673940i	$-0.235399\pi$
$158$		0			0
$159$	5.86351	−	10.1559i	0.465006	−	0.805414i
$160$		0			0
$161$		−	4.17854i		−	0.329315i
$162$		0			0
$163$	−1.11582	−	1.93267i	−0.0873982	−	0.151378i	0.819012	−	0.573776i	$-0.194522\pi$
$163$	−1.11582	−	1.93267i	−0.0873982	−	0.151378i	−0.906411	+	0.422398i	$0.861189\pi$
$164$		0			0
$165$	7.26313	+	0.985375i	0.565434	+	0.0767113i
$166$		0			0
$167$	1.01951	−	1.76584i	0.0788920	−	0.136645i	−0.823880	−	0.566764i	$-0.808195\pi$
$167$	1.01951	−	1.76584i	0.0788920	−	0.136645i	0.902772	+	0.430119i	$0.141528\pi$
$168$		0			0
$169$	6.96658	+	10.9757i	0.535891	+	0.844287i
$170$		0			0
$171$	−12.2436	−	7.06886i	−0.936293	−	0.540569i
$172$		0			0
$173$	−9.41558	+	5.43609i	−0.715854	+	0.413298i	−0.813225	−	0.581950i	$-0.802290\pi$
$173$	−9.41558	+	5.43609i	−0.715854	+	0.413298i	0.0973711	+	0.995248i	$0.468957\pi$
$174$		0			0
$175$	13.1668	−	12.9607i	0.995318	−	0.979734i
$176$		0			0
$177$	−11.0876			−0.833396
$178$		0			0
$179$	−1.95866	+	3.39250i	−0.146397	+	0.253567i	−0.929893	−	0.367829i	$-0.880101\pi$
$179$	−1.95866	+	3.39250i	−0.146397	+	0.253567i	0.783496	+	0.621397i	$0.213434\pi$
$180$		0			0
$181$	−14.1976			−1.05530			−0.527648	−	0.849463i	$-0.676926\pi$
$181$	−14.1976			−1.05530			−0.527648	+	0.849463i	$0.676926\pi$
$182$		0			0
$183$			46.7460i			3.45557i
$184$		0			0
$185$	−8.74609	−	21.3528i	−0.643026	−	1.56989i
$186$		0			0
$187$	2.98795			0.218501
$188$		0			0
$189$	33.7238	−	19.4705i	2.45305	−	1.41627i
$190$		0			0
$191$	−0.168406	−	0.291687i	−0.0121854	−	0.0211057i	0.859868	−	0.510516i	$-0.170545\pi$
$191$	−0.168406	−	0.291687i	−0.0121854	−	0.0211057i	−0.872054	+	0.489410i	$0.837212\pi$
$192$		0			0
$193$	−3.38259	+	5.85881i	−0.243484	+	0.421727i	−0.961704	−	0.274089i	$-0.911624\pi$
$193$	−3.38259	+	5.85881i	−0.243484	+	0.421727i	0.718220	+	0.695816i	$0.244957\pi$
$194$		0			0
$195$	−24.5995	−	2.81314i	−1.76161	−	0.201453i
$196$		0			0
$197$	−7.46816	+	12.9352i	−0.532085	+	0.921598i	0.467214	+	0.884144i	$0.345258\pi$
$197$	−7.46816	+	12.9352i	−0.532085	+	0.921598i	−0.999298	+	0.0374533i	$0.988075\pi$
$198$		0			0
$199$	−0.151290	−	0.262042i	−0.0107247	−	0.0185757i	0.860613	−	0.509259i	$-0.170080\pi$
$199$	−0.151290	−	0.262042i	−0.0107247	−	0.0185757i	−0.871338	+	0.490683i	$0.836747\pi$
$200$		0			0
$201$	10.6385	−	6.14216i	0.750385	−	0.433235i
$202$		0			0
$203$	−10.1114			−0.709682
$204$		0			0
$205$	−10.2182	+	4.18538i	−0.713673	+	0.292320i
$206$		0			0
$207$		−	7.27299i		−	0.505508i
$208$		0			0
$209$	−2.34624			−0.162293
$210$		0			0
$211$	0.202283	−	0.350365i	0.0139258	−	0.0241201i	−0.858979	−	0.512012i	$-0.828900\pi$
$211$	0.202283	−	0.350365i	0.0139258	−	0.0241201i	0.872904	+	0.487891i	$0.162234\pi$
$212$		0			0
$213$	37.7262			2.58495
$214$		0			0
$215$	−1.32159	+	9.74135i	−0.0901316	+	0.664354i
$216$		0			0
$217$	13.4463	−	7.76324i	0.912797	−	0.527003i
$218$		0			0
$219$	3.28191	+	1.89481i	0.221771	+	0.128040i
$220$		0			0
$221$	−10.0912	+	0.211761i	−0.678806	+	0.0142446i
$222$		0			0
$223$	0.416011	−	0.720552i	0.0278581	−	0.0482517i	−0.851760	−	0.523932i	$-0.824465\pi$
$223$	0.416011	−	0.720552i	0.0278581	−	0.0482517i	0.879618	+	0.475680i	$0.157798\pi$
$224$		0			0
$225$	22.9176	−	22.5588i	1.52784	−	1.50392i
$226$		0			0
$227$	3.88773	+	6.73375i	0.258038	+	0.446934i	0.965716	−	0.259600i	$-0.0835908\pi$
$227$	3.88773	+	6.73375i	0.258038	+	0.446934i	−0.707678	+	0.706535i	$0.750257\pi$
$228$		0			0
$229$			7.73762i			0.511316i	0.966767	+	0.255658i	$0.0822921\pi$
$229$			7.73762i			0.511316i	−0.966767	+	0.255658i	$0.917708\pi$
$230$		0			0
$231$	6.05614	−	10.4895i	0.398464	−	0.690161i
$232$		0			0
$233$		−	6.86070i		−	0.449460i	−0.974421	−	0.224730i	$-0.927850\pi$
$233$		−	6.86070i		−	0.449460i	0.974421	−	0.224730i	$-0.0721500\pi$
$234$		0			0
$235$	14.4459	−	18.6733i	0.942347	−	1.21811i
$236$		0			0
$237$	37.8298	+	21.8410i	2.45731	+	1.41873i
$238$		0			0
$239$		−	22.3277i		−	1.44426i	−0.691757	−	0.722130i	$-0.743163\pi$
$239$		−	22.3277i		−	1.44426i	0.691757	−	0.722130i	$-0.256837\pi$
$240$		0			0
$241$	4.92524	−	2.84359i	0.317262	−	0.183172i	−0.332909	−	0.942959i	$-0.608030\pi$
$241$	4.92524	−	2.84359i	0.317262	−	0.183172i	0.650172	+	0.759787i	$0.274697\pi$
$242$		0			0
$243$	7.38171	−	4.26183i	0.473537	−	0.273397i
$244$		0			0
$245$	−5.63939	−	13.7681i	−0.360287	−	0.879610i
$246$		0			0
$247$	7.92393	−	0.166282i	0.504187	−	0.0105803i
$248$		0			0
$249$	−21.7620	−	12.5643i	−1.37911	−	0.796232i
$250$		0			0
$251$	8.80810	+	15.2561i	0.555963	+	0.962955i	0.997828	+	0.0658740i	$0.0209835\pi$
$251$	8.80810	+	15.2561i	0.555963	+	0.962955i	−0.441865	+	0.897081i	$0.645683\pi$
$252$		0			0
$253$	−0.603499	−	1.04529i	−0.0379417	−	0.0657169i
$254$		0			0
$255$	11.7629	−	15.2051i	0.736619	−	0.952179i
$256$		0			0
$257$	−22.3579	−	12.9084i	−1.39465	−	0.805201i	−0.400824	−	0.916155i	$-0.631276\pi$
$257$	−22.3579	−	12.9084i	−1.39465	−	0.805201i	−0.993826	+	0.110954i	$0.964609\pi$
$258$		0			0
$259$	−38.1307			−2.36933
$260$		0			0
$261$	−17.5995			−1.08938
$262$		0			0
$263$	18.3738	+	10.6081i	1.13298	+	0.654125i	0.944682	−	0.327987i	$-0.106370\pi$
$263$	18.3738	+	10.6081i	1.13298	+	0.654125i	0.188296	+	0.982112i	$0.439704\pi$
$264$		0			0
$265$	−6.75348	−	5.22459i	−0.414863	−	0.320944i
$266$		0			0
$267$	13.5204	+	23.4180i	0.827435	+	1.43316i
$268$		0			0
$269$	7.24478	+	12.5483i	0.441722	+	0.765085i	0.997817	−	0.0660332i	$-0.0210343\pi$
$269$	7.24478	+	12.5483i	0.441722	+	0.765085i	−0.556095	+	0.831119i	$0.687701\pi$
$270$		0			0
$271$	25.1873	+	14.5419i	1.53002	+	0.883357i	0.999360	+	0.0357709i	$0.0113887\pi$
$271$	25.1873	+	14.5419i	1.53002	+	0.883357i	0.530659	+	0.847586i	$0.321945\pi$
$272$		0			0
$273$	−19.7099	+	35.8554i	−1.19290	+	2.17007i
$274$		0			0
$275$	1.42189	−	5.14386i	0.0857429	−	0.310187i
$276$		0			0
$277$	2.20097	−	1.27073i	0.132244	−	0.0763510i	−0.432419	−	0.901673i	$-0.642340\pi$
$277$	2.20097	−	1.27073i	0.132244	−	0.0763510i	0.564662	+	0.825322i	$0.309006\pi$
$278$		0			0
$279$	23.4041	−	13.5124i	1.40117	−	0.808965i
$280$		0			0
$281$		−	15.2066i		−	0.907149i	−0.891218	−	0.453574i	$-0.850149\pi$
$281$		−	15.2066i		−	0.907149i	0.891218	−	0.453574i	$-0.149851\pi$
$282$		0			0
$283$	−21.4706	−	12.3960i	−1.27629	−	0.736868i	−0.300128	−	0.953899i	$-0.597029\pi$
$283$	−21.4706	−	12.3960i	−1.27629	−	0.736868i	−0.976165	+	0.217031i	$0.930363\pi$
$284$		0			0
$285$	−9.23659	+	11.9395i	−0.547128	+	0.707237i
$286$		0			0
$287$			18.2472i			1.07710i
$288$		0			0
$289$	−4.58167	+	7.93568i	−0.269510	+	0.466805i
$290$		0			0
$291$			26.8744i			1.57541i
$292$		0			0
$293$	10.5315	+	18.2411i	0.615256	+	1.06565i	0.990340	+	0.138663i	$0.0442806\pi$
$293$	10.5315	+	18.2411i	0.615256	+	1.06565i	−0.375084	+	0.926991i	$0.622386\pi$
$294$		0			0
$295$	−1.08530	+	7.99966i	−0.0631885	+	0.465758i
$296$		0			0
$297$	5.62417	−	9.74135i	0.326347	−	0.565250i
$298$		0			0
$299$	2.11227	+	3.48748i	0.122156	+	0.201686i
$300$		0			0
$301$	14.0686	+	8.12252i	0.810901	+	0.468174i
$302$		0			0
$303$	6.86938	−	3.96604i	0.394636	−	0.227843i
$304$		0			0
$305$	33.7270	+	4.57568i	1.93120	+	0.262003i
$306$		0			0
$307$	8.89181			0.507483			0.253741	−	0.967272i	$-0.418339\pi$
$307$	8.89181			0.507483			0.253741	+	0.967272i	$0.418339\pi$
$308$		0			0
$309$	4.61829	−	7.99912i	0.262726	−	0.455054i
$310$		0			0
$311$	−28.7015			−1.62751			−0.813756	−	0.581206i	$-0.802581\pi$
$311$	−28.7015			−1.62751			−0.813756	+	0.581206i	$0.802581\pi$
$312$		0			0
$313$		−	7.84120i		−	0.443211i	−0.975136	−	0.221606i	$-0.928870\pi$
$313$		−	7.84120i		−	0.443211i	0.975136	−	0.221606i	$-0.0711297\pi$
$314$		0			0
$315$	−20.1422	−	49.1753i	−1.13488	−	2.77071i
$316$		0			0
$317$	6.17741			0.346958			0.173479	−	0.984838i	$-0.444499\pi$
$317$	6.17741			0.346958			0.173479	+	0.984838i	$0.444499\pi$
$318$		0			0
$319$	−2.52944	+	1.46037i	−0.141622	+	0.0817652i
$320$		0			0
$321$	8.40855	+	14.5640i	0.469319	+	0.812885i
$322$		0			0
$323$	−3.07681	+	5.32918i	−0.171198	+	0.296524i
$324$		0			0
$325$	−4.43756	+	17.4731i	−0.246152	+	0.969231i
$326$		0			0
$327$	−18.2533	+	31.6156i	−1.00941	+	1.74835i
$328$		0			0
$329$	−19.5068	−	33.7867i	−1.07544	−	1.86272i
$330$		0			0
$331$	−23.0853	+	13.3283i	−1.26888	+	0.732590i	−0.974777	−	0.223183i	$-0.928355\pi$
$331$	−23.0853	+	13.3283i	−1.26888	+	0.732590i	−0.294106	+	0.955773i	$0.595022\pi$
$332$		0			0
$333$	−66.3688			−3.63699
$334$		0			0
$335$	−3.39020	−	8.27687i	−0.185226	−	0.452214i
$336$		0			0
$337$			22.4283i			1.22175i	0.791728	+	0.610874i	$0.209182\pi$
$337$			22.4283i			1.22175i	−0.791728	+	0.610874i	$0.790818\pi$
$338$		0			0
$339$	28.4474			1.54505
$340$		0			0
$341$	2.24246	−	3.88406i	0.121436	−	0.210334i
$342$		0			0
$343$	1.27939			0.0690808
$344$		0			0
$345$	−7.69510	−	1.04398i	−0.414290	−	0.0562059i
$346$		0			0
$347$	0.357054	−	0.206145i	0.0191677	−	0.0110665i	−0.490386	−	0.871506i	$-0.663144\pi$
$347$	0.357054	−	0.206145i	0.0191677	−	0.0110665i	0.509553	+	0.860439i	$0.329811\pi$
$348$		0			0
$349$	2.89360	+	1.67062i	0.154891	+	0.0894264i	0.575442	−	0.817842i	$-0.304830\pi$
$349$	2.89360	+	1.67062i	0.154891	+	0.0894264i	−0.420551	+	0.907269i	$0.638163\pi$
$350$		0			0
$351$	−18.3040	+	33.2979i	−0.976998	+	1.77731i
$352$		0			0
$353$	−10.5604	+	18.2912i	−0.562075	+	0.973542i	0.435241	+	0.900314i	$0.356663\pi$
$353$	−10.5604	+	18.2912i	−0.562075	+	0.973542i	−0.997315	+	0.0732276i	$0.976670\pi$
$354$		0			0
$355$	3.69278	−	27.2192i	0.195992	−	1.44465i
$356$		0			0
$357$	−15.8837	−	27.5115i	−0.840657	−	1.45606i
$358$		0			0
$359$			5.57954i			0.294477i	0.989101	+	0.147238i	$0.0470384\pi$
$359$			5.57954i			0.294477i	−0.989101	+	0.147238i	$0.952962\pi$
$360$		0			0
$361$	−7.08399	+	12.2698i	−0.372842	+	0.645780i
$362$		0			0
$363$			30.2832i			1.58945i
$364$		0			0
$365$	1.68834	−	2.18241i	0.0883719	−	0.114233i
$366$		0			0
$367$	1.12749	+	0.650958i	0.0588546	+	0.0339797i	0.529139	−	0.848535i	$-0.322515\pi$
$367$	1.12749	+	0.650958i	0.0588546	+	0.0339797i	−0.470284	+	0.882515i	$0.655848\pi$
$368$		0			0
$369$			31.7603i			1.65338i
$370$		0			0
$371$	−12.2195	+	7.05492i	−0.634404	+	0.366273i
$372$		0			0
$373$	29.4424	−	16.9986i	1.52447	−	0.880152i	0.524889	−	0.851171i	$-0.324107\pi$
$373$	29.4424	−	16.9986i	1.52447	−	0.880152i	0.999580	−	0.0289815i	$-0.00922638\pi$
$374$		0			0
$375$	−20.5784	−	27.4858i	−1.06267	−	1.41936i
$376$		0			0
$377$	8.43915	−	5.11137i	0.434638	−	0.263249i
$378$		0			0
$379$	−4.05099	−	2.33884i	−0.208086	−	0.120138i	0.392336	−	0.919822i	$-0.371667\pi$
$379$	−4.05099	−	2.33884i	−0.208086	−	0.120138i	−0.600421	+	0.799684i	$0.705000\pi$
$380$		0			0
$381$	11.3691	+	19.6919i	0.582457	+	1.00884i
$382$		0			0
$383$	−6.86938	−	11.8981i	−0.351009	−	0.607965i	0.635418	−	0.772169i	$-0.280828\pi$
$383$	−6.86938	−	11.8981i	−0.351009	−	0.607965i	−0.986427	+	0.164203i	$0.947495\pi$
$384$		0			0
$385$	−6.97535	−	5.39623i	−0.355497	−	0.275017i
$386$		0			0
$387$	24.4872	+	14.1377i	1.24476	+	0.718661i
$388$		0			0
$389$	17.9138			0.908268			0.454134	−	0.890933i	$-0.349949\pi$
$389$	17.9138			0.908268			0.454134	+	0.890933i	$0.349949\pi$
$390$		0			0
$391$	−3.16566			−0.160094
$392$		0			0
$393$	−19.5704	−	11.2989i	−0.987194	−	0.569957i
$394$		0			0
$395$	19.4611	−	25.1561i	0.979196	−	1.26574i
$396$		0			0
$397$	−0.229256	−	0.397082i	−0.0115060	−	0.0199290i	0.860215	−	0.509931i	$-0.170329\pi$
$397$	−0.229256	−	0.397082i	−0.0115060	−	0.0199290i	−0.871721	+	0.490002i	$0.836996\pi$
$398$		0			0
$399$	12.4725	+	21.6029i	0.624404	+	1.08150i
$400$		0			0
$401$	22.5646	+	13.0277i	1.12682	+	0.650572i	0.943134	−	0.332412i	$-0.107863\pi$
$401$	22.5646	+	13.0277i	1.12682	+	0.650572i	0.183690	+	0.982984i	$0.441196\pi$
$402$		0			0
$403$	−7.29817	+	13.2765i	−0.363548	+	0.661350i
$404$		0			0
$405$	−11.0775	−	27.0448i	−0.550447	−	1.34387i
$406$		0			0
$407$	−9.53867	+	5.50715i	−0.472814	+	0.272979i
$408$		0			0
$409$	0.310497	−	0.179266i	0.0153531	−	0.00886411i	−0.492304	−	0.870423i	$-0.663845\pi$
$409$	0.310497	−	0.179266i	0.0153531	−	0.00886411i	0.507657	+	0.861559i	$0.330512\pi$
$410$		0			0
$411$		−	41.1665i		−	2.03059i
$412$		0			0
$413$	11.5532	+	6.67027i	0.568498	+	0.328222i
$414$		0			0
$415$	−11.1952	+	14.4714i	−0.549553	+	0.710371i
$416$		0			0
$417$			34.8822i			1.70819i
$418$		0			0
$419$	9.65921	−	16.7302i	0.471883	−	0.817326i	−0.527599	−	0.849493i	$-0.676908\pi$
$419$	9.65921	−	16.7302i	0.471883	−	0.817326i	0.999482	+	0.0321678i	$0.0102411\pi$
$420$		0			0
$421$		−	0.220426i		−	0.0107429i	−0.999986	−	0.00537144i	$-0.998290\pi$
$421$		−	0.220426i		−	0.0107429i	0.999986	−	0.00537144i	$-0.00170979\pi$
$422$		0			0
$423$	−33.9527	−	58.8077i	−1.65083	−	2.85933i
$424$		0			0
$425$	−9.81899	−	9.97517i	−0.476291	−	0.483867i
$426$		0			0
$427$	28.1222	−	48.7091i	1.36093	−	2.35720i
$428$		0			0
$429$	0.247959	+	11.8161i	0.0119716	+	0.570488i
$430$		0			0
$431$	17.2942	+	9.98480i	0.833032	+	0.480951i	0.854890	−	0.518810i	$-0.173625\pi$
$431$	17.2942	+	9.98480i	0.833032	+	0.480951i	−0.0218578	+	0.999761i	$0.506958\pi$
$432$		0			0
$433$	27.2066	−	15.7078i	1.30747	−	0.754867i	0.325795	−	0.945440i	$-0.394368\pi$
$433$	27.2066	−	15.7078i	1.30747	−	0.754867i	0.981673	+	0.190573i	$0.0610347\pi$
$434$		0			0
$435$	−2.52627	+	18.6209i	−0.121125	+	0.892806i
$436$		0			0
$437$	2.48578			0.118911
$438$		0			0
$439$	−12.8069	+	22.1823i	−0.611242	+	1.05870i	0.379789	+	0.925073i	$0.375996\pi$
$439$	−12.8069	+	22.1823i	−0.611242	+	1.05870i	−0.991031	+	0.133629i	$0.957337\pi$
$440$		0			0
$441$	−42.7939			−2.03781
$442$		0			0
$443$			28.4024i			1.34944i	0.738074	+	0.674719i	$0.235735\pi$
$443$			28.4024i			1.34944i	−0.738074	+	0.674719i	$0.764265\pi$
$444$		0			0
$445$	18.2194	−	7.46265i	0.863682	−	0.353764i
$446$		0			0
$447$	−21.5016			−1.01699
$448$		0			0
$449$	−19.4178	+	11.2109i	−0.916381	+	0.529073i	−0.882479	−	0.470352i	$-0.844127\pi$
$449$	−19.4178	+	11.2109i	−0.916381	+	0.529073i	−0.0339026	+	0.999425i	$0.510794\pi$
$450$		0			0
$451$	2.63541	+	4.56466i	0.124097	+	0.214942i
$452$		0			0
$453$	−0.298598	+	0.517187i	−0.0140294	+	0.0242996i
$454$		0			0
$455$	23.9402	+	17.7302i	1.12233	+	0.831207i
$456$		0			0
$457$	11.7993	−	20.4370i	0.551949	−	0.956004i	−0.446184	−	0.894941i	$-0.647217\pi$
$457$	11.7993	−	20.4370i	0.551949	−	0.956004i	0.998134	−	0.0610635i	$-0.0194492\pi$
$458$		0			0
$459$	−14.7508	−	25.5491i	−0.688509	−	1.19253i
$460$		0			0
$461$	−28.1513	+	16.2532i	−1.31114	+	0.756986i	−0.982285	−	0.187396i	$-0.939995\pi$
$461$	−28.1513	+	16.2532i	−1.31114	+	0.756986i	−0.328853	+	0.944381i	$0.606662\pi$
$462$		0			0
$463$	−7.70367			−0.358020			−0.179010	−	0.983847i	$-0.557289\pi$
$463$	−7.70367			−0.358020			−0.179010	+	0.983847i	$0.557289\pi$
$464$		0			0
$465$	−10.9371	−	26.7020i	−0.507197	−	1.23828i
$466$		0			0
$467$		−	20.9339i		−	0.968704i	−0.874873	−	0.484352i	$-0.839055\pi$
$467$		−	20.9339i		−	0.968704i	0.874873	−	0.484352i	$-0.160945\pi$
$468$		0			0
$469$	−14.7804			−0.682495
$470$		0			0
$471$	−25.9336	+	44.9183i	−1.19496	+	2.06973i
$472$		0			0
$473$	4.69248			0.215761
$474$		0			0
$475$	7.71020	+	7.83284i	0.353768	+	0.359395i
$476$		0			0
$477$	−21.2687	+	12.2795i	−0.973828	+	0.562240i
$478$		0			0
$479$	0.849137	+	0.490250i	0.0387981	+	0.0224001i	0.519274	−	0.854608i	$-0.326203\pi$
$479$	0.849137	+	0.490250i	0.0387981	+	0.0224001i	−0.480476	+	0.877008i	$0.659536\pi$
$480$		0			0
$481$	31.8245	−	19.2753i	1.45107	−	0.878876i
$482$		0			0
$483$	−6.41632	+	11.1134i	−0.291953	+	0.505677i
$484$		0			0
$485$	19.3898	+	2.63057i	0.880444	+	0.119448i
$486$		0			0
$487$	−19.3141	−	33.4530i	−0.875207	−	1.51590i	−0.856542	−	0.516077i	$-0.827392\pi$
$487$	−19.3141	−	33.4530i	−0.875207	−	1.51590i	−0.0186641	−	0.999826i	$-0.505941\pi$
$488$		0			0
$489$			6.85358i			0.309929i
$490$		0			0
$491$	8.85342	−	15.3346i	0.399549	−	0.692040i	−0.594121	−	0.804376i	$-0.702500\pi$
$491$	8.85342	−	15.3346i	0.399549	−	0.692040i	0.993670	+	0.112336i	$0.0358332\pi$
$492$		0			0
$493$			7.66040i			0.345007i
$494$		0			0
$495$	−12.1410	−	9.39245i	−0.545698	−	0.422159i
$496$		0			0
$497$	−39.3105	−	22.6959i	−1.76331	−	1.01805i
$498$		0			0
$499$			35.5402i			1.59100i	0.605954	+	0.795499i	$0.292791\pi$
$499$			35.5402i			1.59100i	−0.605954	+	0.795499i	$0.707209\pi$
$500$		0			0
$501$	−5.42305	+	3.13100i	−0.242284	+	0.139883i
$502$		0			0
$503$	38.4376	−	22.1920i	1.71385	−	0.989490i	0.784624	−	0.619972i	$-0.212856\pi$
$503$	38.4376	−	22.1920i	1.71385	−	0.989490i	0.929223	−	0.369518i	$-0.120477\pi$
$504$		0			0
$505$	−2.18908	−	5.34443i	−0.0974126	−	0.237824i
$506$		0			0
$507$	−1.67486	−	39.8889i	−0.0743830	−	1.77153i
$508$		0			0
$509$	0.620030	+	0.357975i	0.0274824	+	0.0158669i	0.513678	−	0.857983i	$-0.328283\pi$
$509$	0.620030	+	0.357975i	0.0274824	+	0.0158669i	−0.486196	+	0.873850i	$0.661616\pi$
$510$		0			0
$511$	−2.27982	−	3.94877i	−0.100853	−	0.174683i
$512$		0			0
$513$	11.5828	+	20.0620i	0.511394	+	0.885761i
$514$		0			0
$515$	−5.31927	−	4.11506i	−0.234395	−	0.181331i
$516$		0			0
$517$	−9.75950	−	5.63465i	−0.429222	−	0.247812i
$518$		0			0
$519$	33.3893			1.46563
$520$		0			0
$521$	7.33132			0.321191			0.160595	−	0.987020i	$-0.448659\pi$
$521$	7.33132			0.321191			0.160595	+	0.987020i	$0.448659\pi$
$522$		0			0
$523$	−10.2946	−	5.94360i	−0.450152	−	0.259895i	0.257742	−	0.966214i	$-0.417021\pi$
$523$	−10.2946	−	5.94360i	−0.450152	−	0.259895i	−0.707894	+	0.706318i	$0.750355\pi$
$524$		0			0
$525$	−54.9205	+	14.2524i	−2.39693	+	0.622028i
$526$		0			0
$527$	−5.88143	−	10.1869i	−0.256199	−	0.443750i
$528$		0			0
$529$	−10.8606	−	18.8111i	−0.472200	−	0.817875i
$530$		0			0
$531$	20.1091	+	11.6100i	0.872660	+	0.503831i
$532$		0			0
$533$	−9.22404	−	15.2294i	−0.399537	−	0.659659i
$534$		0			0
$535$	11.3309	−	4.64114i	0.489879	−	0.200654i
$536$		0			0
$537$	10.4186	−	6.01520i	0.449597	−	0.259575i
$538$		0			0
$539$	−6.15044	+	3.55096i	−0.264918	+	0.152950i
$540$		0			0
$541$			20.5115i			0.881856i	0.897542	+	0.440928i	$0.145351\pi$
$541$			20.5115i			0.881856i	−0.897542	+	0.440928i	$0.854649\pi$
$542$		0			0
$543$	37.7603	+	21.8009i	1.62045	+	0.935568i
$544$		0			0
$545$	21.0238	+	16.2643i	0.900561	+	0.696686i
$546$		0			0
$547$		−	16.4268i		−	0.702358i	−0.936308	−	0.351179i	$-0.885781\pi$
$547$		−	16.4268i		−	0.702358i	0.936308	−	0.351179i	$-0.114219\pi$
$548$		0			0
$549$	48.9484	−	84.7811i	2.08907	−	3.61837i
$550$		0			0
$551$		−	6.01520i		−	0.256256i
$552$		0			0
$553$	−26.2790	−	45.5165i	−1.11750	−	1.93556i
$554$		0			0
$555$	−9.52669	+	70.2206i	−0.404386	+	2.98070i
$556$		0			0
$557$	18.0730	−	31.3033i	0.765776	−	1.32636i	−0.174059	−	0.984735i	$-0.555688\pi$
$557$	18.0730	−	31.3033i	0.765776	−	1.32636i	0.939835	−	0.341628i	$-0.110978\pi$
$558$		0			0
$559$	−15.8479	+	0.332564i	−0.670293	+	0.0140659i
$560$		0			0
$561$	−7.94686	−	4.58812i	−0.335517	−	0.193711i
$562$		0			0
$563$	−23.0018	+	13.2801i	−0.969409	+	0.559688i	−0.899056	−	0.437834i	$-0.855746\pi$
$563$	−23.0018	+	13.2801i	−0.969409	+	0.559688i	−0.0703528	+	0.997522i	$0.522413\pi$
$564$		0			0
$565$	2.78454	−	20.5246i	0.117146	−	0.863478i
$566$		0			0
$567$	−48.2952			−2.02821
$568$		0			0
$569$	−21.5921	+	37.3985i	−0.905186	+	1.56783i	−0.0845187	+	0.996422i	$0.526935\pi$
$569$	−21.5921	+	37.3985i	−0.905186	+	1.56783i	−0.820667	+	0.571406i	$0.806398\pi$
$570$		0			0
$571$	31.5110			1.31870			0.659348	−	0.751838i	$-0.270832\pi$
$571$	31.5110			1.31870			0.659348	+	0.751838i	$0.270832\pi$
$572$		0			0
$573$			1.03437i			0.0432116i
$574$		0			0
$575$	−1.50645	+	5.44979i	−0.0628233	+	0.227272i
$576$		0			0
$577$	−26.9555			−1.12217			−0.561086	−	0.827758i	$-0.689616\pi$
$577$	−26.9555			−1.12217			−0.561086	+	0.827758i	$0.689616\pi$
$578$		0			0
$579$	17.9929	−	10.3882i	0.747759	−	0.431719i
$580$		0			0
$581$	15.1173	+	26.1839i	0.627171	+	1.08629i
$582$		0			0
$583$	−2.03786	+	3.52968i	−0.0843995	+	0.146184i
$584$		0			0
$585$	41.6693	+	30.8605i	1.72281	+	1.27593i
$586$		0			0
$587$	−14.8631	+	25.7436i	−0.613465	+	1.06255i	0.377187	+	0.926137i	$0.376891\pi$
$587$	−14.8631	+	25.7436i	−0.613465	+	1.06255i	−0.990652	+	0.136415i	$0.956442\pi$
$588$		0			0
$589$	4.61829	+	7.99912i	0.190293	+	0.329598i
$590$		0			0
$591$	39.7252	−	22.9353i	1.63408	−	0.943434i
$592$		0			0
$593$	15.3561			0.630600			0.315300	−	0.948992i	$-0.397895\pi$
$593$	15.3561			0.630600			0.315300	+	0.948992i	$0.397895\pi$
$594$		0			0
$595$	−21.4041	+	8.76712i	−0.877484	+	0.359417i
$596$		0			0
$597$			0.929248i			0.0380316i
$598$		0			0
$599$	−23.6928			−0.968061			−0.484030	−	0.875051i	$-0.660828\pi$
$599$	−23.6928			−0.968061			−0.484030	+	0.875051i	$0.660828\pi$
$600$		0			0
$601$	1.74834	−	3.02821i	0.0713162	−	0.123523i	−0.828162	−	0.560489i	$-0.810613\pi$
$601$	1.74834	−	3.02821i	0.0713162	−	0.123523i	0.899478	+	0.436965i	$0.143947\pi$
$602$		0			0
$603$	−25.7262			−1.04765
$604$		0			0
$605$	21.8492	+	2.96423i	0.888295	+	0.120513i
$606$		0			0
$607$	−32.3012	+	18.6491i	−1.31107	+	0.756944i	−0.982273	−	0.187457i	$-0.939975\pi$
$607$	−32.3012	+	18.6491i	−1.31107	+	0.756944i	−0.328794	+	0.944402i	$0.606642\pi$
$608$		0			0
$609$	26.8927	+	15.5265i	1.08975	+	0.629165i
$610$		0			0
$611$	33.3600	+	18.3382i	1.34960	+	0.741883i
$612$		0			0
$613$	−7.66210	+	13.2712i	−0.309469	+	0.536017i	−0.978246	−	0.207446i	$-0.933485\pi$
$613$	−7.66210	+	13.2712i	−0.309469	+	0.536017i	0.668777	+	0.743463i	$0.266818\pi$
$614$		0			0
$615$	33.6036	+	4.55893i	1.35503	+	0.183834i
$616$		0			0
$617$	2.53620	+	4.39282i	0.102103	+	0.176848i	0.912551	−	0.408963i	$-0.134109\pi$
$617$	2.53620	+	4.39282i	0.102103	+	0.176848i	−0.810448	+	0.585811i	$0.800776\pi$
$618$		0			0
$619$			20.6770i			0.831079i	0.909575	+	0.415540i	$0.136407\pi$
$619$			20.6770i			0.831079i	−0.909575	+	0.415540i	$0.863593\pi$
$620$		0			0
$621$	−5.95866	+	10.3207i	−0.239113	+	0.414155i
$622$		0			0
$623$		−	32.5352i		−	1.30350i
$624$		0			0
$625$	−21.8452	+	12.1568i	−0.873807	+	0.486272i
$626$		0			0
$627$	6.24014	+	3.60275i	0.249207	+	0.143880i
$628$		0			0
$629$			28.8878i			1.15183i
$630$		0			0
$631$	18.6113	−	10.7452i	0.740903	−	0.427760i	−0.0814946	−	0.996674i	$-0.525969\pi$
$631$	18.6113	−	10.7452i	0.740903	−	0.427760i	0.822397	+	0.568913i	$0.192636\pi$
$632$		0			0
$633$	−1.07600	+	0.621228i	−0.0427671	+	0.0246916i
$634$		0			0
$635$	15.3204	−	6.27524i	0.607973	−	0.249025i
$636$		0			0
$637$	20.5201	−	12.4285i	0.813037	−	0.492435i
$638$		0			0
$639$	−68.4222	−	39.5036i	−2.70674	−	1.56274i
$640$		0			0
$641$	17.8862	+	30.9798i	0.706463	+	1.22363i	0.966161	+	0.257940i	$0.0830437\pi$
$641$	17.8862	+	30.9798i	0.706463	+	1.22363i	−0.259698	+	0.965690i	$0.583623\pi$
$642$		0			0
$643$	14.0108	+	24.2674i	0.552533	+	0.957014i	0.998091	+	0.0617616i	$0.0196718\pi$
$643$	14.0108	+	24.2674i	0.552533	+	0.957014i	−0.445558	+	0.895253i	$0.646995\pi$
$644$		0			0
$645$	18.4732	−	23.8791i	0.727381	−	0.940237i
$646$		0			0
$647$	16.8548	+	9.73113i	0.662631	+	0.382570i	0.793279	−	0.608859i	$-0.208372\pi$
$647$	16.8548	+	9.73113i	0.662631	+	0.382570i	−0.130648	+	0.991429i	$0.541706\pi$
$648$		0			0
$649$	3.85350			0.151263
$650$		0			0
$651$	−47.6831			−1.86885
$652$		0			0
$653$	11.2261	+	6.48138i	0.439310	+	0.253636i	0.703305	−	0.710888i	$-0.251707\pi$
$653$	11.2261	+	6.48138i	0.439310	+	0.253636i	−0.263995	+	0.964524i	$0.585040\pi$
$654$		0			0
$655$	−10.0678	+	13.0139i	−0.393380	+	0.508496i
$656$		0			0
$657$	−3.96816	−	6.87306i	−0.154813	−	0.268144i
$658$		0			0
$659$	−1.10335	−	1.91106i	−0.0429804	−	0.0744443i	0.843735	−	0.536760i	$-0.180352\pi$
$659$	−1.10335	−	1.91106i	−0.0429804	−	0.0744443i	−0.886715	+	0.462316i	$0.847019\pi$
$660$		0			0
$661$	−37.7080	−	21.7707i	−1.46667	−	0.846784i	−0.467367	−	0.884063i	$-0.654797\pi$
$661$	−37.7080	−	21.7707i	−1.46667	−	0.846784i	−0.999305	+	0.0372795i	$0.988131\pi$
$662$		0			0
$663$	27.1640	+	14.9322i	1.05496	+	0.579919i
$664$		0			0
$665$	16.8072	−	6.88424i	0.651757	−	0.266959i
$666$		0			0
$667$	2.67988	−	1.54723i	0.103765	−	0.0599089i
$668$		0			0
$669$	−2.21287	+	1.27760i	−0.0855546	+	0.0493950i
$670$		0			0
$671$		−	16.2466i		−	0.627192i
$672$		0			0
$673$	−0.510080	−	0.294495i	−0.0196621	−	0.0113519i	0.490137	−	0.871646i	$-0.336947\pi$
$673$	−0.510080	−	0.294495i	−0.0196621	−	0.0113519i	−0.509799	+	0.860294i	$0.670280\pi$
$674$		0			0
$675$	−51.0032	+	13.2359i	−1.96312	+	0.509449i
$676$		0			0
$677$		−	7.61779i		−	0.292775i	−0.989227	−	0.146388i	$-0.953235\pi$
$677$		−	7.61779i		−	0.292775i	0.989227	−	0.146388i	$-0.0467647\pi$
$678$		0			0
$679$	16.1676	−	28.0030i	0.620454	−	1.07466i
$680$		0			0
$681$		−	23.8791i		−	0.915048i
$682$		0			0
$683$	−14.1823	−	24.5645i	−0.542672	−	0.939936i	−0.998749	−	0.0499959i	$-0.984079\pi$
$683$	−14.1823	−	24.5645i	−0.542672	−	0.939936i	0.456077	−	0.889940i	$-0.349254\pi$
$684$		0			0
$685$	−29.7014	−	4.02953i	−1.13483	−	0.153961i
$686$		0			0
$687$	11.8814	−	20.5792i	0.453305	−	0.785147i
$688$		0			0
$689$	6.63228	−	12.0652i	0.252670	−	0.459646i
$690$		0			0
$691$	−35.7708	−	20.6523i	−1.36079	−	0.785651i	−0.371058	−	0.928610i	$-0.621005\pi$
$691$	−35.7708	−	20.6523i	−1.36079	−	0.785651i	−0.989729	+	0.142959i	$0.954338\pi$
$692$		0			0
$693$	−21.9675	+	12.6829i	−0.834475	+	0.481784i
$694$		0			0
$695$	25.1673	+	3.41440i	0.954652	+	0.129516i
$696$		0			0
$697$	13.8241			0.523624
$698$		0			0
$699$	−10.5349	+	18.2470i	−0.398466	+	0.690164i
$700$		0			0
$701$	−32.7428			−1.23668			−0.618340	−	0.785911i	$-0.712195\pi$
$701$	−32.7428			−1.23668			−0.618340	+	0.785911i	$0.712195\pi$
$702$		0			0
$703$		−	22.6837i		−	0.855531i
$704$		0			0
$705$	−67.0944	+	27.4818i	−2.52692	+	1.03502i
$706$		0			0
$707$	−9.54381			−0.358932
$708$		0			0
$709$	−18.6615	+	10.7742i	−0.700846	+	0.404633i	−0.807662	−	0.589645i	$-0.799268\pi$
$709$	−18.6615	+	10.7742i	−0.700846	+	0.404633i	0.106817	+	0.994279i	$0.465934\pi$
$710$		0			0
$711$	−45.7401	−	79.2242i	−1.71539	−	2.97114i
$712$		0			0
$713$	−2.37583	+	4.11506i	−0.0889756	+	0.154110i
$714$		0			0
$715$	8.54955	+	0.977707i	0.319735	+	0.0365642i
$716$		0			0
$717$	−34.2851	+	59.3836i	−1.28040	+	2.21772i
$718$		0			0
$719$	21.0431	+	36.4477i	0.784775	+	1.35927i	0.929133	+	0.369745i	$0.120555\pi$
$719$	21.0431	+	36.4477i	0.784775	+	1.35927i	−0.144358	+	0.989526i	$0.546112\pi$
$720$		0			0
$721$	−9.62447	+	5.55669i	−0.358434	+	0.206942i
$722$		0			0
$723$	−17.4658			−0.649559
$724$		0			0
$725$	13.1876	+	3.64538i	0.489777	+	0.135386i
$726$		0			0
$727$			21.7707i			0.807429i	0.914885	+	0.403715i	$0.132281\pi$
$727$			21.7707i			0.807429i	−0.914885	+	0.403715i	$0.867719\pi$
$728$		0			0
$729$	13.0334			0.482718
$730$		0			0
$731$	6.15361	−	10.6584i	0.227600	−	0.394214i
$732$		0			0
$733$	16.2319			0.599541			0.299770	−	0.954011i	$-0.403090\pi$
$733$	16.2319			0.599541			0.299770	+	0.954011i	$0.403090\pi$
$734$		0			0
$735$	−6.14272	+	45.2776i	−0.226577	+	1.67009i
$736$		0			0
$737$	−3.69742	+	2.13471i	−0.136196	+	0.0786329i
$738$		0			0
$739$	−15.9723	−	9.22161i	−0.587550	−	0.339222i	0.176578	−	0.984287i	$-0.443497\pi$
$739$	−15.9723	−	9.22161i	−0.587550	−	0.339222i	−0.764128	+	0.645064i	$0.776831\pi$
$740$		0			0
$741$	−21.3301	−	11.7253i	−0.783580	−	0.430738i
$742$		0			0
$743$	4.10597	−	7.11175i	0.150633	−	0.260905i	−0.780827	−	0.624747i	$-0.785202\pi$
$743$	4.10597	−	7.11175i	0.150633	−	0.260905i	0.931460	+	0.363843i	$0.118535\pi$
$744$		0			0
$745$	−2.10466	+	15.5133i	−0.0771088	+	0.568364i
$746$		0			0
$747$	26.3125	+	45.5747i	0.962725	+	1.66749i
$748$		0			0
$749$		−	20.2342i		−	0.739341i
$750$		0			0
$751$	−19.0454	+	32.9876i	−0.694977	+	1.20374i	0.275211	+	0.961384i	$0.411252\pi$
$751$	−19.0454	+	32.9876i	−0.694977	+	1.20374i	−0.970188	+	0.242352i	$0.922081\pi$
$752$		0			0
$753$		−	54.1008i		−	1.97154i
$754$		0			0
$755$	0.343920	+	0.266061i	0.0125165	+	0.00968297i
$756$		0			0
$757$	21.8817	+	12.6334i	0.795302	+	0.459168i	0.841826	−	0.539749i	$-0.181481\pi$
$757$	21.8817	+	12.6334i	0.795302	+	0.459168i	−0.0465237	+	0.998917i	$0.514814\pi$
$758$		0			0
$759$			3.70679i			0.134548i
$760$		0			0
$761$	31.6134	−	18.2520i	1.14598	−	0.661634i	0.198079	−	0.980186i	$-0.436530\pi$
$761$	31.6134	−	18.2520i	1.14598	−	0.661634i	0.947905	+	0.318552i	$0.103196\pi$
$762$		0			0
$763$	38.0396	−	21.9622i	1.37713	−	0.795085i
$764$		0			0
$765$	−37.2552	+	15.2597i	−1.34696	+	0.551715i
$766$		0			0
$767$	−13.0144	+	0.273103i	−0.469922	+	0.00986120i
$768$		0			0
$769$	−24.0717	−	13.8978i	−0.868049	−	0.501168i	−0.00134961	−	0.999999i	$-0.500430\pi$
$769$	−24.0717	−	13.8978i	−0.868049	−	0.501168i	−0.866699	+	0.498831i	$0.833763\pi$
$770$		0			0
$771$	39.6426	+	68.6630i	1.42769	+	2.47284i
$772$		0			0
$773$	−1.54852	−	2.68212i	−0.0556965	−	0.0964692i	0.836833	−	0.547458i	$-0.184405\pi$
$773$	−1.54852	−	2.68212i	−0.0556965	−	0.0964692i	−0.892529	+	0.450989i	$0.851071\pi$
$774$		0			0
$775$	−20.3360	+	5.27739i	−0.730489	+	0.189569i
$776$		0			0
$777$	101.414	+	58.5513i	3.63820	+	2.10052i
$778$		0			0
$779$	−10.8551			−0.388925
$780$		0			0
$781$	−13.1117			−0.469174
$782$		0			0
$783$	24.9745	+	14.4190i	0.892516	+	0.515294i
$784$		0			0
$785$	29.8698	+	23.1077i	1.06610	+	0.824750i
$786$		0			0
$787$	15.2155	+	26.3540i	0.542374	+	0.939419i	0.998767	+	0.0496407i	$0.0158076\pi$
$787$	15.2155	+	26.3540i	0.542374	+	0.939419i	−0.456393	+	0.889778i	$0.650859\pi$
$788$		0			0
$789$	−32.5784	−	56.4275i	−1.15982	−	2.00887i
$790$		0			0
$791$	−29.6420	−	17.1138i	−1.05395	−	0.608497i
$792$		0			0
$793$	1.15142	+	54.8693i	0.0408881	+	1.94847i
$794$		0			0
$795$	9.93922	+	24.2657i	0.352508	+	0.860617i
$796$		0			0
$797$	−41.1833	+	23.7772i	−1.45879	+	0.842231i	−0.998952	−	0.0457728i	$-0.985425\pi$
$797$	−41.1833	+	23.7772i	−1.45879	+	0.842231i	−0.459836	+	0.888004i	$0.652092\pi$
$798$		0			0
$799$	−25.5968	+	14.7783i	−0.905549	+	0.522819i
$800$		0			0
$801$		−	56.6295i		−	2.00091i
$802$		0			0
$803$	−1.14063	−	0.658541i	−0.0402518	−	0.0232394i
$804$		0			0
$805$	7.39020	+	5.71716i	0.260470	+	0.201503i
$806$		0			0
$807$		−	44.4986i		−	1.56643i
$808$		0			0
$809$	−18.0418	+	31.2493i	−0.634316	+	1.09867i	0.352344	+	0.935871i	$0.385385\pi$
$809$	−18.0418	+	31.2493i	−0.634316	+	1.09867i	−0.986660	+	0.162796i	$0.947949\pi$
$810$		0			0
$811$		−	36.3456i		−	1.27627i	−0.769926	−	0.638134i	$-0.779707\pi$
$811$		−	36.3456i		−	1.27627i	0.769926	−	0.638134i	$-0.220293\pi$
$812$		0			0
$813$	−44.6593	−	77.3522i	−1.56627	−	2.71286i
$814$		0			0
$815$	4.94482	+	0.670854i	0.173210	+	0.0234990i
$816$		0			0
$817$	−4.83202	+	8.36931i	−0.169051	+	0.292805i
$818$		0			0
$819$	73.2915	−	44.3907i	2.56101	−	1.55114i
$820$		0			0
$821$	18.4741	+	10.6660i	0.644751	+	0.372247i	0.786442	−	0.617664i	$-0.211921\pi$
$821$	18.4741	+	10.6660i	0.644751	+	0.372247i	−0.141691	+	0.989911i	$0.545254\pi$
$822$		0			0
$823$	−17.2845	+	9.97923i	−0.602501	+	0.347854i	−0.770025	−	0.638014i	$-0.779756\pi$
$823$	−17.2845	+	9.97923i	−0.602501	+	0.347854i	0.167524	+	0.985868i	$0.446423\pi$
$824$		0			0
$825$	−11.6803	+	11.4974i	−0.406656	+	0.400289i
$826$		0			0
$827$	28.9529			1.00679			0.503395	−	0.864056i	$-0.332084\pi$
$827$	28.9529			1.00679			0.503395	+	0.864056i	$0.332084\pi$
$828$		0			0
$829$	−13.5506	+	23.4703i	−0.470631	+	0.815156i	−0.999436	−	0.0335871i	$-0.989307\pi$
$829$	−13.5506	+	23.4703i	−0.470631	+	0.815156i	0.528805	+	0.848743i	$0.322640\pi$
$830$		0			0
$831$	−7.80505			−0.270754
$832$		0			0
$833$			18.6266i			0.645372i
$834$		0			0
$835$	1.72817	+	4.21917i	0.0598058	+	0.146011i
$836$		0			0
$837$	−44.2820			−1.53061
$838$		0			0
$839$	−29.2035	+	16.8607i	−1.00822	+	0.582095i	−0.910670	−	0.413136i	$-0.864434\pi$
$839$	−29.2035	+	16.8607i	−1.00822	+	0.582095i	−0.0975488	+	0.995231i	$0.531100\pi$
$840$		0			0
$841$	10.7559	+	18.6299i	0.370895	+	0.642409i
$842$		0			0
$843$	−23.3503	+	40.4439i	−0.804228	+	1.39296i
$844$		0			0
$845$	−28.9436	−	2.69608i	−0.995690	−	0.0927479i
$846$		0			0
$847$	18.2182	−	31.5549i	0.625986	−	1.08424i
$848$		0			0
$849$	38.0692	+	65.9378i	1.30653	+	2.26298i
$850$		0			0
$851$	10.1060	−	5.83468i	0.346428	−	0.200010i
$852$		0			0
$853$	−30.0853			−1.03010			−0.515050	−	0.857160i	$-0.672227\pi$
$853$	−30.0853			−1.03010			−0.515050	+	0.857160i	$0.672227\pi$
$854$		0			0
$855$	29.2540	−	11.9824i	1.00047	−	0.409790i
$856$		0			0
$857$			21.6341i			0.739006i	0.929230	+	0.369503i	$0.120472\pi$
$857$			21.6341i			0.739006i	−0.929230	+	0.369503i	$0.879528\pi$
$858$		0			0
$859$	6.57516			0.224342			0.112171	−	0.993689i	$-0.464220\pi$
$859$	6.57516			0.224342			0.112171	+	0.993689i	$0.464220\pi$
$860$		0			0
$861$	28.0193	−	48.5309i	0.954895	−	1.65393i
$862$		0			0
$863$	45.3471			1.54363			0.771817	−	0.635844i	$-0.219348\pi$
$863$	45.3471			1.54363			0.771817	+	0.635844i	$0.219348\pi$
$864$		0			0
$865$	3.26828	−	24.0902i	0.111125	−	0.819093i
$866$		0			0
$867$	24.3711	−	14.0707i	0.827687	−	0.477865i
$868$		0			0
$869$	−13.1477	−	7.59085i	−0.446006	−	0.257502i
$870$		0			0
$871$	12.3360	−	7.47156i	0.417988	−	0.253164i
$872$		0			0
$873$	28.1406	−	48.7409i	0.952414	−	1.64963i
$874$		0			0
$875$	4.90724	+	41.0200i	0.165895	+	1.38673i
$876$		0			0
$877$	23.8945	+	41.3865i	0.806859	+	1.39752i	0.915029	+	0.403389i	$0.132168\pi$
$877$	23.8945	+	41.3865i	0.806859	+	1.39752i	−0.108169	+	0.994133i	$0.534499\pi$
$878$		0			0
$879$		−	64.6861i		−	2.18181i
$880$		0			0
$881$	6.21890	−	10.7714i	0.209520	−	0.362899i	−0.742043	−	0.670352i	$-0.766143\pi$
$881$	6.21890	−	10.7714i	0.209520	−	0.362899i	0.951563	+	0.307453i	$0.0994765\pi$
$882$		0			0
$883$		−	16.6655i		−	0.560840i	−0.959877	−	0.280420i	$-0.909526\pi$
$883$		−	16.6655i		−	0.560840i	0.959877	−	0.280420i	$-0.0904737\pi$
$884$		0			0
$885$	15.1703	−	19.6097i	0.509944	−	0.659171i
$886$		0			0
$887$	−34.5251	−	19.9331i	−1.15924	−	0.669287i	−0.208118	−	0.978104i	$-0.566734\pi$
$887$	−34.5251	−	19.9331i	−1.15924	−	0.669287i	−0.951122	+	0.308816i	$0.900067\pi$
$888$		0			0
$889$		−	27.3584i		−	0.917572i
$890$		0			0
$891$	−12.0814	+	6.97519i	−0.404742	+	0.233678i
$892$		0			0
$893$	20.0994	−	11.6044i	0.672602	−	0.388327i
$894$		0			0
$895$	−3.32012	−	8.10578i	−0.110979	−	0.270947i
$896$		0			0
$897$	−0.262706	−	12.5189i	−0.00877150	−	0.417993i
$898$		0			0
$899$	9.95781	+	5.74914i	0.332111	+	0.191745i
$900$		0			0
$901$	5.34480	+	9.25747i	0.178061	+	0.308411i
$902$		0			0
$903$	−24.9449	−	43.2058i	−0.830114	−	1.43780i
$904$		0			0
$905$	19.4254	−	25.1099i	0.645722	−	0.834682i
$906$		0			0
$907$	10.6324	+	6.13860i	0.353042	+	0.203829i	0.666024	−	0.745930i	$-0.267995\pi$
$907$	10.6324	+	6.13860i	0.353042	+	0.203829i	−0.312982	+	0.949759i	$0.601328\pi$
$908$		0			0
$909$	−16.6116			−0.550971
$910$		0			0
$911$	47.4729			1.57285			0.786423	−	0.617688i	$-0.211930\pi$
$911$	47.4729			1.57285			0.786423	+	0.617688i	$0.211930\pi$
$912$		0			0
$913$	7.56339	+	4.36673i	0.250312	+	0.144518i
$914$		0			0
$915$	−82.6754	−	63.9589i	−2.73317	−	2.11441i
$916$		0			0
$917$	13.5948	+	23.5469i	0.448940	+	0.777587i
$918$		0			0
$919$	−6.03106	−	10.4461i	−0.198946	−	0.344585i	0.749241	−	0.662298i	$-0.230419\pi$
$919$	−6.03106	−	10.4461i	−0.198946	−	0.344585i	−0.948187	+	0.317713i	$0.897085\pi$
$920$		0			0
$921$	−23.6490	−	13.6537i	−0.779260	−	0.449906i
$922$		0			0
$923$	44.2820	−	0.929248i	1.45756	−	0.0305866i
$924$		0			0
$925$	49.7313	+	13.7469i	1.63516	+	0.451996i
$926$		0			0
$927$	−16.7520	+	9.67175i	−0.550207	+	0.317662i
$928$		0			0
$929$	16.6781	−	9.62908i	0.547189	−	0.315920i	−0.200798	−	0.979633i	$-0.564354\pi$
$929$	16.6781	−	9.62908i	0.547189	−	0.315920i	0.747988	+	0.663713i	$0.231020\pi$
$930$		0			0
$931$		−	14.6262i		−	0.479354i
$932$		0			0
$933$	76.3355	+	44.0723i	2.49911	+	1.44286i
$934$		0			0
$935$	−4.08818	+	5.28452i	−0.133698	+	0.172822i
$936$		0			0
$937$		−	17.1012i		−	0.558671i	−0.960194	−	0.279335i	$-0.909886\pi$
$937$		−	17.1012i		−	0.558671i	0.960194	−	0.279335i	$-0.0901141\pi$
$938$		0			0
$939$	−12.0405	+	20.8547i	−0.392926	+	0.680568i
$940$		0			0
$941$		−	12.5077i		−	0.407741i	−0.978998	−	0.203870i	$-0.934648\pi$
$941$		−	12.5077i		−	0.407741i	0.978998	−	0.203870i	$-0.0653521\pi$
$942$		0			0
$943$	−2.79215	−	4.83614i	−0.0909248	−	0.157486i
$944$		0			0
$945$	−11.7060	+	86.2841i	−0.380796	+	2.80682i
$946$		0			0
$947$	−30.1199	+	52.1692i	−0.978766	+	1.69527i	−0.311862	+	0.950127i	$0.600953\pi$
$947$	−30.1199	+	52.1692i	−0.978766	+	1.69527i	−0.666903	+	0.745144i	$0.732381\pi$
$948$		0			0
$949$	3.89890	+	2.14324i	0.126563	+	0.0695726i
$950$		0			0
$951$	−16.4296	−	9.48566i	−0.532768	−	0.307594i
$952$		0			0
$953$	−10.0857	+	5.82300i	−0.326709	+	0.188625i	−0.654379	−	0.756167i	$-0.727070\pi$
$953$	−10.0857	+	5.82300i	−0.326709	+	0.188625i	0.327670	+	0.944792i	$0.393737\pi$
$954$		0			0
$955$	0.746296	+	0.101249i	0.0241496	+	0.00327633i
$956$		0			0
$957$	8.96985			0.289954
$958$		0			0
$959$	−24.7656	+	42.8953i	−0.799723	+	1.38516i
$960$		0			0
$961$	13.3439			0.430449
$962$		0			0
$963$		−	35.2188i		−	1.13491i
$964$		0			0
$965$	−5.73382	−	13.9986i	−0.184578	−	0.450631i
$966$		0			0
$967$	2.95604			0.0950599			0.0475300	−	0.998870i	$-0.484865\pi$
$967$	2.95604			0.0950599			0.0475300	+	0.998870i	$0.484865\pi$
$968$		0			0
$969$	16.3664	−	9.44912i	0.525763	−	0.303549i
$970$		0			0
$971$	16.1211	+	27.9225i	0.517350	+	0.896076i	0.999797	+	0.0201510i	$0.00641469\pi$
$971$	16.1211	+	27.9225i	0.517350	+	0.896076i	−0.482447	+	0.875925i	$0.660252\pi$
$972$		0			0
$973$	20.9850	−	36.3471i	0.672748	−	1.16523i
$974$		0			0
$975$	38.6329	−	39.6579i	1.23724	−	1.27007i
$976$		0			0
$977$	18.6309	−	32.2697i	0.596056	−	1.03240i	−0.397341	−	0.917671i	$-0.630067\pi$
$977$	18.6309	−	32.2697i	0.596056	−	1.03240i	0.993397	−	0.114728i	$-0.0365998\pi$
$978$		0			0
$979$	−4.69901	−	8.13892i	−0.150181	−	0.260121i
$980$		0			0
$981$	66.2102	−	38.2265i	2.11393	−	1.22048i
$982$		0			0
$983$	−31.3081			−0.998574			−0.499287	−	0.866437i	$-0.666405\pi$
$983$	−31.3081			−0.998574			−0.499287	+	0.866437i	$0.666405\pi$
$984$		0			0
$985$	−12.6593	−	30.9065i	−0.403358	−	0.984763i
$986$		0			0
$987$			119.814i			3.81371i
$988$		0			0
$989$	−4.97156			−0.158086
$990$		0			0
$991$	−4.08268	+	7.07141i	−0.129691	+	0.224631i	−0.923557	−	0.383462i	$-0.874732\pi$
$991$	−4.08268	+	7.07141i	−0.129691	+	0.224631i	0.793866	+	0.608093i	$0.208065\pi$
$992$		0			0
$993$	81.8646			2.59789
$994$		0			0
$995$	0.670448	+	0.0909583i	0.0212546	+	0.00288357i
$996$		0			0
$997$	41.1557	−	23.7612i	1.30341	−	0.752526i	0.322425	−	0.946595i	$-0.395502\pi$
$997$	41.1557	−	23.7612i	1.30341	−	0.752526i	0.980988	+	0.194069i	$0.0621687\pi$
$998$		0			0
$999$	94.1802	+	54.3750i	2.97973	+	1.72035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.df.a.849.1		8
4.3	odd	2		130.2.m.b.69.4	yes	8
5.4	even	2		1040.2.df.c.849.4		8
12.11	even	2		1170.2.bj.a.199.3		8
13.10	even	6		1040.2.df.c.49.4		8
20.3	even	4		650.2.m.e.251.1		16
20.7	even	4		650.2.m.e.251.8		16
20.19	odd	2		130.2.m.a.69.1	yes	8
52.7	even	12		1690.2.b.e.339.1		16
52.19	even	12		1690.2.b.e.339.9		16
52.23	odd	6		130.2.m.a.49.1	✓	8
52.35	odd	6		1690.2.c.e.1689.1		8
52.43	odd	6		1690.2.c.f.1689.1		8
60.59	even	2		1170.2.bj.b.199.2		8
65.49	even	6	inner	1040.2.df.a.49.1		8
156.23	even	6		1170.2.bj.b.829.2		8
260.7	odd	12		8450.2.a.cs.1.1		8
260.19	even	12		1690.2.b.e.339.8		16
260.23	even	12		650.2.m.e.101.1		16
260.59	even	12		1690.2.b.e.339.16		16
260.123	odd	12		8450.2.a.cs.1.8		8
260.127	even	12		650.2.m.e.101.8		16
260.139	odd	6		1690.2.c.f.1689.8		8
260.163	odd	12		8450.2.a.cr.1.8		8
260.179	odd	6		130.2.m.b.49.4	yes	8
260.199	odd	6		1690.2.c.e.1689.8		8
260.227	odd	12		8450.2.a.cr.1.1		8
780.179	even	6		1170.2.bj.a.829.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.1	✓	8	52.23	odd	6
130.2.m.a.69.1	yes	8	20.19	odd	2
130.2.m.b.49.4	yes	8	260.179	odd	6
130.2.m.b.69.4	yes	8	4.3	odd	2
650.2.m.e.101.1		16	260.23	even	12
650.2.m.e.101.8		16	260.127	even	12
650.2.m.e.251.1		16	20.3	even	4
650.2.m.e.251.8		16	20.7	even	4
1040.2.df.a.49.1		8	65.49	even	6	inner
1040.2.df.a.849.1		8	1.1	even	1	trivial
1040.2.df.c.49.4		8	13.10	even	6
1040.2.df.c.849.4		8	5.4	even	2
1170.2.bj.a.199.3		8	12.11	even	2
1170.2.bj.a.829.3		8	780.179	even	6
1170.2.bj.b.199.2		8	60.59	even	2
1170.2.bj.b.829.2		8	156.23	even	6
1690.2.b.e.339.1		16	52.7	even	12
1690.2.b.e.339.8		16	260.19	even	12
1690.2.b.e.339.9		16	52.19	even	12
1690.2.b.e.339.16		16	260.59	even	12
1690.2.c.e.1689.1		8	52.35	odd	6
1690.2.c.e.1689.8		8	260.199	odd	6
1690.2.c.f.1689.1		8	52.43	odd	6
1690.2.c.f.1689.8		8	260.139	odd	6
8450.2.a.cr.1.1		8	260.227	odd	12
8450.2.a.cr.1.8		8	260.163	odd	12
8450.2.a.cs.1.1		8	260.7	odd	12
8450.2.a.cs.1.8		8	260.123	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.65963 - 1.53554i) q^{3} +(-1.36822 + 1.76861i) q^{5} +(1.84755 + 3.20005i) q^{7} +(3.21577 + 5.56988i) q^{9} +(0.924355 + 0.533677i) q^{11} +(-3.15963 - 1.73687i) q^{13} +(6.35473 - 2.60289i) q^{15} +(2.42435 - 1.39970i) q^{17} +(-1.90368 + 1.09909i) q^{19} -11.3479i q^{21} +(-0.979330 - 0.565416i) q^{23} +(-1.25595 - 4.83969i) q^{25} -10.5385i q^{27} +(-1.36822 + 2.36983i) q^{29} -4.20191i q^{31} +(-1.63896 - 2.83877i) q^{33} +(-8.18749 - 1.11078i) q^{35} +(-5.15963 + 8.93675i) q^{37} +(5.73644 + 9.47118i) q^{39} +(4.27662 + 2.46911i) q^{41} +(3.80737 - 2.19819i) q^{43} +(-14.2508 - 1.93338i) q^{45} -10.5582 q^{47} +(-3.32688 + 5.76232i) q^{49} -8.59720 q^{51} +3.81853i q^{53} +(-2.20859 + 0.904635i) q^{55} +6.75081 q^{57} +(3.12664 - 1.80517i) q^{59} +(-7.61068 - 13.1821i) q^{61} +(-11.8826 + 20.5812i) q^{63} +(7.39491 - 3.21174i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(1.73644 + 3.00760i) q^{69} +(-10.6385 + 6.14216i) q^{71} -1.23397 q^{73} +(-4.09117 + 14.8004i) q^{75} +3.94398i q^{77} -14.2237 q^{79} +(-6.53504 + 11.3190i) q^{81} +8.18235 q^{83} +(-0.841526 + 6.20283i) q^{85} +(7.27793 - 4.20191i) q^{87} +(-7.62533 - 4.40249i) q^{89} +(-0.279516 - 13.3199i) q^{91} +(-6.45221 + 11.1756i) q^{93} +(0.660795 - 4.87067i) q^{95} +(-4.37540 - 7.57842i) q^{97} +6.86472i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{5} + 5 q^{7} + 8 q^{9} + 3 q^{11} - 4 q^{13} + 10 q^{15} + 15 q^{17} - 9 q^{19} - 6 q^{23} + 5 q^{25} - 3 q^{29} + 10 q^{33} - 15 q^{35} - 20 q^{37} + 30 q^{39} + 21 q^{41} + 18 q^{43} - 36 q^{45}+ \cdots + 4 q^{97}+O(q^{100}) \) 8 * q - 3 * q^5 + 5 * q^7 + 8 * q^9 + 3 * q^11 - 4 * q^13 + 10 * q^15 + 15 * q^17 - 9 * q^19 - 6 * q^23 + 5 * q^25 - 3 * q^29 + 10 * q^33 - 15 * q^35 - 20 * q^37 + 30 * q^39 + 21 * q^41 + 18 * q^43 - 36 * q^45 + 6 * q^47 - 15 * q^49 + 20 * q^51 - 31 * q^55 - 24 * q^57 - 30 * q^59 - 5 * q^61 - 25 * q^63 + 21 * q^65 - 16 * q^67 - 2 * q^69 - 26 * q^73 + 24 * q^75 - 4 * q^79 + 8 * q^81 - 48 * q^83 - 29 * q^85 + 12 * q^87 - 39 * q^89 - 19 * q^91 - 18 * q^93 - 15 * q^95 + 4 * q^97

Introduction

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