LMFDB - Embedded newform 728.2.ds.a.461.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(293,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 6, 11]))

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

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

chi := DirichletCharacter("728.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.ds (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 8x^{12} + 40x^{10} - 161x^{8} + 360x^{6} + 648x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 8x^12 + 40x^10 - 161x^8 + 360x^6 + 648x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			461.1
Root			$1.35670 - 1.07674i$ of defining polynomial
Character	$\chi$	$=$	728.461
Dual form			728.2.ds.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.61083 + 2.79005i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(3.12775 - 3.12775i) q^{5} +(-4.40088 - 1.17921i) q^{6} +(0.684771 - 2.55560i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.68957 - 6.39053i) q^{9} +(5.41743 + 3.12775i) q^{10} -6.44334i q^{12} +(3.60409 - 0.102471i) q^{13} +3.74166 q^{14} +(3.68829 + 13.7649i) q^{15} +(2.00000 - 3.46410i) q^{16} +(7.37915 - 7.37915i) q^{18} +(4.07621 + 1.09222i) q^{19} +(-2.28968 + 8.54518i) q^{20} +(6.02719 + 6.02719i) q^{21} +(-3.01441 - 1.74037i) q^{23} +(8.80176 - 2.35843i) q^{24} -14.5657i q^{25} +(1.45917 + 4.88578i) q^{26} +14.1082 q^{27} +(1.36954 + 5.11120i) q^{28} +(-17.4532 + 10.0766i) q^{30} +(5.46410 + 1.46410i) q^{32} +(-5.85149 - 10.1351i) q^{35} +(12.7811 + 7.37915i) q^{36} +5.96798i q^{38} +(-5.51970 + 10.2207i) q^{39} -12.5110 q^{40} +(-6.02719 + 10.4394i) q^{42} +(-31.5281 - 8.44793i) q^{45} +(1.27404 - 4.75478i) q^{46} +(6.44334 + 11.1602i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(19.8971 - 5.33141i) q^{50} +(-6.14000 + 3.78158i) q^{52} +(5.16395 + 19.2721i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(-9.61343 + 9.61343i) q^{57} +(2.12668 - 7.93688i) q^{59} +(-20.1532 - 20.1532i) q^{60} +(0.749378 + 1.29796i) q^{61} +(-18.8581 + 5.05303i) q^{63} +8.00000i q^{64} +(10.9522 - 11.5932i) q^{65} +(9.71143 - 5.60690i) q^{69} +(11.7030 - 11.7030i) q^{70} +(16.0113 + 4.29022i) q^{71} +(-5.40191 + 20.1602i) q^{72} +(40.6390 + 23.4629i) q^{75} +(-8.15241 + 2.18443i) q^{76} +(-15.9820 - 3.79903i) q^{78} -8.25834 q^{79} +(-4.57935 - 17.0904i) q^{80} +(-11.6572 + 20.1908i) q^{81} +(-12.2473 + 12.2473i) q^{83} +(-16.4666 - 4.41221i) q^{84} -46.1603i q^{90} +(2.20610 - 9.28079i) q^{91} +6.96148 q^{92} +(16.1656 - 9.33319i) q^{95} +(-12.8867 + 12.8867i) q^{96} +(2.56218 - 9.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$	−1.61083	+	2.79005i	−0.930016	+	1.61083i	−0.146726	+	0.989177i	$0.546874\pi$
$3$	−1.61083	+	2.79005i	−0.930016	+	1.61083i	−0.783289	+	0.621657i	$0.786460\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	3.12775	−	3.12775i	1.39877	−	1.39877i	0.595187	−	0.803587i	$-0.297078\pi$
$5$	3.12775	−	3.12775i	1.39877	−	1.39877i	0.803587	−	0.595187i	$-0.202922\pi$
$6$	−4.40088	−	1.17921i	−1.79665	−	0.481411i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−3.68957	−	6.39053i	−1.22986	−	2.13018i
$10$	5.41743	+	3.12775i	1.71314	+	0.989083i
$11$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$11$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$12$		−	6.44334i		−	1.86003i
$13$	3.60409	−	0.102471i	0.999596	−	0.0284203i
$13$	3.60409	−	0.102471i	0.999596	−	0.0284203i
$14$	3.74166			1.00000
$15$	3.68829	+	13.7649i	0.952312	+	3.55408i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	7.37915	−	7.37915i	1.73928	−	1.73928i
$19$	4.07621	+	1.09222i	0.935146	+	0.250572i	0.694048	−	0.719929i	$-0.255826\pi$
$19$	4.07621	+	1.09222i	0.935146	+	0.250572i	0.241098	+	0.970501i	$0.422492\pi$
$20$	−2.28968	+	8.54518i	−0.511987	+	1.91076i
$21$	6.02719	+	6.02719i	1.31524	+	1.31524i
$22$		0			0
$23$	−3.01441	−	1.74037i	−0.628548	−	0.362892i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	−3.01441	−	1.74037i	−0.628548	−	0.362892i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	8.80176	−	2.35843i	1.79665	−	0.481411i
$25$		−	14.5657i		−	2.91314i
$26$	1.45917	+	4.88578i	0.286166	+	0.958180i
$27$	14.1082			2.71512
$28$	1.36954	+	5.11120i	0.258819	+	0.965926i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−17.4532	+	10.0766i	−3.18650	+	1.83972i
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$		0			0
$34$		0			0
$35$	−5.85149	−	10.1351i	−0.989083	−	1.71314i
$36$	12.7811	+	7.37915i	2.13018	+	1.22986i
$37$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$37$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$38$			5.96798i			0.968134i
$39$	−5.51970	+	10.2207i	−0.883860	+	1.63661i
$40$	−12.5110			−1.97817
$41$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$41$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$42$	−6.02719	+	10.4394i	−0.930016	+	1.61083i
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$	−31.5281	−	8.44793i	−4.69993	−	1.25934i
$46$	1.27404	−	4.75478i	0.187847	−	0.701054i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	6.44334	+	11.1602i	0.930016	+	1.61083i
$49$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$50$	19.8971	−	5.33141i	2.81388	−	0.753976i
$51$		0			0
$52$	−6.14000	+	3.78158i	−0.851465	+	0.524411i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	5.16395	+	19.2721i	0.702724	+	2.62260i
$55$		0			0
$56$	−6.48074	+	3.74166i	−0.866025	+	0.500000i
$57$	−9.61343	+	9.61343i	−1.27333	+	1.27333i
$58$		0			0
$59$	2.12668	−	7.93688i	0.276870	−	1.03329i	−0.677707	−	0.735332i	$-0.737026\pi$
$59$	2.12668	−	7.93688i	0.276870	−	1.03329i	0.954578	−	0.297962i	$-0.0963069\pi$
$60$	−20.1532	−	20.1532i	−2.60176	−	2.60176i
$61$	0.749378	+	1.29796i	0.0959480	+	0.166187i	0.910004	−	0.414600i	$-0.136078\pi$
$61$	0.749378	+	1.29796i	0.0959480	+	0.166187i	−0.814056	+	0.580787i	$0.802745\pi$
$62$		0			0
$63$	−18.8581	+	5.05303i	−2.37590	+	0.636621i
$64$			8.00000i			1.00000i
$65$	10.9522	−	11.5932i	1.35846	−	1.43796i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$		0			0
$69$	9.71143	−	5.60690i	1.16912	−	0.674991i
$70$	11.7030	−	11.7030i	1.39877	−	1.39877i
$71$	16.0113	+	4.29022i	1.90020	+	0.509156i	0.996760	+	0.0804327i	$0.0256302\pi$
$71$	16.0113	+	4.29022i	1.90020	+	0.509156i	0.903436	+	0.428723i	$0.141036\pi$
$72$	−5.40191	+	20.1602i	−0.636621	+	2.37590i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	40.6390	+	23.4629i	4.69258	+	2.70926i
$76$	−8.15241	+	2.18443i	−0.935146	+	0.250572i
$77$		0			0
$78$	−15.9820	−	3.79903i	−1.80961	−	0.430156i
$79$	−8.25834			−0.929136			−0.464568	−	0.885537i	$-0.653790\pi$
$79$	−8.25834			−0.929136			−0.464568	+	0.885537i	$0.653790\pi$
$80$	−4.57935	−	17.0904i	−0.511987	−	1.91076i
$81$	−11.6572	+	20.1908i	−1.29524	+	2.24343i
$82$		0			0
$83$	−12.2473	+	12.2473i	−1.34431	+	1.34431i	−0.452598	+	0.891715i	$0.649503\pi$
$83$	−12.2473	+	12.2473i	−1.34431	+	1.34431i	−0.891715	+	0.452598i	$0.850497\pi$
$84$	−16.4666	−	4.41221i	−1.79665	−	0.481411i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$89$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$90$		−	46.1603i		−	4.86573i
$91$	2.20610	−	9.28079i	0.231263	−	0.972891i
$92$	6.96148			0.725785
$93$		0			0
$94$		0			0
$95$	16.1656	−	9.33319i	1.65855	−	0.957565i
$96$	−12.8867	+	12.8867i	−1.31524	+	1.31524i
$97$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$97$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$98$	2.56218	−	9.56218i	0.258819	−	0.965926i
$99$		0			0
$100$	14.5657	+	25.2285i	1.45657	+	2.52285i
$101$	17.3650	+	10.0257i	1.72788	+	0.997594i	0.898607	+	0.438755i	$0.144581\pi$
$101$	17.3650	+	10.0257i	1.72788	+	0.997594i	0.829277	+	0.558838i	$0.188753\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−7.41313	−	7.00325i	−0.726917	−	0.686725i
$105$	37.7031			3.67945
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−24.4361	+	14.1082i	−2.35136	+	1.35756i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$		0			0
$111$		0			0
$112$	−7.48331	−	7.48331i	−0.707107	−	0.707107i
$113$	−0.612486	−	1.06086i	−0.0576178	−	0.0997970i	0.835778	−	0.549068i	$-0.185017\pi$
$113$	−0.612486	−	1.06086i	−0.0576178	−	0.0997970i	−0.893396	+	0.449271i	$0.851684\pi$
$114$	−16.6509	−	9.61343i	−1.55950	−	0.900380i
$115$	−14.8718	+	3.98488i	−1.38680	+	0.371592i
$116$		0			0
$117$	−13.9524	−	22.6540i	−1.28990	−	2.09436i
$118$	11.6204			1.06974
$119$		0			0
$120$	20.1532	−	34.9063i	1.83972	−	3.18650i
$121$	9.52628	−	5.50000i	0.866025	−	0.500000i
$122$	−1.49876	+	1.49876i	−0.135691	+	0.135691i
$123$		0			0
$124$		0			0
$125$	−29.9191	−	29.9191i	−2.67605	−	2.67605i
$126$	−13.8051	−	23.9112i	−1.22986	−	2.13018i
$127$	8.22111	+	4.74646i	0.729506	+	0.421180i	0.818241	−	0.574875i	$-0.194949\pi$
$127$	8.22111	+	4.74646i	0.729506	+	0.421180i	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$		0			0
$130$	19.8454	+	10.7176i	1.74056	+	0.939995i
$131$	−10.5556			−0.922249			−0.461125	−	0.887335i	$-0.652554\pi$
$131$	−10.5556			−0.922249			−0.461125	+	0.887335i	$0.652554\pi$
$132$		0			0
$133$	5.58253	−	9.66923i	0.484067	−	0.838429i
$134$		0			0
$135$	44.1269	−	44.1269i	3.79784	−	3.79784i
$136$		0			0
$137$	−4.94743	+	18.4641i	−0.422687	+	1.57749i	0.346235	+	0.938148i	$0.387460\pi$
$137$	−4.94743	+	18.4641i	−0.422687	+	1.57749i	−0.768922	+	0.639343i	$0.779207\pi$
$138$	11.2138	+	11.2138i	0.954581	+	0.954581i
$139$	−2.66420	−	4.61453i	−0.225974	−	0.391399i	0.730637	−	0.682766i	$-0.239223\pi$
$139$	−2.66420	−	4.61453i	−0.225974	−	0.391399i	−0.956611	+	0.291367i	$0.905890\pi$
$140$	20.2702	+	11.7030i	1.71314	+	0.989083i
$141$		0			0
$142$			23.4422i			1.96723i
$143$		0			0
$144$	−29.5166			−2.45972
$145$		0			0
$146$		0			0
$147$	19.5303	−	11.2758i	1.61083	−	0.930016i
$148$		0			0
$149$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$149$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$150$	−17.1760	+	64.1019i	−1.40242	+	5.23390i
$151$	−10.9388	−	10.9388i	−0.890183	−	0.890183i	0.104357	−	0.994540i	$-0.466722\pi$
$151$	−10.9388	−	10.9388i	−0.890183	−	0.890183i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	−5.96798	−	10.3368i	−0.484067	−	0.838429i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.660254	−	23.2224i	−0.0528626	−	1.85928i
$157$	23.2323			1.85414			0.927071	−	0.374885i	$-0.122318\pi$
$157$	23.2323			1.85414			0.927071	+	0.374885i	$0.122318\pi$
$158$	−3.02276	−	11.2811i	−0.240478	−	0.897477i
$159$		0			0
$160$	21.6697	−	12.5110i	1.71314	−	0.989083i
$161$	−6.51187	+	6.51187i	−0.513207	+	0.513207i
$162$	−31.8480	−	8.53366i	−2.50222	−	0.670467i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$		0			0
$165$		0			0
$166$	−21.2129	−	12.2473i	−1.64644	−	0.950573i
$167$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$167$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$168$		−	24.1088i		−	1.86003i
$169$	12.9790	−	0.738629i	0.998385	−	0.0568176i
$170$		0			0
$171$	−8.05963	−	30.0789i	−0.616335	−	2.30019i
$172$		0			0
$173$	−22.1768	+	12.8038i	−1.68607	+	0.973452i	−0.728588	+	0.684953i	$0.759823\pi$
$173$	−22.1768	+	12.8038i	−1.68607	+	0.973452i	−0.957480	+	0.288499i	$0.906844\pi$
$174$		0			0
$175$	−37.2241	−	9.97416i	−2.81388	−	0.753976i
$176$		0			0
$177$	18.7185	+	18.7185i	1.40697	+	1.40697i
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	63.0562	−	16.8959i	4.69993	−	1.25934i
$181$			23.4886i			1.74589i	0.487818	+	0.872945i	$0.337793\pi$
$181$			23.4886i			1.74589i	−0.487818	+	0.872945i	$0.662207\pi$
$182$	13.4853	−	0.383411i	0.999596	−	0.0284203i
$183$	−4.82850			−0.356933
$184$	2.54808	+	9.50956i	0.187847	+	0.701054i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	9.66086	−	36.0548i	0.702724	−	2.62260i
$190$	18.6664	+	18.6664i	1.35420	+	1.35420i
$191$	−13.6125	−	23.5775i	−0.984965	−	1.70601i	−0.642092	−	0.766627i	$-0.721933\pi$
$191$	−13.6125	−	23.5775i	−0.984965	−	1.70601i	−0.342873	−	0.939382i	$-0.611400\pi$
$192$	−22.3204	−	12.8867i	−1.61083	−	0.930016i
$193$	5.67992	−	1.52193i	0.408850	−	0.109551i	−0.0485316	−	0.998822i	$-0.515454\pi$
$193$	5.67992	−	1.52193i	0.408850	−	0.109551i	0.457381	+	0.889271i	$0.348787\pi$
$194$		0			0
$195$	14.7034	+	49.2320i	1.05293	+	3.52557i
$196$	14.0000			1.00000
$197$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$197$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−29.1314	+	29.1314i	−2.05990	+	2.05990i
$201$		0			0
$202$	−7.33932	+	27.3907i	−0.516393	+	1.92720i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$			25.6849i			1.78522i
$208$	6.85322	−	12.6899i	0.475185	−	0.879886i
$209$		0			0
$210$	13.8003	+	51.5034i	0.952312	+	3.55408i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−37.7615	+	37.7615i	−2.58738	+	2.58738i
$214$		0			0
$215$		0			0
$216$	−28.2163	−	28.2163i	−1.91988	−	1.91988i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$223$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$224$	7.48331	−	12.9615i	0.500000	−	0.866025i
$225$	−93.0825	+	53.7412i	−6.20550	+	3.58275i
$226$	1.22497	−	1.22497i	0.0814839	−	0.0814839i
$227$	26.7472	+	7.16690i	1.77528	+	0.475684i	0.989709	−	0.143094i	$-0.0457050\pi$
$227$	26.7472	+	7.16690i	1.77528	+	0.475684i	0.785566	+	0.618777i	$0.212372\pi$
$228$	7.03752	−	26.2644i	0.466071	−	1.73940i
$229$	16.6904	+	16.6904i	1.10293	+	1.10293i	0.994055	+	0.108880i	$0.0347264\pi$
$229$	16.6904	+	16.6904i	1.10293	+	1.10293i	0.108880	+	0.994055i	$0.465274\pi$
$230$	−10.8869	−	18.8567i	−0.717861	−	1.24337i
$231$		0			0
$232$		0			0
$233$			20.1628i			1.32091i	0.750867	+	0.660454i	$0.229636\pi$
$233$			20.1628i			1.32091i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	25.8390	−	27.3513i	1.68915	−	1.78801i
$235$		0			0
$236$	4.25336	+	15.8738i	0.276870	+	1.03329i
$237$	13.3028	−	23.0412i	0.864111	−	1.49668i
$238$		0			0
$239$	−0.379182	+	0.379182i	−0.0245272	+	0.0245272i	−0.719264	−	0.694737i	$-0.755521\pi$
$239$	−0.379182	+	0.379182i	−0.0245272	+	0.0245272i	0.694737	+	0.719264i	$0.255521\pi$
$240$	55.0595	+	14.7531i	3.55408	+	0.952312i
$241$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$241$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$242$	11.0000	+	11.0000i	0.707107	+	0.707107i
$243$	−16.3934	−	28.3941i	−1.05163	−	1.82148i
$244$	−2.59592	−	1.49876i	−0.166187	−	0.0959480i
$245$	−29.9081	+	8.01386i	−1.91076	+	0.511987i
$246$		0			0
$247$	14.8030	+	3.51876i	0.941890	+	0.223893i
$248$		0			0
$249$	−14.4421	−	53.8988i	−0.915233	−	3.41570i
$250$	29.9191	−	51.8215i	1.89225	−	3.27748i
$251$	−2.57491	+	1.48662i	−0.162527	+	0.0938349i	−0.579057	−	0.815287i	$-0.696579\pi$
$251$	−2.57491	+	1.48662i	−0.162527	+	0.0938349i	0.416530	+	0.909122i	$0.363246\pi$
$252$	27.6102	−	27.6102i	1.73928	−	1.73928i
$253$		0			0
$254$	−3.47465	+	12.9676i	−0.218019	+	0.813658i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$	−7.37657	+	31.0323i	−0.457476	+	1.92454i
$261$		0			0
$262$	−3.86363	−	14.4193i	−0.238696	−	0.890824i
$263$	−11.3271	+	19.6190i	−0.698456	+	1.20976i	0.270546	+	0.962707i	$0.412796\pi$
$263$	−11.3271	+	19.6190i	−0.698456	+	1.20976i	−0.969002	+	0.247054i	$0.920537\pi$
$264$		0			0
$265$		0			0
$266$	15.2518	+	4.08670i	0.935146	+	0.250572i
$267$		0			0
$268$		0			0
$269$	−7.89664	−	13.6774i	−0.481467	−	0.833924i	0.518307	−	0.855194i	$-0.326562\pi$
$269$	−7.89664	−	13.6774i	−0.481467	−	0.833924i	−0.999774	+	0.0212700i	$0.993229\pi$
$270$	76.4300	+	44.1269i	4.65138	+	2.68548i
$271$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$271$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$272$		0			0
$273$	22.3402	+	21.1050i	1.35209	+	1.27733i
$274$	−27.0333			−1.63314
$275$		0			0
$276$	−11.2138	+	19.4229i	−0.674991	+	1.16912i
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	5.32840	−	5.32840i	0.319576	−	0.319576i
$279$		0			0
$280$	−8.56718	+	31.9731i	−0.511987	+	1.91076i
$281$	−22.4833	−	22.4833i	−1.34124	−	1.34124i	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−22.4833	−	22.4833i	−1.34124	−	1.34124i	−0.446417	−	0.894825i	$-0.647300\pi$
$282$		0			0
$283$	−10.2781	−	5.93408i	−0.610971	−	0.352744i	0.162374	−	0.986729i	$-0.448085\pi$
$283$	−10.2781	−	5.93408i	−0.610971	−	0.352744i	−0.773345	+	0.633985i	$0.781418\pi$
$284$	−32.0227	+	8.58045i	−1.90020	+	0.509156i
$285$			60.1369i			3.56220i
$286$		0			0
$287$		0			0
$288$	−10.8038	−	40.3204i	−0.636621	−	2.37590i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.396114	+	1.47832i	−0.0231412	+	0.0863642i	−0.976531	−	0.215378i	$-0.930902\pi$
$293$	−0.396114	+	1.47832i	−0.0231412	+	0.0863642i	0.953390	+	0.301742i	$0.0975682\pi$
$294$	22.5517	+	22.5517i	1.31524	+	1.31524i
$295$	−18.1729	−	31.4763i	−1.05807	−	1.83262i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.0426	−	5.96357i	−0.638608	−	0.344882i
$300$	−93.8517			−5.41853
$301$		0			0
$302$	10.9388	−	18.9465i	0.629454	−	1.09025i
$303$	−55.9443	+	32.2995i	−3.21392	+	1.85556i
$304$	11.9360	−	11.9360i	0.684574	−	0.684574i
$305$	6.40357	+	1.71583i	0.366668	+	0.0982483i
$306$		0			0
$307$	5.97537	+	5.97537i	0.341032	+	0.341032i	0.856755	−	0.515723i	$-0.172477\pi$
$307$	5.97537	+	5.97537i	0.341032	+	0.341032i	−0.515723	+	0.856755i	$0.672477\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	31.4807	−	9.40191i	1.78224	−	0.532278i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	8.50363	+	31.7360i	0.479887	+	1.79096i
$315$	−43.1790	+	74.7883i	−2.43286	+	4.21384i
$316$	14.3039	−	8.25834i	0.804655	−	0.464568i
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$		0			0
$320$	25.0220	+	25.0220i	1.39877	+	1.39877i
$321$		0			0
$322$	−11.2789	−	6.51187i	−0.628548	−	0.362892i
$323$		0			0
$324$		−	46.6288i		−	2.59049i
$325$	−1.49256	−	52.4961i	−0.0827923	−	2.91196i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$331$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$332$	8.96563	−	33.4602i	0.492053	−	1.83637i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	32.9332	−	8.82442i	1.79665	−	0.481411i
$337$		−	36.7083i		−	1.99963i	−0.0192914	−	0.999814i	$-0.506141\pi$
$337$		−	36.7083i		−	1.99963i	0.0192914	−	0.999814i	$-0.493859\pi$
$338$	5.75963	+	17.4593i	0.313283	+	0.949660i
$339$	3.94645			0.214342
$340$		0			0
$341$		0			0
$342$	38.1386	−	22.0193i	2.06230	−	1.19067i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$		0			0
$345$	12.8380	−	47.9120i	0.691173	−	2.57949i
$346$	−25.6075	−	25.6075i	−1.37667	−	1.37667i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	7.82407	−	2.09645i	0.418813	−	0.112221i	−0.0432574	−	0.999064i	$-0.513774\pi$
$349$	7.82407	−	2.09645i	0.418813	−	0.112221i	0.462070	+	0.886843i	$0.347107\pi$
$350$		−	54.4998i		−	2.91314i
$351$	50.8472	−	1.44568i	2.71402	−	0.0771644i
$352$		0			0
$353$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$353$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$354$	−18.7185	+	32.4215i	−0.994879	+	1.72318i
$355$	63.4983	−	36.6608i	3.37014	−	1.94575i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.6541	−	26.6541i	−1.40675	−	1.40675i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	−26.6541	−	26.6541i	−1.40675	−	1.40675i	−0.630814	−	0.775934i	$-0.717279\pi$
$360$	46.1603	+	79.9520i	2.43286	+	4.21384i
$361$	−1.03196	−	0.595801i	−0.0543135	−	0.0313579i
$362$	−32.0860	+	8.59741i	−1.68640	+	0.451870i
$363$			35.4384i			1.86003i
$364$	5.45971	+	18.2809i	0.286166	+	0.958180i
$365$		0			0
$366$	−1.76735	−	6.59585i	−0.0923810	−	0.344770i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−12.0576	+	6.96148i	−0.628548	+	0.362892i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	131.671	−	35.2810i	6.79944	−	1.82190i
$376$		0			0
$377$		0			0
$378$	52.7879			2.71512
$379$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$379$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$380$	−18.6664	+	32.3311i	−0.957565	+	1.65855i
$381$	−26.4857	+	15.2915i	−1.35690	+	0.783408i
$382$	27.2250	−	27.2250i	1.39295	−	1.39295i
$383$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$383$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$384$	9.43370	−	35.2070i	0.481411	−	1.79665i
$385$		0			0
$386$	4.15799	+	7.20185i	0.211636	+	0.366565i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−61.8703	+	38.1054i	−3.13292	+	1.92954i
$391$		0			0
$392$	5.12436	+	19.1244i	0.258819	+	0.965926i
$393$	17.0034	−	29.4507i	0.857706	−	1.48559i
$394$		0			0
$395$	−25.8301	+	25.8301i	−1.29965	+	1.29965i
$396$		0			0
$397$	−4.56394	+	17.0329i	−0.229058	+	0.854855i	0.751680	+	0.659528i	$0.229244\pi$
$397$	−4.56394	+	17.0329i	−0.229058	+	0.854855i	−0.980738	+	0.195327i	$0.937423\pi$
$398$		0			0
$399$	17.9851	+	31.1511i	0.900380	+	1.55950i
$400$	−50.4570	−	29.1314i	−2.52285	−	1.45657i
$401$	−15.3336	+	4.10862i	−0.765723	+	0.205175i	−0.620481	−	0.784221i	$-0.713063\pi$
$401$	−15.3336	+	4.10862i	−0.765723	+	0.205175i	−0.145242	+	0.989396i	$0.546396\pi$
$402$		0			0
$403$		0			0
$404$	−40.1028			−1.99519
$405$	26.6912	+	99.6128i	1.32630	+	4.94980i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$409$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$410$		0			0
$411$	−43.5461	−	43.5461i	−2.14797	−	2.14797i
$412$		0			0
$413$	−18.8272	−	10.8699i	−0.926426	−	0.534872i
$414$	−35.0862	+	9.40133i	−1.72439	+	0.462050i
$415$			76.6129i			3.76078i
$416$	19.8432	+	4.71685i	0.972891	+	0.231263i
$417$	17.1663			0.840639
$418$		0			0
$419$	−13.3866	+	23.1864i	−0.653981	+	1.13273i	0.328168	+	0.944619i	$0.393569\pi$
$419$	−13.3866	+	23.1864i	−0.653981	+	1.13273i	−0.982148	+	0.188108i	$0.939764\pi$
$420$	−65.3038	+	37.7031i	−3.18650	+	1.83972i
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−65.4049	−	37.7615i	−3.16888	−	1.82955i
$427$	3.83022	−	1.02630i	0.185357	−	0.0496664i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.99356	+	7.44009i	0.0960266	+	0.358376i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	1.99356	+	7.44009i	0.0960266	+	0.358376i	−0.901146	+	0.433515i	$0.857273\pi$
$432$	28.2163	−	48.8721i	1.35756	−	2.35136i
$433$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$433$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.3865	−	10.3865i	−0.496854	−	0.496854i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$			51.6540i			2.45972i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	20.4448	+	5.47817i	0.965926	+	0.258819i
$449$	−5.49485	+	20.5071i	−0.259318	+	0.967788i	0.706319	+	0.707894i	$0.250354\pi$
$449$	−5.49485	+	20.5071i	−0.259318	+	0.967788i	−0.965637	+	0.259895i	$0.916312\pi$
$450$	−107.482	−	107.482i	−5.06677	−	5.06677i
$451$		0			0
$452$	2.12171	+	1.22497i	0.0997970	+	0.0576178i
$453$	48.1401	−	12.8991i	2.26182	−	0.606053i
$454$			39.1607i			1.83790i
$455$	−22.1279	−	35.9282i	−1.03737	−	1.68434i
$456$	38.4537			1.80076
$457$	10.1944	+	38.0460i	0.476873	+	1.77972i	0.614157	+	0.789184i	$0.289496\pi$
$457$	10.1944	+	38.0460i	0.476873	+	1.77972i	−0.137283	+	0.990532i	$0.543837\pi$
$458$	−16.6904	+	28.9087i	−0.779893	+	1.35081i
$459$		0			0
$460$	21.7738	−	21.7738i	1.01521	−	1.01521i
$461$	0.570661	+	0.152908i	0.0265783	+	0.00712164i	0.272084	−	0.962274i	$-0.412287\pi$
$461$	0.570661	+	0.152908i	0.0265783	+	0.00712164i	−0.245505	+	0.969395i	$0.578954\pi$
$462$		0			0
$463$	28.2019	+	28.2019i	1.31065	+	1.31065i	0.920935	+	0.389716i	$0.127427\pi$
$463$	28.2019	+	28.2019i	1.31065	+	1.31065i	0.389716	+	0.920935i	$0.372573\pi$
$464$		0			0
$465$		0			0
$466$	−27.5429	+	7.38009i	−1.27590	+	0.341876i
$467$			34.5598i			1.59924i	0.600508	+	0.799618i	$0.294965\pi$
$467$			34.5598i			1.59924i	−0.600508	+	0.799618i	$0.705035\pi$
$468$	46.8203	+	25.2855i	2.16427	+	1.16882i
$469$		0			0
$470$		0			0
$471$	−37.4235	+	64.8193i	−1.72438	+	2.98672i
$472$	−20.1271	+	11.6204i	−0.926426	+	0.534872i
$473$		0			0
$474$	36.3440	+	9.73834i	1.66933	+	0.447297i
$475$	15.9089	−	59.3728i	0.729950	−	2.72421i
$476$		0			0
$477$		0			0
$478$	−0.656763	−	0.379182i	−0.0300396	−	0.0173434i
$479$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$479$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$480$			80.6127i			3.67945i
$481$		0			0
$482$		0			0
$483$	−7.67888	−	28.6580i	−0.349401	−	1.30398i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	32.7867	−	32.7867i	1.48724	−	1.48724i
$487$	−11.4461	−	3.06697i	−0.518672	−	0.138978i	−0.0100195	−	0.999950i	$-0.503189\pi$
$487$	−11.4461	−	3.06697i	−0.518672	−	0.138978i	−0.508652	+	0.860972i	$0.669856\pi$
$488$	1.09717	−	4.09468i	0.0496664	−	0.185357i
$489$		0			0
$490$	−21.8943	−	37.9220i	−0.989083	−	1.71314i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$	0.611544	+	21.5092i	0.0275147	+	0.967743i
$495$		0			0
$496$		0			0
$497$	21.9282	−	37.9807i	0.983614	−	1.70367i
$498$	68.3409	−	39.4567i	3.06243	−	1.76809i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	81.7406	+	21.9023i	3.65555	+	0.979502i
$501$		0			0
$502$	−2.97325	−	2.97325i	−0.132703	−	0.132703i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	47.8223	+	27.6102i	2.13018	+	1.22986i
$505$	85.6714	−	22.9556i	3.81233	−	1.02151i
$506$		0			0
$507$	−18.8462	+	37.4018i	−0.836989	+	1.66107i
$508$	−18.9858			−0.842361
$509$	7.71548	+	28.7946i	0.341983	+	1.27630i	0.896098	+	0.443857i	$0.146390\pi$
$509$	7.71548	+	28.7946i	0.341983	+	1.27630i	−0.554115	+	0.832440i	$0.686943\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	57.5078	+	15.4092i	2.53903	+	0.680331i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	82.4989i		−	3.62130i
$520$	−45.0909	+	1.28201i	−1.97737	+	0.0562200i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	17.3322	−	30.0202i	0.757884	−	1.31269i	−0.186044	−	0.982541i	$-0.559567\pi$
$523$	17.3322	−	30.0202i	0.757884	−	1.31269i	0.943928	−	0.330152i	$-0.107100\pi$
$524$	18.2829	−	10.5556i	0.798691	−	0.461125i
$525$	87.7902	−	87.7902i	3.83148	−	3.83148i
$526$	−30.9461	−	8.29198i	−1.34931	−	0.361547i
$527$		0			0
$528$		0			0
$529$	−5.44222	−	9.42621i	−0.236618	−	0.409835i
$530$		0			0
$531$	−58.5674	+	15.6931i	−2.54161	+	0.681022i
$532$			22.3301i			0.968134i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	15.7933	−	15.7933i	0.680896	−	0.680896i
$539$		0			0
$540$	−32.3031	+	120.557i	−1.39010	+	5.18794i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	−65.5342	−	37.8362i	−2.81234	−	1.62371i
$544$		0			0
$545$		0			0
$546$	−20.6528	+	38.2422i	−0.883860	+	1.63661i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−9.89486	−	36.9281i	−0.422687	−	1.57749i
$549$	5.52977	−	9.57785i	0.236005	−	0.408772i
$550$		0			0
$551$		0			0
$552$	−30.6367	−	8.20907i	−1.30398	−	0.349401i
$553$	−5.65507	+	21.1050i	−0.240478	+	0.897477i
$554$		0			0
$555$		0			0
$556$	9.22906	+	5.32840i	0.391399	+	0.225974i
$557$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$557$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$558$		0			0
$559$		0			0
$560$	−46.8119			−1.97817
$561$		0			0
$562$	22.4833	−	38.9422i	0.948401	−	1.64268i
$563$	−34.5173	+	19.9286i	−1.45473	+	0.839889i	−0.998744	−	0.0500986i	$-0.984046\pi$
$563$	−34.5173	+	19.9286i	−1.45473	+	0.839889i	−0.455985	+	0.889987i	$0.650713\pi$
$564$		0			0
$565$	−5.23381	−	1.40239i	−0.220188	−	0.0589992i
$566$	4.34405	−	16.2122i	0.182594	−	0.681450i
$567$	43.6172	+	43.6172i	1.83175	+	1.83175i
$568$	−23.4422	−	40.6031i	−0.983614	−	1.70367i
$569$	13.0405	+	7.52896i	0.546688	+	0.315631i	0.747785	−	0.663941i	$-0.231117\pi$
$569$	13.0405	+	7.52896i	0.546688	+	0.315631i	−0.201097	+	0.979571i	$0.564451\pi$
$570$	−82.1485	+	22.0116i	−3.44082	+	0.921966i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	87.7098			3.66413
$574$		0			0
$575$	−25.3497	+	43.9070i	−1.05716	+	1.83105i
$576$	51.1242	−	29.5166i	2.13018	−	1.22986i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	23.2224	+	6.22243i	0.965926	+	0.258819i
$579$	−4.90316	+	18.2988i	−0.203768	+	0.760473i
$580$		0			0
$581$	22.9125	+	39.6857i	0.950573	+	1.64644i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−114.496	−	27.2164i	−4.73382	−	1.12526i
$586$	−2.16441			−0.0894108
$587$	−10.4600	−	39.0373i	−0.431731	−	1.61124i	−0.748771	−	0.662829i	$-0.769356\pi$
$587$	−10.4600	−	39.0373i	−0.431731	−	1.61124i	0.317041	−	0.948412i	$-0.397311\pi$
$588$	−22.5517	+	39.0607i	−0.930016	+	1.61083i
$589$		0			0
$590$	36.3458	−	36.3458i	1.49633	−	1.49633i
$591$		0			0
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	4.10453	−	17.2672i	0.167847	−	0.706110i
$599$	48.9290			1.99918			0.999592	−	0.0285537i	$-0.00909015\pi$
$599$	48.9290			1.99918			0.999592	+	0.0285537i	$0.00909015\pi$
$600$	−34.3521	−	128.204i	−1.40242	−	5.23390i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	29.8852	+	8.00772i	1.21601	+	0.325830i
$605$	12.5932	−	46.9985i	0.511987	−	1.91076i
$606$	−64.5989	−	64.5989i	−2.62415	−	2.62415i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	20.6737	+	11.9360i	0.838429	+	0.484067i
$609$		0			0
$610$			9.37548i			0.379602i
$611$		0			0
$612$		0			0
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$	−5.97537	+	10.3496i	−0.241146	+	0.417678i
$615$		0			0
$616$		0			0
$617$	−34.8305	−	9.33281i	−1.40222	−	0.375725i	−0.523081	−	0.852283i	$-0.675218\pi$
$617$	−34.8305	−	9.33281i	−1.40222	−	0.375725i	−0.879143	+	0.476558i	$0.841884\pi$
$618$		0			0
$619$	12.3565	+	12.3565i	0.496650	+	0.496650i	0.910394	−	0.413743i	$-0.135779\pi$
$619$	12.3565	+	12.3565i	0.496650	+	0.496650i	−0.413743	+	0.910394i	$0.635779\pi$
$620$		0			0
$621$	−42.5278	−	24.5534i	−1.70658	−	0.985295i
$622$		0			0
$623$		0			0
$624$	24.3660	+	39.5621i	0.975420	+	1.58375i
$625$	−114.331			−4.57324
$626$		0			0
$627$		0			0
$628$	−40.2396	+	23.2323i	−1.60573	+	0.927071i
$629$		0			0
$630$	−117.967	−	31.6092i	−4.69993	−	1.25934i
$631$	−2.81430	+	10.5031i	−0.112035	+	0.418122i	−0.999048	−	0.0436231i	$-0.986110\pi$
$631$	−2.81430	+	10.5031i	−0.112035	+	0.418122i	0.887013	+	0.461745i	$0.152777\pi$
$632$	16.5167	+	16.5167i	0.656998	+	0.656998i
$633$		0			0
$634$		0			0
$635$	40.5594	−	10.8679i	1.60955	−	0.431278i
$636$		0			0
$637$	−22.2073	−	11.9931i	−0.879886	−	0.475185i
$638$		0			0
$639$	−31.6582	−	118.150i	−1.25238	−	4.67394i
$640$	−25.0220	+	43.3394i	−0.989083	+	1.71314i
$641$	36.6643	−	21.1681i	1.44815	−	0.836090i	0.449780	−	0.893140i	$-0.351502\pi$
$641$	36.6643	−	21.1681i	1.44815	−	0.836090i	0.998371	+	0.0570491i	$0.0181691\pi$
$642$		0			0
$643$	40.1357	+	10.7543i	1.58280	+	0.424109i	0.939790	−	0.341752i	$-0.111020\pi$
$643$	40.1357	+	10.7543i	1.58280	+	0.424109i	0.643006	+	0.765861i	$0.277687\pi$
$644$	4.76702	−	17.7908i	0.187847	−	0.701054i
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	63.6961	−	17.0673i	2.50222	−	0.670467i
$649$		0			0
$650$	71.1648	−	21.2538i	2.79131	−	0.833642i
$651$		0			0
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−33.0154	+	33.0154i	−1.29002	+	1.29002i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−43.4381	+	11.6392i	−1.68955	+	0.452713i	−0.970273	−	0.242012i	$-0.922193\pi$
$661$	−43.4381	+	11.6392i	−1.68955	+	0.452713i	−0.719275	+	0.694725i	$0.755526\pi$
$662$		0			0
$663$		0			0
$664$	48.9891			1.90115
$665$	−12.7822	−	47.7038i	−0.495672	−	1.84987i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	24.1088	+	41.7576i	0.930016	+	1.61083i
$673$	38.8844	+	22.4499i	1.49889	+	0.865382i	0.999999	−	0.00128586i	$-0.000409302\pi$
$673$	38.8844	+	22.4499i	1.49889	+	0.865382i	0.498886	+	0.866668i	$0.333743\pi$
$674$	50.1445	−	13.4362i	1.93149	−	0.517542i
$675$		−	205.495i		−	7.90951i
$676$	−21.7417	+	14.2583i	−0.836218	+	0.548398i
$677$	−23.6537			−0.909087			−0.454543	−	0.890725i	$-0.650198\pi$
$677$	−23.6537			−0.909087			−0.454543	+	0.890725i	$0.650198\pi$
$678$	1.44450	+	5.39096i	0.0554758	+	0.207038i
$679$		0			0
$680$		0			0
$681$	−63.0813	+	63.0813i	−2.41728	+	2.41728i
$682$		0			0
$683$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$683$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$684$	44.0386	+	44.0386i	1.68386	+	1.68386i
$685$	42.2767	+	73.2254i	1.61531	+	2.79780i
$686$	−22.6826	−	13.0958i	−0.866025	−	0.500000i
$687$	−73.4526	+	19.6816i	−2.80239	+	0.750899i
$688$		0			0
$689$		0			0
$690$	70.1480			2.67049
$691$	−9.21525	−	34.3918i	−0.350565	−	1.30833i	−0.885975	−	0.463733i	$-0.846510\pi$
$691$	−9.21525	−	34.3918i	−0.350565	−	1.30833i	0.535410	−	0.844592i	$-0.320157\pi$
$692$	25.6075	−	44.3535i	0.973452	−	1.68607i
$693$		0			0
$694$		0			0
$695$	−22.7661	−	6.10015i	−0.863566	−	0.231392i
$696$		0			0
$697$		0			0
$698$	5.72761	+	9.92052i	0.216793	+	0.375497i
$699$	−56.2551	−	32.4789i	−2.12776	−	1.22846i
$700$	74.4482	−	19.9483i	2.81388	−	0.753976i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	20.5862	+	68.9294i	0.776975	+	2.60157i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.5127	−	37.5127i	1.41081	−	1.41081i
$708$	−51.1400	−	13.7029i	−1.92196	−	0.514987i
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$	73.3215	+	73.3215i	2.75171	+	2.75171i
$711$	30.4698	+	52.7752i	1.14271	+	1.97922i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.447136	−	1.66873i	−0.0166986	−	0.0623200i
$718$	26.6541	−	46.1662i	0.994721	−	1.72291i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−92.3207	+	92.3207i	−3.44059	+	3.44059i
$721$		0			0
$722$	0.436156	−	1.62776i	0.0162321	−	0.0605789i
$723$		0			0
$724$	−23.4886	−	40.6834i	−0.872945	−	1.51199i
$725$		0			0
$726$	−48.4097	+	12.9713i	−1.79665	+	0.481411i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−22.9738	+	14.1494i	−0.851465	+	0.524411i
$729$	35.6848			1.32166
$730$		0			0
$731$		0			0
$732$	8.36320	−	4.82850i	0.309113	−	0.178466i
$733$	−33.1335	+	33.1335i	−1.22381	+	1.22381i	−0.257546	+	0.966266i	$0.582914\pi$
$733$	−33.1335	+	33.1335i	−1.22381	+	1.22381i	−0.966266	+	0.257546i	$0.917086\pi$
$734$		0			0
$735$	25.8180	−	96.3541i	0.952312	−	3.55408i
$736$	−13.9230	−	13.9230i	−0.513207	−	0.513207i
$737$		0			0
$738$		0			0
$739$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$739$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$740$		0			0
$741$	−33.6626	+	35.6328i	−1.23663	+	1.30900i
$742$		0			0
$743$	11.2522	+	41.9939i	0.412804	+	1.54061i	0.789193	+	0.614145i	$0.210499\pi$
$743$	11.2522	+	41.9939i	0.412804	+	1.54061i	−0.376389	+	0.926462i	$0.622834\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	123.454	+	33.0793i	4.51694	+	1.21031i
$748$		0			0
$749$		0			0
$750$	96.3896	+	166.952i	3.51965	+	6.09621i
$751$	47.2211	+	27.2631i	1.72312	+	0.994845i	0.912263	+	0.409605i	$0.134333\pi$
$751$	47.2211	+	27.2631i	1.72312	+	0.994845i	0.810860	+	0.585240i	$0.199000\pi$
$752$		0			0
$753$		−	9.57883i		−	0.349072i
$754$		0			0
$755$	−68.4275			−2.49033
$756$	19.3217	+	72.1096i	0.702724	+	2.62260i
$757$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$757$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$		0			0
$760$	−50.9975	−	13.6647i	−1.84987	−	0.495672i
$761$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$761$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$762$	−30.5830	−	30.5830i	−1.10791	−	1.10791i
$763$		0			0
$764$	47.1550	+	27.2250i	1.70601	+	0.984965i
$765$		0			0
$766$		0			0
$767$	6.85146	−	28.8232i	0.247392	−	1.04075i
$768$	51.5467			1.86003
$769$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$769$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$770$		0			0
$771$		0			0
$772$	−8.31598	+	8.31598i	−0.299299	+	0.299299i
$773$	−4.94989	−	1.32632i	−0.178035	−	0.0477044i	0.168700	−	0.985667i	$-0.446043\pi$
$773$	−4.94989	−	1.32632i	−0.178035	−	0.0477044i	−0.346735	+	0.937963i	$0.612710\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−74.6991	−	70.5688i	−2.67466	−	2.52677i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.2487	+	14.0000i	−0.866025	+	0.500000i
$785$	72.6651	−	72.6651i	2.59353	−	2.59353i
$786$	46.4540	+	12.4473i	1.65696	+	0.443981i
$787$	−10.4819	+	39.1191i	−0.373641	+	1.39445i	0.481680	+	0.876347i	$0.340027\pi$
$787$	−10.4819	+	39.1191i	−0.373641	+	1.39445i	−0.855321	+	0.518099i	$0.826640\pi$
$788$		0			0
$789$	−36.4920	−	63.2060i	−1.29915	−	2.25019i
$790$	−44.7390	−	25.8301i	−1.59174	−	0.918993i
$791$	−3.13054	+	0.838825i	−0.111309	+	0.0298252i
$792$		0			0
$793$	2.83383	+	4.60118i	0.100632	+	0.163393i
$794$	−24.9378			−0.885011
$795$		0			0
$796$		0			0
$797$	13.2267	−	7.63642i	0.468513	−	0.270496i	−0.247104	−	0.968989i	$-0.579479\pi$
$797$	13.2267	−	7.63642i	0.468513	−	0.270496i	0.715617	+	0.698493i	$0.246146\pi$
$798$	−35.9702	+	35.9702i	−1.27333	+	1.27333i
$799$		0			0
$800$	21.3257	−	79.5884i	0.753976	−	2.81388i
$801$		0			0
$802$	−11.2250	−	19.4422i	−0.396368	−	0.686529i
$803$		0			0
$804$		0			0
$805$			40.7351i			1.43572i
$806$		0			0
$807$	50.8807			1.79109
$808$	−14.6786	−	54.7814i	−0.516393	−	1.92720i
$809$	−27.8375	+	48.2159i	−0.978713	+	1.69518i	−0.311619	+	0.950207i	$0.600871\pi$
$809$	−27.8375	+	48.2159i	−0.978713	+	1.69518i	−0.667094	+	0.744973i	$0.732462\pi$
$810$	−126.304	+	72.9217i	−4.43787	+	2.56221i
$811$	−16.5261	+	16.5261i	−0.580310	+	0.580310i	−0.934988	−	0.354679i	$-0.884590\pi$
$811$	−16.5261	+	16.5261i	−0.580310	+	0.580310i	0.354679	+	0.934988i	$0.384590\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−67.4488	+	20.1440i	−2.35685	+	0.703888i
$820$		0			0
$821$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$821$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$822$	43.5461	−	75.4240i	1.51884	−	2.63072i
$823$	−10.7206	+	6.18954i	−0.373697	+	0.215754i	−0.675072	−	0.737752i	$-0.735888\pi$
$823$	−10.7206	+	6.18954i	−0.373697	+	0.215754i	0.301376	+	0.953506i	$0.402554\pi$
$824$		0			0
$825$		0			0
$826$	7.95731	−	29.6971i	0.276870	−	1.03329i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	−25.6849	−	44.4876i	−0.892612	−	1.54605i
$829$	7.64657	+	4.41475i	0.265576	+	0.153331i	0.626876	−	0.779119i	$-0.284333\pi$
$829$	7.64657	+	4.41475i	0.265576	+	0.153331i	−0.361299	+	0.932450i	$0.617667\pi$
$830$	−104.655	+	28.0423i	−3.63263	+	0.973362i
$831$		0			0
$832$	0.819767	+	28.8328i	0.0284203	+	0.999596i
$833$		0			0
$834$	6.28331	+	23.4496i	0.217573	+	0.811995i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−36.5730	−	9.79971i	−1.26339	−	0.338525i
$839$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$839$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$840$	−75.4063	−	75.4063i	−2.60176	−	2.60176i
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$	98.9464	−	26.5126i	3.40789	−	0.913143i
$844$		0			0
$845$	38.2849	−	42.9054i	1.31704	−	1.47599i
$846$		0			0
$847$	−7.53248	−	28.1116i	−0.258819	−	0.965926i
$848$		0			0
$849$	33.1127	−	19.1176i	1.13643	−	0.656116i
$850$		0			0
$851$		0			0
$852$	27.6434	−	103.166i	0.947046	−	3.53442i
$853$	29.1336	+	29.1336i	0.997515	+	0.997515i	0.999997	−	0.00248202i	$-0.000790052\pi$
$853$	29.1336	+	29.1336i	0.997515	+	0.997515i	−0.00248202	+	0.999997i	$0.500790\pi$
$854$	2.80392	+	4.85652i	0.0959480	+	0.166187i
$855$	−119.288	−	68.8710i	−4.07957	−	2.35534i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−41.1363			−1.40355			−0.701776	−	0.712398i	$-0.747609\pi$
$859$	−41.1363			−1.40355			−0.701776	+	0.712398i	$0.747609\pi$
$860$		0			0
$861$		0			0
$862$	−9.43365	+	5.44652i	−0.321311	+	0.185509i
$863$	−29.0285	+	29.0285i	−0.988143	+	0.988143i	−0.999931	−	0.0117879i	$-0.996248\pi$
$863$	−29.0285	+	29.0285i	−0.988143	+	0.988143i	0.0117879	+	0.999931i	$0.496248\pi$
$864$	77.0884	+	20.6558i	2.62260	+	0.702724i
$865$	−29.3164	+	109.410i	−0.996789	+	3.72007i
$866$		0			0
$867$	27.3842	+	47.4308i	0.930016	+	1.61083i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	10.3865	−	17.9899i	0.351329	−	0.608519i
$875$	−96.9491	+	55.9736i	−3.27748	+	1.89225i
$876$		0			0
$877$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$877$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$878$		0			0
$879$	−3.48650	−	3.48650i	−0.117597	−	0.117597i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	−70.5607	+	18.9067i	−2.37590	+	0.636621i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	117.094			3.93607
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	17.7596	−	17.7596i	0.595639	−	0.595639i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$			29.9333i			1.00000i
$897$	34.4264	−	21.2029i	1.14946	−	0.707945i
$898$	−30.0244			−1.00193
$899$		0			0
$900$	107.482	−	186.165i	3.58275	−	6.20550i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.896742	+	3.34669i	−0.0298252	+	0.111309i
$905$	73.4664	+	73.4664i	2.44211	+	2.44211i
$906$	35.2410	+	61.0393i	1.17080	+	2.02789i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	−53.4944	+	14.3338i	−1.77528	+	0.475684i
$909$		−	147.962i		−	4.90759i
$910$	40.9795	−	43.3779i	1.35846	−	1.43796i
$911$	52.1724			1.72855			0.864274	−	0.503022i	$-0.167778\pi$
$911$	52.1724			1.72855			0.864274	+	0.503022i	$0.167778\pi$
$912$	14.0750	+	52.5287i	0.466071	+	1.73940i
$913$		0			0
$914$	−48.2404	+	27.8516i	−1.59565	+	0.921249i
$915$	−15.1023	+	15.1023i	−0.499268	+	0.499268i
$916$	−45.5991	−	12.2182i	−1.50664	−	0.403702i
$917$	−7.22818	+	26.9759i	−0.238696	+	0.890824i
$918$		0			0
$919$	0.663673	+	1.14952i	0.0218926	+	0.0379190i	0.876764	−	0.480921i	$-0.159697\pi$
$919$	0.663673	+	1.14952i	0.0218926	+	0.0379190i	−0.854872	+	0.518840i	$0.826364\pi$
$920$	37.7133	+	21.7738i	1.24337	+	0.717861i
$921$	−26.2969	+	7.04623i	−0.866512	+	0.232181i
$922$			0.835506i			0.0275159i
$923$	58.1460	+	13.8217i	1.91390	+	0.454946i
$924$		0			0
$925$		0			0
$926$	−28.2019	+	48.8470i	−0.926770	+	1.60521i
$927$		0			0
$928$		0			0
$929$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$929$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$930$		0			0
$931$	−20.8879	−	20.8879i	−0.684574	−	0.684574i
$932$	−20.1628	−	34.9230i	−0.660454	−	1.14394i
$933$		0			0
$934$	−47.2096	+	12.6498i	−1.54474	+	0.413913i
$935$		0			0
$936$	−17.4032	+	73.2128i	−0.568840	+	2.39304i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	40.9192	−	40.9192i	1.33393	−	1.33393i	0.432101	−	0.901825i	$-0.357772\pi$
$941$	40.9192	−	40.9192i	1.33393	−	1.33393i	0.901825	−	0.432101i	$-0.142228\pi$
$942$	−102.243	−	27.3959i	−3.33125	−	0.892606i
$943$		0			0
$944$	−23.2408	−	23.2408i	−0.756424	−	0.756424i
$945$	−82.5538	−	142.987i	−2.68548	−	4.65138i
$946$		0			0
$947$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$947$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$948$			53.2113i			1.72822i
$949$		0			0
$950$	86.9278			2.82031
$951$		0			0
$952$		0			0
$953$	−45.8326	+	26.4615i	−1.48466	+	0.857171i	−0.999848	−	0.0174443i	$-0.994447\pi$
$953$	−45.8326	+	26.4615i	−1.48466	+	0.857171i	−0.484817	+	0.874616i	$0.661114\pi$
$954$		0			0
$955$	−116.321	−	31.1682i	−3.76407	−	1.00858i
$956$	0.277580	−	1.03594i	0.00897759	−	0.0335048i
$957$		0			0
$958$		0			0
$959$	43.7989	+	25.2873i	1.41434	+	0.816569i
$960$	−110.119	+	29.5063i	−3.55408	+	0.952312i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.0052	−	22.5256i	0.418651	−	0.725125i
$966$	36.3368	−	20.9791i	1.16912	−	0.674991i
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.360971	−	0.932577i	$-0.382445\pi$
$967$	40.2250	−	40.2250i	1.29355	−	1.29355i	0.932577	−	0.360971i	$-0.117555\pi$
$968$	−30.0526	−	8.05256i	−0.965926	−	0.258819i
$969$		0			0
$970$		0			0
$971$	−30.8853	−	53.4950i	−0.991157	−	1.71673i	−0.610493	−	0.792021i	$-0.709029\pi$
$971$	−30.8853	−	53.4950i	−0.991157	−	1.71673i	−0.380664	−	0.924713i	$-0.624305\pi$
$972$	56.7883	+	32.7867i	1.82148	+	1.05163i
$973$	−13.6173	+	3.64873i	−0.436549	+	0.116973i
$974$		−	16.7582i		−	0.536968i
$975$	148.871	+	80.3983i	4.76769	+	2.57481i
$976$	5.99502			0.191896
$977$	8.51030	+	31.7609i	0.272269	+	1.01612i	0.957650	+	0.287936i	$0.0929689\pi$
$977$	8.51030	+	31.7609i	0.272269	+	1.01612i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$		0			0
$980$	43.7886	−	43.7886i	1.39877	−	1.39877i
$981$		0			0
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−29.1582	+	8.70829i	−0.927647	+	0.277048i
$989$		0			0
$990$		0			0
$991$	19.7951	−	34.2861i	0.628811	−	1.08913i	−0.358980	−	0.933345i	$-0.616875\pi$
$991$	19.7951	−	34.2861i	0.628811	−	1.08913i	0.987791	−	0.155787i	$-0.0497914\pi$
$992$		0			0
$993$		0			0
$994$	59.9089	+	16.0525i	1.90020	+	0.509156i
$995$		0			0
$996$	78.9133	+	78.9133i	2.50046	+	2.50046i
$997$	23.7448	+	41.1271i	0.752004	+	1.30251i	0.946850	+	0.321675i	$0.104246\pi$
$997$	23.7448	+	41.1271i	0.752004	+	1.30251i	−0.194846	+	0.980834i	$0.562421\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.ds.a.461.1	yes	16
7.6	odd	2	inner	728.2.ds.a.461.4	yes	16
8.5	even	2	inner	728.2.ds.a.461.4	yes	16
13.11	odd	12	inner	728.2.ds.a.349.1	✓	16
56.13	odd	2	CM	728.2.ds.a.461.1	yes	16
91.76	even	12	inner	728.2.ds.a.349.4	yes	16
104.37	odd	12	inner	728.2.ds.a.349.4	yes	16
728.349	even	12	inner	728.2.ds.a.349.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.a.349.1	✓	16	13.11	odd	12	inner
728.2.ds.a.349.1	✓	16	728.349	even	12	inner
728.2.ds.a.349.4	yes	16	91.76	even	12	inner
728.2.ds.a.349.4	yes	16	104.37	odd	12	inner
728.2.ds.a.461.1	yes	16	1.1	even	1	trivial
728.2.ds.a.461.1	yes	16	56.13	odd	2	CM
728.2.ds.a.461.4	yes	16	7.6	odd	2	inner
728.2.ds.a.461.4	yes	16	8.5	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.ds (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.61083 + 2.79005i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(3.12775 - 3.12775i) q^{5} +(-4.40088 - 1.17921i) q^{6} +(0.684771 - 2.55560i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.68957 - 6.39053i) q^{9} +(5.41743 + 3.12775i) q^{10} -6.44334i q^{12} +(3.60409 - 0.102471i) q^{13} +3.74166 q^{14} +(3.68829 + 13.7649i) q^{15} +(2.00000 - 3.46410i) q^{16} +(7.37915 - 7.37915i) q^{18} +(4.07621 + 1.09222i) q^{19} +(-2.28968 + 8.54518i) q^{20} +(6.02719 + 6.02719i) q^{21} +(-3.01441 - 1.74037i) q^{23} +(8.80176 - 2.35843i) q^{24} -14.5657i q^{25} +(1.45917 + 4.88578i) q^{26} +14.1082 q^{27} +(1.36954 + 5.11120i) q^{28} +(-17.4532 + 10.0766i) q^{30} +(5.46410 + 1.46410i) q^{32} +(-5.85149 - 10.1351i) q^{35} +(12.7811 + 7.37915i) q^{36} +5.96798i q^{38} +(-5.51970 + 10.2207i) q^{39} -12.5110 q^{40} +(-6.02719 + 10.4394i) q^{42} +(-31.5281 - 8.44793i) q^{45} +(1.27404 - 4.75478i) q^{46} +(6.44334 + 11.1602i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(19.8971 - 5.33141i) q^{50} +(-6.14000 + 3.78158i) q^{52} +(5.16395 + 19.2721i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(-9.61343 + 9.61343i) q^{57} +(2.12668 - 7.93688i) q^{59} +(-20.1532 - 20.1532i) q^{60} +(0.749378 + 1.29796i) q^{61} +(-18.8581 + 5.05303i) q^{63} +8.00000i q^{64} +(10.9522 - 11.5932i) q^{65} +(9.71143 - 5.60690i) q^{69} +(11.7030 - 11.7030i) q^{70} +(16.0113 + 4.29022i) q^{71} +(-5.40191 + 20.1602i) q^{72} +(40.6390 + 23.4629i) q^{75} +(-8.15241 + 2.18443i) q^{76} +(-15.9820 - 3.79903i) q^{78} -8.25834 q^{79} +(-4.57935 - 17.0904i) q^{80} +(-11.6572 + 20.1908i) q^{81} +(-12.2473 + 12.2473i) q^{83} +(-16.4666 - 4.41221i) q^{84} -46.1603i q^{90} +(2.20610 - 9.28079i) q^{91} +6.96148 q^{92} +(16.1656 - 9.33319i) q^{95} +(-12.8867 + 12.8867i) q^{96} +(2.56218 - 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 32 q^{8} - 32 q^{9} + 40 q^{15} + 32 q^{16} + 64 q^{18} - 96 q^{30} + 32 q^{32} - 48 q^{36} + 8 q^{39} + 24 q^{46} + 136 q^{50} - 72 q^{57} - 32 q^{60} - 112 q^{63} - 16 q^{65} + 16 q^{71}+ \cdots - 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 32 * q^8 - 32 * q^9 + 40 * q^15 + 32 * q^16 + 64 * q^18 - 96 * q^30 + 32 * q^32 - 48 * q^36 + 8 * q^39 + 24 * q^46 + 136 * q^50 - 72 * q^57 - 32 * q^60 - 112 * q^63 - 16 * q^65 + 16 * q^71 + 112 * q^72 - 144 * q^78 - 192 * q^79 - 96 * q^81 - 96 * q^92 + 312 * q^95 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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