LMFDB - Embedded newform 728.2.ds.b.461.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(293,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.293"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [16,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 13 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			461.3
Root			$-1.61083 + 0.636563i$ of defining polynomial
Character	$\chi$	$=$	728.461
Dual form			728.2.ds.b.349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.636563 - 1.10256i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.465997 - 0.465997i) q^{5} +(-1.73912 - 0.465997i) q^{6} +(-0.684771 + 2.55560i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.689574 + 1.19438i) q^{9} +(-0.807130 - 0.465997i) q^{10} +2.54625i q^{12} +(0.102471 + 3.60409i) q^{13} +3.74166 q^{14} +(-0.217153 - 0.810426i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.37915 - 1.37915i) q^{18} +(7.36841 + 1.97436i) q^{19} +(-0.341133 + 1.27313i) q^{20} +(2.38180 + 2.38180i) q^{21} +(-3.01441 - 1.74037i) q^{23} +(3.47825 - 0.931993i) q^{24} +4.56569i q^{25} +(4.88578 - 1.45917i) q^{26} +5.57521 q^{27} +(-1.36954 - 5.11120i) q^{28} +(-1.02758 + 0.593273i) q^{30} +(-5.46410 - 1.46410i) q^{32} +(0.871800 + 1.51000i) q^{35} +(-2.38875 - 1.37915i) q^{36} -10.7881i q^{38} +(4.03896 + 2.18125i) q^{39} +1.86399 q^{40} +(2.38180 - 4.12540i) q^{42} +(0.877915 + 0.235237i) q^{45} +(-1.27404 + 4.75478i) q^{46} +(-2.54625 - 4.41024i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(6.23685 - 1.67116i) q^{50} +(-3.78158 - 6.14000i) q^{52} +(-2.04067 - 7.61588i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(6.86731 - 6.86731i) q^{57} +(3.35950 - 12.5378i) q^{59} +(1.18655 + 1.18655i) q^{60} +(7.77422 + 13.4653i) q^{61} +(-3.52455 + 0.944400i) q^{63} +8.00000i q^{64} +(1.72725 + 1.63175i) q^{65} +(-3.83773 + 2.21571i) q^{69} +(1.74360 - 1.74360i) q^{70} +(-16.0113 - 4.29022i) q^{71} +(-1.00961 + 3.76790i) q^{72} +(5.03395 + 2.90635i) q^{75} +(-14.7368 + 3.94872i) q^{76} +(1.50129 - 6.31572i) q^{78} +8.25834 q^{79} +(-0.682267 - 2.54625i) q^{80} +(1.48025 - 2.56387i) q^{81} +(4.00054 - 4.00054i) q^{83} +(-6.50720 - 1.74360i) q^{84} -1.28536i q^{90} +(-9.28079 - 2.20610i) q^{91} +6.96148 q^{92} +(4.35370 - 2.51361i) q^{95} +(-5.09251 + 5.09251i) q^{96} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 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 - 16 * q^9 - 56 * q^15 + 32 * q^16 - 32 * q^18 - 96 * q^30 - 32 * q^32 + 48 * q^36 + 72 * q^39 - 24 * q^46 + 56 * q^50 + 88 * q^57 - 32 * q^60 - 112 * q^63 + 16 * q^65 - 16 * q^71 + 16 * q^72 + 16 * q^78 + 192 * q^79 - 48 * q^81 - 96 * q^92 + 120 * 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
$3$	0.636563	−	1.10256i	0.367520	−	0.636563i	−0.621657	−	0.783289i	$-0.713540\pi$
$3$	0.636563	−	1.10256i	0.367520	−	0.636563i	0.989177	+	0.146726i	$0.0468736\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	0.465997	−	0.465997i	0.208400	−	0.208400i	−0.595187	−	0.803587i	$-0.702922\pi$
$5$	0.465997	−	0.465997i	0.208400	−	0.208400i	0.803587	+	0.595187i	$0.202922\pi$
$6$	−1.73912	−	0.465997i	−0.709994	−	0.190242i
$7$	−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
$9$	0.689574	+	1.19438i	0.229858	+	0.398126i
$10$	−0.807130	−	0.465997i	−0.255237	−	0.147361i
$11$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$11$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$12$			2.54625i			0.735040i
$13$	0.102471	+	3.60409i	0.0284203	+	0.999596i
$13$	0.102471	+	3.60409i	0.0284203	+	0.999596i
$14$	3.74166			1.00000
$15$	−0.217153	−	0.810426i	−0.0560687	−	0.209251i
$16$	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	$0.833333\pi$
$18$	1.37915	−	1.37915i	0.325068	−	0.325068i
$19$	7.36841	+	1.97436i	1.69043	+	0.452949i	0.970501	−	0.241098i	$-0.0775076\pi$
$19$	7.36841	+	1.97436i	1.69043	+	0.452949i	0.719929	+	0.694048i	$0.244174\pi$
$20$	−0.341133	+	1.27313i	−0.0762797	+	0.284680i
$21$	2.38180	+	2.38180i	0.519752	+	0.519752i
$22$		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	$0.784877\pi$
$24$	3.47825	−	0.931993i	0.709994	−	0.190242i
$25$			4.56569i			0.913139i
$26$	4.88578	−	1.45917i	0.958180	−	0.286166i
$27$	5.57521			1.07295
$28$	−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	$0.666667\pi$
$30$	−1.02758	+	0.593273i	−0.187609	+	0.108316i
$31$		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
$35$	0.871800	+	1.51000i	0.147361	+	0.255237i
$36$	−2.38875	−	1.37915i	−0.398126	−	0.229858i
$37$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$37$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$38$		−	10.7881i		−	1.75006i
$39$	4.03896	+	2.18125i	0.646751	+	0.349280i
$40$	1.86399			0.294722
$41$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$41$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$42$	2.38180	−	4.12540i	0.367520	−	0.636563i
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$	0.877915	+	0.235237i	0.130872	+	0.0350670i
$46$	−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	$0.250000\pi$
$48$	−2.54625	−	4.41024i	−0.367520	−	0.636563i
$49$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$50$	6.23685	−	1.67116i	0.882024	−	0.236338i
$51$		0			0
$52$	−3.78158	−	6.14000i	−0.524411	−	0.851465i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−2.04067	−	7.61588i	−0.277700	−	1.03639i
$55$		0			0
$56$	−6.48074	+	3.74166i	−0.866025	+	0.500000i
$57$	6.86731	−	6.86731i	0.909598	−	0.909598i
$58$		0			0
$59$	3.35950	−	12.5378i	0.437369	−	1.63229i	−0.297962	−	0.954578i	$-0.596307\pi$
$59$	3.35950	−	12.5378i	0.437369	−	1.63229i	0.735332	−	0.677707i	$-0.237026\pi$
$60$	1.18655	+	1.18655i	0.153182	+	0.153182i
$61$	7.77422	+	13.4653i	0.995386	+	1.72406i	0.580787	+	0.814056i	$0.302745\pi$
$61$	7.77422	+	13.4653i	0.995386	+	1.72406i	0.414600	+	0.910004i	$0.363922\pi$
$62$		0			0
$63$	−3.52455	+	0.944400i	−0.444052	+	0.118983i
$64$			8.00000i			1.00000i
$65$	1.72725	+	1.63175i	0.214239	+	0.202393i
$66$		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
$69$	−3.83773	+	2.21571i	−0.462008	+	0.266740i
$70$	1.74360	−	1.74360i	0.208400	−	0.208400i
$71$	−16.0113	−	4.29022i	−1.90020	−	0.509156i	−0.996760	−	0.0804327i	$-0.974370\pi$
$71$	−16.0113	−	4.29022i	−1.90020	−	0.509156i	−0.903436	−	0.428723i	$-0.858964\pi$
$72$	−1.00961	+	3.76790i	−0.118983	+	0.444052i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	5.03395	+	2.90635i	0.581271	+	0.335597i
$76$	−14.7368	+	3.94872i	−1.69043	+	0.452949i
$77$		0			0
$78$	1.50129	−	6.31572i	0.169987	−	0.715114i
$79$	8.25834			0.929136			0.464568	−	0.885537i	$-0.346210\pi$
$79$	8.25834			0.929136			0.464568	+	0.885537i	$0.346210\pi$
$80$	−0.682267	−	2.54625i	−0.0762797	−	0.284680i
$81$	1.48025	−	2.56387i	0.164473	−	0.284875i
$82$		0			0
$83$	4.00054	−	4.00054i	0.439116	−	0.439116i	−0.452598	−	0.891715i	$-0.649503\pi$
$83$	4.00054	−	4.00054i	0.439116	−	0.439116i	0.891715	+	0.452598i	$0.149503\pi$
$84$	−6.50720	−	1.74360i	−0.709994	−	0.190242i
$85$		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	$0.916667\pi$
$90$		−	1.28536i		−	0.135489i
$91$	−9.28079	−	2.20610i	−0.972891	−	0.231263i
$92$	6.96148			0.725785
$93$		0			0
$94$		0			0
$95$	4.35370	−	2.51361i	0.446680	−	0.257891i
$96$	−5.09251	+	5.09251i	−0.519752	+	0.519752i
$97$		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
$100$	−4.56569	−	7.90801i	−0.456569	−	0.790801i
$101$	−1.20682	−	0.696757i	−0.120083	−	0.0693299i	0.438755	−	0.898607i	$-0.355419\pi$
$101$	−1.20682	−	0.696757i	−0.120083	−	0.0693299i	−0.558838	+	0.829277i	$0.688753\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−7.00325	+	7.41313i	−0.686725	+	0.726917i
$105$	2.21982			0.216633
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−9.65655	+	5.57521i	−0.929202	+	0.536475i
$109$		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	0.893396	−	0.449271i	$-0.148316\pi$
$113$	0.612486	+	1.06086i	0.0576178	+	0.0997970i	−0.835778	+	0.549068i	$0.814983\pi$
$114$	−11.8945	−	6.86731i	−1.11403	−	0.643183i
$115$	−2.21571	+	0.593698i	−0.206616	+	0.0553626i
$116$		0			0
$117$	−4.23399	+	2.60768i	−0.391432	+	0.241080i
$118$	−18.3566			−1.68987
$119$		0			0
$120$	1.18655	−	2.05516i	0.108316	−	0.187609i
$121$	9.52628	−	5.50000i	0.866025	−	0.500000i
$122$	15.5484	−	15.5484i	1.40769	−	1.40769i
$123$		0			0
$124$		0			0
$125$	4.45758	+	4.45758i	0.398698	+	0.398698i
$126$	2.58015	+	4.46895i	0.229858	+	0.398126i
$127$	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
$130$	1.59679	−	2.95672i	0.140048	−	0.259322i
$131$	20.3120			1.77467			0.887335	−	0.461125i	$-0.152554\pi$
$131$	20.3120			1.77467			0.887335	+	0.461125i	$0.152554\pi$
$132$		0			0
$133$	−10.0913	+	17.4787i	−0.875031	+	1.51560i
$134$		0			0
$135$	2.59803	−	2.59803i	0.223603	−	0.223603i
$136$		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	$0.779207\pi$
$138$	4.43142	+	4.43142i	0.377228	+	0.377228i
$139$	−11.4849	−	19.8924i	−0.974133	−	1.68725i	−0.682766	−	0.730637i	$-0.739223\pi$
$139$	−11.4849	−	19.8924i	−0.974133	−	1.68725i	−0.291367	−	0.956611i	$-0.594110\pi$
$140$	−3.02000	−	1.74360i	−0.255237	−	0.147361i
$141$		0			0
$142$			23.4422i			1.96723i
$143$		0			0
$144$	5.51659			0.459716
$145$		0			0
$146$		0			0
$147$	−7.71792	+	4.45594i	−0.636563	+	0.367520i
$148$		0			0
$149$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$149$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$150$	2.12760	−	7.94031i	0.173718	−	0.648323i
$151$	−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	$0.966722\pi$
$152$	10.7881	+	18.6855i	0.875031	+	1.51560i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−9.17694	+	0.260917i	−0.734743	+	0.0208901i
$157$	−9.39459			−0.749770			−0.374885	−	0.927071i	$-0.622318\pi$
$157$	−9.39459			−0.749770			−0.374885	+	0.927071i	$0.622318\pi$
$158$	−3.02276	−	11.2811i	−0.240478	−	0.897477i
$159$		0			0
$160$	−3.22852	+	1.86399i	−0.255237	+	0.147361i
$161$	6.51187	−	6.51187i	0.513207	−	0.513207i
$162$	−4.04413	−	1.08362i	−0.317737	−	0.0851372i
$163$		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
$166$	−6.92914	−	4.00054i	−0.537805	−	0.310502i
$167$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$167$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$168$			9.52721i			0.735040i
$169$	−12.9790	+	0.738629i	−0.998385	+	0.0568176i
$170$		0			0
$171$	2.72294	+	10.1621i	0.208228	+	0.777118i
$172$		0			0
$173$	−5.21453	+	3.01061i	−0.396454	+	0.228893i	−0.684953	−	0.728588i	$-0.740177\pi$
$173$	−5.21453	+	3.01061i	−0.396454	+	0.228893i	0.288499	+	0.957480i	$0.406844\pi$
$174$		0			0
$175$	−11.6681	−	3.12645i	−0.882024	−	0.236338i
$176$		0			0
$177$	−11.6852	−	11.6852i	−0.878311	−	0.878311i
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	−1.75583	+	0.470473i	−0.130872	+	0.0350670i
$181$			13.1258i			0.975636i	0.872945	+	0.487818i	$0.162207\pi$
$181$			13.1258i			0.975636i	−0.872945	+	0.487818i	$0.837793\pi$
$182$	0.383411	+	13.4853i	0.0284203	+	0.999596i
$183$	19.7951			1.46330
$184$	−2.54808	−	9.50956i	−0.187847	−	0.701054i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−3.81774	+	14.2480i	−0.277700	+	1.03639i
$190$	−5.02722	−	5.02722i	−0.364713	−	0.364713i
$191$	13.6125	+	23.5775i	0.984965	+	1.70601i	0.642092	+	0.766627i	$0.278067\pi$
$191$	13.6125	+	23.5775i	0.984965	+	1.70601i	0.342873	+	0.939382i	$0.388600\pi$
$192$	8.82048	+	5.09251i	0.636563	+	0.367520i
$193$	−5.67992	+	1.52193i	−0.408850	+	0.109551i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	−5.67992	+	1.52193i	−0.408850	+	0.109551i	0.0485316	+	0.998822i	$0.484546\pi$
$194$		0			0
$195$	2.89860	−	0.865685i	0.207573	−	0.0619930i
$196$	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	$0.833333\pi$
$200$	−9.13139	+	9.13139i	−0.645687	+	0.645687i
$201$		0			0
$202$	−0.510061	+	1.90357i	−0.0358878	+	0.133935i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	4.80046i		−	0.333655i
$208$	12.6899	+	6.85322i	0.879886	+	0.475185i
$209$		0			0
$210$	−0.812512	−	3.03234i	−0.0560687	−	0.209251i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−14.9225	+	14.9225i	−1.02247	+	1.02247i
$214$		0			0
$215$		0			0
$216$	11.1504	+	11.1504i	0.758690	+	0.758690i
$217$		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
$225$	−5.45316	+	3.14838i	−0.363544	+	0.209892i
$226$	1.22497	−	1.22497i	0.0814839	−	0.0814839i
$227$	−11.4787	−	3.07572i	−0.761871	−	0.204143i	−0.143094	−	0.989709i	$-0.545705\pi$
$227$	−11.4787	−	3.07572i	−0.761871	−	0.204143i	−0.618777	+	0.785566i	$0.712372\pi$
$228$	−5.02722	+	18.7618i	−0.332936	+	1.24253i
$229$	−13.3951	−	13.3951i	−0.885175	−	0.885175i	0.108880	−	0.994055i	$-0.465274\pi$
$229$	−13.3951	−	13.3951i	−0.885175	−	0.885175i	−0.994055	+	0.108880i	$0.965274\pi$
$230$	1.62201	+	2.80941i	0.106952	+	0.185247i
$231$		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	$0.770364\pi$
$234$	5.11190	+	4.82926i	0.334176	+	0.315699i
$235$		0			0
$236$	6.71900	+	25.0756i	0.437369	+	1.63229i
$237$	5.25696	−	9.10532i	0.341476	−	0.591454i
$238$		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	$0.255521\pi$
$240$	−3.24170	−	0.868612i	−0.209251	−	0.0560687i
$241$		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
$243$	6.47827	+	11.2207i	0.415581	+	0.719807i
$244$	−26.9307	−	15.5484i	−1.72406	−	0.995386i
$245$	−4.45594	+	1.19397i	−0.284680	+	0.0762797i
$246$		0			0
$247$	−6.36073	+	26.7588i	−0.404724	+	1.70262i
$248$		0			0
$249$	−1.86424	−	6.95743i	−0.118141	−	0.440909i
$250$	4.45758	−	7.72076i	0.281922	−	0.488304i
$251$	27.3198	−	15.7731i	1.72441	−	0.995588i	0.815287	−	0.579057i	$-0.196579\pi$
$251$	27.3198	−	15.7731i	1.72441	−	0.995588i	0.909122	−	0.416530i	$-0.136754\pi$
$252$	5.16030	−	5.16030i	0.325068	−	0.325068i
$253$		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
$260$	−4.62343	−	1.09902i	−0.286733	−	0.0681582i
$261$		0			0
$262$	−7.43472	−	27.7468i	−0.459319	−	1.71420i
$263$	11.3271	−	19.6190i	0.698456	−	1.20976i	−0.270546	−	0.962707i	$-0.587204\pi$
$263$	11.3271	−	19.6190i	0.698456	−	1.20976i	0.969002	−	0.247054i	$-0.0794625\pi$
$264$		0			0
$265$		0			0
$266$	27.5701	+	7.38738i	1.69043	+	0.452949i
$267$		0			0
$268$		0			0
$269$	−14.3751	−	24.8984i	−0.876464	−	1.51808i	−0.855194	−	0.518307i	$-0.826562\pi$
$269$	−14.3751	−	24.8984i	−0.876464	−	1.51808i	−0.0212700	−	0.999774i	$-0.506771\pi$
$270$	−4.49992	−	2.59803i	−0.273856	−	0.158111i
$271$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$271$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$272$		0			0
$273$	−8.34018	+	8.82831i	−0.504770	+	0.534313i
$274$	27.0333			1.63314
$275$		0			0
$276$	4.43142	−	7.67545i	0.266740	−	0.462008i
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	−22.9697	+	22.9697i	−1.37763	+	1.37763i
$279$		0			0
$280$	−1.27640	+	4.76360i	−0.0762797	+	0.284680i
$281$	−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
$283$	−27.2646	−	15.7412i	−1.62071	−	0.935720i	−0.986729	−	0.162374i	$-0.948085\pi$
$283$	−27.2646	−	15.7412i	−1.62071	−	0.935720i	−0.633985	−	0.773345i	$-0.718582\pi$
$284$	32.0227	−	8.58045i	1.90020	−	0.509156i
$285$		−	6.40029i		−	0.379120i
$286$		0			0
$287$		0			0
$288$	−2.01921	−	7.53581i	−0.118983	−	0.444052i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.85168	−	33.0349i	0.517121	−	1.92992i	0.215378	−	0.976531i	$-0.430902\pi$
$293$	8.85168	−	33.0349i	0.517121	−	1.92992i	0.301742	−	0.953390i	$-0.402432\pi$
$294$	8.91189	+	8.91189i	0.519752	+	0.519752i
$295$	−4.27707	−	7.40810i	−0.249021	−	0.431316i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.96357	−	11.0426i	0.344882	−	0.638608i
$300$	−11.6254			−0.671194
$301$		0			0
$302$	−10.9388	+	18.9465i	−0.629454	+	1.09025i
$303$	−1.53643	+	0.887060i	−0.0882657	+	0.0509602i
$304$	21.5762	−	21.5762i	1.23748	−	1.23748i
$305$	9.89756	+	2.65204i	0.566733	+	0.151856i
$306$		0			0
$307$	−24.0478	−	24.0478i	−1.37248	−	1.37248i	−0.856755	−	0.515723i	$-0.827523\pi$
$307$	−24.0478	−	24.0478i	−1.37248	−	1.37248i	−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	$0.5\pi$
$312$	3.71541	+	12.4404i	0.210344	+	0.704301i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	3.43866	+	12.8333i	0.194055	+	0.724222i
$315$	−1.20234	+	2.08252i	−0.0677443	+	0.117337i
$316$	−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
$320$	3.72797	+	3.72797i	0.208400	+	0.208400i
$321$		0			0
$322$	−11.2789	−	6.51187i	−0.628548	−	0.362892i
$323$		0			0
$324$			5.92101i			0.328945i
$325$	−16.4552	+	0.467850i	−0.912770	+	0.0259517i
$326$		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	$0.0833333\pi$
$332$	−2.92860	+	10.9297i	−0.160728	+	0.599844i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	13.0144	−	3.48720i	0.709994	−	0.190242i
$337$			36.7083i			1.99963i	0.0192914	+	0.999814i	$0.493859\pi$
$337$			36.7083i			1.99963i	−0.0192914	+	0.999814i	$0.506141\pi$
$338$	5.75963	+	17.4593i	0.313283	+	0.949660i
$339$	1.55954			0.0847028
$340$		0			0
$341$		0			0
$342$	12.8851	−	7.43920i	0.696745	−	0.402266i
$343$	13.0958	−	13.0958i	0.707107	−	0.707107i
$344$		0			0
$345$	−0.755853	+	2.82088i	−0.0406938	+	0.151871i
$346$	6.02122	+	6.02122i	0.323703	+	0.323703i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	35.2317	−	9.44029i	1.88591	−	0.505327i	0.886843	−	0.462070i	$-0.152893\pi$
$349$	35.2317	−	9.44029i	1.88591	−	0.505327i	0.999064	−	0.0432574i	$-0.0137735\pi$
$350$			17.0833i			0.913139i
$351$	0.571296	+	20.0936i	0.0304935	+	1.07252i
$352$		0			0
$353$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$353$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$354$	−11.6852	+	20.2393i	−0.621060	+	1.07571i
$355$	−9.46046	+	5.46200i	−0.502109	+	0.289893i
$356$		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	$-0.717279\pi$
$360$	1.28536	+	2.22630i	0.0677443	+	0.117337i
$361$	33.9409	+	19.5958i	1.78636	+	1.03136i
$362$	17.9302	−	4.80439i	0.942392	−	0.252513i
$363$		−	14.0044i		−	0.735040i
$364$	18.2809	−	5.45971i	0.958180	−	0.286166i
$365$		0			0
$366$	−7.24552	−	27.0406i	−0.378729	−	1.41344i
$367$		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
$375$	7.75229	−	2.07722i	0.400326	−	0.107267i
$376$		0			0
$377$		0			0
$378$	20.8605			1.07295
$379$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$379$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$380$	−5.02722	+	8.70740i	−0.257891	+	0.446680i
$381$	10.4665	−	6.04285i	0.536216	−	0.309584i
$382$	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	$0.0833333\pi$
$384$	3.72797	−	13.9130i	0.190242	−	0.709994i
$385$		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	$0.5\pi$
$390$	−2.24351	−	3.64270i	−0.113604	−	0.184455i
$391$		0			0
$392$	−5.12436	−	19.1244i	−0.258819	−	0.965926i
$393$	12.9299	−	22.3952i	0.652227	−	1.12969i
$394$		0			0
$395$	3.84836	−	3.84836i	0.193632	−	0.193632i
$396$		0			0
$397$	9.24912	−	34.5182i	0.464200	−	1.73242i	−0.195327	−	0.980738i	$-0.562577\pi$
$397$	9.24912	−	34.5182i	0.464200	−	1.73242i	0.659528	−	0.751680i	$-0.270756\pi$
$398$		0			0
$399$	12.8476	+	22.2526i	0.643183	+	1.11403i
$400$	15.8160	+	9.13139i	0.790801	+	0.456569i
$401$	15.3336	−	4.10862i	0.765723	−	0.205175i	0.145242	−	0.989396i	$-0.453604\pi$
$401$	15.3336	−	4.10862i	0.765723	−	0.205175i	0.620481	+	0.784221i	$0.286937\pi$
$402$		0			0
$403$		0			0
$404$	2.78703			0.138660
$405$	−0.504963	−	1.88455i	−0.0250918	−	0.0936440i
$406$		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
$411$	17.2084	+	17.2084i	0.848827	+	0.848827i
$412$		0			0
$413$	29.7412	+	17.1711i	1.46347	+	0.844933i
$414$	−6.55755	+	1.75709i	−0.322286	+	0.0863562i
$415$		−	3.72848i		−	0.183024i
$416$	4.71685	−	19.8432i	0.231263	−	0.972891i
$417$	−29.2434			−1.43205
$418$		0			0
$419$	15.4854	−	26.8215i	0.756511	−	1.31032i	−0.188108	−	0.982148i	$-0.560236\pi$
$419$	15.4854	−	26.8215i	0.756511	−	1.31032i	0.944619	−	0.328168i	$-0.106431\pi$
$420$	−3.84485	+	2.21982i	−0.187609	+	0.108316i
$421$		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
$426$	25.8465	+	14.9225i	1.25227	+	0.722996i
$427$	−39.7356	+	10.6471i	−1.92294	+	0.515250i
$428$		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	$0.857273\pi$
$432$	11.1504	−	19.3131i	0.536475	−	0.929202i
$433$		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
$437$	−18.7753	−	18.7753i	−0.898144	−	0.898144i
$438$		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
$441$		−	9.65404i		−	0.459716i
$442$		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	$0.916312\pi$
$450$	6.29677	+	6.29677i	0.296833	+	0.296833i
$451$		0			0
$452$	−2.12171	−	1.22497i	−0.0997970	−	0.0576178i
$453$	−19.0238	+	5.09742i	−0.893818	+	0.239498i
$454$			16.8061i			0.788747i
$455$	−5.35286	+	3.29678i	−0.250946	+	0.154555i
$456$	27.4692			1.28637
$457$	−10.1944	−	38.0460i	−0.476873	−	1.77972i	−0.614157	−	0.789184i	$-0.710504\pi$
$457$	−10.1944	−	38.0460i	−0.476873	−	1.77972i	0.137283	−	0.990532i	$-0.456163\pi$
$458$	−13.3951	+	23.2010i	−0.625913	+	1.08411i
$459$		0			0
$460$	3.24403	−	3.24403i	0.151254	−	0.151254i
$461$	41.4747	+	11.1131i	1.93167	+	0.517589i	0.969395	+	0.245505i	$0.0789539\pi$
$461$	41.4747	+	11.1131i	1.93167	+	0.517589i	0.962274	+	0.272084i	$0.0877128\pi$
$462$		0			0
$463$	−28.2019	−	28.2019i	−1.31065	−	1.31065i	−0.920935	−	0.389716i	$-0.872573\pi$
$463$	−28.2019	−	28.2019i	−1.31065	−	1.31065i	−0.389716	−	0.920935i	$-0.627427\pi$
$464$		0			0
$465$		0			0
$466$	27.5429	−	7.38009i	1.27590	−	0.341876i
$467$			25.9542i			1.20102i	0.799618	+	0.600508i	$0.205035\pi$
$467$			25.9542i			1.20102i	−0.799618	+	0.600508i	$0.794965\pi$
$468$	4.72580	−	8.75062i	0.218450	−	0.404498i
$469$		0			0
$470$		0			0
$471$	−5.98025	+	10.3581i	−0.275555	+	0.477276i
$472$	31.7946	−	18.3566i	1.46347	−	0.844933i
$473$		0			0
$474$	−14.3623	−	3.84836i	−0.659681	−	0.176761i
$475$	−9.01432	+	33.6419i	−0.413606	+	1.54360i
$476$		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	$0.916667\pi$
$480$			4.74618i			0.216633i
$481$		0			0
$482$		0			0
$483$	−3.03451	−	11.3249i	−0.138075	−	0.515303i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	12.9565	−	12.9565i	0.587720	−	0.587720i
$487$	−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	$0.669856\pi$
$488$	−11.3822	+	42.4791i	−0.515250	+	1.92294i
$489$		0			0
$490$	3.26198	+	5.64991i	0.147361	+	0.255237i
$491$		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
$494$	38.8814	−	1.10547i	1.74935	−	0.0497373i
$495$		0			0
$496$		0			0
$497$	21.9282	−	37.9807i	0.983614	−	1.70367i
$498$	−8.82167	+	5.09319i	−0.395308	+	0.228231i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	−12.1783	−	3.26318i	−0.544632	−	0.145934i
$501$		0			0
$502$	−31.5462	−	31.5462i	−1.40797	−	1.40797i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	−8.93790	−	5.16030i	−0.398126	−	0.229858i
$505$	−0.887060	+	0.237687i	−0.0394736	+	0.0105769i
$506$		0			0
$507$	−7.44757	+	14.7803i	−0.330758	+	0.656417i
$508$	−18.9858			−0.842361
$509$	−8.76684	−	32.7183i	−0.388583	−	1.45021i	−0.832440	−	0.554115i	$-0.813057\pi$
$509$	−8.76684	−	32.7183i	−0.388583	−	1.45021i	0.443857	−	0.896098i	$-0.353610\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	41.0805	+	11.0075i	1.81375	+	0.485992i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$			7.66578i			0.336490i
$520$	0.191004	+	6.71799i	0.00837609	+	0.294603i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−14.9196	+	25.8415i	−0.652390	+	1.12997i	0.330152	+	0.943928i	$0.392900\pi$
$523$	−14.9196	+	25.8415i	−0.652390	+	1.12997i	−0.982541	+	0.186044i	$0.940433\pi$
$524$	−35.1815	+	20.3120i	−1.53691	+	0.887335i
$525$	−10.8746	+	10.8746i	−0.474606	+	0.474606i
$526$	−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
$531$	17.2915	−	4.63325i	0.750388	−	0.201066i
$532$		−	40.3654i		−	1.75006i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−28.7502	+	28.7502i	−1.23951	+	1.23951i
$539$		0			0
$540$	−1.90189	+	7.09795i	−0.0818443	+	0.305447i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	14.4720	+	8.35543i	0.621054	+	0.358566i
$544$		0			0
$545$		0			0
$546$	15.1124	+	8.16151i	0.646751	+	0.349280i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−9.89486	−	36.9281i	−0.422687	−	1.57749i
$549$	−10.7218	+	18.5707i	−0.457595	+	0.792578i
$550$		0			0
$551$		0			0
$552$	−12.1069	−	3.24403i	−0.515303	−	0.138075i
$553$	−5.65507	+	21.1050i	−0.240478	+	0.897477i
$554$		0			0
$555$		0			0
$556$	39.7847	+	22.9697i	1.68725	+	0.974133i
$557$		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
$560$	6.97440			0.294722
$561$		0			0
$562$	−22.4833	+	38.9422i	−0.948401	+	1.64268i
$563$	−22.3060	+	12.8784i	−0.940086	+	0.542759i	−0.889987	−	0.455985i	$-0.849287\pi$
$563$	−22.3060	+	12.8784i	−0.940086	+	0.542759i	−0.0500986	+	0.998744i	$0.515954\pi$
$564$		0			0
$565$	0.779772	+	0.208939i	0.0328053	+	0.00879015i
$566$	−11.5234	+	43.0059i	−0.484364	+	1.80767i
$567$	5.53860	+	5.53860i	0.232599	+	0.232599i
$568$	−23.4422	−	40.6031i	−0.983614	−	1.70367i
$569$	−13.0405	−	7.52896i	−0.546688	−	0.315631i	0.201097	−	0.979571i	$-0.435549\pi$
$569$	−13.0405	−	7.52896i	−0.546688	−	0.315631i	−0.747785	+	0.663941i	$0.768883\pi$
$570$	−8.74296	+	2.34267i	−0.366202	+	0.0981236i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	34.6608			1.44798
$574$		0			0
$575$	7.94600	−	13.7629i	0.331371	−	0.573951i
$576$	−9.55502	+	5.51659i	−0.398126	+	0.229858i
$577$		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
$579$	−1.93761	+	7.23126i	−0.0805243	+	0.300521i
$580$		0			0
$581$	7.48432	+	12.9632i	0.310502	+	0.537805i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.757855	+	3.18819i	−0.0313334	+	0.131816i
$586$	−48.3665			−1.99800
$587$	6.91914	+	25.8226i	0.285583	+	1.06581i	0.948412	+	0.317041i	$0.102689\pi$
$587$	6.91914	+	25.8226i	0.285583	+	1.06581i	−0.662829	+	0.748771i	$0.730644\pi$
$588$	8.91189	−	15.4358i	0.367520	−	0.636563i
$589$		0			0
$590$	−8.55414	+	8.55414i	−0.352168	+	0.352168i
$591$		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
$598$	−17.2672	−	4.10453i	−0.706110	−	0.167847i
$599$	−48.9290			−1.99918			−0.999592	−	0.0285537i	$-0.990910\pi$
$599$	−48.9290			−1.99918			−0.999592	+	0.0285537i	$0.990910\pi$
$600$	4.25520	+	15.8806i	0.173718	+	0.648323i
$601$		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
$605$	1.87623	−	7.00220i	0.0762797	−	0.284680i
$606$	1.77412	+	1.77412i	0.0720687	+	0.0720687i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	−37.3711	−	21.5762i	−1.51560	−	0.875031i
$609$		0			0
$610$		−	14.4910i		−	0.586725i
$611$		0			0
$612$		0			0
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$	−24.0478	+	41.6519i	−0.970489	+	1.68094i
$615$		0			0
$616$		0			0
$617$	34.8305	+	9.33281i	1.40222	+	0.375725i	0.879143	−	0.476558i	$-0.158116\pi$
$617$	34.8305	+	9.33281i	1.40222	+	0.375725i	0.523081	+	0.852283i	$0.324782\pi$
$618$		0			0
$619$	32.9441	+	32.9441i	1.32414	+	1.32414i	0.910394	+	0.413743i	$0.135779\pi$
$619$	32.9441	+	32.9441i	1.32414	+	1.32414i	0.413743	+	0.910394i	$0.364221\pi$
$620$		0			0
$621$	−16.8060	−	9.70293i	−0.674400	−	0.389365i
$622$		0			0
$623$		0			0
$624$	15.6340	−	9.62886i	0.625861	−	0.385463i
$625$	−18.6740			−0.746961
$626$		0			0
$627$		0			0
$628$	16.2719	−	9.39459i	0.649320	−	0.374885i
$629$		0			0
$630$	3.28486	+	0.880175i	0.130872	+	0.0350670i
$631$	2.81430	−	10.5031i	0.112035	−	0.418122i	−0.887013	−	0.461745i	$-0.847223\pi$
$631$	2.81430	−	10.5031i	0.112035	−	0.418122i	0.999048	+	0.0436231i	$0.0138901\pi$
$632$	16.5167	+	16.5167i	0.656998	+	0.656998i
$633$		0			0
$634$		0			0
$635$	6.04285	−	1.61918i	0.239803	−	0.0642550i
$636$		0			0
$637$	11.9931	−	22.2073i	0.475185	−	0.879886i
$638$		0			0
$639$	−5.91686	−	22.0820i	−0.234067	−	0.873551i
$640$	3.72797	−	6.45704i	0.147361	−	0.255237i
$641$	−36.6643	+	21.1681i	−1.44815	+	0.836090i	−0.998371	−	0.0570491i	$-0.981831\pi$
$641$	−36.6643	+	21.1681i	−1.44815	+	0.836090i	−0.449780	+	0.893140i	$0.648498\pi$
$642$		0			0
$643$	−28.0863	−	7.52569i	−1.10761	−	0.296784i	−0.341752	−	0.939790i	$-0.611020\pi$
$643$	−28.0863	−	7.52569i	−1.10761	−	0.296784i	−0.765861	+	0.643006i	$0.777687\pi$
$644$	−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	$0.166667\pi$
$648$	8.08825	−	2.16724i	0.317737	−	0.0851372i
$649$		0			0
$650$	6.66211	+	22.3070i	0.261310	+	0.874951i
$651$		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
$655$	9.46534	−	9.46534i	0.369842	−	0.369842i
$656$		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
$661$	24.0835	−	6.45314i	0.936738	−	0.250998i	0.242012	−	0.970273i	$-0.422193\pi$
$661$	24.0835	−	6.45314i	0.936738	−	0.250998i	0.694725	+	0.719275i	$0.255526\pi$
$662$		0			0
$663$		0			0
$664$	16.0022			0.621004
$665$	3.44249	+	12.8476i	0.133494	+	0.498207i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−9.52721	−	16.5016i	−0.367520	−	0.636563i
$673$	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
$675$			25.4547i			0.979752i
$676$	21.7417	−	14.2583i	0.836218	−	0.548398i
$677$	−46.3519			−1.78145			−0.890725	−	0.454543i	$-0.849802\pi$
$677$	−46.3519			−1.78145			−0.890725	+	0.454543i	$0.849802\pi$
$678$	−0.570833	−	2.13038i	−0.0219227	−	0.0818167i
$679$		0			0
$680$		0			0
$681$	−10.6981	+	10.6981i	−0.409953	+	0.409953i
$682$		0			0
$683$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$683$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$684$	−14.8784	−	14.8784i	−0.568890	−	0.568890i
$685$	6.29870	+	10.9097i	0.240661	+	0.416837i
$686$	−22.6826	−	13.0958i	−0.866025	−	0.500000i
$687$	−23.2958	+	6.24209i	−0.888790	+	0.238150i
$688$		0			0
$689$		0			0
$690$	4.13006			0.157229
$691$	10.0116	+	37.3638i	0.380859	+	1.42139i	0.844592	+	0.535410i	$0.179843\pi$
$691$	10.0116	+	37.3638i	0.380859	+	1.42139i	−0.463733	+	0.885975i	$0.653490\pi$
$692$	6.02122	−	10.4291i	0.228893	−	0.396454i
$693$		0			0
$694$		0			0
$695$	−14.6217	−	3.91787i	−0.554632	−	0.148613i
$696$		0			0
$697$		0			0
$698$	−25.7914	−	44.6720i	−0.976218	−	1.69086i
$699$	22.2307	+	12.8349i	0.840842	+	0.485460i
$700$	23.3362	−	6.25291i	0.882024	−	0.236338i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	27.2392	−	8.13517i	1.02808	−	0.307042i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.60703	−	2.60703i	0.0980473	−	0.0980473i
$708$	31.9245	+	8.55414i	1.19980	+	0.321484i
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$	10.9240	+	10.9240i	0.409970	+	0.409970i
$711$	5.69474	+	9.86358i	0.213569	+	0.369913i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.176698	+	0.659444i	0.00659889	+	0.0246274i
$718$	−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	$0.833333\pi$
$720$	2.57071	−	2.57071i	0.0958049	−	0.0958049i
$721$		0			0
$722$	14.3451	−	53.5367i	0.533870	−	1.99243i
$723$		0			0
$724$	−13.1258	−	22.7346i	−0.487818	−	0.844926i
$725$		0			0
$726$	−19.1304	+	5.12596i	−0.709994	+	0.190242i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−14.1494	−	22.9738i	−0.524411	−	0.851465i
$729$	25.3768			0.939882
$730$		0			0
$731$		0			0
$732$	−34.2862	+	19.7951i	−1.26725	+	0.731649i
$733$	19.1879	−	19.1879i	0.708720	−	0.708720i	−0.257546	−	0.966266i	$-0.582914\pi$
$733$	19.1879	−	19.1879i	0.708720	−	0.708720i	0.966266	+	0.257546i	$0.0829140\pi$
$734$		0			0
$735$	−1.52007	+	5.67298i	−0.0560687	+	0.209251i
$736$	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
$741$	25.4541	+	24.0467i	0.935081	+	0.883379i
$742$		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
$747$	7.53682	+	2.01949i	0.275758	+	0.0738891i
$748$		0			0
$749$		0			0
$750$	−5.67507	−	9.82950i	−0.207224	−	0.358923i
$751$	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
$753$		−	40.1623i		−	1.46359i
$754$		0			0
$755$	−10.1948			−0.371028
$756$	−7.63548	−	28.4960i	−0.277700	−	1.03639i
$757$		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
$760$	13.7346	+	3.68018i	0.498207	+	0.133494i
$761$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$761$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$762$	−12.0857	−	12.0857i	−0.437818	−	0.437818i
$763$		0			0
$764$	−47.1550	−	27.2250i	−1.70601	−	0.984965i
$765$		0			0
$766$		0			0
$767$	45.5317	+	10.8232i	1.64406	+	0.390803i
$768$	−20.3700			−0.735040
$769$		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
$773$	−53.4825	−	14.3306i	−1.92363	−	0.515435i	−0.985667	−	0.168700i	$-0.946043\pi$
$773$	−53.4825	−	14.3306i	−1.92363	−	0.515435i	−0.937963	−	0.346735i	$-0.887290\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−4.15484	+	4.39801i	−0.148767	+	0.157474i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.2487	+	14.0000i	−0.866025	+	0.500000i
$785$	−4.37785	+	4.37785i	−0.156252	+	0.156252i
$786$	−35.3251	−	9.46534i	−1.26001	−	0.337618i
$787$	−10.0501	+	37.5076i	−0.358248	+	1.33700i	0.518099	+	0.855321i	$0.326640\pi$
$787$	−10.0501	+	37.5076i	−0.358248	+	1.33700i	−0.876347	+	0.481680i	$0.840027\pi$
$788$		0			0
$789$	−14.4208	−	24.9775i	−0.513393	−	0.889223i
$790$	−6.66556	−	3.84836i	−0.237150	−	0.136919i
$791$	−3.13054	+	0.838825i	−0.111309	+	0.0298252i
$792$		0			0
$793$	−47.7337	+	29.3988i	−1.69507	+	1.04398i
$794$	−50.5381			−1.79353
$795$		0			0
$796$		0			0
$797$	47.0750	−	27.1788i	1.66748	−	0.962721i	0.698493	−	0.715617i	$-0.253854\pi$
$797$	47.0750	−	27.1788i	1.66748	−	0.962721i	0.968989	−	0.247104i	$-0.0794790\pi$
$798$	25.6951	−	25.6951i	0.909598	−	0.909598i
$799$		0			0
$800$	6.68464	−	24.9474i	0.236338	−	0.882024i
$801$		0			0
$802$	−11.2250	−	19.4422i	−0.396368	−	0.686529i
$803$		0			0
$804$		0			0
$805$		−	6.06902i		−	0.213905i
$806$		0			0
$807$	−36.6026			−1.28847
$808$	−1.02012	−	3.80715i	−0.0358878	−	0.133935i
$809$	27.8375	−	48.2159i	0.978713	−	1.69518i	0.311619	−	0.950207i	$-0.399129\pi$
$809$	27.8375	−	48.2159i	0.978713	−	1.69518i	0.667094	−	0.744973i	$-0.267538\pi$
$810$	−2.38951	+	1.37959i	−0.0839589	+	0.0484737i
$811$	−36.7272	+	36.7272i	−1.28967	+	1.28967i	−0.354679	+	0.934988i	$0.615410\pi$
$811$	−36.7272	+	36.7272i	−1.28967	+	1.28967i	−0.934988	+	0.354679i	$0.884590\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−3.76487	−	12.6060i	−0.131555	−	0.440491i
$820$		0			0
$821$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$821$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$822$	17.2084	−	29.8058i	0.600211	−	1.03960i
$823$	10.7206	−	6.18954i	0.373697	−	0.215754i	−0.301376	−	0.953506i	$-0.597446\pi$
$823$	10.7206	−	6.18954i	0.373697	−	0.215754i	0.675072	+	0.737752i	$0.264112\pi$
$824$		0			0
$825$		0			0
$826$	12.5701	−	46.9122i	0.437369	−	1.63229i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	4.80046	+	8.31464i	0.166827	+	0.288954i
$829$	49.2801	+	28.4519i	1.71157	+	0.988175i	0.932450	+	0.361299i	$0.117667\pi$
$829$	49.2801	+	28.4519i	1.71157	+	0.988175i	0.779119	+	0.626876i	$0.215667\pi$
$830$	−5.09319	+	1.36472i	−0.176787	+	0.0473700i
$831$		0			0
$832$	−28.8328	+	0.819767i	−0.999596	+	0.0284203i
$833$		0			0
$834$	10.7038	+	39.9472i	0.370643	+	1.38326i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−42.3069	−	11.3361i	−1.46147	−	0.391599i
$839$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$839$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$840$	4.43965	+	4.43965i	0.153182	+	0.153182i
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$	−39.1013	+	10.4772i	−1.34672	+	0.360852i
$844$		0			0
$845$	−5.70397	+	6.39237i	−0.196223	+	0.219904i
$846$		0			0
$847$	7.53248	+	28.1116i	0.258819	+	0.965926i
$848$		0			0
$849$	−34.7113	+	20.0406i	−1.19129	+	0.687792i
$850$		0			0
$851$		0			0
$852$	10.9240	−	40.7689i	0.374250	−	1.39672i
$853$	29.2786	+	29.2786i	1.00248	+	1.00248i	0.999997	+	0.00248202i	$0.000790052\pi$
$853$	29.2786	+	29.2786i	1.00248	+	1.00248i	0.00248202	+	0.999997i	$0.499210\pi$
$854$	29.0885	+	50.3827i	0.995386	+	1.72406i
$855$	6.00440	+	3.46664i	0.205346	+	0.118557i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	41.7589			1.42480			0.712398	−	0.701776i	$-0.247609\pi$
$859$	41.7589			1.42480			0.712398	+	0.701776i	$0.247609\pi$
$860$		0			0
$861$		0			0
$862$	9.43365	−	5.44652i	0.321311	−	0.185509i
$863$	29.0285	−	29.0285i	0.988143	−	0.988143i	−0.0117879	−	0.999931i	$-0.503752\pi$
$863$	29.0285	−	29.0285i	0.988143	−	0.988143i	0.999931	+	0.0117879i	$0.00375228\pi$
$864$	−30.4635	−	8.16268i	−1.03639	−	0.277700i
$865$	−1.02702	+	3.83289i	−0.0349197	+	0.130322i
$866$		0			0
$867$	−10.8216	−	18.7435i	−0.367520	−	0.636563i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−18.7753	+	32.5198i	−0.635084	+	1.10000i
$875$	−14.4442	+	8.33937i	−0.488304	+	0.281922i
$876$		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
$879$	−30.7883	−	30.7883i	−1.03846	−	1.03846i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	−13.1877	+	3.53362i	−0.444052	+	0.118983i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	−10.8905			−0.366080
$886$		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
$897$	−8.37889	−	13.6045i	−0.279763	−	0.454240i
$898$	30.0244			1.00193
$899$		0			0
$900$	6.29677	−	10.9063i	0.209892	−	0.363544i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.896742	+	3.34669i	−0.0298252	+	0.111309i
$905$	6.11660	+	6.11660i	0.203323	+	0.203323i
$906$	13.9264	+	24.1213i	0.462674	+	0.801375i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	22.9575	−	6.15144i	0.761871	−	0.204143i
$909$		−	1.92186i		−	0.0637441i
$910$	6.46277	+	6.10543i	0.214239	+	0.202393i
$911$	52.1724			1.72855			0.864274	−	0.503022i	$-0.167778\pi$
$911$	52.1724			1.72855			0.864274	+	0.503022i	$0.167778\pi$
$912$	−10.0544	−	37.5237i	−0.332936	−	1.24253i
$913$		0			0
$914$	−48.2404	+	27.8516i	−1.59565	+	0.921249i
$915$	9.22446	−	9.22446i	0.304951	−	0.304951i
$916$	36.5962	+	9.80592i	1.20917	+	0.323997i
$917$	−13.9091	+	51.9094i	−0.459319	+	1.71420i
$918$		0			0
$919$	−0.663673	−	1.14952i	−0.0218926	−	0.0379190i	0.854872	−	0.518840i	$-0.173636\pi$
$919$	−0.663673	−	1.14952i	−0.0218926	−	0.0379190i	−0.876764	+	0.480921i	$0.840303\pi$
$920$	−5.61882	−	3.24403i	−0.185247	−	0.106952i
$921$	−41.8220	+	11.2062i	−1.37808	+	0.369256i
$922$		−	60.7232i		−	1.99981i
$923$	13.8217	−	58.1460i	0.454946	−	1.91390i
$924$		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
$931$	−37.7584	−	37.7584i	−1.23748	−	1.23748i
$932$	−20.1628	−	34.9230i	−0.660454	−	1.14394i
$933$		0			0
$934$	35.4541	−	9.49989i	1.16009	−	0.310846i
$935$		0			0
$936$	−13.6833	−	3.25262i	−0.447254	−	0.106315i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.4091	−	14.4091i	0.469724	−	0.469724i	−0.432101	−	0.901825i	$-0.642228\pi$
$941$	14.4091	−	14.4091i	0.469724	−	0.469724i	0.901825	+	0.432101i	$0.142228\pi$
$942$	16.3384	+	4.37785i	0.532332	+	0.142638i
$943$		0			0
$944$	−36.7133	−	36.7133i	−1.19492	−	1.19492i
$945$	4.86047	+	8.41858i	0.158111	+	0.273856i
$946$		0			0
$947$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$947$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$948$			21.0278i			0.682952i
$949$		0			0
$950$	49.2552			1.59805
$951$		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
$955$	17.3304	+	4.64367i	0.560799	+	0.150266i
$956$	0.277580	−	1.03594i	0.00897759	−	0.0335048i
$957$		0			0
$958$		0			0
$959$	−43.7989	−	25.2873i	−1.41434	−	0.816569i
$960$	6.48341	−	1.73722i	0.209251	−	0.0560687i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.93761	+	3.35604i	−0.0623739	+	0.108035i
$966$	−14.3595	+	8.29044i	−0.462008	+	0.266740i
$967$	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
$971$	4.13479	+	7.16167i	0.132692	+	0.229829i	0.924713	−	0.380664i	$-0.124305\pi$
$971$	4.13479	+	7.16167i	0.132692	+	0.229829i	−0.792021	+	0.610493i	$0.790971\pi$
$972$	−22.4414	−	12.9565i	−0.719807	−	0.415581i
$973$	58.7014	−	15.7290i	1.88188	−	0.504248i
$974$			16.7582i			0.536968i
$975$	−9.95894	+	18.4407i	−0.318941	+	0.590574i
$976$	62.1937			1.99077
$977$	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
$980$	6.52395	−	6.52395i	0.208400	−	0.208400i
$981$		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
$988$	−15.7417	−	52.7083i	−0.500809	−	1.67687i
$989$		0			0
$990$		0			0
$991$	−19.7951	+	34.2861i	−0.628811	+	1.08913i	0.358980	+	0.933345i	$0.383125\pi$
$991$	−19.7951	+	34.2861i	−0.628811	+	1.08913i	−0.987791	+	0.155787i	$0.950209\pi$
$992$		0			0
$993$		0			0
$994$	−59.9089	−	16.0525i	−1.90020	−	0.509156i
$995$		0			0
$996$	10.1864	+	10.1864i	0.322768	+	0.322768i
$997$	20.8131	+	36.0494i	0.659158	+	1.14170i	0.980834	+	0.194846i	$0.0624207\pi$
$997$	20.8131	+	36.0494i	0.659158	+	1.14170i	−0.321675	+	0.946850i	$0.604246\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.ds.b.461.3	yes	16
7.6	odd	2	inner	728.2.ds.b.461.2	yes	16
8.5	even	2	inner	728.2.ds.b.461.2	yes	16
13.11	odd	12	inner	728.2.ds.b.349.3	yes	16
56.13	odd	2	CM	728.2.ds.b.461.3	yes	16
91.76	even	12	inner	728.2.ds.b.349.2	✓	16
104.37	odd	12	inner	728.2.ds.b.349.2	✓	16
728.349	even	12	inner	728.2.ds.b.349.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.b.349.2	✓	16	91.76	even	12	inner
728.2.ds.b.349.2	✓	16	104.37	odd	12	inner
728.2.ds.b.349.3	yes	16	13.11	odd	12	inner
728.2.ds.b.349.3	yes	16	728.349	even	12	inner
728.2.ds.b.461.2	yes	16	7.6	odd	2	inner
728.2.ds.b.461.2	yes	16	8.5	even	2	inner
728.2.ds.b.461.3	yes	16	1.1	even	1	trivial
728.2.ds.b.461.3	yes	16	56.13	odd	2	CM

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

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(0.636563 - 1.10256i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.465997 - 0.465997i) q^{5} +(-1.73912 - 0.465997i) q^{6} +(-0.684771 + 2.55560i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.689574 + 1.19438i) q^{9} +(-0.807130 - 0.465997i) q^{10} +2.54625i q^{12} +(0.102471 + 3.60409i) q^{13} +3.74166 q^{14} +(-0.217153 - 0.810426i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.37915 - 1.37915i) q^{18} +(7.36841 + 1.97436i) q^{19} +(-0.341133 + 1.27313i) q^{20} +(2.38180 + 2.38180i) q^{21} +(-3.01441 - 1.74037i) q^{23} +(3.47825 - 0.931993i) q^{24} +4.56569i q^{25} +(4.88578 - 1.45917i) q^{26} +5.57521 q^{27} +(-1.36954 - 5.11120i) q^{28} +(-1.02758 + 0.593273i) q^{30} +(-5.46410 - 1.46410i) q^{32} +(0.871800 + 1.51000i) q^{35} +(-2.38875 - 1.37915i) q^{36} -10.7881i q^{38} +(4.03896 + 2.18125i) q^{39} +1.86399 q^{40} +(2.38180 - 4.12540i) q^{42} +(0.877915 + 0.235237i) q^{45} +(-1.27404 + 4.75478i) q^{46} +(-2.54625 - 4.41024i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(6.23685 - 1.67116i) q^{50} +(-3.78158 - 6.14000i) q^{52} +(-2.04067 - 7.61588i) q^{54} +(-6.48074 + 3.74166i) q^{56} +(6.86731 - 6.86731i) q^{57} +(3.35950 - 12.5378i) q^{59} +(1.18655 + 1.18655i) q^{60} +(7.77422 + 13.4653i) q^{61} +(-3.52455 + 0.944400i) q^{63} +8.00000i q^{64} +(1.72725 + 1.63175i) q^{65} +(-3.83773 + 2.21571i) q^{69} +(1.74360 - 1.74360i) q^{70} +(-16.0113 - 4.29022i) q^{71} +(-1.00961 + 3.76790i) q^{72} +(5.03395 + 2.90635i) q^{75} +(-14.7368 + 3.94872i) q^{76} +(1.50129 - 6.31572i) q^{78} +8.25834 q^{79} +(-0.682267 - 2.54625i) q^{80} +(1.48025 - 2.56387i) q^{81} +(4.00054 - 4.00054i) q^{83} +(-6.50720 - 1.74360i) q^{84} -1.28536i q^{90} +(-9.28079 - 2.20610i) q^{91} +6.96148 q^{92} +(4.35370 - 2.51361i) q^{95} +(-5.09251 + 5.09251i) q^{96} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 q^{57} - 32 q^{60} - 112 q^{63} + 16 q^{65} - 16 q^{71}+ \cdots + 56 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 + 32 * q^8 - 16 * q^9 - 56 * q^15 + 32 * q^16 - 32 * q^18 - 96 * q^30 - 32 * q^32 + 48 * q^36 + 72 * q^39 - 24 * q^46 + 56 * q^50 + 88 * q^57 - 32 * q^60 - 112 * q^63 + 16 * q^65 - 16 * q^71 + 16 * q^72 + 16 * q^78 + 192 * q^79 - 48 * q^81 - 96 * q^92 + 120 * q^95 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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