LMFDB - Embedded newform 728.2.ds.b.405.4

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			405.4
Root			$1.35670 + 1.07674i$ of defining polynomial
Character	$\chi$	$=$	728.405
Dual form			728.2.ds.b.293.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 0.366025i) q^{2} +(1.07674 + 1.86497i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-2.94171 + 2.94171i) q^{5} +(0.788230 + 2.94171i) q^{6} +(2.55560 - 0.684771i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-0.818745 + 1.41811i) q^{9} +(-5.09520 + 2.94171i) q^{10} +4.30697i q^{12} +(3.07000 - 1.89079i) q^{13} +3.74166 q^{14} +(-8.65368 - 2.31875i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.63749 + 1.63749i) q^{18} +(-1.97436 - 7.36841i) q^{19} +(-8.03691 + 2.15348i) q^{20} +(4.02880 + 4.02880i) q^{21} +(-8.21056 + 4.74037i) q^{23} +(-1.57646 + 5.88343i) q^{24} -12.3074i q^{25} +(4.88578 - 1.45917i) q^{26} +2.93414 q^{27} +(5.11120 + 1.36954i) q^{28} +(-10.9724 - 6.33493i) q^{30} +(1.46410 + 5.46410i) q^{32} +(-5.50344 + 9.53224i) q^{35} +(-2.83622 + 1.63749i) q^{36} -10.7881i q^{38} +(6.83187 + 3.68957i) q^{39} -11.7669 q^{40} +(4.02880 + 6.97808i) q^{42} +(-1.76315 - 6.58018i) q^{45} +(-12.9509 + 3.47019i) q^{46} +(-4.30697 + 7.45989i) q^{48} +(6.06218 - 3.50000i) q^{49} +(4.50480 - 16.8122i) q^{50} +(7.20819 - 0.204942i) q^{52} +(4.00811 + 1.07397i) q^{54} +(6.48074 + 3.74166i) q^{56} +(11.6160 - 11.6160i) q^{57} +(13.1424 - 3.52151i) q^{59} +(-12.6699 - 12.6699i) q^{60} +(-4.53609 + 7.85674i) q^{61} +(-1.12131 + 4.18477i) q^{63} +8.00000i q^{64} +(-3.46890 + 14.5932i) q^{65} +(-17.6813 - 10.2083i) q^{69} +(-11.0069 + 11.0069i) q^{70} +(-2.82612 - 10.5472i) q^{71} +(-4.47371 + 1.19873i) q^{72} +(22.9529 - 13.2518i) q^{75} +(3.94872 - 14.7368i) q^{76} +(7.98203 + 7.54069i) q^{78} +8.25834 q^{79} +(-16.0738 - 4.30697i) q^{80} +(5.61555 + 9.72641i) q^{81} +(4.00054 - 4.00054i) q^{83} +(2.94929 + 11.0069i) q^{84} -9.63406i q^{90} +(6.55094 - 6.93435i) q^{91} -18.9615 q^{92} +(27.4838 + 15.8678i) q^{95} +(-8.61393 + 8.61393i) q^{96} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$	1.07674	+	1.86497i	0.621657	+	1.07674i	0.989177	+	0.146726i	$0.0468736\pi$
$3$	1.07674	+	1.86497i	0.621657	+	1.07674i	−0.367520	+	0.930016i	$0.619793\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−2.94171	+	2.94171i	−1.31557	+	1.31557i	−0.398333	+	0.917241i	$0.630411\pi$
$5$	−2.94171	+	2.94171i	−1.31557	+	1.31557i	−0.917241	+	0.398333i	$0.869589\pi$
$6$	0.788230	+	2.94171i	0.321793	+	1.20095i
$7$	2.55560	−	0.684771i	0.965926	−	0.258819i
$7$	2.55560	−	0.684771i	0.965926	−	0.258819i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−0.818745	+	1.41811i	−0.272915	+	0.472703i
$10$	−5.09520	+	2.94171i	−1.61124	+	0.930251i
$11$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$11$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$12$			4.30697i			1.24331i
$13$	3.07000	−	1.89079i	0.851465	−	0.524411i
$13$	3.07000	−	1.89079i	0.851465	−	0.524411i
$14$	3.74166			1.00000
$15$	−8.65368	−	2.31875i	−2.23437	−	0.598697i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.63749	+	1.63749i	−0.385960	+	0.385960i
$19$	−1.97436	−	7.36841i	−0.452949	−	1.69043i	−0.694048	−	0.719929i	$-0.744174\pi$
$19$	−1.97436	−	7.36841i	−0.452949	−	1.69043i	0.241098	−	0.970501i	$-0.422492\pi$
$20$	−8.03691	+	2.15348i	−1.79711	+	0.481534i
$21$	4.02880	+	4.02880i	0.879156	+	0.879156i
$22$		0			0
$23$	−8.21056	+	4.74037i	−1.71202	+	0.988436i	−0.780189	+	0.625543i	$0.784877\pi$
$23$	−8.21056	+	4.74037i	−1.71202	+	0.988436i	−0.931831	+	0.362892i	$0.881789\pi$
$24$	−1.57646	+	5.88343i	−0.321793	+	1.20095i
$25$		−	12.3074i		−	2.46147i
$26$	4.88578	−	1.45917i	0.958180	−	0.286166i
$27$	2.93414			0.564676
$28$	5.11120	+	1.36954i	0.965926	+	0.258819i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	−10.9724	−	6.33493i	−2.00328	−	1.15659i
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$		0			0
$34$		0			0
$35$	−5.50344	+	9.53224i	−0.930251	+	1.61124i
$36$	−2.83622	+	1.63749i	−0.472703	+	0.272915i
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$		−	10.7881i		−	1.75006i
$39$	6.83187	+	3.68957i	1.09397	+	0.590805i
$40$	−11.7669			−1.86050
$41$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$41$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$42$	4.02880	+	6.97808i	0.621657	+	1.07674i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$		0			0
$45$	−1.76315	−	6.58018i	−0.262836	−	0.980916i
$46$	−12.9509	+	3.47019i	−1.90951	+	0.511652i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−4.30697	+	7.45989i	−0.621657	+	1.07674i
$49$	6.06218	−	3.50000i	0.866025	−	0.500000i
$50$	4.50480	−	16.8122i	0.637075	−	2.37760i
$51$		0			0
$52$	7.20819	−	0.204942i	0.999596	−	0.0284203i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	4.00811	+	1.07397i	0.545435	+	0.146149i
$55$		0			0
$56$	6.48074	+	3.74166i	0.866025	+	0.500000i
$57$	11.6160	−	11.6160i	1.53858	−	1.53858i
$58$		0			0
$59$	13.1424	−	3.52151i	1.71100	−	0.458461i	0.735332	−	0.677707i	$-0.237026\pi$
$59$	13.1424	−	3.52151i	1.71100	−	0.458461i	0.975670	+	0.219246i	$0.0703597\pi$
$60$	−12.6699	−	12.6699i	−1.63567	−	1.63567i
$61$	−4.53609	+	7.85674i	−0.580787	+	1.00595i	0.414600	+	0.910004i	$0.363922\pi$
$61$	−4.53609	+	7.85674i	−0.580787	+	1.00595i	−0.995386	+	0.0959480i	$0.969412\pi$
$62$		0			0
$63$	−1.12131	+	4.18477i	−0.141271	+	0.527232i
$64$			8.00000i			1.00000i
$65$	−3.46890	+	14.5932i	−0.430265	+	1.81007i
$66$		0			0
$67$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$67$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$68$		0			0
$69$	−17.6813	−	10.2083i	−2.12858	−	1.22894i
$70$	−11.0069	+	11.0069i	−1.31557	+	1.31557i
$71$	−2.82612	−	10.5472i	−0.335399	−	1.25173i	−0.903436	−	0.428723i	$-0.858964\pi$
$71$	−2.82612	−	10.5472i	−0.335399	−	1.25173i	0.568037	−	0.823003i	$-0.307703\pi$
$72$	−4.47371	+	1.19873i	−0.527232	+	0.141271i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	22.9529	−	13.2518i	2.65037	−	1.53019i
$76$	3.94872	−	14.7368i	0.452949	−	1.69043i
$77$		0			0
$78$	7.98203	+	7.54069i	0.903787	+	0.853815i
$79$	8.25834			0.929136			0.464568	−	0.885537i	$-0.346210\pi$
$79$	8.25834			0.929136			0.464568	+	0.885537i	$0.346210\pi$
$80$	−16.0738	−	4.30697i	−1.79711	−	0.481534i
$81$	5.61555	+	9.72641i	0.623950	+	1.08071i
$82$		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	$0.149503\pi$
$84$	2.94929	+	11.0069i	0.321793	+	1.20095i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$89$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$90$		−	9.63406i		−	1.01552i
$91$	6.55094	−	6.93435i	0.686725	−	0.726917i
$92$	−18.9615			−1.97687
$93$		0			0
$94$		0			0
$95$	27.4838	+	15.8678i	2.81977	+	1.62800i
$96$	−8.61393	+	8.61393i	−0.879156	+	0.879156i
$97$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$97$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$98$	9.56218	−	2.56218i	0.965926	−	0.258819i
$99$		0			0
$100$	12.3074	−	21.3170i	1.23074	−	2.13170i
$101$	1.20682	−	0.696757i	0.120083	−	0.0693299i	−0.438755	−	0.898607i	$-0.644581\pi$
$101$	1.20682	−	0.696757i	0.120083	−	0.0693299i	0.558838	+	0.829277i	$0.311247\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	9.92158	+	2.35843i	0.972891	+	0.231263i
$105$	−23.7031			−2.31319
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	5.08208	+	2.93414i	0.489023	+	0.282338i
$109$		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	$-0.814983\pi$
$113$	0.612486	−	1.06086i	0.0576178	−	0.0997970i	0.893396	+	0.449271i	$0.148316\pi$
$114$	20.1195	−	11.6160i	1.88436	−	1.08794i
$115$	10.2083	−	38.0979i	0.951930	−	3.55265i
$116$		0			0
$117$	0.167795	+	5.90167i	0.0155127	+	0.545610i
$118$	19.2419			1.77136
$119$		0			0
$120$	−12.6699	−	21.9448i	−1.15659	−	2.00328i
$121$	−9.52628	−	5.50000i	−0.866025	−	0.500000i
$122$	−9.07218	+	9.07218i	−0.821356	+	0.821356i
$123$		0			0
$124$		0			0
$125$	21.4961	+	21.4961i	1.92267	+	1.92267i
$126$	−3.06346	+	5.30608i	−0.272915	+	0.472703i
$127$	−11.2211	+	6.47851i	−0.995713	+	0.574875i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−11.2211	+	6.47851i	−0.995713	+	0.574875i	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$		0			0
$130$	−10.0801	+	18.6650i	−0.884084	+	1.63703i
$131$	−1.01458			−0.0886442			−0.0443221	−	0.999017i	$-0.514113\pi$
$131$	−1.01458			−0.0886442			−0.0443221	+	0.999017i	$0.514113\pi$
$132$		0			0
$133$	−10.0913	−	17.4787i	−0.875031	−	1.51560i
$134$		0			0
$135$	−8.63140	+	8.63140i	−0.742873	+	0.742873i
$136$		0			0
$137$	−20.5359	+	5.50257i	−1.75450	+	0.470117i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−20.5359	+	5.50257i	−1.75450	+	0.470117i	−0.768922	+	0.639343i	$0.779207\pi$
$138$	−20.4166	−	20.4166i	−1.73798	−	1.73798i
$139$	−11.4849	+	19.8924i	−0.974133	+	1.68725i	−0.291367	+	0.956611i	$0.594110\pi$
$139$	−11.4849	+	19.8924i	−0.974133	+	1.68725i	−0.682766	+	0.730637i	$0.739223\pi$
$140$	−19.0645	+	11.0069i	−1.61124	+	0.930251i
$141$		0			0
$142$		−	15.4422i		−	1.29588i
$143$		0			0
$144$	−6.54996			−0.545830
$145$		0			0
$146$		0			0
$147$	13.0548	+	7.53719i	1.07674	+	0.621657i
$148$		0			0
$149$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$149$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$150$	36.2047	−	9.70102i	2.95610	−	0.792085i
$151$	17.1637	+	17.1637i	1.39676	+	1.39676i	0.809118	+	0.587646i	$0.199945\pi$
$151$	17.1637	+	17.1637i	1.39676	+	1.39676i	0.587646	+	0.809118i	$0.300055\pi$
$152$	10.7881	−	18.6855i	0.875031	−	1.51560i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	8.14357	+	13.2224i	0.652007	+	1.05864i
$157$	−9.39459			−0.749770			−0.374885	−	0.927071i	$-0.622318\pi$
$157$	−9.39459			−0.749770			−0.374885	+	0.927071i	$0.622318\pi$
$158$	11.2811	+	3.02276i	0.897477	+	0.240478i
$159$		0			0
$160$	−20.3808	−	11.7669i	−1.61124	−	0.930251i
$161$	−17.7368	+	17.7368i	−1.39786	+	1.39786i
$162$	4.11087	+	15.3420i	0.322980	+	1.20538i
$163$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$163$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$164$		0			0
$165$		0			0
$166$	6.92914	−	4.00054i	0.537805	−	0.310502i
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$			16.1152i			1.24331i
$169$	5.84983	−	11.6095i	0.449987	−	0.893035i
$170$		0			0
$171$	12.0657	+	3.23300i	0.922688	+	0.247233i
$172$		0			0
$173$	−21.8129	−	12.5937i	−1.65840	−	0.957480i	−0.973452	−	0.228893i	$-0.926490\pi$
$173$	−21.8129	−	12.5937i	−1.65840	−	0.957480i	−0.684953	−	0.728588i	$-0.740177\pi$
$174$		0			0
$175$	−8.42772	−	31.4527i	−0.637075	−	2.37760i
$176$		0			0
$177$	20.7185	+	20.7185i	1.55730	+	1.55730i
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	3.52631	−	13.1604i	0.262836	−	0.980916i
$181$			13.7788i			1.02417i	0.858936	+	0.512084i	$0.171126\pi$
$181$			13.7788i			1.02417i	−0.858936	+	0.512084i	$0.828874\pi$
$182$	11.4869	−	7.07469i	0.851465	−	0.524411i
$183$	−19.5368			−1.44420
$184$	−25.9019	−	6.94038i	−1.90951	−	0.511652i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	7.49849	−	2.00921i	0.545435	−	0.146149i
$190$	31.7355	+	31.7355i	2.30234	+	2.30234i
$191$	13.6125	−	23.5775i	0.984965	−	1.70601i	0.342873	−	0.939382i	$-0.388600\pi$
$191$	13.6125	−	23.5775i	0.984965	−	1.70601i	0.642092	−	0.766627i	$-0.278067\pi$
$192$	−14.9198	+	8.61393i	−1.07674	+	0.621657i
$193$	5.32578	−	19.8761i	0.383358	−	1.43071i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	5.32578	−	19.8761i	0.383358	−	1.43071i	0.840739	−	0.541440i	$-0.182121\pi$
$194$		0			0
$195$	−30.9511	+	9.24373i	−2.21645	+	0.661957i
$196$	14.0000			1.00000
$197$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$197$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	24.6147	−	24.6147i	1.74052	−	1.74052i
$201$		0			0
$202$	1.90357	−	0.510061i	0.133935	−	0.0358878i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	15.5246i		−	1.07904i
$208$	12.6899	+	6.85322i	0.879886	+	0.475185i
$209$		0			0
$210$	−32.3791	−	8.67595i	−2.23437	−	0.598697i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	16.6273	−	16.6273i	1.13928	−	1.13928i
$214$		0			0
$215$		0			0
$216$	5.86828	+	5.86828i	0.399286	+	0.399286i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$223$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$224$	7.48331	+	12.9615i	0.500000	+	0.866025i
$225$	17.4532	+	10.0766i	1.16354	+	0.671773i
$226$	1.22497	−	1.22497i	0.0814839	−	0.0814839i
$227$	−7.74458	−	28.9031i	−0.514025	−	1.91837i	−0.370932	−	0.928660i	$-0.620962\pi$
$227$	−7.74458	−	28.9031i	−0.514025	−	1.91837i	−0.143094	−	0.989709i	$-0.545705\pi$
$228$	31.7355	−	8.50350i	2.10174	−	0.563158i
$229$	−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	$0.965274\pi$
$230$	27.8896	−	48.3062i	1.83899	−	3.18522i
$231$		0			0
$232$		0			0
$233$			9.77048i			0.640085i	0.947403	+	0.320043i	$0.103697\pi$
$233$			9.77048i			0.640085i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−1.93095	+	8.12325i	−0.126230	+	0.531034i
$235$		0			0
$236$	26.2849	+	7.04302i	1.71100	+	0.458461i
$237$	8.89210	+	15.4016i	0.577604	+	1.00044i
$238$		0			0
$239$	19.1208	−	19.1208i	1.23682	−	1.23682i	0.275533	−	0.961292i	$-0.411146\pi$
$239$	19.1208	−	19.1208i	1.23682	−	1.23682i	0.961292	−	0.275533i	$-0.0888542\pi$
$240$	−9.27498	−	34.6147i	−0.598697	−	2.23437i
$241$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$241$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$242$	−11.0000	−	11.0000i	−0.707107	−	0.707107i
$243$	−7.69178	+	13.3226i	−0.493428	+	0.854642i
$244$	−15.7135	+	9.07218i	−1.00595	+	0.580787i
$245$	−7.53719	+	28.1292i	−0.481534	+	1.79711i
$246$		0			0
$247$	−19.9934	−	18.8879i	−1.27215	−	1.20181i
$248$		0			0
$249$	11.7684	+	3.15334i	0.745794	+	0.199835i
$250$	21.4961	+	37.2324i	1.35953	+	2.35478i
$251$	15.8898	+	9.17399i	1.00296	+	0.579057i	0.909122	−	0.416530i	$-0.136754\pi$
$251$	15.8898	+	9.17399i	1.00296	+	0.579057i	0.0938349	+	0.995588i	$0.470087\pi$
$252$	−6.12693	+	6.12693i	−0.385960	+	0.385960i
$253$		0			0
$254$	−17.6996	+	4.74260i	−1.11057	+	0.297577i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$		0			0
$260$	−20.6015	+	21.8073i	−1.27765	+	1.35243i
$261$		0			0
$262$	−1.38594	−	0.371362i	−0.0856237	−	0.0229428i
$263$	−15.7146	−	27.2184i	−0.969002	−	1.67836i	−0.698456	−	0.715653i	$-0.746129\pi$
$263$	−15.7146	−	27.2184i	−0.969002	−	1.67836i	−0.270546	−	0.962707i	$-0.587204\pi$
$264$		0			0
$265$		0			0
$266$	−7.38738	−	27.5701i	−0.452949	−	1.69043i
$267$		0			0
$268$		0			0
$269$	0.348854	−	0.604233i	0.0212700	−	0.0368407i	−0.855194	−	0.518307i	$-0.826562\pi$
$269$	0.348854	−	0.604233i	0.0212700	−	0.0368407i	0.876464	+	0.481467i	$0.159896\pi$
$270$	−14.9500	+	8.63140i	−0.909830	+	0.525290i
$271$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$271$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$272$		0			0
$273$	19.9860	+	4.75081i	1.20961	+	0.287532i
$274$	−30.0666			−1.81639
$275$		0			0
$276$	−20.4166	−	35.3626i	−1.22894	−	2.12858i
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$	−22.9697	+	22.9697i	−1.37763	+	1.37763i
$279$		0			0
$280$	−30.0714	+	8.05760i	−1.79711	+	0.481534i
$281$	−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
$283$	−4.73120	+	2.73156i	−0.281241	+	0.162374i	−0.633985	−	0.773345i	$-0.718582\pi$
$283$	−4.73120	+	2.73156i	−0.281241	+	0.162374i	0.352744	+	0.935720i	$0.385249\pi$
$284$	5.65225	−	21.0945i	0.335399	−	1.25173i
$285$			68.3419i			4.04822i
$286$		0			0
$287$		0			0
$288$	−8.94742	−	2.39745i	−0.527232	−	0.141271i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−33.0349	+	8.85168i	−1.92992	+	0.517121i	−0.953390	+	0.301742i	$0.902432\pi$
$293$	−33.0349	+	8.85168i	−1.92992	+	0.517121i	−0.976531	+	0.215378i	$0.930902\pi$
$294$	15.0744	+	15.0744i	0.879156	+	0.879156i
$295$	−28.3020	+	49.0206i	−1.64781	+	2.85409i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16.2434	+	30.0774i	−0.939380	+	1.73942i
$300$	53.0074			3.06038
$301$		0			0
$302$	17.1637	+	29.7284i	0.987661	+	1.71068i
$303$	2.59886	+	1.50045i	0.149301	+	0.0861988i
$304$	21.5762	−	21.5762i	1.23748	−	1.23748i
$305$	−9.76839	−	36.4561i	−0.559336	−	2.08747i
$306$		0			0
$307$	6.84906	+	6.84906i	0.390896	+	0.390896i	0.875007	−	0.484110i	$-0.160857\pi$
$307$	6.84906	+	6.84906i	0.390896	+	0.390896i	−0.484110	+	0.875007i	$0.660857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	6.28459	+	21.0429i	0.355795	+	1.19132i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−12.8333	−	3.43866i	−0.724222	−	0.194055i
$315$	−9.01183	−	15.6090i	−0.507759	−	0.879465i
$316$	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
$320$	−23.5337	−	23.5337i	−1.31557	−	1.31557i
$321$		0			0
$322$	−30.7211	+	17.7368i	−1.71202	+	0.988436i
$323$		0			0
$324$			22.4622i			1.24790i
$325$	−23.2706	−	37.7836i	−1.29082	−	2.09586i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$331$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$332$	10.9297	−	2.92860i	0.599844	−	0.160728i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−5.89857	+	22.0138i	−0.321793	+	1.20095i
$337$			36.7083i			1.99963i	0.0192914	+	0.999814i	$0.493859\pi$
$337$			36.7083i			1.99963i	−0.0192914	+	0.999814i	$0.506141\pi$
$338$	12.2404	−	13.7176i	0.665788	−	0.746141i
$339$	2.63796			0.143274
$340$		0			0
$341$		0			0
$342$	15.2987	+	8.83271i	0.827259	+	0.477618i
$343$	13.0958	−	13.0958i	0.707107	−	0.707107i
$344$		0			0
$345$	82.0433	−	21.9834i	4.41706	−	1.18355i
$346$	−25.1874	−	25.1874i	−1.35408	−	1.35408i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$	6.53573	−	24.3917i	0.349849	−	1.30566i	−0.536994	−	0.843586i	$-0.680440\pi$
$349$	6.53573	−	24.3917i	0.349849	−	1.30566i	0.886843	−	0.462070i	$-0.152893\pi$
$350$		−	46.0499i		−	2.46147i
$351$	9.00782	−	5.54784i	0.480802	−	0.296122i
$352$		0			0
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$	20.7185	+	35.8856i	1.10118	+	1.90730i
$355$	39.3406	+	22.7133i	2.08798	+	1.20550i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.9458	+	10.9458i	0.577696	+	0.577696i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	10.9458	+	10.9458i	0.577696	+	0.577696i	−0.356572	+	0.934268i	$0.616054\pi$
$360$	9.63406	−	16.6867i	0.507759	−	0.879465i
$361$	−33.9409	+	19.5958i	−1.78636	+	1.03136i
$362$	−5.04338	+	18.8221i	−0.265074	+	0.989270i
$363$		−	23.6883i		−	1.24331i
$364$	18.2809	−	5.45971i	0.958180	−	0.286166i
$365$		0			0
$366$	−26.6877	−	7.15096i	−1.39499	−	0.373787i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$	−32.8422	−	18.9615i	−1.71202	−	0.988436i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−16.9439	+	63.2355i	−0.874979	+	3.26546i
$376$		0			0
$377$		0			0
$378$	10.9785			0.564676
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$	31.7355	+	54.9675i	1.62800	+	2.81977i
$381$	−24.1645	−	13.9514i	−1.23798	−	0.714750i
$382$	27.2250	−	27.2250i	1.39295	−	1.39295i
$383$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$383$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$384$	−23.5337	+	6.30584i	−1.20095	+	0.321793i
$385$		0			0
$386$	14.5503	−	25.2019i	0.740591	−	1.28274i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−45.6634	+	1.29829i	−2.31226	+	0.0657415i
$391$		0			0
$392$	19.1244	+	5.12436i	0.965926	+	0.258819i
$393$	−1.09244	−	1.89216i	−0.0551063	−	0.0954469i
$394$		0			0
$395$	−24.2937	+	24.2937i	−1.22235	+	1.22235i
$396$		0			0
$397$	32.0100	−	8.57705i	1.60654	−	0.430470i	0.659528	−	0.751680i	$-0.270756\pi$
$397$	32.0100	−	8.57705i	1.60654	−	0.430470i	0.947008	+	0.321211i	$0.104090\pi$
$398$		0			0
$399$	21.7316	−	37.6401i	1.08794	−	1.88436i
$400$	42.6339	−	24.6147i	2.13170	−	1.23074i
$401$	−4.10862	+	15.3336i	−0.205175	+	0.765723i	0.784221	+	0.620481i	$0.213063\pi$
$401$	−4.10862	+	15.3336i	−0.205175	+	0.765723i	−0.989396	+	0.145242i	$0.953604\pi$
$402$		0			0
$403$		0			0
$404$	2.78703			0.138660
$405$	−45.1317	−	12.0930i	−2.24261	−	0.600905i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$409$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$410$		0			0
$411$	−32.3740	−	32.3740i	−1.59689	−	1.59689i
$412$		0			0
$413$	31.1754	−	17.9991i	1.53404	−	0.885679i
$414$	5.68241	−	21.2070i	0.279275	−	1.04227i
$415$			23.5369i			1.15538i
$416$	14.8263	+	14.0065i	0.726917	+	0.686725i
$417$	−49.4649			−2.42231
$418$		0			0
$419$	15.4854	+	26.8215i	0.756511	+	1.31032i	0.944619	+	0.328168i	$0.106431\pi$
$419$	15.4854	+	26.8215i	0.756511	+	1.31032i	−0.188108	+	0.982148i	$0.560236\pi$
$420$	−41.0550	−	23.7031i	−2.00328	−	1.15659i
$421$		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
$426$	28.7993	−	16.6273i	1.39533	−	0.805595i
$427$	−6.21236	+	23.1849i	−0.300637	+	1.12199i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−30.4101	−	8.14837i	−1.46480	−	0.392493i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	−30.4101	−	8.14837i	−1.46480	−	0.392493i	−0.901146	+	0.433515i	$0.857273\pi$
$432$	5.86828	+	10.1642i	0.282338	+	0.489023i
$433$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$433$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	51.1396	+	51.1396i	2.44634	+	2.44634i
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$			11.4624i			0.545830i
$442$		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
$448$	5.47817	+	20.4448i	0.258819	+	0.965926i
$449$	20.4281	−	5.47370i	0.964062	−	0.258320i	0.257743	−	0.966213i	$-0.417021\pi$
$449$	20.4281	−	5.47370i	0.964062	−	0.258320i	0.706319	+	0.707894i	$0.250354\pi$
$450$	20.1532	+	20.1532i	0.950030	+	0.950030i
$451$		0			0
$452$	2.12171	−	1.22497i	0.0997970	−	0.0576178i
$453$	−13.5290	+	50.4908i	−0.635646	+	2.37226i
$454$		−	42.3171i		−	1.98604i
$455$	1.12788	+	39.6698i	0.0528760	+	1.85975i
$456$	46.4640			2.17588
$457$	−32.9348	−	8.82485i	−1.54062	−	0.412809i	−0.614157	−	0.789184i	$-0.710504\pi$
$457$	−32.9348	−	8.82485i	−1.54062	−	0.412809i	−0.926467	+	0.376375i	$0.877170\pi$
$458$	−13.3951	−	23.2010i	−0.625913	−	1.08411i
$459$		0			0
$460$	55.7792	−	55.7792i	2.60072	−	2.60072i
$461$	5.42413	+	20.2431i	0.252627	+	0.942817i	0.969395	+	0.245505i	$0.0789539\pi$
$461$	5.42413	+	20.2431i	0.252627	+	0.942817i	−0.716768	+	0.697312i	$0.754379\pi$
$462$		0			0
$463$	4.20185	+	4.20185i	0.195277	+	0.195277i	0.797972	−	0.602695i	$-0.205906\pi$
$463$	4.20185	+	4.20185i	0.195277	+	0.195277i	−0.602695	+	0.797972i	$0.705906\pi$
$464$		0			0
$465$		0			0
$466$	−3.57624	+	13.3467i	−0.165666	+	0.618275i
$467$			16.9526i			0.784471i	0.919865	+	0.392236i	$0.128298\pi$
$467$			16.9526i			0.784471i	−0.919865	+	0.392236i	$0.871702\pi$
$468$	−5.61104	+	10.3898i	−0.259371	+	0.480268i
$469$		0			0
$470$		0			0
$471$	−10.1155	−	17.5206i	−0.466100	−	0.807309i
$472$	33.3279	+	19.2419i	1.53404	+	0.885679i
$473$		0			0
$474$	6.50947	+	24.2937i	0.298990	+	1.11585i
$475$	−90.6856	+	24.2991i	−4.16094	+	1.11492i
$476$		0			0
$477$		0			0
$478$	33.1183	−	19.1208i	1.51479	−	0.874567i
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$		−	50.6794i		−	2.31319i
$481$		0			0
$482$		0			0
$483$	−52.1767	−	13.9807i	−2.37412	−	0.636144i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	−15.3836	+	15.3836i	−0.697812	+	0.697812i
$487$	7.99614	+	29.8420i	0.362340	+	1.35227i	0.870992	+	0.491298i	$0.163477\pi$
$487$	7.99614	+	29.8420i	0.362340	+	1.35227i	−0.508652	+	0.860972i	$0.669856\pi$
$488$	−24.7856	+	6.64129i	−1.12199	+	0.300637i
$489$		0			0
$490$	−20.5920	+	35.6664i	−0.930251	+	1.61124i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$	−20.3980	−	33.1195i	−0.917751	−	1.49012i
$495$		0			0
$496$		0			0
$497$	−14.4449	−	25.0193i	−0.647941	−	1.12227i
$498$	14.9218	+	8.61509i	0.668661	+	0.386052i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	15.7363	+	58.7285i	0.703747	+	2.62642i
$501$		0			0
$502$	18.3480	+	18.3480i	0.818911	+	0.818911i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	−10.6122	+	6.12693i	−0.472703	+	0.272915i
$505$	−1.50045	+	5.59977i	−0.0667693	+	0.249187i
$506$		0			0
$507$	27.9501	−	1.59063i	1.24131	−	0.0706422i
$508$	−25.9140			−1.14975
$509$	−41.2960	−	11.0652i	−1.83041	−	0.490457i	−0.832440	−	0.554115i	$-0.813057\pi$
$509$	−41.2960	−	11.0652i	−1.83041	−	0.490457i	−0.997972	+	0.0636579i	$0.979723\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−5.79305	−	21.6200i	−0.255769	−	0.954545i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	54.2406i		−	2.38090i
$520$	−36.1243	+	22.2486i	−1.58415	+	0.975668i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−7.55031	−	13.0775i	−0.330152	−	0.571840i	0.652390	−	0.757884i	$-0.273767\pi$
$523$	−7.55031	−	13.0775i	−0.330152	−	0.571840i	−0.982541	+	0.186044i	$0.940433\pi$
$524$	−1.75730	−	1.01458i	−0.0767681	−	0.0443221i
$525$	49.5838	−	49.5838i	2.16402	−	2.16402i
$526$	−11.5039	−	42.9330i	−0.501592	−	1.87197i
$527$		0			0
$528$		0			0
$529$	33.4422	−	57.9236i	1.45401	−	2.51842i
$530$		0			0
$531$	−5.76644	+	21.5206i	−0.250242	+	0.933916i
$532$		−	40.3654i		−	1.75006i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.697708	−	0.697708i	0.0300803	−	0.0300803i
$539$		0			0
$540$	−23.5814	+	6.31862i	−1.01478	+	0.271910i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	−25.6970	+	14.8362i	−1.10276	+	0.636681i
$544$		0			0
$545$		0			0
$546$	25.5625	+	13.8051i	1.09397	+	0.590805i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−41.0718	−	11.0051i	−1.75450	−	0.470117i
$549$	−7.42780	−	12.8653i	−0.317011	−	0.549079i
$550$		0			0
$551$		0			0
$552$	−14.9460	−	55.7792i	−0.636144	−	2.37412i
$553$	21.1050	−	5.65507i	0.897477	−	0.240478i
$554$		0			0
$555$		0			0
$556$	−39.7847	+	22.9697i	−1.68725	+	0.974133i
$557$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$557$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$558$		0			0
$559$		0			0
$560$	−44.0275			−1.86050
$561$		0			0
$562$	−22.4833	−	38.9422i	−0.948401	−	1.64268i
$563$	22.3060	+	12.8784i	0.940086	+	0.542759i	0.889987	−	0.455985i	$-0.150713\pi$
$563$	22.3060	+	12.8784i	0.940086	+	0.542759i	0.0500986	+	0.998744i	$0.484046\pi$
$564$		0			0
$565$	1.31898	+	4.92250i	0.0554898	+	0.207091i
$566$	−7.46276	+	1.99964i	−0.313683	+	0.0840511i
$567$	21.0115	+	21.0115i	0.882398	+	0.882398i
$568$	15.4422	−	26.7467i	0.647941	−	1.12227i
$569$	−40.4718	+	23.3664i	−1.69667	+	0.979571i	−0.747785	+	0.663941i	$0.768883\pi$
$569$	−40.4718	+	23.3664i	−1.69667	+	0.979571i	−0.948882	+	0.315631i	$0.897784\pi$
$570$	−25.0149	+	93.3568i	−1.04776	+	3.91028i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	58.6285			2.44924
$574$		0			0
$575$	58.3414	+	101.050i	2.43300	+	4.21409i
$576$	−11.3449	−	6.54996i	−0.472703	−	0.272915i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	6.22243	+	23.2224i	0.258819	+	0.965926i
$579$	42.8028	−	11.4690i	1.77882	−	0.476634i
$580$		0			0
$581$	7.48432	−	12.9632i	0.310502	−	0.537805i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−17.8546	−	16.8674i	−0.738198	−	0.697382i
$586$	−48.3665			−1.99800
$587$	46.7186	+	12.5182i	1.92828	+	0.516681i	0.979869	+	0.199641i	$0.0639775\pi$
$587$	46.7186	+	12.5182i	1.92828	+	0.516681i	0.948412	+	0.317041i	$0.102689\pi$
$588$	15.0744	+	26.1096i	0.621657	+	1.07674i
$589$		0			0
$590$	−56.6041	+	56.6041i	−2.33035	+	2.33035i
$591$		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
$598$	−33.1980	+	35.1410i	−1.35757	+	1.43702i
$599$	23.2541			0.950136			0.475068	−	0.879949i	$-0.342423\pi$
$599$	23.2541			0.950136			0.475068	+	0.879949i	$0.342423\pi$
$600$	72.4094	+	19.4020i	2.95610	+	0.792085i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	12.5647	+	46.8922i	0.511251	+	1.90802i
$605$	44.2030	−	11.8442i	1.79711	−	0.481534i
$606$	3.00091	+	3.00091i	0.121904	+	0.121904i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	37.3711	−	21.5762i	1.51560	−	0.875031i
$609$		0			0
$610$		−	53.3755i		−	2.16111i
$611$		0			0
$612$		0			0
$613$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$613$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$614$	6.84906	+	11.8629i	0.276405	+	0.478748i
$615$		0			0
$616$		0			0
$617$	−2.99306	−	11.1703i	−0.120496	−	0.449698i	0.879143	−	0.476558i	$-0.158116\pi$
$617$	−2.99306	−	11.1703i	−0.120496	−	0.449698i	−0.999639	+	0.0268600i	$0.991449\pi$
$618$		0			0
$619$	−27.1731	−	27.1731i	−1.09218	−	1.09218i	−0.995296	−	0.0968845i	$-0.969112\pi$
$619$	−27.1731	−	27.1731i	−1.09218	−	1.09218i	−0.0968845	−	0.995296i	$-0.530888\pi$
$620$		0			0
$621$	−24.0909	+	13.9089i	−0.966736	+	0.558146i
$622$		0			0
$623$		0			0
$624$	0.882677	+	31.0454i	0.0353354	+	1.24281i
$625$	−64.9341			−2.59737
$626$		0			0
$627$		0			0
$628$	−16.2719	−	9.39459i	−0.649320	−	0.374885i
$629$		0			0
$630$	−6.59712	−	24.6208i	−0.262836	−	0.980916i
$631$	46.2815	−	12.4011i	1.84244	−	0.493680i	0.843389	−	0.537303i	$-0.180557\pi$
$631$	46.2815	−	12.4011i	1.84244	−	0.493680i	0.999048	+	0.0436231i	$0.0138901\pi$
$632$	16.5167	+	16.5167i	0.656998	+	0.656998i
$633$		0			0
$634$		0			0
$635$	13.9514	−	52.0672i	0.553643	−	2.06622i
$636$		0			0
$637$	11.9931	−	22.2073i	0.475185	−	0.879886i
$638$		0			0
$639$	17.2710	+	4.62775i	0.683230	+	0.183071i
$640$	−23.5337	−	40.7616i	−0.930251	−	1.61124i
$641$	2.50172	+	1.44437i	0.0988119	+	0.0570491i	0.548592	−	0.836090i	$-0.315164\pi$
$641$	2.50172	+	1.44437i	0.0988119	+	0.0570491i	−0.449780	+	0.893140i	$0.648498\pi$
$642$		0			0
$643$	5.55067	+	20.7154i	0.218897	+	0.816935i	0.984758	+	0.173929i	$0.0556463\pi$
$643$	5.55067	+	20.7154i	0.218897	+	0.816935i	−0.765861	+	0.643006i	$0.777687\pi$
$644$	−48.4580	+	12.9843i	−1.90951	+	0.511652i
$645$		0			0
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	−8.22173	+	30.6839i	−0.322980	+	1.20538i
$649$		0			0
$650$	−17.9585	−	60.1310i	−0.704390	−	2.35853i
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$	2.98460	−	2.98460i	0.116618	−	0.116618i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	13.3064	−	49.6603i	0.517560	−	1.93156i	0.242012	−	0.970273i	$-0.422193\pi$
$661$	13.3064	−	49.6603i	0.517560	−	1.93156i	0.275548	−	0.961287i	$-0.411141\pi$
$662$		0			0
$663$		0			0
$664$	16.0022			0.621004
$665$	81.1033	+	21.7316i	3.14505	+	0.842713i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−16.1152	+	27.9123i	−0.621657	+	1.07674i
$673$	−38.8844	+	22.4499i	−1.49889	+	0.865382i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−38.8844	+	22.4499i	−1.49889	+	0.865382i	−0.498886	+	0.866668i	$0.666257\pi$
$674$	−13.4362	+	50.1445i	−0.517542	+	1.93149i
$675$		−	36.1115i		−	1.38993i
$676$	21.7417	−	14.2583i	0.836218	−	0.548398i
$677$	2.69123			0.103433			0.0517163	−	0.998662i	$-0.483531\pi$
$677$	2.69123			0.103433			0.0517163	+	0.998662i	$0.483531\pi$
$678$	3.60352	+	0.965559i	0.138392	+	0.0370821i
$679$		0			0
$680$		0			0
$681$	45.5646	−	45.5646i	1.74604	−	1.74604i
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$	17.6654	+	17.6654i	0.675454	+	0.675454i
$685$	44.2237	−	76.5977i	1.68970	−	2.92665i
$686$	22.6826	−	13.0958i	0.866025	−	0.500000i
$687$	10.5584	−	39.4046i	0.402830	−	1.50338i
$688$		0			0
$689$		0			0
$690$	120.120			4.57288
$691$	−11.1023	−	2.97485i	−0.422351	−	0.113168i	0.0413827	−	0.999143i	$-0.486824\pi$
$691$	−11.1023	−	2.97485i	−0.422351	−	0.113168i	−0.463733	+	0.885975i	$0.653490\pi$
$692$	−25.1874	−	43.6258i	−0.957480	−	1.65840i
$693$		0			0
$694$		0			0
$695$	−24.7325	−	92.3028i	−0.938156	−	3.50124i
$696$		0			0
$697$		0			0
$698$	17.8559	−	30.9274i	0.675857	−	1.17062i
$699$	−18.2217	+	10.5203i	−0.689206	+	0.397914i
$700$	16.8554	−	62.9053i	0.637075	−	2.37760i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	14.3356	−	4.28140i	0.541061	−	0.161591i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.60703	−	2.60703i	0.0980473	−	0.0980473i
$708$	15.1670	+	56.6041i	0.570012	+	2.12731i
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$	45.4266	+	45.4266i	1.70483	+	1.70483i
$711$	−6.76148	+	11.7112i	−0.253575	+	0.439205i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	56.2480	+	15.0716i	2.10062	+	0.562860i
$718$	10.9458	+	18.9587i	0.408493	+	0.707531i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	19.2681	−	19.2681i	0.718080	−	0.718080i
$721$		0			0
$722$	−53.5367	+	14.3451i	−1.99243	+	0.533870i
$723$		0			0
$724$	−13.7788	+	23.8655i	−0.512084	+	0.886955i
$725$		0			0
$726$	8.67053	−	32.3588i	0.321793	−	1.20095i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	26.9706	−	0.766821i	0.999596	−	0.0284203i
$729$	0.565054			0.0209279
$730$		0			0
$731$		0			0
$732$	−33.8387	−	19.5368i	−1.25071	−	0.722100i
$733$	−38.2883	+	38.2883i	−1.41421	+	1.41421i	−0.706175	+	0.708038i	$0.749581\pi$
$733$	−38.2883	+	38.2883i	−1.41421	+	1.41421i	−0.708038	+	0.706175i	$0.750419\pi$
$734$		0			0
$735$	−60.5757	+	16.2312i	−2.23437	+	0.598697i
$736$	−37.9230	−	37.9230i	−1.39786	−	1.39786i
$737$		0			0
$738$		0			0
$739$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$739$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$740$		0			0
$741$	13.6977	−	57.6246i	0.503199	−	2.11689i
$742$		0			0
$743$	−41.9939	−	11.2522i	−1.54061	−	0.412804i	−0.614145	−	0.789193i	$-0.710499\pi$
$743$	−41.9939	−	11.2522i	−1.54061	−	0.412804i	−0.926462	+	0.376389i	$0.877166\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.39778	+	8.94862i	0.0877300	+	0.327413i
$748$		0			0
$749$		0			0
$750$	−46.2916	+	80.1793i	−1.69033	+	2.92774i
$751$	27.7789	−	16.0381i	1.01367	−	0.585240i	0.101403	−	0.994845i	$-0.467667\pi$
$751$	27.7789	−	16.0381i	1.01367	−	0.585240i	0.912263	+	0.409605i	$0.134333\pi$
$752$		0			0
$753$			39.5121i			1.43990i
$754$		0			0
$755$	−100.982			−3.67509
$756$	14.9970	+	4.01843i	0.545435	+	0.146149i
$757$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$757$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$758$		0			0
$759$		0			0
$760$	23.2320	+	86.7030i	0.842713	+	3.14505i
$761$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$761$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$762$	−27.9027	−	27.9027i	−1.01081	−	1.01081i
$763$		0			0
$764$	47.1550	−	27.2250i	1.70601	−	0.984965i
$765$		0			0
$766$		0			0
$767$	33.6889	−	35.6606i	1.21644	−	1.28763i
$768$	−34.4557			−1.24331
$769$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$769$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$770$		0			0
$771$		0			0
$772$	29.1006	−	29.1006i	1.04735	−	1.04735i
$773$	14.3306	+	53.4825i	0.515435	+	1.92363i	0.346735	+	0.937963i	$0.387290\pi$
$773$	14.3306	+	53.4825i	0.515435	+	1.92363i	0.168700	+	0.985667i	$0.446043\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−62.8525	−	14.9405i	−2.25048	−	0.534954i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.2487	+	14.0000i	0.866025	+	0.500000i
$785$	27.6362	−	27.6362i	0.986378	−	0.986378i
$786$	−0.799722	−	2.98460i	−0.0285251	−	0.106457i
$787$	15.1244	−	4.05257i	0.539126	−	0.144458i	0.0210268	−	0.999779i	$-0.493306\pi$
$787$	15.1244	−	4.05257i	0.539126	−	0.144458i	0.518099	+	0.855321i	$0.326640\pi$
$788$		0			0
$789$	33.8411	−	58.6144i	1.20477	−	2.08673i
$790$	−42.0779	+	24.2937i	−1.49706	+	0.864330i
$791$	0.838825	−	3.13054i	0.0298252	−	0.111309i
$792$		0			0
$793$	0.929633	+	32.6970i	0.0330122	+	1.16110i
$794$	46.8659			1.66321
$795$		0			0
$796$		0			0
$797$	34.9921	+	20.2027i	1.23948	+	0.715617i	0.968989	−	0.247104i	$-0.0794790\pi$
$797$	34.9921	+	20.2027i	1.23948	+	0.715617i	0.270496	+	0.962721i	$0.412812\pi$
$798$	43.4631	−	43.4631i	1.53858	−	1.53858i
$799$		0			0
$800$	67.2486	−	18.0192i	2.37760	−	0.637075i
$801$		0			0
$802$	−11.2250	+	19.4422i	−0.396368	+	0.686529i
$803$		0			0
$804$		0			0
$805$		−	104.353i		−	3.67797i
$806$		0			0
$807$	1.50250			0.0528906
$808$	3.80715	+	1.02012i	0.133935	+	0.0358878i
$809$	27.8375	+	48.2159i	0.978713	+	1.69518i	0.667094	+	0.744973i	$0.267538\pi$
$809$	27.8375	+	48.2159i	0.978713	+	1.69518i	0.311619	+	0.950207i	$0.399129\pi$
$810$	−57.2246	−	33.0387i	−2.01067	−	1.16086i
$811$	4.05159	−	4.05159i	0.142270	−	0.142270i	−0.632384	−	0.774655i	$-0.717924\pi$
$811$	4.05159	−	4.05159i	0.142270	−	0.142270i	0.774655	+	0.632384i	$0.217924\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	4.47011	+	14.9674i	0.156198	+	0.523004i
$820$		0			0
$821$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$821$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$822$	−32.3740	−	56.0734i	−1.12917	−	1.95578i
$823$	−36.6582	−	21.1646i	−1.27782	−	0.737752i	−0.301376	−	0.953506i	$-0.597446\pi$
$823$	−36.6582	−	21.1646i	−1.27782	−	0.737752i	−0.976448	+	0.215754i	$0.930779\pi$
$824$		0			0
$825$		0			0
$826$	49.1745	−	13.1763i	1.71100	−	0.458461i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	15.5246	−	26.8894i	0.539518	−	0.934473i
$829$	31.2622	−	18.0492i	1.08578	−	0.626876i	0.153331	−	0.988175i	$-0.451000\pi$
$829$	31.2622	−	18.0492i	1.08578	−	0.626876i	0.932450	+	0.361299i	$0.117667\pi$
$830$	−8.61509	+	32.1520i	−0.299034	+	1.11601i
$831$		0			0
$832$	15.1263	+	24.5600i	0.524411	+	0.851465i
$833$		0			0
$834$	−67.5703	−	18.1054i	−2.33977	−	0.626939i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	11.3361	+	42.3069i	0.391599	+	1.46147i
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$	−47.4063	−	47.4063i	−1.63567	−	1.63567i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$	17.7220	−	66.1395i	0.610379	−	2.27796i
$844$		0			0
$845$	16.9432	+	51.3602i	0.582863	+	1.76684i
$846$		0			0
$847$	−28.1116	−	7.53248i	−0.965926	−	0.258819i
$848$		0			0
$849$	−10.1886	−	5.88237i	−0.349670	−	0.201882i
$850$		0			0
$851$		0			0
$852$	45.4266	−	12.1720i	1.55629	−	0.417006i
$853$	−39.8697	−	39.8697i	−1.36511	−	1.36511i	−0.867264	−	0.497849i	$-0.834123\pi$
$853$	−39.8697	−	39.8697i	−1.36511	−	1.36511i	−0.497849	−	0.867264i	$-0.665877\pi$
$854$	−16.9725	+	29.3972i	−0.580787	+	1.00595i
$855$	−45.0044	+	25.9833i	−1.53912	+	0.888610i
$856$		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
$862$	−38.5585	−	22.2618i	−1.31331	−	0.758239i
$863$	−40.2535	+	40.2535i	−1.37025	+	1.37025i	−0.510174	+	0.860071i	$0.670419\pi$
$863$	−40.2535	+	40.2535i	−1.37025	+	1.37025i	−0.860071	+	0.510174i	$0.829581\pi$
$864$	4.29588	+	16.0324i	0.146149	+	0.545435i
$865$	101.214	−	27.1203i	3.44139	−	0.922118i
$866$		0			0
$867$	−18.3046	+	31.7045i	−0.621657	+	1.07674i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	51.1396	+	88.5764i	1.72982	+	2.99614i
$875$	69.6554	+	40.2156i	2.35478	+	1.35953i
$876$		0			0
$877$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$877$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$878$		0			0
$879$	−52.0782	−	52.0782i	−1.75655	−	1.75655i
$880$		0			0
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	−4.19554	+	15.6580i	−0.141271	+	0.527232i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	−121.896			−4.09749
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	−24.2404	+	24.2404i	−0.812996	+	0.812996i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$			29.9333i			1.00000i
$897$	−73.5834	+	2.09211i	−2.45688	+	0.0698534i
$898$	29.9088			0.998071
$899$		0			0
$900$	20.1532	+	34.9063i	0.671773	+	1.16354i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	3.34669	−	0.896742i	0.111309	−	0.0298252i
$905$	−40.5332	−	40.5332i	−1.34737	−	1.34737i
$906$	−36.9618	+	64.0197i	−1.22797	+	2.12691i
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	15.4892	−	57.8063i	0.514025	−	1.91837i
$909$			2.28187i			0.0756847i
$910$	−12.9795	+	54.6029i	−0.430265	+	1.81007i
$911$	0.210840			0.00698543			0.00349271	−	0.999994i	$-0.498888\pi$
$911$	0.210840			0.00698543			0.00349271	+	0.999994i	$0.498888\pi$
$912$	63.4710	+	17.0070i	2.10174	+	0.563158i
$913$		0			0
$914$	−41.7596	−	24.1099i	−1.38129	−	0.797486i
$915$	57.4716	−	57.4716i	1.89995	−	1.89995i
$916$	−9.80592	−	36.5962i	−0.323997	−	1.20917i
$917$	−2.59286	+	0.694754i	−0.0856237	+	0.0229428i
$918$		0			0
$919$	−25.9154	+	44.8869i	−0.854872	+	1.48068i	0.0218926	+	0.999760i	$0.493031\pi$
$919$	−25.9154	+	44.8869i	−0.854872	+	1.48068i	−0.876764	+	0.480921i	$0.840303\pi$
$920$	96.6125	−	55.7792i	3.18522	−	1.83899i
$921$	−5.39863	+	20.1480i	−0.177891	+	0.663898i
$922$			29.6380i			0.976076i
$923$	−28.6188	−	27.0364i	−0.941999	−	0.889915i
$924$		0			0
$925$		0			0
$926$	4.20185	+	7.27782i	0.138081	+	0.239164i
$927$		0			0
$928$		0			0
$929$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$929$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$930$		0			0
$931$	−37.7584	−	37.7584i	−1.23748	−	1.23748i
$932$	−9.77048	+	16.9230i	−0.320043	+	0.554330i
$933$		0			0
$934$	−6.20507	+	23.1576i	−0.203036	+	0.757741i
$935$		0			0
$936$	−11.4678	+	12.1389i	−0.374835	+	0.396773i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−42.6416	+	42.6416i	−1.39008	+	1.39008i	−0.564953	+	0.825123i	$0.691106\pi$
$941$	−42.6416	+	42.6416i	−1.39008	+	1.39008i	−0.825123	+	0.564953i	$0.808894\pi$
$942$	−7.40510	−	27.6362i	−0.241271	−	0.900436i
$943$		0			0
$944$	38.4838	+	38.4838i	1.25254	+	1.25254i
$945$	−16.1479	+	27.9689i	−0.525290	+	0.909830i
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$			35.5684i			1.15521i
$949$		0			0
$950$	−132.773			−4.30772
$951$		0			0
$952$		0			0
$953$	0.932742	+	0.538519i	0.0302145	+	0.0174443i	0.515031	−	0.857171i	$-0.327780\pi$
$953$	0.932742	+	0.538519i	0.0302145	+	0.0174443i	−0.484817	+	0.874616i	$0.661114\pi$
$954$		0			0
$955$	29.3143	+	109.402i	0.948587	+	3.54018i
$956$	52.2391	−	13.9974i	1.68953	−	0.452709i
$957$		0			0
$958$		0			0
$959$	−48.7135	+	28.1248i	−1.57304	+	0.908196i
$960$	18.5500	−	69.2294i	0.598697	−	2.23437i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	42.8028	+	74.1366i	1.37787	+	2.38654i
$966$	−66.1574	−	38.1960i	−2.12858	−	1.22894i
$967$	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	$-0.117555\pi$
$968$	−8.05256	−	30.0526i	−0.258819	−	0.965926i
$969$		0			0
$970$		0			0
$971$	24.6801	−	42.7472i	0.792021	−	1.37182i	−0.132692	−	0.991157i	$-0.542362\pi$
$971$	24.6801	−	42.7472i	0.792021	−	1.37182i	0.924713	−	0.380664i	$-0.124305\pi$
$972$	−26.6451	+	15.3836i	−0.854642	+	0.493428i
$973$	−15.7290	+	58.7014i	−0.504248	+	1.88188i
$974$			43.6917i			1.39997i
$975$	45.4089	−	84.0822i	1.45425	−	2.69279i
$976$	−36.2887			−1.16157
$977$	60.3562	+	16.1724i	1.93097	+	0.517401i	0.973317	+	0.229465i	$0.0736978\pi$
$977$	60.3562	+	16.1724i	1.93097	+	0.517401i	0.957650	+	0.287936i	$0.0929689\pi$
$978$		0			0
$979$		0			0
$980$	−41.1840	+	41.1840i	−1.31557	+	1.31557i
$981$		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
$991$	−11.3007	−	19.5735i	−0.358980	−	0.621771i	0.628811	−	0.777558i	$-0.283542\pi$
$991$	−11.3007	−	19.5735i	−0.358980	−	0.621771i	−0.987791	+	0.155787i	$0.950209\pi$
$992$		0			0
$993$		0			0
$994$	−10.5744	−	39.4641i	−0.335399	−	1.25173i
$995$		0			0
$996$	17.2302	+	17.2302i	0.545959	+	0.545959i
$997$	−30.9701	+	53.6418i	−0.980834	+	1.69885i	−0.321675	+	0.946850i	$0.604246\pi$
$997$	−30.9701	+	53.6418i	−0.980834	+	1.69885i	−0.659158	+	0.752004i	$0.729087\pi$
$998$		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.405.4	yes	16
7.6	odd	2	inner	728.2.ds.b.405.1	yes	16
8.5	even	2	inner	728.2.ds.b.405.1	yes	16
13.7	odd	12	inner	728.2.ds.b.293.4	yes	16
56.13	odd	2	CM	728.2.ds.b.405.4	yes	16
91.20	even	12	inner	728.2.ds.b.293.1	✓	16
104.85	odd	12	inner	728.2.ds.b.293.1	✓	16
728.293	even	12	inner	728.2.ds.b.293.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.b.293.1	✓	16	91.20	even	12	inner
728.2.ds.b.293.1	✓	16	104.85	odd	12	inner
728.2.ds.b.293.4	yes	16	13.7	odd	12	inner
728.2.ds.b.293.4	yes	16	728.293	even	12	inner
728.2.ds.b.405.1	yes	16	7.6	odd	2	inner
728.2.ds.b.405.1	yes	16	8.5	even	2	inner
728.2.ds.b.405.4	yes	16	1.1	even	1	trivial
728.2.ds.b.405.4	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)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.07674 + 1.86497i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-2.94171 + 2.94171i) q^{5} +(0.788230 + 2.94171i) q^{6} +(2.55560 - 0.684771i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-0.818745 + 1.41811i) q^{9} +(-5.09520 + 2.94171i) q^{10} +4.30697i q^{12} +(3.07000 - 1.89079i) q^{13} +3.74166 q^{14} +(-8.65368 - 2.31875i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.63749 + 1.63749i) q^{18} +(-1.97436 - 7.36841i) q^{19} +(-8.03691 + 2.15348i) q^{20} +(4.02880 + 4.02880i) q^{21} +(-8.21056 + 4.74037i) q^{23} +(-1.57646 + 5.88343i) q^{24} -12.3074i q^{25} +(4.88578 - 1.45917i) q^{26} +2.93414 q^{27} +(5.11120 + 1.36954i) q^{28} +(-10.9724 - 6.33493i) q^{30} +(1.46410 + 5.46410i) q^{32} +(-5.50344 + 9.53224i) q^{35} +(-2.83622 + 1.63749i) q^{36} -10.7881i q^{38} +(6.83187 + 3.68957i) q^{39} -11.7669 q^{40} +(4.02880 + 6.97808i) q^{42} +(-1.76315 - 6.58018i) q^{45} +(-12.9509 + 3.47019i) q^{46} +(-4.30697 + 7.45989i) q^{48} +(6.06218 - 3.50000i) q^{49} +(4.50480 - 16.8122i) q^{50} +(7.20819 - 0.204942i) q^{52} +(4.00811 + 1.07397i) q^{54} +(6.48074 + 3.74166i) q^{56} +(11.6160 - 11.6160i) q^{57} +(13.1424 - 3.52151i) q^{59} +(-12.6699 - 12.6699i) q^{60} +(-4.53609 + 7.85674i) q^{61} +(-1.12131 + 4.18477i) q^{63} +8.00000i q^{64} +(-3.46890 + 14.5932i) q^{65} +(-17.6813 - 10.2083i) q^{69} +(-11.0069 + 11.0069i) q^{70} +(-2.82612 - 10.5472i) q^{71} +(-4.47371 + 1.19873i) q^{72} +(22.9529 - 13.2518i) q^{75} +(3.94872 - 14.7368i) q^{76} +(7.98203 + 7.54069i) q^{78} +8.25834 q^{79} +(-16.0738 - 4.30697i) q^{80} +(5.61555 + 9.72641i) q^{81} +(4.00054 - 4.00054i) q^{83} +(2.94929 + 11.0069i) q^{84} -9.63406i q^{90} +(6.55094 - 6.93435i) q^{91} -18.9615 q^{92} +(27.4838 + 15.8678i) q^{95} +(-8.61393 + 8.61393i) q^{96} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 q^{57} - 32 q^{60} - 112 q^{63} + 16 q^{65} - 16 q^{71}+ \cdots + 56 q^{98}+O(q^{100}) \) 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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