LMFDB - Embedded newform 728.2.cy.a.675.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(467,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))

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

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

chi := DirichletCharacter("728.467");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cy (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			675.5
Character	$\chi$	$=$	728.675
Dual form			728.2.cy.a.467.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(2.16895 + 1.25225i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.345317 - 0.199369i) q^{5} -3.54188i q^{6} +(2.63319 - 0.257522i) q^{7} +2.82843 q^{8} +(1.63624 + 2.83404i) q^{9} +(-0.488352 - 0.281950i) q^{10} +(-4.33790 + 2.50449i) q^{12} -3.60555i q^{13} +(-2.17734 - 3.04289i) q^{14} +0.998635 q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.76991 + 2.17656i) q^{17} +(2.31399 - 4.00794i) q^{18} +0.797476i q^{20} +(6.03374 + 2.73885i) q^{21} +(6.13472 + 3.54188i) q^{24} +(-2.42050 + 4.19244i) q^{25} +(-4.41588 + 2.54951i) q^{26} +0.682400i q^{27} +(-2.18715 + 4.81834i) q^{28} +(-0.706142 - 1.22307i) q^{30} +(-3.24146 - 1.87146i) q^{31} +(-2.82843 + 4.89898i) q^{32} -6.15623i q^{34} +(0.857944 - 0.613903i) q^{35} -6.54494 q^{36} +(2.44361 + 4.23246i) q^{37} +(4.51503 - 7.82027i) q^{39} +(0.976705 - 0.563901i) q^{40} +(-0.912112 - 9.32645i) q^{42} +9.68172 q^{43} +(1.13004 + 0.652429i) q^{45} +(-6.18224 + 3.56932i) q^{47} -10.0180i q^{48} +(6.86737 - 1.35621i) q^{49} +6.84622 q^{50} +(5.45116 + 9.44169i) q^{51} +(6.24500 + 3.60555i) q^{52} +(0.835766 - 0.482530i) q^{54} +(7.44778 - 0.728381i) q^{56} +(-0.998635 + 1.72969i) q^{60} +5.29329i q^{62} +(5.03834 + 7.04120i) q^{63} +8.00000 q^{64} +(-0.718835 - 1.24506i) q^{65} +(-7.53981 + 4.35311i) q^{68} +(-1.35853 - 0.616667i) q^{70} -16.8514 q^{71} +(4.62797 + 8.01588i) q^{72} +(3.45579 - 5.98560i) q^{74} +(-10.4999 + 6.06213i) q^{75} -12.7704 q^{78} +(-1.38127 - 0.797476i) q^{80} +(4.05417 - 7.02204i) q^{81} +(-10.7776 + 7.71190i) q^{84} +1.73575 q^{85} +(-6.84601 - 11.8576i) q^{86} -1.84535i q^{90} +(-0.928508 - 9.49410i) q^{91} +(-4.68705 - 8.11821i) q^{93} +(8.74301 + 5.04778i) q^{94} +(-12.2694 + 7.08377i) q^{96} +(-6.51697 - 7.45179i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 36 q^{9} - 48 q^{16} + 60 q^{25} - 24 q^{30} - 72 q^{35} - 144 q^{36} + 96 q^{42} + 60 q^{51} + 192 q^{64} - 108 q^{81}+O(q^{100}) $ 24 * q - 24 * q^4 + 36 * q^9 - 48 * q^16 + 60 * q^25 - 24 * q^30 - 72 * q^35 - 144 * q^36 + 96 * q^42 + 60 * q^51 + 192 * q^64 - 108 * q^81

Character values

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

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$2$	−0.707107	−	1.22474i	−0.500000	−	0.866025i
$3$	2.16895	+	1.25225i	1.25225	+	0.722984i	0.971555	−	0.236814i	$-0.0761033\pi$
$3$	2.16895	+	1.25225i	1.25225	+	0.722984i	0.280690	+	0.959798i	$0.409437\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.345317	−	0.199369i	0.154431	−	0.0891605i	−0.420793	−	0.907157i	$-0.638248\pi$
$5$	0.345317	−	0.199369i	0.154431	−	0.0891605i	0.575224	+	0.817996i	$0.304915\pi$
$6$		−	3.54188i		−	1.44597i
$7$	2.63319	−	0.257522i	0.995252	−	0.0973341i
$7$	2.63319	−	0.257522i	0.995252	−	0.0973341i
$8$	2.82843			1.00000
$9$	1.63624	+	2.83404i	0.545412	+	0.944681i
$10$	−0.488352	−	0.281950i	−0.154431	−	0.0891605i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−4.33790	+	2.50449i	−1.25225	+	0.722984i
$13$		−	3.60555i		−	1.00000i
$13$		−	3.60555i		−	1.00000i
$14$	−2.17734	−	3.04289i	−0.581920	−	0.813246i
$15$	0.998635			0.257847
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	3.76991	+	2.17656i	0.914336	+	0.527892i	0.881824	−	0.471579i	$-0.156316\pi$
$17$	3.76991	+	2.17656i	0.914336	+	0.527892i	0.0325125	+	0.999471i	$0.489649\pi$
$18$	2.31399	−	4.00794i	0.545412	−	0.944681i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$			0.797476i			0.178321i
$21$	6.03374	+	2.73885i	1.31667	+	0.597665i
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	6.13472	+	3.54188i	1.25225	+	0.722984i
$25$	−2.42050	+	4.19244i	−0.484101	+	0.838487i
$26$	−4.41588	+	2.54951i	−0.866025	+	0.500000i
$27$			0.682400i			0.131328i
$28$	−2.18715	+	4.81834i	−0.413332	+	0.910580i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−0.706142	−	1.22307i	−0.128923	−	0.223302i
$31$	−3.24146	−	1.87146i	−0.582184	−	0.336124i	0.179817	−	0.983700i	$-0.442449\pi$
$31$	−3.24146	−	1.87146i	−0.582184	−	0.336124i	−0.762001	+	0.647576i	$0.775783\pi$
$32$	−2.82843	+	4.89898i	−0.500000	+	0.866025i
$33$		0			0
$34$		−	6.15623i		−	1.05578i
$35$	0.857944	−	0.613903i	0.145019	−	0.103769i
$36$	−6.54494			−1.09082
$37$	2.44361	+	4.23246i	0.401727	+	0.695812i	0.993934	−	0.109974i	$-0.0350768\pi$
$37$	2.44361	+	4.23246i	0.401727	+	0.695812i	−0.592207	+	0.805786i	$0.701743\pi$
$38$		0			0
$39$	4.51503	−	7.82027i	0.722984	−	1.25225i
$40$	0.976705	−	0.563901i	0.154431	−	0.0891605i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.912112	−	9.32645i	−0.140742	−	1.43910i
$43$	9.68172			1.47645			0.738224	−	0.674556i	$-0.235665\pi$
$43$	9.68172			1.47645			0.738224	+	0.674556i	$0.235665\pi$
$44$		0			0
$45$	1.13004	+	0.652429i	0.168457	+	0.0972584i
$46$		0			0
$47$	−6.18224	+	3.56932i	−0.901772	+	0.520639i	−0.877775	−	0.479073i	$-0.840973\pi$
$47$	−6.18224	+	3.56932i	−0.901772	+	0.520639i	−0.0239976	+	0.999712i	$0.507639\pi$
$48$		−	10.0180i		−	1.44597i
$49$	6.86737	−	1.35621i	0.981052	−	0.193744i
$50$	6.84622			0.968202
$51$	5.45116	+	9.44169i	0.763315	+	1.32210i
$52$	6.24500	+	3.60555i	0.866025	+	0.500000i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	0.835766	−	0.482530i	0.113733	−	0.0656640i
$55$		0			0
$56$	7.44778	−	0.728381i	0.995252	−	0.0973341i
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−0.998635	+	1.72969i	−0.128923	+	0.223302i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$			5.29329i			0.672248i
$63$	5.03834	+	7.04120i	0.634772	+	0.887108i
$64$	8.00000			1.00000
$65$	−0.718835	−	1.24506i	−0.0891605	−	0.154431i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−7.53981	+	4.35311i	−0.914336	+	0.527892i
$69$		0			0
$70$	−1.35853	−	0.616667i	−0.162376	−	0.0737058i
$71$	−16.8514			−1.99989			−0.999944	−	0.0105471i	$-0.996643\pi$
$71$	−16.8514			−1.99989			−0.999944	+	0.0105471i	$0.996643\pi$
$72$	4.62797	+	8.01588i	0.545412	+	0.944681i
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$	3.45579	−	5.98560i	0.401727	−	0.695812i
$75$	−10.4999	+	6.06213i	−1.21243	+	0.699994i
$76$		0			0
$77$		0			0
$78$	−12.7704			−1.44597
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−1.38127	−	0.797476i	−0.154431	−	0.0891605i
$81$	4.05417	−	7.02204i	0.450464	−	0.780226i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	−10.7776	+	7.71190i	−1.17593	+	0.841437i
$85$	1.73575			0.188269
$86$	−6.84601	−	11.8576i	−0.738224	−	1.27864i
$87$		0			0
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		−	1.84535i		−	0.194517i
$91$	−0.928508	−	9.49410i	−0.0973341	−	0.995252i
$92$		0			0
$93$	−4.68705	−	8.11821i	−0.486024	−	0.841819i
$94$	8.74301	+	5.04778i	0.901772	+	0.520639i
$95$		0			0
$96$	−12.2694	+	7.08377i	−1.25225	+	0.722984i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	−6.51697	−	7.45179i	−0.658313	−	0.752744i
$99$		0			0
$100$	−4.84101	−	8.38487i	−0.484101	−	0.838487i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	7.70911	−	13.3526i	0.763315	−	1.32210i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$		−	10.1980i		−	1.00000i
$105$	2.62960	−	0.257170i	0.256622	−	0.0250973i
$106$		0			0
$107$	−0.0841196	−	0.145699i	−0.00813215	−	0.0140853i	0.861931	−	0.507026i	$-0.169255\pi$
$107$	−0.0841196	−	0.145699i	−0.00813215	−	0.0140853i	−0.870063	+	0.492941i	$0.835922\pi$
$108$	−1.18195	−	0.682400i	−0.113733	−	0.0656640i
$109$	9.76072	−	16.9061i	0.934907	−	1.61931i	0.160108	−	0.987100i	$-0.448816\pi$
$109$	9.76072	−	16.9061i	0.934907	−	1.61931i	0.774800	−	0.632207i	$-0.217851\pi$
$110$		0			0
$111$			12.2400i			1.16177i
$112$	−6.15846	−	8.60659i	−0.581920	−	0.813246i
$113$	−20.6635			−1.94386			−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−20.6635			−1.94386			−0.971930	+	0.235269i	$0.924403\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.2183	−	5.89953i	0.944681	−	0.545412i
$118$		0			0
$119$	10.4874	+	4.76045i	0.961377	+	0.436390i
$120$	2.82457			0.257847
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$	6.48292	−	3.74292i	0.582184	−	0.336124i
$125$			3.92398i			0.350972i
$126$	5.06103	−	11.1496i	0.450872	−	0.993282i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−5.65685	−	9.79796i	−0.500000	−	0.866025i
$129$	20.9992	+	12.1239i	1.84887	+	1.06745i
$130$	−1.01659	+	1.76078i	−0.0891605	+	0.154431i
$131$	−19.1791	+	11.0730i	−1.67568	+	0.967456i	−0.711321	+	0.702867i	$0.751903\pi$
$131$	−19.1791	+	11.0730i	−1.67568	+	0.967456i	−0.964361	+	0.264588i	$0.914764\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.136049	+	0.235644i	0.0117093	+	0.0202810i
$136$	10.6629	+	6.15623i	0.914336	+	0.527892i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		−	23.1549i		−	1.96397i	−0.188953	−	0.981986i	$-0.560509\pi$
$139$		−	23.1549i		−	1.96397i	0.188953	−	0.981986i	$-0.439491\pi$
$140$	0.205367	+	2.09990i	0.0173567	+	0.177474i
$141$	−17.8786			−1.50565
$142$	11.9157	+	20.6386i	0.999944	+	1.73195i
$143$		0			0
$144$	6.54494	−	11.3362i	0.545412	−	0.944681i
$145$		0			0
$146$		0			0
$147$	16.5933	+	5.65808i	1.36859	+	0.466670i
$148$	−9.77444			−0.803454
$149$	−12.1959	−	21.1240i	−0.999129	−	1.73054i	−0.535701	−	0.844407i	$-0.679953\pi$
$149$	−12.1959	−	21.1240i	−0.999129	−	1.73054i	−0.463428	−	0.886135i	$-0.653381\pi$
$150$	14.8491	+	8.57314i	1.21243	+	0.699994i
$151$	−8.81101	+	15.2611i	−0.717030	+	1.24193i	0.245141	+	0.969487i	$0.421166\pi$
$151$	−8.81101	+	15.2611i	−0.717030	+	1.24193i	−0.962171	+	0.272445i	$0.912168\pi$
$152$		0			0
$153$			14.2454i			1.15167i
$154$		0			0
$155$	−1.49244			−0.119876
$156$	9.03007	+	15.6405i	0.722984	+	1.25225i
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$		0			0
$159$		0			0
$160$			2.25560i			0.178321i
$161$		0			0
$162$	−11.4669			−0.900928
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			23.0641i			1.78475i	0.451291	+	0.892377i	$0.350964\pi$
$167$			23.0641i			1.78475i	−0.451291	+	0.892377i	$0.649036\pi$
$168$	17.0660	+	7.74662i	1.31667	+	0.597665i
$169$	−13.0000			−1.00000
$170$	−1.22736	−	2.12585i	−0.0941343	−	0.163045i
$171$		0			0
$172$	−9.68172	+	16.7692i	−0.738224	+	1.27864i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	−5.29400	+	11.6628i	−0.400189	+	0.881625i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.0849	+	22.6637i	−0.978012	+	1.69397i	−0.308395	+	0.951258i	$0.599792\pi$
$179$	−13.0849	+	22.6637i	−0.978012	+	1.69397i	−0.669616	+	0.742707i	$0.733541\pi$
$180$	−2.26008	+	1.30486i	−0.168457	+	0.0972584i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−10.9713	+	7.85053i	−0.813246	+	0.581920i
$183$		0			0
$184$		0			0
$185$	1.68764	+	0.974360i	0.124078	+	0.0716364i
$186$	−6.62849	+	11.4809i	−0.486024	+	0.841819i
$187$		0			0
$188$		−	14.2773i		−	1.04128i
$189$	0.175733	+	1.79689i	0.0127827	+	0.130704i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	17.3516	+	10.0180i	1.25225	+	0.722984i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		−	3.60063i		−	0.257847i
$196$	−4.51835	+	13.2508i	−0.322739	+	0.946488i
$197$	−3.79625			−0.270471			−0.135236	−	0.990813i	$-0.543179\pi$
$197$	−3.79625			−0.270471			−0.135236	+	0.990813i	$0.543179\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−6.84622	+	11.8580i	−0.484101	+	0.838487i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−21.8047			−1.52663
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−12.4900	+	7.21110i	−0.866025	+	0.500000i
$209$		0			0
$210$	−2.17437	−	3.03874i	−0.150046	−	0.209693i
$211$	23.0140			1.58435			0.792175	−	0.610294i	$-0.208949\pi$
$211$	23.0140			1.58435			0.792175	+	0.610294i	$0.208949\pi$
$212$		0			0
$213$	−36.5498	−	21.1020i	−2.50435	−	1.44589i
$214$	−0.118963	+	0.206050i	−0.00813215	+	0.0140853i
$215$	3.34326	−	1.93023i	0.228009	−	0.131641i
$216$			1.93012i			0.131328i
$217$	−9.01732	−	4.09316i	−0.612136	−	0.277862i
$218$	−27.6075			−1.86981
$219$		0			0
$220$		0			0
$221$	7.84768	−	13.5926i	0.527892	−	0.914336i
$222$	14.9909	−	8.65498i	1.00612	−	0.580884i
$223$			24.8566i			1.66452i	0.554384	+	0.832261i	$0.312954\pi$
$223$			24.8566i			1.66452i	−0.554384	+	0.832261i	$0.687046\pi$
$224$	−6.18619	+	13.6283i	−0.413332	+	0.910580i
$225$	−15.8421			−1.05614
$226$	14.6113	+	25.3075i	0.971930	+	1.68343i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	12.3244	−	7.11548i	0.814417	−	0.470204i	−0.0340703	−	0.999419i	$-0.510847\pi$
$229$	12.3244	−	7.11548i	0.814417	−	0.470204i	0.848487	+	0.529215i	$0.177514\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.84994	+	13.5965i	0.514267	+	0.890736i	0.999863	+	0.0165528i	$0.00526917\pi$
$233$	7.84994	+	13.5965i	0.514267	+	0.890736i	−0.485596	+	0.874183i	$0.661397\pi$
$234$	−14.4508	−	8.34320i	−0.944681	−	0.545412i
$235$	−1.42322	+	2.46509i	−0.0928408	+	0.160805i
$236$		0			0
$237$		0			0
$238$	−1.58536	−	16.2105i	−0.102764	−	1.05077i
$239$	0.744372			0.0481494			0.0240747	−	0.999710i	$-0.492336\pi$
$239$	0.744372			0.0481494			0.0240747	+	0.999710i	$0.492336\pi$
$240$	−1.99727	−	3.45937i	−0.128923	−	0.223302i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	−7.77817	+	13.4722i	−0.500000	+	0.866025i
$243$	19.3595	−	11.1772i	1.24192	−	0.717020i
$244$		0			0
$245$	2.10103	−	1.83746i	0.134230	−	0.117391i
$246$		0			0
$247$		0			0
$248$	−9.16824	−	5.29329i	−0.582184	−	0.336124i
$249$		0			0
$250$	4.80588	−	2.77468i	0.303951	−	0.175486i
$251$		−	31.0798i		−	1.96174i	−0.194668	−	0.980869i	$-0.562363\pi$
$251$		−	31.0798i		−	1.96174i	0.194668	−	0.980869i	$-0.437637\pi$
$252$	−17.2341	+	1.68546i	−1.08564	+	0.106174i
$253$		0			0
$254$		0			0
$255$	3.76476	+	2.17359i	0.235758	+	0.136115i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	17.7140	−	10.2272i	1.10497	−	0.637954i	0.167448	−	0.985881i	$-0.446448\pi$
$257$	17.7140	−	10.2272i	1.10497	−	0.637954i	0.937522	+	0.347927i	$0.113114\pi$
$258$		−	34.2915i		−	2.13490i
$259$	7.52443	+	10.5156i	0.467546	+	0.653406i
$260$	2.87534			0.178321
$261$		0			0
$262$	27.1233	+	15.6596i	1.67568	+	0.967456i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	0.192403	−	0.333252i	0.0117093	−	0.0202810i
$271$	−28.1592	+	16.2577i	−1.71055	+	0.987588i	−0.776742	+	0.629819i	$0.783129\pi$
$271$	−28.1592	+	16.2577i	−1.71055	+	0.987588i	−0.933810	+	0.357769i	$0.883538\pi$
$272$		−	17.4124i		−	1.05578i
$273$	9.87505	−	21.7550i	0.597665	−	1.31667i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	−28.3588	+	16.3730i	−1.70085	+	0.981986i
$279$		−	12.2486i		−	0.733304i
$280$	2.42663	−	1.73638i	0.145019	−	0.103769i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	12.6421	+	21.8968i	0.752827	+	1.30393i
$283$	−26.4953	−	15.2971i	−1.57498	−	0.909316i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−26.4953	−	15.2971i	−1.57498	−	0.909316i	−0.579437	−	0.815017i	$-0.696728\pi$
$284$	16.8514	−	29.1874i	0.999944	−	1.73195i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−18.5119			−1.09082
$289$	0.974791	+	1.68839i	0.0573406	+	0.0993169i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	7.14719i		−	0.417543i	−0.977964	−	0.208772i	$-0.933053\pi$
$293$		−	7.14719i		−	0.417543i	0.977964	−	0.208772i	$-0.0669465\pi$
$294$	−4.80353	−	24.3234i	−0.280147	−	1.41857i
$295$		0			0
$296$	6.91157	+	11.9712i	0.401727	+	0.695812i
$297$		0			0
$298$	−17.2476	+	29.8738i	−0.999129	+	1.73054i
$299$		0			0
$300$		−	24.2485i		−	1.39999i
$301$	25.4938	−	2.49325i	1.46944	−	0.143709i
$302$	24.9213			1.43406
$303$		0			0
$304$		0			0
$305$		0			0
$306$	17.4470	−	10.0730i	0.997380	−	0.575837i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$	1.05532	+	1.82786i	0.0599380	+	0.103816i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	12.7704	−	22.1191i	0.722984	−	1.25225i
$313$	28.7957	−	16.6252i	1.62763	−	0.939713i	0.642834	−	0.766006i	$-0.277759\pi$
$313$	28.7957	−	16.6252i	1.62763	−	0.939713i	0.984797	−	0.173707i	$-0.0555747\pi$
$314$		0			0
$315$	3.14362	+	1.42696i	0.177123	+	0.0804000i
$316$		0			0
$317$	−2.29643	−	3.97753i	−0.128980	−	0.223400i	0.794301	−	0.607524i	$-0.207837\pi$
$317$	−2.29643	−	3.97753i	−0.128980	−	0.223400i	−0.923282	+	0.384123i	$0.874504\pi$
$318$		0			0
$319$		0			0
$320$	2.76254	−	1.59495i	0.154431	−	0.0891605i
$321$		−	0.421353i		−	0.0235176i
$322$		0			0
$323$		0			0
$324$	8.10835	+	14.0441i	0.450464	+	0.780226i
$325$	15.1160	+	8.72725i	0.838487	+	0.484101i
$326$		0			0
$327$	42.3411	−	24.4456i	2.34147	−	1.35185i
$328$		0			0
$329$	−15.3598	+	10.9907i	−0.846815	+	0.605940i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	−7.99664	+	13.8506i	−0.438213	+	0.759008i
$334$	28.2476	−	16.3088i	1.54564	−	0.892377i
$335$		0			0
$336$	−2.57984	−	26.3792i	−0.140742	−	1.43910i
$337$	−34.4138			−1.87464			−0.937321	−	0.348467i	$-0.886702\pi$
$337$	−34.4138			−1.87464			−0.937321	+	0.348467i	$0.886702\pi$
$338$	9.19239	+	15.9217i	0.500000	+	0.866025i
$339$	−44.8182	−	25.8758i	−2.43419	−	1.40538i
$340$	−1.73575	+	3.00641i	−0.0941343	+	0.163045i
$341$		0			0
$342$		0			0
$343$	17.7338	−	5.33964i	0.957536	−	0.288314i
$344$	27.3840			1.47645
$345$		0			0
$346$		0			0
$347$	−11.2345	+	19.4588i	−0.603101	+	1.04460i	0.389247	+	0.921133i	$0.372735\pi$
$347$	−11.2345	+	19.4588i	−0.603101	+	1.04460i	−0.992348	+	0.123469i	$0.960598\pi$
$348$		0			0
$349$			27.5721i			1.47590i	0.674854	+	0.737951i	$0.264207\pi$
$349$			27.5721i			1.47590i	−0.674854	+	0.737951i	$0.735793\pi$
$350$	18.0274	−	1.76305i	0.963604	−	0.0942390i
$351$	2.46043			0.131328
$352$		0			0
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$	−5.81907	+	3.35964i	−0.308844	+	0.178311i
$356$		0			0
$357$	16.7854	+	23.4580i	0.888377	+	1.24153i
$358$	37.0097			1.95602
$359$	−17.1457	−	29.6972i	−0.904914	−	1.56736i	−0.821033	−	0.570881i	$-0.806602\pi$
$359$	−17.1457	−	29.6972i	−0.904914	−	1.56736i	−0.0838812	−	0.996476i	$-0.526732\pi$
$360$	3.19624	+	1.84535i	0.168457	+	0.0972584i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$		−	27.5494i		−	1.44597i
$364$	17.3728	+	7.88587i	0.910580	+	0.413332i
$365$		0			0
$366$		0			0
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$		0			0
$369$		0			0
$370$		−	2.75591i		−	0.143273i
$371$		0			0
$372$	18.7482			0.972049
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−4.91379	+	8.51093i	−0.253747	+	0.439503i
$376$	−17.4860	+	10.0956i	−0.901772	+	0.520639i
$377$		0			0
$378$	2.07647	−	1.48582i	0.106802	−	0.0764223i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	33.7959	−	19.5121i	1.72689	−	0.997020i	0.824875	−	0.565315i	$-0.191246\pi$
$383$	33.7959	−	19.5121i	1.72689	−	0.997020i	0.902015	−	0.431705i	$-0.142088\pi$
$384$		−	28.3351i		−	1.44597i
$385$		0			0
$386$		0			0
$387$	15.8416	+	27.4384i	0.805272	+	1.39477i
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	−4.40985	+	2.54603i	−0.223302	+	0.128923i
$391$		0			0
$392$	19.4238	−	3.83593i	0.981052	−	0.193744i
$393$	−55.4646			−2.79782
$394$	2.68435	+	4.64943i	0.135236	+	0.234235i
$395$		0			0
$396$		0			0
$397$	28.3404	−	16.3623i	1.42236	−	0.821203i	0.425864	−	0.904787i	$-0.359970\pi$
$397$	28.3404	−	16.3623i	1.42236	−	0.821203i	0.996501	+	0.0835845i	$0.0266368\pi$
$398$		0			0
$399$		0			0
$400$	19.3640			0.968202
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−6.74764	+	11.6873i	−0.336124	+	0.582184i
$404$		0			0
$405$		−	3.23311i		−	0.160654i
$406$		0			0
$407$		0			0
$408$	15.4182	+	26.7051i	0.763315	+	1.32210i
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	17.6635	+	10.1980i	0.866025	+	0.500000i
$417$	28.9956	−	50.2218i	1.41992	−	2.45937i
$418$		0			0
$419$			25.5295i			1.24720i	0.781745	+	0.623598i	$0.214330\pi$
$419$			25.5295i			1.24720i	−0.781745	+	0.623598i	$0.785670\pi$
$420$	−2.18416	+	4.81176i	−0.106576	+	0.234790i
$421$	15.4551			0.753235			0.376617	−	0.926369i	$-0.377087\pi$
$421$	15.4551			0.753235			0.376617	+	0.926369i	$0.377087\pi$
$422$	−16.2734	−	28.1863i	−0.792175	−	1.37209i
$423$	−20.2312	−	11.6805i	−0.983675	−	0.567925i
$424$		0			0
$425$	−18.2501	+	10.5367i	−0.885262	+	0.511106i
$426$			59.6856i			2.89178i
$427$		0			0
$428$	0.336478			0.0162643
$429$		0			0
$430$	−4.72809	−	2.72976i	−0.228009	−	0.131641i
$431$	4.94788	−	8.56998i	0.238331	−	0.412802i	−0.721904	−	0.691993i	$-0.756733\pi$
$431$	4.94788	−	8.56998i	0.238331	−	0.412802i	0.960236	+	0.279191i	$0.0900663\pi$
$432$	2.36390	−	1.36480i	0.113733	−	0.0656640i
$433$		−	32.6481i		−	1.56897i	−0.620151	−	0.784483i	$-0.712928\pi$
$433$		−	32.6481i		−	1.56897i	0.620151	−	0.784483i	$-0.287072\pi$
$434$	1.36314	+	13.9382i	0.0654326	+	0.669056i
$435$		0			0
$436$	19.5214	+	33.8121i	0.934907	+	1.61931i
$437$		0			0
$438$		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
$441$	15.0802	+	17.2433i	0.718103	+	0.821111i
$442$	−22.1966			−1.05578
$443$	−18.2173	−	31.5533i	−0.865530	−	1.49914i	−0.866520	−	0.499142i	$-0.833648\pi$
$443$	−18.2173	−	31.5533i	−0.865530	−	1.49914i	0.000990059	−	1.00000i	$-0.499685\pi$
$444$	−21.2003	−	12.2400i	−1.00612	−	0.580884i
$445$		0			0
$446$	30.4430	−	17.5763i	1.44152	−	0.832261i
$447$		−	61.0891i		−	2.88942i
$448$	21.0655	−	2.06017i	0.995252	−	0.0973341i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	11.2020	+	19.4025i	0.528069	+	0.914642i
$451$		0			0
$452$	20.6635	−	35.7903i	0.971930	−	1.68343i
$453$	−38.2213	+	22.0671i	−1.79579	+	1.03680i
$454$		0			0
$455$	−2.21346	−	3.09336i	−0.103769	−	0.145019i
$456$		0			0
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$	−17.4293	−	10.0628i	−0.814417	−	0.470204i
$459$	−1.48528	+	2.57258i	−0.0693270	+	0.120078i
$460$		0			0
$461$			11.3301i			0.527693i	0.964565	+	0.263847i	$0.0849913\pi$
$461$			11.3301i			0.527693i	−0.964565	+	0.263847i	$0.915009\pi$
$462$		0			0
$463$	14.9682			0.695631			0.347816	−	0.937563i	$-0.386923\pi$
$463$	14.9682			0.695631			0.347816	+	0.937563i	$0.386923\pi$
$464$		0			0
$465$	−3.23704	−	1.86891i	−0.150114	−	0.0866684i
$466$	11.1015	−	19.2283i	0.514267	−	0.890736i
$467$	−8.83176	+	5.09902i	−0.408685	+	0.235954i	−0.690225	−	0.723595i	$-0.742488\pi$
$467$	−8.83176	+	5.09902i	−0.408685	+	0.235954i	0.281539	+	0.959550i	$0.409155\pi$
$468$			23.5981i			1.09082i
$469$		0			0
$470$	4.02548			0.185682
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−18.7327	+	13.4042i	−0.858613	+	0.614382i
$477$		0			0
$478$	−0.526350	−	0.911665i	−0.0240747	−	0.0416986i
$479$	3.01244	+	1.73923i	0.137642	+	0.0794675i	0.567240	−	0.823553i	$-0.308011\pi$
$479$	3.01244	+	1.73923i	0.137642	+	0.0794675i	−0.429598	+	0.903020i	$0.641345\pi$
$480$	−2.82457	+	4.89229i	−0.128923	+	0.223302i
$481$	15.2603	−	8.81056i	0.695812	−	0.401727i
$482$		0			0
$483$		0			0
$484$	22.0000			1.00000
$485$		0			0
$486$	−27.3785	−	15.8070i	−1.24192	−	0.717020i
$487$	−21.9765	+	38.0643i	−0.995848	+	1.72486i	−0.419091	+	0.907944i	$0.637651\pi$
$487$	−21.9765	+	38.0643i	−0.995848	+	1.72486i	−0.576757	+	0.816916i	$0.695682\pi$
$488$		0			0
$489$		0			0
$490$	−3.73608	−	1.27395i	−0.168779	−	0.0575512i
$491$	23.2945			1.05126			0.525632	−	0.850712i	$-0.323829\pi$
$491$	23.2945			1.05126			0.525632	+	0.850712i	$0.323829\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$			14.9717i			0.672248i
$497$	−44.3728	+	4.33959i	−1.99039	+	0.194657i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−6.79654	−	3.92398i	−0.303951	−	0.175486i
$501$	−28.8819	+	50.0249i	−1.29035	+	2.23495i
$502$	−38.0648	+	21.9767i	−1.69892	+	0.980869i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	14.2506	+	19.9155i	0.634772	+	0.887108i
$505$		0			0
$506$		0			0
$507$	−28.1964	−	16.2792i	−1.25225	−	0.722984i
$508$		0			0
$509$	18.7350	−	10.8167i	0.830414	−	0.479440i	−0.0235804	−	0.999722i	$-0.507507\pi$
$509$	18.7350	−	10.8167i	0.830414	−	0.479440i	0.853994	+	0.520282i	$0.174173\pi$
$510$		−	6.14783i		−	0.272230i
$511$		0			0
$512$	22.6274			1.00000
$513$		0			0
$514$	−25.0514	−	14.4634i	−1.10497	−	0.637954i
$515$		0			0
$516$	−41.9984	+	24.2478i	−1.84887	+	1.06745i
$517$		0			0
$518$	7.55832	−	16.6511i	0.332093	−	0.731609i
$519$		0			0
$520$	−2.03317	−	3.52156i	−0.0891605	−	0.154431i
$521$	36.9499	+	21.3330i	1.61880	+	0.934616i	0.987230	+	0.159299i	$0.0509235\pi$
$521$	36.9499	+	21.3330i	1.61880	+	0.934616i	0.631572	+	0.775317i	$0.282410\pi$
$522$		0			0
$523$	38.7476	−	22.3710i	1.69432	−	0.978214i	0.743358	−	0.668894i	$-0.233232\pi$
$523$	38.7476	−	22.3710i	1.69432	−	0.978214i	0.950958	−	0.309320i	$-0.100101\pi$
$524$		−	44.2921i		−	1.93491i
$525$	−26.0871	+	18.6667i	−1.13854	+	0.814681i
$526$		0			0
$527$	−8.14667	−	14.1104i	−0.354875	−	0.614661i
$528$		0			0
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.0580959	−	0.0335417i	−0.00251170	−	0.00145013i
$536$		0			0
$537$	−56.7611	+	32.7710i	−2.44942	+	1.41417i
$538$		0			0
$539$		0			0
$540$	−0.544198			−0.0234185
$541$	9.38901	+	16.2622i	0.403665	+	0.699168i	0.994165	−	0.107869i	$-0.0344028\pi$
$541$	9.38901	+	16.2622i	0.403665	+	0.699168i	−0.590500	+	0.807038i	$0.701069\pi$
$542$	39.8232	+	22.9919i	1.71055	+	0.987588i
$543$		0			0
$544$	−21.3258	+	12.3125i	−0.914336	+	0.527892i
$545$		−	7.78394i		−	0.333427i
$546$	−33.6270	+	3.28867i	−1.43910	+	0.140742i
$547$	−10.8937			−0.465781			−0.232891	−	0.972503i	$-0.574818\pi$
$547$	−10.8937			−0.465781			−0.232891	+	0.972503i	$0.574818\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.44028	+	4.22668i	0.103584	+	0.179413i
$556$	40.1054	+	23.1549i	1.70085	+	0.981986i
$557$	−20.5037	+	35.5135i	−0.868772	+	1.50476i	−0.00551865	+	0.999985i	$0.501757\pi$
$557$	−20.5037	+	35.5135i	−0.868772	+	1.50476i	−0.863253	+	0.504772i	$0.831577\pi$
$558$	−15.0014	+	8.66106i	−0.635060	+	0.366652i
$559$		−	34.9079i		−	1.47645i
$560$	−3.84251	−	1.74420i	−0.162376	−	0.0737058i
$561$		0			0
$562$		0			0
$563$	16.2489	+	9.38133i	0.684812	+	0.395376i	0.801665	−	0.597773i	$-0.203948\pi$
$563$	16.2489	+	9.38133i	0.684812	+	0.395376i	−0.116854	+	0.993149i	$0.537281\pi$
$564$	17.8786	−	30.9667i	0.752827	−	1.30393i
$565$	−7.13547	+	4.11967i	−0.300192	+	0.173316i
$566$			43.2666i			1.81863i
$567$	8.86708	−	19.5344i	0.372382	−	0.820367i
$568$	−47.6628			−1.99989
$569$	23.6952	+	41.0413i	0.993354	+	1.72054i	0.596356	+	0.802720i	$0.296615\pi$
$569$	23.6952	+	41.0413i	0.993354	+	1.72054i	0.396998	+	0.917819i	$0.370052\pi$
$570$		0			0
$571$	−14.2352	+	24.6560i	−0.595723	+	1.03182i	0.397721	+	0.917506i	$0.369801\pi$
$571$	−14.2352	+	24.6560i	−0.595723	+	1.03182i	−0.993444	+	0.114316i	$0.963532\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	13.0899	+	22.6723i	0.545412	+	0.944681i
$577$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$577$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$578$	1.37856	−	2.38774i	0.0573406	−	0.0993169i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.35237	−	4.07442i	0.0972584	−	0.168457i
$586$	−8.75348	+	5.05383i	−0.361603	+	0.208772i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$	−26.3934	+	23.0823i	−1.08844	+	0.951900i
$589$		0			0
$590$		0			0
$591$	−8.23388	−	4.75383i	−0.338696	−	0.195546i
$592$	9.77444	−	16.9298i	0.401727	−	0.695812i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	4.57056	−	0.446994i	0.187375	−	0.0183250i
$596$	48.7837			1.99826
$597$		0			0
$598$		0			0
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$	−29.6982	+	17.1463i	−1.21243	+	0.699994i
$601$			47.6750i			1.94470i	0.233520	+	0.972352i	$0.424975\pi$
$601$			47.6750i			1.94470i	−0.233520	+	0.972352i	$0.575025\pi$
$602$	−21.0804	−	29.4604i	−0.859174	−	1.20072i
$603$		0			0
$604$	−17.6220	−	30.5222i	−0.717030	−	1.24193i
$605$	−3.79849	−	2.19306i	−0.154431	−	0.0891605i
$606$		0			0
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.8694	+	22.2904i	0.520639	+	0.901772i
$612$	−24.6738	−	14.2454i	−0.997380	−	0.575837i
$613$	−7.12721	+	12.3447i	−0.287865	+	0.498598i	−0.973300	−	0.229537i	$-0.926279\pi$
$613$	−7.12721	+	12.3447i	−0.287865	+	0.498598i	0.685435	+	0.728134i	$0.259612\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$	1.49244	−	2.58499i	0.0599380	−	0.103816i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−36.1203			−1.44597
$625$	−11.3202	−	19.6072i	−0.452808	−	0.784286i
$626$	−40.7233	−	23.5116i	−1.62763	−	0.939713i
$627$		0			0
$628$		0			0
$629$			21.2746i			0.848274i
$630$	−0.475217	−	4.85915i	−0.0189331	−	0.193593i
$631$	−46.6391			−1.85667			−0.928336	−	0.371742i	$-0.878761\pi$
$631$	−46.6391			−1.85667			−0.928336	+	0.371742i	$0.878761\pi$
$632$		0			0
$633$	49.9163	+	28.8192i	1.98399	+	1.14546i
$634$	−3.24764	+	5.62508i	−0.128980	+	0.223400i
$635$		0			0
$636$		0			0
$637$	−4.88987	−	24.7606i	−0.193744	−	0.981052i
$638$		0			0
$639$	−27.5728	−	47.7575i	−1.09076	−	1.88926i
$640$	−3.90682	−	2.25560i	−0.154431	−	0.0891605i
$641$	10.1635	−	17.6037i	0.401435	−	0.695306i	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	10.1635	−	17.6037i	0.401435	−	0.695306i	0.993899	+	0.110291i	$0.0351782\pi$
$642$	−0.516050	+	0.297942i	−0.0203669	+	0.0117588i
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$	9.66850			0.380697
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	11.4669	−	19.8613i	0.450464	−	0.780226i
$649$		0			0
$650$		−	24.6844i		−	0.968202i
$651$	−14.4325	−	20.1698i	−0.565654	−	0.790515i
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	−59.8793	−	34.5713i	−2.34147	−	1.35185i
$655$	−4.41524	+	7.64742i	−0.172518	+	0.298809i
$656$		0			0
$657$		0			0
$658$	24.3219	+	11.0402i	0.948166	+	0.430393i
$659$	41.1588			1.60332			0.801660	−	0.597781i	$-0.203951\pi$
$659$	41.1588			1.60332			0.801660	+	0.597781i	$0.203951\pi$
$660$		0			0
$661$	41.3063	+	23.8482i	1.60663	+	0.927587i	0.990118	+	0.140240i	$0.0447873\pi$
$661$	41.3063	+	23.8482i	1.60663	+	0.927587i	0.616510	+	0.787347i	$0.288546\pi$
$662$		0			0
$663$	34.0425	−	19.6544i	1.32210	−	0.763315i
$664$		0			0
$665$		0			0
$666$	22.6179			0.876426
$667$		0			0
$668$	−39.9482	−	23.0641i	−1.54564	−	0.892377i
$669$	−31.1266	+	53.9128i	−1.20342	+	2.08439i
$670$		0			0
$671$		0			0
$672$	−30.4835	+	21.8125i	−1.17593	+	0.841437i
$673$	48.4803			1.86878			0.934388	−	0.356256i	$-0.115947\pi$
$673$	48.4803			1.86878			0.934388	+	0.356256i	$0.115947\pi$
$674$	24.3343	+	42.1482i	0.937321	+	1.62349i
$675$	−2.86092	−	1.65175i	−0.110117	−	0.0635760i
$676$	13.0000	−	22.5167i	0.500000	−	0.866025i
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$			73.1878i			2.81076i
$679$		0			0
$680$	4.90945			0.188269
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$	−19.0794	−	17.9437i	−0.728455	−	0.685094i
$687$	35.6413			1.35980
$688$	−19.3634	−	33.5384i	−0.738224	−	1.27864i
$689$		0			0
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$		0			0
$694$	31.7761			1.20620
$695$	−4.61637	−	7.99578i	−0.175109	−	0.303297i
$696$		0			0
$697$		0			0
$698$	33.7688	−	19.4964i	1.27817	−	0.737951i
$699$			39.3202i			1.48723i
$700$	−14.9066	−	20.8323i	−0.563416	−	0.787386i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.73979	−	3.01340i	−0.0656640	−	0.113733i
$703$		0			0
$704$		0			0
$705$	−6.17380	+	3.56445i	−0.232519	+	0.134245i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.48528	+	14.6969i	0.318671	+	0.551955i	0.980211	−	0.197955i	$-0.0634300\pi$
$709$	8.48528	+	14.6969i	0.318671	+	0.551955i	−0.661540	+	0.749910i	$0.730097\pi$
$710$	8.22940	+	4.75125i	0.308844	+	0.178311i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	16.8610	−	37.1451i	0.631006	−	1.39012i
$715$		0			0
$716$	−26.1698	−	45.3274i	−0.978012	−	1.69397i
$717$	1.61451	+	0.932136i	0.0602948	+	0.0348112i
$718$	−24.2476	+	41.9981i	−0.904914	+	1.56736i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		−	5.21943i		−	0.194517i
$721$		0			0
$722$	−26.8701			−1.00000
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−33.7410	+	19.4804i	−1.25225	+	0.722984i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−2.62622	−	26.8534i	−0.0973341	−	0.995252i
$729$	31.6615			1.17265
$730$		0			0
$731$	36.4991	+	21.0728i	1.34997	+	0.779405i
$732$		0			0
$733$	45.2040	−	26.0985i	1.66965	−	0.963971i	0.701820	−	0.712354i	$-0.252371\pi$
$733$	45.2040	−	26.0985i	1.66965	−	0.963971i	0.967827	−	0.251617i	$-0.0809623\pi$
$734$		0			0
$735$	6.85799	−	1.35436i	0.252961	−	0.0499562i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	−3.37528	+	1.94872i	−0.124078	+	0.0716364i
$741$		0			0
$742$		0			0
$743$	19.1634			0.703035			0.351518	−	0.936181i	$-0.385666\pi$
$743$	19.1634			0.703035			0.351518	+	0.936181i	$0.385666\pi$
$744$	−13.2570	−	22.9618i	−0.486024	−	0.841819i
$745$	−8.42293	−	4.86298i	−0.308592	−	0.178166i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.259023	−	0.361991i	−0.00946451	−	0.0132269i
$750$	13.8983			0.507494
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	24.7290	+	14.2773i	0.901772	+	0.520639i
$753$	38.9195	−	67.4106i	1.41831	−	2.45658i
$754$		0			0
$755$			7.02657i			0.255723i
$756$	−3.28803	−	1.49251i	−0.119585	−	0.0542821i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	21.3481	−	47.0304i	0.772854	−	1.70262i
$764$		0			0
$765$	2.84010	+	4.91919i	0.102684	+	0.177854i
$766$	−47.7946	−	27.5942i	−1.72689	−	0.997020i
$767$		0			0
$768$	−34.7032	+	20.0359i	−1.25225	+	0.722984i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	51.2278			1.84492
$772$		0			0
$773$	−12.2145	−	7.05206i	−0.439326	−	0.253645i	0.263986	−	0.964527i	$-0.414963\pi$
$773$	−12.2145	−	7.05206i	−0.439326	−	0.253645i	−0.703312	+	0.710882i	$0.748296\pi$
$774$	22.4034	−	38.8037i	0.805272	−	1.39477i
$775$	15.6919	−	9.05975i	0.563671	−	0.325436i
$776$		0			0
$777$	3.15206	+	32.2302i	0.113080	+	1.15625i
$778$		0			0
$779$		0			0
$780$	6.23648	+	3.60063i	0.223302	+	0.128923i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−18.4328	−	21.0768i	−0.658313	−	0.752744i
$785$		0			0
$786$	39.2194	+	67.9300i	1.39891	+	2.42298i
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	3.79625	−	6.57529i	0.135236	−	0.234235i
$789$		0			0
$790$		0			0
$791$	−54.4110	+	5.32131i	−1.93463	+	0.189204i
$792$		0			0
$793$		0			0
$794$	−40.0794	−	23.1399i	−1.42236	−	0.821203i
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−31.0753			−1.09936
$800$	−13.6924	−	23.7160i	−0.484101	−	0.838487i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	19.0852			0.672248
$807$		0			0
$808$		0			0
$809$	−21.6731	+	37.5389i	−0.761985	+	1.31980i	0.179841	+	0.983696i	$0.442442\pi$
$809$	−21.6731	+	37.5389i	−0.761985	+	1.31980i	−0.941826	+	0.336101i	$0.890892\pi$
$810$	−3.95973	+	2.28615i	−0.139131	+	0.0803272i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−81.4347			−2.85604
$814$		0			0
$815$		0			0
$816$	21.8047	−	37.7668i	0.763315	−	1.32210i
$817$		0			0
$818$		0			0
$819$	25.3874	−	18.1660i	0.887108	−	0.634772i
$820$		0			0
$821$	−21.2481	−	36.8028i	−0.741564	−	1.28443i	−0.951783	−	0.306773i	$-0.900751\pi$
$821$	−21.2481	−	36.8028i	−0.741564	−	1.28443i	0.210218	−	0.977654i	$-0.432582\pi$
$822$		0			0
$823$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$823$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$829$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$830$		0			0
$831$		0			0
$832$		−	28.8444i		−	1.00000i
$833$	28.8412	+	9.83443i	0.999287	+	0.340743i
$834$	−82.0119			−2.83984
$835$	4.59827	+	7.96443i	0.159130	+	0.275621i
$836$		0			0
$837$	1.27708	−	2.21197i	0.0441425	−	0.0764570i
$838$	31.2671	−	18.0521i	1.08010	−	0.623598i
$839$			57.3570i			1.98018i	0.140427	+	0.990091i	$0.455153\pi$
$839$			57.3570i			1.98018i	−0.140427	+	0.990091i	$0.544847\pi$
$840$	7.43762	−	0.727388i	0.256622	−	0.0250973i
$841$	29.0000			1.00000
$842$	−10.9284	−	18.9285i	−0.376617	−	0.652321i
$843$		0			0
$844$	−23.0140	+	39.8614i	−0.792175	+	1.37209i
$845$	−4.48912	+	2.59180i	−0.154431	+	0.0891605i
$846$			33.0374i			1.13585i
$847$	−16.9358	−	23.6681i	−0.581920	−	0.813246i
$848$		0			0
$849$	−38.3113	−	66.3572i	−1.31484	−	2.27737i
$850$	25.8096	+	14.9012i	0.885262	+	0.511106i
$851$		0			0
$852$	73.0996	−	42.2041i	2.50435	−	1.44589i
$853$		−	56.7336i		−	1.94252i	−0.238021	−	0.971260i	$-0.576499\pi$
$853$		−	56.7336i		−	1.94252i	0.238021	−	0.971260i	$-0.423501\pi$
$854$		0			0
$855$		0			0
$856$	−0.237926	−	0.412100i	−0.00813215	−	0.0140853i
$857$	35.3270	+	20.3961i	1.20675	+	0.696717i	0.962048	−	0.272882i	$-0.0879768\pi$
$857$	35.3270	+	20.3961i	1.20675	+	0.696717i	0.244701	+	0.969599i	$0.421310\pi$
$858$		0			0
$859$	−24.2524	+	14.0021i	−0.827480	+	0.477746i	−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−24.2524	+	14.0021i	−0.827480	+	0.477746i	0.0255092	+	0.999675i	$0.491879\pi$
$860$			7.72094i			0.263282i
$861$		0			0
$862$	−13.9947			−0.476662
$863$	27.4624	+	47.5663i	0.934831	+	1.61917i	0.774936	+	0.632040i	$0.217782\pi$
$863$	27.4624	+	47.5663i	0.934831	+	1.61917i	0.159895	+	0.987134i	$0.448885\pi$
$864$	−3.34306	−	1.93012i	−0.113733	−	0.0656640i
$865$		0			0
$866$	−39.9855	+	23.0857i	−1.35876	+	0.784483i
$867$			4.88271i			0.165825i
$868$	16.1069	−	11.5253i	0.546703	−	0.391194i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	27.6075	−	47.8175i	0.934907	−	1.61931i
$873$		0			0
$874$		0			0
$875$	1.01051	+	10.3326i	0.0341615	+	0.349305i
$876$		0			0
$877$	−27.2490	−	47.1966i	−0.920133	−	1.59372i	−0.799208	−	0.601055i	$-0.794747\pi$
$877$	−27.2490	−	47.1966i	−0.920133	−	1.59372i	−0.120925	−	0.992662i	$-0.538586\pi$
$878$		0			0
$879$	8.95003	−	15.5019i	0.301877	−	0.522866i
$880$		0			0
$881$			2.41480i			0.0813567i	0.999172	+	0.0406783i	$0.0129519\pi$
$881$			2.41480i			0.0813567i	−0.999172	+	0.0406783i	$0.987048\pi$
$882$	10.4554	−	30.6622i	0.352051	−	1.03245i
$883$	−48.1523			−1.62046			−0.810228	−	0.586115i	$-0.800657\pi$
$883$	−48.1523			−1.62046			−0.810228	+	0.586115i	$0.800657\pi$
$884$	15.6954	+	27.1852i	0.527892	+	0.914336i
$885$		0			0
$886$	−25.7631	+	44.6231i	−0.865530	+	1.49914i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$			34.6199i			1.16177i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−43.0529	−	24.8566i	−1.44152	−	0.832261i
$893$		0			0
$894$	−74.8186	+	43.1965i	−2.50231	+	1.44471i
$895$			10.4349i			0.348800i
$896$	−17.4188	−	24.3431i	−0.581920	−	0.813246i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	15.8421	−	27.4392i	0.528069	−	0.914642i
$901$		0			0
$902$		0			0
$903$	58.4170	+	26.5167i	1.94399	+	0.882421i
$904$	−58.4453			−1.94386
$905$		0			0
$906$	54.0531	+	31.2076i	1.79579	+	1.03680i
$907$	−13.1418	+	22.7623i	−0.436367	+	0.755810i	−0.997406	−	0.0719791i	$-0.977068\pi$
$907$	−13.1418	+	22.7623i	−0.436367	+	0.755810i	0.561039	+	0.827789i	$0.310402\pi$
$908$		0			0
$909$		0			0
$910$	−2.22343	+	4.89826i	−0.0737058	+	0.162376i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$			28.4619i			0.940408i
$917$	−47.6505	+	34.0964i	−1.57356	+	1.12596i
$918$	4.20101			0.138654
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$		0			0
$922$	13.8764	−	8.01156i	0.456996	−	0.263847i
$923$			60.7585i			1.99989i
$924$		0			0
$925$	−23.6591			−0.777905
$926$	−10.5841	−	18.3322i	−0.347816	−	0.602435i
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$			5.28606i			0.173337i
$931$		0			0
$932$	−31.3998			−1.02853
$933$		0			0
$934$	12.4900	+	7.21110i	0.408685	+	0.235954i
$935$		0			0
$936$	28.9017	−	16.6864i	0.944681	−	0.545412i
$937$			28.8621i			0.942883i	0.881897	+	0.471441i	$0.156266\pi$
$937$			28.8621i			0.942883i	−0.881897	+	0.471441i	$0.843734\pi$
$938$		0			0
$939$	83.2754			2.71759
$940$	−2.84645	−	4.93019i	−0.0928408	−	0.160805i
$941$	46.9056	+	27.0809i	1.52908	+	0.882813i	0.999401	+	0.0346136i	$0.0110201\pi$
$941$	46.9056	+	27.0809i	1.52908	+	0.882813i	0.529677	+	0.848200i	$0.322313\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	0.418927	+	0.585461i	0.0136277	+	0.0190450i
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		−	11.5028i		−	0.373003i
$952$	29.6628	+	13.4646i	0.961377	+	0.436390i
$953$	−45.7556			−1.48217			−0.741084	−	0.671412i	$-0.765688\pi$
$953$	−45.7556			−1.48217			−0.741084	+	0.671412i	$0.765688\pi$
$954$		0			0
$955$		0			0
$956$	−0.744372	+	1.28929i	−0.0240747	+	0.0416986i
$957$		0			0
$958$		−	4.91929i		−	0.158935i
$959$		0			0
$960$	7.98908			0.257847
$961$	−8.49528	−	14.7143i	−0.274041	−	0.474654i
$962$	−21.5814	−	12.4600i	−0.695812	−	0.401727i
$963$	0.275279	−	0.476797i	0.00887074	−	0.0153646i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−13.4219			−0.431620			−0.215810	−	0.976435i	$-0.569239\pi$
$967$	−13.4219			−0.431620			−0.215810	+	0.976435i	$0.569239\pi$
$968$	−15.5563	−	26.9444i	−0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$	−22.4591	+	12.9668i	−0.720747	+	0.416124i	−0.815028	−	0.579422i	$-0.803278\pi$
$971$	−22.4591	+	12.9668i	−0.720747	+	0.416124i	0.0942803	+	0.995546i	$0.469945\pi$
$972$			44.7090i			1.43404i
$973$	−5.96289	−	60.9712i	−0.191161	−	1.95465i
$974$	62.1588			1.99170
$975$	21.8573	+	37.8580i	0.699994	+	1.21243i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$	1.08154	+	5.47656i	0.0345486	+	0.174942i
$981$	63.8833			2.03964
$982$	−16.4717	−	28.5298i	−0.525632	−	0.910422i
$983$	52.2001	+	30.1377i	1.66492	+	0.961244i	0.970311	+	0.241860i	$0.0777574\pi$
$983$	52.2001	+	30.1377i	1.66492	+	0.961244i	0.694612	+	0.719384i	$0.255576\pi$
$984$		0			0
$985$	−1.31091	+	0.756854i	−0.0417691	+	0.0241154i
$986$		0			0
$987$	−47.0778	+	4.60414i	−1.49850	+	0.146551i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$	18.3365	−	10.5866i	0.582184	−	0.336124i
$993$		0			0
$994$	36.6912	+	51.2768i	1.16377	+	1.62640i
$995$		0			0
$996$		0			0
$997$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$997$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$	−2.88823	+	1.66752i	−0.0913795	+	0.0527580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cy.a.675.5	yes	24
7.5	odd	6	inner	728.2.cy.a.467.5	✓	24
8.3	odd	2	inner	728.2.cy.a.675.11	yes	24
13.12	even	2	inner	728.2.cy.a.675.11	yes	24
56.19	even	6	inner	728.2.cy.a.467.11	yes	24
91.12	odd	6	inner	728.2.cy.a.467.11	yes	24
104.51	odd	2	CM	728.2.cy.a.675.5	yes	24
728.467	even	6	inner	728.2.cy.a.467.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cy.a.467.5	✓	24	7.5	odd	6	inner
728.2.cy.a.467.5	✓	24	728.467	even	6	inner
728.2.cy.a.467.11	yes	24	56.19	even	6	inner
728.2.cy.a.467.11	yes	24	91.12	odd	6	inner
728.2.cy.a.675.5	yes	24	1.1	even	1	trivial
728.2.cy.a.675.5	yes	24	104.51	odd	2	CM
728.2.cy.a.675.11	yes	24	8.3	odd	2	inner
728.2.cy.a.675.11	yes	24	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cy (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(2.16895 + 1.25225i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.345317 - 0.199369i) q^{5} -3.54188i q^{6} +(2.63319 - 0.257522i) q^{7} +2.82843 q^{8} +(1.63624 + 2.83404i) q^{9} +(-0.488352 - 0.281950i) q^{10} +(-4.33790 + 2.50449i) q^{12} -3.60555i q^{13} +(-2.17734 - 3.04289i) q^{14} +0.998635 q^{15} +(-2.00000 - 3.46410i) q^{16} +(3.76991 + 2.17656i) q^{17} +(2.31399 - 4.00794i) q^{18} +0.797476i q^{20} +(6.03374 + 2.73885i) q^{21} +(6.13472 + 3.54188i) q^{24} +(-2.42050 + 4.19244i) q^{25} +(-4.41588 + 2.54951i) q^{26} +0.682400i q^{27} +(-2.18715 + 4.81834i) q^{28} +(-0.706142 - 1.22307i) q^{30} +(-3.24146 - 1.87146i) q^{31} +(-2.82843 + 4.89898i) q^{32} -6.15623i q^{34} +(0.857944 - 0.613903i) q^{35} -6.54494 q^{36} +(2.44361 + 4.23246i) q^{37} +(4.51503 - 7.82027i) q^{39} +(0.976705 - 0.563901i) q^{40} +(-0.912112 - 9.32645i) q^{42} +9.68172 q^{43} +(1.13004 + 0.652429i) q^{45} +(-6.18224 + 3.56932i) q^{47} -10.0180i q^{48} +(6.86737 - 1.35621i) q^{49} +6.84622 q^{50} +(5.45116 + 9.44169i) q^{51} +(6.24500 + 3.60555i) q^{52} +(0.835766 - 0.482530i) q^{54} +(7.44778 - 0.728381i) q^{56} +(-0.998635 + 1.72969i) q^{60} +5.29329i q^{62} +(5.03834 + 7.04120i) q^{63} +8.00000 q^{64} +(-0.718835 - 1.24506i) q^{65} +(-7.53981 + 4.35311i) q^{68} +(-1.35853 - 0.616667i) q^{70} -16.8514 q^{71} +(4.62797 + 8.01588i) q^{72} +(3.45579 - 5.98560i) q^{74} +(-10.4999 + 6.06213i) q^{75} -12.7704 q^{78} +(-1.38127 - 0.797476i) q^{80} +(4.05417 - 7.02204i) q^{81} +(-10.7776 + 7.71190i) q^{84} +1.73575 q^{85} +(-6.84601 - 11.8576i) q^{86} -1.84535i q^{90} +(-0.928508 - 9.49410i) q^{91} +(-4.68705 - 8.11821i) q^{93} +(8.74301 + 5.04778i) q^{94} +(-12.2694 + 7.08377i) q^{96} +(-6.51697 - 7.45179i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 36 q^{9} - 48 q^{16} + 60 q^{25} - 24 q^{30} - 72 q^{35} - 144 q^{36} + 96 q^{42} + 60 q^{51} + 192 q^{64} - 108 q^{81}+O(q^{100}) \) 24 * q - 24 * q^4 + 36 * q^9 - 48 * q^16 + 60 * q^25 - 24 * q^30 - 72 * q^35 - 144 * q^36 + 96 * q^42 + 60 * q^51 + 192 * q^64 - 108 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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