LMFDB - Embedded newform 728.2.ds.b.405.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 6, 11])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 8x^{12} + 40x^{10} - 161x^{8} + 360x^{6} + 648x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 8x^12 + 40x^10 - 161x^8 + 360x^6 + 648x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 13 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			405.3
Root			$-1.58915 + 0.688914i$ of defining polynomial
Character	$\chi$	$=$	728.405
Dual form			728.2.ds.b.293.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 0.366025i) q^{2} +(0.688914 + 1.19323i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.88215 + 1.88215i) q^{5} +(0.504320 + 1.88215i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.550796 - 0.954007i) q^{9} +(-3.25997 + 1.88215i) q^{10} +2.75565i q^{12} +(-2.62094 + 2.47602i) q^{13} -3.74166 q^{14} +(-3.54248 - 0.949204i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.10159 - 1.10159i) q^{18} +(0.623770 + 2.32794i) q^{19} +(-5.14212 + 1.37783i) q^{20} +(-2.57768 - 2.57768i) q^{21} +(3.01441 - 1.74037i) q^{23} +(-1.00864 + 3.76429i) q^{24} -2.08495i q^{25} +(-4.48655 + 2.42298i) q^{26} +5.65129 q^{27} +(-5.11120 - 1.36954i) q^{28} +(-4.49168 - 2.59327i) q^{30} +(1.46410 + 5.46410i) q^{32} +(3.52117 - 6.09885i) q^{35} +(1.90801 - 1.10159i) q^{36} +3.40834i q^{38} +(-4.76007 - 1.42162i) q^{39} -7.52859 q^{40} +(-2.57768 - 4.46467i) q^{42} +(0.758902 + 2.83226i) q^{45} +(4.75478 - 1.27404i) q^{46} +(-2.75565 + 4.77293i) q^{48} +(6.06218 - 3.50000i) q^{49} +(0.763146 - 2.84810i) q^{50} +(-7.01562 + 1.66766i) q^{52} +(7.71980 + 2.06851i) q^{54} +(-6.48074 - 3.74166i) q^{56} +(-2.34805 + 2.34805i) q^{57} +(3.25336 - 0.871734i) q^{59} +(-5.18655 - 5.18655i) q^{60} +(6.02709 - 10.4392i) q^{61} +(-0.754338 + 2.81523i) q^{63} +8.00000i q^{64} +(0.272752 - 9.59323i) q^{65} +(4.15334 + 2.39793i) q^{69} +(7.04235 - 7.04235i) q^{70} +(4.29022 + 16.0113i) q^{71} +(3.00961 - 0.806422i) q^{72} +(2.48784 - 1.43635i) q^{75} +(-1.24754 + 4.65588i) q^{76} +(-5.98203 - 3.68428i) q^{78} +15.7417 q^{79} +(-10.2842 - 2.75565i) q^{80} +(2.24086 + 3.88128i) q^{81} +(11.4889 - 11.4889i) q^{83} +(-1.88699 - 7.04235i) q^{84} +4.14672i q^{90} +(5.00256 - 8.12246i) q^{91} +6.96148 q^{92} +(-5.55555 - 3.20750i) q^{95} +(-5.51131 + 5.51131i) q^{96} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.688914	+	1.19323i	0.397744	+	0.688914i	0.993447	−	0.114291i	$-0.0364597\pi$
$3$	0.688914	+	1.19323i	0.397744	+	0.688914i	−0.595703	+	0.803205i	$0.703126\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−1.88215	+	1.88215i	−0.841722	+	0.841722i	−0.989083	−	0.147361i	$-0.952922\pi$
$5$	−1.88215	+	1.88215i	−0.841722	+	0.841722i	0.147361	+	0.989083i	$0.452922\pi$
$6$	0.504320	+	1.88215i	0.205888	+	0.768383i
$7$	−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
$9$	0.550796	−	0.954007i	0.183599	−	0.318002i
$10$	−3.25997	+	1.88215i	−1.03089	+	0.595187i
$11$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$11$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$12$			2.75565i			0.795489i
$13$	−2.62094	+	2.47602i	−0.726917	+	0.686725i
$13$	−2.62094	+	2.47602i	−0.726917	+	0.686725i
$14$	−3.74166			−1.00000
$15$	−3.54248	−	0.949204i	−0.914664	−	0.245083i
$16$	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	$0.166667\pi$
$18$	1.10159	−	1.10159i	0.259648	−	0.259648i
$19$	0.623770	+	2.32794i	0.143103	+	0.534066i	0.999833	+	0.0183009i	$0.00582570\pi$
$19$	0.623770	+	2.32794i	0.143103	+	0.534066i	−0.856730	+	0.515765i	$0.827508\pi$
$20$	−5.14212	+	1.37783i	−1.14981	+	0.308092i
$21$	−2.57768	−	2.57768i	−0.562496	−	0.562496i
$22$		0			0
$23$	3.01441	−	1.74037i	0.628548	−	0.362892i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	3.01441	−	1.74037i	0.628548	−	0.362892i	0.780189	+	0.625543i	$0.215123\pi$
$24$	−1.00864	+	3.76429i	−0.205888	+	0.768383i
$25$		−	2.08495i		−	0.416991i
$26$	−4.48655	+	2.42298i	−0.879886	+	0.475185i
$27$	5.65129			1.08759
$28$	−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	$0.333333\pi$
$30$	−4.49168	−	2.59327i	−0.820065	−	0.473465i
$31$		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
$35$	3.52117	−	6.09885i	0.595187	−	1.03089i
$36$	1.90801	−	1.10159i	0.318002	−	0.183599i
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$			3.40834i			0.552906i
$39$	−4.76007	−	1.42162i	−0.762221	−	0.227642i
$40$	−7.52859			−1.19037
$41$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$41$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$42$	−2.57768	−	4.46467i	−0.397744	−	0.688914i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$		0			0
$45$	0.758902	+	2.83226i	0.113130	+	0.422209i
$46$	4.75478	−	1.27404i	0.701054	−	0.187847i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−2.75565	+	4.77293i	−0.397744	+	0.688914i
$49$	6.06218	−	3.50000i	0.866025	−	0.500000i
$50$	0.763146	−	2.84810i	0.107925	−	0.402782i
$51$		0			0
$52$	−7.01562	+	1.66766i	−0.972891	+	0.231263i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	7.71980	+	2.06851i	1.05053	+	0.281489i
$55$		0			0
$56$	−6.48074	−	3.74166i	−0.866025	−	0.500000i
$57$	−2.34805	+	2.34805i	−0.311007	+	0.311007i
$58$		0			0
$59$	3.25336	−	0.871734i	0.423551	−	0.113490i	−0.0407464	−	0.999170i	$-0.512974\pi$
$59$	3.25336	−	0.871734i	0.423551	−	0.113490i	0.464297	+	0.885679i	$0.346307\pi$
$60$	−5.18655	−	5.18655i	−0.669580	−	0.669580i
$61$	6.02709	−	10.4392i	0.771690	−	1.33661i	−0.164946	−	0.986303i	$-0.552745\pi$
$61$	6.02709	−	10.4392i	0.771690	−	1.33661i	0.936636	−	0.350304i	$-0.113922\pi$
$62$		0			0
$63$	−0.754338	+	2.81523i	−0.0950377	+	0.354686i
$64$			8.00000i			1.00000i
$65$	0.272752	−	9.59323i	0.0338308	−	1.18989i
$66$		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
$69$	4.15334	+	2.39793i	0.500003	+	0.288677i
$70$	7.04235	−	7.04235i	0.841722	−	0.841722i
$71$	4.29022	+	16.0113i	0.509156	+	1.90020i	0.428723	+	0.903436i	$0.358964\pi$
$71$	4.29022	+	16.0113i	0.509156	+	1.90020i	0.0804327	+	0.996760i	$0.474370\pi$
$72$	3.00961	−	0.806422i	0.354686	−	0.0950377i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	2.48784	−	1.43635i	0.287271	−	0.165856i
$76$	−1.24754	+	4.65588i	−0.143103	+	0.534066i
$77$		0			0
$78$	−5.98203	−	3.68428i	−0.677331	−	0.417163i
$79$	15.7417			1.77107			0.885537	−	0.464568i	$-0.153790\pi$
$79$	15.7417			1.77107			0.885537	+	0.464568i	$0.153790\pi$
$80$	−10.2842	−	2.75565i	−1.14981	−	0.308092i
$81$	2.24086	+	3.88128i	0.248984	+	0.431253i
$82$		0			0
$83$	11.4889	−	11.4889i	1.26107	−	1.26107i	0.310502	−	0.950573i	$-0.399503\pi$
$83$	11.4889	−	11.4889i	1.26107	−	1.26107i	0.950573	−	0.310502i	$-0.100497\pi$
$84$	−1.88699	−	7.04235i	−0.205888	−	0.768383i
$85$		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	$0.583333\pi$
$90$			4.14672i			0.437102i
$91$	5.00256	−	8.12246i	0.524411	−	0.851465i
$92$	6.96148			0.725785
$93$		0			0
$94$		0			0
$95$	−5.55555	−	3.20750i	−0.569988	−	0.329083i
$96$	−5.51131	+	5.51131i	−0.562496	+	0.562496i
$97$		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
$100$	2.08495	−	3.61125i	0.208495	−	0.361125i
$101$	−11.4256	+	6.59655i	−1.13689	+	0.656382i	−0.945658	−	0.325164i	$-0.894581\pi$
$101$	−11.4256	+	6.59655i	−1.13689	+	0.656382i	−0.191229	+	0.981546i	$0.561247\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−10.1939	−	0.289831i	−0.999596	−	0.0284203i
$105$	9.70314			0.946929
$106$		0			0
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	9.78831	+	5.65129i	0.941881	+	0.543795i
$109$		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
$113$	−10.6125	+	18.3814i	−0.998339	+	1.72917i	−0.449271	+	0.893396i	$0.648316\pi$
$113$	−10.6125	+	18.3814i	−0.998339	+	1.72917i	−0.549068	+	0.835778i	$0.685017\pi$
$114$	−4.06695	+	2.34805i	−0.380905	+	0.219915i
$115$	−2.39793	+	8.94919i	−0.223608	+	0.834517i
$116$		0			0
$117$	0.918540	+	3.86418i	0.0849190	+	0.357243i
$118$	4.76324			0.438492
$119$		0			0
$120$	−5.18655	−	8.98336i	−0.473465	−	0.820065i
$121$	−9.52628	−	5.50000i	−0.866025	−	0.500000i
$122$	12.0542	−	12.0542i	1.09133	−	1.09133i
$123$		0			0
$124$		0			0
$125$	−5.48655	−	5.48655i	−0.490732	−	0.490732i
$126$	−2.06089	+	3.56957i	−0.183599	+	0.318002i
$127$	8.22111	−	4.74646i	0.729506	−	0.421180i	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	8.22111	−	4.74646i	0.729506	−	0.421180i	0.818241	+	0.574875i	$0.194949\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$		0			0
$130$	3.88395	−	13.0048i	0.340645	−	1.14059i
$131$	6.89883			0.602753			0.301377	−	0.953505i	$-0.402554\pi$
$131$	6.89883			0.602753			0.301377	+	0.953505i	$0.402554\pi$
$132$		0			0
$133$	−3.18821	−	5.52215i	−0.276453	−	0.478831i
$134$		0			0
$135$	−10.6365	+	10.6365i	−0.915448	+	0.915448i
$136$		0			0
$137$	−13.0526	+	3.49743i	−1.11516	+	0.298805i	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−13.0526	+	3.49743i	−1.11516	+	0.298805i	−0.346235	+	0.938148i	$0.612540\pi$
$138$	4.79586	+	4.79586i	0.408251	+	0.408251i
$139$	10.0049	−	17.3290i	0.848604	−	1.46983i	−0.0338497	−	0.999427i	$-0.510777\pi$
$139$	10.0049	−	17.3290i	0.848604	−	1.46983i	0.882454	−	0.470399i	$-0.155890\pi$
$140$	12.1977	−	7.04235i	1.03089	−	0.595187i
$141$		0			0
$142$			23.4422i			1.96723i
$143$		0			0
$144$	4.40637			0.367197
$145$		0			0
$146$		0			0
$147$	8.35263	+	4.82239i	0.688914	+	0.397744i
$148$		0			0
$149$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$149$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$150$	3.92419	−	1.05148i	0.320409	−	0.0858532i
$151$	−13.5035	−	13.5035i	−1.09890	−	1.09890i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−13.5035	−	13.5035i	−1.09890	−	1.09890i	−0.104357	−	0.994540i	$-0.533278\pi$
$152$	−3.40834	+	5.90342i	−0.276453	+	0.478831i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−6.82306	−	7.22240i	−0.546282	−	0.578255i
$157$	−9.78477			−0.780909			−0.390455	−	0.920622i	$-0.627682\pi$
$157$	−9.78477			−0.780909			−0.390455	+	0.920622i	$0.627682\pi$
$158$	21.5035	+	5.76185i	1.71073	+	0.458388i
$159$		0			0
$160$	−13.0399	−	7.52859i	−1.03089	−	0.595187i
$161$	−6.51187	+	6.51187i	−0.513207	+	0.513207i
$162$	1.64042	+	6.12214i	0.128884	+	0.481001i
$163$		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
$166$	19.8994	−	11.4889i	1.54449	−	0.891715i
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$		−	10.3107i		−	0.795489i
$169$	0.738629	−	12.9790i	0.0568176	−	0.998385i
$170$		0			0
$171$	2.56444	+	0.687140i	0.196108	+	0.0525469i
$172$		0			0
$173$	19.3686	+	11.1824i	1.47256	+	0.850186i	0.999524	−	0.0308546i	$-0.00982288\pi$
$173$	19.3686	+	11.1824i	1.47256	+	0.850186i	0.473041	+	0.881040i	$0.343156\pi$
$174$		0			0
$175$	1.42772	+	5.32831i	0.107925	+	0.402782i
$176$		0			0
$177$	3.28146	+	3.28146i	0.246650	+	0.246650i
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	−1.51780	+	5.66452i	−0.113130	+	0.422209i
$181$		−	25.8903i		−	1.92441i	−0.272326	−	0.962205i	$-0.587793\pi$
$181$		−	25.8903i		−	1.92441i	0.272326	−	0.962205i	$-0.412207\pi$
$182$	9.80665	−	9.26443i	0.726917	−	0.686725i
$183$	16.6086			1.22774
$184$	9.50956	+	2.54808i	0.701054	+	0.187847i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−14.4424	+	3.86984i	−1.05053	+	0.281489i
$190$	−6.41500	−	6.41500i	−0.465393	−	0.465393i
$191$	2.38751	−	4.13530i	0.172754	−	0.299219i	−0.766627	−	0.642092i	$-0.778067\pi$
$191$	2.38751	−	4.13530i	0.172754	−	0.299219i	0.939382	+	0.342873i	$0.111400\pi$
$192$	−9.54587	+	5.51131i	−0.688914	+	0.397744i
$193$	−1.52193	+	5.67992i	−0.109551	+	0.408850i	−0.998822	−	0.0485316i	$-0.984546\pi$
$193$	−1.52193	+	5.67992i	−0.109551	+	0.408850i	0.889271	+	0.457381i	$0.151213\pi$
$194$		0			0
$195$	11.6349	−	6.28345i	0.833190	−	0.449967i
$196$	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	$0.166667\pi$
$200$	4.16991	−	4.16991i	0.294857	−	0.294857i
$201$		0			0
$202$	−18.0221	+	4.82901i	−1.26803	+	0.339768i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	3.83436i		−	0.266506i
$208$	−13.8191	−	4.12715i	−0.958180	−	0.286166i
$209$		0			0
$210$	13.2547	+	3.55160i	0.914664	+	0.245083i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	−16.1497	+	16.1497i	−1.10656	+	1.10656i
$214$		0			0
$215$		0			0
$216$	11.3026	+	11.3026i	0.769043	+	0.769043i
$217$		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
$225$	−1.98906	−	1.14838i	−0.132604	−	0.0765590i
$226$	−21.2250	+	21.2250i	−1.41186	+	1.41186i
$227$	7.24262	+	27.0298i	0.480710	+	1.79403i	0.598647	+	0.801013i	$0.295705\pi$
$227$	7.24262	+	27.0298i	0.480710	+	1.79403i	−0.117938	+	0.993021i	$0.537628\pi$
$228$	−6.41500	+	1.71889i	−0.424844	+	0.113837i
$229$	−21.2737	−	21.2737i	−1.40581	−	1.40581i	−0.779893	−	0.625913i	$-0.784726\pi$
$229$	−21.2737	−	21.2737i	−1.40581	−	1.40581i	−0.625913	−	0.779893i	$-0.715274\pi$
$230$	−6.55127	+	11.3471i	−0.431978	+	0.748207i
$231$		0			0
$232$		0			0
$233$		−	20.1628i		−	1.32091i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$		−	20.1628i		−	1.32091i	0.750867	−	0.660454i	$-0.229636\pi$
$234$	−0.159638	+	5.61477i	−0.0104359	+	0.367049i
$235$		0			0
$236$	6.50671	+	1.74347i	0.423551	+	0.113490i
$237$	10.8446	+	18.7835i	0.704435	+	1.22012i
$238$		0			0
$239$	21.8599	−	21.8599i	1.41400	−	1.41400i	0.694737	−	0.719264i	$-0.255521\pi$
$239$	21.8599	−	21.8599i	1.41400	−	1.41400i	0.719264	−	0.694737i	$-0.244479\pi$
$240$	−3.79682	−	14.1699i	−0.245083	−	0.914664i
$241$		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
$243$	5.38941	−	9.33474i	0.345731	−	0.598824i
$244$	20.8785	−	12.0542i	1.33661	−	0.771690i
$245$	−4.82239	+	17.9974i	−0.308092	+	1.14981i
$246$		0			0
$247$	−7.39890	−	4.55692i	−0.470780	−	0.289950i
$248$		0			0
$249$	21.6239	+	5.79410i	1.37036	+	0.367186i
$250$	−5.48655	−	9.50298i	−0.347000	−	0.601021i
$251$	−17.4973	−	10.1020i	−1.10442	−	0.637636i	−0.167039	−	0.985950i	$-0.553421\pi$
$251$	−17.4973	−	10.1020i	−1.10442	−	0.637636i	−0.937378	+	0.348315i	$0.886754\pi$
$252$	−4.12178	+	4.12178i	−0.259648	+	0.259648i
$253$		0			0
$254$	12.9676	−	3.47465i	0.813658	−	0.218019i
$255$		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
$260$	10.0656	−	16.3432i	0.624245	−	1.01356i
$261$		0			0
$262$	9.42397	+	2.52515i	0.582215	+	0.156004i
$263$	−11.6059	−	20.1021i	−0.715653	−	1.23955i	−0.962707	−	0.270546i	$-0.912796\pi$
$263$	−11.6059	−	20.1021i	−0.715653	−	1.23955i	0.247054	−	0.969002i	$-0.420537\pi$
$264$		0			0
$265$		0			0
$266$	−2.33393	−	8.71036i	−0.143103	−	0.534066i
$267$		0			0
$268$		0			0
$269$	−15.7485	+	27.2772i	−0.960202	+	1.66312i	−0.238215	+	0.971212i	$0.576562\pi$
$269$	−15.7485	+	27.2772i	−0.960202	+	1.66312i	−0.721987	+	0.691907i	$0.756771\pi$
$270$	−18.4230	+	10.6365i	−1.12119	+	0.647320i
$271$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$271$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$272$		0			0
$273$	13.1383	+	0.373546i	0.795168	+	0.0226080i
$274$	−19.1103			−1.15449
$275$		0			0
$276$	4.79586	+	8.30667i	0.288677	+	0.500003i
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$	20.0098	−	20.0098i	1.20011	−	1.20011i
$279$		0			0
$280$	19.2401	−	5.15536i	1.14981	−	0.308092i
$281$	−7.51669	−	7.51669i	−0.448408	−	0.448408i	0.446417	−	0.894825i	$-0.352700\pi$
$281$	−7.51669	−	7.51669i	−0.448408	−	0.448408i	−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	−26.5467	+	15.3268i	−1.57804	+	0.911082i	−0.582907	+	0.812539i	$0.698085\pi$
$283$	−26.5467	+	15.3268i	−1.57804	+	0.911082i	−0.995133	+	0.0985428i	$0.968582\pi$
$284$	−8.58045	+	32.0227i	−0.509156	+	1.90020i
$285$		−	8.83876i		−	0.523563i
$286$		0			0
$287$		0			0
$288$	6.01921	+	1.61284i	0.354686	+	0.0950377i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−24.4045	+	6.53918i	−1.42573	+	0.382023i	−0.887512	−	0.460784i	$-0.847568\pi$
$293$	−24.4045	+	6.53918i	−1.42573	+	0.382023i	−0.538216	+	0.842807i	$0.680902\pi$
$294$	9.64479	+	9.64479i	0.562496	+	0.562496i
$295$	−4.48256	+	7.76402i	−0.260985	+	0.452039i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.59139	+	12.0251i	−0.207695	+	0.695432i
$300$	5.74541			0.331711
$301$		0			0
$302$	−13.5035	−	23.3887i	−0.777037	−	1.34587i
$303$	−15.7425	−	9.08891i	−0.904380	−	0.522144i
$304$	−6.81668	+	6.81668i	−0.390964	+	0.390964i
$305$	8.30429	+	30.9920i	0.475502	+	1.77460i
$306$		0			0
$307$	21.2296	+	21.2296i	1.21164	+	1.21164i	0.970489	+	0.241146i	$0.0775234\pi$
$307$	21.2296	+	21.2296i	1.21164	+	1.21164i	0.241146	+	0.970489i	$0.422477\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−6.67689	−	12.3634i	−0.378005	−	0.699939i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−13.3662	−	3.58147i	−0.754301	−	0.202114i
$315$	−3.87890	−	6.71845i	−0.218551	−	0.378542i
$316$	27.2654	+	15.7417i	1.53380	+	0.885537i
$317$		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
$320$	−15.0572	−	15.0572i	−0.841722	−	0.841722i
$321$		0			0
$322$	−11.2789	+	6.51187i	−0.628548	+	0.362892i
$323$		0			0
$324$			8.96343i			0.497969i
$325$	5.16239	+	5.46453i	0.286358	+	0.303118i
$326$		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	$0.416667\pi$
$332$	31.3884	−	8.41049i	1.72266	−	0.461585i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	3.77398	−	14.0847i	0.205888	−	0.768383i
$337$		−	0.708287i		−	0.0385828i	−0.999814	−	0.0192914i	$-0.993859\pi$
$337$		−	0.708287i		−	0.0385828i	0.999814	−	0.0192914i	$-0.00614103\pi$
$338$	5.75963	−	17.4593i	0.313283	−	0.949660i
$339$	−29.2443			−1.58833
$340$		0			0
$341$		0			0
$342$	3.25158	+	1.87730i	0.175825	+	0.101513i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$		0			0
$345$	−12.3304	+	3.30393i	−0.663849	+	0.177878i
$346$	22.3649	+	22.3649i	1.20234	+	1.20234i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$	5.19288	−	19.3801i	0.277969	−	1.03739i	−0.675857	−	0.737032i	$-0.736226\pi$
$349$	5.19288	−	19.3801i	0.277969	−	1.03739i	0.953826	−	0.300360i	$-0.0971069\pi$
$350$			7.80118i			0.416991i
$351$	−14.8117	+	13.9927i	−0.790588	+	0.746875i
$352$		0			0
$353$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$353$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$354$	3.28146	+	5.68366i	0.174408	+	0.302083i
$355$	−38.2105	−	22.0609i	−2.02800	−	1.17087i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.74963	−	2.74963i	−0.145120	−	0.145120i	0.630814	−	0.775934i	$-0.282721\pi$
$359$	−2.74963	−	2.74963i	−0.145120	−	0.145120i	−0.775934	+	0.630814i	$0.782721\pi$
$360$	−4.14672	+	7.18233i	−0.218551	+	0.378542i
$361$	11.4243	−	6.59580i	0.601277	−	0.347147i
$362$	9.47650	−	35.3668i	0.498074	−	1.85884i
$363$		−	15.1561i		−	0.795489i
$364$	16.7871	−	9.06596i	0.879886	−	0.475185i
$365$		0			0
$366$	22.6877	+	6.07916i	1.18591	+	0.317763i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$	12.0576	+	6.96148i	0.628548	+	0.362892i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	2.76697	−	10.3265i	0.142886	−	0.533257i
$376$		0			0
$377$		0			0
$378$	−21.1452			−1.08759
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$	−6.41500	−	11.1111i	−0.329083	−	0.569988i
$381$	11.3273	+	6.53980i	0.580314	+	0.335044i
$382$	4.77503	−	4.77503i	0.244312	−	0.244312i
$383$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$383$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$384$	−15.0572	+	4.03456i	−0.768383	+	0.205888i
$385$		0			0
$386$	−4.15799	+	7.20185i	−0.211636	+	0.366565i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	18.1934	−	4.32469i	0.921259	−	0.218989i
$391$		0			0
$392$	19.1244	+	5.12436i	0.965926	+	0.258819i
$393$	4.75269	+	8.23191i	0.239742	+	0.415245i
$394$		0			0
$395$	−29.6281	+	29.6281i	−1.49075	+	1.49075i
$396$		0			0
$397$	36.4521	−	9.76731i	1.82948	−	0.490207i	0.831604	−	0.555369i	$-0.187423\pi$
$397$	36.4521	−	9.76731i	1.82948	−	0.490207i	0.997875	+	0.0651619i	$0.0207564\pi$
$398$		0			0
$399$	4.39281	−	7.60856i	0.219915	−	0.380905i
$400$	7.22249	−	4.16991i	0.361125	−	0.208495i
$401$	4.10862	−	15.3336i	0.205175	−	0.765723i	−0.784221	−	0.620481i	$-0.786937\pi$
$401$	4.10862	−	15.3336i	0.205175	−	0.765723i	0.989396	−	0.145242i	$-0.0463961\pi$
$402$		0			0
$403$		0			0
$404$	−26.3862			−1.31276
$405$	−11.5228	−	3.08752i	−0.572571	−	0.153420i
$406$		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
$411$	−13.1653	−	13.1653i	−0.649398	−	0.649398i
$412$		0			0
$413$	−7.71734	+	4.45561i	−0.379745	+	0.219246i
$414$	1.40347	−	5.23783i	0.0689769	−	0.257425i
$415$			43.2477i			2.12295i
$416$	−17.3666	−	10.6959i	−0.851465	−	0.524411i
$417$	27.5700			1.35011
$418$		0			0
$419$	1.48404	+	2.57043i	0.0725002	+	0.125574i	0.899996	−	0.435897i	$-0.143569\pi$
$419$	1.48404	+	2.57043i	0.0725002	+	0.125574i	−0.827496	+	0.561471i	$0.810236\pi$
$420$	16.8063	+	9.70314i	0.820065	+	0.473465i
$421$		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
$426$	−27.9720	+	16.1497i	−1.35525	+	0.782454i
$427$	−8.25435	+	30.8057i	−0.399456	+	1.49079i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	39.4101	+	10.5599i	1.89832	+	0.508653i	0.997173	+	0.0751385i	$0.0239399\pi$
$431$	39.4101	+	10.5599i	1.89832	+	0.508653i	0.901146	+	0.433515i	$0.142727\pi$
$432$	11.3026	+	19.5766i	0.543795	+	0.941881i
$433$		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
$437$	5.93178	+	5.93178i	0.283755	+	0.283755i
$438$		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
$441$		−	7.71115i		−	0.367197i
$442$		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
$449$	−35.4281	+	9.49293i	−1.67196	+	0.447999i	−0.965637	−	0.259895i	$-0.916312\pi$
$449$	−35.4281	+	9.49293i	−1.67196	+	0.447999i	−0.706319	+	0.707894i	$0.749646\pi$
$450$	−2.29677	−	2.29677i	−0.108271	−	0.108271i
$451$		0			0
$452$	−36.7627	+	21.2250i	−1.72917	+	0.998339i
$453$	6.81007	−	25.4155i	0.319965	−	1.19412i
$454$			39.5744i			1.85732i
$455$	5.87212	+	24.7032i	0.275289	+	1.15810i
$456$	−9.39221			−0.439831
$457$	−38.0460	−	10.1944i	−1.77972	−	0.476873i	−0.789184	−	0.614157i	$-0.789496\pi$
$457$	−38.0460	−	10.1944i	−1.77972	−	0.476873i	−0.990532	+	0.137283i	$0.956163\pi$
$458$	−21.2737	−	36.8471i	−0.994055	−	1.72175i
$459$		0			0
$460$	−13.1025	+	13.1025i	−0.610909	+	0.610909i
$461$	7.75003	+	28.9235i	0.360955	+	1.34710i	0.872822	+	0.488038i	$0.162287\pi$
$461$	7.75003	+	28.9235i	0.360955	+	1.34710i	−0.511867	+	0.859064i	$0.671046\pi$
$462$		0			0
$463$	−28.2019	−	28.2019i	−1.31065	−	1.31065i	−0.920935	−	0.389716i	$-0.872573\pi$
$463$	−28.2019	−	28.2019i	−1.31065	−	1.31065i	−0.389716	−	0.920935i	$-0.627427\pi$
$464$		0			0
$465$		0			0
$466$	7.38009	−	27.5429i	0.341876	−	1.27590i
$467$			42.7899i			1.98008i	0.140792	+	0.990039i	$0.455035\pi$
$467$			42.7899i			1.98008i	−0.140792	+	0.990039i	$0.544965\pi$
$468$	−2.27322	+	7.61149i	−0.105080	+	0.351841i
$469$		0			0
$470$		0			0
$471$	−6.74086	−	11.6755i	−0.310602	−	0.537979i
$472$	8.25018	+	4.76324i	0.379745	+	0.219246i
$473$		0			0
$474$	7.93883	+	29.6281i	0.364642	+	1.36086i
$475$	4.85365	−	1.30053i	0.222701	−	0.0596725i
$476$		0			0
$477$		0			0
$478$	37.8625	−	21.8599i	1.73179	−	0.999850i
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$		−	20.7462i		−	0.946929i
$481$		0			0
$482$		0			0
$483$	−12.2563	−	3.28406i	−0.557681	−	0.149430i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	10.7788	−	10.7788i	0.488937	−	0.488937i
$487$	11.0039	+	41.0670i	0.498633	+	1.86092i	0.508652	+	0.860972i	$0.330144\pi$
$487$	11.0039	+	41.0670i	0.498633	+	1.86092i	−0.0100195	+	0.999950i	$0.503189\pi$
$488$	32.9326	−	8.82427i	1.49079	−	0.399456i
$489$		0			0
$490$	−13.1750	+	22.8198i	−0.595187	+	1.03089i
$491$		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
$494$	−8.43913	−	8.93305i	−0.379694	−	0.401917i
$495$		0			0
$496$		0			0
$497$	−21.9282	−	37.9807i	−0.983614	−	1.70367i
$498$	27.4180	+	15.8298i	1.22863	+	0.709349i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	−4.01643	−	14.9895i	−0.179620	−	0.670352i
$501$		0			0
$502$	−20.2041	−	20.2041i	−0.901753	−	0.901753i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	−7.13914	+	4.12178i	−0.318002	+	0.183599i
$505$	9.08891	−	33.9203i	0.404451	−	1.50943i
$506$		0			0
$507$	15.9958	−	8.06005i	0.710400	−	0.357959i
$508$	18.9858			0.842361
$509$	43.4962	+	11.6548i	1.92793	+	0.516588i	0.980443	+	0.196805i	$0.0630567\pi$
$509$	43.4962	+	11.6548i	1.92793	+	0.516588i	0.947491	+	0.319783i	$0.103610\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	3.52510	+	13.1559i	0.155637	+	0.580845i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$			30.8150i			1.35263i
$520$	19.7320	−	18.6409i	0.865304	−	0.817460i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	1.70594	+	2.95478i	0.0745957	+	0.129204i	0.900910	−	0.434005i	$-0.142900\pi$
$523$	1.70594	+	2.95478i	0.0745957	+	0.129204i	−0.826315	+	0.563209i	$0.809567\pi$
$524$	11.9491	+	6.89883i	0.522000	+	0.301377i
$525$	−5.37434	+	5.37434i	−0.234555	+	0.234555i
$526$	−8.49614	−	31.7080i	−0.370449	−	1.38254i
$527$		0			0
$528$		0			0
$529$	−5.44222	+	9.42621i	−0.236618	+	0.409835i
$530$		0			0
$531$	0.960296	−	3.58387i	0.0416733	−	0.155527i
$532$		−	12.7528i		−	0.552906i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−31.4970	+	31.4970i	−1.35793	+	1.35793i
$539$		0			0
$540$	−29.0596	+	7.78649i	−1.25053	+	0.335077i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	30.8932	−	17.8362i	1.32575	−	0.765423i
$544$		0			0
$545$		0			0
$546$	17.8106	+	5.31923i	0.762221	+	0.227642i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	−26.1051	−	6.99485i	−1.11516	−	0.298805i
$549$	−6.63940	−	11.4998i	−0.283363	−	0.490798i
$550$		0			0
$551$		0			0
$552$	3.51081	+	13.1025i	0.149430	+	0.557681i
$553$	−40.2294	+	10.7794i	−1.71073	+	0.458388i
$554$		0			0
$555$		0			0
$556$	34.6580	−	20.0098i	1.46983	−	0.848604i
$557$		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
$560$	28.1694			1.19037
$561$		0			0
$562$	−7.51669	−	13.0193i	−0.317072	−	0.549185i
$563$	−40.1801	−	23.1980i	−1.69339	−	0.977679i	−0.951746	−	0.306886i	$-0.900713\pi$
$563$	−40.1801	−	23.1980i	−1.69339	−	0.977679i	−0.741644	−	0.670794i	$-0.765954\pi$
$564$		0			0
$565$	−14.6222	−	54.5707i	−0.615159	−	2.29581i
$566$	−41.8735	+	11.2200i	−1.76007	+	0.471611i
$567$	−8.38452	−	8.38452i	−0.352117	−	0.352117i
$568$	−23.4422	+	40.6031i	−0.983614	+	1.70367i
$569$	39.2039	−	22.6344i	1.64351	−	0.948882i	0.663941	−	0.747785i	$-0.268883\pi$
$569$	39.2039	−	22.6344i	1.64351	−	0.948882i	0.979571	−	0.201097i	$-0.0644506\pi$
$570$	3.23521	−	12.0740i	0.135508	−	0.505723i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	6.57916			0.274848
$574$		0			0
$575$	−3.62859	−	6.28490i	−0.151323	−	0.262099i
$576$	7.63206	+	4.40637i	0.318002	+	0.183599i
$577$		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
$579$	−7.82595	+	2.09696i	−0.325235	+	0.0871466i
$580$		0			0
$581$	−21.4938	+	37.2284i	−0.891715	+	1.54449i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−9.00178	−	5.54412i	−0.372178	−	0.229221i
$586$	−35.7307			−1.47602
$587$	45.8628	+	12.2889i	1.89296	+	0.507218i	0.998152	+	0.0607706i	$0.0193558\pi$
$587$	45.8628	+	12.2889i	1.89296	+	0.507218i	0.894810	+	0.446447i	$0.147311\pi$
$588$	9.64479	+	16.7053i	0.397744	+	0.688914i
$589$		0			0
$590$	−8.96512	+	8.96512i	−0.369088	+	0.369088i
$591$		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
$598$	−9.30743	+	15.1121i	−0.380609	+	0.617981i
$599$	−1.39767			−0.0571073			−0.0285537	−	0.999592i	$-0.509090\pi$
$599$	−1.39767			−0.0571073			−0.0285537	+	0.999592i	$0.509090\pi$
$600$	7.84838	+	2.10297i	0.320409	+	0.0858532i
$601$		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
$604$	−9.88523	−	36.8922i	−0.402224	−	1.50112i
$605$	28.2817	−	7.57805i	1.14981	−	0.308092i
$606$	−18.1778	−	18.1778i	−0.738424	−	0.738424i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−11.8068	+	6.81668i	−0.478831	+	0.276453i
$609$		0			0
$610$			45.3755i			1.83720i
$611$		0			0
$612$		0			0
$613$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$613$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$614$	21.2296	+	36.7707i	0.856755	+	1.48394i
$615$		0			0
$616$		0			0
$617$	9.33281	+	34.8305i	0.375725	+	1.40222i	0.852283	+	0.523081i	$0.175218\pi$
$617$	9.33281	+	34.8305i	0.375725	+	1.40222i	−0.476558	+	0.879143i	$0.658116\pi$
$618$		0			0
$619$	14.5577	+	14.5577i	0.585121	+	0.585121i	0.936306	−	0.351185i	$-0.114221\pi$
$619$	14.5577	+	14.5577i	0.585121	+	0.585121i	−0.351185	+	0.936306i	$0.614221\pi$
$620$		0			0
$621$	17.0353	−	9.83533i	0.683603	−	0.394678i
$622$		0			0
$623$		0			0
$624$	−4.59549	−	19.3326i	−0.183967	−	0.773924i
$625$	31.0777			1.24311
$626$		0			0
$627$		0			0
$628$	−16.9477	−	9.78477i	−0.676287	−	0.390455i
$629$		0			0
$630$	−2.83955	−	10.5973i	−0.113130	−	0.422209i
$631$	10.5031	−	2.81430i	0.418122	−	0.112035i	−0.0436231	−	0.999048i	$-0.513890\pi$
$631$	10.5031	−	2.81430i	0.418122	−	0.112035i	0.461745	+	0.887013i	$0.347223\pi$
$632$	31.4833	+	31.4833i	1.25234	+	1.25234i
$633$		0			0
$634$		0			0
$635$	−6.53980	+	24.4069i	−0.259524	+	0.968557i
$636$		0			0
$637$	−7.22251	+	24.1834i	−0.286166	+	0.958180i
$638$		0			0
$639$	17.6380	+	4.72608i	0.697747	+	0.186961i
$640$	−15.0572	−	26.0798i	−0.595187	−	1.03089i
$641$	−24.0569	−	13.8892i	−0.950189	−	0.548592i	−0.0570491	−	0.998371i	$-0.518169\pi$
$641$	−24.0569	−	13.8892i	−0.950189	−	0.548592i	−0.893140	+	0.449780i	$0.851502\pi$
$642$		0			0
$643$	−12.9259	−	48.2402i	−0.509748	−	1.90241i	−0.422876	−	0.906187i	$-0.638980\pi$
$643$	−12.9259	−	48.2402i	−0.509748	−	1.90241i	−0.0868719	−	0.996219i	$-0.527687\pi$
$644$	−17.7908	+	4.76702i	−0.701054	+	0.187847i
$645$		0			0
$646$		0			0
$647$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$647$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$648$	−3.28084	+	12.2443i	−0.128884	+	0.481001i
$649$		0			0
$650$	5.05180	+	9.35426i	0.198148	+	0.366904i
$651$		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
$655$	−12.9846	+	12.9846i	−0.507350	+	0.507350i
$656$		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
$661$	12.7932	−	47.7450i	0.497599	−	1.85706i	−0.0173592	−	0.999849i	$-0.505526\pi$
$661$	12.7932	−	47.7450i	0.497599	−	1.85706i	0.514958	−	0.857215i	$-0.327807\pi$
$662$		0			0
$663$		0			0
$664$	45.9558			1.78343
$665$	16.3942	+	4.39281i	0.635739	+	0.170346i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	10.3107	−	17.8587i	0.397744	−	0.688914i
$673$	38.8844	−	22.4499i	1.49889	−	0.865382i	0.498886	−	0.866668i	$-0.333743\pi$
$673$	38.8844	−	22.4499i	1.49889	−	0.865382i	0.999999	+	0.00128586i	$0.000409302\pi$
$674$	0.259251	−	0.967538i	0.00998598	−	0.0372682i
$675$		−	11.7827i		−	0.453515i
$676$	14.2583	−	21.7417i	0.548398	−	0.836218i
$677$	49.5015			1.90250			0.951248	−	0.308427i	$-0.0998025\pi$
$677$	49.5015			1.90250			0.951248	+	0.308427i	$0.0998025\pi$
$678$	−39.9485	−	10.7042i	−1.53421	−	0.411091i
$679$		0			0
$680$		0			0
$681$	−27.2634	+	27.2634i	−1.04473	+	1.04473i
$682$		0			0
$683$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$683$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$684$	3.75460	+	3.75460i	0.143561	+	0.143561i
$685$	17.9842	−	31.1495i	0.687140	−	1.19016i
$686$	−22.6826	+	13.0958i	−0.866025	+	0.500000i
$687$	10.7287	−	40.0402i	0.409327	−	1.52763i
$688$		0			0
$689$		0			0
$690$	−18.0530			−0.687267
$691$	−50.7388	−	13.5954i	−1.93020	−	0.517195i	−0.975809	−	0.218625i	$-0.929843\pi$
$691$	−50.7388	−	13.5954i	−1.93020	−	0.517195i	−0.954388	−	0.298570i	$-0.903490\pi$
$692$	22.3649	+	38.7371i	0.850186	+	1.47256i
$693$		0			0
$694$		0			0
$695$	13.7850	+	51.4464i	0.522896	+	1.95147i
$696$		0			0
$697$		0			0
$698$	14.1872	−	24.5730i	0.536994	−	0.930101i
$699$	24.0589	−	13.8904i	0.909991	−	0.525384i
$700$	−2.85543	+	10.6566i	−0.107925	+	0.402782i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−25.3548	+	13.6929i	−0.956955	+	0.516807i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	24.6820	−	24.6820i	0.928264	−	0.928264i
$708$	2.40220	+	8.96512i	0.0902801	+	0.336930i
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$	−44.1217	−	44.1217i	−1.65586	−	1.65586i
$711$	8.67045	−	15.0177i	0.325167	−	0.563206i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	41.1436	+	11.0244i	1.53654	+	0.411713i
$718$	−2.74963	−	4.76250i	−0.102615	−	0.177735i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−8.29344	+	8.29344i	−0.309078	+	0.309078i
$721$		0			0
$722$	18.0201	−	4.82846i	0.670637	−	0.179697i
$723$		0			0
$724$	25.8903	−	44.8433i	0.962205	−	1.66659i
$725$		0			0
$726$	5.54752	−	20.7036i	0.205888	−	0.768383i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	26.2500	−	6.23981i	0.972891	−	0.231263i
$729$	28.2965			1.04802
$730$		0			0
$731$		0			0
$732$	28.7669	+	16.6086i	1.06326	+	0.613871i
$733$	36.9968	−	36.9968i	1.36651	−	1.36651i	0.501140	−	0.865366i	$-0.332914\pi$
$733$	36.9968	−	36.9968i	1.36651	−	1.36651i	0.865366	−	0.501140i	$-0.167086\pi$
$734$		0			0
$735$	−24.7973	+	6.64443i	−0.914664	+	0.245083i
$736$	13.9230	+	13.9230i	0.513207	+	0.513207i
$737$		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
$741$	0.340270	−	11.9679i	0.0125001	−	0.439653i
$742$		0			0
$743$	−31.7715	−	8.51314i	−1.16558	−	0.312317i	−0.376389	−	0.926462i	$-0.622834\pi$
$743$	−31.7715	−	8.51314i	−1.16558	−	0.312317i	−0.789193	+	0.614145i	$0.789501\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.63246	−	17.2886i	−0.169493	−	0.632556i
$748$		0			0
$749$		0			0
$750$	7.55951	−	13.0935i	0.276034	−	0.478105i
$751$	47.2211	−	27.2631i	1.72312	−	0.994845i	0.810860	−	0.585240i	$-0.199000\pi$
$751$	47.2211	−	27.2631i	1.72312	−	0.994845i	0.912263	−	0.409605i	$-0.134333\pi$
$752$		0			0
$753$		−	27.8377i		−	1.01446i
$754$		0			0
$755$	50.8310			1.84993
$756$	−28.8848	−	7.73967i	−1.05053	−	0.281489i
$757$		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
$760$	−4.69611	−	17.5261i	−0.170346	−	0.635739i
$761$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$761$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$762$	13.0796	+	13.0796i	0.473824	+	0.473824i
$763$		0			0
$764$	8.27059	−	4.77503i	0.299219	−	0.172754i
$765$		0			0
$766$		0			0
$767$	−6.36841	+	10.3401i	−0.229950	+	0.373361i
$768$	−22.0452			−0.795489
$769$		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
$772$	−8.31598	+	8.31598i	−0.299299	+	0.299299i
$773$	−9.19540	−	34.3177i	−0.330736	−	1.23432i	−0.908419	−	0.418061i	$-0.862710\pi$
$773$	−9.19540	−	34.3177i	−0.330736	−	1.23432i	0.577683	−	0.816261i	$-0.303957\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	26.4356	+	0.751612i	0.946547	+	0.0269120i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.2487	+	14.0000i	0.866025	+	0.500000i
$785$	18.4164	−	18.4164i	0.657308	−	0.657308i
$786$	3.47921	+	12.9846i	0.124099	+	0.463145i
$787$	−1.13955	+	0.305342i	−0.0406207	+	0.0108843i	−0.279072	−	0.960270i	$-0.590027\pi$
$787$	−1.13955	+	0.305342i	−0.0406207	+	0.0108843i	0.238451	+	0.971154i	$0.423360\pi$
$788$		0			0
$789$	15.9910	−	27.6972i	0.569294	−	0.986046i
$790$	−51.3174	+	29.6281i	−1.82579	+	1.05412i
$791$	14.5342	−	54.2425i	0.516778	−	1.92864i
$792$		0			0
$793$	10.0511	+	42.2838i	0.356926	+	1.50154i
$794$	53.3696			1.89402
$795$		0			0
$796$		0			0
$797$	42.6397	+	24.6181i	1.51038	+	0.872016i	0.999927	+	0.0121083i	$0.00385430\pi$
$797$	42.6397	+	24.6181i	1.51038	+	0.872016i	0.510449	+	0.859908i	$0.329479\pi$
$798$	8.78561	−	8.78561i	0.311007	−	0.311007i
$799$		0			0
$800$	11.3924	−	3.05258i	0.402782	−	0.107925i
$801$		0			0
$802$	11.2250	−	19.4422i	0.396368	−	0.686529i
$803$		0			0
$804$		0			0
$805$		−	24.5126i		−	0.863955i
$806$		0			0
$807$	−43.3974			−1.52766
$808$	−36.0442	−	9.65803i	−1.26803	−	0.339768i
$809$	−5.83746	−	10.1108i	−0.205234	−	0.355476i	0.744973	−	0.667094i	$-0.232462\pi$
$809$	−5.83746	−	10.1108i	−0.205234	−	0.355476i	−0.950207	+	0.311619i	$0.899129\pi$
$810$	−14.6103	−	8.43525i	−0.513353	−	0.296384i
$811$	14.2843	−	14.2843i	0.501591	−	0.501591i	−0.410341	−	0.911932i	$-0.634590\pi$
$811$	14.2843	−	14.2843i	0.501591	−	0.501591i	0.911932	+	0.410341i	$0.134590\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−4.99350	−	9.24630i	−0.174487	−	0.323092i
$820$		0			0
$821$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$821$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$822$	−13.1653	−	22.8030i	−0.459194	−	0.795347i
$823$	−48.5187	−	28.0123i	−1.69126	−	0.976448i	−0.953506	−	0.301376i	$-0.902554\pi$
$823$	−48.5187	−	28.0123i	−1.69126	−	0.976448i	−0.737752	−	0.675072i	$-0.764112\pi$
$824$		0			0
$825$		0			0
$826$	−12.1729	+	3.26173i	−0.423551	+	0.113490i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	3.83436	−	6.64130i	0.133253	−	0.230801i
$829$	40.2532	−	23.2402i	1.39805	−	0.807166i	0.403864	−	0.914819i	$-0.367667\pi$
$829$	40.2532	−	23.2402i	1.39805	−	0.807166i	0.994189	+	0.107653i	$0.0343334\pi$
$830$	−15.8298	+	59.0775i	−0.549459	+	2.05061i
$831$		0			0
$832$	−19.8082	−	20.9675i	−0.686725	−	0.726917i
$833$		0			0
$834$	37.6614	+	10.0913i	1.30411	+	0.349434i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	1.08639	+	4.05448i	0.0375288	+	0.140060i
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$	19.4063	+	19.4063i	0.669580	+	0.669580i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$		0			0
$843$	3.79081	−	14.1475i	0.130563	−	0.487266i
$844$		0			0
$845$	23.0382	+	25.8186i	0.792537	+	0.888187i
$846$		0			0
$847$	28.1116	+	7.53248i	0.965926	+	0.258819i
$848$		0			0
$849$	−36.5768	−	21.1176i	−1.25531	−	0.724755i
$850$		0			0
$851$		0			0
$852$	−44.1217	+	11.8224i	−1.51158	+	0.405028i
$853$	−0.102517	−	0.102517i	−0.00351011	−	0.00351011i	0.705350	−	0.708860i	$-0.250790\pi$
$853$	−0.102517	−	0.102517i	−0.00351011	−	0.00351011i	−0.708860	+	0.705350i	$0.750790\pi$
$854$	−22.5513	+	39.0600i	−0.771690	+	1.33661i
$855$	−6.11996	+	3.53336i	−0.209298	+	0.120838i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−0.440260			−0.0150215			−0.00751074	−	0.999972i	$-0.502391\pi$
$859$	−0.440260			−0.0150215			−0.00751074	+	0.999972i	$0.502391\pi$
$860$		0			0
$861$		0			0
$862$	49.9701	+	28.8502i	1.70199	+	0.982643i
$863$	−29.0285	+	29.0285i	−0.988143	+	0.988143i	−0.999931	−	0.0117879i	$-0.996248\pi$
$863$	−29.0285	+	29.0285i	−0.988143	+	0.988143i	0.0117879	+	0.999931i	$0.496248\pi$
$864$	8.27406	+	30.8792i	0.281489	+	1.05053i
$865$	−57.5015	+	15.4075i	−1.95511	+	0.523870i
$866$		0			0
$867$	−11.7115	+	20.2850i	−0.397744	+	0.688914i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	5.93178	+	10.2741i	0.200645	+	0.347528i
$875$	17.7784	+	10.2644i	0.601021	+	0.347000i
$876$		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
$879$	−24.6154	−	24.6154i	−0.830256	−	0.830256i
$880$		0			0
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	2.82248	−	10.5336i	0.0950377	−	0.354686i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	−12.3524			−0.415221
$886$		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
$889$	−17.7596	+	17.7596i	−0.595639	+	0.595639i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	29.9333i		−	1.00000i
$897$	−16.8230	+	3.99893i	−0.561702	+	0.133520i
$898$	−51.8704			−1.73094
$899$		0			0
$900$	−2.29677	−	3.97812i	−0.0765590	−	0.132604i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−57.9877	+	15.5378i	−1.92864	+	0.516778i
$905$	48.7293	+	48.7293i	1.61982	+	1.61982i
$906$	18.6054	−	32.2256i	0.618125	−	1.07062i
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	−14.4852	+	54.0597i	−0.480710	+	1.79403i
$909$			14.5334i			0.482043i
$910$	−1.02055	+	35.8946i	−0.0338308	+	1.18989i
$911$	−52.1724			−1.72855			−0.864274	−	0.503022i	$-0.832222\pi$
$911$	−52.1724			−1.72855			−0.864274	+	0.503022i	$0.832222\pi$
$912$	−12.8300	−	3.43779i	−0.424844	−	0.113837i
$913$		0			0
$914$	−48.2404	−	27.8516i	−1.59565	−	0.921249i
$915$	−31.2598	+	31.2598i	−1.03342	+	1.03342i
$916$	−15.5734	−	58.1208i	−0.514561	−	1.92037i
$917$	−17.6306	+	4.72411i	−0.582215	+	0.156004i
$918$		0			0
$919$	30.3077	−	52.4946i	0.999760	−	1.73164i	0.480921	−	0.876764i	$-0.340303\pi$
$919$	30.3077	−	52.4946i	0.999760	−	1.73164i	0.518840	−	0.854872i	$-0.326364\pi$
$920$	−22.6942	+	13.1025i	−0.748207	+	0.431978i
$921$	−10.7065	+	39.9572i	−0.352791	+	1.31663i
$922$			42.3470i			1.39462i
$923$	−50.8888	−	31.3420i	−1.67503	−	1.03164i
$924$		0			0
$925$		0			0
$926$	−28.2019	−	48.8470i	−0.926770	−	1.60521i
$927$		0			0
$928$		0			0
$929$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$929$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$930$		0			0
$931$	11.9292	+	11.9292i	0.390964	+	0.390964i
$932$	20.1628	−	34.9230i	0.660454	−	1.14394i
$933$		0			0
$934$	−15.6622	+	58.4520i	−0.512482	+	1.91261i
$935$		0			0
$936$	−5.89127	+	9.56543i	−0.192562	+	0.312656i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.7454	−	18.7454i	0.611083	−	0.611083i	−0.332145	−	0.943228i	$-0.607772\pi$
$941$	18.7454	−	18.7454i	0.611083	−	0.611083i	0.943228	+	0.332145i	$0.107772\pi$
$942$	−4.93465	−	18.4164i	−0.160780	−	0.600038i
$943$		0			0
$944$	9.52649	+	9.52649i	0.310061	+	0.310061i
$945$	19.8992	−	34.4664i	0.647320	−	1.12119i
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$			43.3786i			1.40887i
$949$		0			0
$950$	7.10623			0.230557
$951$		0			0
$952$		0			0
$953$	45.8326	+	26.4615i	1.48466	+	0.857171i	0.999848	−	0.0174443i	$-0.00555298\pi$
$953$	45.8326	+	26.4615i	1.48466	+	0.857171i	0.484817	+	0.874616i	$0.338886\pi$
$954$		0			0
$955$	3.28958	+	12.2769i	0.106448	+	0.397271i
$956$	59.7224	−	16.0026i	1.93156	−	0.517560i
$957$		0			0
$958$		0			0
$959$	30.9622	−	17.8760i	0.999822	−	0.577247i
$960$	7.59363	−	28.3398i	0.245083	−	0.914664i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.82595	−	13.5549i	−0.251926	−	0.436349i
$966$	−15.5404	−	8.97223i	−0.500003	−	0.288677i
$967$	17.7750	−	17.7750i	0.571606	−	0.571606i	−0.360971	−	0.932577i	$-0.617555\pi$
$967$	17.7750	−	17.7750i	0.571606	−	0.571606i	0.932577	+	0.360971i	$0.117555\pi$
$968$	−8.05256	−	30.0526i	−0.258819	−	0.965926i
$969$		0			0
$970$		0			0
$971$	−18.9155	+	32.7626i	−0.607027	+	1.05140i	0.384701	+	0.923041i	$0.374305\pi$
$971$	−18.9155	+	32.7626i	−0.607027	+	1.05140i	−0.991728	+	0.128360i	$0.959029\pi$
$972$	18.6695	−	10.7788i	0.598824	−	0.345731i
$973$	−13.7021	+	51.1370i	−0.439270	+	1.63938i
$974$			60.1262i			1.92657i
$975$	−2.96402	+	9.92453i	−0.0949247	+	0.317839i
$976$	48.2167			1.54338
$977$	−51.3562	−	13.7609i	−1.64303	−	0.440249i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	−51.3562	−	13.7609i	−1.64303	−	0.440249i	−0.957650	+	0.287936i	$0.907031\pi$
$978$		0			0
$979$		0			0
$980$	−26.3501	+	26.3501i	−0.841722	+	0.841722i
$981$		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
$988$	−8.25834	−	15.2917i	−0.262733	−	0.486494i
$989$		0			0
$990$		0			0
$991$	24.4777	+	42.3965i	0.777558	+	1.34677i	0.933345	+	0.358980i	$0.116875\pi$
$991$	24.4777	+	42.3965i	0.777558	+	1.34677i	−0.155787	+	0.987791i	$0.549791\pi$
$992$		0			0
$993$		0			0
$994$	−16.0525	−	59.9089i	−0.509156	−	1.90020i
$995$		0			0
$996$	31.6595	+	31.6595i	1.00317	+	1.00317i
$997$	−31.5072	+	54.5720i	−0.997843	+	1.72831i	−0.442065	+	0.896983i	$0.645754\pi$
$997$	−31.5072	+	54.5720i	−0.997843	+	1.72831i	−0.555777	+	0.831331i	$0.687579\pi$
$998$		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.405.3	yes	16
7.6	odd	2	inner	728.2.ds.b.405.2	yes	16
8.5	even	2	inner	728.2.ds.b.405.2	yes	16
13.7	odd	12	inner	728.2.ds.b.293.3	yes	16
56.13	odd	2	CM	728.2.ds.b.405.3	yes	16
91.20	even	12	inner	728.2.ds.b.293.2	✓	16
104.85	odd	12	inner	728.2.ds.b.293.2	✓	16
728.293	even	12	inner	728.2.ds.b.293.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.b.293.2	✓	16	91.20	even	12	inner
728.2.ds.b.293.2	✓	16	104.85	odd	12	inner
728.2.ds.b.293.3	yes	16	13.7	odd	12	inner
728.2.ds.b.293.3	yes	16	728.293	even	12	inner
728.2.ds.b.405.2	yes	16	7.6	odd	2	inner
728.2.ds.b.405.2	yes	16	8.5	even	2	inner
728.2.ds.b.405.3	yes	16	1.1	even	1	trivial
728.2.ds.b.405.3	yes	16	56.13	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(0.688914 + 1.19323i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.88215 + 1.88215i) q^{5} +(0.504320 + 1.88215i) q^{6} +(-2.55560 + 0.684771i) q^{7} +(2.00000 + 2.00000i) q^{8} +(0.550796 - 0.954007i) q^{9} +(-3.25997 + 1.88215i) q^{10} +2.75565i q^{12} +(-2.62094 + 2.47602i) q^{13} -3.74166 q^{14} +(-3.54248 - 0.949204i) q^{15} +(2.00000 + 3.46410i) q^{16} +(1.10159 - 1.10159i) q^{18} +(0.623770 + 2.32794i) q^{19} +(-5.14212 + 1.37783i) q^{20} +(-2.57768 - 2.57768i) q^{21} +(3.01441 - 1.74037i) q^{23} +(-1.00864 + 3.76429i) q^{24} -2.08495i q^{25} +(-4.48655 + 2.42298i) q^{26} +5.65129 q^{27} +(-5.11120 - 1.36954i) q^{28} +(-4.49168 - 2.59327i) q^{30} +(1.46410 + 5.46410i) q^{32} +(3.52117 - 6.09885i) q^{35} +(1.90801 - 1.10159i) q^{36} +3.40834i q^{38} +(-4.76007 - 1.42162i) q^{39} -7.52859 q^{40} +(-2.57768 - 4.46467i) q^{42} +(0.758902 + 2.83226i) q^{45} +(4.75478 - 1.27404i) q^{46} +(-2.75565 + 4.77293i) q^{48} +(6.06218 - 3.50000i) q^{49} +(0.763146 - 2.84810i) q^{50} +(-7.01562 + 1.66766i) q^{52} +(7.71980 + 2.06851i) q^{54} +(-6.48074 - 3.74166i) q^{56} +(-2.34805 + 2.34805i) q^{57} +(3.25336 - 0.871734i) q^{59} +(-5.18655 - 5.18655i) q^{60} +(6.02709 - 10.4392i) q^{61} +(-0.754338 + 2.81523i) q^{63} +8.00000i q^{64} +(0.272752 - 9.59323i) q^{65} +(4.15334 + 2.39793i) q^{69} +(7.04235 - 7.04235i) q^{70} +(4.29022 + 16.0113i) q^{71} +(3.00961 - 0.806422i) q^{72} +(2.48784 - 1.43635i) q^{75} +(-1.24754 + 4.65588i) q^{76} +(-5.98203 - 3.68428i) q^{78} +15.7417 q^{79} +(-10.2842 - 2.75565i) q^{80} +(2.24086 + 3.88128i) q^{81} +(11.4889 - 11.4889i) q^{83} +(-1.88699 - 7.04235i) q^{84} +4.14672i q^{90} +(5.00256 - 8.12246i) q^{91} +6.96148 q^{92} +(-5.55555 - 3.20750i) q^{95} +(-5.51131 + 5.51131i) q^{96} +(9.56218 - 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 q^{57} - 32 q^{60} - 112 q^{63} + 16 q^{65} - 16 q^{71}+ \cdots + 56 q^{98}+O(q^{100}) \) 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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