LMFDB - Embedded newform 3620.1.dy.a.1699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3620,1,Mod(219,3620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3620, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([45, 45, 68]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3620.219");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3620 = 2^{2} \cdot 5 \cdot 181 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3620.dy (of order $90$, degree $24$, 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:	$1.80661534573$
Analytic rank:	$0$
Dimension:	$24$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			1699.1
Root			$-0.997564 - 0.0697565i$ of defining polynomial
Character	$\chi$	$=$	3620.1699
Dual form			3620.1.dy.a.799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.990268 + 0.139173i) q^{2} +(-0.0467046 + 1.33745i) q^{3} +(0.961262 - 0.275637i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-0.139886 - 1.33093i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-0.913545 + 0.406737i) q^{8} +(-0.789016 - 0.0551734i) q^{9} +O(q^{10})$	\(q+(-0.990268 + 0.139173i) q^{2} +(-0.0467046 + 1.33745i) q^{3} +(0.961262 - 0.275637i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-0.139886 - 1.33093i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-0.913545 + 0.406737i) q^{8} +(-0.789016 - 0.0551734i) q^{9} +(0.997564 + 0.0697565i) q^{10} +(0.323755 + 1.29851i) q^{12} +(-0.943248 - 1.20730i) q^{14} +(0.323755 - 1.29851i) q^{15} +(0.848048 - 0.529919i) q^{16} +(0.789016 - 0.0551734i) q^{18} +(-0.997564 + 0.0697565i) q^{20} +(-1.81034 + 0.962574i) q^{21} +(-0.0305979 + 0.0627349i) q^{23} +(-0.501321 - 1.24081i) q^{24} +(0.913545 + 0.406737i) q^{25} +(-0.0292442 + 0.278240i) q^{27} +(1.10209 + 1.06428i) q^{28} +(-1.61323 + 0.718254i) q^{29} +(-0.139886 + 1.33093i) q^{30} +(-0.766044 + 0.642788i) q^{32} +(-0.473442 - 1.45710i) q^{35} +(-0.773659 + 0.164446i) q^{36} +(0.978148 - 0.207912i) q^{40} +(0.194206 + 0.287922i) q^{41} +(1.65876 - 1.20516i) q^{42} +(-0.704030 - 0.256246i) q^{43} +(0.760303 + 0.218013i) q^{45} +(0.0215691 - 0.0663828i) q^{46} +(0.442013 + 1.77282i) q^{47} +(0.669131 + 1.15897i) q^{48} +(-0.673648 + 1.16679i) q^{49} +(-0.961262 - 0.275637i) q^{50} +(-0.00976393 - 0.279602i) q^{54} +(-1.23949 - 0.900539i) q^{56} +(1.49756 - 0.935782i) q^{58} +(-0.0467046 - 1.33745i) q^{60} +(0.194206 + 1.10140i) q^{61} +(-0.531216 - 1.08915i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-0.204489 - 1.94558i) q^{67} +(-0.0824755 - 0.0438530i) q^{69} +(0.671624 + 1.37703i) q^{70} +(0.743243 - 0.270518i) q^{72} +(-0.586655 + 1.20282i) q^{75} +(-0.939693 + 0.342020i) q^{80} +(-1.15401 - 0.162186i) q^{81} +(-0.232387 - 0.258091i) q^{82} +(-0.606126 + 1.50021i) q^{83} +(-1.47489 + 1.42428i) q^{84} +(0.732841 + 0.155770i) q^{86} +(-0.885281 - 2.19115i) q^{87} +(0.333843 - 1.89332i) q^{89} +(-0.783246 - 0.110078i) q^{90} +(-0.0121205 + 0.0687386i) q^{92} +(-0.684440 - 1.69405i) q^{94} +(-0.823916 - 1.05456i) q^{96} +(0.504706 - 1.24919i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) $ 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8	$ 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{14} - 18 q^{21} - 3 q^{23} + 3 q^{25} + 12 q^{27} - 3 q^{28} - 3 q^{30} - 3 q^{40} + 3 q^{41} - 3 q^{43} + 3 q^{48} - 12 q^{49} + 12 q^{58} + 3 q^{61} + 15 q^{63} + 3 q^{64} + 3 q^{67} - 3 q^{69} + 3 q^{70} - 3 q^{84} + 3 q^{87} + 3 q^{89} - 3 q^{92} - 3 q^{98}+O(q^{100}) $ 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^14 - 18 * q^21 - 3 * q^23 + 3 * q^25 + 12 * q^27 - 3 * q^28 - 3 * q^30 - 3 * q^40 + 3 * q^41 - 3 * q^43 + 3 * q^48 - 12 * q^49 + 12 * q^58 + 3 * q^61 + 15 * q^63 + 3 * q^64 + 3 * q^67 - 3 * q^69 + 3 * q^70 - 3 * q^84 + 3 * q^87 + 3 * q^89 - 3 * q^92 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{43}{45}\right)$

Coefficient data

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

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

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

$2$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$2$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$3$	−0.0467046	+	1.33745i	−0.0467046	+	1.33745i	0.719340	+	0.694658i	$0.244444\pi$
$3$	−0.0467046	+	1.33745i	−0.0467046	+	1.33745i	−0.766044	+	0.642788i	$0.777778\pi$
$4$	0.961262	−	0.275637i	0.961262	−	0.275637i
$5$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$5$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$6$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$7$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$7$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$8$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$9$	−0.789016	−	0.0551734i	−0.789016	−	0.0551734i
$10$	0.997564	+	0.0697565i	0.997564	+	0.0697565i
$11$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$11$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$12$	0.323755	+	1.29851i	0.323755	+	1.29851i
$13$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$13$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$14$	−0.943248	−	1.20730i	−0.943248	−	1.20730i
$15$	0.323755	−	1.29851i	0.323755	−	1.29851i
$16$	0.848048	−	0.529919i	0.848048	−	0.529919i
$17$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$17$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$18$	0.789016	−	0.0551734i	0.789016	−	0.0551734i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$21$	−1.81034	+	0.962574i	−1.81034	+	0.962574i
$22$		0			0
$23$	−0.0305979	+	0.0627349i	−0.0305979	+	0.0627349i	−0.913545	−	0.406737i	$-0.866667\pi$
$23$	−0.0305979	+	0.0627349i	−0.0305979	+	0.0627349i	0.882948	+	0.469472i	$0.155556\pi$
$24$	−0.501321	−	1.24081i	−0.501321	−	1.24081i
$25$	0.913545	+	0.406737i	0.913545	+	0.406737i
$26$		0			0
$27$	−0.0292442	+	0.278240i	−0.0292442	+	0.278240i
$28$	1.10209	+	1.06428i	1.10209	+	1.06428i
$29$	−1.61323	+	0.718254i	−1.61323	+	0.718254i	−0.997564	−	0.0697565i	$-0.977778\pi$
$29$	−1.61323	+	0.718254i	−1.61323	+	0.718254i	−0.615661	+	0.788011i	$0.711111\pi$
$30$	−0.139886	+	1.33093i	−0.139886	+	1.33093i
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$33$		0			0
$34$		0			0
$35$	−0.473442	−	1.45710i	−0.473442	−	1.45710i
$36$	−0.773659	+	0.164446i	−0.773659	+	0.164446i
$37$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$37$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$38$		0			0
$39$		0			0
$40$	0.978148	−	0.207912i	0.978148	−	0.207912i
$41$	0.194206	+	0.287922i	0.194206	+	0.287922i	0.913545	−	0.406737i	$-0.133333\pi$
$41$	0.194206	+	0.287922i	0.194206	+	0.287922i	−0.719340	+	0.694658i	$0.755556\pi$
$42$	1.65876	−	1.20516i	1.65876	−	1.20516i
$43$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.0348995	−	0.999391i	$-0.511111\pi$
$43$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.669131	+	0.743145i	$0.733333\pi$
$44$		0			0
$45$	0.760303	+	0.218013i	0.760303	+	0.218013i
$46$	0.0215691	−	0.0663828i	0.0215691	−	0.0663828i
$47$	0.442013	+	1.77282i	0.442013	+	1.77282i	0.615661	+	0.788011i	$0.288889\pi$
$47$	0.442013	+	1.77282i	0.442013	+	1.77282i	−0.173648	+	0.984808i	$0.555556\pi$
$48$	0.669131	+	1.15897i	0.669131	+	1.15897i
$49$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$50$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$51$		0			0
$52$		0			0
$53$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$53$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$54$	−0.00976393	−	0.279602i	−0.00976393	−	0.279602i
$55$		0			0
$56$	−1.23949	−	0.900539i	−1.23949	−	0.900539i
$57$		0			0
$58$	1.49756	−	0.935782i	1.49756	−	0.935782i
$59$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$59$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$60$	−0.0467046	−	1.33745i	−0.0467046	−	1.33745i
$61$	0.194206	+	1.10140i	0.194206	+	1.10140i	0.913545	+	0.406737i	$0.133333\pi$
$61$	0.194206	+	1.10140i	0.194206	+	1.10140i	−0.719340	+	0.694658i	$0.755556\pi$
$62$		0			0
$63$	−0.531216	−	1.08915i	−0.531216	−	1.08915i
$64$	0.669131	−	0.743145i	0.669131	−	0.743145i
$65$		0			0
$66$		0			0
$67$	−0.204489	−	1.94558i	−0.204489	−	1.94558i	−0.309017	−	0.951057i	$-0.600000\pi$
$67$	−0.204489	−	1.94558i	−0.204489	−	1.94558i	0.104528	−	0.994522i	$-0.466667\pi$
$68$		0			0
$69$	−0.0824755	−	0.0438530i	−0.0824755	−	0.0438530i
$70$	0.671624	+	1.37703i	0.671624	+	1.37703i
$71$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$71$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$72$	0.743243	−	0.270518i	0.743243	−	0.270518i
$73$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$73$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$74$		0			0
$75$	−0.586655	+	1.20282i	−0.586655	+	1.20282i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$79$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$80$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$81$	−1.15401	−	0.162186i	−1.15401	−	0.162186i
$82$	−0.232387	−	0.258091i	−0.232387	−	0.258091i
$83$	−0.606126	+	1.50021i	−0.606126	+	1.50021i	0.241922	+	0.970296i	$0.422222\pi$
$83$	−0.606126	+	1.50021i	−0.606126	+	1.50021i	−0.848048	+	0.529919i	$0.822222\pi$
$84$	−1.47489	+	1.42428i	−1.47489	+	1.42428i
$85$		0			0
$86$	0.732841	+	0.155770i	0.732841	+	0.155770i
$87$	−0.885281	−	2.19115i	−0.885281	−	2.19115i
$88$		0			0
$89$	0.333843	−	1.89332i	0.333843	−	1.89332i	−0.104528	−	0.994522i	$-0.533333\pi$
$89$	0.333843	−	1.89332i	0.333843	−	1.89332i	0.438371	−	0.898794i	$-0.355556\pi$
$90$	−0.783246	−	0.110078i	−0.783246	−	0.110078i
$91$		0			0
$92$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i
$93$		0			0
$94$	−0.684440	−	1.69405i	−0.684440	−	1.69405i
$95$		0			0
$96$	−0.823916	−	1.05456i	−0.823916	−	1.05456i
$97$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$97$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$98$	0.504706	−	1.24919i	0.504706	−	1.24919i
$99$		0			0
$100$	0.990268	+	0.139173i	0.990268	+	0.139173i
$101$	0.454664	−	0.165484i	0.454664	−	0.165484i	−0.104528	−	0.994522i	$-0.533333\pi$
$101$	0.454664	−	0.165484i	0.454664	−	0.165484i	0.559193	+	0.829038i	$0.311111\pi$
$102$		0			0
$103$	−1.13491	−	0.709170i	−1.13491	−	0.709170i	−0.173648	−	0.984808i	$-0.555556\pi$
$103$	−1.13491	−	0.709170i	−1.13491	−	0.709170i	−0.961262	+	0.275637i	$0.911111\pi$
$104$		0			0
$105$	1.97091	−	0.565149i	1.97091	−	0.565149i
$106$		0			0
$107$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$107$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$108$	0.0485820	+	0.275522i	0.0485820	+	0.275522i
$109$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.719340	−	0.694658i	$-0.755556\pi$
$109$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.104528	+	0.994522i	$0.533333\pi$
$110$		0			0
$111$		0			0
$112$	1.35275	+	0.719272i	1.35275	+	0.719272i
$113$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$113$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$114$		0			0
$115$	0.0429726	−	0.0550024i	0.0429726	−	0.0550024i
$116$	−1.35275	+	1.13510i	−1.35275	+	1.13510i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.232387	+	1.31793i	0.232387	+	1.31793i
$121$	0.0348995	+	0.999391i	0.0348995	+	0.999391i
$122$	−0.345600	−	1.06365i	−0.345600	−	1.06365i
$123$	−0.394150	+	0.246292i	−0.394150	+	0.246292i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$126$	0.677627	+	1.00462i	0.677627	+	1.00462i
$127$	0.0655896	+	1.87824i	0.0655896	+	1.87824i	0.374607	+	0.927184i	$0.377778\pi$
$127$	0.0655896	+	1.87824i	0.0655896	+	1.87824i	−0.309017	+	0.951057i	$0.600000\pi$
$128$	−0.559193	+	0.829038i	−0.559193	+	0.829038i
$129$	0.375597	−	0.929634i	0.375597	−	0.929634i
$130$		0			0
$131$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$131$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$132$		0			0
$133$		0			0
$134$	0.473271	+	1.89818i	0.473271	+	1.89818i
$135$	0.0864545	−	0.266080i	0.0864545	−	0.266080i
$136$		0			0
$137$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$137$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$138$	0.0877760	+	0.0319479i	0.0877760	+	0.0319479i
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$	−0.856733	−	1.27016i	−0.856733	−	1.27016i
$141$	−2.39169	+	0.508370i	−2.39169	+	0.508370i
$142$		0			0
$143$		0			0
$144$	−0.698361	+	0.371325i	−0.698361	+	0.371325i
$145$	1.72731	−	0.367150i	1.72731	−	0.367150i
$146$		0			0
$147$	−1.52906	−	0.955463i	−1.52906	−	0.955463i
$148$		0			0
$149$	1.29929	−	1.09023i	1.29929	−	1.09023i	0.309017	−	0.951057i	$-0.400000\pi$
$149$	1.29929	−	1.09023i	1.29929	−	1.09023i	0.990268	−	0.139173i	$-0.0444444\pi$
$150$	0.413545	−	1.27276i	0.413545	−	1.27276i
$151$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$151$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$157$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$158$		0			0
$159$		0			0
$160$	0.882948	−	0.469472i	0.882948	−	0.469472i
$161$	−0.106678	+	0.00745964i	−0.106678	+	0.00745964i
$162$	1.16535			1.16535
$163$	−1.99027	+	0.139173i	−1.99027	+	0.139173i	−0.990268	+	0.139173i	$0.955556\pi$
$163$	−1.99027	+	0.139173i	−1.99027	+	0.139173i	−1.00000			$1.00000\pi$
$164$	0.266044	+	0.223238i	0.266044	+	0.223238i
$165$		0			0
$166$	0.391438	−	1.56997i	0.391438	−	1.56997i
$167$	0.539776	+	0.690882i	0.539776	+	0.690882i	0.978148	−	0.207912i	$-0.0666667\pi$
$167$	0.539776	+	0.690882i	0.539776	+	0.690882i	−0.438371	+	0.898794i	$0.644444\pi$
$168$	1.26231	−	1.61569i	1.26231	−	1.61569i
$169$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$170$		0			0
$171$		0			0
$172$	−0.747388	−	0.0522625i	−0.747388	−	0.0522625i
$173$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$173$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$174$	1.18161	+	2.04662i	1.18161	+	2.04662i
$175$	0.160147	+	1.52370i	0.160147	+	1.52370i
$176$		0			0
$177$		0			0
$178$	−0.0670951	+	1.92135i	−0.0670951	+	1.92135i
$179$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$179$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$180$	0.790943			0.790943
$181$	0.961262	−	0.275637i	0.961262	−	0.275637i
$181$	0.961262	−	0.275637i	0.961262	−	0.275637i
$182$		0			0
$183$	−1.48213	+	0.208299i	−1.48213	+	0.208299i
$184$	0.00243595	−	0.0697565i	0.00243595	−	0.0697565i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.913545	+	1.58231i	0.913545	+	1.58231i
$189$	−0.391579	+	0.174342i	−0.391579	+	0.174342i
$190$		0			0
$191$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$191$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$192$	0.962665	+	0.929634i	0.962665	+	0.929634i
$193$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$193$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$194$		0			0
$195$		0			0
$196$	−0.325940	+	1.30728i	−0.325940	+	1.30728i
$197$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$197$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$198$		0			0
$199$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$199$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$200$	−1.00000			−1.00000
$201$	2.61166	−	0.182625i	2.61166	−	0.182625i
$202$	−0.427209	+	0.227151i	−0.427209	+	0.227151i
$203$	−2.18880	−	1.59026i	−2.18880	−	1.59026i
$204$		0			0
$205$	−0.130100	−	0.322008i	−0.130100	−	0.322008i
$206$	1.22256	+	0.544320i	1.22256	+	0.544320i
$207$	0.0276035	−	0.0478107i	0.0276035	−	0.0478107i
$208$		0			0
$209$		0			0
$210$	−1.87307	+	0.833946i	−1.87307	+	0.833946i
$211$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$211$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$212$		0			0
$213$		0			0
$214$	−0.444576	+	0.429322i	−0.444576	+	0.429322i
$215$	0.635369	+	0.397023i	0.635369	+	0.397023i
$216$	−0.0864545	−	0.266080i	−0.0864545	−	0.266080i
$217$		0			0
$218$	0.774117	−	0.411606i	0.774117	−	0.411606i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.996161	+	0.723753i	−0.996161	+	0.723753i	−0.961262	−	0.275637i	$-0.911111\pi$
$223$	−0.996161	+	0.723753i	−0.996161	+	0.723753i	−0.0348995	+	0.999391i	$0.511111\pi$
$224$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$225$	−0.698361	−	0.371325i	−0.698361	−	0.371325i
$226$		0			0
$227$	0.616528	−	1.89748i	0.616528	−	1.89748i	0.241922	−	0.970296i	$-0.422222\pi$
$227$	0.616528	−	1.89748i	0.616528	−	1.89748i	0.374607	−	0.927184i	$-0.377778\pi$
$228$		0			0
$229$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$229$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$230$	−0.0348995	+	0.0604477i	−0.0348995	+	0.0604477i
$231$		0			0
$232$	1.18161	−	1.31232i	1.18161	−	1.31232i
$233$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$233$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$234$		0			0
$235$	−0.0637646	−	1.82598i	−0.0637646	−	1.82598i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$239$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$240$	−0.413545	−	1.27276i	−0.413545	−	1.27276i
$241$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i	−0.882948	−	0.469472i	$-0.844444\pi$
$241$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i	0.848048	−	0.529919i	$-0.177778\pi$
$242$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$243$	0.222230	−	1.26033i	0.222230	−	1.26033i
$244$	0.490268	+	1.00520i	0.490268	+	1.00520i
$245$	0.901517	−	1.00124i	0.901517	−	1.00124i
$246$	0.356037	−	0.298750i	0.356037	−	0.298750i
$247$		0			0
$248$		0			0
$249$	−1.97815	−	0.880728i	−1.97815	−	0.880728i
$250$	0.882948	+	0.469472i	0.882948	+	0.469472i
$251$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$251$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$252$	−0.810849	−	0.900539i	−0.810849	−	0.900539i
$253$		0			0
$254$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$255$		0			0
$256$	0.438371	−	0.898794i	0.438371	−	0.898794i
$257$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$257$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$258$	−0.242561	+	0.972860i	−0.242561	+	0.972860i
$259$		0			0
$260$		0			0
$261$	1.31249	−	0.477707i	1.31249	−	0.477707i
$262$		0			0
$263$	−1.22256	−	1.35779i	−1.22256	−	1.35779i	−0.913545	−	0.406737i	$-0.866667\pi$
$263$	−1.22256	−	1.35779i	−1.22256	−	1.35779i	−0.309017	−	0.951057i	$-0.600000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.51662	+	0.534923i	2.51662	+	0.534923i
$268$	−0.732841	−	1.81385i	−0.732841	−	1.81385i
$269$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$269$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$270$	−0.0485820	+	0.275522i	−0.0485820	+	0.275522i
$271$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$271$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.0913681	−	0.0194209i	−0.0913681	−	0.0194209i
$277$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$277$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$278$		0			0
$279$		0			0
$280$	1.02517	+	1.13856i	1.02517	+	1.13856i
$281$	−1.42468	−	0.200226i	−1.42468	−	0.200226i	−0.615661	−	0.788011i	$-0.711111\pi$
$281$	−1.42468	−	0.200226i	−1.42468	−	0.200226i	−0.809017	+	0.587785i	$0.800000\pi$
$282$	2.29767	−	0.836282i	2.29767	−	0.836282i
$283$	−0.345600	+	0.512373i	−0.345600	+	0.512373i	−0.961262	−	0.275637i	$-0.911111\pi$
$283$	−0.345600	+	0.512373i	−0.345600	+	0.512373i	0.615661	+	0.788011i	$0.288889\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.233252	+	0.478238i	−0.233252	+	0.478238i
$288$	0.639886	−	0.464905i	0.639886	−	0.464905i
$289$	0.173648	+	0.984808i	0.173648	+	0.984808i
$290$	−1.65940	+	0.603972i	−1.65940	+	0.603972i
$291$		0			0
$292$		0			0
$293$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$293$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$294$	1.64715	+	0.733360i	1.64715	+	0.733360i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.13491	+	1.26045i	−1.13491	+	1.26045i
$299$		0			0
$300$	−0.232387	+	1.31793i	−0.232387	+	1.31793i
$301$	−0.199324	−	1.13042i	−0.199324	−	1.13042i
$302$		0			0
$303$	0.200091	+	0.615818i	0.200091	+	0.615818i
$304$		0			0
$305$	0.0390311	−	1.11770i	0.0390311	−	1.11770i
$306$		0			0
$307$	0.116903	+	0.173316i	0.116903	+	0.173316i	0.882948	−	0.469472i	$-0.155556\pi$
$307$	0.116903	+	0.173316i	0.116903	+	0.173316i	−0.766044	+	0.642788i	$0.777778\pi$
$308$		0			0
$309$	1.00148	−	1.48476i	1.00148	−	1.48476i
$310$		0			0
$311$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$311$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	0.293160	+	1.17580i	0.293160	+	1.17580i
$316$		0			0
$317$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$317$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$318$		0			0
$319$		0			0
$320$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$321$	0.462503	+	0.685689i	0.462503	+	0.685689i
$322$	0.104601	−	0.0222337i	0.104601	−	0.0222337i
$323$		0			0
$324$	−1.15401	+	0.162186i	−1.15401	+	0.162186i
$325$		0			0
$326$	1.95153	−	0.414810i	1.95153	−	0.414810i
$327$	−0.362573	−	1.11588i	−0.362573	−	1.11588i
$328$	−0.294524	−	0.184039i	−0.294524	−	0.184039i
$329$	−2.01362	+	1.94453i	−2.01362	+	1.94453i
$330$		0			0
$331$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$331$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$332$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$333$		0			0
$334$	−0.630676	−	0.609036i	−0.630676	−	0.609036i
$335$	−0.204489	+	1.94558i	−0.204489	+	1.94558i
$336$	−1.02517	+	1.77564i	−1.02517	+	1.77564i
$337$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$337$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$338$	0.374607	+	0.927184i	0.374607	+	0.927184i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.532089			−0.532089
$344$	0.747388	−	0.0522625i	0.747388	−	0.0522625i
$345$	0.0715557	+	0.0600423i	0.0715557	+	0.0600423i
$346$		0			0
$347$	−0.348048	+	1.39594i	−0.348048	+	1.39594i	0.500000	+	0.866025i	$0.333333\pi$
$347$	−0.348048	+	1.39594i	−0.348048	+	1.39594i	−0.848048	+	0.529919i	$0.822222\pi$
$348$	−1.45495	−	1.86225i	−1.45495	−	1.86225i
$349$	−1.12487	+	1.43977i	−1.12487	+	1.43977i	−0.241922	+	0.970296i	$0.577778\pi$
$349$	−1.12487	+	1.43977i	−1.12487	+	1.43977i	−0.882948	+	0.469472i	$0.844444\pi$
$350$	−0.370646	−	1.48658i	−0.370646	−	1.48658i
$351$		0			0
$352$		0			0
$353$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$353$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$354$		0			0
$355$		0			0
$356$	−0.200958	−	1.91199i	−0.200958	−	1.91199i
$357$		0			0
$358$		0			0
$359$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$359$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$360$	−0.783246	+	0.110078i	−0.783246	+	0.110078i
$361$	1.00000			1.00000
$362$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$363$	−1.33826			−1.33826
$364$		0			0
$365$		0			0
$366$	1.43871	−	0.412544i	1.43871	−	0.412544i
$367$	1.95630	+	0.415823i	1.95630	+	0.415823i	0.978148	+	0.207912i	$0.0666667\pi$
$367$	1.95630	+	0.415823i	1.95630	+	0.415823i	0.978148	+	0.207912i	$0.0666667\pi$
$368$	0.00729598	+	0.0694166i	0.00729598	+	0.0694166i
$369$	−0.137346	−	0.237890i	−0.137346	−	0.237890i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$373$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$374$		0			0
$375$	0.823916	−	1.05456i	0.823916	−	1.05456i
$376$	−1.12487	−	1.43977i	−1.12487	−	1.43977i
$377$		0			0
$378$	0.363505	−	0.227143i	0.363505	−	0.227143i
$379$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$379$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$380$		0			0
$381$	−2.51511			−2.51511
$382$		0			0
$383$	1.69749	−	0.902570i	1.69749	−	0.902570i	0.719340	−	0.694658i	$-0.244444\pi$
$383$	1.69749	−	0.902570i	1.69749	−	0.902570i	0.978148	−	0.207912i	$-0.0666667\pi$
$384$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$385$		0			0
$386$		0			0
$387$	0.541353	+	0.241026i	0.541353	+	0.241026i
$388$		0			0
$389$	−0.200958	+	1.91199i	−0.200958	+	1.91199i	0.173648	+	0.984808i	$0.444444\pi$
$389$	−0.200958	+	1.91199i	−0.200958	+	1.91199i	−0.374607	+	0.927184i	$0.622222\pi$
$390$		0			0
$391$		0			0
$392$	0.140831	−	1.33992i	0.140831	−	1.33992i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$397$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$398$		0			0
$399$		0			0
$400$	0.990268	−	0.139173i	0.990268	−	0.139173i
$401$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.848048	+	0.529919i	$0.177778\pi$
$401$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.669131	+	0.743145i	$0.266667\pi$
$402$	−2.56082	+	0.544320i	−2.56082	+	0.544320i
$403$		0			0
$404$	0.391438	−	0.284396i	0.391438	−	0.284396i
$405$	1.09507	+	0.398574i	1.09507	+	0.398574i
$406$	2.38882	+	1.27016i	2.38882	+	1.27016i
$407$		0			0
$408$		0			0
$409$	0.241922	+	0.970296i	0.241922	+	0.970296i	0.961262	+	0.275637i	$0.0888889\pi$
$409$	0.241922	+	0.970296i	0.241922	+	0.970296i	−0.719340	+	0.694658i	$0.755556\pi$
$410$	0.173648	+	0.300767i	0.173648	+	0.300767i
$411$		0			0
$412$	−1.28642	−	0.368875i	−1.28642	−	0.368875i
$413$		0			0
$414$	−0.0206809	+	0.0511871i	−0.0206809	+	0.0511871i
$415$	0.904793	−	1.34141i	0.904793	−	1.34141i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$419$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$420$	1.73878	−	1.08651i	1.73878	−	1.08651i
$421$	0.524123	+	1.61308i	0.524123	+	1.61308i	0.766044	+	0.642788i	$0.222222\pi$
$421$	0.524123	+	1.61308i	0.524123	+	1.61308i	−0.241922	+	0.970296i	$0.577778\pi$
$422$		0			0
$423$	−0.250943	−	1.42317i	−0.250943	−	1.42317i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.31259	+	1.10140i	−1.31259	+	1.10140i
$428$	0.380500	−	0.487017i	0.380500	−	0.487017i
$429$		0			0
$430$	−0.684440	−	0.304732i	−0.684440	−	0.304732i
$431$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$431$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$432$	0.122644	+	0.251458i	0.122644	+	0.251458i
$433$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$433$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$434$		0			0
$435$	0.410370	+	2.32733i	0.410370	+	2.32733i
$436$	−0.709299	+	0.515336i	−0.709299	+	0.515336i
$437$		0			0
$438$		0			0
$439$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$439$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$440$		0			0
$441$	0.595895	−	0.883451i	0.595895	−	0.883451i
$442$		0			0
$443$	1.86110	+	0.261560i	1.86110	+	0.261560i	0.978148	−	0.207912i	$-0.0666667\pi$
$443$	1.86110	+	0.261560i	1.86110	+	0.261560i	0.882948	+	0.469472i	$0.155556\pi$
$444$		0			0
$445$	−0.720190	+	1.78253i	−0.720190	+	1.78253i
$446$	0.885740	−	0.855349i	0.885740	−	0.855349i
$447$	1.39744	+	1.78864i	1.39744	+	1.78864i
$448$	1.49861	+	0.318539i	1.49861	+	0.318539i
$449$	−0.741922	−	1.83632i	−0.741922	−	1.83632i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−0.741922	−	1.83632i	−0.741922	−	1.83632i	−0.241922	−	0.970296i	$-0.577778\pi$
$450$	0.743243	+	0.270518i	0.743243	+	0.270518i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.346450	+	1.96482i	−0.346450	+	1.96482i
$455$		0			0
$456$		0			0
$457$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$457$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$458$	0.380500	+	0.487017i	0.380500	+	0.487017i
$459$		0			0
$460$	0.0261472	−	0.0647165i	0.0261472	−	0.0647165i
$461$	1.13491	+	1.26045i	1.13491	+	1.26045i	0.961262	+	0.275637i	$0.0888889\pi$
$461$	1.13491	+	1.26045i	1.13491	+	1.26045i	0.173648	+	0.984808i	$0.444444\pi$
$462$		0			0
$463$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.990268	−	0.139173i	$-0.955556\pi$
$463$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.669131	+	0.743145i	$0.733333\pi$
$464$	−0.987476	+	1.46399i	−0.987476	+	1.46399i
$465$		0			0
$466$		0			0
$467$	−0.333843	+	0.0957278i	−0.333843	+	0.0957278i	−0.438371	−	0.898794i	$-0.644444\pi$
$467$	−0.333843	+	0.0957278i	−0.333843	+	0.0957278i	0.104528	+	0.994522i	$0.466667\pi$
$468$		0			0
$469$	2.42480	−	1.76172i	2.42480	−	1.76172i
$470$	0.317271	+	1.79933i	0.317271	+	1.79933i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$479$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$480$	0.586655	+	1.20282i	0.586655	+	1.20282i
$481$		0			0
$482$	0.173648	+	0.984808i	0.173648	+	0.984808i
$483$	−0.00499451	−	0.143024i	−0.00499451	−	0.143024i
$484$	0.309017	+	0.951057i	0.309017	+	0.951057i
$485$		0			0
$486$	−0.0446634	+	1.27899i	−0.0446634	+	1.27899i
$487$	−1.16392	−	0.845635i	−1.16392	−	0.845635i	−0.173648	−	0.984808i	$-0.555556\pi$
$487$	−1.16392	−	0.845635i	−1.16392	−	0.845635i	−0.990268	+	0.139173i	$0.955556\pi$
$488$	−0.625393	−	0.927184i	−0.625393	−	0.927184i
$489$	−0.0931817	−	2.66838i	−0.0931817	−	2.66838i
$490$	−0.753399	+	1.11696i	−0.753399	+	1.11696i
$491$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$491$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$492$	−0.310994	+	0.345394i	−0.310994	+	0.345394i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.08147	+	0.596852i	2.08147	+	0.596852i
$499$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$499$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$500$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$501$	−0.949228	+	0.689654i	−0.949228	+	0.689654i
$502$		0			0
$503$	1.88051	−	0.399715i	1.88051	−	0.399715i	0.882948	−	0.469472i	$-0.155556\pi$
$503$	1.88051	−	0.399715i	1.88051	−	0.399715i	0.997564	+	0.0697565i	$0.0222222\pi$
$504$	0.928289	+	0.778927i	0.928289	+	0.778927i
$505$	−0.479135	+	0.0673380i	−0.479135	+	0.0673380i
$506$		0			0
$507$	1.30902	−	0.278240i	1.30902	−	0.278240i
$508$	0.580762	+	1.78740i	0.580762	+	1.78740i
$509$	−0.635369	−	0.397023i	−0.635369	−	0.397023i	0.173648	−	0.984808i	$-0.444444\pi$
$509$	−0.635369	−	0.397023i	−0.635369	−	0.397023i	−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$513$		0			0
$514$		0			0
$515$	0.962665	+	0.929634i	0.962665	+	0.929634i
$516$	0.104805	−	0.997150i	0.104805	−	0.997150i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$521$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$522$	−1.23323	+	0.655722i	−1.23323	+	0.655722i
$523$	0.346450	−	0.0242262i	0.346450	−	0.0242262i	0.104528	−	0.994522i	$-0.466667\pi$
$523$	0.346450	−	0.0242262i	0.346450	−	0.0242262i	0.241922	+	0.970296i	$0.422222\pi$
$524$		0			0
$525$	−2.04534	+	0.143024i	−2.04534	+	0.143024i
$526$	1.39963	+	1.17443i	1.39963	+	1.17443i
$527$		0			0
$528$		0			0
$529$	0.612662	+	0.784172i	0.612662	+	0.784172i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−2.56657	−	0.179472i	−2.56657	−	0.179472i
$535$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$536$	0.978148	+	1.69420i	0.978148	+	1.69420i
$537$		0			0
$538$	−1.83832	−	0.390746i	−1.83832	−	0.390746i
$539$		0			0
$540$	0.00976393	−	0.279602i	0.00976393	−	0.279602i
$541$	1.98054	−	0.278346i	1.98054	−	0.278346i	0.990268	−	0.139173i	$-0.0444444\pi$
$541$	1.98054	−	0.278346i	1.98054	−	0.278346i	0.990268	−	0.139173i	$-0.0444444\pi$
$542$		0			0
$543$	0.323755	+	1.29851i	0.323755	+	1.29851i
$544$		0			0
$545$	0.868210	−	0.122019i	0.868210	−	0.122019i
$546$		0			0
$547$	1.69749	−	0.486747i	1.69749	−	0.486747i	0.719340	−	0.694658i	$-0.244444\pi$
$547$	1.69749	−	0.486747i	1.69749	−	0.486747i	0.978148	+	0.207912i	$0.0666667\pi$
$548$		0			0
$549$	−0.0924637	−	0.879734i	−0.0924637	−	0.879734i
$550$		0			0
$551$		0			0
$552$	0.0931817	+	0.00651590i	0.0931817	+	0.00651590i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$557$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$558$		0			0
$559$		0			0
$560$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$561$		0			0
$562$	1.43868			1.43868
$563$	1.69196	−	0.118314i	1.69196	−	0.118314i	0.809017	−	0.587785i	$-0.200000\pi$
$563$	1.69196	−	0.118314i	1.69196	−	0.118314i	0.882948	+	0.469472i	$0.155556\pi$
$564$	−2.15892	+	1.14792i	−2.15892	+	1.14792i
$565$		0			0
$566$	0.270928	−	0.555485i	0.270928	−	0.555485i
$567$	−0.668831	−	1.65542i	−0.668831	−	1.65542i
$568$		0			0
$569$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	0.0348995	+	0.999391i	$0.488889\pi$
$569$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	−0.882948	+	0.469472i	$0.844444\pi$
$570$		0			0
$571$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$571$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$572$		0			0
$573$		0			0
$574$	0.164425	−	0.506047i	0.164425	−	0.506047i
$575$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i
$576$	−0.568957	+	0.549435i	−0.568957	+	0.549435i
$577$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$577$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$578$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$579$		0			0
$580$	1.55919	−	0.829038i	1.55919	−	0.829038i
$581$	−2.45485	+	0.345006i	−2.45485	+	0.345006i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.76159	−	0.936656i	−1.76159	−	0.936656i	−0.913545	−	0.406737i	$-0.866667\pi$
$587$	−1.76159	−	0.936656i	−1.76159	−	0.936656i	−0.848048	−	0.529919i	$-0.822222\pi$
$588$	−1.73319	−	0.496984i	−1.73319	−	0.496984i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$593$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$594$		0			0
$595$		0			0
$596$	0.948445	−	1.40613i	0.948445	−	1.40613i
$597$		0			0
$598$		0			0
$599$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$599$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$600$	0.0467046	−	1.33745i	0.0467046	−	1.33745i
$601$	−0.177290	+	0.110783i	−0.177290	+	0.110783i	−0.615661	−	0.788011i	$-0.711111\pi$
$601$	−0.177290	+	0.110783i	−0.177290	+	0.110783i	0.438371	+	0.898794i	$0.355556\pi$
$602$	0.354709	+	1.09168i	0.354709	+	1.09168i
$603$	0.0540006	+	1.54638i	0.0540006	+	1.54638i
$604$		0			0
$605$	0.173648	−	0.984808i	0.173648	−	0.984808i
$606$	−0.283849	−	0.581978i	−0.283849	−	0.581978i
$607$	−1.02517	+	1.13856i	−1.02517	+	1.13856i	−0.0348995	+	0.999391i	$0.511111\pi$
$607$	−1.02517	+	1.13856i	−1.02517	+	1.13856i	−0.990268	+	0.139173i	$0.955556\pi$
$608$		0			0
$609$	2.22911	−	2.85313i	2.22911	−	2.85313i
$610$	0.116903	+	1.11226i	0.116903	+	1.11226i
$611$		0			0
$612$		0			0
$613$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$613$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$614$	−0.139886	−	0.155360i	−0.139886	−	0.155360i
$615$	0.436744	−	0.158962i	0.436744	−	0.158962i
$616$		0			0
$617$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$617$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$618$	−0.785098	+	1.60969i	−0.785098	+	1.60969i
$619$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$619$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$620$		0			0
$621$	−0.0165606	−	0.0103482i	−0.0165606	−	0.0103482i
$622$		0			0
$623$	2.76784	−	1.00741i	2.76784	−	1.00741i
$624$		0			0
$625$	0.669131	+	0.743145i	0.669131	+	0.743145i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.453946	−	1.12356i	−0.453946	−	1.12356i
$631$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$631$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.326352	−	1.85083i	0.326352	−	1.85083i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.719340	−	0.694658i	0.719340	−	0.694658i
$641$	0.461262	−	1.14166i	0.461262	−	1.14166i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.461262	−	1.14166i	0.461262	−	1.14166i	0.961262	−	0.275637i	$-0.0888889\pi$
$642$	−0.553432	−	0.614648i	−0.553432	−	0.614648i
$643$	0.990268	+	0.139173i	0.990268	+	0.139173i	0.615661	−	0.788011i	$-0.288889\pi$
$643$	0.990268	+	0.139173i	0.990268	+	0.139173i	0.374607	+	0.927184i	$0.377778\pi$
$644$	−0.100489	+	0.0365750i	−0.100489	+	0.0365750i
$645$	−0.560671	+	0.831229i	−0.560671	+	0.831229i
$646$		0			0
$647$	−0.348048	+	1.39594i	−0.348048	+	1.39594i	0.500000	+	0.866025i	$0.333333\pi$
$647$	−0.348048	+	1.39594i	−0.348048	+	1.39594i	−0.848048	+	0.529919i	$0.822222\pi$
$648$	1.12021	−	0.321215i	1.12021	−	0.321215i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.87481	+	0.682374i	−1.87481	+	0.682374i
$653$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$653$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$654$	0.514345	+	1.05456i	0.514345	+	1.05456i
$655$		0			0
$656$	0.317271	+	0.141258i	0.317271	+	0.141258i
$657$		0			0
$658$	1.72340	−	2.20585i	1.72340	−	2.20585i
$659$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$659$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$660$		0			0
$661$	−0.0916445	−	0.187899i	−0.0916445	−	0.187899i	0.848048	−	0.529919i	$-0.177778\pi$
$661$	−0.0916445	−	0.187899i	−0.0916445	−	0.187899i	−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$	−0.0564686	−	1.61705i	−0.0564686	−	1.61705i
$665$		0			0
$666$		0			0
$667$	0.00430163	−	0.123183i	0.00430163	−	0.123183i
$668$	0.709299	+	0.515336i	0.709299	+	0.515336i
$669$	−0.921456	−	1.36611i	−0.921456	−	1.36611i
$670$	−0.0682737	−	1.95510i	−0.0682737	−	1.95510i
$671$		0			0
$672$	0.768069	−	1.90104i	0.768069	−	1.90104i
$673$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$673$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$674$		0			0
$675$	−0.139886	+	0.242290i	−0.139886	+	0.242290i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$677$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.50898	+	0.913195i	2.50898	+	0.913195i
$682$		0			0
$683$	0.418955	+	0.621126i	0.418955	+	0.621126i	0.978148	−	0.207912i	$-0.0666667\pi$
$683$	0.418955	+	0.621126i	0.418955	+	0.621126i	−0.559193	+	0.829038i	$0.688889\pi$
$684$		0			0
$685$		0			0
$686$	0.526911	−	0.0740525i	0.526911	−	0.0740525i
$687$	0.730278	−	0.388296i	0.730278	−	0.388296i
$688$	−0.732841	+	0.155770i	−0.732841	+	0.155770i
$689$		0			0
$690$	−0.0792156	−	0.0494994i	−0.0792156	−	0.0494994i
$691$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$691$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$692$		0			0
$693$		0			0
$694$	0.150383	−	1.43080i	0.150383	−	1.43080i
$695$		0			0
$696$	1.69996	+	1.64164i	1.69996	+	1.64164i
$697$		0			0
$698$	0.913545	−	1.58231i	0.913545	−	1.58231i
$699$		0			0
$700$	0.573931	+	1.42053i	0.573931	+	1.42053i
$701$	−0.874607	+	1.79321i	−0.874607	+	1.79321i	−0.374607	+	0.927184i	$0.622222\pi$
$701$	−0.874607	+	1.79321i	−0.874607	+	1.79321i	−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	2.44512			2.44512
$706$		0			0
$707$	0.567862	+	0.476493i	0.567862	+	0.476493i
$708$		0			0
$709$	−0.410323	+	1.64571i	−0.410323	+	1.64571i	0.309017	+	0.951057i	$0.400000\pi$
$709$	−0.410323	+	1.64571i	−0.410323	+	1.64571i	−0.719340	+	0.694658i	$0.755556\pi$
$710$		0			0
$711$		0			0
$712$	0.465101	+	1.86542i	0.465101	+	1.86542i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$719$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$720$	0.760303	−	0.218013i	0.760303	−	0.218013i
$721$	0.0715557	−	2.04909i	0.0715557	−	2.04909i
$722$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$723$	1.33826			1.33826
$724$	0.848048	−	0.529919i	0.848048	−	0.529919i
$725$	−1.76590			−1.76590
$726$	1.32524	−	0.186250i	1.32524	−	0.186250i
$727$	−0.0215691	+	0.617657i	−0.0215691	+	0.617657i	0.939693	+	0.342020i	$0.111111\pi$
$727$	−0.0215691	+	0.617657i	−0.0215691	+	0.617657i	−0.961262	+	0.275637i	$0.911111\pi$
$728$		0			0
$729$	0.535358	+	0.113794i	0.535358	+	0.113794i
$730$		0			0
$731$		0			0
$732$	−1.36730	+	0.608760i	−1.36730	+	0.608760i
$733$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$733$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$734$	−1.99513	−	0.139513i	−1.99513	−	0.139513i
$735$	1.29699	+	1.25249i	1.29699	+	1.25249i
$736$	−0.0168859	−	0.0677257i	−0.0168859	−	0.0677257i
$737$		0			0
$738$	0.169117	+	0.216460i	0.169117	+	0.216460i
$739$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$739$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.876742			−0.876742			−0.438371	−	0.898794i	$-0.644444\pi$
$743$	−0.876742			−0.876742			−0.438371	+	0.898794i	$0.644444\pi$
$744$		0			0
$745$	−1.49756	+	0.796269i	−1.49756	+	0.796269i
$746$		0			0
$747$	0.561015	−	1.15025i	0.561015	−	1.15025i
$748$		0			0
$749$	0.865021	+	0.385132i	0.865021	+	0.385132i
$750$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$751$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$751$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$752$	1.31430	+	1.26920i	1.31430	+	1.26920i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.328355	+	0.275522i	−0.328355	+	0.275522i
$757$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$757$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.72731	−	0.918425i	1.72731	−	0.918425i	0.766044	−	0.642788i	$-0.222222\pi$
$761$	1.72731	−	0.918425i	1.72731	−	0.918425i	0.961262	−	0.275637i	$-0.0888889\pi$
$762$	2.49063	−	0.350035i	2.49063	−	0.350035i
$763$	−1.02899	−	0.863423i	−1.02899	−	0.863423i
$764$		0			0
$765$		0			0
$766$	−1.55535	+	1.13003i	−1.55535	+	1.13003i
$767$		0			0
$768$	1.18161	+	0.628276i	1.18161	+	0.628276i
$769$	1.90381	+	0.545910i	1.90381	+	0.545910i	0.990268	+	0.139173i	$0.0444444\pi$
$769$	1.90381	+	0.545910i	1.90381	+	0.545910i	0.913545	+	0.406737i	$0.133333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	−0.569629	−	0.163339i	−0.569629	−	0.163339i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.0670951	−	1.92135i	−0.0670951	−	1.92135i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.152670	−	0.469869i	−0.152670	−	0.469869i
$784$	0.0470200	+	1.34648i	0.0470200	+	1.34648i
$785$		0			0
$786$		0			0
$787$	−0.490268	−	1.00520i	−0.490268	−	1.00520i	−0.990268	−	0.139173i	$-0.955556\pi$
$787$	−0.490268	−	1.00520i	−0.490268	−	1.00520i	0.500000	−	0.866025i	$-0.333333\pi$
$788$		0			0
$789$	1.87307	−	1.57170i	1.87307	−	1.57170i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$797$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$798$		0			0
$799$		0			0
$800$	−0.961262	+	0.275637i	−0.961262	+	0.275637i
$801$	−0.367868	+	1.47544i	−0.367868	+	1.47544i
$802$	−1.67959	−	1.04952i	−1.67959	−	1.04952i
$803$		0			0
$804$	2.46015	−	0.895420i	2.46015	−	0.895420i
$805$	0.105898	+	0.0148829i	0.105898	+	0.0148829i
$806$		0			0
$807$	−0.942176	+	2.33197i	−0.942176	+	2.33197i
$808$	−0.348048	+	0.336106i	−0.348048	+	0.336106i
$809$	1.20442	+	1.54158i	1.20442	+	1.54158i	0.766044	+	0.642788i	$0.222222\pi$
$809$	1.20442	+	1.54158i	1.20442	+	1.54158i	0.438371	+	0.898794i	$0.355556\pi$
$810$	−1.13989	−	0.242290i	−1.13989	−	0.242290i
$811$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$811$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$812$	−2.54235	−	0.925338i	−2.54235	−	0.925338i
$813$		0			0
$814$		0			0
$815$	1.97571	+	0.277668i	1.97571	+	0.277668i
$816$		0			0
$817$		0			0
$818$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$819$		0			0
$820$	−0.213817	−	0.273673i	−0.213817	−	0.273673i
$821$	0.538939	−	0.520447i	0.538939	−	0.520447i	−0.374607	−	0.927184i	$-0.622222\pi$
$821$	0.538939	−	0.520447i	0.538939	−	0.520447i	0.913545	+	0.406737i	$0.133333\pi$
$822$		0			0
$823$	−0.0467046	−	0.0518708i	−0.0467046	−	0.0518708i	0.719340	−	0.694658i	$-0.244444\pi$
$823$	−0.0467046	−	0.0518708i	−0.0467046	−	0.0518708i	−0.766044	+	0.642788i	$0.777778\pi$
$824$	1.32524	+	0.186250i	1.32524	+	0.186250i
$825$		0			0
$826$		0			0
$827$	0.410323	+	0.256398i	0.410323	+	0.256398i	0.719340	−	0.694658i	$-0.244444\pi$
$827$	0.410323	+	0.256398i	0.410323	+	0.256398i	−0.309017	+	0.951057i	$0.600000\pi$
$828$	0.0133558	−	0.0535671i	0.0133558	−	0.0535671i
$829$	−1.55535	+	0.445991i	−1.55535	+	0.445991i	−0.939693	−	0.342020i	$-0.888889\pi$
$829$	−1.55535	+	0.445991i	−1.55535	+	0.445991i	−0.615661	+	0.788011i	$0.711111\pi$
$830$	−0.709299	+	1.45428i	−0.709299	+	1.45428i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.384339	−	0.788011i	−0.384339	−	0.788011i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$839$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$840$	−1.57065	+	1.31793i	−1.57065	+	1.31793i
$841$	1.41748	−	1.57427i	1.41748	−	1.57427i
$842$	−0.743520	−	1.52444i	−0.743520	−	1.52444i
$843$	0.334330	−	1.89608i	0.334330	−	1.89608i
$844$		0			0
$845$	0.0348995	+	0.999391i	0.0348995	+	0.999391i
$846$	0.446568	+	1.37440i	0.446568	+	1.37440i
$847$	−1.29929	+	0.811883i	−1.29929	+	0.811883i
$848$		0			0
$849$	−0.669131	−	0.486152i	−0.669131	−	0.486152i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$853$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$854$	1.14653	−	1.27335i	1.14653	−	1.27335i
$855$		0			0
$856$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$859$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$860$	0.720190	+	0.206511i	0.720190	+	0.206511i
$861$	−0.628724	−	0.334298i	−0.628724	−	0.334298i
$862$		0			0
$863$	−0.391438	+	0.284396i	−0.391438	+	0.284396i	−0.766044	−	0.642788i	$-0.777778\pi$
$863$	−0.391438	+	0.284396i	−0.391438	+	0.284396i	0.374607	+	0.927184i	$0.377778\pi$
$864$	−0.156447	−	0.231942i	−0.156447	−	0.231942i
$865$		0			0
$866$		0			0
$867$	−1.32524	+	0.186250i	−1.32524	+	0.186250i
$868$		0			0
$869$		0			0
$870$	−0.730278	−	2.24756i	−0.730278	−	2.24756i
$871$		0			0
$872$	0.630676	−	0.609036i	0.630676	−	0.609036i
$873$		0			0
$874$		0			0
$875$	0.160147	−	1.52370i	0.160147	−	1.52370i
$876$		0			0
$877$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$877$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.747388	+	1.84985i	0.747388	+	1.84985i	0.438371	+	0.898794i	$0.355556\pi$
$881$	0.747388	+	1.84985i	0.747388	+	1.84985i	0.309017	+	0.951057i	$0.400000\pi$
$882$	−0.467144	+	0.957786i	−0.467144	+	0.957786i
$883$	−1.52045	−	1.10467i	−1.52045	−	1.10467i	−0.961262	−	0.275637i	$-0.911111\pi$
$883$	−1.52045	−	1.10467i	−1.52045	−	1.10467i	−0.559193	−	0.829038i	$-0.688889\pi$
$884$		0			0
$885$		0			0
$886$	−1.87939			−1.87939
$887$	1.11566	−	0.0780147i	1.11566	−	0.0780147i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	1.11566	−	0.0780147i	1.11566	−	0.0780147i	0.615661	+	0.788011i	$0.288889\pi$
$888$		0			0
$889$	−2.44186	+	1.52584i	−2.44186	+	1.52584i
$890$	0.465101	−	1.86542i	0.465101	−	1.86542i
$891$		0			0
$892$	−0.758078	+	0.970296i	−0.758078	+	0.970296i
$893$		0			0
$894$	−1.63277	−	1.57675i	−1.63277	−	1.57675i
$895$		0			0
$896$	−1.52836	−	0.106873i	−1.52836	−	0.106873i
$897$		0			0
$898$	0.990268	+	1.71519i	0.990268	+	1.71519i
$899$		0			0
$900$	−0.773659	−	0.164446i	−0.773659	−	0.164446i
$901$		0			0
$902$		0			0
$903$	1.52119	−	0.213789i	1.52119	−	0.213789i
$904$		0			0
$905$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$906$		0			0
$907$	1.74871	−	0.245765i	1.74871	−	0.245765i	0.809017	−	0.587785i	$-0.200000\pi$
$907$	1.74871	−	0.245765i	1.74871	−	0.245765i	0.939693	+	0.342020i	$0.111111\pi$
$908$	0.0696290	−	1.99391i	0.0696290	−	1.99391i
$909$	−0.367868	+	0.105484i	−0.367868	+	0.105484i
$910$		0			0
$911$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$911$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.49305	+	0.104404i	1.49305	+	0.104404i
$916$	−0.444576	−	0.429322i	−0.444576	−	0.429322i
$917$		0			0
$918$		0			0
$919$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$919$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$920$	−0.0168859	+	0.0677257i	−0.0168859	+	0.0677257i
$921$	−0.237261	+	0.148257i	−0.237261	+	0.148257i
$922$	−1.29929	−	1.09023i	−1.29929	−	1.09023i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.55919	−	0.829038i	1.55919	−	0.829038i
$927$	0.856335	+	0.622164i	0.856335	+	0.622164i
$928$	0.774117	−	1.58718i	0.774117	−	1.58718i
$929$	0.606126	+	1.50021i	0.606126	+	1.50021i	0.848048	+	0.529919i	$0.177778\pi$
$929$	0.606126	+	1.50021i	0.606126	+	1.50021i	−0.241922	+	0.970296i	$0.577778\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.317271	−	0.141258i	0.317271	−	0.141258i
$935$		0			0
$936$		0			0
$937$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$937$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$938$	−2.15602	+	2.08204i	−2.15602	+	2.08204i
$939$		0			0
$940$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$941$	−1.09395	+	0.232525i	−1.09395	+	0.232525i	−0.719340	−	0.694658i	$-0.755556\pi$
$941$	−1.09395	+	0.232525i	−1.09395	+	0.232525i	−0.374607	+	0.927184i	$0.622222\pi$
$942$		0			0
$943$	−0.0240050	+	0.00337369i	−0.0240050	+	0.00337369i
$944$		0			0
$945$	0.419270	−	0.0891186i	0.419270	−	0.0891186i
$946$		0			0
$947$	1.55535	−	1.13003i	1.55535	−	1.13003i	0.615661	−	0.788011i	$-0.288889\pi$
$947$	1.55535	−	1.13003i	1.55535	−	1.13003i	0.939693	−	0.342020i	$-0.111111\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.748346	−	1.10947i	−0.748346	−	1.10947i
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$		0			0
$963$	−0.414551	+	0.259040i	−0.414551	+	0.259040i
$964$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$965$		0			0
$966$	0.0248510	+	0.140937i	0.0248510	+	0.140937i
$967$	0.130100	−	0.737831i	0.130100	−	0.737831i	−0.848048	−	0.529919i	$-0.822222\pi$
$967$	0.130100	−	0.737831i	0.130100	−	0.737831i	0.978148	−	0.207912i	$-0.0666667\pi$
$968$	−0.438371	−	0.898794i	−0.438371	−	0.898794i
$969$		0			0
$970$		0			0
$971$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$971$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$972$	−0.133773	−	1.27276i	−0.133773	−	1.27276i
$973$		0			0
$974$	1.27028	+	0.675419i	1.27028	+	0.675419i
$975$		0			0
$976$	0.748346	+	0.831123i	0.748346	+	0.831123i
$977$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$977$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$978$	0.463641	+	2.62944i	0.463641	+	2.62944i
$979$		0			0
$980$	0.590616	−	1.21094i	0.590616	−	1.21094i
$981$	0.666590	−	0.191142i	0.666590	−	0.191142i
$982$		0			0
$983$	0.848048	+	0.529919i	0.848048	+	0.529919i	0.882948	−	0.469472i	$-0.155556\pi$
$983$	0.848048	+	0.529919i	0.848048	+	0.529919i	−0.0348995	+	0.999391i	$0.511111\pi$
$984$	0.259898	−	0.385314i	0.259898	−	0.385314i
$985$		0			0
$986$		0			0
$987$	−2.50666	−	2.78393i	−2.50666	−	2.78393i
$988$		0			0
$989$	0.0376174	−	0.0363267i	0.0376174	−	0.0363267i
$990$		0			0
$991$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$991$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−2.14428	−	0.301359i	−2.14428	−	0.301359i
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3620.1.dy.a.1699.1	yes	24
4.3	odd	2		3620.1.dy.b.1699.1	yes	24
5.4	even	2		3620.1.dy.b.1699.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.1699.1	yes	24
181.75	even	45	inner	3620.1.dy.a.799.1	✓	24
724.75	odd	90		3620.1.dy.b.799.1	yes	24
905.799	even	90		3620.1.dy.b.799.1	yes	24
3620.799	odd	90	inner	3620.1.dy.a.799.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.799.1	✓	24	181.75	even	45	inner
3620.1.dy.a.799.1	✓	24	3620.799	odd	90	inner
3620.1.dy.a.1699.1	yes	24	1.1	even	1	trivial
3620.1.dy.a.1699.1	yes	24	20.19	odd	2	CM
3620.1.dy.b.799.1	yes	24	724.75	odd	90
3620.1.dy.b.799.1	yes	24	905.799	even	90
3620.1.dy.b.1699.1	yes	24	4.3	odd	2
3620.1.dy.b.1699.1	yes	24	5.4	even	2

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:	\( N \)	\(=\)	\( 3620 = 2^{2} \cdot 5 \cdot 181 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3620.dy (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.990268 + 0.139173i) q^{2} +(-0.0467046 + 1.33745i) q^{3} +(0.961262 - 0.275637i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-0.139886 - 1.33093i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-0.913545 + 0.406737i) q^{8} +(-0.789016 - 0.0551734i) q^{9} +O(q^{10})\)	\(q+(-0.990268 + 0.139173i) q^{2} +(-0.0467046 + 1.33745i) q^{3} +(0.961262 - 0.275637i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-0.139886 - 1.33093i) q^{6} +(0.766044 + 1.32683i) q^{7} +(-0.913545 + 0.406737i) q^{8} +(-0.789016 - 0.0551734i) q^{9} +(0.997564 + 0.0697565i) q^{10} +(0.323755 + 1.29851i) q^{12} +(-0.943248 - 1.20730i) q^{14} +(0.323755 - 1.29851i) q^{15} +(0.848048 - 0.529919i) q^{16} +(0.789016 - 0.0551734i) q^{18} +(-0.997564 + 0.0697565i) q^{20} +(-1.81034 + 0.962574i) q^{21} +(-0.0305979 + 0.0627349i) q^{23} +(-0.501321 - 1.24081i) q^{24} +(0.913545 + 0.406737i) q^{25} +(-0.0292442 + 0.278240i) q^{27} +(1.10209 + 1.06428i) q^{28} +(-1.61323 + 0.718254i) q^{29} +(-0.139886 + 1.33093i) q^{30} +(-0.766044 + 0.642788i) q^{32} +(-0.473442 - 1.45710i) q^{35} +(-0.773659 + 0.164446i) q^{36} +(0.978148 - 0.207912i) q^{40} +(0.194206 + 0.287922i) q^{41} +(1.65876 - 1.20516i) q^{42} +(-0.704030 - 0.256246i) q^{43} +(0.760303 + 0.218013i) q^{45} +(0.0215691 - 0.0663828i) q^{46} +(0.442013 + 1.77282i) q^{47} +(0.669131 + 1.15897i) q^{48} +(-0.673648 + 1.16679i) q^{49} +(-0.961262 - 0.275637i) q^{50} +(-0.00976393 - 0.279602i) q^{54} +(-1.23949 - 0.900539i) q^{56} +(1.49756 - 0.935782i) q^{58} +(-0.0467046 - 1.33745i) q^{60} +(0.194206 + 1.10140i) q^{61} +(-0.531216 - 1.08915i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-0.204489 - 1.94558i) q^{67} +(-0.0824755 - 0.0438530i) q^{69} +(0.671624 + 1.37703i) q^{70} +(0.743243 - 0.270518i) q^{72} +(-0.586655 + 1.20282i) q^{75} +(-0.939693 + 0.342020i) q^{80} +(-1.15401 - 0.162186i) q^{81} +(-0.232387 - 0.258091i) q^{82} +(-0.606126 + 1.50021i) q^{83} +(-1.47489 + 1.42428i) q^{84} +(0.732841 + 0.155770i) q^{86} +(-0.885281 - 2.19115i) q^{87} +(0.333843 - 1.89332i) q^{89} +(-0.783246 - 0.110078i) q^{90} +(-0.0121205 + 0.0687386i) q^{92} +(-0.684440 - 1.69405i) q^{94} +(-0.823916 - 1.05456i) q^{96} +(0.504706 - 1.24919i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{14} - 18 q^{21} - 3 q^{23} + 3 q^{25} + 12 q^{27} - 3 q^{28} - 3 q^{30} - 3 q^{40} + 3 q^{41} - 3 q^{43} + 3 q^{48} - 12 q^{49} + 12 q^{58} + 3 q^{61} + 15 q^{63} + 3 q^{64} + 3 q^{67} - 3 q^{69} + 3 q^{70} - 3 q^{84} + 3 q^{87} + 3 q^{89} - 3 q^{92} - 3 q^{98}+O(q^{100}) \) 24 * q + 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^14 - 18 * q^21 - 3 * q^23 + 3 * q^25 + 12 * q^27 - 3 * q^28 - 3 * q^30 - 3 * q^40 + 3 * q^41 - 3 * q^43 + 3 * q^48 - 12 * q^49 + 12 * q^58 + 3 * q^61 + 15 * q^63 + 3 * q^64 + 3 * q^67 - 3 * q^69 + 3 * q^70 - 3 * q^84 + 3 * q^87 + 3 * q^89 - 3 * q^92 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more