LMFDB - Embedded newform 3620.1.dy.a.2479.1

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			2479.1
Root			$0.438371 - 0.898794i$ of defining polynomial
Character	$\chi$	$=$	3620.2479
Dual form			3620.1.dy.a.3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.615661 - 0.788011i) q^{2} +(-1.13491 + 0.709170i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(-0.139886 + 1.33093i) q^{6} +(0.173648 - 0.300767i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(0.346727 - 0.710895i) q^{9} +O(q^{10})$	\(q+(0.615661 - 0.788011i) q^{2} +(-1.13491 + 0.709170i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(-0.139886 + 1.33093i) q^{6} +(0.173648 - 0.300767i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(0.346727 - 0.710895i) q^{9} +(-0.438371 + 0.898794i) q^{10} +(0.962665 + 0.929634i) q^{12} +(-0.130100 - 0.322008i) q^{14} +(0.962665 - 0.929634i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(-0.346727 - 0.710895i) q^{18} +(0.438371 + 0.898794i) q^{20} +(0.0162204 + 0.464490i) q^{21} +(-0.948445 + 1.40613i) q^{23} +(1.32524 - 0.186250i) q^{24} +(0.913545 - 0.406737i) q^{25} +(-0.0292442 - 0.278240i) q^{27} +(-0.333843 - 0.0957278i) q^{28} +(0.0637646 + 0.0283898i) q^{29} +(-0.139886 - 1.33093i) q^{30} +(-0.173648 + 0.984808i) q^{32} +(-0.107320 + 0.330298i) q^{35} +(-0.773659 - 0.164446i) q^{36} +(0.978148 + 0.207912i) q^{40} +(1.87481 + 0.131099i) q^{41} +(0.376009 + 0.273187i) q^{42} +(-1.51718 - 1.27306i) q^{43} +(-0.191346 + 0.767449i) q^{45} +(0.524123 + 1.61308i) q^{46} +(1.31430 + 1.26920i) q^{47} +(0.669131 - 1.15897i) q^{48} +(0.439693 + 0.761570i) q^{49} +(0.241922 - 0.970296i) q^{50} +(-0.237261 - 0.148257i) q^{54} +(-0.280969 + 0.204136i) q^{56} +(0.0616289 - 0.0327686i) q^{58} +(-1.13491 - 0.709170i) q^{60} +(1.87481 - 0.682374i) q^{61} +(-0.153606 - 0.227730i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-0.204489 + 1.94558i) q^{67} +(0.0792156 - 2.26844i) q^{69} +(0.194206 + 0.287922i) q^{70} +(-0.605898 + 0.508408i) q^{72} +(-0.748346 + 1.10947i) q^{75} +(0.766044 - 0.642788i) q^{80} +(0.717462 + 0.918310i) q^{81} +(1.25755 - 1.39666i) q^{82} +(1.60229 + 0.225187i) q^{83} +(0.446769 - 0.128109i) q^{84} +(-1.93726 + 0.411777i) q^{86} +(-0.0925002 + 0.0130001i) q^{87} +(0.454664 + 0.165484i) q^{89} +(0.486953 + 0.623272i) q^{90} +(1.59381 + 0.580099i) q^{92} +(1.80931 - 0.254282i) q^{94} +(-0.501321 - 1.24081i) q^{96} +(0.870827 + 0.122387i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{32}{45}\right)$

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 $

$2$	0.615661	−	0.788011i	0.615661	−	0.788011i
$2$	0.615661	−	0.788011i	0.615661	−	0.788011i
$3$	−1.13491	+	0.709170i	−1.13491	+	0.709170i	−0.961262	−	0.275637i	$-0.911111\pi$
$3$	−1.13491	+	0.709170i	−1.13491	+	0.709170i	−0.173648	+	0.984808i	$0.555556\pi$
$4$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$5$	−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
$7$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$7$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$8$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$9$	0.346727	−	0.710895i	0.346727	−	0.710895i
$10$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$11$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$11$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$12$	0.962665	+	0.929634i	0.962665	+	0.929634i
$13$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$13$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$14$	−0.130100	−	0.322008i	−0.130100	−	0.322008i
$15$	0.962665	−	0.929634i	0.962665	−	0.929634i
$16$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$17$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$17$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$18$	−0.346727	−	0.710895i	−0.346727	−	0.710895i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.438371	+	0.898794i	0.438371	+	0.898794i
$21$	0.0162204	+	0.464490i	0.0162204	+	0.464490i
$22$		0			0
$23$	−0.948445	+	1.40613i	−0.948445	+	1.40613i	−0.0348995	+	0.999391i	$0.511111\pi$
$23$	−0.948445	+	1.40613i	−0.948445	+	1.40613i	−0.913545	+	0.406737i	$0.866667\pi$
$24$	1.32524	−	0.186250i	1.32524	−	0.186250i
$25$	0.913545	−	0.406737i	0.913545	−	0.406737i
$26$		0			0
$27$	−0.0292442	−	0.278240i	−0.0292442	−	0.278240i
$28$	−0.333843	−	0.0957278i	−0.333843	−	0.0957278i
$29$	0.0637646	+	0.0283898i	0.0637646	+	0.0283898i	0.438371	−	0.898794i	$-0.355556\pi$
$29$	0.0637646	+	0.0283898i	0.0637646	+	0.0283898i	−0.374607	+	0.927184i	$0.622222\pi$
$30$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$33$		0			0
$34$		0			0
$35$	−0.107320	+	0.330298i	−0.107320	+	0.330298i
$36$	−0.773659	−	0.164446i	−0.773659	−	0.164446i
$37$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$37$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$38$		0			0
$39$		0			0
$40$	0.978148	+	0.207912i	0.978148	+	0.207912i
$41$	1.87481	+	0.131099i	1.87481	+	0.131099i	0.961262	−	0.275637i	$-0.0888889\pi$
$41$	1.87481	+	0.131099i	1.87481	+	0.131099i	0.913545	+	0.406737i	$0.133333\pi$
$42$	0.376009	+	0.273187i	0.376009	+	0.273187i
$43$	−1.51718	−	1.27306i	−1.51718	−	1.27306i	−0.848048	−	0.529919i	$-0.822222\pi$
$43$	−1.51718	−	1.27306i	−1.51718	−	1.27306i	−0.669131	−	0.743145i	$-0.733333\pi$
$44$		0			0
$45$	−0.191346	+	0.767449i	−0.191346	+	0.767449i
$46$	0.524123	+	1.61308i	0.524123	+	1.61308i
$47$	1.31430	+	1.26920i	1.31430	+	1.26920i	0.939693	+	0.342020i	$0.111111\pi$
$47$	1.31430	+	1.26920i	1.31430	+	1.26920i	0.374607	+	0.927184i	$0.377778\pi$
$48$	0.669131	−	1.15897i	0.669131	−	1.15897i
$49$	0.439693	+	0.761570i	0.439693	+	0.761570i
$50$	0.241922	−	0.970296i	0.241922	−	0.970296i
$51$		0			0
$52$		0			0
$53$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$53$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$54$	−0.237261	−	0.148257i	−0.237261	−	0.148257i
$55$		0			0
$56$	−0.280969	+	0.204136i	−0.280969	+	0.204136i
$57$		0			0
$58$	0.0616289	−	0.0327686i	0.0616289	−	0.0327686i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−1.13491	−	0.709170i	−1.13491	−	0.709170i
$61$	1.87481	−	0.682374i	1.87481	−	0.682374i	0.913545	−	0.406737i	$-0.133333\pi$
$61$	1.87481	−	0.682374i	1.87481	−	0.682374i	0.961262	−	0.275637i	$-0.0888889\pi$
$62$		0			0
$63$	−0.153606	−	0.227730i	−0.153606	−	0.227730i
$64$	0.669131	+	0.743145i	0.669131	+	0.743145i
$65$		0			0
$66$		0			0
$67$	−0.204489	+	1.94558i	−0.204489	+	1.94558i	0.104528	+	0.994522i	$0.466667\pi$
$67$	−0.204489	+	1.94558i	−0.204489	+	1.94558i	−0.309017	+	0.951057i	$0.600000\pi$
$68$		0			0
$69$	0.0792156	−	2.26844i	0.0792156	−	2.26844i
$70$	0.194206	+	0.287922i	0.194206	+	0.287922i
$71$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$71$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$72$	−0.605898	+	0.508408i	−0.605898	+	0.508408i
$73$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$73$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$74$		0			0
$75$	−0.748346	+	1.10947i	−0.748346	+	1.10947i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$79$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$80$	0.766044	−	0.642788i	0.766044	−	0.642788i
$81$	0.717462	+	0.918310i	0.717462	+	0.918310i
$82$	1.25755	−	1.39666i	1.25755	−	1.39666i
$83$	1.60229	+	0.225187i	1.60229	+	0.225187i	0.882948	−	0.469472i	$-0.155556\pi$
$83$	1.60229	+	0.225187i	1.60229	+	0.225187i	0.719340	+	0.694658i	$0.244444\pi$
$84$	0.446769	−	0.128109i	0.446769	−	0.128109i
$85$		0			0
$86$	−1.93726	+	0.411777i	−1.93726	+	0.411777i
$87$	−0.0925002	+	0.0130001i	−0.0925002	+	0.0130001i
$88$		0			0
$89$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$89$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$90$	0.486953	+	0.623272i	0.486953	+	0.623272i
$91$		0			0
$92$	1.59381	+	0.580099i	1.59381	+	0.580099i
$93$		0			0
$94$	1.80931	−	0.254282i	1.80931	−	0.254282i
$95$		0			0
$96$	−0.501321	−	1.24081i	−0.501321	−	1.24081i
$97$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$97$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$98$	0.870827	+	0.122387i	0.870827	+	0.122387i
$99$		0			0
$100$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$101$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.997564	−	0.0697565i	$-0.977778\pi$
$101$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.104528	+	0.994522i	$0.533333\pi$
$102$		0			0
$103$	1.18161	+	0.628276i	1.18161	+	0.628276i	0.939693	−	0.342020i	$-0.111111\pi$
$103$	1.18161	+	0.628276i	1.18161	+	0.628276i	0.241922	+	0.970296i	$0.422222\pi$
$104$		0			0
$105$	−0.112439	−	0.450967i	−0.112439	−	0.450967i
$106$		0			0
$107$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$107$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$108$	−0.262900	+	0.0956879i	−0.262900	+	0.0956879i
$109$	0.856733	−	0.718885i	0.856733	−	0.718885i	−0.104528	−	0.994522i	$-0.533333\pi$
$109$	0.856733	−	0.718885i	0.856733	−	0.718885i	0.961262	+	0.275637i	$0.0888889\pi$
$110$		0			0
$111$		0			0
$112$	−0.0121205	+	0.347085i	−0.0121205	+	0.347085i
$113$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$113$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$114$		0			0
$115$	0.635369	−	1.57259i	0.635369	−	1.57259i
$116$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.25755	+	0.457712i	−1.25755	+	0.457712i
$121$	0.848048	+	0.529919i	0.848048	+	0.529919i
$122$	0.616528	−	1.89748i	0.616528	−	1.89748i
$123$	−2.22071	+	1.18077i	−2.22071	+	1.18077i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$126$	−0.274023	−	0.0191615i	−0.274023	−	0.0191615i
$127$	−1.29929	−	0.811883i	−1.29929	−	0.811883i	−0.309017	−	0.951057i	$-0.600000\pi$
$127$	−1.29929	−	0.811883i	−1.29929	−	0.811883i	−0.990268	+	0.139173i	$0.955556\pi$
$128$	0.997564	−	0.0697565i	0.997564	−	0.0697565i
$129$	2.62468	+	0.368875i	2.62468	+	0.368875i
$130$		0			0
$131$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$131$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$132$		0			0
$133$		0			0
$134$	1.40724	+	1.35896i	1.40724	+	1.35896i
$135$	0.0864545	+	0.266080i	0.0864545	+	0.266080i
$136$		0			0
$137$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$137$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$138$	−1.73878	−	1.45901i	−1.73878	−	1.45901i
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$	0.346450	+	0.0242262i	0.346450	+	0.0242262i
$141$	−2.39169	−	0.508370i	−2.39169	−	0.508370i
$142$		0			0
$143$		0			0
$144$	0.0276035	+	0.790461i	0.0276035	+	0.790461i
$145$	−0.0682737	−	0.0145120i	−0.0682737	−	0.0145120i
$146$		0			0
$147$	−1.03909	−	0.552496i	−1.03909	−	0.552496i
$148$		0			0
$149$	−0.306644	+	1.73907i	−0.306644	+	1.73907i	0.309017	+	0.951057i	$0.400000\pi$
$149$	−0.306644	+	1.73907i	−0.306644	+	1.73907i	−0.615661	+	0.788011i	$0.711111\pi$
$150$	0.413545	+	1.27276i	0.413545	+	1.27276i
$151$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$151$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$157$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$158$		0			0
$159$		0			0
$160$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$161$	0.258222	+	0.529433i	0.258222	+	0.529433i
$162$	1.16535			1.16535
$163$	−0.384339	−	0.788011i	−0.384339	−	0.788011i	0.615661	−	0.788011i	$-0.288889\pi$
$163$	−0.384339	−	0.788011i	−0.384339	−	0.788011i	−1.00000			$\pi$
$164$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$165$		0			0
$166$	1.16392	−	1.12398i	1.16392	−	1.12398i
$167$	0.418955	+	1.03695i	0.418955	+	1.03695i	0.978148	+	0.207912i	$0.0666667\pi$
$167$	0.418955	+	1.03695i	0.418955	+	1.03695i	−0.559193	+	0.829038i	$0.688889\pi$
$168$	0.174107	−	0.430930i	0.174107	−	0.430930i
$169$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$170$		0			0
$171$		0			0
$172$	−0.868210	+	1.78009i	−0.868210	+	1.78009i
$173$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$173$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$174$	−0.0467046	+	0.0808948i	−0.0467046	+	0.0808948i
$175$	0.0363024	−	0.345394i	0.0363024	−	0.345394i
$176$		0			0
$177$		0			0
$178$	0.410323	−	0.256398i	0.410323	−	0.256398i
$179$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$179$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$180$	0.790943			0.790943
$181$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$181$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$182$		0			0
$183$	−1.64382	+	2.10399i	−1.64382	+	2.10399i
$184$	1.43837	−	0.898794i	1.43837	−	0.898794i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.913545	−	1.58231i	0.913545	−	1.58231i
$189$	−0.0887638	−	0.0395202i	−0.0887638	−	0.0395202i
$190$		0			0
$191$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$191$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$192$	−1.28642	−	0.368875i	−1.28642	−	0.368875i
$193$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$193$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$194$		0			0
$195$		0			0
$196$	0.632577	−	0.610872i	0.632577	−	0.610872i
$197$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$197$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$198$		0			0
$199$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$199$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$200$	−1.00000			−1.00000
$201$	−1.14767	−	2.35307i	−1.14767	−	2.35307i
$202$	0.0502092	+	1.43780i	0.0502092	+	1.43780i
$203$	0.0196113	−	0.0142485i	0.0196113	−	0.0142485i
$204$		0			0
$205$	−1.86110	+	0.261560i	−1.86110	+	0.261560i
$206$	1.22256	−	0.544320i	1.22256	−	0.544320i
$207$	0.670758	+	1.16179i	0.670758	+	1.16179i
$208$		0			0
$209$		0			0
$210$	−0.424591	−	0.189040i	−0.424591	−	0.189040i
$211$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$211$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$212$		0			0
$213$		0			0
$214$	0.594092	−	0.170353i	0.594092	−	0.170353i
$215$	1.74871	+	0.929805i	1.74871	+	0.929805i
$216$	−0.0864545	+	0.266080i	−0.0864545	+	0.266080i
$217$		0			0
$218$	−0.0390311	−	1.11770i	−0.0390311	−	1.11770i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.606126	−	0.440376i	−0.606126	−	0.440376i	0.241922	−	0.970296i	$-0.422222\pi$
$223$	−0.606126	−	0.440376i	−0.606126	−	0.440376i	−0.848048	+	0.529919i	$0.822222\pi$
$224$	0.266044	+	0.223238i	0.266044	+	0.223238i
$225$	0.0276035	−	0.790461i	0.0276035	−	0.790461i
$226$		0			0
$227$	−0.270928	−	0.833831i	−0.270928	−	0.833831i	−0.990268	−	0.139173i	$-0.955556\pi$
$227$	−0.270928	−	0.833831i	−0.270928	−	0.833831i	0.719340	−	0.694658i	$-0.244444\pi$
$228$		0			0
$229$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$229$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$230$	−0.848048	−	1.46886i	−0.848048	−	1.46886i
$231$		0			0
$232$	−0.0467046	−	0.0518708i	−0.0467046	−	0.0518708i
$233$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$233$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$234$		0			0
$235$	−1.54946	−	0.968211i	−1.54946	−	0.968211i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$239$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$240$	−0.413545	+	1.27276i	−0.413545	+	1.27276i
$241$	−0.848048	−	0.529919i	−0.848048	−	0.529919i	0.0348995	−	0.999391i	$-0.488889\pi$
$241$	−0.848048	−	0.529919i	−0.848048	−	0.529919i	−0.882948	+	0.469472i	$0.844444\pi$
$242$	0.939693	−	0.342020i	0.939693	−	0.342020i
$243$	−1.20259	−	0.437708i	−1.20259	−	0.437708i
$244$	−1.11566	−	1.65404i	−1.11566	−	1.65404i
$245$	−0.588424	−	0.653511i	−0.588424	−	0.653511i
$246$	−0.436744	+	2.47690i	−0.436744	+	2.47690i
$247$		0			0
$248$		0			0
$249$	−1.97815	+	0.880728i	−1.97815	+	0.880728i
$250$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$251$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$251$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$252$	−0.183805	+	0.204136i	−0.183805	+	0.204136i
$253$		0			0
$254$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$255$		0			0
$256$	0.559193	−	0.829038i	0.559193	−	0.829038i
$257$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$257$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$258$	1.90659	−	1.84117i	1.90659	−	1.84117i
$259$		0			0
$260$		0			0
$261$	0.0422910	−	0.0354864i	0.0422910	−	0.0354864i
$262$		0			0
$263$	−1.22256	+	1.35779i	−1.22256	+	1.35779i	−0.309017	+	0.951057i	$0.600000\pi$
$263$	−1.22256	+	1.35779i	−1.22256	+	1.35779i	−0.913545	+	0.406737i	$0.866667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.633360	+	0.134625i	−0.633360	+	0.134625i
$268$	1.93726	−	0.272264i	1.93726	−	0.272264i
$269$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$269$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$270$	0.262900	+	0.0956879i	0.262900	+	0.0956879i
$271$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$271$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−2.22022	+	0.471922i	−2.22022	+	0.471922i
$277$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$277$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$278$		0			0
$279$		0			0
$280$	0.232387	−	0.258091i	0.232387	−	0.258091i
$281$	−1.18362	−	1.51497i	−1.18362	−	1.51497i	−0.809017	−	0.587785i	$-0.800000\pi$
$281$	−1.18362	−	1.51497i	−1.18362	−	1.51497i	−0.374607	−	0.927184i	$-0.622222\pi$
$282$	−1.87307	+	1.57170i	−1.87307	+	1.57170i
$283$	0.616528	−	0.0431119i	0.616528	−	0.0431119i	0.241922	−	0.970296i	$-0.422222\pi$
$283$	0.616528	−	0.0431119i	0.616528	−	0.0431119i	0.374607	+	0.927184i	$0.377778\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.364987	−	0.541116i	0.364987	−	0.541116i
$288$	0.639886	+	0.464905i	0.639886	+	0.464905i
$289$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$290$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i
$291$		0			0
$292$		0			0
$293$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$293$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$294$	−1.07510	+	0.478667i	−1.07510	+	0.478667i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.18161	+	1.31232i	1.18161	+	1.31232i
$299$		0			0
$300$	1.25755	+	0.457712i	1.25755	+	0.457712i
$301$	−0.646352	+	0.235253i	−0.646352	+	0.235253i
$302$		0			0
$303$	0.594959	−	1.83110i	0.594959	−	1.83110i
$304$		0			0
$305$	−1.69196	+	1.05726i	−1.69196	+	1.05726i
$306$		0			0
$307$	−0.208548	−	0.0145831i	−0.208548	−	0.0145831i	−0.0348995	−	0.999391i	$-0.511111\pi$
$307$	−0.208548	−	0.0145831i	−0.208548	−	0.0145831i	−0.173648	+	0.984808i	$0.555556\pi$
$308$		0			0
$309$	−1.78658	+	0.124930i	−1.78658	+	0.124930i
$310$		0			0
$311$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$311$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		0			0
$315$	0.197597	+	0.190817i	0.197597	+	0.190817i
$316$		0			0
$317$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$317$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$318$		0			0
$319$		0			0
$320$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$321$	−0.825076	−	0.0576949i	−0.825076	−	0.0576949i
$322$	0.576176	+	0.122470i	0.576176	+	0.122470i
$323$		0			0
$324$	0.717462	−	0.918310i	0.717462	−	0.918310i
$325$		0			0
$326$	−0.857583	−	0.182285i	−0.857583	−	0.182285i
$327$	−0.462503	+	1.42344i	−0.462503	+	1.42344i
$328$	−1.65940	−	0.882318i	−1.65940	−	0.882318i
$329$	0.609961	−	0.174903i	0.609961	−	0.174903i
$330$		0			0
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$333$		0			0
$334$	1.07506	+	0.308269i	1.07506	+	0.308269i
$335$	−0.204489	−	1.94558i	−0.204489	−	1.94558i
$336$	−0.232387	−	0.402505i	−0.232387	−	0.402505i
$337$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$337$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$338$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.652704			0.652704
$344$	0.868210	+	1.78009i	0.868210	+	1.78009i
$345$	0.394150	+	2.23534i	0.394150	+	2.23534i
$346$		0			0
$347$	1.38295	−	1.33550i	1.38295	−	1.33550i	0.500000	−	0.866025i	$-0.333333\pi$
$347$	1.38295	−	1.33550i	1.38295	−	1.33550i	0.882948	−	0.469472i	$-0.155556\pi$
$348$	0.0349917	+	0.0866076i	0.0349917	+	0.0866076i
$349$	−0.684440	+	1.69405i	−0.684440	+	1.69405i	0.0348995	+	0.999391i	$0.488889\pi$
$349$	−0.684440	+	1.69405i	−0.684440	+	1.69405i	−0.719340	+	0.694658i	$0.755556\pi$
$350$	−0.249824	−	0.241252i	−0.249824	−	0.241252i
$351$		0			0
$352$		0			0
$353$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$353$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$354$		0			0
$355$		0			0
$356$	0.0505754	−	0.481193i	0.0505754	−	0.481193i
$357$		0			0
$358$		0			0
$359$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$359$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$360$	0.486953	−	0.623272i	0.486953	−	0.623272i
$361$	1.00000			1.00000
$362$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$363$	−1.33826			−1.33826
$364$		0			0
$365$		0			0
$366$	0.645932	+	2.59069i	0.645932	+	2.59069i
$367$	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	$-0.0666667\pi$
$368$	0.177290	−	1.68680i	0.177290	−	1.68680i
$369$	0.743243	−	1.28734i	0.743243	−	1.28734i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$373$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$374$		0			0
$375$	0.501321	−	1.24081i	0.501321	−	1.24081i
$376$	−0.684440	−	1.69405i	−0.684440	−	1.69405i
$377$		0			0
$378$	−0.0857908	+	0.0456158i	−0.0857908	+	0.0456158i
$379$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$379$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$380$		0			0
$381$	2.05034			2.05034
$382$		0			0
$383$	0.0168859	+	0.483549i	0.0168859	+	0.483549i	0.978148	+	0.207912i	$0.0666667\pi$
$383$	0.0168859	+	0.483549i	0.0168859	+	0.483549i	−0.961262	+	0.275637i	$0.911111\pi$
$384$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$385$		0			0
$386$		0			0
$387$	−1.43106	+	0.637149i	−1.43106	+	0.637149i
$388$		0			0
$389$	0.0505754	+	0.481193i	0.0505754	+	0.481193i	0.990268	+	0.139173i	$0.0444444\pi$
$389$	0.0505754	+	0.481193i	0.0505754	+	0.481193i	−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	−0.0919208	−	0.874568i	−0.0919208	−	0.874568i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$397$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$398$		0			0
$399$		0			0
$400$	−0.615661	+	0.788011i	−0.615661	+	0.788011i
$401$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	−0.882948	−	0.469472i	$-0.844444\pi$
$401$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	0.669131	−	0.743145i	$-0.266667\pi$
$402$	−2.56082	−	0.544320i	−2.56082	−	0.544320i
$403$		0			0
$404$	1.16392	+	0.845635i	1.16392	+	0.845635i
$405$	−0.892712	−	0.749074i	−0.892712	−	0.749074i
$406$	0.000845996	−	0.0242262i	0.000845996	−	0.0242262i
$407$		0			0
$408$		0			0
$409$	0.719340	+	0.694658i	0.719340	+	0.694658i	0.961262	−	0.275637i	$-0.0888889\pi$
$409$	0.719340	+	0.694658i	0.719340	+	0.694658i	−0.241922	+	0.970296i	$0.577778\pi$
$410$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$411$		0			0
$412$	0.323755	−	1.29851i	0.323755	−	1.29851i
$413$		0			0
$414$	1.32846	+	0.186703i	1.32846	+	0.186703i
$415$	−1.61409	+	0.112868i	−1.61409	+	0.112868i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$419$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$420$	−0.410370	+	0.218198i	−0.410370	+	0.218198i
$421$	−0.545692	+	1.67947i	−0.545692	+	1.67947i	0.173648	+	0.984808i	$0.444444\pi$
$421$	−0.545692	+	1.67947i	−0.545692	+	1.67947i	−0.719340	+	0.694658i	$0.755556\pi$
$422$		0			0
$423$	1.35797	−	0.494262i	1.35797	−	0.494262i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.120321	−	0.682374i	0.120321	−	0.682374i
$428$	0.231520	−	0.573031i	0.231520	−	0.573031i
$429$		0			0
$430$	1.80931	−	0.805557i	1.80931	−	0.805557i
$431$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$431$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$432$	0.156447	+	0.231942i	0.156447	+	0.231942i
$433$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$433$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$434$		0			0
$435$	0.0877760	−	0.0319479i	0.0877760	−	0.0319479i
$436$	−0.904793	−	0.657371i	−0.904793	−	0.657371i
$437$		0			0
$438$		0			0
$439$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$439$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$440$		0			0
$441$	0.693849	−	0.0485187i	0.693849	−	0.0485187i
$442$		0			0
$443$	0.943248	+	1.20730i	0.943248	+	1.20730i	0.978148	+	0.207912i	$0.0666667\pi$
$443$	0.943248	+	1.20730i	0.943248	+	1.20730i	−0.0348995	+	0.999391i	$0.511111\pi$
$444$		0			0
$445$	−0.479135	−	0.0673380i	−0.479135	−	0.0673380i
$446$	−0.720190	+	0.206511i	−0.720190	+	0.206511i
$447$	−0.885281	−	2.19115i	−0.885281	−	2.19115i
$448$	0.339707	−	0.0722070i	0.339707	−	0.0722070i
$449$	−1.21934	+	0.171367i	−1.21934	+	0.171367i	−0.719340	−	0.694658i	$-0.755556\pi$
$449$	−1.21934	+	0.171367i	−1.21934	+	0.171367i	−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.605898	−	0.508408i	−0.605898	−	0.508408i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.823868	−	0.299864i	−0.823868	−	0.299864i
$455$		0			0
$456$		0			0
$457$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$457$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$458$	0.231520	+	0.573031i	0.231520	+	0.573031i
$459$		0			0
$460$	−1.67959	−	0.236051i	−1.67959	−	0.236051i
$461$	−1.18161	+	1.31232i	−1.18161	+	1.31232i	−0.241922	+	0.970296i	$0.577778\pi$
$461$	−1.18161	+	1.31232i	−1.18161	+	1.31232i	−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	−0.669131	−	0.743145i	$-0.733333\pi$
$463$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	0.615661	+	0.788011i	$0.288889\pi$
$464$	−0.0696290	+	0.00486893i	−0.0696290	+	0.00486893i
$465$		0			0
$466$		0			0
$467$	−0.454664	−	1.82356i	−0.454664	−	1.82356i	−0.559193	−	0.829038i	$-0.688889\pi$
$467$	−0.454664	−	1.82356i	−0.454664	−	1.82356i	0.104528	−	0.994522i	$-0.466667\pi$
$468$		0			0
$469$	0.549658	+	0.399350i	0.549658	+	0.399350i
$470$	−1.71690	+	0.624902i	−1.71690	+	0.624902i
$471$		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	$-0.733333\pi$
$479$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$480$	0.748346	+	1.10947i	0.748346	+	1.10947i
$481$		0			0
$482$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$483$	−0.668516	−	0.417735i	−0.668516	−	0.417735i
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$	−1.08531	+	0.678176i	−1.08531	+	0.678176i
$487$	1.55535	−	1.13003i	1.55535	−	1.13003i	0.615661	−	0.788011i	$-0.288889\pi$
$487$	1.55535	−	1.13003i	1.55535	−	1.13003i	0.939693	−	0.342020i	$-0.111111\pi$
$488$	−1.99027	−	0.139173i	−1.99027	−	0.139173i
$489$	0.995023	+	0.621760i	0.995023	+	0.621760i
$490$	−0.877243	+	0.0613428i	−0.877243	+	0.0613428i
$491$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$491$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$492$	1.68294	+	1.86909i	1.68294	+	1.86909i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.523846	+	2.10103i	−0.523846	+	2.10103i
$499$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$499$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$500$	0.766044	+	0.642788i	0.766044	+	0.642788i
$501$	−1.21085	−	0.879734i	−1.21085	−	0.879734i
$502$		0			0
$503$	−0.473271	−	0.100597i	−0.473271	−	0.100597i	−0.0348995	−	0.999391i	$-0.511111\pi$
$503$	−0.473271	−	0.100597i	−0.473271	−	0.100597i	−0.438371	+	0.898794i	$0.644444\pi$
$504$	0.0476997	+	0.270518i	0.0476997	+	0.270518i
$505$	0.885740	−	1.13369i	0.885740	−	1.13369i
$506$		0			0
$507$	1.30902	+	0.278240i	1.30902	+	0.278240i
$508$	−0.473442	+	1.45710i	−0.473442	+	1.45710i
$509$	−1.74871	−	0.929805i	−1.74871	−	0.929805i	−0.939693	−	0.342020i	$-0.888889\pi$
$509$	−1.74871	−	0.929805i	−1.74871	−	0.929805i	−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
$515$	−1.28642	−	0.368875i	−1.28642	−	0.368875i
$516$	−0.277050	−	2.63596i	−0.277050	−	2.63596i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$521$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$522$	−0.00192670	−	0.0551734i	−0.00192670	−	0.0551734i
$523$	0.823868	+	1.68918i	0.823868	+	1.68918i	0.719340	+	0.694658i	$0.244444\pi$
$523$	0.823868	+	1.68918i	0.823868	+	1.68918i	0.104528	+	0.994522i	$0.466667\pi$
$524$		0			0
$525$	0.203743	+	0.417735i	0.203743	+	0.417735i
$526$	0.317271	+	1.79933i	0.317271	+	1.79933i
$527$		0			0
$528$		0			0
$529$	−0.703040	−	1.74009i	−0.703040	−	1.74009i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.283849	+	0.581978i	−0.283849	+	0.581978i
$535$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$536$	0.978148	−	1.69420i	0.978148	−	1.69420i
$537$		0			0
$538$	1.49861	−	0.318539i	1.49861	−	0.318539i
$539$		0			0
$540$	0.237261	−	0.148257i	0.237261	−	0.148257i
$541$	−1.23132	+	1.57602i	−1.23132	+	1.57602i	−0.615661	+	0.788011i	$0.711111\pi$
$541$	−1.23132	+	1.57602i	−1.23132	+	1.57602i	−0.615661	+	0.788011i	$0.711111\pi$
$542$		0			0
$543$	0.962665	+	0.929634i	0.962665	+	0.929634i
$544$		0			0
$545$	−0.688547	+	0.881300i	−0.688547	+	0.881300i
$546$		0			0
$547$	0.0168859	+	0.0677257i	0.0168859	+	0.0677257i	0.978148	−	0.207912i	$-0.0666667\pi$
$547$	0.0168859	+	0.0677257i	0.0168859	+	0.0677257i	−0.961262	+	0.275637i	$0.911111\pi$
$548$		0			0
$549$	0.164949	−	1.56939i	0.164949	−	1.56939i
$550$		0			0
$551$		0			0
$552$	−0.995023	+	2.04010i	−0.995023	+	2.04010i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$557$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$558$		0			0
$559$		0			0
$560$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$561$		0			0
$562$	−1.92252			−1.92252
$563$	0.774117	+	1.58718i	0.774117	+	1.58718i	0.809017	+	0.587785i	$0.200000\pi$
$563$	0.774117	+	1.58718i	0.774117	+	1.58718i	−0.0348995	+	0.999391i	$0.511111\pi$
$564$	0.0853336	+	2.44364i	0.0853336	+	2.44364i
$565$		0			0
$566$	0.345600	−	0.512373i	0.345600	−	0.512373i
$567$	0.400784	−	0.0563265i	0.400784	−	0.0563265i
$568$		0			0
$569$	0.882948	+	1.52931i	0.882948	+	1.52931i	0.848048	+	0.529919i	$0.177778\pi$
$569$	0.882948	+	1.52931i	0.882948	+	1.52931i	0.0348995	+	0.999391i	$0.488889\pi$
$570$		0			0
$571$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$571$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$572$		0			0
$573$		0			0
$574$	−0.201697	−	0.620758i	−0.201697	−	0.620758i
$575$	−0.294524	+	1.67033i	−0.294524	+	1.67033i
$576$	0.760303	−	0.218013i	0.760303	−	0.218013i
$577$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$577$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$578$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$579$		0			0
$580$	0.00243595	+	0.0697565i	0.00243595	+	0.0697565i
$581$	0.345963	−	0.442813i	0.345963	−	0.442813i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0305979	+	0.876208i	−0.0305979	+	0.876208i	0.882948	+	0.469472i	$0.155556\pi$
$587$	−0.0305979	+	0.876208i	−0.0305979	+	0.876208i	−0.913545	+	0.406737i	$0.866667\pi$
$588$	−0.284705	+	1.14189i	−0.284705	+	1.14189i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$593$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$594$		0			0
$595$		0			0
$596$	1.76159	−	0.123183i	1.76159	−	0.123183i
$597$		0			0
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	1.13491	−	0.709170i	1.13491	−	0.709170i
$601$	0.184586	−	0.0981463i	0.184586	−	0.0981463i	−0.374607	−	0.927184i	$-0.622222\pi$
$601$	0.184586	−	0.0981463i	0.184586	−	0.0981463i	0.559193	+	0.829038i	$0.311111\pi$
$602$	−0.212552	+	0.654168i	−0.212552	+	0.654168i
$603$	1.31220	+	0.819954i	1.31220	+	0.819954i
$604$		0			0
$605$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$606$	−1.07663	−	1.59617i	−1.07663	−	1.59617i
$607$	−0.232387	−	0.258091i	−0.232387	−	0.258091i	0.615661	−	0.788011i	$-0.288889\pi$
$607$	−0.232387	−	0.258091i	−0.232387	−	0.258091i	−0.848048	+	0.529919i	$0.822222\pi$
$608$		0			0
$609$	−0.0121525	+	0.0300785i	−0.0121525	+	0.0300785i
$610$	−0.208548	+	1.98420i	−0.208548	+	1.98420i
$611$		0			0
$612$		0			0
$613$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$613$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$614$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$615$	1.92668	−	1.61668i	1.92668	−	1.61668i
$616$		0			0
$617$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$617$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$618$	−1.00148	+	1.48476i	−1.00148	+	1.48476i
$619$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$619$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$620$		0			0
$621$	0.418978	+	0.222774i	0.418978	+	0.222774i
$622$		0			0
$623$	0.128724	−	0.108012i	0.128724	−	0.108012i
$624$		0			0
$625$	0.669131	−	0.743145i	0.669131	−	0.743145i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.272018	−	0.0382297i	0.272018	−	0.0382297i
$631$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$631$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.43969	+	0.524005i	1.43969	+	0.524005i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.961262	+	0.275637i	−0.961262	+	0.275637i
$641$	−0.741922	−	0.104270i	−0.741922	−	0.104270i	−0.241922	−	0.970296i	$-0.577778\pi$
$641$	−0.741922	−	0.104270i	−0.741922	−	0.104270i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	−0.553432	+	0.614648i	−0.553432	+	0.614648i
$643$	−0.615661	−	0.788011i	−0.615661	−	0.788011i	0.374607	−	0.927184i	$-0.377778\pi$
$643$	−0.615661	−	0.788011i	−0.615661	−	0.788011i	−0.990268	+	0.139173i	$0.955556\pi$
$644$	0.451237	−	0.378633i	0.451237	−	0.378633i
$645$	−2.64402	+	0.184888i	−2.64402	+	0.184888i
$646$		0			0
$647$	1.38295	−	1.33550i	1.38295	−	1.33550i	0.500000	−	0.866025i	$-0.333333\pi$
$647$	1.38295	−	1.33550i	1.38295	−	1.33550i	0.882948	−	0.469472i	$-0.155556\pi$
$648$	−0.281924	−	1.13074i	−0.281924	−	1.13074i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.671624	+	0.563559i	−0.671624	+	0.563559i
$653$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$653$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$654$	0.836940	+	1.24081i	0.836940	+	1.24081i
$655$		0			0
$656$	−1.71690	+	0.764415i	−1.71690	+	0.764415i
$657$		0			0
$658$	0.237704	−	0.588337i	0.237704	−	0.588337i
$659$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$659$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$660$		0			0
$661$	−0.116903	−	0.173316i	−0.116903	−	0.173316i	0.766044	−	0.642788i	$-0.222222\pi$
$661$	−0.116903	−	0.173316i	−0.116903	−	0.173316i	−0.882948	+	0.469472i	$0.844444\pi$
$662$		0			0
$663$		0			0
$664$	−1.37217	−	0.857427i	−1.37217	−	0.857427i
$665$		0			0
$666$		0			0
$667$	−0.100397	+	0.0627349i	−0.100397	+	0.0627349i
$668$	0.904793	−	0.657371i	0.904793	−	0.657371i
$669$	1.00020	+	0.0699408i	1.00020	+	0.0699408i
$670$	−1.65903	−	1.03668i	−1.65903	−	1.03668i
$671$		0			0
$672$	−0.460250	−	0.0646839i	−0.460250	−	0.0646839i
$673$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$673$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$674$		0			0
$675$	−0.139886	−	0.242290i	−0.139886	−	0.242290i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$677$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.898808	+	0.754189i	0.898808	+	0.754189i
$682$		0			0
$683$	1.97571	+	0.138155i	1.97571	+	0.138155i	0.997564	−	0.0697565i	$-0.0222222\pi$
$683$	1.97571	+	0.138155i	1.97571	+	0.138155i	0.978148	+	0.207912i	$0.0666667\pi$
$684$		0			0
$685$		0			0
$686$	0.401844	−	0.514337i	0.401844	−	0.514337i
$687$	−0.0288651	−	0.826587i	−0.0288651	−	0.826587i
$688$	1.93726	+	0.411777i	1.93726	+	0.411777i
$689$		0			0
$690$	2.00413	+	1.06562i	2.00413	+	1.06562i
$691$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$691$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$692$		0			0
$693$		0			0
$694$	−0.200958	−	1.91199i	−0.200958	−	1.91199i
$695$		0			0
$696$	0.0897908	+	0.0257471i	0.0897908	+	0.0257471i
$697$		0			0
$698$	0.913545	+	1.58231i	0.913545	+	1.58231i
$699$		0			0
$700$	−0.343916	+	0.0483343i	−0.343916	+	0.0483343i
$701$	0.490268	−	0.726852i	0.490268	−	0.726852i	−0.500000	−	0.866025i	$-0.666667\pi$
$701$	0.490268	−	0.726852i	0.490268	−	0.726852i	0.990268	+	0.139173i	$0.0444444\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	2.44512			2.44512
$706$		0			0
$707$	0.0867630	+	0.492057i	0.0867630	+	0.492057i
$708$		0			0
$709$	1.27028	−	1.22669i	1.27028	−	1.22669i	0.309017	−	0.951057i	$-0.400000\pi$
$709$	1.27028	−	1.22669i	1.27028	−	1.22669i	0.961262	−	0.275637i	$-0.0888889\pi$
$710$		0			0
$711$		0			0
$712$	−0.348048	−	0.336106i	−0.348048	−	0.336106i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$719$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$720$	−0.191346	−	0.767449i	−0.191346	−	0.767449i
$721$	0.394150	−	0.246292i	0.394150	−	0.246292i
$722$	0.615661	−	0.788011i	0.615661	−	0.788011i
$723$	1.33826			1.33826
$724$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$725$	0.0697990			0.0697990
$726$	−0.823916	+	1.05456i	−0.823916	+	1.05456i
$727$	−0.524123	+	0.327508i	−0.524123	+	0.327508i	−0.766044	−	0.642788i	$-0.777778\pi$
$727$	−0.524123	+	0.327508i	−0.524123	+	0.327508i	0.241922	+	0.970296i	$0.422222\pi$
$728$		0			0
$729$	0.535358	−	0.113794i	0.535358	−	0.113794i
$730$		0			0
$731$		0			0
$732$	2.43917	+	1.08599i	2.43917	+	1.08599i
$733$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$733$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$734$	0.876742	−	1.79759i	0.876742	−	1.79759i
$735$	1.13126	+	0.324383i	1.13126	+	0.324383i
$736$	−1.22007	−	1.17821i	−1.22007	−	1.17821i
$737$		0			0
$738$	−0.556848	−	1.37825i	−0.556848	−	1.37825i
$739$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$739$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.11839			−1.11839			−0.559193	−	0.829038i	$-0.688889\pi$
$743$	−1.11839			−1.11839			−0.559193	+	0.829038i	$0.688889\pi$
$744$		0			0
$745$	−0.0616289	−	1.76482i	−0.0616289	−	1.76482i
$746$		0			0
$747$	0.715640	−	1.06098i	0.715640	−	1.06098i
$748$		0			0
$749$	0.196084	−	0.0873023i	0.196084	−	0.0873023i
$750$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$751$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$751$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$752$	−1.75631	−	0.503615i	−1.75631	−	0.503615i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.0168724	+	0.0956879i	−0.0168724	+	0.0956879i
$757$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$757$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.0682737	−	1.95510i	−0.0682737	−	1.95510i	−0.241922	−	0.970296i	$-0.577778\pi$
$761$	−0.0682737	−	1.95510i	−0.0682737	−	1.95510i	0.173648	−	0.984808i	$-0.444444\pi$
$762$	1.26231	−	1.61569i	1.26231	−	1.61569i
$763$	−0.0674469	−	0.382510i	−0.0674469	−	0.382510i
$764$		0			0
$765$		0			0
$766$	0.391438	+	0.284396i	0.391438	+	0.284396i
$767$		0			0
$768$	−0.0467046	+	1.33745i	−0.0467046	+	1.33745i
$769$	0.297884	−	1.19475i	0.297884	−	1.19475i	−0.615661	−	0.788011i	$-0.711111\pi$
$769$	0.297884	−	1.19475i	0.297884	−	1.19475i	0.913545	−	0.406737i	$-0.133333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	−0.378969	+	1.51996i	−0.378969	+	1.51996i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.410323	+	0.256398i	0.410323	+	0.256398i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.00603444	−	0.0185721i	0.00603444	−	0.0185721i
$784$	−0.745761	−	0.466003i	−0.745761	−	0.466003i
$785$		0			0
$786$		0			0
$787$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.615661	+	0.788011i	$0.288889\pi$
$787$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	0.424591	−	2.40798i	0.424591	−	2.40798i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$797$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$798$		0			0
$799$		0			0
$800$	0.241922	+	0.970296i	0.241922	+	0.970296i
$801$	0.275286	−	0.265841i	0.275286	−	0.265841i
$802$	−1.08719	−	0.578071i	−1.08719	−	0.578071i
$803$		0			0
$804$	−2.00553	+	1.68284i	−2.00553	+	1.68284i
$805$	−0.362654	−	0.464176i	−0.362654	−	0.464176i
$806$		0			0
$807$	−2.03038	−	0.285351i	−2.03038	−	0.285351i
$808$	1.38295	−	0.396554i	1.38295	−	0.396554i
$809$	0.732841	+	1.81385i	0.732841	+	1.81385i	0.559193	+	0.829038i	$0.311111\pi$
$809$	0.732841	+	1.81385i	0.732841	+	1.81385i	0.173648	+	0.984808i	$0.444444\pi$
$810$	−1.13989	+	0.242290i	−1.13989	+	0.242290i
$811$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$811$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$812$	−0.0185696	−	0.0155818i	−0.0185696	−	0.0155818i
$813$		0			0
$814$		0			0
$815$	0.539776	+	0.690882i	0.539776	+	0.690882i
$816$		0			0
$817$		0			0
$818$	0.990268	−	0.139173i	0.990268	−	0.139173i
$819$		0			0
$820$	0.704030	+	1.74254i	0.704030	+	1.74254i
$821$	1.90381	−	0.545910i	1.90381	−	0.545910i	0.913545	−	0.406737i	$-0.133333\pi$
$821$	1.90381	−	0.545910i	1.90381	−	0.545910i	0.990268	−	0.139173i	$-0.0444444\pi$
$822$		0			0
$823$	−1.13491	+	1.26045i	−1.13491	+	1.26045i	−0.173648	+	0.984808i	$0.555556\pi$
$823$	−1.13491	+	1.26045i	−1.13491	+	1.26045i	−0.961262	+	0.275637i	$0.911111\pi$
$824$	−0.823916	−	1.05456i	−0.823916	−	1.05456i
$825$		0			0
$826$		0			0
$827$	−1.27028	−	0.675419i	−1.27028	−	0.675419i	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	−1.27028	−	0.675419i	−1.27028	−	0.675419i	−0.961262	+	0.275637i	$0.911111\pi$
$828$	0.965006	−	0.931895i	0.965006	−	0.931895i
$829$	0.391438	+	1.56997i	0.391438	+	1.56997i	0.766044	+	0.642788i	$0.222222\pi$
$829$	0.391438	+	1.56997i	0.391438	+	1.56997i	−0.374607	+	0.927184i	$0.622222\pi$
$830$	−0.904793	+	1.34141i	−0.904793	+	1.34141i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.625393	−	0.927184i	−0.625393	−	0.927184i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$839$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$840$	−0.0807070	+	0.457712i	−0.0807070	+	0.457712i
$841$	−0.665871	−	0.739524i	−0.665871	−	0.739524i
$842$	0.987476	+	1.46399i	0.987476	+	1.46399i
$843$	2.41768	+	0.879963i	2.41768	+	0.879963i
$844$		0			0
$845$	0.848048	+	0.529919i	0.848048	+	0.529919i
$846$	0.446568	−	1.37440i	0.446568	−	1.37440i
$847$	0.306644	−	0.163046i	0.306644	−	0.163046i
$848$		0			0
$849$	−0.669131	+	0.486152i	−0.669131	+	0.486152i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$853$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$854$	−0.463641	−	0.514926i	−0.463641	−	0.514926i
$855$		0			0
$856$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$859$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$860$	0.479135	−	1.92171i	0.479135	−	1.92171i
$861$	−0.0304843	+	0.872956i	−0.0304843	+	0.872956i
$862$		0			0
$863$	−1.16392	−	0.845635i	−1.16392	−	0.845635i	−0.173648	−	0.984808i	$-0.555556\pi$
$863$	−1.16392	−	0.845635i	−1.16392	−	0.845635i	−0.990268	+	0.139173i	$0.955556\pi$
$864$	0.279091	+	0.0195160i	0.279091	+	0.0195160i
$865$		0			0
$866$		0			0
$867$	0.823916	−	1.05456i	0.823916	−	1.05456i
$868$		0			0
$869$		0			0
$870$	0.0288651	−	0.0888375i	0.0288651	−	0.0888375i
$871$		0			0
$872$	−1.07506	+	0.308269i	−1.07506	+	0.308269i
$873$		0			0
$874$		0			0
$875$	0.0363024	+	0.345394i	0.0363024	+	0.345394i
$876$		0			0
$877$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$877$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.868210	−	0.122019i	0.868210	−	0.122019i	0.309017	−	0.951057i	$-0.400000\pi$
$881$	0.868210	−	0.122019i	0.868210	−	0.122019i	0.559193	+	0.829038i	$0.311111\pi$
$882$	0.388943	−	0.576632i	0.388943	−	0.576632i
$883$	1.23949	−	0.900539i	1.23949	−	0.900539i	0.241922	−	0.970296i	$-0.422222\pi$
$883$	1.23949	−	0.900539i	1.23949	−	0.900539i	0.997564	+	0.0697565i	$0.0222222\pi$
$884$		0			0
$885$		0			0
$886$	1.53209			1.53209
$887$	0.874607	+	1.79321i	0.874607	+	1.79321i	0.500000	+	0.866025i	$0.333333\pi$
$887$	0.874607	+	1.79321i	0.874607	+	1.79321i	0.374607	+	0.927184i	$0.377778\pi$
$888$		0			0
$889$	−0.469807	+	0.249801i	−0.469807	+	0.249801i
$890$	−0.348048	+	0.336106i	−0.348048	+	0.336106i
$891$		0			0
$892$	−0.280660	+	0.694658i	−0.280660	+	0.694658i
$893$		0			0
$894$	−2.27168	−	0.651394i	−2.27168	−	0.651394i
$895$		0			0
$896$	0.152245	−	0.312148i	0.152245	−	0.312148i
$897$		0			0
$898$	−0.615661	+	1.06636i	−0.615661	+	1.06636i
$899$		0			0
$900$	−0.773659	+	0.164446i	−0.773659	+	0.164446i
$901$		0			0
$902$		0			0
$903$	0.566717	−	0.725364i	0.566717	−	0.725364i
$904$		0			0
$905$	0.438371	+	0.898794i	0.438371	+	0.898794i
$906$		0			0
$907$	0.0429726	−	0.0550024i	0.0429726	−	0.0550024i	−0.766044	−	0.642788i	$-0.777778\pi$
$907$	0.0429726	−	0.0550024i	0.0429726	−	0.0550024i	0.809017	+	0.587785i	$0.200000\pi$
$908$	−0.743520	+	0.464603i	−0.743520	+	0.464603i
$909$	0.275286	+	1.10411i	0.275286	+	1.10411i
$910$		0			0
$911$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$911$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.17045	−	2.39978i	1.17045	−	2.39978i
$916$	0.594092	+	0.170353i	0.594092	+	0.170353i
$917$		0			0
$918$		0			0
$919$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$919$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$920$	−1.22007	+	1.17821i	−1.22007	+	1.17821i
$921$	0.247025	−	0.131345i	0.247025	−	0.131345i
$922$	0.306644	+	1.73907i	0.306644	+	1.73907i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.00243595	+	0.0697565i	0.00243595	+	0.0697565i
$927$	0.856335	−	0.622164i	0.856335	−	0.622164i
$928$	−0.0390311	+	0.0578660i	−0.0390311	+	0.0578660i
$929$	−1.60229	+	0.225187i	−1.60229	+	0.225187i	−0.882948	−	0.469472i	$-0.844444\pi$
$929$	−1.60229	+	0.225187i	−1.60229	+	0.225187i	−0.719340	+	0.694658i	$0.755556\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.71690	−	0.764415i	−1.71690	−	0.764415i
$935$		0			0
$936$		0			0
$937$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$937$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$938$	0.653095	−	0.187272i	0.653095	−	0.187272i
$939$		0			0
$940$	−0.564602	+	1.73767i	−0.564602	+	1.73767i
$941$	1.95153	+	0.414810i	1.95153	+	0.414810i	0.990268	+	0.139173i	$0.0444444\pi$
$941$	1.95153	+	0.414810i	1.95153	+	0.414810i	0.961262	+	0.275637i	$0.0888889\pi$
$942$		0			0
$943$	−1.96249	+	2.51188i	−1.96249	+	2.51188i
$944$		0			0
$945$	0.0950408	+	0.0202015i	0.0950408	+	0.0202015i
$946$		0			0
$947$	−0.391438	−	0.284396i	−0.391438	−	0.284396i	0.374607	−	0.927184i	$-0.377778\pi$
$947$	−0.391438	−	0.284396i	−0.391438	−	0.284396i	−0.766044	+	0.642788i	$0.777778\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$953$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.33500	+	0.0933524i	1.33500	+	0.0933524i
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$	0.431611	−	0.229492i	0.431611	−	0.229492i
$964$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$965$		0			0
$966$	−0.740760	+	0.269615i	−0.740760	+	0.269615i
$967$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.978148	+	0.207912i	$0.0666667\pi$
$967$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.882948	+	0.469472i	$0.155556\pi$
$968$	−0.559193	−	0.829038i	−0.559193	−	0.829038i
$969$		0			0
$970$		0			0
$971$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$971$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$972$	−0.133773	+	1.27276i	−0.133773	+	1.27276i
$973$		0			0
$974$	0.0670951	−	1.92135i	0.0670951	−	1.92135i
$975$		0			0
$976$	−1.33500	+	1.48267i	−1.33500	+	1.48267i
$977$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$977$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$978$	1.10255	−	0.401296i	1.10255	−	0.401296i
$979$		0			0
$980$	−0.491746	+	0.729043i	−0.491746	+	0.729043i
$981$	−0.213999	−	0.858304i	−0.213999	−	0.858304i
$982$		0			0
$983$	−0.882948	−	0.469472i	−0.882948	−	0.469472i	−0.0348995	−	0.999391i	$-0.511111\pi$
$983$	−0.882948	−	0.469472i	−0.882948	−	0.469472i	−0.848048	+	0.529919i	$0.822222\pi$
$984$	2.50898	−	0.175445i	2.50898	−	0.175445i
$985$		0			0
$986$		0			0
$987$	−0.568214	+	0.631066i	−0.568214	+	0.631066i
$988$		0			0
$989$	3.22905	−	0.925915i	3.22905	−	0.925915i
$990$		0			0
$991$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$991$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.33312	+	1.70632i	1.33312	+	1.70632i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		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.2479.1	✓	24
4.3	odd	2		3620.1.dy.b.2479.1	yes	24
5.4	even	2		3620.1.dy.b.2479.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.2479.1	✓	24
181.102	even	45	inner	3620.1.dy.a.3179.1	yes	24
724.283	odd	90		3620.1.dy.b.3179.1	yes	24
905.464	even	90		3620.1.dy.b.3179.1	yes	24
3620.3179	odd	90	inner	3620.1.dy.a.3179.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.2479.1	✓	24	1.1	even	1	trivial
3620.1.dy.a.2479.1	✓	24	20.19	odd	2	CM
3620.1.dy.a.3179.1	yes	24	181.102	even	45	inner
3620.1.dy.a.3179.1	yes	24	3620.3179	odd	90	inner
3620.1.dy.b.2479.1	yes	24	4.3	odd	2
3620.1.dy.b.2479.1	yes	24	5.4	even	2
3620.1.dy.b.3179.1	yes	24	724.283	odd	90
3620.1.dy.b.3179.1	yes	24	905.464	even	90

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)

\(f(q)\)	\(=\)	\(q+(0.615661 - 0.788011i) q^{2} +(-1.13491 + 0.709170i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(-0.139886 + 1.33093i) q^{6} +(0.173648 - 0.300767i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(0.346727 - 0.710895i) q^{9} +O(q^{10})\)	\(q+(0.615661 - 0.788011i) q^{2} +(-1.13491 + 0.709170i) q^{3} +(-0.241922 - 0.970296i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(-0.139886 + 1.33093i) q^{6} +(0.173648 - 0.300767i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(0.346727 - 0.710895i) q^{9} +(-0.438371 + 0.898794i) q^{10} +(0.962665 + 0.929634i) q^{12} +(-0.130100 - 0.322008i) q^{14} +(0.962665 - 0.929634i) q^{15} +(-0.882948 + 0.469472i) q^{16} +(-0.346727 - 0.710895i) q^{18} +(0.438371 + 0.898794i) q^{20} +(0.0162204 + 0.464490i) q^{21} +(-0.948445 + 1.40613i) q^{23} +(1.32524 - 0.186250i) q^{24} +(0.913545 - 0.406737i) q^{25} +(-0.0292442 - 0.278240i) q^{27} +(-0.333843 - 0.0957278i) q^{28} +(0.0637646 + 0.0283898i) q^{29} +(-0.139886 - 1.33093i) q^{30} +(-0.173648 + 0.984808i) q^{32} +(-0.107320 + 0.330298i) q^{35} +(-0.773659 - 0.164446i) q^{36} +(0.978148 + 0.207912i) q^{40} +(1.87481 + 0.131099i) q^{41} +(0.376009 + 0.273187i) q^{42} +(-1.51718 - 1.27306i) q^{43} +(-0.191346 + 0.767449i) q^{45} +(0.524123 + 1.61308i) q^{46} +(1.31430 + 1.26920i) q^{47} +(0.669131 - 1.15897i) q^{48} +(0.439693 + 0.761570i) q^{49} +(0.241922 - 0.970296i) q^{50} +(-0.237261 - 0.148257i) q^{54} +(-0.280969 + 0.204136i) q^{56} +(0.0616289 - 0.0327686i) q^{58} +(-1.13491 - 0.709170i) q^{60} +(1.87481 - 0.682374i) q^{61} +(-0.153606 - 0.227730i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-0.204489 + 1.94558i) q^{67} +(0.0792156 - 2.26844i) q^{69} +(0.194206 + 0.287922i) q^{70} +(-0.605898 + 0.508408i) q^{72} +(-0.748346 + 1.10947i) q^{75} +(0.766044 - 0.642788i) q^{80} +(0.717462 + 0.918310i) q^{81} +(1.25755 - 1.39666i) q^{82} +(1.60229 + 0.225187i) q^{83} +(0.446769 - 0.128109i) q^{84} +(-1.93726 + 0.411777i) q^{86} +(-0.0925002 + 0.0130001i) q^{87} +(0.454664 + 0.165484i) q^{89} +(0.486953 + 0.623272i) q^{90} +(1.59381 + 0.580099i) q^{92} +(1.80931 - 0.254282i) q^{94} +(-0.501321 - 1.24081i) q^{96} +(0.870827 + 0.122387i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 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

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