LMFDB - Embedded newform 3620.1.dy.a.2859.1

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			2859.1
Root			$0.848048 + 0.529919i$ of defining polynomial
Character	$\chi$	$=$	3620.2859
Dual form			3620.1.dy.a.2759.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.438371 + 0.898794i) q^{2} +(-1.75631 - 0.503615i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.104528 + 0.994522i) q^{5} +(1.22256 - 1.35779i) q^{6} +(0.766044 - 1.32683i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.98296 + 1.23909i) q^{9} +O(q^{10})$	\(q+(-0.438371 + 0.898794i) q^{2} +(-1.75631 - 0.503615i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.104528 + 0.994522i) q^{5} +(1.22256 - 1.35779i) q^{6} +(0.766044 - 1.32683i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.98296 + 1.23909i) q^{9} +(-0.848048 - 0.529919i) q^{10} +(0.684440 + 1.69405i) q^{12} +(0.856733 + 1.27016i) q^{14} +(0.684440 - 1.69405i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-1.98296 + 1.23909i) q^{18} +(0.848048 - 0.529919i) q^{20} +(-2.01362 + 1.94453i) q^{21} +(1.69749 + 0.902570i) q^{23} +(-1.82264 - 0.127451i) q^{24} +(-0.978148 - 0.207912i) q^{25} +(-1.63611 - 1.81708i) q^{27} +(-1.51718 + 0.213226i) q^{28} +(1.40724 - 0.299118i) q^{29} +(1.22256 + 1.35779i) q^{30} +(-0.766044 - 0.642788i) q^{32} +(1.23949 + 0.900539i) q^{35} +(-0.244415 - 2.32545i) q^{36} +(0.104528 + 0.994522i) q^{40} +(0.0121205 + 0.347085i) q^{41} +(-0.865021 - 2.66226i) q^{42} +(-1.87481 + 0.682374i) q^{43} +(-1.43958 + 1.84257i) q^{45} +(-1.55535 + 1.13003i) q^{46} +(-0.732841 - 1.81385i) q^{47} +(0.913545 - 1.58231i) q^{48} +(-0.673648 - 1.16679i) q^{49} +(0.615661 - 0.788011i) q^{50} +(2.35040 - 0.673968i) q^{54} +(0.473442 - 1.45710i) q^{56} +(-0.348048 + 1.39594i) q^{58} +(-1.75631 + 0.503615i) q^{60} +(0.0121205 - 0.0687386i) q^{61} +(3.16309 - 1.68185i) q^{63} +(0.913545 - 0.406737i) q^{64} +(0.139886 - 0.155360i) q^{67} +(-2.52677 - 2.44007i) q^{69} +(-1.35275 + 0.719272i) q^{70} +(2.19725 + 0.799732i) q^{72} +(1.61323 + 0.857767i) q^{75} +(-0.939693 - 0.342020i) q^{80} +(0.933382 + 1.91372i) q^{81} +(-0.317271 - 0.141258i) q^{82} +(0.616528 - 0.0431119i) q^{83} +(2.77202 + 0.389582i) q^{84} +(0.208548 - 1.98420i) q^{86} +(-2.62220 - 0.183362i) q^{87} +(-0.213817 - 1.21262i) q^{89} +(-1.02503 - 2.10162i) q^{90} +(-0.333843 - 1.89332i) q^{92} +(1.95153 + 0.136464i) q^{94} +(1.02170 + 1.51473i) q^{96} +(1.34401 - 0.0939826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{29}{45}\right)$

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 $

$2$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$2$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$3$	−1.75631	−	0.503615i	−1.75631	−	0.503615i	−0.766044	−	0.642788i	$-0.777778\pi$
$3$	−1.75631	−	0.503615i	−1.75631	−	0.503615i	−0.990268	+	0.139173i	$0.955556\pi$
$4$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$5$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$5$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$6$	1.22256	−	1.35779i	1.22256	−	1.35779i
$7$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$7$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$8$	0.978148	−	0.207912i	0.978148	−	0.207912i
$9$	1.98296	+	1.23909i	1.98296	+	1.23909i
$10$	−0.848048	−	0.529919i	−0.848048	−	0.529919i
$11$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$11$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$12$	0.684440	+	1.69405i	0.684440	+	1.69405i
$13$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$13$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$14$	0.856733	+	1.27016i	0.856733	+	1.27016i
$15$	0.684440	−	1.69405i	0.684440	−	1.69405i
$16$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$17$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$17$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$18$	−1.98296	+	1.23909i	−1.98296	+	1.23909i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.848048	−	0.529919i	0.848048	−	0.529919i
$21$	−2.01362	+	1.94453i	−2.01362	+	1.94453i
$22$		0			0
$23$	1.69749	+	0.902570i	1.69749	+	0.902570i	0.978148	+	0.207912i	$0.0666667\pi$
$23$	1.69749	+	0.902570i	1.69749	+	0.902570i	0.719340	+	0.694658i	$0.244444\pi$
$24$	−1.82264	−	0.127451i	−1.82264	−	0.127451i
$25$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$26$		0			0
$27$	−1.63611	−	1.81708i	−1.63611	−	1.81708i
$28$	−1.51718	+	0.213226i	−1.51718	+	0.213226i
$29$	1.40724	−	0.299118i	1.40724	−	0.299118i	0.559193	−	0.829038i	$-0.311111\pi$
$29$	1.40724	−	0.299118i	1.40724	−	0.299118i	0.848048	+	0.529919i	$0.177778\pi$
$30$	1.22256	+	1.35779i	1.22256	+	1.35779i
$31$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$31$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$32$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$33$		0			0
$34$		0			0
$35$	1.23949	+	0.900539i	1.23949	+	0.900539i
$36$	−0.244415	−	2.32545i	−0.244415	−	2.32545i
$37$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$37$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$38$		0			0
$39$		0			0
$40$	0.104528	+	0.994522i	0.104528	+	0.994522i
$41$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	0.990268	+	0.139173i	$0.0444444\pi$
$41$	0.0121205	+	0.347085i	0.0121205	+	0.347085i	−0.978148	+	0.207912i	$0.933333\pi$
$42$	−0.865021	−	2.66226i	−0.865021	−	2.66226i
$43$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.913545	+	0.406737i	$0.866667\pi$
$43$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.961262	+	0.275637i	$0.911111\pi$
$44$		0			0
$45$	−1.43958	+	1.84257i	−1.43958	+	1.84257i
$46$	−1.55535	+	1.13003i	−1.55535	+	1.13003i
$47$	−0.732841	−	1.81385i	−0.732841	−	1.81385i	−0.559193	−	0.829038i	$-0.688889\pi$
$47$	−0.732841	−	1.81385i	−0.732841	−	1.81385i	−0.173648	−	0.984808i	$-0.555556\pi$
$48$	0.913545	−	1.58231i	0.913545	−	1.58231i
$49$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$50$	0.615661	−	0.788011i	0.615661	−	0.788011i
$51$		0			0
$52$		0			0
$53$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$53$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$54$	2.35040	−	0.673968i	2.35040	−	0.673968i
$55$		0			0
$56$	0.473442	−	1.45710i	0.473442	−	1.45710i
$57$		0			0
$58$	−0.348048	+	1.39594i	−0.348048	+	1.39594i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	−1.75631	+	0.503615i	−1.75631	+	0.503615i
$61$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$61$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$62$		0			0
$63$	3.16309	−	1.68185i	3.16309	−	1.68185i
$64$	0.913545	−	0.406737i	0.913545	−	0.406737i
$65$		0			0
$66$		0			0
$67$	0.139886	−	0.155360i	0.139886	−	0.155360i	−0.669131	−	0.743145i	$-0.733333\pi$
$67$	0.139886	−	0.155360i	0.139886	−	0.155360i	0.809017	+	0.587785i	$0.200000\pi$
$68$		0			0
$69$	−2.52677	−	2.44007i	−2.52677	−	2.44007i
$70$	−1.35275	+	0.719272i	−1.35275	+	0.719272i
$71$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$71$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$72$	2.19725	+	0.799732i	2.19725	+	0.799732i
$73$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$73$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$74$		0			0
$75$	1.61323	+	0.857767i	1.61323	+	0.857767i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$79$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$80$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$81$	0.933382	+	1.91372i	0.933382	+	1.91372i
$82$	−0.317271	−	0.141258i	−0.317271	−	0.141258i
$83$	0.616528	−	0.0431119i	0.616528	−	0.0431119i	0.241922	−	0.970296i	$-0.422222\pi$
$83$	0.616528	−	0.0431119i	0.616528	−	0.0431119i	0.374607	+	0.927184i	$0.377778\pi$
$84$	2.77202	+	0.389582i	2.77202	+	0.389582i
$85$		0			0
$86$	0.208548	−	1.98420i	0.208548	−	1.98420i
$87$	−2.62220	−	0.183362i	−2.62220	−	0.183362i
$88$		0			0
$89$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	−0.882948	−	0.469472i	$-0.844444\pi$
$89$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	0.669131	−	0.743145i	$-0.266667\pi$
$90$	−1.02503	−	2.10162i	−1.02503	−	2.10162i
$91$		0			0
$92$	−0.333843	−	1.89332i	−0.333843	−	1.89332i
$93$		0			0
$94$	1.95153	+	0.136464i	1.95153	+	0.136464i
$95$		0			0
$96$	1.02170	+	1.51473i	1.02170	+	1.51473i
$97$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$97$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$98$	1.34401	−	0.0939826i	1.34401	−	0.0939826i
$99$		0			0
$100$	0.438371	+	0.898794i	0.438371	+	0.898794i
$101$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.669131	−	0.743145i	$-0.266667\pi$
$101$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.0348995	+	0.999391i	$0.488889\pi$
$102$		0			0
$103$	0.442013	+	1.77282i	0.442013	+	1.77282i	0.615661	+	0.788011i	$0.288889\pi$
$103$	0.442013	+	1.77282i	0.442013	+	1.77282i	−0.173648	+	0.984808i	$0.555556\pi$
$104$		0			0
$105$	−1.72340	−	2.20585i	−1.72340	−	2.20585i
$106$		0			0
$107$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$107$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$108$	−0.424591	+	2.40798i	−0.424591	+	2.40798i
$109$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.990268	−	0.139173i	$-0.0444444\pi$
$109$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.669131	+	0.743145i	$0.266667\pi$
$110$		0			0
$111$		0			0
$112$	1.10209	+	1.06428i	1.10209	+	1.06428i
$113$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$113$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$114$		0			0
$115$	−1.07506	+	1.59384i	−1.07506	+	1.59384i
$116$	−1.10209	−	0.924765i	−1.10209	−	0.924765i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.317271	−	1.79933i	0.317271	−	1.79933i
$121$	0.961262	−	0.275637i	0.961262	−	0.275637i
$122$	0.0564686	+	0.0410268i	0.0564686	+	0.0410268i
$123$	0.153510	−	0.615693i	0.153510	−	0.615693i
$124$		0			0
$125$	0.309017	−	0.951057i	0.309017	−	0.951057i
$126$	0.125025	+	3.58024i	0.125025	+	3.58024i
$127$	1.80658	−	0.518029i	1.80658	−	0.518029i	0.809017	−	0.587785i	$-0.200000\pi$
$127$	1.80658	−	0.518029i	1.80658	−	0.518029i	0.997564	+	0.0697565i	$0.0222222\pi$
$128$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$129$	3.63640	−	0.254282i	3.63640	−	0.254282i
$130$		0			0
$131$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$131$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$132$		0			0
$133$		0			0
$134$	0.0783141	+	0.193834i	0.0783141	+	0.193834i
$135$	1.97815	−	1.43721i	1.97815	−	1.43721i
$136$		0			0
$137$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$137$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$138$	3.30079	−	1.20139i	3.30079	−	1.20139i
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$	−0.0534691	−	1.53116i	−0.0534691	−	1.53116i
$141$	0.373619	+	3.55475i	0.373619	+	3.55475i
$142$		0			0
$143$		0			0
$144$	−1.68200	+	1.62429i	−1.68200	+	1.62429i
$145$	0.150383	+	1.43080i	0.150383	+	1.43080i
$146$		0			0
$147$	0.595523	+	2.38851i	0.595523	+	2.38851i
$148$		0			0
$149$	−0.370646	−	0.311009i	−0.370646	−	0.311009i	0.438371	−	0.898794i	$-0.355556\pi$
$149$	−0.370646	−	0.311009i	−0.370646	−	0.311009i	−0.809017	+	0.587785i	$0.800000\pi$
$150$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$151$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$151$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$157$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$158$		0			0
$159$		0			0
$160$	0.719340	−	0.694658i	0.719340	−	0.694658i
$161$	2.49791	−	1.56086i	2.49791	−	1.56086i
$162$	−2.12920			−2.12920
$163$	−1.43837	+	0.898794i	−1.43837	+	0.898794i	−0.438371	+	0.898794i	$0.644444\pi$
$163$	−1.43837	+	0.898794i	−1.43837	+	0.898794i	−1.00000			$1.00000\pi$
$164$	0.266044	−	0.223238i	0.266044	−	0.223238i
$165$		0			0
$166$	−0.231520	+	0.573031i	−0.231520	+	0.573031i
$167$	0.987476	+	1.46399i	0.987476	+	1.46399i	0.882948	+	0.469472i	$0.155556\pi$
$167$	0.987476	+	1.46399i	0.987476	+	1.46399i	0.104528	+	0.994522i	$0.466667\pi$
$168$	−1.56533	+	2.32070i	−1.56533	+	2.32070i
$169$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$170$		0			0
$171$		0			0
$172$	1.69196	+	1.05726i	1.69196	+	1.05726i
$173$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$173$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$174$	1.31430	−	2.27643i	1.31430	−	2.27643i
$175$	−1.02517	+	1.13856i	−1.02517	+	1.13856i
$176$		0			0
$177$		0			0
$178$	1.18362	+	0.339399i	1.18362	+	0.339399i
$179$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$179$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$180$	2.33826			2.33826
$181$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$181$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$182$		0			0
$183$	−0.0559051	+	0.114622i	−0.0559051	+	0.114622i
$184$	1.84805	+	0.529919i	1.84805	+	0.529919i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.978148	+	1.69420i	−0.978148	+	1.69420i
$189$	−3.66429	+	0.778868i	−3.66429	+	0.778868i
$190$		0			0
$191$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$191$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$192$	−1.80931	+	0.254282i	−1.80931	+	0.254282i
$193$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$193$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$194$		0			0
$195$		0			0
$196$	−0.504706	+	1.24919i	−0.504706	+	1.24919i
$197$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$197$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$198$		0			0
$199$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$199$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$200$	−1.00000			−1.00000
$201$	−0.323926	+	0.202411i	−0.323926	+	0.202411i
$202$	−0.538939	+	0.520447i	−0.538939	+	0.520447i
$203$	0.681131	−	2.09630i	0.681131	−	2.09630i
$204$		0			0
$205$	−0.346450	−	0.0242262i	−0.346450	−	0.0242262i
$206$	−1.78716	−	0.379874i	−1.78716	−	0.379874i
$207$	2.24768	+	3.89310i	2.24768	+	3.89310i
$208$		0			0
$209$		0			0
$210$	2.73810	−	0.582000i	2.73810	−	0.582000i
$211$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$211$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$212$		0			0
$213$		0			0
$214$	−1.60229	−	0.225187i	−1.60229	−	0.225187i
$215$	−0.482665	−	1.93586i	−0.482665	−	1.93586i
$216$	−1.97815	−	1.43721i	−1.97815	−	1.43721i
$217$		0			0
$218$	−1.27028	+	1.22669i	−1.27028	+	1.22669i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.345600	−	1.06365i	−0.345600	−	1.06365i	−0.961262	−	0.275637i	$-0.911111\pi$
$223$	−0.345600	−	1.06365i	−0.345600	−	1.06365i	0.615661	−	0.788011i	$-0.288889\pi$
$224$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$225$	−1.68200	−	1.62429i	−1.68200	−	1.62429i
$226$		0			0
$227$	1.37217	−	0.996940i	1.37217	−	0.996940i	0.374607	−	0.927184i	$-0.377778\pi$
$227$	1.37217	−	0.996940i	1.37217	−	0.996940i	0.997564	−	0.0697565i	$-0.0222222\pi$
$228$		0			0
$229$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$229$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$230$	−0.961262	−	1.66495i	−0.961262	−	1.66495i
$231$		0			0
$232$	1.31430	−	0.585164i	1.31430	−	0.585164i
$233$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$233$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$234$		0			0
$235$	1.88051	−	0.539228i	1.88051	−	0.539228i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$239$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$240$	1.47815	+	1.07394i	1.47815	+	1.07394i
$241$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.719340	−	0.694658i	$-0.755556\pi$
$241$	−0.961262	+	0.275637i	−0.961262	+	0.275637i	−0.241922	+	0.970296i	$0.577778\pi$
$242$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$243$	−0.250943	−	1.42317i	−0.250943	−	1.42317i
$244$	−0.0616289	+	0.0327686i	−0.0616289	+	0.0327686i
$245$	1.23082	−	0.547995i	1.23082	−	0.547995i
$246$	0.486087	+	0.407876i	0.486087	+	0.407876i
$247$		0			0
$248$		0			0
$249$	−1.10453	−	0.234775i	−1.10453	−	0.234775i
$250$	0.719340	+	0.694658i	0.719340	+	0.694658i
$251$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$251$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$252$	−3.27271	−	1.45710i	−3.27271	−	1.45710i
$253$		0			0
$254$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$255$		0			0
$256$	−0.882948	−	0.469472i	−0.882948	−	0.469472i
$257$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$257$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$258$	−1.36555	+	3.37985i	−1.36555	+	3.37985i
$259$		0			0
$260$		0			0
$261$	3.16113	+	1.15056i	3.16113	+	1.15056i
$262$		0			0
$263$	1.78716	+	0.795697i	1.78716	+	0.795697i	0.978148	+	0.207912i	$0.0666667\pi$
$263$	1.78716	+	0.795697i	1.78716	+	0.795697i	0.809017	+	0.587785i	$0.200000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.235162	+	2.23741i	−0.235162	+	2.23741i
$268$	−0.208548	−	0.0145831i	−0.208548	−	0.0145831i
$269$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$269$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$270$	0.424591	+	2.40798i	0.424591	+	2.40798i
$271$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$271$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.367169	+	3.49338i	−0.367169	+	3.49338i
$277$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$277$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$278$		0			0
$279$		0			0
$280$	1.39963	+	0.623157i	1.39963	+	0.623157i
$281$	0.868210	+	1.78009i	0.868210	+	1.78009i	0.559193	+	0.829038i	$0.311111\pi$
$281$	0.868210	+	1.78009i	0.868210	+	1.78009i	0.309017	+	0.951057i	$0.400000\pi$
$282$	−3.35877	−	1.22249i	−3.35877	−	1.22249i
$283$	0.0564686	−	1.61705i	0.0564686	−	1.61705i	−0.559193	−	0.829038i	$-0.688889\pi$
$283$	0.0564686	−	1.61705i	0.0564686	−	1.61705i	0.615661	−	0.788011i	$-0.288889\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.469807	+	0.249801i	0.469807	+	0.249801i
$288$	−0.722562	−	2.22382i	−0.722562	−	2.22382i
$289$	0.173648	−	0.984808i	0.173648	−	0.984808i
$290$	−1.35192	−	0.492057i	−1.35192	−	0.492057i
$291$		0			0
$292$		0			0
$293$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$293$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$294$	−2.40784	−	0.511802i	−2.40784	−	0.511802i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.442013	−	0.196797i	0.442013	−	0.196797i
$299$		0			0
$300$	−0.317271	−	1.79933i	−0.317271	−	1.79933i
$301$	−0.530793	+	3.01028i	−0.530793	+	3.01028i
$302$		0			0
$303$	−1.10745	−	0.804608i	−1.10745	−	0.804608i
$304$		0			0
$305$	0.0670951	+	0.0192392i	0.0670951	+	0.0192392i
$306$		0			0
$307$	−0.0467046	−	1.33745i	−0.0467046	−	1.33745i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	−0.0467046	−	1.33745i	−0.0467046	−	1.33745i	0.719340	−	0.694658i	$-0.244444\pi$
$308$		0			0
$309$	0.116504	−	3.33623i	0.116504	−	3.33623i
$310$		0			0
$311$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$311$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$312$		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
$315$	1.34200	+	3.32157i	1.34200	+	3.32157i
$316$		0			0
$317$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$317$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$318$		0			0
$319$		0			0
$320$	0.309017	+	0.951057i	0.309017	+	0.951057i
$321$	−0.103173	−	2.95449i	−0.103173	−	2.95449i
$322$	0.307886	+	2.92934i	0.307886	+	2.92934i
$323$		0			0
$324$	0.933382	−	1.91372i	0.933382	−	1.91372i
$325$		0			0
$326$	−0.177290	−	1.68680i	−0.177290	−	1.68680i
$327$	−2.61025	−	1.89646i	−2.61025	−	1.89646i
$328$	0.0840186	+	0.336980i	0.0840186	+	0.336980i
$329$	−2.96805	−	0.417132i	−2.96805	−	0.417132i
$330$		0			0
$331$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$331$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$332$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$333$		0			0
$334$	−1.74871	+	0.245765i	−1.74871	+	0.245765i
$335$	0.139886	+	0.155360i	0.139886	+	0.155360i
$336$	−1.39963	−	2.42424i	−1.39963	−	2.42424i
$337$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$337$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$338$	0.997564	+	0.0697565i	0.997564	+	0.0697565i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.532089			−0.532089
$344$	−1.69196	+	1.05726i	−1.69196	+	1.05726i
$345$	2.69083	−	2.25787i	2.69083	−	2.25787i
$346$		0			0
$347$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.241922	−	0.970296i	$-0.422222\pi$
$347$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.500000	−	0.866025i	$-0.333333\pi$
$348$	1.46989	+	2.17921i	1.46989	+	2.17921i
$349$	−1.09395	+	1.62184i	−1.09395	+	1.62184i	−0.374607	+	0.927184i	$0.622222\pi$
$349$	−1.09395	+	1.62184i	−1.09395	+	1.62184i	−0.719340	+	0.694658i	$0.755556\pi$
$350$	−0.573931	−	1.42053i	−0.573931	−	1.42053i
$351$		0			0
$352$		0			0
$353$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$353$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$354$		0			0
$355$		0			0
$356$	−0.823916	+	0.915051i	−0.823916	+	0.915051i
$357$		0			0
$358$		0			0
$359$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$359$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$360$	−1.02503	+	2.10162i	−1.02503	+	2.10162i
$361$	1.00000			1.00000
$362$	0.978148	−	0.207912i	0.978148	−	0.207912i
$363$	−1.82709			−1.82709
$364$		0			0
$365$		0			0
$366$	−0.0785148	−	0.100494i	−0.0785148	−	0.100494i
$367$	0.209057	−	1.98904i	0.209057	−	1.98904i	0.104528	−	0.994522i	$-0.466667\pi$
$367$	0.209057	−	1.98904i	0.209057	−	1.98904i	0.104528	−	0.994522i	$-0.466667\pi$
$368$	−1.28642	+	1.42871i	−1.28642	+	1.42871i
$369$	−0.406035	+	0.703273i	−0.406035	+	0.703273i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$373$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$374$		0			0
$375$	−1.02170	+	1.51473i	−1.02170	+	1.51473i
$376$	−1.09395	−	1.62184i	−1.09395	−	1.62184i
$377$		0			0
$378$	0.906275	−	3.63487i	0.906275	−	3.63487i
$379$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$379$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$380$		0			0
$381$	−3.43381			−3.43381
$382$		0			0
$383$	−0.885740	+	0.855349i	−0.885740	+	0.855349i	−0.990268	−	0.139173i	$-0.955556\pi$
$383$	−0.885740	+	0.855349i	−0.885740	+	0.855349i	0.104528	+	0.994522i	$0.466667\pi$
$384$	0.564602	−	1.73767i	0.564602	−	1.73767i
$385$		0			0
$386$		0			0
$387$	−4.56319	−	0.969935i	−4.56319	−	0.969935i
$388$		0			0
$389$	−0.823916	−	0.915051i	−0.823916	−	0.915051i	0.173648	−	0.984808i	$-0.444444\pi$
$389$	−0.823916	−	0.915051i	−0.823916	−	0.915051i	−0.997564	+	0.0697565i	$0.977778\pi$
$390$		0			0
$391$		0			0
$392$	−0.901517	−	1.00124i	−0.901517	−	1.00124i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$397$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$398$		0			0
$399$		0			0
$400$	0.438371	−	0.898794i	0.438371	−	0.898794i
$401$	0.671624	−	0.563559i	0.671624	−	0.563559i	−0.241922	−	0.970296i	$-0.577778\pi$
$401$	0.671624	−	0.563559i	0.671624	−	0.563559i	0.913545	+	0.406737i	$0.133333\pi$
$402$	−0.0399263	−	0.379874i	−0.0399263	−	0.379874i
$403$		0			0
$404$	−0.231520	−	0.712544i	−0.231520	−	0.712544i
$405$	−2.00080	+	0.728231i	−2.00080	+	0.728231i
$406$	1.58556	+	1.53116i	1.58556	+	1.53116i
$407$		0			0
$408$		0			0
$409$	0.374607	+	0.927184i	0.374607	+	0.927184i	0.990268	+	0.139173i	$0.0444444\pi$
$409$	0.374607	+	0.927184i	0.374607	+	0.927184i	−0.615661	+	0.788011i	$0.711111\pi$
$410$	0.173648	−	0.300767i	0.173648	−	0.300767i
$411$		0			0
$412$	1.12487	−	1.43977i	1.12487	−	1.43977i
$413$		0			0
$414$	−4.48441	+	0.313581i	−4.48441	+	0.313581i
$415$	−0.0215691	+	0.617657i	−0.0215691	+	0.617657i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$419$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$420$	−0.677204	+	2.71612i	−0.677204	+	2.71612i
$421$	0.391438	+	0.284396i	0.391438	+	0.284396i	0.766044	−	0.642788i	$-0.222222\pi$
$421$	0.391438	+	0.284396i	0.391438	+	0.284396i	−0.374607	+	0.927184i	$0.622222\pi$
$422$		0			0
$423$	0.794324	−	4.50483i	0.794324	−	4.50483i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.0819195	−	0.0687386i	−0.0819195	−	0.0687386i
$428$	0.904793	−	1.34141i	0.904793	−	1.34141i
$429$		0			0
$430$	1.95153	+	0.414810i	1.95153	+	0.414810i
$431$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$431$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$432$	2.15892	−	1.14792i	2.15892	−	1.14792i
$433$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$433$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$434$		0			0
$435$	0.456451	−	2.58866i	0.456451	−	2.58866i
$436$	−0.545692	−	1.67947i	−0.545692	−	1.67947i
$437$		0			0
$438$		0			0
$439$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$439$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$440$		0			0
$441$	0.109945	−	3.14841i	0.109945	−	3.14841i
$442$		0			0
$443$	0.823868	+	1.68918i	0.823868	+	1.68918i	0.719340	+	0.694658i	$0.244444\pi$
$443$	0.823868	+	1.68918i	0.823868	+	1.68918i	0.104528	+	0.994522i	$0.466667\pi$
$444$		0			0
$445$	1.22832	−	0.0858927i	1.22832	−	0.0858927i
$446$	1.10750	+	0.155649i	1.10750	+	0.155649i
$447$	0.494341	+	0.732891i	0.494341	+	0.732891i
$448$	0.160147	−	1.52370i	0.160147	−	1.52370i
$449$	−0.874607	−	0.0611585i	−0.874607	−	0.0611585i	−0.374607	−	0.927184i	$-0.622222\pi$
$449$	−0.874607	−	0.0611585i	−0.874607	−	0.0611585i	−0.500000	+	0.866025i	$0.666667\pi$
$450$	2.19725	−	0.799732i	2.19725	−	0.799732i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.294524	+	1.67033i	0.294524	+	1.67033i
$455$		0			0
$456$		0			0
$457$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$457$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$458$	0.904793	+	1.34141i	0.904793	+	1.34141i
$459$		0			0
$460$	1.91784	−	0.134108i	1.91784	−	0.134108i
$461$	−0.442013	−	0.196797i	−0.442013	−	0.196797i	0.173648	−	0.984808i	$-0.444444\pi$
$461$	−0.442013	−	0.196797i	−0.442013	−	0.196797i	−0.615661	+	0.788011i	$0.711111\pi$
$462$		0			0
$463$	−1.35192	−	0.492057i	−1.35192	−	0.492057i	−0.438371	−	0.898794i	$-0.644444\pi$
$463$	−1.35192	−	0.492057i	−1.35192	−	0.492057i	−0.913545	+	0.406737i	$0.866667\pi$
$464$	−0.0502092	+	1.43780i	−0.0502092	+	1.43780i
$465$		0			0
$466$		0			0
$467$	0.213817	+	0.273673i	0.213817	+	0.273673i	0.882948	−	0.469472i	$-0.155556\pi$
$467$	0.213817	+	0.273673i	0.213817	+	0.273673i	−0.669131	+	0.743145i	$0.733333\pi$
$468$		0			0
$469$	−0.0989762	−	0.304617i	−0.0989762	−	0.304617i
$470$	−0.339707	+	1.92657i	−0.339707	+	1.92657i
$471$		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		0.913545	−	0.406737i	$-0.133333\pi$
$479$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$480$	−1.61323	+	0.857767i	−1.61323	+	0.857767i
$481$		0			0
$482$	0.173648	−	0.984808i	0.173648	−	0.984808i
$483$	−5.17318	+	1.48338i	−5.17318	+	1.48338i
$484$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$485$		0			0
$486$	1.38914	+	0.398330i	1.38914	+	0.398330i
$487$	−0.612019	+	1.88360i	−0.612019	+	1.88360i	−0.173648	+	0.984808i	$0.555556\pi$
$487$	−0.612019	+	1.88360i	−0.612019	+	1.88360i	−0.438371	+	0.898794i	$0.644444\pi$
$488$	−0.00243595	−	0.0697565i	−0.00243595	−	0.0697565i
$489$	2.97887	−	0.854179i	2.97887	−	0.854179i
$490$	−0.0470200	+	1.34648i	−0.0470200	+	1.34648i
$491$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$491$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$492$	−0.579683	+	0.258091i	−0.579683	+	0.258091i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.695208	−	0.889825i	0.695208	−	0.889825i
$499$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$499$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$500$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$501$	−0.997028	−	3.06854i	−0.997028	−	3.06854i
$502$		0			0
$503$	−0.128708	−	1.22458i	−0.128708	−	1.22458i	−0.848048	−	0.529919i	$-0.822222\pi$
$503$	−0.128708	−	1.22458i	−0.128708	−	1.22458i	0.719340	−	0.694658i	$-0.244444\pi$
$504$	2.74430	−	2.30274i	2.74430	−	2.30274i
$505$	−0.328433	+	0.673388i	−0.328433	+	0.673388i
$506$		0			0
$507$	0.190983	+	1.81708i	0.190983	+	1.81708i
$508$	−1.52045	−	1.10467i	−1.52045	−	1.10467i
$509$	0.482665	+	1.93586i	0.482665	+	1.93586i	0.309017	+	0.951057i	$0.400000\pi$
$509$	0.482665	+	1.93586i	0.482665	+	1.93586i	0.173648	+	0.984808i	$0.444444\pi$
$510$		0			0
$511$		0			0
$512$	0.809017	−	0.587785i	0.809017	−	0.587785i
$513$		0			0
$514$		0			0
$515$	−1.80931	+	0.254282i	−1.80931	+	0.254282i
$516$	−2.43917	−	2.70897i	−2.43917	−	2.70897i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$521$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$522$	−2.41987	+	2.33684i	−2.41987	+	2.33684i
$523$	−0.294524	+	0.184039i	−0.294524	+	0.184039i	−0.669131	−	0.743145i	$-0.733333\pi$
$523$	−0.294524	+	0.184039i	−0.294524	+	0.184039i	0.374607	+	0.927184i	$0.377778\pi$
$524$		0			0
$525$	2.37391	−	1.48338i	2.37391	−	1.48338i
$526$	−1.49861	+	1.25748i	−1.49861	+	1.25748i
$527$		0			0
$528$		0			0
$529$	1.50764	+	2.23517i	1.50764	+	2.23517i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.90789	−	1.19218i	−1.90789	−	1.19218i
$535$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$536$	0.104528	−	0.181049i	0.104528	−	0.181049i
$537$		0			0
$538$	−0.196449	+	1.86909i	−0.196449	+	1.86909i
$539$		0			0
$540$	−2.35040	−	0.673968i	−2.35040	−	0.673968i
$541$	0.876742	−	1.79759i	0.876742	−	1.79759i	0.438371	−	0.898794i	$-0.355556\pi$
$541$	0.876742	−	1.79759i	0.876742	−	1.79759i	0.438371	−	0.898794i	$-0.355556\pi$
$542$		0			0
$543$	0.684440	+	1.69405i	0.684440	+	1.69405i
$544$		0			0
$545$	−0.774117	+	1.58718i	−0.774117	+	1.58718i
$546$		0			0
$547$	−0.885740	−	1.13369i	−0.885740	−	1.13369i	−0.990268	−	0.139173i	$-0.955556\pi$
$547$	−0.885740	−	1.13369i	−0.885740	−	1.13369i	0.104528	−	0.994522i	$-0.466667\pi$
$548$		0			0
$549$	0.109208	−	0.121287i	0.109208	−	0.121287i
$550$		0			0
$551$		0			0
$552$	−2.97887	−	1.86141i	−2.97887	−	1.86141i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$557$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$558$		0			0
$559$		0			0
$560$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$561$		0			0
$562$	−1.98054			−1.98054
$563$	0.410323	−	0.256398i	0.410323	−	0.256398i	−0.309017	−	0.951057i	$-0.600000\pi$
$563$	0.410323	−	0.256398i	0.410323	−	0.256398i	0.719340	+	0.694658i	$0.244444\pi$
$564$	2.57116	−	2.48294i	2.57116	−	2.48294i
$565$		0			0
$566$	1.42864	+	0.759621i	1.42864	+	0.759621i
$567$	3.25418	+	0.227555i	3.25418	+	0.227555i
$568$		0			0
$569$	0.241922	+	0.419021i	0.241922	+	0.419021i	0.961262	−	0.275637i	$-0.0888889\pi$
$569$	0.241922	+	0.419021i	0.241922	+	0.419021i	−0.719340	+	0.694658i	$0.755556\pi$
$570$		0			0
$571$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$571$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$572$		0			0
$573$		0			0
$574$	−0.430469	+	0.312754i	−0.430469	+	0.312754i
$575$	−1.47274	−	1.23577i	−1.47274	−	1.23577i
$576$	2.31551	+	0.325423i	2.31551	+	0.325423i
$577$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$577$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$578$	0.809017	+	0.587785i	0.809017	+	0.587785i
$579$		0			0
$580$	1.03490	−	0.999391i	1.03490	−	0.999391i
$581$	0.415086	−	0.851053i	0.415086	−	0.851053i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.22007	+	1.17821i	1.22007	+	1.17821i	0.978148	+	0.207912i	$0.0666667\pi$
$587$	1.22007	+	1.17821i	1.22007	+	1.17821i	0.241922	+	0.970296i	$0.422222\pi$
$588$	1.51553	−	1.93979i	1.51553	−	1.93979i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$593$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$594$		0			0
$595$		0			0
$596$	−0.0168859	+	0.483549i	−0.0168859	+	0.483549i
$597$		0			0
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	1.75631	+	0.503615i	1.75631	+	0.503615i
$601$	−0.323755	+	1.29851i	−0.323755	+	1.29851i	0.559193	+	0.829038i	$0.311111\pi$
$601$	−0.323755	+	1.29851i	−0.323755	+	1.29851i	−0.882948	+	0.469472i	$0.844444\pi$
$602$	−2.47293	−	1.79669i	−2.47293	−	1.79669i
$603$	0.469893	−	0.134740i	0.469893	−	0.134740i
$604$		0			0
$605$	0.173648	+	0.984808i	0.173648	+	0.984808i
$606$	1.20865	−	0.642651i	1.20865	−	0.642651i
$607$	−1.39963	+	0.623157i	−1.39963	+	0.623157i	−0.961262	−	0.275637i	$-0.911111\pi$
$607$	−1.39963	+	0.623157i	−1.39963	+	0.623157i	−0.438371	+	0.898794i	$0.644444\pi$
$608$		0			0
$609$	−2.25201	+	3.33874i	−2.25201	+	3.33874i
$610$	−0.0467046	+	0.0518708i	−0.0467046	+	0.0518708i
$611$		0			0
$612$		0			0
$613$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$613$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$614$	1.22256	+	0.544320i	1.22256	+	0.544320i
$615$	0.596274	+	0.217026i	0.596274	+	0.217026i
$616$		0			0
$617$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$617$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$618$	2.94751	+	1.56722i	2.94751	+	1.56722i
$619$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$619$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$620$		0			0
$621$	−1.13723	−	4.56118i	−1.13723	−	4.56118i
$622$		0			0
$623$	−1.77273	−	0.645220i	−1.77273	−	0.645220i
$624$		0			0
$625$	0.913545	+	0.406737i	0.913545	+	0.406737i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−3.57370	−	0.249897i	−3.57370	−	0.249897i
$631$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$631$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$632$		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
$640$	−0.990268	−	0.139173i	−0.990268	−	0.139173i
$641$	−1.11566	+	0.0780147i	−1.11566	+	0.0780147i	−0.615661	−	0.788011i	$-0.711111\pi$
$641$	−1.11566	+	0.0780147i	−1.11566	+	0.0780147i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	2.70071	+	1.20243i	2.70071	+	1.20243i
$643$	0.438371	+	0.898794i	0.438371	+	0.898794i	0.997564	+	0.0697565i	$0.0222222\pi$
$643$	0.438371	+	0.898794i	0.438371	+	0.898794i	−0.559193	+	0.829038i	$0.688889\pi$
$644$	−2.76784	−	1.00741i	−2.76784	−	1.00741i
$645$	−0.127218	+	3.64306i	−0.127218	+	3.64306i
$646$		0			0
$647$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.241922	−	0.970296i	$-0.422222\pi$
$647$	0.741922	−	1.83632i	0.741922	−	1.83632i	0.500000	−	0.866025i	$-0.333333\pi$
$648$	1.31087	+	1.67784i	1.31087	+	1.67784i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.59381	+	0.580099i	1.59381	+	0.580099i
$653$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$653$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$654$	2.84879	−	1.51473i	2.84879	−	1.51473i
$655$		0			0
$656$	−0.339707	−	0.0722070i	−0.339707	−	0.0722070i
$657$		0			0
$658$	1.67602	−	2.48481i	1.67602	−	2.48481i
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$	−1.18161	+	0.628276i	−1.18161	+	0.628276i	−0.939693	−	0.342020i	$-0.888889\pi$
$661$	−1.18161	+	0.628276i	−1.18161	+	0.628276i	−0.241922	+	0.970296i	$0.577778\pi$
$662$		0			0
$663$		0			0
$664$	0.594092	−	0.170353i	0.594092	−	0.170353i
$665$		0			0
$666$		0			0
$667$	2.65875	+	0.762384i	2.65875	+	0.762384i
$668$	0.545692	−	1.67947i	0.545692	−	1.67947i
$669$	0.0713134	+	2.04215i	0.0713134	+	2.04215i
$670$	−0.200958	+	0.0576239i	−0.200958	+	0.0576239i
$671$		0			0
$672$	2.79245	−	0.195267i	2.79245	−	0.195267i
$673$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$673$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$674$		0			0
$675$	1.22256	+	2.11754i	1.22256	+	2.11754i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$677$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.91203	+	1.05989i	−2.91203	+	1.05989i
$682$		0			0
$683$	0.0696290	+	1.99391i	0.0696290	+	1.99391i	0.104528	+	0.994522i	$0.466667\pi$
$683$	0.0696290	+	1.99391i	0.0696290	+	1.99391i	−0.0348995	+	0.999391i	$0.511111\pi$
$684$		0			0
$685$		0			0
$686$	0.233252	−	0.478238i	0.233252	−	0.478238i
$687$	−2.12658	+	2.05362i	−2.12658	+	2.05362i
$688$	−0.208548	−	1.98420i	−0.208548	−	1.98420i
$689$		0			0
$690$	0.849781	+	3.40829i	0.849781	+	3.40829i
$691$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$691$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$692$		0			0
$693$		0			0
$694$	1.32524	+	1.47183i	1.32524	+	1.47183i
$695$		0			0
$696$	−2.60302	+	0.365830i	−2.60302	+	0.365830i
$697$		0			0
$698$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$699$		0			0
$700$	1.52836	+	0.106873i	1.52836	+	0.106873i
$701$	−1.49756	−	0.796269i	−1.49756	−	0.796269i	−0.500000	−	0.866025i	$-0.666667\pi$
$701$	−1.49756	−	0.796269i	−1.49756	−	0.796269i	−0.997564	+	0.0697565i	$0.977778\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−3.57433			−3.57433
$706$		0			0
$707$	0.879313	−	0.737831i	0.879313	−	0.737831i
$708$		0			0
$709$	0.181251	−	0.448612i	0.181251	−	0.448612i	−0.809017	−	0.587785i	$-0.800000\pi$
$709$	0.181251	−	0.448612i	0.181251	−	0.448612i	0.990268	+	0.139173i	$0.0444444\pi$
$710$		0			0
$711$		0			0
$712$	−0.461262	−	1.14166i	−0.461262	−	1.14166i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$719$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$720$	−1.43958	−	1.84257i	−1.43958	−	1.84257i
$721$	2.69083	+	0.771582i	2.69083	+	0.771582i
$722$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$723$	1.82709			1.82709
$724$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$725$	−1.43868			−1.43868
$726$	0.800944	−	1.64218i	0.800944	−	1.64218i
$727$	1.55535	+	0.445991i	1.55535	+	0.445991i	0.939693	−	0.342020i	$-0.111111\pi$
$727$	1.55535	+	0.445991i	1.55535	+	0.445991i	0.615661	+	0.788011i	$0.288889\pi$
$728$		0			0
$729$	−0.0534318	+	0.508370i	−0.0534318	+	0.508370i
$730$		0			0
$731$		0			0
$732$	0.124742	−	0.0265148i	0.124742	−	0.0265148i
$733$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$733$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$734$	1.69610	+	1.05984i	1.69610	+	1.05984i
$735$	−2.43768	+	0.342593i	−2.43768	+	0.342593i
$736$	−0.720190	−	1.78253i	−0.720190	−	1.78253i
$737$		0			0
$738$	−0.454104	−	0.673236i	−0.454104	−	0.673236i
$739$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$739$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.76590			1.76590			0.882948	−	0.469472i	$-0.155556\pi$
$743$	1.76590			1.76590			0.882948	+	0.469472i	$0.155556\pi$
$744$		0			0
$745$	0.348048	−	0.336106i	0.348048	−	0.336106i
$746$		0			0
$747$	1.27597	+	0.678445i	1.27597	+	0.678445i
$748$		0			0
$749$	2.42480	+	0.515407i	2.42480	+	0.515407i
$750$	−0.913545	−	1.58231i	−0.913545	−	1.58231i
$751$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$751$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$752$	1.93726	−	0.272264i	1.93726	−	0.272264i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	2.86972	+	2.40798i	2.86972	+	2.40798i
$757$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$757$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.150383	−	0.145223i	0.150383	−	0.145223i	−0.615661	−	0.788011i	$-0.711111\pi$
$761$	0.150383	−	0.145223i	0.150383	−	0.145223i	0.766044	+	0.642788i	$0.222222\pi$
$762$	1.50528	−	3.08629i	1.50528	−	3.08629i
$763$	2.07254	−	1.73907i	2.07254	−	1.73907i
$764$		0			0
$765$		0			0
$766$	−0.380500	−	1.17106i	−0.380500	−	1.17106i
$767$		0			0
$768$	1.31430	+	1.26920i	1.31430	+	1.26920i
$769$	−0.539776	+	0.690882i	−0.539776	+	0.690882i	−0.978148	−	0.207912i	$-0.933333\pi$
$769$	−0.539776	+	0.690882i	−0.539776	+	0.690882i	0.438371	+	0.898794i	$0.355556\pi$
$770$		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	$0.333333\pi$
$774$	2.87214	−	3.67617i	2.87214	−	3.67617i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.18362	−	0.339399i	1.18362	−	0.339399i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.84592	−	2.06768i	−2.84592	−	2.06768i
$784$	1.29510	−	0.371365i	1.29510	−	0.371365i
$785$		0			0
$786$		0			0
$787$	0.0616289	−	0.0327686i	0.0616289	−	0.0327686i	−0.438371	−	0.898794i	$-0.644444\pi$
$787$	0.0616289	−	0.0327686i	0.0616289	−	0.0327686i	0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	−2.73810	−	2.29753i	−2.73810	−	2.29753i
$790$		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	$-0.444444\pi$
$797$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$798$		0			0
$799$		0			0
$800$	0.615661	+	0.788011i	0.615661	+	0.788011i
$801$	1.07855	−	2.66951i	1.07855	−	2.66951i
$802$	0.212103	+	0.850699i	0.212103	+	0.850699i
$803$		0			0
$804$	0.358931	+	0.130640i	0.358931	+	0.130640i
$805$	1.29121	+	2.64738i	1.29121	+	2.64738i
$806$		0			0
$807$	−3.42544	+	0.239530i	−3.42544	+	0.239530i
$808$	0.741922	+	0.104270i	0.741922	+	0.104270i
$809$	−0.116903	−	0.173316i	−0.116903	−	0.173316i	0.766044	−	0.642788i	$-0.222222\pi$
$809$	−0.116903	−	0.173316i	−0.116903	−	0.173316i	−0.882948	+	0.469472i	$0.844444\pi$
$810$	0.222562	−	2.11754i	0.222562	−	2.11754i
$811$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$811$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$812$	−2.07126	+	0.753876i	−2.07126	+	0.753876i
$813$		0			0
$814$		0			0
$815$	−0.743520	−	1.52444i	−0.743520	−	1.52444i
$816$		0			0
$817$		0			0
$818$	−0.997564	−	0.0697565i	−0.997564	−	0.0697565i
$819$		0			0
$820$	0.194206	+	0.287922i	0.194206	+	0.287922i
$821$	−1.97571	−	0.277668i	−1.97571	−	0.277668i	−0.997564	−	0.0697565i	$-0.977778\pi$
$821$	−1.97571	−	0.277668i	−1.97571	−	0.277668i	−0.978148	−	0.207912i	$-0.933333\pi$
$822$		0			0
$823$	−1.75631	−	0.781961i	−1.75631	−	0.781961i	−0.990268	−	0.139173i	$-0.955556\pi$
$823$	−1.75631	−	0.781961i	−1.75631	−	0.781961i	−0.766044	−	0.642788i	$-0.777778\pi$
$824$	0.800944	+	1.64218i	0.800944	+	1.64218i
$825$		0			0
$826$		0			0
$827$	−0.181251	−	0.726958i	−0.181251	−	0.726958i	−0.990268	−	0.139173i	$-0.955556\pi$
$827$	−0.181251	−	0.726958i	−0.181251	−	0.726958i	0.809017	−	0.587785i	$-0.200000\pi$
$828$	1.68399	−	4.16803i	1.68399	−	4.16803i
$829$	−0.380500	−	0.487017i	−0.380500	−	0.487017i	0.559193	−	0.829038i	$-0.311111\pi$
$829$	−0.380500	−	0.487017i	−0.380500	−	0.487017i	−0.939693	+	0.342020i	$0.888889\pi$
$830$	−0.545692	−	0.290149i	−0.545692	−	0.290149i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.55919	+	0.829038i	−1.55919	+	0.829038i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$839$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$840$	−2.14436	−	1.79933i	−2.14436	−	1.79933i
$841$	0.977310	−	0.435126i	0.977310	−	0.435126i
$842$	−0.427209	+	0.227151i	−0.427209	+	0.227151i
$843$	−0.628367	−	3.56364i	−0.628367	−	3.56364i
$844$		0			0
$845$	0.961262	−	0.275637i	0.961262	−	0.275637i
$846$	3.70071	+	2.68872i	3.70071	+	2.68872i
$847$	0.370646	−	1.48658i	0.370646	−	1.48658i
$848$		0			0
$849$	−0.913545	+	2.81160i	−0.913545	+	2.81160i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$853$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$854$	0.0976930	−	0.0434957i	0.0976930	−	0.0434957i
$855$		0			0
$856$	0.809017	+	1.40126i	0.809017	+	1.40126i
$857$		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		0.809017	−	0.587785i	$-0.200000\pi$
$859$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$860$	−1.22832	+	1.57218i	−1.22832	+	1.57218i
$861$	−0.699324	−	0.675329i	−0.699324	−	0.675329i
$862$		0			0
$863$	0.231520	+	0.712544i	0.231520	+	0.712544i	0.997564	+	0.0697565i	$0.0222222\pi$
$863$	0.231520	+	0.712544i	0.231520	+	0.712544i	−0.766044	+	0.642788i	$0.777778\pi$
$864$	0.0853336	+	2.44364i	0.0853336	+	2.44364i
$865$		0			0
$866$		0			0
$867$	−0.800944	+	1.64218i	−0.800944	+	1.64218i
$868$		0			0
$869$		0			0
$870$	2.12658	+	1.54505i	2.12658	+	1.54505i
$871$		0			0
$872$	1.74871	+	0.245765i	1.74871	+	0.245765i
$873$		0			0
$874$		0			0
$875$	−1.02517	−	1.13856i	−1.02517	−	1.13856i
$876$		0			0
$877$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$877$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.69196	−	0.118314i	−1.69196	−	0.118314i	−0.809017	−	0.587785i	$-0.800000\pi$
$881$	−1.69196	−	0.118314i	−1.69196	−	0.118314i	−0.882948	+	0.469472i	$0.844444\pi$
$882$	2.78158	+	1.47899i	2.78158	+	1.47899i
$883$	0.580762	−	1.78740i	0.580762	−	1.78740i	−0.0348995	−	0.999391i	$-0.511111\pi$
$883$	0.580762	−	1.78740i	0.580762	−	1.78740i	0.615661	−	0.788011i	$-0.288889\pi$
$884$		0			0
$885$		0			0
$886$	−1.87939			−1.87939
$887$	−0.0591929	+	0.0369878i	−0.0591929	+	0.0369878i	−0.559193	−	0.829038i	$-0.688889\pi$
$887$	−0.0591929	+	0.0369878i	−0.0591929	+	0.0369878i	0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	0.696586	−	2.79386i	0.696586	−	2.79386i
$890$	−0.461262	+	1.14166i	−0.461262	+	1.14166i
$891$		0			0
$892$	−0.625393	+	0.927184i	−0.625393	+	0.927184i
$893$		0			0
$894$	−0.875423	+	0.123033i	−0.875423	+	0.123033i
$895$		0			0
$896$	1.29929	+	0.811883i	1.29929	+	0.811883i
$897$		0			0
$898$	0.438371	−	0.759281i	0.438371	−	0.759281i
$899$		0			0
$900$	−0.244415	+	2.32545i	−0.244415	+	2.32545i
$901$		0			0
$902$		0			0
$903$	2.44826	−	5.01967i	2.44826	−	5.01967i
$904$		0			0
$905$	0.848048	−	0.529919i	0.848048	−	0.529919i
$906$		0			0
$907$	0.630676	−	1.29308i	0.630676	−	1.29308i	−0.309017	−	0.951057i	$-0.600000\pi$
$907$	0.630676	−	1.29308i	0.630676	−	1.29308i	0.939693	−	0.342020i	$-0.111111\pi$
$908$	−1.63039	−	0.467507i	−1.63039	−	0.467507i
$909$	1.07855	+	1.38048i	1.07855	+	1.38048i
$910$		0			0
$911$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$911$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.108151	−	0.0675801i	−0.108151	−	0.0675801i
$916$	−1.60229	+	0.225187i	−1.60229	+	0.225187i
$917$		0			0
$918$		0			0
$919$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$919$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$920$	−0.720190	+	1.78253i	−0.720190	+	1.78253i
$921$	−0.591529	+	2.37249i	−0.591529	+	2.37249i
$922$	0.370646	−	0.311009i	0.370646	−	0.311009i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.03490	−	0.999391i	1.03490	−	0.999391i
$927$	−1.32019	+	4.06312i	−1.32019	+	4.06312i
$928$	−1.27028	−	0.675419i	−1.27028	−	0.675419i
$929$	−0.616528	−	0.0431119i	−0.616528	−	0.0431119i	−0.241922	−	0.970296i	$-0.577778\pi$
$929$	−0.616528	−	0.0431119i	−0.616528	−	0.0431119i	−0.374607	+	0.927184i	$0.622222\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.339707	+	0.0722070i	−0.339707	+	0.0722070i
$935$		0			0
$936$		0			0
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$	0.317177	+	0.0445763i	0.317177	+	0.0445763i
$939$		0			0
$940$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$941$	−0.00729598	−	0.0694166i	−0.00729598	−	0.0694166i	0.990268	−	0.139173i	$-0.0444444\pi$
$941$	−0.00729598	−	0.0694166i	−0.00729598	−	0.0694166i	−0.997564	+	0.0697565i	$0.977778\pi$
$942$		0			0
$943$	−0.292694	+	0.600112i	−0.292694	+	0.600112i
$944$		0			0
$945$	−0.391579	−	3.72563i	−0.391579	−	3.72563i
$946$		0			0
$947$	0.380500	+	1.17106i	0.380500	+	1.17106i	0.939693	+	0.342020i	$0.111111\pi$
$947$	0.380500	+	1.17106i	0.380500	+	1.17106i	−0.559193	+	0.829038i	$0.688889\pi$
$948$		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
$960$	−0.0637646	−	1.82598i	−0.0637646	−	1.82598i
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$		0			0
$963$	−0.915284	+	3.67100i	−0.915284	+	3.67100i
$964$	0.809017	+	0.587785i	0.809017	+	0.587785i
$965$		0			0
$966$	0.934514	−	5.29989i	0.934514	−	5.29989i
$967$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.241922	+	0.970296i	$0.422222\pi$
$967$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.104528	+	0.994522i	$0.466667\pi$
$968$	0.882948	−	0.469472i	0.882948	−	0.469472i
$969$		0			0
$970$		0			0
$971$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$971$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$972$	−0.966977	+	1.07394i	−0.966977	+	1.07394i
$973$		0			0
$974$	−1.42468	−	1.37580i	−1.42468	−	1.37580i
$975$		0			0
$976$	0.0637646	+	0.0283898i	0.0637646	+	0.0283898i
$977$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$977$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$978$	−0.538122	+	3.05184i	−0.538122	+	3.05184i
$979$		0			0
$980$	−1.18959	−	0.632517i	−1.18959	−	0.632517i
$981$	2.54214	+	3.25379i	2.54214	+	3.25379i
$982$		0			0
$983$	−0.241922	−	0.970296i	−0.241922	−	0.970296i	−0.961262	−	0.275637i	$-0.911111\pi$
$983$	−0.241922	−	0.970296i	−0.241922	−	0.970296i	0.719340	−	0.694658i	$-0.244444\pi$
$984$	0.0221452	−	0.634155i	0.0221452	−	0.634155i
$985$		0			0
$986$		0			0
$987$	5.00275	+	2.22737i	5.00275	+	2.22737i
$988$		0			0
$989$	−3.79835	−	0.533824i	−3.79835	−	0.533824i
$990$		0			0
$991$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$991$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.495011	+	1.01492i	0.495011	+	1.01492i
$997$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$997$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$998$		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.2859.1	yes	24
4.3	odd	2		3620.1.dy.b.2859.1	yes	24
5.4	even	2		3620.1.dy.b.2859.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.2859.1	yes	24
181.44	even	45	inner	3620.1.dy.a.2759.1	✓	24
724.587	odd	90		3620.1.dy.b.2759.1	yes	24
905.44	even	90		3620.1.dy.b.2759.1	yes	24
3620.2759	odd	90	inner	3620.1.dy.a.2759.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.2759.1	✓	24	181.44	even	45	inner
3620.1.dy.a.2759.1	✓	24	3620.2759	odd	90	inner
3620.1.dy.a.2859.1	yes	24	1.1	even	1	trivial
3620.1.dy.a.2859.1	yes	24	20.19	odd	2	CM
3620.1.dy.b.2759.1	yes	24	724.587	odd	90
3620.1.dy.b.2759.1	yes	24	905.44	even	90
3620.1.dy.b.2859.1	yes	24	4.3	odd	2
3620.1.dy.b.2859.1	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)

\(f(q)\)	\(=\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-1.75631 - 0.503615i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.104528 + 0.994522i) q^{5} +(1.22256 - 1.35779i) q^{6} +(0.766044 - 1.32683i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.98296 + 1.23909i) q^{9} +O(q^{10})\)	\(q+(-0.438371 + 0.898794i) q^{2} +(-1.75631 - 0.503615i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-0.104528 + 0.994522i) q^{5} +(1.22256 - 1.35779i) q^{6} +(0.766044 - 1.32683i) q^{7} +(0.978148 - 0.207912i) q^{8} +(1.98296 + 1.23909i) q^{9} +(-0.848048 - 0.529919i) q^{10} +(0.684440 + 1.69405i) q^{12} +(0.856733 + 1.27016i) q^{14} +(0.684440 - 1.69405i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(-1.98296 + 1.23909i) q^{18} +(0.848048 - 0.529919i) q^{20} +(-2.01362 + 1.94453i) q^{21} +(1.69749 + 0.902570i) q^{23} +(-1.82264 - 0.127451i) q^{24} +(-0.978148 - 0.207912i) q^{25} +(-1.63611 - 1.81708i) q^{27} +(-1.51718 + 0.213226i) q^{28} +(1.40724 - 0.299118i) q^{29} +(1.22256 + 1.35779i) q^{30} +(-0.766044 - 0.642788i) q^{32} +(1.23949 + 0.900539i) q^{35} +(-0.244415 - 2.32545i) q^{36} +(0.104528 + 0.994522i) q^{40} +(0.0121205 + 0.347085i) q^{41} +(-0.865021 - 2.66226i) q^{42} +(-1.87481 + 0.682374i) q^{43} +(-1.43958 + 1.84257i) q^{45} +(-1.55535 + 1.13003i) q^{46} +(-0.732841 - 1.81385i) q^{47} +(0.913545 - 1.58231i) q^{48} +(-0.673648 - 1.16679i) q^{49} +(0.615661 - 0.788011i) q^{50} +(2.35040 - 0.673968i) q^{54} +(0.473442 - 1.45710i) q^{56} +(-0.348048 + 1.39594i) q^{58} +(-1.75631 + 0.503615i) q^{60} +(0.0121205 - 0.0687386i) q^{61} +(3.16309 - 1.68185i) q^{63} +(0.913545 - 0.406737i) q^{64} +(0.139886 - 0.155360i) q^{67} +(-2.52677 - 2.44007i) q^{69} +(-1.35275 + 0.719272i) q^{70} +(2.19725 + 0.799732i) q^{72} +(1.61323 + 0.857767i) q^{75} +(-0.939693 - 0.342020i) q^{80} +(0.933382 + 1.91372i) q^{81} +(-0.317271 - 0.141258i) q^{82} +(0.616528 - 0.0431119i) q^{83} +(2.77202 + 0.389582i) q^{84} +(0.208548 - 1.98420i) q^{86} +(-2.62220 - 0.183362i) q^{87} +(-0.213817 - 1.21262i) q^{89} +(-1.02503 - 2.10162i) q^{90} +(-0.333843 - 1.89332i) q^{92} +(1.95153 + 0.136464i) q^{94} +(1.02170 + 1.51473i) q^{96} +(1.34401 - 0.0939826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 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

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