LMFDB - Embedded newform 3620.1.dy.a.2579.1

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			2579.1
Root			$-0.719340 + 0.694658i$ of defining polynomial
Character	$\chi$	$=$	3620.2579
Dual form			3620.1.dy.a.539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0348995 - 0.999391i) q^{2} +(-0.732841 - 1.81385i) q^{3} +(-0.997564 + 0.0697565i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(0.173648 + 0.300767i) q^{7} +(0.104528 + 0.994522i) q^{8} +(-2.03364 + 1.96386i) q^{9} +O(q^{10})$	\(q+(-0.0348995 - 0.999391i) q^{2} +(-0.732841 - 1.81385i) q^{3} +(-0.997564 + 0.0697565i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(0.173648 + 0.300767i) q^{7} +(0.104528 + 0.994522i) q^{8} +(-2.03364 + 1.96386i) q^{9} +(0.719340 - 0.694658i) q^{10} +(0.857583 + 1.75831i) q^{12} +(0.294524 - 0.184039i) q^{14} +(0.857583 - 1.75831i) q^{15} +(0.990268 - 0.139173i) q^{16} +(2.03364 + 1.96386i) q^{18} +(-0.719340 - 0.694658i) q^{20} +(0.418289 - 0.535386i) q^{21} +(0.720190 - 0.206511i) q^{23} +(1.72731 - 0.918425i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(3.26531 + 1.45381i) q^{27} +(-0.194206 - 0.287922i) q^{28} +(0.128708 + 1.22458i) q^{29} +(-1.78716 - 0.795697i) q^{30} +(-0.173648 - 0.984808i) q^{32} +(-0.107320 + 0.330298i) q^{35} +(1.89169 - 2.10094i) q^{36} +(-0.669131 + 0.743145i) q^{40} +(0.454664 - 1.82356i) q^{41} +(-0.549658 - 0.399350i) q^{42} +(1.35275 - 1.13510i) q^{43} +(-2.82020 - 0.197208i) q^{45} +(-0.231520 - 0.712544i) q^{46} +(0.0916445 + 0.187899i) q^{47} +(-0.978148 - 1.69420i) q^{48} +(0.439693 - 0.761570i) q^{49} +(0.997564 + 0.0697565i) q^{50} +(1.33897 - 3.31406i) q^{54} +(-0.280969 + 0.204136i) q^{56} +(1.21934 - 0.171367i) q^{58} +(-0.732841 + 1.81385i) q^{60} +(0.454664 + 0.165484i) q^{61} +(-0.943804 - 0.270631i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(-1.22256 + 0.544320i) q^{67} +(-0.902364 - 1.15497i) q^{69} +(0.333843 + 0.0957278i) q^{70} +(-2.16568 - 1.81722i) q^{72} +(1.88051 - 0.539228i) q^{75} +(0.766044 + 0.642788i) q^{80} +(0.145369 - 4.16281i) q^{81} +(-1.83832 - 0.390746i) q^{82} +(-1.42864 - 0.759621i) q^{83} +(-0.379924 + 0.563260i) q^{84} +(-1.18161 - 1.31232i) q^{86} +(2.12687 - 1.13088i) q^{87} +(1.87481 - 0.682374i) q^{89} +(-0.0986641 + 2.82537i) q^{90} +(-0.704030 + 0.256246i) q^{92} +(0.184586 - 0.0981463i) q^{94} +(-1.65903 + 1.03668i) q^{96} +(-0.776451 - 0.412846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{22}{45}\right)$

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 $

$2$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$2$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$3$	−0.732841	−	1.81385i	−0.732841	−	1.81385i	−0.559193	−	0.829038i	$-0.688889\pi$
$3$	−0.732841	−	1.81385i	−0.732841	−	1.81385i	−0.173648	−	0.984808i	$-0.555556\pi$
$4$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$5$	0.669131	+	0.743145i	0.669131	+	0.743145i
$5$	0.669131	+	0.743145i	0.669131	+	0.743145i
$6$	−1.78716	+	0.795697i	−1.78716	+	0.795697i
$7$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$7$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$8$	0.104528	+	0.994522i	0.104528	+	0.994522i
$9$	−2.03364	+	1.96386i	−2.03364	+	1.96386i
$10$	0.719340	−	0.694658i	0.719340	−	0.694658i
$11$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$11$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$12$	0.857583	+	1.75831i	0.857583	+	1.75831i
$13$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$13$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$14$	0.294524	−	0.184039i	0.294524	−	0.184039i
$15$	0.857583	−	1.75831i	0.857583	−	1.75831i
$16$	0.990268	−	0.139173i	0.990268	−	0.139173i
$17$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$17$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$18$	2.03364	+	1.96386i	2.03364	+	1.96386i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$21$	0.418289	−	0.535386i	0.418289	−	0.535386i
$22$		0			0
$23$	0.720190	−	0.206511i	0.720190	−	0.206511i	0.104528	−	0.994522i	$-0.466667\pi$
$23$	0.720190	−	0.206511i	0.720190	−	0.206511i	0.615661	+	0.788011i	$0.288889\pi$
$24$	1.72731	−	0.918425i	1.72731	−	0.918425i
$25$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$26$		0			0
$27$	3.26531	+	1.45381i	3.26531	+	1.45381i
$28$	−0.194206	−	0.287922i	−0.194206	−	0.287922i
$29$	0.128708	+	1.22458i	0.128708	+	1.22458i	0.848048	+	0.529919i	$0.177778\pi$
$29$	0.128708	+	1.22458i	0.128708	+	1.22458i	−0.719340	+	0.694658i	$0.755556\pi$
$30$	−1.78716	−	0.795697i	−1.78716	−	0.795697i
$31$		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
$36$	1.89169	−	2.10094i	1.89169	−	2.10094i
$37$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$37$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$38$		0			0
$39$		0			0
$40$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$41$	0.454664	−	1.82356i	0.454664	−	1.82356i	−0.104528	−	0.994522i	$-0.533333\pi$
$41$	0.454664	−	1.82356i	0.454664	−	1.82356i	0.559193	−	0.829038i	$-0.311111\pi$
$42$	−0.549658	−	0.399350i	−0.549658	−	0.399350i
$43$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.374607	−	0.927184i	$-0.377778\pi$
$43$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.978148	−	0.207912i	$-0.0666667\pi$
$44$		0			0
$45$	−2.82020	−	0.197208i	−2.82020	−	0.197208i
$46$	−0.231520	−	0.712544i	−0.231520	−	0.712544i
$47$	0.0916445	+	0.187899i	0.0916445	+	0.187899i	0.939693	−	0.342020i	$-0.111111\pi$
$47$	0.0916445	+	0.187899i	0.0916445	+	0.187899i	−0.848048	+	0.529919i	$0.822222\pi$
$48$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$49$	0.439693	−	0.761570i	0.439693	−	0.761570i
$50$	0.997564	+	0.0697565i	0.997564	+	0.0697565i
$51$		0			0
$52$		0			0
$53$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$53$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$54$	1.33897	−	3.31406i	1.33897	−	3.31406i
$55$		0			0
$56$	−0.280969	+	0.204136i	−0.280969	+	0.204136i
$57$		0			0
$58$	1.21934	−	0.171367i	1.21934	−	0.171367i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	−0.732841	+	1.81385i	−0.732841	+	1.81385i
$61$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$61$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$62$		0			0
$63$	−0.943804	−	0.270631i	−0.943804	−	0.270631i
$64$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$65$		0			0
$66$		0			0
$67$	−1.22256	+	0.544320i	−1.22256	+	0.544320i	−0.913545	−	0.406737i	$-0.866667\pi$
$67$	−1.22256	+	0.544320i	−1.22256	+	0.544320i	−0.309017	+	0.951057i	$0.600000\pi$
$68$		0			0
$69$	−0.902364	−	1.15497i	−0.902364	−	1.15497i
$70$	0.333843	+	0.0957278i	0.333843	+	0.0957278i
$71$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$71$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$72$	−2.16568	−	1.81722i	−2.16568	−	1.81722i
$73$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$73$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$74$		0			0
$75$	1.88051	−	0.539228i	1.88051	−	0.539228i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$79$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$80$	0.766044	+	0.642788i	0.766044	+	0.642788i
$81$	0.145369	−	4.16281i	0.145369	−	4.16281i
$82$	−1.83832	−	0.390746i	−1.83832	−	0.390746i
$83$	−1.42864	−	0.759621i	−1.42864	−	0.759621i	−0.438371	−	0.898794i	$-0.644444\pi$
$83$	−1.42864	−	0.759621i	−1.42864	−	0.759621i	−0.990268	+	0.139173i	$0.955556\pi$
$84$	−0.379924	+	0.563260i	−0.379924	+	0.563260i
$85$		0			0
$86$	−1.18161	−	1.31232i	−1.18161	−	1.31232i
$87$	2.12687	−	1.13088i	2.12687	−	1.13088i
$88$		0			0
$89$	1.87481	−	0.682374i	1.87481	−	0.682374i	0.913545	−	0.406737i	$-0.133333\pi$
$89$	1.87481	−	0.682374i	1.87481	−	0.682374i	0.961262	−	0.275637i	$-0.0888889\pi$
$90$	−0.0986641	+	2.82537i	−0.0986641	+	2.82537i
$91$		0			0
$92$	−0.704030	+	0.256246i	−0.704030	+	0.256246i
$93$		0			0
$94$	0.184586	−	0.0981463i	0.184586	−	0.0981463i
$95$		0			0
$96$	−1.65903	+	1.03668i	−1.65903	+	1.03668i
$97$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$97$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$98$	−0.776451	−	0.412846i	−0.776451	−	0.412846i
$99$		0			0
$100$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$101$	0.671624	+	0.563559i	0.671624	+	0.563559i	0.913545	−	0.406737i	$-0.133333\pi$
$101$	0.671624	+	0.563559i	0.671624	+	0.563559i	−0.241922	+	0.970296i	$0.577778\pi$
$102$		0			0
$103$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.997564	−	0.0697565i	$-0.0222222\pi$
$103$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.939693	+	0.342020i	$0.111111\pi$
$104$		0			0
$105$	0.677759	−	0.0473935i	0.677759	−	0.0473935i
$106$		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	$0.600000\pi$
$108$	−3.35877	−	1.22249i	−3.35877	−	1.22249i
$109$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.913545	+	0.406737i	$0.133333\pi$
$109$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.559193	+	0.829038i	$0.311111\pi$
$110$		0			0
$111$		0			0
$112$	0.213817	+	0.273673i	0.213817	+	0.273673i
$113$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$113$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$114$		0			0
$115$	0.635369	+	0.397023i	0.635369	+	0.397023i
$116$	−0.213817	−	1.21262i	−0.213817	−	1.21262i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.83832	+	0.669092i	1.83832	+	0.669092i
$121$	−0.374607	+	0.927184i	−0.374607	+	0.927184i
$122$	0.149516	−	0.460163i	0.149516	−	0.460163i
$123$	−3.64085	+	0.511688i	−3.64085	+	0.511688i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$126$	−0.237528	+	0.952674i	−0.237528	+	0.952674i
$127$	0.573931	−	1.42053i	0.573931	−	1.42053i	−0.309017	−	0.951057i	$-0.600000\pi$
$127$	0.573931	−	1.42053i	0.573931	−	1.42053i	0.882948	−	0.469472i	$-0.155556\pi$
$128$	0.241922	+	0.970296i	0.241922	+	0.970296i
$129$	−3.05024	−	1.62184i	−3.05024	−	1.62184i
$130$		0			0
$131$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$131$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$132$		0			0
$133$		0			0
$134$	0.586655	+	1.20282i	0.586655	+	1.20282i
$135$	1.10453	+	3.39939i	1.10453	+	3.39939i
$136$		0			0
$137$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$137$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$138$	−1.12278	+	0.942122i	−1.12278	+	0.942122i
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$	0.0840186	−	0.336980i	0.0840186	−	0.336980i
$141$	0.273659	−	0.303929i	0.273659	−	0.303929i
$142$		0			0
$143$		0			0
$144$	−1.74053	+	2.22778i	−1.74053	+	2.22778i
$145$	−0.823916	+	0.915051i	−0.823916	+	0.915051i
$146$		0			0
$147$	−1.70359	−	0.239425i	−1.70359	−	0.239425i
$148$		0			0
$149$	0.343916	+	1.95045i	0.343916	+	1.95045i	0.309017	+	0.951057i	$0.400000\pi$
$149$	0.343916	+	1.95045i	0.343916	+	1.95045i	0.0348995	+	0.999391i	$0.488889\pi$
$150$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$151$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$151$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$157$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$158$		0			0
$159$		0			0
$160$	0.615661	−	0.788011i	0.615661	−	0.788011i
$161$	0.187172	+	0.180749i	0.187172	+	0.180749i
$162$	−4.16535			−4.16535
$163$	−1.03490	−	0.999391i	−1.03490	−	0.999391i	−0.0348995	−	0.999391i	$-0.511111\pi$
$163$	−1.03490	−	0.999391i	−1.03490	−	0.999391i	−1.00000			$\pi$
$164$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$165$		0			0
$166$	−0.709299	+	1.45428i	−0.709299	+	1.45428i
$167$	−1.63039	+	1.01878i	−1.63039	+	1.01878i	−0.669131	+	0.743145i	$0.733333\pi$
$167$	−1.63039	+	1.01878i	−1.63039	+	1.01878i	−0.961262	+	0.275637i	$0.911111\pi$
$168$	0.576176	+	0.360035i	0.576176	+	0.360035i
$169$	0.438371	+	0.898794i	0.438371	+	0.898794i
$170$		0			0
$171$		0			0
$172$	−1.27028	+	1.22669i	−1.27028	+	1.22669i
$173$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$173$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$174$	−1.20442	−	2.08611i	−1.20442	−	2.08611i
$175$	−0.317271	+	0.141258i	−0.317271	+	0.141258i
$176$		0			0
$177$		0			0
$178$	−0.747388	−	1.84985i	−0.747388	−	1.84985i
$179$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$179$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$180$	2.82709			2.82709
$181$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$181$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$182$		0			0
$183$	−0.0330338	−	0.945965i	−0.0330338	−	0.945965i
$184$	0.280660	+	0.694658i	0.280660	+	0.694658i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$189$	0.129757	+	1.23455i	0.129757	+	1.23455i
$190$		0			0
$191$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$191$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$192$	1.09395	+	1.62184i	1.09395	+	1.62184i
$193$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$193$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$194$		0			0
$195$		0			0
$196$	−0.385497	+	0.790386i	−0.385497	+	0.790386i
$197$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$197$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$198$		0			0
$199$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$199$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$200$	−1.00000			−1.00000
$201$	1.88326	+	1.81864i	1.88326	+	1.81864i
$202$	0.539776	−	0.690882i	0.539776	−	0.690882i
$203$	−0.345963	+	0.251357i	−0.345963	+	0.251357i
$204$		0			0
$205$	1.65940	−	0.882318i	1.65940	−	0.882318i
$206$	0.204489	−	1.94558i	0.204489	−	1.94558i
$207$	−1.05905	+	1.83432i	−1.05905	+	1.83432i
$208$		0			0
$209$		0			0
$210$	−0.0710181	−	0.675692i	−0.0710181	−	0.675692i
$211$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$211$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$212$		0			0
$213$		0			0
$214$	0.345600	−	0.512373i	0.345600	−	0.512373i
$215$	1.74871	+	0.245765i	1.74871	+	0.245765i
$216$	−1.10453	+	3.39939i	−1.10453	+	3.39939i
$217$		0			0
$218$	1.18362	−	1.51497i	1.18362	−	1.51497i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.37217	+	0.996940i	1.37217	+	0.996940i	0.997564	+	0.0697565i	$0.0222222\pi$
$223$	1.37217	+	0.996940i	1.37217	+	0.996940i	0.374607	+	0.927184i	$0.377778\pi$
$224$	0.266044	−	0.223238i	0.266044	−	0.223238i
$225$	−1.74053	−	2.22778i	−1.74053	−	2.22778i
$226$		0			0
$227$	0.444576	+	1.36827i	0.444576	+	1.36827i	0.882948	+	0.469472i	$0.155556\pi$
$227$	0.444576	+	1.36827i	0.444576	+	1.36827i	−0.438371	+	0.898794i	$0.644444\pi$
$228$		0			0
$229$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$229$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$230$	0.374607	−	0.648838i	0.374607	−	0.648838i
$231$		0			0
$232$	−1.20442	+	0.256006i	−1.20442	+	0.256006i
$233$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$233$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$234$		0			0
$235$	−0.0783141	+	0.193834i	−0.0783141	+	0.193834i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$239$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$240$	0.604528	−	1.86055i	0.604528	−	1.86055i
$241$	0.374607	−	0.927184i	0.374607	−	0.927184i	−0.615661	−	0.788011i	$-0.711111\pi$
$241$	0.374607	−	0.927184i	0.374607	−	0.927184i	0.990268	−	0.139173i	$-0.0444444\pi$
$242$	0.939693	+	0.342020i	0.939693	+	0.342020i
$243$	−4.29846	+	1.56451i	−4.29846	+	1.56451i
$244$	−0.465101	−	0.133365i	−0.465101	−	0.133365i
$245$	0.860169	−	0.182834i	0.860169	−	0.182834i
$246$	0.638441	+	3.62078i	0.638441	+	3.62078i
$247$		0			0
$248$		0			0
$249$	−0.330869	+	3.14801i	−0.330869	+	3.14801i
$250$	0.615661	+	0.788011i	0.615661	+	0.788011i
$251$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$251$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$252$	0.960383	+	0.204136i	0.960383	+	0.204136i
$253$		0			0
$254$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$255$		0			0
$256$	0.961262	−	0.275637i	0.961262	−	0.275637i
$257$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$257$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$258$	−1.51440	+	3.10498i	−1.51440	+	3.10498i
$259$		0			0
$260$		0			0
$261$	−2.66665	−	2.23758i	−2.66665	−	2.23758i
$262$		0			0
$263$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	0.104528	−	0.994522i	$-0.466667\pi$
$263$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	−0.309017	+	0.951057i	$0.600000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.61166	−	2.90054i	−2.61166	−	2.90054i
$268$	1.18161	−	0.628276i	1.18161	−	0.628276i
$269$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$269$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$270$	3.35877	−	1.22249i	3.35877	−	1.22249i
$271$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$271$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.980733	+	1.08921i	0.980733	+	1.08921i
$277$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$277$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$278$		0			0
$279$		0			0
$280$	−0.339707	−	0.0722070i	−0.339707	−	0.0722070i
$281$	0.0390311	−	1.11770i	0.0390311	−	1.11770i	−0.809017	−	0.587785i	$-0.800000\pi$
$281$	0.0390311	−	1.11770i	0.0390311	−	1.11770i	0.848048	−	0.529919i	$-0.177778\pi$
$282$	−0.313295	−	0.262885i	−0.313295	−	0.262885i
$283$	0.149516	+	0.599676i	0.149516	+	0.599676i	0.997564	+	0.0697565i	$0.0222222\pi$
$283$	0.149516	+	0.599676i	0.149516	+	0.599676i	−0.848048	+	0.529919i	$0.822222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.627419	−	0.179910i	0.627419	−	0.179910i
$288$	2.28716	+	1.66172i	2.28716	+	1.66172i
$289$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$290$	0.943248	+	0.791479i	0.943248	+	0.791479i
$291$		0			0
$292$		0			0
$293$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$293$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$294$	−0.179824	+	1.71091i	−0.179824	+	1.71091i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.93726	−	0.411777i	1.93726	−	0.411777i
$299$		0			0
$300$	−1.83832	+	0.669092i	−1.83832	+	0.669092i
$301$	0.576303	+	0.209757i	0.576303	+	0.209757i
$302$		0			0
$303$	0.530016	−	1.63122i	0.530016	−	1.63122i
$304$		0			0
$305$	0.181251	+	0.448612i	0.181251	+	0.448612i
$306$		0			0
$307$	0.442013	−	1.77282i	0.442013	−	1.77282i	−0.173648	−	0.984808i	$-0.555556\pi$
$307$	0.442013	−	1.77282i	0.442013	−	1.77282i	0.615661	−	0.788011i	$-0.288889\pi$
$308$		0			0
$309$	−0.925857	−	3.71341i	−0.925857	−	3.71341i
$310$		0			0
$311$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$311$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	−0.430410	−	0.882470i	−0.430410	−	0.882470i
$316$		0			0
$317$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$317$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$318$		0			0
$319$		0			0
$320$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$321$	0.292497	−	1.17314i	0.292497	−	1.17314i
$322$	0.174107	−	0.193366i	0.174107	−	0.193366i
$323$		0			0
$324$	0.145369	+	4.16281i	0.145369	+	4.16281i
$325$		0			0
$326$	−0.962665	+	1.06915i	−0.962665	+	1.06915i
$327$	1.16222	−	3.57695i	1.16222	−	3.57695i
$328$	1.86110	+	0.261560i	1.86110	+	0.261560i
$329$	−0.0406000	+	0.0601920i	−0.0406000	+	0.0601920i
$330$		0			0
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	1.47815	+	0.658114i	1.47815	+	0.658114i
$333$		0			0
$334$	1.07506	+	1.59384i	1.07506	+	1.59384i
$335$	−1.22256	−	0.544320i	−1.22256	−	0.544320i
$336$	0.339707	−	0.588390i	0.339707	−	0.588390i
$337$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$337$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$338$	0.882948	−	0.469472i	0.882948	−	0.469472i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.652704			0.652704
$344$	1.27028	+	1.22669i	1.27028	+	1.22669i
$345$	0.254513	−	1.44342i	0.254513	−	1.44342i
$346$		0			0
$347$	−0.490268	+	1.00520i	−0.490268	+	1.00520i	0.500000	+	0.866025i	$0.333333\pi$
$347$	−0.490268	+	1.00520i	−0.490268	+	1.00520i	−0.990268	+	0.139173i	$0.955556\pi$
$348$	−2.04280	+	1.27649i	−2.04280	+	1.27649i
$349$	−0.177290	−	0.110783i	−0.177290	−	0.110783i	0.438371	−	0.898794i	$-0.355556\pi$
$349$	−0.177290	−	0.110783i	−0.177290	−	0.110783i	−0.615661	+	0.788011i	$0.711111\pi$
$350$	0.152245	+	0.312148i	0.152245	+	0.312148i
$351$		0			0
$352$		0			0
$353$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$353$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$354$		0			0
$355$		0			0
$356$	−1.82264	+	0.811492i	−1.82264	+	0.811492i
$357$		0			0
$358$		0			0
$359$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$359$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$360$	−0.0986641	−	2.82537i	−0.0986641	−	2.82537i
$361$	1.00000			1.00000
$362$	0.104528	+	0.994522i	0.104528	+	0.994522i
$363$	1.95630			1.95630
$364$		0			0
$365$		0			0
$366$	−0.944236	+	0.0660274i	−0.944236	+	0.0660274i
$367$	−1.33826	−	1.48629i	−1.33826	−	1.48629i	−0.669131	−	0.743145i	$-0.733333\pi$
$367$	−1.33826	−	1.48629i	−1.33826	−	1.48629i	−0.669131	−	0.743145i	$-0.733333\pi$
$368$	0.684440	−	0.304732i	0.684440	−	0.304732i
$369$	2.65660	+	4.60136i	2.65660	+	4.60136i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$373$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$374$		0			0
$375$	1.65903	+	1.03668i	1.65903	+	1.03668i
$376$	−0.177290	+	0.110783i	−0.177290	+	0.110783i
$377$		0			0
$378$	1.22927	−	0.172763i	1.22927	−	0.172763i
$379$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$379$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$380$		0			0
$381$	−2.99722			−2.99722
$382$		0			0
$383$	−1.22832	+	1.57218i	−1.22832	+	1.57218i	−0.559193	+	0.829038i	$0.688889\pi$
$383$	−1.22832	+	1.57218i	−1.22832	+	1.57218i	−0.669131	+	0.743145i	$0.733333\pi$
$384$	1.58268	−	1.14988i	1.58268	−	1.14988i
$385$		0			0
$386$		0			0
$387$	−0.521842	+	4.96500i	−0.521842	+	4.96500i
$388$		0			0
$389$	−1.82264	−	0.811492i	−1.82264	−	0.811492i	−0.939693	−	0.342020i	$-0.888889\pi$
$389$	−1.82264	−	0.811492i	−1.82264	−	0.811492i	−0.882948	−	0.469472i	$-0.844444\pi$
$390$		0			0
$391$		0			0
$392$	0.803358	+	0.357678i	0.803358	+	0.357678i
$393$		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
$400$	0.0348995	+	0.999391i	0.0348995	+	0.999391i
$401$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$401$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$402$	1.75181	−	1.94558i	1.75181	−	1.94558i
$403$		0			0
$404$	−0.709299	−	0.515336i	−0.709299	−	0.515336i
$405$	3.19084	−	2.67744i	3.19084	−	2.67744i
$406$	0.263278	+	0.336980i	0.263278	+	0.336980i
$407$		0			0
$408$		0			0
$409$	−0.438371	−	0.898794i	−0.438371	−	0.898794i	−0.997564	−	0.0697565i	$-0.977778\pi$
$409$	−0.438371	−	0.898794i	−0.438371	−	0.898794i	0.559193	−	0.829038i	$-0.311111\pi$
$410$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$411$		0			0
$412$	−1.95153	−	0.136464i	−1.95153	−	0.136464i
$413$		0			0
$414$	1.87017	+	0.994385i	1.87017	+	0.994385i
$415$	−0.391438	−	1.56997i	−0.391438	−	1.56997i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$419$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$420$	−0.672802	+	0.0945562i	−0.672802	+	0.0945562i
$421$	0.612019	−	1.88360i	0.612019	−	1.88360i	0.173648	−	0.984808i	$-0.444444\pi$
$421$	0.612019	−	1.88360i	0.612019	−	1.88360i	0.438371	−	0.898794i	$-0.355556\pi$
$422$		0			0
$423$	−0.555380	−	0.202142i	−0.555380	−	0.202142i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.0291794	+	0.165484i	0.0291794	+	0.165484i
$428$	−0.524123	−	0.327508i	−0.524123	−	0.327508i
$429$		0			0
$430$	0.184586	−	1.75622i	0.184586	−	1.75622i
$431$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$431$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$432$	3.43587	+	0.985219i	3.43587	+	0.985219i
$433$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$433$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$434$		0			0
$435$	2.26356	+	0.823869i	2.26356	+	0.823869i
$436$	−1.55535	−	1.13003i	−1.55535	−	1.13003i
$437$		0			0
$438$		0			0
$439$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$439$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$440$		0			0
$441$	0.601443	+	2.41225i	0.601443	+	2.41225i
$442$		0			0
$443$	−0.0534691	+	1.53116i	−0.0534691	+	1.53116i	0.615661	+	0.788011i	$0.288889\pi$
$443$	−0.0534691	+	1.53116i	−0.0534691	+	1.53116i	−0.669131	+	0.743145i	$0.733333\pi$
$444$		0			0
$445$	1.76159	+	0.936656i	1.76159	+	0.936656i
$446$	0.948445	−	1.40613i	0.948445	−	1.40613i
$447$	3.28577	−	2.05318i	3.28577	−	2.05318i
$448$	−0.232387	−	0.258091i	−0.232387	−	0.258091i
$449$	−0.0616289	+	0.0327686i	−0.0616289	+	0.0327686i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−0.0616289	+	0.0327686i	−0.0616289	+	0.0327686i	0.438371	+	0.898794i	$0.355556\pi$
$450$	−2.16568	+	1.81722i	−2.16568	+	1.81722i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.35192	−	0.492057i	1.35192	−	0.492057i
$455$		0			0
$456$		0			0
$457$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$457$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$458$	−0.524123	+	0.327508i	−0.524123	+	0.327508i
$459$		0			0
$460$	−0.661516	−	0.351734i	−0.661516	−	0.351734i
$461$	−1.93726	−	0.411777i	−1.93726	−	0.411777i	−0.997564	−	0.0697565i	$-0.977778\pi$
$461$	−1.93726	−	0.411777i	−1.93726	−	0.411777i	−0.939693	−	0.342020i	$-0.888889\pi$
$462$		0			0
$463$	0.943248	+	0.791479i	0.943248	+	0.791479i	0.978148	−	0.207912i	$-0.0666667\pi$
$463$	0.943248	+	0.791479i	0.943248	+	0.791479i	−0.0348995	+	0.999391i	$0.511111\pi$
$464$	0.297884	+	1.19475i	0.297884	+	1.19475i
$465$		0			0
$466$		0			0
$467$	−1.87481	+	0.131099i	−1.87481	+	0.131099i	−0.961262	−	0.275637i	$-0.911111\pi$
$467$	−1.87481	+	0.131099i	−1.87481	+	0.131099i	−0.913545	+	0.406737i	$0.866667\pi$
$468$		0			0
$469$	−0.376009	−	0.273187i	−0.376009	−	0.273187i
$470$	0.196449	+	0.0715017i	0.196449	+	0.0715017i
$471$		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		0.978148	−	0.207912i	$-0.0666667\pi$
$479$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$480$	−1.88051	−	0.539228i	−1.88051	−	0.539228i
$481$		0			0
$482$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$483$	0.190685	−	0.471961i	0.190685	−	0.471961i
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$	1.71357	+	4.24124i	1.71357	+	4.24124i
$487$	0.904793	−	0.657371i	0.904793	−	0.657371i	−0.0348995	−	0.999391i	$-0.511111\pi$
$487$	0.904793	−	0.657371i	0.904793	−	0.657371i	0.939693	+	0.342020i	$0.111111\pi$
$488$	−0.117052	+	0.469472i	−0.117052	+	0.469472i
$489$	−1.05432	+	2.60954i	−1.05432	+	2.60954i
$490$	−0.212743	−	0.853264i	−0.212743	−	0.853264i
$491$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$491$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$492$	3.59629	−	0.764415i	3.59629	−	0.764415i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.15764	+	0.220804i	3.15764	+	0.220804i
$499$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$499$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$500$	0.766044	−	0.642788i	0.766044	−	0.642788i
$501$	3.04273	+	2.21067i	3.04273	+	2.21067i
$502$		0			0
$503$	1.33500	−	1.48267i	1.33500	−	1.48267i	0.615661	−	0.788011i	$-0.288889\pi$
$503$	1.33500	−	1.48267i	1.33500	−	1.48267i	0.719340	−	0.694658i	$-0.244444\pi$
$504$	0.170494	−	0.966922i	0.170494	−	0.966922i
$505$	0.0305979	+	0.876208i	0.0305979	+	0.876208i
$506$		0			0
$507$	1.30902	−	1.45381i	1.30902	−	1.45381i
$508$	−0.473442	+	1.45710i	−0.473442	+	1.45710i
$509$	−1.74871	−	0.245765i	−1.74871	−	0.245765i	−0.809017	−	0.587785i	$-0.800000\pi$
$509$	−1.74871	−	0.245765i	−1.74871	−	0.245765i	−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$513$		0			0
$514$		0			0
$515$	1.09395	+	1.62184i	1.09395	+	1.62184i
$516$	3.15595	+	1.40512i	3.15595	+	1.40512i
$517$		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	$0.133333\pi$
$522$	−2.14316	+	2.74311i	−2.14316	+	2.74311i
$523$	−1.35192	−	1.30553i	−1.35192	−	1.30553i	−0.913545	−	0.406737i	$-0.866667\pi$
$523$	−1.35192	−	1.30553i	−1.35192	−	1.30553i	−0.438371	−	0.898794i	$-0.644444\pi$
$524$		0			0
$525$	0.488730	+	0.471961i	0.488730	+	0.471961i
$526$	−0.0363024	+	0.205881i	−0.0363024	+	0.205881i
$527$		0			0
$528$		0			0
$529$	−0.372021	+	0.232465i	−0.372021	+	0.232465i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−2.80763	+	2.71129i	−2.80763	+	2.71129i
$535$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$536$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$537$		0			0
$538$	−1.02517	−	1.13856i	−1.02517	−	1.13856i
$539$		0			0
$540$	−1.33897	−	3.31406i	−1.33897	−	3.31406i
$541$	0.0697990	+	1.99878i	0.0697990	+	1.99878i	0.0348995	+	0.999391i	$0.488889\pi$
$541$	0.0697990	+	1.99878i	0.0697990	+	1.99878i	0.0348995	+	0.999391i	$0.488889\pi$
$542$		0			0
$543$	0.857583	+	1.75831i	0.857583	+	1.75831i
$544$		0			0
$545$	0.0670951	+	1.92135i	0.0670951	+	1.92135i
$546$		0			0
$547$	−1.22832	+	0.0858927i	−1.22832	+	0.0858927i	−0.669131	−	0.743145i	$-0.733333\pi$
$547$	−1.22832	+	0.0858927i	−1.22832	+	0.0858927i	−0.559193	+	0.829038i	$0.688889\pi$
$548$		0			0
$549$	−1.24961	+	0.556363i	−1.24961	+	0.556363i
$550$		0			0
$551$		0			0
$552$	1.05432	−	1.01815i	1.05432	−	1.01815i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$557$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$558$		0			0
$559$		0			0
$560$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$561$		0			0
$562$	−1.11839			−1.11839
$563$	1.42468	+	1.37580i	1.42468	+	1.37580i	0.809017	+	0.587785i	$0.200000\pi$
$563$	1.42468	+	1.37580i	1.42468	+	1.37580i	0.615661	+	0.788011i	$0.288889\pi$
$564$	−0.251791	+	0.322278i	−0.251791	+	0.322278i
$565$		0			0
$566$	0.594092	−	0.170353i	0.594092	−	0.170353i
$567$	1.27728	−	0.679143i	1.27728	−	0.679143i
$568$		0			0
$569$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.374607	+	0.927184i	$0.622222\pi$
$569$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.615661	+	0.788011i	$0.711111\pi$
$570$		0			0
$571$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$571$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$572$		0			0
$573$		0			0
$574$	−0.201697	−	0.620758i	−0.201697	−	0.620758i
$575$	0.130100	+	0.737831i	0.130100	+	0.737831i
$576$	1.58089	−	2.34376i	1.58089	−	2.34376i
$577$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$577$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$578$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$579$		0			0
$580$	0.758078	−	0.970296i	0.758078	−	0.970296i
$581$	−0.0196113	−	0.561595i	−0.0196113	−	0.561595i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.885740	−	1.13369i	−0.885740	−	1.13369i	−0.990268	−	0.139173i	$-0.955556\pi$
$587$	−0.885740	−	1.13369i	−0.885740	−	1.13369i	0.104528	−	0.994522i	$-0.466667\pi$
$588$	1.71615	+	0.120005i	1.71615	+	0.120005i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$593$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$594$		0			0
$595$		0			0
$596$	−0.479135	−	1.92171i	−0.479135	−	1.92171i
$597$		0			0
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	0.732841	+	1.81385i	0.732841	+	1.81385i
$601$	1.80931	−	0.254282i	1.80931	−	0.254282i	0.848048	−	0.529919i	$-0.177778\pi$
$601$	1.80931	−	0.254282i	1.80931	−	0.254282i	0.961262	+	0.275637i	$0.0888889\pi$
$602$	0.189517	−	0.583272i	0.189517	−	0.583272i
$603$	1.41728	−	3.50789i	1.41728	−	3.50789i
$604$		0			0
$605$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$606$	−1.64872	−	0.472764i	−1.64872	−	0.472764i
$607$	0.339707	−	0.0722070i	0.339707	−	0.0722070i	−0.0348995	−	0.999391i	$-0.511111\pi$
$607$	0.339707	−	0.0722070i	0.339707	−	0.0722070i	0.374607	+	0.927184i	$0.377778\pi$
$608$		0			0
$609$	0.709459	+	0.443319i	0.709459	+	0.443319i
$610$	0.442013	−	0.196797i	0.442013	−	0.196797i
$611$		0			0
$612$		0			0
$613$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$613$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$614$	−1.78716	−	0.379874i	−1.78716	−	0.379874i
$615$	−2.81646	−	2.36329i	−2.81646	−	2.36329i
$616$		0			0
$617$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$617$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$618$	−3.67884	+	1.05489i	−3.67884	+	1.05489i
$619$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$619$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$620$		0			0
$621$	2.65187	+	0.372696i	2.65187	+	0.372696i
$622$		0			0
$623$	0.530793	+	0.445388i	0.530793	+	0.445388i
$624$		0			0
$625$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.866912	+	0.460945i	−0.866912	+	0.460945i
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		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
$640$	−0.559193	+	0.829038i	−0.559193	+	0.829038i
$641$	−1.49756	−	0.796269i	−1.49756	−	0.796269i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−1.49756	−	0.796269i	−1.49756	−	0.796269i	−0.997564	+	0.0697565i	$0.977778\pi$
$642$	−1.18264	−	0.251377i	−1.18264	−	0.251377i
$643$	0.0348995	−	0.999391i	0.0348995	−	0.999391i	−0.848048	−	0.529919i	$-0.822222\pi$
$643$	0.0348995	−	0.999391i	0.0348995	−	0.999391i	0.882948	−	0.469472i	$-0.155556\pi$
$644$	−0.199324	−	0.167253i	−0.199324	−	0.167253i
$645$	−0.835746	−	3.35200i	−0.835746	−	3.35200i
$646$		0			0
$647$	−0.490268	+	1.00520i	−0.490268	+	1.00520i	0.500000	+	0.866025i	$0.333333\pi$
$647$	−0.490268	+	1.00520i	−0.490268	+	1.00520i	−0.990268	+	0.139173i	$0.955556\pi$
$648$	4.15521	−	0.290560i	4.15521	−	0.290560i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.10209	+	0.924765i	1.10209	+	0.924765i
$653$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$653$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$654$	−3.61533	−	1.03668i	−3.61533	−	1.03668i
$655$		0			0
$656$	0.196449	−	1.86909i	0.196449	−	1.86909i
$657$		0			0
$658$	0.0615723	+	0.0384746i	0.0615723	+	0.0384746i
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$	1.75631	+	0.503615i	1.75631	+	0.503615i	0.990268	−	0.139173i	$-0.0444444\pi$
$661$	1.75631	+	0.503615i	1.75631	+	0.503615i	0.766044	+	0.642788i	$0.222222\pi$
$662$		0			0
$663$		0			0
$664$	0.606126	−	1.50021i	0.606126	−	1.50021i
$665$		0			0
$666$		0			0
$667$	0.345583	+	0.855349i	0.345583	+	0.855349i
$668$	1.55535	−	1.13003i	1.55535	−	1.13003i
$669$	0.802713	−	3.21950i	0.802713	−	3.21950i
$670$	−0.501321	+	1.24081i	−0.501321	+	1.24081i
$671$		0			0
$672$	−0.599887	−	0.318966i	−0.599887	−	0.318966i
$673$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$673$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$674$		0			0
$675$	−1.78716	+	3.09546i	−1.78716	+	3.09546i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$677$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.15602	−	1.80911i	2.15602	−	1.80911i
$682$		0			0
$683$	−0.427209	+	1.71344i	−0.427209	+	1.71344i	0.241922	+	0.970296i	$0.422222\pi$
$683$	−0.427209	+	1.71344i	−0.427209	+	1.71344i	−0.669131	+	0.743145i	$0.733333\pi$
$684$		0			0
$685$		0			0
$686$	−0.0227790	−	0.652306i	−0.0227790	−	0.652306i
$687$	−0.744370	+	0.952750i	−0.744370	+	0.952750i
$688$	1.18161	−	1.31232i	1.18161	−	1.31232i
$689$		0			0
$690$	−1.45142	−	0.203984i	−1.45142	−	0.203984i
$691$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$691$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$692$		0			0
$693$		0			0
$694$	1.02170	+	0.454888i	1.02170	+	0.454888i
$695$		0			0
$696$	1.34700	+	1.99701i	1.34700	+	1.99701i
$697$		0			0
$698$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$699$		0			0
$700$	0.306644	−	0.163046i	0.306644	−	0.163046i
$701$	−1.38295	+	0.396554i	−1.38295	+	0.396554i	−0.882948	−	0.469472i	$-0.844444\pi$
$701$	−1.38295	+	0.396554i	−1.38295	+	0.396554i	−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.408977			0.408977
$706$		0			0
$707$	−0.0528740	+	0.299864i	−0.0528740	+	0.299864i
$708$		0			0
$709$	0.868210	−	1.78009i	0.868210	−	1.78009i	0.309017	−	0.951057i	$-0.400000\pi$
$709$	0.868210	−	1.78009i	0.868210	−	1.78009i	0.559193	−	0.829038i	$-0.311111\pi$
$710$		0			0
$711$		0			0
$712$	0.874607	+	1.79321i	0.874607	+	1.79321i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$719$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$720$	−2.82020	+	0.197208i	−2.82020	+	0.197208i
$721$	0.254513	+	0.629942i	0.254513	+	0.629942i
$722$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$723$	−1.95630			−1.95630
$724$	0.990268	−	0.139173i	0.990268	−	0.139173i
$725$	−1.23132			−1.23132
$726$	−0.0682737	−	1.95510i	−0.0682737	−	1.95510i
$727$	0.231520	+	0.573031i	0.231520	+	0.573031i	0.997564	−	0.0697565i	$-0.0222222\pi$
$727$	0.231520	+	0.573031i	0.231520	+	0.573031i	−0.766044	+	0.642788i	$0.777778\pi$
$728$		0			0
$729$	3.20071	+	3.55475i	3.20071	+	3.55475i
$730$		0			0
$731$		0			0
$732$	0.0989405	+	0.941356i	0.0989405	+	0.941356i
$733$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$733$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$734$	−1.43868	+	1.38932i	−1.43868	+	1.38932i
$735$	−0.962000	−	1.42622i	−0.962000	−	1.42622i
$736$	−0.328433	−	0.673388i	−0.328433	−	0.673388i
$737$		0			0
$738$	4.50584	−	2.81556i	4.50584	−	2.81556i
$739$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$739$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.92252			−1.92252			−0.961262	−	0.275637i	$-0.911111\pi$
$743$	−1.92252			−1.92252			−0.961262	+	0.275637i	$0.911111\pi$
$744$		0			0
$745$	−1.21934	+	1.56068i	−1.21934	+	1.56068i
$746$		0			0
$747$	4.39713	−	1.26086i	4.39713	−	1.26086i
$748$		0			0
$749$	−0.0224361	+	0.213465i	−0.0224361	+	0.213465i
$750$	0.978148	−	1.69420i	0.978148	−	1.69420i
$751$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$751$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$752$	0.116903	+	0.173316i	0.116903	+	0.173316i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.215558	−	1.22249i	−0.215558	−	1.22249i
$757$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$757$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.823916	+	1.05456i	−0.823916	+	1.05456i	0.173648	+	0.984808i	$0.444444\pi$
$761$	−0.823916	+	1.05456i	−0.823916	+	1.05456i	−0.997564	+	0.0697565i	$0.977778\pi$
$762$	0.104601	+	2.99539i	0.104601	+	2.99539i
$763$	−0.115942	+	0.657542i	−0.115942	+	0.657542i
$764$		0			0
$765$		0			0
$766$	1.61409	+	1.17271i	1.61409	+	1.17271i
$767$		0			0
$768$	−1.20442	−	1.54158i	−1.20442	−	1.54158i
$769$	−0.0696290	−	0.00486893i	−0.0696290	−	0.00486893i	0.0348995	−	0.999391i	$-0.488889\pi$
$769$	−0.0696290	−	0.00486893i	−0.0696290	−	0.00486893i	−0.104528	+	0.994522i	$0.533333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	4.98019	+	0.348248i	4.98019	+	0.348248i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.747388	+	1.84985i	−0.747388	+	1.84985i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.36003	+	4.18575i	−1.36003	+	4.18575i
$784$	0.329424	−	0.815352i	0.329424	−	0.815352i
$785$		0			0
$786$		0			0
$787$	0.465101	+	0.133365i	0.465101	+	0.133365i	0.500000	−	0.866025i	$-0.333333\pi$
$787$	0.465101	+	0.133365i	0.465101	+	0.133365i	−0.0348995	+	0.999391i	$0.511111\pi$
$788$		0			0
$789$	0.0710181	+	0.402764i	0.0710181	+	0.402764i
$790$		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	$-0.888889\pi$
$797$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$798$		0			0
$799$		0			0
$800$	0.997564	−	0.0697565i	0.997564	−	0.0697565i
$801$	−2.47259	+	5.06957i	−2.47259	+	5.06957i
$802$	−0.0691197	−	0.00971414i	−0.0691197	−	0.00971414i
$803$		0			0
$804$	−2.00553	−	1.68284i	−2.00553	−	1.68284i
$805$	−0.00908081	+	0.260041i	−0.00908081	+	0.260041i
$806$		0			0
$807$	−2.64639	−	1.40711i	−2.64639	−	1.40711i
$808$	−0.490268	+	0.726852i	−0.490268	+	0.726852i
$809$	1.13491	−	0.709170i	1.13491	−	0.709170i	0.173648	−	0.984808i	$-0.444444\pi$
$809$	1.13491	−	0.709170i	1.13491	−	0.709170i	0.961262	+	0.275637i	$0.0888889\pi$
$810$	−2.78716	−	3.09546i	−2.78716	−	3.09546i
$811$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$811$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$812$	0.327587	−	0.274878i	0.327587	−	0.274878i
$813$		0			0
$814$		0			0
$815$	0.0502092	−	1.43780i	0.0502092	−	1.43780i
$816$		0			0
$817$		0			0
$818$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$819$		0			0
$820$	−1.59381	+	0.995922i	−1.59381	+	0.995922i
$821$	−0.987476	+	1.46399i	−0.987476	+	1.46399i	−0.104528	+	0.994522i	$0.533333\pi$
$821$	−0.987476	+	1.46399i	−0.987476	+	1.46399i	−0.882948	+	0.469472i	$0.844444\pi$
$822$		0			0
$823$	−0.732841	−	0.155770i	−0.732841	−	0.155770i	−0.173648	−	0.984808i	$-0.555556\pi$
$823$	−0.732841	−	0.155770i	−0.732841	−	0.155770i	−0.559193	+	0.829038i	$0.688889\pi$
$824$	−0.0682737	+	1.95510i	−0.0682737	+	1.95510i
$825$		0			0
$826$		0			0
$827$	−0.868210	−	0.122019i	−0.868210	−	0.122019i	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	−0.868210	−	0.122019i	−0.868210	−	0.122019i	−0.559193	+	0.829038i	$0.688889\pi$
$828$	0.928511	−	1.90373i	0.928511	−	1.90373i
$829$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.766044	−	0.642788i	$-0.222222\pi$
$829$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.848048	+	0.529919i	$0.177778\pi$
$830$	−1.55535	+	0.445991i	−1.55535	+	0.445991i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.84805	−	0.529919i	−1.84805	−	0.529919i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$839$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$840$	0.117979	+	0.669092i	0.117979	+	0.669092i
$841$	−0.504877	+	0.107315i	−0.504877	+	0.107315i
$842$	−1.90381	−	0.545910i	−1.90381	−	0.545910i
$843$	−2.05595	+	0.748303i	−2.05595	+	0.748303i
$844$		0			0
$845$	−0.374607	+	0.927184i	−0.374607	+	0.927184i
$846$	−0.182636	+	0.562096i	−0.182636	+	0.562096i
$847$	−0.343916	+	0.0483343i	−0.343916	+	0.0483343i
$848$		0			0
$849$	0.978148	−	0.710666i	0.978148	−	0.710666i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$853$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$854$	0.164365	−	0.0349369i	0.164365	−	0.0349369i
$855$		0			0
$856$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$859$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$860$	−1.76159	−	0.123183i	−1.76159	−	0.123183i
$861$	−0.786126	−	1.00620i	−0.786126	−	1.00620i
$862$		0			0
$863$	0.709299	+	0.515336i	0.709299	+	0.515336i	0.882948	−	0.469472i	$-0.155556\pi$
$863$	0.709299	+	0.515336i	0.709299	+	0.515336i	−0.173648	+	0.984808i	$0.555556\pi$
$864$	0.864708	−	3.46816i	0.864708	−	3.46816i
$865$		0			0
$866$		0			0
$867$	0.0682737	+	1.95510i	0.0682737	+	1.95510i
$868$		0			0
$869$		0			0
$870$	0.744370	−	2.29093i	0.744370	−	2.29093i
$871$		0			0
$872$	−1.07506	+	1.59384i	−1.07506	+	1.59384i
$873$		0			0
$874$		0			0
$875$	−0.317271	−	0.141258i	−0.317271	−	0.141258i
$876$		0			0
$877$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$877$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.27028	−	0.675419i	1.27028	−	0.675419i	0.309017	−	0.951057i	$-0.400000\pi$
$881$	1.27028	−	0.675419i	1.27028	−	0.675419i	0.961262	+	0.275637i	$0.0888889\pi$
$882$	2.38979	−	0.685263i	2.38979	−	0.685263i
$883$	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
$887$	−0.348048	−	0.336106i	−0.348048	−	0.336106i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	−0.348048	−	0.336106i	−0.348048	−	0.336106i	−0.848048	+	0.529919i	$0.822222\pi$
$888$		0			0
$889$	0.526911	−	0.0740525i	0.526911	−	0.0740525i
$890$	0.874607	−	1.79321i	0.874607	−	1.79321i
$891$		0			0
$892$	−1.43837	−	0.898794i	−1.43837	−	0.898794i
$893$		0			0
$894$	−2.16660	−	3.21212i	−2.16660	−	3.21212i
$895$		0			0
$896$	−0.249824	+	0.241252i	−0.249824	+	0.241252i
$897$		0			0
$898$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i
$899$		0			0
$900$	1.89169	+	2.10094i	1.89169	+	2.10094i
$901$		0			0
$902$		0			0
$903$	−0.0418715	−	1.19904i	−0.0418715	−	1.19904i
$904$		0			0
$905$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$906$		0			0
$907$	0.0429726	+	1.23057i	0.0429726	+	1.23057i	0.809017	+	0.587785i	$0.200000\pi$
$907$	0.0429726	+	1.23057i	0.0429726	+	1.23057i	−0.766044	+	0.642788i	$0.777778\pi$
$908$	−0.538939	−	1.33392i	−0.538939	−	1.33392i
$909$	−2.47259	+	0.172901i	−2.47259	+	0.172901i
$910$		0			0
$911$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$911$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.680885	−	0.657523i	0.680885	−	0.657523i
$916$	0.345600	+	0.512373i	0.345600	+	0.512373i
$917$		0			0
$918$		0			0
$919$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$919$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$920$	−0.328433	+	0.673388i	−0.328433	+	0.673388i
$921$	−3.53954	+	0.497450i	−3.53954	+	0.497450i
$922$	−0.343916	+	1.95045i	−0.343916	+	1.95045i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.758078	−	0.970296i	0.758078	−	0.970296i
$927$	−4.47437	+	3.25082i	−4.47437	+	3.25082i
$928$	1.18362	−	0.339399i	1.18362	−	0.339399i
$929$	1.42864	−	0.759621i	1.42864	−	0.759621i	0.438371	−	0.898794i	$-0.355556\pi$
$929$	1.42864	−	0.759621i	1.42864	−	0.759621i	0.990268	+	0.139173i	$0.0444444\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.196449	+	1.86909i	0.196449	+	1.86909i
$935$		0			0
$936$		0			0
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$	−0.259898	+	0.385314i	−0.259898	+	0.385314i
$939$		0			0
$940$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$941$	−0.323755	+	0.359566i	−0.323755	+	0.359566i	−0.882948	−	0.469472i	$-0.844444\pi$
$941$	−0.323755	+	0.359566i	−0.323755	+	0.359566i	0.559193	+	0.829038i	$0.311111\pi$
$942$		0			0
$943$	−0.0491406	−	1.40720i	−0.0491406	−	1.40720i
$944$		0			0
$945$	−0.830626	+	0.922504i	−0.830626	+	0.922504i
$946$		0			0
$947$	−1.61409	−	1.17271i	−1.61409	−	1.17271i	−0.848048	−	0.529919i	$-0.822222\pi$
$947$	−1.61409	−	1.17271i	−1.61409	−	1.17271i	−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	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.473271	+	1.89818i	−0.473271	+	1.89818i
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$	−1.73023	+	0.243169i	−1.73023	+	0.243169i
$964$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$965$		0			0
$966$	−0.478328	−	0.174097i	−0.478328	−	0.174097i
$967$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.990268	−	0.139173i	$-0.955556\pi$
$967$	−1.65940	+	0.603972i	−1.65940	+	0.603972i	−0.669131	+	0.743145i	$0.733333\pi$
$968$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$969$		0			0
$970$		0			0
$971$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$971$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$972$	4.17886	−	1.86055i	4.17886	−	1.86055i
$973$		0			0
$974$	−0.688547	−	0.881300i	−0.688547	−	0.881300i
$975$		0			0
$976$	0.473271	+	0.100597i	0.473271	+	0.100597i
$977$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$977$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$978$	2.64475	+	0.962610i	2.64475	+	0.962610i
$979$		0			0
$980$	−0.845319	+	0.242391i	−0.845319	+	0.242391i
$981$	−5.42191	+	0.379137i	−5.42191	+	0.379137i
$982$		0			0
$983$	0.990268	+	0.139173i	0.990268	+	0.139173i	0.615661	−	0.788011i	$-0.288889\pi$
$983$	0.990268	+	0.139173i	0.990268	+	0.139173i	0.374607	+	0.927184i	$0.377778\pi$
$984$	−0.889458	−	3.56742i	−0.889458	−	3.56742i
$985$		0			0
$986$		0			0
$987$	0.138932	+	0.0295310i	0.138932	+	0.0295310i
$988$		0			0
$989$	0.739830	−	1.09684i	0.739830	−	1.09684i
$990$		0			0
$991$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$991$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.110469	−	3.16342i	0.110469	−	3.16342i
$997$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$997$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$998$		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.2579.1	yes	24
4.3	odd	2		3620.1.dy.b.2579.1	yes	24
5.4	even	2		3620.1.dy.b.2579.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.2579.1	yes	24
181.177	even	45	inner	3620.1.dy.a.539.1	✓	24
724.539	odd	90		3620.1.dy.b.539.1	yes	24
905.539	even	90		3620.1.dy.b.539.1	yes	24
3620.539	odd	90	inner	3620.1.dy.a.539.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.539.1	✓	24	181.177	even	45	inner
3620.1.dy.a.539.1	✓	24	3620.539	odd	90	inner
3620.1.dy.a.2579.1	yes	24	1.1	even	1	trivial
3620.1.dy.a.2579.1	yes	24	20.19	odd	2	CM
3620.1.dy.b.539.1	yes	24	724.539	odd	90
3620.1.dy.b.539.1	yes	24	905.539	even	90
3620.1.dy.b.2579.1	yes	24	4.3	odd	2
3620.1.dy.b.2579.1	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)

\(f(q)\)	\(=\)	\(q+(-0.0348995 - 0.999391i) q^{2} +(-0.732841 - 1.81385i) q^{3} +(-0.997564 + 0.0697565i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(0.173648 + 0.300767i) q^{7} +(0.104528 + 0.994522i) q^{8} +(-2.03364 + 1.96386i) q^{9} +O(q^{10})\)	\(q+(-0.0348995 - 0.999391i) q^{2} +(-0.732841 - 1.81385i) q^{3} +(-0.997564 + 0.0697565i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(0.173648 + 0.300767i) q^{7} +(0.104528 + 0.994522i) q^{8} +(-2.03364 + 1.96386i) q^{9} +(0.719340 - 0.694658i) q^{10} +(0.857583 + 1.75831i) q^{12} +(0.294524 - 0.184039i) q^{14} +(0.857583 - 1.75831i) q^{15} +(0.990268 - 0.139173i) q^{16} +(2.03364 + 1.96386i) q^{18} +(-0.719340 - 0.694658i) q^{20} +(0.418289 - 0.535386i) q^{21} +(0.720190 - 0.206511i) q^{23} +(1.72731 - 0.918425i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(3.26531 + 1.45381i) q^{27} +(-0.194206 - 0.287922i) q^{28} +(0.128708 + 1.22458i) q^{29} +(-1.78716 - 0.795697i) q^{30} +(-0.173648 - 0.984808i) q^{32} +(-0.107320 + 0.330298i) q^{35} +(1.89169 - 2.10094i) q^{36} +(-0.669131 + 0.743145i) q^{40} +(0.454664 - 1.82356i) q^{41} +(-0.549658 - 0.399350i) q^{42} +(1.35275 - 1.13510i) q^{43} +(-2.82020 - 0.197208i) q^{45} +(-0.231520 - 0.712544i) q^{46} +(0.0916445 + 0.187899i) q^{47} +(-0.978148 - 1.69420i) q^{48} +(0.439693 - 0.761570i) q^{49} +(0.997564 + 0.0697565i) q^{50} +(1.33897 - 3.31406i) q^{54} +(-0.280969 + 0.204136i) q^{56} +(1.21934 - 0.171367i) q^{58} +(-0.732841 + 1.81385i) q^{60} +(0.454664 + 0.165484i) q^{61} +(-0.943804 - 0.270631i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(-1.22256 + 0.544320i) q^{67} +(-0.902364 - 1.15497i) q^{69} +(0.333843 + 0.0957278i) q^{70} +(-2.16568 - 1.81722i) q^{72} +(1.88051 - 0.539228i) q^{75} +(0.766044 + 0.642788i) q^{80} +(0.145369 - 4.16281i) q^{81} +(-1.83832 - 0.390746i) q^{82} +(-1.42864 - 0.759621i) q^{83} +(-0.379924 + 0.563260i) q^{84} +(-1.18161 - 1.31232i) q^{86} +(2.12687 - 1.13088i) q^{87} +(1.87481 - 0.682374i) q^{89} +(-0.0986641 + 2.82537i) q^{90} +(-0.704030 + 0.256246i) q^{92} +(0.184586 - 0.0981463i) q^{94} +(-1.65903 + 1.03668i) q^{96} +(-0.776451 - 0.412846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 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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