LMFDB - Embedded newform 3620.1.dy.a.1979.1

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			1979.1
Root			$0.961262 + 0.275637i$ of defining polynomial
Character	$\chi$	$=$	3620.1979
Dual form			3620.1.dy.a.739.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.848048 + 0.529919i) q^{2} +(1.93726 + 0.272264i) q^{3} +(0.438371 - 0.898794i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(0.104528 + 0.994522i) q^{8} +(2.71757 + 0.779252i) q^{9} +O(q^{10})$	\(q+(-0.848048 + 0.529919i) q^{2} +(1.93726 + 0.272264i) q^{3} +(0.438371 - 0.898794i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(0.104528 + 0.994522i) q^{8} +(2.71757 + 0.779252i) q^{9} +(-0.961262 - 0.275637i) q^{10} +(1.09395 - 1.62184i) q^{12} +(1.65940 + 0.882318i) q^{14} +(1.09395 + 1.62184i) q^{15} +(-0.615661 - 0.788011i) q^{16} +(-2.71757 + 0.779252i) q^{18} +(0.961262 - 0.275637i) q^{20} +(-1.37729 - 3.40891i) q^{21} +(0.479135 - 1.92171i) q^{23} +(-0.0682737 + 1.95510i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(3.26531 + 1.45381i) q^{27} +(-1.87481 + 0.131099i) q^{28} +(0.0783141 + 0.745109i) q^{29} +(-1.78716 - 0.795697i) q^{30} +(0.939693 + 0.342020i) q^{32} +(0.580762 - 1.78740i) q^{35} +(1.89169 - 2.10094i) q^{36} +(-0.669131 + 0.743145i) q^{40} +(-1.10209 - 1.06428i) q^{41} +(2.97446 + 2.16107i) q^{42} +(-0.0121205 - 0.0687386i) q^{43} +(1.23932 + 2.54097i) q^{45} +(0.612019 + 1.88360i) q^{46} +(0.116903 - 0.173316i) q^{47} +(-0.978148 - 1.69420i) q^{48} +(-1.26604 + 2.19285i) q^{49} +(-0.438371 - 0.898794i) q^{50} +(-3.53954 + 0.497450i) q^{54} +(1.52045 - 1.10467i) q^{56} +(-0.461262 - 0.590388i) q^{58} +(1.93726 - 0.272264i) q^{60} +(-1.10209 + 0.924765i) q^{61} +(-1.28538 - 5.15537i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(-1.22256 + 0.544320i) q^{67} +(1.45142 - 3.59239i) q^{69} +(0.454664 + 1.82356i) q^{70} +(-0.490919 + 2.78414i) q^{72} +(-0.473271 + 1.89818i) q^{75} +(0.173648 - 0.984808i) q^{80} +(3.53242 + 2.20730i) q^{81} +(1.49861 + 0.318539i) q^{82} +(0.0564686 + 1.61705i) q^{83} +(-3.66768 - 0.256469i) q^{84} +(0.0467046 + 0.0518708i) q^{86} +(-0.0511516 + 1.46479i) q^{87} +(0.671624 + 0.563559i) q^{89} +(-2.39751 - 1.49813i) q^{90} +(-1.51718 - 1.27306i) q^{92} +(-0.00729598 + 0.208930i) q^{94} +(1.72731 + 0.918425i) q^{96} +(-0.0883686 - 2.53055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3620\mathbb{Z}\right)^\times$.

$n$	$1811$	$2897$	$3441$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{37}{45}\right)$

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 $

$2$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$2$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$3$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.997564	−	0.0697565i	$-0.0222222\pi$
$3$	1.93726	+	0.272264i	1.93726	+	0.272264i	0.939693	+	0.342020i	$0.111111\pi$
$4$	0.438371	−	0.898794i	0.438371	−	0.898794i
$5$	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
$7$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$7$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$8$	0.104528	+	0.994522i	0.104528	+	0.994522i
$9$	2.71757	+	0.779252i	2.71757	+	0.779252i
$10$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$11$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$11$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$12$	1.09395	−	1.62184i	1.09395	−	1.62184i
$13$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$13$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$14$	1.65940	+	0.882318i	1.65940	+	0.882318i
$15$	1.09395	+	1.62184i	1.09395	+	1.62184i
$16$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	−2.71757	+	0.779252i	−2.71757	+	0.779252i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.961262	−	0.275637i	0.961262	−	0.275637i
$21$	−1.37729	−	3.40891i	−1.37729	−	3.40891i
$22$		0			0
$23$	0.479135	−	1.92171i	0.479135	−	1.92171i	0.104528	−	0.994522i	$-0.466667\pi$
$23$	0.479135	−	1.92171i	0.479135	−	1.92171i	0.374607	−	0.927184i	$-0.377778\pi$
$24$	−0.0682737	+	1.95510i	−0.0682737	+	1.95510i
$25$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$26$		0			0
$27$	3.26531	+	1.45381i	3.26531	+	1.45381i
$28$	−1.87481	+	0.131099i	−1.87481	+	0.131099i
$29$	0.0783141	+	0.745109i	0.0783141	+	0.745109i	0.961262	+	0.275637i	$0.0888889\pi$
$29$	0.0783141	+	0.745109i	0.0783141	+	0.745109i	−0.882948	+	0.469472i	$0.844444\pi$
$30$	−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	$0.400000\pi$
$32$	0.939693	+	0.342020i	0.939693	+	0.342020i
$33$		0			0
$34$		0			0
$35$	0.580762	−	1.78740i	0.580762	−	1.78740i
$36$	1.89169	−	2.10094i	1.89169	−	2.10094i
$37$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$37$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$38$		0			0
$39$		0			0
$40$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$41$	−1.10209	−	1.06428i	−1.10209	−	1.06428i	−0.997564	−	0.0697565i	$-0.977778\pi$
$41$	−1.10209	−	1.06428i	−1.10209	−	1.06428i	−0.104528	−	0.994522i	$-0.533333\pi$
$42$	2.97446	+	2.16107i	2.97446	+	2.16107i
$43$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	0.978148	−	0.207912i	$-0.0666667\pi$
$43$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	−0.990268	+	0.139173i	$0.955556\pi$
$44$		0			0
$45$	1.23932	+	2.54097i	1.23932	+	2.54097i
$46$	0.612019	+	1.88360i	0.612019	+	1.88360i
$47$	0.116903	−	0.173316i	0.116903	−	0.173316i	−0.766044	−	0.642788i	$-0.777778\pi$
$47$	0.116903	−	0.173316i	0.116903	−	0.173316i	0.882948	+	0.469472i	$0.155556\pi$
$48$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$49$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$50$	−0.438371	−	0.898794i	−0.438371	−	0.898794i
$51$		0			0
$52$		0			0
$53$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$53$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$54$	−3.53954	+	0.497450i	−3.53954	+	0.497450i
$55$		0			0
$56$	1.52045	−	1.10467i	1.52045	−	1.10467i
$57$		0			0
$58$	−0.461262	−	0.590388i	−0.461262	−	0.590388i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	1.93726	−	0.272264i	1.93726	−	0.272264i
$61$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.997564	−	0.0697565i	$-0.977778\pi$
$61$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.104528	+	0.994522i	$0.533333\pi$
$62$		0			0
$63$	−1.28538	−	5.15537i	−1.28538	−	5.15537i
$64$	−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
$69$	1.45142	−	3.59239i	1.45142	−	3.59239i
$70$	0.454664	+	1.82356i	0.454664	+	1.82356i
$71$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$71$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$72$	−0.490919	+	2.78414i	−0.490919	+	2.78414i
$73$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$73$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$74$		0			0
$75$	−0.473271	+	1.89818i	−0.473271	+	1.89818i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$79$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$80$	0.173648	−	0.984808i	0.173648	−	0.984808i
$81$	3.53242	+	2.20730i	3.53242	+	2.20730i
$82$	1.49861	+	0.318539i	1.49861	+	0.318539i
$83$	0.0564686	+	1.61705i	0.0564686	+	1.61705i	0.615661	+	0.788011i	$0.288889\pi$
$83$	0.0564686	+	1.61705i	0.0564686	+	1.61705i	−0.559193	+	0.829038i	$0.688889\pi$
$84$	−3.66768	−	0.256469i	−3.66768	−	0.256469i
$85$		0			0
$86$	0.0467046	+	0.0518708i	0.0467046	+	0.0518708i
$87$	−0.0511516	+	1.46479i	−0.0511516	+	1.46479i
$88$		0			0
$89$	0.671624	+	0.563559i	0.671624	+	0.563559i	0.913545	−	0.406737i	$-0.133333\pi$
$89$	0.671624	+	0.563559i	0.671624	+	0.563559i	−0.241922	+	0.970296i	$0.577778\pi$
$90$	−2.39751	−	1.49813i	−2.39751	−	1.49813i
$91$		0			0
$92$	−1.51718	−	1.27306i	−1.51718	−	1.27306i
$93$		0			0
$94$	−0.00729598	+	0.208930i	−0.00729598	+	0.208930i
$95$		0			0
$96$	1.72731	+	0.918425i	1.72731	+	0.918425i
$97$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$97$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$98$	−0.0883686	−	2.53055i	−0.0883686	−	2.53055i
$99$		0			0
$100$	0.848048	+	0.529919i	0.848048	+	0.529919i
$101$	0.194206	−	1.10140i	0.194206	−	1.10140i	−0.719340	−	0.694658i	$-0.755556\pi$
$101$	0.194206	−	1.10140i	0.194206	−	1.10140i	0.913545	−	0.406737i	$-0.133333\pi$
$102$		0			0
$103$	−1.20442	+	1.54158i	−1.20442	+	1.54158i	−0.438371	+	0.898794i	$0.644444\pi$
$103$	−1.20442	+	1.54158i	−1.20442	+	1.54158i	−0.766044	+	0.642788i	$0.777778\pi$
$104$		0			0
$105$	1.61173	−	3.30454i	1.61173	−	3.30454i
$106$		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	$0.600000\pi$
$108$	2.73810	−	2.29753i	2.73810	−	2.29753i
$109$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$109$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$110$		0			0
$111$		0			0
$112$	−0.704030	+	1.74254i	−0.704030	+	1.74254i
$113$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$113$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$114$		0			0
$115$	1.74871	−	0.929805i	1.74871	−	0.929805i
$116$	0.704030	+	0.256246i	0.704030	+	0.256246i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.49861	+	1.25748i	−1.49861	+	1.25748i
$121$	0.990268	−	0.139173i	0.990268	−	0.139173i
$122$	0.444576	−	1.36827i	0.444576	−	1.36827i
$123$	−1.84527	−	2.36184i	−1.84527	−	2.36184i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$126$	3.82199	+	3.69085i	3.82199	+	3.69085i
$127$	−0.343916	+	0.0483343i	−0.343916	+	0.0483343i	−0.309017	−	0.951057i	$-0.600000\pi$
$127$	−0.343916	+	0.0483343i	−0.343916	+	0.0483343i	−0.0348995	+	0.999391i	$0.511111\pi$
$128$	0.719340	−	0.694658i	0.719340	−	0.694658i
$129$	−0.00476544	−	0.136464i	−0.00476544	−	0.136464i
$130$		0			0
$131$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$131$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$132$		0			0
$133$		0			0
$134$	0.748346	−	1.10947i	0.748346	−	1.10947i
$135$	1.10453	+	3.39939i	1.10453	+	3.39939i
$136$		0			0
$137$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$137$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$138$	0.672802	+	3.81565i	0.672802	+	3.81565i
$139$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$139$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$140$	−1.35192	−	1.30553i	−1.35192	−	1.30553i
$141$	0.273659	−	0.303929i	0.273659	−	0.303929i
$142$		0			0
$143$		0			0
$144$	−1.05905	−	2.62123i	−1.05905	−	2.62123i
$145$	−0.501321	+	0.556774i	−0.501321	+	0.556774i
$146$		0			0
$147$	−3.04969	+	3.90342i	−3.04969	+	3.90342i
$148$		0			0
$149$	1.15707	+	0.421137i	1.15707	+	0.421137i	0.848048	−	0.529919i	$-0.177778\pi$
$149$	1.15707	+	0.421137i	1.15707	+	0.421137i	0.309017	+	0.951057i	$0.400000\pi$
$150$	−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		0.0348995	−	0.999391i	$-0.488889\pi$
$157$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$158$		0			0
$159$		0			0
$160$	0.374607	+	0.927184i	0.374607	+	0.927184i
$161$	−3.57800	+	1.02597i	−3.57800	+	1.02597i
$162$	−4.16535			−4.16535
$163$	−1.84805	+	0.529919i	−1.84805	+	0.529919i	−0.848048	+	0.529919i	$0.822222\pi$
$163$	−1.84805	+	0.529919i	−1.84805	+	0.529919i	−1.00000			$\pi$
$164$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$165$		0			0
$166$	−0.904793	−	1.34141i	−0.904793	−	1.34141i
$167$	−0.427209	−	0.227151i	−0.427209	−	0.227151i	0.241922	−	0.970296i	$-0.422222\pi$
$167$	−0.427209	−	0.227151i	−0.427209	−	0.227151i	−0.669131	+	0.743145i	$0.733333\pi$
$168$	3.24627	−	1.72607i	3.24627	−	1.72607i
$169$	0.559193	−	0.829038i	0.559193	−	0.829038i
$170$		0			0
$171$		0			0
$172$	−0.0670951	−	0.0192392i	−0.0670951	−	0.0192392i
$173$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$173$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$174$	−0.732841	−	1.26932i	−0.732841	−	1.26932i
$175$	1.71690	−	0.764415i	1.71690	−	0.764415i
$176$		0			0
$177$		0			0
$178$	−0.868210	−	0.122019i	−0.868210	−	0.122019i
$179$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$179$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$180$	2.82709			2.82709
$181$	0.438371	−	0.898794i	0.438371	−	0.898794i
$181$	0.438371	−	0.898794i	0.438371	−	0.898794i
$182$		0			0
$183$	−2.38682	+	1.49145i	−2.38682	+	1.49145i
$184$	1.96126	+	0.275637i	1.96126	+	0.275637i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$189$	−0.702174	−	6.68074i	−0.702174	−	6.68074i
$190$		0			0
$191$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$191$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$192$	−1.95153	+	0.136464i	−1.95153	+	0.136464i
$193$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$193$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$194$		0			0
$195$		0			0
$196$	1.41593	+	2.09920i	1.41593	+	2.09920i
$197$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$197$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$198$		0			0
$199$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$199$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$200$	−1.00000			−1.00000
$201$	−2.51662	+	0.721628i	−2.51662	+	0.721628i
$202$	0.418955	+	1.03695i	0.418955	+	1.03695i
$203$	1.13914	−	0.827637i	1.13914	−	0.827637i
$204$		0			0
$205$	0.0534691	−	1.53116i	0.0534691	−	1.53116i
$206$	0.204489	−	1.94558i	0.204489	−	1.94558i
$207$	2.79958	−	4.84901i	2.79958	−	4.84901i
$208$		0			0
$209$		0			0
$210$	0.384313	+	3.65649i	0.384313	+	3.65649i
$211$		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
$214$	−0.616528	−	0.0431119i	−0.616528	−	0.0431119i
$215$	0.0429726	−	0.0550024i	0.0429726	−	0.0550024i
$216$	−1.10453	+	3.39939i	−1.10453	+	3.39939i
$217$		0			0
$218$	−0.181251	−	0.448612i	−0.181251	−	0.448612i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1.42864	−	1.03797i	−1.42864	−	1.03797i	−0.990268	−	0.139173i	$-0.955556\pi$
$223$	−1.42864	−	1.03797i	−1.42864	−	1.03797i	−0.438371	−	0.898794i	$-0.644444\pi$
$224$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$225$	−1.05905	+	2.62123i	−1.05905	+	2.62123i
$226$		0			0
$227$	−0.594092	−	1.82843i	−0.594092	−	1.82843i	−0.559193	−	0.829038i	$-0.688889\pi$
$227$	−0.594092	−	1.82843i	−0.594092	−	1.82843i	−0.0348995	−	0.999391i	$-0.511111\pi$
$228$		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	$0.933333\pi$
$230$	−0.990268	+	1.71519i	−0.990268	+	1.71519i
$231$		0			0
$232$	−0.732841	+	0.155770i	−0.732841	+	0.155770i
$233$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$233$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$234$		0			0
$235$	0.207022	−	0.0290951i	0.207022	−	0.0290951i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$239$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$240$	0.604528	−	1.86055i	0.604528	−	1.86055i
$241$	−0.990268	+	0.139173i	−0.990268	+	0.139173i	−0.615661	−	0.788011i	$-0.711111\pi$
$241$	−0.990268	+	0.139173i	−0.990268	+	0.139173i	−0.374607	+	0.927184i	$0.622222\pi$
$242$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$243$	3.50414	+	2.94032i	3.50414	+	2.94032i
$244$	0.348048	+	1.39594i	0.348048	+	1.39594i
$245$	−2.47676	+	0.526451i	−2.47676	+	0.526451i
$246$	2.81646	+	1.02511i	2.81646	+	1.02511i
$247$		0			0
$248$		0			0
$249$	−0.330869	+	3.14801i	−0.330869	+	3.14801i
$250$	0.374607	−	0.927184i	0.374607	−	0.927184i
$251$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$251$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$252$	−5.19709	−	1.10467i	−5.19709	−	1.10467i
$253$		0			0
$254$	0.266044	−	0.223238i	0.266044	−	0.223238i
$255$		0			0
$256$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$257$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$257$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$258$	0.0763564	+	0.113203i	0.0763564	+	0.113203i
$259$		0			0
$260$		0			0
$261$	−0.367803	+	2.08592i	−0.367803	+	2.08592i
$262$		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
$267$	1.14767	+	1.27462i	1.14767	+	1.27462i
$268$	−0.0467046	+	1.33745i	−0.0467046	+	1.33745i
$269$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$269$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$270$	−2.73810	−	2.29753i	−2.73810	−	2.29753i
$271$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$271$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−2.59256	−	2.87932i	−2.59256	−	2.87932i
$277$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$277$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$278$		0			0
$279$		0			0
$280$	1.83832	+	0.390746i	1.83832	+	0.390746i
$281$	−1.69196	−	1.05726i	−1.69196	−	1.05726i	−0.882948	−	0.469472i	$-0.844444\pi$
$281$	−1.69196	−	1.05726i	−1.69196	−	1.05726i	−0.809017	−	0.587785i	$-0.800000\pi$
$282$	−0.0710181	+	0.402764i	−0.0710181	+	0.402764i
$283$	0.444576	−	0.429322i	0.444576	−	0.429322i	−0.438371	−	0.898794i	$-0.644444\pi$
$283$	0.444576	−	0.429322i	0.444576	−	0.429322i	0.882948	+	0.469472i	$0.155556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.696586	+	2.79386i	−0.696586	+	2.79386i
$288$	2.28716	+	1.66172i	2.28716	+	1.66172i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$	0.130100	−	0.737831i	0.130100	−	0.737831i
$291$		0			0
$292$		0			0
$293$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$293$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$294$	0.517783	−	4.92638i	0.517783	−	4.92638i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.20442	+	0.256006i	−1.20442	+	0.256006i
$299$		0			0
$300$	1.49861	+	1.25748i	1.49861	+	1.25748i
$301$	−0.100489	+	0.0843204i	−0.100489	+	0.0843204i
$302$		0			0
$303$	0.676096	−	2.08081i	0.676096	−	2.08081i
$304$		0			0
$305$	−1.42468	−	0.200226i	−1.42468	−	0.200226i
$306$		0			0
$307$	1.31430	+	1.26920i	1.31430	+	1.26920i	0.939693	+	0.342020i	$0.111111\pi$
$307$	1.31430	+	1.26920i	1.31430	+	1.26920i	0.374607	+	0.927184i	$0.377778\pi$
$308$		0			0
$309$	−2.75298	+	2.65852i	−2.75298	+	2.65852i
$310$		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
$315$	2.97110	−	4.40484i	2.97110	−	4.40484i
$316$		0			0
$317$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$317$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$318$		0			0
$319$		0			0
$320$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$321$	0.869723	+	0.839882i	0.869723	+	0.839882i
$322$	2.49063	−	2.76613i	2.49063	−	2.76613i
$323$		0			0
$324$	3.53242	−	2.20730i	3.53242	−	2.20730i
$325$		0			0
$326$	1.28642	−	1.42871i	1.28642	−	1.42871i
$327$	−0.292497	+	0.900214i	−0.292497	+	0.900214i
$328$	0.943248	−	1.20730i	0.943248	−	1.20730i
$329$	−0.391941	−	0.0274072i	−0.391941	−	0.0274072i
$330$		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
$334$	0.482665	−	0.0337512i	0.482665	−	0.0337512i
$335$	−1.22256	−	0.544320i	−1.22256	−	0.544320i
$336$	−1.83832	+	3.18406i	−1.83832	+	3.18406i
$337$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$337$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$338$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	2.87939			2.87939
$344$	0.0670951	−	0.0192392i	0.0670951	−	0.0192392i
$345$	3.64085	−	1.32516i	3.64085	−	1.32516i
$346$		0			0
$347$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.615661	+	0.788011i	$0.288889\pi$
$347$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.500000	+	0.866025i	$0.333333\pi$
$348$	1.29412	+	0.688096i	1.29412	+	0.688096i
$349$	0.184586	−	0.0981463i	0.184586	−	0.0981463i	−0.374607	−	0.927184i	$-0.622222\pi$
$349$	0.184586	−	0.0981463i	0.184586	−	0.0981463i	0.559193	+	0.829038i	$0.311111\pi$
$350$	−1.05094	+	1.55808i	−1.05094	+	1.55808i
$351$		0			0
$352$		0			0
$353$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$353$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$354$		0			0
$355$		0			0
$356$	0.800944	−	0.356603i	0.800944	−	0.356603i
$357$		0			0
$358$		0			0
$359$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$359$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$360$	−2.39751	+	1.49813i	−2.39751	+	1.49813i
$361$	1.00000			1.00000
$362$	0.104528	+	0.994522i	0.104528	+	0.994522i
$363$	1.95630			1.95630
$364$		0			0
$365$		0			0
$366$	1.23379	−	2.52964i	1.23379	−	2.52964i
$367$	−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	$-0.733333\pi$
$368$	−1.80931	+	0.805557i	−1.80931	+	0.805557i
$369$	−2.16568	−	3.75106i	−2.16568	−	3.75106i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$373$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$374$		0			0
$375$	−1.72731	+	0.918425i	−1.72731	+	0.918425i
$376$	0.184586	+	0.0981463i	0.184586	+	0.0981463i
$377$		0			0
$378$	4.13573	+	5.29349i	4.13573	+	5.29349i
$379$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$379$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$380$		0			0
$381$	−0.679414			−0.679414
$382$		0			0
$383$	0.328433	+	0.812901i	0.328433	+	0.812901i	0.997564	+	0.0697565i	$0.0222222\pi$
$383$	0.328433	+	0.812901i	0.328433	+	0.812901i	−0.669131	+	0.743145i	$0.733333\pi$
$384$	1.58268	−	1.14988i	1.58268	−	1.14988i
$385$		0			0
$386$		0			0
$387$	0.0206264	−	0.196247i	0.0206264	−	0.196247i
$388$		0			0
$389$	0.800944	+	0.356603i	0.800944	+	0.356603i	0.766044	−	0.642788i	$-0.222222\pi$
$389$	0.800944	+	0.356603i	0.800944	+	0.356603i	0.0348995	+	0.999391i	$0.488889\pi$
$390$		0			0
$391$		0			0
$392$	−2.31318	−	1.02989i	−2.31318	−	1.02989i
$393$		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
$400$	0.848048	−	0.529919i	0.848048	−	0.529919i
$401$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.978148	−	0.207912i	$-0.933333\pi$
$401$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.615661	+	0.788011i	$0.711111\pi$
$402$	1.75181	−	1.94558i	1.75181	−	1.94558i
$403$		0			0
$404$	−0.904793	−	0.657371i	−0.904793	−	0.657371i
$405$	0.723306	+	4.10207i	0.723306	+	4.10207i
$406$	−0.527469	+	1.30553i	−0.527469	+	1.30553i
$407$		0			0
$408$		0			0
$409$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	−0.997564	−	0.0697565i	$-0.977778\pi$
$409$	−0.559193	+	0.829038i	−0.559193	+	0.829038i	0.438371	+	0.898794i	$0.355556\pi$
$410$	0.766044	+	1.32683i	0.766044	+	1.32683i
$411$		0			0
$412$	0.857583	+	1.75831i	0.857583	+	1.75831i
$413$		0			0
$414$	0.195408	+	5.59574i	0.195408	+	5.59574i
$415$	−1.16392	+	1.12398i	−1.16392	+	1.12398i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$419$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$420$	−2.26356	−	2.89723i	−2.26356	−	2.89723i
$421$	−0.380500	+	1.17106i	−0.380500	+	1.17106i	0.559193	+	0.829038i	$0.311111\pi$
$421$	−0.380500	+	1.17106i	−0.380500	+	1.17106i	−0.939693	+	0.342020i	$0.888889\pi$
$422$		0			0
$423$	0.452750	−	0.379902i	0.452750	−	0.379902i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.54077	+	0.924765i	2.54077	+	0.924765i
$428$	0.545692	−	0.290149i	0.545692	−	0.290149i
$429$		0			0
$430$	−0.00729598	+	0.0694166i	−0.00729598	+	0.0694166i
$431$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$431$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$432$	−0.864708	−	3.46816i	−0.864708	−	3.46816i
$433$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$433$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$434$		0			0
$435$	−1.12278	+	0.942122i	−1.12278	+	0.942122i
$436$	0.391438	+	0.284396i	0.391438	+	0.284396i
$437$		0			0
$438$		0			0
$439$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$439$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$440$		0			0
$441$	−5.14935	+	4.97267i	−5.14935	+	4.97267i
$442$		0			0
$443$	−0.294524	−	0.184039i	−0.294524	−	0.184039i	0.374607	−	0.927184i	$-0.377778\pi$
$443$	−0.294524	−	0.184039i	−0.294524	−	0.184039i	−0.669131	+	0.743145i	$0.733333\pi$
$444$		0			0
$445$	0.0305979	+	0.876208i	0.0305979	+	0.876208i
$446$	1.76159	+	0.123183i	1.76159	+	0.123183i
$447$	2.12687	+	1.13088i	2.12687	+	1.13088i
$448$	1.25755	+	1.39666i	1.25755	+	1.39666i
$449$	0.0591929	−	1.69506i	0.0591929	−	1.69506i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	0.0591929	−	1.69506i	0.0591929	−	1.69506i	0.559193	−	0.829038i	$-0.311111\pi$
$450$	−0.490919	−	2.78414i	−0.490919	−	2.78414i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.47274	+	1.23577i	1.47274	+	1.23577i
$455$		0			0
$456$		0			0
$457$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$457$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$458$	0.545692	+	0.290149i	0.545692	+	0.290149i
$459$		0			0
$460$	−0.0691197	−	1.97933i	−0.0691197	−	1.97933i
$461$	1.20442	+	0.256006i	1.20442	+	0.256006i	0.766044	−	0.642788i	$-0.222222\pi$
$461$	1.20442	+	0.256006i	1.20442	+	0.256006i	0.438371	+	0.898794i	$0.355556\pi$
$462$		0			0
$463$	0.130100	−	0.737831i	0.130100	−	0.737831i	−0.848048	−	0.529919i	$-0.822222\pi$
$463$	0.130100	−	0.737831i	0.130100	−	0.737831i	0.978148	−	0.207912i	$-0.0666667\pi$
$464$	0.538939	−	0.520447i	0.538939	−	0.520447i
$465$		0			0
$466$		0			0
$467$	−0.671624	+	1.37703i	−0.671624	+	1.37703i	0.241922	+	0.970296i	$0.422222\pi$
$467$	−0.671624	+	1.37703i	−0.671624	+	1.37703i	−0.913545	+	0.406737i	$0.866667\pi$
$468$		0			0
$469$	2.03477	+	1.47834i	2.03477	+	1.47834i
$470$	−0.160147	+	0.134379i	−0.160147	+	0.134379i
$471$		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	$0.933333\pi$
$480$	0.473271	+	1.89818i	0.473271	+	1.89818i
$481$		0			0
$482$	0.766044	−	0.642788i	0.766044	−	0.642788i
$483$	−7.21084	+	1.01342i	−7.21084	+	1.01342i
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$	−4.52981	−	0.636624i	−4.52981	−	0.636624i
$487$	−1.61409	+	1.17271i	−1.61409	+	1.17271i	−0.766044	+	0.642788i	$0.777778\pi$
$487$	−1.61409	+	1.17271i	−1.61409	+	1.17271i	−0.848048	+	0.529919i	$0.822222\pi$
$488$	−1.03490	−	0.999391i	−1.03490	−	0.999391i
$489$	−3.72442	+	0.523433i	−3.72442	+	0.523433i
$490$	1.82143	−	1.75894i	1.82143	−	1.75894i
$491$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$491$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$492$	−2.93172	+	0.623157i	−2.93172	+	0.623157i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.38760	−	2.84500i	−1.38760	−	2.84500i
$499$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$499$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$500$	0.173648	+	0.984808i	0.173648	+	0.984808i
$501$	−0.765768	−	0.556363i	−0.765768	−	0.556363i
$502$		0			0
$503$	−0.586655	+	0.651546i	−0.586655	+	0.651546i	−0.961262	−	0.275637i	$-0.911111\pi$
$503$	−0.586655	+	0.651546i	−0.586655	+	0.651546i	0.374607	+	0.927184i	$0.377778\pi$
$504$	4.99277	−	1.81722i	4.99277	−	1.81722i
$505$	0.948445	−	0.592654i	0.948445	−	0.592654i
$506$		0			0
$507$	1.30902	−	1.45381i	1.30902	−	1.45381i
$508$	−0.107320	+	0.330298i	−0.107320	+	0.330298i
$509$	−0.0429726	+	0.0550024i	−0.0429726	+	0.0550024i	−0.809017	−	0.587785i	$-0.800000\pi$
$509$	−0.0429726	+	0.0550024i	−0.0429726	+	0.0550024i	0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$513$		0			0
$514$		0			0
$515$	−1.95153	+	0.136464i	−1.95153	+	0.136464i
$516$	−0.124742	−	0.0555388i	−0.124742	−	0.0555388i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$521$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$522$	−0.793452	−	1.96386i	−0.793452	−	1.96386i
$523$	−1.47274	+	0.422301i	−1.47274	+	0.422301i	−0.913545	−	0.406737i	$-0.866667\pi$
$523$	−1.47274	+	0.422301i	−1.47274	+	0.422301i	−0.559193	+	0.829038i	$0.688889\pi$
$524$		0			0
$525$	3.53421	−	1.01342i	3.53421	−	1.01342i
$526$	0.196449	−	0.0715017i	0.196449	−	0.0715017i
$527$		0			0
$528$		0			0
$529$	−2.58043	−	1.37204i	−2.58043	−	1.37204i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−1.64872	−	0.472764i	−1.64872	−	0.472764i
$535$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$536$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$537$		0			0
$538$	−0.232387	−	0.258091i	−0.232387	−	0.258091i
$539$		0			0
$540$	3.53954	+	0.497450i	3.53954	+	0.497450i
$541$	1.69610	−	1.05984i	1.69610	−	1.05984i	0.848048	−	0.529919i	$-0.177778\pi$
$541$	1.69610	−	1.05984i	1.69610	−	1.05984i	0.848048	−	0.529919i	$-0.177778\pi$
$542$		0			0
$543$	1.09395	−	1.62184i	1.09395	−	1.62184i
$544$		0			0
$545$	−0.410323	+	0.256398i	−0.410323	+	0.256398i
$546$		0			0
$547$	0.328433	−	0.673388i	0.328433	−	0.673388i	−0.669131	−	0.743145i	$-0.733333\pi$
$547$	0.328433	−	0.673388i	0.328433	−	0.673388i	0.997564	+	0.0697565i	$0.0222222\pi$
$548$		0			0
$549$	−3.71564	+	1.65431i	−3.71564	+	1.65431i
$550$		0			0
$551$		0			0
$552$	3.72442	+	1.06796i	3.72442	+	1.06796i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$557$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$558$		0			0
$559$		0			0
$560$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$561$		0			0
$562$	1.99513			1.99513
$563$	1.18362	−	0.339399i	1.18362	−	0.339399i	0.374607	−	0.927184i	$-0.377778\pi$
$563$	1.18362	−	0.339399i	1.18362	−	0.339399i	0.809017	+	0.587785i	$0.200000\pi$
$564$	−0.153206	−	0.379197i	−0.153206	−	0.379197i
$565$		0			0
$566$	−0.149516	+	0.599676i	−0.149516	+	0.599676i
$567$	0.273204	−	7.82353i	0.273204	−	7.82353i
$568$		0			0
$569$	0.615661	−	1.06636i	0.615661	−	1.06636i	−0.374607	−	0.927184i	$-0.622222\pi$
$569$	0.615661	−	1.06636i	0.615661	−	1.06636i	0.990268	−	0.139173i	$-0.0444444\pi$
$570$		0			0
$571$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$571$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$572$		0			0
$573$		0			0
$574$	−0.889779	−	2.73846i	−0.889779	−	2.73846i
$575$	1.86110	+	0.677383i	1.86110	+	0.677383i
$576$	−2.82020	−	0.197208i	−2.82020	−	0.197208i
$577$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$577$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$578$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$579$		0			0
$580$	0.280660	+	0.694658i	0.280660	+	0.694658i
$581$	2.57884	−	1.61144i	2.57884	−	1.61144i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.720190	−	1.78253i	0.720190	−	1.78253i	0.104528	−	0.994522i	$-0.466667\pi$
$587$	0.720190	−	1.78253i	0.720190	−	1.78253i	0.615661	−	0.788011i	$-0.288889\pi$
$588$	2.17148	+	4.45219i	2.17148	+	4.45219i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$593$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$594$		0			0
$595$		0			0
$596$	0.885740	−	0.855349i	0.885740	−	0.855349i
$597$		0			0
$598$		0			0
$599$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$599$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$600$	−1.93726	−	0.272264i	−1.93726	−	0.272264i
$601$	−1.12487	−	1.43977i	−1.12487	−	1.43977i	−0.882948	−	0.469472i	$-0.844444\pi$
$601$	−1.12487	−	1.43977i	−1.12487	−	1.43977i	−0.241922	−	0.970296i	$-0.577778\pi$
$602$	0.0405366	−	0.124759i	0.0405366	−	0.124759i
$603$	−3.74657	+	0.526546i	−3.74657	+	0.526546i
$604$		0			0
$605$	0.766044	+	0.642788i	0.766044	+	0.642788i
$606$	0.529299	+	2.12290i	0.529299	+	2.12290i
$607$	−1.83832	+	0.390746i	−1.83832	+	0.390746i	−0.990268	−	0.139173i	$-0.955556\pi$
$607$	−1.83832	+	0.390746i	−1.83832	+	0.390746i	−0.848048	+	0.529919i	$0.822222\pi$
$608$		0			0
$609$	2.43215	−	1.29320i	2.43215	−	1.29320i
$610$	1.31430	−	0.585164i	1.31430	−	0.585164i
$611$		0			0
$612$		0			0
$613$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$613$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$614$	−1.78716	−	0.379874i	−1.78716	−	0.379874i
$615$	0.520461	−	2.95168i	0.520461	−	2.95168i
$616$		0			0
$617$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$617$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$618$	0.925857	−	3.71341i	0.925857	−	3.71341i
$619$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$619$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$620$		0			0
$621$	4.35832	−	5.57840i	4.35832	−	5.57840i
$622$		0			0
$623$	0.286126	−	1.62270i	0.286126	−	1.62270i
$624$		0			0
$625$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.185428	+	5.30996i	−0.185428	+	5.30996i
$631$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$631$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.997564	+	0.0697565i	0.997564	+	0.0697565i
$641$	−0.0616289	−	1.76482i	−0.0616289	−	1.76482i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−0.0616289	−	1.76482i	−0.0616289	−	1.76482i	0.438371	−	0.898794i	$-0.355556\pi$
$642$	−1.18264	−	0.251377i	−1.18264	−	0.251377i
$643$	0.848048	+	0.529919i	0.848048	+	0.529919i	0.882948	−	0.469472i	$-0.155556\pi$
$643$	0.848048	+	0.529919i	0.848048	+	0.529919i	−0.0348995	+	0.999391i	$0.511111\pi$
$644$	−0.646352	+	3.66564i	−0.646352	+	3.66564i
$645$	0.0982240	−	0.0948538i	0.0982240	−	0.0948538i
$646$		0			0
$647$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.615661	+	0.788011i	$0.288889\pi$
$647$	1.11566	+	1.65404i	1.11566	+	1.65404i	0.500000	+	0.866025i	$0.333333\pi$
$648$	−1.82597	+	3.74379i	−1.82597	+	3.74379i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.333843	+	1.89332i	−0.333843	+	1.89332i
$653$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$653$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$654$	−0.228989	−	0.918425i	−0.228989	−	0.918425i
$655$		0			0
$656$	−0.160147	+	1.52370i	−0.160147	+	1.52370i
$657$		0			0
$658$	0.346909	−	0.184455i	0.346909	−	0.184455i
$659$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$659$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$660$		0			0
$661$	−0.442013	−	1.77282i	−0.442013	−	1.77282i	−0.615661	−	0.788011i	$-0.711111\pi$
$661$	−0.442013	−	1.77282i	−0.442013	−	1.77282i	0.173648	−	0.984808i	$-0.444444\pi$
$662$		0			0
$663$		0			0
$664$	−1.60229	+	0.225187i	−1.60229	+	0.225187i
$665$		0			0
$666$		0			0
$667$	1.46940	+	0.206511i	1.46940	+	0.206511i
$668$	−0.391438	+	0.284396i	−0.391438	+	0.284396i
$669$	−2.48504	−	2.39978i	−2.48504	−	2.39978i
$670$	1.32524	−	0.186250i	1.32524	−	0.186250i
$671$		0			0
$672$	−0.128313	−	3.67439i	−0.128313	−	3.67439i
$673$		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		0.559193	−	0.829038i	$-0.311111\pi$
$677$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.653095	−	3.70388i	−0.653095	−	3.70388i
$682$		0			0
$683$	0.0502092	+	0.0484865i	0.0502092	+	0.0484865i	0.719340	−	0.694658i	$-0.244444\pi$
$683$	0.0502092	+	0.0484865i	0.0502092	+	0.0484865i	−0.669131	+	0.743145i	$0.733333\pi$
$684$		0			0
$685$		0			0
$686$	−2.44186	+	1.52584i	−2.44186	+	1.52584i
$687$	−0.452921	−	1.12102i	−0.452921	−	1.12102i
$688$	−0.0467046	+	0.0518708i	−0.0467046	+	0.0518708i
$689$		0			0
$690$	−2.38539	+	3.05316i	−2.38539	+	3.05316i
$691$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$691$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$692$		0			0
$693$		0			0
$694$	−1.82264	−	0.811492i	−1.82264	−	0.811492i
$695$		0			0
$696$	−1.46211	+	0.102241i	−1.46211	+	0.102241i
$697$		0			0
$698$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$699$		0			0
$700$	0.0655896	−	1.87824i	0.0655896	−	1.87824i
$701$	−0.465101	+	1.86542i	−0.465101	+	1.86542i	0.0348995	+	0.999391i	$0.488889\pi$
$701$	−0.465101	+	1.86542i	−0.465101	+	1.86542i	−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.408977			0.408977
$706$		0			0
$707$	−1.97512	+	0.718885i	−1.97512	+	0.718885i
$708$		0			0
$709$	−0.688547	−	1.02081i	−0.688547	−	1.02081i	−0.997564	−	0.0697565i	$-0.977778\pi$
$709$	−0.688547	−	1.02081i	−0.688547	−	1.02081i	0.309017	−	0.951057i	$-0.400000\pi$
$710$		0			0
$711$		0			0
$712$	−0.490268	+	0.726852i	−0.490268	+	0.726852i
$713$		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	$0.266667\pi$
$720$	1.23932	−	2.54097i	1.23932	−	2.54097i
$721$	3.64085	+	0.511688i	3.64085	+	0.511688i
$722$	−0.848048	+	0.529919i	−0.848048	+	0.529919i
$723$	−1.95630			−1.95630
$724$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$725$	−0.749213			−0.749213
$726$	−1.65903	+	1.03668i	−1.65903	+	1.03668i
$727$	−0.612019	−	0.0860137i	−0.612019	−	0.0860137i	−0.173648	−	0.984808i	$-0.555556\pi$
$727$	−0.612019	−	0.0860137i	−0.612019	−	0.0860137i	−0.438371	+	0.898794i	$0.644444\pi$
$728$		0			0
$729$	3.20071	+	3.55475i	3.20071	+	3.55475i
$730$		0			0
$731$		0			0
$732$	0.294193	+	2.79906i	0.294193	+	2.79906i
$733$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$733$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$734$	1.92252	+	0.551275i	1.92252	+	0.551275i
$735$	−4.94145	+	0.345540i	−4.94145	+	0.345540i
$736$	1.10750	−	1.64194i	1.10750	−	1.64194i
$737$		0			0
$738$	3.82436	+	2.03345i	3.82436	+	2.03345i
$739$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$739$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.483844			0.483844			0.241922	−	0.970296i	$-0.422222\pi$
$743$	0.483844			0.483844			0.241922	+	0.970296i	$0.422222\pi$
$744$		0			0
$745$	0.461262	+	1.14166i	0.461262	+	1.14166i
$746$		0			0
$747$	−1.10663	+	4.43845i	−1.10663	+	4.43845i
$748$		0			0
$749$	0.121412	−	1.15516i	0.121412	−	1.15516i
$750$	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	$0.133333\pi$
$752$	−0.208548	+	0.0145831i	−0.208548	+	0.0145831i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−6.31242	−	2.29753i	−6.31242	−	2.29753i
$757$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$757$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.501321	−	1.24081i	−0.501321	−	1.24081i	−0.939693	−	0.342020i	$-0.888889\pi$
$761$	−0.501321	−	1.24081i	−0.501321	−	1.24081i	0.438371	−	0.898794i	$-0.355556\pi$
$762$	0.576176	−	0.360035i	0.576176	−	0.360035i
$763$	0.854490	−	0.311009i	0.854490	−	0.311009i
$764$		0			0
$765$		0			0
$766$	−0.709299	−	0.515336i	−0.709299	−	0.515336i
$767$		0			0
$768$	−0.732841	+	1.81385i	−0.732841	+	1.81385i
$769$	0.743520	+	1.52444i	0.743520	+	1.52444i	0.848048	+	0.529919i	$0.177778\pi$
$769$	0.743520	+	1.52444i	0.743520	+	1.52444i	−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	$0.666667\pi$
$774$	0.0865029	+	0.177357i	0.0865029	+	0.177357i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.868210	+	0.122019i	−0.868210	+	0.122019i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.827527	+	2.54687i	−0.827527	+	2.54687i
$784$	2.50745	−	0.352399i	2.50745	−	0.352399i
$785$		0			0
$786$		0			0
$787$	−0.348048	−	1.39594i	−0.348048	−	1.39594i	−0.848048	−	0.529919i	$-0.822222\pi$
$787$	−0.348048	−	1.39594i	−0.348048	−	1.39594i	0.500000	−	0.866025i	$-0.333333\pi$
$788$		0			0
$789$	−0.384313	−	0.139878i	−0.384313	−	0.139878i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$797$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$798$		0			0
$799$		0			0
$800$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$801$	1.38603	+	2.05488i	1.38603	+	2.05488i
$802$	1.04422	−	1.33654i	1.04422	−	1.33654i
$803$		0			0
$804$	−0.454617	+	2.57826i	−0.454617	+	2.57826i
$805$	−3.15660	−	1.97246i	−3.15660	−	1.97246i
$806$		0			0
$807$	0.0237112	+	0.679000i	0.0237112	+	0.679000i
$808$	1.11566	+	0.0780147i	1.11566	+	0.0780147i
$809$	−1.18161	−	0.628276i	−1.18161	−	0.628276i	−0.241922	−	0.970296i	$-0.577778\pi$
$809$	−1.18161	−	0.628276i	−1.18161	−	0.628276i	−0.939693	+	0.342020i	$0.888889\pi$
$810$	−2.78716	−	3.09546i	−2.78716	−	3.09546i
$811$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$811$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$812$	−0.244507	−	1.38667i	−0.244507	−	1.38667i
$813$		0			0
$814$		0			0
$815$	−1.63039	−	1.01878i	−1.63039	−	1.01878i
$816$		0			0
$817$		0			0
$818$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$819$		0			0
$820$	−1.35275	−	0.719272i	−1.35275	−	0.719272i
$821$	−0.0696290	−	0.00486893i	−0.0696290	−	0.00486893i	0.0348995	−	0.999391i	$-0.488889\pi$
$821$	−0.0696290	−	0.00486893i	−0.0696290	−	0.00486893i	−0.104528	+	0.994522i	$0.533333\pi$
$822$		0			0
$823$	1.93726	+	0.411777i	1.93726	+	0.411777i	0.997564	+	0.0697565i	$0.0222222\pi$
$823$	1.93726	+	0.411777i	1.93726	+	0.411777i	0.939693	+	0.342020i	$0.111111\pi$
$824$	−1.65903	−	1.03668i	−1.65903	−	1.03668i
$825$		0			0
$826$		0			0
$827$	0.688547	−	0.881300i	0.688547	−	0.881300i	−0.309017	−	0.951057i	$-0.600000\pi$
$827$	0.688547	−	0.881300i	0.688547	−	0.881300i	0.997564	+	0.0697565i	$0.0222222\pi$
$828$	−3.13101	−	4.64191i	−3.13101	−	4.64191i
$829$	−0.709299	+	1.45428i	−0.709299	+	1.45428i	0.173648	+	0.984808i	$0.444444\pi$
$829$	−0.709299	+	1.45428i	−0.709299	+	1.45428i	−0.882948	+	0.469472i	$0.844444\pi$
$830$	0.391438	−	1.56997i	0.391438	−	1.56997i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.117052	−	0.469472i	−0.117052	−	0.469472i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$839$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$840$	3.45490	+	1.25748i	3.45490	+	1.25748i
$841$	0.429093	−	0.0912066i	0.429093	−	0.0912066i
$842$	−0.297884	−	1.19475i	−0.297884	−	1.19475i
$843$	−2.98992	−	2.50884i	−2.98992	−	2.50884i
$844$		0			0
$845$	0.990268	−	0.139173i	0.990268	−	0.139173i
$846$	−0.182636	+	0.562096i	−0.182636	+	0.562096i
$847$	−1.15707	−	1.48098i	−1.15707	−	1.48098i
$848$		0			0
$849$	0.978148	−	0.710666i	0.978148	−	0.710666i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.0348995	−	0.999391i	$-0.511111\pi$
$853$		0			0		0.0348995	+	0.999391i	$0.488889\pi$
$854$	−2.64475	+	0.562159i	−2.64475	+	0.562159i
$855$		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	$0.400000\pi$
$860$	−0.0305979	−	0.0627349i	−0.0305979	−	0.0627349i
$861$	−2.11013	+	5.22276i	−2.11013	+	5.22276i
$862$		0			0
$863$	0.904793	+	0.657371i	0.904793	+	0.657371i	0.939693	−	0.342020i	$-0.111111\pi$
$863$	0.904793	+	0.657371i	0.904793	+	0.657371i	−0.0348995	+	0.999391i	$0.511111\pi$
$864$	2.57116	+	2.48294i	2.57116	+	2.48294i
$865$		0			0
$866$		0			0
$867$	1.65903	−	1.03668i	1.65903	−	1.03668i
$868$		0			0
$869$		0			0
$870$	0.452921	−	1.39395i	0.452921	−	1.39395i
$871$		0			0
$872$	−0.482665	−	0.0337512i	−0.482665	−	0.0337512i
$873$		0			0
$874$		0			0
$875$	1.71690	+	0.764415i	1.71690	+	0.764415i
$876$		0			0
$877$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$877$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.0670951	−	1.92135i	0.0670951	−	1.92135i	−0.241922	−	0.970296i	$-0.577778\pi$
$881$	0.0670951	−	1.92135i	0.0670951	−	1.92135i	0.309017	−	0.951057i	$-0.400000\pi$
$882$	1.73178	−	6.94581i	1.73178	−	6.94581i
$883$	0.280969	−	0.204136i	0.280969	−	0.204136i	−0.438371	−	0.898794i	$-0.644444\pi$
$883$	0.280969	−	0.204136i	0.280969	−	0.204136i	0.719340	+	0.694658i	$0.244444\pi$
$884$		0			0
$885$		0			0
$886$	0.347296			0.347296
$887$	1.38295	−	0.396554i	1.38295	−	0.396554i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	1.38295	−	0.396554i	1.38295	−	0.396554i	0.882948	+	0.469472i	$0.155556\pi$
$888$		0			0
$889$	0.401844	+	0.514337i	0.401844	+	0.514337i
$890$	−0.490268	−	0.726852i	−0.490268	−	0.726852i
$891$		0			0
$892$	−1.55919	+	0.829038i	−1.55919	+	0.829038i
$893$		0			0
$894$	−2.40296	+	0.168032i	−2.40296	+	0.168032i
$895$		0			0
$896$	−1.80658	−	0.518029i	−1.80658	−	0.518029i
$897$		0			0
$898$	0.848048	+	1.46886i	0.848048	+	1.46886i
$899$		0			0
$900$	1.89169	+	2.10094i	1.89169	+	2.10094i
$901$		0			0
$902$		0			0
$903$	−0.217631	+	0.135991i	−0.217631	+	0.135991i
$904$		0			0
$905$	0.961262	−	0.275637i	0.961262	−	0.275637i
$906$		0			0
$907$	0.635369	−	0.397023i	0.635369	−	0.397023i	−0.173648	−	0.984808i	$-0.555556\pi$
$907$	0.635369	−	0.397023i	0.635369	−	0.397023i	0.809017	+	0.587785i	$0.200000\pi$
$908$	−1.90381	−	0.267564i	−1.90381	−	0.267564i
$909$	1.38603	−	2.84179i	1.38603	−	2.84179i
$910$		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
$915$	−2.70545	−	0.775776i	−2.70545	−	0.775776i
$916$	−0.616528	+	0.0431119i	−0.616528	+	0.0431119i
$917$		0			0
$918$		0			0
$919$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$919$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$920$	1.10750	+	1.64194i	1.10750	+	1.64194i
$921$	2.20058	+	2.81661i	2.20058	+	2.81661i
$922$	−1.15707	+	0.421137i	−1.15707	+	0.421137i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.280660	+	0.694658i	0.280660	+	0.694658i
$927$	−4.47437	+	3.25082i	−4.47437	+	3.25082i
$928$	−0.181251	+	0.726958i	−0.181251	+	0.726958i
$929$	−0.0564686	+	1.61705i	−0.0564686	+	1.61705i	0.559193	+	0.829038i	$0.311111\pi$
$929$	−0.0564686	+	1.61705i	−0.0564686	+	1.61705i	−0.615661	+	0.788011i	$0.711111\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.160147	−	1.52370i	−0.160147	−	1.52370i
$935$		0			0
$936$		0			0
$937$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$937$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$938$	−2.50898	−	0.175445i	−2.50898	−	0.175445i
$939$		0			0
$940$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$941$	−0.962665	+	1.06915i	−0.962665	+	1.06915i	0.0348995	+	0.999391i	$0.488889\pi$
$941$	−0.962665	+	1.06915i	−0.962665	+	1.06915i	−0.997564	+	0.0697565i	$0.977778\pi$
$942$		0			0
$943$	−2.57328	+	1.60796i	−2.57328	+	1.60796i
$944$		0			0
$945$	4.49491	−	4.99211i	4.49491	−	4.99211i
$946$		0			0
$947$	0.709299	+	0.515336i	0.709299	+	0.515336i	0.882948	−	0.469472i	$-0.155556\pi$
$947$	0.709299	+	0.515336i	0.709299	+	0.515336i	−0.173648	+	0.984808i	$0.555556\pi$
$948$		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
$960$	−1.40724	−	1.35896i	−1.40724	−	1.35896i
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$	1.07571	+	1.37684i	1.07571	+	1.37684i
$964$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$965$		0			0
$966$	5.57811	−	4.68059i	5.57811	−	4.68059i
$967$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	0.615661	−	0.788011i	$-0.288889\pi$
$967$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	−0.669131	+	0.743145i	$0.733333\pi$
$968$	0.241922	+	0.970296i	0.241922	+	0.970296i
$969$		0			0
$970$		0			0
$971$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$971$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$972$	4.17886	−	1.86055i	4.17886	−	1.86055i
$973$		0			0
$974$	0.747388	−	1.84985i	0.747388	−	1.84985i
$975$		0			0
$976$	1.40724	+	0.299118i	1.40724	+	0.299118i
$977$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$977$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$978$	2.88111	−	2.41754i	2.88111	−	2.41754i
$979$		0			0
$980$	−0.612568	+	2.45688i	−0.612568	+	2.45688i
$981$	−0.599635	+	1.22943i	−0.599635	+	1.22943i
$982$		0			0
$983$	−0.615661	+	0.788011i	−0.615661	+	0.788011i	−0.990268	−	0.139173i	$-0.955556\pi$
$983$	−0.615661	+	0.788011i	−0.615661	+	0.788011i	0.374607	+	0.927184i	$0.377778\pi$
$984$	2.15602	−	2.08204i	2.15602	−	2.08204i
$985$		0			0
$986$		0			0
$987$	−0.751829	−	0.159806i	−0.751829	−	0.159806i
$988$		0			0
$989$	−0.137903	−	0.00964310i	−0.137903	−	0.00964310i
$990$		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
$996$	2.68437	+	1.67738i	2.68437	+	1.67738i
$997$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$997$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$998$		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.1979.1	yes	24
4.3	odd	2		3620.1.dy.b.1979.1	yes	24
5.4	even	2		3620.1.dy.b.1979.1	yes	24
20.19	odd	2	CM	3620.1.dy.a.1979.1	yes	24
181.15	even	45	inner	3620.1.dy.a.739.1	✓	24
724.15	odd	90		3620.1.dy.b.739.1	yes	24
905.739	even	90		3620.1.dy.b.739.1	yes	24
3620.739	odd	90	inner	3620.1.dy.a.739.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3620.1.dy.a.739.1	✓	24	181.15	even	45	inner
3620.1.dy.a.739.1	✓	24	3620.739	odd	90	inner
3620.1.dy.a.1979.1	yes	24	1.1	even	1	trivial
3620.1.dy.a.1979.1	yes	24	20.19	odd	2	CM
3620.1.dy.b.739.1	yes	24	724.15	odd	90
3620.1.dy.b.739.1	yes	24	905.739	even	90
3620.1.dy.b.1979.1	yes	24	4.3	odd	2
3620.1.dy.b.1979.1	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)

\(f(q)\)	\(=\)	\(q+(-0.848048 + 0.529919i) q^{2} +(1.93726 + 0.272264i) q^{3} +(0.438371 - 0.898794i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(0.104528 + 0.994522i) q^{8} +(2.71757 + 0.779252i) q^{9} +O(q^{10})\)	\(q+(-0.848048 + 0.529919i) q^{2} +(1.93726 + 0.272264i) q^{3} +(0.438371 - 0.898794i) q^{4} +(0.669131 + 0.743145i) q^{5} +(-1.78716 + 0.795697i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(0.104528 + 0.994522i) q^{8} +(2.71757 + 0.779252i) q^{9} +(-0.961262 - 0.275637i) q^{10} +(1.09395 - 1.62184i) q^{12} +(1.65940 + 0.882318i) q^{14} +(1.09395 + 1.62184i) q^{15} +(-0.615661 - 0.788011i) q^{16} +(-2.71757 + 0.779252i) q^{18} +(0.961262 - 0.275637i) q^{20} +(-1.37729 - 3.40891i) q^{21} +(0.479135 - 1.92171i) q^{23} +(-0.0682737 + 1.95510i) q^{24} +(-0.104528 + 0.994522i) q^{25} +(3.26531 + 1.45381i) q^{27} +(-1.87481 + 0.131099i) q^{28} +(0.0783141 + 0.745109i) q^{29} +(-1.78716 - 0.795697i) q^{30} +(0.939693 + 0.342020i) q^{32} +(0.580762 - 1.78740i) q^{35} +(1.89169 - 2.10094i) q^{36} +(-0.669131 + 0.743145i) q^{40} +(-1.10209 - 1.06428i) q^{41} +(2.97446 + 2.16107i) q^{42} +(-0.0121205 - 0.0687386i) q^{43} +(1.23932 + 2.54097i) q^{45} +(0.612019 + 1.88360i) q^{46} +(0.116903 - 0.173316i) q^{47} +(-0.978148 - 1.69420i) q^{48} +(-1.26604 + 2.19285i) q^{49} +(-0.438371 - 0.898794i) q^{50} +(-3.53954 + 0.497450i) q^{54} +(1.52045 - 1.10467i) q^{56} +(-0.461262 - 0.590388i) q^{58} +(1.93726 - 0.272264i) q^{60} +(-1.10209 + 0.924765i) q^{61} +(-1.28538 - 5.15537i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(-1.22256 + 0.544320i) q^{67} +(1.45142 - 3.59239i) q^{69} +(0.454664 + 1.82356i) q^{70} +(-0.490919 + 2.78414i) q^{72} +(-0.473271 + 1.89818i) q^{75} +(0.173648 - 0.984808i) q^{80} +(3.53242 + 2.20730i) q^{81} +(1.49861 + 0.318539i) q^{82} +(0.0564686 + 1.61705i) q^{83} +(-3.66768 - 0.256469i) q^{84} +(0.0467046 + 0.0518708i) q^{86} +(-0.0511516 + 1.46479i) q^{87} +(0.671624 + 0.563559i) q^{89} +(-2.39751 - 1.49813i) q^{90} +(-1.51718 - 1.27306i) q^{92} +(-0.00729598 + 0.208930i) q^{94} +(1.72731 + 0.918425i) q^{96} +(-0.0883686 - 2.53055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 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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