LMFDB - Embedded newform 3660.1.eb.f.1319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3660,1,Mod(419,3660)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3660, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 10, 11]))

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

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

chi := DirichletCharacter("3660.419");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3660 = 2^{2} \cdot 3 \cdot 5 \cdot 61 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3660.eb (of order $20$, degree $8$, 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:	$1.82657794624$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{20}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{20} - \cdots)$

Embedding invariants

Embedding label			1319.1
Root			$-0.156434 - 0.987688i$ of defining polynomial
Character	$\chi$	$=$	3660.1319
Dual form			3660.1.eb.f.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.453990 - 0.891007i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.610425 - 0.0966818i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.587785 - 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.453990 - 0.891007i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.610425 - 0.0966818i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.587785 - 0.809017i) q^{9} +(0.453990 + 0.891007i) q^{10} +(0.156434 - 0.987688i) q^{12} +0.618034 q^{14} +(-0.987688 - 0.156434i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.707107 + 0.707107i) q^{18} +(-0.587785 - 0.809017i) q^{20} +(-0.363271 + 0.500000i) q^{21} +(-1.04744 - 0.533698i) q^{23} +1.00000i q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.987688 + 0.156434i) q^{27} +(-0.610425 + 0.0966818i) q^{28} +(-0.642040 - 0.642040i) q^{29} +1.00000 q^{30} +(-0.707107 + 0.707107i) q^{32} +(0.0966818 + 0.610425i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.707107 + 0.707107i) q^{40} +(1.30902 - 0.951057i) q^{41} +(0.280582 - 0.550672i) q^{42} +(-0.280582 - 0.550672i) q^{43} +(-0.587785 + 0.809017i) q^{45} +(1.11803 + 0.363271i) q^{46} +1.97538i q^{47} +(-0.156434 - 0.987688i) q^{48} +(-0.587785 - 0.190983i) q^{49} +(0.707107 - 0.707107i) q^{50} +(0.951057 - 0.309017i) q^{54} +(0.587785 - 0.190983i) q^{56} +(0.734572 + 0.533698i) q^{58} +(-0.987688 + 0.156434i) q^{60} +(-0.587785 + 0.809017i) q^{61} +(0.280582 + 0.550672i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-1.78201 - 0.907981i) q^{67} +(-0.951057 + 0.690983i) q^{69} +(-0.190983 - 0.587785i) q^{70} +(0.891007 + 0.453990i) q^{72} +(0.156434 + 0.987688i) q^{75} +(-0.809017 - 0.587785i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-1.14412 + 1.14412i) q^{82} +(0.183900 - 0.253116i) q^{83} +(-0.190983 + 0.587785i) q^{84} +(0.363271 + 0.500000i) q^{86} +(-0.863541 + 0.280582i) q^{87} +(-0.221232 - 1.39680i) q^{89} +(0.453990 - 0.891007i) q^{90} +(-1.16110 - 0.183900i) q^{92} +(-0.309017 - 1.95106i) q^{94} +(0.309017 + 0.951057i) q^{96} +(0.610425 + 0.0966818i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5} + 4 q^{6}+O(q^{10}) $ 16 * q + 4 * q^5 + 4 * q^6	$ 16 q + 4 q^{5} + 4 q^{6} - 8 q^{14} + 4 q^{16} - 4 q^{25} - 4 q^{29} + 16 q^{30} - 4 q^{36} + 12 q^{41} - 12 q^{70} - 4 q^{80} + 4 q^{81} - 12 q^{84} - 4 q^{89} + 4 q^{94} - 4 q^{96}+O(q^{100}) $ 16 * q + 4 * q^5 + 4 * q^6 - 8 * q^14 + 4 * q^16 - 4 * q^25 - 4 * q^29 + 16 * q^30 - 4 * q^36 + 12 * q^41 - 12 * q^70 - 4 * q^80 + 4 * q^81 - 12 * q^84 - 4 * q^89 + 4 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3660\mathbb{Z}\right)^\times$.

$n$	$1831$	$2197$	$2441$	$3601$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$2$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$3$	0.453990	−	0.891007i	0.453990	−	0.891007i
$3$	0.453990	−	0.891007i	0.453990	−	0.891007i
$4$	0.951057	−	0.309017i	0.951057	−	0.309017i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$6$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$7$	−0.610425	−	0.0966818i	−0.610425	−	0.0966818i	−0.156434	−	0.987688i	$-0.550000\pi$
$7$	−0.610425	−	0.0966818i	−0.610425	−	0.0966818i	−0.453990	+	0.891007i	$0.650000\pi$
$8$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$9$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$10$	0.453990	+	0.891007i	0.453990	+	0.891007i
$11$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$11$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$12$	0.156434	−	0.987688i	0.156434	−	0.987688i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	0.618034			0.618034
$15$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$16$	0.809017	−	0.587785i	0.809017	−	0.587785i
$17$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$17$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$18$	0.707107	+	0.707107i	0.707107	+	0.707107i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$21$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$22$		0			0
$23$	−1.04744	−	0.533698i	−1.04744	−	0.533698i	−0.156434	−	0.987688i	$-0.550000\pi$
$23$	−1.04744	−	0.533698i	−1.04744	−	0.533698i	−0.891007	+	0.453990i	$0.850000\pi$
$24$			1.00000i			1.00000i
$25$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$26$		0			0
$27$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$28$	−0.610425	+	0.0966818i	−0.610425	+	0.0966818i
$29$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	0.309017	−	0.951057i	$-0.400000\pi$
$29$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	−0.951057	+	0.309017i	$0.900000\pi$
$30$	1.00000			1.00000
$31$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$31$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$32$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$33$		0			0
$34$		0			0
$35$	0.0966818	+	0.610425i	0.0966818	+	0.610425i
$36$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$37$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$37$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$38$		0			0
$39$		0			0
$40$	0.707107	+	0.707107i	0.707107	+	0.707107i
$41$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$41$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$42$	0.280582	−	0.550672i	0.280582	−	0.550672i
$43$	−0.280582	−	0.550672i	−0.280582	−	0.550672i	0.707107	−	0.707107i	$-0.250000\pi$
$43$	−0.280582	−	0.550672i	−0.280582	−	0.550672i	−0.987688	+	0.156434i	$0.950000\pi$
$44$		0			0
$45$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$46$	1.11803	+	0.363271i	1.11803	+	0.363271i
$47$			1.97538i			1.97538i	0.156434	+	0.987688i	$0.450000\pi$
$47$			1.97538i			1.97538i	−0.156434	+	0.987688i	$0.550000\pi$
$48$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$49$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$50$	0.707107	−	0.707107i	0.707107	−	0.707107i
$51$		0			0
$52$		0			0
$53$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$53$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$54$	0.951057	−	0.309017i	0.951057	−	0.309017i
$55$		0			0
$56$	0.587785	−	0.190983i	0.587785	−	0.190983i
$57$		0			0
$58$	0.734572	+	0.533698i	0.734572	+	0.533698i
$59$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$59$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$60$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$61$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$61$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$62$		0			0
$63$	0.280582	+	0.550672i	0.280582	+	0.550672i
$64$	0.587785	−	0.809017i	0.587785	−	0.809017i
$65$		0			0
$66$		0			0
$67$	−1.78201	−	0.907981i	−1.78201	−	0.907981i	−0.891007	−	0.453990i	$-0.850000\pi$
$67$	−1.78201	−	0.907981i	−1.78201	−	0.907981i	−0.891007	−	0.453990i	$-0.850000\pi$
$68$		0			0
$69$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$70$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$71$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$71$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$72$	0.891007	+	0.453990i	0.891007	+	0.453990i
$73$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$73$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$74$		0			0
$75$	0.156434	+	0.987688i	0.156434	+	0.987688i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$79$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$80$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$81$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$82$	−1.14412	+	1.14412i	−1.14412	+	1.14412i
$83$	0.183900	−	0.253116i	0.183900	−	0.253116i	−0.707107	−	0.707107i	$-0.750000\pi$
$83$	0.183900	−	0.253116i	0.183900	−	0.253116i	0.891007	+	0.453990i	$0.150000\pi$
$84$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$85$		0			0
$86$	0.363271	+	0.500000i	0.363271	+	0.500000i
$87$	−0.863541	+	0.280582i	−0.863541	+	0.280582i
$88$		0			0
$89$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$89$	−0.221232	−	1.39680i	−0.221232	−	1.39680i	0.587785	−	0.809017i	$-0.300000\pi$
$90$	0.453990	−	0.891007i	0.453990	−	0.891007i
$91$		0			0
$92$	−1.16110	−	0.183900i	−1.16110	−	0.183900i
$93$		0			0
$94$	−0.309017	−	1.95106i	−0.309017	−	1.95106i
$95$		0			0
$96$	0.309017	+	0.951057i	0.309017	+	0.951057i
$97$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$97$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$98$	0.610425	+	0.0966818i	0.610425	+	0.0966818i
$99$		0			0
$100$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$101$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$101$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$102$		0			0
$103$	−0.253116	−	0.183900i	−0.253116	−	0.183900i	0.453990	−	0.891007i	$-0.350000\pi$
$103$	−0.253116	−	0.183900i	−0.253116	−	0.183900i	−0.707107	+	0.707107i	$0.750000\pi$
$104$		0			0
$105$	0.587785	+	0.190983i	0.587785	+	0.190983i
$106$		0			0
$107$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$107$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$108$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$109$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$109$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$110$		0			0
$111$		0			0
$112$	−0.550672	+	0.280582i	−0.550672	+	0.280582i
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$	−0.183900	+	1.16110i	−0.183900	+	1.16110i
$116$	−0.809017	−	0.412215i	−0.809017	−	0.412215i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.951057	−	0.309017i	0.951057	−	0.309017i
$121$			1.00000i			1.00000i
$122$	0.453990	−	0.891007i	0.453990	−	0.891007i
$123$	−0.253116	−	1.59811i	−0.253116	−	1.59811i
$124$		0			0
$125$	0.809017	+	0.587785i	0.809017	+	0.587785i
$126$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$127$	1.69480	−	0.550672i	1.69480	−	0.550672i	0.707107	−	0.707107i	$-0.250000\pi$
$127$	1.69480	−	0.550672i	1.69480	−	0.550672i	0.987688	+	0.156434i	$0.0500000\pi$
$128$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$129$	−0.618034			−0.618034
$130$		0			0
$131$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$131$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$132$		0			0
$133$		0			0
$134$	1.90211	+	0.618034i	1.90211	+	0.618034i
$135$	0.453990	+	0.891007i	0.453990	+	0.891007i
$136$		0			0
$137$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$137$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$138$	0.831254	−	0.831254i	0.831254	−	0.831254i
$139$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$139$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$140$	0.280582	+	0.550672i	0.280582	+	0.550672i
$141$	1.76007	+	0.896802i	1.76007	+	0.896802i
$142$		0			0
$143$		0			0
$144$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$145$	−0.412215	+	0.809017i	−0.412215	+	0.809017i
$146$		0			0
$147$	−0.437016	+	0.437016i	−0.437016	+	0.437016i
$148$		0			0
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$157$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$158$		0			0
$159$		0			0
$160$	0.891007	+	0.453990i	0.891007	+	0.453990i
$161$	0.587785	+	0.427051i	0.587785	+	0.427051i
$162$	0.156434	−	0.987688i	0.156434	−	0.987688i
$163$	0.533698	+	0.734572i	0.533698	+	0.734572i	0.987688	−	0.156434i	$-0.0500000\pi$
$163$	0.533698	+	0.734572i	0.533698	+	0.734572i	−0.453990	+	0.891007i	$0.650000\pi$
$164$	0.951057	−	1.30902i	0.951057	−	1.30902i
$165$		0			0
$166$	−0.142040	+	0.278768i	−0.142040	+	0.278768i
$167$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$167$	1.14412	−	0.831254i	1.14412	−	0.831254i	0.987688	+	0.156434i	$0.0500000\pi$
$168$	0.0966818	−	0.610425i	0.0966818	−	0.610425i
$169$	1.00000			1.00000
$170$		0			0
$171$		0			0
$172$	−0.437016	−	0.437016i	−0.437016	−	0.437016i
$173$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$173$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$174$	0.809017	−	0.412215i	0.809017	−	0.412215i
$175$	0.550672	−	0.280582i	0.550672	−	0.280582i
$176$		0			0
$177$		0			0
$178$	0.437016	+	1.34500i	0.437016	+	1.34500i
$179$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$179$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$180$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$181$	−1.76007	+	0.278768i	−1.76007	+	0.278768i	−0.951057	−	0.309017i	$-0.900000\pi$
$181$	−1.76007	+	0.278768i	−1.76007	+	0.278768i	−0.809017	+	0.587785i	$0.800000\pi$
$182$		0			0
$183$	0.453990	+	0.891007i	0.453990	+	0.891007i
$184$	1.17557			1.17557
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.610425	+	1.87869i	0.610425	+	1.87869i
$189$	0.618034			0.618034
$190$		0			0
$191$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$191$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$192$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$193$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$193$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$194$		0			0
$195$		0			0
$196$	−0.618034			−0.618034
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$199$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$200$	0.453990	−	0.891007i	0.453990	−	0.891007i
$201$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$202$	0.831254	−	1.14412i	0.831254	−	1.14412i
$203$	0.329843	+	0.453990i	0.329843	+	0.453990i
$204$		0			0
$205$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$206$	0.278768	+	0.142040i	0.278768	+	0.142040i
$207$	0.183900	+	1.16110i	0.183900	+	1.16110i
$208$		0			0
$209$		0			0
$210$	−0.610425	−	0.0966818i	−0.610425	−	0.0966818i
$211$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$211$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$212$		0			0
$213$		0			0
$214$	−0.221232	+	1.39680i	−0.221232	+	1.39680i
$215$	−0.437016	+	0.437016i	−0.437016	+	0.437016i
$216$	0.809017	−	0.587785i	0.809017	−	0.587785i
$217$		0			0
$218$	−0.183900	−	1.16110i	−0.183900	−	1.16110i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.831254	−	0.831254i	−0.831254	−	0.831254i	0.156434	−	0.987688i	$-0.450000\pi$
$223$	−0.831254	−	0.831254i	−0.831254	−	0.831254i	−0.987688	+	0.156434i	$0.950000\pi$
$224$	0.500000	−	0.363271i	0.500000	−	0.363271i
$225$	0.951057	+	0.309017i	0.951057	+	0.309017i
$226$		0			0
$227$	1.04744	+	0.533698i	1.04744	+	0.533698i	0.891007	−	0.453990i	$-0.150000\pi$
$227$	1.04744	+	0.533698i	1.04744	+	0.533698i	0.156434	+	0.987688i	$0.450000\pi$
$228$		0			0
$229$	−1.80902	−	0.587785i	−1.80902	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$229$	−1.80902	−	0.587785i	−1.80902	−	0.587785i	−1.00000			$\pi$
$230$		−	1.17557i		−	1.17557i
$231$		0			0
$232$	0.863541	+	0.280582i	0.863541	+	0.280582i
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$	1.87869	−	0.610425i	1.87869	−	0.610425i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$241$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$241$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$242$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$243$	0.707107	+	0.707107i	0.707107	+	0.707107i
$244$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$245$			0.618034i			0.618034i
$246$	0.500000	+	1.53884i	0.500000	+	1.53884i
$247$		0			0
$248$		0			0
$249$	−0.142040	−	0.278768i	−0.142040	−	0.278768i
$250$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$251$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$251$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$252$	0.437016	+	0.437016i	0.437016	+	0.437016i
$253$		0			0
$254$	−1.58779	+	0.809017i	−1.58779	+	0.809017i
$255$		0			0
$256$	0.309017	−	0.951057i	0.309017	−	0.951057i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$259$		0			0
$260$		0			0
$261$	−0.142040	+	0.896802i	−0.142040	+	0.896802i
$262$		0			0
$263$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.987688	−	0.156434i	$-0.950000\pi$
$263$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.453990	−	0.891007i	$-0.650000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$268$	−1.97538	−	0.312869i	−1.97538	−	0.312869i
$269$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$269$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$270$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$277$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$277$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$278$		0			0
$279$		0			0
$280$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$281$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$281$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$282$	−1.87869	−	0.610425i	−1.87869	−	0.610425i
$283$	0.533698	−	0.734572i	0.533698	−	0.734572i	−0.453990	−	0.891007i	$-0.650000\pi$
$283$	0.533698	−	0.734572i	0.533698	−	0.734572i	0.987688	+	0.156434i	$0.0500000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$288$	0.987688	+	0.156434i	0.987688	+	0.156434i
$289$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$290$	0.280582	−	0.863541i	0.280582	−	0.863541i
$291$		0			0
$292$		0			0
$293$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$293$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$294$	0.363271	−	0.500000i	0.363271	−	0.500000i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.453990	+	0.891007i	0.453990	+	0.891007i
$301$	0.118034	+	0.363271i	0.118034	+	0.363271i
$302$		0			0
$303$	0.437016	+	1.34500i	0.437016	+	1.34500i
$304$		0			0
$305$	0.951057	+	0.309017i	0.951057	+	0.309017i
$306$		0			0
$307$	−0.297556	−	1.87869i	−0.297556	−	1.87869i	−0.453990	−	0.891007i	$-0.650000\pi$
$307$	−0.297556	−	1.87869i	−0.297556	−	1.87869i	0.156434	−	0.987688i	$-0.450000\pi$
$308$		0			0
$309$	−0.278768	+	0.142040i	−0.278768	+	0.142040i
$310$		0			0
$311$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$311$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$312$		0			0
$313$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$313$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$314$		0			0
$315$	0.437016	−	0.437016i	0.437016	−	0.437016i
$316$		0			0
$317$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$317$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$318$		0			0
$319$		0			0
$320$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$321$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$322$	−0.647354	−	0.329843i	−0.647354	−	0.329843i
$323$		0			0
$324$			1.00000i			1.00000i
$325$		0			0
$326$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$327$	1.04744	+	0.533698i	1.04744	+	0.533698i
$328$	−0.734572	+	1.44168i	−0.734572	+	1.44168i
$329$	0.190983	−	1.20582i	0.190983	−	1.20582i
$330$		0			0
$331$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$331$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$332$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$333$		0			0
$334$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$335$	−0.312869	+	1.97538i	−0.312869	+	1.97538i
$336$			0.618034i			0.618034i
$337$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$337$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$338$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.891007	+	0.453990i	0.891007	+	0.453990i
$344$	0.500000	+	0.363271i	0.500000	+	0.363271i
$345$	0.951057	+	0.690983i	0.951057	+	0.690983i
$346$		0			0
$347$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.156434	−	0.987688i	$-0.450000\pi$
$347$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.891007	−	0.453990i	$-0.150000\pi$
$348$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$349$	0.809017	−	1.58779i	0.809017	−	1.58779i		−	1.00000i	$-0.5\pi$
$349$	0.809017	−	1.58779i	0.809017	−	1.58779i	0.809017	−	0.587785i	$-0.200000\pi$
$350$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$357$		0			0
$358$		0			0
$359$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$359$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$360$	0.156434	−	0.987688i	0.156434	−	0.987688i
$361$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$362$	1.69480	−	0.550672i	1.69480	−	0.550672i
$363$	0.891007	+	0.453990i	0.891007	+	0.453990i
$364$		0			0
$365$		0			0
$366$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$367$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$367$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$368$	−1.16110	+	0.183900i	−1.16110	+	0.183900i
$369$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$373$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$374$		0			0
$375$	0.891007	−	0.453990i	0.891007	−	0.453990i
$376$	−0.896802	−	1.76007i	−0.896802	−	1.76007i
$377$		0			0
$378$	−0.610425	+	0.0966818i	−0.610425	+	0.0966818i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.278768	−	1.76007i	0.278768	−	1.76007i
$382$		0			0
$383$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$383$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$384$	0.587785	+	0.809017i	0.587785	+	0.809017i
$385$		0			0
$386$		0			0
$387$	−0.280582	+	0.550672i	−0.280582	+	0.550672i
$388$		0			0
$389$	−1.58779	−	0.809017i	−1.58779	−	0.809017i	−0.587785	−	0.809017i	$-0.700000\pi$
$389$	−1.58779	−	0.809017i	−1.58779	−	0.809017i	−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$397$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$398$		0			0
$399$		0			0
$400$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$401$	0.309017	+	1.95106i	0.309017	+	1.95106i	0.309017	+	0.951057i	$0.400000\pi$
$401$	0.309017	+	1.95106i	0.309017	+	1.95106i			1.00000i	$0.5\pi$
$402$	1.41421	−	1.41421i	1.41421	−	1.41421i
$403$		0			0
$404$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$405$	1.00000			1.00000
$406$	−0.396802	−	0.396802i	−0.396802	−	0.396802i
$407$		0			0
$408$		0			0
$409$	0.412215	+	0.809017i	0.412215	+	0.809017i	1.00000			$0$
$409$	0.412215	+	0.809017i	0.412215	+	0.809017i	−0.587785	+	0.809017i	$0.700000\pi$
$410$	1.44168	+	0.734572i	1.44168	+	0.734572i
$411$		0			0
$412$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i
$413$		0			0
$414$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$415$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$419$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$420$	0.618034			0.618034
$421$	0.896802	−	1.76007i	0.896802	−	1.76007i	0.309017	−	0.951057i	$-0.400000\pi$
$421$	0.896802	−	1.76007i	0.896802	−	1.76007i	0.587785	−	0.809017i	$-0.300000\pi$
$422$		0			0
$423$	1.59811	−	1.16110i	1.59811	−	1.16110i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.437016	−	0.437016i	0.437016	−	0.437016i
$428$		−	1.41421i		−	1.41421i
$429$		0			0
$430$	0.363271	−	0.500000i	0.363271	−	0.500000i
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$433$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$433$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$434$		0			0
$435$	0.533698	+	0.734572i	0.533698	+	0.734572i
$436$	0.363271	+	1.11803i	0.363271	+	1.11803i
$437$		0			0
$438$		0			0
$439$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$439$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$440$		0			0
$441$	0.190983	+	0.587785i	0.190983	+	0.587785i
$442$		0			0
$443$	−0.533698	−	0.734572i	−0.533698	−	0.734572i	0.453990	−	0.891007i	$-0.350000\pi$
$443$	−0.533698	−	0.734572i	−0.533698	−	0.734572i	−0.987688	+	0.156434i	$0.950000\pi$
$444$		0			0
$445$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$446$	0.951057	+	0.690983i	0.951057	+	0.690983i
$447$		0			0
$448$	−0.437016	+	0.437016i	−0.437016	+	0.437016i
$449$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$449$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$450$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$455$		0			0
$456$		0			0
$457$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$457$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$458$	1.87869	+	0.297556i	1.87869	+	0.297556i
$459$		0			0
$460$	0.183900	+	1.16110i	0.183900	+	1.16110i
$461$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$461$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$462$		0			0
$463$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.707107	+	0.707107i	$0.250000\pi$
$463$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.453990	+	0.891007i	$0.350000\pi$
$464$	−0.896802	−	0.142040i	−0.896802	−	0.142040i
$465$		0			0
$466$		0			0
$467$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.156434	−	0.987688i	$-0.450000\pi$
$467$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$468$		0			0
$469$	1.00000	+	0.726543i	1.00000	+	0.726543i
$470$	−1.76007	+	0.896802i	−1.76007	+	0.896802i
$471$		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		−0.309017	−	0.951057i	$-0.600000\pi$
$479$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$480$	0.809017	−	0.587785i	0.809017	−	0.587785i
$481$		0			0
$482$		0			0
$483$	0.647354	−	0.329843i	0.647354	−	0.329843i
$484$	0.309017	+	0.951057i	0.309017	+	0.951057i
$485$		0			0
$486$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$487$		−	1.78201i		−	1.78201i	−0.453990	−	0.891007i	$-0.650000\pi$
$487$		−	1.78201i		−	1.78201i	0.453990	−	0.891007i	$-0.350000\pi$
$488$	0.156434	−	0.987688i	0.156434	−	0.987688i
$489$	0.896802	−	0.142040i	0.896802	−	0.142040i
$490$	−0.0966818	−	0.610425i	−0.0966818	−	0.610425i
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$	−0.734572	−	1.44168i	−0.734572	−	1.44168i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.183900	+	0.253116i	0.183900	+	0.253116i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	0.951057	+	0.309017i	0.951057	+	0.309017i
$501$	−0.221232	−	1.39680i	−0.221232	−	1.39680i
$502$		0			0
$503$	−1.69480	−	0.550672i	−1.69480	−	0.550672i	−0.707107	−	0.707107i	$-0.750000\pi$
$503$	−1.69480	−	0.550672i	−1.69480	−	0.550672i	−0.987688	+	0.156434i	$0.950000\pi$
$504$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$505$	1.26007	+	0.642040i	1.26007	+	0.642040i
$506$		0			0
$507$	0.453990	−	0.891007i	0.453990	−	0.891007i
$508$	1.44168	−	1.04744i	1.44168	−	1.04744i
$509$	0.221232	+	0.221232i	0.221232	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$509$	0.221232	+	0.221232i	0.221232	+	0.221232i	−0.587785	+	0.809017i	$0.700000\pi$
$510$		0			0
$511$		0			0
$512$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$513$		0			0
$514$		0			0
$515$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$516$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.896802	+	0.142040i	−0.896802	+	0.142040i	−0.587785	−	0.809017i	$-0.700000\pi$
$521$	−0.896802	+	0.142040i	−0.896802	+	0.142040i	−0.309017	+	0.951057i	$0.600000\pi$
$522$		−	0.907981i		−	0.907981i
$523$	1.87869	−	0.297556i	1.87869	−	0.297556i	0.891007	−	0.453990i	$-0.150000\pi$
$523$	1.87869	−	0.297556i	1.87869	−	0.297556i	0.987688	+	0.156434i	$0.0500000\pi$
$524$		0			0
$525$		−	0.618034i		−	0.618034i
$526$	1.58779	+	0.809017i	1.58779	+	0.809017i
$527$		0			0
$528$		0			0
$529$	0.224514	+	0.309017i	0.224514	+	0.309017i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.39680	+	0.221232i	1.39680	+	0.221232i
$535$	−1.41421			−1.41421
$536$	2.00000			2.00000
$537$		0			0
$538$	1.34500	+	1.34500i	1.34500	+	1.34500i
$539$		0			0
$540$	0.707107	+	0.707107i	0.707107	+	0.707107i
$541$	0.809017	−	0.412215i	0.809017	−	0.412215i		−	1.00000i	$-0.5\pi$
$541$	0.809017	−	0.412215i	0.809017	−	0.412215i	0.809017	+	0.587785i	$0.200000\pi$
$542$		0			0
$543$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$544$		0			0
$545$	1.11803	−	0.363271i	1.11803	−	0.363271i
$546$		0			0
$547$	−1.87869	+	0.297556i	−1.87869	+	0.297556i	−0.987688	−	0.156434i	$-0.950000\pi$
$547$	−1.87869	+	0.297556i	−1.87869	+	0.297556i	−0.891007	+	0.453990i	$0.850000\pi$
$548$		0			0
$549$	1.00000			1.00000
$550$		0			0
$551$		0			0
$552$	0.533698	−	1.04744i	0.533698	−	1.04744i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$557$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$558$		0			0
$559$		0			0
$560$	0.437016	+	0.437016i	0.437016	+	0.437016i
$561$		0			0
$562$	−1.41421			−1.41421
$563$	−0.312869			−0.312869			−0.156434	−	0.987688i	$-0.550000\pi$
$563$	−0.312869			−0.312869			−0.156434	+	0.987688i	$0.550000\pi$
$564$	1.95106	+	0.309017i	1.95106	+	0.309017i
$565$		0			0
$566$	−0.412215	+	0.809017i	−0.412215	+	0.809017i
$567$	0.280582	−	0.550672i	0.280582	−	0.550672i
$568$		0			0
$569$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$569$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$570$		0			0
$571$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$571$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$572$		0			0
$573$		0			0
$574$	0.809017	−	0.587785i	0.809017	−	0.587785i
$575$	1.16110	−	0.183900i	1.16110	−	0.183900i
$576$	−1.00000			−1.00000
$577$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$577$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$578$	0.707107	+	0.707107i	0.707107	+	0.707107i
$579$		0			0
$580$	−0.142040	+	0.896802i	−0.142040	+	0.896802i
$581$	−0.136729	+	0.136729i	−0.136729	+	0.136729i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.280582	−	0.550672i	0.280582	−	0.550672i	−0.707107	−	0.707107i	$-0.750000\pi$
$587$	0.280582	−	0.550672i	0.280582	−	0.550672i	0.987688	+	0.156434i	$0.0500000\pi$
$588$	−0.280582	+	0.550672i	−0.280582	+	0.550672i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$593$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$599$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$600$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$601$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$601$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$602$	−0.173409	−	0.340334i	−0.173409	−	0.340334i
$603$	0.312869	+	1.97538i	0.312869	+	1.97538i
$604$		0			0
$605$	0.951057	−	0.309017i	0.951057	−	0.309017i
$606$	−0.642040	−	1.26007i	−0.642040	−	1.26007i
$607$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.987688	+	0.156434i	$0.0500000\pi$
$607$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.453990	+	0.891007i	$0.350000\pi$
$608$		0			0
$609$	0.554254	−	0.0877853i	0.554254	−	0.0877853i
$610$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$611$		0			0
$612$		0			0
$613$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$613$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$614$	0.587785	+	1.80902i	0.587785	+	1.80902i
$615$	−1.44168	+	0.734572i	−1.44168	+	0.734572i
$616$		0			0
$617$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$617$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$618$	0.253116	−	0.183900i	0.253116	−	0.183900i
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$		0			0
$621$	1.11803	+	0.363271i	1.11803	+	0.363271i
$622$		0			0
$623$			0.874032i			0.874032i
$624$		0			0
$625$	0.309017	−	0.951057i	0.309017	−	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$631$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$631$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.04744	−	1.44168i	−1.04744	−	1.44168i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.987688	+	0.156434i	0.987688	+	0.156434i
$641$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i		−	1.00000i	$-0.5\pi$
$641$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i	−0.309017	+	0.951057i	$0.600000\pi$
$642$	1.14412	+	0.831254i	1.14412	+	0.831254i
$643$	−0.183900	−	1.16110i	−0.183900	−	1.16110i	−0.891007	−	0.453990i	$-0.850000\pi$
$643$	−0.183900	−	1.16110i	−0.183900	−	1.16110i	0.707107	−	0.707107i	$-0.250000\pi$
$644$	0.690983	+	0.224514i	0.690983	+	0.224514i
$645$	0.190983	+	0.587785i	0.190983	+	0.587785i
$646$		0			0
$647$	1.87869	+	0.297556i	1.87869	+	0.297556i	0.987688	−	0.156434i	$-0.0500000\pi$
$647$	1.87869	+	0.297556i	1.87869	+	0.297556i	0.891007	+	0.453990i	$0.150000\pi$
$648$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.734572	+	0.533698i	0.734572	+	0.533698i
$653$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$653$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$654$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$655$		0			0
$656$	0.500000	−	1.53884i	0.500000	−	1.53884i
$657$		0			0
$658$			1.22085i			1.22085i
$659$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$659$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$660$		0			0
$661$	1.76007	−	0.896802i	1.76007	−	0.896802i	0.809017	−	0.587785i	$-0.200000\pi$
$661$	1.76007	−	0.896802i	1.76007	−	0.896802i	0.951057	−	0.309017i	$-0.100000\pi$
$662$		0			0
$663$		0			0
$664$	−0.0489435	+	0.309017i	−0.0489435	+	0.309017i
$665$		0			0
$666$		0			0
$667$	0.329843	+	1.01515i	0.329843	+	1.01515i
$668$	0.831254	−	1.14412i	0.831254	−	1.14412i
$669$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$670$		−	2.00000i		−	2.00000i
$671$		0			0
$672$	−0.0966818	−	0.610425i	−0.0966818	−	0.610425i
$673$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$673$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$674$		0			0
$675$	0.707107	−	0.707107i	0.707107	−	0.707107i
$676$	0.951057	−	0.309017i	0.951057	−	0.309017i
$677$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$677$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.951057	−	0.690983i	0.951057	−	0.690983i
$682$		0			0
$683$	0.863541	+	0.280582i	0.863541	+	0.280582i	0.707107	−	0.707107i	$-0.250000\pi$
$683$	0.863541	+	0.280582i	0.863541	+	0.280582i	0.156434	+	0.987688i	$0.450000\pi$
$684$		0			0
$685$		0			0
$686$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$687$	−1.34500	+	1.34500i	−1.34500	+	1.34500i
$688$	−0.550672	−	0.280582i	−0.550672	−	0.280582i
$689$		0			0
$690$	−1.04744	−	0.533698i	−1.04744	−	0.533698i
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$		0			0
$693$		0			0
$694$	−0.809017	+	1.58779i	−0.809017	+	1.58779i
$695$		0			0
$696$	0.642040	−	0.642040i	0.642040	−	0.642040i
$697$		0			0
$698$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$699$		0			0
$700$	0.437016	−	0.437016i	0.437016	−	0.437016i
$701$	0.278768	−	1.76007i	0.278768	−	1.76007i	−0.309017	−	0.951057i	$-0.600000\pi$
$701$	0.278768	−	1.76007i	0.278768	−	1.76007i	0.587785	−	0.809017i	$-0.300000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.309017	−	1.95106i	0.309017	−	1.95106i
$706$		0			0
$707$	0.707107	−	0.513743i	0.707107	−	0.513743i
$708$		0			0
$709$	1.76007	+	0.896802i	1.76007	+	0.896802i	0.951057	+	0.309017i	$0.100000\pi$
$709$	1.76007	+	0.896802i	1.76007	+	0.896802i	0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$		0			0
$712$	0.831254	+	1.14412i	0.831254	+	1.14412i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$			1.00000i			1.00000i
$721$	0.136729	+	0.136729i	0.136729	+	0.136729i
$722$	0.453990	+	0.891007i	0.453990	+	0.891007i
$723$		0			0
$724$	−1.58779	+	0.809017i	−1.58779	+	0.809017i
$725$	0.896802	+	0.142040i	0.896802	+	0.142040i
$726$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$727$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	−0.707107	−	0.707107i	$-0.750000\pi$
$727$	−0.550672	−	1.69480i	−0.550672	−	1.69480i	0.156434	−	0.987688i	$-0.450000\pi$
$728$		0			0
$729$	0.951057	−	0.309017i	0.951057	−	0.309017i
$730$		0			0
$731$		0			0
$732$	0.707107	+	0.707107i	0.707107	+	0.707107i
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$	1.39680	−	0.221232i	1.39680	−	0.221232i
$735$	0.550672	+	0.280582i	0.550672	+	0.280582i
$736$	1.11803	−	0.363271i	1.11803	−	0.363271i
$737$		0			0
$738$	1.59811	+	0.253116i	1.59811	+	0.253116i
$739$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$739$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.987688	+	0.156434i	$0.0500000\pi$
$743$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.156434	+	0.987688i	$0.450000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.312869			−0.312869
$748$		0			0
$749$	−0.396802	+	0.778768i	−0.396802	+	0.778768i
$750$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$751$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$751$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$752$	1.16110	+	1.59811i	1.16110	+	1.59811i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.587785	−	0.190983i	0.587785	−	0.190983i
$757$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$757$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.221232	+	0.221232i	0.221232	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$761$	0.221232	+	0.221232i	0.221232	+	0.221232i	−0.587785	+	0.809017i	$0.700000\pi$
$762$			1.78201i			1.78201i
$763$	0.113656	−	0.717598i	0.113656	−	0.717598i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$769$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$769$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	0.190983	−	0.587785i	0.190983	−	0.587785i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.69480	+	0.550672i	1.69480	+	0.550672i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.734572	+	0.533698i	0.734572	+	0.533698i
$784$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$785$		0			0
$786$		0			0
$787$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$787$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$788$		0			0
$789$	−1.58779	+	0.809017i	−1.58779	+	0.809017i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	0.156434	−	0.987688i	0.156434	−	0.987688i
$801$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$802$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$803$		0			0
$804$	−1.17557	+	1.61803i	−1.17557	+	1.61803i
$805$	0.224514	−	0.690983i	0.224514	−	0.690983i
$806$		0			0
$807$	−1.87869	+	0.297556i	−1.87869	+	0.297556i
$808$	0.437016	−	1.34500i	0.437016	−	1.34500i
$809$	1.11803	+	1.53884i	1.11803	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$809$	1.11803	+	1.53884i	1.11803	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$810$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$811$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$811$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$812$	0.453990	+	0.329843i	0.453990	+	0.329843i
$813$		0			0
$814$		0			0
$815$	0.533698	−	0.734572i	0.533698	−	0.734572i
$816$		0			0
$817$		0			0
$818$	−0.533698	−	0.734572i	−0.533698	−	0.734572i
$819$		0			0
$820$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$821$	−0.0489435	−	0.309017i	−0.0489435	−	0.309017i	0.951057	−	0.309017i	$-0.100000\pi$
$821$	−0.0489435	−	0.309017i	−0.0489435	−	0.309017i	−1.00000			$\pi$
$822$		0			0
$823$	−1.59811	−	0.253116i	−1.59811	−	0.253116i	−0.707107	−	0.707107i	$-0.750000\pi$
$823$	−1.59811	−	0.253116i	−1.59811	−	0.253116i	−0.891007	+	0.453990i	$0.850000\pi$
$824$	0.309017	+	0.0489435i	0.309017	+	0.0489435i
$825$		0			0
$826$		0			0
$827$	−0.863541	−	0.280582i	−0.863541	−	0.280582i	−0.156434	−	0.987688i	$-0.550000\pi$
$827$	−0.863541	−	0.280582i	−0.863541	−	0.280582i	−0.707107	+	0.707107i	$0.750000\pi$
$828$	0.533698	+	1.04744i	0.533698	+	1.04744i
$829$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$829$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$830$	0.309017	+	0.0489435i	0.309017	+	0.0489435i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.14412	−	0.831254i	−1.14412	−	0.831254i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$839$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$840$	−0.610425	+	0.0966818i	−0.610425	+	0.0966818i
$841$		−	0.175571i		−	0.175571i
$842$	−0.610425	+	1.87869i	−0.610425	+	1.87869i
$843$	0.831254	−	1.14412i	0.831254	−	1.14412i
$844$		0			0
$845$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$846$	−1.39680	+	1.39680i	−1.39680	+	1.39680i
$847$	0.0966818	−	0.610425i	0.0966818	−	0.610425i
$848$		0			0
$849$	−0.412215	−	0.809017i	−0.412215	−	0.809017i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$855$		0			0
$856$	0.221232	+	1.39680i	0.221232	+	1.39680i
$857$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$857$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$858$		0			0
$859$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$859$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$860$	−0.280582	+	0.550672i	−0.280582	+	0.550672i
$861$			1.00000i			1.00000i
$862$		0			0
$863$	−1.34500	+	0.437016i	−1.34500	+	0.437016i	−0.891007	−	0.453990i	$-0.850000\pi$
$863$	−1.34500	+	0.437016i	−1.34500	+	0.437016i	−0.453990	+	0.891007i	$0.650000\pi$
$864$	0.587785	−	0.809017i	0.587785	−	0.809017i
$865$		0			0
$866$		0			0
$867$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$868$		0			0
$869$		0			0
$870$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$871$		0			0
$872$	−0.533698	−	1.04744i	−0.533698	−	1.04744i
$873$		0			0
$874$		0			0
$875$	−0.437016	−	0.437016i	−0.437016	−	0.437016i
$876$		0			0
$877$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$877$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$881$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$882$	−0.280582	−	0.550672i	−0.280582	−	0.550672i
$883$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.156434	−	0.987688i	$-0.450000\pi$
$883$	1.14412	−	1.14412i	1.14412	−	1.14412i	0.987688	−	0.156434i	$-0.0500000\pi$
$884$		0			0
$885$		0			0
$886$	0.642040	+	0.642040i	0.642040	+	0.642040i
$887$	−1.16110	+	0.183900i	−1.16110	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$887$	−1.16110	+	0.183900i	−1.16110	+	0.183900i	−0.453990	+	0.891007i	$0.650000\pi$
$888$		0			0
$889$	−1.08779	+	0.172288i	−1.08779	+	0.172288i
$890$	1.14412	−	0.831254i	1.14412	−	0.831254i
$891$		0			0
$892$	−1.04744	−	0.533698i	−1.04744	−	0.533698i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.363271	−	0.500000i	0.363271	−	0.500000i
$897$		0			0
$898$	0.863541	−	1.69480i	0.863541	−	1.69480i
$899$		0			0
$900$	1.00000			1.00000
$901$		0			0
$902$		0			0
$903$	0.377263	+	0.0597526i	0.377263	+	0.0597526i
$904$		0			0
$905$	0.809017	+	1.58779i	0.809017	+	1.58779i
$906$		0			0
$907$	−1.69480	+	0.863541i	−1.69480	+	0.863541i	−0.707107	+	0.707107i	$0.750000\pi$
$907$	−1.69480	+	0.863541i	−1.69480	+	0.863541i	−0.987688	+	0.156434i	$0.950000\pi$
$908$	1.16110	+	0.183900i	1.16110	+	0.183900i
$909$	1.39680	+	0.221232i	1.39680	+	0.221232i
$910$		0			0
$911$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$911$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.707107	−	0.707107i	0.707107	−	0.707107i
$916$	−1.90211			−1.90211
$917$		0			0
$918$		0			0
$919$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$919$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$920$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$921$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$922$	1.59811	+	0.253116i	1.59811	+	0.253116i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−1.39680	−	1.39680i	−1.39680	−	1.39680i
$927$			0.312869i			0.312869i
$928$	0.907981			0.907981
$929$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$929$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$935$		0			0
$936$		0			0
$937$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$937$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$938$	−1.10134	−	0.561163i	−1.10134	−	0.561163i
$939$		0			0
$940$	1.59811	−	1.16110i	1.59811	−	1.16110i
$941$	1.95106	−	0.309017i	1.95106	−	0.309017i	0.951057	−	0.309017i	$-0.100000\pi$
$941$	1.95106	−	0.309017i	1.95106	−	0.309017i	1.00000			$0$
$942$		0			0
$943$	−1.87869	+	0.297556i	−1.87869	+	0.297556i
$944$		0			0
$945$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$946$		0			0
$947$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$947$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$953$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$961$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$962$		0			0
$963$	−1.34500	+	0.437016i	−1.34500	+	0.437016i
$964$		0			0
$965$		0			0
$966$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$967$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.453990	−	0.891007i	$-0.350000\pi$
$967$	1.34500	−	0.437016i	1.34500	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$968$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$969$		0			0
$970$		0			0
$971$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$971$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$972$	0.891007	+	0.453990i	0.891007	+	0.453990i
$973$		0			0
$974$	0.278768	+	1.76007i	0.278768	+	1.76007i
$975$		0			0
$976$			1.00000i			1.00000i
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$	−0.863541	+	0.280582i	−0.863541	+	0.280582i
$979$		0			0
$980$	0.190983	+	0.587785i	0.190983	+	0.587785i
$981$	0.951057	−	0.690983i	0.951057	−	0.690983i
$982$		0			0
$983$	−0.183900	+	1.16110i	−0.183900	+	1.16110i	0.707107	+	0.707107i	$0.250000\pi$
$983$	−0.183900	+	1.16110i	−0.183900	+	1.16110i	−0.891007	+	0.453990i	$0.850000\pi$
$984$	0.951057	+	1.30902i	0.951057	+	1.30902i
$985$		0			0
$986$		0			0
$987$	−0.987688	−	0.717598i	−0.987688	−	0.717598i
$988$		0			0
$989$			0.726543i			0.726543i
$990$		0			0
$991$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$991$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.221232	−	0.221232i	−0.221232	−	0.221232i
$997$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$997$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3660.1.eb.f.1319.1	yes	16
3.2	odd	2		3660.1.eb.e.1319.2	yes	16
4.3	odd	2	inner	3660.1.eb.f.1319.2	yes	16
5.4	even	2	inner	3660.1.eb.f.1319.2	yes	16
12.11	even	2		3660.1.eb.e.1319.1	yes	16
15.14	odd	2		3660.1.eb.e.1319.1	yes	16
20.19	odd	2	CM	3660.1.eb.f.1319.1	yes	16
60.59	even	2		3660.1.eb.e.1319.2	yes	16
61.53	odd	20		3660.1.eb.e.419.2	yes	16
183.53	even	20	inner	3660.1.eb.f.419.1	yes	16
244.175	even	20		3660.1.eb.e.419.1	✓	16
305.114	odd	20		3660.1.eb.e.419.1	✓	16
732.419	odd	20	inner	3660.1.eb.f.419.2	yes	16
915.419	even	20	inner	3660.1.eb.f.419.2	yes	16
1220.419	even	20		3660.1.eb.e.419.2	yes	16
3660.419	odd	20	inner	3660.1.eb.f.419.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3660.1.eb.e.419.1	✓	16	244.175	even	20
3660.1.eb.e.419.1	✓	16	305.114	odd	20
3660.1.eb.e.419.2	yes	16	61.53	odd	20
3660.1.eb.e.419.2	yes	16	1220.419	even	20
3660.1.eb.e.1319.1	yes	16	12.11	even	2
3660.1.eb.e.1319.1	yes	16	15.14	odd	2
3660.1.eb.e.1319.2	yes	16	3.2	odd	2
3660.1.eb.e.1319.2	yes	16	60.59	even	2
3660.1.eb.f.419.1	yes	16	183.53	even	20	inner
3660.1.eb.f.419.1	yes	16	3660.419	odd	20	inner
3660.1.eb.f.419.2	yes	16	732.419	odd	20	inner
3660.1.eb.f.419.2	yes	16	915.419	even	20	inner
3660.1.eb.f.1319.1	yes	16	1.1	even	1	trivial
3660.1.eb.f.1319.1	yes	16	20.19	odd	2	CM
3660.1.eb.f.1319.2	yes	16	4.3	odd	2	inner
3660.1.eb.f.1319.2	yes	16	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3660 = 2^{2} \cdot 3 \cdot 5 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3660.eb (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.453990 - 0.891007i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.610425 - 0.0966818i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.587785 - 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.453990 - 0.891007i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.610425 - 0.0966818i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-0.587785 - 0.809017i) q^{9} +(0.453990 + 0.891007i) q^{10} +(0.156434 - 0.987688i) q^{12} +0.618034 q^{14} +(-0.987688 - 0.156434i) q^{15} +(0.809017 - 0.587785i) q^{16} +(0.707107 + 0.707107i) q^{18} +(-0.587785 - 0.809017i) q^{20} +(-0.363271 + 0.500000i) q^{21} +(-1.04744 - 0.533698i) q^{23} +1.00000i q^{24} +(-0.809017 + 0.587785i) q^{25} +(-0.987688 + 0.156434i) q^{27} +(-0.610425 + 0.0966818i) q^{28} +(-0.642040 - 0.642040i) q^{29} +1.00000 q^{30} +(-0.707107 + 0.707107i) q^{32} +(0.0966818 + 0.610425i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.707107 + 0.707107i) q^{40} +(1.30902 - 0.951057i) q^{41} +(0.280582 - 0.550672i) q^{42} +(-0.280582 - 0.550672i) q^{43} +(-0.587785 + 0.809017i) q^{45} +(1.11803 + 0.363271i) q^{46} +1.97538i q^{47} +(-0.156434 - 0.987688i) q^{48} +(-0.587785 - 0.190983i) q^{49} +(0.707107 - 0.707107i) q^{50} +(0.951057 - 0.309017i) q^{54} +(0.587785 - 0.190983i) q^{56} +(0.734572 + 0.533698i) q^{58} +(-0.987688 + 0.156434i) q^{60} +(-0.587785 + 0.809017i) q^{61} +(0.280582 + 0.550672i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-1.78201 - 0.907981i) q^{67} +(-0.951057 + 0.690983i) q^{69} +(-0.190983 - 0.587785i) q^{70} +(0.891007 + 0.453990i) q^{72} +(0.156434 + 0.987688i) q^{75} +(-0.809017 - 0.587785i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(-1.14412 + 1.14412i) q^{82} +(0.183900 - 0.253116i) q^{83} +(-0.190983 + 0.587785i) q^{84} +(0.363271 + 0.500000i) q^{86} +(-0.863541 + 0.280582i) q^{87} +(-0.221232 - 1.39680i) q^{89} +(0.453990 - 0.891007i) q^{90} +(-1.16110 - 0.183900i) q^{92} +(-0.309017 - 1.95106i) q^{94} +(0.309017 + 0.951057i) q^{96} +(0.610425 + 0.0966818i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5} + 4 q^{6}+O(q^{10}) \) 16 * q + 4 * q^5 + 4 * q^6	\( 16 q + 4 q^{5} + 4 q^{6} - 8 q^{14} + 4 q^{16} - 4 q^{25} - 4 q^{29} + 16 q^{30} - 4 q^{36} + 12 q^{41} - 12 q^{70} - 4 q^{80} + 4 q^{81} - 12 q^{84} - 4 q^{89} + 4 q^{94} - 4 q^{96}+O(q^{100}) \) 16 * q + 4 * q^5 + 4 * q^6 - 8 * q^14 + 4 * q^16 - 4 * q^25 - 4 * q^29 + 16 * q^30 - 4 * q^36 + 12 * q^41 - 12 * q^70 - 4 * q^80 + 4 * q^81 - 12 * q^84 - 4 * q^89 + 4 * q^94 - 4 * q^96

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