LMFDB - Embedded newform 2299.1.w.a.1322.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,1,Mod(239,2299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2299, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 20]))

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

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

chi := DirichletCharacter("2299.239");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2299.w (of order $30$, degree $8$, not 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:	$1.14735046404$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.43681.1

Embedding invariants

Embedding label			1322.1
Root			$0.406737 - 0.913545i$ of defining polynomial
Character	$\chi$	$=$	2299.1322
Dual form			2299.1.w.a.1546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743145 + 0.669131i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(-0.978148 - 0.207912i) q^{5} +(0.743145 + 0.669131i) q^{6} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(-0.978148 - 0.207912i) q^{5} +(0.743145 + 0.669131i) q^{6} +(-0.587785 - 0.809017i) q^{8} +(0.866025 - 0.500000i) q^{10} +(0.207912 + 0.978148i) q^{13} +(-0.104528 + 0.994522i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.207912 + 0.978148i) q^{17} +(0.587785 + 0.809017i) q^{19} +(-0.500000 - 0.866025i) q^{23} +(-0.743145 + 0.669131i) q^{24} +(-0.809017 - 0.587785i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.994522 - 0.104528i) q^{29} +(-0.587785 - 0.809017i) q^{30} +(-0.500000 - 0.866025i) q^{34} +(-0.978148 - 0.207912i) q^{38} +(0.951057 - 0.309017i) q^{39} +(0.406737 + 0.913545i) q^{40} +(0.994522 - 0.104528i) q^{41} +(0.866025 + 0.500000i) q^{43} +(0.951057 + 0.309017i) q^{46} +(0.913545 + 0.406737i) q^{47} +(0.104528 - 0.994522i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.994522 + 0.104528i) q^{51} +(0.978148 - 0.207912i) q^{53} +(0.866025 + 0.500000i) q^{54} +(0.743145 - 0.669131i) q^{57} +(0.809017 - 0.587785i) q^{58} +(0.913545 - 0.406737i) q^{59} +(0.743145 + 0.669131i) q^{61} +(-0.309017 + 0.951057i) q^{64} -1.00000i q^{65} +(0.500000 + 0.866025i) q^{67} +(-0.809017 + 0.587785i) q^{69} +(0.978148 + 0.207912i) q^{71} +(-0.406737 - 0.913545i) q^{73} +(-0.500000 + 0.866025i) q^{78} +(0.743145 - 0.669131i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(-0.913545 + 0.406737i) q^{81} +(-0.669131 + 0.743145i) q^{82} +(0.406737 - 0.913545i) q^{85} +(-0.978148 + 0.207912i) q^{86} +1.00000i q^{87} +(0.500000 + 0.866025i) q^{89} +(-0.951057 + 0.309017i) q^{94} +(-0.406737 - 0.913545i) q^{95} +(-0.669131 - 0.743145i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 16 * q + 2 * q^3 + 2 * q^5	$ 16 q + 2 q^{3} + 2 q^{5} + 2 q^{15} - 2 q^{16} - 8 q^{23} - 4 q^{26} + 4 q^{27} - 8 q^{34} + 2 q^{38} + 2 q^{47} - 2 q^{48} - 4 q^{49} - 2 q^{53} + 4 q^{58} + 2 q^{59} + 4 q^{64} + 8 q^{67} - 4 q^{69} - 2 q^{71} - 8 q^{78} - 2 q^{80} - 2 q^{81} - 2 q^{82} + 2 q^{86} + 8 q^{89} - 2 q^{97}+O(q^{100}) $ 16 * q + 2 * q^3 + 2 * q^5 + 2 * q^15 - 2 * q^16 - 8 * q^23 - 4 * q^26 + 4 * q^27 - 8 * q^34 + 2 * q^38 + 2 * q^47 - 2 * q^48 - 4 * q^49 - 2 * q^53 + 4 * q^58 + 2 * q^59 + 4 * q^64 + 8 * q^67 - 4 * q^69 - 2 * q^71 - 8 * q^78 - 2 * q^80 - 2 * q^81 - 2 * q^82 + 2 * q^86 + 8 * q^89 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2299\mathbb{Z}\right)^\times$.

$n$	$970$	$1332$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$2$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$3$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$3$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$4$		0			0
$5$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$6$	0.743145	+	0.669131i	0.743145	+	0.669131i
$7$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$7$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$8$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$9$		0			0
$10$	0.866025	−	0.500000i	0.866025	−	0.500000i
$11$		0			0
$11$		0			0
$12$		0			0
$13$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$13$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$14$		0			0
$15$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$16$	0.978148	+	0.207912i	0.978148	+	0.207912i
$17$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$17$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$18$		0			0
$19$	0.587785	+	0.809017i	0.587785	+	0.809017i
$19$	0.587785	+	0.809017i	0.587785	+	0.809017i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$24$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$25$		0			0
$26$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$27$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$28$		0			0
$29$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$29$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$30$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$		0			0
$33$		0			0
$34$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$35$		0			0
$36$		0			0
$37$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$37$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$38$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$39$	0.951057	−	0.309017i	0.951057	−	0.309017i
$40$	0.406737	+	0.913545i	0.406737	+	0.913545i
$41$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$41$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$42$		0			0
$43$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$43$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$	0.951057	+	0.309017i	0.951057	+	0.309017i
$47$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$47$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$48$	0.104528	−	0.994522i	0.104528	−	0.994522i
$49$	0.309017	+	0.951057i	0.309017	+	0.951057i
$50$		0			0
$51$	0.994522	+	0.104528i	0.994522	+	0.104528i
$52$		0			0
$53$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$53$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$54$	0.866025	+	0.500000i	0.866025	+	0.500000i
$55$		0			0
$56$		0			0
$57$	0.743145	−	0.669131i	0.743145	−	0.669131i
$58$	0.809017	−	0.587785i	0.809017	−	0.587785i
$59$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$59$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$61$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$62$		0			0
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$65$		−	1.00000i		−	1.00000i
$66$		0			0
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$70$		0			0
$71$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$71$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$72$		0			0
$73$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$73$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$79$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$79$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$80$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$81$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$82$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$83$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$83$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$84$		0			0
$85$	0.406737	−	0.913545i	0.406737	−	0.913545i
$86$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$87$			1.00000i			1.00000i
$88$		0			0
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$95$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$96$		0			0
$97$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$97$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$98$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$99$		0			0
$100$		0			0
$101$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$101$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$102$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$103$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$103$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$104$	0.669131	−	0.743145i	0.669131	−	0.743145i
$105$		0			0
$106$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$107$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$107$	1.17557	+	1.61803i	1.17557	+	1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$108$		0			0
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$113$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$114$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$115$	0.309017	+	0.951057i	0.309017	+	0.951057i
$116$		0			0
$117$		0			0
$118$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$119$		0			0
$120$	0.866025	−	0.500000i	0.866025	−	0.500000i
$121$		0			0
$122$	−1.00000			−1.00000
$123$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$124$		0			0
$125$	0.809017	+	0.587785i	0.809017	+	0.587785i
$126$		0			0
$127$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$127$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$128$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$129$	0.406737	−	0.913545i	0.406737	−	0.913545i
$130$	0.669131	+	0.743145i	0.669131	+	0.743145i
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$135$	0.104528	+	0.994522i	0.104528	+	0.994522i
$136$	0.913545	−	0.406737i	0.913545	−	0.406737i
$137$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$137$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$138$	0.207912	−	0.978148i	0.207912	−	0.978148i
$139$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$139$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$140$		0			0
$141$	0.309017	−	0.951057i	0.309017	−	0.951057i
$142$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$143$		0			0
$144$		0			0
$145$	0.951057	+	0.309017i	0.951057	+	0.309017i
$146$	0.913545	+	0.406737i	0.913545	+	0.406737i
$147$	0.913545	−	0.406737i	0.913545	−	0.406737i
$148$		0			0
$149$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$149$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$150$		0			0
$151$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$151$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$152$	0.309017	−	0.951057i	0.309017	−	0.951057i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$157$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$158$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$159$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$160$		0			0
$161$		0			0
$162$	0.406737	−	0.913545i	0.406737	−	0.913545i
$163$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$163$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$167$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$168$		0			0
$169$		0			0
$170$	0.309017	+	0.951057i	0.309017	+	0.951057i
$171$		0			0
$172$		0			0
$173$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$173$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$174$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$175$		0			0
$176$		0			0
$177$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$178$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$179$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$179$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$180$		0			0
$181$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$181$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$182$		0			0
$183$	0.587785	−	0.809017i	0.587785	−	0.809017i
$184$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.913545	+	0.406737i	0.913545	+	0.406737i
$191$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$191$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$192$	0.978148	+	0.207912i	0.978148	+	0.207912i
$193$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$193$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$194$	0.994522	+	0.104528i	0.994522	+	0.104528i
$195$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$200$		0			0
$201$	0.809017	−	0.587785i	0.809017	−	0.587785i
$202$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$203$		0			0
$204$		0			0
$205$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$206$		0			0
$207$		0			0
$208$			1.00000i			1.00000i
$209$		0			0
$210$		0			0
$211$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$211$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$212$		0			0
$213$	0.104528	−	0.994522i	0.104528	−	0.994522i
$214$	−1.95630	−	0.415823i	−1.95630	−	0.415823i
$215$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$216$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$217$		0			0
$218$	0.978148	−	0.207912i	0.978148	−	0.207912i
$219$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$220$		0			0
$221$	−1.00000			−1.00000
$222$		0			0
$223$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$223$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$229$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$230$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$231$		0			0
$232$	0.500000	+	0.866025i	0.500000	+	0.866025i
$233$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$233$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$234$		0			0
$235$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$236$		0			0
$237$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$238$		0			0
$239$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$239$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$240$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$246$	0.809017	+	0.587785i	0.809017	+	0.587785i
$247$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$248$		0			0
$249$		0			0
$250$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$252$		0			0
$253$		0			0
$254$	1.00000			1.00000
$255$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$256$		0			0
$257$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$257$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$258$	0.309017	+	0.951057i	0.309017	+	0.951057i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.978148	−	0.207912i	0.978148	−	0.207912i
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	−1.00000			−1.00000
$266$		0			0
$267$	0.809017	−	0.587785i	0.809017	−	0.587785i
$268$		0			0
$269$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$269$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$270$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$271$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$271$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$272$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$273$		0			0
$274$			1.00000i			1.00000i
$275$		0			0
$276$		0			0
$277$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$277$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$278$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$279$		0			0
$280$		0			0
$281$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$281$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$282$	0.406737	+	0.913545i	0.406737	+	0.913545i
$283$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$283$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$284$		0			0
$285$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		0			0
$290$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$291$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$292$		0			0
$293$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$293$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$294$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$295$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$296$		0			0
$297$		0			0
$298$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$299$	0.743145	−	0.669131i	0.743145	−	0.669131i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.951057	−	0.309017i	0.951057	−	0.309017i
$304$	0.406737	+	0.913545i	0.406737	+	0.913545i
$305$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$306$		0			0
$307$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$307$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$311$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$312$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$313$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$313$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$314$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$315$		0			0
$316$		0			0
$317$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$317$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$318$	0.866025	+	0.500000i	0.866025	+	0.500000i
$319$		0			0
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$	1.48629	−	1.33826i	1.48629	−	1.33826i
$322$		0			0
$323$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$328$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$329$		0			0
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$		0			0
$334$	0.809017	+	0.587785i	0.809017	+	0.587785i
$335$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$336$		0			0
$337$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$337$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$345$	0.913545	−	0.406737i	0.913545	−	0.406737i
$346$	0.669131	−	0.743145i	0.669131	−	0.743145i
$347$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$347$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$348$		0			0
$349$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$349$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$350$		0			0
$351$	0.866025	−	0.500000i	0.866025	−	0.500000i
$352$		0			0
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$	0.951057	+	0.309017i	0.951057	+	0.309017i
$355$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$356$		0			0
$357$		0			0
$358$	0.415823	−	1.95630i	0.415823	−	1.95630i
$359$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$359$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$360$		0			0
$361$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$362$			1.00000i			1.00000i
$363$		0			0
$364$		0			0
$365$	0.207912	+	0.978148i	0.207912	+	0.978148i
$366$	0.104528	+	0.994522i	0.104528	+	0.994522i
$367$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$367$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$368$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.500000	−	0.866025i
$376$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$377$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$378$		0			0
$379$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$379$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$380$		0			0
$381$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$382$		0			0
$383$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$383$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$384$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$385$		0			0
$386$	0.500000	+	0.866025i	0.500000	+	0.866025i
$387$		0			0
$388$		0			0
$389$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$389$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$390$	0.669131	−	0.743145i	0.669131	−	0.743145i
$391$	0.951057	−	0.309017i	0.951057	−	0.309017i
$392$	0.587785	−	0.809017i	0.587785	−	0.809017i
$393$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$394$		0			0
$395$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$396$		0			0
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$398$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$399$		0			0
$400$		0			0
$401$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$401$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$402$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$403$		0			0
$404$		0			0
$405$	0.978148	−	0.207912i	0.978148	−	0.207912i
$406$		0			0
$407$		0			0
$408$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$409$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$409$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$410$	0.809017	−	0.587785i	0.809017	−	0.587785i
$411$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	1.00000i		−	1.00000i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$421$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$422$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$423$		0			0
$424$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$425$		0			0
$426$	0.587785	+	0.809017i	0.587785	+	0.809017i
$427$		0			0
$428$		0			0
$429$		0			0
$430$	1.00000			1.00000
$431$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$431$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$432$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$433$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$433$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$434$		0			0
$435$	0.207912	−	0.978148i	0.207912	−	0.978148i
$436$		0			0
$437$	0.406737	−	0.913545i	0.406737	−	0.913545i
$438$	0.309017	−	0.951057i	0.309017	−	0.951057i
$439$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$439$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$440$		0			0
$441$		0			0
$442$	0.743145	−	0.669131i	0.743145	−	0.669131i
$443$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$443$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$444$		0			0
$445$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$446$	0.743145	+	0.669131i	0.743145	+	0.669131i
$447$	0.994522	+	0.104528i	0.994522	+	0.104528i
$448$		0			0
$449$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$449$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$457$	−1.90211	+	0.618034i	−1.90211	+	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$457$	−1.90211	+	0.618034i	−1.90211	+	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$458$	−0.813473	−	1.82709i	−0.813473	−	1.82709i
$459$	0.994522	−	0.104528i	0.994522	−	0.104528i
$460$		0			0
$461$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$461$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$465$		0			0
$466$	0.104528	−	0.994522i	0.104528	−	0.994522i
$467$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$467$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$468$		0			0
$469$		0			0
$470$	0.994522	−	0.104528i	0.994522	−	0.104528i
$471$	0.978148	−	0.207912i	0.978148	−	0.207912i
$472$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$473$		0			0
$474$	1.00000			1.00000
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$479$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$480$		0			0
$481$		0			0
$482$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$483$		0			0
$484$		0			0
$485$	0.500000	+	0.866025i	0.500000	+	0.866025i
$486$		0			0
$487$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$487$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$488$	0.104528	−	0.994522i	0.104528	−	0.994522i
$489$		0			0
$490$	0.743145	+	0.669131i	0.743145	+	0.669131i
$491$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$491$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$492$		0			0
$493$	0.309017	−	0.951057i	0.309017	−	0.951057i
$494$		−	1.00000i		−	1.00000i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$499$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$500$		0			0
$501$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$502$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$503$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$503$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$504$		0			0
$505$		−	1.00000i		−	1.00000i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$509$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$510$	0.913545	−	0.406737i	0.913545	−	0.406737i
$511$		0			0
$512$	0.951057	−	0.309017i	0.951057	−	0.309017i
$513$	0.587785	−	0.809017i	0.587785	−	0.809017i
$514$	0.587785	+	0.809017i	0.587785	+	0.809017i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.207912	+	0.978148i	0.207912	+	0.978148i
$520$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$521$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$521$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$522$		0			0
$523$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$523$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$524$		0			0
$525$		0			0
$526$	0.978148	−	0.207912i	0.978148	−	0.207912i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	0.743145	−	0.669131i	0.743145	−	0.669131i
$531$		0			0
$532$		0			0
$533$	0.309017	+	0.951057i	0.309017	+	0.951057i
$534$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$535$	−0.813473	−	1.82709i	−0.813473	−	1.82709i
$536$	0.406737	−	0.913545i	0.406737	−	0.913545i
$537$	1.33826	+	1.48629i	1.33826	+	1.48629i
$538$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$539$		0			0
$540$		0			0
$541$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$541$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$542$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$543$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$544$		0			0
$545$	0.743145	+	0.669131i	0.743145	+	0.669131i
$546$		0			0
$547$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$547$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$552$	0.951057	+	0.309017i	0.951057	+	0.309017i
$553$		0			0
$554$	1.82709	−	0.813473i	1.82709	−	0.813473i
$555$		0			0
$556$		0			0
$557$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$557$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$558$		0			0
$559$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$560$		0			0
$561$		0			0
$562$	1.00000			1.00000
$563$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$563$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$564$		0			0
$565$		0			0
$566$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$567$		0			0
$568$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$569$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$569$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$570$	0.309017	−	0.951057i	0.309017	−	0.951057i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$577$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$578$		0			0
$579$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$580$		0			0
$581$		0			0
$582$		−	1.00000i		−	1.00000i
$583$		0			0
$584$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$585$		0			0
$586$		0			0
$587$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$587$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$588$		0			0
$589$		0			0
$590$	0.587785	−	0.809017i	0.587785	−	0.809017i
$591$		0			0
$592$		0			0
$593$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$593$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.809017	−	0.587785i	0.809017	−	0.587785i
$598$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$599$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$599$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$607$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$607$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$608$		0			0
$609$		0			0
$610$	0.978148	+	0.207912i	0.978148	+	0.207912i
$611$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$612$		0			0
$613$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$613$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$614$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$615$			1.00000i			1.00000i
$616$		0			0
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$619$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$620$		0			0
$621$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$622$		0			0
$623$		0			0
$624$	0.994522	−	0.104528i	0.994522	−	0.104528i
$625$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$626$		−	1.00000i		−	1.00000i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$632$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$633$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$634$	0.587785	−	0.809017i	0.587785	−	0.809017i
$635$	0.587785	+	0.809017i	0.587785	+	0.809017i
$636$		0			0
$637$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$638$		0			0
$639$		0			0
$640$	0.207912	+	0.978148i	0.207912	+	0.978148i
$641$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$641$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$642$	−0.209057	+	1.98904i	−0.209057	+	1.98904i
$643$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$643$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$644$		0			0
$645$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$646$	0.406737	−	0.913545i	0.406737	−	0.913545i
$647$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$647$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$648$	0.866025	+	0.500000i	0.866025	+	0.500000i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$653$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$654$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$655$	0.743145	+	0.669131i	0.743145	+	0.669131i
$656$	0.994522	+	0.104528i	0.994522	+	0.104528i
$657$		0			0
$658$		0			0
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$661$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$662$		0			0
$663$	0.104528	+	0.994522i	0.104528	+	0.994522i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.406737	+	0.913545i	0.406737	+	0.913545i
$668$		0			0
$669$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$670$	0.866025	+	0.500000i	0.866025	+	0.500000i
$671$		0			0
$672$		0			0
$673$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$673$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$674$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$675$		0			0
$676$		0			0
$677$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$677$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$678$		0			0
$679$		0			0
$680$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$686$		0			0
$687$	1.95630	+	0.415823i	1.95630	+	0.415823i
$688$	0.743145	+	0.669131i	0.743145	+	0.669131i
$689$	0.406737	+	0.913545i	0.406737	+	0.913545i
$690$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$691$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$691$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$692$		0			0
$693$		0			0
$694$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$695$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$696$	0.809017	−	0.587785i	0.809017	−	0.587785i
$697$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$698$	1.95630	+	0.415823i	1.95630	+	0.415823i
$699$	0.743145	+	0.669131i	0.743145	+	0.669131i
$700$		0			0
$701$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$701$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$702$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$703$		0			0
$704$		0			0
$705$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$709$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$710$	0.951057	−	0.309017i	0.951057	−	0.309017i
$711$		0			0
$712$	0.406737	−	0.913545i	0.406737	−	0.913545i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.913545	+	0.406737i	0.913545	+	0.406737i
$719$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$719$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$720$		0			0
$721$		0			0
$722$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$723$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$731$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$732$		0			0
$733$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$733$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$734$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$735$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$739$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$740$		0			0
$741$	0.809017	+	0.587785i	0.809017	+	0.587785i
$742$		0			0
$743$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$743$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$744$		0			0
$745$	0.406737	−	0.913545i	0.406737	−	0.913545i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.207912	+	0.978148i	0.207912	+	0.978148i
$751$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$751$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$752$	0.809017	+	0.587785i	0.809017	+	0.587785i
$753$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$754$	0.743145	+	0.669131i	0.743145	+	0.669131i
$755$		0			0
$756$		0			0
$757$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$757$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$758$		0			0
$759$		0			0
$760$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$761$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$761$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$762$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.994522	+	0.104528i	0.994522	+	0.104528i
$767$	0.587785	+	0.809017i	0.587785	+	0.809017i
$768$		0			0
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$		0			0
$773$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$773$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$774$		0			0
$775$		0			0
$776$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$777$		0			0
$778$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$779$	0.669131	+	0.743145i	0.669131	+	0.743145i
$780$		0			0
$781$		0			0
$782$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$783$	0.207912	+	0.978148i	0.207912	+	0.978148i
$784$	0.104528	+	0.994522i	0.104528	+	0.994522i
$785$	0.104528	−	0.994522i	0.104528	−	0.994522i
$786$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$787$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$787$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$788$		0			0
$789$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$790$	0.309017	−	0.951057i	0.309017	−	0.951057i
$791$		0			0
$792$		0			0
$793$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$794$	0.207912	+	0.978148i	0.207912	+	0.978148i
$795$	0.104528	+	0.994522i	0.104528	+	0.994522i
$796$		0			0
$797$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$797$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$798$		0			0
$799$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$800$		0			0
$801$		0			0
$802$	0.866025	−	0.500000i	0.866025	−	0.500000i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.104528	−	0.994522i	0.104528	−	0.994522i
$808$	0.669131	−	0.743145i	0.669131	−	0.743145i
$809$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$809$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$810$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$811$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$811$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$812$		0			0
$813$	0.866025	−	0.500000i	0.866025	−	0.500000i
$814$		0			0
$815$		0			0
$816$	0.951057	+	0.309017i	0.951057	+	0.309017i
$817$	0.104528	+	0.994522i	0.104528	+	0.994522i
$818$	0.809017	+	0.587785i	0.809017	+	0.587785i
$819$		0			0
$820$		0			0
$821$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$821$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$822$	0.994522	−	0.104528i	0.994522	−	0.104528i
$823$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$823$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$827$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$828$		0			0
$829$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$829$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$830$		0			0
$831$	−0.415823	+	1.95630i	−0.415823	+	1.95630i
$832$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$833$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$834$	0.669131	+	0.743145i	0.669131	+	0.743145i
$835$			1.00000i			1.00000i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$839$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$840$		0			0
$841$		0			0
$842$	0.743145	+	0.669131i	0.743145	+	0.669131i
$843$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$	1.00000			1.00000
$849$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$853$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$854$		0			0
$855$		0			0
$856$	0.618034	−	1.90211i	0.618034	−	1.90211i
$857$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$857$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$858$		0			0
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$863$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$863$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$864$		0			0
$865$	0.994522	+	0.104528i	0.994522	+	0.104528i
$866$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$867$		0			0
$868$		0			0
$869$		0			0
$870$	0.500000	+	0.866025i	0.500000	+	0.866025i
$871$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$872$	0.104528	+	0.994522i	0.104528	+	0.994522i
$873$		0			0
$874$	0.309017	+	0.951057i	0.309017	+	0.951057i
$875$		0			0
$876$		0			0
$877$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$877$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$878$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$883$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$884$		0			0
$885$	0.309017	+	0.951057i	0.309017	+	0.951057i
$886$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$887$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$887$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$888$		0			0
$889$		0			0
$890$	0.866025	+	0.500000i	0.866025	+	0.500000i
$891$		0			0
$892$		0			0
$893$	0.207912	+	0.978148i	0.207912	+	0.978148i
$894$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$895$	1.82709	−	0.813473i	1.82709	−	0.813473i
$896$		0			0
$897$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$898$		0			0
$899$		0			0
$900$		0			0
$901$			1.00000i			1.00000i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$906$		0			0
$907$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$907$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$911$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$912$	0.866025	−	0.500000i	0.866025	−	0.500000i
$913$		0			0
$914$	1.00000	−	1.73205i	1.00000	−	1.73205i
$915$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$916$		0			0
$917$		0			0
$918$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$919$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$919$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$920$	0.587785	−	0.809017i	0.587785	−	0.809017i
$921$	0.406737	−	0.913545i	0.406737	−	0.913545i
$922$	0.978148	−	0.207912i	0.978148	−	0.207912i
$923$			1.00000i			1.00000i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$929$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$930$		0			0
$931$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$937$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$938$		0			0
$939$	0.809017	+	0.587785i	0.809017	+	0.587785i
$940$		0			0
$941$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$941$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$942$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$943$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$944$	0.978148	−	0.207912i	0.978148	−	0.207912i
$945$		0			0
$946$		0			0
$947$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$947$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$948$		0			0
$949$	0.809017	−	0.587785i	0.809017	−	0.587785i
$950$		0			0
$951$	0.309017	+	0.951057i	0.309017	+	0.951057i
$952$		0			0
$953$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$953$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	1.00000			1.00000
$959$		0			0
$960$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$961$	0.809017	+	0.587785i	0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$966$		0			0
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$968$		0			0
$969$	0.500000	+	0.866025i	0.500000	+	0.866025i
$970$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$971$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$971$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.587785	+	0.809017i	0.587785	+	0.809017i
$977$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$977$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$983$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$983$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$984$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$985$		0			0
$986$	0.406737	+	0.913545i	0.406737	+	0.913545i
$987$		0			0
$988$		0			0
$989$		−	1.00000i		−	1.00000i
$990$		0			0
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$996$		0			0
$997$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$997$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$998$	0.406737	−	0.913545i	0.406737	−	0.913545i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.1.w.a.1322.1		16
11.2	odd	10	inner	2299.1.w.a.239.1		16
11.3	even	5	inner	2299.1.w.a.524.2		16
11.4	even	5		209.1.h.a.87.1	✓	4
11.5	even	5	inner	2299.1.w.a.2272.2		16
11.6	odd	10	inner	2299.1.w.a.2272.1		16
11.7	odd	10		209.1.h.a.87.2	yes	4
11.8	odd	10	inner	2299.1.w.a.524.1		16
11.9	even	5	inner	2299.1.w.a.239.2		16
11.10	odd	2	inner	2299.1.w.a.1322.2		16
19.7	even	3	inner	2299.1.w.a.596.1		16
33.26	odd	10		1881.1.bc.a.505.2		4
33.29	even	10		1881.1.bc.a.505.1		4
44.7	even	10		3344.1.bb.a.2177.2		4
44.15	odd	10		3344.1.bb.a.2177.1		4
209.4	even	45		3971.1.q.e.1506.1		12
209.7	odd	30		209.1.h.a.197.1	yes	4
209.15	odd	90		3971.1.q.d.1506.2		12
209.18	even	10		3971.1.h.d.2595.1		4
209.26	even	15		209.1.h.a.197.2	yes	4
209.29	even	90		3971.1.q.d.967.2		12
209.37	odd	10		3971.1.h.d.2595.2		4
209.40	even	90		3971.1.q.d.956.2		12
209.48	odd	90		3971.1.q.d.967.1		12
209.51	even	90		3971.1.q.d.54.1		12
209.59	odd	90		3971.1.q.d.956.1		12
209.62	odd	90		3971.1.q.e.3277.2		12
209.64	even	15	inner	2299.1.w.a.1812.1		16
209.70	odd	90		3971.1.q.d.54.2		12
209.73	odd	90		3971.1.q.e.2265.1		12
209.81	even	45		3971.1.q.e.3277.1		12
209.83	odd	30	inner	2299.1.w.a.1546.1		16
209.84	even	30		3971.1.c.b.362.2		2
209.92	even	45		3971.1.q.e.2265.2		12
209.102	even	15	inner	2299.1.w.a.2097.1		16
209.103	odd	30		3971.1.c.b.362.1		2
209.106	odd	30		3971.1.c.e.362.1		2
209.117	even	90		3971.1.q.d.2265.2		12
209.125	even	15		3971.1.c.e.362.2		2
209.128	even	90		3971.1.q.d.3277.1		12
209.136	odd	90		3971.1.q.d.2265.1		12
209.139	odd	90		3971.1.q.e.54.2		12
209.140	odd	30	inner	2299.1.w.a.2097.2		16
209.147	odd	90		3971.1.q.d.3277.2		12
209.150	odd	90		3971.1.q.e.956.1		12
209.158	even	45		3971.1.q.e.54.1		12
209.159	even	15	inner	2299.1.w.a.1546.2		16
209.161	odd	90		3971.1.q.e.967.1		12
209.169	even	45		3971.1.q.e.956.2		12
209.178	odd	30	inner	2299.1.w.a.1812.2		16
209.180	even	45		3971.1.q.e.967.2		12
209.183	even	30		3971.1.h.d.3541.2		4
209.194	odd	90		3971.1.q.e.1506.2		12
209.197	odd	6	inner	2299.1.w.a.596.2		16
209.202	odd	30		3971.1.h.d.3541.1		4
209.205	even	90		3971.1.q.d.1506.1		12
627.26	odd	30		1881.1.bc.a.406.1		4
627.425	even	30		1881.1.bc.a.406.2		4
836.7	even	30		3344.1.bb.a.2705.2		4
836.235	odd	30		3344.1.bb.a.2705.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.1.h.a.87.1	✓	4	11.4	even	5
209.1.h.a.87.2	yes	4	11.7	odd	10
209.1.h.a.197.1	yes	4	209.7	odd	30
209.1.h.a.197.2	yes	4	209.26	even	15
1881.1.bc.a.406.1		4	627.26	odd	30
1881.1.bc.a.406.2		4	627.425	even	30
1881.1.bc.a.505.1		4	33.29	even	10
1881.1.bc.a.505.2		4	33.26	odd	10
2299.1.w.a.239.1		16	11.2	odd	10	inner
2299.1.w.a.239.2		16	11.9	even	5	inner
2299.1.w.a.524.1		16	11.8	odd	10	inner
2299.1.w.a.524.2		16	11.3	even	5	inner
2299.1.w.a.596.1		16	19.7	even	3	inner
2299.1.w.a.596.2		16	209.197	odd	6	inner
2299.1.w.a.1322.1		16	1.1	even	1	trivial
2299.1.w.a.1322.2		16	11.10	odd	2	inner
2299.1.w.a.1546.1		16	209.83	odd	30	inner
2299.1.w.a.1546.2		16	209.159	even	15	inner
2299.1.w.a.1812.1		16	209.64	even	15	inner
2299.1.w.a.1812.2		16	209.178	odd	30	inner
2299.1.w.a.2097.1		16	209.102	even	15	inner
2299.1.w.a.2097.2		16	209.140	odd	30	inner
2299.1.w.a.2272.1		16	11.6	odd	10	inner
2299.1.w.a.2272.2		16	11.5	even	5	inner
3344.1.bb.a.2177.1		4	44.15	odd	10
3344.1.bb.a.2177.2		4	44.7	even	10
3344.1.bb.a.2705.1		4	836.235	odd	30
3344.1.bb.a.2705.2		4	836.7	even	30
3971.1.c.b.362.1		2	209.103	odd	30
3971.1.c.b.362.2		2	209.84	even	30
3971.1.c.e.362.1		2	209.106	odd	30
3971.1.c.e.362.2		2	209.125	even	15
3971.1.h.d.2595.1		4	209.18	even	10
3971.1.h.d.2595.2		4	209.37	odd	10
3971.1.h.d.3541.1		4	209.202	odd	30
3971.1.h.d.3541.2		4	209.183	even	30
3971.1.q.d.54.1		12	209.51	even	90
3971.1.q.d.54.2		12	209.70	odd	90
3971.1.q.d.956.1		12	209.59	odd	90
3971.1.q.d.956.2		12	209.40	even	90
3971.1.q.d.967.1		12	209.48	odd	90
3971.1.q.d.967.2		12	209.29	even	90
3971.1.q.d.1506.1		12	209.205	even	90
3971.1.q.d.1506.2		12	209.15	odd	90
3971.1.q.d.2265.1		12	209.136	odd	90
3971.1.q.d.2265.2		12	209.117	even	90
3971.1.q.d.3277.1		12	209.128	even	90
3971.1.q.d.3277.2		12	209.147	odd	90
3971.1.q.e.54.1		12	209.158	even	45
3971.1.q.e.54.2		12	209.139	odd	90
3971.1.q.e.956.1		12	209.150	odd	90
3971.1.q.e.956.2		12	209.169	even	45
3971.1.q.e.967.1		12	209.161	odd	90
3971.1.q.e.967.2		12	209.180	even	45
3971.1.q.e.1506.1		12	209.4	even	45
3971.1.q.e.1506.2		12	209.194	odd	90
3971.1.q.e.2265.1		12	209.73	odd	90
3971.1.q.e.2265.2		12	209.92	even	45
3971.1.q.e.3277.1		12	209.81	even	45
3971.1.q.e.3277.2		12	209.62	odd	90

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2299.w (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(-0.978148 - 0.207912i) q^{5} +(0.743145 + 0.669131i) q^{6} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.104528 - 0.994522i) q^{3} +(-0.978148 - 0.207912i) q^{5} +(0.743145 + 0.669131i) q^{6} +(-0.587785 - 0.809017i) q^{8} +(0.866025 - 0.500000i) q^{10} +(0.207912 + 0.978148i) q^{13} +(-0.104528 + 0.994522i) q^{15} +(0.978148 + 0.207912i) q^{16} +(-0.207912 + 0.978148i) q^{17} +(0.587785 + 0.809017i) q^{19} +(-0.500000 - 0.866025i) q^{23} +(-0.743145 + 0.669131i) q^{24} +(-0.809017 - 0.587785i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.994522 - 0.104528i) q^{29} +(-0.587785 - 0.809017i) q^{30} +(-0.500000 - 0.866025i) q^{34} +(-0.978148 - 0.207912i) q^{38} +(0.951057 - 0.309017i) q^{39} +(0.406737 + 0.913545i) q^{40} +(0.994522 - 0.104528i) q^{41} +(0.866025 + 0.500000i) q^{43} +(0.951057 + 0.309017i) q^{46} +(0.913545 + 0.406737i) q^{47} +(0.104528 - 0.994522i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.994522 + 0.104528i) q^{51} +(0.978148 - 0.207912i) q^{53} +(0.866025 + 0.500000i) q^{54} +(0.743145 - 0.669131i) q^{57} +(0.809017 - 0.587785i) q^{58} +(0.913545 - 0.406737i) q^{59} +(0.743145 + 0.669131i) q^{61} +(-0.309017 + 0.951057i) q^{64} -1.00000i q^{65} +(0.500000 + 0.866025i) q^{67} +(-0.809017 + 0.587785i) q^{69} +(0.978148 + 0.207912i) q^{71} +(-0.406737 - 0.913545i) q^{73} +(-0.500000 + 0.866025i) q^{78} +(0.743145 - 0.669131i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(-0.913545 + 0.406737i) q^{81} +(-0.669131 + 0.743145i) q^{82} +(0.406737 - 0.913545i) q^{85} +(-0.978148 + 0.207912i) q^{86} +1.00000i q^{87} +(0.500000 + 0.866025i) q^{89} +(-0.951057 + 0.309017i) q^{94} +(-0.406737 - 0.913545i) q^{95} +(-0.669131 - 0.743145i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 16 * q + 2 * q^3 + 2 * q^5	\( 16 q + 2 q^{3} + 2 q^{5} + 2 q^{15} - 2 q^{16} - 8 q^{23} - 4 q^{26} + 4 q^{27} - 8 q^{34} + 2 q^{38} + 2 q^{47} - 2 q^{48} - 4 q^{49} - 2 q^{53} + 4 q^{58} + 2 q^{59} + 4 q^{64} + 8 q^{67} - 4 q^{69} - 2 q^{71} - 8 q^{78} - 2 q^{80} - 2 q^{81} - 2 q^{82} + 2 q^{86} + 8 q^{89} - 2 q^{97}+O(q^{100}) \) 16 * q + 2 * q^3 + 2 * q^5 + 2 * q^15 - 2 * q^16 - 8 * q^23 - 4 * q^26 + 4 * q^27 - 8 * q^34 + 2 * q^38 + 2 * q^47 - 2 * q^48 - 4 * q^49 - 2 * q^53 + 4 * q^58 + 2 * q^59 + 4 * q^64 + 8 * q^67 - 4 * q^69 - 2 * q^71 - 8 * q^78 - 2 * q^80 - 2 * q^81 - 2 * q^82 + 2 * q^86 + 8 * q^89 - 2 * q^97

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