LMFDB - Embedded newform 675.1.o.a.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,1,Mod(161,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("675.161");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	675.o (of order $10$, degree $4$, 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:	$0.336868883527$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.31640625.2

Embedding invariants

Embedding label			161.1
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	675.161
Dual form			675.1.o.a.566.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 1.30902i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(0.587785 - 0.809017i) q^{5} -1.61803 q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.951057 - 1.30902i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(0.587785 - 0.809017i) q^{5} -1.61803 q^{7} +(0.951057 - 0.309017i) q^{8} -1.61803 q^{10} +(-0.587785 - 0.809017i) q^{11} +(1.53884 + 2.11803i) q^{14} +(-0.951057 + 0.309017i) q^{17} +(-0.309017 - 0.951057i) q^{19} +(0.951057 + 1.30902i) q^{20} +(-0.500000 + 1.53884i) q^{22} +(-0.587785 - 0.809017i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(0.809017 - 2.48990i) q^{28} +(-0.587785 - 0.190983i) q^{29} -1.00000i q^{32} +(1.30902 + 0.951057i) q^{34} +(-0.951057 + 1.30902i) q^{35} +(0.500000 + 0.363271i) q^{37} +(-0.951057 + 1.30902i) q^{38} +(0.309017 - 0.951057i) q^{40} +(-0.587785 + 0.809017i) q^{41} +(1.53884 - 0.500000i) q^{44} +(-0.500000 + 1.53884i) q^{46} +(0.587785 + 0.190983i) q^{47} +1.61803 q^{49} +(-0.951057 + 1.30902i) q^{50} +(1.53884 + 0.500000i) q^{53} -1.00000 q^{55} +(-1.53884 + 0.500000i) q^{56} +(0.309017 + 0.951057i) q^{58} +(0.809017 - 0.587785i) q^{61} +(-1.30902 + 0.951057i) q^{64} +(-0.500000 - 1.53884i) q^{67} -1.61803i q^{68} +2.61803 q^{70} +(-0.587785 - 0.190983i) q^{71} -1.00000i q^{74} +1.61803 q^{76} +(0.951057 + 1.30902i) q^{77} +(-0.190983 + 0.587785i) q^{79} +1.61803 q^{82} +(1.53884 - 0.500000i) q^{83} +(-0.309017 + 0.951057i) q^{85} +(-0.809017 - 0.587785i) q^{88} +(-0.587785 - 0.809017i) q^{89} +(1.53884 - 0.500000i) q^{92} +(-0.309017 - 0.951057i) q^{94} +(-0.951057 - 0.309017i) q^{95} +(0.309017 - 0.951057i) q^{97} +(-1.53884 - 2.11803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^4 - 4 * q^7	$ 8 q - 4 q^{4} - 4 q^{7} - 4 q^{10} + 2 q^{19} - 4 q^{22} + 2 q^{25} + 2 q^{28} + 6 q^{34} + 4 q^{37} - 2 q^{40} - 4 q^{46} + 4 q^{49} - 8 q^{55} - 2 q^{58} + 2 q^{61} - 6 q^{64} - 4 q^{67} + 12 q^{70} + 4 q^{76} - 6 q^{79} + 4 q^{82} + 2 q^{85} - 2 q^{88} + 2 q^{94} - 2 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 - 4 * q^7 - 4 * q^10 + 2 * q^19 - 4 * q^22 + 2 * q^25 + 2 * q^28 + 6 * q^34 + 4 * q^37 - 2 * q^40 - 4 * q^46 + 4 * q^49 - 8 * q^55 - 2 * q^58 + 2 * q^61 - 6 * q^64 - 4 * q^67 + 12 * q^70 + 4 * q^76 - 6 * q^79 + 4 * q^82 + 2 * q^85 - 2 * q^88 + 2 * q^94 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$2$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$5$	0.587785	−	0.809017i	0.587785	−	0.809017i
$5$	0.587785	−	0.809017i	0.587785	−	0.809017i
$6$		0			0
$7$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$7$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$8$	0.951057	−	0.309017i	0.951057	−	0.309017i
$9$		0			0
$10$	−1.61803			−1.61803
$11$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$11$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$12$		0			0
$13$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$13$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$14$	1.53884	+	2.11803i	1.53884	+	2.11803i
$15$		0			0
$16$		0			0
$17$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$17$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$18$		0			0
$19$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$19$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$20$	0.951057	+	1.30902i	0.951057	+	1.30902i
$21$		0			0
$22$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$23$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$23$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$26$		0			0
$27$		0			0
$28$	0.809017	−	2.48990i	0.809017	−	2.48990i
$29$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$29$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$30$		0			0
$31$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$31$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$32$		−	1.00000i		−	1.00000i
$33$		0			0
$34$	1.30902	+	0.951057i	1.30902	+	0.951057i
$35$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$36$		0			0
$37$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$37$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$38$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$39$		0			0
$40$	0.309017	−	0.951057i	0.309017	−	0.951057i
$41$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$41$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.53884	−	0.500000i	1.53884	−	0.500000i
$45$		0			0
$46$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$47$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$47$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$48$		0			0
$49$	1.61803			1.61803
$50$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$51$		0			0
$52$		0			0
$53$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$53$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$54$		0			0
$55$	−1.00000			−1.00000
$56$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$57$		0			0
$58$	0.309017	+	0.951057i	0.309017	+	0.951057i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$61$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$62$		0			0
$63$		0			0
$64$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$65$		0			0
$66$		0			0
$67$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$67$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$68$		−	1.61803i		−	1.61803i
$69$		0			0
$70$	2.61803			2.61803
$71$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$71$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$72$		0			0
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$		−	1.00000i		−	1.00000i
$75$		0			0
$76$	1.61803			1.61803
$77$	0.951057	+	1.30902i	0.951057	+	1.30902i
$78$		0			0
$79$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$79$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$80$		0			0
$81$		0			0
$82$	1.61803			1.61803
$83$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$83$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$84$		0			0
$85$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$86$		0			0
$87$		0			0
$88$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$89$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$89$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$90$		0			0
$91$		0			0
$92$	1.53884	−	0.500000i	1.53884	−	0.500000i
$93$		0			0
$94$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$95$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$96$		0			0
$97$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$97$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$98$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$99$		0			0
$100$	1.61803			1.61803
$101$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$101$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$103$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$104$		0			0
$105$		0			0
$106$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$109$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$110$	0.951057	+	1.30902i	0.951057	+	1.30902i
$111$		0			0
$112$		0			0
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$	−1.00000			−1.00000
$116$	0.587785	−	0.809017i	0.587785	−	0.809017i
$117$		0			0
$118$		0			0
$119$	1.53884	−	0.500000i	1.53884	−	0.500000i
$120$		0			0
$121$		0			0
$122$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$123$		0			0
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$126$		0			0
$127$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$127$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$128$	1.53884	+	0.500000i	1.53884	+	0.500000i
$129$		0			0
$130$		0			0
$131$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$131$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$132$		0			0
$133$	0.500000	+	1.53884i	0.500000	+	1.53884i
$134$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$135$		0			0
$136$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$137$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$137$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$138$		0			0
$139$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$139$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$140$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$141$		0			0
$142$	0.309017	+	0.951057i	0.309017	+	0.951057i
$143$		0			0
$144$		0			0
$145$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$146$		0			0
$147$		0			0
$148$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$149$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$149$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$153$		0			0
$154$	0.809017	−	2.48990i	0.809017	−	2.48990i
$155$		0			0
$156$		0			0
$157$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$157$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$158$	0.951057	−	0.309017i	0.951057	−	0.309017i
$159$		0			0
$160$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$161$	0.951057	+	1.30902i	0.951057	+	1.30902i
$162$		0			0
$163$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$163$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$164$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$165$		0			0
$166$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$167$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$167$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$168$		0			0
$169$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$170$	1.53884	−	0.500000i	1.53884	−	0.500000i
$171$		0			0
$172$		0			0
$173$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$173$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$174$		0			0
$175$	0.500000	+	1.53884i	0.500000	+	1.53884i
$176$		0			0
$177$		0			0
$178$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$179$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$179$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$180$		0			0
$181$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$181$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$182$		0			0
$183$		0			0
$184$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$185$	0.587785	−	0.190983i	0.587785	−	0.190983i
$186$		0			0
$187$	0.809017	+	0.587785i	0.809017	+	0.587785i
$188$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$189$		0			0
$190$	0.500000	+	1.53884i	0.500000	+	1.53884i
$191$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$191$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$192$		0			0
$193$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$193$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$194$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$195$		0			0
$196$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$197$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$197$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$201$		0			0
$202$	1.30902	−	0.951057i	1.30902	−	0.951057i
$203$	0.951057	+	0.309017i	0.951057	+	0.309017i
$204$		0			0
$205$	0.309017	+	0.951057i	0.309017	+	0.951057i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$210$		0			0
$211$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$211$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$212$	−1.53884	+	2.11803i	−1.53884	+	2.11803i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$			1.61803i			1.61803i
$219$		0			0
$220$	0.500000	−	1.53884i	0.500000	−	1.53884i
$221$		0			0
$222$		0			0
$223$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$223$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$224$			1.61803i			1.61803i
$225$		0			0
$226$		0			0
$227$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$227$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$228$		0			0
$229$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$229$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$230$	0.951057	+	1.30902i	0.951057	+	1.30902i
$231$		0			0
$232$	−0.618034			−0.618034
$233$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$233$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$234$		0			0
$235$	0.500000	−	0.363271i	0.500000	−	0.363271i
$236$		0			0
$237$		0			0
$238$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$239$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$239$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$240$		0			0
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$242$		0			0
$243$		0			0
$244$	0.500000	+	1.53884i	0.500000	+	1.53884i
$245$	0.951057	−	1.30902i	0.951057	−	1.30902i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.500000	+	1.53884i	0.500000	+	1.53884i
$251$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$251$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$252$		0			0
$253$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$254$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$255$		0			0
$256$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$260$		0			0
$261$		0			0
$262$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$263$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$263$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$264$		0			0
$265$	1.30902	−	0.951057i	1.30902	−	0.951057i
$266$	1.53884	−	2.11803i	1.53884	−	2.11803i
$267$		0			0
$268$	2.61803			2.61803
$269$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$269$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$270$		0			0
$271$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$271$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$272$		0			0
$273$		0			0
$274$	−1.61803			−1.61803
$275$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$276$		0			0
$277$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$277$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$278$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$279$		0			0
$280$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$281$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$281$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$282$		0			0
$283$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$283$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$284$	0.587785	−	0.809017i	0.587785	−	0.809017i
$285$		0			0
$286$		0			0
$287$	0.951057	−	1.30902i	0.951057	−	1.30902i
$288$		0			0
$289$		0			0
$290$	0.951057	+	0.309017i	0.951057	+	0.309017i
$291$		0			0
$292$		0			0
$293$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$293$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$294$		0			0
$295$		0			0
$296$	0.587785	+	0.190983i	0.587785	+	0.190983i
$297$		0			0
$298$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	1.00000i		−	1.00000i
$306$		0			0
$307$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$307$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$308$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$309$		0			0
$310$		0			0
$311$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$311$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$312$		0			0
$313$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$313$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$314$	0.587785	+	0.809017i	0.587785	+	0.809017i
$315$		0			0
$316$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$317$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$317$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$318$		0			0
$319$	0.190983	+	0.587785i	0.190983	+	0.587785i
$320$			1.61803i			1.61803i
$321$		0			0
$322$	0.809017	−	2.48990i	0.809017	−	2.48990i
$323$	0.587785	+	0.809017i	0.587785	+	0.809017i
$324$		0			0
$325$		0			0
$326$		−	1.61803i		−	1.61803i
$327$		0			0
$328$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$329$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$330$		0			0
$331$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$331$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$332$			2.61803i			2.61803i
$333$		0			0
$334$		0			0
$335$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$336$		0			0
$337$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$337$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$338$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$339$		0			0
$340$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$341$		0			0
$342$		0			0
$343$	−1.00000			−1.00000
$344$		0			0
$345$		0			0
$346$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$347$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$347$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	1.53884	−	2.11803i	1.53884	−	2.11803i
$351$		0			0
$352$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$353$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$353$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$354$		0			0
$355$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$356$	1.53884	−	0.500000i	1.53884	−	0.500000i
$357$		0			0
$358$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$359$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$359$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$360$		0			0
$361$		0			0
$362$	0.951057	−	1.30902i	0.951057	−	1.30902i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$367$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$368$		0			0
$369$		0			0
$370$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$371$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$372$		0			0
$373$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$373$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$374$		−	1.61803i		−	1.61803i
$375$		0			0
$376$	0.618034			0.618034
$377$		0			0
$378$		0			0
$379$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$379$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$380$	0.951057	−	1.30902i	0.951057	−	1.30902i
$381$		0			0
$382$	2.61803			2.61803
$383$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$383$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$384$		0			0
$385$	1.61803			1.61803
$386$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$387$		0			0
$388$	1.30902	+	0.951057i	1.30902	+	0.951057i
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$	0.809017	+	0.587785i	0.809017	+	0.587785i
$392$	1.53884	−	0.500000i	1.53884	−	0.500000i
$393$		0			0
$394$		0			0
$395$	0.363271	+	0.500000i	0.363271	+	0.500000i
$396$		0			0
$397$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$397$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$401$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$402$		0			0
$403$		0			0
$404$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$405$		0			0
$406$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$407$		−	0.618034i		−	0.618034i
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$	0.951057	−	1.30902i	0.951057	−	1.30902i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.500000	−	1.53884i	0.500000	−	1.53884i
$416$		0			0
$417$		0			0
$418$	1.61803			1.61803
$419$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$419$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$420$		0			0
$421$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$421$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$422$	2.48990	+	0.809017i	2.48990	+	0.809017i
$423$		0			0
$424$	1.61803			1.61803
$425$	0.587785	+	0.809017i	0.587785	+	0.809017i
$426$		0			0
$427$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$		0			0
$433$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$433$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$434$		0			0
$435$		0			0
$436$	1.30902	−	0.951057i	1.30902	−	0.951057i
$437$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$438$		0			0
$439$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$439$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$440$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$441$		0			0
$442$		0			0
$443$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$443$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$444$		0			0
$445$	−1.00000			−1.00000
$446$	2.48990	+	0.809017i	2.48990	+	0.809017i
$447$		0			0
$448$	2.11803	−	1.53884i	2.11803	−	1.53884i
$449$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$449$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$450$		0			0
$451$	1.00000			1.00000
$452$		0			0
$453$		0			0
$454$	0.809017	−	2.48990i	0.809017	−	2.48990i
$455$		0			0
$456$		0			0
$457$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$457$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$458$		0			0
$459$		0			0
$460$	0.500000	−	1.53884i	0.500000	−	1.53884i
$461$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$461$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$462$		0			0
$463$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$463$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$464$		0			0
$465$		0			0
$466$	1.30902	+	0.951057i	1.30902	+	0.951057i
$467$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$467$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$468$		0			0
$469$	0.809017	+	2.48990i	0.809017	+	2.48990i
$470$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$476$			2.61803i			2.61803i
$477$		0			0
$478$	0.809017	−	2.48990i	0.809017	−	2.48990i
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$		0			0
$481$		0			0
$482$			1.00000i			1.00000i
$483$		0			0
$484$		0			0
$485$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$486$		0			0
$487$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$487$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$488$	0.587785	−	0.809017i	0.587785	−	0.809017i
$489$		0			0
$490$	−2.61803			−2.61803
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$		0			0
$493$	0.618034			0.618034
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.951057	+	0.309017i	0.951057	+	0.309017i
$498$		0			0
$499$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$500$	0.951057	−	1.30902i	0.951057	−	1.30902i
$501$		0			0
$502$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$503$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$503$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$504$		0			0
$505$	0.809017	+	0.587785i	0.809017	+	0.587785i
$506$	1.53884	−	0.500000i	1.53884	−	0.500000i
$507$		0			0
$508$	0.309017	+	0.951057i	0.309017	+	0.951057i
$509$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$509$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$518$			1.61803i			1.61803i
$519$		0			0
$520$		0			0
$521$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$521$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$522$		0			0
$523$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$523$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$524$			1.00000i			1.00000i
$525$		0			0
$526$	1.61803			1.61803
$527$		0			0
$528$		0			0
$529$		0			0
$530$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$531$		0			0
$532$	−2.61803			−2.61803
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$537$		0			0
$538$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$539$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$540$		0			0
$541$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$541$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$542$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$543$		0			0
$544$	0.309017	+	0.951057i	0.309017	+	0.951057i
$545$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$546$		0			0
$547$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$547$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$548$	0.951057	+	1.30902i	0.951057	+	1.30902i
$549$		0			0
$550$	1.61803			1.61803
$551$			0.618034i			0.618034i
$552$		0			0
$553$	0.309017	−	0.951057i	0.309017	−	0.951057i
$554$		0			0
$555$		0			0
$556$	0.500000	+	1.53884i	0.500000	+	1.53884i
$557$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$557$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$563$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$563$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$564$		0			0
$565$		0			0
$566$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$567$		0			0
$568$	−0.618034			−0.618034
$569$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$569$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$571$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$572$		0			0
$573$		0			0
$574$	−2.61803			−2.61803
$575$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$576$		0			0
$577$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$577$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$578$		0			0
$579$		0			0
$580$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$581$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$582$		0			0
$583$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$584$		0			0
$585$		0			0
$586$	1.30902	−	0.951057i	1.30902	−	0.951057i
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$593$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$594$		0			0
$595$	0.500000	−	1.53884i	0.500000	−	1.53884i
$596$	2.48990	+	0.809017i	2.48990	+	0.809017i
$597$		0			0
$598$		0			0
$599$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$599$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$600$		0			0
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$609$		0			0
$610$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$611$		0			0
$612$		0			0
$613$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$613$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$614$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$615$		0			0
$616$	1.30902	+	0.951057i	1.30902	+	0.951057i
$617$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$617$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$618$		0			0
$619$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$619$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$620$		0			0
$621$		0			0
$622$	0.500000	−	1.53884i	0.500000	−	1.53884i
$623$	0.951057	+	1.30902i	0.951057	+	1.30902i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$			2.61803i			2.61803i
$627$		0			0
$628$	0.309017	−	0.951057i	0.309017	−	0.951057i
$629$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$630$		0			0
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$632$			0.618034i			0.618034i
$633$		0			0
$634$	2.11803	+	1.53884i	2.11803	+	1.53884i
$635$		−	0.618034i		−	0.618034i
$636$		0			0
$637$		0			0
$638$	0.587785	−	0.809017i	0.587785	−	0.809017i
$639$		0			0
$640$	1.30902	−	0.951057i	1.30902	−	0.951057i
$641$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$641$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$642$		0			0
$643$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$643$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$644$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$645$		0			0
$646$	0.500000	−	1.53884i	0.500000	−	1.53884i
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$653$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$653$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$654$		0			0
$655$	0.190983	−	0.587785i	0.190983	−	0.587785i
$656$		0			0
$657$		0			0
$658$	0.500000	+	1.53884i	0.500000	+	1.53884i
$659$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$659$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$660$		0			0
$661$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$661$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$662$		0			0
$663$		0			0
$664$	1.30902	−	0.951057i	1.30902	−	0.951057i
$665$	1.53884	+	0.500000i	1.53884	+	0.500000i
$666$		0			0
$667$	0.190983	+	0.587785i	0.190983	+	0.587785i
$668$		0			0
$669$		0			0
$670$	0.809017	+	2.48990i	0.809017	+	2.48990i
$671$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$672$		0			0
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$674$		0			0
$675$		0			0
$676$	1.61803			1.61803
$677$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$677$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$678$		0			0
$679$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$680$			1.00000i			1.00000i
$681$		0			0
$682$		0			0
$683$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$683$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$684$		0			0
$685$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$686$	0.951057	+	1.30902i	0.951057	+	1.30902i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$691$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$692$	0.951057	−	0.309017i	0.951057	−	0.309017i
$693$		0			0
$694$	0.500000	+	1.53884i	0.500000	+	1.53884i
$695$		−	1.00000i		−	1.00000i
$696$		0			0
$697$	0.309017	−	0.951057i	0.309017	−	0.951057i
$698$		0			0
$699$		0			0
$700$	−2.61803			−2.61803
$701$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$701$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$702$		0			0
$703$	0.190983	−	0.587785i	0.190983	−	0.587785i
$704$	1.53884	+	0.500000i	1.53884	+	0.500000i
$705$		0			0
$706$	0.809017	+	2.48990i	0.809017	+	2.48990i
$707$		−	1.61803i		−	1.61803i
$708$		0			0
$709$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$709$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$710$	0.951057	+	0.309017i	0.951057	+	0.309017i
$711$		0			0
$712$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$717$		0			0
$718$	−1.61803			−1.61803
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−1.61803			−1.61803
$725$			0.618034i			0.618034i
$726$		0			0
$727$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$727$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$733$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$734$	0.951057	−	1.30902i	0.951057	−	1.30902i
$735$		0			0
$736$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$737$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$738$		0			0
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$			1.00000i			1.00000i
$741$		0			0
$742$	1.30902	+	4.02874i	1.30902	+	4.02874i
$743$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$744$		0			0
$745$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$746$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$747$		0			0
$748$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$749$		0			0
$750$		0			0
$751$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$757$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$758$	0.951057	−	0.309017i	0.951057	−	0.309017i
$759$		0			0
$760$	−1.00000			−1.00000
$761$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$761$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$762$		0			0
$763$	1.30902	+	0.951057i	1.30902	+	0.951057i
$764$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$765$		0			0
$766$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$767$		0			0
$768$		0			0
$769$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$769$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$770$	−1.53884	−	2.11803i	−1.53884	−	2.11803i
$771$		0			0
$772$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$773$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$773$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$774$		0			0
$775$		0			0
$776$		−	1.00000i		−	1.00000i
$777$		0			0
$778$		0			0
$779$	0.951057	+	0.309017i	0.951057	+	0.309017i
$780$		0			0
$781$	0.190983	+	0.587785i	0.190983	+	0.587785i
$782$		−	1.61803i		−	1.61803i
$783$		0			0
$784$		0			0
$785$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$786$		0			0
$787$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$787$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$788$		0			0
$789$		0			0
$790$	0.309017	−	0.951057i	0.309017	−	0.951057i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	2.48990	−	0.809017i	2.48990	−	0.809017i
$795$		0			0
$796$		0			0
$797$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$797$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$798$		0			0
$799$	−0.618034			−0.618034
$800$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$801$		0			0
$802$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$803$		0			0
$804$		0			0
$805$	1.61803			1.61803
$806$		0			0
$807$		0			0
$808$	0.309017	+	0.951057i	0.309017	+	0.951057i
$809$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$809$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$810$		0			0
$811$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$811$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$812$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$813$		0			0
$814$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$815$	0.951057	−	0.309017i	0.951057	−	0.309017i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−1.61803			−1.61803
$821$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$821$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$822$		0			0
$823$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$823$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$827$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$828$		0			0
$829$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$829$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$830$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$831$		0			0
$832$		0			0
$833$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$834$		0			0
$835$		0			0
$836$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$837$		0			0
$838$	2.11803	+	1.53884i	2.11803	+	1.53884i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$842$	1.53884	−	0.500000i	1.53884	−	0.500000i
$843$		0			0
$844$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$845$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	0.500000	−	1.53884i	0.500000	−	1.53884i
$851$		−	0.618034i		−	0.618034i
$852$		0			0
$853$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$853$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$854$	2.48990	+	0.809017i	2.48990	+	0.809017i
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$859$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$		0			0
$865$	−0.618034			−0.618034
$866$	0.951057	−	1.30902i	0.951057	−	1.30902i
$867$		0			0
$868$		0			0
$869$	0.587785	−	0.190983i	0.587785	−	0.190983i
$870$		0			0
$871$		0			0
$872$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$873$		0			0
$874$	1.61803			1.61803
$875$	1.53884	+	0.500000i	1.53884	+	0.500000i
$876$		0			0
$877$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$877$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$878$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$879$		0			0
$880$		0			0
$881$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$881$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$882$		0			0
$883$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$883$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$884$		0			0
$885$		0			0
$886$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$887$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$887$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$888$		0			0
$889$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$890$	0.951057	+	1.30902i	0.951057	+	1.30902i
$891$		0			0
$892$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$893$		−	0.618034i		−	0.618034i
$894$		0			0
$895$	0.500000	−	0.363271i	0.500000	−	0.363271i
$896$	−2.48990	−	0.809017i	−2.48990	−	0.809017i
$897$		0			0
$898$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$899$		0			0
$900$		0			0
$901$	−1.61803			−1.61803
$902$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$903$		0			0
$904$		0			0
$905$	0.951057	+	0.309017i	0.951057	+	0.309017i
$906$		0			0
$907$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$907$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$908$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$909$		0			0
$910$		0			0
$911$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$911$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$912$		0			0
$913$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$914$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$915$		0			0
$916$		0			0
$917$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$918$		0			0
$919$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$919$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$920$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$921$		0			0
$922$	0.500000	−	1.53884i	0.500000	−	1.53884i
$923$		0			0
$924$		0			0
$925$	0.190983	−	0.587785i	0.190983	−	0.587785i
$926$		−	1.61803i		−	1.61803i
$927$		0			0
$928$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$929$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$929$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$930$		0			0
$931$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$932$		−	1.61803i		−	1.61803i
$933$		0			0
$934$	0.809017	+	0.587785i	0.809017	+	0.587785i
$935$	0.951057	−	0.309017i	0.951057	−	0.309017i
$936$		0			0
$937$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$937$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$938$	2.48990	−	3.42705i	2.48990	−	3.42705i
$939$		0			0
$940$	0.309017	+	0.951057i	0.309017	+	0.951057i
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$	1.00000			1.00000
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$947$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$948$		0			0
$949$		0			0
$950$	1.53884	+	0.500000i	1.53884	+	0.500000i
$951$		0			0
$952$	1.30902	−	0.951057i	1.30902	−	0.951057i
$953$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$953$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$954$		0			0
$955$	0.500000	+	1.53884i	0.500000	+	1.53884i
$956$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$957$		0			0
$958$		0			0
$959$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$960$		0			0
$961$	0.809017	−	0.587785i	0.809017	−	0.587785i
$962$		0			0
$963$		0			0
$964$	0.809017	−	0.587785i	0.809017	−	0.587785i
$965$	0.587785	−	0.809017i	0.587785	−	0.809017i
$966$		0			0
$967$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$967$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$968$		0			0
$969$		0			0
$970$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$971$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$971$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$972$		0			0
$973$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$974$			1.61803i			1.61803i
$975$		0			0
$976$		0			0
$977$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$977$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$978$		0			0
$979$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$980$	1.53884	+	2.11803i	1.53884	+	2.11803i
$981$		0			0
$982$		0			0
$983$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$983$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$992$		0			0
$993$		0			0
$994$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$995$		0			0
$996$		0			0
$997$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$997$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$998$	0.951057	+	1.30902i	0.951057	+	1.30902i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.1.o.a.161.1	✓	8
3.2	odd	2	inner	675.1.o.a.161.2	yes	8
5.2	odd	4		3375.1.m.b.2699.1		8
5.3	odd	4		3375.1.m.a.2699.2		8
5.4	even	2		3375.1.o.a.2051.2		8
9.2	odd	6		2025.1.y.a.1511.2		16
9.4	even	3		2025.1.y.a.836.2		16
9.5	odd	6		2025.1.y.a.836.1		16
9.7	even	3		2025.1.y.a.1511.1		16
15.2	even	4		3375.1.m.a.2699.1		8
15.8	even	4		3375.1.m.b.2699.2		8
15.14	odd	2		3375.1.o.a.2051.1		8
25.9	even	10		3375.1.o.a.701.1		8
25.12	odd	20		3375.1.m.b.674.1		8
25.13	odd	20		3375.1.m.a.674.2		8
25.16	even	5	inner	675.1.o.a.566.2	yes	8
75.38	even	20		3375.1.m.b.674.2		8
75.41	odd	10	inner	675.1.o.a.566.1	yes	8
75.59	odd	10		3375.1.o.a.701.2		8
75.62	even	20		3375.1.m.a.674.1		8
225.16	even	15		2025.1.y.a.1916.1		16
225.41	odd	30		2025.1.y.a.1241.1		16
225.166	even	15		2025.1.y.a.1241.2		16
225.191	odd	30		2025.1.y.a.1916.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.1.o.a.161.1	✓	8	1.1	even	1	trivial
675.1.o.a.161.2	yes	8	3.2	odd	2	inner
675.1.o.a.566.1	yes	8	75.41	odd	10	inner
675.1.o.a.566.2	yes	8	25.16	even	5	inner
2025.1.y.a.836.1		16	9.5	odd	6
2025.1.y.a.836.2		16	9.4	even	3
2025.1.y.a.1241.1		16	225.41	odd	30
2025.1.y.a.1241.2		16	225.166	even	15
2025.1.y.a.1511.1		16	9.7	even	3
2025.1.y.a.1511.2		16	9.2	odd	6
2025.1.y.a.1916.1		16	225.16	even	15
2025.1.y.a.1916.2		16	225.191	odd	30
3375.1.m.a.674.1		8	75.62	even	20
3375.1.m.a.674.2		8	25.13	odd	20
3375.1.m.a.2699.1		8	15.2	even	4
3375.1.m.a.2699.2		8	5.3	odd	4
3375.1.m.b.674.1		8	25.12	odd	20
3375.1.m.b.674.2		8	75.38	even	20
3375.1.m.b.2699.1		8	5.2	odd	4
3375.1.m.b.2699.2		8	15.8	even	4
3375.1.o.a.701.1		8	25.9	even	10
3375.1.o.a.701.2		8	75.59	odd	10
3375.1.o.a.2051.1		8	15.14	odd	2
3375.1.o.a.2051.2		8	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	675.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 1.30902i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(0.587785 - 0.809017i) q^{5} -1.61803 q^{7} +(0.951057 - 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 - 1.30902i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(0.587785 - 0.809017i) q^{5} -1.61803 q^{7} +(0.951057 - 0.309017i) q^{8} -1.61803 q^{10} +(-0.587785 - 0.809017i) q^{11} +(1.53884 + 2.11803i) q^{14} +(-0.951057 + 0.309017i) q^{17} +(-0.309017 - 0.951057i) q^{19} +(0.951057 + 1.30902i) q^{20} +(-0.500000 + 1.53884i) q^{22} +(-0.587785 - 0.809017i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(0.809017 - 2.48990i) q^{28} +(-0.587785 - 0.190983i) q^{29} -1.00000i q^{32} +(1.30902 + 0.951057i) q^{34} +(-0.951057 + 1.30902i) q^{35} +(0.500000 + 0.363271i) q^{37} +(-0.951057 + 1.30902i) q^{38} +(0.309017 - 0.951057i) q^{40} +(-0.587785 + 0.809017i) q^{41} +(1.53884 - 0.500000i) q^{44} +(-0.500000 + 1.53884i) q^{46} +(0.587785 + 0.190983i) q^{47} +1.61803 q^{49} +(-0.951057 + 1.30902i) q^{50} +(1.53884 + 0.500000i) q^{53} -1.00000 q^{55} +(-1.53884 + 0.500000i) q^{56} +(0.309017 + 0.951057i) q^{58} +(0.809017 - 0.587785i) q^{61} +(-1.30902 + 0.951057i) q^{64} +(-0.500000 - 1.53884i) q^{67} -1.61803i q^{68} +2.61803 q^{70} +(-0.587785 - 0.190983i) q^{71} -1.00000i q^{74} +1.61803 q^{76} +(0.951057 + 1.30902i) q^{77} +(-0.190983 + 0.587785i) q^{79} +1.61803 q^{82} +(1.53884 - 0.500000i) q^{83} +(-0.309017 + 0.951057i) q^{85} +(-0.809017 - 0.587785i) q^{88} +(-0.587785 - 0.809017i) q^{89} +(1.53884 - 0.500000i) q^{92} +(-0.309017 - 0.951057i) q^{94} +(-0.951057 - 0.309017i) q^{95} +(0.309017 - 0.951057i) q^{97} +(-1.53884 - 2.11803i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^4 - 4 * q^7	\( 8 q - 4 q^{4} - 4 q^{7} - 4 q^{10} + 2 q^{19} - 4 q^{22} + 2 q^{25} + 2 q^{28} + 6 q^{34} + 4 q^{37} - 2 q^{40} - 4 q^{46} + 4 q^{49} - 8 q^{55} - 2 q^{58} + 2 q^{61} - 6 q^{64} - 4 q^{67} + 12 q^{70} + 4 q^{76} - 6 q^{79} + 4 q^{82} + 2 q^{85} - 2 q^{88} + 2 q^{94} - 2 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 - 4 * q^7 - 4 * q^10 + 2 * q^19 - 4 * q^22 + 2 * q^25 + 2 * q^28 + 6 * q^34 + 4 * q^37 - 2 * q^40 - 4 * q^46 + 4 * q^49 - 8 * q^55 - 2 * q^58 + 2 * q^61 - 6 * q^64 - 4 * q^67 + 12 * q^70 + 4 * q^76 - 6 * q^79 + 4 * q^82 + 2 * q^85 - 2 * q^88 + 2 * q^94 - 2 * q^97

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