LMFDB - Embedded newform 1169.1.f.b.333.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1169,1,Mod(333,1169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("1169.333");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1169 = 7 \cdot 167 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1169.f (of order $6$, degree $2$, 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:	$0.583406999768$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.8183.1

Embedding invariants

Embedding label			333.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1169.333
Dual form			1169.1.f.b.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -1.41421i q^{13} -1.41421i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.22474 + 0.707107i) q^{17} +1.41421i q^{20} +1.00000 q^{21} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -1.00000 q^{28} +1.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{33} +(1.22474 + 0.707107i) q^{35} +(1.22474 - 0.707107i) q^{37} +(1.22474 + 0.707107i) q^{39} -1.41421i q^{41} +1.41421i q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.22474 + 0.707107i) q^{51} +(-1.22474 - 0.707107i) q^{52} +(-1.22474 - 0.707107i) q^{53} +1.41421i q^{55} +(-1.22474 - 0.707107i) q^{60} -1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-1.22474 - 0.707107i) q^{67} +(1.22474 - 0.707107i) q^{68} -1.41421i q^{71} +(0.500000 + 0.866025i) q^{75} -1.00000 q^{77} +(1.22474 + 0.707107i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{84} -2.00000 q^{85} +(-0.500000 + 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{89} +(-1.22474 + 0.707107i) q^{91} +(0.500000 + 0.866025i) q^{93} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^7	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{7} + 2 q^{11} + 2 q^{12} - 2 q^{16} + 4 q^{21} + 2 q^{25} - 4 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{31} + 2 q^{33} - 2 q^{44} + 2 q^{47} + 4 q^{48} - 2 q^{49} - 4 q^{64} + 4 q^{65} + 2 q^{75} - 4 q^{77} + 2 q^{81} + 2 q^{84} - 8 q^{85} - 2 q^{87} + 2 q^{89} + 2 q^{93}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^7 + 2 * q^11 + 2 * q^12 - 2 * q^16 + 4 * q^21 + 2 * q^25 - 4 * q^27 - 4 * q^28 + 4 * q^29 + 2 * q^31 + 2 * q^33 - 2 * q^44 + 2 * q^47 + 4 * q^48 - 2 * q^49 - 4 * q^64 + 4 * q^65 + 2 * q^75 - 4 * q^77 + 2 * q^81 + 2 * q^84 - 8 * q^85 - 2 * q^87 + 2 * q^89 + 2 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1169\mathbb{Z}\right)^\times$.

$n$	$673$	$836$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$5$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$13$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$14$		0			0
$15$		−	1.41421i		−	1.41421i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$17$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$			1.41421i			1.41421i
$21$	1.00000			1.00000
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.500000	−	0.866025i
$26$		0			0
$27$	−1.00000			−1.00000
$28$	−1.00000			−1.00000
$29$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$29$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$31$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$32$		0			0
$33$	0.500000	+	0.866025i	0.500000	+	0.866025i
$34$		0			0
$35$	1.22474	+	0.707107i	1.22474	+	0.707107i
$36$		0			0
$37$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$37$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$38$		0			0
$39$	1.22474	+	0.707107i	1.22474	+	0.707107i
$40$		0			0
$41$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$41$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$42$		0			0
$43$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$43$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$44$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$45$		0			0
$46$		0			0
$47$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$47$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$48$	1.00000			1.00000
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$		0			0
$51$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$52$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$53$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$53$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$54$		0			0
$55$			1.41421i			1.41421i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−1.00000
$65$	1.00000	+	1.73205i	1.00000	+	1.73205i
$66$		0			0
$67$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$67$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$68$	1.22474	−	0.707107i	1.22474	−	0.707107i
$69$		0			0
$70$		0			0
$71$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$71$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$72$		0			0
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.500000	+	0.866025i
$76$		0			0
$77$	−1.00000			−1.00000
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	1.22474	+	0.707107i	1.22474	+	0.707107i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	0.500000	−	0.866025i	0.500000	−	0.866025i
$85$	−2.00000			−2.00000
$86$		0			0
$87$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$88$		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
$91$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$92$		0			0
$93$	0.500000	+	0.866025i	0.500000	+	0.866025i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$106$		0			0
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$108$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$109$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$109$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$110$		0			0
$111$			1.41421i			1.41421i
$112$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$113$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$113$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$114$		0			0
$115$		0			0
$116$	0.500000	−	0.866025i	0.500000	−	0.866025i
$117$		0			0
$118$		0			0
$119$		−	1.41421i		−	1.41421i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	1.22474	+	0.707107i	1.22474	+	0.707107i
$124$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$125$		0			0
$126$		0			0
$127$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$127$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$128$		0			0
$129$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	1.00000			1.00000
$133$		0			0
$134$		0			0
$135$	1.22474	−	0.707107i	1.22474	−	0.707107i
$136$		0			0
$137$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$137$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$138$		0			0
$139$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$139$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$140$	1.22474	−	0.707107i	1.22474	−	0.707107i
$141$	−1.00000			−1.00000
$142$		0			0
$143$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$144$		0			0
$145$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$146$		0			0
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		−	1.41421i		−	1.41421i
$149$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$149$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$150$		0			0
$151$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$151$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1.41421i			1.41421i
$156$	1.22474	−	0.707107i	1.22474	−	0.707107i
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$158$		0			0
$159$	1.22474	−	0.707107i	1.22474	−	0.707107i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$165$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$166$		0			0
$167$	−1.00000			−1.00000
$167$	−1.00000			−1.00000
$168$		0			0
$169$	−1.00000			−1.00000
$170$		0			0
$171$		0			0
$172$	1.22474	+	0.707107i	1.22474	+	0.707107i
$173$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$173$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$	−1.00000			−1.00000
$176$	−1.00000			−1.00000
$177$		0			0
$178$		0			0
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$180$		0			0
$181$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$186$		0			0
$187$	1.22474	−	0.707107i	1.22474	−	0.707107i
$188$	1.00000			1.00000
$189$	0.500000	+	0.866025i	0.500000	+	0.866025i
$190$		0			0
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$193$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$194$		0			0
$195$	−2.00000			−2.00000
$196$	0.500000	+	0.866025i	0.500000	+	0.866025i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$200$		0			0
$201$	1.22474	−	0.707107i	1.22474	−	0.707107i
$202$		0			0
$203$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$204$			1.41421i			1.41421i
$205$	1.00000	+	1.73205i	1.00000	+	1.73205i
$206$		0			0
$207$		0			0
$208$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$209$		0			0
$210$		0			0
$211$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$211$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$212$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$213$	1.22474	+	0.707107i	1.22474	+	0.707107i
$214$		0			0
$215$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$216$		0			0
$217$	−1.00000			−1.00000
$218$		0			0
$219$		0			0
$220$	1.22474	+	0.707107i	1.22474	+	0.707107i
$221$	1.00000	−	1.73205i	1.00000	−	1.73205i
$222$		0			0
$223$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$223$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$229$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$230$		0			0
$231$	0.500000	−	0.866025i	0.500000	−	0.866025i
$232$		0			0
$233$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$233$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$239$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$240$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		−	1.41421i		−	1.41421i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	1.00000	−	1.73205i	1.00000	−	1.73205i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$257$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$258$		0			0
$259$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$260$	2.00000			2.00000
$261$		0			0
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	2.00000			2.00000
$266$		0			0
$267$	−1.00000			−1.00000
$268$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$269$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$269$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		−	1.41421i		−	1.41421i
$273$		−	1.41421i		−	1.41421i
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$283$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$284$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$285$		0			0
$286$		0			0
$287$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$288$		0			0
$289$	0.500000	+	0.866025i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$293$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$298$		0			0
$299$		0			0
$300$	1.00000			1.00000
$301$	1.22474	−	0.707107i	1.22474	−	0.707107i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$307$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$308$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$309$		0			0
$310$		0			0
$311$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$312$		0			0
$313$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$313$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$317$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	0.500000	−	0.866025i	0.500000	−	0.866025i
$320$	1.22474	−	0.707107i	1.22474	−	0.707107i
$321$	1.00000			1.00000
$322$		0			0
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$326$		0			0
$327$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$328$		0			0
$329$	0.500000	−	0.866025i	0.500000	−	0.866025i
$330$		0			0
$331$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$331$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.00000			2.00000
$336$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$		0			0
$339$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$340$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$341$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$342$		0			0
$343$	1.00000			1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$	0.500000	+	0.866025i	0.500000	+	0.866025i
$349$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$349$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$			1.41421i			1.41421i
$352$		0			0
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$354$		0			0
$355$	1.00000	+	1.73205i	1.00000	+	1.73205i
$356$	1.00000			1.00000
$357$	1.22474	+	0.707107i	1.22474	+	0.707107i
$358$		0			0
$359$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$359$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$360$		0			0
$361$	0.500000	−	0.866025i	0.500000	−	0.866025i
$362$		0			0
$363$		0			0
$364$			1.41421i			1.41421i
$365$		0			0
$366$		0			0
$367$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$367$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$368$		0			0
$369$		0			0
$370$		0			0
$371$			1.41421i			1.41421i
$372$	1.00000			1.00000
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.41421i		−	1.41421i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.500000	−	0.866025i	0.500000	−	0.866025i
$382$		0			0
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$384$		0			0
$385$	1.22474	−	0.707107i	1.22474	−	0.707107i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$397$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$404$		0			0
$405$			1.41421i			1.41421i
$406$		0			0
$407$		−	1.41421i		−	1.41421i
$408$		0			0
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$410$		0			0
$411$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.22474	+	0.707107i	1.22474	+	0.707107i
$418$		0			0
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$			1.41421i			1.41421i
$421$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$421$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.22474	−	0.707107i	1.22474	−	0.707107i
$426$		0			0
$427$		0			0
$428$	−1.00000			−1.00000
$429$	1.22474	−	0.707107i	1.22474	−	0.707107i
$430$		0			0
$431$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$431$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$432$	0.500000	+	0.866025i	0.500000	+	0.866025i
$433$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$433$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$		−	1.41421i		−	1.41421i
$436$	1.22474	−	0.707107i	1.22474	−	0.707107i
$437$		0			0
$438$		0			0
$439$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$439$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$443$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$444$	1.22474	+	0.707107i	1.22474	+	0.707107i
$445$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$446$		0			0
$447$		−	1.41421i		−	1.41421i
$448$	0.500000	+	0.866025i	0.500000	+	0.866025i
$449$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$449$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$450$		0			0
$451$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$452$	1.22474	+	0.707107i	1.22474	+	0.707107i
$453$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$454$		0			0
$455$	1.00000	−	1.73205i	1.00000	−	1.73205i
$456$		0			0
$457$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$457$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$458$		0			0
$459$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$460$		0			0
$461$	−2.00000			−2.00000			−1.00000			$\pi$
$461$	−2.00000			−2.00000			−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$465$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$466$		0			0
$467$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$467$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$			1.41421i			1.41421i
$470$		0			0
$471$	0.500000	+	0.866025i	0.500000	+	0.866025i
$472$		0			0
$473$	1.22474	+	0.707107i	1.22474	+	0.707107i
$474$		0			0
$475$		0			0
$476$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$477$		0			0
$478$		0			0
$479$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$479$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$480$		0			0
$481$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$491$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$492$	1.22474	−	0.707107i	1.22474	−	0.707107i
$493$	1.22474	+	0.707107i	1.22474	+	0.707107i
$494$		0			0
$495$		0			0
$496$	−1.00000			−1.00000
$497$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$	0.500000	−	0.866025i	0.500000	−	0.866025i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.500000	−	0.866025i	0.500000	−	0.866025i
$508$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$517$	1.00000			1.00000
$518$		0			0
$519$	−1.00000			−1.00000
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$523$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$524$		0			0
$525$	0.500000	−	0.866025i	0.500000	−	0.866025i
$526$		0			0
$527$	1.22474	−	0.707107i	1.22474	−	0.707107i
$528$	0.500000	−	0.866025i	0.500000	−	0.866025i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.00000			−2.00000
$534$		0			0
$535$	1.22474	+	0.707107i	1.22474	+	0.707107i
$536$		0			0
$537$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$538$		0			0
$539$	0.500000	+	0.866025i	0.500000	+	0.866025i
$540$		−	1.41421i		−	1.41421i
$541$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$541$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$542$		0			0
$543$	0.500000	−	0.866025i	0.500000	−	0.866025i
$544$		0			0
$545$	−2.00000			−2.00000
$546$		0			0
$547$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$547$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$548$	0.500000	+	0.866025i	0.500000	+	0.866025i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$556$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$557$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$557$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$	2.00000			2.00000
$560$		−	1.41421i		−	1.41421i
$561$			1.41421i			1.41421i
$562$		0			0
$563$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$563$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$564$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$565$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$566$		0			0
$567$	−1.00000			−1.00000
$568$		0			0
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$573$	−1.00000			−1.00000
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$577$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$578$		0			0
$579$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$580$			1.41421i			1.41421i
$581$		0			0
$582$		0			0
$583$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−1.00000			−1.00000
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$593$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$593$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$594$		0			0
$595$	1.00000	+	1.73205i	1.00000	+	1.73205i
$596$			1.41421i			1.41421i
$597$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	1.22474	−	0.707107i	1.22474	−	0.707107i
$605$		0			0
$606$		0			0
$607$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$607$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$608$		0			0
$609$	1.00000			1.00000
$610$		0			0
$611$	1.22474	−	0.707107i	1.22474	−	0.707107i
$612$		0			0
$613$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$613$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$614$		0			0
$615$	−2.00000			−2.00000
$616$		0			0
$617$	2.00000			2.00000			1.00000			$0$
$617$	2.00000			2.00000			1.00000			$0$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	1.22474	+	0.707107i	1.22474	+	0.707107i
$621$		0			0
$622$		0			0
$623$	0.500000	−	0.866025i	0.500000	−	0.866025i
$624$		−	1.41421i		−	1.41421i
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$629$	2.00000			2.00000
$630$		0			0
$631$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$	0.500000	−	0.866025i	0.500000	−	0.866025i
$634$		0			0
$635$	1.22474	−	0.707107i	1.22474	−	0.707107i
$636$		−	1.41421i		−	1.41421i
$637$	1.22474	+	0.707107i	1.22474	+	0.707107i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$	2.00000			2.00000
$646$		0			0
$647$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$647$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	0.500000	−	0.866025i	0.500000	−	0.866025i
$652$		0			0
$653$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$653$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$		0			0
$663$	1.00000	+	1.73205i	1.00000	+	1.73205i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$669$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$673$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$677$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		−	1.41421i		−	1.41421i
$686$		0			0
$687$	1.00000			1.00000
$688$	1.22474	−	0.707107i	1.22474	−	0.707107i
$689$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	1.00000			1.00000
$693$		0			0
$694$		0			0
$695$	1.00000	+	1.73205i	1.00000	+	1.73205i
$696$		0			0
$697$	1.00000	−	1.73205i	1.00000	−	1.73205i
$698$		0			0
$699$	−1.00000			−1.00000
$700$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$701$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$701$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$705$	1.22474	−	0.707107i	1.22474	−	0.707107i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$709$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	2.00000			2.00000
$716$	0.500000	+	0.866025i	0.500000	+	0.866025i
$717$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$718$		0			0
$719$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$719$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$725$	0.500000	−	0.866025i	0.500000	−	0.866025i
$726$		0			0
$727$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$727$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$732$		0			0
$733$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$733$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$734$		0			0
$735$	1.22474	+	0.707107i	1.22474	+	0.707107i
$736$		0			0
$737$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$738$		0			0
$739$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$739$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$740$	1.00000	+	1.73205i	1.00000	+	1.73205i
$741$		0			0
$742$		0			0
$743$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$	1.00000	−	1.73205i	1.00000	−	1.73205i
$746$		0			0
$747$		0			0
$748$		−	1.41421i		−	1.41421i
$749$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$750$		0			0
$751$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$751$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$752$	0.500000	−	0.866025i	0.500000	−	0.866025i
$753$		0			0
$754$		0			0
$755$	−2.00000			−2.00000
$756$	1.00000			1.00000
$757$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$757$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$		−	1.41421i		−	1.41421i
$764$	1.00000			1.00000
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		−	1.41421i		−	1.41421i
$772$	1.22474	−	0.707107i	1.22474	−	0.707107i
$773$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$773$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$774$		0			0
$775$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$776$		0			0
$777$	1.22474	−	0.707107i	1.22474	−	0.707107i
$778$		0			0
$779$		0			0
$780$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$781$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$782$		0			0
$783$	−1.00000			−1.00000
$784$	1.00000			1.00000
$785$			1.41421i			1.41421i
$786$		0			0
$787$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$787$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.22474	−	0.707107i	1.22474	−	0.707107i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$796$	0.500000	+	0.866025i	0.500000	+	0.866025i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$			1.41421i			1.41421i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		−	1.41421i		−	1.41421i
$805$		0			0
$806$		0			0
$807$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$808$		0			0
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−1.00000			−1.00000
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.22474	+	0.707107i	1.22474	+	0.707107i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	2.00000			2.00000
$821$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$821$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$822$		0			0
$823$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$823$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$824$		0			0
$825$	1.00000			1.00000
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$829$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$830$		0			0
$831$		0			0
$832$			1.41421i			1.41421i
$833$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$834$		0			0
$835$	1.22474	−	0.707107i	1.22474	−	0.707107i
$836$		0			0
$837$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$838$		0			0
$839$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$845$	1.22474	−	0.707107i	1.22474	−	0.707107i
$846$		0			0
$847$		0			0
$848$			1.41421i			1.41421i
$849$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$850$		0			0
$851$		0			0
$852$	1.22474	−	0.707107i	1.22474	−	0.707107i
$853$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$853$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$	−2.00000			−2.00000
$861$		−	1.41421i		−	1.41421i
$862$		0			0
$863$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$863$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$864$		0			0
$865$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$866$		0			0
$867$	−1.00000			−1.00000
$868$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$869$		0			0
$870$		0			0
$871$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$878$		0			0
$879$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$880$	1.22474	−	0.707107i	1.22474	−	0.707107i
$881$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$881$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$882$		0			0
$883$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$884$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$885$		0			0
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$892$	0.500000	−	0.866025i	0.500000	−	0.866025i
$893$		0			0
$894$		0			0
$895$		−	1.41421i		−	1.41421i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.500000	−	0.866025i	0.500000	−	0.866025i
$900$		0			0
$901$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$902$		0			0
$903$			1.41421i			1.41421i
$904$		0			0
$905$	1.22474	−	0.707107i	1.22474	−	0.707107i
$906$		0			0
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$911$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.00000			−1.00000
$917$		0			0
$918$		0			0
$919$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$919$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$920$		0			0
$921$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$922$		0			0
$923$	−2.00000			−2.00000
$924$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$925$		−	1.41421i		−	1.41421i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$		0			0
$932$	1.00000			1.00000
$933$	0.500000	+	0.866025i	0.500000	+	0.866025i
$934$		0			0
$935$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$			1.41421i			1.41421i
$940$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$941$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$941$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$946$		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			0
$950$		0			0
$951$	−1.00000			−1.00000
$952$		0			0
$953$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$953$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$954$		0			0
$955$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$956$	0.500000	−	0.866025i	0.500000	−	0.866025i
$957$	0.500000	+	0.866025i	0.500000	+	0.866025i
$958$		0			0
$959$	1.00000			1.00000
$960$			1.41421i			1.41421i
$961$		0			0
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.00000			−2.00000
$966$		0			0
$967$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$		0			0
$973$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$974$		0			0
$975$	1.22474	−	0.707107i	1.22474	−	0.707107i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$	1.00000			1.00000
$980$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$981$		0			0
$982$		0			0
$983$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$983$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.500000	+	0.866025i	0.500000	+	0.866025i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$991$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$992$		0			0
$993$			1.41421i			1.41421i
$994$		0			0
$995$		−	1.41421i		−	1.41421i
$996$		0			0
$997$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$997$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$	−1.22474	+	0.707107i	−1.22474	+	0.707107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1169.1.f.b.333.1	✓	4
7.2	even	3	inner	1169.1.f.b.667.2	yes	4
167.166	odd	2	inner	1169.1.f.b.333.2	yes	4
1169.667	odd	6	inner	1169.1.f.b.667.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1169.1.f.b.333.1	✓	4	1.1	even	1	trivial
1169.1.f.b.333.2	yes	4	167.166	odd	2	inner
1169.1.f.b.667.1	yes	4	1169.667	odd	6	inner
1169.1.f.b.667.2	yes	4	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1169 = 7 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1169.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -1.41421i q^{13} -1.41421i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.22474 + 0.707107i) q^{17} +1.41421i q^{20} +1.00000 q^{21} +(0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -1.00000 q^{28} +1.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{33} +(1.22474 + 0.707107i) q^{35} +(1.22474 - 0.707107i) q^{37} +(1.22474 + 0.707107i) q^{39} -1.41421i q^{41} +1.41421i q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{47} +1.00000 q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.22474 + 0.707107i) q^{51} +(-1.22474 - 0.707107i) q^{52} +(-1.22474 - 0.707107i) q^{53} +1.41421i q^{55} +(-1.22474 - 0.707107i) q^{60} -1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-1.22474 - 0.707107i) q^{67} +(1.22474 - 0.707107i) q^{68} -1.41421i q^{71} +(0.500000 + 0.866025i) q^{75} -1.00000 q^{77} +(1.22474 + 0.707107i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{84} -2.00000 q^{85} +(-0.500000 + 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{89} +(-1.22474 + 0.707107i) q^{91} +(0.500000 + 0.866025i) q^{93} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^7	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{7} + 2 q^{11} + 2 q^{12} - 2 q^{16} + 4 q^{21} + 2 q^{25} - 4 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{31} + 2 q^{33} - 2 q^{44} + 2 q^{47} + 4 q^{48} - 2 q^{49} - 4 q^{64} + 4 q^{65} + 2 q^{75} - 4 q^{77} + 2 q^{81} + 2 q^{84} - 8 q^{85} - 2 q^{87} + 2 q^{89} + 2 q^{93}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^7 + 2 * q^11 + 2 * q^12 - 2 * q^16 + 4 * q^21 + 2 * q^25 - 4 * q^27 - 4 * q^28 + 4 * q^29 + 2 * q^31 + 2 * q^33 - 2 * q^44 + 2 * q^47 + 4 * q^48 - 2 * q^49 - 4 * q^64 + 4 * q^65 + 2 * q^75 - 4 * q^77 + 2 * q^81 + 2 * q^84 - 8 * q^85 - 2 * q^87 + 2 * q^89 + 2 * q^93

Introduction

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