LMFDB - Embedded newform 1365.1.cz.d.779.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1365,1,Mod(389,1365)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1365, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 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("1365.389");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1365 = 3 \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1365.cz (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:	$0.681223742244$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.9555.1
Artin image:	$C_6\times S_3$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			779.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1365.779
Dual form			1365.1.cz.d.389.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{35} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{39} +1.00000 q^{41} +(-0.500000 + 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} -1.00000 q^{48} +1.00000 q^{49} +(0.500000 - 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.00000 + 1.73205i) q^{53} -1.00000 q^{55} +(-0.500000 - 0.866025i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{67} +(-0.500000 + 0.866025i) q^{68} -1.00000 q^{69} -2.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{77} +(0.500000 - 0.866025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{84} -1.00000 q^{85} +(-0.500000 + 0.866025i) q^{89} +1.00000 q^{91} +1.00000 q^{92} -1.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{4} + q^{5} + 2 q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 - q^4 + q^5 + 2 * q^7 - q^9	$ 2 q + q^{3} - q^{4} + q^{5} + 2 q^{7} - q^{9} - q^{11} + q^{12} + 2 q^{13} + 2 q^{15} - q^{16} - q^{17} - 2 q^{20} + q^{21} - q^{23} - q^{25} - 2 q^{27} - q^{28} + q^{33} + q^{35} + 2 q^{36} + q^{37} + q^{39} + 2 q^{41} - q^{44} + q^{45} - 2 q^{48} + 2 q^{49} + q^{51} - q^{52} + 2 q^{53} - 2 q^{55} - q^{59} - q^{60} - 2 q^{61} - q^{63} + 2 q^{64} + q^{65} + q^{67} - q^{68} - 2 q^{69} - 4 q^{71} + q^{73} + q^{75} - q^{77} + q^{79} + q^{80} - q^{81} + q^{84} - 2 q^{85} - q^{89} + 2 q^{91} + 2 q^{92} - 2 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^4 + q^5 + 2 * q^7 - q^9 - q^11 + q^12 + 2 * q^13 + 2 * q^15 - q^16 - q^17 - 2 * q^20 + q^21 - q^23 - q^25 - 2 * q^27 - q^28 + q^33 + q^35 + 2 * q^36 + q^37 + q^39 + 2 * q^41 - q^44 + q^45 - 2 * q^48 + 2 * q^49 + q^51 - q^52 + 2 * q^53 - 2 * q^55 - q^59 - q^60 - 2 * q^61 - q^63 + 2 * q^64 + q^65 + q^67 - q^68 - 2 * q^69 - 4 * q^71 + q^73 + q^75 - q^77 + q^79 + q^80 - q^81 + q^84 - 2 * q^85 - q^89 + 2 * q^91 + 2 * q^92 - 2 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1365\mathbb{Z}\right)^\times$.

$n$	$106$	$547$	$911$	$976$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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		0.500000	−	0.866025i	$-0.333333\pi$
$2$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$6$		0			0
$7$	1.00000			1.00000
$7$	1.00000			1.00000
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$11$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$12$	0.500000	−	0.866025i	0.500000	−	0.866025i
$13$	1.00000			1.00000
$13$	1.00000			1.00000
$14$		0			0
$15$	1.00000			1.00000
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$17$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$18$		0			0
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−1.00000			−1.00000
$21$	0.500000	+	0.866025i	0.500000	+	0.866025i
$22$		0			0
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$		0			0
$27$	−1.00000			−1.00000
$28$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$		0			0
$33$	0.500000	−	0.866025i	0.500000	−	0.866025i
$34$		0			0
$35$	0.500000	−	0.866025i	0.500000	−	0.866025i
$36$	1.00000			1.00000
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$38$		0			0
$39$	0.500000	+	0.866025i	0.500000	+	0.866025i
$40$		0			0
$41$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$41$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$45$	0.500000	+	0.866025i	0.500000	+	0.866025i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−1.00000			−1.00000
$49$	1.00000			1.00000
$50$		0			0
$51$	0.500000	−	0.866025i	0.500000	−	0.866025i
$52$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$53$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$53$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$	−1.00000			−1.00000
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$60$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$61$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$61$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$64$	1.00000			1.00000
$65$	0.500000	−	0.866025i	0.500000	−	0.866025i
$66$		0			0
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$69$	−1.00000			−1.00000
$70$		0			0
$71$	−2.00000			−2.00000			−1.00000			$\pi$
$71$	−2.00000			−2.00000			−1.00000			$\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.500000	−	0.866025i
$76$		0			0
$77$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$78$		0			0
$79$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$79$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$80$	0.500000	+	0.866025i	0.500000	+	0.866025i
$81$	−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
$85$	−1.00000			−1.00000
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$89$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$90$		0			0
$91$	1.00000			1.00000
$92$	1.00000			1.00000
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$97$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$98$		0			0
$99$	1.00000			1.00000
$100$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$	1.00000			1.00000
$106$		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
$109$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$109$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$	1.00000			1.00000
$112$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$113$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$113$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.500000	+	0.866025i
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$118$		0			0
$119$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	0.500000	+	0.866025i	0.500000	+	0.866025i
$124$		0			0
$125$	−1.00000			−1.00000
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$131$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$132$	−1.00000			−1.00000
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$140$	−1.00000			−1.00000
$141$		0			0
$142$		0			0
$143$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$144$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$145$		0			0
$146$		0			0
$147$	0.500000	+	0.866025i	0.500000	+	0.866025i
$148$	−1.00000			−1.00000
$149$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$149$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$150$		0			0
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$		0			0
$153$	1.00000			1.00000
$154$		0			0
$155$		0			0
$156$	0.500000	−	0.866025i	0.500000	−	0.866025i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$160$		0			0
$161$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$162$		0			0
$163$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$163$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$164$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$165$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	1.00000			1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$173$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$176$	1.00000			1.00000
$177$	0.500000	−	0.866025i	0.500000	−	0.866025i
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	0.500000	−	0.866025i	0.500000	−	0.866025i
$181$	−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
$183$	−2.00000			−2.00000
$184$		0			0
$185$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$186$		0			0
$187$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$188$		0			0
$189$	−1.00000			−1.00000
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.500000	+	0.866025i	0.500000	+	0.866025i
$193$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$194$		0			0
$195$	1.00000			1.00000
$196$	−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	1.00000			$0$
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$200$		0			0
$201$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$202$		0			0
$203$		0			0
$204$	−1.00000			−1.00000
$205$	0.500000	−	0.866025i	0.500000	−	0.866025i
$206$		0			0
$207$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$208$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$209$		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	$0.666667\pi$
$212$	1.00000	−	1.73205i	1.00000	−	1.73205i
$213$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$220$	0.500000	+	0.866025i	0.500000	+	0.866025i
$221$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$222$		0			0
$223$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$223$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$	1.00000			1.00000
$226$		0			0
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$	0.500000	−	0.866025i	0.500000	−	0.866025i
$232$		0			0
$233$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$233$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$237$	1.00000			1.00000
$238$		0			0
$239$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$239$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$240$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$	2.00000			2.00000
$245$	0.500000	−	0.866025i	0.500000	−	0.866025i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	1.00000			1.00000
$253$	1.00000			1.00000
$254$		0			0
$255$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$258$		0			0
$259$	0.500000	−	0.866025i	0.500000	−	0.866025i
$260$	−1.00000			−1.00000
$261$		0			0
$262$		0			0
$263$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$263$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$264$		0			0
$265$	2.00000			2.00000
$266$		0			0
$267$	−1.00000			−1.00000
$268$	0.500000	−	0.866025i	0.500000	−	0.866025i
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$		0			0
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$	1.00000			1.00000
$273$	0.500000	+	0.866025i	0.500000	+	0.866025i
$274$		0			0
$275$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$276$	0.500000	+	0.866025i	0.500000	+	0.866025i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$281$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$282$		0			0
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$	1.00000	+	1.73205i	1.00000	+	1.73205i
$285$		0			0
$286$		0			0
$287$	1.00000			1.00000
$288$		0			0
$289$		0			0
$290$		0			0
$291$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$292$	0.500000	−	0.866025i	0.500000	−	0.866025i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$	−1.00000			−1.00000
$296$		0			0
$297$	0.500000	+	0.866025i	0.500000	+	0.866025i
$298$		0			0
$299$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$300$	−1.00000			−1.00000
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.00000	+	1.73205i	1.00000	+	1.73205i
$306$		0			0
$307$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$308$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$309$		0			0
$310$		0			0
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	0.500000	+	0.866025i	0.500000	+	0.866025i
$316$	−1.00000			−1.00000
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		0			0
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$	−1.00000			−1.00000
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	0.500000	+	0.866025i	0.500000	+	0.866025i
$334$		0			0
$335$	1.00000			1.00000
$336$	−1.00000			−1.00000
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$		0			0
$339$	0.500000	+	0.866025i	0.500000	+	0.866025i
$340$	0.500000	+	0.866025i	0.500000	+	0.866025i
$341$		0			0
$342$		0			0
$343$	1.00000			1.00000
$344$		0			0
$345$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$346$		0			0
$347$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$347$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$	−1.00000			−1.00000
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$356$	1.00000			1.00000
$357$	0.500000	−	0.866025i	0.500000	−	0.866025i
$358$		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
$364$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$365$	1.00000			1.00000
$366$		0			0
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$369$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$370$		0			0
$371$	1.00000	+	1.73205i	1.00000	+	1.73205i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$		0			0
$385$	−1.00000			−1.00000
$386$		0			0
$387$		0			0
$388$	0.500000	+	0.866025i	0.500000	+	0.866025i
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$		0			0
$391$	1.00000			1.00000
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$396$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$398$		0			0
$399$		0			0
$400$	1.00000			1.00000
$401$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$401$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000			−1.00000
$406$		0			0
$407$	−1.00000			−1.00000
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$426$		0			0
$427$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$428$	1.00000			1.00000
$429$	0.500000	−	0.866025i	0.500000	−	0.866025i
$430$		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
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$440$		0			0
$441$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$442$		0			0
$443$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$444$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$445$	0.500000	+	0.866025i	0.500000	+	0.866025i
$446$		0			0
$447$	2.00000			2.00000
$448$	1.00000			1.00000
$449$	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
$451$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$452$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$453$		0			0
$454$		0			0
$455$	0.500000	−	0.866025i	0.500000	−	0.866025i
$456$		0			0
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$458$		0			0
$459$	0.500000	+	0.866025i	0.500000	+	0.866025i
$460$	0.500000	−	0.866025i	0.500000	−	0.866025i
$461$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$461$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	2.00000			2.00000			1.00000			$0$
$463$	2.00000			2.00000			1.00000			$0$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$468$	1.00000			1.00000
$469$	0.500000	+	0.866025i	0.500000	+	0.866025i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$477$	−2.00000			−2.00000
$478$		0			0
$479$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$479$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$480$		0			0
$481$	0.500000	−	0.866025i	0.500000	−	0.866025i
$482$		0			0
$483$	−1.00000			−1.00000
$484$		0			0
$485$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$486$		0			0
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$	−2.00000			−2.00000
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	0.500000	−	0.866025i	0.500000	−	0.866025i
$493$		0			0
$494$		0			0
$495$	0.500000	−	0.866025i	0.500000	−	0.866025i
$496$		0			0
$497$	−2.00000			−2.00000
$498$		0			0
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	0.500000	+	0.866025i	0.500000	+	0.866025i
$501$		0			0
$502$		0			0
$503$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$503$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.500000	+	0.866025i	0.500000	+	0.866025i
$508$		0			0
$509$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$510$		0			0
$511$	0.500000	+	0.866025i	0.500000	+	0.866025i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.00000			−1.00000
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$523$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$524$		0			0
$525$	0.500000	−	0.866025i	0.500000	−	0.866025i
$526$		0			0
$527$		0			0
$528$	0.500000	+	0.866025i	0.500000	+	0.866025i
$529$		0			0
$530$		0			0
$531$	1.00000			1.00000
$532$		0			0
$533$	1.00000			1.00000
$534$		0			0
$535$	0.500000	+	0.866025i	0.500000	+	0.866025i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$540$	1.00000			1.00000
$541$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$541$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.500000	−	0.866025i	0.500000	−	0.866025i
$554$		0			0
$555$	0.500000	−	0.866025i	0.500000	−	0.866025i
$556$	0.500000	+	0.866025i	0.500000	+	0.866025i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$	0.500000	+	0.866025i	0.500000	+	0.866025i
$561$	−1.00000			−1.00000
$562$		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			0
$565$	0.500000	−	0.866025i	0.500000	−	0.866025i
$566$		0			0
$567$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$572$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$573$		0			0
$574$		0			0
$575$	1.00000			1.00000
$576$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$577$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$577$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$578$		0			0
$579$	1.00000	−	1.73205i	1.00000	−	1.73205i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.00000	−	1.73205i	1.00000	−	1.73205i
$584$		0			0
$585$	0.500000	+	0.866025i	0.500000	+	0.866025i
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.500000	−	0.866025i	0.500000	−	0.866025i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.500000	+	0.866025i	0.500000	+	0.866025i
$593$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$593$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$594$		0			0
$595$	−1.00000			−1.00000
$596$	−2.00000			−2.00000
$597$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$		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
$603$	−1.00000			−1.00000
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$613$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$614$		0			0
$615$	1.00000			1.00000
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.500000	−	0.866025i
$622$		0			0
$623$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$624$	−1.00000			−1.00000
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.00000			−1.00000
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$634$		0			0
$635$		0			0
$636$	2.00000			2.00000
$637$	1.00000			1.00000
$638$		0			0
$639$	1.00000	−	1.73205i	1.00000	−	1.73205i
$640$		0			0
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$643$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$644$	1.00000			1.00000
$645$		0			0
$646$		0			0
$647$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$647$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$648$		0			0
$649$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$650$		0			0
$651$		0			0
$652$	2.00000			2.00000
$653$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$653$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$654$		0			0
$655$		0			0
$656$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$657$	−1.00000			−1.00000
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$	0.500000	−	0.866025i	0.500000	−	0.866025i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$670$		0			0
$671$	2.00000			2.00000
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		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
$679$	−1.00000			−1.00000
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.00000	+	1.73205i	1.00000	+	1.73205i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	1.00000			1.00000
$693$	1.00000			1.00000
$694$		0			0
$695$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$696$		0			0
$697$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$698$		0			0
$699$	−1.00000			−1.00000
$700$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−1.00000			−1.00000
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.500000	+	0.866025i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−1.00000			−1.00000
$716$		0			0
$717$	0.500000	+	0.866025i	0.500000	+	0.866025i
$718$		0			0
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−1.00000			−1.00000
$721$		0			0
$722$		0			0
$723$		0			0
$724$	0.500000	+	0.866025i	0.500000	+	0.866025i
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	1.00000	+	1.73205i	1.00000	+	1.73205i
$733$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$733$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$734$		0			0
$735$	1.00000			1.00000
$736$		0			0
$737$	0.500000	−	0.866025i	0.500000	−	0.866025i
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$746$		0			0
$747$		0			0
$748$	1.00000			1.00000
$749$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$750$		0			0
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.500000	+	0.866025i	0.500000	+	0.866025i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$	0.500000	+	0.866025i	0.500000	+	0.866025i
$760$		0			0
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.500000	−	0.866025i	0.500000	−	0.866025i
$766$		0			0
$767$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$768$	0.500000	−	0.866025i	0.500000	−	0.866025i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.00000			1.00000
$778$		0			0
$779$		0			0
$780$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$781$	1.00000	+	1.73205i	1.00000	+	1.73205i
$782$		0			0
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$		0			0
$787$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$787$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$788$		0			0
$789$	0.500000	−	0.866025i	0.500000	−	0.866025i
$790$		0			0
$791$	1.00000			1.00000
$792$		0			0
$793$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$794$		0			0
$795$	1.00000	+	1.73205i	1.00000	+	1.73205i
$796$	0.500000	−	0.866025i	0.500000	−	0.866025i
$797$	−2.00000			−2.00000			−1.00000			$\pi$
$797$	−2.00000			−2.00000			−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$802$		0			0
$803$	0.500000	−	0.866025i	0.500000	−	0.866025i
$804$	1.00000			1.00000
$805$	0.500000	+	0.866025i	0.500000	+	0.866025i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.00000	+	1.73205i	1.00000	+	1.73205i
$816$	0.500000	+	0.866025i	0.500000	+	0.866025i
$817$		0			0
$818$		0			0
$819$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$820$	−1.00000			−1.00000
$821$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$821$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$822$		0			0
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	−1.00000			−1.00000
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$830$		0			0
$831$		0			0
$832$	1.00000			1.00000
$833$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.00000			−2.00000			−1.00000			$\pi$
$839$	−2.00000			−2.00000			−1.00000			$\pi$
$840$		0			0
$841$	1.00000			1.00000
$842$		0			0
$843$	0.500000	+	0.866025i	0.500000	+	0.866025i
$844$	0.500000	+	0.866025i	0.500000	+	0.866025i
$845$	0.500000	−	0.866025i	0.500000	−	0.866025i
$846$		0			0
$847$		0			0
$848$	−2.00000			−2.00000
$849$		0			0
$850$		0			0
$851$	0.500000	+	0.866025i	0.500000	+	0.866025i
$852$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$853$	−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
$857$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$857$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$860$		0			0
$861$	0.500000	+	0.866025i	0.500000	+	0.866025i
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$	0.500000	+	0.866025i	0.500000	+	0.866025i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.00000			−1.00000
$870$		0			0
$871$	0.500000	+	0.866025i	0.500000	+	0.866025i
$872$		0			0
$873$	0.500000	−	0.866025i	0.500000	−	0.866025i
$874$		0			0
$875$	−1.00000			−1.00000
$876$	1.00000			1.00000
$877$	−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			0
$880$	0.500000	−	0.866025i	0.500000	−	0.866025i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$885$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$886$		0			0
$887$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$888$		0			0
$889$		0			0
$890$		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
$895$		0			0
$896$		0			0
$897$	−1.00000			−1.00000
$898$		0			0
$899$		0			0
$900$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$901$	1.00000	−	1.73205i	1.00000	−	1.73205i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$906$		0			0
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$920$		0			0
$921$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$922$		0			0
$923$	−2.00000			−2.00000
$924$	−1.00000			−1.00000
$925$	−1.00000			−1.00000
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$930$		0			0
$931$		0			0
$932$	1.00000			1.00000
$933$		0			0
$934$		0			0
$935$	0.500000	+	0.866025i	0.500000	+	0.866025i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$941$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$942$		0			0
$943$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$944$	1.00000			1.00000
$945$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$949$	0.500000	+	0.866025i	0.500000	+	0.866025i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$953$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.00000			1.00000
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$964$		0			0
$965$	−2.00000			−2.00000
$966$		0			0
$967$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$967$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$	−1.00000			−1.00000
$973$	−1.00000			−1.00000
$974$		0			0
$975$	0.500000	−	0.866025i	0.500000	−	0.866025i
$976$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	1.00000			1.00000
$980$	−1.00000			−1.00000
$981$		0			0
$982$		0			0
$983$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$983$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$991$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.00000			1.00000
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$	−0.500000	+	0.866025i	−0.500000	+	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1365.1.cz.d.779.1	yes	2
3.2	odd	2		1365.1.cz.a.779.1	yes	2
5.4	even	2		1365.1.cz.b.779.1	yes	2
7.4	even	3	inner	1365.1.cz.d.389.1	yes	2
13.12	even	2		1365.1.cz.c.779.1	yes	2
15.14	odd	2		1365.1.cz.c.779.1	yes	2
21.11	odd	6		1365.1.cz.a.389.1	✓	2
35.4	even	6		1365.1.cz.b.389.1	yes	2
39.38	odd	2		1365.1.cz.b.779.1	yes	2
65.64	even	2		1365.1.cz.a.779.1	yes	2
91.25	even	6		1365.1.cz.c.389.1	yes	2
105.74	odd	6		1365.1.cz.c.389.1	yes	2
195.194	odd	2	CM	1365.1.cz.d.779.1	yes	2
273.116	odd	6		1365.1.cz.b.389.1	yes	2
455.389	even	6		1365.1.cz.a.389.1	✓	2
1365.389	odd	6	inner	1365.1.cz.d.389.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1365.1.cz.a.389.1	✓	2	21.11	odd	6
1365.1.cz.a.389.1	✓	2	455.389	even	6
1365.1.cz.a.779.1	yes	2	3.2	odd	2
1365.1.cz.a.779.1	yes	2	65.64	even	2
1365.1.cz.b.389.1	yes	2	35.4	even	6
1365.1.cz.b.389.1	yes	2	273.116	odd	6
1365.1.cz.b.779.1	yes	2	5.4	even	2
1365.1.cz.b.779.1	yes	2	39.38	odd	2
1365.1.cz.c.389.1	yes	2	91.25	even	6
1365.1.cz.c.389.1	yes	2	105.74	odd	6
1365.1.cz.c.779.1	yes	2	13.12	even	2
1365.1.cz.c.779.1	yes	2	15.14	odd	2
1365.1.cz.d.389.1	yes	2	7.4	even	3	inner
1365.1.cz.d.389.1	yes	2	1365.389	odd	6	inner
1365.1.cz.d.779.1	yes	2	1.1	even	1	trivial
1365.1.cz.d.779.1	yes	2	195.194	odd	2	CM

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:	\( N \)	\(=\)	\( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1365.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{33} +(0.500000 - 0.866025i) q^{35} +1.00000 q^{36} +(0.500000 - 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{39} +1.00000 q^{41} +(-0.500000 + 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{45} -1.00000 q^{48} +1.00000 q^{49} +(0.500000 - 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.00000 + 1.73205i) q^{53} -1.00000 q^{55} +(-0.500000 - 0.866025i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.00000 + 1.73205i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 + 0.866025i) q^{67} +(-0.500000 + 0.866025i) q^{68} -1.00000 q^{69} -2.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{77} +(0.500000 - 0.866025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{84} -1.00000 q^{85} +(-0.500000 + 0.866025i) q^{89} +1.00000 q^{91} +1.00000 q^{92} -1.00000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{4} + q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 - q^4 + q^5 + 2 * q^7 - q^9	\( 2 q + q^{3} - q^{4} + q^{5} + 2 q^{7} - q^{9} - q^{11} + q^{12} + 2 q^{13} + 2 q^{15} - q^{16} - q^{17} - 2 q^{20} + q^{21} - q^{23} - q^{25} - 2 q^{27} - q^{28} + q^{33} + q^{35} + 2 q^{36} + q^{37} + q^{39} + 2 q^{41} - q^{44} + q^{45} - 2 q^{48} + 2 q^{49} + q^{51} - q^{52} + 2 q^{53} - 2 q^{55} - q^{59} - q^{60} - 2 q^{61} - q^{63} + 2 q^{64} + q^{65} + q^{67} - q^{68} - 2 q^{69} - 4 q^{71} + q^{73} + q^{75} - q^{77} + q^{79} + q^{80} - q^{81} + q^{84} - 2 q^{85} - q^{89} + 2 q^{91} + 2 q^{92} - 2 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^4 + q^5 + 2 * q^7 - q^9 - q^11 + q^12 + 2 * q^13 + 2 * q^15 - q^16 - q^17 - 2 * q^20 + q^21 - q^23 - q^25 - 2 * q^27 - q^28 + q^33 + q^35 + 2 * q^36 + q^37 + q^39 + 2 * q^41 - q^44 + q^45 - 2 * q^48 + 2 * q^49 + q^51 - q^52 + 2 * q^53 - 2 * q^55 - q^59 - q^60 - 2 * q^61 - q^63 + 2 * q^64 + q^65 + q^67 - q^68 - 2 * q^69 - 4 * q^71 + q^73 + q^75 - q^77 + q^79 + q^80 - q^81 + q^84 - 2 * q^85 - q^89 + 2 * q^91 + 2 * q^92 - 2 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more