LMFDB - Embedded newform 1197.1.ci.c.1189.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,1,Mod(748,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1197.748");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1197.ci (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:	$0.597380820122$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.17689.1

Embedding invariants

Embedding label			1189.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1197.1189
Dual form			1197.1.ci.c.748.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000 q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.866025 + 0.500000i) q^{13} +(-0.866025 - 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{17} +1.00000i q^{19} +(0.500000 + 0.866025i) q^{23} +1.00000i q^{26} +(-0.500000 - 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{35} +(0.866025 + 0.500000i) q^{38} +(0.866025 + 0.500000i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} +1.00000 q^{46} +(0.866025 - 0.500000i) q^{47} -1.00000 q^{49} +(-0.500000 - 0.866025i) q^{53} -1.00000i q^{56} -1.00000 q^{58} +(0.866025 + 0.500000i) q^{59} +(0.866025 - 0.500000i) q^{61} +1.00000 q^{64} -1.00000 q^{65} +(-0.500000 - 0.866025i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{71} +(-0.866025 - 0.500000i) q^{73} +(-0.500000 + 0.866025i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.866025 + 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{85} +(0.500000 + 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} -1.00000i q^{94} +(-0.500000 + 0.866025i) q^{95} +(0.866025 + 0.500000i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^8	$ 4 q + 2 q^{2} + 4 q^{8} + 2 q^{16} + 2 q^{23} - 2 q^{29} + 2 q^{35} - 2 q^{43} + 4 q^{46} - 4 q^{49} - 2 q^{53} - 4 q^{58} + 4 q^{64} - 4 q^{65} - 2 q^{67} - 2 q^{70} - 2 q^{71} - 2 q^{79} - 2 q^{85} + 2 q^{86} + 2 q^{91} - 2 q^{95} - 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^8 + 2 * q^16 + 2 * q^23 - 2 * q^29 + 2 * q^35 - 2 * q^43 + 4 * q^46 - 4 * q^49 - 2 * q^53 - 4 * q^58 + 4 * q^64 - 4 * q^65 - 2 * q^67 - 2 * q^70 - 2 * q^71 - 2 * q^79 - 2 * q^85 + 2 * q^86 + 2 * q^91 - 2 * q^95 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$		0			0
$7$		−	1.00000i		−	1.00000i
$7$		−	1.00000i		−	1.00000i
$8$	1.00000			1.00000
$9$		0			0
$10$	0.866025	−	0.500000i	0.866025	−	0.500000i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$14$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$15$		0			0
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$17$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$			1.00000i			1.00000i
$19$			1.00000i			1.00000i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$23$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$24$		0			0
$25$		0			0
$26$			1.00000i			1.00000i
$27$		0			0
$28$		0			0
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$		0			0
$34$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$35$	0.500000	−	0.866025i	0.500000	−	0.866025i
$36$		0			0
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.866025	+	0.500000i	0.866025	+	0.500000i
$39$		0			0
$40$	0.866025	+	0.500000i	0.866025	+	0.500000i
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$43$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$44$		0			0
$45$		0			0
$46$	1.00000			1.00000
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−1.00000			−1.00000
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		−	1.00000i		−	1.00000i
$57$		0			0
$58$	−1.00000			−1.00000
$59$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$59$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$60$		0			0
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			1.00000
$65$	−1.00000			−1.00000
$66$		0			0
$67$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$67$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$71$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$71$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$72$		0			0
$73$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$73$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$79$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$80$	0.866025	−	0.500000i	0.866025	−	0.500000i
$81$		0			0
$82$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$		0			0
$88$		0			0
$89$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$89$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$90$		0			0
$91$	0.500000	+	0.866025i	0.500000	+	0.866025i
$92$		0			0
$93$		0			0
$94$		−	1.00000i		−	1.00000i
$95$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$96$		0			0
$97$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$97$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$98$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$99$		0			0
$100$		0			0
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$105$		0			0
$106$	−1.00000			−1.00000
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$109$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$			1.00000i			1.00000i
$116$		0			0
$117$		0			0
$118$	0.866025	−	0.500000i	0.866025	−	0.500000i
$119$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$120$		0			0
$121$	−1.00000			−1.00000
$122$		−	1.00000i		−	1.00000i
$123$		0			0
$124$		0			0
$125$		−	1.00000i		−	1.00000i
$126$		0			0
$127$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$128$	0.500000	−	0.866025i	0.500000	−	0.866025i
$129$		0			0
$130$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$131$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$131$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$132$		0			0
$133$	1.00000			1.00000
$134$	−1.00000			−1.00000
$135$		0			0
$136$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$137$	−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
$139$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$139$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$		0			0
$142$	0.500000	+	0.866025i	0.500000	+	0.866025i
$143$		0			0
$144$		0			0
$145$		−	1.00000i		−	1.00000i
$146$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$147$		0			0
$148$		0			0
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$			1.00000i			1.00000i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$158$	0.500000	+	0.866025i	0.500000	+	0.866025i
$159$		0			0
$160$		0			0
$161$	0.866025	−	0.500000i	0.866025	−	0.500000i
$162$		0			0
$163$	2.00000			2.00000			1.00000			$0$
$163$	2.00000			2.00000			1.00000			$0$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$168$		0			0
$169$		0			0
$170$	−1.00000			−1.00000
$171$		0			0
$172$		0			0
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$			1.00000i			1.00000i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$181$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$182$	1.00000			1.00000
$183$		0			0
$184$	0.500000	+	0.866025i	0.500000	+	0.866025i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	0.500000	+	0.866025i	0.500000	+	0.866025i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$194$	0.866025	−	0.500000i	0.866025	−	0.500000i
$195$		0			0
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$199$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$		0			0
$202$			1.00000i			1.00000i
$203$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$204$		0			0
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$		0			0
$207$		0			0
$208$			1.00000i			1.00000i
$209$		0			0
$210$		0			0
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$216$		0			0
$217$		0			0
$218$	0.500000	+	0.866025i	0.500000	+	0.866025i
$219$		0			0
$220$		0			0
$221$	1.00000			1.00000
$222$		0			0
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$223$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.866025	+	0.500000i	0.866025	+	0.500000i
$231$		0			0
$232$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$233$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$233$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$234$		0			0
$235$	1.00000			1.00000
$236$		0			0
$237$		0			0
$238$	0.500000	+	0.866025i	0.500000	+	0.866025i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$241$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$242$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$243$		0			0
$244$		0			0
$245$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$246$		0			0
$247$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$248$		0			0
$249$		0			0
$250$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$	−1.00000			−1.00000
$255$		0			0
$256$		0			0
$257$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$257$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.866025	−	0.500000i	0.866025	−	0.500000i
$263$	−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
$265$		−	1.00000i		−	1.00000i
$266$	0.500000	−	0.866025i	0.500000	−	0.866025i
$267$		0			0
$268$		0			0
$269$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$269$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$270$		0			0
$271$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$271$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$272$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$273$		0			0
$274$	−1.00000			−1.00000
$275$		0			0
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		−	1.00000i		−	1.00000i
$279$		0			0
$280$	0.500000	−	0.866025i	0.500000	−	0.866025i
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$288$		0			0
$289$		0			0
$290$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$291$		0			0
$292$		0			0
$293$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$293$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$294$		0			0
$295$	0.500000	+	0.866025i	0.500000	+	0.866025i
$296$		0			0
$297$		0			0
$298$	0.500000	+	0.866025i	0.500000	+	0.866025i
$299$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$300$		0			0
$301$	0.866025	+	0.500000i	0.866025	+	0.500000i
$302$		0			0
$303$		0			0
$304$	0.866025	+	0.500000i	0.866025	+	0.500000i
$305$	1.00000			1.00000
$306$		0			0
$307$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$307$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$313$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$314$	0.866025	−	0.500000i	0.866025	−	0.500000i
$315$		0			0
$316$		0			0
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	0.866025	+	0.500000i	0.866025	+	0.500000i
$321$		0			0
$322$		−	1.00000i		−	1.00000i
$323$	0.500000	−	0.866025i	0.500000	−	0.866025i
$324$		0			0
$325$		0			0
$326$	1.00000	−	1.73205i	1.00000	−	1.73205i
$327$		0			0
$328$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$329$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$		0			0
$334$			1.00000i			1.00000i
$335$		−	1.00000i		−	1.00000i
$336$		0			0
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$			1.00000i			1.00000i
$344$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$345$		0			0
$346$	0.866025	−	0.500000i	0.866025	−	0.500000i
$347$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$353$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$354$		0			0
$355$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$359$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$360$		0			0
$361$	−1.00000			−1.00000
$362$			1.00000i			1.00000i
$363$		0			0
$364$		0			0
$365$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$366$		0			0
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$	1.00000			1.00000
$369$		0			0
$370$		0			0
$371$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$		0			0
$376$	0.866025	−	0.500000i	0.866025	−	0.500000i
$377$	0.866025	+	0.500000i	0.866025	+	0.500000i
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$383$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$384$		0			0
$385$		0			0
$386$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$387$		0			0
$388$		0			0
$389$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$389$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		−	1.00000i		−	1.00000i
$392$	−1.00000			−1.00000
$393$		0			0
$394$		0			0
$395$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$396$		0			0
$397$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$397$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$398$		−	1.00000i		−	1.00000i
$399$		0			0
$400$		0			0
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$			1.00000i			1.00000i
$407$		0			0
$408$		0			0
$409$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$409$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$410$	−1.00000			−1.00000
$411$		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			0
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$422$	0.500000	+	0.866025i	0.500000	+	0.866025i
$423$		0			0
$424$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$425$		0			0
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$428$		0			0
$429$		0			0
$430$			1.00000i			1.00000i
$431$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$431$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$432$		0			0
$433$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$433$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$438$		0			0
$439$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$439$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$		0			0
$442$	0.500000	−	0.866025i	0.500000	−	0.866025i
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$	−1.00000			−1.00000
$446$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$447$		0			0
$448$		−	1.00000i		−	1.00000i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$			1.00000i			1.00000i
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	−1.00000			−1.00000
$465$		0			0
$466$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$470$	0.500000	−	0.866025i	0.500000	−	0.866025i
$471$		0			0
$472$	0.866025	+	0.500000i	0.866025	+	0.500000i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$		0			0
$482$			1.00000i			1.00000i
$483$		0			0
$484$		0			0
$485$	0.500000	+	0.866025i	0.500000	+	0.866025i
$486$		0			0
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$	0.866025	−	0.500000i	0.866025	−	0.500000i
$489$		0			0
$490$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$492$		0			0
$493$			1.00000i			1.00000i
$494$	−1.00000			−1.00000
$495$		0			0
$496$		0			0
$497$	0.866025	+	0.500000i	0.866025	+	0.500000i
$498$		0			0
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$		0			0
$501$		0			0
$502$		−	1.00000i		−	1.00000i
$503$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$503$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$504$		0			0
$505$	−1.00000			−1.00000
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$512$	1.00000			1.00000
$513$		0			0
$514$		−	1.00000i		−	1.00000i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.00000			−1.00000
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$523$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$524$		0			0
$525$		0			0
$526$	0.500000	+	0.866025i	0.500000	+	0.866025i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$531$		0			0
$532$		0			0
$533$	1.00000			1.00000
$534$		0			0
$535$		0			0
$536$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$537$		0			0
$538$	0.866025	−	0.500000i	0.866025	−	0.500000i
$539$		0			0
$540$		0			0
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$542$	0.866025	−	0.500000i	0.866025	−	0.500000i
$543$		0			0
$544$		0			0
$545$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$546$		0			0
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.866025	−	0.500000i	0.866025	−	0.500000i
$552$		0			0
$553$	0.866025	+	0.500000i	0.866025	+	0.500000i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$557$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$558$		0			0
$559$		−	1.00000i		−	1.00000i
$560$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$561$		0			0
$562$	1.00000			1.00000
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$567$		0			0
$568$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$	0.500000	+	0.866025i	0.500000	+	0.866025i
$575$		0			0
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$585$		0			0
$586$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$		0			0
$590$	1.00000			1.00000
$591$		0			0
$592$		0			0
$593$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$593$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$594$		0			0
$595$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$596$		0			0
$597$		0			0
$598$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$599$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$599$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	0.866025	−	0.500000i	0.866025	−	0.500000i
$603$		0			0
$604$		0			0
$605$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	0.500000	−	0.866025i	0.500000	−	0.866025i
$611$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$612$		0			0
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$614$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$615$		0			0
$616$		0			0
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.500000	+	0.866025i	0.500000	+	0.866025i
$624$		0			0
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		−	1.00000i		−	1.00000i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$631$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$632$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$633$		0			0
$634$	−1.00000			−1.00000
$635$		−	1.00000i		−	1.00000i
$636$		0			0
$637$	0.866025	−	0.500000i	0.866025	−	0.500000i
$638$		0			0
$639$		0			0
$640$	0.866025	−	0.500000i	0.866025	−	0.500000i
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$642$		0			0
$643$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$643$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$		0			0
$655$	0.500000	+	0.866025i	0.500000	+	0.866025i
$656$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$657$		0			0
$658$	−1.00000			−1.00000
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$661$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.866025	+	0.500000i	0.866025	+	0.500000i
$666$		0			0
$667$	0.500000	−	0.866025i	0.500000	−	0.866025i
$668$		0			0
$669$		0			0
$670$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$671$		0			0
$672$		0			0
$673$	2.00000			2.00000			1.00000			$0$
$673$	2.00000			2.00000			1.00000			$0$
$674$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$675$		0			0
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$	0.500000	−	0.866025i	0.500000	−	0.866025i
$680$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$681$		0			0
$682$		0			0
$683$	2.00000			2.00000			1.00000			$0$
$683$	2.00000			2.00000			1.00000			$0$
$684$		0			0
$685$		−	1.00000i		−	1.00000i
$686$	0.866025	+	0.500000i	0.866025	+	0.500000i
$687$		0			0
$688$	0.500000	+	0.866025i	0.500000	+	0.866025i
$689$	0.866025	+	0.500000i	0.866025	+	0.500000i
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$695$	1.00000			1.00000
$696$		0			0
$697$	0.500000	+	0.866025i	0.500000	+	0.866025i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$701$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.73205	+	1.00000i	1.73205	+	1.00000i
$707$	0.500000	+	0.866025i	0.500000	+	0.866025i
$708$		0			0
$709$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$709$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$710$			1.00000i			1.00000i
$711$		0			0
$712$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$		0			0
$722$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$727$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$	0.500000	+	0.866025i	0.500000	+	0.866025i
$729$		0			0
$730$	−1.00000			−1.00000
$731$	0.866025	−	0.500000i	0.866025	−	0.500000i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$			1.00000i			1.00000i
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$740$		0			0
$741$		0			0
$742$			1.00000i			1.00000i
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$744$		0			0
$745$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$752$		−	1.00000i		−	1.00000i
$753$		0			0
$754$	0.866025	−	0.500000i	0.866025	−	0.500000i
$755$		0			0
$756$		0			0
$757$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$757$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$761$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$761$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$762$		0			0
$763$	0.866025	+	0.500000i	0.866025	+	0.500000i
$764$		0			0
$765$		0			0
$766$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$767$	−1.00000			−1.00000
$768$		0			0
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$773$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$	0.866025	+	0.500000i	0.866025	+	0.500000i
$777$		0			0
$778$	1.00000			1.00000
$779$	0.500000	−	0.866025i	0.500000	−	0.866025i
$780$		0			0
$781$		0			0
$782$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$	0.500000	+	0.866025i	0.500000	+	0.866025i
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$		0			0
$789$		0			0
$790$			1.00000i			1.00000i
$791$		0			0
$792$		0			0
$793$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$794$	0.866025	−	0.500000i	0.866025	−	0.500000i
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−1.00000			−1.00000
$800$		0			0
$801$		0			0
$802$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$803$		0			0
$804$		0			0
$805$	1.00000			1.00000
$806$		0			0
$807$		0			0
$808$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$809$	−2.00000			−2.00000			−1.00000			$\pi$
$809$	−2.00000			−2.00000			−1.00000			$\pi$
$810$		0			0
$811$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$811$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.73205	+	1.00000i	1.73205	+	1.00000i
$816$		0			0
$817$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$818$			1.00000i			1.00000i
$819$		0			0
$820$		0			0
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$827$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$827$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$828$		0			0
$829$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$829$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$830$		0			0
$831$		0			0
$832$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$833$	0.866025	+	0.500000i	0.866025	+	0.500000i
$834$		0			0
$835$	−1.00000			−1.00000
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$839$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$840$		0			0
$841$		0			0
$842$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$			1.00000i			1.00000i
$848$	−1.00000			−1.00000
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$854$	−1.00000			−1.00000
$855$		0			0
$856$		0			0
$857$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$857$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$859$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	1.00000			1.00000
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	0.500000	+	0.866025i	0.500000	+	0.866025i
$866$		−	1.00000i		−	1.00000i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.866025	+	0.500000i	0.866025	+	0.500000i
$872$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$873$		0			0
$874$			1.00000i			1.00000i
$875$	−1.00000			−1.00000
$876$		0			0
$877$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$877$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$878$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$		0			0
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$	1.00000			1.00000
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$		0			0
$889$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$890$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$891$		0			0
$892$		0			0
$893$	0.500000	+	0.866025i	0.500000	+	0.866025i
$894$		0			0
$895$		0			0
$896$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$			1.00000i			1.00000i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.00000			−1.00000
$906$		0			0
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$908$		0			0
$909$		0			0
$910$	0.866025	+	0.500000i	0.866025	+	0.500000i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.500000	−	0.866025i	0.500000	−	0.866025i
$918$		0			0
$919$	−2.00000			−2.00000			−1.00000			$\pi$
$919$	−2.00000			−2.00000			−1.00000			$\pi$
$920$			1.00000i			1.00000i
$921$		0			0
$922$	0.866025	−	0.500000i	0.866025	−	0.500000i
$923$		−	1.00000i		−	1.00000i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$		−	1.00000i		−	1.00000i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$937$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$938$			1.00000i			1.00000i
$939$		0			0
$940$		0			0
$941$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$941$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$942$		0			0
$943$		−	1.00000i		−	1.00000i
$944$	0.866025	−	0.500000i	0.866025	−	0.500000i
$945$		0			0
$946$		0			0
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$948$		0			0
$949$	1.00000			1.00000
$950$		0			0
$951$		0			0
$952$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$953$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		−	1.00000i		−	1.00000i
$959$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$960$		0			0
$961$	1.00000			1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.866025	−	0.500000i	0.866025	−	0.500000i
$966$		0			0
$967$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$967$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$	1.00000			1.00000
$971$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$971$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$974$		0			0
$975$		0			0
$976$		−	1.00000i		−	1.00000i
$977$	2.00000			2.00000			1.00000			$0$
$977$	2.00000			2.00000			1.00000			$0$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$		0			0
$986$	0.866025	+	0.500000i	0.866025	+	0.500000i
$987$		0			0
$988$		0			0
$989$	−1.00000			−1.00000
$990$		0			0
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$	0.866025	−	0.500000i	0.866025	−	0.500000i
$995$	1.00000			1.00000
$996$		0			0
$997$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$998$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.1.ci.c.1189.2		4
3.2	odd	2		133.1.m.a.125.2	yes	4
7.6	odd	2	inner	1197.1.ci.c.1189.1		4
12.11	even	2		2128.1.cy.a.657.1		4
15.2	even	4		3325.1.bi.b.524.1		4
15.8	even	4		3325.1.bi.a.524.2		4
15.14	odd	2		3325.1.bc.a.3051.1		4
19.7	even	3	inner	1197.1.ci.c.748.1		4
21.2	odd	6		931.1.t.a.619.1		4
21.5	even	6		931.1.t.a.619.2		4
21.11	odd	6		931.1.k.a.68.1		4
21.17	even	6		931.1.k.a.68.2		4
21.20	even	2		133.1.m.a.125.1	yes	4
57.2	even	18		2527.1.y.d.2400.2		12
57.5	odd	18		2527.1.y.e.1833.1		12
57.8	even	6		2527.1.d.b.1084.2		2
57.11	odd	6		2527.1.d.e.1084.1		2
57.14	even	18		2527.1.y.d.1833.2		12
57.17	odd	18		2527.1.y.e.2400.1		12
57.23	odd	18		2527.1.y.e.62.1		12
57.26	odd	6		133.1.m.a.83.1	✓	4
57.29	even	18		2527.1.y.d.2050.1		12
57.32	even	18		2527.1.y.d.776.1		12
57.35	odd	18		2527.1.y.e.1182.2		12
57.41	even	18		2527.1.y.d.1182.1		12
57.44	odd	18		2527.1.y.e.776.2		12
57.47	odd	18		2527.1.y.e.2050.2		12
57.50	even	6		2527.1.m.d.1014.2		4
57.53	even	18		2527.1.y.d.62.2		12
57.56	even	2		2527.1.m.d.790.1		4
84.83	odd	2		2128.1.cy.a.657.2		4
105.62	odd	4		3325.1.bi.a.524.1		4
105.83	odd	4		3325.1.bi.b.524.2		4
105.104	even	2		3325.1.bc.a.3051.2		4
133.83	odd	6	inner	1197.1.ci.c.748.2		4
228.83	even	6		2128.1.cy.a.881.2		4
285.83	even	12		3325.1.bi.a.349.1		4
285.197	even	12		3325.1.bi.b.349.2		4
285.254	odd	6		3325.1.bc.a.2876.2		4
399.26	even	6		931.1.k.a.178.2		4
399.41	odd	18		2527.1.y.d.1182.2		12
399.62	even	18		2527.1.y.e.1833.2		12
399.83	even	6		133.1.m.a.83.2	yes	4
399.104	even	18		2527.1.y.e.2050.1		12
399.125	even	6		2527.1.d.e.1084.2		2
399.146	odd	18		2527.1.y.d.776.2		12
399.167	odd	18		2527.1.y.d.62.1		12
399.188	even	18		2527.1.y.e.2400.2		12
399.230	odd	18		2527.1.y.d.2400.1		12
399.251	even	18		2527.1.y.e.62.2		12
399.254	odd	6		931.1.k.a.178.1		4
399.272	even	18		2527.1.y.e.776.1		12
399.293	odd	6		2527.1.d.b.1084.1		2
399.311	even	6		931.1.t.a.558.1		4
399.314	odd	18		2527.1.y.d.2050.2		12
399.335	odd	6		2527.1.m.d.1014.1		4
399.356	odd	18		2527.1.y.d.1833.1		12
399.368	odd	6		931.1.t.a.558.2		4
399.377	even	18		2527.1.y.e.1182.1		12
399.398	odd	2		2527.1.m.d.790.2		4
1596.83	odd	6		2128.1.cy.a.881.1		4
1995.83	odd	12		3325.1.bi.b.349.1		4
1995.482	odd	12		3325.1.bi.a.349.2		4
1995.1679	even	6		3325.1.bc.a.2876.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.1.m.a.83.1	✓	4	57.26	odd	6
133.1.m.a.83.2	yes	4	399.83	even	6
133.1.m.a.125.1	yes	4	21.20	even	2
133.1.m.a.125.2	yes	4	3.2	odd	2
931.1.k.a.68.1		4	21.11	odd	6
931.1.k.a.68.2		4	21.17	even	6
931.1.k.a.178.1		4	399.254	odd	6
931.1.k.a.178.2		4	399.26	even	6
931.1.t.a.558.1		4	399.311	even	6
931.1.t.a.558.2		4	399.368	odd	6
931.1.t.a.619.1		4	21.2	odd	6
931.1.t.a.619.2		4	21.5	even	6
1197.1.ci.c.748.1		4	19.7	even	3	inner
1197.1.ci.c.748.2		4	133.83	odd	6	inner
1197.1.ci.c.1189.1		4	7.6	odd	2	inner
1197.1.ci.c.1189.2		4	1.1	even	1	trivial
2128.1.cy.a.657.1		4	12.11	even	2
2128.1.cy.a.657.2		4	84.83	odd	2
2128.1.cy.a.881.1		4	1596.83	odd	6
2128.1.cy.a.881.2		4	228.83	even	6
2527.1.d.b.1084.1		2	399.293	odd	6
2527.1.d.b.1084.2		2	57.8	even	6
2527.1.d.e.1084.1		2	57.11	odd	6
2527.1.d.e.1084.2		2	399.125	even	6
2527.1.m.d.790.1		4	57.56	even	2
2527.1.m.d.790.2		4	399.398	odd	2
2527.1.m.d.1014.1		4	399.335	odd	6
2527.1.m.d.1014.2		4	57.50	even	6
2527.1.y.d.62.1		12	399.167	odd	18
2527.1.y.d.62.2		12	57.53	even	18
2527.1.y.d.776.1		12	57.32	even	18
2527.1.y.d.776.2		12	399.146	odd	18
2527.1.y.d.1182.1		12	57.41	even	18
2527.1.y.d.1182.2		12	399.41	odd	18
2527.1.y.d.1833.1		12	399.356	odd	18
2527.1.y.d.1833.2		12	57.14	even	18
2527.1.y.d.2050.1		12	57.29	even	18
2527.1.y.d.2050.2		12	399.314	odd	18
2527.1.y.d.2400.1		12	399.230	odd	18
2527.1.y.d.2400.2		12	57.2	even	18
2527.1.y.e.62.1		12	57.23	odd	18
2527.1.y.e.62.2		12	399.251	even	18
2527.1.y.e.776.1		12	399.272	even	18
2527.1.y.e.776.2		12	57.44	odd	18
2527.1.y.e.1182.1		12	399.377	even	18
2527.1.y.e.1182.2		12	57.35	odd	18
2527.1.y.e.1833.1		12	57.5	odd	18
2527.1.y.e.1833.2		12	399.62	even	18
2527.1.y.e.2050.1		12	399.104	even	18
2527.1.y.e.2050.2		12	57.47	odd	18
2527.1.y.e.2400.1		12	57.17	odd	18
2527.1.y.e.2400.2		12	399.188	even	18
3325.1.bc.a.2876.1		4	1995.1679	even	6
3325.1.bc.a.2876.2		4	285.254	odd	6
3325.1.bc.a.3051.1		4	15.14	odd	2
3325.1.bc.a.3051.2		4	105.104	even	2
3325.1.bi.a.349.1		4	285.83	even	12
3325.1.bi.a.349.2		4	1995.482	odd	12
3325.1.bi.a.524.1		4	105.62	odd	4
3325.1.bi.a.524.2		4	15.8	even	4
3325.1.bi.b.349.1		4	1995.83	odd	12
3325.1.bi.b.349.2		4	285.197	even	12
3325.1.bi.b.524.1		4	15.2	even	4
3325.1.bi.b.524.2		4	105.83	odd	4

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1197.ci (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{5} -1.00000i q^{7} +1.00000 q^{8} +(0.866025 - 0.500000i) q^{10} +(-0.866025 + 0.500000i) q^{13} +(-0.866025 - 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{17} +1.00000i q^{19} +(0.500000 + 0.866025i) q^{23} +1.00000i q^{26} +(-0.500000 - 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{34} +(0.500000 - 0.866025i) q^{35} +(0.866025 + 0.500000i) q^{38} +(0.866025 + 0.500000i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} +1.00000 q^{46} +(0.866025 - 0.500000i) q^{47} -1.00000 q^{49} +(-0.500000 - 0.866025i) q^{53} -1.00000i q^{56} -1.00000 q^{58} +(0.866025 + 0.500000i) q^{59} +(0.866025 - 0.500000i) q^{61} +1.00000 q^{64} -1.00000 q^{65} +(-0.500000 - 0.866025i) q^{67} +(-0.500000 - 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{71} +(-0.866025 - 0.500000i) q^{73} +(-0.500000 + 0.866025i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.866025 + 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{85} +(0.500000 + 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} -1.00000i q^{94} +(-0.500000 + 0.866025i) q^{95} +(0.866025 + 0.500000i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^8	\( 4 q + 2 q^{2} + 4 q^{8} + 2 q^{16} + 2 q^{23} - 2 q^{29} + 2 q^{35} - 2 q^{43} + 4 q^{46} - 4 q^{49} - 2 q^{53} - 4 q^{58} + 4 q^{64} - 4 q^{65} - 2 q^{67} - 2 q^{70} - 2 q^{71} - 2 q^{79} - 2 q^{85} + 2 q^{86} + 2 q^{91} - 2 q^{95} - 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^8 + 2 * q^16 + 2 * q^23 - 2 * q^29 + 2 * q^35 - 2 * q^43 + 4 * q^46 - 4 * q^49 - 2 * q^53 - 4 * q^58 + 4 * q^64 - 4 * q^65 - 2 * q^67 - 2 * q^70 - 2 * q^71 - 2 * q^79 - 2 * q^85 + 2 * q^86 + 2 * q^91 - 2 * q^95 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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