LMFDB - Embedded newform 3311.1.h.i.3310.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3311,1,Mod(3310,3311)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3311, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("3311.3310");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3311 = 7 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3311.h (of order $2$, degree $1$, 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:	yes
Analytic conductor:	$1.65240425683$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{6}$
Projective field:	Galois closure of 6.0.76739047.1

Embedding invariants

Embedding label			3310.2
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	3311.3310

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.73205 q^{3} +1.73205 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})$	$q+1.00000 q^{2} +1.73205 q^{3} +1.73205 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +1.73205 q^{10} -1.00000 q^{11} -1.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} +1.73205 q^{17} +2.00000 q^{18} -1.73205 q^{21} -1.00000 q^{22} -2.00000 q^{23} -1.73205 q^{24} +2.00000 q^{25} +1.73205 q^{27} -1.00000 q^{29} +3.00000 q^{30} -1.73205 q^{33} +1.73205 q^{34} -1.73205 q^{35} -1.73205 q^{40} -1.73205 q^{41} -1.73205 q^{42} +1.00000 q^{43} +3.46410 q^{45} -2.00000 q^{46} -1.73205 q^{48} +1.00000 q^{49} +2.00000 q^{50} +3.00000 q^{51} -1.00000 q^{53} +1.73205 q^{54} -1.73205 q^{55} +1.00000 q^{56} -1.00000 q^{58} -2.00000 q^{63} +1.00000 q^{64} -1.73205 q^{66} -1.00000 q^{67} -3.46410 q^{69} -1.73205 q^{70} -2.00000 q^{72} +3.46410 q^{75} +1.00000 q^{77} -1.73205 q^{80} +1.00000 q^{81} -1.73205 q^{82} +1.73205 q^{83} +3.00000 q^{85} +1.00000 q^{86} -1.73205 q^{87} +1.00000 q^{88} +3.46410 q^{90} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^7 - 2 * q^8 + 4 * q^9	$ 2 q + 2 q^{2} - 2 q^{7} - 2 q^{8} + 4 q^{9} - 2 q^{11} - 2 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{18} - 2 q^{22} - 4 q^{23} + 4 q^{25} - 2 q^{29} + 6 q^{30} + 2 q^{43} - 4 q^{46} + 2 q^{49} + 4 q^{50} + 6 q^{51} - 2 q^{53} + 2 q^{56} - 2 q^{58} - 4 q^{63} + 2 q^{64} - 2 q^{67} - 4 q^{72} + 2 q^{77} + 2 q^{81} + 6 q^{85} + 2 q^{86} + 2 q^{88} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^7 - 2 * q^8 + 4 * q^9 - 2 * q^11 - 2 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^18 - 2 * q^22 - 4 * q^23 + 4 * q^25 - 2 * q^29 + 6 * q^30 + 2 * q^43 - 4 * q^46 + 2 * q^49 + 4 * q^50 + 6 * q^51 - 2 * q^53 + 2 * q^56 - 2 * q^58 - 4 * q^63 + 2 * q^64 - 2 * q^67 - 4 * q^72 + 2 * q^77 + 2 * q^81 + 6 * q^85 + 2 * q^86 + 2 * q^88 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times$.

$n$	$904$	$1893$	$2927$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$3$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	0	0
$5$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$5$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$6$	1.73205	1.73205
$7$	−1.00000	−1.00000
$7$	−1.00000	−1.00000
$8$	−1.00000	−1.00000
$9$	2.00000	2.00000
$10$	1.73205	1.73205
$11$	−1.00000	−1.00000
$11$	−1.00000	−1.00000
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	−1.00000	−1.00000
$15$	3.00000	3.00000
$16$	−1.00000	−1.00000
$17$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$17$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$18$	2.00000	2.00000
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	−1.73205	−1.73205
$22$	−1.00000	−1.00000
$23$	−2.00000	−2.00000	−1.00000			$\pi$
$23$	−2.00000	−2.00000	−1.00000			$\pi$
$24$	−1.73205	−1.73205
$25$	2.00000	2.00000
$26$	0	0
$27$	1.73205	1.73205
$28$	0	0
$29$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$30$	3.00000	3.00000
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	−1.73205	−1.73205
$34$	1.73205	1.73205
$35$	−1.73205	−1.73205
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	−1.73205	−1.73205
$41$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$41$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$42$	−1.73205	−1.73205
$43$	1.00000	1.00000
$43$	1.00000	1.00000
$44$	0	0
$45$	3.46410	3.46410
$46$	−2.00000	−2.00000
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	−1.73205	−1.73205
$49$	1.00000	1.00000
$50$	2.00000	2.00000
$51$	3.00000	3.00000
$52$	0	0
$53$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$53$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$54$	1.73205	1.73205
$55$	−1.73205	−1.73205
$56$	1.00000	1.00000
$57$	0	0
$58$	−1.00000	−1.00000
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−2.00000	−2.00000
$64$	1.00000	1.00000
$65$	0	0
$66$	−1.73205	−1.73205
$67$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$68$	0	0
$69$	−3.46410	−3.46410
$70$	−1.73205	−1.73205
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−2.00000	−2.00000
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	3.46410	3.46410
$76$	0	0
$77$	1.00000	1.00000
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	−1.73205	−1.73205
$81$	1.00000	1.00000
$82$	−1.73205	−1.73205
$83$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$83$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$84$	0	0
$85$	3.00000	3.00000
$86$	1.00000	1.00000
$87$	−1.73205	−1.73205
$88$	1.00000	1.00000
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	3.46410	3.46410
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	1.00000	1.00000
$99$	−2.00000	−2.00000
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	3.00000	3.00000
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	−3.00000	−3.00000
$106$	−1.00000	−1.00000
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	−1.73205	−1.73205
$111$	0	0
$112$	1.00000	1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	−3.46410	−3.46410
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−1.73205	−1.73205
$120$	−3.00000	−3.00000
$121$	1.00000	1.00000
$122$	0	0
$123$	−3.00000	−3.00000
$124$	0	0
$125$	1.73205	1.73205
$126$	−2.00000	−2.00000
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	1.00000	1.00000
$129$	1.73205	1.73205
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−1.00000	−1.00000
$135$	3.00000	3.00000
$136$	−1.73205	−1.73205
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	−3.46410	−3.46410
$139$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$139$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	−2.00000	−2.00000
$145$	−1.73205	−1.73205
$146$	0	0
$147$	1.73205	1.73205
$148$	0	0
$149$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$150$	3.46410	3.46410
$151$	−2.00000	−2.00000	−1.00000			$\pi$
$151$	−2.00000	−2.00000	−1.00000			$\pi$
$152$	0	0
$153$	3.46410	3.46410
$154$	1.00000	1.00000
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	−1.73205	−1.73205
$160$	0	0
$161$	2.00000	2.00000
$162$	1.00000	1.00000
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	−3.00000	−3.00000
$166$	1.73205	1.73205
$167$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$168$	1.73205	1.73205
$169$	−1.00000	−1.00000
$170$	3.00000	3.00000
$171$	0	0
$172$	0	0
$173$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$173$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$174$	−1.73205	−1.73205
$175$	−2.00000	−2.00000
$176$	1.00000	1.00000
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	2.00000	2.00000
$185$	0	0
$186$	0	0
$187$	−1.73205	−1.73205
$188$	0	0
$189$	−1.73205	−1.73205
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	1.73205	1.73205
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	−2.00000	−2.00000
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−2.00000	−2.00000
$201$	−1.73205	−1.73205
$202$	0	0
$203$	1.00000	1.00000
$204$	0	0
$205$	−3.00000	−3.00000
$206$	0	0
$207$	−4.00000	−4.00000
$208$	0	0
$209$	0	0
$210$	−3.00000	−3.00000
$211$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	1.73205	1.73205
$216$	−1.73205	−1.73205
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$223$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$224$	0	0
$225$	4.00000	4.00000
$226$	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			$\pi$
$230$	−3.46410	−3.46410
$231$	1.73205	1.73205
$232$	1.00000	1.00000
$233$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$233$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	−1.73205	−1.73205
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	−3.00000	−3.00000
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	1.00000	1.00000
$243$	0	0
$244$	0	0
$245$	1.73205	1.73205
$246$	−3.00000	−3.00000
$247$	0	0
$248$	0	0
$249$	3.00000	3.00000
$250$	1.73205	1.73205
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	2.00000	2.00000
$254$	0	0
$255$	5.19615	5.19615
$256$	0	0
$257$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$257$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$258$	1.73205	1.73205
$259$	0	0
$260$	0	0
$261$	−2.00000	−2.00000
$262$	0	0
$263$	2.00000	2.00000	1.00000			$0$
$263$	2.00000	2.00000	1.00000			$0$
$264$	1.73205	1.73205
$265$	−1.73205	−1.73205
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	3.00000	3.00000
$271$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$271$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$272$	−1.73205	−1.73205
$273$	0	0
$274$	0	0
$275$	−2.00000	−2.00000
$276$	0	0
$277$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$277$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$278$	1.73205	1.73205
$279$	0	0
$280$	1.73205	1.73205
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	1.73205	1.73205
$288$	0	0
$289$	2.00000	2.00000
$290$	−1.73205	−1.73205
$291$	0	0
$292$	0	0
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	1.73205	1.73205
$295$	0	0
$296$	0	0
$297$	−1.73205	−1.73205
$298$	−1.00000	−1.00000
$299$	0	0
$300$	0	0
$301$	−1.00000	−1.00000
$302$	−2.00000	−2.00000
$303$	0	0
$304$	0	0
$305$	0	0
$306$	3.46410	3.46410
$307$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$307$	−1.73205	−1.73205	−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
$313$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$313$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$314$	0	0
$315$	−3.46410	−3.46410
$316$	0	0
$317$	2.00000	2.00000	1.00000			$0$
$317$	2.00000	2.00000	1.00000			$0$
$318$	−1.73205	−1.73205
$319$	1.00000	1.00000
$320$	1.73205	1.73205
$321$	0	0
$322$	2.00000	2.00000
$323$	0	0
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	1.73205	1.73205
$329$	0	0
$330$	−3.00000	−3.00000
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	−1.73205	−1.73205
$335$	−1.73205	−1.73205
$336$	1.73205	1.73205
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	−1.00000	−1.00000
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−1.00000	−1.00000
$344$	−1.00000	−1.00000
$345$	−6.00000	−6.00000
$346$	1.73205	1.73205
$347$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−2.00000	−2.00000
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−3.00000	−3.00000
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	−3.46410	−3.46410
$361$	1.00000	1.00000
$362$	0	0
$363$	1.73205	1.73205
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	2.00000	2.00000
$369$	−3.46410	−3.46410
$370$	0	0
$371$	1.00000	1.00000
$372$	0	0
$373$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$373$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$374$	−1.73205	−1.73205
$375$	3.00000	3.00000
$376$	0	0
$377$	0	0
$378$	−1.73205	−1.73205
$379$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$379$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.73205	1.73205
$385$	1.73205	1.73205
$386$	0	0
$387$	2.00000	2.00000
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	−3.46410	−3.46410
$392$	−1.00000	−1.00000
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	−2.00000	−2.00000
$401$	2.00000	2.00000	1.00000			$0$
$401$	2.00000	2.00000	1.00000			$0$
$402$	−1.73205	−1.73205
$403$	0	0
$404$	0	0
$405$	1.73205	1.73205
$406$	1.00000	1.00000
$407$	0	0
$408$	−3.00000	−3.00000
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	−3.00000	−3.00000
$411$	0	0
$412$	0	0
$413$	0	0
$414$	−4.00000	−4.00000
$415$	3.00000	3.00000
$416$	0	0
$417$	3.00000	3.00000
$418$	0	0
$419$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$419$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	−1.00000	−1.00000
$423$	0	0
$424$	1.00000	1.00000
$425$	3.46410	3.46410
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	1.73205	1.73205
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−1.73205	−1.73205
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	−3.00000	−3.00000
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	1.73205	1.73205
$441$	2.00000	2.00000
$442$	0	0
$443$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$444$	0	0
$445$	0	0
$446$	1.73205	1.73205
$447$	−1.73205	−1.73205
$448$	−1.00000	−1.00000
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	4.00000	4.00000
$451$	1.73205	1.73205
$452$	0	0
$453$	−3.46410	−3.46410
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$457$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$458$	0	0
$459$	3.00000	3.00000
$460$	0	0
$461$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$461$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$462$	1.73205	1.73205
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	1.00000	1.00000
$465$	0	0
$466$	1.00000	1.00000
$467$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$467$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$468$	0	0
$469$	1.00000	1.00000
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−1.00000	−1.00000
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−2.00000	−2.00000
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	3.46410	3.46410
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$487$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$488$	0	0
$489$	0	0
$490$	1.73205	1.73205
$491$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$492$	0	0
$493$	−1.73205	−1.73205
$494$	0	0
$495$	−3.46410	−3.46410
$496$	0	0
$497$	0	0
$498$	3.00000	3.00000
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	−3.00000	−3.00000
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	2.00000	2.00000
$505$	0	0
$506$	2.00000	2.00000
$507$	−1.73205	−1.73205
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	5.19615	5.19615
$511$	0	0
$512$	−1.00000	−1.00000
$513$	0	0
$514$	−1.73205	−1.73205
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	3.00000	3.00000
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	−2.00000	−2.00000
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−3.46410	−3.46410
$526$	2.00000	2.00000
$527$	0	0
$528$	1.73205	1.73205
$529$	3.00000	3.00000
$530$	−1.73205	−1.73205
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	1.00000	1.00000
$537$	0	0
$538$	0	0
$539$	−1.00000	−1.00000
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	1.73205	1.73205
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	−2.00000	−2.00000
$551$	0	0
$552$	3.46410	3.46410
$553$	0	0
$554$	1.00000	1.00000
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	1.73205	1.73205
$561$	−3.00000	−3.00000
$562$	0	0
$563$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$563$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−1.00000	−1.00000
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$572$	0	0
$573$	0	0
$574$	1.73205	1.73205
$575$	−4.00000	−4.00000
$576$	2.00000	2.00000
$577$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$577$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$578$	2.00000	2.00000
$579$	0	0
$580$	0	0
$581$	−1.73205	−1.73205
$582$	0	0
$583$	1.00000	1.00000
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	−1.73205	−1.73205
$595$	−3.00000	−3.00000
$596$	0	0
$597$	0	0
$598$	0	0
$599$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$599$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$600$	−3.46410	−3.46410
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−1.00000	−1.00000
$603$	−2.00000	−2.00000
$604$	0	0
$605$	1.73205	1.73205
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	1.73205	1.73205
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	−1.73205	−1.73205
$615$	−5.19615	−5.19615
$616$	−1.00000	−1.00000
$617$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	−3.46410	−3.46410
$622$	0	0
$623$	0	0
$624$	0	0
$625$	1.00000	1.00000
$626$	1.73205	1.73205
$627$	0	0
$628$	0	0
$629$	0	0
$630$	−3.46410	−3.46410
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	−1.73205	−1.73205
$634$	2.00000	2.00000
$635$	0	0
$636$	0	0
$637$	0	0
$638$	1.00000	1.00000
$639$	0	0
$640$	1.73205	1.73205
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	3.00000	3.00000
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−1.00000	−1.00000
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	1.73205	1.73205
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	−1.73205	−1.73205
$665$	0	0
$666$	0	0
$667$	2.00000	2.00000
$668$	0	0
$669$	3.00000	3.00000
$670$	−1.73205	−1.73205
$671$	0	0
$672$	0	0
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$673$	−2.00000	−2.00000	−1.00000			$\pi$
$674$	0	0
$675$	3.46410	3.46410
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	−3.00000	−3.00000
$681$	0	0
$682$	0	0
$683$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$684$	0	0
$685$	0	0
$686$	−1.00000	−1.00000
$687$	0	0
$688$	−1.00000	−1.00000
$689$	0	0
$690$	−6.00000	−6.00000
$691$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$691$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$692$	0	0
$693$	2.00000	2.00000
$694$	−1.00000	−1.00000
$695$	3.00000	3.00000
$696$	1.73205	1.73205
$697$	−3.00000	−3.00000
$698$	0	0
$699$	1.73205	1.73205
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	−1.00000	−1.00000
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−2.00000	−2.00000	−1.00000			$\pi$
$709$	−2.00000	−2.00000	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	−3.00000	−3.00000
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−3.46410	−3.46410
$721$	0	0
$722$	1.00000	1.00000
$723$	0	0
$724$	0	0
$725$	−2.00000	−2.00000
$726$	1.73205	1.73205
$727$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$727$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$728$	0	0
$729$	−1.00000	−1.00000
$730$	0	0
$731$	1.73205	1.73205
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	3.00000	3.00000
$736$	0	0
$737$	1.00000	1.00000
$738$	−3.46410	−3.46410
$739$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$739$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$740$	0	0
$741$	0	0
$742$	1.00000	1.00000
$743$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$744$	0	0
$745$	−1.73205	−1.73205
$746$	−1.00000	−1.00000
$747$	3.46410	3.46410
$748$	0	0
$749$	0	0
$750$	3.00000	3.00000
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−3.46410	−3.46410
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	1.00000	1.00000
$759$	3.46410	3.46410
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	6.00000	6.00000
$766$	0	0
$767$	0	0
$768$	0	0
$769$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$769$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$770$	1.73205	1.73205
$771$	−3.00000	−3.00000
$772$	0	0
$773$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$773$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$774$	2.00000	2.00000
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−3.46410	−3.46410
$783$	−1.73205	−1.73205
$784$	−1.00000	−1.00000
$785$	0	0
$786$	0	0
$787$	0	0		−	1.00000i	$-0.5\pi$
$787$	0	0			1.00000i	$0.5\pi$
$788$	0	0
$789$	3.46410	3.46410
$790$	0	0
$791$	0	0
$792$	2.00000	2.00000
$793$	0	0
$794$	0	0
$795$	−3.00000	−3.00000
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	2.00000	2.00000
$803$	0	0
$804$	0	0
$805$	3.46410	3.46410
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	1.73205	1.73205
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	3.00000	3.00000
$814$	0	0
$815$	0	0
$816$	−3.00000	−3.00000
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$823$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$824$	0	0
$825$	−3.46410	−3.46410
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$829$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$830$	3.00000	3.00000
$831$	1.73205	1.73205
$832$	0	0
$833$	1.73205	1.73205
$834$	3.00000	3.00000
$835$	−3.00000	−3.00000
$836$	0	0
$837$	0	0
$838$	−1.73205	−1.73205
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	3.00000	3.00000
$841$	0	0
$842$	0	0
$843$	0	0
$844$	0	0
$845$	−1.73205	−1.73205
$846$	0	0
$847$	−1.00000	−1.00000
$848$	1.00000	1.00000
$849$	0	0
$850$	3.46410	3.46410
$851$	0	0
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$857$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$858$	0	0
$859$	1.73205	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$859$	1.73205	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$860$	0	0
$861$	3.00000	3.00000
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	3.00000	3.00000
$866$	0	0
$867$	3.46410	3.46410
$868$	0	0
$869$	0	0
$870$	−3.00000	−3.00000
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−1.73205	−1.73205
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	1.73205	1.73205
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	2.00000	2.00000
$883$	2.00000	2.00000	1.00000			$0$
$883$	2.00000	2.00000	1.00000			$0$
$884$	0	0
$885$	0	0
$886$	1.00000	1.00000
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.00000	−1.00000
$892$	0	0
$893$	0	0
$894$	−1.73205	−1.73205
$895$	0	0
$896$	−1.00000	−1.00000
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	−1.73205	−1.73205
$902$	1.73205	1.73205
$903$	−1.73205	−1.73205
$904$	0	0
$905$	0	0
$906$	−3.46410	−3.46410
$907$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$907$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	−1.73205	−1.73205
$914$	−1.00000	−1.00000
$915$	0	0
$916$	0	0
$917$	0	0
$918$	3.00000	3.00000
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	3.46410	3.46410
$921$	−3.00000	−3.00000
$922$	1.73205	1.73205
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	−1.73205	−1.73205
$935$	−3.00000	−3.00000
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	1.00000	1.00000
$939$	3.00000	3.00000
$940$	0	0
$941$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$941$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$942$	0	0
$943$	3.46410	3.46410
$944$	0	0
$945$	−3.00000	−3.00000
$946$	−1.00000	−1.00000
$947$	2.00000	2.00000	1.00000			$0$
$947$	2.00000	2.00000	1.00000			$0$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	3.46410	3.46410
$952$	1.73205	1.73205
$953$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$954$	−2.00000	−2.00000
$955$	0	0
$956$	0	0
$957$	1.73205	1.73205
$958$	0	0
$959$	0	0
$960$	3.00000	3.00000
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	3.46410	3.46410
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−1.00000	−1.00000
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	−1.73205	−1.73205
$974$	−1.00000	−1.00000
$975$	0	0
$976$	0	0
$977$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	−1.00000	−1.00000
$983$	−1.73205	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−1.73205	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$984$	3.00000	3.00000
$985$	0	0
$986$	−1.73205	−1.73205
$987$	0	0
$988$	0	0
$989$	−2.00000	−2.00000
$990$	−3.46410	−3.46410
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3311.1.h.i.3310.2	yes	2
7.6	odd	2	inner	3311.1.h.i.3310.1	yes	2
11.10	odd	2		3311.1.h.h.3310.2	yes	2
43.42	odd	2		3311.1.h.h.3310.1	✓	2
77.76	even	2		3311.1.h.h.3310.1	✓	2
301.300	even	2		3311.1.h.h.3310.2	yes	2
473.472	even	2	inner	3311.1.h.i.3310.1	yes	2
3311.3310	odd	2	CM	3311.1.h.i.3310.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3311.1.h.h.3310.1	✓	2	43.42	odd	2
3311.1.h.h.3310.1	✓	2	77.76	even	2
3311.1.h.h.3310.2	yes	2	11.10	odd	2
3311.1.h.h.3310.2	yes	2	301.300	even	2
3311.1.h.i.3310.1	yes	2	7.6	odd	2	inner
3311.1.h.i.3310.1	yes	2	473.472	even	2	inner
3311.1.h.i.3310.2	yes	2	1.1	even	1	trivial
3311.1.h.i.3310.2	yes	2	3311.3310	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:	\( N \)	\(=\)	\( 3311 = 7 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3311.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.73205 q^{3} +1.73205 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.73205 q^{3} +1.73205 q^{5} +1.73205 q^{6} -1.00000 q^{7} -1.00000 q^{8} +2.00000 q^{9} +1.73205 q^{10} -1.00000 q^{11} -1.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} +1.73205 q^{17} +2.00000 q^{18} -1.73205 q^{21} -1.00000 q^{22} -2.00000 q^{23} -1.73205 q^{24} +2.00000 q^{25} +1.73205 q^{27} -1.00000 q^{29} +3.00000 q^{30} -1.73205 q^{33} +1.73205 q^{34} -1.73205 q^{35} -1.73205 q^{40} -1.73205 q^{41} -1.73205 q^{42} +1.00000 q^{43} +3.46410 q^{45} -2.00000 q^{46} -1.73205 q^{48} +1.00000 q^{49} +2.00000 q^{50} +3.00000 q^{51} -1.00000 q^{53} +1.73205 q^{54} -1.73205 q^{55} +1.00000 q^{56} -1.00000 q^{58} -2.00000 q^{63} +1.00000 q^{64} -1.73205 q^{66} -1.00000 q^{67} -3.46410 q^{69} -1.73205 q^{70} -2.00000 q^{72} +3.46410 q^{75} +1.00000 q^{77} -1.73205 q^{80} +1.00000 q^{81} -1.73205 q^{82} +1.73205 q^{83} +3.00000 q^{85} +1.00000 q^{86} -1.73205 q^{87} +1.00000 q^{88} +3.46410 q^{90} +1.00000 q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{7} - 2 q^{8} + 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^7 - 2 * q^8 + 4 * q^9	\( 2 q + 2 q^{2} - 2 q^{7} - 2 q^{8} + 4 q^{9} - 2 q^{11} - 2 q^{14} + 6 q^{15} - 2 q^{16} + 4 q^{18} - 2 q^{22} - 4 q^{23} + 4 q^{25} - 2 q^{29} + 6 q^{30} + 2 q^{43} - 4 q^{46} + 2 q^{49} + 4 q^{50} + 6 q^{51} - 2 q^{53} + 2 q^{56} - 2 q^{58} - 4 q^{63} + 2 q^{64} - 2 q^{67} - 4 q^{72} + 2 q^{77} + 2 q^{81} + 6 q^{85} + 2 q^{86} + 2 q^{88} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^7 - 2 * q^8 + 4 * q^9 - 2 * q^11 - 2 * q^14 + 6 * q^15 - 2 * q^16 + 4 * q^18 - 2 * q^22 - 4 * q^23 + 4 * q^25 - 2 * q^29 + 6 * q^30 + 2 * q^43 - 4 * q^46 + 2 * q^49 + 4 * q^50 + 6 * q^51 - 2 * q^53 + 2 * q^56 - 2 * q^58 - 4 * q^63 + 2 * q^64 - 2 * q^67 - 4 * q^72 + 2 * q^77 + 2 * q^81 + 6 * q^85 + 2 * q^86 + 2 * q^88 + 2 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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