LMFDB - Embedded newform 1475.1.d.a.1474.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1475,1,Mod(1474,1475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1475, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1475.1474");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1475 = 5^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1475.d (of order $2$, degree $1$, not 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:	$0.736120893634$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 59)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.59.1
Artin image:	$C_4\times S_3$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			1474.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1475.1474
Dual form			1475.1.d.a.1474.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{3} -1.00000 q^{4} -1.00000i q^{7} +O(q^{10})$	$q+1.00000i q^{3} -1.00000 q^{4} -1.00000i q^{7} -1.00000i q^{12} +1.00000 q^{16} +2.00000i q^{17} +1.00000 q^{19} +1.00000 q^{21} +1.00000i q^{27} +1.00000i q^{28} +1.00000 q^{29} -1.00000 q^{41} +1.00000i q^{48} -2.00000 q^{51} +1.00000i q^{53} +1.00000i q^{57} -1.00000 q^{59} -1.00000 q^{64} -2.00000i q^{68} +2.00000 q^{71} -1.00000 q^{76} +1.00000 q^{79} -1.00000 q^{81} -1.00000 q^{84} +1.00000i q^{87} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4}+O(q^{10}) $ 2 * q - 2 * q^4	$ 2 q - 2 q^{4} + 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{29} - 2 q^{41} - 4 q^{51} - 2 q^{59} - 2 q^{64} + 4 q^{71} - 2 q^{76} + 2 q^{79} - 2 q^{81} - 2 q^{84}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^29 - 2 * q^41 - 4 * q^51 - 2 * q^59 - 2 * q^64 + 4 * q^71 - 2 * q^76 + 2 * q^79 - 2 * q^81 - 2 * q^84

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1475\mathbb{Z}\right)^\times$.

$n$	$651$	$827$
$\chi(n)$	$-1$	$-1$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	− 1.00000i	− 1.00000i
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	1.00000
$17$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$17$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$18$	0	0
$19$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$19$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$20$	0	0
$21$	1.00000	1.00000
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.00000i	1.00000i
$28$	1.00000i	1.00000i
$29$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$29$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000i	1.00000i
$49$	0	0
$50$	0	0
$51$	−2.00000	−2.00000
$52$	0	0
$53$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$53$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.00000i	1.00000i
$58$	0	0
$59$	−1.00000	−1.00000
$59$	−1.00000	−1.00000
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	−1.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	− 2.00000i	− 2.00000i
$69$	0	0
$70$	0	0
$71$	2.00000	2.00000	1.00000			$0$
$71$	2.00000	2.00000	1.00000			$0$
$72$	0	0
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	0	0
$75$	0	0
$76$	−1.00000	−1.00000
$77$	0	0
$78$	0	0
$79$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$79$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$80$	0	0
$81$	−1.00000	−1.00000
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−1.00000	−1.00000
$85$	0	0
$86$	0	0
$87$	1.00000i	1.00000i
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$107$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$108$	− 1.00000i	− 1.00000i
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	− 1.00000i	− 1.00000i
$113$	0	0		−	1.00000i	$-0.5\pi$
$113$	0	0			1.00000i	$0.5\pi$
$114$	0	0
$115$	0	0
$116$	−1.00000	−1.00000
$117$	0	0
$118$	0	0
$119$	2.00000	2.00000
$120$	0	0
$121$	1.00000	1.00000
$122$	0	0
$123$	− 1.00000i	− 1.00000i
$124$	0	0
$125$	0	0
$126$	0	0
$127$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$127$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	− 1.00000i	− 1.00000i
$134$	0	0
$135$	0	0
$136$	0	0
$137$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$137$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$138$	0	0
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$139$	−2.00000	−2.00000	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0		−	1.00000i	$-0.5\pi$
$157$	0	0			1.00000i	$0.5\pi$
$158$	0	0
$159$	−1.00000	−1.00000
$160$	0	0
$161$	0	0
$162$	0	0
$163$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$163$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$164$	1.00000	1.00000
$165$	0	0
$166$	0	0
$167$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	0	0
$169$	−1.00000	−1.00000
$170$	0	0
$171$	0	0
$172$	0	0
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	− 1.00000i	− 1.00000i
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	1.00000	1.00000
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	− 1.00000i	− 1.00000i
$193$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$193$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$197$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$198$	0	0
$199$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$199$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	− 1.00000i	− 1.00000i
$204$	2.00000	2.00000
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	− 1.00000i	− 1.00000i
$213$	2.00000i	2.00000i
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$223$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	− 1.00000i	− 1.00000i
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	0	0
$235$	0	0
$236$	1.00000	1.00000
$237$	1.00000i	1.00000i
$238$	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	0
$241$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	1.00000	1.00000
$257$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$257$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$263$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$271$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$272$	2.00000i	2.00000i
$273$	0	0
$274$	0	0
$275$	0	0
$276$	0	0
$277$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$282$	0	0
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−2.00000	−2.00000
$285$	0	0
$286$	0	0
$287$	1.00000i	1.00000i
$288$	0	0
$289$	−3.00000	−3.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$293$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	1.00000	1.00000
$305$	0	0
$306$	0	0
$307$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$307$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$312$	0	0
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	0	0
$315$	0	0
$316$	−1.00000	−1.00000
$317$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$317$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	1.00000	1.00000
$322$	0	0
$323$	2.00000i	2.00000i
$324$	1.00000	1.00000
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	1.00000	1.00000
$337$	0	0		−	1.00000i	$-0.5\pi$
$337$	0	0			1.00000i	$0.5\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	− 1.00000i	− 1.00000i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	− 1.00000i	− 1.00000i
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	2.00000i	2.00000i
$358$	0	0
$359$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$359$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$360$	0	0
$361$	0	0
$362$	0	0
$363$	1.00000i	1.00000i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	1.00000	1.00000
$372$	0	0
$373$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$373$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	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
$381$	1.00000	1.00000
$382$	0	0
$383$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$383$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−2.00000	−2.00000	−1.00000			$\pi$
$389$	−2.00000	−2.00000	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0		−	1.00000i	$-0.5\pi$
$397$	0	0			1.00000i	$0.5\pi$
$398$	0	0
$399$	1.00000	1.00000
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	1.00000	1.00000
$412$	0	0
$413$	1.00000i	1.00000i
$414$	0	0
$415$	0	0
$416$	0	0
$417$	− 2.00000i	− 2.00000i
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	1.00000i	1.00000i
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	1.00000i	1.00000i
$433$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$433$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−2.00000	−2.00000	−1.00000			$\pi$
$439$	−2.00000	−2.00000	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	1.00000i	1.00000i
$449$	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	0
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0		−	1.00000i	$-0.5\pi$
$457$	0	0			1.00000i	$0.5\pi$
$458$	0	0
$459$	−2.00000	−2.00000
$460$	0	0
$461$	2.00000	2.00000	1.00000			$0$
$461$	2.00000	2.00000	1.00000			$0$
$462$	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	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	−2.00000	−2.00000
$477$	0	0
$478$	0	0
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$479$	−2.00000	−2.00000	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−1.00000	−1.00000
$485$	0	0
$486$	0	0
$487$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$488$	0	0
$489$	2.00000	2.00000
$490$	0	0
$491$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$492$	1.00000i	1.00000i
$493$	2.00000i	2.00000i
$494$	0	0
$495$	0	0
$496$	0	0
$497$	− 2.00000i	− 2.00000i
$498$	0	0
$499$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$499$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$500$	0	0
$501$	1.00000	1.00000
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	− 1.00000i	− 1.00000i
$508$	1.00000i	1.00000i
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	1.00000i	1.00000i
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	2.00000	2.00000	1.00000			$0$
$521$	2.00000	2.00000	1.00000			$0$
$522$	0	0
$523$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$523$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−1.00000	−1.00000
$530$	0	0
$531$	0	0
$532$	1.00000i	1.00000i
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	− 1.00000i	− 1.00000i
$544$	0	0
$545$	0	0
$546$	0	0
$547$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$547$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$548$	1.00000i	1.00000i
$549$	0	0
$550$	0	0
$551$	1.00000	1.00000
$552$	0	0
$553$	− 1.00000i	− 1.00000i
$554$	0	0
$555$	0	0
$556$	2.00000	2.00000
$557$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.00000i	1.00000i
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$577$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$578$	0	0
$579$	−1.00000	−1.00000
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	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
$591$	−2.00000	−2.00000
$592$	0	0
$593$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$593$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	1.00000i	1.00000i
$598$	0	0
$599$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$599$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	0	0
$606$	0	0
$607$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$607$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$608$	0	0
$609$	1.00000	1.00000
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$617$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$618$	0	0
$619$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$619$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	2.00000	2.00000	1.00000			$0$
$631$	2.00000	2.00000	1.00000			$0$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	1.00000	1.00000
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	2.00000	2.00000	1.00000			$0$
$641$	2.00000	2.00000	1.00000			$0$
$642$	0	0
$643$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$643$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$647$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	2.00000i	2.00000i
$653$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$653$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$654$	0	0
$655$	0	0
$656$	−1.00000	−1.00000
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	1.00000i	1.00000i
$669$	2.00000	2.00000
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	0	0
$675$	0	0
$676$	1.00000	1.00000
$677$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$677$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	− 2.00000i	− 2.00000i
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	1.00000i	1.00000i
$709$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$709$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	1.00000i	1.00000i
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	− 1.00000i	− 1.00000i
$724$	1.00000	1.00000
$725$	0	0
$726$	0	0
$727$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$727$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$728$	0	0
$729$	−1.00000	−1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$733$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$743$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−1.00000	−1.00000
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	− 1.00000i	− 1.00000i
$754$	0	0
$755$	0	0
$756$	−1.00000	−1.00000
$757$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$757$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	1.00000i	1.00000i
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	1.00000	1.00000
$772$	− 1.00000i	− 1.00000i
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−1.00000	−1.00000
$780$	0	0
$781$	0	0
$782$	0	0
$783$	1.00000i	1.00000i
$784$	0	0
$785$	0	0
$786$	0	0
$787$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$787$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$788$	− 2.00000i	− 2.00000i
$789$	−1.00000	−1.00000
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−1.00000	−1.00000
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	1.00000i	1.00000i
$813$	− 1.00000i	− 1.00000i
$814$	0	0
$815$	0	0
$816$	−2.00000	−2.00000
$817$	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
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$827$	2.00000i	2.00000i			1.00000i	$0.5\pi$
$828$	0	0
$829$	1.00000	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$829$	1.00000	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$830$	0	0
$831$	1.00000	1.00000
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	0	0
$842$	0	0
$843$	− 1.00000i	− 1.00000i
$844$	0	0
$845$	0	0
$846$	0	0
$847$	− 1.00000i	− 1.00000i
$848$	1.00000i	1.00000i
$849$	0	0
$850$	0	0
$851$	0	0
$852$	− 2.00000i	− 2.00000i
$853$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$853$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	−1.00000	−1.00000
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 3.00000i	− 3.00000i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$877$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$878$	0	0
$879$	−1.00000	−1.00000
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$883$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	−1.00000	−1.00000
$890$	0	0
$891$	0	0
$892$	2.00000i	2.00000i
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	−2.00000	−2.00000
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$907$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$911$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$912$	1.00000i	1.00000i
$913$	0	0
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	1.00000	1.00000
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	− 1.00000i	− 1.00000i
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0		−	1.00000i	$-0.5\pi$
$937$	0	0			1.00000i	$0.5\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−1.00000	−1.00000
$945$	0	0
$946$	0	0
$947$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$947$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$948$	− 1.00000i	− 1.00000i
$949$	0	0
$950$	0	0
$951$	−2.00000	−2.00000
$952$	0	0
$953$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$953$	− 2.00000i	− 2.00000i		−	1.00000i	$-0.5\pi$
$954$	0	0
$955$	0	0
$956$	−1.00000	−1.00000
$957$	0	0
$958$	0	0
$959$	−1.00000	−1.00000
$960$	0	0
$961$	1.00000	1.00000
$962$	0	0
$963$	0	0
$964$	1.00000	1.00000
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	−2.00000	−2.00000
$970$	0	0
$971$	−1.00000	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$972$	0	0
$973$	2.00000i	2.00000i
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0		−	1.00000i	$-0.5\pi$
$977$	0	0			1.00000i	$0.5\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	− 1.00000i	− 1.00000i
$994$	0	0
$995$	0	0
$996$	0	0
$997$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1475.1.d.a.1474.2		2
5.2	odd	4		1475.1.c.b.176.1		1
5.3	odd	4		59.1.b.a.58.1	✓	1
5.4	even	2	inner	1475.1.d.a.1474.1		2
15.8	even	4		531.1.c.a.235.1		1
20.3	even	4		944.1.h.a.353.1		1
35.3	even	12		2891.1.g.b.471.1		2
35.13	even	4		2891.1.c.e.589.1		1
35.18	odd	12		2891.1.g.d.471.1		2
35.23	odd	12		2891.1.g.d.2713.1		2
35.33	even	12		2891.1.g.b.2713.1		2
40.3	even	4		3776.1.h.a.2241.1		1
40.13	odd	4		3776.1.h.b.2241.1		1
59.58	odd	2	CM	1475.1.d.a.1474.2		2
295.3	odd	116		3481.1.d.a.1702.1		28
295.8	even	116		3481.1.d.a.3181.1		28
295.13	even	116		3481.1.d.a.893.1		28
295.18	even	116		3481.1.d.a.1505.1		28
295.23	even	116		3481.1.d.a.946.1		28
295.28	odd	116		3481.1.d.a.809.1		28
295.33	even	116		3481.1.d.a.2451.1		28
295.38	even	116		3481.1.d.a.2922.1		28
295.43	even	116		3481.1.d.a.806.1		28
295.48	odd	116		3481.1.d.a.3183.1		28
295.53	odd	116		3481.1.d.a.672.1		28
295.58	even	4		59.1.b.a.58.1	✓	1
295.63	odd	116		3481.1.d.a.1105.1		28
295.68	odd	116		3481.1.d.a.2869.1		28
295.73	even	116		3481.1.d.a.3344.1		28
295.78	odd	116		3481.1.d.a.2117.1		28
295.83	even	116		3481.1.d.a.2374.1		28
295.88	odd	116		3481.1.d.a.1106.1		28
295.93	even	116		3481.1.d.a.1558.1		28
295.98	even	116		3481.1.d.a.1311.1		28
295.103	even	116		3481.1.d.a.2076.1		28
295.108	odd	116		3481.1.d.a.1611.1		28
295.113	even	116		3481.1.d.a.506.1		28
295.117	even	4		1475.1.c.b.176.1		1
295.123	odd	116		3481.1.d.a.506.1		28
295.128	even	116		3481.1.d.a.1611.1		28
295.133	odd	116		3481.1.d.a.2076.1		28
295.138	odd	116		3481.1.d.a.1311.1		28
295.143	odd	116		3481.1.d.a.1558.1		28
295.148	even	116		3481.1.d.a.1106.1		28
295.153	odd	116		3481.1.d.a.2374.1		28
295.158	even	116		3481.1.d.a.2117.1		28
295.163	odd	116		3481.1.d.a.3344.1		28
295.168	even	116		3481.1.d.a.2869.1		28
295.173	even	116		3481.1.d.a.1105.1		28
295.183	even	116		3481.1.d.a.672.1		28
295.188	even	116		3481.1.d.a.3183.1		28
295.193	odd	116		3481.1.d.a.806.1		28
295.198	odd	116		3481.1.d.a.2922.1		28
295.203	odd	116		3481.1.d.a.2451.1		28
295.208	even	116		3481.1.d.a.809.1		28
295.213	odd	116		3481.1.d.a.946.1		28
295.218	odd	116		3481.1.d.a.1505.1		28
295.223	odd	116		3481.1.d.a.893.1		28
295.228	odd	116		3481.1.d.a.3181.1		28
295.233	even	116		3481.1.d.a.1702.1		28
295.238	even	116		3481.1.d.a.3182.1		28
295.243	odd	116		3481.1.d.a.1839.1		28
295.248	odd	116		3481.1.d.a.2511.1		28
295.253	odd	116		3481.1.d.a.3428.1		28
295.258	odd	116		3481.1.d.a.1404.1		28
295.263	odd	116		3481.1.d.a.805.1		28
295.268	even	116		3481.1.d.a.805.1		28
295.273	even	116		3481.1.d.a.1404.1		28
295.278	even	116		3481.1.d.a.3428.1		28
295.283	even	116		3481.1.d.a.2511.1		28
295.288	even	116		3481.1.d.a.1839.1		28
295.293	odd	116		3481.1.d.a.3182.1		28
295.294	odd	2	inner	1475.1.d.a.1474.1		2
885.353	odd	4		531.1.c.a.235.1		1
1180.943	odd	4		944.1.h.a.353.1		1
2065.58	even	12		2891.1.g.d.2713.1		2
2065.353	odd	12		2891.1.g.b.471.1		2
2065.648	even	12		2891.1.g.d.471.1		2
2065.943	odd	12		2891.1.g.b.2713.1		2
2065.1238	odd	4		2891.1.c.e.589.1		1
2360.1533	even	4		3776.1.h.b.2241.1		1
2360.2123	odd	4		3776.1.h.a.2241.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.1.b.a.58.1	✓	1	5.3	odd	4
59.1.b.a.58.1	✓	1	295.58	even	4
531.1.c.a.235.1		1	15.8	even	4
531.1.c.a.235.1		1	885.353	odd	4
944.1.h.a.353.1		1	20.3	even	4
944.1.h.a.353.1		1	1180.943	odd	4
1475.1.c.b.176.1		1	5.2	odd	4
1475.1.c.b.176.1		1	295.117	even	4
1475.1.d.a.1474.1		2	5.4	even	2	inner
1475.1.d.a.1474.1		2	295.294	odd	2	inner
1475.1.d.a.1474.2		2	1.1	even	1	trivial
1475.1.d.a.1474.2		2	59.58	odd	2	CM
2891.1.c.e.589.1		1	35.13	even	4
2891.1.c.e.589.1		1	2065.1238	odd	4
2891.1.g.b.471.1		2	35.3	even	12
2891.1.g.b.471.1		2	2065.353	odd	12
2891.1.g.b.2713.1		2	35.33	even	12
2891.1.g.b.2713.1		2	2065.943	odd	12
2891.1.g.d.471.1		2	35.18	odd	12
2891.1.g.d.471.1		2	2065.648	even	12
2891.1.g.d.2713.1		2	35.23	odd	12
2891.1.g.d.2713.1		2	2065.58	even	12
3481.1.d.a.506.1		28	295.113	even	116
3481.1.d.a.506.1		28	295.123	odd	116
3481.1.d.a.672.1		28	295.53	odd	116
3481.1.d.a.672.1		28	295.183	even	116
3481.1.d.a.805.1		28	295.263	odd	116
3481.1.d.a.805.1		28	295.268	even	116
3481.1.d.a.806.1		28	295.43	even	116
3481.1.d.a.806.1		28	295.193	odd	116
3481.1.d.a.809.1		28	295.28	odd	116
3481.1.d.a.809.1		28	295.208	even	116
3481.1.d.a.893.1		28	295.13	even	116
3481.1.d.a.893.1		28	295.223	odd	116
3481.1.d.a.946.1		28	295.23	even	116
3481.1.d.a.946.1		28	295.213	odd	116
3481.1.d.a.1105.1		28	295.63	odd	116
3481.1.d.a.1105.1		28	295.173	even	116
3481.1.d.a.1106.1		28	295.88	odd	116
3481.1.d.a.1106.1		28	295.148	even	116
3481.1.d.a.1311.1		28	295.98	even	116
3481.1.d.a.1311.1		28	295.138	odd	116
3481.1.d.a.1404.1		28	295.258	odd	116
3481.1.d.a.1404.1		28	295.273	even	116
3481.1.d.a.1505.1		28	295.18	even	116
3481.1.d.a.1505.1		28	295.218	odd	116
3481.1.d.a.1558.1		28	295.93	even	116
3481.1.d.a.1558.1		28	295.143	odd	116
3481.1.d.a.1611.1		28	295.108	odd	116
3481.1.d.a.1611.1		28	295.128	even	116
3481.1.d.a.1702.1		28	295.3	odd	116
3481.1.d.a.1702.1		28	295.233	even	116
3481.1.d.a.1839.1		28	295.243	odd	116
3481.1.d.a.1839.1		28	295.288	even	116
3481.1.d.a.2076.1		28	295.103	even	116
3481.1.d.a.2076.1		28	295.133	odd	116
3481.1.d.a.2117.1		28	295.78	odd	116
3481.1.d.a.2117.1		28	295.158	even	116
3481.1.d.a.2374.1		28	295.83	even	116
3481.1.d.a.2374.1		28	295.153	odd	116
3481.1.d.a.2451.1		28	295.33	even	116
3481.1.d.a.2451.1		28	295.203	odd	116
3481.1.d.a.2511.1		28	295.248	odd	116
3481.1.d.a.2511.1		28	295.283	even	116
3481.1.d.a.2869.1		28	295.68	odd	116
3481.1.d.a.2869.1		28	295.168	even	116
3481.1.d.a.2922.1		28	295.38	even	116
3481.1.d.a.2922.1		28	295.198	odd	116
3481.1.d.a.3181.1		28	295.8	even	116
3481.1.d.a.3181.1		28	295.228	odd	116
3481.1.d.a.3182.1		28	295.238	even	116
3481.1.d.a.3182.1		28	295.293	odd	116
3481.1.d.a.3183.1		28	295.48	odd	116
3481.1.d.a.3183.1		28	295.188	even	116
3481.1.d.a.3344.1		28	295.73	even	116
3481.1.d.a.3344.1		28	295.163	odd	116
3481.1.d.a.3428.1		28	295.253	odd	116
3481.1.d.a.3428.1		28	295.278	even	116
3776.1.h.a.2241.1		1	40.3	even	4
3776.1.h.a.2241.1		1	2360.2123	odd	4
3776.1.h.b.2241.1		1	40.13	odd	4
3776.1.h.b.2241.1		1	2360.1533	even	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:	\( N \)	\(=\)	\( 1475 = 5^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1475.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} -1.00000 q^{4} -1.00000i q^{7} +O(q^{10})\)	\(q+1.00000i q^{3} -1.00000 q^{4} -1.00000i q^{7} -1.00000i q^{12} +1.00000 q^{16} +2.00000i q^{17} +1.00000 q^{19} +1.00000 q^{21} +1.00000i q^{27} +1.00000i q^{28} +1.00000 q^{29} -1.00000 q^{41} +1.00000i q^{48} -2.00000 q^{51} +1.00000i q^{53} +1.00000i q^{57} -1.00000 q^{59} -1.00000 q^{64} -2.00000i q^{68} +2.00000 q^{71} -1.00000 q^{76} +1.00000 q^{79} -1.00000 q^{81} -1.00000 q^{84} +1.00000i q^{87} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4}+O(q^{10}) \) 2 * q - 2 * q^4	\( 2 q - 2 q^{4} + 2 q^{16} + 2 q^{19} + 2 q^{21} + 2 q^{29} - 2 q^{41} - 4 q^{51} - 2 q^{59} - 2 q^{64} + 4 q^{71} - 2 q^{76} + 2 q^{79} - 2 q^{81} - 2 q^{84}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^16 + 2 * q^19 + 2 * q^21 + 2 * q^29 - 2 * q^41 - 4 * q^51 - 2 * q^59 - 2 * q^64 + 4 * q^71 - 2 * q^76 + 2 * q^79 - 2 * q^81 - 2 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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