LMFDB - Embedded newform 1475.1.d.a.1474.1

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{7} +O(q^{10})$	$q-1.00000i q^{3} -1.00000 q^{4} +1.00000i q^{7} +1.00000i q^{12} +1.00000 q^{16} -2.00000i q^{17} +1.00000 q^{19} +1.00000 q^{21} -1.00000i q^{27} -1.00000i q^{28} +1.00000 q^{29} -1.00000 q^{41} -1.00000i q^{48} -2.00000 q^{51} -1.00000i q^{53} -1.00000i q^{57} -1.00000 q^{59} -1.00000 q^{64} +2.00000i q^{68} +2.00000 q^{71} -1.00000 q^{76} +1.00000 q^{79} -1.00000 q^{81} -1.00000 q^{84} -1.00000i q^{87} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.833333\pi$
$3$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−1.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$7$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$8$	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	$-0.833333\pi$
$53$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$54$	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	$0.166667\pi$
$107$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$108$	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	$0.166667\pi$
$127$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$128$	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	$0.166667\pi$
$137$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$138$	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	$0.166667\pi$
$167$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$168$	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	$-0.833333\pi$
$193$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$194$	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	$0.166667\pi$
$257$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	− 1.00000i	− 1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$264$	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	$0.166667\pi$
$277$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$278$	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	$-0.833333\pi$
$293$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$294$	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	$0.166667\pi$
$307$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$308$	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	$-0.833333\pi$
$433$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$434$	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	$0.166667\pi$
$487$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$488$	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	$-0.833333\pi$
$523$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$524$	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	$0.166667\pi$
$557$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$558$	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	$0.166667\pi$
$577$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$578$	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	$-0.833333\pi$
$593$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$594$	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	$0.166667\pi$
$607$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$608$	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	$0.166667\pi$
$617$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$618$	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	$-0.833333\pi$
$643$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	1.00000i	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$647$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$648$	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	$-0.833333\pi$
$653$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$654$	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	$0.166667\pi$
$757$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$758$	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	$-0.833333\pi$
$853$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$854$	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	$0.166667\pi$
$877$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$878$	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	$-0.833333\pi$
$883$	− 1.00000i	− 1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$884$	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	$0.166667\pi$
$907$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$908$	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	$0.166667\pi$
$947$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$948$	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	$0.166667\pi$
$997$	1.00000i	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$998$	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.1474.1		2
5.2	odd	4		59.1.b.a.58.1	✓	1
5.3	odd	4		1475.1.c.b.176.1		1
5.4	even	2	inner	1475.1.d.a.1474.2		2
15.2	even	4		531.1.c.a.235.1		1
20.7	even	4		944.1.h.a.353.1		1
35.2	odd	12		2891.1.g.d.2713.1		2
35.12	even	12		2891.1.g.b.2713.1		2
35.17	even	12		2891.1.g.b.471.1		2
35.27	even	4		2891.1.c.e.589.1		1
35.32	odd	12		2891.1.g.d.471.1		2
40.27	even	4		3776.1.h.a.2241.1		1
40.37	odd	4		3776.1.h.b.2241.1		1
59.58	odd	2	CM	1475.1.d.a.1474.1		2
295.2	even	116		3481.1.d.a.3182.1		28
295.7	odd	116		3481.1.d.a.1839.1		28
295.12	odd	116		3481.1.d.a.2511.1		28
295.17	odd	116		3481.1.d.a.3428.1		28
295.22	odd	116		3481.1.d.a.1404.1		28
295.27	odd	116		3481.1.d.a.805.1		28
295.32	even	116		3481.1.d.a.805.1		28
295.37	even	116		3481.1.d.a.1404.1		28
295.42	even	116		3481.1.d.a.3428.1		28
295.47	even	116		3481.1.d.a.2511.1		28
295.52	even	116		3481.1.d.a.1839.1		28
295.57	odd	116		3481.1.d.a.3182.1		28
295.58	even	4		1475.1.c.b.176.1		1
295.62	odd	116		3481.1.d.a.1702.1		28
295.67	even	116		3481.1.d.a.3181.1		28
295.72	even	116		3481.1.d.a.893.1		28
295.77	even	116		3481.1.d.a.1505.1		28
295.82	even	116		3481.1.d.a.946.1		28
295.87	odd	116		3481.1.d.a.809.1		28
295.92	even	116		3481.1.d.a.2451.1		28
295.97	even	116		3481.1.d.a.2922.1		28
295.102	even	116		3481.1.d.a.806.1		28
295.107	odd	116		3481.1.d.a.3183.1		28
295.112	odd	116		3481.1.d.a.672.1		28
295.117	even	4		59.1.b.a.58.1	✓	1
295.122	odd	116		3481.1.d.a.1105.1		28
295.127	odd	116		3481.1.d.a.2869.1		28
295.132	even	116		3481.1.d.a.3344.1		28
295.137	odd	116		3481.1.d.a.2117.1		28
295.142	even	116		3481.1.d.a.2374.1		28
295.147	odd	116		3481.1.d.a.1106.1		28
295.152	even	116		3481.1.d.a.1558.1		28
295.157	even	116		3481.1.d.a.1311.1		28
295.162	even	116		3481.1.d.a.2076.1		28
295.167	odd	116		3481.1.d.a.1611.1		28
295.172	even	116		3481.1.d.a.506.1		28
295.182	odd	116		3481.1.d.a.506.1		28
295.187	even	116		3481.1.d.a.1611.1		28
295.192	odd	116		3481.1.d.a.2076.1		28
295.197	odd	116		3481.1.d.a.1311.1		28
295.202	odd	116		3481.1.d.a.1558.1		28
295.207	even	116		3481.1.d.a.1106.1		28
295.212	odd	116		3481.1.d.a.2374.1		28
295.217	even	116		3481.1.d.a.2117.1		28
295.222	odd	116		3481.1.d.a.3344.1		28
295.227	even	116		3481.1.d.a.2869.1		28
295.232	even	116		3481.1.d.a.1105.1		28
295.242	even	116		3481.1.d.a.672.1		28
295.247	even	116		3481.1.d.a.3183.1		28
295.252	odd	116		3481.1.d.a.806.1		28
295.257	odd	116		3481.1.d.a.2922.1		28
295.262	odd	116		3481.1.d.a.2451.1		28
295.267	even	116		3481.1.d.a.809.1		28
295.272	odd	116		3481.1.d.a.946.1		28
295.277	odd	116		3481.1.d.a.1505.1		28
295.282	odd	116		3481.1.d.a.893.1		28
295.287	odd	116		3481.1.d.a.3181.1		28
295.292	even	116		3481.1.d.a.1702.1		28
295.294	odd	2	inner	1475.1.d.a.1474.2		2
885.707	odd	4		531.1.c.a.235.1		1
1180.707	odd	4		944.1.h.a.353.1		1
2065.117	odd	12		2891.1.g.b.2713.1		2
2065.412	odd	4		2891.1.c.e.589.1		1
2065.1297	even	12		2891.1.g.d.2713.1		2
2065.1592	odd	12		2891.1.g.b.471.1		2
2065.1887	even	12		2891.1.g.d.471.1		2
2360.117	even	4		3776.1.h.b.2241.1		1
2360.707	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	5.2	odd	4
59.1.b.a.58.1	✓	1	295.117	even	4
531.1.c.a.235.1		1	15.2	even	4
531.1.c.a.235.1		1	885.707	odd	4
944.1.h.a.353.1		1	20.7	even	4
944.1.h.a.353.1		1	1180.707	odd	4
1475.1.c.b.176.1		1	5.3	odd	4
1475.1.c.b.176.1		1	295.58	even	4
1475.1.d.a.1474.1		2	1.1	even	1	trivial
1475.1.d.a.1474.1		2	59.58	odd	2	CM
1475.1.d.a.1474.2		2	5.4	even	2	inner
1475.1.d.a.1474.2		2	295.294	odd	2	inner
2891.1.c.e.589.1		1	35.27	even	4
2891.1.c.e.589.1		1	2065.412	odd	4
2891.1.g.b.471.1		2	35.17	even	12
2891.1.g.b.471.1		2	2065.1592	odd	12
2891.1.g.b.2713.1		2	35.12	even	12
2891.1.g.b.2713.1		2	2065.117	odd	12
2891.1.g.d.471.1		2	35.32	odd	12
2891.1.g.d.471.1		2	2065.1887	even	12
2891.1.g.d.2713.1		2	35.2	odd	12
2891.1.g.d.2713.1		2	2065.1297	even	12
3481.1.d.a.506.1		28	295.172	even	116
3481.1.d.a.506.1		28	295.182	odd	116
3481.1.d.a.672.1		28	295.112	odd	116
3481.1.d.a.672.1		28	295.242	even	116
3481.1.d.a.805.1		28	295.27	odd	116
3481.1.d.a.805.1		28	295.32	even	116
3481.1.d.a.806.1		28	295.102	even	116
3481.1.d.a.806.1		28	295.252	odd	116
3481.1.d.a.809.1		28	295.87	odd	116
3481.1.d.a.809.1		28	295.267	even	116
3481.1.d.a.893.1		28	295.72	even	116
3481.1.d.a.893.1		28	295.282	odd	116
3481.1.d.a.946.1		28	295.82	even	116
3481.1.d.a.946.1		28	295.272	odd	116
3481.1.d.a.1105.1		28	295.122	odd	116
3481.1.d.a.1105.1		28	295.232	even	116
3481.1.d.a.1106.1		28	295.147	odd	116
3481.1.d.a.1106.1		28	295.207	even	116
3481.1.d.a.1311.1		28	295.157	even	116
3481.1.d.a.1311.1		28	295.197	odd	116
3481.1.d.a.1404.1		28	295.22	odd	116
3481.1.d.a.1404.1		28	295.37	even	116
3481.1.d.a.1505.1		28	295.77	even	116
3481.1.d.a.1505.1		28	295.277	odd	116
3481.1.d.a.1558.1		28	295.152	even	116
3481.1.d.a.1558.1		28	295.202	odd	116
3481.1.d.a.1611.1		28	295.167	odd	116
3481.1.d.a.1611.1		28	295.187	even	116
3481.1.d.a.1702.1		28	295.62	odd	116
3481.1.d.a.1702.1		28	295.292	even	116
3481.1.d.a.1839.1		28	295.7	odd	116
3481.1.d.a.1839.1		28	295.52	even	116
3481.1.d.a.2076.1		28	295.162	even	116
3481.1.d.a.2076.1		28	295.192	odd	116
3481.1.d.a.2117.1		28	295.137	odd	116
3481.1.d.a.2117.1		28	295.217	even	116
3481.1.d.a.2374.1		28	295.142	even	116
3481.1.d.a.2374.1		28	295.212	odd	116
3481.1.d.a.2451.1		28	295.92	even	116
3481.1.d.a.2451.1		28	295.262	odd	116
3481.1.d.a.2511.1		28	295.12	odd	116
3481.1.d.a.2511.1		28	295.47	even	116
3481.1.d.a.2869.1		28	295.127	odd	116
3481.1.d.a.2869.1		28	295.227	even	116
3481.1.d.a.2922.1		28	295.97	even	116
3481.1.d.a.2922.1		28	295.257	odd	116
3481.1.d.a.3181.1		28	295.67	even	116
3481.1.d.a.3181.1		28	295.287	odd	116
3481.1.d.a.3182.1		28	295.2	even	116
3481.1.d.a.3182.1		28	295.57	odd	116
3481.1.d.a.3183.1		28	295.107	odd	116
3481.1.d.a.3183.1		28	295.247	even	116
3481.1.d.a.3344.1		28	295.132	even	116
3481.1.d.a.3344.1		28	295.222	odd	116
3481.1.d.a.3428.1		28	295.17	odd	116
3481.1.d.a.3428.1		28	295.42	even	116
3776.1.h.a.2241.1		1	40.27	even	4
3776.1.h.a.2241.1		1	2360.707	odd	4
3776.1.h.b.2241.1		1	40.37	odd	4
3776.1.h.b.2241.1		1	2360.117	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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