# Properties

 Label 2888.1.f.a.723.1 Level $2888$ Weight $1$ Character 2888.723 Self dual yes Analytic conductor $1.441$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -8 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(723,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("2888.723");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2888 = 2^{3} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2888.f (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: $$1.44129975648$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 152) Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.2888.1 Artin image: $D_6$ Artin field: Galois closure of 6.0.158470336.1

## Embedding invariants

 Embedding label 723.1 Character $$\chi$$ $$=$$ 2888.72

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} -1.00000 q^{11} +1.00000 q^{12} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{22} -1.00000 q^{24} +1.00000 q^{25} -1.00000 q^{27} -1.00000 q^{32} -1.00000 q^{33} -2.00000 q^{34} +1.00000 q^{41} +2.00000 q^{43} -1.00000 q^{44} +1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} +1.00000 q^{54} +1.00000 q^{59} +1.00000 q^{64} +1.00000 q^{66} +1.00000 q^{67} +2.00000 q^{68} -1.00000 q^{73} +1.00000 q^{75} -1.00000 q^{81} -1.00000 q^{82} -1.00000 q^{83} -2.00000 q^{86} +1.00000 q^{88} -2.00000 q^{89} -1.00000 q^{96} +1.00000 q^{97} -1.00000 q^{98} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$$.

 $$n$$ $$1445$$ $$2167$$ $$2529$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −1.00000
$$3$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ −1.00000 −1.00000
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ 1.00000 1.00000
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.00000 1.00000
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ −1.00000 −1.00000
$$25$$ 1.00000 1.00000
$$26$$ 0 0
$$27$$ −1.00000 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ −1.00000 −1.00000
$$34$$ −2.00000 −2.00000
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$42$$ 0 0
$$43$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$44$$ −1.00000 −1.00000
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 1.00000 1.00000
$$49$$ 1.00000 1.00000
$$50$$ −1.00000 −1.00000
$$51$$ 2.00000 2.00000
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 1.00000 1.00000
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 1.00000 1.00000
$$67$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$68$$ 2.00000 2.00000
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ 1.00000 1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −1.00000
$$82$$ −1.00000 −1.00000
$$83$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 −2.00000
$$87$$ 0 0
$$88$$ 1.00000 1.00000
$$89$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ −1.00000 −1.00000
$$97$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$98$$ −1.00000 −1.00000
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ −2.00000 −2.00000
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$108$$ −1.00000 −1.00000
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −1.00000 −1.00000
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 1.00000 1.00000
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 2.00000 2.00000
$$130$$ 0 0
$$131$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$132$$ −1.00000 −1.00000
$$133$$ 0 0
$$134$$ −1.00000 −1.00000
$$135$$ 0 0
$$136$$ −2.00000 −2.00000
$$137$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 0 0
$$139$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 1.00000 1.00000
$$147$$ 1.00000 1.00000
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ −1.00000 −1.00000
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 1.00000 1.00000
$$163$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 1.00000 1.00000
$$165$$ 0 0
$$166$$ 1.00000 1.00000
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 2.00000 2.00000
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −1.00000
$$177$$ 1.00000 1.00000
$$178$$ 2.00000 2.00000
$$179$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −2.00000 −2.00000
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 1.00000 1.00000
$$193$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$194$$ −1.00000 −1.00000
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ −1.00000 −1.00000
$$201$$ 1.00000 1.00000
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 2.00000 2.00000
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 2.00000 2.00000
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −1.00000 −1.00000
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1.00000 −1.00000
$$227$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 1.00000 1.00000
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −1.00000 −1.00000
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.00000 −1.00000
$$250$$ 0 0
$$251$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ −2.00000 −2.00000
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 1.00000 1.00000
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 1.00000 1.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −2.00000 −2.00000
$$268$$ 1.00000 1.00000
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 2.00000 2.00000
$$273$$ 0 0
$$274$$ 1.00000 1.00000
$$275$$ −1.00000 −1.00000
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 1.00000 1.00000
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$282$$ 0 0
$$283$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 3.00000 3.00000
$$290$$ 0 0
$$291$$ 1.00000 1.00000
$$292$$ −1.00000 −1.00000
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ −1.00000 −1.00000
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1.00000 1.00000
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 1.00000 1.00000
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −2.00000 −2.00000
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ 0 0
$$326$$ 1.00000 1.00000
$$327$$ 0 0
$$328$$ −1.00000 −1.00000
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ −1.00000 −1.00000
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$338$$ −1.00000 −1.00000
$$339$$ 1.00000 1.00000
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −2.00000 −2.00000
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.00000 1.00000
$$353$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ −1.00000 −1.00000
$$355$$ 0 0
$$356$$ −2.00000 −2.00000
$$357$$ 0 0
$$358$$ −1.00000 −1.00000
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 2.00000 2.00000
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ −1.00000 −1.00000
$$385$$ 0 0
$$386$$ 2.00000 2.00000
$$387$$ 0 0
$$388$$ 1.00000 1.00000
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 −1.00000
$$393$$ −1.00000 −1.00000
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$402$$ −1.00000 −1.00000
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −2.00000 −2.00000
$$409$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$410$$ 0 0
$$411$$ −1.00000 −1.00000
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −1.00000 −1.00000
$$418$$ 0 0
$$419$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 2.00000 2.00000
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 2.00000 2.00000
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2.00000 −2.00000
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ −1.00000 −1.00000
$$433$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 1.00000 1.00000
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$450$$ 0 0
$$451$$ −1.00000 −1.00000
$$452$$ 1.00000 1.00000
$$453$$ 0 0
$$454$$ −1.00000 −1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$458$$ 0 0
$$459$$ −2.00000 −2.00000
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 1.00000 1.00000
$$467$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.00000 −1.00000
$$473$$ −2.00000 −2.00000
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −1.00000 −1.00000
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ −1.00000 −1.00000
$$490$$ 0 0
$$491$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$492$$ 1.00000 1.00000
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 1.00000 1.00000
$$499$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1.00000 1.00000
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.00000 1.00000
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −1.00000
$$513$$ 0 0
$$514$$ −1.00000 −1.00000
$$515$$ 0 0
$$516$$ 2.00000 2.00000
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$522$$ 0 0
$$523$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$524$$ −1.00000 −1.00000
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −1.00000 −1.00000
$$529$$ 1.00000 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 2.00000 2.00000
$$535$$ 0 0
$$536$$ −1.00000 −1.00000
$$537$$ 1.00000 1.00000
$$538$$ 0 0
$$539$$ −1.00000 −1.00000
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −2.00000 −2.00000
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$548$$ −1.00000 −1.00000
$$549$$ 0 0
$$550$$ 1.00000 1.00000
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.00000 −1.00000
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −2.00000 −2.00000
$$562$$ −1.00000 −1.00000
$$563$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.00000 1.00000
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ −3.00000 −3.00000
$$579$$ −2.00000 −2.00000
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −1.00000 −1.00000
$$583$$ 0 0
$$584$$ 1.00000 1.00000
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$588$$ 1.00000 1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$594$$ −1.00000 −1.00000
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ −1.00000 −1.00000
$$601$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ −1.00000 −1.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$618$$ 0 0
$$619$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ 1.00000 1.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ −2.00000 −2.00000
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ 2.00000 2.00000
$$643$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 1.00000 1.00000
$$649$$ −1.00000 −1.00000
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −1.00000 −1.00000
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 1.00000 1.00000
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ −1.00000 −1.00000
$$663$$ 0 0
$$664$$ 1.00000 1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$674$$ −1.00000 −1.00000
$$675$$ −1.00000 −1.00000
$$676$$ 1.00000 1.00000
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ −1.00000 −1.00000
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.00000 1.00000
$$682$$ 0 0
$$683$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 2.00000 2.00000
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 1.00000 1.00000
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 2.00000 2.00000
$$698$$ 0 0
$$699$$ −1.00000 −1.00000
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −1.00000 −1.00000
$$705$$ 0 0
$$706$$ 1.00000 1.00000
$$707$$ 0 0
$$708$$ 1.00000 1.00000
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 2.00000 2.00000
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 1.00000 1.00000
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 1.00000 1.00000
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 4.00000 4.00000
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.00000 −1.00000
$$738$$ 0 0
$$739$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −2.00000 −2.00000
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ −1.00000 −1.00000
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 2.00000 2.00000
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−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
$$768$$ 1.00000 1.00000
$$769$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$770$$ 0 0
$$771$$ 1.00000 1.00000
$$772$$ −2.00000 −2.00000
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −1.00000 −1.00000
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ 0 0
$$786$$ 1.00000 1.00000
$$787$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −1.00000 −1.00000
$$801$$ 0 0
$$802$$ −1.00000 −1.00000
$$803$$ 1.00000 1.00000
$$804$$ 1.00000 1.00000
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$810$$ 0 0
$$811$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 2.00000 2.00000
$$817$$ 0 0
$$818$$ −1.00000 −1.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 1.00000 1.00000
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ −1.00000 −1.00000
$$826$$ 0 0
$$827$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 2.00000 2.00000
$$834$$ 1.00000 1.00000
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −2.00000 −2.00000
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 0 0
$$843$$ 1.00000 1.00000
$$844$$ −2.00000 −2.00000
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ −1.00000 −1.00000
$$850$$ −2.00000 −2.00000
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 2.00000 2.00000
$$857$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$858$$ 0 0
$$859$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 1.00000 1.00000
$$865$$ 0 0
$$866$$ 2.00000 2.00000
$$867$$ 3.00000 3.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ −1.00000 −1.00000
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$882$$ 0 0
$$883$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 1.00000 1.00000
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 1.00000 1.00000
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −1.00000 −1.00000
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 1.00000 1.00000
$$903$$ 0 0
$$904$$ −1.00000 −1.00000
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$908$$ 1.00000 1.00000
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 1.00000 1.00000
$$914$$ 1.00000 1.00000
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 2.00000 2.00000
$$919$$ 0 0 1.00000 $$0$$
−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
$$929$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −1.00000 −1.00000
$$933$$ 0 0
$$934$$ 1.00000 1.00000
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$938$$ 0 0
$$939$$ −1.00000 −1.00000
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 1.00000 1.00000
$$945$$ 0 0
$$946$$ 2.00000 2.00000
$$947$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$978$$ 1.00000 1.00000
$$979$$ 2.00000 2.00000
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −2.00000 −2.00000
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ −1.00000 −1.00000
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 1.00000 1.00000
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −1.00000 −1.00000
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 1.00000 1.00000
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2888.1.f.a.723.1 1
8.3 odd 2 CM 2888.1.f.a.723.1 1
19.2 odd 18 2888.1.u.c.99.1 6
19.3 odd 18 2888.1.u.c.2555.1 6
19.4 even 9 2888.1.u.d.1859.1 6
19.5 even 9 2888.1.u.d.595.1 6
19.6 even 9 2888.1.u.d.2411.1 6
19.7 even 3 2888.1.k.a.2595.1 2
19.8 odd 6 152.1.k.a.83.1 yes 2
19.9 even 9 2888.1.u.d.1867.1 6
19.10 odd 18 2888.1.u.c.1867.1 6
19.11 even 3 2888.1.k.a.2819.1 2
19.12 odd 6 152.1.k.a.11.1 2
19.13 odd 18 2888.1.u.c.2411.1 6
19.14 odd 18 2888.1.u.c.595.1 6
19.15 odd 18 2888.1.u.c.1859.1 6
19.16 even 9 2888.1.u.d.2555.1 6
19.17 even 9 2888.1.u.d.99.1 6
19.18 odd 2 2888.1.f.b.723.1 1
57.8 even 6 1368.1.bz.a.235.1 2
57.50 even 6 1368.1.bz.a.163.1 2
76.27 even 6 608.1.o.a.463.1 2
76.31 even 6 608.1.o.a.239.1 2
95.8 even 12 3800.1.bn.b.1299.1 4
95.12 even 12 3800.1.bn.b.2899.1 4
95.27 even 12 3800.1.bn.b.1299.2 4
95.69 odd 6 3800.1.bd.c.3051.1 2
95.84 odd 6 3800.1.bd.c.1451.1 2
95.88 even 12 3800.1.bn.b.2899.2 4
152.3 even 18 2888.1.u.c.2555.1 6
152.11 odd 6 2888.1.k.a.2819.1 2
152.27 even 6 152.1.k.a.83.1 yes 2
152.35 odd 18 2888.1.u.d.2555.1 6
152.43 odd 18 2888.1.u.d.595.1 6
152.51 even 18 2888.1.u.c.2411.1 6
152.59 even 18 2888.1.u.c.99.1 6
152.67 even 18 2888.1.u.c.1867.1 6
152.69 odd 6 608.1.o.a.239.1 2
152.75 even 2 2888.1.f.b.723.1 1
152.83 odd 6 2888.1.k.a.2595.1 2
152.91 even 18 2888.1.u.c.1859.1 6
152.99 odd 18 2888.1.u.d.1859.1 6
152.107 even 6 152.1.k.a.11.1 2
152.123 odd 18 2888.1.u.d.1867.1 6
152.131 odd 18 2888.1.u.d.99.1 6
152.139 odd 18 2888.1.u.d.2411.1 6
152.141 odd 6 608.1.o.a.463.1 2
152.147 even 18 2888.1.u.c.595.1 6
456.107 odd 6 1368.1.bz.a.163.1 2
456.179 odd 6 1368.1.bz.a.235.1 2
760.27 odd 12 3800.1.bn.b.1299.2 4
760.107 odd 12 3800.1.bn.b.2899.1 4
760.179 even 6 3800.1.bd.c.1451.1 2
760.259 even 6 3800.1.bd.c.3051.1 2
760.483 odd 12 3800.1.bn.b.1299.1 4
760.563 odd 12 3800.1.bn.b.2899.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
152.1.k.a.11.1 2 19.12 odd 6
152.1.k.a.11.1 2 152.107 even 6
152.1.k.a.83.1 yes 2 19.8 odd 6
152.1.k.a.83.1 yes 2 152.27 even 6
608.1.o.a.239.1 2 76.31 even 6
608.1.o.a.239.1 2 152.69 odd 6
608.1.o.a.463.1 2 76.27 even 6
608.1.o.a.463.1 2 152.141 odd 6
1368.1.bz.a.163.1 2 57.50 even 6
1368.1.bz.a.163.1 2 456.107 odd 6
1368.1.bz.a.235.1 2 57.8 even 6
1368.1.bz.a.235.1 2 456.179 odd 6
2888.1.f.a.723.1 1 1.1 even 1 trivial
2888.1.f.a.723.1 1 8.3 odd 2 CM
2888.1.f.b.723.1 1 19.18 odd 2
2888.1.f.b.723.1 1 152.75 even 2
2888.1.k.a.2595.1 2 19.7 even 3
2888.1.k.a.2595.1 2 152.83 odd 6
2888.1.k.a.2819.1 2 19.11 even 3
2888.1.k.a.2819.1 2 152.11 odd 6
2888.1.u.c.99.1 6 19.2 odd 18
2888.1.u.c.99.1 6 152.59 even 18
2888.1.u.c.595.1 6 19.14 odd 18
2888.1.u.c.595.1 6 152.147 even 18
2888.1.u.c.1859.1 6 19.15 odd 18
2888.1.u.c.1859.1 6 152.91 even 18
2888.1.u.c.1867.1 6 19.10 odd 18
2888.1.u.c.1867.1 6 152.67 even 18
2888.1.u.c.2411.1 6 19.13 odd 18
2888.1.u.c.2411.1 6 152.51 even 18
2888.1.u.c.2555.1 6 19.3 odd 18
2888.1.u.c.2555.1 6 152.3 even 18
2888.1.u.d.99.1 6 19.17 even 9
2888.1.u.d.99.1 6 152.131 odd 18
2888.1.u.d.595.1 6 19.5 even 9
2888.1.u.d.595.1 6 152.43 odd 18
2888.1.u.d.1859.1 6 19.4 even 9
2888.1.u.d.1859.1 6 152.99 odd 18
2888.1.u.d.1867.1 6 19.9 even 9
2888.1.u.d.1867.1 6 152.123 odd 18
2888.1.u.d.2411.1 6 19.6 even 9
2888.1.u.d.2411.1 6 152.139 odd 18
2888.1.u.d.2555.1 6 19.16 even 9
2888.1.u.d.2555.1 6 152.35 odd 18
3800.1.bd.c.1451.1 2 95.84 odd 6
3800.1.bd.c.1451.1 2 760.179 even 6
3800.1.bd.c.3051.1 2 95.69 odd 6
3800.1.bd.c.3051.1 2 760.259 even 6
3800.1.bn.b.1299.1 4 95.8 even 12
3800.1.bn.b.1299.1 4 760.483 odd 12
3800.1.bn.b.1299.2 4 95.27 even 12
3800.1.bn.b.1299.2 4 760.27 odd 12
3800.1.bn.b.2899.1 4 95.12 even 12
3800.1.bn.b.2899.1 4 760.107 odd 12
3800.1.bn.b.2899.2 4 95.88 even 12
3800.1.bn.b.2899.2 4 760.563 odd 12