# Properties

 Label 1080.1.i.a.269.1 Level $1080$ Weight $1$ Character 1080.269 Self dual yes Analytic conductor $0.539$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -120 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,1,Mod(269,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1080.269");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1080 = 2^{3} \cdot 3^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1080.i (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: $$0.538990213644$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{3}$$ Projective field: Galois closure of 3.1.1080.1 Artin image: $D_6$ Artin field: Galois closure of 6.0.3499200.1

## Embedding invariants

 Embedding label 269.1 Character $$\chi$$ $$=$$ 1080.27

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{8} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{20} -1.00000 q^{22} +1.00000 q^{23} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{29} -1.00000 q^{31} -1.00000 q^{32} -1.00000 q^{34} +2.00000 q^{37} +1.00000 q^{40} -1.00000 q^{43} +1.00000 q^{44} -1.00000 q^{46} +1.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} -1.00000 q^{52} -1.00000 q^{55} -1.00000 q^{58} -2.00000 q^{59} +1.00000 q^{62} +1.00000 q^{64} +1.00000 q^{65} +2.00000 q^{67} +1.00000 q^{68} -2.00000 q^{74} -1.00000 q^{79} -1.00000 q^{80} -1.00000 q^{85} +1.00000 q^{86} -1.00000 q^{88} +1.00000 q^{92} -1.00000 q^{94} -1.00000 q^{98} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$$.

 $$n$$ $$217$$ $$271$$ $$541$$ $$1001$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$

## 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
$$3$$ 0 0
$$4$$ 1.00000 1.00000
$$5$$ −1.00000 −1.00000
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 0 0
$$10$$ 1.00000 1.00000
$$11$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ −1.00000 −1.00000
$$21$$ 0 0
$$22$$ −1.00000 −1.00000
$$23$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ 1.00000 1.00000
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ 0 0
$$34$$ −1.00000 −1.00000
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 1.00000 1.00000
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$44$$ 1.00000 1.00000
$$45$$ 0 0
$$46$$ −1.00000 −1.00000
$$47$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ −1.00000 −1.00000
$$51$$ 0 0
$$52$$ −1.00000 −1.00000
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ −1.00000 −1.00000
$$56$$ 0 0
$$57$$ 0 0
$$58$$ −1.00000 −1.00000
$$59$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 1.00000 1.00000
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 1.00000 1.00000
$$66$$ 0 0
$$67$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$68$$ 1.00000 1.00000
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ −2.00000 −2.00000
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$80$$ −1.00000 −1.00000
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ −1.00000 −1.00000
$$86$$ 1.00000 1.00000
$$87$$ 0 0
$$88$$ −1.00000 −1.00000
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.00000 1.00000
$$93$$ 0 0
$$94$$ −1.00000 −1.00000
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −1.00000 −1.00000
$$99$$ 0 0
$$100$$ 1.00000 1.00000
$$101$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 1.00000 1.00000
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 1.00000 1.00000
$$111$$ 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
$$115$$ −1.00000 −1.00000
$$116$$ 1.00000 1.00000
$$117$$ 0 0
$$118$$ 2.00000 2.00000
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 0 0
$$124$$ −1.00000 −1.00000
$$125$$ −1.00000 −1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 0 0
$$130$$ −1.00000 −1.00000
$$131$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −2.00000 −2.00000
$$135$$ 0 0
$$136$$ −1.00000 −1.00000
$$137$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −1.00000 −1.00000
$$144$$ 0 0
$$145$$ −1.00000 −1.00000
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 2.00000 2.00000
$$149$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1.00000 1.00000
$$156$$ 0 0
$$157$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ 1.00000 1.00000
$$159$$ 0 0
$$160$$ 1.00000 1.00000
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 1.00000 1.00000
$$171$$ 0 0
$$172$$ −1.00000 −1.00000
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.00000 1.00000
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −1.00000 −1.00000
$$185$$ −2.00000 −2.00000
$$186$$ 0 0
$$187$$ 1.00000 1.00000
$$188$$ 1.00000 1.00000
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ −1.00000 −1.00000
$$201$$ 0 0
$$202$$ −1.00000 −1.00000
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.00000 −1.00000
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.00000 1.00000
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −1.00000 −1.00000
$$221$$ −1.00000 −1.00000
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1.00000 −1.00000
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 1.00000 1.00000
$$231$$ 0 0
$$232$$ −1.00000 −1.00000
$$233$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ −1.00000 −1.00000
$$236$$ −2.00000 −2.00000
$$237$$ 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 $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.00000 −1.00000
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 1.00000 1.00000
$$249$$ 0 0
$$250$$ 1.00000 1.00000
$$251$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$252$$ 0 0
$$253$$ 1.00000 1.00000
$$254$$ 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 $$0.333333\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 1.00000 1.00000
$$261$$ 0 0
$$262$$ −1.00000 −1.00000
$$263$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 2.00000 2.00000
$$269$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$270$$ 0 0
$$271$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$272$$ 1.00000 1.00000
$$273$$ 0 0
$$274$$ 2.00000 2.00000
$$275$$ 1.00000 1.00000
$$276$$ 0 0
$$277$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 1.00000 1.00000
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 1.00000 1.00000
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 2.00000 2.00000
$$296$$ −2.00000 −2.00000
$$297$$ 0 0
$$298$$ −1.00000 −1.00000
$$299$$ −1.00000 −1.00000
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 1.00000 1.00000
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −1.00000 −1.00000
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 1.00000 1.00000
$$315$$ 0 0
$$316$$ −1.00000 −1.00000
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 1.00000 1.00000
$$320$$ −1.00000 −1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −1.00000 −1.00000
$$326$$ 1.00000 1.00000
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 2.00000 2.00000
$$335$$ −2.00000 −2.00000
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ −1.00000 −1.00000
$$341$$ −1.00000 −1.00000
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 1.00000 1.00000
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 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 $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 2.00000 2.00000
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 1.00000 1.00000
$$369$$ 0 0
$$370$$ 2.00000 2.00000
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ −1.00000 −1.00000
$$375$$ 0 0
$$376$$ −1.00000 −1.00000
$$377$$ −1.00000 −1.00000
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 1.00000 1.00000
$$392$$ −1.00000 −1.00000
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 1.00000 1.00000
$$396$$ 0 0
$$397$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$398$$ 1.00000 1.00000
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 1.00000 1.00000
$$404$$ 1.00000 1.00000
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.00000 2.00000
$$408$$ 0 0
$$409$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 1.00000 1.00000
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.00000 1.00000
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ −1.00000 −1.00000
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$440$$ 1.00000 1.00000
$$441$$ 0 0
$$442$$ 1.00000 1.00000
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 1.00000 1.00000
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ −1.00000 −1.00000
$$461$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 1.00000 1.00000
$$465$$ 0 0
$$466$$ 2.00000 2.00000
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 1.00000 1.00000
$$471$$ 0 0
$$472$$ 2.00000 2.00000
$$473$$ −1.00000 −1.00000
$$474$$ 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
$$481$$ −2.00000 −2.00000
$$482$$ 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
$$489$$ 0 0
$$490$$ 1.00000 1.00000
$$491$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 1.00000 1.00000
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −1.00000 −1.00000
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ −1.00000 −1.00000
$$501$$ 0 0
$$502$$ −1.00000 −1.00000
$$503$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$504$$ 0 0
$$505$$ −1.00000 −1.00000
$$506$$ −1.00000 −1.00000
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −1.00000
$$513$$ 0 0
$$514$$ −1.00000 −1.00000
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 1.00000 1.00000
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −1.00000 −1.00000
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$524$$ 1.00000 1.00000
$$525$$ 0 0
$$526$$ 2.00000 2.00000
$$527$$ −1.00000 −1.00000
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −2.00000 −2.00000
$$537$$ 0 0
$$538$$ −1.00000 −1.00000
$$539$$ 1.00000 1.00000
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ −2.00000 −2.00000
$$543$$ 0 0
$$544$$ −1.00000 −1.00000
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$548$$ −2.00000 −2.00000
$$549$$ 0 0
$$550$$ −1.00000 −1.00000
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −2.00000 −2.00000
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 1.00000 1.00000
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ −1.00000 −1.00000
$$566$$ −2.00000 −2.00000
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ −1.00000 −1.00000
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.00000 1.00000
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ −1.00000 −1.00000
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −2.00000 −2.00000
$$591$$ 0 0
$$592$$ 2.00000 2.00000
$$593$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1.00000 1.00000
$$597$$ 0 0
$$598$$ 1.00000 1.00000
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1.00000 −1.00000
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −1.00000 −1.00000
$$612$$ 0 0
$$613$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 1.00000 1.00000
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 1.00000 1.00000
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −1.00000 −1.00000
$$629$$ 2.00000 2.00000
$$630$$ 0 0
$$631$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$632$$ 1.00000 1.00000
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1.00000 −1.00000
$$638$$ −1.00000 −1.00000
$$639$$ 0 0
$$640$$ 1.00000 1.00000
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −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
$$647$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ −2.00000 −2.00000
$$650$$ 1.00000 1.00000
$$651$$ 0 0
$$652$$ −1.00000 −1.00000
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ −1.00000 −1.00000
$$656$$ 0 0
$$657$$ 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 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000 1.00000
$$668$$ −2.00000 −2.00000
$$669$$ 0 0
$$670$$ 2.00000 2.00000
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 1.00000 1.00000
$$681$$ 0 0
$$682$$ 1.00000 1.00000
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 2.00000 2.00000
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.00000 −1.00000
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.00000 1.00000
$$705$$ 0 0
$$706$$ −1.00000 −1.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −1.00000 −1.00000
$$714$$ 0 0
$$715$$ 1.00000 1.00000
$$716$$ −2.00000 −2.00000
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −1.00000 −1.00000
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 1.00000 1.00000
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −1.00000 −1.00000
$$732$$ 0 0
$$733$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −1.00000 −1.00000
$$737$$ 2.00000 2.00000
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ −2.00000 −2.00000
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$744$$ 0 0
$$745$$ −1.00000 −1.00000
$$746$$ 1.00000 1.00000
$$747$$ 0 0
$$748$$ 1.00000 1.00000
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ 1.00000 1.00000
$$753$$ 0 0
$$754$$ 1.00000 1.00000
$$755$$ 1.00000 1.00000
$$756$$ 0 0
$$757$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −1.00000 −1.00000
$$767$$ 2.00000 2.00000
$$768$$ 0 0
$$769$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ −1.00000 −1.00000
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.00000 −1.00000
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ −1.00000 −1.00000
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ 1.00000 1.00000
$$786$$ 0 0
$$787$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ −1.00000 −1.00000
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 1.00000 1.00000
$$795$$ 0 0
$$796$$ −1.00000 −1.00000
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 1.00000 1.00000
$$800$$ −1.00000 −1.00000
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ −1.00000 −1.00000
$$807$$ 0 0
$$808$$ −1.00000 −1.00000
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ −2.00000 −2.00000
$$815$$ 1.00000 1.00000
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 1.00000 1.00000
$$819$$ 0 0
$$820$$ 0 0
$$821$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −1.00000
$$833$$ 1.00000 1.00000
$$834$$ 0 0
$$835$$ 2.00000 2.00000
$$836$$ 0 0
$$837$$ 0 0
$$838$$ −1.00000 −1.00000
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 0 0
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ −1.00000 −1.00000
$$851$$ 2.00000 2.00000
$$852$$ 0 0
$$853$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 1.00000 1.00000
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −1.00000 −1.00000
$$870$$ 0 0
$$871$$ −2.00000 −2.00000
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$878$$ −2.00000 −2.00000
$$879$$ 0 0
$$880$$ −1.00000 −1.00000
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$884$$ −1.00000 −1.00000
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 2.00000 2.00000
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ −1.00000 −1.00000
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −1.00000 −1.00000
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$920$$ 1.00000 1.00000
$$921$$ 0 0
$$922$$ 2.00000 2.00000
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 2.00000 2.00000
$$926$$ 0 0
$$927$$ 0 0
$$928$$ −1.00000 −1.00000
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ −2.00000 −2.00000
$$933$$ 0 0
$$934$$ 0 0
$$935$$ −1.00000 −1.00000
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ −1.00000 −1.00000
$$941$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ −2.00000 −2.00000
$$945$$ 0 0
$$946$$ 1.00000 1.00000
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 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
$$961$$ 0 0
$$962$$ 2.00000 2.00000
$$963$$ 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 $$0.333333\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ −1.00000 −1.00000
$$981$$ 0 0
$$982$$ 2.00000 2.00000
$$983$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −1.00000 −1.00000
$$987$$ 0 0
$$988$$ 0 0
$$989$$ −1.00000 −1.00000
$$990$$ 0 0
$$991$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$992$$ 1.00000 1.00000
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 1.00000 1.00000
$$996$$ 0 0
$$997$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$998$$ 0 0
$$999$$ 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 1080.1.i.a.269.1 1
3.2 odd 2 1080.1.i.d.269.1 yes 1
5.4 even 2 1080.1.i.c.269.1 yes 1
8.5 even 2 1080.1.i.b.269.1 yes 1
9.2 odd 6 3240.1.bh.a.1349.1 2
9.4 even 3 3240.1.bh.d.269.1 2
9.5 odd 6 3240.1.bh.a.269.1 2
9.7 even 3 3240.1.bh.d.1349.1 2
15.14 odd 2 1080.1.i.b.269.1 yes 1
24.5 odd 2 1080.1.i.c.269.1 yes 1
40.29 even 2 1080.1.i.d.269.1 yes 1
45.4 even 6 3240.1.bh.b.269.1 2
45.14 odd 6 3240.1.bh.c.269.1 2
45.29 odd 6 3240.1.bh.c.1349.1 2
45.34 even 6 3240.1.bh.b.1349.1 2
72.5 odd 6 3240.1.bh.b.269.1 2
72.13 even 6 3240.1.bh.c.269.1 2
72.29 odd 6 3240.1.bh.b.1349.1 2
72.61 even 6 3240.1.bh.c.1349.1 2
120.29 odd 2 CM 1080.1.i.a.269.1 1
360.29 odd 6 3240.1.bh.d.1349.1 2
360.149 odd 6 3240.1.bh.d.269.1 2
360.229 even 6 3240.1.bh.a.269.1 2
360.349 even 6 3240.1.bh.a.1349.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
1080.1.i.a.269.1 1 1.1 even 1 trivial
1080.1.i.a.269.1 1 120.29 odd 2 CM
1080.1.i.b.269.1 yes 1 8.5 even 2
1080.1.i.b.269.1 yes 1 15.14 odd 2
1080.1.i.c.269.1 yes 1 5.4 even 2
1080.1.i.c.269.1 yes 1 24.5 odd 2
1080.1.i.d.269.1 yes 1 3.2 odd 2
1080.1.i.d.269.1 yes 1 40.29 even 2
3240.1.bh.a.269.1 2 9.5 odd 6
3240.1.bh.a.269.1 2 360.229 even 6
3240.1.bh.a.1349.1 2 9.2 odd 6
3240.1.bh.a.1349.1 2 360.349 even 6
3240.1.bh.b.269.1 2 45.4 even 6
3240.1.bh.b.269.1 2 72.5 odd 6
3240.1.bh.b.1349.1 2 45.34 even 6
3240.1.bh.b.1349.1 2 72.29 odd 6
3240.1.bh.c.269.1 2 45.14 odd 6
3240.1.bh.c.269.1 2 72.13 even 6
3240.1.bh.c.1349.1 2 45.29 odd 6
3240.1.bh.c.1349.1 2 72.61 even 6
3240.1.bh.d.269.1 2 9.4 even 3
3240.1.bh.d.269.1 2 360.149 odd 6
3240.1.bh.d.1349.1 2 9.7 even 3
3240.1.bh.d.1349.1 2 360.29 odd 6