# Properties

 Label 2200.1.d.c.901.1 Level $2200$ Weight $1$ Character 2200.901 Self dual yes Analytic conductor $1.098$ Analytic rank $0$ Dimension $1$ Projective image $D_{3}$ CM discriminant -88 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2200,1,Mod(901,2200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2200.901");

S:= CuspForms(chi, 1);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2200 = 2^{3} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2200.d (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: $$1.09794302779$$ 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 3.1.2200.1 Artin image: $D_6$ Artin field: Galois closure of 6.2.193600000.1

## Embedding invariants

 Embedding label 901.1 Character $$\chi$$ $$=$$ 2200.9

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} -1.00000 q^{13} +1.00000 q^{16} +1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{26} +1.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} +1.00000 q^{36} +1.00000 q^{38} -1.00000 q^{43} -1.00000 q^{44} +1.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} -1.00000 q^{52} +1.00000 q^{58} -2.00000 q^{61} -1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{71} +1.00000 q^{72} +1.00000 q^{76} +1.00000 q^{81} -1.00000 q^{83} -1.00000 q^{86} -1.00000 q^{88} -1.00000 q^{89} +1.00000 q^{92} -2.00000 q^{94} +1.00000 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2200\mathbb{Z}\right)^\times$$.

 $$n$$ $$177$$ $$551$$ $$1101$$ $$1201$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$-1$$

## 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 1.00000 1.00000
$$9$$ 1.00000 1.00000
$$10$$ 0 0
$$11$$ −1.00000 −1.00000
$$12$$ 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
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 1.00000 1.00000
$$19$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$20$$ 0 0
$$21$$ 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
$$25$$ 0 0
$$26$$ −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
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 1.00000 1.00000
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 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
$$47$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ −1.00000 −1.00000
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 1.00000 1.00000
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$62$$ −1.00000 −1.00000
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$72$$ 1.00000 1.00000
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.00000 1.00000
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ 0 0
$$83$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −1.00000 −1.00000
$$87$$ 0 0
$$88$$ −1.00000 −1.00000
$$89$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.00000 1.00000
$$93$$ 0 0
$$94$$ −2.00000 −2.00000
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$98$$ 1.00000 1.00000
$$99$$ −1.00000 −1.00000
$$100$$ 0 0
$$101$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$102$$ 0 0
$$103$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$104$$ −1.00000 −1.00000
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$108$$ 0 0
$$109$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.00000 1.00000
$$117$$ −1.00000 −1.00000
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ −2.00000 −2.00000
$$123$$ 0 0
$$124$$ −1.00000 −1.00000
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 1.00000 1.00000
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0 0
$$139$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −1.00000 −1.00000
$$143$$ 1.00000 1.00000
$$144$$ 1.00000 1.00000
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 1.00000 1.00000
$$153$$ 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
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −1.00000 −1.00000
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 1.00000 1.00000
$$172$$ −1.00000 −1.00000
$$173$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −1.00000 −1.00000
$$177$$ 0 0
$$178$$ −1.00000 −1.00000
$$179$$ 0 0 1.00000 $$0$$
−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
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −2.00000 −2.00000
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 1.00000 1.00000
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$198$$ −1.00000 −1.00000
$$199$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 1.00000 1.00000
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.00000 1.00000
$$207$$ 1.00000 1.00000
$$208$$ −1.00000 −1.00000
$$209$$ −1.00000 −1.00000
$$210$$ 0 0
$$211$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −1.00000 −1.00000
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 1.00000 1.00000
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −2.00000 −2.00000
$$227$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.00000 1.00000
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ −1.00000 −1.00000
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.00000 1.00000
$$243$$ 0 0
$$244$$ −2.00000 −2.00000
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.00000 −1.00000
$$248$$ −1.00000 −1.00000
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 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
$$260$$ 0 0
$$261$$ 1.00000 1.00000
$$262$$ 1.00000 1.00000
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 1.00000 1.00000
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$278$$ 1.00000 1.00000
$$279$$ −1.00000 −1.00000
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$284$$ −1.00000 −1.00000
$$285$$ 0 0
$$286$$ 1.00000 1.00000
$$287$$ 0 0
$$288$$ 1.00000 1.00000
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −2.00000 −2.00000
$$299$$ −1.00000 −1.00000
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 1.00000 1.00000
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ −1.00000 −1.00000
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ −1.00000 −1.00000
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.00000 1.00000
$$342$$ 1.00000 1.00000
$$343$$ 0 0
$$344$$ −1.00000 −1.00000
$$345$$ 0 0
$$346$$ −1.00000 −1.00000
$$347$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$348$$ 0 0
$$349$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 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
$$356$$ −1.00000 −1.00000
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 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
$$367$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$368$$ 1.00000 1.00000
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −2.00000 −2.00000
$$377$$ −1.00000 −1.00000
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −1.00000 −1.00000
$$383$$ 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
$$387$$ −1.00000 −1.00000
$$388$$ 1.00000 1.00000
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 1.00000
$$393$$ 0 0
$$394$$ −1.00000 −1.00000
$$395$$ 0 0
$$396$$ −1.00000 −1.00000
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ −1.00000 −1.00000
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0 0
$$403$$ 1.00000 1.00000
$$404$$ 1.00000 1.00000
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 1.00000 1.00000
$$413$$ 0 0
$$414$$ 1.00000 1.00000
$$415$$ 0 0
$$416$$ −1.00000 −1.00000
$$417$$ 0 0
$$418$$ −1.00000 −1.00000
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ −2.00000 −2.00000
$$423$$ −2.00000 −2.00000
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −1.00000 −1.00000
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 1.00000 1.00000
$$437$$ 1.00000 1.00000
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −2.00000 −2.00000
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −2.00000 −2.00000
$$453$$ 0 0
$$454$$ −1.00000 −1.00000
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$464$$ 1.00000 1.00000
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ −1.00000 −1.00000
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 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
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$488$$ −2.00000 −2.00000
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −1.00000 −1.00000
$$495$$ 0 0
$$496$$ −1.00000 −1.00000
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −1.00000 −1.00000
$$507$$ 0 0
$$508$$ 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
$$516$$ 0 0
$$517$$ 2.00000 2.00000
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 1.00000 1.00000
$$523$$ −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
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −1.00000 −1.00000
$$540$$ 0 0
$$541$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$548$$ 1.00000 1.00000
$$549$$ −2.00000 −2.00000
$$550$$ 0 0
$$551$$ 1.00000 1.00000
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 2.00000 2.00000
$$555$$ 0 0
$$556$$ 1.00000 1.00000
$$557$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ −1.00000 −1.00000
$$559$$ 1.00000 1.00000
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 2.00000 2.00000
$$567$$ 0 0
$$568$$ −1.00000 −1.00000
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 1.00000 1.00000
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 1.00000
$$577$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$578$$ 1.00000 1.00000
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 2.00000 2.00000
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ −1.00000 −1.00000
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −2.00000 −2.00000
$$597$$ 0 0
$$598$$ −1.00000 −1.00000
$$599$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 1.00000 1.00000
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 2.00000 2.00000
$$612$$ 0 0
$$613$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$614$$ 2.00000 2.00000
$$615$$ 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 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −1.00000 −1.00000
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −2.00000 −2.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1.00000 −1.00000
$$638$$ −1.00000 −1.00000
$$639$$ −1.00000 −1.00000
$$640$$ 0 0
$$641$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$648$$ 1.00000 1.00000
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −1.00000 −1.00000
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000 1.00000
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 2.00000 2.00000
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 1.00000 1.00000
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 1.00000 1.00000
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.00000 −1.00000
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ −1.00000 −1.00000
$$693$$ 0 0
$$694$$ 2.00000 2.00000
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 1.00000 1.00000
$$699$$ 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
$$712$$ −1.00000 −1.00000
$$713$$ −1.00000 −1.00000
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$734$$ 1.00000 1.00000
$$735$$ 0 0
$$736$$ 1.00000 1.00000
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 2.00000 2.00000
$$747$$ −1.00000 −1.00000
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$752$$ −2.00000 −2.00000
$$753$$ 0 0
$$754$$ −1.00000 −1.00000
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ −1.00000 −1.00000
$$765$$ 0 0
$$766$$ 1.00000 1.00000
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ −1.00000 −1.00000
$$775$$ 0 0
$$776$$ 1.00000 1.00000
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 1.00000 1.00000
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 1.00000 1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$788$$ −1.00000 −1.00000
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −1.00000 −1.00000
$$793$$ 2.00000 2.00000
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −1.00000 −1.00000
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −1.00000 −1.00000
$$802$$ −1.00000 −1.00000
$$803$$ 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
$$811$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −1.00000 −1.00000
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$822$$ 0 0
$$823$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$824$$ 1.00000 1.00000
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$828$$ 1.00000 1.00000
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −1.00000
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −1.00000 −1.00000
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$840$$ 0 0
$$841$$ 0 0
$$842$$ 0 0
$$843$$ 0 0
$$844$$ −2.00000 −2.00000
$$845$$ 0 0
$$846$$ −2.00000 −2.00000
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ −1.00000 −1.00000
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 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
$$866$$ 1.00000 1.00000
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 1.00000 1.00000
$$873$$ 1.00000 1.00000
$$874$$ 1.00000 1.00000
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$882$$ 1.00000 1.00000
$$883$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ −1.00000 −1.00000
$$892$$ −2.00000 −2.00000
$$893$$ −2.00000 −2.00000
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −1.00000 −1.00000
$$899$$ −1.00000 −1.00000
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −2.00000 −2.00000
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ −1.00000 −1.00000
$$909$$ 1.00000 1.00000
$$910$$ 0 0
$$911$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$912$$ 0 0
$$913$$ 1.00000 1.00000
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ −2.00000 −2.00000
$$923$$ 1.00000 1.00000
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 1.00000 1.00000
$$927$$ 1.00000 1.00000
$$928$$ 1.00000 1.00000
$$929$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$930$$ 0 0
$$931$$ 1.00000 1.00000
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ −1.00000 −1.00000
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 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
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 0 0
$$962$$ 0 0
$$963$$ −1.00000 −1.00000
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 1.00000 1.00000
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 1.00000 1.00000
$$975$$ 0 0
$$976$$ −2.00000 −2.00000
$$977$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 1.00000 1.00000
$$980$$ 0 0
$$981$$ 1.00000 1.00000
$$982$$ 1.00000 1.00000
$$983$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −1.00000 −1.00000
$$989$$ −1.00000 −1.00000
$$990$$ 0 0
$$991$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$992$$ −1.00000 −1.00000
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$998$$ 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 2200.1.d.c.901.1 yes 1
5.2 odd 4 2200.1.o.a.549.2 2
5.3 odd 4 2200.1.o.a.549.1 2
5.4 even 2 2200.1.d.a.901.1 1
8.5 even 2 2200.1.d.b.901.1 yes 1
11.10 odd 2 2200.1.d.b.901.1 yes 1
40.13 odd 4 2200.1.o.b.549.2 2
40.29 even 2 2200.1.d.d.901.1 yes 1
40.37 odd 4 2200.1.o.b.549.1 2
55.32 even 4 2200.1.o.b.549.1 2
55.43 even 4 2200.1.o.b.549.2 2
55.54 odd 2 2200.1.d.d.901.1 yes 1
88.21 odd 2 CM 2200.1.d.c.901.1 yes 1
440.109 odd 2 2200.1.d.a.901.1 1
440.197 even 4 2200.1.o.a.549.2 2
440.373 even 4 2200.1.o.a.549.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
2200.1.d.a.901.1 1 5.4 even 2
2200.1.d.a.901.1 1 440.109 odd 2
2200.1.d.b.901.1 yes 1 8.5 even 2
2200.1.d.b.901.1 yes 1 11.10 odd 2
2200.1.d.c.901.1 yes 1 1.1 even 1 trivial
2200.1.d.c.901.1 yes 1 88.21 odd 2 CM
2200.1.d.d.901.1 yes 1 40.29 even 2
2200.1.d.d.901.1 yes 1 55.54 odd 2
2200.1.o.a.549.1 2 5.3 odd 4
2200.1.o.a.549.1 2 440.373 even 4
2200.1.o.a.549.2 2 5.2 odd 4
2200.1.o.a.549.2 2 440.197 even 4
2200.1.o.b.549.1 2 40.37 odd 4
2200.1.o.b.549.1 2 55.32 even 4
2200.1.o.b.549.2 2 40.13 odd 4
2200.1.o.b.549.2 2 55.43 even 4