# Properties

 Label 1521.4.a.g.1.1 Level $1521$ Weight $4$ Character 1521.1 Self dual yes Analytic conductor $89.742$ Analytic rank $0$ Dimension $1$ CM discriminant -3 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1521,4,Mod(1,1521)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1521, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1521.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1521 = 3^{2} \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1521.a (trivial)

## 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: $$89.7419051187$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 9) Fricke sign: $$+1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1521.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-8.00000 q^{4} -20.0000 q^{7} +O(q^{10})$$ $$q-8.00000 q^{4} -20.0000 q^{7} +64.0000 q^{16} -56.0000 q^{19} -125.000 q^{25} +160.000 q^{28} -308.000 q^{31} -110.000 q^{37} -520.000 q^{43} +57.0000 q^{49} +182.000 q^{61} -512.000 q^{64} +880.000 q^{67} -1190.00 q^{73} +448.000 q^{76} +884.000 q^{79} +1330.00 q^{97} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$3$$ 0 0
$$4$$ −8.00000 −1.00000
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −20.0000 −1.07990 −0.539949 0.841698i $$-0.681557\pi$$
−0.539949 + 0.841698i $$0.681557\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 0 0
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 64.0000 1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ −56.0000 −0.676173 −0.338086 0.941115i $$-0.609780\pi$$
−0.338086 + 0.941115i $$0.609780\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −125.000 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 160.000 1.07990
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −308.000 −1.78447 −0.892233 0.451576i $$-0.850862\pi$$
−0.892233 + 0.451576i $$0.850862\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −110.000 −0.488754 −0.244377 0.969680i $$-0.578583\pi$$
−0.244377 + 0.969680i $$0.578583\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −520.000 −1.84417 −0.922084 0.386989i $$-0.873515\pi$$
−0.922084 + 0.386989i $$0.873515\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 57.0000 0.166181
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 182.000 0.382012 0.191006 0.981589i $$-0.438825\pi$$
0.191006 + 0.981589i $$0.438825\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −512.000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 880.000 1.60461 0.802307 0.596912i $$-0.203606\pi$$
0.802307 + 0.596912i $$0.203606\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −1190.00 −1.90793 −0.953966 0.299916i $$-0.903041\pi$$
−0.953966 + 0.299916i $$0.903041\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 448.000 0.676173
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 884.000 1.25896 0.629480 0.777017i $$-0.283268\pi$$
0.629480 + 0.777017i $$0.283268\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 1330.00 1.39218 0.696088 0.717957i $$-0.254922\pi$$
0.696088 + 0.717957i $$0.254922\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 1000.00 1.00000
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 1820.00 1.74107 0.870534 0.492109i $$-0.163774\pi$$
0.870534 + 0.492109i $$0.163774\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 646.000 0.567666 0.283833 0.958874i $$-0.408394\pi$$
0.283833 + 0.958874i $$0.408394\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1280.00 −1.07990
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1331.00 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 2464.00 1.78447
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 380.000 0.265508 0.132754 0.991149i $$-0.457618\pi$$
0.132754 + 0.991149i $$0.457618\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 1120.00 0.730198
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ 2576.00 1.57190 0.785948 0.618293i $$-0.212175\pi$$
0.785948 + 0.618293i $$0.212175\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 880.000 0.488754
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ −1748.00 −0.942054 −0.471027 0.882119i $$-0.656117\pi$$
−0.471027 + 0.882119i $$0.656117\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −3850.00 −1.95709 −0.978546 0.206028i $$-0.933946\pi$$
−0.978546 + 0.206028i $$0.933946\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 3400.00 1.63379 0.816897 0.576783i $$-0.195692\pi$$
0.816897 + 0.576783i $$0.195692\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 4160.00 1.84417
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 2500.00 1.07990
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 3458.00 1.42006 0.710031 0.704171i $$-0.248681\pi$$
0.710031 + 0.704171i $$0.248681\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 1150.00 0.428906 0.214453 0.976734i $$-0.431203\pi$$
0.214453 + 0.976734i $$0.431203\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −456.000 −0.166181
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ −5236.00 −1.86518 −0.932588 0.360942i $$-0.882455\pi$$
−0.932588 + 0.360942i $$0.882455\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 6032.00 1.96806 0.984028 0.178011i $$-0.0569664\pi$$
0.984028 + 0.178011i $$0.0569664\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 6160.00 1.92704
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 3220.00 0.966938 0.483469 0.875362i $$-0.339377\pi$$
0.483469 + 0.875362i $$0.339377\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ −4466.00 −1.28874 −0.644370 0.764714i $$-0.722880\pi$$
−0.644370 + 0.764714i $$0.722880\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 7378.00 1.97203 0.986014 0.166662i $$-0.0532990\pi$$
0.986014 + 0.166662i $$0.0532990\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ −1456.00 −0.382012
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 4096.00 1.00000
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 2200.00 0.527804
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −7040.00 −1.60461
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ −812.000 −0.182013 −0.0910064 0.995850i $$-0.529008\pi$$
−0.0910064 + 0.995850i $$0.529008\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −4030.00 −0.874149 −0.437074 0.899425i $$-0.643985\pi$$
−0.437074 + 0.899425i $$0.643985\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ 5600.00 1.17627 0.588137 0.808761i $$-0.299862\pi$$
0.588137 + 0.808761i $$0.299862\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4913.00 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 9520.00 1.90793
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 10400.0 1.99152
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −3584.00 −0.676173
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −10640.0 −1.97804 −0.989018 0.147797i $$-0.952782\pi$$
−0.989018 + 0.147797i $$0.952782\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 10010.0 1.80766 0.903832 0.427888i $$-0.140742\pi$$
0.903832 + 0.427888i $$0.140742\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −7072.00 −1.25896
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −992.000 −0.164729 −0.0823644 0.996602i $$-0.526247\pi$$
−0.0823644 + 0.996602i $$0.526247\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −4930.00 −0.796897 −0.398448 0.917191i $$-0.630451\pi$$
−0.398448 + 0.917191i $$0.630451\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 5720.00 0.900440
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 11914.0 1.82734 0.913670 0.406456i $$-0.133236\pi$$
0.913670 + 0.406456i $$0.133236\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −3723.00 −0.542790
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4340.00 0.617292 0.308646 0.951177i $$-0.400124\pi$$
0.308646 + 0.951177i $$0.400124\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 12350.0 1.71437 0.857183 0.515011i $$-0.172212\pi$$
0.857183 + 0.515011i $$0.172212\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8584.00 1.16340 0.581702 0.813402i $$-0.302387\pi$$
0.581702 + 0.813402i $$0.302387\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ −10640.0 −1.39218
$$389$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1190.00 −0.150439 −0.0752196 0.997167i $$-0.523966\pi$$
−0.0752196 + 0.997167i $$0.523966\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −8000.00 −1.00000
$$401$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −8246.00 −0.996916 −0.498458 0.866914i $$-0.666100\pi$$
−0.498458 + 0.866914i $$0.666100\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −14560.0 −1.74107
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ −17138.0 −1.98398 −0.991989 0.126322i $$-0.959683\pi$$
−0.991989 + 0.126322i $$0.959683\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −3640.00 −0.412534
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ −2590.00 −0.287454 −0.143727 0.989617i $$-0.545909\pi$$
−0.143727 + 0.989617i $$0.545909\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −5168.00 −0.567666
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 14924.0 1.62251 0.811257 0.584690i $$-0.198784\pi$$
0.811257 + 0.584690i $$0.198784\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 10240.0 1.07990
$$449$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −12710.0 −1.30098 −0.650491 0.759514i $$-0.725437\pi$$
−0.650491 + 0.759514i $$0.725437\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ 19780.0 1.98543 0.992716 0.120482i $$-0.0384440\pi$$
0.992716 + 0.120482i $$0.0384440\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ −17600.0 −1.73282
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 7000.00 0.676173
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 10648.0 1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −20900.0 −1.94470 −0.972351 0.233526i $$-0.924974\pi$$
−0.972351 + 0.233526i $$0.924974\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −19712.0 −1.78447
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 15136.0 1.35788 0.678938 0.734195i $$-0.262440\pi$$
0.678938 + 0.734195i $$0.262440\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ −3040.00 −0.265508
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 23800.0 2.06037
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ −12040.0 −1.00664 −0.503320 0.864100i $$-0.667888\pi$$
−0.503320 + 0.864100i $$0.667888\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −12167.0 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −8960.00 −0.730198
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 22678.0 1.80222 0.901112 0.433586i $$-0.142752\pi$$
0.901112 + 0.433586i $$0.142752\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 1640.00 0.128193 0.0640963 0.997944i $$-0.479584\pi$$
0.0640963 + 0.997944i $$0.479584\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −17680.0 −1.35955
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −20608.0 −1.57190
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$570$$ 0 0
$$571$$ 23312.0 1.70854 0.854270 0.519829i $$-0.174004\pi$$
0.854270 + 0.519829i $$0.174004\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 17710.0 1.27778 0.638888 0.769300i $$-0.279395\pi$$
0.638888 + 0.769300i $$0.279395\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 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 $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 17248.0 1.20661
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −7040.00 −0.488754
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −29302.0 −1.98877 −0.994387 0.105801i $$-0.966259\pi$$
−0.994387 + 0.105801i $$0.966259\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 13984.0 0.942054
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −28420.0 −1.90038 −0.950191 0.311667i $$-0.899113\pi$$
−0.950191 + 0.311667i $$0.899113\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −17390.0 −1.14580 −0.572900 0.819625i $$-0.694182\pi$$
−0.572900 + 0.819625i $$0.694182\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 26656.0 1.73085 0.865424 0.501040i $$-0.167049\pi$$
0.865424 + 0.501040i $$0.167049\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15625.0 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 30800.0 1.95709
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1892.00 −0.119365 −0.0596825 0.998217i $$-0.519009\pi$$
−0.0596825 + 0.998217i $$0.519009\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ −13160.0 −0.807122 −0.403561 0.914953i $$-0.632228\pi$$
−0.403561 + 0.914953i $$0.632228\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −27200.0 −1.63379
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 20482.0 1.20523 0.602615 0.798032i $$-0.294125\pi$$
0.602615 + 0.798032i $$0.294125\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 24050.0 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ −26600.0 −1.50341
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −33280.0 −1.84417
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 16072.0 0.884816 0.442408 0.896814i $$-0.354124\pi$$
0.442408 + 0.896814i $$0.354124\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ −20000.0 −1.07990
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 6160.00 0.330482
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −36146.0 −1.91466 −0.957328 0.289003i $$-0.906676\pi$$
−0.957328 + 0.289003i $$0.906676\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −36400.0 −1.88018
$$722$$ 0 0
$$723$$ 0 0
$$724$$ −27664.0 −1.42006
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −10780.0 −0.549942 −0.274971 0.961452i $$-0.588668\pi$$
−0.274971 + 0.961452i $$0.588668\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −15050.0 −0.758369 −0.379184 0.925321i $$-0.623795\pi$$
−0.379184 + 0.925321i $$0.623795\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −31376.0 −1.56182 −0.780910 0.624644i $$-0.785244\pi$$
−0.780910 + 0.624644i $$0.785244\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −23452.0 −1.13951 −0.569757 0.821813i $$-0.692963\pi$$
−0.569757 + 0.821813i $$0.692963\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −41470.0 −1.99109 −0.995543 0.0943039i $$-0.969937\pi$$
−0.995543 + 0.0943039i $$0.969937\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ −12920.0 −0.613022
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 4606.00 0.215990 0.107995 0.994151i $$-0.465557\pi$$
0.107995 + 0.994151i $$0.465557\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −9200.00 −0.428906
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 38500.0 1.78447
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 3648.00 0.166181
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −43400.0 −1.96575 −0.982874 0.184281i $$-0.941004\pi$$
−0.982874 + 0.184281i $$0.941004\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 41888.0 1.86518
$$797$$ 0 0 1.00000i $$-0.5\pi$$
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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$810$$ 0 0
$$811$$ −39368.0 −1.70456 −0.852280 0.523087i $$-0.824780\pi$$
−0.852280 + 0.523087i $$0.824780\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 29120.0 1.24698
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ −12220.0 −0.517573 −0.258786 0.965935i $$-0.583323\pi$$
−0.258786 + 0.965935i $$0.583323\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 17066.0 0.714990 0.357495 0.933915i $$-0.383631\pi$$
0.357495 + 0.933915i $$0.383631\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −24389.0 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ −48256.0 −1.96806
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 26620.0 1.07990
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 46690.0 1.87413 0.937066 0.349151i $$-0.113530\pi$$
0.937066 + 0.349151i $$0.113530\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 31304.0 1.24340 0.621699 0.783256i $$-0.286443\pi$$
0.621699 + 0.783256i $$0.286443\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ −49280.0 −1.92704
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −50150.0 −1.93095 −0.965476 0.260491i $$-0.916115\pi$$
−0.965476 + 0.260491i $$0.916115\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ −20680.0 −0.788151 −0.394076 0.919078i $$-0.628935\pi$$
−0.394076 + 0.919078i $$0.628935\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ −7600.00 −0.286722
$$890$$ 0 0
$$891$$ 0 0
$$892$$ −25760.0 −0.966938
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 44840.0 1.64155 0.820776 0.571250i $$-0.193541\pi$$
0.820776 + 0.571250i $$0.193541\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 35728.0 1.28874
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 2756.00 0.0989250 0.0494625 0.998776i $$-0.484249\pi$$
0.0494625 + 0.998776i $$0.484249\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 13750.0 0.488754
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ −3192.00 −0.112367
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −55510.0 −1.93536 −0.967680 0.252181i $$-0.918852\pi$$
−0.967680 + 0.252181i $$0.918852\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 65073.0 2.18432
$$962$$ 0 0
$$963$$ 0 0
$$964$$ −59024.0 −1.97203
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 50020.0 1.66343 0.831714 0.555204i $$-0.187360\pi$$
0.831714 + 0.555204i $$0.187360\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −51520.0 −1.69749
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 11648.0 0.382012
$$977$$ 0 0 1.00000i $$-0.5\pi$$
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 $$-0.5\pi$$
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
$$991$$ −45628.0 −1.46258 −0.731292 0.682064i $$-0.761082\pi$$
−0.731292 + 0.682064i $$0.761082\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 28910.0 0.918344 0.459172 0.888347i $$-0.348146\pi$$
0.459172 + 0.888347i $$0.348146\pi$$
$$998$$ 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 1521.4.a.g.1.1 1
3.2 odd 2 CM 1521.4.a.g.1.1 1
13.12 even 2 9.4.a.a.1.1 1
39.38 odd 2 9.4.a.a.1.1 1
52.51 odd 2 144.4.a.d.1.1 1
65.12 odd 4 225.4.b.g.199.2 2
65.38 odd 4 225.4.b.g.199.1 2
65.64 even 2 225.4.a.d.1.1 1
91.12 odd 6 441.4.e.j.361.1 2
91.25 even 6 441.4.e.i.226.1 2
91.38 odd 6 441.4.e.j.226.1 2
91.51 even 6 441.4.e.i.361.1 2
91.90 odd 2 441.4.a.f.1.1 1
104.51 odd 2 576.4.a.l.1.1 1
104.77 even 2 576.4.a.m.1.1 1
117.25 even 6 81.4.c.b.28.1 2
117.38 odd 6 81.4.c.b.28.1 2
117.77 odd 6 81.4.c.b.55.1 2
117.103 even 6 81.4.c.b.55.1 2
143.142 odd 2 1089.4.a.g.1.1 1
156.155 even 2 144.4.a.d.1.1 1
195.38 even 4 225.4.b.g.199.1 2
195.77 even 4 225.4.b.g.199.2 2
195.194 odd 2 225.4.a.d.1.1 1
273.38 even 6 441.4.e.j.226.1 2
273.116 odd 6 441.4.e.i.226.1 2
273.194 even 6 441.4.e.j.361.1 2
273.233 odd 6 441.4.e.i.361.1 2
273.272 even 2 441.4.a.f.1.1 1
312.77 odd 2 576.4.a.m.1.1 1
312.155 even 2 576.4.a.l.1.1 1
429.428 even 2 1089.4.a.g.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
9.4.a.a.1.1 1 13.12 even 2
9.4.a.a.1.1 1 39.38 odd 2
81.4.c.b.28.1 2 117.25 even 6
81.4.c.b.28.1 2 117.38 odd 6
81.4.c.b.55.1 2 117.77 odd 6
81.4.c.b.55.1 2 117.103 even 6
144.4.a.d.1.1 1 52.51 odd 2
144.4.a.d.1.1 1 156.155 even 2
225.4.a.d.1.1 1 65.64 even 2
225.4.a.d.1.1 1 195.194 odd 2
225.4.b.g.199.1 2 65.38 odd 4
225.4.b.g.199.1 2 195.38 even 4
225.4.b.g.199.2 2 65.12 odd 4
225.4.b.g.199.2 2 195.77 even 4
441.4.a.f.1.1 1 91.90 odd 2
441.4.a.f.1.1 1 273.272 even 2
441.4.e.i.226.1 2 91.25 even 6
441.4.e.i.226.1 2 273.116 odd 6
441.4.e.i.361.1 2 91.51 even 6
441.4.e.i.361.1 2 273.233 odd 6
441.4.e.j.226.1 2 91.38 odd 6
441.4.e.j.226.1 2 273.38 even 6
441.4.e.j.361.1 2 91.12 odd 6
441.4.e.j.361.1 2 273.194 even 6
576.4.a.l.1.1 1 104.51 odd 2
576.4.a.l.1.1 1 312.155 even 2
576.4.a.m.1.1 1 104.77 even 2
576.4.a.m.1.1 1 312.77 odd 2
1089.4.a.g.1.1 1 143.142 odd 2
1089.4.a.g.1.1 1 429.428 even 2
1521.4.a.g.1.1 1 1.1 even 1 trivial
1521.4.a.g.1.1 1 3.2 odd 2 CM