# Properties

 Label 176.9.h.a.65.1 Level $176$ Weight $9$ Character 176.65 Self dual yes Analytic conductor $71.699$ Analytic rank $0$ Dimension $1$ CM discriminant -11 Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,9,Mod(65,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("176.65");

S:= CuspForms(chi, 9);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$176 = 2^{4} \cdot 11$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 176.h (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: yes Analytic conductor: $$71.6986353708$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 11) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 65.1 Character $$\chi$$ $$=$$ 176.65

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+113.000 q^{3} +1151.00 q^{5} +6208.00 q^{9} +O(q^{10})$$ $$q+113.000 q^{3} +1151.00 q^{5} +6208.00 q^{9} -14641.0 q^{11} +130063. q^{15} +531793. q^{23} +934176. q^{25} -39889.0 q^{27} +1.54123e6 q^{31} -1.65443e6 q^{33} +716447. q^{37} +7.14541e6 q^{45} +6.08064e6 q^{47} +5.76480e6 q^{49} -1.52654e7 q^{53} -1.68518e7 q^{55} +4.10155e6 q^{59} -1.98068e7 q^{67} +6.00926e7 q^{69} -7.04309e6 q^{71} +1.05562e8 q^{75} -4.52381e7 q^{81} -8.41010e7 q^{89} +1.74159e8 q^{93} -8.11557e7 q^{97} -9.08913e7 q^{99} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$$.

 $$n$$ $$111$$ $$133$$ $$145$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 113.000 1.39506 0.697531 0.716555i $$-0.254282\pi$$
0.697531 + 0.716555i $$0.254282\pi$$
$$4$$ 0 0
$$5$$ 1151.00 1.84160 0.920800 0.390035i $$-0.127537\pi$$
0.920800 + 0.390035i $$0.127537\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ 6208.00 0.946197
$$10$$ 0 0
$$11$$ −14641.0 −1.00000
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 130063. 2.56915
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 531793. 1.90034 0.950170 0.311732i $$-0.100909\pi$$
0.950170 + 0.311732i $$0.100909\pi$$
$$24$$ 0 0
$$25$$ 934176. 2.39149
$$26$$ 0 0
$$27$$ −39889.0 −0.0750582
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 1.54123e6 1.66887 0.834433 0.551109i $$-0.185795\pi$$
0.834433 + 0.551109i $$0.185795\pi$$
$$32$$ 0 0
$$33$$ −1.65443e6 −1.39506
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 716447. 0.382276 0.191138 0.981563i $$-0.438782\pi$$
0.191138 + 0.981563i $$0.438782\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 7.14541e6 1.74252
$$46$$ 0 0
$$47$$ 6.08064e6 1.24611 0.623057 0.782177i $$-0.285890\pi$$
0.623057 + 0.782177i $$0.285890\pi$$
$$48$$ 0 0
$$49$$ 5.76480e6 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −1.52654e7 −1.93467 −0.967333 0.253511i $$-0.918415\pi$$
−0.967333 + 0.253511i $$0.918415\pi$$
$$54$$ 0 0
$$55$$ −1.68518e7 −1.84160
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.10155e6 0.338486 0.169243 0.985574i $$-0.445868\pi$$
0.169243 + 0.985574i $$0.445868\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.98068e7 −0.982911 −0.491456 0.870903i $$-0.663535\pi$$
−0.491456 + 0.870903i $$0.663535\pi$$
$$68$$ 0 0
$$69$$ 6.00926e7 2.65109
$$70$$ 0 0
$$71$$ −7.04309e6 −0.277159 −0.138580 0.990351i $$-0.544254\pi$$
−0.138580 + 0.990351i $$0.544254\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 1.05562e8 3.33628
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ −4.52381e7 −1.05091
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −8.41010e7 −1.34042 −0.670210 0.742171i $$-0.733796\pi$$
−0.670210 + 0.742171i $$0.733796\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 1.74159e8 2.32817
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −8.11557e7 −0.916710 −0.458355 0.888769i $$-0.651561\pi$$
−0.458355 + 0.888769i $$0.651561\pi$$
$$98$$ 0 0
$$99$$ −9.08913e7 −0.946197
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 3.62784e6 0.0322329 0.0161164 0.999870i $$-0.494870\pi$$
0.0161164 + 0.999870i $$0.494870\pi$$
$$104$$ 0 0
$$105$$ 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 $$\pi$$
$$110$$ 0 0
$$111$$ 8.09585e7 0.533299
$$112$$ 0 0
$$113$$ 1.01857e8 0.624710 0.312355 0.949966i $$-0.398882\pi$$
0.312355 + 0.949966i $$0.398882\pi$$
$$114$$ 0 0
$$115$$ 6.12094e8 3.49967
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 2.14359e8 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 6.25627e8 2.56257
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −4.59122e7 −0.138227
$$136$$ 0 0
$$137$$ 3.63889e8 1.03297 0.516484 0.856297i $$-0.327241\pi$$
0.516484 + 0.856297i $$0.327241\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 6.87112e8 1.73841
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 6.51423e8 1.39506
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1.77396e9 3.07338
$$156$$ 0 0
$$157$$ −1.20570e9 −1.98446 −0.992229 0.124428i $$-0.960290\pi$$
−0.992229 + 0.124428i $$0.960290\pi$$
$$158$$ 0 0
$$159$$ −1.72499e9 −2.69898
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −9.15081e8 −1.29631 −0.648155 0.761508i $$-0.724459\pi$$
−0.648155 + 0.761508i $$0.724459\pi$$
$$164$$ 0 0
$$165$$ −1.90425e9 −2.56915
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 8.15731e8 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 4.63475e8 0.472208
$$178$$ 0 0
$$179$$ −1.21779e9 −1.18620 −0.593102 0.805127i $$-0.702097\pi$$
−0.593102 + 0.805127i $$0.702097\pi$$
$$180$$ 0 0
$$181$$ −2.13327e9 −1.98761 −0.993804 0.111149i $$-0.964547\pi$$
−0.993804 + 0.111149i $$0.964547\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 8.24630e8 0.704000
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 3.27581e8 0.246142 0.123071 0.992398i $$-0.460726\pi$$
0.123071 + 0.992398i $$0.460726\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −3.13584e9 −1.99960 −0.999798 0.0200992i $$-0.993602\pi$$
−0.999798 + 0.0200992i $$0.993602\pi$$
$$200$$ 0 0
$$201$$ −2.23816e9 −1.37122
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 3.30137e9 1.79810
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ −7.95869e8 −0.386655
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −4.76951e9 −1.92865 −0.964326 0.264716i $$-0.914722\pi$$
−0.964326 + 0.264716i $$0.914722\pi$$
$$224$$ 0 0
$$225$$ 5.79936e9 2.26282
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 1.32380e9 0.481371 0.240686 0.970603i $$-0.422628\pi$$
0.240686 + 0.970603i $$0.422628\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 6.99881e9 2.29484
$$236$$ 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 $$\pi$$
$$242$$ 0 0
$$243$$ −4.85020e9 −1.39102
$$244$$ 0 0
$$245$$ 6.63529e9 1.84160
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.39202e9 0.602658 0.301329 0.953520i $$-0.402570\pi$$
0.301329 + 0.953520i $$0.402570\pi$$
$$252$$ 0 0
$$253$$ −7.78598e9 −1.90034
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.90675e8 0.112476 0.0562382 0.998417i $$-0.482089\pi$$
0.0562382 + 0.998417i $$0.482089\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ −1.75705e10 −3.56288
$$266$$ 0 0
$$267$$ −9.50341e9 −1.86997
$$268$$ 0 0
$$269$$ −1.02851e10 −1.96427 −0.982135 0.188178i $$-0.939742\pi$$
−0.982135 + 0.188178i $$0.939742\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.36773e10 −2.39149
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 9.56797e9 1.57908
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 6.97576e9 1.00000
$$290$$ 0 0
$$291$$ −9.17060e9 −1.27887
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 4.72089e9 0.623355
$$296$$ 0 0
$$297$$ 5.84015e8 0.0750582
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 4.09946e8 0.0449668
$$310$$ 0 0
$$311$$ 1.74820e10 1.86874 0.934369 0.356306i $$-0.115964\pi$$
0.934369 + 0.356306i $$0.115964\pi$$
$$312$$ 0 0
$$313$$ −3.39209e9 −0.353419 −0.176710 0.984263i $$-0.556545\pi$$
−0.176710 + 0.984263i $$0.556545\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.66499e10 1.64882 0.824411 0.565991i $$-0.191506\pi$$
0.824411 + 0.565991i $$0.191506\pi$$
$$318$$ 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
$$331$$ 1.44332e10 1.20240 0.601202 0.799097i $$-0.294689\pi$$
0.601202 + 0.799097i $$0.294689\pi$$
$$332$$ 0 0
$$333$$ 4.44770e9 0.361709
$$334$$ 0 0
$$335$$ −2.27976e10 −1.81013
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 1.15099e10 0.871508
$$340$$ 0 0
$$341$$ −2.25652e10 −1.66887
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 6.91666e10 4.88225
$$346$$ 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
$$352$$ 0 0
$$353$$ −1.10589e10 −0.712216 −0.356108 0.934445i $$-0.615896\pi$$
−0.356108 + 0.934445i $$0.615896\pi$$
$$354$$ 0 0
$$355$$ −8.10659e9 −0.510417
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.69836e10 1.00000
$$362$$ 0 0
$$363$$ 2.42226e10 1.39506
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.83672e10 1.01246 0.506232 0.862397i $$-0.331038\pi$$
0.506232 + 0.862397i $$0.331038\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 7.06959e10 3.57494
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −3.14149e10 −1.52258 −0.761288 0.648414i $$-0.775433\pi$$
−0.761288 + 0.648414i $$0.775433\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −3.34982e10 −1.55678 −0.778389 0.627782i $$-0.783963\pi$$
−0.778389 + 0.627782i $$0.783963\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −4.57861e10 −1.99956 −0.999781 0.0209279i $$-0.993338\pi$$
−0.999781 + 0.0209279i $$0.993338\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 4.57269e10 1.84081 0.920407 0.390963i $$-0.127858\pi$$
0.920407 + 0.390963i $$0.127858\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 4.56288e10 1.76466 0.882332 0.470628i $$-0.155973\pi$$
0.882332 + 0.470628i $$0.155973\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −5.20691e10 −1.93535
$$406$$ 0 0
$$407$$ −1.04895e10 −0.382276
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 4.11195e10 1.44105
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1.81505e10 −0.588887 −0.294444 0.955669i $$-0.595134\pi$$
−0.294444 + 0.955669i $$0.595134\pi$$
$$420$$ 0 0
$$421$$ −2.43806e10 −0.776097 −0.388048 0.921639i $$-0.626851\pi$$
−0.388048 + 0.921639i $$0.626851\pi$$
$$422$$ 0 0
$$423$$ 3.77486e10 1.17907
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 6.98359e10 1.98668 0.993338 0.115233i $$-0.0367614\pi$$
0.993338 + 0.115233i $$0.0367614\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 3.57879e10 0.946197
$$442$$ 0 0
$$443$$ 3.92076e10 1.01802 0.509009 0.860761i $$-0.330012\pi$$
0.509009 + 0.860761i $$0.330012\pi$$
$$444$$ 0 0
$$445$$ −9.68002e10 −2.46852
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −8.10587e10 −1.99441 −0.997205 0.0747142i $$-0.976196\pi$$
−0.997205 + 0.0747142i $$0.976196\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −9.08592e10 −1.97717 −0.988587 0.150648i $$-0.951864\pi$$
−0.988587 + 0.150648i $$0.951864\pi$$
$$464$$ 0 0
$$465$$ 2.00457e11 4.28756
$$466$$ 0 0
$$467$$ −8.08102e10 −1.69902 −0.849510 0.527573i $$-0.823102\pi$$
−0.849510 + 0.527573i $$0.823102\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −1.36244e11 −2.76844
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −9.47678e10 −1.83057
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −9.34102e10 −1.68821
$$486$$ 0 0
$$487$$ 2.76502e10 0.491566 0.245783 0.969325i $$-0.420955\pi$$
0.245783 + 0.969325i $$0.420955\pi$$
$$488$$ 0 0
$$489$$ −1.03404e11 −1.80843
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −1.04616e11 −1.74252
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1.05616e11 1.70345 0.851723 0.523993i $$-0.175558\pi$$
0.851723 + 0.523993i $$0.175558\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 9.21776e10 1.39506
$$508$$ 0 0
$$509$$ 1.11658e11 1.66348 0.831742 0.555162i $$-0.187344\pi$$
0.831742 + 0.555162i $$0.187344\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 4.17564e9 0.0593601
$$516$$ 0 0
$$517$$ −8.90266e10 −1.24611
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.31834e11 −1.78927 −0.894633 0.446801i $$-0.852563\pi$$
−0.894633 + 0.446801i $$0.852563\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 2.04493e11 2.61129
$$530$$ 0 0
$$531$$ 2.54624e10 0.320274
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −1.37610e11 −1.65483
$$538$$ 0 0
$$539$$ −8.44025e10 −1.00000
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ −2.41059e11 −2.77284
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 9.31832e10 0.982123
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 1.17238e11 1.15047
$$566$$ 0 0
$$567$$ 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 $$\pi$$
$$572$$ 0 0
$$573$$ 3.70166e10 0.343383
$$574$$ 0 0
$$575$$ 4.96788e11 4.54464
$$576$$ 0 0
$$577$$ −2.17251e10 −0.196001 −0.0980006 0.995186i $$-0.531245\pi$$
−0.0980006 + 0.995186i $$0.531245\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 2.23501e11 1.93467
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.08009e11 −0.909716 −0.454858 0.890564i $$-0.650310\pi$$
−0.454858 + 0.890564i $$0.650310\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −3.54350e11 −2.78956
$$598$$ 0 0
$$599$$ −2.43785e11 −1.89365 −0.946824 0.321751i $$-0.895729\pi$$
−0.946824 + 0.321751i $$0.895729\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ −1.22960e11 −0.930028
$$604$$ 0 0
$$605$$ 2.46727e11 1.84160
$$606$$ 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 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −5.89891e10 −0.407035 −0.203517 0.979071i $$-0.565237\pi$$
−0.203517 + 0.979071i $$0.565237\pi$$
$$618$$ 0 0
$$619$$ −2.89838e11 −1.97420 −0.987102 0.160093i $$-0.948821\pi$$
−0.987102 + 0.160093i $$0.948821\pi$$
$$620$$ 0 0
$$621$$ −2.12127e10 −0.142636
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 3.55184e11 2.32774
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −1.38624e11 −0.874422 −0.437211 0.899359i $$-0.644034\pi$$
−0.437211 + 0.899359i $$0.644034\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −4.37235e10 −0.262247
$$640$$ 0 0
$$641$$ −2.64901e11 −1.56910 −0.784552 0.620063i $$-0.787107\pi$$
−0.784552 + 0.620063i $$0.787107\pi$$
$$642$$ 0 0
$$643$$ −1.08190e11 −0.632914 −0.316457 0.948607i $$-0.602493\pi$$
−0.316457 + 0.948607i $$0.602493\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8.21502e10 0.468804 0.234402 0.972140i $$-0.424687\pi$$
0.234402 + 0.972140i $$0.424687\pi$$
$$648$$ 0 0
$$649$$ −6.00508e10 −0.338486
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3.15668e11 1.73611 0.868056 0.496466i $$-0.165369\pi$$
0.868056 + 0.496466i $$0.165369\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −1.74259e11 −0.912827 −0.456413 0.889768i $$-0.650866\pi$$
−0.456413 + 0.889768i $$0.650866\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −5.38954e11 −2.69059
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −3.72633e10 −0.179501
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 3.39818e11 1.56158 0.780790 0.624794i $$-0.214817\pi$$
0.780790 + 0.624794i $$0.214817\pi$$
$$684$$ 0 0
$$685$$ 4.18837e11 1.90231
$$686$$ 0 0
$$687$$ 1.49589e11 0.671543
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 3.98526e11 1.74801 0.874007 0.485914i $$-0.161513\pi$$
0.874007 + 0.485914i $$0.161513\pi$$
$$692$$ 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
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 7.90866e11 3.20145
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −4.92858e11 −1.95046 −0.975229 0.221198i $$-0.929003\pi$$
−0.975229 + 0.221198i $$0.929003\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 8.19617e11 3.17141
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 4.32961e11 1.62007 0.810035 0.586382i $$-0.199448\pi$$
0.810035 + 0.586382i $$0.199448\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −4.81038e10 −0.172203 −0.0861017 0.996286i $$-0.527441\pi$$
−0.0861017 + 0.996286i $$0.527441\pi$$
$$728$$ 0 0
$$729$$ −2.51265e11 −0.889655
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 7.49787e11 2.56915
$$736$$ 0 0
$$737$$ 2.89991e11 0.982911
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−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
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 6.03334e11 1.89670 0.948349 0.317228i $$-0.102752\pi$$
0.948349 + 0.317228i $$0.102752\pi$$
$$752$$ 0 0
$$753$$ 2.70299e11 0.840745
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 6.45563e11 1.96587 0.982935 0.183953i $$-0.0588894\pi$$
0.982935 + 0.183953i $$0.0588894\pi$$
$$758$$ 0 0
$$759$$ −8.79816e11 −2.65109
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 5.54463e10 0.156912
$$772$$ 0 0
$$773$$ −2.49173e11 −0.697884 −0.348942 0.937144i $$-0.613459\pi$$
−0.348942 + 0.937144i $$0.613459\pi$$
$$774$$ 0 0
$$775$$ 1.43978e12 3.99108
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 1.03118e11 0.277159
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1.38776e12 −3.65458
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ −1.98547e12 −4.97044
$$796$$ 0 0
$$797$$ 7.35104e11 1.82186 0.910931 0.412560i $$-0.135365\pi$$
0.910931 + 0.412560i $$0.135365\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −5.22099e11 −1.26830
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ −1.16222e12 −2.74028
$$808$$ 0 0
$$809$$ 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
$$814$$ 0 0
$$815$$ −1.05326e12 −2.38729
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 3.01900e11 0.658058 0.329029 0.944320i $$-0.393279\pi$$
0.329029 + 0.944320i $$0.393279\pi$$
$$824$$ 0 0
$$825$$ −1.54553e12 −3.33628
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ −4.44761e11 −0.941692 −0.470846 0.882215i $$-0.656051\pi$$
−0.470846 + 0.882215i $$0.656051\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ −6.14782e10 −0.125262
$$838$$ 0 0
$$839$$ −6.66474e11 −1.34504 −0.672520 0.740079i $$-0.734788\pi$$
−0.672520 + 0.740079i $$0.734788\pi$$
$$840$$ 0 0
$$841$$ 5.00246e11 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 9.38906e11 1.84160
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 3.81001e11 0.726455
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 2.74046e11 0.503328 0.251664 0.967815i $$-0.419022\pi$$
0.251664 + 0.967815i $$0.419022\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −5.92719e11 −1.06858 −0.534288 0.845303i $$-0.679420\pi$$
−0.534288 + 0.845303i $$0.679420\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 7.88261e11 1.39506
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −5.03815e11 −0.867389
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −7.70772e11 −1.27945 −0.639724 0.768605i $$-0.720951\pi$$
−0.639724 + 0.768605i $$0.720951\pi$$
$$882$$ 0 0
$$883$$ 1.11501e12 1.83415 0.917077 0.398710i $$-0.130542\pi$$
0.917077 + 0.398710i $$0.130542\pi$$
$$884$$ 0 0
$$885$$ 5.33460e11 0.869619
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 6.62332e11 1.05091
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ −1.40167e12 −2.18451
$$896$$ 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
$$905$$ −2.45539e12 −3.66038
$$906$$ 0 0
$$907$$ −6.54959e11 −0.967798 −0.483899 0.875124i $$-0.660780\pi$$
−0.483899 + 0.875124i $$0.660780\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −8.76790e11 −1.27298 −0.636491 0.771284i $$-0.719615\pi$$
−0.636491 + 0.771284i $$0.719615\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 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
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 6.69288e11 0.914210
$$926$$ 0 0
$$927$$ 2.25216e10 0.0304987
$$928$$ 0 0
$$929$$ −8.36302e11 −1.12279 −0.561397 0.827547i $$-0.689736\pi$$
−0.561397 + 0.827547i $$0.689736\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 1.97546e12 2.60701
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ −3.83306e11 −0.493042
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.60673e12 1.99776 0.998882 0.0472733i $$-0.0150532\pi$$
0.998882 + 0.0472733i $$0.0150532\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 1.88144e12 2.30021
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 3.77045e11 0.453294
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.52251e12 1.78511
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −1.75196e12 −1.97083 −0.985413 0.170178i $$-0.945566\pi$$
−0.985413 + 0.170178i $$0.945566\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −1.65543e12 −1.81691 −0.908455 0.417982i $$-0.862737\pi$$
−0.908455 + 0.417982i $$0.862737\pi$$
$$978$$ 0 0
$$979$$ 1.23132e12 1.34042
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −4.71492e11 −0.504964 −0.252482 0.967602i $$-0.581247\pi$$
−0.252482 + 0.967602i $$0.581247\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 1.63892e12 1.69927 0.849635 0.527371i $$-0.176822\pi$$
0.849635 + 0.527371i $$0.176822\pi$$
$$992$$ 0 0
$$993$$ 1.63095e12 1.67743
$$994$$ 0 0
$$995$$ −3.60936e12 −3.68246
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ −2.85784e10 −0.0286930
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 176.9.h.a.65.1 1
4.3 odd 2 11.9.b.a.10.1 1
11.10 odd 2 CM 176.9.h.a.65.1 1
12.11 even 2 99.9.c.a.10.1 1
44.43 even 2 11.9.b.a.10.1 1
132.131 odd 2 99.9.c.a.10.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
11.9.b.a.10.1 1 4.3 odd 2
11.9.b.a.10.1 1 44.43 even 2
99.9.c.a.10.1 1 12.11 even 2
99.9.c.a.10.1 1 132.131 odd 2
176.9.h.a.65.1 1 1.1 even 1 trivial
176.9.h.a.65.1 1 11.10 odd 2 CM