# Properties

 Label 128.3.d.a.63.1 Level $128$ Weight $3$ Character 128.63 Analytic conductor $3.488$ Analytic rank $0$ Dimension $2$ CM discriminant -4 Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(63,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.63");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$128 = 2^{7}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 128.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: no Analytic conductor: $$3.48774738381$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 63.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 128.63 Dual form 128.3.d.a.63.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-8.00000i q^{5} -9.00000 q^{9} +O(q^{10})$$ $$q-8.00000i q^{5} -9.00000 q^{9} -24.0000i q^{13} +30.0000 q^{17} -39.0000 q^{25} +40.0000i q^{29} +24.0000i q^{37} +18.0000 q^{41} +72.0000i q^{45} +49.0000 q^{49} +56.0000i q^{53} -120.000i q^{61} -192.000 q^{65} +110.000 q^{73} +81.0000 q^{81} -240.000i q^{85} +78.0000 q^{89} -130.000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 18 q^{9}+O(q^{10})$$ 2 * q - 18 * q^9 $$2 q - 18 q^{9} + 60 q^{17} - 78 q^{25} + 36 q^{41} + 98 q^{49} - 384 q^{65} + 220 q^{73} + 162 q^{81} + 156 q^{89} - 260 q^{97}+O(q^{100})$$ 2 * q - 18 * q^9 + 60 * q^17 - 78 * q^25 + 36 * q^41 + 98 * q^49 - 384 * q^65 + 220 * q^73 + 162 * q^81 + 156 * q^89 - 260 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$127$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0 0
$$5$$ − 8.00000i − 1.60000i −0.600000 0.800000i $$-0.704833\pi$$
0.600000 0.800000i $$-0.295167\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ − 24.0000i − 1.84615i −0.384615 0.923077i $$-0.625666\pi$$
0.384615 0.923077i $$-0.374334\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 30.0000 1.76471 0.882353 0.470588i $$-0.155958\pi$$
0.882353 + 0.470588i $$0.155958\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ −39.0000 −1.56000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 40.0000i 1.37931i 0.724138 + 0.689655i $$0.242238\pi$$
−0.724138 + 0.689655i $$0.757762\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 24.0000i 0.648649i 0.945946 + 0.324324i $$0.105137\pi$$
−0.945946 + 0.324324i $$0.894863\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 18.0000 0.439024 0.219512 0.975610i $$-0.429553\pi$$
0.219512 + 0.975610i $$0.429553\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 72.0000i 1.60000i
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 49.0000 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 56.0000i 1.05660i 0.849057 + 0.528302i $$0.177171\pi$$
−0.849057 + 0.528302i $$0.822829\pi$$
$$54$$ 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
$$61$$ − 120.000i − 1.96721i −0.180328 0.983607i $$-0.557716\pi$$
0.180328 0.983607i $$-0.442284\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −192.000 −2.95385
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 110.000 1.50685 0.753425 0.657534i $$-0.228401\pi$$
0.753425 + 0.657534i $$0.228401\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ − 240.000i − 2.82353i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 78.0000 0.876404 0.438202 0.898876i $$-0.355615\pi$$
0.438202 + 0.898876i $$0.355615\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −130.000 −1.34021 −0.670103 0.742268i $$-0.733750\pi$$
−0.670103 + 0.742268i $$0.733750\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ − 40.0000i − 0.396040i −0.980198 0.198020i $$-0.936549\pi$$
0.980198 0.198020i $$-0.0634510\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ − 120.000i − 1.10092i −0.834862 0.550459i $$-0.814453\pi$$
0.834862 0.550459i $$-0.185547\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −30.0000 −0.265487 −0.132743 0.991150i $$-0.542379\pi$$
−0.132743 + 0.991150i $$0.542379\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 216.000i 1.84615i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −121.000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 112.000i 0.896000i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 210.000 1.53285 0.766423 0.642336i $$-0.222035\pi$$
0.766423 + 0.642336i $$0.222035\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 320.000 2.20690
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 280.000i 1.87919i 0.342282 + 0.939597i $$0.388800\pi$$
−0.342282 + 0.939597i $$0.611200\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ −270.000 −1.76471
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 264.000i 1.68153i 0.541401 + 0.840764i $$0.317894\pi$$
−0.541401 + 0.840764i $$0.682106\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −407.000 −2.40828
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 104.000i 0.601156i 0.953757 + 0.300578i $$0.0971796\pi$$
−0.953757 + 0.300578i $$0.902820\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ − 360.000i − 1.98895i −0.104972 0.994475i $$-0.533475\pi$$
0.104972 0.994475i $$-0.466525\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 192.000 1.03784
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 190.000 0.984456 0.492228 0.870466i $$-0.336183\pi$$
0.492228 + 0.870466i $$0.336183\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 56.0000i 0.284264i 0.989848 + 0.142132i $$0.0453957\pi$$
−0.989848 + 0.142132i $$0.954604\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ − 144.000i − 0.702439i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ − 720.000i − 3.25792i
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 351.000 1.56000
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 120.000i 0.524017i 0.965066 + 0.262009i $$0.0843849\pi$$
−0.965066 + 0.262009i $$0.915615\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −210.000 −0.901288 −0.450644 0.892704i $$-0.648806\pi$$
−0.450644 + 0.892704i $$0.648806\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −418.000 −1.73444 −0.867220 0.497925i $$-0.834095\pi$$
−0.867220 + 0.497925i $$0.834095\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ − 392.000i − 1.60000i
$$246$$ 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
$$256$$ 0 0
$$257$$ −510.000 −1.98444 −0.992218 0.124514i $$-0.960263\pi$$
−0.992218 + 0.124514i $$0.960263\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ − 360.000i − 1.37931i
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 448.000 1.69057
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 520.000i 1.93309i 0.256506 + 0.966543i $$0.417429\pi$$
−0.256506 + 0.966543i $$0.582571\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 504.000i 1.81949i 0.415162 + 0.909747i $$0.363725\pi$$
−0.415162 + 0.909747i $$0.636275\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 462.000 1.64413 0.822064 0.569395i $$-0.192822\pi$$
0.822064 + 0.569395i $$0.192822\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 611.000 2.11419
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ − 136.000i − 0.464164i −0.972696 0.232082i $$-0.925446\pi$$
0.972696 0.232082i $$-0.0745537\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −960.000 −3.14754
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 50.0000 0.159744 0.0798722 0.996805i $$-0.474549\pi$$
0.0798722 + 0.996805i $$0.474549\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 616.000i 1.94322i 0.236593 + 0.971609i $$0.423969\pi$$
−0.236593 + 0.971609i $$0.576031\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 936.000i 2.88000i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ − 216.000i − 0.648649i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −350.000 −1.03858 −0.519288 0.854599i $$-0.673803\pi$$
−0.519288 + 0.854599i $$0.673803\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 360.000i 1.03152i 0.856734 + 0.515759i $$0.172490\pi$$
−0.856734 + 0.515759i $$0.827510\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 450.000 1.27479 0.637394 0.770538i $$-0.280012\pi$$
0.637394 + 0.770538i $$0.280012\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ −361.000 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ − 880.000i − 2.41096i
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ −162.000 −0.439024
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 504.000i 1.35121i 0.737265 + 0.675603i $$0.236117\pi$$
−0.737265 + 0.675603i $$0.763883\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 960.000 2.54642
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ − 680.000i − 1.74807i −0.485861 0.874036i $$-0.661494\pi$$
0.485861 0.874036i $$-0.338506\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 456.000i 1.14861i 0.818640 + 0.574307i $$0.194729\pi$$
−0.818640 + 0.574307i $$0.805271\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 798.000 1.99002 0.995012 0.0997506i $$-0.0318045\pi$$
0.995012 + 0.0997506i $$0.0318045\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ − 648.000i − 1.60000i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −782.000 −1.91198 −0.955990 0.293399i $$-0.905214\pi$$
−0.955990 + 0.293399i $$0.905214\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 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
$$421$$ − 840.000i − 1.99525i −0.0688836 0.997625i $$-0.521944\pi$$
0.0688836 0.997625i $$-0.478056\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −1170.00 −2.75294
$$426$$ 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
$$433$$ −290.000 −0.669746 −0.334873 0.942263i $$-0.608693\pi$$
−0.334873 + 0.942263i $$0.608693\pi$$
$$434$$ 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
$$441$$ −441.000 −1.00000
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ − 624.000i − 1.40225i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 702.000 1.56347 0.781737 0.623608i $$-0.214334\pi$$
0.781737 + 0.623608i $$0.214334\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 850.000 1.85996 0.929978 0.367615i $$-0.119826\pi$$
0.929978 + 0.367615i $$0.119826\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ − 760.000i − 1.64859i −0.566161 0.824295i $$-0.691572\pi$$
0.566161 0.824295i $$-0.308428\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ − 504.000i − 1.05660i
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 576.000 1.19751
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 1040.00i 2.14433i
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 1200.00i 2.43408i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ −320.000 −0.633663
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ − 440.000i − 0.864440i −0.901768 0.432220i $$-0.857730\pi$$
0.901768 0.432220i $$-0.142270\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 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
$$521$$ −558.000 −1.07102 −0.535509 0.844530i $$-0.679880\pi$$
−0.535509 + 0.844530i $$0.679880\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 529.000 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ − 432.000i − 0.810507i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 840.000i 1.55268i 0.630314 + 0.776340i $$0.282926\pi$$
−0.630314 + 0.776340i $$0.717074\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −960.000 −1.76147
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 1080.00i 1.96721i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1064.00i 1.91023i 0.296230 + 0.955117i $$0.404271\pi$$
−0.296230 + 0.955117i $$0.595729\pi$$
$$558$$ 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
$$565$$ 240.000i 0.424779i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −462.000 −0.811951 −0.405975 0.913884i $$-0.633068\pi$$
−0.405975 + 0.913884i $$0.633068\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −1150.00 −1.99307 −0.996534 0.0831889i $$-0.973490\pi$$
−0.996534 + 0.0831889i $$0.973490\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 1728.00 2.95385
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 930.000 1.56830 0.784148 0.620573i $$-0.213100\pi$$
0.784148 + 0.620573i $$0.213100\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 1102.00 1.83361 0.916805 0.399334i $$-0.130759\pi$$
0.916805 + 0.399334i $$0.130759\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 968.000i 1.60000i
$$606$$ 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
$$613$$ − 1224.00i − 1.99674i −0.0570962 0.998369i $$-0.518184\pi$$
0.0570962 0.998369i $$-0.481816\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −210.000 −0.340357 −0.170178 0.985413i $$-0.554434\pi$$
−0.170178 + 0.985413i $$0.554434\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −79.0000 −0.126400
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 720.000i 1.14467i
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 1176.00i − 1.84615i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1218.00 −1.90016 −0.950078 0.312012i $$-0.898997\pi$$
−0.950078 + 0.312012i $$0.898997\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 1144.00i − 1.75191i −0.482389 0.875957i $$-0.660231\pi$$
0.482389 0.875957i $$-0.339769\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −990.000 −1.50685
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 600.000i 0.907716i 0.891074 + 0.453858i $$0.149953\pi$$
−0.891074 + 0.453858i $$0.850047\pi$$
$$662$$ 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
$$673$$ −770.000 −1.14413 −0.572065 0.820208i $$-0.693858\pi$$
−0.572065 + 0.820208i $$0.693858\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ − 104.000i − 0.153619i −0.997046 0.0768095i $$-0.975527\pi$$
0.997046 0.0768095i $$-0.0244733\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ − 1680.00i − 2.45255i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 1344.00 1.95065
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 540.000 0.774749
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 520.000i 0.741797i 0.928673 + 0.370899i $$0.120950\pi$$
−0.928673 + 0.370899i $$0.879050\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ − 1320.00i − 1.86178i −0.365303 0.930889i $$-0.619035\pi$$
0.365303 0.930889i $$-0.380965\pi$$
$$710$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ − 1560.00i − 2.15172i
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 216.000i − 0.294679i −0.989086 0.147340i $$-0.952929\pi$$
0.989086 0.147340i $$-0.0470711\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 2240.00 3.00671
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 936.000i − 1.23646i −0.785997 0.618230i $$-0.787850\pi$$
0.785997 0.618230i $$-0.212150\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −78.0000 −0.102497 −0.0512484 0.998686i $$-0.516320\pi$$
−0.0512484 + 0.998686i $$0.516320\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 2160.00i 2.82353i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −962.000 −1.25098 −0.625488 0.780234i $$-0.715100\pi$$
−0.625488 + 0.780234i $$0.715100\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1496.00i 1.93532i 0.252264 + 0.967658i $$0.418825\pi$$
−0.252264 + 0.967658i $$0.581175\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2112.00 2.69045
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −2880.00 −3.63178
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ − 1144.00i − 1.43538i −0.696361 0.717691i $$-0.745199\pi$$
0.696361 0.717691i $$-0.254801\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −702.000 −0.876404
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1518.00 −1.87639 −0.938195 0.346106i $$-0.887504\pi$$
−0.938195 + 0.346106i $$0.887504\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1400.00i 1.70524i 0.522533 + 0.852619i $$0.324987\pi$$
−0.522533 + 0.852619i $$0.675013\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ − 1080.00i − 1.30277i −0.758745 0.651387i $$-0.774187\pi$$
0.758745 0.651387i $$-0.225813\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 1470.00 1.76471
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ −759.000 −0.902497
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 3256.00i 3.85325i
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 1656.00i 1.94138i 0.240328 + 0.970692i $$0.422745\pi$$
−0.240328 + 0.970692i $$0.577255\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 1650.00 1.92532 0.962660 0.270712i $$-0.0872590\pi$$
0.962660 + 0.270712i $$0.0872590\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 832.000 0.961850
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 1170.00 1.34021
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 696.000i − 0.793615i −0.917902 0.396807i $$-0.870118\pi$$
0.917902 0.396807i $$-0.129882\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 738.000 0.837684 0.418842 0.908059i $$-0.362436\pi$$
0.418842 + 0.908059i $$0.362436\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 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
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 1680.00i 1.86459i
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ −2880.00 −3.18232
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 360.000i 0.396040i
$$910$$ 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
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ − 936.000i − 1.01189i
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ −258.000 −0.277718 −0.138859 0.990312i $$-0.544343\pi$$
−0.138859 + 0.990312i $$0.544343\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 430.000 0.458911 0.229456 0.973319i $$-0.426305\pi$$
0.229456 + 0.973319i $$0.426305\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 1160.00i 1.23273i 0.787460 + 0.616366i $$0.211396\pi$$
−0.787460 + 0.616366i $$0.788604\pi$$
$$942$$ 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
$$949$$ − 2640.00i − 2.78188i
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1230.00 −1.29066 −0.645331 0.763903i $$-0.723280\pi$$
−0.645331 + 0.763903i $$0.723280\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 961.000 1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ − 1520.00i − 1.57513i
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ −1890.00 −1.93449 −0.967247 0.253838i $$-0.918307\pi$$
−0.967247 + 0.253838i $$0.918307\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 1080.00i 1.10092i
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 448.000 0.454822
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ − 744.000i − 0.746239i −0.927783 0.373119i $$-0.878288\pi$$
0.927783 0.373119i $$-0.121712\pi$$
$$998$$ 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 128.3.d.a.63.1 2
3.2 odd 2 1152.3.b.a.703.2 2
4.3 odd 2 CM 128.3.d.a.63.1 2
8.3 odd 2 inner 128.3.d.a.63.2 yes 2
8.5 even 2 inner 128.3.d.a.63.2 yes 2
12.11 even 2 1152.3.b.a.703.2 2
16.3 odd 4 256.3.c.a.255.1 1
16.5 even 4 256.3.c.b.255.1 1
16.11 odd 4 256.3.c.b.255.1 1
16.13 even 4 256.3.c.a.255.1 1
24.5 odd 2 1152.3.b.a.703.1 2
24.11 even 2 1152.3.b.a.703.1 2
48.5 odd 4 2304.3.g.a.1279.1 1
48.11 even 4 2304.3.g.a.1279.1 1
48.29 odd 4 2304.3.g.f.1279.1 1
48.35 even 4 2304.3.g.f.1279.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
128.3.d.a.63.1 2 1.1 even 1 trivial
128.3.d.a.63.1 2 4.3 odd 2 CM
128.3.d.a.63.2 yes 2 8.3 odd 2 inner
128.3.d.a.63.2 yes 2 8.5 even 2 inner
256.3.c.a.255.1 1 16.3 odd 4
256.3.c.a.255.1 1 16.13 even 4
256.3.c.b.255.1 1 16.5 even 4
256.3.c.b.255.1 1 16.11 odd 4
1152.3.b.a.703.1 2 24.5 odd 2
1152.3.b.a.703.1 2 24.11 even 2
1152.3.b.a.703.2 2 3.2 odd 2
1152.3.b.a.703.2 2 12.11 even 2
2304.3.g.a.1279.1 1 48.5 odd 4
2304.3.g.a.1279.1 1 48.11 even 4
2304.3.g.f.1279.1 1 48.29 odd 4
2304.3.g.f.1279.1 1 48.35 even 4