# Properties

 Label 12.3.c.a.5.1 Level $12$ Weight $3$ Character 12.5 Self dual yes Analytic conductor $0.327$ 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] = [12,3,Mod(5,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("12.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 12.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: yes Analytic conductor: $$0.326976317232$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 5.1 Character $$\chi$$ $$=$$ 12.5

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-3.00000 q^{3} +2.00000 q^{7} +9.00000 q^{9} +O(q^{10})$$ $$q-3.00000 q^{3} +2.00000 q^{7} +9.00000 q^{9} -22.0000 q^{13} +26.0000 q^{19} -6.00000 q^{21} +25.0000 q^{25} -27.0000 q^{27} -46.0000 q^{31} +26.0000 q^{37} +66.0000 q^{39} -22.0000 q^{43} -45.0000 q^{49} -78.0000 q^{57} +74.0000 q^{61} +18.0000 q^{63} +122.000 q^{67} -46.0000 q^{73} -75.0000 q^{75} -142.000 q^{79} +81.0000 q^{81} -44.0000 q^{91} +138.000 q^{93} +2.00000 q^{97} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$$.

 $$n$$ $$5$$ $$7$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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
$$3$$ −3.00000 −1.00000
$$4$$ 0 0
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 0 0
$$7$$ 2.00000 0.285714 0.142857 0.989743i $$-0.454371\pi$$
0.142857 + 0.989743i $$0.454371\pi$$
$$8$$ 0 0
$$9$$ 9.00000 1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ −22.0000 −1.69231 −0.846154 0.532939i $$-0.821088\pi$$
−0.846154 + 0.532939i $$0.821088\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 26.0000 1.36842 0.684211 0.729285i $$-0.260147\pi$$
0.684211 + 0.729285i $$0.260147\pi$$
$$20$$ 0 0
$$21$$ −6.00000 −0.285714
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 25.0000 1.00000
$$26$$ 0 0
$$27$$ −27.0000 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −46.0000 −1.48387 −0.741935 0.670471i $$-0.766092\pi$$
−0.741935 + 0.670471i $$0.766092\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 26.0000 0.702703 0.351351 0.936244i $$-0.385722\pi$$
0.351351 + 0.936244i $$0.385722\pi$$
$$38$$ 0 0
$$39$$ 66.0000 1.69231
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −22.0000 −0.511628 −0.255814 0.966726i $$-0.582343\pi$$
−0.255814 + 0.966726i $$0.582343\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ −45.0000 −0.918367
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −78.0000 −1.36842
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 74.0000 1.21311 0.606557 0.795040i $$-0.292550\pi$$
0.606557 + 0.795040i $$0.292550\pi$$
$$62$$ 0 0
$$63$$ 18.0000 0.285714
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 122.000 1.82090 0.910448 0.413624i $$-0.135737\pi$$
0.910448 + 0.413624i $$0.135737\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ −46.0000 −0.630137 −0.315068 0.949069i $$-0.602027\pi$$
−0.315068 + 0.949069i $$0.602027\pi$$
$$74$$ 0 0
$$75$$ −75.0000 −1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −142.000 −1.79747 −0.898734 0.438494i $$-0.855512\pi$$
−0.898734 + 0.438494i $$0.855512\pi$$
$$80$$ 0 0
$$81$$ 81.0000 1.00000
$$82$$ 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
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ −44.0000 −0.483516
$$92$$ 0 0
$$93$$ 138.000 1.48387
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 2.00000 0.0206186 0.0103093 0.999947i $$-0.496718\pi$$
0.0103093 + 0.999947i $$0.496718\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 194.000 1.88350 0.941748 0.336321i $$-0.109183\pi$$
0.941748 + 0.336321i $$0.109183\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ −214.000 −1.96330 −0.981651 0.190684i $$-0.938929\pi$$
−0.981651 + 0.190684i $$0.938929\pi$$
$$110$$ 0 0
$$111$$ −78.0000 −0.702703
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −198.000 −1.69231
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 146.000 1.14961 0.574803 0.818292i $$-0.305079\pi$$
0.574803 + 0.818292i $$0.305079\pi$$
$$128$$ 0 0
$$129$$ 66.0000 0.511628
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 52.0000 0.390977
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −22.0000 −0.158273 −0.0791367 0.996864i $$-0.525216\pi$$
−0.0791367 + 0.996864i $$0.525216\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 135.000 0.918367
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ −286.000 −1.89404 −0.947020 0.321175i $$-0.895922\pi$$
−0.947020 + 0.321175i $$0.895922\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −118.000 −0.751592 −0.375796 0.926702i $$-0.622631\pi$$
−0.375796 + 0.926702i $$0.622631\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −262.000 −1.60736 −0.803681 0.595060i $$-0.797128\pi$$
−0.803681 + 0.595060i $$0.797128\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ 315.000 1.86391
$$170$$ 0 0
$$171$$ 234.000 1.36842
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 50.0000 0.285714
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 314.000 1.73481 0.867403 0.497606i $$-0.165787\pi$$
0.867403 + 0.497606i $$0.165787\pi$$
$$182$$ 0 0
$$183$$ −222.000 −1.21311
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −54.0000 −0.285714
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ −382.000 −1.97927 −0.989637 0.143590i $$-0.954135\pi$$
−0.989637 + 0.143590i $$0.954135\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 386.000 1.93970 0.969849 0.243706i $$-0.0783631\pi$$
0.969849 + 0.243706i $$0.0783631\pi$$
$$200$$ 0 0
$$201$$ −366.000 −1.82090
$$202$$ 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
$$211$$ −166.000 −0.786730 −0.393365 0.919382i $$-0.628689\pi$$
−0.393365 + 0.919382i $$0.628689\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −92.0000 −0.423963
$$218$$ 0 0
$$219$$ 138.000 0.630137
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 338.000 1.51570 0.757848 0.652432i $$-0.226251\pi$$
0.757848 + 0.652432i $$0.226251\pi$$
$$224$$ 0 0
$$225$$ 225.000 1.00000
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 26.0000 0.113537 0.0567686 0.998387i $$-0.481920\pi$$
0.0567686 + 0.998387i $$0.481920\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 426.000 1.79747
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −286.000 −1.18672 −0.593361 0.804936i $$-0.702199\pi$$
−0.593361 + 0.804936i $$0.702199\pi$$
$$242$$ 0 0
$$243$$ −243.000 −1.00000
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −572.000 −2.31579
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 52.0000 0.200772
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 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
$$271$$ 242.000 0.892989 0.446494 0.894786i $$-0.352672\pi$$
0.446494 + 0.894786i $$0.352672\pi$$
$$272$$ 0 0
$$273$$ 132.000 0.483516
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 122.000 0.440433 0.220217 0.975451i $$-0.429324\pi$$
0.220217 + 0.975451i $$0.429324\pi$$
$$278$$ 0 0
$$279$$ −414.000 −1.48387
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 458.000 1.61837 0.809187 0.587551i $$-0.199908\pi$$
0.809187 + 0.587551i $$0.199908\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 289.000 1.00000
$$290$$ 0 0
$$291$$ −6.00000 −0.0206186
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −44.0000 −0.146179
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −358.000 −1.16612 −0.583062 0.812428i $$-0.698145\pi$$
−0.583062 + 0.812428i $$0.698145\pi$$
$$308$$ 0 0
$$309$$ −582.000 −1.88350
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ −142.000 −0.453674 −0.226837 0.973933i $$-0.572838\pi$$
−0.226837 + 0.973933i $$0.572838\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −550.000 −1.69231
$$326$$ 0 0
$$327$$ 642.000 1.96330
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 362.000 1.09366 0.546828 0.837245i $$-0.315835\pi$$
0.546828 + 0.837245i $$0.315835\pi$$
$$332$$ 0 0
$$333$$ 234.000 0.702703
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 482.000 1.43027 0.715134 0.698988i $$-0.246366\pi$$
0.715134 + 0.698988i $$0.246366\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −188.000 −0.548105
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −502.000 −1.43840 −0.719198 0.694805i $$-0.755490\pi$$
−0.719198 + 0.694805i $$0.755490\pi$$
$$350$$ 0 0
$$351$$ 594.000 1.69231
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 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
$$361$$ 315.000 0.872576
$$362$$ 0 0
$$363$$ −363.000 −1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −718.000 −1.95640 −0.978202 0.207657i $$-0.933416\pi$$
−0.978202 + 0.207657i $$0.933416\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 698.000 1.87131 0.935657 0.352911i $$-0.114808\pi$$
0.935657 + 0.352911i $$0.114808\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −694.000 −1.83113 −0.915567 0.402165i $$-0.868258\pi$$
−0.915567 + 0.402165i $$0.868258\pi$$
$$380$$ 0 0
$$381$$ −438.000 −1.14961
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −198.000 −0.511628
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 362.000 0.911839 0.455919 0.890021i $$-0.349311\pi$$
0.455919 + 0.890021i $$0.349311\pi$$
$$398$$ 0 0
$$399$$ −156.000 −0.390977
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 1012.00 2.51117
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 626.000 1.53056 0.765281 0.643696i $$-0.222600\pi$$
0.765281 + 0.643696i $$0.222600\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 66.0000 0.158273
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −358.000 −0.850356 −0.425178 0.905110i $$-0.639789\pi$$
−0.425178 + 0.905110i $$0.639789\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 148.000 0.346604
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ −862.000 −1.99076 −0.995381 0.0960028i $$-0.969394\pi$$
−0.995381 + 0.0960028i $$0.969394\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −94.0000 −0.214123 −0.107062 0.994252i $$-0.534144\pi$$
−0.107062 + 0.994252i $$0.534144\pi$$
$$440$$ 0 0
$$441$$ −405.000 −0.918367
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 858.000 1.89404
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −814.000 −1.78118 −0.890591 0.454805i $$-0.849709\pi$$
−0.890591 + 0.454805i $$0.849709\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −526.000 −1.13607 −0.568035 0.823005i $$-0.692296\pi$$
−0.568035 + 0.823005i $$0.692296\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 244.000 0.520256
$$470$$ 0 0
$$471$$ 354.000 0.751592
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 650.000 1.36842
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ −572.000 −1.18919
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 962.000 1.97536 0.987680 0.156489i $$-0.0500176\pi$$
0.987680 + 0.156489i $$0.0500176\pi$$
$$488$$ 0 0
$$489$$ 786.000 1.60736
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 26.0000 0.0521042 0.0260521 0.999661i $$-0.491706\pi$$
0.0260521 + 0.999661i $$0.491706\pi$$
$$500$$ 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
$$507$$ −945.000 −1.86391
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ −92.0000 −0.180039
$$512$$ 0 0
$$513$$ −702.000 −1.36842
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ −982.000 −1.87763 −0.938815 0.344423i $$-0.888075\pi$$
−0.938815 + 0.344423i $$0.888075\pi$$
$$524$$ 0 0
$$525$$ −150.000 −0.285714
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 529.000 1.00000
$$530$$ 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
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1034.00 1.91128 0.955638 0.294545i $$-0.0951680\pi$$
0.955638 + 0.294545i $$0.0951680\pi$$
$$542$$ 0 0
$$543$$ −942.000 −1.73481
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 506.000 0.925046 0.462523 0.886607i $$-0.346944\pi$$
0.462523 + 0.886607i $$0.346944\pi$$
$$548$$ 0 0
$$549$$ 666.000 1.21311
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −284.000 −0.513562
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 484.000 0.865832
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 162.000 0.285714
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −886.000 −1.55166 −0.775832 0.630940i $$-0.782670\pi$$
−0.775832 + 0.630940i $$0.782670\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 962.000 1.66724 0.833622 0.552335i $$-0.186263\pi$$
0.833622 + 0.552335i $$0.186263\pi$$
$$578$$ 0 0
$$579$$ 1146.00 1.97927
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ −1196.00 −2.03056
$$590$$ 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
$$597$$ −1158.00 −1.93970
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −526.000 −0.875208 −0.437604 0.899168i $$-0.644173\pi$$
−0.437604 + 0.899168i $$0.644173\pi$$
$$602$$ 0 0
$$603$$ 1098.00 1.82090
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −814.000 −1.34102 −0.670511 0.741900i $$-0.733925\pi$$
−0.670511 + 0.741900i $$0.733925\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −1126.00 −1.83687 −0.918434 0.395574i $$-0.870546\pi$$
−0.918434 + 0.395574i $$0.870546\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ −214.000 −0.345719 −0.172859 0.984947i $$-0.555301\pi$$
−0.172859 + 0.984947i $$0.555301\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 625.000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 674.000 1.06815 0.534073 0.845438i $$-0.320661\pi$$
0.534073 + 0.845438i $$0.320661\pi$$
$$632$$ 0 0
$$633$$ 498.000 0.786730
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 990.000 1.55416
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 314.000 0.488336 0.244168 0.969733i $$-0.421485\pi$$
0.244168 + 0.969733i $$0.421485\pi$$
$$644$$ 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
$$651$$ 276.000 0.423963
$$652$$ 0 0
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −414.000 −0.630137
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 122.000 0.184569 0.0922844 0.995733i $$-0.470583\pi$$
0.0922844 + 0.995733i $$0.470583\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −1014.00 −1.51570
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 1154.00 1.71471 0.857355 0.514725i $$-0.172106\pi$$
0.857355 + 0.514725i $$0.172106\pi$$
$$674$$ 0 0
$$675$$ −675.000 −1.00000
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 4.00000 0.00589102
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −78.0000 −0.113537
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −1318.00 −1.90738 −0.953690 0.300790i $$-0.902750\pi$$
−0.953690 + 0.300790i $$0.902750\pi$$
$$692$$ 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
$$703$$ 676.000 0.961593
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −934.000 −1.31735 −0.658674 0.752428i $$-0.728882\pi$$
−0.658674 + 0.752428i $$0.728882\pi$$
$$710$$ 0 0
$$711$$ −1278.00 −1.79747
$$712$$ 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
$$721$$ 388.000 0.538141
$$722$$ 0 0
$$723$$ 858.000 1.18672
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 482.000 0.662999 0.331499 0.943455i $$-0.392446\pi$$
0.331499 + 0.943455i $$0.392446\pi$$
$$728$$ 0 0
$$729$$ 729.000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1034.00 1.41064 0.705321 0.708888i $$-0.250803\pi$$
0.705321 + 0.708888i $$0.250803\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −1222.00 −1.65359 −0.826793 0.562506i $$-0.809837\pi$$
−0.826793 + 0.562506i $$0.809837\pi$$
$$740$$ 0 0
$$741$$ 1716.00 2.31579
$$742$$ 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
$$751$$ 1202.00 1.60053 0.800266 0.599645i $$-0.204691\pi$$
0.800266 + 0.599645i $$0.204691\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −838.000 −1.10700 −0.553501 0.832849i $$-0.686708\pi$$
−0.553501 + 0.832849i $$0.686708\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ −428.000 −0.560944
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1534.00 −1.99480 −0.997399 0.0720749i $$-0.977038\pi$$
−0.997399 + 0.0720749i $$0.977038\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 0 0
$$775$$ −1150.00 −1.48387
$$776$$ 0 0
$$777$$ −156.000 −0.200772
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1562.00 1.98475 0.992376 0.123246i $$-0.0393305\pi$$
0.992376 + 0.123246i $$0.0393305\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −1628.00 −2.05296
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 1514.00 1.86683 0.933416 0.358797i $$-0.116813\pi$$
0.933416 + 0.358797i $$0.116813\pi$$
$$812$$ 0 0
$$813$$ −726.000 −0.892989
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −572.000 −0.700122
$$818$$ 0 0
$$819$$ −396.000 −0.483516
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 1058.00 1.28554 0.642770 0.766059i $$-0.277785\pi$$
0.642770 + 0.766059i $$0.277785\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 458.000 0.552473 0.276236 0.961090i $$-0.410913\pi$$
0.276236 + 0.961090i $$0.410913\pi$$
$$830$$ 0 0
$$831$$ −366.000 −0.440433
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 1242.00 1.48387
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 841.000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 242.000 0.285714
$$848$$ 0 0
$$849$$ −1374.00 −1.61837
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 1658.00 1.94373 0.971864 0.235543i $$-0.0756867\pi$$
0.971864 + 0.235543i $$0.0756867\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 1418.00 1.65076 0.825378 0.564580i $$-0.190962\pi$$
0.825378 + 0.564580i $$0.190962\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −867.000 −1.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ −2684.00 −3.08152
$$872$$ 0 0
$$873$$ 18.0000 0.0206186
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −598.000 −0.681870 −0.340935 0.940087i $$-0.610744\pi$$
−0.340935 + 0.940087i $$0.610744\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ −1702.00 −1.92752 −0.963760 0.266771i $$-0.914043\pi$$
−0.963760 + 0.266771i $$0.914043\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 292.000 0.328459
$$890$$ 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
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 132.000 0.146179
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −214.000 −0.235943 −0.117971 0.993017i $$-0.537639\pi$$
−0.117971 + 0.993017i $$0.537639\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 866.000 0.942329 0.471164 0.882045i $$-0.343834\pi$$
0.471164 + 0.882045i $$0.343834\pi$$
$$920$$ 0 0
$$921$$ 1074.00 1.16612
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 650.000 0.702703
$$926$$ 0 0
$$927$$ 1746.00 1.88350
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −1170.00 −1.25671
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −1198.00 −1.27855 −0.639274 0.768979i $$-0.720765\pi$$
−0.639274 + 0.768979i $$0.720765\pi$$
$$938$$ 0 0
$$939$$ 426.000 0.453674
$$940$$ 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
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ 1012.00 1.06639
$$950$$ 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
$$961$$ 1155.00 1.20187
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −1534.00 −1.58635 −0.793175 0.608994i $$-0.791573\pi$$
−0.793175 + 0.608994i $$0.791573\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ −44.0000 −0.0452210
$$974$$ 0 0
$$975$$ 1650.00 1.69231
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −1926.00 −1.96330
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ −46.0000 −0.0464178 −0.0232089 0.999731i $$-0.507388\pi$$
−0.0232089 + 0.999731i $$0.507388\pi$$
$$992$$ 0 0
$$993$$ −1086.00 −1.09366
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ −1894.00 −1.89970 −0.949850 0.312707i $$-0.898764\pi$$
−0.949850 + 0.312707i $$0.898764\pi$$
$$998$$ 0 0
$$999$$ −702.000 −0.702703
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 12.3.c.a.5.1 1
3.2 odd 2 CM 12.3.c.a.5.1 1
4.3 odd 2 48.3.e.a.17.1 1
5.2 odd 4 300.3.b.a.149.2 2
5.3 odd 4 300.3.b.a.149.1 2
5.4 even 2 300.3.g.b.101.1 1
7.2 even 3 588.3.p.c.557.1 2
7.3 odd 6 588.3.p.b.569.1 2
7.4 even 3 588.3.p.c.569.1 2
7.5 odd 6 588.3.p.b.557.1 2
7.6 odd 2 588.3.c.c.197.1 1
8.3 odd 2 192.3.e.a.65.1 1
8.5 even 2 192.3.e.b.65.1 1
9.2 odd 6 324.3.g.b.53.1 2
9.4 even 3 324.3.g.b.269.1 2
9.5 odd 6 324.3.g.b.269.1 2
9.7 even 3 324.3.g.b.53.1 2
11.10 odd 2 1452.3.e.b.485.1 1
12.11 even 2 48.3.e.a.17.1 1
15.2 even 4 300.3.b.a.149.2 2
15.8 even 4 300.3.b.a.149.1 2
15.14 odd 2 300.3.g.b.101.1 1
16.3 odd 4 768.3.h.b.641.2 2
16.5 even 4 768.3.h.a.641.2 2
16.11 odd 4 768.3.h.b.641.1 2
16.13 even 4 768.3.h.a.641.1 2
20.3 even 4 1200.3.c.c.449.2 2
20.7 even 4 1200.3.c.c.449.1 2
20.19 odd 2 1200.3.l.b.401.1 1
21.2 odd 6 588.3.p.c.557.1 2
21.5 even 6 588.3.p.b.557.1 2
21.11 odd 6 588.3.p.c.569.1 2
21.17 even 6 588.3.p.b.569.1 2
21.20 even 2 588.3.c.c.197.1 1
24.5 odd 2 192.3.e.b.65.1 1
24.11 even 2 192.3.e.a.65.1 1
33.32 even 2 1452.3.e.b.485.1 1
36.7 odd 6 1296.3.q.b.1025.1 2
36.11 even 6 1296.3.q.b.1025.1 2
36.23 even 6 1296.3.q.b.593.1 2
36.31 odd 6 1296.3.q.b.593.1 2
48.5 odd 4 768.3.h.a.641.2 2
48.11 even 4 768.3.h.b.641.1 2
48.29 odd 4 768.3.h.a.641.1 2
48.35 even 4 768.3.h.b.641.2 2
60.23 odd 4 1200.3.c.c.449.2 2
60.47 odd 4 1200.3.c.c.449.1 2
60.59 even 2 1200.3.l.b.401.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
12.3.c.a.5.1 1 1.1 even 1 trivial
12.3.c.a.5.1 1 3.2 odd 2 CM
48.3.e.a.17.1 1 4.3 odd 2
48.3.e.a.17.1 1 12.11 even 2
192.3.e.a.65.1 1 8.3 odd 2
192.3.e.a.65.1 1 24.11 even 2
192.3.e.b.65.1 1 8.5 even 2
192.3.e.b.65.1 1 24.5 odd 2
300.3.b.a.149.1 2 5.3 odd 4
300.3.b.a.149.1 2 15.8 even 4
300.3.b.a.149.2 2 5.2 odd 4
300.3.b.a.149.2 2 15.2 even 4
300.3.g.b.101.1 1 5.4 even 2
300.3.g.b.101.1 1 15.14 odd 2
324.3.g.b.53.1 2 9.2 odd 6
324.3.g.b.53.1 2 9.7 even 3
324.3.g.b.269.1 2 9.4 even 3
324.3.g.b.269.1 2 9.5 odd 6
588.3.c.c.197.1 1 7.6 odd 2
588.3.c.c.197.1 1 21.20 even 2
588.3.p.b.557.1 2 7.5 odd 6
588.3.p.b.557.1 2 21.5 even 6
588.3.p.b.569.1 2 7.3 odd 6
588.3.p.b.569.1 2 21.17 even 6
588.3.p.c.557.1 2 7.2 even 3
588.3.p.c.557.1 2 21.2 odd 6
588.3.p.c.569.1 2 7.4 even 3
588.3.p.c.569.1 2 21.11 odd 6
768.3.h.a.641.1 2 16.13 even 4
768.3.h.a.641.1 2 48.29 odd 4
768.3.h.a.641.2 2 16.5 even 4
768.3.h.a.641.2 2 48.5 odd 4
768.3.h.b.641.1 2 16.11 odd 4
768.3.h.b.641.1 2 48.11 even 4
768.3.h.b.641.2 2 16.3 odd 4
768.3.h.b.641.2 2 48.35 even 4
1200.3.c.c.449.1 2 20.7 even 4
1200.3.c.c.449.1 2 60.47 odd 4
1200.3.c.c.449.2 2 20.3 even 4
1200.3.c.c.449.2 2 60.23 odd 4
1200.3.l.b.401.1 1 20.19 odd 2
1200.3.l.b.401.1 1 60.59 even 2
1296.3.q.b.593.1 2 36.23 even 6
1296.3.q.b.593.1 2 36.31 odd 6
1296.3.q.b.1025.1 2 36.7 odd 6
1296.3.q.b.1025.1 2 36.11 even 6
1452.3.e.b.485.1 1 11.10 odd 2
1452.3.e.b.485.1 1 33.32 even 2