# Properties

 Label 768.3.h.a.641.1 Level $768$ Weight $3$ Character 768.641 Analytic conductor $20.926$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 768.h (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$20.9264843029$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 12) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 641.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 768.641 Dual form 768.3.h.a.641.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000i q^{3} -2.00000 q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q-3.00000i q^{3} -2.00000 q^{7} -9.00000 q^{9} -22.0000i q^{13} +26.0000i q^{19} +6.00000i q^{21} -25.0000 q^{25} +27.0000i q^{27} -46.0000 q^{31} -26.0000i q^{37} -66.0000 q^{39} +22.0000i q^{43} -45.0000 q^{49} +78.0000 q^{57} +74.0000i q^{61} +18.0000 q^{63} +122.000i q^{67} +46.0000 q^{73} +75.0000i q^{75} -142.000 q^{79} +81.0000 q^{81} +44.0000i q^{91} +138.000i q^{93} +2.00000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 4q^{7} - 18q^{9} + O(q^{10})$$ $$2q - 4q^{7} - 18q^{9} - 50q^{25} - 92q^{31} - 132q^{39} - 90q^{49} + 156q^{57} + 36q^{63} + 92q^{73} - 284q^{79} + 162q^{81} + 4q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$511$$ $$517$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$

## 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
$$3$$ − 3.00000i − 1.00000i
$$4$$ 0 0
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ −2.00000 −0.285714 −0.142857 0.989743i $$-0.545629\pi$$
−0.142857 + 0.989743i $$0.545629\pi$$
$$8$$ 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
$$13$$ − 22.0000i − 1.69231i −0.532939 0.846154i $$-0.678912\pi$$
0.532939 0.846154i $$-0.321088\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 26.0000i 1.36842i 0.729285 + 0.684211i $$0.239853\pi$$
−0.729285 + 0.684211i $$0.760147\pi$$
$$20$$ 0 0
$$21$$ 6.00000i 0.285714i
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ −25.0000 −1.00000
$$26$$ 0 0
$$27$$ 27.0000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 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
$$37$$ − 26.0000i − 0.702703i −0.936244 0.351351i $$-0.885722\pi$$
0.936244 0.351351i $$-0.114278\pi$$
$$38$$ 0 0
$$39$$ −66.0000 −1.69231
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ 22.0000i 0.511628i 0.966726 + 0.255814i $$0.0823435\pi$$
−0.966726 + 0.255814i $$0.917657\pi$$
$$44$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 78.0000 1.36842
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 74.0000i 1.21311i 0.795040 + 0.606557i $$0.207450\pi$$
−0.795040 + 0.606557i $$0.792550\pi$$
$$62$$ 0 0
$$63$$ 18.0000 0.285714
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 122.000i 1.82090i 0.413624 + 0.910448i $$0.364263\pi$$
−0.413624 + 0.910448i $$0.635737\pi$$
$$68$$ 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 $$-0.397973\pi$$
0.315068 + 0.949069i $$0.397973\pi$$
$$74$$ 0 0
$$75$$ 75.0000i 1.00000i
$$76$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 44.0000i 0.483516i
$$92$$ 0 0
$$93$$ 138.000i 1.48387i
$$94$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ −194.000 −1.88350 −0.941748 0.336321i $$-0.890817\pi$$
−0.941748 + 0.336321i $$0.890817\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ − 214.000i − 1.96330i −0.190684 0.981651i $$-0.561071\pi$$
0.190684 0.981651i $$-0.438929\pi$$
$$110$$ 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
$$117$$ 198.000i 1.69231i
$$118$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ − 52.0000i − 0.390977i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 22.0000i 0.158273i 0.996864 + 0.0791367i $$0.0252164\pi$$
−0.996864 + 0.0791367i $$0.974784\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 135.000i 0.918367i
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 286.000 1.89404 0.947020 0.321175i $$-0.104078\pi$$
0.947020 + 0.321175i $$0.104078\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 118.000i − 0.751592i −0.926702 0.375796i $$-0.877369\pi$$
0.926702 0.375796i $$-0.122631\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ − 262.000i − 1.60736i −0.595060 0.803681i $$-0.702872\pi$$
0.595060 0.803681i $$-0.297128\pi$$
$$164$$ 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
$$171$$ − 234.000i − 1.36842i
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 50.0000 0.285714
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ − 314.000i − 1.73481i −0.497606 0.867403i $$-0.665787\pi$$
0.497606 0.867403i $$-0.334213\pi$$
$$182$$ 0 0
$$183$$ 222.000 1.21311
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ − 54.0000i − 0.285714i
$$190$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ −386.000 −1.93970 −0.969849 0.243706i $$-0.921637\pi$$
−0.969849 + 0.243706i $$0.921637\pi$$
$$200$$ 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
$$211$$ − 166.000i − 0.786730i −0.919382 0.393365i $$-0.871311\pi$$
0.919382 0.393365i $$-0.128689\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 92.0000 0.423963
$$218$$ 0 0
$$219$$ − 138.000i − 0.630137i
$$220$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ − 26.0000i − 0.113537i −0.998387 0.0567686i $$-0.981920\pi$$
0.998387 0.0567686i $$-0.0180797\pi$$
$$230$$ 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
$$237$$ 426.000i 1.79747i
$$238$$ 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
$$243$$ − 243.000i − 1.00000i
$$244$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 52.0000i 0.200772i
$$260$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 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
$$277$$ − 122.000i − 0.440433i −0.975451 0.220217i $$-0.929324\pi$$
0.975451 0.220217i $$-0.0706764\pi$$
$$278$$ 0 0
$$279$$ 414.000 1.48387
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ − 458.000i − 1.61837i −0.587551 0.809187i $$-0.699908\pi$$
0.587551 0.809187i $$-0.300092\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 289.000 1.00000
$$290$$ 0 0
$$291$$ − 6.00000i − 0.0206186i
$$292$$ 0 0
$$293$$ 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
$$301$$ − 44.0000i − 0.146179i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ − 358.000i − 1.16612i −0.812428 0.583062i $$-0.801855\pi$$
0.812428 0.583062i $$-0.198145\pi$$
$$308$$ 0 0
$$309$$ 582.000i 1.88350i
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 142.000 0.453674 0.226837 0.973933i $$-0.427162\pi$$
0.226837 + 0.973933i $$0.427162\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 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
$$325$$ 550.000i 1.69231i
$$326$$ 0 0
$$327$$ −642.000 −1.96330
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ − 362.000i − 1.09366i −0.837245 0.546828i $$-0.815835\pi$$
0.837245 0.546828i $$-0.184165\pi$$
$$332$$ 0 0
$$333$$ 234.000i 0.702703i
$$334$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ − 502.000i − 1.43840i −0.694805 0.719198i $$-0.744510\pi$$
0.694805 0.719198i $$-0.255490\pi$$
$$350$$ 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
$$363$$ 363.000i 1.00000i
$$364$$ 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
$$373$$ − 698.000i − 1.87131i −0.352911 0.935657i $$-0.614808\pi$$
0.352911 0.935657i $$-0.385192\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 694.000i 1.83113i 0.402165 + 0.915567i $$0.368258\pi$$
−0.402165 + 0.915567i $$0.631742\pi$$
$$380$$ 0 0
$$381$$ − 438.000i − 1.14961i
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ − 198.000i − 0.511628i
$$388$$ 0 0
$$389$$ 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
$$397$$ 362.000i 0.911839i 0.890021 + 0.455919i $$0.150689\pi$$
−0.890021 + 0.455919i $$0.849311\pi$$
$$398$$ 0 0
$$399$$ −156.000 −0.390977
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 1012.00i 2.51117i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −626.000 −1.53056 −0.765281 0.643696i $$-0.777400\pi$$
−0.765281 + 0.643696i $$0.777400\pi$$
$$410$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 358.000i 0.850356i 0.905110 + 0.425178i $$0.139789\pi$$
−0.905110 + 0.425178i $$0.860211\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 148.000i − 0.346604i
$$428$$ 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 $$-0.465856\pi$$
0.107062 + 0.994252i $$0.465856\pi$$
$$440$$ 0 0
$$441$$ 405.000 0.918367
$$442$$ 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
$$448$$ 0 0
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ − 858.000i − 1.89404i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 814.000 1.78118 0.890591 0.454805i $$-0.150291\pi$$
0.890591 + 0.454805i $$0.150291\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ −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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ − 244.000i − 0.520256i
$$470$$ 0 0
$$471$$ −354.000 −0.751592
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ − 650.000i − 1.36842i
$$476$$ 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 $$-0.949982\pi$$
−0.987680 + 0.156489i $$0.949982\pi$$
$$488$$ 0 0
$$489$$ −786.000 −1.60736
$$490$$ 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
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 26.0000i 0.0521042i 0.999661 + 0.0260521i $$0.00829358\pi$$
−0.999661 + 0.0260521i $$0.991706\pi$$
$$500$$ 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
$$507$$ 945.000i 1.86391i
$$508$$ 0 0
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 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
$$523$$ 982.000i 1.87763i 0.344423 + 0.938815i $$0.388075\pi$$
−0.344423 + 0.938815i $$0.611925\pi$$
$$524$$ 0 0
$$525$$ − 150.000i − 0.285714i
$$526$$ 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
$$541$$ 1034.00i 1.91128i 0.294545 + 0.955638i $$0.404832\pi$$
−0.294545 + 0.955638i $$0.595168\pi$$
$$542$$ 0 0
$$543$$ −942.000 −1.73481
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 506.000i 0.925046i 0.886607 + 0.462523i $$0.153056\pi$$
−0.886607 + 0.462523i $$0.846944\pi$$
$$548$$ 0 0
$$549$$ − 666.000i − 1.21311i
$$550$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 484.000 0.865832
$$560$$ 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
$$567$$ −162.000 −0.285714
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 886.000i 1.55166i 0.630940 + 0.775832i $$0.282670\pi$$
−0.630940 + 0.775832i $$0.717330\pi$$
$$572$$ 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
$$579$$ 1146.00i 1.97927i
$$580$$ 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
$$589$$ − 1196.00i − 2.03056i
$$590$$ 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
$$597$$ 1158.00i 1.93970i
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 526.000 0.875208 0.437604 0.899168i $$-0.355827\pi$$
0.437604 + 0.899168i $$0.355827\pi$$
$$602$$ 0 0
$$603$$ − 1098.00i − 1.82090i
$$604$$ 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
$$613$$ 1126.00i 1.83687i 0.395574 + 0.918434i $$0.370546\pi$$
−0.395574 + 0.918434i $$0.629454\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 214.000i 0.345719i 0.984947 + 0.172859i $$0.0553006\pi$$
−0.984947 + 0.172859i $$0.944699\pi$$
$$620$$ 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 $$-0.679339\pi$$
−0.534073 + 0.845438i $$0.679339\pi$$
$$632$$ 0 0
$$633$$ −498.000 −0.786730
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 990.000i 1.55416i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 314.000i 0.488336i 0.969733 + 0.244168i $$0.0785148\pi$$
−0.969733 + 0.244168i $$0.921485\pi$$
$$644$$ 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
$$651$$ − 276.000i − 0.423963i
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −414.000 −0.630137
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ − 122.000i − 0.184569i −0.995733 0.0922844i $$-0.970583\pi$$
0.995733 0.0922844i $$-0.0294169\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ − 1014.00i − 1.51570i
$$670$$ 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
$$675$$ − 675.000i − 1.00000i
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ −4.00000 −0.00589102
$$680$$ 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
$$687$$ −78.0000 −0.113537
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ − 1318.00i − 1.90738i −0.300790 0.953690i $$-0.597250\pi$$
0.300790 0.953690i $$-0.402750\pi$$
$$692$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 676.000 0.961593
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 934.000i 1.31735i 0.752428 + 0.658674i $$0.228882\pi$$
−0.752428 + 0.658674i $$0.771118\pi$$
$$710$$ 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
$$723$$ 858.000i 1.18672i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −482.000 −0.662999 −0.331499 0.943455i $$-0.607554\pi$$
−0.331499 + 0.943455i $$0.607554\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1034.00i 1.41064i 0.708888 + 0.705321i $$0.249197\pi$$
−0.708888 + 0.705321i $$0.750803\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ − 1222.00i − 1.65359i −0.562506 0.826793i $$-0.690163\pi$$
0.562506 0.826793i $$-0.309837\pi$$
$$740$$ 0 0
$$741$$ − 1716.00i − 2.31579i
$$742$$ 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
$$757$$ 838.000i 1.10700i 0.832849 + 0.553501i $$0.186708\pi$$
−0.832849 + 0.553501i $$0.813292\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 428.000i 0.560944i
$$764$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 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
$$787$$ 1562.00i 1.98475i 0.123246 + 0.992376i $$0.460669\pi$$
−0.123246 + 0.992376i $$0.539331\pi$$
$$788$$ 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 1.00000i $$-0.5\pi$$
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 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ − 1514.00i − 1.86683i −0.358797 0.933416i $$-0.616813\pi$$
0.358797 0.933416i $$-0.383187\pi$$
$$812$$ 0 0
$$813$$ − 726.000i − 0.892989i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ −572.000 −0.700122
$$818$$ 0 0
$$819$$ − 396.000i − 0.483516i
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ −1058.00 −1.28554 −0.642770 0.766059i $$-0.722215\pi$$
−0.642770 + 0.766059i $$0.722215\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 458.000i 0.552473i 0.961090 + 0.276236i $$0.0890873\pi$$
−0.961090 + 0.276236i $$0.910913\pi$$
$$830$$ 0 0
$$831$$ −366.000 −0.440433
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ − 1242.00i − 1.48387i
$$838$$ 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
$$853$$ − 1658.00i − 1.94373i −0.235543 0.971864i $$-0.575687\pi$$
0.235543 0.971864i $$-0.424313\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ − 1418.00i − 1.65076i −0.564580 0.825378i $$-0.690962\pi$$
0.564580 0.825378i $$-0.309038\pi$$
$$860$$ 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
$$867$$ − 867.000i − 1.00000i
$$868$$ 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
$$877$$ − 598.000i − 0.681870i −0.940087 0.340935i $$-0.889256\pi$$
0.940087 0.340935i $$-0.110744\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ − 1702.00i − 1.92752i −0.266771 0.963760i $$-0.585957\pi$$
0.266771 0.963760i $$-0.414043\pi$$
$$884$$ 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
$$907$$ 214.000i 0.235943i 0.993017 + 0.117971i $$0.0376391\pi$$
−0.993017 + 0.117971i $$0.962361\pi$$
$$908$$ 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 $$-0.656166\pi$$
−0.471164 + 0.882045i $$0.656166\pi$$
$$920$$ 0 0
$$921$$ −1074.00 −1.16612
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 650.000i 0.702703i
$$926$$ 0 0
$$927$$ 1746.00 1.88350
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ − 1170.00i − 1.25671i
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 1198.00 1.27855 0.639274 0.768979i $$-0.279235\pi$$
0.639274 + 0.768979i $$0.279235\pi$$
$$938$$ 0 0
$$939$$ − 426.000i − 0.453674i
$$940$$ 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
$$949$$ − 1012.00i − 1.06639i
$$950$$ 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 $$-0.208427\pi$$
0.793175 + 0.608994i $$0.208427\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ − 44.0000i − 0.0452210i
$$974$$ 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
$$981$$ 1926.00i 1.96330i
$$982$$ 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
$$997$$ 1894.00i 1.89970i 0.312707 + 0.949850i $$0.398764\pi$$
−0.312707 + 0.949850i $$0.601236\pi$$
$$998$$ 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 768.3.h.a.641.1 2
3.2 odd 2 CM 768.3.h.a.641.1 2
4.3 odd 2 768.3.h.b.641.2 2
8.3 odd 2 768.3.h.b.641.1 2
8.5 even 2 inner 768.3.h.a.641.2 2
12.11 even 2 768.3.h.b.641.2 2
16.3 odd 4 192.3.e.a.65.1 1
16.5 even 4 12.3.c.a.5.1 1
16.11 odd 4 48.3.e.a.17.1 1
16.13 even 4 192.3.e.b.65.1 1
24.5 odd 2 inner 768.3.h.a.641.2 2
24.11 even 2 768.3.h.b.641.1 2
48.5 odd 4 12.3.c.a.5.1 1
48.11 even 4 48.3.e.a.17.1 1
48.29 odd 4 192.3.e.b.65.1 1
48.35 even 4 192.3.e.a.65.1 1
80.27 even 4 1200.3.c.c.449.1 2
80.37 odd 4 300.3.b.a.149.2 2
80.43 even 4 1200.3.c.c.449.2 2
80.53 odd 4 300.3.b.a.149.1 2
80.59 odd 4 1200.3.l.b.401.1 1
80.69 even 4 300.3.g.b.101.1 1
112.5 odd 12 588.3.p.b.557.1 2
112.37 even 12 588.3.p.c.557.1 2
112.53 even 12 588.3.p.c.569.1 2
112.69 odd 4 588.3.c.c.197.1 1
112.101 odd 12 588.3.p.b.569.1 2
144.5 odd 12 324.3.g.b.269.1 2
144.11 even 12 1296.3.q.b.1025.1 2
144.43 odd 12 1296.3.q.b.1025.1 2
144.59 even 12 1296.3.q.b.593.1 2
144.85 even 12 324.3.g.b.269.1 2
144.101 odd 12 324.3.g.b.53.1 2
144.133 even 12 324.3.g.b.53.1 2
144.139 odd 12 1296.3.q.b.593.1 2
176.21 odd 4 1452.3.e.b.485.1 1
240.53 even 4 300.3.b.a.149.1 2
240.59 even 4 1200.3.l.b.401.1 1
240.107 odd 4 1200.3.c.c.449.1 2
240.149 odd 4 300.3.g.b.101.1 1
240.197 even 4 300.3.b.a.149.2 2
240.203 odd 4 1200.3.c.c.449.2 2
336.5 even 12 588.3.p.b.557.1 2
336.53 odd 12 588.3.p.c.569.1 2
336.101 even 12 588.3.p.b.569.1 2
336.149 odd 12 588.3.p.c.557.1 2
336.293 even 4 588.3.c.c.197.1 1
528.197 even 4 1452.3.e.b.485.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
12.3.c.a.5.1 1 16.5 even 4
12.3.c.a.5.1 1 48.5 odd 4
48.3.e.a.17.1 1 16.11 odd 4
48.3.e.a.17.1 1 48.11 even 4
192.3.e.a.65.1 1 16.3 odd 4
192.3.e.a.65.1 1 48.35 even 4
192.3.e.b.65.1 1 16.13 even 4
192.3.e.b.65.1 1 48.29 odd 4
300.3.b.a.149.1 2 80.53 odd 4
300.3.b.a.149.1 2 240.53 even 4
300.3.b.a.149.2 2 80.37 odd 4
300.3.b.a.149.2 2 240.197 even 4
300.3.g.b.101.1 1 80.69 even 4
300.3.g.b.101.1 1 240.149 odd 4
324.3.g.b.53.1 2 144.101 odd 12
324.3.g.b.53.1 2 144.133 even 12
324.3.g.b.269.1 2 144.5 odd 12
324.3.g.b.269.1 2 144.85 even 12
588.3.c.c.197.1 1 112.69 odd 4
588.3.c.c.197.1 1 336.293 even 4
588.3.p.b.557.1 2 112.5 odd 12
588.3.p.b.557.1 2 336.5 even 12
588.3.p.b.569.1 2 112.101 odd 12
588.3.p.b.569.1 2 336.101 even 12
588.3.p.c.557.1 2 112.37 even 12
588.3.p.c.557.1 2 336.149 odd 12
588.3.p.c.569.1 2 112.53 even 12
588.3.p.c.569.1 2 336.53 odd 12
768.3.h.a.641.1 2 1.1 even 1 trivial
768.3.h.a.641.1 2 3.2 odd 2 CM
768.3.h.a.641.2 2 8.5 even 2 inner
768.3.h.a.641.2 2 24.5 odd 2 inner
768.3.h.b.641.1 2 8.3 odd 2
768.3.h.b.641.1 2 24.11 even 2
768.3.h.b.641.2 2 4.3 odd 2
768.3.h.b.641.2 2 12.11 even 2
1200.3.c.c.449.1 2 80.27 even 4
1200.3.c.c.449.1 2 240.107 odd 4
1200.3.c.c.449.2 2 80.43 even 4
1200.3.c.c.449.2 2 240.203 odd 4
1200.3.l.b.401.1 1 80.59 odd 4
1200.3.l.b.401.1 1 240.59 even 4
1296.3.q.b.593.1 2 144.59 even 12
1296.3.q.b.593.1 2 144.139 odd 12
1296.3.q.b.1025.1 2 144.11 even 12
1296.3.q.b.1025.1 2 144.43 odd 12
1452.3.e.b.485.1 1 176.21 odd 4
1452.3.e.b.485.1 1 528.197 even 4