# Properties

 Label 768.3.h.b.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.b.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 $$-0.454371\pi$$
0.142857 + 0.989743i $$0.454371\pi$$
$$8$$ 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 $$0.321088\pi$$
−0.532939 + 0.846154i $$0.678912\pi$$
$$14$$ 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 $$-0.233908\pi$$
0.741935 + 0.670471i $$0.233908\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 26.0000i 0.702703i 0.936244 + 0.351351i $$0.114278\pi$$
−0.936244 + 0.351351i $$0.885722\pi$$
$$38$$ 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 $$-0.792550\pi$$
0.795040 0.606557i $$-0.207450\pi$$
$$62$$ 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 $$-0.144488\pi$$
0.898734 + 0.438494i $$0.144488\pi$$
$$80$$ 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 $$-0.109183\pi$$
0.941748 + 0.336321i $$0.109183\pi$$
$$104$$ 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 $$0.438929\pi$$
−0.190684 + 0.981651i $$0.561071\pi$$
$$110$$ 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 $$-0.694921\pi$$
−0.574803 + 0.818292i $$0.694921\pi$$
$$128$$ 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 $$-0.895922\pi$$
−0.947020 + 0.321175i $$0.895922\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 118.000i 0.751592i 0.926702 + 0.375796i $$0.122631\pi$$
−0.926702 + 0.375796i $$0.877369\pi$$
$$158$$ 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 $$0.334213\pi$$
−0.497606 + 0.867403i $$0.665787\pi$$
$$182$$ 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 $$-0.0783631\pi$$
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
$$211$$ − 166.000i − 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 $$-0.773749\pi$$
−0.757848 + 0.652432i $$0.773749\pi$$
$$224$$ 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 $$0.0180797\pi$$
−0.998387 + 0.0567686i $$0.981920\pi$$
$$230$$ 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 $$-0.647328\pi$$
−0.446494 + 0.894786i $$0.647328\pi$$
$$272$$ 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 $$0.0706764\pi$$
−0.975451 + 0.220217i $$0.929324\pi$$
$$278$$ 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 $$0.255490\pi$$
−0.694805 + 0.719198i $$0.744510\pi$$
$$350$$ 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 $$-0.0665839\pi$$
0.978202 + 0.207657i $$0.0665839\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 698.000i 1.87131i 0.352911 + 0.935657i $$0.385192\pi$$
−0.352911 + 0.935657i $$0.614808\pi$$
$$374$$ 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 $$-0.849311\pi$$
0.890021 0.455919i $$-0.150689\pi$$
$$398$$ 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 $$-0.860211\pi$$
0.905110 0.425178i $$-0.139789\pi$$
$$422$$ 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 $$-0.534144\pi$$
−0.107062 + 0.994252i $$0.534144\pi$$
$$440$$ 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 $$-0.307704\pi$$
0.568035 + 0.823005i $$0.307704\pi$$
$$464$$ 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 $$-0.0500176\pi$$
0.987680 + 0.156489i $$0.0500176\pi$$
$$488$$ 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 $$-0.595168\pi$$
0.294545 0.955638i $$-0.404832\pi$$
$$542$$ 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 $$-0.266075\pi$$
0.670511 + 0.741900i $$0.266075\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 1126.00i − 1.83687i −0.395574 0.918434i $$-0.629454\pi$$
0.395574 0.918434i $$-0.370546\pi$$
$$614$$ 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 $$-0.320661\pi$$
0.534073 + 0.845438i $$0.320661\pi$$
$$632$$ 0 0
$$633$$ −498.000 −0.786730
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 990.000i − 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 $$0.0294169\pi$$
−0.995733 + 0.0922844i $$0.970583\pi$$
$$662$$ 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 $$-0.771118\pi$$
0.752428 0.658674i $$-0.228882\pi$$
$$710$$ 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 $$-0.392446\pi$$
0.331499 + 0.943455i $$0.392446\pi$$
$$728$$ 0 0
$$729$$ −729.000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 1034.00i − 1.41064i −0.708888 0.705321i $$-0.750803\pi$$
0.708888 0.705321i $$-0.249197\pi$$
$$734$$ 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 $$-0.795309\pi$$
−0.800266 + 0.599645i $$0.795309\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 838.000i − 1.10700i −0.832849 0.553501i $$-0.813292\pi$$
0.832849 0.553501i $$-0.186708\pi$$
$$758$$ 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 $$-0.277785\pi$$
0.642770 + 0.766059i $$0.277785\pi$$
$$824$$ 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 $$-0.910913\pi$$
0.961090 0.276236i $$-0.0890873\pi$$
$$830$$ 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 $$0.424313\pi$$
−0.235543 + 0.971864i $$0.575687\pi$$
$$854$$ 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 $$0.110744\pi$$
−0.940087 + 0.340935i $$0.889256\pi$$
$$878$$ 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 $$-0.343834\pi$$
0.471164 + 0.882045i $$0.343834\pi$$
$$920$$ 0 0
$$921$$ −1074.00 −1.16612
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ − 650.000i − 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 $$-0.791573\pi$$
−0.793175 + 0.608994i $$0.791573\pi$$
$$968$$ 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 $$-0.492612\pi$$
0.0232089 + 0.999731i $$0.492612\pi$$
$$992$$ 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 $$-0.601236\pi$$
0.312707 0.949850i $$-0.398764\pi$$
$$998$$ 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.b.641.1 2
3.2 odd 2 CM 768.3.h.b.641.1 2
4.3 odd 2 768.3.h.a.641.2 2
8.3 odd 2 768.3.h.a.641.1 2
8.5 even 2 inner 768.3.h.b.641.2 2
12.11 even 2 768.3.h.a.641.2 2
16.3 odd 4 12.3.c.a.5.1 1
16.5 even 4 192.3.e.a.65.1 1
16.11 odd 4 192.3.e.b.65.1 1
16.13 even 4 48.3.e.a.17.1 1
24.5 odd 2 inner 768.3.h.b.641.2 2
24.11 even 2 768.3.h.a.641.1 2
48.5 odd 4 192.3.e.a.65.1 1
48.11 even 4 192.3.e.b.65.1 1
48.29 odd 4 48.3.e.a.17.1 1
48.35 even 4 12.3.c.a.5.1 1
80.3 even 4 300.3.b.a.149.1 2
80.13 odd 4 1200.3.c.c.449.2 2
80.19 odd 4 300.3.g.b.101.1 1
80.29 even 4 1200.3.l.b.401.1 1
80.67 even 4 300.3.b.a.149.2 2
80.77 odd 4 1200.3.c.c.449.1 2
112.3 even 12 588.3.p.b.569.1 2
112.19 even 12 588.3.p.b.557.1 2
112.51 odd 12 588.3.p.c.557.1 2
112.67 odd 12 588.3.p.c.569.1 2
112.83 even 4 588.3.c.c.197.1 1
144.13 even 12 1296.3.q.b.593.1 2
144.29 odd 12 1296.3.q.b.1025.1 2
144.61 even 12 1296.3.q.b.1025.1 2
144.67 odd 12 324.3.g.b.269.1 2
144.77 odd 12 1296.3.q.b.593.1 2
144.83 even 12 324.3.g.b.53.1 2
144.115 odd 12 324.3.g.b.53.1 2
144.131 even 12 324.3.g.b.269.1 2
176.131 even 4 1452.3.e.b.485.1 1
240.29 odd 4 1200.3.l.b.401.1 1
240.77 even 4 1200.3.c.c.449.1 2
240.83 odd 4 300.3.b.a.149.1 2
240.173 even 4 1200.3.c.c.449.2 2
240.179 even 4 300.3.g.b.101.1 1
240.227 odd 4 300.3.b.a.149.2 2
336.83 odd 4 588.3.c.c.197.1 1
336.131 odd 12 588.3.p.b.557.1 2
336.179 even 12 588.3.p.c.569.1 2
336.227 odd 12 588.3.p.b.569.1 2
336.275 even 12 588.3.p.c.557.1 2
528.131 odd 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 16.3 odd 4
12.3.c.a.5.1 1 48.35 even 4
48.3.e.a.17.1 1 16.13 even 4
48.3.e.a.17.1 1 48.29 odd 4
192.3.e.a.65.1 1 16.5 even 4
192.3.e.a.65.1 1 48.5 odd 4
192.3.e.b.65.1 1 16.11 odd 4
192.3.e.b.65.1 1 48.11 even 4
300.3.b.a.149.1 2 80.3 even 4
300.3.b.a.149.1 2 240.83 odd 4
300.3.b.a.149.2 2 80.67 even 4
300.3.b.a.149.2 2 240.227 odd 4
300.3.g.b.101.1 1 80.19 odd 4
300.3.g.b.101.1 1 240.179 even 4
324.3.g.b.53.1 2 144.83 even 12
324.3.g.b.53.1 2 144.115 odd 12
324.3.g.b.269.1 2 144.67 odd 12
324.3.g.b.269.1 2 144.131 even 12
588.3.c.c.197.1 1 112.83 even 4
588.3.c.c.197.1 1 336.83 odd 4
588.3.p.b.557.1 2 112.19 even 12
588.3.p.b.557.1 2 336.131 odd 12
588.3.p.b.569.1 2 112.3 even 12
588.3.p.b.569.1 2 336.227 odd 12
588.3.p.c.557.1 2 112.51 odd 12
588.3.p.c.557.1 2 336.275 even 12
588.3.p.c.569.1 2 112.67 odd 12
588.3.p.c.569.1 2 336.179 even 12
768.3.h.a.641.1 2 8.3 odd 2
768.3.h.a.641.1 2 24.11 even 2
768.3.h.a.641.2 2 4.3 odd 2
768.3.h.a.641.2 2 12.11 even 2
768.3.h.b.641.1 2 1.1 even 1 trivial
768.3.h.b.641.1 2 3.2 odd 2 CM
768.3.h.b.641.2 2 8.5 even 2 inner
768.3.h.b.641.2 2 24.5 odd 2 inner
1200.3.c.c.449.1 2 80.77 odd 4
1200.3.c.c.449.1 2 240.77 even 4
1200.3.c.c.449.2 2 80.13 odd 4
1200.3.c.c.449.2 2 240.173 even 4
1200.3.l.b.401.1 1 80.29 even 4
1200.3.l.b.401.1 1 240.29 odd 4
1296.3.q.b.593.1 2 144.13 even 12
1296.3.q.b.593.1 2 144.77 odd 12
1296.3.q.b.1025.1 2 144.29 odd 12
1296.3.q.b.1025.1 2 144.61 even 12
1452.3.e.b.485.1 1 176.131 even 4
1452.3.e.b.485.1 1 528.131 odd 4