Properties

 Label 1200.3.c.c.449.1 Level $1200$ Weight $3$ Character 1200.449 Analytic conductor $32.698$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 1200.c (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$32.6976317232$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 12) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

 Embedding label 449.1 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1200.449 Dual form 1200.3.c.c.449.2

$q$-expansion

 $$f(q)$$ $$=$$ $$q-3.00000i q^{3} -2.00000i q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q-3.00000i q^{3} -2.00000i q^{7} -9.00000 q^{9} +22.0000i q^{13} +26.0000 q^{19} -6.00000 q^{21} +27.0000i q^{27} +46.0000 q^{31} +26.0000i q^{37} +66.0000 q^{39} -22.0000i q^{43} +45.0000 q^{49} -78.0000i q^{57} +74.0000 q^{61} +18.0000i q^{63} -122.000i q^{67} +46.0000i q^{73} -142.000 q^{79} +81.0000 q^{81} +44.0000 q^{91} -138.000i q^{93} +2.00000i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 18q^{9} + O(q^{10})$$ $$2q - 18q^{9} + 52q^{19} - 12q^{21} + 92q^{31} + 132q^{39} + 90q^{49} + 148q^{61} - 284q^{79} + 162q^{81} + 88q^{91} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$ $$1$$

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
$$6$$ 0 0
$$7$$ − 2.00000i − 0.285714i −0.989743 0.142857i $$-0.954371\pi$$
0.989743 0.142857i $$-0.0456289\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 22.0000i 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 27.0000i 1.00000i
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 46.0000 1.48387 0.741935 0.670471i $$-0.233908\pi$$
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 $$-0.917657\pi$$
0.966726 0.255814i $$-0.0823435\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 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
$$57$$ − 78.0000i − 1.36842i
$$58$$ 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
$$63$$ 18.0000i 0.285714i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 122.000i − 1.82090i −0.413624 0.910448i $$-0.635737\pi$$
0.413624 0.910448i $$-0.364263\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 46.0000i 0.630137i 0.949069 + 0.315068i $$0.102027\pi$$
−0.949069 + 0.315068i $$0.897973\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 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
$$91$$ 44.0000 0.483516
$$92$$ 0 0
$$93$$ − 138.000i − 1.48387i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 2.00000i 0.0206186i 0.999947 + 0.0103093i $$0.00328160\pi$$
−0.999947 + 0.0103093i $$0.996718\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 194.000i 1.88350i 0.336321 + 0.941748i $$0.390817\pi$$
−0.336321 + 0.941748i $$0.609183\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 214.000 1.96330 0.981651 0.190684i $$-0.0610707\pi$$
0.981651 + 0.190684i $$0.0610707\pi$$
$$110$$ 0 0
$$111$$ 78.0000 0.702703
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 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
$$127$$ − 146.000i − 1.14961i −0.818292 0.574803i $$-0.805079\pi$$
0.818292 0.574803i $$-0.194921\pi$$
$$128$$ 0 0
$$129$$ −66.0000 −0.511628
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ − 52.0000i − 0.390977i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 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
$$147$$ − 135.000i − 0.918367i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ 286.000 1.89404 0.947020 0.321175i $$-0.104078\pi$$
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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −315.000 −1.86391
$$170$$ 0 0
$$171$$ −234.000 −1.36842
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 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
$$183$$ − 222.000i − 1.21311i
$$184$$ 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
$$193$$ 382.000i 1.97927i 0.143590 + 0.989637i $$0.454135\pi$$
−0.143590 + 0.989637i $$0.545865\pi$$
$$194$$ 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
$$211$$ 166.000 0.786730 0.393365 0.919382i $$-0.371311\pi$$
0.393365 + 0.919382i $$0.371311\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ − 92.0000i − 0.423963i
$$218$$ 0 0
$$219$$ 138.000 0.630137
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 338.000i 1.51570i 0.652432 + 0.757848i $$0.273749\pi$$
−0.652432 + 0.757848i $$0.726251\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ −26.0000 −0.113537 −0.0567686 0.998387i $$-0.518080\pi$$
−0.0567686 + 0.998387i $$0.518080\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 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
$$247$$ 572.000i 2.31579i
$$248$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 52.0000 0.200772
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 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 $$-0.647328\pi$$
−0.446494 + 0.894786i $$0.647328\pi$$
$$272$$ 0 0
$$273$$ − 132.000i − 0.483516i
$$274$$ 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 $$0.300092\pi$$
−0.587551 + 0.809187i $$0.699908\pi$$
$$284$$ 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 1.00000i $$-0.5\pi$$
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
$$301$$ −44.0000 −0.146179
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 358.000i 1.16612i 0.812428 + 0.583062i $$0.198145\pi$$
−0.812428 + 0.583062i $$0.801855\pi$$
$$308$$ 0 0
$$309$$ 582.000 1.88350
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 142.000i 0.453674i 0.973933 + 0.226837i $$0.0728385\pi$$
−0.973933 + 0.226837i $$0.927162\pi$$
$$314$$ 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
$$325$$ 0 0
$$326$$ 0 0
$$327$$ − 642.000i − 1.96330i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −362.000 −1.09366 −0.546828 0.837245i $$-0.684165\pi$$
−0.546828 + 0.837245i $$0.684165\pi$$
$$332$$ 0 0
$$333$$ − 234.000i − 0.702703i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 482.000i 1.43027i 0.698988 + 0.715134i $$0.253634\pi$$
−0.698988 + 0.715134i $$0.746366\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 188.000i − 0.548105i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 502.000 1.43840 0.719198 0.694805i $$-0.244510\pi$$
0.719198 + 0.694805i $$0.244510\pi$$
$$350$$ 0 0
$$351$$ −594.000 −1.69231
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 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
$$367$$ 718.000i 1.95640i 0.207657 + 0.978202i $$0.433416\pi$$
−0.207657 + 0.978202i $$0.566584\pi$$
$$368$$ 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
$$379$$ −694.000 −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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 198.000i 0.511628i
$$388$$ 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
$$397$$ 362.000i 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
$$417$$ 66.0000i 0.158273i
$$418$$ 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
$$427$$ − 148.000i − 0.346604i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 862.000i 1.99076i 0.0960028 + 0.995381i $$0.469394\pi$$
−0.0960028 + 0.995381i $$0.530606\pi$$
$$434$$ 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
$$457$$ − 814.000i − 1.78118i −0.454805 0.890591i $$-0.650291\pi$$
0.454805 0.890591i $$-0.349709\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ − 526.000i − 1.13607i −0.823005 0.568035i $$-0.807704\pi$$
0.823005 0.568035i $$-0.192296\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ −244.000 −0.520256
$$470$$ 0 0
$$471$$ −354.000 −0.751592
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 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
$$487$$ − 962.000i − 1.97536i −0.156489 0.987680i $$-0.550018\pi$$
0.156489 0.987680i $$-0.449982\pi$$
$$488$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 945.000i 1.86391i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 92.0000 0.180039
$$512$$ 0 0
$$513$$ 702.000i 1.36842i
$$514$$ 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 $$-0.611925\pi$$
0.344423 0.938815i $$-0.388075\pi$$
$$524$$ 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
$$533$$ 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
$$543$$ − 942.000i − 1.73481i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ − 506.000i − 0.925046i −0.886607 0.462523i $$-0.846944\pi$$
0.886607 0.462523i $$-0.153056\pi$$
$$548$$ 0 0
$$549$$ −666.000 −1.21311
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 284.000i 0.513562i
$$554$$ 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
$$567$$ − 162.000i − 0.285714i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 886.000 1.55166 0.775832 0.630940i $$-0.217330\pi$$
0.775832 + 0.630940i $$0.217330\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 962.000i 1.66724i 0.552335 + 0.833622i $$0.313737\pi$$
−0.552335 + 0.833622i $$0.686263\pi$$
$$578$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 1196.00 2.03056
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 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 $$-0.644173\pi$$
−0.437604 + 0.899168i $$0.644173\pi$$
$$602$$ 0 0
$$603$$ 1098.00i 1.82090i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 814.000i 1.34102i 0.741900 + 0.670511i $$0.233925\pi$$
−0.741900 + 0.670511i $$0.766075\pi$$
$$608$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 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
$$625$$ 0 0
$$626$$ 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
$$633$$ − 498.000i − 0.786730i
$$634$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ −276.000 −0.423963
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ − 414.000i − 0.630137i
$$658$$ 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
$$673$$ − 1154.00i − 1.71471i −0.514725 0.857355i $$-0.672106\pi$$
0.514725 0.857355i $$-0.327894\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 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
$$687$$ 78.0000i 0.113537i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 1318.00 1.90738 0.953690 0.300790i $$-0.0972504\pi$$
0.953690 + 0.300790i $$0.0972504\pi$$
$$692$$ 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
$$703$$ 676.000i 0.961593i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 934.000 1.31735 0.658674 0.752428i $$-0.271118\pi$$
0.658674 + 0.752428i $$0.271118\pi$$
$$710$$ 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
$$727$$ − 482.000i − 0.662999i −0.943455 0.331499i $$-0.892446\pi$$
0.943455 0.331499i $$-0.107554\pi$$
$$728$$ 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
$$739$$ −1222.00 −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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 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 $$-0.0229621\pi$$
0.997399 + 0.0720749i $$0.0229621\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ − 156.000i − 0.200772i
$$778$$ 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 $$-0.539331\pi$$
0.123246 0.992376i $$-0.460669\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1628.00i 2.05296i
$$794$$ 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
$$811$$ −1514.00 −1.86683 −0.933416 0.358797i $$-0.883187\pi$$
−0.933416 + 0.358797i $$0.883187\pi$$
$$812$$ 0 0
$$813$$ 726.000i 0.892989i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ − 572.000i − 0.700122i
$$818$$ 0 0
$$819$$ −396.000 −0.483516
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ 1058.00i 1.28554i 0.766059 + 0.642770i $$0.222215\pi$$
−0.766059 + 0.642770i $$0.777785\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ −458.000 −0.552473 −0.276236 0.961090i $$-0.589087\pi$$
−0.276236 + 0.961090i $$0.589087\pi$$
$$830$$ 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
$$847$$ − 242.000i − 0.285714i
$$848$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 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
$$873$$ − 18.0000i − 0.0206186i
$$874$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 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
$$903$$ 132.000i 0.146179i
$$904$$ 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
$$925$$ 0 0
$$926$$ 0 0
$$927$$ − 1746.00i − 1.88350i
$$928$$ 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
$$937$$ − 1198.00i − 1.27855i −0.768979 0.639274i $$-0.779235\pi$$
0.768979 0.639274i $$-0.220765\pi$$
$$938$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ −1012.00 −1.06639
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 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
$$967$$ 1534.00i 1.58635i 0.608994 + 0.793175i $$0.291573\pi$$
−0.608994 + 0.793175i $$0.708427\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 44.0000i 0.0452210i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −1926.00 −1.96330
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 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
$$993$$ 1086.00i 1.09366i
$$994$$ 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 1200.3.c.c.449.1 2
3.2 odd 2 CM 1200.3.c.c.449.1 2
4.3 odd 2 300.3.b.a.149.2 2
5.2 odd 4 1200.3.l.b.401.1 1
5.3 odd 4 48.3.e.a.17.1 1
5.4 even 2 inner 1200.3.c.c.449.2 2
12.11 even 2 300.3.b.a.149.2 2
15.2 even 4 1200.3.l.b.401.1 1
15.8 even 4 48.3.e.a.17.1 1
15.14 odd 2 inner 1200.3.c.c.449.2 2
20.3 even 4 12.3.c.a.5.1 1
20.7 even 4 300.3.g.b.101.1 1
20.19 odd 2 300.3.b.a.149.1 2
40.3 even 4 192.3.e.b.65.1 1
40.13 odd 4 192.3.e.a.65.1 1
45.13 odd 12 1296.3.q.b.593.1 2
45.23 even 12 1296.3.q.b.593.1 2
45.38 even 12 1296.3.q.b.1025.1 2
45.43 odd 12 1296.3.q.b.1025.1 2
60.23 odd 4 12.3.c.a.5.1 1
60.47 odd 4 300.3.g.b.101.1 1
60.59 even 2 300.3.b.a.149.1 2
80.3 even 4 768.3.h.a.641.1 2
80.13 odd 4 768.3.h.b.641.2 2
80.43 even 4 768.3.h.a.641.2 2
80.53 odd 4 768.3.h.b.641.1 2
120.53 even 4 192.3.e.a.65.1 1
120.83 odd 4 192.3.e.b.65.1 1
140.3 odd 12 588.3.p.b.569.1 2
140.23 even 12 588.3.p.c.557.1 2
140.83 odd 4 588.3.c.c.197.1 1
140.103 odd 12 588.3.p.b.557.1 2
140.123 even 12 588.3.p.c.569.1 2
180.23 odd 12 324.3.g.b.269.1 2
180.43 even 12 324.3.g.b.53.1 2
180.83 odd 12 324.3.g.b.53.1 2
180.103 even 12 324.3.g.b.269.1 2
220.43 odd 4 1452.3.e.b.485.1 1
240.53 even 4 768.3.h.b.641.1 2
240.83 odd 4 768.3.h.a.641.1 2
240.173 even 4 768.3.h.b.641.2 2
240.203 odd 4 768.3.h.a.641.2 2
420.23 odd 12 588.3.p.c.557.1 2
420.83 even 4 588.3.c.c.197.1 1
420.143 even 12 588.3.p.b.569.1 2
420.263 odd 12 588.3.p.c.569.1 2
420.383 even 12 588.3.p.b.557.1 2
660.263 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 20.3 even 4
12.3.c.a.5.1 1 60.23 odd 4
48.3.e.a.17.1 1 5.3 odd 4
48.3.e.a.17.1 1 15.8 even 4
192.3.e.a.65.1 1 40.13 odd 4
192.3.e.a.65.1 1 120.53 even 4
192.3.e.b.65.1 1 40.3 even 4
192.3.e.b.65.1 1 120.83 odd 4
300.3.b.a.149.1 2 20.19 odd 2
300.3.b.a.149.1 2 60.59 even 2
300.3.b.a.149.2 2 4.3 odd 2
300.3.b.a.149.2 2 12.11 even 2
300.3.g.b.101.1 1 20.7 even 4
300.3.g.b.101.1 1 60.47 odd 4
324.3.g.b.53.1 2 180.43 even 12
324.3.g.b.53.1 2 180.83 odd 12
324.3.g.b.269.1 2 180.23 odd 12
324.3.g.b.269.1 2 180.103 even 12
588.3.c.c.197.1 1 140.83 odd 4
588.3.c.c.197.1 1 420.83 even 4
588.3.p.b.557.1 2 140.103 odd 12
588.3.p.b.557.1 2 420.383 even 12
588.3.p.b.569.1 2 140.3 odd 12
588.3.p.b.569.1 2 420.143 even 12
588.3.p.c.557.1 2 140.23 even 12
588.3.p.c.557.1 2 420.23 odd 12
588.3.p.c.569.1 2 140.123 even 12
588.3.p.c.569.1 2 420.263 odd 12
768.3.h.a.641.1 2 80.3 even 4
768.3.h.a.641.1 2 240.83 odd 4
768.3.h.a.641.2 2 80.43 even 4
768.3.h.a.641.2 2 240.203 odd 4
768.3.h.b.641.1 2 80.53 odd 4
768.3.h.b.641.1 2 240.53 even 4
768.3.h.b.641.2 2 80.13 odd 4
768.3.h.b.641.2 2 240.173 even 4
1200.3.c.c.449.1 2 1.1 even 1 trivial
1200.3.c.c.449.1 2 3.2 odd 2 CM
1200.3.c.c.449.2 2 5.4 even 2 inner
1200.3.c.c.449.2 2 15.14 odd 2 inner
1200.3.l.b.401.1 1 5.2 odd 4
1200.3.l.b.401.1 1 15.2 even 4
1296.3.q.b.593.1 2 45.13 odd 12
1296.3.q.b.593.1 2 45.23 even 12
1296.3.q.b.1025.1 2 45.38 even 12
1296.3.q.b.1025.1 2 45.43 odd 12
1452.3.e.b.485.1 1 220.43 odd 4
1452.3.e.b.485.1 1 660.263 even 4