# Properties

 Label 900.3.f.b.199.2 Level $900$ Weight $3$ Character 900.199 Analytic conductor $24.523$ Analytic rank $0$ Dimension $2$ CM discriminant -4 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 900.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$24.5232237924$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 36) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 199.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 900.199 Dual form 900.3.f.b.199.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+2.00000i q^{2} -4.00000 q^{4} -8.00000i q^{8} +O(q^{10})$$ $$q+2.00000i q^{2} -4.00000 q^{4} -8.00000i q^{8} -10.0000i q^{13} +16.0000 q^{16} +16.0000i q^{17} +20.0000 q^{26} +40.0000 q^{29} +32.0000i q^{32} -32.0000 q^{34} +70.0000i q^{37} +80.0000 q^{41} -49.0000 q^{49} +40.0000i q^{52} +56.0000i q^{53} +80.0000i q^{58} -22.0000 q^{61} -64.0000 q^{64} -64.0000i q^{68} +110.000i q^{73} -140.000 q^{74} +160.000i q^{82} +160.000 q^{89} +130.000i q^{97} -98.0000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 8 q^{4} + O(q^{10})$$ $$2 q - 8 q^{4} + 32 q^{16} + 40 q^{26} + 80 q^{29} - 64 q^{34} + 160 q^{41} - 98 q^{49} - 44 q^{61} - 128 q^{64} - 280 q^{74} + 320 q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$451$$ $$577$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000i 1.00000i
$$3$$ 0 0
$$4$$ −4.00000 −1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ − 8.00000i − 1.00000i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ − 10.0000i − 0.769231i −0.923077 0.384615i $$-0.874334\pi$$
0.923077 0.384615i $$-0.125666\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ 16.0000i 0.941176i 0.882353 + 0.470588i $$0.155958\pi$$
−0.882353 + 0.470588i $$0.844042\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 20.0000 0.769231
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 40.0000 1.37931 0.689655 0.724138i $$-0.257762\pi$$
0.689655 + 0.724138i $$0.257762\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 32.0000i 1.00000i
$$33$$ 0 0
$$34$$ −32.0000 −0.941176
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 70.0000i 1.89189i 0.324324 + 0.945946i $$0.394863\pi$$
−0.324324 + 0.945946i $$0.605137\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 80.0000 1.95122 0.975610 0.219512i $$-0.0704466\pi$$
0.975610 + 0.219512i $$0.0704466\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −49.0000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 40.0000i 0.769231i
$$53$$ 56.0000i 1.05660i 0.849057 + 0.528302i $$0.177171\pi$$
−0.849057 + 0.528302i $$0.822829\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 80.0000i 1.37931i
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −22.0000 −0.360656 −0.180328 0.983607i $$-0.557716\pi$$
−0.180328 + 0.983607i $$0.557716\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −64.0000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ − 64.0000i − 0.941176i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 110.000i 1.50685i 0.657534 + 0.753425i $$0.271599\pi$$
−0.657534 + 0.753425i $$0.728401\pi$$
$$74$$ −140.000 −1.89189
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 160.000i 1.95122i
$$83$$ 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
$$89$$ 160.000 1.79775 0.898876 0.438202i $$-0.144385\pi$$
0.898876 + 0.438202i $$0.144385\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 130.000i 1.34021i 0.742268 + 0.670103i $$0.233750\pi$$
−0.742268 + 0.670103i $$0.766250\pi$$
$$98$$ − 98.0000i − 1.00000i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −40.0000 −0.396040 −0.198020 0.980198i $$-0.563451\pi$$
−0.198020 + 0.980198i $$0.563451\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ −80.0000 −0.769231
$$105$$ 0 0
$$106$$ −112.000 −1.05660
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ −182.000 −1.66972 −0.834862 0.550459i $$-0.814453\pi$$
−0.834862 + 0.550459i $$0.814453\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 224.000i 1.98230i 0.132743 + 0.991150i $$0.457621\pi$$
−0.132743 + 0.991150i $$0.542379\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −160.000 −1.37931
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 121.000 1.00000
$$122$$ − 44.0000i − 0.360656i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ − 128.000i − 1.00000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 128.000 0.941176
$$137$$ − 176.000i − 1.28467i −0.766423 0.642336i $$-0.777965\pi$$
0.766423 0.642336i $$-0.222035\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −220.000 −1.50685
$$147$$ 0 0
$$148$$ − 280.000i − 1.89189i
$$149$$ 280.000 1.87919 0.939597 0.342282i $$-0.111200\pi$$
0.939597 + 0.342282i $$0.111200\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 170.000i − 1.08280i −0.840764 0.541401i $$-0.817894\pi$$
0.840764 0.541401i $$-0.182106\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ −320.000 −1.95122
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 69.0000 0.408284
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 104.000i 0.601156i 0.953757 + 0.300578i $$0.0971796\pi$$
−0.953757 + 0.300578i $$0.902820\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 320.000i 1.79775i
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 38.0000 0.209945 0.104972 0.994475i $$-0.466525\pi$$
0.104972 + 0.994475i $$0.466525\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ − 190.000i − 0.984456i −0.870466 0.492228i $$-0.836183\pi$$
0.870466 0.492228i $$-0.163817\pi$$
$$194$$ −260.000 −1.34021
$$195$$ 0 0
$$196$$ 196.000 1.00000
$$197$$ − 56.0000i − 0.284264i −0.989848 0.142132i $$-0.954604\pi$$
0.989848 0.142132i $$-0.0453957\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ − 80.0000i − 0.396040i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ − 160.000i − 0.769231i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ − 224.000i − 1.05660i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ − 364.000i − 1.66972i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 160.000 0.723982
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −448.000 −1.98230
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 442.000 1.93013 0.965066 0.262009i $$-0.0843849\pi$$
0.965066 + 0.262009i $$0.0843849\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ − 320.000i − 1.37931i
$$233$$ 416.000i 1.78541i 0.450644 + 0.892704i $$0.351194\pi$$
−0.450644 + 0.892704i $$0.648806\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −418.000 −1.73444 −0.867220 0.497925i $$-0.834095\pi$$
−0.867220 + 0.497925i $$0.834095\pi$$
$$242$$ 242.000i 1.00000i
$$243$$ 0 0
$$244$$ 88.0000 0.360656
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 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
$$256$$ 256.000 1.00000
$$257$$ 64.0000i 0.249027i 0.992218 + 0.124514i $$0.0397370\pi$$
−0.992218 + 0.124514i $$0.960263\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 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
$$269$$ 520.000 1.93309 0.966543 0.256506i $$-0.0825712\pi$$
0.966543 + 0.256506i $$0.0825712\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 256.000i 0.941176i
$$273$$ 0 0
$$274$$ 352.000 1.28467
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 230.000i − 0.830325i −0.909747 0.415162i $$-0.863725\pi$$
0.909747 0.415162i $$-0.136275\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 320.000 1.13879 0.569395 0.822064i $$-0.307178\pi$$
0.569395 + 0.822064i $$0.307178\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 33.0000 0.114187
$$290$$ 0 0
$$291$$ 0 0
$$292$$ − 440.000i − 1.50685i
$$293$$ − 136.000i − 0.464164i −0.972696 0.232082i $$-0.925446\pi$$
0.972696 0.232082i $$-0.0745537\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 560.000 1.89189
$$297$$ 0 0
$$298$$ 560.000i 1.87919i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 50.0000i 0.159744i 0.996805 + 0.0798722i $$0.0254512\pi$$
−0.996805 + 0.0798722i $$0.974549\pi$$
$$314$$ 340.000 1.08280
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 616.000i 1.94322i 0.236593 + 0.971609i $$0.423969\pi$$
−0.236593 + 0.971609i $$0.576031\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ − 640.000i − 1.95122i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ − 350.000i − 1.03858i −0.854599 0.519288i $$-0.826197\pi$$
0.854599 0.519288i $$-0.173803\pi$$
$$338$$ 138.000i 0.408284i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −208.000 −0.601156
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 598.000 1.71347 0.856734 0.515759i $$-0.172490\pi$$
0.856734 + 0.515759i $$0.172490\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ − 544.000i − 1.54108i −0.637394 0.770538i $$-0.719988\pi$$
0.637394 0.770538i $$-0.280012\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −640.000 −1.79775
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 361.000 1.00000
$$362$$ 76.0000i 0.209945i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ − 550.000i − 1.47453i −0.675603 0.737265i $$-0.736117\pi$$
0.675603 0.737265i $$-0.263883\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ − 400.000i − 1.06101i
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 380.000 0.984456
$$387$$ 0 0
$$388$$ − 520.000i − 1.34021i
$$389$$ −680.000 −1.74807 −0.874036 0.485861i $$-0.838506\pi$$
−0.874036 + 0.485861i $$0.838506\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 392.000i 1.00000i
$$393$$ 0 0
$$394$$ 112.000 0.284264
$$395$$ 0 0
$$396$$ 0 0
$$397$$ − 650.000i − 1.63728i −0.574307 0.818640i $$-0.694729\pi$$
0.574307 0.818640i $$-0.305271\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 80.0000 0.199501 0.0997506 0.995012i $$-0.468195\pi$$
0.0997506 + 0.995012i $$0.468195\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 160.000 0.396040
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −782.000 −1.91198 −0.955990 0.293399i $$-0.905214\pi$$
−0.955990 + 0.293399i $$0.905214\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 320.000 0.769231
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −58.0000 −0.137767 −0.0688836 0.997625i $$-0.521944\pi$$
−0.0688836 + 0.997625i $$0.521944\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 448.000 1.05660
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 290.000i 0.669746i 0.942263 + 0.334873i $$0.108693\pi$$
−0.942263 + 0.334873i $$0.891307\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 728.000 1.66972
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 320.000i 0.723982i
$$443$$ 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
$$449$$ −560.000 −1.24722 −0.623608 0.781737i $$-0.714334\pi$$
−0.623608 + 0.781737i $$0.714334\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ − 896.000i − 1.98230i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 850.000i 1.85996i 0.367615 + 0.929978i $$0.380174\pi$$
−0.367615 + 0.929978i $$0.619826\pi$$
$$458$$ 884.000i 1.93013i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −760.000 −1.64859 −0.824295 0.566161i $$-0.808428\pi$$
−0.824295 + 0.566161i $$0.808428\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 640.000 1.37931
$$465$$ 0 0
$$466$$ −832.000 −1.78541
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 700.000 1.45530
$$482$$ − 836.000i − 1.73444i
$$483$$ 0 0
$$484$$ −484.000 −1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 176.000i 0.360656i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 640.000i 1.29817i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 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
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −440.000 −0.864440 −0.432220 0.901768i $$-0.642270\pi$$
−0.432220 + 0.901768i $$0.642270\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 512.000i 1.00000i
$$513$$ 0 0
$$514$$ −128.000 −0.249027
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −880.000 −1.68906 −0.844530 0.535509i $$-0.820120\pi$$
−0.844530 + 0.535509i $$0.820120\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −529.000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ − 800.000i − 1.50094i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 1040.00i 1.93309i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −682.000 −1.26063 −0.630314 0.776340i $$-0.717074\pi$$
−0.630314 + 0.776340i $$0.717074\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −512.000 −0.941176
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 704.000i 1.28467i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 460.000 0.830325
$$555$$ 0 0
$$556$$ 0 0
$$557$$ − 1064.00i − 1.91023i −0.296230 0.955117i $$-0.595729\pi$$
0.296230 0.955117i $$-0.404271\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 640.000i 1.13879i
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1040.00 −1.82777 −0.913884 0.405975i $$-0.866932\pi$$
−0.913884 + 0.405975i $$0.866932\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 1150.00i 1.99307i 0.0831889 + 0.996534i $$0.473490\pi$$
−0.0831889 + 0.996534i $$0.526510\pi$$
$$578$$ 66.0000i 0.114187i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 880.000 1.50685
$$585$$ 0 0
$$586$$ 272.000 0.464164
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1120.00i 1.89189i
$$593$$ − 736.000i − 1.24115i −0.784148 0.620573i $$-0.786900\pi$$
0.784148 0.620573i $$-0.213100\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −1120.00 −1.87919
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1102.00 −1.83361 −0.916805 0.399334i $$-0.869241\pi$$
−0.916805 + 0.399334i $$0.869241\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 70.0000i − 0.114192i −0.998369 0.0570962i $$-0.981816\pi$$
0.998369 0.0570962i $$-0.0181842\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1216.00i 1.97083i 0.170178 + 0.985413i $$0.445566\pi$$
−0.170178 + 0.985413i $$0.554434\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −100.000 −0.159744
$$627$$ 0 0
$$628$$ 680.000i 1.08280i
$$629$$ −1120.00 −1.78060
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −1232.00 −1.94322
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 490.000i 0.769231i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −400.000 −0.624025 −0.312012 0.950078i $$-0.601003\pi$$
−0.312012 + 0.950078i $$0.601003\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ − 1144.00i − 1.75191i −0.482389 0.875957i $$-0.660231\pi$$
0.482389 0.875957i $$-0.339769\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 1280.00 1.95122
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 1178.00 1.78215 0.891074 0.453858i $$-0.149953\pi$$
0.891074 + 0.453858i $$0.149953\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 770.000i 1.14413i 0.820208 + 0.572065i $$0.193858\pi$$
−0.820208 + 0.572065i $$0.806142\pi$$
$$674$$ 700.000 1.03858
$$675$$ 0 0
$$676$$ −276.000 −0.408284
$$677$$ − 104.000i − 0.153619i −0.997046 0.0768095i $$-0.975527\pi$$
0.997046 0.0768095i $$-0.0244733\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 560.000 0.812772
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ − 416.000i − 0.601156i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1280.00i 1.83644i
$$698$$ 1196.00i 1.71347i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −520.000 −0.741797 −0.370899 0.928673i $$-0.620950\pi$$
−0.370899 + 0.928673i $$0.620950\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 1088.00 1.54108
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −518.000 −0.730606 −0.365303 0.930889i $$-0.619035\pi$$
−0.365303 + 0.930889i $$0.619035\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ − 1280.00i − 1.79775i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 722.000i 1.00000i
$$723$$ 0 0
$$724$$ −152.000 −0.209945
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ − 1450.00i − 1.97817i −0.147340 0.989086i $$-0.547071\pi$$
0.147340 0.989086i $$-0.452929\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 1100.00 1.47453
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 800.000 1.06101
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 1190.00i − 1.57199i −0.618230 0.785997i $$-0.712150\pi$$
0.618230 0.785997i $$-0.287850\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 1520.00 1.99737 0.998686 0.0512484i $$-0.0163200\pi$$
0.998686 + 0.0512484i $$0.0163200\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −962.000 −1.25098 −0.625488 0.780234i $$-0.715100\pi$$
−0.625488 + 0.780234i $$0.715100\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 760.000i 0.984456i
$$773$$ 1496.00i 1.93532i 0.252264 + 0.967658i $$0.418825\pi$$
−0.252264 + 0.967658i $$0.581175\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1040.00 1.34021
$$777$$ 0 0
$$778$$ − 1360.00i − 1.74807i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −784.000 −1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 224.000i 0.284264i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 220.000i 0.277427i
$$794$$ 1300.00 1.63728
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1144.00i 1.43538i 0.696361 + 0.717691i $$0.254801\pi$$
−0.696361 + 0.717691i $$0.745199\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 160.000i 0.199501i
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 320.000i 0.396040i
$$809$$ −560.000 −0.692213 −0.346106 0.938195i $$-0.612496\pi$$
−0.346106 + 0.938195i $$0.612496\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ − 1564.00i − 1.91198i
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 1400.00 1.70524 0.852619 0.522533i $$-0.175013\pi$$
0.852619 + 0.522533i $$0.175013\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 1258.00 1.51749 0.758745 0.651387i $$-0.225813\pi$$
0.758745 + 0.651387i $$0.225813\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 640.000i 0.769231i
$$833$$ − 784.000i − 0.941176i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 759.000 0.902497
$$842$$ − 116.000i − 0.137767i
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 896.000i 1.05660i
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 410.000i 0.480657i 0.970692 + 0.240328i $$0.0772551\pi$$
−0.970692 + 0.240328i $$0.922745\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ − 464.000i − 0.541424i −0.962660 0.270712i $$-0.912741\pi$$
0.962660 0.270712i $$-0.0872590\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 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
$$866$$ −580.000 −0.669746
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 1456.00i 1.66972i
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ − 1610.00i − 1.83580i −0.396807 0.917902i $$-0.629882\pi$$
0.396807 0.917902i $$-0.370118\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −1600.00 −1.81612 −0.908059 0.418842i $$-0.862436\pi$$
−0.908059 + 0.418842i $$0.862436\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ −640.000 −0.723982
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ − 1120.00i − 1.24722i
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −896.000 −0.994451
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 1792.00 1.98230
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −1700.00 −1.85996
$$915$$ 0 0
$$916$$ −1768.00 −1.93013
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ − 1520.00i − 1.64859i
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 1280.00i 1.37931i
$$929$$ 1840.00 1.98062 0.990312 0.138859i $$-0.0443435\pi$$
0.990312 + 0.138859i $$0.0443435\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ − 1664.00i − 1.78541i
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 430.000i 0.458911i 0.973319 + 0.229456i $$0.0736946\pi$$
−0.973319 + 0.229456i $$0.926305\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 1160.00 1.23273 0.616366 0.787460i $$-0.288604\pi$$
0.616366 + 0.787460i $$0.288604\pi$$
$$942$$ 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
$$949$$ 1100.00 1.15911
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ − 1456.00i − 1.52781i −0.645331 0.763903i $$-0.723280\pi$$
0.645331 0.763903i $$-0.276720\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 961.000 1.00000
$$962$$ 1400.00i 1.45530i
$$963$$ 0 0
$$964$$ 1672.00 1.73444
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ − 968.000i − 1.00000i
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −352.000 −0.360656
$$977$$ 496.000i 0.507677i 0.967247 + 0.253838i $$0.0816931\pi$$
−0.967247 + 0.253838i $$0.918307\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ −1280.00 −1.29817
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ − 1850.00i − 1.85557i −0.373119 0.927783i $$-0.621712\pi$$
0.373119 0.927783i $$-0.378288\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 900.3.f.b.199.2 2
3.2 odd 2 900.3.f.a.199.1 2
4.3 odd 2 CM 900.3.f.b.199.2 2
5.2 odd 4 36.3.d.a.19.1 1
5.3 odd 4 900.3.c.c.451.1 1
5.4 even 2 inner 900.3.f.b.199.1 2
12.11 even 2 900.3.f.a.199.1 2
15.2 even 4 36.3.d.b.19.1 yes 1
15.8 even 4 900.3.c.b.451.1 1
15.14 odd 2 900.3.f.a.199.2 2
20.3 even 4 900.3.c.c.451.1 1
20.7 even 4 36.3.d.a.19.1 1
20.19 odd 2 inner 900.3.f.b.199.1 2
40.27 even 4 576.3.g.a.127.1 1
40.37 odd 4 576.3.g.a.127.1 1
45.2 even 12 324.3.f.e.271.1 2
45.7 odd 12 324.3.f.f.271.1 2
45.22 odd 12 324.3.f.f.55.1 2
45.32 even 12 324.3.f.e.55.1 2
60.23 odd 4 900.3.c.b.451.1 1
60.47 odd 4 36.3.d.b.19.1 yes 1
60.59 even 2 900.3.f.a.199.2 2
80.27 even 4 2304.3.b.d.127.2 2
80.37 odd 4 2304.3.b.d.127.2 2
80.67 even 4 2304.3.b.d.127.1 2
80.77 odd 4 2304.3.b.d.127.1 2
120.77 even 4 576.3.g.c.127.1 1
120.107 odd 4 576.3.g.c.127.1 1
180.7 even 12 324.3.f.f.271.1 2
180.47 odd 12 324.3.f.e.271.1 2
180.67 even 12 324.3.f.f.55.1 2
180.167 odd 12 324.3.f.e.55.1 2
240.77 even 4 2304.3.b.e.127.2 2
240.107 odd 4 2304.3.b.e.127.1 2
240.197 even 4 2304.3.b.e.127.1 2
240.227 odd 4 2304.3.b.e.127.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
36.3.d.a.19.1 1 5.2 odd 4
36.3.d.a.19.1 1 20.7 even 4
36.3.d.b.19.1 yes 1 15.2 even 4
36.3.d.b.19.1 yes 1 60.47 odd 4
324.3.f.e.55.1 2 45.32 even 12
324.3.f.e.55.1 2 180.167 odd 12
324.3.f.e.271.1 2 45.2 even 12
324.3.f.e.271.1 2 180.47 odd 12
324.3.f.f.55.1 2 45.22 odd 12
324.3.f.f.55.1 2 180.67 even 12
324.3.f.f.271.1 2 45.7 odd 12
324.3.f.f.271.1 2 180.7 even 12
576.3.g.a.127.1 1 40.27 even 4
576.3.g.a.127.1 1 40.37 odd 4
576.3.g.c.127.1 1 120.77 even 4
576.3.g.c.127.1 1 120.107 odd 4
900.3.c.b.451.1 1 15.8 even 4
900.3.c.b.451.1 1 60.23 odd 4
900.3.c.c.451.1 1 5.3 odd 4
900.3.c.c.451.1 1 20.3 even 4
900.3.f.a.199.1 2 3.2 odd 2
900.3.f.a.199.1 2 12.11 even 2
900.3.f.a.199.2 2 15.14 odd 2
900.3.f.a.199.2 2 60.59 even 2
900.3.f.b.199.1 2 5.4 even 2 inner
900.3.f.b.199.1 2 20.19 odd 2 inner
900.3.f.b.199.2 2 1.1 even 1 trivial
900.3.f.b.199.2 2 4.3 odd 2 CM
2304.3.b.d.127.1 2 80.67 even 4
2304.3.b.d.127.1 2 80.77 odd 4
2304.3.b.d.127.2 2 80.27 even 4
2304.3.b.d.127.2 2 80.37 odd 4
2304.3.b.e.127.1 2 240.107 odd 4
2304.3.b.e.127.1 2 240.197 even 4
2304.3.b.e.127.2 2 240.77 even 4
2304.3.b.e.127.2 2 240.227 odd 4