# Properties

 Label 36.3.d.a.19.1 Level $36$ Weight $3$ Character 36.19 Self dual yes Analytic conductor $0.981$ Analytic rank $0$ Dimension $1$ CM discriminant -4 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$36 = 2^{2} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 36.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$0.980928951697$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 19.1 Character $$\chi$$ $$=$$ 36.19

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.00000 q^{2} +4.00000 q^{4} +8.00000 q^{5} -8.00000 q^{8} +O(q^{10})$$ $$q-2.00000 q^{2} +4.00000 q^{4} +8.00000 q^{5} -8.00000 q^{8} -16.0000 q^{10} -10.0000 q^{13} +16.0000 q^{16} -16.0000 q^{17} +32.0000 q^{20} +39.0000 q^{25} +20.0000 q^{26} -40.0000 q^{29} -32.0000 q^{32} +32.0000 q^{34} -70.0000 q^{37} -64.0000 q^{40} +80.0000 q^{41} +49.0000 q^{49} -78.0000 q^{50} -40.0000 q^{52} +56.0000 q^{53} +80.0000 q^{58} -22.0000 q^{61} +64.0000 q^{64} -80.0000 q^{65} -64.0000 q^{68} +110.000 q^{73} +140.000 q^{74} +128.000 q^{80} -160.000 q^{82} -128.000 q^{85} -160.000 q^{89} -130.000 q^{97} -98.0000 q^{98} +O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$$.

 $$n$$ $$19$$ $$29$$ $$\chi(n)$$ $$-1$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 −1.00000
$$3$$ 0 0
$$4$$ 4.00000 1.00000
$$5$$ 8.00000 1.60000 0.800000 0.600000i $$-0.204833\pi$$
0.800000 + 0.600000i $$0.204833\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −8.00000 −1.00000
$$9$$ 0 0
$$10$$ −16.0000 −1.60000
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ −10.0000 −0.769231 −0.384615 0.923077i $$-0.625666\pi$$
−0.384615 + 0.923077i $$0.625666\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 16.0000 1.00000
$$17$$ −16.0000 −0.941176 −0.470588 0.882353i $$-0.655958\pi$$
−0.470588 + 0.882353i $$0.655958\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 32.0000 1.60000
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 39.0000 1.56000
$$26$$ 20.0000 0.769231
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −40.0000 −1.37931 −0.689655 0.724138i $$-0.742238\pi$$
−0.689655 + 0.724138i $$0.742238\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −32.0000 −1.00000
$$33$$ 0 0
$$34$$ 32.0000 0.941176
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −70.0000 −1.89189 −0.945946 0.324324i $$-0.894863\pi$$
−0.945946 + 0.324324i $$0.894863\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −64.0000 −1.60000
$$41$$ 80.0000 1.95122 0.975610 0.219512i $$-0.0704466\pi$$
0.975610 + 0.219512i $$0.0704466\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ 49.0000 1.00000
$$50$$ −78.0000 −1.56000
$$51$$ 0 0
$$52$$ −40.0000 −0.769231
$$53$$ 56.0000 1.05660 0.528302 0.849057i $$-0.322829\pi$$
0.528302 + 0.849057i $$0.322829\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 80.0000 1.37931
$$59$$ 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
$$65$$ −80.0000 −1.23077
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ −64.0000 −0.941176
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 0 0
$$73$$ 110.000 1.50685 0.753425 0.657534i $$-0.228401\pi$$
0.753425 + 0.657534i $$0.228401\pi$$
$$74$$ 140.000 1.89189
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 128.000 1.60000
$$81$$ 0 0
$$82$$ −160.000 −1.95122
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ −128.000 −1.50588
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −160.000 −1.79775 −0.898876 0.438202i $$-0.855615\pi$$
−0.898876 + 0.438202i $$0.855615\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −130.000 −1.34021 −0.670103 0.742268i $$-0.733750\pi$$
−0.670103 + 0.742268i $$0.733750\pi$$
$$98$$ −98.0000 −1.00000
$$99$$ 0 0
$$100$$ 156.000 1.56000
$$101$$ −40.0000 −0.396040 −0.198020 0.980198i $$-0.563451\pi$$
−0.198020 + 0.980198i $$0.563451\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 80.0000 0.769231
$$105$$ 0 0
$$106$$ −112.000 −1.05660
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 182.000 1.66972 0.834862 0.550459i $$-0.185547\pi$$
0.834862 + 0.550459i $$0.185547\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 224.000 1.98230 0.991150 0.132743i $$-0.0423786\pi$$
0.991150 + 0.132743i $$0.0423786\pi$$
$$114$$ 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
$$122$$ 44.0000 0.360656
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 112.000 0.896000
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −128.000 −1.00000
$$129$$ 0 0
$$130$$ 160.000 1.23077
$$131$$ 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
$$137$$ 176.000 1.28467 0.642336 0.766423i $$-0.277965\pi$$
0.642336 + 0.766423i $$0.277965\pi$$
$$138$$ 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
$$145$$ −320.000 −2.20690
$$146$$ −220.000 −1.50685
$$147$$ 0 0
$$148$$ −280.000 −1.89189
$$149$$ −280.000 −1.87919 −0.939597 0.342282i $$-0.888800\pi$$
−0.939597 + 0.342282i $$0.888800\pi$$
$$150$$ 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
$$157$$ 170.000 1.08280 0.541401 0.840764i $$-0.317894\pi$$
0.541401 + 0.840764i $$0.317894\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −256.000 −1.60000
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 320.000 1.95122
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −69.0000 −0.408284
$$170$$ 256.000 1.50588
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 104.000 0.601156 0.300578 0.953757i $$-0.402820\pi$$
0.300578 + 0.953757i $$0.402820\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 320.000 1.79775
$$179$$ 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
$$185$$ −560.000 −3.02703
$$186$$ 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
$$193$$ −190.000 −0.984456 −0.492228 0.870466i $$-0.663817\pi$$
−0.492228 + 0.870466i $$0.663817\pi$$
$$194$$ 260.000 1.34021
$$195$$ 0 0
$$196$$ 196.000 1.00000
$$197$$ 56.0000 0.284264 0.142132 0.989848i $$-0.454604\pi$$
0.142132 + 0.989848i $$0.454604\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ −312.000 −1.56000
$$201$$ 0 0
$$202$$ 80.0000 0.396040
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 640.000 3.12195
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −160.000 −0.769231
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 224.000 1.05660
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −364.000 −1.66972
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 160.000 0.723982
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −448.000 −1.98230
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ −442.000 −1.93013 −0.965066 0.262009i $$-0.915615\pi$$
−0.965066 + 0.262009i $$0.915615\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 320.000 1.37931
$$233$$ 416.000 1.78541 0.892704 0.450644i $$-0.148806\pi$$
0.892704 + 0.450644i $$0.148806\pi$$
$$234$$ 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 $$0.834095\pi$$
$$242$$ −242.000 −1.00000
$$243$$ 0 0
$$244$$ −88.0000 −0.360656
$$245$$ 392.000 1.60000
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −224.000 −0.896000
$$251$$ 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
$$257$$ −64.0000 −0.249027 −0.124514 0.992218i $$-0.539737\pi$$
−0.124514 + 0.992218i $$0.539737\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −320.000 −1.23077
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ 0 0
$$265$$ 448.000 1.69057
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −520.000 −1.93309 −0.966543 0.256506i $$-0.917429\pi$$
−0.966543 + 0.256506i $$0.917429\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −256.000 −0.941176
$$273$$ 0 0
$$274$$ −352.000 −1.28467
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 230.000 0.830325 0.415162 0.909747i $$-0.363725\pi$$
0.415162 + 0.909747i $$0.363725\pi$$
$$278$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −33.0000 −0.114187
$$290$$ 640.000 2.20690
$$291$$ 0 0
$$292$$ 440.000 1.50685
$$293$$ −136.000 −0.464164 −0.232082 0.972696i $$-0.574554\pi$$
−0.232082 + 0.972696i $$0.574554\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 560.000 1.89189
$$297$$ 0 0
$$298$$ 560.000 1.87919
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −176.000 −0.577049
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 50.0000 0.159744 0.0798722 0.996805i $$-0.474549\pi$$
0.0798722 + 0.996805i $$0.474549\pi$$
$$314$$ −340.000 −1.08280
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −616.000 −1.94322 −0.971609 0.236593i $$-0.923969\pi$$
−0.971609 + 0.236593i $$0.923969\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 512.000 1.60000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −390.000 −1.20000
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −640.000 −1.95122
$$329$$ 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
$$337$$ 350.000 1.03858 0.519288 0.854599i $$-0.326197\pi$$
0.519288 + 0.854599i $$0.326197\pi$$
$$338$$ 138.000 0.408284
$$339$$ 0 0
$$340$$ −512.000 −1.50588
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −208.000 −0.601156
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ −598.000 −1.71347 −0.856734 0.515759i $$-0.827510\pi$$
−0.856734 + 0.515759i $$0.827510\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −544.000 −1.54108 −0.770538 0.637394i $$-0.780012\pi$$
−0.770538 + 0.637394i $$0.780012\pi$$
$$354$$ 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
$$362$$ −76.0000 −0.209945
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 880.000 2.41096
$$366$$ 0 0
$$367$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 1120.00 3.02703
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −550.000 −1.47453 −0.737265 0.675603i $$-0.763883\pi$$
−0.737265 + 0.675603i $$0.763883\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 400.000 1.06101
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 380.000 0.984456
$$387$$ 0 0
$$388$$ −520.000 −1.34021
$$389$$ 680.000 1.74807 0.874036 0.485861i $$-0.161494\pi$$
0.874036 + 0.485861i $$0.161494\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −392.000 −1.00000
$$393$$ 0 0
$$394$$ −112.000 −0.284264
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 650.000 1.63728 0.818640 0.574307i $$-0.194729\pi$$
0.818640 + 0.574307i $$0.194729\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 624.000 1.56000
$$401$$ 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 $$-0.0947863\pi$$
0.955990 + 0.293399i $$0.0947863\pi$$
$$410$$ −1280.00 −3.12195
$$411$$ 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
$$425$$ −624.000 −1.46824
$$426$$ 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
$$433$$ 290.000 0.669746 0.334873 0.942263i $$-0.391307\pi$$
0.334873 + 0.942263i $$0.391307\pi$$
$$434$$ 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
$$442$$ −320.000 −0.723982
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ −1280.00 −2.87640
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 560.000 1.24722 0.623608 0.781737i $$-0.285666\pi$$
0.623608 + 0.781737i $$0.285666\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 896.000 1.98230
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −850.000 −1.85996 −0.929978 0.367615i $$-0.880174\pi$$
−0.929978 + 0.367615i $$0.880174\pi$$
$$458$$ 884.000 1.93013
$$459$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ −640.000 −1.37931
$$465$$ 0 0
$$466$$ −832.000 −1.78541
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 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
$$482$$ 836.000 1.73444
$$483$$ 0 0
$$484$$ 484.000 1.00000
$$485$$ −1040.00 −2.14433
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 176.000 0.360656
$$489$$ 0 0
$$490$$ −784.000 −1.60000
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 640.000 1.29817
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 448.000 0.896000
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ −320.000 −0.633663
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 440.000 0.864440 0.432220 0.901768i $$-0.357730\pi$$
0.432220 + 0.901768i $$0.357730\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −512.000 −1.00000
$$513$$ 0 0
$$514$$ 128.000 0.249027
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 640.000 1.23077
$$521$$ −880.000 −1.68906 −0.844530 0.535509i $$-0.820120\pi$$
−0.844530 + 0.535509i $$0.820120\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 529.000 1.00000
$$530$$ −896.000 −1.69057
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −800.000 −1.50094
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 1040.00 1.93309
$$539$$ 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
$$545$$ 1456.00 2.67156
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 704.000 1.28467
$$549$$ 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
$$557$$ 1064.00 1.91023 0.955117 0.296230i $$-0.0957294\pi$$
0.955117 + 0.296230i $$0.0957294\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −640.000 −1.13879
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 1792.00 3.17168
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1040.00 1.82777 0.913884 0.405975i $$-0.133068\pi$$
0.913884 + 0.405975i $$0.133068\pi$$
$$570$$ 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
$$577$$ −1150.00 −1.99307 −0.996534 0.0831889i $$-0.973490\pi$$
−0.996534 + 0.0831889i $$0.973490\pi$$
$$578$$ 66.0000 0.114187
$$579$$ 0 0
$$580$$ −1280.00 −2.20690
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −880.000 −1.50685
$$585$$ 0 0
$$586$$ 272.000 0.464164
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1120.00 −1.89189
$$593$$ −736.000 −1.24115 −0.620573 0.784148i $$-0.713100\pi$$
−0.620573 + 0.784148i $$0.713100\pi$$
$$594$$ 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
$$605$$ 968.000 1.60000
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 352.000 0.577049
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −70.0000 −0.114192 −0.0570962 0.998369i $$-0.518184\pi$$
−0.0570962 + 0.998369i $$0.518184\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1216.00 −1.97083 −0.985413 0.170178i $$-0.945566\pi$$
−0.985413 + 0.170178i $$0.945566\pi$$
$$618$$ 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
$$625$$ −79.0000 −0.126400
$$626$$ −100.000 −0.159744
$$627$$ 0 0
$$628$$ 680.000 1.08280
$$629$$ 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
$$637$$ −490.000 −0.769231
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −1024.00 −1.60000
$$641$$ −400.000 −0.624025 −0.312012 0.950078i $$-0.601003\pi$$
−0.312012 + 0.950078i $$0.601003\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 780.000 1.20000
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1144.00 −1.75191 −0.875957 0.482389i $$-0.839769\pi$$
−0.875957 + 0.482389i $$0.839769\pi$$
$$654$$ 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
$$673$$ 770.000 1.14413 0.572065 0.820208i $$-0.306142\pi$$
0.572065 + 0.820208i $$0.306142\pi$$
$$674$$ −700.000 −1.03858
$$675$$ 0 0
$$676$$ −276.000 −0.408284
$$677$$ 104.000 0.153619 0.0768095 0.997046i $$-0.475527\pi$$
0.0768095 + 0.997046i $$0.475527\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 1024.00 1.50588
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 1408.00 2.05547
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −560.000 −0.812772
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 416.000 0.601156
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1280.00 −1.83644
$$698$$ 1196.00 1.71347
$$699$$ 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 $$-0.380965\pi$$
0.365303 + 0.930889i $$0.380965\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 1280.00 1.79775
$$713$$ 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
$$722$$ −722.000 −1.00000
$$723$$ 0 0
$$724$$ 152.000 0.209945
$$725$$ −1560.00 −2.15172
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −1760.00 −2.41096
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1450.00 −1.97817 −0.989086 0.147340i $$-0.952929\pi$$
−0.989086 + 0.147340i $$0.952929\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ −2240.00 −3.02703
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ −2240.00 −3.00671
$$746$$ 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
$$757$$ 1190.00 1.57199 0.785997 0.618230i $$-0.212150\pi$$
0.785997 + 0.618230i $$0.212150\pi$$
$$758$$ 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 $$-0.284900\pi$$
0.625488 + 0.780234i $$0.284900\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −760.000 −0.984456
$$773$$ 1496.00 1.93532 0.967658 0.252264i $$-0.0811751\pi$$
0.967658 + 0.252264i $$0.0811751\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1040.00 1.34021
$$777$$ 0 0
$$778$$ −1360.00 −1.74807
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 784.000 1.00000
$$785$$ 1360.00 1.73248
$$786$$ 0 0
$$787$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$788$$ 224.000 0.284264
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 220.000 0.277427
$$794$$ −1300.00 −1.63728
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −1144.00 −1.43538 −0.717691 0.696361i $$-0.754801\pi$$
−0.717691 + 0.696361i $$0.754801\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ −1248.00 −1.56000
$$801$$ 0 0
$$802$$ −160.000 −0.199501
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 320.000 0.396040
$$809$$ 560.000 0.692213 0.346106 0.938195i $$-0.387504\pi$$
0.346106 + 0.938195i $$0.387504\pi$$
$$810$$ 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
$$818$$ −1564.00 −1.91198
$$819$$ 0 0
$$820$$ 2560.00 3.12195
$$821$$ 1400.00 1.70524 0.852619 0.522533i $$-0.175013\pi$$
0.852619 + 0.522533i $$0.175013\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ −1258.00 −1.51749 −0.758745 0.651387i $$-0.774187\pi$$
−0.758745 + 0.651387i $$0.774187\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −640.000 −0.769231
$$833$$ −784.000 −0.941176
$$834$$ 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
$$842$$ 116.000 0.137767
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −552.000 −0.653254
$$846$$ 0 0
$$847$$ 0 0
$$848$$ 896.000 1.05660
$$849$$ 0 0
$$850$$ 1248.00 1.46824
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 410.000 0.480657 0.240328 0.970692i $$-0.422745\pi$$
0.240328 + 0.970692i $$0.422745\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 464.000 0.541424 0.270712 0.962660i $$-0.412741\pi$$
0.270712 + 0.962660i $$0.412741\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 832.000 0.961850
$$866$$ −580.000 −0.669746
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −1456.00 −1.66972
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 1610.00 1.83580 0.917902 0.396807i $$-0.129882\pi$$
0.917902 + 0.396807i $$0.129882\pi$$
$$878$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$884$$ 640.000 0.723982
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 2560.00 2.87640
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −1120.00 −1.24722
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −896.000 −0.994451
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −1792.00 −1.98230
$$905$$ 304.000 0.335912
$$906$$ 0 0
$$907$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$908$$ 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
$$922$$ 1520.00 1.64859
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −2730.00 −2.95135
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 1280.00 1.37931
$$929$$ −1840.00 −1.98062 −0.990312 0.138859i $$-0.955657\pi$$
−0.990312 + 0.138859i $$0.955657\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 1664.00 1.78541
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −430.000 −0.458911 −0.229456 0.973319i $$-0.573695\pi$$
−0.229456 + 0.973319i $$0.573695\pi$$
$$938$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ −1100.00 −1.15911
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −1456.00 −1.52781 −0.763903 0.645331i $$-0.776720\pi$$
−0.763903 + 0.645331i $$0.776720\pi$$
$$954$$ 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
$$962$$ −1400.00 −1.45530
$$963$$ 0 0
$$964$$ −1672.00 −1.73444
$$965$$ −1520.00 −1.57513
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ −968.000 −1.00000
$$969$$ 0 0
$$970$$ 2080.00 2.14433
$$971$$ 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
$$977$$ −496.000 −0.507677 −0.253838 0.967247i $$-0.581693\pi$$
−0.253838 + 0.967247i $$0.581693\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 1568.00 1.60000
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$984$$ 0 0
$$985$$ 448.000 0.454822
$$986$$ −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
$$997$$ 1850.00 1.85557 0.927783 0.373119i $$-0.121712\pi$$
0.927783 + 0.373119i $$0.121712\pi$$
$$998$$ 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 36.3.d.a.19.1 1
3.2 odd 2 36.3.d.b.19.1 yes 1
4.3 odd 2 CM 36.3.d.a.19.1 1
5.2 odd 4 900.3.f.b.199.1 2
5.3 odd 4 900.3.f.b.199.2 2
5.4 even 2 900.3.c.c.451.1 1
8.3 odd 2 576.3.g.a.127.1 1
8.5 even 2 576.3.g.a.127.1 1
9.2 odd 6 324.3.f.e.271.1 2
9.4 even 3 324.3.f.f.55.1 2
9.5 odd 6 324.3.f.e.55.1 2
9.7 even 3 324.3.f.f.271.1 2
12.11 even 2 36.3.d.b.19.1 yes 1
15.2 even 4 900.3.f.a.199.2 2
15.8 even 4 900.3.f.a.199.1 2
15.14 odd 2 900.3.c.b.451.1 1
16.3 odd 4 2304.3.b.d.127.1 2
16.5 even 4 2304.3.b.d.127.2 2
16.11 odd 4 2304.3.b.d.127.2 2
16.13 even 4 2304.3.b.d.127.1 2
20.3 even 4 900.3.f.b.199.2 2
20.7 even 4 900.3.f.b.199.1 2
20.19 odd 2 900.3.c.c.451.1 1
24.5 odd 2 576.3.g.c.127.1 1
24.11 even 2 576.3.g.c.127.1 1
36.7 odd 6 324.3.f.f.271.1 2
36.11 even 6 324.3.f.e.271.1 2
36.23 even 6 324.3.f.e.55.1 2
36.31 odd 6 324.3.f.f.55.1 2
48.5 odd 4 2304.3.b.e.127.1 2
48.11 even 4 2304.3.b.e.127.1 2
48.29 odd 4 2304.3.b.e.127.2 2
48.35 even 4 2304.3.b.e.127.2 2
60.23 odd 4 900.3.f.a.199.1 2
60.47 odd 4 900.3.f.a.199.2 2
60.59 even 2 900.3.c.b.451.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
36.3.d.a.19.1 1 1.1 even 1 trivial
36.3.d.a.19.1 1 4.3 odd 2 CM
36.3.d.b.19.1 yes 1 3.2 odd 2
36.3.d.b.19.1 yes 1 12.11 even 2
324.3.f.e.55.1 2 9.5 odd 6
324.3.f.e.55.1 2 36.23 even 6
324.3.f.e.271.1 2 9.2 odd 6
324.3.f.e.271.1 2 36.11 even 6
324.3.f.f.55.1 2 9.4 even 3
324.3.f.f.55.1 2 36.31 odd 6
324.3.f.f.271.1 2 9.7 even 3
324.3.f.f.271.1 2 36.7 odd 6
576.3.g.a.127.1 1 8.3 odd 2
576.3.g.a.127.1 1 8.5 even 2
576.3.g.c.127.1 1 24.5 odd 2
576.3.g.c.127.1 1 24.11 even 2
900.3.c.b.451.1 1 15.14 odd 2
900.3.c.b.451.1 1 60.59 even 2
900.3.c.c.451.1 1 5.4 even 2
900.3.c.c.451.1 1 20.19 odd 2
900.3.f.a.199.1 2 15.8 even 4
900.3.f.a.199.1 2 60.23 odd 4
900.3.f.a.199.2 2 15.2 even 4
900.3.f.a.199.2 2 60.47 odd 4
900.3.f.b.199.1 2 5.2 odd 4
900.3.f.b.199.1 2 20.7 even 4
900.3.f.b.199.2 2 5.3 odd 4
900.3.f.b.199.2 2 20.3 even 4
2304.3.b.d.127.1 2 16.3 odd 4
2304.3.b.d.127.1 2 16.13 even 4
2304.3.b.d.127.2 2 16.5 even 4
2304.3.b.d.127.2 2 16.11 odd 4
2304.3.b.e.127.1 2 48.5 odd 4
2304.3.b.e.127.1 2 48.11 even 4
2304.3.b.e.127.2 2 48.29 odd 4
2304.3.b.e.127.2 2 48.35 even 4