# Properties

 Label 441.4.a.m.1.1 Level $441$ Weight $4$ Character 441.1 Self dual yes Analytic conductor $26.020$ Analytic rank $0$ Dimension $1$ CM discriminant -7 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$26.0198423125$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 49) Fricke sign: $$1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 441.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+5.00000 q^{2} +17.0000 q^{4} +45.0000 q^{8} +O(q^{10})$$ $$q+5.00000 q^{2} +17.0000 q^{4} +45.0000 q^{8} +68.0000 q^{11} +89.0000 q^{16} +340.000 q^{22} +40.0000 q^{23} -125.000 q^{25} +166.000 q^{29} +85.0000 q^{32} +450.000 q^{37} -180.000 q^{43} +1156.00 q^{44} +200.000 q^{46} -625.000 q^{50} -590.000 q^{53} +830.000 q^{58} -287.000 q^{64} -740.000 q^{67} -688.000 q^{71} +2250.00 q^{74} -1384.00 q^{79} -900.000 q^{86} +3060.00 q^{88} +680.000 q^{92} +O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 5.00000 1.76777 0.883883 0.467707i $$-0.154920\pi$$
0.883883 + 0.467707i $$0.154920\pi$$
$$3$$ 0 0
$$4$$ 17.0000 2.12500
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 45.0000 1.98874
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 68.0000 1.86389 0.931944 0.362602i $$-0.118111\pi$$
0.931944 + 0.362602i $$0.118111\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 89.0000 1.39062
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 340.000 3.29492
$$23$$ 40.0000 0.362634 0.181317 0.983425i $$-0.441964\pi$$
0.181317 + 0.983425i $$0.441964\pi$$
$$24$$ 0 0
$$25$$ −125.000 −1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 166.000 1.06295 0.531473 0.847075i $$-0.321639\pi$$
0.531473 + 0.847075i $$0.321639\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 85.0000 0.469563
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 450.000 1.99945 0.999724 0.0235113i $$-0.00748457\pi$$
0.999724 + 0.0235113i $$0.00748457\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −180.000 −0.638366 −0.319183 0.947693i $$-0.603408\pi$$
−0.319183 + 0.947693i $$0.603408\pi$$
$$44$$ 1156.00 3.96076
$$45$$ 0 0
$$46$$ 200.000 0.641052
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −625.000 −1.76777
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −590.000 −1.52911 −0.764554 0.644560i $$-0.777041\pi$$
−0.764554 + 0.644560i $$0.777041\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 830.000 1.87904
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −287.000 −0.560547
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −740.000 −1.34933 −0.674667 0.738122i $$-0.735713\pi$$
−0.674667 + 0.738122i $$0.735713\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −688.000 −1.15001 −0.575004 0.818151i $$-0.695000\pi$$
−0.575004 + 0.818151i $$0.695000\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 2250.00 3.53456
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −1384.00 −1.97104 −0.985520 0.169559i $$-0.945766\pi$$
−0.985520 + 0.169559i $$0.945766\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −900.000 −1.12848
$$87$$ 0 0
$$88$$ 3060.00 3.70679
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 680.000 0.770597
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −2125.00 −2.12500
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −2950.00 −2.70311
$$107$$ 1580.00 1.42752 0.713759 0.700392i $$-0.246991\pi$$
0.713759 + 0.700392i $$0.246991\pi$$
$$108$$ 0 0
$$109$$ −54.0000 −0.0474519 −0.0237260 0.999718i $$-0.507553\pi$$
−0.0237260 + 0.999718i $$0.507553\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 670.000 0.557773 0.278886 0.960324i $$-0.410035\pi$$
0.278886 + 0.960324i $$0.410035\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 2822.00 2.25876
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 3293.00 2.47408
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2000.00 −1.39741 −0.698706 0.715409i $$-0.746240\pi$$
−0.698706 + 0.715409i $$0.746240\pi$$
$$128$$ −2115.00 −1.46048
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −3700.00 −2.38531
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −3110.00 −1.93945 −0.969727 0.244191i $$-0.921478\pi$$
−0.969727 + 0.244191i $$0.921478\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −3440.00 −2.03295
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 7650.00 4.24883
$$149$$ −814.000 −0.447554 −0.223777 0.974640i $$-0.571839\pi$$
−0.223777 + 0.974640i $$0.571839\pi$$
$$150$$ 0 0
$$151$$ −2952.00 −1.59093 −0.795465 0.606000i $$-0.792773\pi$$
−0.795465 + 0.606000i $$0.792773\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ −6920.00 −3.48434
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 1780.00 0.855340 0.427670 0.903935i $$-0.359335\pi$$
0.427670 + 0.903935i $$0.359335\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −2197.00 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −3060.00 −1.35653
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 6052.00 2.59197
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 2084.00 0.870198 0.435099 0.900383i $$-0.356713\pi$$
0.435099 + 0.900383i $$0.356713\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 1800.00 0.721183
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4072.00 1.54262 0.771308 0.636462i $$-0.219603\pi$$
0.771308 + 0.636462i $$0.219603\pi$$
$$192$$ 0 0
$$193$$ −4590.00 −1.71189 −0.855947 0.517064i $$-0.827025\pi$$
−0.855947 + 0.517064i $$0.827025\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2210.00 0.799269 0.399634 0.916675i $$-0.369137\pi$$
0.399634 + 0.916675i $$0.369137\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ −5625.00 −1.98874
$$201$$ 0 0
$$202$$ 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
$$211$$ 5868.00 1.91455 0.957274 0.289181i $$-0.0933830\pi$$
0.957274 + 0.289181i $$0.0933830\pi$$
$$212$$ −10030.0 −3.24935
$$213$$ 0 0
$$214$$ 7900.00 2.52352
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −270.000 −0.0838840
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 3350.00 0.986012
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 7470.00 2.11392
$$233$$ 4730.00 1.32993 0.664963 0.746877i $$-0.268447\pi$$
0.664963 + 0.746877i $$0.268447\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 7376.00 1.99629 0.998146 0.0608655i $$-0.0193861\pi$$
0.998146 + 0.0608655i $$0.0193861\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$242$$ 16465.0 4.37360
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 2720.00 0.675909
$$254$$ −10000.0 −2.47030
$$255$$ 0 0
$$256$$ −8279.00 −2.02124
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −7520.00 −1.76313 −0.881565 0.472063i $$-0.843509\pi$$
−0.881565 + 0.472063i $$0.843509\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −12580.0 −2.86734
$$269$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −15550.0 −3.42850
$$275$$ −8500.00 −1.86389
$$276$$ 0 0
$$277$$ 7310.00 1.58561 0.792807 0.609472i $$-0.208619\pi$$
0.792807 + 0.609472i $$0.208619\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −4342.00 −0.921786 −0.460893 0.887456i $$-0.652471\pi$$
−0.460893 + 0.887456i $$0.652471\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ −11696.0 −2.44377
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4913.00 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 20250.0 3.97638
$$297$$ 0 0
$$298$$ −4070.00 −0.791170
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −14760.0 −2.81239
$$303$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −23528.0 −4.18846
$$317$$ 6970.00 1.23493 0.617467 0.786597i $$-0.288159\pi$$
0.617467 + 0.786597i $$0.288159\pi$$
$$318$$ 0 0
$$319$$ 11288.0 1.98121
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 8900.00 1.51204
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 10908.0 1.81135 0.905677 0.423969i $$-0.139364\pi$$
0.905677 + 0.423969i $$0.139364\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −3330.00 −0.538269 −0.269135 0.963103i $$-0.586738\pi$$
−0.269135 + 0.963103i $$0.586738\pi$$
$$338$$ −10985.0 −1.76777
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −8100.00 −1.26954
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 4100.00 0.634293 0.317146 0.948377i $$-0.397275\pi$$
0.317146 + 0.948377i $$0.397275\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 5780.00 0.875213
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 10420.0 1.53831
$$359$$ 8104.00 1.19140 0.595700 0.803207i $$-0.296875\pi$$
0.595700 + 0.803207i $$0.296875\pi$$
$$360$$ 0 0
$$361$$ −6859.00 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 3560.00 0.504288
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −13970.0 −1.93925 −0.969624 0.244602i $$-0.921343\pi$$
−0.969624 + 0.244602i $$0.921343\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 11916.0 1.61500 0.807498 0.589870i $$-0.200821\pi$$
0.807498 + 0.589870i $$0.200821\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 20360.0 2.72698
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −22950.0 −3.02623
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 10526.0 1.37195 0.685976 0.727624i $$-0.259375\pi$$
0.685976 + 0.727624i $$0.259375\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 11050.0 1.41292
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −11125.0 −1.39062
$$401$$ −1598.00 −0.199003 −0.0995016 0.995037i $$-0.531725\pi$$
−0.0995016 + 0.995037i $$0.531725\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 30600.0 3.72675
$$408$$ 0 0
$$409$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 15262.0 1.76680 0.883402 0.468616i $$-0.155247\pi$$
0.883402 + 0.468616i $$0.155247\pi$$
$$422$$ 29340.0 3.38448
$$423$$ 0 0
$$424$$ −26550.0 −3.04100
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 26860.0 3.03347
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 8608.00 0.962025 0.481012 0.876714i $$-0.340269\pi$$
0.481012 + 0.876714i $$0.340269\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −918.000 −0.100835
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −18580.0 −1.99269 −0.996346 0.0854102i $$-0.972780\pi$$
−0.996346 + 0.0854102i $$0.972780\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 2686.00 0.282317 0.141158 0.989987i $$-0.454917\pi$$
0.141158 + 0.989987i $$0.454917\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 11390.0 1.18527
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 8010.00 0.819895 0.409947 0.912109i $$-0.365547\pi$$
0.409947 + 0.912109i $$0.365547\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ −8440.00 −0.847171 −0.423585 0.905856i $$-0.639229\pi$$
−0.423585 + 0.905856i $$0.639229\pi$$
$$464$$ 14774.0 1.47816
$$465$$ 0 0
$$466$$ 23650.0 2.35100
$$467$$ 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
$$473$$ −12240.0 −1.18984
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 36880.0 3.52898
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 55981.0 5.25742
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 21240.0 1.97634 0.988169 0.153371i $$-0.0490130\pi$$
0.988169 + 0.153371i $$0.0490130\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −20372.0 −1.87246 −0.936228 0.351394i $$-0.885708\pi$$
−0.936228 + 0.351394i $$0.885708\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −7236.00 −0.649154 −0.324577 0.945859i $$-0.605222\pi$$
−0.324577 + 0.945859i $$0.605222\pi$$
$$500$$ 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
$$506$$ 13600.0 1.19485
$$507$$ 0 0
$$508$$ −34000.0 −2.96950
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −24475.0 −2.11260
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −37600.0 −3.11680
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −10567.0 −0.868497
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −33300.0 −2.68347
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 15878.0 1.26183 0.630914 0.775853i $$-0.282680\pi$$
0.630914 + 0.775853i $$0.282680\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 12980.0 1.01460 0.507299 0.861770i $$-0.330644\pi$$
0.507299 + 0.861770i $$0.330644\pi$$
$$548$$ −52870.0 −4.12134
$$549$$ 0 0
$$550$$ −42500.0 −3.29492
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 36550.0 2.80300
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −20470.0 −1.55717 −0.778583 0.627541i $$-0.784061\pi$$
−0.778583 + 0.627541i $$0.784061\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −21710.0 −1.62950
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ −30960.0 −2.28706
$$569$$ 26906.0 1.98235 0.991176 0.132553i $$-0.0423175\pi$$
0.991176 + 0.132553i $$0.0423175\pi$$
$$570$$ 0 0
$$571$$ −6788.00 −0.497494 −0.248747 0.968569i $$-0.580019\pi$$
−0.248747 + 0.968569i $$0.580019\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −5000.00 −0.362634
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ −24565.0 −1.76777
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −40120.0 −2.85009
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 40050.0 2.78048
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −13838.0 −0.951051
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24736.0 1.68729 0.843644 0.536903i $$-0.180406\pi$$
0.843644 + 0.536903i $$0.180406\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −50184.0 −3.38073
$$605$$ 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
$$613$$ 15010.0 0.988986 0.494493 0.869182i $$-0.335354\pi$$
0.494493 + 0.869182i $$0.335354\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −30550.0 −1.99335 −0.996675 0.0814823i $$-0.974035\pi$$
−0.996675 + 0.0814823i $$0.974035\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15625.0 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −26192.0 −1.65244 −0.826218 0.563351i $$-0.809512\pi$$
−0.826218 + 0.563351i $$0.809512\pi$$
$$632$$ −62280.0 −3.91988
$$633$$ 0 0
$$634$$ 34850.0 2.18308
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 56440.0 3.50232
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −8878.00 −0.547051 −0.273526 0.961865i $$-0.588190\pi$$
−0.273526 + 0.961865i $$0.588190\pi$$
$$642$$ 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
$$652$$ 30260.0 1.81760
$$653$$ −27050.0 −1.62105 −0.810527 0.585701i $$-0.800819\pi$$
−0.810527 + 0.585701i $$0.800819\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 1804.00 0.106637 0.0533186 0.998578i $$-0.483020\pi$$
0.0533186 + 0.998578i $$0.483020\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$662$$ 54540.0 3.20205
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 6640.00 0.385460
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −33570.0 −1.92278 −0.961388 0.275196i $$-0.911257\pi$$
−0.961388 + 0.275196i $$0.911257\pi$$
$$674$$ −16650.0 −0.951534
$$675$$ 0 0
$$676$$ −37349.0 −2.12500
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 34060.0 1.90815 0.954077 0.299560i $$-0.0968400\pi$$
0.954077 + 0.299560i $$0.0968400\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −16020.0 −0.887728
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 20500.0 1.12128
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 4198.00 0.226186 0.113093 0.993584i $$-0.463924\pi$$
0.113093 + 0.993584i $$0.463924\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −19516.0 −1.04480
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 12546.0 0.664563 0.332281 0.943180i $$-0.392182\pi$$
0.332281 + 0.943180i $$0.392182\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 35428.0 1.84917
$$717$$ 0 0
$$718$$ 40520.0 2.10612
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −34295.0 −1.76777
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −20750.0 −1.06295
$$726$$ 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
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 3400.00 0.170279
$$737$$ −50320.0 −2.51501
$$738$$ 0 0
$$739$$ −25324.0 −1.26057 −0.630283 0.776365i $$-0.717061\pi$$
−0.630283 + 0.776365i $$0.717061\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −25160.0 −1.24230 −0.621151 0.783691i $$-0.713335\pi$$
−0.621151 + 0.783691i $$0.713335\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −69850.0 −3.42814
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2448.00 −0.118946 −0.0594732 0.998230i $$-0.518942\pi$$
−0.0594732 + 0.998230i $$0.518942\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −34830.0 −1.67228 −0.836141 0.548514i $$-0.815194\pi$$
−0.836141 + 0.548514i $$0.815194\pi$$
$$758$$ 59580.0 2.85494
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 69224.0 3.27806
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −78030.0 −3.63777
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 52630.0 2.42529
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −46784.0 −2.14349
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 37570.0 1.69845
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 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
$$800$$ −10625.0 −0.469563
$$801$$ 0 0
$$802$$ −7990.00 −0.351791
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −37354.0 −1.62336 −0.811679 0.584104i $$-0.801446\pi$$
−0.811679 + 0.584104i $$0.801446\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 153000. 6.58802
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 43538.0 1.85078 0.925388 0.379022i $$-0.123739\pi$$
0.925388 + 0.379022i $$0.123739\pi$$
$$822$$ 0 0
$$823$$ −46240.0 −1.95848 −0.979238 0.202716i $$-0.935023\pi$$
−0.979238 + 0.202716i $$0.935023\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 23980.0 1.00830 0.504151 0.863615i $$-0.331805\pi$$
0.504151 + 0.863615i $$0.331805\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 3167.00 0.129854
$$842$$ 76310.0 3.12330
$$843$$ 0 0
$$844$$ 99756.0 4.06842
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ −52510.0 −2.12642
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 18000.0 0.725067
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 71100.0 2.83896
$$857$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 43040.0 1.70064
$$863$$ 20200.0 0.796774 0.398387 0.917217i $$-0.369570\pi$$
0.398387 + 0.917217i $$0.369570\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −94112.0 −3.67380
$$870$$ 0 0
$$871$$ 0 0
$$872$$ −2430.00 −0.0943695
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −6550.00 −0.252198 −0.126099 0.992018i $$-0.540246\pi$$
−0.126099 + 0.992018i $$0.540246\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$882$$ 0 0
$$883$$ 30060.0 1.14564 0.572820 0.819681i $$-0.305850\pi$$
0.572820 + 0.819681i $$0.305850\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ −92900.0 −3.52261
$$887$$ 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
$$898$$ 13430.0 0.499070
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 30150.0 1.10926
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 52740.0 1.93076 0.965382 0.260840i $$-0.0839996\pi$$
0.965382 + 0.260840i $$0.0839996\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 39632.0 1.44135 0.720673 0.693275i $$-0.243833\pi$$
0.720673 + 0.693275i $$0.243833\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 40050.0 1.44938
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 21744.0 0.780488 0.390244 0.920711i $$-0.372391\pi$$
0.390244 + 0.920711i $$0.372391\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −56250.0 −1.99945
$$926$$ −42200.0 −1.49760
$$927$$ 0 0
$$928$$ 14110.0 0.499120
$$929$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 80410.0 2.82609
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 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
$$946$$ −61200.0 −2.10337
$$947$$ −48820.0 −1.67522 −0.837612 0.546266i $$-0.816049\pi$$
−0.837612 + 0.546266i $$0.816049\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −29290.0 −0.995589 −0.497794 0.867295i $$-0.665857\pi$$
−0.497794 + 0.867295i $$0.665857\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 125392. 4.24212
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −29791.0 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 52040.0 1.73060 0.865302 0.501251i $$-0.167127\pi$$
0.865302 + 0.501251i $$0.167127\pi$$
$$968$$ 148185. 4.92030
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 106200. 3.49370
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 37490.0 1.22765 0.613824 0.789443i $$-0.289631\pi$$
0.613824 + 0.789443i $$0.289631\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ −101860. −3.31006
$$983$$ 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
$$989$$ −7200.00 −0.231493
$$990$$ 0 0
$$991$$ 57528.0 1.84403 0.922017 0.387150i $$-0.126540\pi$$
0.922017 + 0.387150i $$0.126540\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ −36180.0 −1.14755
$$999$$ 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 441.4.a.m.1.1 1
3.2 odd 2 49.4.a.a.1.1 1
7.2 even 3 441.4.e.a.361.1 2
7.3 odd 6 441.4.e.a.226.1 2
7.4 even 3 441.4.e.a.226.1 2
7.5 odd 6 441.4.e.a.361.1 2
7.6 odd 2 CM 441.4.a.m.1.1 1
12.11 even 2 784.4.a.k.1.1 1
15.14 odd 2 1225.4.a.l.1.1 1
21.2 odd 6 49.4.c.d.18.1 2
21.5 even 6 49.4.c.d.18.1 2
21.11 odd 6 49.4.c.d.30.1 2
21.17 even 6 49.4.c.d.30.1 2
21.20 even 2 49.4.a.a.1.1 1
84.83 odd 2 784.4.a.k.1.1 1
105.104 even 2 1225.4.a.l.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.a.a.1.1 1 3.2 odd 2
49.4.a.a.1.1 1 21.20 even 2
49.4.c.d.18.1 2 21.2 odd 6
49.4.c.d.18.1 2 21.5 even 6
49.4.c.d.30.1 2 21.11 odd 6
49.4.c.d.30.1 2 21.17 even 6
441.4.a.m.1.1 1 1.1 even 1 trivial
441.4.a.m.1.1 1 7.6 odd 2 CM
441.4.e.a.226.1 2 7.3 odd 6
441.4.e.a.226.1 2 7.4 even 3
441.4.e.a.361.1 2 7.2 even 3
441.4.e.a.361.1 2 7.5 odd 6
784.4.a.k.1.1 1 12.11 even 2
784.4.a.k.1.1 1 84.83 odd 2
1225.4.a.l.1.1 1 15.14 odd 2
1225.4.a.l.1.1 1 105.104 even 2