# Properties

 Label 768.2.f.d.383.1 Level $768$ Weight $2$ Character 768.383 Analytic conductor $6.133$ Analytic rank $0$ Dimension $4$ CM discriminant -3 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$768 = 2^{8} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 768.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.13251087523$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 383.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 768.383 Dual form 768.2.f.d.383.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} -3.46410i q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.73205 q^{3} -3.46410i q^{7} +3.00000 q^{9} +2.00000i q^{13} -3.46410 q^{19} +6.00000i q^{21} -5.00000 q^{25} -5.19615 q^{27} -10.3923i q^{31} -10.0000i q^{37} -3.46410i q^{39} -10.3923 q^{43} -5.00000 q^{49} +6.00000 q^{57} -14.0000i q^{61} -10.3923i q^{63} -3.46410 q^{67} -10.0000 q^{73} +8.66025 q^{75} +17.3205i q^{79} +9.00000 q^{81} +6.92820 q^{91} +18.0000i q^{93} -14.0000 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 12 q^{9} + O(q^{10})$$ $$4 q + 12 q^{9} - 20 q^{25} - 20 q^{49} + 24 q^{57} - 40 q^{73} + 36 q^{81} - 56 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$511$$ $$517$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.73205 −1.00000
$$4$$ 0 0
$$5$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ − 3.46410i − 1.30931i −0.755929 0.654654i $$-0.772814\pi$$
0.755929 0.654654i $$-0.227186\pi$$
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 2.00000i 0.554700i 0.960769 + 0.277350i $$0.0894562\pi$$
−0.960769 + 0.277350i $$0.910544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ −3.46410 −0.794719 −0.397360 0.917663i $$-0.630073\pi$$
−0.397360 + 0.917663i $$0.630073\pi$$
$$20$$ 0 0
$$21$$ 6.00000i 1.30931i
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ −5.19615 −1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ − 10.3923i − 1.86651i −0.359211 0.933257i $$-0.616954\pi$$
0.359211 0.933257i $$-0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ − 10.0000i − 1.64399i −0.569495 0.821995i $$-0.692861\pi$$
0.569495 0.821995i $$-0.307139\pi$$
$$38$$ 0 0
$$39$$ − 3.46410i − 0.554700i
$$40$$ 0 0
$$41$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$42$$ 0 0
$$43$$ −10.3923 −1.58481 −0.792406 0.609994i $$-0.791172\pi$$
−0.792406 + 0.609994i $$0.791172\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −5.00000 −0.714286
$$50$$ 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
$$57$$ 6.00000 0.794719
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ − 14.0000i − 1.79252i −0.443533 0.896258i $$-0.646275\pi$$
0.443533 0.896258i $$-0.353725\pi$$
$$62$$ 0 0
$$63$$ − 10.3923i − 1.30931i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.46410 −0.423207 −0.211604 0.977356i $$-0.567869\pi$$
−0.211604 + 0.977356i $$0.567869\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −10.0000 −1.17041 −0.585206 0.810885i $$-0.698986\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 0 0
$$75$$ 8.66025 1.00000
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 17.3205i 1.94871i 0.225018 + 0.974355i $$0.427756\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 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
$$91$$ 6.92820 0.726273
$$92$$ 0 0
$$93$$ 18.0000i 1.86651i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$102$$ 0 0
$$103$$ − 3.46410i − 0.341328i −0.985329 0.170664i $$-0.945409\pi$$
0.985329 0.170664i $$-0.0545913\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 2.00000i 0.191565i 0.995402 + 0.0957826i $$0.0305354\pi$$
−0.995402 + 0.0957826i $$0.969465\pi$$
$$110$$ 0 0
$$111$$ 17.3205i 1.64399i
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 6.00000i 0.554700i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ − 10.3923i − 0.922168i −0.887357 0.461084i $$-0.847461\pi$$
0.887357 0.461084i $$-0.152539\pi$$
$$128$$ 0 0
$$129$$ 18.0000 1.58481
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 12.0000i 1.04053i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 17.3205 1.46911 0.734553 0.678551i $$-0.237392\pi$$
0.734553 + 0.678551i $$0.237392\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 8.66025 0.714286
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 24.2487i 1.97333i 0.162758 + 0.986666i $$0.447961\pi$$
−0.162758 + 0.986666i $$0.552039\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 14.0000i − 1.11732i −0.829396 0.558661i $$-0.811315\pi$$
0.829396 0.558661i $$-0.188685\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 24.2487 1.89931 0.949653 0.313304i $$-0.101436\pi$$
0.949653 + 0.313304i $$0.101436\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ −10.3923 −0.794719
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 17.3205i 1.30931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ − 26.0000i − 1.93256i −0.257485 0.966282i $$-0.582894\pi$$
0.257485 0.966282i $$-0.417106\pi$$
$$182$$ 0 0
$$183$$ 24.2487i 1.79252i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 18.0000i 1.30931i
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 2.00000 0.143963 0.0719816 0.997406i $$-0.477068\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ − 3.46410i − 0.245564i −0.992434 0.122782i $$-0.960818\pi$$
0.992434 0.122782i $$-0.0391815\pi$$
$$200$$ 0 0
$$201$$ 6.00000 0.423207
$$202$$ 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
$$211$$ 24.2487 1.66935 0.834675 0.550743i $$-0.185655\pi$$
0.834675 + 0.550743i $$0.185655\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −36.0000 −2.44384
$$218$$ 0 0
$$219$$ 17.3205 1.17041
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ − 10.3923i − 0.695920i −0.937509 0.347960i $$-0.886874\pi$$
0.937509 0.347960i $$-0.113126\pi$$
$$224$$ 0 0
$$225$$ −15.0000 −1.00000
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ 22.0000i 1.45380i 0.686743 + 0.726900i $$0.259040\pi$$
−0.686743 + 0.726900i $$0.740960\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ − 30.0000i − 1.94871i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −14.0000 −0.901819 −0.450910 0.892570i $$-0.648900\pi$$
−0.450910 + 0.892570i $$0.648900\pi$$
$$242$$ 0 0
$$243$$ −15.5885 −1.00000
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ − 6.92820i − 0.440831i
$$248$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ −34.6410 −2.15249
$$260$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$270$$ 0 0
$$271$$ 17.3205i 1.05215i 0.850439 + 0.526073i $$0.176336\pi$$
−0.850439 + 0.526073i $$0.823664\pi$$
$$272$$ 0 0
$$273$$ −12.0000 −0.726273
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 26.0000i − 1.56219i −0.624413 0.781094i $$-0.714662\pi$$
0.624413 0.781094i $$-0.285338\pi$$
$$278$$ 0 0
$$279$$ − 31.1769i − 1.86651i
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ −10.3923 −0.617758 −0.308879 0.951101i $$-0.599954\pi$$
−0.308879 + 0.951101i $$0.599954\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 17.0000 1.00000
$$290$$ 0 0
$$291$$ 24.2487 1.42148
$$292$$ 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
$$301$$ 36.0000i 2.07501i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −31.1769 −1.77936 −0.889680 0.456584i $$-0.849073\pi$$
−0.889680 + 0.456584i $$0.849073\pi$$
$$308$$ 0 0
$$309$$ 6.00000i 0.341328i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 22.0000 1.24351 0.621757 0.783210i $$-0.286419\pi$$
0.621757 + 0.783210i $$0.286419\pi$$
$$314$$ 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
$$325$$ − 10.0000i − 0.554700i
$$326$$ 0 0
$$327$$ − 3.46410i − 0.191565i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 17.3205 0.952021 0.476011 0.879440i $$-0.342082\pi$$
0.476011 + 0.879440i $$0.342082\pi$$
$$332$$ 0 0
$$333$$ − 30.0000i − 1.64399i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 34.0000 1.85210 0.926049 0.377403i $$-0.123183\pi$$
0.926049 + 0.377403i $$0.123183\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 6.92820i − 0.374088i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ − 14.0000i − 0.749403i −0.927146 0.374701i $$-0.877745\pi$$
0.927146 0.374701i $$-0.122255\pi$$
$$350$$ 0 0
$$351$$ − 10.3923i − 0.554700i
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −7.00000 −0.368421
$$362$$ 0 0
$$363$$ −19.0526 −1.00000
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 38.1051i − 1.98907i −0.104399 0.994535i $$-0.533292\pi$$
0.104399 0.994535i $$-0.466708\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 38.0000i 1.96757i 0.179364 + 0.983783i $$0.442596\pi$$
−0.179364 + 0.983783i $$0.557404\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −38.1051 −1.95733 −0.978664 0.205466i $$-0.934129\pi$$
−0.978664 + 0.205466i $$0.934129\pi$$
$$380$$ 0 0
$$381$$ 18.0000i 0.922168i
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −31.1769 −1.58481
$$388$$ 0 0
$$389$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 34.0000i 1.70641i 0.521575 + 0.853206i $$0.325345\pi$$
−0.521575 + 0.853206i $$0.674655\pi$$
$$398$$ 0 0
$$399$$ − 20.7846i − 1.04053i
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 20.7846 1.03536
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 38.0000 1.87898 0.939490 0.342578i $$-0.111300\pi$$
0.939490 + 0.342578i $$0.111300\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −30.0000 −1.46911
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 22.0000i 1.07221i 0.844150 + 0.536107i $$0.180106\pi$$
−0.844150 + 0.536107i $$0.819894\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −48.4974 −2.34695
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ − 31.1769i − 1.48799i −0.668184 0.743996i $$-0.732928\pi$$
0.668184 0.743996i $$-0.267072\pi$$
$$440$$ 0 0
$$441$$ −15.0000 −0.714286
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 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
$$453$$ − 42.0000i − 1.97333i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −10.0000 −0.467780 −0.233890 0.972263i $$-0.575146\pi$$
−0.233890 + 0.972263i $$0.575146\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$462$$ 0 0
$$463$$ − 38.1051i − 1.77090i −0.464739 0.885448i $$-0.653852\pi$$
0.464739 0.885448i $$-0.346148\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 12.0000i 0.554109i
$$470$$ 0 0
$$471$$ 24.2487i 1.11732i
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 17.3205 0.794719
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 20.0000 0.911922
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 3.46410i − 0.156973i −0.996915 0.0784867i $$-0.974991\pi$$
0.996915 0.0784867i $$-0.0250088\pi$$
$$488$$ 0 0
$$489$$ −42.0000 −1.89931
$$490$$ 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
$$499$$ −31.1769 −1.39567 −0.697835 0.716258i $$-0.745853\pi$$
−0.697835 + 0.716258i $$0.745853\pi$$
$$500$$ 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
$$507$$ −15.5885 −0.692308
$$508$$ 0 0
$$509$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$510$$ 0 0
$$511$$ 34.6410i 1.53243i
$$512$$ 0 0
$$513$$ 18.0000 0.794719
$$514$$ 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
$$523$$ 45.0333 1.96917 0.984585 0.174908i $$-0.0559627\pi$$
0.984585 + 0.174908i $$0.0559627\pi$$
$$524$$ 0 0
$$525$$ − 30.0000i − 1.30931i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −23.0000 −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
$$541$$ − 46.0000i − 1.97769i −0.148933 0.988847i $$-0.547584\pi$$
0.148933 0.988847i $$-0.452416\pi$$
$$542$$ 0 0
$$543$$ 45.0333i 1.93256i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 24.2487 1.03680 0.518400 0.855138i $$-0.326528\pi$$
0.518400 + 0.855138i $$0.326528\pi$$
$$548$$ 0 0
$$549$$ − 42.0000i − 1.79252i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 60.0000 2.55146
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ − 20.7846i − 0.879095i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 31.1769i − 1.30931i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 45.0333 1.88459 0.942293 0.334790i $$-0.108665\pi$$
0.942293 + 0.334790i $$0.108665\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −46.0000 −1.91501 −0.957503 0.288425i $$-0.906868\pi$$
−0.957503 + 0.288425i $$0.906868\pi$$
$$578$$ 0 0
$$579$$ −3.46410 −0.143963
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 36.0000i 1.48335i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 6.00000i 0.245564i
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ −10.3923 −0.423207
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 45.0333i 1.82785i 0.405887 + 0.913923i $$0.366962\pi$$
−0.405887 + 0.913923i $$0.633038\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ − 10.0000i − 0.403896i −0.979396 0.201948i $$-0.935273\pi$$
0.979396 0.201948i $$-0.0647272\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ −38.1051 −1.53157 −0.765787 0.643094i $$-0.777650\pi$$
−0.765787 + 0.643094i $$0.777650\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 24.2487i 0.965326i 0.875806 + 0.482663i $$0.160330\pi$$
−0.875806 + 0.482663i $$0.839670\pi$$
$$632$$ 0 0
$$633$$ −42.0000 −1.66935
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ − 10.0000i − 0.396214i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ −31.1769 −1.22950 −0.614749 0.788723i $$-0.710743\pi$$
−0.614749 + 0.788723i $$0.710743\pi$$
$$644$$ 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
$$651$$ 62.3538 2.44384
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −30.0000 −1.17041
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 38.0000i 1.47803i 0.673690 + 0.739014i $$0.264708\pi$$
−0.673690 + 0.739014i $$0.735292\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 18.0000i 0.695920i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 50.0000 1.92736 0.963679 0.267063i $$-0.0860531\pi$$
0.963679 + 0.267063i $$0.0860531\pi$$
$$674$$ 0 0
$$675$$ 25.9808 1.00000
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 48.4974i 1.86116i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ − 38.1051i − 1.45380i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 51.9615 1.97671 0.988355 0.152167i $$-0.0486252\pi$$
0.988355 + 0.152167i $$0.0486252\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 34.6410i 1.30651i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 22.0000i 0.826227i 0.910679 + 0.413114i $$0.135559\pi$$
−0.910679 + 0.413114i $$0.864441\pi$$
$$710$$ 0 0
$$711$$ 51.9615i 1.94871i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ −12.0000 −0.446903
$$722$$ 0 0
$$723$$ 24.2487 0.901819
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ − 31.1769i − 1.15629i −0.815935 0.578144i $$-0.803777\pi$$
0.815935 0.578144i $$-0.196223\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 50.0000i 1.84679i 0.383849 + 0.923396i $$0.374598\pi$$
−0.383849 + 0.923396i $$0.625402\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 51.9615 1.91144 0.955718 0.294285i $$-0.0950814\pi$$
0.955718 + 0.294285i $$0.0950814\pi$$
$$740$$ 0 0
$$741$$ 12.0000i 0.440831i
$$742$$ 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
$$751$$ 17.3205i 0.632034i 0.948753 + 0.316017i $$0.102346\pi$$
−0.948753 + 0.316017i $$0.897654\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ − 26.0000i − 0.944986i −0.881334 0.472493i $$-0.843354\pi$$
0.881334 0.472493i $$-0.156646\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 6.92820 0.250818
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 2.00000 0.0721218 0.0360609 0.999350i $$-0.488519\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 51.9615i 1.86651i
$$776$$ 0 0
$$777$$ 60.0000 2.15249
$$778$$ 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
$$787$$ −3.46410 −0.123482 −0.0617409 0.998092i $$-0.519665\pi$$
−0.0617409 + 0.998092i $$0.519665\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 28.0000 0.994309
$$794$$ 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
$$811$$ −10.3923 −0.364923 −0.182462 0.983213i $$-0.558407\pi$$
−0.182462 + 0.983213i $$0.558407\pi$$
$$812$$ 0 0
$$813$$ − 30.0000i − 1.05215i
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 36.0000 1.25948
$$818$$ 0 0
$$819$$ 20.7846 0.726273
$$820$$ 0 0
$$821$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$822$$ 0 0
$$823$$ 24.2487i 0.845257i 0.906303 + 0.422628i $$0.138892\pi$$
−0.906303 + 0.422628i $$0.861108\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ − 46.0000i − 1.59765i −0.601566 0.798823i $$-0.705456\pi$$
0.601566 0.798823i $$-0.294544\pi$$
$$830$$ 0 0
$$831$$ 45.0333i 1.56219i
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 54.0000i 1.86651i
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ −29.0000 −1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ − 38.1051i − 1.30931i
$$848$$ 0 0
$$849$$ 18.0000 0.617758
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ − 58.0000i − 1.98588i −0.118609 0.992941i $$-0.537843\pi$$
0.118609 0.992941i $$-0.462157\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 17.3205 0.590968 0.295484 0.955348i $$-0.404519\pi$$
0.295484 + 0.955348i $$0.404519\pi$$
$$860$$ 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
$$867$$ −29.4449 −1.00000
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ − 6.92820i − 0.234753i
$$872$$ 0 0
$$873$$ −42.0000 −1.42148
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 34.0000i 1.14810i 0.818821 + 0.574049i $$0.194628\pi$$
−0.818821 + 0.574049i $$0.805372\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ −58.8897 −1.98180 −0.990899 0.134611i $$-0.957022\pi$$
−0.990899 + 0.134611i $$0.957022\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ −36.0000 −1.20740
$$890$$ 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
$$903$$ − 62.3538i − 2.07501i
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 45.0333 1.49531 0.747653 0.664089i $$-0.231180\pi$$
0.747653 + 0.664089i $$0.231180\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ − 31.1769i − 1.02843i −0.857661 0.514216i $$-0.828083\pi$$
0.857661 0.514216i $$-0.171917\pi$$
$$920$$ 0 0
$$921$$ 54.0000 1.77936
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 50.0000i 1.64399i
$$926$$ 0 0
$$927$$ − 10.3923i − 0.341328i
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ 17.3205 0.567657
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ −26.0000 −0.849383 −0.424691 0.905338i $$-0.639617\pi$$
−0.424691 + 0.905338i $$0.639617\pi$$
$$938$$ 0 0
$$939$$ −38.1051 −1.24351
$$940$$ 0 0
$$941$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ − 20.0000i − 0.649227i
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −77.0000 −2.48387
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 58.8897i − 1.89377i −0.321578 0.946883i $$-0.604213\pi$$
0.321578 0.946883i $$-0.395787\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ − 60.0000i − 1.92351i
$$974$$ 0 0
$$975$$ 17.3205i 0.554700i
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 6.00000i 0.191565i
$$982$$ 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
$$991$$ 45.0333i 1.43053i 0.698853 + 0.715265i $$0.253694\pi$$
−0.698853 + 0.715265i $$0.746306\pi$$
$$992$$ 0 0
$$993$$ −30.0000 −0.952021
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ − 10.0000i − 0.316703i −0.987383 0.158352i $$-0.949382\pi$$
0.987383 0.158352i $$-0.0506179\pi$$
$$998$$ 0 0
$$999$$ 51.9615i 1.64399i
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 768.2.f.d.383.1 4
3.2 odd 2 CM 768.2.f.d.383.1 4
4.3 odd 2 inner 768.2.f.d.383.4 4
8.3 odd 2 inner 768.2.f.d.383.2 4
8.5 even 2 inner 768.2.f.d.383.3 4
12.11 even 2 inner 768.2.f.d.383.4 4
16.3 odd 4 48.2.c.a.47.2 yes 2
16.5 even 4 192.2.c.a.191.2 2
16.11 odd 4 192.2.c.a.191.1 2
16.13 even 4 48.2.c.a.47.1 2
24.5 odd 2 inner 768.2.f.d.383.3 4
24.11 even 2 inner 768.2.f.d.383.2 4
48.5 odd 4 192.2.c.a.191.2 2
48.11 even 4 192.2.c.a.191.1 2
48.29 odd 4 48.2.c.a.47.1 2
48.35 even 4 48.2.c.a.47.2 yes 2
80.3 even 4 1200.2.o.i.1199.1 4
80.13 odd 4 1200.2.o.i.1199.3 4
80.19 odd 4 1200.2.h.e.1151.1 2
80.29 even 4 1200.2.h.e.1151.2 2
80.67 even 4 1200.2.o.i.1199.4 4
80.77 odd 4 1200.2.o.i.1199.2 4
112.13 odd 4 2352.2.h.c.2255.2 2
112.83 even 4 2352.2.h.c.2255.1 2
144.13 even 12 1296.2.s.b.431.1 2
144.29 odd 12 1296.2.s.e.863.1 2
144.61 even 12 1296.2.s.e.863.1 2
144.67 odd 12 1296.2.s.e.431.1 2
144.77 odd 12 1296.2.s.b.431.1 2
144.83 even 12 1296.2.s.b.863.1 2
144.115 odd 12 1296.2.s.b.863.1 2
144.131 even 12 1296.2.s.e.431.1 2
240.29 odd 4 1200.2.h.e.1151.2 2
240.77 even 4 1200.2.o.i.1199.2 4
240.83 odd 4 1200.2.o.i.1199.1 4
240.173 even 4 1200.2.o.i.1199.3 4
240.179 even 4 1200.2.h.e.1151.1 2
240.227 odd 4 1200.2.o.i.1199.4 4
336.83 odd 4 2352.2.h.c.2255.1 2
336.125 even 4 2352.2.h.c.2255.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
48.2.c.a.47.1 2 16.13 even 4
48.2.c.a.47.1 2 48.29 odd 4
48.2.c.a.47.2 yes 2 16.3 odd 4
48.2.c.a.47.2 yes 2 48.35 even 4
192.2.c.a.191.1 2 16.11 odd 4
192.2.c.a.191.1 2 48.11 even 4
192.2.c.a.191.2 2 16.5 even 4
192.2.c.a.191.2 2 48.5 odd 4
768.2.f.d.383.1 4 1.1 even 1 trivial
768.2.f.d.383.1 4 3.2 odd 2 CM
768.2.f.d.383.2 4 8.3 odd 2 inner
768.2.f.d.383.2 4 24.11 even 2 inner
768.2.f.d.383.3 4 8.5 even 2 inner
768.2.f.d.383.3 4 24.5 odd 2 inner
768.2.f.d.383.4 4 4.3 odd 2 inner
768.2.f.d.383.4 4 12.11 even 2 inner
1200.2.h.e.1151.1 2 80.19 odd 4
1200.2.h.e.1151.1 2 240.179 even 4
1200.2.h.e.1151.2 2 80.29 even 4
1200.2.h.e.1151.2 2 240.29 odd 4
1200.2.o.i.1199.1 4 80.3 even 4
1200.2.o.i.1199.1 4 240.83 odd 4
1200.2.o.i.1199.2 4 80.77 odd 4
1200.2.o.i.1199.2 4 240.77 even 4
1200.2.o.i.1199.3 4 80.13 odd 4
1200.2.o.i.1199.3 4 240.173 even 4
1200.2.o.i.1199.4 4 80.67 even 4
1200.2.o.i.1199.4 4 240.227 odd 4
1296.2.s.b.431.1 2 144.13 even 12
1296.2.s.b.431.1 2 144.77 odd 12
1296.2.s.b.863.1 2 144.83 even 12
1296.2.s.b.863.1 2 144.115 odd 12
1296.2.s.e.431.1 2 144.67 odd 12
1296.2.s.e.431.1 2 144.131 even 12
1296.2.s.e.863.1 2 144.29 odd 12
1296.2.s.e.863.1 2 144.61 even 12
2352.2.h.c.2255.1 2 112.83 even 4
2352.2.h.c.2255.1 2 336.83 odd 4
2352.2.h.c.2255.2 2 112.13 odd 4
2352.2.h.c.2255.2 2 336.125 even 4