Properties

 Label 1840.2.m.e.1839.2 Level $1840$ Weight $2$ Character 1840.1839 Analytic conductor $14.692$ Analytic rank $0$ Dimension $8$ CM discriminant -115 Inner twists $8$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1840 = 2^{4} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1840.m (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$14.6924739719$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.14166950625.1 Defining polynomial: $$x^{8} - 9 x^{6} + 32 x^{4} - 441 x^{2} + 2401$$ Coefficient ring: $$\Z[a_1, \ldots, a_{23}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

 Embedding label 1839.2 Root $$-1.51764 - 2.16720i$$ of defining polynomial Character $$\chi$$ $$=$$ 1840.1839 Dual form 1840.2.m.e.1839.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q-2.23607 q^{5} -0.461424i q^{7} -3.00000 q^{9} +O(q^{10})$$ $$q-2.23607 q^{5} -0.461424i q^{7} -3.00000 q^{9} -0.799210 q^{17} -4.79583i q^{23} +5.00000 q^{25} +9.78709 q^{29} +7.95998i q^{31} +1.03178i q^{35} -9.74348 q^{37} +5.78709 q^{41} +9.59166i q^{43} +6.70820 q^{45} +6.78709 q^{49} +11.3419 q^{53} +14.8882i q^{59} +1.38427i q^{63} -15.9534i q^{67} -5.89643i q^{71} +9.00000 q^{81} +16.8762i q^{83} +1.78709 q^{85} +4.47214 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 24q^{9} + O(q^{10})$$ $$8q - 24q^{9} + 40q^{25} + 4q^{29} - 28q^{41} - 20q^{49} + 72q^{81} - 60q^{85} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times$$.

 $$n$$ $$737$$ $$1151$$ $$1201$$ $$1381$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$ $$1$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0 0
$$5$$ −2.23607 −1.00000
$$6$$ 0 0
$$7$$ − 0.461424i − 0.174402i −0.996191 0.0872010i $$-0.972208\pi$$
0.996191 0.0872010i $$-0.0277922\pi$$
$$8$$ 0 0
$$9$$ −3.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −0.799210 −0.193837 −0.0969184 0.995292i $$-0.530899\pi$$
−0.0969184 + 0.995292i $$0.530899\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ − 4.79583i − 1.00000i
$$24$$ 0 0
$$25$$ 5.00000 1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 9.78709 1.81742 0.908708 0.417432i $$-0.137070\pi$$
0.908708 + 0.417432i $$0.137070\pi$$
$$30$$ 0 0
$$31$$ 7.95998i 1.42965i 0.699301 + 0.714827i $$0.253495\pi$$
−0.699301 + 0.714827i $$0.746505\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.03178i 0.174402i
$$36$$ 0 0
$$37$$ −9.74348 −1.60182 −0.800909 0.598786i $$-0.795650\pi$$
−0.800909 + 0.598786i $$0.795650\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 5.78709 0.903791 0.451896 0.892071i $$-0.350748\pi$$
0.451896 + 0.892071i $$0.350748\pi$$
$$42$$ 0 0
$$43$$ 9.59166i 1.46271i 0.681994 + 0.731357i $$0.261113\pi$$
−0.681994 + 0.731357i $$0.738887\pi$$
$$44$$ 0 0
$$45$$ 6.70820 1.00000
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 6.78709 0.969584
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 11.3419 1.55793 0.778965 0.627067i $$-0.215745\pi$$
0.778965 + 0.627067i $$0.215745\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 14.8882i 1.93828i 0.246518 + 0.969138i $$0.420713\pi$$
−0.246518 + 0.969138i $$0.579287\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 1.38427i 0.174402i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 15.9534i − 1.94901i −0.224360 0.974506i $$-0.572029\pi$$
0.224360 0.974506i $$-0.427971\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ − 5.89643i − 0.699777i −0.936791 0.349889i $$-0.886219\pi$$
0.936791 0.349889i $$-0.113781\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 16.8762i 1.85240i 0.377027 + 0.926202i $$0.376946\pi$$
−0.377027 + 0.926202i $$0.623054\pi$$
$$84$$ 0 0
$$85$$ 1.78709 0.193837
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 4.47214 0.454077 0.227038 0.973886i $$-0.427096\pi$$
0.227038 + 0.973886i $$0.427096\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 17.7871 1.76988 0.884941 0.465704i $$-0.154199\pi$$
0.884941 + 0.465704i $$0.154199\pi$$
$$102$$ 0 0
$$103$$ − 9.59166i − 0.945095i −0.881305 0.472547i $$-0.843335\pi$$
0.881305 0.472547i $$-0.156665\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 15.0305i 1.45305i 0.687138 + 0.726527i $$0.258867\pi$$
−0.687138 + 0.726527i $$0.741133\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 20.2862 1.90836 0.954181 0.299229i $$-0.0967294\pi$$
0.954181 + 0.299229i $$0.0967294\pi$$
$$114$$ 0 0
$$115$$ 10.7238i 1.00000i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0.368775i 0.0338055i
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −11.1803 −1.00000
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 21.4476i 1.87389i 0.349482 + 0.936943i $$0.386358\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −13.4164 −1.14624 −0.573121 0.819471i $$-0.694267\pi$$
−0.573121 + 0.819471i $$0.694267\pi$$
$$138$$ 0 0
$$139$$ − 12.8246i − 1.08777i −0.839159 0.543885i $$-0.816953\pi$$
0.839159 0.543885i $$-0.183047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −21.8846 −1.81742
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 0 0
$$151$$ − 21.4476i − 1.74538i −0.488273 0.872691i $$-0.662373\pi$$
0.488273 0.872691i $$-0.337627\pi$$
$$152$$ 0 0
$$153$$ 2.39763 0.193837
$$154$$ 0 0
$$155$$ − 17.7991i − 1.42965i
$$156$$ 0 0
$$157$$ 8.14506 0.650047 0.325023 0.945706i $$-0.394628\pi$$
0.325023 + 0.945706i $$0.394628\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −2.21291 −0.174402
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ − 2.30712i − 0.174402i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 21.4476i 1.60307i 0.597948 + 0.801535i $$0.295983\pi$$
−0.597948 + 0.801535i $$0.704017\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 21.7871 1.60182
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ − 4.51600i − 0.316961i
$$204$$ 0 0
$$205$$ −12.9403 −0.903791
$$206$$ 0 0
$$207$$ 14.3875i 1.00000i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 28.7446i 1.97886i 0.145014 + 0.989430i $$0.453677\pi$$
−0.145014 + 0.989430i $$0.546323\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ − 21.4476i − 1.46271i
$$216$$ 0 0
$$217$$ 3.67293 0.249334
$$218$$ 0 0
$$219$$ 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
$$225$$ −15.0000 −1.00000
$$226$$ 0 0
$$227$$ − 28.7750i − 1.90986i −0.296826 0.954932i $$-0.595928\pi$$
0.296826 0.954932i $$-0.404072\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 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
$$237$$ 0 0
$$238$$ 0 0
$$239$$ − 19.7528i − 1.27770i −0.769329 0.638852i $$-0.779409\pi$$
0.769329 0.638852i $$-0.220591\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −15.1764 −0.969584
$$246$$ 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
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 4.49588i 0.279360i
$$260$$ 0 0
$$261$$ −29.3613 −1.81742
$$262$$ 0 0
$$263$$ 32.3681i 1.99590i 0.0639598 + 0.997952i $$0.479627\pi$$
−0.0639598 + 0.997952i $$0.520373\pi$$
$$264$$ 0 0
$$265$$ −25.3613 −1.55793
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −6.21291 −0.378808 −0.189404 0.981899i $$-0.560656\pi$$
−0.189404 + 0.981899i $$0.560656\pi$$
$$270$$ 0 0
$$271$$ − 10.0235i − 0.608886i −0.952531 0.304443i $$-0.901530\pi$$
0.952531 0.304443i $$-0.0984703\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ − 23.8799i − 1.42965i
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 18.7219i 1.11290i 0.830881 + 0.556451i $$0.187837\pi$$
−0.830881 + 0.556451i $$0.812163\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ − 2.67030i − 0.157623i
$$288$$ 0 0
$$289$$ −16.3613 −0.962427
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 32.4273 1.89442 0.947211 0.320610i $$-0.103888\pi$$
0.947211 + 0.320610i $$0.103888\pi$$
$$294$$ 0 0
$$295$$ − 33.2910i − 1.93828i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 4.42582 0.255100
$$302$$ 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
$$311$$ − 21.4476i − 1.21618i −0.793867 0.608091i $$-0.791935\pi$$
0.793867 0.608091i $$-0.208065\pi$$
$$312$$ 0 0
$$313$$ 23.4830 1.32734 0.663669 0.748026i $$-0.268998\pi$$
0.663669 + 0.748026i $$0.268998\pi$$
$$314$$ 0 0
$$315$$ − 3.09533i − 0.174402i
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 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
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ − 30.8081i − 1.69337i −0.532096 0.846684i $$-0.678595\pi$$
0.532096 0.846684i $$-0.321405\pi$$
$$332$$ 0 0
$$333$$ 29.2304 1.60182
$$334$$ 0 0
$$335$$ 35.6728i 1.94901i
$$336$$ 0 0
$$337$$ −31.3050 −1.70529 −0.852645 0.522491i $$-0.825003\pi$$
−0.852645 + 0.522491i $$0.825003\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ − 6.36169i − 0.343499i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ −37.3613 −1.99990 −0.999951 0.00987003i $$-0.996858\pi$$
−0.999951 + 0.00987003i $$0.996858\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 13.1848i 0.699777i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 30.5224i 1.59326i 0.604468 + 0.796629i $$0.293386\pi$$
−0.604468 + 0.796629i $$0.706614\pi$$
$$368$$ 0 0
$$369$$ −17.3613 −0.903791
$$370$$ 0 0
$$371$$ − 5.23343i − 0.271706i
$$372$$ 0 0
$$373$$ −4.47214 −0.231558 −0.115779 0.993275i $$-0.536937\pi$$
−0.115779 + 0.993275i $$0.536937\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 34.2138i 1.74825i 0.485705 + 0.874123i $$0.338563\pi$$
−0.485705 + 0.874123i $$0.661437\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ − 28.7750i − 1.46271i
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 3.83288i 0.193837i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −20.1246 −1.00000
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −10.2129 −0.504996 −0.252498 0.967597i $$-0.581252\pi$$
−0.252498 + 0.967597i $$0.581252\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 6.86977 0.338039
$$414$$ 0 0
$$415$$ − 37.7363i − 1.85240i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −3.99605 −0.193837
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 41.3716 1.98819 0.994095 0.108513i $$-0.0346088\pi$$
0.994095 + 0.108513i $$0.0346088\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ − 21.4476i − 1.02364i −0.859093 0.511819i $$-0.828972\pi$$
0.859093 0.511819i $$-0.171028\pi$$
$$440$$ 0 0
$$441$$ −20.3613 −0.969584
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 29.7871 1.40574 0.702870 0.711319i $$-0.251902\pi$$
0.702870 + 0.711319i $$0.251902\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.0893 0.799405 0.399703 0.916645i $$-0.369113\pi$$
0.399703 + 0.916645i $$0.369113\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −0.0931493 −0.0465746 0.998915i $$-0.514831\pi$$
−0.0465746 + 0.998915i $$0.514831\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ − 19.6448i − 0.909051i −0.890734 0.454525i $$-0.849809\pi$$
0.890734 0.454525i $$-0.150191\pi$$
$$468$$ 0 0
$$469$$ −7.36126 −0.339912
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −34.0257 −1.55793
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −10.0000 −0.454077
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 42.6010i 1.92256i 0.275581 + 0.961278i $$0.411130\pi$$
−0.275581 + 0.961278i $$0.588870\pi$$
$$492$$ 0 0
$$493$$ −7.82194 −0.352282
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −2.72075 −0.122042
$$498$$ 0 0
$$499$$ 10.7611i 0.481732i 0.970558 + 0.240866i $$0.0774314\pi$$
−0.970558 + 0.240866i $$0.922569\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ − 29.5996i − 1.31978i −0.751362 0.659890i $$-0.770603\pi$$
0.751362 0.659890i $$-0.229397\pi$$
$$504$$ 0 0
$$505$$ −39.7731 −1.76988
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 14.0000 0.620539 0.310270 0.950649i $$-0.399581\pi$$
0.310270 + 0.950649i $$0.399581\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 21.4476i 0.945095i
$$516$$ 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
$$523$$ 9.59166i 0.419414i 0.977764 + 0.209707i $$0.0672510\pi$$
−0.977764 + 0.209707i $$0.932749\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ − 6.36169i − 0.277120i
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ 0 0
$$531$$ − 44.6645i − 1.93828i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ − 33.6092i − 1.45305i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −18.0000 −0.773880 −0.386940 0.922105i $$-0.626468\pi$$
−0.386940 + 0.922105i $$0.626468\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −27.6320 −1.17081 −0.585403 0.810742i $$-0.699064\pi$$
−0.585403 + 0.810742i $$0.699064\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ − 12.2620i − 0.516780i −0.966041 0.258390i $$-0.916808\pi$$
0.966041 0.258390i $$-0.0831920\pi$$
$$564$$ 0 0
$$565$$ −45.3613 −1.90836
$$566$$ 0 0
$$567$$ − 4.15282i − 0.174402i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ − 23.9792i − 1.00000i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 7.78709 0.323063
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ − 0.824605i − 0.0338055i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ − 21.4476i − 0.876326i −0.898896 0.438163i $$-0.855629\pi$$
0.898896 0.438163i $$-0.144371\pi$$
$$600$$ 0 0
$$601$$ −9.36126 −0.381854 −0.190927 0.981604i $$-0.561149\pi$$
−0.190927 + 0.981604i $$0.561149\pi$$
$$602$$ 0 0
$$603$$ 47.8601i 1.94901i
$$604$$ 0 0
$$605$$ 24.5967 1.00000
$$606$$ 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
$$613$$ 31.3050 1.26440 0.632198 0.774807i $$-0.282153\pi$$
0.632198 + 0.774807i $$0.282153\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −25.0814 −1.00974 −0.504870 0.863195i $$-0.668460\pi$$
−0.504870 + 0.863195i $$0.668460\pi$$
$$618$$ 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
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 7.78709 0.310492
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 17.6893i 0.699777i
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 49.7058i 1.96020i 0.198494 + 0.980102i $$0.436395\pi$$
−0.198494 + 0.980102i $$0.563605\pi$$
$$644$$ 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
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ − 47.9583i − 1.87389i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ − 46.9372i − 1.81742i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −51.9142 −1.99523 −0.997613 0.0690480i $$-0.978004\pi$$
−0.997613 + 0.0690480i $$0.978004\pi$$
$$678$$ 0 0
$$679$$ − 2.06355i − 0.0791918i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 30.0000 1.14624
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 21.4476i 0.815906i 0.913003 + 0.407953i $$0.133757\pi$$
−0.913003 + 0.407953i $$0.866243\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 28.6767i 1.08777i
$$696$$ 0 0
$$697$$ −4.62510 −0.175188
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ − 8.20739i − 0.308671i
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 38.1747 1.42965
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 25.9435i 0.967529i 0.875198 + 0.483764i $$0.160731\pi$$
−0.875198 + 0.483764i $$0.839269\pi$$
$$720$$ 0 0
$$721$$ −4.42582 −0.164826
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 48.9354 1.81742
$$726$$ 0 0
$$727$$ 36.0595i 1.33737i 0.743544 + 0.668687i $$0.233143\pi$$
−0.743544 + 0.668687i $$0.766857\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ − 7.66575i − 0.283528i
$$732$$ 0 0
$$733$$ 50.3158 1.85846 0.929229 0.369505i $$-0.120473\pi$$
0.929229 + 0.369505i $$0.120473\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 19.0153i 0.699489i 0.936845 + 0.349744i $$0.113732\pi$$
−0.936845 + 0.349744i $$0.886268\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 9.59166i − 0.351884i −0.984401 0.175942i $$-0.943703\pi$$
0.984401 0.175942i $$-0.0562971\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ − 50.6286i − 1.85240i
$$748$$ 0 0
$$749$$ 6.93544 0.253415
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 47.9583i 1.74538i
$$756$$ 0 0
$$757$$ 53.5127 1.94495 0.972476 0.233005i $$-0.0748559\pi$$
0.972476 + 0.233005i $$0.0748559\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 52.9354 1.91891 0.959454 0.281865i $$-0.0909530\pi$$
0.959454 + 0.281865i $$0.0909530\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −5.36126 −0.193837
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −40.2492 −1.44766 −0.723832 0.689976i $$-0.757621\pi$$
−0.723832 + 0.689976i $$0.757621\pi$$
$$774$$ 0 0
$$775$$ 39.7999i 1.42965i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −18.2129 −0.650047
$$786$$ 0 0
$$787$$ 46.0144i 1.64024i 0.572195 + 0.820118i $$0.306092\pi$$
−0.572195 + 0.820118i $$0.693908\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ − 9.36053i − 0.332822i
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 35.6241 1.26187 0.630936 0.775835i $$-0.282671\pi$$
0.630936 + 0.775835i $$0.282671\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 4.94822 0.174402
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 36.9354 1.29858 0.649290 0.760541i $$-0.275066\pi$$
0.649290 + 0.760541i $$0.275066\pi$$
$$810$$ 0 0
$$811$$ 24.6175i 0.864437i 0.901769 + 0.432218i $$0.142269\pi$$
−0.901769 + 0.432218i $$0.857731\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 38.0000 1.32621 0.663105 0.748527i $$-0.269238\pi$$
0.663105 + 0.748527i $$0.269238\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 11.3391i 0.394300i 0.980373 + 0.197150i $$0.0631686\pi$$
−0.980373 + 0.197150i $$0.936831\pi$$
$$828$$ 0 0
$$829$$ 56.9354 1.97745 0.988725 0.149744i $$-0.0478450\pi$$
0.988725 + 0.149744i $$0.0478450\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ −5.42431 −0.187941
$$834$$ 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
$$841$$ 66.7871 2.30300
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ −29.0689 −1.00000
$$846$$ 0 0
$$847$$ 5.07566i 0.174402i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 46.7281i 1.60182i
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ − 58.5210i − 1.99671i −0.0573424 0.998355i $$-0.518263\pi$$
0.0573424 0.998355i $$-0.481737\pi$$
$$860$$ 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
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ −13.4164 −0.454077
$$874$$ 0 0
$$875$$ 5.15888i 0.174402i
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ − 47.9583i − 1.60307i
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 77.9050i 2.59828i
$$900$$ 0 0
$$901$$ −9.06456 −0.301984
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 51.5515i 1.71174i 0.517192 + 0.855869i $$0.326977\pi$$
−0.517192 + 0.855869i $$0.673023\pi$$
$$908$$ 0 0
$$909$$ −53.3613 −1.76988
$$910$$ 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
$$917$$ 9.89644 0.326809
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −48.7174 −1.60182
$$926$$ 0 0
$$927$$ 28.7750i 0.945095i
$$928$$ 0 0
$$929$$ 60.9354 1.99923 0.999613 0.0278019i $$-0.00885076\pi$$
0.999613 + 0.0278019i $$0.00885076\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 58.1378 1.89928 0.949639 0.313346i $$-0.101450\pi$$
0.949639 + 0.313346i $$0.101450\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ − 27.7539i − 0.903791i
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 22.3607 0.724333 0.362167 0.932113i $$-0.382037\pi$$
0.362167 + 0.932113i $$0.382037\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 6.19065i 0.199907i
$$960$$ 0 0
$$961$$ −32.3613 −1.04391
$$962$$ 0 0
$$963$$ − 45.0915i − 1.45305i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ −5.91759 −0.189709
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 62.4569 1.99817 0.999087 0.0427153i $$-0.0136008\pi$$
0.999087 + 0.0427153i $$0.0136008\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ − 36.9824i − 1.17955i −0.807566 0.589777i $$-0.799215\pi$$
0.807566 0.589777i $$-0.200785\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 46.0000 1.46271
$$990$$ 0 0
$$991$$ − 1.76933i − 0.0562045i −0.999605 0.0281022i $$-0.991054\pi$$
0.999605 0.0281022i $$-0.00894640\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 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 1840.2.m.e.1839.2 8
4.3 odd 2 inner 1840.2.m.e.1839.3 yes 8
5.4 even 2 inner 1840.2.m.e.1839.7 yes 8
20.19 odd 2 inner 1840.2.m.e.1839.6 yes 8
23.22 odd 2 inner 1840.2.m.e.1839.7 yes 8
92.91 even 2 inner 1840.2.m.e.1839.6 yes 8
115.114 odd 2 CM 1840.2.m.e.1839.2 8
460.459 even 2 inner 1840.2.m.e.1839.3 yes 8

By twisted newform
Twist Min Dim Char Parity Ord Type
1840.2.m.e.1839.2 8 1.1 even 1 trivial
1840.2.m.e.1839.2 8 115.114 odd 2 CM
1840.2.m.e.1839.3 yes 8 4.3 odd 2 inner
1840.2.m.e.1839.3 yes 8 460.459 even 2 inner
1840.2.m.e.1839.6 yes 8 20.19 odd 2 inner
1840.2.m.e.1839.6 yes 8 92.91 even 2 inner
1840.2.m.e.1839.7 yes 8 5.4 even 2 inner
1840.2.m.e.1839.7 yes 8 23.22 odd 2 inner