# Properties

 Label 1600.2.a.bd.1.1 Level $1600$ Weight $2$ Character 1600.1 Self dual yes Analytic conductor $12.776$ Analytic rank $0$ Dimension $2$ CM discriminant -20 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1600 = 2^{6} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1600.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$12.7760643234$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: no (minimal twist has level 160) Fricke sign: $$-1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 1600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.23607 q^{3} -5.23607 q^{7} -1.47214 q^{9} +O(q^{10})$$ $$q-1.23607 q^{3} -5.23607 q^{7} -1.47214 q^{9} +6.47214 q^{21} -7.70820 q^{23} +5.52786 q^{27} +6.00000 q^{29} +4.47214 q^{41} +6.76393 q^{43} -0.291796 q^{47} +20.4164 q^{49} -13.4164 q^{61} +7.70820 q^{63} +14.1803 q^{67} +9.52786 q^{69} -2.41641 q^{81} -4.29180 q^{83} -7.41641 q^{87} +6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 6 q^{7} + 6 q^{9} + O(q^{10})$$ $$2 q + 2 q^{3} - 6 q^{7} + 6 q^{9} + 4 q^{21} - 2 q^{23} + 20 q^{27} + 12 q^{29} + 18 q^{43} - 14 q^{47} + 14 q^{49} + 2 q^{63} + 6 q^{67} + 28 q^{69} + 22 q^{81} - 22 q^{83} + 12 q^{87} + 12 q^{89} + O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.23607 −0.713644 −0.356822 0.934172i $$-0.616140\pi$$
−0.356822 + 0.934172i $$0.616140\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −5.23607 −1.97905 −0.989524 0.144370i $$-0.953885\pi$$
−0.989524 + 0.144370i $$0.953885\pi$$
$$8$$ 0 0
$$9$$ −1.47214 −0.490712
$$10$$ 0 0
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 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
$$21$$ 6.47214 1.41234
$$22$$ 0 0
$$23$$ −7.70820 −1.60727 −0.803636 0.595121i $$-0.797104\pi$$
−0.803636 + 0.595121i $$0.797104\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.52786 1.06384
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.47214 0.698430 0.349215 0.937043i $$-0.386448\pi$$
0.349215 + 0.937043i $$0.386448\pi$$
$$42$$ 0 0
$$43$$ 6.76393 1.03149 0.515745 0.856742i $$-0.327515\pi$$
0.515745 + 0.856742i $$0.327515\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −0.291796 −0.0425628 −0.0212814 0.999774i $$-0.506775\pi$$
−0.0212814 + 0.999774i $$0.506775\pi$$
$$48$$ 0 0
$$49$$ 20.4164 2.91663
$$50$$ 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
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −13.4164 −1.71780 −0.858898 0.512148i $$-0.828850\pi$$
−0.858898 + 0.512148i $$0.828850\pi$$
$$62$$ 0 0
$$63$$ 7.70820 0.971142
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 14.1803 1.73240 0.866202 0.499694i $$-0.166554\pi$$
0.866202 + 0.499694i $$0.166554\pi$$
$$68$$ 0 0
$$69$$ 9.52786 1.14702
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 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
$$81$$ −2.41641 −0.268490
$$82$$ 0 0
$$83$$ −4.29180 −0.471086 −0.235543 0.971864i $$-0.575687\pi$$
−0.235543 + 0.971864i $$0.575687\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −7.41641 −0.795122
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 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
$$100$$ 0 0
$$101$$ 18.0000 1.79107 0.895533 0.444994i $$-0.146794\pi$$
0.895533 + 0.444994i $$0.146794\pi$$
$$102$$ 0 0
$$103$$ 2.18034 0.214835 0.107418 0.994214i $$-0.465742\pi$$
0.107418 + 0.994214i $$0.465742\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −19.7082 −1.90526 −0.952632 0.304125i $$-0.901636\pi$$
−0.952632 + 0.304125i $$0.901636\pi$$
$$108$$ 0 0
$$109$$ 13.4164 1.28506 0.642529 0.766261i $$-0.277885\pi$$
0.642529 + 0.766261i $$0.277885\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ −5.52786 −0.498431
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 12.6525 1.12273 0.561363 0.827570i $$-0.310277\pi$$
0.561363 + 0.827570i $$0.310277\pi$$
$$128$$ 0 0
$$129$$ −8.36068 −0.736117
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0.360680 0.0303747
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −25.2361 −2.08144
$$148$$ 0 0
$$149$$ −4.47214 −0.366372 −0.183186 0.983078i $$-0.558641\pi$$
−0.183186 + 0.983078i $$0.558641\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 40.3607 3.18087
$$162$$ 0 0
$$163$$ 24.6525 1.93093 0.965465 0.260531i $$-0.0838976\pi$$
0.965465 + 0.260531i $$0.0838976\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 23.7082 1.83460 0.917298 0.398202i $$-0.130366\pi$$
0.917298 + 0.398202i $$0.130366\pi$$
$$168$$ 0 0
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 16.5836 1.22589
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −28.9443 −2.10539
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −17.5279 −1.23632
$$202$$ 0 0
$$203$$ −31.4164 −2.20500
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 11.3475 0.788707
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −18.7639 −1.25653 −0.628263 0.778001i $$-0.716234\pi$$
−0.628263 + 0.778001i $$0.716234\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 27.1246 1.80032 0.900162 0.435556i $$-0.143448\pi$$
0.900162 + 0.435556i $$0.143448\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ −13.4164 −0.864227 −0.432113 0.901819i $$-0.642232\pi$$
−0.432113 + 0.901819i $$0.642232\pi$$
$$242$$ 0 0
$$243$$ −13.5967 −0.872232
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 5.30495 0.336188
$$250$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −8.83282 −0.546738
$$262$$ 0 0
$$263$$ 31.1246 1.91923 0.959613 0.281324i $$-0.0907735\pi$$
0.959613 + 0.281324i $$0.0907735\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −7.41641 −0.453877
$$268$$ 0 0
$$269$$ −22.3607 −1.36335 −0.681677 0.731653i $$-0.738749\pi$$
−0.681677 + 0.731653i $$0.738749\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −31.3050 −1.86750 −0.933748 0.357930i $$-0.883483\pi$$
−0.933748 + 0.357930i $$0.883483\pi$$
$$282$$ 0 0
$$283$$ 9.81966 0.583718 0.291859 0.956461i $$-0.405726\pi$$
0.291859 + 0.956461i $$0.405726\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −23.4164 −1.38223
$$288$$ 0 0
$$289$$ −17.0000 −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
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −35.4164 −2.04137
$$302$$ 0 0
$$303$$ −22.2492 −1.27818
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −21.5967 −1.23259 −0.616296 0.787515i $$-0.711367\pi$$
−0.616296 + 0.787515i $$0.711367\pi$$
$$308$$ 0 0
$$309$$ −2.69505 −0.153316
$$310$$ 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
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 24.3607 1.35968
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −16.5836 −0.917075
$$328$$ 0 0
$$329$$ 1.52786 0.0842339
$$330$$ 0 0
$$331$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −70.2492 −3.79310
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 3.12461 0.167738 0.0838690 0.996477i $$-0.473272\pi$$
0.0838690 + 0.996477i $$0.473272\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 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
$$363$$ 13.5967 0.713644
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −29.2361 −1.52611 −0.763055 0.646333i $$-0.776302\pi$$
−0.763055 + 0.646333i $$0.776302\pi$$
$$368$$ 0 0
$$369$$ −6.58359 −0.342728
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 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
$$381$$ −15.6393 −0.801227
$$382$$ 0 0
$$383$$ 39.1246 1.99917 0.999587 0.0287325i $$-0.00914709\pi$$
0.999587 + 0.0287325i $$0.00914709\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −9.95743 −0.506164
$$388$$ 0 0
$$389$$ 31.3050 1.58722 0.793612 0.608424i $$-0.208198\pi$$
0.793612 + 0.608424i $$0.208198\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −40.2492 −1.99020 −0.995098 0.0988936i $$-0.968470\pi$$
−0.995098 + 0.0988936i $$0.968470\pi$$
$$410$$ 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
$$421$$ 40.2492 1.96163 0.980814 0.194948i $$-0.0624538\pi$$
0.980814 + 0.194948i $$0.0624538\pi$$
$$422$$ 0 0
$$423$$ 0.429563 0.0208861
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 70.2492 3.39960
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ −30.0557 −1.43123
$$442$$ 0 0
$$443$$ 35.7082 1.69655 0.848274 0.529558i $$-0.177642\pi$$
0.848274 + 0.529558i $$0.177642\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 5.52786 0.261459
$$448$$ 0 0
$$449$$ −22.3607 −1.05527 −0.527633 0.849473i $$-0.676920\pi$$
−0.527633 + 0.849473i $$0.676920\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 42.0000 1.95614 0.978068 0.208288i $$-0.0667892\pi$$
0.978068 + 0.208288i $$0.0667892\pi$$
$$462$$ 0 0
$$463$$ 20.0689 0.932680 0.466340 0.884606i $$-0.345572\pi$$
0.466340 + 0.884606i $$0.345572\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 43.1246 1.99557 0.997785 0.0665285i $$-0.0211923\pi$$
0.997785 + 0.0665285i $$0.0211923\pi$$
$$468$$ 0 0
$$469$$ −74.2492 −3.42851
$$470$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −49.8885 −2.27001
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −11.3475 −0.514205 −0.257103 0.966384i $$-0.582768\pi$$
−0.257103 + 0.966384i $$0.582768\pi$$
$$488$$ 0 0
$$489$$ −30.4721 −1.37800
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ 0 0
$$501$$ −29.3050 −1.30925
$$502$$ 0 0
$$503$$ 24.2918 1.08312 0.541559 0.840663i $$-0.317834\pi$$
0.541559 + 0.840663i $$0.317834\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 16.0689 0.713644
$$508$$ 0 0
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 42.0000 1.84005 0.920027 0.391856i $$-0.128167\pi$$
0.920027 + 0.391856i $$0.128167\pi$$
$$522$$ 0 0
$$523$$ 45.5967 1.99381 0.996903 0.0786374i $$-0.0250569\pi$$
0.996903 + 0.0786374i $$0.0250569\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 36.4164 1.58332
$$530$$ 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
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 0 0
$$543$$ −2.47214 −0.106090
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −30.7639 −1.31537 −0.657685 0.753293i $$-0.728464\pi$$
−0.657685 + 0.753293i $$0.728464\pi$$
$$548$$ 0 0
$$549$$ 19.7508 0.842943
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 34.5410 1.45573 0.727865 0.685720i $$-0.240513\pi$$
0.727865 + 0.685720i $$0.240513\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 12.6525 0.531354
$$568$$ 0 0
$$569$$ 31.3050 1.31237 0.656186 0.754599i $$-0.272169\pi$$
0.656186 + 0.754599i $$0.272169\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 22.4721 0.932301
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −26.5410 −1.09547 −0.547733 0.836653i $$-0.684509\pi$$
−0.547733 + 0.836653i $$0.684509\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 40.2492 1.64180 0.820900 0.571072i $$-0.193472\pi$$
0.820900 + 0.571072i $$0.193472\pi$$
$$602$$ 0 0
$$603$$ −20.8754 −0.850112
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 21.8197 0.885633 0.442816 0.896612i $$-0.353979\pi$$
0.442816 + 0.896612i $$0.353979\pi$$
$$608$$ 0 0
$$609$$ 38.8328 1.57359
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ −42.6099 −1.70988
$$622$$ 0 0
$$623$$ −31.4164 −1.25867
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 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
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −49.1935 −1.94303 −0.971513 0.236986i $$-0.923841\pi$$
−0.971513 + 0.236986i $$0.923841\pi$$
$$642$$ 0 0
$$643$$ −8.06888 −0.318206 −0.159103 0.987262i $$-0.550860\pi$$
−0.159103 + 0.987262i $$0.550860\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 46.5410 1.82972 0.914858 0.403775i $$-0.132302\pi$$
0.914858 + 0.403775i $$0.132302\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 40.2492 1.56551 0.782757 0.622328i $$-0.213813\pi$$
0.782757 + 0.622328i $$0.213813\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −46.2492 −1.79078
$$668$$ 0 0
$$669$$ 23.1935 0.896712
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −33.5279 −1.28479
$$682$$ 0 0
$$683$$ −51.1246 −1.95623 −0.978114 0.208068i $$-0.933283\pi$$
−0.978114 + 0.208068i $$0.933283\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −17.3050 −0.660225
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 22.3607 0.844551 0.422276 0.906467i $$-0.361231\pi$$
0.422276 + 0.906467i $$0.361231\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −94.2492 −3.54461
$$708$$ 0 0
$$709$$ 46.0000 1.72757 0.863783 0.503864i $$-0.168089\pi$$
0.863783 + 0.503864i $$0.168089\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 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
$$721$$ −11.4164 −0.425169
$$722$$ 0 0
$$723$$ 16.5836 0.616750
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −41.0132 −1.52109 −0.760547 0.649283i $$-0.775069\pi$$
−0.760547 + 0.649283i $$0.775069\pi$$
$$728$$ 0 0
$$729$$ 24.0557 0.890953
$$730$$ 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
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −14.5410 −0.533458 −0.266729 0.963772i $$-0.585943\pi$$
−0.266729 + 0.963772i $$0.585943\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 6.31811 0.231167
$$748$$ 0 0
$$749$$ 103.193 3.77061
$$750$$ 0 0
$$751$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ −70.2492 −2.54319
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 33.1672 1.18530
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 56.0689 1.99864 0.999320 0.0368739i $$-0.0117400\pi$$
0.999320 + 0.0368739i $$0.0117400\pi$$
$$788$$ 0 0
$$789$$ −38.4721 −1.36964
$$790$$ 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
$$800$$ 0 0
$$801$$ −8.83282 −0.312092
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 27.6393 0.972950
$$808$$ 0 0
$$809$$ 54.0000 1.89854 0.949269 0.314464i $$-0.101825\pi$$
0.949269 + 0.314464i $$0.101825\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$812$$ 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
$$821$$ −31.3050 −1.09255 −0.546275 0.837606i $$-0.683955\pi$$
−0.546275 + 0.837606i $$0.683955\pi$$
$$822$$ 0 0
$$823$$ 50.1803 1.74918 0.874588 0.484866i $$-0.161132\pi$$
0.874588 + 0.484866i $$0.161132\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −10.5410 −0.366547 −0.183274 0.983062i $$-0.558669\pi$$
−0.183274 + 0.983062i $$0.558669\pi$$
$$828$$ 0 0
$$829$$ 13.4164 0.465971 0.232986 0.972480i $$-0.425151\pi$$
0.232986 + 0.972480i $$0.425151\pi$$
$$830$$ 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
$$841$$ 7.00000 0.241379
$$842$$ 0 0
$$843$$ 38.6950 1.33273
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 57.5967 1.97905
$$848$$ 0 0
$$849$$ −12.1378 −0.416567
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 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
$$861$$ 28.9443 0.986418
$$862$$ 0 0
$$863$$ −47.7082 −1.62401 −0.812003 0.583653i $$-0.801623\pi$$
−0.812003 + 0.583653i $$0.801623\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 21.0132 0.713644
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 58.1378 1.95871 0.979356 0.202145i $$-0.0647913\pi$$
0.979356 + 0.202145i $$0.0647913\pi$$
$$882$$ 0 0
$$883$$ −23.3475 −0.785707 −0.392853 0.919601i $$-0.628512\pi$$
−0.392853 + 0.919601i $$0.628512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 16.8754 0.566620 0.283310 0.959028i $$-0.408567\pi$$
0.283310 + 0.959028i $$0.408567\pi$$
$$888$$ 0 0
$$889$$ −66.2492 −2.22193
$$890$$ 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
$$903$$ 43.7771 1.45681
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −39.4853 −1.31109 −0.655544 0.755157i $$-0.727561\pi$$
−0.655544 + 0.755157i $$0.727561\pi$$
$$908$$ 0 0
$$909$$ −26.4984 −0.878898
$$910$$ 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
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 26.6950 0.879632
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −3.20976 −0.105422
$$928$$ 0 0
$$929$$ 49.1935 1.61399 0.806993 0.590561i $$-0.201093\pi$$
0.806993 + 0.590561i $$0.201093\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 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
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 0 0
$$943$$ −34.4721 −1.12257
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 36.2918 1.17932 0.589662 0.807650i $$-0.299261\pi$$
0.589662 + 0.807650i $$0.299261\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 29.0132 0.934936
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 3.93112 0.126416 0.0632081 0.998000i $$-0.479867\pi$$
0.0632081 + 0.998000i $$0.479867\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −19.7508 −0.630594
$$982$$ 0 0
$$983$$ −62.5410 −1.99475 −0.997374 0.0724180i $$-0.976928\pi$$
−0.997374 + 0.0724180i $$0.976928\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −1.88854 −0.0601130
$$988$$ 0 0
$$989$$ −52.1378 −1.65788
$$990$$ 0 0
$$991$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 1600.2.a.bd.1.1 2
4.3 odd 2 1600.2.a.z.1.2 2
5.2 odd 4 320.2.c.d.129.3 4
5.3 odd 4 320.2.c.d.129.2 4
5.4 even 2 1600.2.a.z.1.2 2
8.3 odd 2 800.2.a.n.1.1 2
8.5 even 2 800.2.a.j.1.2 2
15.2 even 4 2880.2.f.w.1729.1 4
15.8 even 4 2880.2.f.w.1729.2 4
20.3 even 4 320.2.c.d.129.3 4
20.7 even 4 320.2.c.d.129.2 4
20.19 odd 2 CM 1600.2.a.bd.1.1 2
24.5 odd 2 7200.2.a.cb.1.1 2
24.11 even 2 7200.2.a.cr.1.2 2
40.3 even 4 160.2.c.b.129.2 4
40.13 odd 4 160.2.c.b.129.3 yes 4
40.19 odd 2 800.2.a.j.1.2 2
40.27 even 4 160.2.c.b.129.3 yes 4
40.29 even 2 800.2.a.n.1.1 2
40.37 odd 4 160.2.c.b.129.2 4
60.23 odd 4 2880.2.f.w.1729.1 4
60.47 odd 4 2880.2.f.w.1729.2 4
80.3 even 4 1280.2.f.h.129.1 4
80.13 odd 4 1280.2.f.g.129.3 4
80.27 even 4 1280.2.f.h.129.2 4
80.37 odd 4 1280.2.f.g.129.4 4
80.43 even 4 1280.2.f.g.129.4 4
80.53 odd 4 1280.2.f.h.129.2 4
80.67 even 4 1280.2.f.g.129.3 4
80.77 odd 4 1280.2.f.h.129.1 4
120.29 odd 2 7200.2.a.cr.1.2 2
120.53 even 4 1440.2.f.i.289.4 4
120.59 even 2 7200.2.a.cb.1.1 2
120.77 even 4 1440.2.f.i.289.3 4
120.83 odd 4 1440.2.f.i.289.3 4
120.107 odd 4 1440.2.f.i.289.4 4

By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.2 4 40.3 even 4
160.2.c.b.129.2 4 40.37 odd 4
160.2.c.b.129.3 yes 4 40.13 odd 4
160.2.c.b.129.3 yes 4 40.27 even 4
320.2.c.d.129.2 4 5.3 odd 4
320.2.c.d.129.2 4 20.7 even 4
320.2.c.d.129.3 4 5.2 odd 4
320.2.c.d.129.3 4 20.3 even 4
800.2.a.j.1.2 2 8.5 even 2
800.2.a.j.1.2 2 40.19 odd 2
800.2.a.n.1.1 2 8.3 odd 2
800.2.a.n.1.1 2 40.29 even 2
1280.2.f.g.129.3 4 80.13 odd 4
1280.2.f.g.129.3 4 80.67 even 4
1280.2.f.g.129.4 4 80.37 odd 4
1280.2.f.g.129.4 4 80.43 even 4
1280.2.f.h.129.1 4 80.3 even 4
1280.2.f.h.129.1 4 80.77 odd 4
1280.2.f.h.129.2 4 80.27 even 4
1280.2.f.h.129.2 4 80.53 odd 4
1440.2.f.i.289.3 4 120.77 even 4
1440.2.f.i.289.3 4 120.83 odd 4
1440.2.f.i.289.4 4 120.53 even 4
1440.2.f.i.289.4 4 120.107 odd 4
1600.2.a.z.1.2 2 4.3 odd 2
1600.2.a.z.1.2 2 5.4 even 2
1600.2.a.bd.1.1 2 1.1 even 1 trivial
1600.2.a.bd.1.1 2 20.19 odd 2 CM
2880.2.f.w.1729.1 4 15.2 even 4
2880.2.f.w.1729.1 4 60.23 odd 4
2880.2.f.w.1729.2 4 15.8 even 4
2880.2.f.w.1729.2 4 60.47 odd 4
7200.2.a.cb.1.1 2 24.5 odd 2
7200.2.a.cb.1.1 2 120.59 even 2
7200.2.a.cr.1.2 2 24.11 even 2
7200.2.a.cr.1.2 2 120.29 odd 2