# Properties

 Label 1600.2.a.bd.1.2 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 1.2 Root $$1.61803$$ of defining polynomial Character $$\chi$$ $$=$$ 1600.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.23607 q^{3} -0.763932 q^{7} +7.47214 q^{9} +O(q^{10})$$ $$q+3.23607 q^{3} -0.763932 q^{7} +7.47214 q^{9} -2.47214 q^{21} +5.70820 q^{23} +14.4721 q^{27} +6.00000 q^{29} -4.47214 q^{41} +11.2361 q^{43} -13.7082 q^{47} -6.41641 q^{49} +13.4164 q^{61} -5.70820 q^{63} -8.18034 q^{67} +18.4721 q^{69} +24.4164 q^{81} -17.7082 q^{83} +19.4164 q^{87} +6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{3} - 6 q^{7} + 6 q^{9} + O(q^{10})$$ $$2 q + 2 q^{3} - 6 q^{7} + 6 q^{9} + 4 q^{21} - 2 q^{23} + 20 q^{27} + 12 q^{29} + 18 q^{43} - 14 q^{47} + 14 q^{49} + 2 q^{63} + 6 q^{67} + 28 q^{69} + 22 q^{81} - 22 q^{83} + 12 q^{87} + 12 q^{89} + O(q^{100})$$

## 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
$$3$$ 3.23607 1.86834 0.934172 0.356822i $$-0.116140\pi$$
0.934172 + 0.356822i $$0.116140\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.763932 −0.288739 −0.144370 0.989524i $$-0.546115\pi$$
−0.144370 + 0.989524i $$0.546115\pi$$
$$8$$ 0 0
$$9$$ 7.47214 2.49071
$$10$$ 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
$$21$$ −2.47214 −0.539464
$$22$$ 0 0
$$23$$ 5.70820 1.19024 0.595121 0.803636i $$-0.297104\pi$$
0.595121 + 0.803636i $$0.297104\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 14.4721 2.78516
$$28$$ 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 $$-0.613552\pi$$
−0.349215 + 0.937043i $$0.613552\pi$$
$$42$$ 0 0
$$43$$ 11.2361 1.71348 0.856742 0.515745i $$-0.172485\pi$$
0.856742 + 0.515745i $$0.172485\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −13.7082 −1.99955 −0.999774 0.0212814i $$-0.993225\pi$$
−0.999774 + 0.0212814i $$0.993225\pi$$
$$48$$ 0 0
$$49$$ −6.41641 −0.916630
$$50$$ 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 $$-0.171150\pi$$
0.858898 + 0.512148i $$0.171150\pi$$
$$62$$ 0 0
$$63$$ −5.70820 −0.719166
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −8.18034 −0.999388 −0.499694 0.866202i $$-0.666554\pi$$
−0.499694 + 0.866202i $$0.666554\pi$$
$$68$$ 0 0
$$69$$ 18.4721 2.22378
$$70$$ 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
$$81$$ 24.4164 2.71293
$$82$$ 0 0
$$83$$ −17.7082 −1.94373 −0.971864 0.235543i $$-0.924313\pi$$
−0.971864 + 0.235543i $$0.924313\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 19.4164 2.08166
$$88$$ 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
$$103$$ −20.1803 −1.98843 −0.994214 0.107418i $$-0.965742\pi$$
−0.994214 + 0.107418i $$0.965742\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.29180 −0.608251 −0.304125 0.952632i $$-0.598364\pi$$
−0.304125 + 0.952632i $$0.598364\pi$$
$$108$$ 0 0
$$109$$ −13.4164 −1.28506 −0.642529 0.766261i $$-0.722115\pi$$
−0.642529 + 0.766261i $$0.722115\pi$$
$$110$$ 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
$$123$$ −14.4721 −1.30491
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −18.6525 −1.65514 −0.827570 0.561363i $$-0.810277\pi$$
−0.827570 + 0.561363i $$0.810277\pi$$
$$128$$ 0 0
$$129$$ 36.3607 3.20138
$$130$$ 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
$$141$$ −44.3607 −3.73584
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −20.7639 −1.71258
$$148$$ 0 0
$$149$$ 4.47214 0.366372 0.183186 0.983078i $$-0.441359\pi$$
0.183186 + 0.983078i $$0.441359\pi$$
$$150$$ 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
$$161$$ −4.36068 −0.343670
$$162$$ 0 0
$$163$$ −6.65248 −0.521062 −0.260531 0.965465i $$-0.583898\pi$$
−0.260531 + 0.965465i $$0.583898\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 10.2918 0.796403 0.398202 0.917298i $$-0.369634\pi$$
0.398202 + 0.917298i $$0.369634\pi$$
$$168$$ 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
$$183$$ 43.4164 3.20943
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −11.0557 −0.804186
$$190$$ 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
$$201$$ −26.4721 −1.86720
$$202$$ 0 0
$$203$$ −4.58359 −0.321705
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 42.6525 2.96455
$$208$$ 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
$$223$$ −23.2361 −1.55600 −0.778001 0.628263i $$-0.783766\pi$$
−0.778001 + 0.628263i $$0.783766\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −13.1246 −0.871111 −0.435556 0.900162i $$-0.643448\pi$$
−0.435556 + 0.900162i $$0.643448\pi$$
$$228$$ 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 $$-0.357768\pi$$
0.432113 + 0.901819i $$0.357768\pi$$
$$242$$ 0 0
$$243$$ 35.5967 2.28353
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −57.3050 −3.63155
$$250$$ 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
$$261$$ 44.8328 2.77508
$$262$$ 0 0
$$263$$ −9.12461 −0.562648 −0.281324 0.959613i $$-0.590774\pi$$
−0.281324 + 0.959613i $$0.590774\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 19.4164 1.18826
$$268$$ 0 0
$$269$$ 22.3607 1.36335 0.681677 0.731653i $$-0.261251\pi$$
0.681677 + 0.731653i $$0.261251\pi$$
$$270$$ 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 $$-0.116517\pi$$
0.933748 + 0.357930i $$0.116517\pi$$
$$282$$ 0 0
$$283$$ 32.1803 1.91292 0.956461 0.291859i $$-0.0942738\pi$$
0.956461 + 0.291859i $$0.0942738\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 3.41641 0.201664
$$288$$ 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
$$301$$ −8.58359 −0.494750
$$302$$ 0 0
$$303$$ 58.2492 3.34633
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 27.5967 1.57503 0.787515 0.616296i $$-0.211367\pi$$
0.787515 + 0.616296i $$0.211367\pi$$
$$308$$ 0 0
$$309$$ −65.3050 −3.71507
$$310$$ 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
$$321$$ −20.3607 −1.13642
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ −43.4164 −2.40093
$$328$$ 0 0
$$329$$ 10.4721 0.577348
$$330$$ 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
$$343$$ 10.2492 0.553406
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −37.1246 −1.99295 −0.996477 0.0838690i $$-0.973272\pi$$
−0.996477 + 0.0838690i $$0.973272\pi$$
$$348$$ 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
$$363$$ −35.5967 −1.86834
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −24.7639 −1.29267 −0.646333 0.763055i $$-0.723698\pi$$
−0.646333 + 0.763055i $$0.723698\pi$$
$$368$$ 0 0
$$369$$ −33.4164 −1.73959
$$370$$ 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
$$381$$ −60.3607 −3.09237
$$382$$ 0 0
$$383$$ −1.12461 −0.0574650 −0.0287325 0.999587i $$-0.509147\pi$$
−0.0287325 + 0.999587i $$0.509147\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 83.9574 4.26780
$$388$$ 0 0
$$389$$ −31.3050 −1.58722 −0.793612 0.608424i $$-0.791802\pi$$
−0.793612 + 0.608424i $$0.791802\pi$$
$$390$$ 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 $$-0.0315304\pi$$
0.995098 + 0.0988936i $$0.0315304\pi$$
$$410$$ 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 $$-0.937546\pi$$
−0.980814 + 0.194948i $$0.937546\pi$$
$$422$$ 0 0
$$423$$ −102.430 −4.98030
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −10.2492 −0.495995
$$428$$ 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
$$441$$ −47.9443 −2.28306
$$442$$ 0 0
$$443$$ 22.2918 1.05912 0.529558 0.848274i $$-0.322358\pi$$
0.529558 + 0.848274i $$0.322358\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 14.4721 0.684509
$$448$$ 0 0
$$449$$ 22.3607 1.05527 0.527633 0.849473i $$-0.323080\pi$$
0.527633 + 0.849473i $$0.323080\pi$$
$$450$$ 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
$$463$$ −38.0689 −1.76921 −0.884606 0.466340i $$-0.845572\pi$$
−0.884606 + 0.466340i $$0.845572\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2.87539 0.133057 0.0665285 0.997785i $$-0.478808\pi$$
0.0665285 + 0.997785i $$0.478808\pi$$
$$468$$ 0 0
$$469$$ 6.24922 0.288562
$$470$$ 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
$$483$$ −14.1115 −0.642093
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −42.6525 −1.93277 −0.966384 0.257103i $$-0.917232\pi$$
−0.966384 + 0.257103i $$0.917232\pi$$
$$488$$ 0 0
$$489$$ −21.5279 −0.973524
$$490$$ 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
$$501$$ 33.3050 1.48796
$$502$$ 0 0
$$503$$ 37.7082 1.68133 0.840663 0.541559i $$-0.182166\pi$$
0.840663 + 0.541559i $$0.182166\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −42.0689 −1.86834
$$508$$ 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
$$523$$ −3.59675 −0.157275 −0.0786374 0.996903i $$-0.525057\pi$$
−0.0786374 + 0.996903i $$0.525057\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 9.58359 0.416678
$$530$$ 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
$$543$$ 6.47214 0.277746
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −35.2361 −1.50659 −0.753293 0.657685i $$-0.771536\pi$$
−0.753293 + 0.657685i $$0.771536\pi$$
$$548$$ 0 0
$$549$$ 100.249 4.27853
$$550$$ 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
$$563$$ −32.5410 −1.37144 −0.685720 0.727865i $$-0.740513\pi$$
−0.685720 + 0.727865i $$0.740513\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −18.6525 −0.783330
$$568$$ 0 0
$$569$$ −31.3050 −1.31237 −0.656186 0.754599i $$-0.727831\pi$$
−0.656186 + 0.754599i $$0.727831\pi$$
$$570$$ 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
$$581$$ 13.5279 0.561230
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 40.5410 1.67331 0.836653 0.547733i $$-0.184509\pi$$
0.836653 + 0.547733i $$0.184509\pi$$
$$588$$ 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 $$-0.806528\pi$$
−0.820900 + 0.571072i $$0.806528\pi$$
$$602$$ 0 0
$$603$$ −61.1246 −2.48919
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 44.1803 1.79322 0.896612 0.442816i $$-0.146021\pi$$
0.896612 + 0.442816i $$0.146021\pi$$
$$608$$ 0 0
$$609$$ −14.8328 −0.601056
$$610$$ 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
$$621$$ 82.6099 3.31502
$$622$$ 0 0
$$623$$ −4.58359 −0.183638
$$624$$ 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 $$-0.0761595\pi$$
0.971513 + 0.236986i $$0.0761595\pi$$
$$642$$ 0 0
$$643$$ 50.0689 1.97452 0.987262 0.159103i $$-0.0508601\pi$$
0.987262 + 0.159103i $$0.0508601\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −20.5410 −0.807551 −0.403775 0.914858i $$-0.632302\pi$$
−0.403775 + 0.914858i $$0.632302\pi$$
$$648$$ 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 $$-0.786187\pi$$
−0.782757 + 0.622328i $$0.786187\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 34.2492 1.32614
$$668$$ 0 0
$$669$$ −75.1935 −2.90715
$$670$$ 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
$$681$$ −42.4721 −1.62754
$$682$$ 0 0
$$683$$ −10.8754 −0.416135 −0.208068 0.978114i $$-0.566717\pi$$
−0.208068 + 0.978114i $$0.566717\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 45.3050 1.72849
$$688$$ 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 $$-0.638769\pi$$
−0.422276 + 0.906467i $$0.638769\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −13.7508 −0.517151
$$708$$ 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
$$721$$ 15.4164 0.574137
$$722$$ 0 0
$$723$$ 43.4164 1.61467
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 35.0132 1.29857 0.649283 0.760547i $$-0.275069\pi$$
0.649283 + 0.760547i $$0.275069\pi$$
$$728$$ 0 0
$$729$$ 41.9443 1.55349
$$730$$ 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
$$743$$ 52.5410 1.92754 0.963772 0.266729i $$-0.0859429\pi$$
0.963772 + 0.266729i $$0.0859429\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −132.318 −4.84127
$$748$$ 0 0
$$749$$ 4.80650 0.175626
$$750$$ 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
$$763$$ 10.2492 0.371047
$$764$$ 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
$$783$$ 86.8328 3.10315
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −2.06888 −0.0737477 −0.0368739 0.999320i $$-0.511740\pi$$
−0.0368739 + 0.999320i $$0.511740\pi$$
$$788$$ 0 0
$$789$$ −29.5279 −1.05122
$$790$$ 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
$$801$$ 44.8328 1.58409
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 72.3607 2.54722
$$808$$ 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 $$-0.316045\pi$$
0.546275 + 0.837606i $$0.316045\pi$$
$$822$$ 0 0
$$823$$ 27.8197 0.969732 0.484866 0.874588i $$-0.338868\pi$$
0.484866 + 0.874588i $$0.338868\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 56.5410 1.96612 0.983062 0.183274i $$-0.0586694\pi$$
0.983062 + 0.183274i $$0.0586694\pi$$
$$828$$ 0 0
$$829$$ −13.4164 −0.465971 −0.232986 0.972480i $$-0.574849\pi$$
−0.232986 + 0.972480i $$0.574849\pi$$
$$830$$ 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
$$843$$ 101.305 3.48913
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 8.40325 0.288739
$$848$$ 0 0
$$849$$ 104.138 3.57400
$$850$$ 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
$$861$$ 11.0557 0.376778
$$862$$ 0 0
$$863$$ −34.2918 −1.16731 −0.583653 0.812003i $$-0.698377\pi$$
−0.583653 + 0.812003i $$0.698377\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ −55.0132 −1.86834
$$868$$ 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 $$-0.935209\pi$$
−0.979356 + 0.202145i $$0.935209\pi$$
$$882$$ 0 0
$$883$$ −54.6525 −1.83920 −0.919601 0.392853i $$-0.871488\pi$$
−0.919601 + 0.392853i $$0.871488\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 57.1246 1.91806 0.959028 0.283310i $$-0.0914325\pi$$
0.959028 + 0.283310i $$0.0914325\pi$$
$$888$$ 0 0
$$889$$ 14.2492 0.477904
$$890$$ 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
$$903$$ −27.7771 −0.924364
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 45.4853 1.51031 0.755157 0.655544i $$-0.227561\pi$$
0.755157 + 0.655544i $$0.227561\pi$$
$$908$$ 0 0
$$909$$ 134.498 4.46103
$$910$$ 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
$$921$$ 89.3050 2.94270
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ −150.790 −4.95260
$$928$$ 0 0
$$929$$ −49.1935 −1.61399 −0.806993 0.590561i $$-0.798907\pi$$
−0.806993 + 0.590561i $$0.798907\pi$$
$$930$$ 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
$$943$$ −25.5279 −0.831302
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 49.7082 1.61530 0.807650 0.589662i $$-0.200739\pi$$
0.807650 + 0.589662i $$0.200739\pi$$
$$948$$ 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
$$963$$ −47.0132 −1.51498
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 62.0689 1.99600 0.998000 0.0632081i $$-0.0201332\pi$$
0.998000 + 0.0632081i $$0.0201332\pi$$
$$968$$ 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
$$981$$ −100.249 −3.20071
$$982$$ 0 0
$$983$$ 4.54102 0.144836 0.0724180 0.997374i $$-0.476928\pi$$
0.0724180 + 0.997374i $$0.476928\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 33.8885 1.07868
$$988$$ 0 0
$$989$$ 64.1378 2.03946
$$990$$ 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.1.2 2
4.3 odd 2 1600.2.a.z.1.1 2
5.2 odd 4 320.2.c.d.129.1 4
5.3 odd 4 320.2.c.d.129.4 4
5.4 even 2 1600.2.a.z.1.1 2
8.3 odd 2 800.2.a.n.1.2 2
8.5 even 2 800.2.a.j.1.1 2
15.2 even 4 2880.2.f.w.1729.3 4
15.8 even 4 2880.2.f.w.1729.4 4
20.3 even 4 320.2.c.d.129.1 4
20.7 even 4 320.2.c.d.129.4 4
20.19 odd 2 CM 1600.2.a.bd.1.2 2
24.5 odd 2 7200.2.a.cb.1.2 2
24.11 even 2 7200.2.a.cr.1.1 2
40.3 even 4 160.2.c.b.129.4 yes 4
40.13 odd 4 160.2.c.b.129.1 4
40.19 odd 2 800.2.a.j.1.1 2
40.27 even 4 160.2.c.b.129.1 4
40.29 even 2 800.2.a.n.1.2 2
40.37 odd 4 160.2.c.b.129.4 yes 4
60.23 odd 4 2880.2.f.w.1729.3 4
60.47 odd 4 2880.2.f.w.1729.4 4
80.3 even 4 1280.2.f.h.129.4 4
80.13 odd 4 1280.2.f.g.129.2 4
80.27 even 4 1280.2.f.h.129.3 4
80.37 odd 4 1280.2.f.g.129.1 4
80.43 even 4 1280.2.f.g.129.1 4
80.53 odd 4 1280.2.f.h.129.3 4
80.67 even 4 1280.2.f.g.129.2 4
80.77 odd 4 1280.2.f.h.129.4 4
120.29 odd 2 7200.2.a.cr.1.1 2
120.53 even 4 1440.2.f.i.289.2 4
120.59 even 2 7200.2.a.cb.1.2 2
120.77 even 4 1440.2.f.i.289.1 4
120.83 odd 4 1440.2.f.i.289.1 4
120.107 odd 4 1440.2.f.i.289.2 4

By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 40.13 odd 4
160.2.c.b.129.1 4 40.27 even 4
160.2.c.b.129.4 yes 4 40.3 even 4
160.2.c.b.129.4 yes 4 40.37 odd 4
320.2.c.d.129.1 4 5.2 odd 4
320.2.c.d.129.1 4 20.3 even 4
320.2.c.d.129.4 4 5.3 odd 4
320.2.c.d.129.4 4 20.7 even 4
800.2.a.j.1.1 2 8.5 even 2
800.2.a.j.1.1 2 40.19 odd 2
800.2.a.n.1.2 2 8.3 odd 2
800.2.a.n.1.2 2 40.29 even 2
1280.2.f.g.129.1 4 80.37 odd 4
1280.2.f.g.129.1 4 80.43 even 4
1280.2.f.g.129.2 4 80.13 odd 4
1280.2.f.g.129.2 4 80.67 even 4
1280.2.f.h.129.3 4 80.27 even 4
1280.2.f.h.129.3 4 80.53 odd 4
1280.2.f.h.129.4 4 80.3 even 4
1280.2.f.h.129.4 4 80.77 odd 4
1440.2.f.i.289.1 4 120.77 even 4
1440.2.f.i.289.1 4 120.83 odd 4
1440.2.f.i.289.2 4 120.53 even 4
1440.2.f.i.289.2 4 120.107 odd 4
1600.2.a.z.1.1 2 4.3 odd 2
1600.2.a.z.1.1 2 5.4 even 2
1600.2.a.bd.1.2 2 1.1 even 1 trivial
1600.2.a.bd.1.2 2 20.19 odd 2 CM
2880.2.f.w.1729.3 4 15.2 even 4
2880.2.f.w.1729.3 4 60.23 odd 4
2880.2.f.w.1729.4 4 15.8 even 4
2880.2.f.w.1729.4 4 60.47 odd 4
7200.2.a.cb.1.2 2 24.5 odd 2
7200.2.a.cb.1.2 2 120.59 even 2
7200.2.a.cr.1.1 2 24.11 even 2
7200.2.a.cr.1.1 2 120.29 odd 2