# Properties

 Label 6400.2.a.cv.1.1 Level $6400$ Weight $2$ Character 6400.1 Self dual yes Analytic conductor $51.104$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$6400 = 2^{8} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 6400.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$51.1042572936$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{5})$$ Defining polynomial: $$x^{4} - 6 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{23}]$$ Coefficient ring index: $$2^{3}$$ Twist minimal: no (minimal twist has level 640) Fricke sign: $$-1$$ Sato-Tate group: $N(\mathrm{U}(1))$

## Embedding invariants

 Embedding label 1.1 Root $$-0.874032$$ of defining polynomial Character $$\chi$$ $$=$$ 6400.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.16228 q^{3} -4.24264 q^{7} +7.00000 q^{9} +O(q^{10})$$ $$q-3.16228 q^{3} -4.24264 q^{7} +7.00000 q^{9} +13.4164 q^{21} +1.41421 q^{23} -12.6491 q^{27} -8.94427 q^{29} +12.0000 q^{41} +3.16228 q^{43} -9.89949 q^{47} +11.0000 q^{49} -13.4164 q^{61} -29.6985 q^{63} -15.8114 q^{67} -4.47214 q^{69} +19.0000 q^{81} -9.48683 q^{83} +28.2843 q^{87} -6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 28 q^{9} + O(q^{10})$$ $$4 q + 28 q^{9} + 48 q^{41} + 44 q^{49} + 76 q^{81} - 24 q^{89} + O(q^{100})$$

## 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
$$3$$ −3.16228 −1.82574 −0.912871 0.408248i $$-0.866140\pi$$
−0.912871 + 0.408248i $$0.866140\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −4.24264 −1.60357 −0.801784 0.597614i $$-0.796115\pi$$
−0.801784 + 0.597614i $$0.796115\pi$$
$$8$$ 0 0
$$9$$ 7.00000 2.33333
$$10$$ 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
$$21$$ 13.4164 2.92770
$$22$$ 0 0
$$23$$ 1.41421 0.294884 0.147442 0.989071i $$-0.452896\pi$$
0.147442 + 0.989071i $$0.452896\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ −12.6491 −2.43432
$$28$$ 0 0
$$29$$ −8.94427 −1.66091 −0.830455 0.557086i $$-0.811919\pi$$
−0.830455 + 0.557086i $$0.811919\pi$$
$$30$$ 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
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ 0 0
$$43$$ 3.16228 0.482243 0.241121 0.970495i $$-0.422485\pi$$
0.241121 + 0.970495i $$0.422485\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −9.89949 −1.44399 −0.721995 0.691898i $$-0.756775\pi$$
−0.721995 + 0.691898i $$0.756775\pi$$
$$48$$ 0 0
$$49$$ 11.0000 1.57143
$$50$$ 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
$$63$$ −29.6985 −3.74166
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −15.8114 −1.93167 −0.965834 0.259161i $$-0.916554\pi$$
−0.965834 + 0.259161i $$0.916554\pi$$
$$68$$ 0 0
$$69$$ −4.47214 −0.538382
$$70$$ 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
$$81$$ 19.0000 2.11111
$$82$$ 0 0
$$83$$ −9.48683 −1.04132 −0.520658 0.853766i $$-0.674313\pi$$
−0.520658 + 0.853766i $$0.674313\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 28.2843 3.03239
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 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
$$101$$ 8.94427 0.889988 0.444994 0.895533i $$-0.353206\pi$$
0.444994 + 0.895533i $$0.353206\pi$$
$$102$$ 0 0
$$103$$ 12.7279 1.25412 0.627060 0.778971i $$-0.284258\pi$$
0.627060 + 0.778971i $$0.284258\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −9.48683 −0.917127 −0.458563 0.888662i $$-0.651636\pi$$
−0.458563 + 0.888662i $$0.651636\pi$$
$$108$$ 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
$$123$$ −37.9473 −3.42160
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 4.24264 0.376473 0.188237 0.982124i $$-0.439723\pi$$
0.188237 + 0.982124i $$0.439723\pi$$
$$128$$ 0 0
$$129$$ −10.0000 −0.880451
$$130$$ 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
$$141$$ 31.3050 2.63635
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −34.7851 −2.86902
$$148$$ 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
$$161$$ −6.00000 −0.472866
$$162$$ 0 0
$$163$$ 22.1359 1.73382 0.866910 0.498464i $$-0.166102\pi$$
0.866910 + 0.498464i $$0.166102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −24.0416 −1.86040 −0.930199 0.367057i $$-0.880366\pi$$
−0.930199 + 0.367057i $$0.880366\pi$$
$$168$$ 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
$$181$$ −26.8328 −1.99447 −0.997234 0.0743294i $$-0.976318\pi$$
−0.997234 + 0.0743294i $$0.976318\pi$$
$$182$$ 0 0
$$183$$ 42.4264 3.13625
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 53.6656 3.90360
$$190$$ 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
$$201$$ 50.0000 3.52673
$$202$$ 0 0
$$203$$ 37.9473 2.66338
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 9.89949 0.688062
$$208$$ 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
$$223$$ 29.6985 1.98876 0.994379 0.105881i $$-0.0337662\pi$$
0.994379 + 0.105881i $$0.0337662\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 28.4605 1.88899 0.944495 0.328526i $$-0.106552\pi$$
0.944495 + 0.328526i $$0.106552\pi$$
$$228$$ 0 0
$$229$$ 26.8328 1.77316 0.886581 0.462573i $$-0.153074\pi$$
0.886581 + 0.462573i $$0.153074\pi$$
$$230$$ 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
$$241$$ 28.0000 1.80364 0.901819 0.432113i $$-0.142232\pi$$
0.901819 + 0.432113i $$0.142232\pi$$
$$242$$ 0 0
$$243$$ −22.1359 −1.42002
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 30.0000 1.90117
$$250$$ 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
$$261$$ −62.6099 −3.87546
$$262$$ 0 0
$$263$$ 15.5563 0.959246 0.479623 0.877475i $$-0.340774\pi$$
0.479623 + 0.877475i $$0.340774\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 18.9737 1.16117
$$268$$ 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
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ 0 0
$$283$$ −15.8114 −0.939889 −0.469945 0.882696i $$-0.655726\pi$$
−0.469945 + 0.882696i $$0.655726\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −50.9117 −3.00522
$$288$$ 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
$$301$$ −13.4164 −0.773309
$$302$$ 0 0
$$303$$ −28.2843 −1.62489
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 34.7851 1.98529 0.992644 0.121070i $$-0.0386326\pi$$
0.992644 + 0.121070i $$0.0386326\pi$$
$$308$$ 0 0
$$309$$ −40.2492 −2.28970
$$310$$ 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
$$321$$ 30.0000 1.67444
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 42.4264 2.34619
$$328$$ 0 0
$$329$$ 42.0000 2.31553
$$330$$ 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
$$343$$ −16.9706 −0.916324
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −28.4605 −1.52784 −0.763920 0.645311i $$-0.776728\pi$$
−0.763920 + 0.645311i $$0.776728\pi$$
$$348$$ 0 0
$$349$$ 26.8328 1.43633 0.718164 0.695874i $$-0.244983\pi$$
0.718164 + 0.695874i $$0.244983\pi$$
$$350$$ 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
$$363$$ 34.7851 1.82574
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 38.1838 1.99318 0.996588 0.0825348i $$-0.0263016\pi$$
0.996588 + 0.0825348i $$0.0263016\pi$$
$$368$$ 0 0
$$369$$ 84.0000 4.37287
$$370$$ 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
$$381$$ −13.4164 −0.687343
$$382$$ 0 0
$$383$$ −26.8701 −1.37300 −0.686498 0.727132i $$-0.740853\pi$$
−0.686498 + 0.727132i $$0.740853\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 22.1359 1.12523
$$388$$ 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
$$409$$ 4.00000 0.197787 0.0988936 0.995098i $$-0.468470\pi$$
0.0988936 + 0.995098i $$0.468470\pi$$
$$410$$ 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
$$423$$ −69.2965 −3.36931
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 56.9210 2.75460
$$428$$ 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
$$441$$ 77.0000 3.66667
$$442$$ 0 0
$$443$$ 9.48683 0.450733 0.225367 0.974274i $$-0.427642\pi$$
0.225367 + 0.974274i $$0.427642\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 14.1421 0.668900
$$448$$ 0 0
$$449$$ 36.0000 1.69895 0.849473 0.527633i $$-0.176920\pi$$
0.849473 + 0.527633i $$0.176920\pi$$
$$450$$ 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
$$461$$ 8.94427 0.416576 0.208288 0.978068i $$-0.433211\pi$$
0.208288 + 0.978068i $$0.433211\pi$$
$$462$$ 0 0
$$463$$ −12.7279 −0.591517 −0.295758 0.955263i $$-0.595572\pi$$
−0.295758 + 0.955263i $$0.595572\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 28.4605 1.31699 0.658497 0.752583i $$-0.271192\pi$$
0.658497 + 0.752583i $$0.271192\pi$$
$$468$$ 0 0
$$469$$ 67.0820 3.09756
$$470$$ 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
$$483$$ 18.9737 0.863332
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −38.1838 −1.73027 −0.865136 0.501538i $$-0.832768\pi$$
−0.865136 + 0.501538i $$0.832768\pi$$
$$488$$ 0 0
$$489$$ −70.0000 −3.16551
$$490$$ 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
$$501$$ 76.0263 3.39661
$$502$$ 0 0
$$503$$ −43.8406 −1.95476 −0.977378 0.211498i $$-0.932166\pi$$
−0.977378 + 0.211498i $$0.932166\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 41.1096 1.82574
$$508$$ 0 0
$$509$$ −44.7214 −1.98224 −0.991120 0.132973i $$-0.957548\pi$$
−0.991120 + 0.132973i $$0.957548\pi$$
$$510$$ 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 $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ 0 0
$$523$$ 34.7851 1.52104 0.760522 0.649312i $$-0.224943\pi$$
0.760522 + 0.649312i $$0.224943\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −21.0000 −0.913043
$$530$$ 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
$$541$$ −26.8328 −1.15363 −0.576816 0.816874i $$-0.695705\pi$$
−0.576816 + 0.816874i $$0.695705\pi$$
$$542$$ 0 0
$$543$$ 84.8528 3.64138
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 3.16228 0.135209 0.0676046 0.997712i $$-0.478464\pi$$
0.0676046 + 0.997712i $$0.478464\pi$$
$$548$$ 0 0
$$549$$ −93.9149 −4.00819
$$550$$ 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
$$563$$ 47.4342 1.99911 0.999556 0.0298010i $$-0.00948736\pi$$
0.999556 + 0.0298010i $$0.00948736\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −80.6102 −3.38531
$$568$$ 0 0
$$569$$ 36.0000 1.50920 0.754599 0.656186i $$-0.227831\pi$$
0.754599 + 0.656186i $$0.227831\pi$$
$$570$$ 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
$$581$$ 40.2492 1.66982
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 47.4342 1.95782 0.978909 0.204298i $$-0.0654911\pi$$
0.978909 + 0.204298i $$0.0654911\pi$$
$$588$$ 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
$$601$$ 28.0000 1.14214 0.571072 0.820900i $$-0.306528\pi$$
0.571072 + 0.820900i $$0.306528\pi$$
$$602$$ 0 0
$$603$$ −110.680 −4.50723
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 46.6690 1.89424 0.947119 0.320882i $$-0.103979\pi$$
0.947119 + 0.320882i $$0.103979\pi$$
$$608$$ 0 0
$$609$$ −120.000 −4.86265
$$610$$ 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
$$621$$ −17.8885 −0.717843
$$622$$ 0 0
$$623$$ 25.4558 1.01987
$$624$$ 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
$$641$$ 12.0000 0.473972 0.236986 0.971513i $$-0.423841\pi$$
0.236986 + 0.971513i $$0.423841\pi$$
$$642$$ 0 0
$$643$$ 41.1096 1.62120 0.810602 0.585597i $$-0.199140\pi$$
0.810602 + 0.585597i $$0.199140\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.3848 0.722780 0.361390 0.932415i $$-0.382302\pi$$
0.361390 + 0.932415i $$0.382302\pi$$
$$648$$ 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
$$667$$ −12.6491 −0.489776
$$668$$ 0 0
$$669$$ −93.9149 −3.63096
$$670$$ 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
$$681$$ −90.0000 −3.44881
$$682$$ 0 0
$$683$$ 28.4605 1.08901 0.544505 0.838757i $$-0.316717\pi$$
0.544505 + 0.838757i $$0.316717\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −84.8528 −3.23734
$$688$$ 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
$$707$$ −37.9473 −1.42716
$$708$$ 0 0
$$709$$ 26.8328 1.00773 0.503864 0.863783i $$-0.331911\pi$$
0.503864 + 0.863783i $$0.331911\pi$$
$$710$$ 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
$$721$$ −54.0000 −2.01107
$$722$$ 0 0
$$723$$ −88.5438 −3.29298
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −4.24264 −0.157351 −0.0786754 0.996900i $$-0.525069\pi$$
−0.0786754 + 0.996900i $$0.525069\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 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
$$743$$ 26.8701 0.985767 0.492883 0.870095i $$-0.335943\pi$$
0.492883 + 0.870095i $$0.335943\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −66.4078 −2.42974
$$748$$ 0 0
$$749$$ 40.2492 1.47067
$$750$$ 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
$$763$$ 56.9210 2.06068
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 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
$$783$$ 113.137 4.04319
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −41.1096 −1.46540 −0.732700 0.680552i $$-0.761740\pi$$
−0.732700 + 0.680552i $$0.761740\pi$$
$$788$$ 0 0
$$789$$ −49.1935 −1.75133
$$790$$ 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
$$801$$ −42.0000 −1.48400
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 70.7107 2.48913
$$808$$ 0 0
$$809$$ −54.0000 −1.89854 −0.949269 0.314464i $$-0.898175\pi$$
−0.949269 + 0.314464i $$0.898175\pi$$
$$810$$ 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
$$823$$ −55.1543 −1.92256 −0.961280 0.275575i $$-0.911132\pi$$
−0.961280 + 0.275575i $$0.911132\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 47.4342 1.64945 0.824724 0.565536i $$-0.191331\pi$$
0.824724 + 0.565536i $$0.191331\pi$$
$$828$$ 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
$$841$$ 51.0000 1.75862
$$842$$ 0 0
$$843$$ −37.9473 −1.30698
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 46.6690 1.60357
$$848$$ 0 0
$$849$$ 50.0000 1.71600
$$850$$ 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
$$861$$ 160.997 5.48676
$$862$$ 0 0
$$863$$ −57.9828 −1.97376 −0.986878 0.161468i $$-0.948377\pi$$
−0.986878 + 0.161468i $$0.948377\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 53.7587 1.82574
$$868$$ 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
$$881$$ 12.0000 0.404290 0.202145 0.979356i $$-0.435209\pi$$
0.202145 + 0.979356i $$0.435209\pi$$
$$882$$ 0 0
$$883$$ 22.1359 0.744934 0.372467 0.928045i $$-0.378512\pi$$
0.372467 + 0.928045i $$0.378512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 52.3259 1.75693 0.878466 0.477805i $$-0.158567\pi$$
0.878466 + 0.477805i $$0.158567\pi$$
$$888$$ 0 0
$$889$$ −18.0000 −0.603701
$$890$$ 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
$$903$$ 42.4264 1.41186
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −60.0833 −1.99503 −0.997516 0.0704373i $$-0.977561\pi$$
−0.997516 + 0.0704373i $$0.977561\pi$$
$$908$$ 0 0
$$909$$ 62.6099 2.07664
$$910$$ 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
$$921$$ −110.000 −3.62462
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 89.0955 2.92628
$$928$$ 0 0
$$929$$ 36.0000 1.18112 0.590561 0.806993i $$-0.298907\pi$$
0.590561 + 0.806993i $$0.298907\pi$$
$$930$$ 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
$$941$$ 44.7214 1.45787 0.728937 0.684580i $$-0.240015\pi$$
0.728937 + 0.684580i $$0.240015\pi$$
$$942$$ 0 0
$$943$$ 16.9706 0.552638
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 9.48683 0.308281 0.154140 0.988049i $$-0.450739\pi$$
0.154140 + 0.988049i $$0.450739\pi$$
$$948$$ 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
$$963$$ −66.4078 −2.13996
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ −46.6690 −1.50078 −0.750388 0.660998i $$-0.770133\pi$$
−0.750388 + 0.660998i $$0.770133\pi$$
$$968$$ 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
$$981$$ −93.9149 −2.99847
$$982$$ 0 0
$$983$$ −41.0122 −1.30809 −0.654043 0.756457i $$-0.726928\pi$$
−0.654043 + 0.756457i $$0.726928\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −132.816 −4.22757
$$988$$ 0 0
$$989$$ 4.47214 0.142206
$$990$$ 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 6400.2.a.cv.1.1 4
4.3 odd 2 inner 6400.2.a.cv.1.4 4
5.2 odd 4 1280.2.c.f.769.3 4
5.3 odd 4 1280.2.c.f.769.1 4
5.4 even 2 inner 6400.2.a.cv.1.4 4
8.3 odd 2 inner 6400.2.a.cv.1.2 4
8.5 even 2 inner 6400.2.a.cv.1.3 4
16.3 odd 4 3200.2.d.i.1601.3 4
16.5 even 4 3200.2.d.i.1601.4 4
16.11 odd 4 3200.2.d.i.1601.1 4
16.13 even 4 3200.2.d.i.1601.2 4
20.3 even 4 1280.2.c.f.769.3 4
20.7 even 4 1280.2.c.f.769.1 4
20.19 odd 2 CM 6400.2.a.cv.1.1 4
40.3 even 4 1280.2.c.f.769.2 4
40.13 odd 4 1280.2.c.f.769.4 4
40.19 odd 2 inner 6400.2.a.cv.1.3 4
40.27 even 4 1280.2.c.f.769.4 4
40.29 even 2 inner 6400.2.a.cv.1.2 4
40.37 odd 4 1280.2.c.f.769.2 4
80.3 even 4 640.2.f.f.449.2 yes 4
80.13 odd 4 640.2.f.f.449.4 yes 4
80.19 odd 4 3200.2.d.i.1601.2 4
80.27 even 4 640.2.f.f.449.1 4
80.29 even 4 3200.2.d.i.1601.3 4
80.37 odd 4 640.2.f.f.449.3 yes 4
80.43 even 4 640.2.f.f.449.3 yes 4
80.53 odd 4 640.2.f.f.449.1 4
80.59 odd 4 3200.2.d.i.1601.4 4
80.67 even 4 640.2.f.f.449.4 yes 4
80.69 even 4 3200.2.d.i.1601.1 4
80.77 odd 4 640.2.f.f.449.2 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.f.f.449.1 4 80.27 even 4
640.2.f.f.449.1 4 80.53 odd 4
640.2.f.f.449.2 yes 4 80.3 even 4
640.2.f.f.449.2 yes 4 80.77 odd 4
640.2.f.f.449.3 yes 4 80.37 odd 4
640.2.f.f.449.3 yes 4 80.43 even 4
640.2.f.f.449.4 yes 4 80.13 odd 4
640.2.f.f.449.4 yes 4 80.67 even 4
1280.2.c.f.769.1 4 5.3 odd 4
1280.2.c.f.769.1 4 20.7 even 4
1280.2.c.f.769.2 4 40.3 even 4
1280.2.c.f.769.2 4 40.37 odd 4
1280.2.c.f.769.3 4 5.2 odd 4
1280.2.c.f.769.3 4 20.3 even 4
1280.2.c.f.769.4 4 40.13 odd 4
1280.2.c.f.769.4 4 40.27 even 4
3200.2.d.i.1601.1 4 16.11 odd 4
3200.2.d.i.1601.1 4 80.69 even 4
3200.2.d.i.1601.2 4 16.13 even 4
3200.2.d.i.1601.2 4 80.19 odd 4
3200.2.d.i.1601.3 4 16.3 odd 4
3200.2.d.i.1601.3 4 80.29 even 4
3200.2.d.i.1601.4 4 16.5 even 4
3200.2.d.i.1601.4 4 80.59 odd 4
6400.2.a.cv.1.1 4 1.1 even 1 trivial
6400.2.a.cv.1.1 4 20.19 odd 2 CM
6400.2.a.cv.1.2 4 8.3 odd 2 inner
6400.2.a.cv.1.2 4 40.29 even 2 inner
6400.2.a.cv.1.3 4 8.5 even 2 inner
6400.2.a.cv.1.3 4 40.19 odd 2 inner
6400.2.a.cv.1.4 4 4.3 odd 2 inner
6400.2.a.cv.1.4 4 5.4 even 2 inner