# Properties

 Label 1280.2.f.g.129.1 Level $1280$ Weight $2$ Character 1280.129 Analytic conductor $10.221$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1280.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.2208514587$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 129.1 Root $$0.618034i$$ of defining polynomial Character $$\chi$$ $$=$$ 1280.129 Dual form 1280.2.f.g.129.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.23607 q^{3} -2.23607i q^{5} +0.763932i q^{7} +7.47214 q^{9} +O(q^{10})$$ $$q-3.23607 q^{3} -2.23607i q^{5} +0.763932i q^{7} +7.47214 q^{9} +7.23607i q^{15} -2.47214i q^{21} +5.70820i q^{23} -5.00000 q^{25} -14.4721 q^{27} +6.00000i q^{29} +1.70820 q^{35} +4.47214 q^{41} +11.2361 q^{43} -16.7082i q^{45} -13.7082i q^{47} +6.41641 q^{49} -13.4164i q^{61} +5.70820i q^{63} -8.18034 q^{67} -18.4721i q^{69} +16.1803 q^{75} +24.4164 q^{81} +17.7082 q^{83} -19.4164i q^{87} +6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{3} + 12 q^{9} + O(q^{10})$$ $$4 q - 4 q^{3} + 12 q^{9} - 20 q^{25} - 40 q^{27} - 20 q^{35} + 36 q^{43} - 28 q^{49} + 12 q^{67} + 20 q^{75} + 44 q^{81} + 44 q^{83} + 24 q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$261$$ $$511$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −3.23607 −1.86834 −0.934172 0.356822i $$-0.883860\pi$$
−0.934172 + 0.356822i $$0.883860\pi$$
$$4$$ 0 0
$$5$$ − 2.23607i − 1.00000i
$$6$$ 0 0
$$7$$ 0.763932i 0.288739i 0.989524 + 0.144370i $$0.0461154\pi$$
−0.989524 + 0.144370i $$0.953885\pi$$
$$8$$ 0 0
$$9$$ 7.47214 2.49071
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 7.23607i 1.86834i
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ − 2.47214i − 0.539464i
$$22$$ 0 0
$$23$$ 5.70820i 1.19024i 0.803636 + 0.595121i $$0.202896\pi$$
−0.803636 + 0.595121i $$0.797104\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ −14.4721 −2.78516
$$28$$ 0 0
$$29$$ 6.00000i 1.11417i 0.830455 + 0.557086i $$0.188081\pi$$
−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
$$35$$ 1.70820 0.288739
$$36$$ 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
$$43$$ 11.2361 1.71348 0.856742 0.515745i $$-0.172485\pi$$
0.856742 + 0.515745i $$0.172485\pi$$
$$44$$ 0 0
$$45$$ − 16.7082i − 2.49071i
$$46$$ 0 0
$$47$$ − 13.7082i − 1.99955i −0.0212814 0.999774i $$-0.506775\pi$$
0.0212814 0.999774i $$-0.493225\pi$$
$$48$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ − 13.4164i − 1.71780i −0.512148 0.858898i $$-0.671150\pi$$
0.512148 0.858898i $$-0.328850\pi$$
$$62$$ 0 0
$$63$$ 5.70820i 0.719166i
$$64$$ 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
$$69$$ − 18.4721i − 2.22378i
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 16.1803 1.86834
$$76$$ 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 $$-0.0756868\pi$$
0.971864 + 0.235543i $$0.0756868\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ − 19.4164i − 2.08166i
$$88$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 18.0000i 1.79107i 0.444994 + 0.895533i $$0.353206\pi$$
−0.444994 + 0.895533i $$0.646794\pi$$
$$102$$ 0 0
$$103$$ − 20.1803i − 1.98843i −0.107418 0.994214i $$-0.534258\pi$$
0.107418 0.994214i $$-0.465742\pi$$
$$104$$ 0 0
$$105$$ −5.52786 −0.539464
$$106$$ 0 0
$$107$$ 6.29180 0.608251 0.304125 0.952632i $$-0.401636\pi$$
0.304125 + 0.952632i $$0.401636\pi$$
$$108$$ 0 0
$$109$$ − 13.4164i − 1.28506i −0.766261 0.642529i $$-0.777885\pi$$
0.766261 0.642529i $$-0.222115\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 12.7639 1.19024
$$116$$ 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
$$125$$ 11.1803i 1.00000i
$$126$$ 0 0
$$127$$ − 18.6525i − 1.65514i −0.561363 0.827570i $$-0.689723\pi$$
0.561363 0.827570i $$-0.310277\pi$$
$$128$$ 0 0
$$129$$ −36.3607 −3.20138
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 32.3607i 2.78516i
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 44.3607i 3.73584i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.4164 1.11417
$$146$$ 0 0
$$147$$ −20.7639 −1.71258
$$148$$ 0 0
$$149$$ − 4.47214i − 0.366372i −0.983078 0.183186i $$-0.941359\pi$$
0.983078 0.183186i $$-0.0586410\pi$$
$$150$$ 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 $$-0.416102\pi$$
0.260531 + 0.965465i $$0.416102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ − 10.2918i − 0.796403i −0.917298 0.398202i $$-0.869634\pi$$
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
$$175$$ − 3.81966i − 0.288739i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 2.00000i 0.148659i 0.997234 + 0.0743294i $$0.0236816\pi$$
−0.997234 + 0.0743294i $$0.976318\pi$$
$$182$$ 0 0
$$183$$ 43.4164i 3.20943i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ − 11.0557i − 0.804186i
$$190$$ 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 1.00000i $$-0.5\pi$$
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
$$205$$ − 10.0000i − 0.698430i
$$206$$ 0 0
$$207$$ 42.6525i 2.96455i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ − 25.1246i − 1.71348i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 23.2361i 1.55600i 0.628263 + 0.778001i $$0.283766\pi$$
−0.628263 + 0.778001i $$0.716234\pi$$
$$224$$ 0 0
$$225$$ −37.3607 −2.49071
$$226$$ 0 0
$$227$$ −13.1246 −0.871111 −0.435556 0.900162i $$-0.643448\pi$$
−0.435556 + 0.900162i $$0.643448\pi$$
$$228$$ 0 0
$$229$$ − 14.0000i − 0.925146i −0.886581 0.462573i $$-0.846926\pi$$
0.886581 0.462573i $$-0.153074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ −30.6525 −1.99955
$$236$$ 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
$$245$$ − 14.3475i − 0.916630i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −57.3050 −3.63155
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 44.8328i 2.77508i
$$262$$ 0 0
$$263$$ − 9.12461i − 0.562648i −0.959613 0.281324i $$-0.909226\pi$$
0.959613 0.281324i $$-0.0907735\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −19.4164 −1.18826
$$268$$ 0 0
$$269$$ 22.3607i 1.36335i 0.731653 + 0.681677i $$0.238749\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 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
$$283$$ 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
$$287$$ 3.41641i 0.201664i
$$288$$ 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
$$301$$ 8.58359i 0.494750i
$$302$$ 0 0
$$303$$ − 58.2492i − 3.34633i
$$304$$ 0 0
$$305$$ −30.0000 −1.71780
$$306$$ 0 0
$$307$$ 27.5967 1.57503 0.787515 0.616296i $$-0.211367\pi$$
0.787515 + 0.616296i $$0.211367\pi$$
$$308$$ 0 0
$$309$$ 65.3050i 3.71507i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 12.7639 0.719166
$$316$$ 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
$$327$$ 43.4164i 2.40093i
$$328$$ 0 0
$$329$$ 10.4721 0.577348
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 18.2918i 0.999388i
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 10.2492i 0.553406i
$$344$$ 0 0
$$345$$ −41.3050 −2.22378
$$346$$ 0 0
$$347$$ 37.1246 1.99295 0.996477 0.0838690i $$-0.0267277\pi$$
0.996477 + 0.0838690i $$0.0267277\pi$$
$$348$$ 0 0
$$349$$ − 26.0000i − 1.39175i −0.718164 0.695874i $$-0.755017\pi$$
0.718164 0.695874i $$-0.244983\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ 19.0000 1.00000
$$362$$ 0 0
$$363$$ −35.5967 −1.86834
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ − 24.7639i − 1.29267i −0.763055 0.646333i $$-0.776302\pi$$
0.763055 0.646333i $$-0.223698\pi$$
$$368$$ 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
$$375$$ − 36.1803i − 1.86834i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 60.3607i 3.09237i
$$382$$ 0 0
$$383$$ 1.12461i 0.0574650i 0.999587 + 0.0287325i $$0.00914709\pi$$
−0.999587 + 0.0287325i $$0.990853\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 83.9574 4.26780
$$388$$ 0 0
$$389$$ 31.3050i 1.58722i 0.608424 + 0.793612i $$0.291802\pi$$
−0.608424 + 0.793612i $$0.708198\pi$$
$$390$$ 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
$$405$$ − 54.5967i − 2.71293i
$$406$$ 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
$$415$$ − 39.5967i − 1.94373i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ − 40.2492i − 1.96163i −0.194948 0.980814i $$-0.562454\pi$$
0.194948 0.980814i $$-0.437546\pi$$
$$422$$ 0 0
$$423$$ − 102.430i − 4.98030i
$$424$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ −43.4164 −2.08166
$$436$$ 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
$$445$$ − 13.4164i − 0.635999i
$$446$$ 0 0
$$447$$ 14.4721i 0.684509i
$$448$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ − 42.0000i − 1.95614i −0.208288 0.978068i $$-0.566789\pi$$
0.208288 0.978068i $$-0.433211\pi$$
$$462$$ 0 0
$$463$$ 38.0689i 1.76921i 0.466340 + 0.884606i $$0.345572\pi$$
−0.466340 + 0.884606i $$0.654428\pi$$
$$464$$ 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
$$469$$ − 6.24922i − 0.288562i
$$470$$ 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
$$487$$ 42.6525i 1.93277i 0.257103 + 0.966384i $$0.417232\pi$$
−0.257103 + 0.966384i $$0.582768\pi$$
$$488$$ 0 0
$$489$$ −21.5279 −0.973524
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 33.3050i 1.48796i
$$502$$ 0 0
$$503$$ 37.7082i 1.68133i 0.541559 + 0.840663i $$0.317834\pi$$
−0.541559 + 0.840663i $$0.682166\pi$$
$$504$$ 0 0
$$505$$ 40.2492 1.79107
$$506$$ 0 0
$$507$$ 42.0689 1.86834
$$508$$ 0 0
$$509$$ 6.00000i 0.265945i 0.991120 + 0.132973i $$0.0424523\pi$$
−0.991120 + 0.132973i $$0.957548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −45.1246 −1.98843
$$516$$ 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
$$523$$ −3.59675 −0.157275 −0.0786374 0.996903i $$-0.525057\pi$$
−0.0786374 + 0.996903i $$0.525057\pi$$
$$524$$ 0 0
$$525$$ 12.3607i 0.539464i
$$526$$ 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
$$535$$ − 14.0689i − 0.608251i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 38.0000i 1.63375i 0.576816 + 0.816874i $$0.304295\pi$$
−0.576816 + 0.816874i $$0.695705\pi$$
$$542$$ 0 0
$$543$$ − 6.47214i − 0.277746i
$$544$$ 0 0
$$545$$ −30.0000 −1.28506
$$546$$ 0 0
$$547$$ −35.2361 −1.50659 −0.753293 0.657685i $$-0.771536\pi$$
−0.753293 + 0.657685i $$0.771536\pi$$
$$548$$ 0 0
$$549$$ − 100.249i − 4.27853i
$$550$$ 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 $$-0.259487\pi$$
0.685720 + 0.727865i $$0.259487\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 18.6525i 0.783330i
$$568$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ − 28.5410i − 1.19024i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 13.5279i 0.561230i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −40.5410 −1.67331 −0.836653 0.547733i $$-0.815491\pi$$
−0.836653 + 0.547733i $$0.815491\pi$$
$$588$$ 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 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
$$603$$ −61.1246 −2.48919
$$604$$ 0 0
$$605$$ − 24.5967i − 1.00000i
$$606$$ 0 0
$$607$$ 44.1803i 1.79322i 0.442816 + 0.896612i $$0.353979\pi$$
−0.442816 + 0.896612i $$0.646021\pi$$
$$608$$ 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
$$615$$ 32.3607i 1.30491i
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ − 82.6099i − 3.31502i
$$622$$ 0 0
$$623$$ 4.58359i 0.183638i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 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
$$635$$ −41.7082 −1.65514
$$636$$ 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 $$-0.949140\pi$$
−0.987262 + 0.159103i $$0.949140\pi$$
$$644$$ 0 0
$$645$$ 81.3050i 3.20138i
$$646$$ 0 0
$$647$$ 20.5410i 0.807551i 0.914858 + 0.403775i $$0.132302\pi$$
−0.914858 + 0.403775i $$0.867698\pi$$
$$648$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ − 40.2492i − 1.56551i −0.622328 0.782757i $$-0.713813\pi$$
0.622328 0.782757i $$-0.286187\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −34.2492 −1.32614
$$668$$ 0 0
$$669$$ − 75.1935i − 2.90715i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 72.3607 2.78516
$$676$$ 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
$$687$$ 45.3050i 1.72849i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 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
$$701$$ 22.3607i 0.844551i 0.906467 + 0.422276i $$0.138769\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 99.1935 3.73584
$$706$$ 0 0
$$707$$ −13.7508 −0.517151
$$708$$ 0 0
$$709$$ − 46.0000i − 1.72757i −0.503864 0.863783i $$-0.668089\pi$$
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
$$721$$ 15.4164 0.574137
$$722$$ 0 0
$$723$$ −43.4164 −1.61467
$$724$$ 0 0
$$725$$ − 30.0000i − 1.11417i
$$726$$ 0 0
$$727$$ − 35.0132i − 1.29857i −0.760547 0.649283i $$-0.775069\pi$$
0.760547 0.649283i $$-0.224931\pi$$
$$728$$ 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
$$735$$ 46.4296i 1.71258i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 52.5410i 1.92754i 0.266729 + 0.963772i $$0.414057\pi$$
−0.266729 + 0.963772i $$0.585943\pi$$
$$744$$ 0 0
$$745$$ −10.0000 −0.366372
$$746$$ 0 0
$$747$$ 132.318 4.84127
$$748$$ 0 0
$$749$$ 4.80650i 0.175626i
$$750$$ 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 $$-0.775414\pi$$
−0.761249 + 0.648459i $$0.775414\pi$$
$$762$$ 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 $$-0.581229\pi$$
−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
$$783$$ − 86.8328i − 3.10315i
$$784$$ 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
$$789$$ 29.5279i 1.05122i
$$790$$ 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
$$805$$ 9.75078i 0.343670i
$$806$$ 0 0
$$807$$ − 72.3607i − 2.54722i
$$808$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ − 14.8754i − 0.521062i
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 31.3050i 1.09255i 0.837606 + 0.546275i $$0.183955\pi$$
−0.837606 + 0.546275i $$0.816045\pi$$
$$822$$ 0 0
$$823$$ 27.8197i 0.969732i 0.874588 + 0.484866i $$0.161132\pi$$
−0.874588 + 0.484866i $$0.838868\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −56.5410 −1.96612 −0.983062 0.183274i $$-0.941331\pi$$
−0.983062 + 0.183274i $$0.941331\pi$$
$$828$$ 0 0
$$829$$ − 13.4164i − 0.465971i −0.972480 0.232986i $$-0.925151\pi$$
0.972480 0.232986i $$-0.0748495\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ −23.0132 −0.796403
$$836$$ 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
$$845$$ 29.0689i 1.00000i
$$846$$ 0 0
$$847$$ 8.40325i 0.288739i
$$848$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ − 11.0557i − 0.376778i
$$862$$ 0 0
$$863$$ 34.2918i 1.16731i 0.812003 + 0.583653i $$0.198377\pi$$
−0.812003 + 0.583653i $$0.801623\pi$$
$$864$$ 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
$$875$$ −8.54102 −0.288739
$$876$$ 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 $$-0.128512\pi$$
0.919601 + 0.392853i $$0.128512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ − 57.1246i − 1.91806i −0.283310 0.959028i $$-0.591433\pi$$
0.283310 0.959028i $$-0.408567\pi$$
$$888$$ 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
$$903$$ − 27.7771i − 0.924364i
$$904$$ 0 0
$$905$$ 4.47214 0.148659
$$906$$ 0 0
$$907$$ −45.4853 −1.51031 −0.755157 0.655544i $$-0.772439\pi$$
−0.755157 + 0.655544i $$0.772439\pi$$
$$908$$ 0 0
$$909$$ 134.498i 4.46103i
$$910$$ 0 0
$$911$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 97.0820 3.20943
$$916$$ 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
$$927$$ − 150.790i − 4.95260i
$$928$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ − 42.0000i − 1.36916i −0.728937 0.684580i $$-0.759985\pi$$
0.728937 0.684580i $$-0.240015\pi$$
$$942$$ 0 0
$$943$$ 25.5279i 0.831302i
$$944$$ 0 0
$$945$$ −24.7214 −0.804186
$$946$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ −31.0000 −1.00000
$$962$$ 0 0
$$963$$ 47.0132 1.51498
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 62.0689i − 1.99600i −0.0632081 0.998000i $$-0.520133\pi$$
0.0632081 0.998000i $$-0.479867\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ − 100.249i − 3.20071i
$$982$$ 0 0
$$983$$ 4.54102i 0.144836i 0.997374 + 0.0724180i $$0.0230716\pi$$
−0.997374 + 0.0724180i $$0.976928\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −33.8885 −1.07868
$$988$$ 0 0
$$989$$ 64.1378i 2.03946i
$$990$$ 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 1280.2.f.g.129.1 4
4.3 odd 2 1280.2.f.h.129.3 4
5.4 even 2 1280.2.f.h.129.3 4
8.3 odd 2 inner 1280.2.f.g.129.2 4
8.5 even 2 1280.2.f.h.129.4 4
16.3 odd 4 320.2.c.d.129.4 4
16.5 even 4 160.2.c.b.129.4 yes 4
16.11 odd 4 160.2.c.b.129.1 4
16.13 even 4 320.2.c.d.129.1 4
20.19 odd 2 CM 1280.2.f.g.129.1 4
40.19 odd 2 1280.2.f.h.129.4 4
40.29 even 2 inner 1280.2.f.g.129.2 4
48.5 odd 4 1440.2.f.i.289.1 4
48.11 even 4 1440.2.f.i.289.2 4
48.29 odd 4 2880.2.f.w.1729.3 4
48.35 even 4 2880.2.f.w.1729.4 4
80.3 even 4 1600.2.a.z.1.1 2
80.13 odd 4 1600.2.a.bd.1.2 2
80.19 odd 4 320.2.c.d.129.1 4
80.27 even 4 800.2.a.j.1.1 2
80.29 even 4 320.2.c.d.129.4 4
80.37 odd 4 800.2.a.n.1.2 2
80.43 even 4 800.2.a.n.1.2 2
80.53 odd 4 800.2.a.j.1.1 2
80.59 odd 4 160.2.c.b.129.4 yes 4
80.67 even 4 1600.2.a.bd.1.2 2
80.69 even 4 160.2.c.b.129.1 4
80.77 odd 4 1600.2.a.z.1.1 2
240.29 odd 4 2880.2.f.w.1729.4 4
240.53 even 4 7200.2.a.cb.1.2 2
240.59 even 4 1440.2.f.i.289.1 4
240.107 odd 4 7200.2.a.cb.1.2 2
240.149 odd 4 1440.2.f.i.289.2 4
240.179 even 4 2880.2.f.w.1729.3 4
240.197 even 4 7200.2.a.cr.1.1 2
240.203 odd 4 7200.2.a.cr.1.1 2

By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 16.11 odd 4
160.2.c.b.129.1 4 80.69 even 4
160.2.c.b.129.4 yes 4 16.5 even 4
160.2.c.b.129.4 yes 4 80.59 odd 4
320.2.c.d.129.1 4 16.13 even 4
320.2.c.d.129.1 4 80.19 odd 4
320.2.c.d.129.4 4 16.3 odd 4
320.2.c.d.129.4 4 80.29 even 4
800.2.a.j.1.1 2 80.27 even 4
800.2.a.j.1.1 2 80.53 odd 4
800.2.a.n.1.2 2 80.37 odd 4
800.2.a.n.1.2 2 80.43 even 4
1280.2.f.g.129.1 4 1.1 even 1 trivial
1280.2.f.g.129.1 4 20.19 odd 2 CM
1280.2.f.g.129.2 4 8.3 odd 2 inner
1280.2.f.g.129.2 4 40.29 even 2 inner
1280.2.f.h.129.3 4 4.3 odd 2
1280.2.f.h.129.3 4 5.4 even 2
1280.2.f.h.129.4 4 8.5 even 2
1280.2.f.h.129.4 4 40.19 odd 2
1440.2.f.i.289.1 4 48.5 odd 4
1440.2.f.i.289.1 4 240.59 even 4
1440.2.f.i.289.2 4 48.11 even 4
1440.2.f.i.289.2 4 240.149 odd 4
1600.2.a.z.1.1 2 80.3 even 4
1600.2.a.z.1.1 2 80.77 odd 4
1600.2.a.bd.1.2 2 80.13 odd 4
1600.2.a.bd.1.2 2 80.67 even 4
2880.2.f.w.1729.3 4 48.29 odd 4
2880.2.f.w.1729.3 4 240.179 even 4
2880.2.f.w.1729.4 4 48.35 even 4
2880.2.f.w.1729.4 4 240.29 odd 4
7200.2.a.cb.1.2 2 240.53 even 4
7200.2.a.cb.1.2 2 240.107 odd 4
7200.2.a.cr.1.1 2 240.197 even 4
7200.2.a.cr.1.1 2 240.203 odd 4