# Properties

 Label 320.2.c.d.129.1 Level $320$ Weight $2$ Character 320.129 Analytic conductor $2.555$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 320.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.55521286468$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 129.1 Root $$-1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.129 Dual form 320.2.c.d.129.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.23607i q^{3} -2.23607 q^{5} -0.763932i q^{7} -7.47214 q^{9} +O(q^{10})$$ $$q-3.23607i q^{3} -2.23607 q^{5} -0.763932i q^{7} -7.47214 q^{9} +7.23607i q^{15} -2.47214 q^{21} -5.70820i q^{23} +5.00000 q^{25} +14.4721i q^{27} -6.00000 q^{29} +1.70820i q^{35} -4.47214 q^{41} -11.2361i q^{43} +16.7082 q^{45} -13.7082i q^{47} +6.41641 q^{49} +13.4164 q^{61} +5.70820i q^{63} -8.18034i q^{67} -18.4721 q^{69} -16.1803i q^{75} +24.4164 q^{81} +17.7082i q^{83} +19.4164i q^{87} -6.00000 q^{89} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 12 q^{9} + O(q^{10})$$ $$4 q - 12 q^{9} + 8 q^{21} + 20 q^{25} - 24 q^{29} + 40 q^{45} - 28 q^{49} - 56 q^{69} + 44 q^{81} - 24 q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$257$$ $$261$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ − 3.23607i − 1.86834i −0.356822 0.934172i $$-0.616140\pi$$
0.356822 0.934172i $$-0.383860\pi$$
$$4$$ 0 0
$$5$$ −2.23607 −1.00000
$$6$$ 0 0
$$7$$ − 0.763932i − 0.288739i −0.989524 0.144370i $$-0.953885\pi$$
0.989524 0.144370i $$-0.0461154\pi$$
$$8$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ −2.47214 −0.539464
$$22$$ 0 0
$$23$$ − 5.70820i − 1.19024i −0.803636 0.595121i $$-0.797104\pi$$
0.803636 0.595121i $$-0.202896\pi$$
$$24$$ 0 0
$$25$$ 5.00000 1.00000
$$26$$ 0 0
$$27$$ 14.4721i 2.78516i
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.70820i 0.288739i
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 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
$$43$$ − 11.2361i − 1.71348i −0.515745 0.856742i $$-0.672485\pi$$
0.515745 0.856742i $$-0.327515\pi$$
$$44$$ 0 0
$$45$$ 16.7082 2.49071
$$46$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 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
$$63$$ 5.70820i 0.719166i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ − 8.18034i − 0.999388i −0.866202 0.499694i $$-0.833446\pi$$
0.866202 0.499694i $$-0.166554\pi$$
$$68$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ − 16.1803i − 1.86834i
$$76$$ 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
$$83$$ 17.7082i 1.94373i 0.235543 + 0.971864i $$0.424313\pi$$
−0.235543 + 0.971864i $$0.575687\pi$$
$$84$$ 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 $$-0.603011\pi$$
−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 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 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
$$103$$ 20.1803i 1.98843i 0.107418 + 0.994214i $$0.465742\pi$$
−0.107418 + 0.994214i $$0.534258\pi$$
$$104$$ 0 0
$$105$$ 5.52786 0.539464
$$106$$ 0 0
$$107$$ − 6.29180i − 0.608251i −0.952632 0.304125i $$-0.901636\pi$$
0.952632 0.304125i $$-0.0983642\pi$$
$$108$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 12.7639i 1.19024i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 0 0
$$123$$ 14.4721i 1.30491i
$$124$$ 0 0
$$125$$ −11.1803 −1.00000
$$126$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ −44.3607 −3.73584
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.4164 1.11417
$$146$$ 0 0
$$147$$ − 20.7639i − 1.71258i
$$148$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4.36068 −0.343670
$$162$$ 0 0
$$163$$ 6.65248i 0.521062i 0.965465 + 0.260531i $$0.0838976\pi$$
−0.965465 + 0.260531i $$0.916102\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 10.2918i 0.796403i 0.917298 + 0.398202i $$0.130366\pi$$
−0.917298 + 0.398202i $$0.869634\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ − 3.81966i − 0.288739i
$$176$$ 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
$$183$$ − 43.4164i − 3.20943i
$$184$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ −26.4721 −1.86720
$$202$$ 0 0
$$203$$ 4.58359i 0.321705i
$$204$$ 0 0
$$205$$ 10.0000 0.698430
$$206$$ 0 0
$$207$$ 42.6525i 2.96455i
$$208$$ 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
$$215$$ 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
$$227$$ − 13.1246i − 0.871111i −0.900162 0.435556i $$-0.856552\pi$$
0.900162 0.435556i $$-0.143448\pi$$
$$228$$ 0 0
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 30.6525i 1.99955i
$$236$$ 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
$$243$$ − 35.5967i − 2.28353i
$$244$$ 0 0
$$245$$ −14.3475 −0.916630
$$246$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 44.8328 2.77508
$$262$$ 0 0
$$263$$ 9.12461i 0.562648i 0.959613 + 0.281324i $$0.0907735\pi$$
−0.959613 + 0.281324i $$0.909226\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 19.4164i 1.18826i
$$268$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 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
$$283$$ − 32.1803i − 1.91292i −0.291859 0.956461i $$-0.594274\pi$$
0.291859 0.956461i $$-0.405726\pi$$
$$284$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 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
$$303$$ − 58.2492i − 3.34633i
$$304$$ 0 0
$$305$$ −30.0000 −1.71780
$$306$$ 0 0
$$307$$ 27.5967i 1.57503i 0.616296 + 0.787515i $$0.288633\pi$$
−0.616296 + 0.787515i $$0.711367\pi$$
$$308$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ − 12.7639i − 0.719166i
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$332$$ 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
$$347$$ − 37.1246i − 1.99295i −0.0838690 0.996477i $$-0.526728\pi$$
0.0838690 0.996477i $$-0.473272\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 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
$$363$$ 35.5967i 1.86834i
$$364$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 36.1803i 1.86834i
$$376$$ 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
$$383$$ 1.12461i 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
$$387$$ 83.9574i 4.26780i
$$388$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 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
$$405$$ −54.5967 −2.71293
$$406$$ 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
$$415$$ − 39.5967i − 1.94373i
$$416$$ 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
$$423$$ 102.430i 4.98030i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ − 10.2492i − 0.495995i
$$428$$ 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
$$435$$ − 43.4164i − 2.08166i
$$436$$ 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
$$443$$ − 22.2918i − 1.05912i −0.848274 0.529558i $$-0.822358\pi$$
0.848274 0.529558i $$-0.177642\pi$$
$$444$$ 0 0
$$445$$ 13.4164 0.635999
$$446$$ 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
$$461$$ 42.0000 1.95614 0.978068 0.208288i $$-0.0667892\pi$$
0.978068 + 0.208288i $$0.0667892\pi$$
$$462$$ 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
$$467$$ 2.87539i 0.133057i 0.997785 + 0.0665285i $$0.0211923\pi$$
−0.997785 + 0.0665285i $$0.978808\pi$$
$$468$$ 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
$$483$$ 14.1115i 0.642093i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ − 42.6525i − 1.93277i −0.257103 0.966384i $$-0.582768\pi$$
0.257103 0.966384i $$-0.417232\pi$$
$$488$$ 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
$$503$$ − 37.7082i − 1.68133i −0.541559 0.840663i $$-0.682166\pi$$
0.541559 0.840663i $$-0.317834\pi$$
$$504$$ 0 0
$$505$$ −40.2492 −1.79107
$$506$$ 0 0
$$507$$ − 42.0689i − 1.86834i
$$508$$ 0 0
$$509$$ −6.00000 −0.265945 −0.132973 0.991120i $$-0.542452\pi$$
−0.132973 + 0.991120i $$0.542452\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ − 45.1246i − 1.98843i
$$516$$ 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
$$523$$ 3.59675i 0.157275i 0.996903 + 0.0786374i $$0.0250569\pi$$
−0.996903 + 0.0786374i $$0.974943\pi$$
$$524$$ 0 0
$$525$$ −12.3607 −0.539464
$$526$$ 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
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 0 0
$$543$$ − 6.47214i − 0.277746i
$$544$$ 0 0
$$545$$ −30.0000 −1.28506
$$546$$ 0 0
$$547$$ − 35.2361i − 1.50659i −0.657685 0.753293i $$-0.728464\pi$$
0.657685 0.753293i $$-0.271536\pi$$
$$548$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 32.5410i 1.37144i 0.727865 + 0.685720i $$0.240513\pi$$
−0.727865 + 0.685720i $$0.759487\pi$$
$$564$$ 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 $$-0.272169\pi$$
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
$$575$$ − 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
$$581$$ 13.5279 0.561230
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 40.5410i 1.67331i 0.547733 + 0.836653i $$0.315491\pi$$
−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 1.00000 $$0$$
−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 $$-0.806528\pi$$
−0.820900 + 0.571072i $$0.806528\pi$$
$$602$$ 0 0
$$603$$ 61.1246i 2.48919i
$$604$$ 0 0
$$605$$ 24.5967 1.00000
$$606$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$620$$ 0 0
$$621$$ 82.6099 3.31502
$$622$$ 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
$$635$$ 41.7082i 1.65514i
$$636$$ 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
$$643$$ − 50.0689i − 1.97452i −0.159103 0.987262i $$-0.550860\pi$$
0.159103 0.987262i $$-0.449140\pi$$
$$644$$ 0 0
$$645$$ 81.3050 3.20138
$$646$$ 0 0
$$647$$ − 20.5410i − 0.807551i −0.914858 0.403775i $$-0.867698\pi$$
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 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 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
$$667$$ 34.2492i 1.32614i
$$668$$ 0 0
$$669$$ 75.1935 2.90715
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 72.3607i 2.78516i
$$676$$ 0 0
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −42.4721 −1.62754
$$682$$ 0 0
$$683$$ 10.8754i 0.416135i 0.978114 + 0.208068i $$0.0667174\pi$$
−0.978114 + 0.208068i $$0.933283\pi$$
$$684$$ 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 1.00000i $$-0.5\pi$$
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
$$705$$ 99.1935 3.73584
$$706$$ 0 0
$$707$$ − 13.7508i − 0.517151i
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 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
$$723$$ − 43.4164i − 1.61467i
$$724$$ 0 0
$$725$$ −30.0000 −1.11417
$$726$$ 0 0
$$727$$ 35.0132i 1.29857i 0.760547 + 0.649283i $$0.224931\pi$$
−0.760547 + 0.649283i $$0.775069\pi$$
$$728$$ 0 0
$$729$$ −41.9443 −1.55349
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 46.4296i 1.71258i
$$736$$ 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
$$743$$ − 52.5410i − 1.92754i −0.266729 0.963772i $$-0.585943\pi$$
0.266729 0.963772i $$-0.414057\pi$$
$$744$$ 0 0
$$745$$ 10.0000 0.366372
$$746$$ 0 0
$$747$$ − 132.318i − 4.84127i
$$748$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 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
$$763$$ − 10.2492i − 0.371047i
$$764$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ 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
$$787$$ − 2.06888i − 0.0737477i −0.999320 0.0368739i $$-0.988260\pi$$
0.999320 0.0368739i $$-0.0117400\pi$$
$$788$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 44.8328 1.58409
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 9.75078 0.343670
$$806$$ 0 0
$$807$$ 72.3607i 2.54722i
$$808$$ 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
$$815$$ − 14.8754i − 0.521062i
$$816$$ 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
$$823$$ − 27.8197i − 0.969732i −0.874588 0.484866i $$-0.838868\pi$$
0.874588 0.484866i $$-0.161132\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 56.5410i 1.96612i 0.183274 + 0.983062i $$0.441331\pi$$
−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
$$835$$ − 23.0132i − 0.796403i
$$836$$ 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
$$843$$ − 101.305i − 3.48913i
$$844$$ 0 0
$$845$$ −29.0689 −1.00000
$$846$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$860$$ 0 0
$$861$$ 11.0557 0.376778
$$862$$ 0 0
$$863$$ 34.2918i 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
$$867$$ − 55.0132i − 1.86834i
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 8.54102i 0.288739i
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 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
$$883$$ 54.6525i 1.83920i 0.392853 + 0.919601i $$0.371488\pi$$
−0.392853 + 0.919601i $$0.628512\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 57.1246i 1.91806i 0.283310 + 0.959028i $$0.408567\pi$$
−0.283310 + 0.959028i $$0.591433\pi$$
$$888$$ 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
$$907$$ 45.4853i 1.51031i 0.655544 + 0.755157i $$0.272439\pi$$
−0.655544 + 0.755157i $$0.727561\pi$$
$$908$$ 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
$$915$$ 97.0820i 3.20943i
$$916$$ 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
$$941$$ 42.0000 1.36916 0.684580 0.728937i $$-0.259985\pi$$
0.684580 + 0.728937i $$0.259985\pi$$
$$942$$ 0 0
$$943$$ 25.5279i 0.831302i
$$944$$ 0 0
$$945$$ −24.7214 −0.804186
$$946$$ 0 0
$$947$$ 49.7082i 1.61530i 0.589662 + 0.807650i $$0.299261\pi$$
−0.589662 + 0.807650i $$0.700739\pi$$
$$948$$ 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
$$963$$ 47.0132i 1.51498i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 62.0689i 1.99600i 0.0632081 + 0.998000i $$0.479867\pi$$
−0.0632081 + 0.998000i $$0.520133\pi$$
$$968$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −100.249 −3.20071
$$982$$ 0 0
$$983$$ − 4.54102i − 0.144836i −0.997374 0.0724180i $$-0.976928\pi$$
0.997374 0.0724180i $$-0.0230716\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 33.8885i 1.07868i
$$988$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 320.2.c.d.129.1 4
3.2 odd 2 2880.2.f.w.1729.3 4
4.3 odd 2 inner 320.2.c.d.129.4 4
5.2 odd 4 1600.2.a.z.1.1 2
5.3 odd 4 1600.2.a.bd.1.2 2
5.4 even 2 inner 320.2.c.d.129.4 4
8.3 odd 2 160.2.c.b.129.1 4
8.5 even 2 160.2.c.b.129.4 yes 4
12.11 even 2 2880.2.f.w.1729.4 4
15.14 odd 2 2880.2.f.w.1729.4 4
16.3 odd 4 1280.2.f.g.129.2 4
16.5 even 4 1280.2.f.g.129.1 4
16.11 odd 4 1280.2.f.h.129.3 4
16.13 even 4 1280.2.f.h.129.4 4
20.3 even 4 1600.2.a.z.1.1 2
20.7 even 4 1600.2.a.bd.1.2 2
20.19 odd 2 CM 320.2.c.d.129.1 4
24.5 odd 2 1440.2.f.i.289.1 4
24.11 even 2 1440.2.f.i.289.2 4
40.3 even 4 800.2.a.n.1.2 2
40.13 odd 4 800.2.a.j.1.1 2
40.19 odd 2 160.2.c.b.129.4 yes 4
40.27 even 4 800.2.a.j.1.1 2
40.29 even 2 160.2.c.b.129.1 4
40.37 odd 4 800.2.a.n.1.2 2
60.59 even 2 2880.2.f.w.1729.3 4
80.19 odd 4 1280.2.f.h.129.4 4
80.29 even 4 1280.2.f.g.129.2 4
80.59 odd 4 1280.2.f.g.129.1 4
80.69 even 4 1280.2.f.h.129.3 4
120.29 odd 2 1440.2.f.i.289.2 4
120.53 even 4 7200.2.a.cb.1.2 2
120.59 even 2 1440.2.f.i.289.1 4
120.77 even 4 7200.2.a.cr.1.1 2
120.83 odd 4 7200.2.a.cr.1.1 2
120.107 odd 4 7200.2.a.cb.1.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.c.b.129.1 4 8.3 odd 2
160.2.c.b.129.1 4 40.29 even 2
160.2.c.b.129.4 yes 4 8.5 even 2
160.2.c.b.129.4 yes 4 40.19 odd 2
320.2.c.d.129.1 4 1.1 even 1 trivial
320.2.c.d.129.1 4 20.19 odd 2 CM
320.2.c.d.129.4 4 4.3 odd 2 inner
320.2.c.d.129.4 4 5.4 even 2 inner
800.2.a.j.1.1 2 40.13 odd 4
800.2.a.j.1.1 2 40.27 even 4
800.2.a.n.1.2 2 40.3 even 4
800.2.a.n.1.2 2 40.37 odd 4
1280.2.f.g.129.1 4 16.5 even 4
1280.2.f.g.129.1 4 80.59 odd 4
1280.2.f.g.129.2 4 16.3 odd 4
1280.2.f.g.129.2 4 80.29 even 4
1280.2.f.h.129.3 4 16.11 odd 4
1280.2.f.h.129.3 4 80.69 even 4
1280.2.f.h.129.4 4 16.13 even 4
1280.2.f.h.129.4 4 80.19 odd 4
1440.2.f.i.289.1 4 24.5 odd 2
1440.2.f.i.289.1 4 120.59 even 2
1440.2.f.i.289.2 4 24.11 even 2
1440.2.f.i.289.2 4 120.29 odd 2
1600.2.a.z.1.1 2 5.2 odd 4
1600.2.a.z.1.1 2 20.3 even 4
1600.2.a.bd.1.2 2 5.3 odd 4
1600.2.a.bd.1.2 2 20.7 even 4
2880.2.f.w.1729.3 4 3.2 odd 2
2880.2.f.w.1729.3 4 60.59 even 2
2880.2.f.w.1729.4 4 12.11 even 2
2880.2.f.w.1729.4 4 15.14 odd 2
7200.2.a.cb.1.2 2 120.53 even 4
7200.2.a.cb.1.2 2 120.107 odd 4
7200.2.a.cr.1.1 2 120.77 even 4
7200.2.a.cr.1.1 2 120.83 odd 4