# Properties

 Label 320.6.f.a.289.1 Level 320 Weight 6 Character 320.289 Analytic conductor 51.323 Analytic rank 0 Dimension 4 CM discriminant -40 Inner twists 8

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{4}\cdot 5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 289.1 Root $$1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.289 Dual form 320.6.f.a.289.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-55.9017 q^{5} -245.967i q^{7} -243.000 q^{9} +O(q^{10})$$ $$q-55.9017 q^{5} -245.967i q^{7} -243.000 q^{9} -802.000i q^{11} +245.967 q^{13} -1914.00i q^{19} +3331.74i q^{23} +3125.00 q^{25} +13750.0i q^{35} -15853.7 q^{37} +15202.0 q^{41} +13584.1 q^{45} -15361.8i q^{47} -43693.0 q^{49} -16837.6 q^{53} +44833.2i q^{55} -27986.0i q^{59} +59770.1i q^{63} -13750.0 q^{65} -197266. q^{77} +59049.0 q^{81} +128786. q^{89} -60500.0i q^{91} +106996. i q^{95} +194886. i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 972q^{9} + O(q^{10})$$ $$4q - 972q^{9} + 12500q^{25} + 60808q^{41} - 174772q^{49} - 55000q^{65} + 236196q^{81} + 515144q^{89} + O(q^{100})$$

## 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
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0 0
$$5$$ −55.9017 −1.00000
$$6$$ 0 0
$$7$$ − 245.967i − 1.89729i −0.316350 0.948643i $$-0.602457\pi$$
0.316350 0.948643i $$-0.397543\pi$$
$$8$$ 0 0
$$9$$ −243.000 −1.00000
$$10$$ 0 0
$$11$$ − 802.000i − 1.99845i −0.0393993 0.999224i $$-0.512544\pi$$
0.0393993 0.999224i $$-0.487456\pi$$
$$12$$ 0 0
$$13$$ 245.967 0.403663 0.201832 0.979420i $$-0.435311\pi$$
0.201832 + 0.979420i $$0.435311\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ 0 0
$$19$$ − 1914.00i − 1.21635i −0.793804 0.608174i $$-0.791902\pi$$
0.793804 0.608174i $$-0.208098\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 3331.74i 1.31326i 0.754212 + 0.656631i $$0.228019\pi$$
−0.754212 + 0.656631i $$0.771981\pi$$
$$24$$ 0 0
$$25$$ 3125.00 1.00000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 13750.0i 1.89729i
$$36$$ 0 0
$$37$$ −15853.7 −1.90382 −0.951912 0.306371i $$-0.900885\pi$$
−0.951912 + 0.306371i $$0.900885\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 15202.0 1.41235 0.706173 0.708039i $$-0.250420\pi$$
0.706173 + 0.708039i $$0.250420\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 13584.1 1.00000
$$46$$ 0 0
$$47$$ − 15361.8i − 1.01437i −0.861837 0.507186i $$-0.830686\pi$$
0.861837 0.507186i $$-0.169314\pi$$
$$48$$ 0 0
$$49$$ −43693.0 −2.59969
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −16837.6 −0.823361 −0.411681 0.911328i $$-0.635058\pi$$
−0.411681 + 0.911328i $$0.635058\pi$$
$$54$$ 0 0
$$55$$ 44833.2i 1.99845i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ − 27986.0i − 1.04667i −0.852126 0.523336i $$-0.824687\pi$$
0.852126 0.523336i $$-0.175313\pi$$
$$60$$ 0 0
$$61$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$62$$ 0 0
$$63$$ 59770.1i 1.89729i
$$64$$ 0 0
$$65$$ −13750.0 −0.403663
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 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
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −197266. −3.79162
$$78$$ 0 0
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 59049.0 1.00000
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 128786. 1.72343 0.861715 0.507393i $$-0.169391\pi$$
0.861715 + 0.507393i $$0.169391\pi$$
$$90$$ 0 0
$$91$$ − 60500.0i − 0.765864i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 106996.i 1.21635i
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 194886.i 1.99845i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 192950.i 1.79206i 0.443994 + 0.896030i $$0.353561\pi$$
−0.443994 + 0.896030i $$0.646439\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ − 186250.i − 1.31326i
$$116$$ 0 0
$$117$$ −59770.1 −0.403663
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −482153. −2.99379
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −174693. −1.00000
$$126$$ 0 0
$$127$$ 293931.i 1.61710i 0.588429 + 0.808549i $$0.299747\pi$$
−0.588429 + 0.808549i $$0.700253\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 66902.0i 0.340613i 0.985391 + 0.170306i $$0.0544757\pi$$
−0.985391 + 0.170306i $$0.945524\pi$$
$$132$$ 0 0
$$133$$ −470782. −2.30776
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ − 16786.0i − 0.0736903i −0.999321 0.0368451i $$-0.988269\pi$$
0.999321 0.0368451i $$-0.0117308\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ − 197266.i − 0.806700i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ 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
$$157$$ 430555. 1.39405 0.697027 0.717045i $$-0.254506\pi$$
0.697027 + 0.717045i $$0.254506\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 819500. 2.49163
$$162$$ 0 0
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 550721.i 1.52806i 0.645180 + 0.764030i $$0.276782\pi$$
−0.645180 + 0.764030i $$0.723218\pi$$
$$168$$ 0 0
$$169$$ −310793. −0.837056
$$170$$ 0 0
$$171$$ 465102.i 1.21635i
$$172$$ 0 0
$$173$$ 353455. 0.897882 0.448941 0.893561i $$-0.351801\pi$$
0.448941 + 0.893561i $$0.351801\pi$$
$$174$$ 0 0
$$175$$ − 768648.i − 1.89729i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ − 316186.i − 0.737582i −0.929512 0.368791i $$-0.879772\pi$$
0.929512 0.368791i $$-0.120228\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 886250. 1.90382
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 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
$$197$$ 1.08349e6 1.98911 0.994553 0.104230i $$-0.0332377\pi$$
0.994553 + 0.104230i $$0.0332377\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −849818. −1.41235
$$206$$ 0 0
$$207$$ − 809613.i − 1.31326i
$$208$$ 0 0
$$209$$ −1.53503e6 −2.43081
$$210$$ 0 0
$$211$$ − 1.18270e6i − 1.82881i −0.404805 0.914403i $$-0.632660\pi$$
0.404805 0.914403i $$-0.367340\pi$$
$$212$$ 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
$$223$$ − 1.31604e6i − 1.77217i −0.463520 0.886087i $$-0.653414\pi$$
0.463520 0.886087i $$-0.346586\pi$$
$$224$$ 0 0
$$225$$ −759375. −1.00000
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 858750.i 1.01437i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 89298.0 0.0990374 0.0495187 0.998773i $$-0.484231\pi$$
0.0495187 + 0.998773i $$0.484231\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.44251e6 2.59969
$$246$$ 0 0
$$247$$ − 470782.i − 0.490995i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ − 620002.i − 0.621168i −0.950546 0.310584i $$-0.899475\pi$$
0.950546 0.310584i $$-0.100525\pi$$
$$252$$ 0 0
$$253$$ 2.67206e6 2.62449
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 3.89950e6i 3.61210i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ − 549245.i − 0.489640i −0.969569 0.244820i $$-0.921271\pi$$
0.969569 0.244820i $$-0.0787289\pi$$
$$264$$ 0 0
$$265$$ 941250. 0.823361
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ − 2.50625e6i − 1.99845i
$$276$$ 0 0
$$277$$ −414947. −0.324933 −0.162466 0.986714i $$-0.551945\pi$$
−0.162466 + 0.986714i $$0.551945\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.12110e6 0.846989 0.423495 0.905899i $$-0.360803\pi$$
0.423495 + 0.905899i $$0.360803\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ − 3.73920e6i − 2.67962i
$$288$$ 0 0
$$289$$ 1.41986e6 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.79040e6 −1.21837 −0.609187 0.793027i $$-0.708504\pi$$
−0.609187 + 0.793027i $$0.708504\pi$$
$$294$$ 0 0
$$295$$ 1.56446e6i 1.04667i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 819500.i 0.530116i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 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
$$315$$ − 3.34125e6i − 1.89729i
$$316$$ 0 0
$$317$$ −2.83169e6 −1.58270 −0.791348 0.611366i $$-0.790620\pi$$
−0.791348 + 0.611366i $$0.790620\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 768648. 0.403663
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −3.77850e6 −1.92455
$$330$$ 0 0
$$331$$ − 2.09810e6i − 1.05258i −0.850305 0.526291i $$-0.823582\pi$$
0.850305 0.526291i $$-0.176418\pi$$
$$332$$ 0 0
$$333$$ 3.85245e6 1.90382
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 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
$$343$$ 6.61308e6i 3.03507i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 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
$$361$$ −1.18730e6 −0.479503
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 132934.i 0.0515195i 0.999668 + 0.0257598i $$0.00820049\pi$$
−0.999668 + 0.0257598i $$0.991800\pi$$
$$368$$ 0 0
$$369$$ −3.69409e6 −1.41235
$$370$$ 0 0
$$371$$ 4.14150e6i 1.56215i
$$372$$ 0 0
$$373$$ −5.37365e6 −1.99985 −0.999925 0.0122483i $$-0.996101\pi$$
−0.999925 + 0.0122483i $$0.996101\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 4.62669e6i 1.65452i 0.561819 + 0.827260i $$0.310102\pi$$
−0.561819 + 0.827260i $$0.689898\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ − 5.65025e6i − 1.96821i −0.177593 0.984104i $$-0.556831\pi$$
0.177593 0.984104i $$-0.443169\pi$$
$$384$$ 0 0
$$385$$ 1.10275e7 3.79162
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −3.34849e6 −1.06628 −0.533142 0.846026i $$-0.678989\pi$$
−0.533142 + 0.846026i $$0.678989\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 231002. 0.0717389 0.0358695 0.999356i $$-0.488580\pi$$
0.0358695 + 0.999356i $$0.488580\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −3.30094e6 −1.00000
$$406$$ 0 0
$$407$$ 1.27147e7i 3.80469i
$$408$$ 0 0
$$409$$ −6.63601e6 −1.96155 −0.980774 0.195146i $$-0.937482\pi$$
−0.980774 + 0.195146i $$0.937482\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −6.88365e6 −1.98584
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 2.11741e6i 0.589211i 0.955619 + 0.294605i $$0.0951882\pi$$
−0.955619 + 0.294605i $$0.904812\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 3.73291e6i 1.01437i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 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
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 6.37695e6 1.59739
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ 0 0
$$441$$ 1.06174e7 2.59969
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ −7.19936e6 −1.72343
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −8.52989e6 −1.99677 −0.998383 0.0568371i $$-0.981898\pi$$
−0.998383 + 0.0568371i $$0.981898\pi$$
$$450$$ 0 0
$$451$$ − 1.21920e7i − 2.82250i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3.38205e6i 0.765864i
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 3.67487e6i 0.796689i 0.917236 + 0.398345i $$0.130415\pi$$
−0.917236 + 0.398345i $$0.869585\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ − 5.98125e6i − 1.21635i
$$476$$ 0 0
$$477$$ 4.09153e6 0.823361
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 0 0
$$481$$ −3.89950e6 −0.768504
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 7.51491e6i 1.43582i 0.696134 + 0.717912i $$0.254902\pi$$
−0.696134 + 0.717912i $$0.745098\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ − 2.39120e6i − 0.447623i −0.974632 0.223812i $$-0.928150\pi$$
0.974632 0.223812i $$-0.0718500\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ − 1.08945e7i − 1.99845i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 6.93889e6i 1.24749i 0.781626 + 0.623747i $$0.214390\pi$$
−0.781626 + 0.623747i $$0.785610\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ − 7.44027e6i − 1.31120i −0.755109 0.655600i $$-0.772416\pi$$
0.755109 0.655600i $$-0.227584\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ − 1.07863e7i − 1.79206i
$$516$$ 0 0
$$517$$ −1.23202e7 −2.02717
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.21326e7 1.95821 0.979106 0.203351i $$-0.0651833\pi$$
0.979106 + 0.203351i $$0.0651833\pi$$
$$522$$ 0 0
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −4.66416e6 −0.724659
$$530$$ 0 0
$$531$$ 6.80060e6i 1.04667i
$$532$$ 0 0
$$533$$ 3.73920e6 0.570112
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3.50418e7i 5.19534i
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 1.45212e7 1.98319 0.991594 0.129387i $$-0.0413008\pi$$
0.991594 + 0.129387i $$0.0413008\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 1.45241e7i − 1.89729i
$$568$$ 0 0
$$569$$ −3.50709e6 −0.454115 −0.227057 0.973881i $$-0.572911\pi$$
−0.227057 + 0.973881i $$0.572911\pi$$
$$570$$ 0 0
$$571$$ − 1.45829e7i − 1.87177i −0.352299 0.935887i $$-0.614600\pi$$
0.352299 0.935887i $$-0.385400\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.04117e7i 1.31326i
$$576$$ 0 0
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 1.35037e7i 1.64544i
$$584$$ 0 0
$$585$$ 3.34125e6 0.403663
$$586$$ 0 0
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 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
$$601$$ −1.60910e7 −1.81718 −0.908588 0.417694i $$-0.862838\pi$$
−0.908588 + 0.417694i $$0.862838\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.69532e7 2.99379
$$606$$ 0 0
$$607$$ − 1.74118e7i − 1.91810i −0.283233 0.959051i $$-0.591407\pi$$
0.283233 0.959051i $$-0.408593\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ − 3.77850e6i − 0.409465i
$$612$$ 0 0
$$613$$ 1.56408e7 1.68116 0.840579 0.541689i $$-0.182215\pi$$
0.840579 + 0.541689i $$0.182215\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ − 7.16491e6i − 0.751596i −0.926702 0.375798i $$-0.877369\pi$$
0.926702 0.375798i $$-0.122631\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ − 3.16772e7i − 3.26984i
$$624$$ 0 0
$$625$$ 9.76562e6 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
$$635$$ − 1.64313e7i − 1.61710i
$$636$$ 0 0
$$637$$ −1.07471e7 −1.04940
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.08320e6 0.392515 0.196257 0.980552i $$-0.437121\pi$$
0.196257 + 0.980552i $$0.437121\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ − 2.10606e7i − 1.97793i −0.148160 0.988963i $$-0.547335\pi$$
0.148160 0.988963i $$-0.452665\pi$$
$$648$$ 0 0
$$649$$ −2.24448e7 −2.09172
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −9.24455e6 −0.848405 −0.424202 0.905567i $$-0.639445\pi$$
−0.424202 + 0.905567i $$0.639445\pi$$
$$654$$ 0 0
$$655$$ − 3.73994e6i − 0.340613i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ − 1.04250e7i − 0.935108i −0.883964 0.467554i $$-0.845135\pi$$
0.883964 0.467554i $$-0.154865\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 2.63175e7 2.30776
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −2.14754e6 −0.180082 −0.0900409 0.995938i $$-0.528700\pi$$
−0.0900409 + 0.995938i $$0.528700\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −4.14150e6 −0.332361
$$690$$ 0 0
$$691$$ 2.50118e7i 1.99274i 0.0851509 + 0.996368i $$0.472863\pi$$
−0.0851509 + 0.996368i $$0.527137\pi$$
$$692$$ 0 0
$$693$$ 4.79356e7 3.79162
$$694$$ 0 0
$$695$$ 938366.i 0.0736903i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 3.03440e7i 2.31571i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 1.10275e7i 0.806700i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 4.74595e7 3.40005
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 1.14949e7i 0.806623i 0.915063 + 0.403311i $$0.132141\pi$$
−0.915063 + 0.403311i $$0.867859\pi$$
$$728$$ 0 0
$$729$$ −1.43489e7 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −1.60595e7 −1.10401 −0.552003 0.833842i $$-0.686136\pi$$
−0.552003 + 0.833842i $$0.686136\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 2.47882e7i 1.66968i 0.550490 + 0.834842i $$0.314441\pi$$
−0.550490 + 0.834842i $$0.685559\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ − 2.55041e7i − 1.69488i −0.530893 0.847439i $$-0.678143\pi$$
0.530893 0.847439i $$-0.321857\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 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
$$757$$ 3.64217e6 0.231005 0.115502 0.993307i $$-0.463152\pi$$
0.115502 + 0.993307i $$0.463152\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −2.83413e7 −1.77402 −0.887009 0.461752i $$-0.847221\pi$$
−0.887009 + 0.461752i $$0.847221\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ − 6.88365e6i − 0.422503i
$$768$$ 0 0
$$769$$ −1.33834e7 −0.816114 −0.408057 0.912956i $$-0.633794\pi$$
−0.408057 + 0.912956i $$0.633794\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.91839e7 −1.75669 −0.878345 0.478028i $$-0.841352\pi$$
−0.878345 + 0.478028i $$0.841352\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ − 2.90966e7i − 1.71790i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −2.40688e7 −1.39405
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.63735e7 1.47069 0.735347 0.677691i $$-0.237019\pi$$
0.735347 + 0.677691i $$0.237019\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ −3.12950e7 −1.72343
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0
$$805$$ −4.58114e7 −2.49163
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 2.58690e7 1.38966 0.694829 0.719175i $$-0.255480\pi$$
0.694829 + 0.719175i $$0.255480\pi$$
$$810$$ 0 0
$$811$$ − 6.54480e6i − 0.349417i −0.984620 0.174709i $$-0.944102\pi$$
0.984620 0.174709i $$-0.0558984\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 1.47015e7i 0.765864i
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ − 9.84056e6i − 0.506431i −0.967410 0.253215i $$-0.918512\pi$$
0.967410 0.253215i $$-0.0814881\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 0 0
$$835$$ − 3.07862e7i − 1.52806i
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$840$$ 0 0
$$841$$ 2.05111e7 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 1.73739e7 0.837056
$$846$$ 0 0
$$847$$ 1.18594e8i 5.68007i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ − 5.28205e7i − 2.50022i
$$852$$ 0 0
$$853$$ −3.76003e7 −1.76937 −0.884685 0.466189i $$-0.845627\pi$$
−0.884685 + 0.466189i $$0.845627\pi$$
$$854$$ 0 0
$$855$$ − 2.60000e7i − 1.21635i
$$856$$ 0 0
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 4.04040e7i 1.86828i 0.356909 + 0.934139i $$0.383831\pi$$
−0.356909 + 0.934139i $$0.616169\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 3.27632e7i 1.49748i 0.662866 + 0.748738i $$0.269340\pi$$
−0.662866 + 0.748738i $$0.730660\pi$$
$$864$$ 0 0
$$865$$ −1.97588e7 −0.897882
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 4.29688e7i 1.89729i
$$876$$ 0 0
$$877$$ −2.60890e7 −1.14540 −0.572702 0.819763i $$-0.694105\pi$$
−0.572702 + 0.819763i $$0.694105\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.19751e7 0.953874 0.476937 0.878937i $$-0.341747\pi$$
0.476937 + 0.878937i $$0.341747\pi$$
$$882$$ 0 0
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 1.71978e7i 0.733946i 0.930232 + 0.366973i $$0.119606\pi$$
−0.930232 + 0.366973i $$0.880394\pi$$
$$888$$ 0 0
$$889$$ 7.22975e7 3.06810
$$890$$ 0 0
$$891$$ − 4.73573e7i − 1.99845i
$$892$$ 0 0
$$893$$ −2.94025e7 −1.23383
$$894$$ 0 0
$$895$$ 1.76753e7i 0.737582i
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 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
$$917$$ 1.64557e7 0.646239
$$918$$ 0 0
$$919$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ 0 0
$$924$$ 0 0
$$925$$ −4.95429e7 −1.90382
$$926$$ 0 0
$$927$$ − 4.68869e7i − 1.79206i
$$928$$ 0 0
$$929$$ 9.58531e6 0.364391 0.182195 0.983262i $$-0.441680\pi$$
0.182195 + 0.983262i $$0.441680\pi$$
$$930$$ 0 0
$$931$$ 8.36284e7i 3.16213i
$$932$$ 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
$$941$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$942$$ 0 0
$$943$$ 5.06491e7i 1.85478i
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 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
$$961$$ −2.86292e7 −1.00000
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ − 2.80976e7i − 0.966280i −0.875543 0.483140i $$-0.839496\pi$$
0.875543 0.483140i $$-0.160504\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 5.13311e7i 1.74716i 0.486681 + 0.873580i $$0.338207\pi$$
−0.486681 + 0.873580i $$0.661793\pi$$
$$972$$ 0 0
$$973$$ −4.12881e6 −0.139811
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 0 0
$$979$$ − 1.03286e8i − 3.44418i
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ − 2.03844e7i − 0.672844i −0.941711 0.336422i $$-0.890783\pi$$
0.941711 0.336422i $$-0.109217\pi$$
$$984$$ 0 0
$$985$$ −6.05687e7 −1.98911
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 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
$$997$$ −6.08649e7 −1.93923 −0.969614 0.244639i $$-0.921331\pi$$
−0.969614 + 0.244639i $$0.921331\pi$$
$$998$$ 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 320.6.f.a.289.1 4
4.3 odd 2 inner 320.6.f.a.289.2 yes 4
5.4 even 2 inner 320.6.f.a.289.4 yes 4
8.3 odd 2 inner 320.6.f.a.289.4 yes 4
8.5 even 2 inner 320.6.f.a.289.3 yes 4
20.19 odd 2 inner 320.6.f.a.289.3 yes 4
40.19 odd 2 CM 320.6.f.a.289.1 4
40.29 even 2 inner 320.6.f.a.289.2 yes 4

By twisted newform
Twist Min Dim Char Parity Ord Type
320.6.f.a.289.1 4 1.1 even 1 trivial
320.6.f.a.289.1 4 40.19 odd 2 CM
320.6.f.a.289.2 yes 4 4.3 odd 2 inner
320.6.f.a.289.2 yes 4 40.29 even 2 inner
320.6.f.a.289.3 yes 4 8.5 even 2 inner
320.6.f.a.289.3 yes 4 20.19 odd 2 inner
320.6.f.a.289.4 yes 4 5.4 even 2 inner
320.6.f.a.289.4 yes 4 8.3 odd 2 inner