# Properties

 Label 1440.2.x.i.127.1 Level $1440$ Weight $2$ Character 1440.127 Analytic conductor $11.498$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1440.x (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.4984578911$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 160) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 127.1 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1440.127 Dual form 1440.2.x.i.703.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +O(q^{10})$$ $$q+(2.00000 - 1.00000i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-1.00000 + 1.00000i) q^{13} +(5.00000 + 5.00000i) q^{17} -4.00000 q^{19} +(2.00000 + 2.00000i) q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000i q^{29} +4.00000i q^{31} +(-2.00000 + 6.00000i) q^{35} +(1.00000 + 1.00000i) q^{37} +(6.00000 + 6.00000i) q^{43} +(-2.00000 + 2.00000i) q^{47} -1.00000i q^{49} +(7.00000 - 7.00000i) q^{53} +4.00000 q^{59} -4.00000 q^{61} +(-1.00000 + 3.00000i) q^{65} +(10.0000 - 10.0000i) q^{67} +12.0000i q^{71} +(-3.00000 + 3.00000i) q^{73} -16.0000 q^{79} +(-2.00000 - 2.00000i) q^{83} +(15.0000 + 5.00000i) q^{85} -4.00000i q^{91} +(-8.00000 + 4.00000i) q^{95} +(-3.00000 - 3.00000i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{5} - 4 q^{7} + O(q^{10})$$ $$2 q + 4 q^{5} - 4 q^{7} - 2 q^{13} + 10 q^{17} - 8 q^{19} + 4 q^{23} + 6 q^{25} - 4 q^{35} + 2 q^{37} + 12 q^{43} - 4 q^{47} + 14 q^{53} + 8 q^{59} - 8 q^{61} - 2 q^{65} + 20 q^{67} - 6 q^{73} - 32 q^{79} - 4 q^{83} + 30 q^{85} - 16 q^{95} - 6 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$$.

 $$n$$ $$577$$ $$641$$ $$901$$ $$991$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$ $$1$$ $$-1$$

## 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
$$4$$ 0 0
$$5$$ 2.00000 1.00000i 0.894427 0.447214i
$$6$$ 0 0
$$7$$ −2.00000 + 2.00000i −0.755929 + 0.755929i −0.975579 0.219650i $$-0.929509\pi$$
0.219650 + 0.975579i $$0.429509\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 1.00000i −0.277350 + 0.277350i −0.832050 0.554700i $$-0.812833\pi$$
0.554700 + 0.832050i $$0.312833\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 5.00000 + 5.00000i 1.21268 + 1.21268i 0.970143 + 0.242536i $$0.0779791\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.00000 + 2.00000i 0.417029 + 0.417029i 0.884178 0.467150i $$-0.154719\pi$$
−0.467150 + 0.884178i $$0.654719\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.00000i 0.742781i 0.928477 + 0.371391i $$0.121119\pi$$
−0.928477 + 0.371391i $$0.878881\pi$$
$$30$$ 0 0
$$31$$ 4.00000i 0.718421i 0.933257 + 0.359211i $$0.116954\pi$$
−0.933257 + 0.359211i $$0.883046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −2.00000 + 6.00000i −0.338062 + 1.01419i
$$36$$ 0 0
$$37$$ 1.00000 + 1.00000i 0.164399 + 0.164399i 0.784512 0.620113i $$-0.212913\pi$$
−0.620113 + 0.784512i $$0.712913\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ 6.00000 + 6.00000i 0.914991 + 0.914991i 0.996660 0.0816682i $$-0.0260248\pi$$
−0.0816682 + 0.996660i $$0.526025\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −2.00000 + 2.00000i −0.291730 + 0.291730i −0.837763 0.546033i $$-0.816137\pi$$
0.546033 + 0.837763i $$0.316137\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 0.142857i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 7.00000 7.00000i 0.961524 0.961524i −0.0377628 0.999287i $$-0.512023\pi$$
0.999287 + 0.0377628i $$0.0120231\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ −4.00000 −0.512148 −0.256074 0.966657i $$-0.582429\pi$$
−0.256074 + 0.966657i $$0.582429\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.00000 + 3.00000i −0.124035 + 0.372104i
$$66$$ 0 0
$$67$$ 10.0000 10.0000i 1.22169 1.22169i 0.254665 0.967029i $$-0.418035\pi$$
0.967029 0.254665i $$-0.0819652\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000i 1.42414i 0.702109 + 0.712069i $$0.252242\pi$$
−0.702109 + 0.712069i $$0.747758\pi$$
$$72$$ 0 0
$$73$$ −3.00000 + 3.00000i −0.351123 + 0.351123i −0.860527 0.509404i $$-0.829866\pi$$
0.509404 + 0.860527i $$0.329866\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −16.0000 −1.80014 −0.900070 0.435745i $$-0.856485\pi$$
−0.900070 + 0.435745i $$0.856485\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −2.00000 2.00000i −0.219529 0.219529i 0.588771 0.808300i $$-0.299612\pi$$
−0.808300 + 0.588771i $$0.799612\pi$$
$$84$$ 0 0
$$85$$ 15.0000 + 5.00000i 1.62698 + 0.542326i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 4.00000i 0.419314i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −8.00000 + 4.00000i −0.820783 + 0.410391i
$$96$$ 0 0
$$97$$ −3.00000 3.00000i −0.304604 0.304604i 0.538208 0.842812i $$-0.319101\pi$$
−0.842812 + 0.538208i $$0.819101\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 0 0
$$103$$ 6.00000 + 6.00000i 0.591198 + 0.591198i 0.937955 0.346757i $$-0.112717\pi$$
−0.346757 + 0.937955i $$0.612717\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 6.00000 6.00000i 0.580042 0.580042i −0.354873 0.934915i $$-0.615476\pi$$
0.934915 + 0.354873i $$0.115476\pi$$
$$108$$ 0 0
$$109$$ 10.0000i 0.957826i 0.877862 + 0.478913i $$0.158969\pi$$
−0.877862 + 0.478913i $$0.841031\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.00000 9.00000i 0.846649 0.846649i −0.143065 0.989713i $$-0.545696\pi$$
0.989713 + 0.143065i $$0.0456957\pi$$
$$114$$ 0 0
$$115$$ 6.00000 + 2.00000i 0.559503 + 0.186501i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −20.0000 −1.83340
$$120$$ 0 0
$$121$$ 11.0000 1.00000
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 2.00000 11.0000i 0.178885 0.983870i
$$126$$ 0 0
$$127$$ −10.0000 + 10.0000i −0.887357 + 0.887357i −0.994268 0.106912i $$-0.965904\pi$$
0.106912 + 0.994268i $$0.465904\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 8.00000i 0.698963i 0.936943 + 0.349482i $$0.113642\pi$$
−0.936943 + 0.349482i $$0.886358\pi$$
$$132$$ 0 0
$$133$$ 8.00000 8.00000i 0.693688 0.693688i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.00000 1.00000i −0.0854358 0.0854358i 0.663097 0.748533i $$-0.269242\pi$$
−0.748533 + 0.663097i $$0.769242\pi$$
$$138$$ 0 0
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 4.00000 + 8.00000i 0.332182 + 0.664364i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 18.0000i 1.47462i 0.675556 + 0.737309i $$0.263904\pi$$
−0.675556 + 0.737309i $$0.736096\pi$$
$$150$$ 0 0
$$151$$ 12.0000i 0.976546i −0.872691 0.488273i $$-0.837627\pi$$
0.872691 0.488273i $$-0.162373\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.00000 + 8.00000i 0.321288 + 0.642575i
$$156$$ 0 0
$$157$$ −9.00000 9.00000i −0.718278 0.718278i 0.249974 0.968252i $$-0.419578\pi$$
−0.968252 + 0.249974i $$0.919578\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −8.00000 −0.630488
$$162$$ 0 0
$$163$$ −2.00000 2.00000i −0.156652 0.156652i 0.624429 0.781081i $$-0.285332\pi$$
−0.781081 + 0.624429i $$0.785332\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.00000 + 2.00000i −0.154765 + 0.154765i −0.780242 0.625478i $$-0.784904\pi$$
0.625478 + 0.780242i $$0.284904\pi$$
$$168$$ 0 0
$$169$$ 11.0000i 0.846154i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −13.0000 + 13.0000i −0.988372 + 0.988372i −0.999933 0.0115615i $$-0.996320\pi$$
0.0115615 + 0.999933i $$0.496320\pi$$
$$174$$ 0 0
$$175$$ 2.00000 + 14.0000i 0.151186 + 1.05830i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 3.00000 + 1.00000i 0.220564 + 0.0735215i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 20.0000i 1.44715i −0.690246 0.723575i $$-0.742498\pi$$
0.690246 0.723575i $$-0.257502\pi$$
$$192$$ 0 0
$$193$$ −5.00000 + 5.00000i −0.359908 + 0.359908i −0.863779 0.503871i $$-0.831909\pi$$
0.503871 + 0.863779i $$0.331909\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −5.00000 5.00000i −0.356235 0.356235i 0.506188 0.862423i $$-0.331054\pi$$
−0.862423 + 0.506188i $$0.831054\pi$$
$$198$$ 0 0
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −8.00000 8.00000i −0.561490 0.561490i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 16.0000i 1.10149i −0.834675 0.550743i $$-0.814345\pi$$
0.834675 0.550743i $$-0.185655\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 18.0000 + 6.00000i 1.22759 + 0.409197i
$$216$$ 0 0
$$217$$ −8.00000 8.00000i −0.543075 0.543075i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −10.0000 −0.672673
$$222$$ 0 0
$$223$$ 10.0000 + 10.0000i 0.669650 + 0.669650i 0.957635 0.287985i $$-0.0929854\pi$$
−0.287985 + 0.957635i $$0.592985\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 10.0000 10.0000i 0.663723 0.663723i −0.292532 0.956256i $$-0.594498\pi$$
0.956256 + 0.292532i $$0.0944979\pi$$
$$228$$ 0 0
$$229$$ 20.0000i 1.32164i −0.750546 0.660819i $$-0.770209\pi$$
0.750546 0.660819i $$-0.229791\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 5.00000 5.00000i 0.327561 0.327561i −0.524097 0.851658i $$-0.675597\pi$$
0.851658 + 0.524097i $$0.175597\pi$$
$$234$$ 0 0
$$235$$ −2.00000 + 6.00000i −0.130466 + 0.391397i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 8.00000 0.517477 0.258738 0.965947i $$-0.416693\pi$$
0.258738 + 0.965947i $$0.416693\pi$$
$$240$$ 0 0
$$241$$ −16.0000 −1.03065 −0.515325 0.856995i $$-0.672329\pi$$
−0.515325 + 0.856995i $$0.672329\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.00000 2.00000i −0.0638877 0.127775i
$$246$$ 0 0
$$247$$ 4.00000 4.00000i 0.254514 0.254514i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 24.0000i 1.51487i −0.652913 0.757433i $$-0.726453\pi$$
0.652913 0.757433i $$-0.273547\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −7.00000 7.00000i −0.436648 0.436648i 0.454234 0.890882i $$-0.349913\pi$$
−0.890882 + 0.454234i $$0.849913\pi$$
$$258$$ 0 0
$$259$$ −4.00000 −0.248548
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 6.00000 + 6.00000i 0.369976 + 0.369976i 0.867468 0.497492i $$-0.165746\pi$$
−0.497492 + 0.867468i $$0.665746\pi$$
$$264$$ 0 0
$$265$$ 7.00000 21.0000i 0.430007 1.29002i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.0000i 0.609711i 0.952399 + 0.304855i $$0.0986081\pi$$
−0.952399 + 0.304855i $$0.901392\pi$$
$$270$$ 0 0
$$271$$ 20.0000i 1.21491i −0.794353 0.607457i $$-0.792190\pi$$
0.794353 0.607457i $$-0.207810\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −9.00000 9.00000i −0.540758 0.540758i 0.382993 0.923751i $$-0.374893\pi$$
−0.923751 + 0.382993i $$0.874893\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −8.00000 −0.477240 −0.238620 0.971113i $$-0.576695\pi$$
−0.238620 + 0.971113i $$0.576695\pi$$
$$282$$ 0 0
$$283$$ −6.00000 6.00000i −0.356663 0.356663i 0.505918 0.862581i $$-0.331154\pi$$
−0.862581 + 0.505918i $$0.831154\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 33.0000i 1.94118i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 5.00000 5.00000i 0.292103 0.292103i −0.545807 0.837911i $$-0.683777\pi$$
0.837911 + 0.545807i $$0.183777\pi$$
$$294$$ 0 0
$$295$$ 8.00000 4.00000i 0.465778 0.232889i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −4.00000 −0.231326
$$300$$ 0 0
$$301$$ −24.0000 −1.38334
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −8.00000 + 4.00000i −0.458079 + 0.229039i
$$306$$ 0 0
$$307$$ 10.0000 10.0000i 0.570730 0.570730i −0.361602 0.932332i $$-0.617770\pi$$
0.932332 + 0.361602i $$0.117770\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 28.0000i 1.58773i −0.608091 0.793867i $$-0.708065\pi$$
0.608091 0.793867i $$-0.291935\pi$$
$$312$$ 0 0
$$313$$ 15.0000 15.0000i 0.847850 0.847850i −0.142014 0.989865i $$-0.545358\pi$$
0.989865 + 0.142014i $$0.0453579\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −11.0000 11.0000i −0.617822 0.617822i 0.327151 0.944972i $$-0.393912\pi$$
−0.944972 + 0.327151i $$0.893912\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −20.0000 20.0000i −1.11283 1.11283i
$$324$$ 0 0
$$325$$ 1.00000 + 7.00000i 0.0554700 + 0.388290i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 8.00000i 0.441054i
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 10.0000 30.0000i 0.546358 1.63908i
$$336$$ 0 0
$$337$$ −23.0000 23.0000i −1.25289 1.25289i −0.954419 0.298471i $$-0.903523\pi$$
−0.298471 0.954419i $$-0.596477\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −12.0000 12.0000i −0.647939 0.647939i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 18.0000 18.0000i 0.966291 0.966291i −0.0331594 0.999450i $$-0.510557\pi$$
0.999450 + 0.0331594i $$0.0105569\pi$$
$$348$$ 0 0
$$349$$ 20.0000i 1.07058i 0.844670 + 0.535288i $$0.179797\pi$$
−0.844670 + 0.535288i $$0.820203\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −9.00000 + 9.00000i −0.479022 + 0.479022i −0.904819 0.425797i $$-0.859994\pi$$
0.425797 + 0.904819i $$0.359994\pi$$
$$354$$ 0 0
$$355$$ 12.0000 + 24.0000i 0.636894 + 1.27379i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −16.0000 −0.844448 −0.422224 0.906492i $$-0.638750\pi$$
−0.422224 + 0.906492i $$0.638750\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −3.00000 + 9.00000i −0.157027 + 0.471082i
$$366$$ 0 0
$$367$$ 22.0000 22.0000i 1.14839 1.14839i 0.161521 0.986869i $$-0.448360\pi$$
0.986869 0.161521i $$-0.0516401\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 28.0000i 1.45369i
$$372$$ 0 0
$$373$$ 21.0000 21.0000i 1.08734 1.08734i 0.0915371 0.995802i $$-0.470822\pi$$
0.995802 0.0915371i $$-0.0291780\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 4.00000i −0.206010 0.206010i
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 22.0000 + 22.0000i 1.12415 + 1.12415i 0.991111 + 0.133036i $$0.0424727\pi$$
0.133036 + 0.991111i $$0.457527\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 18.0000i 0.912636i −0.889817 0.456318i $$-0.849168\pi$$
0.889817 0.456318i $$-0.150832\pi$$
$$390$$ 0 0
$$391$$ 20.0000i 1.01144i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −32.0000 + 16.0000i −1.61009 + 0.805047i
$$396$$ 0 0
$$397$$ 13.0000 + 13.0000i 0.652451 + 0.652451i 0.953583 0.301131i $$-0.0973643\pi$$
−0.301131 + 0.953583i $$0.597364\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −34.0000 −1.69788 −0.848939 0.528490i $$-0.822758\pi$$
−0.848939 + 0.528490i $$0.822758\pi$$
$$402$$ 0 0
$$403$$ −4.00000 4.00000i −0.199254 0.199254i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 2.00000i 0.0988936i 0.998777 + 0.0494468i $$0.0157458\pi$$
−0.998777 + 0.0494468i $$0.984254\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −8.00000 + 8.00000i −0.393654 + 0.393654i
$$414$$ 0 0
$$415$$ −6.00000 2.00000i −0.294528 0.0981761i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 20.0000 0.974740 0.487370 0.873195i $$-0.337956\pi$$
0.487370 + 0.873195i $$0.337956\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 35.0000 5.00000i 1.69775 0.242536i
$$426$$ 0 0
$$427$$ 8.00000 8.00000i 0.387147 0.387147i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4.00000i 0.192673i 0.995349 + 0.0963366i $$0.0307125\pi$$
−0.995349 + 0.0963366i $$0.969287\pi$$
$$432$$ 0 0
$$433$$ −19.0000 + 19.0000i −0.913082 + 0.913082i −0.996513 0.0834318i $$-0.973412\pi$$
0.0834318 + 0.996513i $$0.473412\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −8.00000 8.00000i −0.382692 0.382692i
$$438$$ 0 0
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 22.0000 + 22.0000i 1.04525 + 1.04525i 0.998926 + 0.0463251i $$0.0147510\pi$$
0.0463251 + 0.998926i $$0.485249\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 26.0000i 1.22702i 0.789689 + 0.613508i $$0.210242\pi$$
−0.789689 + 0.613508i $$0.789758\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −4.00000 8.00000i −0.187523 0.375046i
$$456$$ 0 0
$$457$$ 15.0000 + 15.0000i 0.701670 + 0.701670i 0.964769 0.263099i $$-0.0847444\pi$$
−0.263099 + 0.964769i $$0.584744\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 14.0000 0.652045 0.326023 0.945362i $$-0.394291\pi$$
0.326023 + 0.945362i $$0.394291\pi$$
$$462$$ 0 0
$$463$$ 22.0000 + 22.0000i 1.02243 + 1.02243i 0.999743 + 0.0226840i $$0.00722117\pi$$
0.0226840 + 0.999743i $$0.492779\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 2.00000 2.00000i 0.0925490 0.0925490i −0.659317 0.751865i $$-0.729154\pi$$
0.751865 + 0.659317i $$0.229154\pi$$
$$468$$ 0 0
$$469$$ 40.0000i 1.84703i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −12.0000 + 16.0000i −0.550598 + 0.734130i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 0 0
$$481$$ −2.00000 −0.0911922
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −9.00000 3.00000i −0.408669 0.136223i
$$486$$ 0 0
$$487$$ 6.00000 6.00000i 0.271886 0.271886i −0.557973 0.829859i $$-0.688421\pi$$
0.829859 + 0.557973i $$0.188421\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 16.0000i 0.722070i −0.932552 0.361035i $$-0.882424\pi$$
0.932552 0.361035i $$-0.117576\pi$$
$$492$$ 0 0
$$493$$ −20.0000 + 20.0000i −0.900755 + 0.900755i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −24.0000 24.0000i −1.07655 1.07655i
$$498$$ 0 0
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 10.0000 + 10.0000i 0.445878 + 0.445878i 0.893982 0.448104i $$-0.147900\pi$$
−0.448104 + 0.893982i $$0.647900\pi$$
$$504$$ 0 0
$$505$$ 12.0000 6.00000i 0.533993 0.266996i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 36.0000i 1.59567i −0.602875 0.797836i $$-0.705978\pi$$
0.602875 0.797836i $$-0.294022\pi$$
$$510$$ 0 0
$$511$$ 12.0000i 0.530849i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 18.0000 + 6.00000i 0.793175 + 0.264392i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −14.0000 14.0000i −0.612177 0.612177i 0.331336 0.943513i $$-0.392501\pi$$
−0.943513 + 0.331336i $$0.892501\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −20.0000 + 20.0000i −0.871214 + 0.871214i
$$528$$ 0 0
$$529$$ 15.0000i 0.652174i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 6.00000 18.0000i 0.259403 0.778208i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −30.0000 −1.28980 −0.644900 0.764267i $$-0.723101\pi$$
−0.644900 + 0.764267i $$0.723101\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 10.0000 + 20.0000i 0.428353 + 0.856706i
$$546$$ 0 0
$$547$$ 6.00000 6.00000i 0.256541 0.256541i −0.567104 0.823646i $$-0.691936\pi$$
0.823646 + 0.567104i $$0.191936\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 16.0000i 0.681623i
$$552$$ 0 0
$$553$$ 32.0000 32.0000i 1.36078 1.36078i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 15.0000 + 15.0000i 0.635570 + 0.635570i 0.949460 0.313889i $$-0.101632\pi$$
−0.313889 + 0.949460i $$0.601632\pi$$
$$558$$ 0 0
$$559$$ −12.0000 −0.507546
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −6.00000 6.00000i −0.252870 0.252870i 0.569276 0.822146i $$-0.307223\pi$$
−0.822146 + 0.569276i $$0.807223\pi$$
$$564$$ 0 0
$$565$$ 9.00000 27.0000i 0.378633 1.13590i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2.00000i 0.0838444i 0.999121 + 0.0419222i $$0.0133482\pi$$
−0.999121 + 0.0419222i $$0.986652\pi$$
$$570$$ 0 0
$$571$$ 16.0000i 0.669579i 0.942293 + 0.334790i $$0.108665\pi$$
−0.942293 + 0.334790i $$0.891335\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 14.0000 2.00000i 0.583840 0.0834058i
$$576$$ 0 0
$$577$$ 15.0000 + 15.0000i 0.624458 + 0.624458i 0.946668 0.322210i $$-0.104426\pi$$
−0.322210 + 0.946668i $$0.604426\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −14.0000 + 14.0000i −0.577842 + 0.577842i −0.934308 0.356466i $$-0.883981\pi$$
0.356466 + 0.934308i $$0.383981\pi$$
$$588$$ 0 0
$$589$$ 16.0000i 0.659269i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −1.00000 + 1.00000i −0.0410651 + 0.0410651i −0.727341 0.686276i $$-0.759244\pi$$
0.686276 + 0.727341i $$0.259244\pi$$
$$594$$ 0 0
$$595$$ −40.0000 + 20.0000i −1.63984 + 0.819920i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −8.00000 −0.326871 −0.163436 0.986554i $$-0.552258\pi$$
−0.163436 + 0.986554i $$0.552258\pi$$
$$600$$ 0 0
$$601$$ −8.00000 −0.326327 −0.163163 0.986599i $$-0.552170\pi$$
−0.163163 + 0.986599i $$0.552170\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 22.0000 11.0000i 0.894427 0.447214i
$$606$$ 0 0
$$607$$ 18.0000 18.0000i 0.730597 0.730597i −0.240141 0.970738i $$-0.577194\pi$$
0.970738 + 0.240141i $$0.0771936\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.00000i 0.161823i
$$612$$ 0 0
$$613$$ −9.00000 + 9.00000i −0.363507 + 0.363507i −0.865102 0.501596i $$-0.832747\pi$$
0.501596 + 0.865102i $$0.332747\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 29.0000 + 29.0000i 1.16750 + 1.16750i 0.982795 + 0.184701i $$0.0591318\pi$$
0.184701 + 0.982795i $$0.440868\pi$$
$$618$$ 0 0
$$619$$ 28.0000 1.12542 0.562708 0.826656i $$-0.309760\pi$$
0.562708 + 0.826656i $$0.309760\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 10.0000i 0.398726i
$$630$$ 0 0
$$631$$ 4.00000i 0.159237i −0.996825 0.0796187i $$-0.974630\pi$$
0.996825 0.0796187i $$-0.0253703\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −10.0000 + 30.0000i −0.396838 + 1.19051i
$$636$$ 0 0
$$637$$ 1.00000 + 1.00000i 0.0396214 + 0.0396214i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 48.0000 1.89589 0.947943 0.318440i $$-0.103159\pi$$
0.947943 + 0.318440i $$0.103159\pi$$
$$642$$ 0 0
$$643$$ 10.0000 + 10.0000i 0.394362 + 0.394362i 0.876239 0.481877i $$-0.160045\pi$$
−0.481877 + 0.876239i $$0.660045\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 10.0000 10.0000i 0.393141 0.393141i −0.482665 0.875805i $$-0.660331\pi$$
0.875805 + 0.482665i $$0.160331\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.00000 + 1.00000i −0.0391330 + 0.0391330i −0.726403 0.687270i $$-0.758809\pi$$
0.687270 + 0.726403i $$0.258809\pi$$
$$654$$ 0 0
$$655$$ 8.00000 + 16.0000i 0.312586 + 0.625172i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 12.0000 0.466746 0.233373 0.972387i $$-0.425024\pi$$
0.233373 + 0.972387i $$0.425024\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 8.00000 24.0000i 0.310227 0.930680i
$$666$$ 0 0
$$667$$ −8.00000 + 8.00000i −0.309761 + 0.309761i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 5.00000 5.00000i 0.192736 0.192736i −0.604141 0.796877i $$-0.706484\pi$$
0.796877 + 0.604141i $$0.206484\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 3.00000 + 3.00000i 0.115299 + 0.115299i 0.762402 0.647103i $$-0.224020\pi$$
−0.647103 + 0.762402i $$0.724020\pi$$
$$678$$ 0 0
$$679$$ 12.0000 0.460518
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −22.0000 22.0000i −0.841807 0.841807i 0.147287 0.989094i $$-0.452946\pi$$
−0.989094 + 0.147287i $$0.952946\pi$$
$$684$$ 0 0
$$685$$ −3.00000 1.00000i −0.114624 0.0382080i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 14.0000i 0.533358i
$$690$$ 0 0
$$691$$ 32.0000i 1.21734i 0.793424 + 0.608669i $$0.208296\pi$$
−0.793424 + 0.608669i $$0.791704\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 24.0000 12.0000i 0.910372 0.455186i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −20.0000 −0.755390 −0.377695 0.925930i $$-0.623283\pi$$
−0.377695 + 0.925930i $$0.623283\pi$$
$$702$$ 0 0
$$703$$ −4.00000 4.00000i −0.150863 0.150863i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −12.0000 + 12.0000i −0.451306 + 0.451306i
$$708$$ 0 0
$$709$$ 12.0000i 0.450669i −0.974281 0.225335i $$-0.927652\pi$$
0.974281 0.225335i $$-0.0723476\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −8.00000 + 8.00000i −0.299602 + 0.299602i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ −24.0000 −0.893807
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 16.0000 + 12.0000i 0.594225 + 0.445669i
$$726$$ 0 0
$$727$$ −18.0000 + 18.0000i −0.667583 + 0.667583i −0.957156 0.289573i $$-0.906487\pi$$
0.289573 + 0.957156i $$0.406487\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 60.0000i 2.21918i
$$732$$ 0 0
$$733$$ 21.0000 21.0000i 0.775653 0.775653i −0.203436 0.979088i $$-0.565211\pi$$
0.979088 + 0.203436i $$0.0652108\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −44.0000 −1.61857 −0.809283 0.587419i $$-0.800144\pi$$
−0.809283 + 0.587419i $$0.800144\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 30.0000 + 30.0000i 1.10059 + 1.10059i 0.994339 + 0.106254i $$0.0338857\pi$$
0.106254 + 0.994339i $$0.466114\pi$$
$$744$$ 0 0
$$745$$ 18.0000 + 36.0000i 0.659469 + 1.31894i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 24.0000i 0.876941i
$$750$$ 0 0
$$751$$ 44.0000i 1.60558i −0.596260 0.802791i $$-0.703347\pi$$
0.596260 0.802791i $$-0.296653\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12.0000 24.0000i −0.436725 0.873449i
$$756$$ 0 0
$$757$$ −1.00000 1.00000i −0.0363456 0.0363456i 0.688700 0.725046i $$-0.258182\pi$$
−0.725046 + 0.688700i $$0.758182\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 22.0000 0.797499 0.398750 0.917060i $$-0.369444\pi$$
0.398750 + 0.917060i $$0.369444\pi$$
$$762$$ 0 0
$$763$$ −20.0000 20.0000i −0.724049 0.724049i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −4.00000 + 4.00000i −0.144432 + 0.144432i
$$768$$ 0 0
$$769$$ 40.0000i 1.44244i 0.692708 + 0.721218i $$0.256418\pi$$
−0.692708 + 0.721218i $$0.743582\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 1.00000 1.00000i 0.0359675 0.0359675i −0.688894 0.724862i $$-0.741904\pi$$
0.724862 + 0.688894i $$0.241904\pi$$
$$774$$ 0 0
$$775$$ 16.0000 + 12.0000i 0.574737 + 0.431053i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −27.0000 9.00000i −0.963671 0.321224i
$$786$$ 0 0
$$787$$ −30.0000 + 30.0000i −1.06938 + 1.06938i −0.0719783 + 0.997406i $$0.522931\pi$$
−0.997406 + 0.0719783i $$0.977069\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 36.0000i 1.28001i
$$792$$ 0 0
$$793$$ 4.00000 4.00000i 0.142044 0.142044i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 29.0000 + 29.0000i 1.02723 + 1.02723i 0.999619 + 0.0276140i $$0.00879094\pi$$
0.0276140 + 0.999619i $$0.491209\pi$$
$$798$$ 0 0
$$799$$ −20.0000 −0.707549
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0 0
$$804$$ 0 0