# Properties

 Label 1444.1.j.b.1029.1 Level $1444$ Weight $1$ Character 1444.1029 Analytic conductor $0.721$ Analytic rank $0$ Dimension $12$ Projective image $S_{4}$ CM/RM no Inner twists $12$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1444 = 2^{2} \cdot 19^{2}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1444.j (of order $$18$$, degree $$6$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.720649878242$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{18})$$ Coefficient field: 12.0.101559956668416.1 Defining polynomial: $$x^{12} - 8 x^{6} + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$S_{4}$$ Projective field: Galois closure of 4.2.27436.1

## Embedding invariants

 Embedding label 1029.1 Root $$0.483690 - 1.32893i$$ of defining polynomial Character $$\chi$$ $$=$$ 1444.1029 Dual form 1444.1.j.b.849.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.483690 - 1.32893i) q^{3} +(0.173648 - 0.984808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.766044 + 0.642788i) q^{9} +O(q^{10})$$ $$q+(-0.483690 - 1.32893i) q^{3} +(0.173648 - 0.984808i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.766044 + 0.642788i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-1.39273 + 0.245576i) q^{15} +(0.766044 + 0.642788i) q^{17} +(-0.909039 + 1.08335i) q^{21} +(-0.909039 - 1.08335i) q^{29} +(-1.39273 - 0.245576i) q^{33} +(-0.939693 + 0.342020i) q^{35} +1.41421i q^{37} +(0.483690 + 1.32893i) q^{41} +(-0.173648 + 0.984808i) q^{43} +(0.500000 + 0.866025i) q^{45} +(-0.766044 + 0.642788i) q^{47} +(0.483690 - 1.32893i) q^{51} +(-0.766044 - 0.642788i) q^{55} +(0.909039 - 1.08335i) q^{59} +(-0.173648 - 0.984808i) q^{61} +(0.939693 + 0.342020i) q^{63} +(1.39273 + 0.245576i) q^{71} +(-0.939693 + 0.342020i) q^{73} -1.00000 q^{77} +(-0.173648 + 0.984808i) q^{81} +(0.766044 - 0.642788i) q^{85} +(-1.00000 + 1.73205i) q^{87} +(0.173648 + 0.984808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 6q^{7} + O(q^{10})$$ $$12q - 6q^{7} + 6q^{11} + 6q^{45} - 12q^{77} - 12q^{87} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1444\mathbb{Z}\right)^\times$$.

 $$n$$ $$723$$ $$1085$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{13}{18}\right)$$

## 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
$$3$$ −0.483690 1.32893i −0.483690 1.32893i −0.906308 0.422618i $$-0.861111\pi$$
0.422618 0.906308i $$-0.361111\pi$$
$$4$$ 0 0
$$5$$ 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i $$-0.777778\pi$$
0.939693 0.342020i $$-0.111111\pi$$
$$6$$ 0 0
$$7$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$8$$ 0 0
$$9$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$10$$ 0 0
$$11$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$12$$ 0 0
$$13$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$14$$ 0 0
$$15$$ −1.39273 + 0.245576i −1.39273 + 0.245576i
$$16$$ 0 0
$$17$$ 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i $$-0.111111\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$18$$ 0 0
$$19$$ 0 0
$$20$$ 0 0
$$21$$ −0.909039 + 1.08335i −0.909039 + 1.08335i
$$22$$ 0 0
$$23$$ 0 0 0.984808 0.173648i $$-0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −0.909039 1.08335i −0.909039 1.08335i −0.996195 0.0871557i $$-0.972222\pi$$
0.0871557 0.996195i $$-0.472222\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ 0 0
$$33$$ −1.39273 0.245576i −1.39273 0.245576i
$$34$$ 0 0
$$35$$ −0.939693 + 0.342020i −0.939693 + 0.342020i
$$36$$ 0 0
$$37$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.483690 + 1.32893i 0.483690 + 1.32893i 0.906308 + 0.422618i $$0.138889\pi$$
−0.422618 + 0.906308i $$0.638889\pi$$
$$42$$ 0 0
$$43$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$44$$ 0 0
$$45$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$46$$ 0 0
$$47$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0.483690 1.32893i 0.483690 1.32893i
$$52$$ 0 0
$$53$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$54$$ 0 0
$$55$$ −0.766044 0.642788i −0.766044 0.642788i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.909039 1.08335i 0.909039 1.08335i −0.0871557 0.996195i $$-0.527778\pi$$
0.996195 0.0871557i $$-0.0277778\pi$$
$$60$$ 0 0
$$61$$ −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i $$-0.888889\pi$$
0.766044 0.642788i $$-0.222222\pi$$
$$62$$ 0 0
$$63$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.39273 + 0.245576i 1.39273 + 0.245576i 0.819152 0.573576i $$-0.194444\pi$$
0.573576 + 0.819152i $$0.305556\pi$$
$$72$$ 0 0
$$73$$ −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i $$-0.777778\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −1.00000 −1.00000
$$78$$ 0 0
$$79$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$80$$ 0 0
$$81$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$82$$ 0 0
$$83$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$84$$ 0 0
$$85$$ 0.766044 0.642788i 0.766044 0.642788i
$$86$$ 0 0
$$87$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$88$$ 0 0
$$89$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$98$$ 0 0
$$99$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$100$$ 0 0
$$101$$ 0 0 0.342020 0.939693i $$-0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$102$$ 0 0
$$103$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$104$$ 0 0
$$105$$ 0.909039 + 1.08335i 0.909039 + 1.08335i
$$106$$ 0 0
$$107$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$108$$ 0 0
$$109$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$110$$ 0 0
$$111$$ 1.87939 0.684040i 1.87939 0.684040i
$$112$$ 0 0
$$113$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0.173648 0.984808i 0.173648 0.984808i
$$120$$ 0 0
$$121$$ 0 0
$$122$$ 0 0
$$123$$ 1.53209 1.28558i 1.53209 1.28558i
$$124$$ 0 0
$$125$$ 0.500000 0.866025i 0.500000 0.866025i
$$126$$ 0 0
$$127$$ −0.483690 + 1.32893i −0.483690 + 1.32893i 0.422618 + 0.906308i $$0.361111\pi$$
−0.906308 + 0.422618i $$0.861111\pi$$
$$128$$ 0 0
$$129$$ 1.39273 0.245576i 1.39273 0.245576i
$$130$$ 0 0
$$131$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i $$0.111111\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$138$$ 0 0
$$139$$ −0.939693 0.342020i −0.939693 0.342020i −0.173648 0.984808i $$-0.555556\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$140$$ 0 0
$$141$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$150$$ 0 0
$$151$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$152$$ 0 0
$$153$$ −1.00000 −1.00000
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 −0.984808 0.173648i $$-0.944444\pi$$
0.984808 + 0.173648i $$0.0555556\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$164$$ 0 0
$$165$$ −0.483690 + 1.32893i −0.483690 + 1.32893i
$$166$$ 0 0
$$167$$ 1.39273 0.245576i 1.39273 0.245576i 0.573576 0.819152i $$-0.305556\pi$$
0.819152 + 0.573576i $$0.194444\pi$$
$$168$$ 0 0
$$169$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0.909039 1.08335i 0.909039 1.08335i −0.0871557 0.996195i $$-0.527778\pi$$
0.996195 0.0871557i $$-0.0277778\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −1.87939 0.684040i −1.87939 0.684040i
$$178$$ 0 0
$$179$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$180$$ 0 0
$$181$$ 0.909039 + 1.08335i 0.909039 + 1.08335i 0.996195 + 0.0871557i $$0.0277778\pi$$
−0.0871557 + 0.996195i $$0.527778\pi$$
$$182$$ 0 0
$$183$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$184$$ 0 0
$$185$$ 1.39273 + 0.245576i 1.39273 + 0.245576i
$$186$$ 0 0
$$187$$ 0.939693 0.342020i 0.939693 0.342020i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ 0 0
$$193$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$198$$ 0 0
$$199$$ 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i $$-0.555556\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −0.483690 + 1.32893i −0.483690 + 1.32893i
$$204$$ 0 0
$$205$$ 1.39273 0.245576i 1.39273 0.245576i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −0.909039 + 1.08335i −0.909039 + 1.08335i 0.0871557 + 0.996195i $$0.472222\pi$$
−0.996195 + 0.0871557i $$0.972222\pi$$
$$212$$ 0 0
$$213$$ −0.347296 1.96962i −0.347296 1.96962i
$$214$$ 0 0
$$215$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0.909039 + 1.08335i 0.909039 + 1.08335i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −1.39273 0.245576i −1.39273 0.245576i −0.573576 0.819152i $$-0.694444\pi$$
−0.819152 + 0.573576i $$0.805556\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$228$$ 0 0
$$229$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 0.483690 + 1.32893i 0.483690 + 1.32893i
$$232$$ 0 0
$$233$$ 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i $$-0.777778\pi$$
0.939693 0.342020i $$-0.111111\pi$$
$$234$$ 0 0
$$235$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0.483690 1.32893i 0.483690 1.32893i −0.422618 0.906308i $$-0.638889\pi$$
0.906308 0.422618i $$-0.138889\pi$$
$$242$$ 0 0
$$243$$ 1.39273 0.245576i 1.39273 0.245576i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i $$0.111111\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ −1.22474 0.707107i −1.22474 0.707107i
$$256$$ 0 0
$$257$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$258$$ 0 0
$$259$$ 1.22474 0.707107i 1.22474 0.707107i
$$260$$ 0 0
$$261$$ 1.39273 + 0.245576i 1.39273 + 0.245576i
$$262$$ 0 0
$$263$$ −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i $$-0.777778\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$270$$ 0 0
$$271$$ 0 0 −0.984808 0.173648i $$-0.944444\pi$$
0.984808 + 0.173648i $$0.0555556\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.39273 + 0.245576i −1.39273 + 0.245576i −0.819152 0.573576i $$-0.805556\pi$$
−0.573576 + 0.819152i $$0.694444\pi$$
$$282$$ 0 0
$$283$$ 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i $$-0.111111\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0.909039 1.08335i 0.909039 1.08335i
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ −0.909039 1.08335i −0.909039 1.08335i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0.939693 0.342020i 0.939693 0.342020i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −1.00000 −1.00000
$$306$$ 0 0
$$307$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$308$$ 0 0
$$309$$ −0.347296 + 1.96962i −0.347296 + 1.96962i
$$310$$ 0 0
$$311$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.642788 0.766044i $$-0.722222\pi$$
0.642788 + 0.766044i $$0.277778\pi$$
$$314$$ 0 0
$$315$$ 0.500000 0.866025i 0.500000 0.866025i
$$316$$ 0 0
$$317$$ 0.483690 1.32893i 0.483690 1.32893i −0.422618 0.906308i $$-0.638889\pi$$
0.906308 0.422618i $$-0.138889\pi$$
$$318$$ 0 0
$$319$$ −1.39273 + 0.245576i −1.39273 + 0.245576i
$$320$$ 0 0
$$321$$ −1.53209 1.28558i −1.53209 1.28558i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$330$$ 0 0
$$331$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 0 0
$$333$$ −0.909039 1.08335i −0.909039 1.08335i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$338$$ 0 0
$$339$$ −1.87939 + 0.684040i −1.87939 + 0.684040i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −1.00000 −1.00000
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$348$$ 0 0
$$349$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$354$$ 0 0
$$355$$ 0.483690 1.32893i 0.483690 1.32893i
$$356$$ 0 0
$$357$$ −1.39273 + 0.245576i −1.39273 + 0.245576i
$$358$$ 0 0
$$359$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$366$$ 0 0
$$367$$ 0 0 0.342020 0.939693i $$-0.388889\pi$$
−0.342020 + 0.939693i $$0.611111\pi$$
$$368$$ 0 0
$$369$$ −1.22474 0.707107i −1.22474 0.707107i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$374$$ 0 0
$$375$$ −1.39273 0.245576i −1.39273 0.245576i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$380$$ 0 0
$$381$$ 2.00000 2.00000
$$382$$ 0 0
$$383$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$384$$ 0 0
$$385$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$386$$ 0 0
$$387$$ −0.500000 0.866025i −0.500000 0.866025i
$$388$$ 0 0
$$389$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −0.483690 + 1.32893i −0.483690 + 1.32893i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.939693 + 0.342020i 0.939693 + 0.342020i
$$406$$ 0 0
$$407$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$408$$ 0 0
$$409$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$410$$ 0 0
$$411$$ 1.22474 0.707107i 1.22474 0.707107i
$$412$$ 0 0
$$413$$ −1.39273 0.245576i −1.39273 0.245576i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 1.41421i 1.41421i
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 0 0 0.939693 0.342020i $$-0.111111\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$422$$ 0 0
$$423$$ 0.173648 0.984808i 0.173648 0.984808i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.939693 0.342020i $$-0.888889\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$432$$ 0 0
$$433$$ −1.39273 + 0.245576i −1.39273 + 0.245576i −0.819152 0.573576i $$-0.805556\pi$$
−0.573576 + 0.819152i $$0.694444\pi$$
$$434$$ 0 0
$$435$$ 1.53209 + 1.28558i 1.53209 + 1.28558i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −0.909039 + 1.08335i −0.909039 + 1.08335i 0.0871557 + 0.996195i $$0.472222\pi$$
−0.996195 + 0.0871557i $$0.972222\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i $$-0.222222\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ −0.909039 1.08335i −0.909039 1.08335i
$$448$$ 0 0
$$449$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$450$$ 0 0
$$451$$ 1.39273 + 0.245576i 1.39273 + 0.245576i
$$452$$ 0 0
$$453$$ −1.87939 + 0.684040i −1.87939 + 0.684040i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i $$-0.777778\pi$$
0.939693 0.342020i $$-0.111111\pi$$
$$462$$ 0 0
$$463$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −0.347296 1.96962i −0.347296 1.96962i −0.173648 0.984808i $$-0.555556\pi$$
−0.173648 0.984808i $$-0.555556\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 −0.342020 0.939693i $$-0.611111\pi$$
0.342020 + 0.939693i $$0.388889\pi$$
$$492$$ 0 0
$$493$$ 1.41421i 1.41421i
$$494$$ 0 0
$$495$$ 1.00000 1.00000
$$496$$ 0 0
$$497$$ −0.483690 1.32893i −0.483690 1.32893i
$$498$$ 0 0
$$499$$ 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i $$-0.777778\pi$$
0.939693 0.342020i $$-0.111111\pi$$
$$500$$ 0 0
$$501$$ −1.00000 1.73205i −1.00000 1.73205i
$$502$$ 0 0
$$503$$ −1.53209 + 1.28558i −1.53209 + 1.28558i −0.766044 + 0.642788i $$0.777778\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.483690 1.32893i 0.483690 1.32893i
$$508$$ 0 0
$$509$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$510$$ 0 0
$$511$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −0.909039 + 1.08335i −0.909039 + 1.08335i
$$516$$ 0 0
$$517$$ 0.173648 + 0.984808i 0.173648 + 0.984808i
$$518$$ 0 0
$$519$$ −1.87939 0.684040i −1.87939 0.684040i
$$520$$ 0 0
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ 0.909039 + 1.08335i 0.909039 + 1.08335i 0.996195 + 0.0871557i $$0.0277778\pi$$
−0.0871557 + 0.996195i $$0.527778\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.939693 0.342020i 0.939693 0.342020i
$$530$$ 0 0
$$531$$ 1.41421i 1.41421i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −0.483690 1.32893i −0.483690 1.32893i
$$536$$ 0 0
$$537$$ 0.347296 1.96962i 0.347296 1.96962i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i $$-0.888889\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$542$$ 0 0
$$543$$ 1.00000 1.73205i 1.00000 1.73205i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$548$$ 0 0
$$549$$ 0.766044 + 0.642788i 0.766044 + 0.642788i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −0.347296 1.96962i −0.347296 1.96962i
$$556$$ 0 0
$$557$$ −0.939693 0.342020i −0.939693 0.342020i −0.173648 0.984808i $$-0.555556\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −0.909039 1.08335i −0.909039 1.08335i
$$562$$ 0 0
$$563$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$564$$ 0 0
$$565$$ −1.39273 0.245576i −1.39273 0.245576i
$$566$$ 0 0
$$567$$ 0.939693 0.342020i 0.939693 0.342020i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$572$$ 0 0
$$573$$ −0.483690 1.32893i −0.483690 1.32893i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 0.766044 + 0.642788i 0.766044 + 0.642788i 0.939693 0.342020i $$-0.111111\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 0.984808 0.173648i $$-0.0555556\pi$$
−0.984808 + 0.173648i $$0.944444\pi$$
$$594$$ 0 0
$$595$$ −0.939693 0.342020i −0.939693 0.342020i
$$596$$ 0 0
$$597$$ −1.22474 0.707107i −1.22474 0.707107i
$$598$$ 0 0
$$599$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$600$$ 0 0
$$601$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 2.00000 2.00000
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i $$-0.777778\pi$$
0.939693 0.342020i $$-0.111111\pi$$
$$614$$ 0 0
$$615$$ −1.00000 1.73205i −1.00000 1.73205i
$$616$$ 0 0
$$617$$ 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i $$-0.555556\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −0.766044 0.642788i −0.766044 0.642788i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −0.909039 + 1.08335i −0.909039 + 1.08335i
$$630$$ 0 0
$$631$$ 0.173648 + 0.984808i 0.173648 + 0.984808i 0.939693 + 0.342020i $$0.111111\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$632$$ 0 0
$$633$$ 1.87939 + 0.684040i 1.87939 + 0.684040i
$$634$$ 0 0
$$635$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$640$$ 0 0
$$641$$ 0 0 0.173648 0.984808i $$-0.444444\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$642$$ 0 0
$$643$$ −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i $$-0.777778\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$644$$ 0 0
$$645$$ 1.41421i 1.41421i
$$646$$ 0 0
$$647$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$648$$ 0 0
$$649$$ −0.483690 1.32893i −0.483690 1.32893i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$654$$ 0 0
$$655$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$656$$ 0 0
$$657$$ 0.500000 0.866025i 0.500000 0.866025i
$$658$$ 0 0
$$659$$ −0.483690 + 1.32893i −0.483690 + 1.32893i 0.422618 + 0.906308i $$0.361111\pi$$
−0.906308 + 0.422618i $$0.861111\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.173648 0.984808i $$-0.555556\pi$$
0.173648 + 0.984808i $$0.444444\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0.347296 + 1.96962i 0.347296 + 1.96962i
$$670$$ 0 0
$$671$$ −0.939693 0.342020i −0.939693 0.342020i
$$672$$ 0 0
$$673$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ 0 0
$$685$$ 1.00000 1.00000
$$686$$ 0 0
$$687$$ 0.483690 + 1.32893i 0.483690 + 1.32893i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0.766044 0.642788i 0.766044 0.642788i
$$694$$ 0 0
$$695$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$696$$ 0 0
$$697$$ −0.483690 + 1.32893i −0.483690 + 1.32893i
$$698$$ 0 0
$$699$$ −1.39273 + 0.245576i −1.39273 + 0.245576i
$$700$$ 0 0
$$701$$ 0 0 0.642788 0.766044i $$-0.277778\pi$$
−0.642788 + 0.766044i $$0.722222\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0.909039 1.08335i 0.909039 1.08335i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.87939 + 0.684040i 1.87939 + 0.684040i 0.939693 + 0.342020i $$0.111111\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 1.39273 + 0.245576i 1.39273 + 0.245576i
$$718$$ 0 0
$$719$$ 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i $$-0.444444\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$720$$ 0 0
$$721$$ 1.41421i 1.41421i
$$722$$ 0 0
$$723$$ −2.00000 −2.00000
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i $$0.222222\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$728$$ 0 0
$$729$$ −0.500000 0.866025i −0.500000 0.866025i
$$730$$ 0 0
$$731$$ −0.766044 + 0.642788i −0.766044 + 0.642788i
$$732$$ 0 0
$$733$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i $$-0.444444\pi$$
−0.939693 + 0.342020i $$0.888889\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.766044 0.642788i $$-0.777778\pi$$
0.766044 + 0.642788i $$0.222222\pi$$
$$744$$ 0 0
$$745$$ −0.173648 0.984808i −0.173648 0.984808i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −1.22474 0.707107i −1.22474 0.707107i
$$750$$ 0 0
$$751$$ 0 0 0.766044 0.642788i $$-0.222222\pi$$
−0.766044 + 0.642788i $$0.777778\pi$$
$$752$$ 0 0
$$753$$ 1.22474 0.707107i 1.22474 0.707107i
$$754$$ 0 0
$$755$$ −1.39273 0.245576i −1.39273 0.245576i
$$756$$ 0 0
$$757$$ −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i $$-0.777778\pi$$
−0.173648 + 0.984808i $$0.555556\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i $$-0.555556\pi$$
0.939693 + 0.342020i $$0.111111\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.483690 1.32893i 0.483690 1.32893i −0.422618 0.906308i $$-0.638889\pi$$
0.906308 0.422618i $$-0.138889\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −1.53209 1.28558i −1.53209 1.28558i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0.909039 1.08335i 0.909039 1.08335i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 0 0
$$789$$ 0.909039 + 1.08335i 0.909039 + 1.08335i
$$790$$ 0 0
$$791$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$792$$ 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
$$799$$ −1.00000 −1.00000
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −0.173648 + 0.984808i −0.173648 + 0.984808i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0