# Properties

 Label 500.1.j.a.151.1 Level $500$ Weight $1$ Character 500.151 Analytic conductor $0.250$ Analytic rank $0$ Dimension $4$ Projective image $D_{5}$ CM discriminant -4 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$500 = 2^{2} \cdot 5^{3}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 500.j (of order $$10$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.249532506317$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ x^4 - x^3 + x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 100) Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.6250000.1

## Embedding invariants

 Embedding label 151.1 Root $$-0.309017 + 0.951057i$$ of defining polynomial Character $$\chi$$ $$=$$ 500.151 Dual form 500.1.j.a.351.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$$ $$q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.500000 - 1.53884i) q^{13} +(0.309017 - 0.951057i) q^{16} +(0.500000 + 0.363271i) q^{17} -1.00000 q^{18} -1.61803 q^{26} +(-0.500000 + 0.363271i) q^{29} -1.00000 q^{32} +(0.190983 - 0.587785i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-0.190983 + 0.587785i) q^{37} +(-0.500000 + 1.53884i) q^{41} +1.00000 q^{49} +(0.500000 + 1.53884i) q^{52} +(-1.30902 + 0.951057i) q^{53} +(0.500000 + 0.363271i) q^{58} +(-0.500000 - 1.53884i) q^{61} +(0.309017 + 0.951057i) q^{64} -0.618034 q^{68} +(0.809017 - 0.587785i) q^{72} +(0.500000 + 1.53884i) q^{73} +0.618034 q^{74} +(-0.809017 - 0.587785i) q^{81} +1.61803 q^{82} +(0.190983 + 0.587785i) q^{89} +(0.500000 - 0.363271i) q^{97} +(-0.309017 - 0.951057i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{2} - q^{4} + q^{8} - q^{9}+O(q^{10})$$ 4 * q + q^2 - q^4 + q^8 - q^9 $$4 q + q^{2} - q^{4} + q^{8} - q^{9} + 2 q^{13} - q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{26} - 2 q^{29} - 4 q^{32} + 3 q^{34} - q^{36} - 3 q^{37} - 2 q^{41} + 4 q^{49} + 2 q^{52} - 3 q^{53} + 2 q^{58} - 2 q^{61} - q^{64} + 2 q^{68} + q^{72} + 2 q^{73} - 2 q^{74} - q^{81} + 2 q^{82} + 3 q^{89} + 2 q^{97} + q^{98}+O(q^{100})$$ 4 * q + q^2 - q^4 + q^8 - q^9 + 2 * q^13 - q^16 + 2 * q^17 - 4 * q^18 - 2 * q^26 - 2 * q^29 - 4 * q^32 + 3 * q^34 - q^36 - 3 * q^37 - 2 * q^41 + 4 * q^49 + 2 * q^52 - 3 * q^53 + 2 * q^58 - 2 * q^61 - q^64 + 2 * q^68 + q^72 + 2 * q^73 - 2 * q^74 - q^81 + 2 * q^82 + 3 * q^89 + 2 * q^97 + q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$$.

 $$n$$ $$251$$ $$377$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.309017 0.951057i −0.309017 0.951057i
$$3$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$4$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$9$$ 0.309017 0.951057i 0.309017 0.951057i
$$10$$ 0 0
$$11$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$12$$ 0 0
$$13$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0.309017 0.951057i 0.309017 0.951057i
$$17$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$18$$ −1.00000 −1.00000
$$19$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −1.61803 −1.61803
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ 0 0
$$34$$ 0.190983 0.587785i 0.190983 0.587785i
$$35$$ 0 0
$$36$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$37$$ −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i $$0.200000\pi$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$53$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$59$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$60$$ 0 0
$$61$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$68$$ −0.618034 −0.618034
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$72$$ 0.809017 0.587785i 0.809017 0.587785i
$$73$$ 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i $$0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$74$$ 0.618034 0.618034
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$80$$ 0 0
$$81$$ −0.809017 0.587785i −0.809017 0.587785i
$$82$$ 1.61803 1.61803
$$83$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$98$$ −0.309017 0.951057i −0.309017 0.951057i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$104$$ 1.30902 0.951057i 1.30902 0.951057i
$$105$$ 0 0
$$106$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i $$0.200000\pi$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.190983 0.587785i 0.190983 0.587785i
$$117$$ −1.30902 0.951057i −1.30902 0.951057i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$122$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$128$$ 0.809017 0.587785i 0.809017 0.587785i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$137$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$138$$ 0 0
$$139$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.809017 0.587785i −0.809017 0.587785i
$$145$$ 0 0
$$146$$ 1.30902 0.951057i 1.30902 0.951057i
$$147$$ 0 0
$$148$$ −0.190983 0.587785i −0.190983 0.587785i
$$149$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0.500000 0.363271i 0.500000 0.363271i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$163$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$164$$ −0.500000 1.53884i −0.500000 1.53884i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$168$$ 0 0
$$169$$ −1.30902 0.951057i −1.30902 0.951057i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.500000 0.363271i 0.500000 0.363271i
$$179$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$180$$ 0 0
$$181$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$192$$ 0 0
$$193$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$194$$ −0.500000 0.363271i −0.500000 0.363271i
$$195$$ 0 0
$$196$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$197$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −0.190983 0.587785i −0.190983 0.587785i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −1.30902 0.951057i −1.30902 0.951057i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$212$$ 0.500000 1.53884i 0.500000 1.53884i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 1.61803 1.61803
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0.809017 0.587785i 0.809017 0.587785i
$$222$$ 0 0
$$223$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0.618034 0.618034
$$227$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$228$$ 0 0
$$229$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −0.618034 −0.618034
$$233$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$234$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$240$$ 0 0
$$241$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$242$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$243$$ 0 0
$$244$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.809017 0.587785i −0.809017 0.587785i
$$257$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$262$$ 0 0
$$263$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$272$$ 0.500000 0.363271i 0.500000 0.363271i
$$273$$ 0 0
$$274$$ −1.61803 −1.61803
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$289$$ −0.190983 0.587785i −0.190983 0.587785i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −1.30902 0.951057i −1.30902 0.951057i
$$293$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$297$$ 0 0
$$298$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −0.500000 0.363271i −0.500000 0.363271i
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$312$$ 0 0
$$313$$ −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i $$0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$314$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i $$0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 1.00000 1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$332$$ 0 0
$$333$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i $$0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$338$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$347$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$348$$ 0 0
$$349$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i $$-0.200000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −0.500000 0.363271i −0.500000 0.363271i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$360$$ 0 0
$$361$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$362$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$368$$ 0 0
$$369$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 0.951057i $$-0.600000\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$378$$ 0 0
$$379$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −0.500000 1.53884i −0.500000 1.53884i
$$387$$ 0 0
$$388$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$389$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$393$$ 0 0
$$394$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i $$-0.200000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$420$$ 0 0
$$421$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ −1.61803 −1.61803
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$432$$ 0 0
$$433$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −0.500000 1.53884i −0.500000 1.53884i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$440$$ 0 0
$$441$$ 0.309017 0.951057i 0.309017 0.951057i
$$442$$ −0.809017 0.587785i −0.809017 0.587785i
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −0.190983 0.587785i −0.190983 0.587785i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$458$$ −1.30902 0.951057i −1.30902 0.951057i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$462$$ 0 0
$$463$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$464$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$465$$ 0 0
$$466$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$467$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$468$$ 1.61803 1.61803
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$478$$ 0 0
$$479$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$480$$ 0 0
$$481$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$482$$ −0.618034 −0.618034
$$483$$ 0 0
$$484$$ 0.309017 0.951057i 0.309017 0.951057i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$488$$ 0.500000 1.53884i 0.500000 1.53884i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$492$$ 0 0
$$493$$ −0.381966 −0.381966
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$513$$ 0 0
$$514$$ −0.500000 1.53884i −0.500000 1.53884i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$522$$ 0.500000 0.363271i 0.500000 0.363271i
$$523$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0.500000 1.53884i 0.500000 1.53884i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −0.500000 0.363271i −0.500000 0.363271i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$548$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$549$$ −1.61803 −1.61803
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0.500000 1.53884i 0.500000 1.53884i
$$563$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$570$$ 0 0
$$571$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 1.00000
$$577$$ −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 0.951057i $$-0.600000\pi$$
$$578$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$585$$ 0 0
$$586$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$587$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$593$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 1.30902 0.951057i 1.30902 0.951057i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$602$$ 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
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$613$$ −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i $$0.200000\pi$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 2.00000 2.00000
$$627$$ 0 0
$$628$$ 0.500000 0.363271i 0.500000 0.363271i
$$629$$ −0.309017 + 0.224514i −0.309017 + 0.224514i
$$630$$ 0 0
$$631$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0.618034 1.90211i 0.618034 1.90211i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.500000 1.53884i 0.500000 1.53884i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i $$-0.400000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$648$$ −0.309017 0.951057i −0.309017 0.951057i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$657$$ 1.61803 1.61803
$$658$$ 0 0
$$659$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$660$$ 0 0
$$661$$ 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i $$0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0.190983 0.587785i 0.190983 0.587785i
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$674$$ 2.00000 2.00000
$$675$$ 0 0
$$676$$ 1.61803 1.61803
$$677$$ −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 0.951057i $$-0.600000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$690$$ 0 0
$$691$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$692$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$698$$ −0.190983 0.587785i −0.190983 0.587785i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ −1.61803 1.17557i −1.61803 1.17557i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.809017 0.587785i 0.809017 0.587785i
$$723$$ 0 0
$$724$$ 0.618034 0.618034
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$728$$ 0 0
$$729$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i $$0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0.500000 1.53884i 0.500000 1.53884i
$$739$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −1.61803 + 1.17557i −1.61803 + 1.17557i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0.809017 0.587785i 0.809017 0.587785i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$773$$ 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i $$0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0.618034 0.618034
$$777$$ 0 0
$$778$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.309017 0.951057i 0.309017 0.951057i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$788$$ 0.500000 1.53884i 0.500000 1.53884i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −2.61803 −2.61803
$$794$$ −1.61803 1.17557i −1.61803 1.17557i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0.618034 0.618034
$$802$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0