# Properties

 Label 429.1.v.a.311.1 Level $429$ Weight $1$ Character 429.311 Analytic conductor $0.214$ Analytic rank $0$ Dimension $4$ Projective image $D_{5}$ CM discriminant -39 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$429 = 3 \cdot 11 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 429.v (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.214098890420$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.22268961.1

## Embedding invariants

 Embedding label 311.1 Root $$0.809017 + 0.587785i$$ of defining polynomial Character $$\chi$$ $$=$$ 429.311 Dual form 429.1.v.a.389.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.500000 - 1.53884i) q^{4} +(0.500000 + 0.363271i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$$ $$q+(-1.30902 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.500000 - 1.53884i) q^{4} +(0.500000 + 0.363271i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +(0.809017 + 0.587785i) q^{11} +1.61803 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.190983 + 0.587785i) q^{15} +(0.500000 - 1.53884i) q^{18} +(0.809017 - 0.587785i) q^{20} -1.61803 q^{22} +(-0.809017 + 0.587785i) q^{24} +(-0.190983 - 0.587785i) q^{25} +(0.500000 - 1.53884i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.309017 - 0.951057i) q^{30} -1.00000 q^{32} +(-0.309017 + 0.951057i) q^{33} +(0.500000 + 1.53884i) q^{36} +(-0.809017 - 0.587785i) q^{39} +(-0.190983 + 0.587785i) q^{40} +(-0.618034 - 1.90211i) q^{41} +0.618034 q^{43} +(1.30902 - 0.951057i) q^{44} -0.618034 q^{45} +(0.500000 + 1.53884i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.500000 + 1.53884i) q^{52} +1.61803 q^{54} +(0.190983 + 0.587785i) q^{55} +(0.500000 - 1.53884i) q^{59} +(0.809017 + 0.587785i) q^{60} +(1.30902 + 0.951057i) q^{61} +(1.30902 - 0.951057i) q^{64} -0.618034 q^{65} +(-0.500000 - 1.53884i) q^{66} +(1.61803 + 1.17557i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(0.500000 - 0.363271i) q^{75} +1.61803 q^{78} +(1.30902 - 0.951057i) q^{79} +(0.309017 - 0.951057i) q^{81} +(2.61803 + 1.90211i) q^{82} +(0.500000 + 0.363271i) q^{83} +(-0.809017 + 0.587785i) q^{86} +(-0.309017 + 0.951057i) q^{88} -2.00000 q^{89} +(0.809017 - 0.587785i) q^{90} +(-2.11803 - 1.53884i) q^{94} +(-0.309017 - 0.951057i) q^{96} +1.61803 q^{98} -1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 3q^{2} - q^{3} + 2q^{4} + 2q^{5} - 3q^{6} - q^{8} - q^{9} + O(q^{10})$$ $$4q - 3q^{2} - q^{3} + 2q^{4} + 2q^{5} - 3q^{6} - q^{8} - q^{9} - 4q^{10} + q^{11} + 2q^{12} - q^{13} - 3q^{15} + 2q^{18} + q^{20} - 2q^{22} - q^{24} - 3q^{25} + 2q^{26} - q^{27} + q^{30} - 4q^{32} + q^{33} + 2q^{36} - q^{39} - 3q^{40} + 2q^{41} - 2q^{43} + 3q^{44} + 2q^{45} + 2q^{47} - q^{49} + q^{50} + 2q^{52} + 2q^{54} + 3q^{55} + 2q^{59} + q^{60} + 3q^{61} + 3q^{64} + 2q^{65} - 2q^{66} + 2q^{71} - q^{72} + 2q^{75} + 2q^{78} + 3q^{79} - q^{81} + 6q^{82} + 2q^{83} - q^{86} + q^{88} - 8q^{89} + q^{90} - 4q^{94} + q^{96} + 2q^{98} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$$.

 $$n$$ $$67$$ $$79$$ $$287$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$3$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$4$$ 0.500000 1.53884i 0.500000 1.53884i
$$5$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$6$$ −1.30902 0.951057i −1.30902 0.951057i
$$7$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$8$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$9$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$10$$ −1.00000 −1.00000
$$11$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$12$$ 1.61803 1.61803
$$13$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$14$$ 0 0
$$15$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$16$$ 0 0
$$17$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$18$$ 0.500000 1.53884i 0.500000 1.53884i
$$19$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$20$$ 0.809017 0.587785i 0.809017 0.587785i
$$21$$ 0 0
$$22$$ −1.61803 −1.61803
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$25$$ −0.190983 0.587785i −0.190983 0.587785i
$$26$$ 0.500000 1.53884i 0.500000 1.53884i
$$27$$ −0.809017 0.587785i −0.809017 0.587785i
$$28$$ 0 0
$$29$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$30$$ −0.309017 0.951057i −0.309017 0.951057i
$$31$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$37$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$38$$ 0 0
$$39$$ −0.809017 0.587785i −0.809017 0.587785i
$$40$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$41$$ −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 0.951057i $$-0.600000\pi$$
$$42$$ 0 0
$$43$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$44$$ 1.30902 0.951057i 1.30902 0.951057i
$$45$$ −0.618034 −0.618034
$$46$$ 0 0
$$47$$ 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i $$0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$48$$ 0 0
$$49$$ −0.809017 0.587785i −0.809017 0.587785i
$$50$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$51$$ 0 0
$$52$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$53$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$54$$ 1.61803 1.61803
$$55$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$60$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$61$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.30902 0.951057i 1.30902 0.951057i
$$65$$ −0.618034 −0.618034
$$66$$ −0.500000 1.53884i −0.500000 1.53884i
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i $$0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$72$$ −0.809017 0.587785i −0.809017 0.587785i
$$73$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$74$$ 0 0
$$75$$ 0.500000 0.363271i 0.500000 0.363271i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 1.61803 1.61803
$$79$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$80$$ 0 0
$$81$$ 0.309017 0.951057i 0.309017 0.951057i
$$82$$ 2.61803 + 1.90211i 2.61803 + 1.90211i
$$83$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$87$$ 0 0
$$88$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$89$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$90$$ 0.809017 0.587785i 0.809017 0.587785i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −2.11803 1.53884i −2.11803 1.53884i
$$95$$ 0 0
$$96$$ −0.309017 0.951057i −0.309017 0.951057i
$$97$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$98$$ 1.61803 1.61803
$$99$$ −1.00000 −1.00000
$$100$$ −1.00000 −1.00000
$$101$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$102$$ 0 0
$$103$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$104$$ −0.809017 0.587785i −0.809017 0.587785i
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$108$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ −0.809017 0.587785i −0.809017 0.587785i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.309017 0.951057i 0.309017 0.951057i
$$118$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$119$$ 0 0
$$120$$ −0.618034 −0.618034
$$121$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$122$$ −2.61803 −2.61803
$$123$$ 1.61803 1.17557i 1.61803 1.17557i
$$124$$ 0 0
$$125$$ 0.309017 0.951057i 0.309017 0.951057i
$$126$$ 0 0
$$127$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$128$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$129$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$130$$ 0.809017 0.587785i 0.809017 0.587785i
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −0.190983 0.587785i −0.190983 0.587785i
$$136$$ 0 0
$$137$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$140$$ 0 0
$$141$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$142$$ −3.23607 −3.23607
$$143$$ −1.00000 −1.00000
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0.309017 0.951057i 0.309017 0.951057i
$$148$$ 0 0
$$149$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$150$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$151$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$157$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$158$$ −0.809017 + 2.48990i −0.809017 + 2.48990i
$$159$$ 0 0
$$160$$ −0.500000 0.363271i −0.500000 0.363271i
$$161$$ 0 0
$$162$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$163$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$164$$ −3.23607 −3.23607
$$165$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$166$$ −1.00000 −1.00000
$$167$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$168$$ 0 0
$$169$$ 0.309017 0.951057i 0.309017 0.951057i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0.309017 0.951057i 0.309017 0.951057i
$$173$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 1.61803 1.61803
$$178$$ 2.61803 1.90211i 2.61803 1.90211i
$$179$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$180$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$181$$ −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
$$183$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 2.61803 2.61803
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$192$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$193$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$194$$ 0 0
$$195$$ −0.190983 0.587785i −0.190983 0.587785i
$$196$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$197$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$198$$ 1.30902 0.951057i 1.30902 0.951057i
$$199$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$200$$ 0.500000 0.363271i 0.500000 0.363271i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0.381966 1.17557i 0.381966 1.17557i
$$206$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$212$$ 0 0
$$213$$ −0.618034 + 1.90211i −0.618034 + 1.90211i
$$214$$ 0 0
$$215$$ 0.309017 + 0.224514i 0.309017 + 0.224514i
$$216$$ 0.309017 0.951057i 0.309017 0.951057i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 1.00000 1.00000
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$224$$ 0 0
$$225$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$226$$ 0 0
$$227$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$234$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$235$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$236$$ −2.11803 1.53884i −2.11803 1.53884i
$$237$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$238$$ 0 0
$$239$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ −1.30902 0.951057i −1.30902 0.951057i
$$243$$ 1.00000 1.00000
$$244$$ 2.11803 1.53884i 2.11803 1.53884i
$$245$$ −0.190983 0.587785i −0.190983 0.587785i
$$246$$ −1.00000 + 3.07768i −1.00000 + 3.07768i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$250$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$251$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 1.00000 1.00000
$$255$$ 0 0
$$256$$ −0.309017 0.951057i −0.309017 0.951057i
$$257$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$258$$ −0.809017 0.587785i −0.809017 0.587785i
$$259$$ 0 0
$$260$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$264$$ −1.00000 −1.00000
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.618034 1.90211i −0.618034 1.90211i
$$268$$ 0 0
$$269$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$270$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$271$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 2.61803 2.61803
$$275$$ 0.190983 0.587785i 0.190983 0.587785i
$$276$$ 0 0
$$277$$ −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i $$0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$278$$ −0.809017 2.48990i −0.809017 2.48990i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$282$$ 0.809017 2.48990i 0.809017 2.48990i
$$283$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$284$$ 2.61803 1.90211i 2.61803 1.90211i
$$285$$ 0 0
$$286$$ 1.30902 0.951057i 1.30902 0.951057i
$$287$$ 0 0
$$288$$ 0.809017 0.587785i 0.809017 0.587785i
$$289$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i $$0.200000\pi$$
−1.00000 $$\pi$$
$$294$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$295$$ 0.809017 0.587785i 0.809017 0.587785i
$$296$$ 0 0
$$297$$ −0.309017 0.951057i −0.309017 0.951057i
$$298$$ −1.00000 −1.00000
$$299$$ 0 0
$$300$$ −0.309017 0.951057i −0.309017 0.951057i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0.618034 0.618034
$$310$$ 0 0
$$311$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$312$$ 0.309017 0.951057i 0.309017 0.951057i
$$313$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$314$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$315$$ 0 0
$$316$$ −0.809017 2.48990i −0.809017 2.48990i
$$317$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 1.00000 1.00000
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.30902 0.951057i −1.30902 0.951057i
$$325$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 1.61803 1.17557i 1.61803 1.17557i
$$329$$ 0 0
$$330$$ 0.309017 0.951057i 0.309017 0.951057i
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0.809017 0.587785i 0.809017 0.587785i
$$333$$ 0 0
$$334$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$338$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$348$$ 0 0
$$349$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$350$$ 0 0
$$351$$ 1.00000 1.00000
$$352$$ −0.809017 0.587785i −0.809017 0.587785i
$$353$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$354$$ −2.11803 + 1.53884i −2.11803 + 1.53884i
$$355$$ 0.381966 + 1.17557i 0.381966 + 1.17557i
$$356$$ −1.00000 + 3.07768i −1.00000 + 3.07768i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i $$0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$360$$ −0.190983 0.587785i −0.190983 0.587785i
$$361$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$362$$ 1.00000 1.00000
$$363$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −0.809017 2.48990i −0.809017 2.48990i
$$367$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$368$$ 0 0
$$369$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$374$$ 0 0
$$375$$ 1.00000 1.00000
$$376$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$380$$ 0 0
$$381$$ 0.190983 0.587785i 0.190983 0.587785i
$$382$$ 0 0
$$383$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$384$$ −1.61803 −1.61803
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$388$$ 0 0
$$389$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$390$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$391$$ 0 0
$$392$$ 0.309017 0.951057i 0.309017 0.951057i
$$393$$ 0 0
$$394$$ −2.11803 + 1.53884i −2.11803 + 1.53884i
$$395$$ 1.00000 1.00000
$$396$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 2.11803 1.53884i 2.11803 1.53884i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0.500000 0.363271i 0.500000 0.363271i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$410$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$411$$ 0.500000 1.53884i 0.500000 1.53884i
$$412$$ −0.809017 0.587785i −0.809017 0.587785i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0.118034 + 0.363271i 0.118034 + 0.363271i
$$416$$ 0.809017 0.587785i 0.809017 0.587785i
$$417$$ −1.61803 −1.61803
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$422$$ 0.309017 0.951057i 0.309017 0.951057i
$$423$$ −1.30902 0.951057i −1.30902 0.951057i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ −1.00000 3.07768i −1.00000 3.07768i
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −0.309017 0.951057i −0.309017 0.951057i
$$430$$ −0.618034 −0.618034
$$431$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$440$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$441$$ 1.00000 1.00000
$$442$$ 0 0
$$443$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$444$$ 0 0
$$445$$ −1.00000 0.726543i −1.00000 0.726543i
$$446$$ 0 0
$$447$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$448$$ 0 0
$$449$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$450$$ −1.00000 −1.00000
$$451$$ 0.618034 1.90211i 0.618034 1.90211i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$468$$ −1.30902 0.951057i −1.30902 0.951057i
$$469$$ 0 0
$$470$$ −0.500000 1.53884i −0.500000 1.53884i
$$471$$ 1.30902 0.951057i 1.30902 0.951057i
$$472$$ 1.61803 1.61803
$$473$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$474$$ −2.61803 −2.61803
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$479$$ 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i $$-0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$480$$ 0.190983 0.587785i 0.190983 0.587785i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 1.61803 1.61803
$$485$$ 0 0
$$486$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$487$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$488$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$489$$ 0 0
$$490$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$491$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$492$$ −1.00000 3.07768i −1.00000 3.07768i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −0.500000 0.363271i −0.500000 0.363271i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −0.309017 0.951057i −0.309017 0.951057i
$$499$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$500$$ −1.30902 0.951057i −1.30902 0.951057i
$$501$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$502$$ 0 0
$$503$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.00000 1.00000
$$508$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$509$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0.309017 0.224514i 0.309017 0.224514i
$$516$$ 1.00000 1.00000
$$517$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −0.190983 0.587785i −0.190983 0.587785i
$$521$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$522$$ 0 0
$$523$$ −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 1.00000
$$530$$ 0 0
$$531$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$532$$ 0 0
$$533$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$534$$ 2.61803 + 1.90211i 2.61803 + 1.90211i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −0.309017 0.951057i −0.309017 0.951057i
$$540$$ −1.00000 −1.00000
$$541$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$542$$ 0 0
$$543$$ 0.190983 0.587785i 0.190983 0.587785i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$548$$ −2.11803 + 1.53884i −2.11803 + 1.53884i
$$549$$ −1.61803 −1.61803
$$550$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 1.00000 3.07768i 1.00000 3.07768i
$$555$$ 0 0
$$556$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$557$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$558$$ 0 0
$$559$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 2.61803 2.61803
$$563$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$564$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$565$$ 0 0
$$566$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$567$$ 0 0
$$568$$ −0.618034 + 1.90211i −0.618034 + 1.90211i
$$569$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$570$$ 0 0
$$571$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$572$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$577$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$578$$ −1.30902 0.951057i −1.30902 0.951057i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0.500000 0.363271i 0.500000 0.363271i
$$586$$ −0.309017 0.951057i −0.309017 0.951057i
$$587$$ −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i $$0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$588$$ −1.30902 0.951057i −1.30902 0.951057i
$$589$$ 0 0
$$590$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$591$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$592$$ 0 0
$$593$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$594$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$595$$ 0 0
$$596$$ 0.809017 0.587785i 0.809017 0.587785i
$$597$$ −0.500000 1.53884i −0.500000 1.53884i
$$598$$ 0 0
$$599$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$600$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$601$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$606$$ 0 0
$$607$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ −1.30902 0.951057i −1.30902 0.951057i
$$611$$ −1.30902 0.951057i −1.30902 0.951057i
$$612$$ 0 0
$$613$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$614$$ 0 0
$$615$$ 1.23607 1.23607
$$616$$ 0 0
$$617$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$618$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$619$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 1.00000 1.00000
$$627$$ 0 0
$$628$$ −2.61803 −2.61803
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$632$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$633$$ −0.500000 0.363271i −0.500000 0.363271i
$$634$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$635$$ −0.118034 0.363271i −0.118034 0.363271i
$$636$$ 0 0
$$637$$ 1.00000 1.00000
$$638$$ 0 0
$$639$$ −2.00000 −2.00000
$$640$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$641$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$642$$ 0 0
$$643$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$644$$ 0 0
$$645$$ −0.118034 + 0.363271i −0.118034 + 0.363271i
$$646$$ 0 0
$$647$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$648$$ 1.00000 1.00000
$$649$$ 1.30902 0.951057i 1.30902 0.951057i
$$650$$ −1.00000 −1.00000
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −0.309017 0.951057i −0.309017 0.951057i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$672$$ 0 0
$$673$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$674$$ −0.809017 2.48990i −0.809017 2.48990i
$$675$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$676$$ −1.30902 0.951057i −1.30902 0.951057i
$$677$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.61803 1.61803
$$682$$ 0 0
$$683$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$684$$ 0 0
$$685$$ −0.309017 0.951057i −0.309017 0.951057i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$702$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$703$$ 0 0
$$704$$ 1.61803 1.61803
$$705$$ −1.00000 −1.00000
$$706$$ 0.809017 0.587785i 0.809017 0.587785i
$$707$$ 0 0
$$708$$ 0.809017 2.48990i 0.809017 2.48990i
$$709$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$710$$ −1.61803 1.17557i −1.61803 1.17557i
$$711$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$712$$ −0.618034 1.90211i −0.618034 1.90211i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −0.500000 0.363271i −0.500000 0.363271i
$$716$$ 0 0
$$717$$ 0.500000 0.363271i 0.500000 0.363271i
$$718$$ −1.00000 3.07768i −1.00000 3.07768i
$$719$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0.500000 1.53884i 0.500000 1.53884i
$$723$$ 0 0
$$724$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$725$$ 0 0
$$726$$ 0.500000 1.53884i 0.500000 1.53884i
$$727$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$728$$ 0 0
$$729$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$733$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$734$$ −0.809017 2.48990i −0.809017 2.48990i
$$735$$ 0.500000 0.363271i 0.500000 0.363271i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −3.23607 −3.23607
$$739$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i $$-0.600000\pi$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0.118034 + 0.363271i 0.118034 + 0.363271i
$$746$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$747$$ −0.618034 −0.618034
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$751$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$762$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0.809017 2.48990i 0.809017 2.48990i
$$767$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$768$$ 0.809017 0.587785i 0.809017 0.587785i
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i $$0.200000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$774$$ 0.309017 0.951057i 0.309017 0.951057i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ −1.00000 −1.00000
$$781$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0.309017 0.951057i 0.309017 0.951057i
$$786$$ 0 0
$$787$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$788$$ 0.809017 2.48990i 0.809017 2.48990i
$$789$$ 0 0
$$790$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$791$$ 0 0
$$792$$ −0.309017 0.951057i −0.309017 0.951057i
$$793$$ −1.61803 −1.61803
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −0.809017 + 2.48990i −0.809017 + 2.48990i
$$797$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$798$$ 0 0