# Properties

 Label 2008.1.j.a.651.1 Level 2008 Weight 1 Character 2008.651 Analytic conductor 1.002 Analytic rank 0 Dimension 4 Projective image $$D_{5}$$ CM discriminant -8 Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2008 = 2^{3} \cdot 251$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2008.j (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.00212254537$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image $$D_{5}$$ Projective field Galois closure of 5.1.254024064064.1

## Embedding invariants

 Embedding label 651.1 Root $$0.809017 + 0.587785i$$ of defining polynomial Character $$\chi$$ $$=$$ 2008.651 Dual form 2008.1.j.a.219.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(-0.500000 + 0.363271i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.363271i) q^{6} +1.00000 q^{8} +(-0.190983 + 0.587785i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(-0.500000 + 0.363271i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.363271i) q^{6} +1.00000 q^{8} +(-0.190983 + 0.587785i) q^{9} +(1.30902 - 0.951057i) q^{11} +(-0.500000 + 0.363271i) q^{12} +1.00000 q^{16} +(-1.61803 - 1.17557i) q^{17} +(-0.190983 + 0.587785i) q^{18} +(0.618034 + 1.90211i) q^{19} +(1.30902 - 0.951057i) q^{22} +(-0.500000 + 0.363271i) q^{24} +1.00000 q^{25} +(-0.309017 - 0.951057i) q^{27} +1.00000 q^{32} +(-0.309017 + 0.951057i) q^{33} +(-1.61803 - 1.17557i) q^{34} +(-0.190983 + 0.587785i) q^{36} +(0.618034 + 1.90211i) q^{38} +(-0.500000 - 0.363271i) q^{41} +(-0.500000 + 1.53884i) q^{43} +(1.30902 - 0.951057i) q^{44} +(-0.500000 + 0.363271i) q^{48} +(-0.809017 + 0.587785i) q^{49} +1.00000 q^{50} +1.23607 q^{51} +(-0.309017 - 0.951057i) q^{54} +(-1.00000 - 0.726543i) q^{57} +(1.30902 - 0.951057i) q^{59} +1.00000 q^{64} +(-0.309017 + 0.951057i) q^{66} +(-0.500000 - 0.363271i) q^{67} +(-1.61803 - 1.17557i) q^{68} +(-0.190983 + 0.587785i) q^{72} +(-1.61803 - 1.17557i) q^{73} +(-0.500000 + 0.363271i) q^{75} +(0.618034 + 1.90211i) q^{76} +(-0.500000 - 0.363271i) q^{82} +(1.30902 + 0.951057i) q^{83} +(-0.500000 + 1.53884i) q^{86} +(1.30902 - 0.951057i) q^{88} +(-0.500000 - 0.363271i) q^{89} +(-0.500000 + 0.363271i) q^{96} +(-0.500000 - 0.363271i) q^{97} +(-0.809017 + 0.587785i) q^{98} +(0.309017 + 0.951057i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + O(q^{10})$$ $$4q + 4q^{2} - 2q^{3} + 4q^{4} - 2q^{6} + 4q^{8} - 3q^{9} + 3q^{11} - 2q^{12} + 4q^{16} - 2q^{17} - 3q^{18} - 2q^{19} + 3q^{22} - 2q^{24} + 4q^{25} + q^{27} + 4q^{32} + q^{33} - 2q^{34} - 3q^{36} - 2q^{38} - 2q^{41} - 2q^{43} + 3q^{44} - 2q^{48} - q^{49} + 4q^{50} - 4q^{51} + q^{54} - 4q^{57} + 3q^{59} + 4q^{64} + q^{66} - 2q^{67} - 2q^{68} - 3q^{72} - 2q^{73} - 2q^{75} - 2q^{76} - 2q^{82} + 3q^{83} - 2q^{86} + 3q^{88} - 2q^{89} - 2q^{96} - 2q^{97} - q^{98} - q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$$.

 $$n$$ $$257$$ $$503$$ $$1005$$ $$\chi(n)$$ $$e\left(\frac{4}{5}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.00000
$$3$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$7$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$8$$ 1.00000 1.00000
$$9$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$10$$ 0 0
$$11$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$12$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$13$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$18$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$19$$ 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i $$0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.30902 0.951057i 1.30902 0.951057i
$$23$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$24$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$25$$ 1.00000 1.00000
$$26$$ 0 0
$$27$$ −0.309017 0.951057i −0.309017 0.951057i
$$28$$ 0 0
$$29$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$30$$ 0 0
$$31$$ 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
$$34$$ −1.61803 1.17557i −1.61803 1.17557i
$$35$$ 0 0
$$36$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$37$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$38$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$42$$ 0 0
$$43$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$44$$ 1.30902 0.951057i 1.30902 0.951057i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$49$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$50$$ 1.00000 1.00000
$$51$$ 1.23607 1.23607
$$52$$ 0 0
$$53$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$54$$ −0.309017 0.951057i −0.309017 0.951057i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −1.00000 0.726543i −1.00000 0.726543i
$$58$$ 0 0
$$59$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$60$$ 0 0
$$61$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$67$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$68$$ −1.61803 1.17557i −1.61803 1.17557i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$72$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$73$$ −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 0.587785i $$-0.800000\pi$$
$$74$$ 0 0
$$75$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$76$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −0.500000 0.363271i −0.500000 0.363271i
$$83$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$87$$ 0 0
$$88$$ 1.30902 0.951057i 1.30902 0.951057i
$$89$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−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
$$96$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$97$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$98$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$99$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$100$$ 1.00000 1.00000
$$101$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$102$$ 1.23607 1.23607
$$103$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$108$$ −0.309017 0.951057i −0.309017 0.951057i
$$109$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$114$$ −1.00000 0.726543i −1.00000 0.726543i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 1.30902 0.951057i 1.30902 0.951057i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.500000 1.53884i 0.500000 1.53884i
$$122$$ 0 0
$$123$$ 0.381966 0.381966
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$128$$ 1.00000 1.00000
$$129$$ −0.309017 0.951057i −0.309017 0.951057i
$$130$$ 0 0
$$131$$ −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i $$0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$132$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$133$$ 0 0
$$134$$ −0.500000 0.363271i −0.500000 0.363271i
$$135$$ 0 0
$$136$$ −1.61803 1.17557i −1.61803 1.17557i
$$137$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$138$$ 0 0
$$139$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$145$$ 0 0
$$146$$ −1.61803 1.17557i −1.61803 1.17557i
$$147$$ 0.190983 0.587785i 0.190983 0.587785i
$$148$$ 0 0
$$149$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$150$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$153$$ 1.00000 0.726543i 1.00000 0.726543i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$164$$ −0.500000 0.363271i −0.500000 0.363271i
$$165$$ 0 0
$$166$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$167$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$168$$ 0 0
$$169$$ −0.809017 0.587785i −0.809017 0.587785i
$$170$$ 0 0
$$171$$ −1.23607 −1.23607
$$172$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$173$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.30902 0.951057i 1.30902 0.951057i
$$177$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$178$$ −0.500000 0.363271i −0.500000 0.363271i
$$179$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$180$$ 0 0
$$181$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.23607 −3.23607
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$192$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$193$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$194$$ −0.500000 0.363271i −0.500000 0.363271i
$$195$$ 0 0
$$196$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$197$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$198$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$199$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$200$$ 1.00000 1.00000
$$201$$ 0.381966 0.381966
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 1.23607 1.23607
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 2.61803 + 1.90211i 2.61803 + 1.90211i
$$210$$ 0 0
$$211$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0.190983 0.587785i 0.190983 0.587785i
$$215$$ 0 0
$$216$$ −0.309017 0.951057i −0.309017 0.951057i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 1.23607 1.23607
$$220$$ 0 0
$$221$$ 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
$$225$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$226$$ −1.61803 −1.61803
$$227$$ −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i $$0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$228$$ −1.00000 0.726543i −1.00000 0.726543i
$$229$$ 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
$$233$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 1.30902 0.951057i 1.30902 0.951057i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$240$$ 0 0
$$241$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$242$$ 0.500000 1.53884i 0.500000 1.53884i
$$243$$ 1.00000 1.00000
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.381966 0.381966
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.00000 −1.00000
$$250$$ 0 0
$$251$$ 0.309017 0.951057i 0.309017 0.951057i
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$258$$ −0.309017 0.951057i −0.309017 0.951057i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1.61803 + 1.17557i −1.61803 + 1.17557i
$$263$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$264$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0.381966 0.381966
$$268$$ −0.500000 0.363271i −0.500000 0.363271i
$$269$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ −1.61803 1.17557i −1.61803 1.17557i
$$273$$ 0 0
$$274$$ −0.500000 0.363271i −0.500000 0.363271i
$$275$$ 1.30902 0.951057i 1.30902 0.951057i
$$276$$ 0 0
$$277$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$278$$ −0.500000 1.53884i −0.500000 1.53884i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$282$$ 0 0
$$283$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$289$$ 0.927051 + 2.85317i 0.927051 + 2.85317i
$$290$$ 0 0
$$291$$ 0.381966 0.381966
$$292$$ −1.61803 1.17557i −1.61803 1.17557i
$$293$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$294$$ 0.190983 0.587785i 0.190983 0.587785i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −1.30902 0.951057i −1.30902 0.951057i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$305$$ 0 0
$$306$$ 1.00000 0.726543i 1.00000 0.726543i
$$307$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$312$$ 0 0
$$313$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0.118034 + 0.363271i 0.118034 + 0.363271i
$$322$$ 0 0
$$323$$ 1.23607 3.80423i 1.23607 3.80423i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$327$$ 0 0
$$328$$ −0.500000 0.363271i −0.500000 0.363271i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$332$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 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 $$0.800000\pi$$
$$338$$ −0.809017 0.587785i −0.809017 0.587785i
$$339$$ 0.809017 0.587785i 0.809017 0.587785i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −1.23607 −1.23607
$$343$$ 0 0
$$344$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$348$$ 0 0
$$349$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.30902 0.951057i 1.30902 0.951057i
$$353$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$354$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$355$$ 0 0
$$356$$ −0.500000 0.363271i −0.500000 0.363271i
$$357$$ 0 0
$$358$$ 0.190983 0.587785i 0.190983 0.587785i
$$359$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$360$$ 0 0
$$361$$ −2.42705 + 1.76336i −2.42705 + 1.76336i
$$362$$ 0 0
$$363$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$368$$ 0 0
$$369$$ 0.309017 0.224514i 0.309017 0.224514i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$374$$ −3.23607 −3.23607
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$384$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$385$$ 0 0
$$386$$ −0.500000 1.53884i −0.500000 1.53884i
$$387$$ −0.809017 0.587785i −0.809017 0.587785i
$$388$$ −0.500000 0.363271i −0.500000 0.363271i
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$393$$ 0.381966 1.17557i 0.381966 1.17557i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$397$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$402$$ 0.381966 0.381966
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 1.23607 1.23607
$$409$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$410$$ 0 0
$$411$$ 0.381966 0.381966
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$418$$ 2.61803 + 1.90211i 2.61803 + 1.90211i
$$419$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$420$$ 0 0
$$421$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$422$$ 0.618034 0.618034
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −1.61803 1.17557i −1.61803 1.17557i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0.190983 0.587785i 0.190983 0.587785i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$432$$ −0.309017 0.951057i −0.309017 0.951057i
$$433$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 1.23607 1.23607
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ −0.190983 0.587785i −0.190983 0.587785i
$$442$$ 0 0
$$443$$ −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i $$0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$450$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$451$$ −1.00000 −1.00000
$$452$$ −1.61803 −1.61803
$$453$$ 0 0
$$454$$ −1.61803 + 1.17557i −1.61803 + 1.17557i
$$455$$ 0 0
$$456$$ −1.00000 0.726543i −1.00000 0.726543i
$$457$$ 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i $$-0.400000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$458$$ 0 0
$$459$$ −0.618034 + 1.90211i −0.618034 + 1.90211i
$$460$$ 0 0
$$461$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$462$$ 0 0
$$463$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$467$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.30902 0.951057i 1.30902 0.951057i
$$473$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$474$$ 0 0
$$475$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0.618034 0.618034
$$483$$ 0 0
$$484$$ 0.500000 1.53884i 0.500000 1.53884i
$$485$$ 0 0
$$486$$ 1.00000 1.00000
$$487$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$488$$ 0 0
$$489$$ 0.118034 0.363271i 0.118034 0.363271i
$$490$$ 0 0
$$491$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$492$$ 0.381966 0.381966
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −1.00000 −1.00000
$$499$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0.309017 0.951057i 0.309017 0.951057i
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0.618034 0.618034
$$508$$ 0 0
$$509$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 1.00000
$$513$$ 1.61803 1.17557i 1.61803 1.17557i
$$514$$ 1.30902 0.951057i 1.30902 0.951057i
$$515$$ 0 0
$$516$$ −0.309017 0.951057i −0.309017 0.951057i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$522$$ 0 0
$$523$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$524$$ −1.61803 + 1.17557i −1.61803 + 1.17557i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$529$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$530$$ 0 0
$$531$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0.381966 0.381966
$$535$$ 0 0
$$536$$ −0.500000 0.363271i −0.500000 0.363271i
$$537$$ 0.118034 + 0.363271i 0.118034 + 0.363271i
$$538$$ 0 0
$$539$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$540$$ 0 0
$$541$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ −1.61803 1.17557i −1.61803 1.17557i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$548$$ −0.500000 0.363271i −0.500000 0.363271i
$$549$$ 0 0
$$550$$ 1.30902 0.951057i 1.30902 0.951057i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.500000 1.53884i −0.500000 1.53884i
$$557$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 1.61803 1.17557i 1.61803 1.17557i
$$562$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$563$$ 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i $$0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0.618034 0.618034
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$570$$ 0 0
$$571$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$577$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$578$$ 0.927051 + 2.85317i 0.927051 + 2.85317i
$$579$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0.381966 0.381966
$$583$$ 0 0
$$584$$ −1.61803 1.17557i −1.61803 1.17557i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$588$$ 0.190983 0.587785i 0.190983 0.587785i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$594$$ −1.30902 0.951057i −1.30902 0.951057i
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 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
$$601$$ 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i $$0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$602$$ 0 0
$$603$$ 0.309017 0.224514i 0.309017 0.224514i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$608$$ 0.618034 + 1.90211i 0.618034 + 1.90211i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 1.00000 0.726543i 1.00000 0.726543i
$$613$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$614$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$618$$ 0 0
$$619$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$627$$ −2.00000 −2.00000
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$632$$ 0 0
$$633$$ −0.309017 + 0.224514i −0.309017 + 0.224514i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 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 $$0.400000\pi$$
$$642$$ 0.118034 + 0.363271i 0.118034 + 0.363271i
$$643$$ 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i $$-0.400000\pi$$
1.00000 $$0$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 1.23607 3.80423i 1.23607 3.80423i
$$647$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$648$$ 0 0
$$649$$ 0.809017 2.48990i 0.809017 2.48990i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −0.500000 0.363271i −0.500000 0.363271i
$$657$$ 1.00000 0.726543i 1.00000 0.726543i
$$658$$ 0 0
$$659$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$660$$ 0 0
$$661$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$662$$ −1.61803 −1.61803
$$663$$ 0 0
$$664$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$674$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$675$$ −0.309017 0.951057i −0.309017 0.951057i
$$676$$ −0.809017 0.587785i −0.809017 0.587785i
$$677$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$678$$ 0.809017 0.587785i 0.809017 0.587785i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.381966 1.17557i 0.381966 1.17557i
$$682$$ 0 0
$$683$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$684$$ −1.23607 −1.23607
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 1.30902 0.951057i 1.30902 0.951057i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0.381966 + 1.17557i 0.381966 + 1.17557i
$$698$$ 0 0
$$699$$ −0.309017 0.951057i −0.309017 0.951057i
$$700$$ 0 0
$$701$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 1.30902 0.951057i 1.30902 0.951057i
$$705$$ 0 0
$$706$$ 2.00000 2.00000
$$707$$ 0 0
$$708$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$709$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −0.500000 0.363271i −0.500000 0.363271i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0.190983 0.587785i 0.190983 0.587785i
$$717$$ 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
$$722$$ −2.42705 + 1.76336i −2.42705 + 1.76336i
$$723$$ −0.309017 + 0.224514i −0.309017 + 0.224514i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$727$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$728$$ 0 0
$$729$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$730$$ 0 0
$$731$$ 2.61803 1.90211i 2.61803 1.90211i
$$732$$ 0 0
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.00000 −1.00000
$$738$$ 0.309017 0.224514i 0.309017 0.224514i
$$739$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
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
$$746$$ 0 0
$$747$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$748$$ −3.23607 −3.23607
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0.618034 0.618034
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$769$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$770$$ 0 0
$$771$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$772$$ −0.500000 1.53884i −0.500000 1.53884i
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ −0.809017 0.587785i −0.809017 0.587785i
$$775$$ 0 0
$$776$$ −0.500000 0.363271i −0.500000 0.363271i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0.381966 1.17557i 0.381966 1.17557i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$785$$ 0 0
$$786$$ 0.381966 1.17557i 0.381966 1.17557i
$$787$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 1.00000 1.00000
$$801$$ 0.309017 0.224514i 0.309017 0.224514i
$$802$$ 1.30902 0.951057i 1.30902 0.951057i
$$803$$ −3.23607 −3.23607
$$804$$ 0.381966 0.381966
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$810$$ 0 0