# Properties

 Label 633.1.m.b.71.2 Level 633 Weight 1 Character 633.71 Analytic conductor 0.316 Analytic rank 0 Dimension 8 Projective image $$A_{5}$$ CM/RM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$633 = 3 \cdot 211$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 633.m (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.315908152997$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{10})$$ Coefficient field: $$\Q(\zeta_{20})$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image $$A_{5}$$ Projective field Galois closure of 5.1.17839074969.1

## Embedding invariants

 Embedding label 71.2 Root $$-0.951057 + 0.309017i$$ of $$x^{8} - x^{6} + x^{4} - x^{2} + 1$$ Character $$\chi$$ $$=$$ 633.71 Dual form 633.1.m.b.107.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.951057 + 1.30902i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(0.951057 + 0.309017i) q^{5} +(0.951057 - 1.30902i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$$ $$q+(0.951057 + 1.30902i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 + 1.53884i) q^{4} +(0.951057 + 0.309017i) q^{5} +(0.951057 - 1.30902i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.500000 + 1.53884i) q^{10} +(0.587785 + 0.190983i) q^{11} +1.61803 q^{12} +(0.809017 + 0.587785i) q^{13} -1.61803i q^{14} -1.00000i q^{15} +(-0.363271 + 0.500000i) q^{17} +(-1.53884 - 0.500000i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.951057 + 1.30902i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(0.309017 + 0.951057i) q^{22} +(-0.587785 - 0.809017i) q^{23} +(0.587785 + 0.809017i) q^{24} +1.61803i q^{26} +(0.809017 + 0.587785i) q^{27} +(1.30902 - 0.951057i) q^{28} +(0.951057 - 1.30902i) q^{29} +(1.30902 - 0.951057i) q^{30} -1.61803 q^{31} +1.00000i q^{32} -0.618034i q^{33} -1.00000 q^{34} +(-0.587785 - 0.809017i) q^{35} +(-0.500000 - 1.53884i) q^{36} -1.61803i q^{38} +(0.309017 - 0.951057i) q^{39} -1.00000 q^{40} +(-0.587785 - 0.190983i) q^{41} +(-1.53884 + 0.500000i) q^{42} -1.00000 q^{43} +(-0.587785 + 0.809017i) q^{44} +(-0.951057 + 0.309017i) q^{45} +(0.500000 - 1.53884i) q^{46} +(-0.951057 + 1.30902i) q^{47} +(0.587785 + 0.190983i) q^{51} +(-1.30902 + 0.951057i) q^{52} +1.61803i q^{54} +(0.500000 + 0.363271i) q^{55} +(0.951057 + 0.309017i) q^{56} +(-0.309017 + 0.951057i) q^{57} +2.61803 q^{58} +(1.53884 + 0.500000i) q^{60} +(-0.190983 - 0.587785i) q^{61} +(-1.53884 - 2.11803i) q^{62} +1.00000 q^{63} +(-1.30902 + 0.951057i) q^{64} +(0.587785 + 0.809017i) q^{65} +(0.809017 - 0.587785i) q^{66} +(-0.587785 - 0.809017i) q^{68} +(-0.587785 + 0.809017i) q^{69} +(0.500000 - 1.53884i) q^{70} +(1.53884 - 0.500000i) q^{71} +(0.587785 - 0.809017i) q^{72} -1.00000 q^{73} +(1.30902 - 0.951057i) q^{76} +(-0.363271 - 0.500000i) q^{77} +(1.53884 - 0.500000i) q^{78} +(0.309017 - 0.951057i) q^{81} +(-0.309017 - 0.951057i) q^{82} +(1.53884 + 0.500000i) q^{83} +(-1.30902 - 0.951057i) q^{84} +(-0.500000 + 0.363271i) q^{85} +(-0.951057 - 1.30902i) q^{86} +(-1.53884 - 0.500000i) q^{87} -0.618034 q^{88} +(0.587785 - 0.809017i) q^{89} +(-1.30902 - 0.951057i) q^{90} +(-0.309017 - 0.951057i) q^{91} +(1.53884 - 0.500000i) q^{92} +(0.500000 + 1.53884i) q^{93} -2.61803 q^{94} +(-0.587785 - 0.809017i) q^{95} +(0.951057 - 0.309017i) q^{96} +(-0.587785 + 0.190983i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 2q^{3} - 4q^{4} - 2q^{7} - 2q^{9} + O(q^{10})$$ $$8q + 2q^{3} - 4q^{4} - 2q^{7} - 2q^{9} + 4q^{10} + 4q^{12} + 2q^{13} - 2q^{19} + 2q^{21} - 2q^{22} + 2q^{27} + 6q^{28} + 6q^{30} - 4q^{31} - 8q^{34} - 4q^{36} - 2q^{39} - 8q^{40} - 8q^{43} + 4q^{46} - 6q^{52} + 4q^{55} + 2q^{57} + 12q^{58} - 6q^{61} + 8q^{63} - 6q^{64} + 2q^{66} + 4q^{70} - 8q^{73} + 6q^{76} - 2q^{81} + 2q^{82} - 6q^{84} - 4q^{85} + 4q^{88} - 6q^{90} + 2q^{91} + 4q^{93} - 12q^{94} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$$.

 $$n$$ $$212$$ $$424$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i $$0.100000\pi$$
1.00000i $$0.5\pi$$
$$3$$ −0.309017 0.951057i −0.309017 0.951057i
$$4$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$5$$ 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i $$-0.233333\pi$$
0.207912 + 0.978148i $$0.433333\pi$$
$$6$$ 0.951057 1.30902i 0.951057 1.30902i
$$7$$ −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i $$-0.466667\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$8$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$9$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$10$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$11$$ 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i $$-0.300000\pi$$
1.00000i $$0.5\pi$$
$$12$$ 1.61803 1.61803
$$13$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$14$$ 1.61803i 1.61803i
$$15$$ 1.00000i 1.00000i
$$16$$ 0 0
$$17$$ −0.363271 + 0.500000i −0.363271 + 0.500000i −0.951057 0.309017i $$-0.900000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$18$$ −1.53884 0.500000i −1.53884 0.500000i
$$19$$ −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i $$-0.466667\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$20$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$21$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$22$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$23$$ −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i $$-0.366667\pi$$
−0.994522 + 0.104528i $$0.966667\pi$$
$$24$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$25$$ 0 0
$$26$$ 1.61803i 1.61803i
$$27$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$28$$ 1.30902 0.951057i 1.30902 0.951057i
$$29$$ 0.951057 1.30902i 0.951057 1.30902i 1.00000i $$-0.5\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$30$$ 1.30902 0.951057i 1.30902 0.951057i
$$31$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$32$$ 1.00000i 1.00000i
$$33$$ 0.618034i 0.618034i
$$34$$ −1.00000 −1.00000
$$35$$ −0.587785 0.809017i −0.587785 0.809017i
$$36$$ −0.500000 1.53884i −0.500000 1.53884i
$$37$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$38$$ 1.61803i 1.61803i
$$39$$ 0.309017 0.951057i 0.309017 0.951057i
$$40$$ −1.00000 −1.00000
$$41$$ −0.587785 0.190983i −0.587785 0.190983i 1.00000i $$-0.5\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$42$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$43$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$44$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$45$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$46$$ 0.500000 1.53884i 0.500000 1.53884i
$$47$$ −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i $$0.5\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 0.587785 + 0.190983i 0.587785 + 0.190983i
$$52$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$53$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$54$$ 1.61803i 1.61803i
$$55$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$56$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$57$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$58$$ 2.61803 2.61803
$$59$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$60$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$61$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$62$$ −1.53884 2.11803i −1.53884 2.11803i
$$63$$ 1.00000 1.00000
$$64$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$65$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$66$$ 0.809017 0.587785i 0.809017 0.587785i
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ −0.587785 0.809017i −0.587785 0.809017i
$$69$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$70$$ 0.500000 1.53884i 0.500000 1.53884i
$$71$$ 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i $$-0.300000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$72$$ 0.587785 0.809017i 0.587785 0.809017i
$$73$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.30902 0.951057i 1.30902 0.951057i
$$77$$ −0.363271 0.500000i −0.363271 0.500000i
$$78$$ 1.53884 0.500000i 1.53884 0.500000i
$$79$$ 0 0 −0.951057 0.309017i $$-0.900000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$80$$ 0 0
$$81$$ 0.309017 0.951057i 0.309017 0.951057i
$$82$$ −0.309017 0.951057i −0.309017 0.951057i
$$83$$ 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i $$-0.100000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$84$$ −1.30902 0.951057i −1.30902 0.951057i
$$85$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$86$$ −0.951057 1.30902i −0.951057 1.30902i
$$87$$ −1.53884 0.500000i −1.53884 0.500000i
$$88$$ −0.618034 −0.618034
$$89$$ 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i $$-0.633333\pi$$
0.994522 + 0.104528i $$0.0333333\pi$$
$$90$$ −1.30902 0.951057i −1.30902 0.951057i
$$91$$ −0.309017 0.951057i −0.309017 0.951057i
$$92$$ 1.53884 0.500000i 1.53884 0.500000i
$$93$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$94$$ −2.61803 −2.61803
$$95$$ −0.587785 0.809017i −0.587785 0.809017i
$$96$$ 0.951057 0.309017i 0.951057 0.309017i
$$97$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$98$$ 0 0
$$99$$ −0.587785 + 0.190983i −0.587785 + 0.190983i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$103$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$104$$ −0.951057 0.309017i −0.951057 0.309017i
$$105$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$106$$ 0 0
$$107$$ 1.90211 + 0.618034i 1.90211 + 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$108$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$109$$ 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i $$0.0666667\pi$$
−0.669131 + 0.743145i $$0.733333\pi$$
$$110$$ 1.00000i 1.00000i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$114$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$115$$ −0.309017 0.951057i −0.309017 0.951057i
$$116$$ 1.53884 + 2.11803i 1.53884 + 2.11803i
$$117$$ −1.00000 −1.00000
$$118$$ 0 0
$$119$$ 0.587785 0.190983i 0.587785 0.190983i
$$120$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$121$$ −0.500000 0.363271i −0.500000 0.363271i
$$122$$ 0.587785 0.809017i 0.587785 0.809017i
$$123$$ 0.618034i 0.618034i
$$124$$ 0.809017 2.48990i 0.809017 2.48990i
$$125$$ −0.587785 0.809017i −0.587785 0.809017i
$$126$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$127$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$128$$ −1.53884 0.500000i −1.53884 0.500000i
$$129$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$130$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$131$$ −0.363271 0.500000i −0.363271 0.500000i 0.587785 0.809017i $$-0.300000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$132$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$133$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$134$$ 0 0
$$135$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$136$$ 0.190983 0.587785i 0.190983 0.587785i
$$137$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$138$$ −1.61803 −1.61803
$$139$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$140$$ 1.53884 0.500000i 1.53884 0.500000i
$$141$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$142$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$143$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$144$$ 0 0
$$145$$ 1.30902 0.951057i 1.30902 0.951057i
$$146$$ −0.951057 1.30902i −0.951057 1.30902i
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0.951057 + 1.30902i 0.951057 + 1.30902i 0.951057 + 0.309017i $$0.100000\pi$$
1.00000i $$0.5\pi$$
$$150$$ 0 0
$$151$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$152$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$153$$ 0.618034i 0.618034i
$$154$$ 0.309017 0.951057i 0.309017 0.951057i
$$155$$ −1.53884 0.500000i −1.53884 0.500000i
$$156$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$157$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$161$$ 1.00000i 1.00000i
$$162$$ 1.53884 0.500000i 1.53884 0.500000i
$$163$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$164$$ 0.587785 0.809017i 0.587785 0.809017i
$$165$$ 0.190983 0.587785i 0.190983 0.587785i
$$166$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$167$$ −0.951057 + 1.30902i −0.951057 + 1.30902i 1.00000i $$0.5\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$168$$ 1.00000i 1.00000i
$$169$$ 0 0
$$170$$ −0.951057 0.309017i −0.951057 0.309017i
$$171$$ 1.00000 1.00000
$$172$$ 0.500000 1.53884i 0.500000 1.53884i
$$173$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$174$$ −0.809017 2.48990i −0.809017 2.48990i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 1.61803 1.61803
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 1.61803i 1.61803i
$$181$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$182$$ 0.951057 1.30902i 0.951057 1.30902i
$$183$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$184$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$185$$ 0 0
$$186$$ −1.53884 + 2.11803i −1.53884 + 2.11803i
$$187$$ −0.309017 + 0.224514i −0.309017 + 0.224514i
$$188$$ −1.53884 2.11803i −1.53884 2.11803i
$$189$$ −0.309017 0.951057i −0.309017 0.951057i
$$190$$ 0.500000 1.53884i 0.500000 1.53884i
$$191$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$192$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$193$$ 0 0 −0.951057 0.309017i $$-0.900000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$194$$ 0 0
$$195$$ 0.587785 0.809017i 0.587785 0.809017i
$$196$$ 0 0
$$197$$ 1.61803i 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$198$$ −0.809017 0.587785i −0.809017 0.587785i
$$199$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$204$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$205$$ −0.500000 0.363271i −0.500000 0.363271i
$$206$$ 0 0
$$207$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$208$$ 0 0
$$209$$ −0.363271 0.500000i −0.363271 0.500000i
$$210$$ −1.61803 −1.61803
$$211$$ −0.809017 0.587785i −0.809017 0.587785i
$$212$$ 0 0
$$213$$ −0.951057 1.30902i −0.951057 1.30902i
$$214$$ 1.00000 + 3.07768i 1.00000 + 3.07768i
$$215$$ −0.951057 0.309017i −0.951057 0.309017i
$$216$$ −0.951057 0.309017i −0.951057 0.309017i
$$217$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$218$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$219$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$220$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$221$$ −0.587785 + 0.190983i −0.587785 + 0.190983i
$$222$$ 0 0
$$223$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$224$$ 0.587785 0.809017i 0.587785 0.809017i
$$225$$ 0 0
$$226$$ −1.61803 −1.61803
$$227$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$228$$ −1.30902 0.951057i −1.30902 0.951057i
$$229$$ −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i $$0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$230$$ 0.951057 1.30902i 0.951057 1.30902i
$$231$$ −0.363271 + 0.500000i −0.363271 + 0.500000i
$$232$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$233$$ 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i $$-0.300000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$234$$ −0.951057 1.30902i −0.951057 1.30902i
$$235$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$239$$ 0 0 0.809017 0.587785i $$-0.200000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$240$$ 0 0
$$241$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ −1.00000 −1.00000
$$244$$ 1.00000 1.00000
$$245$$ 0 0
$$246$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$247$$ −0.309017 0.951057i −0.309017 0.951057i
$$248$$ 1.53884 0.500000i 1.53884 0.500000i
$$249$$ 1.61803i 1.61803i
$$250$$ 0.500000 1.53884i 0.500000 1.53884i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$253$$ −0.190983 0.587785i −0.190983 0.587785i
$$254$$ 1.61803i 1.61803i
$$255$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$256$$ −0.309017 0.951057i −0.309017 0.951057i
$$257$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$258$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$259$$ 0 0
$$260$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$261$$ 1.61803i 1.61803i
$$262$$ 0.309017 0.951057i 0.309017 0.951057i
$$263$$ 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i $$-0.0333333\pi$$
−0.406737 + 0.913545i $$0.633333\pi$$
$$264$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$265$$ 0 0
$$266$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$267$$ −0.951057 0.309017i −0.951057 0.309017i
$$268$$ 0 0
$$269$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$270$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$271$$ 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i $$-0.800000\pi$$
1.00000 $$0$$
$$272$$ 0 0
$$273$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$274$$ −1.61803 −1.61803
$$275$$ 0 0
$$276$$ −0.951057 1.30902i −0.951057 1.30902i
$$277$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$278$$ 1.61803i 1.61803i
$$279$$ 1.30902 0.951057i 1.30902 0.951057i
$$280$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$281$$ −0.587785 0.190983i −0.587785 0.190983i 1.00000i $$-0.5\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$282$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$283$$ −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i $$-0.466667\pi$$
−0.913545 + 0.406737i $$0.866667\pi$$
$$284$$ 2.61803i 2.61803i
$$285$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$286$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$287$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$288$$ −0.587785 0.809017i −0.587785 0.809017i
$$289$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$290$$ 2.48990 + 0.809017i 2.48990 + 0.809017i
$$291$$ 0 0
$$292$$ 0.500000 1.53884i 0.500000 1.53884i
$$293$$ −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i $$-0.766667\pi$$
−0.207912 + 0.978148i $$0.566667\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$298$$ −0.809017 + 2.48990i −0.809017 + 2.48990i
$$299$$ 1.00000i 1.00000i
$$300$$ 0 0
$$301$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$302$$ 0.951057 0.309017i 0.951057 0.309017i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0.618034i 0.618034i
$$306$$ 0.809017 0.587785i 0.809017 0.587785i
$$307$$ −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i $$-0.933333\pi$$
0.669131 0.743145i $$-0.266667\pi$$
$$308$$ 0.951057 0.309017i 0.951057 0.309017i
$$309$$ 0 0
$$310$$ −0.809017 2.48990i −0.809017 2.48990i
$$311$$ −0.587785 0.809017i −0.587785 0.809017i 0.406737 0.913545i $$-0.366667\pi$$
−0.994522 + 0.104528i $$0.966667\pi$$
$$312$$ 1.00000i 1.00000i
$$313$$ −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 0.951057i $$-0.400000\pi$$
$$314$$ −0.951057 1.30902i −0.951057 1.30902i
$$315$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$316$$ 0 0
$$317$$ 0.587785 0.809017i 0.587785 0.809017i −0.406737 0.913545i $$-0.633333\pi$$
0.994522 + 0.104528i $$0.0333333\pi$$
$$318$$ 0 0
$$319$$ 0.809017 0.587785i 0.809017 0.587785i
$$320$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$321$$ 2.00000i 2.00000i
$$322$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$323$$ 0.587785 0.190983i 0.587785 0.190983i
$$324$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$325$$ 0 0
$$326$$ 1.53884 0.500000i 1.53884 0.500000i
$$327$$ 0.809017 0.587785i 0.809017 0.587785i
$$328$$ 0.618034 0.618034
$$329$$ 1.53884 0.500000i 1.53884 0.500000i
$$330$$ 0.951057 0.309017i 0.951057 0.309017i
$$331$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$332$$ −1.53884 + 2.11803i −1.53884 + 2.11803i
$$333$$ 0 0
$$334$$ −2.61803 −2.61803
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i $$-0.533333\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$338$$ 0 0
$$339$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$340$$ −0.309017 0.951057i −0.309017 0.951057i
$$341$$ −0.951057 0.309017i −0.951057 0.309017i
$$342$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$343$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$344$$ 0.951057 0.309017i 0.951057 0.309017i
$$345$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$346$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$347$$ 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i $$-0.300000\pi$$
1.00000i $$0.5\pi$$
$$348$$ 1.53884 2.11803i 1.53884 2.11803i
$$349$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$350$$ 0 0
$$351$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$352$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$353$$ 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i $$-0.700000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$354$$ 0 0
$$355$$ 1.61803 1.61803
$$356$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$357$$ −0.363271 0.500000i −0.363271 0.500000i
$$358$$ 0 0
$$359$$ 0.618034i 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$360$$ 0.809017 0.587785i 0.809017 0.587785i
$$361$$ 0 0
$$362$$ 0 0
$$363$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$364$$ 1.61803 1.61803
$$365$$ −0.951057 0.309017i −0.951057 0.309017i
$$366$$ −0.951057 0.309017i −0.951057 0.309017i
$$367$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$368$$ 0 0
$$369$$ 0.587785 0.190983i 0.587785 0.190983i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ −2.61803 −2.61803
$$373$$ −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i $$-0.200000\pi$$
−1.00000 $$\pi$$
$$374$$ −0.587785 0.190983i −0.587785 0.190983i
$$375$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$376$$ 0.500000 1.53884i 0.500000 1.53884i
$$377$$ 1.53884 0.500000i 1.53884 0.500000i
$$378$$ 0.951057 1.30902i 0.951057 1.30902i
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 1.53884 0.500000i 1.53884 0.500000i
$$381$$ 0.309017 0.951057i 0.309017 0.951057i
$$382$$ −1.61803 −1.61803
$$383$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$384$$ 1.61803i 1.61803i
$$385$$ −0.190983 0.587785i −0.190983 0.587785i
$$386$$ 0 0
$$387$$ 0.809017 0.587785i 0.809017 0.587785i
$$388$$ 0 0
$$389$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$390$$ 1.61803 1.61803
$$391$$ 0.618034 0.618034
$$392$$ 0 0
$$393$$ −0.363271 + 0.500000i −0.363271 + 0.500000i
$$394$$ 2.11803 1.53884i 2.11803 1.53884i
$$395$$ 0 0
$$396$$ 1.00000i 1.00000i
$$397$$ −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i $$-0.400000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$398$$ 1.53884 + 2.11803i 1.53884 + 2.11803i
$$399$$ 0.809017 0.587785i 0.809017 0.587785i
$$400$$ 0 0
$$401$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$402$$ 0 0
$$403$$ −1.30902 0.951057i −1.30902 0.951057i
$$404$$ 0 0
$$405$$ 0.587785 0.809017i 0.587785 0.809017i
$$406$$ −2.11803 1.53884i −2.11803 1.53884i
$$407$$ 0 0
$$408$$ −0.618034 −0.618034
$$409$$ 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 $$0$$
0.309017 + 0.951057i $$0.400000\pi$$
$$410$$ 1.00000i 1.00000i
$$411$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$415$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$416$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$417$$ 0.309017 0.951057i 0.309017 0.951057i
$$418$$ 0.309017 0.951057i 0.309017 0.951057i
$$419$$ 1.53884 0.500000i 1.53884 0.500000i 0.587785 0.809017i $$-0.300000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$420$$ −0.951057 1.30902i −0.951057 1.30902i
$$421$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$422$$ 1.61803i 1.61803i
$$423$$ 1.61803i 1.61803i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0.809017 2.48990i 0.809017 2.48990i
$$427$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$428$$ −1.90211 + 2.61803i −1.90211 + 2.61803i
$$429$$ 0.363271 0.500000i 0.363271 0.500000i
$$430$$ −0.500000 1.53884i −0.500000 1.53884i
$$431$$ 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i $$-0.0333333\pi$$
−0.406737 + 0.913545i $$0.633333\pi$$
$$432$$ 0 0
$$433$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$434$$ 2.61803i 2.61803i
$$435$$ −1.30902 0.951057i −1.30902 0.951057i
$$436$$ −1.61803 −1.61803
$$437$$ 1.00000i 1.00000i
$$438$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$439$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$440$$ −0.587785 0.190983i −0.587785 0.190983i
$$441$$ 0 0
$$442$$ −0.809017 0.587785i −0.809017 0.587785i
$$443$$ −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i $$-0.566667\pi$$
−0.743145 + 0.669131i $$0.766667\pi$$
$$444$$ 0 0
$$445$$ 0.809017 0.587785i 0.809017 0.587785i
$$446$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$447$$ 0.951057 1.30902i 0.951057 1.30902i
$$448$$ 1.61803 1.61803
$$449$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$450$$ 0 0
$$451$$ −0.309017 0.224514i −0.309017 0.224514i
$$452$$ −0.951057 1.30902i −0.951057 1.30902i
$$453$$ −0.618034 −0.618034
$$454$$ −1.61803 −1.61803
$$455$$ 1.00000i 1.00000i
$$456$$ 1.00000i 1.00000i
$$457$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$458$$ −2.48990 + 0.809017i −2.48990 + 0.809017i
$$459$$ −0.587785 + 0.190983i −0.587785 + 0.190983i
$$460$$ 1.61803 1.61803
$$461$$ 0.951057 + 0.309017i 0.951057 + 0.309017i 0.743145 0.669131i $$-0.233333\pi$$
0.207912 + 0.978148i $$0.433333\pi$$
$$462$$ −1.00000 −1.00000
$$463$$ −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i $$0.266667\pi$$
−0.978148 + 0.207912i $$0.933333\pi$$
$$464$$ 0 0
$$465$$ 1.61803i 1.61803i
$$466$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$467$$ −0.951057 + 0.309017i −0.951057 + 0.309017i −0.743145 0.669131i $$-0.766667\pi$$
−0.207912 + 0.978148i $$0.566667\pi$$
$$468$$ 0.500000 1.53884i 0.500000 1.53884i
$$469$$ 0 0
$$470$$ −2.48990 0.809017i −2.48990 0.809017i
$$471$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$472$$ 0 0
$$473$$ −0.587785 0.190983i −0.587785 0.190983i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 1.00000i 1.00000i
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0.587785 + 0.190983i 0.587785 + 0.190983i 0.587785 0.809017i $$-0.300000\pi$$
1.00000i $$0.5\pi$$
$$480$$ 1.00000 1.00000
$$481$$ 0 0
$$482$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$483$$ 0.951057 0.309017i 0.951057 0.309017i
$$484$$ 0.809017 0.587785i 0.809017 0.587785i
$$485$$ 0 0
$$486$$ −0.951057 1.30902i −0.951057 1.30902i
$$487$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$488$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$489$$ −1.00000 −1.00000
$$490$$ 0 0
$$491$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$492$$ −0.951057 0.309017i −0.951057 0.309017i
$$493$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$494$$ 0.951057 1.30902i 0.951057 1.30902i
$$495$$ −0.618034 −0.618034
$$496$$ 0 0
$$497$$ −1.53884 0.500000i −1.53884 0.500000i
$$498$$ 2.11803 1.53884i 2.11803 1.53884i
$$499$$ 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i $$-0.533333\pi$$
0.913545 + 0.406737i $$0.133333\pi$$
$$500$$ 1.53884 0.500000i 1.53884 0.500000i
$$501$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$502$$ 0 0
$$503$$ 1.53884 + 0.500000i 1.53884 + 0.500000i 0.951057 0.309017i $$-0.100000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$504$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$505$$ 0 0
$$506$$ 0.587785 0.809017i 0.587785 0.809017i
$$507$$ 0 0
$$508$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$509$$ −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i $$-0.566667\pi$$
−0.743145 + 0.669131i $$0.766667\pi$$
$$510$$ 1.00000i 1.00000i
$$511$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$512$$ 0 0
$$513$$ −0.309017 0.951057i −0.309017 0.951057i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ −1.61803 −1.61803
$$517$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$518$$ 0 0
$$519$$ 0.951057 0.309017i 0.951057 0.309017i
$$520$$ −0.809017 0.587785i −0.809017 0.587785i
$$521$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$522$$ −2.11803 + 1.53884i −2.11803 + 1.53884i
$$523$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$524$$ 0.951057 0.309017i 0.951057 0.309017i
$$525$$ 0 0
$$526$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$527$$ 0.587785 0.809017i 0.587785 0.809017i
$$528$$ 0 0
$$529$$ 0 0
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −1.61803 −1.61803
$$533$$ −0.363271 0.500000i −0.363271 0.500000i
$$534$$ −0.500000 1.53884i −0.500000 1.53884i
$$535$$ 1.61803 + 1.17557i 1.61803 + 1.17557i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$541$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$542$$ 0.951057 0.309017i 0.951057 0.309017i
$$543$$ 0 0
$$544$$ −0.500000 0.363271i −0.500000 0.363271i
$$545$$ 1.00000i 1.00000i
$$546$$ −1.53884 0.500000i −1.53884 0.500000i
$$547$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$548$$ −0.951057 1.30902i −0.951057 1.30902i
$$549$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$550$$ 0 0
$$551$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$552$$ 0.309017 0.951057i 0.309017 0.951057i
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$557$$ 0.363271 + 0.500000i 0.363271 + 0.500000i 0.951057 0.309017i $$-0.100000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$558$$ 2.48990 + 0.809017i 2.48990 + 0.809017i
$$559$$ −0.809017 0.587785i −0.809017 0.587785i
$$560$$ 0 0
$$561$$ 0.309017 + 0.224514i 0.309017 + 0.224514i
$$562$$ −0.309017 0.951057i −0.309017 0.951057i
$$563$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$564$$ −1.53884 + 2.11803i −1.53884 + 2.11803i
$$565$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$566$$ 1.61803i 1.61803i
$$567$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$568$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$569$$ −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i $$-0.900000\pi$$
1.00000i $$-0.5\pi$$
$$570$$ −1.61803 −1.61803
$$571$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$572$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$573$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$574$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$575$$ 0 0
$$576$$ 0.500000 1.53884i 0.500000 1.53884i
$$577$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$578$$ −0.587785 + 0.809017i −0.587785 + 0.809017i
$$579$$ 0 0
$$580$$ 0.809017 + 2.48990i 0.809017 + 2.48990i
$$581$$ −0.951057 1.30902i −0.951057 1.30902i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0.951057 0.309017i 0.951057 0.309017i
$$585$$ −0.951057 0.309017i −0.951057 0.309017i
$$586$$ −1.30902 0.951057i −1.30902 0.951057i
$$587$$ −0.951057 0.309017i −0.951057 0.309017i −0.207912 0.978148i $$-0.566667\pi$$
−0.743145 + 0.669131i $$0.766667\pi$$
$$588$$ 0 0
$$589$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$590$$ 0 0
$$591$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$595$$ 0.618034 0.618034
$$596$$ −2.48990 + 0.809017i −2.48990 + 0.809017i
$$597$$ −0.500000 1.53884i −0.500000 1.53884i
$$598$$ 1.30902 0.951057i 1.30902 0.951057i
$$599$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 1.61803i 1.61803i
$$603$$ 0 0
$$604$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$605$$ −0.363271 0.500000i −0.363271 0.500000i
$$606$$ 0 0
$$607$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$608$$ 0.587785 0.809017i 0.587785 0.809017i
$$609$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$610$$ 0.809017 0.587785i 0.809017 0.587785i
$$611$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$612$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$613$$ 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i $$-0.133333\pi$$
−0.104528 + 0.994522i $$0.533333\pi$$
$$614$$ 0.951057 1.30902i 0.951057 1.30902i
$$615$$ −0.190983 + 0.587785i −0.190983 + 0.587785i
$$616$$ 0.500000 + 0.363271i 0.500000 + 0.363271i
$$617$$ 0 0 −0.809017 0.587785i $$-0.800000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$618$$ 0 0
$$619$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$620$$ 1.53884 2.11803i 1.53884 2.11803i
$$621$$ 1.00000i 1.00000i
$$622$$ 0.500000 1.53884i 0.500000 1.53884i
$$623$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$624$$ 0 0
$$625$$ −0.309017 0.951057i −0.309017 0.951057i
$$626$$ 1.53884 2.11803i 1.53884 2.11803i
$$627$$ −0.363271 + 0.500000i −0.363271 + 0.500000i
$$628$$ 0.500000 1.53884i 0.500000 1.53884i
$$629$$ 0 0
$$630$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$631$$ −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i $$0.600000\pi$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$634$$ 1.61803 1.61803
$$635$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$639$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$640$$ −1.30902 0.951057i −1.30902 0.951057i
$$641$$ 0.951057 0.309017i 0.951057 0.309017i 0.207912 0.978148i $$-0.433333\pi$$
0.743145 + 0.669131i $$0.233333\pi$$
$$642$$ 2.61803 1.90211i 2.61803 1.90211i
$$643$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$644$$ −1.53884 0.500000i −1.53884 0.500000i
$$645$$ 1.00000i 1.00000i
$$646$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$647$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$648$$ 1.00000i 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0.500000 1.53884i 0.500000 1.53884i
$$652$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$653$$ 0.363271 0.500000i 0.363271 0.500000i −0.587785 0.809017i $$-0.700000\pi$$
0.951057 + 0.309017i $$0.100000\pi$$
$$654$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$655$$ −0.190983 0.587785i −0.190983 0.587785i
$$656$$ 0 0
$$657$$ 0.809017 0.587785i 0.809017 0.587785i
$$658$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$661$$ 0 0 −0.587785 0.809017i $$-0.700000\pi$$
0.587785 + 0.809017i $$0.300000\pi$$
$$662$$ 0 0
$$663$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$664$$ −1.61803 −1.61803
$$665$$ 1.00000i 1.00000i
$$666$$ 0 0
$$667$$ −1.61803 −1.61803
$$668$$ −1.53884 2.11803i −1.53884 2.11803i
$$669$$ −0.309017 0.951057i −0.309017 0.951057i
$$670$$ 0 0
$$671$$ 0.381966i 0.381966i
$$672$$ −0.951057 0.309017i −0.951057 0.309017i
$$673$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$674$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −0.587785 + 0.809017i −0.587785 + 0.809017i −0.994522 0.104528i $$-0.966667\pi$$
0.406737 + 0.913545i $$0.366667\pi$$
$$678$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$679$$ 0 0
$$680$$ 0.363271 0.500000i 0.363271 0.500000i
$$681$$ 0.951057 + 0.309017i 0.951057 + 0.309017i
$$682$$ −0.500000 1.53884i −0.500000 1.53884i
$$683$$ 1.61803i 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$684$$ −0.500000 + 1.53884i −0.500000 + 1.53884i
$$685$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$686$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$687$$ 1.61803 1.61803
$$688$$ 0 0
$$689$$ 0 0
$$690$$ −1.53884 0.500000i −1.53884 0.500000i
$$691$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ −1.53884 0.500000i −1.53884 0.500000i
$$693$$ 0.587785 + 0.190983i 0.587785 + 0.190983i
$$694$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$695$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$696$$ 1.61803 1.61803
$$697$$ 0.309017 0.224514i 0.309017 0.224514i
$$698$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$699$$ −0.951057 1.30902i −0.951057 1.30902i
$$700$$ 0 0
$$701$$ 0.587785 + 0.809017i 0.587785 + 0.809017i 0.994522 0.104528i $$-0.0333333\pi$$
−0.406737 + 0.913545i $$0.633333\pi$$
$$702$$ −0.951057 + 1.30902i −0.951057 + 1.30902i
$$703$$ 0 0
$$704$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$705$$ 1.30902 + 0.951057i 1.30902 + 0.951057i
$$706$$ 1.00000 1.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i $$-0.800000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$710$$ 1.53884 + 2.11803i 1.53884 + 2.11803i
$$711$$ 0 0
$$712$$ −0.309017 + 0.951057i −0.309017 + 0.951057i
$$713$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$714$$ 0.309017 0.951057i 0.309017 0.951057i
$$715$$ 0.190983 + 0.587785i 0.190983 + 0.587785i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0.809017 0.587785i 0.809017 0.587785i
$$719$$ −0.951057 1.30902i −0.951057 1.30902i −0.951057 0.309017i $$-0.900000\pi$$
1.00000i $$-0.5\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −0.500000 0.363271i −0.500000 0.363271i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −0.951057 + 0.309017i −0.951057 + 0.309017i
$$727$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$728$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$729$$ 0.309017 + 0.951057i 0.309017 + 0.951057i
$$730$$ −0.500000 1.53884i −0.500000 1.53884i
$$731$$ 0.363271 0.500000i 0.363271 0.500000i
$$732$$ −0.309017 0.951057i −0.309017 0.951057i
$$733$$ 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$734$$ 1.61803i 1.61803i
$$735$$ 0 0
$$736$$ 0.809017 0.587785i 0.809017 0.587785i
$$737$$ 0 0
$$738$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$739$$ 0 0 0.587785 0.809017i $$-0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$740$$ 0 0
$$741$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ −0.951057 1.30902i −0.951057 1.30902i
$$745$$ 0.500000 + 1.53884i 0.500000 + 1.53884i
$$746$$ 0.587785 0.809017i 0.587785 0.809017i
$$747$$ −1.53884 + 0.500000i −1.53884 + 0.500000i
$$748$$ −0.190983 0.587785i −0.190983 0.587785i
$$749$$ −1.17557 1.61803i −1.17557 1.61803i
$$750$$ −1.61803 −1.61803
$$751$$ 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 $$0$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 2.11803 + 1.53884i 2.11803 + 1.53884i
$$755$$ 0.363271 0.500000i 0.363271 0.500000i
$$756$$ 1.61803 1.61803
$$757$$ 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i $$-0.733333\pi$$
0.978148 0.207912i $$-0.0666667\pi$$
$$758$$ 0 0
$$759$$ −0.500000 + 0.363271i −0.500000 + 0.363271i
$$760$$ 0.809017 + 0.587785i 0.809017 + 0.587785i
$$761$$ 0 0 0.309017 0.951057i $$-0.400000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$762$$ 1.53884 0.500000i 1.53884 0.500000i
$$763$$ 0.309017 0.951057i 0.309017 0.951057i
$$764$$ −0.951057 1.30902i −0.951057 1.30902i
$$765$$ 0.190983 0.587785i 0.190983 0.587785i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −0.809017 + 0.587785i −0.809017 + 0.587785i
$$769$$ 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i $$-0.600000\pi$$
0.809017 0.587785i $$-0.200000\pi$$
$$770$$ 0.587785 0.809017i 0.587785 0.809017i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 −0.309017 0.951057i $$-0.600000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$774$$ 1.53884 + 0.500000i 1.53884 + 0.500000i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.30902 + 0.951057i −1.30902 + 0.951057i
$$779$$ 0.363271 + 0.500000i 0.363271 + 0.500000i
$$780$$ 0.951057 + 1.30902i 0.951057 + 1.30902i
$$781$$ 1.00000 1.00000
$$782$$ 0.587785 + 0.809017i 0.587785 + 0.809017i
$$783$$ 1.53884 0.500000i 1.53884 0.500000i
$$784$$ 0 0
$$785$$ −0.951057 0.309017i −0.951057 0.309017i
$$786$$ −1.00000 −1.00000
$$787$$ −0.190983 + 0.587785i