# Properties

 Label 2520.1.fw.b.349.2 Level $2520$ Weight $1$ Character 2520.349 Analytic conductor $1.258$ Analytic rank $0$ Dimension $8$ Projective image $D_{12}$ CM discriminant -56 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2520.fw (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.25764383184$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{12}$$ Projective field: Galois closure of $$\mathbb{Q}[x]/(x^{12} - \cdots)$$

## Embedding invariants

 Embedding label 349.2 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 2520.349 Dual form 2520.1.fw.b.2029.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.965926 + 0.258819i) q^{10} +(-0.258819 + 0.965926i) q^{12} +(-1.22474 + 0.707107i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{18} -0.517638 q^{19} +(-0.707107 - 0.707107i) q^{20} +(0.258819 + 0.965926i) q^{21} +(-1.50000 + 0.866025i) q^{23} +(0.707107 - 0.707107i) q^{24} +(0.866025 - 0.500000i) q^{25} +1.41421 q^{26} +(-0.707107 + 0.707107i) q^{27} +1.00000i q^{28} +(0.500000 + 0.866025i) q^{30} +(0.866025 - 0.500000i) q^{32} +(-0.965926 - 0.258819i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(0.448288 + 0.258819i) q^{38} +(-1.36603 - 0.366025i) q^{39} +(0.258819 + 0.965926i) q^{40} +(0.258819 - 0.965926i) q^{42} +(-0.258819 - 0.965926i) q^{45} +1.73205 q^{46} +(-0.965926 + 0.258819i) q^{48} +(0.500000 + 0.866025i) q^{49} -1.00000 q^{50} +(-1.22474 - 0.707107i) q^{52} +(0.965926 - 0.258819i) q^{54} +(0.500000 - 0.866025i) q^{56} +(-0.366025 - 0.366025i) q^{57} +(-0.707107 - 1.22474i) q^{59} -1.00000i q^{60} +(0.258819 - 0.448288i) q^{61} +(-0.500000 + 0.866025i) q^{63} -1.00000 q^{64} +(1.00000 - 1.00000i) q^{65} +(-1.67303 - 0.448288i) q^{69} +(0.707107 + 0.707107i) q^{70} +1.73205 q^{71} +1.00000 q^{72} +(0.965926 + 0.258819i) q^{75} +(-0.258819 - 0.448288i) q^{76} +(1.00000 + 1.00000i) q^{78} +(-0.866025 + 1.50000i) q^{79} +(0.258819 - 0.965926i) q^{80} -1.00000 q^{81} +(1.22474 + 0.707107i) q^{83} +(-0.707107 + 0.707107i) q^{84} +(-0.258819 + 0.965926i) q^{90} -1.41421 q^{91} +(-1.50000 - 0.866025i) q^{92} +(0.500000 - 0.133975i) q^{95} +(0.965926 + 0.258819i) q^{96} -1.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} + O(q^{10})$$ $$8q + 4q^{4} - 4q^{14} - 4q^{16} + 4q^{18} - 12q^{23} + 4q^{30} - 4q^{39} + 4q^{49} - 8q^{50} + 4q^{56} + 4q^{57} - 4q^{63} - 8q^{64} + 8q^{65} + 8q^{72} + 8q^{78} - 8q^{81} - 12q^{92} + 4q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$$.

 $$n$$ $$281$$ $$631$$ $$1081$$ $$1261$$ $$2017$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 0.500000i −0.866025 0.500000i
$$3$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$4$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$5$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$6$$ −0.258819 0.965926i −0.258819 0.965926i
$$7$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$8$$ 1.00000i 1.00000i
$$9$$ 1.00000i 1.00000i
$$10$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$11$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$12$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$13$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$14$$ −0.500000 0.866025i −0.500000 0.866025i
$$15$$ −0.866025 0.500000i −0.866025 0.500000i
$$16$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0.500000 0.866025i 0.500000 0.866025i
$$19$$ −0.517638 −0.517638 −0.258819 0.965926i $$-0.583333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$20$$ −0.707107 0.707107i −0.707107 0.707107i
$$21$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$22$$ 0 0
$$23$$ −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i $$0.666667\pi$$
−1.00000 $$\pi$$
$$24$$ 0.707107 0.707107i 0.707107 0.707107i
$$25$$ 0.866025 0.500000i 0.866025 0.500000i
$$26$$ 1.41421 1.41421
$$27$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$28$$ 1.00000i 1.00000i
$$29$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$30$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$31$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$32$$ 0.866025 0.500000i 0.866025 0.500000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −0.965926 0.258819i −0.965926 0.258819i
$$36$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$39$$ −1.36603 0.366025i −1.36603 0.366025i
$$40$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$41$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$42$$ 0.258819 0.965926i 0.258819 0.965926i
$$43$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$44$$ 0 0
$$45$$ −0.258819 0.965926i −0.258819 0.965926i
$$46$$ 1.73205 1.73205
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$49$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$50$$ −1.00000 −1.00000
$$51$$ 0 0
$$52$$ −1.22474 0.707107i −1.22474 0.707107i
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0.965926 0.258819i 0.965926 0.258819i
$$55$$ 0 0
$$56$$ 0.500000 0.866025i 0.500000 0.866025i
$$57$$ −0.366025 0.366025i −0.366025 0.366025i
$$58$$ 0 0
$$59$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$60$$ 1.00000i 1.00000i
$$61$$ 0.258819 0.448288i 0.258819 0.448288i −0.707107 0.707107i $$-0.750000\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$62$$ 0 0
$$63$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$64$$ −1.00000 −1.00000
$$65$$ 1.00000 1.00000i 1.00000 1.00000i
$$66$$ 0 0
$$67$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$68$$ 0 0
$$69$$ −1.67303 0.448288i −1.67303 0.448288i
$$70$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$71$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ 1.00000 1.00000
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$76$$ −0.258819 0.448288i −0.258819 0.448288i
$$77$$ 0 0
$$78$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$79$$ −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i $$0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ 0.258819 0.965926i 0.258819 0.965926i
$$81$$ −1.00000 −1.00000
$$82$$ 0 0
$$83$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$84$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$91$$ −1.41421 −1.41421
$$92$$ −1.50000 0.866025i −1.50000 0.866025i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0.500000 0.133975i 0.500000 0.133975i
$$96$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$97$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$98$$ 1.00000i 1.00000i
$$99$$ 0 0
$$100$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$101$$ −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i $$0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$102$$ 0 0
$$103$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$104$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$105$$ −0.500000 0.866025i −0.500000 0.866025i
$$106$$ 0 0
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ −0.965926 0.258819i −0.965926 0.258819i
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$113$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0.133975 + 0.500000i 0.133975 + 0.500000i
$$115$$ 1.22474 1.22474i 1.22474 1.22474i
$$116$$ 0 0
$$117$$ −0.707107 1.22474i −0.707107 1.22474i
$$118$$ 1.41421i 1.41421i
$$119$$ 0 0
$$120$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$121$$ −0.500000 0.866025i −0.500000 0.866025i
$$122$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$126$$ 0.866025 0.500000i 0.866025 0.500000i
$$127$$ 1.73205i 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$128$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$129$$ 0 0
$$130$$ −1.36603 + 0.366025i −1.36603 + 0.366025i
$$131$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$132$$ 0 0
$$133$$ −0.448288 0.258819i −0.448288 0.258819i
$$134$$ 0 0
$$135$$ 0.500000 0.866025i 0.500000 0.866025i
$$136$$ 0 0
$$137$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$138$$ 1.22474 + 1.22474i 1.22474 + 1.22474i
$$139$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$140$$ −0.258819 0.965926i −0.258819 0.965926i
$$141$$ 0 0
$$142$$ −1.50000 0.866025i −1.50000 0.866025i
$$143$$ 0 0
$$144$$ −0.866025 0.500000i −0.866025 0.500000i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$148$$ 0 0
$$149$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$150$$ −0.707107 0.707107i −0.707107 0.707107i
$$151$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$152$$ 0.517638i 0.517638i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.366025 1.36603i −0.366025 1.36603i
$$157$$ 1.67303 0.965926i 1.67303 0.965926i 0.707107 0.707107i $$-0.250000\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$158$$ 1.50000 0.866025i 1.50000 0.866025i
$$159$$ 0 0
$$160$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$161$$ −1.73205 −1.73205
$$162$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −0.707107 1.22474i −0.707107 1.22474i
$$167$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$168$$ 0.965926 0.258819i 0.965926 0.258819i
$$169$$ 0.500000 0.866025i 0.500000 0.866025i
$$170$$ 0 0
$$171$$ 0.517638i 0.517638i
$$172$$ 0 0
$$173$$ −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$174$$ 0 0
$$175$$ 1.00000 1.00000
$$176$$ 0 0
$$177$$ 0.366025 1.36603i 0.366025 1.36603i
$$178$$ 0 0
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0.707107 0.707107i 0.707107 0.707107i
$$181$$ −1.93185 −1.93185 −0.965926 0.258819i $$-0.916667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$182$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$183$$ 0.500000 0.133975i 0.500000 0.133975i
$$184$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$190$$ −0.500000 0.133975i −0.500000 0.133975i
$$191$$ 0.866025 1.50000i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$192$$ −0.707107 0.707107i −0.707107 0.707107i
$$193$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$194$$ 0 0
$$195$$ 1.41421 1.41421
$$196$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ −0.500000 0.866025i −0.500000 0.866025i
$$201$$ 0 0
$$202$$ 1.67303 0.965926i 1.67303 0.965926i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −0.866025 1.50000i −0.866025 1.50000i
$$208$$ 1.41421i 1.41421i
$$209$$ 0 0
$$210$$ 1.00000i 1.00000i
$$211$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$212$$ 0 0
$$213$$ 1.22474 + 1.22474i 1.22474 + 1.22474i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$224$$ 1.00000 1.00000
$$225$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$226$$ 1.00000 1.00000
$$227$$ 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$228$$ 0.133975 0.500000i 0.133975 0.500000i
$$229$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$230$$ −1.67303 + 0.448288i −1.67303 + 0.448288i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$234$$ 1.41421i 1.41421i
$$235$$ 0 0
$$236$$ 0.707107 1.22474i 0.707107 1.22474i
$$237$$ −1.67303 + 0.448288i −1.67303 + 0.448288i
$$238$$ 0 0
$$239$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$240$$ 0.866025 0.500000i 0.866025 0.500000i
$$241$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ 1.00000i 1.00000i
$$243$$ −0.707107 0.707107i −0.707107 0.707107i
$$244$$ 0.517638 0.517638
$$245$$ −0.707107 0.707107i −0.707107 0.707107i
$$246$$ 0 0
$$247$$ 0.633975 0.366025i 0.633975 0.366025i
$$248$$ 0 0
$$249$$ 0.366025 + 1.36603i 0.366025 + 1.36603i
$$250$$ 0.965926 0.258819i 0.965926 0.258819i
$$251$$ −0.517638 −0.517638 −0.258819 0.965926i $$-0.583333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$252$$ −1.00000 −1.00000
$$253$$ 0 0
$$254$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.500000 0.866025i
$$257$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$261$$ 0 0
$$262$$ 1.93185i 1.93185i
$$263$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0.258819 + 0.448288i 0.258819 + 0.448288i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.93185 1.93185 0.965926 0.258819i $$-0.0833333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$270$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ −1.00000 1.00000i −1.00000 1.00000i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −0.448288 1.67303i −0.448288 1.67303i
$$277$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$278$$ 1.93185i 1.93185i
$$279$$ 0 0
$$280$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$281$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 1.67303 0.965926i 1.67303 0.965926i 0.707107 0.707107i $$-0.250000\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$284$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$285$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$289$$ −1.00000 −1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$294$$ 0.707107 0.707107i 0.707107 0.707107i
$$295$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 1.22474 2.12132i 1.22474 2.12132i
$$300$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$301$$ 0 0
$$302$$ 0.866025 0.500000i 0.866025 0.500000i
$$303$$ −1.86603 + 0.500000i −1.86603 + 0.500000i
$$304$$ 0.258819 0.448288i 0.258819 0.448288i
$$305$$ −0.133975 + 0.500000i −0.133975 + 0.500000i
$$306$$ 0 0
$$307$$ 0.517638i 0.517638i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$312$$ −0.366025 + 1.36603i −0.366025 + 1.36603i
$$313$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$314$$ −1.93185 −1.93185
$$315$$ 0.258819 0.965926i 0.258819 0.965926i
$$316$$ −1.73205 −1.73205
$$317$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.965926 0.258819i 0.965926 0.258819i
$$321$$ 0 0
$$322$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$323$$ 0 0
$$324$$ −0.500000 0.866025i −0.500000 0.866025i
$$325$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 1.41421i 1.41421i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −0.965926 0.258819i −0.965926 0.258819i
$$337$$ 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i $$-0.166667\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$338$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$339$$ −0.965926 0.258819i −0.965926 0.258819i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −0.258819 + 0.448288i −0.258819 + 0.448288i
$$343$$ 1.00000i 1.00000i
$$344$$ 0 0
$$345$$ 1.73205 1.73205
$$346$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$347$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$348$$ 0 0
$$349$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$350$$ −0.866025 0.500000i −0.866025 0.500000i
$$351$$ 0.366025 1.36603i 0.366025 1.36603i
$$352$$ 0 0
$$353$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$354$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$355$$ −1.67303 + 0.448288i −1.67303 + 0.448288i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$360$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$361$$ −0.732051 −0.732051
$$362$$ 1.67303 + 0.965926i 1.67303 + 0.965926i
$$363$$ 0.258819 0.965926i 0.258819 0.965926i
$$364$$ −0.707107 1.22474i −0.707107 1.22474i
$$365$$ 0 0
$$366$$ −0.500000 0.133975i −0.500000 0.133975i
$$367$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$368$$ 1.73205i 1.73205i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$374$$ 0 0
$$375$$ −1.00000 −1.00000
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$381$$ 1.22474 1.22474i 1.22474 1.22474i
$$382$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$385$$ 0 0
$$386$$ −1.00000 −1.00000
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ −1.22474 0.707107i −1.22474 0.707107i
$$391$$ 0 0
$$392$$ 0.866025 0.500000i 0.866025 0.500000i
$$393$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$394$$ 0 0
$$395$$ 0.448288 1.67303i 0.448288 1.67303i
$$396$$ 0 0
$$397$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$398$$ 0 0
$$399$$ −0.133975 0.500000i −0.133975 0.500000i
$$400$$ 1.00000i 1.00000i
$$401$$ −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ −1.93185 −1.93185
$$405$$ 0.965926 0.258819i 0.965926 0.258819i
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 1.41421i 1.41421i
$$414$$ 1.73205i 1.73205i
$$415$$ −1.36603 0.366025i −1.36603 0.366025i
$$416$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$417$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$418$$ 0 0
$$419$$ 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i $$-0.0833333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$420$$ 0.500000 0.866025i 0.500000 0.866025i
$$421$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ −0.448288 1.67303i −0.448288 1.67303i
$$427$$ 0.448288 0.258819i 0.448288 0.258819i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$432$$ −0.258819 0.965926i −0.258819 0.965926i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0.776457 0.448288i 0.776457 0.448288i
$$438$$ 0 0
$$439$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$440$$ 0 0
$$441$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$442$$ 0 0
$$443$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ −0.866025 0.500000i −0.866025 0.500000i
$$449$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$450$$ 1.00000i 1.00000i
$$451$$ 0 0
$$452$$ −0.866025 0.500000i −0.866025 0.500000i
$$453$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$454$$ −0.965926 1.67303i −0.965926 1.67303i
$$455$$ 1.36603 0.366025i 1.36603 0.366025i
$$456$$ −0.366025 + 0.366025i −0.366025 + 0.366025i
$$457$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$458$$ 1.93185i 1.93185i
$$459$$ 0 0
$$460$$ 1.67303 + 0.448288i 1.67303 + 0.448288i
$$461$$ 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i $$-0.416667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$462$$ 0 0
$$463$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0.866025 1.50000i 0.866025 1.50000i
$$467$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$468$$ 0.707107 1.22474i 0.707107 1.22474i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 1.86603 + 0.500000i 1.86603 + 0.500000i
$$472$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$473$$ 0 0
$$474$$ 1.67303 + 0.448288i 1.67303 + 0.448288i
$$475$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 1.00000i 1.00000i
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ −1.00000 −1.00000
$$481$$ 0 0
$$482$$ 0 0
$$483$$ −1.22474 1.22474i −1.22474 1.22474i
$$484$$ 0.500000 0.866025i 0.500000 0.866025i
$$485$$ 0 0
$$486$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$487$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$488$$ −0.448288 0.258819i −0.448288 0.258819i
$$489$$ 0 0
$$490$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$491$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −0.732051 −0.732051
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$498$$ 0.366025 1.36603i 0.366025 1.36603i
$$499$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$500$$ −0.965926 0.258819i −0.965926 0.258819i
$$501$$ 0 0
$$502$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$505$$ 0.500000 1.86603i 0.500000 1.86603i
$$506$$ 0 0
$$507$$ 0.965926 0.258819i 0.965926 0.258819i
$$508$$ 1.50000 0.866025i 1.50000 0.866025i
$$509$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 1.00000i
$$513$$ 0.366025 0.366025i 0.366025 0.366025i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −0.366025 1.36603i −0.366025 1.36603i
$$520$$ −1.00000 1.00000i −1.00000 1.00000i
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 0.517638i 0.517638i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$524$$ −0.965926 + 1.67303i −0.965926 + 1.67303i
$$525$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$526$$ −0.500000 0.866025i −0.500000 0.866025i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 1.73205i 1.00000 1.73205i
$$530$$ 0 0
$$531$$ 1.22474 0.707107i 1.22474 0.707107i
$$532$$ 0.517638i 0.517638i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −1.67303 0.965926i −1.67303 0.965926i
$$539$$ 0 0
$$540$$ 1.00000 1.00000
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ 0 0
$$543$$ −1.36603 1.36603i −1.36603 1.36603i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0.366025 + 1.36603i 0.366025 + 1.36603i
$$547$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$548$$ 0 0
$$549$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ −0.448288 + 1.67303i −0.448288 + 1.67303i
$$553$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.965926 + 1.67303i −0.965926 + 1.67303i
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0.707107 0.707107i 0.707107 0.707107i
$$561$$ 0 0
$$562$$ 0.866025 0.500000i 0.866025 0.500000i
$$563$$ −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i $$0.750000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$564$$ 0 0
$$565$$ 0.707107 0.707107i 0.707107 0.707107i
$$566$$ −1.93185 −1.93185
$$567$$ −0.866025 0.500000i −0.866025 0.500000i
$$568$$ 1.73205i 1.73205i
$$569$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$570$$ −0.258819 0.448288i −0.258819 0.448288i
$$571$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 0 0
$$573$$ 1.67303 0.448288i 1.67303 0.448288i
$$574$$ 0 0
$$575$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$576$$ 1.00000i 1.00000i
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$579$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$580$$ 0 0
$$581$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 1.00000 + 1.00000i 1.00000 + 1.00000i
$$586$$ −0.517638 −0.517638
$$587$$ 0.448288 + 0.258819i 0.448288 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$588$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$589$$ 0 0
$$590$$ −0.366025 1.36603i −0.366025 1.36603i
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −2.12132 + 1.22474i −2.12132 + 1.22474i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0.258819 0.965926i 0.258819 0.965926i
$$601$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1.00000 −1.00000
$$605$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$606$$ 1.86603 + 0.500000i 1.86603 + 0.500000i
$$607$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$608$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$609$$ 0 0
$$610$$ 0.366025 0.366025i 0.366025 0.366025i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$614$$ 0.258819 0.448288i 0.258819 0.448288i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$618$$ 0 0
$$619$$ −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$620$$ 0 0
$$621$$ 0.448288 1.67303i 0.448288 1.67303i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 1.00000 1.00000i 1.00000 1.00000i
$$625$$ 0.500000 0.866025i 0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.67303 + 0.965926i 1.67303 + 0.965926i
$$629$$ 0 0
$$630$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$631$$ 1.73205 1.73205 0.866025 0.500000i $$-0.166667\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$632$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.448288 + 1.67303i 0.448288 + 1.67303i
$$636$$ 0 0
$$637$$ −1.22474 0.707107i −1.22474 0.707107i
$$638$$ 0 0
$$639$$ 1.73205i 1.73205i
$$640$$ −0.965926 0.258819i −0.965926 0.258819i
$$641$$ −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i $$0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$642$$ 0 0
$$643$$ 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$644$$ −0.866025 1.50000i −0.866025 1.50000i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 1.00000i 1.00000i
$$649$$ 0 0
$$650$$ 1.22474 0.707107i 1.22474 0.707107i
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$654$$ 0 0
$$655$$ −1.36603 1.36603i −1.36603 1.36603i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$660$$ 0 0
$$661$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0.707107 1.22474i 0.707107 1.22474i
$$665$$ 0.500000 + 0.133975i 0.500000 + 0.133975i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$673$$ −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
−1.00000 $$\pi$$
$$674$$ −2.00000 −2.00000
$$675$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$676$$ 1.00000 1.00000
$$677$$ 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$678$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0.500000 + 1.86603i 0.500000 + 1.86603i
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0.448288 0.258819i 0.448288 0.258819i
$$685$$ 0 0
$$686$$ 0.500000 0.866025i 0.500000 0.866025i
$$687$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ −1.50000 0.866025i −1.50000 0.866025i
$$691$$ 0.965926 1.67303i 0.965926 1.67303i 0.258819 0.965926i $$-0.416667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$692$$ 1.41421i 1.41421i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.36603 1.36603i −1.36603 1.36603i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$699$$ −1.22474 + 1.22474i −1.22474 + 1.22474i
$$700$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ −1.00000 + 1.00000i −1.00000 + 1.00000i
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.67303 + 0.965926i −1.67303 + 0.965926i
$$708$$ 1.36603 0.366025i 1.36603 0.366025i
$$709$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 1.67303 + 0.448288i 1.67303 + 0.448288i
$$711$$ −1.50000 0.866025i −1.50000 0.866025i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$718$$ −0.866025 0.500000i −0.866025 0.500000i
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$721$$ 0 0
$$722$$ 0.633975 + 0.366025i 0.633975 + 0.366025i
$$723$$ 0 0
$$724$$ −0.965926 1.67303i −0.965926 1.67303i
$$725$$ 0 0
$$726$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$727$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$728$$ 1.41421i 1.41421i
$$729$$ 1.00000i 1.00000i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0.366025 + 0.366025i 0.366025 + 0.366025i
$$733$$ −1.67303 + 0.965926i −1.67303 + 0.965926i −0.707107 + 0.707107i $$0.750000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$734$$ 0 0
$$735$$ 1.00000i 1.00000i
$$736$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0.707107 + 0.189469i 0.707107 + 0.189469i
$$742$$ 0 0
$$743$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$751$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ −0.366025 0.366025i −0.366025 0.366025i
$$754$$ 0 0
$$755$$ 0.258819 0.965926i 0.258819 0.965926i
$$756$$ −0.707107 0.707107i −0.707107 0.707107i
$$757$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ −0.133975 0.500000i −0.133975 0.500000i
$$761$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$762$$ −1.67303 + 0.448288i −1.67303 + 0.448288i
$$763$$ 0 0
$$764$$ 1.73205 1.73205
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1.73205 + 1.00000i 1.73205 + 1.00000i
$$768$$ 0.258819 0.965926i 0.258819 0.965926i
$$769$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$773$$ 0.517638i 0.517638i −0.965926 0.258819i $$-0.916667\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ −1.36603 + 1.36603i −1.36603 + 1.36603i
$$786$$ 1.36603 1.36603i 1.36603 1.36603i
$$787$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$788$$ 0 0
$$789$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$790$$ −1.22474 + 1.22474i −1.22474 + 1.22474i
$$791$$ −1.00000 −1.00000
$$792$$ 0 0
$$793$$ 0.732051i 0.732051i
$$794$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$795$$ 0 0
$$796$$ 0 0