# Properties

 Label 1148.1.bj.a.319.2 Level $1148$ Weight $1$ Character 1148.319 Analytic conductor $0.573$ Analytic rank $0$ Dimension $8$ Projective image $S_{4}$ CM/RM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1148 = 2^{2} \cdot 7 \cdot 41$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1148.bj (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.572926634503$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{12})$$ 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: $$S_{4}$$ Projective field: Galois closure of 4.2.13508516.2

## Embedding invariants

 Embedding label 319.2 Root $$0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 1148.319 Dual form 1148.1.bj.a.583.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.965926 - 0.258819i) q^{11} +(0.258819 - 0.965926i) q^{12} +(-1.00000 + 1.00000i) q^{13} +(-0.258819 - 0.965926i) q^{14} +(-0.707107 + 0.707107i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.965926 + 0.258819i) q^{19} +1.00000i q^{20} -1.00000i q^{21} +(0.707107 - 0.707107i) q^{22} +(-0.258819 - 0.965926i) q^{24} +(-0.366025 + 1.36603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-0.258819 + 0.965926i) q^{30} +(-1.22474 - 0.707107i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +(0.258819 + 0.965926i) q^{35} +(0.965926 - 0.258819i) q^{38} +(-0.707107 + 1.22474i) q^{39} +(0.500000 + 0.866025i) q^{40} +1.00000i q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.258819 - 0.965926i) q^{44} +(-0.707107 - 0.707107i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.366025 + 1.36603i) q^{52} +(0.366025 + 1.36603i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-0.707107 + 0.707107i) q^{55} +(-0.965926 - 0.258819i) q^{56} +1.00000 q^{57} +(1.22474 + 0.707107i) q^{59} +(0.258819 + 0.965926i) q^{60} +(0.866025 - 0.500000i) q^{61} -1.41421 q^{62} -1.00000 q^{64} +(0.366025 - 1.36603i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-0.517638 - 1.93185i) q^{67} +(0.707107 + 0.707107i) q^{70} +(0.707107 + 0.707107i) q^{71} +(0.707107 - 0.707107i) q^{76} -1.00000i q^{77} +1.41421i q^{78} +(-0.258819 + 0.965926i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +1.41421i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-0.258819 - 0.965926i) q^{88} +(-1.36603 - 0.366025i) q^{89} +(0.707107 + 1.22474i) q^{91} +(-1.36603 - 0.366025i) q^{93} +(-0.965926 + 0.258819i) q^{95} +(-0.965926 - 0.258819i) q^{96} -1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} + O(q^{10})$$ $$8q + 4q^{4} - 4q^{10} - 8q^{13} - 4q^{16} + 4q^{26} + 4q^{40} - 4q^{42} - 4q^{52} - 4q^{53} + 8q^{57} - 8q^{64} - 4q^{65} + 4q^{66} - 4q^{81} + 4q^{82} - 4q^{89} - 4q^{93} - 8q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$$.

 $$n$$ $$493$$ $$575$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

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