# Properties

 Label 1575.1.cb.a.907.2 Level 1575 Weight 1 Character 1575.907 Analytic conductor 0.786 Analytic rank 0 Dimension 8 Projective image $$A_{4}$$ CM/RM no Inner twists 8

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1575.cb (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.786027394897$$ 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 $$A_{4}$$ Projective field Galois closure of 4.0.99225.1

## Embedding invariants

 Embedding label 907.2 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 1575.907 Dual form 1575.1.cb.a.1318.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.965926 - 0.258819i) q^{13} +(-0.866025 + 0.500000i) q^{14} +1.00000 q^{16} +(-0.965926 + 0.258819i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.866025 - 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{21} +(0.866025 - 0.500000i) q^{24} +(-0.500000 - 0.866025i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.866025 + 0.500000i) q^{29} -1.00000 q^{31} +(-0.866025 - 0.500000i) q^{34} +(-0.258819 + 0.965926i) q^{37} +(0.965926 + 0.258819i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-0.965926 + 0.258819i) q^{42} +(-0.258819 - 0.965926i) q^{43} +(-0.707107 - 0.707107i) q^{47} +(0.965926 + 0.258819i) q^{48} +(-0.866025 - 0.500000i) q^{49} -1.00000 q^{51} +(-0.258819 - 0.965926i) q^{53} +1.00000i q^{54} +(0.500000 + 0.866025i) q^{56} +(0.965926 - 0.258819i) q^{57} +(0.258819 + 0.965926i) q^{58} -1.00000i q^{59} +1.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-0.707107 + 0.707107i) q^{63} -1.00000i q^{64} +(0.707107 + 0.707107i) q^{67} -2.00000 q^{71} +(0.965926 - 0.258819i) q^{72} +(0.258819 + 0.965926i) q^{73} +(-0.866025 + 0.500000i) q^{74} +(-0.258819 - 0.965926i) q^{78} +1.00000i q^{79} +(0.500000 + 0.866025i) q^{81} +(0.258819 - 0.965926i) q^{82} +(0.258819 + 0.965926i) q^{83} +(0.500000 - 0.866025i) q^{86} +(0.707107 + 0.707107i) q^{87} +(-0.866025 + 0.500000i) q^{89} +(0.500000 - 0.866025i) q^{91} +(-0.965926 - 0.258819i) q^{93} -1.00000i q^{94} +(0.965926 - 0.258819i) q^{97} +(-0.258819 - 0.965926i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{6} + O(q^{10})$$ $$8q + 4q^{6} + 8q^{16} - 4q^{21} - 4q^{26} - 8q^{31} - 4q^{41} - 8q^{51} + 4q^{56} + 8q^{61} - 16q^{71} + 4q^{81} + 4q^{86} + 4q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$1226$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$3$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$7$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$8$$ 0.707107 0.707107i 0.707107 0.707107i
$$9$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$10$$ 0 0
$$11$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$12$$ 0 0
$$13$$ −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$14$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$18$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$19$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$20$$ 0 0
$$21$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$22$$ 0 0
$$23$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$24$$ 0.866025 0.500000i 0.866025 0.500000i
$$25$$ 0 0
$$26$$ −0.500000 0.866025i −0.500000 0.866025i
$$27$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$28$$ 0 0
$$29$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$30$$ 0 0
$$31$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ −0.866025 0.500000i −0.866025 0.500000i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$38$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$39$$ −0.866025 0.500000i −0.866025 0.500000i
$$40$$ 0 0
$$41$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$-1.00000\pi$$
$$42$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$43$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$48$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$49$$ −0.866025 0.500000i −0.866025 0.500000i
$$50$$ 0 0
$$51$$ −1.00000 −1.00000
$$52$$ 0 0
$$53$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$54$$ 1.00000i 1.00000i
$$55$$ 0 0
$$56$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$57$$ 0.965926 0.258819i 0.965926 0.258819i
$$58$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$59$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$60$$ 0 0
$$61$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$62$$ −0.707107 0.707107i −0.707107 0.707107i
$$63$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$64$$ 1.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$72$$ 0.965926 0.258819i 0.965926 0.258819i
$$73$$ 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$74$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ −0.258819 0.965926i −0.258819 0.965926i
$$79$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ 0 0
$$81$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$82$$ 0.258819 0.965926i 0.258819 0.965926i
$$83$$ 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0.500000 0.866025i 0.500000 0.866025i
$$87$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$88$$ 0 0
$$89$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$90$$ 0 0
$$91$$ 0.500000 0.866025i 0.500000 0.866025i
$$92$$ 0 0
$$93$$ −0.965926 0.258819i −0.965926 0.258819i
$$94$$ 1.00000i 1.00000i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i $$-0.416667\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$98$$ −0.258819 0.965926i −0.258819 0.965926i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$102$$ −0.707107 0.707107i −0.707107 0.707107i
$$103$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$104$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$105$$ 0 0
$$106$$ 0.500000 0.866025i 0.500000 0.866025i
$$107$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$108$$ 0 0
$$109$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$110$$ 0 0
$$111$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$112$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$113$$ −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$114$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −0.707107 0.707107i −0.707107 0.707107i
$$118$$ 0.707107 0.707107i 0.707107 0.707107i
$$119$$ 1.00000i 1.00000i
$$120$$ 0 0
$$121$$ 0.500000 0.866025i 0.500000 0.866025i
$$122$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$123$$ −0.258819 0.965926i −0.258819 0.965926i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −1.00000 −1.00000
$$127$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ 0.707107 0.707107i 0.707107 0.707107i
$$129$$ 1.00000i 1.00000i
$$130$$ 0 0
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ 0 0
$$133$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$134$$ 1.00000i 1.00000i
$$135$$ 0 0
$$136$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$137$$ 0.517638 1.93185i 0.517638 1.93185i 0.258819 0.965926i $$-0.416667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$138$$ 0 0
$$139$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$140$$ 0 0
$$141$$ −0.500000 0.866025i −0.500000 0.866025i
$$142$$ −1.41421 1.41421i −1.41421 1.41421i
$$143$$ 0 0
$$144$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$145$$ 0 0
$$146$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$147$$ −0.707107 0.707107i −0.707107 0.707107i
$$148$$ 0 0
$$149$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$150$$ 0 0
$$151$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$152$$ 0.258819 0.965926i 0.258819 0.965926i
$$153$$ −0.965926 0.258819i −0.965926 0.258819i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$158$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$159$$ 1.00000i 1.00000i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$163$$ −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$167$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$168$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$169$$ 0 0
$$170$$ 0 0
$$171$$ 1.00000 1.00000
$$172$$ 0 0
$$173$$ −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$174$$ 1.00000i 1.00000i
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0.258819 0.965926i 0.258819 0.965926i
$$178$$ −0.965926 0.258819i −0.965926 0.258819i
$$179$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0.965926 0.258819i 0.965926 0.258819i
$$183$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ −0.500000 0.866025i −0.500000 0.866025i
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$190$$ 0 0
$$191$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ 0.258819 0.965926i 0.258819 0.965926i
$$193$$ 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$194$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$198$$ 0 0
$$199$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$200$$ 0 0
$$201$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$202$$ 0.517638 1.93185i 0.517638 1.93185i
$$203$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ −0.965926 0.258819i −0.965926 0.258819i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0 0
$$213$$ −1.93185 0.517638i −1.93185 0.517638i
$$214$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$215$$ 0 0
$$216$$ 1.00000 1.00000
$$217$$ 0.258819 0.965926i 0.258819 0.965926i
$$218$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$219$$ 1.00000i 1.00000i
$$220$$ 0 0
$$221$$ 1.00000 1.00000
$$222$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$223$$ 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −0.500000 0.866025i −0.500000 0.866025i
$$227$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0.965926 0.258819i 0.965926 0.258819i
$$233$$ 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$234$$ 1.00000i 1.00000i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$238$$ 0.707107 0.707107i 0.707107 0.707107i
$$239$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$240$$ 0 0
$$241$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$242$$ 0.965926 0.258819i 0.965926 0.258819i
$$243$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0.500000 0.866025i 0.500000 0.866025i
$$247$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$248$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$249$$ 1.00000i 1.00000i
$$250$$ 0 0
$$251$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 0 0 −0.258819 0.965926i $$-0.583333\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$258$$ 0.707107 0.707107i 0.707107 0.707107i
$$259$$ −0.866025 0.500000i −0.866025 0.500000i
$$260$$ 0 0
$$261$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$262$$ 0 0
$$263$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$267$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$268$$ 0 0
$$269$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$270$$ 0 0
$$271$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$272$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$273$$ 0.707107 0.707107i 0.707107 0.707107i
$$274$$ 1.73205 1.00000i 1.73205 1.00000i
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$278$$ −0.965926 0.258819i −0.965926 0.258819i
$$279$$ −0.866025 0.500000i −0.866025 0.500000i
$$280$$ 0 0
$$281$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$282$$ 0.258819 0.965926i 0.258819 0.965926i
$$283$$ 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0.965926 0.258819i 0.965926 0.258819i
$$288$$ 0 0
$$289$$ 0 0
$$290$$ 0 0
$$291$$ 1.00000 1.00000
$$292$$ 0 0
$$293$$ −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$294$$ 1.00000i 1.00000i
$$295$$ 0 0
$$296$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 1.00000 1.00000
$$302$$ 0 0
$$303$$ −0.517638 1.93185i −0.517638 1.93185i
$$304$$ 0.866025 0.500000i 0.866025 0.500000i
$$305$$ 0 0
$$306$$ −0.500000 0.866025i −0.500000 0.866025i
$$307$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$313$$ 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$314$$ 1.00000i 1.00000i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$318$$ 0.707107 0.707107i 0.707107 0.707107i
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$322$$ 0 0
$$323$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −0.500000 0.866025i −0.500000 0.866025i
$$327$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$328$$ −0.965926 0.258819i −0.965926 0.258819i
$$329$$ 0.866025 0.500000i 0.866025 0.500000i
$$330$$ 0 0
$$331$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 0 0
$$333$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$334$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$335$$ 0 0
$$336$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$337$$ 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i $$-0.750000\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$338$$ 0 0
$$339$$ −0.866025 0.500000i −0.866025 0.500000i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$343$$ 0.707107 0.707107i 0.707107 0.707107i
$$344$$ −0.866025 0.500000i −0.866025 0.500000i
$$345$$ 0 0
$$346$$ −1.00000 −1.00000
$$347$$ 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$348$$ 0 0
$$349$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$350$$ 0 0
$$351$$ −0.500000 0.866025i −0.500000 0.866025i
$$352$$ 0 0
$$353$$ 0 0 0.258819 0.965926i $$-0.416667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$354$$ 0.866025 0.500000i 0.866025 0.500000i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0.258819 0.965926i 0.258819 0.965926i
$$358$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$359$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0.707107 0.707107i 0.707107 0.707107i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$367$$ 0 0 −0.965926 0.258819i $$-0.916667\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$368$$ 0 0
$$369$$ 1.00000i 1.00000i
$$370$$ 0 0
$$371$$ 1.00000 1.00000
$$372$$ 0 0
$$373$$ 0.517638 + 1.93185i 0.517638 + 1.93185i 0.258819 + 0.965926i $$0.416667\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.00000 −1.00000
$$377$$ −0.707107 0.707107i −0.707107 0.707107i
$$378$$ −0.965926 0.258819i −0.965926 0.258819i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$383$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$384$$ 0.866025 0.500000i 0.866025 0.500000i
$$385$$ 0 0
$$386$$ 1.00000 1.00000
$$387$$ 0.258819 0.965926i 0.258819 0.965926i
$$388$$ 0 0
$$389$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$398$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$399$$ 1.00000i 1.00000i
$$400$$ 0 0
$$401$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$402$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$403$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ −1.00000 −1.00000
$$407$$ 0 0
$$408$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$409$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$410$$ 0 0
$$411$$ 1.00000 1.73205i 1.00000 1.73205i
$$412$$ 0 0
$$413$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$418$$ 0 0
$$419$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.500000\pi$$
$$420$$ 0 0
$$421$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$422$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$423$$ −0.258819 0.965926i −0.258819 0.965926i
$$424$$ −0.866025 0.500000i −0.866025 0.500000i
$$425$$ 0 0
$$426$$ −1.00000 1.73205i −1.00000 1.73205i
$$427$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$432$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$433$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$434$$ 0.866025 0.500000i 0.866025 0.500000i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$439$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 0 0
$$441$$ −0.500000 0.866025i −0.500000 0.866025i
$$442$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$443$$ 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$447$$ 0 0
$$448$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0.500000 0.866025i 0.500000 0.866025i
$$457$$ −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$458$$ 0 0
$$459$$ −0.866025 0.500000i −0.866025 0.500000i
$$460$$ 0 0
$$461$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$462$$ 0 0
$$463$$ 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$464$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$465$$ 0 0
$$466$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$467$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$468$$ 0 0
$$469$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$470$$ 0 0
$$471$$ −0.500000 0.866025i −0.500000 0.866025i
$$472$$ −0.707107 0.707107i −0.707107 0.707107i
$$473$$ 0 0
$$474$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0.258819 0.965926i 0.258819 0.965926i
$$478$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$479$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$480$$ 0 0
$$481$$ 0.500000 0.866025i 0.500000 0.866025i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$487$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$488$$ 0.707107 0.707107i 0.707107 0.707107i
$$489$$ −0.866025 0.500000i −0.866025 0.500000i
$$490$$ 0 0
$$491$$ 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 $$0$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$492$$ 0 0
$$493$$ −0.965926 0.258819i −0.965926 0.258819i
$$494$$ −0.866025 0.500000i −0.866025 0.500000i
$$495$$ 0 0
$$496$$ −1.00000 −1.00000
$$497$$ 0.517638 1.93185i 0.517638 1.93185i
$$498$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$499$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ 0 0
$$501$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$502$$ 1.41421 + 1.41421i 1.41421 + 1.41421i
$$503$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$504$$ 1.00000i 1.00000i
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$510$$ 0 0
$$511$$ −1.00000 −1.00000
$$512$$ −0.707107 0.707107i −0.707107 0.707107i
$$513$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ −0.258819 0.965926i −0.258819 0.965926i
$$519$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$520$$ 0 0
$$521$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$522$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$523$$ 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0.965926 0.258819i 0.965926 0.258819i
$$528$$ 0 0
$$529$$ 0.866025 0.500000i 0.866025 0.500000i
$$530$$ 0 0
$$531$$ 0.500000 0.866025i 0.500000 0.866025i
$$532$$ 0 0
$$533$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$534$$ −0.866025 0.500000i −0.866025 0.500000i
$$535$$ 0 0
$$536$$ 1.00000 1.00000
$$537$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$538$$ −0.258819 0.965926i −0.258819 0.965926i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$-1.00000\pi$$
$$542$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 1.00000 1.00000
$$547$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$548$$ 0 0
$$549$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$550$$ 0 0
$$551$$ 1.00000 1.00000
$$552$$ 0 0
$$553$$ −0.965926 0.258819i −0.965926 0.258819i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$558$$ −0.258819 0.965926i −0.258819 0.965926i
$$559$$ 1.00000i 1.00000i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$563$$ 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 1.00000 1.00000
$$567$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$568$$ −1.41421 + 1.41421i −1.41421 + 1.41421i
$$569$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$570$$ 0 0
$$571$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$572$$ 0 0
$$573$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$574$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$575$$ 0 0
$$576$$ 0.500000 0.866025i 0.500000 0.866025i
$$577$$ 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i $$-0.416667\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$578$$ 0 0
$$579$$ 0.866025 0.500000i 0.866025 0.500000i
$$580$$ 0 0
$$581$$ −1.00000 −1.00000
$$582$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$583$$ 0 0
$$584$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$585$$ 0 0
$$586$$ −0.500000 0.866025i −0.500000 0.866025i
$$587$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$588$$ 0 0
$$589$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$593$$ 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$598$$ 0 0
$$599$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$600$$ 0 0
$$601$$ −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i $$0.333333\pi$$
−1.00000 $$1.00000\pi$$
$$602$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$603$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 1.00000 1.73205i 1.00000 1.73205i
$$607$$ 1.93185 0.517638i 1.93185 0.517638i 0.965926 0.258819i $$-0.0833333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$608$$ 0 0
$$609$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$610$$ 0 0
$$611$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$612$$ 0 0
$$613$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i $$0.250000\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$618$$ 0 0
$$619$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −0.707107 0.707107i −0.707107 0.707107i
$$623$$ −0.258819 0.965926i −0.258819 0.965926i
$$624$$ −0.866025 0.500000i −0.866025 0.500000i
$$625$$ 0 0
$$626$$ 1.00000 1.00000
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.00000i 1.00000i
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$633$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$634$$ 1.00000i 1.00000i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$638$$ 0 0
$$639$$ −1.73205 1.00000i −1.73205 1.00000i
$$640$$ 0 0
$$641$$ −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 0.866025i $$-0.666667\pi$$
$$642$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$643$$ −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −1.00000 −1.00000
$$647$$ −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$648$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0.500000 0.866025i 0.500000 0.866025i
$$652$$ 0 0
$$653$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$654$$ 1.00000i 1.00000i
$$655$$ 0 0
$$656$$ −0.500000 0.866025i −0.500000 0.866025i
$$657$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$658$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$659$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.500000\pi$$
$$660$$ 0 0
$$661$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$662$$ −0.707107 0.707107i −0.707107 0.707107i
$$663$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$664$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$665$$ 0 0
$$666$$ −1.00000 −1.00000
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 1.00000i 1.00000i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$674$$ 0.866025 0.500000i 0.866025 0.500000i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i $$-0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$678$$ −0.258819 0.965926i −0.258819 0.965926i
$$679$$ 1.00000i 1.00000i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.00000 1.00000
$$687$$ 0 0
$$688$$ −0.258819 0.965926i −0.258819 0.965926i
$$689$$ 1.00000i 1.00000i
$$690$$ 0 0
$$691$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 1.00000i 1.00000i
$$695$$ 0 0
$$696$$ 1.00000 1.00000
$$697$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$698$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$699$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0.258819 0.965926i 0.258819 0.965926i
$$703$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 1.93185 0.517638i 1.93185 0.517638i
$$708$$ 0 0
$$709$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$710$$ 0 0
$$711$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$712$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$713$$ 0 0
$$714$$ 0.866025 0.500000i 0.866025 0.500000i
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0.965926 0.258819i 0.965926 0.258819i
$$718$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$719$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 1.00000 1.00000
$$727$$ 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i $$-0.416667\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$728$$ −0.258819 0.965926i −0.258819 0.965926i
$$729$$ 1.00000i 1.00000i
$$730$$ 0 0
$$731$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$732$$ 0 0
$$733$$ 0 0 0.965926 0.258819i $$-0.0833333\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0.707107 0.707107i 0.707107 0.707107i
$$739$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$740$$ 0 0
$$741$$ −1.00000 −1.00000
$$742$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$743$$ 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$744$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$745$$ 0 0
$$746$$ −1.00000 + 1.73205i −1.00000 + 1.73205i
$$747$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$748$$ 0 0
$$749$$ −0.866025 0.500000i −0.866025 0.500000i
$$750$$ 0 0
$$751$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$752$$ −0.707107 0.707107i −0.707107 0.707107i
$$753$$ 1.93185 + 0.517638i 1.93185 + 0.517638i
$$754$$ 1.00000i 1.00000i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 0.707107i $$-0.750000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i $$0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$762$$ 0 0
$$763$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$768$$ 0 0
$$769$$ 0.866025 0.500000i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$774$$ 0.866025 0.500000i 0.866025 0.500000i
$$775$$ 0 0
$$776$$ 0.500000 0.866025i 0.500000 0.866025i
$$777$$ −0.707107 0.707107i −0.707107 0.707107i
$$778$$ 0 0
$$779$$ −0.866025 0.500000i −0.866025 0.500000i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$784$$ −0.866025 0.500000i −0.866025 0.500000i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i $$-0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0.500000 0.866025i 0.500000 0.866025i
$$792$$ 0 0
$$793$$ −0.965926 0.258819i −0.965926 0.258819i
$$794$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0.258819 0.965926i 0.258819