Properties

 Label 2520.1.eq.b.899.3 Level $2520$ Weight $1$ Character 2520.899 Analytic conductor $1.258$ Analytic rank $0$ Dimension $8$ Projective image $D_{12}$ CM discriminant -40 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.eq (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: $$\Z[a_1, \ldots, a_{7}]$$ 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 899.3 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 2520.899 Dual form 2520.1.eq.b.1979.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(0.448288 + 0.258819i) q^{11} -1.93185i q^{13} +(-0.965926 - 0.258819i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{19} +1.00000 q^{20} +0.517638 q^{22} +(1.50000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.965926 - 1.67303i) q^{26} +(-0.965926 + 0.258819i) q^{28} +(-0.866025 - 0.500000i) q^{32} +(0.258819 - 0.965926i) q^{35} +(0.965926 + 1.67303i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(0.866025 - 0.500000i) q^{40} +0.517638 q^{41} +(0.448288 - 0.258819i) q^{44} +(0.866025 - 1.50000i) q^{46} +(-0.866025 - 1.50000i) q^{47} +1.00000i q^{49} +1.00000i q^{50} +(-1.67303 - 0.965926i) q^{52} +(0.866025 + 0.500000i) q^{53} +0.517638i q^{55} +(-0.707107 + 0.707107i) q^{56} +(-0.707107 + 1.22474i) q^{59} -1.00000 q^{64} +(1.67303 - 0.965926i) q^{65} +(-0.258819 - 0.965926i) q^{70} +(1.67303 + 0.965926i) q^{74} +1.00000i q^{76} +(-0.133975 - 0.500000i) q^{77} +(0.500000 - 0.866025i) q^{80} +(0.448288 - 0.258819i) q^{82} +(0.258819 - 0.448288i) q^{88} +(0.707107 + 1.22474i) q^{89} +(-1.36603 + 1.36603i) q^{91} -1.73205i q^{92} +(-1.50000 - 0.866025i) q^{94} +(-0.866025 - 0.500000i) q^{95} +(0.500000 + 0.866025i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} + 4q^{5} + O(q^{10})$$ $$8q + 4q^{4} + 4q^{5} - 4q^{16} + 8q^{20} + 12q^{23} - 4q^{25} - 4q^{38} - 8q^{64} - 8q^{77} + 4q^{80} - 4q^{91} - 12q^{94} + 4q^{98} + O(q^{100})$$

Character values

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

 $$n$$ $$281$$ $$631$$ $$1081$$ $$1261$$ $$2017$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 0.500000i 0.866025 0.500000i
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.500000 0.866025i
$$5$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$6$$ 0 0
$$7$$ −0.707107 0.707107i −0.707107 0.707107i
$$8$$ 1.00000i 1.00000i
$$9$$ 0 0
$$10$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$11$$ 0.448288 + 0.258819i 0.448288 + 0.258819i 0.707107 0.707107i $$-0.250000\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$12$$ 0 0
$$13$$ 1.93185i 1.93185i −0.258819 0.965926i $$-0.583333\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$14$$ −0.965926 0.258819i −0.965926 0.258819i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.500000 0.866025i
$$17$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0 0
$$19$$ −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$0.5\pi$$
$$20$$ 1.00000 1.00000
$$21$$ 0 0
$$22$$ 0.517638 0.517638
$$23$$ 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$26$$ −0.965926 1.67303i −0.965926 1.67303i
$$27$$ 0 0
$$28$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ −0.866025 0.500000i −0.866025 0.500000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0.258819 0.965926i 0.258819 0.965926i
$$36$$ 0 0
$$37$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$38$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$39$$ 0 0
$$40$$ 0.866025 0.500000i 0.866025 0.500000i
$$41$$ 0.517638 0.517638 0.258819 0.965926i $$-0.416667\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0.448288 0.258819i 0.448288 0.258819i
$$45$$ 0 0
$$46$$ 0.866025 1.50000i 0.866025 1.50000i
$$47$$ −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000i 1.00000i
$$50$$ 1.00000i 1.00000i
$$51$$ 0 0
$$52$$ −1.67303 0.965926i −1.67303 0.965926i
$$53$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0.517638i 0.517638i
$$56$$ −0.707107 + 0.707107i −0.707107 + 0.707107i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i $$0.416667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 1.67303 0.965926i 1.67303 0.965926i
$$66$$ 0 0
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −0.258819 0.965926i −0.258819 0.965926i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$74$$ 1.67303 + 0.965926i 1.67303 + 0.965926i
$$75$$ 0 0
$$76$$ 1.00000i 1.00000i
$$77$$ −0.133975 0.500000i −0.133975 0.500000i
$$78$$ 0 0
$$79$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$80$$ 0.500000 0.866025i 0.500000 0.866025i
$$81$$ 0 0
$$82$$ 0.448288 0.258819i 0.448288 0.258819i
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0.258819 0.448288i 0.258819 0.448288i
$$89$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$90$$ 0 0
$$91$$ −1.36603 + 1.36603i −1.36603 + 1.36603i
$$92$$ 1.73205i 1.73205i
$$93$$ 0 0
$$94$$ −1.50000 0.866025i −1.50000 0.866025i
$$95$$ −0.866025 0.500000i −0.866025 0.500000i
$$96$$ 0 0
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$99$$ 0 0
$$100$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$101$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$102$$ 0 0
$$103$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$104$$ −1.93185 −1.93185
$$105$$ 0 0
$$106$$ 1.00000 1.00000
$$107$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$108$$ 0 0
$$109$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ 0.258819 + 0.448288i 0.258819 + 0.448288i
$$111$$ 0 0
$$112$$ −0.258819 + 0.965926i −0.258819 + 0.965926i
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 1.41421i 1.41421i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.366025 0.633975i −0.366025 0.633975i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −1.00000
$$126$$ 0 0
$$127$$ −1.93185 −1.93185 −0.965926 0.258819i $$-0.916667\pi$$
−0.965926 + 0.258819i $$0.916667\pi$$
$$128$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$129$$ 0 0
$$130$$ 0.965926 1.67303i 0.965926 1.67303i
$$131$$ 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i $$-0.0833333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$132$$ 0 0
$$133$$ 0.965926 + 0.258819i 0.965926 + 0.258819i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ −0.707107 0.707107i −0.707107 0.707107i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0.500000 0.866025i 0.500000 0.866025i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 1.93185 1.93185
$$149$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$150$$ 0 0
$$151$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$152$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$153$$ 0 0
$$154$$ −0.366025 0.366025i −0.366025 0.366025i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −0.448288 0.258819i −0.448288 0.258819i 0.258819 0.965926i $$-0.416667\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 1.00000i 1.00000i
$$161$$ −1.67303 0.448288i −1.67303 0.448288i
$$162$$ 0 0
$$163$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$164$$ 0.258819 0.448288i 0.258819 0.448288i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$168$$ 0 0
$$169$$ −2.73205 −2.73205
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i $$0.166667\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0.965926 0.258819i 0.965926 0.258819i
$$176$$ 0.517638i 0.517638i
$$177$$ 0 0
$$178$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$179$$ 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ −0.500000 + 1.86603i −0.500000 + 1.86603i
$$183$$ 0 0
$$184$$ −0.866025 1.50000i −0.866025 1.50000i
$$185$$ −0.965926 + 1.67303i −0.965926 + 1.67303i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −1.73205 −1.73205
$$189$$ 0 0
$$190$$ −1.00000 −1.00000
$$191$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$192$$ 0 0
$$193$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$197$$ 1.73205i 1.73205i 0.500000 + 0.866025i $$0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0.258819 + 0.448288i 0.258819 + 0.448288i
$$206$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$207$$ 0 0
$$208$$ −1.67303 + 0.965926i −1.67303 + 0.965926i
$$209$$ −0.517638 −0.517638
$$210$$ 0 0
$$211$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$212$$ 0.866025 0.500000i 0.866025 0.500000i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$224$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ 0 0
$$229$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$230$$ 1.73205 1.73205
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$234$$ 0 0
$$235$$ 0.866025 1.50000i 0.866025 1.50000i
$$236$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i $$-0.166667\pi$$
1.00000i $$0.5\pi$$
$$242$$ −0.633975 0.366025i −0.633975 0.366025i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$246$$ 0 0
$$247$$ 0.965926 + 1.67303i 0.965926 + 1.67303i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$251$$ 1.93185 1.93185 0.965926 0.258819i $$-0.0833333\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$252$$ 0 0
$$253$$ 0.896575 0.896575
$$254$$ −1.67303 + 0.965926i −1.67303 + 0.965926i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$257$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$258$$ 0 0
$$259$$ 0.500000 1.86603i 0.500000 1.86603i
$$260$$ 1.93185i 1.93185i
$$261$$ 0 0
$$262$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ 1.00000i 1.00000i
$$266$$ 0.965926 0.258819i 0.965926 0.258819i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ 0 0
$$271$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$276$$ 0 0
$$277$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ −0.965926 0.258819i −0.965926 0.258819i
$$281$$ 1.93185i 1.93185i −0.258819 0.965926i $$-0.583333\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$282$$ 0 0
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 1.00000i 1.00000i
$$287$$ −0.366025 0.366025i −0.366025 0.366025i
$$288$$ 0 0
$$289$$ −0.500000 0.866025i −0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.00000 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$294$$ 0 0
$$295$$ −1.41421 −1.41421
$$296$$ 1.67303 0.965926i 1.67303 0.965926i
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −1.67303 2.89778i −1.67303 2.89778i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0.866025 + 0.500000i 0.866025 + 0.500000i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ −0.500000 0.133975i −0.500000 0.133975i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0 0
$$313$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ −0.517638 −0.517638
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −0.500000 0.866025i −0.500000 0.866025i
$$321$$ 0 0
$$322$$ −1.67303 + 0.448288i −1.67303 + 0.448288i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 1.67303 + 0.965926i 1.67303 + 0.965926i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0.517638i 0.517638i
$$329$$ −0.448288 + 1.67303i −0.448288 + 1.67303i
$$330$$ 0 0
$$331$$ 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i $$0.166667\pi$$
1.00000i $$0.5\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −2.36603 + 1.36603i −2.36603 + 1.36603i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0.707107 0.707107i 0.707107 0.707107i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$347$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ 0.707107 0.707107i 0.707107 0.707107i
$$351$$ 0 0
$$352$$ −0.258819 0.448288i −0.258819 0.448288i
$$353$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 1.41421 1.41421
$$357$$ 0 0
$$358$$ 1.93185 1.93185
$$359$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$360$$ 0 0
$$361$$ 0 0
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0.500000 + 1.86603i 0.500000 + 1.86603i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i $$0.0833333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$368$$ −1.50000 0.866025i −1.50000 0.866025i
$$369$$ 0 0
$$370$$ 1.93185i 1.93185i
$$371$$ −0.258819 0.965926i −0.258819 0.965926i
$$372$$ 0 0
$$373$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.50000 + 0.866025i −1.50000 + 0.866025i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 1.00000 1.00000 0.500000 0.866025i $$-0.333333\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$380$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i $$0.166667\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0.366025 0.366025i 0.366025 0.366025i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.00000 1.00000
$$393$$ 0 0
$$394$$ 0.866025 + 1.50000i 0.866025 + 1.50000i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 1.00000 1.00000
$$401$$ 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.00000i 1.00000i
$$408$$ 0 0
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 0.448288 + 0.258819i 0.448288 + 0.258819i
$$411$$ 0 0
$$412$$ 1.41421i 1.41421i
$$413$$ 1.36603 0.366025i 1.36603 0.366025i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.965926 + 1.67303i −0.965926 + 1.67303i
$$417$$ 0 0
$$418$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$419$$ −0.517638 −0.517638 −0.258819 0.965926i $$-0.583333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$423$$ 0 0
$$424$$ 0.500000 0.866025i 0.500000 0.866025i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$438$$ 0 0
$$439$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$440$$ 0.517638 0.517638
$$441$$ 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
$$445$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$446$$ −0.707107 1.22474i −0.707107 1.22474i
$$447$$ 0 0
$$448$$ 0.707107 + 0.707107i 0.707107 + 0.707107i
$$449$$ 0.517638i 0.517638i −0.965926 0.258819i $$-0.916667\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$450$$ 0 0
$$451$$ 0.232051 + 0.133975i 0.232051 + 0.133975i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −1.86603 0.500000i −1.86603 0.500000i
$$456$$ 0 0
$$457$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 1.50000 0.866025i 1.50000 0.866025i
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −0.517638 −0.517638 −0.258819 0.965926i $$-0.583333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 1.73205i 1.73205i
$$471$$ 0 0
$$472$$ 1.22474 + 0.707107i 1.22474 + 0.707107i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 1.00000i 1.00000i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$480$$ 0 0
$$481$$ 3.23205 1.86603i 3.23205 1.86603i
$$482$$ 1.00000 1.00000
$$483$$ 0 0
$$484$$ −0.732051 −0.732051
$$485$$ 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 0
$$489$$ 0 0
$$490$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$491$$ 1.41421i 1.41421i 0.707107 + 0.707107i $$0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 1.67303 + 0.965926i 1.67303 + 0.965926i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$500$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$501$$ 0 0
$$502$$ 1.67303 0.965926i 1.67303 0.965926i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0.776457 0.448288i 0.776457 0.448288i
$$507$$ 0 0
$$508$$ −0.965926 + 1.67303i −0.965926 + 1.67303i
$$509$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.22474 0.707107i −1.22474 0.707107i
$$516$$ 0 0
$$517$$ 0.896575i 0.896575i
$$518$$ −0.500000 1.86603i −0.500000 1.86603i
$$519$$ 0 0
$$520$$ −0.965926 1.67303i −0.965926 1.67303i
$$521$$ 0.258819 0.448288i 0.258819 0.448288i −0.707107 0.707107i $$-0.750000\pi$$
0.965926 + 0.258819i $$0.0833333\pi$$
$$522$$ 0 0
$$523$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$524$$ 0.517638 0.517638
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 1.00000 1.73205i 1.00000 1.73205i
$$530$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$531$$ 0 0
$$532$$ 0.707107 0.707107i 0.707107 0.707107i
$$533$$ 1.00000i 1.00000i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −0.258819 + 0.448288i −0.258819 + 0.448288i
$$540$$ 0 0
$$541$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ −0.258819 + 0.448288i −0.258819 + 0.448288i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 1.41421i 1.41421i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −0.866025 0.500000i −0.866025 0.500000i 1.00000i $$-0.5\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −0.965926 + 0.258819i −0.965926 + 0.258819i
$$561$$ 0 0
$$562$$ −0.965926 1.67303i −0.965926 1.67303i
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 0.448288 0.258819i 0.448288 0.258819i −0.258819 0.965926i $$-0.583333\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$572$$ −0.500000 0.866025i −0.500000 0.866025i
$$573$$ 0 0
$$574$$ −0.500000 0.133975i −0.500000 0.133975i
$$575$$ 1.73205i 1.73205i
$$576$$ 0 0
$$577$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$578$$ −0.866025 0.500000i −0.866025 0.500000i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0.258819 + 0.448288i 0.258819 + 0.448288i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −0.866025 + 0.500000i −0.866025 + 0.500000i
$$587$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −1.22474 + 0.707107i −1.22474 + 0.707107i
$$591$$ 0 0
$$592$$ 0.965926 1.67303i 0.965926 1.67303i
$$593$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ −2.89778 1.67303i −2.89778 1.67303i
$$599$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$600$$ 0 0
$$601$$ 2.00000i 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0.366025 0.633975i 0.366025 0.633975i
$$606$$ 0 0
$$607$$ 1.67303 0.965926i 1.67303 0.965926i 0.707107 0.707107i $$-0.250000\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$608$$ 1.00000 1.00000
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −2.89778 + 1.67303i −2.89778 + 1.67303i
$$612$$ 0 0
$$613$$ −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i $$0.583333\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ −0.500000 + 0.133975i −0.500000 + 0.133975i
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0.366025 1.36603i 0.366025 1.36603i
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −0.965926 1.67303i −0.965926 1.67303i
$$636$$ 0 0
$$637$$ 1.93185 1.93185
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −0.866025 0.500000i −0.866025 0.500000i
$$641$$ −1.67303 0.965926i −1.67303 0.965926i −0.965926 0.258819i $$-0.916667\pi$$
−0.707107 0.707107i $$-0.750000\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ −1.22474 + 1.22474i −1.22474 + 1.22474i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0.866025 1.50000i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$648$$ 0 0
$$649$$ −0.633975 + 0.366025i −0.633975 + 0.366025i
$$650$$ 1.93185 1.93185
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$654$$ 0 0
$$655$$ −0.258819 + 0.448288i −0.258819 + 0.448288i
$$656$$ −0.258819 0.448288i −0.258819 0.448288i
$$657$$ 0 0
$$658$$ 0.448288 + 1.67303i 0.448288 + 1.67303i
$$659$$ 1.41421i 1.41421i −0.707107 0.707107i $$-0.750000\pi$$
0.707107 0.707107i $$-0.250000\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$662$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0.258819 + 0.965926i 0.258819 + 0.965926i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −1.36603 + 2.36603i −1.36603 + 2.36603i
$$677$$ −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0.258819 0.965926i 0.258819 0.965926i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0.965926 1.67303i 0.965926 1.67303i
$$690$$ 0 0
$$691$$ −1.73205 + 1.00000i −1.73205 + 1.00000i −0.866025 + 0.500000i $$0.833333\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$692$$ 1.73205 1.73205
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0.258819 0.965926i 0.258819 0.965926i
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −1.67303 0.965926i −1.67303 0.965926i
$$704$$ −0.448288 0.258819i −0.448288 0.258819i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 1.22474 0.707107i 1.22474 0.707107i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 1.00000 1.00000
$$716$$ 1.67303 0.965926i 1.67303 0.965926i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0 0
$$721$$ 1.36603 + 0.366025i 1.36603 + 0.366025i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 1.93185i 1.93185i −0.258819 0.965926i $$-0.583333\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$728$$ 1.36603 + 1.36603i 1.36603 + 1.36603i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −0.448288 + 0.258819i −0.448288 + 0.258819i −0.707107 0.707107i $$-0.750000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$734$$ 1.93185 1.93185
$$735$$ 0 0
$$736$$ −1.73205 −1.73205
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0.866025 1.50000i 0.866025 1.50000i 1.00000i $$-0.5\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$740$$ 0.965926 + 1.67303i 0.965926 + 1.67303i
$$741$$ 0 0
$$742$$ −0.707107 0.707107i −0.707107 0.707107i
$$743$$ 1.00000i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −1.22474 0.707107i −1.22474 0.707107i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$752$$ −0.866025 + 1.50000i −0.866025 + 1.50000i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$758$$ 0.866025 0.500000i 0.866025 0.500000i
$$759$$ 0 0
$$760$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$761$$ 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$767$$ 2.36603 + 1.36603i 2.36603 + 1.36603i
$$768$$ 0 0
$$769$$ 1.00000i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$770$$ 0.133975 0.500000i 0.133975 0.500000i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i $$-0.666667\pi$$
1.00000 $$0$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.448288 + 0.258819i −0.448288 + 0.258819i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0.866025 0.500000i 0.866025 0.500000i
$$785$$ 0.517638i 0.517638i
$$786$$ 0 0
$$787$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$788$$ 1.50000 + 0.866025i 1.50000 + 0.866025i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0.866025 0.500000i 0.866025 0.500000i
$$801$$ 0 0
$$802$$ 0.258819 0.448288i 0.258819 0.448288i
$$803$$ 0 0