# Properties

 Label 1911.1.w.e.116.3 Level $1911$ Weight $1$ Character 1911.116 Analytic conductor $0.954$ Analytic rank $0$ Dimension $8$ Projective image $D_{8}$ CM discriminant -39 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1911 = 3 \cdot 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 1911.w (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.953713239142$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.339738624.2 Defining polynomial: $$x^{8} + 4x^{6} + 14x^{4} + 8x^{2} + 4$$ x^8 + 4*x^6 + 14*x^4 + 8*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{8}$$ Projective field: Galois closure of 8.2.90724673403.2

## Embedding invariants

 Embedding label 116.3 Root $$0.923880 + 1.60021i$$ of defining polynomial Character $$\chi$$ $$=$$ 1911.116 Dual form 1911.1.w.e.1598.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.382683 + 0.662827i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.207107 - 0.358719i) q^{4} +(0.923880 + 1.60021i) q^{5} -0.765367 q^{6} +1.08239 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.382683 + 0.662827i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.207107 - 0.358719i) q^{4} +(0.923880 + 1.60021i) q^{5} -0.765367 q^{6} +1.08239 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(-0.382683 + 0.662827i) q^{11} +(0.207107 + 0.358719i) q^{12} -1.00000 q^{13} -1.84776 q^{15} +(0.207107 + 0.358719i) q^{16} +(0.382683 - 0.662827i) q^{18} +0.765367 q^{20} -0.585786 q^{22} +(-0.541196 + 0.937379i) q^{24} +(-1.20711 + 2.09077i) q^{25} +(-0.382683 - 0.662827i) q^{26} +1.00000 q^{27} +(-0.707107 - 1.22474i) q^{30} +(0.382683 - 0.662827i) q^{32} +(-0.382683 - 0.662827i) q^{33} -0.414214 q^{36} +(0.500000 - 0.866025i) q^{39} +(1.00000 + 1.73205i) q^{40} +1.84776 q^{41} +(0.158513 + 0.274552i) q^{44} +(0.923880 - 1.60021i) q^{45} +(-0.923880 - 1.60021i) q^{47} -0.414214 q^{48} -1.84776 q^{50} +(-0.207107 + 0.358719i) q^{52} +(0.382683 + 0.662827i) q^{54} -1.41421 q^{55} +(-0.382683 + 0.662827i) q^{59} +(-0.382683 + 0.662827i) q^{60} +1.00000 q^{64} +(-0.923880 - 1.60021i) q^{65} +(0.292893 - 0.507306i) q^{66} +1.84776 q^{71} +(-0.541196 - 0.937379i) q^{72} +(-1.20711 - 2.09077i) q^{75} +0.765367 q^{78} +(-0.707107 - 1.22474i) q^{79} +(-0.382683 + 0.662827i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.707107 + 1.22474i) q^{82} -0.765367 q^{83} +(-0.414214 + 0.717439i) q^{88} +(0.382683 + 0.662827i) q^{89} +1.41421 q^{90} +(0.707107 - 1.22474i) q^{94} +(0.382683 + 0.662827i) q^{96} +0.765367 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 4 q^{3} - 4 q^{4} - 4 q^{9}+O(q^{10})$$ 8 * q - 4 * q^3 - 4 * q^4 - 4 * q^9 $$8 q - 4 q^{3} - 4 q^{4} - 4 q^{9} - 4 q^{12} - 8 q^{13} - 4 q^{16} - 16 q^{22} - 4 q^{25} + 8 q^{27} + 8 q^{36} + 4 q^{39} + 8 q^{40} + 8 q^{48} + 4 q^{52} + 8 q^{64} + 8 q^{66} - 4 q^{75} - 4 q^{81} + 8 q^{88}+O(q^{100})$$ 8 * q - 4 * q^3 - 4 * q^4 - 4 * q^9 - 4 * q^12 - 8 * q^13 - 4 * q^16 - 16 * q^22 - 4 * q^25 + 8 * q^27 + 8 * q^36 + 4 * q^39 + 8 * q^40 + 8 * q^48 + 4 * q^52 + 8 * q^64 + 8 * q^66 - 4 * q^75 - 4 * q^81 + 8 * q^88

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times$$.

 $$n$$ $$638$$ $$1471$$ $$1522$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i $$-0.0416667\pi$$
−0.608761 + 0.793353i $$0.708333\pi$$
$$3$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$4$$ 0.207107 0.358719i 0.207107 0.358719i
$$5$$ 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i $$0.208333\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$6$$ −0.765367 −0.765367
$$7$$ 0 0
$$8$$ 1.08239 1.08239
$$9$$ −0.500000 0.866025i −0.500000 0.866025i
$$10$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$11$$ −0.382683 + 0.662827i −0.382683 + 0.662827i −0.991445 0.130526i $$-0.958333\pi$$
0.608761 + 0.793353i $$0.291667\pi$$
$$12$$ 0.207107 + 0.358719i 0.207107 + 0.358719i
$$13$$ −1.00000 −1.00000
$$14$$ 0 0
$$15$$ −1.84776 −1.84776
$$16$$ 0.207107 + 0.358719i 0.207107 + 0.358719i
$$17$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0.382683 0.662827i 0.382683 0.662827i
$$19$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$20$$ 0.765367 0.765367
$$21$$ 0 0
$$22$$ −0.585786 −0.585786
$$23$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$24$$ −0.541196 + 0.937379i −0.541196 + 0.937379i
$$25$$ −1.20711 + 2.09077i −1.20711 + 2.09077i
$$26$$ −0.382683 0.662827i −0.382683 0.662827i
$$27$$ 1.00000 1.00000
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ −0.707107 1.22474i −0.707107 1.22474i
$$31$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$32$$ 0.382683 0.662827i 0.382683 0.662827i
$$33$$ −0.382683 0.662827i −0.382683 0.662827i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −0.414214 −0.414214
$$37$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$38$$ 0 0
$$39$$ 0.500000 0.866025i 0.500000 0.866025i
$$40$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$41$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0.158513 + 0.274552i 0.158513 + 0.274552i
$$45$$ 0.923880 1.60021i 0.923880 1.60021i
$$46$$ 0 0
$$47$$ −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i $$-0.791667\pi$$
−0.130526 0.991445i $$-0.541667\pi$$
$$48$$ −0.414214 −0.414214
$$49$$ 0 0
$$50$$ −1.84776 −1.84776
$$51$$ 0 0
$$52$$ −0.207107 + 0.358719i −0.207107 + 0.358719i
$$53$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$54$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$55$$ −1.41421 −1.41421
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −0.382683 + 0.662827i −0.382683 + 0.662827i −0.991445 0.130526i $$-0.958333\pi$$
0.608761 + 0.793353i $$0.291667\pi$$
$$60$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$61$$ 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
$$65$$ −0.923880 1.60021i −0.923880 1.60021i
$$66$$ 0.292893 0.507306i 0.292893 0.507306i
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 1.84776 1.84776 0.923880 0.382683i $$-0.125000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$72$$ −0.541196 0.937379i −0.541196 0.937379i
$$73$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$74$$ 0 0
$$75$$ −1.20711 2.09077i −1.20711 2.09077i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0.765367 0.765367
$$79$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$80$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$81$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$82$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$83$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.414214 + 0.717439i −0.414214 + 0.717439i
$$89$$ 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i $$-0.0416667\pi$$
−0.608761 + 0.793353i $$0.708333\pi$$
$$90$$ 1.41421 1.41421
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0.707107 1.22474i 0.707107 1.22474i
$$95$$ 0 0
$$96$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0 0
$$99$$ 0.765367 0.765367
$$100$$ 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
$$103$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$104$$ −1.08239 −1.08239
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ 0.207107 0.358719i 0.207107 0.358719i
$$109$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$110$$ −0.541196 0.937379i −0.541196 0.937379i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$118$$ −0.585786 −0.585786
$$119$$ 0 0
$$120$$ −2.00000 −2.00000
$$121$$ 0.207107 + 0.358719i 0.207107 + 0.358719i
$$122$$ 0 0
$$123$$ −0.923880 + 1.60021i −0.923880 + 1.60021i
$$124$$ 0 0
$$125$$ −2.61313 −2.61313
$$126$$ 0 0
$$127$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0.707107 1.22474i 0.707107 1.22474i
$$131$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$132$$ −0.317025 −0.317025
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$136$$ 0 0
$$137$$ 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i $$-0.458333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$138$$ 0 0
$$139$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$140$$ 0 0
$$141$$ 1.84776 1.84776
$$142$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$143$$ 0.382683 0.662827i 0.382683 0.662827i
$$144$$ 0.207107 0.358719i 0.207107 0.358719i
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i $$0.208333\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$150$$ 0.923880 1.60021i 0.923880 1.60021i
$$151$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −0.207107 0.358719i −0.207107 0.358719i
$$157$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$158$$ 0.541196 0.937379i 0.541196 0.937379i
$$159$$ 0 0
$$160$$ 1.41421 1.41421
$$161$$ 0 0
$$162$$ −0.765367 −0.765367
$$163$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$164$$ 0.382683 0.662827i 0.382683 0.662827i
$$165$$ 0.707107 1.22474i 0.707107 1.22474i
$$166$$ −0.292893 0.507306i −0.292893 0.507306i
$$167$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$168$$ 0 0
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −0.317025 −0.317025
$$177$$ −0.382683 0.662827i −0.382683 0.662827i
$$178$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$179$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$180$$ −0.382683 0.662827i −0.382683 0.662827i
$$181$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −0.765367 −0.765367
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$192$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$193$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$194$$ 0 0
$$195$$ 1.84776 1.84776
$$196$$ 0 0
$$197$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$198$$ 0.292893 + 0.507306i 0.292893 + 0.507306i
$$199$$ 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i $$-0.333333\pi$$
0.500000 0.866025i $$-0.333333\pi$$
$$200$$ −1.30656 + 2.26303i −1.30656 + 2.26303i
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 1.70711 + 2.95680i 1.70711 + 2.95680i
$$206$$ 0.541196 0.937379i 0.541196 0.937379i
$$207$$ 0 0
$$208$$ −0.207107 0.358719i −0.207107 0.358719i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 1.41421 1.41421 0.707107 0.707107i $$-0.250000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$212$$ 0 0
$$213$$ −0.923880 + 1.60021i −0.923880 + 1.60021i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 1.08239 1.08239
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 2.41421 2.41421
$$226$$ 0 0
$$227$$ −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i $$0.541667\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$234$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$235$$ 1.70711 2.95680i 1.70711 2.95680i
$$236$$ 0.158513 + 0.274552i 0.158513 + 0.274552i
$$237$$ 1.41421 1.41421
$$238$$ 0 0
$$239$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$240$$ −0.382683 0.662827i −0.382683 0.662827i
$$241$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$242$$ −0.158513 + 0.274552i −0.158513 + 0.274552i
$$243$$ −0.500000 0.866025i −0.500000 0.866025i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ −1.41421 −1.41421
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0.382683 0.662827i 0.382683 0.662827i
$$250$$ −1.00000 1.73205i −1.00000 1.73205i
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −0.541196 0.937379i −0.541196 0.937379i
$$255$$ 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 0
$$260$$ −0.765367 −0.765367
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ −0.414214 0.717439i −0.414214 0.717439i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −0.765367 −0.765367
$$268$$ 0 0
$$269$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$270$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$271$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 1.41421 1.41421
$$275$$ −0.923880 1.60021i −0.923880 1.60021i
$$276$$ 0 0
$$277$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$278$$ −0.541196 0.937379i −0.541196 0.937379i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$282$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$283$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$284$$ 0.382683 0.662827i 0.382683 0.662827i
$$285$$ 0 0
$$286$$ 0.585786 0.585786
$$287$$ 0 0
$$288$$ −0.765367 −0.765367
$$289$$ −0.500000 0.866025i −0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$294$$ 0 0
$$295$$ −1.41421 −1.41421
$$296$$ 0 0
$$297$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$298$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$299$$ 0 0
$$300$$ −1.00000 −1.00000
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 1.41421 1.41421
$$310$$ 0 0
$$311$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$312$$ 0.541196 0.937379i 0.541196 0.937379i
$$313$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ 1.08239 1.08239
$$315$$ 0 0
$$316$$ −0.585786 −0.585786
$$317$$ 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i $$-0.0416667\pi$$
−0.608761 + 0.793353i $$0.708333\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0.207107 + 0.358719i 0.207107 + 0.358719i
$$325$$ 1.20711 2.09077i 1.20711 2.09077i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 2.00000 2.00000
$$329$$ 0 0
$$330$$ 1.08239 1.08239
$$331$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$332$$ −0.158513 + 0.274552i −0.158513 + 0.274552i
$$333$$ 0 0
$$334$$ 0.292893 + 0.507306i 0.292893 + 0.507306i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −1.41421 −1.41421 −0.707107 0.707107i $$-0.750000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$338$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −1.00000
$$352$$ 0.292893 + 0.507306i 0.292893 + 0.507306i
$$353$$ 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i $$-0.708333\pi$$
0.991445 + 0.130526i $$0.0416667\pi$$
$$354$$ 0.292893 0.507306i 0.292893 0.507306i
$$355$$ 1.70711 + 2.95680i 1.70711 + 2.95680i
$$356$$ 0.317025 0.317025
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i $$-0.0416667\pi$$
−0.608761 + 0.793353i $$0.708333\pi$$
$$360$$ 1.00000 1.73205i 1.00000 1.73205i
$$361$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$362$$ 0.541196 + 0.937379i 0.541196 + 0.937379i
$$363$$ −0.414214 −0.414214
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −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
$$369$$ −0.923880 1.60021i −0.923880 1.60021i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 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
$$375$$ 1.30656 2.26303i 1.30656 2.26303i
$$376$$ −1.00000 1.73205i −1.00000 1.73205i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0.707107 1.22474i 0.707107 1.22474i
$$382$$ 0 0
$$383$$ 0.923880 + 1.60021i 0.923880 + 1.60021i 0.793353 + 0.608761i $$0.208333\pi$$
0.130526 + 0.991445i $$0.458333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$390$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0.292893 + 0.507306i 0.292893 + 0.507306i
$$395$$ 1.30656 2.26303i 1.30656 2.26303i
$$396$$ 0.158513 0.274552i 0.158513 0.274552i
$$397$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$398$$ 1.53073 1.53073
$$399$$ 0 0
$$400$$ −1.00000 −1.00000
$$401$$ −0.382683 0.662827i −0.382683 0.662827i 0.608761 0.793353i $$-0.291667\pi$$
−0.991445 + 0.130526i $$0.958333\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.84776 −1.84776
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ −1.30656 + 2.26303i −1.30656 + 2.26303i
$$411$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$412$$ −0.585786 −0.585786
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −0.707107 1.22474i −0.707107 1.22474i
$$416$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$417$$ 0.707107 1.22474i 0.707107 1.22474i
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0.541196 + 0.937379i 0.541196 + 0.937379i
$$423$$ −0.923880 + 1.60021i −0.923880 + 1.60021i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ −1.41421 −1.41421
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$430$$ 0 0
$$431$$ −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i $$0.541667\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$432$$ 0.207107 + 0.358719i 0.207107 + 0.358719i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$440$$ −1.53073 −1.53073
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$444$$ 0 0
$$445$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$446$$ 0 0
$$447$$ −1.84776 −1.84776
$$448$$ 0 0
$$449$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$450$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$451$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ −1.41421 −1.41421
$$455$$ 0 0
$$456$$ 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
$$460$$ 0 0
$$461$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$468$$ 0.414214 0.414214
$$469$$ 0 0
$$470$$ 2.61313 2.61313
$$471$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$472$$ −0.414214 + 0.717439i −0.414214 + 0.717439i
$$473$$ 0 0
$$474$$ 0.541196 + 0.937379i 0.541196 + 0.937379i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −0.292893 0.507306i −0.292893 0.507306i
$$479$$ 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i $$-0.458333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$480$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0.171573 0.171573
$$485$$ 0 0
$$486$$ 0.382683 0.662827i 0.382683 0.662827i
$$487$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0.707107 + 1.22474i 0.707107 + 1.22474i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0.585786 0.585786
$$499$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$500$$ −0.541196 + 0.937379i −0.541196 + 0.937379i
$$501$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$502$$ 0 0
$$503$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$508$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$509$$ −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i $$-0.791667\pi$$
−0.130526 0.991445i $$-0.541667\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0.765367 0.765367
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 1.30656 2.26303i 1.30656 2.26303i
$$516$$ 0 0
$$517$$ 1.41421 1.41421
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −1.00000 1.73205i −1.00000 1.73205i
$$521$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$522$$ 0 0
$$523$$ −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i $$-0.916667\pi$$
0.258819 0.965926i $$-0.416667\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0.158513 0.274552i 0.158513 0.274552i
$$529$$ −0.500000 + 0.866025i −0.500000 + 0.866025i
$$530$$ 0 0
$$531$$ 0.765367 0.765367
$$532$$ 0 0
$$533$$ −1.84776 −1.84776
$$534$$ −0.292893 0.507306i −0.292893 0.507306i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0.765367 0.765367
$$541$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$542$$ 0 0
$$543$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$548$$ −0.382683 0.662827i −0.382683 0.662827i
$$549$$ 0 0
$$550$$ 0.707107 1.22474i 0.707107 1.22474i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$557$$ −0.923880 + 1.60021i −0.923880 + 1.60021i −0.130526 + 0.991445i $$0.541667\pi$$
−0.793353 + 0.608761i $$0.791667\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.707107 1.22474i −0.707107 1.22474i
$$563$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$564$$ 0.382683 0.662827i 0.382683 0.662827i
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 2.00000 2.00000
$$569$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$570$$ 0 0
$$571$$ 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$572$$ −0.158513 0.274552i −0.158513 0.274552i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.500000 0.866025i
$$577$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$578$$ 0.382683 0.662827i 0.382683 0.662827i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ −0.923880 + 1.60021i −0.923880 + 1.60021i
$$586$$ 0.292893 + 0.507306i 0.292893 + 0.507306i
$$587$$ −1.84776 −1.84776 −0.923880 0.382683i $$-0.875000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −0.541196 0.937379i −0.541196 0.937379i
$$591$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$592$$ 0 0
$$593$$ 0.382683 + 0.662827i 0.382683 + 0.662827i 0.991445 0.130526i $$-0.0416667\pi$$
−0.608761 + 0.793353i $$0.708333\pi$$
$$594$$ −0.585786 −0.585786
$$595$$ 0 0
$$596$$ 0.765367 0.765367
$$597$$ 1.00000 + 1.73205i 1.00000 + 1.73205i
$$598$$ 0 0
$$599$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$600$$ −1.30656 2.26303i −1.30656 2.26303i
$$601$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$606$$ 0 0
$$607$$ 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0.923880 + 1.60021i 0.923880 + 1.60021i
$$612$$ 0 0
$$613$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$614$$ 0 0
$$615$$ −3.41421 −3.41421
$$616$$ 0 0
$$617$$ −0.765367 −0.765367 −0.382683 0.923880i $$-0.625000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$618$$ 0.541196 + 0.937379i 0.541196 + 0.937379i
$$619$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0.414214 0.414214
$$625$$ −1.20711 2.09077i −1.20711 2.09077i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ −0.292893 0.507306i −0.292893 0.507306i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ −0.765367 1.32565i −0.765367 1.32565i
$$633$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$634$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$635$$ −1.30656 2.26303i −1.30656 2.26303i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ −0.923880 1.60021i −0.923880 1.60021i
$$640$$ 0 0
$$641$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$642$$ 0 0
$$643$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$648$$ −0.541196 + 0.937379i −0.541196 + 0.937379i
$$649$$ −0.292893 0.507306i −0.292893 0.507306i
$$650$$ 1.84776 1.84776
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ −0.292893 0.507306i −0.292893 0.507306i
$$661$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −0.828427 −0.828427
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0.158513 0.274552i 0.158513 0.274552i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$674$$ −0.541196 0.937379i −0.541196 0.937379i
$$675$$ −1.20711 + 2.09077i −1.20711 + 2.09077i
$$676$$ 0.207107 0.358719i 0.207107 0.358719i
$$677$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −0.923880 1.60021i −0.923880 1.60021i
$$682$$ 0 0
$$683$$ 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i $$-0.458333\pi$$
0.793353 0.608761i $$-0.208333\pi$$
$$684$$ 0 0
$$685$$ 3.41421 3.41421
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.30656 2.26303i −1.30656 2.26303i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ −0.382683 0.662827i −0.382683 0.662827i
$$703$$ 0 0
$$704$$ −0.382683 + 0.662827i −0.382683 + 0.662827i
$$705$$ 1.70711 + 2.95680i 1.70711 + 2.95680i
$$706$$ 0.585786 0.585786
$$707$$ 0 0
$$708$$ −0.317025 −0.317025
$$709$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$710$$ −1.30656 + 2.26303i −1.30656 + 2.26303i
$$711$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$712$$ 0.414214 + 0.717439i 0.414214 + 0.717439i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 1.41421 1.41421
$$716$$ 0 0
$$717$$ 0.382683 0.662827i 0.382683 0.662827i
$$718$$ −0.292893 + 0.507306i −0.292893 + 0.507306i
$$719$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$720$$ 0.765367 0.765367
$$721$$ 0 0
$$722$$ −0.765367 −0.765367
$$723$$ 0 0
$$724$$ 0.292893 0.507306i 0.292893 0.507306i
$$725$$ 0 0
$$726$$ −0.158513 0.274552i −0.158513 0.274552i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$734$$ −1.08239 −1.08239
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0.707107 1.22474i 0.707107 1.22474i
$$739$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.765367 0.765367 0.382683 0.923880i $$-0.375000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$744$$ 0 0
$$745$$ −1.70711 + 2.95680i −1.70711 + 2.95680i
$$746$$ 0.541196 0.937379i 0.541196 0.937379i
$$747$$ 0.382683 + 0.662827i 0.382683 + 0.662827i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 2.00000 2.00000
$$751$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$752$$ 0.382683 0.662827i 0.382683 0.662827i
$$753$$ 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 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.923880 1.60021i −0.923880 1.60021i −0.793353 0.608761i $$-0.791667\pi$$
−0.130526 0.991445i $$-0.541667\pi$$
$$762$$ 1.08239 1.08239
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$767$$ 0.382683 0.662827i 0.382683 0.662827i
$$768$$ 0.500000 + 0.866025i 0.500000 + 0.866025i
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0.382683 0.662827i 0.382683 0.662827i −0.608761 0.793353i $$-0.708333\pi$$
0.991445 + 0.130526i $$0.0416667\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0.382683 0.662827i 0.382683 0.662827i
$$781$$ −0.707107 + 1.22474i −0.707107 + 1.22474i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.61313 2.61313
$$786$$ 0 0
$$787$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$788$$ 0.158513 0.274552i 0.158513 0.274552i
$$789$$ 0 0
$$790$$ 2.00000 2.00000
$$791$$ 0 0
$$792$$ 0.828427 0.828427
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ −0.414214 0.717439i −0.414214 0.717439i
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0.923880 + 1.60021i 0.923880 +