# Properties

 Label 168.2.ba.a.5.1 Level $168$ Weight $2$ Character 168.5 Analytic conductor $1.341$ Analytic rank $0$ Dimension $4$ CM discriminant -24 Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 168.ba (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.34148675396$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

## Embedding invariants

 Embedding label 5.1 Root $$-0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 168.5 Dual form 168.2.ba.a.101.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.621320 - 0.358719i) q^{5} -2.44949i q^{6} +(-2.62132 + 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.621320 - 0.358719i) q^{5} -2.44949i q^{6} +(-2.62132 + 0.358719i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.878680 - 0.507306i) q^{10} +(-2.91421 - 5.04757i) q^{11} +(3.00000 + 1.73205i) q^{12} +(1.41421 - 3.46410i) q^{14} +1.24264 q^{15} +(-2.00000 + 3.46410i) q^{16} +(2.12132 + 3.67423i) q^{18} +1.43488i q^{20} +(3.62132 - 2.80821i) q^{21} +8.24264 q^{22} +(-4.24264 + 2.44949i) q^{24} +(-2.24264 - 3.88437i) q^{25} +5.19615i q^{27} +(3.24264 + 4.18154i) q^{28} -7.58579 q^{29} +(-0.878680 + 1.52192i) q^{30} +(-9.62132 + 5.55487i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(8.74264 + 5.04757i) q^{33} +(1.75736 + 0.717439i) q^{35} -6.00000 q^{36} +(-1.75736 - 1.01461i) q^{40} +(0.878680 + 6.42090i) q^{42} +(-5.82843 + 10.0951i) q^{44} +(-1.86396 + 1.07616i) q^{45} -6.92820i q^{48} +(6.74264 - 1.88064i) q^{49} +6.34315 q^{50} +(2.03553 + 3.52565i) q^{53} +(-6.36396 - 3.67423i) q^{54} +4.18154i q^{55} +(-7.41421 + 1.01461i) q^{56} +(5.36396 - 9.29065i) q^{58} +(12.9853 - 7.49706i) q^{59} +(-1.24264 - 2.15232i) q^{60} -15.7116i q^{62} +(-3.00000 + 7.34847i) q^{63} +8.00000 q^{64} +(-12.3640 + 7.13834i) q^{66} +(-2.12132 + 1.64501i) q^{70} +(4.24264 - 7.34847i) q^{72} +(-8.48528 + 4.89898i) q^{73} +(6.72792 + 3.88437i) q^{75} +(9.44975 + 12.1859i) q^{77} +(8.86396 - 15.3528i) q^{79} +(2.48528 - 1.43488i) q^{80} +(-4.50000 - 7.79423i) q^{81} +13.5592i q^{83} +(-8.48528 - 3.46410i) q^{84} +(11.3787 - 6.56948i) q^{87} +(-8.24264 - 14.2767i) q^{88} -3.04384i q^{90} +(9.62132 - 16.6646i) q^{93} +(8.48528 + 4.89898i) q^{96} -8.06591i q^{97} +(-2.46447 + 9.58783i) q^{98} -17.4853 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9}+O(q^{10})$$ 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9 $$4 q - 6 q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{7} + 6 q^{9} + 12 q^{10} - 6 q^{11} + 12 q^{12} - 12 q^{15} - 8 q^{16} + 6 q^{21} + 16 q^{22} + 8 q^{25} - 4 q^{28} - 36 q^{29} - 12 q^{30} - 30 q^{31} + 18 q^{33} + 24 q^{35} - 24 q^{36} - 24 q^{40} + 12 q^{42} - 12 q^{44} + 18 q^{45} + 10 q^{49} + 48 q^{50} - 6 q^{53} - 24 q^{56} - 4 q^{58} + 18 q^{59} + 12 q^{60} - 12 q^{63} + 32 q^{64} - 24 q^{66} - 24 q^{75} + 18 q^{77} + 10 q^{79} - 24 q^{80} - 18 q^{81} + 54 q^{87} - 16 q^{88} + 30 q^{93} - 24 q^{98} - 36 q^{99}+O(q^{100})$$ 4 * q - 6 * q^3 - 4 * q^4 + 6 * q^5 - 2 * q^7 + 6 * q^9 + 12 * q^10 - 6 * q^11 + 12 * q^12 - 12 * q^15 - 8 * q^16 + 6 * q^21 + 16 * q^22 + 8 * q^25 - 4 * q^28 - 36 * q^29 - 12 * q^30 - 30 * q^31 + 18 * q^33 + 24 * q^35 - 24 * q^36 - 24 * q^40 + 12 * q^42 - 12 * q^44 + 18 * q^45 + 10 * q^49 + 48 * q^50 - 6 * q^53 - 24 * q^56 - 4 * q^58 + 18 * q^59 + 12 * q^60 - 12 * q^63 + 32 * q^64 - 24 * q^66 - 24 * q^75 + 18 * q^77 + 10 * q^79 - 24 * q^80 - 18 * q^81 + 54 * q^87 - 16 * q^88 + 30 * q^93 - 24 * q^98 - 36 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$$.

 $$n$$ $$73$$ $$85$$ $$113$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 1.22474i −0.500000 + 0.866025i
$$3$$ −1.50000 + 0.866025i −0.866025 + 0.500000i
$$4$$ −1.00000 1.73205i −0.500000 0.866025i
$$5$$ −0.621320 0.358719i −0.277863 0.160424i 0.354593 0.935021i $$-0.384620\pi$$
−0.632456 + 0.774597i $$0.717953\pi$$
$$6$$ 2.44949i 1.00000i
$$7$$ −2.62132 + 0.358719i −0.990766 + 0.135583i
$$8$$ 2.82843 1.00000
$$9$$ 1.50000 2.59808i 0.500000 0.866025i
$$10$$ 0.878680 0.507306i 0.277863 0.160424i
$$11$$ −2.91421 5.04757i −0.878668 1.52190i −0.852803 0.522233i $$-0.825099\pi$$
−0.0258656 0.999665i $$-0.508234\pi$$
$$12$$ 3.00000 + 1.73205i 0.866025 + 0.500000i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 1.41421 3.46410i 0.377964 0.925820i
$$15$$ 1.24264 0.320848
$$16$$ −2.00000 + 3.46410i −0.500000 + 0.866025i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 2.12132 + 3.67423i 0.500000 + 0.866025i
$$19$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$20$$ 1.43488i 0.320848i
$$21$$ 3.62132 2.80821i 0.790237 0.612801i
$$22$$ 8.24264 1.75734
$$23$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$24$$ −4.24264 + 2.44949i −0.866025 + 0.500000i
$$25$$ −2.24264 3.88437i −0.448528 0.776874i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 3.24264 + 4.18154i 0.612801 + 0.790237i
$$29$$ −7.58579 −1.40865 −0.704323 0.709880i $$-0.748749\pi$$
−0.704323 + 0.709880i $$0.748749\pi$$
$$30$$ −0.878680 + 1.52192i −0.160424 + 0.277863i
$$31$$ −9.62132 + 5.55487i −1.72804 + 0.997684i −0.830014 + 0.557743i $$0.811667\pi$$
−0.898027 + 0.439941i $$0.854999\pi$$
$$32$$ −2.82843 4.89898i −0.500000 0.866025i
$$33$$ 8.74264 + 5.04757i 1.52190 + 0.878668i
$$34$$ 0 0
$$35$$ 1.75736 + 0.717439i 0.297048 + 0.121269i
$$36$$ −6.00000 −1.00000
$$37$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ −1.75736 1.01461i −0.277863 0.160424i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0.878680 + 6.42090i 0.135583 + 0.990766i
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −5.82843 + 10.0951i −0.878668 + 1.52190i
$$45$$ −1.86396 + 1.07616i −0.277863 + 0.160424i
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 6.92820i 1.00000i
$$49$$ 6.74264 1.88064i 0.963234 0.268662i
$$50$$ 6.34315 0.897056
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.03553 + 3.52565i 0.279602 + 0.484285i 0.971286 0.237915i $$-0.0764641\pi$$
−0.691684 + 0.722200i $$0.743131\pi$$
$$54$$ −6.36396 3.67423i −0.866025 0.500000i
$$55$$ 4.18154i 0.563839i
$$56$$ −7.41421 + 1.01461i −0.990766 + 0.135583i
$$57$$ 0 0
$$58$$ 5.36396 9.29065i 0.704323 1.21992i
$$59$$ 12.9853 7.49706i 1.69054 0.976034i 0.736460 0.676481i $$-0.236496\pi$$
0.954080 0.299552i $$-0.0968372\pi$$
$$60$$ −1.24264 2.15232i −0.160424 0.277863i
$$61$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$62$$ 15.7116i 1.99537i
$$63$$ −3.00000 + 7.34847i −0.377964 + 0.925820i
$$64$$ 8.00000 1.00000
$$65$$ 0 0
$$66$$ −12.3640 + 7.13834i −1.52190 + 0.878668i
$$67$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −2.12132 + 1.64501i −0.253546 + 0.196616i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 4.24264 7.34847i 0.500000 0.866025i
$$73$$ −8.48528 + 4.89898i −0.993127 + 0.573382i −0.906208 0.422833i $$-0.861036\pi$$
−0.0869195 + 0.996215i $$0.527702\pi$$
$$74$$ 0 0
$$75$$ 6.72792 + 3.88437i 0.776874 + 0.448528i
$$76$$ 0 0
$$77$$ 9.44975 + 12.1859i 1.07690 + 1.38871i
$$78$$ 0 0
$$79$$ 8.86396 15.3528i 0.997274 1.72733i 0.434730 0.900561i $$-0.356844\pi$$
0.562544 0.826767i $$-0.309823\pi$$
$$80$$ 2.48528 1.43488i 0.277863 0.160424i
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 13.5592i 1.48832i 0.668002 + 0.744160i $$0.267150\pi$$
−0.668002 + 0.744160i $$0.732850\pi$$
$$84$$ −8.48528 3.46410i −0.925820 0.377964i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 11.3787 6.56948i 1.21992 0.704323i
$$88$$ −8.24264 14.2767i −0.878668 1.52190i
$$89$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$90$$ 3.04384i 0.320848i
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 9.62132 16.6646i 0.997684 1.72804i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 8.48528 + 4.89898i 0.866025 + 0.500000i
$$97$$ 8.06591i 0.818969i −0.912317 0.409484i $$-0.865709\pi$$
0.912317 0.409484i $$-0.134291\pi$$
$$98$$ −2.46447 + 9.58783i −0.248949 + 0.968517i
$$99$$ −17.4853 −1.75734
$$100$$ −4.48528 + 7.76874i −0.448528 + 0.776874i
$$101$$ −3.00000 + 1.73205i −0.298511 + 0.172345i −0.641774 0.766894i $$-0.721801\pi$$
0.343263 + 0.939239i $$0.388468\pi$$
$$102$$ 0 0
$$103$$ −12.7279 7.34847i −1.25412 0.724066i −0.282194 0.959357i $$-0.591062\pi$$
−0.971925 + 0.235291i $$0.924396\pi$$
$$104$$ 0 0
$$105$$ −3.25736 + 0.445759i −0.317886 + 0.0435017i
$$106$$ −5.75736 −0.559204
$$107$$ 4.67157 8.09140i 0.451618 0.782225i −0.546869 0.837218i $$-0.684180\pi$$
0.998487 + 0.0549930i $$0.0175137\pi$$
$$108$$ 9.00000 5.19615i 0.866025 0.500000i
$$109$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$110$$ −5.12132 2.95680i −0.488299 0.281919i
$$111$$ 0 0
$$112$$ 4.00000 9.79796i 0.377964 0.925820i
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 7.58579 + 13.1390i 0.704323 + 1.21992i
$$117$$ 0 0
$$118$$ 21.2049i 1.95207i
$$119$$ 0 0
$$120$$ 3.51472 0.320848
$$121$$ −11.4853 + 19.8931i −1.04412 + 1.80846i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 19.2426 + 11.1097i 1.72804 + 0.997684i
$$125$$ 6.80511i 0.608668i
$$126$$ −6.87868 8.87039i −0.612801 0.790237i
$$127$$ 15.2426 1.35257 0.676283 0.736642i $$-0.263590\pi$$
0.676283 + 0.736642i $$0.263590\pi$$
$$128$$ −5.65685 + 9.79796i −0.500000 + 0.866025i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −15.4706 8.93193i −1.35167 0.780387i −0.363186 0.931717i $$-0.618311\pi$$
−0.988483 + 0.151330i $$0.951644\pi$$
$$132$$ 20.1903i 1.75734i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.86396 3.22848i 0.160424 0.277863i
$$136$$ 0 0
$$137$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ −0.514719 3.76127i −0.0435017 0.317886i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 6.00000 + 10.3923i 0.500000 + 0.866025i
$$145$$ 4.71320 + 2.72117i 0.391410 + 0.225981i
$$146$$ 13.8564i 1.14676i
$$147$$ −8.48528 + 8.66025i −0.699854 + 0.714286i
$$148$$ 0 0
$$149$$ −1.41421 + 2.44949i −0.115857 + 0.200670i −0.918122 0.396298i $$-0.870295\pi$$
0.802265 + 0.596968i $$0.203628\pi$$
$$150$$ −9.51472 + 5.49333i −0.776874 + 0.448528i
$$151$$ 10.1066 + 17.5051i 0.822464 + 1.42455i 0.903842 + 0.427865i $$0.140734\pi$$
−0.0813788 + 0.996683i $$0.525932\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ −21.6066 + 2.95680i −1.74111 + 0.238265i
$$155$$ 7.97056 0.640211
$$156$$ 0 0
$$157$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$158$$ 12.5355 + 21.7122i 0.997274 + 1.72733i
$$159$$ −6.10660 3.52565i −0.484285 0.279602i
$$160$$ 4.05845i 0.320848i
$$161$$ 0 0
$$162$$ 12.7279 1.00000
$$163$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$164$$ 0 0
$$165$$ −3.62132 6.27231i −0.281919 0.488299i
$$166$$ −16.6066 9.58783i −1.28892 0.744160i
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 10.2426 7.94282i 0.790237 0.612801i
$$169$$ −13.0000 −1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −15.0000 8.66025i −1.14043 0.658427i −0.193892 0.981023i $$-0.562111\pi$$
−0.946537 + 0.322596i $$0.895445\pi$$
$$174$$ 18.5813i 1.40865i
$$175$$ 7.27208 + 9.37769i 0.549717 + 0.708887i
$$176$$ 23.3137 1.75734
$$177$$ −12.9853 + 22.4912i −0.976034 + 1.69054i
$$178$$ 0 0
$$179$$ −5.65685 9.79796i −0.422813 0.732334i 0.573400 0.819275i $$-0.305624\pi$$
−0.996213 + 0.0869415i $$0.972291\pi$$
$$180$$ 3.72792 + 2.15232i 0.277863 + 0.160424i
$$181$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 13.6066 + 23.5673i 0.997684 + 1.72804i
$$187$$ 0 0
$$188$$ 0 0
$$189$$ −1.86396 13.6208i −0.135583 0.990766i
$$190$$ 0 0
$$191$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$192$$ −12.0000 + 6.92820i −0.866025 + 0.500000i
$$193$$ 2.25736 + 3.90986i 0.162488 + 0.281438i 0.935760 0.352636i $$-0.114715\pi$$
−0.773272 + 0.634074i $$0.781381\pi$$
$$194$$ 9.87868 + 5.70346i 0.709248 + 0.409484i
$$195$$ 0 0
$$196$$ −10.0000 9.79796i −0.714286 0.699854i
$$197$$ −14.1421 −1.00759 −0.503793 0.863825i $$-0.668062\pi$$
−0.503793 + 0.863825i $$0.668062\pi$$
$$198$$ 12.3640 21.4150i 0.878668 1.52190i
$$199$$ 21.2132 12.2474i 1.50376 0.868199i 0.503774 0.863836i $$-0.331945\pi$$
0.999990 0.00436292i $$-0.00138876\pi$$
$$200$$ −6.34315 10.9867i −0.448528 0.776874i
$$201$$ 0 0
$$202$$ 4.89898i 0.344691i
$$203$$ 19.8848 2.72117i 1.39564 0.190989i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 18.0000 10.3923i 1.25412 0.724066i
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 1.75736 4.30463i 0.121269 0.297048i
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 4.07107 7.05130i 0.279602 0.484285i
$$213$$ 0 0
$$214$$ 6.60660 + 11.4430i 0.451618 + 0.782225i
$$215$$ 0 0
$$216$$ 14.6969i 1.00000i
$$217$$ 23.2279 18.0125i 1.57681 1.22277i
$$218$$ 0 0
$$219$$ 8.48528 14.6969i 0.573382 0.993127i
$$220$$ 7.24264 4.18154i 0.488299 0.281919i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 15.1682i 1.01574i −0.861435 0.507869i $$-0.830434\pi$$
0.861435 0.507869i $$-0.169566\pi$$
$$224$$ 9.17157 + 11.8272i 0.612801 + 0.790237i
$$225$$ −13.4558 −0.897056
$$226$$ 0 0
$$227$$ −16.7132 + 9.64937i −1.10929 + 0.640451i −0.938647 0.344881i $$-0.887919\pi$$
−0.170648 + 0.985332i $$0.554586\pi$$
$$228$$ 0 0
$$229$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$230$$ 0 0
$$231$$ −24.7279 10.0951i −1.62698 0.664211i
$$232$$ −21.4558 −1.40865
$$233$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −25.9706 14.9941i −1.69054 0.976034i
$$237$$ 30.7057i 1.99455i
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ −2.48528 + 4.30463i −0.160424 + 0.277863i
$$241$$ 5.22792 3.01834i 0.336760 0.194429i −0.322078 0.946713i $$-0.604381\pi$$
0.658838 + 0.752285i $$0.271048\pi$$
$$242$$ −16.2426 28.1331i −1.04412 1.80846i
$$243$$ 13.5000 + 7.79423i 0.866025 + 0.500000i
$$244$$ 0 0
$$245$$ −4.86396 1.25024i −0.310747 0.0798748i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ −27.2132 + 15.7116i −1.72804 + 0.997684i
$$249$$ −11.7426 20.3389i −0.744160 1.28892i
$$250$$ −8.33452 4.81194i −0.527122 0.304334i
$$251$$ 10.6895i 0.674714i −0.941377 0.337357i $$-0.890467\pi$$
0.941377 0.337357i $$-0.109533\pi$$
$$252$$ 15.7279 2.15232i 0.990766 0.135583i
$$253$$ 0 0
$$254$$ −10.7782 + 18.6683i −0.676283 + 1.17136i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −11.3787 + 19.7085i −0.704323 + 1.21992i
$$262$$ 21.8787 12.6317i 1.35167 0.780387i
$$263$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$264$$ 24.7279 + 14.2767i 1.52190 + 0.878668i
$$265$$ 2.92074i 0.179420i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 27.8345 16.0703i 1.69710 0.979822i 0.748614 0.663007i $$-0.230720\pi$$
0.948487 0.316815i $$-0.102613\pi$$
$$270$$ 2.63604 + 4.56575i 0.160424 + 0.277863i
$$271$$ −27.1066 15.6500i −1.64661 0.950670i −0.978406 0.206691i $$-0.933731\pi$$
−0.668202 0.743980i $$-0.732936\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −13.0711 + 22.6398i −0.788215 + 1.36523i
$$276$$ 0 0
$$277$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$278$$ 0 0
$$279$$ 33.3292i 1.99537i
$$280$$ 4.97056 + 2.02922i 0.297048 + 0.121269i
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −16.9706 −1.00000
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ −6.66548 + 3.84831i −0.391410 + 0.225981i
$$291$$ 6.98528 + 12.0989i 0.409484 + 0.709248i
$$292$$ 16.9706 + 9.79796i 0.993127 + 0.573382i
$$293$$ 27.8359i 1.62619i −0.582130 0.813095i $$-0.697781\pi$$
0.582130 0.813095i $$-0.302219\pi$$
$$294$$ −4.60660 16.5160i −0.268662 0.963234i
$$295$$ −10.7574 −0.626318
$$296$$ 0 0
$$297$$ 26.2279 15.1427i 1.52190 0.878668i
$$298$$ −2.00000 3.46410i −0.115857 0.200670i
$$299$$ 0 0
$$300$$ 15.5375i 0.897056i
$$301$$ 0 0
$$302$$ −28.5858 −1.64493
$$303$$ 3.00000 5.19615i 0.172345 0.298511i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 11.6569 28.5533i 0.664211 1.62698i
$$309$$ 25.4558 1.44813
$$310$$ −5.63604 + 9.76191i −0.320106 + 0.554439i
$$311$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$312$$ 0 0
$$313$$ 29.7426 + 17.1719i 1.68115 + 0.970614i 0.960897 + 0.276907i $$0.0893093\pi$$
0.720257 + 0.693708i $$0.244024\pi$$
$$314$$ 0 0
$$315$$ 4.50000 3.48960i 0.253546 0.196616i
$$316$$ −35.4558 −1.99455
$$317$$ −0.278175 + 0.481813i −0.0156238 + 0.0270613i −0.873732 0.486408i $$-0.838307\pi$$
0.858108 + 0.513470i $$0.171640\pi$$
$$318$$ 8.63604 4.98602i 0.484285 0.279602i
$$319$$ 22.1066 + 38.2898i 1.23773 + 2.14381i
$$320$$ −4.97056 2.86976i −0.277863 0.160424i
$$321$$ 16.1828i 0.903236i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −9.00000 + 15.5885i −0.500000 + 0.866025i
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 10.2426 0.563839
$$331$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$332$$ 23.4853 13.5592i 1.28892 0.744160i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 2.48528 + 18.1610i 0.135583 + 0.990766i
$$337$$ −14.4558 −0.787460 −0.393730 0.919226i $$-0.628816\pi$$
−0.393730 + 0.919226i $$0.628816\pi$$
$$338$$ 9.19239 15.9217i 0.500000 0.866025i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 56.0772 + 32.3762i 3.03675 + 1.75327i
$$342$$ 0 0
$$343$$ −17.0000 + 7.34847i −0.917914 + 0.396780i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 21.2132 12.2474i 1.14043 0.658427i
$$347$$ 14.1421 + 24.4949i 0.759190 + 1.31495i 0.943264 + 0.332043i $$0.107738\pi$$
−0.184075 + 0.982912i $$0.558929\pi$$
$$348$$ −22.7574 13.1390i −1.21992 0.704323i
$$349$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$350$$ −16.6274 + 2.27541i −0.888773 + 0.121626i
$$351$$ 0 0
$$352$$ −16.4853 + 28.5533i −0.878668 + 1.52190i
$$353$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$354$$ −18.3640 31.8073i −0.976034 1.69054i
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 16.0000 0.845626
$$359$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$360$$ −5.27208 + 3.04384i −0.277863 + 0.160424i
$$361$$ 9.50000 + 16.4545i 0.500000 + 0.866025i
$$362$$ 0 0
$$363$$ 39.7862i 2.08823i
$$364$$ 0 0
$$365$$ 7.02944 0.367938
$$366$$ 0 0
$$367$$ −30.6213 + 17.6792i −1.59842 + 0.922848i −0.606628 + 0.794986i $$0.707478\pi$$
−0.991792 + 0.127862i $$0.959188\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −6.60051 8.51167i −0.342681 0.441904i
$$372$$ −38.4853 −1.99537
$$373$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$374$$ 0 0
$$375$$ −5.89340 10.2077i −0.304334 0.527122i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 18.0000 + 7.34847i 0.925820 + 0.377964i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ −22.8640 + 13.2005i −1.17136 + 0.676283i
$$382$$ 0 0
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 19.5959i 1.00000i
$$385$$ −1.50000 10.9612i −0.0764471 0.558632i
$$386$$ −6.38478 −0.324977
$$387$$ 0 0
$$388$$ −13.9706 + 8.06591i −0.709248 + 0.409484i
$$389$$ −15.5563 26.9444i −0.788738 1.36613i −0.926740 0.375703i $$-0.877401\pi$$
0.138002 0.990432i $$-0.455932\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 19.0711 5.31925i 0.963234 0.268662i
$$393$$ 30.9411 1.56077
$$394$$ 10.0000 17.3205i 0.503793 0.872595i
$$395$$ −11.0147 + 6.35935i −0.554211 + 0.319974i
$$396$$ 17.4853 + 30.2854i 0.878668 + 1.52190i
$$397$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$398$$ 34.6410i 1.73640i
$$399$$ 0 0
$$400$$ 17.9411 0.897056
$$401$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 6.00000 + 3.46410i 0.298511 + 0.172345i
$$405$$ 6.45695i 0.320848i
$$406$$ −10.7279 + 26.2779i −0.532418 + 1.30415i
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −24.4706 + 14.1281i −1.20999 + 0.698589i −0.962757 0.270367i $$-0.912855\pi$$
−0.247234 + 0.968956i $$0.579522\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 29.3939i 1.44813i
$$413$$ −31.3492 + 24.3103i −1.54260 + 1.19623i
$$414$$ 0 0
$$415$$ 4.86396 8.42463i 0.238762 0.413549i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 10.3923i 0.507697i 0.967244 + 0.253849i $$0.0816965\pi$$
−0.967244 + 0.253849i $$0.918303\pi$$
$$420$$ 4.02944 + 5.19615i 0.196616 + 0.253546i
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 5.75736 + 9.97204i 0.279602 + 0.484285i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −18.6863 −0.903236
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$432$$ −18.0000 10.3923i −0.866025 0.500000i
$$433$$ 39.1918i 1.88344i −0.336399 0.941720i $$-0.609209\pi$$
0.336399 0.941720i $$-0.390791\pi$$
$$434$$ 5.63604 + 41.1850i 0.270539 + 1.97694i
$$435$$ −9.42641 −0.451962
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 12.0000 + 20.7846i 0.573382 + 0.993127i
$$439$$ 14.8934 + 8.59871i 0.710823 + 0.410394i 0.811366 0.584539i $$-0.198725\pi$$
−0.100543 + 0.994933i $$0.532058\pi$$
$$440$$ 11.8272i 0.563839i
$$441$$ 5.22792 20.3389i 0.248949 0.968517i
$$442$$ 0 0
$$443$$ −6.42893 + 11.1352i −0.305448 + 0.529051i −0.977361 0.211579i $$-0.932139\pi$$
0.671913 + 0.740630i $$0.265473\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 18.5772 + 10.7255i 0.879654 + 0.507869i
$$447$$ 4.89898i 0.231714i
$$448$$ −20.9706 + 2.86976i −0.990766 + 0.135583i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 9.51472 16.4800i 0.448528 0.776874i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ −30.3198 17.5051i −1.42455 0.822464i
$$454$$ 27.2925i 1.28090i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 1.01472 1.75754i 0.0474665 0.0822145i −0.841316 0.540544i $$-0.818219\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 38.1051i 1.77473i −0.461065 0.887366i $$-0.652533\pi$$
0.461065 0.887366i $$-0.347467\pi$$
$$462$$ 29.8492 23.1471i 1.38871 1.07690i
$$463$$ −26.0000 −1.20832 −0.604161 0.796862i $$-0.706492\pi$$
−0.604161 + 0.796862i $$0.706492\pi$$
$$464$$ 15.1716 26.2779i 0.704323 1.21992i
$$465$$ −11.9558 + 6.90271i −0.554439 + 0.320106i
$$466$$ 0 0
$$467$$ −15.0000 8.66025i −0.694117 0.400749i 0.111035 0.993816i $$-0.464583\pi$$
−0.805153 + 0.593068i $$0.797917\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 36.7279 21.2049i 1.69054 0.976034i
$$473$$ 0 0
$$474$$ −37.6066 21.7122i −1.72733 0.997274i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 12.2132 0.559204
$$478$$ 0 0
$$479$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$480$$ −3.51472 6.08767i −0.160424 0.277863i
$$481$$ 0 0
$$482$$ 8.53716i 0.388857i
$$483$$ 0 0
$$484$$ 45.9411 2.08823
$$485$$ −2.89340 + 5.01151i −0.131382 + 0.227561i
$$486$$ −19.0919 + 11.0227i −0.866025 + 0.500000i
$$487$$ −19.5919 33.9341i −0.887793 1.53770i −0.842479 0.538730i $$-0.818904\pi$$
−0.0453143 0.998973i $$-0.514429\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 4.97056 5.07306i 0.224547 0.229177i
$$491$$ 44.3137 1.99985 0.999925 0.0122607i $$-0.00390281\pi$$
0.999925 + 0.0122607i $$0.00390281\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 10.8640 + 6.27231i 0.488299 + 0.281919i
$$496$$ 44.4390i 1.99537i
$$497$$ 0 0
$$498$$ 33.2132 1.48832
$$499$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$500$$ 11.7868 6.80511i 0.527122 0.304334i
$$501$$ 0 0
$$502$$ 13.0919 + 7.55860i 0.584319 + 0.337357i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ −8.48528 + 20.7846i −0.377964 + 0.925820i
$$505$$ 2.48528 0.110594
$$506$$ 0 0
$$507$$ 19.5000 11.2583i 0.866025 0.500000i
$$508$$ −15.2426 26.4010i −0.676283 1.17136i
$$509$$ −21.6213 12.4831i −0.958348 0.553303i −0.0626839 0.998033i $$-0.519966\pi$$
−0.895664 + 0.444731i $$0.853299\pi$$
$$510$$ 0 0
$$511$$ 20.4853 15.8856i 0.906215 0.702739i
$$512$$ 22.6274 1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5.27208 + 9.13151i 0.232316 + 0.402382i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 30.0000 1.31685
$$520$$ 0 0
$$521$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$522$$ −16.0919 27.8720i −0.704323 1.21992i
$$523$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$524$$ 35.7277i 1.56077i
$$525$$ −19.0294 7.76874i −0.830513 0.339055i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −34.9706 + 20.1903i −1.52190 + 0.878668i
$$529$$ −11.5000 19.9186i −0.500000 0.866025i
$$530$$ 3.57716 + 2.06528i 0.155382 + 0.0897099i
$$531$$ 44.9823i 1.95207i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −5.80509 + 3.35157i −0.250976 + 0.144901i
$$536$$ 0 0
$$537$$ 16.9706 + 9.79796i 0.732334 + 0.422813i
$$538$$ 45.4536i 1.95964i
$$539$$ −29.1421 28.5533i −1.25524 1.22988i
$$540$$ −7.45584 −0.320848
$$541$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$542$$ 38.3345 22.1324i 1.64661 0.950670i
$$543$$ 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
$$550$$ −18.4853 32.0174i −0.788215 1.36523i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −17.7279 + 43.4244i −0.753868 + 1.84659i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 23.0355 + 39.8987i 0.976047 + 1.69056i 0.676436 + 0.736501i $$0.263523\pi$$
0.299611 + 0.954062i $$0.403143\pi$$
$$558$$ −40.8198 23.5673i −1.72804 0.997684i
$$559$$ 0 0
$$560$$ −6.00000 + 4.65279i −0.253546 + 0.196616i
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −37.7132 + 21.7737i −1.58942 + 0.917653i −0.596020 + 0.802970i $$0.703252\pi$$
−0.993402 + 0.114684i $$0.963415\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 14.5919 + 18.8169i 0.612801 + 0.790237i
$$568$$ 0 0
$$569$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$570$$ 0 0
$$571$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 12.0000 20.7846i 0.500000 0.866025i
$$577$$ −15.7721 + 9.10601i −0.656600 + 0.379088i −0.790980 0.611842i $$-0.790429\pi$$
0.134380 + 0.990930i $$0.457096\pi$$
$$578$$ 12.0208 + 20.8207i 0.500000 + 0.866025i
$$579$$ −6.77208 3.90986i −0.281438 0.162488i
$$580$$ 10.8847i 0.451962i
$$581$$ −4.86396 35.5431i −0.201791 1.47458i
$$582$$ −19.7574 −0.818969
$$583$$ 11.8640 20.5490i 0.491355 0.851052i
$$584$$ −24.0000 + 13.8564i −0.993127 + 0.573382i
$$585$$ 0 0
$$586$$ 34.0919 + 19.6830i 1.40832 + 0.813095i
$$587$$ 47.8521i 1.97507i 0.157409 + 0.987534i $$0.449686\pi$$
−0.157409 + 0.987534i $$0.550314\pi$$
$$588$$ 23.4853 + 6.03668i 0.968517 + 0.248949i
$$589$$ 0 0
$$590$$ 7.60660 13.1750i 0.313159 0.542407i
$$591$$ 21.2132 12.2474i 0.872595 0.503793i
$$592$$ 0 0
$$593$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$594$$ 42.8300i 1.75734i
$$595$$ 0 0
$$596$$ 5.65685 0.231714
$$597$$ −21.2132 + 36.7423i −0.868199 + 1.50376i
$$598$$ 0 0
$$599$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$600$$ 19.0294 + 10.9867i 0.776874 + 0.448528i
$$601$$ 26.2269i 1.06982i 0.844909 + 0.534910i $$0.179654\pi$$
−0.844909 + 0.534910i $$0.820346\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 20.2132 35.0103i 0.822464 1.42455i
$$605$$ 14.2721 8.23999i 0.580242 0.335003i
$$606$$ 4.24264 + 7.34847i 0.172345 + 0.298511i
$$607$$ 2.59188 + 1.49642i 0.105201 + 0.0607380i 0.551678 0.834058i $$-0.313988\pi$$
−0.446476 + 0.894795i $$0.647321\pi$$
$$608$$ 0 0
$$609$$ −27.4706 + 21.3025i −1.11316 + 0.863220i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 26.7279 + 34.4669i 1.07690 + 1.38871i
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ −18.0000 + 31.1769i −0.724066 + 1.25412i
$$619$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$620$$ −7.97056 13.8054i −0.320106 0.554439i
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −8.77208 + 15.1937i −0.350883 + 0.607747i
$$626$$ −42.0624 + 24.2848i −1.68115 + 0.970614i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 1.09188 + 7.97887i 0.0435017 + 0.317886i
$$631$$ 29.2426 1.16413 0.582066 0.813142i $$-0.302245\pi$$
0.582066 + 0.813142i $$0.302245\pi$$
$$632$$ 25.0711 43.4244i 0.997274 1.72733i
$$633$$ 0 0
$$634$$ −0.393398 0.681386i −0.0156238 0.0270613i
$$635$$ −9.47056 5.46783i −0.375828 0.216984i
$$636$$ 14.1026i 0.559204i
$$637$$ 0 0
$$638$$ −62.5269 −2.47546
$$639$$ 0 0
$$640$$ 7.02944 4.05845i 0.277863 0.160424i
$$641$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$642$$ −19.8198 11.4430i −0.782225 0.451618i
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ −12.7279 22.0454i −0.500000 0.866025i
$$649$$ −75.6838 43.6960i −2.97085 1.71522i
$$650$$ 0 0
$$651$$ −19.2426 + 47.1347i −0.754179 + 1.84735i
$$652$$ 0 0
$$653$$ 19.5208 33.8110i 0.763909 1.32313i −0.176913 0.984226i $$-0.556611\pi$$
0.940822 0.338902i $$-0.110055\pi$$
$$654$$ 0 0
$$655$$ 6.40812 + 11.0992i 0.250386 + 0.433681i
$$656$$ 0 0
$$657$$ 29.3939i 1.14676i
$$658$$ 0 0
$$659$$ 45.2548 1.76288 0.881439 0.472298i $$-0.156575\pi$$
0.881439 + 0.472298i $$0.156575\pi$$
$$660$$ −7.24264 + 12.5446i −0.281919 + 0.488299i
$$661$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 38.3513i 1.48832i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 13.1360 + 22.7523i 0.507869 + 0.879654i
$$670$$ 0 0
$$671$$ 0 0
$$672$$ −24.0000 9.79796i −0.925820 0.377964i
$$673$$ 16.9411 0.653032 0.326516 0.945192i $$-0.394125\pi$$
0.326516 + 0.945192i $$0.394125\pi$$
$$674$$ 10.2218 17.7047i 0.393730 0.681960i
$$675$$ 20.1838 11.6531i 0.776874 0.448528i
$$676$$ 13.0000 + 22.5167i 0.500000 + 0.866025i
$$677$$ 20.3787 + 11.7656i 0.783216 + 0.452190i 0.837569 0.546332i $$-0.183976\pi$$
−0.0543526 + 0.998522i $$0.517310\pi$$
$$678$$ 0 0
$$679$$ 2.89340 + 21.1433i 0.111038 + 0.811407i
$$680$$ 0 0
$$681$$ 16.7132 28.9481i 0.640451 1.10929i
$$682$$ −79.3051 + 45.7868i −3.03675 + 1.75327i
$$683$$ −23.9142 41.4206i −0.915052 1.58492i −0.806825 0.590790i $$-0.798816\pi$$
−0.108227 0.994126i $$-0.534517\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 3.02082 26.0168i 0.115335 0.993327i
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$692$$ 34.6410i 1.31685i
$$693$$ 45.8345 6.27231i 1.74111 0.238265i
$$694$$ −40.0000 −1.51838
$$695$$ 0 0
$$696$$ 32.1838 18.5813i 1.21992 0.704323i
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 8.97056 21.9733i 0.339055 0.830513i
$$701$$ 14.6152 0.552009 0.276005 0.961156i $$-0.410989\pi$$
0.276005 + 0.961156i $$0.410989\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −23.3137 40.3805i −0.878668 1.52190i
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 7.24264 5.61642i 0.272388 0.211227i
$$708$$ 51.9411 1.95207
$$709$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$710$$ 0 0
$$711$$ −26.5919 46.0585i −0.997274 1.72733i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −11.3137 + 19.5959i −0.422813 + 0.732334i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$720$$ 8.60927i 0.320848i
$$721$$ 36.0000 + 14.6969i 1.34071 + 0.547343i
$$722$$ −26.8701 −1.00000
$$723$$ −5.22792 + 9.05503i −0.194429 + 0.336760i
$$724$$ 0 0
$$725$$ 17.0122 + 29.4660i 0.631817 + 1.09434i
$$726$$ 48.7279 + 28.1331i 1.80846 + 1.04412i
$$727$$ 25.2123i 0.935074i −0.883974 0.467537i $$-0.845142\pi$$
0.883974 0.467537i $$-0.154858\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ −4.97056 + 8.60927i −0.183969 + 0.318643i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$734$$ 50.0044i 1.84570i
$$735$$ 8.37868 2.33696i 0.309052 0.0861999i
$$736$$ 0 0
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 15.0919 2.06528i 0.554040 0.0758187i
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 27.2132 47.1347i 0.997684 1.72804i
$$745$$ 1.75736 1.01461i 0.0643847 0.0371725i
$$746$$ 0 0
$$747$$ 35.2279 + 20.3389i 1.28892 + 0.744160i
$$748$$ 0 0
$$749$$ −9.34315 + 22.8859i −0.341391 + 0.836234i
$$750$$ 16.6690 0.608668
$$751$$ −20.8345 + 36.0865i −0.760263 + 1.31681i 0.182453 + 0.983215i $$0.441596\pi$$
−0.942715 + 0.333599i $$0.891737\pi$$
$$752$$ 0 0
$$753$$ 9.25736 + 16.0342i 0.337357 + 0.584319i
$$754$$ 0 0
$$755$$ 14.5017i 0.527772i
$$756$$ −21.7279 + 16.8493i −0.790237 + 0.612801i
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$762$$ 37.3367i 1.35257i
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 24.0000 + 13.8564i 0.866025 + 0.500000i
$$769$$ 1.97824i 0.0713370i 0.999364 + 0.0356685i $$0.0113561\pi$$
−0.999364 + 0.0356685i $$0.988644\pi$$
$$770$$ 14.4853 + 5.91359i 0.522013 + 0.213111i
$$771$$ 0 0
$$772$$ 4.51472 7.81972i 0.162488 0.281438i
$$773$$ −45.0000 + 25.9808i −1.61854 + 0.934463i −0.631239 + 0.775589i $$0.717453\pi$$
−0.987299 + 0.158874i $$0.949213\pi$$
$$774$$ 0 0
$$775$$ 43.1543 + 24.9152i 1.55015 + 0.894979i
$$776$$ 22.8138i 0.818969i
$$777$$ 0 0
$$778$$ 44.0000 1.57748
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 39.4169i 1.40865i
$$784$$ −6.97056 + 27.1185i −0.248949 + 0.968517i
$$785$$ 0 0
$$786$$ −21.8787 + 37.8950i −0.780387 + 1.35167i
$$787$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$788$$ 14.1421 + 24.4949i 0.503793 + 0.872595i
$$789$$ 0 0
$$790$$ 17.9870i 0.639947i
$$791$$ 0 0
$$792$$