# Properties

 Label 546.2.l.c.211.1 Level $546$ Weight $2$ Character 546.211 Analytic conductor $4.360$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.l (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 211.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.211 Dual form 546.2.l.c.295.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(1.00000 - 1.73205i) q^{20} -1.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-2.50000 - 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} -2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +5.00000 q^{38} +(-1.00000 - 3.46410i) q^{39} +2.00000 q^{40} +(2.50000 + 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +(1.00000 - 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{46} -1.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} -7.00000 q^{51} +(-2.50000 + 2.59808i) q^{52} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{55} +(-0.500000 + 0.866025i) q^{56} -5.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.00000 - 1.73205i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-7.00000 - 1.73205i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(3.50000 + 6.06218i) q^{68} +(-3.00000 + 5.19615i) q^{69} -2.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} -3.00000 q^{77} +(2.50000 - 2.59808i) q^{78} +3.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50000 + 4.33013i) q^{82} -8.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(-7.00000 + 12.1244i) q^{85} -2.00000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +2.00000 q^{90} +(2.50000 - 2.59808i) q^{91} +6.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-5.00000 + 8.66025i) q^{95} -1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(0.500000 - 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9 $$2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + 2 q^{12} + 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} + 7 q^{17} - 2 q^{18} + 5 q^{19} + 2 q^{20} - 2 q^{21} + 3 q^{22} - 6 q^{23} + q^{24} - 2 q^{25} + 2 q^{26} + 2 q^{27} + q^{28} - 5 q^{29} - 2 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} + 14 q^{34} - 2 q^{35} - q^{36} + 2 q^{37} + 10 q^{38} - 2 q^{39} + 4 q^{40} + 5 q^{41} - q^{42} - 2 q^{43} + 6 q^{44} + 2 q^{45} + 6 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 14 q^{51} - 5 q^{52} + 6 q^{53} + q^{54} + 6 q^{55} - q^{56} - 10 q^{57} + 5 q^{58} + 6 q^{59} - 4 q^{60} - 7 q^{61} - 2 q^{62} + q^{63} + 2 q^{64} - 14 q^{65} - 6 q^{66} - 2 q^{67} + 7 q^{68} - 6 q^{69} - 4 q^{70} - 8 q^{71} + q^{72} + 24 q^{73} - 2 q^{74} + q^{75} + 5 q^{76} - 6 q^{77} + 5 q^{78} + 6 q^{79} + 2 q^{80} - q^{81} - 5 q^{82} - 16 q^{83} + q^{84} - 14 q^{85} - 4 q^{86} - 5 q^{87} + 3 q^{88} + 11 q^{89} + 4 q^{90} + 5 q^{91} + 12 q^{92} + 2 q^{93} - q^{94} - 10 q^{95} - 2 q^{96} + 2 q^{97} + q^{98} + 6 q^{99}+O(q^{100})$$ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 + 2 * q^12 + 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 + 7 * q^17 - 2 * q^18 + 5 * q^19 + 2 * q^20 - 2 * q^21 + 3 * q^22 - 6 * q^23 + q^24 - 2 * q^25 + 2 * q^26 + 2 * q^27 + q^28 - 5 * q^29 - 2 * q^30 - 4 * q^31 + q^32 - 3 * q^33 + 14 * q^34 - 2 * q^35 - q^36 + 2 * q^37 + 10 * q^38 - 2 * q^39 + 4 * q^40 + 5 * q^41 - q^42 - 2 * q^43 + 6 * q^44 + 2 * q^45 + 6 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 14 * q^51 - 5 * q^52 + 6 * q^53 + q^54 + 6 * q^55 - q^56 - 10 * q^57 + 5 * q^58 + 6 * q^59 - 4 * q^60 - 7 * q^61 - 2 * q^62 + q^63 + 2 * q^64 - 14 * q^65 - 6 * q^66 - 2 * q^67 + 7 * q^68 - 6 * q^69 - 4 * q^70 - 8 * q^71 + q^72 + 24 * q^73 - 2 * q^74 + q^75 + 5 * q^76 - 6 * q^77 + 5 * q^78 + 6 * q^79 + 2 * q^80 - q^81 - 5 * q^82 - 16 * q^83 + q^84 - 14 * q^85 - 4 * q^86 - 5 * q^87 + 3 * q^88 + 11 * q^89 + 4 * q^90 + 5 * q^91 + 12 * q^92 + 2 * q^93 - q^94 - 10 * q^95 - 2 * q^96 + 2 * q^97 + q^98 + 6 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −2.00000 −0.894427 −0.447214 0.894427i $$-0.647584\pi$$
−0.447214 + 0.894427i $$0.647584\pi$$
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ 0.500000 0.866025i 0.188982 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −1.00000 1.73205i −0.316228 0.547723i
$$11$$ −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i $$-0.316051\pi$$
−0.998526 + 0.0542666i $$0.982718\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.50000 + 0.866025i 0.970725 + 0.240192i
$$14$$ 1.00000 0.267261
$$15$$ 1.00000 + 1.73205i 0.258199 + 0.447214i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i $$-0.510614\pi$$
0.882213 0.470850i $$-0.156053\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i $$-0.638903\pi$$
0.996199 0.0871106i $$-0.0277634\pi$$
$$20$$ 1.00000 1.73205i 0.223607 0.387298i
$$21$$ −1.00000 −0.218218
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ −1.00000 −0.200000
$$26$$ 1.00000 + 3.46410i 0.196116 + 0.679366i
$$27$$ 1.00000 0.192450
$$28$$ 0.500000 + 0.866025i 0.0944911 + 0.163663i
$$29$$ −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i $$-0.320339\pi$$
−0.999167 + 0.0408130i $$0.987005\pi$$
$$30$$ −1.00000 + 1.73205i −0.182574 + 0.316228i
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ 7.00000 1.20049
$$35$$ −1.00000 + 1.73205i −0.169031 + 0.292770i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i $$-0.114098\pi$$
−0.772043 + 0.635571i $$0.780765\pi$$
$$38$$ 5.00000 0.811107
$$39$$ −1.00000 3.46410i −0.160128 0.554700i
$$40$$ 2.00000 0.316228
$$41$$ 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i $$-0.0389915\pi$$
−0.602072 + 0.798441i $$0.705658\pi$$
$$42$$ −0.500000 0.866025i −0.0771517 0.133631i
$$43$$ −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i $$-0.882065\pi$$
0.779647 + 0.626219i $$0.215399\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 1.00000 1.73205i 0.149071 0.258199i
$$46$$ 3.00000 5.19615i 0.442326 0.766131i
$$47$$ −1.00000 −0.145865 −0.0729325 0.997337i $$-0.523236\pi$$
−0.0729325 + 0.997337i $$0.523236\pi$$
$$48$$ −0.500000 + 0.866025i −0.0721688 + 0.125000i
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ −0.500000 0.866025i −0.0707107 0.122474i
$$51$$ −7.00000 −0.980196
$$52$$ −2.50000 + 2.59808i −0.346688 + 0.360288i
$$53$$ 3.00000 0.412082 0.206041 0.978543i $$-0.433942\pi$$
0.206041 + 0.978543i $$0.433942\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 3.00000 + 5.19615i 0.404520 + 0.700649i
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ −5.00000 −0.662266
$$58$$ 2.50000 4.33013i 0.328266 0.568574i
$$59$$ 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i $$-0.705612\pi$$
0.992524 + 0.122047i $$0.0389457\pi$$
$$60$$ −2.00000 −0.258199
$$61$$ −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i $$-0.981243\pi$$
0.550135 + 0.835076i $$0.314576\pi$$
$$62$$ −1.00000 1.73205i −0.127000 0.219971i
$$63$$ 0.500000 + 0.866025i 0.0629941 + 0.109109i
$$64$$ 1.00000 0.125000
$$65$$ −7.00000 1.73205i −0.868243 0.214834i
$$66$$ −3.00000 −0.369274
$$67$$ −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i $$-0.205652\pi$$
−0.920623 + 0.390453i $$0.872318\pi$$
$$68$$ 3.50000 + 6.06218i 0.424437 + 0.735147i
$$69$$ −3.00000 + 5.19615i −0.361158 + 0.625543i
$$70$$ −2.00000 −0.239046
$$71$$ −4.00000 + 6.92820i −0.474713 + 0.822226i −0.999581 0.0289572i $$-0.990781\pi$$
0.524868 + 0.851184i $$0.324115\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ 12.0000 1.40449 0.702247 0.711934i $$-0.252180\pi$$
0.702247 + 0.711934i $$0.252180\pi$$
$$74$$ −1.00000 + 1.73205i −0.116248 + 0.201347i
$$75$$ 0.500000 + 0.866025i 0.0577350 + 0.100000i
$$76$$ 2.50000 + 4.33013i 0.286770 + 0.496700i
$$77$$ −3.00000 −0.341882
$$78$$ 2.50000 2.59808i 0.283069 0.294174i
$$79$$ 3.00000 0.337526 0.168763 0.985657i $$-0.446023\pi$$
0.168763 + 0.985657i $$0.446023\pi$$
$$80$$ 1.00000 + 1.73205i 0.111803 + 0.193649i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −2.50000 + 4.33013i −0.276079 + 0.478183i
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0.500000 0.866025i 0.0545545 0.0944911i
$$85$$ −7.00000 + 12.1244i −0.759257 + 1.31507i
$$86$$ −2.00000 −0.215666
$$87$$ −2.50000 + 4.33013i −0.268028 + 0.464238i
$$88$$ 1.50000 + 2.59808i 0.159901 + 0.276956i
$$89$$ 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i $$0.0314541\pi$$
−0.412123 + 0.911128i $$0.635213\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 2.50000 2.59808i 0.262071 0.272352i
$$92$$ 6.00000 0.625543
$$93$$ 1.00000 + 1.73205i 0.103695 + 0.179605i
$$94$$ −0.500000 0.866025i −0.0515711 0.0893237i
$$95$$ −5.00000 + 8.66025i −0.512989 + 0.888523i
$$96$$ −1.00000 −0.102062
$$97$$ 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i $$-0.800958\pi$$
0.912317 + 0.409484i $$0.134291\pi$$
$$98$$ 0.500000 0.866025i 0.0505076 0.0874818i
$$99$$ 3.00000 0.301511
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i $$-0.921395\pi$$
0.273138 0.961975i $$-0.411939\pi$$
$$102$$ −3.50000 6.06218i −0.346552 0.600245i
$$103$$ 10.0000 0.985329 0.492665 0.870219i $$-0.336023\pi$$
0.492665 + 0.870219i $$0.336023\pi$$
$$104$$ −3.50000 0.866025i −0.343203 0.0849208i
$$105$$ 2.00000 0.195180
$$106$$ 1.50000 + 2.59808i 0.145693 + 0.252347i
$$107$$ −7.50000 12.9904i −0.725052 1.25583i −0.958952 0.283567i $$-0.908482\pi$$
0.233900 0.972261i $$-0.424851\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ −3.00000 + 5.19615i −0.286039 + 0.495434i
$$111$$ 1.00000 1.73205i 0.0949158 0.164399i
$$112$$ −1.00000 −0.0944911
$$113$$ −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i $$-0.924403\pi$$
0.689714 + 0.724082i $$0.257736\pi$$
$$114$$ −2.50000 4.33013i −0.234146 0.405554i
$$115$$ 6.00000 + 10.3923i 0.559503 + 0.969087i
$$116$$ 5.00000 0.464238
$$117$$ −2.50000 + 2.59808i −0.231125 + 0.240192i
$$118$$ 6.00000 0.552345
$$119$$ −3.50000 6.06218i −0.320844 0.555719i
$$120$$ −1.00000 1.73205i −0.0912871 0.158114i
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ −7.00000 −0.633750
$$123$$ 2.50000 4.33013i 0.225417 0.390434i
$$124$$ 1.00000 1.73205i 0.0898027 0.155543i
$$125$$ 12.0000 1.07331
$$126$$ −0.500000 + 0.866025i −0.0445435 + 0.0771517i
$$127$$ 6.00000 + 10.3923i 0.532414 + 0.922168i 0.999284 + 0.0378419i $$0.0120483\pi$$
−0.466870 + 0.884326i $$0.654618\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 2.00000 0.176090
$$130$$ −2.00000 6.92820i −0.175412 0.607644i
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ −1.50000 2.59808i −0.130558 0.226134i
$$133$$ −2.50000 4.33013i −0.216777 0.375470i
$$134$$ 1.00000 1.73205i 0.0863868 0.149626i
$$135$$ −2.00000 −0.172133
$$136$$ −3.50000 + 6.06218i −0.300123 + 0.519827i
$$137$$ −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i $$0.445873\pi$$
−0.938148 + 0.346235i $$0.887460\pi$$
$$138$$ −6.00000 −0.510754
$$139$$ 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i $$-0.535080\pi$$
0.915764 0.401718i $$-0.131587\pi$$
$$140$$ −1.00000 1.73205i −0.0845154 0.146385i
$$141$$ 0.500000 + 0.866025i 0.0421076 + 0.0729325i
$$142$$ −8.00000 −0.671345
$$143$$ −3.00000 10.3923i −0.250873 0.869048i
$$144$$ 1.00000 0.0833333
$$145$$ 5.00000 + 8.66025i 0.415227 + 0.719195i
$$146$$ 6.00000 + 10.3923i 0.496564 + 0.860073i
$$147$$ −0.500000 + 0.866025i −0.0412393 + 0.0714286i
$$148$$ −2.00000 −0.164399
$$149$$ −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i $$0.361067\pi$$
−0.996207 + 0.0870170i $$0.972267\pi$$
$$150$$ −0.500000 + 0.866025i −0.0408248 + 0.0707107i
$$151$$ 13.0000 1.05792 0.528962 0.848645i $$-0.322581\pi$$
0.528962 + 0.848645i $$0.322581\pi$$
$$152$$ −2.50000 + 4.33013i −0.202777 + 0.351220i
$$153$$ 3.50000 + 6.06218i 0.282958 + 0.490098i
$$154$$ −1.50000 2.59808i −0.120873 0.209359i
$$155$$ 4.00000 0.321288
$$156$$ 3.50000 + 0.866025i 0.280224 + 0.0693375i
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 1.50000 + 2.59808i 0.119334 + 0.206692i
$$159$$ −1.50000 2.59808i −0.118958 0.206041i
$$160$$ −1.00000 + 1.73205i −0.0790569 + 0.136931i
$$161$$ −6.00000 −0.472866
$$162$$ 0.500000 0.866025i 0.0392837 0.0680414i
$$163$$ 7.00000 12.1244i 0.548282 0.949653i −0.450110 0.892973i $$-0.648615\pi$$
0.998392 0.0566798i $$-0.0180514\pi$$
$$164$$ −5.00000 −0.390434
$$165$$ 3.00000 5.19615i 0.233550 0.404520i
$$166$$ −4.00000 6.92820i −0.310460 0.537733i
$$167$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ 11.5000 + 6.06218i 0.884615 + 0.466321i
$$170$$ −14.0000 −1.07375
$$171$$ 2.50000 + 4.33013i 0.191180 + 0.331133i
$$172$$ −1.00000 1.73205i −0.0762493 0.132068i
$$173$$ −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i $$-0.984113\pi$$
0.542583 + 0.840002i $$0.317446\pi$$
$$174$$ −5.00000 −0.379049
$$175$$ −0.500000 + 0.866025i −0.0377964 + 0.0654654i
$$176$$ −1.50000 + 2.59808i −0.113067 + 0.195837i
$$177$$ −6.00000 −0.450988
$$178$$ −5.50000 + 9.52628i −0.412242 + 0.714025i
$$179$$ −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i $$-0.897952\pi$$
0.201613 0.979465i $$-0.435382\pi$$
$$180$$ 1.00000 + 1.73205i 0.0745356 + 0.129099i
$$181$$ −9.00000 −0.668965 −0.334482 0.942402i $$-0.608561\pi$$
−0.334482 + 0.942402i $$0.608561\pi$$
$$182$$ 3.50000 + 0.866025i 0.259437 + 0.0641941i
$$183$$ 7.00000 0.517455
$$184$$ 3.00000 + 5.19615i 0.221163 + 0.383065i
$$185$$ −2.00000 3.46410i −0.147043 0.254686i
$$186$$ −1.00000 + 1.73205i −0.0733236 + 0.127000i
$$187$$ −21.0000 −1.53567
$$188$$ 0.500000 0.866025i 0.0364662 0.0631614i
$$189$$ 0.500000 0.866025i 0.0363696 0.0629941i
$$190$$ −10.0000 −0.725476
$$191$$ 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i $$-0.787107\pi$$
0.929267 + 0.369410i $$0.120440\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −6.50000 11.2583i −0.467880 0.810392i 0.531446 0.847092i $$-0.321649\pi$$
−0.999326 + 0.0366998i $$0.988315\pi$$
$$194$$ 2.00000 0.143592
$$195$$ 2.00000 + 6.92820i 0.143223 + 0.496139i
$$196$$ 1.00000 0.0714286
$$197$$ 4.50000 + 7.79423i 0.320612 + 0.555316i 0.980614 0.195947i $$-0.0627782\pi$$
−0.660003 + 0.751263i $$0.729445\pi$$
$$198$$ 1.50000 + 2.59808i 0.106600 + 0.184637i
$$199$$ 13.0000 22.5167i 0.921546 1.59616i 0.124521 0.992217i $$-0.460261\pi$$
0.797025 0.603947i $$-0.206406\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ −1.00000 + 1.73205i −0.0705346 + 0.122169i
$$202$$ 7.00000 12.1244i 0.492518 0.853067i
$$203$$ −5.00000 −0.350931
$$204$$ 3.50000 6.06218i 0.245049 0.424437i
$$205$$ −5.00000 8.66025i −0.349215 0.604858i
$$206$$ 5.00000 + 8.66025i 0.348367 + 0.603388i
$$207$$ 6.00000 0.417029
$$208$$ −1.00000 3.46410i −0.0693375 0.240192i
$$209$$ −15.0000 −1.03757
$$210$$ 1.00000 + 1.73205i 0.0690066 + 0.119523i
$$211$$ 5.00000 + 8.66025i 0.344214 + 0.596196i 0.985211 0.171347i $$-0.0548120\pi$$
−0.640996 + 0.767544i $$0.721479\pi$$
$$212$$ −1.50000 + 2.59808i −0.103020 + 0.178437i
$$213$$ 8.00000 0.548151
$$214$$ 7.50000 12.9904i 0.512689 0.888004i
$$215$$ 2.00000 3.46410i 0.136399 0.236250i
$$216$$ −1.00000 −0.0680414
$$217$$ −1.00000 + 1.73205i −0.0678844 + 0.117579i
$$218$$ −8.00000 13.8564i −0.541828 0.938474i
$$219$$ −6.00000 10.3923i −0.405442 0.702247i
$$220$$ −6.00000 −0.404520
$$221$$ 17.5000 18.1865i 1.17718 1.22336i
$$222$$ 2.00000 0.134231
$$223$$ 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i $$-0.123907\pi$$
−0.791258 + 0.611482i $$0.790574\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ 0.500000 0.866025i 0.0333333 0.0577350i
$$226$$ −6.00000 −0.399114
$$227$$ −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i $$-0.987137\pi$$
0.534577 + 0.845120i $$0.320471\pi$$
$$228$$ 2.50000 4.33013i 0.165567 0.286770i
$$229$$ 27.0000 1.78421 0.892105 0.451828i $$-0.149228\pi$$
0.892105 + 0.451828i $$0.149228\pi$$
$$230$$ −6.00000 + 10.3923i −0.395628 + 0.685248i
$$231$$ 1.50000 + 2.59808i 0.0986928 + 0.170941i
$$232$$ 2.50000 + 4.33013i 0.164133 + 0.284287i
$$233$$ 26.0000 1.70332 0.851658 0.524097i $$-0.175597\pi$$
0.851658 + 0.524097i $$0.175597\pi$$
$$234$$ −3.50000 0.866025i −0.228802 0.0566139i
$$235$$ 2.00000 0.130466
$$236$$ 3.00000 + 5.19615i 0.195283 + 0.338241i
$$237$$ −1.50000 2.59808i −0.0974355 0.168763i
$$238$$ 3.50000 6.06218i 0.226871 0.392953i
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 1.00000 1.73205i 0.0645497 0.111803i
$$241$$ −14.0000 + 24.2487i −0.901819 + 1.56200i −0.0766885 + 0.997055i $$0.524435\pi$$
−0.825131 + 0.564942i $$0.808899\pi$$
$$242$$ 2.00000 0.128565
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ −3.50000 6.06218i −0.224065 0.388091i
$$245$$ 1.00000 + 1.73205i 0.0638877 + 0.110657i
$$246$$ 5.00000 0.318788
$$247$$ 12.5000 12.9904i 0.795356 0.826558i
$$248$$ 2.00000 0.127000
$$249$$ 4.00000 + 6.92820i 0.253490 + 0.439057i
$$250$$ 6.00000 + 10.3923i 0.379473 + 0.657267i
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ −1.00000 −0.0629941
$$253$$ −9.00000 + 15.5885i −0.565825 + 0.980038i
$$254$$ −6.00000 + 10.3923i −0.376473 + 0.652071i
$$255$$ 14.0000 0.876714
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i $$-0.0117000\pi$$
−0.531487 + 0.847066i $$0.678367\pi$$
$$258$$ 1.00000 + 1.73205i 0.0622573 + 0.107833i
$$259$$ 2.00000 0.124274
$$260$$ 5.00000 5.19615i 0.310087 0.322252i
$$261$$ 5.00000 0.309492
$$262$$ 4.00000 + 6.92820i 0.247121 + 0.428026i
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 1.50000 2.59808i 0.0923186 0.159901i
$$265$$ −6.00000 −0.368577
$$266$$ 2.50000 4.33013i 0.153285 0.265497i
$$267$$ 5.50000 9.52628i 0.336595 0.582999i
$$268$$ 2.00000 0.122169
$$269$$ 12.0000 20.7846i 0.731653 1.26726i −0.224523 0.974469i $$-0.572083\pi$$
0.956176 0.292791i $$-0.0945841\pi$$
$$270$$ −1.00000 1.73205i −0.0608581 0.105409i
$$271$$ −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i $$-0.186015\pi$$
−0.894799 + 0.446469i $$0.852681\pi$$
$$272$$ −7.00000 −0.424437
$$273$$ −3.50000 0.866025i −0.211830 0.0524142i
$$274$$ −18.0000 −1.08742
$$275$$ 1.50000 + 2.59808i 0.0904534 + 0.156670i
$$276$$ −3.00000 5.19615i −0.180579 0.312772i
$$277$$ −3.00000 + 5.19615i −0.180253 + 0.312207i −0.941966 0.335707i $$-0.891025\pi$$
0.761714 + 0.647913i $$0.224358\pi$$
$$278$$ 19.0000 1.13954
$$279$$ 1.00000 1.73205i 0.0598684 0.103695i
$$280$$ 1.00000 1.73205i 0.0597614 0.103510i
$$281$$ 16.0000 0.954480 0.477240 0.878773i $$-0.341637\pi$$
0.477240 + 0.878773i $$0.341637\pi$$
$$282$$ −0.500000 + 0.866025i −0.0297746 + 0.0515711i
$$283$$ −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i $$-0.853740\pi$$
0.0640654 0.997946i $$-0.479593\pi$$
$$284$$ −4.00000 6.92820i −0.237356 0.411113i
$$285$$ 10.0000 0.592349
$$286$$ 7.50000 7.79423i 0.443484 0.460882i
$$287$$ 5.00000 0.295141
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ −16.0000 27.7128i −0.941176 1.63017i
$$290$$ −5.00000 + 8.66025i −0.293610 + 0.508548i
$$291$$ −2.00000 −0.117242
$$292$$ −6.00000 + 10.3923i −0.351123 + 0.608164i
$$293$$ −6.00000 + 10.3923i −0.350524 + 0.607125i −0.986341 0.164714i $$-0.947330\pi$$
0.635818 + 0.771839i $$0.280663\pi$$
$$294$$ −1.00000 −0.0583212
$$295$$ −6.00000 + 10.3923i −0.349334 + 0.605063i
$$296$$ −1.00000 1.73205i −0.0581238 0.100673i
$$297$$ −1.50000 2.59808i −0.0870388 0.150756i
$$298$$ −14.0000 −0.810998
$$299$$ −6.00000 20.7846i −0.346989 1.20201i
$$300$$ −1.00000 −0.0577350
$$301$$ 1.00000 + 1.73205i 0.0576390 + 0.0998337i
$$302$$ 6.50000 + 11.2583i 0.374033 + 0.647844i
$$303$$ −7.00000 + 12.1244i −0.402139 + 0.696526i
$$304$$ −5.00000 −0.286770
$$305$$ 7.00000 12.1244i 0.400819 0.694239i
$$306$$ −3.50000 + 6.06218i −0.200082 + 0.346552i
$$307$$ 9.00000 0.513657 0.256829 0.966457i $$-0.417322\pi$$
0.256829 + 0.966457i $$0.417322\pi$$
$$308$$ 1.50000 2.59808i 0.0854704 0.148039i
$$309$$ −5.00000 8.66025i −0.284440 0.492665i
$$310$$ 2.00000 + 3.46410i 0.113592 + 0.196748i
$$311$$ 23.0000 1.30421 0.652105 0.758129i $$-0.273886\pi$$
0.652105 + 0.758129i $$0.273886\pi$$
$$312$$ 1.00000 + 3.46410i 0.0566139 + 0.196116i
$$313$$ 28.0000 1.58265 0.791327 0.611393i $$-0.209391\pi$$
0.791327 + 0.611393i $$0.209391\pi$$
$$314$$ −9.00000 15.5885i −0.507899 0.879708i
$$315$$ −1.00000 1.73205i −0.0563436 0.0975900i
$$316$$ −1.50000 + 2.59808i −0.0843816 + 0.146153i
$$317$$ 30.0000 1.68497 0.842484 0.538721i $$-0.181092\pi$$
0.842484 + 0.538721i $$0.181092\pi$$
$$318$$ 1.50000 2.59808i 0.0841158 0.145693i
$$319$$ −7.50000 + 12.9904i −0.419919 + 0.727322i
$$320$$ −2.00000 −0.111803
$$321$$ −7.50000 + 12.9904i −0.418609 + 0.725052i
$$322$$ −3.00000 5.19615i −0.167183 0.289570i
$$323$$ −17.5000 30.3109i −0.973726 1.68654i
$$324$$ 1.00000 0.0555556
$$325$$ −3.50000 0.866025i −0.194145 0.0480384i
$$326$$ 14.0000 0.775388
$$327$$ 8.00000 + 13.8564i 0.442401 + 0.766261i
$$328$$ −2.50000 4.33013i −0.138039 0.239091i
$$329$$ −0.500000 + 0.866025i −0.0275659 + 0.0477455i
$$330$$ 6.00000 0.330289
$$331$$ −11.0000 + 19.0526i −0.604615 + 1.04722i 0.387498 + 0.921871i $$0.373340\pi$$
−0.992112 + 0.125353i $$0.959994\pi$$
$$332$$ 4.00000 6.92820i 0.219529 0.380235i
$$333$$ −2.00000 −0.109599
$$334$$ 0 0
$$335$$ 2.00000 + 3.46410i 0.109272 + 0.189264i
$$336$$ 0.500000 + 0.866025i 0.0272772 + 0.0472456i
$$337$$ −17.0000 −0.926049 −0.463025 0.886345i $$-0.653236\pi$$
−0.463025 + 0.886345i $$0.653236\pi$$
$$338$$ 0.500000 + 12.9904i 0.0271964 + 0.706584i
$$339$$ 6.00000 0.325875
$$340$$ −7.00000 12.1244i −0.379628 0.657536i
$$341$$ 3.00000 + 5.19615i 0.162459 + 0.281387i
$$342$$ −2.50000 + 4.33013i −0.135185 + 0.234146i
$$343$$ −1.00000 −0.0539949
$$344$$ 1.00000 1.73205i 0.0539164 0.0933859i
$$345$$ 6.00000 10.3923i 0.323029 0.559503i
$$346$$ −12.0000 −0.645124
$$347$$ −8.50000 + 14.7224i −0.456304 + 0.790342i −0.998762 0.0497412i $$-0.984160\pi$$
0.542458 + 0.840083i $$0.317494\pi$$
$$348$$ −2.50000 4.33013i −0.134014 0.232119i
$$349$$ 9.00000 + 15.5885i 0.481759 + 0.834431i 0.999781 0.0209364i $$-0.00666475\pi$$
−0.518022 + 0.855367i $$0.673331\pi$$
$$350$$ −1.00000 −0.0534522
$$351$$ 3.50000 + 0.866025i 0.186816 + 0.0462250i
$$352$$ −3.00000 −0.159901
$$353$$ −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i $$-0.288191\pi$$
−0.989960 + 0.141344i $$0.954858\pi$$
$$354$$ −3.00000 5.19615i −0.159448 0.276172i
$$355$$ 8.00000 13.8564i 0.424596 0.735422i
$$356$$ −11.0000 −0.582999
$$357$$ −3.50000 + 6.06218i −0.185240 + 0.320844i
$$358$$ 10.0000 17.3205i 0.528516 0.915417i
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ −1.00000 + 1.73205i −0.0527046 + 0.0912871i
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ −4.50000 7.79423i −0.236515 0.409656i
$$363$$ −2.00000 −0.104973
$$364$$ 1.00000 + 3.46410i 0.0524142 + 0.181568i
$$365$$ −24.0000 −1.25622
$$366$$ 3.50000 + 6.06218i 0.182948 + 0.316875i
$$367$$ 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i $$-0.0826151\pi$$
−0.705509 + 0.708700i $$0.749282\pi$$
$$368$$ −3.00000 + 5.19615i −0.156386 + 0.270868i
$$369$$ −5.00000 −0.260290
$$370$$ 2.00000 3.46410i 0.103975 0.180090i
$$371$$ 1.50000 2.59808i 0.0778761 0.134885i
$$372$$ −2.00000 −0.103695
$$373$$ −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i $$-0.866355\pi$$
0.809591 + 0.586994i $$0.199689\pi$$
$$374$$ −10.5000 18.1865i −0.542942 0.940403i
$$375$$ −6.00000 10.3923i −0.309839 0.536656i
$$376$$ 1.00000 0.0515711
$$377$$ −5.00000 17.3205i −0.257513 0.892052i
$$378$$ 1.00000 0.0514344
$$379$$ 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i $$0.00504609\pi$$
−0.486209 + 0.873843i $$0.661621\pi$$
$$380$$ −5.00000 8.66025i −0.256495 0.444262i
$$381$$ 6.00000 10.3923i 0.307389 0.532414i
$$382$$ 4.00000 0.204658
$$383$$ −15.5000 + 26.8468i −0.792013 + 1.37181i 0.132706 + 0.991155i $$0.457633\pi$$
−0.924719 + 0.380651i $$0.875700\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ 6.00000 0.305788
$$386$$ 6.50000 11.2583i 0.330841 0.573034i
$$387$$ −1.00000 1.73205i −0.0508329 0.0880451i
$$388$$ 1.00000 + 1.73205i 0.0507673 + 0.0879316i
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ −5.00000 + 5.19615i −0.253185 + 0.263117i
$$391$$ −42.0000 −2.12403
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ −4.00000 6.92820i −0.201773 0.349482i
$$394$$ −4.50000 + 7.79423i −0.226707 + 0.392668i
$$395$$ −6.00000 −0.301893
$$396$$ −1.50000 + 2.59808i −0.0753778 + 0.130558i
$$397$$ 7.50000 12.9904i 0.376414 0.651969i −0.614123 0.789210i $$-0.710490\pi$$
0.990538 + 0.137241i $$0.0438236\pi$$
$$398$$ 26.0000 1.30326
$$399$$ −2.50000 + 4.33013i −0.125157 + 0.216777i
$$400$$ 0.500000 + 0.866025i 0.0250000 + 0.0433013i
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ −2.00000 −0.0997509
$$403$$ −7.00000 1.73205i −0.348695 0.0862796i
$$404$$ 14.0000 0.696526
$$405$$ 1.00000 + 1.73205i 0.0496904 + 0.0860663i
$$406$$ −2.50000 4.33013i −0.124073 0.214901i
$$407$$ 3.00000 5.19615i 0.148704 0.257564i
$$408$$ 7.00000 0.346552
$$409$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$410$$ 5.00000 8.66025i 0.246932 0.427699i
$$411$$ 18.0000 0.887875
$$412$$ −5.00000 + 8.66025i −0.246332 + 0.426660i
$$413$$ −3.00000 5.19615i −0.147620 0.255686i
$$414$$ 3.00000 + 5.19615i 0.147442 + 0.255377i
$$415$$ 16.0000 0.785409
$$416$$ 2.50000 2.59808i 0.122573 0.127381i
$$417$$ −19.0000 −0.930434
$$418$$ −7.50000 12.9904i −0.366837 0.635380i
$$419$$ −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i $$-0.197817\pi$$
−0.910735 + 0.412991i $$0.864484\pi$$
$$420$$ −1.00000 + 1.73205i −0.0487950 + 0.0845154i
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ −5.00000 + 8.66025i −0.243396 + 0.421575i
$$423$$ 0.500000 0.866025i 0.0243108 0.0421076i
$$424$$ −3.00000 −0.145693
$$425$$ −3.50000 + 6.06218i −0.169775 + 0.294059i
$$426$$ 4.00000 + 6.92820i 0.193801 + 0.335673i
$$427$$ 3.50000 + 6.06218i 0.169377 + 0.293369i
$$428$$ 15.0000 0.725052
$$429$$ −7.50000 + 7.79423i −0.362103 + 0.376309i
$$430$$ 4.00000 0.192897
$$431$$ 4.00000 + 6.92820i 0.192673 + 0.333720i 0.946135 0.323772i $$-0.104951\pi$$
−0.753462 + 0.657491i $$0.771618\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i $$0.381462\pi$$
−0.988591 + 0.150624i $$0.951872\pi$$
$$434$$ −2.00000 −0.0960031
$$435$$ 5.00000 8.66025i 0.239732 0.415227i
$$436$$ 8.00000 13.8564i 0.383131 0.663602i
$$437$$ −30.0000 −1.43509
$$438$$ 6.00000 10.3923i 0.286691 0.496564i
$$439$$ −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i $$-0.197097\pi$$
−0.909798 + 0.415051i $$0.863764\pi$$
$$440$$ −3.00000 5.19615i −0.143019 0.247717i
$$441$$ 1.00000 0.0476190
$$442$$ 24.5000 + 6.06218i 1.16535 + 0.288348i
$$443$$ 15.0000 0.712672 0.356336 0.934358i $$-0.384026\pi$$
0.356336 + 0.934358i $$0.384026\pi$$
$$444$$ 1.00000 + 1.73205i 0.0474579 + 0.0821995i
$$445$$ −11.0000 19.0526i −0.521450 0.903178i
$$446$$ −2.00000 + 3.46410i −0.0947027 + 0.164030i
$$447$$ 14.0000 0.662177
$$448$$ 0.500000 0.866025i 0.0236228 0.0409159i
$$449$$ 19.0000 32.9090i 0.896665 1.55307i 0.0649356 0.997889i $$-0.479316\pi$$
0.831730 0.555181i $$-0.187351\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ 7.50000 12.9904i 0.353161 0.611693i
$$452$$ −3.00000 5.19615i −0.141108 0.244406i
$$453$$ −6.50000 11.2583i −0.305397 0.528962i
$$454$$ −14.0000 −0.657053
$$455$$ −5.00000 + 5.19615i −0.234404 + 0.243599i
$$456$$ 5.00000 0.234146
$$457$$ −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i $$-0.958593\pi$$
0.383437 0.923567i $$-0.374740\pi$$
$$458$$ 13.5000 + 23.3827i 0.630814 + 1.09260i
$$459$$ 3.50000 6.06218i 0.163366 0.282958i
$$460$$ −12.0000 −0.559503
$$461$$ −4.00000 + 6.92820i −0.186299 + 0.322679i −0.944013 0.329907i $$-0.892983\pi$$
0.757715 + 0.652586i $$0.226316\pi$$
$$462$$ −1.50000 + 2.59808i −0.0697863 + 0.120873i
$$463$$ −31.0000 −1.44069 −0.720346 0.693615i $$-0.756017\pi$$
−0.720346 + 0.693615i $$0.756017\pi$$
$$464$$ −2.50000 + 4.33013i −0.116060 + 0.201021i
$$465$$ −2.00000 3.46410i −0.0927478 0.160644i
$$466$$ 13.0000 + 22.5167i 0.602213 + 1.04306i
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ −1.00000 3.46410i −0.0462250 0.160128i
$$469$$ −2.00000 −0.0923514
$$470$$ 1.00000 + 1.73205i 0.0461266 + 0.0798935i
$$471$$ 9.00000 + 15.5885i 0.414698 + 0.718278i
$$472$$ −3.00000 + 5.19615i −0.138086 + 0.239172i
$$473$$ 6.00000 0.275880
$$474$$ 1.50000 2.59808i 0.0688973 0.119334i
$$475$$ −2.50000 + 4.33013i −0.114708 + 0.198680i
$$476$$ 7.00000 0.320844
$$477$$ −1.50000 + 2.59808i −0.0686803 + 0.118958i
$$478$$ 6.00000 + 10.3923i 0.274434 + 0.475333i
$$479$$ −10.5000 18.1865i −0.479757 0.830964i 0.519973 0.854183i $$-0.325942\pi$$
−0.999730 + 0.0232187i $$0.992609\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ 2.00000 + 6.92820i 0.0911922 + 0.315899i
$$482$$ −28.0000 −1.27537
$$483$$ 3.00000 + 5.19615i 0.136505 + 0.236433i
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ −2.00000 + 3.46410i −0.0908153 + 0.157297i
$$486$$ −1.00000 −0.0453609
$$487$$ −17.5000 + 30.3109i −0.793001 + 1.37352i 0.131100 + 0.991369i $$0.458149\pi$$
−0.924101 + 0.382148i $$0.875184\pi$$
$$488$$ 3.50000 6.06218i 0.158438 0.274422i
$$489$$ −14.0000 −0.633102
$$490$$ −1.00000 + 1.73205i −0.0451754 + 0.0782461i
$$491$$ 4.00000 + 6.92820i 0.180517 + 0.312665i 0.942057 0.335453i $$-0.108889\pi$$
−0.761539 + 0.648119i $$0.775556\pi$$
$$492$$ 2.50000 + 4.33013i 0.112709 + 0.195217i
$$493$$ −35.0000 −1.57632
$$494$$ 17.5000 + 4.33013i 0.787362 + 0.194822i
$$495$$ −6.00000 −0.269680
$$496$$ 1.00000 + 1.73205i 0.0449013 + 0.0777714i
$$497$$ 4.00000 + 6.92820i 0.179425 + 0.310772i
$$498$$ −4.00000 + 6.92820i −0.179244 + 0.310460i
$$499$$ 14.0000 0.626726 0.313363 0.949633i $$-0.398544\pi$$
0.313363 + 0.949633i $$0.398544\pi$$
$$500$$ −6.00000 + 10.3923i −0.268328 + 0.464758i
$$501$$ 0 0
$$502$$ 12.0000 0.535586
$$503$$ −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i $$0.346375\pi$$
−0.999161 + 0.0409609i $$0.986958\pi$$
$$504$$ −0.500000 0.866025i −0.0222718 0.0385758i
$$505$$ 14.0000 + 24.2487i 0.622992 + 1.07905i
$$506$$ −18.0000 −0.800198
$$507$$ −0.500000 12.9904i −0.0222058 0.576923i
$$508$$ −12.0000 −0.532414
$$509$$ 20.0000 + 34.6410i 0.886484 + 1.53544i 0.844003 + 0.536339i $$0.180193\pi$$
0.0424816 + 0.999097i $$0.486474\pi$$
$$510$$ 7.00000 + 12.1244i 0.309965 + 0.536875i
$$511$$ 6.00000 10.3923i 0.265424 0.459728i
$$512$$ −1.00000 −0.0441942
$$513$$ 2.50000 4.33013i 0.110378 0.191180i
$$514$$ −7.50000 + 12.9904i −0.330811 + 0.572981i
$$515$$ −20.0000 −0.881305
$$516$$ −1.00000 + 1.73205i −0.0440225 + 0.0762493i
$$517$$ 1.50000 + 2.59808i 0.0659699 + 0.114263i
$$518$$ 1.00000 + 1.73205i 0.0439375 + 0.0761019i
$$519$$ 12.0000 0.526742
$$520$$ 7.00000 + 1.73205i 0.306970 + 0.0759555i
$$521$$ 21.0000 0.920027 0.460013 0.887912i $$-0.347845\pi$$
0.460013 + 0.887912i $$0.347845\pi$$
$$522$$ 2.50000 + 4.33013i 0.109422 + 0.189525i
$$523$$ −19.5000 33.7750i −0.852675 1.47688i −0.878785 0.477218i $$-0.841645\pi$$
0.0261094 0.999659i $$-0.491688\pi$$
$$524$$ −4.00000 + 6.92820i −0.174741 + 0.302660i
$$525$$ 1.00000 0.0436436
$$526$$ −12.0000 + 20.7846i −0.523225 + 0.906252i
$$527$$ −7.00000 + 12.1244i −0.304925 + 0.528145i
$$528$$ 3.00000 0.130558
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ −3.00000 5.19615i −0.130312 0.225706i
$$531$$ 3.00000 + 5.19615i 0.130189 + 0.225494i
$$532$$ 5.00000 0.216777
$$533$$ 5.00000 + 17.3205i 0.216574 + 0.750234i
$$534$$ 11.0000 0.476017
$$535$$ 15.0000 + 25.9808i 0.648507 + 1.12325i
$$536$$ 1.00000 + 1.73205i 0.0431934 + 0.0748132i
$$537$$ −10.0000 + 17.3205i −0.431532 + 0.747435i
$$538$$ 24.0000 1.03471
$$539$$ −1.50000 + 2.59808i −0.0646096 + 0.111907i
$$540$$ 1.00000 1.73205i 0.0430331 0.0745356i
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ 1.00000 1.73205i 0.0429537 0.0743980i
$$543$$ 4.50000 + 7.79423i 0.193113 + 0.334482i
$$544$$ −3.50000 6.06218i −0.150061 0.259914i
$$545$$ 32.0000 1.37073
$$546$$ −1.00000 3.46410i −0.0427960 0.148250i
$$547$$ −32.0000 −1.36822 −0.684111 0.729378i $$-0.739809\pi$$
−0.684111 + 0.729378i $$0.739809\pi$$
$$548$$ −9.00000 15.5885i −0.384461 0.665906i
$$549$$ −3.50000 6.06218i −0.149376 0.258727i
$$550$$ −1.50000 + 2.59808i −0.0639602 + 0.110782i
$$551$$ −25.0000 −1.06504
$$552$$ 3.00000 5.19615i 0.127688 0.221163i
$$553$$ 1.50000 2.59808i 0.0637865 0.110481i
$$554$$ −6.00000 −0.254916
$$555$$ −2.00000 + 3.46410i −0.0848953 + 0.147043i
$$556$$ 9.50000 + 16.4545i 0.402890 + 0.697826i
$$557$$ 7.50000 + 12.9904i 0.317785 + 0.550420i 0.980026 0.198871i $$-0.0637276\pi$$
−0.662240 + 0.749291i $$0.730394\pi$$
$$558$$ 2.00000 0.0846668
$$559$$ −5.00000 + 5.19615i −0.211477 + 0.219774i
$$560$$ 2.00000 0.0845154
$$561$$ 10.5000 + 18.1865i 0.443310 + 0.767836i
$$562$$ 8.00000 + 13.8564i 0.337460 + 0.584497i
$$563$$ −15.0000 + 25.9808i −0.632175 + 1.09496i 0.354932 + 0.934892i $$0.384504\pi$$
−0.987106 + 0.160066i $$0.948829\pi$$
$$564$$ −1.00000 −0.0421076
$$565$$ 6.00000 10.3923i 0.252422 0.437208i
$$566$$ 14.0000 24.2487i 0.588464 1.01925i
$$567$$ −1.00000 −0.0419961
$$568$$ 4.00000 6.92820i 0.167836 0.290701i
$$569$$ 22.0000 + 38.1051i 0.922288 + 1.59745i 0.795866 + 0.605473i $$0.207016\pi$$
0.126422 + 0.991977i $$0.459651\pi$$
$$570$$ 5.00000 + 8.66025i 0.209427 + 0.362738i
$$571$$ −12.0000 −0.502184 −0.251092 0.967963i $$-0.580790\pi$$
−0.251092 + 0.967963i $$0.580790\pi$$
$$572$$ 10.5000 + 2.59808i 0.439027 + 0.108631i
$$573$$ −4.00000 −0.167102
$$574$$ 2.50000 + 4.33013i 0.104348 + 0.180736i
$$575$$ 3.00000 + 5.19615i 0.125109 + 0.216695i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 20.0000 0.832611 0.416305 0.909225i $$-0.363325\pi$$
0.416305 + 0.909225i $$0.363325\pi$$
$$578$$ 16.0000 27.7128i 0.665512 1.15270i
$$579$$ −6.50000 + 11.2583i −0.270131 + 0.467880i
$$580$$ −10.0000 −0.415227
$$581$$ −4.00000 + 6.92820i −0.165948 + 0.287430i
$$582$$ −1.00000 1.73205i −0.0414513 0.0717958i
$$583$$ −4.50000 7.79423i −0.186371 0.322804i
$$584$$ −12.0000 −0.496564
$$585$$ 5.00000 5.19615i 0.206725 0.214834i
$$586$$ −12.0000 −0.495715
$$587$$ −5.00000 8.66025i −0.206372 0.357447i 0.744197 0.667960i $$-0.232832\pi$$
−0.950569 + 0.310513i $$0.899499\pi$$
$$588$$ −0.500000 0.866025i −0.0206197 0.0357143i
$$589$$ −5.00000 + 8.66025i −0.206021 + 0.356840i
$$590$$ −12.0000 −0.494032
$$591$$ 4.50000 7.79423i 0.185105 0.320612i
$$592$$ 1.00000 1.73205i 0.0410997 0.0711868i
$$593$$ −13.0000 −0.533846 −0.266923 0.963718i $$-0.586007\pi$$
−0.266923 + 0.963718i $$0.586007\pi$$
$$594$$ 1.50000 2.59808i 0.0615457 0.106600i
$$595$$ 7.00000 + 12.1244i 0.286972 + 0.497050i
$$596$$ −7.00000 12.1244i −0.286731 0.496633i
$$597$$ −26.0000 −1.06411
$$598$$ 15.0000 15.5885i 0.613396 0.637459i
$$599$$ −26.0000 −1.06233 −0.531166 0.847268i $$-0.678246\pi$$
−0.531166 + 0.847268i $$0.678246\pi$$
$$600$$ −0.500000 0.866025i −0.0204124 0.0353553i
$$601$$ −19.0000 32.9090i −0.775026 1.34238i −0.934780 0.355228i $$-0.884403\pi$$
0.159754 0.987157i $$-0.448930\pi$$
$$602$$ −1.00000 + 1.73205i −0.0407570 + 0.0705931i
$$603$$ 2.00000 0.0814463
$$604$$ −6.50000 + 11.2583i −0.264481 + 0.458095i
$$605$$ −2.00000 + 3.46410i −0.0813116 + 0.140836i
$$606$$ −14.0000 −0.568711
$$607$$ 15.0000 25.9808i 0.608831 1.05453i −0.382602 0.923913i $$-0.624972\pi$$
0.991433 0.130613i $$-0.0416947\pi$$
$$608$$ −2.50000 4.33013i −0.101388 0.175610i
$$609$$ 2.50000 + 4.33013i 0.101305 + 0.175466i
$$610$$ 14.0000 0.566843
$$611$$ −3.50000 0.866025i −0.141595 0.0350356i
$$612$$ −7.00000 −0.282958
$$613$$ 14.0000 + 24.2487i 0.565455 + 0.979396i 0.997007 + 0.0773084i $$0.0246326\pi$$
−0.431553 + 0.902088i $$0.642034\pi$$
$$614$$ 4.50000 + 7.79423i 0.181605 + 0.314549i
$$615$$ −5.00000 + 8.66025i −0.201619 + 0.349215i
$$616$$ 3.00000 0.120873
$$617$$ 10.0000 17.3205i 0.402585 0.697297i −0.591452 0.806340i $$-0.701445\pi$$
0.994037 + 0.109043i $$0.0347785\pi$$
$$618$$ 5.00000 8.66025i 0.201129 0.348367i
$$619$$ 41.0000 1.64793 0.823965 0.566641i $$-0.191757\pi$$
0.823965 + 0.566641i $$0.191757\pi$$
$$620$$ −2.00000 + 3.46410i −0.0803219 + 0.139122i
$$621$$ −3.00000 5.19615i −0.120386 0.208514i
$$622$$ 11.5000 + 19.9186i 0.461108 + 0.798662i
$$623$$ 11.0000 0.440706
$$624$$ −2.50000 + 2.59808i −0.100080 + 0.104006i
$$625$$ −19.0000 −0.760000
$$626$$ 14.0000 + 24.2487i 0.559553 + 0.969173i
$$627$$ 7.50000 + 12.9904i 0.299521 + 0.518786i
$$628$$ 9.00000 15.5885i 0.359139 0.622047i
$$629$$ 14.0000 0.558217
$$630$$ 1.00000 1.73205i 0.0398410 0.0690066i
$$631$$ −7.50000 + 12.9904i −0.298570 + 0.517139i −0.975809 0.218624i $$-0.929843\pi$$
0.677239 + 0.735763i $$0.263176\pi$$
$$632$$ −3.00000 −0.119334
$$633$$ 5.00000 8.66025i 0.198732 0.344214i
$$634$$ 15.0000 + 25.9808i 0.595726 + 1.03183i
$$635$$ −12.0000 20.7846i −0.476205 0.824812i
$$636$$ 3.00000 0.118958
$$637$$ −1.00000 3.46410i −0.0396214 0.137253i
$$638$$ −15.0000 −0.593856
$$639$$ −4.00000 6.92820i −0.158238 0.274075i
$$640$$ −1.00000 1.73205i −0.0395285 0.0684653i
$$641$$ −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i $$-0.949015\pi$$
0.631721 + 0.775196i $$0.282349\pi$$
$$642$$ −15.0000 −0.592003
$$643$$ 24.5000 42.4352i 0.966186 1.67348i 0.259791 0.965665i $$-0.416346\pi$$
0.706395 0.707818i $$-0.250320\pi$$
$$644$$ 3.00000 5.19615i 0.118217 0.204757i
$$645$$ −4.00000 −0.157500
$$646$$ 17.5000 30.3109i 0.688528 1.19257i
$$647$$ −0.500000 0.866025i −0.0196570 0.0340470i 0.856030 0.516927i $$-0.172924\pi$$
−0.875687 + 0.482880i $$0.839591\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ −18.0000 −0.706562
$$650$$ −1.00000 3.46410i −0.0392232 0.135873i
$$651$$ 2.00000 0.0783862
$$652$$ 7.00000 + 12.1244i 0.274141 + 0.474826i
$$653$$ −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i $$-0.989498\pi$$
0.471160 0.882048i $$-0.343835\pi$$
$$654$$ −8.00000 + 13.8564i −0.312825 + 0.541828i
$$655$$ −16.0000 −0.625172
$$656$$ 2.50000 4.33013i 0.0976086 0.169063i
$$657$$ −6.00000 + 10.3923i −0.234082 + 0.405442i
$$658$$ −1.00000 −0.0389841
$$659$$ 13.5000 23.3827i 0.525885 0.910860i −0.473660 0.880708i $$-0.657067\pi$$
0.999545 0.0301523i $$-0.00959924\pi$$
$$660$$ 3.00000 + 5.19615i 0.116775 + 0.202260i
$$661$$ 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i $$-0.0788928\pi$$
−0.697174 + 0.716902i $$0.745559\pi$$
$$662$$ −22.0000 −0.855054
$$663$$ −24.5000 6.06218i −0.951501 0.235435i
$$664$$ 8.00000 0.310460
$$665$$ 5.00000 + 8.66025i 0.193892 + 0.335830i
$$666$$ −1.00000 1.73205i −0.0387492 0.0671156i
$$667$$ −15.0000 + 25.9808i −0.580802 + 1.00598i
$$668$$ 0 0
$$669$$ 2.00000 3.46410i 0.0773245 0.133930i
$$670$$ −2.00000 + 3.46410i −0.0772667 + 0.133830i
$$671$$ 21.0000 0.810696
$$672$$ −0.500000 + 0.866025i −0.0192879 + 0.0334077i
$$673$$ −11.5000 19.9186i −0.443292 0.767805i 0.554639 0.832091i $$-0.312856\pi$$
−0.997932 + 0.0642860i $$0.979523\pi$$
$$674$$ −8.50000 14.7224i −0.327408 0.567087i
$$675$$ −1.00000 −0.0384900
$$676$$ −11.0000 + 6.92820i −0.423077 + 0.266469i
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 3.00000 + 5.19615i 0.115214 + 0.199557i
$$679$$ −1.00000 1.73205i −0.0383765 0.0664700i
$$680$$ 7.00000 12.1244i 0.268438 0.464948i
$$681$$ 14.0000 0.536481
$$682$$ −3.00000 + 5.19615i −0.114876 + 0.198971i
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ −5.00000 −0.191180
$$685$$ 18.0000 31.1769i 0.687745 1.19121i
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ −13.5000 23.3827i −0.515057 0.892105i
$$688$$ 2.00000 0.0762493
$$689$$ 10.5000 + 2.59808i 0.400018 + 0.0989788i
$$690$$ 12.0000 0.456832
$$691$$ −20.0000 34.6410i −0.760836 1.31781i −0.942420 0.334431i $$-0.891456\pi$$
0.181584 0.983375i $$-0.441877\pi$$
$$692$$ −6.00000 10.3923i −0.228086 0.395056i
$$693$$ 1.50000 2.59808i 0.0569803 0.0986928i
$$694$$ −17.0000 −0.645311
$$695$$ −19.0000 + 32.9090i −0.720711 + 1.24831i
$$696$$ 2.50000 4.33013i 0.0947623 0.164133i
$$697$$ 35.0000 1.32572
$$698$$ −9.00000 + 15.5885i −0.340655 + 0.590032i
$$699$$ −13.0000 22.5167i −0.491705 0.851658i
$$700$$ −0.500000 0.866025i −0.0188982 0.0327327i
$$701$$ 13.0000 0.491003 0.245502 0.969396i $$-0.421047\pi$$
0.245502 + 0.969396i $$0.421047\pi$$
$$702$$ 1.00000 + 3.46410i 0.0377426 + 0.130744i
$$703$$ 10.0000 0.377157
$$704$$ −1.50000 2.59808i −0.0565334 0.0979187i
$$705$$ −1.00000 1.73205i −0.0376622 0.0652328i
$$706$$ 7.00000 12.1244i 0.263448 0.456306i
$$707$$ −14.0000 −0.526524
$$708$$ 3.00000 5.19615i 0.112747 0.195283i
$$709$$ 14.0000 24.2487i 0.525781 0.910679i −0.473768 0.880650i $$-0.657106\pi$$
0.999549 0.0300298i $$-0.00956021\pi$$
$$710$$ 16.0000 0.600469
$$711$$ −1.50000 + 2.59808i −0.0562544 + 0.0974355i
$$712$$ −5.50000 9.52628i −0.206121 0.357012i
$$713$$ 6.00000 + 10.3923i 0.224702 + 0.389195i
$$714$$ −7.00000 −0.261968
$$715$$ 6.00000 + 20.7846i 0.224387 + 0.777300i
$$716$$ 20.0000 0.747435
$$717$$ −6.00000 10.3923i −0.224074 0.388108i
$$718$$ 9.00000 + 15.5885i 0.335877 + 0.581756i
$$719$$ 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i $$-0.743097\pi$$
0.971311 + 0.237814i $$0.0764307\pi$$
$$720$$ −2.00000 −0.0745356
$$721$$ 5.00000 8.66025i 0.186210 0.322525i
$$722$$ 3.00000 5.19615i 0.111648 0.193381i
$$723$$ 28.0000 1.04133
$$724$$ 4.50000 7.79423i 0.167241 0.289670i
$$725$$ 2.50000 + 4.33013i 0.0928477 + 0.160817i
$$726$$ −1.00000 1.73205i −0.0371135 0.0642824i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ −2.50000 + 2.59808i −0.0926562 + 0.0962911i
$$729$$ 1.00000 0.0370370
$$730$$ −12.0000 20.7846i −0.444140 0.769273i
$$731$$ 7.00000 + 12.1244i 0.258904 + 0.448435i
$$732$$ −3.50000 + 6.06218i −0.129364 + 0.224065i
$$733$$ −7.00000 −0.258551 −0.129275 0.991609i $$-0.541265\pi$$
−0.129275 + 0.991609i $$0.541265\pi$$
$$734$$ −5.00000 + 8.66025i −0.184553 + 0.319656i
$$735$$ 1.00000 1.73205i 0.0368856 0.0638877i
$$736$$ −6.00000 −0.221163
$$737$$ −3.00000 + 5.19615i −0.110506 + 0.191403i
$$738$$ −2.50000 4.33013i −0.0920263 0.159394i
$$739$$ 7.00000 + 12.1244i 0.257499 + 0.446002i 0.965571 0.260138i $$-0.0837682\pi$$
−0.708072 + 0.706140i $$0.750435\pi$$
$$740$$ 4.00000 0.147043
$$741$$ −17.5000 4.33013i −0.642879 0.159071i
$$742$$ 3.00000 0.110133
$$743$$ 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i $$-0.131563\pi$$
−0.805735 + 0.592277i $$0.798229\pi$$
$$744$$ −1.00000 1.73205i −0.0366618 0.0635001i
$$745$$ 14.0000 24.2487i 0.512920 0.888404i
$$746$$ −4.00000 −0.146450
$$747$$ 4.00000 6.92820i 0.146352 0.253490i
$$748$$ 10.5000 18.1865i 0.383918 0.664966i
$$749$$ −15.0000 −0.548088
$$750$$ 6.00000 10.3923i 0.219089 0.379473i
$$751$$ 16.5000 + 28.5788i 0.602094 + 1.04286i 0.992504 + 0.122216i $$0.0389999\pi$$
−0.390410 + 0.920641i $$0.627667\pi$$
$$752$$ 0.500000 + 0.866025i 0.0182331 + 0.0315807i
$$753$$ −12.0000 −0.437304
$$754$$ 12.5000 12.9904i 0.455223 0.473082i
$$755$$ −26.0000 −0.946237
$$756$$ 0.500000 + 0.866025i 0.0181848 + 0.0314970i
$$757$$ −16.0000 27.7128i −0.581530 1.00724i −0.995298 0.0968571i $$-0.969121\pi$$
0.413768 0.910382i $$-0.364212\pi$$
$$758$$ −10.0000 + 17.3205i −0.363216 + 0.629109i
$$759$$ 18.0000 0.653359
$$760$$ 5.00000 8.66025i 0.181369 0.314140i
$$761$$ 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i $$-0.727548\pi$$
0.981764 + 0.190101i $$0.0608816\pi$$
$$762$$ 12.0000 0.434714
$$763$$ −8.00000 + 13.8564i −0.289619 + 0.501636i
$$764$$ 2.00000 + 3.46410i 0.0723575 + 0.125327i
$$765$$ −7.00000 12.1244i −0.253086 0.438357i
$$766$$ −31.0000 −1.12008
$$767$$ 15.0000 15.5885i 0.541619 0.562867i
$$768$$ 1.00000 0.0360844
$$769$$ −23.0000 39.8372i −0.829401 1.43657i −0.898509 0.438956i $$-0.855348\pi$$
0.0691074 0.997609i $$-0.477985\pi$$
$$770$$ 3.00000 + 5.19615i 0.108112 + 0.187256i
$$771$$ 7.50000 12.9904i 0.270106 0.467837i
$$772$$ 13.0000 0.467880
$$773$$ 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i $$-0.775776\pi$$
0.941825 + 0.336104i $$0.109109\pi$$
$$774$$ 1.00000 1.73205i 0.0359443 0.0622573i