# Properties

 Label 78.2.e.b.55.1 Level $78$ Weight $2$ Character 78.55 Analytic conductor $0.623$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$78 = 2 \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 78.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.622833135766$$ 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 55.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 78.55 Dual form 78.2.e.b.61.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +2.00000 q^{38} +(3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(1.00000 + 3.46410i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(1.00000 + 1.73205i) q^{76} -4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} -10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(-2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 $$2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{12} + 5 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} - 6 q^{23} - q^{24} - 8 q^{25} + 7 q^{26} - 2 q^{27} + 2 q^{28} + 9 q^{29} + q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 10 q^{34} - 2 q^{35} - q^{36} + 11 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 5 q^{41} + 2 q^{42} - 10 q^{43} + 4 q^{44} + q^{45} + 6 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} + 2 q^{52} - 2 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} + 4 q^{57} - 9 q^{58} + 8 q^{59} + 2 q^{60} + 11 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{65} + 4 q^{66} - 2 q^{67} - 5 q^{68} + 6 q^{69} - 4 q^{70} + 14 q^{71} + q^{72} - 26 q^{73} - 11 q^{74} - 4 q^{75} + 2 q^{76} - 8 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} - 20 q^{86} - 9 q^{87} + 2 q^{88} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 12 q^{92} - 4 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100})$$ 2 * q + q^2 + q^3 - q^4 - 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 - q^10 - 2 * q^11 - 2 * q^12 + 5 * q^13 + 4 * q^14 - q^15 - q^16 - 5 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 4 * q^21 + 2 * q^22 - 6 * q^23 - q^24 - 8 * q^25 + 7 * q^26 - 2 * q^27 + 2 * q^28 + 9 * q^29 + q^30 - 8 * q^31 + q^32 + 2 * q^33 - 10 * q^34 - 2 * q^35 - q^36 + 11 * q^37 + 4 * q^38 + 7 * q^39 + 2 * q^40 - 5 * q^41 + 2 * q^42 - 10 * q^43 + 4 * q^44 + q^45 + 6 * q^46 + 4 * q^47 + q^48 + 3 * q^49 - 4 * q^50 - 10 * q^51 + 2 * q^52 - 2 * q^53 - q^54 + 2 * q^55 - 2 * q^56 + 4 * q^57 - 9 * q^58 + 8 * q^59 + 2 * q^60 + 11 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 5 * q^65 + 4 * q^66 - 2 * q^67 - 5 * q^68 + 6 * q^69 - 4 * q^70 + 14 * q^71 + q^72 - 26 * q^73 - 11 * q^74 - 4 * q^75 + 2 * q^76 - 8 * q^77 + 2 * q^78 - 8 * q^79 + q^80 - q^81 + 5 * q^82 + 12 * q^83 - 2 * q^84 + 5 * q^85 - 20 * q^86 - 9 * q^87 + 2 * q^88 - 2 * q^89 + 2 * q^90 - 4 * q^91 + 12 * q^92 - 4 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 + 2 * q^97 - 3 * q^98 + 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$$.

 $$n$$ $$53$$ $$67$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ −1.00000 −0.447214 −0.223607 0.974679i $$-0.571783\pi$$
−0.223607 + 0.974679i $$0.571783\pi$$
$$6$$ −0.500000 + 0.866025i −0.204124 + 0.353553i
$$7$$ 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i $$-0.709957\pi$$
0.990766 + 0.135583i $$0.0432908\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ 2.50000 2.59808i 0.693375 0.720577i
$$14$$ 2.00000 0.534522
$$15$$ −0.500000 0.866025i −0.129099 0.223607i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −2.50000 + 4.33013i −0.606339 + 1.05021i 0.385499 + 0.922708i $$0.374029\pi$$
−0.991838 + 0.127502i $$0.959304\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i $$-0.759652\pi$$
0.957635 + 0.287984i $$0.0929851\pi$$
$$20$$ 0.500000 0.866025i 0.111803 0.193649i
$$21$$ 2.00000 0.436436
$$22$$ 1.00000 1.73205i 0.213201 0.369274i
$$23$$ −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
$$25$$ −4.00000 −0.800000
$$26$$ 3.50000 + 0.866025i 0.686406 + 0.169842i
$$27$$ −1.00000 −0.192450
$$28$$ 1.00000 + 1.73205i 0.188982 + 0.327327i
$$29$$ 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i $$0.148230\pi$$
−0.0578882 + 0.998323i $$0.518437\pi$$
$$30$$ 0.500000 0.866025i 0.0912871 0.158114i
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 1.00000 1.73205i 0.174078 0.301511i
$$34$$ −5.00000 −0.857493
$$35$$ −1.00000 + 1.73205i −0.169031 + 0.292770i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 5.50000 + 9.52628i 0.904194 + 1.56611i 0.821995 + 0.569495i $$0.192861\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 2.00000 0.324443
$$39$$ 3.50000 + 0.866025i 0.560449 + 0.138675i
$$40$$ 1.00000 0.158114
$$41$$ −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i $$-0.294342\pi$$
−0.992507 + 0.122189i $$0.961009\pi$$
$$42$$ 1.00000 + 1.73205i 0.154303 + 0.267261i
$$43$$ −5.00000 + 8.66025i −0.762493 + 1.32068i 0.179069 + 0.983836i $$0.442691\pi$$
−0.941562 + 0.336840i $$0.890642\pi$$
$$44$$ 2.00000 0.301511
$$45$$ 0.500000 0.866025i 0.0745356 0.129099i
$$46$$ 3.00000 5.19615i 0.442326 0.766131i
$$47$$ 2.00000 0.291730 0.145865 0.989305i $$-0.453403\pi$$
0.145865 + 0.989305i $$0.453403\pi$$
$$48$$ 0.500000 0.866025i 0.0721688 0.125000i
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ −5.00000 −0.700140
$$52$$ 1.00000 + 3.46410i 0.138675 + 0.480384i
$$53$$ −1.00000 −0.137361 −0.0686803 0.997639i $$-0.521879\pi$$
−0.0686803 + 0.997639i $$0.521879\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 1.00000 + 1.73205i 0.134840 + 0.233550i
$$56$$ −1.00000 + 1.73205i −0.133631 + 0.231455i
$$57$$ 2.00000 0.264906
$$58$$ −4.50000 + 7.79423i −0.590879 + 1.02343i
$$59$$ 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i $$-0.658984\pi$$
0.999709 0.0241347i $$-0.00768307\pi$$
$$60$$ 1.00000 0.129099
$$61$$ 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i $$-0.584638\pi$$
0.966978 0.254858i $$-0.0820288\pi$$
$$62$$ −2.00000 3.46410i −0.254000 0.439941i
$$63$$ 1.00000 + 1.73205i 0.125988 + 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ −2.50000 + 2.59808i −0.310087 + 0.322252i
$$66$$ 2.00000 0.246183
$$67$$ −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i $$-0.205652\pi$$
−0.920623 + 0.390453i $$0.872318\pi$$
$$68$$ −2.50000 4.33013i −0.303170 0.525105i
$$69$$ 3.00000 5.19615i 0.361158 0.625543i
$$70$$ −2.00000 −0.239046
$$71$$ 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i $$-0.521247\pi$$
0.897447 0.441123i $$-0.145420\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −13.0000 −1.52153 −0.760767 0.649025i $$-0.775177\pi$$
−0.760767 + 0.649025i $$0.775177\pi$$
$$74$$ −5.50000 + 9.52628i −0.639362 + 1.10741i
$$75$$ −2.00000 3.46410i −0.230940 0.400000i
$$76$$ 1.00000 + 1.73205i 0.114708 + 0.198680i
$$77$$ −4.00000 −0.455842
$$78$$ 1.00000 + 3.46410i 0.113228 + 0.392232i
$$79$$ −4.00000 −0.450035 −0.225018 0.974355i $$-0.572244\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0.500000 + 0.866025i 0.0559017 + 0.0968246i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 2.50000 4.33013i 0.276079 0.478183i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ −1.00000 + 1.73205i −0.109109 + 0.188982i
$$85$$ 2.50000 4.33013i 0.271163 0.469668i
$$86$$ −10.0000 −1.07833
$$87$$ −4.50000 + 7.79423i −0.482451 + 0.835629i
$$88$$ 1.00000 + 1.73205i 0.106600 + 0.184637i
$$89$$ −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i $$-0.200471\pi$$
−0.914146 + 0.405385i $$0.867138\pi$$
$$90$$ 1.00000 0.105409
$$91$$ −2.00000 6.92820i −0.209657 0.726273i
$$92$$ 6.00000 0.625543
$$93$$ −2.00000 3.46410i −0.207390 0.359211i
$$94$$ 1.00000 + 1.73205i 0.103142 + 0.178647i
$$95$$ −1.00000 + 1.73205i −0.102598 + 0.177705i
$$96$$ 1.00000 0.102062
$$97$$ 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i $$-0.800958\pi$$
0.912317 + 0.409484i $$0.134291\pi$$
$$98$$ −1.50000 + 2.59808i −0.151523 + 0.262445i
$$99$$ 2.00000 0.201008
$$100$$ 2.00000 3.46410i 0.200000 0.346410i
$$101$$ 2.50000 + 4.33013i 0.248759 + 0.430864i 0.963182 0.268851i $$-0.0866439\pi$$
−0.714423 + 0.699715i $$0.753311\pi$$
$$102$$ −2.50000 4.33013i −0.247537 0.428746i
$$103$$ 10.0000 0.985329 0.492665 0.870219i $$-0.336023\pi$$
0.492665 + 0.870219i $$0.336023\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ −2.00000 −0.195180
$$106$$ −0.500000 0.866025i −0.0485643 0.0841158i
$$107$$ 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i $$0.169255\pi$$
0.00813215 + 0.999967i $$0.497411\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ −1.00000 + 1.73205i −0.0953463 + 0.165145i
$$111$$ −5.50000 + 9.52628i −0.522037 + 0.904194i
$$112$$ −2.00000 −0.188982
$$113$$ 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i $$-0.788267\pi$$
0.927914 + 0.372794i $$0.121600\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ 3.00000 + 5.19615i 0.279751 + 0.484544i
$$116$$ −9.00000 −0.835629
$$117$$ 1.00000 + 3.46410i 0.0924500 + 0.320256i
$$118$$ 8.00000 0.736460
$$119$$ 5.00000 + 8.66025i 0.458349 + 0.793884i
$$120$$ 0.500000 + 0.866025i 0.0456435 + 0.0790569i
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 11.0000 0.995893
$$123$$ 2.50000 4.33013i 0.225417 0.390434i
$$124$$ 2.00000 3.46410i 0.179605 0.311086i
$$125$$ 9.00000 0.804984
$$126$$ −1.00000 + 1.73205i −0.0890871 + 0.154303i
$$127$$ 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
$$129$$ −10.0000 −0.880451
$$130$$ −3.50000 0.866025i −0.306970 0.0759555i
$$131$$ −8.00000 −0.698963 −0.349482 0.936943i $$-0.613642\pi$$
−0.349482 + 0.936943i $$0.613642\pi$$
$$132$$ 1.00000 + 1.73205i 0.0870388 + 0.150756i
$$133$$ −2.00000 3.46410i −0.173422 0.300376i
$$134$$ 1.00000 1.73205i 0.0863868 0.149626i
$$135$$ 1.00000 0.0860663
$$136$$ 2.50000 4.33013i 0.214373 0.371305i
$$137$$ −8.50000 + 14.7224i −0.726204 + 1.25782i 0.232273 + 0.972651i $$0.425384\pi$$
−0.958477 + 0.285171i $$0.907949\pi$$
$$138$$ 6.00000 0.510754
$$139$$ 6.00000 10.3923i 0.508913 0.881464i −0.491033 0.871141i $$-0.663381\pi$$
0.999947 0.0103230i $$-0.00328598\pi$$
$$140$$ −1.00000 1.73205i −0.0845154 0.146385i
$$141$$ 1.00000 + 1.73205i 0.0842152 + 0.145865i
$$142$$ 14.0000 1.17485
$$143$$ −7.00000 1.73205i −0.585369 0.144841i
$$144$$ 1.00000 0.0833333
$$145$$ −4.50000 7.79423i −0.373705 0.647275i
$$146$$ −6.50000 11.2583i −0.537944 0.931746i
$$147$$ −1.50000 + 2.59808i −0.123718 + 0.214286i
$$148$$ −11.0000 −0.904194
$$149$$ −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i $$-0.872548\pi$$
0.798019 + 0.602632i $$0.205881\pi$$
$$150$$ 2.00000 3.46410i 0.163299 0.282843i
$$151$$ −6.00000 −0.488273 −0.244137 0.969741i $$-0.578505\pi$$
−0.244137 + 0.969741i $$0.578505\pi$$
$$152$$ −1.00000 + 1.73205i −0.0811107 + 0.140488i
$$153$$ −2.50000 4.33013i −0.202113 0.350070i
$$154$$ −2.00000 3.46410i −0.161165 0.279145i
$$155$$ 4.00000 0.321288
$$156$$ −2.50000 + 2.59808i −0.200160 + 0.208013i
$$157$$ −7.00000 −0.558661 −0.279330 0.960195i $$-0.590112\pi$$
−0.279330 + 0.960195i $$0.590112\pi$$
$$158$$ −2.00000 3.46410i −0.159111 0.275589i
$$159$$ −0.500000 0.866025i −0.0396526 0.0686803i
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ −12.0000 −0.945732
$$162$$ 0.500000 0.866025i 0.0392837 0.0680414i
$$163$$ −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i $$0.453112\pi$$
−0.930033 + 0.367477i $$0.880222\pi$$
$$164$$ 5.00000 0.390434
$$165$$ −1.00000 + 1.73205i −0.0778499 + 0.134840i
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ −12.0000 20.7846i −0.928588 1.60836i −0.785687 0.618624i $$-0.787690\pi$$
−0.142901 0.989737i $$-0.545643\pi$$
$$168$$ −2.00000 −0.154303
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 5.00000 0.383482
$$171$$ 1.00000 + 1.73205i 0.0764719 + 0.132453i
$$172$$ −5.00000 8.66025i −0.381246 0.660338i
$$173$$ 11.0000 19.0526i 0.836315 1.44854i −0.0566411 0.998395i $$-0.518039\pi$$
0.892956 0.450145i $$-0.148628\pi$$
$$174$$ −9.00000 −0.682288
$$175$$ −4.00000 + 6.92820i −0.302372 + 0.523723i
$$176$$ −1.00000 + 1.73205i −0.0753778 + 0.130558i
$$177$$ 8.00000 0.601317
$$178$$ 1.00000 1.73205i 0.0749532 0.129823i
$$179$$ 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i $$-0.0946798\pi$$
−0.731858 + 0.681457i $$0.761346\pi$$
$$180$$ 0.500000 + 0.866025i 0.0372678 + 0.0645497i
$$181$$ 5.00000 0.371647 0.185824 0.982583i $$-0.440505\pi$$
0.185824 + 0.982583i $$0.440505\pi$$
$$182$$ 5.00000 5.19615i 0.370625 0.385164i
$$183$$ 11.0000 0.813143
$$184$$ 3.00000 + 5.19615i 0.221163 + 0.383065i
$$185$$ −5.50000 9.52628i −0.404368 0.700386i
$$186$$ 2.00000 3.46410i 0.146647 0.254000i
$$187$$ 10.0000 0.731272
$$188$$ −1.00000 + 1.73205i −0.0729325 + 0.126323i
$$189$$ −1.00000 + 1.73205i −0.0727393 + 0.125988i
$$190$$ −2.00000 −0.145095
$$191$$ −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i $$-0.879560\pi$$
0.784552 + 0.620063i $$0.212893\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ 8.50000 + 14.7224i 0.611843 + 1.05974i 0.990930 + 0.134382i $$0.0429051\pi$$
−0.379086 + 0.925361i $$0.623762\pi$$
$$194$$ 2.00000 0.143592
$$195$$ −3.50000 0.866025i −0.250640 0.0620174i
$$196$$ −3.00000 −0.214286
$$197$$ −3.00000 5.19615i −0.213741 0.370211i 0.739141 0.673550i $$-0.235232\pi$$
−0.952882 + 0.303340i $$0.901898\pi$$
$$198$$ 1.00000 + 1.73205i 0.0710669 + 0.123091i
$$199$$ −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i $$-0.948662\pi$$
0.632581 + 0.774494i $$0.281995\pi$$
$$200$$ 4.00000 0.282843
$$201$$ 1.00000 1.73205i 0.0705346 0.122169i
$$202$$ −2.50000 + 4.33013i −0.175899 + 0.304667i
$$203$$ 18.0000 1.26335
$$204$$ 2.50000 4.33013i 0.175035 0.303170i
$$205$$ 2.50000 + 4.33013i 0.174608 + 0.302429i
$$206$$ 5.00000 + 8.66025i 0.348367 + 0.603388i
$$207$$ 6.00000 0.417029
$$208$$ −3.50000 0.866025i −0.242681 0.0600481i
$$209$$ −4.00000 −0.276686
$$210$$ −1.00000 1.73205i −0.0690066 0.119523i
$$211$$ −12.0000 20.7846i −0.826114 1.43087i −0.901065 0.433684i $$-0.857213\pi$$
0.0749508 0.997187i $$-0.476120\pi$$
$$212$$ 0.500000 0.866025i 0.0343401 0.0594789i
$$213$$ 14.0000 0.959264
$$214$$ −9.00000 + 15.5885i −0.615227 + 1.06561i
$$215$$ 5.00000 8.66025i 0.340997 0.590624i
$$216$$ 1.00000 0.0680414
$$217$$ −4.00000 + 6.92820i −0.271538 + 0.470317i
$$218$$ −1.00000 1.73205i −0.0677285 0.117309i
$$219$$ −6.50000 11.2583i −0.439229 0.760767i
$$220$$ −2.00000 −0.134840
$$221$$ 5.00000 + 17.3205i 0.336336 + 1.16510i
$$222$$ −11.0000 −0.738272
$$223$$ 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i $$0.0132929\pi$$
−0.463409 + 0.886145i $$0.653374\pi$$
$$224$$ −1.00000 1.73205i −0.0668153 0.115728i
$$225$$ 2.00000 3.46410i 0.133333 0.230940i
$$226$$ 3.00000 0.199557
$$227$$ −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i $$-0.987137\pi$$
0.534577 + 0.845120i $$0.320471\pi$$
$$228$$ −1.00000 + 1.73205i −0.0662266 + 0.114708i
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ −3.00000 + 5.19615i −0.197814 + 0.342624i
$$231$$ −2.00000 3.46410i −0.131590 0.227921i
$$232$$ −4.50000 7.79423i −0.295439 0.511716i
$$233$$ −6.00000 −0.393073 −0.196537 0.980497i $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ −2.50000 + 2.59808i −0.163430 + 0.169842i
$$235$$ −2.00000 −0.130466
$$236$$ 4.00000 + 6.92820i 0.260378 + 0.450988i
$$237$$ −2.00000 3.46410i −0.129914 0.225018i
$$238$$ −5.00000 + 8.66025i −0.324102 + 0.561361i
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ −0.500000 + 0.866025i −0.0322749 + 0.0559017i
$$241$$ −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i $$-0.905720\pi$$
0.731001 + 0.682376i $$0.239053\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 5.50000 + 9.52628i 0.352101 + 0.609858i
$$245$$ −1.50000 2.59808i −0.0958315 0.165985i
$$246$$ 5.00000 0.318788
$$247$$ −2.00000 6.92820i −0.127257 0.440831i
$$248$$ 4.00000 0.254000
$$249$$ 3.00000 + 5.19615i 0.190117 + 0.329293i
$$250$$ 4.50000 + 7.79423i 0.284605 + 0.492950i
$$251$$ −2.00000 + 3.46410i −0.126239 + 0.218652i −0.922217 0.386674i $$-0.873624\pi$$
0.795978 + 0.605326i $$0.206957\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ −6.00000 + 10.3923i −0.377217 + 0.653359i
$$254$$ −6.00000 + 10.3923i −0.376473 + 0.652071i
$$255$$ 5.00000 0.313112
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i $$-0.136840\pi$$
−0.815442 + 0.578838i $$0.803506\pi$$
$$258$$ −5.00000 8.66025i −0.311286 0.539164i
$$259$$ 22.0000 1.36701
$$260$$ −1.00000 3.46410i −0.0620174 0.214834i
$$261$$ −9.00000 −0.557086
$$262$$ −4.00000 6.92820i −0.247121 0.428026i
$$263$$ −7.00000 12.1244i −0.431638 0.747620i 0.565376 0.824833i $$-0.308731\pi$$
−0.997015 + 0.0772134i $$0.975398\pi$$
$$264$$ −1.00000 + 1.73205i −0.0615457 + 0.106600i
$$265$$ 1.00000 0.0614295
$$266$$ 2.00000 3.46410i 0.122628 0.212398i
$$267$$ 1.00000 1.73205i 0.0611990 0.106000i
$$268$$ 2.00000 0.122169
$$269$$ 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i $$-0.692975\pi$$
0.996586 + 0.0825561i $$0.0263084\pi$$
$$270$$ 0.500000 + 0.866025i 0.0304290 + 0.0527046i
$$271$$ −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i $$-0.244792\pi$$
−0.961563 + 0.274586i $$0.911459\pi$$
$$272$$ 5.00000 0.303170
$$273$$ 5.00000 5.19615i 0.302614 0.314485i
$$274$$ −17.0000 −1.02701
$$275$$ 4.00000 + 6.92820i 0.241209 + 0.417786i
$$276$$ 3.00000 + 5.19615i 0.180579 + 0.312772i
$$277$$ 5.50000 9.52628i 0.330463 0.572379i −0.652140 0.758099i $$-0.726128\pi$$
0.982603 + 0.185720i $$0.0594618\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 2.00000 3.46410i 0.119737 0.207390i
$$280$$ 1.00000 1.73205i 0.0597614 0.103510i
$$281$$ 25.0000 1.49137 0.745687 0.666296i $$-0.232121\pi$$
0.745687 + 0.666296i $$0.232121\pi$$
$$282$$ −1.00000 + 1.73205i −0.0595491 + 0.103142i
$$283$$ −13.0000 22.5167i −0.772770 1.33848i −0.936039 0.351895i $$-0.885537\pi$$
0.163270 0.986581i $$-0.447796\pi$$
$$284$$ 7.00000 + 12.1244i 0.415374 + 0.719448i
$$285$$ −2.00000 −0.118470
$$286$$ −2.00000 6.92820i −0.118262 0.409673i
$$287$$ −10.0000 −0.590281
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ −4.00000 6.92820i −0.235294 0.407541i
$$290$$ 4.50000 7.79423i 0.264249 0.457693i
$$291$$ 2.00000 0.117242
$$292$$ 6.50000 11.2583i 0.380384 0.658844i
$$293$$ 0.500000 0.866025i 0.0292103 0.0505937i −0.851051 0.525084i $$-0.824034\pi$$
0.880261 + 0.474490i $$0.157367\pi$$
$$294$$ −3.00000 −0.174964
$$295$$ −4.00000 + 6.92820i −0.232889 + 0.403376i
$$296$$ −5.50000 9.52628i −0.319681 0.553704i
$$297$$ 1.00000 + 1.73205i 0.0580259 + 0.100504i
$$298$$ −3.00000 −0.173785
$$299$$ −21.0000 5.19615i −1.21446 0.300501i
$$300$$ 4.00000 0.230940
$$301$$ 10.0000 + 17.3205i 0.576390 + 0.998337i
$$302$$ −3.00000 5.19615i −0.172631 0.299005i
$$303$$ −2.50000 + 4.33013i −0.143621 + 0.248759i
$$304$$ −2.00000 −0.114708
$$305$$ −5.50000 + 9.52628i −0.314929 + 0.545473i
$$306$$ 2.50000 4.33013i 0.142915 0.247537i
$$307$$ −14.0000 −0.799022 −0.399511 0.916728i $$-0.630820\pi$$
−0.399511 + 0.916728i $$0.630820\pi$$
$$308$$ 2.00000 3.46410i 0.113961 0.197386i
$$309$$ 5.00000 + 8.66025i 0.284440 + 0.492665i
$$310$$ 2.00000 + 3.46410i 0.113592 + 0.196748i
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ −3.50000 0.866025i −0.198148 0.0490290i
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ −3.50000 6.06218i −0.197516 0.342108i
$$315$$ −1.00000 1.73205i −0.0563436 0.0975900i
$$316$$ 2.00000 3.46410i 0.112509 0.194871i
$$317$$ −33.0000 −1.85346 −0.926732 0.375722i $$-0.877395\pi$$
−0.926732 + 0.375722i $$0.877395\pi$$
$$318$$ 0.500000 0.866025i 0.0280386 0.0485643i
$$319$$ 9.00000 15.5885i 0.503903 0.872786i
$$320$$ −1.00000 −0.0559017
$$321$$ −9.00000 + 15.5885i −0.502331 + 0.870063i
$$322$$ −6.00000 10.3923i −0.334367 0.579141i
$$323$$ 5.00000 + 8.66025i 0.278207 + 0.481869i
$$324$$ 1.00000 0.0555556
$$325$$ −10.0000 + 10.3923i −0.554700 + 0.576461i
$$326$$ −20.0000 −1.10770
$$327$$ −1.00000 1.73205i −0.0553001 0.0957826i
$$328$$ 2.50000 + 4.33013i 0.138039 + 0.239091i
$$329$$ 2.00000 3.46410i 0.110264 0.190982i
$$330$$ −2.00000 −0.110096
$$331$$ 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i $$-0.553834\pi$$
0.937829 0.347097i $$-0.112833\pi$$
$$332$$ −3.00000 + 5.19615i −0.164646 + 0.285176i
$$333$$ −11.0000 −0.602796
$$334$$ 12.0000 20.7846i 0.656611 1.13728i
$$335$$ 1.00000 + 1.73205i 0.0546358 + 0.0946320i
$$336$$ −1.00000 1.73205i −0.0545545 0.0944911i
$$337$$ −9.00000 −0.490261 −0.245131 0.969490i $$-0.578831\pi$$
−0.245131 + 0.969490i $$0.578831\pi$$
$$338$$ 11.0000 6.92820i 0.598321 0.376845i
$$339$$ 3.00000 0.162938
$$340$$ 2.50000 + 4.33013i 0.135582 + 0.234834i
$$341$$ 4.00000 + 6.92820i 0.216612 + 0.375183i
$$342$$ −1.00000 + 1.73205i −0.0540738 + 0.0936586i
$$343$$ 20.0000 1.07990
$$344$$ 5.00000 8.66025i 0.269582 0.466930i
$$345$$ −3.00000 + 5.19615i −0.161515 + 0.279751i
$$346$$ 22.0000 1.18273
$$347$$ −3.00000 + 5.19615i −0.161048 + 0.278944i −0.935245 0.354001i $$-0.884821\pi$$
0.774197 + 0.632945i $$0.218154\pi$$
$$348$$ −4.50000 7.79423i −0.241225 0.417815i
$$349$$ −3.00000 5.19615i −0.160586 0.278144i 0.774493 0.632583i $$-0.218005\pi$$
−0.935079 + 0.354439i $$0.884672\pi$$
$$350$$ −8.00000 −0.427618
$$351$$ −2.50000 + 2.59808i −0.133440 + 0.138675i
$$352$$ −2.00000 −0.106600
$$353$$ −8.50000 14.7224i −0.452409 0.783596i 0.546126 0.837703i $$-0.316102\pi$$
−0.998535 + 0.0541072i $$0.982769\pi$$
$$354$$ 4.00000 + 6.92820i 0.212598 + 0.368230i
$$355$$ −7.00000 + 12.1244i −0.371521 + 0.643494i
$$356$$ 2.00000 0.106000
$$357$$ −5.00000 + 8.66025i −0.264628 + 0.458349i
$$358$$ −3.00000 + 5.19615i −0.158555 + 0.274625i
$$359$$ −30.0000 −1.58334 −0.791670 0.610949i $$-0.790788\pi$$
−0.791670 + 0.610949i $$0.790788\pi$$
$$360$$ −0.500000 + 0.866025i −0.0263523 + 0.0456435i
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 2.50000 + 4.33013i 0.131397 + 0.227586i
$$363$$ 7.00000 0.367405
$$364$$ 7.00000 + 1.73205i 0.366900 + 0.0907841i
$$365$$ 13.0000 0.680451
$$366$$ 5.50000 + 9.52628i 0.287490 + 0.497947i
$$367$$ 1.00000 + 1.73205i 0.0521996 + 0.0904123i 0.890945 0.454112i $$-0.150043\pi$$
−0.838745 + 0.544524i $$0.816710\pi$$
$$368$$ −3.00000 + 5.19615i −0.156386 + 0.270868i
$$369$$ 5.00000 0.260290
$$370$$ 5.50000 9.52628i 0.285931 0.495248i
$$371$$ −1.00000 + 1.73205i −0.0519174 + 0.0899236i
$$372$$ 4.00000 0.207390
$$373$$ −4.50000 + 7.79423i −0.233001 + 0.403570i −0.958690 0.284453i $$-0.908188\pi$$
0.725689 + 0.688023i $$0.241521\pi$$
$$374$$ 5.00000 + 8.66025i 0.258544 + 0.447811i
$$375$$ 4.50000 + 7.79423i 0.232379 + 0.402492i
$$376$$ −2.00000 −0.103142
$$377$$ 31.5000 + 7.79423i 1.62233 + 0.401423i
$$378$$ −2.00000 −0.102869
$$379$$ −6.00000 10.3923i −0.308199 0.533817i 0.669769 0.742569i $$-0.266393\pi$$
−0.977969 + 0.208752i $$0.933060\pi$$
$$380$$ −1.00000 1.73205i −0.0512989 0.0888523i
$$381$$ −6.00000 + 10.3923i −0.307389 + 0.532414i
$$382$$ −4.00000 −0.204658
$$383$$ −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i $$0.376773\pi$$
−0.990702 + 0.136047i $$0.956560\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 4.00000 0.203859
$$386$$ −8.50000 + 14.7224i −0.432639 + 0.749352i
$$387$$ −5.00000 8.66025i −0.254164 0.440225i
$$388$$ 1.00000 + 1.73205i 0.0507673 + 0.0879316i
$$389$$ 19.0000 0.963338 0.481669 0.876353i $$-0.340031\pi$$
0.481669 + 0.876353i $$0.340031\pi$$
$$390$$ −1.00000 3.46410i −0.0506370 0.175412i
$$391$$ 30.0000 1.51717
$$392$$ −1.50000 2.59808i −0.0757614 0.131223i
$$393$$ −4.00000 6.92820i −0.201773 0.349482i
$$394$$ 3.00000 5.19615i 0.151138 0.261778i
$$395$$ 4.00000 0.201262
$$396$$ −1.00000 + 1.73205i −0.0502519 + 0.0870388i
$$397$$ 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i $$-0.684152\pi$$
0.998492 + 0.0549046i $$0.0174855\pi$$
$$398$$ −10.0000 −0.501255
$$399$$ 2.00000 3.46410i 0.100125 0.173422i
$$400$$ 2.00000 + 3.46410i 0.100000 + 0.173205i
$$401$$ 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i $$0.0688266\pi$$
−0.302556 + 0.953131i $$0.597840\pi$$
$$402$$ 2.00000 0.0997509
$$403$$ −10.0000 + 10.3923i −0.498135 + 0.517678i
$$404$$ −5.00000 −0.248759
$$405$$ 0.500000 + 0.866025i 0.0248452 + 0.0430331i
$$406$$ 9.00000 + 15.5885i 0.446663 + 0.773642i
$$407$$ 11.0000 19.0526i 0.545250 0.944400i
$$408$$ 5.00000 0.247537
$$409$$ −11.5000 + 19.9186i −0.568638 + 0.984911i 0.428063 + 0.903749i $$0.359196\pi$$
−0.996701 + 0.0811615i $$0.974137\pi$$
$$410$$ −2.50000 + 4.33013i −0.123466 + 0.213850i
$$411$$ −17.0000 −0.838548
$$412$$ −5.00000 + 8.66025i −0.246332 + 0.426660i
$$413$$ −8.00000 13.8564i −0.393654 0.681829i
$$414$$ 3.00000 + 5.19615i 0.147442 + 0.255377i
$$415$$ −6.00000 −0.294528
$$416$$ −1.00000 3.46410i −0.0490290 0.169842i
$$417$$ 12.0000 0.587643
$$418$$ −2.00000 3.46410i −0.0978232 0.169435i
$$419$$ 16.0000 + 27.7128i 0.781651 + 1.35386i 0.930979 + 0.365072i $$0.118956\pi$$
−0.149328 + 0.988788i $$0.547711\pi$$
$$420$$ 1.00000 1.73205i 0.0487950 0.0845154i
$$421$$ −23.0000 −1.12095 −0.560476 0.828171i $$-0.689382\pi$$
−0.560476 + 0.828171i $$0.689382\pi$$
$$422$$ 12.0000 20.7846i 0.584151 1.01178i
$$423$$ −1.00000 + 1.73205i −0.0486217 + 0.0842152i
$$424$$ 1.00000 0.0485643
$$425$$ 10.0000 17.3205i 0.485071 0.840168i
$$426$$ 7.00000 + 12.1244i 0.339151 + 0.587427i
$$427$$ −11.0000 19.0526i −0.532327 0.922018i
$$428$$ −18.0000 −0.870063
$$429$$ −2.00000 6.92820i −0.0965609 0.334497i
$$430$$ 10.0000 0.482243
$$431$$ 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i $$-0.151328\pi$$
−0.840936 + 0.541135i $$0.817995\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 10.5000 18.1865i 0.504598 0.873989i −0.495388 0.868672i $$-0.664974\pi$$
0.999986 0.00531724i $$-0.00169254\pi$$
$$434$$ −8.00000 −0.384012
$$435$$ 4.50000 7.79423i 0.215758 0.373705i
$$436$$ 1.00000 1.73205i 0.0478913 0.0829502i
$$437$$ −12.0000 −0.574038
$$438$$ 6.50000 11.2583i 0.310582 0.537944i
$$439$$ −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i $$-0.243367\pi$$
−0.960323 + 0.278889i $$0.910034\pi$$
$$440$$ −1.00000 1.73205i −0.0476731 0.0825723i
$$441$$ −3.00000 −0.142857
$$442$$ −12.5000 + 12.9904i −0.594564 + 0.617889i
$$443$$ 20.0000 0.950229 0.475114 0.879924i $$-0.342407\pi$$
0.475114 + 0.879924i $$0.342407\pi$$
$$444$$ −5.50000 9.52628i −0.261018 0.452097i
$$445$$ 1.00000 + 1.73205i 0.0474045 + 0.0821071i
$$446$$ −8.00000 + 13.8564i −0.378811 + 0.656120i
$$447$$ −3.00000 −0.141895
$$448$$ 1.00000 1.73205i 0.0472456 0.0818317i
$$449$$ 15.0000 25.9808i 0.707894 1.22611i −0.257743 0.966213i $$-0.582979\pi$$
0.965637 0.259895i $$-0.0836878\pi$$
$$450$$ 4.00000 0.188562
$$451$$ −5.00000 + 8.66025i −0.235441 + 0.407795i
$$452$$ 1.50000 + 2.59808i 0.0705541 + 0.122203i
$$453$$ −3.00000 5.19615i −0.140952 0.244137i
$$454$$ −14.0000 −0.657053
$$455$$ 2.00000 + 6.92820i 0.0937614 + 0.324799i
$$456$$ −2.00000 −0.0936586
$$457$$ −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i $$-0.189020\pi$$
−0.898974 + 0.438001i $$0.855687\pi$$
$$458$$ 5.00000 + 8.66025i 0.233635 + 0.404667i
$$459$$ 2.50000 4.33013i 0.116690 0.202113i
$$460$$ −6.00000 −0.279751
$$461$$ −1.50000 + 2.59808i −0.0698620 + 0.121004i −0.898840 0.438276i $$-0.855589\pi$$
0.828978 + 0.559281i $$0.188923\pi$$
$$462$$ 2.00000 3.46410i 0.0930484 0.161165i
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ 4.50000 7.79423i 0.208907 0.361838i
$$465$$ 2.00000 + 3.46410i 0.0927478 + 0.160644i
$$466$$ −3.00000 5.19615i −0.138972 0.240707i
$$467$$ −22.0000 −1.01804 −0.509019 0.860755i $$-0.669992\pi$$
−0.509019 + 0.860755i $$0.669992\pi$$
$$468$$ −3.50000 0.866025i −0.161788 0.0400320i
$$469$$ −4.00000 −0.184703
$$470$$ −1.00000 1.73205i −0.0461266 0.0798935i
$$471$$ −3.50000 6.06218i −0.161271 0.279330i
$$472$$ −4.00000 + 6.92820i −0.184115 + 0.318896i
$$473$$ 20.0000 0.919601
$$474$$ 2.00000 3.46410i 0.0918630 0.159111i
$$475$$ −4.00000 + 6.92820i −0.183533 + 0.317888i
$$476$$ −10.0000 −0.458349
$$477$$ 0.500000 0.866025i 0.0228934 0.0396526i
$$478$$ −3.00000 5.19615i −0.137217 0.237666i
$$479$$ −16.0000 27.7128i −0.731059 1.26623i −0.956431 0.291958i $$-0.905693\pi$$
0.225372 0.974273i $$-0.427640\pi$$
$$480$$ −1.00000 −0.0456435
$$481$$ 38.5000 + 9.52628i 1.75545 + 0.434361i
$$482$$ −7.00000 −0.318841
$$483$$ −6.00000 10.3923i −0.273009 0.472866i
$$484$$ 3.50000 + 6.06218i 0.159091 + 0.275554i
$$485$$ −1.00000 + 1.73205i −0.0454077 + 0.0786484i
$$486$$ 1.00000 0.0453609
$$487$$ 13.0000 22.5167i 0.589086 1.02033i −0.405266 0.914199i $$-0.632821\pi$$
0.994352 0.106129i $$-0.0338455\pi$$
$$488$$ −5.50000 + 9.52628i −0.248973 + 0.431234i
$$489$$ −20.0000 −0.904431
$$490$$ 1.50000 2.59808i 0.0677631 0.117369i
$$491$$ 15.0000 + 25.9808i 0.676941 + 1.17250i 0.975898 + 0.218229i $$0.0700279\pi$$
−0.298957 + 0.954267i $$0.596639\pi$$
$$492$$ 2.50000 + 4.33013i 0.112709 + 0.195217i
$$493$$ −45.0000 −2.02670
$$494$$ 5.00000 5.19615i 0.224961 0.233786i
$$495$$ −2.00000 −0.0898933
$$496$$ 2.00000 + 3.46410i 0.0898027 + 0.155543i
$$497$$ −14.0000 24.2487i −0.627986 1.08770i
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$500$$ −4.50000 + 7.79423i −0.201246 + 0.348569i
$$501$$ 12.0000 20.7846i 0.536120 0.928588i
$$502$$ −4.00000 −0.178529
$$503$$ 7.00000 12.1244i 0.312115 0.540598i −0.666705 0.745321i $$-0.732296\pi$$
0.978820 + 0.204723i $$0.0656294\pi$$
$$504$$ −1.00000 1.73205i −0.0445435 0.0771517i
$$505$$ −2.50000 4.33013i −0.111249 0.192688i
$$506$$ −12.0000 −0.533465
$$507$$ 11.0000 6.92820i 0.488527 0.307692i
$$508$$ −12.0000 −0.532414
$$509$$ −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i $$-0.274536\pi$$
−0.982988 + 0.183669i $$0.941202\pi$$
$$510$$ 2.50000 + 4.33013i 0.110702 + 0.191741i
$$511$$ −13.0000 + 22.5167i −0.575086 + 0.996078i
$$512$$ −1.00000 −0.0441942
$$513$$ −1.00000 + 1.73205i −0.0441511 + 0.0764719i
$$514$$ −1.50000 + 2.59808i −0.0661622 + 0.114596i
$$515$$ −10.0000 −0.440653
$$516$$ 5.00000 8.66025i 0.220113 0.381246i
$$517$$ −2.00000 3.46410i −0.0879599 0.152351i
$$518$$ 11.0000 + 19.0526i 0.483312 + 0.837121i
$$519$$ 22.0000 0.965693
$$520$$ 2.50000 2.59808i 0.109632 0.113933i
$$521$$ 25.0000 1.09527 0.547635 0.836717i $$-0.315528\pi$$
0.547635 + 0.836717i $$0.315528\pi$$
$$522$$ −4.50000 7.79423i −0.196960 0.341144i
$$523$$ 19.0000 + 32.9090i 0.830812 + 1.43901i 0.897395 + 0.441228i $$0.145457\pi$$
−0.0665832 + 0.997781i $$0.521210\pi$$
$$524$$ 4.00000 6.92820i 0.174741 0.302660i
$$525$$ −8.00000 −0.349149
$$526$$ 7.00000 12.1244i 0.305215 0.528647i
$$527$$ 10.0000 17.3205i 0.435607 0.754493i
$$528$$ −2.00000 −0.0870388
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0.500000 + 0.866025i 0.0217186 + 0.0376177i
$$531$$ 4.00000 + 6.92820i 0.173585 + 0.300658i
$$532$$ 4.00000 0.173422
$$533$$ −17.5000 4.33013i −0.758009 0.187559i
$$534$$ 2.00000 0.0865485
$$535$$ −9.00000 15.5885i −0.389104 0.673948i
$$536$$ 1.00000 + 1.73205i 0.0431934 + 0.0748132i
$$537$$ −3.00000 + 5.19615i −0.129460 + 0.224231i
$$538$$ 14.0000 0.603583
$$539$$ 3.00000 5.19615i 0.129219 0.223814i
$$540$$ −0.500000 + 0.866025i −0.0215166 + 0.0372678i
$$541$$ −7.00000 −0.300954 −0.150477 0.988614i $$-0.548081\pi$$
−0.150477 + 0.988614i $$0.548081\pi$$
$$542$$ 4.00000 6.92820i 0.171815 0.297592i
$$543$$ 2.50000 + 4.33013i 0.107285 + 0.185824i
$$544$$ 2.50000 + 4.33013i 0.107187 + 0.185653i
$$545$$ 2.00000 0.0856706
$$546$$ 7.00000 + 1.73205i 0.299572 + 0.0741249i
$$547$$ 2.00000 0.0855138 0.0427569 0.999086i $$-0.486386\pi$$
0.0427569 + 0.999086i $$0.486386\pi$$
$$548$$ −8.50000 14.7224i −0.363102 0.628911i
$$549$$ 5.50000 + 9.52628i 0.234734 + 0.406572i
$$550$$ −4.00000 + 6.92820i −0.170561 + 0.295420i
$$551$$ 18.0000 0.766826
$$552$$ −3.00000 + 5.19615i −0.127688 + 0.221163i
$$553$$ −4.00000 + 6.92820i −0.170097 + 0.294617i
$$554$$ 11.0000 0.467345
$$555$$ 5.50000 9.52628i 0.233462 0.404368i
$$556$$ 6.00000 + 10.3923i 0.254457 + 0.440732i
$$557$$ 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i $$-0.105600\pi$$
−0.754802 + 0.655953i $$0.772267\pi$$
$$558$$ 4.00000 0.169334
$$559$$ 10.0000 + 34.6410i 0.422955 + 1.46516i
$$560$$ 2.00000 0.0845154
$$561$$ 5.00000 + 8.66025i 0.211100 + 0.365636i
$$562$$ 12.5000 + 21.6506i 0.527281 + 0.913277i
$$563$$ −20.0000 + 34.6410i −0.842900 + 1.45994i 0.0445334 + 0.999008i $$0.485820\pi$$
−0.887433 + 0.460937i $$0.847513\pi$$
$$564$$ −2.00000 −0.0842152
$$565$$ −1.50000 + 2.59808i −0.0631055 + 0.109302i
$$566$$ 13.0000 22.5167i 0.546431 0.946446i
$$567$$ −2.00000 −0.0839921
$$568$$ −7.00000 + 12.1244i −0.293713 + 0.508727i
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ −1.00000 1.73205i −0.0418854 0.0725476i
$$571$$ −2.00000 −0.0836974 −0.0418487 0.999124i $$-0.513325\pi$$
−0.0418487 + 0.999124i $$0.513325\pi$$
$$572$$ 5.00000 5.19615i 0.209061 0.217262i
$$573$$ −4.00000 −0.167102
$$574$$ −5.00000 8.66025i −0.208696 0.361472i
$$575$$ 12.0000 + 20.7846i 0.500435 + 0.866778i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 27.0000 1.12402 0.562012 0.827129i $$-0.310027\pi$$
0.562012 + 0.827129i $$0.310027\pi$$
$$578$$ 4.00000 6.92820i 0.166378 0.288175i
$$579$$ −8.50000 + 14.7224i −0.353248 + 0.611843i
$$580$$ 9.00000 0.373705
$$581$$ 6.00000 10.3923i 0.248922 0.431145i
$$582$$ 1.00000 + 1.73205i 0.0414513 + 0.0717958i
$$583$$ 1.00000 + 1.73205i 0.0414158 + 0.0717342i
$$584$$ 13.0000 0.537944
$$585$$ −1.00000 3.46410i −0.0413449 0.143223i
$$586$$ 1.00000 0.0413096
$$587$$ 16.0000 + 27.7128i 0.660391 + 1.14383i 0.980513 + 0.196454i $$0.0629426\pi$$
−0.320122 + 0.947376i $$0.603724\pi$$
$$588$$ −1.50000 2.59808i −0.0618590 0.107143i
$$589$$ −4.00000 + 6.92820i −0.164817 + 0.285472i
$$590$$ −8.00000 −0.329355
$$591$$ 3.00000 5.19615i 0.123404 0.213741i
$$592$$ 5.50000 9.52628i 0.226049 0.391528i
$$593$$ −39.0000 −1.60154 −0.800769 0.598973i $$-0.795576\pi$$
−0.800769 + 0.598973i $$0.795576\pi$$
$$594$$ −1.00000 + 1.73205i −0.0410305 + 0.0710669i
$$595$$ −5.00000 8.66025i −0.204980 0.355036i
$$596$$ −1.50000 2.59808i −0.0614424 0.106421i
$$597$$ −10.0000 −0.409273
$$598$$ −6.00000 20.7846i −0.245358 0.849946i
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 2.00000 + 3.46410i 0.0816497 + 0.141421i
$$601$$ −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i $$-0.238692\pi$$
−0.956124 + 0.292962i $$0.905359\pi$$
$$602$$ −10.0000 + 17.3205i −0.407570 + 0.705931i
$$603$$ 2.00000 0.0814463
$$604$$ 3.00000 5.19615i 0.122068 0.211428i
$$605$$ −3.50000 + 6.06218i −0.142295 + 0.246463i
$$606$$ −5.00000 −0.203111
$$607$$ −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i $$0.391655\pi$$
−0.983262 + 0.182199i $$0.941678\pi$$
$$608$$ −1.00000 1.73205i −0.0405554 0.0702439i
$$609$$ 9.00000 + 15.5885i 0.364698 + 0.631676i
$$610$$ −11.0000 −0.445377
$$611$$ 5.00000 5.19615i 0.202278 0.210214i
$$612$$ 5.00000 0.202113
$$613$$ −6.50000 11.2583i −0.262533 0.454720i 0.704382 0.709821i $$-0.251224\pi$$
−0.966914 + 0.255102i $$0.917891\pi$$
$$614$$ −7.00000 12.1244i −0.282497 0.489299i
$$615$$ −2.50000 + 4.33013i −0.100810 + 0.174608i
$$616$$ 4.00000 0.161165
$$617$$ 7.50000 12.9904i 0.301939 0.522973i −0.674636 0.738150i $$-0.735700\pi$$
0.976575 + 0.215177i $$0.0690329\pi$$
$$618$$ −5.00000 + 8.66025i −0.201129 + 0.348367i
$$619$$ 32.0000 1.28619 0.643094 0.765787i $$-0.277650\pi$$
0.643094 + 0.765787i $$0.277650\pi$$
$$620$$ −2.00000 + 3.46410i −0.0803219 + 0.139122i
$$621$$ 3.00000 + 5.19615i 0.120386 + 0.208514i
$$622$$ 3.00000 + 5.19615i 0.120289 + 0.208347i
$$623$$ −4.00000 −0.160257
$$624$$ −1.00000 3.46410i −0.0400320 0.138675i
$$625$$ 11.0000 0.440000
$$626$$ 3.00000 + 5.19615i 0.119904 + 0.207680i
$$627$$ −2.00000 3.46410i −0.0798723 0.138343i
$$628$$ 3.50000 6.06218i 0.139665 0.241907i
$$629$$ −55.0000 −2.19299
$$630$$ 1.00000 1.73205i 0.0398410 0.0690066i
$$631$$ −6.00000 + 10.3923i −0.238856 + 0.413711i −0.960386 0.278672i $$-0.910106\pi$$
0.721530 + 0.692383i $$0.243439\pi$$
$$632$$ 4.00000 0.159111
$$633$$ 12.0000 20.7846i 0.476957 0.826114i
$$634$$ −16.5000 28.5788i −0.655299 1.13501i
$$635$$ −6.00000 10.3923i −0.238103 0.412406i
$$636$$ 1.00000 0.0396526
$$637$$ 10.5000 + 2.59808i 0.416025 + 0.102940i
$$638$$ 18.0000 0.712627
$$639$$ 7.00000 + 12.1244i 0.276916 + 0.479632i
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i $$-0.864816\pi$$
0.812421 + 0.583071i $$0.198149\pi$$
$$642$$ −18.0000 −0.710403
$$643$$ −4.00000 + 6.92820i −0.157745 + 0.273222i −0.934055 0.357129i $$-0.883756\pi$$
0.776310 + 0.630351i $$0.217089\pi$$
$$644$$ 6.00000 10.3923i 0.236433 0.409514i
$$645$$ 10.0000 0.393750
$$646$$ −5.00000 + 8.66025i −0.196722 + 0.340733i
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ −16.0000 −0.628055
$$650$$ −14.0000 3.46410i −0.549125 0.135873i
$$651$$ −8.00000 −0.313545
$$652$$ −10.0000 17.3205i −0.391630 0.678323i
$$653$$ 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i $$-0.0250169\pi$$
−0.566450 + 0.824096i $$0.691684\pi$$
$$654$$ 1.00000 1.73205i 0.0391031 0.0677285i
$$655$$ 8.00000 0.312586
$$656$$ −2.50000 + 4.33013i −0.0976086 + 0.169063i
$$657$$ 6.50000 11.2583i 0.253589 0.439229i
$$658$$ 4.00000 0.155936
$$659$$ −12.0000 + 20.7846i −0.467454 + 0.809653i −0.999309 0.0371821i $$-0.988162\pi$$
0.531855 + 0.846836i $$0.321495\pi$$
$$660$$ −1.00000 1.73205i −0.0389249 0.0674200i
$$661$$ −12.5000 21.6506i −0.486194 0.842112i 0.513680 0.857982i $$-0.328282\pi$$
−0.999874 + 0.0158695i $$0.994948\pi$$
$$662$$ 28.0000 1.08825
$$663$$ −12.5000 + 12.9904i −0.485460 + 0.504505i
$$664$$ −6.00000 −0.232845
$$665$$ 2.00000 + 3.46410i 0.0775567 + 0.134332i
$$666$$ −5.50000 9.52628i −0.213121 0.369136i
$$667$$ 27.0000 46.7654i 1.04544 1.81076i
$$668$$ 24.0000 0.928588
$$669$$ −8.00000 + 13.8564i −0.309298 + 0.535720i
$$670$$ −1.00000 + 1.73205i −0.0386334 + 0.0669150i
$$671$$ −22.0000 −0.849301
$$672$$ 1.00000 1.73205i 0.0385758 0.0668153i
$$673$$ −21.5000 37.2391i −0.828764 1.43546i −0.899008 0.437932i $$-0.855711\pi$$
0.0702442 0.997530i $$-0.477622\pi$$
$$674$$ −4.50000 7.79423i −0.173334 0.300222i
$$675$$ 4.00000 0.153960
$$676$$ 11.5000 + 6.06218i 0.442308 + 0.233161i
$$677$$ −46.0000 −1.76792 −0.883962 0.467559i $$-0.845134\pi$$
−0.883962 + 0.467559i $$0.845134\pi$$
$$678$$ 1.50000 + 2.59808i 0.0576072 + 0.0997785i
$$679$$ −2.00000 3.46410i −0.0767530 0.132940i
$$680$$ −2.50000 + 4.33013i −0.0958706 + 0.166053i
$$681$$ −14.0000 −0.536481
$$682$$ −4.00000 + 6.92820i −0.153168 + 0.265295i
$$683$$ 20.0000 34.6410i 0.765279 1.32550i −0.174820 0.984600i $$-0.555934\pi$$
0.940099 0.340901i $$-0.110732\pi$$
$$684$$ −2.00000 −0.0764719
$$685$$ 8.50000 14.7224i 0.324768 0.562515i
$$686$$ 10.0000 + 17.3205i 0.381802 + 0.661300i
$$687$$ 5.00000 + 8.66025i 0.190762 + 0.330409i
$$688$$ 10.0000 0.381246
$$689$$ −2.50000 + 2.59808i −0.0952424 + 0.0989788i
$$690$$ −6.00000 −0.228416
$$691$$ 1.00000 + 1.73205i 0.0380418 + 0.0658903i 0.884419 0.466693i $$-0.154555\pi$$
−0.846378 + 0.532583i $$0.821221\pi$$
$$692$$ 11.0000 + 19.0526i 0.418157 + 0.724270i
$$693$$ 2.00000 3.46410i 0.0759737 0.131590i
$$694$$ −6.00000 −0.227757
$$695$$ −6.00000 + 10.3923i −0.227593 + 0.394203i
$$696$$ 4.50000 7.79423i 0.170572 0.295439i
$$697$$ 25.0000 0.946943
$$698$$ 3.00000 5.19615i 0.113552 0.196677i
$$699$$ −3.00000 5.19615i −0.113470 0.196537i
$$700$$ −4.00000 6.92820i −0.151186 0.261861i
$$701$$ 34.0000 1.28416 0.642081 0.766637i $$-0.278071\pi$$
0.642081 + 0.766637i $$0.278071\pi$$
$$702$$ −3.50000 0.866025i −0.132099 0.0326860i
$$703$$ 22.0000 0.829746
$$704$$ −1.00000 1.73205i −0.0376889 0.0652791i
$$705$$ −1.00000 1.73205i −0.0376622 0.0652328i
$$706$$ 8.50000 14.7224i 0.319902 0.554086i
$$707$$ 10.0000 0.376089
$$708$$ −4.00000 + 6.92820i −0.150329 + 0.260378i
$$709$$ 7.50000 12.9904i 0.281668 0.487864i −0.690127 0.723688i $$-0.742446\pi$$
0.971796 + 0.235824i $$0.0757789\pi$$
$$710$$ −14.0000 −0.525411
$$711$$ 2.00000 3.46410i 0.0750059 0.129914i
$$712$$ 1.00000 + 1.73205i 0.0374766 + 0.0649113i
$$713$$ 12.0000 + 20.7846i 0.449404 + 0.778390i
$$714$$ −10.0000 −0.374241
$$715$$ 7.00000 + 1.73205i 0.261785 + 0.0647750i
$$716$$ −6.00000 −0.224231
$$717$$ −3.00000 5.19615i −0.112037 0.194054i
$$718$$ −15.0000 25.9808i −0.559795 0.969593i
$$719$$ −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i $$-0.981028\pi$$
0.550700 + 0.834703i $$0.314361\pi$$
$$720$$ −1.00000 −0.0372678
$$721$$ 10.0000 17.3205i 0.372419 0.645049i
$$722$$ −7.50000 + 12.9904i −0.279121 + 0.483452i
$$723$$ −7.00000 −0.260333
$$724$$ −2.50000 + 4.33013i −0.0929118 + 0.160928i
$$725$$ −18.0000 31.1769i −0.668503 1.15788i
$$726$$ 3.50000 + 6.06218i 0.129897 + 0.224989i
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 2.00000 + 6.92820i 0.0741249 + 0.256776i
$$729$$ 1.00000 0.0370370
$$730$$ 6.50000 + 11.2583i 0.240576 + 0.416689i
$$731$$ −25.0000 43.3013i −0.924658 1.60156i
$$732$$ −5.50000 + 9.52628i −0.203286 + 0.352101i
$$733$$ 13.0000 0.480166 0.240083 0.970752i $$-0.422825\pi$$
0.240083 + 0.970752i $$0.422825\pi$$
$$734$$ −1.00000 + 1.73205i −0.0369107 + 0.0639312i
$$735$$ 1.50000 2.59808i 0.0553283 0.0958315i
$$736$$ −6.00000 −0.221163
$$737$$ −2.00000 + 3.46410i −0.0736709 + 0.127602i
$$738$$ 2.50000 + 4.33013i 0.0920263 + 0.159394i
$$739$$ −8.00000 13.8564i −0.294285 0.509716i 0.680534 0.732717i $$-0.261748\pi$$
−0.974818 + 0.223001i $$0.928415\pi$$
$$740$$ 11.0000 0.404368
$$741$$ 5.00000 5.19615i 0.183680 0.190885i
$$742$$ −2.00000 −0.0734223
$$743$$ 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i $$-0.0960222\pi$$
−0.734725 + 0.678365i $$0.762689\pi$$
$$744$$ 2.00000 + 3.46410i 0.0733236 + 0.127000i
$$745$$ 1.50000 2.59808i 0.0549557 0.0951861i
$$746$$ −9.00000 −0.329513
$$747$$ −3.00000 + 5.19615i −0.109764 + 0.190117i
$$748$$ −5.00000 + 8.66025i −0.182818 + 0.316650i
$$749$$ 36.0000 1.31541
$$750$$ −4.50000 + 7.79423i −0.164317 + 0.284605i
$$751$$ −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i $$-0.323993\pi$$
−0.999570 + 0.0293387i $$0.990660\pi$$
$$752$$ −1.00000 1.73205i −0.0364662 0.0631614i
$$753$$ −4.00000 −0.145768
$$754$$ 9.00000 + 31.1769i 0.327761 + 1.13540i
$$755$$ 6.00000 0.218362
$$756$$ −1.00000 1.73205i −0.0363696 0.0629941i
$$757$$ 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i $$-0.0605917\pi$$
−0.654827 + 0.755779i $$0.727258\pi$$
$$758$$ 6.00000 10.3923i 0.217930 0.377466i
$$759$$ −12.0000 −0.435572
$$760$$ 1.00000 1.73205i 0.0362738 0.0628281i
$$761$$ −17.0000 + 29.4449i −0.616250 + 1.06738i 0.373914 + 0.927463i $$0.378015\pi$$
−0.990164 + 0.139912i $$0.955318\pi$$
$$762$$ −12.0000 −0.434714
$$763$$ −2.00000 + 3.46410i −0.0724049 + 0.125409i
$$764$$ −2.00000 3.46410i −0.0723575 0.125327i
$$765$$ 2.50000 + 4.33013i 0.0903877 + 0.156556i
$$766$$ −24.0000 −0.867155
$$767$$ −8.00000 27.7128i −0.288863 1.00065i
$$768$$ −1.00000 −0.0360844
$$769$$ 17.0000 + 29.4449i 0.613036 + 1.06181i 0.990726 + 0.135877i $$0.0433852\pi$$
−0.377690 + 0.925932i $$0.623282\pi$$
$$770$$ 2.00000 + 3.46410i 0.0720750 + 0.124838i
$$771$$ −1.50000 + 2.59808i −0.0540212 + 0.0935674i
$$772$$ −17.0000 −0.611843
$$773$$ −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i $$-0.938263\pi$$
0.657542 + 0.753418i $$0.271596\pi$$
$$774$$ 5.00000 8.66025i 0.179721 0.311286i
$$775$$ 16.0000 0.574737