# Properties

 Label 546.2.l.d.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.d.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} +(2.00000 + 3.46410i) 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} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{20} -1.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{29} +(-1.00000 + 1.73205i) q^{30} -9.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} -2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +2.00000 q^{40} +(-1.00000 - 1.73205i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(2.50000 - 4.33013i) q^{43} -4.00000 q^{44} +(1.00000 - 1.73205i) q^{45} +(-0.500000 + 0.866025i) q^{46} +6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +7.00000 q^{51} +(1.00000 - 3.46410i) q^{52} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(-0.500000 + 0.866025i) q^{56} +2.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-7.50000 + 12.9904i) q^{59} -2.00000 q^{60} +(3.50000 - 6.06218i) q^{61} +(-4.50000 - 7.79423i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(7.00000 - 1.73205i) q^{65} +4.00000 q^{66} +(2.50000 + 4.33013i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(0.500000 - 0.866025i) q^{69} -2.00000 q^{70} +(-0.500000 + 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -1.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(7.00000 - 12.1244i) q^{85} +5.00000 q^{86} +(1.00000 - 1.73205i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-1.50000 - 2.59808i) q^{89} +2.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} -1.00000 q^{92} +(4.50000 + 7.79423i) q^{93} +(3.00000 + 5.19615i) q^{94} +(2.00000 - 3.46410i) q^{95} -1.00000 q^{96} +(8.00000 - 13.8564i) q^{97} +(0.500000 - 0.866025i) q^{98} -4.00000 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 $$2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - 2 q^{10} + 4 q^{11} + 2 q^{12} - 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} - 7 q^{17} - 2 q^{18} - 2 q^{19} + 2 q^{20} - 2 q^{21} - 4 q^{22} + q^{23} + q^{24} - 2 q^{25} - 5 q^{26} + 2 q^{27} + q^{28} + 2 q^{29} - 2 q^{30} - 18 q^{31} + q^{32} + 4 q^{33} - 14 q^{34} - 2 q^{35} - q^{36} + 2 q^{37} - 4 q^{38} + 5 q^{39} + 4 q^{40} - 2 q^{41} - q^{42} + 5 q^{43} - 8 q^{44} + 2 q^{45} - q^{46} + 12 q^{47} - q^{48} - q^{49} - q^{50} + 14 q^{51} + 2 q^{52} + 6 q^{53} + q^{54} - 8 q^{55} - q^{56} + 4 q^{57} - 2 q^{58} - 15 q^{59} - 4 q^{60} + 7 q^{61} - 9 q^{62} + q^{63} + 2 q^{64} + 14 q^{65} + 8 q^{66} + 5 q^{67} - 7 q^{68} + q^{69} - 4 q^{70} - q^{71} + q^{72} + 24 q^{73} - 2 q^{74} + q^{75} - 2 q^{76} + 8 q^{77} - 2 q^{78} - 8 q^{79} + 2 q^{80} - q^{81} + 2 q^{82} - 2 q^{83} + q^{84} + 14 q^{85} + 10 q^{86} + 2 q^{87} - 4 q^{88} - 3 q^{89} + 4 q^{90} - 2 q^{91} - 2 q^{92} + 9 q^{93} + 6 q^{94} + 4 q^{95} - 2 q^{96} + 16 q^{97} + q^{98} - 8 q^{99}+O(q^{100})$$ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9 - 2 * q^10 + 4 * q^11 + 2 * q^12 - 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 - 7 * q^17 - 2 * q^18 - 2 * q^19 + 2 * q^20 - 2 * q^21 - 4 * q^22 + q^23 + q^24 - 2 * q^25 - 5 * q^26 + 2 * q^27 + q^28 + 2 * q^29 - 2 * q^30 - 18 * q^31 + q^32 + 4 * q^33 - 14 * q^34 - 2 * q^35 - q^36 + 2 * q^37 - 4 * q^38 + 5 * q^39 + 4 * q^40 - 2 * q^41 - q^42 + 5 * q^43 - 8 * q^44 + 2 * q^45 - q^46 + 12 * q^47 - q^48 - q^49 - q^50 + 14 * q^51 + 2 * q^52 + 6 * q^53 + q^54 - 8 * q^55 - q^56 + 4 * q^57 - 2 * q^58 - 15 * q^59 - 4 * q^60 + 7 * q^61 - 9 * q^62 + q^63 + 2 * q^64 + 14 * q^65 + 8 * q^66 + 5 * q^67 - 7 * q^68 + q^69 - 4 * q^70 - q^71 + q^72 + 24 * q^73 - 2 * q^74 + q^75 - 2 * q^76 + 8 * q^77 - 2 * q^78 - 8 * q^79 + 2 * q^80 - q^81 + 2 * q^82 - 2 * q^83 + q^84 + 14 * q^85 + 10 * q^86 + 2 * q^87 - 4 * q^88 - 3 * q^89 + 4 * q^90 - 2 * q^91 - 2 * q^92 + 9 * q^93 + 6 * q^94 + 4 * q^95 - 2 * q^96 + 16 * q^97 + q^98 - 8 * 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
$$11$$ 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i $$0.0393705\pi$$
−0.389338 + 0.921095i $$0.627296\pi$$
$$12$$ 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 $$0.489386\pi$$
−0.882213 + 0.470850i $$0.843947\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 1.00000 1.73205i 0.223607 0.387298i
$$21$$ −1.00000 −0.218218
$$22$$ −2.00000 + 3.46410i −0.426401 + 0.738549i
$$23$$ 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i $$-0.133420\pi$$
−0.809177 + 0.587565i $$0.800087\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ −1.00000 −0.200000
$$26$$ −2.50000 2.59808i −0.490290 0.509525i
$$27$$ 1.00000 0.192450
$$28$$ 0.500000 + 0.866025i 0.0944911 + 0.163663i
$$29$$ 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i $$-0.107213\pi$$
−0.758115 + 0.652121i $$0.773880\pi$$
$$30$$ −1.00000 + 1.73205i −0.182574 + 0.316228i
$$31$$ −9.00000 −1.61645 −0.808224 0.588875i $$-0.799571\pi$$
−0.808224 + 0.588875i $$0.799571\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 2.00000 3.46410i 0.348155 0.603023i
$$34$$ −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 $$0.780765\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ 2.50000 + 2.59808i 0.400320 + 0.416025i
$$40$$ 2.00000 0.316228
$$41$$ −1.00000 1.73205i −0.156174 0.270501i 0.777312 0.629115i $$-0.216583\pi$$
−0.933486 + 0.358614i $$0.883249\pi$$
$$42$$ −0.500000 0.866025i −0.0771517 0.133631i
$$43$$ 2.50000 4.33013i 0.381246 0.660338i −0.609994 0.792406i $$-0.708828\pi$$
0.991241 + 0.132068i $$0.0421616\pi$$
$$44$$ −4.00000 −0.603023
$$45$$ 1.00000 1.73205i 0.149071 0.258199i
$$46$$ −0.500000 + 0.866025i −0.0737210 + 0.127688i
$$47$$ 6.00000 0.875190 0.437595 0.899172i $$-0.355830\pi$$
0.437595 + 0.899172i $$0.355830\pi$$
$$48$$ −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
$$52$$ 1.00000 3.46410i 0.138675 0.480384i
$$53$$ 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
$$55$$ −4.00000 6.92820i −0.539360 0.934199i
$$56$$ −0.500000 + 0.866025i −0.0668153 + 0.115728i
$$57$$ 2.00000 0.264906
$$58$$ −1.00000 + 1.73205i −0.131306 + 0.227429i
$$59$$ −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i $$0.597400\pi$$
−0.675178 + 0.737655i $$0.735933\pi$$
$$60$$ −2.00000 −0.258199
$$61$$ 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i $$-0.685424\pi$$
0.998264 + 0.0588933i $$0.0187572\pi$$
$$62$$ −4.50000 7.79423i −0.571501 0.989868i
$$63$$ 0.500000 + 0.866025i 0.0629941 + 0.109109i
$$64$$ 1.00000 0.125000
$$65$$ 7.00000 1.73205i 0.868243 0.214834i
$$66$$ 4.00000 0.492366
$$67$$ 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i $$-0.0678686\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ −3.50000 6.06218i −0.424437 0.735147i
$$69$$ 0.500000 0.866025i 0.0601929 0.104257i
$$70$$ −2.00000 −0.239046
$$71$$ −0.500000 + 0.866025i −0.0593391 + 0.102778i −0.894169 0.447730i $$-0.852233\pi$$
0.834830 + 0.550508i $$0.185566\pi$$
$$72$$ 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
$$76$$ −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 $$0.572244\pi$$
$$80$$ 1.00000 + 1.73205i 0.111803 + 0.193649i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 1.00000 1.73205i 0.110432 0.191273i
$$83$$ −1.00000 −0.109764 −0.0548821 0.998493i $$-0.517478\pi$$
−0.0548821 + 0.998493i $$0.517478\pi$$
$$84$$ 0.500000 0.866025i 0.0545545 0.0944911i
$$85$$ 7.00000 12.1244i 0.759257 1.31507i
$$86$$ 5.00000 0.539164
$$87$$ 1.00000 1.73205i 0.107211 0.185695i
$$88$$ −2.00000 3.46410i −0.213201 0.369274i
$$89$$ −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i $$-0.217494\pi$$
−0.934508 + 0.355942i $$0.884160\pi$$
$$90$$ 2.00000 0.210819
$$91$$ −1.00000 + 3.46410i −0.104828 + 0.363137i
$$92$$ −1.00000 −0.104257
$$93$$ 4.50000 + 7.79423i 0.466628 + 0.808224i
$$94$$ 3.00000 + 5.19615i 0.309426 + 0.535942i
$$95$$ 2.00000 3.46410i 0.205196 0.355409i
$$96$$ −1.00000 −0.102062
$$97$$ 8.00000 13.8564i 0.812277 1.40690i −0.0989899 0.995088i $$-0.531561\pi$$
0.911267 0.411816i $$-0.135106\pi$$
$$98$$ 0.500000 0.866025i 0.0505076 0.0874818i
$$99$$ −4.00000 −0.402015
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$102$$ 3.50000 + 6.06218i 0.346552 + 0.600245i
$$103$$ −11.0000 −1.08386 −0.541931 0.840423i $$-0.682307\pi$$
−0.541931 + 0.840423i $$0.682307\pi$$
$$104$$ 3.50000 0.866025i 0.343203 0.0849208i
$$105$$ 2.00000 0.195180
$$106$$ 1.50000 + 2.59808i 0.145693 + 0.252347i
$$107$$ 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i $$-0.0730044\pi$$
−0.683793 + 0.729676i $$0.739671\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 4.00000 6.92820i 0.381385 0.660578i
$$111$$ 1.00000 1.73205i 0.0949158 0.164399i
$$112$$ −1.00000 −0.0944911
$$113$$ 4.00000 6.92820i 0.376288 0.651751i −0.614231 0.789127i $$-0.710534\pi$$
0.990519 + 0.137376i $$0.0438669\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ −1.00000 1.73205i −0.0932505 0.161515i
$$116$$ −2.00000 −0.185695
$$117$$ 1.00000 3.46410i 0.0924500 0.320256i
$$118$$ −15.0000 −1.38086
$$119$$ 3.50000 + 6.06218i 0.320844 + 0.555719i
$$120$$ −1.00000 1.73205i −0.0912871 0.158114i
$$121$$ −2.50000 + 4.33013i −0.227273 + 0.393648i
$$122$$ 7.00000 0.633750
$$123$$ −1.00000 + 1.73205i −0.0901670 + 0.156174i
$$124$$ 4.50000 7.79423i 0.404112 0.699942i
$$125$$ 12.0000 1.07331
$$126$$ −0.500000 + 0.866025i −0.0445435 + 0.0771517i
$$127$$ −8.00000 13.8564i −0.709885 1.22956i −0.964899 0.262620i $$-0.915413\pi$$
0.255014 0.966937i $$-0.417920\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −5.00000 −0.440225
$$130$$ 5.00000 + 5.19615i 0.438529 + 0.455733i
$$131$$ 15.0000 1.31056 0.655278 0.755388i $$-0.272551\pi$$
0.655278 + 0.755388i $$0.272551\pi$$
$$132$$ 2.00000 + 3.46410i 0.174078 + 0.301511i
$$133$$ 1.00000 + 1.73205i 0.0867110 + 0.150188i
$$134$$ −2.50000 + 4.33013i −0.215967 + 0.374066i
$$135$$ −2.00000 −0.172133
$$136$$ 3.50000 6.06218i 0.300123 0.519827i
$$137$$ −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i $$-0.887992\pi$$
0.767853 + 0.640626i $$0.221325\pi$$
$$138$$ 1.00000 0.0851257
$$139$$ −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i $$0.404058\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ −1.00000 1.73205i −0.0845154 0.146385i
$$141$$ −3.00000 5.19615i −0.252646 0.437595i
$$142$$ −1.00000 −0.0839181
$$143$$ −10.0000 10.3923i −0.836242 0.869048i
$$144$$ 1.00000 0.0833333
$$145$$ −2.00000 3.46410i −0.166091 0.287678i
$$146$$ 6.00000 + 10.3923i 0.496564 + 0.860073i
$$147$$ −0.500000 + 0.866025i −0.0412393 + 0.0714286i
$$148$$ −2.00000 −0.164399
$$149$$ −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i $$0.496324\pi$$
−0.871742 + 0.489966i $$0.837009\pi$$
$$150$$ −0.500000 + 0.866025i −0.0408248 + 0.0707107i
$$151$$ 20.0000 1.62758 0.813788 0.581161i $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ 1.00000 1.73205i 0.0811107 0.140488i
$$153$$ −3.50000 6.06218i −0.282958 0.490098i
$$154$$ 2.00000 + 3.46410i 0.161165 + 0.279145i
$$155$$ 18.0000 1.44579
$$156$$ −3.50000 + 0.866025i −0.280224 + 0.0693375i
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ −2.00000 3.46410i −0.159111 0.275589i
$$159$$ −1.50000 2.59808i −0.118958 0.206041i
$$160$$ −1.00000 + 1.73205i −0.0790569 + 0.136931i
$$161$$ 1.00000 0.0788110
$$162$$ 0.500000 0.866025i 0.0392837 0.0680414i
$$163$$ −10.5000 + 18.1865i −0.822423 + 1.42448i 0.0814491 + 0.996678i $$0.474045\pi$$
−0.903873 + 0.427802i $$0.859288\pi$$
$$164$$ 2.00000 0.156174
$$165$$ −4.00000 + 6.92820i −0.311400 + 0.539360i
$$166$$ −0.500000 0.866025i −0.0388075 0.0672166i
$$167$$ 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
$$171$$ −1.00000 1.73205i −0.0764719 0.132453i
$$172$$ 2.50000 + 4.33013i 0.190623 + 0.330169i
$$173$$ 8.00000 13.8564i 0.608229 1.05348i −0.383304 0.923622i $$-0.625214\pi$$
0.991532 0.129861i $$-0.0414530\pi$$
$$174$$ 2.00000 0.151620
$$175$$ −0.500000 + 0.866025i −0.0377964 + 0.0654654i
$$176$$ 2.00000 3.46410i 0.150756 0.261116i
$$177$$ 15.0000 1.12747
$$178$$ 1.50000 2.59808i 0.112430 0.194734i
$$179$$ −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i $$-0.238654\pi$$
−0.956088 + 0.293079i $$0.905320\pi$$
$$180$$ 1.00000 + 1.73205i 0.0745356 + 0.129099i
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ −3.50000 + 0.866025i −0.259437 + 0.0641941i
$$183$$ −7.00000 −0.517455
$$184$$ −0.500000 0.866025i −0.0368605 0.0638442i
$$185$$ −2.00000 3.46410i −0.147043 0.254686i
$$186$$ −4.50000 + 7.79423i −0.329956 + 0.571501i
$$187$$ −28.0000 −2.04756
$$188$$ −3.00000 + 5.19615i −0.218797 + 0.378968i
$$189$$ 0.500000 0.866025i 0.0363696 0.0629941i
$$190$$ 4.00000 0.290191
$$191$$ −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i $$-0.867950\pi$$
0.806641 + 0.591041i $$0.201283\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i $$0.124188\pi$$
−0.133056 + 0.991109i $$0.542479\pi$$
$$194$$ 16.0000 1.14873
$$195$$ −5.00000 5.19615i −0.358057 0.372104i
$$196$$ 1.00000 0.0714286
$$197$$ 4.50000 + 7.79423i 0.320612 + 0.555316i 0.980614 0.195947i $$-0.0627782\pi$$
−0.660003 + 0.751263i $$0.729445\pi$$
$$198$$ −2.00000 3.46410i −0.142134 0.246183i
$$199$$ 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i $$-0.776623\pi$$
0.940927 + 0.338608i $$0.109956\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 2.50000 4.33013i 0.176336 0.305424i
$$202$$ 0 0
$$203$$ 2.00000 0.140372
$$204$$ −3.50000 + 6.06218i −0.245049 + 0.424437i
$$205$$ 2.00000 + 3.46410i 0.139686 + 0.241943i
$$206$$ −5.50000 9.52628i −0.383203 0.663727i
$$207$$ −1.00000 −0.0695048
$$208$$ 2.50000 + 2.59808i 0.173344 + 0.180144i
$$209$$ −8.00000 −0.553372
$$210$$ 1.00000 + 1.73205i 0.0690066 + 0.119523i
$$211$$ −2.00000 3.46410i −0.137686 0.238479i 0.788935 0.614477i $$-0.210633\pi$$
−0.926620 + 0.375999i $$0.877300\pi$$
$$212$$ −1.50000 + 2.59808i −0.103020 + 0.178437i
$$213$$ 1.00000 0.0685189
$$214$$ −3.00000 + 5.19615i −0.205076 + 0.355202i
$$215$$ −5.00000 + 8.66025i −0.340997 + 0.590624i
$$216$$ −1.00000 −0.0680414
$$217$$ −4.50000 + 7.79423i −0.305480 + 0.529107i
$$218$$ −8.00000 13.8564i −0.541828 0.938474i
$$219$$ −6.00000 10.3923i −0.405442 0.702247i
$$220$$ 8.00000 0.539360
$$221$$ 7.00000 24.2487i 0.470871 1.63114i
$$222$$ 2.00000 0.134231
$$223$$ −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i $$-0.198694\pi$$
−0.911869 + 0.410481i $$0.865361\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ 0.500000 0.866025i 0.0333333 0.0577350i
$$226$$ 8.00000 0.532152
$$227$$ −14.0000 + 24.2487i −0.929213 + 1.60944i −0.144571 + 0.989494i $$0.546180\pi$$
−0.784642 + 0.619949i $$0.787153\pi$$
$$228$$ −1.00000 + 1.73205i −0.0662266 + 0.114708i
$$229$$ 13.0000 0.859064 0.429532 0.903052i $$-0.358679\pi$$
0.429532 + 0.903052i $$0.358679\pi$$
$$230$$ 1.00000 1.73205i 0.0659380 0.114208i
$$231$$ −2.00000 3.46410i −0.131590 0.227921i
$$232$$ −1.00000 1.73205i −0.0656532 0.113715i
$$233$$ −16.0000 −1.04819 −0.524097 0.851658i $$-0.675597\pi$$
−0.524097 + 0.851658i $$0.675597\pi$$
$$234$$ 3.50000 0.866025i 0.228802 0.0566139i
$$235$$ −12.0000 −0.782794
$$236$$ −7.50000 12.9904i −0.488208 0.845602i
$$237$$ 2.00000 + 3.46410i 0.129914 + 0.225018i
$$238$$ −3.50000 + 6.06218i −0.226871 + 0.392953i
$$239$$ −9.00000 −0.582162 −0.291081 0.956698i $$-0.594015\pi$$
−0.291081 + 0.956698i $$0.594015\pi$$
$$240$$ 1.00000 1.73205i 0.0645497 0.111803i
$$241$$ −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i $$-0.982234\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ −5.00000 −0.321412
$$243$$ −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
$$246$$ −2.00000 −0.127515
$$247$$ 2.00000 6.92820i 0.127257 0.440831i
$$248$$ 9.00000 0.571501
$$249$$ 0.500000 + 0.866025i 0.0316862 + 0.0548821i
$$250$$ 6.00000 + 10.3923i 0.379473 + 0.657267i
$$251$$ −11.5000 + 19.9186i −0.725874 + 1.25725i 0.232740 + 0.972539i $$0.425231\pi$$
−0.958613 + 0.284711i $$0.908102\pi$$
$$252$$ −1.00000 −0.0629941
$$253$$ −2.00000 + 3.46410i −0.125739 + 0.217786i
$$254$$ 8.00000 13.8564i 0.501965 0.869428i
$$255$$ −14.0000 −0.876714
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −13.5000 23.3827i −0.842107 1.45857i −0.888110 0.459631i $$-0.847982\pi$$
0.0460033 0.998941i $$-0.485352\pi$$
$$258$$ −2.50000 4.33013i −0.155643 0.269582i
$$259$$ 2.00000 0.124274
$$260$$ −2.00000 + 6.92820i −0.124035 + 0.429669i
$$261$$ −2.00000 −0.123797
$$262$$ 7.50000 + 12.9904i 0.463352 + 0.802548i
$$263$$ −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i $$-0.206023\pi$$
−0.921077 + 0.389380i $$0.872689\pi$$
$$264$$ −2.00000 + 3.46410i −0.123091 + 0.213201i
$$265$$ −6.00000 −0.368577
$$266$$ −1.00000 + 1.73205i −0.0613139 + 0.106199i
$$267$$ −1.50000 + 2.59808i −0.0917985 + 0.159000i
$$268$$ −5.00000 −0.305424
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ −1.00000 1.73205i −0.0608581 0.105409i
$$271$$ −4.50000 7.79423i −0.273356 0.473466i 0.696363 0.717689i $$-0.254800\pi$$
−0.969719 + 0.244224i $$0.921467\pi$$
$$272$$ 7.00000 0.424437
$$273$$ 3.50000 0.866025i 0.211830 0.0524142i
$$274$$ −4.00000 −0.241649
$$275$$ −2.00000 3.46410i −0.120605 0.208893i
$$276$$ 0.500000 + 0.866025i 0.0300965 + 0.0521286i
$$277$$ 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i $$-0.756075\pi$$
0.960810 + 0.277207i $$0.0894088\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 4.50000 7.79423i 0.269408 0.466628i
$$280$$ 1.00000 1.73205i 0.0597614 0.103510i
$$281$$ −26.0000 −1.55103 −0.775515 0.631329i $$-0.782510\pi$$
−0.775515 + 0.631329i $$0.782510\pi$$
$$282$$ 3.00000 5.19615i 0.178647 0.309426i
$$283$$ −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i $$-0.303272\pi$$
−0.995544 + 0.0942988i $$0.969939\pi$$
$$284$$ −0.500000 0.866025i −0.0296695 0.0513892i
$$285$$ −4.00000 −0.236940
$$286$$ 4.00000 13.8564i 0.236525 0.819346i
$$287$$ −2.00000 −0.118056
$$288$$ 0.500000 + 0.866025i 0.0294628 + 0.0510310i
$$289$$ −16.0000 27.7128i −0.941176 1.63017i
$$290$$ 2.00000 3.46410i 0.117444 0.203419i
$$291$$ −16.0000 −0.937937
$$292$$ −6.00000 + 10.3923i −0.351123 + 0.608164i
$$293$$ 8.00000 13.8564i 0.467365 0.809500i −0.531940 0.846782i $$-0.678537\pi$$
0.999305 + 0.0372823i $$0.0118701\pi$$
$$294$$ −1.00000 −0.0583212
$$295$$ 15.0000 25.9808i 0.873334 1.51266i
$$296$$ −1.00000 1.73205i −0.0581238 0.100673i
$$297$$ 2.00000 + 3.46410i 0.116052 + 0.201008i
$$298$$ −21.0000 −1.21650
$$299$$ −2.50000 2.59808i −0.144579 0.150251i
$$300$$ −1.00000 −0.0577350
$$301$$ −2.50000 4.33013i −0.144098 0.249584i
$$302$$ 10.0000 + 17.3205i 0.575435 + 0.996683i
$$303$$ 0 0
$$304$$ 2.00000 0.114708
$$305$$ −7.00000 + 12.1244i −0.400819 + 0.694239i
$$306$$ 3.50000 6.06218i 0.200082 0.346552i
$$307$$ 30.0000 1.71219 0.856095 0.516818i $$-0.172884\pi$$
0.856095 + 0.516818i $$0.172884\pi$$
$$308$$ −2.00000 + 3.46410i −0.113961 + 0.197386i
$$309$$ 5.50000 + 9.52628i 0.312884 + 0.541931i
$$310$$ 9.00000 + 15.5885i 0.511166 + 0.885365i
$$311$$ 30.0000 1.70114 0.850572 0.525859i $$-0.176256\pi$$
0.850572 + 0.525859i $$0.176256\pi$$
$$312$$ −2.50000 2.59808i −0.141535 0.147087i
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ 5.00000 + 8.66025i 0.282166 + 0.488726i
$$315$$ −1.00000 1.73205i −0.0563436 0.0975900i
$$316$$ 2.00000 3.46410i 0.112509 0.194871i
$$317$$ 23.0000 1.29181 0.645904 0.763418i $$-0.276480\pi$$
0.645904 + 0.763418i $$0.276480\pi$$
$$318$$ 1.50000 2.59808i 0.0841158 0.145693i
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ −2.00000 −0.111803
$$321$$ 3.00000 5.19615i 0.167444 0.290021i
$$322$$ 0.500000 + 0.866025i 0.0278639 + 0.0482617i
$$323$$ −7.00000 12.1244i −0.389490 0.674617i
$$324$$ 1.00000 0.0555556
$$325$$ 3.50000 0.866025i 0.194145 0.0480384i
$$326$$ −21.0000 −1.16308
$$327$$ 8.00000 + 13.8564i 0.442401 + 0.766261i
$$328$$ 1.00000 + 1.73205i 0.0552158 + 0.0956365i
$$329$$ 3.00000 5.19615i 0.165395 0.286473i
$$330$$ −8.00000 −0.440386
$$331$$ −18.0000 + 31.1769i −0.989369 + 1.71364i −0.368744 + 0.929531i $$0.620212\pi$$
−0.620625 + 0.784107i $$0.713121\pi$$
$$332$$ 0.500000 0.866025i 0.0274411 0.0475293i
$$333$$ −2.00000 −0.109599
$$334$$ 0 0
$$335$$ −5.00000 8.66025i −0.273179 0.473160i
$$336$$ 0.500000 + 0.866025i 0.0272772 + 0.0472456i
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 11.0000 + 6.92820i 0.598321 + 0.376845i
$$339$$ −8.00000 −0.434500
$$340$$ 7.00000 + 12.1244i 0.379628 + 0.657536i
$$341$$ −18.0000 31.1769i −0.974755 1.68832i
$$342$$ 1.00000 1.73205i 0.0540738 0.0936586i
$$343$$ −1.00000 −0.0539949
$$344$$ −2.50000 + 4.33013i −0.134791 + 0.233465i
$$345$$ −1.00000 + 1.73205i −0.0538382 + 0.0932505i
$$346$$ 16.0000 0.860165
$$347$$ −5.00000 + 8.66025i −0.268414 + 0.464907i −0.968452 0.249198i $$-0.919833\pi$$
0.700038 + 0.714105i $$0.253166\pi$$
$$348$$ 1.00000 + 1.73205i 0.0536056 + 0.0928477i
$$349$$ 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i $$0.0666577\pi$$
−0.309044 + 0.951048i $$0.600009\pi$$
$$350$$ −1.00000 −0.0534522
$$351$$ −3.50000 + 0.866025i −0.186816 + 0.0462250i
$$352$$ 4.00000 0.213201
$$353$$ 17.5000 + 30.3109i 0.931431 + 1.61329i 0.780878 + 0.624684i $$0.214772\pi$$
0.150553 + 0.988602i $$0.451894\pi$$
$$354$$ 7.50000 + 12.9904i 0.398621 + 0.690431i
$$355$$ 1.00000 1.73205i 0.0530745 0.0919277i
$$356$$ 3.00000 0.159000
$$357$$ 3.50000 6.06218i 0.185240 0.320844i
$$358$$ 3.00000 5.19615i 0.158555 0.274625i
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ −1.00000 + 1.73205i −0.0527046 + 0.0912871i
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ −1.00000 1.73205i −0.0525588 0.0910346i
$$363$$ 5.00000 0.262432
$$364$$ −2.50000 2.59808i −0.131036 0.136176i
$$365$$ −24.0000 −1.25622
$$366$$ −3.50000 6.06218i −0.182948 0.316875i
$$367$$ 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i $$-0.141718\pi$$
−0.824217 + 0.566274i $$0.808384\pi$$
$$368$$ 0.500000 0.866025i 0.0260643 0.0451447i
$$369$$ 2.00000 0.104116
$$370$$ 2.00000 3.46410i 0.103975 0.180090i
$$371$$ 1.50000 2.59808i 0.0778761 0.134885i
$$372$$ −9.00000 −0.466628
$$373$$ −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i $$-0.866355\pi$$
0.809591 + 0.586994i $$0.199689\pi$$
$$374$$ −14.0000 24.2487i −0.723923 1.25387i
$$375$$ −6.00000 10.3923i −0.309839 0.536656i
$$376$$ −6.00000 −0.309426
$$377$$ −5.00000 5.19615i −0.257513 0.267615i
$$378$$ 1.00000 0.0514344
$$379$$ 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i $$0.00504609\pi$$
−0.486209 + 0.873843i $$0.661621\pi$$
$$380$$ 2.00000 + 3.46410i 0.102598 + 0.177705i
$$381$$ −8.00000 + 13.8564i −0.409852 + 0.709885i
$$382$$ −3.00000 −0.153493
$$383$$ −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
$$385$$ −8.00000 −0.407718
$$386$$ −11.0000 + 19.0526i −0.559885 + 0.969750i
$$387$$ 2.50000 + 4.33013i 0.127082 + 0.220113i
$$388$$ 8.00000 + 13.8564i 0.406138 + 0.703452i
$$389$$ −1.00000 −0.0507020 −0.0253510 0.999679i $$-0.508070\pi$$
−0.0253510 + 0.999679i $$0.508070\pi$$
$$390$$ 2.00000 6.92820i 0.101274 0.350823i
$$391$$ −7.00000 −0.354005
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ −7.50000 12.9904i −0.378325 0.655278i
$$394$$ −4.50000 + 7.79423i −0.226707 + 0.392668i
$$395$$ 8.00000 0.402524
$$396$$ 2.00000 3.46410i 0.100504 0.174078i
$$397$$ 0.500000 0.866025i 0.0250943 0.0434646i −0.853206 0.521575i $$-0.825345\pi$$
0.878300 + 0.478110i $$0.158678\pi$$
$$398$$ 5.00000 0.250627
$$399$$ 1.00000 1.73205i 0.0500626 0.0867110i
$$400$$ 0.500000 + 0.866025i 0.0250000 + 0.0433013i
$$401$$ −16.0000 27.7128i −0.799002 1.38391i −0.920267 0.391292i $$-0.872028\pi$$
0.121265 0.992620i $$-0.461305\pi$$
$$402$$ 5.00000 0.249377
$$403$$ 31.5000 7.79423i 1.56913 0.388258i
$$404$$ 0 0
$$405$$ 1.00000 + 1.73205i 0.0496904 + 0.0860663i
$$406$$ 1.00000 + 1.73205i 0.0496292 + 0.0859602i
$$407$$ −4.00000 + 6.92820i −0.198273 + 0.343418i
$$408$$ −7.00000 −0.346552
$$409$$ −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i $$-0.945837\pi$$
0.639430 + 0.768849i $$0.279170\pi$$
$$410$$ −2.00000 + 3.46410i −0.0987730 + 0.171080i
$$411$$ 4.00000 0.197305
$$412$$ 5.50000 9.52628i 0.270966 0.469326i
$$413$$ 7.50000 + 12.9904i 0.369051 + 0.639215i
$$414$$ −0.500000 0.866025i −0.0245737 0.0425628i
$$415$$ 2.00000 0.0981761
$$416$$ −1.00000 + 3.46410i −0.0490290 + 0.169842i
$$417$$ 16.0000 0.783523
$$418$$ −4.00000 6.92820i −0.195646 0.338869i
$$419$$ 15.5000 + 26.8468i 0.757225 + 1.31155i 0.944261 + 0.329198i $$0.106778\pi$$
−0.187036 + 0.982353i $$0.559888\pi$$
$$420$$ −1.00000 + 1.73205i −0.0487950 + 0.0845154i
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 2.00000 3.46410i 0.0973585 0.168630i
$$423$$ −3.00000 + 5.19615i −0.145865 + 0.252646i
$$424$$ −3.00000 −0.145693
$$425$$ 3.50000 6.06218i 0.169775 0.294059i
$$426$$ 0.500000 + 0.866025i 0.0242251 + 0.0419591i
$$427$$ −3.50000 6.06218i −0.169377 0.293369i
$$428$$ −6.00000 −0.290021
$$429$$ −4.00000 + 13.8564i −0.193122 + 0.668994i
$$430$$ −10.0000 −0.482243
$$431$$ 0.500000 + 0.866025i 0.0240842 + 0.0417150i 0.877816 0.478997i $$-0.159000\pi$$
−0.853732 + 0.520712i $$0.825666\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −6.00000 + 10.3923i −0.288342 + 0.499422i −0.973414 0.229053i $$-0.926437\pi$$
0.685072 + 0.728475i $$0.259771\pi$$
$$434$$ −9.00000 −0.432014
$$435$$ −2.00000 + 3.46410i −0.0958927 + 0.166091i
$$436$$ 8.00000 13.8564i 0.383131 0.663602i
$$437$$ −2.00000 −0.0956730
$$438$$ 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 $$0.863764\pi$$
$$440$$ 4.00000 + 6.92820i 0.190693 + 0.330289i
$$441$$ 1.00000 0.0476190
$$442$$ 24.5000 6.06218i 1.16535 0.288348i
$$443$$ −6.00000 −0.285069 −0.142534 0.989790i $$-0.545525\pi$$
−0.142534 + 0.989790i $$0.545525\pi$$
$$444$$ 1.00000 + 1.73205i 0.0474579 + 0.0821995i
$$445$$ 3.00000 + 5.19615i 0.142214 + 0.246321i
$$446$$ 1.50000 2.59808i 0.0710271 0.123022i
$$447$$ 21.0000 0.993266
$$448$$ 0.500000 0.866025i 0.0236228 0.0409159i
$$449$$ −9.00000 + 15.5885i −0.424736 + 0.735665i −0.996396 0.0848262i $$-0.972967\pi$$
0.571660 + 0.820491i $$0.306300\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ 4.00000 6.92820i 0.188353 0.326236i
$$452$$ 4.00000 + 6.92820i 0.188144 + 0.325875i
$$453$$ −10.0000 17.3205i −0.469841 0.813788i
$$454$$ −28.0000 −1.31411
$$455$$ 2.00000 6.92820i 0.0937614 0.324799i
$$456$$ −2.00000 −0.0936586
$$457$$ 4.50000 + 7.79423i 0.210501 + 0.364599i 0.951871 0.306497i $$-0.0991571\pi$$
−0.741370 + 0.671096i $$0.765824\pi$$
$$458$$ 6.50000 + 11.2583i 0.303725 + 0.526067i
$$459$$ −3.50000 + 6.06218i −0.163366 + 0.282958i
$$460$$ 2.00000 0.0932505
$$461$$ 10.0000 17.3205i 0.465746 0.806696i −0.533488 0.845807i $$-0.679119\pi$$
0.999235 + 0.0391109i $$0.0124526\pi$$
$$462$$ 2.00000 3.46410i 0.0930484 0.161165i
$$463$$ 18.0000 0.836531 0.418265 0.908325i $$-0.362638\pi$$
0.418265 + 0.908325i $$0.362638\pi$$
$$464$$ 1.00000 1.73205i 0.0464238 0.0804084i
$$465$$ −9.00000 15.5885i −0.417365 0.722897i
$$466$$ −8.00000 13.8564i −0.370593 0.641886i
$$467$$ 37.0000 1.71216 0.856078 0.516847i $$-0.172894\pi$$
0.856078 + 0.516847i $$0.172894\pi$$
$$468$$ 2.50000 + 2.59808i 0.115563 + 0.120096i
$$469$$ 5.00000 0.230879
$$470$$ −6.00000 10.3923i −0.276759 0.479361i
$$471$$ −5.00000 8.66025i −0.230388 0.399043i
$$472$$ 7.50000 12.9904i 0.345215 0.597931i
$$473$$ 20.0000 0.919601
$$474$$ −2.00000 + 3.46410i −0.0918630 + 0.159111i
$$475$$ 1.00000 1.73205i 0.0458831 0.0794719i
$$476$$ −7.00000 −0.320844
$$477$$ −1.50000 + 2.59808i −0.0686803 + 0.118958i
$$478$$ −4.50000 7.79423i −0.205825 0.356500i
$$479$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$480$$ 2.00000 0.0912871
$$481$$ −5.00000 5.19615i −0.227980 0.236924i
$$482$$ −14.0000 −0.637683
$$483$$ −0.500000 0.866025i −0.0227508 0.0394055i
$$484$$ −2.50000 4.33013i −0.113636 0.196824i
$$485$$ −16.0000 + 27.7128i −0.726523 + 1.25837i
$$486$$ −1.00000 −0.0453609
$$487$$ 14.0000 24.2487i 0.634401 1.09881i −0.352241 0.935909i $$-0.614580\pi$$
0.986642 0.162905i $$-0.0520863\pi$$
$$488$$ −3.50000 + 6.06218i −0.158438 + 0.274422i
$$489$$ 21.0000 0.949653
$$490$$ −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 $$0.775556\pi$$
$$492$$ −1.00000 1.73205i −0.0450835 0.0780869i
$$493$$ −14.0000 −0.630528
$$494$$ 7.00000 1.73205i 0.314945 0.0779287i
$$495$$ 8.00000 0.359573
$$496$$ 4.50000 + 7.79423i 0.202056 + 0.349971i
$$497$$ 0.500000 + 0.866025i 0.0224281 + 0.0388465i
$$498$$ −0.500000 + 0.866025i −0.0224055 + 0.0388075i
$$499$$ 7.00000 0.313363 0.156682 0.987649i $$-0.449920\pi$$
0.156682 + 0.987649i $$0.449920\pi$$
$$500$$ −6.00000 + 10.3923i −0.268328 + 0.464758i
$$501$$ 0 0
$$502$$ −23.0000 −1.02654
$$503$$ 2.00000 3.46410i 0.0891756 0.154457i −0.817987 0.575236i $$-0.804910\pi$$
0.907163 + 0.420780i $$0.138243\pi$$
$$504$$ −0.500000 0.866025i −0.0222718 0.0385758i
$$505$$ 0 0
$$506$$ −4.00000 −0.177822
$$507$$ −11.0000 6.92820i −0.488527 0.307692i
$$508$$ 16.0000 0.709885
$$509$$ 6.00000 + 10.3923i 0.265945 + 0.460631i 0.967811 0.251679i $$-0.0809826\pi$$
−0.701866 + 0.712309i $$0.747649\pi$$
$$510$$ −7.00000 12.1244i −0.309965 0.536875i
$$511$$ 6.00000 10.3923i 0.265424 0.459728i
$$512$$ −1.00000 −0.0441942
$$513$$ −1.00000 + 1.73205i −0.0441511 + 0.0764719i
$$514$$ 13.5000 23.3827i 0.595459 1.03137i
$$515$$ 22.0000 0.969436
$$516$$ 2.50000 4.33013i 0.110056 0.190623i
$$517$$ 12.0000 + 20.7846i 0.527759 + 0.914106i
$$518$$ 1.00000 + 1.73205i 0.0439375 + 0.0761019i
$$519$$ −16.0000 −0.702322
$$520$$ −7.00000 + 1.73205i −0.306970 + 0.0759555i
$$521$$ −42.0000 −1.84005 −0.920027 0.391856i $$-0.871833\pi$$
−0.920027 + 0.391856i $$0.871833\pi$$
$$522$$ −1.00000 1.73205i −0.0437688 0.0758098i
$$523$$ 12.0000 + 20.7846i 0.524723 + 0.908848i 0.999586 + 0.0287874i $$0.00916457\pi$$
−0.474862 + 0.880060i $$0.657502\pi$$
$$524$$ −7.50000 + 12.9904i −0.327639 + 0.567487i
$$525$$ 1.00000 0.0436436
$$526$$ 2.00000 3.46410i 0.0872041 0.151042i
$$527$$ 31.5000 54.5596i 1.37216 2.37665i
$$528$$ −4.00000 −0.174078
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ −3.00000 5.19615i −0.130312 0.225706i
$$531$$ −7.50000 12.9904i −0.325472 0.563735i
$$532$$ −2.00000 −0.0867110
$$533$$ 5.00000 + 5.19615i 0.216574 + 0.225070i
$$534$$ −3.00000 −0.129823
$$535$$ −6.00000 10.3923i −0.259403 0.449299i
$$536$$ −2.50000 4.33013i −0.107984 0.187033i
$$537$$ −3.00000 + 5.19615i −0.129460 + 0.224231i
$$538$$ −18.0000 −0.776035
$$539$$ 2.00000 3.46410i 0.0861461 0.149209i
$$540$$ 1.00000 1.73205i 0.0430331 0.0745356i
$$541$$ 34.0000 1.46177 0.730887 0.682498i $$-0.239107\pi$$
0.730887 + 0.682498i $$0.239107\pi$$
$$542$$ 4.50000 7.79423i 0.193292 0.334791i
$$543$$ 1.00000 + 1.73205i 0.0429141 + 0.0743294i
$$544$$ 3.50000 + 6.06218i 0.150061 + 0.259914i
$$545$$ 32.0000 1.37073
$$546$$ 2.50000 + 2.59808i 0.106990 + 0.111187i
$$547$$ −4.00000 −0.171028 −0.0855138 0.996337i $$-0.527253\pi$$
−0.0855138 + 0.996337i $$0.527253\pi$$
$$548$$ −2.00000 3.46410i −0.0854358 0.147979i
$$549$$ 3.50000 + 6.06218i 0.149376 + 0.258727i
$$550$$ 2.00000 3.46410i 0.0852803 0.147710i
$$551$$ −4.00000 −0.170406
$$552$$ −0.500000 + 0.866025i −0.0212814 + 0.0368605i
$$553$$ −2.00000 + 3.46410i −0.0850487 + 0.147309i
$$554$$ 8.00000 0.339887
$$555$$ −2.00000 + 3.46410i −0.0848953 + 0.147043i
$$556$$ −8.00000 13.8564i −0.339276 0.587643i
$$557$$ −6.50000 11.2583i −0.275414 0.477031i 0.694826 0.719178i $$-0.255482\pi$$
−0.970239 + 0.242147i $$0.922148\pi$$
$$558$$ 9.00000 0.381000
$$559$$ −5.00000 + 17.3205i −0.211477 + 0.732579i
$$560$$ 2.00000 0.0845154
$$561$$ 14.0000 + 24.2487i 0.591080 + 1.02378i
$$562$$ −13.0000 22.5167i −0.548372 0.949808i
$$563$$ 20.0000 34.6410i 0.842900 1.45994i −0.0445334 0.999008i $$-0.514180\pi$$
0.887433 0.460937i $$-0.152487\pi$$
$$564$$ 6.00000 0.252646
$$565$$ −8.00000 + 13.8564i −0.336563 + 0.582943i
$$566$$ 7.00000 12.1244i 0.294232 0.509625i
$$567$$ −1.00000 −0.0419961
$$568$$ 0.500000 0.866025i 0.0209795 0.0363376i
$$569$$ −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i $$-0.983201\pi$$
0.453619 0.891196i $$-0.350133\pi$$
$$570$$ −2.00000 3.46410i −0.0837708 0.145095i
$$571$$ 23.0000 0.962520 0.481260 0.876578i $$-0.340179\pi$$
0.481260 + 0.876578i $$0.340179\pi$$
$$572$$ 14.0000 3.46410i 0.585369 0.144841i
$$573$$ 3.00000 0.125327
$$574$$ −1.00000 1.73205i −0.0417392 0.0722944i
$$575$$ −0.500000 0.866025i −0.0208514 0.0361158i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 6.00000 0.249783 0.124892 0.992170i $$-0.460142\pi$$
0.124892 + 0.992170i $$0.460142\pi$$
$$578$$ 16.0000 27.7128i 0.665512 1.15270i
$$579$$ 11.0000 19.0526i 0.457144 0.791797i
$$580$$ 4.00000 0.166091
$$581$$ −0.500000 + 0.866025i −0.0207435 + 0.0359288i
$$582$$ −8.00000 13.8564i −0.331611 0.574367i
$$583$$ 6.00000 + 10.3923i 0.248495 + 0.430405i
$$584$$ −12.0000 −0.496564
$$585$$ −2.00000 + 6.92820i −0.0826898 + 0.286446i
$$586$$ 16.0000 0.660954
$$587$$ −22.5000 38.9711i −0.928674 1.60851i −0.785543 0.618808i $$-0.787616\pi$$
−0.143132 0.989704i $$-0.545717\pi$$
$$588$$ −0.500000 0.866025i −0.0206197 0.0357143i
$$589$$ 9.00000 15.5885i 0.370839 0.642311i
$$590$$ 30.0000 1.23508
$$591$$ 4.50000 7.79423i 0.185105 0.320612i
$$592$$ 1.00000 1.73205i 0.0410997 0.0711868i
$$593$$ 29.0000 1.19089 0.595444 0.803397i $$-0.296976\pi$$
0.595444 + 0.803397i $$0.296976\pi$$
$$594$$ −2.00000 + 3.46410i −0.0820610 + 0.142134i
$$595$$ −7.00000 12.1244i −0.286972 0.497050i
$$596$$ −10.5000 18.1865i −0.430097 0.744949i
$$597$$ −5.00000 −0.204636
$$598$$ 1.00000 3.46410i 0.0408930 0.141658i
$$599$$ 9.00000 0.367730 0.183865 0.982952i $$-0.441139\pi$$
0.183865 + 0.982952i $$0.441139\pi$$
$$600$$ −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 $$-0.448930\pi$$
$$602$$ 2.50000 4.33013i 0.101892 0.176483i
$$603$$ −5.00000 −0.203616
$$604$$ −10.0000 + 17.3205i −0.406894 + 0.704761i
$$605$$ 5.00000 8.66025i 0.203279 0.352089i
$$606$$ 0 0
$$607$$ −23.5000 + 40.7032i −0.953836 + 1.65209i −0.216825 + 0.976210i $$0.569570\pi$$
−0.737011 + 0.675881i $$0.763763\pi$$
$$608$$ 1.00000 + 1.73205i 0.0405554 + 0.0702439i
$$609$$ −1.00000 1.73205i −0.0405220 0.0701862i
$$610$$ −14.0000 −0.566843
$$611$$ −21.0000 + 5.19615i −0.849569 + 0.210214i
$$612$$ 7.00000 0.282958
$$613$$ −7.00000 12.1244i −0.282727 0.489698i 0.689328 0.724449i $$-0.257906\pi$$
−0.972056 + 0.234751i $$0.924572\pi$$
$$614$$ 15.0000 + 25.9808i 0.605351 + 1.04850i
$$615$$ 2.00000 3.46410i 0.0806478 0.139686i
$$616$$ −4.00000 −0.161165
$$617$$ 10.0000 17.3205i 0.402585 0.697297i −0.591452 0.806340i $$-0.701445\pi$$
0.994037 + 0.109043i $$0.0347785\pi$$
$$618$$ −5.50000 + 9.52628i −0.221242 + 0.383203i
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ −9.00000 + 15.5885i −0.361449 + 0.626048i
$$621$$ 0.500000 + 0.866025i 0.0200643 + 0.0347524i
$$622$$ 15.0000 + 25.9808i 0.601445 + 1.04173i
$$623$$ −3.00000 −0.120192
$$624$$ 1.00000 3.46410i 0.0400320 0.138675i
$$625$$ −19.0000 −0.760000
$$626$$ 0 0
$$627$$ 4.00000 + 6.92820i 0.159745 + 0.276686i
$$628$$ −5.00000 + 8.66025i −0.199522 + 0.345582i
$$629$$ −14.0000 −0.558217
$$630$$ 1.00000 1.73205i 0.0398410 0.0690066i
$$631$$ 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i $$-0.703005\pi$$
0.993491 + 0.113913i $$0.0363385\pi$$
$$632$$ 4.00000 0.159111
$$633$$ −2.00000 + 3.46410i −0.0794929 + 0.137686i
$$634$$ 11.5000 + 19.9186i 0.456723 + 0.791068i
$$635$$ 16.0000 + 27.7128i 0.634941 + 1.09975i
$$636$$ 3.00000 0.118958
$$637$$ 2.50000 + 2.59808i 0.0990536 + 0.102940i
$$638$$ −8.00000 −0.316723
$$639$$ −0.500000 0.866025i −0.0197797 0.0342594i
$$640$$ −1.00000 1.73205i −0.0395285 0.0684653i
$$641$$ −16.0000 + 27.7128i −0.631962 + 1.09459i 0.355188 + 0.934795i $$0.384417\pi$$
−0.987150 + 0.159795i $$0.948917\pi$$
$$642$$ 6.00000 0.236801
$$643$$ −7.00000 + 12.1244i −0.276053 + 0.478138i −0.970400 0.241502i $$-0.922360\pi$$
0.694347 + 0.719640i $$0.255693\pi$$
$$644$$ −0.500000 + 0.866025i −0.0197028 + 0.0341262i
$$645$$ 10.0000 0.393750
$$646$$ 7.00000 12.1244i 0.275411 0.477026i
$$647$$ 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i $$-0.129037\pi$$
−0.801010 + 0.598651i $$0.795704\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ −60.0000 −2.35521
$$650$$ 2.50000 + 2.59808i 0.0980581 + 0.101905i
$$651$$ 9.00000 0.352738
$$652$$ −10.5000 18.1865i −0.411212 0.712240i
$$653$$ −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
$$655$$ −30.0000 −1.17220
$$656$$ −1.00000 + 1.73205i −0.0390434 + 0.0676252i
$$657$$ −6.00000 + 10.3923i −0.234082 + 0.405442i
$$658$$ 6.00000 0.233904
$$659$$ 3.00000 5.19615i 0.116863 0.202413i −0.801660 0.597781i $$-0.796049\pi$$
0.918523 + 0.395367i $$0.129383\pi$$
$$660$$ −4.00000 6.92820i −0.155700 0.269680i
$$661$$ 17.5000 + 30.3109i 0.680671 + 1.17896i 0.974776 + 0.223184i $$0.0716450\pi$$
−0.294105 + 0.955773i $$0.595022\pi$$
$$662$$ −36.0000 −1.39918
$$663$$ −24.5000 + 6.06218i −0.951501 + 0.235435i
$$664$$ 1.00000 0.0388075
$$665$$ −2.00000 3.46410i −0.0775567 0.134332i
$$666$$ −1.00000 1.73205i −0.0387492 0.0671156i
$$667$$ −1.00000 + 1.73205i −0.0387202 + 0.0670653i
$$668$$ 0 0
$$669$$ −1.50000 + 2.59808i −0.0579934 + 0.100447i
$$670$$ 5.00000 8.66025i 0.193167 0.334575i
$$671$$ 28.0000 1.08093
$$672$$ −0.500000 + 0.866025i −0.0192879 + 0.0334077i
$$673$$ 16.5000 + 28.5788i 0.636028 + 1.10163i 0.986296 + 0.164984i $$0.0527572\pi$$
−0.350268 + 0.936650i $$0.613909\pi$$
$$674$$ 9.00000 + 15.5885i 0.346667 + 0.600445i
$$675$$ −1.00000 −0.0384900
$$676$$ −0.500000 + 12.9904i −0.0192308 + 0.499630i
$$677$$ 28.0000 1.07613 0.538064 0.842904i $$-0.319156\pi$$
0.538064 + 0.842904i $$0.319156\pi$$
$$678$$ −4.00000 6.92820i −0.153619 0.266076i
$$679$$ −8.00000 13.8564i −0.307012 0.531760i
$$680$$ −7.00000 + 12.1244i −0.268438 + 0.464948i
$$681$$ 28.0000 1.07296
$$682$$ 18.0000 31.1769i 0.689256 1.19383i
$$683$$ −11.0000 + 19.0526i −0.420903 + 0.729026i −0.996028 0.0890398i $$-0.971620\pi$$
0.575125 + 0.818066i $$0.304953\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 4.00000 6.92820i 0.152832 0.264713i
$$686$$ −0.500000 0.866025i −0.0190901 0.0330650i
$$687$$ −6.50000 11.2583i −0.247990 0.429532i
$$688$$ −5.00000 −0.190623
$$689$$ −10.5000 + 2.59808i −0.400018 + 0.0989788i
$$690$$ −2.00000 −0.0761387
$$691$$ 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i $$0.148979\pi$$
−0.0555386 + 0.998457i $$0.517688\pi$$
$$692$$ 8.00000 + 13.8564i 0.304114 + 0.526742i
$$693$$ −2.00000 + 3.46410i −0.0759737 + 0.131590i
$$694$$ −10.0000 −0.379595
$$695$$ 16.0000 27.7128i 0.606915 1.05121i
$$696$$ −1.00000 + 1.73205i −0.0379049 + 0.0656532i
$$697$$ 14.0000 0.530288
$$698$$ −12.5000 + 21.6506i −0.473132 + 0.819489i
$$699$$ 8.00000 + 13.8564i 0.302588 + 0.524097i
$$700$$ −0.500000 0.866025i −0.0188982 0.0327327i
$$701$$ −15.0000 −0.566542 −0.283271 0.959040i $$-0.591420\pi$$
−0.283271 + 0.959040i $$0.591420\pi$$
$$702$$ −2.50000 2.59808i −0.0943564 0.0980581i
$$703$$ −4.00000 −0.150863
$$704$$ 2.00000 + 3.46410i 0.0753778 + 0.130558i
$$705$$ 6.00000 + 10.3923i 0.225973 + 0.391397i
$$706$$ −17.5000 + 30.3109i −0.658621 + 1.14077i
$$707$$ 0 0
$$708$$ −7.50000 + 12.9904i −0.281867 + 0.488208i
$$709$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$710$$ 2.00000 0.0750587
$$711$$ 2.00000 3.46410i 0.0750059 0.129914i
$$712$$ 1.50000 + 2.59808i 0.0562149 + 0.0973670i
$$713$$ −4.50000 7.79423i −0.168526 0.291896i
$$714$$ 7.00000 0.261968
$$715$$ 20.0000 + 20.7846i 0.747958 + 0.777300i
$$716$$ 6.00000 0.224231
$$717$$ 4.50000 + 7.79423i 0.168056 + 0.291081i
$$718$$ −12.0000 20.7846i −0.447836 0.775675i
$$719$$ −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i $$-0.954983\pi$$
0.617079 + 0.786901i $$0.288316\pi$$
$$720$$ −2.00000 −0.0745356
$$721$$ −5.50000 + 9.52628i −0.204831 + 0.354777i
$$722$$ −7.50000 + 12.9904i −0.279121 + 0.483452i
$$723$$ 14.0000 0.520666
$$724$$ 1.00000 1.73205i 0.0371647 0.0643712i
$$725$$ −1.00000 1.73205i −0.0371391 0.0643268i
$$726$$ 2.50000 + 4.33013i 0.0927837 + 0.160706i
$$727$$ −21.0000 −0.778847 −0.389423 0.921059i $$-0.627326\pi$$
−0.389423 + 0.921059i $$0.627326\pi$$
$$728$$ 1.00000 3.46410i 0.0370625 0.128388i
$$729$$ 1.00000 0.0370370
$$730$$ −12.0000 20.7846i −0.444140 0.769273i
$$731$$ 17.5000 + 30.3109i 0.647261 + 1.12109i
$$732$$ 3.50000 6.06218i 0.129364 0.224065i
$$733$$ −21.0000 −0.775653 −0.387826 0.921732i $$-0.626774\pi$$
−0.387826 + 0.921732i $$0.626774\pi$$
$$734$$ −1.50000 + 2.59808i −0.0553660 + 0.0958967i
$$735$$ 1.00000 1.73205i 0.0368856 0.0638877i
$$736$$ 1.00000 0.0368605
$$737$$ −10.0000 + 17.3205i −0.368355 + 0.638009i
$$738$$ 1.00000 + 1.73205i 0.0368105 + 0.0637577i
$$739$$ −24.5000 42.4352i −0.901247 1.56101i −0.825877 0.563850i $$-0.809320\pi$$
−0.0753699 0.997156i $$-0.524014\pi$$
$$740$$ 4.00000 0.147043
$$741$$ −7.00000 + 1.73205i −0.257151 + 0.0636285i
$$742$$ 3.00000 0.110133
$$743$$ 20.5000 + 35.5070i 0.752072 + 1.30263i 0.946817 + 0.321773i $$0.104279\pi$$
−0.194745 + 0.980854i $$0.562388\pi$$
$$744$$ −4.50000 7.79423i −0.164978 0.285750i
$$745$$ 21.0000 36.3731i 0.769380 1.33261i
$$746$$ −4.00000 −0.146450
$$747$$ 0.500000 0.866025i 0.0182940 0.0316862i
$$748$$ 14.0000 24.2487i 0.511891 0.886621i
$$749$$ 6.00000 0.219235
$$750$$ 6.00000 10.3923i 0.219089 0.379473i
$$751$$ 13.0000 + 22.5167i 0.474377 + 0.821645i 0.999570 0.0293387i $$-0.00934013\pi$$
−0.525193 + 0.850983i $$0.676007\pi$$
$$752$$ −3.00000 5.19615i −0.109399 0.189484i
$$753$$ 23.0000 0.838167
$$754$$ 2.00000 6.92820i 0.0728357 0.252310i
$$755$$ −40.0000 −1.45575
$$756$$ 0.500000 + 0.866025i 0.0181848 + 0.0314970i
$$757$$ −23.0000 39.8372i −0.835949 1.44791i −0.893255 0.449550i $$-0.851584\pi$$
0.0573060 0.998357i $$-0.481749\pi$$
$$758$$ −10.0000 + 17.3205i −0.363216 + 0.629109i
$$759$$ 4.00000 0.145191
$$760$$ −2.00000 + 3.46410i −0.0725476 + 0.125656i
$$761$$ −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i $$-0.891348\pi$$
0.761057 + 0.648686i $$0.224681\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ −8.00000 + 13.8564i −0.289619 + 0.501636i
$$764$$ −1.50000 2.59808i −0.0542681 0.0939951i
$$765$$ 7.00000 + 12.1244i 0.253086 + 0.438357i
$$766$$ −24.0000 −0.867155
$$767$$ 15.0000 51.9615i 0.541619 1.87622i
$$768$$ 1.00000 0.0360844
$$769$$ −2.00000 3.46410i −0.0721218 0.124919i 0.827709 0.561157i $$-0.189644\pi$$
−0.899831 + 0.436239i $$0.856310\pi$$
$$770$$ −4.00000 6.92820i −0.144150 0.249675i
$$771$$ −13.5000 + 23.3827i −0.486191 + 0.842107i
$$772$$ −22.0000 −0.791797
$$773$$ 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i $$-0.775776\pi$$
0.941825 + 0.336104i $$0.109109\pi$$
$$774$$ −2.50000 + 4.33013i −0.0898606 + 0.155643i