# Properties

 Label 546.2.s.e.43.3 Level $546$ Weight $2$ Character 546.43 Analytic conductor $4.360$ Analytic rank $0$ Dimension $8$ 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.s (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: 8.0.195105024.2 Defining polynomial: $$x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 43.3 Root $$-1.58726 - 0.693255i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.43 Dual form 546.2.s.e.127.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.05596i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.52798 - 2.64654i) q^{10} +(-2.98127 - 1.72124i) q^{11} +1.00000 q^{12} +(3.25253 + 1.55596i) q^{13} +1.00000 q^{14} +(-2.64654 - 1.52798i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.41449 - 2.44997i) q^{17} -1.00000i q^{18} +(1.49425 - 0.862708i) q^{19} +(2.64654 - 1.52798i) q^{20} -1.00000i q^{21} +(-1.72124 - 2.98127i) q^{22} +(1.53130 - 2.65229i) q^{23} +(0.866025 + 0.500000i) q^{24} -4.33891 q^{25} +(2.03880 + 2.97377i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(-1.92531 + 3.33473i) q^{29} +(-1.52798 - 2.64654i) q^{30} -0.978370i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.98127 + 1.72124i) q^{33} -2.82898i q^{34} +(-1.52798 - 2.64654i) q^{35} +(0.500000 - 0.866025i) q^{36} +(4.58394 + 2.64654i) q^{37} +1.72542 q^{38} +(2.97377 - 2.03880i) q^{39} +3.05596 q^{40} +(8.62781 + 4.98127i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-1.51082 - 2.61681i) q^{43} -3.44247i q^{44} +(-2.64654 + 1.52798i) q^{45} +(2.65229 - 1.53130i) q^{46} +8.04447i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.75760 - 2.16945i) q^{50} -2.82898 q^{51} +(0.278764 + 3.59476i) q^{52} -8.33405 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-5.26003 + 9.11064i) q^{55} +(0.500000 + 0.866025i) q^{56} -1.72542i q^{57} +(-3.33473 + 1.92531i) q^{58} +(8.64080 - 4.98877i) q^{59} -3.05596i q^{60} +(5.77260 + 9.99843i) q^{61} +(0.489185 - 0.847293i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(4.75496 - 9.93962i) q^{65} -3.44247 q^{66} +(4.11410 + 2.37527i) q^{67} +(1.41449 - 2.44997i) q^{68} +(-1.53130 - 2.65229i) q^{69} -3.05596i q^{70} +(-3.17784 + 1.83473i) q^{71} +(0.866025 - 0.500000i) q^{72} +10.1119i q^{73} +(2.64654 + 4.58394i) q^{74} +(-2.16945 + 3.75760i) q^{75} +(1.49425 + 0.862708i) q^{76} -3.44247 q^{77} +(3.59476 - 0.278764i) q^{78} -4.49843 q^{79} +(2.64654 + 1.52798i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.98127 + 8.62781i) q^{82} +7.15869i q^{83} +(0.866025 - 0.500000i) q^{84} +(-7.48701 + 4.32263i) q^{85} -3.02163i q^{86} +(1.92531 + 3.33473i) q^{87} +(1.72124 - 2.98127i) q^{88} +(-6.84426 - 3.95154i) q^{89} -3.05596 q^{90} +(3.59476 - 0.278764i) q^{91} +3.06260 q^{92} +(-0.847293 - 0.489185i) q^{93} +(-4.02224 + 6.96672i) q^{94} +(-2.63640 - 4.56638i) q^{95} +1.00000i q^{96} +(-7.88016 + 4.54961i) q^{97} +(0.866025 - 0.500000i) q^{98} +3.44247i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$8 q + 4 q^{3} + 4 q^{4} - 4 q^{9} + 6 q^{10} + 6 q^{11} + 8 q^{12} + 12 q^{13} + 8 q^{14} + 6 q^{15} - 4 q^{16} + 2 q^{17} - 12 q^{19} - 6 q^{20} - 4 q^{22} + 8 q^{23} - 24 q^{25} + 6 q^{26} - 8 q^{27} + 2 q^{29} - 6 q^{30} + 6 q^{33} - 6 q^{35} + 4 q^{36} + 18 q^{37} - 4 q^{38} + 12 q^{40} + 12 q^{41} + 4 q^{42} - 8 q^{43} + 6 q^{45} + 18 q^{46} + 4 q^{48} + 4 q^{49} + 12 q^{50} + 4 q^{51} + 12 q^{52} - 12 q^{53} - 22 q^{55} + 4 q^{56} - 24 q^{58} + 18 q^{59} - 8 q^{61} + 8 q^{62} - 8 q^{64} + 46 q^{65} - 8 q^{66} + 18 q^{67} - 2 q^{68} - 8 q^{69} + 6 q^{71} - 6 q^{74} - 12 q^{75} - 12 q^{76} - 8 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} - 4 q^{81} + 10 q^{82} - 54 q^{85} - 2 q^{87} + 4 q^{88} - 18 q^{89} - 12 q^{90} + 6 q^{91} + 16 q^{92} + 30 q^{93} - 2 q^{94} - 50 q^{95} - 54 q^{97} + O(q^{100})$$

## Character values

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

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 + 0.500000i 0.612372 + 0.353553i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0.500000 + 0.866025i 0.250000 + 0.433013i
$$5$$ 3.05596i 1.36667i −0.730106 0.683334i $$-0.760529\pi$$
0.730106 0.683334i $$-0.239471\pi$$
$$6$$ 0.866025 0.500000i 0.353553 0.204124i
$$7$$ 0.866025 0.500000i 0.327327 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 1.52798 2.64654i 0.483190 0.836910i
$$11$$ −2.98127 1.72124i −0.898886 0.518972i −0.0220475 0.999757i $$-0.507018\pi$$
−0.876839 + 0.480785i $$0.840352\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.25253 + 1.55596i 0.902091 + 0.431546i
$$14$$ 1.00000 0.267261
$$15$$ −2.64654 1.52798i −0.683334 0.394523i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.41449 2.44997i −0.343064 0.594205i 0.641936 0.766758i $$-0.278132\pi$$
−0.985000 + 0.172554i $$0.944798\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.49425 0.862708i 0.342805 0.197919i −0.318707 0.947853i $$-0.603248\pi$$
0.661512 + 0.749935i $$0.269915\pi$$
$$20$$ 2.64654 1.52798i 0.591785 0.341667i
$$21$$ 1.00000i 0.218218i
$$22$$ −1.72124 2.98127i −0.366969 0.635608i
$$23$$ 1.53130 2.65229i 0.319298 0.553040i −0.661044 0.750347i $$-0.729886\pi$$
0.980342 + 0.197307i $$0.0632196\pi$$
$$24$$ 0.866025 + 0.500000i 0.176777 + 0.102062i
$$25$$ −4.33891 −0.867781
$$26$$ 2.03880 + 2.97377i 0.399841 + 0.583204i
$$27$$ −1.00000 −0.192450
$$28$$ 0.866025 + 0.500000i 0.163663 + 0.0944911i
$$29$$ −1.92531 + 3.33473i −0.357520 + 0.619243i −0.987546 0.157331i $$-0.949711\pi$$
0.630026 + 0.776574i $$0.283044\pi$$
$$30$$ −1.52798 2.64654i −0.278970 0.483190i
$$31$$ 0.978370i 0.175720i −0.996133 0.0878602i $$-0.971997\pi$$
0.996133 0.0878602i $$-0.0280029\pi$$
$$32$$ −0.866025 + 0.500000i −0.153093 + 0.0883883i
$$33$$ −2.98127 + 1.72124i −0.518972 + 0.299629i
$$34$$ 2.82898i 0.485166i
$$35$$ −1.52798 2.64654i −0.258276 0.447347i
$$36$$ 0.500000 0.866025i 0.0833333 0.144338i
$$37$$ 4.58394 + 2.64654i 0.753596 + 0.435089i 0.826992 0.562214i $$-0.190050\pi$$
−0.0733959 + 0.997303i $$0.523384\pi$$
$$38$$ 1.72542 0.279899
$$39$$ 2.97377 2.03880i 0.476184 0.326469i
$$40$$ 3.05596 0.483190
$$41$$ 8.62781 + 4.98127i 1.34744 + 0.777943i 0.987886 0.155182i $$-0.0495964\pi$$
0.359551 + 0.933125i $$0.382930\pi$$
$$42$$ 0.500000 0.866025i 0.0771517 0.133631i
$$43$$ −1.51082 2.61681i −0.230397 0.399060i 0.727528 0.686078i $$-0.240669\pi$$
−0.957925 + 0.287019i $$0.907336\pi$$
$$44$$ 3.44247i 0.518972i
$$45$$ −2.64654 + 1.52798i −0.394523 + 0.227778i
$$46$$ 2.65229 1.53130i 0.391058 0.225778i
$$47$$ 8.04447i 1.17341i 0.809802 + 0.586703i $$0.199575\pi$$
−0.809802 + 0.586703i $$0.800425\pi$$
$$48$$ 0.500000 + 0.866025i 0.0721688 + 0.125000i
$$49$$ 0.500000 0.866025i 0.0714286 0.123718i
$$50$$ −3.75760 2.16945i −0.531405 0.306807i
$$51$$ −2.82898 −0.396137
$$52$$ 0.278764 + 3.59476i 0.0386576 + 0.498503i
$$53$$ −8.33405 −1.14477 −0.572385 0.819985i $$-0.693982\pi$$
−0.572385 + 0.819985i $$0.693982\pi$$
$$54$$ −0.866025 0.500000i −0.117851 0.0680414i
$$55$$ −5.26003 + 9.11064i −0.709263 + 1.22848i
$$56$$ 0.500000 + 0.866025i 0.0668153 + 0.115728i
$$57$$ 1.72542i 0.228537i
$$58$$ −3.33473 + 1.92531i −0.437871 + 0.252805i
$$59$$ 8.64080 4.98877i 1.12494 0.649482i 0.182279 0.983247i $$-0.441652\pi$$
0.942656 + 0.333765i $$0.108319\pi$$
$$60$$ 3.05596i 0.394523i
$$61$$ 5.77260 + 9.99843i 0.739106 + 1.28017i 0.952899 + 0.303289i $$0.0980849\pi$$
−0.213793 + 0.976879i $$0.568582\pi$$
$$62$$ 0.489185 0.847293i 0.0621266 0.107606i
$$63$$ −0.866025 0.500000i −0.109109 0.0629941i
$$64$$ −1.00000 −0.125000
$$65$$ 4.75496 9.93962i 0.589781 1.23286i
$$66$$ −3.44247 −0.423739
$$67$$ 4.11410 + 2.37527i 0.502617 + 0.290186i 0.729794 0.683668i $$-0.239616\pi$$
−0.227177 + 0.973854i $$0.572950\pi$$
$$68$$ 1.41449 2.44997i 0.171532 0.297102i
$$69$$ −1.53130 2.65229i −0.184347 0.319298i
$$70$$ 3.05596i 0.365257i
$$71$$ −3.17784 + 1.83473i −0.377140 + 0.217742i −0.676573 0.736375i $$-0.736536\pi$$
0.299433 + 0.954117i $$0.403202\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ 10.1119i 1.18351i 0.806117 + 0.591756i $$0.201565\pi$$
−0.806117 + 0.591756i $$0.798435\pi$$
$$74$$ 2.64654 + 4.58394i 0.307654 + 0.532873i
$$75$$ −2.16945 + 3.75760i −0.250507 + 0.433891i
$$76$$ 1.49425 + 0.862708i 0.171403 + 0.0989594i
$$77$$ −3.44247 −0.392306
$$78$$ 3.59476 0.278764i 0.407026 0.0315638i
$$79$$ −4.49843 −0.506113 −0.253057 0.967451i $$-0.581436\pi$$
−0.253057 + 0.967451i $$0.581436\pi$$
$$80$$ 2.64654 + 1.52798i 0.295892 + 0.170833i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 4.98127 + 8.62781i 0.550089 + 0.952782i
$$83$$ 7.15869i 0.785768i 0.919588 + 0.392884i $$0.128523\pi$$
−0.919588 + 0.392884i $$0.871477\pi$$
$$84$$ 0.866025 0.500000i 0.0944911 0.0545545i
$$85$$ −7.48701 + 4.32263i −0.812081 + 0.468855i
$$86$$ 3.02163i 0.325831i
$$87$$ 1.92531 + 3.33473i 0.206414 + 0.357520i
$$88$$ 1.72124 2.98127i 0.183484 0.317804i
$$89$$ −6.84426 3.95154i −0.725490 0.418862i 0.0912800 0.995825i $$-0.470904\pi$$
−0.816770 + 0.576963i $$0.804238\pi$$
$$90$$ −3.05596 −0.322127
$$91$$ 3.59476 0.278764i 0.376833 0.0292224i
$$92$$ 3.06260 0.319298
$$93$$ −0.847293 0.489185i −0.0878602 0.0507261i
$$94$$ −4.02224 + 6.96672i −0.414862 + 0.718562i
$$95$$ −2.63640 4.56638i −0.270489 0.468501i
$$96$$ 1.00000i 0.102062i
$$97$$ −7.88016 + 4.54961i −0.800109 + 0.461943i −0.843509 0.537115i $$-0.819514\pi$$
0.0434004 + 0.999058i $$0.486181\pi$$
$$98$$ 0.866025 0.500000i 0.0874818 0.0505076i
$$99$$ 3.44247i 0.345981i
$$100$$ −2.16945 3.75760i −0.216945 0.375760i
$$101$$ 9.42664 16.3274i 0.937985 1.62464i 0.168764 0.985657i $$-0.446023\pi$$
0.769222 0.638982i $$-0.220644\pi$$
$$102$$ −2.44997 1.41449i −0.242583 0.140055i
$$103$$ −13.7079 −1.35068 −0.675338 0.737509i $$-0.736002\pi$$
−0.675338 + 0.737509i $$0.736002\pi$$
$$104$$ −1.55596 + 3.25253i −0.152575 + 0.318937i
$$105$$ −3.05596 −0.298231
$$106$$ −7.21750 4.16702i −0.701025 0.404737i
$$107$$ 1.65736 2.87063i 0.160223 0.277514i −0.774726 0.632297i $$-0.782112\pi$$
0.934948 + 0.354784i $$0.115445\pi$$
$$108$$ −0.500000 0.866025i −0.0481125 0.0833333i
$$109$$ 8.67525i 0.830938i 0.909607 + 0.415469i $$0.136383\pi$$
−0.909607 + 0.415469i $$0.863617\pi$$
$$110$$ −9.11064 + 5.26003i −0.868666 + 0.501524i
$$111$$ 4.58394 2.64654i 0.435089 0.251199i
$$112$$ 1.00000i 0.0944911i
$$113$$ 5.60557 + 9.70914i 0.527328 + 0.913359i 0.999493 + 0.0318486i $$0.0101394\pi$$
−0.472165 + 0.881510i $$0.656527\pi$$
$$114$$ 0.862708 1.49425i 0.0808000 0.139950i
$$115$$ −8.10529 4.67959i −0.755822 0.436374i
$$116$$ −3.85061 −0.357520
$$117$$ −0.278764 3.59476i −0.0257718 0.332336i
$$118$$ 9.97753 0.918506
$$119$$ −2.44997 1.41449i −0.224588 0.129666i
$$120$$ 1.52798 2.64654i 0.139485 0.241595i
$$121$$ 0.425305 + 0.736650i 0.0386641 + 0.0669682i
$$122$$ 11.5452i 1.04525i
$$123$$ 8.62781 4.98127i 0.777943 0.449146i
$$124$$ 0.847293 0.489185i 0.0760892 0.0439301i
$$125$$ 2.02028i 0.180699i
$$126$$ −0.500000 0.866025i −0.0445435 0.0771517i
$$127$$ 2.55753 4.42977i 0.226944 0.393078i −0.729957 0.683493i $$-0.760460\pi$$
0.956901 + 0.290415i $$0.0937932\pi$$
$$128$$ −0.866025 0.500000i −0.0765466 0.0441942i
$$129$$ −3.02163 −0.266040
$$130$$ 9.08773 6.23048i 0.797047 0.546450i
$$131$$ −18.7757 −1.64044 −0.820219 0.572049i $$-0.806149\pi$$
−0.820219 + 0.572049i $$0.806149\pi$$
$$132$$ −2.98127 1.72124i −0.259486 0.149814i
$$133$$ 0.862708 1.49425i 0.0748063 0.129568i
$$134$$ 2.37527 + 4.11410i 0.205192 + 0.355404i
$$135$$ 3.05596i 0.263015i
$$136$$ 2.44997 1.41449i 0.210083 0.121292i
$$137$$ 2.30457 1.33055i 0.196893 0.113676i −0.398312 0.917250i $$-0.630404\pi$$
0.595205 + 0.803574i $$0.297071\pi$$
$$138$$ 3.06260i 0.260706i
$$139$$ 8.35322 + 14.4682i 0.708511 + 1.22718i 0.965409 + 0.260739i $$0.0839662\pi$$
−0.256898 + 0.966439i $$0.582700\pi$$
$$140$$ 1.52798 2.64654i 0.129138 0.223674i
$$141$$ 6.96672 + 4.02224i 0.586703 + 0.338733i
$$142$$ −3.66945 −0.307934
$$143$$ −7.01850 10.2371i −0.586916 0.856071i
$$144$$ 1.00000 0.0833333
$$145$$ 10.1908 + 5.88366i 0.846300 + 0.488611i
$$146$$ −5.05596 + 8.75718i −0.418434 + 0.724750i
$$147$$ −0.500000 0.866025i −0.0412393 0.0714286i
$$148$$ 5.29308i 0.435089i
$$149$$ 2.16642 1.25078i 0.177480 0.102468i −0.408628 0.912701i $$-0.633993\pi$$
0.586108 + 0.810233i $$0.300659\pi$$
$$150$$ −3.75760 + 2.16945i −0.306807 + 0.177135i
$$151$$ 12.6465i 1.02916i −0.857444 0.514578i $$-0.827949\pi$$
0.857444 0.514578i $$-0.172051\pi$$
$$152$$ 0.862708 + 1.49425i 0.0699749 + 0.121200i
$$153$$ −1.41449 + 2.44997i −0.114355 + 0.198068i
$$154$$ −2.98127 1.72124i −0.240237 0.138701i
$$155$$ −2.98986 −0.240151
$$156$$ 3.25253 + 1.55596i 0.260411 + 0.124577i
$$157$$ 17.8131 1.42164 0.710822 0.703372i $$-0.248323\pi$$
0.710822 + 0.703372i $$0.248323\pi$$
$$158$$ −3.89576 2.24922i −0.309930 0.178938i
$$159$$ −4.16702 + 7.21750i −0.330467 + 0.572385i
$$160$$ 1.52798 + 2.64654i 0.120798 + 0.209227i
$$161$$ 3.06260i 0.241366i
$$162$$ −0.866025 + 0.500000i −0.0680414 + 0.0392837i
$$163$$ −7.68884 + 4.43915i −0.602236 + 0.347701i −0.769921 0.638139i $$-0.779704\pi$$
0.167684 + 0.985841i $$0.446371\pi$$
$$164$$ 9.96254i 0.777943i
$$165$$ 5.26003 + 9.11064i 0.409493 + 0.709263i
$$166$$ −3.57934 + 6.19961i −0.277811 + 0.481183i
$$167$$ −8.46097 4.88494i −0.654730 0.378008i 0.135536 0.990772i $$-0.456724\pi$$
−0.790266 + 0.612764i $$0.790058\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ 8.15796 + 10.1216i 0.627535 + 0.778588i
$$170$$ −8.64526 −0.663061
$$171$$ −1.49425 0.862708i −0.114268 0.0659729i
$$172$$ 1.51082 2.61681i 0.115199 0.199530i
$$173$$ 4.33762 + 7.51299i 0.329783 + 0.571202i 0.982469 0.186427i $$-0.0596909\pi$$
−0.652685 + 0.757629i $$0.726358\pi$$
$$174$$ 3.85061i 0.291914i
$$175$$ −3.75760 + 2.16945i −0.284048 + 0.163995i
$$176$$ 2.98127 1.72124i 0.224722 0.129743i
$$177$$ 9.97753i 0.749957i
$$178$$ −3.95154 6.84426i −0.296180 0.512999i
$$179$$ −11.7139 + 20.2891i −0.875540 + 1.51648i −0.0193531 + 0.999813i $$0.506161\pi$$
−0.856187 + 0.516667i $$0.827173\pi$$
$$180$$ −2.64654 1.52798i −0.197262 0.113889i
$$181$$ 7.66632 0.569833 0.284917 0.958552i $$-0.408034\pi$$
0.284917 + 0.958552i $$0.408034\pi$$
$$182$$ 3.25253 + 1.55596i 0.241094 + 0.115336i
$$183$$ 11.5452 0.853446
$$184$$ 2.65229 + 1.53130i 0.195529 + 0.112889i
$$185$$ 8.08773 14.0084i 0.594622 1.02992i
$$186$$ −0.489185 0.847293i −0.0358688 0.0621266i
$$187$$ 9.73869i 0.712163i
$$188$$ −6.96672 + 4.02224i −0.508100 + 0.293352i
$$189$$ −0.866025 + 0.500000i −0.0629941 + 0.0363696i
$$190$$ 5.27281i 0.382530i
$$191$$ −12.7472 22.0789i −0.922357 1.59757i −0.795757 0.605616i $$-0.792927\pi$$
−0.126600 0.991954i $$-0.540407\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −7.38361 4.26293i −0.531484 0.306852i 0.210137 0.977672i $$-0.432609\pi$$
−0.741621 + 0.670820i $$0.765942\pi$$
$$194$$ −9.09922 −0.653286
$$195$$ −6.23048 9.08773i −0.446174 0.650786i
$$196$$ 1.00000 0.0714286
$$197$$ 20.5094 + 11.8411i 1.46124 + 0.843645i 0.999069 0.0431470i $$-0.0137384\pi$$
0.462168 + 0.886792i $$0.347072\pi$$
$$198$$ −1.72124 + 2.98127i −0.122323 + 0.211869i
$$199$$ −12.4233 21.5178i −0.880666 1.52536i −0.850602 0.525810i $$-0.823762\pi$$
−0.0300637 0.999548i $$-0.509571\pi$$
$$200$$ 4.33891i 0.306807i
$$201$$ 4.11410 2.37527i 0.290186 0.167539i
$$202$$ 16.3274 9.42664i 1.14879 0.663256i
$$203$$ 3.85061i 0.270260i
$$204$$ −1.41449 2.44997i −0.0990341 0.171532i
$$205$$ 15.2226 26.3663i 1.06319 1.84150i
$$206$$ −11.8714 6.85393i −0.827116 0.477536i
$$207$$ −3.06260 −0.212865
$$208$$ −2.97377 + 2.03880i −0.206194 + 0.141365i
$$209$$ −5.93970 −0.410857
$$210$$ −2.64654 1.52798i −0.182629 0.105441i
$$211$$ −0.386509 + 0.669453i −0.0266084 + 0.0460871i −0.879023 0.476779i $$-0.841804\pi$$
0.852415 + 0.522867i $$0.175137\pi$$
$$212$$ −4.16702 7.21750i −0.286192 0.495700i
$$213$$ 3.66945i 0.251427i
$$214$$ 2.87063 1.65736i 0.196232 0.113295i
$$215$$ −7.99687 + 4.61699i −0.545382 + 0.314876i
$$216$$ 1.00000i 0.0680414i
$$217$$ −0.489185 0.847293i −0.0332080 0.0575180i
$$218$$ −4.33762 + 7.51299i −0.293781 + 0.508844i
$$219$$ 8.75718 + 5.05596i 0.591756 + 0.341650i
$$220$$ −10.5201 −0.709263
$$221$$ −0.788619 10.1695i −0.0530482 0.684075i
$$222$$ 5.29308 0.355248
$$223$$ −18.6502 10.7677i −1.24891 0.721060i −0.278019 0.960575i $$-0.589678\pi$$
−0.970892 + 0.239516i $$0.923011\pi$$
$$224$$ −0.500000 + 0.866025i −0.0334077 + 0.0578638i
$$225$$ 2.16945 + 3.75760i 0.144630 + 0.250507i
$$226$$ 11.2111i 0.745754i
$$227$$ 15.1939 8.77218i 1.00845 0.582230i 0.0977139 0.995215i $$-0.468847\pi$$
0.910738 + 0.412985i $$0.135514\pi$$
$$228$$ 1.49425 0.862708i 0.0989594 0.0571342i
$$229$$ 10.3222i 0.682109i 0.940043 + 0.341055i $$0.110784\pi$$
−0.940043 + 0.341055i $$0.889216\pi$$
$$230$$ −4.67959 8.10529i −0.308563 0.534447i
$$231$$ −1.72124 + 2.98127i −0.113249 + 0.196153i
$$232$$ −3.33473 1.92531i −0.218936 0.126402i
$$233$$ −17.8290 −1.16802 −0.584008 0.811748i $$-0.698516\pi$$
−0.584008 + 0.811748i $$0.698516\pi$$
$$234$$ 1.55596 3.25253i 0.101716 0.212625i
$$235$$ 24.5836 1.60366
$$236$$ 8.64080 + 4.98877i 0.562468 + 0.324741i
$$237$$ −2.24922 + 3.89576i −0.146102 + 0.253057i
$$238$$ −1.41449 2.44997i −0.0916878 0.158808i
$$239$$ 5.71271i 0.369525i 0.982783 + 0.184762i $$0.0591515\pi$$
−0.982783 + 0.184762i $$0.940848\pi$$
$$240$$ 2.64654 1.52798i 0.170833 0.0986308i
$$241$$ 0.868738 0.501566i 0.0559603 0.0323087i −0.471759 0.881728i $$-0.656381\pi$$
0.527719 + 0.849419i $$0.323047\pi$$
$$242$$ 0.850611i 0.0546793i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ −5.77260 + 9.99843i −0.369553 + 0.640084i
$$245$$ −2.64654 1.52798i −0.169081 0.0976191i
$$246$$ 9.96254 0.635188
$$247$$ 6.20245 0.480984i 0.394653 0.0306043i
$$248$$ 0.978370 0.0621266
$$249$$ 6.19961 + 3.57934i 0.392884 + 0.226832i
$$250$$ 1.01014 1.74961i 0.0638867 0.110655i
$$251$$ −0.336293 0.582476i −0.0212266 0.0367656i 0.855217 0.518270i $$-0.173424\pi$$
−0.876444 + 0.481505i $$0.840090\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ −9.13042 + 5.27145i −0.574025 + 0.331413i
$$254$$ 4.42977 2.55753i 0.277948 0.160474i
$$255$$ 8.64526i 0.541387i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 12.1717 21.0820i 0.759248 1.31506i −0.183986 0.982929i $$-0.558900\pi$$
0.943234 0.332128i $$-0.107766\pi$$
$$258$$ −2.61681 1.51082i −0.162915 0.0940592i
$$259$$ 5.29308 0.328896
$$260$$ 10.9854 0.851893i 0.681289 0.0528322i
$$261$$ 3.85061 0.238347
$$262$$ −16.2602 9.38784i −1.00456 0.579983i
$$263$$ 8.54648 14.8029i 0.526999 0.912788i −0.472506 0.881327i $$-0.656651\pi$$
0.999505 0.0314610i $$-0.0100160\pi$$
$$264$$ −1.72124 2.98127i −0.105935 0.183484i
$$265$$ 25.4685i 1.56452i
$$266$$ 1.49425 0.862708i 0.0916186 0.0528960i
$$267$$ −6.84426 + 3.95154i −0.418862 + 0.241830i
$$268$$ 4.75055i 0.290186i
$$269$$ 13.3297 + 23.0877i 0.812727 + 1.40768i 0.910949 + 0.412519i $$0.135351\pi$$
−0.0982223 + 0.995165i $$0.531316\pi$$
$$270$$ −1.52798 + 2.64654i −0.0929900 + 0.161063i
$$271$$ 21.1739 + 12.2247i 1.28622 + 0.742600i 0.977978 0.208708i $$-0.0669257\pi$$
0.308243 + 0.951308i $$0.400259\pi$$
$$272$$ 2.82898 0.171532
$$273$$ 1.55596 3.25253i 0.0941711 0.196852i
$$274$$ 2.66109 0.160763
$$275$$ 12.9354 + 7.46828i 0.780037 + 0.450354i
$$276$$ 1.53130 2.65229i 0.0921734 0.159649i
$$277$$ −14.2406 24.6655i −0.855636 1.48201i −0.876054 0.482214i $$-0.839833\pi$$
0.0204175 0.999792i $$-0.493500\pi$$
$$278$$ 16.7064i 1.00199i
$$279$$ −0.847293 + 0.489185i −0.0507261 + 0.0292867i
$$280$$ 2.64654 1.52798i 0.158161 0.0913143i
$$281$$ 9.76032i 0.582252i 0.956685 + 0.291126i $$0.0940298\pi$$
−0.956685 + 0.291126i $$0.905970\pi$$
$$282$$ 4.02224 + 6.96672i 0.239521 + 0.414862i
$$283$$ 5.83562 10.1076i 0.346891 0.600833i −0.638804 0.769369i $$-0.720571\pi$$
0.985696 + 0.168536i $$0.0539039\pi$$
$$284$$ −3.17784 1.83473i −0.188570 0.108871i
$$285$$ −5.27281 −0.312334
$$286$$ −0.959638 12.3749i −0.0567446 0.731741i
$$287$$ 9.96254 0.588070
$$288$$ 0.866025 + 0.500000i 0.0510310 + 0.0294628i
$$289$$ 4.49843 7.79152i 0.264614 0.458324i
$$290$$ 5.88366 + 10.1908i 0.345500 + 0.598424i
$$291$$ 9.09922i 0.533406i
$$292$$ −8.75718 + 5.05596i −0.512475 + 0.295878i
$$293$$ 18.8968 10.9101i 1.10396 0.637373i 0.166704 0.986007i $$-0.446688\pi$$
0.937259 + 0.348634i $$0.113354\pi$$
$$294$$ 1.00000i 0.0583212i
$$295$$ −15.2455 26.4059i −0.887626 1.53741i
$$296$$ −2.64654 + 4.58394i −0.153827 + 0.266436i
$$297$$ 2.98127 + 1.72124i 0.172991 + 0.0998762i
$$298$$ 2.50157 0.144912
$$299$$ 9.10746 6.24401i 0.526698 0.361101i
$$300$$ −4.33891 −0.250507
$$301$$ −2.61681 1.51082i −0.150830 0.0870819i
$$302$$ 6.32323 10.9522i 0.363861 0.630226i
$$303$$ −9.42664 16.3274i −0.541546 0.937985i
$$304$$ 1.72542i 0.0989594i
$$305$$ 30.5548 17.6408i 1.74957 1.01011i
$$306$$ −2.44997 + 1.41449i −0.140055 + 0.0808610i
$$307$$ 4.87046i 0.277972i −0.990294 0.138986i $$-0.955616\pi$$
0.990294 0.138986i $$-0.0443843\pi$$
$$308$$ −1.72124 2.98127i −0.0980765 0.169874i
$$309$$ −6.85393 + 11.8714i −0.389906 + 0.675338i
$$310$$ −2.58930 1.49493i −0.147062 0.0849064i
$$311$$ −3.90344 −0.221344 −0.110672 0.993857i $$-0.535300\pi$$
−0.110672 + 0.993857i $$0.535300\pi$$
$$312$$ 2.03880 + 2.97377i 0.115424 + 0.168357i
$$313$$ 26.0528 1.47259 0.736297 0.676659i $$-0.236573\pi$$
0.736297 + 0.676659i $$0.236573\pi$$
$$314$$ 15.4266 + 8.90657i 0.870576 + 0.502627i
$$315$$ −1.52798 + 2.64654i −0.0860920 + 0.149116i
$$316$$ −2.24922 3.89576i −0.126528 0.219154i
$$317$$ 11.1107i 0.624040i 0.950076 + 0.312020i $$0.101006\pi$$
−0.950076 + 0.312020i $$0.898994\pi$$
$$318$$ −7.21750 + 4.16702i −0.404737 + 0.233675i
$$319$$ 11.4797 6.62781i 0.642740 0.371086i
$$320$$ 3.05596i 0.170833i
$$321$$ −1.65736 2.87063i −0.0925046 0.160223i
$$322$$ 1.53130 2.65229i 0.0853359 0.147806i
$$323$$ −4.22722 2.44058i −0.235209 0.135798i
$$324$$ −1.00000 −0.0555556
$$325$$ −14.1124 6.75118i −0.782818 0.374488i
$$326$$ −8.87831 −0.491724
$$327$$ 7.51299 + 4.33762i 0.415469 + 0.239871i
$$328$$ −4.98127 + 8.62781i −0.275045 + 0.476391i
$$329$$ 4.02224 + 6.96672i 0.221753 + 0.384087i
$$330$$ 10.5201i 0.579110i
$$331$$ 12.6854 7.32391i 0.697252 0.402559i −0.109071 0.994034i $$-0.534788\pi$$
0.806323 + 0.591475i $$0.201454\pi$$
$$332$$ −6.19961 + 3.57934i −0.340248 + 0.196442i
$$333$$ 5.29308i 0.290059i
$$334$$ −4.88494 8.46097i −0.267292 0.462964i
$$335$$ 7.25875 12.5725i 0.396588 0.686910i
$$336$$ 0.866025 + 0.500000i 0.0472456 + 0.0272772i
$$337$$ −27.5456 −1.50050 −0.750251 0.661153i $$-0.770068\pi$$
−0.750251 + 0.661153i $$0.770068\pi$$
$$338$$ 2.00418 + 12.8446i 0.109013 + 0.698653i
$$339$$ 11.2111 0.608906
$$340$$ −7.48701 4.32263i −0.406040 0.234427i
$$341$$ −1.68401 + 2.91678i −0.0911940 + 0.157953i
$$342$$ −0.862708 1.49425i −0.0466499 0.0808000i
$$343$$ 1.00000i 0.0539949i
$$344$$ 2.61681 1.51082i 0.141089 0.0814577i
$$345$$ −8.10529 + 4.67959i −0.436374 + 0.251941i
$$346$$ 8.67525i 0.466384i
$$347$$ −2.62073 4.53924i −0.140688 0.243679i 0.787068 0.616867i $$-0.211598\pi$$
−0.927756 + 0.373187i $$0.878265\pi$$
$$348$$ −1.92531 + 3.33473i −0.103207 + 0.178760i
$$349$$ −4.52901 2.61482i −0.242432 0.139968i 0.373862 0.927484i $$-0.378033\pi$$
−0.616294 + 0.787516i $$0.711367\pi$$
$$350$$ −4.33891 −0.231924
$$351$$ −3.25253 1.55596i −0.173607 0.0830511i
$$352$$ 3.44247 0.183484
$$353$$ 3.26227 + 1.88348i 0.173633 + 0.100247i 0.584298 0.811539i $$-0.301370\pi$$
−0.410665 + 0.911786i $$0.634703\pi$$
$$354$$ 4.98877 8.64080i 0.265150 0.459253i
$$355$$ 5.60686 + 9.71136i 0.297581 + 0.515425i
$$356$$ 7.90307i 0.418862i
$$357$$ −2.44997 + 1.41449i −0.129666 + 0.0748628i
$$358$$ −20.2891 + 11.7139i −1.07231 + 0.619100i
$$359$$ 20.6003i 1.08724i 0.839330 + 0.543622i $$0.182947\pi$$
−0.839330 + 0.543622i $$0.817053\pi$$
$$360$$ −1.52798 2.64654i −0.0805317 0.139485i
$$361$$ −8.01147 + 13.8763i −0.421656 + 0.730330i
$$362$$ 6.63923 + 3.83316i 0.348950 + 0.201466i
$$363$$ 0.850611 0.0446455
$$364$$ 2.03880 + 2.97377i 0.106862 + 0.155868i
$$365$$ 30.9017 1.61747
$$366$$ 9.99843 + 5.77260i 0.522627 + 0.301739i
$$367$$ 13.9579 24.1759i 0.728598 1.26197i −0.228877 0.973455i $$-0.573505\pi$$
0.957476 0.288514i $$-0.0931612\pi$$
$$368$$ 1.53130 + 2.65229i 0.0798245 + 0.138260i
$$369$$ 9.96254i 0.518629i
$$370$$ 14.0084 8.08773i 0.728260 0.420461i
$$371$$ −7.21750 + 4.16702i −0.374714 + 0.216341i
$$372$$ 0.978370i 0.0507261i
$$373$$ −15.7091 27.2090i −0.813388 1.40883i −0.910479 0.413554i $$-0.864287\pi$$
0.0970910 0.995276i $$-0.469046\pi$$
$$374$$ −4.86934 + 8.43395i −0.251788 + 0.436109i
$$375$$ −1.74961 1.01014i −0.0903495 0.0521633i
$$376$$ −8.04447 −0.414862
$$377$$ −11.4508 + 7.85061i −0.589748 + 0.404327i
$$378$$ −1.00000 −0.0514344
$$379$$ −27.5747 15.9203i −1.41642 0.817770i −0.420437 0.907322i $$-0.638123\pi$$
−0.995982 + 0.0895514i $$0.971457\pi$$
$$380$$ 2.63640 4.56638i 0.135245 0.234251i
$$381$$ −2.55753 4.42977i −0.131026 0.226944i
$$382$$ 25.4945i 1.30441i
$$383$$ −4.08962 + 2.36114i −0.208970 + 0.120649i −0.600832 0.799375i $$-0.705164\pi$$
0.391863 + 0.920024i $$0.371831\pi$$
$$384$$ −0.866025 + 0.500000i −0.0441942 + 0.0255155i
$$385$$ 10.5201i 0.536152i
$$386$$ −4.26293 7.38361i −0.216977 0.375816i
$$387$$ −1.51082 + 2.61681i −0.0767990 + 0.133020i
$$388$$ −7.88016 4.54961i −0.400054 0.230972i
$$389$$ −30.5902 −1.55099 −0.775493 0.631356i $$-0.782499\pi$$
−0.775493 + 0.631356i $$0.782499\pi$$
$$390$$ −0.851893 10.9854i −0.0431373 0.556270i
$$391$$ −8.66403 −0.438159
$$392$$ 0.866025 + 0.500000i 0.0437409 + 0.0252538i
$$393$$ −9.38784 + 16.2602i −0.473554 + 0.820219i
$$394$$ 11.8411 + 20.5094i 0.596547 + 1.03325i
$$395$$ 13.7470i 0.691689i
$$396$$ −2.98127 + 1.72124i −0.149814 + 0.0864954i
$$397$$ 10.1133 5.83891i 0.507571 0.293046i −0.224264 0.974529i $$-0.571998\pi$$
0.731835 + 0.681482i $$0.238664\pi$$
$$398$$ 24.8466i 1.24545i
$$399$$ −0.862708 1.49425i −0.0431894 0.0748063i
$$400$$ 2.16945 3.75760i 0.108473 0.187880i
$$401$$ 8.01677 + 4.62849i 0.400339 + 0.231136i 0.686630 0.727007i $$-0.259089\pi$$
−0.286292 + 0.958143i $$0.592423\pi$$
$$402$$ 4.75055 0.236936
$$403$$ 1.52231 3.18218i 0.0758315 0.158516i
$$404$$ 18.8533 0.937985
$$405$$ 2.64654 + 1.52798i 0.131508 + 0.0759260i
$$406$$ −1.92531 + 3.33473i −0.0955513 + 0.165500i
$$407$$ −9.11064 15.7801i −0.451598 0.782190i
$$408$$ 2.82898i 0.140055i
$$409$$ −22.1693 + 12.7994i −1.09620 + 0.632891i −0.935220 0.354066i $$-0.884799\pi$$
−0.160980 + 0.986958i $$0.551465\pi$$
$$410$$ 26.3663 15.2226i 1.30214 0.751789i
$$411$$ 2.66109i 0.131262i
$$412$$ −6.85393 11.8714i −0.337669 0.584860i
$$413$$ 4.98877 8.64080i 0.245481 0.425186i
$$414$$ −2.65229 1.53130i −0.130353 0.0752592i
$$415$$ 21.8767 1.07388
$$416$$ −3.59476 + 0.278764i −0.176248 + 0.0136675i
$$417$$ 16.7064 0.818118
$$418$$ −5.14393 2.96985i −0.251598 0.145260i
$$419$$ −14.1018 + 24.4251i −0.688920 + 1.19324i 0.283268 + 0.959041i $$0.408581\pi$$
−0.972188 + 0.234203i $$0.924752\pi$$
$$420$$ −1.52798 2.64654i −0.0745579 0.129138i
$$421$$ 5.07012i 0.247102i 0.992338 + 0.123551i $$0.0394283\pi$$
−0.992338 + 0.123551i $$0.960572\pi$$
$$422$$ −0.669453 + 0.386509i −0.0325885 + 0.0188150i
$$423$$ 6.96672 4.02224i 0.338733 0.195568i
$$424$$ 8.33405i 0.404737i
$$425$$ 6.13734 + 10.6302i 0.297705 + 0.515640i
$$426$$ −1.83473 + 3.17784i −0.0888928 + 0.153967i
$$427$$ 9.99843 + 5.77260i 0.483858 + 0.279356i
$$428$$ 3.31471 0.160223
$$429$$ −12.3749 + 0.959638i −0.597464 + 0.0463318i
$$430$$ −9.23399 −0.445302
$$431$$ −13.9808 8.07185i −0.673434 0.388807i 0.123943 0.992289i $$-0.460446\pi$$
−0.797376 + 0.603482i $$0.793779\pi$$
$$432$$ 0.500000 0.866025i 0.0240563 0.0416667i
$$433$$ −11.3014 19.5747i −0.543113 0.940699i −0.998723 0.0505195i $$-0.983912\pi$$
0.455610 0.890179i $$-0.349421\pi$$
$$434$$ 0.978370i 0.0469633i
$$435$$ 10.1908 5.88366i 0.488611 0.282100i
$$436$$ −7.51299 + 4.33762i −0.359807 + 0.207735i
$$437$$ 5.28425i 0.252780i
$$438$$ 5.05596 + 8.75718i 0.241583 + 0.418434i
$$439$$ 14.1486 24.5060i 0.675273 1.16961i −0.301115 0.953588i $$-0.597359\pi$$
0.976389 0.216020i $$-0.0693077\pi$$
$$440$$ −9.11064 5.26003i −0.434333 0.250762i
$$441$$ −1.00000 −0.0476190
$$442$$ 4.40179 9.20136i 0.209372 0.437664i
$$443$$ −1.38096 −0.0656112 −0.0328056 0.999462i $$-0.510444\pi$$
−0.0328056 + 0.999462i $$0.510444\pi$$
$$444$$ 4.58394 + 2.64654i 0.217544 + 0.125599i
$$445$$ −12.0757 + 20.9158i −0.572445 + 0.991504i
$$446$$ −10.7677 18.6502i −0.509866 0.883114i
$$447$$ 2.50157i 0.118320i
$$448$$ −0.866025 + 0.500000i −0.0409159 + 0.0236228i
$$449$$ −32.0480 + 18.5029i −1.51244 + 0.873208i −0.512547 + 0.858659i $$0.671298\pi$$
−0.999894 + 0.0145487i $$0.995369\pi$$
$$450$$ 4.33891i 0.204538i
$$451$$ −17.1479 29.7010i −0.807462 1.39856i
$$452$$ −5.60557 + 9.70914i −0.263664 + 0.456679i
$$453$$ −10.9522 6.32323i −0.514578 0.297091i
$$454$$ 17.5444 0.823398
$$455$$ −0.851893 10.9854i −0.0399374 0.515006i
$$456$$ 1.72542 0.0808000
$$457$$ 12.0530 + 6.95878i 0.563813 + 0.325518i 0.754675 0.656099i $$-0.227795\pi$$
−0.190861 + 0.981617i $$0.561128\pi$$
$$458$$ −5.16109 + 8.93928i −0.241162 + 0.417705i
$$459$$ 1.41449 + 2.44997i 0.0660228 + 0.114355i
$$460$$ 9.35918i 0.436374i
$$461$$ 4.19845 2.42397i 0.195541 0.112896i −0.399033 0.916937i $$-0.630654\pi$$
0.594574 + 0.804041i $$0.297321\pi$$
$$462$$ −2.98127 + 1.72124i −0.138701 + 0.0800791i
$$463$$ 24.4377i 1.13571i 0.823127 + 0.567857i $$0.192227\pi$$
−0.823127 + 0.567857i $$0.807773\pi$$
$$464$$ −1.92531 3.33473i −0.0893801 0.154811i
$$465$$ −1.49493 + 2.58930i −0.0693258 + 0.120076i
$$466$$ −15.4404 8.91449i −0.715260 0.412956i
$$467$$ −36.0027 −1.66600 −0.833002 0.553270i $$-0.813380\pi$$
−0.833002 + 0.553270i $$0.813380\pi$$
$$468$$ 2.97377 2.03880i 0.137463 0.0942434i
$$469$$ 4.75055 0.219360
$$470$$ 21.2900 + 12.2918i 0.982035 + 0.566978i
$$471$$ 8.90657 15.4266i 0.410393 0.710822i
$$472$$ 4.98877 + 8.64080i 0.229627 + 0.397725i
$$473$$ 10.4019i 0.478279i
$$474$$ −3.89576 + 2.24922i −0.178938 + 0.103310i
$$475$$ −6.48343 + 3.74321i −0.297480 + 0.171750i
$$476$$ 2.82898i 0.129666i
$$477$$ 4.16702 + 7.21750i 0.190795 + 0.330467i
$$478$$ −2.85636 + 4.94735i −0.130647 + 0.226287i
$$479$$ −8.22108 4.74644i −0.375631 0.216870i 0.300285 0.953850i $$-0.402918\pi$$
−0.675915 + 0.736979i $$0.736252\pi$$
$$480$$ 3.05596 0.139485
$$481$$ 10.7915 + 15.7404i 0.492051 + 0.717701i
$$482$$ 1.00313 0.0456914
$$483$$ −2.65229 1.53130i −0.120683 0.0696765i
$$484$$ −0.425305 + 0.736650i −0.0193321 + 0.0334841i
$$485$$ 13.9034 + 24.0815i 0.631323 + 1.09348i
$$486$$ 1.00000i 0.0453609i
$$487$$ −35.4383 + 20.4603i −1.60586 + 0.927144i −0.615578 + 0.788076i $$0.711078\pi$$
−0.990283 + 0.139069i $$0.955589\pi$$
$$488$$ −9.99843 + 5.77260i −0.452608 + 0.261313i
$$489$$ 8.87831i 0.401491i
$$490$$ −1.52798 2.64654i −0.0690272 0.119559i
$$491$$ −2.55753 + 4.42977i −0.115420 + 0.199913i −0.917947 0.396702i $$-0.870155\pi$$
0.802528 + 0.596615i $$0.203488\pi$$
$$492$$ 8.62781 + 4.98127i 0.388972 + 0.224573i
$$493$$ 10.8933 0.490610
$$494$$ 5.61197 + 2.68468i 0.252495 + 0.120790i
$$495$$ 10.5201 0.472842
$$496$$ 0.847293 + 0.489185i 0.0380446 + 0.0219651i
$$497$$ −1.83473 + 3.17784i −0.0822987 + 0.142546i
$$498$$ 3.57934 + 6.19961i 0.160394 + 0.277811i
$$499$$ 19.5827i 0.876640i 0.898819 + 0.438320i $$0.144426\pi$$
−0.898819 + 0.438320i $$0.855574\pi$$
$$500$$ 1.74961 1.01014i 0.0782450 0.0451747i
$$501$$ −8.46097 + 4.88494i −0.378008 + 0.218243i
$$502$$ 0.672585i 0.0300189i
$$503$$ 14.5429 + 25.1890i 0.648436 + 1.12312i 0.983496 + 0.180928i $$0.0579100\pi$$
−0.335060 + 0.942197i $$0.608757\pi$$
$$504$$ 0.500000 0.866025i 0.0222718 0.0385758i
$$505$$ −49.8960 28.8075i −2.22034 1.28191i
$$506$$ −10.5429 −0.468689
$$507$$ 12.8446 2.00418i 0.570448 0.0890088i
$$508$$ 5.11506 0.226944
$$509$$ −4.52051 2.60992i −0.200368 0.115682i 0.396459 0.918052i $$-0.370239\pi$$
−0.596827 + 0.802370i $$0.703572\pi$$
$$510$$ −4.32263 + 7.48701i −0.191409 + 0.331531i
$$511$$ 5.05596 + 8.75718i 0.223663 + 0.387395i
$$512$$ 1.00000i 0.0441942i
$$513$$ −1.49425 + 0.862708i −0.0659729 + 0.0380895i
$$514$$ 21.0820 12.1717i 0.929885 0.536870i
$$515$$ 41.8907i 1.84592i
$$516$$ −1.51082 2.61681i −0.0665099 0.115199i
$$517$$ 13.8464 23.9827i 0.608965 1.05476i
$$518$$ 4.58394 + 2.64654i 0.201407 + 0.116282i
$$519$$ 8.67525 0.380801
$$520$$ 9.93962 + 4.75496i 0.435881 + 0.208519i
$$521$$ −14.5259 −0.636389 −0.318195 0.948025i $$-0.603077\pi$$
−0.318195 + 0.948025i $$0.603077\pi$$
$$522$$ 3.33473 + 1.92531i 0.145957 + 0.0842683i
$$523$$ −13.9367 + 24.1391i −0.609410 + 1.05553i 0.381927 + 0.924192i $$0.375260\pi$$
−0.991338 + 0.131337i $$0.958073\pi$$
$$524$$ −9.38784 16.2602i −0.410110 0.710331i
$$525$$ 4.33891i 0.189365i
$$526$$ 14.8029 8.54648i 0.645439 0.372644i
$$527$$ −2.39698 + 1.38389i −0.104414 + 0.0602834i
$$528$$ 3.44247i 0.149814i
$$529$$ 6.81025 + 11.7957i 0.296098 + 0.512856i
$$530$$ −12.7343 + 22.0564i −0.553141 + 0.958069i
$$531$$ −8.64080 4.98877i −0.374979 0.216494i
$$532$$ 1.72542 0.0748063
$$533$$ 20.3116 + 29.6263i 0.879792 + 1.28326i
$$534$$ −7.90307 −0.341999
$$535$$ −8.77252 5.06482i −0.379269 0.218971i
$$536$$ −2.37527 + 4.11410i −0.102596 + 0.177702i
$$537$$ 11.7139 + 20.2891i 0.505493 + 0.875540i
$$538$$ 26.6594i 1.14937i
$$539$$ −2.98127 + 1.72124i −0.128412 + 0.0741389i
$$540$$ −2.64654 + 1.52798i −0.113889 + 0.0657538i
$$541$$ 1.42341i 0.0611970i −0.999532 0.0305985i $$-0.990259\pi$$
0.999532 0.0305985i $$-0.00974133\pi$$
$$542$$ 12.2247 + 21.1739i 0.525097 + 0.909496i
$$543$$ 3.83316 6.63923i 0.164497 0.284917i
$$544$$ 2.44997 + 1.41449i 0.105042 + 0.0606458i
$$545$$ 26.5112 1.13562
$$546$$ 2.97377 2.03880i 0.127266 0.0872524i
$$547$$ −9.33008 −0.398925 −0.199463 0.979905i $$-0.563920\pi$$
−0.199463 + 0.979905i $$0.563920\pi$$
$$548$$ 2.30457 + 1.33055i 0.0984465 + 0.0568381i
$$549$$ 5.77260 9.99843i 0.246369 0.426723i
$$550$$ 7.46828 + 12.9354i 0.318449 + 0.551569i
$$551$$ 6.64390i 0.283040i
$$552$$ 2.65229 1.53130i 0.112889 0.0651764i
$$553$$ −3.89576 + 2.24922i −0.165664 + 0.0956464i
$$554$$ 28.4812i 1.21005i
$$555$$ −8.08773 14.0084i −0.343305 0.594622i
$$556$$ −8.35322 + 14.4682i −0.354256 + 0.613589i
$$557$$ 9.34071 + 5.39286i 0.395779 + 0.228503i 0.684661 0.728862i $$-0.259950\pi$$
−0.288882 + 0.957365i $$0.593284\pi$$
$$558$$ −0.978370 −0.0414177
$$559$$ −0.842322 10.8620i −0.0356264 0.459415i
$$560$$ 3.05596 0.129138
$$561$$ 8.43395 + 4.86934i 0.356082 + 0.205584i
$$562$$ −4.88016 + 8.45268i −0.205857 + 0.356555i
$$563$$ 12.7541 + 22.0908i 0.537522 + 0.931016i 0.999037 + 0.0438831i $$0.0139729\pi$$
−0.461514 + 0.887133i $$0.652694\pi$$
$$564$$ 8.04447i 0.338733i
$$565$$ 29.6708 17.1304i 1.24826 0.720682i
$$566$$ 10.1076 5.83562i 0.424853 0.245289i
$$567$$ 1.00000i 0.0419961i
$$568$$ −1.83473 3.17784i −0.0769834 0.133339i
$$569$$ −4.10835 + 7.11587i −0.172231 + 0.298313i −0.939200 0.343372i $$-0.888431\pi$$
0.766969 + 0.641685i $$0.221764\pi$$
$$570$$ −4.56638 2.63640i −0.191265 0.110427i
$$571$$ 2.70500 0.113201 0.0566003 0.998397i $$-0.481974\pi$$
0.0566003 + 0.998397i $$0.481974\pi$$
$$572$$ 5.35636 11.1968i 0.223961 0.468160i
$$573$$ −25.4945 −1.06505
$$574$$ 8.62781 + 4.98127i 0.360118 + 0.207914i
$$575$$ −6.64416 + 11.5080i −0.277081 + 0.479918i
$$576$$ 0.500000 + 0.866025i 0.0208333 + 0.0360844i
$$577$$ 21.4253i 0.891946i 0.895046 + 0.445973i $$0.147142\pi$$
−0.895046 + 0.445973i $$0.852858\pi$$
$$578$$ 7.79152 4.49843i 0.324084 0.187110i
$$579$$ −7.38361 + 4.26293i −0.306852 + 0.177161i
$$580$$ 11.7673i 0.488611i
$$581$$ 3.57934 + 6.19961i 0.148496 + 0.257203i
$$582$$ −4.54961 + 7.88016i −0.188587 + 0.326643i
$$583$$ 24.8460 + 14.3449i 1.02902 + 0.594104i
$$584$$ −10.1119 −0.418434
$$585$$ −10.9854 + 0.851893i −0.454192 + 0.0352214i
$$586$$ 21.8202 0.901382
$$587$$ −4.96515 2.86663i −0.204934 0.118319i 0.394021 0.919101i $$-0.371084\pi$$
−0.598955 + 0.800783i $$0.704417\pi$$
$$588$$ 0.500000 0.866025i 0.0206197 0.0357143i
$$589$$ −0.844048 1.46193i −0.0347784 0.0602379i
$$590$$ 30.4910i 1.25529i
$$591$$ 20.5094 11.8411i 0.843645 0.487079i
$$592$$ −4.58394 + 2.64654i −0.188399 + 0.108772i
$$593$$ 17.3442i 0.712240i −0.934440 0.356120i $$-0.884099\pi$$
0.934440 0.356120i $$-0.115901\pi$$
$$594$$ 1.72124 + 2.98127i 0.0706232 + 0.122323i
$$595$$ −4.32263 + 7.48701i −0.177211 + 0.306938i
$$596$$ 2.16642 + 1.25078i 0.0887400 + 0.0512341i
$$597$$ −24.8466 −1.01691
$$598$$ 11.0093 0.853743i 0.450204 0.0349121i
$$599$$ −31.5835 −1.29047 −0.645234 0.763985i $$-0.723240\pi$$
−0.645234 + 0.763985i $$0.723240\pi$$
$$600$$ −3.75760 2.16945i −0.153404 0.0885676i
$$601$$ −12.4478 + 21.5603i −0.507757 + 0.879462i 0.492202 + 0.870481i $$0.336192\pi$$
−0.999960 + 0.00898069i $$0.997141\pi$$
$$602$$ −1.51082 2.61681i −0.0615762 0.106653i
$$603$$ 4.75055i 0.193457i
$$604$$ 10.9522 6.32323i 0.445637 0.257289i
$$605$$ 2.25118 1.29972i 0.0915233 0.0528410i
$$606$$ 18.8533i 0.765862i
$$607$$ −7.62951 13.2147i −0.309672 0.536368i 0.668618 0.743606i $$-0.266886\pi$$
−0.978291 + 0.207238i $$0.933553\pi$$
$$608$$ −0.862708 + 1.49425i −0.0349874 + 0.0606000i
$$609$$ 3.33473 + 1.92531i 0.135130 + 0.0780173i
$$610$$ 35.2817 1.42851
$$611$$ −12.5169 + 26.1649i −0.506379 + 1.05852i
$$612$$ −2.82898 −0.114355
$$613$$ −39.6220 22.8757i −1.60032 0.923943i −0.991423 0.130690i $$-0.958281\pi$$
−0.608892 0.793253i $$-0.708386\pi$$
$$614$$ 2.43523 4.21794i 0.0982779 0.170222i
$$615$$ −15.2226 26.3663i −0.613833 1.06319i
$$616$$ 3.44247i 0.138701i
$$617$$ 36.6167 21.1406i 1.47413 0.851090i 0.474555 0.880226i $$-0.342609\pi$$
0.999575 + 0.0291358i $$0.00927553\pi$$
$$618$$ −11.8714 + 6.85393i −0.477536 + 0.275705i
$$619$$ 22.0261i 0.885303i 0.896694 + 0.442651i $$0.145962\pi$$
−0.896694 + 0.442651i $$0.854038\pi$$
$$620$$ −1.49493 2.58930i −0.0600379 0.103989i
$$621$$ −1.53130 + 2.65229i −0.0614489 + 0.106433i
$$622$$ −3.38048 1.95172i −0.135545 0.0782569i
$$623$$ −7.90307 −0.316630
$$624$$ 0.278764 + 3.59476i 0.0111595 + 0.143906i
$$625$$ −27.8684 −1.11474
$$626$$ 22.5624 + 13.0264i 0.901775 + 0.520640i
$$627$$ −2.96985 + 5.14393i −0.118604 + 0.205429i
$$628$$ 8.90657 + 15.4266i 0.355411 + 0.615590i
$$629$$ 14.9740i 0.597054i
$$630$$ −2.64654 + 1.52798i −0.105441 + 0.0608762i
$$631$$ 18.0721 10.4339i 0.719440 0.415369i −0.0951064 0.995467i $$-0.530319\pi$$
0.814547 + 0.580098i $$0.196986\pi$$
$$632$$ 4.49843i 0.178938i
$$633$$ 0.386509 + 0.669453i 0.0153624 + 0.0266084i
$$634$$ −5.55536 + 9.62216i −0.220631 + 0.382145i
$$635$$ −13.5372 7.81571i −0.537208 0.310157i
$$636$$ −8.33405 −0.330467
$$637$$ 2.97377 2.03880i 0.117825 0.0807800i
$$638$$ 13.2556 0.524795
$$639$$ 3.17784 + 1.83473i 0.125713 + 0.0725807i
$$640$$ −1.52798 + 2.64654i −0.0603988 + 0.104614i
$$641$$ −10.4526 18.1045i −0.412853 0.715083i 0.582347 0.812940i $$-0.302134\pi$$
−0.995200 + 0.0978574i $$0.968801\pi$$
$$642$$ 3.31471i 0.130821i
$$643$$ 33.8703 19.5550i 1.33571 0.771174i 0.349544 0.936920i $$-0.386337\pi$$
0.986168 + 0.165746i $$0.0530032\pi$$
$$644$$ 2.65229 1.53130i 0.104515 0.0603416i
$$645$$ 9.23399i 0.363588i
$$646$$ −2.44058 4.22722i −0.0960235 0.166318i
$$647$$ −3.96755 + 6.87201i −0.155981 + 0.270166i −0.933416 0.358797i $$-0.883187\pi$$
0.777435 + 0.628963i $$0.216520\pi$$
$$648$$ −0.866025 0.500000i −0.0340207 0.0196419i
$$649$$ −34.3474 −1.34825
$$650$$ −8.84615 12.9029i −0.346974 0.506094i
$$651$$ −0.978370 −0.0383453
$$652$$ −7.68884 4.43915i −0.301118 0.173851i
$$653$$ −21.3998 + 37.0655i −0.837439 + 1.45049i 0.0545901 + 0.998509i $$0.482615\pi$$
−0.892029 + 0.451978i $$0.850719\pi$$
$$654$$ 4.33762 + 7.51299i 0.169615 + 0.293781i
$$655$$ 57.3778i 2.24194i
$$656$$ −8.62781 + 4.98127i −0.336859 + 0.194486i
$$657$$ 8.75718 5.05596i 0.341650 0.197252i
$$658$$ 8.04447i 0.313606i
$$659$$ −0.364274 0.630941i −0.0141901 0.0245780i 0.858843 0.512239i $$-0.171184\pi$$
−0.873033 + 0.487661i $$0.837850\pi$$
$$660$$ −5.26003 + 9.11064i −0.204746 + 0.354631i
$$661$$ −2.04352 1.17983i −0.0794836 0.0458899i 0.459731 0.888058i $$-0.347946\pi$$
−0.539215 + 0.842168i $$0.681279\pi$$
$$662$$ 14.6478 0.569304
$$663$$ −9.20136 4.40179i −0.357351 0.170951i
$$664$$ −7.15869 −0.277811
$$665$$ −4.56638 2.63640i −0.177077 0.102235i
$$666$$ 2.64654 4.58394i 0.102551 0.177624i
$$667$$ 5.89644 + 10.2129i 0.228311 + 0.395446i
$$668$$ 9.76989i 0.378008i
$$669$$ −18.6502 + 10.7677i −0.721060 + 0.416304i
$$670$$ 12.5725 7.25875i 0.485719 0.280430i
$$671$$ 39.7440i 1.53430i
$$672$$ 0.500000 + 0.866025i 0.0192879 + 0.0334077i
$$673$$ 15.6279 27.0682i 0.602410 1.04340i −0.390045 0.920796i $$-0.627541\pi$$
0.992455 0.122609i $$-0.0391260\pi$$
$$674$$ −23.8552 13.7728i −0.918867 0.530508i
$$675$$ 4.33891 0.167005
$$676$$ −4.68662 + 12.1258i −0.180255 + 0.466378i
$$677$$ −41.7294 −1.60379 −0.801895 0.597464i $$-0.796175\pi$$
−0.801895 + 0.597464i $$0.796175\pi$$
$$678$$ 9.70914 + 5.60557i 0.372877 + 0.215281i
$$679$$ −4.54961 + 7.88016i −0.174598 + 0.302413i
$$680$$ −4.32263 7.48701i −0.165765 0.287114i
$$681$$ 17.5444i 0.672301i
$$682$$ −2.91678 + 1.68401i −0.111689 + 0.0644839i
$$683$$ −7.98473 + 4.60999i −0.305527 + 0.176396i −0.644923 0.764247i $$-0.723111\pi$$
0.339396 + 0.940644i $$0.389777\pi$$
$$684$$ 1.72542i 0.0659729i
$$685$$ −4.06610 7.04269i −0.155358 0.269087i
$$686$$ 0.500000 0.866025i 0.0190901 0.0330650i
$$687$$ 8.93928 + 5.16109i 0.341055 + 0.196908i
$$688$$ 3.02163 0.115199
$$689$$ −27.1068 12.9675i −1.03269 0.494021i
$$690$$ −9.35918 −0.356298
$$691$$ −7.97487 4.60429i −0.303378 0.175156i 0.340581 0.940215i $$-0.389376\pi$$
−0.643960 + 0.765060i $$0.722709\pi$$
$$692$$ −4.33762 + 7.51299i −0.164892 + 0.285601i
$$693$$ 1.72124 + 2.98127i 0.0653843 + 0.113249i
$$694$$ 5.24146i 0.198963i
$$695$$ 44.2143 25.5271i 1.67714 0.968300i
$$696$$ −3.33473 + 1.92531i −0.126402 + 0.0729785i
$$697$$ 28.1838i 1.06754i
$$698$$ −2.61482 4.52901i −0.0989725 0.171425i
$$699$$ −8.91449 + 15.4404i −0.337177 + 0.584008i
$$700$$ −3.75760 2.16945i −0.142024 0.0819976i
$$701$$ 20.8683 0.788184 0.394092 0.919071i $$-0.371059\pi$$
0.394092 + 0.919071i $$0.371059\pi$$
$$702$$ −2.03880 2.97377i −0.0769494 0.112238i
$$703$$ 9.13277 0.344449
$$704$$ 2.98127 + 1.72124i 0.112361 + 0.0648715i
$$705$$ 12.2918 21.2900i 0.462936 0.801829i
$$706$$ 1.88348 + 3.26227i 0.0708855 + 0.122777i
$$707$$ 18.8533i 0.709050i
$$708$$ 8.64080 4.98877i 0.324741 0.187489i
$$709$$ −12.8731 + 7.43226i −0.483458 + 0.279124i −0.721856 0.692043i $$-0.756711\pi$$
0.238399 + 0.971167i $$0.423378\pi$$
$$710$$ 11.2137i 0.420843i
$$711$$ 2.24922 + 3.89576i 0.0843522 + 0.146102i
$$712$$ 3.95154 6.84426i 0.148090 0.256499i
$$713$$ −2.59492 1.49818i −0.0971804 0.0561072i
$$714$$ −2.82898 −0.105872
$$715$$ −31.2843 + 21.4483i −1.16996 + 0.802120i
$$716$$ −23.4278 −0.875540
$$717$$ 4.94735 + 2.85636i 0.184762 + 0.106673i
$$718$$ −10.3002 + 17.8404i −0.384399 + 0.665798i
$$719$$ −12.8265 22.2162i −0.478349 0.828524i 0.521343 0.853347i $$-0.325431\pi$$
−0.999692 + 0.0248229i $$0.992098\pi$$
$$720$$ 3.05596i 0.113889i
$$721$$ −11.8714 + 6.85393i −0.442112 + 0.255254i
$$722$$ −13.8763 + 8.01147i −0.516421 + 0.298156i
$$723$$ 1.00313i 0.0373069i
$$724$$ 3.83316 + 6.63923i 0.142458 + 0.246745i
$$725$$ 8.35372 14.4691i 0.310249 0.537368i
$$726$$ 0.736650 + 0.425305i 0.0273397 + 0.0157846i
$$727$$ 41.6568 1.54497 0.772483 0.635036i $$-0.219015\pi$$
0.772483 + 0.635036i $$0.219015\pi$$
$$728$$ 0.278764 + 3.59476i 0.0103317 + 0.133231i
$$729$$ 1.00000 0.0370370
$$730$$ 26.7616 + 15.4508i 0.990492 + 0.571861i
$$731$$ −4.27407 + 7.40290i −0.158082 + 0.273806i
$$732$$ 5.77260 + 9.99843i 0.213361 + 0.369553i
$$733$$ 26.4965i 0.978671i −0.872096 0.489336i $$-0.837239\pi$$
0.872096 0.489336i $$-0.162761\pi$$
$$734$$ 24.1759 13.9579i 0.892347 0.515197i
$$735$$ −2.64654 + 1.52798i −0.0976191 + 0.0563604i
$$736$$ 3.06260i 0.112889i
$$737$$ −8.17682 14.1627i −0.301197 0.521688i
$$738$$ 4.98127 8.62781i 0.183363 0.317594i
$$739$$ 18.1009 + 10.4506i 0.665853 + 0.384431i 0.794504 0.607259i $$-0.207731\pi$$
−0.128650 + 0.991690i $$0.541064\pi$$
$$740$$ 16.1755 0.594622
$$741$$ 2.68468 5.61197i 0.0986243 0.206161i
$$742$$ −8.33405 −0.305953
$$743$$ 4.88999 + 2.82323i 0.179396 + 0.103574i 0.587009 0.809580i $$-0.300305\pi$$
−0.407613 + 0.913155i $$0.633639\pi$$
$$744$$ 0.489185 0.847293i 0.0179344 0.0310633i
$$745$$ −3.82235 6.62050i −0.140040 0.242556i
$$746$$ 31.4183i 1.15030i
$$747$$ 6.19961 3.57934i 0.226832 0.130961i
$$748$$ −8.43395 + 4.86934i −0.308376 + 0.178041i
$$749$$ 3.31471i 0.121117i
$$750$$ −1.01014 1.74961i −0.0368850 0.0638867i
$$751$$ 7.70439 13.3444i 0.281137 0.486944i −0.690528 0.723306i $$-0.742622\pi$$
0.971665 + 0.236362i $$0.0759551\pi$$
$$752$$ −6.96672 4.02224i −0.254050 0.146676i
$$753$$ −0.672585 −0.0245104
$$754$$ −13.8420 + 1.07341i −0.504097 + 0.0390914i
$$755$$ −38.6471 −1.40651
$$756$$ −0.866025 0.500000i −0.0314970 0.0181848i
$$757$$ 17.7686 30.7761i 0.645811 1.11858i −0.338303 0.941037i $$-0.609853\pi$$
0.984114 0.177540i $$-0.0568139\pi$$
$$758$$ −15.9203 27.5747i −0.578251 1.00156i
$$759$$ 10.5429i 0.382683i
$$760$$ 4.56638 2.63640i 0.165640 0.0956324i
$$761$$ 36.2213 20.9124i 1.31302 0.758073i 0.330425 0.943832i $$-0.392808\pi$$
0.982595 + 0.185759i $$0.0594745\pi$$
$$762$$ 5.11506i 0.185299i
$$763$$ 4.33762 + 7.51299i 0.157033 + 0.271988i
$$764$$ 12.7472 22.0789i 0.461179 0.798785i
$$765$$ 7.48701 + 4.32263i 0.270694 + 0.156285i
$$766$$ −4.72228 −0.170623
$$767$$ 35.8668 2.78138i 1.29508 0.100430i
$$768$$ −1.00000 −0.0360844
$$769$$ 15.4609 + 8.92635i 0.557534 + 0.321893i 0.752155 0.658986i $$-0.229014\pi$$
−0.194621 + 0.980879i $$0.562348\pi$$
$$770$$ −5.26003 + 9.11064i −0.189558 + 0.328325i
$$771$$ −12.1717 21.0820i −0.438352 0.759248i
$$772$$ 8.52586i 0.306852i
$$773$$ 10.4892 6.05596i 0.377272 0.217818i −0.299359 0.954141i $$-0.596773\pi$$
0.676630 + 0.736323i $$0.263439\pi$$
$$774$$ −2.61681 + 1.51082i −0.0940592 + 0.0543051i
$$775$$ 4.24506i 0.152487i
$$776$$ −4.54961