# Properties

 Label 189.2.h.a.37.1 Level $189$ Weight $2$ Character 189.37 Analytic conductor $1.509$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.h (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.50917259820$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 37.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 189.37 Dual form 189.2.h.a.46.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(-0.500000 - 0.866025i) q^{29} -5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.00000 + 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-2.50000 + 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(6.00000 + 5.19615i) q^{56} +(0.500000 + 0.866025i) q^{58} -14.0000 q^{61} +7.00000 q^{64} -5.00000 q^{65} +4.00000 q^{67} +(-1.50000 - 2.59808i) q^{68} +(-0.500000 + 2.59808i) q^{70} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.50000 - 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{76} +(12.5000 - 4.33013i) q^{77} +8.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(2.50000 - 4.33013i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{88} +(-6.50000 + 11.2583i) q^{89} +(12.5000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +1.00000 q^{95} +(4.50000 + 7.79423i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 2q^{2} - 2q^{4} - q^{5} + 4q^{7} + 6q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 2q^{4} - q^{5} + 4q^{7} + 6q^{8} + q^{10} + 5q^{11} + 5q^{13} - 4q^{14} - 2q^{16} + 3q^{17} - q^{19} + q^{20} - 5q^{22} + 3q^{23} + 4q^{25} - 5q^{26} - 4q^{28} - q^{29} - 10q^{32} - 3q^{34} + q^{35} - 3q^{37} + q^{38} - 3q^{40} - 5q^{41} + q^{43} - 5q^{44} - 3q^{46} + 2q^{49} - 4q^{50} - 5q^{52} - 9q^{53} - 10q^{55} + 12q^{56} + q^{58} - 28q^{61} + 14q^{64} - 10q^{65} + 8q^{67} - 3q^{68} - q^{70} + 24q^{71} - 3q^{73} + 3q^{74} + q^{76} + 25q^{77} + 16q^{79} + q^{80} + 5q^{82} - 9q^{83} + 3q^{85} - q^{86} + 15q^{88} - 13q^{89} + 25q^{91} - 3q^{92} + 2q^{95} + 9q^{97} - 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$136$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107 −0.353553 0.935414i $$-0.615027\pi$$
−0.353553 + 0.935414i $$0.615027\pi$$
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i $$-0.238450\pi$$
−0.955901 + 0.293691i $$0.905116\pi$$
$$6$$ 0 0
$$7$$ 2.00000 + 1.73205i 0.755929 + 0.654654i
$$8$$ 3.00000 1.06066
$$9$$ 0 0
$$10$$ 0.500000 + 0.866025i 0.158114 + 0.273861i
$$11$$ 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i $$-0.561563\pi$$
0.945979 0.324227i $$-0.105104\pi$$
$$12$$ 0 0
$$13$$ 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i $$-0.589456\pi$$
0.970725 0.240192i $$-0.0772105\pi$$
$$14$$ −2.00000 1.73205i −0.534522 0.462910i
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i $$-0.0481447\pi$$
−0.624780 + 0.780801i $$0.714811\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0.500000 + 0.866025i 0.111803 + 0.193649i
$$21$$ 0 0
$$22$$ −2.50000 + 4.33013i −0.533002 + 0.923186i
$$23$$ 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i $$-0.0654092\pi$$
−0.666190 + 0.745782i $$0.732076\pi$$
$$24$$ 0 0
$$25$$ 2.00000 3.46410i 0.400000 0.692820i
$$26$$ −2.50000 + 4.33013i −0.490290 + 0.849208i
$$27$$ 0 0
$$28$$ −2.00000 1.73205i −0.377964 0.327327i
$$29$$ −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i $$-0.196264\pi$$
−0.908708 + 0.417432i $$0.862930\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −5.00000 −0.883883
$$33$$ 0 0
$$34$$ −1.50000 2.59808i −0.257248 0.445566i
$$35$$ 0.500000 2.59808i 0.0845154 0.439155i
$$36$$ 0 0
$$37$$ −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i $$-0.912646\pi$$
0.715981 + 0.698119i $$0.245980\pi$$
$$38$$ 0.500000 0.866025i 0.0811107 0.140488i
$$39$$ 0 0
$$40$$ −1.50000 2.59808i −0.237171 0.410792i
$$41$$ −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i $$-0.961009\pi$$
0.602072 + 0.798441i $$0.294342\pi$$
$$42$$ 0 0
$$43$$ 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i $$-0.142372\pi$$
−0.825380 + 0.564578i $$0.809039\pi$$
$$44$$ −2.50000 + 4.33013i −0.376889 + 0.652791i
$$45$$ 0 0
$$46$$ −1.50000 2.59808i −0.221163 0.383065i
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ −2.00000 + 3.46410i −0.282843 + 0.489898i
$$51$$ 0 0
$$52$$ −2.50000 + 4.33013i −0.346688 + 0.600481i
$$53$$ −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i $$-0.954560\pi$$
0.371706 0.928351i $$-0.378773\pi$$
$$54$$ 0 0
$$55$$ −5.00000 −0.674200
$$56$$ 6.00000 + 5.19615i 0.801784 + 0.694365i
$$57$$ 0 0
$$58$$ 0.500000 + 0.866025i 0.0656532 + 0.113715i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ −14.0000 −1.79252 −0.896258 0.443533i $$-0.853725\pi$$
−0.896258 + 0.443533i $$0.853725\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ −5.00000 −0.620174
$$66$$ 0 0
$$67$$ 4.00000 0.488678 0.244339 0.969690i $$-0.421429\pi$$
0.244339 + 0.969690i $$0.421429\pi$$
$$68$$ −1.50000 2.59808i −0.181902 0.315063i
$$69$$ 0 0
$$70$$ −0.500000 + 2.59808i −0.0597614 + 0.310530i
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i $$-0.222841\pi$$
−0.940356 + 0.340193i $$0.889507\pi$$
$$74$$ 1.50000 2.59808i 0.174371 0.302020i
$$75$$ 0 0
$$76$$ 0.500000 0.866025i 0.0573539 0.0993399i
$$77$$ 12.5000 4.33013i 1.42451 0.493464i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0.500000 + 0.866025i 0.0559017 + 0.0968246i
$$81$$ 0 0
$$82$$ 2.50000 4.33013i 0.276079 0.478183i
$$83$$ −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i $$-0.331110\pi$$
−0.999976 + 0.00698436i $$0.997777\pi$$
$$84$$ 0 0
$$85$$ 1.50000 2.59808i 0.162698 0.281801i
$$86$$ −0.500000 0.866025i −0.0539164 0.0933859i
$$87$$ 0 0
$$88$$ 7.50000 12.9904i 0.799503 1.38478i
$$89$$ −6.50000 + 11.2583i −0.688999 + 1.19338i 0.283164 + 0.959072i $$0.408616\pi$$
−0.972162 + 0.234309i $$0.924717\pi$$
$$90$$ 0 0
$$91$$ 12.5000 4.33013i 1.31036 0.453921i
$$92$$ −1.50000 2.59808i −0.156386 0.270868i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 1.00000 0.102598
$$96$$ 0 0
$$97$$ 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i $$-0.0156243\pi$$
−0.541890 + 0.840450i $$0.682291\pi$$
$$98$$ −1.00000 6.92820i −0.101015 0.699854i
$$99$$ 0 0
$$100$$ −2.00000 + 3.46410i −0.200000 + 0.346410i
$$101$$ −8.50000 + 14.7224i −0.845782 + 1.46494i 0.0391591 + 0.999233i $$0.487532\pi$$
−0.884941 + 0.465704i $$0.845801\pi$$
$$102$$ 0 0
$$103$$ 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i $$-0.150978\pi$$
−0.840341 + 0.542059i $$0.817645\pi$$
$$104$$ 7.50000 12.9904i 0.735436 1.27381i
$$105$$ 0 0
$$106$$ 4.50000 + 7.79423i 0.437079 + 0.757042i
$$107$$ 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i $$-0.526345\pi$$
0.904396 0.426694i $$-0.140322\pi$$
$$108$$ 0 0
$$109$$ 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i $$-0.0248199\pi$$
−0.565940 + 0.824447i $$0.691487\pi$$
$$110$$ 5.00000 0.476731
$$111$$ 0 0
$$112$$ −2.00000 1.73205i −0.188982 0.163663i
$$113$$ −0.500000 + 0.866025i −0.0470360 + 0.0814688i −0.888585 0.458712i $$-0.848311\pi$$
0.841549 + 0.540181i $$0.181644\pi$$
$$114$$ 0 0
$$115$$ 1.50000 2.59808i 0.139876 0.242272i
$$116$$ 0.500000 + 0.866025i 0.0464238 + 0.0804084i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −1.50000 + 7.79423i −0.137505 + 0.714496i
$$120$$ 0 0
$$121$$ −7.00000 12.1244i −0.636364 1.10221i
$$122$$ 14.0000 1.26750
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.00000 −0.804984
$$126$$ 0 0
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ 3.00000 0.265165
$$129$$ 0 0
$$130$$ 5.00000 0.438529
$$131$$ −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i $$-0.180577\pi$$
−0.887041 + 0.461690i $$0.847243\pi$$
$$132$$ 0 0
$$133$$ −2.50000 + 0.866025i −0.216777 + 0.0750939i
$$134$$ −4.00000 −0.345547
$$135$$ 0 0
$$136$$ 4.50000 + 7.79423i 0.385872 + 0.668350i
$$137$$ −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i $$-0.958946\pi$$
0.607233 + 0.794524i $$0.292279\pi$$
$$138$$ 0 0
$$139$$ −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i $$-0.957989\pi$$
0.609618 + 0.792695i $$0.291323\pi$$
$$140$$ −0.500000 + 2.59808i −0.0422577 + 0.219578i
$$141$$ 0 0
$$142$$ −12.0000 −1.00702
$$143$$ −12.5000 21.6506i −1.04530 1.81052i
$$144$$ 0 0
$$145$$ −0.500000 + 0.866025i −0.0415227 + 0.0719195i
$$146$$ 1.50000 + 2.59808i 0.124141 + 0.215018i
$$147$$ 0 0
$$148$$ 1.50000 2.59808i 0.123299 0.213561i
$$149$$ 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i $$-0.127452\pi$$
−0.798019 + 0.602632i $$0.794119\pi$$
$$150$$ 0 0
$$151$$ −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i $$-0.898548\pi$$
0.746190 + 0.665733i $$0.231881\pi$$
$$152$$ −1.50000 + 2.59808i −0.121666 + 0.210732i
$$153$$ 0 0
$$154$$ −12.5000 + 4.33013i −1.00728 + 0.348932i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −14.0000 −1.11732 −0.558661 0.829396i $$-0.688685\pi$$
−0.558661 + 0.829396i $$0.688685\pi$$
$$158$$ −8.00000 −0.636446
$$159$$ 0 0
$$160$$ 2.50000 + 4.33013i 0.197642 + 0.342327i
$$161$$ −1.50000 + 7.79423i −0.118217 + 0.614271i
$$162$$ 0 0
$$163$$ 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i $$-0.691567\pi$$
0.996942 + 0.0781474i $$0.0249005\pi$$
$$164$$ 2.50000 4.33013i 0.195217 0.338126i
$$165$$ 0 0
$$166$$ 4.50000 + 7.79423i 0.349268 + 0.604949i
$$167$$ −9.50000 + 16.4545i −0.735132 + 1.27329i 0.219533 + 0.975605i $$0.429547\pi$$
−0.954665 + 0.297681i $$0.903787\pi$$
$$168$$ 0 0
$$169$$ −6.00000 10.3923i −0.461538 0.799408i
$$170$$ −1.50000 + 2.59808i −0.115045 + 0.199263i
$$171$$ 0 0
$$172$$ −0.500000 0.866025i −0.0381246 0.0660338i
$$173$$ 14.0000 1.06440 0.532200 0.846619i $$-0.321365\pi$$
0.532200 + 0.846619i $$0.321365\pi$$
$$174$$ 0 0
$$175$$ 10.0000 3.46410i 0.755929 0.261861i
$$176$$ −2.50000 + 4.33013i −0.188445 + 0.326396i
$$177$$ 0 0
$$178$$ 6.50000 11.2583i 0.487196 0.843848i
$$179$$ 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i $$0.0846670\pi$$
−0.254770 + 0.967002i $$0.582000\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ −12.5000 + 4.33013i −0.926562 + 0.320970i
$$183$$ 0 0
$$184$$ 4.50000 + 7.79423i 0.331744 + 0.574598i
$$185$$ 3.00000 0.220564
$$186$$ 0 0
$$187$$ 15.0000 1.09691
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −1.00000 −0.0725476
$$191$$ −8.00000 −0.578860 −0.289430 0.957199i $$-0.593466\pi$$
−0.289430 + 0.957199i $$0.593466\pi$$
$$192$$ 0 0
$$193$$ −10.0000 −0.719816 −0.359908 0.932988i $$-0.617192\pi$$
−0.359908 + 0.932988i $$0.617192\pi$$
$$194$$ −4.50000 7.79423i −0.323081 0.559593i
$$195$$ 0 0
$$196$$ −1.00000 6.92820i −0.0714286 0.494872i
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ −1.50000 2.59808i −0.106332 0.184173i 0.807950 0.589252i $$-0.200577\pi$$
−0.914282 + 0.405079i $$0.867244\pi$$
$$200$$ 6.00000 10.3923i 0.424264 0.734847i
$$201$$ 0 0
$$202$$ 8.50000 14.7224i 0.598058 1.03587i
$$203$$ 0.500000 2.59808i 0.0350931 0.182349i
$$204$$ 0 0
$$205$$ 5.00000 0.349215
$$206$$ −0.500000 0.866025i −0.0348367 0.0603388i
$$207$$ 0 0
$$208$$ −2.50000 + 4.33013i −0.173344 + 0.300240i
$$209$$ 2.50000 + 4.33013i 0.172929 + 0.299521i
$$210$$ 0 0
$$211$$ −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i $$-0.981011\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ 4.50000 + 7.79423i 0.309061 + 0.535310i
$$213$$ 0 0
$$214$$ −8.50000 + 14.7224i −0.581048 + 1.00640i
$$215$$ 0.500000 0.866025i 0.0340997 0.0590624i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −4.50000 7.79423i −0.304778 0.527892i
$$219$$ 0 0
$$220$$ 5.00000 0.337100
$$221$$ 15.0000 1.00901
$$222$$ 0 0
$$223$$ −9.50000 16.4545i −0.636167 1.10187i −0.986267 0.165161i $$-0.947186\pi$$
0.350100 0.936713i $$-0.386148\pi$$
$$224$$ −10.0000 8.66025i −0.668153 0.578638i
$$225$$ 0 0
$$226$$ 0.500000 0.866025i 0.0332595 0.0576072i
$$227$$ −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i $$-0.865076\pi$$
0.811943 + 0.583736i $$0.198410\pi$$
$$228$$ 0 0
$$229$$ 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i $$-0.156147\pi$$
−0.849032 + 0.528341i $$0.822814\pi$$
$$230$$ −1.50000 + 2.59808i −0.0989071 + 0.171312i
$$231$$ 0 0
$$232$$ −1.50000 2.59808i −0.0984798 0.170572i
$$233$$ 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i $$-0.802003\pi$$
0.910968 + 0.412477i $$0.135336\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 1.50000 7.79423i 0.0972306 0.505225i
$$239$$ −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i $$-0.994563\pi$$
0.514719 + 0.857359i $$0.327896\pi$$
$$240$$ 0 0
$$241$$ −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i $$-0.948609\pi$$
0.632709 + 0.774389i $$0.281943\pi$$
$$242$$ 7.00000 + 12.1244i 0.449977 + 0.779383i
$$243$$ 0 0
$$244$$ 14.0000 0.896258
$$245$$ 5.50000 4.33013i 0.351382 0.276642i
$$246$$ 0 0
$$247$$ 2.50000 + 4.33013i 0.159071 + 0.275519i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 9.00000 0.569210
$$251$$ 28.0000 1.76734 0.883672 0.468106i $$-0.155064\pi$$
0.883672 + 0.468106i $$0.155064\pi$$
$$252$$ 0 0
$$253$$ 15.0000 0.943042
$$254$$ 12.0000 0.752947
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ −14.5000 25.1147i −0.904485 1.56661i −0.821607 0.570055i $$-0.806922\pi$$
−0.0828783 0.996560i $$-0.526411\pi$$
$$258$$ 0 0
$$259$$ −7.50000 + 2.59808i −0.466027 + 0.161437i
$$260$$ 5.00000 0.310087
$$261$$ 0 0
$$262$$ 0.500000 + 0.866025i 0.0308901 + 0.0535032i
$$263$$ 2.50000 4.33013i 0.154157 0.267007i −0.778595 0.627527i $$-0.784067\pi$$
0.932752 + 0.360520i $$0.117401\pi$$
$$264$$ 0 0
$$265$$ −4.50000 + 7.79423i −0.276433 + 0.478796i
$$266$$ 2.50000 0.866025i 0.153285 0.0530994i
$$267$$ 0 0
$$268$$ −4.00000 −0.244339
$$269$$ 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i $$-0.137514\pi$$
−0.816668 + 0.577108i $$0.804181\pi$$
$$270$$ 0 0
$$271$$ −0.500000 + 0.866025i −0.0303728 + 0.0526073i −0.880812 0.473466i $$-0.843003\pi$$
0.850439 + 0.526073i $$0.176336\pi$$
$$272$$ −1.50000 2.59808i −0.0909509 0.157532i
$$273$$ 0 0
$$274$$ 4.50000 7.79423i 0.271855 0.470867i
$$275$$ −10.0000 17.3205i −0.603023 1.04447i
$$276$$ 0 0
$$277$$ −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i $$0.360033\pi$$
−0.996484 + 0.0837823i $$0.973300\pi$$
$$278$$ 4.50000 7.79423i 0.269892 0.467467i
$$279$$ 0 0
$$280$$ 1.50000 7.79423i 0.0896421 0.465794i
$$281$$ −14.5000 25.1147i −0.864997 1.49822i −0.867050 0.498222i $$-0.833987\pi$$
0.00205220 0.999998i $$-0.499347\pi$$
$$282$$ 0 0
$$283$$ 28.0000 1.66443 0.832214 0.554455i $$-0.187073\pi$$
0.832214 + 0.554455i $$0.187073\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ 0 0
$$286$$ 12.5000 + 21.6506i 0.739140 + 1.28023i
$$287$$ −12.5000 + 4.33013i −0.737852 + 0.255599i
$$288$$ 0 0
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 0.500000 0.866025i 0.0293610 0.0508548i
$$291$$ 0 0
$$292$$ 1.50000 + 2.59808i 0.0877809 + 0.152041i
$$293$$ −2.50000 + 4.33013i −0.146052 + 0.252969i −0.929765 0.368154i $$-0.879990\pi$$
0.783713 + 0.621123i $$0.213323\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −4.50000 + 7.79423i −0.261557 + 0.453030i
$$297$$ 0 0
$$298$$ −1.50000 2.59808i −0.0868927 0.150503i
$$299$$ 15.0000 0.867472
$$300$$ 0 0
$$301$$ −0.500000 + 2.59808i −0.0288195 + 0.149751i
$$302$$ 2.50000 4.33013i 0.143859 0.249171i
$$303$$ 0 0
$$304$$ 0.500000 0.866025i 0.0286770 0.0496700i
$$305$$ 7.00000 + 12.1244i 0.400819 + 0.694239i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ −12.5000 + 4.33013i −0.712254 + 0.246732i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 6.00000 0.336994 0.168497 0.985702i $$-0.446109\pi$$
0.168497 + 0.985702i $$0.446109\pi$$
$$318$$ 0 0
$$319$$ −5.00000 −0.279946
$$320$$ −3.50000 6.06218i −0.195656 0.338886i
$$321$$ 0 0
$$322$$ 1.50000 7.79423i 0.0835917 0.434355i
$$323$$ −3.00000 −0.166924
$$324$$ 0 0
$$325$$ −10.0000 17.3205i −0.554700 0.960769i
$$326$$ −5.50000 + 9.52628i −0.304617 + 0.527612i
$$327$$ 0 0
$$328$$ −7.50000 + 12.9904i −0.414118 + 0.717274i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 4.50000 + 7.79423i 0.246970 + 0.427764i
$$333$$ 0 0
$$334$$ 9.50000 16.4545i 0.519817 0.900349i
$$335$$ −2.00000 3.46410i −0.109272 0.189264i
$$336$$ 0 0
$$337$$ 14.5000 25.1147i 0.789865 1.36809i −0.136184 0.990684i $$-0.543484\pi$$
0.926049 0.377403i $$-0.123183\pi$$
$$338$$ 6.00000 + 10.3923i 0.326357 + 0.565267i
$$339$$ 0 0
$$340$$ −1.50000 + 2.59808i −0.0813489 + 0.140900i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 1.50000 + 2.59808i 0.0808746 + 0.140079i
$$345$$ 0 0
$$346$$ −14.0000 −0.752645
$$347$$ −4.00000 −0.214731 −0.107366 0.994220i $$-0.534242\pi$$
−0.107366 + 0.994220i $$0.534242\pi$$
$$348$$ 0 0
$$349$$ −9.50000 16.4545i −0.508523 0.880788i −0.999951 0.00987003i $$-0.996858\pi$$
0.491428 0.870918i $$-0.336475\pi$$
$$350$$ −10.0000 + 3.46410i −0.534522 + 0.185164i
$$351$$ 0 0
$$352$$ −12.5000 + 21.6506i −0.666252 + 1.15398i
$$353$$ 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i $$-0.738768\pi$$
0.974456 + 0.224580i $$0.0721011\pi$$
$$354$$ 0 0
$$355$$ −6.00000 10.3923i −0.318447 0.551566i
$$356$$ 6.50000 11.2583i 0.344499 0.596690i
$$357$$ 0 0
$$358$$ −9.50000 16.4545i −0.502091 0.869646i
$$359$$ −5.50000 + 9.52628i −0.290279 + 0.502778i −0.973876 0.227082i $$-0.927081\pi$$
0.683597 + 0.729860i $$0.260415\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 14.0000 0.735824
$$363$$ 0 0
$$364$$ −12.5000 + 4.33013i −0.655178 + 0.226960i
$$365$$ −1.50000 + 2.59808i −0.0785136 + 0.135990i
$$366$$ 0 0
$$367$$ 1.50000 2.59808i 0.0782994 0.135618i −0.824217 0.566274i $$-0.808384\pi$$
0.902516 + 0.430656i $$0.141718\pi$$
$$368$$ −1.50000 2.59808i −0.0781929 0.135434i
$$369$$ 0 0
$$370$$ −3.00000 −0.155963
$$371$$ 4.50000 23.3827i 0.233628 1.21397i
$$372$$ 0 0
$$373$$ 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i $$0.0574041\pi$$
−0.336557 + 0.941663i $$0.609263\pi$$
$$374$$ −15.0000 −0.775632
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −5.00000 −0.257513
$$378$$ 0 0
$$379$$ −12.0000 −0.616399 −0.308199 0.951322i $$-0.599726\pi$$
−0.308199 + 0.951322i $$0.599726\pi$$
$$380$$ −1.00000 −0.0512989
$$381$$ 0 0
$$382$$ 8.00000 0.409316
$$383$$ 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i $$0.0756427\pi$$
−0.282079 + 0.959391i $$0.591024\pi$$
$$384$$ 0 0
$$385$$ −10.0000 8.66025i −0.509647 0.441367i
$$386$$ 10.0000 0.508987
$$387$$ 0 0
$$388$$ −4.50000 7.79423i −0.228453 0.395692i
$$389$$ −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i $$-0.906604\pi$$
0.729103 + 0.684403i $$0.239937\pi$$
$$390$$ 0 0
$$391$$ −4.50000 + 7.79423i −0.227575 + 0.394171i
$$392$$ 3.00000 + 20.7846i 0.151523 + 1.04978i
$$393$$ 0 0
$$394$$ 2.00000 0.100759
$$395$$ −4.00000 6.92820i −0.201262 0.348596i
$$396$$ 0 0
$$397$$ −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i $$-0.956176\pi$$
0.614123 + 0.789210i $$0.289510\pi$$
$$398$$ 1.50000 + 2.59808i 0.0751882 + 0.130230i
$$399$$ 0 0
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i $$-0.142801\pi$$
−0.826139 + 0.563466i $$0.809468\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 8.50000 14.7224i 0.422891 0.732468i
$$405$$ 0 0
$$406$$ −0.500000 + 2.59808i −0.0248146 + 0.128940i
$$407$$ 7.50000 + 12.9904i 0.371761 + 0.643909i
$$408$$ 0 0
$$409$$ 14.0000 0.692255 0.346128 0.938187i $$-0.387496\pi$$
0.346128 + 0.938187i $$0.387496\pi$$
$$410$$ −5.00000 −0.246932
$$411$$ 0 0
$$412$$ −0.500000 0.866025i −0.0246332 0.0426660i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −4.50000 + 7.79423i −0.220896 + 0.382604i
$$416$$ −12.5000 + 21.6506i −0.612863 + 1.06151i
$$417$$ 0 0
$$418$$ −2.50000 4.33013i −0.122279 0.211793i
$$419$$ 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i $$-0.762780\pi$$
0.954759 + 0.297382i $$0.0961133\pi$$
$$420$$ 0 0
$$421$$ 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i $$-0.158909\pi$$
−0.853584 + 0.520955i $$0.825576\pi$$
$$422$$ 6.50000 11.2583i 0.316415 0.548047i
$$423$$ 0 0
$$424$$ −13.5000 23.3827i −0.655618 1.13556i
$$425$$ 12.0000 0.582086
$$426$$ 0 0
$$427$$ −28.0000 24.2487i −1.35501 1.17348i
$$428$$ −8.50000 + 14.7224i −0.410863 + 0.711636i
$$429$$ 0 0
$$430$$ −0.500000 + 0.866025i −0.0241121 + 0.0417635i
$$431$$ −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i $$-0.236215\pi$$
−0.953815 + 0.300395i $$0.902881\pi$$
$$432$$ 0 0
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −4.50000 7.79423i −0.215511 0.373276i
$$437$$ −3.00000 −0.143509
$$438$$ 0 0
$$439$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$440$$ −15.0000 −0.715097
$$441$$ 0 0
$$442$$ −15.0000 −0.713477
$$443$$ −36.0000 −1.71041 −0.855206 0.518289i $$-0.826569\pi$$
−0.855206 + 0.518289i $$0.826569\pi$$
$$444$$ 0 0
$$445$$ 13.0000 0.616259
$$446$$ 9.50000 + 16.4545i 0.449838 + 0.779142i
$$447$$ 0 0
$$448$$ 14.0000 + 12.1244i 0.661438 + 0.572822i
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ 12.5000 + 21.6506i 0.588602 + 1.01949i
$$452$$ 0.500000 0.866025i 0.0235180 0.0407344i
$$453$$ 0 0
$$454$$ 1.50000 2.59808i 0.0703985 0.121934i
$$455$$ −10.0000 8.66025i −0.468807 0.405999i
$$456$$ 0 0
$$457$$ 22.0000 1.02912 0.514558 0.857455i $$-0.327956\pi$$
0.514558 + 0.857455i $$0.327956\pi$$
$$458$$ −0.500000 0.866025i −0.0233635 0.0404667i
$$459$$ 0 0
$$460$$ −1.50000 + 2.59808i −0.0699379 + 0.121136i
$$461$$ 9.50000 + 16.4545i 0.442459 + 0.766362i 0.997871 0.0652135i $$-0.0207728\pi$$
−0.555412 + 0.831575i $$0.687440\pi$$
$$462$$ 0 0
$$463$$ −6.50000 + 11.2583i −0.302081 + 0.523219i −0.976607 0.215032i $$-0.931015\pi$$
0.674526 + 0.738251i $$0.264348\pi$$
$$464$$ 0.500000 + 0.866025i 0.0232119 + 0.0402042i
$$465$$ 0 0
$$466$$ −1.50000 + 2.59808i −0.0694862 + 0.120354i
$$467$$ −13.5000 + 23.3827i −0.624705 + 1.08202i 0.363892 + 0.931441i $$0.381448\pi$$
−0.988598 + 0.150581i $$0.951886\pi$$
$$468$$ 0 0
$$469$$ 8.00000 + 6.92820i 0.369406 + 0.319915i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 5.00000 0.229900
$$474$$ 0 0
$$475$$ 2.00000 + 3.46410i 0.0917663 + 0.158944i
$$476$$ 1.50000 7.79423i 0.0687524 0.357248i
$$477$$ 0 0
$$478$$ 7.50000 12.9904i 0.343042 0.594166i
$$479$$ 12.5000 21.6506i 0.571140 0.989243i −0.425310 0.905048i $$-0.639835\pi$$
0.996449 0.0841949i $$-0.0268318\pi$$
$$480$$ 0 0
$$481$$ 7.50000 + 12.9904i 0.341971 + 0.592310i
$$482$$ 5.50000 9.52628i 0.250518 0.433910i
$$483$$ 0 0
$$484$$ 7.00000 + 12.1244i 0.318182 + 0.551107i
$$485$$ 4.50000 7.79423i 0.204334 0.353918i
$$486$$ 0 0
$$487$$ −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i $$-0.308325\pi$$
−0.996915 + 0.0784867i $$0.974991\pi$$
$$488$$ −42.0000 −1.90125
$$489$$ 0 0
$$490$$ −5.50000 + 4.33013i −0.248465 + 0.195615i
$$491$$ 6.50000 11.2583i 0.293341 0.508081i −0.681257 0.732045i $$-0.738566\pi$$
0.974598 + 0.223963i $$0.0718996\pi$$
$$492$$ 0 0
$$493$$ 1.50000 2.59808i 0.0675566 0.117011i
$$494$$ −2.50000 4.33013i −0.112480 0.194822i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 24.0000 + 20.7846i 1.07655 + 0.932317i
$$498$$ 0 0
$$499$$ −15.5000 26.8468i −0.693875 1.20183i −0.970558 0.240866i $$-0.922569\pi$$
0.276683 0.960961i $$-0.410765\pi$$
$$500$$ 9.00000 0.402492
$$501$$ 0 0
$$502$$ −28.0000 −1.24970
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 17.0000 0.756490
$$506$$ −15.0000 −0.666831
$$507$$ 0 0
$$508$$ 12.0000 0.532414
$$509$$ −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i $$-0.944480\pi$$
0.342126 0.939654i $$-0.388853\pi$$
$$510$$ 0 0
$$511$$ 1.50000 7.79423i 0.0663561 0.344796i
$$512$$ 11.0000 0.486136
$$513$$ 0 0
$$514$$ 14.5000 + 25.1147i 0.639568 + 1.10776i
$$515$$ 0.500000 0.866025i 0.0220326 0.0381616i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 7.50000 2.59808i 0.329531 0.114153i
$$519$$ 0 0
$$520$$ −15.0000 −0.657794
$$521$$ 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i $$-0.145733\pi$$
−0.831295 + 0.555831i $$0.812400\pi$$
$$522$$ 0 0
$$523$$ −0.500000 + 0.866025i −0.0218635 + 0.0378686i −0.876750 0.480946i $$-0.840293\pi$$
0.854887 + 0.518815i $$0.173627\pi$$
$$524$$ 0.500000 + 0.866025i 0.0218426 + 0.0378325i
$$525$$ 0 0
$$526$$ −2.50000 + 4.33013i −0.109005 + 0.188803i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 7.00000 12.1244i 0.304348 0.527146i
$$530$$ 4.50000 7.79423i 0.195468 0.338560i
$$531$$ 0 0
$$532$$ 2.50000 0.866025i 0.108389 0.0375470i
$$533$$ 12.5000 + 21.6506i 0.541435 + 0.937793i
$$534$$ 0 0
$$535$$ −17.0000 −0.734974
$$536$$ 12.0000 0.518321
$$537$$ 0 0
$$538$$ −1.50000 2.59808i −0.0646696 0.112011i
$$539$$ 32.5000 + 12.9904i 1.39987 + 0.559535i
$$540$$ 0 0
$$541$$ 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i $$-0.652733\pi$$
0.999042 0.0437584i $$-0.0139332\pi$$
$$542$$ 0.500000 0.866025i 0.0214768 0.0371990i
$$543$$ 0 0
$$544$$ −7.50000 12.9904i −0.321560 0.556958i
$$545$$ 4.50000 7.79423i 0.192759 0.333868i
$$546$$ 0 0
$$547$$ 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i $$0.0461907\pi$$
−0.369514 + 0.929225i $$0.620476\pi$$
$$548$$ 4.50000 7.79423i 0.192230 0.332953i
$$549$$ 0 0
$$550$$ 10.0000 + 17.3205i 0.426401 + 0.738549i
$$551$$ 1.00000 0.0426014
$$552$$ 0 0
$$553$$ 16.0000 + 13.8564i 0.680389 + 0.589234i
$$554$$ 9.50000 16.4545i 0.403616 0.699084i
$$555$$ 0 0
$$556$$ 4.50000 7.79423i 0.190843 0.330549i
$$557$$ −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i $$-0.879909\pi$$
0.145802 0.989314i $$-0.453424\pi$$
$$558$$ 0 0
$$559$$ 5.00000 0.211477
$$560$$ −0.500000 + 2.59808i −0.0211289 + 0.109789i
$$561$$ 0 0
$$562$$ 14.5000 + 25.1147i 0.611646 + 1.05940i
$$563$$ 28.0000 1.18006 0.590030 0.807382i $$-0.299116\pi$$
0.590030 + 0.807382i $$0.299116\pi$$
$$564$$ 0 0
$$565$$ 1.00000 0.0420703
$$566$$ −28.0000 −1.17693
$$567$$ 0 0
$$568$$ 36.0000 1.51053
$$569$$ 34.0000 1.42535 0.712677 0.701492i $$-0.247483\pi$$
0.712677 + 0.701492i $$0.247483\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 12.5000 + 21.6506i 0.522651 + 0.905259i
$$573$$ 0 0
$$574$$ 12.5000 4.33013i 0.521740 0.180736i
$$575$$ 12.0000 0.500435
$$576$$ 0 0
$$577$$ −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i $$-0.943410\pi$$
0.338965 0.940799i $$-0.389923\pi$$
$$578$$ −4.00000 + 6.92820i −0.166378 + 0.288175i
$$579$$ 0 0
$$580$$ 0.500000 0.866025i 0.0207614 0.0359597i
$$581$$ 4.50000 23.3827i 0.186691 0.970077i
$$582$$ 0 0
$$583$$ −45.0000 −1.86371
$$584$$ −4.50000 7.79423i −0.186211 0.322527i
$$585$$ 0 0
$$586$$ 2.50000 4.33013i 0.103274 0.178876i
$$587$$ −18.5000 32.0429i −0.763577 1.32255i −0.940996 0.338418i $$-0.890108\pi$$
0.177419 0.984135i $$-0.443225\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 1.50000 2.59808i 0.0616496 0.106780i
$$593$$ 7.50000 12.9904i 0.307988 0.533451i −0.669934 0.742421i $$-0.733678\pi$$
0.977922 + 0.208970i $$0.0670110\pi$$
$$594$$ 0 0
$$595$$ 7.50000 2.59808i 0.307470 0.106511i
$$596$$ −1.50000 2.59808i −0.0614424 0.106421i
$$597$$ 0 0
$$598$$ −15.0000 −0.613396
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i $$-0.107905\pi$$
−0.759531 + 0.650471i $$0.774572\pi$$
$$602$$ 0.500000 2.59808i 0.0203785 0.105890i
$$603$$ 0 0
$$604$$ 2.50000 4.33013i 0.101724 0.176190i
$$605$$ −7.00000 + 12.1244i −0.284590 + 0.492925i
$$606$$ 0 0
$$607$$ 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i $$-0.160206\pi$$
−0.855700 + 0.517472i $$0.826873\pi$$
$$608$$ 2.50000 4.33013i 0.101388 0.175610i
$$609$$ 0 0
$$610$$ −7.00000 12.1244i −0.283422 0.490901i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −9.50000 16.4545i −0.383701 0.664590i 0.607887 0.794024i $$-0.292017\pi$$
−0.991588 + 0.129433i $$0.958684\pi$$
$$614$$ −28.0000 −1.12999
$$615$$ 0 0
$$616$$ 37.5000 12.9904i 1.51092 0.523397i
$$617$$ 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i $$-0.650436\pi$$
0.998700 0.0509678i $$-0.0162306\pi$$
$$618$$ 0 0
$$619$$ −12.5000 + 21.6506i −0.502417 + 0.870212i 0.497579 + 0.867419i $$0.334223\pi$$
−0.999996 + 0.00279365i $$0.999111\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −32.5000 + 11.2583i −1.30209 + 0.451055i
$$624$$ 0 0
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ −14.0000 −0.559553
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ −9.00000 −0.358854
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 24.0000 0.954669
$$633$$ 0 0
$$634$$ −6.00000 −0.238290
$$635$$ 6.00000 + 10.3923i 0.238103 + 0.412406i
$$636$$ 0 0
$$637$$ 32.5000 + 12.9904i 1.28770 + 0.514698i
$$638$$ 5.00000 0.197952
$$639$$ 0 0
$$640$$ −1.50000 2.59808i −0.0592927 0.102698i
$$641$$ −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i $$-0.890212\pi$$
0.763367 + 0.645966i $$0.223545\pi$$
$$642$$ 0 0
$$643$$ 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i $$-0.711098\pi$$
0.990274 + 0.139134i $$0.0444318\pi$$
$$644$$ 1.50000 7.79423i 0.0591083 0.307136i
$$645$$ 0 0
$$646$$ 3.00000 0.118033
$$647$$ 15.5000 + 26.8468i 0.609368 + 1.05546i 0.991345 + 0.131284i $$0.0419101\pi$$
−0.381977 + 0.924172i $$0.624757\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 10.0000 + 17.3205i 0.392232 + 0.679366i
$$651$$ 0 0
$$652$$ −5.50000 + 9.52628i −0.215397 + 0.373078i
$$653$$ 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i $$-0.147971\pi$$
−0.835182 + 0.549973i $$0.814638\pi$$
$$654$$ 0 0
$$655$$ −0.500000 + 0.866025i −0.0195366 + 0.0338384i
$$656$$ 2.50000 4.33013i 0.0976086 0.169063i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 13.5000 + 23.3827i 0.525885 + 0.910860i 0.999545 + 0.0301523i $$0.00959924\pi$$
−0.473660 + 0.880708i $$0.657067\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ −8.00000 −0.310929
$$663$$ 0 0
$$664$$ −13.5000 23.3827i −0.523902 0.907424i
$$665$$ 2.00000 + 1.73205i 0.0775567 + 0.0671660i
$$666$$ 0 0
$$667$$ 1.50000 2.59808i 0.0580802 0.100598i
$$668$$ 9.50000 16.4545i 0.367566 0.636643i
$$669$$ 0 0
$$670$$ 2.00000 + 3.46410i 0.0772667 + 0.133830i
$$671$$ −35.0000 + 60.6218i −1.35116 + 2.34028i
$$672$$ 0 0
$$673$$ 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i $$0.0221228\pi$$
−0.438652 + 0.898657i $$0.644544\pi$$
$$674$$ −14.5000 + 25.1147i −0.558519 + 0.967384i
$$675$$ 0 0
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ 0 0
$$679$$ −4.50000 + 23.3827i −0.172694 + 0.897345i
$$680$$ 4.50000 7.79423i 0.172567 0.298895i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i $$-0.221750\pi$$
−0.939184 + 0.343413i $$0.888417\pi$$
$$684$$ 0 0
$$685$$ 9.00000 0.343872
$$686$$ 10.0000 15.5885i 0.381802 0.595170i
$$687$$ 0 0
$$688$$ −0.500000 0.866025i −0.0190623 0.0330169i
$$689$$ −45.0000 −1.71436
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ 4.00000 0.151838
$$695$$ 9.00000 0.341389
$$696$$ 0 0
$$697$$ −15.0000 −0.568166
$$698$$ 9.50000 + 16.4545i 0.359580 + 0.622811i
$$699$$ 0 0
$$700$$ −10.0000 + 3.46410i −0.377964 + 0.130931i
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 0 0
$$703$$ −1.50000 2.59808i −0.0565736 0.0979883i
$$704$$ 17.5000 30.3109i 0.659556 1.14238i
$$705$$ 0 0
$$706$$ −5.50000 + 9.52628i −0.206995 + 0.358526i
$$707$$ −42.5000 + 14.7224i −1.59838 + 0.553694i
$$708$$ 0 0
$$709$$ −6.00000 −0.225335 −0.112667 0.993633i $$-0.535939\pi$$
−0.112667 + 0.993633i $$0.535939\pi$$
$$710$$ 6.00000 + 10.3923i 0.225176 + 0.390016i
$$711$$ 0 0
$$712$$ −19.5000 + 33.7750i −0.730793 + 1.26577i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −12.5000 + 21.6506i −0.467473 + 0.809688i
$$716$$ −9.50000 16.4545i −0.355032 0.614933i
$$717$$ 0 0
$$718$$ 5.50000 9.52628i 0.205258 0.355518i
$$719$$ −13.5000 + 23.3827i −0.503465 + 0.872027i 0.496527 + 0.868021i $$0.334608\pi$$
−0.999992 + 0.00400572i $$0.998725\pi$$
$$720$$ 0 0
$$721$$ −0.500000 + 2.59808i −0.0186210 + 0.0967574i
$$722$$ −9.00000 15.5885i −0.334945 0.580142i
$$723$$ 0 0
$$724$$ 14.0000 0.520306
$$725$$ −4.00000 −0.148556
$$726$$ 0 0
$$727$$ −23.5000 40.7032i −0.871567 1.50960i −0.860376 0.509661i $$-0.829771\pi$$
−0.0111912 0.999937i $$-0.503562\pi$$
$$728$$ 37.5000 12.9904i 1.38984 0.481456i
$$729$$ 0 0
$$730$$ 1.50000 2.59808i 0.0555175 0.0961591i
$$731$$ −1.50000 + 2.59808i −0.0554795 + 0.0960933i
$$732$$ 0 0
$$733$$ −13.5000 23.3827i −0.498634 0.863659i 0.501365 0.865236i $$-0.332831\pi$$
−0.999999 + 0.00157675i $$0.999498\pi$$
$$734$$ −1.50000 + 2.59808i −0.0553660 + 0.0958967i
$$735$$ 0 0
$$736$$ −7.50000 12.9904i −0.276454 0.478832i
$$737$$ 10.0000 17.3205i 0.368355 0.638009i
$$738$$ 0 0
$$739$$ 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i $$-0.113732\pi$$
−0.771310 + 0.636460i $$0.780398\pi$$
$$740$$ −3.00000 −0.110282
$$741$$ 0 0
$$742$$ −4.50000 + 23.3827i −0.165200 + 0.858405i
$$743$$ −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i $$-0.922060\pi$$
0.695024 + 0.718986i $$0.255394\pi$$
$$744$$ 0 0
$$745$$ 1.50000 2.59808i 0.0549557 0.0951861i
$$746$$ −12.5000 21.6506i −0.457658 0.792686i
$$747$$ 0 0
$$748$$ −15.0000 −0.548454
$$749$$ 42.5000 14.7224i 1.55292 0.537946i
$$750$$ 0 0
$$751$$ −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i $$-0.975310\pi$$
0.431390 0.902165i $$-0.358023\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 5.00000 0.182089
$$755$$ 5.00000 0.181969
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 12.0000 0.435860
$$759$$ 0 0
$$760$$ 3.00000 0.108821
$$761$$ 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i $$-0.00389175\pi$$
−0.510551 + 0.859848i $$0.670558\pi$$
$$762$$ 0 0
$$763$$ −4.50000 + 23.3827i −0.162911 + 0.846510i
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ −13.5000 23.3827i −0.487775 0.844851i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i $$-0.969447\pi$$
0.580696 + 0.814120i $$0.302780\pi$$
$$770$$ 10.0000 + 8.66025i 0.360375 + 0.312094i
$$771$$ 0 0
$$772$$ 10.0000 0.359908
$$773$$ 15.5000 + 26.8468i 0.557496 + 0.965612i 0.997705 + 0.0677162i $$0.0215712\pi$$
−0.440208 + 0.897896i $$0.645095\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 13.5000 + 23.3827i 0.484622 + 0.839390i
$$777$$ 0 0
$$778$$ 4.50000 7.79423i 0.161333 0.279437i
$$779$$ −2.50000 4.33013i −0.0895718 0.155143i
$$780$$ 0 0
$$781$$ 30.0000 51.9615i 1.07348 1.85933i
$$782$$ 4.50000 7.79423i 0.160920 0.278721i
$$783$$ 0 0
$$784$$ −1.00000 6.92820i −0.0357143 0.247436i
$$785$$ 7.00000 + 12.1244i 0.249841 + 0.432737i
$$786$$ 0 0
$$787$$ 28.0000 0.998092 0.499046 0.866575i $$-0.333684\pi$$
0.499046 + 0.866575i $$0.333684\pi$$
$$788$$ 2.00000 0.0712470
$$789$$ 0 0
$$790$$ 4.00000 + 6.92820i 0.142314 + 0.246494i
$$791$$ −2.50000 +