# Properties

 Label 43.2.c.a.36.1 Level $43$ Weight $2$ Character 43.36 Analytic conductor $0.343$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 43.c (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.343356728692$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 36.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 43.36 Dual form 43.2.c.a.6.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(0.500000 - 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +3.00000 q^{21} +(3.50000 + 6.06218i) q^{23} +(1.50000 + 2.59808i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.50000 - 4.33013i) q^{26} -5.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(0.500000 - 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +5.00000 q^{32} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{35} +(-1.00000 + 1.73205i) q^{36} +(4.50000 + 7.79423i) q^{37} +(-0.500000 - 0.866025i) q^{38} -5.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} -10.0000 q^{41} +3.00000 q^{42} +(-4.00000 - 5.19615i) q^{43} +2.00000 q^{45} +(3.50000 + 6.06218i) q^{46} -8.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(2.00000 - 3.46410i) q^{50} +3.00000 q^{51} +(-2.50000 + 4.33013i) q^{52} +(2.50000 + 4.33013i) q^{53} -5.00000 q^{54} +(4.50000 - 7.79423i) q^{56} +(-0.500000 + 0.866025i) q^{57} +(-1.50000 + 2.59808i) q^{58} +12.0000 q^{59} +(-0.500000 + 0.866025i) q^{60} +(6.50000 - 11.2583i) q^{61} +(-2.50000 - 4.33013i) q^{62} +(3.00000 + 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(1.50000 + 2.59808i) q^{67} +(1.50000 - 2.59808i) q^{68} +(3.50000 - 6.06218i) q^{69} -3.00000 q^{70} +(0.500000 - 0.866025i) q^{71} +(-3.00000 + 5.19615i) q^{72} +(-5.50000 + 9.52628i) q^{73} +(4.50000 + 7.79423i) q^{74} -4.00000 q^{75} +(0.500000 + 0.866025i) q^{76} -5.00000 q^{78} +(2.50000 - 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} -10.0000 q^{82} +(-4.50000 - 7.79423i) q^{83} -3.00000 q^{84} -3.00000 q^{85} +(-4.00000 - 5.19615i) q^{86} +3.00000 q^{87} +(0.500000 + 0.866025i) q^{89} +2.00000 q^{90} +(7.50000 + 12.9904i) q^{91} +(-3.50000 - 6.06218i) q^{92} +(-2.50000 + 4.33013i) q^{93} -8.00000 q^{94} +(0.500000 - 0.866025i) q^{95} +(-2.50000 - 4.33013i) q^{96} -2.00000 q^{97} +(-1.00000 - 1.73205i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} + q^{12} + 5 q^{13} - 3 q^{14} + q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - q^{19} - q^{20} + 6 q^{21} + 7 q^{23} + 3 q^{24} + 4 q^{25} + 5 q^{26} - 10 q^{27} + 3 q^{28} - 3 q^{29} + q^{30} - 5 q^{31} + 10 q^{32} - 3 q^{34} - 6 q^{35} - 2 q^{36} + 9 q^{37} - q^{38} - 10 q^{39} - 3 q^{40} - 20 q^{41} + 6 q^{42} - 8 q^{43} + 4 q^{45} + 7 q^{46} - 16 q^{47} + q^{48} - 2 q^{49} + 4 q^{50} + 6 q^{51} - 5 q^{52} + 5 q^{53} - 10 q^{54} + 9 q^{56} - q^{57} - 3 q^{58} + 24 q^{59} - q^{60} + 13 q^{61} - 5 q^{62} + 6 q^{63} + 14 q^{64} + 10 q^{65} + 3 q^{67} + 3 q^{68} + 7 q^{69} - 6 q^{70} + q^{71} - 6 q^{72} - 11 q^{73} + 9 q^{74} - 8 q^{75} + q^{76} - 10 q^{78} + 5 q^{79} - q^{80} - q^{81} - 20 q^{82} - 9 q^{83} - 6 q^{84} - 6 q^{85} - 8 q^{86} + 6 q^{87} + q^{89} + 4 q^{90} + 15 q^{91} - 7 q^{92} - 5 q^{93} - 16 q^{94} + q^{95} - 5 q^{96} - 4 q^{97} - 2 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$$.

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

## 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 $$-0.384973\pi$$
0.353553 + 0.935414i $$0.384973\pi$$
$$3$$ −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i $$-0.259881\pi$$
−0.973494 + 0.228714i $$0.926548\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i $$-0.0948835\pi$$
−0.732294 + 0.680989i $$0.761550\pi$$
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i $$0.358542\pi$$
−0.996866 + 0.0791130i $$0.974791\pi$$
$$8$$ −3.00000 −1.06066
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ 0.500000 + 0.866025i 0.158114 + 0.273861i
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i $$-0.589456\pi$$
0.970725 0.240192i $$-0.0772105\pi$$
$$14$$ −1.50000 + 2.59808i −0.400892 + 0.694365i
$$15$$ 0.500000 0.866025i 0.129099 0.223607i
$$16$$ −1.00000 −0.250000
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 1.00000 1.73205i 0.235702 0.408248i
$$19$$ −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i $$-0.203260\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −0.500000 0.866025i −0.111803 0.193649i
$$21$$ 3.00000 0.654654
$$22$$ 0 0
$$23$$ 3.50000 + 6.06218i 0.729800 + 1.26405i 0.956967 + 0.290196i $$0.0937204\pi$$
−0.227167 + 0.973856i $$0.572946\pi$$
$$24$$ 1.50000 + 2.59808i 0.306186 + 0.530330i
$$25$$ 2.00000 3.46410i 0.400000 0.692820i
$$26$$ 2.50000 4.33013i 0.490290 0.849208i
$$27$$ −5.00000 −0.962250
$$28$$ 1.50000 2.59808i 0.283473 0.490990i
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 0.500000 0.866025i 0.0912871 0.158114i
$$31$$ −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i $$-0.314891\pi$$
−0.998322 + 0.0579057i $$0.981558\pi$$
$$32$$ 5.00000 0.883883
$$33$$ 0 0
$$34$$ −1.50000 + 2.59808i −0.257248 + 0.445566i
$$35$$ −3.00000 −0.507093
$$36$$ −1.00000 + 1.73205i −0.166667 + 0.288675i
$$37$$ 4.50000 + 7.79423i 0.739795 + 1.28136i 0.952587 + 0.304266i $$0.0984111\pi$$
−0.212792 + 0.977098i $$0.568256\pi$$
$$38$$ −0.500000 0.866025i −0.0811107 0.140488i
$$39$$ −5.00000 −0.800641
$$40$$ −1.50000 2.59808i −0.237171 0.410792i
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 3.00000 0.462910
$$43$$ −4.00000 5.19615i −0.609994 0.792406i
$$44$$ 0 0
$$45$$ 2.00000 0.298142
$$46$$ 3.50000 + 6.06218i 0.516047 + 0.893819i
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0.500000 + 0.866025i 0.0721688 + 0.125000i
$$49$$ −1.00000 1.73205i −0.142857 0.247436i
$$50$$ 2.00000 3.46410i 0.282843 0.489898i
$$51$$ 3.00000 0.420084
$$52$$ −2.50000 + 4.33013i −0.346688 + 0.600481i
$$53$$ 2.50000 + 4.33013i 0.343401 + 0.594789i 0.985062 0.172200i $$-0.0550875\pi$$
−0.641661 + 0.766989i $$0.721754\pi$$
$$54$$ −5.00000 −0.680414
$$55$$ 0 0
$$56$$ 4.50000 7.79423i 0.601338 1.04155i
$$57$$ −0.500000 + 0.866025i −0.0662266 + 0.114708i
$$58$$ −1.50000 + 2.59808i −0.196960 + 0.341144i
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ −0.500000 + 0.866025i −0.0645497 + 0.111803i
$$61$$ 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i $$-0.520392\pi$$
0.896258 0.443533i $$-0.146275\pi$$
$$62$$ −2.50000 4.33013i −0.317500 0.549927i
$$63$$ 3.00000 + 5.19615i 0.377964 + 0.654654i
$$64$$ 7.00000 0.875000
$$65$$ 5.00000 0.620174
$$66$$ 0 0
$$67$$ 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i $$-0.108004\pi$$
−0.759733 + 0.650236i $$0.774670\pi$$
$$68$$ 1.50000 2.59808i 0.181902 0.315063i
$$69$$ 3.50000 6.06218i 0.421350 0.729800i
$$70$$ −3.00000 −0.358569
$$71$$ 0.500000 0.866025i 0.0593391 0.102778i −0.834830 0.550508i $$-0.814434\pi$$
0.894169 + 0.447730i $$0.147767\pi$$
$$72$$ −3.00000 + 5.19615i −0.353553 + 0.612372i
$$73$$ −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i $$0.389279\pi$$
−0.984594 + 0.174855i $$0.944054\pi$$
$$74$$ 4.50000 + 7.79423i 0.523114 + 0.906061i
$$75$$ −4.00000 −0.461880
$$76$$ 0.500000 + 0.866025i 0.0573539 + 0.0993399i
$$77$$ 0 0
$$78$$ −5.00000 −0.566139
$$79$$ 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i $$-0.742577\pi$$
0.971698 + 0.236225i $$0.0759104\pi$$
$$80$$ −0.500000 0.866025i −0.0559017 0.0968246i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ −10.0000 −1.10432
$$83$$ −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i $$-0.331110\pi$$
−0.999976 + 0.00698436i $$0.997777\pi$$
$$84$$ −3.00000 −0.327327
$$85$$ −3.00000 −0.325396
$$86$$ −4.00000 5.19615i −0.431331 0.560316i
$$87$$ 3.00000 0.321634
$$88$$ 0 0
$$89$$ 0.500000 + 0.866025i 0.0529999 + 0.0917985i 0.891308 0.453398i $$-0.149788\pi$$
−0.838308 + 0.545197i $$0.816455\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 7.50000 + 12.9904i 0.786214 + 1.36176i
$$92$$ −3.50000 6.06218i −0.364900 0.632026i
$$93$$ −2.50000 + 4.33013i −0.259238 + 0.449013i
$$94$$ −8.00000 −0.825137
$$95$$ 0.500000 0.866025i 0.0512989 0.0888523i
$$96$$ −2.50000 4.33013i −0.255155 0.441942i
$$97$$ −2.00000 −0.203069 −0.101535 0.994832i $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ −1.00000 1.73205i −0.101015 0.174964i
$$99$$ 0 0
$$100$$ −2.00000 + 3.46410i −0.200000 + 0.346410i
$$101$$ 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i $$-0.685553\pi$$
0.998240 + 0.0592978i $$0.0188862\pi$$
$$102$$ 3.00000 0.297044
$$103$$ −3.50000 + 6.06218i −0.344865 + 0.597324i −0.985329 0.170664i $$-0.945409\pi$$
0.640464 + 0.767988i $$0.278742\pi$$
$$104$$ −7.50000 + 12.9904i −0.735436 + 1.27381i
$$105$$ 1.50000 + 2.59808i 0.146385 + 0.253546i
$$106$$ 2.50000 + 4.33013i 0.242821 + 0.420579i
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 5.00000 0.481125
$$109$$ −3.50000 6.06218i −0.335239 0.580651i 0.648292 0.761392i $$-0.275484\pi$$
−0.983531 + 0.180741i $$0.942150\pi$$
$$110$$ 0 0
$$111$$ 4.50000 7.79423i 0.427121 0.739795i
$$112$$ 1.50000 2.59808i 0.141737 0.245495i
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ −0.500000 + 0.866025i −0.0468293 + 0.0811107i
$$115$$ −3.50000 + 6.06218i −0.326377 + 0.565301i
$$116$$ 1.50000 2.59808i 0.139272 0.241225i
$$117$$ −5.00000 8.66025i −0.462250 0.800641i
$$118$$ 12.0000 1.10469
$$119$$ −4.50000 7.79423i −0.412514 0.714496i
$$120$$ −1.50000 + 2.59808i −0.136931 + 0.237171i
$$121$$ −11.0000 −1.00000
$$122$$ 6.50000 11.2583i 0.588482 1.01928i
$$123$$ 5.00000 + 8.66025i 0.450835 + 0.780869i
$$124$$ 2.50000 + 4.33013i 0.224507 + 0.388857i
$$125$$ 9.00000 0.804984
$$126$$ 3.00000 + 5.19615i 0.267261 + 0.462910i
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ −3.00000 −0.265165
$$129$$ −2.50000 + 6.06218i −0.220113 + 0.533745i
$$130$$ 5.00000 0.438529
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ 3.00000 0.260133
$$134$$ 1.50000 + 2.59808i 0.129580 + 0.224440i
$$135$$ −2.50000 4.33013i −0.215166 0.372678i
$$136$$ 4.50000 7.79423i 0.385872 0.668350i
$$137$$ −18.0000 −1.53784 −0.768922 0.639343i $$-0.779207\pi$$
−0.768922 + 0.639343i $$0.779207\pi$$
$$138$$ 3.50000 6.06218i 0.297940 0.516047i
$$139$$ −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i $$-0.980790\pi$$
0.446857 0.894606i $$-0.352543\pi$$
$$140$$ 3.00000 0.253546
$$141$$ 4.00000 + 6.92820i 0.336861 + 0.583460i
$$142$$ 0.500000 0.866025i 0.0419591 0.0726752i
$$143$$ 0 0
$$144$$ −1.00000 + 1.73205i −0.0833333 + 0.144338i
$$145$$ −3.00000 −0.249136
$$146$$ −5.50000 + 9.52628i −0.455183 + 0.788400i
$$147$$ −1.00000 + 1.73205i −0.0824786 + 0.142857i
$$148$$ −4.50000 7.79423i −0.369898 0.640682i
$$149$$ 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i $$0.162991\pi$$
−0.0115483 + 0.999933i $$0.503676\pi$$
$$150$$ −4.00000 −0.326599
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 1.50000 + 2.59808i 0.121666 + 0.210732i
$$153$$ 3.00000 + 5.19615i 0.242536 + 0.420084i
$$154$$ 0 0
$$155$$ 2.50000 4.33013i 0.200805 0.347804i
$$156$$ 5.00000 0.400320
$$157$$ 0.500000 0.866025i 0.0399043 0.0691164i −0.845383 0.534160i $$-0.820628\pi$$
0.885288 + 0.465044i $$0.153961\pi$$
$$158$$ 2.50000 4.33013i 0.198889 0.344486i
$$159$$ 2.50000 4.33013i 0.198263 0.343401i
$$160$$ 2.50000 + 4.33013i 0.197642 + 0.342327i
$$161$$ −21.0000 −1.65503
$$162$$ −0.500000 0.866025i −0.0392837 0.0680414i
$$163$$ 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i $$-0.820864\pi$$
0.884943 + 0.465700i $$0.154198\pi$$
$$164$$ 10.0000 0.780869
$$165$$ 0 0
$$166$$ −4.50000 7.79423i −0.349268 0.604949i
$$167$$ 1.50000 + 2.59808i 0.116073 + 0.201045i 0.918208 0.396098i $$-0.129636\pi$$
−0.802135 + 0.597143i $$0.796303\pi$$
$$168$$ −9.00000 −0.694365
$$169$$ −6.00000 10.3923i −0.461538 0.799408i
$$170$$ −3.00000 −0.230089
$$171$$ −2.00000 −0.152944
$$172$$ 4.00000 + 5.19615i 0.304997 + 0.396203i
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 3.00000 0.227429
$$175$$ 6.00000 + 10.3923i 0.453557 + 0.785584i
$$176$$ 0 0
$$177$$ −6.00000 10.3923i −0.450988 0.781133i
$$178$$ 0.500000 + 0.866025i 0.0374766 + 0.0649113i
$$179$$ 0.500000 0.866025i 0.0373718 0.0647298i −0.846735 0.532016i $$-0.821435\pi$$
0.884106 + 0.467286i $$0.154768\pi$$
$$180$$ −2.00000 −0.149071
$$181$$ −3.50000 + 6.06218i −0.260153 + 0.450598i −0.966282 0.257485i $$-0.917106\pi$$
0.706129 + 0.708083i $$0.250440\pi$$
$$182$$ 7.50000 + 12.9904i 0.555937 + 0.962911i
$$183$$ −13.0000 −0.960988
$$184$$ −10.5000 18.1865i −0.774070 1.34073i
$$185$$ −4.50000 + 7.79423i −0.330847 + 0.573043i
$$186$$ −2.50000 + 4.33013i −0.183309 + 0.317500i
$$187$$ 0 0
$$188$$ 8.00000 0.583460
$$189$$ 7.50000 12.9904i 0.545545 0.944911i
$$190$$ 0.500000 0.866025i 0.0362738 0.0628281i
$$191$$ 9.50000 + 16.4545i 0.687396 + 1.19060i 0.972677 + 0.232161i $$0.0745796\pi$$
−0.285282 + 0.958444i $$0.592087\pi$$
$$192$$ −3.50000 6.06218i −0.252591 0.437500i
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ −2.00000 −0.143592
$$195$$ −2.50000 4.33013i −0.179029 0.310087i
$$196$$ 1.00000 + 1.73205i 0.0714286 + 0.123718i
$$197$$ −5.50000 + 9.52628i −0.391859 + 0.678719i −0.992695 0.120653i $$-0.961501\pi$$
0.600836 + 0.799372i $$0.294834\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −6.00000 + 10.3923i −0.424264 + 0.734847i
$$201$$ 1.50000 2.59808i 0.105802 0.183254i
$$202$$ 4.50000 7.79423i 0.316619 0.548400i
$$203$$ −4.50000 7.79423i −0.315838 0.547048i
$$204$$ −3.00000 −0.210042
$$205$$ −5.00000 8.66025i −0.349215 0.604858i
$$206$$ −3.50000 + 6.06218i −0.243857 + 0.422372i
$$207$$ 14.0000 0.973067
$$208$$ −2.50000 + 4.33013i −0.173344 + 0.300240i
$$209$$ 0 0
$$210$$ 1.50000 + 2.59808i 0.103510 + 0.179284i
$$211$$ 8.00000 0.550743 0.275371 0.961338i $$-0.411199\pi$$
0.275371 + 0.961338i $$0.411199\pi$$
$$212$$ −2.50000 4.33013i −0.171701 0.297394i
$$213$$ −1.00000 −0.0685189
$$214$$ 12.0000 0.820303
$$215$$ 2.50000 6.06218i 0.170499 0.413437i
$$216$$ 15.0000 1.02062
$$217$$ 15.0000 1.01827
$$218$$ −3.50000 6.06218i −0.237050 0.410582i
$$219$$ 11.0000 0.743311
$$220$$ 0 0
$$221$$ 7.50000 + 12.9904i 0.504505 + 0.873828i
$$222$$ 4.50000 7.79423i 0.302020 0.523114i
$$223$$ 20.0000 1.33930 0.669650 0.742677i $$-0.266444\pi$$
0.669650 + 0.742677i $$0.266444\pi$$
$$224$$ −7.50000 + 12.9904i −0.501115 + 0.867956i
$$225$$ −4.00000 6.92820i −0.266667 0.461880i
$$226$$ −2.00000 −0.133038
$$227$$ 3.50000 + 6.06218i 0.232303 + 0.402361i 0.958485 0.285141i $$-0.0920405\pi$$
−0.726182 + 0.687502i $$0.758707\pi$$
$$228$$ 0.500000 0.866025i 0.0331133 0.0573539i
$$229$$ 4.50000 7.79423i 0.297368 0.515057i −0.678165 0.734910i $$-0.737224\pi$$
0.975533 + 0.219853i $$0.0705577\pi$$
$$230$$ −3.50000 + 6.06218i −0.230783 + 0.399728i
$$231$$ 0 0
$$232$$ 4.50000 7.79423i 0.295439 0.511716i
$$233$$ 4.50000 7.79423i 0.294805 0.510617i −0.680135 0.733087i $$-0.738079\pi$$
0.974939 + 0.222470i $$0.0714120\pi$$
$$234$$ −5.00000 8.66025i −0.326860 0.566139i
$$235$$ −4.00000 6.92820i −0.260931 0.451946i
$$236$$ −12.0000 −0.781133
$$237$$ −5.00000 −0.324785
$$238$$ −4.50000 7.79423i −0.291692 0.505225i
$$239$$ −12.5000 21.6506i −0.808558 1.40046i −0.913863 0.406023i $$-0.866915\pi$$
0.105305 0.994440i $$-0.466418\pi$$
$$240$$ −0.500000 + 0.866025i −0.0322749 + 0.0559017i
$$241$$ −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i $$-0.993829\pi$$
0.516695 + 0.856170i $$0.327162\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ −8.00000 + 13.8564i −0.513200 + 0.888889i
$$244$$ −6.50000 + 11.2583i −0.416120 + 0.720741i
$$245$$ 1.00000 1.73205i 0.0638877 0.110657i
$$246$$ 5.00000 + 8.66025i 0.318788 + 0.552158i
$$247$$ −5.00000 −0.318142
$$248$$ 7.50000 + 12.9904i 0.476250 + 0.824890i
$$249$$ −4.50000 + 7.79423i −0.285176 + 0.493939i
$$250$$ 9.00000 0.569210
$$251$$ −3.50000 + 6.06218i −0.220918 + 0.382641i −0.955087 0.296326i $$-0.904239\pi$$
0.734169 + 0.678967i $$0.237572\pi$$
$$252$$ −3.00000 5.19615i −0.188982 0.327327i
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 1.50000 + 2.59808i 0.0939336 + 0.162698i
$$256$$ −17.0000 −1.06250
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ −2.50000 + 6.06218i −0.155643 + 0.377415i
$$259$$ −27.0000 −1.67770
$$260$$ −5.00000 −0.310087
$$261$$ 3.00000 + 5.19615i 0.185695 + 0.321634i
$$262$$ −4.00000 −0.247121
$$263$$ −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i $$-0.942499\pi$$
0.336270 0.941766i $$-0.390834\pi$$
$$264$$ 0 0
$$265$$ −2.50000 + 4.33013i −0.153574 + 0.265998i
$$266$$ 3.00000 0.183942
$$267$$ 0.500000 0.866025i 0.0305995 0.0529999i
$$268$$ −1.50000 2.59808i −0.0916271 0.158703i
$$269$$ 14.0000 0.853595 0.426798 0.904347i $$-0.359642\pi$$
0.426798 + 0.904347i $$0.359642\pi$$
$$270$$ −2.50000 4.33013i −0.152145 0.263523i
$$271$$ −11.5000 + 19.9186i −0.698575 + 1.20997i 0.270385 + 0.962752i $$0.412849\pi$$
−0.968960 + 0.247216i $$0.920484\pi$$
$$272$$ 1.50000 2.59808i 0.0909509 0.157532i
$$273$$ 7.50000 12.9904i 0.453921 0.786214i
$$274$$ −18.0000 −1.08742
$$275$$ 0 0
$$276$$ −3.50000 + 6.06218i −0.210675 + 0.364900i
$$277$$ −3.50000 6.06218i −0.210295 0.364241i 0.741512 0.670940i $$-0.234109\pi$$
−0.951807 + 0.306699i $$0.900776\pi$$
$$278$$ −6.50000 11.2583i −0.389844 0.675230i
$$279$$ −10.0000 −0.598684
$$280$$ 9.00000 0.537853
$$281$$ 8.50000 + 14.7224i 0.507067 + 0.878267i 0.999967 + 0.00818015i $$0.00260385\pi$$
−0.492899 + 0.870087i $$0.664063\pi$$
$$282$$ 4.00000 + 6.92820i 0.238197 + 0.412568i
$$283$$ −1.50000 + 2.59808i −0.0891657 + 0.154440i −0.907159 0.420789i $$-0.861753\pi$$
0.817993 + 0.575228i $$0.195087\pi$$
$$284$$ −0.500000 + 0.866025i −0.0296695 + 0.0513892i
$$285$$ −1.00000 −0.0592349
$$286$$ 0 0
$$287$$ 15.0000 25.9808i 0.885422 1.53360i
$$288$$ 5.00000 8.66025i 0.294628 0.510310i
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ −3.00000 −0.176166
$$291$$ 1.00000 + 1.73205i 0.0586210 + 0.101535i
$$292$$ 5.50000 9.52628i 0.321863 0.557483i
$$293$$ −14.0000 −0.817889 −0.408944 0.912559i $$-0.634103\pi$$
−0.408944 + 0.912559i $$0.634103\pi$$
$$294$$ −1.00000 + 1.73205i −0.0583212 + 0.101015i
$$295$$ 6.00000 + 10.3923i 0.349334 + 0.605063i
$$296$$ −13.5000 23.3827i −0.784672 1.35909i
$$297$$ 0 0
$$298$$ 10.5000 + 18.1865i 0.608249 + 1.05352i
$$299$$ 35.0000 2.02410
$$300$$ 4.00000 0.230940
$$301$$ 19.5000 2.59808i 1.12396 0.149751i
$$302$$ −8.00000 −0.460348
$$303$$ −9.00000 −0.517036
$$304$$ 0.500000 + 0.866025i 0.0286770 + 0.0496700i
$$305$$ 13.0000 0.744378
$$306$$ 3.00000 + 5.19615i 0.171499 + 0.297044i
$$307$$ −2.50000 4.33013i −0.142683 0.247133i 0.785823 0.618451i $$-0.212239\pi$$
−0.928506 + 0.371318i $$0.878906\pi$$
$$308$$ 0 0
$$309$$ 7.00000 0.398216
$$310$$ 2.50000 4.33013i 0.141990 0.245935i
$$311$$ 1.50000 + 2.59808i 0.0850572 + 0.147323i 0.905416 0.424526i $$-0.139559\pi$$
−0.820358 + 0.571850i $$0.806226\pi$$
$$312$$ 15.0000 0.849208
$$313$$ 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i $$-0.00714060\pi$$
−0.519300 + 0.854592i $$0.673807\pi$$
$$314$$ 0.500000 0.866025i 0.0282166 0.0488726i
$$315$$ −3.00000 + 5.19615i −0.169031 + 0.292770i
$$316$$ −2.50000 + 4.33013i −0.140636 + 0.243589i
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 2.50000 4.33013i 0.140193 0.242821i
$$319$$ 0 0
$$320$$ 3.50000 + 6.06218i 0.195656 + 0.338886i
$$321$$ −6.00000 10.3923i −0.334887 0.580042i
$$322$$ −21.0000 −1.17028
$$323$$ 3.00000 0.166924
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ −10.0000 17.3205i −0.554700 0.960769i
$$326$$ 0.500000 0.866025i 0.0276924 0.0479647i
$$327$$ −3.50000 + 6.06218i −0.193550 + 0.335239i
$$328$$ 30.0000 1.65647
$$329$$ 12.0000 20.7846i 0.661581 1.14589i
$$330$$ 0 0
$$331$$ −9.50000 + 16.4545i −0.522167 + 0.904420i 0.477500 + 0.878632i $$0.341543\pi$$
−0.999667 + 0.0257885i $$0.991790\pi$$
$$332$$ 4.50000 + 7.79423i 0.246970 + 0.427764i
$$333$$ 18.0000 0.986394
$$334$$ 1.50000 + 2.59808i 0.0820763 + 0.142160i
$$335$$ −1.50000 + 2.59808i −0.0819538 + 0.141948i
$$336$$ −3.00000 −0.163663
$$337$$ −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i $$-0.859372\pi$$
0.822274 + 0.569091i $$0.192705\pi$$
$$338$$ −6.00000 10.3923i −0.326357 0.565267i
$$339$$ 1.00000 + 1.73205i 0.0543125 + 0.0940721i
$$340$$ 3.00000 0.162698
$$341$$ 0 0
$$342$$ −2.00000 −0.108148
$$343$$ −15.0000 −0.809924
$$344$$ 12.0000 + 15.5885i 0.646997 + 0.840473i
$$345$$ 7.00000 0.376867
$$346$$ −6.00000 −0.322562
$$347$$ −18.5000 32.0429i −0.993132 1.72016i −0.597890 0.801578i $$-0.703994\pi$$
−0.395242 0.918577i $$-0.629339\pi$$
$$348$$ −3.00000 −0.160817
$$349$$ 0.500000 + 0.866025i 0.0267644 + 0.0463573i 0.879097 0.476642i $$-0.158146\pi$$
−0.852333 + 0.523000i $$0.824813\pi$$
$$350$$ 6.00000 + 10.3923i 0.320713 + 0.555492i
$$351$$ −12.5000 + 21.6506i −0.667201 + 1.15563i
$$352$$ 0 0
$$353$$ 12.5000 21.6506i 0.665308 1.15235i −0.313894 0.949458i $$-0.601634\pi$$
0.979202 0.202889i $$-0.0650330\pi$$
$$354$$ −6.00000 10.3923i −0.318896 0.552345i
$$355$$ 1.00000 0.0530745
$$356$$ −0.500000 0.866025i −0.0264999 0.0458993i
$$357$$ −4.50000 + 7.79423i −0.238165 + 0.412514i
$$358$$ 0.500000 0.866025i 0.0264258 0.0457709i
$$359$$ −9.50000 + 16.4545i −0.501391 + 0.868434i 0.498608 + 0.866828i $$0.333845\pi$$
−0.999999 + 0.00160673i $$0.999489\pi$$
$$360$$ −6.00000 −0.316228
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ −3.50000 + 6.06218i −0.183956 + 0.318621i
$$363$$ 5.50000 + 9.52628i 0.288675 + 0.500000i
$$364$$ −7.50000 12.9904i −0.393107 0.680881i
$$365$$ −11.0000 −0.575766
$$366$$ −13.0000 −0.679521
$$367$$ −6.50000 11.2583i −0.339297 0.587680i 0.645003 0.764180i $$-0.276856\pi$$
−0.984301 + 0.176500i $$0.943523\pi$$
$$368$$ −3.50000 6.06218i −0.182450 0.316013i
$$369$$ −10.0000 + 17.3205i −0.520579 + 0.901670i
$$370$$ −4.50000 + 7.79423i −0.233944 + 0.405203i
$$371$$ −15.0000 −0.778761
$$372$$ 2.50000 4.33013i 0.129619 0.224507i
$$373$$ −5.50000 + 9.52628i −0.284779 + 0.493252i −0.972556 0.232671i $$-0.925254\pi$$
0.687776 + 0.725923i $$0.258587\pi$$
$$374$$ 0 0
$$375$$ −4.50000 7.79423i −0.232379 0.402492i
$$376$$ 24.0000 1.23771
$$377$$ 7.50000 + 12.9904i 0.386270 + 0.669039i
$$378$$ 7.50000 12.9904i 0.385758 0.668153i
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ −0.500000 + 0.866025i −0.0256495 + 0.0444262i
$$381$$ −8.00000 13.8564i −0.409852 0.709885i
$$382$$ 9.50000 + 16.4545i 0.486062 + 0.841885i
$$383$$ 8.00000 0.408781 0.204390 0.978889i $$-0.434479\pi$$
0.204390 + 0.978889i $$0.434479\pi$$
$$384$$ 1.50000 + 2.59808i 0.0765466 + 0.132583i
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ −13.0000 + 1.73205i −0.660827 + 0.0880451i
$$388$$ 2.00000 0.101535
$$389$$ −6.00000 −0.304212 −0.152106 0.988364i $$-0.548606\pi$$
−0.152106 + 0.988364i $$0.548606\pi$$
$$390$$ −2.50000 4.33013i −0.126592 0.219265i
$$391$$ −21.0000 −1.06202
$$392$$ 3.00000 + 5.19615i 0.151523 + 0.262445i
$$393$$ 2.00000 + 3.46410i 0.100887 + 0.174741i
$$394$$ −5.50000 + 9.52628i −0.277086 + 0.479927i
$$395$$ 5.00000 0.251577
$$396$$ 0 0
$$397$$ 10.5000 + 18.1865i 0.526980 + 0.912756i 0.999506 + 0.0314391i $$0.0100090\pi$$
−0.472526 + 0.881317i $$0.656658\pi$$
$$398$$ 8.00000 0.401004
$$399$$ −1.50000 2.59808i −0.0750939 0.130066i
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ 18.5000 32.0429i 0.923846 1.60015i 0.130439 0.991456i $$-0.458361\pi$$
0.793407 0.608692i $$-0.208305\pi$$
$$402$$ 1.50000 2.59808i 0.0748132 0.129580i
$$403$$ −25.0000 −1.24534
$$404$$ −4.50000 + 7.79423i −0.223883 + 0.387777i
$$405$$ 0.500000 0.866025i 0.0248452 0.0430331i
$$406$$ −4.50000 7.79423i −0.223331 0.386821i
$$407$$ 0 0
$$408$$ −9.00000 −0.445566
$$409$$ −18.0000 −0.890043 −0.445021 0.895520i $$-0.646804\pi$$
−0.445021 + 0.895520i $$0.646804\pi$$
$$410$$ −5.00000 8.66025i −0.246932 0.427699i
$$411$$ 9.00000 + 15.5885i 0.443937 + 0.768922i
$$412$$ 3.50000 6.06218i 0.172433 0.298662i
$$413$$ −18.0000 + 31.1769i −0.885722 + 1.53412i
$$414$$ 14.0000 0.688062
$$415$$ 4.50000 7.79423i 0.220896 0.382604i
$$416$$ 12.5000 21.6506i 0.612863 1.06151i
$$417$$ −6.50000 + 11.2583i −0.318306 + 0.551323i
$$418$$ 0 0
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ −1.50000 2.59808i −0.0731925 0.126773i
$$421$$ 18.5000 32.0429i 0.901635 1.56168i 0.0762630 0.997088i $$-0.475701\pi$$
0.825372 0.564590i $$-0.190966\pi$$
$$422$$ 8.00000 0.389434
$$423$$ −8.00000 + 13.8564i −0.388973 + 0.673722i
$$424$$ −7.50000 12.9904i −0.364232 0.630869i
$$425$$ 6.00000 + 10.3923i 0.291043 + 0.504101i
$$426$$ −1.00000 −0.0484502
$$427$$ 19.5000 + 33.7750i 0.943671 + 1.63449i
$$428$$ −12.0000 −0.580042
$$429$$ 0 0
$$430$$ 2.50000 6.06218i 0.120561 0.292344i
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 5.00000 0.240563
$$433$$ −13.5000 23.3827i −0.648769 1.12370i −0.983417 0.181357i $$-0.941951\pi$$
0.334649 0.942343i $$-0.391382\pi$$
$$434$$ 15.0000 0.720023
$$435$$ 1.50000 + 2.59808i 0.0719195 + 0.124568i
$$436$$ 3.50000 + 6.06218i 0.167620 + 0.290326i
$$437$$ 3.50000 6.06218i 0.167428 0.289993i
$$438$$ 11.0000 0.525600
$$439$$ 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i $$-0.732928\pi$$
0.978412 + 0.206666i $$0.0662612\pi$$
$$440$$ 0 0
$$441$$ −4.00000 −0.190476
$$442$$ 7.50000 + 12.9904i 0.356739 + 0.617889i
$$443$$ 18.5000 32.0429i 0.878962 1.52241i 0.0264796 0.999649i $$-0.491570\pi$$
0.852482 0.522757i $$-0.175096\pi$$
$$444$$ −4.50000 + 7.79423i −0.213561 + 0.369898i
$$445$$ −0.500000 + 0.866025i −0.0237023 + 0.0410535i
$$446$$ 20.0000 0.947027
$$447$$ 10.5000 18.1865i 0.496633 0.860194i
$$448$$ −10.5000 + 18.1865i −0.496078 + 0.859233i
$$449$$ 10.5000 + 18.1865i 0.495526 + 0.858276i 0.999987 0.00515887i $$-0.00164213\pi$$
−0.504461 + 0.863434i $$0.668309\pi$$
$$450$$ −4.00000 6.92820i −0.188562 0.326599i
$$451$$ 0 0
$$452$$ 2.00000 0.0940721
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 3.50000 + 6.06218i 0.164263 + 0.284512i
$$455$$ −7.50000 + 12.9904i −0.351605 + 0.608998i
$$456$$ 1.50000 2.59808i 0.0702439 0.121666i
$$457$$ 6.00000 0.280668 0.140334 0.990104i $$-0.455182\pi$$
0.140334 + 0.990104i $$0.455182\pi$$
$$458$$ 4.50000 7.79423i 0.210271 0.364200i
$$459$$ 7.50000 12.9904i 0.350070 0.606339i
$$460$$ 3.50000 6.06218i 0.163188 0.282650i
$$461$$ −1.50000 2.59808i −0.0698620 0.121004i 0.828978 0.559281i $$-0.188923\pi$$
−0.898840 + 0.438276i $$0.855589\pi$$
$$462$$ 0 0
$$463$$ 11.5000 + 19.9186i 0.534450 + 0.925695i 0.999190 + 0.0402476i $$0.0128147\pi$$
−0.464739 + 0.885448i $$0.653852\pi$$
$$464$$ 1.50000 2.59808i 0.0696358 0.120613i
$$465$$ −5.00000 −0.231869
$$466$$ 4.50000 7.79423i 0.208458 0.361061i
$$467$$ −10.5000 18.1865i −0.485882 0.841572i 0.513986 0.857798i $$-0.328168\pi$$
−0.999868 + 0.0162260i $$0.994835\pi$$
$$468$$ 5.00000 + 8.66025i 0.231125 + 0.400320i
$$469$$ −9.00000 −0.415581
$$470$$ −4.00000 6.92820i −0.184506 0.319574i
$$471$$ −1.00000 −0.0460776
$$472$$ −36.0000 −1.65703
$$473$$ 0 0
$$474$$ −5.00000 −0.229658
$$475$$ −4.00000 −0.183533
$$476$$ 4.50000 + 7.79423i 0.206257 + 0.357248i
$$477$$ 10.0000 0.457869
$$478$$ −12.5000 21.6506i −0.571737 0.990277i
$$479$$ 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i $$-0.0553307\pi$$
−0.642246 + 0.766498i $$0.721997\pi$$
$$480$$ 2.50000 4.33013i 0.114109 0.197642i
$$481$$ 45.0000 2.05182
$$482$$ −7.50000 + 12.9904i −0.341616 + 0.591696i
$$483$$ 10.5000 + 18.1865i 0.477767 + 0.827516i
$$484$$ 11.0000 0.500000
$$485$$ −1.00000 1.73205i −0.0454077 0.0786484i
$$486$$ −8.00000 + 13.8564i −0.362887 + 0.628539i
$$487$$ 4.50000 7.79423i 0.203914 0.353190i −0.745872 0.666089i $$-0.767967\pi$$
0.949786 + 0.312899i $$0.101300\pi$$
$$488$$ −19.5000 + 33.7750i −0.882724 + 1.52892i
$$489$$ −1.00000 −0.0452216
$$490$$ 1.00000 1.73205i 0.0451754 0.0782461i
$$491$$ 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i $$-0.768237\pi$$
0.949520 + 0.313707i $$0.101571\pi$$
$$492$$ −5.00000 8.66025i −0.225417 0.390434i
$$493$$ −4.50000 7.79423i −0.202670 0.351034i
$$494$$ −5.00000 −0.224961
$$495$$ 0 0
$$496$$ 2.50000 + 4.33013i 0.112253 + 0.194428i
$$497$$ 1.50000 + 2.59808i 0.0672842 + 0.116540i
$$498$$ −4.50000 + 7.79423i −0.201650 + 0.349268i
$$499$$ 8.50000 14.7224i 0.380512 0.659067i −0.610623 0.791921i $$-0.709081\pi$$
0.991136 + 0.132855i $$0.0424144\pi$$
$$500$$ −9.00000 −0.402492
$$501$$ 1.50000 2.59808i 0.0670151 0.116073i
$$502$$ −3.50000 + 6.06218i −0.156213 + 0.270568i
$$503$$ 4.50000 7.79423i 0.200645 0.347527i −0.748091 0.663596i $$-0.769030\pi$$
0.948736 + 0.316068i $$0.102363\pi$$
$$504$$ −9.00000 15.5885i −0.400892 0.694365i
$$505$$ 9.00000 0.400495
$$506$$ 0 0
$$507$$ −6.00000 + 10.3923i −0.266469 + 0.461538i
$$508$$ −16.0000 −0.709885
$$509$$ −13.5000 + 23.3827i −0.598377 + 1.03642i 0.394684 + 0.918817i $$0.370854\pi$$
−0.993061 + 0.117602i $$0.962479\pi$$
$$510$$ 1.50000 + 2.59808i 0.0664211 + 0.115045i
$$511$$ −16.5000 28.5788i −0.729917 1.26425i
$$512$$ −11.0000 −0.486136
$$513$$ 2.50000 + 4.33013i 0.110378 + 0.191180i
$$514$$ 6.00000 0.264649
$$515$$ −7.00000 −0.308457
$$516$$ 2.50000 6.06218i 0.110056 0.266872i
$$517$$ 0 0
$$518$$ −27.0000 −1.18631
$$519$$ 3.00000 + 5.19615i 0.131685 + 0.228086i
$$520$$ −15.0000 −0.657794
$$521$$ −17.5000 30.3109i −0.766689 1.32794i −0.939349 0.342963i $$-0.888570\pi$$
0.172660 0.984981i $$-0.444764\pi$$
$$522$$ 3.00000 + 5.19615i 0.131306 + 0.227429i
$$523$$ 10.5000 18.1865i 0.459133 0.795242i −0.539782 0.841805i $$-0.681493\pi$$
0.998915 + 0.0465630i $$0.0148268\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 6.00000 10.3923i 0.261861 0.453557i
$$526$$ −10.5000 18.1865i −0.457822 0.792971i
$$527$$ 15.0000 0.653410
$$528$$ 0 0
$$529$$ −13.0000 + 22.5167i −0.565217 + 0.978985i
$$530$$ −2.50000 + 4.33013i −0.108593 + 0.188089i
$$531$$ 12.0000 20.7846i 0.520756 0.901975i
$$532$$ −3.00000 −0.130066
$$533$$ −25.0000 + 43.3013i −1.08287 + 1.87559i
$$534$$ 0.500000 0.866025i 0.0216371 0.0374766i
$$535$$ 6.00000 + 10.3923i 0.259403 + 0.449299i
$$536$$ −4.50000 7.79423i −0.194370 0.336659i
$$537$$ −1.00000 −0.0431532
$$538$$ 14.0000 0.603583
$$539$$ 0 0
$$540$$ 2.50000 + 4.33013i 0.107583 + 0.186339i
$$541$$ −15.5000 + 26.8468i −0.666397 + 1.15423i 0.312507 + 0.949915i $$0.398831\pi$$
−0.978905 + 0.204318i $$0.934502\pi$$
$$542$$ −11.5000 + 19.9186i −0.493967 + 0.855576i
$$543$$ 7.00000 0.300399
$$544$$ −7.50000 + 12.9904i −0.321560 + 0.556958i
$$545$$ 3.50000 6.06218i 0.149924 0.259675i
$$546$$ 7.50000 12.9904i 0.320970 0.555937i
$$547$$ −0.500000 0.866025i −0.0213785 0.0370286i 0.855138 0.518400i $$-0.173472\pi$$
−0.876517 + 0.481371i $$0.840139\pi$$
$$548$$ 18.0000 0.768922
$$549$$ −13.0000 22.5167i −0.554826 0.960988i
$$550$$ 0 0
$$551$$ 3.00000 0.127804
$$552$$ −10.5000 + 18.1865i −0.446910 + 0.774070i
$$553$$ 7.50000 + 12.9904i 0.318932 + 0.552407i
$$554$$ −3.50000 6.06218i −0.148701 0.257557i
$$555$$ 9.00000 0.382029
$$556$$ 6.50000 + 11.2583i 0.275661 + 0.477460i
$$557$$ −6.00000 −0.254228 −0.127114 0.991888i $$-0.540571\pi$$
−0.127114 + 0.991888i $$0.540571\pi$$
$$558$$ −10.0000 −0.423334
$$559$$ −32.5000 + 4.33013i −1.37460 + 0.183145i
$$560$$ 3.00000 0.126773
$$561$$ 0 0
$$562$$ 8.50000 + 14.7224i 0.358551 + 0.621028i
$$563$$ 4.00000 0.168580 0.0842900 0.996441i $$-0.473138\pi$$
0.0842900 + 0.996441i $$0.473138\pi$$
$$564$$ −4.00000 6.92820i −0.168430 0.291730i
$$565$$ −1.00000 1.73205i −0.0420703 0.0728679i
$$566$$ −1.50000 + 2.59808i −0.0630497 + 0.109205i
$$567$$ 3.00000 0.125988
$$568$$ −1.50000 + 2.59808i −0.0629386 + 0.109013i
$$569$$ 8.50000 + 14.7224i 0.356339 + 0.617196i 0.987346 0.158580i $$-0.0506917\pi$$
−0.631008 + 0.775777i $$0.717358\pi$$
$$570$$ −1.00000 −0.0418854
$$571$$ −6.50000 11.2583i −0.272017 0.471146i 0.697362 0.716720i $$-0.254357\pi$$
−0.969378 + 0.245573i $$0.921024\pi$$
$$572$$ 0 0
$$573$$ 9.50000 16.4545i 0.396868 0.687396i
$$574$$ 15.0000 25.9808i 0.626088 1.08442i
$$575$$ 28.0000 1.16768
$$576$$ 7.00000 12.1244i 0.291667 0.505181i
$$577$$ 2.50000 4.33013i 0.104076 0.180266i −0.809284 0.587417i $$-0.800145\pi$$
0.913360 + 0.407152i $$0.133478\pi$$
$$578$$ 4.00000 + 6.92820i 0.166378 + 0.288175i
$$579$$ −3.00000 5.19615i −0.124676 0.215945i
$$580$$ 3.00000 0.124568
$$581$$ 27.0000 1.12015
$$582$$ 1.00000 + 1.73205i 0.0414513 + 0.0717958i
$$583$$ 0 0
$$584$$ 16.5000 28.5788i 0.682775 1.18260i
$$585$$ 5.00000 8.66025i 0.206725 0.358057i
$$586$$ −14.0000 −0.578335
$$587$$ 6.50000 11.2583i 0.268284 0.464681i −0.700135 0.714010i $$-0.746877\pi$$
0.968419 + 0.249329i $$0.0802102\pi$$
$$588$$ 1.00000 1.73205i 0.0412393 0.0714286i
$$589$$ −2.50000 + 4.33013i −0.103011 + 0.178420i
$$590$$ 6.00000 + 10.3923i 0.247016 + 0.427844i
$$591$$ 11.0000 0.452480
$$592$$ −4.50000 7.79423i −0.184949 0.320341i
$$593$$ 0.500000 0.866025i 0.0205325 0.0355634i −0.855577 0.517676i $$-0.826797\pi$$
0.876109 + 0.482113i $$0.160130\pi$$
$$594$$ 0 0
$$595$$ 4.50000 7.79423i 0.184482 0.319532i
$$596$$ −10.5000 18.1865i −0.430097 0.744949i
$$597$$ −4.00000 6.92820i −0.163709 0.283552i
$$598$$ 35.0000 1.43126
$$599$$ 15.5000 + 26.8468i 0.633313 + 1.09693i 0.986870 + 0.161517i $$0.0516387\pi$$
−0.353557 + 0.935413i $$0.615028\pi$$
$$600$$ 12.0000 0.489898
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 19.5000 2.59808i 0.794761 0.105890i
$$603$$ 6.00000 0.244339
$$604$$ 8.00000 0.325515
$$605$$ −5.50000 9.52628i −0.223607 0.387298i
$$606$$ −9.00000 −0.365600
$$607$$ 21.5000 + 37.2391i 0.872658 + 1.51149i 0.859237 + 0.511578i $$0.170939\pi$$
0.0134214 + 0.999910i $$0.495728\pi$$
$$608$$ −2.50000 4.33013i −0.101388 0.175610i
$$609$$ −4.50000 + 7.79423i −0.182349 + 0.315838i
$$610$$ 13.0000 0.526355
$$611$$ −20.0000 + 34.6410i −0.809113 + 1.40143i
$$612$$ −3.00000 5.19615i −0.121268 0.210042i
$$613$$ −30.0000 −1.21169 −0.605844 0.795583i $$-0.707165\pi$$
−0.605844 + 0.795583i $$0.707165\pi$$
$$614$$ −2.50000 4.33013i −0.100892 0.174750i
$$615$$ −5.00000 + 8.66025i −0.201619 + 0.349215i
$$616$$ 0 0
$$617$$ −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i $$-0.852567\pi$$
0.834251 + 0.551385i $$0.185900\pi$$
$$618$$ 7.00000 0.281581
$$619$$ 10.5000 18.1865i 0.422031 0.730978i −0.574107 0.818780i $$-0.694651\pi$$
0.996138 + 0.0878015i $$0.0279841\pi$$
$$620$$ −2.50000 + 4.33013i −0.100402 + 0.173902i
$$621$$ −17.5000 30.3109i −0.702251 1.21633i
$$622$$ 1.50000 + 2.59808i 0.0601445 + 0.104173i
$$623$$ −3.00000 −0.120192
$$624$$ 5.00000 0.200160
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ 8.50000 + 14.7224i 0.339728 + 0.588427i
$$627$$ 0 0
$$628$$ −0.500000 + 0.866025i −0.0199522 + 0.0345582i
$$629$$ −27.0000 −1.07656
$$630$$ −3.00000 + 5.19615i −0.119523 + 0.207020i
$$631$$ 4.50000 7.79423i 0.179142 0.310283i −0.762445 0.647053i $$-0.776001\pi$$
0.941587 + 0.336770i $$0.109334\pi$$
$$632$$ −7.50000 + 12.9904i −0.298334 + 0.516730i
$$633$$ −4.00000 6.92820i −0.158986 0.275371i
$$634$$ −18.0000 −0.714871
$$635$$ 8.00000 + 13.8564i 0.317470 + 0.549875i
$$636$$ −2.50000 + 4.33013i −0.0991314 + 0.171701i
$$637$$ −10.0000 −0.396214
$$638$$ 0 0
$$639$$ −1.00000 1.73205i −0.0395594 0.0685189i
$$640$$ −1.50000 2.59808i −0.0592927 0.102698i
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ 12.0000 0.473234 0.236617 0.971603i $$-0.423961\pi$$
0.236617 + 0.971603i $$0.423961\pi$$
$$644$$ 21.0000 0.827516
$$645$$ −6.50000 + 0.866025i −0.255937 + 0.0340997i
$$646$$ 3.00000 0.118033
$$647$$ −12.0000 −0.471769 −0.235884 0.971781i $$-0.575799\pi$$
−0.235884 + 0.971781i $$0.575799\pi$$
$$648$$ 1.50000 + 2.59808i 0.0589256 + 0.102062i
$$649$$ 0 0
$$650$$ −10.0000 17.3205i −0.392232 0.679366i
$$651$$ −7.50000 12.9904i −0.293948 0.509133i
$$652$$ −0.500000 + 0.866025i −0.0195815 + 0.0339162i
$$653$$ −50.0000 −1.95665 −0.978326 0.207072i $$-0.933606\pi$$
−0.978326 + 0.207072i $$0.933606\pi$$
$$654$$ −3.50000 + 6.06218i −0.136861 + 0.237050i
$$655$$ −2.00000 3.46410i −0.0781465 0.135354i
$$656$$ 10.0000 0.390434
$$657$$ 11.0000 + 19.0526i 0.429151 + 0.743311i
$$658$$ 12.0000 20.7846i 0.467809 0.810268i
$$659$$ −11.5000 + 19.9186i −0.447976 + 0.775918i −0.998254 0.0590638i $$-0.981188\pi$$
0.550278 + 0.834982i $$0.314522\pi$$
$$660$$ 0 0
$$661$$ −14.0000 −0.544537 −0.272268 0.962221i $$-0.587774\pi$$
−0.272268 + 0.962221i $$0.587774\pi$$
$$662$$ −9.50000 + 16.4545i −0.369228 + 0.639522i
$$663$$ 7.50000 12.9904i 0.291276 0.504505i
$$664$$ 13.5000 + 23.3827i 0.523902 + 0.907424i
$$665$$ 1.50000 + 2.59808i 0.0581675 + 0.100749i
$$666$$ 18.0000 0.697486
$$667$$ −21.0000 −0.813123
$$668$$ −1.50000 2.59808i −0.0580367 0.100523i
$$669$$ −10.0000 17.3205i −0.386622 0.669650i
$$670$$ −1.50000 + 2.59808i −0.0579501 + 0.100372i
$$671$$ 0 0
$$672$$ 15.0000 0.578638
$$673$$ −23.5000 + 40.7032i −0.905858 + 1.56899i −0.0860977 + 0.996287i $$0.527440\pi$$
−0.819761 + 0.572706i $$0.805894\pi$$
$$674$$ −1.50000 + 2.59808i −0.0577778 + 0.100074i
$$675$$ −10.0000 + 17.3205i −0.384900 + 0.666667i
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ −14.0000 −0.538064 −0.269032 0.963131i $$-0.586704\pi$$
−0.269032 + 0.963131i $$0.586704\pi$$
$$678$$ 1.00000 + 1.73205i 0.0384048 + 0.0665190i
$$679$$ 3.00000 5.19615i 0.115129 0.199410i
$$680$$ 9.00000 0.345134
$$681$$ 3.50000 6.06218i 0.134120 0.232303i
$$682$$ 0 0
$$683$$ −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i $$-0.221750\pi$$
−0.939184 + 0.343413i $$0.888417\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ −9.00000 15.5885i −0.343872 0.595604i
$$686$$ −15.0000 −0.572703
$$687$$ −9.00000 −0.343371
$$688$$ 4.00000 + 5.19615i 0.152499 + 0.198101i
$$689$$ 25.0000 0.952424
$$690$$ 7.00000 0.266485
$$691$$ −2.50000 4.33013i −0.0951045 0.164726i 0.814548 0.580097i $$-0.196985\pi$$
−0.909652 + 0.415371i $$0.863652\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ −18.5000 32.0429i −0.702250 1.21633i
$$695$$ 6.50000 11.2583i 0.246559 0.427053i
$$696$$ −9.00000 −0.341144
$$697$$ 15.0000 25.9808i 0.568166 0.984092i
$$698$$ 0.500000 + 0.866025i 0.0189253 + 0.0327795i
$$699$$ −9.00000 −0.340411
$$700$$ −6.00000 10.3923i −0.226779 0.392792i
$$701$$ −3.50000 + 6.06218i −0.132193 + 0.228965i −0.924522 0.381129i $$-0.875535\pi$$
0.792329 + 0.610095i $$0.208869\pi$$
$$702$$ −12.5000 + 21.6506i −0.471782 + 0.817151i
$$703$$ 4.50000 7.79423i 0.169721 0.293965i
$$704$$ 0 0
$$705$$ −4.00000 + 6.92820i −0.150649 + 0.260931i
$$706$$ 12.5000 21.6506i 0.470444 0.814832i
$$707$$ 13.5000 + 23.3827i 0.507720 + 0.879396i
$$708$$ 6.00000 + 10.3923i 0.225494 + 0.390567i
$$709$$ 26.0000 0.976450 0.488225 0.872718i $$-0.337644\pi$$
0.488225 + 0.872718i $$0.337644\pi$$
$$710$$ 1.00000 0.0375293
$$711$$ −5.00000 8.66025i −0.187515 0.324785i
$$712$$ −1.50000 2.59808i −0.0562149 0.0973670i
$$713$$ 17.5000 30.3109i 0.655380 1.13515i
$$714$$ −4.50000 + 7.79423i −0.168408 + 0.291692i
$$715$$ 0 0
$$716$$ −0.500000 + 0.866025i −0.0186859 + 0.0323649i
$$717$$ −12.5000 + 21.6506i −0.466821 + 0.808558i
$$718$$ −9.50000 + 16.4545i −0.354537 + 0.614076i
$$719$$ 15.5000 + 26.8468i 0.578052 + 1.00122i 0.995703 + 0.0926083i $$0.0295204\pi$$
−0.417650 + 0.908608i $$0.637146\pi$$
$$720$$ −2.00000 −0.0745356
$$721$$ −10.5000 18.1865i −0.391040 0.677302i
$$722$$ 9.00000 15.5885i 0.334945 0.580142i
$$723$$ 15.0000 0.557856
$$724$$ 3.50000 6.06218i 0.130076 0.225299i
$$725$$ 6.00000 + 10.3923i 0.222834 + 0.385961i
$$726$$ 5.50000 + 9.52628i 0.204124 + 0.353553i
$$727$$ −32.0000 −1.18681 −0.593407 0.804902i $$-0.702218\pi$$
−0.593407 + 0.804902i $$0.702218\pi$$
$$728$$ −22.5000 38.9711i −0.833905 1.44437i
$$729$$ 13.0000 0.481481
$$730$$ −11.0000 −0.407128
$$731$$ 19.5000 2.59808i 0.721234 0.0960933i
$$732$$ 13.0000 0.480494
$$733$$ 26.0000 0.960332 0.480166 0.877178i $$-0.340576\pi$$
0.480166 + 0.877178i $$0.340576\pi$$
$$734$$ −6.50000 11.2583i −0.239919 0.415553i
$$735$$ −2.00000 −0.0737711
$$736$$ 17.5000 + 30.3109i 0.645059 + 1.11727i
$$737$$ 0 0
$$738$$ −10.0000 + 17.3205i −0.368105 + 0.637577i
$$739$$ −4.00000 −0.147142 −0.0735712 0.997290i $$-0.523440\pi$$
−0.0735712 + 0.997290i $$0.523440\pi$$
$$740$$ 4.50000 7.79423i 0.165423 0.286522i
$$741$$ 2.50000 + 4.33013i 0.0918398 + 0.159071i
$$742$$ −15.0000 −0.550667
$$743$$ −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i $$-0.292537\pi$$
−0.991798 + 0.127815i $$0.959204\pi$$
$$744$$ 7.50000 12.9904i 0.274963 0.476250i
$$745$$ −10.5000 + 18.1865i −0.384690 + 0.666303i
$$746$$ −5.50000 + 9.52628i −0.201369 + 0.348782i
$$747$$ −18.0000 −0.658586
$$748$$ 0 0
$$749$$ −18.0000 + 31.1769i −0.657706 + 1.13918i
$$750$$ −4.50000 7.79423i −0.164317 0.284605i
$$751$$ 13.5000 + 23.3827i 0.492622 + 0.853246i 0.999964 0.00849853i $$-0.00270520\pi$$
−0.507342 + 0.861745i $$0.669372\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 7.00000 0.255094
$$754$$ 7.50000 + 12.9904i 0.273134 + 0.473082i
$$755$$ −4.00000 6.92820i −0.145575 0.252143i
$$756$$ −7.50000 + 12.9904i −0.272772 + 0.472456i
$$757$$ 2.50000 4.33013i 0.0908640 0.157381i −0.817011 0.576622i $$-0.804370\pi$$
0.907875 + 0.419241i $$0.137704\pi$$
$$758$$ 20.0000 0.726433
$$759$$ 0 0
$$760$$ −1.50000 + 2.59808i −0.0544107 + 0.0942421i
$$761$$ 18.5000 32.0429i 0.670624 1.16156i −0.307103 0.951676i $$-0.599360\pi$$
0.977727 0.209879i $$-0.0673071\pi$$
$$762$$ −8.00000 13.8564i −0.289809 0.501965i
$$763$$ 21.0000 0.760251
$$764$$ −9.50000 16.4545i −0.343698 0.595302i
$$765$$ −3.00000 + 5.19615i −0.108465 + 0.187867i
$$766$$ 8.00000 0.289052
$$767$$ 30.0000 51.9615i 1.08324 1.87622i
$$768$$ 8.50000 + 14.7224i 0.306717 + 0.531250i
$$769$$ 16.5000 + 28.5788i 0.595005 + 1.03058i 0.993546 + 0.113429i $$0.0361834\pi$$
−0.398541 + 0.917151i $$0.630483\pi$$
$$770$$ 0 0
$$771$$ −3.00000 5.19615i −0.108042 0.187135i
$$772$$ −6.00000 −0.215945
$$773$$ 26.0000 0.935155 0.467578 0.883952i $$-0.345127\pi$$
0.467578 + 0.883952i $$0.345127\pi$$
$$774$$ −13.0000 + 1.73205i −0.467275 + 0.0622573i
$$775$$ −20.0000 −0.718421
$$776$$ 6.00000 0.215387
$$777$$ 13.5000 + 23.3827i 0.484310 + 0.838849i
$$778$$ −6.00000 −0.215110
$$779$$ 5.00000 + 8.66025i 0.179144 + 0.310286i
$$780$$ 2.50000