# Properties

 Label 585.2.bt.a.571.1 Level $585$ Weight $2$ Character 585.571 Analytic conductor $4.671$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$585 = 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 585.bt (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.67124851824$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 571.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 585.571 Dual form 585.2.bt.a.376.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} -3.46410 q^{6} +(-1.73205 + 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-1.73205 + 1.00000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.866025 - 0.500000i) q^{5} -3.46410 q^{6} +(-1.73205 + 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +2.00000 q^{10} +(5.19615 - 3.00000i) q^{11} +(3.00000 - 1.73205i) q^{12} +(3.23205 - 1.59808i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.866025 - 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} -1.00000 q^{17} +(-5.19615 - 3.00000i) q^{18} +8.00000i q^{19} +(-1.73205 + 1.00000i) q^{20} -3.46410 q^{21} +(-6.00000 + 10.3923i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-4.00000 + 6.00000i) q^{26} +5.19615i q^{27} +4.00000i q^{28} +(-1.00000 - 1.73205i) q^{29} +(3.00000 + 1.73205i) q^{30} +(6.92820 + 4.00000i) q^{31} +(-6.92820 - 4.00000i) q^{32} +10.3923 q^{33} +(1.73205 - 1.00000i) q^{34} +2.00000 q^{35} +6.00000 q^{36} -2.00000i q^{37} +(-8.00000 - 13.8564i) q^{38} +(6.23205 + 0.401924i) q^{39} +(1.73205 + 1.00000i) q^{41} +(6.00000 - 3.46410i) q^{42} +(-2.50000 - 4.33013i) q^{43} -12.0000i q^{44} -3.00000i q^{45} -2.00000i q^{46} +(-8.66025 + 5.00000i) q^{47} +6.92820i q^{48} +(-1.50000 + 2.59808i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(-1.50000 - 0.866025i) q^{51} +(0.464102 - 7.19615i) q^{52} +9.00000 q^{53} +(-5.19615 - 9.00000i) q^{54} -6.00000 q^{55} +(-6.92820 + 12.0000i) q^{57} +(3.46410 + 2.00000i) q^{58} +(5.19615 + 3.00000i) q^{59} -3.46410 q^{60} +(2.50000 + 4.33013i) q^{61} -16.0000 q^{62} +(-5.19615 - 3.00000i) q^{63} +8.00000 q^{64} +(-3.59808 - 0.232051i) q^{65} +(-18.0000 + 10.3923i) q^{66} +(-1.00000 + 1.73205i) q^{68} +(-1.50000 + 0.866025i) q^{69} +(-3.46410 + 2.00000i) q^{70} -10.0000i q^{71} +4.00000i q^{73} +(2.00000 + 3.46410i) q^{74} +1.73205i q^{75} +(13.8564 + 8.00000i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(-11.1962 + 5.53590i) q^{78} +(-0.500000 - 0.866025i) q^{79} -4.00000i q^{80} +(-4.50000 + 7.79423i) q^{81} -4.00000 q^{82} +(-3.46410 + 6.00000i) q^{84} +(0.866025 + 0.500000i) q^{85} +(8.66025 + 5.00000i) q^{86} -3.46410i q^{87} +(3.00000 + 5.19615i) q^{90} +(-4.00000 + 6.00000i) q^{91} +(1.00000 + 1.73205i) q^{92} +(6.92820 + 12.0000i) q^{93} +(10.0000 - 17.3205i) q^{94} +(4.00000 - 6.92820i) q^{95} +(-6.92820 - 12.0000i) q^{96} +(8.66025 - 5.00000i) q^{97} -6.00000i q^{98} +(15.5885 + 9.00000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{3} + 4 q^{4} + 6 q^{9}+O(q^{10})$$ 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9 $$4 q + 6 q^{3} + 4 q^{4} + 6 q^{9} + 8 q^{10} + 12 q^{12} + 6 q^{13} + 8 q^{14} + 8 q^{16} - 4 q^{17} - 24 q^{22} - 2 q^{23} + 2 q^{25} - 16 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{35} + 24 q^{36} - 32 q^{38} + 18 q^{39} + 24 q^{42} - 10 q^{43} - 6 q^{49} - 6 q^{51} - 12 q^{52} + 36 q^{53} - 24 q^{55} + 10 q^{61} - 64 q^{62} + 32 q^{64} - 4 q^{65} - 72 q^{66} - 4 q^{68} - 6 q^{69} + 8 q^{74} - 24 q^{77} - 24 q^{78} - 2 q^{79} - 18 q^{81} - 16 q^{82} + 12 q^{90} - 16 q^{91} + 4 q^{92} + 40 q^{94} + 16 q^{95}+O(q^{100})$$ 4 * q + 6 * q^3 + 4 * q^4 + 6 * q^9 + 8 * q^10 + 12 * q^12 + 6 * q^13 + 8 * q^14 + 8 * q^16 - 4 * q^17 - 24 * q^22 - 2 * q^23 + 2 * q^25 - 16 * q^26 - 4 * q^29 + 12 * q^30 + 8 * q^35 + 24 * q^36 - 32 * q^38 + 18 * q^39 + 24 * q^42 - 10 * q^43 - 6 * q^49 - 6 * q^51 - 12 * q^52 + 36 * q^53 - 24 * q^55 + 10 * q^61 - 64 * q^62 + 32 * q^64 - 4 * q^65 - 72 * q^66 - 4 * q^68 - 6 * q^69 + 8 * q^74 - 24 * q^77 - 24 * q^78 - 2 * q^79 - 18 * q^81 - 16 * q^82 + 12 * q^90 - 16 * q^91 + 4 * q^92 + 40 * q^94 + 16 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$$.

 $$n$$ $$326$$ $$352$$ $$496$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.73205 + 1.00000i −1.22474 + 0.707107i −0.965926 0.258819i $$-0.916667\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$3$$ 1.50000 + 0.866025i 0.866025 + 0.500000i
$$4$$ 1.00000 1.73205i 0.500000 0.866025i
$$5$$ −0.866025 0.500000i −0.387298 0.223607i
$$6$$ −3.46410 −1.41421
$$7$$ −1.73205 + 1.00000i −0.654654 + 0.377964i −0.790237 0.612801i $$-0.790043\pi$$
0.135583 + 0.990766i $$0.456709\pi$$
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 2.00000 0.632456
$$11$$ 5.19615 3.00000i 1.56670 0.904534i 0.570149 0.821541i $$-0.306886\pi$$
0.996550 0.0829925i $$-0.0264478\pi$$
$$12$$ 3.00000 1.73205i 0.866025 0.500000i
$$13$$ 3.23205 1.59808i 0.896410 0.443227i
$$14$$ 2.00000 3.46410i 0.534522 0.925820i
$$15$$ −0.866025 1.50000i −0.223607 0.387298i
$$16$$ 2.00000 + 3.46410i 0.500000 + 0.866025i
$$17$$ −1.00000 −0.242536 −0.121268 0.992620i $$-0.538696\pi$$
−0.121268 + 0.992620i $$0.538696\pi$$
$$18$$ −5.19615 3.00000i −1.22474 0.707107i
$$19$$ 8.00000i 1.83533i 0.397360 + 0.917663i $$0.369927\pi$$
−0.397360 + 0.917663i $$0.630073\pi$$
$$20$$ −1.73205 + 1.00000i −0.387298 + 0.223607i
$$21$$ −3.46410 −0.755929
$$22$$ −6.00000 + 10.3923i −1.27920 + 2.21565i
$$23$$ −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i $$-0.866580\pi$$
0.809177 + 0.587565i $$0.199913\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −4.00000 + 6.00000i −0.784465 + 1.17670i
$$27$$ 5.19615i 1.00000i
$$28$$ 4.00000i 0.755929i
$$29$$ −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i $$-0.226120\pi$$
−0.943811 + 0.330487i $$0.892787\pi$$
$$30$$ 3.00000 + 1.73205i 0.547723 + 0.316228i
$$31$$ 6.92820 + 4.00000i 1.24434 + 0.718421i 0.969975 0.243204i $$-0.0781984\pi$$
0.274367 + 0.961625i $$0.411532\pi$$
$$32$$ −6.92820 4.00000i −1.22474 0.707107i
$$33$$ 10.3923 1.80907
$$34$$ 1.73205 1.00000i 0.297044 0.171499i
$$35$$ 2.00000 0.338062
$$36$$ 6.00000 1.00000
$$37$$ 2.00000i 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ −8.00000 13.8564i −1.29777 2.24781i
$$39$$ 6.23205 + 0.401924i 0.997927 + 0.0643593i
$$40$$ 0 0
$$41$$ 1.73205 + 1.00000i 0.270501 + 0.156174i 0.629115 0.777312i $$-0.283417\pi$$
−0.358614 + 0.933486i $$0.616751\pi$$
$$42$$ 6.00000 3.46410i 0.925820 0.534522i
$$43$$ −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i $$-0.291172\pi$$
−0.991241 + 0.132068i $$0.957838\pi$$
$$44$$ 12.0000i 1.80907i
$$45$$ 3.00000i 0.447214i
$$46$$ 2.00000i 0.294884i
$$47$$ −8.66025 + 5.00000i −1.26323 + 0.729325i −0.973698 0.227844i $$-0.926832\pi$$
−0.289530 + 0.957169i $$0.593499\pi$$
$$48$$ 6.92820i 1.00000i
$$49$$ −1.50000 + 2.59808i −0.214286 + 0.371154i
$$50$$ −1.73205 1.00000i −0.244949 0.141421i
$$51$$ −1.50000 0.866025i −0.210042 0.121268i
$$52$$ 0.464102 7.19615i 0.0643593 0.997927i
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ −5.19615 9.00000i −0.707107 1.22474i
$$55$$ −6.00000 −0.809040
$$56$$ 0 0
$$57$$ −6.92820 + 12.0000i −0.917663 + 1.58944i
$$58$$ 3.46410 + 2.00000i 0.454859 + 0.262613i
$$59$$ 5.19615 + 3.00000i 0.676481 + 0.390567i 0.798528 0.601958i $$-0.205612\pi$$
−0.122047 + 0.992524i $$0.538946\pi$$
$$60$$ −3.46410 −0.447214
$$61$$ 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i $$-0.0629528\pi$$
−0.660415 + 0.750901i $$0.729619\pi$$
$$62$$ −16.0000 −2.03200
$$63$$ −5.19615 3.00000i −0.654654 0.377964i
$$64$$ 8.00000 1.00000
$$65$$ −3.59808 0.232051i −0.446286 0.0287824i
$$66$$ −18.0000 + 10.3923i −2.21565 + 1.27920i
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ −1.00000 + 1.73205i −0.121268 + 0.210042i
$$69$$ −1.50000 + 0.866025i −0.180579 + 0.104257i
$$70$$ −3.46410 + 2.00000i −0.414039 + 0.239046i
$$71$$ 10.0000i 1.18678i −0.804914 0.593391i $$-0.797789\pi$$
0.804914 0.593391i $$-0.202211\pi$$
$$72$$ 0 0
$$73$$ 4.00000i 0.468165i 0.972217 + 0.234082i $$0.0752085\pi$$
−0.972217 + 0.234082i $$0.924791\pi$$
$$74$$ 2.00000 + 3.46410i 0.232495 + 0.402694i
$$75$$ 1.73205i 0.200000i
$$76$$ 13.8564 + 8.00000i 1.58944 + 0.917663i
$$77$$ −6.00000 + 10.3923i −0.683763 + 1.18431i
$$78$$ −11.1962 + 5.53590i −1.26771 + 0.626817i
$$79$$ −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i $$-0.184582\pi$$
−0.892781 + 0.450490i $$0.851249\pi$$
$$80$$ 4.00000i 0.447214i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −4.00000 −0.441726
$$83$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$84$$ −3.46410 + 6.00000i −0.377964 + 0.654654i
$$85$$ 0.866025 + 0.500000i 0.0939336 + 0.0542326i
$$86$$ 8.66025 + 5.00000i 0.933859 + 0.539164i
$$87$$ 3.46410i 0.371391i
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 3.00000 + 5.19615i 0.316228 + 0.547723i
$$91$$ −4.00000 + 6.00000i −0.419314 + 0.628971i
$$92$$ 1.00000 + 1.73205i 0.104257 + 0.180579i
$$93$$ 6.92820 + 12.0000i 0.718421 + 1.24434i
$$94$$ 10.0000 17.3205i 1.03142 1.78647i
$$95$$ 4.00000 6.92820i 0.410391 0.710819i
$$96$$ −6.92820 12.0000i −0.707107 1.22474i
$$97$$ 8.66025 5.00000i 0.879316 0.507673i 0.00888289 0.999961i $$-0.497172\pi$$
0.870433 + 0.492287i $$0.163839\pi$$
$$98$$ 6.00000i 0.606092i
$$99$$ 15.5885 + 9.00000i 1.56670 + 0.904534i
$$100$$ 2.00000 0.200000
$$101$$ −3.50000 6.06218i −0.348263 0.603209i 0.637678 0.770303i $$-0.279895\pi$$
−0.985941 + 0.167094i $$0.946562\pi$$
$$102$$ 3.46410 0.342997
$$103$$ −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i $$0.455686\pi$$
−0.927030 + 0.374987i $$0.877647\pi$$
$$104$$ 0 0
$$105$$ 3.00000 + 1.73205i 0.292770 + 0.169031i
$$106$$ −15.5885 + 9.00000i −1.51408 + 0.874157i
$$107$$ 17.0000 1.64345 0.821726 0.569883i $$-0.193011\pi$$
0.821726 + 0.569883i $$0.193011\pi$$
$$108$$ 9.00000 + 5.19615i 0.866025 + 0.500000i
$$109$$ 20.0000i 1.91565i −0.287348 0.957826i $$-0.592774\pi$$
0.287348 0.957826i $$-0.407226\pi$$
$$110$$ 10.3923 6.00000i 0.990867 0.572078i
$$111$$ 1.73205 3.00000i 0.164399 0.284747i
$$112$$ −6.92820 4.00000i −0.654654 0.377964i
$$113$$ −9.50000 + 16.4545i −0.893685 + 1.54791i −0.0582609 + 0.998301i $$0.518556\pi$$
−0.835424 + 0.549606i $$0.814778\pi$$
$$114$$ 27.7128i 2.59554i
$$115$$ 0.866025 0.500000i 0.0807573 0.0466252i
$$116$$ −4.00000 −0.371391
$$117$$ 9.00000 + 6.00000i 0.832050 + 0.554700i
$$118$$ −12.0000 −1.10469
$$119$$ 1.73205 1.00000i 0.158777 0.0916698i
$$120$$ 0 0
$$121$$ 12.5000 21.6506i 1.13636 1.96824i
$$122$$ −8.66025 5.00000i −0.784063 0.452679i
$$123$$ 1.73205 + 3.00000i 0.156174 + 0.270501i
$$124$$ 13.8564 8.00000i 1.24434 0.718421i
$$125$$ 1.00000i 0.0894427i
$$126$$ 12.0000 1.06904
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0 0
$$129$$ 8.66025i 0.762493i
$$130$$ 6.46410 3.19615i 0.566939 0.280321i
$$131$$ −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i $$0.394115\pi$$
−0.981824 + 0.189794i $$0.939218\pi$$
$$132$$ 10.3923 18.0000i 0.904534 1.56670i
$$133$$ −8.00000 13.8564i −0.693688 1.20150i
$$134$$ 0 0
$$135$$ 2.59808 4.50000i 0.223607 0.387298i
$$136$$ 0 0
$$137$$ −5.19615 + 3.00000i −0.443937 + 0.256307i −0.705266 0.708942i $$-0.749173\pi$$
0.261329 + 0.965250i $$0.415839\pi$$
$$138$$ 1.73205 3.00000i 0.147442 0.255377i
$$139$$ 5.50000 9.52628i 0.466504 0.808008i −0.532764 0.846264i $$-0.678847\pi$$
0.999268 + 0.0382553i $$0.0121800\pi$$
$$140$$ 2.00000 3.46410i 0.169031 0.292770i
$$141$$ −17.3205 −1.45865
$$142$$ 10.0000 + 17.3205i 0.839181 + 1.45350i
$$143$$ 12.0000 18.0000i 1.00349 1.50524i
$$144$$ −6.00000 + 10.3923i −0.500000 + 0.866025i
$$145$$ 2.00000i 0.166091i
$$146$$ −4.00000 6.92820i −0.331042 0.573382i
$$147$$ −4.50000 + 2.59808i −0.371154 + 0.214286i
$$148$$ −3.46410 2.00000i −0.284747 0.164399i
$$149$$ 1.73205 + 1.00000i 0.141895 + 0.0819232i 0.569267 0.822153i $$-0.307227\pi$$
−0.427372 + 0.904076i $$0.640560\pi$$
$$150$$ −1.73205 3.00000i −0.141421 0.244949i
$$151$$ −3.46410 + 2.00000i −0.281905 + 0.162758i −0.634285 0.773099i $$-0.718706\pi$$
0.352381 + 0.935857i $$0.385372\pi$$
$$152$$ 0 0
$$153$$ −1.50000 2.59808i −0.121268 0.210042i
$$154$$ 24.0000i 1.93398i
$$155$$ −4.00000 6.92820i −0.321288 0.556487i
$$156$$ 6.92820 10.3923i 0.554700 0.832050i
$$157$$ 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i $$-0.659728\pi$$
0.999762 0.0217953i $$-0.00693820\pi$$
$$158$$ 1.73205 + 1.00000i 0.137795 + 0.0795557i
$$159$$ 13.5000 + 7.79423i 1.07062 + 0.618123i
$$160$$ 4.00000 + 6.92820i 0.316228 + 0.547723i
$$161$$ 2.00000i 0.157622i
$$162$$ 18.0000i 1.41421i
$$163$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$164$$ 3.46410 2.00000i 0.270501 0.156174i
$$165$$ −9.00000 5.19615i −0.700649 0.404520i
$$166$$ 0 0
$$167$$ 1.73205 + 1.00000i 0.134030 + 0.0773823i 0.565516 0.824737i $$-0.308677\pi$$
−0.431486 + 0.902120i $$0.642010\pi$$
$$168$$ 0 0
$$169$$ 7.89230 10.3301i 0.607100 0.794625i
$$170$$ −2.00000 −0.153393
$$171$$ −20.7846 + 12.0000i −1.58944 + 0.917663i
$$172$$ −10.0000 −0.762493
$$173$$ −6.50000 11.2583i −0.494186 0.855955i 0.505792 0.862656i $$-0.331200\pi$$
−0.999978 + 0.00670064i $$0.997867\pi$$
$$174$$ 3.46410 + 6.00000i 0.262613 + 0.454859i
$$175$$ −1.73205 1.00000i −0.130931 0.0755929i
$$176$$ 20.7846 + 12.0000i 1.56670 + 0.904534i
$$177$$ 5.19615 + 9.00000i 0.390567 + 0.676481i
$$178$$ 0 0
$$179$$ 15.0000 1.12115 0.560576 0.828103i $$-0.310580\pi$$
0.560576 + 0.828103i $$0.310580\pi$$
$$180$$ −5.19615 3.00000i −0.387298 0.223607i
$$181$$ 21.0000 1.56092 0.780459 0.625207i $$-0.214986\pi$$
0.780459 + 0.625207i $$0.214986\pi$$
$$182$$ 0.928203 14.3923i 0.0688030 1.06683i
$$183$$ 8.66025i 0.640184i
$$184$$ 0 0
$$185$$ −1.00000 + 1.73205i −0.0735215 + 0.127343i
$$186$$ −24.0000 13.8564i −1.75977 1.01600i
$$187$$ −5.19615 + 3.00000i −0.379980 + 0.219382i
$$188$$ 20.0000i 1.45865i
$$189$$ −5.19615 9.00000i −0.377964 0.654654i
$$190$$ 16.0000i 1.16076i
$$191$$ −9.50000 16.4545i −0.687396 1.19060i −0.972677 0.232161i $$-0.925420\pi$$
0.285282 0.958444i $$-0.407913\pi$$
$$192$$ 12.0000 + 6.92820i 0.866025 + 0.500000i
$$193$$ −3.46410 2.00000i −0.249351 0.143963i 0.370116 0.928986i $$-0.379318\pi$$
−0.619467 + 0.785022i $$0.712651\pi$$
$$194$$ −10.0000 + 17.3205i −0.717958 + 1.24354i
$$195$$ −5.19615 3.46410i −0.372104 0.248069i
$$196$$ 3.00000 + 5.19615i 0.214286 + 0.371154i
$$197$$ 20.0000i 1.42494i −0.701702 0.712470i $$-0.747576\pi$$
0.701702 0.712470i $$-0.252424\pi$$
$$198$$ −36.0000 −2.55841
$$199$$ 3.00000 0.212664 0.106332 0.994331i $$-0.466089\pi$$
0.106332 + 0.994331i $$0.466089\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 12.1244 + 7.00000i 0.853067 + 0.492518i
$$203$$ 3.46410 + 2.00000i 0.243132 + 0.140372i
$$204$$ −3.00000 + 1.73205i −0.210042 + 0.121268i
$$205$$ −1.00000 1.73205i −0.0698430 0.120972i
$$206$$ 32.0000i 2.22955i
$$207$$ −3.00000 −0.208514
$$208$$ 12.0000 + 8.00000i 0.832050 + 0.554700i
$$209$$ 24.0000 + 41.5692i 1.66011 + 2.87540i
$$210$$ −6.92820 −0.478091
$$211$$ 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i $$-0.660634\pi$$
0.999820 0.0189499i $$-0.00603229\pi$$
$$212$$ 9.00000 15.5885i 0.618123 1.07062i
$$213$$ 8.66025 15.0000i 0.593391 1.02778i
$$214$$ −29.4449 + 17.0000i −2.01281 + 1.16210i
$$215$$ 5.00000i 0.340997i
$$216$$ 0 0
$$217$$ −16.0000 −1.08615
$$218$$ 20.0000 + 34.6410i 1.35457 + 2.34619i
$$219$$ −3.46410 + 6.00000i −0.234082 + 0.405442i
$$220$$ −6.00000 + 10.3923i −0.404520 + 0.700649i
$$221$$ −3.23205 + 1.59808i −0.217411 + 0.107498i
$$222$$ 6.92820i 0.464991i
$$223$$ 12.1244 7.00000i 0.811907 0.468755i −0.0357107 0.999362i $$-0.511370\pi$$
0.847618 + 0.530607i $$0.178036\pi$$
$$224$$ 16.0000 1.06904
$$225$$ −1.50000 + 2.59808i −0.100000 + 0.173205i
$$226$$ 38.0000i 2.52772i
$$227$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$228$$ 13.8564 + 24.0000i 0.917663 + 1.58944i
$$229$$ −22.5167 13.0000i −1.48794 0.859064i −0.488037 0.872823i $$-0.662287\pi$$
−0.999905 + 0.0137585i $$0.995620\pi$$
$$230$$ −1.00000 + 1.73205i −0.0659380 + 0.114208i
$$231$$ −18.0000 + 10.3923i −1.18431 + 0.683763i
$$232$$ 0 0
$$233$$ −19.0000 −1.24473 −0.622366 0.782727i $$-0.713828\pi$$
−0.622366 + 0.782727i $$0.713828\pi$$
$$234$$ −21.5885 1.39230i −1.41128 0.0910178i
$$235$$ 10.0000 0.652328
$$236$$ 10.3923 6.00000i 0.676481 0.390567i
$$237$$ 1.73205i 0.112509i
$$238$$ −2.00000 + 3.46410i −0.129641 + 0.224544i
$$239$$ −17.3205 10.0000i −1.12037 0.646846i −0.178875 0.983872i $$-0.557246\pi$$
−0.941495 + 0.337026i $$0.890579\pi$$
$$240$$ 3.46410 6.00000i 0.223607 0.387298i
$$241$$ −25.9808 + 15.0000i −1.67357 + 0.966235i −0.707953 + 0.706260i $$0.750381\pi$$
−0.965615 + 0.259975i $$0.916286\pi$$
$$242$$ 50.0000i 3.21412i
$$243$$ −13.5000 + 7.79423i −0.866025 + 0.500000i
$$244$$ 10.0000 0.640184
$$245$$ 2.59808 1.50000i 0.165985 0.0958315i
$$246$$ −6.00000 3.46410i −0.382546 0.220863i
$$247$$ 12.7846 + 25.8564i 0.813465 + 1.64520i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 1.00000 + 1.73205i 0.0632456 + 0.109545i
$$251$$ 3.00000 0.189358 0.0946792 0.995508i $$-0.469817\pi$$
0.0946792 + 0.995508i $$0.469817\pi$$
$$252$$ −10.3923 + 6.00000i −0.654654 + 0.377964i
$$253$$ 6.00000i 0.377217i
$$254$$ 0 0
$$255$$ 0.866025 + 1.50000i 0.0542326 + 0.0939336i
$$256$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$257$$ 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i $$-0.803506\pi$$
0.909010 + 0.416775i $$0.136840\pi$$
$$258$$ 8.66025 + 15.0000i 0.539164 + 0.933859i
$$259$$ 2.00000 + 3.46410i 0.124274 + 0.215249i
$$260$$ −4.00000 + 6.00000i −0.248069 + 0.372104i
$$261$$ 3.00000 5.19615i 0.185695 0.321634i
$$262$$ 30.0000i 1.85341i
$$263$$ −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i $$-0.256167\pi$$
−0.970758 + 0.240059i $$0.922833\pi$$
$$264$$ 0 0
$$265$$ −7.79423 4.50000i −0.478796 0.276433i
$$266$$ 27.7128 + 16.0000i 1.69918 + 0.981023i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −14.0000 −0.853595 −0.426798 0.904347i $$-0.640358\pi$$
−0.426798 + 0.904347i $$0.640358\pi$$
$$270$$ 10.3923i 0.632456i
$$271$$ 28.0000i 1.70088i 0.526073 + 0.850439i $$0.323664\pi$$
−0.526073 + 0.850439i $$0.676336\pi$$
$$272$$ −2.00000 3.46410i −0.121268 0.210042i
$$273$$ −11.1962 + 5.53590i −0.677622 + 0.335048i
$$274$$ 6.00000 10.3923i 0.362473 0.627822i
$$275$$ 5.19615 + 3.00000i 0.313340 + 0.180907i
$$276$$ 3.46410i 0.208514i
$$277$$ −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i $$-0.263794\pi$$
−0.976231 + 0.216731i $$0.930460\pi$$
$$278$$ 22.0000i 1.31947i
$$279$$ 24.0000i 1.43684i
$$280$$ 0 0
$$281$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$282$$ 30.0000 17.3205i 1.78647 1.03142i
$$283$$ 15.5000 26.8468i 0.921379 1.59588i 0.124096 0.992270i $$-0.460397\pi$$
0.797283 0.603606i $$-0.206270\pi$$
$$284$$ −17.3205 10.0000i −1.02778 0.593391i
$$285$$ 12.0000 6.92820i 0.710819 0.410391i
$$286$$ −2.78461 + 43.1769i −0.164657 + 2.55310i
$$287$$ −4.00000 −0.236113
$$288$$ 24.0000i 1.41421i
$$289$$ −16.0000 −0.941176
$$290$$ −2.00000 3.46410i −0.117444 0.203419i
$$291$$ 17.3205 1.01535
$$292$$ 6.92820 + 4.00000i 0.405442 + 0.234082i
$$293$$ −5.19615 3.00000i −0.303562 0.175262i 0.340480 0.940252i $$-0.389411\pi$$
−0.644042 + 0.764990i $$0.722744\pi$$
$$294$$ 5.19615 9.00000i 0.303046 0.524891i
$$295$$ −3.00000 5.19615i −0.174667 0.302532i
$$296$$ 0 0
$$297$$ 15.5885 + 27.0000i 0.904534 + 1.56670i
$$298$$ −4.00000 −0.231714
$$299$$ −0.232051 + 3.59808i −0.0134198 + 0.208082i
$$300$$ 3.00000 + 1.73205i 0.173205 + 0.100000i
$$301$$ 8.66025 + 5.00000i 0.499169 + 0.288195i
$$302$$ 4.00000 6.92820i 0.230174 0.398673i
$$303$$ 12.1244i 0.696526i
$$304$$ −27.7128 + 16.0000i −1.58944 + 0.917663i
$$305$$ 5.00000i 0.286299i
$$306$$ 5.19615 + 3.00000i 0.297044 + 0.171499i
$$307$$ 4.00000i 0.228292i −0.993464 0.114146i $$-0.963587\pi$$
0.993464 0.114146i $$-0.0364132\pi$$
$$308$$ 12.0000 + 20.7846i 0.683763 + 1.18431i
$$309$$ −24.0000 + 13.8564i −1.36531 + 0.788263i
$$310$$ 13.8564 + 8.00000i 0.786991 + 0.454369i
$$311$$ 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i $$-0.760501\pi$$
0.956864 + 0.290537i $$0.0938340\pi$$
$$312$$ 0 0
$$313$$ 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i $$-0.0754642\pi$$
−0.689412 + 0.724370i $$0.742131\pi$$
$$314$$ 26.0000i 1.46726i
$$315$$ 3.00000 + 5.19615i 0.169031 + 0.292770i
$$316$$ −2.00000 −0.112509
$$317$$ −22.5167 + 13.0000i −1.26466 + 0.730153i −0.973973 0.226665i $$-0.927218\pi$$
−0.290689 + 0.956818i $$0.593884\pi$$
$$318$$ −31.1769 −1.74831
$$319$$ −10.3923 6.00000i −0.581857 0.335936i
$$320$$ −6.92820 4.00000i −0.387298 0.223607i
$$321$$ 25.5000 + 14.7224i 1.42327 + 0.821726i
$$322$$ 2.00000 + 3.46410i 0.111456 + 0.193047i
$$323$$ 8.00000i 0.445132i
$$324$$ 9.00000 + 15.5885i 0.500000 + 0.866025i
$$325$$ 3.00000 + 2.00000i 0.166410 + 0.110940i
$$326$$ 0 0
$$327$$ 17.3205 30.0000i 0.957826 1.65900i
$$328$$ 0 0
$$329$$ 10.0000 17.3205i 0.551318 0.954911i
$$330$$ 20.7846 1.14416
$$331$$ −6.92820 + 4.00000i −0.380808 + 0.219860i −0.678170 0.734905i $$-0.737227\pi$$
0.297361 + 0.954765i $$0.403893\pi$$
$$332$$ 0 0
$$333$$ 5.19615 3.00000i 0.284747 0.164399i
$$334$$ −4.00000 −0.218870
$$335$$ 0 0
$$336$$ −6.92820 12.0000i −0.377964 0.654654i
$$337$$ −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i $$-0.859372\pi$$
0.822274 + 0.569091i $$0.192705\pi$$
$$338$$ −3.33975 + 25.7846i −0.181658 + 1.40250i
$$339$$ −28.5000 + 16.4545i −1.54791 + 0.893685i
$$340$$ 1.73205 1.00000i 0.0939336 0.0542326i
$$341$$ 48.0000 2.59935
$$342$$ 24.0000 41.5692i 1.29777 2.24781i
$$343$$ 20.0000i 1.07990i
$$344$$ 0 0
$$345$$ 1.73205 0.0932505
$$346$$ 22.5167 + 13.0000i 1.21050 + 0.698884i
$$347$$ 2.50000 4.33013i 0.134207 0.232453i −0.791087 0.611703i $$-0.790485\pi$$
0.925294 + 0.379250i $$0.123818\pi$$
$$348$$ −6.00000 3.46410i −0.321634 0.185695i
$$349$$ −1.73205 + 1.00000i −0.0927146 + 0.0535288i −0.545640 0.838019i $$-0.683714\pi$$
0.452926 + 0.891548i $$0.350380\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 8.30385 + 16.7942i 0.443227 + 0.896410i
$$352$$ −48.0000 −2.55841
$$353$$ −5.19615 + 3.00000i −0.276563 + 0.159674i −0.631867 0.775077i $$-0.717711\pi$$
0.355303 + 0.934751i $$0.384378\pi$$
$$354$$ −18.0000 10.3923i −0.956689 0.552345i
$$355$$ −5.00000 + 8.66025i −0.265372 + 0.459639i
$$356$$ 0 0
$$357$$ 3.46410 0.183340
$$358$$ −25.9808 + 15.0000i −1.37313 + 0.792775i
$$359$$ 10.0000i 0.527780i 0.964553 + 0.263890i $$0.0850056\pi$$
−0.964553 + 0.263890i $$0.914994\pi$$
$$360$$ 0 0
$$361$$ −45.0000 −2.36842
$$362$$ −36.3731 + 21.0000i −1.91173 + 1.10374i
$$363$$ 37.5000 21.6506i 1.96824 1.13636i
$$364$$ 6.39230 + 12.9282i 0.335048 + 0.677622i
$$365$$ 2.00000 3.46410i 0.104685 0.181319i
$$366$$ −8.66025 15.0000i −0.452679 0.784063i
$$367$$ −10.5000 18.1865i −0.548096 0.949329i −0.998405 0.0564568i $$-0.982020\pi$$
0.450310 0.892873i $$-0.351314\pi$$
$$368$$ −4.00000 −0.208514
$$369$$ 6.00000i 0.312348i
$$370$$ 4.00000i 0.207950i
$$371$$ −15.5885 + 9.00000i −0.809312 + 0.467257i
$$372$$ 27.7128 1.43684
$$373$$ −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i $$-0.997028\pi$$
0.508065 + 0.861319i $$0.330361\pi$$
$$374$$ 6.00000 10.3923i 0.310253 0.537373i
$$375$$ 0.866025 1.50000i 0.0447214 0.0774597i
$$376$$ 0 0
$$377$$ −6.00000 4.00000i −0.309016 0.206010i
$$378$$ 18.0000 + 10.3923i 0.925820 + 0.534522i
$$379$$ 18.0000i 0.924598i −0.886724 0.462299i $$-0.847025\pi$$
0.886724 0.462299i $$-0.152975\pi$$
$$380$$ −8.00000 13.8564i −0.410391 0.710819i
$$381$$ 0 0
$$382$$ 32.9090 + 19.0000i 1.68377 + 0.972125i
$$383$$ 22.5167 + 13.0000i 1.15055 + 0.664269i 0.949021 0.315214i $$-0.102076\pi$$
0.201527 + 0.979483i $$0.435410\pi$$
$$384$$ 0 0
$$385$$ 10.3923 6.00000i 0.529641 0.305788i
$$386$$ 8.00000 0.407189
$$387$$ 7.50000 12.9904i 0.381246 0.660338i
$$388$$ 20.0000i 1.01535i
$$389$$ 11.5000 + 19.9186i 0.583073 + 1.00991i 0.995113 + 0.0987463i $$0.0314832\pi$$
−0.412039 + 0.911166i $$0.635183\pi$$
$$390$$ 12.4641 + 0.803848i 0.631144 + 0.0407044i
$$391$$ 0.500000 0.866025i 0.0252861 0.0437968i
$$392$$ 0 0
$$393$$ −22.5000 + 12.9904i −1.13497 + 0.655278i
$$394$$ 20.0000 + 34.6410i 1.00759 + 1.74519i
$$395$$ 1.00000i 0.0503155i
$$396$$ 31.1769 18.0000i 1.56670 0.904534i
$$397$$ 28.0000i 1.40528i −0.711546 0.702640i $$-0.752005\pi$$
0.711546 0.702640i $$-0.247995\pi$$
$$398$$ −5.19615 + 3.00000i −0.260460 + 0.150376i
$$399$$ 27.7128i 1.38738i
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ −27.7128 16.0000i −1.38391 0.799002i −0.391292 0.920267i $$-0.627972\pi$$
−0.992620 + 0.121265i $$0.961305\pi$$
$$402$$ 0 0
$$403$$ 28.7846 + 1.85641i 1.43386 + 0.0924742i
$$404$$ −14.0000 −0.696526
$$405$$ 7.79423 4.50000i 0.387298 0.223607i
$$406$$ −8.00000 −0.397033
$$407$$ −6.00000 10.3923i −0.297409 0.515127i
$$408$$ 0 0
$$409$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$410$$ 3.46410 + 2.00000i 0.171080 + 0.0987730i
$$411$$ −10.3923 −0.512615
$$412$$ 16.0000 + 27.7128i 0.788263 + 1.36531i
$$413$$ −12.0000 −0.590481
$$414$$ 5.19615 3.00000i 0.255377 0.147442i
$$415$$ 0 0
$$416$$ −28.7846 1.85641i −1.41128 0.0910178i
$$417$$ 16.5000 9.52628i 0.808008 0.466504i
$$418$$ −83.1384 48.0000i −4.06643 2.34776i
$$419$$ −7.50000 + 12.9904i −0.366399 + 0.634622i −0.989000 0.147918i $$-0.952743\pi$$
0.622601 + 0.782540i $$0.286076\pi$$
$$420$$ 6.00000 3.46410i 0.292770 0.169031i
$$421$$ 6.92820 4.00000i 0.337660 0.194948i −0.321577 0.946883i $$-0.604213\pi$$
0.659237 + 0.751935i $$0.270879\pi$$
$$422$$ 30.0000i 1.46038i
$$423$$ −25.9808 15.0000i −1.26323 0.729325i
$$424$$ 0 0
$$425$$ −0.500000 0.866025i −0.0242536 0.0420084i
$$426$$ 34.6410i 1.67836i
$$427$$ −8.66025 5.00000i −0.419099 0.241967i
$$428$$ 17.0000 29.4449i 0.821726 1.42327i
$$429$$ 33.5885 16.6077i 1.62167 0.801827i
$$430$$ −5.00000 8.66025i −0.241121 0.417635i
$$431$$ 24.0000i 1.15604i −0.816023 0.578020i $$-0.803826\pi$$
0.816023 0.578020i $$-0.196174\pi$$
$$432$$ −18.0000 + 10.3923i −0.866025 + 0.500000i
$$433$$ 5.00000 0.240285 0.120142 0.992757i $$-0.461665\pi$$
0.120142 + 0.992757i $$0.461665\pi$$
$$434$$ 27.7128 16.0000i 1.33026 0.768025i
$$435$$ −1.73205 + 3.00000i −0.0830455 + 0.143839i
$$436$$ −34.6410 20.0000i −1.65900 0.957826i
$$437$$ −6.92820 4.00000i −0.331421 0.191346i
$$438$$ 13.8564i 0.662085i
$$439$$ −12.5000 21.6506i −0.596592 1.03333i −0.993320 0.115392i $$-0.963188\pi$$
0.396728 0.917936i $$-0.370146\pi$$
$$440$$ 0 0
$$441$$ −9.00000 −0.428571
$$442$$ 4.00000 6.00000i 0.190261 0.285391i
$$443$$ −10.5000 18.1865i −0.498870 0.864068i 0.501129 0.865373i $$-0.332918\pi$$
−0.999999 + 0.00130426i $$0.999585\pi$$
$$444$$ −3.46410 6.00000i −0.164399 0.284747i
$$445$$ 0 0
$$446$$ −14.0000 + 24.2487i −0.662919 + 1.14821i
$$447$$ 1.73205 + 3.00000i 0.0819232 + 0.141895i
$$448$$ −13.8564 + 8.00000i −0.654654 + 0.377964i
$$449$$ 36.0000i 1.69895i 0.527633 + 0.849473i $$0.323080\pi$$
−0.527633 + 0.849473i $$0.676920\pi$$
$$450$$ 6.00000i 0.282843i
$$451$$ 12.0000 0.565058
$$452$$ 19.0000 + 32.9090i 0.893685 + 1.54791i
$$453$$ −6.92820 −0.325515
$$454$$ 0 0
$$455$$ 6.46410 3.19615i 0.303042 0.149838i
$$456$$ 0 0
$$457$$ 6.92820 4.00000i 0.324088 0.187112i −0.329125 0.944286i $$-0.606754\pi$$
0.653213 + 0.757174i $$0.273421\pi$$
$$458$$ 52.0000 2.42980
$$459$$ 5.19615i 0.242536i
$$460$$ 2.00000i 0.0932505i
$$461$$ 1.73205 1.00000i 0.0806696 0.0465746i −0.459123 0.888373i $$-0.651836\pi$$
0.539792 + 0.841798i $$0.318503\pi$$
$$462$$ 20.7846 36.0000i 0.966988 1.67487i
$$463$$ 19.0526 + 11.0000i 0.885448 + 0.511213i 0.872451 0.488702i $$-0.162530\pi$$
0.0129968 + 0.999916i $$0.495863\pi$$
$$464$$ 4.00000 6.92820i 0.185695 0.321634i
$$465$$ 13.8564i 0.642575i
$$466$$ 32.9090 19.0000i 1.52448 0.880158i
$$467$$ −21.0000 −0.971764 −0.485882 0.874024i $$-0.661502\pi$$
−0.485882 + 0.874024i $$0.661502\pi$$
$$468$$ 19.3923 9.58846i 0.896410 0.443227i
$$469$$ 0 0
$$470$$ −17.3205 + 10.0000i −0.798935 + 0.461266i
$$471$$ 19.5000 11.2583i 0.898513 0.518756i
$$472$$ 0 0
$$473$$ −25.9808 15.0000i −1.19460 0.689701i
$$474$$ 1.73205 + 3.00000i 0.0795557 + 0.137795i
$$475$$ −6.92820 + 4.00000i −0.317888 + 0.183533i
$$476$$ 4.00000i 0.183340i
$$477$$ 13.5000 + 23.3827i 0.618123 + 1.07062i
$$478$$ 40.0000 1.82956
$$479$$ 15.5885 9.00000i 0.712255 0.411220i −0.0996406 0.995023i $$-0.531769\pi$$
0.811895 + 0.583803i $$0.198436\pi$$
$$480$$ 13.8564i 0.632456i
$$481$$ −3.19615 6.46410i −0.145732 0.294738i
$$482$$ 30.0000 51.9615i 1.36646 2.36678i
$$483$$ 1.73205 3.00000i 0.0788110 0.136505i
$$484$$ −25.0000 43.3013i −1.13636 1.96824i
$$485$$ −10.0000 −0.454077
$$486$$ 15.5885 27.0000i 0.707107 1.22474i
$$487$$ 24.0000i 1.08754i 0.839233 + 0.543772i $$0.183004\pi$$
−0.839233 + 0.543772i $$0.816996\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −3.00000 + 5.19615i −0.135526 + 0.234738i
$$491$$ 8.00000 13.8564i 0.361035 0.625331i −0.627096 0.778942i $$-0.715757\pi$$
0.988131 + 0.153611i $$0.0490902\pi$$
$$492$$ 6.92820 0.312348
$$493$$ 1.00000 + 1.73205i 0.0450377 + 0.0780076i
$$494$$ −48.0000 32.0000i −2.15962 1.43975i
$$495$$ −9.00000 15.5885i −0.404520 0.700649i
$$496$$ 32.0000i 1.43684i
$$497$$ 10.0000 + 17.3205i 0.448561 + 0.776931i
$$498$$ 0 0
$$499$$ 24.2487 + 14.0000i 1.08552 + 0.626726i 0.932381 0.361478i $$-0.117728\pi$$
0.153141 + 0.988204i $$0.451061\pi$$
$$500$$ −1.73205 1.00000i −0.0774597 0.0447214i
$$501$$ 1.73205 + 3.00000i 0.0773823 + 0.134030i
$$502$$ −5.19615 + 3.00000i −0.231916 + 0.133897i
$$503$$ −25.0000 −1.11469 −0.557347 0.830279i $$-0.688181\pi$$
−0.557347 + 0.830279i $$0.688181\pi$$
$$504$$ 0 0
$$505$$ 7.00000i 0.311496i
$$506$$ −6.00000 10.3923i −0.266733 0.461994i
$$507$$ 20.7846 8.66025i 0.923077 0.384615i
$$508$$ 0 0
$$509$$ −5.19615 3.00000i −0.230315 0.132973i 0.380402 0.924821i $$-0.375786\pi$$
−0.610718 + 0.791849i $$0.709119\pi$$
$$510$$ −3.00000 1.73205i −0.132842 0.0766965i
$$511$$ −4.00000 6.92820i −0.176950 0.306486i
$$512$$ 32.0000i 1.41421i
$$513$$ −41.5692 −1.83533
$$514$$ 6.00000i 0.264649i
$$515$$ 13.8564 8.00000i 0.610586 0.352522i
$$516$$ −15.0000 8.66025i −0.660338 0.381246i
$$517$$ −30.0000 + 51.9615i −1.31940 + 2.28527i
$$518$$ −6.92820 4.00000i −0.304408 0.175750i
$$519$$ 22.5167i 0.988372i
$$520$$ 0 0
$$521$$ 10.0000 0.438108 0.219054 0.975713i $$-0.429703\pi$$
0.219054 + 0.975713i $$0.429703\pi$$
$$522$$ 12.0000i 0.525226i
$$523$$ 20.0000 0.874539 0.437269 0.899331i $$-0.355946\pi$$
0.437269 + 0.899331i $$0.355946\pi$$
$$524$$ 15.0000 + 25.9808i 0.655278 + 1.13497i
$$525$$ −1.73205 3.00000i −0.0755929 0.130931i
$$526$$ 15.5885 + 9.00000i 0.679689 + 0.392419i
$$527$$ −6.92820 4.00000i −0.301797 0.174243i
$$528$$ 20.7846 + 36.0000i 0.904534 + 1.56670i
$$529$$ 11.0000 + 19.0526i 0.478261 + 0.828372i
$$530$$ 18.0000 0.781870
$$531$$ 18.0000i 0.781133i
$$532$$ −32.0000 −1.38738
$$533$$ 7.19615 + 0.464102i 0.311700 + 0.0201025i
$$534$$ 0 0
$$535$$ −14.7224 8.50000i −0.636506 0.367487i
$$536$$ 0 0
$$537$$ 22.5000 + 12.9904i 0.970947 + 0.560576i
$$538$$ 24.2487 14.0000i 1.04544 0.603583i
$$539$$ 18.0000i 0.775315i
$$540$$ −5.19615 9.00000i −0.223607 0.387298i
$$541$$ 32.0000i 1.37579i −0.725811 0.687894i $$-0.758536\pi$$
0.725811 0.687894i $$-0.241464\pi$$
$$542$$ −28.0000 48.4974i −1.20270 2.08314i
$$543$$ 31.5000 + 18.1865i 1.35179 + 0.780459i
$$544$$ 6.92820 + 4.00000i 0.297044 + 0.171499i
$$545$$ −10.0000 + 17.3205i −0.428353 + 0.741929i
$$546$$ 13.8564 20.7846i 0.592999 0.889499i
$$547$$ 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i $$-0.139413\pi$$
−0.820096 + 0.572226i $$0.806080\pi$$
$$548$$ 12.0000i 0.512615i
$$549$$ −7.50000 + 12.9904i −0.320092 + 0.554416i
$$550$$ −12.0000 −0.511682
$$551$$ 13.8564 8.00000i 0.590303 0.340811i
$$552$$ 0 0
$$553$$ 1.73205 + 1.00000i 0.0736543 + 0.0425243i
$$554$$ 17.3205 + 10.0000i 0.735878 + 0.424859i
$$555$$ −3.00000 + 1.73205i −0.127343 + 0.0735215i
$$556$$ −11.0000 19.0526i −0.466504 0.808008i
$$557$$ 12.0000i 0.508456i 0.967144 + 0.254228i $$0.0818214\pi$$
−0.967144 + 0.254228i $$0.918179\pi$$
$$558$$ −24.0000 41.5692i −1.01600 1.75977i
$$559$$ −15.0000 10.0000i −0.634432 0.422955i
$$560$$ 4.00000 + 6.92820i 0.169031 + 0.292770i
$$561$$ −10.3923 −0.438763
$$562$$ 0 0
$$563$$ −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i $$0.473712\pi$$
−0.904320 + 0.426855i $$0.859622\pi$$
$$564$$ −17.3205 + 30.0000i −0.729325 + 1.26323i
$$565$$ 16.4545 9.50000i 0.692245 0.399668i
$$566$$ 62.0000i 2.60605i
$$567$$ 18.0000i 0.755929i
$$568$$ 0 0
$$569$$ −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i $$-0.950200\pi$$
0.358954 0.933355i $$-0.383134\pi$$
$$570$$ −13.8564 + 24.0000i −0.580381 + 1.00525i
$$571$$ −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i $$-0.970773\pi$$
0.577301 + 0.816532i $$0.304106\pi$$
$$572$$ −19.1769 38.7846i −0.801827 1.62167i
$$573$$ 32.9090i 1.37479i
$$574$$ 6.92820 4.00000i 0.289178 0.166957i
$$575$$ −1.00000 −0.0417029
$$576$$ 12.0000 + 20.7846i 0.500000 + 0.866025i
$$577$$ 28.0000i 1.16566i 0.812596 + 0.582828i $$0.198054\pi$$
−0.812596 + 0.582828i $$0.801946\pi$$
$$578$$ 27.7128 16.0000i 1.15270 0.665512i
$$579$$ −3.46410 6.00000i −0.143963 0.249351i
$$580$$ 3.46410 + 2.00000i 0.143839 + 0.0830455i
$$581$$ 0 0
$$582$$ −30.0000 + 17.3205i −1.24354 + 0.717958i
$$583$$ 46.7654 27.0000i 1.93682 1.11823i
$$584$$ 0 0
$$585$$ −4.79423 9.69615i −0.198217 0.400887i
$$586$$ 12.0000 0.495715
$$587$$ 24.2487 14.0000i 1.00085 0.577842i 0.0923513 0.995726i $$-0.470562\pi$$
0.908500 + 0.417885i $$0.137228\pi$$
$$588$$ 10.3923i 0.428571i
$$589$$ −32.0000 + 55.4256i −1.31854 + 2.28377i
$$590$$ 10.3923 + 6.00000i 0.427844 + 0.247016i
$$591$$ 17.3205 30.0000i 0.712470 1.23404i
$$592$$ 6.92820 4.00000i 0.284747 0.164399i
$$593$$ 16.0000i 0.657041i −0.944497 0.328521i $$-0.893450\pi$$
0.944497 0.328521i $$-0.106550\pi$$
$$594$$ −54.0000 31.1769i −2.21565 1.27920i
$$595$$ −2.00000 −0.0819920
$$596$$ 3.46410 2.00000i 0.141895 0.0819232i
$$597$$ 4.50000 + 2.59808i 0.184173 + 0.106332i
$$598$$ −3.19615 6.46410i −0.130700 0.264337i
$$599$$ −3.50000 + 6.06218i −0.143006 + 0.247694i −0.928627 0.371014i $$-0.879010\pi$$
0.785621 + 0.618708i $$0.212344\pi$$
$$600$$ 0 0
$$601$$ −2.50000 4.33013i −0.101977 0.176630i 0.810522 0.585708i $$-0.199184\pi$$
−0.912499 + 0.409079i $$0.865850\pi$$
$$602$$ −20.0000 −0.815139
$$603$$ 0 0
$$604$$ 8.00000i 0.325515i
$$605$$ −21.6506 + 12.5000i −0.880223 + 0.508197i
$$606$$ 12.1244 + 21.0000i 0.492518 + 0.853067i
$$607$$ 5.50000 9.52628i 0.223238 0.386660i −0.732551 0.680712i $$-0.761671\pi$$
0.955789 + 0.294052i $$0.0950039\pi$$
$$608$$ 32.0000 55.4256i 1.29777 2.24781i
$$609$$ 3.46410 + 6.00000i 0.140372 + 0.243132i
$$610$$ 5.00000 + 8.66025i 0.202444 + 0.350643i
$$611$$ −20.0000 + 30.0000i −0.809113 + 1.21367i
$$612$$ −6.00000 −0.242536
$$613$$ 28.0000i 1.13091i 0.824779 + 0.565455i $$0.191299\pi$$
−0.824779 + 0.565455i $$0.808701\pi$$
$$614$$ 4.00000 + 6.92820i 0.161427 + 0.279600i
$$615$$ 3.46410i 0.139686i
$$616$$ 0 0
$$617$$ −1.73205 1.00000i −0.0697297 0.0402585i 0.464730 0.885453i $$-0.346151\pi$$
−0.534460 + 0.845194i $$0.679485\pi$$
$$618$$ 27.7128 48.0000i 1.11477 1.93084i
$$619$$ −8.66025 + 5.00000i −0.348085 + 0.200967i −0.663842 0.747873i $$-0.731075\pi$$
0.315757 + 0.948840i $$0.397742\pi$$
$$620$$ −16.0000 −0.642575
$$621$$ −4.50000 2.59808i −0.180579 0.104257i
$$622$$ 16.0000i 0.641542i
$$623$$ 0 0
$$624$$ 11.0718 + 22.3923i 0.443227 + 0.896410i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ −17.3205 10.0000i −0.692267 0.399680i
$$627$$ 83.1384i 3.32023i
$$628$$ −13.0000 22.5167i −0.518756 0.898513i
$$629$$ 2.00000i 0.0797452i
$$630$$ −10.3923 6.00000i −0.414039 0.239046i
$$631$$ 2.00000i 0.0796187i 0.999207 + 0.0398094i $$0.0126751\pi$$
−0.999207 + 0.0398094i $$0.987325\pi$$
$$632$$ 0 0
$$633$$ 22.5000 12.9904i 0.894295 0.516321i
$$634$$ 26.0000 45.0333i 1.03259 1.78850i
$$635$$ 0 0
$$636$$ 27.0000 15.5885i 1.07062 0.618123i
$$637$$ −0.696152 + 10.7942i −0.0275826 + 0.427683i
$$638$$ 24.0000 0.950169
$$639$$ 25.9808 15.0000i 1.02778 0.593391i
$$640$$ 0 0
$$641$$ 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i $$-0.128860\pi$$
−0.800678 + 0.599095i $$0.795527\pi$$
$$642$$ −58.8897 −2.32419
$$643$$ 27.7128 + 16.0000i 1.09289 + 0.630978i 0.934344 0.356374i $$-0.115987\pi$$
0.158543 + 0.987352i $$0.449320\pi$$
$$644$$ −3.46410 2.00000i −0.136505 0.0788110i
$$645$$ −4.33013 + 7.50000i −0.170499 + 0.295312i
$$646$$ 8.00000 + 13.8564i 0.314756 + 0.545173i
$$647$$ −17.0000 −0.668339 −0.334169 0.942513i $$-0.608456\pi$$
−0.334169 + 0.942513i $$0.608456\pi$$
$$648$$ 0 0
$$649$$ 36.0000 1.41312
$$650$$ −7.19615 0.464102i −0.282256 0.0182036i
$$651$$ −24.0000 13.8564i −0.940634 0.543075i
$$652$$ 0 0
$$653$$ −17.0000 + 29.4449i −0.665261 + 1.15227i 0.313953 + 0.949439i $$0.398347\pi$$
−0.979214 + 0.202828i $$0.934987\pi$$
$$654$$ 69.2820i 2.70914i
$$655$$ 12.9904 7.50000i 0.507576 0.293049i
$$656$$ 8.00000i 0.312348i
$$657$$ −10.3923 + 6.00000i −0.405442 + 0.234082i
$$658$$ 40.0000i 1.55936i
$$659$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$660$$ −18.0000 + 10.3923i −0.700649 + 0.404520i
$$661$$ −1.73205 1.00000i −0.0673690 0.0388955i 0.465937 0.884818i $$-0.345717\pi$$
−0.533306 + 0.845922i $$0.679051\pi$$
$$662$$ 8.00000 13.8564i 0.310929 0.538545i
$$663$$ −6.23205 0.401924i −0.242033 0.0156094i
$$664$$ 0 0
$$665$$ 16.0000i 0.620453i
$$666$$ −6.00000 + 10.3923i −0.232495 + 0.402694i
$$667$$ 2.00000 0.0774403
$$668$$ 3.46410 2.00000i 0.134030 0.0773823i
$$669$$ 24.2487 0.937509
$$670$$ 0 0
$$671$$ 25.9808 + 15.0000i 1.00298 + 0.579069i
$$672$$ 24.0000 + 13.8564i 0.925820 + 0.534522i
$$673$$ −15.5000 26.8468i −0.597481 1.03487i −0.993192 0.116492i $$-0.962835\pi$$
0.395711 0.918375i $$-0.370498\pi$$
$$674$$ 6.00000i 0.231111i
$$675$$ −4.50000 + 2.59808i −0.173205 + 0.100000i
$$676$$ −10.0000 24.0000i −0.384615 0.923077i
$$677$$ 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i $$-0.129884\pi$$
−0.802600 + 0.596518i $$0.796551\pi$$
$$678$$ 32.9090 57.0000i 1.26386 2.18907i
$$679$$ −10.0000 + 17.3205i −0.383765 + 0.664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −83.1384 + 48.0000i −3.18354 + 1.83801i
$$683$$ 34.0000i 1.30097i −0.759517 0.650487i $$-0.774565\pi$$
0.759517 0.650487i $$-0.225435\pi$$
$$684$$ 48.0000i 1.83533i
$$685$$ 6.00000 0.229248
$$686$$ 20.0000 + 34.6410i 0.763604 + 1.32260i
$$687$$ −22.5167 39.0000i −0.859064 1.48794i
$$688$$ 10.0000 17.3205i 0.381246 0.660338i
$$689$$ 29.0885 14.3827i 1.10818 0.547937i
$$690$$ −3.00000 + 1.73205i −0.114208 + 0.0659380i
$$691$$ −8.66025 + 5.00000i −0.329452 + 0.190209i −0.655598 0.755110i $$-0.727583\pi$$
0.326146 + 0.945319i $$0.394250\pi$$
$$692$$ −26.0000 −0.988372
$$693$$ −36.0000 −1.36753
$$694$$ 10.0000i 0.379595i
$$695$$ −9.52628 + 5.50000i −0.361352 + 0.208627i
$$696$$ 0 0
$$697$$ −1.73205 1.00000i −0.0656061 0.0378777i
$$698$$ 2.00000 3.46410i 0.0757011 0.131118i
$$699$$ −28.5000 16.4545i −1.07797 0.622366i
$$700$$ −3.46410 + 2.00000i −0.130931 + 0.0755929i
$$701$$ −39.0000 −1.47301 −0.736505 0.676432i $$-0.763525\pi$$
−0.736505 + 0.676432i $$0.763525\pi$$
$$702$$ −31.1769 20.7846i −1.17670 0.784465i
$$703$$ 16.0000 0.603451
$$704$$ 41.5692 24.0000i 1.56670 0.904534i
$$705$$ 15.0000 + 8.66025i 0.564933 + 0.326164i
$$706$$ 6.00000 10.3923i 0.225813 0.391120i
$$707$$ 12.1244 + 7.00000i 0.455983 + 0.263262i
$$708$$ 20.7846 0.781133
$$709$$ −6.92820 + 4.00000i −0.260194 + 0.150223i −0.624423 0.781086i $$-0.714666\pi$$
0.364229 + 0.931309i $$0.381333\pi$$
$$710$$ 20.0000i 0.750587i
$$711$$ 1.50000 2.59808i 0.0562544 0.0974355i
$$712$$ 0 0
$$713$$ −6.92820 + 4.00000i −0.259463 + 0.149801i
$$714$$ −6.00000 + 3.46410i −0.224544 + 0.129641i
$$715$$ −19.3923 + 9.58846i −0.725231 + 0.358588i
$$716$$ 15.0000 25.9808i 0.560576 0.970947i
$$717$$ −17.3205 30.0000i −0.646846 1.12037i
$$718$$ −10.0000 17.3205i −0.373197 0.646396i
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ 10.3923 6.00000i 0.387298 0.223607i
$$721$$ 32.0000i 1.19174i
$$722$$ 77.9423 45.0000i 2.90071 1.67473i
$$723$$ −51.9615 −1.93247
$$724$$ 21.0000 36.3731i 0.780459 1.35179i
$$725$$ 1.00000 1.73205i 0.0371391 0.0643268i
$$726$$ −43.3013 + 75.0000i −1.60706 + 2.78351i
$$727$$ 18.5000 + 32.0429i 0.686127 + 1.18841i 0.973081 + 0.230463i $$0.0740239\pi$$
−0.286954 + 0.957944i $$0.592643\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 8.00000i 0.296093i
$$731$$ 2.50000 + 4.33013i 0.0924658 + 0.160156i
$$732$$ 15.0000 + 8.66025i 0.554416 + 0.320092i
$$733$$ −20.7846 12.0000i −0.767697 0.443230i 0.0643554 0.997927i $$-0.479501\pi$$
−0.832052 + 0.554697i $$0.812834\pi$$
$$734$$ 36.3731 + 21.0000i 1.34255 + 0.775124i
$$735$$ 5.19615 0.191663
$$736$$ 6.92820 4.00000i 0.255377 0.147442i
$$737$$ 0 0
$$738$$ −6.00000 10.3923i −0.220863 0.382546i
$$739$$ 12.0000i 0.441427i 0.975339 + 0.220714i $$0.0708386\pi$$
−0.975339 + 0.220714i $$0.929161\pi$$
$$740$$ 2.00000 + 3.46410i 0.0735215 + 0.127343i
$$741$$ −3.21539 + 49.8564i −0.118120 + 1.83152i
$$742$$ 18.0000 31.1769i 0.660801 1.14454i
$$743$$ 38.1051 + 22.0000i 1.39794 + 0.807102i 0.994177 0.107761i $$-0.0343682\pi$$
0.403764 + 0.914863i $$0.367702\pi$$
$$744$$ 0 0
$$745$$ −1.00000 1.73205i −0.0366372 0.0634574i
$$746$$ 38.0000i 1.39128i
$$747$$ 0 0
$$748$$ 12.0000i 0.438763i
$$749$$ −29.4449 + 17.0000i −1.07589 + 0.621166i
$$750$$ 3.46410i 0.126491i
$$751$$ 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i $$-0.634880\pi$$
0.995018 0.0996961i $$-0.0317870\pi$$
$$752$$ −34.6410 20.0000i −1.26323 0.729325i
$$753$$ 4.50000 + 2.59808i 0.163989 + 0.0946792i
$$754$$ 14.3923 + 0.928203i 0.524137 + 0.0338032i
$$755$$ 4.00000 0.145575
$$756$$ −20.7846 −0.755929
$$757$$ 29.0000 1.05402 0.527011 0.849858i $$-0.323312\pi$$
0.527011 + 0.849858i $$0.323312\pi$$
$$758$$ 18.0000 + 31.1769i 0.653789 + 1.13240i
$$759$$ −5.19615 + 9.00000i −0.188608 + 0.326679i
$$760$$ 0 0
$$761$$ −39.8372 23.0000i −1.44410 0.833749i −0.445977 0.895045i $$-0.647144\pi$$
−0.998120 + 0.0612953i $$0.980477\pi$$
$$762$$ 0 0
$$763$$ 20.0000 + 34.6410i 0.724049 + 1.25409i
$$764$$ −38.0000 −1.37479
$$765$$ 3.00000i 0.108465i
$$766$$ −52.0000 −1.87884
$$767$$ 21.5885 + 1.39230i 0.779514 + 0.0502732i
$$768$$ −24.0000 + 13.8564i −0.866025 + 0.500000i
$$769$$ −34.6410 20.0000i −1.24919 0.721218i −0.278240 0.960512i $$-0.589751\pi$$
−0.970947 + 0.239293i $$0.923084\pi$$
$$770$$ −12.0000 + 20.7846i −0.432450 + 0.749025i
$$771$$ 4.50000 2.59808i 0.162064 0.0935674i
$$772$$ −6.92820 + 4.00000i −0.249351 + 0.143963i
$$773$$ 18.0000i 0.647415i −0.946157 0.323708i $$-0.895071\pi$$
0.946157 0.323708i $$-0.104929\pi$$
$$774$$ 30.0000i 1.07833i
$$775$$ 8.00000i 0.287368i
$$776$$ 0 0
$$777$$ 6.92820i 0.248548i
$$778$$ −39.8372 23.0000i −1.42823 0.824590i