# Properties

 Label 570.2.i.d.391.1 Level $570$ Weight $2$ Character 570.391 Analytic conductor $4.551$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 391.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.391 Dual form 570.2.i.d.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +6.00000 q^{11} +1.00000 q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +(4.00000 - 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 - 0.866025i) q^{21} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.00000 q^{30} +5.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 + 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +11.0000 q^{37} +(0.500000 - 4.33013i) q^{38} +5.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +(-3.00000 - 5.19615i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(-0.500000 - 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(-2.50000 + 4.33013i) q^{52} +(6.00000 + 10.3923i) q^{53} +(0.500000 - 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{55} +1.00000 q^{56} +(-0.500000 + 4.33013i) q^{57} -6.00000 q^{58} +(-3.00000 + 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{60} +(3.50000 + 6.06218i) q^{61} +(2.50000 - 4.33013i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(3.00000 + 5.19615i) q^{66} +(0.500000 + 0.866025i) q^{67} +6.00000 q^{69} +(0.500000 + 0.866025i) q^{70} +(0.500000 + 0.866025i) q^{72} +(0.500000 - 0.866025i) q^{73} +(5.50000 - 9.52628i) q^{74} +1.00000 q^{75} +(-3.50000 - 2.59808i) q^{76} -6.00000 q^{77} +(2.50000 - 4.33013i) q^{78} +(3.50000 - 6.06218i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -6.00000 q^{83} -1.00000 q^{84} +(-0.500000 - 0.866025i) q^{86} +6.00000 q^{87} -6.00000 q^{88} +(6.00000 + 10.3923i) q^{89} +(-0.500000 + 0.866025i) q^{90} +(2.50000 + 4.33013i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(-2.50000 + 4.33013i) q^{93} -12.0000 q^{94} +(0.500000 - 4.33013i) q^{95} -1.00000 q^{96} +(-7.00000 + 12.1244i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} + O(q^{10})$$ $$2q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} - q^{10} + 12q^{11} + 2q^{12} - 5q^{13} - q^{14} + q^{15} - q^{16} - 2q^{18} + 8q^{19} - 2q^{20} + q^{21} + 6q^{22} - 6q^{23} + q^{24} - q^{25} - 10q^{26} + 2q^{27} + q^{28} - 6q^{29} + 2q^{30} + 10q^{31} + q^{32} - 6q^{33} - q^{35} - q^{36} + 22q^{37} + q^{38} + 10q^{39} - q^{40} - 6q^{41} - q^{42} + q^{43} - 6q^{44} - 2q^{45} - 12q^{46} - 12q^{47} - q^{48} - 12q^{49} - 2q^{50} - 5q^{52} + 12q^{53} + q^{54} + 6q^{55} + 2q^{56} - q^{57} - 12q^{58} - 6q^{59} + q^{60} + 7q^{61} + 5q^{62} + q^{63} + 2q^{64} - 10q^{65} + 6q^{66} + q^{67} + 12q^{69} + q^{70} + q^{72} + q^{73} + 11q^{74} + 2q^{75} - 7q^{76} - 12q^{77} + 5q^{78} + 7q^{79} + q^{80} - q^{81} + 6q^{82} - 12q^{83} - 2q^{84} - q^{86} + 12q^{87} - 12q^{88} + 12q^{89} - q^{90} + 5q^{91} - 6q^{92} - 5q^{93} - 24q^{94} + q^{95} - 2q^{96} - 14q^{97} - 6q^{98} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0.500000 + 0.866025i 0.204124 + 0.353553i
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 1.00000 0.288675
$$13$$ −2.50000 4.33013i −0.693375 1.20096i −0.970725 0.240192i $$-0.922790\pi$$
0.277350 0.960769i $$-0.410544\pi$$
$$14$$ −0.500000 + 0.866025i −0.133631 + 0.231455i
$$15$$ 0.500000 + 0.866025i 0.129099 + 0.223607i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ 4.00000 1.73205i 0.917663 0.397360i
$$20$$ −1.00000 −0.223607
$$21$$ 0.500000 0.866025i 0.109109 0.188982i
$$22$$ 3.00000 5.19615i 0.639602 1.10782i
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −5.00000 −0.980581
$$27$$ 1.00000 0.192450
$$28$$ 0.500000 + 0.866025i 0.0944911 + 0.163663i
$$29$$ −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i $$-0.978586\pi$$
0.440652 0.897678i $$-0.354747\pi$$
$$30$$ 1.00000 0.182574
$$31$$ 5.00000 0.898027 0.449013 0.893525i $$-0.351776\pi$$
0.449013 + 0.893525i $$0.351776\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −3.00000 + 5.19615i −0.522233 + 0.904534i
$$34$$ 0 0
$$35$$ −0.500000 + 0.866025i −0.0845154 + 0.146385i
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ 11.0000 1.80839 0.904194 0.427121i $$-0.140472\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 0.500000 4.33013i 0.0811107 0.702439i
$$39$$ 5.00000 0.800641
$$40$$ −0.500000 + 0.866025i −0.0790569 + 0.136931i
$$41$$ −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i $$-0.988546\pi$$
0.530831 + 0.847477i $$0.321880\pi$$
$$42$$ −0.500000 0.866025i −0.0771517 0.133631i
$$43$$ 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i $$-0.809039\pi$$
0.901629 + 0.432511i $$0.142372\pi$$
$$44$$ −3.00000 5.19615i −0.452267 0.783349i
$$45$$ −1.00000 −0.149071
$$46$$ −6.00000 −0.884652
$$47$$ −6.00000 10.3923i −0.875190 1.51587i −0.856560 0.516047i $$-0.827403\pi$$
−0.0186297 0.999826i $$-0.505930\pi$$
$$48$$ −0.500000 0.866025i −0.0721688 0.125000i
$$49$$ −6.00000 −0.857143
$$50$$ −1.00000 −0.141421
$$51$$ 0 0
$$52$$ −2.50000 + 4.33013i −0.346688 + 0.600481i
$$53$$ 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i $$0.141688\pi$$
−0.0783936 + 0.996922i $$0.524979\pi$$
$$54$$ 0.500000 0.866025i 0.0680414 0.117851i
$$55$$ 3.00000 5.19615i 0.404520 0.700649i
$$56$$ 1.00000 0.133631
$$57$$ −0.500000 + 4.33013i −0.0662266 + 0.573539i
$$58$$ −6.00000 −0.787839
$$59$$ −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i $$-0.961054\pi$$
0.601958 + 0.798528i $$0.294388\pi$$
$$60$$ 0.500000 0.866025i 0.0645497 0.111803i
$$61$$ 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i $$-0.0187572\pi$$
−0.550135 + 0.835076i $$0.685424\pi$$
$$62$$ 2.50000 4.33013i 0.317500 0.549927i
$$63$$ 0.500000 + 0.866025i 0.0629941 + 0.109109i
$$64$$ 1.00000 0.125000
$$65$$ −5.00000 −0.620174
$$66$$ 3.00000 + 5.19615i 0.369274 + 0.639602i
$$67$$ 0.500000 + 0.866025i 0.0610847 + 0.105802i 0.894951 0.446165i $$-0.147211\pi$$
−0.833866 + 0.551967i $$0.813877\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 0.500000 + 0.866025i 0.0597614 + 0.103510i
$$71$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i $$-0.814695\pi$$
0.893801 + 0.448463i $$0.148028\pi$$
$$74$$ 5.50000 9.52628i 0.639362 1.10741i
$$75$$ 1.00000 0.115470
$$76$$ −3.50000 2.59808i −0.401478 0.298020i
$$77$$ −6.00000 −0.683763
$$78$$ 2.50000 4.33013i 0.283069 0.490290i
$$79$$ 3.50000 6.06218i 0.393781 0.682048i −0.599164 0.800626i $$-0.704500\pi$$
0.992945 + 0.118578i $$0.0378336\pi$$
$$80$$ 0.500000 + 0.866025i 0.0559017 + 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 3.00000 + 5.19615i 0.331295 + 0.573819i
$$83$$ −6.00000 −0.658586 −0.329293 0.944228i $$-0.606810\pi$$
−0.329293 + 0.944228i $$0.606810\pi$$
$$84$$ −1.00000 −0.109109
$$85$$ 0 0
$$86$$ −0.500000 0.866025i −0.0539164 0.0933859i
$$87$$ 6.00000 0.643268
$$88$$ −6.00000 −0.639602
$$89$$ 6.00000 + 10.3923i 0.635999 + 1.10158i 0.986303 + 0.164946i $$0.0527450\pi$$
−0.350304 + 0.936636i $$0.613922\pi$$
$$90$$ −0.500000 + 0.866025i −0.0527046 + 0.0912871i
$$91$$ 2.50000 + 4.33013i 0.262071 + 0.453921i
$$92$$ −3.00000 + 5.19615i −0.312772 + 0.541736i
$$93$$ −2.50000 + 4.33013i −0.259238 + 0.449013i
$$94$$ −12.0000 −1.23771
$$95$$ 0.500000 4.33013i 0.0512989 0.444262i
$$96$$ −1.00000 −0.102062
$$97$$ −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i $$0.418307\pi$$
−0.964579 + 0.263795i $$0.915026\pi$$
$$98$$ −3.00000 + 5.19615i −0.303046 + 0.524891i
$$99$$ −3.00000 5.19615i −0.301511 0.522233i
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i $$-0.0701767\pi$$
−0.677284 + 0.735721i $$0.736843\pi$$
$$102$$ 0 0
$$103$$ 11.0000 1.08386 0.541931 0.840423i $$-0.317693\pi$$
0.541931 + 0.840423i $$0.317693\pi$$
$$104$$ 2.50000 + 4.33013i 0.245145 + 0.424604i
$$105$$ −0.500000 0.866025i −0.0487950 0.0845154i
$$106$$ 12.0000 1.16554
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ −0.500000 0.866025i −0.0481125 0.0833333i
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ −3.00000 5.19615i −0.286039 0.495434i
$$111$$ −5.50000 + 9.52628i −0.522037 + 0.904194i
$$112$$ 0.500000 0.866025i 0.0472456 0.0818317i
$$113$$ −18.0000 −1.69330 −0.846649 0.532152i $$-0.821383\pi$$
−0.846649 + 0.532152i $$0.821383\pi$$
$$114$$ 3.50000 + 2.59808i 0.327805 + 0.243332i
$$115$$ −6.00000 −0.559503
$$116$$ −3.00000 + 5.19615i −0.278543 + 0.482451i
$$117$$ −2.50000 + 4.33013i −0.231125 + 0.400320i
$$118$$ 3.00000 + 5.19615i 0.276172 + 0.478345i
$$119$$ 0 0
$$120$$ −0.500000 0.866025i −0.0456435 0.0790569i
$$121$$ 25.0000 2.27273
$$122$$ 7.00000 0.633750
$$123$$ −3.00000 5.19615i −0.270501 0.468521i
$$124$$ −2.50000 4.33013i −0.224507 0.388857i
$$125$$ −1.00000 −0.0894427
$$126$$ 1.00000 0.0890871
$$127$$ 8.00000 + 13.8564i 0.709885 + 1.22956i 0.964899 + 0.262620i $$0.0845865\pi$$
−0.255014 + 0.966937i $$0.582080\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0.500000 + 0.866025i 0.0440225 + 0.0762493i
$$130$$ −2.50000 + 4.33013i −0.219265 + 0.379777i
$$131$$ −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 6.00000 0.522233
$$133$$ −4.00000 + 1.73205i −0.346844 + 0.150188i
$$134$$ 1.00000 0.0863868
$$135$$ 0.500000 0.866025i 0.0430331 0.0745356i
$$136$$ 0 0
$$137$$ 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i $$-0.0841608\pi$$
−0.708942 + 0.705266i $$0.750827\pi$$
$$138$$ 3.00000 5.19615i 0.255377 0.442326i
$$139$$ 0.500000 + 0.866025i 0.0424094 + 0.0734553i 0.886451 0.462822i $$-0.153163\pi$$
−0.844042 + 0.536278i $$0.819830\pi$$
$$140$$ 1.00000 0.0845154
$$141$$ 12.0000 1.01058
$$142$$ 0 0
$$143$$ −15.0000 25.9808i −1.25436 2.17262i
$$144$$ 1.00000 0.0833333
$$145$$ −6.00000 −0.498273
$$146$$ −0.500000 0.866025i −0.0413803 0.0716728i
$$147$$ 3.00000 5.19615i 0.247436 0.428571i
$$148$$ −5.50000 9.52628i −0.452097 0.783055i
$$149$$ 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i $$-0.569430\pi$$
0.953703 0.300750i $$-0.0972370\pi$$
$$150$$ 0.500000 0.866025i 0.0408248 0.0707107i
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −4.00000 + 1.73205i −0.324443 + 0.140488i
$$153$$ 0 0
$$154$$ −3.00000 + 5.19615i −0.241747 + 0.418718i
$$155$$ 2.50000 4.33013i 0.200805 0.347804i
$$156$$ −2.50000 4.33013i −0.200160 0.346688i
$$157$$ 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i $$-0.659728\pi$$
0.999762 0.0217953i $$-0.00693820\pi$$
$$158$$ −3.50000 6.06218i −0.278445 0.482281i
$$159$$ −12.0000 −0.951662
$$160$$ 1.00000 0.0790569
$$161$$ 3.00000 + 5.19615i 0.236433 + 0.409514i
$$162$$ 0.500000 + 0.866025i 0.0392837 + 0.0680414i
$$163$$ 11.0000 0.861586 0.430793 0.902451i $$-0.358234\pi$$
0.430793 + 0.902451i $$0.358234\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 3.00000 + 5.19615i 0.233550 + 0.404520i
$$166$$ −3.00000 + 5.19615i −0.232845 + 0.403300i
$$167$$ 9.00000 + 15.5885i 0.696441 + 1.20627i 0.969693 + 0.244328i $$0.0785675\pi$$
−0.273252 + 0.961943i $$0.588099\pi$$
$$168$$ −0.500000 + 0.866025i −0.0385758 + 0.0668153i
$$169$$ −6.00000 + 10.3923i −0.461538 + 0.799408i
$$170$$ 0 0
$$171$$ −3.50000 2.59808i −0.267652 0.198680i
$$172$$ −1.00000 −0.0762493
$$173$$ −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i $$-0.906580\pi$$
0.729155 + 0.684349i $$0.239913\pi$$
$$174$$ 3.00000 5.19615i 0.227429 0.393919i
$$175$$ 0.500000 + 0.866025i 0.0377964 + 0.0654654i
$$176$$ −3.00000 + 5.19615i −0.226134 + 0.391675i
$$177$$ −3.00000 5.19615i −0.225494 0.390567i
$$178$$ 12.0000 0.899438
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0.500000 + 0.866025i 0.0372678 + 0.0645497i
$$181$$ −13.0000 22.5167i −0.966282 1.67365i −0.706129 0.708083i $$-0.749560\pi$$
−0.260153 0.965567i $$-0.583773\pi$$
$$182$$ 5.00000 0.370625
$$183$$ −7.00000 −0.517455
$$184$$ 3.00000 + 5.19615i 0.221163 + 0.383065i
$$185$$ 5.50000 9.52628i 0.404368 0.700386i
$$186$$ 2.50000 + 4.33013i 0.183309 + 0.317500i
$$187$$ 0 0
$$188$$ −6.00000 + 10.3923i −0.437595 + 0.757937i
$$189$$ −1.00000 −0.0727393
$$190$$ −3.50000 2.59808i −0.253917 0.188484i
$$191$$ 12.0000 0.868290 0.434145 0.900843i $$-0.357051\pi$$
0.434145 + 0.900843i $$0.357051\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i $$-0.890928\pi$$
0.761911 + 0.647682i $$0.224262\pi$$
$$194$$ 7.00000 + 12.1244i 0.502571 + 0.870478i
$$195$$ 2.50000 4.33013i 0.179029 0.310087i
$$196$$ 3.00000 + 5.19615i 0.214286 + 0.371154i
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ −6.00000 −0.426401
$$199$$ 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i $$-0.0868577\pi$$
−0.714893 + 0.699234i $$0.753524\pi$$
$$200$$ 0.500000 + 0.866025i 0.0353553 + 0.0612372i
$$201$$ −1.00000 −0.0705346
$$202$$ 6.00000 0.422159
$$203$$ 3.00000 + 5.19615i 0.210559 + 0.364698i
$$204$$ 0 0
$$205$$ 3.00000 + 5.19615i 0.209529 + 0.362915i
$$206$$ 5.50000 9.52628i 0.383203 0.663727i
$$207$$ −3.00000 + 5.19615i −0.208514 + 0.361158i
$$208$$ 5.00000 0.346688
$$209$$ 24.0000 10.3923i 1.66011 0.718851i
$$210$$ −1.00000 −0.0690066
$$211$$ 6.50000 11.2583i 0.447478 0.775055i −0.550743 0.834675i $$-0.685655\pi$$
0.998221 + 0.0596196i $$0.0189888\pi$$
$$212$$ 6.00000 10.3923i 0.412082 0.713746i
$$213$$ 0 0
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ −0.500000 0.866025i −0.0340997 0.0590624i
$$216$$ −1.00000 −0.0680414
$$217$$ −5.00000 −0.339422
$$218$$ 7.00000 + 12.1244i 0.474100 + 0.821165i
$$219$$ 0.500000 + 0.866025i 0.0337869 + 0.0585206i
$$220$$ −6.00000 −0.404520
$$221$$ 0 0
$$222$$ 5.50000 + 9.52628i 0.369136 + 0.639362i
$$223$$ 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i $$-0.822674\pi$$
0.882281 + 0.470723i $$0.156007\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ −0.500000 + 0.866025i −0.0333333 + 0.0577350i
$$226$$ −9.00000 + 15.5885i −0.598671 + 1.03693i
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 4.00000 1.73205i 0.264906 0.114708i
$$229$$ −25.0000 −1.65205 −0.826023 0.563636i $$-0.809402\pi$$
−0.826023 + 0.563636i $$0.809402\pi$$
$$230$$ −3.00000 + 5.19615i −0.197814 + 0.342624i
$$231$$ 3.00000 5.19615i 0.197386 0.341882i
$$232$$ 3.00000 + 5.19615i 0.196960 + 0.341144i
$$233$$ 6.00000 10.3923i 0.393073 0.680823i −0.599780 0.800165i $$-0.704745\pi$$
0.992853 + 0.119342i $$0.0380786\pi$$
$$234$$ 2.50000 + 4.33013i 0.163430 + 0.283069i
$$235$$ −12.0000 −0.782794
$$236$$ 6.00000 0.390567
$$237$$ 3.50000 + 6.06218i 0.227349 + 0.393781i
$$238$$ 0 0
$$239$$ −18.0000 −1.16432 −0.582162 0.813073i $$-0.697793\pi$$
−0.582162 + 0.813073i $$0.697793\pi$$
$$240$$ −1.00000 −0.0645497
$$241$$ −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i $$-0.218151\pi$$
−0.935242 + 0.354010i $$0.884818\pi$$
$$242$$ 12.5000 21.6506i 0.803530 1.39176i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 3.50000 6.06218i 0.224065 0.388091i
$$245$$ −3.00000 + 5.19615i −0.191663 + 0.331970i
$$246$$ −6.00000 −0.382546
$$247$$ −17.5000 12.9904i −1.11350 0.826558i
$$248$$ −5.00000 −0.317500
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ −0.500000 + 0.866025i −0.0316228 + 0.0547723i
$$251$$ −3.00000 5.19615i −0.189358 0.327978i 0.755678 0.654943i $$-0.227307\pi$$
−0.945036 + 0.326965i $$0.893974\pi$$
$$252$$ 0.500000 0.866025i 0.0314970 0.0545545i
$$253$$ −18.0000 31.1769i −1.13165 1.96008i
$$254$$ 16.0000 1.00393
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i $$-0.226587\pi$$
−0.944294 + 0.329104i $$0.893253\pi$$
$$258$$ 1.00000 0.0622573
$$259$$ −11.0000 −0.683507
$$260$$ 2.50000 + 4.33013i 0.155043 + 0.268543i
$$261$$ −3.00000 + 5.19615i −0.185695 + 0.321634i
$$262$$ 3.00000 + 5.19615i 0.185341 + 0.321019i
$$263$$ 3.00000 5.19615i 0.184988 0.320408i −0.758585 0.651575i $$-0.774109\pi$$
0.943572 + 0.331166i $$0.107442\pi$$
$$264$$ 3.00000 5.19615i 0.184637 0.319801i
$$265$$ 12.0000 0.737154
$$266$$ −0.500000 + 4.33013i −0.0306570 + 0.265497i
$$267$$ −12.0000 −0.734388
$$268$$ 0.500000 0.866025i 0.0305424 0.0529009i
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ −0.500000 0.866025i −0.0304290 0.0527046i
$$271$$ 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i $$-0.671801\pi$$
0.999870 + 0.0161307i $$0.00513477\pi$$
$$272$$ 0 0
$$273$$ −5.00000 −0.302614
$$274$$ 6.00000 0.362473
$$275$$ −3.00000 5.19615i −0.180907 0.313340i
$$276$$ −3.00000 5.19615i −0.180579 0.312772i
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ 1.00000 0.0599760
$$279$$ −2.50000 4.33013i −0.149671 0.259238i
$$280$$ 0.500000 0.866025i 0.0298807 0.0517549i
$$281$$ −9.00000 15.5885i −0.536895 0.929929i −0.999069 0.0431402i $$-0.986264\pi$$
0.462174 0.886789i $$-0.347070\pi$$
$$282$$ 6.00000 10.3923i 0.357295 0.618853i
$$283$$ 8.00000 13.8564i 0.475551 0.823678i −0.524057 0.851683i $$-0.675582\pi$$
0.999608 + 0.0280052i $$0.00891551\pi$$
$$284$$ 0 0
$$285$$ 3.50000 + 2.59808i 0.207322 + 0.153897i
$$286$$ −30.0000 −1.77394
$$287$$ 3.00000 5.19615i 0.177084 0.306719i
$$288$$ 0.500000 0.866025i 0.0294628 0.0510310i
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ −3.00000 + 5.19615i −0.176166 + 0.305129i
$$291$$ −7.00000 12.1244i −0.410347 0.710742i
$$292$$ −1.00000 −0.0585206
$$293$$ −18.0000 −1.05157 −0.525786 0.850617i $$-0.676229\pi$$
−0.525786 + 0.850617i $$0.676229\pi$$
$$294$$ −3.00000 5.19615i −0.174964 0.303046i
$$295$$ 3.00000 + 5.19615i 0.174667 + 0.302532i
$$296$$ −11.0000 −0.639362
$$297$$ 6.00000 0.348155
$$298$$ −9.00000 15.5885i −0.521356 0.903015i
$$299$$ −15.0000 + 25.9808i −0.867472 + 1.50251i
$$300$$ −0.500000 0.866025i −0.0288675 0.0500000i
$$301$$ −0.500000 + 0.866025i −0.0288195 + 0.0499169i
$$302$$ 4.00000 6.92820i 0.230174 0.398673i
$$303$$ −6.00000 −0.344691
$$304$$ −0.500000 + 4.33013i −0.0286770 + 0.248350i
$$305$$ 7.00000 0.400819
$$306$$ 0 0
$$307$$ −10.0000 + 17.3205i −0.570730 + 0.988534i 0.425761 + 0.904836i $$0.360006\pi$$
−0.996491 + 0.0836980i $$0.973327\pi$$
$$308$$ 3.00000 + 5.19615i 0.170941 + 0.296078i
$$309$$ −5.50000 + 9.52628i −0.312884 + 0.541931i
$$310$$ −2.50000 4.33013i −0.141990 0.245935i
$$311$$ 6.00000 0.340229 0.170114 0.985424i $$-0.445586\pi$$
0.170114 + 0.985424i $$0.445586\pi$$
$$312$$ −5.00000 −0.283069
$$313$$ 11.0000 + 19.0526i 0.621757 + 1.07691i 0.989158 + 0.146852i $$0.0469141\pi$$
−0.367402 + 0.930062i $$0.619753\pi$$
$$314$$ −6.50000 11.2583i −0.366816 0.635344i
$$315$$ 1.00000 0.0563436
$$316$$ −7.00000 −0.393781
$$317$$ 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i $$0.00202172\pi$$
−0.494489 + 0.869184i $$0.664645\pi$$
$$318$$ −6.00000 + 10.3923i −0.336463 + 0.582772i
$$319$$ −18.0000 31.1769i −1.00781 1.74557i
$$320$$ 0.500000 0.866025i 0.0279508 0.0484123i
$$321$$ 6.00000 10.3923i 0.334887 0.580042i
$$322$$ 6.00000 0.334367
$$323$$ 0 0
$$324$$ 1.00000 0.0555556
$$325$$ −2.50000 + 4.33013i −0.138675 + 0.240192i
$$326$$ 5.50000 9.52628i 0.304617 0.527612i
$$327$$ −7.00000 12.1244i −0.387101 0.670478i
$$328$$ 3.00000 5.19615i 0.165647 0.286910i
$$329$$ 6.00000 + 10.3923i 0.330791 + 0.572946i
$$330$$ 6.00000 0.330289
$$331$$ 29.0000 1.59398 0.796992 0.603990i $$-0.206423\pi$$
0.796992 + 0.603990i $$0.206423\pi$$
$$332$$ 3.00000 + 5.19615i 0.164646 + 0.285176i
$$333$$ −5.50000 9.52628i −0.301398 0.522037i
$$334$$ 18.0000 0.984916
$$335$$ 1.00000 0.0546358
$$336$$ 0.500000 + 0.866025i 0.0272772 + 0.0472456i
$$337$$ −5.50000 + 9.52628i −0.299604 + 0.518930i −0.976045 0.217567i $$-0.930188\pi$$
0.676441 + 0.736497i $$0.263521\pi$$
$$338$$ 6.00000 + 10.3923i 0.326357 + 0.565267i
$$339$$ 9.00000 15.5885i 0.488813 0.846649i
$$340$$ 0 0
$$341$$ 30.0000 1.62459
$$342$$ −4.00000 + 1.73205i −0.216295 + 0.0936586i
$$343$$ 13.0000 0.701934
$$344$$ −0.500000 + 0.866025i −0.0269582 + 0.0466930i
$$345$$ 3.00000 5.19615i 0.161515 0.279751i
$$346$$ 3.00000 + 5.19615i 0.161281 + 0.279347i
$$347$$ 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i $$-0.728946\pi$$
0.980921 + 0.194409i $$0.0622790\pi$$
$$348$$ −3.00000 5.19615i −0.160817 0.278543i
$$349$$ −19.0000 −1.01705 −0.508523 0.861048i $$-0.669808\pi$$
−0.508523 + 0.861048i $$0.669808\pi$$
$$350$$ 1.00000 0.0534522
$$351$$ −2.50000 4.33013i −0.133440 0.231125i
$$352$$ 3.00000 + 5.19615i 0.159901 + 0.276956i
$$353$$ 18.0000 0.958043 0.479022 0.877803i $$-0.340992\pi$$
0.479022 + 0.877803i $$0.340992\pi$$
$$354$$ −6.00000 −0.318896
$$355$$ 0 0
$$356$$ 6.00000 10.3923i 0.317999 0.550791i
$$357$$ 0 0
$$358$$ 9.00000 15.5885i 0.475665 0.823876i
$$359$$ 3.00000 5.19615i 0.158334 0.274242i −0.775934 0.630814i $$-0.782721\pi$$
0.934268 + 0.356572i $$0.116054\pi$$
$$360$$ 1.00000 0.0527046
$$361$$ 13.0000 13.8564i 0.684211 0.729285i
$$362$$ −26.0000 −1.36653
$$363$$ −12.5000 + 21.6506i −0.656080 + 1.13636i
$$364$$ 2.50000 4.33013i 0.131036 0.226960i
$$365$$ −0.500000 0.866025i −0.0261712 0.0453298i
$$366$$ −3.50000 + 6.06218i −0.182948 + 0.316875i
$$367$$ −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i $$-0.313000\pi$$
−0.997960 + 0.0638362i $$0.979666\pi$$
$$368$$ 6.00000 0.312772
$$369$$ 6.00000 0.312348
$$370$$ −5.50000 9.52628i −0.285931 0.495248i
$$371$$ −6.00000 10.3923i −0.311504 0.539542i
$$372$$ 5.00000 0.259238
$$373$$ 2.00000 0.103556 0.0517780 0.998659i $$-0.483511\pi$$
0.0517780 + 0.998659i $$0.483511\pi$$
$$374$$ 0 0
$$375$$ 0.500000 0.866025i 0.0258199 0.0447214i
$$376$$ 6.00000 + 10.3923i 0.309426 + 0.535942i
$$377$$ −15.0000 + 25.9808i −0.772539 + 1.33808i
$$378$$ −0.500000 + 0.866025i −0.0257172 + 0.0445435i
$$379$$ −19.0000 −0.975964 −0.487982 0.872854i $$-0.662267\pi$$
−0.487982 + 0.872854i $$0.662267\pi$$
$$380$$ −4.00000 + 1.73205i −0.205196 + 0.0888523i
$$381$$ −16.0000 −0.819705
$$382$$ 6.00000 10.3923i 0.306987 0.531717i
$$383$$ 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i $$-0.734147\pi$$
0.977613 + 0.210411i $$0.0674801\pi$$
$$384$$ 0.500000 + 0.866025i 0.0255155 + 0.0441942i
$$385$$ −3.00000 + 5.19615i −0.152894 + 0.264820i
$$386$$ 2.50000 + 4.33013i 0.127247 + 0.220398i
$$387$$ −1.00000 −0.0508329
$$388$$ 14.0000 0.710742
$$389$$ 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i $$-0.118061\pi$$
−0.779895 + 0.625910i $$0.784728\pi$$
$$390$$ −2.50000 4.33013i −0.126592 0.219265i
$$391$$ 0 0
$$392$$ 6.00000 0.303046
$$393$$ −3.00000 5.19615i −0.151330 0.262111i
$$394$$ −9.00000 + 15.5885i −0.453413 + 0.785335i
$$395$$ −3.50000 6.06218i −0.176104 0.305021i
$$396$$ −3.00000 + 5.19615i −0.150756 + 0.261116i
$$397$$ 12.5000 21.6506i 0.627357 1.08661i −0.360723 0.932673i $$-0.617470\pi$$
0.988080 0.153941i $$-0.0491966\pi$$
$$398$$ 7.00000 0.350878
$$399$$ 0.500000 4.33013i 0.0250313 0.216777i
$$400$$ 1.00000 0.0500000
$$401$$ −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i $$-0.981709\pi$$
0.548911 + 0.835881i $$0.315043\pi$$
$$402$$ −0.500000 + 0.866025i −0.0249377 + 0.0431934i
$$403$$ −12.5000 21.6506i −0.622669 1.07849i
$$404$$ 3.00000 5.19615i 0.149256 0.258518i
$$405$$ 0.500000 + 0.866025i 0.0248452 + 0.0430331i
$$406$$ 6.00000 0.297775
$$407$$ 66.0000 3.27150
$$408$$ 0 0
$$409$$ −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i $$-0.182412\pi$$
−0.889689 + 0.456566i $$0.849079\pi$$
$$410$$ 6.00000 0.296319
$$411$$ −6.00000 −0.295958
$$412$$ −5.50000 9.52628i −0.270966 0.469326i
$$413$$ 3.00000 5.19615i 0.147620 0.255686i
$$414$$ 3.00000 + 5.19615i 0.147442 + 0.255377i
$$415$$ −3.00000 + 5.19615i −0.147264 + 0.255069i
$$416$$ 2.50000 4.33013i 0.122573 0.212302i
$$417$$ −1.00000 −0.0489702
$$418$$ 3.00000 25.9808i 0.146735 1.27076i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ −0.500000 + 0.866025i −0.0243975 + 0.0422577i
$$421$$ −13.0000 + 22.5167i −0.633581 + 1.09739i 0.353233 + 0.935536i $$0.385082\pi$$
−0.986814 + 0.161859i $$0.948251\pi$$
$$422$$ −6.50000 11.2583i −0.316415 0.548047i
$$423$$ −6.00000 + 10.3923i −0.291730 + 0.505291i
$$424$$ −6.00000 10.3923i −0.291386 0.504695i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −3.50000 6.06218i −0.169377 0.293369i
$$428$$ 6.00000 + 10.3923i 0.290021 + 0.502331i
$$429$$ 30.0000 1.44841
$$430$$ −1.00000 −0.0482243
$$431$$ 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i $$0.0295076\pi$$
−0.417687 + 0.908591i $$0.637159\pi$$
$$432$$ −0.500000 + 0.866025i −0.0240563 + 0.0416667i
$$433$$ 3.50000 + 6.06218i 0.168199 + 0.291330i 0.937787 0.347212i $$-0.112871\pi$$
−0.769588 + 0.638541i $$0.779538\pi$$
$$434$$ −2.50000 + 4.33013i −0.120004 + 0.207853i
$$435$$ 3.00000 5.19615i 0.143839 0.249136i
$$436$$ 14.0000 0.670478
$$437$$ −21.0000 15.5885i −1.00457 0.745697i
$$438$$ 1.00000 0.0477818
$$439$$ −5.50000 + 9.52628i −0.262501 + 0.454665i −0.966906 0.255134i $$-0.917881\pi$$
0.704405 + 0.709798i $$0.251214\pi$$
$$440$$ −3.00000 + 5.19615i −0.143019 + 0.247717i
$$441$$ 3.00000 + 5.19615i 0.142857 + 0.247436i
$$442$$ 0 0
$$443$$ 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i $$0.0264433\pi$$
−0.426414 + 0.904528i $$0.640223\pi$$
$$444$$ 11.0000 0.522037
$$445$$ 12.0000 0.568855
$$446$$ −0.500000 0.866025i −0.0236757 0.0410075i
$$447$$ 9.00000 + 15.5885i 0.425685 + 0.737309i
$$448$$ −1.00000 −0.0472456
$$449$$ 24.0000 1.13263 0.566315 0.824189i $$-0.308369\pi$$
0.566315 + 0.824189i $$0.308369\pi$$
$$450$$ 0.500000 + 0.866025i 0.0235702 + 0.0408248i
$$451$$ −18.0000 + 31.1769i −0.847587 + 1.46806i
$$452$$ 9.00000 + 15.5885i 0.423324 + 0.733219i
$$453$$ −4.00000 + 6.92820i −0.187936 + 0.325515i
$$454$$ −9.00000 + 15.5885i −0.422391 + 0.731603i
$$455$$ 5.00000 0.234404
$$456$$ 0.500000 4.33013i 0.0234146 0.202777i
$$457$$ 11.0000 0.514558 0.257279 0.966337i $$-0.417174\pi$$
0.257279 + 0.966337i $$0.417174\pi$$
$$458$$ −12.5000 + 21.6506i −0.584087 + 1.01167i
$$459$$ 0 0
$$460$$ 3.00000 + 5.19615i 0.139876 + 0.242272i
$$461$$ −18.0000 + 31.1769i −0.838344 + 1.45205i 0.0529352 + 0.998598i $$0.483142\pi$$
−0.891279 + 0.453456i $$0.850191\pi$$
$$462$$ −3.00000 5.19615i −0.139573 0.241747i
$$463$$ 17.0000 0.790057 0.395029 0.918669i $$-0.370735\pi$$
0.395029 + 0.918669i $$0.370735\pi$$
$$464$$ 6.00000 0.278543
$$465$$ 2.50000 + 4.33013i 0.115935 + 0.200805i
$$466$$ −6.00000 10.3923i −0.277945 0.481414i
$$467$$ −6.00000 −0.277647 −0.138823 0.990317i $$-0.544332\pi$$
−0.138823 + 0.990317i $$0.544332\pi$$
$$468$$ 5.00000 0.231125
$$469$$ −0.500000 0.866025i −0.0230879 0.0399893i
$$470$$ −6.00000 + 10.3923i −0.276759 + 0.479361i
$$471$$ 6.50000 + 11.2583i 0.299504 + 0.518756i
$$472$$ 3.00000 5.19615i 0.138086 0.239172i
$$473$$ 3.00000 5.19615i 0.137940 0.238919i
$$474$$ 7.00000 0.321521
$$475$$ −3.50000 2.59808i −0.160591 0.119208i
$$476$$ 0 0
$$477$$ 6.00000 10.3923i 0.274721 0.475831i
$$478$$ −9.00000 + 15.5885i −0.411650 + 0.712999i
$$479$$ −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i $$-0.210436\pi$$
−0.926388 + 0.376571i $$0.877103\pi$$
$$480$$ −0.500000 + 0.866025i −0.0228218 + 0.0395285i
$$481$$ −27.5000 47.6314i −1.25389 2.17180i
$$482$$ −5.00000 −0.227744
$$483$$ −6.00000 −0.273009
$$484$$ −12.5000 21.6506i −0.568182 0.984120i
$$485$$ 7.00000 + 12.1244i 0.317854 + 0.550539i
$$486$$ −1.00000 −0.0453609
$$487$$ 32.0000 1.45006 0.725029 0.688718i $$-0.241826\pi$$
0.725029 + 0.688718i $$0.241826\pi$$
$$488$$ −3.50000 6.06218i −0.158438 0.274422i
$$489$$ −5.50000 + 9.52628i −0.248719 + 0.430793i
$$490$$ 3.00000 + 5.19615i 0.135526 + 0.234738i
$$491$$ 6.00000 10.3923i 0.270776 0.468998i −0.698285 0.715820i $$-0.746053\pi$$
0.969061 + 0.246822i $$0.0793863\pi$$
$$492$$ −3.00000 + 5.19615i −0.135250 + 0.234261i
$$493$$ 0 0
$$494$$ −20.0000 + 8.66025i −0.899843 + 0.389643i
$$495$$ −6.00000 −0.269680
$$496$$ −2.50000 + 4.33013i −0.112253 + 0.194428i
$$497$$ 0 0
$$498$$ −3.00000 5.19615i −0.134433 0.232845i
$$499$$ 0.500000 0.866025i 0.0223831 0.0387686i −0.854617 0.519259i $$-0.826208\pi$$
0.877000 + 0.480490i $$0.159541\pi$$
$$500$$ 0.500000 + 0.866025i 0.0223607 + 0.0387298i
$$501$$ −18.0000 −0.804181
$$502$$ −6.00000 −0.267793
$$503$$ 12.0000 + 20.7846i 0.535054 + 0.926740i 0.999161 + 0.0409609i $$0.0130419\pi$$
−0.464107 + 0.885779i $$0.653625\pi$$
$$504$$ −0.500000 0.866025i −0.0222718 0.0385758i
$$505$$ 6.00000 0.266996
$$506$$ −36.0000 −1.60040
$$507$$ −6.00000 10.3923i −0.266469 0.461538i
$$508$$ 8.00000 13.8564i 0.354943 0.614779i
$$509$$ 18.0000 + 31.1769i 0.797836 + 1.38189i 0.921023 + 0.389509i $$0.127355\pi$$
−0.123187 + 0.992384i $$0.539311\pi$$
$$510$$ 0 0
$$511$$ −0.500000 + 0.866025i −0.0221187 + 0.0383107i
$$512$$ −1.00000 −0.0441942
$$513$$ 4.00000 1.73205i 0.176604 0.0764719i
$$514$$ −6.00000 −0.264649
$$515$$ 5.50000 9.52628i 0.242359 0.419778i
$$516$$ 0.500000 0.866025i 0.0220113 0.0381246i
$$517$$ −36.0000 62.3538i −1.58328 2.74232i
$$518$$ −5.50000 + 9.52628i −0.241656 + 0.418561i
$$519$$ −3.00000 5.19615i −0.131685 0.228086i
$$520$$ 5.00000 0.219265
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 3.00000 + 5.19615i 0.131306 + 0.227429i
$$523$$ 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i $$0.0703858\pi$$
−0.297884 + 0.954602i $$0.596281\pi$$
$$524$$ 6.00000 0.262111
$$525$$ −1.00000 −0.0436436
$$526$$ −3.00000 5.19615i −0.130806 0.226563i
$$527$$ 0 0
$$528$$ −3.00000 5.19615i −0.130558 0.226134i
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 6.00000 10.3923i 0.260623 0.451413i
$$531$$ 6.00000 0.260378
$$532$$ 3.50000 + 2.59808i 0.151744 + 0.112641i
$$533$$ 30.0000 1.29944
$$534$$ −6.00000 + 10.3923i −0.259645 + 0.449719i
$$535$$ −6.00000 + 10.3923i −0.259403 + 0.449299i
$$536$$ −0.500000 0.866025i −0.0215967 0.0374066i
$$537$$ −9.00000 + 15.5885i −0.388379 + 0.672692i
$$538$$ 9.00000 + 15.5885i 0.388018 + 0.672066i
$$539$$ −36.0000 −1.55063
$$540$$ −1.00000 −0.0430331
$$541$$ −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i $$-0.242655\pi$$
−0.959697 + 0.281037i $$0.909322\pi$$
$$542$$ −8.00000 13.8564i −0.343629 0.595184i
$$543$$ 26.0000 1.11577
$$544$$ 0 0
$$545$$ 7.00000 + 12.1244i 0.299847 + 0.519350i
$$546$$ −2.50000 + 4.33013i −0.106990 + 0.185312i
$$547$$ 6.50000 + 11.2583i 0.277920 + 0.481371i 0.970868 0.239616i $$-0.0770217\pi$$
−0.692948 + 0.720988i $$0.743688\pi$$
$$548$$ 3.00000 5.19615i 0.128154 0.221969i
$$549$$ 3.50000 6.06218i 0.149376 0.258727i
$$550$$ −6.00000 −0.255841
$$551$$ −21.0000 15.5885i −0.894630 0.664091i
$$552$$ −6.00000 −0.255377
$$553$$ −3.50000 + 6.06218i −0.148835 + 0.257790i
$$554$$ 7.00000 12.1244i 0.297402 0.515115i
$$555$$ 5.50000 + 9.52628i 0.233462 + 0.404368i
$$556$$ 0.500000 0.866025i 0.0212047 0.0367277i
$$557$$ 6.00000 + 10.3923i 0.254228 + 0.440336i 0.964686 0.263404i $$-0.0848453\pi$$
−0.710457 + 0.703740i $$0.751512\pi$$
$$558$$ −5.00000 −0.211667
$$559$$ −5.00000 −0.211477
$$560$$ −0.500000 0.866025i −0.0211289 0.0365963i
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ −6.00000 −0.252870 −0.126435 0.991975i $$-0.540353\pi$$
−0.126435 + 0.991975i $$0.540353\pi$$
$$564$$ −6.00000 10.3923i −0.252646 0.437595i
$$565$$ −9.00000 + 15.5885i −0.378633 + 0.655811i
$$566$$ −8.00000 13.8564i −0.336265 0.582428i
$$567$$ 0.500000 0.866025i 0.0209980 0.0363696i
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 4.00000 1.73205i 0.167542 0.0725476i
$$571$$ 23.0000 0.962520 0.481260 0.876578i $$-0.340179\pi$$
0.481260 + 0.876578i $$0.340179\pi$$
$$572$$ −15.0000 + 25.9808i −0.627182 + 1.08631i
$$573$$ −6.00000 + 10.3923i −0.250654 + 0.434145i
$$574$$ −3.00000 5.19615i −0.125218 0.216883i
$$575$$ −3.00000 + 5.19615i −0.125109 + 0.216695i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −34.0000 −1.41544 −0.707719 0.706494i $$-0.750276\pi$$
−0.707719 + 0.706494i $$0.750276\pi$$
$$578$$ 17.0000 0.707107
$$579$$ −2.50000 4.33013i −0.103896 0.179954i
$$580$$ 3.00000 + 5.19615i 0.124568 + 0.215758i
$$581$$ 6.00000 0.248922
$$582$$ −14.0000 −0.580319
$$583$$ 36.0000 + 62.3538i 1.49097 + 2.58243i
$$584$$ −0.500000 + 0.866025i −0.0206901 + 0.0358364i
$$585$$ 2.50000 + 4.33013i 0.103362 + 0.179029i
$$586$$ −9.00000 + 15.5885i −0.371787 + 0.643953i
$$587$$ −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i $$-0.954479\pi$$
0.618322 + 0.785925i $$0.287813\pi$$
$$588$$ −6.00000 −0.247436
$$589$$ 20.0000 8.66025i 0.824086 0.356840i
$$590$$ 6.00000 0.247016
$$591$$ 9.00000 15.5885i 0.370211 0.641223i
$$592$$ −5.50000 + 9.52628i −0.226049 + 0.391528i
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 3.00000 5.19615i 0.123091 0.213201i
$$595$$ 0 0
$$596$$ −18.0000 −0.737309
$$597$$ −7.00000 −0.286491
$$598$$ 15.0000 + 25.9808i 0.613396 + 1.06243i
$$599$$ −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i $$-0.729446\pi$$
−0.320607 0.947212i $$-0.603887\pi$$
$$600$$ −1.00000 −0.0408248
$$601$$ −1.00000 −0.0407909 −0.0203954 0.999792i $$-0.506493\pi$$
−0.0203954 + 0.999792i $$0.506493\pi$$
$$602$$ 0.500000 + 0.866025i 0.0203785 + 0.0352966i
$$603$$ 0.500000 0.866025i 0.0203616 0.0352673i
$$604$$ −4.00000 6.92820i −0.162758 0.281905i
$$605$$ 12.5000 21.6506i 0.508197 0.880223i
$$606$$ −3.00000 + 5.19615i −0.121867 + 0.211079i
$$607$$ −1.00000 −0.0405887 −0.0202944 0.999794i $$-0.506460\pi$$
−0.0202944 + 0.999794i $$0.506460\pi$$
$$608$$ 3.50000 + 2.59808i 0.141944 + 0.105366i
$$609$$ −6.00000 −0.243132
$$610$$ 3.50000 6.06218i 0.141711 0.245450i
$$611$$ −30.0000 + 51.9615i −1.21367 + 2.10214i
$$612$$ 0 0
$$613$$ −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i $$-0.846193\pi$$
0.845124 + 0.534570i $$0.179527\pi$$
$$614$$ 10.0000 + 17.3205i 0.403567 + 0.698999i
$$615$$ −6.00000 −0.241943
$$616$$ 6.00000 0.241747
$$617$$ 12.0000 + 20.7846i 0.483102 + 0.836757i 0.999812 0.0194037i $$-0.00617676\pi$$
−0.516710 + 0.856161i $$0.672843\pi$$
$$618$$ 5.50000 + 9.52628i 0.221242 + 0.383203i
$$619$$ 11.0000 0.442127 0.221064 0.975259i $$-0.429047\pi$$
0.221064 + 0.975259i $$0.429047\pi$$
$$620$$ −5.00000 −0.200805
$$621$$ −3.00000 5.19615i −0.120386 0.208514i
$$622$$ 3.00000 5.19615i 0.120289 0.208347i
$$623$$ −6.00000 10.3923i −0.240385 0.416359i
$$624$$ −2.50000 + 4.33013i −0.100080 + 0.173344i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 22.0000 0.879297
$$627$$ −3.00000 + 25.9808i −0.119808 + 1.03757i
$$628$$ −13.0000 −0.518756
$$629$$ 0 0
$$630$$ 0.500000 0.866025i 0.0199205 0.0345033i
$$631$$ 3.50000 + 6.06218i 0.139333 + 0.241331i 0.927244 0.374457i $$-0.122171\pi$$
−0.787911 + 0.615789i $$0.788838\pi$$
$$632$$ −3.50000 + 6.06218i −0.139223 + 0.241140i
$$633$$ 6.50000 + 11.2583i 0.258352 + 0.447478i
$$634$$ 18.0000 0.714871
$$635$$ 16.0000 0.634941
$$636$$ 6.00000 + 10.3923i 0.237915 + 0.412082i
$$637$$ 15.0000 + 25.9808i 0.594322 + 1.02940i
$$638$$ −36.0000 −1.42525
$$639$$ 0 0
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ 18.0000 31.1769i 0.710957 1.23141i −0.253541 0.967325i $$-0.581595\pi$$
0.964498 0.264089i $$-0.0850714\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ −14.5000 + 25.1147i −0.571824 + 0.990429i 0.424555 + 0.905402i $$0.360431\pi$$
−0.996379 + 0.0850262i $$0.972903\pi$$
$$644$$ 3.00000 5.19615i 0.118217 0.204757i
$$645$$ 1.00000 0.0393750
$$646$$ 0 0
$$647$$ −42.0000 −1.65119 −0.825595 0.564263i $$-0.809160\pi$$
−0.825595 + 0.564263i $$0.809160\pi$$
$$648$$ 0.500000 0.866025i 0.0196419 0.0340207i
$$649$$ −18.0000 + 31.1769i −0.706562 + 1.22380i
$$650$$ 2.50000 + 4.33013i 0.0980581 + 0.169842i
$$651$$ 2.50000 4.33013i 0.0979827 0.169711i
$$652$$ −5.50000 9.52628i −0.215397 0.373078i
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ −14.0000 −0.547443
$$655$$ 3.00000 + 5.19615i 0.117220 + 0.203030i
$$656$$ −3.00000 5.19615i −0.117130 0.202876i
$$657$$ −1.00000 −0.0390137
$$658$$ 12.0000 0.467809
$$659$$ −15.0000 25.9808i −0.584317 1.01207i −0.994960 0.100271i $$-0.968029\pi$$
0.410643 0.911796i $$-0.365304\pi$$
$$660$$ 3.00000 5.19615i 0.116775 0.202260i
$$661$$ −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i $$-0.254441\pi$$
−0.969442 + 0.245319i $$0.921107\pi$$
$$662$$ 14.5000 25.1147i 0.563559 0.976112i
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ −0.500000 + 4.33013i −0.0193892 + 0.167915i
$$666$$ −11.0000 −0.426241
$$667$$ −18.0000 + 31.1769i −0.696963 + 1.20717i
$$668$$ 9.00000 15.5885i 0.348220 0.603136i
$$669$$ 0.500000 + 0.866025i 0.0193311 + 0.0334825i
$$670$$ 0.500000 0.866025i 0.0193167 0.0334575i
$$671$$ 21.0000 + 36.3731i 0.810696 + 1.40417i
$$672$$ 1.00000 0.0385758
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ 5.50000 + 9.52628i 0.211852 + 0.366939i
$$675$$ −0.500000 0.866025i −0.0192450 0.0333333i
$$676$$ 12.0000 0.461538
$$677$$ −12.0000 −0.461197 −0.230599 0.973049i $$-0.574068\pi$$
−0.230599 + 0.973049i $$0.574068\pi$$
$$678$$ −9.00000 15.5885i −0.345643 0.598671i
$$679$$ 7.00000 12.1244i 0.268635 0.465290i
$$680$$ 0 0
$$681$$ 9.00000 15.5885i 0.344881 0.597351i
$$682$$ 15.0000 25.9808i 0.574380 0.994855i
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ −0.500000 + 4.33013i −0.0191180 + 0.165567i
$$685$$ 6.00000 0.229248
$$686$$ 6.50000 11.2583i 0.248171 0.429845i
$$687$$ 12.5000 21.6506i 0.476905 0.826023i
$$688$$ 0.500000 + 0.866025i 0.0190623 + 0.0330169i
$$689$$ 30.0000 51.9615i 1.14291 1.97958i
$$690$$ −3.00000 5.19615i −0.114208 0.197814i
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 3.00000 + 5.19615i 0.113961 + 0.197386i
$$694$$ −6.00000 10.3923i −0.227757 0.394486i
$$695$$ 1.00000 0.0379322
$$696$$ −6.00000 −0.227429
$$697$$ 0 0
$$698$$ −9.50000 + 16.4545i −0.359580 + 0.622811i
$$699$$ 6.00000 + 10.3923i 0.226941 + 0.393073i
$$700$$ 0.500000 0.866025i 0.0188982 0.0327327i
$$701$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 44.0000 19.0526i 1.65949 0.718581i
$$704$$ 6.00000 0.226134
$$705$$ 6.00000 10.3923i 0.225973 0.391397i
$$706$$ 9.00000 15.5885i 0.338719 0.586679i
$$707$$ −3.00000 5.19615i −0.112827 0.195421i
$$708$$ −3.00000 + 5.19615i −0.112747 + 0.195283i
$$709$$ 0.500000 + 0.866025i 0.0187779 + 0.0325243i 0.875262 0.483650i $$-0.160689\pi$$
−0.856484 + 0.516174i $$0.827356\pi$$
$$710$$ 0 0
$$711$$ −7.00000 −0.262521
$$712$$ −6.00000 10.3923i −0.224860 0.389468i
$$713$$ −15.0000 25.9808i −0.561754 0.972987i
$$714$$ 0 0
$$715$$ −30.0000 −1.12194
$$716$$ −9.00000 15.5885i −0.336346 0.582568i
$$717$$ 9.00000 15.5885i 0.336111 0.582162i
$$718$$ −3.00000 5.19615i −0.111959 0.193919i
$$719$$ 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i $$-0.546936\pi$$
0.930087 0.367338i $$-0.119731\pi$$
$$720$$ 0.500000 0.866025i 0.0186339 0.0322749i
$$721$$ −11.0000 −0.409661
$$722$$ −5.50000 18.1865i −0.204689 0.676833i
$$723$$ 5.00000 0.185952
$$724$$ −13.0000 + 22.5167i −0.483141 + 0.836825i
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 12.5000 + 21.6506i 0.463919 + 0.803530i
$$727$$ −17.5000 + 30.3109i −0.649039 + 1.12417i 0.334314 + 0.942462i $$0.391496\pi$$
−0.983353 + 0.181707i $$0.941838\pi$$
$$728$$ −2.50000 4.33013i −0.0926562 0.160485i
$$729$$ 1.00000 0.0370370
$$730$$ −1.00000 −0.0370117
$$731$$ 0 0
$$732$$ 3.50000 + 6.06218i 0.129364 + 0.224065i
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ −17.0000 −0.627481
$$735$$ −3.00000 5.19615i −0.110657 0.191663i
$$736$$ 3.00000 5.19615i 0.110581 0.191533i
$$737$$ 3.00000 + 5.19615i 0.110506 + 0.191403i
$$738$$ 3.00000 5.19615i 0.110432 0.191273i
$$739$$ −20.5000 + 35.5070i −0.754105 + 1.30615i 0.191714 + 0.981451i $$0.438596\pi$$
−0.945818 + 0.324697i $$0.894738\pi$$
$$740$$ −11.0000 −0.404368
$$741$$ 20.0000 8.66025i 0.734718 0.318142i
$$742$$ −12.0000 −0.440534
$$743$$ −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i $$-0.940442\pi$$
0.652369 + 0.757902i $$0.273775\pi$$
$$744$$ 2.50000 4.33013i 0.0916544 0.158750i
$$745$$ −9.00000 15.5885i −0.329734 0.571117i
$$746$$ 1.00000 1.73205i 0.0366126 0.0634149i
$$747$$ 3.00000 + 5.19615i 0.109764 + 0.190117i
$$748$$ 0 0
$$749$$ 12.0000 0.438470
$$750$$ −0.500000 0.866025i −0.0182574 0.0316228i
$$751$$ −2.50000 4.33013i −0.0912263 0.158009i 0.816801 0.576919i $$-0.195745\pi$$
−0.908027 + 0.418911i $$0.862412\pi$$
$$752$$ 12.0000 0.437595
$$753$$ 6.00000 0.218652
$$754$$ 15.0000 + 25.9808i 0.546268 + 0.946164i
$$755$$ 4.00000 6.92820i 0.145575 0.252143i
$$756$$ 0.500000 + 0.866025i 0.0181848 + 0.0314970i
$$757$$ 15.5000 26.8468i 0.563357 0.975763i −0.433843 0.900988i $$-0.642843\pi$$
0.997200 0.0747748i $$-0.0238238\pi$$
$$758$$ −9.50000 + 16.4545i −0.345056 + 0.597654i
$$759$$ 36.0000 1.30672
$$760$$ −0.500000 + 4.33013i −0.0181369 + 0.157070i
$$761$$ −6.00000 −0.217500 −0.108750 0.994069i $$-0.534685\pi$$
−0.108750 + 0.994069i $$0.534685\pi$$
$$762$$ −8.00000 + 13.8564i −0.289809 + 0.501965i
$$763$$ 7.00000 12.1244i 0.253417 0.438931i
$$764$$ −6.00000 10.3923i −0.217072 0.375980i
$$765$$ 0 0
$$766$$ −6.00000 10.3923i −0.216789 0.375489i
$$767$$ 30.0000 1.08324
$$768$$ 1.00000 0.0360844
$$769$$ −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i $$-0.302780\pi$$
−0.995397 + 0.0958377i $$0.969447\pi$$
$$770$$ 3.00000 + 5.19615i 0.108112 + 0.187256i
$$771$$ 6.00000 0.216085
$$772$$ 5.00000 0.179954
$$773$$ 15.0000 + 25.9808i 0.539513 + 0.934463i 0.998930 + 0.0462427i $$0.0147248\pi$$
−0.459418 + 0.888220i $$0.651942\pi$$
$$774$$ −0.500000 + 0.866025i −0.0179721 + 0.0311286i
$$775$$ −2.50000 4.33013i −0.0898027 0.155543i
$$776$$ 7.00000 12.1244i 0.251285 0.435239i
$$777$$ 5.50000 9.52628i 0.197311 0.341753i
$$778$$ 6.00000 0.215110
$$779$$ −3.00000 + 25.9808i −0.107486 + 0.930857i