# Properties

 Label 1950.2.i.n.601.1 Level $1950$ Weight $2$ Character 1950.601 Analytic conductor $15.571$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ 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: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 601.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.601 Dual form 1950.2.i.n.451.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.50000 + 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -6.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(-0.500000 + 0.866025i) q^{43} -3.00000 q^{44} +(1.50000 - 2.59808i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +6.00000 q^{51} +(3.50000 + 0.866025i) q^{52} +6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 + 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-2.50000 - 4.33013i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(6.00000 - 10.3923i) q^{71} +(-0.500000 + 0.866025i) q^{72} -14.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +6.00000 q^{77} +(-3.50000 - 0.866025i) q^{78} +5.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +1.00000 q^{86} +(1.50000 - 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(9.00000 + 15.5885i) q^{89} +(-7.00000 - 1.73205i) q^{91} -3.00000 q^{92} +(2.50000 + 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(7.00000 - 12.1244i) q^{97} +(1.50000 - 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{7} + 2q^{8} - q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{3} - q^{4} + q^{6} + 2q^{7} + 2q^{8} - q^{9} + 3q^{11} - 2q^{12} - 2q^{13} - 4q^{14} - q^{16} + 6q^{17} + 2q^{18} - 2q^{19} + 4q^{21} + 3q^{22} + 3q^{23} + q^{24} - 5q^{26} - 2q^{27} + 2q^{28} - 3q^{29} + 10q^{31} - q^{32} - 3q^{33} - 12q^{34} - q^{36} - 7q^{37} + 4q^{38} + 5q^{39} - 6q^{41} - 2q^{42} - q^{43} - 6q^{44} + 3q^{46} + 6q^{47} + q^{48} + 3q^{49} + 12q^{51} + 7q^{52} + 12q^{53} + q^{54} + 2q^{56} - 4q^{57} - 3q^{58} + 9q^{59} - 2q^{61} - 5q^{62} + 2q^{63} + 2q^{64} + 6q^{66} + 8q^{67} + 6q^{68} - 3q^{69} + 12q^{71} - q^{72} - 28q^{73} - 7q^{74} - 2q^{76} + 12q^{77} - 7q^{78} + 10q^{79} - q^{81} - 6q^{82} + 12q^{83} - 2q^{84} + 2q^{86} + 3q^{87} + 3q^{88} + 18q^{89} - 14q^{91} - 6q^{92} + 5q^{93} - 3q^{94} - 2q^{96} + 14q^{97} + 3q^{98} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −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 0
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i $$-0.709957\pi$$
0.990766 + 0.135583i $$0.0432908\pi$$
$$8$$ 1.00000 0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −1.00000 3.46410i −0.277350 0.960769i
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i $$-0.573966\pi$$
0.957892 0.287129i $$-0.0927008\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i $$-0.907015\pi$$
0.728219 + 0.685344i $$0.240348\pi$$
$$20$$ 0 0
$$21$$ 2.00000 0.436436
$$22$$ 1.50000 2.59808i 0.319801 0.553912i
$$23$$ 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i $$-0.0654092\pi$$
−0.666190 + 0.745782i $$0.732076\pi$$
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ −2.50000 + 2.59808i −0.490290 + 0.509525i
$$27$$ −1.00000 −0.192450
$$28$$ 1.00000 + 1.73205i 0.188982 + 0.327327i
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ 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
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ −6.00000 −1.02899
$$35$$ 0 0
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i $$-0.971514\pi$$
0.420602 0.907245i $$-0.361819\pi$$
$$38$$ 2.00000 0.324443
$$39$$ 2.50000 2.59808i 0.400320 0.416025i
$$40$$ 0 0
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ −1.00000 1.73205i −0.154303 0.267261i
$$43$$ −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i $$-0.857628\pi$$
0.825380 + 0.564578i $$0.190961\pi$$
$$44$$ −3.00000 −0.452267
$$45$$ 0 0
$$46$$ 1.50000 2.59808i 0.221163 0.383065i
$$47$$ 3.00000 0.437595 0.218797 0.975770i $$-0.429787\pi$$
0.218797 + 0.975770i $$0.429787\pi$$
$$48$$ 0.500000 0.866025i 0.0721688 0.125000i
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ 0 0
$$51$$ 6.00000 0.840168
$$52$$ 3.50000 + 0.866025i 0.485363 + 0.120096i
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 0 0
$$56$$ 1.00000 1.73205i 0.133631 0.231455i
$$57$$ −2.00000 −0.264906
$$58$$ −1.50000 + 2.59808i −0.196960 + 0.341144i
$$59$$ 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i $$-0.634094\pi$$
0.994769 0.102151i $$-0.0325726\pi$$
$$60$$ 0 0
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ −2.50000 4.33013i −0.317500 0.549927i
$$63$$ 1.00000 + 1.73205i 0.125988 + 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 3.00000 0.369274
$$67$$ 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i $$-0.00414604\pi$$
−0.511237 + 0.859440i $$0.670813\pi$$
$$68$$ 3.00000 + 5.19615i 0.363803 + 0.630126i
$$69$$ −1.50000 + 2.59808i −0.180579 + 0.312772i
$$70$$ 0 0
$$71$$ 6.00000 10.3923i 0.712069 1.23334i −0.252010 0.967725i $$-0.581092\pi$$
0.964079 0.265615i $$-0.0855750\pi$$
$$72$$ −0.500000 + 0.866025i −0.0589256 + 0.102062i
$$73$$ −14.0000 −1.63858 −0.819288 0.573382i $$-0.805631\pi$$
−0.819288 + 0.573382i $$0.805631\pi$$
$$74$$ −3.50000 + 6.06218i −0.406867 + 0.704714i
$$75$$ 0 0
$$76$$ −1.00000 1.73205i −0.114708 0.198680i
$$77$$ 6.00000 0.683763
$$78$$ −3.50000 0.866025i −0.396297 0.0980581i
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ 0 0
$$81$$ −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 $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ −1.00000 + 1.73205i −0.109109 + 0.188982i
$$85$$ 0 0
$$86$$ 1.00000 0.107833
$$87$$ 1.50000 2.59808i 0.160817 0.278543i
$$88$$ 1.50000 + 2.59808i 0.159901 + 0.276956i
$$89$$ 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i $$0.236409\pi$$
0.217354 + 0.976093i $$0.430258\pi$$
$$90$$ 0 0
$$91$$ −7.00000 1.73205i −0.733799 0.181568i
$$92$$ −3.00000 −0.312772
$$93$$ 2.50000 + 4.33013i 0.259238 + 0.449013i
$$94$$ −1.50000 2.59808i −0.154713 0.267971i
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 7.00000 12.1244i 0.710742 1.23104i −0.253837 0.967247i $$-0.581693\pi$$
0.964579 0.263795i $$-0.0849741\pi$$
$$98$$ 1.50000 2.59808i 0.151523 0.262445i
$$99$$ −3.00000 −0.301511
$$100$$ 0 0
$$101$$ −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i $$-0.263157\pi$$
−0.975796 + 0.218685i $$0.929823\pi$$
$$102$$ −3.00000 5.19615i −0.297044 0.514496i
$$103$$ −14.0000 −1.37946 −0.689730 0.724066i $$-0.742271\pi$$
−0.689730 + 0.724066i $$0.742271\pi$$
$$104$$ −1.00000 3.46410i −0.0980581 0.339683i
$$105$$ 0 0
$$106$$ −3.00000 5.19615i −0.291386 0.504695i
$$107$$ −3.00000 5.19615i −0.290021 0.502331i 0.683793 0.729676i $$-0.260329\pi$$
−0.973814 + 0.227345i $$0.926996\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ 3.50000 6.06218i 0.332205 0.575396i
$$112$$ −2.00000 −0.188982
$$113$$ 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i $$-0.584038\pi$$
0.966496 0.256681i $$-0.0826291\pi$$
$$114$$ 1.00000 + 1.73205i 0.0936586 + 0.162221i
$$115$$ 0 0
$$116$$ 3.00000 0.278543
$$117$$ 3.50000 + 0.866025i 0.323575 + 0.0800641i
$$118$$ −9.00000 −0.828517
$$119$$ −6.00000 10.3923i −0.550019 0.952661i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 2.00000 0.181071
$$123$$ 3.00000 5.19615i 0.270501 0.468521i
$$124$$ −2.50000 + 4.33013i −0.224507 + 0.388857i
$$125$$ 0 0
$$126$$ 1.00000 1.73205i 0.0890871 0.154303i
$$127$$ 7.00000 + 12.1244i 0.621150 + 1.07586i 0.989272 + 0.146085i $$0.0466674\pi$$
−0.368122 + 0.929777i $$0.619999\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ −1.00000 −0.0880451
$$130$$ 0 0
$$131$$ 9.00000 0.786334 0.393167 0.919467i $$-0.371379\pi$$
0.393167 + 0.919467i $$0.371379\pi$$
$$132$$ −1.50000 2.59808i −0.130558 0.226134i
$$133$$ 2.00000 + 3.46410i 0.173422 + 0.300376i
$$134$$ 4.00000 6.92820i 0.345547 0.598506i
$$135$$ 0 0
$$136$$ 3.00000 5.19615i 0.257248 0.445566i
$$137$$ 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i $$-0.707721\pi$$
0.991694 + 0.128618i $$0.0410540\pi$$
$$138$$ 3.00000 0.255377
$$139$$ −7.00000 + 12.1244i −0.593732 + 1.02837i 0.399992 + 0.916519i $$0.369013\pi$$
−0.993724 + 0.111856i $$0.964321\pi$$
$$140$$ 0 0
$$141$$ 1.50000 + 2.59808i 0.126323 + 0.218797i
$$142$$ −12.0000 −1.00702
$$143$$ 7.50000 7.79423i 0.627182 0.651786i
$$144$$ 1.00000 0.0833333
$$145$$ 0 0
$$146$$ 7.00000 + 12.1244i 0.579324 + 1.00342i
$$147$$ −1.50000 + 2.59808i −0.123718 + 0.214286i
$$148$$ 7.00000 0.575396
$$149$$ 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i $$-0.713152\pi$$
0.989355 + 0.145519i $$0.0464853\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −1.00000 + 1.73205i −0.0811107 + 0.140488i
$$153$$ 3.00000 + 5.19615i 0.242536 + 0.420084i
$$154$$ −3.00000 5.19615i −0.241747 0.418718i
$$155$$ 0 0
$$156$$ 1.00000 + 3.46410i 0.0800641 + 0.277350i
$$157$$ 13.0000 1.03751 0.518756 0.854922i $$-0.326395\pi$$
0.518756 + 0.854922i $$0.326395\pi$$
$$158$$ −2.50000 4.33013i −0.198889 0.344486i
$$159$$ 3.00000 + 5.19615i 0.237915 + 0.412082i
$$160$$ 0 0
$$161$$ 6.00000 0.472866
$$162$$ −0.500000 + 0.866025i −0.0392837 + 0.0680414i
$$163$$ −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i $$0.336695\pi$$
−0.999944 + 0.0105623i $$0.996638\pi$$
$$164$$ 6.00000 0.468521
$$165$$ 0 0
$$166$$ −3.00000 5.19615i −0.232845 0.403300i
$$167$$ −4.50000 7.79423i −0.348220 0.603136i 0.637713 0.770274i $$-0.279881\pi$$
−0.985933 + 0.167139i $$0.946547\pi$$
$$168$$ 2.00000 0.154303
$$169$$ −11.0000 + 6.92820i −0.846154 + 0.532939i
$$170$$ 0 0
$$171$$ −1.00000 1.73205i −0.0764719 0.132453i
$$172$$ −0.500000 0.866025i −0.0381246 0.0660338i
$$173$$ 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i $$-0.682554\pi$$
0.998755 + 0.0498898i $$0.0158870\pi$$
$$174$$ −3.00000 −0.227429
$$175$$ 0 0
$$176$$ 1.50000 2.59808i 0.113067 0.195837i
$$177$$ 9.00000 0.676481
$$178$$ 9.00000 15.5885i 0.674579 1.16840i
$$179$$ 1.50000 + 2.59808i 0.112115 + 0.194189i 0.916623 0.399753i $$-0.130904\pi$$
−0.804508 + 0.593942i $$0.797571\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 2.00000 + 6.92820i 0.148250 + 0.513553i
$$183$$ −2.00000 −0.147844
$$184$$ 1.50000 + 2.59808i 0.110581 + 0.191533i
$$185$$ 0 0
$$186$$ 2.50000 4.33013i 0.183309 0.317500i
$$187$$ 18.0000 1.31629
$$188$$ −1.50000 + 2.59808i −0.109399 + 0.189484i
$$189$$ −1.00000 + 1.73205i −0.0727393 + 0.125988i
$$190$$ 0 0
$$191$$ 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i $$-0.690384\pi$$
0.997225 + 0.0744412i $$0.0237173\pi$$
$$192$$ 0.500000 + 0.866025i 0.0360844 + 0.0625000i
$$193$$ −2.00000 3.46410i −0.143963 0.249351i 0.785022 0.619467i $$-0.212651\pi$$
−0.928986 + 0.370116i $$0.879318\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ 12.0000 + 20.7846i 0.854965 + 1.48084i 0.876678 + 0.481078i $$0.159755\pi$$
−0.0217133 + 0.999764i $$0.506912\pi$$
$$198$$ 1.50000 + 2.59808i 0.106600 + 0.184637i
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ 0 0
$$201$$ −4.00000 + 6.92820i −0.282138 + 0.488678i
$$202$$ −3.00000 + 5.19615i −0.211079 + 0.365600i
$$203$$ −6.00000 −0.421117
$$204$$ −3.00000 + 5.19615i −0.210042 + 0.363803i
$$205$$ 0 0
$$206$$ 7.00000 + 12.1244i 0.487713 + 0.844744i
$$207$$ −3.00000 −0.208514
$$208$$ −2.50000 + 2.59808i −0.173344 + 0.180144i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i $$-0.924968\pi$$
0.283918 0.958849i $$-0.408366\pi$$
$$212$$ −3.00000 + 5.19615i −0.206041 + 0.356873i
$$213$$ 12.0000 0.822226
$$214$$ −3.00000 + 5.19615i −0.205076 + 0.355202i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 5.00000 8.66025i 0.339422 0.587896i
$$218$$ −7.00000 12.1244i −0.474100 0.821165i
$$219$$ −7.00000 12.1244i −0.473016 0.819288i
$$220$$ 0 0
$$221$$ −21.0000 5.19615i −1.41261 0.349531i
$$222$$ −7.00000 −0.469809
$$223$$ −5.00000 8.66025i −0.334825 0.579934i 0.648626 0.761107i $$-0.275344\pi$$
−0.983451 + 0.181173i $$0.942010\pi$$
$$224$$ 1.00000 + 1.73205i 0.0668153 + 0.115728i
$$225$$ 0 0
$$226$$ −15.0000 −0.997785
$$227$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$228$$ 1.00000 1.73205i 0.0662266 0.114708i
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 3.00000 + 5.19615i 0.197386 + 0.341882i
$$232$$ −1.50000 2.59808i −0.0984798 0.170572i
$$233$$ −21.0000 −1.37576 −0.687878 0.725826i $$-0.741458\pi$$
−0.687878 + 0.725826i $$0.741458\pi$$
$$234$$ −1.00000 3.46410i −0.0653720 0.226455i
$$235$$ 0 0
$$236$$ 4.50000 + 7.79423i 0.292925 + 0.507361i
$$237$$ 2.50000 + 4.33013i 0.162392 + 0.281272i
$$238$$ −6.00000 + 10.3923i −0.388922 + 0.673633i
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ −8.50000 + 14.7224i −0.547533 + 0.948355i 0.450910 + 0.892570i $$0.351100\pi$$
−0.998443 + 0.0557856i $$0.982234\pi$$
$$242$$ −2.00000 −0.128565
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ −1.00000 1.73205i −0.0640184 0.110883i
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ 7.00000 + 1.73205i 0.445399 + 0.110208i
$$248$$ 5.00000 0.317500
$$249$$ 3.00000 + 5.19615i 0.190117 + 0.329293i
$$250$$ 0 0
$$251$$ −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i $$-0.990305\pi$$
0.526140 + 0.850398i $$0.323639\pi$$
$$252$$ −2.00000 −0.125988
$$253$$ −4.50000 + 7.79423i −0.282913 + 0.490019i
$$254$$ 7.00000 12.1244i 0.439219 0.760750i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i $$-0.939347\pi$$
0.326929 0.945049i $$-0.393986\pi$$
$$258$$ 0.500000 + 0.866025i 0.0311286 + 0.0539164i
$$259$$ −14.0000 −0.869918
$$260$$ 0 0
$$261$$ 3.00000 0.185695
$$262$$ −4.50000 7.79423i −0.278011 0.481529i
$$263$$ −7.50000 12.9904i −0.462470 0.801021i 0.536614 0.843828i $$-0.319703\pi$$
−0.999083 + 0.0428069i $$0.986370\pi$$
$$264$$ −1.50000 + 2.59808i −0.0923186 + 0.159901i
$$265$$ 0 0
$$266$$ 2.00000 3.46410i 0.122628 0.212398i
$$267$$ −9.00000 + 15.5885i −0.550791 + 0.953998i
$$268$$ −8.00000 −0.488678
$$269$$ −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i $$0.351559\pi$$
−0.998361 + 0.0572259i $$0.981774\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ −6.00000 −0.363803
$$273$$ −2.00000 6.92820i −0.121046 0.419314i
$$274$$ −9.00000 −0.543710
$$275$$ 0 0
$$276$$ −1.50000 2.59808i −0.0902894 0.156386i
$$277$$ −0.500000 + 0.866025i −0.0300421 + 0.0520344i −0.880656 0.473757i $$-0.842897\pi$$
0.850613 + 0.525792i $$0.176231\pi$$
$$278$$ 14.0000 0.839664
$$279$$ −2.50000 + 4.33013i −0.149671 + 0.259238i
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ 1.50000 2.59808i 0.0893237 0.154713i
$$283$$ −15.5000 26.8468i −0.921379 1.59588i −0.797283 0.603606i $$-0.793730\pi$$
−0.124096 0.992270i $$-0.539603\pi$$
$$284$$ 6.00000 + 10.3923i 0.356034 + 0.616670i
$$285$$ 0 0
$$286$$ −10.5000 2.59808i −0.620878 0.153627i
$$287$$ −12.0000 −0.708338
$$288$$ −0.500000 0.866025i −0.0294628 0.0510310i
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 0 0
$$291$$ 14.0000 0.820695
$$292$$ 7.00000 12.1244i 0.409644 0.709524i
$$293$$ −15.0000 + 25.9808i −0.876309 + 1.51781i −0.0209480 + 0.999781i $$0.506668\pi$$
−0.855361 + 0.518032i $$0.826665\pi$$
$$294$$ 3.00000 0.174964
$$295$$ 0 0
$$296$$ −3.50000 6.06218i −0.203433 0.352357i
$$297$$ −1.50000 2.59808i −0.0870388 0.150756i
$$298$$ −9.00000 −0.521356
$$299$$ 7.50000 7.79423i 0.433736 0.450752i
$$300$$ 0 0
$$301$$ 1.00000 + 1.73205i 0.0576390 + 0.0998337i
$$302$$ −4.00000 6.92820i −0.230174 0.398673i
$$303$$ 3.00000 5.19615i 0.172345 0.298511i
$$304$$ 2.00000 0.114708
$$305$$ 0 0
$$306$$ 3.00000 5.19615i 0.171499 0.297044i
$$307$$ −8.00000 −0.456584 −0.228292 0.973593i $$-0.573314\pi$$
−0.228292 + 0.973593i $$0.573314\pi$$
$$308$$ −3.00000 + 5.19615i −0.170941 + 0.296078i
$$309$$ −7.00000 12.1244i −0.398216 0.689730i
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 2.50000 2.59808i 0.141535 0.147087i
$$313$$ −8.00000 −0.452187 −0.226093 0.974106i $$-0.572595\pi$$
−0.226093 + 0.974106i $$0.572595\pi$$
$$314$$ −6.50000 11.2583i −0.366816 0.635344i
$$315$$ 0 0
$$316$$ −2.50000 + 4.33013i −0.140636 + 0.243589i
$$317$$ −12.0000 −0.673987 −0.336994 0.941507i $$-0.609410\pi$$
−0.336994 + 0.941507i $$0.609410\pi$$
$$318$$ 3.00000 5.19615i 0.168232 0.291386i
$$319$$ 4.50000 7.79423i 0.251952 0.436393i
$$320$$ 0 0
$$321$$ 3.00000 5.19615i 0.167444 0.290021i
$$322$$ −3.00000 5.19615i −0.167183 0.289570i
$$323$$ 6.00000 + 10.3923i 0.333849 + 0.578243i
$$324$$ 1.00000 0.0555556
$$325$$ 0 0
$$326$$ 13.0000 0.720003
$$327$$ 7.00000 + 12.1244i 0.387101 + 0.670478i
$$328$$ −3.00000 5.19615i −0.165647 0.286910i
$$329$$ 3.00000 5.19615i 0.165395 0.286473i
$$330$$ 0 0
$$331$$ −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i $$0.508749\pi$$
−0.851957 + 0.523612i $$0.824584\pi$$
$$332$$ −3.00000 + 5.19615i −0.164646 + 0.285176i
$$333$$ 7.00000 0.383598
$$334$$ −4.50000 + 7.79423i −0.246229 + 0.426481i
$$335$$ 0 0
$$336$$ −1.00000 1.73205i −0.0545545 0.0944911i
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ 11.5000 + 6.06218i 0.625518 + 0.329739i
$$339$$ 15.0000 0.814688
$$340$$ 0 0
$$341$$ 7.50000 + 12.9904i 0.406148 + 0.703469i
$$342$$ −1.00000 + 1.73205i −0.0540738 + 0.0936586i
$$343$$ 20.0000 1.07990
$$344$$ −0.500000 + 0.866025i −0.0269582 + 0.0466930i
$$345$$ 0 0
$$346$$ −12.0000 −0.645124
$$347$$ −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i $$0.464631\pi$$
−0.916127 + 0.400887i $$0.868702\pi$$
$$348$$ 1.50000 + 2.59808i 0.0804084 + 0.139272i
$$349$$ −4.00000 6.92820i −0.214115 0.370858i 0.738883 0.673833i $$-0.235353\pi$$
−0.952998 + 0.302975i $$0.902020\pi$$
$$350$$ 0 0
$$351$$ 1.00000 + 3.46410i 0.0533761 + 0.184900i
$$352$$ −3.00000 −0.159901
$$353$$ 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i $$0.127637\pi$$
−0.122308 + 0.992492i $$0.539030\pi$$
$$354$$ −4.50000 7.79423i −0.239172 0.414259i
$$355$$ 0 0
$$356$$ −18.0000 −0.953998
$$357$$ 6.00000 10.3923i 0.317554 0.550019i
$$358$$ 1.50000 2.59808i 0.0792775 0.137313i
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 8.00000 + 13.8564i 0.420471 + 0.728277i
$$363$$ 2.00000 0.104973
$$364$$ 5.00000 5.19615i 0.262071 0.272352i
$$365$$ 0 0
$$366$$ 1.00000 + 1.73205i 0.0522708 + 0.0905357i
$$367$$ 10.0000 + 17.3205i 0.521996 + 0.904123i 0.999673 + 0.0255875i $$0.00814566\pi$$
−0.477677 + 0.878536i $$0.658521\pi$$
$$368$$ 1.50000 2.59808i 0.0781929 0.135434i
$$369$$ 6.00000 0.312348
$$370$$ 0 0
$$371$$ 6.00000 10.3923i 0.311504 0.539542i
$$372$$ −5.00000 −0.259238
$$373$$ −12.5000 + 21.6506i −0.647225 + 1.12103i 0.336557 + 0.941663i $$0.390737\pi$$
−0.983783 + 0.179364i $$0.942596\pi$$
$$374$$ −9.00000 15.5885i −0.465379 0.806060i
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ −7.50000 + 7.79423i −0.386270 + 0.401423i
$$378$$ 2.00000 0.102869
$$379$$ −19.0000 32.9090i −0.975964 1.69042i −0.676715 0.736245i $$-0.736597\pi$$
−0.299249 0.954175i $$-0.596736\pi$$
$$380$$ 0 0
$$381$$ −7.00000 + 12.1244i −0.358621 + 0.621150i
$$382$$ −12.0000 −0.613973
$$383$$ −10.5000 + 18.1865i −0.536525 + 0.929288i 0.462563 + 0.886586i $$0.346930\pi$$
−0.999088 + 0.0427020i $$0.986403\pi$$
$$384$$ 0.500000 0.866025i 0.0255155 0.0441942i
$$385$$ 0 0
$$386$$ −2.00000 + 3.46410i −0.101797 + 0.176318i
$$387$$ −0.500000 0.866025i −0.0254164 0.0440225i
$$388$$ 7.00000 + 12.1244i 0.355371 + 0.615521i
$$389$$ 3.00000 0.152106 0.0760530 0.997104i $$-0.475768\pi$$
0.0760530 + 0.997104i $$0.475768\pi$$
$$390$$ 0 0
$$391$$ 18.0000 0.910299
$$392$$ 1.50000 + 2.59808i 0.0757614 + 0.131223i
$$393$$ 4.50000 + 7.79423i 0.226995 + 0.393167i
$$394$$ 12.0000 20.7846i 0.604551 1.04711i
$$395$$ 0 0
$$396$$ 1.50000 2.59808i 0.0753778 0.130558i
$$397$$ −15.5000 + 26.8468i −0.777923 + 1.34740i 0.155214 + 0.987881i $$0.450393\pi$$
−0.933137 + 0.359521i $$0.882940\pi$$
$$398$$ 8.00000 0.401004
$$399$$ −2.00000 + 3.46410i −0.100125 + 0.173422i
$$400$$ 0 0
$$401$$ 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i $$-0.0698049\pi$$
−0.676425 + 0.736512i $$0.736472\pi$$
$$402$$ 8.00000 0.399004
$$403$$ −5.00000 17.3205i −0.249068 0.862796i
$$404$$ 6.00000 0.298511
$$405$$ 0 0
$$406$$ 3.00000 + 5.19615i 0.148888 + 0.257881i
$$407$$ 10.5000 18.1865i 0.520466 0.901473i
$$408$$ 6.00000 0.297044
$$409$$ 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i $$-0.753812\pi$$
0.962757 + 0.270367i $$0.0871450\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 7.00000 12.1244i 0.344865 0.597324i
$$413$$ −9.00000 15.5885i −0.442861 0.767058i
$$414$$ 1.50000 + 2.59808i 0.0737210 + 0.127688i
$$415$$ 0 0
$$416$$ 3.50000 + 0.866025i 0.171602 + 0.0424604i
$$417$$ −14.0000 −0.685583
$$418$$ 3.00000 + 5.19615i 0.146735 + 0.254152i
$$419$$ 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i $$-0.0719734\pi$$
−0.681426 + 0.731887i $$0.738640\pi$$
$$420$$ 0 0
$$421$$ −16.0000 −0.779792 −0.389896 0.920859i $$-0.627489\pi$$
−0.389896 + 0.920859i $$0.627489\pi$$
$$422$$ −10.0000 + 17.3205i −0.486792 + 0.843149i
$$423$$ −1.50000 + 2.59808i −0.0729325 + 0.126323i
$$424$$ 6.00000 0.291386
$$425$$ 0 0
$$426$$ −6.00000 10.3923i −0.290701 0.503509i
$$427$$ 2.00000 + 3.46410i 0.0967868 + 0.167640i
$$428$$ 6.00000 0.290021
$$429$$ 10.5000 + 2.59808i 0.506945 + 0.125436i
$$430$$ 0 0
$$431$$ −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i $$-0.259993\pi$$
−0.973574 + 0.228373i $$0.926659\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ −20.0000 + 34.6410i −0.961139 + 1.66474i −0.241489 + 0.970404i $$0.577636\pi$$
−0.719650 + 0.694337i $$0.755698\pi$$
$$434$$ −10.0000 −0.480015
$$435$$ 0 0
$$436$$ −7.00000 + 12.1244i −0.335239 + 0.580651i
$$437$$ −6.00000 −0.287019
$$438$$ −7.00000 + 12.1244i −0.334473 + 0.579324i
$$439$$ 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i $$-0.136236\pi$$
−0.814344 + 0.580383i $$0.802903\pi$$
$$440$$ 0 0
$$441$$ −3.00000 −0.142857
$$442$$ 6.00000 + 20.7846i 0.285391 + 0.988623i
$$443$$ 36.0000 1.71041 0.855206 0.518289i $$-0.173431\pi$$
0.855206 + 0.518289i $$0.173431\pi$$
$$444$$ 3.50000 + 6.06218i 0.166103 + 0.287698i
$$445$$ 0 0
$$446$$ −5.00000 + 8.66025i −0.236757 + 0.410075i
$$447$$ 9.00000 0.425685
$$448$$ 1.00000 1.73205i 0.0472456 0.0818317i
$$449$$ −18.0000 + 31.1769i −0.849473 + 1.47133i 0.0322072 + 0.999481i $$0.489746\pi$$
−0.881680 + 0.471848i $$0.843587\pi$$
$$450$$ 0 0
$$451$$ 9.00000 15.5885i 0.423793 0.734032i
$$452$$ 7.50000 + 12.9904i 0.352770 + 0.611016i
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ 1.00000 + 1.73205i 0.0467780 + 0.0810219i 0.888466 0.458942i $$-0.151771\pi$$
−0.841688 + 0.539964i $$0.818438\pi$$
$$458$$ −7.00000 12.1244i −0.327089 0.566534i
$$459$$ −3.00000 + 5.19615i −0.140028 + 0.242536i
$$460$$ 0 0
$$461$$ −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i $$-0.946917\pi$$
0.636817 + 0.771015i $$0.280251\pi$$
$$462$$ 3.00000 5.19615i 0.139573 0.241747i
$$463$$ 34.0000 1.58011 0.790057 0.613033i $$-0.210051\pi$$
0.790057 + 0.613033i $$0.210051\pi$$
$$464$$ −1.50000 + 2.59808i −0.0696358 + 0.120613i
$$465$$ 0 0
$$466$$ 10.5000 + 18.1865i 0.486403 + 0.842475i
$$467$$ −18.0000 −0.832941 −0.416470 0.909149i $$-0.636733\pi$$
−0.416470 + 0.909149i $$0.636733\pi$$
$$468$$ −2.50000 + 2.59808i −0.115563 + 0.120096i
$$469$$ 16.0000 0.738811
$$470$$ 0 0
$$471$$ 6.50000 + 11.2583i 0.299504 + 0.518756i
$$472$$ 4.50000 7.79423i 0.207129 0.358758i
$$473$$ −3.00000 −0.137940
$$474$$ 2.50000 4.33013i 0.114829 0.198889i
$$475$$ 0 0
$$476$$ 12.0000 0.550019
$$477$$ −3.00000 + 5.19615i −0.137361 + 0.237915i
$$478$$ −12.0000 20.7846i −0.548867 0.950666i
$$479$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$480$$ 0 0
$$481$$ −17.5000 + 18.1865i −0.797931 + 0.829235i
$$482$$ 17.0000 0.774329
$$483$$ 3.00000 + 5.19615i 0.136505 + 0.236433i
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ 1.00000 1.73205i 0.0453143 0.0784867i −0.842479 0.538730i $$-0.818904\pi$$
0.887793 + 0.460243i $$0.152238\pi$$
$$488$$ −1.00000 + 1.73205i −0.0452679 + 0.0784063i
$$489$$ −13.0000 −0.587880
$$490$$ 0 0
$$491$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$492$$ 3.00000 + 5.19615i 0.135250 + 0.234261i
$$493$$ −18.0000 −0.810679
$$494$$ −2.00000 6.92820i −0.0899843 0.311715i
$$495$$ 0 0
$$496$$ −2.50000 4.33013i −0.112253 0.194428i
$$497$$ −12.0000 20.7846i −0.538274 0.932317i
$$498$$ 3.00000 5.19615i 0.134433 0.232845i
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ 0 0
$$501$$ 4.50000 7.79423i 0.201045 0.348220i
$$502$$ 15.0000 0.669483
$$503$$ 12.0000 20.7846i 0.535054 0.926740i −0.464107 0.885779i $$-0.653625\pi$$
0.999161 0.0409609i $$-0.0130419\pi$$
$$504$$ 1.00000 + 1.73205i 0.0445435 + 0.0771517i
$$505$$ 0 0
$$506$$ 9.00000 0.400099
$$507$$ −11.5000 6.06218i −0.510733 0.269231i
$$508$$ −14.0000 −0.621150
$$509$$ −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i $$-0.187846\pi$$
−0.897352 + 0.441315i $$0.854512\pi$$
$$510$$ 0 0
$$511$$ −14.0000 + 24.2487i −0.619324 + 1.07270i
$$512$$ 1.00000 0.0441942
$$513$$ 1.00000 1.73205i 0.0441511 0.0764719i
$$514$$ −10.5000 + 18.1865i −0.463135 + 0.802174i
$$515$$ 0 0
$$516$$ 0.500000 0.866025i 0.0220113 0.0381246i
$$517$$ 4.50000 + 7.79423i 0.197910 + 0.342790i
$$518$$ 7.00000 + 12.1244i 0.307562 + 0.532714i
$$519$$ 12.0000 0.526742
$$520$$ 0 0
$$521$$ −30.0000 −1.31432 −0.657162 0.753749i $$-0.728243\pi$$
−0.657162 + 0.753749i $$0.728243\pi$$
$$522$$ −1.50000 2.59808i −0.0656532 0.113715i
$$523$$ 5.50000 + 9.52628i 0.240498 + 0.416555i 0.960856 0.277047i $$-0.0893559\pi$$
−0.720358 + 0.693602i $$0.756023\pi$$
$$524$$ −4.50000 + 7.79423i −0.196583 + 0.340492i
$$525$$ 0 0
$$526$$ −7.50000 + 12.9904i −0.327016 + 0.566408i
$$527$$ 15.0000 25.9808i 0.653410 1.13174i
$$528$$ 3.00000 0.130558
$$529$$ 7.00000 12.1244i 0.304348 0.527146i
$$530$$ 0 0
$$531$$ 4.50000 + 7.79423i 0.195283 + 0.338241i
$$532$$ −4.00000 −0.173422
$$533$$ −15.0000 + 15.5885i −0.649722 + 0.675211i
$$534$$ 18.0000 0.778936
$$535$$ 0 0
$$536$$ 4.00000 + 6.92820i 0.172774 + 0.299253i
$$537$$ −1.50000 + 2.59808i −0.0647298 + 0.112115i
$$538$$ 18.0000 0.776035
$$539$$ −4.50000 + 7.79423i −0.193829 + 0.335721i
$$540$$ 0 0
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ −5.50000 + 9.52628i −0.236245 + 0.409189i
$$543$$ −8.00000 13.8564i −0.343313 0.594635i
$$544$$ 3.00000 + 5.19615i 0.128624 + 0.222783i
$$545$$ 0 0
$$546$$ −5.00000 + 5.19615i −0.213980 + 0.222375i
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ 4.50000 + 7.79423i 0.192230 + 0.332953i
$$549$$ −1.00000 1.73205i −0.0426790 0.0739221i
$$550$$ 0 0
$$551$$ 6.00000 0.255609
$$552$$ −1.50000 + 2.59808i −0.0638442 + 0.110581i
$$553$$ 5.00000 8.66025i 0.212622 0.368271i
$$554$$ 1.00000 0.0424859
$$555$$ 0 0
$$556$$ −7.00000 12.1244i −0.296866 0.514187i
$$557$$ −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i $$-0.207238\pi$$
−0.922557 + 0.385860i $$0.873905\pi$$
$$558$$ 5.00000 0.211667
$$559$$ 3.50000 + 0.866025i 0.148034 + 0.0366290i
$$560$$ 0 0
$$561$$ 9.00000 + 15.5885i 0.379980 + 0.658145i
$$562$$ −9.00000 15.5885i −0.379642 0.657559i
$$563$$ 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i $$-0.559212\pi$$
0.943560 0.331202i $$-0.107454\pi$$
$$564$$ −3.00000 −0.126323
$$565$$ 0 0
$$566$$ −15.5000 + 26.8468i −0.651514 + 1.12845i
$$567$$ −2.00000 −0.0839921
$$568$$ 6.00000 10.3923i 0.251754 0.436051i
$$569$$ −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i $$-0.206806\pi$$
−0.922032 + 0.387113i $$0.873472\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 3.00000 + 10.3923i 0.125436 + 0.434524i
$$573$$ 12.0000 0.501307
$$574$$ 6.00000 + 10.3923i 0.250435 + 0.433766i
$$575$$ 0 0
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ −9.50000 + 16.4545i −0.395148 + 0.684416i
$$579$$ 2.00000 3.46410i 0.0831172 0.143963i
$$580$$ 0 0
$$581$$ 6.00000 10.3923i 0.248922 0.431145i
$$582$$ −7.00000 12.1244i −0.290159 0.502571i
$$583$$ 9.00000 + 15.5885i 0.372742 + 0.645608i
$$584$$ −14.0000 −0.579324
$$585$$ 0 0
$$586$$ 30.0000 1.23929
$$587$$ 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i $$-0.0455206\pi$$
−0.618322 + 0.785925i $$0.712187\pi$$
$$588$$ −1.50000 2.59808i −0.0618590 0.107143i
$$589$$ −5.00000 + 8.66025i −0.206021 + 0.356840i
$$590$$ 0 0
$$591$$ −12.0000 + 20.7846i −0.493614 + 0.854965i
$$592$$ −3.50000 + 6.06218i −0.143849 + 0.249154i
$$593$$ −27.0000 −1.10876 −0.554379 0.832265i $$-0.687044\pi$$
−0.554379 + 0.832265i $$0.687044\pi$$
$$594$$ −1.50000 + 2.59808i −0.0615457 + 0.106600i
$$595$$ 0 0
$$596$$ 4.50000 + 7.79423i 0.184327 + 0.319264i
$$597$$ −8.00000 −0.327418
$$598$$ −10.5000 2.59808i −0.429377 0.106243i
$$599$$ 6.00000 0.245153 0.122577 0.992459i $$-0.460884\pi$$
0.122577 + 0.992459i $$0.460884\pi$$
$$600$$ 0 0
$$601$$ 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i $$-0.0400009\pi$$
−0.604601 + 0.796528i $$0.706668\pi$$
$$602$$ 1.00000 1.73205i 0.0407570 0.0705931i
$$603$$ −8.00000 −0.325785
$$604$$ −4.00000 + 6.92820i −0.162758 + 0.281905i
$$605$$ 0 0
$$606$$ −6.00000 −0.243733
$$607$$ −11.0000 + 19.0526i −0.446476 + 0.773320i −0.998154 0.0607380i $$-0.980655\pi$$
0.551678 + 0.834058i $$0.313988\pi$$
$$608$$ −1.00000 1.73205i −0.0405554 0.0702439i
$$609$$ −3.00000 5.19615i −0.121566 0.210559i
$$610$$ 0 0
$$611$$ −3.00000 10.3923i −0.121367 0.420428i
$$612$$ −6.00000 −0.242536
$$613$$ −15.5000 26.8468i −0.626039 1.08433i −0.988339 0.152270i $$-0.951342\pi$$
0.362300 0.932062i $$-0.381992\pi$$
$$614$$ 4.00000 + 6.92820i 0.161427 + 0.279600i
$$615$$ 0 0
$$616$$ 6.00000 0.241747
$$617$$ 10.5000 18.1865i 0.422714 0.732162i −0.573490 0.819213i $$-0.694411\pi$$
0.996204 + 0.0870504i $$0.0277441\pi$$
$$618$$ −7.00000 + 12.1244i −0.281581 + 0.487713i
$$619$$ −46.0000 −1.84890 −0.924448 0.381308i $$-0.875474\pi$$
−0.924448 + 0.381308i $$0.875474\pi$$
$$620$$ 0 0
$$621$$ −1.50000 2.59808i −0.0601929 0.104257i
$$622$$ 6.00000 + 10.3923i 0.240578 + 0.416693i
$$623$$ 36.0000 1.44231
$$624$$ −3.50000 0.866025i −0.140112 0.0346688i
$$625$$ 0 0
$$626$$ 4.00000 + 6.92820i 0.159872 + 0.276907i
$$627$$ −3.00000 5.19615i −0.119808 0.207514i
$$628$$ −6.50000 + 11.2583i −0.259378 + 0.449256i
$$629$$ −42.0000 −1.67465
$$630$$ 0 0
$$631$$ 8.00000 13.8564i 0.318475 0.551615i −0.661695 0.749773i $$-0.730163\pi$$
0.980170 + 0.198158i $$0.0634960\pi$$
$$632$$ 5.00000 0.198889
$$633$$ 10.0000 17.3205i 0.397464 0.688428i
$$634$$ 6.00000 + 10.3923i 0.238290 + 0.412731i
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 7.50000 7.79423i 0.297161 0.308819i
$$638$$ −9.00000 −0.356313
$$639$$ 6.00000 + 10.3923i 0.237356 + 0.411113i
$$640$$ 0 0
$$641$$ −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i $$-0.871140\pi$$
0.800678 + 0.599095i $$0.204473\pi$$
$$642$$ −6.00000 −0.236801
$$643$$ −8.00000 + 13.8564i −0.315489 + 0.546443i −0.979541 0.201243i $$-0.935502\pi$$
0.664052 + 0.747686i $$0.268835\pi$$
$$644$$ −3.00000 + 5.19615i −0.118217 + 0.204757i
$$645$$ 0 0
$$646$$ 6.00000 10.3923i 0.236067 0.408880i
$$647$$ 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i $$-0.0102824\pi$$
−0.527710 + 0.849425i $$0.676949\pi$$
$$648$$ −0.500000 0.866025i −0.0196419 0.0340207i
$$649$$ 27.0000 1.05984
$$650$$ 0 0
$$651$$ 10.0000 0.391931
$$652$$ −6.50000 11.2583i −0.254560 0.440910i
$$653$$ 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i $$-0.129211\pi$$
−0.801337 + 0.598213i $$0.795878\pi$$
$$654$$ 7.00000 12.1244i 0.273722 0.474100i
$$655$$ 0 0
$$656$$ −3.00000 + 5.19615i −0.117130 + 0.202876i
$$657$$ 7.00000 12.1244i 0.273096 0.473016i
$$658$$ −6.00000 −0.233904
$$659$$ −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i $$-0.927707\pi$$
0.682161 + 0.731202i $$0.261040\pi$$
$$660$$ 0 0
$$661$$ −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i $$-0.952854\pi$$
0.366723 0.930330i $$-0.380480\pi$$
$$662$$ 32.0000 1.24372
$$663$$ −6.00000 20.7846i −0.233021 0.807207i
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ −3.50000 6.06218i −0.135622 0.234905i
$$667$$ 4.50000 7.79423i 0.174241 0.301794i
$$668$$ 9.00000 0.348220
$$669$$ 5.00000 8.66025i 0.193311 0.334825i
$$670$$ 0 0
$$671$$ −6.00000 −0.231627
$$672$$ −1.00000 + 1.73205i −0.0385758 + 0.0668153i
$$673$$ −2.00000 3.46410i −0.0770943 0.133531i 0.824901 0.565278i $$-0.191231\pi$$
−0.901995 + 0.431746i $$0.857898\pi$$
$$674$$ 7.00000 + 12.1244i 0.269630 + 0.467013i
$$675$$ 0 0
$$676$$ −0.500000 12.9904i −0.0192308 0.499630i
$$677$$ 36.0000 1.38359 0.691796 0.722093i $$-0.256820\pi$$
0.691796 + 0.722093i $$0.256820\pi$$
$$678$$ −7.50000 12.9904i −0.288036 0.498893i
$$679$$ −14.0000 24.2487i −0.537271 0.930580i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 7.50000 12.9904i 0.287190 0.497427i
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ 2.00000 0.0764719
$$685$$ 0 0
$$686$$ −10.0000 17.3205i −0.381802 0.661300i
$$687$$ 7.00000 + 12.1244i 0.267067 + 0.462573i
$$688$$ 1.00000 0.0381246
$$689$$ −6.00000 20.7846i −0.228582 0.791831i
$$690$$ 0 0
$$691$$ 23.0000 + 39.8372i 0.874961 + 1.51548i 0.856804 + 0.515642i $$0.172447\pi$$
0.0181572 + 0.999835i $$0.494220\pi$$
$$692$$ 6.00000 + 10.3923i 0.228086 + 0.395056i
$$693$$ −3.00000 + 5.19615i −0.113961 + 0.197386i
$$694$$ 30.0000 1.13878
$$695$$ 0 0
$$696$$ 1.50000 2.59808i 0.0568574 0.0984798i
$$697$$ −36.0000 −1.36360
$$698$$ −4.00000 + 6.92820i −0.151402 + 0.262236i
$$699$$ −10.5000 18.1865i −0.397146 0.687878i
$$700$$ 0 0
$$701$$ −21.0000 −0.793159 −0.396580 0.918000i $$-0.629803\pi$$
−0.396580 + 0.918000i $$0.629803\pi$$
$$702$$ 2.50000 2.59808i 0.0943564 0.0980581i
$$703$$ 14.0000 0.528020
$$704$$ 1.50000 + 2.59808i 0.0565334 + 0.0979187i
$$705$$ 0 0
$$706$$ 15.0000 25.9808i 0.564532 0.977799i
$$707$$ −12.0000 −0.451306
$$708$$ −4.50000 + 7.79423i −0.169120 + 0.292925i
$$709$$ −16.0000 + 27.7128i −0.600893 + 1.04078i 0.391794 + 0.920053i $$0.371855\pi$$
−0.992686 + 0.120723i $$0.961479\pi$$
$$710$$ 0 0
$$711$$ −2.50000 + 4.33013i −0.0937573 + 0.162392i
$$712$$ 9.00000 + 15.5885i 0.337289 + 0.584202i
$$713$$ 7.50000 + 12.9904i 0.280877 + 0.486494i
$$714$$ −12.0000 −0.449089
$$715$$ 0 0
$$716$$ −3.00000 −0.112115
$$717$$ 12.0000 + 20.7846i 0.448148 + 0.776215i
$$718$$ −12.0000 20.7846i −0.447836 0.775675i
$$719$$ −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i $$0.400925\pi$$
−0.977539 + 0.210752i $$0.932409\pi$$
$$720$$ 0 0
$$721$$ −14.0000 + 24.2487i −0.521387 + 0.903069i
$$722$$ 7.50000 12.9904i 0.279121 0.483452i
$$723$$ −17.0000 −0.632237
$$724$$ 8.00000 13.8564i 0.297318 0.514969i
$$725$$ 0 0
$$726$$ −1.00000 1.73205i −0.0371135 0.0642824i
$$727$$ 4.00000 0.148352 0.0741759 0.997245i $$-0.476367\pi$$
0.0741759 + 0.997245i $$0.476367\pi$$
$$728$$ −7.00000 1.73205i −0.259437 0.0641941i
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 3.00000 + 5.19615i 0.110959 + 0.192187i
$$732$$ 1.00000 1.73205i 0.0369611 0.0640184i
$$733$$ 22.0000 0.812589 0.406294 0.913742i $$-0.366821\pi$$
0.406294 + 0.913742i $$0.366821\pi$$
$$734$$ 10.0000 17.3205i 0.369107 0.639312i
$$735$$ 0 0
$$736$$ −3.00000 −0.110581
$$737$$ −12.0000 + 20.7846i −0.442026 + 0.765611i
$$738$$ −3.00000 5.19615i −0.110432 0.191273i
$$739$$ 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i $$-0.0715853\pi$$
−0.680534 + 0.732717i $$0.738252\pi$$
$$740$$ 0 0
$$741$$ 2.00000 + 6.92820i 0.0734718 + 0.254514i
$$742$$ −12.0000 −0.440534
$$743$$ −4.50000 7.79423i −0.165089 0.285943i 0.771598 0.636111i $$-0.219458\pi$$
−0.936687 + 0.350168i $$0.886124\pi$$
$$744$$ 2.50000 + 4.33013i 0.0916544 + 0.158750i
$$745$$ 0 0
$$746$$ 25.0000 0.915315
$$747$$ −3.00000 + 5.19615i −0.109764 + 0.190117i
$$748$$ −9.00000 + 15.5885i −0.329073 + 0.569970i
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i $$-0.897654\pi$$
0.200698 0.979653i $$-0.435679\pi$$
$$752$$ −1.50000 2.59808i −0.0546994 0.0947421i
$$753$$ −15.0000 −0.546630
$$754$$ 10.5000 + 2.59808i 0.382387 + 0.0946164i
$$755$$ 0 0
$$756$$ −1.00000 1.73205i −0.0363696 0.0629941i
$$757$$ 19.0000 + 32.9090i 0.690567 + 1.19610i 0.971652 + 0.236414i $$0.0759722\pi$$
−0.281086 + 0.959683i $$0.590695\pi$$
$$758$$ −19.0000 + 32.9090i −0.690111 + 1.19531i
$$759$$ −9.00000 −0.326679
$$760$$ 0 0
$$761$$ 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i $$-0.763543\pi$$
0.954043 + 0.299670i $$0.0968765\pi$$
$$762$$ 14.0000 0.507166
$$763$$ 14.0000 24.2487i 0.506834 0.877862i
$$764$$ 6.00000 + 10.3923i 0.217072 + 0.375980i
$$765$$ 0 0
$$766$$ 21.0000 0.758761
$$767$$ −31.5000 7.79423i −1.13740 0.281433i
$$768$$ −1.00000 −0.0360844
$$769$$ 6.50000 + 11.2583i 0.234396 + 0.405986i 0.959097 0.283078i $$-0.0913554\pi$$
−0.724701 + 0.689063i $$0.758022\pi$$
$$770$$ 0 0
$$771$$ 10.5000 18.1865i 0.378148 0.654972i
$$772$$ 4.00000 0.143963
$$773$$ −24.0000 + 41.5692i −0.863220 + 1.49514i 0.00558380 + 0.999984i $$0.498223\pi$$
−0.868804 + 0.495156i $$0.835111\pi$$
$$774$$ −0.500000 + 0.866025i −0.0179721 + 0.0311286i
$$775$$ 0 0
$$776$$ 7.00000 12.1244i 0.251285 0.435239i
$$777$$ −7.00000 12.1244i −0.251124 0.434959i
$$778$$ −1.50000 2.59808i −0.0537776 0.0931455i
$$779$$ 12.0000 0.429945
$$780$$ 0 0
$$781$$ 36.0000 1.28818
$$782$$ −9.00000 15.5885i −0.321839 0.557442i
$$783$$ 1.50000 + 2.59808i 0.0536056 + 0.0928477i
$$784$$ 1.50000 2.59808i 0.0535714 0.0927884i
$$785$$ 0 0
$$786$$ 4.50000 7.79423i