# Properties

 Label 546.2.bi.c.257.1 Level $546$ Weight $2$ Character 546.257 Analytic conductor $4.360$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bi (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 257.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.257 Dual form 546.2.bi.c.17.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(-3.00000 - 1.73205i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(-3.00000 + 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(-0.500000 - 2.59808i) q^{14} +(3.00000 + 5.19615i) q^{15} +1.00000 q^{16} +(1.50000 + 2.59808i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-1.50000 + 4.33013i) q^{21} +(-3.00000 + 5.19615i) q^{22} -3.46410i q^{23} +(-1.50000 - 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} +(-2.50000 + 2.59808i) q^{26} -5.19615i q^{27} +(-0.500000 - 2.59808i) q^{28} +(-6.00000 + 3.46410i) q^{29} +(3.00000 + 5.19615i) q^{30} +(-4.00000 - 6.92820i) q^{31} +1.00000 q^{32} +(9.00000 - 5.19615i) q^{33} +(-3.00000 + 8.66025i) q^{35} +(1.50000 + 2.59808i) q^{36} -8.66025i q^{37} +(2.50000 + 4.33013i) q^{38} +(6.00000 - 1.73205i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(-9.00000 + 5.19615i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} -10.3923i q^{45} -3.46410i q^{46} +(-6.00000 - 3.46410i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(3.50000 + 6.06218i) q^{50} +(-2.50000 + 2.59808i) q^{52} +(-3.00000 + 1.73205i) q^{53} -5.19615i q^{54} +(18.0000 - 10.3923i) q^{55} +(-0.500000 - 2.59808i) q^{56} -8.66025i q^{57} +(-6.00000 + 3.46410i) q^{58} +(3.00000 + 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(-4.00000 - 6.92820i) q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(12.0000 - 3.46410i) q^{65} +(9.00000 - 5.19615i) q^{66} +(-3.00000 - 1.73205i) q^{67} +(-3.00000 + 5.19615i) q^{69} +(-3.00000 + 8.66025i) q^{70} +(1.50000 + 2.59808i) q^{72} +(3.50000 + 6.06218i) q^{73} -8.66025i q^{74} -12.1244i q^{75} +(2.50000 + 4.33013i) q^{76} +(15.0000 + 5.19615i) q^{77} +(6.00000 - 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-3.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 + 5.19615i) q^{82} -3.46410i q^{83} +(-1.50000 + 4.33013i) q^{84} +(-0.500000 + 0.866025i) q^{86} +12.0000 q^{87} +(-3.00000 + 5.19615i) q^{88} -3.46410i q^{89} -10.3923i q^{90} +(8.00000 + 5.19615i) q^{91} -3.46410i q^{92} +13.8564i q^{93} +(-6.00000 - 3.46410i) q^{94} -17.3205i q^{95} +(-1.50000 - 0.866025i) q^{96} +(-3.50000 + 6.06218i) q^{97} +(-6.50000 + 2.59808i) q^{98} -18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} - 3q^{3} + 2q^{4} - 6q^{5} - 3q^{6} - q^{7} + 2q^{8} + 3q^{9} + O(q^{10})$$ $$2q + 2q^{2} - 3q^{3} + 2q^{4} - 6q^{5} - 3q^{6} - q^{7} + 2q^{8} + 3q^{9} - 6q^{10} - 6q^{11} - 3q^{12} - 5q^{13} - q^{14} + 6q^{15} + 2q^{16} + 3q^{18} + 5q^{19} - 6q^{20} - 3q^{21} - 6q^{22} - 3q^{24} + 7q^{25} - 5q^{26} - q^{28} - 12q^{29} + 6q^{30} - 8q^{31} + 2q^{32} + 18q^{33} - 6q^{35} + 3q^{36} + 5q^{38} + 12q^{39} - 6q^{40} - 18q^{41} - 3q^{42} - q^{43} - 6q^{44} - 12q^{47} - 3q^{48} - 13q^{49} + 7q^{50} - 5q^{52} - 6q^{53} + 36q^{55} - q^{56} - 12q^{58} + 6q^{60} + 9q^{61} - 8q^{62} + 12q^{63} + 2q^{64} + 24q^{65} + 18q^{66} - 6q^{67} - 6q^{69} - 6q^{70} + 3q^{72} + 7q^{73} + 5q^{76} + 30q^{77} + 12q^{78} + 8q^{79} - 6q^{80} - 9q^{81} - 18q^{82} - 3q^{84} - q^{86} + 24q^{87} - 6q^{88} + 16q^{91} - 12q^{94} - 3q^{96} - 7q^{97} - 13q^{98} - 36q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −1.50000 0.866025i −0.866025 0.500000i
$$4$$ 1.00000 0.500000
$$5$$ −3.00000 1.73205i −1.34164 0.774597i −0.354593 0.935021i $$-0.615380\pi$$
−0.987048 + 0.160424i $$0.948714\pi$$
$$6$$ −1.50000 0.866025i −0.612372 0.353553i
$$7$$ −0.500000 2.59808i −0.188982 0.981981i
$$8$$ 1.00000 0.353553
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ −3.00000 1.73205i −0.948683 0.547723i
$$11$$ −3.00000 + 5.19615i −0.904534 + 1.56670i −0.0829925 + 0.996550i $$0.526448\pi$$
−0.821541 + 0.570149i $$0.806886\pi$$
$$12$$ −1.50000 0.866025i −0.433013 0.250000i
$$13$$ −2.50000 + 2.59808i −0.693375 + 0.720577i
$$14$$ −0.500000 2.59808i −0.133631 0.694365i
$$15$$ 3.00000 + 5.19615i 0.774597 + 1.34164i
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 1.50000 + 2.59808i 0.353553 + 0.612372i
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ −3.00000 1.73205i −0.670820 0.387298i
$$21$$ −1.50000 + 4.33013i −0.327327 + 0.944911i
$$22$$ −3.00000 + 5.19615i −0.639602 + 1.10782i
$$23$$ 3.46410i 0.722315i −0.932505 0.361158i $$-0.882382\pi$$
0.932505 0.361158i $$-0.117618\pi$$
$$24$$ −1.50000 0.866025i −0.306186 0.176777i
$$25$$ 3.50000 + 6.06218i 0.700000 + 1.21244i
$$26$$ −2.50000 + 2.59808i −0.490290 + 0.509525i
$$27$$ 5.19615i 1.00000i
$$28$$ −0.500000 2.59808i −0.0944911 0.490990i
$$29$$ −6.00000 + 3.46410i −1.11417 + 0.643268i −0.939907 0.341431i $$-0.889088\pi$$
−0.174265 + 0.984699i $$0.555755\pi$$
$$30$$ 3.00000 + 5.19615i 0.547723 + 0.948683i
$$31$$ −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i $$-0.911532\pi$$
0.243204 0.969975i $$-0.421802\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 9.00000 5.19615i 1.56670 0.904534i
$$34$$ 0 0
$$35$$ −3.00000 + 8.66025i −0.507093 + 1.46385i
$$36$$ 1.50000 + 2.59808i 0.250000 + 0.433013i
$$37$$ 8.66025i 1.42374i −0.702313 0.711868i $$-0.747849\pi$$
0.702313 0.711868i $$-0.252151\pi$$
$$38$$ 2.50000 + 4.33013i 0.405554 + 0.702439i
$$39$$ 6.00000 1.73205i 0.960769 0.277350i
$$40$$ −3.00000 1.73205i −0.474342 0.273861i
$$41$$ −9.00000 + 5.19615i −1.40556 + 0.811503i −0.994956 0.100309i $$-0.968017\pi$$
−0.410608 + 0.911812i $$0.634683\pi$$
$$42$$ −1.50000 + 4.33013i −0.231455 + 0.668153i
$$43$$ −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 + 5.19615i −0.452267 + 0.783349i
$$45$$ 10.3923i 1.54919i
$$46$$ 3.46410i 0.510754i
$$47$$ −6.00000 3.46410i −0.875190 0.505291i −0.00612051 0.999981i $$-0.501948\pi$$
−0.869069 + 0.494690i $$0.835282\pi$$
$$48$$ −1.50000 0.866025i −0.216506 0.125000i
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 3.50000 + 6.06218i 0.494975 + 0.857321i
$$51$$ 0 0
$$52$$ −2.50000 + 2.59808i −0.346688 + 0.360288i
$$53$$ −3.00000 + 1.73205i −0.412082 + 0.237915i −0.691684 0.722200i $$-0.743131\pi$$
0.279602 + 0.960116i $$0.409797\pi$$
$$54$$ 5.19615i 0.707107i
$$55$$ 18.0000 10.3923i 2.42712 1.40130i
$$56$$ −0.500000 2.59808i −0.0668153 0.347183i
$$57$$ 8.66025i 1.14708i
$$58$$ −6.00000 + 3.46410i −0.787839 + 0.454859i
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 3.00000 + 5.19615i 0.387298 + 0.670820i
$$61$$ 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i $$-0.558724\pi$$
0.759608 + 0.650381i $$0.225391\pi$$
$$62$$ −4.00000 6.92820i −0.508001 0.879883i
$$63$$ 6.00000 5.19615i 0.755929 0.654654i
$$64$$ 1.00000 0.125000
$$65$$ 12.0000 3.46410i 1.48842 0.429669i
$$66$$ 9.00000 5.19615i 1.10782 0.639602i
$$67$$ −3.00000 1.73205i −0.366508 0.211604i 0.305424 0.952217i $$-0.401202\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ 0 0
$$69$$ −3.00000 + 5.19615i −0.361158 + 0.625543i
$$70$$ −3.00000 + 8.66025i −0.358569 + 1.03510i
$$71$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$72$$ 1.50000 + 2.59808i 0.176777 + 0.306186i
$$73$$ 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i $$-0.0323196\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 8.66025i 1.00673i
$$75$$ 12.1244i 1.40000i
$$76$$ 2.50000 + 4.33013i 0.286770 + 0.496700i
$$77$$ 15.0000 + 5.19615i 1.70941 + 0.592157i
$$78$$ 6.00000 1.73205i 0.679366 0.196116i
$$79$$ 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i $$-0.684745\pi$$
0.998388 + 0.0567635i $$0.0180781\pi$$
$$80$$ −3.00000 1.73205i −0.335410 0.193649i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −9.00000 + 5.19615i −0.993884 + 0.573819i
$$83$$ 3.46410i 0.380235i −0.981761 0.190117i $$-0.939113\pi$$
0.981761 0.190117i $$-0.0608868\pi$$
$$84$$ −1.50000 + 4.33013i −0.163663 + 0.472456i
$$85$$ 0 0
$$86$$ −0.500000 + 0.866025i −0.0539164 + 0.0933859i
$$87$$ 12.0000 1.28654
$$88$$ −3.00000 + 5.19615i −0.319801 + 0.553912i
$$89$$ 3.46410i 0.367194i −0.983002 0.183597i $$-0.941226\pi$$
0.983002 0.183597i $$-0.0587741\pi$$
$$90$$ 10.3923i 1.09545i
$$91$$ 8.00000 + 5.19615i 0.838628 + 0.544705i
$$92$$ 3.46410i 0.361158i
$$93$$ 13.8564i 1.43684i
$$94$$ −6.00000 3.46410i −0.618853 0.357295i
$$95$$ 17.3205i 1.77705i
$$96$$ −1.50000 0.866025i −0.153093 0.0883883i
$$97$$ −3.50000 + 6.06218i −0.355371 + 0.615521i −0.987181 0.159602i $$-0.948979\pi$$
0.631810 + 0.775123i $$0.282312\pi$$
$$98$$ −6.50000 + 2.59808i −0.656599 + 0.262445i
$$99$$ −18.0000 −1.80907
$$100$$ 3.50000 + 6.06218i 0.350000 + 0.606218i
$$101$$ −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i $$-0.929823\pi$$
0.677284 + 0.735721i $$0.263157\pi$$
$$102$$ 0 0
$$103$$ 4.50000 + 2.59808i 0.443398 + 0.255996i 0.705038 0.709170i $$-0.250930\pi$$
−0.261640 + 0.965166i $$0.584263\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 12.0000 10.3923i 1.17108 1.01419i
$$106$$ −3.00000 + 1.73205i −0.291386 + 0.168232i
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 5.19615i 0.500000i
$$109$$ −10.5000 + 6.06218i −1.00572 + 0.580651i −0.909935 0.414751i $$-0.863869\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 18.0000 10.3923i 1.71623 0.990867i
$$111$$ −7.50000 + 12.9904i −0.711868 + 1.23299i
$$112$$ −0.500000 2.59808i −0.0472456 0.245495i
$$113$$ 6.00000 + 3.46410i 0.564433 + 0.325875i 0.754923 0.655814i $$-0.227674\pi$$
−0.190490 + 0.981689i $$0.561008\pi$$
$$114$$ 8.66025i 0.811107i
$$115$$ −6.00000 + 10.3923i −0.559503 + 0.969087i
$$116$$ −6.00000 + 3.46410i −0.557086 + 0.321634i
$$117$$ −10.5000 2.59808i −0.970725 0.240192i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 3.00000 + 5.19615i 0.273861 + 0.474342i
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ 4.50000 2.59808i 0.407411 0.235219i
$$123$$ 18.0000 1.62301
$$124$$ −4.00000 6.92820i −0.359211 0.622171i
$$125$$ 6.92820i 0.619677i
$$126$$ 6.00000 5.19615i 0.534522 0.462910i
$$127$$ −0.500000 0.866025i −0.0443678 0.0768473i 0.842989 0.537931i $$-0.180794\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 1.50000 0.866025i 0.132068 0.0762493i
$$130$$ 12.0000 3.46410i 1.05247 0.303822i
$$131$$ 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i $$-0.545310\pi$$
0.928199 0.372084i $$-0.121357\pi$$
$$132$$ 9.00000 5.19615i 0.783349 0.452267i
$$133$$ 10.0000 8.66025i 0.867110 0.750939i
$$134$$ −3.00000 1.73205i −0.259161 0.149626i
$$135$$ −9.00000 + 15.5885i −0.774597 + 1.34164i
$$136$$ 0 0
$$137$$ −6.00000 −0.512615 −0.256307 0.966595i $$-0.582506\pi$$
−0.256307 + 0.966595i $$0.582506\pi$$
$$138$$ −3.00000 + 5.19615i −0.255377 + 0.442326i
$$139$$ −3.00000 1.73205i −0.254457 0.146911i 0.367347 0.930084i $$-0.380266\pi$$
−0.621803 + 0.783174i $$0.713600\pi$$
$$140$$ −3.00000 + 8.66025i −0.253546 + 0.731925i
$$141$$ 6.00000 + 10.3923i 0.505291 + 0.875190i
$$142$$ 0 0
$$143$$ −6.00000 20.7846i −0.501745 1.73810i
$$144$$ 1.50000 + 2.59808i 0.125000 + 0.216506i
$$145$$ 24.0000 1.99309
$$146$$ 3.50000 + 6.06218i 0.289662 + 0.501709i
$$147$$ 12.0000 + 1.73205i 0.989743 + 0.142857i
$$148$$ 8.66025i 0.711868i
$$149$$ −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i $$-0.902763\pi$$
0.216394 0.976306i $$-0.430570\pi$$
$$150$$ 12.1244i 0.989949i
$$151$$ 3.00000 1.73205i 0.244137 0.140952i −0.372940 0.927855i $$-0.621650\pi$$
0.617076 + 0.786903i $$0.288317\pi$$
$$152$$ 2.50000 + 4.33013i 0.202777 + 0.351220i
$$153$$ 0 0
$$154$$ 15.0000 + 5.19615i 1.20873 + 0.418718i
$$155$$ 27.7128i 2.22595i
$$156$$ 6.00000 1.73205i 0.480384 0.138675i
$$157$$ −16.5000 + 9.52628i −1.31684 + 0.760280i −0.983220 0.182426i $$-0.941605\pi$$
−0.333624 + 0.942706i $$0.608272\pi$$
$$158$$ 4.00000 6.92820i 0.318223 0.551178i
$$159$$ 6.00000 0.475831
$$160$$ −3.00000 1.73205i −0.237171 0.136931i
$$161$$ −9.00000 + 1.73205i −0.709299 + 0.136505i
$$162$$ −4.50000 + 7.79423i −0.353553 + 0.612372i
$$163$$ 1.50000 0.866025i 0.117489 0.0678323i −0.440104 0.897947i $$-0.645058\pi$$
0.557593 + 0.830115i $$0.311725\pi$$
$$164$$ −9.00000 + 5.19615i −0.702782 + 0.405751i
$$165$$ −36.0000 −2.80260
$$166$$ 3.46410i 0.268866i
$$167$$ 3.00000 1.73205i 0.232147 0.134030i −0.379415 0.925227i $$-0.623875\pi$$
0.611562 + 0.791196i $$0.290541\pi$$
$$168$$ −1.50000 + 4.33013i −0.115728 + 0.334077i
$$169$$ −0.500000 12.9904i −0.0384615 0.999260i
$$170$$ 0 0
$$171$$ −7.50000 + 12.9904i −0.573539 + 0.993399i
$$172$$ −0.500000 + 0.866025i −0.0381246 + 0.0660338i
$$173$$ 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i $$-0.0934200\pi$$
−0.729155 + 0.684349i $$0.760087\pi$$
$$174$$ 12.0000 0.909718
$$175$$ 14.0000 12.1244i 1.05830 0.916515i
$$176$$ −3.00000 + 5.19615i −0.226134 + 0.391675i
$$177$$ 0 0
$$178$$ 3.46410i 0.259645i
$$179$$ 21.0000 + 12.1244i 1.56961 + 0.906217i 0.996213 + 0.0869415i $$0.0277093\pi$$
0.573400 + 0.819275i $$0.305624\pi$$
$$180$$ 10.3923i 0.774597i
$$181$$ 15.5885i 1.15868i 0.815086 + 0.579340i $$0.196690\pi$$
−0.815086 + 0.579340i $$0.803310\pi$$
$$182$$ 8.00000 + 5.19615i 0.592999 + 0.385164i
$$183$$ −9.00000 −0.665299
$$184$$ 3.46410i 0.255377i
$$185$$ −15.0000 + 25.9808i −1.10282 + 1.91014i
$$186$$ 13.8564i 1.01600i
$$187$$ 0 0
$$188$$ −6.00000 3.46410i −0.437595 0.252646i
$$189$$ −13.5000 + 2.59808i −0.981981 + 0.188982i
$$190$$ 17.3205i 1.25656i
$$191$$ 18.0000 10.3923i 1.30243 0.751961i 0.321613 0.946871i $$-0.395775\pi$$
0.980821 + 0.194910i $$0.0624416\pi$$
$$192$$ −1.50000 0.866025i −0.108253 0.0625000i
$$193$$ −4.50000 2.59808i −0.323917 0.187014i 0.329220 0.944253i $$-0.393214\pi$$
−0.653137 + 0.757240i $$0.726548\pi$$
$$194$$ −3.50000 + 6.06218i −0.251285 + 0.435239i
$$195$$ −21.0000 5.19615i −1.50384 0.372104i
$$196$$ −6.50000 + 2.59808i −0.464286 + 0.185577i
$$197$$ −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i $$-0.307266\pi$$
−0.996649 + 0.0818013i $$0.973933\pi$$
$$198$$ −18.0000 −1.27920
$$199$$ 15.5885i 1.10504i 0.833501 + 0.552518i $$0.186333\pi$$
−0.833501 + 0.552518i $$0.813667\pi$$
$$200$$ 3.50000 + 6.06218i 0.247487 + 0.428661i
$$201$$ 3.00000 + 5.19615i 0.211604 + 0.366508i
$$202$$ −3.00000 + 5.19615i −0.211079 + 0.365600i
$$203$$ 12.0000 + 13.8564i 0.842235 + 0.972529i
$$204$$ 0 0
$$205$$ 36.0000 2.51435
$$206$$ 4.50000 + 2.59808i 0.313530 + 0.181017i
$$207$$ 9.00000 5.19615i 0.625543 0.361158i
$$208$$ −2.50000 + 2.59808i −0.173344 + 0.180144i
$$209$$ −30.0000 −2.07514
$$210$$ 12.0000 10.3923i 0.828079 0.717137i
$$211$$ −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i $$-0.221724\pi$$
−0.939156 + 0.343490i $$0.888391\pi$$
$$212$$ −3.00000 + 1.73205i −0.206041 + 0.118958i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 3.00000 1.73205i 0.204598 0.118125i
$$216$$ 5.19615i 0.353553i
$$217$$ −16.0000 + 13.8564i −1.08615 + 0.940634i
$$218$$ −10.5000 + 6.06218i −0.711150 + 0.410582i
$$219$$ 12.1244i 0.819288i
$$220$$ 18.0000 10.3923i 1.21356 0.700649i
$$221$$ 0 0
$$222$$ −7.50000 + 12.9904i −0.503367 + 0.871857i
$$223$$ −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i $$-0.986707\pi$$
0.463409 0.886145i $$-0.346626\pi$$
$$224$$ −0.500000 2.59808i −0.0334077 0.173591i
$$225$$ −10.5000 + 18.1865i −0.700000 + 1.21244i
$$226$$ 6.00000 + 3.46410i 0.399114 + 0.230429i
$$227$$ 10.3923i 0.689761i −0.938647 0.344881i $$-0.887919\pi$$
0.938647 0.344881i $$-0.112081\pi$$
$$228$$ 8.66025i 0.573539i
$$229$$ −14.5000 + 25.1147i −0.958187 + 1.65963i −0.231287 + 0.972886i $$0.574293\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ −6.00000 + 10.3923i −0.395628 + 0.685248i
$$231$$ −18.0000 20.7846i −1.18431 1.36753i
$$232$$ −6.00000 + 3.46410i −0.393919 + 0.227429i
$$233$$ 6.00000 + 3.46410i 0.393073 + 0.226941i 0.683491 0.729959i $$-0.260461\pi$$
−0.290418 + 0.956900i $$0.593794\pi$$
$$234$$ −10.5000 2.59808i −0.686406 0.169842i
$$235$$ 12.0000 + 20.7846i 0.782794 + 1.35584i
$$236$$ 0 0
$$237$$ −12.0000 + 6.92820i −0.779484 + 0.450035i
$$238$$ 0 0
$$239$$ −6.00000 −0.388108 −0.194054 0.980991i $$-0.562164\pi$$
−0.194054 + 0.980991i $$0.562164\pi$$
$$240$$ 3.00000 + 5.19615i 0.193649 + 0.335410i
$$241$$ 26.0000 1.67481 0.837404 0.546585i $$-0.184072\pi$$
0.837404 + 0.546585i $$0.184072\pi$$
$$242$$ −12.5000 21.6506i −0.803530 1.39176i
$$243$$ 13.5000 7.79423i 0.866025 0.500000i
$$244$$ 4.50000 2.59808i 0.288083 0.166325i
$$245$$ 24.0000 + 3.46410i 1.53330 + 0.221313i
$$246$$ 18.0000 1.14764
$$247$$ −17.5000 4.33013i −1.11350 0.275519i
$$248$$ −4.00000 6.92820i −0.254000 0.439941i
$$249$$ −3.00000 + 5.19615i −0.190117 + 0.329293i
$$250$$ 6.92820i 0.438178i
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ 6.00000 5.19615i 0.377964 0.327327i
$$253$$ 18.0000 + 10.3923i 1.13165 + 0.653359i
$$254$$ −0.500000 0.866025i −0.0313728 0.0543393i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000 1.12281 0.561405 0.827541i $$-0.310261\pi$$
0.561405 + 0.827541i $$0.310261\pi$$
$$258$$ 1.50000 0.866025i 0.0933859 0.0539164i
$$259$$ −22.5000 + 4.33013i −1.39808 + 0.269061i
$$260$$ 12.0000 3.46410i 0.744208 0.214834i
$$261$$ −18.0000 10.3923i −1.11417 0.643268i
$$262$$ 9.00000 15.5885i 0.556022 0.963058i
$$263$$ −12.0000 6.92820i −0.739952 0.427211i 0.0821001 0.996624i $$-0.473837\pi$$
−0.822052 + 0.569413i $$0.807171\pi$$
$$264$$ 9.00000 5.19615i 0.553912 0.319801i
$$265$$ 12.0000 0.737154
$$266$$ 10.0000 8.66025i 0.613139 0.530994i
$$267$$ −3.00000 + 5.19615i −0.183597 + 0.317999i
$$268$$ −3.00000 1.73205i −0.183254 0.105802i
$$269$$ −12.0000 −0.731653 −0.365826 0.930683i $$-0.619214\pi$$
−0.365826 + 0.930683i $$0.619214\pi$$
$$270$$ −9.00000 + 15.5885i −0.547723 + 0.948683i
$$271$$ 1.00000 0.0607457 0.0303728 0.999539i $$-0.490331\pi$$
0.0303728 + 0.999539i $$0.490331\pi$$
$$272$$ 0 0
$$273$$ −7.50000 14.7224i −0.453921 0.891042i
$$274$$ −6.00000 −0.362473
$$275$$ −42.0000 −2.53270
$$276$$ −3.00000 + 5.19615i −0.180579 + 0.312772i
$$277$$ 17.0000 1.02143 0.510716 0.859750i $$-0.329381\pi$$
0.510716 + 0.859750i $$0.329381\pi$$
$$278$$ −3.00000 1.73205i −0.179928 0.103882i
$$279$$ 12.0000 20.7846i 0.718421 1.24434i
$$280$$ −3.00000 + 8.66025i −0.179284 + 0.517549i
$$281$$ 12.0000 0.715860 0.357930 0.933748i $$-0.383483\pi$$
0.357930 + 0.933748i $$0.383483\pi$$
$$282$$ 6.00000 + 10.3923i 0.357295 + 0.618853i
$$283$$ −1.50000 0.866025i −0.0891657 0.0514799i 0.454754 0.890617i $$-0.349727\pi$$
−0.543920 + 0.839137i $$0.683060\pi$$
$$284$$ 0 0
$$285$$ −15.0000 + 25.9808i −0.888523 + 1.53897i
$$286$$ −6.00000 20.7846i −0.354787 1.22902i
$$287$$ 18.0000 + 20.7846i 1.06251 + 1.22688i
$$288$$ 1.50000 + 2.59808i 0.0883883 + 0.153093i
$$289$$ −17.0000 −1.00000
$$290$$ 24.0000 1.40933
$$291$$ 10.5000 6.06218i 0.615521 0.355371i
$$292$$ 3.50000 + 6.06218i 0.204822 + 0.354762i
$$293$$ −6.00000 3.46410i −0.350524 0.202375i 0.314392 0.949293i $$-0.398199\pi$$
−0.664916 + 0.746918i $$0.731533\pi$$
$$294$$ 12.0000 + 1.73205i 0.699854 + 0.101015i
$$295$$ 0 0
$$296$$ 8.66025i 0.503367i
$$297$$ 27.0000 + 15.5885i 1.56670 + 0.904534i
$$298$$ −9.00000 15.5885i −0.521356 0.903015i
$$299$$ 9.00000 + 8.66025i 0.520483 + 0.500835i
$$300$$ 12.1244i 0.700000i
$$301$$ 2.50000 + 0.866025i 0.144098 + 0.0499169i
$$302$$ 3.00000 1.73205i 0.172631 0.0996683i
$$303$$ 9.00000 5.19615i 0.517036 0.298511i
$$304$$ 2.50000 + 4.33013i 0.143385 + 0.248350i
$$305$$ −18.0000 −1.03068
$$306$$ 0 0
$$307$$ −4.00000 −0.228292 −0.114146 0.993464i $$-0.536413\pi$$
−0.114146 + 0.993464i $$0.536413\pi$$
$$308$$ 15.0000 + 5.19615i 0.854704 + 0.296078i
$$309$$ −4.50000 7.79423i −0.255996 0.443398i
$$310$$ 27.7128i 1.57398i
$$311$$ −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i $$-0.221080\pi$$
−0.938460 + 0.345389i $$0.887747\pi$$
$$312$$ 6.00000 1.73205i 0.339683 0.0980581i
$$313$$ −28.5000 16.4545i −1.61092 0.930062i −0.989158 0.146852i $$-0.953086\pi$$
−0.621757 0.783210i $$-0.713581\pi$$
$$314$$ −16.5000 + 9.52628i −0.931149 + 0.537599i
$$315$$ −27.0000 + 5.19615i −1.52128 + 0.292770i
$$316$$ 4.00000 6.92820i 0.225018 0.389742i
$$317$$ −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i $$0.335355\pi$$
−0.999980 + 0.00635137i $$0.997978\pi$$
$$318$$ 6.00000 0.336463
$$319$$ 41.5692i 2.32743i
$$320$$ −3.00000 1.73205i −0.167705 0.0968246i
$$321$$ 0 0
$$322$$ −9.00000 + 1.73205i −0.501550 + 0.0965234i
$$323$$ 0 0
$$324$$ −4.50000 + 7.79423i −0.250000 + 0.433013i
$$325$$ −24.5000 6.06218i −1.35902 0.336269i
$$326$$ 1.50000 0.866025i 0.0830773 0.0479647i
$$327$$ 21.0000 1.16130
$$328$$ −9.00000 + 5.19615i −0.496942 + 0.286910i
$$329$$ −6.00000 + 17.3205i −0.330791 + 0.954911i
$$330$$ −36.0000 −1.98173
$$331$$ −16.5000 + 9.52628i −0.906922 + 0.523612i −0.879440 0.476011i $$-0.842082\pi$$
−0.0274825 + 0.999622i $$0.508749\pi$$
$$332$$ 3.46410i 0.190117i
$$333$$ 22.5000 12.9904i 1.23299 0.711868i
$$334$$ 3.00000 1.73205i 0.164153 0.0947736i
$$335$$ 6.00000 + 10.3923i 0.327815 + 0.567792i
$$336$$ −1.50000 + 4.33013i −0.0818317 + 0.236228i
$$337$$ 5.00000 0.272367 0.136184 0.990684i $$-0.456516\pi$$
0.136184 + 0.990684i $$0.456516\pi$$
$$338$$ −0.500000 12.9904i −0.0271964 0.706584i
$$339$$ −6.00000 10.3923i −0.325875 0.564433i
$$340$$ 0 0
$$341$$ 48.0000 2.59935
$$342$$ −7.50000 + 12.9904i −0.405554 + 0.702439i
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ −0.500000 + 0.866025i −0.0269582 + 0.0466930i
$$345$$ 18.0000 10.3923i 0.969087 0.559503i
$$346$$ 3.00000 + 5.19615i 0.161281 + 0.279347i
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 12.0000 0.643268
$$349$$ −5.50000 9.52628i −0.294408 0.509930i 0.680439 0.732805i $$-0.261789\pi$$
−0.974847 + 0.222875i $$0.928456\pi$$
$$350$$ 14.0000 12.1244i 0.748331 0.648074i
$$351$$ 13.5000 + 12.9904i 0.720577 + 0.693375i
$$352$$ −3.00000 + 5.19615i −0.159901 + 0.276956i
$$353$$ −9.00000 5.19615i −0.479022 0.276563i 0.240987 0.970528i $$-0.422529\pi$$
−0.720009 + 0.693965i $$0.755862\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 3.46410i 0.183597i
$$357$$ 0 0
$$358$$ 21.0000 + 12.1244i 1.10988 + 0.640792i
$$359$$ −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i $$0.384981\pi$$
−0.986865 + 0.161546i $$0.948352\pi$$
$$360$$ 10.3923i 0.547723i
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 15.5885i 0.819311i
$$363$$ 43.3013i 2.27273i
$$364$$ 8.00000 + 5.19615i 0.419314 + 0.272352i
$$365$$ 24.2487i 1.26924i
$$366$$ −9.00000 −0.470438
$$367$$ 1.50000 + 0.866025i 0.0782994 + 0.0452062i 0.538639 0.842537i $$-0.318939\pi$$
−0.460339 + 0.887743i $$0.652272\pi$$
$$368$$ 3.46410i 0.180579i
$$369$$ −27.0000 15.5885i −1.40556 0.811503i
$$370$$ −15.0000 + 25.9808i −0.779813 + 1.35068i
$$371$$ 6.00000 + 6.92820i 0.311504 + 0.359694i
$$372$$ 13.8564i 0.718421i
$$373$$ 1.00000 + 1.73205i 0.0517780 + 0.0896822i 0.890753 0.454488i $$-0.150178\pi$$
−0.838975 + 0.544170i $$0.816844\pi$$
$$374$$ 0 0
$$375$$ −6.00000 + 10.3923i −0.309839 + 0.536656i
$$376$$ −6.00000 3.46410i −0.309426 0.178647i
$$377$$ 6.00000 24.2487i 0.309016 1.24887i
$$378$$ −13.5000 + 2.59808i −0.694365 + 0.133631i
$$379$$ −15.0000 + 8.66025i −0.770498 + 0.444847i −0.833052 0.553194i $$-0.813409\pi$$
0.0625541 + 0.998042i $$0.480075\pi$$
$$380$$ 17.3205i 0.888523i
$$381$$ 1.73205i 0.0887357i
$$382$$ 18.0000 10.3923i 0.920960 0.531717i
$$383$$ −18.0000 + 10.3923i −0.919757 + 0.531022i −0.883558 0.468323i $$-0.844859\pi$$
−0.0361995 + 0.999345i $$0.511525\pi$$
$$384$$ −1.50000 0.866025i −0.0765466 0.0441942i
$$385$$ −36.0000 41.5692i −1.83473 2.11856i
$$386$$ −4.50000 2.59808i −0.229044 0.132239i
$$387$$ −3.00000 −0.152499
$$388$$ −3.50000 + 6.06218i −0.177686 + 0.307760i
$$389$$ 9.00000 5.19615i 0.456318 0.263455i −0.254177 0.967158i $$-0.581804\pi$$
0.710495 + 0.703702i $$0.248471\pi$$
$$390$$ −21.0000 5.19615i −1.06338 0.263117i
$$391$$ 0 0
$$392$$ −6.50000 + 2.59808i −0.328300 + 0.131223i
$$393$$ −27.0000 + 15.5885i −1.36197 + 0.786334i
$$394$$ −6.00000 10.3923i −0.302276 0.523557i
$$395$$ −24.0000 + 13.8564i −1.20757 + 0.697191i
$$396$$ −18.0000 −0.904534
$$397$$ 5.50000 + 9.52628i 0.276037 + 0.478110i 0.970396 0.241518i $$-0.0776454\pi$$
−0.694359 + 0.719629i $$0.744312\pi$$
$$398$$ 15.5885i 0.781379i
$$399$$ −22.5000 + 4.33013i −1.12641 + 0.216777i
$$400$$ 3.50000 + 6.06218i 0.175000 + 0.303109i
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 3.00000 + 5.19615i 0.149626 + 0.259161i
$$403$$ 28.0000 + 6.92820i 1.39478 + 0.345118i
$$404$$ −3.00000 + 5.19615i −0.149256 + 0.258518i
$$405$$ 27.0000 15.5885i 1.34164 0.774597i
$$406$$ 12.0000 + 13.8564i 0.595550 + 0.687682i
$$407$$ 45.0000 + 25.9808i 2.23057 + 1.28782i
$$408$$ 0 0
$$409$$ 19.0000 0.939490 0.469745 0.882802i $$-0.344346\pi$$
0.469745 + 0.882802i $$0.344346\pi$$
$$410$$ 36.0000 1.77791
$$411$$ 9.00000 + 5.19615i 0.443937 + 0.256307i
$$412$$ 4.50000 + 2.59808i 0.221699 + 0.127998i
$$413$$ 0 0
$$414$$ 9.00000 5.19615i 0.442326 0.255377i
$$415$$ −6.00000 + 10.3923i −0.294528 + 0.510138i
$$416$$ −2.50000 + 2.59808i −0.122573 + 0.127381i
$$417$$ 3.00000 + 5.19615i 0.146911 + 0.254457i
$$418$$ −30.0000 −1.46735
$$419$$ −15.0000 25.9808i −0.732798 1.26924i −0.955683 0.294398i $$-0.904881\pi$$
0.222885 0.974845i $$-0.428453\pi$$
$$420$$ 12.0000 10.3923i 0.585540 0.507093i
$$421$$ 27.7128i 1.35064i 0.737525 + 0.675320i $$0.235994\pi$$
−0.737525 + 0.675320i $$0.764006\pi$$
$$422$$ −2.50000 4.33013i −0.121698 0.210787i
$$423$$ 20.7846i 1.01058i
$$424$$ −3.00000 + 1.73205i −0.145693 + 0.0841158i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −9.00000 10.3923i −0.435541 0.502919i
$$428$$ 0 0
$$429$$ −9.00000 + 36.3731i −0.434524 + 1.75611i
$$430$$ 3.00000 1.73205i 0.144673 0.0835269i
$$431$$ 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i $$-0.690607\pi$$
0.997173 + 0.0751385i $$0.0239399\pi$$
$$432$$ 5.19615i 0.250000i
$$433$$ 18.0000 + 10.3923i 0.865025 + 0.499422i 0.865692 0.500577i $$-0.166879\pi$$
−0.000666943 1.00000i $$0.500212\pi$$
$$434$$ −16.0000 + 13.8564i −0.768025 + 0.665129i
$$435$$ −36.0000 20.7846i −1.72607 0.996546i
$$436$$ −10.5000 + 6.06218i −0.502859 + 0.290326i
$$437$$ 15.0000 8.66025i 0.717547 0.414276i
$$438$$ 12.1244i 0.579324i
$$439$$ 12.1244i 0.578664i 0.957229 + 0.289332i $$0.0934331\pi$$
−0.957229 + 0.289332i $$0.906567\pi$$
$$440$$ 18.0000 10.3923i 0.858116 0.495434i
$$441$$ −16.5000 12.9904i −0.785714 0.618590i
$$442$$ 0 0
$$443$$ 33.0000 + 19.0526i 1.56788 + 0.905214i 0.996416 + 0.0845852i $$0.0269565\pi$$
0.571461 + 0.820629i $$0.306377\pi$$
$$444$$ −7.50000 + 12.9904i −0.355934 + 0.616496i
$$445$$ −6.00000 + 10.3923i −0.284427 + 0.492642i
$$446$$ −8.00000 13.8564i −0.378811 0.656120i
$$447$$ 31.1769i 1.47462i
$$448$$ −0.500000 2.59808i −0.0236228 0.122748i
$$449$$ 15.0000 25.9808i 0.707894 1.22611i −0.257743 0.966213i $$-0.582979\pi$$
0.965637 0.259895i $$-0.0836878\pi$$
$$450$$ −10.5000 + 18.1865i −0.494975 + 0.857321i
$$451$$ 62.3538i 2.93613i
$$452$$ 6.00000 + 3.46410i 0.282216 + 0.162938i
$$453$$ −6.00000 −0.281905
$$454$$ 10.3923i 0.487735i
$$455$$ −15.0000 29.4449i −0.703211 1.38040i
$$456$$ 8.66025i 0.405554i
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ −14.5000 + 25.1147i −0.677541 + 1.17353i
$$459$$ 0 0
$$460$$ −6.00000 + 10.3923i −0.279751 + 0.484544i
$$461$$ 18.0000 + 10.3923i 0.838344 + 0.484018i 0.856701 0.515814i $$-0.172510\pi$$
−0.0183573 + 0.999831i $$0.505844\pi$$
$$462$$ −18.0000 20.7846i −0.837436 0.966988i
$$463$$ 19.0526i 0.885448i 0.896658 + 0.442724i $$0.145988\pi$$
−0.896658 + 0.442724i $$0.854012\pi$$
$$464$$ −6.00000 + 3.46410i −0.278543 + 0.160817i
$$465$$ 24.0000 41.5692i 1.11297 1.92773i
$$466$$ 6.00000 + 3.46410i 0.277945 + 0.160471i
$$467$$ −9.00000 + 15.5885i −0.416470 + 0.721348i −0.995582 0.0939008i $$-0.970066\pi$$
0.579111 + 0.815249i $$0.303400\pi$$
$$468$$ −10.5000 2.59808i −0.485363 0.120096i
$$469$$ −3.00000 + 8.66025i −0.138527 + 0.399893i
$$470$$ 12.0000 + 20.7846i 0.553519 + 0.958723i
$$471$$ 33.0000 1.52056
$$472$$ 0 0
$$473$$ −3.00000 5.19615i −0.137940 0.238919i
$$474$$ −12.0000 + 6.92820i −0.551178 + 0.318223i
$$475$$ −17.5000 + 30.3109i −0.802955 + 1.39076i
$$476$$ 0 0
$$477$$ −9.00000 5.19615i −0.412082 0.237915i
$$478$$ −6.00000 −0.274434
$$479$$ −6.00000 3.46410i −0.274147 0.158279i 0.356624 0.934248i $$-0.383928\pi$$
−0.630771 + 0.775969i $$0.717261\pi$$
$$480$$ 3.00000 + 5.19615i 0.136931 + 0.237171i
$$481$$ 22.5000 + 21.6506i 1.02591 + 0.987184i
$$482$$ 26.0000 1.18427
$$483$$ 15.0000 + 5.19615i 0.682524 + 0.236433i
$$484$$ −12.5000 21.6506i −0.568182 0.984120i
$$485$$ 21.0000 12.1244i 0.953561 0.550539i
$$486$$ 13.5000 7.79423i 0.612372 0.353553i
$$487$$ 15.5885i 0.706380i −0.935552 0.353190i $$-0.885097\pi$$
0.935552 0.353190i $$-0.114903\pi$$
$$488$$ 4.50000 2.59808i 0.203705 0.117609i
$$489$$ −3.00000 −0.135665
$$490$$ 24.0000 + 3.46410i 1.08421 + 0.156492i
$$491$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$492$$ 18.0000 0.811503
$$493$$ 0 0
$$494$$ −17.5000 4.33013i −0.787362 0.194822i
$$495$$ 54.0000 + 31.1769i 2.42712 + 1.40130i
$$496$$ −4.00000 6.92820i −0.179605 0.311086i
$$497$$ 0 0
$$498$$ −3.00000 + 5.19615i −0.134433 + 0.232845i
$$499$$ −7.50000 4.33013i −0.335746 0.193843i 0.322643 0.946521i $$-0.395429\pi$$
−0.658389 + 0.752678i $$0.728762\pi$$
$$500$$ 6.92820i 0.309839i
$$501$$ −6.00000 −0.268060
$$502$$ 6.00000 10.3923i 0.267793 0.463831i
$$503$$ −15.0000 + 25.9808i −0.668817 + 1.15842i 0.309418 + 0.950926i $$0.399866\pi$$
−0.978235 + 0.207499i $$0.933468\pi$$
$$504$$ 6.00000 5.19615i 0.267261 0.231455i
$$505$$ 18.0000 10.3923i 0.800989 0.462451i
$$506$$ 18.0000 + 10.3923i 0.800198 + 0.461994i
$$507$$ −10.5000 + 19.9186i −0.466321 + 0.884615i
$$508$$ −0.500000 0.866025i −0.0221839 0.0384237i
$$509$$ 24.2487i 1.07481i −0.843326 0.537403i $$-0.819406\pi$$
0.843326 0.537403i $$-0.180594\pi$$
$$510$$ 0 0
$$511$$ 14.0000 12.1244i 0.619324 0.536350i
$$512$$ 1.00000 0.0441942
$$513$$ 22.5000 12.9904i 0.993399 0.573539i
$$514$$ 18.0000 0.793946
$$515$$ −9.00000 15.5885i −0.396587 0.686909i
$$516$$ 1.50000 0.866025i 0.0660338 0.0381246i
$$517$$ 36.0000 20.7846i 1.58328 0.914106i
$$518$$ −22.5000 + 4.33013i −0.988593 + 0.190255i
$$519$$ 10.3923i 0.456172i
$$520$$ 12.0000 3.46410i 0.526235 0.151911i
$$521$$ 6.00000 + 10.3923i 0.262865 + 0.455295i 0.967002 0.254769i $$-0.0819994\pi$$
−0.704137 + 0.710064i $$0.748666\pi$$
$$522$$ −18.0000 10.3923i −0.787839 0.454859i
$$523$$ 8.66025i 0.378686i 0.981911 + 0.189343i $$0.0606359\pi$$
−0.981911 + 0.189343i $$0.939364\pi$$
$$524$$ 9.00000 15.5885i 0.393167 0.680985i
$$525$$ −31.5000 + 6.06218i −1.37477 + 0.264575i
$$526$$ −12.0000 6.92820i −0.523225 0.302084i
$$527$$ 0 0
$$528$$ 9.00000 5.19615i 0.391675 0.226134i
$$529$$ 11.0000 0.478261
$$530$$ 12.0000 0.521247
$$531$$ 0 0
$$532$$ 10.0000 8.66025i 0.433555 0.375470i
$$533$$ 9.00000 36.3731i 0.389833 1.57549i
$$534$$ −3.00000 + 5.19615i −0.129823 + 0.224860i
$$535$$ 0 0
$$536$$ −3.00000 1.73205i −0.129580 0.0748132i
$$537$$ −21.0000 36.3731i −0.906217 1.56961i
$$538$$ −12.0000 −0.517357
$$539$$ 6.00000 41.5692i 0.258438 1.79051i
$$540$$ −9.00000 + 15.5885i −0.387298 + 0.670820i
$$541$$ 1.50000 + 0.866025i 0.0644900 + 0.0372333i 0.531898 0.846808i $$-0.321479\pi$$
−0.467408 + 0.884042i $$0.654812\pi$$
$$542$$ 1.00000 0.0429537
$$543$$ 13.5000 23.3827i 0.579340 1.00345i
$$544$$ 0 0
$$545$$ 42.0000 1.79908
$$546$$ −7.50000 14.7224i −0.320970 0.630062i
$$547$$ −25.0000 −1.06892 −0.534461 0.845193i $$-0.679486\pi$$
−0.534461 + 0.845193i $$0.679486\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 13.5000 + 7.79423i 0.576166 + 0.332650i
$$550$$ −42.0000 −1.79089
$$551$$ −30.0000 17.3205i −1.27804 0.737878i
$$552$$ −3.00000 + 5.19615i −0.127688 + 0.221163i
$$553$$ −20.0000 6.92820i −0.850487 0.294617i
$$554$$ 17.0000 0.722261
$$555$$ 45.0000 25.9808i 1.91014 1.10282i
$$556$$ −3.00000 1.73205i −0.127228 0.0734553i
$$557$$ 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i $$-0.708795\pi$$
0.991254 + 0.131965i $$0.0421286\pi$$
$$558$$ 12.0000 20.7846i 0.508001 0.879883i
$$559$$ −1.00000 3.46410i −0.0422955 0.146516i
$$560$$ −3.00000 + 8.66025i −0.126773 + 0.365963i
$$561$$ 0 0
$$562$$ 12.0000 0.506189
$$563$$ 18.0000 0.758610 0.379305 0.925272i $$-0.376163\pi$$
0.379305 + 0.925272i $$0.376163\pi$$
$$564$$ 6.00000 + 10.3923i 0.252646 + 0.437595i
$$565$$ −12.0000 20.7846i −0.504844 0.874415i
$$566$$ −1.50000 0.866025i −0.0630497 0.0364018i
$$567$$ 22.5000 + 7.79423i 0.944911 + 0.327327i
$$568$$ 0 0
$$569$$ 27.7128i 1.16178i −0.813982 0.580891i $$-0.802704\pi$$
0.813982 0.580891i $$-0.197296\pi$$
$$570$$ −15.0000 + 25.9808i −0.628281 + 1.08821i
$$571$$ −9.50000 16.4545i −0.397563 0.688599i 0.595862 0.803087i $$-0.296811\pi$$
−0.993425 + 0.114488i $$0.963477\pi$$
$$572$$ −6.00000 20.7846i −0.250873 0.869048i
$$573$$ −36.0000 −1.50392
$$574$$ 18.0000 + 20.7846i 0.751305 + 0.867533i
$$575$$ 21.0000 12.1244i 0.875761 0.505621i
$$576$$ 1.50000 + 2.59808i 0.0625000 + 0.108253i
$$577$$ −18.5000 32.0429i −0.770165 1.33397i −0.937472 0.348060i $$-0.886840\pi$$
0.167307 0.985905i $$-0.446493\pi$$
$$578$$ −17.0000 −0.707107
$$579$$ 4.50000 + 7.79423i 0.187014 + 0.323917i
$$580$$ 24.0000 0.996546
$$581$$ −9.00000 + 1.73205i −0.373383 + 0.0718576i
$$582$$ 10.5000 6.06218i 0.435239 0.251285i
$$583$$ 20.7846i 0.860811i
$$584$$ 3.50000 + 6.06218i 0.144831 + 0.250855i
$$585$$ 27.0000 + 25.9808i 1.11631 + 1.07417i
$$586$$ −6.00000 3.46410i −0.247858 0.143101i
$$587$$ 39.0000 22.5167i 1.60970 0.929362i 0.620266 0.784391i $$-0.287025\pi$$
0.989436 0.144971i $$-0.0463088\pi$$
$$588$$ 12.0000 + 1.73205i 0.494872 + 0.0714286i
$$589$$ 20.0000 34.6410i 0.824086 1.42736i
$$590$$ 0 0
$$591$$ 20.7846i 0.854965i
$$592$$ 8.66025i 0.355934i
$$593$$ −6.00000 3.46410i −0.246390 0.142254i 0.371720 0.928345i $$-0.378768\pi$$
−0.618110 + 0.786091i $$0.712102\pi$$
$$594$$ 27.0000 + 15.5885i 1.10782 + 0.639602i
$$595$$ 0 0
$$596$$ −9.00000 15.5885i −0.368654 0.638528i
$$597$$ 13.5000 23.3827i 0.552518 0.956990i
$$598$$ 9.00000 + 8.66025i 0.368037 + 0.354144i
$$599$$ −24.0000 + 13.8564i −0.980613 + 0.566157i −0.902455 0.430784i $$-0.858237\pi$$
−0.0781581 + 0.996941i $$0.524904\pi$$
$$600$$ 12.1244i 0.494975i
$$601$$ 1.50000 0.866025i 0.0611863 0.0353259i −0.469095 0.883148i $$-0.655420\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 2.50000 + 0.866025i 0.101892 + 0.0352966i
$$603$$ 10.3923i 0.423207i
$$604$$ 3.00000 1.73205i 0.122068 0.0704761i
$$605$$ 86.6025i 3.52089i
$$606$$ 9.00000 5.19615i 0.365600 0.211079i
$$607$$ −13.5000 + 7.79423i −0.547948 + 0.316358i −0.748294 0.663367i $$-0.769127\pi$$
0.200346 + 0.979725i $$0.435793\pi$$
$$608$$ 2.50000 + 4.33013i 0.101388 + 0.175610i
$$609$$ −6.00000 31.1769i −0.243132 1.26335i
$$610$$ −18.0000 −0.728799
$$611$$ 24.0000 6.92820i 0.970936 0.280285i
$$612$$ 0 0
$$613$$ 22.5000 + 12.9904i 0.908766 + 0.524677i 0.880034 0.474911i $$-0.157520\pi$$
0.0287324 + 0.999587i $$0.490853\pi$$
$$614$$ −4.00000 −0.161427
$$615$$ −54.0000 31.1769i −2.17749 1.25717i
$$616$$ 15.0000 + 5.19615i 0.604367 + 0.209359i
$$617$$ −18.0000 + 31.1769i −0.724653 + 1.25514i 0.234464 + 0.972125i $$0.424666\pi$$
−0.959117 + 0.283011i $$0.908667\pi$$
$$618$$ −4.50000 7.79423i −0.181017 0.313530i
$$619$$ 8.50000 + 14.7224i 0.341644 + 0.591744i 0.984738 0.174042i $$-0.0556830\pi$$
−0.643094 + 0.765787i $$0.722350\pi$$
$$620$$ 27.7128i 1.11297i
$$621$$ −18.0000 −0.722315
$$622$$ −3.00000 5.19615i −0.120289 0.208347i
$$623$$ −9.00000 + 1.73205i −0.360577 + 0.0693932i
$$624$$ 6.00000 1.73205i 0.240192 0.0693375i
$$625$$ 5.50000 9.52628i 0.220000 0.381051i
$$626$$ −28.5000 16.4545i −1.13909 0.657653i
$$627$$ 45.0000 + 25.9808i 1.79713 + 1.03757i
$$628$$ −16.5000 + 9.52628i −0.658422 + 0.380140i
$$629$$ 0 0
$$630$$ −27.0000 + 5.19615i −1.07571 + 0.207020i
$$631$$ 22.5000 + 12.9904i 0.895711 + 0.517139i 0.875806 0.482663i $$-0.160330\pi$$
0.0199047 + 0.999802i $$0.493664\pi$$
$$632$$ 4.00000 6.92820i 0.159111 0.275589i
$$633$$ 8.66025i 0.344214i
$$634$$ −9.00000 + 15.5885i −0.357436 + 0.619097i
$$635$$ 3.46410i 0.137469i
$$636$$ 6.00000 0.237915
$$637$$ 9.50000 23.3827i 0.376404 0.926456i
$$638$$ 41.5692i 1.64574i
$$639$$ 0 0
$$640$$ −3.00000 1.73205i −0.118585 0.0684653i
$$641$$ 38.1051i 1.50506i 0.658557 + 0.752531i $$0.271167\pi$$
−0.658557 + 0.752531i $$0.728833\pi$$
$$642$$ 0 0
$$643$$ −5.50000 + 9.52628i −0.216899 + 0.375680i −0.953858 0.300257i $$-0.902928\pi$$
0.736959 + 0.675937i $$0.236261\pi$$
$$644$$ −9.00000 + 1.73205i −0.354650 + 0.0682524i
$$645$$ −6.00000 −0.236250
$$646$$ 0 0
$$647$$ −18.0000 + 31.1769i −0.707653 + 1.22569i 0.258073 + 0.966126i $$0.416913\pi$$
−0.965726 + 0.259565i $$0.916421\pi$$
$$648$$ −4.50000 + 7.79423i −0.176777 + 0.306186i
$$649$$ 0 0
$$650$$ −24.5000 6.06218i −0.960969 0.237778i
$$651$$ 36.0000 6.92820i 1.41095 0.271538i
$$652$$ 1.50000 0.866025i 0.0587445 0.0339162i
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 21.0000 0.821165
$$655$$ −54.0000 + 31.1769i −2.10995 + 1.21818i
$$656$$ −9.00000 + 5.19615i −0.351391 + 0.202876i
$$657$$ −10.5000 + 18.1865i −0.409644 + 0.709524i
$$658$$ −6.00000 + 17.3205i −0.233904 + 0.675224i
$$659$$ −24.0000 13.8564i −0.934907 0.539769i −0.0465470 0.998916i $$-0.514822\pi$$
−0.888360 + 0.459147i $$0.848155\pi$$
$$660$$ −36.0000 −1.40130
$$661$$ −25.0000 + 43.3013i −0.972387 + 1.68422i −0.284087 + 0.958799i $$0.591690\pi$$
−0.688301 + 0.725426i $$0.741643\pi$$
$$662$$ −16.5000 + 9.52628i −0.641291 + 0.370249i
$$663$$ 0 0
$$664$$ 3.46410i 0.134433i
$$665$$ −45.0000 + 8.66025i −1.74503 + 0.335830i
$$666$$ 22.5000 12.9904i 0.871857 0.503367i
$$667$$ 12.0000 + 20.7846i 0.464642 + 0.804783i
$$668$$ 3.00000 1.73205i 0.116073 0.0670151i
$$669$$ 27.7128i 1.07144i
$$670$$ 6.00000 + 10.3923i 0.231800 + 0.401490i
$$671$$ 31.1769i 1.20357i
$$672$$ −1.50000 + 4.33013i −0.0578638 + 0.167038i
$$673$$ −0.500000 0.866025i −0.0192736 0.0333828i 0.856228 0.516599i $$-0.172802\pi$$
−0.875501 + 0.483216i $$0.839469\pi$$
$$674$$ 5.00000 0.192593
$$675$$ 31.5000 18.1865i 1.21244 0.700000i
$$676$$ −0.500000 12.9904i −0.0192308 0.499630i
$$677$$ −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i $$-0.945759\pi$$
0.639618 + 0.768693i $$0.279092\pi$$
$$678$$ −6.00000 10.3923i −0.230429 0.399114i
$$679$$ 17.5000 + 6.06218i 0.671588 + 0.232645i
$$680$$ 0 0
$$681$$ −9.00000 + 15.5885i −0.344881 + 0.597351i
$$682$$ 48.0000 1.83801
$$683$$ −18.0000 −0.688751 −0.344375 0.938832i $$-0.611909\pi$$
−0.344375 + 0.938832i $$0.611909\pi$$
$$684$$ −7.50000 + 12.9904i −0.286770 + 0.496700i
$$685$$ 18.0000 + 10.3923i 0.687745 + 0.397070i
$$686$$ 10.0000 + 15.5885i 0.381802 + 0.595170i
$$687$$ 43.5000 25.1147i 1.65963 0.958187i
$$688$$ −0.500000 + 0.866025i −0.0190623 + 0.0330169i
$$689$$ 3.00000 12.1244i 0.114291 0.461901i
$$690$$ 18.0000 10.3923i 0.685248 0.395628i
$$691$$ −17.0000 −0.646710 −0.323355 0.946278i $$-0.604811\pi$$
−0.323355 + 0.946278i $$0.604811\pi$$
$$692$$ 3.00000 + 5.19615i 0.114043 + 0.197528i
$$693$$ 9.00000 + 46.7654i 0.341882 + 1.77647i
$$694$$ 0 0
$$695$$ 6.00000 + 10.3923i 0.227593 + 0.394203i
$$696$$ 12.0000 0.454859
$$697$$ 0 0
$$698$$ −5.50000 9.52628i −0.208178 0.360575i
$$699$$ −6.00000 10.3923i −0.226941 0.393073i
$$700$$ 14.0000 12.1244i 0.529150 0.458258i
$$701$$ 13.8564i 0.523349i 0.965156 + 0.261675i $$0.0842747\pi$$
−0.965156 + 0.261675i $$0.915725\pi$$
$$702$$ 13.5000 + 12.9904i 0.509525 + 0.490290i
$$703$$ 37.5000 21.6506i 1.41434 0.816569i
$$704$$ −3.00000 + 5.19615i −0.113067 + 0.195837i
$$705$$ 41.5692i 1.56559i
$$706$$ −9.00000 5.19615i −0.338719 0.195560i
$$707$$ 15.0000 + 5.19615i 0.564133 + 0.195421i
$$708$$ 0 0
$$709$$ −34.5000 + 19.9186i −1.29567 + 0.748058i −0.979654 0.200694i $$-0.935680\pi$$
−0.316021 + 0.948752i $$0.602347\pi$$
$$710$$ 0 0
$$711$$ 24.0000 0.900070
$$712$$ 3.46410i 0.129823i
$$713$$ −24.0000 + 13.8564i −0.898807 + 0.518927i
$$714$$ 0 0
$$715$$ −18.0000 + 72.7461i −0.673162 + 2.72055i
$$716$$ 21.0000 + 12.1244i 0.784807 + 0.453108i
$$717$$ 9.00000 + 5.19615i 0.336111 + 0.194054i
$$718$$ −12.0000 + 20.7846i −0.447836 + 0.775675i
$$719$$ 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i $$0.0223039\pi$$
−0.438141 + 0.898906i $$0.644363\pi$$
$$720$$ 10.3923i 0.387298i
$$721$$ 4.50000 12.9904i 0.167589 0.483787i
$$722$$ −3.00000 + 5.19615i −0.111648 + 0.193381i
$$723$$ −39.0000 22.5167i −1.45043 0.837404i
$$724$$ 15.5885i 0.579340i
$$725$$ −42.0000 24.2487i −1.55984 0.900575i
$$726$$ 43.3013i 1.60706i
$$727$$ 10.3923i 0.385429i −0.981255 0.192715i $$-0.938271\pi$$
0.981255 0.192715i $$-0.0617292\pi$$
$$728$$ 8.00000 + 5.19615i 0.296500 + 0.192582i
$$729$$ −27.0000 −1.00000
$$730$$ 24.2487i 0.897485i
$$731$$ 0 0
$$732$$ −9.00000 −0.332650
$$733$$ 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i $$-0.510222\pi$$
0.881633 0.471935i $$-0.156444\pi$$
$$734$$ 1.50000 + 0.866025i 0.0553660 + 0.0319656i
$$735$$ −33.0000 25.9808i −1.21722 0.958315i
$$736$$ 3.46410i 0.127688i
$$737$$ 18.0000 10.3923i 0.663039 0.382805i
$$738$$ −27.0000 15.5885i −0.993884 0.573819i
$$739$$ −28.5000 16.4545i −1.04839 0.605288i −0.126191 0.992006i $$-0.540275\pi$$
−0.922198 + 0.386718i $$0.873609\pi$$
$$740$$ −15.0000 + 25.9808i −0.551411 + 0.955072i
$$741$$ 22.5000 + 21.6506i 0.826558 + 0.795356i
$$742$$ 6.00000 + 6.92820i 0.220267 + 0.254342i
$$743$$ −15.0000 25.9808i −0.550297 0.953142i −0.998253 0.0590862i $$-0.981181\pi$$
0.447956 0.894055i $$-0.352152\pi$$
$$744$$ 13.8564i 0.508001i
$$745$$ 62.3538i 2.28447i
$$746$$ 1.00000 + 1.73205i 0.0366126 + 0.0634149i
$$747$$ 9.00000 5.19615i 0.329293 0.190117i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −6.00000 + 10.3923i −0.219089 + 0.379473i
$$751$$ −17.0000 −0.620339 −0.310169 0.950681i $$-0.600386\pi$$
−0.310169 + 0.950681i $$0.600386\pi$$
$$752$$ −6.00000 3.46410i −0.218797 0.126323i
$$753$$ −18.0000 + 10.3923i −0.655956 + 0.378717i
$$754$$ 6.00000 24.2487i 0.218507 0.883086i
$$755$$ −12.0000 −0.436725
$$756$$ −13.5000 + 2.59808i −0.490990 + 0.0944911i
$$757$$ −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i $$-0.924028\pi$$
0.281086 0.959683i $$-0.409305\pi$$
$$758$$ −15.0000 + 8.66025i −0.544825 + 0.314555i
$$759$$ −18.0000 31.1769i −0.653359 1.13165i
$$760$$ 17.3205i 0.628281i
$$761$$ 3.00000 1.73205i 0.108750 0.0627868i −0.444639 0.895710i $$-0.646668\pi$$
0.553388 + 0.832923i $$0.313335\pi$$
$$762$$ 1.73205i 0.0627456i
$$763$$ 21.0000 + 24.2487i 0.760251 + 0.877862i
$$764$$ 18.0000 10.3923i 0.651217 0.375980i
$$765$$ 0 0
$$766$$ −18.0000 + 10.3923i −0.650366 + 0.375489i
$$767$$ 0 0
$$768$$ −1.50000 0.866025i −0.0541266 0.0312500i
$$769$$ 0.500000 + 0.866025i 0.0180305 + 0.0312297i 0.874900 0.484304i $$-0.160927\pi$$
−0.856869 + 0.515534i $$0.827594\pi$$
$$770$$ −36.0000 41.5692i −1.29735 1.49805i
$$771$$ −27.0000 15.5885i −0.972381 0.561405i
$$772$$ −4.50000 2.59808i −0.161959 0.0935068i
$$773$$ 41.5692i 1.49514i −0.664183 0.747570i $$-0.731220\pi$$
0.664183 0.747570i $$-0.268780\pi$$
$$774$$ −3.00000 −0.107833
$$775$$ 28.0000 48.4974i 1.00579 1.74208i
$$776$$ −3.50000 + 6.06218i −0.125643 + 0.217620i
\(7