# Properties

 Label 966.2.i.f.415.1 Level $966$ Weight $2$ Character 966.415 Analytic conductor $7.714$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.71354883526$$ 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 415.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 966.415 Dual form 966.2.i.f.277.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +2.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(2.50000 - 0.866025i) q^{21} +3.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(2.50000 - 0.866025i) q^{28} +3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-1.00000 - 1.73205i) q^{39} +6.00000 q^{41} +(0.500000 - 2.59808i) q^{42} +2.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 - 2.59808i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-1.00000 + 1.73205i) q^{61} -2.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 - 2.59808i) q^{68} -1.00000 q^{69} +3.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{75} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} -2.00000 q^{78} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +(-2.00000 - 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-1.00000 + 5.19615i) q^{91} -1.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + O(q^{10})$$ $$2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - q^{7} - 2 q^{8} - q^{9} + 3 q^{11} - q^{12} + 4 q^{13} + 4 q^{14} - q^{16} + 3 q^{17} + q^{18} - 2 q^{19} + 5 q^{21} + 6 q^{22} + q^{23} + q^{24} + 5 q^{25} + 2 q^{26} + 2 q^{27} + 5 q^{28} + 6 q^{29} - 2 q^{31} + q^{32} + 3 q^{33} + 6 q^{34} + 2 q^{36} - 2 q^{37} + 2 q^{38} - 2 q^{39} + 12 q^{41} + q^{42} + 4 q^{43} + 3 q^{44} - q^{46} + 3 q^{47} + 2 q^{48} - 13 q^{49} + 10 q^{50} + 3 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} + q^{56} + 4 q^{57} + 3 q^{58} - 2 q^{61} - 4 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{66} - 2 q^{67} + 3 q^{68} - 2 q^{69} + 6 q^{71} + q^{72} - 11 q^{73} + 2 q^{74} + 5 q^{75} + 4 q^{76} - 15 q^{77} - 4 q^{78} - 11 q^{79} - q^{81} + 6 q^{82} - 4 q^{84} + 2 q^{86} - 3 q^{87} - 3 q^{88} + 6 q^{89} - 2 q^{91} - 2 q^{92} - 2 q^{93} - 3 q^{94} + q^{96} + 16 q^{97} - 11 q^{98} - 6 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$$.

 $$n$$ $$323$$ $$829$$ $$925$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ −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 $$0.683949\pi$$
$$12$$ −0.500000 + 0.866025i −0.144338 + 0.250000i
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 2.00000 + 1.73205i 0.534522 + 0.462910i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i $$-0.0481447\pi$$
−0.624780 + 0.780801i $$0.714811\pi$$
$$18$$ 0.500000 + 0.866025i 0.117851 + 0.204124i
$$19$$ −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
$$21$$ 2.50000 0.866025i 0.545545 0.188982i
$$22$$ 3.00000 0.639602
$$23$$ 0.500000 0.866025i 0.104257 0.180579i
$$24$$ 0.500000 + 0.866025i 0.102062 + 0.176777i
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 1.00000 1.73205i 0.196116 0.339683i
$$27$$ 1.00000 0.192450
$$28$$ 2.50000 0.866025i 0.472456 0.163663i
$$29$$ 3.00000 0.557086 0.278543 0.960424i $$-0.410149\pi$$
0.278543 + 0.960424i $$0.410149\pi$$
$$30$$ 0 0
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 1.50000 2.59808i 0.261116 0.452267i
$$34$$ 3.00000 0.514496
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i $$-0.885902\pi$$
0.772043 + 0.635571i $$0.219235\pi$$
$$38$$ 1.00000 + 1.73205i 0.162221 + 0.280976i
$$39$$ −1.00000 1.73205i −0.160128 0.277350i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0.500000 2.59808i 0.0771517 0.400892i
$$43$$ 2.00000 0.304997 0.152499 0.988304i $$-0.451268\pi$$
0.152499 + 0.988304i $$0.451268\pi$$
$$44$$ 1.50000 2.59808i 0.226134 0.391675i
$$45$$ 0 0
$$46$$ −0.500000 0.866025i −0.0737210 0.127688i
$$47$$ 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i $$-0.763120\pi$$
0.954441 + 0.298401i $$0.0964533\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 5.00000 0.707107
$$51$$ 1.50000 2.59808i 0.210042 0.363803i
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i $$-0.0314685\pi$$
−0.583036 + 0.812447i $$0.698135\pi$$
$$54$$ 0.500000 0.866025i 0.0680414 0.117851i
$$55$$ 0 0
$$56$$ 0.500000 2.59808i 0.0668153 0.347183i
$$57$$ 2.00000 0.264906
$$58$$ 1.50000 2.59808i 0.196960 0.341144i
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ −2.00000 1.73205i −0.251976 0.218218i
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ −1.50000 2.59808i −0.184637 0.319801i
$$67$$ −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i $$-0.205652\pi$$
−0.920623 + 0.390453i $$0.872318\pi$$
$$68$$ 1.50000 2.59808i 0.181902 0.315063i
$$69$$ −1.00000 −0.120386
$$70$$ 0 0
$$71$$ 3.00000 0.356034 0.178017 0.984027i $$-0.443032\pi$$
0.178017 + 0.984027i $$0.443032\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i $$-0.944054\pi$$
0.340868 0.940111i $$-0.389279\pi$$
$$74$$ 1.00000 + 1.73205i 0.116248 + 0.201347i
$$75$$ 2.50000 4.33013i 0.288675 0.500000i
$$76$$ 2.00000 0.229416
$$77$$ −7.50000 + 2.59808i −0.854704 + 0.296078i
$$78$$ −2.00000 −0.226455
$$79$$ −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i $$0.379047\pi$$
−0.989705 + 0.143120i $$0.954286\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 3.00000 5.19615i 0.331295 0.573819i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ −2.00000 1.73205i −0.218218 0.188982i
$$85$$ 0 0
$$86$$ 1.00000 1.73205i 0.107833 0.186772i
$$87$$ −1.50000 2.59808i −0.160817 0.278543i
$$88$$ −1.50000 2.59808i −0.159901 0.276956i
$$89$$ 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i $$-0.730322\pi$$
0.980071 + 0.198650i $$0.0636557\pi$$
$$90$$ 0 0
$$91$$ −1.00000 + 5.19615i −0.104828 + 0.544705i
$$92$$ −1.00000 −0.104257
$$93$$ −1.00000 + 1.73205i −0.103695 + 0.179605i
$$94$$ −1.50000 2.59808i −0.154713 0.267971i
$$95$$ 0 0
$$96$$ 0.500000 0.866025i 0.0510310 0.0883883i
$$97$$ 8.00000 0.812277 0.406138 0.913812i $$-0.366875\pi$$
0.406138 + 0.913812i $$0.366875\pi$$
$$98$$ −5.50000 + 4.33013i −0.555584 + 0.437409i
$$99$$ −3.00000 −0.301511
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i $$-0.118979\pi$$
−0.781697 + 0.623658i $$0.785646\pi$$
$$102$$ −1.50000 2.59808i −0.148522 0.257248i
$$103$$ −2.50000 + 4.33013i −0.246332 + 0.426660i −0.962505 0.271263i $$-0.912559\pi$$
0.716173 + 0.697923i $$0.245892\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i $$0.363630\pi$$
−0.995474 + 0.0950377i $$0.969703\pi$$
$$108$$ −0.500000 0.866025i −0.0481125 0.0833333i
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ −2.00000 1.73205i −0.188982 0.163663i
$$113$$ 18.0000 1.69330 0.846649 0.532152i $$-0.178617\pi$$
0.846649 + 0.532152i $$0.178617\pi$$
$$114$$ 1.00000 1.73205i 0.0936586 0.162221i
$$115$$ 0 0
$$116$$ −1.50000 2.59808i −0.139272 0.241225i
$$117$$ −1.00000 + 1.73205i −0.0924500 + 0.160128i
$$118$$ 0 0
$$119$$ −7.50000 + 2.59808i −0.687524 + 0.238165i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 1.00000 + 1.73205i 0.0905357 + 0.156813i
$$123$$ −3.00000 5.19615i −0.270501 0.468521i
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ 0 0
$$126$$ −2.50000 + 0.866025i −0.222718 + 0.0771517i
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ −1.00000 1.73205i −0.0880451 0.152499i
$$130$$ 0 0
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ −3.00000 −0.261116
$$133$$ −4.00000 3.46410i −0.346844 0.300376i
$$134$$ −2.00000 −0.172774
$$135$$ 0 0
$$136$$ −1.50000 2.59808i −0.128624 0.222783i
$$137$$ 10.5000 + 18.1865i 0.897076 + 1.55378i 0.831215 + 0.555952i $$0.187646\pi$$
0.0658609 + 0.997829i $$0.479021\pi$$
$$138$$ −0.500000 + 0.866025i −0.0425628 + 0.0737210i
$$139$$ −13.0000 −1.10265 −0.551323 0.834292i $$-0.685877\pi$$
−0.551323 + 0.834292i $$0.685877\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 1.50000 2.59808i 0.125877 0.218026i
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ 0 0
$$146$$ −11.0000 −0.910366
$$147$$ 1.00000 + 6.92820i 0.0824786 + 0.571429i
$$148$$ 2.00000 0.164399
$$149$$ −6.00000 + 10.3923i −0.491539 + 0.851371i −0.999953 0.00974235i $$-0.996899\pi$$
0.508413 + 0.861113i $$0.330232\pi$$
$$150$$ −2.50000 4.33013i −0.204124 0.353553i
$$151$$ 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i $$-0.114628\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 1.00000 1.73205i 0.0811107 0.140488i
$$153$$ −3.00000 −0.242536
$$154$$ −1.50000 + 7.79423i −0.120873 + 0.628077i
$$155$$ 0 0
$$156$$ −1.00000 + 1.73205i −0.0800641 + 0.138675i
$$157$$ −11.5000 19.9186i −0.917800 1.58968i −0.802749 0.596316i $$-0.796630\pi$$
−0.115050 0.993360i $$-0.536703\pi$$
$$158$$ 5.50000 + 9.52628i 0.437557 + 0.757870i
$$159$$ 3.00000 5.19615i 0.237915 0.412082i
$$160$$ 0 0
$$161$$ 2.00000 + 1.73205i 0.157622 + 0.136505i
$$162$$ −1.00000 −0.0785674
$$163$$ −11.5000 + 19.9186i −0.900750 + 1.56014i −0.0742262 + 0.997241i $$0.523649\pi$$
−0.826523 + 0.562902i $$0.809685\pi$$
$$164$$ −3.00000 5.19615i −0.234261 0.405751i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ −2.50000 + 0.866025i −0.192879 + 0.0668153i
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −1.00000 1.73205i −0.0764719 0.132453i
$$172$$ −1.00000 1.73205i −0.0762493 0.132068i
$$173$$ 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i $$-0.640193\pi$$
0.996544 0.0830722i $$-0.0264732\pi$$
$$174$$ −3.00000 −0.227429
$$175$$ −12.5000 + 4.33013i −0.944911 + 0.327327i
$$176$$ −3.00000 −0.226134
$$177$$ 0 0
$$178$$ −3.00000 5.19615i −0.224860 0.389468i
$$179$$ −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i $$-0.238654\pi$$
−0.956088 + 0.293079i $$0.905320\pi$$
$$180$$ 0 0
$$181$$ 11.0000 0.817624 0.408812 0.912619i $$-0.365943\pi$$
0.408812 + 0.912619i $$0.365943\pi$$
$$182$$ 4.00000 + 3.46410i 0.296500 + 0.256776i
$$183$$ 2.00000 0.147844
$$184$$ −0.500000 + 0.866025i −0.0368605 + 0.0638442i
$$185$$ 0 0
$$186$$ 1.00000 + 1.73205i 0.0733236 + 0.127000i
$$187$$ −4.50000 + 7.79423i −0.329073 + 0.569970i
$$188$$ −3.00000 −0.218797
$$189$$ −0.500000 + 2.59808i −0.0363696 + 0.188982i
$$190$$ 0 0
$$191$$ −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i $$-0.976283\pi$$
0.563081 + 0.826402i $$0.309616\pi$$
$$192$$ −0.500000 0.866025i −0.0360844 0.0625000i
$$193$$ −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i $$-0.998575\pi$$
0.496119 0.868255i $$-0.334758\pi$$
$$194$$ 4.00000 6.92820i 0.287183 0.497416i
$$195$$ 0 0
$$196$$ 1.00000 + 6.92820i 0.0714286 + 0.494872i
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ −1.50000 + 2.59808i −0.106600 + 0.184637i
$$199$$ −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i $$-0.960818\pi$$
0.389885 0.920864i $$-0.372515\pi$$
$$200$$ −2.50000 4.33013i −0.176777 0.306186i
$$201$$ −1.00000 + 1.73205i −0.0705346 + 0.122169i
$$202$$ 3.00000 0.211079
$$203$$ −1.50000 + 7.79423i −0.105279 + 0.547048i
$$204$$ −3.00000 −0.210042
$$205$$ 0 0
$$206$$ 2.50000 + 4.33013i 0.174183 + 0.301694i
$$207$$ 0.500000 + 0.866025i 0.0347524 + 0.0601929i
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ −6.00000 −0.415029
$$210$$ 0 0
$$211$$ −19.0000 −1.30801 −0.654007 0.756489i $$-0.726913\pi$$
−0.654007 + 0.756489i $$0.726913\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ −1.50000 2.59808i −0.102778 0.178017i
$$214$$ 6.00000 + 10.3923i 0.410152 + 0.710403i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 5.00000 1.73205i 0.339422 0.117579i
$$218$$ 1.00000 0.0677285
$$219$$ −5.50000 + 9.52628i −0.371656 + 0.643726i
$$220$$ 0 0
$$221$$ 3.00000 + 5.19615i 0.201802 + 0.349531i
$$222$$ 1.00000 1.73205i 0.0671156 0.116248i
$$223$$ −10.0000 −0.669650 −0.334825 0.942280i $$-0.608677\pi$$
−0.334825 + 0.942280i $$0.608677\pi$$
$$224$$ −2.50000 + 0.866025i −0.167038 + 0.0578638i
$$225$$ −5.00000 −0.333333
$$226$$ 9.00000 15.5885i 0.598671 1.03693i
$$227$$ 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i $$-0.134924\pi$$
−0.811943 + 0.583736i $$0.801590\pi$$
$$228$$ −1.00000 1.73205i −0.0662266 0.114708i
$$229$$ 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i $$-0.822814\pi$$
0.882073 + 0.471113i $$0.156147\pi$$
$$230$$ 0 0
$$231$$ 6.00000 + 5.19615i 0.394771 + 0.341882i
$$232$$ −3.00000 −0.196960
$$233$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$234$$ 1.00000 + 1.73205i 0.0653720 + 0.113228i
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 11.0000 0.714527
$$238$$ −1.50000 + 7.79423i −0.0972306 + 0.505225i
$$239$$ 15.0000 0.970269 0.485135 0.874439i $$-0.338771\pi$$
0.485135 + 0.874439i $$0.338771\pi$$
$$240$$ 0 0
$$241$$ −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i $$-0.187185\pi$$
−0.896435 + 0.443176i $$0.853852\pi$$
$$242$$ −1.00000 1.73205i −0.0642824 0.111340i
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 2.00000 0.128037
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ −2.00000 + 3.46410i −0.127257 + 0.220416i
$$248$$ 1.00000 + 1.73205i 0.0635001 + 0.109985i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3.00000 0.189358 0.0946792 0.995508i $$-0.469817\pi$$
0.0946792 + 0.995508i $$0.469817\pi$$
$$252$$ −0.500000 + 2.59808i −0.0314970 + 0.163663i
$$253$$ 3.00000 0.188608
$$254$$ 1.00000 1.73205i 0.0627456 0.108679i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i $$-0.893253\pi$$
0.757159 + 0.653231i $$0.226587\pi$$
$$258$$ −2.00000 −0.124515
$$259$$ −4.00000 3.46410i −0.248548 0.215249i
$$260$$ 0 0
$$261$$ −1.50000 + 2.59808i −0.0928477 + 0.160817i
$$262$$ 0 0
$$263$$ −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i $$-0.901515\pi$$
0.212565 0.977147i $$-0.431818\pi$$
$$264$$ −1.50000 + 2.59808i −0.0923186 + 0.159901i
$$265$$ 0 0
$$266$$ −5.00000 + 1.73205i −0.306570 + 0.106199i
$$267$$ −6.00000 −0.367194
$$268$$ −1.00000 + 1.73205i −0.0610847 + 0.105802i
$$269$$ −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i $$-0.317844\pi$$
−0.998816 + 0.0486418i $$0.984511\pi$$
$$270$$ 0 0
$$271$$ 11.0000 19.0526i 0.668202 1.15736i −0.310204 0.950670i $$-0.600397\pi$$
0.978406 0.206691i $$-0.0662693\pi$$
$$272$$ −3.00000 −0.181902
$$273$$ 5.00000 1.73205i 0.302614 0.104828i
$$274$$ 21.0000 1.26866
$$275$$ −7.50000 + 12.9904i −0.452267 + 0.783349i
$$276$$ 0.500000 + 0.866025i 0.0300965 + 0.0521286i
$$277$$ −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i $$-0.243925\pi$$
−0.960810 + 0.277207i $$0.910591\pi$$
$$278$$ −6.50000 + 11.2583i −0.389844 + 0.675230i
$$279$$ 2.00000 0.119737
$$280$$ 0 0
$$281$$ −3.00000 −0.178965 −0.0894825 0.995988i $$-0.528521\pi$$
−0.0894825 + 0.995988i $$0.528521\pi$$
$$282$$ −1.50000 + 2.59808i −0.0893237 + 0.154713i
$$283$$ −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i $$-0.243085\pi$$
−0.960076 + 0.279741i $$0.909752\pi$$
$$284$$ −1.50000 2.59808i −0.0890086 0.154167i
$$285$$ 0 0
$$286$$ 6.00000 0.354787
$$287$$ −3.00000 + 15.5885i −0.177084 + 0.920158i
$$288$$ −1.00000 −0.0589256
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 0 0
$$291$$ −4.00000 6.92820i −0.234484 0.406138i
$$292$$ −5.50000 + 9.52628i −0.321863 + 0.557483i
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 6.50000 + 2.59808i 0.379088 + 0.151523i
$$295$$ 0 0
$$296$$ 1.00000 1.73205i 0.0581238 0.100673i
$$297$$ 1.50000 + 2.59808i 0.0870388 + 0.150756i
$$298$$ 6.00000 + 10.3923i 0.347571 + 0.602010i
$$299$$ 1.00000 1.73205i 0.0578315 0.100167i
$$300$$ −5.00000 −0.288675
$$301$$ −1.00000 + 5.19615i −0.0576390 + 0.299501i
$$302$$ 4.00000 0.230174
$$303$$ 1.50000 2.59808i 0.0861727 0.149256i
$$304$$ −1.00000 1.73205i −0.0573539 0.0993399i
$$305$$ 0 0
$$306$$ −1.50000 + 2.59808i −0.0857493 + 0.148522i
$$307$$ 11.0000 0.627803 0.313902 0.949456i $$-0.398364\pi$$
0.313902 + 0.949456i $$0.398364\pi$$
$$308$$ 6.00000 + 5.19615i 0.341882 + 0.296078i
$$309$$ 5.00000 0.284440
$$310$$ 0 0
$$311$$ 1.50000 + 2.59808i 0.0850572 + 0.147323i 0.905416 0.424526i $$-0.139559\pi$$
−0.820358 + 0.571850i $$0.806226\pi$$
$$312$$ 1.00000 + 1.73205i 0.0566139 + 0.0980581i
$$313$$ −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i $$-0.905929\pi$$
0.730554 + 0.682855i $$0.239262\pi$$
$$314$$ −23.0000 −1.29797
$$315$$ 0 0
$$316$$ 11.0000 0.618798
$$317$$ 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i $$-0.664645\pi$$
0.999980 0.00635137i $$-0.00202172\pi$$
$$318$$ −3.00000 5.19615i −0.168232 0.291386i
$$319$$ 4.50000 + 7.79423i 0.251952 + 0.436393i
$$320$$ 0 0
$$321$$ 12.0000 0.669775
$$322$$ 2.50000 0.866025i 0.139320 0.0482617i
$$323$$ −6.00000 −0.333849
$$324$$ −0.500000 + 0.866025i −0.0277778 + 0.0481125i
$$325$$ 5.00000 + 8.66025i 0.277350 + 0.480384i
$$326$$ 11.5000 + 19.9186i 0.636926 + 1.10319i
$$327$$ 0.500000 0.866025i 0.0276501 0.0478913i
$$328$$ −6.00000 −0.331295
$$329$$ 6.00000 + 5.19615i 0.330791 + 0.286473i
$$330$$ 0 0
$$331$$ −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i $$-0.903893\pi$$
0.734905 + 0.678170i $$0.237227\pi$$
$$332$$ 0 0
$$333$$ −1.00000 1.73205i −0.0547997 0.0949158i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ −0.500000 + 2.59808i −0.0272772 + 0.141737i
$$337$$ 14.0000 0.762629 0.381314 0.924445i $$-0.375472\pi$$
0.381314 + 0.924445i $$0.375472\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ −9.00000 15.5885i −0.488813 0.846649i
$$340$$ 0 0
$$341$$ 3.00000 5.19615i 0.162459 0.281387i
$$342$$ −2.00000 −0.108148
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ −2.00000 −0.107833
$$345$$ 0 0
$$346$$ −7.50000 12.9904i −0.403202 0.698367i
$$347$$ −3.00000 5.19615i −0.161048 0.278944i 0.774197 0.632945i $$-0.218154\pi$$
−0.935245 + 0.354001i $$0.884821\pi$$
$$348$$ −1.50000 + 2.59808i −0.0804084 + 0.139272i
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ −2.50000 + 12.9904i −0.133631 + 0.694365i
$$351$$ 2.00000 0.106752
$$352$$ −1.50000 + 2.59808i −0.0799503 + 0.138478i
$$353$$ 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i $$-0.00765819\pi$$
−0.520689 + 0.853746i $$0.674325\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −6.00000 −0.317999
$$357$$ 6.00000 + 5.19615i 0.317554 + 0.275010i
$$358$$ −6.00000 −0.317110
$$359$$ 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i $$-0.730769\pi$$
0.979791 + 0.200026i $$0.0641026\pi$$
$$360$$ 0 0
$$361$$ 7.50000 + 12.9904i 0.394737 + 0.683704i
$$362$$ 5.50000 9.52628i 0.289074 0.500690i
$$363$$ −2.00000 −0.104973
$$364$$ 5.00000 1.73205i 0.262071 0.0907841i
$$365$$ 0 0
$$366$$ 1.00000 1.73205i 0.0522708 0.0905357i
$$367$$ −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i $$-0.233622\pi$$
−0.951336 + 0.308155i $$0.900289\pi$$
$$368$$ 0.500000 + 0.866025i 0.0260643 + 0.0451447i
$$369$$ −3.00000 + 5.19615i −0.156174 + 0.270501i
$$370$$ 0 0
$$371$$ −15.0000 + 5.19615i −0.778761 + 0.269771i
$$372$$ 2.00000 0.103695
$$373$$ 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i $$-0.724071\pi$$
0.983783 + 0.179364i $$0.0574041\pi$$
$$374$$ 4.50000 + 7.79423i 0.232689 + 0.403030i
$$375$$ 0 0
$$376$$ −1.50000 + 2.59808i −0.0773566 + 0.133986i
$$377$$ 6.00000 0.309016
$$378$$ 2.00000 + 1.73205i 0.102869 + 0.0890871i
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ 0 0
$$381$$ −1.00000 1.73205i −0.0512316 0.0887357i
$$382$$ 6.00000 + 10.3923i 0.306987 + 0.531717i
$$383$$ 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i $$-0.784346\pi$$
0.932436 + 0.361335i $$0.117679\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −14.0000 −0.712581
$$387$$ −1.00000 + 1.73205i −0.0508329 + 0.0880451i
$$388$$ −4.00000 6.92820i −0.203069 0.351726i
$$389$$ −12.0000 20.7846i −0.608424 1.05382i −0.991500 0.130105i $$-0.958469\pi$$
0.383076 0.923717i $$-0.374865\pi$$
$$390$$ 0 0
$$391$$ 3.00000 0.151717
$$392$$ 6.50000 + 2.59808i 0.328300 + 0.131223i
$$393$$ 0 0
$$394$$ 7.50000 12.9904i 0.377845 0.654446i
$$395$$ 0 0
$$396$$ 1.50000 + 2.59808i 0.0753778 + 0.130558i
$$397$$ 17.0000 29.4449i 0.853206 1.47780i −0.0250943 0.999685i $$-0.507989\pi$$
0.878300 0.478110i $$-0.158678\pi$$
$$398$$ −17.0000 −0.852133
$$399$$ −1.00000 + 5.19615i −0.0500626 + 0.260133i
$$400$$ −5.00000 −0.250000
$$401$$ 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i $$-0.711137\pi$$
0.990257 + 0.139253i $$0.0444700\pi$$
$$402$$ 1.00000 + 1.73205i 0.0498755 + 0.0863868i
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ 1.50000 2.59808i 0.0746278 0.129259i
$$405$$ 0 0
$$406$$ 6.00000 + 5.19615i 0.297775 + 0.257881i
$$407$$ −6.00000 −0.297409
$$408$$ −1.50000 + 2.59808i −0.0742611 + 0.128624i
$$409$$ −14.5000 25.1147i −0.716979 1.24184i −0.962191 0.272374i $$-0.912191\pi$$
0.245212 0.969469i $$-0.421142\pi$$
$$410$$ 0 0
$$411$$ 10.5000 18.1865i 0.517927 0.897076i
$$412$$ 5.00000 0.246332
$$413$$ 0 0
$$414$$ 1.00000 0.0491473
$$415$$ 0 0
$$416$$ 1.00000 + 1.73205i 0.0490290 + 0.0849208i
$$417$$ 6.50000 + 11.2583i 0.318306 + 0.551323i
$$418$$ −3.00000 + 5.19615i −0.146735 + 0.254152i
$$419$$ −21.0000 −1.02592 −0.512959 0.858413i $$-0.671451\pi$$
−0.512959 + 0.858413i $$0.671451\pi$$
$$420$$ 0 0
$$421$$ 17.0000 0.828529 0.414265 0.910156i $$-0.364039\pi$$
0.414265 + 0.910156i $$0.364039\pi$$
$$422$$ −9.50000 + 16.4545i −0.462453 + 0.800992i
$$423$$ 1.50000 + 2.59808i 0.0729325 + 0.126323i
$$424$$ −3.00000 5.19615i −0.145693 0.252347i
$$425$$ −7.50000 + 12.9904i −0.363803 + 0.630126i
$$426$$ −3.00000 −0.145350
$$427$$ −4.00000 3.46410i −0.193574 0.167640i
$$428$$ 12.0000 0.580042
$$429$$ 3.00000 5.19615i 0.144841 0.250873i
$$430$$ 0 0
$$431$$ −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i $$-0.909648\pi$$
0.237460 0.971397i $$-0.423685\pi$$
$$432$$ −0.500000 + 0.866025i −0.0240563 + 0.0416667i
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 1.00000 5.19615i 0.0480015 0.249423i
$$435$$ 0 0
$$436$$ 0.500000 0.866025i 0.0239457 0.0414751i
$$437$$ 1.00000 + 1.73205i 0.0478365 + 0.0828552i
$$438$$ 5.50000 + 9.52628i 0.262800 + 0.455183i
$$439$$ −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i $$-0.894477\pi$$
0.754642 + 0.656136i $$0.227810\pi$$
$$440$$ 0 0
$$441$$ 5.50000 4.33013i 0.261905 0.206197i
$$442$$ 6.00000 0.285391
$$443$$ 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i $$-0.640223\pi$$
0.996551 0.0829786i $$-0.0264433\pi$$
$$444$$ −1.00000 1.73205i −0.0474579 0.0821995i
$$445$$ 0 0
$$446$$ −5.00000 + 8.66025i −0.236757 + 0.410075i
$$447$$ 12.0000 0.567581
$$448$$ −0.500000 + 2.59808i −0.0236228 + 0.122748i
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ −2.50000 + 4.33013i −0.117851 + 0.204124i
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ −9.00000 15.5885i −0.423324 0.733219i
$$453$$ 2.00000 3.46410i 0.0939682 0.162758i
$$454$$ 3.00000 0.140797
$$455$$ 0 0
$$456$$ −2.00000 −0.0936586
$$457$$ −10.0000 + 17.3205i −0.467780 + 0.810219i −0.999322 0.0368128i $$-0.988279\pi$$
0.531542 + 0.847032i $$0.321613\pi$$
$$458$$ −0.500000 0.866025i −0.0233635 0.0404667i
$$459$$ 1.50000 + 2.59808i 0.0700140 + 0.121268i
$$460$$ 0 0
$$461$$ −30.0000 −1.39724 −0.698620 0.715493i $$-0.746202\pi$$
−0.698620 + 0.715493i $$0.746202\pi$$
$$462$$ 7.50000 2.59808i 0.348932 0.120873i
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ −1.50000 + 2.59808i −0.0696358 + 0.120613i
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 10.5000 18.1865i 0.485882 0.841572i −0.513986 0.857798i $$-0.671832\pi$$
0.999868 + 0.0162260i $$0.00516512\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ 5.00000 1.73205i 0.230879 0.0799787i
$$470$$ 0 0
$$471$$ −11.5000 + 19.9186i −0.529892 + 0.917800i
$$472$$ 0 0
$$473$$ 3.00000 + 5.19615i 0.137940 + 0.238919i
$$474$$ 5.50000 9.52628i 0.252623 0.437557i
$$475$$ −10.0000 −0.458831
$$476$$ 6.00000 + 5.19615i 0.275010 + 0.238165i
$$477$$ −6.00000 −0.274721
$$478$$ 7.50000 12.9904i 0.343042 0.594166i
$$479$$ −15.0000 25.9808i −0.685367 1.18709i −0.973321 0.229447i $$-0.926308\pi$$
0.287954 0.957644i $$-0.407025\pi$$
$$480$$ 0 0
$$481$$ −2.00000 + 3.46410i −0.0911922 + 0.157949i
$$482$$ −2.00000 −0.0910975
$$483$$ 0.500000 2.59808i 0.0227508 0.118217i
$$484$$ −2.00000 −0.0909091
$$485$$ 0 0
$$486$$ 0.500000 + 0.866025i 0.0226805 + 0.0392837i
$$487$$ −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i $$-0.181096\pi$$
−0.887793 + 0.460243i $$0.847762\pi$$
$$488$$ 1.00000 1.73205i 0.0452679 0.0784063i
$$489$$ 23.0000 1.04010
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ −3.00000 + 5.19615i −0.135250 + 0.234261i
$$493$$ 4.50000 + 7.79423i 0.202670 + 0.351034i
$$494$$ 2.00000 + 3.46410i 0.0899843 + 0.155857i
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ −1.50000 + 7.79423i −0.0672842 + 0.349619i
$$498$$ 0 0
$$499$$ −17.5000 + 30.3109i −0.783408 + 1.35690i 0.146538 + 0.989205i $$0.453187\pi$$
−0.929946 + 0.367697i $$0.880146\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 1.50000 2.59808i 0.0669483 0.115958i
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 2.00000 + 1.73205i 0.0890871 + 0.0771517i
$$505$$ 0 0
$$506$$ 1.50000 2.59808i 0.0666831 0.115499i
$$507$$ 4.50000 + 7.79423i 0.199852 + 0.346154i
$$508$$ −1.00000 1.73205i −0.0443678 0.0768473i
$$509$$ 10.5000 18.1865i 0.465404 0.806104i −0.533815 0.845601i $$-0.679242\pi$$
0.999220 + 0.0394971i $$0.0125756\pi$$
$$510$$ 0 0
$$511$$ 27.5000 9.52628i 1.21653 0.421418i
$$512$$ −1.00000 −0.0441942
$$513$$ −1.00000 + 1.73205i −0.0441511 + 0.0764719i
$$514$$ 3.00000 + 5.19615i 0.132324 + 0.229192i
$$515$$ 0 0
$$516$$ −1.00000 + 1.73205i −0.0440225 + 0.0762493i
$$517$$ 9.00000 0.395820
$$518$$ −5.00000 + 1.73205i −0.219687 + 0.0761019i
$$519$$ −15.0000 −0.658427
$$520$$ 0 0
$$521$$ 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i $$0.205167\pi$$
0.120656 + 0.992694i $$0.461500\pi$$
$$522$$ 1.50000 + 2.59808i 0.0656532 + 0.113715i
$$523$$ 11.0000 19.0526i 0.480996 0.833110i −0.518766 0.854916i $$-0.673608\pi$$
0.999762 + 0.0218062i $$0.00694167\pi$$
$$524$$ 0 0
$$525$$ 10.0000 + 8.66025i 0.436436 + 0.377964i
$$526$$ −24.0000 −1.04645
$$527$$ 3.00000 5.19615i 0.130682 0.226348i
$$528$$ 1.50000 + 2.59808i 0.0652791 + 0.113067i
$$529$$ −0.500000 0.866025i −0.0217391 0.0376533i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −1.00000 + 5.19615i −0.0433555 + 0.225282i
$$533$$ 12.0000 0.519778
$$534$$ −3.00000 + 5.19615i −0.129823 + 0.224860i
$$535$$ 0 0
$$536$$ 1.00000 + 1.73205i 0.0431934 + 0.0748132i
$$537$$ −3.00000 + 5.19615i −0.129460 + 0.224231i
$$538$$ −15.0000 −0.646696
$$539$$ −3.00000 20.7846i −0.129219 0.895257i
$$540$$ 0 0
$$541$$ −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i $$-0.974796\pi$$
0.566933 + 0.823764i $$0.308130\pi$$
$$542$$ −11.0000 19.0526i −0.472490 0.818377i
$$543$$ −5.50000 9.52628i −0.236028 0.408812i
$$544$$ −1.50000 + 2.59808i −0.0643120 + 0.111392i
$$545$$ 0 0
$$546$$ 1.00000 5.19615i 0.0427960 0.222375i
$$547$$ 17.0000 0.726868 0.363434 0.931620i $$-0.381604\pi$$
0.363434 + 0.931620i $$0.381604\pi$$
$$548$$ 10.5000 18.1865i 0.448538 0.776890i
$$549$$ −1.00000 1.73205i −0.0426790 0.0739221i
$$550$$ 7.50000 + 12.9904i 0.319801 + 0.553912i
$$551$$ −3.00000 + 5.19615i −0.127804 + 0.221364i
$$552$$ 1.00000 0.0425628
$$553$$ −22.0000 19.0526i −0.935535 0.810197i
$$554$$ −8.00000 −0.339887
$$555$$ 0 0
$$556$$ 6.50000 + 11.2583i 0.275661 + 0.477460i
$$557$$ −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i $$-0.947432\pi$$
0.350824 0.936442i $$-0.385902\pi$$
$$558$$ 1.00000 1.73205i 0.0423334 0.0733236i
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 9.00000 0.379980
$$562$$ −1.50000 + 2.59808i −0.0632737 + 0.109593i
$$563$$ 4.50000 + 7.79423i 0.189652 + 0.328488i 0.945134 0.326682i $$-0.105931\pi$$
−0.755482 + 0.655169i $$0.772597\pi$$
$$564$$ 1.50000 + 2.59808i 0.0631614 + 0.109399i
$$565$$ 0 0
$$566$$ −8.00000 −0.336265
$$567$$ 2.50000 0.866025i 0.104990 0.0363696i
$$568$$ −3.00000 −0.125877
$$569$$ 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i $$-0.793194\pi$$
0.922032 + 0.387113i $$0.126528\pi$$
$$570$$ 0 0
$$571$$ 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i $$-0.139994\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$572$$ 3.00000 5.19615i 0.125436 0.217262i
$$573$$ 12.0000 0.501307
$$574$$ 12.0000 + 10.3923i 0.500870 + 0.433766i
$$575$$ 5.00000 0.208514
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i $$0.0565899\pi$$
−0.338965 + 0.940799i $$0.610077\pi$$
$$578$$ −4.00000 6.92820i −0.166378 0.288175i
$$579$$ −7.00000 + 12.1244i −0.290910 + 0.503871i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ −8.00000 −0.331611
$$583$$ −9.00000 + 15.5885i −0.372742 + 0.645608i
$$584$$ 5.50000 + 9.52628i 0.227592 + 0.394200i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 5.50000 4.33013i 0.226816 0.178571i
$$589$$ 4.00000 0.164817
$$590$$ 0 0
$$591$$ −7.50000 12.9904i −0.308509 0.534353i
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ 21.0000 36.3731i 0.862367 1.49366i −0.00727173 0.999974i $$-0.502315\pi$$
0.869638 0.493689i $$-0.164352\pi$$
$$594$$ 3.00000 0.123091
$$595$$ 0 0
$$596$$ 12.0000 0.491539
$$597$$ −8.50000 + 14.7224i −0.347882 + 0.602549i
$$598$$ −1.00000 1.73205i −0.0408930 0.0708288i
$$599$$ −7.50000 12.9904i −0.306442 0.530773i 0.671140 0.741331i $$-0.265805\pi$$
−0.977581 + 0.210558i $$0.932472\pi$$
$$600$$ −2.50000 + 4.33013i −0.102062 + 0.176777i
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 4.00000 + 3.46410i 0.163028 + 0.141186i
$$603$$ 2.00000 0.0814463
$$604$$ 2.00000 3.46410i 0.0813788 0.140952i
$$605$$ 0 0
$$606$$ −1.50000 2.59808i −0.0609333 0.105540i
$$607$$ −7.00000 + 12.1244i −0.284121 + 0.492112i −0.972396 0.233338i $$-0.925035\pi$$
0.688274 + 0.725450i $$0.258368\pi$$
$$608$$ −2.00000 −0.0811107
$$609$$ 7.50000 2.59808i 0.303915 0.105279i
$$610$$ 0 0
$$611$$ 3.00000 5.19615i 0.121367 0.210214i
$$612$$ 1.50000 + 2.59808i 0.0606339 + 0.105021i
$$613$$ −2.50000 4.33013i −0.100974 0.174892i 0.811112 0.584891i $$-0.198863\pi$$
−0.912086 + 0.409998i $$0.865529\pi$$
$$614$$ 5.50000 9.52628i 0.221962 0.384449i
$$615$$ 0 0
$$616$$ 7.50000 2.59808i 0.302184 0.104679i
$$617$$ 33.0000 1.32853 0.664265 0.747497i $$-0.268745\pi$$
0.664265 + 0.747497i $$0.268745\pi$$
$$618$$ 2.50000 4.33013i 0.100565 0.174183i
$$619$$ −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i $$-0.944317\pi$$
0.341644 0.939829i $$-0.389016\pi$$
$$620$$ 0 0
$$621$$ 0.500000 0.866025i 0.0200643 0.0347524i
$$622$$ 3.00000 0.120289
$$623$$ 12.0000 + 10.3923i 0.480770 + 0.416359i
$$624$$ 2.00000 0.0800641
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 4.00000 + 6.92820i 0.159872 + 0.276907i
$$627$$ 3.00000 + 5.19615i 0.119808 + 0.207514i
$$628$$ −11.5000 + 19.9186i −0.458900 + 0.794838i
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ 5.50000 9.52628i 0.218778 0.378935i
$$633$$ 9.50000 + 16.4545i 0.377591 + 0.654007i
$$634$$ −9.00000 15.5885i −0.357436 0.619097i
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ −13.0000 5.19615i −0.515079 0.205879i
$$638$$ 9.00000 0.356313
$$639$$ −1.50000 + 2.59808i −0.0593391 + 0.102778i
$$640$$ 0 0
$$641$$ 1.50000 + 2.59808i 0.0592464 + 0.102618i 0.894127 0.447813i $$-0.147797\pi$$
−0.834881 + 0.550431i $$0.814464\pi$$
$$642$$ 6.00000 10.3923i 0.236801 0.410152i
$$643$$ −28.0000 −1.10421 −0.552106 0.833774i $$-0.686176\pi$$
−0.552106 + 0.833774i $$0.686176\pi$$
$$644$$ 0.500000 2.59808i 0.0197028 0.102379i
$$645$$ 0 0
$$646$$ −3.00000 + 5.19615i −0.118033 + 0.204440i
$$647$$ 7.50000 + 12.9904i 0.294855 + 0.510705i 0.974951 0.222419i $$-0.0713952\pi$$
−0.680096 + 0.733123i $$0.738062\pi$$
$$648$$ 0.500000 + 0.866025i 0.0196419 + 0.0340207i
$$649$$ 0 0
$$650$$ 10.0000 0.392232
$$651$$ −4.00000 3.46410i −0.156772 0.135769i
$$652$$ 23.0000 0.900750
$$653$$ −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i $$-0.852029\pi$$
0.835182 + 0.549973i $$0.185362\pi$$
$$654$$ −0.500000 0.866025i −0.0195515 0.0338643i
$$655$$ 0 0
$$656$$ −3.00000 + 5.19615i −0.117130 + 0.202876i
$$657$$ 11.0000 0.429151
$$658$$ 7.50000 2.59808i 0.292380 0.101284i
$$659$$ 3.00000 0.116863 0.0584317 0.998291i $$-0.481390\pi$$
0.0584317 + 0.998291i $$0.481390\pi$$
$$660$$ 0 0
$$661$$ −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i $$-0.197668\pi$$
−0.910541 + 0.413419i $$0.864334\pi$$
$$662$$ 4.00000 + 6.92820i 0.155464 + 0.269272i
$$663$$ 3.00000 5.19615i 0.116510 0.201802i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ 1.50000 2.59808i 0.0580802 0.100598i
$$668$$ 0 0
$$669$$ 5.00000 + 8.66025i 0.193311 + 0.334825i
$$670$$ 0 0
$$671$$ −6.00000 −0.231627
$$672$$ 2.00000 + 1.73205i 0.0771517 + 0.0668153i
$$673$$ −19.0000 −0.732396 −0.366198 0.930537i $$-0.619341\pi$$
−0.366198 + 0.930537i $$0.619341\pi$$
$$674$$ 7.00000 12.1244i 0.269630 0.467013i
$$675$$ 2.50000 + 4.33013i 0.0962250 + 0.166667i
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i $$-0.720908\pi$$
0.985517 + 0.169580i $$0.0542410\pi$$
$$678$$ −18.0000 −0.691286
$$679$$ −4.00000 + 20.7846i −0.153506 + 0.797640i
$$680$$ 0 0
$$681$$ 1.50000 2.59808i 0.0574801 0.0995585i
$$682$$ −3.00000 5.19615i −0.114876 0.198971i
$$683$$ −24.0000 41.5692i −0.918334 1.59060i −0.801945 0.597398i $$-0.796201\pi$$
−0.116390 0.993204i $$-0.537132\pi$$
$$684$$ −1.00000 + 1.73205i −0.0382360 + 0.0662266i
$$685$$ 0 0
$$686$$ −8.50000 16.4545i −0.324532 0.628235i
$$687$$ −1.00000 −0.0381524
$$688$$ −1.00000 + 1.73205i −0.0381246 + 0.0660338i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i $$-0.938144\pi$$
0.657823 + 0.753173i $$0.271478\pi$$
$$692$$ −15.0000 −0.570214
$$693$$ 1.50000 7.79423i 0.0569803 0.296078i
$$694$$ −6.00000 −0.227757
$$695$$ 0 0
$$696$$ 1.50000 + 2.59808i 0.0568574 + 0.0984798i
$$697$$ 9.00000 + 15.5885i 0.340899 + 0.590455i
$$698$$ −11.0000 + 19.0526i −0.416356 + 0.721150i
$$699$$ 0 0
$$700$$ 10.0000 + 8.66025i 0.377964 + 0.327327i
$$701$$ −42.0000 −1.58632 −0.793159 0.609015i $$-0.791565\pi$$
−0.793159 + 0.609015i $$0.791565\pi$$
$$702$$ 1.00000 1.73205i 0.0377426 0.0653720i
$$703$$ −2.00000 3.46410i −0.0754314 0.130651i
$$704$$ 1.50000 + 2.59808i 0.0565334 + 0.0979187i
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ −7.50000 + 2.59808i −0.282067 + 0.0977107i
$$708$$ 0 0
$$709$$ 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i $$-0.635559\pi$$
0.995228 0.0975728i $$-0.0311079\pi$$
$$710$$ 0 0
$$711$$ −5.50000 9.52628i −0.206266 0.357263i
$$712$$ −3.00000 + 5.19615i −0.112430 + 0.194734i
$$713$$ −2.00000 −0.0749006
$$714$$ 7.50000 2.59808i 0.280680 0.0972306i
$$715$$ 0 0
$$716$$ −3.00000 + 5.19615i −0.112115 + 0.194189i
$$717$$ −7.50000 12.9904i −0.280093 0.485135i
$$718$$ −6.00000 10.3923i −0.223918 0.387837i
$$719$$ 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i $$-0.480474\pi$$
0.833744 0.552151i $$-0.186193\pi$$
$$720$$ 0 0
$$721$$ −10.0000 8.66025i −0.372419 0.322525i
$$722$$ 15.0000 0.558242
$$723$$ −1.00000 + 1.73205i −0.0371904 + 0.0644157i
$$724$$ −5.50000 9.52628i −0.204406 0.354041i
$$725$$ 7.50000 + 12.9904i 0.278543 + 0.482451i
$$726$$ −1.00000 + 1.73205i −0.0371135 + 0.0642824i
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 1.00000 5.19615i 0.0370625 0.192582i
$$729$$ 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
$$733$$ −20.5000 + 35.5070i −0.757185 + 1.31148i 0.187096 + 0.982342i $$0.440092\pi$$
−0.944281 + 0.329141i $$0.893241\pi$$
$$734$$ −8.00000 −0.295285
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ 3.00000 5.19615i 0.110506 0.191403i
$$738$$ 3.00000 + 5.19615i 0.110432 + 0.191273i
$$739$$ 12.5000 + 21.6506i 0.459820 + 0.796431i 0.998951 0.0457903i $$-0.0145806\pi$$
−0.539131 + 0.842222i $$0.681247\pi$$
$$740$$ 0 0
$$741$$ 4.00000 0.146944
$$742$$ −3.00000 + 15.5885i −0.110133 + 0.572270i
$$743$$ −12.0000 −0.440237 −0.220119 0.975473i $$-0.570644\pi$$
−0.220119 + 0.975473i $$0.570644\pi$$
$$744$$ 1.00000 1.73205i 0.0366618 0.0635001i
$$745$$ 0 0
$$746$$ −6.50000 11.2583i −0.237982 0.412197i
$$747$$ 0 0
$$748$$ 9.00000 0.329073
$$749$$ −24.0000 20.7846i −0.876941 0.759453i
$$750$$ 0 0
$$751$$ −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i $$0.365120\pi$$
−0.995018 + 0.0996961i $$0.968213\pi$$
$$752$$ 1.50000 + 2.59808i 0.0546994 + 0.0947421i
$$753$$ −1.50000 2.59808i −0.0546630 0.0946792i
$$754$$ 3.00000 5.19615i 0.109254 0.189233i
$$755$$ 0 0
$$756$$ 2.50000 0.866025i 0.0909241 0.0314970i
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 10.0000 17.3205i 0.363216 0.629109i
$$759$$ −1.50000 2.59808i −0.0544466 0.0943042i
$$760$$ 0 0
$$761$$ −24.0000 + 41.5692i −0.869999 + 1.50688i −0.00800331 + 0.999968i $$0.502548\pi$$
−0.861996 + 0.506915i $$0.830786\pi$$
$$762$$ −2.00000 −0.0724524
$$763$$ −2.50000 + 0.866025i −0.0905061 + 0.0313522i
$$764$$ 12.0000 0.434145
$$765$$ 0 0
$$766$$ −3.00000 5.19615i −0.108394 0.187745i
$$767$$ 0 0
$$768$$ −0.500000 + 0.866025i −0.0180422 + 0.0312500i
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ −7.00000 + 12.1244i −0.251936 + 0.436365i
$$773$$ 18.0000 + 31.1769i 0.647415 + 1.12136i 0.983738 + 0.179609i $$0.0574833\pi$$
−0.336323 + 0.941747i $$0.609183\pi$$
$$774$$ 1.00000 + 1.73205i 0.0359443 + 0.0622573i
$$775$$ 5.00000 8.66025i 0.179605 0.311086i
$$776$$ −8.00000 −0.287183
$$777$$ −1.00000 + 5.19615i −0.0358748 + 0.186411i
$$778$$ −24.0000 −0.860442
$$779$$ −6.00000 + 10.3923i −0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 4.50000 + 7.79423i 0.161023 + 0.278899i
$$782$$ 1.50000 2.59808i 0.0536399 0.0929070i
$$783$$ 3.00000 0.107211
$$784$$ 5.50000 4.33013i 0.196429 0.154647i