# Properties

 Label 735.2.i.l.361.2 Level $735$ Weight $2$ Character 735.361 Analytic conductor $5.869$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.86900454856$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.2 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 735.361 Dual form 735.2.i.l.226.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.36603 + 2.36603i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.73205 q^{6} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(1.36603 + 2.36603i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.73205 q^{6} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(-2.73205 - 4.73205i) q^{12} -2.26795 q^{13} -1.00000 q^{15} +(-7.46410 - 12.9282i) q^{16} +(1.63397 - 2.83013i) q^{17} +(1.36603 - 2.36603i) q^{18} +(2.23205 + 3.86603i) q^{19} -5.46410 q^{20} -2.00000 q^{22} +(2.36603 + 4.09808i) q^{23} +(4.73205 - 8.19615i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-3.09808 - 5.36603i) q^{26} +1.00000 q^{27} -4.19615 q^{29} +(-1.36603 - 2.36603i) q^{30} +(-0.232051 + 0.401924i) q^{31} +(10.9282 - 18.9282i) q^{32} +(-0.366025 - 0.633975i) q^{33} +8.92820 q^{34} +5.46410 q^{36} +(1.59808 + 2.76795i) q^{37} +(-6.09808 + 10.5622i) q^{38} +(1.13397 - 1.96410i) q^{39} +(-4.73205 - 8.19615i) q^{40} +0.732051 q^{41} +3.19615 q^{43} +(-2.00000 - 3.46410i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-6.46410 + 11.1962i) q^{46} +(1.00000 + 1.73205i) q^{47} +14.9282 q^{48} -2.73205 q^{50} +(1.63397 + 2.83013i) q^{51} +(6.19615 - 10.7321i) q^{52} +(-6.19615 + 10.7321i) q^{53} +(1.36603 + 2.36603i) q^{54} -0.732051 q^{55} -4.46410 q^{57} +(-5.73205 - 9.92820i) q^{58} +(-0.0980762 + 0.169873i) q^{59} +(2.73205 - 4.73205i) q^{60} +(2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +29.8564 q^{64} +(-1.13397 - 1.96410i) q^{65} +(1.00000 - 1.73205i) q^{66} +(7.33013 - 12.6962i) q^{67} +(8.92820 + 15.4641i) q^{68} -4.73205 q^{69} +6.19615 q^{71} +(4.73205 + 8.19615i) q^{72} +(6.33013 - 10.9641i) q^{73} +(-4.36603 + 7.56218i) q^{74} +(-0.500000 - 0.866025i) q^{75} -24.3923 q^{76} +6.19615 q^{78} +(3.69615 + 6.40192i) q^{79} +(7.46410 - 12.9282i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} -15.1244 q^{83} +3.26795 q^{85} +(4.36603 + 7.56218i) q^{86} +(2.09808 - 3.63397i) q^{87} +(3.46410 - 6.00000i) q^{88} +(7.56218 + 13.0981i) q^{89} +2.73205 q^{90} -25.8564 q^{92} +(-0.232051 - 0.401924i) q^{93} +(-2.73205 + 4.73205i) q^{94} +(-2.23205 + 3.86603i) q^{95} +(10.9282 + 18.9282i) q^{96} -14.9282 q^{97} +0.732051 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 4q^{6} - 24q^{8} - 2q^{9} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{3} - 4q^{4} + 2q^{5} - 4q^{6} - 24q^{8} - 2q^{9} - 2q^{10} + 2q^{11} - 4q^{12} - 16q^{13} - 4q^{15} - 16q^{16} + 10q^{17} + 2q^{18} + 2q^{19} - 8q^{20} - 8q^{22} + 6q^{23} + 12q^{24} - 2q^{25} - 2q^{26} + 4q^{27} + 4q^{29} - 2q^{30} + 6q^{31} + 16q^{32} + 2q^{33} + 8q^{34} + 8q^{36} - 4q^{37} - 14q^{38} + 8q^{39} - 12q^{40} - 4q^{41} - 8q^{43} - 8q^{44} + 2q^{45} - 12q^{46} + 4q^{47} + 32q^{48} - 4q^{50} + 10q^{51} + 4q^{52} - 4q^{53} + 2q^{54} + 4q^{55} - 4q^{57} - 16q^{58} + 10q^{59} + 4q^{60} + 8q^{61} - 12q^{62} + 64q^{64} - 8q^{65} + 4q^{66} + 12q^{67} + 8q^{68} - 12q^{69} + 4q^{71} + 12q^{72} + 8q^{73} - 14q^{74} - 2q^{75} - 56q^{76} + 4q^{78} - 6q^{79} + 16q^{80} - 2q^{81} + 4q^{82} - 12q^{83} + 20q^{85} + 14q^{86} - 2q^{87} + 6q^{89} + 4q^{90} - 48q^{92} + 6q^{93} - 4q^{94} - 2q^{95} + 16q^{96} - 32q^{97} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$$.

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36603 + 2.36603i 0.965926 + 1.67303i 0.707107 + 0.707107i $$0.250000\pi$$
0.258819 + 0.965926i $$0.416667\pi$$
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −2.73205 + 4.73205i −1.36603 + 2.36603i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ −2.73205 −1.11536
$$7$$ 0 0
$$8$$ −9.46410 −3.34607
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −1.36603 + 2.36603i −0.431975 + 0.748203i
$$11$$ −0.366025 + 0.633975i −0.110361 + 0.191151i −0.915916 0.401371i $$-0.868534\pi$$
0.805555 + 0.592521i $$0.201867\pi$$
$$12$$ −2.73205 4.73205i −0.788675 1.36603i
$$13$$ −2.26795 −0.629016 −0.314508 0.949255i $$-0.601840\pi$$
−0.314508 + 0.949255i $$0.601840\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ −7.46410 12.9282i −1.86603 3.23205i
$$17$$ 1.63397 2.83013i 0.396297 0.686407i −0.596969 0.802264i $$-0.703628\pi$$
0.993266 + 0.115858i $$0.0369617\pi$$
$$18$$ 1.36603 2.36603i 0.321975 0.557678i
$$19$$ 2.23205 + 3.86603i 0.512068 + 0.886927i 0.999902 + 0.0139909i $$0.00445360\pi$$
−0.487835 + 0.872936i $$0.662213\pi$$
$$20$$ −5.46410 −1.22181
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ 2.36603 + 4.09808i 0.493350 + 0.854508i 0.999971 0.00766135i $$-0.00243871\pi$$
−0.506620 + 0.862169i $$0.669105\pi$$
$$24$$ 4.73205 8.19615i 0.965926 1.67303i
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ −3.09808 5.36603i −0.607583 1.05236i
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −4.19615 −0.779206 −0.389603 0.920983i $$-0.627388\pi$$
−0.389603 + 0.920983i $$0.627388\pi$$
$$30$$ −1.36603 2.36603i −0.249401 0.431975i
$$31$$ −0.232051 + 0.401924i −0.0416776 + 0.0721876i −0.886112 0.463472i $$-0.846604\pi$$
0.844434 + 0.535659i $$0.179937\pi$$
$$32$$ 10.9282 18.9282i 1.93185 3.34607i
$$33$$ −0.366025 0.633975i −0.0637168 0.110361i
$$34$$ 8.92820 1.53117
$$35$$ 0 0
$$36$$ 5.46410 0.910684
$$37$$ 1.59808 + 2.76795i 0.262722 + 0.455048i 0.966964 0.254912i $$-0.0820464\pi$$
−0.704242 + 0.709960i $$0.748713\pi$$
$$38$$ −6.09808 + 10.5622i −0.989239 + 1.71341i
$$39$$ 1.13397 1.96410i 0.181581 0.314508i
$$40$$ −4.73205 8.19615i −0.748203 1.29593i
$$41$$ 0.732051 0.114327 0.0571636 0.998365i $$-0.481794\pi$$
0.0571636 + 0.998365i $$0.481794\pi$$
$$42$$ 0 0
$$43$$ 3.19615 0.487409 0.243704 0.969850i $$-0.421637\pi$$
0.243704 + 0.969850i $$0.421637\pi$$
$$44$$ −2.00000 3.46410i −0.301511 0.522233i
$$45$$ 0.500000 0.866025i 0.0745356 0.129099i
$$46$$ −6.46410 + 11.1962i −0.953080 + 1.65078i
$$47$$ 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i $$-0.120070\pi$$
−0.783830 + 0.620975i $$0.786737\pi$$
$$48$$ 14.9282 2.15470
$$49$$ 0 0
$$50$$ −2.73205 −0.386370
$$51$$ 1.63397 + 2.83013i 0.228802 + 0.396297i
$$52$$ 6.19615 10.7321i 0.859252 1.48827i
$$53$$ −6.19615 + 10.7321i −0.851107 + 1.47416i 0.0291032 + 0.999576i $$0.490735\pi$$
−0.880210 + 0.474584i $$0.842598\pi$$
$$54$$ 1.36603 + 2.36603i 0.185893 + 0.321975i
$$55$$ −0.732051 −0.0987097
$$56$$ 0 0
$$57$$ −4.46410 −0.591285
$$58$$ −5.73205 9.92820i −0.752655 1.30364i
$$59$$ −0.0980762 + 0.169873i −0.0127684 + 0.0221156i −0.872339 0.488901i $$-0.837398\pi$$
0.859571 + 0.511017i $$0.170731\pi$$
$$60$$ 2.73205 4.73205i 0.352706 0.610905i
$$61$$ 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i $$-0.0842377\pi$$
−0.709113 + 0.705095i $$0.750904\pi$$
$$62$$ −1.26795 −0.161030
$$63$$ 0 0
$$64$$ 29.8564 3.73205
$$65$$ −1.13397 1.96410i −0.140652 0.243617i
$$66$$ 1.00000 1.73205i 0.123091 0.213201i
$$67$$ 7.33013 12.6962i 0.895518 1.55108i 0.0623548 0.998054i $$-0.480139\pi$$
0.833163 0.553028i $$-0.186528\pi$$
$$68$$ 8.92820 + 15.4641i 1.08270 + 1.87530i
$$69$$ −4.73205 −0.569672
$$70$$ 0 0
$$71$$ 6.19615 0.735348 0.367674 0.929955i $$-0.380154\pi$$
0.367674 + 0.929955i $$0.380154\pi$$
$$72$$ 4.73205 + 8.19615i 0.557678 + 0.965926i
$$73$$ 6.33013 10.9641i 0.740885 1.28325i −0.211207 0.977441i $$-0.567740\pi$$
0.952093 0.305810i $$-0.0989271\pi$$
$$74$$ −4.36603 + 7.56218i −0.507540 + 0.879085i
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ −24.3923 −2.79799
$$77$$ 0 0
$$78$$ 6.19615 0.701576
$$79$$ 3.69615 + 6.40192i 0.415850 + 0.720273i 0.995517 0.0945803i $$-0.0301509\pi$$
−0.579668 + 0.814853i $$0.696818\pi$$
$$80$$ 7.46410 12.9282i 0.834512 1.44542i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 1.00000 + 1.73205i 0.110432 + 0.191273i
$$83$$ −15.1244 −1.66011 −0.830057 0.557679i $$-0.811692\pi$$
−0.830057 + 0.557679i $$0.811692\pi$$
$$84$$ 0 0
$$85$$ 3.26795 0.354459
$$86$$ 4.36603 + 7.56218i 0.470801 + 0.815451i
$$87$$ 2.09808 3.63397i 0.224937 0.389603i
$$88$$ 3.46410 6.00000i 0.369274 0.639602i
$$89$$ 7.56218 + 13.0981i 0.801589 + 1.38839i 0.918570 + 0.395259i $$0.129345\pi$$
−0.116980 + 0.993134i $$0.537321\pi$$
$$90$$ 2.73205 0.287983
$$91$$ 0 0
$$92$$ −25.8564 −2.69572
$$93$$ −0.232051 0.401924i −0.0240625 0.0416776i
$$94$$ −2.73205 + 4.73205i −0.281790 + 0.488074i
$$95$$ −2.23205 + 3.86603i −0.229004 + 0.396646i
$$96$$ 10.9282 + 18.9282i 1.11536 + 1.93185i
$$97$$ −14.9282 −1.51573 −0.757865 0.652412i $$-0.773757\pi$$
−0.757865 + 0.652412i $$0.773757\pi$$
$$98$$ 0 0
$$99$$ 0.732051 0.0735739
$$100$$ −2.73205 4.73205i −0.273205 0.473205i
$$101$$ −3.63397 + 6.29423i −0.361594 + 0.626299i −0.988223 0.153018i $$-0.951101\pi$$
0.626629 + 0.779317i $$0.284434\pi$$
$$102$$ −4.46410 + 7.73205i −0.442012 + 0.765587i
$$103$$ −4.59808 7.96410i −0.453062 0.784726i 0.545513 0.838103i $$-0.316335\pi$$
−0.998574 + 0.0533764i $$0.983002\pi$$
$$104$$ 21.4641 2.10473
$$105$$ 0 0
$$106$$ −33.8564 −3.28842
$$107$$ −1.09808 1.90192i −0.106155 0.183866i 0.808054 0.589108i $$-0.200521\pi$$
−0.914210 + 0.405242i $$0.867187\pi$$
$$108$$ −2.73205 + 4.73205i −0.262892 + 0.455342i
$$109$$ −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i $$0.343277\pi$$
−0.999512 + 0.0312328i $$0.990057\pi$$
$$110$$ −1.00000 1.73205i −0.0953463 0.165145i
$$111$$ −3.19615 −0.303365
$$112$$ 0 0
$$113$$ 8.92820 0.839895 0.419947 0.907548i $$-0.362049\pi$$
0.419947 + 0.907548i $$0.362049\pi$$
$$114$$ −6.09808 10.5622i −0.571137 0.989239i
$$115$$ −2.36603 + 4.09808i −0.220633 + 0.382148i
$$116$$ 11.4641 19.8564i 1.06442 1.84362i
$$117$$ 1.13397 + 1.96410i 0.104836 + 0.181581i
$$118$$ −0.535898 −0.0493334
$$119$$ 0 0
$$120$$ 9.46410 0.863950
$$121$$ 5.23205 + 9.06218i 0.475641 + 0.823834i
$$122$$ −5.46410 + 9.46410i −0.494697 + 0.856840i
$$123$$ −0.366025 + 0.633975i −0.0330034 + 0.0571636i
$$124$$ −1.26795 2.19615i −0.113865 0.197220i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 4.80385 0.426273 0.213136 0.977022i $$-0.431632\pi$$
0.213136 + 0.977022i $$0.431632\pi$$
$$128$$ 18.9282 + 32.7846i 1.67303 + 2.89778i
$$129$$ −1.59808 + 2.76795i −0.140703 + 0.243704i
$$130$$ 3.09808 5.36603i 0.271719 0.470632i
$$131$$ 7.73205 + 13.3923i 0.675552 + 1.17009i 0.976307 + 0.216390i $$0.0694281\pi$$
−0.300755 + 0.953702i $$0.597239\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 0 0
$$134$$ 40.0526 3.46001
$$135$$ 0.500000 + 0.866025i 0.0430331 + 0.0745356i
$$136$$ −15.4641 + 26.7846i −1.32604 + 2.29676i
$$137$$ −1.09808 + 1.90192i −0.0938150 + 0.162492i −0.909113 0.416549i $$-0.863240\pi$$
0.815298 + 0.579041i $$0.196573\pi$$
$$138$$ −6.46410 11.1962i −0.550261 0.953080i
$$139$$ −5.92820 −0.502824 −0.251412 0.967880i $$-0.580895\pi$$
−0.251412 + 0.967880i $$0.580895\pi$$
$$140$$ 0 0
$$141$$ −2.00000 −0.168430
$$142$$ 8.46410 + 14.6603i 0.710292 + 1.23026i
$$143$$ 0.830127 1.43782i 0.0694187 0.120237i
$$144$$ −7.46410 + 12.9282i −0.622008 + 1.07735i
$$145$$ −2.09808 3.63397i −0.174236 0.301785i
$$146$$ 34.5885 2.86256
$$147$$ 0 0
$$148$$ −17.4641 −1.43554
$$149$$ −2.92820 5.07180i −0.239888 0.415498i 0.720794 0.693149i $$-0.243777\pi$$
−0.960682 + 0.277651i $$0.910444\pi$$
$$150$$ 1.36603 2.36603i 0.111536 0.193185i
$$151$$ 4.46410 7.73205i 0.363283 0.629225i −0.625216 0.780452i $$-0.714989\pi$$
0.988499 + 0.151227i $$0.0483223\pi$$
$$152$$ −21.1244 36.5885i −1.71341 2.96772i
$$153$$ −3.26795 −0.264198
$$154$$ 0 0
$$155$$ −0.464102 −0.0372775
$$156$$ 6.19615 + 10.7321i 0.496089 + 0.859252i
$$157$$ 3.19615 5.53590i 0.255081 0.441813i −0.709837 0.704366i $$-0.751231\pi$$
0.964917 + 0.262553i $$0.0845646\pi$$
$$158$$ −10.0981 + 17.4904i −0.803360 + 1.39146i
$$159$$ −6.19615 10.7321i −0.491387 0.851107i
$$160$$ 21.8564 1.72790
$$161$$ 0 0
$$162$$ −2.73205 −0.214650
$$163$$ −10.9282 18.9282i −0.855963 1.48257i −0.875749 0.482767i $$-0.839632\pi$$
0.0197859 0.999804i $$-0.493702\pi$$
$$164$$ −2.00000 + 3.46410i −0.156174 + 0.270501i
$$165$$ 0.366025 0.633975i 0.0284950 0.0493549i
$$166$$ −20.6603 35.7846i −1.60355 2.77742i
$$167$$ 17.6603 1.36659 0.683296 0.730142i $$-0.260546\pi$$
0.683296 + 0.730142i $$0.260546\pi$$
$$168$$ 0 0
$$169$$ −7.85641 −0.604339
$$170$$ 4.46410 + 7.73205i 0.342381 + 0.593021i
$$171$$ 2.23205 3.86603i 0.170689 0.295642i
$$172$$ −8.73205 + 15.1244i −0.665813 + 1.15322i
$$173$$ 7.26795 + 12.5885i 0.552572 + 0.957083i 0.998088 + 0.0618087i $$0.0196869\pi$$
−0.445516 + 0.895274i $$0.646980\pi$$
$$174$$ 11.4641 0.869091
$$175$$ 0 0
$$176$$ 10.9282 0.823744
$$177$$ −0.0980762 0.169873i −0.00737186 0.0127684i
$$178$$ −20.6603 + 35.7846i −1.54855 + 2.68217i
$$179$$ 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i $$-0.711416\pi$$
0.990134 + 0.140122i $$0.0447496\pi$$
$$180$$ 2.73205 + 4.73205i 0.203635 + 0.352706i
$$181$$ 24.3205 1.80773 0.903865 0.427819i $$-0.140718\pi$$
0.903865 + 0.427819i $$0.140718\pi$$
$$182$$ 0 0
$$183$$ −4.00000 −0.295689
$$184$$ −22.3923 38.7846i −1.65078 2.85924i
$$185$$ −1.59808 + 2.76795i −0.117493 + 0.203504i
$$186$$ 0.633975 1.09808i 0.0464853 0.0805149i
$$187$$ 1.19615 + 2.07180i 0.0874713 + 0.151505i
$$188$$ −10.9282 −0.797021
$$189$$ 0 0
$$190$$ −12.1962 −0.884802
$$191$$ 4.46410 + 7.73205i 0.323011 + 0.559472i 0.981108 0.193462i $$-0.0619716\pi$$
−0.658097 + 0.752933i $$0.728638\pi$$
$$192$$ −14.9282 + 25.8564i −1.07735 + 1.86603i
$$193$$ −0.598076 + 1.03590i −0.0430505 + 0.0745656i −0.886748 0.462254i $$-0.847041\pi$$
0.843697 + 0.536819i $$0.180374\pi$$
$$194$$ −20.3923 35.3205i −1.46408 2.53586i
$$195$$ 2.26795 0.162411
$$196$$ 0 0
$$197$$ −0.339746 −0.0242059 −0.0121029 0.999927i $$-0.503853\pi$$
−0.0121029 + 0.999927i $$0.503853\pi$$
$$198$$ 1.00000 + 1.73205i 0.0710669 + 0.123091i
$$199$$ 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i $$-0.548670\pi$$
0.932075 0.362267i $$-0.117997\pi$$
$$200$$ 4.73205 8.19615i 0.334607 0.579555i
$$201$$ 7.33013 + 12.6962i 0.517027 + 0.895518i
$$202$$ −19.8564 −1.39709
$$203$$ 0 0
$$204$$ −17.8564 −1.25020
$$205$$ 0.366025 + 0.633975i 0.0255643 + 0.0442787i
$$206$$ 12.5622 21.7583i 0.875248 1.51597i
$$207$$ 2.36603 4.09808i 0.164450 0.284836i
$$208$$ 16.9282 + 29.3205i 1.17376 + 2.03301i
$$209$$ −3.26795 −0.226049
$$210$$ 0 0
$$211$$ 7.07180 0.486843 0.243421 0.969921i $$-0.421730\pi$$
0.243421 + 0.969921i $$0.421730\pi$$
$$212$$ −33.8564 58.6410i −2.32527 4.02748i
$$213$$ −3.09808 + 5.36603i −0.212277 + 0.367674i
$$214$$ 3.00000 5.19615i 0.205076 0.355202i
$$215$$ 1.59808 + 2.76795i 0.108988 + 0.188773i
$$216$$ −9.46410 −0.643951
$$217$$ 0 0
$$218$$ −30.0526 −2.03542
$$219$$ 6.33013 + 10.9641i 0.427750 + 0.740885i
$$220$$ 2.00000 3.46410i 0.134840 0.233550i
$$221$$ −3.70577 + 6.41858i −0.249277 + 0.431761i
$$222$$ −4.36603 7.56218i −0.293028 0.507540i
$$223$$ 20.3923 1.36557 0.682785 0.730619i $$-0.260769\pi$$
0.682785 + 0.730619i $$0.260769\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 12.1962 + 21.1244i 0.811276 + 1.40517i
$$227$$ −0.830127 + 1.43782i −0.0550975 + 0.0954316i −0.892259 0.451525i $$-0.850880\pi$$
0.837161 + 0.546956i $$0.184214\pi$$
$$228$$ 12.1962 21.1244i 0.807710 1.39899i
$$229$$ −1.50000 2.59808i −0.0991228 0.171686i 0.812199 0.583380i $$-0.198270\pi$$
−0.911322 + 0.411695i $$0.864937\pi$$
$$230$$ −12.9282 −0.852460
$$231$$ 0 0
$$232$$ 39.7128 2.60727
$$233$$ −8.66025 15.0000i −0.567352 0.982683i −0.996827 0.0796037i $$-0.974635\pi$$
0.429474 0.903079i $$-0.358699\pi$$
$$234$$ −3.09808 + 5.36603i −0.202528 + 0.350788i
$$235$$ −1.00000 + 1.73205i −0.0652328 + 0.112987i
$$236$$ −0.535898 0.928203i −0.0348840 0.0604209i
$$237$$ −7.39230 −0.480182
$$238$$ 0 0
$$239$$ 7.07180 0.457437 0.228718 0.973493i $$-0.426547\pi$$
0.228718 + 0.973493i $$0.426547\pi$$
$$240$$ 7.46410 + 12.9282i 0.481806 + 0.834512i
$$241$$ 6.73205 11.6603i 0.433650 0.751103i −0.563535 0.826092i $$-0.690559\pi$$
0.997184 + 0.0749893i $$0.0238923\pi$$
$$242$$ −14.2942 + 24.7583i −0.918868 + 1.59153i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ −21.8564 −1.39921
$$245$$ 0 0
$$246$$ −2.00000 −0.127515
$$247$$ −5.06218 8.76795i −0.322099 0.557891i
$$248$$ 2.19615 3.80385i 0.139456 0.241545i
$$249$$ 7.56218 13.0981i 0.479234 0.830057i
$$250$$ −1.36603 2.36603i −0.0863950 0.149641i
$$251$$ 24.5885 1.55201 0.776005 0.630727i $$-0.217243\pi$$
0.776005 + 0.630727i $$0.217243\pi$$
$$252$$ 0 0
$$253$$ −3.46410 −0.217786
$$254$$ 6.56218 + 11.3660i 0.411748 + 0.713168i
$$255$$ −1.63397 + 2.83013i −0.102323 + 0.177229i
$$256$$ −21.8564 + 37.8564i −1.36603 + 2.36603i
$$257$$ −2.83013 4.90192i −0.176538 0.305774i 0.764154 0.645034i $$-0.223157\pi$$
−0.940693 + 0.339260i $$0.889823\pi$$
$$258$$ −8.73205 −0.543634
$$259$$ 0 0
$$260$$ 12.3923 0.768538
$$261$$ 2.09808 + 3.63397i 0.129868 + 0.224937i
$$262$$ −21.1244 + 36.5885i −1.30507 + 2.26044i
$$263$$ −4.19615 + 7.26795i −0.258746 + 0.448161i −0.965906 0.258892i $$-0.916643\pi$$
0.707160 + 0.707053i $$0.249976\pi$$
$$264$$ 3.46410 + 6.00000i 0.213201 + 0.369274i
$$265$$ −12.3923 −0.761253
$$266$$ 0 0
$$267$$ −15.1244 −0.925596
$$268$$ 40.0526 + 69.3731i 2.44660 + 4.23763i
$$269$$ −6.26795 + 10.8564i −0.382164 + 0.661927i −0.991371 0.131084i $$-0.958154\pi$$
0.609208 + 0.793011i $$0.291488\pi$$
$$270$$ −1.36603 + 2.36603i −0.0831337 + 0.143992i
$$271$$ 1.53590 + 2.66025i 0.0932992 + 0.161599i 0.908897 0.417020i $$-0.136925\pi$$
−0.815598 + 0.578619i $$0.803592\pi$$
$$272$$ −48.7846 −2.95800
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ −0.366025 0.633975i −0.0220722 0.0382301i
$$276$$ 12.9282 22.3923i 0.778186 1.34786i
$$277$$ 7.33013 12.6962i 0.440425 0.762838i −0.557296 0.830314i $$-0.688161\pi$$
0.997721 + 0.0674759i $$0.0214946\pi$$
$$278$$ −8.09808 14.0263i −0.485690 0.841240i
$$279$$ 0.464102 0.0277850
$$280$$ 0 0
$$281$$ 13.8564 0.826604 0.413302 0.910594i $$-0.364375\pi$$
0.413302 + 0.910594i $$0.364375\pi$$
$$282$$ −2.73205 4.73205i −0.162691 0.281790i
$$283$$ −12.0622 + 20.8923i −0.717022 + 1.24192i 0.245152 + 0.969485i $$0.421162\pi$$
−0.962174 + 0.272434i $$0.912171\pi$$
$$284$$ −16.9282 + 29.3205i −1.00450 + 1.73985i
$$285$$ −2.23205 3.86603i −0.132215 0.229004i
$$286$$ 4.53590 0.268213
$$287$$ 0 0
$$288$$ −21.8564 −1.28790
$$289$$ 3.16025 + 5.47372i 0.185897 + 0.321984i
$$290$$ 5.73205 9.92820i 0.336598 0.583004i
$$291$$ 7.46410 12.9282i 0.437553 0.757865i
$$292$$ 34.5885 + 59.9090i 2.02414 + 3.50591i
$$293$$ −18.9282 −1.10580 −0.552899 0.833248i $$-0.686478\pi$$
−0.552899 + 0.833248i $$0.686478\pi$$
$$294$$ 0 0
$$295$$ −0.196152 −0.0114204
$$296$$ −15.1244 26.1962i −0.879085 1.52262i
$$297$$ −0.366025 + 0.633975i −0.0212389 + 0.0367869i
$$298$$ 8.00000 13.8564i 0.463428 0.802680i
$$299$$ −5.36603 9.29423i −0.310325 0.537499i
$$300$$ 5.46410 0.315470
$$301$$ 0 0
$$302$$ 24.3923 1.40362
$$303$$ −3.63397 6.29423i −0.208766 0.361594i
$$304$$ 33.3205 57.7128i 1.91106 3.31006i
$$305$$ −2.00000 + 3.46410i −0.114520 + 0.198354i
$$306$$ −4.46410 7.73205i −0.255196 0.442012i
$$307$$ 32.1244 1.83343 0.916717 0.399537i $$-0.130829\pi$$
0.916717 + 0.399537i $$0.130829\pi$$
$$308$$ 0 0
$$309$$ 9.19615 0.523151
$$310$$ −0.633975 1.09808i −0.0360073 0.0623665i
$$311$$ 4.56218 7.90192i 0.258697 0.448077i −0.707196 0.707018i $$-0.750040\pi$$
0.965893 + 0.258941i $$0.0833734\pi$$
$$312$$ −10.7321 + 18.5885i −0.607583 + 1.05236i
$$313$$ −6.33013 10.9641i −0.357800 0.619728i 0.629793 0.776763i $$-0.283140\pi$$
−0.987593 + 0.157035i $$0.949806\pi$$
$$314$$ 17.4641 0.985556
$$315$$ 0 0
$$316$$ −40.3923 −2.27224
$$317$$ 14.2224 + 24.6340i 0.798811 + 1.38358i 0.920391 + 0.391000i $$0.127871\pi$$
−0.121579 + 0.992582i $$0.538796\pi$$
$$318$$ 16.9282 29.3205i 0.949286 1.64421i
$$319$$ 1.53590 2.66025i 0.0859938 0.148946i
$$320$$ 14.9282 + 25.8564i 0.834512 + 1.44542i
$$321$$ 2.19615 0.122577
$$322$$ 0 0
$$323$$ 14.5885 0.811723
$$324$$ −2.73205 4.73205i −0.151781 0.262892i
$$325$$ 1.13397 1.96410i 0.0629016 0.108949i
$$326$$ 29.8564 51.7128i 1.65359 2.86411i
$$327$$ −5.50000 9.52628i −0.304151 0.526804i
$$328$$ −6.92820 −0.382546
$$329$$ 0 0
$$330$$ 2.00000 0.110096
$$331$$ −4.03590 6.99038i −0.221833 0.384226i 0.733532 0.679655i $$-0.237871\pi$$
−0.955365 + 0.295429i $$0.904537\pi$$
$$332$$ 41.3205 71.5692i 2.26776 3.92787i
$$333$$ 1.59808 2.76795i 0.0875740 0.151683i
$$334$$ 24.1244 + 41.7846i 1.32003 + 2.28635i
$$335$$ 14.6603 0.800975
$$336$$ 0 0
$$337$$ 17.9808 0.979475 0.489737 0.871870i $$-0.337093\pi$$
0.489737 + 0.871870i $$0.337093\pi$$
$$338$$ −10.7321 18.5885i −0.583747 1.01108i
$$339$$ −4.46410 + 7.73205i −0.242457 + 0.419947i
$$340$$ −8.92820 + 15.4641i −0.484200 + 0.838659i
$$341$$ −0.169873 0.294229i −0.00919914 0.0159334i
$$342$$ 12.1962 0.659492
$$343$$ 0 0
$$344$$ −30.2487 −1.63090
$$345$$ −2.36603 4.09808i −0.127383 0.220633i
$$346$$ −19.8564 + 34.3923i −1.06749 + 1.84894i
$$347$$ 10.5359 18.2487i 0.565597 0.979642i −0.431397 0.902162i $$-0.641979\pi$$
0.996994 0.0774801i $$-0.0246874\pi$$
$$348$$ 11.4641 + 19.8564i 0.614540 + 1.06442i
$$349$$ −22.0000 −1.17763 −0.588817 0.808267i $$-0.700406\pi$$
−0.588817 + 0.808267i $$0.700406\pi$$
$$350$$ 0 0
$$351$$ −2.26795 −0.121054
$$352$$ 8.00000 + 13.8564i 0.426401 + 0.738549i
$$353$$ −1.56218 + 2.70577i −0.0831463 + 0.144014i −0.904600 0.426262i $$-0.859830\pi$$
0.821453 + 0.570276i $$0.193164\pi$$
$$354$$ 0.267949 0.464102i 0.0142413 0.0246667i
$$355$$ 3.09808 + 5.36603i 0.164429 + 0.284799i
$$356$$ −82.6410 −4.37997
$$357$$ 0 0
$$358$$ 27.3205 1.44393
$$359$$ 0.633975 + 1.09808i 0.0334599 + 0.0579542i 0.882270 0.470743i $$-0.156014\pi$$
−0.848811 + 0.528697i $$0.822681\pi$$
$$360$$ −4.73205 + 8.19615i −0.249401 + 0.431975i
$$361$$ −0.464102 + 0.803848i −0.0244264 + 0.0423078i
$$362$$ 33.2224 + 57.5429i 1.74613 + 3.02439i
$$363$$ −10.4641 −0.549223
$$364$$ 0 0
$$365$$ 12.6603 0.662668
$$366$$ −5.46410 9.46410i −0.285613 0.494697i
$$367$$ 5.59808 9.69615i 0.292217 0.506135i −0.682117 0.731244i $$-0.738940\pi$$
0.974334 + 0.225108i $$0.0722736\pi$$
$$368$$ 35.3205 61.1769i 1.84121 3.18907i
$$369$$ −0.366025 0.633975i −0.0190545 0.0330034i
$$370$$ −8.73205 −0.453958
$$371$$ 0 0
$$372$$ 2.53590 0.131480
$$373$$ −13.2583 22.9641i −0.686490 1.18904i −0.972966 0.230949i $$-0.925817\pi$$
0.286476 0.958088i $$-0.407516\pi$$
$$374$$ −3.26795 + 5.66025i −0.168982 + 0.292685i
$$375$$ 0.500000 0.866025i 0.0258199 0.0447214i
$$376$$ −9.46410 16.3923i −0.488074 0.845369i
$$377$$ 9.51666 0.490133
$$378$$ 0 0
$$379$$ 6.32051 0.324663 0.162331 0.986736i $$-0.448099\pi$$
0.162331 + 0.986736i $$0.448099\pi$$
$$380$$ −12.1962 21.1244i −0.625649 1.08366i
$$381$$ −2.40192 + 4.16025i −0.123054 + 0.213136i
$$382$$ −12.1962 + 21.1244i −0.624009 + 1.08082i
$$383$$ −11.6603 20.1962i −0.595811 1.03198i −0.993432 0.114425i $$-0.963497\pi$$
0.397621 0.917550i $$-0.369836\pi$$
$$384$$ −37.8564 −1.93185
$$385$$ 0 0
$$386$$ −3.26795 −0.166334
$$387$$ −1.59808 2.76795i −0.0812348 0.140703i
$$388$$ 40.7846 70.6410i 2.07052 3.58625i
$$389$$ −2.70577 + 4.68653i −0.137188 + 0.237617i −0.926431 0.376464i $$-0.877140\pi$$
0.789243 + 0.614081i $$0.210473\pi$$
$$390$$ 3.09808 + 5.36603i 0.156877 + 0.271719i
$$391$$ 15.4641 0.782053
$$392$$ 0 0
$$393$$ −15.4641 −0.780061
$$394$$ −0.464102 0.803848i −0.0233811 0.0404973i
$$395$$ −3.69615 + 6.40192i −0.185974 + 0.322116i
$$396$$ −2.00000 + 3.46410i −0.100504 + 0.174078i
$$397$$ −15.5981 27.0167i −0.782845 1.35593i −0.930278 0.366855i $$-0.880434\pi$$
0.147433 0.989072i $$-0.452899\pi$$
$$398$$ 60.1051 3.01280
$$399$$ 0 0
$$400$$ 14.9282 0.746410
$$401$$ 8.19615 + 14.1962i 0.409296 + 0.708922i 0.994811 0.101740i $$-0.0324409\pi$$
−0.585515 + 0.810662i $$0.699108\pi$$
$$402$$ −20.0263 + 34.6865i −0.998820 + 1.73001i
$$403$$ 0.526279 0.911543i 0.0262158 0.0454072i
$$404$$ −19.8564 34.3923i −0.987893 1.71108i
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ −2.33975 −0.115977
$$408$$ −15.4641 26.7846i −0.765587 1.32604i
$$409$$ 1.57180 2.72243i 0.0777203 0.134616i −0.824546 0.565795i $$-0.808569\pi$$
0.902266 + 0.431180i $$0.141903\pi$$
$$410$$ −1.00000 + 1.73205i −0.0493865 + 0.0855399i
$$411$$ −1.09808 1.90192i −0.0541641 0.0938150i
$$412$$ 50.2487 2.47558
$$413$$ 0 0
$$414$$ 12.9282 0.635387
$$415$$ −7.56218 13.0981i −0.371213 0.642959i
$$416$$ −24.7846 + 42.9282i −1.21517 + 2.10473i
$$417$$ 2.96410 5.13397i 0.145153 0.251412i
$$418$$ −4.46410 7.73205i −0.218346 0.378187i
$$419$$ 35.4641 1.73253 0.866267 0.499581i $$-0.166513\pi$$
0.866267 + 0.499581i $$0.166513\pi$$
$$420$$ 0 0
$$421$$ 0.0717968 0.00349916 0.00174958 0.999998i $$-0.499443\pi$$
0.00174958 + 0.999998i $$0.499443\pi$$
$$422$$ 9.66025 + 16.7321i 0.470254 + 0.814503i
$$423$$ 1.00000 1.73205i 0.0486217 0.0842152i
$$424$$ 58.6410 101.569i 2.84786 4.93264i
$$425$$ 1.63397 + 2.83013i 0.0792594 + 0.137281i
$$426$$ −16.9282 −0.820174
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 0.830127 + 1.43782i 0.0400789 + 0.0694187i
$$430$$ −4.36603 + 7.56218i −0.210548 + 0.364681i
$$431$$ −8.66025 + 15.0000i −0.417150 + 0.722525i −0.995651 0.0931566i $$-0.970304\pi$$
0.578502 + 0.815681i $$0.303638\pi$$
$$432$$ −7.46410 12.9282i −0.359117 0.622008i
$$433$$ −15.1962 −0.730280 −0.365140 0.930953i $$-0.618979\pi$$
−0.365140 + 0.930953i $$0.618979\pi$$
$$434$$ 0 0
$$435$$ 4.19615 0.201190
$$436$$ −30.0526 52.0526i −1.43926 2.49287i
$$437$$ −10.5622 + 18.2942i −0.505257 + 0.875132i
$$438$$ −17.2942 + 29.9545i −0.826350 + 1.43128i
$$439$$ 0.267949 + 0.464102i 0.0127885 + 0.0221504i 0.872349 0.488884i $$-0.162596\pi$$
−0.859560 + 0.511034i $$0.829263\pi$$
$$440$$ 6.92820 0.330289
$$441$$ 0 0
$$442$$ −20.2487 −0.963133
$$443$$ −4.73205 8.19615i −0.224827 0.389411i 0.731441 0.681905i $$-0.238848\pi$$
−0.956267 + 0.292494i $$0.905515\pi$$
$$444$$ 8.73205 15.1244i 0.414405 0.717770i
$$445$$ −7.56218 + 13.0981i −0.358482 + 0.620908i
$$446$$ 27.8564 + 48.2487i 1.31904 + 2.28464i
$$447$$ 5.85641 0.276999
$$448$$ 0 0
$$449$$ −35.8564 −1.69217 −0.846084 0.533049i $$-0.821046\pi$$
−0.846084 + 0.533049i $$0.821046\pi$$
$$450$$ 1.36603 + 2.36603i 0.0643951 + 0.111536i
$$451$$ −0.267949 + 0.464102i −0.0126172 + 0.0218537i
$$452$$ −24.3923 + 42.2487i −1.14732 + 1.98721i
$$453$$ 4.46410 + 7.73205i 0.209742 + 0.363283i
$$454$$ −4.53590 −0.212880
$$455$$ 0 0
$$456$$ 42.2487 1.97848
$$457$$ 8.33013 + 14.4282i 0.389667 + 0.674923i 0.992405 0.123016i $$-0.0392568\pi$$
−0.602738 + 0.797939i $$0.705923\pi$$
$$458$$ 4.09808 7.09808i 0.191491 0.331671i
$$459$$ 1.63397 2.83013i 0.0762674 0.132099i
$$460$$ −12.9282 22.3923i −0.602781 1.04405i
$$461$$ −16.9808 −0.790873 −0.395436 0.918493i $$-0.629407\pi$$
−0.395436 + 0.918493i $$0.629407\pi$$
$$462$$ 0 0
$$463$$ 25.7321 1.19587 0.597935 0.801545i $$-0.295988\pi$$
0.597935 + 0.801545i $$0.295988\pi$$
$$464$$ 31.3205 + 54.2487i 1.45402 + 2.51843i
$$465$$ 0.232051 0.401924i 0.0107611 0.0186388i
$$466$$ 23.6603 40.9808i 1.09604 1.89840i
$$467$$ −0.0717968 0.124356i −0.00332236 0.00575449i 0.864359 0.502874i $$-0.167724\pi$$
−0.867682 + 0.497120i $$0.834391\pi$$
$$468$$ −12.3923 −0.572834
$$469$$ 0 0
$$470$$ −5.46410 −0.252040
$$471$$ 3.19615 + 5.53590i 0.147271 + 0.255081i
$$472$$ 0.928203 1.60770i 0.0427240 0.0740002i
$$473$$ −1.16987 + 2.02628i −0.0537908 + 0.0931684i
$$474$$ −10.0981 17.4904i −0.463820 0.803360i
$$475$$ −4.46410 −0.204827
$$476$$ 0 0
$$477$$ 12.3923 0.567405
$$478$$ 9.66025 + 16.7321i 0.441850 + 0.765306i
$$479$$ 4.39230 7.60770i 0.200690 0.347604i −0.748061 0.663630i $$-0.769015\pi$$
0.948751 + 0.316025i $$0.102348\pi$$
$$480$$ −10.9282 + 18.9282i −0.498802 + 0.863950i
$$481$$ −3.62436 6.27757i −0.165256 0.286232i
$$482$$ 36.7846 1.67549
$$483$$ 0 0
$$484$$ −57.1769 −2.59895
$$485$$ −7.46410 12.9282i −0.338927 0.587039i
$$486$$ 1.36603 2.36603i 0.0619642 0.107325i
$$487$$ 0.205771 0.356406i 0.00932439 0.0161503i −0.861326 0.508053i $$-0.830365\pi$$
0.870650 + 0.491903i $$0.163699\pi$$
$$488$$ −18.9282 32.7846i −0.856840 1.48409i
$$489$$ 21.8564 0.988381
$$490$$ 0 0
$$491$$ −38.2487 −1.72614 −0.863070 0.505084i $$-0.831461\pi$$
−0.863070 + 0.505084i $$0.831461\pi$$
$$492$$ −2.00000 3.46410i −0.0901670 0.156174i
$$493$$ −6.85641 + 11.8756i −0.308797 + 0.534852i
$$494$$ 13.8301 23.9545i 0.622247 1.07776i
$$495$$ 0.366025 + 0.633975i 0.0164516 + 0.0284950i
$$496$$ 6.92820 0.311086
$$497$$ 0 0
$$498$$ 41.3205 1.85162
$$499$$ 6.76795 + 11.7224i 0.302975 + 0.524768i 0.976808 0.214115i $$-0.0686868\pi$$
−0.673833 + 0.738883i $$0.735353\pi$$
$$500$$ 2.73205 4.73205i 0.122181 0.211624i
$$501$$ −8.83013 + 15.2942i −0.394501 + 0.683296i
$$502$$ 33.5885 + 58.1769i 1.49913 + 2.59656i
$$503$$ −14.3923 −0.641721 −0.320861 0.947126i $$-0.603972\pi$$
−0.320861 + 0.947126i $$0.603972\pi$$
$$504$$ 0 0
$$505$$ −7.26795 −0.323419
$$506$$ −4.73205 8.19615i −0.210365 0.364363i
$$507$$ 3.92820 6.80385i 0.174458 0.302169i
$$508$$ −13.1244 + 22.7321i −0.582299 + 1.00857i
$$509$$ 2.26795 + 3.92820i 0.100525 + 0.174115i 0.911901 0.410410i $$-0.134614\pi$$
−0.811376 + 0.584525i $$0.801281\pi$$
$$510$$ −8.92820 −0.395347
$$511$$ 0 0
$$512$$ −43.7128 −1.93185
$$513$$ 2.23205 + 3.86603i 0.0985475 + 0.170689i
$$514$$ 7.73205 13.3923i 0.341046 0.590709i
$$515$$ 4.59808 7.96410i 0.202615 0.350940i
$$516$$ −8.73205 15.1244i −0.384407 0.665813i
$$517$$ −1.46410 −0.0643911
$$518$$ 0 0
$$519$$ −14.5359 −0.638055
$$520$$ 10.7321 + 18.5885i 0.470632 + 0.815158i
$$521$$ −2.73205 + 4.73205i −0.119693 + 0.207315i −0.919646 0.392748i $$-0.871524\pi$$
0.799953 + 0.600063i $$0.204858\pi$$
$$522$$ −5.73205 + 9.92820i −0.250885 + 0.434546i
$$523$$ −13.8660 24.0167i −0.606319 1.05018i −0.991842 0.127477i $$-0.959312\pi$$
0.385523 0.922698i $$-0.374021\pi$$
$$524$$ −84.4974 −3.69129
$$525$$ 0 0
$$526$$ −22.9282 −0.999717
$$527$$ 0.758330 + 1.31347i 0.0330334 + 0.0572155i
$$528$$ −5.46410 + 9.46410i −0.237795 + 0.411872i
$$529$$ 0.303848 0.526279i 0.0132108 0.0228817i
$$530$$ −16.9282 29.3205i −0.735314 1.27360i
$$531$$ 0.196152 0.00851229
$$532$$ 0 0
$$533$$ −1.66025 −0.0719136
$$534$$ −20.6603 35.7846i −0.894057 1.54855i
$$535$$ 1.09808 1.90192i 0.0474740 0.0822273i
$$536$$ −69.3731 + 120.158i −2.99646 + 5.19002i
$$537$$ 5.00000 + 8.66025i 0.215766 + 0.373718i
$$538$$ −34.2487 −1.47657
$$539$$ 0 0
$$540$$ −5.46410 −0.235137
$$541$$ −2.89230 5.00962i −0.124350 0.215380i 0.797129 0.603809i $$-0.206351\pi$$
−0.921479 + 0.388429i $$0.873018\pi$$
$$542$$ −4.19615 + 7.26795i −0.180240 + 0.312185i
$$543$$ −12.1603 + 21.0622i −0.521846 + 0.903865i
$$544$$ −35.7128 61.8564i −1.53117 2.65207i
$$545$$ −11.0000 −0.471188
$$546$$ 0 0
$$547$$ −26.2487 −1.12231 −0.561157 0.827709i $$-0.689644\pi$$
−0.561157 + 0.827709i $$0.689644\pi$$
$$548$$ −6.00000 10.3923i −0.256307 0.443937i
$$549$$ 2.00000 3.46410i 0.0853579 0.147844i
$$550$$ 1.00000 1.73205i 0.0426401 0.0738549i
$$551$$ −9.36603 16.2224i −0.399006 0.691099i
$$552$$ 44.7846 1.90616
$$553$$ 0 0
$$554$$ 40.0526 1.70167
$$555$$ −1.59808 2.76795i −0.0678346 0.117493i
$$556$$ 16.1962 28.0526i 0.686870 1.18969i
$$557$$ −7.39230 + 12.8038i −0.313222 + 0.542516i −0.979058 0.203582i $$-0.934742\pi$$
0.665836 + 0.746098i $$0.268075\pi$$
$$558$$ 0.633975 + 1.09808i 0.0268383 + 0.0464853i
$$559$$ −7.24871 −0.306588
$$560$$ 0 0
$$561$$ −2.39230 −0.101003
$$562$$ 18.9282 + 32.7846i 0.798438 + 1.38294i
$$563$$ −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i $$-0.957170\pi$$
0.611656 + 0.791123i $$0.290503\pi$$
$$564$$ 5.46410 9.46410i 0.230080 0.398511i
$$565$$ 4.46410 + 7.73205i 0.187806 + 0.325290i
$$566$$ −65.9090 −2.77036
$$567$$ 0 0
$$568$$ −58.6410 −2.46052
$$569$$ −16.2224 28.0981i −0.680080 1.17793i −0.974956 0.222397i $$-0.928612\pi$$
0.294876 0.955535i $$-0.404722\pi$$
$$570$$ 6.09808 10.5622i 0.255420 0.442401i
$$571$$ −9.30385 + 16.1147i −0.389354 + 0.674381i −0.992363 0.123354i $$-0.960635\pi$$
0.603009 + 0.797734i $$0.293968\pi$$
$$572$$ 4.53590 + 7.85641i 0.189655 + 0.328493i
$$573$$ −8.92820 −0.372981
$$574$$ 0 0
$$575$$ −4.73205 −0.197340
$$576$$ −14.9282 25.8564i −0.622008 1.07735i
$$577$$ 14.3301 24.8205i 0.596571 1.03329i −0.396752 0.917926i $$-0.629863\pi$$
0.993323 0.115365i $$-0.0368039\pi$$
$$578$$ −8.63397 + 14.9545i −0.359126 + 0.622024i
$$579$$ −0.598076 1.03590i −0.0248552 0.0430505i
$$580$$ 22.9282 0.952042
$$581$$ 0 0
$$582$$ 40.7846 1.69058
$$583$$ −4.53590 7.85641i −0.187858 0.325379i
$$584$$ −59.9090 + 103.765i −2.47905 + 4.29384i
$$585$$ −1.13397 + 1.96410i −0.0468841 + 0.0812056i
$$586$$ −25.8564 44.7846i −1.06812 1.85004i
$$587$$ −40.7321 −1.68119 −0.840596 0.541663i $$-0.817795\pi$$
−0.840596 + 0.541663i $$0.817795\pi$$
$$588$$ 0 0
$$589$$ −2.07180 −0.0853669
$$590$$ −0.267949 0.464102i −0.0110313 0.0191068i
$$591$$ 0.169873 0.294229i 0.00698764 0.0121029i
$$592$$ 23.8564 41.3205i 0.980492 1.69826i
$$593$$ 13.9545 + 24.1699i 0.573042 + 0.992538i 0.996251 + 0.0865058i $$0.0275701\pi$$
−0.423209 + 0.906032i $$0.639097\pi$$
$$594$$ −2.00000 −0.0820610
$$595$$ 0 0
$$596$$ 32.0000 1.31077
$$597$$ 11.0000 + 19.0526i 0.450200 + 0.779769i
$$598$$ 14.6603 25.3923i 0.599502 1.03837i
$$599$$ 19.1244 33.1244i 0.781400 1.35342i −0.149726 0.988727i $$-0.547839\pi$$
0.931126 0.364697i $$-0.118827\pi$$
$$600$$ 4.73205 + 8.19615i 0.193185 + 0.334607i
$$601$$ 0.0717968 0.00292865 0.00146433 0.999999i $$-0.499534\pi$$
0.00146433 + 0.999999i $$0.499534\pi$$
$$602$$ 0 0
$$603$$ −14.6603 −0.597012
$$604$$ 24.3923 + 42.2487i 0.992509 + 1.71908i
$$605$$ −5.23205 + 9.06218i −0.212713 + 0.368430i
$$606$$ 9.92820 17.1962i 0.403306 0.698546i
$$607$$ 1.59808 + 2.76795i 0.0648639 + 0.112348i 0.896634 0.442773i $$-0.146005\pi$$
−0.831770 + 0.555121i $$0.812672\pi$$
$$608$$ 97.5692 3.95695
$$609$$ 0 0
$$610$$ −10.9282 −0.442470
$$611$$ −2.26795 3.92820i −0.0917514 0.158918i
$$612$$ 8.92820 15.4641i 0.360901 0.625099i
$$613$$ 13.4641 23.3205i 0.543810 0.941906i −0.454871 0.890557i $$-0.650315\pi$$
0.998681 0.0513490i $$-0.0163521\pi$$
$$614$$ 43.8827 + 76.0070i 1.77096 + 3.06739i
$$615$$ −0.732051 −0.0295191
$$616$$ 0 0
$$617$$ −36.2487 −1.45932 −0.729659 0.683811i $$-0.760321\pi$$
−0.729659 + 0.683811i $$0.760321\pi$$
$$618$$ 12.5622 + 21.7583i 0.505325 + 0.875248i
$$619$$ −15.0359 + 26.0429i −0.604344 + 1.04675i 0.387811 + 0.921739i $$0.373231\pi$$
−0.992155 + 0.125015i $$0.960102\pi$$
$$620$$ 1.26795 2.19615i 0.0509221 0.0881996i
$$621$$ 2.36603 + 4.09808i 0.0949453 + 0.164450i
$$622$$ 24.9282 0.999530
$$623$$ 0 0
$$624$$ −33.8564 −1.35534
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 17.2942 29.9545i 0.691216 1.19722i
$$627$$ 1.63397 2.83013i 0.0652547 0.113024i
$$628$$ 17.4641 + 30.2487i 0.696894 + 1.20705i
$$629$$ 10.4449 0.416464
$$630$$ 0 0
$$631$$ 48.7846 1.94208 0.971042 0.238908i $$-0.0767893\pi$$
0.971042 + 0.238908i $$0.0767893\pi$$
$$632$$ −34.9808 60.5885i −1.39146 2.41008i
$$633$$ −3.53590 + 6.12436i −0.140539 + 0.243421i
$$634$$ −38.8564 + 67.3013i −1.54319 + 2.67287i
$$635$$ 2.40192 + 4.16025i 0.0953174 + 0.165095i
$$636$$ 67.7128 2.68499
$$637$$ 0 0
$$638$$ 8.39230 0.332255
$$639$$ −3.09808 5.36603i −0.122558 0.212277i
$$640$$ −18.9282 + 32.7846i −0.748203 + 1.29593i
$$641$$ −1.90192 + 3.29423i −0.0751215 + 0.130114i −0.901139 0.433530i $$-0.857268\pi$$
0.826018 + 0.563644i $$0.190601\pi$$
$$642$$ 3.00000 + 5.19615i 0.118401 + 0.205076i
$$643$$ −4.51666 −0.178120 −0.0890599 0.996026i $$-0.528386\pi$$
−0.0890599 + 0.996026i $$0.528386\pi$$
$$644$$ 0 0
$$645$$ −3.19615 −0.125848
$$646$$ 19.9282 + 34.5167i 0.784065 + 1.35804i
$$647$$ −13.9545 + 24.1699i −0.548607 + 0.950216i 0.449763 + 0.893148i $$0.351508\pi$$
−0.998370 + 0.0570678i $$0.981825\pi$$
$$648$$ 4.73205 8.19615i 0.185893 0.321975i
$$649$$ −0.0717968 0.124356i −0.00281827 0.00488139i
$$650$$ 6.19615 0.243033
$$651$$ 0 0
$$652$$ 119.426 4.67707
$$653$$ 22.2942 + 38.6147i 0.872441 + 1.51111i 0.859464 + 0.511196i $$0.170797\pi$$
0.0129762 + 0.999916i $$0.495869\pi$$
$$654$$ 15.0263 26.0263i 0.587574 1.01771i
$$655$$ −7.73205 + 13.3923i −0.302116 + 0.523281i
$$656$$ −5.46410 9.46410i −0.213337 0.369511i
$$657$$ −12.6603 −0.493924
$$658$$ 0 0
$$659$$ 2.92820 0.114067 0.0570333 0.998372i $$-0.481836\pi$$
0.0570333 + 0.998372i $$0.481836\pi$$
$$660$$ 2.00000 + 3.46410i 0.0778499 + 0.134840i
$$661$$ 5.23205 9.06218i 0.203503 0.352478i −0.746152 0.665776i $$-0.768101\pi$$
0.949655 + 0.313298i $$0.101434\pi$$
$$662$$ 11.0263 19.0981i 0.428549 0.742268i
$$663$$ −3.70577 6.41858i −0.143920 0.249277i
$$664$$ 143.138 5.55485
$$665$$ 0 0
$$666$$ 8.73205 0.338360
$$667$$ −9.92820 17.1962i −0.384422 0.665838i
$$668$$ −48.2487 + 83.5692i −1.86680 + 3.23339i
$$669$$ −10.1962 + 17.6603i −0.394206 + 0.682785i
$$670$$ 20.0263 + 34.6865i 0.773683 + 1.34006i
$$671$$ −2.92820 −0.113042
$$672$$ 0 0
$$673$$ −27.3397 −1.05387 −0.526935 0.849906i $$-0.676659\pi$$
−0.526935 + 0.849906i $$0.676659\pi$$
$$674$$ 24.5622 + 42.5429i 0.946100 + 1.63869i
$$675$$ −0.500000 + 0.866025i −0.0192450 + 0.0333333i
$$676$$ 21.4641 37.1769i 0.825542 1.42988i
$$677$$ −16.5622 28.6865i −0.636536 1.10251i −0.986187 0.165633i $$-0.947033\pi$$
0.349651 0.936880i $$-0.386300\pi$$
$$678$$ −24.3923 −0.936781
$$679$$ 0 0
$$680$$ −30.9282 −1.18604
$$681$$ −0.830127 1.43782i −0.0318105 0.0550975i
$$682$$ 0.464102 0.803848i 0.0177714 0.0307809i
$$683$$ 14.0263 24.2942i 0.536701 0.929593i −0.462378 0.886683i $$-0.653004\pi$$
0.999079 0.0429101i $$-0.0136629\pi$$
$$684$$ 12.1962 + 21.1244i 0.466332 + 0.807710i
$$685$$ −2.19615 −0.0839107
$$686$$ 0 0
$$687$$ 3.00000 0.114457
$$688$$ −23.8564 41.3205i −0.909517 1.57533i
$$689$$ 14.0526 24.3397i 0.535360 0.927270i
$$690$$ 6.46410 11.1962i 0.246084 0.426230i
$$691$$ 4.42820 + 7.66987i 0.168457 + 0.291776i 0.937877 0.346967i $$-0.112788\pi$$
−0.769421 + 0.638742i $$0.779455\pi$$
$$692$$ −79.4256 −3.01931
$$693$$ 0 0
$$694$$ 57.5692 2.18530
$$695$$ −2.96410 5.13397i −0.112435 0.194743i
$$696$$ −19.8564 + 34.3923i −0.752655 + 1.30364i
$$697$$ 1.19615 2.07180i 0.0453075 0.0784749i
$$698$$ −30.0526 52.0526i −1.13751 1.97022i
$$699$$ 17.3205 0.655122
$$700$$ 0 0
$$701$$ −8.58846 −0.324382 −0.162191 0.986759i $$-0.551856\pi$$
−0.162191 + 0.986759i $$0.551856\pi$$
$$702$$ −3.09808 5.36603i −0.116929 0.202528i
$$703$$ −7.13397 + 12.3564i −0.269063 + 0.466031i
$$704$$ −10.9282 + 18.9282i −0.411872 + 0.713384i
$$705$$ −1.00000 1.73205i −0.0376622 0.0652328i
$$706$$ −8.53590 −0.321253
$$707$$ 0 0
$$708$$ 1.07180 0.0402806
$$709$$ 0.535898 + 0.928203i 0.0201261 + 0.0348594i 0.875913 0.482469i $$-0.160260\pi$$
−0.855787 + 0.517328i $$0.826927\pi$$
$$710$$ −8.46410 + 14.6603i −0.317652 + 0.550190i
$$711$$ 3.69615 6.40192i 0.138617 0.240091i
$$712$$ −71.5692 123.962i −2.68217 4.64565i
$$713$$ −2.19615 −0.0822466
$$714$$ 0 0
$$715$$ 1.66025 0.0620900
$$716$$ 27.3205 + 47.3205i 1.02102 + 1.76845i
$$717$$ −3.53590 + 6.12436i −0.132051 + 0.228718i
$$718$$ −1.73205 + 3.00000i −0.0646396 + 0.111959i
$$719$$ −10.2679 17.7846i −0.382930 0.663254i 0.608550 0.793516i $$-0.291752\pi$$
−0.991480 + 0.130262i $$0.958418\pi$$
$$720$$ −14.9282 −0.556341
$$721$$ 0 0
$$722$$ −2.53590 −0.0943764
$$723$$ 6.73205 + 11.6603i 0.250368 + 0.433650i
$$724$$ −66.4449 + 115.086i −2.46940 + 4.27713i
$$725$$ 2.09808 3.63397i 0.0779206 0.134962i
$$726$$ −14.2942 24.7583i −0.530509 0.918868i
$$727$$ 13.3397 0.494744 0.247372 0.968921i $$-0.420433\pi$$
0.247372 + 0.968921i $$0.420433\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 17.2942 + 29.9545i 0.640088 + 1.10867i
$$731$$ 5.22243 9.04552i 0.193159 0.334561i
$$732$$ 10.9282 18.9282i 0.403918 0.699607i
$$733$$ −0.669873 1.16025i −0.0247423 0.0428550i 0.853389 0.521274i $$-0.174543\pi$$
−0.878131 + 0.478419i $$0.841210\pi$$
$$734$$ 30.5885 1.12904
$$735$$ 0 0
$$736$$ 103.426 3.81232
$$737$$ 5.36603 + 9.29423i 0.197660 + 0.342357i
$$738$$ 1.00000 1.73205i 0.0368105 0.0637577i
$$739$$ −13.8923 + 24.0622i −0.511037 + 0.885142i 0.488881 + 0.872350i $$0.337405\pi$$
−0.999918 + 0.0127913i $$0.995928\pi$$
$$740$$ −8.73205 15.1244i −0.320997 0.555982i
$$741$$ 10.1244 0.371927
$$742$$ 0 0
$$743$$ −15.9090 −0.583643 −0.291822 0.956473i $$-0.594261\pi$$
−0.291822 + 0.956473i $$0.594261\pi$$
$$744$$ 2.19615 + 3.80385i 0.0805149 + 0.139456i
$$745$$ 2.92820 5.07180i 0.107281 0.185816i
$$746$$ 36.2224 62.7391i 1.32620 2.29704i
$$747$$ 7.56218 + 13.0981i 0.276686 + 0.479234i
$$748$$ −13.0718 −0.477952
$$749$$ 0 0
$$750$$ 2.73205 0.0997604
$$751$$ −9.03590 15.6506i −0.329725 0.571100i 0.652732 0.757588i $$-0.273623\pi$$
−0.982457 + 0.186489i $$0.940289\pi$$
$$752$$ 14.9282 25.8564i 0.544376 0.942886i
$$753$$ −12.2942 + 21.2942i −0.448027 + 0.776005i
$$754$$ 13.0000 + 22.5167i 0.473432 + 0.820008i
$$755$$ 8.92820 0.324931
$$756$$ 0 0
$$757$$ −27.8564 −1.01246 −0.506229 0.862399i $$-0.668961\pi$$
−0.506229 + 0.862399i $$0.668961\pi$$
$$758$$ 8.63397 + 14.9545i 0.313600 + 0.543171i
$$759$$ 1.73205 3.00000i 0.0628695 0.108893i
$$760$$ 21.1244 36.5885i 0.766261 1.32720i
$$761$$ 23.3660 + 40.4711i 0.847018 + 1.46708i 0.883857 + 0.467757i $$0.154938\pi$$
−0.0368396 + 0.999321i $$0.511729\pi$$
$$762$$ −13.1244 −0.475445
$$763$$ 0 0
$$764$$ −48.7846 −1.76497
$$765$$ −1.63397 2.83013i −0.0590765 0.102323i
$$766$$ 31.8564 55.1769i 1.15102 1.99362i
$$767$$ 0.222432 0.385263i 0.00803155 0.0139111i
$$768$$ −21.8564 37.8564i −0.788675 1.36603i
$$769$$ −52.3205 −1.88673 −0.943363 0.331763i $$-0.892357\pi$$
−0.943363 + 0.331763i $$0.892357\pi$$
$$770$$ 0 0
$$771$$ 5.66025 0.203849
$$772$$ −3.26795 5.66025i −0.117616 0.203717i
$$773$$ 21.7583 37.6865i 0.782593 1.35549i −0.147834 0.989012i $$-0.547230\pi$$
0.930427 0.366478i $$-0.119437\pi$$
$$774$$ 4.36603 7.56218i 0.156934 0.271817i
$$775$$ −0.232051 0.401924i −0.00833551 0.0144375i
$$776$$ 141.282 5.07173
$$777$$ 0 0
$$778$$ −14.7846 −0.530054
$$779$$ 1.63397 + 2.83013i 0.0585432 + 0.101400i
$$780$$ −6.19615 + 10.7321i −0.221858 + 0.384269i
$$781$$ −2.26795 + 3.92820i −0.0811536 + 0.140562i
$$782$$ 21.1244 + 36.5885i 0.75