# Properties

 Label 1386.2.k.a.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 793.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1386.793 Dual form 1386.2.k.a.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{19} +4.00000 q^{20} +1.00000 q^{22} +(-1.00000 + 1.73205i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.00000 + 1.73205i) q^{28} -1.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +(2.00000 - 10.3923i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 + 3.46410i) q^{40} +2.00000 q^{41} +4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{46} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +11.0000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(4.50000 + 7.79423i) q^{59} +(2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(4.50000 + 7.79423i) q^{67} +(1.00000 - 1.73205i) q^{68} +(8.00000 + 6.92820i) q^{70} -4.00000 q^{71} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(2.00000 + 1.73205i) q^{77} +(7.50000 - 12.9904i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-1.00000 + 1.73205i) q^{82} +6.00000 q^{83} -8.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(2.50000 - 0.866025i) q^{91} +2.00000 q^{92} +(1.00000 + 1.73205i) q^{94} +(-12.0000 - 20.7846i) q^{95} -5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} - 4q^{5} - 5q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} - 4q^{5} - 5q^{7} + 2q^{8} - 4q^{10} - q^{11} - 2q^{13} + q^{14} - q^{16} + 2q^{17} - 6q^{19} + 8q^{20} + 2q^{22} - 2q^{23} - 11q^{25} + q^{26} + 4q^{28} - 2q^{29} - 4q^{31} - q^{32} - 4q^{34} + 4q^{35} + 2q^{37} - 6q^{38} - 4q^{40} + 4q^{41} + 8q^{43} - q^{44} - 2q^{46} + 2q^{47} + 11q^{49} + 22q^{50} + q^{52} - 12q^{53} + 8q^{55} - 5q^{56} + q^{58} + 9q^{59} + 5q^{61} + 8q^{62} + 2q^{64} + 4q^{65} + 9q^{67} + 2q^{68} + 16q^{70} - 8q^{71} + 2q^{73} + 2q^{74} + 12q^{76} + 4q^{77} + 15q^{79} - 4q^{80} - 2q^{82} + 12q^{83} - 16q^{85} - 4q^{86} - q^{88} + 6q^{89} + 5q^{91} + 4q^{92} + 2q^{94} - 24q^{95} - 10q^{97} + 2q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −2.00000 + 3.46410i −0.894427 + 1.54919i −0.0599153 + 0.998203i $$0.519083\pi$$
−0.834512 + 0.550990i $$0.814250\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −2.00000 3.46410i −0.632456 1.09545i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 0 0
$$13$$ −1.00000 −0.277350 −0.138675 0.990338i $$-0.544284\pi$$
−0.138675 + 0.990338i $$0.544284\pi$$
$$14$$ 0.500000 2.59808i 0.133631 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i $$-0.0886875\pi$$
−0.718900 + 0.695113i $$0.755354\pi$$
$$18$$ 0 0
$$19$$ −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i $$0.408286\pi$$
−0.972404 + 0.233301i $$0.925047\pi$$
$$20$$ 4.00000 0.894427
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i $$-0.900196\pi$$
0.742732 + 0.669588i $$0.233529\pi$$
$$24$$ 0 0
$$25$$ −5.50000 9.52628i −1.10000 1.90526i
$$26$$ 0.500000 0.866025i 0.0980581 0.169842i
$$27$$ 0 0
$$28$$ 2.00000 + 1.73205i 0.377964 + 0.327327i
$$29$$ −1.00000 −0.185695 −0.0928477 0.995680i $$-0.529597\pi$$
−0.0928477 + 0.995680i $$0.529597\pi$$
$$30$$ 0 0
$$31$$ −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i $$-0.283621\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 2.00000 10.3923i 0.338062 1.75662i
$$36$$ 0 0
$$37$$ 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i $$-0.780765\pi$$
0.936442 + 0.350823i $$0.114098\pi$$
$$38$$ −3.00000 5.19615i −0.486664 0.842927i
$$39$$ 0 0
$$40$$ −2.00000 + 3.46410i −0.316228 + 0.547723i
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ −1.00000 1.73205i −0.147442 0.255377i
$$47$$ 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i $$-0.786737\pi$$
0.929695 + 0.368329i $$0.120070\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 11.0000 1.55563
$$51$$ 0 0
$$52$$ 0.500000 + 0.866025i 0.0693375 + 0.120096i
$$53$$ −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i $$-0.858312\pi$$
0.0783936 0.996922i $$-0.475021\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ −2.50000 + 0.866025i −0.334077 + 0.115728i
$$57$$ 0 0
$$58$$ 0.500000 0.866025i 0.0656532 0.113715i
$$59$$ 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i $$0.0325726\pi$$
−0.408919 + 0.912571i $$0.634094\pi$$
$$60$$ 0 0
$$61$$ 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i $$-0.729619\pi$$
0.980507 + 0.196485i $$0.0629528\pi$$
$$62$$ 4.00000 0.508001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 2.00000 3.46410i 0.248069 0.429669i
$$66$$ 0 0
$$67$$ 4.50000 + 7.79423i 0.549762 + 0.952217i 0.998290 + 0.0584478i $$0.0186151\pi$$
−0.448528 + 0.893769i $$0.648052\pi$$
$$68$$ 1.00000 1.73205i 0.121268 0.210042i
$$69$$ 0 0
$$70$$ 8.00000 + 6.92820i 0.956183 + 0.828079i
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i $$-0.129326\pi$$
−0.801553 + 0.597924i $$0.795992\pi$$
$$74$$ 1.00000 + 1.73205i 0.116248 + 0.201347i
$$75$$ 0 0
$$76$$ 6.00000 0.688247
$$77$$ 2.00000 + 1.73205i 0.227921 + 0.197386i
$$78$$ 0 0
$$79$$ 7.50000 12.9904i 0.843816 1.46153i −0.0428296 0.999082i $$-0.513637\pi$$
0.886646 0.462450i $$-0.153029\pi$$
$$80$$ −2.00000 3.46410i −0.223607 0.387298i
$$81$$ 0 0
$$82$$ −1.00000 + 1.73205i −0.110432 + 0.191273i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ −8.00000 −0.867722
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ 0 0
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ 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
$$91$$ 2.50000 0.866025i 0.262071 0.0907841i
$$92$$ 2.00000 0.208514
$$93$$ 0 0
$$94$$ 1.00000 + 1.73205i 0.103142 + 0.178647i
$$95$$ −12.0000 20.7846i −1.23117 2.13246i
$$96$$ 0 0
$$97$$ −5.00000 −0.507673 −0.253837 0.967247i $$-0.581693\pi$$
−0.253837 + 0.967247i $$0.581693\pi$$
$$98$$ 1.00000 + 6.92820i 0.101015 + 0.699854i
$$99$$ 0 0
$$100$$ −5.50000 + 9.52628i −0.550000 + 0.952628i
$$101$$ −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i $$-0.898506\pi$$
0.203317 0.979113i $$-0.434828\pi$$
$$102$$ 0 0
$$103$$ −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i $$0.368011\pi$$
−0.994071 + 0.108729i $$0.965322\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 12.0000 1.16554
$$107$$ 4.00000 6.92820i 0.386695 0.669775i −0.605308 0.795991i $$-0.706950\pi$$
0.992003 + 0.126217i $$0.0402834\pi$$
$$108$$ 0 0
$$109$$ −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i $$-0.325636\pi$$
−0.999708 + 0.0241802i $$0.992302\pi$$
$$110$$ −2.00000 + 3.46410i −0.190693 + 0.330289i
$$111$$ 0 0
$$112$$ 0.500000 2.59808i 0.0472456 0.245495i
$$113$$ −17.0000 −1.59923 −0.799613 0.600516i $$-0.794962\pi$$
−0.799613 + 0.600516i $$0.794962\pi$$
$$114$$ 0 0
$$115$$ −4.00000 6.92820i −0.373002 0.646058i
$$116$$ 0.500000 + 0.866025i 0.0464238 + 0.0804084i
$$117$$ 0 0
$$118$$ −9.00000 −0.828517
$$119$$ −4.00000 3.46410i −0.366679 0.317554i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ 2.50000 + 4.33013i 0.226339 + 0.392031i
$$123$$ 0 0
$$124$$ −2.00000 + 3.46410i −0.179605 + 0.311086i
$$125$$ 24.0000 2.14663
$$126$$ 0 0
$$127$$ 5.00000 0.443678 0.221839 0.975083i $$-0.428794\pi$$
0.221839 + 0.975083i $$0.428794\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 2.00000 + 3.46410i 0.175412 + 0.303822i
$$131$$ −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i $$0.454690\pi$$
−0.928199 + 0.372084i $$0.878643\pi$$
$$132$$ 0 0
$$133$$ 3.00000 15.5885i 0.260133 1.35169i
$$134$$ −9.00000 −0.777482
$$135$$ 0 0
$$136$$ 1.00000 + 1.73205i 0.0857493 + 0.148522i
$$137$$ −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i $$-0.292279\pi$$
−0.991694 + 0.128618i $$0.958946\pi$$
$$138$$ 0 0
$$139$$ 8.00000 0.678551 0.339276 0.940687i $$-0.389818\pi$$
0.339276 + 0.940687i $$0.389818\pi$$
$$140$$ −10.0000 + 3.46410i −0.845154 + 0.292770i
$$141$$ 0 0
$$142$$ 2.00000 3.46410i 0.167836 0.290701i
$$143$$ 0.500000 + 0.866025i 0.0418121 + 0.0724207i
$$144$$ 0 0
$$145$$ 2.00000 3.46410i 0.166091 0.287678i
$$146$$ −2.00000 −0.165521
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i $$-0.967671\pi$$
0.585231 + 0.810867i $$0.301004\pi$$
$$150$$ 0 0
$$151$$ −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i $$-0.286010\pi$$
−0.988969 + 0.148124i $$0.952676\pi$$
$$152$$ −3.00000 + 5.19615i −0.243332 + 0.421464i
$$153$$ 0 0
$$154$$ −2.50000 + 0.866025i −0.201456 + 0.0697863i
$$155$$ 16.0000 1.28515
$$156$$ 0 0
$$157$$ −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i $$-0.217693\pi$$
−0.934731 + 0.355357i $$0.884359\pi$$
$$158$$ 7.50000 + 12.9904i 0.596668 + 1.03346i
$$159$$ 0 0
$$160$$ 4.00000 0.316228
$$161$$ 1.00000 5.19615i 0.0788110 0.409514i
$$162$$ 0 0
$$163$$ −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i $$0.336695\pi$$
−0.999944 + 0.0105623i $$0.996638\pi$$
$$164$$ −1.00000 1.73205i −0.0780869 0.135250i
$$165$$ 0 0
$$166$$ −3.00000 + 5.19615i −0.232845 + 0.403300i
$$167$$ 17.0000 1.31550 0.657750 0.753237i $$-0.271508\pi$$
0.657750 + 0.753237i $$0.271508\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 4.00000 6.92820i 0.306786 0.531369i
$$171$$ 0 0
$$172$$ −2.00000 3.46410i −0.152499 0.264135i
$$173$$ −2.50000 + 4.33013i −0.190071 + 0.329213i −0.945274 0.326278i $$-0.894205\pi$$
0.755202 + 0.655492i $$0.227539\pi$$
$$174$$ 0 0
$$175$$ 22.0000 + 19.0526i 1.66304 + 1.44024i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ 3.00000 + 5.19615i 0.224860 + 0.389468i
$$179$$ 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i $$-0.00518305\pi$$
−0.514035 + 0.857769i $$0.671850\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ −0.500000 + 2.59808i −0.0370625 + 0.192582i
$$183$$ 0 0
$$184$$ −1.00000 + 1.73205i −0.0737210 + 0.127688i
$$185$$ 4.00000 + 6.92820i 0.294086 + 0.509372i
$$186$$ 0 0
$$187$$ 1.00000 1.73205i 0.0731272 0.126660i
$$188$$ −2.00000 −0.145865
$$189$$ 0 0
$$190$$ 24.0000 1.74114
$$191$$ 7.00000 12.1244i 0.506502 0.877288i −0.493469 0.869763i $$-0.664272\pi$$
0.999972 0.00752447i $$-0.00239513\pi$$
$$192$$ 0 0
$$193$$ 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i $$0.124188\pi$$
−0.133056 + 0.991109i $$0.542479\pi$$
$$194$$ 2.50000 4.33013i 0.179490 0.310885i
$$195$$ 0 0
$$196$$ −6.50000 2.59808i −0.464286 0.185577i
$$197$$ 3.00000 0.213741 0.106871 0.994273i $$-0.465917\pi$$
0.106871 + 0.994273i $$0.465917\pi$$
$$198$$ 0 0
$$199$$ −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i $$-0.281995\pi$$
−0.987022 + 0.160585i $$0.948662\pi$$
$$200$$ −5.50000 9.52628i −0.388909 0.673610i
$$201$$ 0 0
$$202$$ 15.0000 1.05540
$$203$$ 2.50000 0.866025i 0.175466 0.0607831i
$$204$$ 0 0
$$205$$ −4.00000 + 6.92820i −0.279372 + 0.483887i
$$206$$ −6.00000 10.3923i −0.418040 0.724066i
$$207$$ 0 0
$$208$$ 0.500000 0.866025i 0.0346688 0.0600481i
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ −14.0000 −0.963800 −0.481900 0.876226i $$-0.660053\pi$$
−0.481900 + 0.876226i $$0.660053\pi$$
$$212$$ −6.00000 + 10.3923i −0.412082 + 0.713746i
$$213$$ 0 0
$$214$$ 4.00000 + 6.92820i 0.273434 + 0.473602i
$$215$$ −8.00000 + 13.8564i −0.545595 + 0.944999i
$$216$$ 0 0
$$217$$ 8.00000 + 6.92820i 0.543075 + 0.470317i
$$218$$ 10.0000 0.677285
$$219$$ 0 0
$$220$$ −2.00000 3.46410i −0.134840 0.233550i
$$221$$ −1.00000 1.73205i −0.0672673 0.116510i
$$222$$ 0 0
$$223$$ −26.0000 −1.74109 −0.870544 0.492090i $$-0.836233\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ 2.00000 + 1.73205i 0.133631 + 0.115728i
$$225$$ 0 0
$$226$$ 8.50000 14.7224i 0.565412 0.979322i
$$227$$ 5.00000 + 8.66025i 0.331862 + 0.574801i 0.982877 0.184263i $$-0.0589899\pi$$
−0.651015 + 0.759065i $$0.725657\pi$$
$$228$$ 0 0
$$229$$ 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i $$-0.656030\pi$$
0.999442 0.0334101i $$-0.0106368\pi$$
$$230$$ 8.00000 0.527504
$$231$$ 0 0
$$232$$ −1.00000 −0.0656532
$$233$$ 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i $$-0.770364\pi$$
0.947403 + 0.320043i $$0.103697\pi$$
$$234$$ 0 0
$$235$$ 4.00000 + 6.92820i 0.260931 + 0.451946i
$$236$$ 4.50000 7.79423i 0.292925 0.507361i
$$237$$ 0 0
$$238$$ 5.00000 1.73205i 0.324102 0.112272i
$$239$$ −19.0000 −1.22901 −0.614504 0.788914i $$-0.710644\pi$$
−0.614504 + 0.788914i $$0.710644\pi$$
$$240$$ 0 0
$$241$$ −15.0000 25.9808i −0.966235 1.67357i −0.706260 0.707953i $$-0.749619\pi$$
−0.259975 0.965615i $$-0.583714\pi$$
$$242$$ −0.500000 0.866025i −0.0321412 0.0556702i
$$243$$ 0 0
$$244$$ −5.00000 −0.320092
$$245$$ 4.00000 + 27.7128i 0.255551 + 1.77051i
$$246$$ 0 0
$$247$$ 3.00000 5.19615i 0.190885 0.330623i
$$248$$ −2.00000 3.46410i −0.127000 0.219971i
$$249$$ 0 0
$$250$$ −12.0000 + 20.7846i −0.758947 + 1.31453i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 2.00000 0.125739
$$254$$ −2.50000 + 4.33013i −0.156864 + 0.271696i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −10.5000 + 18.1865i −0.654972 + 1.13444i 0.326929 + 0.945049i $$0.393986\pi$$
−0.981901 + 0.189396i $$0.939347\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 5.19615i −0.0621370 + 0.322873i
$$260$$ −4.00000 −0.248069
$$261$$ 0 0
$$262$$ −9.00000 15.5885i −0.556022 0.963058i
$$263$$ 1.50000 + 2.59808i 0.0924940 + 0.160204i 0.908560 0.417755i $$-0.137183\pi$$
−0.816066 + 0.577959i $$0.803849\pi$$
$$264$$ 0 0
$$265$$ 48.0000 2.94862
$$266$$ 12.0000 + 10.3923i 0.735767 + 0.637193i
$$267$$ 0 0
$$268$$ 4.50000 7.79423i 0.274881 0.476108i
$$269$$ 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i $$-0.0474530\pi$$
−0.623082 + 0.782157i $$0.714120\pi$$
$$270$$ 0 0
$$271$$ −12.5000 + 21.6506i −0.759321 + 1.31518i 0.183876 + 0.982949i $$0.441135\pi$$
−0.943197 + 0.332233i $$0.892198\pi$$
$$272$$ −2.00000 −0.121268
$$273$$ 0 0
$$274$$ 9.00000 0.543710
$$275$$ −5.50000 + 9.52628i −0.331662 + 0.574456i
$$276$$ 0 0
$$277$$ 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i $$-0.137940\pi$$
−0.817438 + 0.576017i $$0.804606\pi$$
$$278$$ −4.00000 + 6.92820i −0.239904 + 0.415526i
$$279$$ 0 0
$$280$$ 2.00000 10.3923i 0.119523 0.621059i
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i $$-0.109597\pi$$
−0.762978 + 0.646425i $$0.776263\pi$$
$$284$$ 2.00000 + 3.46410i 0.118678 + 0.205557i
$$285$$ 0 0
$$286$$ −1.00000 −0.0591312
$$287$$ −5.00000 + 1.73205i −0.295141 + 0.102240i
$$288$$ 0 0
$$289$$ 6.50000 11.2583i 0.382353 0.662255i
$$290$$ 2.00000 + 3.46410i 0.117444 + 0.203419i
$$291$$ 0 0
$$292$$ 1.00000 1.73205i 0.0585206 0.101361i
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 0 0
$$295$$ −36.0000 −2.09600
$$296$$ 1.00000 1.73205i 0.0581238 0.100673i
$$297$$ 0 0
$$298$$ −5.00000 8.66025i −0.289642 0.501675i
$$299$$ 1.00000 1.73205i 0.0578315 0.100167i
$$300$$ 0 0
$$301$$ −10.0000 + 3.46410i −0.576390 + 0.199667i
$$302$$ 9.00000 0.517892
$$303$$ 0 0
$$304$$ −3.00000 5.19615i −0.172062 0.298020i
$$305$$ 10.0000 + 17.3205i 0.572598 + 0.991769i
$$306$$ 0 0
$$307$$ 32.0000 1.82634 0.913168 0.407583i $$-0.133628\pi$$
0.913168 + 0.407583i $$0.133628\pi$$
$$308$$ 0.500000 2.59808i 0.0284901 0.148039i
$$309$$ 0 0
$$310$$ −8.00000 + 13.8564i −0.454369 + 0.786991i
$$311$$ −14.0000 24.2487i −0.793867 1.37502i −0.923556 0.383464i $$-0.874731\pi$$
0.129689 0.991555i $$-0.458602\pi$$
$$312$$ 0 0
$$313$$ −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i $$-0.842331\pi$$
0.851549 + 0.524276i $$0.175664\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 0 0
$$316$$ −15.0000 −0.843816
$$317$$ −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i $$-0.942743\pi$$
0.646872 + 0.762598i $$0.276077\pi$$
$$318$$ 0 0
$$319$$ 0.500000 + 0.866025i 0.0279946 + 0.0484881i
$$320$$ −2.00000 + 3.46410i −0.111803 + 0.193649i
$$321$$ 0 0
$$322$$ 4.00000 + 3.46410i 0.222911 + 0.193047i
$$323$$ −12.0000 −0.667698
$$324$$ 0 0
$$325$$ 5.50000 + 9.52628i 0.305085 + 0.528423i
$$326$$ −6.50000 11.2583i −0.360002 0.623541i
$$327$$ 0 0
$$328$$ 2.00000 0.110432
$$329$$ −1.00000 + 5.19615i −0.0551318 + 0.286473i
$$330$$ 0 0
$$331$$ −3.50000 + 6.06218i −0.192377 + 0.333207i −0.946038 0.324057i $$-0.894953\pi$$
0.753660 + 0.657264i $$0.228286\pi$$
$$332$$ −3.00000 5.19615i −0.164646 0.285176i
$$333$$ 0 0
$$334$$ −8.50000 + 14.7224i −0.465099 + 0.805576i
$$335$$ −36.0000 −1.96689
$$336$$ 0 0
$$337$$ −30.0000 −1.63420 −0.817102 0.576493i $$-0.804421\pi$$
−0.817102 + 0.576493i $$0.804421\pi$$
$$338$$ 6.00000 10.3923i 0.326357 0.565267i
$$339$$ 0 0
$$340$$ 4.00000 + 6.92820i 0.216930 + 0.375735i
$$341$$ −2.00000 + 3.46410i −0.108306 + 0.187592i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 4.00000 0.215666
$$345$$ 0 0
$$346$$ −2.50000 4.33013i −0.134401 0.232789i
$$347$$ −14.0000 24.2487i −0.751559 1.30174i −0.947067 0.321037i $$-0.895969\pi$$
0.195507 0.980702i $$-0.437365\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ −27.5000 + 9.52628i −1.46994 + 0.509201i
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i $$-0.325675\pi$$
−0.999711 + 0.0240566i $$0.992342\pi$$
$$354$$ 0 0
$$355$$ 8.00000 13.8564i 0.424596 0.735422i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −13.0000 −0.687071
$$359$$ −15.5000 + 26.8468i −0.818059 + 1.41692i 0.0890519 + 0.996027i $$0.471616\pi$$
−0.907111 + 0.420892i $$0.861717\pi$$
$$360$$ 0 0
$$361$$ −8.50000 14.7224i −0.447368 0.774865i
$$362$$ 11.0000 19.0526i 0.578147 1.00138i
$$363$$ 0 0
$$364$$ −2.00000 1.73205i −0.104828 0.0907841i
$$365$$ −8.00000 −0.418739
$$366$$ 0 0
$$367$$ 7.00000 + 12.1244i 0.365397 + 0.632886i 0.988840 0.148983i $$-0.0475999\pi$$
−0.623443 + 0.781869i $$0.714267\pi$$
$$368$$ −1.00000 1.73205i −0.0521286 0.0902894i
$$369$$ 0 0
$$370$$ −8.00000 −0.415900
$$371$$ 24.0000 + 20.7846i 1.24602 + 1.07908i
$$372$$ 0 0
$$373$$ 3.50000 6.06218i 0.181223 0.313888i −0.761074 0.648665i $$-0.775328\pi$$
0.942297 + 0.334777i $$0.108661\pi$$
$$374$$ 1.00000 + 1.73205i 0.0517088 + 0.0895622i
$$375$$ 0 0
$$376$$ 1.00000 1.73205i 0.0515711 0.0893237i
$$377$$ 1.00000 0.0515026
$$378$$ 0 0
$$379$$ −29.0000 −1.48963 −0.744815 0.667271i $$-0.767462\pi$$
−0.744815 + 0.667271i $$0.767462\pi$$
$$380$$ −12.0000 + 20.7846i −0.615587 + 1.06623i
$$381$$ 0 0
$$382$$ 7.00000 + 12.1244i 0.358151 + 0.620336i
$$383$$ 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i $$-0.767812\pi$$
0.949938 + 0.312437i $$0.101145\pi$$
$$384$$ 0 0
$$385$$ −10.0000 + 3.46410i −0.509647 + 0.176547i
$$386$$ −22.0000 −1.11977
$$387$$ 0 0
$$388$$ 2.50000 + 4.33013i 0.126918 + 0.219829i
$$389$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 5.50000 4.33013i 0.277792 0.218704i
$$393$$ 0 0
$$394$$ −1.50000 + 2.59808i −0.0755689 + 0.130889i
$$395$$ 30.0000 + 51.9615i 1.50946 + 2.61447i
$$396$$ 0 0
$$397$$ 15.0000 25.9808i 0.752828 1.30394i −0.193618 0.981077i $$-0.562022\pi$$
0.946447 0.322860i $$-0.104644\pi$$
$$398$$ 10.0000 0.501255
$$399$$ 0 0
$$400$$ 11.0000 0.550000
$$401$$ 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i $$-0.711137\pi$$
0.990257 + 0.139253i $$0.0444700\pi$$
$$402$$ 0 0
$$403$$ 2.00000 + 3.46410i 0.0996271 + 0.172559i
$$404$$ −7.50000 + 12.9904i −0.373139 + 0.646296i
$$405$$ 0 0
$$406$$ −0.500000 + 2.59808i −0.0248146 + 0.128940i
$$407$$ −2.00000 −0.0991363
$$408$$ 0 0
$$409$$ 16.0000 + 27.7128i 0.791149 + 1.37031i 0.925256 + 0.379344i $$0.123850\pi$$
−0.134107 + 0.990967i $$0.542817\pi$$
$$410$$ −4.00000 6.92820i −0.197546 0.342160i
$$411$$ 0 0
$$412$$ 12.0000 0.591198
$$413$$ −18.0000 15.5885i −0.885722 0.767058i
$$414$$ 0 0
$$415$$ −12.0000 + 20.7846i −0.589057 + 1.02028i
$$416$$ 0.500000 + 0.866025i 0.0245145 + 0.0424604i
$$417$$ 0 0
$$418$$ −3.00000 + 5.19615i −0.146735 + 0.254152i
$$419$$ 20.0000 0.977064 0.488532 0.872546i $$-0.337533\pi$$
0.488532 + 0.872546i $$0.337533\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ 7.00000 12.1244i 0.340755 0.590204i
$$423$$ 0 0
$$424$$ −6.00000 10.3923i −0.291386 0.504695i
$$425$$ 11.0000 19.0526i 0.533578 0.924185i
$$426$$ 0 0
$$427$$ −2.50000 + 12.9904i −0.120983 + 0.628649i
$$428$$ −8.00000 −0.386695
$$429$$ 0 0
$$430$$ −8.00000 13.8564i −0.385794 0.668215i
$$431$$ 0.500000 + 0.866025i 0.0240842 + 0.0417150i 0.877816 0.478997i $$-0.159000\pi$$
−0.853732 + 0.520712i $$0.825666\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ −10.0000 + 3.46410i −0.480015 + 0.166282i
$$435$$ 0 0
$$436$$ −5.00000 + 8.66025i −0.239457 + 0.414751i
$$437$$ −6.00000 10.3923i −0.287019 0.497131i
$$438$$ 0 0
$$439$$ 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i $$-0.795262\pi$$
0.919498 + 0.393095i $$0.128596\pi$$
$$440$$ 4.00000 0.190693
$$441$$ 0 0
$$442$$ 2.00000 0.0951303
$$443$$ −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i $$-0.925350\pi$$
0.687557 + 0.726130i $$0.258683\pi$$
$$444$$ 0 0
$$445$$ 12.0000 + 20.7846i 0.568855 + 0.985285i
$$446$$ 13.0000 22.5167i 0.615568 1.06619i
$$447$$ 0 0
$$448$$ −2.50000 + 0.866025i −0.118114 + 0.0409159i
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 0 0
$$451$$ −1.00000 1.73205i −0.0470882 0.0815591i
$$452$$ 8.50000 + 14.7224i 0.399806 + 0.692485i
$$453$$ 0 0
$$454$$ −10.0000 −0.469323
$$455$$ −2.00000 + 10.3923i −0.0937614 + 0.487199i
$$456$$ 0 0
$$457$$ −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i $$-0.848229\pi$$
0.841688 + 0.539964i $$0.181562\pi$$
$$458$$ 8.00000 + 13.8564i 0.373815 + 0.647467i
$$459$$ 0 0
$$460$$ −4.00000 + 6.92820i −0.186501 + 0.323029i
$$461$$ 3.00000 0.139724 0.0698620 0.997557i $$-0.477744\pi$$
0.0698620 + 0.997557i $$0.477744\pi$$
$$462$$ 0 0
$$463$$ −14.0000 −0.650635 −0.325318 0.945605i $$-0.605471\pi$$
−0.325318 + 0.945605i $$0.605471\pi$$
$$464$$ 0.500000 0.866025i 0.0232119 0.0402042i
$$465$$ 0 0
$$466$$ 3.00000 + 5.19615i 0.138972 + 0.240707i
$$467$$ −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i $$-0.922888\pi$$
0.693153 + 0.720791i $$0.256221\pi$$
$$468$$ 0 0
$$469$$ −18.0000 15.5885i −0.831163 0.719808i
$$470$$ −8.00000 −0.369012
$$471$$ 0 0
$$472$$ 4.50000 + 7.79423i 0.207129 + 0.358758i
$$473$$ −2.00000 3.46410i −0.0919601 0.159280i
$$474$$ 0 0
$$475$$ 66.0000 3.02829
$$476$$ −1.00000 + 5.19615i −0.0458349 + 0.238165i
$$477$$ 0 0
$$478$$ 9.50000 16.4545i 0.434520 0.752611i
$$479$$ −18.5000 32.0429i −0.845287 1.46408i −0.885372 0.464883i $$-0.846096\pi$$
0.0400855 0.999196i $$-0.487237\pi$$
$$480$$ 0 0
$$481$$ −1.00000 + 1.73205i −0.0455961 + 0.0789747i
$$482$$ 30.0000 1.36646
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 10.0000 17.3205i 0.454077 0.786484i
$$486$$ 0 0
$$487$$ 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i $$-0.137779\pi$$
−0.817147 + 0.576429i $$0.804446\pi$$
$$488$$ 2.50000 4.33013i 0.113170 0.196016i
$$489$$ 0 0
$$490$$ −26.0000 10.3923i −1.17456 0.469476i
$$491$$ −18.0000 −0.812329 −0.406164 0.913800i $$-0.633134\pi$$
−0.406164 + 0.913800i $$0.633134\pi$$
$$492$$ 0 0
$$493$$ −1.00000 1.73205i −0.0450377 0.0780076i
$$494$$ 3.00000 + 5.19615i 0.134976 + 0.233786i
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 10.0000 3.46410i 0.448561 0.155386i
$$498$$ 0 0
$$499$$ 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i $$-0.716748\pi$$
0.987648 + 0.156687i $$0.0500814\pi$$
$$500$$ −12.0000 20.7846i −0.536656 0.929516i
$$501$$ 0 0
$$502$$ 6.00000 10.3923i 0.267793 0.463831i
$$503$$ 21.0000 0.936344 0.468172 0.883637i $$-0.344913\pi$$
0.468172 + 0.883637i $$0.344913\pi$$
$$504$$ 0 0
$$505$$ 60.0000 2.66996
$$506$$ −1.00000 + 1.73205i −0.0444554 + 0.0769991i
$$507$$ 0 0
$$508$$ −2.50000 4.33013i −0.110920 0.192118i
$$509$$ 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i $$-0.819220\pi$$
0.887336 + 0.461123i $$0.152553\pi$$
$$510$$ 0 0
$$511$$ −4.00000 3.46410i −0.176950 0.153243i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −10.5000 18.1865i −0.463135 0.802174i
$$515$$ −24.0000 41.5692i −1.05757 1.83176i
$$516$$ 0 0
$$517$$ −2.00000 −0.0879599
$$518$$ −4.00000 3.46410i −0.175750 0.152204i
$$519$$ 0 0
$$520$$ 2.00000 3.46410i 0.0877058 0.151911i
$$521$$ −13.0000 22.5167i −0.569540 0.986473i −0.996611 0.0822547i $$-0.973788\pi$$
0.427071 0.904218i $$-0.359545\pi$$
$$522$$ 0 0
$$523$$ −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i $$-0.977388\pi$$
0.560208 + 0.828352i $$0.310721\pi$$
$$524$$ 18.0000 0.786334
$$525$$ 0 0
$$526$$ −3.00000 −0.130806
$$527$$ 4.00000 6.92820i 0.174243 0.301797i
$$528$$ 0 0
$$529$$ 9.50000 + 16.4545i 0.413043 + 0.715412i
$$530$$ −24.0000 + 41.5692i −1.04249 + 1.80565i
$$531$$ 0 0
$$532$$ −15.0000 + 5.19615i −0.650332 + 0.225282i
$$533$$ −2.00000 −0.0866296
$$534$$ 0 0
$$535$$ 16.0000 + 27.7128i 0.691740 + 1.19813i
$$536$$ 4.50000 + 7.79423i 0.194370 + 0.336659i
$$537$$ 0 0
$$538$$ −12.0000 −0.517357
$$539$$ −6.50000 2.59808i −0.279975 0.111907i
$$540$$ 0 0
$$541$$ 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i $$-0.652733\pi$$
0.999042 0.0437584i $$-0.0139332\pi$$
$$542$$ −12.5000 21.6506i −0.536921 0.929974i
$$543$$ 0 0
$$544$$ 1.00000 1.73205i 0.0428746 0.0742611i
$$545$$ 40.0000 1.71341
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ −4.50000 + 7.79423i −0.192230 + 0.332953i
$$549$$ 0 0
$$550$$ −5.50000 9.52628i −0.234521 0.406202i
$$551$$ 3.00000 5.19615i 0.127804 0.221364i
$$552$$ 0 0
$$553$$ −7.50000 + 38.9711i −0.318932 + 1.65722i
$$554$$ −3.00000 −0.127458
$$555$$ 0 0
$$556$$ −4.00000 6.92820i −0.169638 0.293821i
$$557$$ 19.0000 + 32.9090i 0.805056 + 1.39440i 0.916253 + 0.400599i $$0.131198\pi$$
−0.111198 + 0.993798i $$0.535469\pi$$
$$558$$ 0 0
$$559$$ −4.00000 −0.169182
$$560$$ 8.00000 + 6.92820i 0.338062 + 0.292770i
$$561$$ 0 0
$$562$$ −5.00000 + 8.66025i −0.210912 + 0.365311i
$$563$$ 13.0000 + 22.5167i 0.547885 + 0.948964i 0.998419 + 0.0562051i $$0.0179001\pi$$
−0.450535 + 0.892759i $$0.648767\pi$$
$$564$$ 0 0
$$565$$ 34.0000 58.8897i 1.43039 2.47751i
$$566$$ −6.00000 −0.252199
$$567$$ 0 0
$$568$$ −4.00000 −0.167836
$$569$$ 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i $$-0.561165\pi$$
0.945573 0.325409i $$-0.105502\pi$$
$$570$$ 0 0
$$571$$ 10.0000 + 17.3205i 0.418487 + 0.724841i 0.995788 0.0916910i $$-0.0292272\pi$$
−0.577301 + 0.816532i $$0.695894\pi$$
$$572$$ 0.500000 0.866025i 0.0209061 0.0362103i
$$573$$ 0 0
$$574$$ 1.00000 5.19615i 0.0417392 0.216883i
$$575$$ 22.0000 0.917463
$$576$$ 0 0
$$577$$ 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i $$-0.120121\pi$$
−0.783930 + 0.620850i $$0.786788\pi$$
$$578$$ 6.50000 + 11.2583i 0.270364 + 0.468285i
$$579$$ 0 0
$$580$$ −4.00000 −0.166091
$$581$$ −15.0000 + 5.19615i −0.622305 + 0.215573i
$$582$$ 0 0
$$583$$ −6.00000 + 10.3923i −0.248495 + 0.430405i
$$584$$ 1.00000 + 1.73205i 0.0413803 + 0.0716728i
$$585$$ 0 0
$$586$$ −3.00000 + 5.19615i −0.123929 + 0.214651i
$$587$$ 3.00000 0.123823 0.0619116 0.998082i $$-0.480280\pi$$
0.0619116 + 0.998082i $$0.480280\pi$$
$$588$$ 0 0
$$589$$ 24.0000 0.988903
$$590$$ 18.0000 31.1769i 0.741048 1.28353i
$$591$$ 0 0
$$592$$ 1.00000 + 1.73205i 0.0410997 + 0.0711868i
$$593$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$594$$ 0 0
$$595$$ 20.0000 6.92820i 0.819920 0.284029i
$$596$$ 10.0000 0.409616
$$597$$ 0 0
$$598$$ 1.00000 + 1.73205i 0.0408930 + 0.0708288i
$$599$$ −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i $$-0.329782\pi$$
−0.999938 + 0.0111569i $$0.996449\pi$$
$$600$$ 0 0
$$601$$ 26.0000 1.06056 0.530281 0.847822i $$-0.322086\pi$$
0.530281 + 0.847822i $$0.322086\pi$$
$$602$$ 2.00000 10.3923i 0.0815139 0.423559i
$$603$$ 0 0
$$604$$ −4.50000 + 7.79423i −0.183102 + 0.317143i
$$605$$ −2.00000 3.46410i −0.0813116 0.140836i
$$606$$ 0 0
$$607$$ 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i $$-0.728067\pi$$
0.981454 + 0.191700i $$0.0614000\pi$$
$$608$$ 6.00000 0.243332
$$609$$ 0 0
$$610$$ −20.0000 −0.809776
$$611$$ −1.00000 + 1.73205i −0.0404557 + 0.0700713i
$$612$$ 0 0
$$613$$ −11.0000 19.0526i −0.444286 0.769526i 0.553716 0.832705i $$-0.313209\pi$$
−0.998002 + 0.0631797i $$0.979876\pi$$
$$614$$ −16.0000 + 27.7128i −0.645707 + 1.11840i
$$615$$ 0 0
$$616$$ 2.00000 + 1.73205i 0.0805823 + 0.0697863i
$$617$$ 27.0000 1.08698 0.543490 0.839416i $$-0.317103\pi$$
0.543490 + 0.839416i $$0.317103\pi$$
$$618$$ 0 0
$$619$$ −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i $$-0.298329\pi$$
−0.993959 + 0.109749i $$0.964995\pi$$
$$620$$ −8.00000 13.8564i −0.321288 0.556487i
$$621$$ 0 0
$$622$$ 28.0000 1.12270
$$623$$ −3.00000 + 15.5885i −0.120192 + 0.624538i
$$624$$ 0 0
$$625$$ −20.5000 + 35.5070i −0.820000 + 1.42028i
$$626$$ −0.500000 0.866025i −0.0199840 0.0346133i
$$627$$ 0 0
$$628$$ −2.00000 + 3.46410i −0.0798087 + 0.138233i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 7.50000 12.9904i 0.298334 0.516730i
$$633$$ 0 0
$$634$$ −6.00000 10.3923i −0.238290 0.412731i
$$635$$ −10.0000 + 17.3205i −0.396838 + 0.687343i
$$636$$ 0 0
$$637$$ −5.50000 + 4.33013i −0.217918 + 0.171566i
$$638$$ −1.00000 −0.0395904
$$639$$ 0 0
$$640$$ −2.00000 3.46410i −0.0790569 0.136931i
$$641$$ 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i $$-0.109788\pi$$
−0.763367 + 0.645966i $$0.776455\pi$$
$$642$$ 0 0
$$643$$ 1.00000 0.0394362 0.0197181 0.999806i $$-0.493723\pi$$
0.0197181 + 0.999806i $$0.493723\pi$$
$$644$$ −5.00000 + 1.73205i −0.197028 + 0.0682524i
$$645$$ 0 0
$$646$$ 6.00000 10.3923i 0.236067 0.408880i
$$647$$ 12.0000 + 20.7846i 0.471769 + 0.817127i 0.999478 0.0322975i $$-0.0102824\pi$$
−0.527710 + 0.849425i $$0.676949\pi$$
$$648$$ 0 0
$$649$$ 4.50000 7.79423i 0.176640 0.305950i
$$650$$ −11.0000 −0.431455
$$651$$ 0 0
$$652$$ 13.0000 0.509119
$$653$$ 11.0000 19.0526i 0.430463 0.745584i −0.566450 0.824096i $$-0.691684\pi$$
0.996913 + 0.0785119i $$0.0250169\pi$$
$$654$$ 0 0
$$655$$ −36.0000 62.3538i −1.40664 2.43637i
$$656$$ −1.00000 + 1.73205i −0.0390434 + 0.0676252i
$$657$$ 0 0
$$658$$ −4.00000 3.46410i −0.155936 0.135045i
$$659$$ 32.0000 1.24654 0.623272 0.782006i $$-0.285803\pi$$
0.623272 + 0.782006i $$0.285803\pi$$
$$660$$ 0 0
$$661$$ 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i $$-0.104366\pi$$
−0.752252 + 0.658876i $$0.771032\pi$$
$$662$$ −3.50000 6.06218i −0.136031 0.235613i
$$663$$ 0 0
$$664$$ 6.00000 0.232845
$$665$$ 48.0000 + 41.5692i 1.86136 + 1.61199i
$$666$$ 0 0
$$667$$ 1.00000 1.73205i 0.0387202 0.0670653i
$$668$$ −8.50000 14.7224i −0.328875 0.569628i
$$669$$ 0 0
$$670$$ 18.0000 31.1769i 0.695401 1.20447i
$$671$$ −5.00000 −0.193023
$$672$$ 0 0
$$673$$ 16.0000 0.616755 0.308377 0.951264i $$-0.400214\pi$$
0.308377 + 0.951264i $$0.400214\pi$$
$$674$$ 15.0000 25.9808i 0.577778 1.00074i
$$675$$ 0 0
$$676$$ 6.00000 + 10.3923i 0.230769 + 0.399704i
$$677$$ 19.0000 32.9090i 0.730229 1.26479i −0.226556 0.973998i $$-0.572747\pi$$
0.956785 0.290796i $$-0.0939201\pi$$
$$678$$ 0 0
$$679$$ 12.5000 4.33013i 0.479706 0.166175i
$$680$$ −8.00000 −0.306786
$$681$$ 0 0
$$682$$ −2.00000 3.46410i −0.0765840 0.132647i
$$683$$ −16.5000 28.5788i −0.631355 1.09354i −0.987275 0.159022i $$-0.949166\pi$$
0.355920 0.934516i $$-0.384168\pi$$
$$684$$ 0 0
$$685$$ 36.0000 1.37549
$$686$$ −8.50000 16.4545i −0.324532 0.628235i
$$687$$ 0 0
$$688$$ −2.00000 + 3.46410i −0.0762493 + 0.132068i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −7.50000 + 12.9904i −0.285313 + 0.494177i −0.972685 0.232128i $$-0.925431\pi$$
0.687372 + 0.726306i $$0.258764\pi$$
$$692$$ 5.00000 0.190071
$$693$$ 0 0
$$694$$ 28.0000 1.06287
$$695$$ −16.0000 + 27.7128i −0.606915 + 1.05121i
$$696$$ 0 0
$$697$$ 2.00000 + 3.46410i 0.0757554 + 0.131212i
$$698$$ −1.00000 + 1.73205i −0.0378506 + 0.0655591i
$$699$$ 0 0
$$700$$ 5.50000 28.5788i 0.207880 1.08018i
$$701$$ −39.0000 −1.47301 −0.736505 0.676432i $$-0.763525\pi$$
−0.736505 + 0.676432i $$0.763525\pi$$
$$702$$ 0 0
$$703$$ 6.00000 + 10.3923i 0.226294 + 0.391953i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 18.0000 0.677439
$$707$$ 30.0000 + 25.9808i 1.12827 + 0.977107i
$$708$$ 0 0
$$709$$ −3.00000 + 5.19615i −0.112667 + 0.195146i −0.916845 0.399244i $$-0.869273\pi$$
0.804178 + 0.594389i $$0.202606\pi$$
$$710$$ 8.00000 + 13.8564i 0.300235 + 0.520022i
$$711$$ 0 0
$$712$$ 3.00000 5.19615i 0.112430 0.194734i
$$713$$ 8.00000 0.299602
$$714$$ 0 0
$$715$$ −4.00000 −0.149592
$$716$$ 6.50000 11.2583i 0.242916 0.420744i
$$717$$ 0 0
$$718$$ −15.5000 26.8468i −0.578455 1.00191i
$$719$$ −13.0000 + 22.5167i −0.484818 + 0.839730i −0.999848 0.0174426i $$-0.994448\pi$$
0.515030 + 0.857172i $$0.327781\pi$$
$$720$$ 0 0
$$721$$ 6.00000 31.1769i 0.223452 1.16109i
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ 11.0000 + 19.0526i 0.408812 + 0.708083i
$$725$$ 5.50000 + 9.52628i 0.204265 + 0.353797i
$$726$$ 0 0
$$727$$ −34.0000 −1.26099 −0.630495 0.776193i $$-0.717148\pi$$
−0.630495 + 0.776193i $$0.717148\pi$$
$$728$$ 2.50000 0.866025i 0.0926562 0.0320970i
$$729$$ 0 0
$$730$$ 4.00000 6.92820i 0.148047 0.256424i
$$731$$ 4.00000 + 6.92820i 0.147945 + 0.256249i
$$732$$ 0 0
$$733$$ 0.500000 0.866025i 0.0184679 0.0319874i −0.856644 0.515908i $$-0.827454\pi$$
0.875112 + 0.483921i $$0.160788\pi$$
$$734$$ −14.0000 −0.516749
$$735$$ 0 0
$$736$$ 2.00000 0.0737210
$$737$$ 4.50000 7.79423i 0.165760 0.287104i
$$738$$ 0 0
$$739$$ −9.00000 15.5885i −0.331070 0.573431i 0.651652 0.758518i $$-0.274076\pi$$
−0.982722 + 0.185088i $$0.940743\pi$$
$$740$$ 4.00000 6.92820i 0.147043 0.254686i
$$741$$ 0 0
$$742$$ −30.0000 + 10.3923i −1.10133 + 0.381514i
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ −20.0000 34.6410i −0.732743 1.26915i
$$746$$ 3.50000 + 6.06218i 0.128144 + 0.221952i
$$747$$ 0 0
$$748$$ −2.00000 −0.0731272
$$749$$ −4.00000 + 20.7846i −0.146157 + 0.759453i
$$750$$ 0 0
$$751$$ 22.0000 38.1051i 0.802791 1.39048i −0.114981 0.993368i $$-0.536681\pi$$
0.917772 0.397108i $$-0.129986\pi$$
$$752$$ 1.00000 + 1.73205i 0.0364662 + 0.0631614i
$$753$$ 0 0
$$754$$ −0.500000 + 0.866025i −0.0182089 + 0.0315388i
$$755$$ 36.0000 1.31017
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 14.5000 25.1147i 0.526664 0.912208i
$$759$$ 0 0
$$760$$ −12.0000 20.7846i −0.435286 0.753937i
$$761$$ 27.0000 46.7654i 0.978749 1.69524i 0.311787 0.950152i $$-0.399073\pi$$
0.666962 0.745091i $$-0.267594\pi$$
$$762$$ 0 0
$$763$$ 20.0000 + 17.3205i 0.724049 + 0.627044i
$$764$$ −14.0000 −0.506502
$$765$$ 0 0
$$766$$ 4.00000 + 6.92820i 0.144526 + 0.250326i
$$767$$ −4.50000 7.79423i −0.162486 0.281433i
$$768$$ 0 0
$$769$$ −38.0000 −1.37032 −0.685158 0.728395i $$-0.740267\pi$$
−0.685158 + 0.728395i $$0.740267\pi$$
$$770$$ 2.00000 10.3923i 0.0720750 0.374513i
$$771$$ 0 0
$$772$$ 11.0000 19.0526i 0.395899 0.685717i
$$773$$ −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i $$-0.308721\pi$$
−0.997012 + 0.0772449i $$0.975388\pi$$
$$774$$ 0 0
$$775$$ −22.0000 + 38.1051i −0.790263 + 1.36878i
$$776$$ −5.00000 −0.179490
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −6.00000 + 10.3923i −0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 2.00000 + 3.46410i 0.0715656 + 0.123955i
$$782$$ 2.00000 3.46410i 0.0715199 0.123876i
$$783$$ 0 0
$$784$$ 1.00000 + 6.92820i 0.0357143 + 0.247436i
$$785$$ 16.0000 0.571064
$$786$$ 0 0
$$787$$ 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i $$-0.0384127\pi$$
−0.600620 + 0.799535i $$0.705079\pi$$
$$788$$ −1.50000 2.59808i −0.0534353 0.0925526i
$$789$$