# Properties

 Label 1386.2.k.j.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $0$ 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: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 462) 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.j.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-0.500000 - 0.866025i) q^{11} +6.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-3.00000 + 5.19615i) q^{19} -3.00000 q^{20} +1.00000 q^{22} +(2.50000 - 4.33013i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-3.00000 + 5.19615i) q^{26} +(2.00000 + 1.73205i) q^{28} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +5.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(1.50000 - 2.59808i) q^{40} -5.00000 q^{41} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(2.50000 + 4.33013i) q^{46} +(4.50000 - 7.79423i) q^{47} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} -3.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(9.00000 - 15.5885i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(-6.00000 - 5.19615i) q^{70} -4.00000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(2.00000 + 1.73205i) q^{77} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 - 4.33013i) q^{82} -1.00000 q^{83} -15.0000 q^{85} +(5.00000 - 8.66025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-15.0000 + 5.19615i) q^{91} -5.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(9.00000 + 15.5885i) q^{95} +9.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{2} - q^{4} + 3 q^{5} - 5 q^{7} + 2 q^{8} + O(q^{10})$$ $$2 q - q^{2} - q^{4} + 3 q^{5} - 5 q^{7} + 2 q^{8} + 3 q^{10} - q^{11} + 12 q^{13} + q^{14} - q^{16} - 5 q^{17} - 6 q^{19} - 6 q^{20} + 2 q^{22} + 5 q^{23} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 12 q^{29} - 4 q^{31} - q^{32} + 10 q^{34} - 3 q^{35} + 2 q^{37} - 6 q^{38} + 3 q^{40} - 10 q^{41} - 20 q^{43} - q^{44} + 5 q^{46} + 9 q^{47} + 11 q^{49} + 8 q^{50} - 6 q^{52} + 2 q^{53} - 6 q^{55} - 5 q^{56} - 6 q^{58} - 12 q^{59} + 5 q^{61} + 8 q^{62} + 2 q^{64} + 18 q^{65} - 5 q^{67} - 5 q^{68} - 12 q^{70} - 8 q^{71} - 12 q^{73} + 2 q^{74} + 12 q^{76} + 4 q^{77} + q^{79} + 3 q^{80} + 5 q^{82} - 2 q^{83} - 30 q^{85} + 10 q^{86} - q^{88} + 6 q^{89} - 30 q^{91} - 10 q^{92} + 9 q^{94} + 18 q^{95} + 18 q^{97} + 2 q^{98} + O(q^{100})$$

## 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
$$5$$ 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i $$-0.599275\pi$$
0.977672 0.210138i $$-0.0673912\pi$$
$$6$$ 0 0
$$7$$ −2.50000 + 0.866025i −0.944911 + 0.327327i
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 1.50000 + 2.59808i 0.474342 + 0.821584i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ 0 0
$$13$$ 6.00000 1.66410 0.832050 0.554700i $$-0.187167\pi$$
0.832050 + 0.554700i $$0.187167\pi$$
$$14$$ 0.500000 2.59808i 0.133631 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i $$-0.959304\pi$$
0.385499 0.922708i $$-0.374029\pi$$
$$18$$ 0 0
$$19$$ −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i $$0.408286\pi$$
−0.972404 + 0.233301i $$0.925047\pi$$
$$20$$ −3.00000 −0.670820
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ 2.50000 4.33013i 0.521286 0.902894i −0.478407 0.878138i $$-0.658786\pi$$
0.999694 0.0247559i $$-0.00788087\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ −3.00000 + 5.19615i −0.588348 + 1.01905i
$$27$$ 0 0
$$28$$ 2.00000 + 1.73205i 0.377964 + 0.327327i
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 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
$$34$$ 5.00000 0.857493
$$35$$ −1.50000 + 7.79423i −0.253546 + 1.31747i
$$36$$ 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
$$40$$ 1.50000 2.59808i 0.237171 0.410792i
$$41$$ −5.00000 −0.780869 −0.390434 0.920631i $$-0.627675\pi$$
−0.390434 + 0.920631i $$0.627675\pi$$
$$42$$ 0 0
$$43$$ −10.0000 −1.52499 −0.762493 0.646997i $$-0.776025\pi$$
−0.762493 + 0.646997i $$0.776025\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ 2.50000 + 4.33013i 0.368605 + 0.638442i
$$47$$ 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i $$-0.605415\pi$$
0.981543 0.191243i $$-0.0612518\pi$$
$$48$$ 0 0
$$49$$ 5.50000 4.33013i 0.785714 0.618590i
$$50$$ 4.00000 0.565685
$$51$$ 0 0
$$52$$ −3.00000 5.19615i −0.416025 0.720577i
$$53$$ 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ 0 0
$$55$$ −3.00000 −0.404520
$$56$$ −2.50000 + 0.866025i −0.334077 + 0.115728i
$$57$$ 0 0
$$58$$ −3.00000 + 5.19615i −0.393919 + 0.682288i
$$59$$ −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i $$-0.881308\pi$$
0.150148 0.988663i $$-0.452025\pi$$
$$60$$ 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
$$65$$ 9.00000 15.5885i 1.11631 1.93351i
$$66$$ 0 0
$$67$$ −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i $$-0.265465\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ −2.50000 + 4.33013i −0.303170 + 0.525105i
$$69$$ 0 0
$$70$$ −6.00000 5.19615i −0.717137 0.621059i
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0 0
$$73$$ −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i $$-0.918847\pi$$
0.265429 0.964130i $$-0.414486\pi$$
$$74$$ 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
$$79$$ 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i $$-0.815418\pi$$
0.892781 + 0.450490i $$0.148751\pi$$
$$80$$ 1.50000 + 2.59808i 0.167705 + 0.290474i
$$81$$ 0 0
$$82$$ 2.50000 4.33013i 0.276079 0.478183i
$$83$$ −1.00000 −0.109764 −0.0548821 0.998493i $$-0.517478\pi$$
−0.0548821 + 0.998493i $$0.517478\pi$$
$$84$$ 0 0
$$85$$ −15.0000 −1.62698
$$86$$ 5.00000 8.66025i 0.539164 0.933859i
$$87$$ 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
$$91$$ −15.0000 + 5.19615i −1.57243 + 0.544705i
$$92$$ −5.00000 −0.521286
$$93$$ 0 0
$$94$$ 4.50000 + 7.79423i 0.464140 + 0.803913i
$$95$$ 9.00000 + 15.5885i 0.923381 + 1.59934i
$$96$$ 0 0
$$97$$ 9.00000 0.913812 0.456906 0.889515i $$-0.348958\pi$$
0.456906 + 0.889515i $$0.348958\pi$$
$$98$$ 1.00000 + 6.92820i 0.101015 + 0.699854i
$$99$$ 0 0
$$100$$ −2.00000 + 3.46410i −0.200000 + 0.346410i
$$101$$ −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i $$-0.296967\pi$$
−0.993481 + 0.113998i $$0.963634\pi$$
$$102$$ 0 0
$$103$$ 1.00000 1.73205i 0.0985329 0.170664i −0.812545 0.582899i $$-0.801918\pi$$
0.911078 + 0.412235i $$0.135252\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ −2.00000 −0.194257
$$107$$ −6.50000 + 11.2583i −0.628379 + 1.08838i 0.359498 + 0.933146i $$0.382948\pi$$
−0.987877 + 0.155238i $$0.950386\pi$$
$$108$$ 0 0
$$109$$ 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i $$0.00994332\pi$$
−0.472708 + 0.881219i $$0.656723\pi$$
$$110$$ 1.50000 2.59808i 0.143019 0.247717i
$$111$$ 0 0
$$112$$ 0.500000 2.59808i 0.0472456 0.245495i
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ 0 0
$$115$$ −7.50000 12.9904i −0.699379 1.21136i
$$116$$ −3.00000 5.19615i −0.278543 0.482451i
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 10.0000 + 8.66025i 0.916698 + 0.793884i
$$120$$ 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
$$125$$ 3.00000 0.268328
$$126$$ 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
$$130$$ 9.00000 + 15.5885i 0.789352 + 1.36720i
$$131$$ −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i $$-0.889242\pi$$
0.765331 + 0.643637i $$0.222575\pi$$
$$132$$ 0 0
$$133$$ 3.00000 15.5885i 0.260133 1.35169i
$$134$$ 5.00000 0.431934
$$135$$ 0 0
$$136$$ −2.50000 4.33013i −0.214373 0.371305i
$$137$$ −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i $$-0.193895\pi$$
−0.905577 + 0.424182i $$0.860562\pi$$
$$138$$ 0 0
$$139$$ 22.0000 1.86602 0.933008 0.359856i $$-0.117174\pi$$
0.933008 + 0.359856i $$0.117174\pi$$
$$140$$ 7.50000 2.59808i 0.633866 0.219578i
$$141$$ 0 0
$$142$$ 2.00000 3.46410i 0.167836 0.290701i
$$143$$ −3.00000 5.19615i −0.250873 0.434524i
$$144$$ 0 0
$$145$$ 9.00000 15.5885i 0.747409 1.29455i
$$146$$ 12.0000 0.993127
$$147$$ 0 0
$$148$$ −2.00000 −0.164399
$$149$$ 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i $$-0.569430\pi$$
0.953703 0.300750i $$-0.0972370\pi$$
$$150$$ 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
$$155$$ −12.0000 −0.963863
$$156$$ 0 0
$$157$$ 12.0000 + 20.7846i 0.957704 + 1.65879i 0.728055 + 0.685519i $$0.240425\pi$$
0.229650 + 0.973273i $$0.426242\pi$$
$$158$$ 0.500000 + 0.866025i 0.0397779 + 0.0688973i
$$159$$ 0 0
$$160$$ −3.00000 −0.237171
$$161$$ −2.50000 + 12.9904i −0.197028 + 1.02379i
$$162$$ 0 0
$$163$$ 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i $$-0.820864\pi$$
0.884943 + 0.465700i $$0.154198\pi$$
$$164$$ 2.50000 + 4.33013i 0.195217 + 0.338126i
$$165$$ 0 0
$$166$$ 0.500000 0.866025i 0.0388075 0.0672166i
$$167$$ 24.0000 1.85718 0.928588 0.371113i $$-0.121024\pi$$
0.928588 + 0.371113i $$0.121024\pi$$
$$168$$ 0 0
$$169$$ 23.0000 1.76923
$$170$$ 7.50000 12.9904i 0.575224 0.996317i
$$171$$ 0 0
$$172$$ 5.00000 + 8.66025i 0.381246 + 0.660338i
$$173$$ −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i $$-0.984113\pi$$
0.542583 + 0.840002i $$0.317446\pi$$
$$174$$ 0 0
$$175$$ 8.00000 + 6.92820i 0.604743 + 0.523723i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ 3.00000 + 5.19615i 0.224860 + 0.389468i
$$179$$ −4.00000 6.92820i −0.298974 0.517838i 0.676927 0.736050i $$-0.263311\pi$$
−0.975901 + 0.218212i $$0.929978\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 3.00000 15.5885i 0.222375 1.15549i
$$183$$ 0 0
$$184$$ 2.50000 4.33013i 0.184302 0.319221i
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ −2.50000 + 4.33013i −0.182818 + 0.316650i
$$188$$ −9.00000 −0.656392
$$189$$ 0 0
$$190$$ −18.0000 −1.30586
$$191$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$192$$ 0 0
$$193$$ −3.00000 5.19615i −0.215945 0.374027i 0.737620 0.675216i $$-0.235950\pi$$
−0.953564 + 0.301189i $$0.902616\pi$$
$$194$$ −4.50000 + 7.79423i −0.323081 + 0.559593i
$$195$$ 0 0
$$196$$ −6.50000 2.59808i −0.464286 0.185577i
$$197$$ 24.0000 1.70993 0.854965 0.518686i $$-0.173579\pi$$
0.854965 + 0.518686i $$0.173579\pi$$
$$198$$ 0 0
$$199$$ −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i $$-0.281995\pi$$
−0.987022 + 0.160585i $$0.948662\pi$$
$$200$$ −2.00000 3.46410i −0.141421 0.244949i
$$201$$ 0 0
$$202$$ 8.00000 0.562878
$$203$$ −15.0000 + 5.19615i −1.05279 + 0.364698i
$$204$$ 0 0
$$205$$ −7.50000 + 12.9904i −0.523823 + 0.907288i
$$206$$ 1.00000 + 1.73205i 0.0696733 + 0.120678i
$$207$$ 0 0
$$208$$ −3.00000 + 5.19615i −0.208013 + 0.360288i
$$209$$ 6.00000 0.415029
$$210$$ 0 0
$$211$$ 14.0000 0.963800 0.481900 0.876226i $$-0.339947\pi$$
0.481900 + 0.876226i $$0.339947\pi$$
$$212$$ 1.00000 1.73205i 0.0686803 0.118958i
$$213$$ 0 0
$$214$$ −6.50000 11.2583i −0.444331 0.769604i
$$215$$ −15.0000 + 25.9808i −1.02299 + 1.77187i
$$216$$ 0 0
$$217$$ 8.00000 + 6.92820i 0.543075 + 0.470317i
$$218$$ −11.0000 −0.745014
$$219$$ 0 0
$$220$$ 1.50000 + 2.59808i 0.101130 + 0.175162i
$$221$$ −15.0000 25.9808i −1.00901 1.74766i
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 2.00000 + 1.73205i 0.133631 + 0.115728i
$$225$$ 0 0
$$226$$ 5.00000 8.66025i 0.332595 0.576072i
$$227$$ 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i $$-0.134924\pi$$
−0.811943 + 0.583736i $$0.801590\pi$$
$$228$$ 0 0
$$229$$ −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i $$0.495620\pi$$
−0.872823 + 0.488037i $$0.837713\pi$$
$$230$$ 15.0000 0.989071
$$231$$ 0 0
$$232$$ 6.00000 0.393919
$$233$$ −14.5000 + 25.1147i −0.949927 + 1.64532i −0.204354 + 0.978897i $$0.565509\pi$$
−0.745573 + 0.666424i $$0.767824\pi$$
$$234$$ 0 0
$$235$$ −13.5000 23.3827i −0.880643 1.52532i
$$236$$ −6.00000 + 10.3923i −0.390567 + 0.676481i
$$237$$ 0 0
$$238$$ −12.5000 + 4.33013i −0.810255 + 0.280680i
$$239$$ −26.0000 −1.68180 −0.840900 0.541190i $$-0.817974\pi$$
−0.840900 + 0.541190i $$0.817974\pi$$
$$240$$ 0 0
$$241$$ 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i $$0.149261\pi$$
−0.0546547 + 0.998505i $$0.517406\pi$$
$$242$$ −0.500000 0.866025i −0.0321412 0.0556702i
$$243$$ 0 0
$$244$$ −5.00000 −0.320092
$$245$$ −3.00000 20.7846i −0.191663 1.32788i
$$246$$ 0 0
$$247$$ −18.0000 + 31.1769i −1.14531 + 1.98374i
$$248$$ −2.00000 3.46410i −0.127000 0.219971i
$$249$$ 0 0
$$250$$ −1.50000 + 2.59808i −0.0948683 + 0.164317i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ −5.00000 −0.314347
$$254$$ −2.50000 + 4.33013i −0.156864 + 0.271696i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i $$-0.977168\pi$$
0.560781 + 0.827964i $$0.310501\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 5.19615i −0.0621370 + 0.322873i
$$260$$ −18.0000 −1.11631
$$261$$ 0 0
$$262$$ −2.00000 3.46410i −0.123560 0.214013i
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 0 0
$$265$$ 6.00000 0.368577
$$266$$ 12.0000 + 10.3923i 0.735767 + 0.637193i
$$267$$ 0 0
$$268$$ −2.50000 + 4.33013i −0.152712 + 0.264505i
$$269$$ −4.50000 7.79423i −0.274370 0.475223i 0.695606 0.718423i $$-0.255136\pi$$
−0.969976 + 0.243201i $$0.921803\pi$$
$$270$$ 0 0
$$271$$ 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i $$-0.573343\pi$$
0.957328 0.289003i $$-0.0933238\pi$$
$$272$$ 5.00000 0.303170
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ −2.00000 + 3.46410i −0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ −9.00000 15.5885i −0.540758 0.936620i −0.998861 0.0477206i $$-0.984804\pi$$
0.458103 0.888899i $$-0.348529\pi$$
$$278$$ −11.0000 + 19.0526i −0.659736 + 1.14270i
$$279$$ 0 0
$$280$$ −1.50000 + 7.79423i −0.0896421 + 0.465794i
$$281$$ −11.0000 −0.656205 −0.328102 0.944642i $$-0.606409\pi$$
−0.328102 + 0.944642i $$0.606409\pi$$
$$282$$ 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
$$286$$ 6.00000 0.354787
$$287$$ 12.5000 4.33013i 0.737852 0.255599i
$$288$$ 0 0
$$289$$ −4.00000 + 6.92820i −0.235294 + 0.407541i
$$290$$ 9.00000 + 15.5885i 0.528498 + 0.915386i
$$291$$ 0 0
$$292$$ −6.00000 + 10.3923i −0.351123 + 0.608164i
$$293$$ −8.00000 −0.467365 −0.233682 0.972313i $$-0.575078\pi$$
−0.233682 + 0.972313i $$0.575078\pi$$
$$294$$ 0 0
$$295$$ −36.0000 −2.09600
$$296$$ 1.00000 1.73205i 0.0581238 0.100673i
$$297$$ 0 0
$$298$$ 9.00000 + 15.5885i 0.521356 + 0.903015i
$$299$$ 15.0000 25.9808i 0.867472 1.50251i
$$300$$ 0 0
$$301$$ 25.0000 8.66025i 1.44098 0.499169i
$$302$$ 9.00000 0.517892
$$303$$ 0 0
$$304$$ −3.00000 5.19615i −0.172062 0.298020i
$$305$$ −7.50000 12.9904i −0.429449 0.743827i
$$306$$ 0 0
$$307$$ 18.0000 1.02731 0.513657 0.857996i $$-0.328290\pi$$
0.513657 + 0.857996i $$0.328290\pi$$
$$308$$ 0.500000 2.59808i 0.0284901 0.148039i
$$309$$ 0 0
$$310$$ 6.00000 10.3923i 0.340777 0.590243i
$$311$$ −10.5000 18.1865i −0.595400 1.03126i −0.993490 0.113917i $$-0.963660\pi$$
0.398090 0.917346i $$-0.369673\pi$$
$$312$$ 0 0
$$313$$ 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i $$-0.779095\pi$$
0.938269 + 0.345907i $$0.112429\pi$$
$$314$$ −24.0000 −1.35440
$$315$$ 0 0
$$316$$ −1.00000 −0.0562544
$$317$$ 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i $$-0.752000\pi$$
0.964281 + 0.264883i $$0.0853332\pi$$
$$318$$ 0 0
$$319$$ −3.00000 5.19615i −0.167968 0.290929i
$$320$$ 1.50000 2.59808i 0.0838525 0.145237i
$$321$$ 0 0
$$322$$ −10.0000 8.66025i −0.557278 0.482617i
$$323$$ 30.0000 1.66924
$$324$$ 0 0
$$325$$ −12.0000 20.7846i −0.665640 1.15292i
$$326$$ 0.500000 + 0.866025i 0.0276924 + 0.0479647i
$$327$$ 0 0
$$328$$ −5.00000 −0.276079
$$329$$ −4.50000 + 23.3827i −0.248093 + 1.28913i
$$330$$ 0 0
$$331$$ −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i $$0.578503\pi$$
−0.717756 + 0.696295i $$0.754831\pi$$
$$332$$ 0.500000 + 0.866025i 0.0274411 + 0.0475293i
$$333$$ 0 0
$$334$$ −12.0000 + 20.7846i −0.656611 + 1.13728i
$$335$$ −15.0000 −0.819538
$$336$$ 0 0
$$337$$ −2.00000 −0.108947 −0.0544735 0.998515i $$-0.517348\pi$$
−0.0544735 + 0.998515i $$0.517348\pi$$
$$338$$ −11.5000 + 19.9186i −0.625518 + 1.08343i
$$339$$ 0 0
$$340$$ 7.50000 + 12.9904i 0.406745 + 0.704502i
$$341$$ −2.00000 + 3.46410i −0.108306 + 0.187592i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ −10.0000 −0.539164
$$345$$ 0 0
$$346$$ −6.00000 10.3923i −0.322562 0.558694i
$$347$$ 3.50000 + 6.06218i 0.187890 + 0.325435i 0.944547 0.328378i $$-0.106502\pi$$
−0.756657 + 0.653812i $$0.773169\pi$$
$$348$$ 0 0
$$349$$ −19.0000 −1.01705 −0.508523 0.861048i $$-0.669808\pi$$
−0.508523 + 0.861048i $$0.669808\pi$$
$$350$$ −10.0000 + 3.46410i −0.534522 + 0.185164i
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i $$0.0538590\pi$$
−0.347024 + 0.937856i $$0.612808\pi$$
$$354$$ 0 0
$$355$$ −6.00000 + 10.3923i −0.318447 + 0.551566i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 8.00000 0.422813
$$359$$ −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i $$-0.918339\pi$$
0.703382 + 0.710812i $$0.251672\pi$$
$$360$$ 0 0
$$361$$ −8.50000 14.7224i −0.447368 0.774865i
$$362$$ 11.0000 19.0526i 0.578147 1.00138i
$$363$$ 0 0
$$364$$ 12.0000 + 10.3923i 0.628971 + 0.544705i
$$365$$ −36.0000 −1.88433
$$366$$ 0 0
$$367$$ 7.00000 + 12.1244i 0.365397 + 0.632886i 0.988840 0.148983i $$-0.0475999\pi$$
−0.623443 + 0.781869i $$0.714267\pi$$
$$368$$ 2.50000 + 4.33013i 0.130322 + 0.225723i
$$369$$ 0 0
$$370$$ 6.00000 0.311925
$$371$$ −4.00000 3.46410i −0.207670 0.179847i
$$372$$ 0 0
$$373$$ 3.50000 6.06218i 0.181223 0.313888i −0.761074 0.648665i $$-0.775328\pi$$
0.942297 + 0.334777i $$0.108661\pi$$
$$374$$ −2.50000 4.33013i −0.129272 0.223906i
$$375$$ 0 0
$$376$$ 4.50000 7.79423i 0.232070 0.401957i
$$377$$ 36.0000 1.85409
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 9.00000 15.5885i 0.461690 0.799671i
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 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
$$385$$ 7.50000 2.59808i 0.382235 0.132410i
$$386$$ 6.00000 0.305392
$$387$$ 0 0
$$388$$ −4.50000 7.79423i −0.228453 0.395692i
$$389$$ −10.5000 18.1865i −0.532371 0.922094i −0.999286 0.0377914i $$-0.987968\pi$$
0.466915 0.884302i $$-0.345366\pi$$
$$390$$ 0 0
$$391$$ −25.0000 −1.26430
$$392$$ 5.50000 4.33013i 0.277792 0.218704i
$$393$$ 0 0
$$394$$ −12.0000 + 20.7846i −0.604551 + 1.04711i
$$395$$ −1.50000 2.59808i −0.0754732 0.130723i
$$396$$ 0 0
$$397$$ −13.0000 + 22.5167i −0.652451 + 1.13008i 0.330075 + 0.943955i $$0.392926\pi$$
−0.982526 + 0.186124i $$0.940407\pi$$
$$398$$ 10.0000 0.501255
$$399$$ 0 0
$$400$$ 4.00000 0.200000
$$401$$ −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i $$-0.881200\pi$$
0.781345 + 0.624099i $$0.214534\pi$$
$$402$$ 0 0
$$403$$ −12.0000 20.7846i −0.597763 1.03536i
$$404$$ −4.00000 + 6.92820i −0.199007 + 0.344691i
$$405$$ 0 0
$$406$$ 3.00000 15.5885i 0.148888 0.773642i
$$407$$ −2.00000 −0.0991363
$$408$$ 0 0
$$409$$ −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i $$-0.246188\pi$$
−0.962757 + 0.270367i $$0.912855\pi$$
$$410$$ −7.50000 12.9904i −0.370399 0.641549i
$$411$$ 0 0
$$412$$ −2.00000 −0.0985329
$$413$$ 24.0000 + 20.7846i 1.18096 + 1.02274i
$$414$$ 0 0
$$415$$ −1.50000 + 2.59808i −0.0736321 + 0.127535i
$$416$$ −3.00000 5.19615i −0.147087 0.254762i
$$417$$ 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
$$421$$ 8.00000 0.389896 0.194948 0.980814i $$-0.437546\pi$$
0.194948 + 0.980814i $$0.437546\pi$$
$$422$$ −7.00000 + 12.1244i −0.340755 + 0.590204i
$$423$$ 0 0
$$424$$ 1.00000 + 1.73205i 0.0485643 + 0.0841158i
$$425$$ −10.0000 + 17.3205i −0.485071 + 0.840168i
$$426$$ 0 0
$$427$$ −2.50000 + 12.9904i −0.120983 + 0.628649i
$$428$$ 13.0000 0.628379
$$429$$ 0 0
$$430$$ −15.0000 25.9808i −0.723364 1.25290i
$$431$$ 11.0000 + 19.0526i 0.529851 + 0.917729i 0.999394 + 0.0348195i $$0.0110856\pi$$
−0.469542 + 0.882910i $$0.655581\pi$$
$$432$$ 0 0
$$433$$ 11.0000 0.528626 0.264313 0.964437i $$-0.414855\pi$$
0.264313 + 0.964437i $$0.414855\pi$$
$$434$$ −10.0000 + 3.46410i −0.480015 + 0.166282i
$$435$$ 0 0
$$436$$ 5.50000 9.52628i 0.263402 0.456226i
$$437$$ 15.0000 + 25.9808i 0.717547 + 1.24283i
$$438$$ 0 0
$$439$$ 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i $$-0.795262\pi$$
0.919498 + 0.393095i $$0.128596\pi$$
$$440$$ −3.00000 −0.143019
$$441$$ 0 0
$$442$$ 30.0000 1.42695
$$443$$ 1.00000 1.73205i 0.0475114 0.0822922i −0.841292 0.540581i $$-0.818204\pi$$
0.888803 + 0.458289i $$0.151538\pi$$
$$444$$ 0 0
$$445$$ −9.00000 15.5885i −0.426641 0.738964i
$$446$$ −8.00000 + 13.8564i −0.378811 + 0.656120i
$$447$$ 0 0
$$448$$ −2.50000 + 0.866025i −0.118114 + 0.0409159i
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 2.50000 + 4.33013i 0.117720 + 0.203898i
$$452$$ 5.00000 + 8.66025i 0.235180 + 0.407344i
$$453$$ 0 0
$$454$$ −3.00000 −0.140797
$$455$$ −9.00000 + 46.7654i −0.421927 + 2.19239i
$$456$$ 0 0
$$457$$ 13.0000 22.5167i 0.608114 1.05328i −0.383437 0.923567i $$-0.625260\pi$$
0.991551 0.129718i $$-0.0414071\pi$$
$$458$$ −13.0000 22.5167i −0.607450 1.05213i
$$459$$ 0 0
$$460$$ −7.50000 + 12.9904i −0.349689 + 0.605680i
$$461$$ 10.0000 0.465746 0.232873 0.972507i $$-0.425187\pi$$
0.232873 + 0.972507i $$0.425187\pi$$
$$462$$ 0 0
$$463$$ 28.0000 1.30127 0.650635 0.759390i $$-0.274503\pi$$
0.650635 + 0.759390i $$0.274503\pi$$
$$464$$ −3.00000 + 5.19615i −0.139272 + 0.241225i
$$465$$ 0 0
$$466$$ −14.5000 25.1147i −0.671700 1.16342i
$$467$$ 8.00000 13.8564i 0.370196 0.641198i −0.619400 0.785076i $$-0.712624\pi$$
0.989595 + 0.143878i $$0.0459572\pi$$
$$468$$ 0 0
$$469$$ 10.0000 + 8.66025i 0.461757 + 0.399893i
$$470$$ 27.0000 1.24542
$$471$$ 0 0
$$472$$ −6.00000 10.3923i −0.276172 0.478345i
$$473$$ 5.00000 + 8.66025i 0.229900 + 0.398199i
$$474$$ 0 0
$$475$$ 24.0000 1.10120
$$476$$ 2.50000 12.9904i 0.114587 0.595413i
$$477$$ 0 0
$$478$$ 13.0000 22.5167i 0.594606 1.02989i
$$479$$ 6.00000 + 10.3923i 0.274147 + 0.474837i 0.969920 0.243426i $$-0.0782712\pi$$
−0.695773 + 0.718262i $$0.744938\pi$$
$$480$$ 0 0
$$481$$ 6.00000 10.3923i 0.273576 0.473848i
$$482$$ −26.0000 −1.18427
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ 13.5000 23.3827i 0.613003 1.06175i
$$486$$ 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
$$490$$ 19.5000 + 7.79423i 0.880920 + 0.352107i
$$491$$ 3.00000 0.135388 0.0676941 0.997706i $$-0.478436\pi$$
0.0676941 + 0.997706i $$0.478436\pi$$
$$492$$ 0 0
$$493$$ −15.0000 25.9808i −0.675566 1.17011i
$$494$$ −18.0000 31.1769i −0.809858 1.40272i
$$495$$ 0 0
$$496$$ 4.00000 0.179605
$$497$$ 10.0000 3.46410i 0.448561 0.155386i
$$498$$ 0 0
$$499$$ −6.00000 + 10.3923i −0.268597 + 0.465223i −0.968500 0.249015i $$-0.919893\pi$$
0.699903 + 0.714238i $$0.253227\pi$$
$$500$$ −1.50000 2.59808i −0.0670820 0.116190i
$$501$$ 0 0
$$502$$ 6.00000 10.3923i 0.267793 0.463831i
$$503$$ 42.0000 1.87269 0.936344 0.351085i $$-0.114187\pi$$
0.936344 + 0.351085i $$0.114187\pi$$
$$504$$ 0 0
$$505$$ −24.0000 −1.06799
$$506$$ 2.50000 4.33013i 0.111139 0.192498i
$$507$$ 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
$$511$$ 24.0000 + 20.7846i 1.06170 + 0.919457i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −7.00000 12.1244i −0.308757 0.534782i
$$515$$ −3.00000 5.19615i −0.132196 0.228970i
$$516$$ 0 0
$$517$$ −9.00000 −0.395820
$$518$$ −4.00000 3.46410i −0.175750 0.152204i
$$519$$ 0 0
$$520$$ 9.00000 15.5885i 0.394676 0.683599i
$$521$$ 1.00000 + 1.73205i 0.0438108 + 0.0758825i 0.887099 0.461579i $$-0.152717\pi$$
−0.843288 + 0.537461i $$0.819383\pi$$
$$522$$ 0 0
$$523$$ −3.00000 + 5.19615i −0.131181 + 0.227212i −0.924132 0.382073i $$-0.875210\pi$$
0.792951 + 0.609285i $$0.208544\pi$$
$$524$$ 4.00000 0.174741
$$525$$ 0 0
$$526$$ −24.0000 −1.04645
$$527$$ −10.0000 + 17.3205i −0.435607 + 0.754493i
$$528$$ 0 0
$$529$$ −1.00000 1.73205i −0.0434783 0.0753066i
$$530$$ −3.00000 + 5.19615i −0.130312 + 0.225706i
$$531$$ 0 0
$$532$$ −15.0000 + 5.19615i −0.650332 + 0.225282i
$$533$$ −30.0000 −1.29944
$$534$$ 0 0
$$535$$ 19.5000 + 33.7750i 0.843059 + 1.46022i
$$536$$ −2.50000 4.33013i −0.107984 0.187033i
$$537$$ 0 0
$$538$$ 9.00000 0.388018
$$539$$ −6.50000 2.59808i −0.279975 0.111907i
$$540$$ 0 0
$$541$$ 19.5000 33.7750i 0.838370 1.45210i −0.0528859 0.998601i $$-0.516842\pi$$
0.891256 0.453500i $$-0.149825\pi$$
$$542$$ 12.0000 + 20.7846i 0.515444 + 0.892775i
$$543$$ 0 0
$$544$$ −2.50000 + 4.33013i −0.107187 + 0.185653i
$$545$$ 33.0000 1.41356
$$546$$ 0 0
$$547$$ −42.0000 −1.79579 −0.897895 0.440209i $$-0.854904\pi$$
−0.897895 + 0.440209i $$0.854904\pi$$
$$548$$ −1.00000 + 1.73205i −0.0427179 + 0.0739895i
$$549$$ 0 0
$$550$$ −2.00000 3.46410i −0.0852803 0.147710i
$$551$$ −18.0000 + 31.1769i −0.766826 + 1.32818i
$$552$$ 0 0
$$553$$ −0.500000 + 2.59808i −0.0212622 + 0.110481i
$$554$$ 18.0000 0.764747
$$555$$ 0 0
$$556$$ −11.0000 19.0526i −0.466504 0.808008i
$$557$$ −16.0000 27.7128i −0.677942 1.17423i −0.975600 0.219557i $$-0.929539\pi$$
0.297658 0.954673i $$-0.403795\pi$$
$$558$$ 0 0
$$559$$ −60.0000 −2.53773
$$560$$ −6.00000 5.19615i −0.253546 0.219578i
$$561$$ 0 0
$$562$$ 5.50000 9.52628i 0.232003 0.401842i
$$563$$ −8.00000 13.8564i −0.337160 0.583978i 0.646737 0.762713i $$-0.276133\pi$$
−0.983897 + 0.178735i $$0.942800\pi$$
$$564$$ 0 0
$$565$$ −15.0000 + 25.9808i −0.631055 + 1.09302i
$$566$$ −6.00000 −0.252199
$$567$$ 0 0
$$568$$ −4.00000 −0.167836
$$569$$ −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i $$-0.873472\pi$$
0.796266 + 0.604947i $$0.206806\pi$$
$$570$$ 0 0
$$571$$ 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i $$0.0852845\pi$$
−0.252893 + 0.967494i $$0.581382\pi$$
$$572$$ −3.00000 + 5.19615i −0.125436 + 0.217262i
$$573$$ 0 0
$$574$$ −2.50000 + 12.9904i −0.104348 + 0.542208i
$$575$$ −20.0000 −0.834058
$$576$$ 0 0
$$577$$ 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i $$-0.120121\pi$$
−0.783930 + 0.620850i $$0.786788\pi$$
$$578$$ −4.00000 6.92820i −0.166378 0.288175i
$$579$$ 0 0
$$580$$ −18.0000 −0.747409
$$581$$ 2.50000 0.866025i 0.103717 0.0359288i
$$582$$ 0 0
$$583$$ 1.00000 1.73205i 0.0414158 0.0717342i
$$584$$ −6.00000 10.3923i −0.248282 0.430037i
$$585$$ 0 0
$$586$$ 4.00000 6.92820i 0.165238 0.286201i
$$587$$ 24.0000 0.990586 0.495293 0.868726i $$-0.335061\pi$$
0.495293 + 0.868726i $$0.335061\pi$$
$$588$$ 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
$$593$$ 7.00000 12.1244i 0.287456 0.497888i −0.685746 0.727841i $$-0.740524\pi$$
0.973202 + 0.229953i $$0.0738573\pi$$
$$594$$ 0 0
$$595$$ 37.5000 12.9904i 1.53735 0.532554i
$$596$$ −18.0000 −0.737309
$$597$$ 0 0
$$598$$ 15.0000 + 25.9808i 0.613396 + 1.06243i
$$599$$ −1.50000 2.59808i −0.0612883 0.106155i 0.833753 0.552137i $$-0.186188\pi$$
−0.895042 + 0.445983i $$0.852854\pi$$
$$600$$ 0 0
$$601$$ −44.0000 −1.79480 −0.897399 0.441221i $$-0.854546\pi$$
−0.897399 + 0.441221i $$0.854546\pi$$
$$602$$ −5.00000 + 25.9808i −0.203785 + 1.05890i
$$603$$ 0 0
$$604$$ −4.50000 + 7.79423i −0.183102 + 0.317143i
$$605$$ 1.50000 + 2.59808i 0.0609837 + 0.105627i
$$606$$ 0 0
$$607$$ −16.5000 + 28.5788i −0.669714 + 1.15998i 0.308270 + 0.951299i $$0.400250\pi$$
−0.977984 + 0.208680i $$0.933083\pi$$
$$608$$ 6.00000 0.243332
$$609$$ 0 0
$$610$$ 15.0000 0.607332
$$611$$ 27.0000 46.7654i 1.09230 1.89192i
$$612$$ 0 0
$$613$$ 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i $$0.143847\pi$$
−0.0716275 + 0.997431i $$0.522819\pi$$
$$614$$ −9.00000 + 15.5885i −0.363210 + 0.629099i
$$615$$ 0 0
$$616$$ 2.00000 + 1.73205i 0.0805823 + 0.0697863i
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i $$0.0313779\pi$$
−0.412341 + 0.911030i $$0.635289\pi$$
$$620$$ 6.00000 + 10.3923i 0.240966 + 0.417365i
$$621$$ 0 0
$$622$$ 21.0000 0.842023
$$623$$ −3.00000 + 15.5885i −0.120192 + 0.624538i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 3.00000 + 5.19615i 0.119904 + 0.207680i
$$627$$ 0 0
$$628$$ 12.0000 20.7846i 0.478852 0.829396i
$$629$$ −10.0000 −0.398726
$$630$$ 0 0
$$631$$ 28.0000 1.11466 0.557331 0.830290i $$-0.311825\pi$$
0.557331 + 0.830290i $$0.311825\pi$$
$$632$$ 0.500000 0.866025i 0.0198889 0.0344486i
$$633$$ 0 0
$$634$$ 4.50000 + 7.79423i 0.178718 + 0.309548i
$$635$$ 7.50000 12.9904i 0.297628 0.515508i
$$636$$ 0 0
$$637$$ 33.0000 25.9808i 1.30751 1.02940i
$$638$$ 6.00000 0.237542
$$639$$ 0 0
$$640$$ 1.50000 + 2.59808i 0.0592927 + 0.102698i
$$641$$ −20.0000 34.6410i −0.789953 1.36824i −0.925995 0.377535i $$-0.876772\pi$$
0.136043 0.990703i $$-0.456562\pi$$
$$642$$ 0 0
$$643$$ 36.0000 1.41970 0.709851 0.704352i $$-0.248762\pi$$
0.709851 + 0.704352i $$0.248762\pi$$
$$644$$ 12.5000 4.33013i 0.492569 0.170631i
$$645$$ 0 0
$$646$$ −15.0000 + 25.9808i −0.590167 + 1.02220i
$$647$$ 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i $$-0.0582109\pi$$
−0.649155 + 0.760656i $$0.724878\pi$$
$$648$$ 0 0
$$649$$ −6.00000 + 10.3923i −0.235521 + 0.407934i
$$650$$ 24.0000 0.941357
$$651$$ 0 0
$$652$$ −1.00000 −0.0391630
$$653$$ −13.5000 + 23.3827i −0.528296 + 0.915035i 0.471160 + 0.882048i $$0.343835\pi$$
−0.999456 + 0.0329874i $$0.989498\pi$$
$$654$$ 0 0
$$655$$ 6.00000 + 10.3923i 0.234439 + 0.406061i
$$656$$ 2.50000 4.33013i 0.0976086 0.169063i
$$657$$ 0 0
$$658$$ −18.0000 15.5885i −0.701713 0.607701i
$$659$$ −31.0000 −1.20759 −0.603794 0.797140i $$-0.706345\pi$$
−0.603794 + 0.797140i $$0.706345\pi$$
$$660$$ 0 0
$$661$$ −2.00000 3.46410i −0.0777910 0.134738i 0.824506 0.565854i $$-0.191453\pi$$
−0.902297 + 0.431116i $$0.858120\pi$$
$$662$$ −17.5000 30.3109i −0.680157 1.17807i
$$663$$ 0 0
$$664$$ −1.00000 −0.0388075
$$665$$ −36.0000 31.1769i −1.39602 1.20899i
$$666$$ 0 0
$$667$$ 15.0000 25.9808i 0.580802 1.00598i
$$668$$ −12.0000 20.7846i −0.464294 0.804181i
$$669$$ 0 0
$$670$$ 7.50000 12.9904i 0.289750 0.501862i
$$671$$ −5.00000 −0.193023
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 1.00000 1.73205i 0.0385186 0.0667161i
$$675$$ 0 0
$$676$$ −11.5000 19.9186i −0.442308 0.766099i
$$677$$ −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i $$-0.945759\pi$$
0.639618 + 0.768693i $$0.279092\pi$$
$$678$$ 0 0
$$679$$ −22.5000 + 7.79423i −0.863471 + 0.299115i
$$680$$ −15.0000 −0.575224
$$681$$ 0 0
$$682$$ −2.00000 3.46410i −0.0765840 0.132647i
$$683$$ −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i $$-0.240403\pi$$
−0.957685 + 0.287819i $$0.907070\pi$$
$$684$$ 0 0
$$685$$ −6.00000 −0.229248
$$686$$ −8.50000 16.4545i −0.324532 0.628235i
$$687$$ 0 0
$$688$$ 5.00000 8.66025i 0.190623 0.330169i
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ 13.5000 23.3827i 0.513564 0.889519i −0.486312 0.873785i $$-0.661658\pi$$
0.999876 0.0157341i $$-0.00500851\pi$$
$$692$$ 12.0000 0.456172
$$693$$ 0 0
$$694$$ −7.00000 −0.265716
$$695$$ 33.0000 57.1577i 1.25176 2.16811i
$$696$$ 0 0
$$697$$ 12.5000 + 21.6506i 0.473471 + 0.820076i
$$698$$ 9.50000 16.4545i 0.359580 0.622811i
$$699$$ 0 0
$$700$$ 2.00000 10.3923i 0.0755929 0.392792i
$$701$$ 10.0000 0.377695 0.188847 0.982006i $$-0.439525\pi$$
0.188847 + 0.982006i $$0.439525\pi$$
$$702$$ 0 0
$$703$$ 6.00000 + 10.3923i 0.226294 + 0.391953i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ −24.0000 −0.903252
$$707$$ 16.0000 + 13.8564i 0.601742 + 0.521124i
$$708$$ 0 0
$$709$$ −10.0000 + 17.3205i −0.375558 + 0.650485i −0.990410 0.138157i $$-0.955882\pi$$
0.614852 + 0.788642i $$0.289216\pi$$
$$710$$ −6.00000 10.3923i −0.225176 0.390016i
$$711$$ 0 0
$$712$$ 3.00000 5.19615i 0.112430 0.194734i
$$713$$ −20.0000 −0.749006
$$714$$ 0 0
$$715$$ −18.0000 −0.673162
$$716$$ −4.00000 + 6.92820i −0.149487 + 0.258919i
$$717$$ 0 0
$$718$$ −5.00000 8.66025i −0.186598 0.323198i
$$719$$ 18.5000 32.0429i 0.689934 1.19500i −0.281925 0.959436i $$-0.590973\pi$$
0.971859 0.235564i $$-0.0756936\pi$$
$$720$$ 0 0
$$721$$ −1.00000 + 5.19615i −0.0372419 + 0.193515i
$$722$$ 17.0000 0.632674
$$723$$ 0 0
$$724$$ 11.0000 + 19.0526i 0.408812 + 0.708083i
$$725$$ −12.0000 20.7846i −0.445669 0.771921i
$$726$$ 0 0
$$727$$ 22.0000 0.815935 0.407967 0.912996i $$-0.366238\pi$$
0.407967 + 0.912996i $$0.366238\pi$$
$$728$$ −15.0000 + 5.19615i −0.555937 + 0.192582i
$$729$$ 0 0
$$730$$ 18.0000 31.1769i 0.666210 1.15391i
$$731$$ 25.0000 + 43.3013i 0.924658 + 1.60156i
$$732$$ 0 0
$$733$$ 7.50000 12.9904i 0.277019 0.479811i −0.693624 0.720338i $$-0.743987\pi$$
0.970642 + 0.240527i $$0.0773202\pi$$
$$734$$ −14.0000 −0.516749
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ −2.50000 + 4.33013i −0.0920887 + 0.159502i
$$738$$ 0 0
$$739$$ 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i $$-0.107785\pi$$
−0.759287 + 0.650756i $$0.774452\pi$$
$$740$$ −3.00000 + 5.19615i −0.110282 + 0.191014i
$$741$$ 0 0
$$742$$ 5.00000 1.73205i 0.183556 0.0635856i
$$743$$ −22.0000 −0.807102 −0.403551 0.914957i $$-0.632224\pi$$
−0.403551 + 0.914957i $$0.632224\pi$$
$$744$$ 0 0
$$745$$ −27.0000 46.7654i −0.989203 1.71335i
$$746$$ 3.50000 + 6.06218i 0.128144 + 0.221952i
$$747$$ 0 0
$$748$$ 5.00000 0.182818
$$749$$ 6.50000 33.7750i 0.237505 1.23411i
$$750$$ 0 0
$$751$$ 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i $$-0.821715\pi$$
0.883694 + 0.468065i $$0.155049\pi$$
$$752$$ 4.50000 + 7.79423i 0.164098 + 0.284226i
$$753$$ 0 0
$$754$$ −18.0000 + 31.1769i −0.655521 + 1.13540i
$$755$$ −27.0000 −0.982631
$$756$$ 0 0
$$757$$ −2.00000 −0.0726912 −0.0363456 0.999339i $$-0.511572\pi$$
−0.0363456 + 0.999339i $$0.511572\pi$$
$$758$$ −6.50000 + 11.2583i −0.236091 + 0.408921i
$$759$$ 0 0
$$760$$ 9.00000 + 15.5885i 0.326464 + 0.565453i
$$761$$ 23.5000 40.7032i 0.851874 1.47549i −0.0276404 0.999618i $$-0.508799\pi$$
0.879515 0.475872i $$-0.157867\pi$$
$$762$$ 0 0
$$763$$ −22.0000 19.0526i −0.796453 0.689749i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 4.00000 + 6.92820i 0.144526 + 0.250326i
$$767$$ −36.0000 62.3538i −1.29988 2.25147i
$$768$$ 0 0
$$769$$ 46.0000 1.65880 0.829401 0.558653i $$-0.188682\pi$$
0.829401 + 0.558653i $$0.188682\pi$$
$$770$$ −1.50000 + 7.79423i −0.0540562 + 0.280885i
$$771$$ 0 0
$$772$$ −3.00000 + 5.19615i −0.107972 + 0.187014i
$$773$$ 5.50000 + 9.52628i 0.197821 + 0.342636i 0.947822 0.318801i $$-0.103280\pi$$
−0.750000 + 0.661437i $$0.769947\pi$$
$$774$$ 0 0
$$775$$ −8.00000 + 13.8564i −0.287368 + 0.497737i
$$776$$ 9.00000 0.323081
$$777$$ 0 0
$$778$$ 21.0000 0.752886
$$779$$ 15.0000 25.9808i 0.537431 0.930857i
$$780$$ 0 0
$$781$$ 2.00000 + 3.46410i 0.0715656 + 0.123955i
$$782$$ 12.5000 21.6506i 0.446999 0.774225i
$$783$$ 0 0
$$784$$ 1.00000 + 6.92820i 0.0357143 + 0.247436i
$$785$$ 72.0000 2.56979
$$786$$ 0 0
$$787$$ 25.0000 + 43.3013i 0.891154 + 1.54352i 0.838494 + 0.544911i $$0.183437\pi$$
0.0526599 + 0.998613i $$0.483230\pi$$
$$788$$ −12.0000 20.7846i −0.427482 0.740421i
$$789$$