Properties

 Label 2340.2.q.a.2161.1 Level $2340$ Weight $2$ Character 2340.2161 Analytic conductor $18.685$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2340.q (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$18.6849940730$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 260) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 2161.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2340.2161 Dual form 2340.2.q.a.1621.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +O(q^{10})$$ $$q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.50000 - 6.06218i) q^{23} +1.00000 q^{25} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(1.50000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{41} +(4.50000 - 7.79423i) q^{43} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-1.00000 + 3.46410i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{71} -14.0000 q^{73} -9.00000 q^{77} -8.00000 q^{79} -12.0000 q^{83} +(3.50000 - 6.06218i) q^{85} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(0.500000 - 0.866025i) q^{95} +(5.50000 - 9.52628i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{5} - 3 q^{7}+O(q^{10})$$ 2 * q - 2 * q^5 - 3 * q^7 $$2 q - 2 q^{5} - 3 q^{7} + 3 q^{11} + 2 q^{13} - 7 q^{17} - q^{19} - 7 q^{23} + 2 q^{25} - 5 q^{29} - 8 q^{31} + 3 q^{35} + 3 q^{37} + 7 q^{41} + 9 q^{43} - 16 q^{47} - 2 q^{49} + 12 q^{53} - 3 q^{55} + 5 q^{59} + 5 q^{61} - 2 q^{65} - 13 q^{67} - 3 q^{71} - 28 q^{73} - 18 q^{77} - 16 q^{79} - 24 q^{83} + 7 q^{85} + 7 q^{89} + 15 q^{91} + q^{95} + 11 q^{97}+O(q^{100})$$ 2 * q - 2 * q^5 - 3 * q^7 + 3 * q^11 + 2 * q^13 - 7 * q^17 - q^19 - 7 * q^23 + 2 * q^25 - 5 * q^29 - 8 * q^31 + 3 * q^35 + 3 * q^37 + 7 * q^41 + 9 * q^43 - 16 * q^47 - 2 * q^49 + 12 * q^53 - 3 * q^55 + 5 * q^59 + 5 * q^61 - 2 * q^65 - 13 * q^67 - 3 * q^71 - 28 * q^73 - 18 * q^77 - 16 * q^79 - 24 * q^83 + 7 * q^85 + 7 * q^89 + 15 * q^91 + q^95 + 11 * q^97

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$$.

 $$n$$ $$937$$ $$1081$$ $$1171$$ $$2081$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −1.00000 −0.447214
$$6$$ 0 0
$$7$$ −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i $$0.358542\pi$$
−0.996866 + 0.0791130i $$0.974791\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ 0 0
$$13$$ 1.00000 3.46410i 0.277350 0.960769i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i $$0.489386\pi$$
−0.882213 + 0.470850i $$0.843947\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i $$-0.906280\pi$$
0.227167 0.973856i $$-0.427054\pi$$
$$24$$ 0 0
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i $$-0.320339\pi$$
−0.999167 + 0.0408130i $$0.987005\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.50000 2.59808i 0.253546 0.439155i
$$36$$ 0 0
$$37$$ 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i $$-0.0873538\pi$$
−0.715981 + 0.698119i $$0.754020\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.50000 + 6.06218i 0.546608 + 0.946753i 0.998504 + 0.0546823i $$0.0174146\pi$$
−0.451896 + 0.892071i $$0.649252\pi$$
$$42$$ 0 0
$$43$$ 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i $$-0.592592\pi$$
0.973044 0.230618i $$-0.0740749\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0 0
$$49$$ −1.00000 1.73205i −0.142857 0.247436i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ −1.50000 2.59808i −0.202260 0.350325i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i $$-0.727810\pi$$
0.981608 + 0.190909i $$0.0611434\pi$$
$$60$$ 0 0
$$61$$ 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i $$-0.729619\pi$$
0.980507 + 0.196485i $$0.0629528\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −1.00000 + 3.46410i −0.124035 + 0.429669i
$$66$$ 0 0
$$67$$ −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i $$-0.874609\pi$$
0.129307 0.991605i $$-0.458725\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.50000 + 2.59808i −0.178017 + 0.308335i −0.941201 0.337846i $$-0.890302\pi$$
0.763184 + 0.646181i $$0.223635\pi$$
$$72$$ 0 0
$$73$$ −14.0000 −1.63858 −0.819288 0.573382i $$-0.805631\pi$$
−0.819288 + 0.573382i $$0.805631\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −9.00000 −1.02565
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 3.50000 6.06218i 0.379628 0.657536i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i $$-0.0456819\pi$$
−0.618720 + 0.785611i $$0.712349\pi$$
$$90$$ 0 0
$$91$$ 7.50000 + 7.79423i 0.786214 + 0.817057i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0.500000 0.866025i 0.0512989 0.0888523i
$$96$$ 0 0
$$97$$ 5.50000 9.52628i 0.558440 0.967247i −0.439187 0.898396i $$-0.644733\pi$$
0.997627 0.0688512i $$-0.0219334\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i $$-0.314447\pi$$
−0.998240 + 0.0592978i $$0.981114\pi$$
$$102$$ 0 0
$$103$$ −16.0000 −1.57653 −0.788263 0.615338i $$-0.789020\pi$$
−0.788263 + 0.615338i $$0.789020\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i $$-0.212988\pi$$
−0.929377 + 0.369132i $$0.879655\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 6.50000 11.2583i 0.611469 1.05909i −0.379525 0.925182i $$-0.623912\pi$$
0.990993 0.133913i $$-0.0427543\pi$$
$$114$$ 0 0
$$115$$ 3.50000 + 6.06218i 0.326377 + 0.565301i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −10.5000 18.1865i −0.962533 1.66716i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −0.500000 0.866025i −0.0443678 0.0768473i 0.842989 0.537931i $$-0.180794\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −4.00000 −0.349482 −0.174741 0.984614i $$-0.555909\pi$$
−0.174741 + 0.984614i $$0.555909\pi$$
$$132$$ 0 0
$$133$$ −1.50000 2.59808i −0.130066 0.225282i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i $$-0.874238\pi$$
0.794808 + 0.606861i $$0.207572\pi$$
$$138$$ 0 0
$$139$$ −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i $$0.352543\pi$$
−0.998179 + 0.0603135i $$0.980790\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 10.5000 2.59808i 0.878054 0.217262i
$$144$$ 0 0
$$145$$ 2.50000 + 4.33013i 0.207614 + 0.359597i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i $$-0.794119\pi$$
0.920904 + 0.389789i $$0.127452\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.00000 0.321288
$$156$$ 0 0
$$157$$ 6.00000 0.478852 0.239426 0.970915i $$-0.423041\pi$$
0.239426 + 0.970915i $$0.423041\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 21.0000 1.65503
$$162$$ 0 0
$$163$$ −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i $$-0.975100\pi$$
0.566149 + 0.824303i $$0.308433\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.500000 + 0.866025i 0.0386912 + 0.0670151i 0.884723 0.466118i $$-0.154348\pi$$
−0.846031 + 0.533133i $$0.821014\pi$$
$$168$$ 0 0
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i $$0.359807\pi$$
−0.996544 + 0.0830722i $$0.973527\pi$$
$$174$$ 0 0
$$175$$ −1.50000 + 2.59808i −0.113389 + 0.196396i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i $$0.0846670\pi$$
−0.254770 + 0.967002i $$0.582000\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −1.50000 2.59808i −0.110282 0.191014i
$$186$$ 0 0
$$187$$ −21.0000 −1.53567
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i $$-0.867950\pi$$
0.806641 + 0.591041i $$0.201283\pi$$
$$192$$ 0 0
$$193$$ 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i $$0.0148568\pi$$
−0.459049 + 0.888411i $$0.651810\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −11.5000 19.9186i −0.819341 1.41914i −0.906168 0.422917i $$-0.861006\pi$$
0.0868274 0.996223i $$-0.472327\pi$$
$$198$$ 0 0
$$199$$ −4.50000 + 7.79423i −0.318997 + 0.552518i −0.980279 0.197619i $$-0.936679\pi$$
0.661282 + 0.750137i $$0.270013\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 15.0000 1.05279
$$204$$ 0 0
$$205$$ −3.50000 6.06218i −0.244451 0.423401i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −3.00000 −0.207514
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −4.50000 + 7.79423i −0.306897 + 0.531562i
$$216$$ 0 0
$$217$$ 6.00000 10.3923i 0.407307 0.705476i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 17.5000 + 18.1865i 1.17718 + 1.22336i
$$222$$ 0 0
$$223$$ 11.5000 + 19.9186i 0.770097 + 1.33385i 0.937509 + 0.347960i $$0.113126\pi$$
−0.167412 + 0.985887i $$0.553541\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −0.500000 + 0.866025i −0.0331862 + 0.0574801i −0.882141 0.470985i $$-0.843899\pi$$
0.848955 + 0.528465i $$0.177232\pi$$
$$228$$ 0 0
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 0 0
$$235$$ 8.00000 0.521862
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 1.00000 + 1.73205i 0.0638877 + 0.110657i
$$246$$ 0 0
$$247$$ 2.50000 + 2.59808i 0.159071 + 0.165312i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 2.50000 4.33013i 0.157799 0.273315i −0.776276 0.630393i $$-0.782894\pi$$
0.934075 + 0.357078i $$0.116227\pi$$
$$252$$ 0 0
$$253$$ 10.5000 18.1865i 0.660129 1.14338i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.50000 16.4545i −0.592594 1.02640i −0.993882 0.110450i $$-0.964771\pi$$
0.401288 0.915952i $$-0.368563\pi$$
$$258$$ 0 0
$$259$$ −9.00000 −0.559233
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3.50000 6.06218i −0.215819 0.373810i 0.737706 0.675122i $$-0.235909\pi$$
−0.953526 + 0.301312i $$0.902576\pi$$
$$264$$ 0 0
$$265$$ −6.00000 −0.368577
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i $$-0.804181\pi$$
0.908124 + 0.418701i $$0.137514\pi$$
$$270$$ 0 0
$$271$$ −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i $$-0.920484\pi$$
0.270385 0.962752i $$-0.412849\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1.50000 + 2.59808i 0.0904534 + 0.156670i
$$276$$ 0 0
$$277$$ 11.5000 19.9186i 0.690968 1.19679i −0.280553 0.959839i $$-0.590518\pi$$
0.971521 0.236953i $$-0.0761488\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 0 0
$$283$$ −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i $$-0.176129\pi$$
−0.880504 + 0.474039i $$0.842796\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −21.0000 −1.23959
$$288$$ 0 0
$$289$$ −16.0000 27.7128i −0.941176 1.63017i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i $$-0.748657\pi$$
0.967009 + 0.254741i $$0.0819901\pi$$
$$294$$ 0 0
$$295$$ −2.50000 + 4.33013i −0.145556 + 0.252110i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −24.5000 + 6.06218i −1.41687 + 0.350585i
$$300$$ 0 0
$$301$$ 13.5000 + 23.3827i 0.778127 + 1.34776i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2.50000 + 4.33013i −0.143150 + 0.247942i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 0 0
$$319$$ 7.50000 12.9904i 0.419919 0.727322i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3.50000 6.06218i −0.194745 0.337309i
$$324$$ 0 0
$$325$$ 1.00000 3.46410i 0.0554700 0.192154i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 12.0000 20.7846i 0.661581 1.14589i
$$330$$ 0 0
$$331$$ −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i $$-0.949627\pi$$
0.630232 + 0.776407i $$0.282960\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 6.50000 + 11.2583i 0.355133 + 0.615108i
$$336$$ 0 0
$$337$$ −18.0000 −0.980522 −0.490261 0.871576i $$-0.663099\pi$$
−0.490261 + 0.871576i $$0.663099\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −6.00000 10.3923i −0.324918 0.562775i
$$342$$ 0 0
$$343$$ −15.0000 −0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.50000 + 11.2583i −0.348938 + 0.604379i −0.986061 0.166383i $$-0.946791\pi$$
0.637123 + 0.770762i $$0.280124\pi$$
$$348$$ 0 0
$$349$$ 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i $$0.0666577\pi$$
−0.309044 + 0.951048i $$0.600009\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i $$0.0220939\pi$$
−0.438733 + 0.898617i $$0.644573\pi$$
$$354$$ 0 0
$$355$$ 1.50000 2.59808i 0.0796117 0.137892i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 14.0000 0.732793
$$366$$ 0 0
$$367$$ −4.50000 7.79423i −0.234898 0.406855i 0.724345 0.689438i $$-0.242142\pi$$
−0.959243 + 0.282582i $$0.908809\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −9.00000 + 15.5885i −0.467257 + 0.809312i
$$372$$ 0 0
$$373$$ 13.5000 23.3827i 0.699004 1.21071i −0.269809 0.962914i $$-0.586961\pi$$
0.968812 0.247796i $$-0.0797062\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −17.5000 + 4.33013i −0.901296 + 0.223013i
$$378$$ 0 0
$$379$$ 4.50000 + 7.79423i 0.231149 + 0.400363i 0.958147 0.286278i $$-0.0924180\pi$$
−0.726997 + 0.686640i $$0.759085\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i $$-0.941102\pi$$
0.650796 + 0.759253i $$0.274435\pi$$
$$384$$ 0 0
$$385$$ 9.00000 0.458682
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 49.0000 2.47804
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 8.00000 0.402524
$$396$$ 0 0
$$397$$ −16.5000 + 28.5788i −0.828111 + 1.43433i 0.0714068 + 0.997447i $$0.477251\pi$$
−0.899518 + 0.436884i $$0.856082\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i $$-0.0444700\pi$$
−0.615725 + 0.787961i $$0.711137\pi$$
$$402$$ 0 0
$$403$$ −4.00000 + 13.8564i −0.199254 + 0.690237i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.50000 + 7.79423i −0.223057 + 0.386346i
$$408$$ 0 0
$$409$$ 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i $$-0.825463\pi$$
0.878122 + 0.478436i $$0.158796\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 7.50000 + 12.9904i 0.369051 + 0.639215i
$$414$$ 0 0
$$415$$ 12.0000 0.589057
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i $$-0.868253\pi$$
0.109483 0.993989i $$-0.465080\pi$$
$$420$$ 0 0
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −3.50000 + 6.06218i −0.169775 + 0.294059i
$$426$$ 0 0
$$427$$ 7.50000 + 12.9904i 0.362950 + 0.628649i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i $$-0.236215\pi$$
−0.953815 + 0.300395i $$0.902881\pi$$
$$432$$ 0 0
$$433$$ −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i $$-0.840983\pi$$
0.853761 + 0.520665i $$0.174316\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 7.00000 0.334855
$$438$$ 0 0
$$439$$ −1.50000 2.59808i −0.0715911 0.123999i 0.828008 0.560717i $$-0.189474\pi$$
−0.899599 + 0.436717i $$0.856141\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ −3.50000 6.06218i −0.165916 0.287375i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i $$-0.998358\pi$$
0.504461 + 0.863434i $$0.331691\pi$$
$$450$$ 0 0
$$451$$ −10.5000 + 18.1865i −0.494426 + 0.856370i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −7.50000 7.79423i −0.351605 0.365399i
$$456$$ 0 0
$$457$$ 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i $$0.0141334\pi$$
−0.461067 + 0.887365i $$0.652533\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 5.50000 9.52628i 0.256161 0.443683i −0.709050 0.705159i $$-0.750876\pi$$
0.965210 + 0.261476i $$0.0842091\pi$$
$$462$$ 0 0
$$463$$ −28.0000 −1.30127 −0.650635 0.759390i $$-0.725497\pi$$
−0.650635 + 0.759390i $$0.725497\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −20.0000 −0.925490 −0.462745 0.886492i $$-0.653135\pi$$
−0.462745 + 0.886492i $$0.653135\pi$$
$$468$$ 0 0
$$469$$ 39.0000 1.80085
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 27.0000 1.24146
$$474$$ 0 0
$$475$$ −0.500000 + 0.866025i −0.0229416 + 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i $$-0.173939\pi$$
−0.877222 + 0.480085i $$0.840606\pi$$
$$480$$ 0 0
$$481$$ 10.5000 2.59808i 0.478759 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −5.50000 + 9.52628i −0.249742 + 0.432566i
$$486$$ 0 0
$$487$$ 8.50000 14.7224i 0.385172 0.667137i −0.606621 0.794991i $$-0.707476\pi$$
0.991793 + 0.127854i $$0.0408089\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11.5000 + 19.9186i 0.518988 + 0.898913i 0.999757 + 0.0220657i $$0.00702431\pi$$
−0.480769 + 0.876847i $$0.659642\pi$$
$$492$$ 0 0
$$493$$ 35.0000 1.57632
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4.50000 7.79423i −0.201853 0.349619i
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i $$-0.754469\pi$$
0.962197 + 0.272354i $$0.0878022\pi$$
$$504$$ 0 0
$$505$$ 4.50000 + 7.79423i 0.200247 + 0.346839i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i $$-0.0587976\pi$$
−0.650556 + 0.759458i $$0.725464\pi$$
$$510$$ 0 0
$$511$$ 21.0000 36.3731i 0.928985 1.60905i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 16.0000 0.705044
$$516$$ 0 0
$$517$$ −12.0000 20.7846i −0.527759 0.914106i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 34.0000 1.48957 0.744784 0.667306i $$-0.232553\pi$$
0.744784 + 0.667306i $$0.232553\pi$$
$$522$$ 0 0
$$523$$ 11.5000 + 19.9186i 0.502860 + 0.870979i 0.999995 + 0.00330547i $$0.00105217\pi$$
−0.497135 + 0.867673i $$0.665615\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 14.0000 24.2487i 0.609850 1.05629i
$$528$$ 0 0
$$529$$ −13.0000 + 22.5167i −0.565217 + 0.978985i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 24.5000 6.06218i 1.06121 0.262582i
$$534$$ 0 0
$$535$$ 1.50000 + 2.59808i 0.0648507 + 0.112325i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 3.00000 5.19615i 0.129219 0.223814i
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 14.0000 0.599694
$$546$$ 0 0
$$547$$ −16.0000 −0.684111 −0.342055 0.939680i $$-0.611123\pi$$
−0.342055 + 0.939680i $$0.611123\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 5.00000 0.213007
$$552$$ 0 0
$$553$$ 12.0000 20.7846i 0.510292 0.883852i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −9.50000 16.4545i −0.402528 0.697199i 0.591502 0.806303i $$-0.298535\pi$$
−0.994030 + 0.109104i $$0.965202\pi$$
$$558$$ 0 0
$$559$$ −22.5000 23.3827i −0.951649 0.988982i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −22.5000 + 38.9711i −0.948262 + 1.64244i −0.199177 + 0.979963i $$0.563827\pi$$
−0.749085 + 0.662474i $$0.769506\pi$$
$$564$$ 0 0
$$565$$ −6.50000 + 11.2583i −0.273457 + 0.473642i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 9.50000 + 16.4545i 0.398261 + 0.689808i 0.993511 0.113732i $$-0.0362806\pi$$
−0.595251 + 0.803540i $$0.702947\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −3.50000 6.06218i −0.145960 0.252810i
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 18.0000 31.1769i 0.746766 1.29344i
$$582$$ 0 0
$$583$$ 9.00000 + 15.5885i 0.372742 + 0.645608i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i $$0.109892\pi$$
−0.177419 + 0.984135i $$0.556775\pi$$
$$588$$ 0 0
$$589$$ 2.00000 3.46410i 0.0824086 0.142736i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −26.0000 −1.06769 −0.533846 0.845582i $$-0.679254\pi$$
−0.533846 + 0.845582i $$0.679254\pi$$
$$594$$ 0 0
$$595$$ 10.5000 + 18.1865i 0.430458 + 0.745575i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −8.00000 −0.326871 −0.163436 0.986554i $$-0.552258\pi$$
−0.163436 + 0.986554i $$0.552258\pi$$
$$600$$ 0 0
$$601$$ 6.50000 + 11.2583i 0.265141 + 0.459237i 0.967600 0.252486i $$-0.0812483\pi$$
−0.702460 + 0.711723i $$0.747915\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −1.00000 + 1.73205i −0.0406558 + 0.0704179i
$$606$$ 0 0
$$607$$ 4.50000 7.79423i 0.182649 0.316358i −0.760133 0.649768i $$-0.774866\pi$$
0.942782 + 0.333410i $$0.108199\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.00000 + 27.7128i −0.323645 + 1.12114i
$$612$$ 0 0
$$613$$ 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i $$0.0486583\pi$$
−0.362300 + 0.932062i $$0.618008\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 14.5000 25.1147i 0.583748 1.01108i −0.411282 0.911508i $$-0.634919\pi$$
0.995030 0.0995732i $$-0.0317477\pi$$
$$618$$ 0 0
$$619$$ 12.0000 0.482321 0.241160 0.970485i $$-0.422472\pi$$
0.241160 + 0.970485i $$0.422472\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −21.0000 −0.841347
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −21.0000 −0.837325
$$630$$ 0 0
$$631$$ 7.50000 12.9904i 0.298570 0.517139i −0.677239 0.735763i $$-0.736824\pi$$
0.975809 + 0.218624i $$0.0701569\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.500000 + 0.866025i 0.0198419 + 0.0343672i
$$636$$ 0 0
$$637$$ −7.00000 + 1.73205i −0.277350 + 0.0686264i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i $$-0.969456\pi$$
0.580674 + 0.814136i $$0.302789\pi$$
$$642$$ 0 0
$$643$$ −3.50000 + 6.06218i −0.138027 + 0.239069i −0.926750 0.375680i $$-0.877409\pi$$
0.788723 + 0.614749i $$0.210743\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 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
$$649$$ 15.0000 0.588802
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −5.50000 9.52628i −0.215232 0.372792i 0.738113 0.674678i $$-0.235717\pi$$
−0.953344 + 0.301885i $$0.902384\pi$$
$$654$$ 0 0
$$655$$ 4.00000 0.156293
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i $$-0.927707\pi$$
0.682161 + 0.731202i $$0.261040\pi$$
$$660$$ 0 0
$$661$$ 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i $$-0.0594116\pi$$
−0.652020 + 0.758202i $$0.726078\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 1.50000 + 2.59808i 0.0581675 + 0.100749i
$$666$$ 0 0
$$667$$ −17.5000 + 30.3109i −0.677603 + 1.17364i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 15.0000 0.579069
$$672$$ 0 0
$$673$$ −6.50000 11.2583i −0.250557 0.433977i 0.713123 0.701039i $$-0.247280\pi$$
−0.963679 + 0.267063i $$0.913947\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −22.0000 −0.845529 −0.422764 0.906240i $$-0.638940\pi$$
−0.422764 + 0.906240i $$0.638940\pi$$
$$678$$ 0 0
$$679$$ 16.5000 + 28.5788i 0.633212 + 1.09676i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 15.5000 26.8468i 0.593091 1.02726i −0.400722 0.916200i $$-0.631241\pi$$
0.993813 0.111064i $$-0.0354259\pi$$
$$684$$ 0 0
$$685$$ 1.50000 2.59808i 0.0573121 0.0992674i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 6.00000 20.7846i 0.228582 0.791831i
$$690$$ 0 0
$$691$$ 12.5000 + 21.6506i 0.475522 + 0.823629i 0.999607 0.0280373i $$-0.00892572\pi$$
−0.524084 + 0.851666i $$0.675592\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.50000 11.2583i 0.246559 0.427053i
$$696$$ 0 0
$$697$$ −49.0000 −1.85601
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 0 0
$$703$$ −3.00000 −0.113147
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.0000 1.01544
$$708$$ 0 0
$$709$$ −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i $$0.394937\pi$$
−0.981331 + 0.192328i $$0.938396\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 14.0000 + 24.2487i 0.524304 + 0.908121i
$$714$$ 0 0
$$715$$ −10.5000 + 2.59808i −0.392678 + 0.0971625i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0.500000 0.866025i 0.0186469 0.0322973i −0.856551 0.516062i $$-0.827398\pi$$
0.875198 + 0.483764i $$0.160731\pi$$
$$720$$ 0 0
$$721$$ 24.0000 41.5692i 0.893807 1.54812i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −2.50000 4.33013i −0.0928477 0.160817i
$$726$$ 0 0
$$727$$ −28.0000 −1.03846 −0.519231 0.854634i $$-0.673782\pi$$
−0.519231 + 0.854634i $$0.673782\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 31.5000 + 54.5596i 1.16507 + 2.01796i
$$732$$ 0 0
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 19.5000 33.7750i 0.718292 1.24412i
$$738$$ 0 0
$$739$$ −19.5000 33.7750i −0.717319 1.24243i −0.962058 0.272844i $$-0.912036\pi$$
0.244739 0.969589i $$-0.421298\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0.500000 + 0.866025i 0.0183432 + 0.0317714i 0.875051 0.484030i $$-0.160828\pi$$
−0.856708 + 0.515802i $$0.827494\pi$$
$$744$$ 0 0
$$745$$ −1.50000 + 2.59808i −0.0549557 + 0.0951861i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 9.00000 0.328853
$$750$$ 0 0
$$751$$ 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i $$-0.0904408\pi$$
−0.722718 + 0.691143i $$0.757107\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −0.500000 0.866025i −0.0181728 0.0314762i 0.856796 0.515656i $$-0.172452\pi$$
−0.874969 + 0.484179i $$0.839118\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 25.5000 44.1673i 0.924374 1.60106i 0.131810 0.991275i $$-0.457921\pi$$
0.792564 0.609788i $$-0.208745\pi$$
$$762$$ 0 0
$$763$$ 21.0000 36.3731i 0.760251 1.31679i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −12.5000 12.9904i −0.451349 0.469055i
$$768$$ 0 0
$$769$$ 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i $$-0.137931\pi$$
−0.817423 + 0.576038i $$0.804598\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 12.5000 21.6506i 0.449594 0.778719i −0.548766 0.835976i $$-0.684902\pi$$
0.998359 + 0.0572570i $$0.0182354\pi$$
$$774$$ 0 0
$$775$$ −4.00000 −0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −7.00000 −0.250801
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.00000 −0.214149
$$786$$ 0 0
$$787$$ 0.500000 0.866025i 0.0178231 0.0308705i −0.856976 0.515356i $$-0.827660\pi$$
0.874799 + 0.484485i $$0.160993\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 19.5000 + 33.7750i 0.693340 + 1.20090i
$$792$$ 0 0
$$793$$ −12.5000 12.9904i −0.443888 0.461302i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −3.50000 + 6.06218i −0.123976 + 0.214733i −0.921332 0.388776i $$-0.872898\pi$$
0.797356 + 0.603509i $$0.206231\pi$$
$$798$$ 0 0
$$799$$ 28.0000 48.4974i 0.990569 1.71572i
$$800$$ 0 0
$$801$$ 0 0