# Properties

 Label 432.2.s.a.143.1 Level $432$ Weight $2$ Character 432.143 Analytic conductor $3.450$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 432.s (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.44953736732$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 144) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 143.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 432.143 Dual form 432.2.s.a.287.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{7} +O(q^{10})$$ $$q+(-1.50000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{7} +(-1.50000 + 2.59808i) q^{11} +(2.50000 + 4.33013i) q^{13} +6.92820i q^{17} +3.46410i q^{19} +(-4.50000 - 7.79423i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-1.50000 - 0.866025i) q^{29} +(-4.50000 + 2.59808i) q^{31} +3.00000 q^{35} +2.00000 q^{37} +(4.50000 - 2.59808i) q^{41} +(4.50000 + 2.59808i) q^{43} +(-1.50000 + 2.59808i) q^{47} +(-2.00000 - 3.46410i) q^{49} -5.19615i q^{55} +(1.50000 + 2.59808i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-7.50000 - 4.33013i) q^{65} +(7.50000 - 4.33013i) q^{67} +12.0000 q^{71} -2.00000 q^{73} +(4.50000 - 2.59808i) q^{77} +(-7.50000 - 4.33013i) q^{79} +(-7.50000 + 12.9904i) q^{83} +(-6.00000 - 10.3923i) q^{85} -6.92820i q^{89} -8.66025i q^{91} +(-3.00000 - 5.19615i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{5} - 3 q^{7}+O(q^{10})$$ 2 * q - 3 * q^5 - 3 * q^7 $$2 q - 3 q^{5} - 3 q^{7} - 3 q^{11} + 5 q^{13} - 9 q^{23} - 2 q^{25} - 3 q^{29} - 9 q^{31} + 6 q^{35} + 4 q^{37} + 9 q^{41} + 9 q^{43} - 3 q^{47} - 4 q^{49} + 3 q^{59} + q^{61} - 15 q^{65} + 15 q^{67} + 24 q^{71} - 4 q^{73} + 9 q^{77} - 15 q^{79} - 15 q^{83} - 12 q^{85} - 6 q^{95} + 5 q^{97}+O(q^{100})$$ 2 * q - 3 * q^5 - 3 * q^7 - 3 * q^11 + 5 * q^13 - 9 * q^23 - 2 * q^25 - 3 * q^29 - 9 * q^31 + 6 * q^35 + 4 * q^37 + 9 * q^41 + 9 * q^43 - 3 * q^47 - 4 * q^49 + 3 * q^59 + q^61 - 15 * q^65 + 15 * q^67 + 24 * q^71 - 4 * q^73 + 9 * q^77 - 15 * q^79 - 15 * q^83 - 12 * q^85 - 6 * q^95 + 5 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$$.

 $$n$$ $$271$$ $$325$$ $$353$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$5$$ −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i $$-0.793258\pi$$
0.125567 + 0.992085i $$0.459925\pi$$
$$6$$ 0 0
$$7$$ −1.50000 0.866025i −0.566947 0.327327i 0.188982 0.981981i $$-0.439481\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.92820i 1.68034i 0.542326 + 0.840168i $$0.317544\pi$$
−0.542326 + 0.840168i $$0.682456\pi$$
$$18$$ 0 0
$$19$$ 3.46410i 0.794719i 0.917663 + 0.397360i $$0.130073\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i $$-0.779053\pi$$
−0.169701 0.985496i $$-0.554280\pi$$
$$24$$ 0 0
$$25$$ −1.00000 + 1.73205i −0.200000 + 0.346410i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1.50000 0.866025i −0.278543 0.160817i 0.354221 0.935162i $$-0.384746\pi$$
−0.632764 + 0.774345i $$0.718080\pi$$
$$30$$ 0 0
$$31$$ −4.50000 + 2.59808i −0.808224 + 0.466628i −0.846339 0.532645i $$-0.821198\pi$$
0.0381148 + 0.999273i $$0.487865\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 3.00000 0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.50000 2.59808i 0.702782 0.405751i −0.105601 0.994409i $$-0.533677\pi$$
0.808383 + 0.588657i $$0.200343\pi$$
$$42$$ 0 0
$$43$$ 4.50000 + 2.59808i 0.686244 + 0.396203i 0.802203 0.597051i $$-0.203661\pi$$
−0.115960 + 0.993254i $$0.536994\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i $$-0.903547\pi$$
0.735643 + 0.677369i $$0.236880\pi$$
$$48$$ 0 0
$$49$$ −2.00000 3.46410i −0.285714 0.494872i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 5.19615i 0.700649i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i $$-0.104104\pi$$
−0.751710 + 0.659494i $$0.770771\pi$$
$$60$$ 0 0
$$61$$ 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i $$-0.812942\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −7.50000 4.33013i −0.930261 0.537086i
$$66$$ 0 0
$$67$$ 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i $$-0.489230\pi$$
0.882443 + 0.470418i $$0.155897\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 4.50000 2.59808i 0.512823 0.296078i
$$78$$ 0 0
$$79$$ −7.50000 4.33013i −0.843816 0.487177i 0.0147436 0.999891i $$-0.495307\pi$$
−0.858559 + 0.512714i $$0.828640\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −7.50000 + 12.9904i −0.823232 + 1.42588i 0.0800311 + 0.996792i $$0.474498\pi$$
−0.903263 + 0.429087i $$0.858835\pi$$
$$84$$ 0 0
$$85$$ −6.00000 10.3923i −0.650791 1.12720i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.92820i 0.734388i −0.930144 0.367194i $$-0.880318\pi$$
0.930144 0.367194i $$-0.119682\pi$$
$$90$$ 0 0
$$91$$ 8.66025i 0.907841i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −3.00000 5.19615i −0.307794 0.533114i
$$96$$ 0 0
$$97$$ 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i $$-0.751641\pi$$
0.964579 + 0.263795i $$0.0849741\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 4.50000 + 2.59808i 0.447767 + 0.258518i 0.706887 0.707327i $$-0.250099\pi$$
−0.259120 + 0.965845i $$0.583432\pi$$
$$102$$ 0 0
$$103$$ 1.50000 0.866025i 0.147799 0.0853320i −0.424277 0.905533i $$-0.639472\pi$$
0.572076 + 0.820201i $$0.306138\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 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
$$113$$ 10.5000 6.06218i 0.987757 0.570282i 0.0831539 0.996537i $$-0.473501\pi$$
0.904603 + 0.426255i $$0.140167\pi$$
$$114$$ 0 0
$$115$$ 13.5000 + 7.79423i 1.25888 + 0.726816i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 6.00000 10.3923i 0.550019 0.952661i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 12.1244i 1.08444i
$$126$$ 0 0
$$127$$ 10.3923i 0.922168i 0.887357 + 0.461084i $$0.152539\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i $$-0.124830\pi$$
−0.793028 + 0.609185i $$0.791497\pi$$
$$132$$ 0 0
$$133$$ 3.00000 5.19615i 0.260133 0.450564i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −7.50000 4.33013i −0.640768 0.369948i 0.144142 0.989557i $$-0.453958\pi$$
−0.784910 + 0.619609i $$0.787291\pi$$
$$138$$ 0 0
$$139$$ 1.50000 0.866025i 0.127228 0.0734553i −0.435035 0.900414i $$-0.643264\pi$$
0.562263 + 0.826958i $$0.309931\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −15.0000 −1.25436
$$144$$ 0 0
$$145$$ 3.00000 0.249136
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −7.50000 + 4.33013i −0.614424 + 0.354738i −0.774695 0.632335i $$-0.782097\pi$$
0.160271 + 0.987073i $$0.448763\pi$$
$$150$$ 0 0
$$151$$ −7.50000 4.33013i −0.610341 0.352381i 0.162758 0.986666i $$-0.447961\pi$$
−0.773099 + 0.634285i $$0.781294\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.50000 7.79423i 0.361449 0.626048i
$$156$$ 0 0
$$157$$ 0.500000 + 0.866025i 0.0399043 + 0.0691164i 0.885288 0.465044i $$-0.153961\pi$$
−0.845383 + 0.534160i $$0.820628\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 15.5885i 1.22854i
$$162$$ 0 0
$$163$$ 17.3205i 1.35665i 0.734763 + 0.678323i $$0.237293\pi$$
−0.734763 + 0.678323i $$0.762707\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 1.50000 + 2.59808i 0.116073 + 0.201045i 0.918208 0.396098i $$-0.129636\pi$$
−0.802135 + 0.597143i $$0.796303\pi$$
$$168$$ 0 0
$$169$$ −6.00000 + 10.3923i −0.461538 + 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 16.5000 + 9.52628i 1.25447 + 0.724270i 0.971994 0.235004i $$-0.0755104\pi$$
0.282477 + 0.959274i $$0.408844\pi$$
$$174$$ 0 0
$$175$$ 3.00000 1.73205i 0.226779 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3.00000 + 1.73205i −0.220564 + 0.127343i
$$186$$ 0 0
$$187$$ −18.0000 10.3923i −1.31629 0.759961i
$$188$$ 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
$$193$$ 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i $$-0.0116845\pi$$
−0.531446 + 0.847092i $$0.678351\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 6.92820i 0.493614i 0.969065 + 0.246807i $$0.0793814\pi$$
−0.969065 + 0.246807i $$0.920619\pi$$
$$198$$ 0 0
$$199$$ 24.2487i 1.71895i −0.511182 0.859473i $$-0.670792\pi$$
0.511182 0.859473i $$-0.329208\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 1.50000 + 2.59808i 0.105279 + 0.182349i
$$204$$ 0 0
$$205$$ −4.50000 + 7.79423i −0.314294 + 0.544373i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −9.00000 5.19615i −0.622543 0.359425i
$$210$$ 0 0
$$211$$ −16.5000 + 9.52628i −1.13591 + 0.655816i −0.945414 0.325872i $$-0.894342\pi$$
−0.190493 + 0.981689i $$0.561009\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −9.00000 −0.613795
$$216$$ 0 0
$$217$$ 9.00000 0.610960
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −30.0000 + 17.3205i −2.01802 + 1.16510i
$$222$$ 0 0
$$223$$ 22.5000 + 12.9904i 1.50671 + 0.869900i 0.999970 + 0.00780243i $$0.00248362\pi$$
0.506742 + 0.862098i $$0.330850\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i $$-0.865076\pi$$
0.811943 + 0.583736i $$0.198410\pi$$
$$228$$ 0 0
$$229$$ 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i $$0.0231842\pi$$
−0.435653 + 0.900115i $$0.643482\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 13.8564i 0.907763i 0.891062 + 0.453882i $$0.149961\pi$$
−0.891062 + 0.453882i $$0.850039\pi$$
$$234$$ 0 0
$$235$$ 5.19615i 0.338960i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i $$-0.00543724\pi$$
−0.514719 + 0.857359i $$0.672104\pi$$
$$240$$ 0 0
$$241$$ 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i $$-0.648900\pi$$
0.998443 0.0557856i $$-0.0177663\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 6.00000 + 3.46410i 0.383326 + 0.221313i
$$246$$ 0 0
$$247$$ −15.0000 + 8.66025i −0.954427 + 0.551039i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 27.0000 1.69748
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.50000 + 0.866025i −0.0935674 + 0.0540212i −0.546054 0.837750i $$-0.683871\pi$$
0.452486 + 0.891771i $$0.350537\pi$$
$$258$$ 0 0
$$259$$ −3.00000 1.73205i −0.186411 0.107624i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i $$-0.743833\pi$$
0.970758 + 0.240059i $$0.0771668\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 27.7128i 1.68968i −0.535019 0.844840i $$-0.679696\pi$$
0.535019 0.844840i $$-0.320304\pi$$
$$270$$ 0 0
$$271$$ 24.2487i 1.47300i 0.676435 + 0.736502i $$0.263524\pi$$
−0.676435 + 0.736502i $$0.736476\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −3.00000 5.19615i −0.180907 0.313340i
$$276$$ 0 0
$$277$$ −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i $$0.360033\pi$$
−0.996484 + 0.0837823i $$0.973300\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 16.5000 + 9.52628i 0.984307 + 0.568290i 0.903568 0.428445i $$-0.140938\pi$$
0.0807396 + 0.996735i $$0.474272\pi$$
$$282$$ 0 0
$$283$$ 13.5000 7.79423i 0.802492 0.463319i −0.0418500 0.999124i $$-0.513325\pi$$
0.844342 + 0.535805i $$0.179992\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −9.00000 −0.531253
$$288$$ 0 0
$$289$$ −31.0000 −1.82353
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.50000 + 0.866025i −0.0876309 + 0.0505937i −0.543175 0.839619i $$-0.682778\pi$$
0.455544 + 0.890213i $$0.349445\pi$$
$$294$$ 0 0
$$295$$ −4.50000 2.59808i −0.262000 0.151266i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 22.5000 38.9711i 1.30121 2.25376i
$$300$$ 0 0
$$301$$ −4.50000 7.79423i −0.259376 0.449252i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 1.73205i 0.0991769i
$$306$$ 0 0
$$307$$ 10.3923i 0.593120i −0.955014 0.296560i $$-0.904160\pi$$
0.955014 0.296560i $$-0.0958395\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 7.50000 + 12.9904i 0.425286 + 0.736617i 0.996447 0.0842210i $$-0.0268402\pi$$
−0.571161 + 0.820838i $$0.693507\pi$$
$$312$$ 0 0
$$313$$ 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i $$-0.824336\pi$$
0.879810 + 0.475325i $$0.157669\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 10.5000 + 6.06218i 0.589739 + 0.340486i 0.764994 0.644037i $$-0.222742\pi$$
−0.175255 + 0.984523i $$0.556075\pi$$
$$318$$ 0 0
$$319$$ 4.50000 2.59808i 0.251952 0.145464i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −24.0000 −1.33540
$$324$$ 0 0
$$325$$ −10.0000 −0.554700
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 4.50000 2.59808i 0.248093 0.143237i
$$330$$ 0 0
$$331$$ −1.50000 0.866025i −0.0824475 0.0476011i 0.458209 0.888844i $$-0.348491\pi$$
−0.540657 + 0.841243i $$0.681824\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −7.50000 + 12.9904i −0.409769 + 0.709740i
$$336$$ 0 0
$$337$$ −3.50000 6.06218i −0.190657 0.330228i 0.754811 0.655942i $$-0.227729\pi$$
−0.945468 + 0.325714i $$0.894395\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 15.5885i 0.844162i
$$342$$ 0 0
$$343$$ 19.0526i 1.02874i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i $$-0.244330\pi$$
−0.961162 + 0.275983i $$0.910997\pi$$
$$348$$ 0 0
$$349$$ 6.50000 11.2583i 0.347937 0.602645i −0.637946 0.770081i $$-0.720216\pi$$
0.985883 + 0.167437i $$0.0535490\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 4.50000 + 2.59808i 0.239511 + 0.138282i 0.614952 0.788565i $$-0.289175\pi$$
−0.375441 + 0.926846i $$0.622509\pi$$
$$354$$ 0 0
$$355$$ −18.0000 + 10.3923i −0.955341 + 0.551566i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ 7.00000 0.368421
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.00000 1.73205i 0.157027 0.0906597i
$$366$$ 0 0
$$367$$ 16.5000 + 9.52628i 0.861293 + 0.497268i 0.864445 0.502727i $$-0.167670\pi$$
−0.00315207 + 0.999995i $$0.501003\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i $$-0.258587\pi$$
−0.972556 + 0.232671i $$0.925254\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 8.66025i 0.446026i
$$378$$ 0 0
$$379$$ 17.3205i 0.889695i −0.895606 0.444847i $$-0.853258\pi$$
0.895606 0.444847i $$-0.146742\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i $$0.0756427\pi$$
−0.282079 + 0.959391i $$0.591024\pi$$
$$384$$ 0 0
$$385$$ −4.50000 + 7.79423i −0.229341 + 0.397231i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −31.5000 18.1865i −1.59711 0.922094i −0.992040 0.125924i $$-0.959810\pi$$
−0.605074 0.796170i $$-0.706856\pi$$
$$390$$ 0 0
$$391$$ 54.0000 31.1769i 2.73090 1.57668i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 15.0000 0.754732
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 16.5000 9.52628i 0.823971 0.475720i −0.0278131 0.999613i $$-0.508854\pi$$
0.851784 + 0.523893i $$0.175521\pi$$
$$402$$ 0 0
$$403$$ −22.5000 12.9904i −1.12080 0.647097i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −3.00000 + 5.19615i −0.148704 + 0.257564i
$$408$$ 0 0
$$409$$ −15.5000 26.8468i −0.766426 1.32749i −0.939490 0.342578i $$-0.888700\pi$$
0.173064 0.984911i $$-0.444633\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 5.19615i 0.255686i
$$414$$ 0 0
$$415$$ 25.9808i 1.27535i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i $$-0.0472572\pi$$
−0.622601 + 0.782540i $$0.713924\pi$$
$$420$$ 0 0
$$421$$ 8.50000 14.7224i 0.414265 0.717527i −0.581086 0.813842i $$-0.697372\pi$$
0.995351 + 0.0963145i $$0.0307055\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −12.0000 6.92820i −0.582086 0.336067i
$$426$$ 0 0
$$427$$ −1.50000 + 0.866025i −0.0725901 + 0.0419099i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 27.0000 15.5885i 1.29159 0.745697i
$$438$$ 0 0
$$439$$ 4.50000 + 2.59808i 0.214773 + 0.123999i 0.603528 0.797342i $$-0.293761\pi$$
−0.388755 + 0.921341i $$0.627095\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i $$-0.764749\pi$$
0.952901 + 0.303281i $$0.0980821\pi$$
$$444$$ 0 0
$$445$$ 6.00000 + 10.3923i 0.284427 + 0.492642i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 20.7846i 0.980886i −0.871473 0.490443i $$-0.836835\pi$$
0.871473 0.490443i $$-0.163165\pi$$
$$450$$ 0 0
$$451$$ 15.5885i 0.734032i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 7.50000 + 12.9904i 0.351605 + 0.608998i
$$456$$ 0 0
$$457$$ 14.5000 25.1147i 0.678281 1.17482i −0.297217 0.954810i $$-0.596058\pi$$
0.975498 0.220008i $$-0.0706083\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 22.5000 + 12.9904i 1.04793 + 0.605022i 0.922069 0.387026i $$-0.126497\pi$$
0.125860 + 0.992048i $$0.459831\pi$$
$$462$$ 0 0
$$463$$ −16.5000 + 9.52628i −0.766820 + 0.442724i −0.831739 0.555167i $$-0.812654\pi$$
0.0649190 + 0.997891i $$0.479321\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 12.0000 0.555294 0.277647 0.960683i $$-0.410445\pi$$
0.277647 + 0.960683i $$0.410445\pi$$
$$468$$ 0 0
$$469$$ −15.0000 −0.692636
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −13.5000 + 7.79423i −0.620731 + 0.358379i
$$474$$ 0 0
$$475$$ −6.00000 3.46410i −0.275299 0.158944i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −7.50000 + 12.9904i −0.342684 + 0.593546i −0.984930 0.172953i $$-0.944669\pi$$
0.642246 + 0.766498i $$0.278003\pi$$
$$480$$ 0 0
$$481$$ 5.00000 + 8.66025i 0.227980 + 0.394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 8.66025i 0.393242i
$$486$$ 0 0
$$487$$ 3.46410i 0.156973i −0.996915 0.0784867i $$-0.974991\pi$$
0.996915 0.0784867i $$-0.0250088\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i $$-0.323806\pi$$
−0.999552 + 0.0299272i $$0.990472\pi$$
$$492$$ 0 0
$$493$$ 6.00000 10.3923i 0.270226 0.468046i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −18.0000 10.3923i −0.807410 0.466159i
$$498$$ 0 0
$$499$$ 13.5000 7.79423i 0.604343 0.348918i −0.166405 0.986057i $$-0.553216\pi$$
0.770748 + 0.637140i $$0.219883\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ −9.00000 −0.400495
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −31.5000 + 18.1865i −1.39621 + 0.806104i −0.993993 0.109439i $$-0.965094\pi$$
−0.402219 + 0.915543i $$0.631761\pi$$
$$510$$ 0 0
$$511$$ 3.00000 + 1.73205i 0.132712 + 0.0766214i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −1.50000 + 2.59808i −0.0660979 + 0.114485i
$$516$$ 0 0
$$517$$ −4.50000 7.79423i −0.197910 0.342790i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ 0 0
$$523$$ 17.3205i 0.757373i −0.925525 0.378686i $$-0.876376\pi$$
0.925525 0.378686i $$-0.123624\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −18.0000 31.1769i −0.784092 1.35809i
$$528$$ 0 0
$$529$$ −29.0000 + 50.2295i −1.26087 + 2.18389i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 22.5000 + 12.9904i 0.974583 + 0.562676i
$$534$$ 0 0
$$535$$ −18.0000 + 10.3923i −0.778208 + 0.449299i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 12.0000 0.516877
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 21.0000 12.1244i 0.899541 0.519350i
$$546$$ 0 0
$$547$$ 34.5000 + 19.9186i 1.47511 + 0.851657i 0.999606 0.0280547i $$-0.00893127\pi$$
0.475507 + 0.879712i $$0.342265\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 3.00000 5.19615i 0.127804 0.221364i
$$552$$ 0 0
$$553$$ 7.50000 + 12.9904i 0.318932 + 0.552407i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 27.7128i 1.17423i 0.809504 + 0.587115i $$0.199736\pi$$
−0.809504 + 0.587115i $$0.800264\pi$$
$$558$$ 0 0
$$559$$ 25.9808i 1.09887i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −4.50000 7.79423i −0.189652 0.328488i 0.755482 0.655169i $$-0.227403\pi$$
−0.945134 + 0.326682i $$0.894069\pi$$
$$564$$ 0 0
$$565$$ −10.5000 + 18.1865i −0.441738 + 0.765113i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.50000 0.866025i −0.0628833 0.0363057i 0.468229 0.883607i $$-0.344892\pi$$
−0.531112 + 0.847302i $$0.678226\pi$$
$$570$$ 0 0
$$571$$ −28.5000 + 16.4545i −1.19269 + 0.688599i −0.958915 0.283693i $$-0.908440\pi$$
−0.233773 + 0.972291i $$0.575107\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 18.0000 0.750652
$$576$$ 0 0
$$577$$ 38.0000 1.58196 0.790980 0.611842i $$-0.209571\pi$$
0.790980 + 0.611842i $$0.209571\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 22.5000 12.9904i 0.933457 0.538932i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −19.5000 + 33.7750i −0.804851 + 1.39404i 0.111540 + 0.993760i $$0.464422\pi$$
−0.916392 + 0.400283i $$0.868912\pi$$
$$588$$ 0 0
$$589$$ −9.00000 15.5885i −0.370839 0.642311i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 34.6410i 1.42254i 0.702921 + 0.711268i $$0.251879\pi$$
−0.702921 + 0.711268i $$0.748121\pi$$
$$594$$ 0 0
$$595$$ 20.7846i 0.852086i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ −22.5000 38.9711i −0.919325 1.59232i −0.800443 0.599409i $$-0.795402\pi$$
−0.118882 0.992908i $$-0.537931\pi$$
$$600$$ 0 0
$$601$$ −5.50000 + 9.52628i −0.224350 + 0.388585i −0.956124 0.292962i $$-0.905359\pi$$
0.731774 + 0.681547i $$0.238692\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.00000 1.73205i −0.121967 0.0704179i
$$606$$ 0 0
$$607$$ 1.50000 0.866025i 0.0608831 0.0351509i −0.469249 0.883066i $$-0.655475\pi$$
0.530133 + 0.847915i $$0.322142\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −15.0000 −0.606835
$$612$$ 0 0
$$613$$ 26.0000 1.05013 0.525065 0.851062i $$-0.324041\pi$$
0.525065 + 0.851062i $$0.324041\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −19.5000 + 11.2583i −0.785040 + 0.453243i −0.838214 0.545342i $$-0.816400\pi$$
0.0531732 + 0.998585i $$0.483066\pi$$
$$618$$ 0 0
$$619$$ −25.5000 14.7224i −1.02493 0.591744i −0.109403 0.993997i $$-0.534894\pi$$
−0.915529 + 0.402253i $$0.868227\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −6.00000 + 10.3923i −0.240385 + 0.416359i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 13.8564i 0.552491i
$$630$$ 0 0
$$631$$ 17.3205i 0.689519i −0.938691 0.344759i $$-0.887961\pi$$
0.938691 0.344759i $$-0.112039\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −9.00000 15.5885i −0.357154 0.618609i
$$636$$ 0 0
$$637$$ 10.0000 17.3205i 0.396214 0.686264i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −25.5000 14.7224i −1.00719 0.581501i −0.0968219 0.995302i $$-0.530868\pi$$
−0.910368 + 0.413801i $$0.864201\pi$$
$$642$$ 0 0
$$643$$ −4.50000 + 2.59808i −0.177463 + 0.102458i −0.586100 0.810239i $$-0.699337\pi$$
0.408637 + 0.912697i $$0.366004\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 24.0000 0.943537 0.471769 0.881722i $$-0.343616\pi$$
0.471769 + 0.881722i $$0.343616\pi$$
$$648$$ 0 0
$$649$$ −9.00000 −0.353281
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −13.5000 + 7.79423i −0.528296 + 0.305012i −0.740322 0.672252i $$-0.765327\pi$$
0.212026 + 0.977264i $$0.431994\pi$$
$$654$$ 0 0
$$655$$ −4.50000 2.59808i −0.175830 0.101515i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i $$-0.851943\pi$$
0.835330 + 0.549749i $$0.185277\pi$$
$$660$$ 0 0
$$661$$ 24.5000 + 42.4352i 0.952940 + 1.65054i 0.739014 + 0.673690i $$0.235292\pi$$
0.213925 + 0.976850i $$0.431375\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 10.3923i 0.402996i
$$666$$ 0 0
$$667$$ 15.5885i 0.603587i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1.50000 + 2.59808i 0.0579069 + 0.100298i
$$672$$ 0 0
$$673$$ 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i $$-0.580614\pi$$
0.963679 0.267063i $$-0.0860531\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −31.5000 18.1865i −1.21064 0.698965i −0.247744 0.968826i $$-0.579689\pi$$
−0.962899 + 0.269860i $$0.913022\pi$$
$$678$$ 0 0
$$679$$ −7.50000 + 4.33013i −0.287824 + 0.166175i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 15.0000 0.573121
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 4.50000 + 2.59808i 0.171188 + 0.0988355i 0.583146 0.812367i $$-0.301822\pi$$
−0.411958 + 0.911203i $$0.635155\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.50000 + 2.59808i −0.0568982 + 0.0985506i
$$696$$ 0 0
$$697$$ 18.0000 + 31.1769i 0.681799 + 1.18091i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 13.8564i 0.523349i 0.965156 + 0.261675i $$0.0842747\pi$$
−0.965156 + 0.261675i $$0.915725\pi$$
$$702$$ 0 0
$$703$$ 6.92820i 0.261302i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −4.50000 7.79423i −0.169240 0.293132i
$$708$$ 0 0
$$709$$ −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i $$-0.949459\pi$$
0.630641 + 0.776075i $$0.282792\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 40.5000 + 23.3827i 1.51674 + 0.875688i
$$714$$ 0 0
$$715$$ 22.5000 12.9904i 0.841452 0.485813i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −24.0000 −0.895049 −0.447524 0.894272i $$-0.647694\pi$$
−0.447524 + 0.894272i $$0.647694\pi$$
$$720$$ 0 0
$$721$$ −3.00000 −0.111726
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 3.00000 1.73205i 0.111417 0.0643268i
$$726$$ 0 0
$$727$$ −31.5000 18.1865i −1.16827 0.674501i −0.214998 0.976614i $$-0.568975\pi$$
−0.953272 + 0.302113i $$0.902308\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −18.0000 + 31.1769i −0.665754 + 1.15312i
$$732$$ 0 0
$$733$$ 2.50000 + 4.33013i 0.0923396 + 0.159937i 0.908495 0.417895i $$-0.137232\pi$$
−0.816156 + 0.577832i $$0.803899\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 25.9808i 0.957014i
$$738$$ 0 0
$$739$$ 31.1769i 1.14686i −0.819254 0.573431i $$-0.805612\pi$$
0.819254 0.573431i $$-0.194388\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 13.5000 + 23.3827i 0.495267 + 0.857828i 0.999985 0.00545664i $$-0.00173691\pi$$
−0.504718 + 0.863284i $$0.668404\pi$$
$$744$$ 0 0
$$745$$ 7.50000 12.9904i 0.274779 0.475931i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −18.0000 10.3923i −0.657706 0.379727i
$$750$$ 0 0
$$751$$ −10.5000 + 6.06218i −0.383150 + 0.221212i −0.679188 0.733964i $$-0.737668\pi$$
0.296038 + 0.955176i $$0.404335\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 15.0000 0.545906
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −19.5000 + 11.2583i −0.706874 + 0.408114i −0.809903 0.586564i $$-0.800480\pi$$
0.103028 + 0.994678i $$0.467147\pi$$
$$762$$ 0 0
$$763$$ 21.0000 + 12.1244i 0.760251 + 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −7.50000 + 12.9904i −0.270809 + 0.469055i
$$768$$ 0 0
$$769$$ −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i $$-0.302780\pi$$
−0.995397 + 0.0958377i $$0.969447\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 27.7128i 0.996761i 0.866959 + 0.498380i $$0.166072\pi$$
−0.866959 + 0.498380i $$0.833928\pi$$
$$774$$ 0 0
$$775$$ 10.3923i 0.373303i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 9.00000 + 15.5885i 0.322458 + 0.558514i
$$780$$ 0 0
$$781$$ −18.0000 + 31.1769i −0.644091 + 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1.50000 0.866025i −0.0535373 0.0309098i
$$786$$ 0 0
$$787$$ 25.5000 14.7224i 0.908977 0.524798i 0.0288750 0.999583i $$-0.490808\pi$$
0.880102 + 0.474785i $$0.157474\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −21.0000 −0.746674
$$792$$ 0 0
$$793$$ 5.00000 0.177555
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 28.5000 16.4545i 1.00952 0.582848i 0.0984702 0.995140i $$-0.468605\pi$$
0.911052 + 0.412292i $$0.135272\pi$$
$$798$$ 0 0
$$799$$ −18.0000 10.3923i −0.636794 0.367653i
$$800$$ 0 0
$$801$$