# Properties

 Label 1296.2.i.p.865.1 Level $1296$ Weight $2$ Character 1296.865 Analytic conductor $10.349$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1296 = 2^{4} \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1296.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.3486121020$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 324) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 865.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1296.865 Dual form 1296.2.i.p.433.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +O(q^{10})$$ $$q+(1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{7} +(3.00000 - 5.19615i) q^{11} +(-2.50000 - 4.33013i) q^{13} +3.00000 q^{17} -2.00000 q^{19} +(-3.00000 - 5.19615i) q^{23} +(-2.00000 + 3.46410i) q^{25} +(1.50000 - 2.59808i) q^{29} +(-2.00000 - 3.46410i) q^{31} +6.00000 q^{35} +5.00000 q^{37} +(-3.00000 - 5.19615i) q^{41} +(-5.00000 + 8.66025i) q^{43} +(1.50000 + 2.59808i) q^{49} +6.00000 q^{53} +18.0000 q^{55} +(6.00000 + 10.3923i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(7.50000 - 12.9904i) q^{65} +(1.00000 + 1.73205i) q^{67} +6.00000 q^{71} -1.00000 q^{73} +(-6.00000 - 10.3923i) q^{77} +(-5.00000 + 8.66025i) q^{79} +(4.50000 + 7.79423i) q^{85} +3.00000 q^{89} -10.0000 q^{91} +(-3.00000 - 5.19615i) q^{95} +(5.00000 - 8.66025i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{5} + 2 q^{7}+O(q^{10})$$ 2 * q + 3 * q^5 + 2 * q^7 $$2 q + 3 q^{5} + 2 q^{7} + 6 q^{11} - 5 q^{13} + 6 q^{17} - 4 q^{19} - 6 q^{23} - 4 q^{25} + 3 q^{29} - 4 q^{31} + 12 q^{35} + 10 q^{37} - 6 q^{41} - 10 q^{43} + 3 q^{49} + 12 q^{53} + 36 q^{55} + 12 q^{59} - 5 q^{61} + 15 q^{65} + 2 q^{67} + 12 q^{71} - 2 q^{73} - 12 q^{77} - 10 q^{79} + 9 q^{85} + 6 q^{89} - 20 q^{91} - 6 q^{95} + 10 q^{97}+O(q^{100})$$ 2 * q + 3 * q^5 + 2 * q^7 + 6 * q^11 - 5 * q^13 + 6 * q^17 - 4 * q^19 - 6 * q^23 - 4 * q^25 + 3 * q^29 - 4 * q^31 + 12 * q^35 + 10 * q^37 - 6 * q^41 - 10 * q^43 + 3 * q^49 + 12 * q^53 + 36 * q^55 + 12 * q^59 - 5 * q^61 + 15 * q^65 + 2 * q^67 + 12 * q^71 - 2 * q^73 - 12 * q^77 - 10 * q^79 + 9 * q^85 + 6 * q^89 - 20 * q^91 - 6 * q^95 + 10 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$1135$$ $$1217$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i $$0.0673912\pi$$
−0.306851 + 0.951757i $$0.599275\pi$$
$$6$$ 0 0
$$7$$ 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i $$-0.709957\pi$$
0.990766 + 0.135583i $$0.0432908\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.00000 5.19615i 0.904534 1.56670i 0.0829925 0.996550i $$-0.473552\pi$$
0.821541 0.570149i $$-0.193114\pi$$
$$12$$ 0 0
$$13$$ −2.50000 4.33013i −0.693375 1.20096i −0.970725 0.240192i $$-0.922790\pi$$
0.277350 0.960769i $$-0.410544\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 3.00000 0.727607 0.363803 0.931476i $$-0.381478\pi$$
0.363803 + 0.931476i $$0.381478\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0 0
$$25$$ −2.00000 + 3.46410i −0.400000 + 0.692820i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i $$-0.743482\pi$$
0.971023 + 0.238987i $$0.0768152\pi$$
$$30$$ 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 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 6.00000 1.01419
$$36$$ 0 0
$$37$$ 5.00000 0.821995 0.410997 0.911636i $$-0.365181\pi$$
0.410997 + 0.911636i $$0.365181\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ 0 0
$$43$$ −5.00000 + 8.66025i −0.762493 + 1.32068i 0.179069 + 0.983836i $$0.442691\pi$$
−0.941562 + 0.336840i $$0.890642\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0 0
$$49$$ 1.50000 + 2.59808i 0.214286 + 0.371154i
$$50$$ 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
$$55$$ 18.0000 2.42712
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i $$0.118692\pi$$
−0.150148 + 0.988663i $$0.547975\pi$$
$$60$$ 0 0
$$61$$ −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i $$-0.937047\pi$$
0.660415 + 0.750901i $$0.270381\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 7.50000 12.9904i 0.930261 1.61126i
$$66$$ 0 0
$$67$$ 1.00000 + 1.73205i 0.122169 + 0.211604i 0.920623 0.390453i $$-0.127682\pi$$
−0.798454 + 0.602056i $$0.794348\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ −1.00000 −0.117041 −0.0585206 0.998286i $$-0.518638\pi$$
−0.0585206 + 0.998286i $$0.518638\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −6.00000 10.3923i −0.683763 1.18431i
$$78$$ 0 0
$$79$$ −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i $$0.356844\pi$$
−0.997274 + 0.0737937i $$0.976489\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$84$$ 0 0
$$85$$ 4.50000 + 7.79423i 0.488094 + 0.845403i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 3.00000 0.317999 0.159000 0.987279i $$-0.449173\pi$$
0.159000 + 0.987279i $$0.449173\pi$$
$$90$$ 0 0
$$91$$ −10.0000 −1.04828
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −3.00000 5.19615i −0.307794 0.533114i
$$96$$ 0 0
$$97$$ 5.00000 8.66025i 0.507673 0.879316i −0.492287 0.870433i $$-0.663839\pi$$
0.999961 0.00888289i $$-0.00282755\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ 0 0
$$103$$ −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i $$-0.877647\pi$$
0.138767 0.990325i $$-0.455686\pi$$
$$104$$ 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
$$109$$ −7.00000 −0.670478 −0.335239 0.942133i $$-0.608817\pi$$
−0.335239 + 0.942133i $$0.608817\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i $$-0.0275297\pi$$
−0.572938 + 0.819599i $$0.694196\pi$$
$$114$$ 0 0
$$115$$ 9.00000 15.5885i 0.839254 1.45363i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 3.00000 5.19615i 0.275010 0.476331i
$$120$$ 0 0
$$121$$ −12.5000 21.6506i −1.13636 1.96824i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 3.00000 0.268328
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i $$-0.0822479\pi$$
−0.704692 + 0.709514i $$0.748915\pi$$
$$132$$ 0 0
$$133$$ −2.00000 + 3.46410i −0.173422 + 0.300376i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −7.50000 + 12.9904i −0.640768 + 1.10984i 0.344493 + 0.938789i $$0.388051\pi$$
−0.985262 + 0.171054i $$0.945283\pi$$
$$138$$ 0 0
$$139$$ 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i $$-0.0564848\pi$$
−0.645021 + 0.764165i $$0.723151\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −30.0000 −2.50873
$$144$$ 0 0
$$145$$ 9.00000 0.747409
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 7.50000 + 12.9904i 0.614424 + 1.06421i 0.990485 + 0.137619i $$0.0439449\pi$$
−0.376061 + 0.926595i $$0.622722\pi$$
$$150$$ 0 0
$$151$$ −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i $$-0.885372\pi$$
0.773099 + 0.634285i $$0.218706\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.00000 10.3923i 0.481932 0.834730i
$$156$$ 0 0
$$157$$ −2.50000 4.33013i −0.199522 0.345582i 0.748852 0.662738i $$-0.230606\pi$$
−0.948373 + 0.317156i $$0.897272\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −12.0000 −0.945732
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i $$-0.921432\pi$$
0.273252 0.961943i $$-0.411901\pi$$
$$168$$ 0 0
$$169$$ −6.00000 + 10.3923i −0.461538 + 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i $$-0.944481\pi$$
0.642699 + 0.766119i $$0.277815\pi$$
$$174$$ 0 0
$$175$$ 4.00000 + 6.92820i 0.302372 + 0.523723i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 7.50000 + 12.9904i 0.551411 + 0.955072i
$$186$$ 0 0
$$187$$ 9.00000 15.5885i 0.658145 1.13994i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i $$-0.902984\pi$$
0.736839 + 0.676068i $$0.236317\pi$$
$$192$$ 0 0
$$193$$ 12.5000 + 21.6506i 0.899770 + 1.55845i 0.827788 + 0.561041i $$0.189599\pi$$
0.0719816 + 0.997406i $$0.477068\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ 0 0
$$199$$ −20.0000 −1.41776 −0.708881 0.705328i $$-0.750800\pi$$
−0.708881 + 0.705328i $$0.750800\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −3.00000 5.19615i −0.210559 0.364698i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −6.00000 + 10.3923i −0.415029 + 0.718851i
$$210$$ 0 0
$$211$$ 7.00000 + 12.1244i 0.481900 + 0.834675i 0.999784 0.0207756i $$-0.00661356\pi$$
−0.517884 + 0.855451i $$0.673280\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −30.0000 −2.04598
$$216$$ 0 0
$$217$$ −8.00000 −0.543075
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −7.50000 12.9904i −0.504505 0.873828i
$$222$$ 0 0
$$223$$ −5.00000 + 8.66025i −0.334825 + 0.579934i −0.983451 0.181173i $$-0.942010\pi$$
0.648626 + 0.761107i $$0.275344\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i $$0.370447\pi$$
−0.993210 + 0.116331i $$0.962887\pi$$
$$228$$ 0 0
$$229$$ −2.50000 4.33013i −0.165205 0.286143i 0.771523 0.636201i $$-0.219495\pi$$
−0.936728 + 0.350058i $$0.886162\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 15.0000 0.982683 0.491341 0.870967i $$-0.336507\pi$$
0.491341 + 0.870967i $$0.336507\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$240$$ 0 0
$$241$$ −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i $$-0.948609\pi$$
0.632709 + 0.774389i $$0.281943\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −4.50000 + 7.79423i −0.287494 + 0.497955i
$$246$$ 0 0
$$247$$ 5.00000 + 8.66025i 0.318142 + 0.551039i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 30.0000 1.89358 0.946792 0.321847i $$-0.104304\pi$$
0.946792 + 0.321847i $$0.104304\pi$$
$$252$$ 0 0
$$253$$ −36.0000 −2.26330
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −13.5000 23.3827i −0.842107 1.45857i −0.888110 0.459631i $$-0.847982\pi$$
0.0460033 0.998941i $$-0.485352\pi$$
$$258$$ 0 0
$$259$$ 5.00000 8.66025i 0.310685 0.538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 0 0
$$265$$ 9.00000 + 15.5885i 0.552866 + 0.957591i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −3.00000 −0.182913 −0.0914566 0.995809i $$-0.529152\pi$$
−0.0914566 + 0.995809i $$0.529152\pi$$
$$270$$ 0 0
$$271$$ 10.0000 0.607457 0.303728 0.952759i $$-0.401768\pi$$
0.303728 + 0.952759i $$0.401768\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 12.0000 + 20.7846i 0.723627 + 1.25336i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i $$-0.980988\pi$$
0.550804 + 0.834634i $$0.314321\pi$$
$$282$$ 0 0
$$283$$ −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i $$-0.204600\pi$$
−0.919327 + 0.393494i $$0.871266\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −12.0000 −0.708338
$$288$$ 0 0
$$289$$ −8.00000 −0.470588
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 7.50000 + 12.9904i 0.438155 + 0.758906i 0.997547 0.0699967i $$-0.0222989\pi$$
−0.559393 + 0.828903i $$0.688966\pi$$
$$294$$ 0 0
$$295$$ −18.0000 + 31.1769i −1.04800 + 1.81519i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −15.0000 + 25.9808i −0.867472 + 1.50251i
$$300$$ 0 0
$$301$$ 10.0000 + 17.3205i 0.576390 + 0.998337i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −15.0000 −0.858898
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i $$0.0715523\pi$$
−0.294384 + 0.955687i $$0.595114\pi$$
$$312$$ 0 0
$$313$$ 12.5000 21.6506i 0.706542 1.22377i −0.259590 0.965719i $$-0.583588\pi$$
0.966132 0.258047i $$-0.0830791\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7.50000 12.9904i 0.421242 0.729612i −0.574819 0.818280i $$-0.694928\pi$$
0.996061 + 0.0886679i $$0.0282610\pi$$
$$318$$ 0 0
$$319$$ −9.00000 15.5885i −0.503903 0.872786i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −6.00000 −0.333849
$$324$$ 0 0
$$325$$ 20.0000 1.10940
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 13.0000 22.5167i 0.714545 1.23763i −0.248590 0.968609i $$-0.579967\pi$$
0.963135 0.269019i $$-0.0866994\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −3.00000 + 5.19615i −0.163908 + 0.283896i
$$336$$ 0 0
$$337$$ 5.00000 + 8.66025i 0.272367 + 0.471754i 0.969468 0.245220i $$-0.0788601\pi$$
−0.697100 + 0.716974i $$0.745527\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −24.0000 −1.29967
$$342$$ 0 0
$$343$$ 20.0000 1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i $$-0.00616095\pi$$
−0.516667 + 0.856186i $$0.672828\pi$$
$$348$$ 0 0
$$349$$ −1.00000 + 1.73205i −0.0535288 + 0.0927146i −0.891548 0.452926i $$-0.850380\pi$$
0.838019 + 0.545640i $$0.183714\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i $$-0.539030\pi$$
0.920677 0.390324i $$-0.127637\pi$$
$$354$$ 0 0
$$355$$ 9.00000 + 15.5885i 0.477670 + 0.827349i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −18.0000 −0.950004 −0.475002 0.879985i $$-0.657553\pi$$
−0.475002 + 0.879985i $$0.657553\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −1.50000 2.59808i −0.0785136 0.135990i
$$366$$ 0 0
$$367$$ 16.0000 27.7128i 0.835193 1.44660i −0.0586798 0.998277i $$-0.518689\pi$$
0.893873 0.448320i $$-0.147978\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.00000 10.3923i 0.311504 0.539542i
$$372$$ 0 0
$$373$$ −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i $$-0.284725\pi$$
−0.988363 + 0.152115i $$0.951392\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −15.0000 −0.772539
$$378$$ 0 0
$$379$$ 4.00000 0.205466 0.102733 0.994709i $$-0.467241\pi$$
0.102733 + 0.994709i $$0.467241\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −15.0000 25.9808i −0.766464 1.32755i −0.939469 0.342634i $$-0.888681\pi$$
0.173005 0.984921i $$-0.444652\pi$$
$$384$$ 0 0
$$385$$ 18.0000 31.1769i 0.917365 1.58892i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −15.0000 + 25.9808i −0.760530 + 1.31728i 0.182047 + 0.983290i $$0.441728\pi$$
−0.942578 + 0.333987i $$0.891606\pi$$
$$390$$ 0 0
$$391$$ −9.00000 15.5885i −0.455150 0.788342i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −30.0000 −1.50946
$$396$$ 0 0
$$397$$ −7.00000 −0.351320 −0.175660 0.984451i $$-0.556206\pi$$
−0.175660 + 0.984451i $$0.556206\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i $$-0.288863\pi$$
−0.990257 + 0.139253i $$0.955530\pi$$
$$402$$ 0 0
$$403$$ −10.0000 + 17.3205i −0.498135 + 0.862796i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 15.0000 25.9808i 0.743522 1.28782i
$$408$$ 0 0
$$409$$ −17.5000 30.3109i −0.865319 1.49878i −0.866730 0.498778i $$-0.833782\pi$$
0.00141047 0.999999i $$-0.499551\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 24.0000 1.18096
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$420$$ 0 0
$$421$$ −14.5000 + 25.1147i −0.706687 + 1.22402i 0.259393 + 0.965772i $$0.416478\pi$$
−0.966079 + 0.258245i $$0.916856\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −6.00000 + 10.3923i −0.291043 + 0.504101i
$$426$$ 0 0
$$427$$ 5.00000 + 8.66025i 0.241967 + 0.419099i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ 0 0
$$433$$ 11.0000 0.528626 0.264313 0.964437i $$-0.414855\pi$$
0.264313 + 0.964437i $$0.414855\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 6.00000 + 10.3923i 0.287019 + 0.497131i
$$438$$ 0 0
$$439$$ 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i $$-0.772190\pi$$
0.945552 + 0.325471i $$0.105523\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$444$$ 0 0
$$445$$ 4.50000 + 7.79423i 0.213320 + 0.369482i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ −36.0000 −1.69517
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −15.0000 25.9808i −0.703211 1.21800i
$$456$$ 0 0
$$457$$ −17.5000 + 30.3109i −0.818615 + 1.41788i 0.0880870 + 0.996113i $$0.471925\pi$$
−0.906702 + 0.421771i $$0.861409\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i $$-0.877955\pi$$
0.787668 + 0.616100i $$0.211288\pi$$
$$462$$ 0 0
$$463$$ −2.00000 3.46410i −0.0929479 0.160990i 0.815802 0.578331i $$-0.196296\pi$$
−0.908750 + 0.417340i $$0.862962\pi$$
$$464$$ 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
$$469$$ 4.00000 0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 30.0000 + 51.9615i 1.37940 + 2.38919i
$$474$$ 0 0
$$475$$ 4.00000 6.92820i 0.183533 0.317888i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −9.00000 + 15.5885i −0.411220 + 0.712255i −0.995023 0.0996406i $$-0.968231\pi$$
0.583803 + 0.811895i $$0.301564\pi$$
$$480$$ 0 0
$$481$$ −12.5000 21.6506i −0.569951 0.987184i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 30.0000 1.36223
$$486$$ 0 0
$$487$$ −20.0000 −0.906287 −0.453143 0.891438i $$-0.649697\pi$$
−0.453143 + 0.891438i $$0.649697\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −3.00000 5.19615i −0.135388 0.234499i 0.790358 0.612646i $$-0.209895\pi$$
−0.925746 + 0.378147i $$0.876561\pi$$
$$492$$ 0 0
$$493$$ 4.50000 7.79423i 0.202670 0.351034i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 6.00000 10.3923i 0.269137 0.466159i
$$498$$ 0 0
$$499$$ −11.0000 19.0526i −0.492428 0.852910i 0.507534 0.861632i $$-0.330557\pi$$
−0.999962 + 0.00872186i $$0.997224\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i $$-0.209119\pi$$
−0.924821 + 0.380402i $$0.875786\pi$$
$$510$$ 0 0
$$511$$ −1.00000 + 1.73205i −0.0442374 + 0.0766214i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 24.0000 41.5692i 1.05757 1.83176i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ 10.0000 0.437269 0.218635 0.975807i $$-0.429840\pi$$
0.218635 + 0.975807i $$0.429840\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −6.00000 10.3923i −0.261364 0.452696i
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −15.0000 + 25.9808i −0.649722 + 1.12535i
$$534$$ 0 0
$$535$$ 18.0000 + 31.1769i 0.778208 + 1.34790i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 18.0000 0.775315
$$540$$ 0 0
$$541$$ 41.0000 1.76273 0.881364 0.472438i $$-0.156626\pi$$
0.881364 + 0.472438i $$0.156626\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −10.5000 18.1865i −0.449771 0.779026i
$$546$$ 0 0
$$547$$ −20.0000 + 34.6410i −0.855138 + 1.48114i 0.0213785 + 0.999771i $$0.493195\pi$$
−0.876517 + 0.481371i $$0.840139\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3.00000 + 5.19615i −0.127804 + 0.221364i
$$552$$ 0 0
$$553$$ 10.0000 + 17.3205i 0.425243 + 0.736543i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −15.0000 −0.635570 −0.317785 0.948163i $$-0.602939\pi$$
−0.317785 + 0.948163i $$0.602939\pi$$
$$558$$ 0 0
$$559$$ 50.0000 2.11477
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$564$$ 0 0
$$565$$ −13.5000 + 23.3827i −0.567949 + 0.983717i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.50000 + 2.59808i −0.0628833 + 0.108917i −0.895753 0.444552i $$-0.853363\pi$$
0.832870 + 0.553469i $$0.186696\pi$$
$$570$$ 0 0
$$571$$ 22.0000 + 38.1051i 0.920671 + 1.59465i 0.798379 + 0.602155i $$0.205691\pi$$
0.122292 + 0.992494i $$0.460975\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 24.0000 1.00087
$$576$$ 0 0
$$577$$ −37.0000 −1.54033 −0.770165 0.637845i $$-0.779826\pi$$
−0.770165 + 0.637845i $$0.779826\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 18.0000 31.1769i 0.745484 1.29122i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 15.0000 25.9808i 0.619116 1.07234i −0.370531 0.928820i $$-0.620824\pi$$
0.989647 0.143521i $$-0.0458424\pi$$
$$588$$ 0 0
$$589$$ 4.00000 + 6.92820i 0.164817 + 0.285472i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 39.0000 1.60154 0.800769 0.598973i $$-0.204424\pi$$
0.800769 + 0.598973i $$0.204424\pi$$
$$594$$ 0 0
$$595$$ 18.0000 0.737928
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i $$-0.0878284\pi$$
−0.717021 + 0.697051i $$0.754495\pi$$
$$600$$ 0 0
$$601$$ 0.500000 0.866025i 0.0203954 0.0353259i −0.855648 0.517559i $$-0.826841\pi$$
0.876043 + 0.482233i $$0.160174\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 37.5000 64.9519i 1.52459 2.64067i
$$606$$ 0 0
$$607$$ −5.00000 8.66025i −0.202944 0.351509i 0.746532 0.665350i $$-0.231718\pi$$
−0.949476 + 0.313841i $$0.898384\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −10.0000 −0.403896 −0.201948 0.979396i $$-0.564727\pi$$
−0.201948 + 0.979396i $$0.564727\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7.50000 12.9904i −0.301939 0.522973i 0.674636 0.738150i $$-0.264300\pi$$
−0.976575 + 0.215177i $$0.930967\pi$$
$$618$$ 0 0
$$619$$ −20.0000 + 34.6410i −0.803868 + 1.39234i 0.113185 + 0.993574i $$0.463895\pi$$
−0.917053 + 0.398766i $$0.869439\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 3.00000 5.19615i 0.120192 0.208179i
$$624$$ 0 0
$$625$$ 14.5000 + 25.1147i 0.580000 + 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 15.0000 0.598089
$$630$$ 0 0
$$631$$ 4.00000 0.159237 0.0796187 0.996825i $$-0.474630\pi$$
0.0796187 + 0.996825i $$0.474630\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −3.00000 5.19615i −0.119051 0.206203i
$$636$$ 0 0
$$637$$ 7.50000 12.9904i 0.297161 0.514698i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i $$-0.697211\pi$$
0.995400 + 0.0958109i $$0.0305444\pi$$
$$642$$ 0 0
$$643$$ −20.0000 34.6410i −0.788723 1.36611i −0.926750 0.375680i $$-0.877409\pi$$
0.138027 0.990429i $$-0.455924\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000 0.707653 0.353827 0.935311i $$-0.384880\pi$$
0.353827 + 0.935311i $$0.384880\pi$$
$$648$$ 0 0
$$649$$ 72.0000 2.82625
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i $$-0.966977\pi$$
0.407628 0.913148i $$-0.366356\pi$$
$$654$$ 0 0
$$655$$ −9.00000 + 15.5885i −0.351659 + 0.609091i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −3.00000 + 5.19615i −0.116863 + 0.202413i −0.918523 0.395367i $$-0.870617\pi$$
0.801660 + 0.597781i $$0.203951\pi$$
$$660$$ 0 0
$$661$$ −14.5000 25.1147i −0.563985 0.976850i −0.997143 0.0755324i $$-0.975934\pi$$
0.433159 0.901318i $$-0.357399\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −12.0000 −0.465340
$$666$$ 0 0
$$667$$ −18.0000 −0.696963
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 15.0000 + 25.9808i 0.579069 + 1.00298i
$$672$$ 0 0
$$673$$ 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i $$-0.827198\pi$$
0.875501 + 0.483216i $$0.160531\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 21.0000 36.3731i 0.807096 1.39793i −0.107772 0.994176i $$-0.534372\pi$$
0.914867 0.403755i $$-0.132295\pi$$
$$678$$ 0 0
$$679$$ −10.0000 17.3205i −0.383765 0.664700i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ −45.0000 −1.71936
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −15.0000 25.9808i −0.571454 0.989788i
$$690$$ 0 0
$$691$$ −5.00000 + 8.66025i −0.190209 + 0.329452i −0.945319 0.326146i $$-0.894250\pi$$
0.755110 + 0.655598i $$0.227583\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −12.0000 + 20.7846i −0.455186 + 0.788405i
$$696$$ 0 0
$$697$$ −9.00000 15.5885i −0.340899 0.590455i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −39.0000 −1.47301 −0.736505 0.676432i $$-0.763525\pi$$
−0.736505 + 0.676432i $$0.763525\pi$$
$$702$$ 0 0
$$703$$ −10.0000 −0.377157
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.00000 10.3923i −0.225653 0.390843i
$$708$$ 0 0
$$709$$ 9.50000 16.4545i 0.356780 0.617961i −0.630641 0.776075i $$-0.717208\pi$$
0.987421 + 0.158114i $$0.0505412\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −12.0000 + 20.7846i −0.449404 + 0.778390i
$$714$$ 0 0
$$715$$ −45.0000 77.9423i −1.68290 2.91488i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 18.0000 0.671287 0.335643 0.941989i $$-0.391046\pi$$
0.335643 + 0.941989i $$0.391046\pi$$
$$720$$ 0 0
$$721$$ −32.0000 −1.19174
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 6.00000 + 10.3923i 0.222834 + 0.385961i
$$726$$ 0 0
$$727$$ −5.00000 + 8.66025i −0.185440 + 0.321191i −0.943725 0.330732i $$-0.892704\pi$$
0.758285 + 0.651923i $$0.226038\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −15.0000 + 25.9808i −0.554795 + 0.960933i
$$732$$ 0 0
$$733$$ −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i $$-0.249912\pi$$
−0.965854 + 0.259087i $$0.916578\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 12.0000 0.442026
$$738$$ 0 0
$$739$$ 52.0000 1.91285 0.956425 0.291977i $$-0.0943129\pi$$
0.956425 + 0.291977i $$0.0943129\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i $$0.0629279\pi$$
−0.320166 + 0.947361i $$0.603739\pi$$
$$744$$ 0 0
$$745$$ −22.5000 + 38.9711i −0.824336 + 1.42779i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 12.0000 20.7846i 0.438470 0.759453i
$$750$$ 0 0
$$751$$ −5.00000 8.66025i −0.182453 0.316017i 0.760263 0.649616i $$-0.225070\pi$$
−0.942715 + 0.333599i $$0.891737\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12.0000 −0.436725
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 4.50000 + 7.79423i 0.163125 + 0.282541i 0.935988 0.352032i $$-0.114509\pi$$
−0.772863 + 0.634573i $$0.781176\pi$$
$$762$$ 0 0
$$763$$ −7.00000 + 12.1244i −0.253417 + 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 30.0000 51.9615i 1.08324 1.87622i
$$768$$ 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
$$773$$ 45.0000 1.61854 0.809269 0.587439i $$-0.199864\pi$$
0.809269 + 0.587439i $$0.199864\pi$$
$$774$$ 0 0
$$775$$ 16.0000 0.574737
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 6.00000 + 10.3923i 0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 18.0000 31.1769i 0.644091 1.11560i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 7.50000 12.9904i 0.267686 0.463647i
$$786$$ 0 0
$$787$$ 19.0000 + 32.9090i 0.677277 + 1.17308i 0.975798 + 0.218675i $$0.0701734\pi$$
−0.298521 + 0.954403i $$0.596493\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 18.0000 0.640006
$$792$$ 0 0
$$793$$ 25.0000 0.887776
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −22.5000 38.9711i −0.796991 1.38043i −0.921567 0.388219i $$-0.873091\pi$$
0.124576 0.992210i $$-0.460243\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0