# Properties

 Label 1296.2.i.d.433.1 Level $1296$ Weight $2$ Character 1296.433 Analytic conductor $10.349$ Analytic rank $1$ 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: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 324) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 433.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1296.433 Dual form 1296.2.i.d.865.1

## $q$-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 $$\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$$.

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

## 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 0.306851 + 0.951757i $$0.400725\pi$$
−0.977672 + 0.210138i $$0.932609\pi$$
$$6$$ 0 0
$$7$$ 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i $$-0.0432908\pi$$
−0.612801 + 0.790237i $$0.709957\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i $$-0.806886\pi$$
−0.0829925 0.996550i $$-0.526448\pi$$
$$12$$ 0 0
$$13$$ −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i $$0.410544\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.00000 −0.727607 −0.363803 0.931476i $$-0.618522\pi$$
−0.363803 + 0.931476i $$0.618522\pi$$
$$18$$ 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 −0.362892 0.931831i $$-0.618211\pi$$
0.988436 0.151642i $$-0.0484560\pi$$
$$24$$ 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 $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i $$-0.950287\pi$$
0.628619 + 0.777714i $$0.283621\pi$$
$$32$$ 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 $$-0.678120\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ −5.00000 8.66025i −0.762493 1.32068i −0.941562 0.336840i $$-0.890642\pi$$
0.179069 0.983836i $$-0.442691\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 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 $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 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 0.150148 + 0.988663i $$0.452025\pi$$
−0.931282 + 0.364299i $$0.881308\pi$$
$$60$$ 0 0
$$61$$ −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i $$-0.270381\pi$$
−0.980507 + 0.196485i $$0.937047\pi$$
$$62$$ 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 −0.798454 0.602056i $$-0.794348\pi$$
0.920623 + 0.390453i $$0.127682\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −6.00000 −0.712069 −0.356034 0.934473i $$-0.615871\pi$$
−0.356034 + 0.934473i $$0.615871\pi$$
$$72$$ 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 −0.997274 0.0737937i $$-0.976489\pi$$
0.434730 0.900561i $$-0.356844\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$84$$ 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 $$-0.550827\pi$$
−0.159000 + 0.987279i $$0.550827\pi$$
$$90$$ 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 0.999961 + 0.00888289i $$0.00282755\pi$$
−0.492287 + 0.870433i $$0.663839\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i $$-0.263157\pi$$
−0.975796 + 0.218685i $$0.929823\pi$$
$$102$$ 0 0
$$103$$ −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i $$0.455686\pi$$
−0.927030 + 0.374987i $$0.877647\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −12.0000 −1.16008 −0.580042 0.814587i $$-0.696964\pi$$
−0.580042 + 0.814587i $$0.696964\pi$$
$$108$$ 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 $$-0.972470\pi$$
0.572938 + 0.819599i $$0.305804\pi$$
$$114$$ 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 $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 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 0.985262 + 0.171054i $$0.0547174\pi$$
−0.344493 + 0.938789i $$0.611949\pi$$
$$138$$ 0 0
$$139$$ 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i $$-0.723151\pi$$
0.984297 + 0.176522i $$0.0564848\pi$$
$$140$$ 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 0.376061 + 0.926595i $$0.377278\pi$$
−0.990485 + 0.137619i $$0.956055\pi$$
$$150$$ 0 0
$$151$$ −2.00000 3.46410i −0.162758 0.281905i 0.773099 0.634285i $$-0.218706\pi$$
−0.935857 + 0.352381i $$0.885372\pi$$
$$152$$ 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 −0.948373 0.317156i $$-0.897272\pi$$
0.748852 + 0.662738i $$0.230606\pi$$
$$158$$ 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 −0.273252 0.961943i $$-0.588099\pi$$
0.969693 0.244328i $$-0.0785675\pi$$
$$168$$ 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 $$-0.0555188\pi$$
−0.642699 + 0.766119i $$0.722185\pi$$
$$174$$ 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 $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 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 $$-0.0970159\pi$$
−0.736839 + 0.676068i $$0.763683\pi$$
$$192$$ 0 0
$$193$$ 12.5000 21.6506i 0.899770 1.55845i 0.0719816 0.997406i $$-0.477068\pi$$
0.827788 0.561041i $$-0.189599\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 15.0000 1.06871 0.534353 0.845262i $$-0.320555\pi$$
0.534353 + 0.845262i $$0.320555\pi$$
$$198$$ 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 −0.517884 0.855451i $$-0.673280\pi$$
0.999784 + 0.0207756i $$0.00661356\pi$$
$$212$$ 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 0.648626 0.761107i $$-0.275344\pi$$
−0.983451 + 0.181173i $$0.942010\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i $$0.0371134\pi$$
−0.395860 + 0.918311i $$0.629553\pi$$
$$228$$ 0 0
$$229$$ −2.50000 + 4.33013i −0.165205 + 0.286143i −0.936728 0.350058i $$-0.886162\pi$$
0.771523 + 0.636201i $$0.219495\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −15.0000 −0.982683 −0.491341 0.870967i $$-0.663493\pi$$
−0.491341 + 0.870967i $$0.663493\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$240$$ 0 0
$$241$$ −5.50000 9.52628i −0.354286 0.613642i 0.632709 0.774389i $$-0.281943\pi$$
−0.986996 + 0.160748i $$0.948609\pi$$
$$242$$ 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 $$-0.895696\pi$$
−0.946792 + 0.321847i $$0.895696\pi$$
$$252$$ 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 −0.0460033 0.998941i $$-0.514648\pi$$
0.888110 0.459631i $$-0.152018\pi$$
$$258$$ 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 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 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 $$-0.470848\pi$$
0.0914566 + 0.995809i $$0.470848\pi$$
$$270$$ 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 0.976231 0.216731i $$-0.0695395\pi$$
−0.675810 + 0.737075i $$0.736206\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7.50000 + 12.9904i 0.447412 + 0.774941i 0.998217 0.0596933i $$-0.0190123\pi$$
−0.550804 + 0.834634i $$0.685679\pi$$
$$282$$ 0 0
$$283$$ −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i $$-0.871266\pi$$
0.800439 + 0.599414i $$0.204600\pi$$
$$284$$ 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 $$-0.977701\pi$$
0.559393 + 0.828903i $$0.311034\pi$$
$$294$$ 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 0.294384 + 0.955687i $$0.404886\pi$$
−0.974841 + 0.222900i $$0.928448\pi$$
$$312$$ 0 0
$$313$$ 12.5000 + 21.6506i 0.706542 + 1.22377i 0.966132 + 0.258047i $$0.0830791\pi$$
−0.259590 + 0.965719i $$0.583588\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7.50000 12.9904i −0.421242 0.729612i 0.574819 0.818280i $$-0.305072\pi$$
−0.996061 + 0.0886679i $$0.971739\pi$$
$$318$$ 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 0.963135 + 0.269019i $$0.0866994\pi$$
−0.248590 + 0.968609i $$0.579967\pi$$
$$332$$ 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 −0.697100 0.716974i $$-0.745527\pi$$
0.969468 + 0.245220i $$0.0788601\pi$$
$$338$$ 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 $$-0.993839\pi$$
0.516667 + 0.856186i $$0.327172\pi$$
$$348$$ 0 0
$$349$$ −1.00000 1.73205i −0.0535288 0.0927146i 0.838019 0.545640i $$-0.183714\pi$$
−0.891548 + 0.452926i $$0.850380\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i $$-0.872363\pi$$
0.122308 0.992492i $$-0.460970\pi$$
$$354$$ 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 $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 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 0.893873 + 0.448320i $$0.147978\pi$$
−0.0586798 + 0.998277i $$0.518689\pi$$
$$368$$ 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 −0.988363 0.152115i $$-0.951392\pi$$
0.625917 + 0.779890i $$0.284725\pi$$
$$374$$ 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 −0.173005 0.984921i $$-0.555348\pi$$
0.939469 0.342634i $$-0.111319\pi$$
$$384$$ 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 0.942578 + 0.333987i $$0.108394\pi$$
−0.182047 + 0.983290i $$0.558272\pi$$
$$390$$ 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 $$-0.711137\pi$$
0.990257 + 0.139253i $$0.0444700\pi$$
$$402$$ 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 0.00141047 + 0.999999i $$0.499551\pi$$
−0.866730 + 0.498778i $$0.833782\pi$$
$$410$$ 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 $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$420$$ 0 0
$$421$$ −14.5000 25.1147i −0.706687 1.22402i −0.966079 0.258245i $$-0.916856\pi$$
0.259393 0.965772i $$-0.416478\pi$$
$$422$$ 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 $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 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 0.945552 0.325471i $$-0.105523\pi$$
−0.754642 + 0.656136i $$0.772190\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$444$$ 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 $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 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 −0.906702 0.421771i $$-0.861409\pi$$
0.0880870 0.996113i $$-0.471925\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 3.00000 + 5.19615i 0.139724 + 0.242009i 0.927392 0.374091i $$-0.122045\pi$$
−0.787668 + 0.616100i $$0.788712\pi$$
$$462$$ 0 0
$$463$$ −2.00000 + 3.46410i −0.0929479 + 0.160990i −0.908750 0.417340i $$-0.862962\pi$$
0.815802 + 0.578331i $$0.196296\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 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 $$-0.0317693\pi$$
−0.583803 + 0.811895i $$0.698436\pi$$
$$480$$ 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 $$-0.790105\pi$$
0.925746 + 0.378147i $$0.123439\pi$$
$$492$$ 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 −0.999962 0.00872186i $$-0.997224\pi$$
0.507534 + 0.861632i $$0.330557\pi$$
$$500$$ 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 $$-0.790881\pi$$
0.924821 + 0.380402i $$0.124214\pi$$
$$510$$ 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 $$-0.728243\pi$$
−0.657162 + 0.753749i $$0.728243\pi$$
$$522$$ 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 −0.876517 0.481371i $$-0.840139\pi$$
0.0213785 0.999771i $$-0.493195\pi$$
$$548$$ 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 $$-0.397061\pi$$
0.317785 + 0.948163i $$0.397061\pi$$
$$558$$ 0 0
$$559$$ 50.0000 2.11477
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$564$$ 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 $$-0.146637\pi$$
−0.832870 + 0.553469i $$0.813304\pi$$
$$570$$ 0 0
$$571$$ 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i $$-0.460975\pi$$
0.798379 0.602155i $$-0.205691\pi$$
$$572$$ 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 −0.989647 0.143521i $$-0.954158\pi$$
0.370531 0.928820i $$-0.379176\pi$$
$$588$$ 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 $$-0.795576\pi$$
−0.800769 + 0.598973i $$0.795576\pi$$
$$594$$ 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 $$-0.912172\pi$$
0.717021 + 0.697051i $$0.245505\pi$$
$$600$$ 0 0
$$601$$ 0.500000 + 0.866025i 0.0203954 + 0.0353259i 0.876043 0.482233i $$-0.160174\pi$$
−0.855648 + 0.517559i $$0.826841\pi$$
$$602$$ 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 −0.949476 0.313841i $$-0.898384\pi$$
0.746532 + 0.665350i $$0.231718\pi$$
$$608$$ 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 $$-0.735700\pi$$
0.976575 + 0.215177i $$0.0690329\pi$$
$$618$$ 0 0
$$619$$ −20.0000 34.6410i −0.803868 1.39234i −0.917053 0.398766i $$-0.869439\pi$$
0.113185 0.993574i $$-0.463895\pi$$
$$620$$ 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 $$-0.302789\pi$$
−0.995400 + 0.0958109i $$0.969456\pi$$
$$642$$ 0 0
$$643$$ −20.0000 + 34.6410i −0.788723 + 1.36611i 0.138027 + 0.990429i $$0.455924\pi$$
−0.926750 + 0.375680i $$0.877409\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −18.0000 −0.707653 −0.353827 0.935311i $$-0.615120\pi$$
−0.353827 + 0.935311i $$0.615120\pi$$
$$648$$ 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 −0.407628 0.913148i $$-0.633644\pi$$
0.994623 0.103558i $$-0.0330227\pi$$
$$654$$ 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 $$-0.129383\pi$$
−0.801660 + 0.597781i $$0.796049\pi$$
$$660$$ 0 0
$$661$$ −14.5000 + 25.1147i −0.563985 + 0.976850i 0.433159 + 0.901318i $$0.357399\pi$$
−0.997143 + 0.0755324i $$0.975934\pi$$
$$662$$ 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 0.875501 0.483216i $$-0.160531\pi$$
−0.856228 + 0.516599i $$0.827198\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i $$-0.867705\pi$$
0.107772 0.994176i $$-0.465628\pi$$
$$678$$ 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 0.755110 0.655598i $$-0.227583\pi$$
−0.945319 + 0.326146i $$0.894250\pi$$
$$692$$ 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 $$-0.236475\pi$$
0.736505 + 0.676432i $$0.236475\pi$$
$$702$$ 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 0.987421 0.158114i $$-0.0505412\pi$$
−0.630641 + 0.776075i $$0.717208\pi$$
$$710$$ 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 $$-0.608954\pi$$
−0.335643 + 0.941989i $$0.608954\pi$$
$$720$$ 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 0.758285 0.651923i $$-0.226038\pi$$
−0.943725 + 0.330732i $$0.892704\pi$$
$$728$$ 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 −0.965854 0.259087i $$-0.916578\pi$$
0.707303 + 0.706910i $$0.249912\pi$$
$$734$$ 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 0.320166 + 0.947361i $$0.396261\pi$$
−0.980522 + 0.196409i $$0.937072\pi$$
$$744$$ 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 −0.942715 0.333599i $$-0.891737\pi$$
0.760263 + 0.649616i $$0.225070\pi$$
$$752$$ 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 $$-0.885491\pi$$
0.772863 + 0.634573i $$0.218824\pi$$
$$762$$ 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 −0.995397 0.0958377i $$-0.969447\pi$$
0.580696 + 0.814120i $$0.302780\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −45.0000 −1.61854 −0.809269 0.587439i $$-0.800136\pi$$
−0.809269 + 0.587439i $$0.800136\pi$$
$$774$$ 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 −0.298521 0.954403i $$-0.596493\pi$$
0.975798 0.218675i $$-0.0701734\pi$$
$$788$$ 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 −0.124576 0.992210i $$-0.539757\pi$$
0.921567 0.388219i $$-0.126909\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$