# Properties

 Label 3240.2.q.n.1081.1 Level $3240$ Weight $2$ Character 3240.1081 Analytic conductor $25.872$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3240 = 2^{3} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3240.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.8715302549$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 360) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1081.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 3240.1081 Dual form 3240.2.q.n.2161.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(-2.00000 + 3.46410i) q^{13} -2.00000 q^{17} +4.00000 q^{19} +(-4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.00000 + 8.66025i) q^{29} +(-2.00000 + 3.46410i) q^{31} -2.00000 q^{35} +(4.00000 + 6.92820i) q^{43} +(-4.00000 - 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{53} -2.00000 q^{55} +(7.00000 - 12.1244i) q^{59} +(7.00000 + 12.1244i) q^{61} +(2.00000 + 3.46410i) q^{65} +(2.00000 - 3.46410i) q^{67} +12.0000 q^{71} +6.00000 q^{73} +(-2.00000 + 3.46410i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-2.00000 - 3.46410i) q^{83} +(-1.00000 + 1.73205i) q^{85} -12.0000 q^{89} +8.00000 q^{91} +(2.00000 - 3.46410i) q^{95} +(7.00000 + 12.1244i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{5} - 2q^{7} + O(q^{10})$$ $$2q + q^{5} - 2q^{7} - 2q^{11} - 4q^{13} - 4q^{17} + 8q^{19} - 8q^{23} - q^{25} + 10q^{29} - 4q^{31} - 4q^{35} + 8q^{43} - 8q^{47} + 3q^{49} + 12q^{53} - 4q^{55} + 14q^{59} + 14q^{61} + 4q^{65} + 4q^{67} + 24q^{71} + 12q^{73} - 4q^{77} + 12q^{79} - 4q^{83} - 2q^{85} - 24q^{89} + 16q^{91} + 4q^{95} + 14q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$$.

 $$n$$ $$1297$$ $$1621$$ $$2431$$ $$3161$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0 0
$$7$$ −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i $$-0.290043\pi$$
−0.990766 + 0.135583i $$0.956709\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i $$-0.264158\pi$$
−0.976478 + 0.215615i $$0.930824\pi$$
$$12$$ 0 0
$$13$$ −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i $$0.353834\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 −0.485071 −0.242536 0.970143i $$-0.577979\pi$$
−0.242536 + 0.970143i $$0.577979\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i $$0.480655\pi$$
−0.894795 + 0.446476i $$0.852679\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 5.00000 + 8.66025i 0.928477 + 1.60817i 0.785872 + 0.618389i $$0.212214\pi$$
0.142605 + 0.989780i $$0.454452\pi$$
$$30$$ 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
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$42$$ 0 0
$$43$$ 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i $$0.0421616\pi$$
−0.381246 + 0.924473i $$0.624505\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i $$-0.968365\pi$$
0.411606 0.911362i $$-0.364968\pi$$
$$48$$ 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
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i $$-0.468396\pi$$
0.812198 0.583382i $$-0.198271\pi$$
$$60$$ 0 0
$$61$$ 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i $$0.187058\pi$$
0.0640184 + 0.997949i $$0.479608\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 2.00000 + 3.46410i 0.248069 + 0.429669i
$$66$$ 0 0
$$67$$ 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i $$-0.754762\pi$$
0.961946 + 0.273241i $$0.0880957\pi$$
$$68$$ 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
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −2.00000 + 3.46410i −0.227921 + 0.394771i
$$78$$ 0 0
$$79$$ 6.00000 + 10.3923i 0.675053 + 1.16923i 0.976453 + 0.215728i $$0.0692125\pi$$
−0.301401 + 0.953498i $$0.597454\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −2.00000 3.46410i −0.219529 0.380235i 0.735135 0.677920i $$-0.237119\pi$$
−0.954664 + 0.297686i $$0.903785\pi$$
$$84$$ 0 0
$$85$$ −1.00000 + 1.73205i −0.108465 + 0.187867i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −12.0000 −1.27200 −0.635999 0.771690i $$-0.719412\pi$$
−0.635999 + 0.771690i $$0.719412\pi$$
$$90$$ 0 0
$$91$$ 8.00000 0.838628
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 2.00000 3.46410i 0.205196 0.355409i
$$96$$ 0 0
$$97$$ 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i $$0.0849741\pi$$
−0.253837 + 0.967247i $$0.581693\pi$$
$$98$$ 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
$$103$$ 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i $$-0.591062\pi$$
0.971925 0.235291i $$-0.0756043\pi$$
$$104$$ 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
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −9.00000 + 15.5885i −0.846649 + 1.46644i 0.0375328 + 0.999295i $$0.488050\pi$$
−0.884182 + 0.467143i $$0.845283\pi$$
$$114$$ 0 0
$$115$$ 4.00000 + 6.92820i 0.373002 + 0.646058i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 2.00000 + 3.46410i 0.183340 + 0.317554i
$$120$$ 0 0
$$121$$ 3.50000 6.06218i 0.318182 0.551107i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 18.0000 1.59724 0.798621 0.601834i $$-0.205563\pi$$
0.798621 + 0.601834i $$0.205563\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i $$-0.545310\pi$$
0.928199 0.372084i $$-0.121357\pi$$
$$132$$ 0 0
$$133$$ −4.00000 6.92820i −0.346844 0.600751i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i $$-0.193895\pi$$
−0.905577 + 0.424182i $$0.860562\pi$$
$$138$$ 0 0
$$139$$ −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i $$0.336619\pi$$
−0.999947 + 0.0103230i $$0.996714\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 8.00000 0.668994
$$144$$ 0 0
$$145$$ 10.0000 0.830455
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i $$-0.967671\pi$$
0.585231 + 0.810867i $$0.301004\pi$$
$$150$$ 0 0
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 2.00000 + 3.46410i 0.160644 + 0.278243i
$$156$$ 0 0
$$157$$ −2.00000 + 3.46410i −0.159617 + 0.276465i −0.934731 0.355357i $$-0.884359\pi$$
0.775113 + 0.631822i $$0.217693\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 16.0000 1.26098
$$162$$ 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
$$167$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$168$$ 0 0
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i $$-0.142443\pi$$
−0.825505 + 0.564396i $$0.809109\pi$$
$$174$$ 0 0
$$175$$ −1.00000 + 1.73205i −0.0755929 + 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −14.0000 −1.04641 −0.523205 0.852207i $$-0.675264\pi$$
−0.523205 + 0.852207i $$0.675264\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 2.00000 + 3.46410i 0.146254 + 0.253320i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i $$-0.212893\pi$$
−0.929267 + 0.369410i $$0.879560\pi$$
$$192$$ 0 0
$$193$$ −11.0000 + 19.0526i −0.791797 + 1.37143i 0.133056 + 0.991109i $$0.457521\pi$$
−0.924853 + 0.380325i $$0.875812\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 10.0000 17.3205i 0.701862 1.21566i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −4.00000 6.92820i −0.276686 0.479234i
$$210$$ 0 0
$$211$$ −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i $$0.408366\pi$$
−0.972346 + 0.233544i $$0.924968\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 8.00000 0.545595
$$216$$ 0 0
$$217$$ 8.00000 0.543075
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 4.00000 6.92820i 0.269069 0.466041i
$$222$$ 0 0
$$223$$ 11.0000 + 19.0526i 0.736614 + 1.27585i 0.954011 + 0.299770i $$0.0969101\pi$$
−0.217397 + 0.976083i $$0.569757\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$228$$ 0 0
$$229$$ 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i $$-0.812283\pi$$
0.897173 + 0.441679i $$0.145617\pi$$
$$230$$ 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
$$239$$ −6.00000 + 10.3923i −0.388108 + 0.672222i −0.992195 0.124696i $$-0.960204\pi$$
0.604087 + 0.796918i $$0.293538\pi$$
$$240$$ 0 0
$$241$$ 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i $$-0.0622852\pi$$
−0.658838 + 0.752285i $$0.728952\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −1.50000 2.59808i −0.0958315 0.165985i
$$246$$ 0 0
$$247$$ −8.00000 + 13.8564i −0.509028 + 0.881662i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 6.00000 0.378717 0.189358 0.981908i $$-0.439359\pi$$
0.189358 + 0.981908i $$0.439359\pi$$
$$252$$ 0 0
$$253$$ 16.0000 1.00591
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i $$0.356405\pi$$
−0.997374 + 0.0724199i $$0.976928\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$264$$ 0 0
$$265$$ 3.00000 5.19615i 0.184289 0.319197i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −2.00000 −0.121942 −0.0609711 0.998140i $$-0.519420\pi$$
−0.0609711 + 0.998140i $$0.519420\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.00000 + 1.73205i −0.0603023 + 0.104447i
$$276$$ 0 0
$$277$$ 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i $$-0.00705893\pi$$
−0.519081 + 0.854725i $$0.673726\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 14.0000 + 24.2487i 0.835170 + 1.44656i 0.893892 + 0.448282i $$0.147964\pi$$
−0.0587220 + 0.998274i $$0.518703\pi$$
$$282$$ 0 0
$$283$$ 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i $$-0.795400\pi$$
0.919327 + 0.393494i $$0.128734\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −13.0000 −0.764706
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −1.00000 + 1.73205i −0.0584206 + 0.101187i −0.893757 0.448552i $$-0.851940\pi$$
0.835336 + 0.549740i $$0.185273\pi$$
$$294$$ 0 0
$$295$$ −7.00000 12.1244i −0.407556 0.705907i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −16.0000 27.7128i −0.925304 1.60267i
$$300$$ 0 0
$$301$$ 8.00000 13.8564i 0.461112 0.798670i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 14.0000 0.801638
$$306$$ 0 0
$$307$$ −32.0000 −1.82634 −0.913168 0.407583i $$-0.866372\pi$$
−0.913168 + 0.407583i $$0.866372\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 10.0000 17.3205i 0.567048 0.982156i −0.429808 0.902920i $$-0.641419\pi$$
0.996856 0.0792356i $$-0.0252479\pi$$
$$312$$ 0 0
$$313$$ 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i $$-0.0754642\pi$$
−0.689412 + 0.724370i $$0.742131\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i $$0.152241\pi$$
−0.0453045 + 0.998973i $$0.514426\pi$$
$$318$$ 0 0
$$319$$ 10.0000 17.3205i 0.559893 0.969762i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8.00000 −0.445132
$$324$$ 0 0
$$325$$ 4.00000 0.221880
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −8.00000 + 13.8564i −0.441054 + 0.763928i
$$330$$ 0 0
$$331$$ 6.00000 + 10.3923i 0.329790 + 0.571213i 0.982470 0.186421i $$-0.0596888\pi$$
−0.652680 + 0.757634i $$0.726355\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −2.00000 3.46410i −0.109272 0.189264i
$$336$$ 0 0
$$337$$ 1.00000 1.73205i 0.0544735 0.0943508i −0.837503 0.546433i $$-0.815985\pi$$
0.891976 + 0.452082i $$0.149319\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 8.00000 0.433224
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i $$-0.974630\pi$$
0.567363 + 0.823468i $$0.307964\pi$$
$$348$$ 0 0
$$349$$ 3.00000 + 5.19615i 0.160586 + 0.278144i 0.935079 0.354439i $$-0.115328\pi$$
−0.774493 + 0.632583i $$0.781995\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 13.0000 + 22.5167i 0.691920 + 1.19844i 0.971208 + 0.238233i $$0.0765683\pi$$
−0.279288 + 0.960207i $$0.590098\pi$$
$$354$$ 0 0
$$355$$ 6.00000 10.3923i 0.318447 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
$$361$$ −3.00000 −0.157895
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.00000 5.19615i 0.157027 0.271979i
$$366$$ 0 0
$$367$$ −13.0000 22.5167i −0.678594 1.17536i −0.975404 0.220423i $$-0.929256\pi$$
0.296810 0.954937i $$-0.404077\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −6.00000 10.3923i −0.311504 0.539542i
$$372$$ 0 0
$$373$$ 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i $$-0.660092\pi$$
0.999787 0.0206542i $$-0.00657489\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −40.0000 −2.06010
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i $$-0.623227\pi$$
0.990702 0.136047i $$-0.0434398\pi$$
$$384$$ 0 0
$$385$$ 2.00000 + 3.46410i 0.101929 + 0.176547i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i $$-0.317499\pi$$
−0.998763 + 0.0497253i $$0.984165\pi$$
$$390$$ 0 0
$$391$$ 8.00000 13.8564i 0.404577 0.700749i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 12.0000 0.603786
$$396$$ 0 0
$$397$$ −8.00000 −0.401508 −0.200754 0.979642i $$-0.564339\pi$$
−0.200754 + 0.979642i $$0.564339\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i $$-0.736472\pi$$
0.976050 + 0.217545i $$0.0698049\pi$$
$$402$$ 0 0
$$403$$ −8.00000 13.8564i −0.398508 0.690237i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i $$-0.912855\pi$$
0.715523 + 0.698589i $$0.246188\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −28.0000 −1.37779
$$414$$ 0 0
$$415$$ −4.00000 −0.196352
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −15.0000 + 25.9808i −0.732798 + 1.26924i 0.222885 + 0.974845i $$0.428453\pi$$
−0.955683 + 0.294398i $$0.904881\pi$$
$$420$$ 0 0
$$421$$ −15.0000 25.9808i −0.731055 1.26622i −0.956433 0.291953i $$-0.905695\pi$$
0.225377 0.974272i $$-0.427639\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.00000 + 1.73205i 0.0485071 + 0.0840168i
$$426$$ 0 0
$$427$$ 14.0000 24.2487i 0.677507 1.17348i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −16.0000 + 27.7128i −0.765384 + 1.32568i
$$438$$ 0 0
$$439$$ 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i $$0.109922\pi$$
−0.177325 + 0.984152i $$0.556744\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i $$-0.973557\pi$$
0.426414 0.904528i $$-0.359777\pi$$
$$444$$ 0 0
$$445$$ −6.00000 + 10.3923i −0.284427 + 0.492642i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 4.00000 6.92820i 0.187523 0.324799i
$$456$$ 0 0
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i $$0.0795353\pi$$
−0.270326 + 0.962769i $$0.587131\pi$$
$$462$$ 0 0
$$463$$ −15.0000 + 25.9808i −0.697109 + 1.20743i 0.272355 + 0.962197i $$0.412197\pi$$
−0.969465 + 0.245232i $$0.921136\pi$$
$$464$$ 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
$$469$$ −8.00000 −0.369406
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 8.00000 13.8564i 0.367840 0.637118i
$$474$$ 0 0
$$475$$ −2.00000 3.46410i −0.0917663 0.158944i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.00000 + 3.46410i 0.0913823 + 0.158279i 0.908093 0.418769i $$-0.137538\pi$$
−0.816711 + 0.577047i $$0.804205\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 14.0000 0.635707
$$486$$ 0 0
$$487$$ 22.0000 0.996915 0.498458 0.866914i $$-0.333900\pi$$
0.498458 + 0.866914i $$0.333900\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 9.00000 15.5885i 0.406164 0.703497i −0.588292 0.808649i $$-0.700199\pi$$
0.994456 + 0.105151i $$0.0335327\pi$$
$$492$$ 0 0
$$493$$ −10.0000 17.3205i −0.450377 0.780076i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −12.0000 20.7846i −0.538274 0.932317i
$$498$$ 0 0
$$499$$ −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i $$-0.981076\pi$$
0.550572 + 0.834788i $$0.314410\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −7.00000 + 12.1244i −0.310270 + 0.537403i −0.978421 0.206623i $$-0.933753\pi$$
0.668151 + 0.744026i $$0.267086\pi$$
$$510$$ 0 0
$$511$$ −6.00000 10.3923i −0.265424 0.459728i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −7.00000 12.1244i −0.308457 0.534263i
$$516$$ 0 0
$$517$$ −8.00000 + 13.8564i −0.351840 + 0.609404i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 20.0000 0.876216 0.438108 0.898922i $$-0.355649\pi$$
0.438108 + 0.898922i $$0.355649\pi$$
$$522$$ 0 0
$$523$$ 28.0000 1.22435 0.612177 0.790721i $$-0.290294\pi$$
0.612177 + 0.790721i $$0.290294\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 4.00000 6.92820i 0.174243 0.301797i
$$528$$ 0 0
$$529$$ −20.5000 35.5070i −0.891304 1.54378i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ −6.00000 + 10.3923i −0.259403 + 0.449299i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −6.00000 −0.258438
$$540$$ 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
$$545$$ 1.00000 1.73205i 0.0428353 0.0741929i
$$546$$ 0 0
$$547$$ −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i $$-0.221375\pi$$
−0.938779 + 0.344519i $$0.888042\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 20.0000 + 34.6410i 0.852029 + 1.47576i
$$552$$ 0 0
$$553$$ 12.0000 20.7846i 0.510292 0.883852i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −26.0000 −1.10166 −0.550828 0.834619i $$-0.685688\pi$$
−0.550828 + 0.834619i $$0.685688\pi$$
$$558$$ 0 0
$$559$$ −32.0000 −1.35346
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −4.00000 + 6.92820i −0.168580 + 0.291989i −0.937921 0.346850i $$-0.887251\pi$$
0.769341 + 0.638838i $$0.220585\pi$$
$$564$$ 0 0
$$565$$ 9.00000 + 15.5885i 0.378633 + 0.655811i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 10.0000 + 17.3205i 0.419222 + 0.726113i 0.995861 0.0908852i $$-0.0289696\pi$$
−0.576640 + 0.816999i $$0.695636\pi$$
$$570$$ 0 0
$$571$$ −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i $$-0.860006\pi$$
0.821138 + 0.570730i $$0.193340\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 8.00000 0.333623
$$576$$ 0 0
$$577$$ 26.0000 1.08239 0.541197 0.840896i $$-0.317971\pi$$
0.541197 + 0.840896i $$0.317971\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −4.00000 + 6.92820i −0.165948 + 0.287430i
$$582$$ 0 0
$$583$$ −6.00000 10.3923i −0.248495 0.430405i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −18.0000 31.1769i −0.742940 1.28681i −0.951151 0.308725i $$-0.900098\pi$$
0.208212 0.978084i $$-0.433236\pi$$
$$588$$ 0 0
$$589$$ −8.00000 + 13.8564i −0.329634 + 0.570943i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 42.0000 1.72473 0.862367 0.506284i $$-0.168981\pi$$
0.862367 + 0.506284i $$0.168981\pi$$
$$594$$ 0 0
$$595$$ 4.00000 0.163984
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i $$-0.670218\pi$$
0.999938 + 0.0111569i $$0.00355143\pi$$
$$600$$ 0 0
$$601$$ −11.0000 19.0526i −0.448699 0.777170i 0.549602 0.835426i $$-0.314779\pi$$
−0.998302 + 0.0582563i $$0.981446\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −3.50000 6.06218i −0.142295 0.246463i
$$606$$ 0 0
$$607$$ −3.00000 + 5.19615i −0.121766 + 0.210905i −0.920464 0.390827i $$-0.872189\pi$$
0.798698 + 0.601732i $$0.205522\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 32.0000 1.29458
$$612$$ 0 0
$$613$$ −48.0000 −1.93870 −0.969351 0.245680i $$-0.920989\pi$$
−0.969351 + 0.245680i $$0.920989\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −3.00000 + 5.19615i −0.120775 + 0.209189i −0.920074 0.391745i $$-0.871871\pi$$
0.799298 + 0.600935i $$0.205205\pi$$
$$618$$ 0 0
$$619$$ −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i $$-0.821334\pi$$
−0.0376891 0.999290i $$-0.512000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 12.0000 + 20.7846i 0.480770 + 0.832718i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −20.0000 −0.796187 −0.398094 0.917345i $$-0.630328\pi$$
−0.398094 + 0.917345i $$0.630328\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 9.00000 15.5885i 0.357154 0.618609i
$$636$$ 0 0
$$637$$ 6.00000 + 10.3923i 0.237729 + 0.411758i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i $$-0.323847\pi$$
−0.999556 + 0.0297987i $$0.990513\pi$$
$$642$$ 0 0
$$643$$ −6.00000 + 10.3923i −0.236617 + 0.409832i −0.959741 0.280885i $$-0.909372\pi$$
0.723124 + 0.690718i $$0.242705\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −24.0000 −0.943537 −0.471769 0.881722i $$-0.656384\pi$$
−0.471769 + 0.881722i $$0.656384\pi$$
$$648$$ 0 0
$$649$$ −28.0000 −1.09910
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 7.00000 12.1244i 0.273931 0.474463i −0.695934 0.718106i $$-0.745009\pi$$
0.969865 + 0.243643i $$0.0783426\pi$$
$$654$$ 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 0.801660 0.597781i $$-0.203951\pi$$
−0.918523 + 0.395367i $$0.870617\pi$$
$$660$$ 0 0
$$661$$ −9.00000 + 15.5885i −0.350059 + 0.606321i −0.986260 0.165203i $$-0.947172\pi$$
0.636200 + 0.771524i $$0.280505\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ −80.0000 −3.09761
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 14.0000 24.2487i 0.540464 0.936111i
$$672$$ 0 0
$$673$$ −15.0000 25.9808i −0.578208 1.00148i −0.995685 0.0927975i $$-0.970419\pi$$
0.417477 0.908687i $$-0.362914\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −13.0000 22.5167i −0.499631 0.865386i 0.500369 0.865812i $$-0.333198\pi$$
−1.00000 0.000426509i $$0.999864\pi$$
$$678$$ 0 0
$$679$$ 14.0000 24.2487i 0.537271 0.930580i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −12.0000 + 20.7846i −0.457164 + 0.791831i
$$690$$ 0 0
$$691$$ 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i $$0.0121127\pi$$
−0.466691 + 0.884420i $$0.654554\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.00000 + 10.3923i 0.227593 + 0.394203i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 22.0000 0.830929 0.415464 0.909610i $$-0.363619\pi$$
0.415464 + 0.909610i $$0.363619\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −6.00000 + 10.3923i −0.225653 + 0.390843i
$$708$$ 0 0
$$709$$ −7.00000 12.1244i −0.262891 0.455340i 0.704118 0.710083i $$-0.251342\pi$$
−0.967009 + 0.254743i $$0.918009\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −16.0000 27.7128i −0.599205 1.03785i
$$714$$ 0 0
$$715$$ 4.00000 6.92820i 0.149592 0.259100i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −40.0000 −1.49175 −0.745874 0.666087i $$-0.767968\pi$$
−0.745874 + 0.666087i $$0.767968\pi$$
$$720$$ 0 0
$$721$$ −28.0000 −1.04277
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 5.00000 8.66025i 0.185695 0.321634i
$$726$$ 0 0
$$727$$ −19.0000 32.9090i −0.704671 1.22053i −0.966810 0.255496i $$-0.917761\pi$$
0.262139 0.965030i $$-0.415572\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −8.00000 13.8564i −0.295891 0.512498i
$$732$$ 0 0
$$733$$ 12.0000 20.7846i 0.443230 0.767697i −0.554697 0.832052i $$-0.687166\pi$$
0.997927 + 0.0643554i $$0.0204991\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −8.00000 −0.294684
$$738$$ 0 0
$$739$$ 12.0000 0.441427 0.220714 0.975339i $$-0.429161\pi$$
0.220714 + 0.975339i $$0.429161\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −12.0000 + 20.7846i −0.440237 + 0.762513i −0.997707 0.0676840i $$-0.978439\pi$$
0.557470 + 0.830197i $$0.311772\pi$$
$$744$$ 0 0
$$745$$ 5.00000 + 8.66025i 0.183186 + 0.317287i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 12.0000 + 20.7846i 0.438470 + 0.759453i
$$750$$ 0 0
$$751$$ 18.0000 31.1769i 0.656829 1.13766i −0.324603 0.945851i $$-0.605231\pi$$
0.981432 0.191811i $$-0.0614361\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ 32.0000 1.16306 0.581530 0.813525i $$-0.302454\pi$$
0.581530 + 0.813525i $$0.302454\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 18.0000 31.1769i 0.652499 1.13016i −0.330015 0.943976i $$-0.607054\pi$$
0.982514 0.186187i $$-0.0596129\pi$$
$$762$$ 0 0
$$763$$ −2.00000 3.46410i −0.0724049 0.125409i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 28.0000 + 48.4974i 1.01102 + 1.75114i
$$768$$ 0 0
$$769$$ 25.0000 43.3013i 0.901523 1.56148i 0.0760054 0.997107i $$-0.475783\pi$$
0.825518 0.564376i $$-0.190883\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 42.0000 1.51064 0.755318 0.655359i $$-0.227483\pi$$
0.755318 + 0.655359i $$0.227483\pi$$
$$774$$ 0 0
$$775$$ 4.00000 0.143684
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −12.0000 20.7846i −0.429394 0.743732i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 2.00000 + 3.46410i 0.0713831 + 0.123639i
$$786$$ 0 0
$$787$$ 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i $$-0.667017\pi$$
0.999999 + 0.00110111i $$0.000350496\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 36.0000 1.28001
$$792$$ 0 0
$$793$$ −56.0000 −1.98862
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −15.0000 + 25.9808i −0.531327 + 0.920286i 0.468004 + 0.883726i $$0.344973\pi$$
−0.999331 + 0.0365596i $$0.988360\pi$$
$$798$$ 0 0
$$799$$ 8.00000 + 13.8564i 0.283020 + 0.490204i
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ −6.00000 10.3923i −0.211735 0.366736i
$$804$$ 0 0
$$805$$