# Properties

 Label 546.2.c.e.337.1 Level $546$ Weight $2$ Character 546.337 Analytic conductor $4.360$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{17})$$ Defining polynomial: $$x^{4} + 9x^{2} + 16$$ x^4 + 9*x^2 + 16 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 337.1 Root $$-2.56155i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.337 Dual form 546.2.c.e.337.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} -3.56155 q^{10} -5.56155i q^{11} +1.00000 q^{12} +(3.56155 + 0.561553i) q^{13} +1.00000 q^{14} +3.56155i q^{15} +1.00000 q^{16} -6.68466 q^{17} -1.00000i q^{18} +1.56155i q^{19} +3.56155i q^{20} -1.00000i q^{21} -5.56155 q^{22} -6.68466 q^{23} -1.00000i q^{24} -7.68466 q^{25} +(0.561553 - 3.56155i) q^{26} -1.00000 q^{27} -1.00000i q^{28} +1.56155 q^{29} +3.56155 q^{30} +6.24621i q^{31} -1.00000i q^{32} +5.56155i q^{33} +6.68466i q^{34} +3.56155 q^{35} -1.00000 q^{36} -10.6847i q^{37} +1.56155 q^{38} +(-3.56155 - 0.561553i) q^{39} +3.56155 q^{40} -4.00000i q^{41} -1.00000 q^{42} -6.43845 q^{43} +5.56155i q^{44} -3.56155i q^{45} +6.68466i q^{46} +10.2462i q^{47} -1.00000 q^{48} -1.00000 q^{49} +7.68466i q^{50} +6.68466 q^{51} +(-3.56155 - 0.561553i) q^{52} +4.87689 q^{53} +1.00000i q^{54} -19.8078 q^{55} -1.00000 q^{56} -1.56155i q^{57} -1.56155i q^{58} -4.24621i q^{59} -3.56155i q^{60} -1.56155 q^{61} +6.24621 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(2.00000 - 12.6847i) q^{65} +5.56155 q^{66} +1.12311i q^{67} +6.68466 q^{68} +6.68466 q^{69} -3.56155i q^{70} -9.36932i q^{71} +1.00000i q^{72} -11.5616i q^{73} -10.6847 q^{74} +7.68466 q^{75} -1.56155i q^{76} +5.56155 q^{77} +(-0.561553 + 3.56155i) q^{78} +16.0000 q^{79} -3.56155i q^{80} +1.00000 q^{81} -4.00000 q^{82} +2.00000i q^{83} +1.00000i q^{84} +23.8078i q^{85} +6.43845i q^{86} -1.56155 q^{87} +5.56155 q^{88} +8.00000i q^{89} -3.56155 q^{90} +(-0.561553 + 3.56155i) q^{91} +6.68466 q^{92} -6.24621i q^{93} +10.2462 q^{94} +5.56155 q^{95} +1.00000i q^{96} -10.0000i q^{97} +1.00000i q^{98} -5.56155i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 $$4 q - 4 q^{3} - 4 q^{4} + 4 q^{9} - 6 q^{10} + 4 q^{12} + 6 q^{13} + 4 q^{14} + 4 q^{16} - 2 q^{17} - 14 q^{22} - 2 q^{23} - 6 q^{25} - 6 q^{26} - 4 q^{27} - 2 q^{29} + 6 q^{30} + 6 q^{35} - 4 q^{36} - 2 q^{38} - 6 q^{39} + 6 q^{40} - 4 q^{42} - 34 q^{43} - 4 q^{48} - 4 q^{49} + 2 q^{51} - 6 q^{52} + 36 q^{53} - 38 q^{55} - 4 q^{56} + 2 q^{61} - 8 q^{62} - 4 q^{64} + 8 q^{65} + 14 q^{66} + 2 q^{68} + 2 q^{69} - 18 q^{74} + 6 q^{75} + 14 q^{77} + 6 q^{78} + 64 q^{79} + 4 q^{81} - 16 q^{82} + 2 q^{87} + 14 q^{88} - 6 q^{90} + 6 q^{91} + 2 q^{92} + 8 q^{94} + 14 q^{95}+O(q^{100})$$ 4 * q - 4 * q^3 - 4 * q^4 + 4 * q^9 - 6 * q^10 + 4 * q^12 + 6 * q^13 + 4 * q^14 + 4 * q^16 - 2 * q^17 - 14 * q^22 - 2 * q^23 - 6 * q^25 - 6 * q^26 - 4 * q^27 - 2 * q^29 + 6 * q^30 + 6 * q^35 - 4 * q^36 - 2 * q^38 - 6 * q^39 + 6 * q^40 - 4 * q^42 - 34 * q^43 - 4 * q^48 - 4 * q^49 + 2 * q^51 - 6 * q^52 + 36 * q^53 - 38 * q^55 - 4 * q^56 + 2 * q^61 - 8 * q^62 - 4 * q^64 + 8 * q^65 + 14 * q^66 + 2 * q^68 + 2 * q^69 - 18 * q^74 + 6 * q^75 + 14 * q^77 + 6 * q^78 + 64 * q^79 + 4 * q^81 - 16 * q^82 + 2 * q^87 + 14 * q^88 - 6 * q^90 + 6 * q^91 + 2 * q^92 + 8 * q^94 + 14 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ −1.00000 −0.577350
$$4$$ −1.00000 −0.500000
$$5$$ 3.56155i 1.59277i −0.604787 0.796387i $$-0.706742\pi$$
0.604787 0.796387i $$-0.293258\pi$$
$$6$$ 1.00000i 0.408248i
$$7$$ 1.00000i 0.377964i
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000 0.333333
$$10$$ −3.56155 −1.12626
$$11$$ 5.56155i 1.67687i −0.545001 0.838436i $$-0.683471\pi$$
0.545001 0.838436i $$-0.316529\pi$$
$$12$$ 1.00000 0.288675
$$13$$ 3.56155 + 0.561553i 0.987797 + 0.155747i
$$14$$ 1.00000 0.267261
$$15$$ 3.56155i 0.919589i
$$16$$ 1.00000 0.250000
$$17$$ −6.68466 −1.62127 −0.810634 0.585553i $$-0.800877\pi$$
−0.810634 + 0.585553i $$0.800877\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.56155i 0.358245i 0.983827 + 0.179122i $$0.0573258\pi$$
−0.983827 + 0.179122i $$0.942674\pi$$
$$20$$ 3.56155i 0.796387i
$$21$$ 1.00000i 0.218218i
$$22$$ −5.56155 −1.18573
$$23$$ −6.68466 −1.39385 −0.696924 0.717145i $$-0.745448\pi$$
−0.696924 + 0.717145i $$0.745448\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ −7.68466 −1.53693
$$26$$ 0.561553 3.56155i 0.110130 0.698478i
$$27$$ −1.00000 −0.192450
$$28$$ 1.00000i 0.188982i
$$29$$ 1.56155 0.289973 0.144987 0.989434i $$-0.453686\pi$$
0.144987 + 0.989434i $$0.453686\pi$$
$$30$$ 3.56155 0.650248
$$31$$ 6.24621i 1.12185i 0.827866 + 0.560926i $$0.189555\pi$$
−0.827866 + 0.560926i $$0.810445\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 5.56155i 0.968142i
$$34$$ 6.68466i 1.14641i
$$35$$ 3.56155 0.602012
$$36$$ −1.00000 −0.166667
$$37$$ 10.6847i 1.75655i −0.478159 0.878274i $$-0.658696\pi$$
0.478159 0.878274i $$-0.341304\pi$$
$$38$$ 1.56155 0.253317
$$39$$ −3.56155 0.561553i −0.570305 0.0899204i
$$40$$ 3.56155 0.563131
$$41$$ 4.00000i 0.624695i −0.949968 0.312348i $$-0.898885\pi$$
0.949968 0.312348i $$-0.101115\pi$$
$$42$$ −1.00000 −0.154303
$$43$$ −6.43845 −0.981854 −0.490927 0.871201i $$-0.663342\pi$$
−0.490927 + 0.871201i $$0.663342\pi$$
$$44$$ 5.56155i 0.838436i
$$45$$ 3.56155i 0.530925i
$$46$$ 6.68466i 0.985599i
$$47$$ 10.2462i 1.49456i 0.664507 + 0.747282i $$0.268641\pi$$
−0.664507 + 0.747282i $$0.731359\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −1.00000 −0.142857
$$50$$ 7.68466i 1.08677i
$$51$$ 6.68466 0.936039
$$52$$ −3.56155 0.561553i −0.493899 0.0778734i
$$53$$ 4.87689 0.669893 0.334946 0.942237i $$-0.391282\pi$$
0.334946 + 0.942237i $$0.391282\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ −19.8078 −2.67088
$$56$$ −1.00000 −0.133631
$$57$$ 1.56155i 0.206833i
$$58$$ 1.56155i 0.205042i
$$59$$ 4.24621i 0.552810i −0.961041 0.276405i $$-0.910857\pi$$
0.961041 0.276405i $$-0.0891431\pi$$
$$60$$ 3.56155i 0.459794i
$$61$$ −1.56155 −0.199936 −0.0999682 0.994991i $$-0.531874\pi$$
−0.0999682 + 0.994991i $$0.531874\pi$$
$$62$$ 6.24621 0.793270
$$63$$ 1.00000i 0.125988i
$$64$$ −1.00000 −0.125000
$$65$$ 2.00000 12.6847i 0.248069 1.57334i
$$66$$ 5.56155 0.684580
$$67$$ 1.12311i 0.137209i 0.997644 + 0.0686046i $$0.0218547\pi$$
−0.997644 + 0.0686046i $$0.978145\pi$$
$$68$$ 6.68466 0.810634
$$69$$ 6.68466 0.804738
$$70$$ 3.56155i 0.425687i
$$71$$ 9.36932i 1.11193i −0.831205 0.555967i $$-0.812348\pi$$
0.831205 0.555967i $$-0.187652\pi$$
$$72$$ 1.00000i 0.117851i
$$73$$ 11.5616i 1.35318i −0.736361 0.676589i $$-0.763458\pi$$
0.736361 0.676589i $$-0.236542\pi$$
$$74$$ −10.6847 −1.24207
$$75$$ 7.68466 0.887348
$$76$$ 1.56155i 0.179122i
$$77$$ 5.56155 0.633798
$$78$$ −0.561553 + 3.56155i −0.0635833 + 0.403266i
$$79$$ 16.0000 1.80014 0.900070 0.435745i $$-0.143515\pi$$
0.900070 + 0.435745i $$0.143515\pi$$
$$80$$ 3.56155i 0.398194i
$$81$$ 1.00000 0.111111
$$82$$ −4.00000 −0.441726
$$83$$ 2.00000i 0.219529i 0.993958 + 0.109764i $$0.0350096\pi$$
−0.993958 + 0.109764i $$0.964990\pi$$
$$84$$ 1.00000i 0.109109i
$$85$$ 23.8078i 2.58231i
$$86$$ 6.43845i 0.694276i
$$87$$ −1.56155 −0.167416
$$88$$ 5.56155 0.592864
$$89$$ 8.00000i 0.847998i 0.905663 + 0.423999i $$0.139374\pi$$
−0.905663 + 0.423999i $$0.860626\pi$$
$$90$$ −3.56155 −0.375421
$$91$$ −0.561553 + 3.56155i −0.0588667 + 0.373352i
$$92$$ 6.68466 0.696924
$$93$$ 6.24621i 0.647702i
$$94$$ 10.2462 1.05682
$$95$$ 5.56155 0.570603
$$96$$ 1.00000i 0.102062i
$$97$$ 10.0000i 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 1.00000i 0.101015i
$$99$$ 5.56155i 0.558957i
$$100$$ 7.68466 0.768466
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ 6.68466i 0.661880i
$$103$$ 1.80776 0.178124 0.0890621 0.996026i $$-0.471613\pi$$
0.0890621 + 0.996026i $$0.471613\pi$$
$$104$$ −0.561553 + 3.56155i −0.0550648 + 0.349239i
$$105$$ −3.56155 −0.347572
$$106$$ 4.87689i 0.473686i
$$107$$ −4.87689 −0.471467 −0.235734 0.971818i $$-0.575749\pi$$
−0.235734 + 0.971818i $$0.575749\pi$$
$$108$$ 1.00000 0.0962250
$$109$$ 12.9309i 1.23855i −0.785173 0.619276i $$-0.787426\pi$$
0.785173 0.619276i $$-0.212574\pi$$
$$110$$ 19.8078i 1.88860i
$$111$$ 10.6847i 1.01414i
$$112$$ 1.00000i 0.0944911i
$$113$$ 20.2462 1.90460 0.952302 0.305158i $$-0.0987093\pi$$
0.952302 + 0.305158i $$0.0987093\pi$$
$$114$$ −1.56155 −0.146253
$$115$$ 23.8078i 2.22009i
$$116$$ −1.56155 −0.144987
$$117$$ 3.56155 + 0.561553i 0.329266 + 0.0519156i
$$118$$ −4.24621 −0.390895
$$119$$ 6.68466i 0.612782i
$$120$$ −3.56155 −0.325124
$$121$$ −19.9309 −1.81190
$$122$$ 1.56155i 0.141376i
$$123$$ 4.00000i 0.360668i
$$124$$ 6.24621i 0.560926i
$$125$$ 9.56155i 0.855211i
$$126$$ 1.00000 0.0890871
$$127$$ 10.2462 0.909204 0.454602 0.890695i $$-0.349781\pi$$
0.454602 + 0.890695i $$0.349781\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 6.43845 0.566874
$$130$$ −12.6847 2.00000i −1.11252 0.175412i
$$131$$ −1.56155 −0.136434 −0.0682168 0.997671i $$-0.521731\pi$$
−0.0682168 + 0.997671i $$0.521731\pi$$
$$132$$ 5.56155i 0.484071i
$$133$$ −1.56155 −0.135404
$$134$$ 1.12311 0.0970215
$$135$$ 3.56155i 0.306530i
$$136$$ 6.68466i 0.573205i
$$137$$ 6.68466i 0.571109i −0.958362 0.285554i $$-0.907822\pi$$
0.958362 0.285554i $$-0.0921777\pi$$
$$138$$ 6.68466i 0.569036i
$$139$$ 10.2462 0.869072 0.434536 0.900654i $$-0.356912\pi$$
0.434536 + 0.900654i $$0.356912\pi$$
$$140$$ −3.56155 −0.301006
$$141$$ 10.2462i 0.862887i
$$142$$ −9.36932 −0.786256
$$143$$ 3.12311 19.8078i 0.261167 1.65641i
$$144$$ 1.00000 0.0833333
$$145$$ 5.56155i 0.461862i
$$146$$ −11.5616 −0.956841
$$147$$ 1.00000 0.0824786
$$148$$ 10.6847i 0.878274i
$$149$$ 10.0000i 0.819232i −0.912258 0.409616i $$-0.865663\pi$$
0.912258 0.409616i $$-0.134337\pi$$
$$150$$ 7.68466i 0.627450i
$$151$$ 16.6847i 1.35778i −0.734241 0.678889i $$-0.762462\pi$$
0.734241 0.678889i $$-0.237538\pi$$
$$152$$ −1.56155 −0.126659
$$153$$ −6.68466 −0.540423
$$154$$ 5.56155i 0.448163i
$$155$$ 22.2462 1.78686
$$156$$ 3.56155 + 0.561553i 0.285152 + 0.0449602i
$$157$$ −11.8078 −0.942362 −0.471181 0.882037i $$-0.656172\pi$$
−0.471181 + 0.882037i $$0.656172\pi$$
$$158$$ 16.0000i 1.27289i
$$159$$ −4.87689 −0.386763
$$160$$ −3.56155 −0.281565
$$161$$ 6.68466i 0.526825i
$$162$$ 1.00000i 0.0785674i
$$163$$ 9.12311i 0.714577i −0.933994 0.357288i $$-0.883701\pi$$
0.933994 0.357288i $$-0.116299\pi$$
$$164$$ 4.00000i 0.312348i
$$165$$ 19.8078 1.54203
$$166$$ 2.00000 0.155230
$$167$$ 11.8078i 0.913712i 0.889541 + 0.456856i $$0.151025\pi$$
−0.889541 + 0.456856i $$0.848975\pi$$
$$168$$ 1.00000 0.0771517
$$169$$ 12.3693 + 4.00000i 0.951486 + 0.307692i
$$170$$ 23.8078 1.82597
$$171$$ 1.56155i 0.119415i
$$172$$ 6.43845 0.490927
$$173$$ −3.75379 −0.285395 −0.142698 0.989766i $$-0.545578\pi$$
−0.142698 + 0.989766i $$0.545578\pi$$
$$174$$ 1.56155i 0.118381i
$$175$$ 7.68466i 0.580906i
$$176$$ 5.56155i 0.419218i
$$177$$ 4.24621i 0.319165i
$$178$$ 8.00000 0.599625
$$179$$ 11.1231 0.831380 0.415690 0.909506i $$-0.363540\pi$$
0.415690 + 0.909506i $$0.363540\pi$$
$$180$$ 3.56155i 0.265462i
$$181$$ −13.3693 −0.993733 −0.496867 0.867827i $$-0.665516\pi$$
−0.496867 + 0.867827i $$0.665516\pi$$
$$182$$ 3.56155 + 0.561553i 0.264000 + 0.0416251i
$$183$$ 1.56155 0.115433
$$184$$ 6.68466i 0.492800i
$$185$$ −38.0540 −2.79778
$$186$$ −6.24621 −0.457994
$$187$$ 37.1771i 2.71866i
$$188$$ 10.2462i 0.747282i
$$189$$ 1.00000i 0.0727393i
$$190$$ 5.56155i 0.403477i
$$191$$ −24.0540 −1.74048 −0.870242 0.492624i $$-0.836038\pi$$
−0.870242 + 0.492624i $$0.836038\pi$$
$$192$$ 1.00000 0.0721688
$$193$$ 12.0000i 0.863779i 0.901927 + 0.431889i $$0.142153\pi$$
−0.901927 + 0.431889i $$0.857847\pi$$
$$194$$ −10.0000 −0.717958
$$195$$ −2.00000 + 12.6847i −0.143223 + 0.908367i
$$196$$ 1.00000 0.0714286
$$197$$ 6.00000i 0.427482i 0.976890 + 0.213741i $$0.0685649\pi$$
−0.976890 + 0.213741i $$0.931435\pi$$
$$198$$ −5.56155 −0.395242
$$199$$ 4.93087 0.349540 0.174770 0.984609i $$-0.444082\pi$$
0.174770 + 0.984609i $$0.444082\pi$$
$$200$$ 7.68466i 0.543387i
$$201$$ 1.12311i 0.0792178i
$$202$$ 6.00000i 0.422159i
$$203$$ 1.56155i 0.109600i
$$204$$ −6.68466 −0.468020
$$205$$ −14.2462 −0.994999
$$206$$ 1.80776i 0.125953i
$$207$$ −6.68466 −0.464616
$$208$$ 3.56155 + 0.561553i 0.246949 + 0.0389367i
$$209$$ 8.68466 0.600730
$$210$$ 3.56155i 0.245770i
$$211$$ 7.80776 0.537509 0.268754 0.963209i $$-0.413388\pi$$
0.268754 + 0.963209i $$0.413388\pi$$
$$212$$ −4.87689 −0.334946
$$213$$ 9.36932i 0.641975i
$$214$$ 4.87689i 0.333378i
$$215$$ 22.9309i 1.56387i
$$216$$ 1.00000i 0.0680414i
$$217$$ −6.24621 −0.424020
$$218$$ −12.9309 −0.875789
$$219$$ 11.5616i 0.781257i
$$220$$ 19.8078 1.33544
$$221$$ −23.8078 3.75379i −1.60148 0.252507i
$$222$$ 10.6847 0.717107
$$223$$ 1.75379i 0.117442i 0.998274 + 0.0587212i $$0.0187023\pi$$
−0.998274 + 0.0587212i $$0.981298\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ −7.68466 −0.512311
$$226$$ 20.2462i 1.34676i
$$227$$ 17.6155i 1.16918i 0.811328 + 0.584592i $$0.198745\pi$$
−0.811328 + 0.584592i $$0.801255\pi$$
$$228$$ 1.56155i 0.103416i
$$229$$ 2.00000i 0.132164i −0.997814 0.0660819i $$-0.978950\pi$$
0.997814 0.0660819i $$-0.0210498\pi$$
$$230$$ 23.8078 1.56984
$$231$$ −5.56155 −0.365923
$$232$$ 1.56155i 0.102521i
$$233$$ 2.00000 0.131024 0.0655122 0.997852i $$-0.479132\pi$$
0.0655122 + 0.997852i $$0.479132\pi$$
$$234$$ 0.561553 3.56155i 0.0367099 0.232826i
$$235$$ 36.4924 2.38050
$$236$$ 4.24621i 0.276405i
$$237$$ −16.0000 −1.03931
$$238$$ −6.68466 −0.433302
$$239$$ 14.2462i 0.921511i −0.887527 0.460755i $$-0.847579\pi$$
0.887527 0.460755i $$-0.152421\pi$$
$$240$$ 3.56155i 0.229897i
$$241$$ 6.00000i 0.386494i −0.981150 0.193247i $$-0.938098\pi$$
0.981150 0.193247i $$-0.0619019\pi$$
$$242$$ 19.9309i 1.28120i
$$243$$ −1.00000 −0.0641500
$$244$$ 1.56155 0.0999682
$$245$$ 3.56155i 0.227539i
$$246$$ 4.00000 0.255031
$$247$$ −0.876894 + 5.56155i −0.0557955 + 0.353873i
$$248$$ −6.24621 −0.396635
$$249$$ 2.00000i 0.126745i
$$250$$ 9.56155 0.604726
$$251$$ 22.0540 1.39203 0.696017 0.718025i $$-0.254954\pi$$
0.696017 + 0.718025i $$0.254954\pi$$
$$252$$ 1.00000i 0.0629941i
$$253$$ 37.1771i 2.33730i
$$254$$ 10.2462i 0.642904i
$$255$$ 23.8078i 1.49090i
$$256$$ 1.00000 0.0625000
$$257$$ −26.0000 −1.62184 −0.810918 0.585160i $$-0.801032\pi$$
−0.810918 + 0.585160i $$0.801032\pi$$
$$258$$ 6.43845i 0.400840i
$$259$$ 10.6847 0.663912
$$260$$ −2.00000 + 12.6847i −0.124035 + 0.786669i
$$261$$ 1.56155 0.0966577
$$262$$ 1.56155i 0.0964731i
$$263$$ −23.3693 −1.44101 −0.720507 0.693448i $$-0.756091\pi$$
−0.720507 + 0.693448i $$0.756091\pi$$
$$264$$ −5.56155 −0.342290
$$265$$ 17.3693i 1.06699i
$$266$$ 1.56155i 0.0957449i
$$267$$ 8.00000i 0.489592i
$$268$$ 1.12311i 0.0686046i
$$269$$ 31.3693 1.91262 0.956311 0.292353i $$-0.0944382\pi$$
0.956311 + 0.292353i $$0.0944382\pi$$
$$270$$ 3.56155 0.216749
$$271$$ 8.00000i 0.485965i 0.970031 + 0.242983i $$0.0781258\pi$$
−0.970031 + 0.242983i $$0.921874\pi$$
$$272$$ −6.68466 −0.405317
$$273$$ 0.561553 3.56155i 0.0339867 0.215555i
$$274$$ −6.68466 −0.403835
$$275$$ 42.7386i 2.57724i
$$276$$ −6.68466 −0.402369
$$277$$ −10.8769 −0.653529 −0.326765 0.945106i $$-0.605958\pi$$
−0.326765 + 0.945106i $$0.605958\pi$$
$$278$$ 10.2462i 0.614527i
$$279$$ 6.24621i 0.373951i
$$280$$ 3.56155i 0.212843i
$$281$$ 6.00000i 0.357930i −0.983855 0.178965i $$-0.942725\pi$$
0.983855 0.178965i $$-0.0572749\pi$$
$$282$$ −10.2462 −0.610153
$$283$$ −4.87689 −0.289901 −0.144951 0.989439i $$-0.546302\pi$$
−0.144951 + 0.989439i $$0.546302\pi$$
$$284$$ 9.36932i 0.555967i
$$285$$ −5.56155 −0.329438
$$286$$ −19.8078 3.12311i −1.17126 0.184673i
$$287$$ 4.00000 0.236113
$$288$$ 1.00000i 0.0589256i
$$289$$ 27.6847 1.62851
$$290$$ −5.56155 −0.326586
$$291$$ 10.0000i 0.586210i
$$292$$ 11.5616i 0.676589i
$$293$$ 7.75379i 0.452981i 0.974013 + 0.226491i $$0.0727253\pi$$
−0.974013 + 0.226491i $$0.927275\pi$$
$$294$$ 1.00000i 0.0583212i
$$295$$ −15.1231 −0.880501
$$296$$ 10.6847 0.621033
$$297$$ 5.56155i 0.322714i
$$298$$ −10.0000 −0.579284
$$299$$ −23.8078 3.75379i −1.37684 0.217087i
$$300$$ −7.68466 −0.443674
$$301$$ 6.43845i 0.371106i
$$302$$ −16.6847 −0.960094
$$303$$ −6.00000 −0.344691
$$304$$ 1.56155i 0.0895612i
$$305$$ 5.56155i 0.318454i
$$306$$ 6.68466i 0.382136i
$$307$$ 26.2462i 1.49795i −0.662598 0.748975i $$-0.730546\pi$$
0.662598 0.748975i $$-0.269454\pi$$
$$308$$ −5.56155 −0.316899
$$309$$ −1.80776 −0.102840
$$310$$ 22.2462i 1.26350i
$$311$$ −0.492423 −0.0279227 −0.0139614 0.999903i $$-0.504444\pi$$
−0.0139614 + 0.999903i $$0.504444\pi$$
$$312$$ 0.561553 3.56155i 0.0317917 0.201633i
$$313$$ 32.2462 1.82266 0.911332 0.411673i $$-0.135055\pi$$
0.911332 + 0.411673i $$0.135055\pi$$
$$314$$ 11.8078i 0.666351i
$$315$$ 3.56155 0.200671
$$316$$ −16.0000 −0.900070
$$317$$ 3.36932i 0.189240i 0.995513 + 0.0946198i $$0.0301636\pi$$
−0.995513 + 0.0946198i $$0.969836\pi$$
$$318$$ 4.87689i 0.273483i
$$319$$ 8.68466i 0.486248i
$$320$$ 3.56155i 0.199097i
$$321$$ 4.87689 0.272202
$$322$$ −6.68466 −0.372521
$$323$$ 10.4384i 0.580811i
$$324$$ −1.00000 −0.0555556
$$325$$ −27.3693 4.31534i −1.51818 0.239372i
$$326$$ −9.12311 −0.505282
$$327$$ 12.9309i 0.715079i
$$328$$ 4.00000 0.220863
$$329$$ −10.2462 −0.564892
$$330$$ 19.8078i 1.09038i
$$331$$ 1.12311i 0.0617315i 0.999524 + 0.0308657i $$0.00982643\pi$$
−0.999524 + 0.0308657i $$0.990174\pi$$
$$332$$ 2.00000i 0.109764i
$$333$$ 10.6847i 0.585516i
$$334$$ 11.8078 0.646092
$$335$$ 4.00000 0.218543
$$336$$ 1.00000i 0.0545545i
$$337$$ 20.0540 1.09241 0.546205 0.837652i $$-0.316072\pi$$
0.546205 + 0.837652i $$0.316072\pi$$
$$338$$ 4.00000 12.3693i 0.217571 0.672802i
$$339$$ −20.2462 −1.09962
$$340$$ 23.8078i 1.29116i
$$341$$ 34.7386 1.88120
$$342$$ 1.56155 0.0844391
$$343$$ 1.00000i 0.0539949i
$$344$$ 6.43845i 0.347138i
$$345$$ 23.8078i 1.28177i
$$346$$ 3.75379i 0.201805i
$$347$$ −24.4924 −1.31482 −0.657411 0.753532i $$-0.728348\pi$$
−0.657411 + 0.753532i $$0.728348\pi$$
$$348$$ 1.56155 0.0837080
$$349$$ 3.36932i 0.180355i −0.995926 0.0901777i $$-0.971256\pi$$
0.995926 0.0901777i $$-0.0287435\pi$$
$$350$$ −7.68466 −0.410762
$$351$$ −3.56155 0.561553i −0.190102 0.0299735i
$$352$$ −5.56155 −0.296432
$$353$$ 18.2462i 0.971148i 0.874196 + 0.485574i $$0.161389\pi$$
−0.874196 + 0.485574i $$0.838611\pi$$
$$354$$ 4.24621 0.225684
$$355$$ −33.3693 −1.77106
$$356$$ 8.00000i 0.423999i
$$357$$ 6.68466i 0.353790i
$$358$$ 11.1231i 0.587874i
$$359$$ 23.6155i 1.24638i −0.782071 0.623190i $$-0.785836\pi$$
0.782071 0.623190i $$-0.214164\pi$$
$$360$$ 3.56155 0.187710
$$361$$ 16.5616 0.871661
$$362$$ 13.3693i 0.702676i
$$363$$ 19.9309 1.04610
$$364$$ 0.561553 3.56155i 0.0294334 0.186676i
$$365$$ −41.1771 −2.15531
$$366$$ 1.56155i 0.0816237i
$$367$$ 0.630683 0.0329214 0.0164607 0.999865i $$-0.494760\pi$$
0.0164607 + 0.999865i $$0.494760\pi$$
$$368$$ −6.68466 −0.348462
$$369$$ 4.00000i 0.208232i
$$370$$ 38.0540i 1.97833i
$$371$$ 4.87689i 0.253196i
$$372$$ 6.24621i 0.323851i
$$373$$ −6.00000 −0.310668 −0.155334 0.987862i $$-0.549645\pi$$
−0.155334 + 0.987862i $$0.549645\pi$$
$$374$$ 37.1771 1.92238
$$375$$ 9.56155i 0.493756i
$$376$$ −10.2462 −0.528408
$$377$$ 5.56155 + 0.876894i 0.286435 + 0.0451624i
$$378$$ −1.00000 −0.0514344
$$379$$ 18.8769i 0.969641i 0.874614 + 0.484820i $$0.161115\pi$$
−0.874614 + 0.484820i $$0.838885\pi$$
$$380$$ −5.56155 −0.285302
$$381$$ −10.2462 −0.524929
$$382$$ 24.0540i 1.23071i
$$383$$ 17.5616i 0.897353i −0.893694 0.448677i $$-0.851895\pi$$
0.893694 0.448677i $$-0.148105\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 19.8078i 1.00950i
$$386$$ 12.0000 0.610784
$$387$$ −6.43845 −0.327285
$$388$$ 10.0000i 0.507673i
$$389$$ 27.1231 1.37520 0.687598 0.726092i $$-0.258665\pi$$
0.687598 + 0.726092i $$0.258665\pi$$
$$390$$ 12.6847 + 2.00000i 0.642313 + 0.101274i
$$391$$ 44.6847 2.25980
$$392$$ 1.00000i 0.0505076i
$$393$$ 1.56155 0.0787699
$$394$$ 6.00000 0.302276
$$395$$ 56.9848i 2.86722i
$$396$$ 5.56155i 0.279479i
$$397$$ 15.3693i 0.771364i −0.922632 0.385682i $$-0.873966\pi$$
0.922632 0.385682i $$-0.126034\pi$$
$$398$$ 4.93087i 0.247162i
$$399$$ 1.56155 0.0781754
$$400$$ −7.68466 −0.384233
$$401$$ 30.9848i 1.54731i 0.633608 + 0.773655i $$0.281573\pi$$
−0.633608 + 0.773655i $$0.718427\pi$$
$$402$$ −1.12311 −0.0560154
$$403$$ −3.50758 + 22.2462i −0.174725 + 1.10816i
$$404$$ −6.00000 −0.298511
$$405$$ 3.56155i 0.176975i
$$406$$ 1.56155 0.0774986
$$407$$ −59.4233 −2.94550
$$408$$ 6.68466i 0.330940i
$$409$$ 13.8078i 0.682750i −0.939927 0.341375i $$-0.889107\pi$$
0.939927 0.341375i $$-0.110893\pi$$
$$410$$ 14.2462i 0.703570i
$$411$$ 6.68466i 0.329730i
$$412$$ −1.80776 −0.0890621
$$413$$ 4.24621 0.208942
$$414$$ 6.68466i 0.328533i
$$415$$ 7.12311 0.349660
$$416$$ 0.561553 3.56155i 0.0275324 0.174619i
$$417$$ −10.2462 −0.501759
$$418$$ 8.68466i 0.424781i
$$419$$ −20.6847 −1.01051 −0.505256 0.862970i $$-0.668602\pi$$
−0.505256 + 0.862970i $$0.668602\pi$$
$$420$$ 3.56155 0.173786
$$421$$ 10.0000i 0.487370i 0.969854 + 0.243685i $$0.0783563\pi$$
−0.969854 + 0.243685i $$0.921644\pi$$
$$422$$ 7.80776i 0.380076i
$$423$$ 10.2462i 0.498188i
$$424$$ 4.87689i 0.236843i
$$425$$ 51.3693 2.49178
$$426$$ 9.36932 0.453945
$$427$$ 1.56155i 0.0755688i
$$428$$ 4.87689 0.235734
$$429$$ −3.12311 + 19.8078i −0.150785 + 0.956328i
$$430$$ 22.9309 1.10582
$$431$$ 29.8617i 1.43839i −0.694809 0.719195i $$-0.744511\pi$$
0.694809 0.719195i $$-0.255489\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 23.3693 1.12306 0.561529 0.827457i $$-0.310213\pi$$
0.561529 + 0.827457i $$0.310213\pi$$
$$434$$ 6.24621i 0.299828i
$$435$$ 5.56155i 0.266656i
$$436$$ 12.9309i 0.619276i
$$437$$ 10.4384i 0.499339i
$$438$$ 11.5616 0.552432
$$439$$ −8.93087 −0.426247 −0.213124 0.977025i $$-0.568364\pi$$
−0.213124 + 0.977025i $$0.568364\pi$$
$$440$$ 19.8078i 0.944298i
$$441$$ −1.00000 −0.0476190
$$442$$ −3.75379 + 23.8078i −0.178550 + 1.13242i
$$443$$ 6.63068 0.315033 0.157517 0.987516i $$-0.449651\pi$$
0.157517 + 0.987516i $$0.449651\pi$$
$$444$$ 10.6847i 0.507071i
$$445$$ 28.4924 1.35067
$$446$$ 1.75379 0.0830443
$$447$$ 10.0000i 0.472984i
$$448$$ 1.00000i 0.0472456i
$$449$$ 9.31534i 0.439618i 0.975543 + 0.219809i $$0.0705434\pi$$
−0.975543 + 0.219809i $$0.929457\pi$$
$$450$$ 7.68466i 0.362258i
$$451$$ −22.2462 −1.04753
$$452$$ −20.2462 −0.952302
$$453$$ 16.6847i 0.783914i
$$454$$ 17.6155 0.826738
$$455$$ 12.6847 + 2.00000i 0.594666 + 0.0937614i
$$456$$ 1.56155 0.0731264
$$457$$ 16.0000i 0.748448i 0.927338 + 0.374224i $$0.122091\pi$$
−0.927338 + 0.374224i $$0.877909\pi$$
$$458$$ −2.00000 −0.0934539
$$459$$ 6.68466 0.312013
$$460$$ 23.8078i 1.11004i
$$461$$ 36.9309i 1.72004i −0.510259 0.860021i $$-0.670450\pi$$
0.510259 0.860021i $$-0.329550\pi$$
$$462$$ 5.56155i 0.258747i
$$463$$ 30.5464i 1.41961i 0.704397 + 0.709806i $$0.251217\pi$$
−0.704397 + 0.709806i $$0.748783\pi$$
$$464$$ 1.56155 0.0724933
$$465$$ −22.2462 −1.03164
$$466$$ 2.00000i 0.0926482i
$$467$$ 1.56155 0.0722600 0.0361300 0.999347i $$-0.488497\pi$$
0.0361300 + 0.999347i $$0.488497\pi$$
$$468$$ −3.56155 0.561553i −0.164633 0.0259578i
$$469$$ −1.12311 −0.0518602
$$470$$ 36.4924i 1.68327i
$$471$$ 11.8078 0.544073
$$472$$ 4.24621 0.195448
$$473$$ 35.8078i 1.64644i
$$474$$ 16.0000i 0.734904i
$$475$$ 12.0000i 0.550598i
$$476$$ 6.68466i 0.306391i
$$477$$ 4.87689 0.223298
$$478$$ −14.2462 −0.651607
$$479$$ 12.3002i 0.562010i −0.959706 0.281005i $$-0.909332\pi$$
0.959706 0.281005i $$-0.0906677\pi$$
$$480$$ 3.56155 0.162562
$$481$$ 6.00000 38.0540i 0.273576 1.73511i
$$482$$ −6.00000 −0.273293
$$483$$ 6.68466i 0.304162i
$$484$$ 19.9309 0.905949
$$485$$ −35.6155 −1.61722
$$486$$ 1.00000i 0.0453609i
$$487$$ 13.7538i 0.623244i 0.950206 + 0.311622i $$0.100872\pi$$
−0.950206 + 0.311622i $$0.899128\pi$$
$$488$$ 1.56155i 0.0706882i
$$489$$ 9.12311i 0.412561i
$$490$$ 3.56155 0.160895
$$491$$ −10.2462 −0.462405 −0.231203 0.972906i $$-0.574266\pi$$
−0.231203 + 0.972906i $$0.574266\pi$$
$$492$$ 4.00000i 0.180334i
$$493$$ −10.4384 −0.470124
$$494$$ 5.56155 + 0.876894i 0.250226 + 0.0394533i
$$495$$ −19.8078 −0.890293
$$496$$ 6.24621i 0.280463i
$$497$$ 9.36932 0.420271
$$498$$ −2.00000 −0.0896221
$$499$$ 1.50758i 0.0674884i 0.999431 + 0.0337442i $$0.0107432\pi$$
−0.999431 + 0.0337442i $$0.989257\pi$$
$$500$$ 9.56155i 0.427606i
$$501$$ 11.8078i 0.527532i
$$502$$ 22.0540i 0.984317i
$$503$$ 35.6155 1.58802 0.794009 0.607906i $$-0.207990\pi$$
0.794009 + 0.607906i $$0.207990\pi$$
$$504$$ −1.00000 −0.0445435
$$505$$ 21.3693i 0.950922i
$$506$$ 37.1771 1.65272
$$507$$ −12.3693 4.00000i −0.549341 0.177646i
$$508$$ −10.2462 −0.454602
$$509$$ 2.68466i 0.118995i −0.998228 0.0594977i $$-0.981050\pi$$
0.998228 0.0594977i $$-0.0189499\pi$$
$$510$$ −23.8078 −1.05423
$$511$$ 11.5616 0.511453
$$512$$ 1.00000i 0.0441942i
$$513$$ 1.56155i 0.0689442i
$$514$$ 26.0000i 1.14681i
$$515$$ 6.43845i 0.283712i
$$516$$ −6.43845 −0.283437
$$517$$ 56.9848 2.50619
$$518$$ 10.6847i 0.469457i
$$519$$ 3.75379 0.164773
$$520$$ 12.6847 + 2.00000i 0.556259 + 0.0877058i
$$521$$ 8.05398 0.352851 0.176426 0.984314i $$-0.443547\pi$$
0.176426 + 0.984314i $$0.443547\pi$$
$$522$$ 1.56155i 0.0683473i
$$523$$ −8.49242 −0.371348 −0.185674 0.982611i $$-0.559447\pi$$
−0.185674 + 0.982611i $$0.559447\pi$$
$$524$$ 1.56155 0.0682168
$$525$$ 7.68466i 0.335386i
$$526$$ 23.3693i 1.01895i
$$527$$ 41.7538i 1.81882i
$$528$$ 5.56155i 0.242036i
$$529$$ 21.6847 0.942811
$$530$$ −17.3693 −0.754475
$$531$$ 4.24621i 0.184270i
$$532$$ 1.56155 0.0677019
$$533$$ 2.24621 14.2462i 0.0972942 0.617072i
$$534$$ −8.00000 −0.346194
$$535$$ 17.3693i 0.750941i
$$536$$ −1.12311 −0.0485108
$$537$$ −11.1231 −0.479997
$$538$$ 31.3693i 1.35243i
$$539$$ 5.56155i 0.239553i
$$540$$ 3.56155i 0.153265i
$$541$$ 6.19224i 0.266225i 0.991101 + 0.133113i $$0.0424972\pi$$
−0.991101 + 0.133113i $$0.957503\pi$$
$$542$$ 8.00000 0.343629
$$543$$ 13.3693 0.573732
$$544$$ 6.68466i 0.286602i
$$545$$ −46.0540 −1.97274
$$546$$ −3.56155 0.561553i −0.152420 0.0240322i
$$547$$ 28.9848 1.23930 0.619651 0.784877i $$-0.287274\pi$$
0.619651 + 0.784877i $$0.287274\pi$$
$$548$$ 6.68466i 0.285554i
$$549$$ −1.56155 −0.0666455
$$550$$ 42.7386 1.82238
$$551$$ 2.43845i 0.103881i
$$552$$ 6.68466i 0.284518i
$$553$$ 16.0000i 0.680389i
$$554$$ 10.8769i 0.462115i
$$555$$ 38.0540 1.61530
$$556$$ −10.2462 −0.434536
$$557$$ 16.2462i 0.688374i −0.938901 0.344187i $$-0.888155\pi$$
0.938901 0.344187i $$-0.111845\pi$$
$$558$$ 6.24621 0.264423
$$559$$ −22.9309 3.61553i −0.969872 0.152921i
$$560$$ 3.56155 0.150503
$$561$$ 37.1771i 1.56962i
$$562$$ −6.00000 −0.253095
$$563$$ 38.0540 1.60378 0.801892 0.597469i $$-0.203827\pi$$
0.801892 + 0.597469i $$0.203827\pi$$
$$564$$ 10.2462i 0.431443i
$$565$$ 72.1080i 3.03360i
$$566$$ 4.87689i 0.204991i
$$567$$ 1.00000i 0.0419961i
$$568$$ 9.36932 0.393128
$$569$$ −18.0000 −0.754599 −0.377300 0.926091i $$-0.623147\pi$$
−0.377300 + 0.926091i $$0.623147\pi$$
$$570$$ 5.56155i 0.232948i
$$571$$ −18.2462 −0.763580 −0.381790 0.924249i $$-0.624692\pi$$
−0.381790 + 0.924249i $$0.624692\pi$$
$$572$$ −3.12311 + 19.8078i −0.130584 + 0.828204i
$$573$$ 24.0540 1.00487
$$574$$ 4.00000i 0.166957i
$$575$$ 51.3693 2.14225
$$576$$ −1.00000 −0.0416667
$$577$$ 7.75379i 0.322794i −0.986890 0.161397i $$-0.948400\pi$$
0.986890 0.161397i $$-0.0516000\pi$$
$$578$$ 27.6847i 1.15153i
$$579$$ 12.0000i 0.498703i
$$580$$ 5.56155i 0.230931i
$$581$$ −2.00000 −0.0829740
$$582$$ 10.0000 0.414513
$$583$$ 27.1231i 1.12332i
$$584$$ 11.5616 0.478420
$$585$$ 2.00000 12.6847i 0.0826898 0.524446i
$$586$$ 7.75379 0.320306
$$587$$ 37.1231i 1.53223i 0.642701 + 0.766117i $$0.277814\pi$$
−0.642701 + 0.766117i $$0.722186\pi$$
$$588$$ −1.00000 −0.0412393
$$589$$ −9.75379 −0.401898
$$590$$ 15.1231i 0.622608i
$$591$$ 6.00000i 0.246807i
$$592$$ 10.6847i 0.439137i
$$593$$ 28.0000i 1.14982i 0.818216 + 0.574911i $$0.194963\pi$$
−0.818216 + 0.574911i $$0.805037\pi$$
$$594$$ 5.56155 0.228193
$$595$$ −23.8078 −0.976023
$$596$$ 10.0000i 0.409616i
$$597$$ −4.93087 −0.201807
$$598$$ −3.75379 + 23.8078i −0.153504 + 0.973572i
$$599$$ 30.3002 1.23803 0.619016 0.785378i $$-0.287532\pi$$
0.619016 + 0.785378i $$0.287532\pi$$
$$600$$ 7.68466i 0.313725i
$$601$$ −31.8617 −1.29967 −0.649834 0.760076i $$-0.725161\pi$$
−0.649834 + 0.760076i $$0.725161\pi$$
$$602$$ −6.43845 −0.262412
$$603$$ 1.12311i 0.0457364i
$$604$$ 16.6847i 0.678889i
$$605$$ 70.9848i 2.88594i
$$606$$ 6.00000i 0.243733i
$$607$$ −28.5464 −1.15866 −0.579331 0.815092i $$-0.696686\pi$$
−0.579331 + 0.815092i $$0.696686\pi$$
$$608$$ 1.56155 0.0633293
$$609$$ 1.56155i 0.0632773i
$$610$$ 5.56155 0.225181
$$611$$ −5.75379 + 36.4924i −0.232773 + 1.47633i
$$612$$ 6.68466 0.270211
$$613$$ 1.80776i 0.0730149i 0.999333 + 0.0365075i $$0.0116233\pi$$
−0.999333 + 0.0365075i $$0.988377\pi$$
$$614$$ −26.2462 −1.05921
$$615$$ 14.2462 0.574463
$$616$$ 5.56155i 0.224081i
$$617$$ 6.19224i 0.249290i −0.992201 0.124645i $$-0.960221\pi$$
0.992201 0.124645i $$-0.0397792\pi$$
$$618$$ 1.80776i 0.0727189i
$$619$$ 30.9309i 1.24322i 0.783328 + 0.621608i $$0.213520\pi$$
−0.783328 + 0.621608i $$0.786480\pi$$
$$620$$ −22.2462 −0.893429
$$621$$ 6.68466 0.268246
$$622$$ 0.492423i 0.0197443i
$$623$$ −8.00000 −0.320513
$$624$$ −3.56155 0.561553i −0.142576 0.0224801i
$$625$$ −4.36932 −0.174773
$$626$$ 32.2462i 1.28882i
$$627$$ −8.68466 −0.346832
$$628$$ 11.8078 0.471181
$$629$$ 71.4233i 2.84783i
$$630$$ 3.56155i 0.141896i
$$631$$ 12.6847i 0.504968i −0.967601 0.252484i $$-0.918752\pi$$
0.967601 0.252484i $$-0.0812476\pi$$
$$632$$ 16.0000i 0.636446i
$$633$$ −7.80776 −0.310331
$$634$$ 3.36932 0.133813
$$635$$ 36.4924i 1.44816i
$$636$$ 4.87689 0.193381
$$637$$ −3.56155 0.561553i −0.141114 0.0222495i
$$638$$ −8.68466 −0.343829
$$639$$ 9.36932i 0.370644i
$$640$$ 3.56155 0.140783
$$641$$ 30.1080 1.18919 0.594596 0.804024i $$-0.297312\pi$$
0.594596 + 0.804024i $$0.297312\pi$$
$$642$$ 4.87689i 0.192476i
$$643$$ 0.192236i 0.00758105i 0.999993 + 0.00379052i $$0.00120656\pi$$
−0.999993 + 0.00379052i $$0.998793\pi$$
$$644$$ 6.68466i 0.263412i
$$645$$ 22.9309i 0.902902i
$$646$$ −10.4384 −0.410695
$$647$$ 10.6307 0.417935 0.208968 0.977923i $$-0.432990\pi$$
0.208968 + 0.977923i $$0.432990\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ −23.6155 −0.926991
$$650$$ −4.31534 + 27.3693i −0.169262 + 1.07351i
$$651$$ 6.24621 0.244808
$$652$$ 9.12311i 0.357288i
$$653$$ −29.5616 −1.15683 −0.578416 0.815742i $$-0.696329\pi$$
−0.578416 + 0.815742i $$0.696329\pi$$
$$654$$ 12.9309 0.505637
$$655$$ 5.56155i 0.217308i
$$656$$ 4.00000i 0.156174i
$$657$$ 11.5616i 0.451059i
$$658$$ 10.2462i 0.399439i
$$659$$ 12.8769 0.501613 0.250806 0.968037i $$-0.419304\pi$$
0.250806 + 0.968037i $$0.419304\pi$$
$$660$$ −19.8078 −0.771016
$$661$$ 44.7386i 1.74013i 0.492936 + 0.870066i $$0.335924\pi$$
−0.492936 + 0.870066i $$0.664076\pi$$
$$662$$ 1.12311 0.0436507
$$663$$ 23.8078 + 3.75379i 0.924617 + 0.145785i
$$664$$ −2.00000 −0.0776151
$$665$$ 5.56155i 0.215668i
$$666$$ −10.6847 −0.414022
$$667$$ −10.4384 −0.404178
$$668$$ 11.8078i 0.456856i
$$669$$ 1.75379i 0.0678054i
$$670$$ 4.00000i 0.154533i
$$671$$ 8.68466i 0.335268i
$$672$$ −1.00000 −0.0385758
$$673$$ 37.8078 1.45738 0.728691 0.684843i $$-0.240129\pi$$
0.728691 + 0.684843i $$0.240129\pi$$
$$674$$ 20.0540i 0.772450i
$$675$$ 7.68466 0.295783
$$676$$ −12.3693 4.00000i −0.475743 0.153846i
$$677$$ 31.3693 1.20562 0.602810 0.797884i $$-0.294048\pi$$
0.602810 + 0.797884i $$0.294048\pi$$
$$678$$ 20.2462i 0.777551i
$$679$$ 10.0000 0.383765
$$680$$ −23.8078 −0.912986
$$681$$ 17.6155i 0.675029i
$$682$$ 34.7386i 1.33021i
$$683$$ 0.684658i 0.0261977i −0.999914 0.0130989i $$-0.995830\pi$$
0.999914 0.0130989i $$-0.00416962\pi$$
$$684$$ 1.56155i 0.0597075i
$$685$$ −23.8078 −0.909648
$$686$$ −1.00000 −0.0381802
$$687$$ 2.00000i 0.0763048i
$$688$$ −6.43845 −0.245463
$$689$$ 17.3693 + 2.73863i 0.661718 + 0.104334i
$$690$$ −23.8078 −0.906346
$$691$$ 36.4924i 1.38824i −0.719861 0.694119i $$-0.755794\pi$$
0.719861 0.694119i $$-0.244206\pi$$
$$692$$ 3.75379 0.142698
$$693$$ 5.56155 0.211266
$$694$$ 24.4924i 0.929720i
$$695$$ 36.4924i 1.38424i
$$696$$ 1.56155i 0.0591905i
$$697$$ 26.7386i 1.01280i
$$698$$ −3.36932 −0.127531
$$699$$ −2.00000 −0.0756469
$$700$$ 7.68466i 0.290453i
$$701$$ −3.61553 −0.136557 −0.0682783 0.997666i $$-0.521751\pi$$
−0.0682783 + 0.997666i $$0.521751\pi$$
$$702$$ −0.561553 + 3.56155i −0.0211944 + 0.134422i
$$703$$ 16.6847 0.629274
$$704$$ 5.56155i 0.209609i
$$705$$ −36.4924 −1.37438
$$706$$ 18.2462 0.686705
$$707$$ 6.00000i 0.225653i
$$708$$ 4.24621i 0.159582i
$$709$$ 31.7538i 1.19254i −0.802784 0.596269i $$-0.796649\pi$$
0.802784 0.596269i $$-0.203351\pi$$
$$710$$ 33.3693i 1.25233i
$$711$$ 16.0000 0.600047
$$712$$ −8.00000 −0.299813
$$713$$ 41.7538i 1.56369i
$$714$$ 6.68466 0.250167
$$715$$ −70.5464 11.1231i −2.63829 0.415981i
$$716$$ −11.1231 −0.415690
$$717$$ 14.2462i 0.532035i
$$718$$ −23.6155 −0.881324
$$719$$ 13.7538 0.512930 0.256465 0.966554i $$-0.417442\pi$$
0.256465 + 0.966554i $$0.417442\pi$$
$$720$$ 3.56155i 0.132731i
$$721$$ 1.80776i 0.0673247i
$$722$$ 16.5616i 0.616357i
$$723$$ 6.00000i 0.223142i
$$724$$ 13.3693 0.496867
$$725$$ −12.0000 −0.445669
$$726$$ 19.9309i 0.739704i
$$727$$ −48.9309 −1.81475 −0.907373 0.420327i $$-0.861915\pi$$
−0.907373 + 0.420327i $$0.861915\pi$$
$$728$$ −3.56155 0.561553i −0.132000 0.0208125i
$$729$$ 1.00000 0.0370370
$$730$$ 41.1771i 1.52403i
$$731$$ 43.0388 1.59185
$$732$$ −1.56155 −0.0577167
$$733$$ 22.8769i 0.844977i 0.906368 + 0.422489i $$0.138843\pi$$
−0.906368 + 0.422489i $$0.861157\pi$$
$$734$$ 0.630683i 0.0232789i
$$735$$ 3.56155i 0.131370i
$$736$$ 6.68466i 0.246400i
$$737$$ 6.24621 0.230082
$$738$$ −4.00000 −0.147242
$$739$$ 17.6155i 0.647998i 0.946057 + 0.323999i $$0.105027\pi$$
−0.946057 + 0.323999i $$0.894973\pi$$
$$740$$ 38.0540 1.39889
$$741$$ 0.876894 5.56155i 0.0322135 0.204309i
$$742$$ 4.87689 0.179036
$$743$$ 16.0000i 0.586983i 0.955962 + 0.293492i $$0.0948173\pi$$
−0.955962 + 0.293492i $$0.905183\pi$$
$$744$$ 6.24621 0.228997
$$745$$ −35.6155 −1.30485
$$746$$ 6.00000i 0.219676i
$$747$$ 2.00000i 0.0731762i
$$748$$ 37.1771i 1.35933i
$$749$$ 4.87689i 0.178198i
$$750$$ −9.56155 −0.349139
$$751$$ 2.24621 0.0819654 0.0409827 0.999160i $$-0.486951\pi$$
0.0409827 + 0.999160i $$0.486951\pi$$
$$752$$ 10.2462i 0.373641i
$$753$$ −22.0540 −0.803692
$$754$$ 0.876894 5.56155i 0.0319346 0.202540i
$$755$$ −59.4233 −2.16264
$$756$$ 1.00000i 0.0363696i
$$757$$ 38.0000 1.38113 0.690567 0.723269i $$-0.257361\pi$$
0.690567 + 0.723269i $$0.257361\pi$$
$$758$$ 18.8769 0.685640
$$759$$ 37.1771i 1.34944i
$$760$$ 5.56155i 0.201739i
$$761$$ 39.1231i 1.41821i 0.705102 + 0.709106i $$0.250901\pi$$
−0.705102 + 0.709106i $$0.749099\pi$$
$$762$$ 10.2462i 0.371181i
$$763$$ 12.9309 0.468129
$$764$$ 24.0540 0.870242
$$765$$ 23.8078i 0.860772i
$$766$$ −17.5616 −0.634525
$$767$$ 2.38447 15.1231i 0.0860983 0.546064i
$$768$$ −1.00000 −0.0360844
$$769$$ 8.43845i 0.304298i 0.988358 + 0.152149i $$0.0486194\pi$$
−0.988358 + 0.152149i $$0.951381\pi$$
$$770$$ −19.8078 −0.713822
$$771$$ 26.0000 0.936367
$$772$$ 12.0000i 0.431889i
$$773$$ 12.9309i 0.465091i −0.972586 0.232546i $$-0.925295\pi$$
0.972586 0.232546i $$-0.0747055\pi$$
$$774$$ 6.43845i 0.231425i
$$775$$ 48.0000i 1.72421i
$$776$$ 10.0000 0.358979
$$777$$ −10.6847 −0.383310
$$778$$ 27.1231i 0.972410i
$$779$$ 6.24621 0.223794
$$780$$ 2.00000 12.6847i 0.0716115 0.454184i
$$781$$ −52.1080 −1.86457
$$782$$ 44.6847i 1.59792i
$$783$$ −1.56155 −0.0558053
$$784$$ −1.00000 −0.0357143
$$785$$ 42.0540i 1.50097i
$$786$$ 1.56155i 0.0556987i
$$787$$ 17.0691i 0.608449i −0.952600 0.304224i $$-0.901603\pi$$
0.952600 0.304224i $$-0.0983973\pi$$
$$788$$ 6.00000i 0.213741i
$$789$$