Properties

 Label 304.2.i.b.49.1 Level $304$ Weight $2$ Character 304.49 Analytic conductor $2.427$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$304 = 2^{4} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 304.i (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$2.42745222145$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 152) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 49.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 304.49 Dual form 304.2.i.b.273.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(1.00000 + 1.73205i) q^{9} +4.00000 q^{11} +(2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{15} +(2.50000 - 4.33013i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{23} +(-2.00000 - 3.46410i) q^{25} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{37} +5.00000 q^{39} +(2.50000 - 4.33013i) q^{41} +(-5.50000 + 9.52628i) q^{43} -6.00000 q^{45} +(-2.50000 - 4.33013i) q^{47} -7.00000 q^{49} +(-2.50000 - 4.33013i) q^{51} +(4.50000 + 7.79423i) q^{53} +(-6.00000 + 10.3923i) q^{55} +(-0.500000 + 4.33013i) q^{57} +(6.50000 - 11.2583i) q^{59} +(0.500000 + 0.866025i) q^{61} -15.0000 q^{65} +(-2.50000 - 4.33013i) q^{67} -1.00000 q^{69} +(0.500000 - 0.866025i) q^{71} +(4.50000 - 7.79423i) q^{73} -4.00000 q^{75} +(8.50000 - 14.7224i) q^{79} +(-0.500000 + 0.866025i) q^{81} -16.0000 q^{83} +(7.50000 + 12.9904i) q^{85} -3.00000 q^{87} +(-1.50000 - 2.59808i) q^{89} +(-2.00000 + 3.46410i) q^{93} +(1.50000 - 12.9904i) q^{95} +(6.50000 - 11.2583i) q^{97} +(4.00000 + 6.92820i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - 3 q^{5} + 2 q^{9} + O(q^{10})$$ $$2 q + q^{3} - 3 q^{5} + 2 q^{9} + 8 q^{11} + 5 q^{13} + 3 q^{15} + 5 q^{17} - 8 q^{19} - q^{23} - 4 q^{25} + 10 q^{27} - 3 q^{29} - 8 q^{31} + 4 q^{33} + 4 q^{37} + 10 q^{39} + 5 q^{41} - 11 q^{43} - 12 q^{45} - 5 q^{47} - 14 q^{49} - 5 q^{51} + 9 q^{53} - 12 q^{55} - q^{57} + 13 q^{59} + q^{61} - 30 q^{65} - 5 q^{67} - 2 q^{69} + q^{71} + 9 q^{73} - 8 q^{75} + 17 q^{79} - q^{81} - 32 q^{83} + 15 q^{85} - 6 q^{87} - 3 q^{89} - 4 q^{93} + 3 q^{95} + 13 q^{97} + 8 q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$191$$ $$229$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i $$-0.740119\pi$$
0.973494 + 0.228714i $$0.0734519\pi$$
$$4$$ 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
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 0 0
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 4.00000 1.20605 0.603023 0.797724i $$-0.293963\pi$$
0.603023 + 0.797724i $$0.293963\pi$$
$$12$$ 0 0
$$13$$ 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 1.50000 + 2.59808i 0.387298 + 0.670820i
$$16$$ 0 0
$$17$$ 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i $$-0.625971\pi$$
0.991838 0.127502i $$-0.0406959\pi$$
$$18$$ 0 0
$$19$$ −4.00000 + 1.73205i −0.917663 + 0.397360i
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i $$-0.199913\pi$$
−0.913434 + 0.406986i $$0.866580\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 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
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 2.00000 3.46410i 0.348155 0.603023i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 0 0
$$39$$ 5.00000 0.800641
$$40$$ 0 0
$$41$$ 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i $$-0.705658\pi$$
0.992507 + 0.122189i $$0.0389915\pi$$
$$42$$ 0 0
$$43$$ −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i $$0.483375\pi$$
−0.890947 + 0.454108i $$0.849958\pi$$
$$44$$ 0 0
$$45$$ −6.00000 −0.894427
$$46$$ 0 0
$$47$$ −2.50000 4.33013i −0.364662 0.631614i 0.624059 0.781377i $$-0.285482\pi$$
−0.988722 + 0.149763i $$0.952149\pi$$
$$48$$ 0 0
$$49$$ −7.00000 −1.00000
$$50$$ 0 0
$$51$$ −2.50000 4.33013i −0.350070 0.606339i
$$52$$ 0 0
$$53$$ 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i $$0.0454398\pi$$
−0.371706 + 0.928351i $$0.621227\pi$$
$$54$$ 0 0
$$55$$ −6.00000 + 10.3923i −0.809040 + 1.40130i
$$56$$ 0 0
$$57$$ −0.500000 + 4.33013i −0.0662266 + 0.573539i
$$58$$ 0 0
$$59$$ 6.50000 11.2583i 0.846228 1.46571i −0.0383226 0.999265i $$-0.512201\pi$$
0.884551 0.466444i $$-0.154465\pi$$
$$60$$ 0 0
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −15.0000 −1.86052
$$66$$ 0 0
$$67$$ −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i $$-0.265465\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ −1.00000 −0.120386
$$70$$ 0 0
$$71$$ 0.500000 0.866025i 0.0593391 0.102778i −0.834830 0.550508i $$-0.814434\pi$$
0.894169 + 0.447730i $$0.147767\pi$$
$$72$$ 0 0
$$73$$ 4.50000 7.79423i 0.526685 0.912245i −0.472831 0.881153i $$-0.656768\pi$$
0.999517 0.0310925i $$-0.00989865\pi$$
$$74$$ 0 0
$$75$$ −4.00000 −0.461880
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 8.50000 14.7224i 0.956325 1.65640i 0.225018 0.974355i $$-0.427756\pi$$
0.731307 0.682048i $$-0.238911\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −16.0000 −1.75623 −0.878114 0.478451i $$-0.841198\pi$$
−0.878114 + 0.478451i $$0.841198\pi$$
$$84$$ 0 0
$$85$$ 7.50000 + 12.9904i 0.813489 + 1.40900i
$$86$$ 0 0
$$87$$ −3.00000 −0.321634
$$88$$ 0 0
$$89$$ −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i $$-0.217494\pi$$
−0.934508 + 0.355942i $$0.884160\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −2.00000 + 3.46410i −0.207390 + 0.359211i
$$94$$ 0 0
$$95$$ 1.50000 12.9904i 0.153897 1.33278i
$$96$$ 0 0
$$97$$ 6.50000 11.2583i 0.659975 1.14311i −0.320647 0.947199i $$-0.603900\pi$$
0.980622 0.195911i $$-0.0627665\pi$$
$$98$$ 0 0
$$99$$ 4.00000 + 6.92820i 0.402015 + 0.696311i
$$100$$ 0 0
$$101$$ −9.50000 16.4545i −0.945285 1.63728i −0.755179 0.655519i $$-0.772450\pi$$
−0.190106 0.981763i $$-0.560883\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 12.0000 1.16008 0.580042 0.814587i $$-0.303036\pi$$
0.580042 + 0.814587i $$0.303036\pi$$
$$108$$ 0 0
$$109$$ −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i $$-0.942150\pi$$
0.648292 + 0.761392i $$0.275484\pi$$
$$110$$ 0 0
$$111$$ 1.00000 1.73205i 0.0949158 0.164399i
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ 3.00000 0.279751
$$116$$ 0 0
$$117$$ −5.00000 + 8.66025i −0.462250 + 0.800641i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.00000 0.454545
$$122$$ 0 0
$$123$$ −2.50000 4.33013i −0.225417 0.390434i
$$124$$ 0 0
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 7.50000 + 12.9904i 0.665517 + 1.15271i 0.979145 + 0.203164i $$0.0651224\pi$$
−0.313627 + 0.949546i $$0.601544\pi$$
$$128$$ 0 0
$$129$$ 5.50000 + 9.52628i 0.484248 + 0.838742i
$$130$$ 0 0
$$131$$ −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i $$0.394115\pi$$
−0.981824 + 0.189794i $$0.939218\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −7.50000 + 12.9904i −0.645497 + 1.11803i
$$136$$ 0 0
$$137$$ 2.50000 + 4.33013i 0.213589 + 0.369948i 0.952835 0.303488i $$-0.0981512\pi$$
−0.739246 + 0.673436i $$0.764818\pi$$
$$138$$ 0 0
$$139$$ 7.50000 + 12.9904i 0.636142 + 1.10183i 0.986272 + 0.165129i $$0.0528040\pi$$
−0.350130 + 0.936701i $$0.613863\pi$$
$$140$$ 0 0
$$141$$ −5.00000 −0.421076
$$142$$ 0 0
$$143$$ 10.0000 + 17.3205i 0.836242 + 1.44841i
$$144$$ 0 0
$$145$$ 9.00000 0.747409
$$146$$ 0 0
$$147$$ −3.50000 + 6.06218i −0.288675 + 0.500000i
$$148$$ 0 0
$$149$$ 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i $$-0.588141\pi$$
0.969724 0.244202i $$-0.0785259\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 10.0000 0.808452
$$154$$ 0 0
$$155$$ 6.00000 10.3923i 0.481932 0.834730i
$$156$$ 0 0
$$157$$ 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i $$-0.659728\pi$$
0.999762 0.0217953i $$-0.00693820\pi$$
$$158$$ 0 0
$$159$$ 9.00000 0.713746
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ 0 0
$$165$$ 6.00000 + 10.3923i 0.467099 + 0.809040i
$$166$$ 0 0
$$167$$ −2.50000 4.33013i −0.193456 0.335075i 0.752937 0.658092i $$-0.228636\pi$$
−0.946393 + 0.323017i $$0.895303\pi$$
$$168$$ 0 0
$$169$$ −6.00000 + 10.3923i −0.461538 + 0.799408i
$$170$$ 0 0
$$171$$ −7.00000 5.19615i −0.535303 0.397360i
$$172$$ 0 0
$$173$$ 2.50000 4.33013i 0.190071 0.329213i −0.755202 0.655492i $$-0.772461\pi$$
0.945274 + 0.326278i $$0.105795\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −6.50000 11.2583i −0.488570 0.846228i
$$178$$ 0 0
$$179$$ 12.0000 0.896922 0.448461 0.893802i $$-0.351972\pi$$
0.448461 + 0.893802i $$0.351972\pi$$
$$180$$ 0 0
$$181$$ −3.50000 6.06218i −0.260153 0.450598i 0.706129 0.708083i $$-0.250440\pi$$
−0.966282 + 0.257485i $$0.917106\pi$$
$$182$$ 0 0
$$183$$ 1.00000 0.0739221
$$184$$ 0 0
$$185$$ −3.00000 + 5.19615i −0.220564 + 0.382029i
$$186$$ 0 0
$$187$$ 10.0000 17.3205i 0.731272 1.26660i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 16.0000 1.15772 0.578860 0.815427i $$-0.303498\pi$$
0.578860 + 0.815427i $$0.303498\pi$$
$$192$$ 0 0
$$193$$ −7.50000 + 12.9904i −0.539862 + 0.935068i 0.459049 + 0.888411i $$0.348190\pi$$
−0.998911 + 0.0466572i $$0.985143\pi$$
$$194$$ 0 0
$$195$$ −7.50000 + 12.9904i −0.537086 + 0.930261i
$$196$$ 0 0
$$197$$ 10.0000 0.712470 0.356235 0.934396i $$-0.384060\pi$$
0.356235 + 0.934396i $$0.384060\pi$$
$$198$$ 0 0
$$199$$ 1.50000 + 2.59808i 0.106332 + 0.184173i 0.914282 0.405079i $$-0.132756\pi$$
−0.807950 + 0.589252i $$0.799423\pi$$
$$200$$ 0 0
$$201$$ −5.00000 −0.352673
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 7.50000 + 12.9904i 0.523823 + 0.907288i
$$206$$ 0 0
$$207$$ 1.00000 1.73205i 0.0695048 0.120386i
$$208$$ 0 0
$$209$$ −16.0000 + 6.92820i −1.10674 + 0.479234i
$$210$$ 0 0
$$211$$ 4.50000 7.79423i 0.309793 0.536577i −0.668524 0.743690i $$-0.733074\pi$$
0.978317 + 0.207114i $$0.0664070\pi$$
$$212$$ 0 0
$$213$$ −0.500000 0.866025i −0.0342594 0.0593391i
$$214$$ 0 0
$$215$$ −16.5000 28.5788i −1.12529 1.94906i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −4.50000 7.79423i −0.304082 0.526685i
$$220$$ 0 0
$$221$$ 25.0000 1.68168
$$222$$ 0 0
$$223$$ −5.50000 + 9.52628i −0.368307 + 0.637927i −0.989301 0.145889i $$-0.953396\pi$$
0.620994 + 0.783815i $$0.286729\pi$$
$$224$$ 0 0
$$225$$ 4.00000 6.92820i 0.266667 0.461880i
$$226$$ 0 0
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −5.50000 + 9.52628i −0.360317 + 0.624087i −0.988013 0.154371i $$-0.950665\pi$$
0.627696 + 0.778459i $$0.283998\pi$$
$$234$$ 0 0
$$235$$ 15.0000 0.978492
$$236$$ 0 0
$$237$$ −8.50000 14.7224i −0.552134 0.956325i
$$238$$ 0 0
$$239$$ −12.0000 −0.776215 −0.388108 0.921614i $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 10.5000 + 18.1865i 0.676364 + 1.17150i 0.976068 + 0.217465i $$0.0697789\pi$$
−0.299704 + 0.954032i $$0.596888\pi$$
$$242$$ 0 0
$$243$$ 8.00000 + 13.8564i 0.513200 + 0.888889i
$$244$$ 0 0
$$245$$ 10.5000 18.1865i 0.670820 1.16190i
$$246$$ 0 0
$$247$$ −17.5000 12.9904i −1.11350 0.826558i
$$248$$ 0 0
$$249$$ −8.00000 + 13.8564i −0.506979 + 0.878114i
$$250$$ 0 0
$$251$$ −4.50000 7.79423i −0.284037 0.491967i 0.688338 0.725390i $$-0.258341\pi$$
−0.972375 + 0.233423i $$0.925007\pi$$
$$252$$ 0 0
$$253$$ −2.00000 3.46410i −0.125739 0.217786i
$$254$$ 0 0
$$255$$ 15.0000 0.939336
$$256$$ 0 0
$$257$$ 12.5000 + 21.6506i 0.779729 + 1.35053i 0.932098 + 0.362206i $$0.117976\pi$$
−0.152370 + 0.988324i $$0.548690\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 3.00000 5.19615i 0.185695 0.321634i
$$262$$ 0 0
$$263$$ −9.50000 + 16.4545i −0.585795 + 1.01463i 0.408981 + 0.912543i $$0.365884\pi$$
−0.994776 + 0.102084i $$0.967449\pi$$
$$264$$ 0 0
$$265$$ −27.0000 −1.65860
$$266$$ 0 0
$$267$$ −3.00000 −0.183597
$$268$$ 0 0
$$269$$ 8.50000 14.7224i 0.518254 0.897643i −0.481521 0.876435i $$-0.659915\pi$$
0.999775 0.0212079i $$-0.00675120\pi$$
$$270$$ 0 0
$$271$$ 14.5000 25.1147i 0.880812 1.52561i 0.0303728 0.999539i $$-0.490331\pi$$
0.850439 0.526073i $$-0.176336\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −8.00000 13.8564i −0.482418 0.835573i
$$276$$ 0 0
$$277$$ −30.0000 −1.80253 −0.901263 0.433273i $$-0.857359\pi$$
−0.901263 + 0.433273i $$0.857359\pi$$
$$278$$ 0 0
$$279$$ −4.00000 6.92820i −0.239474 0.414781i
$$280$$ 0 0
$$281$$ −7.50000 12.9904i −0.447412 0.774941i 0.550804 0.834634i $$-0.314321\pi$$
−0.998217 + 0.0596933i $$0.980988\pi$$
$$282$$ 0 0
$$283$$ −7.50000 + 12.9904i −0.445829 + 0.772198i −0.998110 0.0614601i $$-0.980424\pi$$
0.552281 + 0.833658i $$0.313758\pi$$
$$284$$ 0 0
$$285$$ −10.5000 7.79423i −0.621966 0.461690i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −4.00000 6.92820i −0.235294 0.407541i
$$290$$ 0 0
$$291$$ −6.50000 11.2583i −0.381037 0.659975i
$$292$$ 0 0
$$293$$ 10.0000 0.584206 0.292103 0.956387i $$-0.405645\pi$$
0.292103 + 0.956387i $$0.405645\pi$$
$$294$$ 0 0
$$295$$ 19.5000 + 33.7750i 1.13533 + 1.96646i
$$296$$ 0 0
$$297$$ 20.0000 1.16052
$$298$$ 0 0
$$299$$ 2.50000 4.33013i 0.144579 0.250418i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −19.0000 −1.09152
$$304$$ 0 0
$$305$$ −3.00000 −0.171780
$$306$$ 0 0
$$307$$ −1.50000 + 2.59808i −0.0856095 + 0.148280i −0.905651 0.424024i $$-0.860617\pi$$
0.820041 + 0.572304i $$0.193950\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ 2.50000 + 4.33013i 0.141308 + 0.244753i 0.927990 0.372606i $$-0.121536\pi$$
−0.786681 + 0.617359i $$0.788202\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −13.5000 23.3827i −0.758236 1.31330i −0.943750 0.330661i $$-0.892728\pi$$
0.185514 0.982642i $$-0.440605\pi$$
$$318$$ 0 0
$$319$$ −6.00000 10.3923i −0.335936 0.581857i
$$320$$ 0 0
$$321$$ 6.00000 10.3923i 0.334887 0.580042i
$$322$$ 0 0
$$323$$ −2.50000 + 21.6506i −0.139104 + 1.20467i
$$324$$ 0 0
$$325$$ 10.0000 17.3205i 0.554700 0.960769i
$$326$$ 0 0
$$327$$ 3.50000 + 6.06218i 0.193550 + 0.335239i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −20.0000 −1.09930 −0.549650 0.835395i $$-0.685239\pi$$
−0.549650 + 0.835395i $$0.685239\pi$$
$$332$$ 0 0
$$333$$ 2.00000 + 3.46410i 0.109599 + 0.189832i
$$334$$ 0 0
$$335$$ 15.0000 0.819538
$$336$$ 0 0
$$337$$ −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i $$-0.859372\pi$$
0.822274 + 0.569091i $$0.192705\pi$$
$$338$$ 0 0
$$339$$ 3.00000 5.19615i 0.162938 0.282216i
$$340$$ 0 0
$$341$$ −16.0000 −0.866449
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 1.50000 2.59808i 0.0807573 0.139876i
$$346$$ 0 0
$$347$$ 2.50000 4.33013i 0.134207 0.232453i −0.791087 0.611703i $$-0.790485\pi$$
0.925294 + 0.379250i $$0.123818\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 12.5000 + 21.6506i 0.667201 + 1.15563i
$$352$$ 0 0
$$353$$ −10.0000 −0.532246 −0.266123 0.963939i $$-0.585743\pi$$
−0.266123 + 0.963939i $$0.585743\pi$$
$$354$$ 0 0
$$355$$ 1.50000 + 2.59808i 0.0796117 + 0.137892i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 2.50000 4.33013i 0.131945 0.228535i −0.792481 0.609896i $$-0.791211\pi$$
0.924426 + 0.381361i $$0.124544\pi$$
$$360$$ 0 0
$$361$$ 13.0000 13.8564i 0.684211 0.729285i
$$362$$ 0 0
$$363$$ 2.50000 4.33013i 0.131216 0.227273i
$$364$$ 0 0
$$365$$ 13.5000 + 23.3827i 0.706622 + 1.22391i
$$366$$ 0 0
$$367$$ −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i $$-0.208325\pi$$
−0.923869 + 0.382709i $$0.874991\pi$$
$$368$$ 0 0
$$369$$ 10.0000 0.520579
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −10.0000 −0.517780 −0.258890 0.965907i $$-0.583357\pi$$
−0.258890 + 0.965907i $$0.583357\pi$$
$$374$$ 0 0
$$375$$ −1.50000 + 2.59808i −0.0774597 + 0.134164i
$$376$$ 0 0
$$377$$ 7.50000 12.9904i 0.386270 0.669039i
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ 15.0000 0.768473
$$382$$ 0 0
$$383$$ −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i $$-0.958522\pi$$
0.608290 + 0.793715i $$0.291856\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −22.0000 −1.11832
$$388$$ 0 0
$$389$$ 8.50000 + 14.7224i 0.430967 + 0.746457i 0.996957 0.0779554i $$-0.0248392\pi$$
−0.565990 + 0.824412i $$0.691506\pi$$
$$390$$ 0 0
$$391$$ −5.00000 −0.252861
$$392$$ 0 0
$$393$$ 7.50000 + 12.9904i 0.378325 + 0.655278i
$$394$$ 0 0
$$395$$ 25.5000 + 44.1673i 1.28304 + 2.22230i
$$396$$ 0 0
$$397$$ −17.5000 + 30.3109i −0.878300 + 1.52126i −0.0250943 + 0.999685i $$0.507989\pi$$
−0.853206 + 0.521575i $$0.825345\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −5.50000 + 9.52628i −0.274657 + 0.475720i −0.970049 0.242911i $$-0.921898\pi$$
0.695392 + 0.718631i $$0.255231\pi$$
$$402$$ 0 0
$$403$$ −10.0000 17.3205i −0.498135 0.862796i
$$404$$ 0 0
$$405$$ −1.50000 2.59808i −0.0745356 0.129099i
$$406$$ 0 0
$$407$$ 8.00000 0.396545
$$408$$ 0 0
$$409$$ −3.50000 6.06218i −0.173064 0.299755i 0.766426 0.642333i $$-0.222033\pi$$
−0.939490 + 0.342578i $$0.888700\pi$$
$$410$$ 0 0
$$411$$ 5.00000 0.246632
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 24.0000 41.5692i 1.17811 2.04055i
$$416$$ 0 0
$$417$$ 15.0000 0.734553
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 14.5000 25.1147i 0.706687 1.22402i −0.259393 0.965772i $$-0.583522\pi$$
0.966079 0.258245i $$-0.0831443\pi$$
$$422$$ 0 0
$$423$$ 5.00000 8.66025i 0.243108 0.421076i
$$424$$ 0 0
$$425$$ −20.0000 −0.970143
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 20.0000 0.965609
$$430$$ 0 0
$$431$$ −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i $$-0.236215\pi$$
−0.953815 + 0.300395i $$0.902881\pi$$
$$432$$ 0 0
$$433$$ 12.5000 + 21.6506i 0.600712 + 1.04046i 0.992713 + 0.120499i $$0.0384494\pi$$
−0.392002 + 0.919964i $$0.628217\pi$$
$$434$$ 0 0
$$435$$ 4.50000 7.79423i 0.215758 0.373705i
$$436$$ 0 0
$$437$$ 3.50000 + 2.59808i 0.167428 + 0.124283i
$$438$$ 0 0
$$439$$ −3.50000 + 6.06218i −0.167046 + 0.289332i −0.937380 0.348309i $$-0.886756\pi$$
0.770334 + 0.637641i $$0.220089\pi$$
$$440$$ 0 0
$$441$$ −7.00000 12.1244i −0.333333 0.577350i
$$442$$ 0 0
$$443$$ 7.50000 + 12.9904i 0.356336 + 0.617192i 0.987346 0.158583i $$-0.0506926\pi$$
−0.631010 + 0.775775i $$0.717359\pi$$
$$444$$ 0 0
$$445$$ 9.00000 0.426641
$$446$$ 0 0
$$447$$ −8.50000 14.7224i −0.402036 0.696347i
$$448$$ 0 0
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 10.0000 17.3205i 0.470882 0.815591i
$$452$$ 0 0
$$453$$ −8.00000 + 13.8564i −0.375873 + 0.651031i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 10.0000 0.467780 0.233890 0.972263i $$-0.424854\pi$$
0.233890 + 0.972263i $$0.424854\pi$$
$$458$$ 0 0
$$459$$ 12.5000 21.6506i 0.583450 1.01057i
$$460$$ 0 0
$$461$$ 0.500000 0.866025i 0.0232873 0.0403348i −0.854147 0.520032i $$-0.825920\pi$$
0.877434 + 0.479697i $$0.159253\pi$$
$$462$$ 0 0
$$463$$ 20.0000 0.929479 0.464739 0.885448i $$-0.346148\pi$$
0.464739 + 0.885448i $$0.346148\pi$$
$$464$$ 0 0
$$465$$ −6.00000 10.3923i −0.278243 0.481932i
$$466$$ 0 0
$$467$$ −12.0000 −0.555294 −0.277647 0.960683i $$-0.589555\pi$$
−0.277647 + 0.960683i $$0.589555\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −6.50000 11.2583i −0.299504 0.518756i
$$472$$ 0 0
$$473$$ −22.0000 + 38.1051i −1.01156 + 1.75208i
$$474$$ 0 0
$$475$$ 14.0000 + 10.3923i 0.642364 + 0.476832i
$$476$$ 0 0
$$477$$ −9.00000 + 15.5885i −0.412082 + 0.713746i
$$478$$ 0 0
$$479$$ 13.5000 + 23.3827i 0.616831 + 1.06838i 0.990060 + 0.140643i $$0.0449170\pi$$
−0.373230 + 0.927739i $$0.621750\pi$$
$$480$$ 0 0
$$481$$ 5.00000 + 8.66025i 0.227980 + 0.394874i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 19.5000 + 33.7750i 0.885449 + 1.53364i
$$486$$ 0 0
$$487$$ 40.0000 1.81257 0.906287 0.422664i $$-0.138905\pi$$
0.906287 + 0.422664i $$0.138905\pi$$
$$488$$ 0 0
$$489$$ 2.00000 3.46410i 0.0904431 0.156652i
$$490$$ 0 0
$$491$$ 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i $$-0.768237\pi$$
0.949520 + 0.313707i $$0.101571\pi$$
$$492$$ 0 0
$$493$$ −15.0000 −0.675566
$$494$$ 0 0
$$495$$ −24.0000 −1.07872
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −17.5000 + 30.3109i −0.783408 + 1.35690i 0.146538 + 0.989205i $$0.453187\pi$$
−0.929946 + 0.367697i $$0.880146\pi$$
$$500$$ 0 0
$$501$$ −5.00000 −0.223384
$$502$$ 0 0
$$503$$ 7.50000 + 12.9904i 0.334408 + 0.579212i 0.983371 0.181608i $$-0.0581302\pi$$
−0.648963 + 0.760820i $$0.724797\pi$$
$$504$$ 0 0
$$505$$ 57.0000 2.53647
$$506$$ 0 0
$$507$$ 6.00000 + 10.3923i 0.266469 + 0.461538i
$$508$$ 0 0
$$509$$ 2.50000 + 4.33013i 0.110811 + 0.191930i 0.916097 0.400956i $$-0.131322\pi$$
−0.805287 + 0.592886i $$0.797989\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −20.0000 + 8.66025i −0.883022 + 0.382360i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −10.0000 17.3205i −0.439799 0.761755i
$$518$$ 0 0
$$519$$ −2.50000 4.33013i −0.109738 0.190071i
$$520$$ 0 0
$$521$$ −6.00000 −0.262865 −0.131432 0.991325i $$-0.541958\pi$$
−0.131432 + 0.991325i $$0.541958\pi$$
$$522$$ 0 0
$$523$$ −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i $$-0.948062\pi$$
0.352677 0.935745i $$-0.385272\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.0000 + 17.3205i −0.435607 + 0.754493i
$$528$$ 0 0
$$529$$ 11.0000 19.0526i 0.478261 0.828372i
$$530$$ 0 0
$$531$$ 26.0000 1.12830
$$532$$ 0 0
$$533$$ 25.0000 1.08287
$$534$$ 0 0
$$535$$ −18.0000 + 31.1769i −0.778208 + 1.34790i
$$536$$ 0 0
$$537$$ 6.00000 10.3923i 0.258919 0.448461i
$$538$$ 0 0
$$539$$ −28.0000 −1.20605
$$540$$ 0 0
$$541$$ −5.50000 9.52628i −0.236463 0.409567i 0.723234 0.690604i $$-0.242655\pi$$
−0.959697 + 0.281037i $$0.909322\pi$$
$$542$$ 0 0
$$543$$ −7.00000 −0.300399
$$544$$ 0 0
$$545$$ −10.5000 18.1865i −0.449771 0.779026i
$$546$$ 0 0
$$547$$ 3.50000 + 6.06218i 0.149649 + 0.259200i 0.931098 0.364770i $$-0.118852\pi$$
−0.781449 + 0.623970i $$0.785519\pi$$
$$548$$ 0 0
$$549$$ −1.00000 + 1.73205i −0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ 10.5000 + 7.79423i 0.447315 + 0.332045i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 3.00000 + 5.19615i 0.127343 + 0.220564i
$$556$$ 0 0
$$557$$ 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i $$0.0797613\pi$$
−0.269642 + 0.962961i $$0.586905\pi$$
$$558$$ 0 0
$$559$$ −55.0000 −2.32625
$$560$$ 0 0
$$561$$ −10.0000 17.3205i −0.422200 0.731272i
$$562$$ 0 0
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 0 0
$$565$$ −9.00000 + 15.5885i −0.378633 + 0.655811i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −18.0000 −0.754599 −0.377300 0.926091i $$-0.623147\pi$$
−0.377300 + 0.926091i $$0.623147\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ 8.00000 13.8564i 0.334205 0.578860i
$$574$$ 0 0
$$575$$ −2.00000 + 3.46410i −0.0834058 + 0.144463i
$$576$$ 0 0
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 0 0
$$579$$ 7.50000 + 12.9904i 0.311689 + 0.539862i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 18.0000 + 31.1769i 0.745484 + 1.29122i
$$584$$ 0 0
$$585$$ −15.0000 25.9808i −0.620174 1.07417i
$$586$$ 0 0
$$587$$ 12.5000 21.6506i 0.515930 0.893617i −0.483899 0.875124i $$-0.660780\pi$$
0.999829 0.0184934i $$-0.00588696\pi$$
$$588$$ 0 0
$$589$$ 16.0000 6.92820i 0.659269 0.285472i
$$590$$ 0 0
$$591$$ 5.00000 8.66025i 0.205673 0.356235i
$$592$$ 0 0
$$593$$ −17.5000 30.3109i −0.718639 1.24472i −0.961539 0.274668i $$-0.911432\pi$$
0.242900 0.970051i $$-0.421901\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 3.00000 0.122782
$$598$$ 0 0
$$599$$ −12.5000 21.6506i −0.510736 0.884621i −0.999923 0.0124417i $$-0.996040\pi$$
0.489186 0.872179i $$-0.337294\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 5.00000 8.66025i 0.203616 0.352673i
$$604$$ 0 0
$$605$$ −7.50000 + 12.9904i −0.304918 + 0.528134i
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 12.5000 21.6506i 0.505696 0.875891i
$$612$$ 0 0
$$613$$ 0.500000 0.866025i 0.0201948 0.0349784i −0.855751 0.517387i $$-0.826905\pi$$
0.875946 + 0.482409i $$0.160238\pi$$
$$614$$ 0 0
$$615$$ 15.0000 0.604858
$$616$$ 0 0
$$617$$ −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i $$-0.185900\pi$$
−0.894639 + 0.446790i $$0.852567\pi$$
$$618$$ 0 0
$$619$$ 20.0000 0.803868 0.401934 0.915669i $$-0.368338\pi$$
0.401934 + 0.915669i $$0.368338\pi$$
$$620$$ 0 0
$$621$$ −2.50000 4.33013i −0.100322 0.173762i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 0 0
$$627$$ −2.00000 + 17.3205i −0.0798723 + 0.691714i
$$628$$ 0 0
$$629$$ 5.00000 8.66025i 0.199363 0.345307i
$$630$$ 0 0
$$631$$ −14.5000 25.1147i −0.577236 0.999802i −0.995795 0.0916122i $$-0.970798\pi$$
0.418559 0.908190i $$-0.362535\pi$$
$$632$$ 0 0
$$633$$ −4.50000 7.79423i −0.178859 0.309793i
$$634$$ 0 0
$$635$$ −45.0000 −1.78577
$$636$$ 0 0
$$637$$ −17.5000 30.3109i −0.693375 1.20096i
$$638$$ 0 0
$$639$$ 2.00000 0.0791188
$$640$$ 0 0
$$641$$ 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i $$-0.776455\pi$$
0.941106 + 0.338112i $$0.109788\pi$$
$$642$$ 0 0
$$643$$ 2.50000 4.33013i 0.0985904 0.170764i −0.812511 0.582946i $$-0.801900\pi$$
0.911101 + 0.412182i $$0.135233\pi$$
$$644$$ 0 0
$$645$$ −33.0000 −1.29937
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ 26.0000 45.0333i 1.02059 1.76771i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.00000 −0.234798 −0.117399 0.993085i $$-0.537456\pi$$
−0.117399 + 0.993085i $$0.537456\pi$$
$$654$$ 0 0
$$655$$ −22.5000 38.9711i −0.879148 1.52273i
$$656$$ 0 0
$$657$$ 18.0000 0.702247
$$658$$ 0 0
$$659$$ 9.50000 + 16.4545i 0.370067 + 0.640976i 0.989576 0.144015i $$-0.0460012\pi$$
−0.619508 + 0.784990i $$0.712668\pi$$
$$660$$ 0 0
$$661$$ 14.5000 + 25.1147i 0.563985 + 0.976850i 0.997143 + 0.0755324i $$0.0240656\pi$$
−0.433159 + 0.901318i $$0.642601\pi$$
$$662$$ 0 0
$$663$$ 12.5000 21.6506i 0.485460 0.840841i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −1.50000 + 2.59808i −0.0580802 + 0.100598i
$$668$$ 0 0
$$669$$ 5.50000 + 9.52628i 0.212642 + 0.368307i
$$670$$ 0 0
$$671$$ 2.00000 + 3.46410i 0.0772091 + 0.133730i
$$672$$ 0 0
$$673$$ 30.0000 1.15642 0.578208 0.815890i $$-0.303752\pi$$
0.578208 + 0.815890i $$0.303752\pi$$
$$674$$ 0 0
$$675$$ −10.0000 17.3205i −0.384900 0.666667i
$$676$$ 0 0
$$677$$ −30.0000 −1.15299 −0.576497 0.817099i $$-0.695581\pi$$
−0.576497 + 0.817099i $$0.695581\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −6.00000 + 10.3923i −0.229920 + 0.398234i
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ −15.0000 −0.573121
$$686$$ 0 0
$$687$$ −11.0000 + 19.0526i −0.419676 + 0.726900i
$$688$$ 0 0
$$689$$ −22.5000 + 38.9711i −0.857182 + 1.48468i
$$690$$ 0 0
$$691$$ −36.0000 −1.36950 −0.684752 0.728776i $$-0.740090\pi$$
−0.684752 + 0.728776i $$0.740090\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −45.0000 −1.70695
$$696$$ 0 0
$$697$$ −12.5000 21.6506i −0.473471 0.820076i
$$698$$ 0 0
$$699$$ 5.50000 + 9.52628i 0.208029 + 0.360317i
$$700$$ 0 0
$$701$$ −11.5000 + 19.9186i −0.434349 + 0.752315i −0.997242 0.0742151i $$-0.976355\pi$$
0.562893 + 0.826530i $$0.309688\pi$$
$$702$$ 0 0
$$703$$ −8.00000 + 3.46410i −0.301726 + 0.130651i
$$704$$ 0 0
$$705$$ 7.50000 12.9904i 0.282466 0.489246i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 8.50000 + 14.7224i 0.319224 + 0.552913i 0.980326 0.197383i $$-0.0632444\pi$$
−0.661102 + 0.750296i $$0.729911\pi$$
$$710$$ 0 0
$$711$$ 34.0000 1.27510
$$712$$ 0 0
$$713$$ 2.00000 + 3.46410i 0.0749006 + 0.129732i
$$714$$ 0 0
$$715$$ −60.0000 −2.24387
$$716$$ 0 0
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ 0 0
$$719$$ −13.5000 + 23.3827i −0.503465 + 0.872027i 0.496527 + 0.868021i $$0.334608\pi$$
−0.999992 + 0.00400572i $$0.998725\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 21.0000 0.780998
$$724$$ 0 0
$$725$$ −6.00000 + 10.3923i −0.222834 + 0.385961i
$$726$$ 0 0
$$727$$ 6.50000 11.2583i 0.241072 0.417548i −0.719948 0.694028i $$-0.755834\pi$$
0.961020 + 0.276479i $$0.0891678\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 27.5000 + 47.6314i 1.01712 + 1.76171i
$$732$$ 0 0
$$733$$ −6.00000 −0.221615 −0.110808 0.993842i $$-0.535344\pi$$
−0.110808 + 0.993842i $$0.535344\pi$$
$$734$$ 0 0
$$735$$ −10.5000 18.1865i −0.387298 0.670820i
$$736$$ 0 0
$$737$$ −10.0000 17.3205i −0.368355 0.638009i
$$738$$ 0 0
$$739$$ 18.5000 32.0429i 0.680534 1.17872i −0.294285 0.955718i $$-0.595081\pi$$
0.974818 0.223001i $$-0.0715853\pi$$
$$740$$ 0 0
$$741$$ −20.0000 + 8.66025i −0.734718 + 0.318142i
$$742$$ 0 0
$$743$$ 14.5000 25.1147i 0.531953 0.921370i −0.467351 0.884072i $$-0.654791\pi$$
0.999304 0.0372984i $$-0.0118752\pi$$
$$744$$ 0 0
$$745$$ 25.5000 + 44.1673i 0.934248 + 1.61816i
$$746$$ 0 0
$$747$$ −16.0000 27.7128i −0.585409 1.01396i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i $$0.0246899\pi$$
−0.431390 + 0.902165i $$0.641977\pi$$
$$752$$ 0 0
$$753$$ −9.00000 −0.327978
$$754$$ 0 0
$$755$$ 24.0000 41.5692i 0.873449 1.51286i
$$756$$ 0 0
$$757$$ −17.5000 + 30.3109i −0.636048 + 1.10167i 0.350244 + 0.936659i $$0.386099\pi$$
−0.986292 + 0.165009i $$0.947235\pi$$
$$758$$ 0 0
$$759$$ −4.00000 −0.145191
$$760$$ 0 0
$$761$$ 38.0000 1.37750 0.688749 0.724999i $$-0.258160\pi$$
0.688749 + 0.724999i $$0.258160\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −15.0000 + 25.9808i −0.542326 + 0.939336i
$$766$$ 0 0
$$767$$ 65.0000 2.34701
$$768$$ 0 0
$$769$$ −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i $$-0.302780\pi$$
−0.995397 + 0.0958377i $$0.969447\pi$$
$$770$$ 0 0
$$771$$ 25.0000 0.900353
$$772$$ 0 0
$$773$$ 12.5000 + 21.6506i 0.449594 + 0.778719i 0.998359 0.0572570i $$-0.0182354\pi$$
−0.548766 + 0.835976i $$0.684902\pi$$
$$774$$ 0 0
$$775$$ 8.00000 + 13.8564i 0.287368 + 0.497737i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −2.50000 + 21.6506i −0.0895718 + 0.775715i
$$780$$ 0 0
$$781$$ 2.00000 3.46410i 0.0715656 0.123955i
$$782$$ 0 0
$$783$$ −7.50000 12.9904i −0.268028 0.464238i
$$784$$ 0 0
$$785$$ 19.5000 + 33.7750i 0.695985 + 1.20548i
$$786$$ 0 0
$$787$$ −20.0000 −0.712923 −0.356462 0.934310i $$-0.616017\pi$$
−0.356462 + 0.934310i $$0.616017\pi$$
$$788$$ 0 0
$$789$$ 9.50000 + 16.4545i 0.338209 + 0.585795i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −2.50000 + 4.33013i −0.0887776 + 0.153767i
$$794$$ 0 0
$$795$$ −13.5000 + 23.3827i −0.478796 + 0.829298i
$$796$$ 0 0
$$797$$ 42.0000 1.48772 0.743858 0.668338i $$-0.232994\pi$$
0.743858 + 0.668338i $$0.232994\pi$$
$$798$$ 0