# Properties

 Label 1300.2.bb.e.549.2 Level $1300$ Weight $2$ Character 1300.549 Analytic conductor $10.381$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1300 = 2^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1300.bb (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.3805522628$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 260) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 549.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1300.549 Dual form 1300.2.bb.e.1049.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$$ $$q+(2.59808 - 1.50000i) q^{3} +(-2.59808 - 1.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.46410 - 1.00000i) q^{13} +(6.06218 + 3.50000i) q^{17} +(0.500000 - 0.866025i) q^{19} -9.00000 q^{21} +(6.06218 - 3.50000i) q^{23} -9.00000i q^{27} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(-7.79423 - 4.50000i) q^{33} +(-2.59808 + 1.50000i) q^{37} +(-10.5000 + 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-7.79423 - 4.50000i) q^{43} +8.00000i q^{47} +(1.00000 + 1.73205i) q^{49} +21.0000 q^{51} +6.00000i q^{53} -3.00000i q^{57} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-15.5885 + 9.00000i) q^{63} +(11.2583 - 6.50000i) q^{67} +(10.5000 - 18.1865i) q^{69} +(1.50000 - 2.59808i) q^{71} +14.0000i q^{73} +9.00000i q^{77} +8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000i q^{83} +(-12.9904 - 7.50000i) q^{87} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(-10.3923 + 6.00000i) q^{93} +(9.52628 + 5.50000i) q^{97} -18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 12 q^{9} + O(q^{10})$$ $$4 q + 12 q^{9} - 6 q^{11} + 2 q^{19} - 36 q^{21} - 10 q^{29} - 16 q^{31} - 42 q^{39} - 14 q^{41} + 4 q^{49} + 84 q^{51} + 10 q^{59} + 10 q^{61} + 42 q^{69} + 6 q^{71} + 32 q^{79} - 18 q^{81} + 14 q^{89} + 30 q^{91} - 72 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$651$$ $$677$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$

## 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
$$3$$ 2.59808 1.50000i 1.50000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
1.00000 $$0$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −2.59808 1.50000i −0.981981 0.566947i −0.0791130 0.996866i $$-0.525209\pi$$
−0.902867 + 0.429919i $$0.858542\pi$$
$$8$$ 0 0
$$9$$ 3.00000 5.19615i 1.00000 1.73205i
$$10$$ 0 0
$$11$$ −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i $$-0.316051\pi$$
−0.998526 + 0.0542666i $$0.982718\pi$$
$$12$$ 0 0
$$13$$ −3.46410 1.00000i −0.960769 0.277350i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.06218 + 3.50000i 1.47029 + 0.848875i 0.999444 0.0333386i $$-0.0106140\pi$$
0.470850 + 0.882213i $$0.343947\pi$$
$$18$$ 0 0
$$19$$ 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i $$-0.796740\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ −9.00000 −1.96396
$$22$$ 0 0
$$23$$ 6.06218 3.50000i 1.26405 0.729800i 0.290196 0.956967i $$-0.406280\pi$$
0.973856 + 0.227167i $$0.0729463\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 9.00000i 1.73205i
$$28$$ 0 0
$$29$$ −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i $$-0.320339\pi$$
−0.999167 + 0.0408130i $$0.987005\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ −7.79423 4.50000i −1.35680 0.783349i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i $$-0.745980\pi$$
0.270998 + 0.962580i $$0.412646\pi$$
$$38$$ 0 0
$$39$$ −10.5000 + 2.59808i −1.68135 + 0.416025i
$$40$$ 0 0
$$41$$ −3.50000 6.06218i −0.546608 0.946753i −0.998504 0.0546823i $$-0.982585\pi$$
0.451896 0.892071i $$-0.350748\pi$$
$$42$$ 0 0
$$43$$ −7.79423 4.50000i −1.18861 0.686244i −0.230618 0.973044i $$-0.574075\pi$$
−0.957990 + 0.286801i $$0.907408\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i 0.812142 + 0.583460i $$0.198301\pi$$
−0.812142 + 0.583460i $$0.801699\pi$$
$$48$$ 0 0
$$49$$ 1.00000 + 1.73205i 0.142857 + 0.247436i
$$50$$ 0 0
$$51$$ 21.0000 2.94059
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000i 0.397360i
$$58$$ 0 0
$$59$$ 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i $$-0.727810\pi$$
0.981608 + 0.190909i $$0.0611434\pi$$
$$60$$ 0 0
$$61$$ 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i $$-0.729619\pi$$
0.980507 + 0.196485i $$0.0629528\pi$$
$$62$$ 0 0
$$63$$ −15.5885 + 9.00000i −1.96396 + 1.13389i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 11.2583 6.50000i 1.37542 0.794101i 0.383819 0.923408i $$-0.374609\pi$$
0.991605 + 0.129307i $$0.0412752\pi$$
$$68$$ 0 0
$$69$$ 10.5000 18.1865i 1.26405 2.18940i
$$70$$ 0 0
$$71$$ 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i $$-0.776365\pi$$
0.941201 + 0.337846i $$0.109698\pi$$
$$72$$ 0 0
$$73$$ 14.0000i 1.63858i 0.573382 + 0.819288i $$0.305631\pi$$
−0.573382 + 0.819288i $$0.694369\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 9.00000i 1.02565i
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −12.9904 7.50000i −1.39272 0.804084i
$$88$$ 0 0
$$89$$ 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i $$-0.0456819\pi$$
−0.618720 + 0.785611i $$0.712349\pi$$
$$90$$ 0 0
$$91$$ 7.50000 + 7.79423i 0.786214 + 0.817057i
$$92$$ 0 0
$$93$$ −10.3923 + 6.00000i −1.07763 + 0.622171i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 9.52628 + 5.50000i 0.967247 + 0.558440i 0.898396 0.439187i $$-0.144733\pi$$
0.0688512 + 0.997627i $$0.478067\pi$$
$$98$$ 0 0
$$99$$ −18.0000 −1.80907
$$100$$ 0 0
$$101$$ 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i $$-0.0188862\pi$$
−0.550474 + 0.834853i $$0.685553\pi$$
$$102$$ 0 0
$$103$$ 16.0000i 1.57653i 0.615338 + 0.788263i $$0.289020\pi$$
−0.615338 + 0.788263i $$0.710980\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −2.59808 + 1.50000i −0.251166 + 0.145010i −0.620298 0.784366i $$-0.712988\pi$$
0.369132 + 0.929377i $$0.379655\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ −4.50000 + 7.79423i −0.427121 + 0.739795i
$$112$$ 0 0
$$113$$ 11.2583 + 6.50000i 1.05909 + 0.611469i 0.925182 0.379525i $$-0.123912\pi$$
0.133913 + 0.990993i $$0.457246\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −15.5885 + 15.0000i −1.44115 + 1.38675i
$$118$$ 0 0
$$119$$ −10.5000 18.1865i −0.962533 1.66716i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 0 0
$$123$$ −18.1865 10.5000i −1.63982 0.946753i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.866025 0.500000i 0.0768473 0.0443678i −0.461084 0.887357i $$-0.652539\pi$$
0.537931 + 0.842989i $$0.319206\pi$$
$$128$$ 0 0
$$129$$ −27.0000 −2.37722
$$130$$ 0 0
$$131$$ 4.00000 0.349482 0.174741 0.984614i $$-0.444091\pi$$
0.174741 + 0.984614i $$0.444091\pi$$
$$132$$ 0 0
$$133$$ −2.59808 + 1.50000i −0.225282 + 0.130066i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 2.59808 + 1.50000i 0.221969 + 0.128154i 0.606861 0.794808i $$-0.292428\pi$$
−0.384893 + 0.922961i $$0.625762\pi$$
$$138$$ 0 0
$$139$$ 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i $$-0.647457\pi$$
0.998179 0.0603135i $$-0.0192101\pi$$
$$140$$ 0 0
$$141$$ 12.0000 + 20.7846i 1.01058 + 1.75038i
$$142$$ 0 0
$$143$$ 2.59808 + 10.5000i 0.217262 + 0.878054i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 5.19615 + 3.00000i 0.428571 + 0.247436i
$$148$$ 0 0
$$149$$ 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i $$-0.794119\pi$$
0.920904 + 0.389789i $$0.127452\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ 36.3731 21.0000i 2.94059 1.69775i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 6.00000i 0.478852i 0.970915 + 0.239426i $$0.0769593\pi$$
−0.970915 + 0.239426i $$0.923041\pi$$
$$158$$ 0 0
$$159$$ 9.00000 + 15.5885i 0.713746 + 1.23625i
$$160$$ 0 0
$$161$$ −21.0000 −1.65503
$$162$$ 0 0
$$163$$ 9.52628 + 5.50000i 0.746156 + 0.430793i 0.824303 0.566149i $$-0.191567\pi$$
−0.0781474 + 0.996942i $$0.524900\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.866025 0.500000i 0.0670151 0.0386912i −0.466118 0.884723i $$-0.654348\pi$$
0.533133 + 0.846031i $$0.321014\pi$$
$$168$$ 0 0
$$169$$ 11.0000 + 6.92820i 0.846154 + 0.532939i
$$170$$ 0 0
$$171$$ −3.00000 5.19615i −0.229416 0.397360i
$$172$$ 0 0
$$173$$ −12.9904 7.50000i −0.987640 0.570214i −0.0830722 0.996544i $$-0.526473\pi$$
−0.904568 + 0.426329i $$0.859807\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 15.0000i 1.12747i
$$178$$ 0 0
$$179$$ 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i $$0.0846670\pi$$
−0.254770 + 0.967002i $$0.582000\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ 15.0000i 1.10883i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 21.0000i 1.53567i
$$188$$ 0 0
$$189$$ −13.5000 + 23.3827i −0.981981 + 1.70084i
$$190$$ 0 0
$$191$$ 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i $$-0.798717\pi$$
0.915177 + 0.403051i $$0.132050\pi$$
$$192$$ 0 0
$$193$$ 12.9904 7.50000i 0.935068 0.539862i 0.0466572 0.998911i $$-0.485143\pi$$
0.888411 + 0.459049i $$0.151810\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −19.9186 + 11.5000i −1.41914 + 0.819341i −0.996223 0.0868274i $$-0.972327\pi$$
−0.422917 + 0.906168i $$0.638994\pi$$
$$198$$ 0 0
$$199$$ 4.50000 7.79423i 0.318997 0.552518i −0.661282 0.750137i $$-0.729987\pi$$
0.980279 + 0.197619i $$0.0633208\pi$$
$$200$$ 0 0
$$201$$ 19.5000 33.7750i 1.37542 2.38230i
$$202$$ 0 0
$$203$$ 15.0000i 1.05279i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 42.0000i 2.91920i
$$208$$ 0 0
$$209$$ −3.00000 −0.207514
$$210$$ 0 0
$$211$$ 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i $$-0.111609\pi$$
−0.767049 + 0.641588i $$0.778276\pi$$
$$212$$ 0 0
$$213$$ 9.00000i 0.616670i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 10.3923 + 6.00000i 0.705476 + 0.407307i
$$218$$ 0 0
$$219$$ 21.0000 + 36.3731i 1.41905 + 2.45786i
$$220$$ 0 0
$$221$$ −17.5000 18.1865i −1.17718 1.22336i
$$222$$ 0 0
$$223$$ 19.9186 11.5000i 1.33385 0.770097i 0.347960 0.937509i $$-0.386874\pi$$
0.985887 + 0.167412i $$0.0535411\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0.866025 + 0.500000i 0.0574801 + 0.0331862i 0.528465 0.848955i $$-0.322768\pi$$
−0.470985 + 0.882141i $$0.656101\pi$$
$$228$$ 0 0
$$229$$ −26.0000 −1.71813 −0.859064 0.511868i $$-0.828954\pi$$
−0.859064 + 0.511868i $$0.828954\pi$$
$$230$$ 0 0
$$231$$ 13.5000 + 23.3827i 0.888235 + 1.53847i
$$232$$ 0 0
$$233$$ 18.0000i 1.17922i −0.807688 0.589610i $$-0.799282\pi$$
0.807688 0.589610i $$-0.200718\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 20.7846 12.0000i 1.35011 0.779484i
$$238$$ 0 0
$$239$$ 16.0000 1.03495 0.517477 0.855697i $$-0.326871\pi$$
0.517477 + 0.855697i $$0.326871\pi$$
$$240$$ 0 0
$$241$$ 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −2.59808 + 2.50000i −0.165312 + 0.159071i
$$248$$ 0 0
$$249$$ −18.0000 31.1769i −1.14070 1.97576i
$$250$$ 0 0
$$251$$ −2.50000 + 4.33013i −0.157799 + 0.273315i −0.934075 0.357078i $$-0.883773\pi$$
0.776276 + 0.630393i $$0.217106\pi$$
$$252$$ 0 0
$$253$$ −18.1865 10.5000i −1.14338 0.660129i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −16.4545 + 9.50000i −1.02640 + 0.592594i −0.915952 0.401288i $$-0.868563\pi$$
−0.110450 + 0.993882i $$0.535229\pi$$
$$258$$ 0 0
$$259$$ 9.00000 0.559233
$$260$$ 0 0
$$261$$ −30.0000 −1.85695
$$262$$ 0 0
$$263$$ 6.06218 3.50000i 0.373810 0.215819i −0.301312 0.953526i $$-0.597424\pi$$
0.675122 + 0.737706i $$0.264091\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 18.1865 + 10.5000i 1.11300 + 0.642590i
$$268$$ 0 0
$$269$$ 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i $$-0.804181\pi$$
0.908124 + 0.418701i $$0.137514\pi$$
$$270$$ 0 0
$$271$$ −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i $$-0.920484\pi$$
0.270385 0.962752i $$-0.412849\pi$$
$$272$$ 0 0
$$273$$ 31.1769 + 9.00000i 1.88691 + 0.544705i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 19.9186 + 11.5000i 1.19679 + 0.690968i 0.959839 0.280553i $$-0.0905179\pi$$
0.236953 + 0.971521i $$0.423851\pi$$
$$278$$ 0 0
$$279$$ −12.0000 + 20.7846i −0.718421 + 1.24434i
$$280$$ 0 0
$$281$$ −10.0000 −0.596550 −0.298275 0.954480i $$-0.596411\pi$$
−0.298275 + 0.954480i $$0.596411\pi$$
$$282$$ 0 0
$$283$$ −0.866025 + 0.500000i −0.0514799 + 0.0297219i −0.525519 0.850782i $$-0.676129\pi$$
0.474039 + 0.880504i $$0.342796\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 21.0000i 1.23959i
$$288$$ 0 0
$$289$$ 16.0000 + 27.7128i 0.941176 + 1.63017i
$$290$$ 0 0
$$291$$ 33.0000 1.93449
$$292$$ 0 0
$$293$$ 7.79423 + 4.50000i 0.455344 + 0.262893i 0.710084 0.704117i $$-0.248657\pi$$
−0.254741 + 0.967009i $$0.581990\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −23.3827 + 13.5000i −1.35680 + 0.783349i
$$298$$ 0 0
$$299$$ −24.5000 + 6.06218i −1.41687 + 0.350585i
$$300$$ 0 0
$$301$$ 13.5000 + 23.3827i 0.778127 + 1.34776i
$$302$$ 0 0
$$303$$ 23.3827 + 13.5000i 1.34330 + 0.775555i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 28.0000i 1.59804i 0.601302 + 0.799022i $$0.294649\pi$$
−0.601302 + 0.799022i $$0.705351\pi$$
$$308$$ 0 0
$$309$$ 24.0000 + 41.5692i 1.36531 + 2.36479i
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ 0 0
$$313$$ 6.00000i 0.339140i 0.985518 + 0.169570i $$0.0542379\pi$$
−0.985518 + 0.169570i $$0.945762\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i −0.998421 0.0561656i $$-0.982113\pi$$
0.998421 0.0561656i $$-0.0178875\pi$$
$$318$$ 0 0
$$319$$ −7.50000 + 12.9904i −0.419919 + 0.727322i
$$320$$ 0 0
$$321$$ −4.50000 + 7.79423i −0.251166 + 0.435031i
$$322$$ 0 0
$$323$$ 6.06218 3.50000i 0.337309 0.194745i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 36.3731 21.0000i 2.01144 1.16130i
$$328$$ 0 0
$$329$$ 12.0000 20.7846i 0.661581 1.14589i
$$330$$ 0 0
$$331$$ −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i $$-0.949627\pi$$
0.630232 + 0.776407i $$0.282960\pi$$
$$332$$ 0 0
$$333$$ 18.0000i 0.986394i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 18.0000i 0.980522i −0.871576 0.490261i $$-0.836901\pi$$
0.871576 0.490261i $$-0.163099\pi$$
$$338$$ 0 0
$$339$$ 39.0000 2.11819
$$340$$ 0 0
$$341$$ 6.00000 + 10.3923i 0.324918 + 0.562775i
$$342$$ 0 0
$$343$$ 15.0000i 0.809924i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 11.2583 + 6.50000i 0.604379 + 0.348938i 0.770762 0.637123i $$-0.219876\pi$$
−0.166383 + 0.986061i $$0.553209\pi$$
$$348$$ 0 0
$$349$$ −12.5000 21.6506i −0.669110 1.15893i −0.978153 0.207884i $$-0.933342\pi$$
0.309044 0.951048i $$-0.399991\pi$$
$$350$$ 0 0
$$351$$ −9.00000 + 31.1769i −0.480384 + 1.66410i
$$352$$ 0 0
$$353$$ −18.1865 + 10.5000i −0.967972 + 0.558859i −0.898617 0.438733i $$-0.855427\pi$$
−0.0693543 + 0.997592i $$0.522094\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −54.5596 31.5000i −2.88760 1.66716i
$$358$$ 0 0
$$359$$ 8.00000 0.422224 0.211112 0.977462i $$-0.432292\pi$$
0.211112 + 0.977462i $$0.432292\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ 6.00000i 0.314918i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 7.79423 4.50000i 0.406855 0.234898i −0.282582 0.959243i $$-0.591191\pi$$
0.689438 + 0.724345i $$0.257858\pi$$
$$368$$ 0 0
$$369$$ −42.0000 −2.18643
$$370$$ 0 0
$$371$$ 9.00000 15.5885i 0.467257 0.809312i
$$372$$ 0 0
$$373$$ −23.3827 13.5000i −1.21071 0.699004i −0.247796 0.968812i $$-0.579706\pi$$
−0.962914 + 0.269809i $$0.913039\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 4.33013 + 17.5000i 0.223013 + 0.901296i
$$378$$ 0 0
$$379$$ −4.50000 7.79423i −0.231149 0.400363i 0.726997 0.686640i $$-0.240915\pi$$
−0.958147 + 0.286278i $$0.907582\pi$$
$$380$$ 0 0
$$381$$ 1.50000 2.59808i 0.0768473 0.133103i
$$382$$ 0 0
$$383$$ −11.2583 6.50000i −0.575274 0.332134i 0.183979 0.982930i $$-0.441102\pi$$
−0.759253 + 0.650796i $$0.774435\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −46.7654 + 27.0000i −2.37722 + 1.37249i
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 49.0000 2.47804
$$392$$ 0 0
$$393$$ 10.3923 6.00000i 0.524222 0.302660i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −28.5788 16.5000i −1.43433 0.828111i −0.436884 0.899518i $$-0.643918\pi$$
−0.997447 + 0.0714068i $$0.977251\pi$$
$$398$$ 0 0
$$399$$ −4.50000 + 7.79423i −0.225282 + 0.390199i
$$400$$ 0 0
$$401$$ −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i $$-0.288863\pi$$
−0.990257 + 0.139253i $$0.955530\pi$$
$$402$$ 0 0
$$403$$ 13.8564 + 4.00000i 0.690237 + 0.199254i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 7.79423 + 4.50000i 0.386346 + 0.223057i
$$408$$ 0 0
$$409$$ −0.500000 + 0.866025i −0.0247234 + 0.0428222i −0.878122 0.478436i $$-0.841204\pi$$
0.853399 + 0.521258i $$0.174537\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ −12.9904 + 7.50000i −0.639215 + 0.369051i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 39.0000i 1.90984i
$$418$$ 0 0
$$419$$ −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i $$-0.868253\pi$$
0.109483 0.993989i $$-0.465080\pi$$
$$420$$ 0 0
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 0 0
$$423$$ 41.5692 + 24.0000i 2.02116 + 1.16692i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −12.9904 + 7.50000i −0.628649 + 0.362950i
$$428$$ 0 0
$$429$$ 22.5000 + 23.3827i 1.08631 + 1.12893i
$$430$$ 0 0
$$431$$ 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i $$-0.0971186\pi$$
−0.737057 + 0.675830i $$0.763785\pi$$
$$432$$ 0 0
$$433$$ 0.866025 + 0.500000i 0.0416185 + 0.0240285i 0.520665 0.853761i $$-0.325684\pi$$
−0.479046 + 0.877790i $$0.659017\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 7.00000i 0.334855i
$$438$$ 0 0
$$439$$ 1.50000 + 2.59808i 0.0715911 + 0.123999i 0.899599 0.436717i $$-0.143859\pi$$
−0.828008 + 0.560717i $$0.810526\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ 24.0000i 1.14027i −0.821549 0.570137i $$-0.806890\pi$$
0.821549 0.570137i $$-0.193110\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 9.00000i 0.425685i
$$448$$ 0 0
$$449$$ −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i $$-0.998358\pi$$
0.504461 + 0.863434i $$0.331691\pi$$
$$450$$ 0 0
$$451$$ −10.5000 + 18.1865i −0.494426 + 0.856370i
$$452$$ 0 0
$$453$$ −20.7846 + 12.0000i −0.976546 + 0.563809i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −19.9186 + 11.5000i −0.931752 + 0.537947i −0.887365 0.461067i $$-0.847467\pi$$
−0.0443868 + 0.999014i $$0.514133\pi$$
$$458$$ 0 0
$$459$$ 31.5000 54.5596i 1.47029 2.54662i
$$460$$ 0 0
$$461$$ −5.50000 + 9.52628i −0.256161 + 0.443683i −0.965210 0.261476i $$-0.915791\pi$$
0.709050 + 0.705159i $$0.249124\pi$$
$$462$$ 0 0
$$463$$ 28.0000i 1.30127i 0.759390 + 0.650635i $$0.225497\pi$$
−0.759390 + 0.650635i $$0.774503\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 20.0000i 0.925490i 0.886492 + 0.462745i $$0.153135\pi$$
−0.886492 + 0.462745i $$0.846865\pi$$
$$468$$ 0 0
$$469$$ −39.0000 −1.80085
$$470$$ 0 0
$$471$$ 9.00000 + 15.5885i 0.414698 + 0.718278i
$$472$$ 0 0
$$473$$ 27.0000i 1.24146i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 31.1769 + 18.0000i 1.42749 + 0.824163i
$$478$$ 0 0
$$479$$ −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i $$-0.173939\pi$$
−0.877222 + 0.480085i $$0.840606\pi$$
$$480$$ 0 0
$$481$$ 10.5000 2.59808i 0.478759 0.118462i
$$482$$ 0 0
$$483$$ −54.5596 + 31.5000i −2.48255 + 1.43330i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 14.7224 + 8.50000i 0.667137 + 0.385172i 0.794991 0.606621i $$-0.207476\pi$$
−0.127854 + 0.991793i $$0.540809\pi$$
$$488$$ 0 0
$$489$$ 33.0000 1.49231
$$490$$ 0 0
$$491$$ −11.5000 19.9186i −0.518988 0.898913i −0.999757 0.0220657i $$-0.992976\pi$$
0.480769 0.876847i $$-0.340358\pi$$
$$492$$ 0 0
$$493$$ 35.0000i 1.57632i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −7.79423 + 4.50000i −0.349619 + 0.201853i
$$498$$ 0 0
$$499$$ 16.0000 0.716258 0.358129 0.933672i $$-0.383415\pi$$
0.358129 + 0.933672i $$0.383415\pi$$
$$500$$ 0 0
$$501$$ 1.50000 2.59808i 0.0670151 0.116073i
$$502$$ 0 0
$$503$$ 9.52628 + 5.50000i 0.424756 + 0.245233i 0.697110 0.716964i $$-0.254469\pi$$
−0.272354 + 0.962197i $$0.587802\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 38.9711 + 1.50000i 1.73077 + 0.0666173i
$$508$$ 0 0
$$509$$ 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i $$-0.0587976\pi$$
−0.650556 + 0.759458i $$0.725464\pi$$
$$510$$ 0 0
$$511$$ 21.0000 36.3731i 0.928985 1.60905i
$$512$$ 0 0
$$513$$ −7.79423 4.50000i −0.344124 0.198680i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 20.7846 12.0000i 0.914106 0.527759i
$$518$$ 0 0
$$519$$ −45.0000 −1.97528
$$520$$ 0 0
$$521$$ −34.0000 −1.48957 −0.744784 0.667306i $$-0.767447\pi$$
−0.744784 + 0.667306i $$0.767447\pi$$
$$522$$ 0 0
$$523$$ 19.9186 11.5000i 0.870979 0.502860i 0.00330547 0.999995i $$-0.498948\pi$$
0.867673 + 0.497135i $$0.165615\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −24.2487 14.0000i −1.05629 0.609850i
$$528$$ 0 0
$$529$$ 13.0000 22.5167i 0.565217 0.978985i
$$530$$ 0 0
$$531$$ −15.0000 25.9808i −0.650945 1.12747i
$$532$$ 0 0
$$533$$ 6.06218 + 24.5000i 0.262582 + 1.06121i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 49.3634 + 28.5000i 2.13019 + 1.22987i
$$538$$ 0 0
$$539$$ 3.00000 5.19615i 0.129219 0.223814i
$$540$$ 0 0
$$541$$ 10.0000 0.429934 0.214967 0.976621i $$-0.431036\pi$$
0.214967 + 0.976621i $$0.431036\pi$$
$$542$$ 0 0
$$543$$ −36.3731 + 21.0000i −1.56092 + 0.901196i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 16.0000i 0.684111i −0.939680 0.342055i $$-0.888877\pi$$
0.939680 0.342055i $$-0.111123\pi$$
$$548$$ 0 0
$$549$$ −15.0000 25.9808i −0.640184 1.10883i
$$550$$ 0 0
$$551$$ −5.00000 −0.213007
$$552$$ 0 0
$$553$$ −20.7846 12.0000i −0.883852 0.510292i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −16.4545 + 9.50000i −0.697199 + 0.402528i −0.806303 0.591502i $$-0.798535\pi$$
0.109104 + 0.994030i $$0.465202\pi$$
$$558$$ 0 0
$$559$$ 22.5000 + 23.3827i 0.951649 + 0.988982i
$$560$$ 0 0
$$561$$ −31.5000 54.5596i −1.32993 2.30351i
$$562$$ 0 0
$$563$$ −38.9711 22.5000i −1.64244 0.948262i −0.979963 0.199177i $$-0.936173\pi$$
−0.662474 0.749085i $$-0.730494\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 27.0000i 1.13389i
$$568$$ 0 0
$$569$$ 9.50000 + 16.4545i 0.398261 + 0.689808i 0.993511 0.113732i $$-0.0362806\pi$$
−0.595251 + 0.803540i $$0.702947\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 9.00000i 0.375980i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 2.00000i 0.0832611i 0.999133 + 0.0416305i $$0.0132552\pi$$
−0.999133 + 0.0416305i $$0.986745\pi$$
$$578$$ 0 0
$$579$$ 22.5000 38.9711i 0.935068 1.61959i
$$580$$ 0 0
$$581$$ −18.0000 + 31.1769i −0.746766 + 1.29344i
$$582$$ 0 0
$$583$$ 15.5885 9.00000i 0.645608 0.372742i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 32.0429 18.5000i 1.32255 0.763577i 0.338418 0.940996i $$-0.390108\pi$$
0.984135 + 0.177419i $$0.0567748\pi$$
$$588$$ 0 0
$$589$$ −2.00000 + 3.46410i −0.0824086 + 0.142736i
$$590$$ 0 0
$$591$$ −34.5000 + 59.7558i −1.41914 + 2.45802i
$$592$$ 0 0
$$593$$ 26.0000i 1.06769i −0.845582 0.533846i $$-0.820746\pi$$
0.845582 0.533846i $$-0.179254\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 27.0000i 1.10504i
$$598$$ 0 0
$$599$$ −8.00000 −0.326871 −0.163436 0.986554i $$-0.552258\pi$$
−0.163436 + 0.986554i $$0.552258\pi$$
$$600$$ 0 0
$$601$$ 6.50000 + 11.2583i 0.265141 + 0.459237i 0.967600 0.252486i $$-0.0812483\pi$$
−0.702460 + 0.711723i $$0.747915\pi$$
$$602$$ 0 0
$$603$$ 78.0000i 3.17641i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 7.79423 + 4.50000i 0.316358 + 0.182649i 0.649768 0.760133i $$-0.274866\pi$$
−0.333410 + 0.942782i $$0.608199\pi$$
$$608$$ 0 0
$$609$$ 22.5000 + 38.9711i 0.911746 + 1.57919i
$$610$$ 0 0
$$611$$ 8.00000 27.7128i 0.323645 1.12114i
$$612$$ 0 0
$$613$$ 26.8468 15.5000i 1.08433 0.626039i 0.152270 0.988339i $$-0.451342\pi$$
0.932062 + 0.362300i $$0.118008\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −25.1147 14.5000i −1.01108 0.583748i −0.0995732 0.995030i $$-0.531748\pi$$
−0.911508 + 0.411282i $$0.865081\pi$$
$$618$$ 0 0
$$619$$ −12.0000 −0.482321 −0.241160 0.970485i $$-0.577528\pi$$
−0.241160 + 0.970485i $$0.577528\pi$$
$$620$$ 0 0
$$621$$ −31.5000 54.5596i −1.26405 2.18940i
$$622$$ 0 0
$$623$$ 21.0000i 0.841347i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −7.79423 + 4.50000i −0.311272 + 0.179713i
$$628$$ 0 0
$$629$$ −21.0000 −0.837325
$$630$$ 0 0
$$631$$ 7.50000 12.9904i 0.298570 0.517139i −0.677239 0.735763i $$-0.736824\pi$$
0.975809 + 0.218624i $$0.0701569\pi$$
$$632$$ 0 0
$$633$$ 12.9904 + 7.50000i 0.516321 + 0.298098i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −1.73205 7.00000i −0.0686264 0.277350i
$$638$$ 0 0
$$639$$ −9.00000 15.5885i −0.356034 0.616670i
$$640$$ 0 0
$$641$$ 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i $$-0.697211\pi$$
0.995400 + 0.0958109i $$0.0305444\pi$$
$$642$$ 0 0
$$643$$ 6.06218 + 3.50000i 0.239069 + 0.138027i 0.614749 0.788723i $$-0.289257\pi$$
−0.375680 + 0.926750i $$0.622591\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 14.7224 8.50000i 0.578799 0.334169i −0.181857 0.983325i $$-0.558211\pi$$
0.760656 + 0.649155i $$0.224878\pi$$
$$648$$ 0 0
$$649$$ −15.0000 −0.588802
$$650$$ 0 0
$$651$$ 36.0000 1.41095
$$652$$ 0 0
$$653$$ 9.52628 5.50000i 0.372792 0.215232i −0.301885 0.953344i $$-0.597616\pi$$
0.674678 + 0.738113i $$0.264283\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 72.7461 + 42.0000i 2.83810 + 1.63858i
$$658$$ 0 0
$$659$$ −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i $$-0.927707\pi$$
0.682161 + 0.731202i $$0.261040\pi$$
$$660$$ 0 0
$$661$$ 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i $$-0.0594116\pi$$
−0.652020 + 0.758202i $$0.726078\pi$$
$$662$$ 0 0
$$663$$ −72.7461 21.0000i −2.82523 0.815572i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −30.3109 17.5000i −1.17364 0.677603i
$$668$$ 0 0
$$669$$ 34.5000 59.7558i 1.33385 2.31029i
$$670$$ 0 0
$$671$$ −15.0000 −0.579069
$$672$$ 0 0
$$673$$ −11.2583 + 6.50000i −0.433977 + 0.250557i −0.701039 0.713123i $$-0.747280\pi$$
0.267063 + 0.963679i $$0.413947\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 22.0000i 0.845529i 0.906240 + 0.422764i $$0.138940\pi$$
−0.906240 + 0.422764i $$0.861060\pi$$
$$678$$ 0 0
$$679$$ −16.5000 28.5788i −0.633212 1.09676i
$$680$$ 0 0
$$681$$ 3.00000 0.114960
$$682$$ 0 0
$$683$$ 26.8468 + 15.5000i 1.02726 + 0.593091i 0.916200 0.400722i $$-0.131241\pi$$
0.111064 + 0.993813i $$0.464574\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −67.5500 + 39.0000i −2.57719 + 1.48794i
$$688$$ 0 0
$$689$$ 6.00000 20.7846i 0.228582 0.791831i
$$690$$ 0 0
$$691$$ 12.5000 + 21.6506i 0.475522 + 0.823629i 0.999607 0.0280373i $$-0.00892572\pi$$
−0.524084 + 0.851666i $$0.675592\pi$$
$$692$$ 0 0
$$693$$ 46.7654 + 27.0000i 1.77647 + 1.02565i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 49.0000i 1.85601i
$$698$$ 0 0
$$699$$ −27.0000 46.7654i −1.02123 1.76883i
$$700$$ 0 0
$$701$$ 2.00000 0.0755390 0.0377695 0.999286i $$-0.487975\pi$$
0.0377695 + 0.999286i $$0.487975\pi$$
$$702$$ 0 0
$$703$$ 3.00000i 0.113147i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.0000i 1.01544i
$$708$$ 0 0
$$709$$ 17.5000 30.3109i 0.657226 1.13835i −0.324104 0.946021i $$-0.605063\pi$$
0.981331 0.192328i $$-0.0616038\pi$$
$$710$$ 0 0
$$711$$ 24.0000 41.5692i 0.900070 1.55897i
$$712$$ 0 0
$$713$$ −24.2487 + 14.0000i −0.908121 + 0.524304i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 41.5692 24.0000i 1.55243 0.896296i
$$718$$ 0 0
$$719$$ 0.500000 0.866025i 0.0186469 0.0322973i −0.856551 0.516062i $$-0.827398\pi$$
0.875198 + 0.483764i $$0.160731\pi$$
$$720$$ 0 0
$$721$$ 24.0000 41.5692i 0.893807 1.54812i
$$722$$ 0 0
$$723$$ 3.00000i 0.111571i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 28.0000i 1.03846i −0.854634 0.519231i $$-0.826218\pi$$
0.854634 0.519231i $$-0.173782\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ −31.5000 54.5596i −1.16507 2.01796i
$$732$$ 0 0
$$733$$ 14.0000i 0.517102i −0.965998 0.258551i $$-0.916755\pi$$
0.965998 0.258551i $$-0.0832450\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −33.7750 19.5000i −1.24412 0.718292i
$$738$$ 0 0
$$739$$ 19.5000 + 33.7750i 0.717319 + 1.24243i 0.962058 + 0.272844i $$0.0879643\pi$$
−0.244739 + 0.969589i $$0.578702\pi$$
$$740$$ 0 0
$$741$$ −3.00000 + 10.3923i −0.110208 + 0.381771i
$$742$$ 0 0
$$743$$ −0.866025 + 0.500000i −0.0317714 + 0.0183432i −0.515802 0.856708i $$-0.672506\pi$$
0.484030 + 0.875051i $$0.339172\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −62.3538 36.0000i −2.28141 1.31717i
$$748$$ 0 0
$$749$$ 9.00000 0.328853
$$750$$ 0 0
$$751$$ 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i $$-0.0904408\pi$$
−0.722718 + 0.691143i $$0.757107\pi$$
$$752$$ 0 0
$$753$$ 15.0000i 0.546630i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0.866025 0.500000i 0.0314762 0.0181728i −0.484179 0.874969i $$-0.660882\pi$$
0.515656 + 0.856796i $$0.327548\pi$$
$$758$$ 0 0
$$759$$ −63.0000 −2.28676
$$760$$ 0 0
$$761$$ −25.5000 + 44.1673i −0.924374 + 1.60106i −0.131810 + 0.991275i $$0.542079\pi$$
−0.792564 + 0.609788i $$0.791255\pi$$
$$762$$ 0 0
$$763$$ −36.3731 21.0000i −1.31679 0.760251i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −12.9904 + 12.5000i −0.469055 + 0.451349i
$$768$$ 0 0
$$769$$ −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i $$-0.195402\pi$$
−0.907575 + 0.419890i $$0.862069\pi$$
$$770$$ 0 0
$$771$$ −28.5000 + 49.3634i −1.02640 + 1.77778i
$$772$$ 0 0
$$773$$ 21.6506 + 12.5000i 0.778719 + 0.449594i 0.835976 0.548766i $$-0.184902\pi$$
−0.0572570 + 0.998359i $$0.518235\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 23.3827 13.5000i 0.838849 0.484310i
$$778$$ 0 0
$$779$$ −7.00000 −0.250801
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ −38.9711 + 22.5000i −1.39272 + 0.804084i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0.866025 + 0.500000i 0.0308705 + 0.0178231i 0.515356 0.856976i $$-0.327660\pi$$
−0.484485 + 0.874799i $$0.660993\pi$$
$$788$$ 0 0
$$789$$ 10.5000 18.1865i 0.373810 0.647458i
$$790$$ 0 0
$$791$$ −19.5000 33.7750i −0.693340 1.20090i
$$792$$ 0 0
$$793$$ −12.9904 + 12.5000i −0.461302 + 0.443888i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 6.06218 + 3.50000i 0.214733 + 0.123976i 0.603509 0.797356i $$-0.293769\pi$$
−0.388776 + 0.921332i $$0.627102\pi$$
$$798$$ 0 0
$$799$$ −28.0000 +