Properties

 Label 1300.2.i.a.601.1 Level $1300$ Weight $2$ Character 1300.601 Analytic conductor $10.381$ Analytic rank $1$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1300 = 2^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1300.i (of order $$3$$, degree $$2$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$10.3805522628$$ Analytic rank: $$1$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 260) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 601.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1300.601 Dual form 1300.2.i.a.1101.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.50000 - 2.59808i) q^{3} +(1.50000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$$ $$q+(-1.50000 - 2.59808i) q^{3} +(1.50000 - 2.59808i) q^{7} +(-3.00000 + 5.19615i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 + 0.866025i) q^{19} -9.00000 q^{21} +(-3.50000 - 6.06218i) q^{23} +9.00000 q^{27} +(2.50000 + 4.33013i) q^{29} -4.00000 q^{31} +(-4.50000 + 7.79423i) q^{33} +(-1.50000 - 2.59808i) q^{37} +(10.5000 - 2.59808i) q^{39} +(-3.50000 - 6.06218i) q^{41} +(-4.50000 + 7.79423i) q^{43} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +21.0000 q^{51} +6.00000 q^{53} +3.00000 q^{57} +(-2.50000 + 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(9.00000 + 15.5885i) q^{63} +(6.50000 + 11.2583i) q^{67} +(-10.5000 + 18.1865i) q^{69} +(1.50000 - 2.59808i) q^{71} +14.0000 q^{73} -9.00000 q^{77} -8.00000 q^{79} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{83} +(7.50000 - 12.9904i) q^{87} +(-3.50000 - 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(6.00000 + 10.3923i) q^{93} +(-5.50000 + 9.52628i) q^{97} +18.0000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 3 q^{3} + 3 q^{7} - 6 q^{9} + O(q^{10})$$ $$2 q - 3 q^{3} + 3 q^{7} - 6 q^{9} - 3 q^{11} - 2 q^{13} - 7 q^{17} - q^{19} - 18 q^{21} - 7 q^{23} + 18 q^{27} + 5 q^{29} - 8 q^{31} - 9 q^{33} - 3 q^{37} + 21 q^{39} - 7 q^{41} - 9 q^{43} - 16 q^{47} - 2 q^{49} + 42 q^{51} + 12 q^{53} + 6 q^{57} - 5 q^{59} + 5 q^{61} + 18 q^{63} + 13 q^{67} - 21 q^{69} + 3 q^{71} + 28 q^{73} - 18 q^{77} - 16 q^{79} - 9 q^{81} - 24 q^{83} + 15 q^{87} - 7 q^{89} + 15 q^{91} + 12 q^{93} - 11 q^{97} + 36 q^{99} + O(q^{100})$$

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
$$3$$ −1.50000 2.59808i −0.866025 1.50000i −0.866025 0.500000i $$-0.833333\pi$$
1.00000i $$-0.5\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i $$-0.641458\pi$$
0.996866 0.0791130i $$-0.0252088\pi$$
$$8$$ 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
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i $$0.489386\pi$$
−0.882213 + 0.470850i $$0.843947\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0 0
$$21$$ −9.00000 −1.96396
$$22$$ 0 0
$$23$$ −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i $$-0.906280\pi$$
0.227167 0.973856i $$-0.427054\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 9.00000 1.73205
$$28$$ 0 0
$$29$$ 2.50000 + 4.33013i 0.464238 + 0.804084i 0.999167 0.0408130i $$-0.0129948\pi$$
−0.534928 + 0.844897i $$0.679661\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ −4.50000 + 7.79423i −0.783349 + 1.35680i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i $$-0.245980\pi$$
−0.962580 + 0.270998i $$0.912646\pi$$
$$38$$ 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
$$43$$ −4.50000 + 7.79423i −0.686244 + 1.18861i 0.286801 + 0.957990i $$0.407408\pi$$
−0.973044 + 0.230618i $$0.925925\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −8.00000 −1.16692 −0.583460 0.812142i $$-0.698301\pi$$
−0.583460 + 0.812142i $$0.698301\pi$$
$$48$$ 0 0
$$49$$ −1.00000 1.73205i −0.142857 0.247436i
$$50$$ 0 0
$$51$$ 21.0000 2.94059
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.00000 0.397360
$$58$$ 0 0
$$59$$ −2.50000 + 4.33013i −0.325472 + 0.563735i −0.981608 0.190909i $$-0.938857\pi$$
0.656136 + 0.754643i $$0.272190\pi$$
$$60$$ 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
$$63$$ 9.00000 + 15.5885i 1.13389 + 1.96396i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i $$0.125391\pi$$
−0.129307 + 0.991605i $$0.541275\pi$$
$$68$$ 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
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −9.00000 −1.02565
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ −4.50000 7.79423i −0.500000 0.866025i
$$82$$ 0 0
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 7.50000 12.9904i 0.804084 1.39272i
$$88$$ 0 0
$$89$$ −3.50000 6.06218i −0.370999 0.642590i 0.618720 0.785611i $$-0.287651\pi$$
−0.989720 + 0.143022i $$0.954318\pi$$
$$90$$ 0 0
$$91$$ 7.50000 + 7.79423i 0.786214 + 0.817057i
$$92$$ 0 0
$$93$$ 6.00000 + 10.3923i 0.622171 + 1.07763i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −5.50000 + 9.52628i −0.558440 + 0.967247i 0.439187 + 0.898396i $$0.355267\pi$$
−0.997627 + 0.0688512i $$0.978067\pi$$
$$98$$ 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
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i $$-0.212988\pi$$
−0.929377 + 0.369132i $$0.879655\pi$$
$$108$$ 0 0
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ −4.50000 + 7.79423i −0.427121 + 0.739795i
$$112$$ 0 0
$$113$$ 6.50000 11.2583i 0.611469 1.05909i −0.379525 0.925182i $$-0.623912\pi$$
0.990993 0.133913i $$-0.0427543\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −15.0000 15.5885i −1.38675 1.44115i
$$118$$ 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
$$123$$ −10.5000 + 18.1865i −0.946753 + 1.63982i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0.500000 + 0.866025i 0.0443678 + 0.0768473i 0.887357 0.461084i $$-0.152539\pi$$
−0.842989 + 0.537931i $$0.819206\pi$$
$$128$$ 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
$$133$$ 1.50000 + 2.59808i 0.130066 + 0.225282i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i $$-0.874238\pi$$
0.794808 + 0.606861i $$0.207572\pi$$
$$138$$ 0 0
$$139$$ −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i $$0.352543\pi$$
−0.998179 + 0.0603135i $$0.980790\pi$$
$$140$$ 0 0
$$141$$ 12.0000 + 20.7846i 1.01058 + 1.75038i
$$142$$ 0 0
$$143$$ 10.5000 2.59808i 0.878054 0.217262i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −3.00000 + 5.19615i −0.247436 + 0.428571i
$$148$$ 0 0
$$149$$ −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i $$-0.872548\pi$$
0.798019 + 0.602632i $$0.205881\pi$$
$$150$$ 0 0
$$151$$ −8.00000 −0.651031 −0.325515 0.945537i $$-0.605538\pi$$
−0.325515 + 0.945537i $$0.605538\pi$$
$$152$$ 0 0
$$153$$ −21.0000 36.3731i −1.69775 2.94059i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −6.00000 −0.478852 −0.239426 0.970915i $$-0.576959\pi$$
−0.239426 + 0.970915i $$0.576959\pi$$
$$158$$ 0 0
$$159$$ −9.00000 15.5885i −0.713746 1.23625i
$$160$$ 0 0
$$161$$ −21.0000 −1.65503
$$162$$ 0 0
$$163$$ 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i $$-0.691567\pi$$
0.996942 + 0.0781474i $$0.0249005\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0.500000 + 0.866025i 0.0386912 + 0.0670151i 0.884723 0.466118i $$-0.154348\pi$$
−0.846031 + 0.533133i $$0.821014\pi$$
$$168$$ 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
$$173$$ −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i $$0.359807\pi$$
−0.996544 + 0.0830722i $$0.973527\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 15.0000 1.12747
$$178$$ 0 0
$$179$$ −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i $$-0.915333\pi$$
0.254770 0.967002i $$-0.418000\pi$$
$$180$$ 0 0
$$181$$ −14.0000 −1.04061 −0.520306 0.853980i $$-0.674182\pi$$
−0.520306 + 0.853980i $$0.674182\pi$$
$$182$$ 0 0
$$183$$ −15.0000 −1.10883
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 21.0000 1.53567
$$188$$ 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
$$193$$ −7.50000 12.9904i −0.539862 0.935068i −0.998911 0.0466572i $$-0.985143\pi$$
0.459049 0.888411i $$-0.348190\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −11.5000 19.9186i −0.819341 1.41914i −0.906168 0.422917i $$-0.861006\pi$$
0.0868274 0.996223i $$-0.472327\pi$$
$$198$$ 0 0
$$199$$ −4.50000 + 7.79423i −0.318997 + 0.552518i −0.980279 0.197619i $$-0.936679\pi$$
0.661282 + 0.750137i $$0.270013\pi$$
$$200$$ 0 0
$$201$$ 19.5000 33.7750i 1.37542 2.38230i
$$202$$ 0 0
$$203$$ 15.0000 1.05279
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 42.0000 2.91920
$$208$$ 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
$$213$$ −9.00000 −0.616670
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −6.00000 + 10.3923i −0.407307 + 0.705476i
$$218$$ 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
$$223$$ −11.5000 19.9186i −0.770097 1.33385i −0.937509 0.347960i $$-0.886874\pi$$
0.167412 0.985887i $$-0.446459\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −0.500000 + 0.866025i −0.0331862 + 0.0574801i −0.882141 0.470985i $$-0.843899\pi$$
0.848955 + 0.528465i $$0.177232\pi$$
$$228$$ 0 0
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ 0 0
$$231$$ 13.5000 + 23.3827i 0.888235 + 1.53847i
$$232$$ 0 0
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 12.0000 + 20.7846i 0.779484 + 1.35011i
$$238$$ 0 0
$$239$$ −16.0000 −1.03495 −0.517477 0.855697i $$-0.673129\pi$$
−0.517477 + 0.855697i $$0.673129\pi$$
$$240$$ 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
$$247$$ −2.50000 2.59808i −0.159071 0.165312i
$$248$$ 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
$$253$$ −10.5000 + 18.1865i −0.660129 + 1.14338i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −9.50000 16.4545i −0.592594 1.02640i −0.993882 0.110450i $$-0.964771\pi$$
0.401288 0.915952i $$-0.368563\pi$$
$$258$$ 0 0
$$259$$ −9.00000 −0.559233
$$260$$ 0 0
$$261$$ −30.0000 −1.85695
$$262$$ 0 0
$$263$$ −3.50000 6.06218i −0.215819 0.373810i 0.737706 0.675122i $$-0.235909\pi$$
−0.953526 + 0.301312i $$0.902576\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −10.5000 + 18.1865i −0.642590 + 1.11300i
$$268$$ 0 0
$$269$$ −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i $$-0.862486\pi$$
0.816668 + 0.577108i $$0.195819\pi$$
$$270$$ 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
$$273$$ 9.00000 31.1769i 0.544705 1.88691i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i $$0.409482\pi$$
−0.971521 + 0.236953i $$0.923851\pi$$
$$278$$ 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
$$283$$ 0.500000 + 0.866025i 0.0297219 + 0.0514799i 0.880504 0.474039i $$-0.157204\pi$$
−0.850782 + 0.525519i $$0.823871\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −21.0000 −1.23959
$$288$$ 0 0
$$289$$ −16.0000 27.7128i −0.941176 1.63017i
$$290$$ 0 0
$$291$$ 33.0000 1.93449
$$292$$ 0 0
$$293$$ 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i $$-0.748657\pi$$
0.967009 + 0.254741i $$0.0819901\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −13.5000 23.3827i −0.783349 1.35680i
$$298$$ 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
$$303$$ 13.5000 23.3827i 0.775555 1.34330i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 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
$$313$$ 6.00000 0.339140 0.169570 0.985518i $$-0.445762\pi$$
0.169570 + 0.985518i $$0.445762\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 2.00000 0.112331 0.0561656 0.998421i $$-0.482113\pi$$
0.0561656 + 0.998421i $$0.482113\pi$$
$$318$$ 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
$$323$$ −3.50000 6.06218i −0.194745 0.337309i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 21.0000 + 36.3731i 1.16130 + 2.01144i
$$328$$ 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
$$333$$ 18.0000 0.986394
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 18.0000 0.980522 0.490261 0.871576i $$-0.336901\pi$$
0.490261 + 0.871576i $$0.336901\pi$$
$$338$$ 0 0
$$339$$ −39.0000 −2.11819
$$340$$ 0 0
$$341$$ 6.00000 + 10.3923i 0.324918 + 0.562775i
$$342$$ 0 0
$$343$$ 15.0000 0.809924
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.50000 + 11.2583i −0.348938 + 0.604379i −0.986061 0.166383i $$-0.946791\pi$$
0.637123 + 0.770762i $$0.280124\pi$$
$$348$$ 0 0
$$349$$ 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i $$0.0666577\pi$$
−0.309044 + 0.951048i $$0.600009\pi$$
$$350$$ 0 0
$$351$$ −9.00000 + 31.1769i −0.480384 + 1.66410i
$$352$$ 0 0
$$353$$ 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i $$0.0220939\pi$$
−0.438733 + 0.898617i $$0.644573\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 31.5000 54.5596i 1.66716 2.88760i
$$358$$ 0 0
$$359$$ −8.00000 −0.422224 −0.211112 0.977462i $$-0.567708\pi$$
−0.211112 + 0.977462i $$0.567708\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ −6.00000 −0.314918
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.50000 + 7.79423i 0.234898 + 0.406855i 0.959243 0.282582i $$-0.0911910\pi$$
−0.724345 + 0.689438i $$0.757858\pi$$
$$368$$ 0 0
$$369$$ 42.0000 2.18643
$$370$$ 0 0
$$371$$ 9.00000 15.5885i 0.467257 0.809312i
$$372$$ 0 0
$$373$$ −13.5000 + 23.3827i −0.699004 + 1.21071i 0.269809 + 0.962914i $$0.413039\pi$$
−0.968812 + 0.247796i $$0.920294\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −17.5000 + 4.33013i −0.901296 + 0.223013i
$$378$$ 0 0
$$379$$ 4.50000 + 7.79423i 0.231149 + 0.400363i 0.958147 0.286278i $$-0.0924180\pi$$
−0.726997 + 0.686640i $$0.759085\pi$$
$$380$$ 0 0
$$381$$ 1.50000 2.59808i 0.0768473 0.133103i
$$382$$ 0 0
$$383$$ −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i $$-0.941102\pi$$
0.650796 + 0.759253i $$0.274435\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −27.0000 46.7654i −1.37249 2.37722i
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ 49.0000 2.47804
$$392$$ 0 0
$$393$$ −6.00000 10.3923i −0.302660 0.524222i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 16.5000 28.5788i 0.828111 1.43433i −0.0714068 0.997447i $$-0.522749\pi$$
0.899518 0.436884i $$-0.143918\pi$$
$$398$$ 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
$$403$$ 4.00000 13.8564i 0.199254 0.690237i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −4.50000 + 7.79423i −0.223057 + 0.386346i
$$408$$ 0 0
$$409$$ 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i $$-0.825463\pi$$
0.878122 + 0.478436i $$0.158796\pi$$
$$410$$ 0 0
$$411$$ 9.00000 0.443937
$$412$$ 0 0
$$413$$ 7.50000 + 12.9904i 0.369051 + 0.639215i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 39.0000 1.90984
$$418$$ 0 0
$$419$$ 16.5000 + 28.5788i 0.806078 + 1.39617i 0.915561 + 0.402179i $$0.131747\pi$$
−0.109483 + 0.993989i $$0.534920\pi$$
$$420$$ 0 0
$$421$$ 34.0000 1.65706 0.828529 0.559946i $$-0.189178\pi$$
0.828529 + 0.559946i $$0.189178\pi$$
$$422$$ 0 0
$$423$$ 24.0000 41.5692i 1.16692 2.02116i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −7.50000 12.9904i −0.362950 0.628649i
$$428$$ 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
$$433$$ 0.500000 0.866025i 0.0240285 0.0416185i −0.853761 0.520665i $$-0.825684\pi$$
0.877790 + 0.479046i $$0.159017\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 7.00000 0.334855
$$438$$ 0 0
$$439$$ −1.50000 2.59808i −0.0715911 0.123999i 0.828008 0.560717i $$-0.189474\pi$$
−0.899599 + 0.436717i $$0.856141\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ −24.0000 −1.14027 −0.570137 0.821549i $$-0.693110\pi$$
−0.570137 + 0.821549i $$0.693110\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 9.00000 0.425685
$$448$$ 0 0
$$449$$ 10.5000 18.1865i 0.495526 0.858276i −0.504461 0.863434i $$-0.668309\pi$$
0.999987 + 0.00515887i $$0.00164213\pi$$
$$450$$ 0 0
$$451$$ −10.5000 + 18.1865i −0.494426 + 0.856370i
$$452$$ 0 0
$$453$$ 12.0000 + 20.7846i 0.563809 + 0.976546i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −11.5000 19.9186i −0.537947 0.931752i −0.999014 0.0443868i $$-0.985867\pi$$
0.461067 0.887365i $$-0.347467\pi$$
$$458$$ 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
$$463$$ 28.0000 1.30127 0.650635 0.759390i $$-0.274503\pi$$
0.650635 + 0.759390i $$0.274503\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −20.0000 −0.925490 −0.462745 0.886492i $$-0.653135\pi$$
−0.462745 + 0.886492i $$0.653135\pi$$
$$468$$ 0 0
$$469$$ 39.0000 1.80085
$$470$$ 0 0
$$471$$ 9.00000 + 15.5885i 0.414698 + 0.718278i
$$472$$ 0 0
$$473$$ 27.0000 1.24146
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −18.0000 + 31.1769i −0.824163 + 1.42749i
$$478$$ 0 0
$$479$$ 0.500000 + 0.866025i 0.0228456 + 0.0395697i 0.877222 0.480085i $$-0.159394\pi$$
−0.854377 + 0.519654i $$0.826061\pi$$
$$480$$ 0 0
$$481$$ 10.5000 2.59808i 0.478759 0.118462i
$$482$$ 0 0
$$483$$ 31.5000 + 54.5596i 1.43330 + 2.48255i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i $$-0.959191\pi$$
0.606621 + 0.794991i $$0.292524\pi$$
$$488$$ 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
$$493$$ −35.0000 −1.57632
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −4.50000 7.79423i −0.201853 0.349619i
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 0 0
$$501$$ 1.50000 2.59808i 0.0670151 0.116073i
$$502$$ 0 0
$$503$$ 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i $$-0.754469\pi$$
0.962197 + 0.272354i $$0.0878022\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −1.50000 + 38.9711i −0.0666173 + 1.73077i
$$508$$ 0 0
$$509$$ −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i $$-0.274536\pi$$
−0.982988 + 0.183669i $$0.941202\pi$$
$$510$$ 0 0
$$511$$ 21.0000 36.3731i 0.928985 1.60905i
$$512$$ 0 0
$$513$$ −4.50000 + 7.79423i −0.198680 + 0.344124i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 12.0000 + 20.7846i 0.527759 + 0.914106i
$$518$$ 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
$$523$$ −11.5000 19.9186i −0.502860 0.870979i −0.999995 0.00330547i $$-0.998948\pi$$
0.497135 0.867673i $$-0.334385\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 14.0000 24.2487i 0.609850 1.05629i
$$528$$ 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
$$533$$ 24.5000 6.06218i 1.06121 0.262582i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −28.5000 + 49.3634i −1.22987 + 2.13019i
$$538$$ 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
$$543$$ 21.0000 + 36.3731i 0.901196 + 1.56092i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 16.0000 0.684111 0.342055 0.939680i $$-0.388877\pi$$
0.342055 + 0.939680i $$0.388877\pi$$
$$548$$ 0 0
$$549$$ 15.0000 + 25.9808i 0.640184 + 1.10883i
$$550$$ 0 0
$$551$$ −5.00000 −0.213007
$$552$$ 0 0
$$553$$ −12.0000 + 20.7846i −0.510292 + 0.883852i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −9.50000 16.4545i −0.402528 0.697199i 0.591502 0.806303i $$-0.298535\pi$$
−0.994030 + 0.109104i $$0.965202\pi$$
$$558$$ 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
$$563$$ −22.5000 + 38.9711i −0.948262 + 1.64244i −0.199177 + 0.979963i $$0.563827\pi$$
−0.749085 + 0.662474i $$0.769506\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −27.0000 −1.13389
$$568$$ 0 0
$$569$$ −9.50000 16.4545i −0.398261 0.689808i 0.595251 0.803540i $$-0.297053\pi$$
−0.993511 + 0.113732i $$0.963719\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ −9.00000 −0.375980
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 0 0
$$579$$ −22.5000 + 38.9711i −0.935068 + 1.61959i
$$580$$ 0 0
$$581$$ −18.0000 + 31.1769i −0.746766 + 1.29344i
$$582$$ 0 0
$$583$$ −9.00000 15.5885i −0.372742 0.645608i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i $$0.109892\pi$$
−0.177419 + 0.984135i $$0.556775\pi$$
$$588$$ 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
$$593$$ −26.0000 −1.06769 −0.533846 0.845582i $$-0.679254\pi$$
−0.533846 + 0.845582i $$0.679254\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 27.0000 1.10504
$$598$$ 0 0
$$599$$ 8.00000 0.326871 0.163436 0.986554i $$-0.447742\pi$$
0.163436 + 0.986554i $$0.447742\pi$$
$$600$$ 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
$$603$$ −78.0000 −3.17641
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −4.50000 + 7.79423i −0.182649 + 0.316358i −0.942782 0.333410i $$-0.891801\pi$$
0.760133 + 0.649768i $$0.225134\pi$$
$$608$$ 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
$$613$$ −15.5000 26.8468i −0.626039 1.08433i −0.988339 0.152270i $$-0.951342\pi$$
0.362300 0.932062i $$-0.381992\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 14.5000 25.1147i 0.583748 1.01108i −0.411282 0.911508i $$-0.634919\pi$$
0.995030 0.0995732i $$-0.0317477\pi$$
$$618$$ 0 0
$$619$$ 12.0000 0.482321 0.241160 0.970485i $$-0.422472\pi$$
0.241160 + 0.970485i $$0.422472\pi$$
$$620$$ 0 0
$$621$$ −31.5000 54.5596i −1.26405 2.18940i
$$622$$ 0 0
$$623$$ −21.0000 −0.841347
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −4.50000 7.79423i −0.179713 0.311272i
$$628$$ 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
$$633$$ 7.50000 12.9904i 0.298098 0.516321i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 7.00000 1.73205i 0.277350 0.0686264i
$$638$$ 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
$$643$$ 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i $$-0.789257\pi$$
0.926750 + 0.375680i $$0.122591\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i $$-0.0582109\pi$$
−0.649155 + 0.760656i $$0.724878\pi$$
$$648$$ 0 0
$$649$$ 15.0000 0.588802
$$650$$ 0 0
$$651$$ 36.0000 1.41095
$$652$$ 0 0
$$653$$ −5.50000 9.52628i −0.215232 0.372792i 0.738113 0.674678i $$-0.235717\pi$$
−0.953344 + 0.301885i $$0.902384\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −42.0000 + 72.7461i −1.63858 + 2.83810i
$$658$$ 0 0
$$659$$ 7.50000 12.9904i 0.292159 0.506033i −0.682161 0.731202i $$-0.738960\pi$$
0.974320 + 0.225168i $$0.0722932\pi$$
$$660$$ 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
$$663$$ −21.0000 + 72.7461i −0.815572 + 2.82523i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 17.5000 30.3109i 0.677603 1.17364i
$$668$$ 0 0
$$669$$ −34.5000 + 59.7558i −1.33385 + 2.31029i
$$670$$ 0 0
$$671$$ −15.0000 −0.579069
$$672$$ 0 0
$$673$$ 6.50000 + 11.2583i 0.250557 + 0.433977i 0.963679 0.267063i $$-0.0860531\pi$$
−0.713123 + 0.701039i $$0.752720\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −22.0000 −0.845529 −0.422764 0.906240i $$-0.638940\pi$$
−0.422764 + 0.906240i $$0.638940\pi$$
$$678$$ 0 0
$$679$$ 16.5000 + 28.5788i 0.633212 + 1.09676i
$$680$$ 0 0
$$681$$ 3.00000 0.114960
$$682$$ 0 0
$$683$$ 15.5000 26.8468i 0.593091 1.02726i −0.400722 0.916200i $$-0.631241\pi$$
0.993813 0.111064i $$-0.0354259\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −39.0000 67.5500i −1.48794 2.57719i
$$688$$ 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
$$693$$ 27.0000 46.7654i 1.02565 1.77647i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 49.0000 1.85601
$$698$$ 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
$$703$$ 3.00000 0.113147
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 27.0000 1.01544
$$708$$ 0 0
$$709$$ −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i $$0.394937\pi$$
−0.981331 + 0.192328i $$0.938396\pi$$
$$710$$ 0 0
$$711$$ 24.0000 41.5692i 0.900070 1.55897i
$$712$$ 0 0
$$713$$ 14.0000 + 24.2487i 0.524304 + 0.908121i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 24.0000 + 41.5692i 0.896296 + 1.55243i
$$718$$ 0 0
$$719$$ −0.500000 + 0.866025i −0.0186469 + 0.0322973i −0.875198 0.483764i $$-0.839269\pi$$
0.856551 + 0.516062i $$0.172602\pi$$
$$720$$ 0 0
$$721$$ 24.0000 41.5692i 0.893807 1.54812i
$$722$$ 0 0
$$723$$ −3.00000 −0.111571
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 28.0000 1.03846 0.519231 0.854634i $$-0.326218\pi$$
0.519231 + 0.854634i $$0.326218\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −31.5000 54.5596i −1.16507 2.01796i
$$732$$ 0 0
$$733$$ −14.0000 −0.517102 −0.258551 0.965998i $$-0.583245\pi$$
−0.258551 + 0.965998i $$0.583245\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 19.5000 33.7750i 0.718292 1.24412i
$$738$$ 0 0
$$739$$ −19.5000 33.7750i −0.717319 1.24243i −0.962058 0.272844i $$-0.912036\pi$$
0.244739 0.969589i $$-0.421298\pi$$
$$740$$ 0 0
$$741$$ −3.00000 + 10.3923i −0.110208 + 0.381771i
$$742$$ 0 0
$$743$$ 0.500000 + 0.866025i 0.0183432 + 0.0317714i 0.875051 0.484030i $$-0.160828\pi$$
−0.856708 + 0.515802i $$0.827494\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 36.0000 62.3538i 1.31717 2.28141i
$$748$$ 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
$$753$$ 15.0000 0.546630
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0.500000 + 0.866025i 0.0181728 + 0.0314762i 0.874969 0.484179i $$-0.160882\pi$$
−0.856796 + 0.515656i $$0.827548\pi$$
$$758$$ 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
$$763$$ −21.0000 + 36.3731i −0.760251 + 1.31679i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −12.5000 12.9904i −0.451349 0.469055i
$$768$$ 0 0
$$769$$ 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i $$-0.137931\pi$$
−0.817423 + 0.576038i $$0.804598\pi$$
$$770$$ 0 0
$$771$$ −28.5000 + 49.3634i −1.02640 + 1.77778i
$$772$$ 0 0
$$773$$ 12.5000 21.6506i 0.449594 0.778719i −0.548766 0.835976i $$-0.684902\pi$$
0.998359 + 0.0572570i $$0.0182354\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 13.5000 + 23.3827i 0.484310 + 0.838849i
$$778$$ 0 0
$$779$$ 7.00000 0.250801
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ 22.5000 + 38.9711i 0.804084 + 1.39272i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −0.500000 + 0.866025i −0.0178231 + 0.0308705i −0.874799 0.484485i $$-0.839007\pi$$
0.856976 + 0.515356i $$0.172340\pi$$
$$788$$ 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
$$793$$ 12.5000 + 12.9904i 0.443888 + 0.461302i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −3.50000 + 6.06218i −0.123976 + 0.214733i −0.921332 0.388776i $$-0.872898\pi$$
0.797356 + 0.603509i $$0.206231\pi$$
$$798$$ 0 0