# Properties

 Label 912.2.q.b.49.1 Level $912$ Weight $2$ Character 912.49 Analytic conductor $7.282$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.28235666434$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 49.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.49 Dual form 912.2.q.b.577.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} -1.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +2.00000 q^{11} +(1.50000 + 2.59808i) q^{13} +(-2.00000 + 3.46410i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{21} +(2.00000 + 3.46410i) q^{23} +(2.50000 + 4.33013i) q^{25} +1.00000 q^{27} +3.00000 q^{31} +(-1.00000 + 1.73205i) q^{33} -5.00000 q^{37} -3.00000 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-4.50000 + 7.79423i) q^{43} +(5.00000 + 8.66025i) q^{47} -6.00000 q^{49} +(-2.00000 - 3.46410i) q^{51} +(2.00000 + 3.46410i) q^{53} +(3.50000 - 2.59808i) q^{57} +(-7.00000 + 12.1244i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(0.500000 + 0.866025i) q^{63} +(1.50000 + 2.59808i) q^{67} -4.00000 q^{69} +(7.00000 - 12.1244i) q^{71} +(5.50000 - 9.52628i) q^{73} -5.00000 q^{75} -2.00000 q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} -8.00000 q^{83} +(7.00000 + 12.1244i) q^{89} +(-1.50000 - 2.59808i) q^{91} +(-1.50000 + 2.59808i) q^{93} +(-1.00000 + 1.73205i) q^{97} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{3} - 2 q^{7} - q^{9}+O(q^{10})$$ 2 * q - q^3 - 2 * q^7 - q^9 $$2 q - q^{3} - 2 q^{7} - q^{9} + 4 q^{11} + 3 q^{13} - 4 q^{17} - 8 q^{19} + q^{21} + 4 q^{23} + 5 q^{25} + 2 q^{27} + 6 q^{31} - 2 q^{33} - 10 q^{37} - 6 q^{39} - 4 q^{41} - 9 q^{43} + 10 q^{47} - 12 q^{49} - 4 q^{51} + 4 q^{53} + 7 q^{57} - 14 q^{59} - 11 q^{61} + q^{63} + 3 q^{67} - 8 q^{69} + 14 q^{71} + 11 q^{73} - 10 q^{75} - 4 q^{77} + q^{79} - q^{81} - 16 q^{83} + 14 q^{89} - 3 q^{91} - 3 q^{93} - 2 q^{97} - 2 q^{99}+O(q^{100})$$ 2 * q - q^3 - 2 * q^7 - q^9 + 4 * q^11 + 3 * q^13 - 4 * q^17 - 8 * q^19 + q^21 + 4 * q^23 + 5 * q^25 + 2 * q^27 + 6 * q^31 - 2 * q^33 - 10 * q^37 - 6 * q^39 - 4 * q^41 - 9 * q^43 + 10 * q^47 - 12 * q^49 - 4 * q^51 + 4 * q^53 + 7 * q^57 - 14 * q^59 - 11 * q^61 + q^63 + 3 * q^67 - 8 * q^69 + 14 * q^71 + 11 * q^73 - 10 * q^75 - 4 * q^77 + q^79 - q^81 - 16 * q^83 + 14 * q^89 - 3 * q^91 - 3 * q^93 - 2 * q^97 - 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$229$$ $$305$$ $$799$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ 1.50000 + 2.59808i 0.416025 + 0.720577i 0.995535 0.0943882i $$-0.0300895\pi$$
−0.579510 + 0.814965i $$0.696756\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ −4.00000 1.73205i −0.917663 0.397360i
$$20$$ 0 0
$$21$$ 0.500000 0.866025i 0.109109 0.188982i
$$22$$ 0 0
$$23$$ 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i $$-0.0297381\pi$$
−0.578610 + 0.815604i $$0.696405\pi$$
$$24$$ 0 0
$$25$$ 2.50000 + 4.33013i 0.500000 + 0.866025i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$30$$ 0 0
$$31$$ 3.00000 0.538816 0.269408 0.963026i $$-0.413172\pi$$
0.269408 + 0.963026i $$0.413172\pi$$
$$32$$ 0 0
$$33$$ −1.00000 + 1.73205i −0.174078 + 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −5.00000 −0.821995 −0.410997 0.911636i $$-0.634819\pi$$
−0.410997 + 0.911636i $$0.634819\pi$$
$$38$$ 0 0
$$39$$ −3.00000 −0.480384
$$40$$ 0 0
$$41$$ −2.00000 + 3.46410i −0.312348 + 0.541002i −0.978870 0.204483i $$-0.934449\pi$$
0.666523 + 0.745485i $$0.267782\pi$$
$$42$$ 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
$$47$$ 5.00000 + 8.66025i 0.729325 + 1.26323i 0.957169 + 0.289530i $$0.0934991\pi$$
−0.227844 + 0.973698i $$0.573168\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ −2.00000 3.46410i −0.280056 0.485071i
$$52$$ 0 0
$$53$$ 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i $$-0.0780811\pi$$
−0.695344 + 0.718677i $$0.744748\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 3.50000 2.59808i 0.463586 0.344124i
$$58$$ 0 0
$$59$$ −7.00000 + 12.1244i −0.911322 + 1.57846i −0.0991242 + 0.995075i $$0.531604\pi$$
−0.812198 + 0.583382i $$0.801729\pi$$
$$60$$ 0 0
$$61$$ −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i $$-0.917971\pi$$
0.262776 0.964857i $$-0.415362\pi$$
$$62$$ 0 0
$$63$$ 0.500000 + 0.866025i 0.0629941 + 0.109109i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i $$-0.108004\pi$$
−0.759733 + 0.650236i $$0.774670\pi$$
$$68$$ 0 0
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i $$-0.521247\pi$$
0.897447 0.441123i $$-0.145420\pi$$
$$72$$ 0 0
$$73$$ 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i $$-0.610721\pi$$
0.984594 0.174855i $$-0.0559458\pi$$
$$74$$ 0 0
$$75$$ −5.00000 −0.577350
$$76$$ 0 0
$$77$$ −2.00000 −0.227921
$$78$$ 0 0
$$79$$ 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i $$-0.815418\pi$$
0.892781 + 0.450490i $$0.148751\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i $$0.0994552\pi$$
−0.209585 + 0.977790i $$0.567211\pi$$
$$90$$ 0 0
$$91$$ −1.50000 2.59808i −0.157243 0.272352i
$$92$$ 0 0
$$93$$ −1.50000 + 2.59808i −0.155543 + 0.269408i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 0 0
$$99$$ −1.00000 1.73205i −0.100504 0.174078i
$$100$$ 0 0
$$101$$ 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i $$-0.000911295\pi$$
−0.502477 + 0.864590i $$0.667578\pi$$
$$102$$ 0 0
$$103$$ 3.00000 0.295599 0.147799 0.989017i $$-0.452781\pi$$
0.147799 + 0.989017i $$0.452781\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 10.0000 0.966736 0.483368 0.875417i $$-0.339413\pi$$
0.483368 + 0.875417i $$0.339413\pi$$
$$108$$ 0 0
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ 0 0
$$111$$ 2.50000 4.33013i 0.237289 0.410997i
$$112$$ 0 0
$$113$$ 10.0000 0.940721 0.470360 0.882474i $$-0.344124\pi$$
0.470360 + 0.882474i $$0.344124\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 1.50000 2.59808i 0.138675 0.240192i
$$118$$ 0 0
$$119$$ 2.00000 3.46410i 0.183340 0.317554i
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 0 0
$$123$$ −2.00000 3.46410i −0.180334 0.312348i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i $$-0.282166\pi$$
−0.987108 + 0.160055i $$0.948833\pi$$
$$128$$ 0 0
$$129$$ −4.50000 7.79423i −0.396203 0.686244i
$$130$$ 0 0
$$131$$ −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i $$-0.917752\pi$$
0.704692 + 0.709514i $$0.251085\pi$$
$$132$$ 0 0
$$133$$ 4.00000 + 1.73205i 0.346844 + 0.150188i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i $$-0.0841608\pi$$
−0.708942 + 0.705266i $$0.750827\pi$$
$$138$$ 0 0
$$139$$ −9.50000 16.4545i −0.805779 1.39565i −0.915764 0.401718i $$-0.868413\pi$$
0.109984 0.993933i $$-0.464920\pi$$
$$140$$ 0 0
$$141$$ −10.0000 −0.842152
$$142$$ 0 0
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 3.00000 5.19615i 0.247436 0.428571i
$$148$$ 0 0
$$149$$ 11.0000 19.0526i 0.901155 1.56085i 0.0751583 0.997172i $$-0.476054\pi$$
0.825997 0.563675i $$-0.190613\pi$$
$$150$$ 0 0
$$151$$ 20.0000 1.62758 0.813788 0.581161i $$-0.197401\pi$$
0.813788 + 0.581161i $$0.197401\pi$$
$$152$$ 0 0
$$153$$ 4.00000 0.323381
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.5000 18.1865i 0.837991 1.45144i −0.0535803 0.998564i $$-0.517063\pi$$
0.891572 0.452880i $$-0.149603\pi$$
$$158$$ 0 0
$$159$$ −4.00000 −0.317221
$$160$$ 0 0
$$161$$ −2.00000 3.46410i −0.157622 0.273009i
$$162$$ 0 0
$$163$$ −11.0000 −0.861586 −0.430793 0.902451i $$-0.641766\pi$$
−0.430793 + 0.902451i $$0.641766\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 3.00000 + 5.19615i 0.232147 + 0.402090i 0.958440 0.285295i $$-0.0920916\pi$$
−0.726293 + 0.687386i $$0.758758\pi$$
$$168$$ 0 0
$$169$$ 2.00000 3.46410i 0.153846 0.266469i
$$170$$ 0 0
$$171$$ 0.500000 + 4.33013i 0.0382360 + 0.331133i
$$172$$ 0 0
$$173$$ 12.0000 20.7846i 0.912343 1.58022i 0.101598 0.994826i $$-0.467605\pi$$
0.810745 0.585399i $$-0.199062\pi$$
$$174$$ 0 0
$$175$$ −2.50000 4.33013i −0.188982 0.327327i
$$176$$ 0 0
$$177$$ −7.00000 12.1244i −0.526152 0.911322i
$$178$$ 0 0
$$179$$ −4.00000 −0.298974 −0.149487 0.988764i $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 0 0
$$181$$ 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i $$0.0665956\pi$$
−0.309229 + 0.950988i $$0.600071\pi$$
$$182$$ 0 0
$$183$$ 11.0000 0.813143
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −4.00000 + 6.92820i −0.292509 + 0.506640i
$$188$$ 0 0
$$189$$ −1.00000 −0.0727393
$$190$$ 0 0
$$191$$ 8.00000 0.578860 0.289430 0.957199i $$-0.406534\pi$$
0.289430 + 0.957199i $$0.406534\pi$$
$$192$$ 0 0
$$193$$ 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i $$-0.678351\pi$$
0.999326 + 0.0366998i $$0.0116845\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2.00000 −0.142494 −0.0712470 0.997459i $$-0.522698\pi$$
−0.0712470 + 0.997459i $$0.522698\pi$$
$$198$$ 0 0
$$199$$ 2.50000 + 4.33013i 0.177220 + 0.306955i 0.940927 0.338608i $$-0.109956\pi$$
−0.763707 + 0.645563i $$0.776623\pi$$
$$200$$ 0 0
$$201$$ −3.00000 −0.211604
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 2.00000 3.46410i 0.139010 0.240772i
$$208$$ 0 0
$$209$$ −8.00000 3.46410i −0.553372 0.239617i
$$210$$ 0 0
$$211$$ 12.5000 21.6506i 0.860535 1.49049i −0.0108774 0.999941i $$-0.503462\pi$$
0.871413 0.490550i $$-0.163204\pi$$
$$212$$ 0 0
$$213$$ 7.00000 + 12.1244i 0.479632 + 0.830747i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3.00000 −0.203653
$$218$$ 0 0
$$219$$ 5.50000 + 9.52628i 0.371656 + 0.643726i
$$220$$ 0 0
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ 4.50000 7.79423i 0.301342 0.521940i −0.675098 0.737728i $$-0.735899\pi$$
0.976440 + 0.215788i $$0.0692320\pi$$
$$224$$ 0 0
$$225$$ 2.50000 4.33013i 0.166667 0.288675i
$$226$$ 0 0
$$227$$ −8.00000 −0.530979 −0.265489 0.964114i $$-0.585534\pi$$
−0.265489 + 0.964114i $$0.585534\pi$$
$$228$$ 0 0
$$229$$ −11.0000 −0.726900 −0.363450 0.931614i $$-0.618401\pi$$
−0.363450 + 0.931614i $$0.618401\pi$$
$$230$$ 0 0
$$231$$ 1.00000 1.73205i 0.0657952 0.113961i
$$232$$ 0 0
$$233$$ −9.00000 + 15.5885i −0.589610 + 1.02123i 0.404674 + 0.914461i $$0.367385\pi$$
−0.994283 + 0.106773i $$0.965948\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0.500000 + 0.866025i 0.0324785 + 0.0562544i
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i $$-0.868727\pi$$
0.110963 0.993825i $$-0.464606\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.50000 12.9904i −0.0954427 0.826558i
$$248$$ 0 0
$$249$$ 4.00000 6.92820i 0.253490 0.439057i
$$250$$ 0 0
$$251$$ −9.00000 15.5885i −0.568075 0.983935i −0.996756 0.0804789i $$-0.974355\pi$$
0.428681 0.903456i $$-0.358978\pi$$
$$252$$ 0 0
$$253$$ 4.00000 + 6.92820i 0.251478 + 0.435572i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i $$-0.0445601\pi$$
−0.615948 + 0.787787i $$0.711227\pi$$
$$258$$ 0 0
$$259$$ 5.00000 0.310685
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i $$-0.646065\pi$$
0.997906 0.0646755i $$-0.0206012\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −14.0000 −0.856786
$$268$$ 0 0
$$269$$ −1.00000 + 1.73205i −0.0609711 + 0.105605i −0.894900 0.446267i $$-0.852753\pi$$
0.833929 + 0.551872i $$0.186086\pi$$
$$270$$ 0 0
$$271$$ −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i $$-0.994865\pi$$
0.513905 + 0.857847i $$0.328199\pi$$
$$272$$ 0 0
$$273$$ 3.00000 0.181568
$$274$$ 0 0
$$275$$ 5.00000 + 8.66025i 0.301511 + 0.522233i
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ −1.50000 2.59808i −0.0898027 0.155543i
$$280$$ 0 0
$$281$$ 4.00000 + 6.92820i 0.238620 + 0.413302i 0.960319 0.278906i $$-0.0899716\pi$$
−0.721699 + 0.692207i $$0.756638\pi$$
$$282$$ 0 0
$$283$$ −10.0000 + 17.3205i −0.594438 + 1.02960i 0.399188 + 0.916869i $$0.369292\pi$$
−0.993626 + 0.112728i $$0.964041\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.00000 3.46410i 0.118056 0.204479i
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 0 0
$$291$$ −1.00000 1.73205i −0.0586210 0.101535i
$$292$$ 0 0
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 2.00000 0.116052
$$298$$ 0 0
$$299$$ −6.00000 + 10.3923i −0.346989 + 0.601003i
$$300$$ 0 0
$$301$$ 4.50000 7.79423i 0.259376 0.449252i
$$302$$ 0 0
$$303$$ −10.0000 −0.574485
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −6.00000 + 10.3923i −0.342438 + 0.593120i −0.984885 0.173210i $$-0.944586\pi$$
0.642447 + 0.766330i $$0.277919\pi$$
$$308$$ 0 0
$$309$$ −1.50000 + 2.59808i −0.0853320 + 0.147799i
$$310$$ 0 0
$$311$$ −10.0000 −0.567048 −0.283524 0.958965i $$-0.591504\pi$$
−0.283524 + 0.958965i $$0.591504\pi$$
$$312$$ 0 0
$$313$$ −3.00000 5.19615i −0.169570 0.293704i 0.768699 0.639611i $$-0.220905\pi$$
−0.938269 + 0.345907i $$0.887571\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i $$-0.276077\pi$$
−0.983866 + 0.178908i $$0.942743\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ −5.00000 + 8.66025i −0.279073 + 0.483368i
$$322$$ 0 0
$$323$$ 14.0000 10.3923i 0.778981 0.578243i
$$324$$ 0 0
$$325$$ −7.50000 + 12.9904i −0.416025 + 0.720577i
$$326$$ 0 0
$$327$$ −7.00000 12.1244i −0.387101 0.670478i
$$328$$ 0 0
$$329$$ −5.00000 8.66025i −0.275659 0.477455i
$$330$$ 0 0
$$331$$ −15.0000 −0.824475 −0.412237 0.911077i $$-0.635253\pi$$
−0.412237 + 0.911077i $$0.635253\pi$$
$$332$$ 0 0
$$333$$ 2.50000 + 4.33013i 0.136999 + 0.237289i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 9.50000 16.4545i 0.517498 0.896333i −0.482295 0.876009i $$-0.660197\pi$$
0.999793 0.0203242i $$-0.00646983\pi$$
$$338$$ 0 0
$$339$$ −5.00000 + 8.66025i −0.271563 + 0.470360i
$$340$$ 0 0
$$341$$ 6.00000 0.324918
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 8.00000 13.8564i 0.429463 0.743851i −0.567363 0.823468i $$-0.692036\pi$$
0.996826 + 0.0796169i $$0.0253697\pi$$
$$348$$ 0 0
$$349$$ −29.0000 −1.55233 −0.776167 0.630527i $$-0.782839\pi$$
−0.776167 + 0.630527i $$0.782839\pi$$
$$350$$ 0 0
$$351$$ 1.50000 + 2.59808i 0.0800641 + 0.138675i
$$352$$ 0 0
$$353$$ −12.0000 −0.638696 −0.319348 0.947638i $$-0.603464\pi$$
−0.319348 + 0.947638i $$0.603464\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 2.00000 + 3.46410i 0.105851 + 0.183340i
$$358$$ 0 0
$$359$$ −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i $$0.565588\pi$$
−0.745409 + 0.666608i $$0.767746\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 0 0
$$363$$ 3.50000 6.06218i 0.183702 0.318182i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 11.5000 + 19.9186i 0.600295 + 1.03974i 0.992776 + 0.119982i $$0.0382835\pi$$
−0.392481 + 0.919760i $$0.628383\pi$$
$$368$$ 0 0
$$369$$ 4.00000 0.208232
$$370$$ 0 0
$$371$$ −2.00000 3.46410i −0.103835 0.179847i
$$372$$ 0 0
$$373$$ 26.0000 1.34623 0.673114 0.739538i $$-0.264956\pi$$
0.673114 + 0.739538i $$0.264956\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 13.0000 0.667765 0.333883 0.942615i $$-0.391641\pi$$
0.333883 + 0.942615i $$0.391641\pi$$
$$380$$ 0 0
$$381$$ 8.00000 0.409852
$$382$$ 0 0
$$383$$ 7.00000 12.1244i 0.357683 0.619526i −0.629890 0.776684i $$-0.716900\pi$$
0.987573 + 0.157159i $$0.0502334\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 9.00000 0.457496
$$388$$ 0 0
$$389$$ 8.00000 + 13.8564i 0.405616 + 0.702548i 0.994393 0.105748i $$-0.0337237\pi$$
−0.588777 + 0.808296i $$0.700390\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ −3.00000 5.19615i −0.151330 0.262111i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i $$-0.956176\pi$$
0.614123 + 0.789210i $$0.289510\pi$$
$$398$$ 0 0
$$399$$ −3.50000 + 2.59808i −0.175219 + 0.130066i
$$400$$ 0 0
$$401$$ −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i $$-0.981709\pi$$
0.548911 + 0.835881i $$0.315043\pi$$
$$402$$ 0 0
$$403$$ 4.50000 + 7.79423i 0.224161 + 0.388258i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −10.0000 −0.495682
$$408$$ 0 0
$$409$$ 15.0000 + 25.9808i 0.741702 + 1.28467i 0.951720 + 0.306968i $$0.0993146\pi$$
−0.210017 + 0.977698i $$0.567352\pi$$
$$410$$ 0 0
$$411$$ −6.00000 −0.295958
$$412$$ 0 0
$$413$$ 7.00000 12.1244i 0.344447 0.596601i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 19.0000 0.930434
$$418$$ 0 0
$$419$$ −18.0000 −0.879358 −0.439679 0.898155i $$-0.644908\pi$$
−0.439679 + 0.898155i $$0.644908\pi$$
$$420$$ 0 0
$$421$$ −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i $$-0.911690\pi$$
0.718076 + 0.695965i $$0.245023\pi$$
$$422$$ 0 0
$$423$$ 5.00000 8.66025i 0.243108 0.421076i
$$424$$ 0 0
$$425$$ −20.0000 −0.970143
$$426$$ 0 0
$$427$$ 5.50000 + 9.52628i 0.266164 + 0.461009i
$$428$$ 0 0
$$429$$ −6.00000 −0.289683
$$430$$ 0 0
$$431$$ −5.00000 8.66025i −0.240842 0.417150i 0.720113 0.693857i $$-0.244090\pi$$
−0.960954 + 0.276707i $$0.910757\pi$$
$$432$$ 0 0
$$433$$ 4.50000 + 7.79423i 0.216256 + 0.374567i 0.953660 0.300885i $$-0.0972820\pi$$
−0.737404 + 0.675452i $$0.763949\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.00000 17.3205i −0.0956730 0.828552i
$$438$$ 0 0
$$439$$ 9.50000 16.4545i 0.453410 0.785330i −0.545185 0.838316i $$-0.683541\pi$$
0.998595 + 0.0529862i $$0.0168739\pi$$
$$440$$ 0 0
$$441$$ 3.00000 + 5.19615i 0.142857 + 0.247436i
$$442$$ 0 0
$$443$$ 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i $$0.0264433\pi$$
−0.426414 + 0.904528i $$0.640223\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 11.0000 + 19.0526i 0.520282 + 0.901155i
$$448$$ 0 0
$$449$$ −36.0000 −1.69895 −0.849473 0.527633i $$-0.823080\pi$$
−0.849473 + 0.527633i $$0.823080\pi$$
$$450$$ 0 0
$$451$$ −4.00000 + 6.92820i −0.188353 + 0.326236i
$$452$$ 0 0
$$453$$ −10.0000 + 17.3205i −0.469841 + 0.813788i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 5.00000 0.233890 0.116945 0.993138i $$-0.462690\pi$$
0.116945 + 0.993138i $$0.462690\pi$$
$$458$$ 0 0
$$459$$ −2.00000 + 3.46410i −0.0933520 + 0.161690i
$$460$$ 0 0
$$461$$ −3.00000 + 5.19615i −0.139724 + 0.242009i −0.927392 0.374091i $$-0.877955\pi$$
0.787668 + 0.616100i $$0.211288\pi$$
$$462$$ 0 0
$$463$$ 9.00000 0.418265 0.209133 0.977887i $$-0.432936\pi$$
0.209133 + 0.977887i $$0.432936\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −8.00000 −0.370196 −0.185098 0.982720i $$-0.559260\pi$$
−0.185098 + 0.982720i $$0.559260\pi$$
$$468$$ 0 0
$$469$$ −1.50000 2.59808i −0.0692636 0.119968i
$$470$$ 0 0
$$471$$ 10.5000 + 18.1865i 0.483814 + 0.837991i
$$472$$ 0 0
$$473$$ −9.00000 + 15.5885i −0.413820 + 0.716758i
$$474$$ 0 0
$$475$$ −2.50000 21.6506i −0.114708 0.993399i
$$476$$ 0 0
$$477$$ 2.00000 3.46410i 0.0915737 0.158610i
$$478$$ 0 0
$$479$$ 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i $$-0.122897\pi$$
−0.789314 + 0.613990i $$0.789564\pi$$
$$480$$ 0 0
$$481$$ −7.50000 12.9904i −0.341971 0.592310i
$$482$$ 0 0
$$483$$ 4.00000 0.182006
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −32.0000 −1.45006 −0.725029 0.688718i $$-0.758174\pi$$
−0.725029 + 0.688718i $$0.758174\pi$$
$$488$$ 0 0
$$489$$ 5.50000 9.52628i 0.248719 0.430793i
$$490$$ 0 0
$$491$$ 15.0000 25.9808i 0.676941 1.17250i −0.298957 0.954267i $$-0.596639\pi$$
0.975898 0.218229i $$-0.0700279\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −7.00000 + 12.1244i −0.313993 + 0.543852i
$$498$$ 0 0
$$499$$ 2.50000 4.33013i 0.111915 0.193843i −0.804627 0.593780i $$-0.797635\pi$$
0.916542 + 0.399937i $$0.130968\pi$$
$$500$$ 0 0
$$501$$ −6.00000 −0.268060
$$502$$ 0 0
$$503$$ 8.00000 + 13.8564i 0.356702 + 0.617827i 0.987408 0.158196i $$-0.0505677\pi$$
−0.630705 + 0.776022i $$0.717234\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 2.00000 + 3.46410i 0.0888231 + 0.153846i
$$508$$ 0 0
$$509$$ −13.0000 22.5167i −0.576215 0.998033i −0.995908 0.0903676i $$-0.971196\pi$$
0.419694 0.907666i $$-0.362138\pi$$
$$510$$ 0 0
$$511$$ −5.50000 + 9.52628i −0.243306 + 0.421418i
$$512$$ 0 0
$$513$$ −4.00000 1.73205i −0.176604 0.0764719i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 10.0000 + 17.3205i 0.439799 + 0.761755i
$$518$$ 0 0
$$519$$ 12.0000 + 20.7846i 0.526742 + 0.912343i
$$520$$ 0 0
$$521$$ 34.0000 1.48957 0.744784 0.667306i $$-0.232553\pi$$
0.744784 + 0.667306i $$0.232553\pi$$
$$522$$ 0 0
$$523$$ 18.5000 + 32.0429i 0.808949 + 1.40114i 0.913593 + 0.406630i $$0.133296\pi$$
−0.104644 + 0.994510i $$0.533370\pi$$
$$524$$ 0 0
$$525$$ 5.00000 0.218218
$$526$$ 0 0
$$527$$ −6.00000 + 10.3923i −0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 3.50000 6.06218i 0.152174 0.263573i
$$530$$ 0 0
$$531$$ 14.0000 0.607548
$$532$$ 0 0
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 2.00000 3.46410i 0.0863064 0.149487i
$$538$$ 0 0
$$539$$ −12.0000 −0.516877
$$540$$ 0 0
$$541$$ 15.5000 + 26.8468i 0.666397 + 1.15423i 0.978905 + 0.204318i $$0.0654977\pi$$
−0.312507 + 0.949915i $$0.601169\pi$$
$$542$$ 0 0
$$543$$ −18.0000 −0.772454
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 5.50000 + 9.52628i 0.235163 + 0.407314i 0.959320 0.282321i $$-0.0911043\pi$$
−0.724157 + 0.689635i $$0.757771\pi$$
$$548$$ 0 0
$$549$$ −5.50000 + 9.52628i −0.234734 + 0.406572i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −0.500000 + 0.866025i −0.0212622 + 0.0368271i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −17.0000 29.4449i −0.720313 1.24762i −0.960874 0.276985i $$-0.910665\pi$$
0.240561 0.970634i $$-0.422669\pi$$
$$558$$ 0 0
$$559$$ −27.0000 −1.14198
$$560$$ 0 0
$$561$$ −4.00000 6.92820i −0.168880 0.292509i
$$562$$ 0 0
$$563$$ 6.00000 0.252870 0.126435 0.991975i $$-0.459647\pi$$
0.126435 + 0.991975i $$0.459647\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0.500000 0.866025i 0.0209980 0.0363696i
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ 7.00000 0.292941 0.146470 0.989215i $$-0.453209\pi$$
0.146470 + 0.989215i $$0.453209\pi$$
$$572$$ 0 0
$$573$$ −4.00000 + 6.92820i −0.167102 + 0.289430i
$$574$$ 0 0
$$575$$ −10.0000 + 17.3205i −0.417029 + 0.722315i
$$576$$ 0 0
$$577$$ −14.0000 −0.582828 −0.291414 0.956597i $$-0.594126\pi$$
−0.291414 + 0.956597i $$0.594126\pi$$
$$578$$ 0 0
$$579$$ 6.50000 + 11.2583i 0.270131 + 0.467880i
$$580$$ 0 0
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ 4.00000 + 6.92820i 0.165663 + 0.286937i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.00000 + 1.73205i −0.0412744 + 0.0714894i −0.885925 0.463829i $$-0.846475\pi$$
0.844650 + 0.535319i $$0.179808\pi$$
$$588$$ 0 0
$$589$$ −12.0000 5.19615i −0.494451 0.214104i
$$590$$ 0 0
$$591$$ 1.00000 1.73205i 0.0411345 0.0712470i
$$592$$ 0 0
$$593$$ −17.0000 29.4449i −0.698106 1.20916i −0.969122 0.246581i $$-0.920693\pi$$
0.271016 0.962575i $$-0.412640\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −5.00000 −0.204636
$$598$$ 0 0
$$599$$ −23.0000 39.8372i −0.939755 1.62770i −0.765928 0.642926i $$-0.777720\pi$$
−0.173826 0.984776i $$-0.555613\pi$$
$$600$$ 0 0
$$601$$ 27.0000 1.10135 0.550676 0.834719i $$-0.314370\pi$$
0.550676 + 0.834719i $$0.314370\pi$$
$$602$$ 0 0
$$603$$ 1.50000 2.59808i 0.0610847 0.105802i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −5.00000 −0.202944 −0.101472 0.994838i $$-0.532355\pi$$
−0.101472 + 0.994838i $$0.532355\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −15.0000 + 25.9808i −0.606835 + 1.05107i
$$612$$ 0 0
$$613$$ −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i $$-0.846193\pi$$
0.845124 + 0.534570i $$0.179527\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i $$0.153988\pi$$
−0.0398207 + 0.999207i $$0.512679\pi$$
$$618$$ 0 0
$$619$$ −1.00000 −0.0401934 −0.0200967 0.999798i $$-0.506397\pi$$
−0.0200967 + 0.999798i $$0.506397\pi$$
$$620$$ 0 0
$$621$$ 2.00000 + 3.46410i 0.0802572 + 0.139010i
$$622$$ 0 0
$$623$$ −7.00000 12.1244i −0.280449 0.485752i
$$624$$ 0 0
$$625$$ −12.5000 + 21.6506i −0.500000 + 0.866025i
$$626$$ 0 0
$$627$$ 7.00000 5.19615i 0.279553 0.207514i
$$628$$ 0 0
$$629$$ 10.0000 17.3205i 0.398726 0.690614i
$$630$$ 0 0
$$631$$ 8.50000 + 14.7224i 0.338380 + 0.586091i 0.984128 0.177459i $$-0.0567879\pi$$
−0.645748 + 0.763550i $$0.723455\pi$$
$$632$$ 0 0
$$633$$ 12.5000 + 21.6506i 0.496830 + 0.860535i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −9.00000 15.5885i −0.356593 0.617637i
$$638$$ 0 0
$$639$$ −14.0000 −0.553831
$$640$$ 0 0
$$641$$ 7.00000 12.1244i 0.276483 0.478883i −0.694025 0.719951i $$-0.744164\pi$$
0.970508 + 0.241068i $$0.0774976\pi$$
$$642$$ 0 0
$$643$$ 18.5000 32.0429i 0.729569 1.26365i −0.227497 0.973779i $$-0.573054\pi$$
0.957066 0.289871i $$-0.0936125\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −48.0000 −1.88707 −0.943537 0.331266i $$-0.892524\pi$$
−0.943537 + 0.331266i $$0.892524\pi$$
$$648$$ 0 0
$$649$$ −14.0000 + 24.2487i −0.549548 + 0.951845i
$$650$$ 0 0
$$651$$ 1.50000 2.59808i 0.0587896 0.101827i
$$652$$ 0 0
$$653$$ −42.0000 −1.64359 −0.821794 0.569785i $$-0.807026\pi$$
−0.821794 + 0.569785i $$0.807026\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −11.0000 −0.429151
$$658$$ 0 0
$$659$$ −7.00000 12.1244i −0.272681 0.472298i 0.696866 0.717201i $$-0.254577\pi$$
−0.969548 + 0.244903i $$0.921244\pi$$
$$660$$ 0 0
$$661$$ −5.00000 8.66025i −0.194477 0.336845i 0.752252 0.658876i $$-0.228968\pi$$
−0.946729 + 0.322031i $$0.895634\pi$$
$$662$$ 0 0
$$663$$ 6.00000 10.3923i 0.233021 0.403604i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 4.50000 + 7.79423i 0.173980 + 0.301342i
$$670$$ 0 0
$$671$$ −11.0000 19.0526i −0.424650 0.735516i
$$672$$ 0 0
$$673$$ −1.00000 −0.0385472 −0.0192736 0.999814i $$-0.506135\pi$$
−0.0192736 + 0.999814i $$0.506135\pi$$
$$674$$ 0 0
$$675$$ 2.50000 + 4.33013i 0.0962250 + 0.166667i
$$676$$ 0 0
$$677$$ 18.0000 0.691796 0.345898 0.938272i $$-0.387574\pi$$
0.345898 + 0.938272i $$0.387574\pi$$
$$678$$ 0 0
$$679$$ 1.00000 1.73205i 0.0383765 0.0664700i
$$680$$ 0 0
$$681$$ 4.00000 6.92820i 0.153280 0.265489i
$$682$$ 0 0
$$683$$ 36.0000 1.37750 0.688751 0.724998i $$-0.258159\pi$$
0.688751 + 0.724998i $$0.258159\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 5.50000 9.52628i 0.209838 0.363450i
$$688$$ 0 0
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −4.00000 −0.152167 −0.0760836 0.997101i $$-0.524242\pi$$
−0.0760836 + 0.997101i $$0.524242\pi$$
$$692$$ 0 0
$$693$$ 1.00000 + 1.73205i 0.0379869 + 0.0657952i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −8.00000 13.8564i −0.303022 0.524849i
$$698$$ 0 0
$$699$$ −9.00000 15.5885i −0.340411 0.589610i
$$700$$ 0 0
$$701$$ 22.0000 38.1051i 0.830929 1.43921i −0.0663742 0.997795i $$-0.521143\pi$$
0.897303 0.441416i $$-0.145524\pi$$
$$702$$ 0 0
$$703$$ 20.0000 + 8.66025i 0.754314 + 0.326628i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −5.00000 8.66025i −0.188044 0.325702i
$$708$$ 0 0
$$709$$ 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i $$0.0311079\pi$$
−0.413114 + 0.910679i $$0.635559\pi$$
$$710$$ 0 0
$$711$$ −1.00000 −0.0375029
$$712$$ 0 0
$$713$$ 6.00000 + 10.3923i 0.224702 + 0.389195i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −6.00000 + 10.3923i −0.224074 + 0.388108i
$$718$$ 0 0
$$719$$ 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i $$-0.565365\pi$$
0.949785 0.312903i $$-0.101301\pi$$
$$720$$ 0 0
$$721$$ −3.00000 −0.111726
$$722$$ 0 0
$$723$$ 25.0000 0.929760
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 8.50000 14.7224i 0.315248 0.546025i −0.664243 0.747517i $$-0.731246\pi$$
0.979490 + 0.201492i $$0.0645791\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ −18.0000 31.1769i −0.665754 1.15312i
$$732$$ 0 0
$$733$$ −2.00000 −0.0738717 −0.0369358 0.999318i $$-0.511760\pi$$
−0.0369358 + 0.999318i $$0.511760\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 3.00000 + 5.19615i 0.110506 + 0.191403i
$$738$$ 0 0
$$739$$ −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i $$-0.862648\pi$$
0.816373 + 0.577524i $$0.195981\pi$$
$$740$$ 0 0
$$741$$ 12.0000 + 5.19615i 0.440831 + 0.190885i
$$742$$ 0 0
$$743$$ −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i $$-0.940442\pi$$
0.652369 + 0.757902i $$0.273775\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 4.00000 + 6.92820i 0.146352 + 0.253490i
$$748$$ 0 0
$$749$$ −10.0000 −0.365392
$$750$$ 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
$$753$$ 18.0000 0.655956
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −2.50000 + 4.33013i −0.0908640 + 0.157381i −0.907875 0.419241i $$-0.862296\pi$$
0.817011 + 0.576622i $$0.195630\pi$$
$$758$$ 0 0
$$759$$ −8.00000 −0.290382
$$760$$ 0 0
$$761$$ −34.0000 −1.23250 −0.616250 0.787551i $$-0.711349\pi$$
−0.616250 + 0.787551i $$0.711349\pi$$
$$762$$ 0 0
$$763$$ 7.00000 12.1244i 0.253417 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −42.0000 −1.51653
$$768$$ 0 0
$$769$$ −13.5000 23.3827i −0.486822 0.843201i 0.513063 0.858351i $$-0.328511\pi$$
−0.999885 + 0.0151499i $$0.995177\pi$$
$$770$$ 0 0
$$771$$ −12.0000 −0.432169
$$772$$ 0 0
$$773$$ 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i $$-0.0617373\pi$$
−0.657542 + 0.753418i $$0.728404\pi$$
$$774$$ 0 0
$$775$$ 7.50000 + 12.9904i 0.269408 + 0.466628i
$$776$$ 0 0
$$777$$ −2.50000 + 4.33013i −0.0896870 + 0.155342i
$$778$$ 0 0
$$779$$ 14.0000 10.3923i 0.501602 0.372343i
$$780$$ 0 0
$$781$$ 14.0000 24.2487i 0.500959 0.867687i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 47.0000 1.67537 0.837685 0.546154i $$-0.183909\pi$$
0.837685 + 0.546154i $$0.183909\pi$$
$$788$$ 0 0
$$789$$ 9.00000 + 15.5885i 0.320408 + 0.554964i
$$790$$ 0 0
$$791$$ −10.0000 −0.355559
$$792$$ 0 0
$$793$$ 16.5000 28.5788i 0.585932 1.01486i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 26.0000 0.920967 0.460484 0.887668i $$-0.347676\pi$$
0.460484 + 0.887668i $$0.347676\pi$$
$$798$$ 0 0