# Properties

 Label 1386.2.k.l.793.1 Level $1386$ Weight $2$ Character 1386.793 Analytic conductor $11.067$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$11.0672657201$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 793.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1386.793 Dual form 1386.2.k.l.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(1.50000 - 2.59808i) q^{19} +2.00000 q^{20} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +(-2.50000 - 0.866025i) q^{28} +1.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +1.00000 q^{34} +(1.00000 + 5.19615i) q^{35} +(2.50000 - 4.33013i) q^{37} +(-1.50000 - 2.59808i) q^{38} +(1.00000 - 1.73205i) q^{40} +10.0000 q^{41} +1.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.500000 + 0.866025i) q^{46} +(3.50000 - 6.06218i) q^{47} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(6.00000 + 10.3923i) q^{53} -2.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(0.500000 - 0.866025i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(0.500000 - 0.866025i) q^{68} +(5.00000 + 1.73205i) q^{70} -5.00000 q^{71} +(4.00000 + 6.92820i) q^{73} +(-2.50000 - 4.33013i) q^{74} -3.00000 q^{76} +(2.50000 + 0.866025i) q^{77} +(-1.00000 - 1.73205i) q^{80} +(5.00000 - 8.66025i) q^{82} +6.00000 q^{83} -2.00000 q^{85} +(0.500000 - 0.866025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(4.00000 - 3.46410i) q^{91} +1.00000 q^{92} +(-3.50000 - 6.06218i) q^{94} +(3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + O(q^{10})$$ $$2q + q^{2} - q^{4} - 2q^{5} + 4q^{7} - 2q^{8} + 2q^{10} + q^{11} + 4q^{13} - q^{14} - q^{16} + q^{17} + 3q^{19} + 4q^{20} + 2q^{22} - q^{23} + q^{25} + 2q^{26} - 5q^{28} + 2q^{29} + 2q^{31} + q^{32} + 2q^{34} + 2q^{35} + 5q^{37} - 3q^{38} + 2q^{40} + 20q^{41} + 2q^{43} + q^{44} + q^{46} + 7q^{47} + 2q^{49} + 2q^{50} - 2q^{52} + 12q^{53} - 4q^{55} - 4q^{56} + q^{58} - 3q^{59} + 14q^{61} + 4q^{62} + 2q^{64} - 4q^{65} - 12q^{67} + q^{68} + 10q^{70} - 10q^{71} + 8q^{73} - 5q^{74} - 6q^{76} + 5q^{77} - 2q^{80} + 10q^{82} + 12q^{83} - 4q^{85} + q^{86} - q^{88} - 6q^{89} + 8q^{91} + 2q^{92} - 7q^{94} + 6q^{95} + 14q^{97} - 11q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$$.

 $$n$$ $$155$$ $$199$$ $$1135$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i $$-0.980917\pi$$
0.550990 + 0.834512i $$0.314250\pi$$
$$6$$ 0 0
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 1.00000 + 1.73205i 0.316228 + 0.547723i
$$11$$ 0.500000 + 0.866025i 0.150756 + 0.261116i
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ −0.500000 2.59808i −0.133631 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0.500000 + 0.866025i 0.121268 + 0.210042i 0.920268 0.391289i $$-0.127971\pi$$
−0.799000 + 0.601331i $$0.794637\pi$$
$$18$$ 0 0
$$19$$ 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i $$-0.721509\pi$$
0.985194 + 0.171442i $$0.0548427\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ 1.00000 0.213201
$$23$$ −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i $$-0.866580\pi$$
0.809177 + 0.587565i $$0.199913\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ 1.00000 1.73205i 0.196116 0.339683i
$$27$$ 0 0
$$28$$ −2.50000 0.866025i −0.472456 0.163663i
$$29$$ 1.00000 0.185695 0.0928477 0.995680i $$-0.470403\pi$$
0.0928477 + 0.995680i $$0.470403\pi$$
$$30$$ 0 0
$$31$$ 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i $$-0.109185\pi$$
−0.762140 + 0.647412i $$0.775851\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 1.00000 0.171499
$$35$$ 1.00000 + 5.19615i 0.169031 + 0.878310i
$$36$$ 0 0
$$37$$ 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i $$-0.698514\pi$$
0.994999 + 0.0998840i $$0.0318472\pi$$
$$38$$ −1.50000 2.59808i −0.243332 0.421464i
$$39$$ 0 0
$$40$$ 1.00000 1.73205i 0.158114 0.273861i
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ 0.500000 0.866025i 0.0753778 0.130558i
$$45$$ 0 0
$$46$$ 0.500000 + 0.866025i 0.0737210 + 0.127688i
$$47$$ 3.50000 6.06218i 0.510527 0.884260i −0.489398 0.872060i $$-0.662783\pi$$
0.999926 0.0121990i $$-0.00388317\pi$$
$$48$$ 0 0
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i $$0.141688\pi$$
−0.0783936 + 0.996922i $$0.524979\pi$$
$$54$$ 0 0
$$55$$ −2.00000 −0.269680
$$56$$ −2.00000 + 1.73205i −0.267261 + 0.231455i
$$57$$ 0 0
$$58$$ 0.500000 0.866025i 0.0656532 0.113715i
$$59$$ −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i $$-0.229229\pi$$
−0.946993 + 0.321253i $$0.895896\pi$$
$$60$$ 0 0
$$61$$ 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i $$-0.479608\pi$$
0.832240 0.554416i $$-0.187058\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 + 3.46410i −0.248069 + 0.429669i
$$66$$ 0 0
$$67$$ −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i $$-0.904778\pi$$
0.222571 0.974916i $$-0.428555\pi$$
$$68$$ 0.500000 0.866025i 0.0606339 0.105021i
$$69$$ 0 0
$$70$$ 5.00000 + 1.73205i 0.597614 + 0.207020i
$$71$$ −5.00000 −0.593391 −0.296695 0.954972i $$-0.595885\pi$$
−0.296695 + 0.954972i $$0.595885\pi$$
$$72$$ 0 0
$$73$$ 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i $$-0.0115821\pi$$
−0.531174 + 0.847263i $$0.678249\pi$$
$$74$$ −2.50000 4.33013i −0.290619 0.503367i
$$75$$ 0 0
$$76$$ −3.00000 −0.344124
$$77$$ 2.50000 + 0.866025i 0.284901 + 0.0986928i
$$78$$ 0 0
$$79$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$80$$ −1.00000 1.73205i −0.111803 0.193649i
$$81$$ 0 0
$$82$$ 5.00000 8.66025i 0.552158 0.956365i
$$83$$ 6.00000 0.658586 0.329293 0.944228i $$-0.393190\pi$$
0.329293 + 0.944228i $$0.393190\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ 0.500000 0.866025i 0.0539164 0.0933859i
$$87$$ 0 0
$$88$$ −0.500000 0.866025i −0.0533002 0.0923186i
$$89$$ −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i $$-0.936344\pi$$
0.662071 + 0.749441i $$0.269678\pi$$
$$90$$ 0 0
$$91$$ 4.00000 3.46410i 0.419314 0.363137i
$$92$$ 1.00000 0.104257
$$93$$ 0 0
$$94$$ −3.50000 6.06218i −0.360997 0.625266i
$$95$$ 3.00000 + 5.19615i 0.307794 + 0.533114i
$$96$$ 0 0
$$97$$ 7.00000 0.710742 0.355371 0.934725i $$-0.384354\pi$$
0.355371 + 0.934725i $$0.384354\pi$$
$$98$$ −5.50000 4.33013i −0.555584 0.437409i
$$99$$ 0 0
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i $$-0.314447\pi$$
−0.998240 + 0.0592978i $$0.981114\pi$$
$$102$$ 0 0
$$103$$ 3.00000 5.19615i 0.295599 0.511992i −0.679525 0.733652i $$-0.737814\pi$$
0.975124 + 0.221660i $$0.0711475\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ 12.0000 1.16554
$$107$$ −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i $$-0.864154\pi$$
0.813632 + 0.581380i $$0.197487\pi$$
$$108$$ 0 0
$$109$$ 10.0000 + 17.3205i 0.957826 + 1.65900i 0.727764 + 0.685828i $$0.240560\pi$$
0.230063 + 0.973176i $$0.426107\pi$$
$$110$$ −1.00000 + 1.73205i −0.0953463 + 0.165145i
$$111$$ 0 0
$$112$$ 0.500000 + 2.59808i 0.0472456 + 0.245495i
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ 0 0
$$115$$ −1.00000 1.73205i −0.0932505 0.161515i
$$116$$ −0.500000 0.866025i −0.0464238 0.0804084i
$$117$$ 0 0
$$118$$ −3.00000 −0.276172
$$119$$ 2.50000 + 0.866025i 0.229175 + 0.0793884i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ −7.00000 12.1244i −0.633750 1.09769i
$$123$$ 0 0
$$124$$ 1.00000 1.73205i 0.0898027 0.155543i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −1.00000 −0.0887357 −0.0443678 0.999015i $$-0.514127\pi$$
−0.0443678 + 0.999015i $$0.514127\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 2.00000 + 3.46410i 0.175412 + 0.303822i
$$131$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$132$$ 0 0
$$133$$ −1.50000 7.79423i −0.130066 0.675845i
$$134$$ −12.0000 −1.03664
$$135$$ 0 0
$$136$$ −0.500000 0.866025i −0.0428746 0.0742611i
$$137$$ 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
$$139$$ −13.0000 −1.10265 −0.551323 0.834292i $$-0.685877\pi$$
−0.551323 + 0.834292i $$0.685877\pi$$
$$140$$ 4.00000 3.46410i 0.338062 0.292770i
$$141$$ 0 0
$$142$$ −2.50000 + 4.33013i −0.209795 + 0.363376i
$$143$$ 1.00000 + 1.73205i 0.0836242 + 0.144841i
$$144$$ 0 0
$$145$$ −1.00000 + 1.73205i −0.0830455 + 0.143839i
$$146$$ 8.00000 0.662085
$$147$$ 0 0
$$148$$ −5.00000 −0.410997
$$149$$ −5.50000 + 9.52628i −0.450578 + 0.780423i −0.998422 0.0561570i $$-0.982115\pi$$
0.547844 + 0.836580i $$0.315449\pi$$
$$150$$ 0 0
$$151$$ 7.50000 + 12.9904i 0.610341 + 1.05714i 0.991183 + 0.132502i $$0.0423010\pi$$
−0.380841 + 0.924640i $$0.624366\pi$$
$$152$$ −1.50000 + 2.59808i −0.121666 + 0.210732i
$$153$$ 0 0
$$154$$ 2.00000 1.73205i 0.161165 0.139573i
$$155$$ −4.00000 −0.321288
$$156$$ 0 0
$$157$$ −0.500000 0.866025i −0.0399043 0.0691164i 0.845383 0.534160i $$-0.179372\pi$$
−0.885288 + 0.465044i $$0.846039\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −2.00000 −0.158114
$$161$$ 0.500000 + 2.59808i 0.0394055 + 0.204757i
$$162$$ 0 0
$$163$$ −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i $$-0.961422\pi$$
0.601035 + 0.799223i $$0.294755\pi$$
$$164$$ −5.00000 8.66025i −0.390434 0.676252i
$$165$$ 0 0
$$166$$ 3.00000 5.19615i 0.232845 0.403300i
$$167$$ −2.00000 −0.154765 −0.0773823 0.997001i $$-0.524656\pi$$
−0.0773823 + 0.997001i $$0.524656\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ −1.00000 + 1.73205i −0.0766965 + 0.132842i
$$171$$ 0 0
$$172$$ −0.500000 0.866025i −0.0381246 0.0660338i
$$173$$ 7.00000 12.1244i 0.532200 0.921798i −0.467093 0.884208i $$-0.654699\pi$$
0.999293 0.0375896i $$-0.0119679\pi$$
$$174$$ 0 0
$$175$$ 2.50000 + 0.866025i 0.188982 + 0.0654654i
$$176$$ −1.00000 −0.0753778
$$177$$ 0 0
$$178$$ 3.00000 + 5.19615i 0.224860 + 0.389468i
$$179$$ −3.50000 6.06218i −0.261602 0.453108i 0.705066 0.709142i $$-0.250918\pi$$
−0.966668 + 0.256034i $$0.917584\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ −1.00000 5.19615i −0.0741249 0.385164i
$$183$$ 0 0
$$184$$ 0.500000 0.866025i 0.0368605 0.0638442i
$$185$$ 5.00000 + 8.66025i 0.367607 + 0.636715i
$$186$$ 0 0
$$187$$ −0.500000 + 0.866025i −0.0365636 + 0.0633300i
$$188$$ −7.00000 −0.510527
$$189$$ 0 0
$$190$$ 6.00000 0.435286
$$191$$ −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i $$-0.926799\pi$$
0.684244 + 0.729253i $$0.260132\pi$$
$$192$$ 0 0
$$193$$ −4.00000 6.92820i −0.287926 0.498703i 0.685388 0.728178i $$-0.259632\pi$$
−0.973315 + 0.229475i $$0.926299\pi$$
$$194$$ 3.50000 6.06218i 0.251285 0.435239i
$$195$$ 0 0
$$196$$ −6.50000 + 2.59808i −0.464286 + 0.185577i
$$197$$ −27.0000 −1.92367 −0.961835 0.273629i $$-0.911776\pi$$
−0.961835 + 0.273629i $$0.911776\pi$$
$$198$$ 0 0
$$199$$ 1.00000 + 1.73205i 0.0708881 + 0.122782i 0.899291 0.437351i $$-0.144083\pi$$
−0.828403 + 0.560133i $$0.810750\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ −9.00000 −0.633238
$$203$$ 2.00000 1.73205i 0.140372 0.121566i
$$204$$ 0 0
$$205$$ −10.0000 + 17.3205i −0.698430 + 1.20972i
$$206$$ −3.00000 5.19615i −0.209020 0.362033i
$$207$$ 0 0
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ 3.00000 0.207514
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 6.00000 10.3923i 0.412082 0.713746i
$$213$$ 0 0
$$214$$ 1.00000 + 1.73205i 0.0683586 + 0.118401i
$$215$$ −1.00000 + 1.73205i −0.0681994 + 0.118125i
$$216$$ 0 0
$$217$$ 5.00000 + 1.73205i 0.339422 + 0.117579i
$$218$$ 20.0000 1.35457
$$219$$ 0 0
$$220$$ 1.00000 + 1.73205i 0.0674200 + 0.116775i
$$221$$ 1.00000 + 1.73205i 0.0672673 + 0.116510i
$$222$$ 0 0
$$223$$ −26.0000 −1.74109 −0.870544 0.492090i $$-0.836233\pi$$
−0.870544 + 0.492090i $$0.836233\pi$$
$$224$$ 2.50000 + 0.866025i 0.167038 + 0.0578638i
$$225$$ 0 0
$$226$$ −5.00000 + 8.66025i −0.332595 + 0.576072i
$$227$$ −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i $$-0.274343\pi$$
−0.982877 + 0.184263i $$0.941010\pi$$
$$228$$ 0 0
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ −2.00000 −0.131876
$$231$$ 0 0
$$232$$ −1.00000 −0.0656532
$$233$$ −10.5000 + 18.1865i −0.687878 + 1.19144i 0.284645 + 0.958633i $$0.408124\pi$$
−0.972523 + 0.232806i $$0.925209\pi$$
$$234$$ 0 0
$$235$$ 7.00000 + 12.1244i 0.456630 + 0.790906i
$$236$$ −1.50000 + 2.59808i −0.0976417 + 0.169120i
$$237$$ 0 0
$$238$$ 2.00000 1.73205i 0.129641 0.112272i
$$239$$ 22.0000 1.42306 0.711531 0.702655i $$-0.248002\pi$$
0.711531 + 0.702655i $$0.248002\pi$$
$$240$$ 0 0
$$241$$ 6.00000 + 10.3923i 0.386494 + 0.669427i 0.991975 0.126432i $$-0.0403527\pi$$
−0.605481 + 0.795860i $$0.707019\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ −14.0000 −0.896258
$$245$$ 11.0000 + 8.66025i 0.702764 + 0.553283i
$$246$$ 0 0
$$247$$ 3.00000 5.19615i 0.190885 0.330623i
$$248$$ −1.00000 1.73205i −0.0635001 0.109985i
$$249$$ 0 0
$$250$$ −6.00000 + 10.3923i −0.379473 + 0.657267i
$$251$$ 21.0000 1.32551 0.662754 0.748837i $$-0.269387\pi$$
0.662754 + 0.748837i $$0.269387\pi$$
$$252$$ 0 0
$$253$$ −1.00000 −0.0628695
$$254$$ −0.500000 + 0.866025i −0.0313728 + 0.0543393i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i $$-0.893253\pi$$
0.757159 + 0.653231i $$0.226587\pi$$
$$258$$ 0 0
$$259$$ −2.50000 12.9904i −0.155342 0.807183i
$$260$$ 4.00000 0.248069
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i $$-0.225891\pi$$
−0.943572 + 0.331166i $$0.892558\pi$$
$$264$$ 0 0
$$265$$ −24.0000 −1.47431
$$266$$ −7.50000 2.59808i −0.459855 0.159298i
$$267$$ 0 0
$$268$$ −6.00000 + 10.3923i −0.366508 + 0.634811i
$$269$$ 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i $$-0.0474530\pi$$
−0.623082 + 0.782157i $$0.714120\pi$$
$$270$$ 0 0
$$271$$ −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i $$-0.994865\pi$$
0.513905 + 0.857847i $$0.328199\pi$$
$$272$$ −1.00000 −0.0606339
$$273$$ 0 0
$$274$$ 6.00000 0.362473
$$275$$ −0.500000 + 0.866025i −0.0301511 + 0.0522233i
$$276$$ 0 0
$$277$$ 12.0000 + 20.7846i 0.721010 + 1.24883i 0.960595 + 0.277951i $$0.0896552\pi$$
−0.239585 + 0.970875i $$0.577011\pi$$
$$278$$ −6.50000 + 11.2583i −0.389844 + 0.675230i
$$279$$ 0 0
$$280$$ −1.00000 5.19615i −0.0597614 0.310530i
$$281$$ −7.00000 −0.417585 −0.208792 0.977960i $$-0.566953\pi$$
−0.208792 + 0.977960i $$0.566953\pi$$
$$282$$ 0 0
$$283$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 2.50000 + 4.33013i 0.148348 + 0.256946i
$$285$$ 0 0
$$286$$ 2.00000 0.118262
$$287$$ 20.0000 17.3205i 1.18056 1.02240i
$$288$$ 0 0
$$289$$ 8.00000 13.8564i 0.470588 0.815083i
$$290$$ 1.00000 + 1.73205i 0.0587220 + 0.101710i
$$291$$ 0 0
$$292$$ 4.00000 6.92820i 0.234082 0.405442i
$$293$$ −9.00000 −0.525786 −0.262893 0.964825i $$-0.584677\pi$$
−0.262893 + 0.964825i $$0.584677\pi$$
$$294$$ 0 0
$$295$$ 6.00000 0.349334
$$296$$ −2.50000 + 4.33013i −0.145310 + 0.251684i
$$297$$ 0 0
$$298$$ 5.50000 + 9.52628i 0.318606 + 0.551843i
$$299$$ −1.00000 + 1.73205i −0.0578315 + 0.100167i
$$300$$ 0 0
$$301$$ 2.00000 1.73205i 0.115278 0.0998337i
$$302$$ 15.0000 0.863153
$$303$$ 0 0
$$304$$ 1.50000 + 2.59808i 0.0860309 + 0.149010i
$$305$$ 14.0000 + 24.2487i 0.801638 + 1.38848i
$$306$$ 0 0
$$307$$ −4.00000 −0.228292 −0.114146 0.993464i $$-0.536413\pi$$
−0.114146 + 0.993464i $$0.536413\pi$$
$$308$$ −0.500000 2.59808i −0.0284901 0.148039i
$$309$$ 0 0
$$310$$ −2.00000 + 3.46410i −0.113592 + 0.196748i
$$311$$ 6.50000 + 11.2583i 0.368581 + 0.638401i 0.989344 0.145597i $$-0.0465103\pi$$
−0.620763 + 0.783998i $$0.713177\pi$$
$$312$$ 0 0
$$313$$ −3.50000 + 6.06218i −0.197832 + 0.342655i −0.947825 0.318791i $$-0.896723\pi$$
0.749993 + 0.661445i $$0.230057\pi$$
$$314$$ −1.00000 −0.0564333
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i $$-0.779442\pi$$
0.937892 + 0.346929i $$0.112775\pi$$
$$318$$ 0 0
$$319$$ 0.500000 + 0.866025i 0.0279946 + 0.0484881i
$$320$$ −1.00000 + 1.73205i −0.0559017 + 0.0968246i
$$321$$ 0 0
$$322$$ 2.50000 + 0.866025i 0.139320 + 0.0482617i
$$323$$ 3.00000 0.166924
$$324$$ 0 0
$$325$$ 1.00000 + 1.73205i 0.0554700 + 0.0960769i
$$326$$ 5.00000 + 8.66025i 0.276924 + 0.479647i
$$327$$ 0 0
$$328$$ −10.0000 −0.552158
$$329$$ −3.50000 18.1865i −0.192961 1.00266i
$$330$$ 0 0
$$331$$ 1.00000 1.73205i 0.0549650 0.0952021i −0.837234 0.546845i $$-0.815829\pi$$
0.892199 + 0.451643i $$0.149162\pi$$
$$332$$ −3.00000 5.19615i −0.164646 0.285176i
$$333$$ 0 0
$$334$$ −1.00000 + 1.73205i −0.0547176 + 0.0947736i
$$335$$ 24.0000 1.31126
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ 1.00000 + 1.73205i 0.0542326 + 0.0939336i
$$341$$ −1.00000 + 1.73205i −0.0541530 + 0.0937958i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ −1.00000 −0.0539164
$$345$$ 0 0
$$346$$ −7.00000 12.1244i −0.376322 0.651809i
$$347$$ −16.0000 27.7128i −0.858925 1.48770i −0.872955 0.487800i $$-0.837799\pi$$
0.0140303 0.999902i $$-0.495534\pi$$
$$348$$ 0 0
$$349$$ −16.0000 −0.856460 −0.428230 0.903670i $$-0.640863\pi$$
−0.428230 + 0.903670i $$0.640863\pi$$
$$350$$ 2.00000 1.73205i 0.106904 0.0925820i
$$351$$ 0 0
$$352$$ −0.500000 + 0.866025i −0.0266501 + 0.0461593i
$$353$$ −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i $$-0.217711\pi$$
−0.934751 + 0.355303i $$0.884378\pi$$
$$354$$ 0 0
$$355$$ 5.00000 8.66025i 0.265372 0.459639i
$$356$$ 6.00000 0.317999
$$357$$ 0 0
$$358$$ −7.00000 −0.369961
$$359$$ 5.00000 8.66025i 0.263890 0.457071i −0.703382 0.710812i $$-0.748328\pi$$
0.967272 + 0.253741i $$0.0816611\pi$$
$$360$$ 0 0
$$361$$ 5.00000 + 8.66025i 0.263158 + 0.455803i
$$362$$ −5.00000 + 8.66025i −0.262794 + 0.455173i
$$363$$ 0 0
$$364$$ −5.00000 1.73205i −0.262071 0.0907841i
$$365$$ −16.0000 −0.837478
$$366$$ 0 0
$$367$$ 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i $$0.147978\pi$$
−0.0586798 + 0.998277i $$0.518689\pi$$
$$368$$ −0.500000 0.866025i −0.0260643 0.0451447i
$$369$$ 0 0
$$370$$ 10.0000 0.519875
$$371$$ 30.0000 + 10.3923i 1.55752 + 0.539542i
$$372$$ 0 0
$$373$$ −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i $$0.401711\pi$$
−0.977016 + 0.213165i $$0.931623\pi$$
$$374$$ 0.500000 + 0.866025i 0.0258544 + 0.0447811i
$$375$$ 0 0
$$376$$ −3.50000 + 6.06218i −0.180499 + 0.312633i
$$377$$ 2.00000 0.103005
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 3.00000 5.19615i 0.153897 0.266557i
$$381$$ 0 0
$$382$$ 4.00000 + 6.92820i 0.204658 + 0.354478i
$$383$$ 12.5000 21.6506i 0.638720 1.10630i −0.346994 0.937867i $$-0.612797\pi$$
0.985714 0.168428i $$-0.0538692\pi$$
$$384$$ 0 0
$$385$$ −4.00000 + 3.46410i −0.203859 + 0.176547i
$$386$$ −8.00000 −0.407189
$$387$$ 0 0
$$388$$ −3.50000 6.06218i −0.177686 0.307760i
$$389$$ −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i $$-0.891606\pi$$
0.182047 0.983290i $$-0.441728\pi$$
$$390$$ 0 0
$$391$$ −1.00000 −0.0505722
$$392$$ −1.00000 + 6.92820i −0.0505076 + 0.349927i
$$393$$ 0 0
$$394$$ −13.5000 + 23.3827i −0.680120 + 1.17800i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 13.5000 23.3827i 0.677546 1.17354i −0.298172 0.954512i $$-0.596377\pi$$
0.975718 0.219031i $$-0.0702897\pi$$
$$398$$ 2.00000 0.100251
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −12.0000 + 20.7846i −0.599251 + 1.03793i 0.393680 + 0.919247i $$0.371202\pi$$
−0.992932 + 0.118686i $$0.962132\pi$$
$$402$$ 0 0
$$403$$ 2.00000 + 3.46410i 0.0996271 + 0.172559i
$$404$$ −4.50000 + 7.79423i −0.223883 + 0.387777i
$$405$$ 0 0
$$406$$ −0.500000 2.59808i −0.0248146 0.128940i
$$407$$ 5.00000 0.247841
$$408$$ 0 0
$$409$$ −8.00000 13.8564i −0.395575 0.685155i 0.597600 0.801795i $$-0.296121\pi$$
−0.993174 + 0.116639i $$0.962788\pi$$
$$410$$ 10.0000 + 17.3205i 0.493865 + 0.855399i
$$411$$ 0 0
$$412$$ −6.00000 −0.295599
$$413$$ −7.50000 2.59808i −0.369051 0.127843i
$$414$$ 0 0
$$415$$ −6.00000 + 10.3923i −0.294528 + 0.510138i
$$416$$ 1.00000 + 1.73205i 0.0490290 + 0.0849208i
$$417$$ 0 0
$$418$$ 1.50000 2.59808i 0.0733674 0.127076i
$$419$$ −29.0000 −1.41674 −0.708371 0.705840i $$-0.750570\pi$$
−0.708371 + 0.705840i $$0.750570\pi$$
$$420$$ 0 0
$$421$$ −17.0000 −0.828529 −0.414265 0.910156i $$-0.635961\pi$$
−0.414265 + 0.910156i $$0.635961\pi$$
$$422$$ 2.00000 3.46410i 0.0973585 0.168630i
$$423$$ 0 0
$$424$$ −6.00000 10.3923i −0.291386 0.504695i
$$425$$ −0.500000 + 0.866025i −0.0242536 + 0.0420084i
$$426$$ 0 0
$$427$$ −7.00000 36.3731i −0.338754 1.76022i
$$428$$ 2.00000 0.0966736
$$429$$ 0 0
$$430$$ 1.00000 + 1.73205i 0.0482243 + 0.0835269i
$$431$$ −8.00000 13.8564i −0.385346 0.667440i 0.606471 0.795106i $$-0.292585\pi$$
−0.991817 + 0.127666i $$0.959251\pi$$
$$432$$ 0 0
$$433$$ −19.0000 −0.913082 −0.456541 0.889702i $$-0.650912\pi$$
−0.456541 + 0.889702i $$0.650912\pi$$
$$434$$ 4.00000 3.46410i 0.192006 0.166282i
$$435$$ 0 0
$$436$$ 10.0000 17.3205i 0.478913 0.829502i
$$437$$ 1.50000 + 2.59808i 0.0717547 + 0.124283i
$$438$$ 0 0
$$439$$ −15.5000 + 26.8468i −0.739775 + 1.28133i 0.212822 + 0.977091i $$0.431735\pi$$
−0.952597 + 0.304236i $$0.901599\pi$$
$$440$$ 2.00000 0.0953463
$$441$$ 0 0
$$442$$ 2.00000 0.0951303
$$443$$ 7.50000 12.9904i 0.356336 0.617192i −0.631010 0.775775i $$-0.717359\pi$$
0.987346 + 0.158583i $$0.0506926\pi$$
$$444$$ 0 0
$$445$$ −6.00000 10.3923i −0.284427 0.492642i
$$446$$ −13.0000 + 22.5167i −0.615568 + 1.06619i
$$447$$ 0 0
$$448$$ 2.00000 1.73205i 0.0944911 0.0818317i
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 0 0
$$451$$ 5.00000 + 8.66025i 0.235441 + 0.407795i
$$452$$ 5.00000 + 8.66025i 0.235180 + 0.407344i
$$453$$ 0 0
$$454$$ −10.0000 −0.469323
$$455$$ 2.00000 + 10.3923i 0.0937614 + 0.487199i
$$456$$ 0 0
$$457$$ −16.0000 + 27.7128i −0.748448 + 1.29635i 0.200118 + 0.979772i $$0.435868\pi$$
−0.948566 + 0.316579i $$0.897466\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ 0 0
$$460$$ −1.00000 + 1.73205i −0.0466252 + 0.0807573i
$$461$$ −33.0000 −1.53696 −0.768482 0.639872i $$-0.778987\pi$$
−0.768482 + 0.639872i $$0.778987\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −0.500000 + 0.866025i −0.0232119 + 0.0402042i
$$465$$ 0 0
$$466$$ 10.5000 + 18.1865i 0.486403 + 0.842475i
$$467$$ 13.5000 23.3827i 0.624705 1.08202i −0.363892 0.931441i $$-0.618552\pi$$
0.988598 0.150581i $$-0.0481143\pi$$
$$468$$ 0 0
$$469$$ −30.0000 10.3923i −1.38527 0.479872i
$$470$$ 14.0000 0.645772
$$471$$ 0 0
$$472$$ 1.50000 + 2.59808i 0.0690431 + 0.119586i
$$473$$ 0.500000 + 0.866025i 0.0229900 + 0.0398199i
$$474$$ 0 0
$$475$$ 3.00000 0.137649
$$476$$ −0.500000 2.59808i −0.0229175 0.119083i
$$477$$ 0 0
$$478$$ 11.0000 19.0526i 0.503128 0.871444i
$$479$$ −13.0000 22.5167i −0.593985 1.02881i −0.993689 0.112168i $$-0.964220\pi$$
0.399704 0.916644i $$-0.369113\pi$$
$$480$$ 0 0
$$481$$ 5.00000 8.66025i 0.227980 0.394874i
$$482$$ 12.0000 0.546585
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −7.00000 + 12.1244i −0.317854 + 0.550539i
$$486$$ 0 0
$$487$$ 17.0000 + 29.4449i 0.770344 + 1.33427i 0.937375 + 0.348323i $$0.113249\pi$$
−0.167031 + 0.985952i $$0.553418\pi$$
$$488$$ −7.00000 + 12.1244i −0.316875 + 0.548844i
$$489$$ 0 0
$$490$$ 13.0000 5.19615i 0.587280 0.234738i
$$491$$ 6.00000 0.270776 0.135388 0.990793i $$-0.456772\pi$$
0.135388 + 0.990793i $$0.456772\pi$$
$$492$$ 0 0
$$493$$ 0.500000 + 0.866025i 0.0225189 + 0.0390038i
$$494$$ −3.00000 5.19615i −0.134976 0.233786i
$$495$$ 0 0
$$496$$ −2.00000 −0.0898027
$$497$$ −10.0000 + 8.66025i −0.448561 + 0.388465i
$$498$$ 0 0
$$499$$ −4.00000 + 6.92820i −0.179065 + 0.310149i −0.941560 0.336844i $$-0.890640\pi$$
0.762496 + 0.646993i $$0.223974\pi$$
$$500$$ 6.00000 + 10.3923i 0.268328 + 0.464758i
$$501$$ 0 0
$$502$$ 10.5000 18.1865i 0.468638 0.811705i
$$503$$ 42.0000 1.87269 0.936344 0.351085i $$-0.114187\pi$$
0.936344 + 0.351085i $$0.114187\pi$$
$$504$$ 0 0
$$505$$ 18.0000 0.800989
$$506$$ −0.500000 + 0.866025i −0.0222277 + 0.0384995i
$$507$$ 0 0
$$508$$ 0.500000 + 0.866025i 0.0221839 + 0.0384237i
$$509$$ −10.0000 + 17.3205i −0.443242 + 0.767718i −0.997928 0.0643419i $$-0.979505\pi$$
0.554686 + 0.832060i $$0.312839\pi$$
$$510$$ 0 0
$$511$$ 20.0000 + 6.92820i 0.884748 + 0.306486i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 3.00000 + 5.19615i 0.132324 + 0.229192i
$$515$$ 6.00000 + 10.3923i 0.264392 + 0.457940i
$$516$$ 0 0
$$517$$ 7.00000 0.307860
$$518$$ −12.5000 4.33013i −0.549218 0.190255i
$$519$$ 0 0
$$520$$ 2.00000 3.46410i 0.0877058 0.151911i
$$521$$ 7.00000 + 12.1244i 0.306676 + 0.531178i 0.977633 0.210318i $$-0.0674500\pi$$
−0.670957 + 0.741496i $$0.734117\pi$$
$$522$$ 0 0
$$523$$ 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i $$-0.805460\pi$$
0.906434 + 0.422347i $$0.138794\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −6.00000 −0.261612
$$527$$ −1.00000 + 1.73205i −0.0435607 + 0.0754493i
$$528$$ 0 0
$$529$$ 11.0000 + 19.0526i 0.478261 + 0.828372i
$$530$$ −12.0000 + 20.7846i −0.521247 + 0.902826i
$$531$$ 0 0
$$532$$ −6.00000 + 5.19615i −0.260133 + 0.225282i
$$533$$ 20.0000 0.866296
$$534$$ 0 0
$$535$$ −2.00000 3.46410i −0.0864675 0.149766i
$$536$$ 6.00000 + 10.3923i 0.259161 + 0.448879i
$$537$$ 0 0
$$538$$ 12.0000 0.517357
$$539$$ 6.50000 2.59808i 0.279975 0.111907i
$$540$$ 0 0
$$541$$ 8.00000 13.8564i 0.343947 0.595733i −0.641215 0.767361i $$-0.721569\pi$$
0.985162 + 0.171628i $$0.0549027\pi$$
$$542$$ 8.00000 + 13.8564i 0.343629 + 0.595184i
$$543$$ 0 0
$$544$$ −0.500000 + 0.866025i −0.0214373 + 0.0371305i
$$545$$ −40.0000 −1.71341
$$546$$ 0 0
$$547$$ 39.0000 1.66752 0.833760 0.552127i $$-0.186184\pi$$
0.833760 + 0.552127i $$0.186184\pi$$
$$548$$ 3.00000 5.19615i 0.128154 0.221969i
$$549$$ 0 0
$$550$$ 0.500000 + 0.866025i 0.0213201 + 0.0369274i
$$551$$ 1.50000 2.59808i 0.0639021 0.110682i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 24.0000 1.01966
$$555$$ 0 0
$$556$$ 6.50000 + 11.2583i 0.275661 + 0.477460i
$$557$$ −17.5000 30.3109i −0.741499 1.28431i −0.951813 0.306680i $$-0.900782\pi$$
0.210314 0.977634i $$-0.432551\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ −5.00000 1.73205i −0.211289 0.0731925i
$$561$$ 0 0
$$562$$ −3.50000 + 6.06218i −0.147639 + 0.255718i
$$563$$ −19.0000 32.9090i −0.800755 1.38695i −0.919120 0.393977i $$-0.871099\pi$$
0.118366 0.992970i $$-0.462235\pi$$
$$564$$ 0 0
$$565$$ 10.0000 17.3205i 0.420703 0.728679i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 5.00000 0.209795
$$569$$ −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i $$-0.935142\pi$$
0.664897 + 0.746935i $$0.268475\pi$$
$$570$$ 0 0
$$571$$ −3.50000 6.06218i −0.146470 0.253694i 0.783450 0.621455i $$-0.213458\pi$$
−0.929921 + 0.367760i $$0.880125\pi$$
$$572$$ 1.00000 1.73205i 0.0418121 0.0724207i
$$573$$ 0 0
$$574$$ −5.00000 25.9808i −0.208696 1.08442i
$$575$$ −1.00000 −0.0417029
$$576$$ 0 0
$$577$$ −7.00000 12.1244i −0.291414 0.504744i 0.682730 0.730670i $$-0.260792\pi$$
−0.974144 + 0.225927i $$0.927459\pi$$
$$578$$ −8.00000 13.8564i −0.332756 0.576351i
$$579$$ 0 0
$$580$$ 2.00000 0.0830455
$$581$$ 12.0000 10.3923i 0.497844 0.431145i
$$582$$ 0 0
$$583$$ −6.00000 + 10.3923i −0.248495 + 0.430405i
$$584$$ −4.00000 6.92820i −0.165521 0.286691i
$$585$$ 0 0
$$586$$ −4.50000 + 7.79423i −0.185893 + 0.321977i
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 0 0
$$589$$ 6.00000 0.247226
$$590$$ 3.00000 5.19615i 0.123508 0.213922i
$$591$$ 0 0
$$592$$ 2.50000 + 4.33013i 0.102749 + 0.177967i
$$593$$ 7.50000 12.9904i 0.307988 0.533451i −0.669934 0.742421i $$-0.733678\pi$$
0.977922 + 0.208970i $$0.0670110\pi$$
$$594$$ 0 0
$$595$$ −4.00000 + 3.46410i −0.163984 + 0.142014i
$$596$$ 11.0000 0.450578
$$597$$ 0 0
$$598$$ 1.00000 + 1.73205i 0.0408930 + 0.0708288i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0 0
$$601$$ 8.00000 0.326327 0.163163 0.986599i $$-0.447830\pi$$
0.163163 + 0.986599i $$0.447830\pi$$
$$602$$ −0.500000 2.59808i −0.0203785 0.105890i
$$603$$ 0 0
$$604$$ 7.50000 12.9904i 0.305171 0.528571i
$$605$$ −1.00000 1.73205i −0.0406558 0.0704179i
$$606$$ 0 0
$$607$$ 14.0000 24.2487i 0.568242 0.984225i −0.428497 0.903543i $$-0.640957\pi$$
0.996740 0.0806818i $$-0.0257098\pi$$
$$608$$ 3.00000 0.121666
$$609$$ 0 0
$$610$$ 28.0000 1.13369
$$611$$ 7.00000 12.1244i 0.283190 0.490499i
$$612$$ 0 0
$$613$$ 7.00000 + 12.1244i 0.282727 + 0.489698i 0.972056 0.234751i $$-0.0754275\pi$$
−0.689328 + 0.724449i $$0.742094\pi$$
$$614$$ −2.00000 + 3.46410i −0.0807134 + 0.139800i
$$615$$ 0 0
$$616$$ −2.50000 0.866025i −0.100728 0.0348932i
$$617$$ −36.0000 −1.44931 −0.724653 0.689114i $$-0.758000\pi$$
−0.724653 + 0.689114i $$0.758000\pi$$
$$618$$ 0 0
$$619$$ −13.0000 22.5167i −0.522514 0.905021i −0.999657 0.0261952i $$-0.991661\pi$$
0.477143 0.878826i $$-0.341672\pi$$
$$620$$ 2.00000 + 3.46410i 0.0803219 + 0.139122i
$$621$$ 0 0
$$622$$ 13.0000 0.521253
$$623$$ 3.00000 + 15.5885i 0.120192 + 0.624538i
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 3.50000 + 6.06218i 0.139888 + 0.242293i
$$627$$ 0 0
$$628$$ −0.500000 + 0.866025i −0.0199522 + 0.0345582i
$$629$$ 5.00000 0.199363
$$630$$ 0 0
$$631$$ 18.0000 0.716569 0.358284 0.933613i $$-0.383362\pi$$
0.358284 + 0.933613i $$0.383362\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −3.00000 5.19615i −0.119145 0.206366i
$$635$$ 1.00000 1.73205i 0.0396838 0.0687343i
$$636$$ 0 0
$$637$$ 2.00000 13.8564i 0.0792429 0.549011i
$$638$$ 1.00000 0.0395904
$$639$$ 0 0
$$640$$ 1.00000 + 1.73205i 0.0395285 + 0.0684653i
$$641$$ −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i $$-0.242826\pi$$
−0.959848 + 0.280521i $$0.909493\pi$$
$$642$$ 0 0
$$643$$ −32.0000 −1.26196 −0.630978 0.775800i $$-0.717346\pi$$
−0.630978 + 0.775800i $$0.717346\pi$$
$$644$$ 2.00000 1.73205i 0.0788110 0.0682524i
$$645$$ 0 0
$$646$$ 1.50000 2.59808i 0.0590167 0.102220i
$$647$$ 24.0000 + 41.5692i 0.943537 + 1.63425i 0.758654 + 0.651494i $$0.225858\pi$$
0.184884 + 0.982760i $$0.440809\pi$$
$$648$$ 0 0
$$649$$ 1.50000 2.59808i 0.0588802 0.101983i
$$650$$ 2.00000 0.0784465
$$651$$ 0 0
$$652$$ 10.0000 0.391630
$$653$$ 7.00000 12.1244i 0.273931 0.474463i −0.695934 0.718106i $$-0.745009\pi$$
0.969865 + 0.243643i $$0.0783426\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −5.00000 + 8.66025i −0.195217 + 0.338126i
$$657$$ 0 0
$$658$$ −17.5000 6.06218i −0.682221 0.236328i
$$659$$ −44.0000 −1.71400 −0.856998 0.515319i $$-0.827673\pi$$
−0.856998 + 0.515319i $$0.827673\pi$$
$$660$$ 0 0
$$661$$ −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i $$-0.197668\pi$$
−0.910541 + 0.413419i $$0.864334\pi$$
$$662$$ −1.00000 1.73205i −0.0388661 0.0673181i
$$663$$ 0 0
$$664$$ −6.00000 −0.232845
$$665$$ 15.0000 + 5.19615i 0.581675 + 0.201498i
$$666$$ 0 0
$$667$$ −0.500000 + 0.866025i −0.0193601 + 0.0335326i
$$668$$ 1.00000 + 1.73205i 0.0386912 + 0.0670151i
$$669$$ 0 0
$$670$$ 12.0000 20.7846i 0.463600 0.802980i
$$671$$ 14.0000 0.540464
$$672$$ 0 0
$$673$$ 22.0000 0.848038 0.424019 0.905653i $$-0.360619\pi$$
0.424019 + 0.905653i $$0.360619\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ 3.50000 6.06218i 0.134516 0.232988i −0.790897 0.611950i $$-0.790385\pi$$
0.925412 + 0.378962i $$0.123719\pi$$
$$678$$ 0 0
$$679$$ 14.0000 12.1244i 0.537271 0.465290i
$$680$$ 2.00000 0.0766965
$$681$$ 0 0
$$682$$ 1.00000 + 1.73205i 0.0382920 + 0.0663237i
$$683$$ −19.5000 33.7750i −0.746147 1.29236i −0.949657 0.313291i $$-0.898568\pi$$
0.203510 0.979073i $$-0.434765\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ −18.5000 + 0.866025i −0.706333 + 0.0330650i
$$687$$ 0 0
$$688$$ −0.500000 + 0.866025i −0.0190623 + 0.0330169i
$$689$$ 12.0000 + 20.7846i 0.457164 + 0.791831i
$$690$$ 0 0
$$691$$ 9.00000 15.5885i 0.342376 0.593013i −0.642497 0.766288i $$-0.722102\pi$$
0.984873 + 0.173275i $$0.0554350\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ −32.0000 −1.21470
$$695$$ 13.0000 22.5167i 0.493118 0.854106i
$$696$$ 0 0
$$697$$ 5.00000 + 8.66025i 0.189389 + 0.328031i
$$698$$ −8.00000 + 13.8564i −0.302804 + 0.524473i
$$699$$ 0 0
$$700$$ −0.500000 2.59808i −0.0188982 0.0981981i
$$701$$ −9.00000 −0.339925 −0.169963 0.985451i $$-0.554365\pi$$
−0.169963 + 0.985451i $$0.554365\pi$$
$$702$$ 0 0
$$703$$ −7.50000 12.9904i −0.282868 0.489942i
$$704$$ 0.500000 + 0.866025i 0.0188445 + 0.0326396i
$$705$$ 0 0
$$706$$ −6.00000 −0.225813
$$707$$ −22.5000 7.79423i −0.846200 0.293132i
$$708$$ 0 0
$$709$$ −4.50000 + 7.79423i −0.169001 + 0.292718i −0.938069 0.346449i $$-0.887387\pi$$
0.769068 + 0.639167i $$0.220721\pi$$
$$710$$ −5.00000 8.66025i −0.187647 0.325014i
$$711$$ 0 0
$$712$$ 3.00000 5.19615i 0.112430 0.194734i
$$713$$ −2.00000 −0.0749006
$$714$$ 0 0
$$715$$ −4.00000 −0.149592
$$716$$ −3.50000 + 6.06218i −0.130801 + 0.226554i
$$717$$ 0 0
$$718$$ −5.00000 8.66025i −0.186598 0.323198i
$$719$$ 11.5000 19.9186i 0.428878 0.742838i −0.567896 0.823100i $$-0.692242\pi$$
0.996774 + 0.0802624i $$0.0255758\pi$$
$$720$$ 0 0
$$721$$ −3.00000 15.5885i −0.111726 0.580544i
$$722$$ 10.0000 0.372161
$$723$$ 0 0
$$724$$ 5.00000 + 8.66025i 0.185824 + 0.321856i
$$725$$ 0.500000 + 0.866025i 0.0185695 + 0.0321634i
$$726$$ 0 0
$$727$$ 14.0000 0.519231 0.259616 0.965712i $$-0.416404\pi$$
0.259616 + 0.965712i $$0.416404\pi$$
$$728$$ −4.00000 + 3.46410i −0.148250 + 0.128388i
$$729$$ 0 0
$$730$$ −8.00000 + 13.8564i −0.296093 + 0.512849i
$$731$$ 0.500000 + 0.866025i 0.0184932 + 0.0320311i
$$732$$ 0 0
$$733$$ 5.00000 8.66025i 0.184679 0.319874i −0.758789 0.651336i $$-0.774209\pi$$
0.943468 + 0.331463i $$0.107542\pi$$
$$734$$ 32.0000 1.18114
$$735$$ 0 0
$$736$$ −1.00000 −0.0368605
$$737$$ 6.00000 10.3923i 0.221013 0.382805i
$$738$$ 0 0
$$739$$ −18.0000 31.1769i −0.662141 1.14686i −0.980052 0.198741i $$-0.936315\pi$$
0.317911 0.948120i $$-0.397019\pi$$
$$740$$ 5.00000 8.66025i 0.183804 0.318357i
$$741$$ 0 0
$$742$$ 24.0000 20.7846i 0.881068 0.763027i
$$743$$ −36.0000 −1.32071 −0.660356 0.750953i $$-0.729595\pi$$
−0.660356 + 0.750953i $$0.729595\pi$$
$$744$$ 0 0
$$745$$ −11.0000 19.0526i −0.403009 0.698032i
$$746$$ 13.0000 + 22.5167i 0.475964 + 0.824394i
$$747$$ 0 0
$$748$$ 1.00000 0.0365636
$$749$$ 1.00000 + 5.19615i 0.0365392 + 0.189863i
$$750$$ 0 0
$$751$$ 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i $$-0.634880\pi$$
0.995018 0.0996961i $$-0.0317870\pi$$
$$752$$ 3.50000 + 6.06218i 0.127632 + 0.221065i
$$753$$ 0 0
$$754$$ 1.00000 1.73205i 0.0364179 0.0630776i
$$755$$ −30.0000 −1.09181
$$756$$ 0 0
$$757$$ 47.0000 1.70824 0.854122 0.520073i $$-0.174095\pi$$
0.854122 + 0.520073i $$0.174095\pi$$
$$758$$ −4.00000 + 6.92820i −0.145287 + 0.251644i
$$759$$ 0 0
$$760$$ −3.00000 5.19615i −0.108821 0.188484i
$$761$$ 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i $$-0.727548\pi$$
0.981764 + 0.190101i $$0.0608816\pi$$
$$762$$ 0 0
$$763$$ 50.0000 + 17.3205i 1.81012 + 0.627044i
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ −12.5000 21.6506i −0.451643 0.782269i
$$767$$ −3.00000 5.19615i −0.108324 0.187622i
$$768$$ 0 0
$$769$$ −20.0000 −0.721218 −0.360609 0.932717i $$-0.617431\pi$$
−0.360609 + 0.932717i $$0.617431\pi$$
$$770$$ 1.00000 + 5.19615i 0.0360375 + 0.187256i
$$771$$ 0 0
$$772$$ −4.00000 + 6.92820i −0.143963 + 0.249351i
$$773$$ 18.0000 + 31.1769i 0.647415 + 1.12136i 0.983738 + 0.179609i $$0.0574833\pi$$
−0.336323 + 0.941747i $$0.609183\pi$$
$$774$$ 0 0
$$775$$ −1.00000 + 1.73205i −0.0359211 + 0.0622171i
$$776$$ −7.00000 −0.251285
$$777$$ 0 0
$$778$$ −30.0000 −1.07555
$$779$$ 15.0000 25.9808i 0.537431 0.930857i
$$780$$ 0 0
$$781$$ −2.50000 4.33013i −0.0894570 0.154944i
$$782$$ −0.500000 + 0.866025i −0.0178800 + 0.0309690i
$$783$$ 0 0
$$784$$ 5.50000 + 4.33013i 0.196429 + 0.154647i
$$785$$ 2.00000 0.0713831
$$786$$ 0 0
$$787$$ 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i $$0.0196653\pi$$
−0.445577 + 0.895244i $$0.647001\pi$$
$$788$$ 13.5000 + 23.3827i 0.480918 + 0.832974i
$$789$$ 0 0
$$790$$ 0