# Properties

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

# Related objects

## 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.k.991.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +2.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +2.00000 q^{20} -1.00000 q^{22} +(-3.50000 + 6.06218i) q^{23} +(0.500000 + 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +(0.500000 - 2.59808i) q^{28} +5.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +(-5.00000 + 1.73205i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{38} +(1.00000 - 1.73205i) q^{40} -6.00000 q^{41} +11.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-3.50000 + 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-2.00000 - 3.46410i) q^{53} +2.00000 q^{55} +(-2.00000 - 1.73205i) q^{56} +(2.50000 - 4.33013i) q^{58} +(5.50000 + 9.52628i) q^{59} +(-5.00000 + 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(-1.00000 + 5.19615i) q^{70} +5.00000 q^{71} +(4.00000 + 6.92820i) q^{73} +(1.50000 + 2.59808i) q^{74} +7.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-3.00000 + 5.19615i) q^{82} -14.0000 q^{83} +6.00000 q^{85} +(5.50000 - 9.52628i) q^{86} +(0.500000 + 0.866025i) q^{88} +(1.00000 - 1.73205i) q^{89} +(4.00000 + 3.46410i) q^{91} +7.00000 q^{92} +(3.50000 + 6.06218i) q^{94} +(-7.00000 - 12.1244i) q^{95} +15.0000 q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} - 2 q^{5} + 4 q^{7} - 2 q^{8} + O(q^{10})$$ $$2 q + q^{2} - q^{4} - 2 q^{5} + 4 q^{7} - 2 q^{8} + 2 q^{10} - q^{11} + 4 q^{13} + 5 q^{14} - q^{16} - 3 q^{17} - 7 q^{19} + 4 q^{20} - 2 q^{22} - 7 q^{23} + q^{25} + 2 q^{26} + q^{28} + 10 q^{29} - 2 q^{31} + q^{32} - 6 q^{34} - 10 q^{35} - 3 q^{37} + 7 q^{38} + 2 q^{40} - 12 q^{41} + 22 q^{43} - q^{44} + 7 q^{46} - 7 q^{47} + 2 q^{49} + 2 q^{50} - 2 q^{52} - 4 q^{53} + 4 q^{55} - 4 q^{56} + 5 q^{58} + 11 q^{59} - 10 q^{61} - 4 q^{62} + 2 q^{64} - 4 q^{65} + 4 q^{67} - 3 q^{68} - 2 q^{70} + 10 q^{71} + 8 q^{73} + 3 q^{74} + 14 q^{76} + q^{77} + 8 q^{79} - 2 q^{80} - 6 q^{82} - 28 q^{83} + 12 q^{85} + 11 q^{86} + q^{88} + 2 q^{89} + 8 q^{91} + 14 q^{92} + 7 q^{94} - 14 q^{95} + 30 q^{97} + 13 q^{98} + O(q^{100})$$

## 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 $$0.410544\pi$$
$$14$$ 2.50000 0.866025i 0.668153 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ −1.00000 −0.213201
$$23$$ −3.50000 + 6.06218i −0.729800 + 1.26405i 0.227167 + 0.973856i $$0.427054\pi$$
−0.956967 + 0.290196i $$0.906280\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ 1.00000 1.73205i 0.196116 0.339683i
$$27$$ 0 0
$$28$$ 0.500000 2.59808i 0.0944911 0.490990i
$$29$$ 5.00000 0.928477 0.464238 0.885710i $$-0.346328\pi$$
0.464238 + 0.885710i $$0.346328\pi$$
$$30$$ 0 0
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ −3.00000 −0.514496
$$35$$ −5.00000 + 1.73205i −0.845154 + 0.292770i
$$36$$ 0 0
$$37$$ −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i $$-0.912646\pi$$
0.715981 + 0.698119i $$0.245980\pi$$
$$38$$ 3.50000 + 6.06218i 0.567775 + 0.983415i
$$39$$ 0 0
$$40$$ 1.00000 1.73205i 0.158114 0.273861i
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 11.0000 1.67748 0.838742 0.544529i $$-0.183292\pi$$
0.838742 + 0.544529i $$0.183292\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ 0 0
$$46$$ 3.50000 + 6.06218i 0.516047 + 0.893819i
$$47$$ −3.50000 + 6.06218i −0.510527 + 0.884260i 0.489398 + 0.872060i $$0.337217\pi$$
−0.999926 + 0.0121990i $$0.996117\pi$$
$$48$$ 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
$$53$$ −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i $$-0.255252\pi$$
−0.970065 + 0.242846i $$0.921919\pi$$
$$54$$ 0 0
$$55$$ 2.00000 0.269680
$$56$$ −2.00000 1.73205i −0.267261 0.231455i
$$57$$ 0 0
$$58$$ 2.50000 4.33013i 0.328266 0.568574i
$$59$$ 5.50000 + 9.52628i 0.716039 + 1.24022i 0.962557 + 0.271078i $$0.0873801\pi$$
−0.246518 + 0.969138i $$0.579287\pi$$
$$60$$ 0 0
$$61$$ −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i $$0.387809\pi$$
−0.985391 + 0.170305i $$0.945525\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −2.00000 + 3.46410i −0.248069 + 0.429669i
$$66$$ 0 0
$$67$$ 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i $$-0.0880957\pi$$
−0.717607 + 0.696449i $$0.754762\pi$$
$$68$$ −1.50000 + 2.59808i −0.181902 + 0.315063i
$$69$$ 0 0
$$70$$ −1.00000 + 5.19615i −0.119523 + 0.621059i
$$71$$ 5.00000 0.593391 0.296695 0.954972i $$-0.404115\pi$$
0.296695 + 0.954972i $$0.404115\pi$$
$$72$$ 0 0
$$73$$ 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i $$-0.0115821\pi$$
−0.531174 + 0.847263i $$0.678249\pi$$
$$74$$ 1.50000 + 2.59808i 0.174371 + 0.302020i
$$75$$ 0 0
$$76$$ 7.00000 0.802955
$$77$$ 0.500000 2.59808i 0.0569803 0.296078i
$$78$$ 0 0
$$79$$ 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i $$-0.684745\pi$$
0.998388 + 0.0567635i $$0.0180781\pi$$
$$80$$ −1.00000 1.73205i −0.111803 0.193649i
$$81$$ 0 0
$$82$$ −3.00000 + 5.19615i −0.331295 + 0.573819i
$$83$$ −14.0000 −1.53670 −0.768350 0.640030i $$-0.778922\pi$$
−0.768350 + 0.640030i $$0.778922\pi$$
$$84$$ 0 0
$$85$$ 6.00000 0.650791
$$86$$ 5.50000 9.52628i 0.593080 1.02725i
$$87$$ 0 0
$$88$$ 0.500000 + 0.866025i 0.0533002 + 0.0923186i
$$89$$ 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i $$-0.799529\pi$$
0.914146 + 0.405385i $$0.132862\pi$$
$$90$$ 0 0
$$91$$ 4.00000 + 3.46410i 0.419314 + 0.363137i
$$92$$ 7.00000 0.729800
$$93$$ 0 0
$$94$$ 3.50000 + 6.06218i 0.360997 + 0.625266i
$$95$$ −7.00000 12.1244i −0.718185 1.24393i
$$96$$ 0 0
$$97$$ 15.0000 1.52302 0.761510 0.648154i $$-0.224459\pi$$
0.761510 + 0.648154i $$0.224459\pi$$
$$98$$ 6.50000 + 2.59808i 0.656599 + 0.262445i
$$99$$ 0 0
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ 1.50000 + 2.59808i 0.149256 + 0.258518i 0.930953 0.365140i $$-0.118979\pi$$
−0.781697 + 0.623658i $$0.785646\pi$$
$$102$$ 0 0
$$103$$ 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i $$-0.669356\pi$$
0.999964 + 0.00844953i $$0.00268960\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ −4.00000 −0.388514
$$107$$ 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i $$-0.497411\pi$$
0.861931 0.507026i $$-0.169255\pi$$
$$108$$ 0 0
$$109$$ −2.00000 3.46410i −0.191565 0.331801i 0.754204 0.656640i $$-0.228023\pi$$
−0.945769 + 0.324840i $$0.894690\pi$$
$$110$$ 1.00000 1.73205i 0.0953463 0.165145i
$$111$$ 0 0
$$112$$ −2.50000 + 0.866025i −0.236228 + 0.0818317i
$$113$$ −2.00000 −0.188144 −0.0940721 0.995565i $$-0.529988\pi$$
−0.0940721 + 0.995565i $$0.529988\pi$$
$$114$$ 0 0
$$115$$ −7.00000 12.1244i −0.652753 1.13060i
$$116$$ −2.50000 4.33013i −0.232119 0.402042i
$$117$$ 0 0
$$118$$ 11.0000 1.01263
$$119$$ 1.50000 7.79423i 0.137505 0.714496i
$$120$$ 0 0
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ 5.00000 + 8.66025i 0.452679 + 0.784063i
$$123$$ 0 0
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −19.0000 −1.68598 −0.842989 0.537931i $$-0.819206\pi$$
−0.842989 + 0.537931i $$0.819206\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 2.00000 + 3.46410i 0.175412 + 0.303822i
$$131$$ −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i $$-0.946976\pi$$
0.636676 + 0.771132i $$0.280309\pi$$
$$132$$ 0 0
$$133$$ −17.5000 + 6.06218i −1.51744 + 0.525657i
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ 1.50000 + 2.59808i 0.128624 + 0.222783i
$$137$$ 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
$$139$$ 17.0000 1.44192 0.720961 0.692976i $$-0.243701\pi$$
0.720961 + 0.692976i $$0.243701\pi$$
$$140$$ 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
$$145$$ −5.00000 + 8.66025i −0.415227 + 0.719195i
$$146$$ 8.00000 0.662085
$$147$$ 0 0
$$148$$ 3.00000 0.246598
$$149$$ 8.50000 14.7224i 0.696347 1.20611i −0.273377 0.961907i $$-0.588141\pi$$
0.969724 0.244202i $$-0.0785259\pi$$
$$150$$ 0 0
$$151$$ 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i $$-0.101452\pi$$
−0.746190 + 0.665733i $$0.768119\pi$$
$$152$$ 3.50000 6.06218i 0.283887 0.491708i
$$153$$ 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 $$0.846039\pi$$
$$158$$ −4.00000 6.92820i −0.318223 0.551178i
$$159$$ 0 0
$$160$$ −2.00000 −0.158114
$$161$$ −17.5000 + 6.06218i −1.37919 + 0.477767i
$$162$$ 0 0
$$163$$ −3.00000 + 5.19615i −0.234978 + 0.406994i −0.959266 0.282503i $$-0.908835\pi$$
0.724288 + 0.689497i $$0.242169\pi$$
$$164$$ 3.00000 + 5.19615i 0.234261 + 0.405751i
$$165$$ 0 0
$$166$$ −7.00000 + 12.1244i −0.543305 + 0.941033i
$$167$$ 10.0000 0.773823 0.386912 0.922117i $$-0.373542\pi$$
0.386912 + 0.922117i $$0.373542\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 3.00000 5.19615i 0.230089 0.398527i
$$171$$ 0 0
$$172$$ −5.50000 9.52628i −0.419371 0.726372i
$$173$$ 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
$$175$$ −0.500000 + 2.59808i −0.0377964 + 0.196396i
$$176$$ 1.00000 0.0753778
$$177$$ 0 0
$$178$$ −1.00000 1.73205i −0.0749532 0.129823i
$$179$$ −4.50000 7.79423i −0.336346 0.582568i 0.647397 0.762153i $$-0.275858\pi$$
−0.983742 + 0.179585i $$0.942524\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 5.00000 1.73205i 0.370625 0.128388i
$$183$$ 0 0
$$184$$ 3.50000 6.06218i 0.258023 0.446910i
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ −1.50000 + 2.59808i −0.109691 + 0.189990i
$$188$$ 7.00000 0.510527
$$189$$ 0 0
$$190$$ −14.0000 −1.01567
$$191$$ −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
$$193$$ −12.0000 20.7846i −0.863779 1.49611i −0.868255 0.496119i $$-0.834758\pi$$
0.00447566 0.999990i $$-0.498575\pi$$
$$194$$ 7.50000 12.9904i 0.538469 0.932655i
$$195$$ 0 0
$$196$$ 5.50000 4.33013i 0.392857 0.309295i
$$197$$ −15.0000 −1.06871 −0.534353 0.845262i $$-0.679445\pi$$
−0.534353 + 0.845262i $$0.679445\pi$$
$$198$$ 0 0
$$199$$ −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i $$-0.281995\pi$$
−0.987022 + 0.160585i $$0.948662\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ 0 0
$$202$$ 3.00000 0.211079
$$203$$ 10.0000 + 8.66025i 0.701862 + 0.607831i
$$204$$ 0 0
$$205$$ 6.00000 10.3923i 0.419058 0.725830i
$$206$$ −5.00000 8.66025i −0.348367 0.603388i
$$207$$ 0 0
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ 7.00000 0.484200
$$210$$ 0 0
$$211$$ 20.0000 1.37686 0.688428 0.725304i $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ −2.00000 + 3.46410i −0.137361 + 0.237915i
$$213$$ 0 0
$$214$$ −9.00000 15.5885i −0.615227 1.06561i
$$215$$ −11.0000 + 19.0526i −0.750194 + 1.29937i
$$216$$ 0 0
$$217$$ 1.00000 5.19615i 0.0678844 0.352738i
$$218$$ −4.00000 −0.270914
$$219$$ 0 0
$$220$$ −1.00000 1.73205i −0.0674200 0.116775i
$$221$$ −3.00000 5.19615i −0.201802 0.349531i
$$222$$ 0 0
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ −0.500000 + 2.59808i −0.0334077 + 0.173591i
$$225$$ 0 0
$$226$$ −1.00000 + 1.73205i −0.0665190 + 0.115214i
$$227$$ 5.00000 + 8.66025i 0.331862 + 0.574801i 0.982877 0.184263i $$-0.0589899\pi$$
−0.651015 + 0.759065i $$0.725657\pi$$
$$228$$ 0 0
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ −14.0000 −0.923133
$$231$$ 0 0
$$232$$ −5.00000 −0.328266
$$233$$ −4.50000 + 7.79423i −0.294805 + 0.510617i −0.974939 0.222470i $$-0.928588\pi$$
0.680135 + 0.733087i $$0.261921\pi$$
$$234$$ 0 0
$$235$$ −7.00000 12.1244i −0.456630 0.790906i
$$236$$ 5.50000 9.52628i 0.358020 0.620108i
$$237$$ 0 0
$$238$$ −6.00000 5.19615i −0.388922 0.336817i
$$239$$ 10.0000 0.646846 0.323423 0.946254i $$-0.395166\pi$$
0.323423 + 0.946254i $$0.395166\pi$$
$$240$$ 0 0
$$241$$ 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i $$-0.125544\pi$$
−0.794393 + 0.607404i $$0.792211\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 0 0
$$244$$ 10.0000 0.640184
$$245$$ −13.0000 5.19615i −0.830540 0.331970i
$$246$$ 0 0
$$247$$ −7.00000 + 12.1244i −0.445399 + 0.771454i
$$248$$ 1.00000 + 1.73205i 0.0635001 + 0.109985i
$$249$$ 0 0
$$250$$ −6.00000 + 10.3923i −0.379473 + 0.657267i
$$251$$ −5.00000 −0.315597 −0.157799 0.987471i $$-0.550440\pi$$
−0.157799 + 0.987471i $$0.550440\pi$$
$$252$$ 0 0
$$253$$ 7.00000 0.440086
$$254$$ −9.50000 + 16.4545i −0.596083 + 1.03245i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i $$-0.977168\pi$$
0.560781 + 0.827964i $$0.310501\pi$$
$$258$$ 0 0
$$259$$ −7.50000 + 2.59808i −0.466027 + 0.161437i
$$260$$ 4.00000 0.248069
$$261$$ 0 0
$$262$$ 4.00000 + 6.92820i 0.247121 + 0.428026i
$$263$$ 15.0000 + 25.9808i 0.924940 + 1.60204i 0.791658 + 0.610964i $$0.209218\pi$$
0.133281 + 0.991078i $$0.457449\pi$$
$$264$$ 0 0
$$265$$ 8.00000 0.491436
$$266$$ −3.50000 + 18.1865i −0.214599 + 1.11509i
$$267$$ 0 0
$$268$$ 2.00000 3.46410i 0.122169 0.211604i
$$269$$ −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i $$-0.957952\pi$$
0.381577 0.924337i $$-0.375381\pi$$
$$270$$ 0 0
$$271$$ −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i $$-0.911459\pi$$
0.718580 + 0.695444i $$0.244792\pi$$
$$272$$ 3.00000 0.181902
$$273$$ 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 $$-0.910345\pi$$
0.239585 0.970875i $$-0.422989\pi$$
$$278$$ 8.50000 14.7224i 0.509796 0.882993i
$$279$$ 0 0
$$280$$ 5.00000 1.73205i 0.298807 0.103510i
$$281$$ −3.00000 −0.178965 −0.0894825 0.995988i $$-0.528521\pi$$
−0.0894825 + 0.995988i $$0.528521\pi$$
$$282$$ 0 0
$$283$$ −12.0000 20.7846i −0.713326 1.23552i −0.963602 0.267342i $$-0.913855\pi$$
0.250276 0.968175i $$-0.419479\pi$$
$$284$$ −2.50000 4.33013i −0.148348 0.256946i
$$285$$ 0 0
$$286$$ −2.00000 −0.118262
$$287$$ −12.0000 10.3923i −0.708338 0.613438i
$$288$$ 0 0
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 5.00000 + 8.66025i 0.293610 + 0.508548i
$$291$$ 0 0
$$292$$ 4.00000 6.92820i 0.234082 0.405442i
$$293$$ 3.00000 0.175262 0.0876309 0.996153i $$-0.472070\pi$$
0.0876309 + 0.996153i $$0.472070\pi$$
$$294$$ 0 0
$$295$$ −22.0000 −1.28089
$$296$$ 1.50000 2.59808i 0.0871857 0.151010i
$$297$$ 0 0
$$298$$ −8.50000 14.7224i −0.492392 0.852848i
$$299$$ −7.00000 + 12.1244i −0.404820 + 0.701170i
$$300$$ 0 0
$$301$$ 22.0000 + 19.0526i 1.26806 + 1.09817i
$$302$$ 5.00000 0.287718
$$303$$ 0 0
$$304$$ −3.50000 6.06218i −0.200739 0.347690i
$$305$$ −10.0000 17.3205i −0.572598 0.991769i
$$306$$ 0 0
$$307$$ 28.0000 1.59804 0.799022 0.601302i $$-0.205351\pi$$
0.799022 + 0.601302i $$0.205351\pi$$
$$308$$ −2.50000 + 0.866025i −0.142451 + 0.0493464i
$$309$$ 0 0
$$310$$ 2.00000 3.46410i 0.113592 0.196748i
$$311$$ 13.5000 + 23.3827i 0.765515 + 1.32591i 0.939974 + 0.341246i $$0.110849\pi$$
−0.174459 + 0.984664i $$0.555818\pi$$
$$312$$ 0 0
$$313$$ −7.50000 + 12.9904i −0.423925 + 0.734260i −0.996319 0.0857188i $$-0.972681\pi$$
0.572394 + 0.819979i $$0.306015\pi$$
$$314$$ −1.00000 −0.0564333
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i $$-0.514426\pi$$
0.887788 0.460252i $$-0.152241\pi$$
$$318$$ 0 0
$$319$$ −2.50000 4.33013i −0.139973 0.242441i
$$320$$ −1.00000 + 1.73205i −0.0559017 + 0.0968246i
$$321$$ 0 0
$$322$$ −3.50000 + 18.1865i −0.195047 + 1.01350i
$$323$$ 21.0000 1.16847
$$324$$ 0 0
$$325$$ 1.00000 + 1.73205i 0.0554700 + 0.0960769i
$$326$$ 3.00000 + 5.19615i 0.166155 + 0.287788i
$$327$$ 0 0
$$328$$ 6.00000 0.331295
$$329$$ −17.5000 + 6.06218i −0.964806 + 0.334219i
$$330$$ 0 0
$$331$$ 7.00000 12.1244i 0.384755 0.666415i −0.606980 0.794717i $$-0.707619\pi$$
0.991735 + 0.128302i $$0.0409527\pi$$
$$332$$ 7.00000 + 12.1244i 0.384175 + 0.665410i
$$333$$ 0 0
$$334$$ 5.00000 8.66025i 0.273588 0.473868i
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ 8.00000 0.435788 0.217894 0.975972i $$-0.430081\pi$$
0.217894 + 0.975972i $$0.430081\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ 0 0
$$340$$ −3.00000 5.19615i −0.162698 0.281801i
$$341$$ −1.00000 + 1.73205i −0.0541530 + 0.0937958i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ −11.0000 −0.593080
$$345$$ 0 0
$$346$$ −7.00000 12.1244i −0.376322 0.651809i
$$347$$ 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i $$0.0561403\pi$$
−0.340293 + 0.940319i $$0.610526\pi$$
$$348$$ 0 0
$$349$$ 8.00000 0.428230 0.214115 0.976808i $$-0.431313\pi$$
0.214115 + 0.976808i $$0.431313\pi$$
$$350$$ 2.00000 + 1.73205i 0.106904 + 0.0925820i
$$351$$ 0 0
$$352$$ 0.500000 0.866025i 0.0266501 0.0461593i
$$353$$ 5.00000 + 8.66025i 0.266123 + 0.460939i 0.967857 0.251500i $$-0.0809239\pi$$
−0.701734 + 0.712439i $$0.747591\pi$$
$$354$$ 0 0
$$355$$ −5.00000 + 8.66025i −0.265372 + 0.459639i
$$356$$ −2.00000 −0.106000
$$357$$ 0 0
$$358$$ −9.00000 −0.475665
$$359$$ −9.00000 + 15.5885i −0.475002 + 0.822727i −0.999590 0.0286287i $$-0.990886\pi$$
0.524588 + 0.851356i $$0.324219\pi$$
$$360$$ 0 0
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ −5.00000 + 8.66025i −0.262794 + 0.455173i
$$363$$ 0 0
$$364$$ 1.00000 5.19615i 0.0524142 0.272352i
$$365$$ −16.0000 −0.837478
$$366$$ 0 0
$$367$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$368$$ −3.50000 6.06218i −0.182450 0.316013i
$$369$$ 0 0
$$370$$ −6.00000 −0.311925
$$371$$ 2.00000 10.3923i 0.103835 0.539542i
$$372$$ 0 0
$$373$$ 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i $$-0.640448\pi$$
0.996610 0.0822766i $$-0.0262191\pi$$
$$374$$ 1.50000 + 2.59808i 0.0775632 + 0.134343i
$$375$$ 0 0
$$376$$ 3.50000 6.06218i 0.180499 0.312633i
$$377$$ 10.0000 0.515026
$$378$$ 0 0
$$379$$ −16.0000 −0.821865 −0.410932 0.911666i $$-0.634797\pi$$
−0.410932 + 0.911666i $$0.634797\pi$$
$$380$$ −7.00000 + 12.1244i −0.359092 + 0.621966i
$$381$$ 0 0
$$382$$ 4.00000 + 6.92820i 0.204658 + 0.354478i
$$383$$ 15.5000 26.8468i 0.792013 1.37181i −0.132706 0.991155i $$-0.542367\pi$$
0.924719 0.380651i $$-0.124300\pi$$
$$384$$ 0 0
$$385$$ 4.00000 + 3.46410i 0.203859 + 0.176547i
$$386$$ −24.0000 −1.22157
$$387$$ 0 0
$$388$$ −7.50000 12.9904i −0.380755 0.659487i
$$389$$ −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 0 0
$$391$$ 21.0000 1.06202
$$392$$ −1.00000 6.92820i −0.0505076 0.349927i
$$393$$ 0 0
$$394$$ −7.50000 + 12.9904i −0.377845 + 0.654446i
$$395$$ 8.00000 + 13.8564i 0.402524 + 0.697191i
$$396$$ 0 0
$$397$$ 1.50000 2.59808i 0.0752828 0.130394i −0.825926 0.563778i $$-0.809347\pi$$
0.901209 + 0.433384i $$0.142681\pi$$
$$398$$ −10.0000 −0.501255
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ 16.0000 27.7128i 0.799002 1.38391i −0.121265 0.992620i $$-0.538695\pi$$
0.920267 0.391292i $$-0.127972\pi$$
$$402$$ 0 0
$$403$$ −2.00000 3.46410i −0.0996271 0.172559i
$$404$$ 1.50000 2.59808i 0.0746278 0.129259i
$$405$$ 0 0
$$406$$ 12.5000 4.33013i 0.620365 0.214901i
$$407$$ 3.00000 0.148704
$$408$$ 0 0
$$409$$ −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i $$-0.876150\pi$$
0.134107 0.990967i $$-0.457183\pi$$
$$410$$ −6.00000 10.3923i −0.296319 0.513239i
$$411$$ 0 0
$$412$$ −10.0000 −0.492665
$$413$$ −5.50000 + 28.5788i −0.270637 + 1.40627i
$$414$$ 0 0
$$415$$ 14.0000 24.2487i 0.687233 1.19032i
$$416$$ 1.00000 + 1.73205i 0.0490290 + 0.0849208i
$$417$$ 0 0
$$418$$ 3.50000 6.06218i 0.171191 0.296511i
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ 0 0
$$421$$ −17.0000 −0.828529 −0.414265 0.910156i $$-0.635961\pi$$
−0.414265 + 0.910156i $$0.635961\pi$$
$$422$$ 10.0000 17.3205i 0.486792 0.843149i
$$423$$ 0 0
$$424$$ 2.00000 + 3.46410i 0.0971286 + 0.168232i
$$425$$ 1.50000 2.59808i 0.0727607 0.126025i
$$426$$ 0 0
$$427$$ −25.0000 + 8.66025i −1.20983 + 0.419099i
$$428$$ −18.0000 −0.870063
$$429$$ 0 0
$$430$$ 11.0000 + 19.0526i 0.530467 + 0.918796i
$$431$$ 20.0000 + 34.6410i 0.963366 + 1.66860i 0.713942 + 0.700205i $$0.246908\pi$$
0.249424 + 0.968394i $$0.419759\pi$$
$$432$$ 0 0
$$433$$ 5.00000 0.240285 0.120142 0.992757i $$-0.461665\pi$$
0.120142 + 0.992757i $$0.461665\pi$$
$$434$$ −4.00000 3.46410i −0.192006 0.166282i
$$435$$ 0 0
$$436$$ −2.00000 + 3.46410i −0.0957826 + 0.165900i
$$437$$ −24.5000 42.4352i −1.17199 2.02995i
$$438$$ 0 0
$$439$$ −2.50000 + 4.33013i −0.119318 + 0.206666i −0.919498 0.393095i $$-0.871404\pi$$
0.800179 + 0.599761i $$0.204738\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ −6.00000 −0.285391
$$443$$ 20.5000 35.5070i 0.973984 1.68699i 0.290738 0.956803i $$-0.406099\pi$$
0.683247 0.730188i $$-0.260567\pi$$
$$444$$ 0 0
$$445$$ 2.00000 + 3.46410i 0.0948091 + 0.164214i
$$446$$ −7.00000 + 12.1244i −0.331460 + 0.574105i
$$447$$ 0 0
$$448$$ 2.00000 + 1.73205i 0.0944911 + 0.0818317i
$$449$$ 36.0000 1.69895 0.849473 0.527633i $$-0.176920\pi$$
0.849473 + 0.527633i $$0.176920\pi$$
$$450$$ 0 0
$$451$$ 3.00000 + 5.19615i 0.141264 + 0.244677i
$$452$$ 1.00000 + 1.73205i 0.0470360 + 0.0814688i
$$453$$ 0 0
$$454$$ 10.0000 0.469323
$$455$$ −10.0000 + 3.46410i −0.468807 + 0.162400i
$$456$$ 0 0
$$457$$ −20.0000 + 34.6410i −0.935561 + 1.62044i −0.161929 + 0.986802i $$0.551772\pi$$
−0.773631 + 0.633636i $$0.781562\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ 0 0
$$460$$ −7.00000 + 12.1244i −0.326377 + 0.565301i
$$461$$ −13.0000 −0.605470 −0.302735 0.953075i $$-0.597900\pi$$
−0.302735 + 0.953075i $$0.597900\pi$$
$$462$$ 0 0
$$463$$ −24.0000 −1.11537 −0.557687 0.830051i $$-0.688311\pi$$
−0.557687 + 0.830051i $$0.688311\pi$$
$$464$$ −2.50000 + 4.33013i −0.116060 + 0.201021i
$$465$$ 0 0
$$466$$ 4.50000 + 7.79423i 0.208458 + 0.361061i
$$467$$ 6.50000 11.2583i 0.300784 0.520973i −0.675530 0.737333i $$-0.736085\pi$$
0.976314 + 0.216359i $$0.0694183\pi$$
$$468$$ 0 0
$$469$$ −2.00000 + 10.3923i −0.0923514 + 0.479872i
$$470$$ −14.0000 −0.645772
$$471$$ 0 0
$$472$$ −5.50000 9.52628i −0.253158 0.438483i
$$473$$ −5.50000 9.52628i −0.252890 0.438019i
$$474$$ 0 0
$$475$$ −7.00000 −0.321182
$$476$$ −7.50000 + 2.59808i −0.343762 + 0.119083i
$$477$$ 0 0
$$478$$ 5.00000 8.66025i 0.228695 0.396111i
$$479$$ 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i $$-0.0317693\pi$$
−0.583803 + 0.811895i $$0.698436\pi$$
$$480$$ 0 0
$$481$$ −3.00000 + 5.19615i −0.136788 + 0.236924i
$$482$$ 4.00000 0.182195
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −15.0000 + 25.9808i −0.681115 + 1.17973i
$$486$$ 0 0
$$487$$ −9.00000 15.5885i −0.407829 0.706380i 0.586817 0.809719i $$-0.300381\pi$$
−0.994646 + 0.103339i $$0.967047\pi$$
$$488$$ 5.00000 8.66025i 0.226339 0.392031i
$$489$$ 0 0
$$490$$ −11.0000 + 8.66025i −0.496929 + 0.391230i
$$491$$ 26.0000 1.17336 0.586682 0.809818i $$-0.300434\pi$$
0.586682 + 0.809818i $$0.300434\pi$$
$$492$$ 0 0
$$493$$ −7.50000 12.9904i −0.337783 0.585057i
$$494$$ 7.00000 + 12.1244i 0.314945 + 0.545501i
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 10.0000 + 8.66025i 0.448561 + 0.388465i
$$498$$ 0 0
$$499$$ 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i $$-0.480278\pi$$
0.833404 0.552664i $$-0.186389\pi$$
$$500$$ 6.00000 + 10.3923i 0.268328 + 0.464758i
$$501$$ 0 0
$$502$$ −2.50000 + 4.33013i −0.111580 + 0.193263i
$$503$$ 30.0000 1.33763 0.668817 0.743427i $$-0.266801\pi$$
0.668817 + 0.743427i $$0.266801\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 3.50000 6.06218i 0.155594 0.269497i
$$507$$ 0 0
$$508$$ 9.50000 + 16.4545i 0.421494 + 0.730050i
$$509$$ 2.00000 3.46410i 0.0886484 0.153544i −0.818292 0.574803i $$-0.805079\pi$$
0.906940 + 0.421260i $$0.138412\pi$$
$$510$$ 0 0
$$511$$ −4.00000 + 20.7846i −0.176950 + 0.919457i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 7.00000 + 12.1244i 0.308757 + 0.534782i
$$515$$ 10.0000 + 17.3205i 0.440653 + 0.763233i
$$516$$ 0 0
$$517$$ 7.00000 0.307860
$$518$$ −1.50000 + 7.79423i −0.0659062 + 0.342459i
$$519$$ 0 0
$$520$$ 2.00000 3.46410i 0.0877058 0.151911i
$$521$$ −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i $$-0.295679\pi$$
−0.993011 + 0.118020i $$0.962345\pi$$
$$522$$ 0 0
$$523$$ 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i $$-0.689279\pi$$
0.997478 + 0.0709788i $$0.0226123\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ 30.0000 1.30806
$$527$$ −3.00000 + 5.19615i −0.130682 + 0.226348i
$$528$$ 0 0
$$529$$ −13.0000 22.5167i −0.565217 0.978985i
$$530$$ 4.00000 6.92820i 0.173749 0.300942i
$$531$$ 0 0
$$532$$ 14.0000 + 12.1244i 0.606977 + 0.525657i
$$533$$ −12.0000 −0.519778
$$534$$ 0 0
$$535$$ 18.0000 + 31.1769i 0.778208 + 1.34790i
$$536$$ −2.00000 3.46410i −0.0863868 0.149626i
$$537$$ 0 0
$$538$$ −20.0000 −0.862261
$$539$$ 5.50000 4.33013i 0.236902 0.186512i
$$540$$ 0 0
$$541$$ −8.00000 + 13.8564i −0.343947 + 0.595733i −0.985162 0.171628i $$-0.945097\pi$$
0.641215 + 0.767361i $$0.278431\pi$$
$$542$$ 4.00000 + 6.92820i 0.171815 + 0.297592i
$$543$$ 0 0
$$544$$ 1.50000 2.59808i 0.0643120 0.111392i
$$545$$ 8.00000 0.342682
$$546$$ 0 0
$$547$$ −11.0000 −0.470326 −0.235163 0.971956i $$-0.575562\pi$$
−0.235163 + 0.971956i $$0.575562\pi$$
$$548$$ 3.00000 5.19615i 0.128154 0.221969i
$$549$$ 0 0
$$550$$ −0.500000 0.866025i −0.0213201 0.0369274i
$$551$$ −17.5000 + 30.3109i −0.745525 + 1.29129i
$$552$$ 0 0
$$553$$ 20.0000 6.92820i 0.850487 0.294617i
$$554$$ −24.0000 −1.01966
$$555$$ 0 0
$$556$$ −8.50000 14.7224i −0.360480 0.624370i
$$557$$ 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i $$-0.105600\pi$$
−0.754802 + 0.655953i $$0.772267\pi$$
$$558$$ 0 0
$$559$$ 22.0000 0.930501
$$560$$ 1.00000 5.19615i 0.0422577 0.219578i
$$561$$ 0 0
$$562$$ −1.50000 + 2.59808i −0.0632737 + 0.109593i
$$563$$ −21.0000 36.3731i −0.885044 1.53294i −0.845663 0.533718i $$-0.820794\pi$$
−0.0393818 0.999224i $$-0.512539\pi$$
$$564$$ 0 0
$$565$$ 2.00000 3.46410i 0.0841406 0.145736i
$$566$$ −24.0000 −1.00880
$$567$$ 0 0
$$568$$ −5.00000 −0.209795
$$569$$ 6.50000 11.2583i 0.272494 0.471974i −0.697006 0.717066i $$-0.745485\pi$$
0.969500 + 0.245092i $$0.0788181\pi$$
$$570$$ 0 0
$$571$$ 21.5000 + 37.2391i 0.899747 + 1.55841i 0.827817 + 0.560998i $$0.189582\pi$$
0.0719297 + 0.997410i $$0.477084\pi$$
$$572$$ −1.00000 + 1.73205i −0.0418121 + 0.0724207i
$$573$$ 0 0
$$574$$ −15.0000 + 5.19615i −0.626088 + 0.216883i
$$575$$ −7.00000 −0.291920
$$576$$ 0 0
$$577$$ 9.00000 + 15.5885i 0.374675 + 0.648956i 0.990278 0.139100i $$-0.0444210\pi$$
−0.615603 + 0.788056i $$0.711088\pi$$
$$578$$ −4.00000 6.92820i −0.166378 0.288175i
$$579$$ 0 0
$$580$$ 10.0000 0.415227
$$581$$ −28.0000 24.2487i −1.16164 1.00601i
$$582$$ 0 0
$$583$$ −2.00000 + 3.46410i −0.0828315 + 0.143468i
$$584$$ −4.00000 6.92820i −0.165521 0.286691i
$$585$$ 0 0
$$586$$ 1.50000 2.59808i 0.0619644 0.107326i
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 14.0000 0.576860
$$590$$ −11.0000 + 19.0526i −0.452863 + 0.784381i
$$591$$ 0 0
$$592$$ −1.50000 2.59808i −0.0616496 0.106780i
$$593$$ −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i $$-0.975237\pi$$
0.565792 + 0.824548i $$0.308570\pi$$
$$594$$ 0 0
$$595$$ 12.0000 + 10.3923i 0.491952 + 0.426043i
$$596$$ −17.0000 −0.696347
$$597$$ 0 0
$$598$$ 7.00000 + 12.1244i 0.286251 + 0.495802i
$$599$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$602$$ 27.5000 9.52628i 1.12082 0.388262i
$$603$$ 0 0
$$604$$ 2.50000 4.33013i 0.101724 0.176190i
$$605$$ −1.00000 1.73205i −0.0406558 0.0704179i
$$606$$ 0 0
$$607$$ −18.0000 + 31.1769i −0.730597 + 1.26543i 0.226031 + 0.974120i $$0.427425\pi$$
−0.956628 + 0.291312i $$0.905908\pi$$
$$608$$ −7.00000 −0.283887
$$609$$ 0 0
$$610$$ −20.0000 −0.809776
$$611$$ −7.00000 + 12.1244i −0.283190 + 0.490499i
$$612$$ 0 0
$$613$$ −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i $$-0.179527\pi$$
−0.885514 + 0.464614i $$0.846193\pi$$
$$614$$ 14.0000 24.2487i 0.564994 0.978598i
$$615$$ 0 0
$$616$$ −0.500000 + 2.59808i −0.0201456 + 0.104679i
$$617$$ 20.0000 0.805170 0.402585 0.915383i $$-0.368112\pi$$
0.402585 + 0.915383i $$0.368112\pi$$
$$618$$ 0 0
$$619$$ 13.0000 + 22.5167i 0.522514 + 0.905021i 0.999657 + 0.0261952i $$0.00833914\pi$$
−0.477143 + 0.878826i $$0.658328\pi$$
$$620$$ −2.00000 3.46410i −0.0803219 0.139122i
$$621$$ 0 0
$$622$$ 27.0000 1.08260
$$623$$ 5.00000 1.73205i 0.200321 0.0693932i
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 7.50000 + 12.9904i 0.299760 + 0.519200i
$$627$$ 0 0
$$628$$ −0.500000 + 0.866025i −0.0199522 + 0.0345582i
$$629$$ 9.00000 0.358854
$$630$$ 0 0
$$631$$ −10.0000 −0.398094 −0.199047 0.979990i $$-0.563785\pi$$
−0.199047 + 0.979990i $$0.563785\pi$$
$$632$$ −4.00000 + 6.92820i −0.159111 + 0.275589i
$$633$$ 0 0
$$634$$ −15.0000 25.9808i −0.595726 1.03183i
$$635$$ 19.0000 32.9090i 0.753992 1.30595i
$$636$$ 0 0
$$637$$ 2.00000 + 13.8564i 0.0792429 + 0.549011i
$$638$$ −5.00000 −0.197952
$$639$$ 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
$$643$$ 40.0000 1.57745 0.788723 0.614749i $$-0.210743\pi$$
0.788723 + 0.614749i $$0.210743\pi$$
$$644$$ 14.0000 + 12.1244i 0.551677 + 0.477767i
$$645$$ 0 0
$$646$$ 10.5000 18.1865i 0.413117 0.715540i
$$647$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$648$$ 0 0
$$649$$ 5.50000 9.52628i 0.215894 0.373939i
$$650$$ 2.00000 0.0784465
$$651$$ 0 0
$$652$$ 6.00000 0.234978
$$653$$ −5.00000 + 8.66025i −0.195665 + 0.338902i −0.947118 0.320884i $$-0.896020\pi$$
0.751453 + 0.659786i $$0.229353\pi$$
$$654$$ 0 0
$$655$$ −8.00000 13.8564i −0.312586 0.541415i
$$656$$ 3.00000 5.19615i 0.117130 0.202876i
$$657$$ 0 0
$$658$$ −3.50000 + 18.1865i −0.136444 + 0.708985i
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ 0 0
$$661$$ 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i $$-0.0980418\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ −7.00000 12.1244i −0.272063 0.471226i
$$663$$ 0 0
$$664$$ 14.0000 0.543305
$$665$$ 7.00000 36.3731i 0.271448 1.41049i
$$666$$ 0 0
$$667$$ −17.5000 + 30.3109i −0.677603 + 1.17364i
$$668$$ −5.00000 8.66025i −0.193456 0.335075i
$$669$$ 0 0
$$670$$ −4.00000 + 6.92820i −0.154533 + 0.267660i
$$671$$ 10.0000 0.386046
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ 4.00000 6.92820i 0.154074 0.266864i
$$675$$ 0 0
$$676$$ 4.50000 + 7.79423i 0.173077 + 0.299778i
$$677$$ −10.5000 + 18.1865i −0.403548 + 0.698965i −0.994151 0.107997i $$-0.965556\pi$$
0.590603 + 0.806962i $$0.298890\pi$$
$$678$$ 0 0
$$679$$ 30.0000 + 25.9808i 1.15129 + 0.997050i
$$680$$ −6.00000 −0.230089
$$681$$ 0 0
$$682$$ 1.00000 + 1.73205i 0.0382920 + 0.0663237i
$$683$$ 19.5000 + 33.7750i 0.746147 + 1.29236i 0.949657 + 0.313291i $$0.101432\pi$$
−0.203510 + 0.979073i $$0.565235\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 8.50000 + 16.4545i 0.324532 + 0.628235i
$$687$$ 0 0
$$688$$ −5.50000 + 9.52628i −0.209686 + 0.363186i
$$689$$ −4.00000 6.92820i −0.152388 0.263944i
$$690$$ 0 0
$$691$$ −9.00000 + 15.5885i −0.342376 + 0.593013i −0.984873 0.173275i $$-0.944565\pi$$
0.642497 + 0.766288i $$0.277898\pi$$
$$692$$ −14.0000 −0.532200
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ −17.0000 + 29.4449i −0.644847 + 1.11691i
$$696$$ 0 0
$$697$$ 9.00000 + 15.5885i 0.340899 + 0.590455i
$$698$$ 4.00000 6.92820i 0.151402 0.262236i
$$699$$ 0 0
$$700$$ 2.50000 0.866025i 0.0944911 0.0327327i
$$701$$ 27.0000 1.01978 0.509888 0.860241i $$-0.329687\pi$$
0.509888 + 0.860241i $$0.329687\pi$$
$$702$$ 0 0
$$703$$ −10.5000 18.1865i −0.396015 0.685918i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ 0 0
$$706$$ 10.0000 0.376355
$$707$$ −1.50000 + 7.79423i −0.0564133 + 0.293132i
$$708$$ 0 0
$$709$$ 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i $$-0.635559\pi$$
0.995228 0.0975728i $$-0.0311079\pi$$
$$710$$ 5.00000 + 8.66025i 0.187647 + 0.325014i
$$711$$ 0 0
$$712$$ −1.00000 + 1.73205i −0.0374766 + 0.0649113i
$$713$$ 14.0000 0.524304
$$714$$ 0 0
$$715$$ 4.00000 0.149592
$$716$$ −4.50000 + 7.79423i −0.168173 + 0.291284i
$$717$$ 0 0
$$718$$ 9.00000 + 15.5885i 0.335877 + 0.581756i
$$719$$ 4.50000 7.79423i 0.167822 0.290676i −0.769832 0.638247i $$-0.779660\pi$$
0.937654 + 0.347571i $$0.112993\pi$$
$$720$$ 0 0
$$721$$ 25.0000 8.66025i 0.931049 0.322525i
$$722$$ −30.0000 −1.11648
$$723$$ 0 0
$$724$$ 5.00000 + 8.66025i 0.185824 + 0.321856i
$$725$$ 2.50000 + 4.33013i 0.0928477 + 0.160817i
$$726$$ 0 0
$$727$$ −14.0000 −0.519231 −0.259616 0.965712i $$-0.583596\pi$$
−0.259616 + 0.965712i $$0.583596\pi$$
$$728$$ −4.00000 3.46410i −0.148250 0.128388i
$$729$$ 0 0
$$730$$ −8.00000 + 13.8564i −0.296093 + 0.512849i
$$731$$ −16.5000 28.5788i −0.610275 1.05703i
$$732$$ 0 0
$$733$$ −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i $$-0.966513\pi$$
0.588177 + 0.808732i $$0.299846\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ −7.00000 −0.258023
$$737$$ 2.00000 3.46410i 0.0736709 0.127602i
$$738$$ 0 0
$$739$$ −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i $$-0.286575\pi$$
−0.989230 + 0.146369i $$0.953241\pi$$
$$740$$ −3.00000 + 5.19615i −0.110282 + 0.191014i
$$741$$ 0 0
$$742$$ −8.00000 6.92820i −0.293689 0.254342i
$$743$$ 4.00000 0.146746 0.0733729 0.997305i $$-0.476624\pi$$
0.0733729 + 0.997305i $$0.476624\pi$$
$$744$$ 0 0
$$745$$ 17.0000 + 29.4449i 0.622832 + 1.07878i
$$746$$ −11.0000 19.0526i −0.402739 0.697564i
$$747$$ 0 0
$$748$$ 3.00000 0.109691
$$749$$ 45.0000 15.5885i 1.64426 0.569590i
$$750$$ 0 0
$$751$$ 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i $$-0.572942\pi$$
0.956963 0.290209i $$-0.0937250\pi$$
$$752$$ −3.50000 6.06218i −0.127632 0.221065i
$$753$$ 0 0
$$754$$ 5.00000 8.66025i 0.182089 0.315388i
$$755$$ −10.0000 −0.363937
$$756$$ 0 0
$$757$$ 15.0000 0.545184 0.272592 0.962130i $$-0.412119\pi$$
0.272592 + 0.962130i $$0.412119\pi$$
$$758$$ −8.00000 + 13.8564i −0.290573 + 0.503287i
$$759$$ 0 0
$$760$$ 7.00000 + 12.1244i 0.253917 + 0.439797i
$$761$$ −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i $$0.349663\pi$$
−0.998684 + 0.0512772i $$0.983671\pi$$
$$762$$ 0 0
$$763$$ 2.00000 10.3923i 0.0724049 0.376227i
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ −15.5000 26.8468i −0.560038 0.970014i
$$767$$ 11.0000 + 19.0526i 0.397187 + 0.687948i
$$768$$ 0 0
$$769$$ 28.0000 1.00971 0.504853 0.863205i $$-0.331547\pi$$
0.504853 + 0.863205i $$0.331547\pi$$
$$770$$ 5.00000 1.73205i 0.180187 0.0624188i
$$771$$ 0 0
$$772$$ −12.0000 + 20.7846i −0.431889 + 0.748054i
$$773$$ 2.00000 + 3.46410i 0.0719350 + 0.124595i 0.899749 0.436407i $$-0.143749\pi$$
−0.827814 + 0.561002i $$0.810416\pi$$
$$774$$ 0 0
$$775$$ 1.00000 1.73205i 0.0359211 0.0622171i
$$776$$ −15.0000 −0.538469
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ 21.0000 36.3731i 0.752403 1.30320i
$$780$$ 0 0
$$781$$ −2.50000 4.33013i −0.0894570 0.154944i
$$782$$ 10.5000 18.1865i 0.375479 0.650349i
$$783$$ 0 0
$$784$$ −6.50000 2.59808i −0.232143 0.0927884i
$$785$$ 2.00000 0.0713831
$$786$$ 0 0
$$787$$ 18.5000 + 32.0429i 0.659454 + 1.14221i 0.980757 + 0.195231i $$0.0625457\pi$$
−0.321303 + 0.946976i $$0.604121\pi$$
$$788$$ 7.50000 + 12.9904i 0.267176 + 0.462763i
$$789$$ 0 0