# Properties

 Label 162.2.c.c.109.1 Level $162$ Weight $2$ Character 162.109 Analytic conductor $1.294$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 162.c (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.29357651274$$ 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: no (minimal twist has level 54) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 109.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 162.109 Dual form 162.2.c.c.55.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{10} +(1.50000 + 2.59808i) q^{11} +(2.00000 - 3.46410i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(-1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +4.00000 q^{26} -1.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-2.50000 + 4.33013i) q^{31} +(0.500000 - 0.866025i) q^{32} -3.00000 q^{35} +2.00000 q^{37} +(1.00000 + 1.73205i) q^{38} +(1.50000 - 2.59808i) q^{40} +(3.00000 - 5.19615i) q^{41} +(5.00000 + 8.66025i) q^{43} -3.00000 q^{44} +6.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(3.00000 - 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} +(2.00000 + 3.46410i) q^{52} +9.00000 q^{53} -9.00000 q^{55} +(-0.500000 - 0.866025i) q^{56} +(3.00000 - 5.19615i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(-7.00000 + 12.1244i) q^{67} +(-1.50000 - 2.59808i) q^{70} -7.00000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-1.50000 + 2.59808i) q^{77} +(-4.00000 - 6.92820i) q^{79} +3.00000 q^{80} +6.00000 q^{82} +(1.50000 + 2.59808i) q^{83} +(-5.00000 + 8.66025i) q^{86} +(-1.50000 - 2.59808i) q^{88} -18.0000 q^{89} +4.00000 q^{91} +(3.00000 + 5.19615i) q^{92} +(3.00000 - 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} +6.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{4} - 3 q^{5} + q^{7} - 2 q^{8} + O(q^{10})$$ $$2 q + q^{2} - q^{4} - 3 q^{5} + q^{7} - 2 q^{8} - 6 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} - q^{16} + 4 q^{19} - 3 q^{20} - 3 q^{22} + 6 q^{23} - 4 q^{25} + 8 q^{26} - 2 q^{28} - 6 q^{29} - 5 q^{31} + q^{32} - 6 q^{35} + 4 q^{37} + 2 q^{38} + 3 q^{40} + 6 q^{41} + 10 q^{43} - 6 q^{44} + 12 q^{46} - 6 q^{47} + 6 q^{49} + 4 q^{50} + 4 q^{52} + 18 q^{53} - 18 q^{55} - q^{56} + 6 q^{58} - 12 q^{59} - 8 q^{61} - 10 q^{62} + 2 q^{64} + 12 q^{65} - 14 q^{67} - 3 q^{70} - 14 q^{73} + 2 q^{74} - 2 q^{76} - 3 q^{77} - 8 q^{79} + 6 q^{80} + 12 q^{82} + 3 q^{83} - 10 q^{86} - 3 q^{88} - 36 q^{89} + 8 q^{91} + 6 q^{92} + 6 q^{94} - 6 q^{95} + q^{97} + 12 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$$.

 $$n$$ $$83$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i $$0.400725\pi$$
−0.977672 + 0.210138i $$0.932609\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i $$-0.106148\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ −3.00000 −0.948683
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ 0 0
$$13$$ 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i $$-0.646166\pi$$
0.997927 0.0643593i $$-0.0205004\pi$$
$$14$$ −0.500000 + 0.866025i −0.133631 + 0.231455i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ −1.50000 2.59808i −0.335410 0.580948i
$$21$$ 0 0
$$22$$ −1.50000 + 2.59808i −0.319801 + 0.553912i
$$23$$ 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i $$-0.618211\pi$$
0.988436 0.151642i $$-0.0484560\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ 4.00000 0.784465
$$27$$ 0 0
$$28$$ −1.00000 −0.188982
$$29$$ −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i $$-0.978586\pi$$
0.440652 0.897678i $$-0.354747\pi$$
$$30$$ 0 0
$$31$$ −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i $$-0.981558\pi$$
0.549309 + 0.835619i $$0.314891\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −3.00000 −0.507093
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 1.00000 + 1.73205i 0.162221 + 0.280976i
$$39$$ 0 0
$$40$$ 1.50000 2.59808i 0.237171 0.410792i
$$41$$ 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i $$-0.678120\pi$$
0.999353 + 0.0359748i $$0.0114536\pi$$
$$42$$ 0 0
$$43$$ 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i $$0.109358\pi$$
−0.179069 + 0.983836i $$0.557309\pi$$
$$44$$ −3.00000 −0.452267
$$45$$ 0 0
$$46$$ 6.00000 0.884652
$$47$$ −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i $$-0.310836\pi$$
−0.997503 + 0.0706177i $$0.977503\pi$$
$$48$$ 0 0
$$49$$ 3.00000 5.19615i 0.428571 0.742307i
$$50$$ 2.00000 3.46410i 0.282843 0.489898i
$$51$$ 0 0
$$52$$ 2.00000 + 3.46410i 0.277350 + 0.480384i
$$53$$ 9.00000 1.23625 0.618123 0.786082i $$-0.287894\pi$$
0.618123 + 0.786082i $$0.287894\pi$$
$$54$$ 0 0
$$55$$ −9.00000 −1.21356
$$56$$ −0.500000 0.866025i −0.0668153 0.115728i
$$57$$ 0 0
$$58$$ 3.00000 5.19615i 0.393919 0.682288i
$$59$$ −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i $$0.452025\pi$$
−0.931282 + 0.364299i $$0.881308\pi$$
$$60$$ 0 0
$$61$$ −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i $$-0.995517\pi$$
0.487753 0.872982i $$-0.337817\pi$$
$$62$$ −5.00000 −0.635001
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 + 10.3923i 0.744208 + 1.28901i
$$66$$ 0 0
$$67$$ −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i $$0.493224\pi$$
−0.876472 + 0.481452i $$0.840109\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ −1.50000 2.59808i −0.179284 0.310530i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −7.00000 −0.819288 −0.409644 0.912245i $$-0.634347\pi$$
−0.409644 + 0.912245i $$0.634347\pi$$
$$74$$ 1.00000 + 1.73205i 0.116248 + 0.201347i
$$75$$ 0 0
$$76$$ −1.00000 + 1.73205i −0.114708 + 0.198680i
$$77$$ −1.50000 + 2.59808i −0.170941 + 0.296078i
$$78$$ 0 0
$$79$$ −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i $$-0.315255\pi$$
−0.998388 + 0.0567635i $$0.981922\pi$$
$$80$$ 3.00000 0.335410
$$81$$ 0 0
$$82$$ 6.00000 0.662589
$$83$$ 1.50000 + 2.59808i 0.164646 + 0.285176i 0.936530 0.350588i $$-0.114018\pi$$
−0.771883 + 0.635764i $$0.780685\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −5.00000 + 8.66025i −0.539164 + 0.933859i
$$87$$ 0 0
$$88$$ −1.50000 2.59808i −0.159901 0.276956i
$$89$$ −18.0000 −1.90800 −0.953998 0.299813i $$-0.903076\pi$$
−0.953998 + 0.299813i $$0.903076\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 3.00000 + 5.19615i 0.312772 + 0.541736i
$$93$$ 0 0
$$94$$ 3.00000 5.19615i 0.309426 0.535942i
$$95$$ −3.00000 + 5.19615i −0.307794 + 0.533114i
$$96$$ 0 0
$$97$$ 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i $$-0.150500\pi$$
−0.839525 + 0.543321i $$0.817167\pi$$
$$98$$ 6.00000 0.606092
$$99$$ 0 0
$$100$$ 4.00000 0.400000
$$101$$ 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
$$103$$ 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i $$-0.770192\pi$$
0.947576 + 0.319531i $$0.103525\pi$$
$$104$$ −2.00000 + 3.46410i −0.196116 + 0.339683i
$$105$$ 0 0
$$106$$ 4.50000 + 7.79423i 0.437079 + 0.757042i
$$107$$ 9.00000 0.870063 0.435031 0.900415i $$-0.356737\pi$$
0.435031 + 0.900415i $$0.356737\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −4.50000 7.79423i −0.429058 0.743151i
$$111$$ 0 0
$$112$$ 0.500000 0.866025i 0.0472456 0.0818317i
$$113$$ 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i $$-0.742264\pi$$
0.971930 + 0.235269i $$0.0755971\pi$$
$$114$$ 0 0
$$115$$ 9.00000 + 15.5885i 0.839254 + 1.45363i
$$116$$ 6.00000 0.557086
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 4.00000 6.92820i 0.362143 0.627250i
$$123$$ 0 0
$$124$$ −2.50000 4.33013i −0.224507 0.388857i
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ −7.00000 −0.621150 −0.310575 0.950549i $$-0.600522\pi$$
−0.310575 + 0.950549i $$0.600522\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −6.00000 + 10.3923i −0.526235 + 0.911465i
$$131$$ 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i $$-0.605885\pi$$
0.981824 0.189794i $$-0.0607819\pi$$
$$132$$ 0 0
$$133$$ 1.00000 + 1.73205i 0.0867110 + 0.150188i
$$134$$ −14.0000 −1.20942
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i $$-0.249173\pi$$
−0.965250 + 0.261329i $$0.915839\pi$$
$$138$$ 0 0
$$139$$ 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i $$-0.779074\pi$$
0.938293 + 0.345843i $$0.112407\pi$$
$$140$$ 1.50000 2.59808i 0.126773 0.219578i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 12.0000 1.00349
$$144$$ 0 0
$$145$$ 18.0000 1.49482
$$146$$ −3.50000 6.06218i −0.289662 0.501709i
$$147$$ 0 0
$$148$$ −1.00000 + 1.73205i −0.0821995 + 0.142374i
$$149$$ −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i $$-0.872548\pi$$
0.798019 + 0.602632i $$0.205881\pi$$
$$150$$ 0 0
$$151$$ −8.50000 14.7224i −0.691720 1.19809i −0.971274 0.237964i $$-0.923520\pi$$
0.279554 0.960130i $$-0.409814\pi$$
$$152$$ −2.00000 −0.162221
$$153$$ 0 0
$$154$$ −3.00000 −0.241747
$$155$$ −7.50000 12.9904i −0.602414 1.04341i
$$156$$ 0 0
$$157$$ 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i $$-0.782307\pi$$
0.934731 + 0.355357i $$0.115641\pi$$
$$158$$ 4.00000 6.92820i 0.318223 0.551178i
$$159$$ 0 0
$$160$$ 1.50000 + 2.59808i 0.118585 + 0.205396i
$$161$$ 6.00000 0.472866
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 3.00000 + 5.19615i 0.234261 + 0.405751i
$$165$$ 0 0
$$166$$ −1.50000 + 2.59808i −0.116423 + 0.201650i
$$167$$ 3.00000 5.19615i 0.232147 0.402090i −0.726293 0.687386i $$-0.758758\pi$$
0.958440 + 0.285295i $$0.0920916\pi$$
$$168$$ 0 0
$$169$$ −1.50000 2.59808i −0.115385 0.199852i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −10.0000 −0.762493
$$173$$ −7.50000 12.9904i −0.570214 0.987640i −0.996544 0.0830722i $$-0.973527\pi$$
0.426329 0.904568i $$-0.359807\pi$$
$$174$$ 0 0
$$175$$ 2.00000 3.46410i 0.151186 0.261861i
$$176$$ 1.50000 2.59808i 0.113067 0.195837i
$$177$$ 0 0
$$178$$ −9.00000 15.5885i −0.674579 1.16840i
$$179$$ −9.00000 −0.672692 −0.336346 0.941739i $$-0.609191\pi$$
−0.336346 + 0.941739i $$0.609191\pi$$
$$180$$ 0 0
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 2.00000 + 3.46410i 0.148250 + 0.256776i
$$183$$ 0 0
$$184$$ −3.00000 + 5.19615i −0.221163 + 0.383065i
$$185$$ −3.00000 + 5.19615i −0.220564 + 0.382029i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 6.00000 0.437595
$$189$$ 0 0
$$190$$ −6.00000 −0.435286
$$191$$ 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i $$-0.0237173\pi$$
−0.563081 + 0.826402i $$0.690384\pi$$
$$192$$ 0 0
$$193$$ −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i $$-0.890928\pi$$
0.761911 + 0.647682i $$0.224262\pi$$
$$194$$ −0.500000 + 0.866025i −0.0358979 + 0.0621770i
$$195$$ 0 0
$$196$$ 3.00000 + 5.19615i 0.214286 + 0.371154i
$$197$$ 9.00000 0.641223 0.320612 0.947211i $$-0.396112\pi$$
0.320612 + 0.947211i $$0.396112\pi$$
$$198$$ 0 0
$$199$$ −7.00000 −0.496217 −0.248108 0.968732i $$-0.579809\pi$$
−0.248108 + 0.968732i $$0.579809\pi$$
$$200$$ 2.00000 + 3.46410i 0.141421 + 0.244949i
$$201$$ 0 0
$$202$$ −1.50000 + 2.59808i −0.105540 + 0.182800i
$$203$$ 3.00000 5.19615i 0.210559 0.364698i
$$204$$ 0 0
$$205$$ 9.00000 + 15.5885i 0.628587 + 1.08875i
$$206$$ 4.00000 0.278693
$$207$$ 0 0
$$208$$ −4.00000 −0.277350
$$209$$ 3.00000 + 5.19615i 0.207514 + 0.359425i
$$210$$ 0 0
$$211$$ 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i $$-0.559865\pi$$
0.944237 0.329266i $$-0.106801\pi$$
$$212$$ −4.50000 + 7.79423i −0.309061 + 0.535310i
$$213$$ 0 0
$$214$$ 4.50000 + 7.79423i 0.307614 + 0.532803i
$$215$$ −30.0000 −2.04598
$$216$$ 0 0
$$217$$ −5.00000 −0.339422
$$218$$ 1.00000 + 1.73205i 0.0677285 + 0.117309i
$$219$$ 0 0
$$220$$ 4.50000 7.79423i 0.303390 0.525487i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i $$-0.252983\pi$$
−0.968309 + 0.249756i $$0.919650\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ 6.00000 0.399114
$$227$$ 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i $$-0.0362899\pi$$
−0.595274 + 0.803523i $$0.702957\pi$$
$$228$$ 0 0
$$229$$ −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i $$-0.986407\pi$$
0.536515 + 0.843891i $$0.319740\pi$$
$$230$$ −9.00000 + 15.5885i −0.593442 + 1.02787i
$$231$$ 0 0
$$232$$ 3.00000 + 5.19615i 0.196960 + 0.341144i
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ 0 0
$$235$$ 18.0000 1.17419
$$236$$ −6.00000 10.3923i −0.390567 0.676481i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −15.0000 + 25.9808i −0.970269 + 1.68056i −0.275533 + 0.961292i $$0.588854\pi$$
−0.694737 + 0.719264i $$0.744479\pi$$
$$240$$ 0 0
$$241$$ 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i $$-0.0622852\pi$$
−0.658838 + 0.752285i $$0.728952\pi$$
$$242$$ 2.00000 0.128565
$$243$$ 0 0
$$244$$ 8.00000 0.512148
$$245$$ 9.00000 + 15.5885i 0.574989 + 0.995910i
$$246$$ 0 0
$$247$$ 4.00000 6.92820i 0.254514 0.440831i
$$248$$ 2.50000 4.33013i 0.158750 0.274963i
$$249$$ 0 0
$$250$$ −1.50000 2.59808i −0.0948683 0.164317i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ −3.50000 6.06218i −0.219610 0.380375i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i $$-0.955440\pi$$
0.615948 + 0.787787i $$0.288773\pi$$
$$258$$ 0 0
$$259$$ 1.00000 + 1.73205i 0.0621370 + 0.107624i
$$260$$ −12.0000 −0.744208
$$261$$ 0 0
$$262$$ 15.0000 0.926703
$$263$$ 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
$$265$$ −13.5000 + 23.3827i −0.829298 + 1.43639i
$$266$$ −1.00000 + 1.73205i −0.0613139 + 0.106199i
$$267$$ 0 0
$$268$$ −7.00000 12.1244i −0.427593 0.740613i
$$269$$ −18.0000 −1.09748 −0.548740 0.835993i $$-0.684892\pi$$
−0.548740 + 0.835993i $$0.684892\pi$$
$$270$$ 0 0
$$271$$ −25.0000 −1.51864 −0.759321 0.650716i $$-0.774469\pi$$
−0.759321 + 0.650716i $$0.774469\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 3.00000 5.19615i 0.181237 0.313911i
$$275$$ 6.00000 10.3923i 0.361814 0.626680i
$$276$$ 0 0
$$277$$ −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i $$-0.243925\pi$$
−0.960810 + 0.277207i $$0.910591\pi$$
$$278$$ 4.00000 0.239904
$$279$$ 0 0
$$280$$ 3.00000 0.179284
$$281$$ −12.0000 20.7846i −0.715860 1.23991i −0.962627 0.270831i $$-0.912702\pi$$
0.246767 0.969075i $$-0.420632\pi$$
$$282$$ 0 0
$$283$$ −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i $$-0.969939\pi$$
0.579437 + 0.815017i $$0.303272\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 6.00000 + 10.3923i 0.354787 + 0.614510i
$$287$$ 6.00000 0.354169
$$288$$ 0 0
$$289$$ −17.0000 −1.00000
$$290$$ 9.00000 + 15.5885i 0.528498 + 0.915386i
$$291$$ 0 0
$$292$$ 3.50000 6.06218i 0.204822 0.354762i
$$293$$ 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i $$-0.777256\pi$$
0.940252 + 0.340480i $$0.110589\pi$$
$$294$$ 0 0
$$295$$ −18.0000 31.1769i −1.04800 1.81519i
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ −3.00000 −0.173785
$$299$$ −12.0000 20.7846i −0.693978 1.20201i
$$300$$ 0 0
$$301$$ −5.00000 + 8.66025i −0.288195 + 0.499169i
$$302$$ 8.50000 14.7224i 0.489120 0.847181i
$$303$$ 0 0
$$304$$ −1.00000 1.73205i −0.0573539 0.0993399i
$$305$$ 24.0000 1.37424
$$306$$ 0 0
$$307$$ −16.0000 −0.913168 −0.456584 0.889680i $$-0.650927\pi$$
−0.456584 + 0.889680i $$0.650927\pi$$
$$308$$ −1.50000 2.59808i −0.0854704 0.148039i
$$309$$ 0 0
$$310$$ 7.50000 12.9904i 0.425971 0.737804i
$$311$$ 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i $$-0.778920\pi$$
0.938460 + 0.345389i $$0.112253\pi$$
$$312$$ 0 0
$$313$$ 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i $$0.0137652\pi$$
−0.462093 + 0.886831i $$0.652902\pi$$
$$314$$ 4.00000 0.225733
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i $$-0.139818\pi$$
−0.820822 + 0.571184i $$0.806484\pi$$
$$318$$ 0 0
$$319$$ 9.00000 15.5885i 0.503903 0.872786i
$$320$$ −1.50000 + 2.59808i −0.0838525 + 0.145237i
$$321$$ 0 0
$$322$$ 3.00000 + 5.19615i 0.167183 + 0.289570i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −16.0000 −0.887520
$$326$$ 10.0000 + 17.3205i 0.553849 + 0.959294i
$$327$$ 0 0
$$328$$ −3.00000 + 5.19615i −0.165647 + 0.286910i
$$329$$ 3.00000 5.19615i 0.165395 0.286473i
$$330$$ 0 0
$$331$$ 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i $$-0.0780468\pi$$
−0.695266 + 0.718752i $$0.744713\pi$$
$$332$$ −3.00000 −0.164646
$$333$$ 0 0
$$334$$ 6.00000 0.328305
$$335$$ −21.0000 36.3731i −1.14735 1.98727i
$$336$$ 0 0
$$337$$ 11.0000 19.0526i 0.599208 1.03786i −0.393730 0.919226i $$-0.628816\pi$$
0.992938 0.118633i $$-0.0378512\pi$$
$$338$$ 1.50000 2.59808i 0.0815892 0.141317i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −15.0000 −0.812296
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −5.00000 8.66025i −0.269582 0.466930i
$$345$$ 0 0
$$346$$ 7.50000 12.9904i 0.403202 0.698367i
$$347$$ −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i $$-0.858993\pi$$
0.822951 + 0.568112i $$0.192326\pi$$
$$348$$ 0 0
$$349$$ 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i $$-0.0804216\pi$$
−0.700609 + 0.713545i $$0.747088\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ 3.00000 0.159901
$$353$$ −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
$$355$$ 0 0
$$356$$ 9.00000 15.5885i 0.476999 0.826187i
$$357$$ 0 0
$$358$$ −4.50000 7.79423i −0.237832 0.411938i
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ −8.00000 13.8564i −0.420471 0.728277i
$$363$$ 0 0
$$364$$ −2.00000 + 3.46410i −0.104828 + 0.181568i
$$365$$ 10.5000 18.1865i 0.549595 0.951927i
$$366$$ 0 0
$$367$$ −8.50000 14.7224i −0.443696 0.768505i 0.554264 0.832341i $$-0.313000\pi$$
−0.997960 + 0.0638362i $$0.979666\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ −6.00000 −0.311925
$$371$$ 4.50000 + 7.79423i 0.233628 + 0.404656i
$$372$$ 0 0
$$373$$ −16.0000 + 27.7128i −0.828449 + 1.43492i 0.0708063 + 0.997490i $$0.477443\pi$$
−0.899255 + 0.437425i $$0.855891\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ −24.0000 −1.23606
$$378$$ 0 0
$$379$$ 20.0000 1.02733 0.513665 0.857991i $$-0.328287\pi$$
0.513665 + 0.857991i $$0.328287\pi$$
$$380$$ −3.00000 5.19615i −0.153897 0.266557i
$$381$$ 0 0
$$382$$ −6.00000 + 10.3923i −0.306987 + 0.531717i
$$383$$ 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i $$-0.623227\pi$$
0.990702 0.136047i $$-0.0434398\pi$$
$$384$$ 0 0
$$385$$ −4.50000 7.79423i −0.229341 0.397231i
$$386$$ −5.00000 −0.254493
$$387$$ 0 0
$$388$$ −1.00000 −0.0507673
$$389$$ 10.5000 + 18.1865i 0.532371 + 0.922094i 0.999286 + 0.0377914i $$0.0120322\pi$$
−0.466915 + 0.884302i $$0.654634\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −3.00000 + 5.19615i −0.151523 + 0.262445i
$$393$$ 0 0
$$394$$ 4.50000 + 7.79423i 0.226707 + 0.392668i
$$395$$ 24.0000 1.20757
$$396$$ 0 0
$$397$$ 20.0000 1.00377 0.501886 0.864934i $$-0.332640\pi$$
0.501886 + 0.864934i $$0.332640\pi$$
$$398$$ −3.50000 6.06218i −0.175439 0.303870i
$$399$$ 0 0
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i $$-0.930195\pi$$
0.676425 + 0.736512i $$0.263528\pi$$
$$402$$ 0 0
$$403$$ 10.0000 + 17.3205i 0.498135 + 0.862796i
$$404$$ −3.00000 −0.149256
$$405$$ 0 0
$$406$$ 6.00000 0.297775
$$407$$ 3.00000 + 5.19615i 0.148704 + 0.257564i
$$408$$ 0 0
$$409$$ −11.5000 + 19.9186i −0.568638 + 0.984911i 0.428063 + 0.903749i $$0.359196\pi$$
−0.996701 + 0.0811615i $$0.974137\pi$$
$$410$$ −9.00000 + 15.5885i −0.444478 + 0.769859i
$$411$$ 0 0
$$412$$ 2.00000 + 3.46410i 0.0985329 + 0.170664i
$$413$$ −12.0000 −0.590481
$$414$$ 0 0
$$415$$ −9.00000 −0.441793
$$416$$ −2.00000 3.46410i −0.0980581 0.169842i
$$417$$ 0 0
$$418$$ −3.00000 + 5.19615i −0.146735 + 0.254152i
$$419$$ −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i $$-0.928027\pi$$
0.681426 + 0.731887i $$0.261360\pi$$
$$420$$ 0 0
$$421$$ −4.00000 6.92820i −0.194948 0.337660i 0.751935 0.659237i $$-0.229121\pi$$
−0.946883 + 0.321577i $$0.895787\pi$$
$$422$$ 22.0000 1.07094
$$423$$ 0 0
$$424$$ −9.00000 −0.437079
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 4.00000 6.92820i 0.193574 0.335279i
$$428$$ −4.50000 + 7.79423i −0.217516 + 0.376748i
$$429$$ 0 0
$$430$$ −15.0000 25.9808i −0.723364 1.25290i
$$431$$ 18.0000 0.867029 0.433515 0.901146i $$-0.357273\pi$$
0.433515 + 0.901146i $$0.357273\pi$$
$$432$$ 0 0
$$433$$ 29.0000 1.39365 0.696826 0.717241i $$-0.254595\pi$$
0.696826 + 0.717241i $$0.254595\pi$$
$$434$$ −2.50000 4.33013i −0.120004 0.207853i
$$435$$ 0 0
$$436$$ −1.00000 + 1.73205i −0.0478913 + 0.0829502i
$$437$$ 6.00000 10.3923i 0.287019 0.497131i
$$438$$ 0 0
$$439$$ 9.50000 + 16.4545i 0.453410 + 0.785330i 0.998595 0.0529862i $$-0.0168739\pi$$
−0.545185 + 0.838316i $$0.683541\pi$$
$$440$$ 9.00000 0.429058
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i $$-0.0746503\pi$$
−0.687557 + 0.726130i $$0.741317\pi$$
$$444$$ 0 0
$$445$$ 27.0000 46.7654i 1.27992 2.21689i
$$446$$ 4.00000 6.92820i 0.189405 0.328060i
$$447$$ 0 0
$$448$$ 0.500000 + 0.866025i 0.0236228 + 0.0409159i
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 18.0000 0.847587
$$452$$ 3.00000 + 5.19615i 0.141108 + 0.244406i
$$453$$ 0 0
$$454$$ −6.00000 + 10.3923i −0.281594 + 0.487735i
$$455$$ −6.00000 + 10.3923i −0.281284 + 0.487199i
$$456$$ 0 0
$$457$$ 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i $$-0.159221\pi$$
−0.854094 + 0.520119i $$0.825888\pi$$
$$458$$ −14.0000 −0.654177
$$459$$ 0 0
$$460$$ −18.0000 −0.839254
$$461$$ 10.5000 + 18.1865i 0.489034 + 0.847031i 0.999920 0.0126168i $$-0.00401615\pi$$
−0.510887 + 0.859648i $$0.670683\pi$$
$$462$$ 0 0
$$463$$ 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i $$-0.735652\pi$$
0.976607 + 0.215032i $$0.0689855\pi$$
$$464$$ −3.00000 + 5.19615i −0.139272 + 0.241225i
$$465$$ 0 0
$$466$$ 9.00000 + 15.5885i 0.416917 + 0.722121i
$$467$$ −27.0000 −1.24941 −0.624705 0.780860i $$-0.714781\pi$$
−0.624705 + 0.780860i $$0.714781\pi$$
$$468$$ 0 0
$$469$$ −14.0000 −0.646460
$$470$$ 9.00000 + 15.5885i 0.415139 + 0.719042i
$$471$$ 0 0
$$472$$ 6.00000 10.3923i 0.276172 0.478345i
$$473$$ −15.0000 + 25.9808i −0.689701 + 1.19460i
$$474$$ 0 0
$$475$$ −4.00000 6.92820i −0.183533 0.317888i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −30.0000 −1.37217
$$479$$ −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i $$-0.210436\pi$$
−0.926388 + 0.376571i $$0.877103\pi$$
$$480$$ 0 0
$$481$$ 4.00000 6.92820i 0.182384 0.315899i
$$482$$ −5.00000 + 8.66025i −0.227744 + 0.394464i
$$483$$ 0 0
$$484$$ 1.00000 + 1.73205i 0.0454545 + 0.0787296i
$$485$$ −3.00000 −0.136223
$$486$$ 0 0
$$487$$ −16.0000 −0.725029 −0.362515 0.931978i $$-0.618082\pi$$
−0.362515 + 0.931978i $$0.618082\pi$$
$$488$$ 4.00000 + 6.92820i 0.181071 + 0.313625i
$$489$$ 0 0
$$490$$ −9.00000 + 15.5885i −0.406579 + 0.704215i
$$491$$ −19.5000 + 33.7750i −0.880023 + 1.52424i −0.0287085 + 0.999588i $$0.509139\pi$$
−0.851314 + 0.524656i $$0.824194\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 8.00000 0.359937
$$495$$ 0 0
$$496$$ 5.00000 0.224507
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −7.00000 + 12.1244i −0.313363 + 0.542761i −0.979088 0.203436i $$-0.934789\pi$$
0.665725 + 0.746197i $$0.268122\pi$$
$$500$$ 1.50000 2.59808i 0.0670820 0.116190i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −18.0000 −0.802580 −0.401290 0.915951i $$-0.631438\pi$$
−0.401290 + 0.915951i $$0.631438\pi$$
$$504$$ 0 0
$$505$$ −9.00000 −0.400495
$$506$$ 9.00000 + 15.5885i 0.400099 + 0.692991i
$$507$$ 0 0
$$508$$ 3.50000 6.06218i 0.155287 0.268966i
$$509$$ 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i $$-0.725464\pi$$
0.982988 + 0.183669i $$0.0587976\pi$$
$$510$$ 0 0
$$511$$ −3.50000 6.06218i −0.154831 0.268175i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −12.0000 −0.529297
$$515$$ 6.00000 + 10.3923i 0.264392 + 0.457940i
$$516$$ 0 0
$$517$$ 9.00000 15.5885i 0.395820 0.685580i
$$518$$ −1.00000 + 1.73205i −0.0439375 + 0.0761019i
$$519$$ 0 0
$$520$$ −6.00000 10.3923i −0.263117 0.455733i
$$521$$ 36.0000 1.57719 0.788594 0.614914i $$-0.210809\pi$$
0.788594 + 0.614914i $$0.210809\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ 7.50000 + 12.9904i 0.327639 + 0.567487i
$$525$$ 0 0
$$526$$ −15.0000 + 25.9808i −0.654031 + 1.13282i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −6.50000 11.2583i −0.282609 0.489493i
$$530$$ −27.0000 −1.17281
$$531$$ 0 0
$$532$$ −2.00000 −0.0867110
$$533$$ −12.0000 20.7846i −0.519778 0.900281i
$$534$$ 0 0
$$535$$ −13.5000 + 23.3827i −0.583656 + 1.01092i
$$536$$ 7.00000 12.1244i 0.302354 0.523692i
$$537$$ 0 0
$$538$$ −9.00000 15.5885i −0.388018 0.672066i
$$539$$ 18.0000 0.775315
$$540$$ 0 0
$$541$$ 20.0000 0.859867 0.429934 0.902861i $$-0.358537\pi$$
0.429934 + 0.902861i $$0.358537\pi$$
$$542$$ −12.5000 21.6506i −0.536921 0.929974i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −3.00000 + 5.19615i −0.128506 + 0.222579i
$$546$$ 0 0
$$547$$ −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i $$-0.221375\pi$$
−0.938779 + 0.344519i $$0.888042\pi$$
$$548$$ 6.00000 0.256307
$$549$$ 0 0
$$550$$ 12.0000 0.511682
$$551$$ −6.00000 10.3923i −0.255609 0.442727i
$$552$$ 0 0
$$553$$ 4.00000 6.92820i 0.170097 0.294617i
$$554$$ 4.00000 6.92820i 0.169944 0.294351i
$$555$$ 0 0
$$556$$ 2.00000 + 3.46410i 0.0848189 + 0.146911i
$$557$$ 27.0000 1.14403 0.572013 0.820244i $$-0.306163\pi$$
0.572013 + 0.820244i $$0.306163\pi$$
$$558$$ 0 0
$$559$$ 40.0000 1.69182
$$560$$ 1.50000 + 2.59808i 0.0633866 + 0.109789i
$$561$$ 0 0
$$562$$ 12.0000 20.7846i 0.506189 0.876746i
$$563$$ −1.50000 + 2.59808i −0.0632175 + 0.109496i −0.895902 0.444252i $$-0.853470\pi$$
0.832684 + 0.553748i $$0.186803\pi$$
$$564$$ 0 0
$$565$$ 9.00000 + 15.5885i 0.378633 + 0.655811i
$$566$$ −14.0000 −0.588464
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 6.00000 + 10.3923i 0.251533 + 0.435668i 0.963948 0.266090i $$-0.0857319\pi$$
−0.712415 + 0.701758i $$0.752399\pi$$
$$570$$ 0 0
$$571$$ 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i $$-0.806660\pi$$
0.904835 + 0.425762i $$0.139994\pi$$
$$572$$ −6.00000 + 10.3923i −0.250873 + 0.434524i
$$573$$ 0 0
$$574$$ 3.00000 + 5.19615i 0.125218 + 0.216883i
$$575$$ −24.0000 −1.00087
$$576$$ 0 0
$$577$$ 38.0000 1.58196 0.790980 0.611842i $$-0.209571\pi$$
0.790980 + 0.611842i $$0.209571\pi$$
$$578$$ −8.50000 14.7224i −0.353553 0.612372i
$$579$$ 0 0
$$580$$ −9.00000 + 15.5885i −0.373705 + 0.647275i
$$581$$ −1.50000 + 2.59808i −0.0622305 + 0.107786i
$$582$$ 0 0
$$583$$ 13.5000 + 23.3827i 0.559113 + 0.968412i
$$584$$ 7.00000 0.289662
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ 1.50000 + 2.59808i 0.0619116 + 0.107234i 0.895320 0.445424i $$-0.146947\pi$$
−0.833408 + 0.552658i $$0.813614\pi$$
$$588$$ 0 0
$$589$$ −5.00000 + 8.66025i −0.206021 + 0.356840i
$$590$$ 18.0000 31.1769i 0.741048 1.28353i
$$591$$ 0 0
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ 18.0000 0.739171 0.369586 0.929197i $$-0.379500\pi$$
0.369586 + 0.929197i $$0.379500\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −1.50000 2.59808i −0.0614424 0.106421i
$$597$$ 0 0
$$598$$ 12.0000 20.7846i 0.490716 0.849946i
$$599$$ 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i $$-0.505017\pi$$
0.873799 0.486287i $$-0.161649\pi$$
$$600$$ 0 0
$$601$$ −17.5000 30.3109i −0.713840 1.23641i −0.963405 0.268049i $$-0.913621\pi$$
0.249565 0.968358i $$-0.419712\pi$$
$$602$$ −10.0000 −0.407570
$$603$$ 0 0
$$604$$ 17.0000 0.691720
$$605$$ 3.00000 + 5.19615i 0.121967 + 0.211254i
$$606$$ 0 0
$$607$$ −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i $$0.391655\pi$$
−0.983262 + 0.182199i $$0.941678\pi$$
$$608$$ 1.00000 1.73205i 0.0405554 0.0702439i
$$609$$ 0 0
$$610$$ 12.0000 + 20.7846i 0.485866 + 0.841544i
$$611$$ −24.0000 −0.970936
$$612$$ 0 0
$$613$$ −34.0000 −1.37325 −0.686624 0.727013i $$-0.740908\pi$$
−0.686624 + 0.727013i $$0.740908\pi$$
$$614$$ −8.00000 13.8564i −0.322854 0.559199i
$$615$$ 0 0
$$616$$ 1.50000 2.59808i 0.0604367 0.104679i
$$617$$ 21.0000 36.3731i 0.845428 1.46432i −0.0398207 0.999207i $$-0.512679\pi$$
0.885249 0.465118i $$-0.153988\pi$$
$$618$$ 0 0
$$619$$ 14.0000 + 24.2487i 0.562708 + 0.974638i 0.997259 + 0.0739910i $$0.0235736\pi$$
−0.434551 + 0.900647i $$0.643093\pi$$
$$620$$ 15.0000 0.602414
$$621$$ 0 0
$$622$$ 6.00000 0.240578
$$623$$ −9.00000 15.5885i −0.360577 0.624538i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ −9.50000 + 16.4545i −0.379696 + 0.657653i
$$627$$ 0 0
$$628$$ 2.00000 + 3.46410i 0.0798087 + 0.138233i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −25.0000 −0.995234 −0.497617 0.867397i $$-0.665792\pi$$
−0.497617 + 0.867397i $$0.665792\pi$$
$$632$$ 4.00000 + 6.92820i 0.159111 + 0.275589i
$$633$$ 0 0
$$634$$ −1.50000 + 2.59808i −0.0595726 + 0.103183i
$$635$$ 10.5000 18.1865i 0.416680 0.721711i
$$636$$ 0 0
$$637$$ −12.0000 20.7846i −0.475457 0.823516i
$$638$$ 18.0000 0.712627
$$639$$ 0 0
$$640$$ −3.00000 −0.118585
$$641$$ −21.0000 36.3731i −0.829450 1.43665i −0.898470 0.439034i $$-0.855321\pi$$
0.0690201 0.997615i $$-0.478013\pi$$
$$642$$ 0 0
$$643$$ 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i $$-0.808201\pi$$
0.902764 + 0.430137i $$0.141535\pi$$
$$644$$ −3.00000 + 5.19615i −0.118217 + 0.204757i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 0 0
$$649$$ −36.0000 −1.41312
$$650$$ −8.00000 13.8564i −0.313786 0.543493i
$$651$$ 0 0
$$652$$ −10.0000 + 17.3205i −0.391630 + 0.678323i
$$653$$ −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i $$0.442987\pi$$
−0.941248 + 0.337715i $$0.890346\pi$$
$$654$$ 0 0
$$655$$ 22.5000 + 38.9711i 0.879148 + 1.52273i
$$656$$ −6.00000 −0.234261
$$657$$ 0 0
$$658$$ 6.00000 0.233904
$$659$$ 10.5000 + 18.1865i 0.409022 + 0.708447i 0.994780 0.102039i $$-0.0325366\pi$$
−0.585758 + 0.810486i $$0.699203\pi$$
$$660$$ 0 0
$$661$$ −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i $$-0.921107\pi$$
0.697174 + 0.716902i $$0.254441\pi$$
$$662$$ −5.00000 + 8.66025i −0.194331 + 0.336590i
$$663$$ 0 0
$$664$$ −1.50000 2.59808i −0.0582113 0.100825i
$$665$$ −6.00000 −0.232670
$$666$$ 0 0
$$667$$ −36.0000 −1.39393
$$668$$ 3.00000 + 5.19615i 0.116073 + 0.201045i
$$669$$ 0 0
$$670$$ 21.0000 36.3731i 0.811301 1.40521i
$$671$$ 12.0000 20.7846i 0.463255 0.802381i
$$672$$ 0 0
$$673$$ 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i $$-0.0473259\pi$$
−0.622770 + 0.782405i $$0.713993\pi$$
$$674$$ 22.0000 0.847408
$$675$$ 0 0
$$676$$ 3.00000 0.115385
$$677$$ −21.0000 36.3731i −0.807096 1.39793i −0.914867 0.403755i $$-0.867705\pi$$
0.107772 0.994176i $$-0.465628\pi$$
$$678$$ 0 0
$$679$$ −0.500000 + 0.866025i −0.0191882 + 0.0332350i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −7.50000 12.9904i −0.287190 0.497427i
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 18.0000 0.687745
$$686$$ 6.50000 + 11.2583i 0.248171 + 0.429845i
$$687$$ 0 0
$$688$$ 5.00000 8.66025i 0.190623 0.330169i
$$689$$ 18.0000 31.1769i 0.685745 1.18775i
$$690$$ 0 0
$$691$$ −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i $$-0.851021\pi$$
0.0555386 0.998457i $$-0.482312\pi$$
$$692$$ 15.0000 0.570214
$$693$$ 0 0
$$694$$ −3.00000 −0.113878
$$695$$ 6.00000 + 10.3923i 0.227593 + 0.394203i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −5.00000 + 8.66025i −0.189253 + 0.327795i
$$699$$ 0 0
$$700$$ 2.00000 + 3.46410i 0.0755929 + 0.130931i
$$701$$ 9.00000 0.339925 0.169963 0.985451i $$-0.445635\pi$$
0.169963 + 0.985451i $$0.445635\pi$$
$$702$$ 0 0
$$703$$ 4.00000 0.150863
$$704$$ 1.50000 + 2.59808i 0.0565334 + 0.0979187i
$$705$$ 0 0
$$706$$ 3.00000 5.19615i 0.112906 0.195560i
$$707$$ −1.50000 + 2.59808i −0.0564133 + 0.0977107i
$$708$$ 0 0
$$709$$ −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i $$-0.857149\pi$$
0.0747503 0.997202i $$-0.476184\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 18.0000 0.674579
$$713$$ 15.0000 + 25.9808i 0.561754 + 0.972987i
$$714$$ 0 0
$$715$$ −18.0000 + 31.1769i −0.673162 + 1.16595i
$$716$$ 4.50000 7.79423i 0.168173 0.291284i
$$717$$ 0 0
$$718$$ 9.00000 + 15.5885i 0.335877 + 0.581756i
$$719$$ 36.0000 1.34257 0.671287 0.741198i $$-0.265742\pi$$
0.671287 + 0.741198i $$0.265742\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ −7.50000 12.9904i −0.279121 0.483452i
$$723$$ 0 0
$$724$$ 8.00000 13.8564i 0.297318 0.514969i
$$725$$ −12.0000 + 20.7846i −0.445669 + 0.771921i
$$726$$ 0 0
$$727$$ 0.500000 + 0.866025i 0.0185440 + 0.0321191i 0.875148 0.483854i $$-0.160764\pi$$
−0.856605 + 0.515974i $$0.827430\pi$$
$$728$$ −4.00000 −0.148250
$$729$$ 0 0
$$730$$ 21.0000 0.777245
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i $$-0.700154\pi$$
0.994471 + 0.105010i $$0.0334875\pi$$
$$734$$ 8.50000 14.7224i 0.313741 0.543415i
$$735$$ 0 0
$$736$$ −3.00000 5.19615i −0.110581 0.191533i
$$737$$ −42.0000 −1.54709
$$738$$ 0 0
$$739$$ −16.0000 −0.588570 −0.294285 0.955718i $$-0.595081\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ −3.00000 5.19615i −0.110282 0.191014i
$$741$$ 0 0
$$742$$ −4.50000 + 7.79423i −0.165200 + 0.286135i
$$743$$ −6.00000 + 10.3923i −0.220119 + 0.381257i −0.954844 0.297108i $$-0.903978\pi$$
0.734725 + 0.678365i $$0.237311\pi$$
$$744$$ 0 0
$$745$$ −4.50000 7.79423i −0.164867 0.285558i
$$746$$ −32.0000 −1.17160
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.50000 + 7.79423i 0.164426 + 0.284795i
$$750$$ 0 0
$$751$$ −20.5000 + 35.5070i −0.748056 + 1.29567i 0.200698 + 0.979653i $$0.435679\pi$$
−0.948753 + 0.316017i $$0.897654\pi$$
$$752$$ −3.00000 + 5.19615i −0.109399 + 0.189484i
$$753$$ 0 0
$$754$$ −12.0000 20.7846i −0.437014 0.756931i
$$755$$ 51.0000 1.85608
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 10.0000 + 17.3205i 0.363216 + 0.629109i
$$759$$ 0 0
$$760$$ 3.00000 5.19615i 0.108821 0.188484i
$$761$$ −24.0000 + 41.5692i −0.869999 + 1.50688i −0.00800331 + 0.999968i $$0.502548\pi$$
−0.861996 + 0.506915i $$0.830786\pi$$
$$762$$ 0 0
$$763$$ 1.00000 + 1.73205i 0.0362024 + 0.0627044i
$$764$$ −12.0000 −0.434145
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 24.0000 + 41.5692i 0.866590 + 1.50098i
$$768$$ 0 0
$$769$$ 15.5000 26.8468i 0.558944 0.968120i −0.438641 0.898663i $$-0.644540\pi$$
0.997585 0.0694574i $$-0.0221268\pi$$
$$770$$ 4.50000 7.79423i 0.162169 0.280885i
$$771$$ 0 0
$$772$$ −2.50000 4.33013i −0.0899770 0.155845i
$$773$$ −18.0000 −0.647415 −0.323708 0.946157i $$-0.604929\pi$$
−0.323708 + 0.946157i $$0.604929\pi$$
$$774$$ 0 0
$$775$$ 20.0000 0.718421
$$776$$ −0.500000 0.866025i −0.0179490 0.0310885i
$$777$$ 0 0
$$778$$ −10.5000 + 18.1865i −0.376443 + 0.652019i
$$779$$ 6.00000 10.3923i 0.214972 0.372343i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −6.00000 −0.214286
$$785$$ 6.00000 + 10.3923i 0.214149 + 0.370917i
$$786$$ 0 0
$$787$$ −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i $$0.359855\pi$$
−0.996531 + 0.0832226i $$0.973479\pi$$
$$788$$ −4.50000 + 7.79423i −0.160306 + 0.277658i
$$789$$ 0 0
$$790$$ 12.0000 + 20.7846i 0.426941 + 0.739483i
$$791$$ 6.00000 0.213335
$$792$$ 0