Properties

 Label 2646.2.e.f.2125.1 Level $2646$ Weight $2$ Character 2646.2125 Analytic conductor $21.128$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$2646 = 2 \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2646.e (of order $$3$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$21.1284163748$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

 Embedding label 2125.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 2646.2125 Dual form 2646.2.e.f.1549.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(3.00000 - 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} +(3.00000 - 5.19615i) q^{58} +5.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +8.00000 q^{67} +(3.00000 - 5.19615i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-3.00000 - 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} -21.0000 q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} + 2q^{4} - 3q^{5} + 2q^{8} + O(q^{10})$$ $$2q + 2q^{2} + 2q^{4} - 3q^{5} + 2q^{8} - 3q^{10} - 6q^{11} - 2q^{13} + 2q^{16} + 6q^{17} + 7q^{19} - 3q^{20} - 6q^{22} + 3q^{23} - 4q^{25} - 2q^{26} + 6q^{29} + 4q^{31} + 2q^{32} + 6q^{34} - 2q^{37} + 7q^{38} - 3q^{40} - 2q^{43} - 6q^{44} + 3q^{46} - 4q^{50} - 2q^{52} + 6q^{53} + 36q^{55} + 6q^{58} + 10q^{61} + 4q^{62} + 2q^{64} + 12q^{65} + 16q^{67} + 6q^{68} - 6q^{71} - 2q^{73} - 2q^{74} + 7q^{76} + 10q^{79} - 3q^{80} + 12q^{83} + 18q^{85} - 2q^{86} - 6q^{88} + 3q^{92} - 42q^{95} - 2q^{97} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1081$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −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 0
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ −1.50000 + 2.59808i −0.474342 + 0.821584i
$$11$$ −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i $$-0.806886\pi$$
−0.0829925 0.996550i $$-0.526448\pi$$
$$12$$ 0 0
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i $$-0.573966\pi$$
0.957892 0.287129i $$-0.0927008\pi$$
$$18$$ 0 0
$$19$$ 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i $$0.130073\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ −1.50000 + 2.59808i −0.335410 + 0.580948i
$$21$$ 0 0
$$22$$ −3.00000 5.19615i −0.639602 1.10782i
$$23$$ 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i $$-0.732076\pi$$
0.978961 + 0.204046i $$0.0654092\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ −1.00000 1.73205i −0.196116 0.339683i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i $$-0.645253\pi$$
0.997738 0.0672232i $$-0.0214140\pi$$
$$30$$ 0 0
$$31$$ 2.00000 0.359211 0.179605 0.983739i $$-0.442518\pi$$
0.179605 + 0.983739i $$0.442518\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 3.00000 5.19615i 0.514496 0.891133i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i $$-0.219235\pi$$
−0.936442 + 0.350823i $$0.885902\pi$$
$$38$$ 3.50000 + 6.06218i 0.567775 + 0.983415i
$$39$$ 0 0
$$40$$ −1.50000 + 2.59808i −0.237171 + 0.410792i
$$41$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$42$$ 0 0
$$43$$ −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i $$-0.882065\pi$$
0.779647 + 0.626219i $$0.215399\pi$$
$$44$$ −3.00000 5.19615i −0.452267 0.783349i
$$45$$ 0 0
$$46$$ 1.50000 2.59808i 0.221163 0.383065i
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −2.00000 3.46410i −0.282843 0.489898i
$$51$$ 0 0
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i $$-0.698135\pi$$
0.995117 + 0.0987002i $$0.0314685\pi$$
$$54$$ 0 0
$$55$$ 18.0000 2.42712
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 3.00000 5.19615i 0.393919 0.682288i
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 0 0
$$61$$ 5.00000 0.640184 0.320092 0.947386i $$-0.396286\pi$$
0.320092 + 0.947386i $$0.396286\pi$$
$$62$$ 2.00000 0.254000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ 8.00000 0.977356 0.488678 0.872464i $$-0.337479\pi$$
0.488678 + 0.872464i $$0.337479\pi$$
$$68$$ 3.00000 5.19615i 0.363803 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.00000 −0.356034 −0.178017 0.984027i $$-0.556968\pi$$
−0.178017 + 0.984027i $$0.556968\pi$$
$$72$$ 0 0
$$73$$ −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i $$-0.870674\pi$$
0.801553 + 0.597924i $$0.204008\pi$$
$$74$$ −1.00000 1.73205i −0.116248 0.201347i
$$75$$ 0 0
$$76$$ 3.50000 + 6.06218i 0.401478 + 0.695379i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 5.00000 0.562544 0.281272 0.959628i $$-0.409244\pi$$
0.281272 + 0.959628i $$0.409244\pi$$
$$80$$ −1.50000 + 2.59808i −0.167705 + 0.290474i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i $$-0.604488\pi$$
0.980982 0.194099i $$-0.0621783\pi$$
$$84$$ 0 0
$$85$$ 9.00000 + 15.5885i 0.976187 + 1.69081i
$$86$$ −1.00000 + 1.73205i −0.107833 + 0.186772i
$$87$$ 0 0
$$88$$ −3.00000 5.19615i −0.319801 0.553912i
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 1.50000 2.59808i 0.156386 0.270868i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −21.0000 −2.15455
$$96$$ 0 0
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −2.00000 3.46410i −0.200000 0.346410i
$$101$$ 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i $$-0.0188862\pi$$
−0.550474 + 0.834853i $$0.685553\pi$$
$$102$$ 0 0
$$103$$ 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i $$-0.669356\pi$$
0.999964 + 0.00844953i $$0.00268960\pi$$
$$104$$ −1.00000 1.73205i −0.0980581 0.169842i
$$105$$ 0 0
$$106$$ 3.00000 5.19615i 0.291386 0.504695i
$$107$$ −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i $$-0.969703\pi$$
0.415432 0.909624i $$-0.363630\pi$$
$$108$$ 0 0
$$109$$ 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i $$-0.674364\pi$$
0.999708 + 0.0241802i $$0.00769755\pi$$
$$110$$ 18.0000 1.71623
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i $$0.0826291\pi$$
−0.260955 + 0.965351i $$0.584038\pi$$
$$114$$ 0 0
$$115$$ 4.50000 + 7.79423i 0.419627 + 0.726816i
$$116$$ 3.00000 5.19615i 0.278543 0.482451i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −12.5000 + 21.6506i −1.13636 + 1.96824i
$$122$$ 5.00000 0.452679
$$123$$ 0 0
$$124$$ 2.00000 0.179605
$$125$$ −3.00000 −0.268328
$$126$$ 0 0
$$127$$ 17.0000 1.50851 0.754253 0.656584i $$-0.227999\pi$$
0.754253 + 0.656584i $$0.227999\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 6.00000 0.526235
$$131$$ −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i $$-0.961954\pi$$
0.599699 + 0.800226i $$0.295287\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 8.00000 0.691095
$$135$$ 0 0
$$136$$ 3.00000 5.19615i 0.257248 0.445566i
$$137$$ 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
$$139$$ −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i $$-0.234680\pi$$
−0.952355 + 0.304991i $$0.901346\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −3.00000 −0.251754
$$143$$ −6.00000 + 10.3923i −0.501745 + 0.869048i
$$144$$ 0 0
$$145$$ 9.00000 + 15.5885i 0.747409 + 1.29455i
$$146$$ −1.00000 + 1.73205i −0.0827606 + 0.143346i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ 0 0
$$151$$ −11.5000 19.9186i −0.935857 1.62095i −0.773099 0.634285i $$-0.781294\pi$$
−0.162758 0.986666i $$-0.552039\pi$$
$$152$$ 3.50000 + 6.06218i 0.283887 + 0.491708i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.00000 + 5.19615i −0.240966 + 0.417365i
$$156$$ 0 0
$$157$$ −13.0000 −1.03751 −0.518756 0.854922i $$-0.673605\pi$$
−0.518756 + 0.854922i $$0.673605\pi$$
$$158$$ 5.00000 0.397779
$$159$$ 0 0
$$160$$ −1.50000 + 2.59808i −0.118585 + 0.205396i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i $$-0.191624\pi$$
−0.902528 + 0.430632i $$0.858291\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 6.00000 10.3923i 0.465690 0.806599i
$$167$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 9.00000 + 15.5885i 0.690268 + 1.19558i
$$171$$ 0 0
$$172$$ −1.00000 + 1.73205i −0.0762493 + 0.132068i
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −3.00000 5.19615i −0.226134 0.391675i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 9.00000 15.5885i 0.672692 1.16514i −0.304446 0.952529i $$-0.598471\pi$$
0.977138 0.212607i $$-0.0681952\pi$$
$$180$$ 0 0
$$181$$ −25.0000 −1.85824 −0.929118 0.369784i $$-0.879432\pi$$
−0.929118 + 0.369784i $$0.879432\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 1.50000 2.59808i 0.110581 0.191533i
$$185$$ 6.00000 0.441129
$$186$$ 0 0
$$187$$ −36.0000 −2.63258
$$188$$ 0 0
$$189$$ 0 0
$$190$$ −21.0000 −1.52350
$$191$$ 9.00000 0.651217 0.325609 0.945505i $$-0.394431\pi$$
0.325609 + 0.945505i $$0.394431\pi$$
$$192$$ 0 0
$$193$$ 17.0000 1.22369 0.611843 0.790979i $$-0.290428\pi$$
0.611843 + 0.790979i $$0.290428\pi$$
$$194$$ −1.00000 + 1.73205i −0.0717958 + 0.124354i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0 0
$$199$$ −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i $$-0.998611\pi$$
0.503774 + 0.863836i $$0.331945\pi$$
$$200$$ −2.00000 3.46410i −0.141421 0.244949i
$$201$$ 0 0
$$202$$ 4.50000 + 7.79423i 0.316619 + 0.548400i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 5.00000 8.66025i 0.348367 0.603388i
$$207$$ 0 0
$$208$$ −1.00000 1.73205i −0.0693375 0.120096i
$$209$$ 21.0000 36.3731i 1.45260 2.51598i
$$210$$ 0 0
$$211$$ −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i $$-0.255467\pi$$
−0.970229 + 0.242190i $$0.922134\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ −6.00000 10.3923i −0.410152 0.710403i
$$215$$ −3.00000 5.19615i −0.204598 0.354375i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 5.00000 8.66025i 0.338643 0.586546i
$$219$$ 0 0
$$220$$ 18.0000 1.21356
$$221$$ −12.0000 −0.807207
$$222$$ 0 0
$$223$$ 14.0000 24.2487i 0.937509 1.62381i 0.167412 0.985887i $$-0.446459\pi$$
0.770097 0.637927i $$-0.220208\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 7.50000 + 12.9904i 0.498893 + 0.864107i
$$227$$ −7.50000 12.9904i −0.497792 0.862202i 0.502204 0.864749i $$-0.332523\pi$$
−0.999997 + 0.00254715i $$0.999189\pi$$
$$228$$ 0 0
$$229$$ 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i $$-0.822814\pi$$
0.882073 + 0.471113i $$0.156147\pi$$
$$230$$ 4.50000 + 7.79423i 0.296721 + 0.513936i
$$231$$ 0 0
$$232$$ 3.00000 5.19615i 0.196960 0.341144i
$$233$$ 4.50000 + 7.79423i 0.294805 + 0.510617i 0.974939 0.222470i $$-0.0714120\pi$$
−0.680135 + 0.733087i $$0.738079\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i $$-0.327896\pi$$
−0.999854 + 0.0170808i $$0.994563\pi$$
$$240$$ 0 0
$$241$$ −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i $$-0.249619\pi$$
−0.965615 + 0.259975i $$0.916286\pi$$
$$242$$ −12.5000 + 21.6506i −0.803530 + 1.39176i
$$243$$ 0 0
$$244$$ 5.00000 0.320092
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 7.00000 12.1244i 0.445399 0.771454i
$$248$$ 2.00000 0.127000
$$249$$ 0 0
$$250$$ −3.00000 −0.189737
$$251$$ −3.00000 −0.189358 −0.0946792 0.995508i $$-0.530183\pi$$
−0.0946792 + 0.995508i $$0.530183\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 17.0000 1.06667
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i $$-0.643595\pi$$
0.997374 0.0724199i $$-0.0230722\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 6.00000 0.372104
$$261$$ 0 0
$$262$$ −4.50000 + 7.79423i −0.278011 + 0.481529i
$$263$$ −10.5000 18.1865i −0.647458 1.12143i −0.983728 0.179664i $$-0.942499\pi$$
0.336270 0.941766i $$-0.390834\pi$$
$$264$$ 0 0
$$265$$ 9.00000 + 15.5885i 0.552866 + 0.957591i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 8.00000 0.488678
$$269$$ −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i $$-0.921803\pi$$
0.695606 + 0.718423i $$0.255136\pi$$
$$270$$ 0 0
$$271$$ 14.0000 + 24.2487i 0.850439 + 1.47300i 0.880812 + 0.473466i $$0.156997\pi$$
−0.0303728 + 0.999539i $$0.509669\pi$$
$$272$$ 3.00000 5.19615i 0.181902 0.315063i
$$273$$ 0 0
$$274$$ 3.00000 + 5.19615i 0.181237 + 0.313911i
$$275$$ −12.0000 + 20.7846i −0.723627 + 1.25336i
$$276$$ 0 0
$$277$$ 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i $$-0.00705893\pi$$
−0.519081 + 0.854725i $$0.673726\pi$$
$$278$$ −2.50000 4.33013i −0.149940 0.259704i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −13.5000 + 23.3827i −0.805342 + 1.39489i 0.110717 + 0.993852i $$0.464685\pi$$
−0.916060 + 0.401042i $$0.868648\pi$$
$$282$$ 0 0
$$283$$ −19.0000 −1.12943 −0.564716 0.825285i $$-0.691014\pi$$
−0.564716 + 0.825285i $$0.691014\pi$$
$$284$$ −3.00000 −0.178017
$$285$$ 0 0
$$286$$ −6.00000 + 10.3923i −0.354787 + 0.614510i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −9.50000 16.4545i −0.558824 0.967911i
$$290$$ 9.00000 + 15.5885i 0.528498 + 0.915386i
$$291$$ 0 0
$$292$$ −1.00000 + 1.73205i −0.0585206 + 0.101361i
$$293$$ −1.50000 2.59808i −0.0876309 0.151781i 0.818878 0.573967i $$-0.194596\pi$$
−0.906509 + 0.422186i $$0.861263\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −1.00000 1.73205i −0.0581238 0.100673i
$$297$$ 0 0
$$298$$ −3.00000 + 5.19615i −0.173785 + 0.301005i
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −11.5000 19.9186i −0.661751 1.14619i
$$303$$ 0 0
$$304$$ 3.50000 + 6.06218i 0.200739 + 0.347690i
$$305$$ −7.50000 + 12.9904i −0.429449 + 0.743827i
$$306$$ 0 0
$$307$$ −25.0000 −1.42683 −0.713413 0.700744i $$-0.752851\pi$$
−0.713413 + 0.700744i $$0.752851\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −3.00000 + 5.19615i −0.170389 + 0.295122i
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 0 0
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ −13.0000 −0.733632
$$315$$ 0 0
$$316$$ 5.00000 0.281272
$$317$$ −18.0000 −1.01098 −0.505490 0.862832i $$-0.668688\pi$$
−0.505490 + 0.862832i $$0.668688\pi$$
$$318$$ 0 0
$$319$$ −36.0000 −2.01561
$$320$$ −1.50000 + 2.59808i −0.0838525 + 0.145237i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 42.0000 2.33694
$$324$$ 0 0
$$325$$ −4.00000 + 6.92820i −0.221880 + 0.384308i
$$326$$ −1.00000 1.73205i −0.0553849 0.0959294i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 26.0000 1.42909 0.714545 0.699590i $$-0.246634\pi$$
0.714545 + 0.699590i $$0.246634\pi$$
$$332$$ 6.00000 10.3923i 0.329293 0.570352i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −12.0000 + 20.7846i −0.655630 + 1.13558i
$$336$$ 0 0
$$337$$ 11.0000 + 19.0526i 0.599208 + 1.03786i 0.992938 + 0.118633i $$0.0378512\pi$$
−0.393730 + 0.919226i $$0.628816\pi$$
$$338$$ 4.50000 7.79423i 0.244768 0.423950i
$$339$$ 0 0
$$340$$ 9.00000 + 15.5885i 0.488094 + 0.845403i
$$341$$ −6.00000 10.3923i −0.324918 0.562775i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −1.00000 + 1.73205i −0.0539164 + 0.0933859i
$$345$$ 0 0
$$346$$ 6.00000 0.322562
$$347$$ 24.0000 1.28839 0.644194 0.764862i $$-0.277193\pi$$
0.644194 + 0.764862i $$0.277193\pi$$
$$348$$ 0 0
$$349$$ −13.0000 + 22.5167i −0.695874 + 1.20529i 0.274011 + 0.961727i $$0.411649\pi$$
−0.969885 + 0.243563i $$0.921684\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −3.00000 5.19615i −0.159901 0.276956i
$$353$$ −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i $$-0.325675\pi$$
−0.999711 + 0.0240566i $$0.992342\pi$$
$$354$$ 0 0
$$355$$ 4.50000 7.79423i 0.238835 0.413675i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 9.00000 15.5885i 0.475665 0.823876i
$$359$$ −1.50000 2.59808i −0.0791670 0.137121i 0.823724 0.566991i $$-0.191893\pi$$
−0.902891 + 0.429870i $$0.858559\pi$$
$$360$$ 0 0
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ −25.0000 −1.31397
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −3.00000 5.19615i −0.157027 0.271979i
$$366$$ 0 0
$$367$$ −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i $$-0.233622\pi$$
−0.951336 + 0.308155i $$0.900289\pi$$
$$368$$ 1.50000 2.59808i 0.0781929 0.135434i
$$369$$ 0 0
$$370$$ 6.00000 0.311925
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i $$-0.951392\pi$$
0.625917 + 0.779890i $$0.284725\pi$$
$$374$$ −36.0000 −1.86152
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ −21.0000 −1.07728
$$381$$ 0 0
$$382$$ 9.00000 0.460480
$$383$$ −9.00000 + 15.5885i −0.459879 + 0.796533i −0.998954 0.0457244i $$-0.985440\pi$$
0.539076 + 0.842257i $$0.318774\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 17.0000 0.865277
$$387$$ 0 0
$$388$$ −1.00000 + 1.73205i −0.0507673 + 0.0879316i
$$389$$ 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i $$0.0415314\pi$$
−0.383076 + 0.923717i $$0.625135\pi$$
$$390$$ 0 0
$$391$$ −9.00000 15.5885i −0.455150 0.788342i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −18.0000 −0.906827
$$395$$ −7.50000 + 12.9904i −0.377366 + 0.653617i
$$396$$ 0 0
$$397$$ −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i $$-0.940407\pi$$
0.330075 0.943955i $$-0.392926\pi$$
$$398$$ −7.00000 + 12.1244i −0.350878 + 0.607739i
$$399$$ 0 0
$$400$$ −2.00000 3.46410i −0.100000 0.173205i
$$401$$ 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i $$-0.809468\pi$$
0.901046 + 0.433724i $$0.142801\pi$$
$$402$$ 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 0
$$407$$ −6.00000 + 10.3923i −0.297409 + 0.515127i
$$408$$ 0 0
$$409$$ 32.0000 1.58230 0.791149 0.611623i $$-0.209483\pi$$
0.791149 + 0.611623i $$0.209483\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 5.00000 8.66025i 0.246332 0.426660i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 18.0000 + 31.1769i 0.883585 + 1.53041i
$$416$$ −1.00000 1.73205i −0.0490290 0.0849208i
$$417$$ 0 0
$$418$$ 21.0000 36.3731i 1.02714 1.77906i
$$419$$ 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i $$-0.0472572\pi$$
−0.622601 + 0.782540i $$0.713924\pi$$
$$420$$ 0 0
$$421$$ 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i $$-0.754977\pi$$
0.961761 + 0.273890i $$0.0883103\pi$$
$$422$$ −4.00000 6.92820i −0.194717 0.337260i
$$423$$ 0 0
$$424$$ 3.00000 5.19615i 0.145693 0.252347i
$$425$$ −24.0000 −1.16417
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −6.00000 10.3923i −0.290021 0.502331i
$$429$$ 0 0
$$430$$ −3.00000 5.19615i −0.144673 0.250581i
$$431$$ 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i $$-0.740007\pi$$
0.973574 + 0.228373i $$0.0733406\pi$$
$$432$$ 0 0
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 5.00000 8.66025i 0.239457 0.414751i
$$437$$ 21.0000 1.00457
$$438$$ 0 0
$$439$$ 8.00000 0.381819 0.190910 0.981608i $$-0.438856\pi$$
0.190910 + 0.981608i $$0.438856\pi$$
$$440$$ 18.0000 0.858116
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ −18.0000 −0.855206 −0.427603 0.903967i $$-0.640642\pi$$
−0.427603 + 0.903967i $$0.640642\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 14.0000 24.2487i 0.662919 1.14821i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −33.0000 −1.55737 −0.778683 0.627417i $$-0.784112\pi$$
−0.778683 + 0.627417i $$0.784112\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 7.50000 + 12.9904i 0.352770 + 0.611016i
$$453$$ 0 0
$$454$$ −7.50000 12.9904i −0.351992 0.609669i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 29.0000 1.35656 0.678281 0.734802i $$-0.262725\pi$$
0.678281 + 0.734802i $$0.262725\pi$$
$$458$$ 0.500000 0.866025i 0.0233635 0.0404667i
$$459$$ 0 0
$$460$$ 4.50000 + 7.79423i 0.209814 + 0.363408i
$$461$$ −16.5000 + 28.5788i −0.768482 + 1.33105i 0.169904 + 0.985461i $$0.445654\pi$$
−0.938386 + 0.345589i $$0.887679\pi$$
$$462$$ 0 0
$$463$$ 6.50000 + 11.2583i 0.302081 + 0.523219i 0.976607 0.215032i $$-0.0689855\pi$$
−0.674526 + 0.738251i $$0.735652\pi$$
$$464$$ 3.00000 5.19615i 0.139272 0.241225i
$$465$$ 0 0
$$466$$ 4.50000 + 7.79423i 0.208458 + 0.361061i
$$467$$ 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i $$-0.0771121\pi$$
−0.693153 + 0.720791i $$0.743779\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 12.0000 0.551761
$$474$$ 0 0
$$475$$ 14.0000 24.2487i 0.642364 1.11261i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −7.50000 12.9904i −0.343042 0.594166i
$$479$$ −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
$$481$$ −2.00000 + 3.46410i −0.0911922 + 0.157949i
$$482$$ −4.00000 6.92820i −0.182195 0.315571i
$$483$$ 0 0
$$484$$ −12.5000 + 21.6506i −0.568182 + 0.984120i
$$485$$ −3.00000 5.19615i −0.136223 0.235945i
$$486$$ 0 0
$$487$$ −14.5000 + 25.1147i −0.657058 + 1.13806i 0.324316 + 0.945949i $$0.394866\pi$$
−0.981374 + 0.192109i $$0.938467\pi$$
$$488$$ 5.00000 0.226339
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 9.00000 + 15.5885i 0.406164 + 0.703497i 0.994456 0.105151i $$-0.0335327\pi$$
−0.588292 + 0.808649i $$0.700199\pi$$
$$492$$ 0 0
$$493$$ −18.0000 31.1769i −0.810679 1.40414i
$$494$$ 7.00000 12.1244i 0.314945 0.545501i
$$495$$ 0 0
$$496$$ 2.00000 0.0898027
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −16.0000 + 27.7128i −0.716258 + 1.24060i 0.246214 + 0.969216i $$0.420813\pi$$
−0.962472 + 0.271380i $$0.912520\pi$$
$$500$$ −3.00000 −0.134164
$$501$$ 0 0
$$502$$ −3.00000 −0.133897
$$503$$ −12.0000 −0.535054 −0.267527 0.963550i $$-0.586206\pi$$
−0.267527 + 0.963550i $$0.586206\pi$$
$$504$$ 0 0
$$505$$ −27.0000 −1.20148
$$506$$ −18.0000 −0.800198
$$507$$ 0 0
$$508$$ 17.0000 0.754253
$$509$$ 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i $$-0.601823\pi$$
0.979322 0.202306i $$-0.0648436\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 9.00000 15.5885i 0.396973 0.687577i
$$515$$ 15.0000 + 25.9808i 0.660979 + 1.14485i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 6.00000 0.263117
$$521$$ 12.0000 20.7846i 0.525730 0.910590i −0.473821 0.880621i $$-0.657126\pi$$
0.999551 0.0299693i $$-0.00954094\pi$$
$$522$$ 0 0
$$523$$ 6.50000 + 11.2583i 0.284225 + 0.492292i 0.972421 0.233233i $$-0.0749303\pi$$
−0.688196 + 0.725525i $$0.741597\pi$$
$$524$$ −4.50000 + 7.79423i −0.196583 + 0.340492i
$$525$$ 0 0
$$526$$ −10.5000 18.1865i −0.457822 0.792971i
$$527$$ 6.00000 10.3923i 0.261364 0.452696i
$$528$$ 0 0
$$529$$ 7.00000 + 12.1244i 0.304348 + 0.527146i
$$530$$ 9.00000 + 15.5885i 0.390935 + 0.677119i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 36.0000 1.55642
$$536$$ 8.00000 0.345547
$$537$$ 0 0
$$538$$ −4.50000 + 7.79423i −0.194009 + 0.336033i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −19.0000 32.9090i −0.816874 1.41487i −0.907975 0.419025i $$-0.862372\pi$$
0.0911008 0.995842i $$-0.470961\pi$$
$$542$$ 14.0000 + 24.2487i 0.601351 + 1.04157i
$$543$$ 0 0
$$544$$ 3.00000 5.19615i 0.128624 0.222783i
$$545$$ 15.0000 + 25.9808i 0.642529 + 1.11289i
$$546$$ 0 0
$$547$$ −16.0000 + 27.7128i −0.684111 + 1.18491i 0.289605 + 0.957146i $$0.406476\pi$$
−0.973715 + 0.227768i $$0.926857\pi$$
$$548$$ 3.00000 + 5.19615i 0.128154 + 0.221969i
$$549$$ 0 0
$$550$$ −12.0000 + 20.7846i −0.511682 + 0.886259i
$$551$$ 42.0000 1.78926
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 8.00000 + 13.8564i 0.339887 + 0.588702i
$$555$$ 0 0
$$556$$ −2.50000 4.33013i −0.106024 0.183638i
$$557$$ −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i $$0.336450\pi$$
−0.999952 + 0.00979220i $$0.996883\pi$$
$$558$$ 0 0
$$559$$ 4.00000 0.169182
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −13.5000 + 23.3827i −0.569463 + 0.986339i
$$563$$ 33.0000 1.39078 0.695392 0.718631i $$-0.255231\pi$$
0.695392 + 0.718631i $$0.255231\pi$$
$$564$$ 0 0
$$565$$ −45.0000 −1.89316
$$566$$ −19.0000 −0.798630
$$567$$ 0 0
$$568$$ −3.00000 −0.125877
$$569$$ 18.0000 0.754599 0.377300 0.926091i $$-0.376853\pi$$
0.377300 + 0.926091i $$0.376853\pi$$
$$570$$ 0 0
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ −6.00000 + 10.3923i −0.250873 + 0.434524i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ 2.00000 3.46410i 0.0832611 0.144212i −0.821388 0.570370i $$-0.806800\pi$$
0.904649 + 0.426158i $$0.140133\pi$$
$$578$$ −9.50000 16.4545i −0.395148 0.684416i
$$579$$ 0 0
$$580$$ 9.00000 + 15.5885i 0.373705 + 0.647275i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −36.0000 −1.49097
$$584$$ −1.00000 + 1.73205i −0.0413803 + 0.0716728i
$$585$$ 0 0
$$586$$ −1.50000 2.59808i −0.0619644 0.107326i
$$587$$ −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i $$-0.853053\pi$$
0.833408 + 0.552658i $$0.186386\pi$$
$$588$$ 0 0
$$589$$ 7.00000 + 12.1244i 0.288430 + 0.499575i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −1.00000 1.73205i −0.0410997 0.0711868i
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −3.00000 + 5.19615i −0.122885 + 0.212843i
$$597$$ 0 0
$$598$$ −6.00000 −0.245358
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ −7.00000 + 12.1244i −0.285536 + 0.494563i −0.972739 0.231903i $$-0.925505\pi$$
0.687203 + 0.726465i $$0.258838\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −11.5000 19.9186i −0.467928 0.810476i
$$605$$ −37.5000 64.9519i −1.52459 2.64067i
$$606$$ 0 0
$$607$$ 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i $$-0.686012\pi$$
0.998154 + 0.0607380i $$0.0193454\pi$$
$$608$$ 3.50000 + 6.06218i 0.141944 + 0.245854i
$$609$$ 0 0
$$610$$ −7.50000 + 12.9904i −0.303666 + 0.525965i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i $$-0.884985\pi$$
0.773869 + 0.633345i $$0.218319\pi$$
$$614$$ −25.0000 −1.00892
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i $$0.153988\pi$$
−0.0398207 + 0.999207i $$0.512679\pi$$
$$618$$ 0 0
$$619$$ 3.50000 + 6.06218i 0.140677 + 0.243659i 0.927752 0.373198i $$-0.121739\pi$$
−0.787075 + 0.616858i $$0.788405\pi$$
$$620$$ −3.00000 + 5.19615i −0.120483 + 0.208683i
$$621$$ 0 0
$$622$$ −12.0000 −0.481156
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ −10.0000 −0.399680
$$627$$ 0 0
$$628$$ −13.0000 −0.518756
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −7.00000 −0.278666 −0.139333 0.990246i $$-0.544496\pi$$
−0.139333 + 0.990246i $$0.544496\pi$$
$$632$$ 5.00000 0.198889
$$633$$ 0 0
$$634$$ −18.0000 −0.714871
$$635$$ −25.5000 + 44.1673i −1.01194 + 1.75273i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ −36.0000 −1.42525
$$639$$ 0 0
$$640$$ −1.50000 + 2.59808i −0.0592927 + 0.102698i
$$641$$ 13.5000 + 23.3827i 0.533218 + 0.923561i 0.999247 + 0.0387913i $$0.0123508\pi$$
−0.466029 + 0.884769i $$0.654316\pi$$
$$642$$ 0 0
$$643$$ 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i $$-0.141535\pi$$
−0.823891 + 0.566748i $$0.808201\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 42.0000 1.65247
$$647$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −4.00000 + 6.92820i −0.156893 + 0.271746i
$$651$$ 0 0
$$652$$ −1.00000 1.73205i −0.0391630 0.0678323i
$$653$$ −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i $$0.415448\pi$$
−0.966910 + 0.255119i $$0.917885\pi$$
$$654$$ 0 0
$$655$$ −13.5000 23.3827i −0.527489 0.913637i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 21.0000 36.3731i 0.818044 1.41689i −0.0890776 0.996025i $$-0.528392\pi$$
0.907122 0.420869i $$-0.138275\pi$$
$$660$$ 0 0
$$661$$ 5.00000 0.194477 0.0972387 0.995261i $$-0.468999\pi$$
0.0972387 + 0.995261i $$0.468999\pi$$
$$662$$ 26.0000 1.01052
$$663$$ 0 0
$$664$$ 6.00000 10.3923i 0.232845 0.403300i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9.00000 15.5885i −0.348481 0.603587i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ −12.0000 + 20.7846i −0.463600 + 0.802980i
$$671$$ −15.0000 25.9808i −0.579069 1.00298i
$$672$$ 0 0
$$673$$ 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i $$-0.580614\pi$$
0.963679 0.267063i $$-0.0860531\pi$$
$$674$$ 11.0000 + 19.0526i 0.423704 + 0.733877i
$$675$$ 0 0
$$676$$ 4.50000 7.79423i 0.173077 0.299778i
$$677$$ −42.0000 −1.61419 −0.807096 0.590421i $$-0.798962\pi$$
−0.807096 + 0.590421i $$0.798962\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 9.00000 + 15.5885i 0.345134 + 0.597790i
$$681$$ 0 0
$$682$$ −6.00000 10.3923i −0.229752 0.397942i
$$683$$ −3.00000 + 5.19615i −0.114792 + 0.198825i −0.917697 0.397282i $$-0.869953\pi$$
0.802905 + 0.596107i $$0.203287\pi$$
$$684$$ 0 0
$$685$$ −18.0000 −0.687745
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −1.00000 + 1.73205i −0.0381246 + 0.0660338i
$$689$$ −12.0000 −0.457164
$$690$$ 0 0
$$691$$ 47.0000 1.78796 0.893982 0.448103i $$-0.147900\pi$$
0.893982 + 0.448103i $$0.147900\pi$$
$$692$$ 6.00000 0.228086
$$693$$ 0 0
$$694$$ 24.0000 0.911028
$$695$$ 15.0000 0.568982
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −13.0000 + 22.5167i −0.492057 + 0.852268i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ 7.00000 12.1244i 0.264010 0.457279i
$$704$$ −3.00000 5.19615i −0.113067 0.195837i
$$705$$ 0 0
$$706$$ −9.00000 15.5885i −0.338719 0.586679i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −52.0000 −1.95290 −0.976450 0.215742i $$-0.930783\pi$$
−0.976450 + 0.215742i $$0.930783\pi$$
$$710$$ 4.50000 7.79423i 0.168882 0.292512i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 3.00000 5.19615i 0.112351 0.194597i
$$714$$ 0 0
$$715$$ −18.0000 31.1769i −0.673162 1.16595i
$$716$$ 9.00000 15.5885i 0.336346 0.582568i
$$717$$ 0 0
$$718$$ −1.50000 2.59808i −0.0559795 0.0969593i
$$719$$ −18.0000 31.1769i −0.671287 1.16270i −0.977539 0.210752i $$-0.932409\pi$$
0.306253 0.951950i $$-0.400925\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −15.0000 + 25.9808i −0.558242 + 0.966904i
$$723$$ 0 0
$$724$$ −25.0000 −0.929118
$$725$$ −24.0000 −0.891338
$$726$$ 0 0
$$727$$ −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i $$-0.880730\pi$$
0.782267 + 0.622944i $$0.214063\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −3.00000 5.19615i −0.111035 0.192318i
$$731$$ 6.00000 + 10.3923i 0.221918 + 0.384373i
$$732$$ 0 0
$$733$$ −14.5000 + 25.1147i −0.535570 + 0.927634i 0.463566 + 0.886062i $$0.346570\pi$$
−0.999136 + 0.0415715i $$0.986764\pi$$
$$734$$ −4.00000 6.92820i −0.147643 0.255725i
$$735$$ 0 0
$$736$$ 1.50000 2.59808i 0.0552907 0.0957664i
$$737$$ −24.0000 41.5692i −0.884051 1.53122i
$$738$$ 0 0
$$739$$ −13.0000 + 22.5167i −0.478213 + 0.828289i −0.999688 0.0249776i $$-0.992049\pi$$
0.521475 + 0.853266i $$0.325382\pi$$
$$740$$ 6.00000 0.220564
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i $$0.0629279\pi$$
−0.320166 + 0.947361i $$0.603739\pi$$
$$744$$ 0 0
$$745$$ −9.00000 15.5885i −0.329734 0.571117i
$$746$$ −7.00000 + 12.1244i −0.256288 + 0.443904i
$$747$$ 0 0
$$748$$ −36.0000 −1.31629
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i $$-0.641977\pi$$
0.996993 0.0774878i $$-0.0246899\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ −12.0000 −0.437014
$$755$$ 69.0000 2.51117
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 2.00000 0.0726433
$$759$$ 0 0
$$760$$ −21.0000 −0.761750
$$761$$ −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i $$0.442080\pi$$
−0.942207 + 0.335032i $$0.891253\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 9.00000 0.325609
$$765$$ 0 0
$$766$$ −9.00000 + 15.5885i −0.325183 + 0.563234i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i $$-0.247895\pi$$
−0.964193 + 0.265200i $$0.914562\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 17.0000 0.611843
$$773$$ −25.5000 + 44.1673i −0.917171 + 1.58859i −0.113480 + 0.993540i $$0.536200\pi$$
−0.803691 + 0.595047i $$0.797133\pi$$
$$774$$ 0 0
$$775$$ −4.00000 6.92820i −0.143684 0.248868i
$$776$$ −1.00000 + 1.73205i −0.0358979 + 0.0621770i
$$777$$ 0 0
$$778$$ 12.0000 + 20.7846i 0.430221 + 0.745164i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 9.00000 + 15.5885i 0.322045 + 0.557799i
$$782$$ −9.00000 15.5885i −0.321839 0.557442i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 19.5000 33.7750i 0.695985 1.20548i
$$786$$ 0 0
$$787$$ 20.0000 0.712923 0.356462 0.934310i $$-0.383983\pi$$
0.356462 + 0.934310i $$0.383983\pi$$
$$788$$ −18.0000 −0.641223
$$789$$ 0 0
$$790$$ −7.50000 + 12.9904i −0.266838 + 0.462177i
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −5.00000 8.66025i −0.177555 0.307535i
$$794$$ −13.0000 22.5167i −0.461353 0.799086i
$$795$$ 0 0
$$796$$ −7.00000 + 12.1244i −0.2481