# Properties

 Label 1710.2.l.c.1261.1 Level $1710$ Weight $2$ Character 1710.1261 Analytic conductor $13.654$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1710.l (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.6544187456$$ 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 570) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1261.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1710.1261 Dual form 1710.2.l.c.1531.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -5.00000 q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(-3.00000 + 5.19615i) q^{13} +(2.50000 + 4.33013i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 4.33013i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{25} +6.00000 q^{26} +(2.50000 - 4.33013i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{34} +(-2.50000 - 4.33013i) q^{35} +7.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(-2.50000 - 4.33013i) q^{41} +(-3.00000 - 5.19615i) q^{43} +(0.500000 - 0.866025i) q^{44} -7.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +18.0000 q^{49} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(5.50000 - 9.52628i) q^{53} +(-0.500000 - 0.866025i) q^{55} -5.00000 q^{56} -6.00000 q^{58} +(-4.00000 - 6.92820i) q^{59} +(2.00000 - 3.46410i) q^{61} +1.00000 q^{64} -6.00000 q^{65} +(-6.00000 + 10.3923i) q^{67} -4.00000 q^{68} +(-2.50000 + 4.33013i) q^{70} +(1.00000 + 1.73205i) q^{71} +(1.00000 + 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(4.00000 + 1.73205i) q^{76} +5.00000 q^{77} +(-5.00000 - 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-2.50000 + 4.33013i) q^{82} +10.0000 q^{83} +(-2.00000 + 3.46410i) q^{85} +(-3.00000 + 5.19615i) q^{86} -1.00000 q^{88} +(6.50000 - 11.2583i) q^{89} +(15.0000 - 25.9808i) q^{91} +(3.50000 + 6.06218i) q^{92} +8.00000 q^{94} +(3.50000 - 2.59808i) q^{95} +(-1.00000 - 1.73205i) q^{97} +(-9.00000 - 15.5885i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} - q^{4} + q^{5} - 10q^{7} + 2q^{8} + O(q^{10})$$ $$2q - q^{2} - q^{4} + q^{5} - 10q^{7} + 2q^{8} + q^{10} - 2q^{11} - 6q^{13} + 5q^{14} - q^{16} + 4q^{17} - q^{19} - 2q^{20} + q^{22} + 7q^{23} - q^{25} + 12q^{26} + 5q^{28} + 6q^{29} - q^{32} + 4q^{34} - 5q^{35} + 14q^{37} - 7q^{38} + q^{40} - 5q^{41} - 6q^{43} + q^{44} - 14q^{46} - 8q^{47} + 36q^{49} + 2q^{50} - 6q^{52} + 11q^{53} - q^{55} - 10q^{56} - 12q^{58} - 8q^{59} + 4q^{61} + 2q^{64} - 12q^{65} - 12q^{67} - 8q^{68} - 5q^{70} + 2q^{71} + 2q^{73} - 7q^{74} + 8q^{76} + 10q^{77} - 10q^{79} + q^{80} - 5q^{82} + 20q^{83} - 4q^{85} - 6q^{86} - 2q^{88} + 13q^{89} + 30q^{91} + 7q^{92} + 16q^{94} + 7q^{95} - 2q^{97} - 18q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$1027$$ $$1351$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ −5.00000 −1.88982 −0.944911 0.327327i $$-0.893852\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0.500000 0.866025i 0.158114 0.273861i
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 0 0
$$13$$ −3.00000 + 5.19615i −0.832050 + 1.44115i 0.0643593 + 0.997927i $$0.479500\pi$$
−0.896410 + 0.443227i $$0.853834\pi$$
$$14$$ 2.50000 + 4.33013i 0.668153 + 1.15728i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i $$-0.00546033\pi$$
−0.514782 + 0.857321i $$0.672127\pi$$
$$18$$ 0 0
$$19$$ −0.500000 4.33013i −0.114708 0.993399i
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 0.500000 + 0.866025i 0.106600 + 0.184637i
$$23$$ 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i $$-0.572946\pi$$
0.956967 0.290196i $$-0.0937204\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ 6.00000 1.17670
$$27$$ 0 0
$$28$$ 2.50000 4.33013i 0.472456 0.818317i
$$29$$ 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
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ 0 0
$$34$$ 2.00000 3.46410i 0.342997 0.594089i
$$35$$ −2.50000 4.33013i −0.422577 0.731925i
$$36$$ 0 0
$$37$$ 7.00000 1.15079 0.575396 0.817875i $$-0.304848\pi$$
0.575396 + 0.817875i $$0.304848\pi$$
$$38$$ −3.50000 + 2.59808i −0.567775 + 0.421464i
$$39$$ 0 0
$$40$$ 0.500000 + 0.866025i 0.0790569 + 0.136931i
$$41$$ −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i $$-0.294342\pi$$
−0.992507 + 0.122189i $$0.961009\pi$$
$$42$$ 0 0
$$43$$ −3.00000 5.19615i −0.457496 0.792406i 0.541332 0.840809i $$-0.317920\pi$$
−0.998828 + 0.0484030i $$0.984587\pi$$
$$44$$ 0.500000 0.866025i 0.0753778 0.130558i
$$45$$ 0 0
$$46$$ −7.00000 −1.03209
$$47$$ −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i $$0.364968\pi$$
−0.995066 + 0.0992202i $$0.968365\pi$$
$$48$$ 0 0
$$49$$ 18.0000 2.57143
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ −3.00000 5.19615i −0.416025 0.720577i
$$53$$ 5.50000 9.52628i 0.755483 1.30854i −0.189651 0.981852i $$-0.560736\pi$$
0.945134 0.326683i $$-0.105931\pi$$
$$54$$ 0 0
$$55$$ −0.500000 0.866025i −0.0674200 0.116775i
$$56$$ −5.00000 −0.668153
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i $$-0.992317\pi$$
0.478953 0.877841i $$-0.341016\pi$$
$$60$$ 0 0
$$61$$ 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i $$-0.750904\pi$$
0.965187 + 0.261562i $$0.0842377\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −6.00000 −0.744208
$$66$$ 0 0
$$67$$ −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i $$0.428555\pi$$
−0.955588 + 0.294706i $$0.904778\pi$$
$$68$$ −4.00000 −0.485071
$$69$$ 0 0
$$70$$ −2.50000 + 4.33013i −0.298807 + 0.517549i
$$71$$ 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i $$-0.128801\pi$$
−0.800566 + 0.599245i $$0.795468\pi$$
$$72$$ 0 0
$$73$$ 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i $$-0.129326\pi$$
−0.801553 + 0.597924i $$0.795992\pi$$
$$74$$ −3.50000 6.06218i −0.406867 0.704714i
$$75$$ 0 0
$$76$$ 4.00000 + 1.73205i 0.458831 + 0.198680i
$$77$$ 5.00000 0.569803
$$78$$ 0 0
$$79$$ −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i $$-0.976489\pi$$
0.434730 0.900561i $$-0.356844\pi$$
$$80$$ 0.500000 0.866025i 0.0559017 0.0968246i
$$81$$ 0 0
$$82$$ −2.50000 + 4.33013i −0.276079 + 0.478183i
$$83$$ 10.0000 1.09764 0.548821 0.835940i $$-0.315077\pi$$
0.548821 + 0.835940i $$0.315077\pi$$
$$84$$ 0 0
$$85$$ −2.00000 + 3.46410i −0.216930 + 0.375735i
$$86$$ −3.00000 + 5.19615i −0.323498 + 0.560316i
$$87$$ 0 0
$$88$$ −1.00000 −0.106600
$$89$$ 6.50000 11.2583i 0.688999 1.19338i −0.283164 0.959072i $$-0.591384\pi$$
0.972162 0.234309i $$-0.0752827\pi$$
$$90$$ 0 0
$$91$$ 15.0000 25.9808i 1.57243 2.72352i
$$92$$ 3.50000 + 6.06218i 0.364900 + 0.632026i
$$93$$ 0 0
$$94$$ 8.00000 0.825137
$$95$$ 3.50000 2.59808i 0.359092 0.266557i
$$96$$ 0 0
$$97$$ −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i $$-0.199042\pi$$
−0.912317 + 0.409484i $$0.865709\pi$$
$$98$$ −9.00000 15.5885i −0.909137 1.57467i
$$99$$ 0 0
$$100$$ −0.500000 0.866025i −0.0500000 0.0866025i
$$101$$ 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i $$-0.801608\pi$$
0.911479 + 0.411346i $$0.134941\pi$$
$$102$$ 0 0
$$103$$ 15.0000 1.47799 0.738997 0.673709i $$-0.235300\pi$$
0.738997 + 0.673709i $$0.235300\pi$$
$$104$$ −3.00000 + 5.19615i −0.294174 + 0.509525i
$$105$$ 0 0
$$106$$ −11.0000 −1.06841
$$107$$ 4.00000 0.386695 0.193347 0.981130i $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 0 0
$$109$$ 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i $$0.111218\pi$$
−0.173316 + 0.984866i $$0.555448\pi$$
$$110$$ −0.500000 + 0.866025i −0.0476731 + 0.0825723i
$$111$$ 0 0
$$112$$ 2.50000 + 4.33013i 0.236228 + 0.409159i
$$113$$ −4.00000 −0.376288 −0.188144 0.982141i $$-0.560247\pi$$
−0.188144 + 0.982141i $$0.560247\pi$$
$$114$$ 0 0
$$115$$ 7.00000 0.652753
$$116$$ 3.00000 + 5.19615i 0.278543 + 0.482451i
$$117$$ 0 0
$$118$$ −4.00000 + 6.92820i −0.368230 + 0.637793i
$$119$$ −10.0000 17.3205i −0.916698 1.58777i
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ −4.00000 −0.362143
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 2.50000 4.33013i 0.221839 0.384237i −0.733527 0.679660i $$-0.762127\pi$$
0.955366 + 0.295423i $$0.0954607\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ 0 0
$$130$$ 3.00000 + 5.19615i 0.263117 + 0.455733i
$$131$$ −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i $$-0.208503\pi$$
−0.924084 + 0.382190i $$0.875170\pi$$
$$132$$ 0 0
$$133$$ 2.50000 + 21.6506i 0.216777 + 1.87735i
$$134$$ 12.0000 1.03664
$$135$$ 0 0
$$136$$ 2.00000 + 3.46410i 0.171499 + 0.297044i
$$137$$ −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i $$0.337990\pi$$
−0.999893 + 0.0146279i $$0.995344\pi$$
$$138$$ 0 0
$$139$$ 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i $$-0.595942\pi$$
0.975417 0.220366i $$-0.0707252\pi$$
$$140$$ 5.00000 0.422577
$$141$$ 0 0
$$142$$ 1.00000 1.73205i 0.0839181 0.145350i
$$143$$ 3.00000 5.19615i 0.250873 0.434524i
$$144$$ 0 0
$$145$$ 6.00000 0.498273
$$146$$ 1.00000 1.73205i 0.0827606 0.143346i
$$147$$ 0 0
$$148$$ −3.50000 + 6.06218i −0.287698 + 0.498308i
$$149$$ −2.00000 3.46410i −0.163846 0.283790i 0.772399 0.635138i $$-0.219057\pi$$
−0.936245 + 0.351348i $$0.885723\pi$$
$$150$$ 0 0
$$151$$ −20.0000 −1.62758 −0.813788 0.581161i $$-0.802599\pi$$
−0.813788 + 0.581161i $$0.802599\pi$$
$$152$$ −0.500000 4.33013i −0.0405554 0.351220i
$$153$$ 0 0
$$154$$ −2.50000 4.33013i −0.201456 0.348932i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −4.50000 7.79423i −0.359139 0.622047i 0.628678 0.777666i $$-0.283596\pi$$
−0.987817 + 0.155618i $$0.950263\pi$$
$$158$$ −5.00000 + 8.66025i −0.397779 + 0.688973i
$$159$$ 0 0
$$160$$ −1.00000 −0.0790569
$$161$$ −17.5000 + 30.3109i −1.37919 + 2.38883i
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 5.00000 0.390434
$$165$$ 0 0
$$166$$ −5.00000 8.66025i −0.388075 0.672166i
$$167$$ 10.5000 18.1865i 0.812514 1.40732i −0.0985846 0.995129i $$-0.531432\pi$$
0.911099 0.412188i $$-0.135235\pi$$
$$168$$ 0 0
$$169$$ −11.5000 19.9186i −0.884615 1.53220i
$$170$$ 4.00000 0.306786
$$171$$ 0 0
$$172$$ 6.00000 0.457496
$$173$$ −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i $$-0.277815\pi$$
−0.984828 + 0.173534i $$0.944481\pi$$
$$174$$ 0 0
$$175$$ 2.50000 4.33013i 0.188982 0.327327i
$$176$$ 0.500000 + 0.866025i 0.0376889 + 0.0652791i
$$177$$ 0 0
$$178$$ −13.0000 −0.974391
$$179$$ −7.00000 −0.523205 −0.261602 0.965176i $$-0.584251\pi$$
−0.261602 + 0.965176i $$0.584251\pi$$
$$180$$ 0 0
$$181$$ −9.00000 + 15.5885i −0.668965 + 1.15868i 0.309229 + 0.950988i $$0.399929\pi$$
−0.978194 + 0.207693i $$0.933404\pi$$
$$182$$ −30.0000 −2.22375
$$183$$ 0 0
$$184$$ 3.50000 6.06218i 0.258023 0.446910i
$$185$$ 3.50000 + 6.06218i 0.257325 + 0.445700i
$$186$$ 0 0
$$187$$ −2.00000 3.46410i −0.146254 0.253320i
$$188$$ −4.00000 6.92820i −0.291730 0.505291i
$$189$$ 0 0
$$190$$ −4.00000 1.73205i −0.290191 0.125656i
$$191$$ 14.0000 1.01300 0.506502 0.862239i $$-0.330938\pi$$
0.506502 + 0.862239i $$0.330938\pi$$
$$192$$ 0 0
$$193$$ 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i $$-0.120682\pi$$
−0.785022 + 0.619467i $$0.787349\pi$$
$$194$$ −1.00000 + 1.73205i −0.0717958 + 0.124354i
$$195$$ 0 0
$$196$$ −9.00000 + 15.5885i −0.642857 + 1.11346i
$$197$$ −1.00000 −0.0712470 −0.0356235 0.999365i $$-0.511342\pi$$
−0.0356235 + 0.999365i $$0.511342\pi$$
$$198$$ 0 0
$$199$$ 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i $$-0.788052\pi$$
0.928166 + 0.372168i $$0.121385\pi$$
$$200$$ −0.500000 + 0.866025i −0.0353553 + 0.0612372i
$$201$$ 0 0
$$202$$ −2.00000 −0.140720
$$203$$ −15.0000 + 25.9808i −1.05279 + 1.82349i
$$204$$ 0 0
$$205$$ 2.50000 4.33013i 0.174608 0.302429i
$$206$$ −7.50000 12.9904i −0.522550 0.905083i
$$207$$ 0 0
$$208$$ 6.00000 0.416025
$$209$$ 0.500000 + 4.33013i 0.0345857 + 0.299521i
$$210$$ 0 0
$$211$$ −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i $$-0.314345\pi$$
−0.998221 + 0.0596196i $$0.981011\pi$$
$$212$$ 5.50000 + 9.52628i 0.377742 + 0.654268i
$$213$$ 0 0
$$214$$ −2.00000 3.46410i −0.136717 0.236801i
$$215$$ 3.00000 5.19615i 0.204598 0.354375i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 8.00000 13.8564i 0.541828 0.938474i
$$219$$ 0 0
$$220$$ 1.00000 0.0674200
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ 10.5000 + 18.1865i 0.703132 + 1.21786i 0.967361 + 0.253401i $$0.0815490\pi$$
−0.264229 + 0.964460i $$0.585118\pi$$
$$224$$ 2.50000 4.33013i 0.167038 0.289319i
$$225$$ 0 0
$$226$$ 2.00000 + 3.46410i 0.133038 + 0.230429i
$$227$$ −2.00000 −0.132745 −0.0663723 0.997795i $$-0.521143\pi$$
−0.0663723 + 0.997795i $$0.521143\pi$$
$$228$$ 0 0
$$229$$ 10.0000 0.660819 0.330409 0.943838i $$-0.392813\pi$$
0.330409 + 0.943838i $$0.392813\pi$$
$$230$$ −3.50000 6.06218i −0.230783 0.399728i
$$231$$ 0 0
$$232$$ 3.00000 5.19615i 0.196960 0.341144i
$$233$$ −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i $$-0.965948\pi$$
0.404674 0.914461i $$-0.367385\pi$$
$$234$$ 0 0
$$235$$ −8.00000 −0.521862
$$236$$ 8.00000 0.520756
$$237$$ 0 0
$$238$$ −10.0000 + 17.3205i −0.648204 + 1.12272i
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i $$-0.517406\pi$$
0.892058 0.451920i $$-0.149261\pi$$
$$242$$ 5.00000 + 8.66025i 0.321412 + 0.556702i
$$243$$ 0 0
$$244$$ 2.00000 + 3.46410i 0.128037 + 0.221766i
$$245$$ 9.00000 + 15.5885i 0.574989 + 0.995910i
$$246$$ 0 0
$$247$$ 24.0000 + 10.3923i 1.52708 + 0.661247i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0.500000 + 0.866025i 0.0316228 + 0.0547723i
$$251$$ 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i $$-0.709699\pi$$
0.990876 + 0.134778i $$0.0430322\pi$$
$$252$$ 0 0
$$253$$ −3.50000 + 6.06218i −0.220043 + 0.381126i
$$254$$ −5.00000 −0.313728
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 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
$$259$$ −35.0000 −2.17479
$$260$$ 3.00000 5.19615i 0.186052 0.322252i
$$261$$ 0 0
$$262$$ −1.50000 + 2.59808i −0.0926703 + 0.160510i
$$263$$ 10.5000 + 18.1865i 0.647458 + 1.12143i 0.983728 + 0.179664i $$0.0575011\pi$$
−0.336270 + 0.941766i $$0.609166\pi$$
$$264$$ 0 0
$$265$$ 11.0000 0.675725
$$266$$ 17.5000 12.9904i 1.07299 0.796491i
$$267$$ 0 0
$$268$$ −6.00000 10.3923i −0.366508 0.634811i
$$269$$ 16.0000 + 27.7128i 0.975537 + 1.68968i 0.678151 + 0.734923i $$0.262782\pi$$
0.297386 + 0.954757i $$0.403885\pi$$
$$270$$ 0 0
$$271$$ −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i $$-0.186015\pi$$
−0.894799 + 0.446469i $$0.852681\pi$$
$$272$$ 2.00000 3.46410i 0.121268 0.210042i
$$273$$ 0 0
$$274$$ 12.0000 0.724947
$$275$$ 0.500000 0.866025i 0.0301511 0.0522233i
$$276$$ 0 0
$$277$$ −14.0000 −0.841178 −0.420589 0.907251i $$-0.638177\pi$$
−0.420589 + 0.907251i $$0.638177\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 0 0
$$280$$ −2.50000 4.33013i −0.149404 0.258775i
$$281$$ −5.50000 + 9.52628i −0.328102 + 0.568290i −0.982135 0.188176i $$-0.939742\pi$$
0.654033 + 0.756466i $$0.273076\pi$$
$$282$$ 0 0
$$283$$ −11.0000 19.0526i −0.653882 1.13256i −0.982173 0.187980i $$-0.939806\pi$$
0.328291 0.944577i $$-0.393527\pi$$
$$284$$ −2.00000 −0.118678
$$285$$ 0 0
$$286$$ −6.00000 −0.354787
$$287$$ 12.5000 + 21.6506i 0.737852 + 1.27800i
$$288$$ 0 0
$$289$$ 0.500000 0.866025i 0.0294118 0.0509427i
$$290$$ −3.00000 5.19615i −0.176166 0.305129i
$$291$$ 0 0
$$292$$ −2.00000 −0.117041
$$293$$ −5.00000 −0.292103 −0.146052 0.989277i $$-0.546657\pi$$
−0.146052 + 0.989277i $$0.546657\pi$$
$$294$$ 0 0
$$295$$ 4.00000 6.92820i 0.232889 0.403376i
$$296$$ 7.00000 0.406867
$$297$$ 0 0
$$298$$ −2.00000 + 3.46410i −0.115857 + 0.200670i
$$299$$ 21.0000 + 36.3731i 1.21446 + 2.10351i
$$300$$ 0 0
$$301$$ 15.0000 + 25.9808i 0.864586 + 1.49751i
$$302$$ 10.0000 + 17.3205i 0.575435 + 0.996683i
$$303$$ 0 0
$$304$$ −3.50000 + 2.59808i −0.200739 + 0.149010i
$$305$$ 4.00000 0.229039
$$306$$ 0 0
$$307$$ −9.00000 15.5885i −0.513657 0.889680i −0.999875 0.0158424i $$-0.994957\pi$$
0.486217 0.873838i $$-0.338376\pi$$
$$308$$ −2.50000 + 4.33013i −0.142451 + 0.246732i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 20.0000 1.13410 0.567048 0.823685i $$-0.308085\pi$$
0.567048 + 0.823685i $$0.308085\pi$$
$$312$$ 0 0
$$313$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$314$$ −4.50000 + 7.79423i −0.253950 + 0.439854i
$$315$$ 0 0
$$316$$ 10.0000 0.562544
$$317$$ 1.50000 2.59808i 0.0842484 0.145922i −0.820822 0.571184i $$-0.806484\pi$$
0.905071 + 0.425261i $$0.139818\pi$$
$$318$$ 0 0
$$319$$ −3.00000 + 5.19615i −0.167968 + 0.290929i
$$320$$ 0.500000 + 0.866025i 0.0279508 + 0.0484123i
$$321$$ 0 0
$$322$$ 35.0000 1.95047
$$323$$ 14.0000 10.3923i 0.778981 0.578243i
$$324$$ 0 0
$$325$$ −3.00000 5.19615i −0.166410 0.288231i
$$326$$ 5.00000 + 8.66025i 0.276924 + 0.479647i
$$327$$ 0 0
$$328$$ −2.50000 4.33013i −0.138039 0.239091i
$$329$$ 20.0000 34.6410i 1.10264 1.90982i
$$330$$ 0 0
$$331$$ 15.0000 0.824475 0.412237 0.911077i $$-0.364747\pi$$
0.412237 + 0.911077i $$0.364747\pi$$
$$332$$ −5.00000 + 8.66025i −0.274411 + 0.475293i
$$333$$ 0 0
$$334$$ −21.0000 −1.14907
$$335$$ −12.0000 −0.655630
$$336$$ 0 0
$$337$$ −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i $$-0.184015\pi$$
−0.891976 + 0.452082i $$0.850681\pi$$
$$338$$ −11.5000 + 19.9186i −0.625518 + 1.08343i
$$339$$ 0 0
$$340$$ −2.00000 3.46410i −0.108465 0.187867i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −55.0000 −2.96972
$$344$$ −3.00000 5.19615i −0.161749 0.280158i
$$345$$ 0 0
$$346$$ −4.50000 + 7.79423i −0.241921 + 0.419020i
$$347$$ −1.00000 1.73205i −0.0536828 0.0929814i 0.837935 0.545770i $$-0.183763\pi$$
−0.891618 + 0.452788i $$0.850429\pi$$
$$348$$ 0 0
$$349$$ 16.0000 0.856460 0.428230 0.903670i $$-0.359137\pi$$
0.428230 + 0.903670i $$0.359137\pi$$
$$350$$ −5.00000 −0.267261
$$351$$ 0 0
$$352$$ 0.500000 0.866025i 0.0266501 0.0461593i
$$353$$ −36.0000 −1.91609 −0.958043 0.286623i $$-0.907467\pi$$
−0.958043 + 0.286623i $$0.907467\pi$$
$$354$$ 0 0
$$355$$ −1.00000 + 1.73205i −0.0530745 + 0.0919277i
$$356$$ 6.50000 + 11.2583i 0.344499 + 0.596690i
$$357$$ 0 0
$$358$$ 3.50000 + 6.06218i 0.184981 + 0.320396i
$$359$$ −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i $$-0.324219\pi$$
−0.999590 + 0.0286287i $$0.990886\pi$$
$$360$$ 0 0
$$361$$ −18.5000 + 4.33013i −0.973684 + 0.227901i
$$362$$ 18.0000 0.946059
$$363$$ 0 0
$$364$$ 15.0000 + 25.9808i 0.786214 + 1.36176i
$$365$$ −1.00000 + 1.73205i −0.0523424 + 0.0906597i
$$366$$ 0 0
$$367$$ 2.00000 3.46410i 0.104399 0.180825i −0.809093 0.587680i $$-0.800041\pi$$
0.913493 + 0.406855i $$0.133375\pi$$
$$368$$ −7.00000 −0.364900
$$369$$ 0 0
$$370$$ 3.50000 6.06218i 0.181956 0.315158i
$$371$$ −27.5000 + 47.6314i −1.42773 + 2.47290i
$$372$$ 0 0
$$373$$ 5.00000 0.258890 0.129445 0.991587i $$-0.458680\pi$$
0.129445 + 0.991587i $$0.458680\pi$$
$$374$$ −2.00000 + 3.46410i −0.103418 + 0.179124i
$$375$$ 0 0
$$376$$ −4.00000 + 6.92820i −0.206284 + 0.357295i
$$377$$ 18.0000 + 31.1769i 0.927047 + 1.60569i
$$378$$ 0 0
$$379$$ −4.00000 −0.205466 −0.102733 0.994709i $$-0.532759\pi$$
−0.102733 + 0.994709i $$0.532759\pi$$
$$380$$ 0.500000 + 4.33013i 0.0256495 + 0.222131i
$$381$$ 0 0
$$382$$ −7.00000 12.1244i −0.358151 0.620336i
$$383$$ 16.0000 + 27.7128i 0.817562 + 1.41606i 0.907474 + 0.420109i $$0.138008\pi$$
−0.0899119 + 0.995950i $$0.528659\pi$$
$$384$$ 0 0
$$385$$ 2.50000 + 4.33013i 0.127412 + 0.220684i
$$386$$ 2.00000 3.46410i 0.101797 0.176318i
$$387$$ 0 0
$$388$$ 2.00000 0.101535
$$389$$ −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i $$-0.914918\pi$$
0.710980 + 0.703213i $$0.248252\pi$$
$$390$$ 0 0
$$391$$ 28.0000 1.41602
$$392$$ 18.0000 0.909137
$$393$$ 0 0
$$394$$ 0.500000 + 0.866025i 0.0251896 + 0.0436297i
$$395$$ 5.00000 8.66025i 0.251577 0.435745i
$$396$$ 0 0
$$397$$ 16.5000 + 28.5788i 0.828111 + 1.43433i 0.899518 + 0.436884i $$0.143918\pi$$
−0.0714068 + 0.997447i $$0.522749\pi$$
$$398$$ −4.00000 −0.200502
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 1.00000 + 1.73205i 0.0497519 + 0.0861727i
$$405$$ 0 0
$$406$$ 30.0000 1.48888
$$407$$ −7.00000 −0.346977
$$408$$ 0 0
$$409$$ 1.50000 2.59808i 0.0741702 0.128467i −0.826555 0.562856i $$-0.809703\pi$$
0.900725 + 0.434389i $$0.143036\pi$$
$$410$$ −5.00000 −0.246932
$$411$$ 0 0
$$412$$ −7.50000 + 12.9904i −0.369498 + 0.639990i
$$413$$ 20.0000 + 34.6410i 0.984136 + 1.70457i
$$414$$ 0 0
$$415$$ 5.00000 + 8.66025i 0.245440 + 0.425115i
$$416$$ −3.00000 5.19615i −0.147087 0.254762i
$$417$$ 0 0
$$418$$ 3.50000 2.59808i 0.171191 0.127076i
$$419$$ 3.00000 0.146560 0.0732798 0.997311i $$-0.476653\pi$$
0.0732798 + 0.997311i $$0.476653\pi$$
$$420$$ 0 0
$$421$$ 4.00000 + 6.92820i 0.194948 + 0.337660i 0.946883 0.321577i $$-0.104213\pi$$
−0.751935 + 0.659237i $$0.770879\pi$$
$$422$$ −6.50000 + 11.2583i −0.316415 + 0.548047i
$$423$$ 0 0
$$424$$ 5.50000 9.52628i 0.267104 0.462637i
$$425$$ −4.00000 −0.194029
$$426$$ 0 0
$$427$$ −10.0000 + 17.3205i −0.483934 + 0.838198i
$$428$$ −2.00000 + 3.46410i −0.0966736 + 0.167444i
$$429$$ 0 0
$$430$$ −6.00000 −0.289346
$$431$$ −2.00000 + 3.46410i −0.0963366 + 0.166860i −0.910166 0.414244i $$-0.864046\pi$$
0.813829 + 0.581104i $$0.197379\pi$$
$$432$$ 0 0
$$433$$ −3.00000 + 5.19615i −0.144171 + 0.249711i −0.929063 0.369921i $$-0.879385\pi$$
0.784892 + 0.619632i $$0.212718\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −16.0000 −0.766261
$$437$$ −28.0000 12.1244i −1.33942 0.579987i
$$438$$ 0 0
$$439$$ 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i $$0.109922\pi$$
−0.177325 + 0.984152i $$0.556744\pi$$
$$440$$ −0.500000 0.866025i −0.0238366 0.0412861i
$$441$$ 0 0
$$442$$ 12.0000 + 20.7846i 0.570782 + 0.988623i
$$443$$ 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i $$-0.640223\pi$$
0.996551 0.0829786i $$-0.0264433\pi$$
$$444$$ 0 0
$$445$$ 13.0000 0.616259
$$446$$ 10.5000 18.1865i 0.497189 0.861157i
$$447$$ 0 0
$$448$$ −5.00000 −0.236228
$$449$$ 39.0000 1.84052 0.920262 0.391303i $$-0.127976\pi$$
0.920262 + 0.391303i $$0.127976\pi$$
$$450$$ 0 0
$$451$$ 2.50000 + 4.33013i 0.117720 + 0.203898i
$$452$$ 2.00000 3.46410i 0.0940721 0.162938i
$$453$$ 0 0
$$454$$ 1.00000 + 1.73205i 0.0469323 + 0.0812892i
$$455$$ 30.0000 1.40642
$$456$$ 0 0
$$457$$ 8.00000 0.374224 0.187112 0.982339i $$-0.440087\pi$$
0.187112 + 0.982339i $$0.440087\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ 0 0
$$460$$ −3.50000 + 6.06218i −0.163188 + 0.282650i
$$461$$ −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i $$-0.211288\pi$$
−0.927392 + 0.374091i $$0.877955\pi$$
$$462$$ 0 0
$$463$$ −9.00000 −0.418265 −0.209133 0.977887i $$-0.567064\pi$$
−0.209133 + 0.977887i $$0.567064\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ −9.00000 + 15.5885i −0.416917 + 0.722121i
$$467$$ −38.0000 −1.75843 −0.879215 0.476425i $$-0.841932\pi$$
−0.879215 + 0.476425i $$0.841932\pi$$
$$468$$ 0 0
$$469$$ 30.0000 51.9615i 1.38527 2.39936i
$$470$$ 4.00000 + 6.92820i 0.184506 + 0.319574i
$$471$$ 0 0
$$472$$ −4.00000 6.92820i −0.184115 0.318896i
$$473$$ 3.00000 + 5.19615i 0.137940 + 0.238919i
$$474$$ 0 0
$$475$$ 4.00000 + 1.73205i 0.183533 + 0.0794719i
$$476$$ 20.0000 0.916698
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 21.0000 36.3731i 0.959514 1.66193i 0.235833 0.971794i $$-0.424218\pi$$
0.723681 0.690134i $$-0.242449\pi$$
$$480$$ 0 0
$$481$$ −21.0000 + 36.3731i −0.957518 + 1.65847i
$$482$$ −26.0000 −1.18427
$$483$$ 0 0
$$484$$ 5.00000 8.66025i 0.227273 0.393648i
$$485$$ 1.00000 1.73205i 0.0454077 0.0786484i
$$486$$ 0 0
$$487$$ −13.0000 −0.589086 −0.294543 0.955638i $$-0.595167\pi$$
−0.294543 + 0.955638i $$0.595167\pi$$
$$488$$ 2.00000 3.46410i 0.0905357 0.156813i
$$489$$ 0 0
$$490$$ 9.00000 15.5885i 0.406579 0.704215i
$$491$$ −16.5000 28.5788i −0.744635 1.28974i −0.950365 0.311136i $$-0.899290\pi$$
0.205731 0.978609i $$-0.434043\pi$$
$$492$$ 0 0
$$493$$ 24.0000 1.08091
$$494$$ −3.00000 25.9808i −0.134976 1.16893i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −5.00000 8.66025i −0.224281 0.388465i
$$498$$ 0 0
$$499$$ 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i $$-0.116587\pi$$
−0.776989 + 0.629515i $$0.783254\pi$$
$$500$$ 0.500000 0.866025i 0.0223607 0.0387298i
$$501$$ 0 0
$$502$$ −12.0000 −0.535586
$$503$$ 0.500000 0.866025i 0.0222939 0.0386142i −0.854663 0.519183i $$-0.826236\pi$$
0.876957 + 0.480569i $$0.159570\pi$$
$$504$$ 0 0
$$505$$ 2.00000 0.0889988
$$506$$ 7.00000 0.311188
$$507$$ 0 0
$$508$$ 2.50000 + 4.33013i 0.110920 + 0.192118i
$$509$$ 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i $$-0.819220\pi$$
0.887336 + 0.461123i $$0.152553\pi$$
$$510$$ 0 0
$$511$$ −5.00000 8.66025i −0.221187 0.383107i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ 7.50000 + 12.9904i 0.330489 + 0.572425i
$$516$$ 0 0
$$517$$ 4.00000 6.92820i 0.175920 0.304702i
$$518$$ 17.5000 + 30.3109i 0.768906 + 1.33178i
$$519$$ 0 0
$$520$$ −6.00000 −0.263117
$$521$$ 14.0000 0.613351 0.306676 0.951814i $$-0.400783\pi$$
0.306676 + 0.951814i $$0.400783\pi$$
$$522$$ 0 0
$$523$$ 7.00000 12.1244i 0.306089 0.530161i −0.671414 0.741082i $$-0.734313\pi$$
0.977503 + 0.210921i $$0.0676463\pi$$
$$524$$ 3.00000 0.131056
$$525$$ 0 0
$$526$$ 10.5000 18.1865i 0.457822 0.792971i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −13.0000 22.5167i −0.565217 0.978985i
$$530$$ −5.50000 9.52628i −0.238905 0.413795i
$$531$$ 0 0
$$532$$ −20.0000 8.66025i −0.867110 0.375470i
$$533$$ 30.0000 1.29944
$$534$$ 0 0
$$535$$ 2.00000 + 3.46410i 0.0864675 + 0.149766i
$$536$$ −6.00000 + 10.3923i −0.259161 + 0.448879i
$$537$$ 0 0
$$538$$ 16.0000 27.7128i 0.689809 1.19478i
$$539$$ −18.0000 −0.775315
$$540$$ 0 0
$$541$$ −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i $$-0.888348\pi$$
0.767136 + 0.641484i $$0.221681\pi$$
$$542$$ −1.00000 + 1.73205i −0.0429537 + 0.0743980i
$$543$$ 0 0
$$544$$ −4.00000 −0.171499
$$545$$ −8.00000 + 13.8564i −0.342682 + 0.593543i
$$546$$ 0 0
$$547$$ −7.00000 + 12.1244i −0.299298 + 0.518400i −0.975976 0.217880i $$-0.930086\pi$$
0.676677 + 0.736280i $$0.263419\pi$$
$$548$$ −6.00000 10.3923i −0.256307 0.443937i
$$549$$ 0 0
$$550$$ −1.00000 −0.0426401
$$551$$ −24.0000 10.3923i −1.02243 0.442727i
$$552$$ 0 0
$$553$$ 25.0000 + 43.3013i 1.06311 + 1.84136i
$$554$$ 7.00000 + 12.1244i 0.297402 + 0.515115i
$$555$$ 0 0
$$556$$ 8.00000 + 13.8564i 0.339276 + 0.587643i
$$557$$ 0.500000 0.866025i 0.0211857 0.0366947i −0.855238 0.518235i $$-0.826589\pi$$
0.876424 + 0.481540i $$0.159923\pi$$
$$558$$ 0 0
$$559$$ 36.0000 1.52264
$$560$$ −2.50000 + 4.33013i −0.105644 + 0.182981i
$$561$$ 0 0
$$562$$ 11.0000 0.464007
$$563$$ −24.0000 −1.01148 −0.505740 0.862686i $$-0.668780\pi$$
−0.505740 + 0.862686i $$0.668780\pi$$
$$564$$ 0 0
$$565$$ −2.00000 3.46410i −0.0841406 0.145736i
$$566$$ −11.0000 + 19.0526i −0.462364 + 0.800839i
$$567$$ 0 0
$$568$$ 1.00000 + 1.73205i 0.0419591 + 0.0726752i
$$569$$ −33.0000 −1.38343 −0.691716 0.722170i $$-0.743145\pi$$
−0.691716 + 0.722170i $$0.743145\pi$$
$$570$$ 0 0
$$571$$ 20.0000 0.836974 0.418487 0.908223i $$-0.362561\pi$$
0.418487 + 0.908223i $$0.362561\pi$$
$$572$$ 3.00000 + 5.19615i 0.125436 + 0.217262i
$$573$$ 0 0
$$574$$ 12.5000 21.6506i 0.521740 0.903680i
$$575$$ 3.50000 + 6.06218i 0.145960 + 0.252810i
$$576$$ 0 0
$$577$$ −32.0000 −1.33218 −0.666089 0.745873i $$-0.732033\pi$$
−0.666089 + 0.745873i $$0.732033\pi$$
$$578$$ −1.00000 −0.0415945
$$579$$ 0 0
$$580$$ −3.00000 + 5.19615i −0.124568 + 0.215758i
$$581$$ −50.0000 −2.07435
$$582$$ 0 0
$$583$$ −5.50000 + 9.52628i −0.227787 + 0.394538i
$$584$$ 1.00000 + 1.73205i 0.0413803 + 0.0716728i
$$585$$ 0 0
$$586$$ 2.50000 + 4.33013i 0.103274 + 0.178876i
$$587$$ −10.0000 17.3205i −0.412744 0.714894i 0.582445 0.812870i $$-0.302096\pi$$
−0.995189 + 0.0979766i $$0.968763\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −8.00000 −0.329355
$$591$$ 0 0
$$592$$ −3.50000 6.06218i −0.143849 0.249154i
$$593$$ 11.0000 19.0526i 0.451716 0.782395i −0.546777 0.837278i $$-0.684145\pi$$
0.998493 + 0.0548835i $$0.0174787\pi$$
$$594$$ 0 0
$$595$$ 10.0000 17.3205i 0.409960 0.710072i
$$596$$ 4.00000 0.163846
$$597$$ 0 0
$$598$$ 21.0000 36.3731i 0.858754 1.48741i
$$599$$ 4.00000 6.92820i 0.163436 0.283079i −0.772663 0.634816i $$-0.781076\pi$$
0.936099 + 0.351738i $$0.114409\pi$$
$$600$$ 0 0
$$601$$ −3.00000 −0.122373 −0.0611863 0.998126i $$-0.519488\pi$$
−0.0611863 + 0.998126i $$0.519488\pi$$
$$602$$ 15.0000 25.9808i 0.611354 1.05890i
$$603$$ 0 0
$$604$$ 10.0000 17.3205i 0.406894 0.704761i
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ 0 0
$$607$$ −1.00000 −0.0405887 −0.0202944 0.999794i $$-0.506460\pi$$
−0.0202944 + 0.999794i $$0.506460\pi$$
$$608$$ 4.00000 + 1.73205i 0.162221 + 0.0702439i
$$609$$ 0 0
$$610$$ −2.00000 3.46410i −0.0809776 0.140257i
$$611$$ −24.0000 41.5692i −0.970936 1.68171i
$$612$$ 0 0
$$613$$ −17.5000 30.3109i −0.706818 1.22425i −0.966031 0.258425i $$-0.916796\pi$$
0.259213 0.965820i $$-0.416537\pi$$
$$614$$ −9.00000 + 15.5885i −0.363210 + 0.629099i
$$615$$ 0 0
$$616$$ 5.00000 0.201456
$$617$$ 24.0000 41.5692i 0.966204 1.67351i 0.259858 0.965647i $$-0.416324\pi$$
0.706346 0.707867i $$-0.250342\pi$$
$$618$$ 0 0
$$619$$ 43.0000 1.72832 0.864158 0.503221i $$-0.167852\pi$$
0.864158 + 0.503221i $$0.167852\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −10.0000 17.3205i −0.400963 0.694489i
$$623$$ −32.5000 + 56.2917i −1.30209 + 2.25528i
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 9.00000 0.359139
$$629$$ 14.0000 + 24.2487i 0.558217 + 0.966859i
$$630$$ 0 0
$$631$$ −19.0000 + 32.9090i −0.756378 + 1.31009i 0.188308 + 0.982110i $$0.439700\pi$$
−0.944686 + 0.327975i $$0.893634\pi$$
$$632$$ −5.00000 8.66025i −0.198889 0.344486i
$$633$$ 0 0
$$634$$ −3.00000 −0.119145
$$635$$ 5.00000 0.198419
$$636$$ 0 0
$$637$$ −54.0000 + 93.5307i −2.13956 + 3.70582i
$$638$$ 6.00000 0.237542
$$639$$ 0 0
$$640$$ 0.500000 0.866025i 0.0197642 0.0342327i
$$641$$ −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i $$-0.995027\pi$$
0.486409 0.873731i $$-0.338307\pi$$
$$642$$ 0 0
$$643$$ 22.0000 + 38.1051i 0.867595 + 1.50272i 0.864447 + 0.502724i $$0.167669\pi$$
0.00314839 + 0.999995i $$0.498998\pi$$
$$644$$ −17.5000 30.3109i −0.689597 1.19442i
$$645$$ 0 0
$$646$$ −16.0000 6.92820i −0.629512 0.272587i
$$647$$ −3.00000 −0.117942 −0.0589711 0.998260i $$-0.518782\pi$$
−0.0589711 + 0.998260i $$0.518782\pi$$
$$648$$ 0 0
$$649$$ 4.00000 + 6.92820i 0.157014 + 0.271956i
$$650$$ −3.00000 + 5.19615i −0.117670 + 0.203810i
$$651$$ 0 0
$$652$$ 5.00000 8.66025i 0.195815 0.339162i
$$653$$ −9.00000 −0.352197 −0.176099 0.984373i $$-0.556348\pi$$
−0.176099 + 0.984373i $$0.556348\pi$$
$$654$$ 0 0
$$655$$ 1.50000 2.59808i 0.0586098 0.101515i
$$656$$ −2.50000 + 4.33013i −0.0976086 + 0.169063i
$$657$$ 0 0
$$658$$ −40.0000 −1.55936
$$659$$ −5.50000 + 9.52628i −0.214250 + 0.371091i −0.953040 0.302844i $$-0.902064\pi$$
0.738791 + 0.673935i $$0.235397\pi$$
$$660$$ 0 0
$$661$$ 10.0000 17.3205i 0.388955 0.673690i −0.603354 0.797473i $$-0.706170\pi$$
0.992309 + 0.123784i $$0.0395028\pi$$
$$662$$ −7.50000 12.9904i −0.291496 0.504885i
$$663$$ 0 0
$$664$$ 10.0000 0.388075
$$665$$ −17.5000 + 12.9904i −0.678621 + 0.503745i
$$666$$ 0 0
$$667$$ −21.0000 36.3731i −0.813123 1.40837i
$$668$$ 10.5000 + 18.1865i 0.406257 + 0.703658i
$$669$$ 0 0
$$670$$ 6.00000 + 10.3923i 0.231800 + 0.401490i
$$671$$ −2.00000 + 3.46410i −0.0772091 + 0.133730i
$$672$$ 0 0
$$673$$ −40.0000 −1.54189 −0.770943 0.636904i $$-0.780215\pi$$
−0.770943 + 0.636904i $$0.780215\pi$$
$$674$$ −1.00000 + 1.73205i −0.0385186 + 0.0667161i
$$675$$ 0 0
$$676$$ 23.0000 0.884615
$$677$$ −21.0000 −0.807096 −0.403548 0.914959i $$-0.632223\pi$$
−0.403548 + 0.914959i $$0.632223\pi$$
$$678$$ 0 0
$$679$$ 5.00000 + 8.66025i 0.191882 + 0.332350i
$$680$$ −2.00000 + 3.46410i −0.0766965 + 0.132842i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ −12.0000 −0.458496
$$686$$ 27.5000 + 47.6314i 1.04995 + 1.81858i
$$687$$ 0 0
$$688$$ −3.00000 + 5.19615i −0.114374 + 0.198101i
$$689$$ 33.0000 + 57.1577i 1.25720 + 2.17753i
$$690$$ 0 0
$$691$$ 1.00000 0.0380418 0.0190209 0.999819i $$-0.493945\pi$$
0.0190209 + 0.999819i $$0.493945\pi$$
$$692$$ 9.00000 0.342129
$$693$$ 0 0
$$694$$ −1.00000 + 1.73205i −0.0379595 + 0.0657477i
$$695$$ 16.0000 0.606915
$$696$$ 0 0
$$697$$ 10.0000 17.3205i 0.378777 0.656061i
$$698$$ −8.00000 13.8564i −0.302804 0.524473i
$$699$$ 0 0
$$700$$ 2.50000 + 4.33013i 0.0944911 + 0.163663i
$$701$$ 17.0000 + 29.4449i 0.642081 + 1.11212i 0.984967 + 0.172740i $$0.0552621\pi$$
−0.342886 + 0.939377i $$0.611405\pi$$
$$702$$ 0 0
$$703$$ −3.50000 30.3109i −0.132005 1.14320i
$$704$$ −1.00000 −0.0376889
$$705$$ 0 0
$$706$$ 18.0000 + 31.1769i 0.677439 + 1.17336i
$$707$$ −5.00000 + 8.66025i −0.188044 + 0.325702i
$$708$$ 0 0
$$709$$ 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i $$-0.809402\pi$$
0.901135 + 0.433539i $$0.142735\pi$$
$$710$$ 2.00000 0.0750587
$$711$$ 0 0
$$712$$ 6.50000 11.2583i 0.243598 0.421924i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 6.00000 0.224387
$$716$$ 3.50000 6.06218i 0.130801 0.226554i
$$717$$ 0 0
$$718$$ −9.00000 + 15.5885i −0.335877 + 0.581756i
$$719$$ −22.0000 38.1051i −0.820462 1.42108i −0.905339 0.424690i $$-0.860383\pi$$
0.0848774 0.996391i $$-0.472950\pi$$
$$720$$ 0 0
$$721$$ −75.0000 −2.79315
$$722$$ 13.0000 + 13.8564i 0.483810 + 0.515682i
$$723$$ 0 0
$$724$$ −9.00000 15.5885i −0.334482 0.579340i
$$725$$ 3.00000 + 5.19615i 0.111417 + 0.192980i
$$726$$ 0 0
$$727$$ −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i $$-0.964449\pi$$
0.400362 0.916357i $$-0.368884\pi$$
$$728$$ 15.0000 25.9808i 0.555937 0.962911i
$$729$$ 0 0
$$730$$ 2.00000 0.0740233
$$731$$ 12.0000 20.7846i 0.443836 0.768747i
$$732$$ 0 0
$$733$$ 19.0000 0.701781 0.350891 0.936416i $$-0.385879\pi$$
0.350891 + 0.936416i $$0.385879\pi$$
$$734$$ −4.00000 −0.147643
$$735$$ 0 0
$$736$$ 3.50000 + 6.06218i 0.129012 + 0.223455i
$$737$$ 6.00000 10.3923i 0.221013 0.382805i
$$738$$ 0 0
$$739$$ 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i $$0.165674\pi$$
−0.00311943 + 0.999995i $$0.500993\pi$$
$$740$$ −7.00000 −0.257325
$$741$$ 0 0
$$742$$ 55.0000 2.01911
$$743$$ 7.50000 + 12.9904i 0.275148 + 0.476571i 0.970173 0.242415i $$-0.0779397\pi$$
−0.695024 + 0.718986i $$0.744606\pi$$
$$744$$ 0 0
$$745$$ 2.00000 3.46410i 0.0732743 0.126915i
$$746$$ −2.50000 4.33013i −0.0915315 0.158537i
$$747$$ 0 0
$$748$$ 4.00000 0.146254
$$749$$ −20.0000 −0.730784
$$750$$ 0 0
$$751$$ −20.0000 + 34.6410i −0.729810 + 1.26407i 0.227153 + 0.973859i $$0.427058\pi$$
−0.956963 + 0.290209i $$0.906275\pi$$
$$752$$ 8.00000 0.291730
$$753$$ 0 0
$$754$$ 18.0000 31.1769i 0.655521 1.13540i
$$755$$ −10.0000 17.3205i −0.363937 0.630358i
$$756$$ 0 0
$$757$$ 6.50000 + 11.2583i 0.236247 + 0.409191i 0.959634 0.281251i $$-0.0907494\pi$$
−0.723388 + 0.690442i $$0.757416\pi$$
$$758$$ 2.00000 + 3.46410i 0.0726433 + 0.125822i
$$759$$ 0 0
$$760$$ 3.50000 2.59808i 0.126958 0.0942421i
$$761$$ 31.0000 1.12375 0.561875 0.827222i $$-0.310080\pi$$
0.561875 + 0.827222i $$0.310080\pi$$
$$762$$ 0 0
$$763$$ −40.0000 69.2820i −1.44810 2.50818i
$$764$$ −7.00000 + 12.1244i −0.253251 + 0.438644i
$$765$$ 0 0
$$766$$ 16.0000 27.7128i 0.578103 1.00130i
$$767$$ 48.0000 1.73318
$$768$$ 0 0
$$769$$ −3.00000 + 5.19615i −0.108183 + 0.187378i −0.915034 0.403376i $$-0.867837\pi$$
0.806851 + 0.590755i $$0.201170\pi$$
$$770$$ 2.50000 4.33013i 0.0900937 0.156047i
$$771$$ 0 0
$$772$$ −4.00000 −0.143963
$$773$$ −10.5000 + 18.1865i −0.377659 + 0.654124i −0.990721 0.135910i $$-0.956604\pi$$
0.613062 + 0.790034i $$0.289937\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −1.00000 1.73205i −0.0358979 0.0621770i
$$777$$ 0 0
$$778$$ 10.0000 0.358517
$$779$$ −17.5000 + 12.9904i −0.627003 + 0.465429i
$$780$$ 0 0
$$781$$ −1.00000 1.73205i −0.0357828 0.0619777i
$$782$$ −14.0000 24.2487i −0.500639 0.867132i
$$783$$ 0 0
$$784$$ −9.00000 15.5885i −0.321429 0.556731i
$$785$$ 4.50000 7.79423i 0.160612 0.278188i
$$786$$ 0 0
$$787$$ −26.0000 −0.926800 −0.463400 0.886149i $$-0.653371\pi$$
−0.463400 + 0.886149i $$0.653371\pi$$
$$788$$ 0.500000 0.866025i 0.0178118 0.0308509i
$$789$$ 0 0
$$790$$ −10.0000