# Properties

 Label 570.2.i.e.391.1 Level $570$ Weight $2$ Character 570.391 Analytic conductor $4.551$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 391.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.391 Dual form 570.2.i.e.121.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} -5.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.00000 q^{11} -1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(-2.50000 + 4.33013i) q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} -1.00000 q^{18} +(-0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(-2.50000 + 4.33013i) q^{21} +(0.500000 - 0.866025i) q^{22} +(-3.50000 - 6.06218i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.00000 q^{30} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{33} +(2.00000 + 3.46410i) q^{34} +(2.50000 - 4.33013i) q^{35} +(-0.500000 + 0.866025i) q^{36} +7.00000 q^{37} +(3.50000 + 2.59808i) q^{38} -6.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(2.50000 - 4.33013i) q^{41} +(2.50000 + 4.33013i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(-0.500000 - 0.866025i) q^{44} +1.00000 q^{45} -7.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(0.500000 + 0.866025i) q^{48} +18.0000 q^{49} -1.00000 q^{50} +(2.00000 + 3.46410i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-5.50000 - 9.52628i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{55} +5.00000 q^{56} +(3.50000 + 2.59808i) q^{57} -6.00000 q^{58} +(4.00000 - 6.92820i) q^{59} +(0.500000 - 0.866025i) q^{60} +(2.00000 + 3.46410i) q^{61} +(2.50000 + 4.33013i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(-0.500000 - 0.866025i) q^{66} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{68} -7.00000 q^{69} +(-2.50000 - 4.33013i) q^{70} +(-1.00000 + 1.73205i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{75} +(4.00000 - 1.73205i) q^{76} -5.00000 q^{77} +(-3.00000 + 5.19615i) q^{78} +(-5.00000 + 8.66025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -10.0000 q^{83} +5.00000 q^{84} +(-2.00000 - 3.46410i) q^{85} +(3.00000 + 5.19615i) q^{86} -6.00000 q^{87} -1.00000 q^{88} +(-6.50000 - 11.2583i) q^{89} +(0.500000 - 0.866025i) q^{90} +(15.0000 + 25.9808i) q^{91} +(-3.50000 + 6.06218i) q^{92} +8.00000 q^{94} +(-3.50000 - 2.59808i) q^{95} +1.00000 q^{96} +(-1.00000 + 1.73205i) q^{97} +(9.00000 - 15.5885i) q^{98} +(-0.500000 - 0.866025i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10q^{7} - 2q^{8} - q^{9} + O(q^{10})$$ $$2q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 10q^{7} - 2q^{8} - q^{9} + q^{10} + 2q^{11} - 2q^{12} - 6q^{13} - 5q^{14} + q^{15} - q^{16} - 4q^{17} - 2q^{18} - q^{19} + 2q^{20} - 5q^{21} + q^{22} - 7q^{23} - q^{24} - q^{25} - 12q^{26} - 2q^{27} + 5q^{28} - 6q^{29} + 2q^{30} + q^{32} + q^{33} + 4q^{34} + 5q^{35} - q^{36} + 14q^{37} + 7q^{38} - 12q^{39} + q^{40} + 5q^{41} + 5q^{42} - 6q^{43} - q^{44} + 2q^{45} - 14q^{46} + 8q^{47} + q^{48} + 36q^{49} - 2q^{50} + 4q^{51} - 6q^{52} - 11q^{53} - q^{54} - q^{55} + 10q^{56} + 7q^{57} - 12q^{58} + 8q^{59} + q^{60} + 4q^{61} + 5q^{63} + 2q^{64} + 12q^{65} - q^{66} - 12q^{67} + 8q^{68} - 14q^{69} - 5q^{70} - 2q^{71} + q^{72} + 2q^{73} + 7q^{74} - 2q^{75} + 8q^{76} - 10q^{77} - 6q^{78} - 10q^{79} - q^{80} - q^{81} - 5q^{82} - 20q^{83} + 10q^{84} - 4q^{85} + 6q^{86} - 12q^{87} - 2q^{88} - 13q^{89} + q^{90} + 30q^{91} - 7q^{92} + 16q^{94} - 7q^{95} + 2q^{96} - 2q^{97} + 18q^{98} - q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ −0.500000 0.866025i −0.204124 0.353553i
$$7$$ −5.00000 −1.88982 −0.944911 0.327327i $$-0.893852\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0.500000 + 0.866025i 0.158114 + 0.273861i
$$11$$ 1.00000 0.301511 0.150756 0.988571i $$-0.451829\pi$$
0.150756 + 0.988571i $$0.451829\pi$$
$$12$$ −1.00000 −0.288675
$$13$$ −3.00000 5.19615i −0.832050 1.44115i −0.896410 0.443227i $$-0.853834\pi$$
0.0643593 0.997927i $$-0.479500\pi$$
$$14$$ −2.50000 + 4.33013i −0.668153 + 1.15728i
$$15$$ 0.500000 + 0.866025i 0.129099 + 0.223607i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −0.500000 + 4.33013i −0.114708 + 0.993399i
$$20$$ 1.00000 0.223607
$$21$$ −2.50000 + 4.33013i −0.545545 + 0.944911i
$$22$$ 0.500000 0.866025i 0.106600 0.184637i
$$23$$ −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i $$-0.906280\pi$$
0.227167 0.973856i $$-0.427054\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −6.00000 −1.17670
$$27$$ −1.00000 −0.192450
$$28$$ 2.50000 + 4.33013i 0.472456 + 0.818317i
$$29$$ −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i $$-0.978586\pi$$
0.440652 0.897678i $$-0.354747\pi$$
$$30$$ 1.00000 0.182574
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ 0.500000 0.866025i 0.0870388 0.150756i
$$34$$ 2.00000 + 3.46410i 0.342997 + 0.594089i
$$35$$ 2.50000 4.33013i 0.422577 0.731925i
$$36$$ −0.500000 + 0.866025i −0.0833333 + 0.144338i
$$37$$ 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
$$39$$ −6.00000 −0.960769
$$40$$ 0.500000 0.866025i 0.0790569 0.136931i
$$41$$ 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i $$-0.705658\pi$$
0.992507 + 0.122189i $$0.0389915\pi$$
$$42$$ 2.50000 + 4.33013i 0.385758 + 0.668153i
$$43$$ −3.00000 + 5.19615i −0.457496 + 0.792406i −0.998828 0.0484030i $$-0.984587\pi$$
0.541332 + 0.840809i $$0.317920\pi$$
$$44$$ −0.500000 0.866025i −0.0753778 0.130558i
$$45$$ 1.00000 0.149071
$$46$$ −7.00000 −1.03209
$$47$$ 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i $$0.0316348\pi$$
−0.411606 + 0.911362i $$0.635032\pi$$
$$48$$ 0.500000 + 0.866025i 0.0721688 + 0.125000i
$$49$$ 18.0000 2.57143
$$50$$ −1.00000 −0.141421
$$51$$ 2.00000 + 3.46410i 0.280056 + 0.485071i
$$52$$ −3.00000 + 5.19615i −0.416025 + 0.720577i
$$53$$ −5.50000 9.52628i −0.755483 1.30854i −0.945134 0.326683i $$-0.894069\pi$$
0.189651 0.981852i $$-0.439264\pi$$
$$54$$ −0.500000 + 0.866025i −0.0680414 + 0.117851i
$$55$$ −0.500000 + 0.866025i −0.0674200 + 0.116775i
$$56$$ 5.00000 0.668153
$$57$$ 3.50000 + 2.59808i 0.463586 + 0.344124i
$$58$$ −6.00000 −0.787839
$$59$$ 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i $$-0.658984\pi$$
0.999709 0.0241347i $$-0.00768307\pi$$
$$60$$ 0.500000 0.866025i 0.0645497 0.111803i
$$61$$ 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i $$-0.0842377\pi$$
−0.709113 + 0.705095i $$0.750904\pi$$
$$62$$ 0 0
$$63$$ 2.50000 + 4.33013i 0.314970 + 0.545545i
$$64$$ 1.00000 0.125000
$$65$$ 6.00000 0.744208
$$66$$ −0.500000 0.866025i −0.0615457 0.106600i
$$67$$ −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i $$-0.904778\pi$$
0.222571 0.974916i $$-0.428555\pi$$
$$68$$ 4.00000 0.485071
$$69$$ −7.00000 −0.842701
$$70$$ −2.50000 4.33013i −0.298807 0.517549i
$$71$$ −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i $$-0.871199\pi$$
0.800566 + 0.599245i $$0.204532\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i $$-0.795992\pi$$
0.918594 + 0.395203i $$0.129326\pi$$
$$74$$ 3.50000 6.06218i 0.406867 0.704714i
$$75$$ −1.00000 −0.115470
$$76$$ 4.00000 1.73205i 0.458831 0.198680i
$$77$$ −5.00000 −0.569803
$$78$$ −3.00000 + 5.19615i −0.339683 + 0.588348i
$$79$$ −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i $$0.356844\pi$$
−0.997274 + 0.0737937i $$0.976489\pi$$
$$80$$ −0.500000 0.866025i −0.0559017 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −2.50000 4.33013i −0.276079 0.478183i
$$83$$ −10.0000 −1.09764 −0.548821 0.835940i $$-0.684923\pi$$
−0.548821 + 0.835940i $$0.684923\pi$$
$$84$$ 5.00000 0.545545
$$85$$ −2.00000 3.46410i −0.216930 0.375735i
$$86$$ 3.00000 + 5.19615i 0.323498 + 0.560316i
$$87$$ −6.00000 −0.643268
$$88$$ −1.00000 −0.106600
$$89$$ −6.50000 11.2583i −0.688999 1.19338i −0.972162 0.234309i $$-0.924717\pi$$
0.283164 0.959072i $$-0.408616\pi$$
$$90$$ 0.500000 0.866025i 0.0527046 0.0912871i
$$91$$ 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
$$96$$ 1.00000 0.102062
$$97$$ −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i $$-0.865709\pi$$
0.810782 + 0.585348i $$0.199042\pi$$
$$98$$ 9.00000 15.5885i 0.909137 1.57467i
$$99$$ −0.500000 0.866025i −0.0502519 0.0870388i
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i $$-0.198392\pi$$
−0.911479 + 0.411346i $$0.865059\pi$$
$$102$$ 4.00000 0.396059
$$103$$ 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
$$105$$ −2.50000 4.33013i −0.243975 0.422577i
$$106$$ −11.0000 −1.06841
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0.500000 + 0.866025i 0.0481125 + 0.0833333i
$$109$$ 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i $$-0.555448\pi$$
0.939577 0.342337i $$-0.111218\pi$$
$$110$$ 0.500000 + 0.866025i 0.0476731 + 0.0825723i
$$111$$ 3.50000 6.06218i 0.332205 0.575396i
$$112$$ 2.50000 4.33013i 0.236228 0.409159i
$$113$$ 4.00000 0.376288 0.188144 0.982141i $$-0.439753\pi$$
0.188144 + 0.982141i $$0.439753\pi$$
$$114$$ 4.00000 1.73205i 0.374634 0.162221i
$$115$$ 7.00000 0.652753
$$116$$ −3.00000 + 5.19615i −0.278543 + 0.482451i
$$117$$ −3.00000 + 5.19615i −0.277350 + 0.480384i
$$118$$ −4.00000 6.92820i −0.368230 0.637793i
$$119$$ 10.0000 17.3205i 0.916698 1.58777i
$$120$$ −0.500000 0.866025i −0.0456435 0.0790569i
$$121$$ −10.0000 −0.909091
$$122$$ 4.00000 0.362143
$$123$$ −2.50000 4.33013i −0.225417 0.390434i
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 5.00000 0.445435
$$127$$ 2.50000 + 4.33013i 0.221839 + 0.384237i 0.955366 0.295423i $$-0.0954607\pi$$
−0.733527 + 0.679660i $$0.762127\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 3.00000 + 5.19615i 0.264135 + 0.457496i
$$130$$ 3.00000 5.19615i 0.263117 0.455733i
$$131$$ 1.50000 2.59808i 0.131056 0.226995i −0.793028 0.609185i $$-0.791497\pi$$
0.924084 + 0.382190i $$0.124830\pi$$
$$132$$ −1.00000 −0.0870388
$$133$$ 2.50000 21.6506i 0.216777 1.87735i
$$134$$ −12.0000 −1.03664
$$135$$ 0.500000 0.866025i 0.0430331 0.0745356i
$$136$$ 2.00000 3.46410i 0.171499 0.297044i
$$137$$ 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i $$0.00465636\pi$$
−0.487278 + 0.873247i $$0.662010\pi$$
$$138$$ −3.50000 + 6.06218i −0.297940 + 0.516047i
$$139$$ 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i $$0.0707252\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ −5.00000 −0.422577
$$141$$ 8.00000 0.673722
$$142$$ 1.00000 + 1.73205i 0.0839181 + 0.145350i
$$143$$ −3.00000 5.19615i −0.250873 0.434524i
$$144$$ 1.00000 0.0833333
$$145$$ 6.00000 0.498273
$$146$$ −1.00000 1.73205i −0.0827606 0.143346i
$$147$$ 9.00000 15.5885i 0.742307 1.28571i
$$148$$ −3.50000 6.06218i −0.287698 0.498308i
$$149$$ 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i $$-0.780943\pi$$
0.936245 + 0.351348i $$0.114277\pi$$
$$150$$ −0.500000 + 0.866025i −0.0408248 + 0.0707107i
$$151$$ −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
$$153$$ 4.00000 0.323381
$$154$$ −2.50000 + 4.33013i −0.201456 + 0.348932i
$$155$$ 0 0
$$156$$ 3.00000 + 5.19615i 0.240192 + 0.416025i
$$157$$ −4.50000 + 7.79423i −0.359139 + 0.622047i −0.987817 0.155618i $$-0.950263\pi$$
0.628678 + 0.777666i $$0.283596\pi$$
$$158$$ 5.00000 + 8.66025i 0.397779 + 0.688973i
$$159$$ −11.0000 −0.872357
$$160$$ −1.00000 −0.0790569
$$161$$ 17.5000 + 30.3109i 1.37919 + 2.38883i
$$162$$ 0.500000 + 0.866025i 0.0392837 + 0.0680414i
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ −5.00000 −0.390434
$$165$$ 0.500000 + 0.866025i 0.0389249 + 0.0674200i
$$166$$ −5.00000 + 8.66025i −0.388075 + 0.672166i
$$167$$ −10.5000 18.1865i −0.812514 1.40732i −0.911099 0.412188i $$-0.864765\pi$$
0.0985846 0.995129i $$-0.468568\pi$$
$$168$$ 2.50000 4.33013i 0.192879 0.334077i
$$169$$ −11.5000 + 19.9186i −0.884615 + 1.53220i
$$170$$ −4.00000 −0.306786
$$171$$ 4.00000 1.73205i 0.305888 0.132453i
$$172$$ 6.00000 0.457496
$$173$$ 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i $$-0.722185\pi$$
0.984828 + 0.173534i $$0.0555188\pi$$
$$174$$ −3.00000 + 5.19615i −0.227429 + 0.393919i
$$175$$ 2.50000 + 4.33013i 0.188982 + 0.327327i
$$176$$ −0.500000 + 0.866025i −0.0376889 + 0.0652791i
$$177$$ −4.00000 6.92820i −0.300658 0.520756i
$$178$$ −13.0000 −0.974391
$$179$$ 7.00000 0.523205 0.261602 0.965176i $$-0.415749\pi$$
0.261602 + 0.965176i $$0.415749\pi$$
$$180$$ −0.500000 0.866025i −0.0372678 0.0645497i
$$181$$ −9.00000 15.5885i −0.668965 1.15868i −0.978194 0.207693i $$-0.933404\pi$$
0.309229 0.950988i $$-0.399929\pi$$
$$182$$ 30.0000 2.22375
$$183$$ 4.00000 0.295689
$$184$$ 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
$$189$$ 5.00000 0.363696
$$190$$ −4.00000 + 1.73205i −0.290191 + 0.125656i
$$191$$ −14.0000 −1.01300 −0.506502 0.862239i $$-0.669062\pi$$
−0.506502 + 0.862239i $$0.669062\pi$$
$$192$$ 0.500000 0.866025i 0.0360844 0.0625000i
$$193$$ 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i $$-0.787349\pi$$
0.928986 + 0.370116i $$0.120682\pi$$
$$194$$ 1.00000 + 1.73205i 0.0717958 + 0.124354i
$$195$$ 3.00000 5.19615i 0.214834 0.372104i
$$196$$ −9.00000 15.5885i −0.642857 1.11346i
$$197$$ 1.00000 0.0712470 0.0356235 0.999365i $$-0.488658\pi$$
0.0356235 + 0.999365i $$0.488658\pi$$
$$198$$ −1.00000 −0.0710669
$$199$$ 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i $$-0.121385\pi$$
−0.786389 + 0.617731i $$0.788052\pi$$
$$200$$ 0.500000 + 0.866025i 0.0353553 + 0.0612372i
$$201$$ −12.0000 −0.846415
$$202$$ −2.00000 −0.140720
$$203$$ 15.0000 + 25.9808i 1.05279 + 1.82349i
$$204$$ 2.00000 3.46410i 0.140028 0.242536i
$$205$$ 2.50000 + 4.33013i 0.174608 + 0.302429i
$$206$$ 7.50000 12.9904i 0.522550 0.905083i
$$207$$ −3.50000 + 6.06218i −0.243267 + 0.421350i
$$208$$ 6.00000 0.416025
$$209$$ −0.500000 + 4.33013i −0.0345857 + 0.299521i
$$210$$ −5.00000 −0.345033
$$211$$ −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i $$-0.981011\pi$$
0.550743 + 0.834675i $$0.314345\pi$$
$$212$$ −5.50000 + 9.52628i −0.377742 + 0.654268i
$$213$$ 1.00000 + 1.73205i 0.0685189 + 0.118678i
$$214$$ −2.00000 + 3.46410i −0.136717 + 0.236801i
$$215$$ −3.00000 5.19615i −0.204598 0.354375i
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ −8.00000 13.8564i −0.541828 0.938474i
$$219$$ −1.00000 1.73205i −0.0675737 0.117041i
$$220$$ 1.00000 0.0674200
$$221$$ 24.0000 1.61441
$$222$$ −3.50000 6.06218i −0.234905 0.406867i
$$223$$ 10.5000 18.1865i 0.703132 1.21786i −0.264229 0.964460i $$-0.585118\pi$$
0.967361 0.253401i $$-0.0815490\pi$$
$$224$$ −2.50000 4.33013i −0.167038 0.289319i
$$225$$ −0.500000 + 0.866025i −0.0333333 + 0.0577350i
$$226$$ 2.00000 3.46410i 0.133038 0.230429i
$$227$$ 2.00000 0.132745 0.0663723 0.997795i $$-0.478857\pi$$
0.0663723 + 0.997795i $$0.478857\pi$$
$$228$$ 0.500000 4.33013i 0.0331133 0.286770i
$$229$$ 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
$$231$$ −2.50000 + 4.33013i −0.164488 + 0.284901i
$$232$$ 3.00000 + 5.19615i 0.196960 + 0.341144i
$$233$$ 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i $$-0.632615\pi$$
0.994283 0.106773i $$-0.0340517\pi$$
$$234$$ 3.00000 + 5.19615i 0.196116 + 0.339683i
$$235$$ −8.00000 −0.521862
$$236$$ −8.00000 −0.520756
$$237$$ 5.00000 + 8.66025i 0.324785 + 0.562544i
$$238$$ −10.0000 17.3205i −0.648204 1.12272i
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ −1.00000 −0.0645497
$$241$$ 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i $$0.149261\pi$$
−0.0546547 + 0.998505i $$0.517406\pi$$
$$242$$ −5.00000 + 8.66025i −0.321412 + 0.556702i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ 2.00000 3.46410i 0.128037 0.221766i
$$245$$ −9.00000 + 15.5885i −0.574989 + 0.995910i
$$246$$ −5.00000 −0.318788
$$247$$ 24.0000 10.3923i 1.52708 0.661247i
$$248$$ 0 0
$$249$$ −5.00000 + 8.66025i −0.316862 + 0.548821i
$$250$$ 0.500000 0.866025i 0.0316228 0.0547723i
$$251$$ −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i $$-0.290301\pi$$
−0.990876 + 0.134778i $$0.956968\pi$$
$$252$$ 2.50000 4.33013i 0.157485 0.272772i
$$253$$ −3.50000 6.06218i −0.220043 0.381126i
$$254$$ 5.00000 0.313728
$$255$$ −4.00000 −0.250490
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i $$-0.976928\pi$$
0.435970 0.899961i $$-0.356405\pi$$
$$258$$ 6.00000 0.373544
$$259$$ −35.0000 −2.17479
$$260$$ −3.00000 5.19615i −0.186052 0.322252i
$$261$$ −3.00000 + 5.19615i −0.185695 + 0.321634i
$$262$$ −1.50000 2.59808i −0.0926703 0.160510i
$$263$$ −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i $$0.390834\pi$$
−0.983728 + 0.179664i $$0.942499\pi$$
$$264$$ −0.500000 + 0.866025i −0.0307729 + 0.0533002i
$$265$$ 11.0000 0.675725
$$266$$ −17.5000 12.9904i −1.07299 0.796491i
$$267$$ −13.0000 −0.795587
$$268$$ −6.00000 + 10.3923i −0.366508 + 0.634811i
$$269$$ −16.0000 + 27.7128i −0.975537 + 1.68968i −0.297386 + 0.954757i $$0.596115\pi$$
−0.678151 + 0.734923i $$0.737218\pi$$
$$270$$ −0.500000 0.866025i −0.0304290 0.0527046i
$$271$$ −1.00000 + 1.73205i −0.0607457 + 0.105215i −0.894799 0.446469i $$-0.852681\pi$$
0.834053 + 0.551684i $$0.186015\pi$$
$$272$$ −2.00000 3.46410i −0.121268 0.210042i
$$273$$ 30.0000 1.81568
$$274$$ 12.0000 0.724947
$$275$$ −0.500000 0.866025i −0.0301511 0.0522233i
$$276$$ 3.50000 + 6.06218i 0.210675 + 0.364900i
$$277$$ −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 $$-0.0602575\pi$$
−0.654033 + 0.756466i $$0.726924\pi$$
$$282$$ 4.00000 6.92820i 0.238197 0.412568i
$$283$$ −11.0000 + 19.0526i −0.653882 + 1.13256i 0.328291 + 0.944577i $$0.393527\pi$$
−0.982173 + 0.187980i $$0.939806\pi$$
$$284$$ 2.00000 0.118678
$$285$$ −4.00000 + 1.73205i −0.236940 + 0.102598i
$$286$$ −6.00000 −0.354787
$$287$$ −12.5000 + 21.6506i −0.737852 + 1.27800i
$$288$$ 0.500000 0.866025i 0.0294628 0.0510310i
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ 3.00000 5.19615i 0.176166 0.305129i
$$291$$ 1.00000 + 1.73205i 0.0586210 + 0.101535i
$$292$$ −2.00000 −0.117041
$$293$$ 5.00000 0.292103 0.146052 0.989277i $$-0.453343\pi$$
0.146052 + 0.989277i $$0.453343\pi$$
$$294$$ −9.00000 15.5885i −0.524891 0.909137i
$$295$$ 4.00000 + 6.92820i 0.232889 + 0.403376i
$$296$$ −7.00000 −0.406867
$$297$$ −1.00000 −0.0580259
$$298$$ −2.00000 3.46410i −0.115857 0.200670i
$$299$$ −21.0000 + 36.3731i −1.21446 + 2.10351i
$$300$$ 0.500000 + 0.866025i 0.0288675 + 0.0500000i
$$301$$ 15.0000 25.9808i 0.864586 1.49751i
$$302$$ −10.0000 + 17.3205i −0.575435 + 0.996683i
$$303$$ −2.00000 −0.114897
$$304$$ −3.50000 2.59808i −0.200739 0.149010i
$$305$$ −4.00000 −0.229039
$$306$$ 2.00000 3.46410i 0.114332 0.198030i
$$307$$ −9.00000 + 15.5885i −0.513657 + 0.889680i 0.486217 + 0.873838i $$0.338376\pi$$
−0.999875 + 0.0158424i $$0.994957\pi$$
$$308$$ 2.50000 + 4.33013i 0.142451 + 0.246732i
$$309$$ 7.50000 12.9904i 0.426660 0.738997i
$$310$$ 0 0
$$311$$ −20.0000 −1.13410 −0.567048 0.823685i $$-0.691915\pi$$
−0.567048 + 0.823685i $$0.691915\pi$$
$$312$$ 6.00000 0.339683
$$313$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$314$$ 4.50000 + 7.79423i 0.253950 + 0.439854i
$$315$$ −5.00000 −0.281718
$$316$$ 10.0000 0.562544
$$317$$ −1.50000 2.59808i −0.0842484 0.145922i 0.820822 0.571184i $$-0.193516\pi$$
−0.905071 + 0.425261i $$0.860182\pi$$
$$318$$ −5.50000 + 9.52628i −0.308425 + 0.534207i
$$319$$ −3.00000 5.19615i −0.167968 0.290929i
$$320$$ −0.500000 + 0.866025i −0.0279508 + 0.0484123i
$$321$$ −2.00000 + 3.46410i −0.111629 + 0.193347i
$$322$$ 35.0000 1.95047
$$323$$ −14.0000 10.3923i −0.778981 0.578243i
$$324$$ 1.00000 0.0555556
$$325$$ −3.00000 + 5.19615i −0.166410 + 0.288231i
$$326$$ −5.00000 + 8.66025i −0.276924 + 0.479647i
$$327$$ −8.00000 13.8564i −0.442401 0.766261i
$$328$$ −2.50000 + 4.33013i −0.138039 + 0.239091i
$$329$$ −20.0000 34.6410i −1.10264 1.90982i
$$330$$ 1.00000 0.0550482
$$331$$ 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
$$333$$ −3.50000 6.06218i −0.191799 0.332205i
$$334$$ −21.0000 −1.14907
$$335$$ 12.0000 0.655630
$$336$$ −2.50000 4.33013i −0.136386 0.236228i
$$337$$ −1.00000 + 1.73205i −0.0544735 + 0.0943508i −0.891976 0.452082i $$-0.850681\pi$$
0.837503 + 0.546433i $$0.184015\pi$$
$$338$$ 11.5000 + 19.9186i 0.625518 + 1.08343i
$$339$$ 2.00000 3.46410i 0.108625 0.188144i
$$340$$ −2.00000 + 3.46410i −0.108465 + 0.187867i
$$341$$ 0 0
$$342$$ 0.500000 4.33013i 0.0270369 0.234146i
$$343$$ −55.0000 −2.96972
$$344$$ 3.00000 5.19615i 0.161749 0.280158i
$$345$$ 3.50000 6.06218i 0.188434 0.326377i
$$346$$ −4.50000 7.79423i −0.241921 0.419020i
$$347$$ 1.00000 1.73205i 0.0536828 0.0929814i −0.837935 0.545770i $$-0.816237\pi$$
0.891618 + 0.452788i $$0.149571\pi$$
$$348$$ 3.00000 + 5.19615i 0.160817 + 0.278543i
$$349$$ 16.0000 0.856460 0.428230 0.903670i $$-0.359137\pi$$
0.428230 + 0.903670i $$0.359137\pi$$
$$350$$ 5.00000 0.267261
$$351$$ 3.00000 + 5.19615i 0.160128 + 0.277350i
$$352$$ 0.500000 + 0.866025i 0.0266501 + 0.0461593i
$$353$$ 36.0000 1.91609 0.958043 0.286623i $$-0.0925328\pi$$
0.958043 + 0.286623i $$0.0925328\pi$$
$$354$$ −8.00000 −0.425195
$$355$$ −1.00000 1.73205i −0.0530745 0.0919277i
$$356$$ −6.50000 + 11.2583i −0.344499 + 0.596690i
$$357$$ −10.0000 17.3205i −0.529256 0.916698i
$$358$$ 3.50000 6.06218i 0.184981 0.320396i
$$359$$ 9.00000 15.5885i 0.475002 0.822727i −0.524588 0.851356i $$-0.675781\pi$$
0.999590 + 0.0286287i $$0.00911406\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ −18.5000 4.33013i −0.973684 0.227901i
$$362$$ −18.0000 −0.946059
$$363$$ −5.00000 + 8.66025i −0.262432 + 0.454545i
$$364$$ 15.0000 25.9808i 0.786214 1.36176i
$$365$$ 1.00000 + 1.73205i 0.0523424 + 0.0906597i
$$366$$ 2.00000 3.46410i 0.104542 0.181071i
$$367$$ 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i $$-0.133375\pi$$
−0.809093 + 0.587680i $$0.800041\pi$$
$$368$$ 7.00000 0.364900
$$369$$ −5.00000 −0.260290
$$370$$ 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
$$375$$ 0.500000 0.866025i 0.0258199 0.0447214i
$$376$$ −4.00000 6.92820i −0.206284 0.357295i
$$377$$ −18.0000 + 31.1769i −0.927047 + 1.60569i
$$378$$ 2.50000 4.33013i 0.128586 0.222718i
$$379$$ −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
$$381$$ 5.00000 0.256158
$$382$$ −7.00000 + 12.1244i −0.358151 + 0.620336i
$$383$$ −16.0000 + 27.7128i −0.817562 + 1.41606i 0.0899119 + 0.995950i $$0.471341\pi$$
−0.907474 + 0.420109i $$0.861992\pi$$
$$384$$ −0.500000 0.866025i −0.0255155 0.0441942i
$$385$$ 2.50000 4.33013i 0.127412 0.220684i
$$386$$ −2.00000 3.46410i −0.101797 0.176318i
$$387$$ 6.00000 0.304997
$$388$$ 2.00000 0.101535
$$389$$ 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i $$-0.0850816\pi$$
−0.710980 + 0.703213i $$0.751748\pi$$
$$390$$ −3.00000 5.19615i −0.151911 0.263117i
$$391$$ 28.0000 1.41602
$$392$$ −18.0000 −0.909137
$$393$$ −1.50000 2.59808i −0.0756650 0.131056i
$$394$$ 0.500000 0.866025i 0.0251896 0.0436297i
$$395$$ −5.00000 8.66025i −0.251577 0.435745i
$$396$$ −0.500000 + 0.866025i −0.0251259 + 0.0435194i
$$397$$ 16.5000 28.5788i 0.828111 1.43433i −0.0714068 0.997447i $$-0.522749\pi$$
0.899518 0.436884i $$-0.143918\pi$$
$$398$$ 4.00000 0.200502
$$399$$ −17.5000 12.9904i −0.876096 0.650332i
$$400$$ 1.00000 0.0500000
$$401$$ 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i $$-0.684957\pi$$
0.998350 + 0.0574304i $$0.0182907\pi$$
$$402$$ −6.00000 + 10.3923i −0.299253 + 0.518321i
$$403$$ 0 0
$$404$$ −1.00000 + 1.73205i −0.0497519 + 0.0861727i
$$405$$ −0.500000 0.866025i −0.0248452 0.0430331i
$$406$$ 30.0000 1.48888
$$407$$ 7.00000 0.346977
$$408$$ −2.00000 3.46410i −0.0990148 0.171499i
$$409$$ 1.50000 + 2.59808i 0.0741702 + 0.128467i 0.900725 0.434389i $$-0.143036\pi$$
−0.826555 + 0.562856i $$0.809703\pi$$
$$410$$ 5.00000 0.246932
$$411$$ 12.0000 0.591916
$$412$$ −7.50000 12.9904i −0.369498 0.639990i
$$413$$ −20.0000 + 34.6410i −0.984136 + 1.70457i
$$414$$ 3.50000 + 6.06218i 0.172016 + 0.297940i
$$415$$ 5.00000 8.66025i 0.245440 0.425115i
$$416$$ 3.00000 5.19615i 0.147087 0.254762i
$$417$$ 16.0000 0.783523
$$418$$ 3.50000 + 2.59808i 0.171191 + 0.127076i
$$419$$ −3.00000 −0.146560 −0.0732798 0.997311i $$-0.523347\pi$$
−0.0732798 + 0.997311i $$0.523347\pi$$
$$420$$ −2.50000 + 4.33013i −0.121988 + 0.211289i
$$421$$ 4.00000 6.92820i 0.194948 0.337660i −0.751935 0.659237i $$-0.770879\pi$$
0.946883 + 0.321577i $$0.104213\pi$$
$$422$$ 6.50000 + 11.2583i 0.316415 + 0.548047i
$$423$$ 4.00000 6.92820i 0.194487 0.336861i
$$424$$ 5.50000 + 9.52628i 0.267104 + 0.462637i
$$425$$ 4.00000 0.194029
$$426$$ 2.00000 0.0969003
$$427$$ −10.0000 17.3205i −0.483934 0.838198i
$$428$$ 2.00000 + 3.46410i 0.0966736 + 0.167444i
$$429$$ −6.00000 −0.289683
$$430$$ −6.00000 −0.289346
$$431$$ 2.00000 + 3.46410i 0.0963366 + 0.166860i 0.910166 0.414244i $$-0.135954\pi$$
−0.813829 + 0.581104i $$0.802621\pi$$
$$432$$ 0.500000 0.866025i 0.0240563 0.0416667i
$$433$$ −3.00000 5.19615i −0.144171 0.249711i 0.784892 0.619632i $$-0.212718\pi$$
−0.929063 + 0.369921i $$0.879385\pi$$
$$434$$ 0 0
$$435$$ 3.00000 5.19615i 0.143839 0.249136i
$$436$$ −16.0000 −0.766261
$$437$$ 28.0000 12.1244i 1.33942 0.579987i
$$438$$ −2.00000 −0.0955637
$$439$$ 16.0000 27.7128i 0.763638 1.32266i −0.177325 0.984152i $$-0.556744\pi$$
0.940963 0.338508i $$-0.109922\pi$$
$$440$$ 0.500000 0.866025i 0.0238366 0.0412861i
$$441$$ −9.00000 15.5885i −0.428571 0.742307i
$$442$$ 12.0000 20.7846i 0.570782 0.988623i
$$443$$ −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i $$-0.973557\pi$$
0.426414 0.904528i $$-0.359777\pi$$
$$444$$ −7.00000 −0.332205
$$445$$ 13.0000 0.616259
$$446$$ −10.5000 18.1865i −0.497189 0.861157i
$$447$$ −2.00000 3.46410i −0.0945968 0.163846i
$$448$$ −5.00000 −0.236228
$$449$$ −39.0000 −1.84052 −0.920262 0.391303i $$-0.872024\pi$$
−0.920262 + 0.391303i $$0.872024\pi$$
$$450$$ 0.500000 + 0.866025i 0.0235702 + 0.0408248i
$$451$$ 2.50000 4.33013i 0.117720 0.203898i
$$452$$ −2.00000 3.46410i −0.0940721 0.162938i
$$453$$ −10.0000 + 17.3205i −0.469841 + 0.813788i
$$454$$ 1.00000 1.73205i 0.0469323 0.0812892i
$$455$$ −30.0000 −1.40642
$$456$$ −3.50000 2.59808i −0.163903 0.121666i
$$457$$ 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
$$459$$ 2.00000 3.46410i 0.0933520 0.161690i
$$460$$ −3.50000 6.06218i −0.163188 0.282650i
$$461$$ 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i $$-0.788712\pi$$
0.927392 + 0.374091i $$0.122045\pi$$
$$462$$ 2.50000 + 4.33013i 0.116311 + 0.201456i
$$463$$ −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 $$-0.158068\pi$$
0.879215 + 0.476425i $$0.158068\pi$$
$$468$$ 6.00000 0.277350
$$469$$ 30.0000 + 51.9615i 1.38527 + 2.39936i
$$470$$ −4.00000 + 6.92820i −0.184506 + 0.319574i
$$471$$ 4.50000 + 7.79423i 0.207349 + 0.359139i
$$472$$ −4.00000 + 6.92820i −0.184115 + 0.318896i
$$473$$ −3.00000 + 5.19615i −0.137940 + 0.238919i
$$474$$ 10.0000 0.459315
$$475$$ 4.00000 1.73205i 0.183533 0.0794719i
$$476$$ −20.0000 −0.916698
$$477$$ −5.50000 + 9.52628i −0.251828 + 0.436178i
$$478$$ 0 0
$$479$$ −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i $$-0.757551\pi$$
−0.235833 0.971794i $$-0.575782\pi$$
$$480$$ −0.500000 + 0.866025i −0.0228218 + 0.0395285i
$$481$$ −21.0000 36.3731i −0.957518 1.65847i
$$482$$ 26.0000 1.18427
$$483$$ 35.0000 1.59256
$$484$$ 5.00000 + 8.66025i 0.227273 + 0.393648i
$$485$$ −1.00000 1.73205i −0.0454077 0.0786484i
$$486$$ 1.00000 0.0453609
$$487$$ −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
$$489$$ −5.00000 + 8.66025i −0.226108 + 0.391630i
$$490$$ 9.00000 + 15.5885i 0.406579 + 0.704215i
$$491$$ 16.5000 28.5788i 0.744635 1.28974i −0.205731 0.978609i $$-0.565957\pi$$
0.950365 0.311136i $$-0.100710\pi$$
$$492$$ −2.50000 + 4.33013i −0.112709 + 0.195217i
$$493$$ 24.0000 1.08091
$$494$$ 3.00000 25.9808i 0.134976 1.16893i
$$495$$ 1.00000 0.0449467
$$496$$ 0 0
$$497$$ 5.00000 8.66025i 0.224281 0.388465i
$$498$$ 5.00000 + 8.66025i 0.224055 + 0.388075i
$$499$$ 3.50000 6.06218i 0.156682 0.271380i −0.776989 0.629515i $$-0.783254\pi$$
0.933670 + 0.358134i $$0.116587\pi$$
$$500$$ −0.500000 0.866025i −0.0223607 0.0387298i
$$501$$ −21.0000 −0.938211
$$502$$ −12.0000 −0.535586
$$503$$ −0.500000 0.866025i −0.0222939 0.0386142i 0.854663 0.519183i $$-0.173764\pi$$
−0.876957 + 0.480569i $$0.840430\pi$$
$$504$$ −2.50000 4.33013i −0.111359 0.192879i
$$505$$ 2.00000 0.0889988
$$506$$ −7.00000 −0.311188
$$507$$ 11.5000 + 19.9186i 0.510733 + 0.884615i
$$508$$ 2.50000 4.33013i 0.110920 0.192118i
$$509$$ −1.00000 1.73205i −0.0443242 0.0767718i 0.843012 0.537895i $$-0.180780\pi$$
−0.887336 + 0.461123i $$0.847447\pi$$
$$510$$ −2.00000 + 3.46410i −0.0885615 + 0.153393i
$$511$$ −5.00000 + 8.66025i −0.221187 + 0.383107i
$$512$$ −1.00000 −0.0441942
$$513$$ 0.500000 4.33013i 0.0220755 0.191180i
$$514$$ −18.0000 −0.793946
$$515$$ −7.50000 + 12.9904i −0.330489 + 0.572425i
$$516$$ 3.00000 5.19615i 0.132068 0.228748i
$$517$$ 4.00000 + 6.92820i 0.175920 + 0.304702i
$$518$$ −17.5000 + 30.3109i −0.768906 + 1.33178i
$$519$$ −4.50000 7.79423i −0.197528 0.342129i
$$520$$ −6.00000 −0.263117
$$521$$ −14.0000 −0.613351 −0.306676 0.951814i $$-0.599217\pi$$
−0.306676 + 0.951814i $$0.599217\pi$$
$$522$$ 3.00000 + 5.19615i 0.131306 + 0.227429i
$$523$$ 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i $$-0.0676463\pi$$
−0.671414 + 0.741082i $$0.734313\pi$$
$$524$$ −3.00000 −0.131056
$$525$$ 5.00000 0.218218
$$526$$ 10.5000 + 18.1865i 0.457822 + 0.792971i
$$527$$ 0 0
$$528$$ 0.500000 + 0.866025i 0.0217597 + 0.0376889i
$$529$$ −13.0000 + 22.5167i −0.565217 + 0.978985i
$$530$$ 5.50000 9.52628i 0.238905 0.413795i
$$531$$ −8.00000 −0.347170
$$532$$ −20.0000 + 8.66025i −0.867110 + 0.375470i
$$533$$ −30.0000 −1.29944
$$534$$ −6.50000 + 11.2583i −0.281283 + 0.487196i
$$535$$ 2.00000 3.46410i 0.0864675 0.149766i
$$536$$ 6.00000 + 10.3923i 0.259161 + 0.448879i
$$537$$ 3.50000 6.06218i 0.151036 0.261602i
$$538$$ 16.0000 + 27.7128i 0.689809 + 1.19478i
$$539$$ 18.0000 0.775315
$$540$$ −1.00000 −0.0430331
$$541$$ −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i $$-0.221681\pi$$
−0.939110 + 0.343617i $$0.888348\pi$$
$$542$$ 1.00000 + 1.73205i 0.0429537 + 0.0743980i
$$543$$ −18.0000 −0.772454
$$544$$ −4.00000 −0.171499
$$545$$ 8.00000 + 13.8564i 0.342682 + 0.593543i
$$546$$ 15.0000 25.9808i 0.641941 1.11187i
$$547$$ −7.00000 12.1244i −0.299298 0.518400i 0.676677 0.736280i $$-0.263419\pi$$
−0.975976 + 0.217880i $$0.930086\pi$$
$$548$$ 6.00000 10.3923i 0.256307 0.443937i
$$549$$ 2.00000 3.46410i 0.0853579 0.147844i
$$550$$ −1.00000 −0.0426401
$$551$$ 24.0000 10.3923i 1.02243 0.442727i
$$552$$ 7.00000 0.297940
$$553$$ 25.0000 43.3013i 1.06311 1.84136i
$$554$$ −7.00000 + 12.1244i −0.297402 + 0.515115i
$$555$$ 3.50000 + 6.06218i 0.148567 + 0.257325i
$$556$$ 8.00000 13.8564i 0.339276 0.587643i
$$557$$ −0.500000 0.866025i −0.0211857 0.0366947i 0.855238 0.518235i $$-0.173411\pi$$
−0.876424 + 0.481540i $$0.840077\pi$$
$$558$$ 0 0
$$559$$ 36.0000 1.52264
$$560$$ 2.50000 + 4.33013i 0.105644 + 0.182981i
$$561$$ 2.00000 + 3.46410i 0.0844401 + 0.146254i
$$562$$ 11.0000 0.464007
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ −4.00000 6.92820i −0.168430 0.291730i
$$565$$ −2.00000 + 3.46410i −0.0841406 + 0.145736i
$$566$$ 11.0000 + 19.0526i 0.462364 + 0.800839i
$$567$$ 2.50000 4.33013i 0.104990 0.181848i
$$568$$ 1.00000 1.73205i 0.0419591 0.0726752i
$$569$$ 33.0000 1.38343 0.691716 0.722170i $$-0.256855\pi$$
0.691716 + 0.722170i $$0.256855\pi$$
$$570$$ −0.500000 + 4.33013i −0.0209427 + 0.181369i
$$571$$ 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
$$573$$ −7.00000 + 12.1244i −0.292429 + 0.506502i
$$574$$ 12.5000 + 21.6506i 0.521740 + 0.903680i
$$575$$ −3.50000 + 6.06218i −0.145960 + 0.252810i
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −32.0000 −1.33218 −0.666089 0.745873i $$-0.732033\pi$$
−0.666089 + 0.745873i $$0.732033\pi$$
$$578$$ 1.00000 0.0415945
$$579$$ −2.00000 3.46410i −0.0831172 0.143963i
$$580$$ −3.00000 5.19615i −0.124568 0.215758i
$$581$$ 50.0000 2.07435
$$582$$ 2.00000 0.0829027
$$583$$ −5.50000 9.52628i −0.227787 0.394538i
$$584$$ −1.00000 + 1.73205i −0.0413803 + 0.0716728i
$$585$$ −3.00000 5.19615i −0.124035 0.214834i
$$586$$ 2.50000 4.33013i 0.103274 0.178876i
$$587$$ 10.0000 17.3205i 0.412744 0.714894i −0.582445 0.812870i $$-0.697904\pi$$
0.995189 + 0.0979766i $$0.0312370\pi$$
$$588$$ −18.0000 −0.742307
$$589$$ 0 0
$$590$$ 8.00000 0.329355
$$591$$ 0.500000 0.866025i 0.0205673 0.0356235i
$$592$$ −3.50000 + 6.06218i −0.143849 + 0.249154i
$$593$$ −11.0000 19.0526i −0.451716 0.782395i 0.546777 0.837278i $$-0.315855\pi$$
−0.998493 + 0.0548835i $$0.982521\pi$$
$$594$$ −0.500000 + 0.866025i −0.0205152 + 0.0355335i
$$595$$ 10.0000 + 17.3205i 0.409960 + 0.710072i
$$596$$ −4.00000 −0.163846
$$597$$ 4.00000 0.163709
$$598$$ 21.0000 + 36.3731i 0.858754 + 1.48741i
$$599$$ −4.00000 6.92820i −0.163436 0.283079i 0.772663 0.634816i $$-0.218924\pi$$
−0.936099 + 0.351738i $$0.885591\pi$$
$$600$$ 1.00000 0.0408248
$$601$$ −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
$$603$$ −6.00000 + 10.3923i −0.244339 + 0.423207i
$$604$$ 10.0000 + 17.3205i 0.406894 + 0.704761i
$$605$$ 5.00000 8.66025i 0.203279 0.352089i
$$606$$ −1.00000 + 1.73205i −0.0406222 + 0.0703598i
$$607$$ −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
$$609$$ 30.0000 1.21566
$$610$$ −2.00000 + 3.46410i −0.0809776 + 0.140257i
$$611$$ 24.0000 41.5692i 0.970936 1.68171i
$$612$$ −2.00000 3.46410i −0.0808452 0.140028i
$$613$$ −17.5000 + 30.3109i −0.706818 + 1.22425i 0.259213 + 0.965820i $$0.416537\pi$$
−0.966031 + 0.258425i $$0.916796\pi$$
$$614$$ 9.00000 + 15.5885i 0.363210 + 0.629099i
$$615$$ 5.00000 0.201619
$$616$$ 5.00000 0.201456
$$617$$ −24.0000 41.5692i −0.966204 1.67351i −0.706346 0.707867i $$-0.749658\pi$$
−0.259858 0.965647i $$-0.583676\pi$$
$$618$$ −7.50000 12.9904i −0.301694 0.522550i
$$619$$ 43.0000 1.72832 0.864158 0.503221i $$-0.167852\pi$$
0.864158 + 0.503221i $$0.167852\pi$$
$$620$$ 0 0
$$621$$ 3.50000 + 6.06218i 0.140450 + 0.243267i
$$622$$ −10.0000 + 17.3205i −0.400963 + 0.694489i
$$623$$ 32.5000 + 56.2917i 1.30209 + 2.25528i
$$624$$ 3.00000 5.19615i 0.120096 0.208013i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 3.50000 + 2.59808i 0.139777 + 0.103757i
$$628$$ 9.00000 0.359139
$$629$$ −14.0000 + 24.2487i −0.558217 + 0.966859i
$$630$$ −2.50000 + 4.33013i −0.0996024 + 0.172516i
$$631$$ −19.0000 32.9090i −0.756378 1.31009i −0.944686 0.327975i $$-0.893634\pi$$
0.188308 0.982110i $$-0.439700\pi$$
$$632$$ 5.00000 8.66025i 0.198889 0.344486i
$$633$$ 6.50000 + 11.2583i 0.258352 + 0.447478i
$$634$$ −3.00000 −0.119145
$$635$$ −5.00000 −0.198419
$$636$$ 5.50000 + 9.52628i 0.218089 + 0.377742i
$$637$$ −54.0000 93.5307i −2.13956 3.70582i
$$638$$ −6.00000 −0.237542
$$639$$ 2.00000 0.0791188
$$640$$ 0.500000 + 0.866025i 0.0197642 + 0.0342327i
$$641$$ 13.0000 22.5167i 0.513469 0.889355i −0.486409 0.873731i $$-0.661693\pi$$
0.999878 0.0156233i $$-0.00497325\pi$$
$$642$$ 2.00000 + 3.46410i 0.0789337 + 0.136717i
$$643$$ 22.0000 38.1051i 0.867595 1.50272i 0.00314839 0.999995i $$-0.498998\pi$$
0.864447 0.502724i $$-0.167669\pi$$
$$644$$ 17.5000 30.3109i 0.689597 1.19442i
$$645$$ −6.00000 −0.236250
$$646$$ −16.0000 + 6.92820i −0.629512 + 0.272587i
$$647$$ 3.00000 0.117942 0.0589711 0.998260i $$-0.481218\pi$$
0.0589711 + 0.998260i $$0.481218\pi$$
$$648$$ 0.500000 0.866025i 0.0196419 0.0340207i
$$649$$ 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 $$-0.443652\pi$$
0.176099 + 0.984373i $$0.443652\pi$$
$$654$$ −16.0000 −0.625650
$$655$$ 1.50000 + 2.59808i 0.0586098 + 0.101515i
$$656$$ 2.50000 + 4.33013i 0.0976086 + 0.169063i
$$657$$ −2.00000 −0.0780274
$$658$$ −40.0000 −1.55936
$$659$$ 5.50000 + 9.52628i 0.214250 + 0.371091i 0.953040 0.302844i $$-0.0979361\pi$$
−0.738791 + 0.673935i $$0.764603\pi$$
$$660$$ 0.500000 0.866025i 0.0194625 0.0337100i
$$661$$ 10.0000 + 17.3205i 0.388955 + 0.673690i 0.992309 0.123784i $$-0.0395028\pi$$
−0.603354 + 0.797473i $$0.706170\pi$$
$$662$$ 7.50000 12.9904i 0.291496 0.504885i
$$663$$ 12.0000 20.7846i 0.466041 0.807207i
$$664$$ 10.0000 0.388075
$$665$$ 17.5000 + 12.9904i 0.678621 + 0.503745i
$$666$$ −7.00000 −0.271244
$$667$$ −21.0000 + 36.3731i −0.813123 + 1.40837i
$$668$$ −10.5000 + 18.1865i −0.406257 + 0.703658i
$$669$$ −10.5000 18.1865i −0.405953 0.703132i
$$670$$ 6.00000 10.3923i 0.231800 0.401490i
$$671$$ 2.00000 + 3.46410i 0.0772091 + 0.133730i
$$672$$ −5.00000 −0.192879
$$673$$ −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
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ 23.0000 0.884615
$$677$$ 21.0000 0.807096 0.403548 0.914959i $$-0.367777\pi$$
0.403548 + 0.914959i $$0.367777\pi$$
$$678$$ −2.00000 3.46410i −0.0768095 0.133038i
$$679$$ 5.00000 8.66025i 0.191882 0.332350i
$$680$$ 2.00000 + 3.46410i 0.0766965 + 0.132842i
$$681$$ 1.00000 1.73205i 0.0383201 0.0663723i
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ −3.50000 2.59808i −0.133826 0.0993399i
$$685$$ −12.0000 −0.458496
$$686$$ −27.5000 + 47.6314i −1.04995 + 1.81858i
$$687$$ 5.00000 8.66025i 0.190762 0.330409i
$$688$$ −3.00000 5.19615i −0.114374 0.198101i
$$689$$ −33.0000 + 57.1577i −1.25720 + 2.17753i
$$690$$ −3.50000 6.06218i −0.133243 0.230783i
$$691$$ 1.00000 0.0380418 0.0190209 0.999819i $$-0.493945\pi$$
0.0190209 + 0.999819i $$0.493945\pi$$
$$692$$ −9.00000 −0.342129
$$693$$ 2.50000 + 4.33013i 0.0949671 + 0.164488i
$$694$$ −1.00000 1.73205i −0.0379595 0.0657477i
$$695$$ −16.0000 −0.606915
$$696$$ 6.00000 0.227429
$$697$$ 10.0000 + 17.3205i 0.378777 + 0.656061i
$$698$$ 8.00000 13.8564i 0.302804 0.524473i
$$699$$ −9.00000 15.5885i −0.340411 0.589610i
$$700$$ 2.50000 4.33013i 0.0944911 0.163663i
$$701$$ −17.0000 + 29.4449i −0.642081 + 1.11212i 0.342886 + 0.939377i $$0.388595\pi$$
−0.984967 + 0.172740i $$0.944738\pi$$
$$702$$ 6.00000 0.226455
$$703$$ −3.50000 + 30.3109i −0.132005 + 1.14320i
$$704$$ 1.00000 0.0376889
$$705$$ −4.00000 + 6.92820i −0.150649 + 0.260931i
$$706$$ 18.0000 31.1769i 0.677439 1.17336i
$$707$$ 5.00000 + 8.66025i 0.188044 + 0.325702i
$$708$$ −4.00000 + 6.92820i −0.150329 + 0.260378i
$$709$$ 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i $$-0.142735\pi$$
−0.826023 + 0.563636i $$0.809402\pi$$
$$710$$ −2.00000 −0.0750587
$$711$$ 10.0000 0.375029
$$712$$ 6.50000 + 11.2583i 0.243598 + 0.421924i
$$713$$ 0 0
$$714$$ −20.0000 −0.748481
$$715$$ 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 −0.0848774 0.996391i $$-0.527050\pi$$
0.905339 0.424690i $$-0.139617\pi$$
$$720$$ −0.500000 + 0.866025i −0.0186339 + 0.0322749i
$$721$$ −75.0000 −2.79315
$$722$$ −13.0000 + 13.8564i −0.483810 + 0.515682i
$$723$$ 26.0000 0.966950
$$724$$ −9.00000 + 15.5885i −0.334482 + 0.579340i
$$725$$ −3.00000 + 5.19615i −0.111417 + 0.192980i
$$726$$ 5.00000 + 8.66025i 0.185567 + 0.321412i
$$727$$ −16.0000 + 27.7128i −0.593407 + 1.02781i 0.400362 + 0.916357i $$0.368884\pi$$
−0.993770 + 0.111454i $$0.964449\pi$$
$$728$$ −15.0000 25.9808i −0.555937 0.962911i
$$729$$ 1.00000 0.0370370
$$730$$ 2.00000 0.0740233
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ −2.00000 3.46410i −0.0739221 0.128037i
$$733$$ 19.0000 0.701781 0.350891 0.936416i $$-0.385879\pi$$
0.350891 + 0.936416i $$0.385879\pi$$
$$734$$ 4.00000 0.147643
$$735$$ 9.00000 + 15.5885i 0.331970 + 0.574989i
$$736$$ 3.50000 6.06218i 0.129012 0.223455i
$$737$$ −6.00000 10.3923i −0.221013 0.382805i
$$738$$ −2.50000 + 4.33013i −0.0920263 + 0.159394i
$$739$$ 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i $$-0.500993\pi$$
0.867581 0.497296i $$-0.165674\pi$$
$$740$$ 7.00000 0.257325
$$741$$ 3.00000 25.9808i 0.110208 0.954427i
$$742$$ 55.0000 2.01911
$$743$$ −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i $$-0.922060\pi$$
0.695024 + 0.718986i $$0.255394\pi$$
$$744$$ 0 0
$$745$$ 2.00000 + 3.46410i 0.0732743 + 0.126915i
$$746$$ 2.50000 4.33013i 0.0915315 0.158537i
$$747$$ 5.00000 + 8.66025i 0.182940 + 0.316862i
$$748$$ 4.00000 0.146254
$$749$$ 20.0000 0.730784
$$750$$ −0.500000 0.866025i −0.0182574 0.0316228i
$$751$$ −20.0000 34.6410i −0.729810 1.26407i −0.956963 0.290209i $$-0.906275\pi$$
0.227153 0.973859i $$-0.427058\pi$$
$$752$$ −8.00000 −0.291730
$$753$$ −12.0000 −0.437304
$$754$$ 18.0000 + 31.1769i 0.655521 + 1.13540i
$$755$$ 10.0000 17.3205i 0.363937 0.630358i
$$756$$ −2.50000 4.33013i −0.0909241 0.157485i
$$757$$ 6.50000 11.2583i 0.236247 0.409191i −0.723388 0.690442i $$-0.757416\pi$$
0.959634 + 0.281251i $$0.0907494\pi$$
$$758$$ −2.00000 + 3.46410i −0.0726433 + 0.125822i
$$759$$ −7.00000 −0.254084
$$760$$ 3.50000 + 2.59808i 0.126958 + 0.0942421i
$$761$$ −31.0000 −1.12375 −0.561875 0.827222i $$-0.689920\pi$$
−0.561875 + 0.827222i $$0.689920\pi$$
$$762$$ 2.50000 4.33013i 0.0905654 0.156864i
$$763$$ −40.0000 + 69.2820i −1.44810 + 2.50818i
$$764$$ 7.00000 + 12.1244i 0.253251 + 0.438644i
$$765$$ −2.00000 + 3.46410i −0.0723102 + 0.125245i
$$766$$ 16.0000 + 27.7128i 0.578103 + 1.00130i
$$767$$ −48.0000 −1.73318
$$768$$ −1.00000 −0.0360844
$$769$$ −3.00000 5.19615i −0.108183 0.187378i 0.806851 0.590755i $$-0.201170\pi$$
−0.915034 + 0.403376i $$0.867837\pi$$
$$770$$ −2.50000 4.33013i −0.0900937 0.156047i
$$771$$ −18.0000 −0.648254
$$772$$ −4.00000 −0.143963
$$773$$ 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i $$-0.0433959\pi$$
−0.613062 + 0.790034i $$0.710063\pi$$
$$774$$ 3.00000 5.19615i 0.107833 0.186772i
$$775$$ 0 0
$$776$$ 1.00000 1.73205i 0.0358979 0.0621770i
$$777$$ −17.5000 + 30.3109i −0.627809 + 1.08740i
$$778$$ 10.0000 0.358517