# Properties

 Label 570.2.f.d.341.7 Level $570$ Weight $2$ Character 570.341 Analytic conductor $4.551$ Analytic rank $0$ Dimension $8$ 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.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.7278137344.1 Defining polynomial: $$x^{8} - 2 x^{7} + x^{6} + 6 x^{5} - 20 x^{4} + 18 x^{3} + 9 x^{2} - 54 x + 81$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 341.7 Root $$-1.71731 + 0.225499i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.341 Dual form 570.2.f.d.341.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(1.71731 - 0.225499i) q^{12} -2.45100i q^{13} -0.631989 q^{14} +(-0.225499 - 1.71731i) q^{15} +1.00000 q^{16} +3.25363i q^{17} +(2.89830 - 0.774501i) q^{18} +(-2.43462 + 3.61561i) q^{19} -1.00000i q^{20} +(-1.08532 + 0.142513i) q^{21} -2.00000i q^{22} -0.812981i q^{23} +(1.71731 - 0.225499i) q^{24} -1.00000 q^{25} -2.45100i q^{26} +(4.80263 - 1.98362i) q^{27} -0.631989 q^{28} +3.43462 q^{29} +(-0.225499 - 1.71731i) q^{30} +7.16461i q^{31} +1.00000 q^{32} +(-0.450997 - 3.43462i) q^{33} +3.25363i q^{34} +0.631989i q^{35} +(2.89830 - 0.774501i) q^{36} +5.60526i q^{37} +(-2.43462 + 3.61561i) q^{38} +(-0.552696 - 4.20912i) q^{39} -1.00000i q^{40} -0.802629 q^{41} +(-1.08532 + 0.142513i) q^{42} -11.9672 q^{43} -2.00000i q^{44} +(-0.774501 - 2.89830i) q^{45} -0.812981i q^{46} -7.96724i q^{47} +(1.71731 - 0.225499i) q^{48} -6.60059 q^{49} -1.00000 q^{50} +(0.733688 + 5.58748i) q^{51} -2.45100i q^{52} +6.53262 q^{53} +(4.80263 - 1.98362i) q^{54} -2.00000 q^{55} -0.631989 q^{56} +(-3.36568 + 6.75812i) q^{57} +3.43462 q^{58} -2.09198 q^{59} +(-0.225499 - 1.71731i) q^{60} -2.70326 q^{61} +7.16461i q^{62} +(-1.83169 + 0.489476i) q^{63} +1.00000 q^{64} -2.45100 q^{65} +(-0.450997 - 3.43462i) q^{66} +14.9462i q^{67} +3.25363i q^{68} +(-0.183326 - 1.39614i) q^{69} +0.631989i q^{70} +6.16597 q^{71} +(2.89830 - 0.774501i) q^{72} -4.89461 q^{73} +5.60526i q^{74} +(-1.71731 + 0.225499i) q^{75} +(-2.43462 + 3.61561i) q^{76} +1.26398i q^{77} +(-0.552696 - 4.20912i) q^{78} -4.42859i q^{79} -1.00000i q^{80} +(7.80030 - 4.48948i) q^{81} -0.802629 q^{82} -5.86788i q^{83} +(-1.08532 + 0.142513i) q^{84} +3.25363 q^{85} -11.9672 q^{86} +(5.89830 - 0.774501i) q^{87} -2.00000i q^{88} -5.93339 q^{89} +(-0.774501 - 2.89830i) q^{90} +1.54900i q^{91} -0.812981i q^{92} +(1.61561 + 12.3039i) q^{93} -7.96724i q^{94} +(3.61561 + 2.43462i) q^{95} +(1.71731 - 0.225499i) q^{96} +3.26398i q^{97} -6.60059 q^{98} +(-1.54900 - 5.79660i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} + O(q^{10})$$ $$8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} - 2q^{12} + 4q^{14} + 8q^{16} + 2q^{18} + 12q^{19} - 2q^{21} - 2q^{24} - 8q^{25} + 16q^{27} + 4q^{28} - 4q^{29} + 8q^{32} + 2q^{36} + 12q^{38} - 22q^{39} + 16q^{41} - 2q^{42} - 40q^{43} - 8q^{45} - 2q^{48} + 4q^{49} - 8q^{50} + 18q^{51} + 28q^{53} + 16q^{54} - 16q^{55} + 4q^{56} - 30q^{57} - 4q^{58} - 4q^{59} + 16q^{61} - 34q^{63} + 8q^{64} - 16q^{65} - 2q^{69} + 24q^{71} + 2q^{72} - 4q^{73} + 2q^{75} + 12q^{76} - 22q^{78} + 34q^{81} + 16q^{82} - 2q^{84} - 40q^{86} + 26q^{87} - 88q^{89} - 8q^{90} - 24q^{93} - 8q^{95} - 2q^{96} + 4q^{98} - 16q^{99} + O(q^{100})$$

## Character values

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

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 1.71731 0.225499i 0.991489 0.130192i
$$4$$ 1.00000 0.500000
$$5$$ 1.00000i 0.447214i
$$6$$ 1.71731 0.225499i 0.701088 0.0920594i
$$7$$ −0.631989 −0.238869 −0.119435 0.992842i $$-0.538108\pi$$
−0.119435 + 0.992842i $$0.538108\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 2.89830 0.774501i 0.966100 0.258167i
$$10$$ 1.00000i 0.316228i
$$11$$ 2.00000i 0.603023i −0.953463 0.301511i $$-0.902509\pi$$
0.953463 0.301511i $$-0.0974911\pi$$
$$12$$ 1.71731 0.225499i 0.495744 0.0650958i
$$13$$ 2.45100i 0.679784i −0.940464 0.339892i $$-0.889609\pi$$
0.940464 0.339892i $$-0.110391\pi$$
$$14$$ −0.631989 −0.168906
$$15$$ −0.225499 1.71731i −0.0582235 0.443407i
$$16$$ 1.00000 0.250000
$$17$$ 3.25363i 0.789120i 0.918870 + 0.394560i $$0.129103\pi$$
−0.918870 + 0.394560i $$0.870897\pi$$
$$18$$ 2.89830 0.774501i 0.683136 0.182552i
$$19$$ −2.43462 + 3.61561i −0.558540 + 0.829478i
$$20$$ 1.00000i 0.223607i
$$21$$ −1.08532 + 0.142513i −0.236836 + 0.0310988i
$$22$$ 2.00000i 0.426401i
$$23$$ 0.812981i 0.169518i −0.996401 0.0847591i $$-0.972988\pi$$
0.996401 0.0847591i $$-0.0270121\pi$$
$$24$$ 1.71731 0.225499i 0.350544 0.0460297i
$$25$$ −1.00000 −0.200000
$$26$$ 2.45100i 0.480680i
$$27$$ 4.80263 1.98362i 0.924266 0.381748i
$$28$$ −0.631989 −0.119435
$$29$$ 3.43462 0.637793 0.318896 0.947790i $$-0.396688\pi$$
0.318896 + 0.947790i $$0.396688\pi$$
$$30$$ −0.225499 1.71731i −0.0411702 0.313536i
$$31$$ 7.16461i 1.28680i 0.765529 + 0.643401i $$0.222477\pi$$
−0.765529 + 0.643401i $$0.777523\pi$$
$$32$$ 1.00000 0.176777
$$33$$ −0.450997 3.43462i −0.0785085 0.597890i
$$34$$ 3.25363i 0.557992i
$$35$$ 0.631989i 0.106826i
$$36$$ 2.89830 0.774501i 0.483050 0.129084i
$$37$$ 5.60526i 0.921499i 0.887530 + 0.460749i $$0.152419\pi$$
−0.887530 + 0.460749i $$0.847581\pi$$
$$38$$ −2.43462 + 3.61561i −0.394947 + 0.586529i
$$39$$ −0.552696 4.20912i −0.0885022 0.673999i
$$40$$ 1.00000i 0.158114i
$$41$$ −0.802629 −0.125350 −0.0626748 0.998034i $$-0.519963\pi$$
−0.0626748 + 0.998034i $$0.519963\pi$$
$$42$$ −1.08532 + 0.142513i −0.167469 + 0.0219902i
$$43$$ −11.9672 −1.82499 −0.912494 0.409091i $$-0.865846\pi$$
−0.912494 + 0.409091i $$0.865846\pi$$
$$44$$ 2.00000i 0.301511i
$$45$$ −0.774501 2.89830i −0.115456 0.432053i
$$46$$ 0.812981i 0.119867i
$$47$$ 7.96724i 1.16214i −0.813853 0.581071i $$-0.802634\pi$$
0.813853 0.581071i $$-0.197366\pi$$
$$48$$ 1.71731 0.225499i 0.247872 0.0325479i
$$49$$ −6.60059 −0.942941
$$50$$ −1.00000 −0.141421
$$51$$ 0.733688 + 5.58748i 0.102737 + 0.782404i
$$52$$ 2.45100i 0.339892i
$$53$$ 6.53262 0.897325 0.448662 0.893701i $$-0.351901\pi$$
0.448662 + 0.893701i $$0.351901\pi$$
$$54$$ 4.80263 1.98362i 0.653555 0.269937i
$$55$$ −2.00000 −0.269680
$$56$$ −0.631989 −0.0844531
$$57$$ −3.36568 + 6.75812i −0.445795 + 0.895135i
$$58$$ 3.43462 0.450987
$$59$$ −2.09198 −0.272352 −0.136176 0.990685i $$-0.543481\pi$$
−0.136176 + 0.990685i $$0.543481\pi$$
$$60$$ −0.225499 1.71731i −0.0291117 0.221704i
$$61$$ −2.70326 −0.346118 −0.173059 0.984912i $$-0.555365\pi$$
−0.173059 + 0.984912i $$0.555365\pi$$
$$62$$ 7.16461i 0.909907i
$$63$$ −1.83169 + 0.489476i −0.230772 + 0.0616682i
$$64$$ 1.00000 0.125000
$$65$$ −2.45100 −0.304009
$$66$$ −0.450997 3.43462i −0.0555139 0.422772i
$$67$$ 14.9462i 1.82597i 0.407995 + 0.912984i $$0.366228\pi$$
−0.407995 + 0.912984i $$0.633772\pi$$
$$68$$ 3.25363i 0.394560i
$$69$$ −0.183326 1.39614i −0.0220699 0.168075i
$$70$$ 0.631989i 0.0755371i
$$71$$ 6.16597 0.731766 0.365883 0.930661i $$-0.380767\pi$$
0.365883 + 0.930661i $$0.380767\pi$$
$$72$$ 2.89830 0.774501i 0.341568 0.0912759i
$$73$$ −4.89461 −0.572870 −0.286435 0.958100i $$-0.592470\pi$$
−0.286435 + 0.958100i $$0.592470\pi$$
$$74$$ 5.60526i 0.651598i
$$75$$ −1.71731 + 0.225499i −0.198298 + 0.0260383i
$$76$$ −2.43462 + 3.61561i −0.279270 + 0.414739i
$$77$$ 1.26398i 0.144044i
$$78$$ −0.552696 4.20912i −0.0625805 0.476589i
$$79$$ 4.42859i 0.498255i −0.968471 0.249128i $$-0.919856\pi$$
0.968471 0.249128i $$-0.0801439\pi$$
$$80$$ 1.00000i 0.111803i
$$81$$ 7.80030 4.48948i 0.866699 0.498831i
$$82$$ −0.802629 −0.0886356
$$83$$ 5.86788i 0.644083i −0.946726 0.322042i $$-0.895631\pi$$
0.946726 0.322042i $$-0.104369\pi$$
$$84$$ −1.08532 + 0.142513i −0.118418 + 0.0155494i
$$85$$ 3.25363 0.352905
$$86$$ −11.9672 −1.29046
$$87$$ 5.89830 0.774501i 0.632364 0.0830353i
$$88$$ 2.00000i 0.213201i
$$89$$ −5.93339 −0.628938 −0.314469 0.949268i $$-0.601827\pi$$
−0.314469 + 0.949268i $$0.601827\pi$$
$$90$$ −0.774501 2.89830i −0.0816396 0.305508i
$$91$$ 1.54900i 0.162380i
$$92$$ 0.812981i 0.0847591i
$$93$$ 1.61561 + 12.3039i 0.167531 + 1.27585i
$$94$$ 7.96724i 0.821758i
$$95$$ 3.61561 + 2.43462i 0.370954 + 0.249787i
$$96$$ 1.71731 0.225499i 0.175272 0.0230149i
$$97$$ 3.26398i 0.331407i 0.986176 + 0.165703i $$0.0529894\pi$$
−0.986176 + 0.165703i $$0.947011\pi$$
$$98$$ −6.60059 −0.666760
$$99$$ −1.54900 5.79660i −0.155681 0.582580i
$$100$$ −1.00000 −0.100000
$$101$$ 7.45999i 0.742297i 0.928574 + 0.371148i $$0.121036\pi$$
−0.928574 + 0.371148i $$0.878964\pi$$
$$102$$ 0.733688 + 5.58748i 0.0726459 + 0.553243i
$$103$$ 17.9345i 1.76714i −0.468302 0.883569i $$-0.655134\pi$$
0.468302 0.883569i $$-0.344866\pi$$
$$104$$ 2.45100i 0.240340i
$$105$$ 0.142513 + 1.08532i 0.0139078 + 0.105916i
$$106$$ 6.53262 0.634505
$$107$$ −5.63063 −0.544334 −0.272167 0.962250i $$-0.587740\pi$$
−0.272167 + 0.962250i $$0.587740\pi$$
$$108$$ 4.80263 1.98362i 0.462133 0.190874i
$$109$$ 8.71362i 0.834613i −0.908766 0.417307i $$-0.862974\pi$$
0.908766 0.417307i $$-0.137026\pi$$
$$110$$ −2.00000 −0.190693
$$111$$ 1.26398 + 9.62596i 0.119971 + 0.913656i
$$112$$ −0.631989 −0.0597173
$$113$$ −0.705983 −0.0664133 −0.0332066 0.999449i $$-0.510572\pi$$
−0.0332066 + 0.999449i $$0.510572\pi$$
$$114$$ −3.36568 + 6.75812i −0.315225 + 0.632956i
$$115$$ −0.812981 −0.0758108
$$116$$ 3.43462 0.318896
$$117$$ −1.89830 7.10373i −0.175498 0.656740i
$$118$$ −2.09198 −0.192582
$$119$$ 2.05626i 0.188497i
$$120$$ −0.225499 1.71731i −0.0205851 0.156768i
$$121$$ 7.00000 0.636364
$$122$$ −2.70326 −0.244742
$$123$$ −1.37836 + 0.180992i −0.124283 + 0.0163195i
$$124$$ 7.16461i 0.643401i
$$125$$ 1.00000i 0.0894427i
$$126$$ −1.83169 + 0.489476i −0.163180 + 0.0436060i
$$127$$ 4.86924i 0.432075i 0.976385 + 0.216037i $$0.0693133\pi$$
−0.976385 + 0.216037i $$0.930687\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ −20.5515 + 2.69860i −1.80945 + 0.237598i
$$130$$ −2.45100 −0.214967
$$131$$ 20.1005i 1.75618i 0.478491 + 0.878092i $$0.341184\pi$$
−0.478491 + 0.878092i $$0.658816\pi$$
$$132$$ −0.450997 3.43462i −0.0392543 0.298945i
$$133$$ 1.53865 2.28503i 0.133418 0.198137i
$$134$$ 14.9462i 1.29115i
$$135$$ −1.98362 4.80263i −0.170723 0.413345i
$$136$$ 3.25363i 0.278996i
$$137$$ 8.28883i 0.708163i −0.935215 0.354081i $$-0.884794\pi$$
0.935215 0.354081i $$-0.115206\pi$$
$$138$$ −0.183326 1.39614i −0.0156057 0.118847i
$$139$$ −0.196012 −0.0166255 −0.00831274 0.999965i $$-0.502646\pi$$
−0.00831274 + 0.999965i $$0.502646\pi$$
$$140$$ 0.631989i 0.0534128i
$$141$$ −1.79660 13.6822i −0.151301 1.15225i
$$142$$ 6.16597 0.517437
$$143$$ −4.90199 −0.409925
$$144$$ 2.89830 0.774501i 0.241525 0.0645418i
$$145$$ 3.43462i 0.285230i
$$146$$ −4.89461 −0.405081
$$147$$ −11.3353 + 1.48842i −0.934916 + 0.122763i
$$148$$ 5.60526i 0.460749i
$$149$$ 11.4092i 0.934682i −0.884077 0.467341i $$-0.845212\pi$$
0.884077 0.467341i $$-0.154788\pi$$
$$150$$ −1.71731 + 0.225499i −0.140218 + 0.0184119i
$$151$$ 10.2119i 0.831031i 0.909586 + 0.415515i $$0.136399\pi$$
−0.909586 + 0.415515i $$0.863601\pi$$
$$152$$ −2.43462 + 3.61561i −0.197474 + 0.293265i
$$153$$ 2.51994 + 9.42999i 0.203725 + 0.762369i
$$154$$ 1.26398i 0.101854i
$$155$$ 7.16461 0.575476
$$156$$ −0.552696 4.20912i −0.0442511 0.336999i
$$157$$ 14.0338 1.12002 0.560012 0.828485i $$-0.310797\pi$$
0.560012 + 0.828485i $$0.310797\pi$$
$$158$$ 4.42859i 0.352320i
$$159$$ 11.2185 1.47310i 0.889688 0.116824i
$$160$$ 1.00000i 0.0790569i
$$161$$ 0.513795i 0.0404927i
$$162$$ 7.80030 4.48948i 0.612849 0.352727i
$$163$$ −19.3765 −1.51768 −0.758842 0.651275i $$-0.774234\pi$$
−0.758842 + 0.651275i $$0.774234\pi$$
$$164$$ −0.802629 −0.0626748
$$165$$ −3.43462 + 0.450997i −0.267385 + 0.0351101i
$$166$$ 5.86788i 0.455436i
$$167$$ −9.23122 −0.714333 −0.357167 0.934041i $$-0.616257\pi$$
−0.357167 + 0.934041i $$0.616257\pi$$
$$168$$ −1.08532 + 0.142513i −0.0837343 + 0.0109951i
$$169$$ 6.99261 0.537893
$$170$$ 3.25363 0.249542
$$171$$ −4.25596 + 12.3647i −0.325461 + 0.945555i
$$172$$ −11.9672 −0.912494
$$173$$ 1.98794 0.151141 0.0755703 0.997140i $$-0.475922\pi$$
0.0755703 + 0.997140i $$0.475922\pi$$
$$174$$ 5.89830 0.774501i 0.447149 0.0587148i
$$175$$ 0.631989 0.0477739
$$176$$ 2.00000i 0.150756i
$$177$$ −3.59257 + 0.471738i −0.270034 + 0.0354580i
$$178$$ −5.93339 −0.444727
$$179$$ 11.4938 0.859090 0.429545 0.903046i $$-0.358674\pi$$
0.429545 + 0.903046i $$0.358674\pi$$
$$180$$ −0.774501 2.89830i −0.0577279 0.216027i
$$181$$ 18.1671i 1.35035i 0.737659 + 0.675174i $$0.235931\pi$$
−0.737659 + 0.675174i $$0.764069\pi$$
$$182$$ 1.54900i 0.114820i
$$183$$ −4.64234 + 0.609582i −0.343172 + 0.0450616i
$$184$$ 0.812981i 0.0599337i
$$185$$ 5.60526 0.412107
$$186$$ 1.61561 + 12.3039i 0.118462 + 0.902162i
$$187$$ 6.50725 0.475857
$$188$$ 7.96724i 0.581071i
$$189$$ −3.03521 + 1.25363i −0.220779 + 0.0911879i
$$190$$ 3.61561 + 2.43462i 0.262304 + 0.176626i
$$191$$ 2.80093i 0.202668i −0.994852 0.101334i $$-0.967689\pi$$
0.994852 0.101334i $$-0.0323110\pi$$
$$192$$ 1.71731 0.225499i 0.123936 0.0162740i
$$193$$ 15.9552i 1.14848i −0.818687 0.574240i $$-0.805298\pi$$
0.818687 0.574240i $$-0.194702\pi$$
$$194$$ 3.26398i 0.234340i
$$195$$ −4.20912 + 0.552696i −0.301421 + 0.0395794i
$$196$$ −6.60059 −0.471471
$$197$$ 19.0352i 1.35620i −0.734969 0.678101i $$-0.762803\pi$$
0.734969 0.678101i $$-0.237197\pi$$
$$198$$ −1.54900 5.79660i −0.110083 0.411947i
$$199$$ −15.3691 −1.08949 −0.544743 0.838603i $$-0.683373\pi$$
−0.544743 + 0.838603i $$0.683373\pi$$
$$200$$ −1.00000 −0.0707107
$$201$$ 3.37035 + 25.6672i 0.237726 + 1.81043i
$$202$$ 7.45999i 0.524883i
$$203$$ −2.17064 −0.152349
$$204$$ 0.733688 + 5.58748i 0.0513684 + 0.391202i
$$205$$ 0.802629i 0.0560581i
$$206$$ 17.9345i 1.24955i
$$207$$ −0.629655 2.35626i −0.0437640 0.163772i
$$208$$ 2.45100i 0.169946i
$$209$$ 7.23122 + 4.86924i 0.500194 + 0.336812i
$$210$$ 0.142513 + 1.08532i 0.00983430 + 0.0748942i
$$211$$ 2.13976i 0.147307i 0.997284 + 0.0736534i $$0.0234659\pi$$
−0.997284 + 0.0736534i $$0.976534\pi$$
$$212$$ 6.53262 0.448662
$$213$$ 10.5889 1.39042i 0.725538 0.0952699i
$$214$$ −5.63063 −0.384902
$$215$$ 11.9672i 0.816159i
$$216$$ 4.80263 1.98362i 0.326778 0.134968i
$$217$$ 4.52796i 0.307378i
$$218$$ 8.71362i 0.590161i
$$219$$ −8.40555 + 1.10373i −0.567995 + 0.0745830i
$$220$$ −2.00000 −0.134840
$$221$$ 7.97463 0.536432
$$222$$ 1.26398 + 9.62596i 0.0848326 + 0.646052i
$$223$$ 17.9044i 1.19897i −0.800386 0.599485i $$-0.795372\pi$$
0.800386 0.599485i $$-0.204628\pi$$
$$224$$ −0.631989 −0.0422265
$$225$$ −2.89830 + 0.774501i −0.193220 + 0.0516334i
$$226$$ −0.705983 −0.0469613
$$227$$ −3.97463 −0.263805 −0.131903 0.991263i $$-0.542109\pi$$
−0.131903 + 0.991263i $$0.542109\pi$$
$$228$$ −3.36568 + 6.75812i −0.222897 + 0.447568i
$$229$$ 13.5932 0.898264 0.449132 0.893465i $$-0.351733\pi$$
0.449132 + 0.893465i $$0.351733\pi$$
$$230$$ −0.812981 −0.0536064
$$231$$ 0.285025 + 2.17064i 0.0187533 + 0.142818i
$$232$$ 3.43462 0.225494
$$233$$ 21.2323i 1.39097i −0.718538 0.695487i $$-0.755188\pi$$
0.718538 0.695487i $$-0.244812\pi$$
$$234$$ −1.89830 7.10373i −0.124096 0.464385i
$$235$$ −7.96724 −0.519726
$$236$$ −2.09198 −0.136176
$$237$$ −0.998641 7.60526i −0.0648687 0.494015i
$$238$$ 2.05626i 0.133287i
$$239$$ 22.2899i 1.44182i 0.693031 + 0.720908i $$0.256275\pi$$
−0.693031 + 0.720908i $$0.743725\pi$$
$$240$$ −0.225499 1.71731i −0.0145559 0.110852i
$$241$$ 4.19873i 0.270464i −0.990814 0.135232i $$-0.956822\pi$$
0.990814 0.135232i $$-0.0431780\pi$$
$$242$$ 7.00000 0.449977
$$243$$ 12.3831 9.46877i 0.794379 0.607422i
$$244$$ −2.70326 −0.173059
$$245$$ 6.60059i 0.421696i
$$246$$ −1.37836 + 0.180992i −0.0878812 + 0.0115396i
$$247$$ 8.86185 + 5.96724i 0.563866 + 0.379687i
$$248$$ 7.16461i 0.454953i
$$249$$ −1.32320 10.0770i −0.0838543 0.638601i
$$250$$ 1.00000i 0.0632456i
$$251$$ 18.6377i 1.17640i −0.808714 0.588202i $$-0.799836\pi$$
0.808714 0.588202i $$-0.200164\pi$$
$$252$$ −1.83169 + 0.489476i −0.115386 + 0.0308341i
$$253$$ −1.62596 −0.102223
$$254$$ 4.86924i 0.305523i
$$255$$ 5.58748 0.733688i 0.349902 0.0459453i
$$256$$ 1.00000 0.0625000
$$257$$ −5.63802 −0.351690 −0.175845 0.984418i $$-0.556266\pi$$
−0.175845 + 0.984418i $$0.556266\pi$$
$$258$$ −20.5515 + 2.69860i −1.27948 + 0.168007i
$$259$$ 3.54246i 0.220118i
$$260$$ −2.45100 −0.152004
$$261$$ 9.95456 2.66012i 0.616172 0.164657i
$$262$$ 20.1005i 1.24181i
$$263$$ 25.9044i 1.59734i −0.601772 0.798668i $$-0.705538\pi$$
0.601772 0.798668i $$-0.294462\pi$$
$$264$$ −0.450997 3.43462i −0.0277570 0.211386i
$$265$$ 6.53262i 0.401296i
$$266$$ 1.53865 2.28503i 0.0943408 0.140104i
$$267$$ −10.1895 + 1.33797i −0.623585 + 0.0818825i
$$268$$ 14.9462i 0.912984i
$$269$$ 25.3317 1.54450 0.772250 0.635319i $$-0.219131\pi$$
0.772250 + 0.635319i $$0.219131\pi$$
$$270$$ −1.98362 4.80263i −0.120719 0.292279i
$$271$$ 17.5799 1.06790 0.533951 0.845515i $$-0.320707\pi$$
0.533951 + 0.845515i $$0.320707\pi$$
$$272$$ 3.25363i 0.197280i
$$273$$ 0.349298 + 2.66012i 0.0211405 + 0.160998i
$$274$$ 8.28883i 0.500747i
$$275$$ 2.00000i 0.120605i
$$276$$ −0.183326 1.39614i −0.0110349 0.0840377i
$$277$$ 21.6271 1.29944 0.649722 0.760172i $$-0.274885\pi$$
0.649722 + 0.760172i $$0.274885\pi$$
$$278$$ −0.196012 −0.0117560
$$279$$ 5.54900 + 20.7652i 0.332210 + 1.24318i
$$280$$ 0.631989i 0.0377686i
$$281$$ 21.6598 1.29212 0.646058 0.763288i $$-0.276416\pi$$
0.646058 + 0.763288i $$0.276416\pi$$
$$282$$ −1.79660 13.6822i −0.106986 0.814764i
$$283$$ −15.2132 −0.904333 −0.452166 0.891934i $$-0.649349\pi$$
−0.452166 + 0.891934i $$0.649349\pi$$
$$284$$ 6.16597 0.365883
$$285$$ 6.75812 + 3.36568i 0.400317 + 0.199365i
$$286$$ −4.90199 −0.289861
$$287$$ 0.507253 0.0299422
$$288$$ 2.89830 0.774501i 0.170784 0.0456379i
$$289$$ 6.41392 0.377289
$$290$$ 3.43462i 0.201688i
$$291$$ 0.736022 + 5.60526i 0.0431464 + 0.328586i
$$292$$ −4.89461 −0.286435
$$293$$ −5.38980 −0.314876 −0.157438 0.987529i $$-0.550323\pi$$
−0.157438 + 0.987529i $$0.550323\pi$$
$$294$$ −11.3353 + 1.48842i −0.661085 + 0.0868066i
$$295$$ 2.09198i 0.121800i
$$296$$ 5.60526i 0.325799i
$$297$$ −3.96724 9.60526i −0.230203 0.557354i
$$298$$ 11.4092i 0.660920i
$$299$$ −1.99261 −0.115236
$$300$$ −1.71731 + 0.225499i −0.0991489 + 0.0130192i
$$301$$ 7.56316 0.435934
$$302$$ 10.2119i 0.587627i
$$303$$ 1.68222 + 12.8111i 0.0966408 + 0.735979i
$$304$$ −2.43462 + 3.61561i −0.139635 + 0.207369i
$$305$$ 2.70326i 0.154788i
$$306$$ 2.51994 + 9.42999i 0.144055 + 0.539077i
$$307$$ 0.570050i 0.0325345i −0.999868 0.0162672i $$-0.994822\pi$$
0.999868 0.0162672i $$-0.00517825\pi$$
$$308$$ 1.26398i 0.0720218i
$$309$$ −4.04420 30.7991i −0.230067 1.75210i
$$310$$ 7.16461 0.406923
$$311$$ 8.38548i 0.475497i 0.971327 + 0.237749i $$0.0764094\pi$$
−0.971327 + 0.237749i $$0.923591\pi$$
$$312$$ −0.552696 4.20912i −0.0312903 0.238294i
$$313$$ 24.6358 1.39250 0.696249 0.717801i $$-0.254851\pi$$
0.696249 + 0.717801i $$0.254851\pi$$
$$314$$ 14.0338 0.791976
$$315$$ 0.489476 + 1.83169i 0.0275789 + 0.103204i
$$316$$ 4.42859i 0.249128i
$$317$$ 17.0071 0.955215 0.477607 0.878573i $$-0.341504\pi$$
0.477607 + 0.878573i $$0.341504\pi$$
$$318$$ 11.2185 1.47310i 0.629104 0.0826072i
$$319$$ 6.86924i 0.384603i
$$320$$ 1.00000i 0.0559017i
$$321$$ −9.66953 + 1.26970i −0.539701 + 0.0708677i
$$322$$ 0.513795i 0.0286327i
$$323$$ −11.7638 7.92134i −0.654558 0.440755i
$$324$$ 7.80030 4.48948i 0.433350 0.249415i
$$325$$ 2.45100i 0.135957i
$$326$$ −19.3765 −1.07316
$$327$$ −1.96491 14.9640i −0.108660 0.827509i
$$328$$ −0.802629 −0.0443178
$$329$$ 5.03521i 0.277600i
$$330$$ −3.43462 + 0.450997i −0.189070 + 0.0248266i
$$331$$ 9.74773i 0.535784i 0.963449 + 0.267892i $$0.0863270\pi$$
−0.963449 + 0.267892i $$0.913673\pi$$
$$332$$ 5.86788i 0.322042i
$$333$$ 4.34128 + 16.2457i 0.237901 + 0.890260i
$$334$$ −9.23122 −0.505110
$$335$$ 14.9462 0.816598
$$336$$ −1.08532 + 0.142513i −0.0592091 + 0.00777470i
$$337$$ 23.7505i 1.29377i −0.762586 0.646887i $$-0.776071\pi$$
0.762586 0.646887i $$-0.223929\pi$$
$$338$$ 6.99261 0.380348
$$339$$ −1.21239 + 0.159198i −0.0658480 + 0.00864645i
$$340$$ 3.25363 0.176453
$$341$$ 14.3292 0.775971
$$342$$ −4.25596 + 12.3647i −0.230136 + 0.668609i
$$343$$ 8.59542 0.464109
$$344$$ −11.9672 −0.645230
$$345$$ −1.39614 + 0.183326i −0.0751656 + 0.00986994i
$$346$$ 1.98794 0.106873
$$347$$ 22.9031i 1.22950i −0.788721 0.614751i $$-0.789256\pi$$
0.788721 0.614751i $$-0.210744\pi$$
$$348$$ 5.89830 0.774501i 0.316182 0.0415176i
$$349$$ 11.1985 0.599440 0.299720 0.954027i $$-0.403107\pi$$
0.299720 + 0.954027i $$0.403107\pi$$
$$350$$ 0.631989 0.0337812
$$351$$ −4.86185 11.7712i −0.259506 0.628302i
$$352$$ 2.00000i 0.106600i
$$353$$ 1.64837i 0.0877338i −0.999037 0.0438669i $$-0.986032\pi$$
0.999037 0.0438669i $$-0.0139677\pi$$
$$354$$ −3.59257 + 0.471738i −0.190943 + 0.0250726i
$$355$$ 6.16597i 0.327256i
$$356$$ −5.93339 −0.314469
$$357$$ −0.463683 3.53123i −0.0245407 0.186892i
$$358$$ 11.4938 0.607468
$$359$$ 32.3079i 1.70515i 0.522608 + 0.852573i $$0.324959\pi$$
−0.522608 + 0.852573i $$0.675041\pi$$
$$360$$ −0.774501 2.89830i −0.0408198 0.152754i
$$361$$ −7.14527 17.6053i −0.376067 0.926593i
$$362$$ 18.1671i 0.954840i
$$363$$ 12.0212 1.57849i 0.630947 0.0828492i
$$364$$ 1.54900i 0.0811898i
$$365$$ 4.89461i 0.256195i
$$366$$ −4.64234 + 0.609582i −0.242659 + 0.0318634i
$$367$$ −4.78465 −0.249756 −0.124878 0.992172i $$-0.539854\pi$$
−0.124878 + 0.992172i $$0.539854\pi$$
$$368$$ 0.812981i 0.0423795i
$$369$$ −2.32626 + 0.621638i −0.121100 + 0.0323612i
$$370$$ 5.60526 0.291404
$$371$$ −4.12855 −0.214343
$$372$$ 1.61561 + 12.3039i 0.0837655 + 0.637925i
$$373$$ 3.21978i 0.166714i 0.996520 + 0.0833569i $$0.0265641\pi$$
−0.996520 + 0.0833569i $$0.973436\pi$$
$$374$$ 6.50725 0.336482
$$375$$ 0.225499 + 1.71731i 0.0116447 + 0.0886815i
$$376$$ 7.96724i 0.410879i
$$377$$ 8.41824i 0.433561i
$$378$$ −3.03521 + 1.25363i −0.156114 + 0.0644796i
$$379$$ 23.0887i 1.18599i 0.805206 + 0.592995i $$0.202054\pi$$
−0.805206 + 0.592995i $$0.797946\pi$$
$$380$$ 3.61561 + 2.43462i 0.185477 + 0.124893i
$$381$$ 1.09801 + 8.36198i 0.0562525 + 0.428397i
$$382$$ 2.80093i 0.143308i
$$383$$ −28.8124 −1.47224 −0.736122 0.676849i $$-0.763345\pi$$
−0.736122 + 0.676849i $$0.763345\pi$$
$$384$$ 1.71731 0.225499i 0.0876361 0.0115074i
$$385$$ 1.26398 0.0644183
$$386$$ 15.9552i 0.812098i
$$387$$ −34.6847 + 9.26865i −1.76312 + 0.471152i
$$388$$ 3.26398i 0.165703i
$$389$$ 13.5545i 0.687241i −0.939109 0.343621i $$-0.888347\pi$$
0.939109 0.343621i $$-0.111653\pi$$
$$390$$ −4.20912 + 0.552696i −0.213137 + 0.0279869i
$$391$$ 2.64514 0.133770
$$392$$ −6.60059 −0.333380
$$393$$ 4.53262 + 34.5187i 0.228641 + 1.74124i
$$394$$ 19.0352i 0.958980i
$$395$$ −4.42859 −0.222827
$$396$$ −1.54900 5.79660i −0.0778403 0.291290i
$$397$$ 1.51795 0.0761837 0.0380918 0.999274i $$-0.487872\pi$$
0.0380918 + 0.999274i $$0.487872\pi$$
$$398$$ −15.3691 −0.770383
$$399$$ 2.12707 4.27106i 0.106487 0.213820i
$$400$$ −1.00000 −0.0500000
$$401$$ −9.81713 −0.490244 −0.245122 0.969492i $$-0.578828\pi$$
−0.245122 + 0.969492i $$0.578828\pi$$
$$402$$ 3.37035 + 25.6672i 0.168098 + 1.28017i
$$403$$ 17.5604 0.874748
$$404$$ 7.45999i 0.371148i
$$405$$ −4.48948 7.80030i −0.223084 0.387600i
$$406$$ −2.17064 −0.107727
$$407$$ 11.2105 0.555685
$$408$$ 0.733688 + 5.58748i 0.0363230 + 0.276622i
$$409$$ 18.1453i 0.897226i 0.893726 + 0.448613i $$0.148082\pi$$
−0.893726 + 0.448613i $$0.851918\pi$$
$$410$$ 0.802629i 0.0396390i
$$411$$ −1.86912 14.2345i −0.0921969 0.702136i
$$412$$ 17.9345i 0.883569i
$$413$$ 1.32211 0.0650566
$$414$$ −0.629655 2.35626i −0.0309458 0.115804i
$$415$$ −5.86788 −0.288043
$$416$$ 2.45100i 0.120170i
$$417$$ −0.336612 + 0.0442003i −0.0164840 + 0.00216450i
$$418$$ 7.23122 + 4.86924i 0.353691 + 0.238162i
$$419$$ 15.0145i 0.733507i 0.930318 + 0.366753i $$0.119531\pi$$
−0.930318 + 0.366753i $$0.880469\pi$$
$$420$$ 0.142513 + 1.08532i 0.00695390 + 0.0529582i
$$421$$ 24.4341i 1.19085i −0.803413 0.595423i $$-0.796985\pi$$
0.803413 0.595423i $$-0.203015\pi$$
$$422$$ 2.13976i 0.104162i
$$423$$ −6.17064 23.0915i −0.300027 1.12275i
$$424$$ 6.53262 0.317252
$$425$$ 3.25363i 0.157824i
$$426$$ 10.5889 1.39042i 0.513033 0.0673660i
$$427$$ 1.70843 0.0826769
$$428$$ −5.63063 −0.272167
$$429$$ −8.41824 + 1.10539i −0.406436 + 0.0533689i
$$430$$ 11.9672i 0.577112i
$$431$$ −41.0522 −1.97741 −0.988707 0.149864i $$-0.952116\pi$$
−0.988707 + 0.149864i $$0.952116\pi$$
$$432$$ 4.80263 1.98362i 0.231067 0.0954370i
$$433$$ 18.0121i 0.865604i 0.901489 + 0.432802i $$0.142475\pi$$
−0.901489 + 0.432802i $$0.857525\pi$$
$$434$$ 4.52796i 0.217349i
$$435$$ −0.774501 5.89830i −0.0371345 0.282802i
$$436$$ 8.71362i 0.417307i
$$437$$ 2.93942 + 1.97930i 0.140612 + 0.0946826i
$$438$$ −8.40555 + 1.10373i −0.401633 + 0.0527381i
$$439$$ 27.8024i 1.32693i −0.748205 0.663467i $$-0.769084\pi$$
0.748205 0.663467i $$-0.230916\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ −19.1305 + 5.11217i −0.910976 + 0.243437i
$$442$$ 7.97463 0.379314
$$443$$ 10.0366i 0.476852i 0.971161 + 0.238426i $$0.0766314\pi$$
−0.971161 + 0.238426i $$0.923369\pi$$
$$444$$ 1.26398 + 9.62596i 0.0599857 + 0.456828i
$$445$$ 5.93339i 0.281270i
$$446$$ 17.9044i 0.847800i
$$447$$ −2.57277 19.5932i −0.121688 0.926727i
$$448$$ −0.631989 −0.0298587
$$449$$ 33.9055 1.60010 0.800051 0.599933i $$-0.204806\pi$$
0.800051 + 0.599933i $$0.204806\pi$$
$$450$$ −2.89830 + 0.774501i −0.136627 + 0.0365103i
$$451$$ 1.60526i 0.0755887i
$$452$$ −0.705983 −0.0332066
$$453$$ 2.30276 + 17.5369i 0.108193 + 0.823958i
$$454$$ −3.97463 −0.186539
$$455$$ 1.54900 0.0726184
$$456$$ −3.36568 + 6.75812i −0.157612 + 0.316478i
$$457$$ −31.7131 −1.48348 −0.741738 0.670690i $$-0.765998\pi$$
−0.741738 + 0.670690i $$0.765998\pi$$
$$458$$ 13.5932 0.635169
$$459$$ 6.45396 + 15.6260i 0.301245 + 0.729357i
$$460$$ −0.812981 −0.0379054
$$461$$ 23.1029i 1.07601i −0.842942 0.538005i $$-0.819178\pi$$
0.842942 0.538005i $$-0.180822\pi$$
$$462$$ 0.285025 + 2.17064i 0.0132606 + 0.100987i
$$463$$ 32.6950 1.51947 0.759733 0.650235i $$-0.225330\pi$$
0.759733 + 0.650235i $$0.225330\pi$$
$$464$$ 3.43462 0.159448
$$465$$ 12.3039 1.61561i 0.570578 0.0749221i
$$466$$ 21.2323i 0.983568i
$$467$$ 29.2023i 1.35132i 0.737213 + 0.675660i $$0.236141\pi$$
−0.737213 + 0.675660i $$0.763859\pi$$
$$468$$ −1.89830 7.10373i −0.0877490 0.328370i
$$469$$ 9.44583i 0.436168i
$$470$$ −7.96724 −0.367501
$$471$$ 24.1005 3.16461i 1.11049 0.145818i
$$472$$ −2.09198 −0.0962911
$$473$$ 23.9345i 1.10051i
$$474$$ −0.998641 7.60526i −0.0458691 0.349321i
$$475$$ 2.43462 3.61561i 0.111708 0.165896i
$$476$$ 2.05626i 0.0942483i
$$477$$ 18.9335 5.05953i 0.866906 0.231660i
$$478$$ 22.2899i 1.01952i
$$479$$ 17.7712i 0.811988i 0.913876 + 0.405994i $$0.133075\pi$$
−0.913876 + 0.405994i $$0.866925\pi$$
$$480$$ −0.225499 1.71731i −0.0102926 0.0783841i
$$481$$ 13.7385 0.626420
$$482$$ 4.19873i 0.191247i
$$483$$ 0.115860 + 0.882344i 0.00527181 + 0.0401481i
$$484$$ 7.00000 0.318182
$$485$$ 3.26398 0.148210
$$486$$ 12.3831 9.46877i 0.561711 0.429512i
$$487$$ 10.3620i 0.469546i −0.972050 0.234773i $$-0.924565\pi$$
0.972050 0.234773i $$-0.0754347\pi$$
$$488$$ −2.70326 −0.122371
$$489$$ −33.2754 + 4.36937i −1.50477 + 0.197590i
$$490$$ 6.60059i 0.298184i
$$491$$ 16.8993i 0.762654i −0.924440 0.381327i $$-0.875467\pi$$
0.924440 0.381327i $$-0.124533\pi$$
$$492$$ −1.37836 + 0.180992i −0.0621414 + 0.00815974i
$$493$$ 11.1750i 0.503295i
$$494$$ 8.86185 + 5.96724i 0.398713 + 0.268479i
$$495$$ −5.79660 + 1.54900i −0.260538 + 0.0696225i
$$496$$ 7.16461i 0.321701i
$$497$$ −3.89683 −0.174797
$$498$$ −1.32320 10.0770i −0.0592939 0.451559i
$$499$$ 0.364702 0.0163263 0.00816315 0.999967i $$-0.497402\pi$$
0.00816315 + 0.999967i $$0.497402\pi$$
$$500$$ 1.00000i 0.0447214i
$$501$$ −15.8529 + 2.08163i −0.708253 + 0.0930002i
$$502$$ 18.6377i 0.831843i
$$503$$ 30.0939i 1.34182i −0.741538 0.670911i $$-0.765903\pi$$
0.741538 0.670911i $$-0.234097\pi$$
$$504$$ −1.83169 + 0.489476i −0.0815901 + 0.0218030i
$$505$$ 7.45999 0.331965
$$506$$ −1.62596 −0.0722828
$$507$$ 12.0085 1.57682i 0.533315 0.0700292i
$$508$$ 4.86924i 0.216037i
$$509$$ −44.3849 −1.96732 −0.983662 0.180023i $$-0.942383\pi$$
−0.983662 + 0.180023i $$0.942383\pi$$
$$510$$ 5.58748 0.733688i 0.247418 0.0324883i
$$511$$ 3.09334 0.136841
$$512$$ 1.00000 0.0441942
$$513$$ −4.52057 + 22.1938i −0.199588 + 0.979880i
$$514$$ −5.63802 −0.248682
$$515$$ −17.9345 −0.790288
$$516$$ −20.5515 + 2.69860i −0.904727 + 0.118799i
$$517$$ −15.9345 −0.700798
$$518$$ 3.54246i 0.155647i
$$519$$ 3.41392 0.448279i 0.149854 0.0196772i
$$520$$ −2.45100 −0.107483
$$521$$ −17.8472 −0.781899 −0.390949 0.920412i $$-0.627853\pi$$
−0.390949 + 0.920412i $$0.627853\pi$$
$$522$$ 9.95456 2.66012i 0.435699 0.116430i
$$523$$ 14.2222i 0.621895i 0.950427 + 0.310947i $$0.100646\pi$$
−0.950427 + 0.310947i $$0.899354\pi$$
$$524$$ 20.1005i 0.878092i
$$525$$ 1.08532 0.142513i 0.0473673 0.00621976i
$$526$$ 25.9044i 1.12949i
$$527$$ −23.3110 −1.01544
$$528$$ −0.450997 3.43462i −0.0196271 0.149473i
$$529$$ 22.3391 0.971264
$$530$$ 6.53262i 0.283759i
$$531$$ −6.06318 + 1.62024i −0.263120 + 0.0703124i
$$532$$ 1.53865 2.28503i 0.0667090 0.0990684i
$$533$$ 1.96724i 0.0852107i
$$534$$ −10.1895 + 1.33797i −0.440941 + 0.0578997i
$$535$$ 5.63063i 0.243433i
$$536$$ 14.9462i 0.645577i
$$537$$ 19.7385 2.59184i 0.851778 0.111846i
$$538$$ 25.3317 1.09213
$$539$$ 13.2012i 0.568615i
$$540$$ −1.98362 4.80263i −0.0853615 0.206672i
$$541$$ −37.2164 −1.60006 −0.800030 0.599960i $$-0.795183\pi$$
−0.800030 + 0.599960i $$0.795183\pi$$
$$542$$ 17.5799 0.755121
$$543$$ 4.09665 + 31.1985i 0.175804 + 1.33885i
$$544$$ 3.25363i 0.139498i
$$545$$ −8.71362 −0.373250
$$546$$ 0.349298 + 2.66012i 0.0149486 + 0.113842i
$$547$$ 16.3789i 0.700313i −0.936691 0.350156i $$-0.886128\pi$$
0.936691 0.350156i $$-0.113872\pi$$
$$548$$ 8.28883i 0.354081i
$$549$$ −7.83487 + 2.09368i −0.334384 + 0.0893562i
$$550$$ 2.00000i 0.0852803i
$$551$$ −8.36198 + 12.4182i −0.356232 + 0.529035i
$$552$$ −0.183326 1.39614i −0.00780287 0.0594236i
$$553$$ 2.79882i 0.119018i
$$554$$ 21.6271 0.918845
$$555$$ 9.62596 1.26398i 0.408599 0.0536529i
$$556$$ −0.196012 −0.00831274
$$557$$ 36.8244i 1.56030i 0.625592 + 0.780150i $$0.284858\pi$$
−0.625592 + 0.780150i $$0.715142\pi$$
$$558$$ 5.54900 + 20.7652i 0.234908 + 0.879061i
$$559$$ 29.3317i 1.24060i
$$560$$ 0.631989i 0.0267064i
$$561$$ 11.1750 1.46738i 0.471807 0.0619527i
$$562$$ 21.6598 0.913664
$$563$$ −40.0022 −1.68589 −0.842945 0.537999i $$-0.819180\pi$$
−0.842945 + 0.537999i $$0.819180\pi$$
$$564$$ −1.79660 13.6822i −0.0756506 0.576125i
$$565$$ 0.705983i 0.0297009i
$$566$$ −15.2132 −0.639460
$$567$$ −4.92970 + 2.83730i −0.207028 + 0.119155i
$$568$$ 6.16597 0.258718
$$569$$ −21.6953 −0.909514 −0.454757 0.890616i $$-0.650274\pi$$
−0.454757 + 0.890616i $$0.650274\pi$$
$$570$$ 6.75812 + 3.36568i 0.283067 + 0.140973i
$$571$$ 3.37377 0.141188 0.0705940 0.997505i $$-0.477511\pi$$
0.0705940 + 0.997505i $$0.477511\pi$$
$$572$$ −4.90199 −0.204963
$$573$$ −0.631605 4.81005i −0.0263857 0.200943i
$$574$$ 0.507253 0.0211723
$$575$$ 0.812981i 0.0339036i
$$576$$ 2.89830 0.774501i 0.120763 0.0322709i
$$577$$ −31.3740 −1.30612 −0.653058 0.757308i $$-0.726514\pi$$
−0.653058 + 0.757308i $$0.726514\pi$$
$$578$$ 6.41392 0.266784
$$579$$ −3.59787 27.4000i −0.149522 1.13870i
$$580$$ 3.43462i 0.142615i
$$581$$ 3.70843i 0.153852i
$$582$$ 0.736022 + 5.60526i 0.0305091 + 0.232345i
$$583$$ 13.0652i 0.541107i
$$584$$ −4.89461 −0.202540
$$585$$ −7.10373 + 1.89830i −0.293703 + 0.0784851i
$$586$$ −5.38980 −0.222651
$$587$$ 39.0718i 1.61266i 0.591463 + 0.806332i $$0.298551\pi$$
−0.591463 + 0.806332i $$0.701449\pi$$
$$588$$ −11.3353 + 1.48842i −0.467458 + 0.0613816i
$$589$$ −25.9044 17.4431i −1.06737 0.718730i
$$590$$ 2.09198i 0.0861254i
$$591$$ −4.29241 32.6893i −0.176566 1.34466i
$$592$$ 5.60526i 0.230375i
$$593$$ 26.6367i 1.09384i 0.837186 + 0.546918i $$0.184199\pi$$
−0.837186 + 0.546918i $$0.815801\pi$$
$$594$$ −3.96724 9.60526i −0.162778 0.394109i
$$595$$ −2.05626 −0.0842983
$$596$$ 11.4092i 0.467341i
$$597$$ −26.3935 + 3.46571i −1.08021 + 0.141842i
$$598$$ −1.99261 −0.0814840
$$599$$ 0.952736 0.0389278 0.0194639 0.999811i $$-0.493804\pi$$
0.0194639 + 0.999811i $$0.493804\pi$$
$$600$$ −1.71731 + 0.225499i −0.0701088 + 0.00920594i
$$601$$ 14.6050i 0.595750i −0.954605 0.297875i $$-0.903722\pi$$
0.954605 0.297875i $$-0.0962779\pi$$
$$602$$ 7.56316 0.308252
$$603$$ 11.5758 + 43.3186i 0.471405 + 1.76407i
$$604$$ 10.2119i 0.415515i
$$605$$ 7.00000i 0.284590i
$$606$$ 1.68222 + 12.8111i 0.0683354 + 0.520416i
$$607$$ 11.5304i 0.468005i 0.972236 + 0.234002i $$0.0751823\pi$$
−0.972236 + 0.234002i $$0.924818\pi$$
$$608$$ −2.43462 + 3.61561i −0.0987368 + 0.146632i
$$609$$ −3.72766 + 0.489476i −0.151052 + 0.0198346i
$$610$$ 2.70326i 0.109452i
$$611$$ −19.5277 −0.790006
$$612$$ 2.51994 + 9.42999i 0.101862 + 0.381185i
$$613$$ −25.1996 −1.01780 −0.508900 0.860826i $$-0.669948\pi$$
−0.508900 + 0.860826i $$0.669948\pi$$
$$614$$ 0.570050i 0.0230054i
$$615$$ 0.180992 + 1.37836i 0.00729829 + 0.0555809i
$$616$$ 1.26398i 0.0509271i
$$617$$ 18.3724i 0.739645i −0.929102 0.369823i $$-0.879418\pi$$
0.929102 0.369823i $$-0.120582\pi$$
$$618$$ −4.04420 30.7991i −0.162682 1.23892i
$$619$$ −16.4952 −0.662998 −0.331499 0.943456i $$-0.607554\pi$$
−0.331499 + 0.943456i $$0.607554\pi$$
$$620$$ 7.16461 0.287738
$$621$$ −1.61265 3.90444i −0.0647132 0.156680i
$$622$$ 8.38548i 0.336227i
$$623$$ 3.74984 0.150234
$$624$$ −0.552696 4.20912i −0.0221256 0.168500i
$$625$$ 1.00000 0.0400000
$$626$$ 24.6358 0.984645
$$627$$ 13.5162 + 6.73135i 0.539787 + 0.268824i
$$628$$ 14.0338 0.560012
$$629$$ −18.2374 −0.727173
$$630$$ 0.489476 + 1.83169i 0.0195012 + 0.0729764i
$$631$$ −11.0532 −0.440021 −0.220010 0.975498i $$-0.570609\pi$$
−0.220010 + 0.975498i $$0.570609\pi$$
$$632$$ 4.42859i 0.176160i
$$633$$ 0.482512 + 3.67462i 0.0191781 + 0.146053i
$$634$$ 17.0071 0.675439
$$635$$ 4.86924 0.193230
$$636$$ 11.2185 1.47310i 0.444844 0.0584121i
$$637$$ 16.1780i 0.640997i
$$638$$ 6.86924i 0.271956i
$$639$$ 17.8708 4.77555i 0.706960 0.188918i
$$640$$ 1.00000i 0.0395285i
$$641$$ 33.7368 1.33253 0.666263 0.745717i $$-0.267893\pi$$
0.666263 + 0.745717i $$0.267893\pi$$
$$642$$ −9.66953 + 1.26970i −0.381626 + 0.0501110i
$$643$$ −28.9369 −1.14116 −0.570581 0.821242i $$-0.693282\pi$$
−0.570581 + 0.821242i $$0.693282\pi$$
$$644$$ 0.513795i 0.0202463i
$$645$$ 2.69860 + 20.5515i 0.106257 + 0.809213i
$$646$$ −11.7638 7.92134i −0.462842 0.311661i
$$647$$ 35.3409i 1.38940i −0.719302 0.694698i $$-0.755538\pi$$
0.719302 0.694698i $$-0.244462\pi$$
$$648$$ 7.80030 4.48948i 0.306425 0.176363i
$$649$$ 4.18396i 0.164235i
$$650$$ 2.45100i 0.0961360i
$$651$$ −1.02105 7.77590i −0.0400180 0.304762i
$$652$$ −19.3765 −0.758842
$$653$$ 5.41518i 0.211912i −0.994371 0.105956i $$-0.966210\pi$$
0.994371 0.105956i $$-0.0337903\pi$$
$$654$$ −1.96491 14.9640i −0.0768340 0.585138i
$$655$$ 20.1005 0.785390
$$656$$ −0.802629 −0.0313374
$$657$$ −14.1860 + 3.79088i −0.553450 + 0.147896i
$$658$$ 5.03521i 0.196293i
$$659$$ 23.8546 0.929242 0.464621 0.885510i $$-0.346191\pi$$
0.464621 + 0.885510i $$0.346191\pi$$
$$660$$ −3.43462 + 0.450997i −0.133692 + 0.0175550i
$$661$$ 14.3396i 0.557745i 0.960328 + 0.278872i $$0.0899607\pi$$
−0.960328 + 0.278872i $$0.910039\pi$$
$$662$$ 9.74773i 0.378856i
$$663$$ 13.6949 1.79827i 0.531866 0.0698389i
$$664$$ 5.86788i 0.227718i
$$665$$ −2.28503 1.53865i −0.0886095 0.0596663i
$$666$$ 4.34128 + 16.2457i 0.168221 + 0.629509i
$$667$$ 2.79228i 0.108117i
$$668$$ −9.23122 −0.357167
$$669$$ −4.03743 30.7475i −0.156096 1.18877i
$$670$$ 14.9462 0.577422
$$671$$ 5.40653i 0.208717i
$$672$$ −1.08532 + 0.142513i −0.0418671 + 0.00549754i
$$673$$ 49.3290i 1.90149i 0.309972 + 0.950746i $$0.399680\pi$$
−0.309972 + 0.950746i $$0.600320\pi$$
$$674$$ 23.7505i 0.914836i
$$675$$ −4.80263 + 1.98362i −0.184853 + 0.0763496i
$$676$$ 6.99261 0.268947
$$677$$ −23.1431 −0.889460 −0.444730 0.895665i $$-0.646700\pi$$
−0.444730 + 0.895665i $$0.646700\pi$$
$$678$$ −1.21239 + 0.159198i −0.0465616 + 0.00611397i
$$679$$ 2.06280i 0.0791629i
$$680$$ 3.25363 0.124771
$$681$$ −6.82567 + 0.896273i −0.261560 + 0.0343453i
$$682$$ 14.3292 0.548694
$$683$$ 20.2905 0.776396 0.388198 0.921576i $$-0.373098\pi$$
0.388198 + 0.921576i $$0.373098\pi$$
$$684$$ −4.25596 + 12.3647i −0.162731 + 0.472778i
$$685$$ −8.28883 −0.316700
$$686$$ 8.59542 0.328175
$$687$$ 23.3437 3.06525i 0.890619 0.116946i
$$688$$ −11.9672 −0.456247
$$689$$ 16.0114i 0.609987i
$$690$$ −1.39614 + 0.183326i −0.0531501 + 0.00697910i
$$691$$ −18.5280 −0.704837 −0.352418 0.935843i $$-0.614641\pi$$
−0.352418 + 0.935843i $$0.614641\pi$$
$$692$$ 1.98794 0.0755703
$$693$$ 0.978953 + 3.66339i 0.0371873 + 0.139161i
$$694$$ 22.9031i 0.869389i
$$695$$ 0.196012i 0.00743514i
$$696$$ 5.89830 0.774501i 0.223575 0.0293574i
$$697$$ 2.61146i 0.0989159i
$$698$$ 11.1985 0.423868
$$699$$ −4.78786 36.4624i −0.181093 1.37914i
$$700$$ 0.631989 0.0238869
$$701$$ 3.42130i 0.129221i 0.997911 + 0.0646104i $$0.0205805\pi$$
−0.997911 + 0.0646104i $$0.979420\pi$$
$$702$$ −4.86185 11.7712i −0.183499 0.444276i
$$703$$ −20.2664 13.6467i −0.764363 0.514694i
$$704$$ 2.00000i 0.0753778i
$$705$$ −13.6822 + 1.79660i −0.515302 + 0.0676639i
$$706$$ 1.64837i 0.0620371i
$$707$$ 4.71463i 0.177312i
$$708$$ −3.59257 + 0.471738i −0.135017 + 0.0177290i
$$709$$ 15.1329 0.568330 0.284165 0.958775i $$-0.408284\pi$$
0.284165 + 0.958775i $$0.408284\pi$$
$$710$$ 6.16597i 0.231405i
$$711$$ −3.42995 12.8354i −0.128633 0.481365i
$$712$$ −5.93339 −0.222363
$$713$$ 5.82469 0.218136
$$714$$ −0.463683 3.53123i −0.0173529 0.132153i
$$715$$ 4.90199i 0.183324i
$$716$$ 11.4938 0.429545
$$717$$ 5.02635 + 38.2787i 0.187712 + 1.42954i
$$718$$ 32.3079i 1.20572i
$$719$$ 4.37343i 0.163101i 0.996669 + 0.0815506i $$0.0259872\pi$$
−0.996669 + 0.0815506i $$0.974013\pi$$
$$720$$ −0.774501 2.89830i −0.0288640 0.108013i
$$721$$ 11.3344i 0.422115i
$$722$$ −7.14527 17.6053i −0.265919 0.655200i
$$723$$ −0.946808 7.21052i −0.0352122 0.268162i
$$724$$ 18.1671i 0.675174i
$$725$$ −3.43462 −0.127559
$$726$$ 12.0212 1.57849i 0.446147 0.0585833i
$$727$$ 26.6517 0.988455 0.494228 0.869332i $$-0.335451\pi$$
0.494228 + 0.869332i $$0.335451\pi$$
$$728$$ 1.54900i 0.0574099i
$$729$$ 19.1305 19.0532i 0.708537 0.705674i
$$730$$ 4.89461i 0.181158i
$$731$$ 38.9369i 1.44013i
$$732$$ −4.64234 + 0.609582i −0.171586 + 0.0225308i
$$733$$ 14.1501 0.522646 0.261323 0.965251i $$-0.415841\pi$$
0.261323 + 0.965251i $$0.415841\pi$$
$$734$$ −4.78465 −0.176604
$$735$$ 1.48842 + 11.3353i 0.0549013 + 0.418107i
$$736$$ 0.812981i 0.0299669i
$$737$$ 29.8924 1.10110
$$738$$ −2.32626 + 0.621638i −0.0856309 + 0.0228828i
$$739$$ −47.9721 −1.76468 −0.882342 0.470609i $$-0.844034\pi$$
−0.882342 + 0.470609i $$0.844034\pi$$
$$740$$ 5.60526 0.206053
$$741$$ 16.5641 + 8.24926i 0.608499 + 0.303044i
$$742$$ −4.12855 −0.151564
$$743$$ 43.3765 1.59133 0.795665 0.605738i $$-0.207122\pi$$
0.795665 + 0.605738i $$0.207122\pi$$
$$744$$ 1.61561 + 12.3039i 0.0592311 + 0.451081i
$$745$$ −11.4092 −0.418002
$$746$$ 3.21978i 0.117884i
$$747$$ −4.54468 17.0069i −0.166281 0.622249i
$$748$$ 6.50725 0.237929
$$749$$ 3.55850 0.130025
$$750$$ 0.225499 + 1.71731i 0.00823404 + 0.0627073i
$$751$$ 3.58278i 0.130737i −0.997861 0.0653687i $$-0.979178\pi$$
0.997861 0.0653687i $$-0.0208223\pi$$
$$752$$ 7.96724i 0.290535i
$$753$$ −4.20279 32.0068i −0.153158 1.16639i
$$754$$ 8.41824i 0.306574i
$$755$$ 10.2119 0.371648
$$756$$ −3.03521 + 1.25363i −0.110389 + 0.0455940i
$$757$$ −16.5618 −0.601949 −0.300975 0.953632i $$-0.597312\pi$$
−0.300975 + 0.953632i $$0.597312\pi$$
$$758$$ 23.0887i 0.838621i
$$759$$ −2.79228 + 0.366652i −0.101353 + 0.0133086i
$$760$$ 3.61561 + 2.43462i 0.131152 + 0.0883129i
$$761$$ 34.6726i 1.25688i 0.777858 + 0.628441i $$0.216306\pi$$
−0.777858 + 0.628441i $$0.783694\pi$$
$$762$$ 1.09801 + 8.36198i 0.0397766 + 0.302923i
$$763$$ 5.50691i 0.199363i
$$764$$ 2.80093i 0.101334i
$$765$$ 9.42999 2.51994i 0.340942 0.0911086i
$$766$$ −28.8124 −1.04103
$$767$$ 5.12743i 0.185141i
$$768$$ 1.71731 0.225499i 0.0619681 0.00813698i
$$769$$ −20.4698 −0.738161 −0.369080 0.929397i $$-0.620327\pi$$
−0.369080 + 0.929397i $$0.620327\pi$$
$$770$$ 1.26398 0.0455506
$$771$$ −9.68222 + 1.27136i −0.348697 + 0.0457871i
$$772$$ 15.9552i 0.574240i
$$773$$ 27.5738 0.991759 0.495880 0.868391i $$-0.334846\pi$$
0.495880 + 0.868391i $$0.334846\pi$$
$$774$$ −34.6847 + 9.26865i −1.24671 + 0.333155i
$$775$$ 7.16461i 0.257360i
$$776$$ 3.26398i 0.117170i
$$777$$ −0.798820 6.08350i −0.0286575 0.218244i
$$778$$ 13.5545i 0.485953i
$$779$$ 1.95410 2.90199i 0.0700127 0.103975i
$$780$$ −4.20912 + 0.552696i −0.150711 + 0.0197897i
$$781$$ 12.3319i 0.441272i
$$782$$ 2.64514 0.0945898
$$783$$ 16.4952 6.81298i 0.589490 0.243476i
$$784$$ −6.60059