# Properties

 Label 60.3.f.b.19.1 Level $60$ Weight $3$ Character 60.19 Analytic conductor $1.635$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 60.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.63488158616$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.389136420864.4 Defining polynomial: $$x^{8} + 5 x^{6} + 24 x^{4} + 80 x^{2} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 19.1 Root $$-1.52274 - 1.29664i$$ of defining polynomial Character $$\chi$$ $$=$$ 60.19 Dual form 60.3.f.b.19.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.52274 - 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 + 3.94888i) q^{4} +(4.27492 - 2.59328i) q^{5} +(-2.63746 - 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 - 6.83966i) q^{8} +3.00000 q^{9} +O(q^{10})$$ $$q+(-1.52274 - 1.29664i) q^{2} +1.73205 q^{3} +(0.637459 + 3.94888i) q^{4} +(4.27492 - 2.59328i) q^{5} +(-2.63746 - 2.24584i) q^{6} +0.837253 q^{7} +(4.14959 - 6.83966i) q^{8} +3.00000 q^{9} +(-9.87212 - 1.59414i) q^{10} -15.7955i q^{11} +(1.10411 + 6.83966i) q^{12} +5.18655i q^{13} +(-1.27492 - 1.08561i) q^{14} +(7.40437 - 4.49169i) q^{15} +(-15.1873 + 5.03449i) q^{16} +27.3586i q^{17} +(-4.56821 - 3.88991i) q^{18} +17.9667i q^{19} +(12.9656 + 15.2280i) q^{20} +1.45017 q^{21} +(-20.4811 + 24.0524i) q^{22} -19.1101 q^{23} +(7.18729 - 11.8466i) q^{24} +(11.5498 - 22.1721i) q^{25} +(6.72508 - 7.89776i) q^{26} +5.19615 q^{27} +(0.533714 + 3.30621i) q^{28} -45.6495 q^{29} +(-17.0990 - 2.76113i) q^{30} +13.6243i q^{31} +(29.6542 + 12.0262i) q^{32} -27.3586i q^{33} +(35.4743 - 41.6600i) q^{34} +(3.57919 - 2.17123i) q^{35} +(1.91238 + 11.8466i) q^{36} -15.5597i q^{37} +(23.2964 - 27.3586i) q^{38} +8.98337i q^{39} +(0.00200734 - 40.0000i) q^{40} +13.2990 q^{41} +(-2.20822 - 1.88034i) q^{42} +27.9430 q^{43} +(62.3746 - 10.0690i) q^{44} +(12.8248 - 7.77983i) q^{45} +(29.0997 + 24.7789i) q^{46} -55.6558 q^{47} +(-26.3052 + 8.72000i) q^{48} -48.2990 q^{49} +(-46.3365 + 18.7863i) q^{50} +47.3865i q^{51} +(-20.4811 + 3.30621i) q^{52} -15.5597i q^{53} +(-7.91238 - 6.73753i) q^{54} +(-40.9621 - 67.5245i) q^{55} +(3.47425 - 5.72653i) q^{56} +31.1193i q^{57} +(69.5122 + 59.1909i) q^{58} +87.6625i q^{59} +(22.4571 + 26.3757i) q^{60} +38.0000 q^{61} +(17.6658 - 20.7462i) q^{62} +2.51176 q^{63} +(-29.5619 - 56.7635i) q^{64} +(13.4502 + 22.1721i) q^{65} +(-35.4743 + 41.6600i) q^{66} +92.2015 q^{67} +(-108.036 + 17.4400i) q^{68} -33.0997 q^{69} +(-8.26547 - 1.33470i) q^{70} -130.707i q^{71} +(12.4488 - 20.5190i) q^{72} +54.7173i q^{73} +(-20.1752 + 23.6933i) q^{74} +(20.0049 - 38.4032i) q^{75} +(-70.9485 + 11.4531i) q^{76} -13.2249i q^{77} +(11.6482 - 13.6793i) q^{78} -13.6243i q^{79} +(-51.8686 + 60.9069i) q^{80} +9.00000 q^{81} +(-20.2509 - 17.2440i) q^{82} +59.0048 q^{83} +(0.924421 + 5.72653i) q^{84} +(70.9485 + 116.956i) q^{85} +(-42.5498 - 36.2319i) q^{86} -79.0673 q^{87} +(-108.036 - 65.5448i) q^{88} +39.8007 q^{89} +(-29.6164 - 4.78243i) q^{90} +4.34246i q^{91} +(-12.1819 - 75.4635i) q^{92} +23.5980i q^{93} +(84.7492 + 72.1654i) q^{94} +(46.5927 + 76.8064i) q^{95} +(51.3625 + 20.8300i) q^{96} -168.821i q^{97} +(73.5467 + 62.6263i) q^{98} -47.3865i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 10q^{4} + 4q^{5} - 6q^{6} + 24q^{9} + O(q^{10})$$ $$8q - 10q^{4} + 4q^{5} - 6q^{6} + 24q^{9} - 42q^{10} + 20q^{14} - 46q^{16} + 52q^{20} + 72q^{21} - 18q^{24} + 32q^{25} + 84q^{26} - 184q^{29} - 60q^{30} + 12q^{34} - 30q^{36} - 6q^{40} - 256q^{41} + 348q^{44} + 12q^{45} + 112q^{46} - 24q^{49} + 72q^{50} - 18q^{54} - 244q^{56} + 6q^{60} + 304q^{61} - 10q^{64} + 168q^{65} - 12q^{66} - 144q^{69} - 104q^{70} - 252q^{74} - 24q^{76} - 308q^{80} + 72q^{81} - 204q^{84} + 24q^{85} - 280q^{86} + 560q^{89} - 126q^{90} + 376q^{94} + 426q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$37$$ $$41$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.52274 1.29664i −0.761369 0.648319i
$$3$$ 1.73205 0.577350
$$4$$ 0.637459 + 3.94888i 0.159365 + 0.987220i
$$5$$ 4.27492 2.59328i 0.854983 0.518655i
$$6$$ −2.63746 2.24584i −0.439576 0.374307i
$$7$$ 0.837253 0.119608 0.0598038 0.998210i $$-0.480952\pi$$
0.0598038 + 0.998210i $$0.480952\pi$$
$$8$$ 4.14959 6.83966i 0.518698 0.854957i
$$9$$ 3.00000 0.333333
$$10$$ −9.87212 1.59414i −0.987212 0.159414i
$$11$$ 15.7955i 1.43596i −0.696066 0.717978i $$-0.745068\pi$$
0.696066 0.717978i $$-0.254932\pi$$
$$12$$ 1.10411 + 6.83966i 0.0920092 + 0.569972i
$$13$$ 5.18655i 0.398966i 0.979901 + 0.199483i $$0.0639262\pi$$
−0.979901 + 0.199483i $$0.936074\pi$$
$$14$$ −1.27492 1.08561i −0.0910655 0.0775439i
$$15$$ 7.40437 4.49169i 0.493625 0.299446i
$$16$$ −15.1873 + 5.03449i −0.949206 + 0.314656i
$$17$$ 27.3586i 1.60933i 0.593728 + 0.804666i $$0.297656\pi$$
−0.593728 + 0.804666i $$0.702344\pi$$
$$18$$ −4.56821 3.88991i −0.253790 0.216106i
$$19$$ 17.9667i 0.945618i 0.881165 + 0.472809i $$0.156760\pi$$
−0.881165 + 0.472809i $$0.843240\pi$$
$$20$$ 12.9656 + 15.2280i 0.648281 + 0.761401i
$$21$$ 1.45017 0.0690555
$$22$$ −20.4811 + 24.0524i −0.930958 + 1.09329i
$$23$$ −19.1101 −0.830874 −0.415437 0.909622i $$-0.636371\pi$$
−0.415437 + 0.909622i $$0.636371\pi$$
$$24$$ 7.18729 11.8466i 0.299471 0.493610i
$$25$$ 11.5498 22.1721i 0.461993 0.886883i
$$26$$ 6.72508 7.89776i 0.258657 0.303760i
$$27$$ 5.19615 0.192450
$$28$$ 0.533714 + 3.30621i 0.0190612 + 0.118079i
$$29$$ −45.6495 −1.57412 −0.787060 0.616876i $$-0.788398\pi$$
−0.787060 + 0.616876i $$0.788398\pi$$
$$30$$ −17.0990 2.76113i −0.569967 0.0920378i
$$31$$ 13.6243i 0.439493i 0.975557 + 0.219747i $$0.0705230\pi$$
−0.975557 + 0.219747i $$0.929477\pi$$
$$32$$ 29.6542 + 12.0262i 0.926693 + 0.375819i
$$33$$ 27.3586i 0.829050i
$$34$$ 35.4743 41.6600i 1.04336 1.22529i
$$35$$ 3.57919 2.17123i 0.102263 0.0620351i
$$36$$ 1.91238 + 11.8466i 0.0531216 + 0.329073i
$$37$$ 15.5597i 0.420531i −0.977644 0.210266i $$-0.932567\pi$$
0.977644 0.210266i $$-0.0674329\pi$$
$$38$$ 23.2964 27.3586i 0.613062 0.719964i
$$39$$ 8.98337i 0.230343i
$$40$$ 0.00200734 40.0000i 5.01834e−5 1.00000i
$$41$$ 13.2990 0.324366 0.162183 0.986761i $$-0.448147\pi$$
0.162183 + 0.986761i $$0.448147\pi$$
$$42$$ −2.20822 1.88034i −0.0525767 0.0447700i
$$43$$ 27.9430 0.649837 0.324918 0.945742i $$-0.394663\pi$$
0.324918 + 0.945742i $$0.394663\pi$$
$$44$$ 62.3746 10.0690i 1.41760 0.228841i
$$45$$ 12.8248 7.77983i 0.284994 0.172885i
$$46$$ 29.0997 + 24.7789i 0.632601 + 0.538672i
$$47$$ −55.6558 −1.18417 −0.592083 0.805877i $$-0.701694\pi$$
−0.592083 + 0.805877i $$0.701694\pi$$
$$48$$ −26.3052 + 8.72000i −0.548024 + 0.181667i
$$49$$ −48.2990 −0.985694
$$50$$ −46.3365 + 18.7863i −0.926731 + 0.375726i
$$51$$ 47.3865i 0.929148i
$$52$$ −20.4811 + 3.30621i −0.393867 + 0.0635810i
$$53$$ 15.5597i 0.293578i −0.989168 0.146789i $$-0.953106\pi$$
0.989168 0.146789i $$-0.0468939\pi$$
$$54$$ −7.91238 6.73753i −0.146525 0.124769i
$$55$$ −40.9621 67.5245i −0.744766 1.22772i
$$56$$ 3.47425 5.72653i 0.0620403 0.102259i
$$57$$ 31.1193i 0.545953i
$$58$$ 69.5122 + 59.1909i 1.19849 + 1.02053i
$$59$$ 87.6625i 1.48581i 0.669400 + 0.742903i $$0.266551\pi$$
−0.669400 + 0.742903i $$0.733449\pi$$
$$60$$ 22.4571 + 26.3757i 0.374285 + 0.439595i
$$61$$ 38.0000 0.622951 0.311475 0.950254i $$-0.399177\pi$$
0.311475 + 0.950254i $$0.399177\pi$$
$$62$$ 17.6658 20.7462i 0.284932 0.334616i
$$63$$ 2.51176 0.0398692
$$64$$ −29.5619 56.7635i −0.461904 0.886930i
$$65$$ 13.4502 + 22.1721i 0.206926 + 0.341109i
$$66$$ −35.4743 + 41.6600i −0.537489 + 0.631212i
$$67$$ 92.2015 1.37614 0.688071 0.725643i $$-0.258458\pi$$
0.688071 + 0.725643i $$0.258458\pi$$
$$68$$ −108.036 + 17.4400i −1.58876 + 0.256471i
$$69$$ −33.0997 −0.479705
$$70$$ −8.26547 1.33470i −0.118078 0.0190672i
$$71$$ 130.707i 1.84094i −0.390816 0.920469i $$-0.627807\pi$$
0.390816 0.920469i $$-0.372193\pi$$
$$72$$ 12.4488 20.5190i 0.172899 0.284986i
$$73$$ 54.7173i 0.749552i 0.927115 + 0.374776i $$0.122280\pi$$
−0.927115 + 0.374776i $$0.877720\pi$$
$$74$$ −20.1752 + 23.6933i −0.272638 + 0.320179i
$$75$$ 20.0049 38.4032i 0.266732 0.512042i
$$76$$ −70.9485 + 11.4531i −0.933533 + 0.150698i
$$77$$ 13.2249i 0.171751i
$$78$$ 11.6482 13.6793i 0.149336 0.175376i
$$79$$ 13.6243i 0.172459i −0.996275 0.0862297i $$-0.972518\pi$$
0.996275 0.0862297i $$-0.0274819\pi$$
$$80$$ −51.8686 + 60.9069i −0.648357 + 0.761336i
$$81$$ 9.00000 0.111111
$$82$$ −20.2509 17.2440i −0.246962 0.210293i
$$83$$ 59.0048 0.710901 0.355451 0.934695i $$-0.384327\pi$$
0.355451 + 0.934695i $$0.384327\pi$$
$$84$$ 0.924421 + 5.72653i 0.0110050 + 0.0681730i
$$85$$ 70.9485 + 116.956i 0.834688 + 1.37595i
$$86$$ −42.5498 36.2319i −0.494766 0.421302i
$$87$$ −79.0673 −0.908819
$$88$$ −108.036 65.5448i −1.22768 0.744828i
$$89$$ 39.8007 0.447198 0.223599 0.974681i $$-0.428219\pi$$
0.223599 + 0.974681i $$0.428219\pi$$
$$90$$ −29.6164 4.78243i −0.329071 0.0531381i
$$91$$ 4.34246i 0.0477193i
$$92$$ −12.1819 75.4635i −0.132412 0.820255i
$$93$$ 23.5980i 0.253741i
$$94$$ 84.7492 + 72.1654i 0.901587 + 0.767717i
$$95$$ 46.5927 + 76.8064i 0.490450 + 0.808488i
$$96$$ 51.3625 + 20.8300i 0.535026 + 0.216979i
$$97$$ 168.821i 1.74043i −0.492675 0.870214i $$-0.663981\pi$$
0.492675 0.870214i $$-0.336019\pi$$
$$98$$ 73.5467 + 62.6263i 0.750477 + 0.639044i
$$99$$ 47.3865i 0.478652i
$$100$$ 94.9174 + 31.4751i 0.949174 + 0.314751i
$$101$$ 44.5498 0.441087 0.220544 0.975377i $$-0.429217\pi$$
0.220544 + 0.975377i $$0.429217\pi$$
$$102$$ 61.4432 72.1573i 0.602384 0.707424i
$$103$$ −126.466 −1.22782 −0.613911 0.789375i $$-0.710405\pi$$
−0.613911 + 0.789375i $$0.710405\pi$$
$$104$$ 35.4743 + 21.5220i 0.341099 + 0.206943i
$$105$$ 6.19934 3.76068i 0.0590413 0.0358160i
$$106$$ −20.1752 + 23.6933i −0.190333 + 0.223521i
$$107$$ 104.383 0.975546 0.487773 0.872971i $$-0.337809\pi$$
0.487773 + 0.872971i $$0.337809\pi$$
$$108$$ 3.31233 + 20.5190i 0.0306697 + 0.189991i
$$109$$ −0.501656 −0.00460235 −0.00230117 0.999997i $$-0.500732\pi$$
−0.00230117 + 0.999997i $$0.500732\pi$$
$$110$$ −25.1803 + 155.935i −0.228912 + 1.41759i
$$111$$ 26.9501i 0.242794i
$$112$$ −12.7156 + 4.21515i −0.113532 + 0.0376352i
$$113$$ 16.9855i 0.150314i −0.997172 0.0751572i $$-0.976054\pi$$
0.997172 0.0751572i $$-0.0239459\pi$$
$$114$$ 40.3505 47.3865i 0.353952 0.415671i
$$115$$ −81.6941 + 49.5578i −0.710384 + 0.430937i
$$116$$ −29.0997 180.264i −0.250859 1.55400i
$$117$$ 15.5597i 0.132989i
$$118$$ 113.667 133.487i 0.963276 1.13125i
$$119$$ 22.9061i 0.192488i
$$120$$ 0.00347681 69.2820i 2.89734e−5 0.577350i
$$121$$ −128.498 −1.06197
$$122$$ −57.8640 49.2723i −0.474295 0.403871i
$$123$$ 23.0346 0.187273
$$124$$ −53.8007 + 8.68492i −0.433876 + 0.0700397i
$$125$$ −8.12376 124.736i −0.0649901 0.997886i
$$126$$ −3.82475 3.25684i −0.0303552 0.0258480i
$$127$$ 8.45598 0.0665825 0.0332913 0.999446i $$-0.489401\pi$$
0.0332913 + 0.999446i $$0.489401\pi$$
$$128$$ −28.5867 + 124.767i −0.223334 + 0.974742i
$$129$$ 48.3987 0.375184
$$130$$ 8.26810 51.2023i 0.0636008 0.393864i
$$131$$ 51.7290i 0.394878i 0.980315 + 0.197439i $$0.0632624\pi$$
−0.980315 + 0.197439i $$0.936738\pi$$
$$132$$ 108.036 17.4400i 0.818454 0.132121i
$$133$$ 15.0427i 0.113103i
$$134$$ −140.399 119.552i −1.04775 0.892179i
$$135$$ 22.2131 13.4751i 0.164542 0.0998153i
$$136$$ 187.124 + 113.527i 1.37591 + 0.834757i
$$137$$ 53.8083i 0.392762i −0.980528 0.196381i $$-0.937081\pi$$
0.980528 0.196381i $$-0.0629189\pi$$
$$138$$ 50.4021 + 42.9183i 0.365233 + 0.311002i
$$139$$ 13.6243i 0.0980165i 0.998798 + 0.0490082i $$0.0156061\pi$$
−0.998798 + 0.0490082i $$0.984394\pi$$
$$140$$ 10.8555 + 12.7497i 0.0775393 + 0.0910694i
$$141$$ −96.3987 −0.683679
$$142$$ −169.479 + 199.032i −1.19352 + 1.40163i
$$143$$ 81.9243 0.572897
$$144$$ −45.5619 + 15.1035i −0.316402 + 0.104885i
$$145$$ −195.148 + 118.382i −1.34585 + 0.816426i
$$146$$ 70.9485 83.3200i 0.485949 0.570685i
$$147$$ −83.6563 −0.569091
$$148$$ 61.4432 9.91864i 0.415157 0.0670178i
$$149$$ −33.6495 −0.225836 −0.112918 0.993604i $$-0.536020\pi$$
−0.112918 + 0.993604i $$0.536020\pi$$
$$150$$ −80.2572 + 32.5388i −0.535048 + 0.216926i
$$151$$ 139.988i 0.927076i 0.886077 + 0.463538i $$0.153420\pi$$
−0.886077 + 0.463538i $$0.846580\pi$$
$$152$$ 122.886 + 74.5546i 0.808463 + 0.490490i
$$153$$ 82.0759i 0.536444i
$$154$$ −17.1478 + 20.1380i −0.111350 + 0.130766i
$$155$$ 35.3315 + 58.2427i 0.227945 + 0.375759i
$$156$$ −35.4743 + 5.72653i −0.227399 + 0.0367085i
$$157$$ 21.2631i 0.135434i 0.997705 + 0.0677170i $$0.0215715\pi$$
−0.997705 + 0.0677170i $$0.978428\pi$$
$$158$$ −17.6658 + 20.7462i −0.111809 + 0.131305i
$$159$$ 26.9501i 0.169498i
$$160$$ 157.956 25.4904i 0.987228 0.159315i
$$161$$ −16.0000 −0.0993789
$$162$$ −13.7046 11.6697i −0.0845965 0.0720355i
$$163$$ −210.211 −1.28964 −0.644819 0.764335i $$-0.723067\pi$$
−0.644819 + 0.764335i $$0.723067\pi$$
$$164$$ 8.47757 + 52.5162i 0.0516925 + 0.320221i
$$165$$ −70.9485 116.956i −0.429991 0.708824i
$$166$$ −89.8488 76.5079i −0.541258 0.460891i
$$167$$ −238.384 −1.42745 −0.713725 0.700426i $$-0.752994\pi$$
−0.713725 + 0.700426i $$0.752994\pi$$
$$168$$ 6.01759 9.91864i 0.0358190 0.0590395i
$$169$$ 142.100 0.840826
$$170$$ 43.6136 270.088i 0.256550 1.58875i
$$171$$ 53.9002i 0.315206i
$$172$$ 17.8125 + 110.343i 0.103561 + 0.641532i
$$173$$ 2.33481i 0.0134960i −0.999977 0.00674800i $$-0.997852\pi$$
0.999977 0.00674800i $$-0.00214797\pi$$
$$174$$ 120.399 + 102.522i 0.691946 + 0.589205i
$$175$$ 9.67014 18.5637i 0.0552579 0.106078i
$$176$$ 79.5224 + 239.891i 0.451832 + 1.36302i
$$177$$ 151.836i 0.857830i
$$178$$ −60.6060 51.6071i −0.340483 0.289927i
$$179$$ 227.054i 1.26846i −0.773145 0.634229i $$-0.781318\pi$$
0.773145 0.634229i $$-0.218682\pi$$
$$180$$ 38.8969 + 45.6841i 0.216094 + 0.253800i
$$181$$ 114.096 0.630367 0.315183 0.949031i $$-0.397934\pi$$
0.315183 + 0.949031i $$0.397934\pi$$
$$182$$ 5.63060 6.61243i 0.0309374 0.0363320i
$$183$$ 65.8179 0.359661
$$184$$ −79.2990 + 130.707i −0.430973 + 0.710362i
$$185$$ −40.3505 66.5163i −0.218111 0.359547i
$$186$$ 30.5980 35.9335i 0.164505 0.193191i
$$187$$ 432.144 2.31093
$$188$$ −35.4783 219.778i −0.188714 1.16903i
$$189$$ 4.35050 0.0230185
$$190$$ 28.6415 177.370i 0.150745 0.933525i
$$191$$ 139.392i 0.729798i 0.931047 + 0.364899i $$0.118897\pi$$
−0.931047 + 0.364899i $$0.881103\pi$$
$$192$$ −51.2027 98.3173i −0.266681 0.512069i
$$193$$ 182.046i 0.943245i −0.881801 0.471623i $$-0.843669\pi$$
0.881801 0.471623i $$-0.156331\pi$$
$$194$$ −218.900 + 257.071i −1.12835 + 1.32511i
$$195$$ 23.2964 + 38.4032i 0.119469 + 0.196939i
$$196$$ −30.7886 190.727i −0.157085 0.973097i
$$197$$ 258.027i 1.30978i 0.755724 + 0.654890i $$0.227285\pi$$
−0.755724 + 0.654890i $$0.772715\pi$$
$$198$$ −61.4432 + 72.1573i −0.310319 + 0.364431i
$$199$$ 256.474i 1.28881i −0.764683 0.644407i $$-0.777104\pi$$
0.764683 0.644407i $$-0.222896\pi$$
$$200$$ −103.722 171.002i −0.518612 0.855009i
$$201$$ 159.698 0.794516
$$202$$ −67.8377 57.7650i −0.335830 0.285965i
$$203$$ −38.2202 −0.188277
$$204$$ −187.124 + 30.2070i −0.917273 + 0.148073i
$$205$$ 56.8522 34.4880i 0.277328 0.168234i
$$206$$ 192.574 + 163.980i 0.934825 + 0.796020i
$$207$$ −57.3303 −0.276958
$$208$$ −26.1117 78.7697i −0.125537 0.378700i
$$209$$ 283.794 1.35787
$$210$$ −14.3162 2.31177i −0.0681724 0.0110084i
$$211$$ 211.855i 1.00405i −0.864852 0.502027i $$-0.832588\pi$$
0.864852 0.502027i $$-0.167412\pi$$
$$212$$ 61.4432 9.91864i 0.289826 0.0467860i
$$213$$ 226.390i 1.06287i
$$214$$ −158.949 135.348i −0.742750 0.632465i
$$215$$ 119.454 72.4639i 0.555600 0.337041i
$$216$$ 21.5619 35.5399i 0.0998235 0.164537i
$$217$$ 11.4070i 0.0525667i
$$218$$ 0.763890 + 0.650466i 0.00350408 + 0.00298379i
$$219$$ 94.7731i 0.432754i
$$220$$ 240.535 204.799i 1.09334 0.930903i
$$221$$ −141.897 −0.642068
$$222$$ −34.9446 + 41.0380i −0.157408 + 0.184856i
$$223$$ 349.843 1.56880 0.784401 0.620255i $$-0.212971\pi$$
0.784401 + 0.620255i $$0.212971\pi$$
$$224$$ 24.8281 + 10.0690i 0.110840 + 0.0449508i
$$225$$ 34.6495 66.5163i 0.153998 0.295628i
$$226$$ −22.0241 + 25.8645i −0.0974517 + 0.114445i
$$227$$ −185.554 −0.817418 −0.408709 0.912665i $$-0.634021\pi$$
−0.408709 + 0.912665i $$0.634021\pi$$
$$228$$ −122.886 + 19.8373i −0.538976 + 0.0870056i
$$229$$ 263.897 1.15239 0.576194 0.817313i $$-0.304537\pi$$
0.576194 + 0.817313i $$0.304537\pi$$
$$230$$ 188.657 + 30.4642i 0.820249 + 0.132453i
$$231$$ 22.9061i 0.0991607i
$$232$$ −189.427 + 312.227i −0.816494 + 1.34581i
$$233$$ 58.4780i 0.250978i 0.992095 + 0.125489i $$0.0400500\pi$$
−0.992095 + 0.125489i $$0.959950\pi$$
$$234$$ 20.1752 23.6933i 0.0862190 0.101253i
$$235$$ −237.924 + 144.331i −1.01244 + 0.614174i
$$236$$ −346.169 + 55.8812i −1.46682 + 0.236785i
$$237$$ 23.5980i 0.0995694i
$$238$$ 29.7009 34.8800i 0.124794 0.146555i
$$239$$ 113.337i 0.474212i −0.971484 0.237106i $$-0.923801\pi$$
0.971484 0.237106i $$-0.0761989\pi$$
$$240$$ −89.8390 + 105.494i −0.374329 + 0.439558i
$$241$$ −77.7940 −0.322797 −0.161398 0.986889i $$-0.551600\pi$$
−0.161398 + 0.986889i $$0.551600\pi$$
$$242$$ 195.669 + 166.616i 0.808551 + 0.688495i
$$243$$ 15.5885 0.0641500
$$244$$ 24.2234 + 150.057i 0.0992763 + 0.614989i
$$245$$ −206.474 + 125.253i −0.842752 + 0.511235i
$$246$$ −35.0756 29.8675i −0.142584 0.121413i
$$247$$ −93.1855 −0.377269
$$248$$ 93.1855 + 56.5351i 0.375748 + 0.227964i
$$249$$ 102.199 0.410439
$$250$$ −149.367 + 200.473i −0.597467 + 0.801893i
$$251$$ 106.226i 0.423212i 0.977355 + 0.211606i $$0.0678693\pi$$
−0.977355 + 0.211606i $$0.932131\pi$$
$$252$$ 1.60114 + 9.91864i 0.00635374 + 0.0393597i
$$253$$ 301.854i 1.19310i
$$254$$ −12.8762 10.9644i −0.0506939 0.0431667i
$$255$$ 122.886 + 202.574i 0.481908 + 0.794406i
$$256$$ 205.308 152.921i 0.801983 0.597346i
$$257$$ 381.078i 1.48279i 0.671067 + 0.741397i $$0.265836\pi$$
−0.671067 + 0.741397i $$0.734164\pi$$
$$258$$ −73.6985 62.7556i −0.285653 0.243239i
$$259$$ 13.0274i 0.0502988i
$$260$$ −78.9810 + 67.2469i −0.303773 + 0.258642i
$$261$$ −136.949 −0.524707
$$262$$ 67.0738 78.7697i 0.256007 0.300648i
$$263$$ −11.4914 −0.0436934 −0.0218467 0.999761i $$-0.506955\pi$$
−0.0218467 + 0.999761i $$0.506955\pi$$
$$264$$ −187.124 113.527i −0.708802 0.430027i
$$265$$ −40.3505 66.5163i −0.152266 0.251005i
$$266$$ 19.5050 22.9061i 0.0733269 0.0861132i
$$267$$ 68.9368 0.258190
$$268$$ 58.7746 + 364.093i 0.219308 + 1.35855i
$$269$$ −77.9518 −0.289784 −0.144892 0.989447i $$-0.546283\pi$$
−0.144892 + 0.989447i $$0.546283\pi$$
$$270$$ −51.2970 8.28340i −0.189989 0.0306793i
$$271$$ 86.6851i 0.319871i −0.987127 0.159936i $$-0.948871\pi$$
0.987127 0.159936i $$-0.0511287\pi$$
$$272$$ −137.737 415.504i −0.506386 1.52759i
$$273$$ 7.52136i 0.0275508i
$$274$$ −69.7700 + 81.9360i −0.254635 + 0.299036i
$$275$$ −350.220 182.436i −1.27353 0.663402i
$$276$$ −21.0997 130.707i −0.0764481 0.473575i
$$277$$ 287.328i 1.03729i −0.854991 0.518643i $$-0.826437\pi$$
0.854991 0.518643i $$-0.173563\pi$$
$$278$$ 17.6658 20.7462i 0.0635459 0.0746267i
$$279$$ 40.8729i 0.146498i
$$280$$ 0.00168065 33.4901i 6.00232e−6 0.119608i
$$281$$ −224.598 −0.799281 −0.399641 0.916672i $$-0.630865\pi$$
−0.399641 + 0.916672i $$0.630865\pi$$
$$282$$ 146.790 + 124.994i 0.520531 + 0.443242i
$$283$$ −84.1224 −0.297252 −0.148626 0.988893i $$-0.547485\pi$$
−0.148626 + 0.988893i $$0.547485\pi$$
$$284$$ 516.145 83.3200i 1.81741 0.293380i
$$285$$ 80.7010 + 133.033i 0.283161 + 0.466781i
$$286$$ −124.749 106.226i −0.436186 0.371420i
$$287$$ 11.1346 0.0387967
$$288$$ 88.9625 + 36.0786i 0.308898 + 0.125273i
$$289$$ −459.495 −1.58995
$$290$$ 450.657 + 72.7718i 1.55399 + 0.250937i
$$291$$ 292.407i 1.00484i
$$292$$ −216.072 + 34.8800i −0.739972 + 0.119452i
$$293$$ 246.620i 0.841706i −0.907129 0.420853i $$-0.861731\pi$$
0.907129 0.420853i $$-0.138269\pi$$
$$294$$ 127.387 + 108.472i 0.433288 + 0.368952i
$$295$$ 227.333 + 374.750i 0.770621 + 1.27034i
$$296$$ −106.423 64.5661i −0.359536 0.218129i
$$297$$ 82.0759i 0.276350i
$$298$$ 51.2394 + 43.6312i 0.171944 + 0.146414i
$$299$$ 99.1156i 0.331490i
$$300$$ 164.402 + 54.5165i 0.548006 + 0.181722i
$$301$$ 23.3954 0.0777255
$$302$$ 181.514 213.166i 0.601041 0.705846i
$$303$$ 77.1626 0.254662
$$304$$ −90.4535 272.866i −0.297544 0.897586i
$$305$$ 162.447 98.5445i 0.532613 0.323097i
$$306$$ 106.423 124.980i 0.347787 0.408432i
$$307$$ −115.811 −0.377236 −0.188618 0.982051i $$-0.560401\pi$$
−0.188618 + 0.982051i $$0.560401\pi$$
$$308$$ 52.2233 8.43030i 0.169556 0.0273711i
$$309$$ −219.045 −0.708883
$$310$$ 21.7190 134.501i 0.0700614 0.433873i
$$311$$ 203.767i 0.655201i 0.944816 + 0.327600i $$0.106240\pi$$
−0.944816 + 0.327600i $$0.893760\pi$$
$$312$$ 61.4432 + 37.2773i 0.196933 + 0.119478i
$$313$$ 99.0614i 0.316490i −0.987400 0.158245i $$-0.949416\pi$$
0.987400 0.158245i $$-0.0505836\pi$$
$$314$$ 27.5706 32.3782i 0.0878045 0.103115i
$$315$$ 10.7376 6.51369i 0.0340875 0.0206784i
$$316$$ 53.8007 8.68492i 0.170255 0.0274839i
$$317$$ 471.192i 1.48641i −0.669063 0.743206i $$-0.733304\pi$$
0.669063 0.743206i $$-0.266696\pi$$
$$318$$ −34.9446 + 41.0380i −0.109889 + 0.129050i
$$319$$ 721.057i 2.26037i
$$320$$ −273.578 165.997i −0.854931 0.518741i
$$321$$ 180.797 0.563232
$$322$$ 24.3638 + 20.7462i 0.0756640 + 0.0644292i
$$323$$ −491.546 −1.52181
$$324$$ 5.73713 + 35.5399i 0.0177072 + 0.109691i
$$325$$ 114.997 + 59.9038i 0.353836 + 0.184319i
$$326$$ 320.096 + 272.568i 0.981891 + 0.836098i
$$327$$ −0.868893 −0.00265717
$$328$$ 55.1854 90.9607i 0.168248 0.277319i
$$329$$ −46.5980 −0.141635
$$330$$ −43.6136 + 270.088i −0.132162 + 0.818448i
$$331$$ 270.695i 0.817810i 0.912577 + 0.408905i $$0.134089\pi$$
−0.912577 + 0.408905i $$0.865911\pi$$
$$332$$ 37.6131 + 233.003i 0.113293 + 0.701816i
$$333$$ 46.6790i 0.140177i
$$334$$ 362.997 + 309.098i 1.08682 + 0.925444i
$$335$$ 394.154 239.104i 1.17658 0.713743i
$$336$$ −22.0241 + 7.30085i −0.0655479 + 0.0217287i
$$337$$ 377.317i 1.11964i −0.828615 0.559818i $$-0.810871\pi$$
0.828615 0.559818i $$-0.189129\pi$$
$$338$$ −216.380 184.252i −0.640179 0.545124i
$$339$$ 29.4198i 0.0867841i
$$340$$ −416.618 + 354.722i −1.22535 + 1.04330i
$$341$$ 215.203 0.631093
$$342$$ 69.8891 82.0759i 0.204354 0.239988i
$$343$$ −81.4639 −0.237504
$$344$$ 115.952 191.121i 0.337069 0.555583i
$$345$$ −141.498 + 85.8366i −0.410140 + 0.248802i
$$346$$ −3.02740 + 3.55530i −0.00874971 + 0.0102754i
$$347$$ 462.222 1.33205 0.666025 0.745929i $$-0.267994\pi$$
0.666025 + 0.745929i $$0.267994\pi$$
$$348$$ −50.4021 312.227i −0.144834 0.897204i
$$349$$ 200.598 0.574779 0.287390 0.957814i $$-0.407213\pi$$
0.287390 + 0.957814i $$0.407213\pi$$
$$350$$ −38.7954 + 15.7289i −0.110844 + 0.0449397i
$$351$$ 26.9501i 0.0767810i
$$352$$ 189.960 468.403i 0.539660 1.33069i
$$353$$ 250.897i 0.710757i 0.934722 + 0.355379i $$0.115648\pi$$
−0.934722 + 0.355379i $$0.884352\pi$$
$$354$$ 196.876 231.206i 0.556148 0.653125i
$$355$$ −338.958 558.760i −0.954812 1.57397i
$$356$$ 25.3713 + 157.168i 0.0712676 + 0.441483i
$$357$$ 39.6746i 0.111133i
$$358$$ −294.407 + 345.744i −0.822366 + 0.965764i
$$359$$ 215.601i 0.600560i 0.953851 + 0.300280i $$0.0970801\pi$$
−0.953851 + 0.300280i $$0.902920\pi$$
$$360$$ 0.00602201 120.000i 1.67278e−5 0.333333i
$$361$$ 38.1960 0.105806
$$362$$ −173.739 147.942i −0.479941 0.408679i
$$363$$ −222.566 −0.613129
$$364$$ −17.1478 + 2.76814i −0.0471095 + 0.00760478i
$$365$$ 141.897 + 233.912i 0.388759 + 0.640854i
$$366$$ −100.223 85.3420i −0.273835 0.233175i
$$367$$ −67.0637 −0.182735 −0.0913675 0.995817i $$-0.529124\pi$$
−0.0913675 + 0.995817i $$0.529124\pi$$
$$368$$ 290.231 96.2097i 0.788670 0.261439i
$$369$$ 39.8970 0.108122
$$370$$ −24.8043 + 153.607i −0.0670387 + 0.415153i
$$371$$ 13.0274i 0.0351142i
$$372$$ −93.1855 + 15.0427i −0.250499 + 0.0404374i
$$373$$ 567.402i 1.52119i 0.649230 + 0.760593i $$0.275091\pi$$
−0.649230 + 0.760593i $$0.724909\pi$$
$$374$$ −658.042 560.334i −1.75947 1.49822i
$$375$$ −14.0708 216.049i −0.0375220 0.576130i
$$376$$ −230.949 + 380.667i −0.614225 + 1.01241i
$$377$$ 236.764i 0.628020i
$$378$$ −6.62466 5.64102i −0.0175256 0.0149233i
$$379$$ 240.298i 0.634031i −0.948420 0.317016i $$-0.897319\pi$$
0.948420 0.317016i $$-0.102681\pi$$
$$380$$ −273.598 + 232.950i −0.719995 + 0.613026i
$$381$$ 14.6462 0.0384414
$$382$$ 180.740 212.257i 0.473142 0.555646i
$$383$$ 670.068 1.74952 0.874762 0.484553i $$-0.161018\pi$$
0.874762 + 0.484553i $$0.161018\pi$$
$$384$$ −49.5137 + 216.103i −0.128942 + 0.562768i
$$385$$ −34.2957 56.5351i −0.0890797 0.146845i
$$386$$ −236.048 + 277.209i −0.611524 + 0.718157i
$$387$$ 83.8290 0.216612
$$388$$ 666.655 107.617i 1.71818 0.277363i
$$389$$ −474.640 −1.22015 −0.610077 0.792342i $$-0.708861\pi$$
−0.610077 + 0.792342i $$0.708861\pi$$
$$390$$ 14.3208 88.6849i 0.0367199 0.227397i
$$391$$ 522.826i 1.33715i
$$392$$ −200.421 + 330.349i −0.511278 + 0.842726i
$$393$$ 89.5973i 0.227983i
$$394$$ 334.567 392.907i 0.849156 0.997226i
$$395$$ −35.3315 58.2427i −0.0894469 0.147450i
$$396$$ 187.124 30.2070i 0.472535 0.0762802i
$$397$$ 499.460i 1.25809i 0.777371 + 0.629043i $$0.216553\pi$$
−0.777371 + 0.629043i $$0.783447\pi$$
$$398$$ −332.554 + 390.542i −0.835562 + 0.981262i
$$399$$ 26.0548i 0.0653001i
$$400$$ −63.7855 + 394.882i −0.159464 + 0.987204i
$$401$$ 344.694 0.859587 0.429793 0.902927i $$-0.358586\pi$$
0.429793 + 0.902927i $$0.358586\pi$$
$$402$$ −243.178 207.070i −0.604920 0.515100i
$$403$$ −70.6631 −0.175343
$$404$$ 28.3987 + 175.922i 0.0702938 + 0.435450i
$$405$$ 38.4743 23.3395i 0.0949982 0.0576284i
$$406$$ 58.1993 + 49.5578i 0.143348 + 0.122063i
$$407$$ −245.773 −0.603864
$$408$$ 324.108 + 196.635i 0.794382 + 0.481947i
$$409$$ −501.890 −1.22712 −0.613558 0.789650i $$-0.710262\pi$$
−0.613558 + 0.789650i $$0.710262\pi$$
$$410$$ −131.289 21.2005i −0.320218 0.0517085i
$$411$$ 93.1988i 0.226761i
$$412$$ −80.6166 499.397i −0.195671 1.21213i
$$413$$ 73.3957i 0.177714i
$$414$$ 87.2990 + 74.3367i 0.210867 + 0.179557i
$$415$$ 252.241 153.016i 0.607809 0.368713i
$$416$$ −62.3746 + 153.803i −0.149939 + 0.369719i
$$417$$ 23.5980i 0.0565898i
$$418$$ −432.144 367.978i −1.03384 0.880331i
$$419$$ 218.369i 0.521167i 0.965451 + 0.260584i $$0.0839150\pi$$
−0.965451 + 0.260584i $$0.916085\pi$$
$$420$$ 18.8023 + 22.0832i 0.0447674 + 0.0525789i
$$421$$ 281.698 0.669116 0.334558 0.942375i $$-0.391413\pi$$
0.334558 + 0.942375i $$0.391413\pi$$
$$422$$ −274.700 + 322.600i −0.650947 + 0.764455i
$$423$$ −166.967 −0.394722
$$424$$ −106.423 64.5661i −0.250997 0.152279i
$$425$$ 606.598 + 315.988i 1.42729 + 0.743501i
$$426$$ −293.547 + 344.733i −0.689076 + 0.809233i
$$427$$ 31.8156 0.0745097
$$428$$ 66.5401 + 412.197i 0.155468 + 0.963078i
$$429$$ 141.897 0.330762
$$430$$ −275.856 44.5451i −0.641527 0.103593i
$$431$$ 441.081i 1.02339i 0.859167 + 0.511694i $$0.170982\pi$$
−0.859167 + 0.511694i $$0.829018\pi$$
$$432$$ −78.9155 + 26.1600i −0.182675 + 0.0605556i
$$433$$ 123.443i 0.285089i −0.989788 0.142544i $$-0.954472\pi$$
0.989788 0.142544i $$-0.0455283\pi$$
$$434$$ 14.7907 17.3698i 0.0340800 0.0400227i
$$435$$ −338.006 + 205.043i −0.777025 + 0.471364i
$$436$$ −0.319785 1.98098i −0.000733451 0.00454353i
$$437$$ 343.346i 0.785690i
$$438$$ 122.886 144.315i 0.280563 0.329485i
$$439$$ 330.728i 0.753368i −0.926342 0.376684i $$-0.877064\pi$$
0.926342 0.376684i $$-0.122936\pi$$
$$440$$ −631.821 0.0317069i −1.43596 7.20612e-5i
$$441$$ −144.897 −0.328565
$$442$$ 216.072 + 183.989i 0.488850 + 0.416265i
$$443$$ 154.952 0.349780 0.174890 0.984588i $$-0.444043\pi$$
0.174890 + 0.984588i $$0.444043\pi$$
$$444$$ 106.423 17.1796i 0.239691 0.0386928i
$$445$$ 170.145 103.214i 0.382347 0.231942i
$$446$$ −532.718 453.619i −1.19444 1.01708i
$$447$$ −58.2826 −0.130386
$$448$$ −24.7508 47.5254i −0.0552473 0.106084i
$$449$$ −95.8970 −0.213579 −0.106790 0.994282i $$-0.534057\pi$$
−0.106790 + 0.994282i $$0.534057\pi$$
$$450$$ −139.010 + 56.3589i −0.308910 + 0.125242i
$$451$$ 210.065i 0.465775i
$$452$$ 67.0738 10.8276i 0.148393 0.0239548i
$$453$$ 242.467i 0.535247i
$$454$$ 282.550 + 240.596i 0.622356 + 0.529948i
$$455$$ 11.2612 + 18.5637i 0.0247499 + 0.0407992i
$$456$$ 212.846 + 129.132i 0.466767 + 0.283185i
$$457$$ 485.718i 1.06284i 0.847108 + 0.531420i $$0.178341\pi$$
−0.847108 + 0.531420i $$0.821659\pi$$
$$458$$ −401.846 342.179i −0.877393 0.747116i
$$459$$ 142.160i 0.309716i
$$460$$ −247.774 291.009i −0.538640 0.632629i
$$461$$ 353.650 0.767136 0.383568 0.923513i $$-0.374695\pi$$
0.383568 + 0.923513i $$0.374695\pi$$
$$462$$ −29.7009 + 34.8800i −0.0642878 + 0.0754978i
$$463$$ 421.720 0.910842 0.455421 0.890276i $$-0.349489\pi$$
0.455421 + 0.890276i $$0.349489\pi$$
$$464$$ 693.292 229.822i 1.49416 0.495306i
$$465$$ 61.1960 + 100.879i 0.131604 + 0.216945i
$$466$$ 75.8248 89.0466i 0.162714 0.191087i
$$467$$ 640.974 1.37254 0.686268 0.727349i $$-0.259248\pi$$
0.686268 + 0.727349i $$0.259248\pi$$
$$468$$ −61.4432 + 9.91864i −0.131289 + 0.0211937i
$$469$$ 77.1960 0.164597
$$470$$ 549.441 + 88.7232i 1.16902 + 0.188773i
$$471$$ 36.8289i 0.0781929i
$$472$$ 599.582 + 363.763i 1.27030 + 0.770684i
$$473$$ 441.374i 0.933137i
$$474$$ −30.5980 + 35.9335i −0.0645528 + 0.0758091i
$$475$$ 398.360 + 207.513i 0.838653 + 0.436869i
$$476$$ −90.4535 + 14.6017i −0.190028 + 0.0306758i
$$477$$ 46.6790i 0.0978595i
$$478$$ −146.957 + 172.582i −0.307441 + 0.361050i
$$479$$ 221.137i 0.461664i 0.972994 + 0.230832i $$0.0741448\pi$$
−0.972994 + 0.230832i $$0.925855\pi$$
$$480$$ 273.589 44.1507i 0.569976 0.0919806i
$$481$$ 80.7010 0.167778
$$482$$ 118.460 + 100.871i 0.245767 + 0.209275i
$$483$$ −27.7128 −0.0573764
$$484$$ −81.9124 507.424i −0.169240 1.04840i
$$485$$ −437.801 721.698i −0.902682 1.48804i
$$486$$ −23.7371 20.2126i −0.0488418 0.0415897i
$$487$$ −889.949 −1.82741 −0.913705 0.406377i $$-0.866792\pi$$
−0.913705 + 0.406377i $$0.866792\pi$$
$$488$$ 157.684 259.907i 0.323123 0.532596i
$$489$$ −364.096 −0.744573
$$490$$ 476.813 + 76.9955i 0.973089 + 0.157134i
$$491$$ 552.843i 1.12595i −0.826473 0.562977i $$-0.809656\pi$$
0.826473 0.562977i $$-0.190344\pi$$
$$492$$ 14.6836 + 90.9607i 0.0298447 + 0.184879i
$$493$$ 1248.91i 2.53328i
$$494$$ 141.897 + 120.828i 0.287241 + 0.244591i
$$495$$ −122.886 202.574i −0.248255 0.409240i
$$496$$ −68.5914 206.916i −0.138289 0.417169i
$$497$$ 109.435i 0.220190i
$$498$$ −155.623 132.516i −0.312495 0.266096i
$$499$$ 533.302i 1.06874i 0.845250 + 0.534371i $$0.179451\pi$$
−0.845250 + 0.534371i $$0.820549\pi$$
$$500$$ 487.388 111.594i 0.974776 0.223187i
$$501$$ −412.894 −0.824139
$$502$$ 137.737 161.755i 0.274376 0.322220i
$$503$$ −574.914 −1.14297 −0.571485 0.820612i $$-0.693633\pi$$
−0.571485 + 0.820612i $$0.693633\pi$$
$$504$$ 10.4228 17.1796i 0.0206801 0.0340865i
$$505$$ 190.447 115.530i 0.377122 0.228772i
$$506$$ 391.395 459.644i 0.773509 0.908388i
$$507$$ 246.124 0.485451
$$508$$ 5.39034 + 33.3917i 0.0106109 + 0.0657316i
$$509$$ 207.547 0.407753 0.203877 0.978997i $$-0.434646\pi$$
0.203877 + 0.978997i $$0.434646\pi$$
$$510$$ 75.5409 467.806i 0.148119 0.917266i
$$511$$ 45.8122i 0.0896521i
$$512$$ −510.913 33.3518i −0.997876 0.0651403i
$$513$$ 93.3580i 0.181984i
$$514$$ 494.120 580.282i 0.961324 1.12895i
$$515$$ −540.630 + 327.960i −1.04977 + 0.636816i
$$516$$ 30.8522 + 191.121i 0.0597910 + 0.370389i
$$517$$ 879.112i 1.70041i
$$518$$ −16.8918 + 19.8373i −0.0326096 + 0.0382959i
$$519$$ 4.04401i 0.00779192i
$$520$$ 207.462 + 0.0104112i 0.398966 + 2.00214e-5i
$$521$$ −712.900 −1.36833 −0.684165 0.729327i $$-0.739833\pi$$
−0.684165 + 0.729327i $$0.739833\pi$$
$$522$$ 208.537 + 177.573i 0.399495 + 0.340178i
$$523$$ −139.548 −0.266822 −0.133411 0.991061i $$-0.542593\pi$$
−0.133411 + 0.991061i $$0.542593\pi$$
$$524$$ −204.272 + 32.9751i −0.389831 + 0.0629296i
$$525$$ 16.7492 32.1532i 0.0319032 0.0612442i
$$526$$ 17.4983 + 14.9002i 0.0332668 + 0.0283273i
$$527$$ −372.742 −0.707290
$$528$$ 137.737 + 415.504i 0.260865 + 0.786939i
$$529$$ −163.804 −0.309648
$$530$$ −24.8043 + 153.607i −0.0468006 + 0.289824i
$$531$$ 262.988i 0.495268i
$$532$$ −59.4019 + 9.58911i −0.111658 + 0.0180246i
$$533$$ 68.9760i 0.129411i
$$534$$ −104.973 89.3861i −0.196578 0.167390i
$$535$$ 446.230 270.695i 0.834075 0.505972i
$$536$$ 382.598 630.627i 0.713802 1.17654i
$$537$$ 393.269i 0.732345i
$$538$$ 118.700 + 101.075i 0.220632 + 0.187872i
$$539$$ 762.908i 1.41541i
$$540$$ 67.3713 + 79.1271i 0.124762 + 0.146532i
$$541$$ −946.688 −1.74988 −0.874942 0.484227i $$-0.839101\pi$$
−0.874942 + 0.484227i $$0.839101\pi$$
$$542$$ −112.399 + 131.999i −0.207379 + 0.243540i
$$543$$ 197.621 0.363942
$$544$$ −329.021 + 811.298i −0.604818 + 1.49136i
$$545$$ −2.14454 + 1.30093i −0.00393493 + 0.00238703i
$$546$$ 9.75248 11.4531i 0.0178617 0.0209763i
$$547$$ −50.3388 −0.0920271 −0.0460136 0.998941i $$-0.514652\pi$$
−0.0460136 + 0.998941i $$0.514652\pi$$
$$548$$ 212.483 34.3006i 0.387742 0.0625923i
$$549$$ 114.000 0.207650
$$550$$ 296.739 + 731.910i 0.539526 + 1.33074i
$$551$$ 820.173i 1.48852i
$$552$$ −137.350 + 226.390i −0.248822 + 0.410128i
$$553$$ 11.4070i 0.0206275i
$$554$$ −372.561 + 437.525i −0.672492 + 0.789757i
$$555$$ −69.8891 115.210i −0.125926 0.207585i
$$556$$ −53.8007 + 8.68492i −0.0967638 + 0.0156204i
$$557$$ 790.157i 1.41859i 0.704910 + 0.709297i $$0.250987\pi$$
−0.704910 + 0.709297i $$0.749013\pi$$
$$558$$ 52.9973 62.2386i 0.0949773 0.111539i
$$559$$ 144.928i 0.259263i
$$560$$ −43.4272 + 50.9945i −0.0775485 + 0.0910616i
$$561$$ 748.495 1.33422
$$562$$ 342.004 + 291.222i 0.608548 + 0.518189i
$$563$$ 354.133 0.629010 0.314505 0.949256i $$-0.398162\pi$$
0.314505 + 0.949256i $$0.398162\pi$$
$$564$$ −61.4502 380.667i −0.108954 0.674941i
$$565$$ −44.0482 72.6117i −0.0779614 0.128516i
$$566$$ 128.096 + 109.076i 0.226319 + 0.192714i
$$567$$ 7.53528 0.0132897
$$568$$ −893.989 542.378i −1.57392 0.954891i
$$569$$ 55.4983 0.0975366 0.0487683 0.998810i $$-0.484470\pi$$
0.0487683 + 0.998810i $$0.484470\pi$$
$$570$$ 49.6086 307.214i 0.0870326 0.538971i
$$571$$ 791.134i 1.38552i 0.721167 + 0.692762i $$0.243606\pi$$
−0.721167 + 0.692762i $$0.756394\pi$$
$$572$$ 52.2233 + 323.509i 0.0912995 + 0.565575i
$$573$$ 241.433i 0.421349i
$$574$$ −16.9551 14.4376i −0.0295386 0.0251526i
$$575$$ −220.719 + 423.711i −0.383858 + 0.736888i
$$576$$ −88.6856 170.291i −0.153968 0.295643i
$$577$$ 201.759i 0.349668i 0.984598 + 0.174834i $$0.0559389\pi$$
−0.984598 + 0.174834i $$0.944061\pi$$
$$578$$ 699.690 + 595.799i 1.21054 + 1.03079i
$$579$$ 315.313i 0.544583i
$$580$$ −591.874 695.152i −1.02047 1.19854i
$$581$$ 49.4020 0.0850292
$$582$$ −379.146 + 445.260i −0.651454 + 0.765051i
$$583$$ −245.773 −0.421566
$$584$$ 374.248 + 227.054i 0.640835 + 0.388791i
$$585$$ 40.3505 + 66.5163i 0.0689752 + 0.113703i
$$586$$ −319.777 + 375.537i −0.545694 + 0.640848i
$$587$$ 444.556 0.757335 0.378668 0.925533i $$-0.376382\pi$$
0.378668 + 0.925533i $$0.376382\pi$$
$$588$$ −53.3274 330.349i −0.0906929 0.561818i
$$589$$ −244.784 −0.415593
$$590$$ 139.746 865.415i 0.236858 1.46680i
$$591$$ 446.915i 0.756202i
$$592$$ 78.3350 + 236.309i 0.132323 + 0.399171i
$$593$$ 563.908i 0.950942i 0.879731 + 0.475471i $$0.157722\pi$$
−0.879731 + 0.475471i $$0.842278\pi$$
$$594$$ −106.423 + 124.980i −0.179163 + 0.210404i
$$595$$ 59.4019 + 97.9217i 0.0998351 + 0.164574i
$$596$$ −21.4502 132.878i −0.0359902 0.222949i
$$597$$ 444.226i 0.744097i
$$598$$ −128.517 + 150.927i −0.214911 + 0.252386i
$$599$$ 845.034i 1.41074i −0.708839 0.705371i $$-0.750781\pi$$
0.708839 0.705371i $$-0.249219\pi$$
$$600$$ −179.653 296.184i −0.299421 0.493640i
$$601$$ 672.296 1.11863 0.559314 0.828956i $$-0.311065\pi$$
0.559314 + 0.828956i $$0.311065\pi$$
$$602$$ −35.6250 30.3353i −0.0591777 0.0503909i
$$603$$ 276.604 0.458714
$$604$$ −552.797 + 89.2368i −0.915227 + 0.147743i
$$605$$ −549.320 + 333.232i −0.907967 + 0.550796i
$$606$$ −117.498 100.052i −0.193892 0.165102i
$$607$$ −882.664 −1.45414 −0.727071 0.686562i $$-0.759119\pi$$
−0.727071 + 0.686562i $$0.759119\pi$$
$$608$$ −216.072 + 532.789i −0.355381 + 0.876298i
$$609$$ −66.1993 −0.108702
$$610$$ −375.140 60.5774i −0.614984 0.0993072i
$$611$$ 288.662i 0.472442i
$$612$$ −324.108 + 52.3200i −0.529588 + 0.0854902i
$$613$$ 469.374i 0.765701i −0.923810 0.382850i $$-0.874943\pi$$
0.923810 0.382850i $$-0.125057\pi$$
$$614$$ 176.350 + 150.166i 0.287216 + 0.244569i
$$615$$ 98.4708 59.7350i 0.160115 0.0971300i
$$616$$ −90.4535 54.8777i −0.146840 0.0890871i
$$617$$ 218.994i 0.354934i 0.984127 + 0.177467i $$0.0567902\pi$$
−0.984127 + 0.177467i $$0.943210\pi$$
$$618$$ 333.548 + 284.022i 0.539721 + 0.459582i
$$619$$ 879.610i 1.42102i −0.703689 0.710509i $$-0.748465\pi$$
0.703689 0.710509i $$-0.251535\pi$$
$$620$$ −207.471 + 176.647i −0.334631 + 0.284915i
$$621$$ −99.2990 −0.159902
$$622$$ 264.213 310.284i 0.424779 0.498849i
$$623$$ 33.3232 0.0534884
$$624$$ −45.2267 136.433i −0.0724787 0.218643i
$$625$$ −358.203 512.168i −0.573124 0.819468i
$$626$$ −128.447 + 150.845i −0.205187 + 0.240966i
$$627$$ 491.546 0.783964
$$628$$ −83.9656 + 13.5544i −0.133703 + 0.0215834i
$$629$$ 425.691 0.676774
$$630$$ −24.7964 4.00410i −0.0393594 0.00635572i
$$631$$ 635.566i 1.00724i 0.863926 + 0.503618i $$0.167998\pi$$
−0.863926 + 0.503618i $$0.832002\pi$$
$$632$$ −93.1855 56.5351i −0.147445 0.0894543i
$$633$$ 366.944i 0.579691i
$$634$$ −610.966 + 717.502i −0.963669 + 1.13171i
$$635$$ 36.1486 21.9287i 0.0569270 0.0345334i
$$636$$ 106.423 17.1796i 0.167331 0.0270119i
$$637$$ 250.505i 0.393258i
$$638$$ 934.951 1097.98i 1.46544 1.72097i
$$639$$ 392.120i 0.613646i
$$640$$ 201.349 + 607.502i 0.314608 + 0.949222i
$$641$$ −296.309 −0.462260 −0.231130 0.972923i $$-0.574242\pi$$
−0.231130 + 0.972923i $$0.574242\pi$$
$$642$$ −275.307 234.429i −0.428827 0.365154i
$$643$$ 591.032 0.919179 0.459590 0.888131i $$-0.347997\pi$$
0.459590 + 0.888131i $$0.347997\pi$$
$$644$$ −10.1993 63.1821i −0.0158375 0.0981088i
$$645$$ 206.900 125.511i 0.320776 0.194591i
$$646$$ 748.495 + 637.357i 1.15866 + 0.986621i
$$647$$ −166.507 −0.257352 −0.128676 0.991687i $$-0.541073\pi$$
−0.128676 + 0.991687i $$0.541073\pi$$
$$648$$ 37.3463 61.5569i 0.0576331 0.0949953i
$$649$$ 1384.67 2.13355
$$650$$ −97.4362 240.327i −0.149902 0.369734i
$$651$$ 19.7575i 0.0303494i
$$652$$ −134.001 830.098i −0.205523 1.27316i
$$653$$ 621.335i 0.951509i 0.879578 + 0.475754i $$0.157825\pi$$
−0.879578 + 0.475754i $$0.842175\pi$$
$$654$$ 1.32310 + 1.12664i 0.00202308 + 0.00172269i
$$655$$ 134.148 + 221.137i 0.204806 + 0.337614i
$$656$$ −201.976 + 66.9538i −0.307890 + 0.102064i
$$657$$ 164.152i 0.249851i
$$658$$ 70.9565 + 60.4208i 0.107837 + 0.0918249i
$$659$$ 702.113i 1.06542i −0.846297 0.532711i $$-0.821173\pi$$
0.846297 0.532711i $$-0.178827\pi$$
$$660$$ 416.618 354.722i 0.631239 0.537457i
$$661$$ 358.193 0.541895 0.270948 0.962594i $$-0.412663\pi$$
0.270948 + 0.962594i $$0.412663\pi$$
$$662$$ 350.994 412.197i 0.530202 0.622655i
$$663$$ −245.773 −0.370698
$$664$$ 244.846 403.573i 0.368743 0.607790i
$$665$$ 39.0099 + 64.3064i 0.0586616 + 0.0967013i
$$666$$ −60.5257 + 71.0798i −0.0908795 + 0.106726i
$$667$$ 872.367 1.30790
$$668$$ −151.960 941.351i −0.227485 1.40921i
$$669$$ 605.945 0.905748
$$670$$ −910.224 146.982i −1.35854 0.219377i
$$671$$ 600.230i 0.894530i
$$672$$ 43.0035 + 17.4400i 0.0639933 + 0.0259524i
$$673$$ 714.176i 1.06118i 0.847628 + 0.530592i $$0.178030\pi$$
−0.847628 + 0.530592i $$0.821970\pi$$
$$674$$ −489.244 + 574.555i −0.725882 + 0.852456i
$$675$$ 60.0147 115.210i 0.0889107 0.170681i
$$676$$ 90.5827 + 561.134i 0.133998 + 0.830081i
$$677$$ 509.833i 0.753077i −0.926401 0.376538i $$-0.877114\pi$$
0.926401 0.376538i $$-0.122886\pi$$
$$678$$ −38.1468 + 44.7986i −0.0562638 + 0.0660747i
$$679$$ 141.346i 0.208168i
$$680$$ 1094.35 + 0.0549180i 1.60933 + 8.07617e-5i
$$681$$ −321.389 −0.471936
$$682$$ −327.697 279.040i −0.480494 0.409150i
$$683$$ −1263.93 −1.85055 −0.925275 0.379298i $$-0.876166\pi$$
−0.925275 + 0.379298i $$0.876166\pi$$
$$684$$ −212.846 + 34.3592i −0.311178 + 0.0502327i
$$685$$ −139.540 230.026i −0.203708 0.335805i
$$686$$ 124.048 + 105.629i 0.180828 + 0.153978i
$$687$$ 457.083 0.665332
$$688$$ −424.378 + 140.679i −0.616829 + 0.204475i
$$689$$ 80.7010 0.117128
$$690$$ 326.764 + 52.7656i 0.473571 + 0.0764718i
$$691$$ 512.351i 0.741463i 0.928740 + 0.370731i $$0.120893\pi$$
−0.928740 + 0.370731i $$0.879107\pi$$
$$692$$ 9.21987 1.48834i 0.0133235 0.00215078i
$$693$$ 39.6746i 0.0572504i
$$694$$ −703.842 599.334i −1.01418 0.863594i
$$695$$ 35.3315 + 58.2427i 0.0508368 + 0.0838024i
$$696$$ −328.096 + 540.793i −0.471403 + 0.777002i
$$697$$ 363.843i 0.522012i
$$698$$ −305.458 260.103i −0.437619 0.372640i
$$699$$ 101.287i 0.144902i
$$700$$ 79.4699 + 26.3526i 0.113528 + 0.0376466i
$$701$$ 1092.03 1.55781 0.778907 0.627139i $$-0.215774\pi$$
0.778907 + 0.627139i $$0.215774\pi$$
$$702$$ 34.9446 41.0380i 0.0497786 0.0584586i
$$703$$ 279.556 0.397662
$$704$$ −896.609 + 466.945i −1.27359 + 0.663274i
$$705$$ −412.096 + 249.988i −0.584534 + 0.354593i
$$706$$ 325.323 382.051i 0.460798 0.541148i
$$707$$ 37.2995 0.0527574
$$708$$ −599.582 + 96.7891i −0.846867 + 0.136708i
$$709$$ 416.887 0.587993 0.293997 0.955806i $$-0.405015\pi$$
0.293997 + 0.955806i $$0.405015\pi$$
$$710$$ −208.365 + 1290.35i −0.293472 + 1.81740i
$$711$$ 40.8729i 0.0574864i
$$712$$ 165.156 272.223i 0.231961 0.382336i
$$713$$ 260.362i 0.365163i
$$714$$ 51.4435 60.4139i 0.0720498 0.0846133i
$$715$$ 350.220 212.452i 0.489818 0.297136i
$$716$$ 896.609 144.738i 1.25225 0.202147i
$$717$$ 196.305i 0.273787i
$$718$$ 279.556 328.304i 0.389354 0.457247i
$$719$$ 395.268i 0.549747i −0.961480 0.274874i $$-0.911364\pi$$
0.961480 0.274874i $$-0.0886361\pi$$
$$720$$ −155.606 + 182.721i −0.216119 + 0.253779i
$$721$$ −105.884 −0.146857
$$722$$ −58.1625 49.5264i −0.0805575 0.0685962i
$$723$$ −134.743 −0.186367
$$724$$ 72.7317 + 450.553i 0.100458 + 0.622310i
$$725$$ −527.244 + 1012.14i −0.727233 + 1.39606i
$$726$$ 338.909 + 288.587i 0.466817 + 0.397503i
$$727$$ −597.583 −0.821985 −0.410993 0.911639i $$-0.634818\pi$$
−0.410993 + 0.911639i $$0.634818\pi$$
$$728$$ 29.7009 + 18.0194i 0.0407980 + 0.0247519i
$$729$$ 27.0000 0.0370370
$$730$$ 87.2271 540.175i 0.119489 0.739966i
$$731$$ 764.482i 1.04580i
$$732$$ 41.9562 + 259.907i 0.0573172 + 0.355064i
$$733$$ 23.8650i 0.0325580i −0.999867 0.0162790i $$-0.994818\pi$$
0.999867 0.0162790i $$-0.00518200\pi$$
$$734$$ 102.120 + 86.9574i 0.139129 + 0.118471i
$$735$$ −357.624 + 216.944i −0.486563 + 0.295162i
$$736$$ −566.694 229.822i −0.769965 0.312258i
$$737$$ 1456.37i 1.97608i
$$738$$ −60.7527 51.7320i −0.0823207 0.0700976i
$$739$$ 125.767i 0.170186i 0.996373 + 0.0850928i $$0.0271187\pi$$
−0.996373 + 0.0850928i $$0.972881\pi$$
$$740$$ 236.943 201.741i 0.320193 0.272622i
$$741$$ −161.402 −0.217816
$$742$$ −16.8918 + 19.8373i −0.0227652 + 0.0267349i
$$743$$ −148.841 −0.200325 −0.100162 0.994971i $$-0.531936\pi$$
−0.100162 + 0.994971i $$0.531936\pi$$
$$744$$ 161.402 + 97.9217i 0.216938 + 0.131615i
$$745$$ −143.849 + 87.2625i −0.193086 + 0.117131i
$$746$$ 735.715 864.004i 0.986213 1.15818i
$$747$$ 177.014 0.236967
$$748$$ 275.474 + 1706.48i 0.368280 + 2.28140i
$$749$$ 87.3954 0.116683
$$750$$ −258.711 + 347.230i −0.344948 + 0.462973i
$$751$$ 463.390i 0.617030i −0.951219 0.308515i $$-0.900168\pi$$
0.951219 0.308515i $$-0.0998321\pi$$
$$752$$ 845.261 280.199i 1.12402 0.372605i
$$753$$ 183.989i 0.244341i
$$754$$ −306.997 + 360.529i −0.407157 + 0.478155i
$$755$$ 363.029 + 598.439i 0.480833 + 0.792634i
$$756$$ 2.77326 + 17.1796i 0.00366834 + 0.0227243i
$$757$$ 719.363i 0.950281i −0.879910 0.475141i $$-0.842397\pi$$
0.879910 0.475141i $$-0.157603\pi$$
$$758$$ −311.579 + 365.910i −0.411054 + 0.482731i
$$759$$ 522.826i 0.688836i
$$760$$ 718.670 + 0.0360653i 0.945618 + 4.74543e-5i
$$761$$ −1107.49 −1.45530 −0.727651 0.685947i $$-0.759388\pi$$
−0.727651 + 0.685947i $$0.759388\pi$$
$$762$$ −22.3023 18.9908i −0.0292681 0.0249223i
$$763$$ −0.420013 −0.000550476
$$764$$ −550.440 + 88.8563i −0.720472 + 0.116304i
$$765$$ 212.846 + 350.868i 0.278229 + 0.458651i
$$766$$ −1020.34 868.835i −1.33203 1.13425i
$$767$$ −454.666 −0.592785
$$768$$ 355.603 264.866i 0.463025 0.344878i
$$769$$ −231.691 −0.301289 −0.150644 0.988588i $$-0.548135\pi$$
−0.150644 + 0.988588i $$0.548135\pi$$
$$770$$ −21.0823 + 130.557i −0.0273796 + 0.169555i
$$771$$ 660.047i 0.856092i
$$772$$ 718.879 116.047i 0.931190 0.150320i
$$773$$ 519.956i 0.672647i 0.941746 + 0.336324i $$0.109184\pi$$
−0.941746 + 0.336324i $$0.890816\pi$$
$$774$$ −127.650 108.696i −0.164922 0.140434i
$$775$$ 302.079 + 157.358i 0.389779 + 0.203043i
$$776$$ −1154.68 700.539i −1.48799 0.902756i
$$777$$ 22.5641i 0.0290400i