Properties

Label 60.3.f.b.19.2
Level $60$
Weight $3$
Character 60.19
Analytic conductor $1.635$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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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 19.2
Root \(-1.52274 + 1.29664i\) of defining polynomial
Character \(\chi\) \(=\) 60.19
Dual form 60.3.f.b.19.1

$q$-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 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 \(0.254932\pi\)
−0.696066 + 0.717978i \(0.745068\pi\)
\(12\) 1.10411 6.83966i 0.0920092 0.569972i
\(13\) 5.18655i 0.398966i −0.979901 0.199483i \(-0.936074\pi\)
0.979901 0.199483i \(-0.0639262\pi\)
\(14\) −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 \(-0.702344\pi\)
0.593728 0.804666i \(-0.297656\pi\)
\(18\) −4.56821 + 3.88991i −0.253790 + 0.216106i
\(19\) 17.9667i 0.945618i −0.881165 0.472809i \(-0.843240\pi\)
0.881165 0.472809i \(-0.156760\pi\)
\(20\) 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 \(-0.929477\pi\)
0.975557 0.219747i \(-0.0705230\pi\)
\(32\) 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 \(0.0674329\pi\)
−0.977644 + 0.210266i \(0.932567\pi\)
\(38\) 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 \(0.0468939\pi\)
−0.989168 + 0.146789i \(0.953106\pi\)
\(54\) −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 \(-0.733449\pi\)
0.669400 0.742903i \(-0.266551\pi\)
\(60\) 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 \(0.372193\pi\)
−0.390816 + 0.920469i \(0.627807\pi\)
\(72\) 12.4488 + 20.5190i 0.172899 + 0.284986i
\(73\) 54.7173i 0.749552i −0.927115 0.374776i \(-0.877720\pi\)
0.927115 0.374776i \(-0.122280\pi\)
\(74\) −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 \(0.0274819\pi\)
−0.996275 + 0.0862297i \(0.972518\pi\)
\(80\) −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 \(0.336019\pi\)
−0.492675 + 0.870214i \(0.663981\pi\)
\(98\) 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 \(0.0239459\pi\)
−0.997172 + 0.0751572i \(0.976054\pi\)
\(114\) 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 \(-0.936738\pi\)
0.980315 0.197439i \(-0.0632624\pi\)
\(132\) 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 \(0.0629189\pi\)
−0.980528 + 0.196381i \(0.937081\pi\)
\(138\) 50.4021 42.9183i 0.365233 0.311002i
\(139\) 13.6243i 0.0980165i −0.998798 0.0490082i \(-0.984394\pi\)
0.998798 0.0490082i \(-0.0156061\pi\)
\(140\) 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 \(-0.846580\pi\)
0.886077 0.463538i \(-0.153420\pi\)
\(152\) 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 \(-0.978428\pi\)
0.997705 0.0677170i \(-0.0215715\pi\)
\(158\) −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 \(0.00214797\pi\)
−0.999977 + 0.00674800i \(0.997852\pi\)
\(174\) 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 \(0.218682\pi\)
−0.773145 + 0.634229i \(0.781318\pi\)
\(180\) 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 \(-0.881103\pi\)
0.931047 0.364899i \(-0.118897\pi\)
\(192\) −51.2027 + 98.3173i −0.266681 + 0.512069i
\(193\) 182.046i 0.943245i 0.881801 + 0.471623i \(0.156331\pi\)
−0.881801 + 0.471623i \(0.843669\pi\)
\(194\) −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 \(-0.772715\pi\)
0.755724 0.654890i \(-0.227285\pi\)
\(198\) −61.4432 72.1573i −0.310319 0.364431i
\(199\) 256.474i 1.28881i 0.764683 + 0.644407i \(0.222896\pi\)
−0.764683 + 0.644407i \(0.777104\pi\)
\(200\) −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 \(0.167412\pi\)
−0.864852 + 0.502027i \(0.832588\pi\)
\(212\) 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 \(-0.959950\pi\)
0.992095 0.125489i \(-0.0400500\pi\)
\(234\) 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 \(0.0761989\pi\)
−0.971484 + 0.237106i \(0.923801\pi\)
\(240\) −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 \(-0.932131\pi\)
0.977355 0.211606i \(-0.0678693\pi\)
\(252\) 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 \(-0.734164\pi\)
0.671067 0.741397i \(-0.265836\pi\)
\(258\) −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 \(0.0511287\pi\)
−0.987127 + 0.159936i \(0.948871\pi\)
\(272\) −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 \(0.173563\pi\)
−0.854991 + 0.518643i \(0.826437\pi\)
\(278\) 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 \(0.138269\pi\)
−0.907129 + 0.420853i \(0.861731\pi\)
\(294\) 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 \(-0.893760\pi\)
0.944816 0.327600i \(-0.106240\pi\)
\(312\) 61.4432 37.2773i 0.196933 0.119478i
\(313\) 99.0614i 0.316490i 0.987400 + 0.158245i \(0.0505836\pi\)
−0.987400 + 0.158245i \(0.949416\pi\)
\(314\) 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 \(0.266696\pi\)
−0.669063 + 0.743206i \(0.733304\pi\)
\(318\) −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 \(-0.865911\pi\)
0.912577 0.408905i \(-0.134089\pi\)
\(332\) 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 \(0.189129\pi\)
−0.828615 + 0.559818i \(0.810871\pi\)
\(338\) −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 \(-0.884352\pi\)
0.934722 0.355379i \(-0.115648\pi\)
\(354\) 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 \(-0.902920\pi\)
0.953851 0.300280i \(-0.0970801\pi\)
\(360\) 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 \(-0.724909\pi\)
0.649230 0.760593i \(-0.275091\pi\)
\(374\) −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 \(0.102681\pi\)
−0.948420 + 0.317016i \(0.897319\pi\)
\(380\) −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 \(-0.783447\pi\)
0.777371 0.629043i \(-0.216553\pi\)
\(398\) −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 \(-0.916085\pi\)
0.965451 0.260584i \(-0.0839150\pi\)
\(420\) 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 \(-0.829018\pi\)
0.859167 0.511694i \(-0.170982\pi\)
\(432\) −78.9155 26.1600i −0.182675 0.0605556i
\(433\) 123.443i 0.285089i 0.989788 + 0.142544i \(0.0455283\pi\)
−0.989788 + 0.142544i \(0.954472\pi\)
\(434\) 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 \(0.122936\pi\)
−0.926342 + 0.376684i \(0.877064\pi\)
\(440\) −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 \(-0.821659\pi\)
0.847108 0.531420i \(-0.178341\pi\)
\(458\) −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 \(-0.925855\pi\)
0.972994 0.230832i \(-0.0741448\pi\)
\(480\) 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 \(0.190344\pi\)
−0.826473 + 0.562977i \(0.809656\pi\)
\(492\) 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 \(-0.820549\pi\)
0.845250 0.534371i \(-0.179451\pi\)
\(500\) 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 \(-0.749013\pi\)
0.704910 0.709297i \(-0.250987\pi\)
\(558\) 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 \(-0.756394\pi\)
0.721167 0.692762i \(-0.243606\pi\)
\(572\) 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 \(-0.944061\pi\)
0.984598 0.174834i \(-0.0559389\pi\)
\(578\) 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 \(-0.842278\pi\)
0.879731 0.475471i \(-0.157722\pi\)
\(594\) −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 \(0.249219\pi\)
−0.708839 + 0.705371i \(0.750781\pi\)
\(600\) −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 \(0.125057\pi\)
−0.923810 + 0.382850i \(0.874943\pi\)
\(614\) 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 \(-0.943210\pi\)
0.984127 0.177467i \(-0.0567902\pi\)
\(618\) 333.548 284.022i 0.539721 0.459582i
\(619\) 879.610i 1.42102i 0.703689 + 0.710509i \(0.251535\pi\)
−0.703689 + 0.710509i \(0.748465\pi\)
\(620\) −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 \(-0.832002\pi\)
0.863926 0.503618i \(-0.167998\pi\)
\(632\) −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 \(-0.842175\pi\)
0.879578 0.475754i \(-0.157825\pi\)
\(654\) 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 \(0.178827\pi\)
−0.846297 + 0.532711i \(0.821173\pi\)
\(660\) 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 \(-0.821970\pi\)
0.847628 0.530592i \(-0.178030\pi\)
\(674\) −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 \(0.122886\pi\)
−0.926401 + 0.376538i \(0.877114\pi\)
\(678\) −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 \(-0.879107\pi\)
0.928740 0.370731i \(-0.120893\pi\)
\(692\) 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 \(0.0886361\pi\)
−0.961480 + 0.274874i \(0.911364\pi\)
\(720\) −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 \(0.00518200\pi\)
−0.999867 + 0.0162790i \(0.994818\pi\)
\(734\) 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 \(-0.972881\pi\)
0.996373 0.0850928i \(-0.0271187\pi\)
\(740\) 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 \(0.0998321\pi\)
−0.951219 + 0.308515i \(0.900168\pi\)
\(752\) 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 \(0.157603\pi\)
−0.879910 + 0.475141i \(0.842397\pi\)
\(758\) −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 \(-0.890816\pi\)
0.941746 0.336324i \(-0.109184\pi\)
\(774\) −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