Properties

Label 60.3.f.b.19.7
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 19.7
Root \(1.52274 - 1.29664i\) of defining polynomial
Character \(\chi\) \(=\) 60.19
Dual form 60.3.f.b.19.8

$q$-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} +(3.14704 - 9.49190i) 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} +(-7.51545 - 18.5342i) 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} +(-5.45082 + 16.4405i) 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} +(-35.4763 - 18.4780i) 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} +(-11.1618 - 48.7382i) 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} +(13.0171 + 32.1022i) 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} +(-2.63487 + 7.94713i) 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} +(-77.9803 + 17.8628i) 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} +(9.44111 - 28.4757i) 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 \(-0.519048\pi\)
−0.0598038 + 0.998210i \(0.519048\pi\)
\(8\) −4.14959 6.83966i −0.518698 0.854957i
\(9\) 3.00000 0.333333
\(10\) 3.14704 9.49190i 0.314704 0.949190i
\(11\) 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 \(0.0639262\pi\)
−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 \(-0.843240\pi\)
0.881165 0.472809i \(-0.156760\pi\)
\(20\) −7.51545 18.5342i −0.375773 0.926712i
\(21\) 1.45017 0.0690555
\(22\) 20.4811 + 24.0524i 0.930958 + 1.09329i
\(23\) 19.1101 0.830874 0.415437 0.909622i \(-0.363629\pi\)
0.415437 + 0.909622i \(0.363629\pi\)
\(24\) 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 \(0.788398\pi\)
\(30\) −5.45082 + 16.4405i −0.181694 + 0.548015i
\(31\) 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 \(-0.932567\pi\)
0.977644 0.210266i \(-0.0674329\pi\)
\(38\) −23.2964 27.3586i −0.613062 0.719964i
\(39\) 8.98337i 0.230343i
\(40\) −35.4763 18.4780i −0.886907 0.461949i
\(41\) 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 \(-0.605337\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(44\) 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 \(-0.298306\pi\)
0.592083 + 0.805877i \(0.298306\pi\)
\(48\) 26.3052 + 8.72000i 0.548024 + 0.181667i
\(49\) −48.2990 −0.985694
\(50\) −11.1618 48.7382i −0.223236 0.974764i
\(51\) 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 \(-0.733449\pi\)
0.669400 0.742903i \(-0.266551\pi\)
\(60\) 13.0171 + 32.1022i 0.216952 + 0.535037i
\(61\) 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 \(-0.741542\pi\)
−0.688071 + 0.725643i \(0.741542\pi\)
\(68\) 108.036 + 17.4400i 1.58876 + 0.256471i
\(69\) −33.0997 −0.479705
\(70\) −2.63487 + 7.94713i −0.0376409 + 0.113530i
\(71\) 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 \(0.122280\pi\)
−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 \(0.0274819\pi\)
−0.996275 + 0.0862297i \(0.972518\pi\)
\(80\) −77.9803 + 17.8628i −0.974753 + 0.223285i
\(81\) 9.00000 0.111111
\(82\) 20.2509 17.2440i 0.246962 0.210293i
\(83\) −59.0048 −0.710901 −0.355451 0.934695i \(-0.615673\pi\)
−0.355451 + 0.934695i \(0.615673\pi\)
\(84\) 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 \(0.428219\pi\)
\(90\) 9.44111 28.4757i 0.104901 0.316397i
\(91\) 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
\(100\) −80.1923 59.7427i −0.801923 0.597427i
\(101\) 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 \(-0.289595\pi\)
0.613911 + 0.789375i \(0.289595\pi\)
\(104\) 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 \(-0.662191\pi\)
−0.487773 + 0.872971i \(0.662191\pi\)
\(108\) −3.31233 + 20.5190i −0.0306697 + 0.189991i
\(109\) −0.501656 −0.00460235 −0.00230117 0.999997i \(-0.500732\pi\)
−0.00230117 + 0.999997i \(0.500732\pi\)
\(110\) 149.929 + 49.7090i 1.36300 + 0.451900i
\(111\) 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
\(120\) 61.4467 + 32.0048i 0.512056 + 0.266706i
\(121\) −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 \(-0.510599\pi\)
−0.0332913 + 0.999446i \(0.510599\pi\)
\(128\) 28.5867 + 124.767i 0.223334 + 0.974742i
\(129\) 48.3987 0.375184
\(130\) 49.2302 + 16.3223i 0.378694 + 0.125556i
\(131\) 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 \(-0.937081\pi\)
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 \(-0.984394\pi\)
0.998798 0.0490082i \(-0.0156061\pi\)
\(140\) 6.29234 + 15.5179i 0.0449453 + 0.110842i
\(141\) −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 \(0.536020\pi\)
\(150\) 19.3328 + 84.4171i 0.128885 + 0.562780i
\(151\) 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 \(0.0215715\pi\)
−0.997705 + 0.0677170i \(0.978428\pi\)
\(158\) 17.6658 + 20.7462i 0.111809 + 0.131305i
\(159\) 26.9501i 0.169498i
\(160\) −95.5819 + 128.313i −0.597387 + 0.801953i
\(161\) −16.0000 −0.0993789
\(162\) 13.7046 11.6697i 0.0845965 0.0720355i
\(163\) 210.211 1.28964 0.644819 0.764335i \(-0.276933\pi\)
0.644819 + 0.764335i \(0.276933\pi\)
\(164\) 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 \(-0.247006\pi\)
0.713725 + 0.700426i \(0.247006\pi\)
\(168\) −6.01759 9.91864i −0.0358190 0.0590395i
\(169\) 142.100 0.840826
\(170\) 259.685 + 86.0986i 1.52756 + 0.506462i
\(171\) 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 \(0.218682\pi\)
−0.773145 + 0.634229i \(0.781318\pi\)
\(180\) −22.5464 55.6027i −0.125258 0.308904i
\(181\) 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
\(190\) −170.539 56.5420i −0.897571 0.297589i
\(191\) 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 \(-0.843669\pi\)
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 \(0.222896\pi\)
−0.764683 + 0.644407i \(0.777104\pi\)
\(200\) −199.577 + 13.0080i −0.997883 + 0.0650401i
\(201\) 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
\(210\) 4.56372 13.7648i 0.0217320 0.0655468i
\(211\) 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
\(220\) 292.758 118.710i 1.33072 0.539593i
\(221\) −141.897 −0.642068
\(222\) 34.9446 + 41.0380i 0.157408 + 0.184856i
\(223\) −349.843 −1.56880 −0.784401 0.620255i \(-0.787029\pi\)
−0.784401 + 0.620255i \(0.787029\pi\)
\(224\) 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 \(-0.365979\pi\)
0.408709 + 0.912665i \(0.365979\pi\)
\(228\) 122.886 + 19.8373i 0.538976 + 0.0870056i
\(229\) 263.897 1.15239 0.576194 0.817313i \(-0.304537\pi\)
0.576194 + 0.817313i \(0.304537\pi\)
\(230\) 60.1402 181.391i 0.261479 0.788657i
\(231\) 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 \(0.0761989\pi\)
−0.971484 + 0.237106i \(0.923801\pi\)
\(240\) 135.066 30.9393i 0.562774 0.128914i
\(241\) −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
\(250\) −174.107 179.406i −0.696430 0.717625i
\(251\) 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 \(0.265836\pi\)
−0.671067 + 0.741397i \(0.734164\pi\)
\(258\) 73.6985 62.7556i 0.285653 0.243239i
\(259\) 13.0274i 0.0502988i
\(260\) 96.1288 38.9793i 0.369726 0.149920i
\(261\) −136.949 −0.524707
\(262\) −67.0738 78.7697i −0.256007 0.300648i
\(263\) 11.4914 0.0436934 0.0218467 0.999761i \(-0.493045\pi\)
0.0218467 + 0.999761i \(0.493045\pi\)
\(264\) −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 \(0.546283\pi\)
\(270\) −16.3525 + 49.3214i −0.0605647 + 0.182672i
\(271\) 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 \(-0.826437\pi\)
0.854991 0.518643i \(-0.173563\pi\)
\(278\) −17.6658 20.7462i −0.0635459 0.0746267i
\(279\) 40.8729i 0.146498i
\(280\) 29.7026 + 15.4707i 0.106081 + 0.0552526i
\(281\) −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 \(-0.452515\pi\)
0.148626 + 0.988893i \(0.452515\pi\)
\(284\) 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
\(290\) −143.661 + 433.301i −0.495381 + 1.49414i
\(291\) 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
\(300\) 138.897 + 103.477i 0.462991 + 0.344925i
\(301\) 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 \(-0.439599\pi\)
0.188618 + 0.982051i \(0.439599\pi\)
\(308\) −52.2233 8.43030i −0.169556 0.0273711i
\(309\) −219.045 −0.708883
\(310\) −129.320 42.8761i −0.417162 0.138310i
\(311\) 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 \(-0.949416\pi\)
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
\(320\) 20.8289 + 319.321i 0.0650902 + 0.997879i
\(321\) 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
\(330\) −259.685 86.0986i −0.786926 0.260905i
\(331\) 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 \(-0.810871\pi\)
0.828615 0.559818i \(-0.189129\pi\)
\(338\) 216.380 184.252i 0.640179 0.545124i
\(339\) 29.4198i 0.0867841i
\(340\) 507.071 205.613i 1.49139 0.604743i
\(341\) 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 \(-0.732006\pi\)
−0.666025 + 0.745929i \(0.732006\pi\)
\(348\) 50.4021 312.227i 0.144834 0.897204i
\(349\) 200.598 0.574779 0.287390 0.957814i \(-0.407213\pi\)
0.287390 + 0.957814i \(0.407213\pi\)
\(350\) 9.34526 + 40.8062i 0.0267007 + 0.116589i
\(351\) 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 \(-0.902920\pi\)
0.953851 0.300280i \(-0.0970801\pi\)
\(360\) −106.429 55.4339i −0.295636 0.153983i
\(361\) 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 \(-0.470876\pi\)
0.0913675 + 0.995817i \(0.470876\pi\)
\(368\) −290.231 96.2097i −0.788670 0.261439i
\(369\) 39.8970 0.108122
\(370\) −147.691 48.9668i −0.399164 0.132343i
\(371\) 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 \(0.102681\pi\)
−0.948420 + 0.317016i \(0.897319\pi\)
\(380\) −333.000 + 135.028i −0.876316 + 0.355337i
\(381\) 14.6462 0.0384414
\(382\) −180.740 212.257i −0.473142 0.555646i
\(383\) −670.068 −1.74952 −0.874762 0.484553i \(-0.838982\pi\)
−0.874762 + 0.484553i \(0.838982\pi\)
\(384\) −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 \(0.708861\pi\)
\(390\) −85.2693 28.2710i −0.218639 0.0724897i
\(391\) 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
\(400\) −287.036 + 278.586i −0.717590 + 0.696466i
\(401\) 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 \(0.710262\pi\)
\(410\) 41.8524 126.233i 0.102079 0.307885i
\(411\) 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 \(-0.0839150\pi\)
\(420\) −10.8987 26.8777i −0.0259492 0.0639946i
\(421\) 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
\(430\) −87.9376 + 265.232i −0.204506 + 0.616819i
\(431\) 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 \(-0.954472\pi\)
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 \(0.122936\pi\)
−0.926342 + 0.376684i \(0.877064\pi\)
\(440\) 291.869 560.366i 0.663338 1.27356i
\(441\) −144.897 −0.328565
\(442\) −216.072 + 183.989i −0.488850 + 0.416265i
\(443\) −154.952 −0.349780 −0.174890 0.984588i \(-0.555957\pi\)
−0.174890 + 0.984588i \(0.555957\pi\)
\(444\) 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 \(0.534057\pi\)
\(450\) −33.4854 146.215i −0.0744120 0.324921i
\(451\) 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
\(460\) −143.621 354.191i −0.312220 0.769981i
\(461\) 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 \(-0.650511\pi\)
−0.455421 + 0.890276i \(0.650511\pi\)
\(464\) 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 \(-0.740752\pi\)
−0.686268 + 0.727349i \(0.740752\pi\)
\(468\) 61.4432 + 9.91864i 0.131289 + 0.0211937i
\(469\) 77.1960 0.164597
\(470\) 175.151 528.279i 0.372661 1.12400i
\(471\) 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 \(-0.0741448\pi\)
\(480\) 165.553 222.244i 0.344901 0.463008i
\(481\) 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 \(-0.133208\pi\)
0.913705 + 0.406377i \(0.133208\pi\)
\(488\) −157.684 259.907i −0.323123 0.532596i
\(489\) −364.096 −0.744573
\(490\) −151.999 + 458.449i −0.310201 + 0.935611i
\(491\) 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 \(-0.179451\pi\)
\(500\) −497.745 47.4341i −0.995490 0.0948683i
\(501\) −412.894 −0.824139
\(502\) −137.737 161.755i −0.274376 0.322220i
\(503\) 574.914 1.14297 0.571485 0.820612i \(-0.306367\pi\)
0.571485 + 0.820612i \(0.306367\pi\)
\(504\) 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 \(0.434646\pi\)
\(510\) −449.788 149.127i −0.881938 0.292406i
\(511\) 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
\(520\) 95.8369 184.000i 0.184302 0.353845i
\(521\) −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 \(-0.457407\pi\)
0.133411 + 0.991061i \(0.457407\pi\)
\(524\) −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
\(530\) −147.691 48.9668i −0.278662 0.0923902i
\(531\) 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
\(540\) 39.0514 + 96.3067i 0.0723175 + 0.178346i
\(541\) −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 \(-0.485348\pi\)
0.0460136 + 0.998941i \(0.485348\pi\)
\(548\) −212.483 34.3006i −0.387742 0.0625923i
\(549\) 114.000 0.207650
\(550\) 769.845 176.307i 1.39972 0.320557i
\(551\) 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
\(560\) 65.2892 14.9557i 0.116588 0.0267066i
\(561\) 748.495 1.33422
\(562\) −342.004 + 291.222i −0.608548 + 0.518189i
\(563\) −354.133 −0.629010 −0.314505 0.949256i \(-0.601838\pi\)
−0.314505 + 0.949256i \(0.601838\pi\)
\(564\) −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 \(0.484470\pi\)
\(570\) 295.381 + 97.9336i 0.518213 + 0.171813i
\(571\) 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 \(0.0559389\pi\)
−0.984598 + 0.174834i \(0.944061\pi\)
\(578\) −699.690 + 595.799i −1.21054 + 1.03079i
\(579\) 315.313i 0.544583i
\(580\) 343.077 + 846.079i 0.591512 + 1.45876i
\(581\) 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 \(-0.623618\pi\)
−0.378668 + 0.925533i \(0.623618\pi\)
\(588\) 53.3274 330.349i 0.0906929 0.561818i
\(589\) −244.784 −0.415593
\(590\) −832.084 275.877i −1.41031 0.467588i
\(591\) 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 \(0.249219\pi\)
−0.708839 + 0.705371i \(0.750781\pi\)
\(600\) 345.677 22.5306i 0.576128 0.0375509i
\(601\) 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 \(-0.240881\pi\)
0.727071 + 0.686562i \(0.240881\pi\)
\(608\) 216.072 + 532.789i 0.355381 + 0.876298i
\(609\) −66.1993 −0.108702
\(610\) 119.587 360.692i 0.196045 0.591299i
\(611\) 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 \(0.251535\pi\)
−0.703689 + 0.710509i \(0.748465\pi\)
\(620\) −252.516 + 102.393i −0.407284 + 0.165149i
\(621\) −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
\(630\) −7.90460 + 23.8414i −0.0125470 + 0.0378435i
\(631\) 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
\(640\) 445.761 + 459.235i 0.696502 + 0.717555i
\(641\) −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 \(-0.652003\pi\)
−0.459590 + 0.888131i \(0.652003\pi\)
\(644\) −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 \(-0.458927\pi\)
0.128676 + 0.991687i \(0.458927\pi\)
\(648\) −37.3463 61.5569i −0.0576331 0.0949953i
\(649\) 1384.67 2.13355
\(650\) 252.783 57.8913i 0.388897 0.0890635i
\(651\) 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 \(0.178827\pi\)
−0.846297 + 0.532711i \(0.821173\pi\)
\(660\) −507.071 + 205.613i −0.768290 + 0.311534i
\(661\) 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
\(670\) −290.161 + 875.167i −0.433077 + 1.30622i
\(671\) 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
\(680\) 505.532 970.582i 0.743429 1.42733i
\(681\) −321.389 −0.471936
\(682\) 327.697 279.040i 0.480494 0.409150i
\(683\) 1263.93 1.85055 0.925275 0.379298i \(-0.123834\pi\)
0.925275 + 0.379298i \(0.123834\pi\)
\(684\) −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
\(690\) −104.166 + 314.179i −0.150965 + 0.455332i
\(691\) 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
\(700\) 67.1413 + 50.0198i 0.0959162 + 0.0714568i
\(701\) 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 \(0.405015\pi\)
\(710\) 1240.65 + 411.338i 1.74740 + 0.579350i
\(711\) 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 \(0.911364\pi\)
\(720\) −233.941 + 53.5884i −0.324918 + 0.0744284i
\(721\) −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 \(-0.365182\pi\)
0.410993 + 0.911639i \(0.365182\pi\)
\(728\) −29.7009 + 18.0194i −0.0407980 + 0.0247519i
\(729\) 27.0000 0.0370370
\(730\) 519.371 + 172.197i 0.711467 + 0.235887i
\(731\) 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 \(-0.972881\pi\)
0.996373 0.0850928i \(-0.0271187\pi\)
\(740\) −288.386 + 116.938i −0.389711 + 0.158024i
\(741\) −161.402 −0.217816
\(742\) 16.8918 + 19.8373i 0.0227652 + 0.0267349i
\(743\) 148.841 0.200325 0.100162 0.994971i \(-0.468064\pi\)
0.100162 + 0.994971i \(0.468064\pi\)
\(744\) 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
\(750\) 301.563 + 310.741i 0.402084 + 0.414321i
\(751\) 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 \(-0.842397\pi\)
0.879910 0.475141i \(-0.157603\pi\)
\(758\) 311.579 + 365.910i 0.411054 + 0.482731i
\(759\) 522.826i 0.688836i
\(760\) −331.989 + 637.393i −0.436827 + 0.838675i
\(761\) −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 \(0.548135\pi\)
\(770\) −125.529 41.6191i −0.163025 0.0540507i
\(771\) 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