Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 15 x^{9} + 25 x^{8} + 88 x^{7} - 112 x^{6} - 247 x^{5} + 215 x^{4} + 313 x^{3} - 170 x^{2} - 121 x + 57 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.74009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74009 | 1.93753 | 0.968767 | − | 0.247972i | \(-0.0797639\pi\) | ||||
0.968767 | + | 0.247972i | \(0.0797639\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.50808 | 2.75404 | ||||||||
\(5\) | −2.04281 | −0.913570 | −0.456785 | − | 0.889577i | \(-0.650999\pi\) | ||||
−0.456785 | + | 0.889577i | \(0.650999\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 9.61245 | 3.39851 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.59747 | −1.77007 | ||||||||
\(11\) | 0.112732 | 0.0339899 | 0.0169949 | − | 0.999856i | \(-0.494590\pi\) | ||||
0.0169949 | + | 0.999856i | \(0.494590\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24720 | −1.45531 | −0.727655 | − | 0.685943i | \(-0.759390\pi\) | ||||
−0.727655 | + | 0.685943i | \(0.759390\pi\) | |||||||
\(14\) | −2.74009 | −0.732319 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.3228 | 3.83070 | ||||||||
\(17\) | 1.15266 | 0.279561 | 0.139780 | − | 0.990183i | \(-0.455360\pi\) | ||||
0.139780 | + | 0.990183i | \(0.455360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.39631 | −1.69683 | −0.848415 | − | 0.529332i | \(-0.822443\pi\) | ||||
−0.848415 | + | 0.529332i | \(0.822443\pi\) | |||||||
\(20\) | −11.2519 | −2.51601 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.308894 | 0.0658565 | ||||||||
\(23\) | −2.82330 | −0.588698 | −0.294349 | − | 0.955698i | \(-0.595103\pi\) | ||||
−0.294349 | + | 0.955698i | \(0.595103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.826947 | −0.165389 | ||||||||
\(26\) | −14.3778 | −2.81971 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.50808 | −1.04093 | ||||||||
\(29\) | −7.47063 | −1.38726 | −0.693631 | − | 0.720331i | \(-0.743990\pi\) | ||||
−0.693631 | + | 0.720331i | \(0.743990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.42979 | 0.795615 | 0.397807 | − | 0.917469i | \(-0.369771\pi\) | ||||
0.397807 | + | 0.917469i | \(0.369771\pi\) | |||||||
\(32\) | 22.7609 | 4.02360 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.15838 | 0.541658 | ||||||||
\(35\) | 2.04281 | 0.345297 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.52019 | −1.40071 | −0.700355 | − | 0.713795i | \(-0.746975\pi\) | ||||
−0.700355 | + | 0.713795i | \(0.746975\pi\) | |||||||
\(38\) | −20.2665 | −3.28767 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −19.6364 | −3.10478 | ||||||||
\(41\) | −4.19537 | −0.655207 | −0.327603 | − | 0.944815i | \(-0.606241\pi\) | ||||
−0.327603 | + | 0.944815i | \(0.606241\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8938 | 1.66129 | 0.830646 | − | 0.556801i | \(-0.187971\pi\) | ||||
0.830646 | + | 0.556801i | \(0.187971\pi\) | |||||||
\(44\) | 0.620935 | 0.0936094 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.73608 | −1.14062 | ||||||||
\(47\) | −0.534490 | −0.0779633 | −0.0389817 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389817 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.26591 | −0.320448 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −28.9020 | −4.00798 | ||||||||
\(53\) | −1.02108 | −0.140256 | −0.0701282 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701282 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.230289 | −0.0310521 | ||||||||
\(56\) | −9.61245 | −1.28452 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.4702 | −2.68787 | ||||||||
\(59\) | 9.13894 | 1.18979 | 0.594894 | − | 0.803804i | \(-0.297194\pi\) | ||||
0.594894 | + | 0.803804i | \(0.297194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.61416 | −0.846856 | −0.423428 | − | 0.905930i | \(-0.639173\pi\) | ||||
−0.423428 | + | 0.905930i | \(0.639173\pi\) | |||||||
\(62\) | 12.1380 | 1.54153 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31.7213 | 3.96516 | ||||||||
\(65\) | 10.7190 | 1.32953 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00129 | −0.122327 | −0.0611633 | − | 0.998128i | \(-0.519481\pi\) | ||||
−0.0611633 | + | 0.998128i | \(0.519481\pi\) | |||||||
\(68\) | 6.34893 | 0.769921 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.59747 | 0.669025 | ||||||||
\(71\) | 9.18990 | 1.09064 | 0.545320 | − | 0.838228i | \(-0.316408\pi\) | ||||
0.545320 | + | 0.838228i | \(0.316408\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.3691 | −1.56473 | −0.782367 | − | 0.622817i | \(-0.785988\pi\) | ||||
−0.782367 | + | 0.622817i | \(0.785988\pi\) | |||||||
\(74\) | −23.3461 | −2.71392 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.7395 | −4.67314 | ||||||||
\(77\) | −0.112732 | −0.0128470 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0096 | −1.68871 | −0.844355 | − | 0.535785i | \(-0.820016\pi\) | ||||
−0.844355 | + | 0.535785i | \(0.820016\pi\) | |||||||
\(80\) | −31.3015 | −3.49961 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.4957 | −1.26949 | ||||||||
\(83\) | 8.19311 | 0.899310 | 0.449655 | − | 0.893202i | \(-0.351547\pi\) | ||||
0.449655 | + | 0.893202i | \(0.351547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.35466 | −0.255398 | ||||||||
\(86\) | 29.8500 | 3.21881 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.08363 | 0.115515 | ||||||||
\(89\) | −14.8850 | −1.57781 | −0.788906 | − | 0.614514i | \(-0.789352\pi\) | ||||
−0.788906 | + | 0.614514i | \(0.789352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.24720 | 0.550056 | ||||||||
\(92\) | −15.5509 | −1.62130 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.46455 | −0.151057 | ||||||||
\(95\) | 15.1092 | 1.55017 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.69953 | −0.883303 | −0.441652 | − | 0.897187i | \(-0.645607\pi\) | ||||
−0.441652 | + | 0.897187i | \(0.645607\pi\) | |||||||
\(98\) | 2.74009 | 0.276791 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.55489 | −0.455489 | ||||||||
\(101\) | −13.0599 | −1.29950 | −0.649752 | − | 0.760146i | \(-0.725127\pi\) | ||||
−0.649752 | + | 0.760146i | \(0.725127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.177061 | 0.0174463 | 0.00872317 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872317 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(104\) | −50.4384 | −4.94589 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.79786 | −0.271752 | ||||||||
\(107\) | 19.3196 | 1.86769 | 0.933846 | − | 0.357676i | \(-0.116431\pi\) | ||||
0.933846 | + | 0.357676i | \(0.116431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.62043 | −0.729905 | −0.364952 | − | 0.931026i | \(-0.618915\pi\) | ||||
−0.364952 | + | 0.931026i | \(0.618915\pi\) | |||||||
\(110\) | −0.631011 | −0.0601646 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.3228 | −1.44787 | ||||||||
\(113\) | 15.7793 | 1.48439 | 0.742197 | − | 0.670182i | \(-0.233784\pi\) | ||||
0.742197 | + | 0.670182i | \(0.233784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.76744 | 0.537817 | ||||||||
\(116\) | −41.1488 | −3.82057 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 25.0415 | 2.30526 | ||||||||
\(119\) | −1.15266 | −0.105664 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9873 | −0.998845 | ||||||||
\(122\) | −18.1234 | −1.64081 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.3997 | 2.19115 | ||||||||
\(125\) | 11.9033 | 1.06467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 41.3973 | 3.65904 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 29.3710 | 2.57601 | ||||||||
\(131\) | −9.28013 | −0.810809 | −0.405404 | − | 0.914137i | \(-0.632869\pi\) | ||||
−0.405404 | + | 0.914137i | \(0.632869\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.39631 | 0.641341 | ||||||||
\(134\) | −2.74361 | −0.237012 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.0799 | 0.950091 | ||||||||
\(137\) | −7.40716 | −0.632836 | −0.316418 | − | 0.948620i | \(-0.602480\pi\) | ||||
−0.316418 | + | 0.948620i | \(0.602480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7704 | 1.42245 | 0.711225 | − | 0.702965i | \(-0.248141\pi\) | ||||
0.711225 | + | 0.702965i | \(0.248141\pi\) | |||||||
\(140\) | 11.2519 | 0.950962 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.1811 | 2.11315 | ||||||||
\(143\) | −0.591525 | −0.0494658 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2610 | 1.26736 | ||||||||
\(146\) | −36.6325 | −3.03173 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −46.9299 | −3.85761 | ||||||||
\(149\) | 18.5396 | 1.51882 | 0.759410 | − | 0.650612i | \(-0.225488\pi\) | ||||
0.759410 | + | 0.650612i | \(0.225488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.80282 | −0.309469 | −0.154734 | − | 0.987956i | \(-0.549452\pi\) | ||||
−0.154734 | + | 0.987956i | \(0.549452\pi\) | |||||||
\(152\) | −71.0966 | −5.76670 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.308894 | −0.0248914 | ||||||||
\(155\) | −9.04921 | −0.726850 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3952 | −0.909437 | −0.454719 | − | 0.890635i | \(-0.650260\pi\) | ||||
−0.454719 | + | 0.890635i | \(0.650260\pi\) | |||||||
\(158\) | −41.1276 | −3.27193 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −46.4961 | −3.67584 | ||||||||
\(161\) | 2.82330 | 0.222507 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13475 | 0.0888804 | 0.0444402 | − | 0.999012i | \(-0.485850\pi\) | ||||
0.0444402 | + | 0.999012i | \(0.485850\pi\) | |||||||
\(164\) | −23.1084 | −1.80447 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.4498 | 1.74245 | ||||||||
\(167\) | 3.50370 | 0.271125 | 0.135562 | − | 0.990769i | \(-0.456716\pi\) | ||||
0.135562 | + | 0.990769i | \(0.456716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.5331 | 1.11793 | ||||||||
\(170\) | −6.45196 | −0.494843 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60.0040 | 4.57527 | ||||||||
\(173\) | 4.92407 | 0.374370 | 0.187185 | − | 0.982325i | \(-0.440064\pi\) | ||||
0.187185 | + | 0.982325i | \(0.440064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.826947 | 0.0625113 | ||||||||
\(176\) | 1.72736 | 0.130205 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −40.7863 | −3.05706 | ||||||||
\(179\) | 12.5938 | 0.941308 | 0.470654 | − | 0.882318i | \(-0.344018\pi\) | ||||
0.470654 | + | 0.882318i | \(0.344018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.2386 | 1.57865 | 0.789327 | − | 0.613974i | \(-0.210430\pi\) | ||||
0.789327 | + | 0.613974i | \(0.210430\pi\) | |||||||
\(182\) | 14.3778 | 1.06575 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −27.1388 | −2.00070 | ||||||||
\(185\) | 17.4051 | 1.27965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.129941 | 0.00950223 | ||||||||
\(188\) | −2.94401 | −0.214714 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 41.4006 | 3.00351 | ||||||||
\(191\) | 4.80560 | 0.347721 | 0.173861 | − | 0.984770i | \(-0.444376\pi\) | ||||
0.173861 | + | 0.984770i | \(0.444376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4812 | −0.826432 | −0.413216 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413216 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(194\) | −23.8375 | −1.71143 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50808 | 0.393434 | ||||||||
\(197\) | −8.26242 | −0.588673 | −0.294337 | − | 0.955702i | \(-0.595099\pi\) | ||||
−0.294337 | + | 0.955702i | \(0.595099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.57725 | 0.182697 | 0.0913483 | − | 0.995819i | \(-0.470882\pi\) | ||||
0.0913483 | + | 0.995819i | \(0.470882\pi\) | |||||||
\(200\) | −7.94899 | −0.562078 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −35.7851 | −2.51783 | ||||||||
\(203\) | 7.47063 | 0.524336 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.57032 | 0.598577 | ||||||||
\(206\) | 0.485163 | 0.0338029 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −80.4017 | −5.57485 | ||||||||
\(209\) | −0.833797 | −0.0576750 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.95661 | −0.203541 | −0.101771 | − | 0.994808i | \(-0.532451\pi\) | ||||
−0.101771 | + | 0.994808i | \(0.532451\pi\) | |||||||
\(212\) | −5.62421 | −0.386272 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 52.9373 | 3.61872 | ||||||||
\(215\) | −22.2540 | −1.51771 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.42979 | −0.300714 | ||||||||
\(218\) | −20.8806 | −1.41422 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.26845 | −0.0855188 | ||||||||
\(221\) | −6.04822 | −0.406847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.73292 | −0.450870 | −0.225435 | − | 0.974258i | \(-0.572380\pi\) | ||||
−0.225435 | + | 0.974258i | \(0.572380\pi\) | |||||||
\(224\) | −22.7609 | −1.52078 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.2367 | 2.87606 | ||||||||
\(227\) | −11.0498 | −0.733399 | −0.366699 | − | 0.930339i | \(-0.619512\pi\) | ||||
−0.366699 | + | 0.930339i | \(0.619512\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.3402 | −1.34412 | −0.672058 | − | 0.740498i | \(-0.734590\pi\) | ||||
−0.672058 | + | 0.740498i | \(0.734590\pi\) | |||||||
\(230\) | 15.8033 | 1.04204 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −71.8111 | −4.71463 | ||||||||
\(233\) | 3.07642 | 0.201543 | 0.100771 | − | 0.994910i | \(-0.467869\pi\) | ||||
0.100771 | + | 0.994910i | \(0.467869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.09186 | 0.0712250 | ||||||||
\(236\) | 50.3380 | 3.27673 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.15838 | −0.204728 | ||||||||
\(239\) | −7.52434 | −0.486709 | −0.243354 | − | 0.969937i | \(-0.578248\pi\) | ||||
−0.243354 | + | 0.969937i | \(0.578248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5340 | 1.25830 | 0.629148 | − | 0.777286i | \(-0.283404\pi\) | ||||
0.629148 | + | 0.777286i | \(0.283404\pi\) | |||||||
\(242\) | −30.1061 | −1.93530 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −36.4313 | −2.33228 | ||||||||
\(245\) | −2.04281 | −0.130510 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.8099 | 2.46941 | ||||||||
\(248\) | 42.5812 | 2.70391 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 32.6161 | 2.06283 | ||||||||
\(251\) | 20.2651 | 1.27912 | 0.639562 | − | 0.768740i | \(-0.279116\pi\) | ||||
0.639562 | + | 0.768740i | \(0.279116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.318275 | −0.0200098 | ||||||||
\(254\) | 2.74009 | 0.171928 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 49.9896 | 3.12435 | ||||||||
\(257\) | −17.0647 | −1.06447 | −0.532235 | − | 0.846597i | \(-0.678648\pi\) | ||||
−0.532235 | + | 0.846597i | \(0.678648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.52019 | 0.529419 | ||||||||
\(260\) | 59.0411 | 3.66157 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −25.4284 | −1.57097 | ||||||||
\(263\) | 26.4333 | 1.62995 | 0.814975 | − | 0.579496i | \(-0.196751\pi\) | ||||
0.814975 | + | 0.579496i | \(0.196751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.08587 | 0.128134 | ||||||||
\(266\) | 20.2665 | 1.24262 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.51516 | −0.336892 | ||||||||
\(269\) | 0.229249 | 0.0139775 | 0.00698877 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00698877 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2110 | 1.22773 | 0.613865 | − | 0.789411i | \(-0.289614\pi\) | ||||
0.613865 | + | 0.789411i | \(0.289614\pi\) | |||||||
\(272\) | 17.6619 | 1.07091 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2963 | −1.22614 | ||||||||
\(275\) | −0.0932231 | −0.00562156 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3393 | −0.741398 | −0.370699 | − | 0.928753i | \(-0.620882\pi\) | ||||
−0.370699 | + | 0.928753i | \(0.620882\pi\) | |||||||
\(278\) | 45.9524 | 2.75604 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.6364 | 1.17350 | ||||||||
\(281\) | 27.5356 | 1.64264 | 0.821318 | − | 0.570471i | \(-0.193239\pi\) | ||||
0.821318 | + | 0.570471i | \(0.193239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.82223 | −0.167764 | −0.0838822 | − | 0.996476i | \(-0.526732\pi\) | ||||
−0.0838822 | + | 0.996476i | \(0.526732\pi\) | |||||||
\(284\) | 50.6187 | 3.00367 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.62083 | −0.0958417 | ||||||||
\(287\) | 4.19537 | 0.247645 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6714 | −0.921846 | ||||||||
\(290\) | 41.8166 | 2.45556 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −73.6381 | −4.30934 | ||||||||
\(293\) | 2.20100 | 0.128584 | 0.0642918 | − | 0.997931i | \(-0.479521\pi\) | ||||
0.0642918 | + | 0.997931i | \(0.479521\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.6691 | −1.08696 | ||||||||
\(296\) | −81.8999 | −4.76033 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 50.8000 | 2.94277 | ||||||||
\(299\) | 14.8144 | 0.856738 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.8938 | −0.627909 | ||||||||
\(302\) | −10.4200 | −0.599606 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −113.332 | −6.50004 | ||||||||
\(305\) | 13.5114 | 0.773663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6085 | −1.11911 | −0.559557 | − | 0.828792i | \(-0.689029\pi\) | ||||
−0.559557 | + | 0.828792i | \(0.689029\pi\) | |||||||
\(308\) | −0.620935 | −0.0353810 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.7956 | −1.40830 | ||||||||
\(311\) | −27.3394 | −1.55027 | −0.775137 | − | 0.631793i | \(-0.782319\pi\) | ||||
−0.775137 | + | 0.631793i | \(0.782319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.73784 | −0.324322 | −0.162161 | − | 0.986764i | \(-0.551846\pi\) | ||||
−0.162161 | + | 0.986764i | \(0.551846\pi\) | |||||||
\(314\) | −31.2239 | −1.76207 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −82.6740 | −4.65077 | ||||||||
\(317\) | 0.929834 | 0.0522247 | 0.0261123 | − | 0.999659i | \(-0.491687\pi\) | ||||
0.0261123 | + | 0.999659i | \(0.491687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.842176 | −0.0471528 | ||||||||
\(320\) | −64.8004 | −3.62245 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.73608 | 0.431115 | ||||||||
\(323\) | −8.52541 | −0.474367 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.33915 | 0.240693 | ||||||||
\(326\) | 3.10931 | 0.172209 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −40.3278 | −2.22673 | ||||||||
\(329\) | 0.534490 | 0.0294674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.7581 | −0.591317 | −0.295658 | − | 0.955294i | \(-0.595539\pi\) | ||||
−0.295658 | + | 0.955294i | \(0.595539\pi\) | |||||||
\(332\) | 45.1283 | 2.47674 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.60045 | 0.525313 | ||||||||
\(335\) | 2.04543 | 0.111754 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.2782 | −1.64936 | −0.824679 | − | 0.565601i | \(-0.808644\pi\) | ||||
−0.824679 | + | 0.565601i | \(0.808644\pi\) | |||||||
\(338\) | 39.8219 | 2.16602 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.9696 | −0.703377 | ||||||||
\(341\) | 0.499378 | 0.0270428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 104.716 | 5.64592 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.4924 | 0.725355 | ||||||||
\(347\) | −30.1873 | −1.62054 | −0.810269 | − | 0.586058i | \(-0.800679\pi\) | ||||
−0.810269 | + | 0.586058i | \(0.800679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.71098 | −0.252173 | −0.126086 | − | 0.992019i | \(-0.540242\pi\) | ||||
−0.126086 | + | 0.992019i | \(0.540242\pi\) | |||||||
\(350\) | 2.26591 | 0.121118 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.56587 | 0.136761 | ||||||||
\(353\) | −14.8027 | −0.787867 | −0.393934 | − | 0.919139i | \(-0.628886\pi\) | ||||
−0.393934 | + | 0.919139i | \(0.628886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.7732 | −0.996377 | ||||||||
\(356\) | −81.9880 | −4.34536 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.5082 | 1.82382 | ||||||||
\(359\) | −23.9011 | −1.26145 | −0.630726 | − | 0.776005i | \(-0.717243\pi\) | ||||
−0.630726 | + | 0.776005i | \(0.717243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.7054 | 1.87923 | ||||||||
\(362\) | 58.1956 | 3.05869 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 28.9020 | 1.51488 | ||||||||
\(365\) | 27.3105 | 1.42950 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.4281 | 0.961940 | 0.480970 | − | 0.876737i | \(-0.340285\pi\) | ||||
0.480970 | + | 0.876737i | \(0.340285\pi\) | |||||||
\(368\) | −43.2608 | −2.25512 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 47.6915 | 2.47936 | ||||||||
\(371\) | 1.02108 | 0.0530120 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3124 | −0.585732 | −0.292866 | − | 0.956154i | \(-0.594609\pi\) | ||||
−0.292866 | + | 0.956154i | \(0.594609\pi\) | |||||||
\(374\) | 0.356050 | 0.0184109 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.13776 | −0.264960 | ||||||||
\(377\) | 39.1999 | 2.01890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.17198 | 0.471133 | 0.235566 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235566 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(380\) | 83.2228 | 4.26924 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.1678 | 0.673722 | ||||||||
\(383\) | −15.8752 | −0.811183 | −0.405592 | − | 0.914054i | \(-0.632935\pi\) | ||||
−0.405592 | + | 0.914054i | \(0.632935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.230289 | 0.0117366 | ||||||||
\(386\) | −31.4594 | −1.60124 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −47.9177 | −2.43265 | ||||||||
\(389\) | −16.2897 | −0.825920 | −0.412960 | − | 0.910749i | \(-0.635505\pi\) | ||||
−0.412960 | + | 0.910749i | \(0.635505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.25429 | −0.164577 | ||||||||
\(392\) | 9.61245 | 0.485502 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.6398 | −1.14057 | ||||||||
\(395\) | 30.6616 | 1.54275 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.36849 | −0.369814 | −0.184907 | − | 0.982756i | \(-0.559198\pi\) | ||||
−0.184907 | + | 0.982756i | \(0.559198\pi\) | |||||||
\(398\) | 7.06190 | 0.353981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.6711 | −0.633557 | ||||||||
\(401\) | −16.8371 | −0.840804 | −0.420402 | − | 0.907338i | \(-0.638111\pi\) | ||||
−0.420402 | + | 0.907338i | \(0.638111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.2440 | −1.15787 | ||||||||
\(404\) | −71.9347 | −3.57889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.4702 | 1.01592 | ||||||||
\(407\) | −0.960494 | −0.0476099 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.10681 | 0.153622 | 0.0768108 | − | 0.997046i | \(-0.475526\pi\) | ||||
0.0768108 | + | 0.997046i | \(0.475526\pi\) | |||||||
\(410\) | 23.4834 | 1.15976 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.975266 | 0.0480479 | ||||||||
\(413\) | −9.13894 | −0.449698 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.7369 | −0.821583 | ||||||||
\(416\) | −119.431 | −5.85558 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.28468 | −0.111747 | ||||||||
\(419\) | 19.8014 | 0.967359 | 0.483680 | − | 0.875245i | \(-0.339300\pi\) | ||||
0.483680 | + | 0.875245i | \(0.339300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.6093 | 1.68675 | 0.843377 | − | 0.537322i | \(-0.180564\pi\) | ||||
0.843377 | + | 0.537322i | \(0.180564\pi\) | |||||||
\(422\) | −8.10136 | −0.394368 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.81511 | −0.476664 | ||||||||
\(425\) | −0.953187 | −0.0462364 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.61416 | 0.320082 | ||||||||
\(428\) | 106.414 | 5.14370 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −60.9778 | −2.94061 | ||||||||
\(431\) | −13.5389 | −0.652144 | −0.326072 | − | 0.945345i | \(-0.605725\pi\) | ||||
−0.326072 | + | 0.945345i | \(0.605725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6920 | 1.61914 | 0.809568 | − | 0.587026i | \(-0.199702\pi\) | ||||
0.809568 | + | 0.587026i | \(0.199702\pi\) | |||||||
\(434\) | −12.1380 | −0.582644 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −41.9739 | −2.01019 | ||||||||
\(437\) | 20.8820 | 0.998920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6447 | −0.842134 | −0.421067 | − | 0.907029i | \(-0.638344\pi\) | ||||
−0.421067 | + | 0.907029i | \(0.638344\pi\) | |||||||
\(440\) | −2.21364 | −0.105531 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.5727 | −0.788281 | ||||||||
\(443\) | 7.11646 | 0.338113 | 0.169057 | − | 0.985606i | \(-0.445928\pi\) | ||||
0.169057 | + | 0.985606i | \(0.445928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.4072 | 1.44144 | ||||||||
\(446\) | −18.4488 | −0.873576 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −31.7213 | −1.49869 | ||||||||
\(449\) | 39.9935 | 1.88741 | 0.943706 | − | 0.330786i | \(-0.107314\pi\) | ||||
0.943706 | + | 0.330786i | \(0.107314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.472951 | −0.0222704 | ||||||||
\(452\) | 86.9138 | 4.08808 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.2773 | −1.42099 | ||||||||
\(455\) | −10.7190 | −0.502514 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3464 | 0.904987 | 0.452493 | − | 0.891768i | \(-0.350535\pi\) | ||||
0.452493 | + | 0.891768i | \(0.350535\pi\) | |||||||
\(458\) | −55.7339 | −2.60427 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 31.7675 | 1.48117 | ||||||||
\(461\) | 17.9613 | 0.836543 | 0.418271 | − | 0.908322i | \(-0.362636\pi\) | ||||
0.418271 | + | 0.908322i | \(0.362636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.5516 | 1.51280 | 0.756400 | − | 0.654110i | \(-0.226957\pi\) | ||||
0.756400 | + | 0.654110i | \(0.226957\pi\) | |||||||
\(464\) | −114.471 | −5.31418 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.42966 | 0.390496 | ||||||||
\(467\) | −22.3867 | −1.03593 | −0.517965 | − | 0.855402i | \(-0.673310\pi\) | ||||
−0.517965 | + | 0.855402i | \(0.673310\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00129 | 0.0462351 | ||||||||
\(470\) | 2.99179 | 0.138001 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 87.8476 | 4.04351 | ||||||||
\(473\) | 1.22808 | 0.0564671 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.11636 | 0.280638 | ||||||||
\(476\) | −6.34893 | −0.291003 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.6173 | −0.943015 | ||||||||
\(479\) | −8.93937 | −0.408450 | −0.204225 | − | 0.978924i | \(-0.565467\pi\) | ||||
−0.204225 | + | 0.978924i | \(0.565467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.7071 | 2.03847 | ||||||||
\(482\) | 53.5249 | 2.43799 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −60.5189 | −2.75086 | ||||||||
\(485\) | 17.7714 | 0.806960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9076 | −0.539583 | −0.269792 | − | 0.962919i | \(-0.586955\pi\) | ||||
−0.269792 | + | 0.962919i | \(0.586955\pi\) | |||||||
\(488\) | −63.5783 | −2.87805 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.59747 | −0.252868 | ||||||||
\(491\) | −3.26881 | −0.147519 | −0.0737597 | − | 0.997276i | \(-0.523500\pi\) | ||||
−0.0737597 | + | 0.997276i | \(0.523500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.61108 | −0.387824 | ||||||||
\(494\) | 106.342 | 4.78457 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 67.8768 | 3.04776 | ||||||||
\(497\) | −9.18990 | −0.412223 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.83398 | −0.126867 | −0.0634333 | − | 0.997986i | \(-0.520205\pi\) | ||||
−0.0634333 | + | 0.997986i | \(0.520205\pi\) | |||||||
\(500\) | 65.5644 | 2.93213 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 55.5283 | 2.47835 | ||||||||
\(503\) | −39.5073 | −1.76155 | −0.880773 | − | 0.473540i | \(-0.842976\pi\) | ||||
−0.880773 | + | 0.473540i | \(0.842976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.6787 | 1.18719 | ||||||||
\(506\) | −0.872100 | −0.0387696 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.50808 | 0.244382 | ||||||||
\(509\) | −1.82369 | −0.0808337 | −0.0404169 | − | 0.999183i | \(-0.512869\pi\) | ||||
−0.0404169 | + | 0.999183i | \(0.512869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3691 | 0.591414 | ||||||||
\(512\) | 54.1814 | 2.39450 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.7589 | −2.06245 | ||||||||
\(515\) | −0.361701 | −0.0159385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0602539 | −0.00264996 | ||||||||
\(518\) | 23.3461 | 1.02577 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 103.036 | 4.51842 | ||||||||
\(521\) | −2.49558 | −0.109333 | −0.0546667 | − | 0.998505i | \(-0.517410\pi\) | ||||
−0.0546667 | + | 0.998505i | \(0.517410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.6174 | 1.51371 | 0.756857 | − | 0.653580i | \(-0.226734\pi\) | ||||
0.756857 | + | 0.653580i | \(0.226734\pi\) | |||||||
\(524\) | −51.1157 | −2.23300 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 72.4297 | 3.15808 | ||||||||
\(527\) | 5.10604 | 0.222423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0290 | −0.653435 | ||||||||
\(530\) | 5.71547 | 0.248264 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 40.7395 | 1.76628 | ||||||||
\(533\) | 22.0139 | 0.953529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.4661 | −1.70627 | ||||||||
\(536\) | −9.62481 | −0.415729 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.628161 | 0.0270820 | ||||||||
\(539\) | 0.112732 | 0.00485569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.2805 | −0.957914 | −0.478957 | − | 0.877838i | \(-0.658985\pi\) | ||||
−0.478957 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(542\) | 55.3798 | 2.37877 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 26.2355 | 1.12484 | ||||||||
\(545\) | 15.5671 | 0.666819 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.937979 | −0.0401051 | −0.0200526 | − | 0.999799i | \(-0.506383\pi\) | ||||
−0.0200526 | + | 0.999799i | \(0.506383\pi\) | |||||||
\(548\) | −40.7992 | −1.74286 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.255439 | −0.0108920 | ||||||||
\(551\) | 55.2551 | 2.35395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0096 | 0.638272 | ||||||||
\(554\) | −33.8108 | −1.43648 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 92.3729 | 3.91748 | ||||||||
\(557\) | −25.4331 | −1.07763 | −0.538817 | − | 0.842423i | \(-0.681128\pi\) | ||||
−0.538817 | + | 0.842423i | \(0.681128\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.1620 | −2.41770 | ||||||||
\(560\) | 31.3015 | 1.32273 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 75.4499 | 3.18266 | ||||||||
\(563\) | 25.9729 | 1.09463 | 0.547313 | − | 0.836928i | \(-0.315651\pi\) | ||||
0.547313 | + | 0.836928i | \(0.315651\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.2341 | −1.35610 | ||||||||
\(566\) | −7.73317 | −0.325049 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 88.3374 | 3.70656 | ||||||||
\(569\) | 22.4346 | 0.940509 | 0.470254 | − | 0.882531i | \(-0.344162\pi\) | ||||
0.470254 | + | 0.882531i | \(0.344162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.66335 | 0.111458 | 0.0557288 | − | 0.998446i | \(-0.482252\pi\) | ||||
0.0557288 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(572\) | −3.25817 | −0.136231 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.4957 | 0.479821 | ||||||||
\(575\) | 2.33472 | 0.0973644 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.2471 | −1.17594 | −0.587970 | − | 0.808882i | \(-0.700073\pi\) | ||||
−0.587970 | + | 0.808882i | \(0.700073\pi\) | |||||||
\(578\) | −42.9410 | −1.78611 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 84.0591 | 3.49036 | ||||||||
\(581\) | −8.19311 | −0.339907 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.115108 | −0.00476730 | ||||||||
\(584\) | −128.510 | −5.31777 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.03092 | 0.249135 | ||||||||
\(587\) | 44.1126 | 1.82072 | 0.910360 | − | 0.413817i | \(-0.135805\pi\) | ||||
0.910360 | + | 0.413817i | \(0.135805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.7641 | −1.35002 | ||||||||
\(590\) | −51.1549 | −2.10601 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −130.553 | −5.36570 | ||||||||
\(593\) | 23.3655 | 0.959505 | 0.479753 | − | 0.877404i | \(-0.340726\pi\) | ||||
0.479753 | + | 0.877404i | \(0.340726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.35466 | 0.0965315 | ||||||||
\(596\) | 102.117 | 4.18289 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 40.5927 | 1.65996 | ||||||||
\(599\) | −24.3295 | −0.994078 | −0.497039 | − | 0.867728i | \(-0.665579\pi\) | ||||
−0.497039 | + | 0.867728i | \(0.665579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.15886 | 0.251225 | 0.125613 | − | 0.992079i | \(-0.459910\pi\) | ||||
0.125613 | + | 0.992079i | \(0.459910\pi\) | |||||||
\(602\) | −29.8500 | −1.21660 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.9462 | −0.852289 | ||||||||
\(605\) | 22.4449 | 0.912515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0362 | 1.30031 | 0.650154 | − | 0.759802i | \(-0.274704\pi\) | ||||
0.650154 | + | 0.759802i | \(0.274704\pi\) | |||||||
\(608\) | −168.347 | −6.82736 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 37.0225 | 1.49900 | ||||||||
\(611\) | 2.80457 | 0.113461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.3490 | −1.58929 | −0.794645 | − | 0.607074i | \(-0.792343\pi\) | ||||
−0.794645 | + | 0.607074i | \(0.792343\pi\) | |||||||
\(614\) | −53.7289 | −2.16832 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.08363 | −0.0436606 | ||||||||
\(617\) | −41.7994 | −1.68278 | −0.841391 | − | 0.540427i | \(-0.818263\pi\) | ||||
−0.841391 | + | 0.540427i | \(0.818263\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.0712 | 1.73118 | 0.865589 | − | 0.500755i | \(-0.166944\pi\) | ||||
0.865589 | + | 0.500755i | \(0.166944\pi\) | |||||||
\(620\) | −49.8438 | −2.00177 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −74.9123 | −3.00371 | ||||||||
\(623\) | 14.8850 | 0.596357 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1814 | −0.807257 | ||||||||
\(626\) | −15.7222 | −0.628384 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −62.7658 | −2.50463 | ||||||||
\(629\) | −9.82086 | −0.391583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.6791 | −0.584366 | −0.292183 | − | 0.956362i | \(-0.594382\pi\) | ||||
−0.292183 | + | 0.956362i | \(0.594382\pi\) | |||||||
\(632\) | −144.279 | −5.73910 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.54783 | 0.101187 | ||||||||
\(635\) | −2.04281 | −0.0810662 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.24720 | −0.207901 | ||||||||
\(638\) | −2.30764 | −0.0913602 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −84.5666 | −3.34279 | ||||||||
\(641\) | −26.1705 | −1.03367 | −0.516836 | − | 0.856085i | \(-0.672890\pi\) | ||||
−0.516836 | + | 0.856085i | \(0.672890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.9679 | 0.866331 | 0.433166 | − | 0.901314i | \(-0.357397\pi\) | ||||
0.433166 | + | 0.901314i | \(0.357397\pi\) | |||||||
\(644\) | 15.5509 | 0.612793 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.3604 | −0.919102 | ||||||||
\(647\) | −9.64241 | −0.379082 | −0.189541 | − | 0.981873i | \(-0.560700\pi\) | ||||
−0.189541 | + | 0.981873i | \(0.560700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.03025 | 0.0404407 | ||||||||
\(650\) | 11.8897 | 0.466351 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.25029 | 0.244780 | ||||||||
\(653\) | 1.29571 | 0.0507049 | 0.0253524 | − | 0.999679i | \(-0.491929\pi\) | ||||
0.0253524 | + | 0.999679i | \(0.491929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9575 | 0.740731 | ||||||||
\(656\) | −64.2848 | −2.50990 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.46455 | 0.0570941 | ||||||||
\(659\) | −14.1795 | −0.552353 | −0.276177 | − | 0.961107i | \(-0.589067\pi\) | ||||
−0.276177 | + | 0.961107i | \(0.589067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.9298 | 0.969658 | 0.484829 | − | 0.874609i | \(-0.338882\pi\) | ||||
0.484829 | + | 0.874609i | \(0.338882\pi\) | |||||||
\(662\) | −29.4780 | −1.14570 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 78.7558 | 3.05632 | ||||||||
\(665\) | −15.1092 | −0.585910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0918 | 0.816678 | ||||||||
\(668\) | 19.2987 | 0.746688 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.60466 | 0.216527 | ||||||||
\(671\) | −0.745625 | −0.0287845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.9745 | −0.962697 | −0.481349 | − | 0.876529i | \(-0.659853\pi\) | ||||
−0.481349 | + | 0.876529i | \(0.659853\pi\) | |||||||
\(674\) | −82.9649 | −3.19569 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 80.0493 | 3.07882 | ||||||||
\(677\) | 28.5115 | 1.09579 | 0.547893 | − | 0.836548i | \(-0.315430\pi\) | ||||
0.547893 | + | 0.836548i | \(0.315430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.69953 | 0.333857 | ||||||||
\(680\) | −22.6340 | −0.867975 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.36834 | 0.0523964 | ||||||||
\(683\) | −17.8617 | −0.683461 | −0.341730 | − | 0.939798i | \(-0.611013\pi\) | ||||
−0.341730 | + | 0.939798i | \(0.611013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.1314 | 0.578140 | ||||||||
\(686\) | −2.74009 | −0.104617 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 166.924 | 6.36391 | ||||||||
\(689\) | 5.35782 | 0.204117 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.58485 | −0.250500 | −0.125250 | − | 0.992125i | \(-0.539973\pi\) | ||||
−0.125250 | + | 0.992125i | \(0.539973\pi\) | |||||||
\(692\) | 27.1222 | 1.03103 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −82.7158 | −3.13985 | ||||||||
\(695\) | −34.2587 | −1.29951 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.83583 | −0.183170 | ||||||||
\(698\) | −12.9085 | −0.488593 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.55489 | 0.172159 | ||||||||
\(701\) | 39.2478 | 1.48237 | 0.741185 | − | 0.671301i | \(-0.234264\pi\) | ||||
0.741185 | + | 0.671301i | \(0.234264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.0179 | 2.37677 | ||||||||
\(704\) | 3.57599 | 0.134775 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.5606 | −1.52652 | ||||||||
\(707\) | 13.0599 | 0.491166 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.86649 | 0.295432 | 0.147716 | − | 0.989030i | \(-0.452808\pi\) | ||||
0.147716 | + | 0.989030i | \(0.452808\pi\) | |||||||
\(710\) | −51.4401 | −1.93051 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −143.082 | −5.36221 | ||||||||
\(713\) | −12.5066 | −0.468377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.20837 | 0.0451905 | ||||||||
\(716\) | 69.3679 | 2.59240 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −65.4912 | −2.44411 | ||||||||
\(719\) | 8.12303 | 0.302938 | 0.151469 | − | 0.988462i | \(-0.451600\pi\) | ||||
0.151469 | + | 0.988462i | \(0.451600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.177061 | −0.00659410 | ||||||||
\(722\) | 97.8358 | 3.64107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 116.984 | 4.34767 | ||||||||
\(725\) | 6.17782 | 0.229438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.97997 | −0.0734331 | −0.0367166 | − | 0.999326i | \(-0.511690\pi\) | ||||
−0.0367166 | + | 0.999326i | \(0.511690\pi\) | |||||||
\(728\) | 50.4384 | 1.86937 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 74.8331 | 2.76970 | ||||||||
\(731\) | 12.5569 | 0.464432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.5423 | −1.53440 | −0.767199 | − | 0.641409i | \(-0.778350\pi\) | ||||
−0.767199 | + | 0.641409i | \(0.778350\pi\) | |||||||
\(734\) | 50.4946 | 1.86379 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −64.2608 | −2.36868 | ||||||||
\(737\) | −0.112877 | −0.00415786 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.8099 | 1.68514 | 0.842572 | − | 0.538583i | \(-0.181040\pi\) | ||||
0.842572 | + | 0.538583i | \(0.181040\pi\) | |||||||
\(740\) | 95.8686 | 3.52420 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.79786 | 0.102713 | ||||||||
\(743\) | −15.2766 | −0.560444 | −0.280222 | − | 0.959935i | \(-0.590408\pi\) | ||||
−0.280222 | + | 0.959935i | \(0.590408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8727 | −1.38755 | ||||||||
\(746\) | −30.9968 | −1.13488 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.715725 | 0.0261695 | ||||||||
\(749\) | −19.3196 | −0.705921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4752 | −0.820131 | −0.410066 | − | 0.912056i | \(-0.634494\pi\) | ||||
−0.410066 | + | 0.912056i | \(0.634494\pi\) | |||||||
\(752\) | −8.18988 | −0.298654 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 107.411 | 3.91168 | ||||||||
\(755\) | 7.76841 | 0.282721 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.43364 | 0.306526 | 0.153263 | − | 0.988185i | \(-0.451022\pi\) | ||||
0.153263 | + | 0.988185i | \(0.451022\pi\) | |||||||
\(758\) | 25.1320 | 0.912836 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 145.237 | 5.26828 | ||||||||
\(761\) | −15.5995 | −0.565482 | −0.282741 | − | 0.959196i | \(-0.591244\pi\) | ||||
−0.282741 | + | 0.959196i | \(0.591244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.62043 | 0.275878 | ||||||||
\(764\) | 26.4696 | 0.957638 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −43.4994 | −1.57170 | ||||||||
\(767\) | −47.9538 | −1.73151 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9832 | 0.612430 | 0.306215 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306215 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(770\) | 0.631011 | 0.0227401 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −63.2391 | −2.27603 | ||||||||
\(773\) | 48.2227 | 1.73445 | 0.867225 | − | 0.497916i | \(-0.165901\pi\) | ||||
0.867225 | + | 0.497916i | \(0.165901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.66321 | −0.131586 | ||||||||
\(776\) | −83.6238 | −3.00192 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.6352 | −1.60025 | ||||||||
\(779\) | 31.0302 | 1.11177 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03599 | 0.0370707 | ||||||||
\(782\) | −8.91705 | −0.318873 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.3228 | 0.547243 | ||||||||
\(785\) | 23.2782 | 0.830835 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.8280 | 1.49101 | 0.745504 | − | 0.666501i | \(-0.232209\pi\) | ||||
0.745504 | + | 0.666501i | \(0.232209\pi\) | |||||||
\(788\) | −45.5101 | −1.62123 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 84.0156 | 2.98914 | ||||||||
\(791\) | −15.7793 | −0.561048 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.7058 | 1.23244 | ||||||||
\(794\) | −20.1903 | −0.716527 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.1957 | 0.503154 | ||||||||
\(797\) | 36.9157 | 1.30762 | 0.653811 | − | 0.756658i | \(-0.273169\pi\) | ||||
0.653811 | + | 0.756658i | \(0.273169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.616084 | −0.0217955 | ||||||||
\(800\) | −18.8221 | −0.665460 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −46.1351 | −1.62909 | ||||||||
\(803\) | −1.50712 | −0.0531851 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.76744 | −0.203276 | ||||||||
\(806\) | −63.6906 | −2.24341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −125.537 | −4.41638 | ||||||||
\(809\) | −6.95959 | −0.244686 | −0.122343 | − | 0.992488i | \(-0.539041\pi\) | ||||
−0.122343 | + | 0.992488i | \(0.539041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.34138 | −0.257791 | −0.128895 | − | 0.991658i | \(-0.541143\pi\) | ||||
−0.128895 | + | 0.991658i | \(0.541143\pi\) | |||||||
\(812\) | 41.1488 | 1.44404 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.63184 | −0.0922459 | ||||||||
\(815\) | −2.31807 | −0.0811985 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −80.5740 | −2.81893 | ||||||||
\(818\) | 8.51292 | 0.297647 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 47.2060 | 1.64851 | ||||||||
\(821\) | 6.22424 | 0.217227 | 0.108614 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108614 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.8870 | −1.59952 | −0.799760 | − | 0.600320i | \(-0.795040\pi\) | ||||
−0.799760 | + | 0.600320i | \(0.795040\pi\) | |||||||
\(824\) | 1.70199 | 0.0592916 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.0415 | −0.871305 | ||||||||
\(827\) | −46.8185 | −1.62804 | −0.814019 | − | 0.580838i | \(-0.802725\pi\) | ||||
−0.814019 | + | 0.580838i | \(0.802725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1291 | 0.629650 | 0.314825 | − | 0.949150i | \(-0.398054\pi\) | ||||
0.314825 | + | 0.949150i | \(0.398054\pi\) | |||||||
\(830\) | −45.8606 | −1.59185 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −166.448 | −5.77054 | ||||||||
\(833\) | 1.15266 | 0.0399372 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.15738 | −0.247691 | ||||||||
\(836\) | −4.59262 | −0.158839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.2574 | 1.87429 | ||||||||
\(839\) | −31.0024 | −1.07032 | −0.535161 | − | 0.844750i | \(-0.679749\pi\) | ||||
−0.535161 | + | 0.844750i | \(0.679749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.8103 | 0.924494 | ||||||||
\(842\) | 94.8326 | 3.26815 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.2852 | −0.560560 | ||||||||
\(845\) | −29.6882 | −1.02131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9873 | 0.377528 | ||||||||
\(848\) | −15.6458 | −0.537280 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.61182 | −0.0895846 | ||||||||
\(851\) | 24.0550 | 0.824595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.7618 | 1.19022 | 0.595111 | − | 0.803643i | \(-0.297108\pi\) | ||||
0.595111 | + | 0.803643i | \(0.297108\pi\) | |||||||
\(854\) | 18.1234 | 0.620169 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 185.708 | 6.34738 | ||||||||
\(857\) | −3.40035 | −0.116154 | −0.0580768 | − | 0.998312i | \(-0.518497\pi\) | ||||
−0.0580768 | + | 0.998312i | \(0.518497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.1386 | 0.584761 | 0.292381 | − | 0.956302i | \(-0.405553\pi\) | ||||
0.292381 | + | 0.956302i | \(0.405553\pi\) | |||||||
\(860\) | −122.577 | −4.17983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.0977 | −1.26355 | ||||||||
\(863\) | 6.88023 | 0.234206 | 0.117103 | − | 0.993120i | \(-0.462639\pi\) | ||||
0.117103 | + | 0.993120i | \(0.462639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0589 | −0.342013 | ||||||||
\(866\) | 92.3191 | 3.13713 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.3997 | −0.828179 | ||||||||
\(869\) | −1.69205 | −0.0573990 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.25394 | 0.178023 | ||||||||
\(872\) | −73.2510 | −2.48059 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 57.2184 | 1.93544 | ||||||||
\(875\) | −11.9033 | −0.402406 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.2602 | −0.515300 | −0.257650 | − | 0.966238i | \(-0.582948\pi\) | ||||
−0.257650 | + | 0.966238i | \(0.582948\pi\) | |||||||
\(878\) | −48.3479 | −1.63166 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.52867 | −0.118951 | ||||||||
\(881\) | −54.7338 | −1.84403 | −0.922014 | − | 0.387157i | \(-0.873457\pi\) | ||||
−0.922014 | + | 0.387157i | \(0.873457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.8655 | 1.17332 | 0.586659 | − | 0.809834i | \(-0.300443\pi\) | ||||
0.586659 | + | 0.809834i | \(0.300443\pi\) | |||||||
\(884\) | −33.3141 | −1.12047 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.4997 | 0.655106 | ||||||||
\(887\) | 12.8739 | 0.432262 | 0.216131 | − | 0.976364i | \(-0.430656\pi\) | ||||
0.216131 | + | 0.976364i | \(0.430656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 83.3185 | 2.79284 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.0855 | −1.24171 | ||||||||
\(893\) | 3.95325 | 0.132290 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.7268 | −0.859951 | ||||||||
\(896\) | −41.3973 | −1.38299 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 109.586 | 3.65693 | ||||||||
\(899\) | −33.0934 | −1.10373 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.17696 | −0.0392102 | ||||||||
\(902\) | −1.29593 | −0.0431496 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 151.678 | 5.04473 | ||||||||
\(905\) | −43.3863 | −1.44221 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.7867 | −1.52032 | −0.760161 | − | 0.649735i | \(-0.774880\pi\) | ||||
−0.760161 | + | 0.649735i | \(0.774880\pi\) | |||||||
\(908\) | −60.8630 | −2.01981 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −29.3710 | −0.973639 | ||||||||
\(911\) | 31.8369 | 1.05480 | 0.527402 | − | 0.849616i | \(-0.323166\pi\) | ||||
0.527402 | + | 0.849616i | \(0.323166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.923622 | 0.0305674 | ||||||||
\(914\) | 53.0108 | 1.75344 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −112.035 | −3.70175 | ||||||||
\(917\) | 9.28013 | 0.306457 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.8384 | 0.786356 | 0.393178 | − | 0.919462i | \(-0.371376\pi\) | ||||
0.393178 | + | 0.919462i | \(0.371376\pi\) | |||||||
\(920\) | 55.4393 | 1.82778 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 49.2156 | 1.62083 | ||||||||
\(923\) | −48.2212 | −1.58722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.04574 | 0.231663 | ||||||||
\(926\) | 89.1941 | 2.93110 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −170.038 | −5.58178 | ||||||||
\(929\) | 32.6729 | 1.07196 | 0.535982 | − | 0.844229i | \(-0.319942\pi\) | ||||
0.535982 | + | 0.844229i | \(0.319942\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.39631 | −0.242404 | ||||||||
\(932\) | 16.9452 | 0.555057 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −61.3414 | −2.00715 | ||||||||
\(935\) | −0.265444 | −0.00868095 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.8311 | 0.549847 | 0.274924 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274924 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(938\) | 2.74361 | 0.0895821 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.01404 | 0.196156 | ||||||||
\(941\) | −44.8845 | −1.46319 | −0.731597 | − | 0.681738i | \(-0.761225\pi\) | ||||
−0.731597 | + | 0.681738i | \(0.761225\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.8448 | 0.385719 | ||||||||
\(944\) | 140.034 | 4.55772 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.36504 | 0.109407 | ||||||||
\(947\) | 23.1949 | 0.753732 | 0.376866 | − | 0.926268i | \(-0.377002\pi\) | ||||
0.376866 | + | 0.926268i | \(0.377002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 70.1503 | 2.27717 | ||||||||
\(950\) | 16.7594 | 0.543745 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.0799 | −0.359101 | ||||||||
\(953\) | 1.41323 | 0.0457791 | 0.0228895 | − | 0.999738i | \(-0.492713\pi\) | ||||
0.0228895 | + | 0.999738i | \(0.492713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.81691 | −0.317668 | ||||||||
\(956\) | −41.4447 | −1.34042 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.4947 | −0.791386 | ||||||||
\(959\) | 7.40716 | 0.239190 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3769 | −0.366997 | ||||||||
\(962\) | 122.501 | 3.94960 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 107.595 | 3.46540 | ||||||||
\(965\) | 23.4538 | 0.755003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.289444 | −0.00930789 | −0.00465395 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465395 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(968\) | −105.615 | −3.39459 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.6953 | 1.56351 | ||||||||
\(971\) | −7.65950 | −0.245805 | −0.122903 | − | 0.992419i | \(-0.539220\pi\) | ||||
−0.122903 | + | 0.992419i | \(0.539220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.7704 | −0.537635 | ||||||||
\(974\) | −32.6278 | −1.04546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −101.347 | −3.24405 | ||||||||
\(977\) | −21.5704 | −0.690099 | −0.345050 | − | 0.938584i | \(-0.612138\pi\) | ||||
−0.345050 | + | 0.938584i | \(0.612138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.67801 | −0.0536296 | ||||||||
\(980\) | −11.2519 | −0.359430 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.95683 | −0.285824 | ||||||||
\(983\) | −2.55468 | −0.0814816 | −0.0407408 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407408 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.8785 | 0.537794 | ||||||||
\(986\) | −23.5951 | −0.751422 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 213.768 | 6.80086 | ||||||||
\(989\) | −30.7565 | −0.977999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.4736 | 1.03156 | 0.515779 | − | 0.856722i | \(-0.327503\pi\) | ||||
0.515779 | + | 0.856722i | \(0.327503\pi\) | |||||||
\(992\) | 100.826 | 3.20123 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.1811 | −0.798697 | ||||||||
\(995\) | −5.26482 | −0.166906 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.6147 | 1.31795 | 0.658975 | − | 0.752165i | \(-0.270990\pi\) | ||||
0.658975 | + | 0.752165i | \(0.270990\pi\) | |||||||
\(998\) | −7.76536 | −0.245808 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.m.1.11 | 11 | ||
3.2 | odd | 2 | 2667.2.a.k.1.1 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.k.1.1 | ✓ | 11 | 3.2 | odd | 2 | ||
8001.2.a.m.1.11 | 11 | 1.1 | even | 1 | trivial |