Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8027,2,Mod(1,8027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8027 = 23 \cdot 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8027.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: | \(64.0959177025\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60291 | −1.84053 | −0.920267 | − | 0.391292i | \(-0.872028\pi\) | ||||
−0.920267 | + | 0.391292i | \(0.872028\pi\) | |||||||
\(3\) | 2.78039 | 1.60526 | 0.802629 | − | 0.596479i | \(-0.203434\pi\) | ||||
0.802629 | + | 0.596479i | \(0.203434\pi\) | |||||||
\(4\) | 4.77512 | 2.38756 | ||||||||
\(5\) | −1.36371 | −0.609871 | −0.304935 | − | 0.952373i | \(-0.598635\pi\) | ||||
−0.304935 | + | 0.952373i | \(0.598635\pi\) | |||||||
\(6\) | −7.23709 | −2.95453 | ||||||||
\(7\) | −4.03414 | −1.52476 | −0.762381 | − | 0.647128i | \(-0.775970\pi\) | ||||
−0.762381 | + | 0.647128i | \(0.775970\pi\) | |||||||
\(8\) | −7.22339 | −2.55385 | ||||||||
\(9\) | 4.73056 | 1.57685 | ||||||||
\(10\) | 3.54962 | 1.12249 | ||||||||
\(11\) | −3.33382 | −1.00518 | −0.502592 | − | 0.864523i | \(-0.667620\pi\) | ||||
−0.502592 | + | 0.864523i | \(0.667620\pi\) | |||||||
\(12\) | 13.2767 | 3.83265 | ||||||||
\(13\) | 3.04561 | 0.844699 | 0.422350 | − | 0.906433i | \(-0.361205\pi\) | ||||
0.422350 | + | 0.906433i | \(0.361205\pi\) | |||||||
\(14\) | 10.5005 | 2.80638 | ||||||||
\(15\) | −3.79165 | −0.979000 | ||||||||
\(16\) | 9.25157 | 2.31289 | ||||||||
\(17\) | 0.158916 | 0.0385427 | 0.0192714 | − | 0.999814i | \(-0.493865\pi\) | ||||
0.0192714 | + | 0.999814i | \(0.493865\pi\) | |||||||
\(18\) | −12.3132 | −2.90225 | ||||||||
\(19\) | −4.36044 | −1.00035 | −0.500176 | − | 0.865924i | \(-0.666732\pi\) | ||||
−0.500176 | + | 0.865924i | \(0.666732\pi\) | |||||||
\(20\) | −6.51190 | −1.45610 | ||||||||
\(21\) | −11.2165 | −2.44764 | ||||||||
\(22\) | 8.67763 | 1.85008 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −20.0838 | −4.09960 | ||||||||
\(25\) | −3.14029 | −0.628058 | ||||||||
\(26\) | −7.92743 | −1.55470 | ||||||||
\(27\) | 4.81163 | 0.925998 | ||||||||
\(28\) | −19.2635 | −3.64047 | ||||||||
\(29\) | 7.56463 | 1.40472 | 0.702358 | − | 0.711824i | \(-0.252131\pi\) | ||||
0.702358 | + | 0.711824i | \(0.252131\pi\) | |||||||
\(30\) | 9.86931 | 1.80188 | ||||||||
\(31\) | 8.19797 | 1.47240 | 0.736199 | − | 0.676765i | \(-0.236619\pi\) | ||||
0.736199 | + | 0.676765i | \(0.236619\pi\) | |||||||
\(32\) | −9.63419 | −1.70310 | ||||||||
\(33\) | −9.26932 | −1.61358 | ||||||||
\(34\) | −0.413643 | −0.0709391 | ||||||||
\(35\) | 5.50141 | 0.929908 | ||||||||
\(36\) | 22.5890 | 3.76484 | ||||||||
\(37\) | −6.78196 | −1.11495 | −0.557474 | − | 0.830194i | \(-0.688229\pi\) | ||||
−0.557474 | + | 0.830194i | \(0.688229\pi\) | |||||||
\(38\) | 11.3498 | 1.84118 | ||||||||
\(39\) | 8.46797 | 1.35596 | ||||||||
\(40\) | 9.85063 | 1.55752 | ||||||||
\(41\) | 6.49295 | 1.01403 | 0.507014 | − | 0.861938i | \(-0.330749\pi\) | ||||
0.507014 | + | 0.861938i | \(0.330749\pi\) | |||||||
\(42\) | 29.1955 | 4.50496 | ||||||||
\(43\) | 4.80654 | 0.732990 | 0.366495 | − | 0.930420i | \(-0.380558\pi\) | ||||
0.366495 | + | 0.930420i | \(0.380558\pi\) | |||||||
\(44\) | −15.9194 | −2.39994 | ||||||||
\(45\) | −6.45112 | −0.961677 | ||||||||
\(46\) | 2.60291 | 0.383778 | ||||||||
\(47\) | 10.2963 | 1.50187 | 0.750935 | − | 0.660376i | \(-0.229603\pi\) | ||||
0.750935 | + | 0.660376i | \(0.229603\pi\) | |||||||
\(48\) | 25.7230 | 3.71279 | ||||||||
\(49\) | 9.27430 | 1.32490 | ||||||||
\(50\) | 8.17388 | 1.15596 | ||||||||
\(51\) | 0.441847 | 0.0618710 | ||||||||
\(52\) | 14.5431 | 2.01677 | ||||||||
\(53\) | −0.354937 | −0.0487543 | −0.0243771 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243771 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(54\) | −12.5242 | −1.70433 | ||||||||
\(55\) | 4.54637 | 0.613033 | ||||||||
\(56\) | 29.1402 | 3.89402 | ||||||||
\(57\) | −12.1237 | −1.60582 | ||||||||
\(58\) | −19.6900 | −2.58543 | ||||||||
\(59\) | 14.2564 | 1.85602 | 0.928011 | − | 0.372554i | \(-0.121518\pi\) | ||||
0.928011 | + | 0.372554i | \(0.121518\pi\) | |||||||
\(60\) | −18.1056 | −2.33742 | ||||||||
\(61\) | 8.78484 | 1.12478 | 0.562392 | − | 0.826871i | \(-0.309881\pi\) | ||||
0.562392 | + | 0.826871i | \(0.309881\pi\) | |||||||
\(62\) | −21.3386 | −2.71000 | ||||||||
\(63\) | −19.0838 | −2.40433 | ||||||||
\(64\) | 6.57376 | 0.821720 | ||||||||
\(65\) | −4.15333 | −0.515157 | ||||||||
\(66\) | 24.1272 | 2.96985 | ||||||||
\(67\) | −15.5705 | −1.90224 | −0.951121 | − | 0.308818i | \(-0.900067\pi\) | ||||
−0.951121 | + | 0.308818i | \(0.900067\pi\) | |||||||
\(68\) | 0.758842 | 0.0920231 | ||||||||
\(69\) | −2.78039 | −0.334719 | ||||||||
\(70\) | −14.3197 | −1.71153 | ||||||||
\(71\) | −12.1475 | −1.44164 | −0.720821 | − | 0.693121i | \(-0.756235\pi\) | ||||
−0.720821 | + | 0.693121i | \(0.756235\pi\) | |||||||
\(72\) | −34.1707 | −4.02705 | ||||||||
\(73\) | −1.66239 | −0.194569 | −0.0972843 | − | 0.995257i | \(-0.531016\pi\) | ||||
−0.0972843 | + | 0.995257i | \(0.531016\pi\) | |||||||
\(74\) | 17.6528 | 2.05210 | ||||||||
\(75\) | −8.73122 | −1.00819 | ||||||||
\(76\) | −20.8216 | −2.38840 | ||||||||
\(77\) | 13.4491 | 1.53267 | ||||||||
\(78\) | −22.0413 | −2.49569 | ||||||||
\(79\) | 16.4330 | 1.84886 | 0.924431 | − | 0.381350i | \(-0.124541\pi\) | ||||
0.924431 | + | 0.381350i | \(0.124541\pi\) | |||||||
\(80\) | −12.6165 | −1.41057 | ||||||||
\(81\) | −0.813484 | −0.0903871 | ||||||||
\(82\) | −16.9005 | −1.86635 | ||||||||
\(83\) | 4.08140 | 0.447992 | 0.223996 | − | 0.974590i | \(-0.428090\pi\) | ||||
0.223996 | + | 0.974590i | \(0.428090\pi\) | |||||||
\(84\) | −53.5601 | −5.84389 | ||||||||
\(85\) | −0.216715 | −0.0235061 | ||||||||
\(86\) | −12.5110 | −1.34909 | ||||||||
\(87\) | 21.0326 | 2.25493 | ||||||||
\(88\) | 24.0815 | 2.56710 | ||||||||
\(89\) | −2.58156 | −0.273645 | −0.136822 | − | 0.990596i | \(-0.543689\pi\) | ||||
−0.136822 | + | 0.990596i | \(0.543689\pi\) | |||||||
\(90\) | 16.7917 | 1.77000 | ||||||||
\(91\) | −12.2864 | −1.28797 | ||||||||
\(92\) | −4.77512 | −0.497841 | ||||||||
\(93\) | 22.7935 | 2.36358 | ||||||||
\(94\) | −26.8003 | −2.76424 | ||||||||
\(95\) | 5.94638 | 0.610086 | ||||||||
\(96\) | −26.7868 | −2.73391 | ||||||||
\(97\) | −12.3407 | −1.25301 | −0.626503 | − | 0.779419i | \(-0.715515\pi\) | ||||
−0.626503 | + | 0.779419i | \(0.715515\pi\) | |||||||
\(98\) | −24.1401 | −2.43852 | ||||||||
\(99\) | −15.7708 | −1.58503 | ||||||||
\(100\) | −14.9953 | −1.49953 | ||||||||
\(101\) | −11.5044 | −1.14473 | −0.572366 | − | 0.819998i | \(-0.693974\pi\) | ||||
−0.572366 | + | 0.819998i | \(0.693974\pi\) | |||||||
\(102\) | −1.15009 | −0.113876 | ||||||||
\(103\) | −1.39858 | −0.137806 | −0.0689031 | − | 0.997623i | \(-0.521950\pi\) | ||||
−0.0689031 | + | 0.997623i | \(0.521950\pi\) | |||||||
\(104\) | −21.9996 | −2.15724 | ||||||||
\(105\) | 15.2961 | 1.49274 | ||||||||
\(106\) | 0.923867 | 0.0897339 | ||||||||
\(107\) | 7.25864 | 0.701720 | 0.350860 | − | 0.936428i | \(-0.385889\pi\) | ||||
0.350860 | + | 0.936428i | \(0.385889\pi\) | |||||||
\(108\) | 22.9761 | 2.21088 | ||||||||
\(109\) | −12.7326 | −1.21956 | −0.609780 | − | 0.792570i | \(-0.708742\pi\) | ||||
−0.609780 | + | 0.792570i | \(0.708742\pi\) | |||||||
\(110\) | −11.8338 | −1.12831 | ||||||||
\(111\) | −18.8565 | −1.78978 | ||||||||
\(112\) | −37.3221 | −3.52661 | ||||||||
\(113\) | −4.83065 | −0.454429 | −0.227215 | − | 0.973845i | \(-0.572962\pi\) | ||||
−0.227215 | + | 0.973845i | \(0.572962\pi\) | |||||||
\(114\) | 31.5569 | 2.95557 | ||||||||
\(115\) | 1.36371 | 0.127167 | ||||||||
\(116\) | 36.1220 | 3.35385 | ||||||||
\(117\) | 14.4074 | 1.33197 | ||||||||
\(118\) | −37.1080 | −3.41607 | ||||||||
\(119\) | −0.641088 | −0.0587685 | ||||||||
\(120\) | 27.3886 | 2.50022 | ||||||||
\(121\) | 0.114364 | 0.0103967 | ||||||||
\(122\) | −22.8661 | −2.07020 | ||||||||
\(123\) | 18.0529 | 1.62778 | ||||||||
\(124\) | 39.1463 | 3.51544 | ||||||||
\(125\) | 11.1010 | 0.992905 | ||||||||
\(126\) | 49.6732 | 4.42524 | ||||||||
\(127\) | −17.2237 | −1.52836 | −0.764178 | − | 0.645006i | \(-0.776855\pi\) | ||||
−0.764178 | + | 0.645006i | \(0.776855\pi\) | |||||||
\(128\) | 2.15749 | 0.190697 | ||||||||
\(129\) | 13.3640 | 1.17664 | ||||||||
\(130\) | 10.8107 | 0.948164 | ||||||||
\(131\) | −5.41863 | −0.473428 | −0.236714 | − | 0.971579i | \(-0.576070\pi\) | ||||
−0.236714 | + | 0.971579i | \(0.576070\pi\) | |||||||
\(132\) | −44.2622 | −3.85253 | ||||||||
\(133\) | 17.5906 | 1.52530 | ||||||||
\(134\) | 40.5286 | 3.50114 | ||||||||
\(135\) | −6.56168 | −0.564739 | ||||||||
\(136\) | −1.14791 | −0.0984325 | ||||||||
\(137\) | −11.6743 | −0.997404 | −0.498702 | − | 0.866774i | \(-0.666190\pi\) | ||||
−0.498702 | + | 0.866774i | \(0.666190\pi\) | |||||||
\(138\) | 7.23709 | 0.616062 | ||||||||
\(139\) | 10.9603 | 0.929641 | 0.464821 | − | 0.885405i | \(-0.346119\pi\) | ||||
0.464821 | + | 0.885405i | \(0.346119\pi\) | |||||||
\(140\) | 26.2699 | 2.22021 | ||||||||
\(141\) | 28.6277 | 2.41089 | ||||||||
\(142\) | 31.6188 | 2.65339 | ||||||||
\(143\) | −10.1535 | −0.849079 | ||||||||
\(144\) | 43.7651 | 3.64709 | ||||||||
\(145\) | −10.3160 | −0.856695 | ||||||||
\(146\) | 4.32706 | 0.358110 | ||||||||
\(147\) | 25.7862 | 2.12681 | ||||||||
\(148\) | −32.3847 | −2.66201 | ||||||||
\(149\) | 10.6443 | 0.872014 | 0.436007 | − | 0.899943i | \(-0.356392\pi\) | ||||
0.436007 | + | 0.899943i | \(0.356392\pi\) | |||||||
\(150\) | 22.7266 | 1.85562 | ||||||||
\(151\) | −13.0362 | −1.06087 | −0.530434 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530434 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(152\) | 31.4971 | 2.55476 | ||||||||
\(153\) | 0.751760 | 0.0607762 | ||||||||
\(154\) | −35.0068 | −2.82093 | ||||||||
\(155\) | −11.1797 | −0.897973 | ||||||||
\(156\) | 40.4356 | 3.23744 | ||||||||
\(157\) | 11.0360 | 0.880767 | 0.440383 | − | 0.897810i | \(-0.354843\pi\) | ||||
0.440383 | + | 0.897810i | \(0.354843\pi\) | |||||||
\(158\) | −42.7737 | −3.40289 | ||||||||
\(159\) | −0.986862 | −0.0782632 | ||||||||
\(160\) | 13.1383 | 1.03867 | ||||||||
\(161\) | 4.03414 | 0.317935 | ||||||||
\(162\) | 2.11742 | 0.166360 | ||||||||
\(163\) | −17.5860 | −1.37744 | −0.688721 | − | 0.725026i | \(-0.741828\pi\) | ||||
−0.688721 | + | 0.725026i | \(0.741828\pi\) | |||||||
\(164\) | 31.0046 | 2.42106 | ||||||||
\(165\) | 12.6407 | 0.984076 | ||||||||
\(166\) | −10.6235 | −0.824544 | ||||||||
\(167\) | −9.30364 | −0.719937 | −0.359969 | − | 0.932964i | \(-0.617213\pi\) | ||||
−0.359969 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(168\) | 81.0210 | 6.25091 | ||||||||
\(169\) | −3.72429 | −0.286484 | ||||||||
\(170\) | 0.564090 | 0.0432637 | ||||||||
\(171\) | −20.6273 | −1.57741 | ||||||||
\(172\) | 22.9518 | 1.75006 | ||||||||
\(173\) | −18.9570 | −1.44127 | −0.720636 | − | 0.693313i | \(-0.756150\pi\) | ||||
−0.720636 | + | 0.693313i | \(0.756150\pi\) | |||||||
\(174\) | −54.7459 | −4.15028 | ||||||||
\(175\) | 12.6684 | 0.957639 | ||||||||
\(176\) | −30.8431 | −2.32488 | ||||||||
\(177\) | 39.6382 | 2.97939 | ||||||||
\(178\) | 6.71956 | 0.503653 | ||||||||
\(179\) | 15.2536 | 1.14010 | 0.570052 | − | 0.821609i | \(-0.306923\pi\) | ||||
0.570052 | + | 0.821609i | \(0.306923\pi\) | |||||||
\(180\) | −30.8049 | −2.29606 | ||||||||
\(181\) | −20.9167 | −1.55473 | −0.777364 | − | 0.629051i | \(-0.783444\pi\) | ||||
−0.777364 | + | 0.629051i | \(0.783444\pi\) | |||||||
\(182\) | 31.9804 | 2.37054 | ||||||||
\(183\) | 24.4253 | 1.80557 | ||||||||
\(184\) | 7.22339 | 0.532516 | ||||||||
\(185\) | 9.24865 | 0.679974 | ||||||||
\(186\) | −59.3295 | −4.35025 | ||||||||
\(187\) | −0.529796 | −0.0387426 | ||||||||
\(188\) | 49.1661 | 3.58581 | ||||||||
\(189\) | −19.4108 | −1.41193 | ||||||||
\(190\) | −15.4779 | −1.12288 | ||||||||
\(191\) | −14.1508 | −1.02392 | −0.511959 | − | 0.859010i | \(-0.671080\pi\) | ||||
−0.511959 | + | 0.859010i | \(0.671080\pi\) | |||||||
\(192\) | 18.2776 | 1.31907 | ||||||||
\(193\) | −12.5103 | −0.900510 | −0.450255 | − | 0.892900i | \(-0.648667\pi\) | ||||
−0.450255 | + | 0.892900i | \(0.648667\pi\) | |||||||
\(194\) | 32.1217 | 2.30620 | ||||||||
\(195\) | −11.5479 | −0.826960 | ||||||||
\(196\) | 44.2860 | 3.16328 | ||||||||
\(197\) | 18.1564 | 1.29359 | 0.646794 | − | 0.762665i | \(-0.276109\pi\) | ||||
0.646794 | + | 0.762665i | \(0.276109\pi\) | |||||||
\(198\) | 41.0500 | 2.91730 | ||||||||
\(199\) | −27.2662 | −1.93285 | −0.966425 | − | 0.256949i | \(-0.917283\pi\) | ||||
−0.966425 | + | 0.256949i | \(0.917283\pi\) | |||||||
\(200\) | 22.6835 | 1.60397 | ||||||||
\(201\) | −43.2921 | −3.05359 | ||||||||
\(202\) | 29.9449 | 2.10692 | ||||||||
\(203\) | −30.5168 | −2.14186 | ||||||||
\(204\) | 2.10988 | 0.147721 | ||||||||
\(205\) | −8.85452 | −0.618426 | ||||||||
\(206\) | 3.64038 | 0.253637 | ||||||||
\(207\) | −4.73056 | −0.328797 | ||||||||
\(208\) | 28.1766 | 1.95370 | ||||||||
\(209\) | 14.5369 | 1.00554 | ||||||||
\(210\) | −39.8142 | −2.74744 | ||||||||
\(211\) | 23.1335 | 1.59257 | 0.796287 | − | 0.604919i | \(-0.206795\pi\) | ||||
0.796287 | + | 0.604919i | \(0.206795\pi\) | |||||||
\(212\) | −1.69487 | −0.116404 | ||||||||
\(213\) | −33.7747 | −2.31421 | ||||||||
\(214\) | −18.8936 | −1.29154 | ||||||||
\(215\) | −6.55473 | −0.447029 | ||||||||
\(216\) | −34.7563 | −2.36487 | ||||||||
\(217\) | −33.0718 | −2.24506 | ||||||||
\(218\) | 33.1417 | 2.24464 | ||||||||
\(219\) | −4.62210 | −0.312333 | ||||||||
\(220\) | 21.7095 | 1.46365 | ||||||||
\(221\) | 0.483995 | 0.0325570 | ||||||||
\(222\) | 49.0817 | 3.29415 | ||||||||
\(223\) | −23.6814 | −1.58583 | −0.792913 | − | 0.609335i | \(-0.791437\pi\) | ||||
−0.792913 | + | 0.609335i | \(0.791437\pi\) | |||||||
\(224\) | 38.8657 | 2.59682 | ||||||||
\(225\) | −14.8553 | −0.990355 | ||||||||
\(226\) | 12.5737 | 0.836392 | ||||||||
\(227\) | 25.6706 | 1.70382 | 0.851910 | − | 0.523688i | \(-0.175444\pi\) | ||||
0.851910 | + | 0.523688i | \(0.175444\pi\) | |||||||
\(228\) | −57.8922 | −3.83401 | ||||||||
\(229\) | 10.5015 | 0.693959 | 0.346979 | − | 0.937873i | \(-0.387207\pi\) | ||||
0.346979 | + | 0.937873i | \(0.387207\pi\) | |||||||
\(230\) | −3.54962 | −0.234055 | ||||||||
\(231\) | 37.3937 | 2.46033 | ||||||||
\(232\) | −54.6423 | −3.58744 | ||||||||
\(233\) | −20.7921 | −1.36214 | −0.681069 | − | 0.732220i | \(-0.738484\pi\) | ||||
−0.681069 | + | 0.732220i | \(0.738484\pi\) | |||||||
\(234\) | −37.5012 | −2.45153 | ||||||||
\(235\) | −14.0412 | −0.915946 | ||||||||
\(236\) | 68.0760 | 4.43137 | ||||||||
\(237\) | 45.6902 | 2.96790 | ||||||||
\(238\) | 1.66869 | 0.108165 | ||||||||
\(239\) | −29.0262 | −1.87755 | −0.938774 | − | 0.344535i | \(-0.888037\pi\) | ||||
−0.938774 | + | 0.344535i | \(0.888037\pi\) | |||||||
\(240\) | −35.0787 | −2.26432 | ||||||||
\(241\) | 6.23083 | 0.401363 | 0.200681 | − | 0.979657i | \(-0.435684\pi\) | ||||
0.200681 | + | 0.979657i | \(0.435684\pi\) | |||||||
\(242\) | −0.297678 | −0.0191355 | ||||||||
\(243\) | −16.6967 | −1.07109 | ||||||||
\(244\) | 41.9487 | 2.68549 | ||||||||
\(245\) | −12.6475 | −0.808018 | ||||||||
\(246\) | −46.9901 | −2.99598 | ||||||||
\(247\) | −13.2802 | −0.844997 | ||||||||
\(248\) | −59.2171 | −3.76029 | ||||||||
\(249\) | 11.3479 | 0.719143 | ||||||||
\(250\) | −28.8949 | −1.82747 | ||||||||
\(251\) | −0.600486 | −0.0379024 | −0.0189512 | − | 0.999820i | \(-0.506033\pi\) | ||||
−0.0189512 | + | 0.999820i | \(0.506033\pi\) | |||||||
\(252\) | −91.1273 | −5.74048 | ||||||||
\(253\) | 3.33382 | 0.209596 | ||||||||
\(254\) | 44.8317 | 2.81299 | ||||||||
\(255\) | −0.602553 | −0.0377333 | ||||||||
\(256\) | −18.7633 | −1.17270 | ||||||||
\(257\) | 8.60111 | 0.536523 | 0.268261 | − | 0.963346i | \(-0.413551\pi\) | ||||
0.268261 | + | 0.963346i | \(0.413551\pi\) | |||||||
\(258\) | −34.7853 | −2.16564 | ||||||||
\(259\) | 27.3594 | 1.70003 | ||||||||
\(260\) | −19.8327 | −1.22997 | ||||||||
\(261\) | 35.7849 | 2.21503 | ||||||||
\(262\) | 14.1042 | 0.871360 | ||||||||
\(263\) | −26.6833 | −1.64536 | −0.822682 | − | 0.568502i | \(-0.807523\pi\) | ||||
−0.822682 | + | 0.568502i | \(0.807523\pi\) | |||||||
\(264\) | 66.9559 | 4.12085 | ||||||||
\(265\) | 0.484031 | 0.0297338 | ||||||||
\(266\) | −45.7868 | −2.80737 | ||||||||
\(267\) | −7.17774 | −0.439271 | ||||||||
\(268\) | −74.3512 | −4.54172 | ||||||||
\(269\) | −10.8196 | −0.659686 | −0.329843 | − | 0.944036i | \(-0.606996\pi\) | ||||
−0.329843 | + | 0.944036i | \(0.606996\pi\) | |||||||
\(270\) | 17.0794 | 1.03942 | ||||||||
\(271\) | −10.5213 | −0.639124 | −0.319562 | − | 0.947565i | \(-0.603536\pi\) | ||||
−0.319562 | + | 0.947565i | \(0.603536\pi\) | |||||||
\(272\) | 1.47022 | 0.0891451 | ||||||||
\(273\) | −34.1610 | −2.06752 | ||||||||
\(274\) | 30.3871 | 1.83575 | ||||||||
\(275\) | 10.4692 | 0.631314 | ||||||||
\(276\) | −13.2767 | −0.799164 | ||||||||
\(277\) | −8.23535 | −0.494814 | −0.247407 | − | 0.968912i | \(-0.579578\pi\) | ||||
−0.247407 | + | 0.968912i | \(0.579578\pi\) | |||||||
\(278\) | −28.5287 | −1.71104 | ||||||||
\(279\) | 38.7810 | 2.32176 | ||||||||
\(280\) | −39.7388 | −2.37485 | ||||||||
\(281\) | −6.44166 | −0.384277 | −0.192139 | − | 0.981368i | \(-0.561542\pi\) | ||||
−0.192139 | + | 0.981368i | \(0.561542\pi\) | |||||||
\(282\) | −74.5153 | −4.43732 | ||||||||
\(283\) | 6.90455 | 0.410433 | 0.205216 | − | 0.978717i | \(-0.434210\pi\) | ||||
0.205216 | + | 0.978717i | \(0.434210\pi\) | |||||||
\(284\) | −58.0058 | −3.44201 | ||||||||
\(285\) | 16.5333 | 0.979345 | ||||||||
\(286\) | 26.4286 | 1.56276 | ||||||||
\(287\) | −26.1935 | −1.54615 | ||||||||
\(288\) | −45.5751 | −2.68554 | ||||||||
\(289\) | −16.9747 | −0.998514 | ||||||||
\(290\) | 26.8515 | 1.57678 | ||||||||
\(291\) | −34.3119 | −2.01140 | ||||||||
\(292\) | −7.93814 | −0.464545 | ||||||||
\(293\) | 4.43221 | 0.258933 | 0.129466 | − | 0.991584i | \(-0.458674\pi\) | ||||
0.129466 | + | 0.991584i | \(0.458674\pi\) | |||||||
\(294\) | −67.1190 | −3.91446 | ||||||||
\(295\) | −19.4416 | −1.13193 | ||||||||
\(296\) | 48.9888 | 2.84741 | ||||||||
\(297\) | −16.0411 | −0.930800 | ||||||||
\(298\) | −27.7061 | −1.60497 | ||||||||
\(299\) | −3.04561 | −0.176132 | ||||||||
\(300\) | −41.6927 | −2.40713 | ||||||||
\(301\) | −19.3902 | −1.11764 | ||||||||
\(302\) | 33.9319 | 1.95256 | ||||||||
\(303\) | −31.9867 | −1.83759 | ||||||||
\(304\) | −40.3409 | −2.31371 | ||||||||
\(305\) | −11.9800 | −0.685973 | ||||||||
\(306\) | −1.95676 | −0.111861 | ||||||||
\(307\) | −32.1297 | −1.83374 | −0.916870 | − | 0.399185i | \(-0.869293\pi\) | ||||
−0.916870 | + | 0.399185i | \(0.869293\pi\) | |||||||
\(308\) | 64.2212 | 3.65934 | ||||||||
\(309\) | −3.88860 | −0.221215 | ||||||||
\(310\) | 29.0996 | 1.65275 | ||||||||
\(311\) | −10.9159 | −0.618984 | −0.309492 | − | 0.950902i | \(-0.600159\pi\) | ||||
−0.309492 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(312\) | −61.1674 | −3.46292 | ||||||||
\(313\) | 9.80624 | 0.554282 | 0.277141 | − | 0.960829i | \(-0.410613\pi\) | ||||
0.277141 | + | 0.960829i | \(0.410613\pi\) | |||||||
\(314\) | −28.7256 | −1.62108 | ||||||||
\(315\) | 26.0247 | 1.46633 | ||||||||
\(316\) | 78.4698 | 4.41427 | ||||||||
\(317\) | −19.0524 | −1.07009 | −0.535044 | − | 0.844824i | \(-0.679705\pi\) | ||||
−0.535044 | + | 0.844824i | \(0.679705\pi\) | |||||||
\(318\) | 2.56871 | 0.144046 | ||||||||
\(319\) | −25.2191 | −1.41200 | ||||||||
\(320\) | −8.96472 | −0.501143 | ||||||||
\(321\) | 20.1818 | 1.12644 | ||||||||
\(322\) | −10.5005 | −0.585170 | ||||||||
\(323\) | −0.692942 | −0.0385563 | ||||||||
\(324\) | −3.88449 | −0.215805 | ||||||||
\(325\) | −9.56408 | −0.530520 | ||||||||
\(326\) | 45.7747 | 2.53523 | ||||||||
\(327\) | −35.4015 | −1.95771 | ||||||||
\(328\) | −46.9011 | −2.58968 | ||||||||
\(329\) | −41.5367 | −2.28999 | ||||||||
\(330\) | −32.9025 | −1.81122 | ||||||||
\(331\) | 8.08544 | 0.444416 | 0.222208 | − | 0.974999i | \(-0.428674\pi\) | ||||
0.222208 | + | 0.974999i | \(0.428674\pi\) | |||||||
\(332\) | 19.4892 | 1.06961 | ||||||||
\(333\) | −32.0825 | −1.75811 | ||||||||
\(334\) | 24.2165 | 1.32507 | ||||||||
\(335\) | 21.2337 | 1.16012 | ||||||||
\(336\) | −103.770 | −5.66112 | ||||||||
\(337\) | −2.15213 | −0.117234 | −0.0586170 | − | 0.998281i | \(-0.518669\pi\) | ||||
−0.0586170 | + | 0.998281i | \(0.518669\pi\) | |||||||
\(338\) | 9.69397 | 0.527283 | ||||||||
\(339\) | −13.4311 | −0.729476 | ||||||||
\(340\) | −1.03484 | −0.0561222 | ||||||||
\(341\) | −27.3306 | −1.48003 | ||||||||
\(342\) | 53.6910 | 2.90327 | ||||||||
\(343\) | −9.17486 | −0.495396 | ||||||||
\(344\) | −34.7195 | −1.87195 | ||||||||
\(345\) | 3.79165 | 0.204136 | ||||||||
\(346\) | 49.3433 | 2.65271 | ||||||||
\(347\) | 30.9474 | 1.66135 | 0.830673 | − | 0.556761i | \(-0.187956\pi\) | ||||
0.830673 | + | 0.556761i | \(0.187956\pi\) | |||||||
\(348\) | 100.433 | 5.38379 | ||||||||
\(349\) | −1.00000 | −0.0535288 | ||||||||
\(350\) | −32.9746 | −1.76257 | ||||||||
\(351\) | 14.6543 | 0.782190 | ||||||||
\(352\) | 32.1187 | 1.71193 | ||||||||
\(353\) | 32.9297 | 1.75267 | 0.876337 | − | 0.481699i | \(-0.159980\pi\) | ||||
0.876337 | + | 0.481699i | \(0.159980\pi\) | |||||||
\(354\) | −103.175 | −5.48367 | ||||||||
\(355\) | 16.5657 | 0.879215 | ||||||||
\(356\) | −12.3273 | −0.653344 | ||||||||
\(357\) | −1.78247 | −0.0943386 | ||||||||
\(358\) | −39.7036 | −2.09840 | ||||||||
\(359\) | 10.5393 | 0.556245 | 0.278123 | − | 0.960546i | \(-0.410288\pi\) | ||||
0.278123 | + | 0.960546i | \(0.410288\pi\) | |||||||
\(360\) | 46.5990 | 2.45598 | ||||||||
\(361\) | 0.0134087 | 0.000705721 0 | ||||||||
\(362\) | 54.4443 | 2.86153 | ||||||||
\(363\) | 0.317976 | 0.0166894 | ||||||||
\(364\) | −58.6691 | −3.07510 | ||||||||
\(365\) | 2.26703 | 0.118662 | ||||||||
\(366\) | −63.5767 | −3.32321 | ||||||||
\(367\) | 24.2005 | 1.26325 | 0.631627 | − | 0.775272i | \(-0.282387\pi\) | ||||
0.631627 | + | 0.775272i | \(0.282387\pi\) | |||||||
\(368\) | −9.25157 | −0.482271 | ||||||||
\(369\) | 30.7153 | 1.59897 | ||||||||
\(370\) | −24.0734 | −1.25151 | ||||||||
\(371\) | 1.43186 | 0.0743387 | ||||||||
\(372\) | 108.842 | 5.64319 | ||||||||
\(373\) | 11.0453 | 0.571905 | 0.285953 | − | 0.958244i | \(-0.407690\pi\) | ||||
0.285953 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(374\) | 1.37901 | 0.0713070 | ||||||||
\(375\) | 30.8651 | 1.59387 | ||||||||
\(376\) | −74.3742 | −3.83556 | ||||||||
\(377\) | 23.0389 | 1.18656 | ||||||||
\(378\) | 50.5245 | 2.59870 | ||||||||
\(379\) | −24.3895 | −1.25281 | −0.626403 | − | 0.779499i | \(-0.715474\pi\) | ||||
−0.626403 | + | 0.779499i | \(0.715474\pi\) | |||||||
\(380\) | 28.3947 | 1.45662 | ||||||||
\(381\) | −47.8885 | −2.45340 | ||||||||
\(382\) | 36.8333 | 1.88456 | ||||||||
\(383\) | 18.0641 | 0.923030 | 0.461515 | − | 0.887132i | \(-0.347306\pi\) | ||||
0.461515 | + | 0.887132i | \(0.347306\pi\) | |||||||
\(384\) | 5.99867 | 0.306118 | ||||||||
\(385\) | −18.3407 | −0.934729 | ||||||||
\(386\) | 32.5631 | 1.65742 | ||||||||
\(387\) | 22.7376 | 1.15582 | ||||||||
\(388\) | −58.9283 | −2.99163 | ||||||||
\(389\) | 21.4135 | 1.08571 | 0.542854 | − | 0.839827i | \(-0.317344\pi\) | ||||
0.542854 | + | 0.839827i | \(0.317344\pi\) | |||||||
\(390\) | 30.0580 | 1.52205 | ||||||||
\(391\) | −0.158916 | −0.00803671 | ||||||||
\(392\) | −66.9919 | −3.38360 | ||||||||
\(393\) | −15.0659 | −0.759974 | ||||||||
\(394\) | −47.2593 | −2.38089 | ||||||||
\(395\) | −22.4099 | −1.12757 | ||||||||
\(396\) | −75.3077 | −3.78436 | ||||||||
\(397\) | −11.9097 | −0.597733 | −0.298867 | − | 0.954295i | \(-0.596609\pi\) | ||||
−0.298867 | + | 0.954295i | \(0.596609\pi\) | |||||||
\(398\) | 70.9714 | 3.55747 | ||||||||
\(399\) | 48.9088 | 2.44850 | ||||||||
\(400\) | −29.0526 | −1.45263 | ||||||||
\(401\) | −18.6728 | −0.932474 | −0.466237 | − | 0.884660i | \(-0.654391\pi\) | ||||
−0.466237 | + | 0.884660i | \(0.654391\pi\) | |||||||
\(402\) | 112.685 | 5.62023 | ||||||||
\(403\) | 24.9678 | 1.24373 | ||||||||
\(404\) | −54.9350 | −2.73312 | ||||||||
\(405\) | 1.10936 | 0.0551244 | ||||||||
\(406\) | 79.4324 | 3.94216 | ||||||||
\(407\) | 22.6099 | 1.12073 | ||||||||
\(408\) | −3.19164 | −0.158010 | ||||||||
\(409\) | 24.2432 | 1.19875 | 0.599376 | − | 0.800468i | \(-0.295416\pi\) | ||||
0.599376 | + | 0.800468i | \(0.295416\pi\) | |||||||
\(410\) | 23.0475 | 1.13823 | ||||||||
\(411\) | −32.4591 | −1.60109 | ||||||||
\(412\) | −6.67840 | −0.329021 | ||||||||
\(413\) | −57.5122 | −2.82999 | ||||||||
\(414\) | 12.3132 | 0.605161 | ||||||||
\(415\) | −5.56586 | −0.273217 | ||||||||
\(416\) | −29.3419 | −1.43861 | ||||||||
\(417\) | 30.4739 | 1.49231 | ||||||||
\(418\) | −37.8382 | −1.85073 | ||||||||
\(419\) | −30.4515 | −1.48765 | −0.743826 | − | 0.668373i | \(-0.766991\pi\) | ||||
−0.743826 | + | 0.668373i | \(0.766991\pi\) | |||||||
\(420\) | 73.0406 | 3.56402 | ||||||||
\(421\) | 1.41765 | 0.0690921 | 0.0345460 | − | 0.999403i | \(-0.489001\pi\) | ||||
0.0345460 | + | 0.999403i | \(0.489001\pi\) | |||||||
\(422\) | −60.2143 | −2.93119 | ||||||||
\(423\) | 48.7073 | 2.36823 | ||||||||
\(424\) | 2.56385 | 0.124511 | ||||||||
\(425\) | −0.499041 | −0.0242070 | ||||||||
\(426\) | 87.9125 | 4.25938 | ||||||||
\(427\) | −35.4393 | −1.71503 | ||||||||
\(428\) | 34.6609 | 1.67540 | ||||||||
\(429\) | −28.2307 | −1.36299 | ||||||||
\(430\) | 17.0614 | 0.822772 | ||||||||
\(431\) | 7.08869 | 0.341450 | 0.170725 | − | 0.985319i | \(-0.445389\pi\) | ||||
0.170725 | + | 0.985319i | \(0.445389\pi\) | |||||||
\(432\) | 44.5151 | 2.14173 | ||||||||
\(433\) | 0.387898 | 0.0186412 | 0.00932059 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00932059 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(434\) | 86.0827 | 4.13210 | ||||||||
\(435\) | −28.6824 | −1.37522 | ||||||||
\(436\) | −60.7997 | −2.91178 | ||||||||
\(437\) | 4.36044 | 0.208588 | ||||||||
\(438\) | 12.0309 | 0.574859 | ||||||||
\(439\) | −37.6565 | −1.79725 | −0.898624 | − | 0.438719i | \(-0.855432\pi\) | ||||
−0.898624 | + | 0.438719i | \(0.855432\pi\) | |||||||
\(440\) | −32.8402 | −1.56560 | ||||||||
\(441\) | 43.8726 | 2.08917 | ||||||||
\(442\) | −1.25979 | −0.0599222 | ||||||||
\(443\) | −13.5551 | −0.644020 | −0.322010 | − | 0.946736i | \(-0.604358\pi\) | ||||
−0.322010 | + | 0.946736i | \(0.604358\pi\) | |||||||
\(444\) | −90.0421 | −4.27321 | ||||||||
\(445\) | 3.52051 | 0.166888 | ||||||||
\(446\) | 61.6406 | 2.91877 | ||||||||
\(447\) | 29.5953 | 1.39981 | ||||||||
\(448\) | −26.5195 | −1.25293 | ||||||||
\(449\) | −3.82446 | −0.180487 | −0.0902437 | − | 0.995920i | \(-0.528765\pi\) | ||||
−0.0902437 | + | 0.995920i | \(0.528765\pi\) | |||||||
\(450\) | 38.6670 | 1.82278 | ||||||||
\(451\) | −21.6463 | −1.01929 | ||||||||
\(452\) | −23.0670 | −1.08498 | ||||||||
\(453\) | −36.2456 | −1.70297 | ||||||||
\(454\) | −66.8183 | −3.13594 | ||||||||
\(455\) | 16.7551 | 0.785492 | ||||||||
\(456\) | 87.5743 | 4.10104 | ||||||||
\(457\) | −16.9428 | −0.792552 | −0.396276 | − | 0.918131i | \(-0.629698\pi\) | ||||
−0.396276 | + | 0.918131i | \(0.629698\pi\) | |||||||
\(458\) | −27.3344 | −1.27725 | ||||||||
\(459\) | 0.764643 | 0.0356905 | ||||||||
\(460\) | 6.51190 | 0.303619 | ||||||||
\(461\) | −15.4883 | −0.721361 | −0.360681 | − | 0.932689i | \(-0.617456\pi\) | ||||
−0.360681 | + | 0.932689i | \(0.617456\pi\) | |||||||
\(462\) | −97.3324 | −4.52832 | ||||||||
\(463\) | 21.4330 | 0.996076 | 0.498038 | − | 0.867155i | \(-0.334054\pi\) | ||||
0.498038 | + | 0.867155i | \(0.334054\pi\) | |||||||
\(464\) | 69.9847 | 3.24896 | ||||||||
\(465\) | −31.0838 | −1.44148 | ||||||||
\(466\) | 54.1200 | 2.50706 | ||||||||
\(467\) | −13.2395 | −0.612653 | −0.306326 | − | 0.951927i | \(-0.599100\pi\) | ||||
−0.306326 | + | 0.951927i | \(0.599100\pi\) | |||||||
\(468\) | 68.7972 | 3.18015 | ||||||||
\(469\) | 62.8137 | 2.90047 | ||||||||
\(470\) | 36.5479 | 1.68583 | ||||||||
\(471\) | 30.6843 | 1.41386 | ||||||||
\(472\) | −102.979 | −4.74001 | ||||||||
\(473\) | −16.0241 | −0.736790 | ||||||||
\(474\) | −118.927 | −5.46252 | ||||||||
\(475\) | 13.6930 | 0.628279 | ||||||||
\(476\) | −3.06128 | −0.140313 | ||||||||
\(477\) | −1.67905 | −0.0768784 | ||||||||
\(478\) | 75.5524 | 3.45569 | ||||||||
\(479\) | 16.3784 | 0.748348 | 0.374174 | − | 0.927358i | \(-0.377926\pi\) | ||||
0.374174 | + | 0.927358i | \(0.377926\pi\) | |||||||
\(480\) | 36.5295 | 1.66733 | ||||||||
\(481\) | −20.6552 | −0.941795 | ||||||||
\(482\) | −16.2183 | −0.738722 | ||||||||
\(483\) | 11.2165 | 0.510368 | ||||||||
\(484\) | 0.546101 | 0.0248228 | ||||||||
\(485\) | 16.8291 | 0.764172 | ||||||||
\(486\) | 43.4599 | 1.97138 | ||||||||
\(487\) | 18.7581 | 0.850008 | 0.425004 | − | 0.905191i | \(-0.360273\pi\) | ||||
0.425004 | + | 0.905191i | \(0.360273\pi\) | |||||||
\(488\) | −63.4564 | −2.87254 | ||||||||
\(489\) | −48.8959 | −2.21115 | ||||||||
\(490\) | 32.9202 | 1.48718 | ||||||||
\(491\) | 26.8223 | 1.21047 | 0.605236 | − | 0.796046i | \(-0.293079\pi\) | ||||
0.605236 | + | 0.796046i | \(0.293079\pi\) | |||||||
\(492\) | 86.2050 | 3.88642 | ||||||||
\(493\) | 1.20214 | 0.0541416 | ||||||||
\(494\) | 34.5670 | 1.55525 | ||||||||
\(495\) | 21.5069 | 0.966663 | ||||||||
\(496\) | 75.8441 | 3.40550 | ||||||||
\(497\) | 49.0047 | 2.19816 | ||||||||
\(498\) | −29.5375 | −1.32361 | ||||||||
\(499\) | 21.7496 | 0.973646 | 0.486823 | − | 0.873501i | \(-0.338156\pi\) | ||||
0.486823 | + | 0.873501i | \(0.338156\pi\) | |||||||
\(500\) | 53.0087 | 2.37062 | ||||||||
\(501\) | −25.8677 | −1.15569 | ||||||||
\(502\) | 1.56301 | 0.0697606 | ||||||||
\(503\) | 16.1677 | 0.720881 | 0.360441 | − | 0.932782i | \(-0.382626\pi\) | ||||
0.360441 | + | 0.932782i | \(0.382626\pi\) | |||||||
\(504\) | 137.849 | 6.14030 | ||||||||
\(505\) | 15.6887 | 0.698138 | ||||||||
\(506\) | −8.67763 | −0.385768 | ||||||||
\(507\) | −10.3550 | −0.459880 | ||||||||
\(508\) | −82.2453 | −3.64904 | ||||||||
\(509\) | −42.0955 | −1.86585 | −0.932925 | − | 0.360071i | \(-0.882753\pi\) | ||||
−0.932925 | + | 0.360071i | \(0.882753\pi\) | |||||||
\(510\) | 1.56839 | 0.0694494 | ||||||||
\(511\) | 6.70634 | 0.296671 | ||||||||
\(512\) | 44.5241 | 1.96770 | ||||||||
\(513\) | −20.9808 | −0.926325 | ||||||||
\(514\) | −22.3879 | −0.987488 | ||||||||
\(515\) | 1.90726 | 0.0840440 | ||||||||
\(516\) | 63.8149 | 2.80930 | ||||||||
\(517\) | −34.3260 | −1.50966 | ||||||||
\(518\) | −71.2140 | −3.12896 | ||||||||
\(519\) | −52.7078 | −2.31361 | ||||||||
\(520\) | 30.0011 | 1.31564 | ||||||||
\(521\) | −10.3470 | −0.453310 | −0.226655 | − | 0.973975i | \(-0.572779\pi\) | ||||
−0.226655 | + | 0.973975i | \(0.572779\pi\) | |||||||
\(522\) | −93.1448 | −4.07684 | ||||||||
\(523\) | −26.6023 | −1.16324 | −0.581618 | − | 0.813462i | \(-0.697580\pi\) | ||||
−0.581618 | + | 0.813462i | \(0.697580\pi\) | |||||||
\(524\) | −25.8746 | −1.13034 | ||||||||
\(525\) | 35.2230 | 1.53726 | ||||||||
\(526\) | 69.4542 | 3.02835 | ||||||||
\(527\) | 1.30279 | 0.0567502 | ||||||||
\(528\) | −85.7557 | −3.73204 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −1.25989 | −0.0547261 | ||||||||
\(531\) | 67.4406 | 2.92667 | ||||||||
\(532\) | 83.9974 | 3.64175 | ||||||||
\(533\) | 19.7750 | 0.856549 | ||||||||
\(534\) | 18.6830 | 0.808492 | ||||||||
\(535\) | −9.89870 | −0.427958 | ||||||||
\(536\) | 112.472 | 4.85805 | ||||||||
\(537\) | 42.4108 | 1.83016 | ||||||||
\(538\) | 28.1625 | 1.21417 | ||||||||
\(539\) | −30.9189 | −1.33177 | ||||||||
\(540\) | −31.3328 | −1.34835 | ||||||||
\(541\) | 23.2865 | 1.00116 | 0.500582 | − | 0.865689i | \(-0.333119\pi\) | ||||
0.500582 | + | 0.865689i | \(0.333119\pi\) | |||||||
\(542\) | 27.3860 | 1.17633 | ||||||||
\(543\) | −58.1566 | −2.49574 | ||||||||
\(544\) | −1.53102 | −0.0656421 | ||||||||
\(545\) | 17.3636 | 0.743774 | ||||||||
\(546\) | 88.9179 | 3.80533 | ||||||||
\(547\) | 15.5491 | 0.664830 | 0.332415 | − | 0.943133i | \(-0.392137\pi\) | ||||
0.332415 | + | 0.943133i | \(0.392137\pi\) | |||||||
\(548\) | −55.7463 | −2.38136 | ||||||||
\(549\) | 41.5572 | 1.77362 | ||||||||
\(550\) | −27.2502 | −1.16195 | ||||||||
\(551\) | −32.9851 | −1.40521 | ||||||||
\(552\) | 20.0838 | 0.854825 | ||||||||
\(553\) | −66.2932 | −2.81907 | ||||||||
\(554\) | 21.4358 | 0.910722 | ||||||||
\(555\) | 25.7148 | 1.09153 | ||||||||
\(556\) | 52.3369 | 2.21958 | ||||||||
\(557\) | 21.9668 | 0.930762 | 0.465381 | − | 0.885110i | \(-0.345917\pi\) | ||||
0.465381 | + | 0.885110i | \(0.345917\pi\) | |||||||
\(558\) | −100.943 | −4.27327 | ||||||||
\(559\) | 14.6388 | 0.619156 | ||||||||
\(560\) | 50.8967 | 2.15078 | ||||||||
\(561\) | −1.47304 | −0.0621918 | ||||||||
\(562\) | 16.7670 | 0.707275 | ||||||||
\(563\) | 1.00084 | 0.0421803 | 0.0210901 | − | 0.999778i | \(-0.493286\pi\) | ||||
0.0210901 | + | 0.999778i | \(0.493286\pi\) | |||||||
\(564\) | 136.701 | 5.75615 | ||||||||
\(565\) | 6.58762 | 0.277143 | ||||||||
\(566\) | −17.9719 | −0.755415 | ||||||||
\(567\) | 3.28171 | 0.137819 | ||||||||
\(568\) | 87.7461 | 3.68174 | ||||||||
\(569\) | −25.8517 | −1.08376 | −0.541880 | − | 0.840456i | \(-0.682287\pi\) | ||||
−0.541880 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(570\) | −43.0345 | −1.80252 | ||||||||
\(571\) | 36.8534 | 1.54227 | 0.771133 | − | 0.636675i | \(-0.219691\pi\) | ||||
0.771133 | + | 0.636675i | \(0.219691\pi\) | |||||||
\(572\) | −48.4843 | −2.02723 | ||||||||
\(573\) | −39.3448 | −1.64365 | ||||||||
\(574\) | 68.1792 | 2.84574 | ||||||||
\(575\) | 3.14029 | 0.130959 | ||||||||
\(576\) | 31.0976 | 1.29573 | ||||||||
\(577\) | −4.33062 | −0.180286 | −0.0901429 | − | 0.995929i | \(-0.528732\pi\) | ||||
−0.0901429 | + | 0.995929i | \(0.528732\pi\) | |||||||
\(578\) | 44.1837 | 1.83780 | ||||||||
\(579\) | −34.7835 | −1.44555 | ||||||||
\(580\) | −49.2601 | −2.04541 | ||||||||
\(581\) | −16.4650 | −0.683081 | ||||||||
\(582\) | 89.3107 | 3.70205 | ||||||||
\(583\) | 1.18330 | 0.0490071 | ||||||||
\(584\) | 12.0081 | 0.496900 | ||||||||
\(585\) | −19.6476 | −0.812327 | ||||||||
\(586\) | −11.5366 | −0.476574 | ||||||||
\(587\) | 14.2394 | 0.587722 | 0.293861 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(588\) | 123.132 | 5.07788 | ||||||||
\(589\) | −35.7467 | −1.47292 | ||||||||
\(590\) | 50.6047 | 2.08336 | ||||||||
\(591\) | 50.4818 | 2.07654 | ||||||||
\(592\) | −62.7438 | −2.57875 | ||||||||
\(593\) | 30.8143 | 1.26539 | 0.632695 | − | 0.774401i | \(-0.281949\pi\) | ||||
0.632695 | + | 0.774401i | \(0.281949\pi\) | |||||||
\(594\) | 41.7535 | 1.71317 | ||||||||
\(595\) | 0.874260 | 0.0358412 | ||||||||
\(596\) | 50.8278 | 2.08199 | ||||||||
\(597\) | −75.8106 | −3.10272 | ||||||||
\(598\) | 7.92743 | 0.324177 | ||||||||
\(599\) | −5.87754 | −0.240150 | −0.120075 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120075 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(600\) | 63.0690 | 2.57478 | ||||||||
\(601\) | −19.6502 | −0.801549 | −0.400775 | − | 0.916177i | \(-0.631259\pi\) | ||||
−0.400775 | + | 0.916177i | \(0.631259\pi\) | |||||||
\(602\) | 50.4710 | 2.05704 | ||||||||
\(603\) | −73.6573 | −2.99956 | ||||||||
\(604\) | −62.2494 | −2.53289 | ||||||||
\(605\) | −0.155959 | −0.00634064 | ||||||||
\(606\) | 83.2585 | 3.38215 | ||||||||
\(607\) | 15.0478 | 0.610771 | 0.305386 | − | 0.952229i | \(-0.401215\pi\) | ||||
0.305386 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(608\) | 42.0093 | 1.70370 | ||||||||
\(609\) | −84.8485 | −3.43824 | ||||||||
\(610\) | 31.1828 | 1.26256 | ||||||||
\(611\) | 31.3585 | 1.26863 | ||||||||
\(612\) | 3.58975 | 0.145107 | ||||||||
\(613\) | −48.5970 | −1.96282 | −0.981408 | − | 0.191935i | \(-0.938524\pi\) | ||||
−0.981408 | + | 0.191935i | \(0.938524\pi\) | |||||||
\(614\) | 83.6307 | 3.37506 | ||||||||
\(615\) | −24.6190 | −0.992734 | ||||||||
\(616\) | −97.1482 | −3.91421 | ||||||||
\(617\) | −11.6449 | −0.468807 | −0.234404 | − | 0.972139i | \(-0.575314\pi\) | ||||
−0.234404 | + | 0.972139i | \(0.575314\pi\) | |||||||
\(618\) | 10.1217 | 0.407153 | ||||||||
\(619\) | 28.7361 | 1.15500 | 0.577500 | − | 0.816391i | \(-0.304028\pi\) | ||||
0.577500 | + | 0.816391i | \(0.304028\pi\) | |||||||
\(620\) | −53.3843 | −2.14397 | ||||||||
\(621\) | −4.81163 | −0.193084 | ||||||||
\(622\) | 28.4131 | 1.13926 | ||||||||
\(623\) | 10.4144 | 0.417244 | ||||||||
\(624\) | 78.3420 | 3.13619 | ||||||||
\(625\) | 0.562852 | 0.0225141 | ||||||||
\(626\) | −25.5247 | −1.02017 | ||||||||
\(627\) | 40.4183 | 1.61415 | ||||||||
\(628\) | 52.6982 | 2.10289 | ||||||||
\(629\) | −1.07776 | −0.0429731 | ||||||||
\(630\) | −67.7400 | −2.69883 | ||||||||
\(631\) | 28.5390 | 1.13612 | 0.568060 | − | 0.822987i | \(-0.307694\pi\) | ||||
0.568060 | + | 0.822987i | \(0.307694\pi\) | |||||||
\(632\) | −118.702 | −4.72172 | ||||||||
\(633\) | 64.3200 | 2.55649 | ||||||||
\(634\) | 49.5916 | 1.96953 | ||||||||
\(635\) | 23.4882 | 0.932099 | ||||||||
\(636\) | −4.71239 | −0.186858 | ||||||||
\(637\) | 28.2459 | 1.11914 | ||||||||
\(638\) | 65.6430 | 2.59883 | ||||||||
\(639\) | −57.4644 | −2.27326 | ||||||||
\(640\) | −2.94220 | −0.116301 | ||||||||
\(641\) | −48.3855 | −1.91111 | −0.955556 | − | 0.294811i | \(-0.904743\pi\) | ||||
−0.955556 | + | 0.294811i | \(0.904743\pi\) | |||||||
\(642\) | −52.5315 | −2.07325 | ||||||||
\(643\) | −36.9845 | −1.45853 | −0.729263 | − | 0.684233i | \(-0.760137\pi\) | ||||
−0.729263 | + | 0.684233i | \(0.760137\pi\) | |||||||
\(644\) | 19.2635 | 0.759090 | ||||||||
\(645\) | −18.2247 | −0.717597 | ||||||||
\(646\) | 1.80366 | 0.0709642 | ||||||||
\(647\) | −10.3514 | −0.406954 | −0.203477 | − | 0.979080i | \(-0.565224\pi\) | ||||
−0.203477 | + | 0.979080i | \(0.565224\pi\) | |||||||
\(648\) | 5.87611 | 0.230835 | ||||||||
\(649\) | −47.5282 | −1.86564 | ||||||||
\(650\) | 24.8944 | 0.976439 | ||||||||
\(651\) | −91.9524 | −3.60390 | ||||||||
\(652\) | −83.9754 | −3.28873 | ||||||||
\(653\) | 18.0082 | 0.704715 | 0.352358 | − | 0.935865i | \(-0.385380\pi\) | ||||
0.352358 | + | 0.935865i | \(0.385380\pi\) | |||||||
\(654\) | 92.1469 | 3.60323 | ||||||||
\(655\) | 7.38946 | 0.288730 | ||||||||
\(656\) | 60.0700 | 2.34534 | ||||||||
\(657\) | −7.86406 | −0.306806 | ||||||||
\(658\) | 108.116 | 4.21481 | ||||||||
\(659\) | 31.4918 | 1.22675 | 0.613373 | − | 0.789793i | \(-0.289812\pi\) | ||||
0.613373 | + | 0.789793i | \(0.289812\pi\) | |||||||
\(660\) | 60.3608 | 2.34954 | ||||||||
\(661\) | 18.2788 | 0.710965 | 0.355482 | − | 0.934683i | \(-0.384317\pi\) | ||||
0.355482 | + | 0.934683i | \(0.384317\pi\) | |||||||
\(662\) | −21.0457 | −0.817963 | ||||||||
\(663\) | 1.34569 | 0.0522624 | ||||||||
\(664\) | −29.4816 | −1.14411 | ||||||||
\(665\) | −23.9885 | −0.930236 | ||||||||
\(666\) | 83.5077 | 3.23586 | ||||||||
\(667\) | −7.56463 | −0.292904 | ||||||||
\(668\) | −44.4260 | −1.71890 | ||||||||
\(669\) | −65.8436 | −2.54566 | ||||||||
\(670\) | −55.2694 | −2.13524 | ||||||||
\(671\) | −29.2871 | −1.13062 | ||||||||
\(672\) | 108.062 | 4.16857 | ||||||||
\(673\) | −36.1959 | −1.39525 | −0.697625 | − | 0.716463i | \(-0.745760\pi\) | ||||
−0.697625 | + | 0.716463i | \(0.745760\pi\) | |||||||
\(674\) | 5.60179 | 0.215773 | ||||||||
\(675\) | −15.1099 | −0.581580 | ||||||||
\(676\) | −17.7839 | −0.683997 | ||||||||
\(677\) | −4.34341 | −0.166931 | −0.0834653 | − | 0.996511i | \(-0.526599\pi\) | ||||
−0.0834653 | + | 0.996511i | \(0.526599\pi\) | |||||||
\(678\) | 34.9599 | 1.34262 | ||||||||
\(679\) | 49.7841 | 1.91054 | ||||||||
\(680\) | 1.56542 | 0.0600311 | ||||||||
\(681\) | 71.3744 | 2.73507 | ||||||||
\(682\) | 71.1389 | 2.72405 | ||||||||
\(683\) | 11.0265 | 0.421917 | 0.210958 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210958 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(684\) | −98.4980 | −3.76616 | ||||||||
\(685\) | 15.9204 | 0.608287 | ||||||||
\(686\) | 23.8813 | 0.911793 | ||||||||
\(687\) | 29.1982 | 1.11398 | ||||||||
\(688\) | 44.4680 | 1.69533 | ||||||||
\(689\) | −1.08100 | −0.0411827 | ||||||||
\(690\) | −9.86931 | −0.375718 | ||||||||
\(691\) | −24.8647 | −0.945897 | −0.472948 | − | 0.881090i | \(-0.656810\pi\) | ||||
−0.472948 | + | 0.881090i | \(0.656810\pi\) | |||||||
\(692\) | −90.5220 | −3.44113 | ||||||||
\(693\) | 63.6218 | 2.41679 | ||||||||
\(694\) | −80.5533 | −3.05776 | ||||||||
\(695\) | −14.9467 | −0.566961 | ||||||||
\(696\) | −151.927 | −5.75877 | ||||||||
\(697\) | 1.03183 | 0.0390834 | ||||||||
\(698\) | 2.60291 | 0.0985215 | ||||||||
\(699\) | −57.8102 | −2.18658 | ||||||||
\(700\) | 60.4930 | 2.28642 | ||||||||
\(701\) | 15.2705 | 0.576758 | 0.288379 | − | 0.957516i | \(-0.406884\pi\) | ||||
0.288379 | + | 0.957516i | \(0.406884\pi\) | |||||||
\(702\) | −38.1438 | −1.43965 | ||||||||
\(703\) | 29.5723 | 1.11534 | ||||||||
\(704\) | −21.9157 | −0.825980 | ||||||||
\(705\) | −39.0400 | −1.47033 | ||||||||
\(706\) | −85.7131 | −3.22585 | ||||||||
\(707\) | 46.4104 | 1.74544 | ||||||||
\(708\) | 189.278 | 7.11349 | ||||||||
\(709\) | 0.0323175 | 0.00121371 | 0.000606856 | − | 1.00000i | \(-0.499807\pi\) | ||||
0.000606856 | 1.00000i | \(0.499807\pi\) | ||||||||
\(710\) | −43.1189 | −1.61822 | ||||||||
\(711\) | 77.7375 | 2.91538 | ||||||||
\(712\) | 18.6476 | 0.698849 | ||||||||
\(713\) | −8.19797 | −0.307016 | ||||||||
\(714\) | 4.63962 | 0.173633 | ||||||||
\(715\) | 13.8465 | 0.517828 | ||||||||
\(716\) | 72.8376 | 2.72207 | ||||||||
\(717\) | −80.7040 | −3.01395 | ||||||||
\(718\) | −27.4329 | −1.02379 | ||||||||
\(719\) | 14.5959 | 0.544334 | 0.272167 | − | 0.962250i | \(-0.412260\pi\) | ||||
0.272167 | + | 0.962250i | \(0.412260\pi\) | |||||||
\(720\) | −59.6830 | −2.22425 | ||||||||
\(721\) | 5.64207 | 0.210122 | ||||||||
\(722\) | −0.0349016 | −0.00129890 | ||||||||
\(723\) | 17.3241 | 0.644291 | ||||||||
\(724\) | −99.8800 | −3.71201 | ||||||||
\(725\) | −23.7551 | −0.882243 | ||||||||
\(726\) | −0.827661 | −0.0307174 | ||||||||
\(727\) | −9.96456 | −0.369565 | −0.184783 | − | 0.982779i | \(-0.559158\pi\) | ||||
−0.184783 | + | 0.982779i | \(0.559158\pi\) | |||||||
\(728\) | 88.7495 | 3.28928 | ||||||||
\(729\) | −43.9828 | −1.62899 | ||||||||
\(730\) | −5.90086 | −0.218401 | ||||||||
\(731\) | 0.763834 | 0.0282514 | ||||||||
\(732\) | 116.634 | 4.31091 | ||||||||
\(733\) | −38.6023 | −1.42581 | −0.712904 | − | 0.701262i | \(-0.752620\pi\) | ||||
−0.712904 | + | 0.701262i | \(0.752620\pi\) | |||||||
\(734\) | −62.9916 | −2.32506 | ||||||||
\(735\) | −35.1649 | −1.29708 | ||||||||
\(736\) | 9.63419 | 0.355121 | ||||||||
\(737\) | 51.9093 | 1.91211 | ||||||||
\(738\) | −79.9490 | −2.94296 | ||||||||
\(739\) | 34.4926 | 1.26883 | 0.634415 | − | 0.772993i | \(-0.281241\pi\) | ||||
0.634415 | + | 0.772993i | \(0.281241\pi\) | |||||||
\(740\) | 44.1634 | 1.62348 | ||||||||
\(741\) | −36.9240 | −1.35644 | ||||||||
\(742\) | −3.72701 | −0.136823 | ||||||||
\(743\) | −9.18695 | −0.337036 | −0.168518 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168518 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(744\) | −164.647 | −6.03624 | ||||||||
\(745\) | −14.5158 | −0.531816 | ||||||||
\(746\) | −28.7499 | −1.05261 | ||||||||
\(747\) | 19.3073 | 0.706418 | ||||||||
\(748\) | −2.52984 | −0.0925003 | ||||||||
\(749\) | −29.2824 | −1.06996 | ||||||||
\(750\) | −80.3391 | −2.93357 | ||||||||
\(751\) | 10.7256 | 0.391383 | 0.195692 | − | 0.980665i | \(-0.437305\pi\) | ||||
0.195692 | + | 0.980665i | \(0.437305\pi\) | |||||||
\(752\) | 95.2569 | 3.47366 | ||||||||
\(753\) | −1.66959 | −0.0608431 | ||||||||
\(754\) | −59.9681 | −2.18391 | ||||||||
\(755\) | 17.7776 | 0.646993 | ||||||||
\(756\) | −92.6890 | −3.37106 | ||||||||
\(757\) | 46.7619 | 1.69959 | 0.849794 | − | 0.527114i | \(-0.176726\pi\) | ||||
0.849794 | + | 0.527114i | \(0.176726\pi\) | |||||||
\(758\) | 63.4837 | 2.30583 | ||||||||
\(759\) | 9.26932 | 0.336455 | ||||||||
\(760\) | −42.9530 | −1.55807 | ||||||||
\(761\) | 48.5597 | 1.76029 | 0.880145 | − | 0.474706i | \(-0.157445\pi\) | ||||
0.880145 | + | 0.474706i | \(0.157445\pi\) | |||||||
\(762\) | 124.649 | 4.51557 | ||||||||
\(763\) | 51.3651 | 1.85954 | ||||||||
\(764\) | −67.5720 | −2.44467 | ||||||||
\(765\) | −1.02518 | −0.0370656 | ||||||||
\(766\) | −47.0191 | −1.69887 | ||||||||
\(767\) | 43.4193 | 1.56778 | ||||||||
\(768\) | −52.1692 | −1.88249 | ||||||||
\(769\) | 14.0526 | 0.506749 | 0.253374 | − | 0.967368i | \(-0.418460\pi\) | ||||
0.253374 | + | 0.967368i | \(0.418460\pi\) | |||||||
\(770\) | 47.7392 | 1.72040 | ||||||||
\(771\) | 23.9144 | 0.861258 | ||||||||
\(772\) | −59.7382 | −2.15002 | ||||||||
\(773\) | −5.34611 | −0.192286 | −0.0961431 | − | 0.995368i | \(-0.530651\pi\) | ||||
−0.0961431 | + | 0.995368i | \(0.530651\pi\) | |||||||
\(774\) | −59.1839 | −2.12732 | ||||||||
\(775\) | −25.7440 | −0.924751 | ||||||||
\(776\) | 89.1416 | 3.20000 | ||||||||
\(777\) | 76.0698 | 2.72899 | ||||||||
\(778\) | −55.7374 | −1.99828 | ||||||||
\(779\) | −28.3121 | −1.01439 | ||||||||
\(780\) | −55.1425 | −1.97442 | ||||||||
\(781\) | 40.4976 | 1.44912 | ||||||||
\(782\) | 0.413643 | 0.0147918 | ||||||||
\(783\) | 36.3982 | 1.30076 | ||||||||
\(784\) | 85.8018 | 3.06435 | ||||||||
\(785\) | −15.0499 | −0.537154 | ||||||||
\(786\) | 39.2151 | 1.39876 | ||||||||
\(787\) | 38.8629 | 1.38531 | 0.692657 | − | 0.721268i | \(-0.256440\pi\) | ||||
0.692657 | + | 0.721268i | \(0.256440\pi\) | |||||||
\(788\) | 86.6989 | 3.08852 | ||||||||
\(789\) | −74.1900 | −2.64123 | ||||||||
\(790\) | 58.3310 | 2.07532 | ||||||||
\(791\) | 19.4875 | 0.692897 | ||||||||
\(792\) | 113.919 | 4.04793 | ||||||||
\(793\) | 26.7552 | 0.950104 | ||||||||
\(794\) | 31.0000 | 1.10015 | ||||||||
\(795\) | 1.34580 | 0.0477304 | ||||||||
\(796\) | −130.200 | −4.61480 | ||||||||
\(797\) | −13.6058 | −0.481941 | −0.240970 | − | 0.970533i | \(-0.577466\pi\) | ||||
−0.240970 | + | 0.970533i | \(0.577466\pi\) | |||||||
\(798\) | −127.305 | −4.50655 | ||||||||
\(799\) | 1.63624 | 0.0578861 | ||||||||
\(800\) | 30.2541 | 1.06964 | ||||||||
\(801\) | −12.2122 | −0.431498 | ||||||||
\(802\) | 48.6035 | 1.71625 | ||||||||
\(803\) | 5.54213 | 0.195577 | ||||||||
\(804\) | −206.725 | −7.29064 | ||||||||
\(805\) | −5.50141 | −0.193899 | ||||||||
\(806\) | −64.9888 | −2.28913 | ||||||||
\(807\) | −30.0828 | −1.05897 | ||||||||
\(808\) | 83.1009 | 2.92348 | ||||||||
\(809\) | 31.0235 | 1.09073 | 0.545365 | − | 0.838199i | \(-0.316391\pi\) | ||||
0.545365 | + | 0.838199i | \(0.316391\pi\) | |||||||
\(810\) | −2.88755 | −0.101458 | ||||||||
\(811\) | −2.81553 | −0.0988666 | −0.0494333 | − | 0.998777i | \(-0.515742\pi\) | ||||
−0.0494333 | + | 0.998777i | \(0.515742\pi\) | |||||||
\(812\) | −145.721 | −5.11382 | ||||||||
\(813\) | −29.2533 | −1.02596 | ||||||||
\(814\) | −58.8513 | −2.06274 | ||||||||
\(815\) | 23.9823 | 0.840062 | ||||||||
\(816\) | 4.08778 | 0.143101 | ||||||||
\(817\) | −20.9586 | −0.733248 | ||||||||
\(818\) | −63.1029 | −2.20634 | ||||||||
\(819\) | −58.1216 | −2.03093 | ||||||||
\(820\) | −42.2814 | −1.47653 | ||||||||
\(821\) | −17.1795 | −0.599570 | −0.299785 | − | 0.954007i | \(-0.596915\pi\) | ||||
−0.299785 | + | 0.954007i | \(0.596915\pi\) | |||||||
\(822\) | 84.4881 | 2.94686 | ||||||||
\(823\) | 43.4035 | 1.51295 | 0.756476 | − | 0.654021i | \(-0.226919\pi\) | ||||
0.756476 | + | 0.654021i | \(0.226919\pi\) | |||||||
\(824\) | 10.1025 | 0.351937 | ||||||||
\(825\) | 29.1083 | 1.01342 | ||||||||
\(826\) | 149.699 | 5.20869 | ||||||||
\(827\) | −18.8788 | −0.656480 | −0.328240 | − | 0.944594i | \(-0.606455\pi\) | ||||
−0.328240 | + | 0.944594i | \(0.606455\pi\) | |||||||
\(828\) | −22.5890 | −0.785023 | ||||||||
\(829\) | 17.9676 | 0.624041 | 0.312020 | − | 0.950075i | \(-0.398994\pi\) | ||||
0.312020 | + | 0.950075i | \(0.398994\pi\) | |||||||
\(830\) | 14.4874 | 0.502865 | ||||||||
\(831\) | −22.8975 | −0.794304 | ||||||||
\(832\) | 20.0211 | 0.694106 | ||||||||
\(833\) | 1.47383 | 0.0510653 | ||||||||
\(834\) | −79.3208 | −2.74665 | ||||||||
\(835\) | 12.6875 | 0.439069 | ||||||||
\(836\) | 69.4156 | 2.40079 | ||||||||
\(837\) | 39.4456 | 1.36344 | ||||||||
\(838\) | 79.2624 | 2.73807 | ||||||||
\(839\) | −20.8917 | −0.721260 | −0.360630 | − | 0.932709i | \(-0.617438\pi\) | ||||
−0.360630 | + | 0.932709i | \(0.617438\pi\) | |||||||
\(840\) | −110.489 | −3.81225 | ||||||||
\(841\) | 28.2236 | 0.973228 | ||||||||
\(842\) | −3.69001 | −0.127166 | ||||||||
\(843\) | −17.9103 | −0.616864 | ||||||||
\(844\) | 110.465 | 3.80237 | ||||||||
\(845\) | 5.07886 | 0.174718 | ||||||||
\(846\) | −126.780 | −4.35880 | ||||||||
\(847\) | −0.461359 | −0.0158525 | ||||||||
\(848\) | −3.28372 | −0.112763 | ||||||||
\(849\) | 19.1973 | 0.658850 | ||||||||
\(850\) | 1.29896 | 0.0445539 | ||||||||
\(851\) | 6.78196 | 0.232483 | ||||||||
\(852\) | −161.279 | −5.52531 | ||||||||
\(853\) | −2.02790 | −0.0694341 | −0.0347170 | − | 0.999397i | \(-0.511053\pi\) | ||||
−0.0347170 | + | 0.999397i | \(0.511053\pi\) | |||||||
\(854\) | 92.2452 | 3.15657 | ||||||||
\(855\) | 28.1297 | 0.962016 | ||||||||
\(856\) | −52.4320 | −1.79209 | ||||||||
\(857\) | −6.01004 | −0.205299 | −0.102649 | − | 0.994718i | \(-0.532732\pi\) | ||||
−0.102649 | + | 0.994718i | \(0.532732\pi\) | |||||||
\(858\) | 73.4819 | 2.50863 | ||||||||
\(859\) | −14.1592 | −0.483107 | −0.241553 | − | 0.970388i | \(-0.577657\pi\) | ||||
−0.241553 | + | 0.970388i | \(0.577657\pi\) | |||||||
\(860\) | −31.2997 | −1.06731 | ||||||||
\(861\) | −72.8281 | −2.48197 | ||||||||
\(862\) | −18.4512 | −0.628451 | ||||||||
\(863\) | −18.1308 | −0.617181 | −0.308591 | − | 0.951195i | \(-0.599857\pi\) | ||||
−0.308591 | + | 0.951195i | \(0.599857\pi\) | |||||||
\(864\) | −46.3561 | −1.57707 | ||||||||
\(865\) | 25.8519 | 0.878990 | ||||||||
\(866\) | −1.00966 | −0.0343097 | ||||||||
\(867\) | −47.1964 | −1.60287 | ||||||||
\(868\) | −157.922 | −5.36022 | ||||||||
\(869\) | −54.7848 | −1.85845 | ||||||||
\(870\) | 74.6577 | 2.53113 | ||||||||
\(871\) | −47.4217 | −1.60682 | ||||||||
\(872\) | 91.9725 | 3.11458 | ||||||||
\(873\) | −58.3783 | −1.97581 | ||||||||
\(874\) | −11.3498 | −0.383913 | ||||||||
\(875\) | −44.7831 | −1.51394 | ||||||||
\(876\) | −22.0711 | −0.745714 | ||||||||
\(877\) | −8.74218 | −0.295203 | −0.147601 | − | 0.989047i | \(-0.547155\pi\) | ||||
−0.147601 | + | 0.989047i | \(0.547155\pi\) | |||||||
\(878\) | 98.0165 | 3.30789 | ||||||||
\(879\) | 12.3233 | 0.415654 | ||||||||
\(880\) | 42.0611 | 1.41788 | ||||||||
\(881\) | −28.9335 | −0.974793 | −0.487397 | − | 0.873181i | \(-0.662053\pi\) | ||||
−0.487397 | + | 0.873181i | \(0.662053\pi\) | |||||||
\(882\) | −114.196 | −3.84519 | ||||||||
\(883\) | 32.1090 | 1.08055 | 0.540277 | − | 0.841487i | \(-0.318319\pi\) | ||||
0.540277 | + | 0.841487i | \(0.318319\pi\) | |||||||
\(884\) | 2.31113 | 0.0777319 | ||||||||
\(885\) | −54.0552 | −1.81704 | ||||||||
\(886\) | 35.2826 | 1.18534 | ||||||||
\(887\) | −29.2805 | −0.983144 | −0.491572 | − | 0.870837i | \(-0.663577\pi\) | ||||
−0.491572 | + | 0.870837i | \(0.663577\pi\) | |||||||
\(888\) | 136.208 | 4.57084 | ||||||||
\(889\) | 69.4828 | 2.33038 | ||||||||
\(890\) | −9.16355 | −0.307163 | ||||||||
\(891\) | 2.71201 | 0.0908557 | ||||||||
\(892\) | −113.082 | −3.78626 | ||||||||
\(893\) | −44.8964 | −1.50240 | ||||||||
\(894\) | −77.0337 | −2.57639 | ||||||||
\(895\) | −20.8015 | −0.695316 | ||||||||
\(896\) | −8.70363 | −0.290768 | ||||||||
\(897\) | −8.46797 | −0.282737 | ||||||||
\(898\) | 9.95471 | 0.332193 | ||||||||
\(899\) | 62.0146 | 2.06830 | ||||||||
\(900\) | −70.9360 | −2.36453 | ||||||||
\(901\) | −0.0564050 | −0.00187912 | ||||||||
\(902\) | 56.3434 | 1.87603 | ||||||||
\(903\) | −53.9124 | −1.79409 | ||||||||
\(904\) | 34.8937 | 1.16055 | ||||||||
\(905\) | 28.5244 | 0.948183 | ||||||||
\(906\) | 94.3440 | 3.13437 | ||||||||
\(907\) | −33.4901 | −1.11202 | −0.556010 | − | 0.831176i | \(-0.687668\pi\) | ||||
−0.556010 | + | 0.831176i | \(0.687668\pi\) | |||||||
\(908\) | 122.581 | 4.06798 | ||||||||
\(909\) | −54.4223 | −1.80507 | ||||||||
\(910\) | −43.6120 | −1.44572 | ||||||||
\(911\) | −3.23737 | −0.107259 | −0.0536294 | − | 0.998561i | \(-0.517079\pi\) | ||||
−0.0536294 | + | 0.998561i | \(0.517079\pi\) | |||||||
\(912\) | −112.163 | −3.71410 | ||||||||
\(913\) | −13.6067 | −0.450315 | ||||||||
\(914\) | 44.1006 | 1.45872 | ||||||||
\(915\) | −33.3091 | −1.10116 | ||||||||
\(916\) | 50.1460 | 1.65687 | ||||||||
\(917\) | 21.8595 | 0.721865 | ||||||||
\(918\) | −1.99030 | −0.0656895 | ||||||||
\(919\) | −15.0331 | −0.495897 | −0.247949 | − | 0.968773i | \(-0.579756\pi\) | ||||
−0.247949 | + | 0.968773i | \(0.579756\pi\) | |||||||
\(920\) | −9.85063 | −0.324766 | ||||||||
\(921\) | −89.3331 | −2.94363 | ||||||||
\(922\) | 40.3146 | 1.32769 | ||||||||
\(923\) | −36.9965 | −1.21775 | ||||||||
\(924\) | 178.560 | 5.87419 | ||||||||
\(925\) | 21.2973 | 0.700252 | ||||||||
\(926\) | −55.7881 | −1.83331 | ||||||||
\(927\) | −6.61607 | −0.217300 | ||||||||
\(928\) | −72.8791 | −2.39237 | ||||||||
\(929\) | 24.2943 | 0.797069 | 0.398534 | − | 0.917153i | \(-0.369519\pi\) | ||||
0.398534 | + | 0.917153i | \(0.369519\pi\) | |||||||
\(930\) | 80.9083 | 2.65309 | ||||||||
\(931\) | −40.4400 | −1.32537 | ||||||||
\(932\) | −99.2850 | −3.25219 | ||||||||
\(933\) | −30.3504 | −0.993628 | ||||||||
\(934\) | 34.4613 | 1.12761 | ||||||||
\(935\) | 0.722490 | 0.0236280 | ||||||||
\(936\) | −104.070 | −3.40165 | ||||||||
\(937\) | −31.9099 | −1.04245 | −0.521225 | − | 0.853419i | \(-0.674525\pi\) | ||||
−0.521225 | + | 0.853419i | \(0.674525\pi\) | |||||||
\(938\) | −163.498 | −5.33841 | ||||||||
\(939\) | 27.2652 | 0.889765 | ||||||||
\(940\) | −67.0484 | −2.18688 | ||||||||
\(941\) | −47.3623 | −1.54397 | −0.771983 | − | 0.635643i | \(-0.780735\pi\) | ||||
−0.771983 | + | 0.635643i | \(0.780735\pi\) | |||||||
\(942\) | −79.8684 | −2.60225 | ||||||||
\(943\) | −6.49295 | −0.211440 | ||||||||
\(944\) | 131.894 | 4.29278 | ||||||||
\(945\) | 26.4707 | 0.861093 | ||||||||
\(946\) | 41.7093 | 1.35609 | ||||||||
\(947\) | −13.4565 | −0.437278 | −0.218639 | − | 0.975806i | \(-0.570162\pi\) | ||||
−0.218639 | + | 0.975806i | \(0.570162\pi\) | |||||||
\(948\) | 218.177 | 7.08604 | ||||||||
\(949\) | −5.06300 | −0.164352 | ||||||||
\(950\) | −35.6417 | −1.15637 | ||||||||
\(951\) | −52.9730 | −1.71777 | ||||||||
\(952\) | 4.63083 | 0.150086 | ||||||||
\(953\) | 45.5210 | 1.47457 | 0.737286 | − | 0.675581i | \(-0.236107\pi\) | ||||
0.737286 | + | 0.675581i | \(0.236107\pi\) | |||||||
\(954\) | 4.37041 | 0.141497 | ||||||||
\(955\) | 19.2977 | 0.624458 | ||||||||
\(956\) | −138.604 | −4.48276 | ||||||||
\(957\) | −70.1189 | −2.26662 | ||||||||
\(958\) | −42.6315 | −1.37736 | ||||||||
\(959\) | 47.0958 | 1.52080 | ||||||||
\(960\) | −24.9254 | −0.804464 | ||||||||
\(961\) | 36.2067 | 1.16796 | ||||||||
\(962\) | 53.7635 | 1.73341 | ||||||||
\(963\) | 34.3374 | 1.10651 | ||||||||
\(964\) | 29.7530 | 0.958279 | ||||||||
\(965\) | 17.0604 | 0.549195 | ||||||||
\(966\) | −29.1955 | −0.939349 | ||||||||
\(967\) | −51.4672 | −1.65507 | −0.827537 | − | 0.561411i | \(-0.810259\pi\) | ||||
−0.827537 | + | 0.561411i | \(0.810259\pi\) | |||||||
\(968\) | −0.826094 | −0.0265517 | ||||||||
\(969\) | −1.92665 | −0.0618928 | ||||||||
\(970\) | −43.8047 | −1.40648 | ||||||||
\(971\) | 43.6587 | 1.40107 | 0.700537 | − | 0.713617i | \(-0.252944\pi\) | ||||
0.700537 | + | 0.713617i | \(0.252944\pi\) | |||||||
\(972\) | −79.7288 | −2.55730 | ||||||||
\(973\) | −44.2154 | −1.41748 | ||||||||
\(974\) | −48.8255 | −1.56447 | ||||||||
\(975\) | −26.5919 | −0.851621 | ||||||||
\(976\) | 81.2736 | 2.60150 | ||||||||
\(977\) | 3.77898 | 0.120900 | 0.0604502 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604502 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(978\) | 127.272 | 4.06970 | ||||||||
\(979\) | 8.60646 | 0.275064 | ||||||||
\(980\) | −60.3933 | −1.92919 | ||||||||
\(981\) | −60.2323 | −1.92307 | ||||||||
\(982\) | −69.8159 | −2.22792 | ||||||||
\(983\) | −12.8855 | −0.410984 | −0.205492 | − | 0.978659i | \(-0.565879\pi\) | ||||
−0.205492 | + | 0.978659i | \(0.565879\pi\) | |||||||
\(984\) | −130.403 | −4.15711 | ||||||||
\(985\) | −24.7601 | −0.788921 | ||||||||
\(986\) | −3.12905 | −0.0996494 | ||||||||
\(987\) | −115.488 | −3.67603 | ||||||||
\(988\) | −63.4145 | −2.01748 | ||||||||
\(989\) | −4.80654 | −0.152839 | ||||||||
\(990\) | −55.9804 | −1.77918 | ||||||||
\(991\) | −6.94849 | −0.220726 | −0.110363 | − | 0.993891i | \(-0.535201\pi\) | ||||
−0.110363 | + | 0.993891i | \(0.535201\pi\) | |||||||
\(992\) | −78.9808 | −2.50764 | ||||||||
\(993\) | 22.4807 | 0.713402 | ||||||||
\(994\) | −127.555 | −4.04579 | ||||||||
\(995\) | 37.1833 | 1.17879 | ||||||||
\(996\) | 54.1875 | 1.71700 | ||||||||
\(997\) | −61.2404 | −1.93950 | −0.969751 | − | 0.244096i | \(-0.921509\pi\) | ||||
−0.969751 | + | 0.244096i | \(0.921509\pi\) | |||||||
\(998\) | −56.6122 | −1.79203 | ||||||||
\(999\) | −32.6323 | −1.03244 |
(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 | 8027.2.a.d.1.6 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8027.2.a.d.1.6 | ✓ | 149 | 1.1 | even | 1 | trivial |