Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64207 | −1.86823 | −0.934113 | − | 0.356978i | \(-0.883807\pi\) | ||||
−0.934113 | + | 0.356978i | \(0.883807\pi\) | |||||||
\(3\) | 1.02501 | 0.591787 | 0.295894 | − | 0.955221i | \(-0.404383\pi\) | ||||
0.295894 | + | 0.955221i | \(0.404383\pi\) | |||||||
\(4\) | 4.98054 | 2.49027 | ||||||||
\(5\) | 2.32673 | 1.04055 | 0.520273 | − | 0.854000i | \(-0.325830\pi\) | ||||
0.520273 | + | 0.854000i | \(0.325830\pi\) | |||||||
\(6\) | −2.70814 | −1.10559 | ||||||||
\(7\) | −0.493904 | −0.186678 | −0.0933391 | − | 0.995634i | \(-0.529754\pi\) | ||||
−0.0933391 | + | 0.995634i | \(0.529754\pi\) | |||||||
\(8\) | −7.87479 | −2.78416 | ||||||||
\(9\) | −1.94936 | −0.649788 | ||||||||
\(10\) | −6.14739 | −1.94397 | ||||||||
\(11\) | 2.96142 | 0.892902 | 0.446451 | − | 0.894808i | \(-0.352688\pi\) | ||||
0.446451 | + | 0.894808i | \(0.352688\pi\) | |||||||
\(12\) | 5.10508 | 1.47371 | ||||||||
\(13\) | 0.776601 | 0.215390 | 0.107695 | − | 0.994184i | \(-0.465653\pi\) | ||||
0.107695 | + | 0.994184i | \(0.465653\pi\) | |||||||
\(14\) | 1.30493 | 0.348757 | ||||||||
\(15\) | 2.38491 | 0.615781 | ||||||||
\(16\) | 10.8447 | 2.71117 | ||||||||
\(17\) | 6.61446 | 1.60424 | 0.802122 | − | 0.597161i | \(-0.203705\pi\) | ||||
0.802122 | + | 0.597161i | \(0.203705\pi\) | |||||||
\(18\) | 5.15036 | 1.21395 | ||||||||
\(19\) | −7.31111 | −1.67728 | −0.838642 | − | 0.544683i | \(-0.816650\pi\) | ||||
−0.838642 | + | 0.544683i | \(0.816650\pi\) | |||||||
\(20\) | 11.5884 | 2.59124 | ||||||||
\(21\) | −0.506254 | −0.110474 | ||||||||
\(22\) | −7.82428 | −1.66814 | ||||||||
\(23\) | −8.89506 | −1.85475 | −0.927374 | − | 0.374135i | \(-0.877940\pi\) | ||||
−0.927374 | + | 0.374135i | \(0.877940\pi\) | |||||||
\(24\) | −8.07170 | −1.64763 | ||||||||
\(25\) | 0.413674 | 0.0827348 | ||||||||
\(26\) | −2.05183 | −0.402398 | ||||||||
\(27\) | −5.07312 | −0.976323 | ||||||||
\(28\) | −2.45991 | −0.464879 | ||||||||
\(29\) | −2.08930 | −0.387974 | −0.193987 | − | 0.981004i | \(-0.562142\pi\) | ||||
−0.193987 | + | 0.981004i | \(0.562142\pi\) | |||||||
\(30\) | −6.30110 | −1.15042 | ||||||||
\(31\) | 0.878413 | 0.157768 | 0.0788838 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788838 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(32\) | −12.9028 | −2.28091 | ||||||||
\(33\) | 3.03547 | 0.528408 | ||||||||
\(34\) | −17.4759 | −2.99709 | ||||||||
\(35\) | −1.14918 | −0.194247 | ||||||||
\(36\) | −9.70888 | −1.61815 | ||||||||
\(37\) | 4.25838 | 0.700074 | 0.350037 | − | 0.936736i | \(-0.386169\pi\) | ||||
0.350037 | + | 0.936736i | \(0.386169\pi\) | |||||||
\(38\) | 19.3165 | 3.13354 | ||||||||
\(39\) | 0.796020 | 0.127465 | ||||||||
\(40\) | −18.3225 | −2.89704 | ||||||||
\(41\) | −11.1405 | −1.73985 | −0.869926 | − | 0.493183i | \(-0.835833\pi\) | ||||
−0.869926 | + | 0.493183i | \(0.835833\pi\) | |||||||
\(42\) | 1.33756 | 0.206390 | ||||||||
\(43\) | −7.88750 | −1.20283 | −0.601416 | − | 0.798936i | \(-0.705397\pi\) | ||||
−0.601416 | + | 0.798936i | \(0.705397\pi\) | |||||||
\(44\) | 14.7495 | 2.22357 | ||||||||
\(45\) | −4.53564 | −0.676134 | ||||||||
\(46\) | 23.5014 | 3.46509 | ||||||||
\(47\) | 10.9205 | 1.59292 | 0.796460 | − | 0.604691i | \(-0.206704\pi\) | ||||
0.796460 | + | 0.604691i | \(0.206704\pi\) | |||||||
\(48\) | 11.1158 | 1.60443 | ||||||||
\(49\) | −6.75606 | −0.965151 | ||||||||
\(50\) | −1.09296 | −0.154567 | ||||||||
\(51\) | 6.77986 | 0.949370 | ||||||||
\(52\) | 3.86789 | 0.536380 | ||||||||
\(53\) | −10.8022 | −1.48380 | −0.741898 | − | 0.670513i | \(-0.766074\pi\) | ||||
−0.741898 | + | 0.670513i | \(0.766074\pi\) | |||||||
\(54\) | 13.4036 | 1.82399 | ||||||||
\(55\) | 6.89043 | 0.929105 | ||||||||
\(56\) | 3.88939 | 0.519741 | ||||||||
\(57\) | −7.49393 | −0.992595 | ||||||||
\(58\) | 5.52008 | 0.724823 | ||||||||
\(59\) | 2.76488 | 0.359957 | 0.179979 | − | 0.983671i | \(-0.442397\pi\) | ||||
0.179979 | + | 0.983671i | \(0.442397\pi\) | |||||||
\(60\) | 11.8781 | 1.53346 | ||||||||
\(61\) | 8.06297 | 1.03236 | 0.516179 | − | 0.856481i | \(-0.327354\pi\) | ||||
0.516179 | + | 0.856481i | \(0.327354\pi\) | |||||||
\(62\) | −2.32083 | −0.294746 | ||||||||
\(63\) | 0.962798 | 0.121301 | ||||||||
\(64\) | 12.4008 | 1.55010 | ||||||||
\(65\) | 1.80694 | 0.224123 | ||||||||
\(66\) | −8.01993 | −0.987185 | ||||||||
\(67\) | −0.138871 | −0.0169657 | −0.00848287 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848287 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(68\) | 32.9436 | 3.99500 | ||||||||
\(69\) | −9.11748 | −1.09762 | ||||||||
\(70\) | 3.03622 | 0.362897 | ||||||||
\(71\) | −10.2433 | −1.21566 | −0.607829 | − | 0.794068i | \(-0.707960\pi\) | ||||
−0.607829 | + | 0.794068i | \(0.707960\pi\) | |||||||
\(72\) | 15.3508 | 1.80911 | ||||||||
\(73\) | −11.2894 | −1.32132 | −0.660662 | − | 0.750684i | \(-0.729724\pi\) | ||||
−0.660662 | + | 0.750684i | \(0.729724\pi\) | |||||||
\(74\) | −11.2509 | −1.30790 | ||||||||
\(75\) | 0.424018 | 0.0489614 | ||||||||
\(76\) | −36.4132 | −4.17689 | ||||||||
\(77\) | −1.46266 | −0.166685 | ||||||||
\(78\) | −2.10314 | −0.238134 | ||||||||
\(79\) | 12.0755 | 1.35860 | 0.679299 | − | 0.733862i | \(-0.262284\pi\) | ||||
0.679299 | + | 0.733862i | \(0.262284\pi\) | |||||||
\(80\) | 25.2326 | 2.82109 | ||||||||
\(81\) | 0.648113 | 0.0720126 | ||||||||
\(82\) | 29.4339 | 3.25044 | ||||||||
\(83\) | −5.70804 | −0.626539 | −0.313269 | − | 0.949664i | \(-0.601424\pi\) | ||||
−0.313269 | + | 0.949664i | \(0.601424\pi\) | |||||||
\(84\) | −2.52142 | −0.275109 | ||||||||
\(85\) | 15.3901 | 1.66929 | ||||||||
\(86\) | 20.8393 | 2.24716 | ||||||||
\(87\) | −2.14155 | −0.229598 | ||||||||
\(88\) | −23.3206 | −2.48598 | ||||||||
\(89\) | −11.7510 | −1.24560 | −0.622801 | − | 0.782381i | \(-0.714005\pi\) | ||||
−0.622801 | + | 0.782381i | \(0.714005\pi\) | |||||||
\(90\) | 11.9835 | 1.26317 | ||||||||
\(91\) | −0.383566 | −0.0402087 | ||||||||
\(92\) | −44.3022 | −4.61882 | ||||||||
\(93\) | 0.900378 | 0.0933649 | ||||||||
\(94\) | −28.8528 | −2.97593 | ||||||||
\(95\) | −17.0110 | −1.74529 | ||||||||
\(96\) | −13.2254 | −1.34982 | ||||||||
\(97\) | −6.74086 | −0.684431 | −0.342215 | − | 0.939622i | \(-0.611177\pi\) | ||||
−0.342215 | + | 0.939622i | \(0.611177\pi\) | |||||||
\(98\) | 17.8500 | 1.80312 | ||||||||
\(99\) | −5.77289 | −0.580197 | ||||||||
\(100\) | 2.06032 | 0.206032 | ||||||||
\(101\) | −1.13676 | −0.113112 | −0.0565561 | − | 0.998399i | \(-0.518012\pi\) | ||||
−0.0565561 | + | 0.998399i | \(0.518012\pi\) | |||||||
\(102\) | −17.9129 | −1.77364 | ||||||||
\(103\) | −6.15488 | −0.606458 | −0.303229 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303229 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(104\) | −6.11556 | −0.599680 | ||||||||
\(105\) | −1.17792 | −0.114953 | ||||||||
\(106\) | 28.5402 | 2.77207 | ||||||||
\(107\) | 11.1794 | 1.08075 | 0.540374 | − | 0.841425i | \(-0.318283\pi\) | ||||
0.540374 | + | 0.841425i | \(0.318283\pi\) | |||||||
\(108\) | −25.2669 | −2.43131 | ||||||||
\(109\) | 13.4404 | 1.28736 | 0.643679 | − | 0.765295i | \(-0.277407\pi\) | ||||
0.643679 | + | 0.765295i | \(0.277407\pi\) | |||||||
\(110\) | −18.2050 | −1.73578 | ||||||||
\(111\) | 4.36486 | 0.414294 | ||||||||
\(112\) | −5.35622 | −0.506115 | ||||||||
\(113\) | −13.2241 | −1.24402 | −0.622011 | − | 0.783009i | \(-0.713684\pi\) | ||||
−0.622011 | + | 0.783009i | \(0.713684\pi\) | |||||||
\(114\) | 19.7995 | 1.85439 | ||||||||
\(115\) | −20.6964 | −1.92995 | ||||||||
\(116\) | −10.4058 | −0.966158 | ||||||||
\(117\) | −1.51388 | −0.139958 | ||||||||
\(118\) | −7.30501 | −0.672481 | ||||||||
\(119\) | −3.26691 | −0.299477 | ||||||||
\(120\) | −18.7807 | −1.71443 | ||||||||
\(121\) | −2.22999 | −0.202726 | ||||||||
\(122\) | −21.3029 | −1.92868 | ||||||||
\(123\) | −11.4191 | −1.02962 | ||||||||
\(124\) | 4.37497 | 0.392884 | ||||||||
\(125\) | −10.6711 | −0.954456 | ||||||||
\(126\) | −2.54378 | −0.226618 | ||||||||
\(127\) | 0.798224 | 0.0708310 | 0.0354155 | − | 0.999373i | \(-0.488725\pi\) | ||||
0.0354155 | + | 0.999373i | \(0.488725\pi\) | |||||||
\(128\) | −6.95811 | −0.615016 | ||||||||
\(129\) | −8.08473 | −0.711820 | ||||||||
\(130\) | −4.77406 | −0.418713 | ||||||||
\(131\) | −15.7436 | −1.37552 | −0.687760 | − | 0.725938i | \(-0.741406\pi\) | ||||
−0.687760 | + | 0.725938i | \(0.741406\pi\) | |||||||
\(132\) | 15.1183 | 1.31588 | ||||||||
\(133\) | 3.61099 | 0.313112 | ||||||||
\(134\) | 0.366906 | 0.0316958 | ||||||||
\(135\) | −11.8038 | −1.01591 | ||||||||
\(136\) | −52.0875 | −4.46646 | ||||||||
\(137\) | −18.6132 | −1.59023 | −0.795115 | − | 0.606459i | \(-0.792590\pi\) | ||||
−0.795115 | + | 0.606459i | \(0.792590\pi\) | |||||||
\(138\) | 24.0890 | 2.05059 | ||||||||
\(139\) | 10.9726 | 0.930680 | 0.465340 | − | 0.885132i | \(-0.345932\pi\) | ||||
0.465340 | + | 0.885132i | \(0.345932\pi\) | |||||||
\(140\) | −5.72354 | −0.483727 | ||||||||
\(141\) | 11.1936 | 0.942669 | ||||||||
\(142\) | 27.0636 | 2.27113 | ||||||||
\(143\) | 2.29984 | 0.192322 | ||||||||
\(144\) | −21.1402 | −1.76168 | ||||||||
\(145\) | −4.86124 | −0.403704 | ||||||||
\(146\) | 29.8274 | 2.46853 | ||||||||
\(147\) | −6.92500 | −0.571164 | ||||||||
\(148\) | 21.2090 | 1.74337 | ||||||||
\(149\) | 1.99896 | 0.163761 | 0.0818807 | − | 0.996642i | \(-0.473907\pi\) | ||||
0.0818807 | + | 0.996642i | \(0.473907\pi\) | |||||||
\(150\) | −1.12029 | −0.0914710 | ||||||||
\(151\) | −4.34393 | −0.353504 | −0.176752 | − | 0.984255i | \(-0.556559\pi\) | ||||
−0.176752 | + | 0.984255i | \(0.556559\pi\) | |||||||
\(152\) | 57.5734 | 4.66982 | ||||||||
\(153\) | −12.8940 | −1.04242 | ||||||||
\(154\) | 3.86444 | 0.311406 | ||||||||
\(155\) | 2.04383 | 0.164164 | ||||||||
\(156\) | 3.96461 | 0.317422 | ||||||||
\(157\) | 8.39098 | 0.669673 | 0.334837 | − | 0.942276i | \(-0.391319\pi\) | ||||
0.334837 | + | 0.942276i | \(0.391319\pi\) | |||||||
\(158\) | −31.9043 | −2.53817 | ||||||||
\(159\) | −11.0723 | −0.878091 | ||||||||
\(160\) | −30.0213 | −2.37339 | ||||||||
\(161\) | 4.39330 | 0.346241 | ||||||||
\(162\) | −1.71236 | −0.134536 | ||||||||
\(163\) | −4.93579 | −0.386601 | −0.193300 | − | 0.981140i | \(-0.561919\pi\) | ||||
−0.193300 | + | 0.981140i | \(0.561919\pi\) | |||||||
\(164\) | −55.4856 | −4.33270 | ||||||||
\(165\) | 7.06272 | 0.549832 | ||||||||
\(166\) | 15.0810 | 1.17052 | ||||||||
\(167\) | 7.80826 | 0.604221 | 0.302110 | − | 0.953273i | \(-0.402309\pi\) | ||||
0.302110 | + | 0.953273i | \(0.402309\pi\) | |||||||
\(168\) | 3.98664 | 0.307576 | ||||||||
\(169\) | −12.3969 | −0.953607 | ||||||||
\(170\) | −40.6617 | −3.11861 | ||||||||
\(171\) | 14.2520 | 1.08988 | ||||||||
\(172\) | −39.2840 | −2.99537 | ||||||||
\(173\) | 15.1926 | 1.15507 | 0.577535 | − | 0.816366i | \(-0.304015\pi\) | ||||
0.577535 | + | 0.816366i | \(0.304015\pi\) | |||||||
\(174\) | 5.65811 | 0.428941 | ||||||||
\(175\) | −0.204315 | −0.0154448 | ||||||||
\(176\) | 32.1156 | 2.42081 | ||||||||
\(177\) | 2.83402 | 0.213018 | ||||||||
\(178\) | 31.0469 | 2.32706 | ||||||||
\(179\) | 11.6776 | 0.872828 | 0.436414 | − | 0.899746i | \(-0.356248\pi\) | ||||
0.436414 | + | 0.899746i | \(0.356248\pi\) | |||||||
\(180\) | −22.5899 | −1.68375 | ||||||||
\(181\) | 22.1145 | 1.64376 | 0.821878 | − | 0.569663i | \(-0.192926\pi\) | ||||
0.821878 | + | 0.569663i | \(0.192926\pi\) | |||||||
\(182\) | 1.01341 | 0.0751188 | ||||||||
\(183\) | 8.26459 | 0.610936 | ||||||||
\(184\) | 70.0467 | 5.16391 | ||||||||
\(185\) | 9.90811 | 0.728458 | ||||||||
\(186\) | −2.37886 | −0.174427 | ||||||||
\(187\) | 19.5882 | 1.43243 | ||||||||
\(188\) | 54.3900 | 3.96680 | ||||||||
\(189\) | 2.50564 | 0.182258 | ||||||||
\(190\) | 44.9442 | 3.26060 | ||||||||
\(191\) | 3.56942 | 0.258274 | 0.129137 | − | 0.991627i | \(-0.458779\pi\) | ||||
0.129137 | + | 0.991627i | \(0.458779\pi\) | |||||||
\(192\) | 12.7109 | 0.917327 | ||||||||
\(193\) | 14.1884 | 1.02131 | 0.510653 | − | 0.859787i | \(-0.329404\pi\) | ||||
0.510653 | + | 0.859787i | \(0.329404\pi\) | |||||||
\(194\) | 17.8098 | 1.27867 | ||||||||
\(195\) | 1.85212 | 0.132633 | ||||||||
\(196\) | −33.6488 | −2.40349 | ||||||||
\(197\) | −18.4248 | −1.31271 | −0.656356 | − | 0.754452i | \(-0.727903\pi\) | ||||
−0.656356 | + | 0.754452i | \(0.727903\pi\) | |||||||
\(198\) | 15.2524 | 1.08394 | ||||||||
\(199\) | 15.9680 | 1.13194 | 0.565971 | − | 0.824425i | \(-0.308502\pi\) | ||||
0.565971 | + | 0.824425i | \(0.308502\pi\) | |||||||
\(200\) | −3.25760 | −0.230347 | ||||||||
\(201\) | −0.142343 | −0.0100401 | ||||||||
\(202\) | 3.00341 | 0.211319 | ||||||||
\(203\) | 1.03191 | 0.0724262 | ||||||||
\(204\) | 33.7673 | 2.36419 | ||||||||
\(205\) | −25.9209 | −1.81039 | ||||||||
\(206\) | 16.2616 | 1.13300 | ||||||||
\(207\) | 17.3397 | 1.20519 | ||||||||
\(208\) | 8.42198 | 0.583959 | ||||||||
\(209\) | −21.6513 | −1.49765 | ||||||||
\(210\) | 3.11214 | 0.214758 | ||||||||
\(211\) | 8.51245 | 0.586021 | 0.293010 | − | 0.956109i | \(-0.405343\pi\) | ||||
0.293010 | + | 0.956109i | \(0.405343\pi\) | |||||||
\(212\) | −53.8007 | −3.69505 | ||||||||
\(213\) | −10.4995 | −0.719411 | ||||||||
\(214\) | −29.5366 | −2.01908 | ||||||||
\(215\) | −18.3521 | −1.25160 | ||||||||
\(216\) | 39.9498 | 2.71824 | ||||||||
\(217\) | −0.433852 | −0.0294518 | ||||||||
\(218\) | −35.5105 | −2.40508 | ||||||||
\(219\) | −11.5717 | −0.781942 | ||||||||
\(220\) | 34.3180 | 2.31372 | ||||||||
\(221\) | 5.13680 | 0.345538 | ||||||||
\(222\) | −11.5323 | −0.773996 | ||||||||
\(223\) | 13.2510 | 0.887353 | 0.443676 | − | 0.896187i | \(-0.353674\pi\) | ||||
0.443676 | + | 0.896187i | \(0.353674\pi\) | |||||||
\(224\) | 6.37274 | 0.425797 | ||||||||
\(225\) | −0.806402 | −0.0537601 | ||||||||
\(226\) | 34.9391 | 2.32411 | ||||||||
\(227\) | −6.83741 | −0.453815 | −0.226908 | − | 0.973916i | \(-0.572862\pi\) | ||||
−0.226908 | + | 0.973916i | \(0.572862\pi\) | |||||||
\(228\) | −37.3238 | −2.47183 | ||||||||
\(229\) | −19.9059 | −1.31542 | −0.657709 | − | 0.753273i | \(-0.728474\pi\) | ||||
−0.657709 | + | 0.753273i | \(0.728474\pi\) | |||||||
\(230\) | 54.6814 | 3.60558 | ||||||||
\(231\) | −1.49923 | −0.0986422 | ||||||||
\(232\) | 16.4528 | 1.08018 | ||||||||
\(233\) | −13.6658 | −0.895276 | −0.447638 | − | 0.894215i | \(-0.647735\pi\) | ||||
−0.447638 | + | 0.894215i | \(0.647735\pi\) | |||||||
\(234\) | 3.99977 | 0.261473 | ||||||||
\(235\) | 25.4091 | 1.65751 | ||||||||
\(236\) | 13.7706 | 0.896389 | ||||||||
\(237\) | 12.3774 | 0.804001 | ||||||||
\(238\) | 8.63140 | 0.559491 | ||||||||
\(239\) | 15.2687 | 0.987648 | 0.493824 | − | 0.869562i | \(-0.335599\pi\) | ||||
0.493824 | + | 0.869562i | \(0.335599\pi\) | |||||||
\(240\) | 25.8636 | 1.66949 | ||||||||
\(241\) | 4.11200 | 0.264877 | 0.132439 | − | 0.991191i | \(-0.457719\pi\) | ||||
0.132439 | + | 0.991191i | \(0.457719\pi\) | |||||||
\(242\) | 5.89178 | 0.378738 | ||||||||
\(243\) | 15.8837 | 1.01894 | ||||||||
\(244\) | 40.1579 | 2.57085 | ||||||||
\(245\) | −15.7195 | −1.00428 | ||||||||
\(246\) | 30.1700 | 1.92357 | ||||||||
\(247\) | −5.67781 | −0.361271 | ||||||||
\(248\) | −6.91732 | −0.439250 | ||||||||
\(249\) | −5.85077 | −0.370777 | ||||||||
\(250\) | 28.1939 | 1.78314 | ||||||||
\(251\) | 19.8514 | 1.25301 | 0.626504 | − | 0.779418i | \(-0.284485\pi\) | ||||
0.626504 | + | 0.779418i | \(0.284485\pi\) | |||||||
\(252\) | 4.79525 | 0.302073 | ||||||||
\(253\) | −26.3420 | −1.65611 | ||||||||
\(254\) | −2.10896 | −0.132328 | ||||||||
\(255\) | 15.7749 | 0.987863 | ||||||||
\(256\) | −6.41772 | −0.401107 | ||||||||
\(257\) | −23.0628 | −1.43862 | −0.719309 | − | 0.694690i | \(-0.755542\pi\) | ||||
−0.719309 | + | 0.694690i | \(0.755542\pi\) | |||||||
\(258\) | 21.3604 | 1.32984 | ||||||||
\(259\) | −2.10323 | −0.130688 | ||||||||
\(260\) | 8.99953 | 0.558127 | ||||||||
\(261\) | 4.07281 | 0.252101 | ||||||||
\(262\) | 41.5956 | 2.56978 | ||||||||
\(263\) | −5.93944 | −0.366242 | −0.183121 | − | 0.983090i | \(-0.558620\pi\) | ||||
−0.183121 | + | 0.983090i | \(0.558620\pi\) | |||||||
\(264\) | −23.9037 | −1.47117 | ||||||||
\(265\) | −25.1338 | −1.54396 | ||||||||
\(266\) | −9.54048 | −0.584964 | ||||||||
\(267\) | −12.0448 | −0.737131 | ||||||||
\(268\) | −0.691650 | −0.0422493 | ||||||||
\(269\) | −18.0932 | −1.10316 | −0.551582 | − | 0.834120i | \(-0.685976\pi\) | ||||
−0.551582 | + | 0.834120i | \(0.685976\pi\) | |||||||
\(270\) | 31.1865 | 1.89795 | ||||||||
\(271\) | 18.0167 | 1.09444 | 0.547220 | − | 0.836989i | \(-0.315686\pi\) | ||||
0.547220 | + | 0.836989i | \(0.315686\pi\) | |||||||
\(272\) | 71.7316 | 4.34937 | ||||||||
\(273\) | −0.393157 | −0.0237950 | ||||||||
\(274\) | 49.1773 | 2.97091 | ||||||||
\(275\) | 1.22506 | 0.0738741 | ||||||||
\(276\) | −45.4100 | −2.73336 | ||||||||
\(277\) | −29.7144 | −1.78537 | −0.892683 | − | 0.450686i | \(-0.851179\pi\) | ||||
−0.892683 | + | 0.450686i | \(0.851179\pi\) | |||||||
\(278\) | −28.9903 | −1.73872 | ||||||||
\(279\) | −1.71235 | −0.102516 | ||||||||
\(280\) | 9.04955 | 0.540814 | ||||||||
\(281\) | 1.14465 | 0.0682843 | 0.0341421 | − | 0.999417i | \(-0.489130\pi\) | ||||
0.0341421 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(282\) | −29.5742 | −1.76112 | ||||||||
\(283\) | 19.4627 | 1.15694 | 0.578470 | − | 0.815704i | \(-0.303650\pi\) | ||||
0.578470 | + | 0.815704i | \(0.303650\pi\) | |||||||
\(284\) | −51.0172 | −3.02732 | ||||||||
\(285\) | −17.4363 | −1.03284 | ||||||||
\(286\) | −6.07634 | −0.359302 | ||||||||
\(287\) | 5.50233 | 0.324792 | ||||||||
\(288\) | 25.1523 | 1.48211 | ||||||||
\(289\) | 26.7511 | 1.57360 | ||||||||
\(290\) | 12.8437 | 0.754211 | ||||||||
\(291\) | −6.90942 | −0.405037 | ||||||||
\(292\) | −56.2272 | −3.29045 | ||||||||
\(293\) | −2.31783 | −0.135409 | −0.0677046 | − | 0.997705i | \(-0.521568\pi\) | ||||
−0.0677046 | + | 0.997705i | \(0.521568\pi\) | |||||||
\(294\) | 18.2963 | 1.06706 | ||||||||
\(295\) | 6.43314 | 0.374552 | ||||||||
\(296\) | −33.5338 | −1.94911 | ||||||||
\(297\) | −15.0237 | −0.871761 | ||||||||
\(298\) | −5.28140 | −0.305943 | ||||||||
\(299\) | −6.90791 | −0.399495 | ||||||||
\(300\) | 2.11184 | 0.121927 | ||||||||
\(301\) | 3.89566 | 0.224542 | ||||||||
\(302\) | 11.4770 | 0.660425 | ||||||||
\(303\) | −1.16519 | −0.0669384 | ||||||||
\(304\) | −79.2865 | −4.54740 | ||||||||
\(305\) | 18.7604 | 1.07422 | ||||||||
\(306\) | 34.0669 | 1.94747 | ||||||||
\(307\) | −13.0843 | −0.746759 | −0.373380 | − | 0.927679i | \(-0.621801\pi\) | ||||
−0.373380 | + | 0.927679i | \(0.621801\pi\) | |||||||
\(308\) | −7.28482 | −0.415091 | ||||||||
\(309\) | −6.30878 | −0.358894 | ||||||||
\(310\) | −5.39994 | −0.306696 | ||||||||
\(311\) | 15.8629 | 0.899504 | 0.449752 | − | 0.893153i | \(-0.351512\pi\) | ||||
0.449752 | + | 0.893153i | \(0.351512\pi\) | |||||||
\(312\) | −6.26849 | −0.354883 | ||||||||
\(313\) | −6.77606 | −0.383006 | −0.191503 | − | 0.981492i | \(-0.561336\pi\) | ||||
−0.191503 | + | 0.981492i | \(0.561336\pi\) | |||||||
\(314\) | −22.1696 | −1.25110 | ||||||||
\(315\) | 2.24017 | 0.126219 | ||||||||
\(316\) | 60.1424 | 3.38327 | ||||||||
\(317\) | 17.5246 | 0.984278 | 0.492139 | − | 0.870517i | \(-0.336215\pi\) | ||||
0.492139 | + | 0.870517i | \(0.336215\pi\) | |||||||
\(318\) | 29.2538 | 1.64047 | ||||||||
\(319\) | −6.18730 | −0.346422 | ||||||||
\(320\) | 28.8533 | 1.61295 | ||||||||
\(321\) | 11.4589 | 0.639573 | ||||||||
\(322\) | −11.6074 | −0.646856 | ||||||||
\(323\) | −48.3591 | −2.69077 | ||||||||
\(324\) | 3.22795 | 0.179331 | ||||||||
\(325\) | 0.321260 | 0.0178203 | ||||||||
\(326\) | 13.0407 | 0.722257 | ||||||||
\(327\) | 13.7765 | 0.761842 | ||||||||
\(328\) | 87.7289 | 4.84402 | ||||||||
\(329\) | −5.39368 | −0.297363 | ||||||||
\(330\) | −18.6602 | −1.02721 | ||||||||
\(331\) | −12.0475 | −0.662188 | −0.331094 | − | 0.943598i | \(-0.607418\pi\) | ||||
−0.331094 | + | 0.943598i | \(0.607418\pi\) | |||||||
\(332\) | −28.4291 | −1.56025 | ||||||||
\(333\) | −8.30114 | −0.454899 | ||||||||
\(334\) | −20.6300 | −1.12882 | ||||||||
\(335\) | −0.323114 | −0.0176536 | ||||||||
\(336\) | −5.49016 | −0.299513 | ||||||||
\(337\) | 18.8516 | 1.02691 | 0.513457 | − | 0.858115i | \(-0.328365\pi\) | ||||
0.513457 | + | 0.858115i | \(0.328365\pi\) | |||||||
\(338\) | 32.7535 | 1.78155 | ||||||||
\(339\) | −13.5548 | −0.736196 | ||||||||
\(340\) | 76.6508 | 4.15697 | ||||||||
\(341\) | 2.60135 | 0.140871 | ||||||||
\(342\) | −37.6548 | −2.03614 | ||||||||
\(343\) | 6.79417 | 0.366851 | ||||||||
\(344\) | 62.1123 | 3.34887 | ||||||||
\(345\) | −21.2139 | −1.14212 | ||||||||
\(346\) | −40.1399 | −2.15793 | ||||||||
\(347\) | −26.1619 | −1.40445 | −0.702223 | − | 0.711957i | \(-0.747809\pi\) | ||||
−0.702223 | + | 0.711957i | \(0.747809\pi\) | |||||||
\(348\) | −10.6660 | −0.571760 | ||||||||
\(349\) | 12.5396 | 0.671230 | 0.335615 | − | 0.941999i | \(-0.391056\pi\) | ||||
0.335615 | + | 0.941999i | \(0.391056\pi\) | |||||||
\(350\) | 0.539815 | 0.0288543 | ||||||||
\(351\) | −3.93979 | −0.210291 | ||||||||
\(352\) | −38.2106 | −2.03663 | ||||||||
\(353\) | 11.1603 | 0.594001 | 0.297001 | − | 0.954877i | \(-0.404014\pi\) | ||||
0.297001 | + | 0.954877i | \(0.404014\pi\) | |||||||
\(354\) | −7.48768 | −0.397966 | ||||||||
\(355\) | −23.8335 | −1.26495 | ||||||||
\(356\) | −58.5262 | −3.10188 | ||||||||
\(357\) | −3.34860 | −0.177227 | ||||||||
\(358\) | −30.8531 | −1.63064 | ||||||||
\(359\) | 32.8588 | 1.73422 | 0.867110 | − | 0.498117i | \(-0.165975\pi\) | ||||
0.867110 | + | 0.498117i | \(0.165975\pi\) | |||||||
\(360\) | 35.7172 | 1.88246 | ||||||||
\(361\) | 34.4523 | 1.81328 | ||||||||
\(362\) | −58.4280 | −3.07091 | ||||||||
\(363\) | −2.28575 | −0.119971 | ||||||||
\(364\) | −1.91036 | −0.100130 | ||||||||
\(365\) | −26.2674 | −1.37490 | ||||||||
\(366\) | −21.8356 | −1.14137 | ||||||||
\(367\) | −13.3290 | −0.695768 | −0.347884 | − | 0.937538i | \(-0.613100\pi\) | ||||
−0.347884 | + | 0.937538i | \(0.613100\pi\) | |||||||
\(368\) | −96.4640 | −5.02853 | ||||||||
\(369\) | 21.7169 | 1.13053 | ||||||||
\(370\) | −26.1779 | −1.36092 | ||||||||
\(371\) | 5.33525 | 0.276992 | ||||||||
\(372\) | 4.48437 | 0.232504 | ||||||||
\(373\) | 8.88503 | 0.460050 | 0.230025 | − | 0.973185i | \(-0.426119\pi\) | ||||
0.230025 | + | 0.973185i | \(0.426119\pi\) | |||||||
\(374\) | −51.7534 | −2.67611 | ||||||||
\(375\) | −10.9380 | −0.564835 | ||||||||
\(376\) | −85.9967 | −4.43494 | ||||||||
\(377\) | −1.62255 | −0.0835658 | ||||||||
\(378\) | −6.62007 | −0.340499 | ||||||||
\(379\) | 22.6120 | 1.16150 | 0.580750 | − | 0.814082i | \(-0.302759\pi\) | ||||
0.580750 | + | 0.814082i | \(0.302759\pi\) | |||||||
\(380\) | −84.7238 | −4.34624 | ||||||||
\(381\) | 0.818184 | 0.0419168 | ||||||||
\(382\) | −9.43065 | −0.482514 | ||||||||
\(383\) | −0.491019 | −0.0250899 | −0.0125450 | − | 0.999921i | \(-0.503993\pi\) | ||||
−0.0125450 | + | 0.999921i | \(0.503993\pi\) | |||||||
\(384\) | −7.13210 | −0.363959 | ||||||||
\(385\) | −3.40321 | −0.173444 | ||||||||
\(386\) | −37.4868 | −1.90803 | ||||||||
\(387\) | 15.3756 | 0.781586 | ||||||||
\(388\) | −33.5731 | −1.70442 | ||||||||
\(389\) | −33.0524 | −1.67583 | −0.837913 | − | 0.545804i | \(-0.816224\pi\) | ||||
−0.837913 | + | 0.545804i | \(0.816224\pi\) | |||||||
\(390\) | −4.89344 | −0.247789 | ||||||||
\(391\) | −58.8361 | −2.97547 | ||||||||
\(392\) | 53.2025 | 2.68713 | ||||||||
\(393\) | −16.1372 | −0.814016 | ||||||||
\(394\) | 48.6796 | 2.45244 | ||||||||
\(395\) | 28.0964 | 1.41368 | ||||||||
\(396\) | −28.7521 | −1.44485 | ||||||||
\(397\) | −24.9472 | −1.25206 | −0.626031 | − | 0.779798i | \(-0.715322\pi\) | ||||
−0.626031 | + | 0.779798i | \(0.715322\pi\) | |||||||
\(398\) | −42.1886 | −2.11472 | ||||||||
\(399\) | 3.70128 | 0.185296 | ||||||||
\(400\) | 4.48616 | 0.224308 | ||||||||
\(401\) | 4.24375 | 0.211923 | 0.105961 | − | 0.994370i | \(-0.466208\pi\) | ||||
0.105961 | + | 0.994370i | \(0.466208\pi\) | |||||||
\(402\) | 0.376081 | 0.0187572 | ||||||||
\(403\) | 0.682176 | 0.0339816 | ||||||||
\(404\) | −5.66169 | −0.281680 | ||||||||
\(405\) | 1.50798 | 0.0749324 | ||||||||
\(406\) | −2.72639 | −0.135308 | ||||||||
\(407\) | 12.6109 | 0.625097 | ||||||||
\(408\) | −53.3899 | −2.64320 | ||||||||
\(409\) | −9.07084 | −0.448524 | −0.224262 | − | 0.974529i | \(-0.571997\pi\) | ||||
−0.224262 | + | 0.974529i | \(0.571997\pi\) | |||||||
\(410\) | 68.4849 | 3.38223 | ||||||||
\(411\) | −19.0786 | −0.941078 | ||||||||
\(412\) | −30.6546 | −1.51024 | ||||||||
\(413\) | −1.36559 | −0.0671961 | ||||||||
\(414\) | −45.8127 | −2.25157 | ||||||||
\(415\) | −13.2811 | −0.651942 | ||||||||
\(416\) | −10.0203 | −0.491287 | ||||||||
\(417\) | 11.2469 | 0.550765 | ||||||||
\(418\) | 57.2042 | 2.79795 | ||||||||
\(419\) | 22.3057 | 1.08970 | 0.544852 | − | 0.838532i | \(-0.316586\pi\) | ||||
0.544852 | + | 0.838532i | \(0.316586\pi\) | |||||||
\(420\) | −5.86666 | −0.286264 | ||||||||
\(421\) | −19.7844 | −0.964234 | −0.482117 | − | 0.876107i | \(-0.660132\pi\) | ||||
−0.482117 | + | 0.876107i | \(0.660132\pi\) | |||||||
\(422\) | −22.4905 | −1.09482 | ||||||||
\(423\) | −21.2880 | −1.03506 | ||||||||
\(424\) | 85.0650 | 4.13112 | ||||||||
\(425\) | 2.73623 | 0.132727 | ||||||||
\(426\) | 27.7403 | 1.34402 | ||||||||
\(427\) | −3.98233 | −0.192719 | ||||||||
\(428\) | 55.6792 | 2.69135 | ||||||||
\(429\) | 2.35735 | 0.113814 | ||||||||
\(430\) | 48.4875 | 2.33827 | ||||||||
\(431\) | −13.1267 | −0.632289 | −0.316145 | − | 0.948711i | \(-0.602388\pi\) | ||||
−0.316145 | + | 0.948711i | \(0.602388\pi\) | |||||||
\(432\) | −55.0163 | −2.64697 | ||||||||
\(433\) | 23.5459 | 1.13154 | 0.565772 | − | 0.824562i | \(-0.308578\pi\) | ||||
0.565772 | + | 0.824562i | \(0.308578\pi\) | |||||||
\(434\) | 1.14627 | 0.0550226 | ||||||||
\(435\) | −4.98280 | −0.238907 | ||||||||
\(436\) | 66.9405 | 3.20587 | ||||||||
\(437\) | 65.0328 | 3.11094 | ||||||||
\(438\) | 30.5732 | 1.46084 | ||||||||
\(439\) | −5.08283 | −0.242590 | −0.121295 | − | 0.992616i | \(-0.538705\pi\) | ||||
−0.121295 | + | 0.992616i | \(0.538705\pi\) | |||||||
\(440\) | −54.2606 | −2.58677 | ||||||||
\(441\) | 13.1700 | 0.627144 | ||||||||
\(442\) | −13.5718 | −0.645544 | ||||||||
\(443\) | −27.4957 | −1.30636 | −0.653180 | − | 0.757202i | \(-0.726566\pi\) | ||||
−0.653180 | + | 0.757202i | \(0.726566\pi\) | |||||||
\(444\) | 21.7394 | 1.03170 | ||||||||
\(445\) | −27.3414 | −1.29610 | ||||||||
\(446\) | −35.0101 | −1.65778 | ||||||||
\(447\) | 2.04895 | 0.0969119 | ||||||||
\(448\) | −6.12479 | −0.289369 | ||||||||
\(449\) | −20.1737 | −0.952054 | −0.476027 | − | 0.879431i | \(-0.657924\pi\) | ||||
−0.476027 | + | 0.879431i | \(0.657924\pi\) | |||||||
\(450\) | 2.13057 | 0.100436 | ||||||||
\(451\) | −32.9917 | −1.55352 | ||||||||
\(452\) | −65.8632 | −3.09795 | ||||||||
\(453\) | −4.45255 | −0.209199 | ||||||||
\(454\) | 18.0649 | 0.847829 | ||||||||
\(455\) | −0.892455 | −0.0418389 | ||||||||
\(456\) | 59.0131 | 2.76354 | ||||||||
\(457\) | 36.5943 | 1.71181 | 0.855905 | − | 0.517133i | \(-0.173001\pi\) | ||||
0.855905 | + | 0.517133i | \(0.173001\pi\) | |||||||
\(458\) | 52.5927 | 2.45750 | ||||||||
\(459\) | −33.5560 | −1.56626 | ||||||||
\(460\) | −103.079 | −4.80609 | ||||||||
\(461\) | −19.9762 | −0.930385 | −0.465193 | − | 0.885209i | \(-0.654015\pi\) | ||||
−0.465193 | + | 0.885209i | \(0.654015\pi\) | |||||||
\(462\) | 3.96107 | 0.184286 | ||||||||
\(463\) | −26.6366 | −1.23791 | −0.618955 | − | 0.785427i | \(-0.712444\pi\) | ||||
−0.618955 | + | 0.785427i | \(0.712444\pi\) | |||||||
\(464\) | −22.6578 | −1.05186 | ||||||||
\(465\) | 2.09494 | 0.0971504 | ||||||||
\(466\) | 36.1060 | 1.67258 | ||||||||
\(467\) | −21.8308 | −1.01021 | −0.505103 | − | 0.863059i | \(-0.668546\pi\) | ||||
−0.505103 | + | 0.863059i | \(0.668546\pi\) | |||||||
\(468\) | −7.53992 | −0.348533 | ||||||||
\(469\) | 0.0685887 | 0.00316713 | ||||||||
\(470\) | −67.1326 | −3.09659 | ||||||||
\(471\) | 8.60080 | 0.396304 | ||||||||
\(472\) | −21.7729 | −1.00218 | ||||||||
\(473\) | −23.3582 | −1.07401 | ||||||||
\(474\) | −32.7021 | −1.50205 | ||||||||
\(475\) | −3.02442 | −0.138770 | ||||||||
\(476\) | −16.2710 | −0.745778 | ||||||||
\(477\) | 21.0574 | 0.964153 | ||||||||
\(478\) | −40.3409 | −1.84515 | ||||||||
\(479\) | 9.28019 | 0.424023 | 0.212011 | − | 0.977267i | \(-0.431999\pi\) | ||||
0.212011 | + | 0.977267i | \(0.431999\pi\) | |||||||
\(480\) | −30.7720 | −1.40454 | ||||||||
\(481\) | 3.30706 | 0.150789 | ||||||||
\(482\) | −10.8642 | −0.494851 | ||||||||
\(483\) | 4.50316 | 0.204901 | ||||||||
\(484\) | −11.1065 | −0.504842 | ||||||||
\(485\) | −15.6842 | −0.712181 | ||||||||
\(486\) | −41.9658 | −1.90361 | ||||||||
\(487\) | 28.8945 | 1.30934 | 0.654668 | − | 0.755917i | \(-0.272809\pi\) | ||||
0.654668 | + | 0.755917i | \(0.272809\pi\) | |||||||
\(488\) | −63.4942 | −2.87425 | ||||||||
\(489\) | −5.05921 | −0.228785 | ||||||||
\(490\) | 41.5321 | 1.87623 | ||||||||
\(491\) | 22.0320 | 0.994290 | 0.497145 | − | 0.867667i | \(-0.334382\pi\) | ||||
0.497145 | + | 0.867667i | \(0.334382\pi\) | |||||||
\(492\) | −56.8730 | −2.56403 | ||||||||
\(493\) | −13.8196 | −0.622404 | ||||||||
\(494\) | 15.0012 | 0.674935 | ||||||||
\(495\) | −13.4320 | −0.603721 | ||||||||
\(496\) | 9.52610 | 0.427734 | ||||||||
\(497\) | 5.05922 | 0.226937 | ||||||||
\(498\) | 15.4581 | 0.692696 | ||||||||
\(499\) | −13.3085 | −0.595769 | −0.297884 | − | 0.954602i | \(-0.596281\pi\) | ||||
−0.297884 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(500\) | −53.1480 | −2.37685 | ||||||||
\(501\) | 8.00350 | 0.357570 | ||||||||
\(502\) | −52.4487 | −2.34090 | ||||||||
\(503\) | −38.8551 | −1.73246 | −0.866231 | − | 0.499643i | \(-0.833464\pi\) | ||||
−0.866231 | + | 0.499643i | \(0.833464\pi\) | |||||||
\(504\) | −7.58183 | −0.337722 | ||||||||
\(505\) | −2.64494 | −0.117698 | ||||||||
\(506\) | 69.5975 | 3.09398 | ||||||||
\(507\) | −12.7069 | −0.564332 | ||||||||
\(508\) | 3.97559 | 0.176388 | ||||||||
\(509\) | 11.9069 | 0.527765 | 0.263883 | − | 0.964555i | \(-0.414997\pi\) | ||||
0.263883 | + | 0.964555i | \(0.414997\pi\) | |||||||
\(510\) | −41.6784 | −1.84555 | ||||||||
\(511\) | 5.57587 | 0.246662 | ||||||||
\(512\) | 30.8723 | 1.36438 | ||||||||
\(513\) | 37.0902 | 1.63757 | ||||||||
\(514\) | 60.9336 | 2.68766 | ||||||||
\(515\) | −14.3207 | −0.631047 | ||||||||
\(516\) | −40.2663 | −1.77262 | ||||||||
\(517\) | 32.3402 | 1.42232 | ||||||||
\(518\) | 5.55688 | 0.244155 | ||||||||
\(519\) | 15.5725 | 0.683556 | ||||||||
\(520\) | −14.2293 | −0.623995 | ||||||||
\(521\) | 13.1056 | 0.574167 | 0.287083 | − | 0.957906i | \(-0.407314\pi\) | ||||
0.287083 | + | 0.957906i | \(0.407314\pi\) | |||||||
\(522\) | −10.7607 | −0.470981 | ||||||||
\(523\) | 9.88203 | 0.432111 | 0.216056 | − | 0.976381i | \(-0.430681\pi\) | ||||
0.216056 | + | 0.976381i | \(0.430681\pi\) | |||||||
\(524\) | −78.4113 | −3.42542 | ||||||||
\(525\) | −0.209424 | −0.00914002 | ||||||||
\(526\) | 15.6924 | 0.684222 | ||||||||
\(527\) | 5.81023 | 0.253098 | ||||||||
\(528\) | 32.9187 | 1.43260 | ||||||||
\(529\) | 56.1221 | 2.44009 | ||||||||
\(530\) | 66.4053 | 2.88446 | ||||||||
\(531\) | −5.38976 | −0.233896 | ||||||||
\(532\) | 17.9846 | 0.779733 | ||||||||
\(533\) | −8.65171 | −0.374747 | ||||||||
\(534\) | 31.8232 | 1.37713 | ||||||||
\(535\) | 26.0113 | 1.12457 | ||||||||
\(536\) | 1.09358 | 0.0472353 | ||||||||
\(537\) | 11.9696 | 0.516528 | ||||||||
\(538\) | 47.8036 | 2.06096 | ||||||||
\(539\) | −20.0075 | −0.861785 | ||||||||
\(540\) | −58.7892 | −2.52988 | ||||||||
\(541\) | 15.8552 | 0.681669 | 0.340835 | − | 0.940123i | \(-0.389290\pi\) | ||||
0.340835 | + | 0.940123i | \(0.389290\pi\) | |||||||
\(542\) | −47.6015 | −2.04466 | ||||||||
\(543\) | 22.6675 | 0.972754 | ||||||||
\(544\) | −85.3451 | −3.65914 | ||||||||
\(545\) | 31.2722 | 1.33955 | ||||||||
\(546\) | 1.03875 | 0.0444544 | ||||||||
\(547\) | 5.31702 | 0.227339 | 0.113670 | − | 0.993519i | \(-0.463739\pi\) | ||||
0.113670 | + | 0.993519i | \(0.463739\pi\) | |||||||
\(548\) | −92.7035 | −3.96010 | ||||||||
\(549\) | −15.7177 | −0.670814 | ||||||||
\(550\) | −3.23670 | −0.138014 | ||||||||
\(551\) | 15.2751 | 0.650742 | ||||||||
\(552\) | 71.7982 | 3.05594 | ||||||||
\(553\) | −5.96413 | −0.253621 | ||||||||
\(554\) | 78.5075 | 3.33547 | ||||||||
\(555\) | 10.1559 | 0.431092 | ||||||||
\(556\) | 54.6492 | 2.31764 | ||||||||
\(557\) | −36.5698 | −1.54951 | −0.774755 | − | 0.632261i | \(-0.782127\pi\) | ||||
−0.774755 | + | 0.632261i | \(0.782127\pi\) | |||||||
\(558\) | 4.52414 | 0.191522 | ||||||||
\(559\) | −6.12544 | −0.259078 | ||||||||
\(560\) | −12.4625 | −0.526636 | ||||||||
\(561\) | 20.0780 | 0.847695 | ||||||||
\(562\) | −3.02425 | −0.127570 | ||||||||
\(563\) | 27.3771 | 1.15381 | 0.576904 | − | 0.816812i | \(-0.304261\pi\) | ||||
0.576904 | + | 0.816812i | \(0.304261\pi\) | |||||||
\(564\) | 55.7500 | 2.34750 | ||||||||
\(565\) | −30.7690 | −1.29446 | ||||||||
\(566\) | −51.4219 | −2.16142 | ||||||||
\(567\) | −0.320106 | −0.0134432 | ||||||||
\(568\) | 80.6640 | 3.38459 | ||||||||
\(569\) | −12.6810 | −0.531617 | −0.265808 | − | 0.964026i | \(-0.585639\pi\) | ||||
−0.265808 | + | 0.964026i | \(0.585639\pi\) | |||||||
\(570\) | 46.0681 | 1.92958 | ||||||||
\(571\) | 13.2561 | 0.554751 | 0.277376 | − | 0.960762i | \(-0.410535\pi\) | ||||
0.277376 | + | 0.960762i | \(0.410535\pi\) | |||||||
\(572\) | 11.4544 | 0.478934 | ||||||||
\(573\) | 3.65867 | 0.152843 | ||||||||
\(574\) | −14.5375 | −0.606785 | ||||||||
\(575\) | −3.67966 | −0.153452 | ||||||||
\(576\) | −24.1736 | −1.00723 | ||||||||
\(577\) | −41.1712 | −1.71398 | −0.856990 | − | 0.515333i | \(-0.827668\pi\) | ||||
−0.856990 | + | 0.515333i | \(0.827668\pi\) | |||||||
\(578\) | −70.6784 | −2.93983 | ||||||||
\(579\) | 14.5432 | 0.604396 | ||||||||
\(580\) | −24.2116 | −1.00533 | ||||||||
\(581\) | 2.81922 | 0.116961 | ||||||||
\(582\) | 18.2552 | 0.756701 | ||||||||
\(583\) | −31.9898 | −1.32488 | ||||||||
\(584\) | 88.9015 | 3.67877 | ||||||||
\(585\) | −3.52239 | −0.145633 | ||||||||
\(586\) | 6.12387 | 0.252975 | ||||||||
\(587\) | 5.17284 | 0.213506 | 0.106753 | − | 0.994286i | \(-0.465955\pi\) | ||||
0.106753 | + | 0.994286i | \(0.465955\pi\) | |||||||
\(588\) | −34.4902 | −1.42235 | ||||||||
\(589\) | −6.42218 | −0.264621 | ||||||||
\(590\) | −16.9968 | −0.699747 | ||||||||
\(591\) | −18.8855 | −0.776846 | ||||||||
\(592\) | 46.1807 | 1.89802 | ||||||||
\(593\) | −34.4971 | −1.41663 | −0.708313 | − | 0.705899i | \(-0.750543\pi\) | ||||
−0.708313 | + | 0.705899i | \(0.750543\pi\) | |||||||
\(594\) | 39.6936 | 1.62865 | ||||||||
\(595\) | −7.60122 | −0.311619 | ||||||||
\(596\) | 9.95590 | 0.407810 | ||||||||
\(597\) | 16.3673 | 0.669868 | ||||||||
\(598\) | 18.2512 | 0.746346 | ||||||||
\(599\) | 22.3063 | 0.911410 | 0.455705 | − | 0.890131i | \(-0.349387\pi\) | ||||
0.455705 | + | 0.890131i | \(0.349387\pi\) | |||||||
\(600\) | −3.33905 | −0.136316 | ||||||||
\(601\) | −6.22133 | −0.253773 | −0.126887 | − | 0.991917i | \(-0.540498\pi\) | ||||
−0.126887 | + | 0.991917i | \(0.540498\pi\) | |||||||
\(602\) | −10.2926 | −0.419496 | ||||||||
\(603\) | 0.270709 | 0.0110241 | ||||||||
\(604\) | −21.6351 | −0.880319 | ||||||||
\(605\) | −5.18858 | −0.210946 | ||||||||
\(606\) | 3.07851 | 0.125056 | ||||||||
\(607\) | −41.2831 | −1.67563 | −0.837814 | − | 0.545955i | \(-0.816167\pi\) | ||||
−0.837814 | + | 0.545955i | \(0.816167\pi\) | |||||||
\(608\) | 94.3338 | 3.82574 | ||||||||
\(609\) | 1.05772 | 0.0428609 | ||||||||
\(610\) | −49.5662 | −2.00688 | ||||||||
\(611\) | 8.48087 | 0.343099 | ||||||||
\(612\) | −64.2190 | −2.59590 | ||||||||
\(613\) | 25.8987 | 1.04604 | 0.523018 | − | 0.852321i | \(-0.324806\pi\) | ||||
0.523018 | + | 0.852321i | \(0.324806\pi\) | |||||||
\(614\) | 34.5696 | 1.39511 | ||||||||
\(615\) | −26.5691 | −1.07137 | ||||||||
\(616\) | 11.5181 | 0.464078 | ||||||||
\(617\) | 38.4627 | 1.54845 | 0.774225 | − | 0.632910i | \(-0.218140\pi\) | ||||
0.774225 | + | 0.632910i | \(0.218140\pi\) | |||||||
\(618\) | 16.6682 | 0.670495 | ||||||||
\(619\) | −25.8680 | −1.03972 | −0.519860 | − | 0.854251i | \(-0.674016\pi\) | ||||
−0.519860 | + | 0.854251i | \(0.674016\pi\) | |||||||
\(620\) | 10.1794 | 0.408813 | ||||||||
\(621\) | 45.1257 | 1.81083 | ||||||||
\(622\) | −41.9110 | −1.68048 | ||||||||
\(623\) | 5.80385 | 0.232526 | ||||||||
\(624\) | 8.63257 | 0.345579 | ||||||||
\(625\) | −26.8972 | −1.07589 | ||||||||
\(626\) | 17.9028 | 0.715541 | ||||||||
\(627\) | −22.1927 | −0.886290 | ||||||||
\(628\) | 41.7916 | 1.66767 | ||||||||
\(629\) | 28.1669 | 1.12309 | ||||||||
\(630\) | −5.91869 | −0.235806 | ||||||||
\(631\) | −25.1744 | −1.00218 | −0.501088 | − | 0.865396i | \(-0.667067\pi\) | ||||
−0.501088 | + | 0.865396i | \(0.667067\pi\) | |||||||
\(632\) | −95.0918 | −3.78255 | ||||||||
\(633\) | 8.72530 | 0.346800 | ||||||||
\(634\) | −46.3011 | −1.83885 | ||||||||
\(635\) | 1.85725 | 0.0737028 | ||||||||
\(636\) | −55.1460 | −2.18668 | ||||||||
\(637\) | −5.24676 | −0.207884 | ||||||||
\(638\) | 16.3473 | 0.647195 | ||||||||
\(639\) | 19.9680 | 0.789921 | ||||||||
\(640\) | −16.1897 | −0.639952 | ||||||||
\(641\) | 0.360829 | 0.0142519 | 0.00712594 | − | 0.999975i | \(-0.497732\pi\) | ||||
0.00712594 | + | 0.999975i | \(0.497732\pi\) | |||||||
\(642\) | −30.2752 | −1.19487 | ||||||||
\(643\) | 3.78669 | 0.149332 | 0.0746662 | − | 0.997209i | \(-0.476211\pi\) | ||||
0.0746662 | + | 0.997209i | \(0.476211\pi\) | |||||||
\(644\) | 21.8810 | 0.862233 | ||||||||
\(645\) | −18.8110 | −0.740681 | ||||||||
\(646\) | 127.768 | 5.02697 | ||||||||
\(647\) | −11.5272 | −0.453179 | −0.226590 | − | 0.973990i | \(-0.572758\pi\) | ||||
−0.226590 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(648\) | −5.10375 | −0.200494 | ||||||||
\(649\) | 8.18798 | 0.321406 | ||||||||
\(650\) | −0.848791 | −0.0332923 | ||||||||
\(651\) | −0.444700 | −0.0174292 | ||||||||
\(652\) | −24.5829 | −0.962739 | ||||||||
\(653\) | −35.2744 | −1.38039 | −0.690197 | − | 0.723622i | \(-0.742476\pi\) | ||||
−0.690197 | + | 0.723622i | \(0.742476\pi\) | |||||||
\(654\) | −36.3985 | −1.42329 | ||||||||
\(655\) | −36.6310 | −1.43129 | ||||||||
\(656\) | −120.815 | −4.71703 | ||||||||
\(657\) | 22.0071 | 0.858580 | ||||||||
\(658\) | 14.2505 | 0.555542 | ||||||||
\(659\) | −6.14081 | −0.239212 | −0.119606 | − | 0.992821i | \(-0.538163\pi\) | ||||
−0.119606 | + | 0.992821i | \(0.538163\pi\) | |||||||
\(660\) | 35.1762 | 1.36923 | ||||||||
\(661\) | 0.711705 | 0.0276821 | 0.0138411 | − | 0.999904i | \(-0.495594\pi\) | ||||
0.0138411 | + | 0.999904i | \(0.495594\pi\) | |||||||
\(662\) | 31.8302 | 1.23712 | ||||||||
\(663\) | 5.26524 | 0.204485 | ||||||||
\(664\) | 44.9496 | 1.74438 | ||||||||
\(665\) | 8.40179 | 0.325807 | ||||||||
\(666\) | 21.9322 | 0.849855 | ||||||||
\(667\) | 18.5845 | 0.719594 | ||||||||
\(668\) | 38.8893 | 1.50467 | ||||||||
\(669\) | 13.5823 | 0.525124 | ||||||||
\(670\) | 0.853691 | 0.0329810 | ||||||||
\(671\) | 23.8779 | 0.921794 | ||||||||
\(672\) | 6.53209 | 0.251981 | ||||||||
\(673\) | −44.1131 | −1.70043 | −0.850217 | − | 0.526432i | \(-0.823529\pi\) | ||||
−0.850217 | + | 0.526432i | \(0.823529\pi\) | |||||||
\(674\) | −49.8074 | −1.91851 | ||||||||
\(675\) | −2.09862 | −0.0807760 | ||||||||
\(676\) | −61.7432 | −2.37474 | ||||||||
\(677\) | −9.04562 | −0.347652 | −0.173826 | − | 0.984776i | \(-0.555613\pi\) | ||||
−0.173826 | + | 0.984776i | \(0.555613\pi\) | |||||||
\(678\) | 35.8127 | 1.37538 | ||||||||
\(679\) | 3.32934 | 0.127768 | ||||||||
\(680\) | −121.194 | −4.64756 | ||||||||
\(681\) | −7.00839 | −0.268562 | ||||||||
\(682\) | −6.87295 | −0.263179 | ||||||||
\(683\) | −9.59421 | −0.367112 | −0.183556 | − | 0.983009i | \(-0.558761\pi\) | ||||
−0.183556 | + | 0.983009i | \(0.558761\pi\) | |||||||
\(684\) | 70.9827 | 2.71409 | ||||||||
\(685\) | −43.3078 | −1.65471 | ||||||||
\(686\) | −17.9507 | −0.685360 | ||||||||
\(687\) | −20.4036 | −0.778447 | ||||||||
\(688\) | −85.5373 | −3.26108 | ||||||||
\(689\) | −8.38899 | −0.319595 | ||||||||
\(690\) | 56.0487 | 2.13374 | ||||||||
\(691\) | 8.70008 | 0.330967 | 0.165483 | − | 0.986213i | \(-0.447082\pi\) | ||||
0.165483 | + | 0.986213i | \(0.447082\pi\) | |||||||
\(692\) | 75.6672 | 2.87644 | ||||||||
\(693\) | 2.85125 | 0.108310 | ||||||||
\(694\) | 69.1217 | 2.62382 | ||||||||
\(695\) | 25.5302 | 0.968415 | ||||||||
\(696\) | 16.8642 | 0.639236 | ||||||||
\(697\) | −73.6883 | −2.79114 | ||||||||
\(698\) | −33.1305 | −1.25401 | ||||||||
\(699\) | −14.0075 | −0.529813 | ||||||||
\(700\) | −1.01760 | −0.0384617 | ||||||||
\(701\) | −30.4119 | −1.14864 | −0.574321 | − | 0.818630i | \(-0.694734\pi\) | ||||
−0.574321 | + | 0.818630i | \(0.694734\pi\) | |||||||
\(702\) | 10.4092 | 0.392870 | ||||||||
\(703\) | −31.1335 | −1.17422 | ||||||||
\(704\) | 36.7239 | 1.38408 | ||||||||
\(705\) | 26.0444 | 0.980890 | ||||||||
\(706\) | −29.4862 | −1.10973 | ||||||||
\(707\) | 0.561452 | 0.0211156 | ||||||||
\(708\) | 14.1149 | 0.530472 | ||||||||
\(709\) | 44.2104 | 1.66036 | 0.830179 | − | 0.557497i | \(-0.188238\pi\) | ||||
0.830179 | + | 0.557497i | \(0.188238\pi\) | |||||||
\(710\) | 62.9697 | 2.36321 | ||||||||
\(711\) | −23.5395 | −0.882801 | ||||||||
\(712\) | 92.5364 | 3.46795 | ||||||||
\(713\) | −7.81354 | −0.292619 | ||||||||
\(714\) | 8.84723 | 0.331099 | ||||||||
\(715\) | 5.35111 | 0.200120 | ||||||||
\(716\) | 58.1609 | 2.17357 | ||||||||
\(717\) | 15.6505 | 0.584477 | ||||||||
\(718\) | −86.8152 | −3.23991 | ||||||||
\(719\) | −37.5002 | −1.39852 | −0.699261 | − | 0.714866i | \(-0.746488\pi\) | ||||
−0.699261 | + | 0.714866i | \(0.746488\pi\) | |||||||
\(720\) | −49.1876 | −1.83311 | ||||||||
\(721\) | 3.03992 | 0.113212 | ||||||||
\(722\) | −91.0255 | −3.38762 | ||||||||
\(723\) | 4.21482 | 0.156751 | ||||||||
\(724\) | 110.142 | 4.09339 | ||||||||
\(725\) | −0.864291 | −0.0320989 | ||||||||
\(726\) | 6.03911 | 0.224132 | ||||||||
\(727\) | −50.2627 | −1.86414 | −0.932071 | − | 0.362276i | \(-0.882000\pi\) | ||||
−0.932071 | + | 0.362276i | \(0.882000\pi\) | |||||||
\(728\) | 3.02050 | 0.111947 | ||||||||
\(729\) | 14.3365 | 0.530983 | ||||||||
\(730\) | 69.4002 | 2.56862 | ||||||||
\(731\) | −52.1716 | −1.92963 | ||||||||
\(732\) | 41.1621 | 1.52139 | ||||||||
\(733\) | 42.4330 | 1.56730 | 0.783648 | − | 0.621205i | \(-0.213356\pi\) | ||||
0.783648 | + | 0.621205i | \(0.213356\pi\) | |||||||
\(734\) | 35.2162 | 1.29985 | ||||||||
\(735\) | −16.1126 | −0.594322 | ||||||||
\(736\) | 114.771 | 4.23052 | ||||||||
\(737\) | −0.411254 | −0.0151487 | ||||||||
\(738\) | −57.3775 | −2.11209 | ||||||||
\(739\) | 4.92702 | 0.181243 | 0.0906217 | − | 0.995885i | \(-0.471115\pi\) | ||||
0.0906217 | + | 0.995885i | \(0.471115\pi\) | |||||||
\(740\) | 49.3477 | 1.81406 | ||||||||
\(741\) | −5.81979 | −0.213795 | ||||||||
\(742\) | −14.0961 | −0.517484 | ||||||||
\(743\) | −44.3385 | −1.62662 | −0.813310 | − | 0.581830i | \(-0.802337\pi\) | ||||
−0.813310 | + | 0.581830i | \(0.802337\pi\) | |||||||
\(744\) | −7.09029 | −0.259942 | ||||||||
\(745\) | 4.65105 | 0.170401 | ||||||||
\(746\) | −23.4749 | −0.859476 | ||||||||
\(747\) | 11.1270 | 0.407117 | ||||||||
\(748\) | 97.5598 | 3.56714 | ||||||||
\(749\) | −5.52153 | −0.201752 | ||||||||
\(750\) | 28.8989 | 1.05524 | ||||||||
\(751\) | −7.54396 | −0.275283 | −0.137642 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137642 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(752\) | 118.429 | 4.31867 | ||||||||
\(753\) | 20.3478 | 0.741514 | ||||||||
\(754\) | 4.28690 | 0.156120 | ||||||||
\(755\) | −10.1071 | −0.367837 | ||||||||
\(756\) | 12.4794 | 0.453872 | ||||||||
\(757\) | −3.41994 | −0.124300 | −0.0621499 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621499 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(758\) | −59.7425 | −2.16995 | ||||||||
\(759\) | −27.0007 | −0.980064 | ||||||||
\(760\) | 133.958 | 4.85916 | ||||||||
\(761\) | 0.188752 | 0.00684227 | 0.00342113 | − | 0.999994i | \(-0.498911\pi\) | ||||
0.00342113 | + | 0.999994i | \(0.498911\pi\) | |||||||
\(762\) | −2.16170 | −0.0783101 | ||||||||
\(763\) | −6.63827 | −0.240322 | ||||||||
\(764\) | 17.7776 | 0.643171 | ||||||||
\(765\) | −30.0009 | −1.08468 | ||||||||
\(766\) | 1.29731 | 0.0468736 | ||||||||
\(767\) | 2.14721 | 0.0775312 | ||||||||
\(768\) | −6.57819 | −0.237370 | ||||||||
\(769\) | −3.54424 | −0.127809 | −0.0639043 | − | 0.997956i | \(-0.520355\pi\) | ||||
−0.0639043 | + | 0.997956i | \(0.520355\pi\) | |||||||
\(770\) | 8.99152 | 0.324032 | ||||||||
\(771\) | −23.6395 | −0.851356 | ||||||||
\(772\) | 70.6660 | 2.54333 | ||||||||
\(773\) | 46.2757 | 1.66442 | 0.832211 | − | 0.554459i | \(-0.187075\pi\) | ||||
0.832211 | + | 0.554459i | \(0.187075\pi\) | |||||||
\(774\) | −40.6234 | −1.46018 | ||||||||
\(775\) | 0.363377 | 0.0130529 | ||||||||
\(776\) | 53.0828 | 1.90556 | ||||||||
\(777\) | −2.15582 | −0.0773397 | ||||||||
\(778\) | 87.3269 | 3.13082 | ||||||||
\(779\) | 81.4493 | 2.91822 | ||||||||
\(780\) | 9.22457 | 0.330293 | ||||||||
\(781\) | −30.3348 | −1.08546 | ||||||||
\(782\) | 155.449 | 5.55884 | ||||||||
\(783\) | 10.5993 | 0.378788 | ||||||||
\(784\) | −73.2672 | −2.61669 | ||||||||
\(785\) | 19.5236 | 0.696826 | ||||||||
\(786\) | 42.6357 | 1.52076 | ||||||||
\(787\) | −32.9728 | −1.17535 | −0.587677 | − | 0.809095i | \(-0.699958\pi\) | ||||
−0.587677 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(788\) | −91.7653 | −3.26900 | ||||||||
\(789\) | −6.08796 | −0.216737 | ||||||||
\(790\) | −74.2326 | −2.64108 | ||||||||
\(791\) | 6.53145 | 0.232232 | ||||||||
\(792\) | 45.4603 | 1.61536 | ||||||||
\(793\) | 6.26171 | 0.222360 | ||||||||
\(794\) | 65.9122 | 2.33914 | ||||||||
\(795\) | −25.7623 | −0.913694 | ||||||||
\(796\) | 79.5292 | 2.81884 | ||||||||
\(797\) | −22.2197 | −0.787062 | −0.393531 | − | 0.919311i | \(-0.628747\pi\) | ||||
−0.393531 | + | 0.919311i | \(0.628747\pi\) | |||||||
\(798\) | −9.77904 | −0.346174 | ||||||||
\(799\) | 72.2333 | 2.55543 | ||||||||
\(800\) | −5.33756 | −0.188711 | ||||||||
\(801\) | 22.9069 | 0.809377 | ||||||||
\(802\) | −11.2123 | −0.395919 | ||||||||
\(803\) | −33.4326 | −1.17981 | ||||||||
\(804\) | −0.708945 | −0.0250026 | ||||||||
\(805\) | 10.2220 | 0.360279 | ||||||||
\(806\) | −1.80236 | −0.0634854 | ||||||||
\(807\) | −18.5457 | −0.652839 | ||||||||
\(808\) | 8.95177 | 0.314922 | ||||||||
\(809\) | −2.63715 | −0.0927172 | −0.0463586 | − | 0.998925i | \(-0.514762\pi\) | ||||
−0.0463586 | + | 0.998925i | \(0.514762\pi\) | |||||||
\(810\) | −3.98420 | −0.139991 | ||||||||
\(811\) | −0.783721 | −0.0275201 | −0.0137601 | − | 0.999905i | \(-0.504380\pi\) | ||||
−0.0137601 | + | 0.999905i | \(0.504380\pi\) | |||||||
\(812\) | 5.13949 | 0.180361 | ||||||||
\(813\) | 18.4673 | 0.647675 | ||||||||
\(814\) | −33.3188 | −1.16782 | ||||||||
\(815\) | −11.4842 | −0.402275 | ||||||||
\(816\) | 73.5253 | 2.57390 | ||||||||
\(817\) | 57.6664 | 2.01749 | ||||||||
\(818\) | 23.9658 | 0.837945 | ||||||||
\(819\) | 0.747710 | 0.0261271 | ||||||||
\(820\) | −129.100 | −4.50837 | ||||||||
\(821\) | −2.12851 | −0.0742856 | −0.0371428 | − | 0.999310i | \(-0.511826\pi\) | ||||
−0.0371428 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(822\) | 50.4070 | 1.75815 | ||||||||
\(823\) | −31.8659 | −1.11077 | −0.555387 | − | 0.831592i | \(-0.687430\pi\) | ||||
−0.555387 | + | 0.831592i | \(0.687430\pi\) | |||||||
\(824\) | 48.4683 | 1.68847 | ||||||||
\(825\) | 1.25570 | 0.0437177 | ||||||||
\(826\) | 3.60797 | 0.125537 | ||||||||
\(827\) | 32.4426 | 1.12814 | 0.564070 | − | 0.825727i | \(-0.309235\pi\) | ||||
0.564070 | + | 0.825727i | \(0.309235\pi\) | |||||||
\(828\) | 86.3611 | 3.00125 | ||||||||
\(829\) | 38.8086 | 1.34788 | 0.673939 | − | 0.738787i | \(-0.264601\pi\) | ||||
0.673939 | + | 0.738787i | \(0.264601\pi\) | |||||||
\(830\) | 35.0895 | 1.21797 | ||||||||
\(831\) | −30.4574 | −1.05656 | ||||||||
\(832\) | 9.63045 | 0.333876 | ||||||||
\(833\) | −44.6877 | −1.54834 | ||||||||
\(834\) | −29.7152 | −1.02895 | ||||||||
\(835\) | 18.1677 | 0.628719 | ||||||||
\(836\) | −107.835 | −3.72955 | ||||||||
\(837\) | −4.45630 | −0.154032 | ||||||||
\(838\) | −58.9332 | −2.03581 | ||||||||
\(839\) | 24.5690 | 0.848217 | 0.424108 | − | 0.905611i | \(-0.360588\pi\) | ||||
0.424108 | + | 0.905611i | \(0.360588\pi\) | |||||||
\(840\) | 9.27584 | 0.320047 | ||||||||
\(841\) | −24.6348 | −0.849476 | ||||||||
\(842\) | 52.2719 | 1.80141 | ||||||||
\(843\) | 1.17328 | 0.0404098 | ||||||||
\(844\) | 42.3965 | 1.45935 | ||||||||
\(845\) | −28.8442 | −0.992271 | ||||||||
\(846\) | 56.2445 | 1.93373 | ||||||||
\(847\) | 1.10140 | 0.0378445 | ||||||||
\(848\) | −117.146 | −4.02282 | ||||||||
\(849\) | 19.9494 | 0.684662 | ||||||||
\(850\) | −7.22932 | −0.247964 | ||||||||
\(851\) | −37.8786 | −1.29846 | ||||||||
\(852\) | −52.2929 | −1.79153 | ||||||||
\(853\) | 3.84572 | 0.131675 | 0.0658374 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658374 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(854\) | 10.5216 | 0.360042 | ||||||||
\(855\) | 33.1606 | 1.13407 | ||||||||
\(856\) | −88.0350 | −3.00897 | ||||||||
\(857\) | −3.82526 | −0.130668 | −0.0653342 | − | 0.997863i | \(-0.520811\pi\) | ||||
−0.0653342 | + | 0.997863i | \(0.520811\pi\) | |||||||
\(858\) | −6.22828 | −0.212630 | ||||||||
\(859\) | −8.00146 | −0.273006 | −0.136503 | − | 0.990640i | \(-0.543586\pi\) | ||||
−0.136503 | + | 0.990640i | \(0.543586\pi\) | |||||||
\(860\) | −91.4032 | −3.11682 | ||||||||
\(861\) | 5.63992 | 0.192208 | ||||||||
\(862\) | 34.6816 | 1.18126 | ||||||||
\(863\) | 25.1596 | 0.856443 | 0.428221 | − | 0.903674i | \(-0.359140\pi\) | ||||
0.428221 | + | 0.903674i | \(0.359140\pi\) | |||||||
\(864\) | 65.4575 | 2.22691 | ||||||||
\(865\) | 35.3491 | 1.20190 | ||||||||
\(866\) | −62.2100 | −2.11398 | ||||||||
\(867\) | 27.4200 | 0.931234 | ||||||||
\(868\) | −2.16081 | −0.0733428 | ||||||||
\(869\) | 35.7606 | 1.21309 | ||||||||
\(870\) | 13.1649 | 0.446332 | ||||||||
\(871\) | −0.107847 | −0.00365426 | ||||||||
\(872\) | −105.840 | −3.58421 | ||||||||
\(873\) | 13.1404 | 0.444735 | ||||||||
\(874\) | −171.821 | −5.81194 | ||||||||
\(875\) | 5.27052 | 0.178176 | ||||||||
\(876\) | −57.6332 | −1.94725 | ||||||||
\(877\) | 47.0932 | 1.59023 | 0.795113 | − | 0.606462i | \(-0.207412\pi\) | ||||
0.795113 | + | 0.606462i | \(0.207412\pi\) | |||||||
\(878\) | 13.4292 | 0.453213 | ||||||||
\(879\) | −2.37579 | −0.0801334 | ||||||||
\(880\) | 74.7244 | 2.51896 | ||||||||
\(881\) | −32.7410 | −1.10307 | −0.551537 | − | 0.834150i | \(-0.685958\pi\) | ||||
−0.551537 | + | 0.834150i | \(0.685958\pi\) | |||||||
\(882\) | −34.7961 | −1.17165 | ||||||||
\(883\) | 9.65046 | 0.324764 | 0.162382 | − | 0.986728i | \(-0.448082\pi\) | ||||
0.162382 | + | 0.986728i | \(0.448082\pi\) | |||||||
\(884\) | 25.5840 | 0.860483 | ||||||||
\(885\) | 6.59400 | 0.221655 | ||||||||
\(886\) | 72.6456 | 2.44058 | ||||||||
\(887\) | −26.5622 | −0.891871 | −0.445935 | − | 0.895065i | \(-0.647129\pi\) | ||||
−0.445935 | + | 0.895065i | \(0.647129\pi\) | |||||||
\(888\) | −34.3724 | −1.15346 | ||||||||
\(889\) | −0.394246 | −0.0132226 | ||||||||
\(890\) | 72.2378 | 2.42142 | ||||||||
\(891\) | 1.91934 | 0.0643002 | ||||||||
\(892\) | 65.9971 | 2.20975 | ||||||||
\(893\) | −79.8410 | −2.67178 | ||||||||
\(894\) | −5.41346 | −0.181053 | ||||||||
\(895\) | 27.1707 | 0.908217 | ||||||||
\(896\) | 3.43664 | 0.114810 | ||||||||
\(897\) | −7.08064 | −0.236416 | ||||||||
\(898\) | 53.3002 | 1.77865 | ||||||||
\(899\) | −1.83527 | −0.0612097 | ||||||||
\(900\) | −4.01631 | −0.133877 | ||||||||
\(901\) | −71.4507 | −2.38037 | ||||||||
\(902\) | 87.1663 | 2.90232 | ||||||||
\(903\) | 3.99308 | 0.132881 | ||||||||
\(904\) | 104.137 | 3.46355 | ||||||||
\(905\) | 51.4544 | 1.71040 | ||||||||
\(906\) | 11.7639 | 0.390831 | ||||||||
\(907\) | 25.7393 | 0.854660 | 0.427330 | − | 0.904096i | \(-0.359454\pi\) | ||||
0.427330 | + | 0.904096i | \(0.359454\pi\) | |||||||
\(908\) | −34.0540 | −1.13012 | ||||||||
\(909\) | 2.21597 | 0.0734990 | ||||||||
\(910\) | 2.35793 | 0.0781646 | ||||||||
\(911\) | −25.9725 | −0.860507 | −0.430253 | − | 0.902708i | \(-0.641576\pi\) | ||||
−0.430253 | + | 0.902708i | \(0.641576\pi\) | |||||||
\(912\) | −81.2691 | −2.69109 | ||||||||
\(913\) | −16.9039 | −0.559438 | ||||||||
\(914\) | −96.6848 | −3.19805 | ||||||||
\(915\) | 19.2295 | 0.635707 | ||||||||
\(916\) | −99.1419 | −3.27574 | ||||||||
\(917\) | 7.77580 | 0.256780 | ||||||||
\(918\) | 88.6573 | 2.92613 | ||||||||
\(919\) | 14.8970 | 0.491408 | 0.245704 | − | 0.969345i | \(-0.420981\pi\) | ||||
0.245704 | + | 0.969345i | \(0.420981\pi\) | |||||||
\(920\) | 162.980 | 5.37328 | ||||||||
\(921\) | −13.4115 | −0.441922 | ||||||||
\(922\) | 52.7786 | 1.73817 | ||||||||
\(923\) | −7.95497 | −0.261841 | ||||||||
\(924\) | −7.46698 | −0.245645 | ||||||||
\(925\) | 1.76158 | 0.0579205 | ||||||||
\(926\) | 70.3759 | 2.31269 | ||||||||
\(927\) | 11.9981 | 0.394069 | ||||||||
\(928\) | 26.9578 | 0.884935 | ||||||||
\(929\) | −23.8673 | −0.783062 | −0.391531 | − | 0.920165i | \(-0.628054\pi\) | ||||
−0.391531 | + | 0.920165i | \(0.628054\pi\) | |||||||
\(930\) | −5.53497 | −0.181499 | ||||||||
\(931\) | 49.3943 | 1.61883 | ||||||||
\(932\) | −68.0630 | −2.22948 | ||||||||
\(933\) | 16.2596 | 0.532315 | ||||||||
\(934\) | 57.6784 | 1.88729 | ||||||||
\(935\) | 45.5765 | 1.49051 | ||||||||
\(936\) | 11.9215 | 0.389665 | ||||||||
\(937\) | 27.8986 | 0.911407 | 0.455704 | − | 0.890132i | \(-0.349388\pi\) | ||||
0.455704 | + | 0.890132i | \(0.349388\pi\) | |||||||
\(938\) | −0.181216 | −0.00591692 | ||||||||
\(939\) | −6.94550 | −0.226658 | ||||||||
\(940\) | 126.551 | 4.12763 | ||||||||
\(941\) | 56.3426 | 1.83672 | 0.918359 | − | 0.395749i | \(-0.129515\pi\) | ||||
0.918359 | + | 0.395749i | \(0.129515\pi\) | |||||||
\(942\) | −22.7239 | −0.740386 | ||||||||
\(943\) | 99.0953 | 3.22699 | ||||||||
\(944\) | 29.9842 | 0.975903 | ||||||||
\(945\) | 5.82994 | 0.189648 | ||||||||
\(946\) | 61.7140 | 2.00650 | ||||||||
\(947\) | 30.6416 | 0.995717 | 0.497859 | − | 0.867258i | \(-0.334120\pi\) | ||||
0.497859 | + | 0.867258i | \(0.334120\pi\) | |||||||
\(948\) | 61.6463 | 2.00218 | ||||||||
\(949\) | −8.76735 | −0.284600 | ||||||||
\(950\) | 7.99072 | 0.259253 | ||||||||
\(951\) | 17.9628 | 0.582483 | ||||||||
\(952\) | 25.7262 | 0.833791 | ||||||||
\(953\) | −16.6997 | −0.540958 | −0.270479 | − | 0.962726i | \(-0.587182\pi\) | ||||
−0.270479 | + | 0.962726i | \(0.587182\pi\) | |||||||
\(954\) | −55.6352 | −1.80125 | ||||||||
\(955\) | 8.30507 | 0.268746 | ||||||||
\(956\) | 76.0461 | 2.45951 | ||||||||
\(957\) | −6.34202 | −0.205008 | ||||||||
\(958\) | −24.5189 | −0.792170 | ||||||||
\(959\) | 9.19311 | 0.296861 | ||||||||
\(960\) | 29.5747 | 0.954520 | ||||||||
\(961\) | −30.2284 | −0.975109 | ||||||||
\(962\) | −8.73749 | −0.281708 | ||||||||
\(963\) | −21.7926 | −0.702258 | ||||||||
\(964\) | 20.4800 | 0.659616 | ||||||||
\(965\) | 33.0127 | 1.06272 | ||||||||
\(966\) | −11.8977 | −0.382801 | ||||||||
\(967\) | −50.3165 | −1.61807 | −0.809034 | − | 0.587762i | \(-0.800009\pi\) | ||||
−0.809034 | + | 0.587762i | \(0.800009\pi\) | |||||||
\(968\) | 17.5607 | 0.564421 | ||||||||
\(969\) | −49.5683 | −1.59236 | ||||||||
\(970\) | 41.4387 | 1.33052 | ||||||||
\(971\) | −53.8266 | −1.72738 | −0.863689 | − | 0.504026i | \(-0.831852\pi\) | ||||
−0.863689 | + | 0.504026i | \(0.831852\pi\) | |||||||
\(972\) | 79.1093 | 2.53743 | ||||||||
\(973\) | −5.41939 | −0.173738 | ||||||||
\(974\) | −76.3414 | −2.44613 | ||||||||
\(975\) | 0.329293 | 0.0105458 | ||||||||
\(976\) | 87.4402 | 2.79889 | ||||||||
\(977\) | −51.7565 | −1.65584 | −0.827918 | − | 0.560849i | \(-0.810475\pi\) | ||||
−0.827918 | + | 0.560849i | \(0.810475\pi\) | |||||||
\(978\) | 13.3668 | 0.427422 | ||||||||
\(979\) | −34.7996 | −1.11220 | ||||||||
\(980\) | −78.2917 | −2.50094 | ||||||||
\(981\) | −26.2003 | −0.836510 | ||||||||
\(982\) | −58.2101 | −1.85756 | ||||||||
\(983\) | −15.5608 | −0.496312 | −0.248156 | − | 0.968720i | \(-0.579825\pi\) | ||||
−0.248156 | + | 0.968720i | \(0.579825\pi\) | |||||||
\(984\) | 89.9226 | 2.86663 | ||||||||
\(985\) | −42.8695 | −1.36594 | ||||||||
\(986\) | 36.5124 | 1.16279 | ||||||||
\(987\) | −5.52855 | −0.175976 | ||||||||
\(988\) | −28.2786 | −0.899661 | ||||||||
\(989\) | 70.1598 | 2.23095 | ||||||||
\(990\) | 35.4882 | 1.12789 | ||||||||
\(991\) | −9.59922 | −0.304929 | −0.152465 | − | 0.988309i | \(-0.548721\pi\) | ||||
−0.152465 | + | 0.988309i | \(0.548721\pi\) | |||||||
\(992\) | −11.3340 | −0.359855 | ||||||||
\(993\) | −12.3487 | −0.391874 | ||||||||
\(994\) | −13.3668 | −0.423969 | ||||||||
\(995\) | 37.1532 | 1.17784 | ||||||||
\(996\) | −29.1400 | −0.923335 | ||||||||
\(997\) | −41.8528 | −1.32549 | −0.662745 | − | 0.748845i | \(-0.730609\pi\) | ||||
−0.662745 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(998\) | 35.1619 | 1.11303 | ||||||||
\(999\) | −21.6033 | −0.683498 |
(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 | 4003.2.a.b.1.8 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.8 | ✓ | 152 | 1.1 | even | 1 | trivial |