Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.34 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.50132 | 1.76870 | 0.884351 | − | 0.466822i | \(-0.154601\pi\) | ||||
0.884351 | + | 0.466822i | \(0.154601\pi\) | |||||||
\(3\) | 2.36788 | 1.36710 | 0.683548 | − | 0.729906i | \(-0.260436\pi\) | ||||
0.683548 | + | 0.729906i | \(0.260436\pi\) | |||||||
\(4\) | 4.25662 | 2.12831 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 5.92283 | 2.41799 | ||||||||
\(7\) | −2.67178 | −1.00984 | −0.504919 | − | 0.863167i | \(-0.668478\pi\) | ||||
−0.504919 | + | 0.863167i | \(0.668478\pi\) | |||||||
\(8\) | 5.64454 | 1.99565 | ||||||||
\(9\) | 2.60686 | 0.868952 | ||||||||
\(10\) | 2.50132 | 0.790988 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 10.0792 | 2.90960 | ||||||||
\(13\) | 3.48435 | 0.966384 | 0.483192 | − | 0.875514i | \(-0.339477\pi\) | ||||
0.483192 | + | 0.875514i | \(0.339477\pi\) | |||||||
\(14\) | −6.68298 | −1.78610 | ||||||||
\(15\) | 2.36788 | 0.611384 | ||||||||
\(16\) | 5.60558 | 1.40139 | ||||||||
\(17\) | 4.44902 | 1.07905 | 0.539523 | − | 0.841971i | \(-0.318604\pi\) | ||||
0.539523 | + | 0.841971i | \(0.318604\pi\) | |||||||
\(18\) | 6.52059 | 1.53692 | ||||||||
\(19\) | −4.04223 | −0.927350 | −0.463675 | − | 0.886005i | \(-0.653469\pi\) | ||||
−0.463675 | + | 0.886005i | \(0.653469\pi\) | |||||||
\(20\) | 4.25662 | 0.951809 | ||||||||
\(21\) | −6.32645 | −1.38054 | ||||||||
\(22\) | 2.50132 | 0.533284 | ||||||||
\(23\) | 5.55439 | 1.15817 | 0.579085 | − | 0.815267i | \(-0.303410\pi\) | ||||
0.579085 | + | 0.815267i | \(0.303410\pi\) | |||||||
\(24\) | 13.3656 | 2.72824 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.71548 | 1.70925 | ||||||||
\(27\) | −0.930919 | −0.179156 | ||||||||
\(28\) | −11.3727 | −2.14925 | ||||||||
\(29\) | −6.50210 | −1.20741 | −0.603705 | − | 0.797208i | \(-0.706309\pi\) | ||||
−0.603705 | + | 0.797208i | \(0.706309\pi\) | |||||||
\(30\) | 5.92283 | 1.08136 | ||||||||
\(31\) | −2.94433 | −0.528817 | −0.264408 | − | 0.964411i | \(-0.585177\pi\) | ||||
−0.264408 | + | 0.964411i | \(0.585177\pi\) | |||||||
\(32\) | 2.73229 | 0.483004 | ||||||||
\(33\) | 2.36788 | 0.412195 | ||||||||
\(34\) | 11.1284 | 1.90851 | ||||||||
\(35\) | −2.67178 | −0.451613 | ||||||||
\(36\) | 11.0964 | 1.84940 | ||||||||
\(37\) | 0.596335 | 0.0980369 | 0.0490185 | − | 0.998798i | \(-0.484391\pi\) | ||||
0.0490185 | + | 0.998798i | \(0.484391\pi\) | |||||||
\(38\) | −10.1109 | −1.64021 | ||||||||
\(39\) | 8.25052 | 1.32114 | ||||||||
\(40\) | 5.64454 | 0.892480 | ||||||||
\(41\) | 5.28979 | 0.826127 | 0.413063 | − | 0.910702i | \(-0.364459\pi\) | ||||
0.413063 | + | 0.910702i | \(0.364459\pi\) | |||||||
\(42\) | −15.8245 | −2.44177 | ||||||||
\(43\) | 6.60038 | 1.00655 | 0.503274 | − | 0.864127i | \(-0.332129\pi\) | ||||
0.503274 | + | 0.864127i | \(0.332129\pi\) | |||||||
\(44\) | 4.25662 | 0.641710 | ||||||||
\(45\) | 2.60686 | 0.388607 | ||||||||
\(46\) | 13.8933 | 2.04846 | ||||||||
\(47\) | 0.172675 | 0.0251873 | 0.0125937 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125937 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(48\) | 13.2733 | 1.91584 | ||||||||
\(49\) | 0.138402 | 0.0197717 | ||||||||
\(50\) | 2.50132 | 0.353741 | ||||||||
\(51\) | 10.5348 | 1.47516 | ||||||||
\(52\) | 14.8315 | 2.05676 | ||||||||
\(53\) | −4.95784 | −0.681012 | −0.340506 | − | 0.940242i | \(-0.610598\pi\) | ||||
−0.340506 | + | 0.940242i | \(0.610598\pi\) | |||||||
\(54\) | −2.32853 | −0.316873 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −15.0810 | −2.01528 | ||||||||
\(57\) | −9.57150 | −1.26778 | ||||||||
\(58\) | −16.2638 | −2.13555 | ||||||||
\(59\) | −4.38285 | −0.570599 | −0.285299 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285299 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(60\) | 10.0792 | 1.30121 | ||||||||
\(61\) | 2.23428 | 0.286070 | 0.143035 | − | 0.989718i | \(-0.454314\pi\) | ||||
0.143035 | + | 0.989718i | \(0.454314\pi\) | |||||||
\(62\) | −7.36471 | −0.935320 | ||||||||
\(63\) | −6.96494 | −0.877500 | ||||||||
\(64\) | −4.37682 | −0.547103 | ||||||||
\(65\) | 3.48435 | 0.432180 | ||||||||
\(66\) | 5.92283 | 0.729050 | ||||||||
\(67\) | 5.08973 | 0.621809 | 0.310905 | − | 0.950441i | \(-0.399368\pi\) | ||||
0.310905 | + | 0.950441i | \(0.399368\pi\) | |||||||
\(68\) | 18.9378 | 2.29655 | ||||||||
\(69\) | 13.1521 | 1.58333 | ||||||||
\(70\) | −6.68298 | −0.798769 | ||||||||
\(71\) | −3.91570 | −0.464708 | −0.232354 | − | 0.972631i | \(-0.574643\pi\) | ||||
−0.232354 | + | 0.972631i | \(0.574643\pi\) | |||||||
\(72\) | 14.7145 | 1.73412 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | 1.49163 | 0.173398 | ||||||||
\(75\) | 2.36788 | 0.273419 | ||||||||
\(76\) | −17.2062 | −1.97369 | ||||||||
\(77\) | −2.67178 | −0.304477 | ||||||||
\(78\) | 20.6372 | 2.33670 | ||||||||
\(79\) | −13.4294 | −1.51093 | −0.755464 | − | 0.655190i | \(-0.772589\pi\) | ||||
−0.755464 | + | 0.655190i | \(0.772589\pi\) | |||||||
\(80\) | 5.60558 | 0.626723 | ||||||||
\(81\) | −10.0249 | −1.11387 | ||||||||
\(82\) | 13.2315 | 1.46117 | ||||||||
\(83\) | 8.54660 | 0.938111 | 0.469055 | − | 0.883169i | \(-0.344594\pi\) | ||||
0.469055 | + | 0.883169i | \(0.344594\pi\) | |||||||
\(84\) | −26.9293 | −2.93823 | ||||||||
\(85\) | 4.44902 | 0.482564 | ||||||||
\(86\) | 16.5097 | 1.78028 | ||||||||
\(87\) | −15.3962 | −1.65064 | ||||||||
\(88\) | 5.64454 | 0.601710 | ||||||||
\(89\) | −14.7674 | −1.56534 | −0.782671 | − | 0.622436i | \(-0.786143\pi\) | ||||
−0.782671 | + | 0.622436i | \(0.786143\pi\) | |||||||
\(90\) | 6.52059 | 0.687330 | ||||||||
\(91\) | −9.30940 | −0.975891 | ||||||||
\(92\) | 23.6429 | 2.46495 | ||||||||
\(93\) | −6.97181 | −0.722943 | ||||||||
\(94\) | 0.431917 | 0.0445489 | ||||||||
\(95\) | −4.04223 | −0.414724 | ||||||||
\(96\) | 6.46972 | 0.660313 | ||||||||
\(97\) | −8.71708 | −0.885085 | −0.442543 | − | 0.896747i | \(-0.645924\pi\) | ||||
−0.442543 | + | 0.896747i | \(0.645924\pi\) | |||||||
\(98\) | 0.346188 | 0.0349703 | ||||||||
\(99\) | 2.60686 | 0.261999 | ||||||||
\(100\) | 4.25662 | 0.425662 | ||||||||
\(101\) | 3.41038 | 0.339346 | 0.169673 | − | 0.985500i | \(-0.445729\pi\) | ||||
0.169673 | + | 0.985500i | \(0.445729\pi\) | |||||||
\(102\) | 26.3508 | 2.60912 | ||||||||
\(103\) | −6.25577 | −0.616399 | −0.308200 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308200 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(104\) | 19.6675 | 1.92856 | ||||||||
\(105\) | −6.32645 | −0.617398 | ||||||||
\(106\) | −12.4012 | −1.20451 | ||||||||
\(107\) | −1.37862 | −0.133277 | −0.0666383 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666383 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(108\) | −3.96257 | −0.381299 | ||||||||
\(109\) | −16.4165 | −1.57242 | −0.786209 | − | 0.617961i | \(-0.787959\pi\) | ||||
−0.786209 | + | 0.617961i | \(0.787959\pi\) | |||||||
\(110\) | 2.50132 | 0.238492 | ||||||||
\(111\) | 1.41205 | 0.134026 | ||||||||
\(112\) | −14.9769 | −1.41518 | ||||||||
\(113\) | 16.6097 | 1.56251 | 0.781256 | − | 0.624211i | \(-0.214580\pi\) | ||||
0.781256 | + | 0.624211i | \(0.214580\pi\) | |||||||
\(114\) | −23.9414 | −2.24232 | ||||||||
\(115\) | 5.55439 | 0.517949 | ||||||||
\(116\) | −27.6770 | −2.56974 | ||||||||
\(117\) | 9.08319 | 0.839741 | ||||||||
\(118\) | −10.9629 | −1.00922 | ||||||||
\(119\) | −11.8868 | −1.08966 | ||||||||
\(120\) | 13.3656 | 1.22011 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.58866 | 0.505973 | ||||||||
\(123\) | 12.5256 | 1.12939 | ||||||||
\(124\) | −12.5329 | −1.12549 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −17.4216 | −1.55204 | ||||||||
\(127\) | 13.1896 | 1.17039 | 0.585195 | − | 0.810893i | \(-0.301018\pi\) | ||||
0.585195 | + | 0.810893i | \(0.301018\pi\) | |||||||
\(128\) | −16.4124 | −1.45067 | ||||||||
\(129\) | 15.6289 | 1.37605 | ||||||||
\(130\) | 8.71548 | 0.764398 | ||||||||
\(131\) | −7.70878 | −0.673519 | −0.336759 | − | 0.941591i | \(-0.609331\pi\) | ||||
−0.336759 | + | 0.941591i | \(0.609331\pi\) | |||||||
\(132\) | 10.0792 | 0.877279 | ||||||||
\(133\) | 10.7999 | 0.936473 | ||||||||
\(134\) | 12.7311 | 1.09980 | ||||||||
\(135\) | −0.930919 | −0.0801208 | ||||||||
\(136\) | 25.1127 | 2.15339 | ||||||||
\(137\) | 14.5083 | 1.23952 | 0.619762 | − | 0.784790i | \(-0.287229\pi\) | ||||
0.619762 | + | 0.784790i | \(0.287229\pi\) | |||||||
\(138\) | 32.8977 | 2.80044 | ||||||||
\(139\) | 7.51225 | 0.637181 | 0.318590 | − | 0.947892i | \(-0.396791\pi\) | ||||
0.318590 | + | 0.947892i | \(0.396791\pi\) | |||||||
\(140\) | −11.3727 | −0.961173 | ||||||||
\(141\) | 0.408875 | 0.0344335 | ||||||||
\(142\) | −9.79443 | −0.821930 | ||||||||
\(143\) | 3.48435 | 0.291376 | ||||||||
\(144\) | 14.6129 | 1.21774 | ||||||||
\(145\) | −6.50210 | −0.539970 | ||||||||
\(146\) | 2.50132 | 0.207011 | ||||||||
\(147\) | 0.327719 | 0.0270298 | ||||||||
\(148\) | 2.53837 | 0.208653 | ||||||||
\(149\) | −5.63280 | −0.461457 | −0.230729 | − | 0.973018i | \(-0.574111\pi\) | ||||
−0.230729 | + | 0.973018i | \(0.574111\pi\) | |||||||
\(150\) | 5.92283 | 0.483597 | ||||||||
\(151\) | 23.7457 | 1.93240 | 0.966198 | − | 0.257801i | \(-0.0829978\pi\) | ||||
0.966198 | + | 0.257801i | \(0.0829978\pi\) | |||||||
\(152\) | −22.8165 | −1.85066 | ||||||||
\(153\) | 11.5980 | 0.937639 | ||||||||
\(154\) | −6.68298 | −0.538530 | ||||||||
\(155\) | −2.94433 | −0.236494 | ||||||||
\(156\) | 35.1193 | 2.81180 | ||||||||
\(157\) | 3.40138 | 0.271459 | 0.135730 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135730 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(158\) | −33.5913 | −2.67238 | ||||||||
\(159\) | −11.7396 | −0.931009 | ||||||||
\(160\) | 2.73229 | 0.216006 | ||||||||
\(161\) | −14.8401 | −1.16956 | ||||||||
\(162\) | −25.0754 | −1.97011 | ||||||||
\(163\) | −3.18356 | −0.249356 | −0.124678 | − | 0.992197i | \(-0.539790\pi\) | ||||
−0.124678 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(164\) | 22.5166 | 1.75825 | ||||||||
\(165\) | 2.36788 | 0.184339 | ||||||||
\(166\) | 21.3778 | 1.65924 | ||||||||
\(167\) | 1.02167 | 0.0790589 | 0.0395294 | − | 0.999218i | \(-0.487414\pi\) | ||||
0.0395294 | + | 0.999218i | \(0.487414\pi\) | |||||||
\(168\) | −35.7099 | −2.75508 | ||||||||
\(169\) | −0.859326 | −0.0661020 | ||||||||
\(170\) | 11.1284 | 0.853513 | ||||||||
\(171\) | −10.5375 | −0.805823 | ||||||||
\(172\) | 28.0953 | 2.14225 | ||||||||
\(173\) | −3.26504 | −0.248237 | −0.124118 | − | 0.992267i | \(-0.539610\pi\) | ||||
−0.124118 | + | 0.992267i | \(0.539610\pi\) | |||||||
\(174\) | −38.5108 | −2.91950 | ||||||||
\(175\) | −2.67178 | −0.201967 | ||||||||
\(176\) | 5.60558 | 0.422536 | ||||||||
\(177\) | −10.3781 | −0.780063 | ||||||||
\(178\) | −36.9380 | −2.76862 | ||||||||
\(179\) | −16.6425 | −1.24392 | −0.621958 | − | 0.783051i | \(-0.713662\pi\) | ||||
−0.621958 | + | 0.783051i | \(0.713662\pi\) | |||||||
\(180\) | 11.0964 | 0.827076 | ||||||||
\(181\) | −5.99670 | −0.445731 | −0.222865 | − | 0.974849i | \(-0.571541\pi\) | ||||
−0.222865 | + | 0.974849i | \(0.571541\pi\) | |||||||
\(182\) | −23.2858 | −1.72606 | ||||||||
\(183\) | 5.29051 | 0.391085 | ||||||||
\(184\) | 31.3520 | 2.31130 | ||||||||
\(185\) | 0.596335 | 0.0438435 | ||||||||
\(186\) | −17.4388 | −1.27867 | ||||||||
\(187\) | 4.44902 | 0.325345 | ||||||||
\(188\) | 0.735014 | 0.0536064 | ||||||||
\(189\) | 2.48721 | 0.180918 | ||||||||
\(190\) | −10.1109 | −0.733523 | ||||||||
\(191\) | −20.7548 | −1.50177 | −0.750883 | − | 0.660436i | \(-0.770372\pi\) | ||||
−0.750883 | + | 0.660436i | \(0.770372\pi\) | |||||||
\(192\) | −10.3638 | −0.747942 | ||||||||
\(193\) | 10.8308 | 0.779619 | 0.389809 | − | 0.920896i | \(-0.372541\pi\) | ||||
0.389809 | + | 0.920896i | \(0.372541\pi\) | |||||||
\(194\) | −21.8042 | −1.56545 | ||||||||
\(195\) | 8.25052 | 0.590832 | ||||||||
\(196\) | 0.589125 | 0.0420803 | ||||||||
\(197\) | −7.69796 | −0.548457 | −0.274228 | − | 0.961665i | \(-0.588422\pi\) | ||||
−0.274228 | + | 0.961665i | \(0.588422\pi\) | |||||||
\(198\) | 6.52059 | 0.463398 | ||||||||
\(199\) | −14.1572 | −1.00358 | −0.501790 | − | 0.864990i | \(-0.667325\pi\) | ||||
−0.501790 | + | 0.864990i | \(0.667325\pi\) | |||||||
\(200\) | 5.64454 | 0.399129 | ||||||||
\(201\) | 12.0519 | 0.850073 | ||||||||
\(202\) | 8.53047 | 0.600202 | ||||||||
\(203\) | 17.3722 | 1.21929 | ||||||||
\(204\) | 44.8424 | 3.13960 | ||||||||
\(205\) | 5.28979 | 0.369455 | ||||||||
\(206\) | −15.6477 | −1.09023 | ||||||||
\(207\) | 14.4795 | 1.00639 | ||||||||
\(208\) | 19.5318 | 1.35428 | ||||||||
\(209\) | −4.04223 | −0.279607 | ||||||||
\(210\) | −15.8245 | −1.09199 | ||||||||
\(211\) | 25.0038 | 1.72134 | 0.860668 | − | 0.509167i | \(-0.170046\pi\) | ||||
0.860668 | + | 0.509167i | \(0.170046\pi\) | |||||||
\(212\) | −21.1037 | −1.44941 | ||||||||
\(213\) | −9.27190 | −0.635300 | ||||||||
\(214\) | −3.44838 | −0.235727 | ||||||||
\(215\) | 6.60038 | 0.450142 | ||||||||
\(216\) | −5.25461 | −0.357531 | ||||||||
\(217\) | 7.86659 | 0.534019 | ||||||||
\(218\) | −41.0630 | −2.78114 | ||||||||
\(219\) | 2.36788 | 0.160006 | ||||||||
\(220\) | 4.25662 | 0.286981 | ||||||||
\(221\) | 15.5019 | 1.04277 | ||||||||
\(222\) | 3.53200 | 0.237052 | ||||||||
\(223\) | −21.8292 | −1.46179 | −0.730896 | − | 0.682489i | \(-0.760898\pi\) | ||||
−0.730896 | + | 0.682489i | \(0.760898\pi\) | |||||||
\(224\) | −7.30006 | −0.487756 | ||||||||
\(225\) | 2.60686 | 0.173790 | ||||||||
\(226\) | 41.5463 | 2.76362 | ||||||||
\(227\) | 27.1837 | 1.80425 | 0.902124 | − | 0.431477i | \(-0.142007\pi\) | ||||
0.902124 | + | 0.431477i | \(0.142007\pi\) | |||||||
\(228\) | −40.7423 | −2.69822 | ||||||||
\(229\) | 10.0624 | 0.664940 | 0.332470 | − | 0.943114i | \(-0.392118\pi\) | ||||
0.332470 | + | 0.943114i | \(0.392118\pi\) | |||||||
\(230\) | 13.8933 | 0.916099 | ||||||||
\(231\) | −6.32645 | −0.416250 | ||||||||
\(232\) | −36.7013 | −2.40956 | ||||||||
\(233\) | −25.0994 | −1.64431 | −0.822157 | − | 0.569261i | \(-0.807229\pi\) | ||||
−0.822157 | + | 0.569261i | \(0.807229\pi\) | |||||||
\(234\) | 22.7200 | 1.48525 | ||||||||
\(235\) | 0.172675 | 0.0112641 | ||||||||
\(236\) | −18.6561 | −1.21441 | ||||||||
\(237\) | −31.7993 | −2.06558 | ||||||||
\(238\) | −29.7327 | −1.92729 | ||||||||
\(239\) | −12.8094 | −0.828571 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(240\) | 13.2733 | 0.856790 | ||||||||
\(241\) | 13.3242 | 0.858287 | 0.429143 | − | 0.903236i | \(-0.358816\pi\) | ||||
0.429143 | + | 0.903236i | \(0.358816\pi\) | |||||||
\(242\) | 2.50132 | 0.160791 | ||||||||
\(243\) | −20.9449 | −1.34362 | ||||||||
\(244\) | 9.51048 | 0.608846 | ||||||||
\(245\) | 0.138402 | 0.00884218 | ||||||||
\(246\) | 31.3306 | 1.99756 | ||||||||
\(247\) | −14.0845 | −0.896176 | ||||||||
\(248\) | −16.6194 | −1.05533 | ||||||||
\(249\) | 20.2373 | 1.28249 | ||||||||
\(250\) | 2.50132 | 0.158198 | ||||||||
\(251\) | −28.6688 | −1.80956 | −0.904779 | − | 0.425882i | \(-0.859964\pi\) | ||||
−0.904779 | + | 0.425882i | \(0.859964\pi\) | |||||||
\(252\) | −29.6471 | −1.86759 | ||||||||
\(253\) | 5.55439 | 0.349201 | ||||||||
\(254\) | 32.9915 | 2.07007 | ||||||||
\(255\) | 10.5348 | 0.659712 | ||||||||
\(256\) | −32.2991 | −2.01870 | ||||||||
\(257\) | 2.19515 | 0.136929 | 0.0684647 | − | 0.997654i | \(-0.478190\pi\) | ||||
0.0684647 | + | 0.997654i | \(0.478190\pi\) | |||||||
\(258\) | 39.0929 | 2.43382 | ||||||||
\(259\) | −1.59328 | −0.0990014 | ||||||||
\(260\) | 14.8315 | 0.919813 | ||||||||
\(261\) | −16.9500 | −1.04918 | ||||||||
\(262\) | −19.2821 | −1.19125 | ||||||||
\(263\) | 16.1810 | 0.997762 | 0.498881 | − | 0.866670i | \(-0.333744\pi\) | ||||
0.498881 | + | 0.866670i | \(0.333744\pi\) | |||||||
\(264\) | 13.3656 | 0.822595 | ||||||||
\(265\) | −4.95784 | −0.304558 | ||||||||
\(266\) | 27.0141 | 1.65634 | ||||||||
\(267\) | −34.9674 | −2.13997 | ||||||||
\(268\) | 21.6650 | 1.32340 | ||||||||
\(269\) | 7.76730 | 0.473581 | 0.236790 | − | 0.971561i | \(-0.423905\pi\) | ||||
0.236790 | + | 0.971561i | \(0.423905\pi\) | |||||||
\(270\) | −2.32853 | −0.141710 | ||||||||
\(271\) | 12.9838 | 0.788709 | 0.394354 | − | 0.918958i | \(-0.370968\pi\) | ||||
0.394354 | + | 0.918958i | \(0.370968\pi\) | |||||||
\(272\) | 24.9393 | 1.51217 | ||||||||
\(273\) | −22.0436 | −1.33414 | ||||||||
\(274\) | 36.2899 | 2.19235 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 55.9836 | 3.36982 | ||||||||
\(277\) | 0.491802 | 0.0295495 | 0.0147747 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147747 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(278\) | 18.7906 | 1.12698 | ||||||||
\(279\) | −7.67543 | −0.459516 | ||||||||
\(280\) | −15.0810 | −0.901260 | ||||||||
\(281\) | −2.87378 | −0.171435 | −0.0857177 | − | 0.996319i | \(-0.527318\pi\) | ||||
−0.0857177 | + | 0.996319i | \(0.527318\pi\) | |||||||
\(282\) | 1.02273 | 0.0609026 | ||||||||
\(283\) | −30.8900 | −1.83622 | −0.918111 | − | 0.396324i | \(-0.870286\pi\) | ||||
−0.918111 | + | 0.396324i | \(0.870286\pi\) | |||||||
\(284\) | −16.6676 | −0.989042 | ||||||||
\(285\) | −9.57150 | −0.566967 | ||||||||
\(286\) | 8.71548 | 0.515357 | ||||||||
\(287\) | −14.1332 | −0.834254 | ||||||||
\(288\) | 7.12267 | 0.419708 | ||||||||
\(289\) | 2.79380 | 0.164341 | ||||||||
\(290\) | −16.2638 | −0.955046 | ||||||||
\(291\) | −20.6410 | −1.21000 | ||||||||
\(292\) | 4.25662 | 0.249100 | ||||||||
\(293\) | 26.4906 | 1.54760 | 0.773800 | − | 0.633430i | \(-0.218354\pi\) | ||||
0.773800 | + | 0.633430i | \(0.218354\pi\) | |||||||
\(294\) | 0.819732 | 0.0478077 | ||||||||
\(295\) | −4.38285 | −0.255179 | ||||||||
\(296\) | 3.36604 | 0.195647 | ||||||||
\(297\) | −0.930919 | −0.0540174 | ||||||||
\(298\) | −14.0895 | −0.816181 | ||||||||
\(299\) | 19.3534 | 1.11924 | ||||||||
\(300\) | 10.0792 | 0.581921 | ||||||||
\(301\) | −17.6347 | −1.01645 | ||||||||
\(302\) | 59.3956 | 3.41783 | ||||||||
\(303\) | 8.07537 | 0.463918 | ||||||||
\(304\) | −22.6590 | −1.29958 | ||||||||
\(305\) | 2.23428 | 0.127934 | ||||||||
\(306\) | 29.0102 | 1.65841 | ||||||||
\(307\) | −22.5586 | −1.28749 | −0.643744 | − | 0.765241i | \(-0.722620\pi\) | ||||
−0.643744 | + | 0.765241i | \(0.722620\pi\) | |||||||
\(308\) | −11.3727 | −0.648022 | ||||||||
\(309\) | −14.8129 | −0.842677 | ||||||||
\(310\) | −7.36471 | −0.418288 | ||||||||
\(311\) | −2.62013 | −0.148574 | −0.0742870 | − | 0.997237i | \(-0.523668\pi\) | ||||
−0.0742870 | + | 0.997237i | \(0.523668\pi\) | |||||||
\(312\) | 46.5703 | 2.63653 | ||||||||
\(313\) | 23.8061 | 1.34560 | 0.672799 | − | 0.739826i | \(-0.265092\pi\) | ||||
0.672799 | + | 0.739826i | \(0.265092\pi\) | |||||||
\(314\) | 8.50795 | 0.480131 | ||||||||
\(315\) | −6.96494 | −0.392430 | ||||||||
\(316\) | −57.1640 | −3.21572 | ||||||||
\(317\) | −0.622469 | −0.0349613 | −0.0174807 | − | 0.999847i | \(-0.505565\pi\) | ||||
−0.0174807 | + | 0.999847i | \(0.505565\pi\) | |||||||
\(318\) | −29.3645 | −1.64668 | ||||||||
\(319\) | −6.50210 | −0.364048 | ||||||||
\(320\) | −4.37682 | −0.244672 | ||||||||
\(321\) | −3.26442 | −0.182202 | ||||||||
\(322\) | −37.1199 | −2.06861 | ||||||||
\(323\) | −17.9840 | −1.00065 | ||||||||
\(324\) | −42.6721 | −2.37067 | ||||||||
\(325\) | 3.48435 | 0.193277 | ||||||||
\(326\) | −7.96311 | −0.441036 | ||||||||
\(327\) | −38.8724 | −2.14965 | ||||||||
\(328\) | 29.8584 | 1.64866 | ||||||||
\(329\) | −0.461351 | −0.0254351 | ||||||||
\(330\) | 5.92283 | 0.326041 | ||||||||
\(331\) | −4.85370 | −0.266784 | −0.133392 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133392 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(332\) | 36.3796 | 1.99659 | ||||||||
\(333\) | 1.55456 | 0.0851894 | ||||||||
\(334\) | 2.55552 | 0.139832 | ||||||||
\(335\) | 5.08973 | 0.278081 | ||||||||
\(336\) | −35.4634 | −1.93469 | ||||||||
\(337\) | 16.4423 | 0.895668 | 0.447834 | − | 0.894117i | \(-0.352196\pi\) | ||||
0.447834 | + | 0.894117i | \(0.352196\pi\) | |||||||
\(338\) | −2.14945 | −0.116915 | ||||||||
\(339\) | 39.3298 | 2.13610 | ||||||||
\(340\) | 18.9378 | 1.02705 | ||||||||
\(341\) | −2.94433 | −0.159444 | ||||||||
\(342\) | −26.3577 | −1.42526 | ||||||||
\(343\) | 18.3327 | 0.989871 | ||||||||
\(344\) | 37.2561 | 2.00871 | ||||||||
\(345\) | 13.1521 | 0.708087 | ||||||||
\(346\) | −8.16693 | −0.439057 | ||||||||
\(347\) | −24.8517 | −1.33411 | −0.667056 | − | 0.745008i | \(-0.732446\pi\) | ||||
−0.667056 | + | 0.745008i | \(0.732446\pi\) | |||||||
\(348\) | −65.5357 | −3.51308 | ||||||||
\(349\) | −7.61793 | −0.407778 | −0.203889 | − | 0.978994i | \(-0.565358\pi\) | ||||
−0.203889 | + | 0.978994i | \(0.565358\pi\) | |||||||
\(350\) | −6.68298 | −0.357221 | ||||||||
\(351\) | −3.24365 | −0.173133 | ||||||||
\(352\) | 2.73229 | 0.145631 | ||||||||
\(353\) | 13.6194 | 0.724885 | 0.362443 | − | 0.932006i | \(-0.381943\pi\) | ||||
0.362443 | + | 0.932006i | \(0.381943\pi\) | |||||||
\(354\) | −25.9589 | −1.37970 | ||||||||
\(355\) | −3.91570 | −0.207824 | ||||||||
\(356\) | −62.8592 | −3.33153 | ||||||||
\(357\) | −28.1465 | −1.48967 | ||||||||
\(358\) | −41.6282 | −2.20012 | ||||||||
\(359\) | −22.6034 | −1.19296 | −0.596481 | − | 0.802627i | \(-0.703435\pi\) | ||||
−0.596481 | + | 0.802627i | \(0.703435\pi\) | |||||||
\(360\) | 14.7145 | 0.775522 | ||||||||
\(361\) | −2.66041 | −0.140022 | ||||||||
\(362\) | −14.9997 | −0.788366 | ||||||||
\(363\) | 2.36788 | 0.124281 | ||||||||
\(364\) | −39.6266 | −2.07700 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 13.2333 | 0.691714 | ||||||||
\(367\) | 1.63669 | 0.0854346 | 0.0427173 | − | 0.999087i | \(-0.486399\pi\) | ||||
0.0427173 | + | 0.999087i | \(0.486399\pi\) | |||||||
\(368\) | 31.1356 | 1.62305 | ||||||||
\(369\) | 13.7897 | 0.717864 | ||||||||
\(370\) | 1.49163 | 0.0775461 | ||||||||
\(371\) | 13.2463 | 0.687712 | ||||||||
\(372\) | −29.6764 | −1.53865 | ||||||||
\(373\) | 7.41370 | 0.383867 | 0.191934 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191934 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(374\) | 11.1284 | 0.575438 | ||||||||
\(375\) | 2.36788 | 0.122277 | ||||||||
\(376\) | 0.974673 | 0.0502649 | ||||||||
\(377\) | −22.6556 | −1.16682 | ||||||||
\(378\) | 6.22132 | 0.319990 | ||||||||
\(379\) | 17.7378 | 0.911132 | 0.455566 | − | 0.890202i | \(-0.349437\pi\) | ||||
0.455566 | + | 0.890202i | \(0.349437\pi\) | |||||||
\(380\) | −17.2062 | −0.882660 | ||||||||
\(381\) | 31.2314 | 1.60003 | ||||||||
\(382\) | −51.9145 | −2.65618 | ||||||||
\(383\) | −15.0193 | −0.767449 | −0.383725 | − | 0.923448i | \(-0.625359\pi\) | ||||
−0.383725 | + | 0.923448i | \(0.625359\pi\) | |||||||
\(384\) | −38.8626 | −1.98320 | ||||||||
\(385\) | −2.67178 | −0.136166 | ||||||||
\(386\) | 27.0914 | 1.37891 | ||||||||
\(387\) | 17.2062 | 0.874642 | ||||||||
\(388\) | −37.1053 | −1.88374 | ||||||||
\(389\) | 29.6042 | 1.50099 | 0.750495 | − | 0.660876i | \(-0.229815\pi\) | ||||
0.750495 | + | 0.660876i | \(0.229815\pi\) | |||||||
\(390\) | 20.6372 | 1.04501 | ||||||||
\(391\) | 24.7116 | 1.24972 | ||||||||
\(392\) | 0.781215 | 0.0394573 | ||||||||
\(393\) | −18.2535 | −0.920765 | ||||||||
\(394\) | −19.2551 | −0.970057 | ||||||||
\(395\) | −13.4294 | −0.675708 | ||||||||
\(396\) | 11.0964 | 0.557615 | ||||||||
\(397\) | 15.9367 | 0.799838 | 0.399919 | − | 0.916550i | \(-0.369038\pi\) | ||||
0.399919 | + | 0.916550i | \(0.369038\pi\) | |||||||
\(398\) | −35.4118 | −1.77503 | ||||||||
\(399\) | 25.5729 | 1.28025 | ||||||||
\(400\) | 5.60558 | 0.280279 | ||||||||
\(401\) | −2.46612 | −0.123152 | −0.0615762 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615762 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(402\) | 30.1456 | 1.50353 | ||||||||
\(403\) | −10.2591 | −0.511040 | ||||||||
\(404\) | 14.5167 | 0.722233 | ||||||||
\(405\) | −10.0249 | −0.498140 | ||||||||
\(406\) | 43.4534 | 2.15656 | ||||||||
\(407\) | 0.596335 | 0.0295593 | ||||||||
\(408\) | 59.4638 | 2.94390 | ||||||||
\(409\) | −0.380219 | −0.0188006 | −0.00940030 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00940030 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(410\) | 13.2315 | 0.653457 | ||||||||
\(411\) | 34.3538 | 1.69455 | ||||||||
\(412\) | −26.6284 | −1.31189 | ||||||||
\(413\) | 11.7100 | 0.576212 | ||||||||
\(414\) | 36.2179 | 1.78001 | ||||||||
\(415\) | 8.54660 | 0.419536 | ||||||||
\(416\) | 9.52023 | 0.466768 | ||||||||
\(417\) | 17.7881 | 0.871087 | ||||||||
\(418\) | −10.1109 | −0.494541 | ||||||||
\(419\) | −26.5584 | −1.29747 | −0.648733 | − | 0.761017i | \(-0.724701\pi\) | ||||
−0.648733 | + | 0.761017i | \(0.724701\pi\) | |||||||
\(420\) | −26.9293 | −1.31402 | ||||||||
\(421\) | 17.2515 | 0.840785 | 0.420392 | − | 0.907342i | \(-0.361892\pi\) | ||||
0.420392 | + | 0.907342i | \(0.361892\pi\) | |||||||
\(422\) | 62.5427 | 3.04453 | ||||||||
\(423\) | 0.450140 | 0.0218866 | ||||||||
\(424\) | −27.9847 | −1.35906 | ||||||||
\(425\) | 4.44902 | 0.215809 | ||||||||
\(426\) | −23.1920 | −1.12366 | ||||||||
\(427\) | −5.96950 | −0.288884 | ||||||||
\(428\) | −5.86828 | −0.283654 | ||||||||
\(429\) | 8.25052 | 0.398339 | ||||||||
\(430\) | 16.5097 | 0.796167 | ||||||||
\(431\) | −1.65671 | −0.0798008 | −0.0399004 | − | 0.999204i | \(-0.512704\pi\) | ||||
−0.0399004 | + | 0.999204i | \(0.512704\pi\) | |||||||
\(432\) | −5.21834 | −0.251068 | ||||||||
\(433\) | 14.4053 | 0.692273 | 0.346136 | − | 0.938184i | \(-0.387493\pi\) | ||||
0.346136 | + | 0.938184i | \(0.387493\pi\) | |||||||
\(434\) | 19.6769 | 0.944521 | ||||||||
\(435\) | −15.3962 | −0.738191 | ||||||||
\(436\) | −69.8789 | −3.34659 | ||||||||
\(437\) | −22.4521 | −1.07403 | ||||||||
\(438\) | 5.92283 | 0.283004 | ||||||||
\(439\) | 22.8919 | 1.09257 | 0.546284 | − | 0.837600i | \(-0.316042\pi\) | ||||
0.546284 | + | 0.837600i | \(0.316042\pi\) | |||||||
\(440\) | 5.64454 | 0.269093 | ||||||||
\(441\) | 0.360794 | 0.0171807 | ||||||||
\(442\) | 38.7754 | 1.84436 | ||||||||
\(443\) | 12.0384 | 0.571960 | 0.285980 | − | 0.958236i | \(-0.407681\pi\) | ||||
0.285980 | + | 0.958236i | \(0.407681\pi\) | |||||||
\(444\) | 6.01056 | 0.285249 | ||||||||
\(445\) | −14.7674 | −0.700042 | ||||||||
\(446\) | −54.6019 | −2.58548 | ||||||||
\(447\) | −13.3378 | −0.630856 | ||||||||
\(448\) | 11.6939 | 0.552485 | ||||||||
\(449\) | 26.2517 | 1.23889 | 0.619447 | − | 0.785039i | \(-0.287357\pi\) | ||||
0.619447 | + | 0.785039i | \(0.287357\pi\) | |||||||
\(450\) | 6.52059 | 0.307384 | ||||||||
\(451\) | 5.28979 | 0.249087 | ||||||||
\(452\) | 70.7013 | 3.32551 | ||||||||
\(453\) | 56.2269 | 2.64177 | ||||||||
\(454\) | 67.9953 | 3.19118 | ||||||||
\(455\) | −9.30940 | −0.436432 | ||||||||
\(456\) | −54.0267 | −2.53003 | ||||||||
\(457\) | −1.85069 | −0.0865716 | −0.0432858 | − | 0.999063i | \(-0.513783\pi\) | ||||
−0.0432858 | + | 0.999063i | \(0.513783\pi\) | |||||||
\(458\) | 25.1693 | 1.17608 | ||||||||
\(459\) | −4.14168 | −0.193317 | ||||||||
\(460\) | 23.6429 | 1.10236 | ||||||||
\(461\) | −36.6237 | −1.70573 | −0.852867 | − | 0.522129i | \(-0.825138\pi\) | ||||
−0.852867 | + | 0.522129i | \(0.825138\pi\) | |||||||
\(462\) | −15.8245 | −0.736223 | ||||||||
\(463\) | −15.6303 | −0.726403 | −0.363202 | − | 0.931711i | \(-0.618316\pi\) | ||||
−0.363202 | + | 0.931711i | \(0.618316\pi\) | |||||||
\(464\) | −36.4480 | −1.69206 | ||||||||
\(465\) | −6.97181 | −0.323310 | ||||||||
\(466\) | −62.7816 | −2.90830 | ||||||||
\(467\) | 15.8465 | 0.733288 | 0.366644 | − | 0.930361i | \(-0.380507\pi\) | ||||
0.366644 | + | 0.930361i | \(0.380507\pi\) | |||||||
\(468\) | 38.6637 | 1.78723 | ||||||||
\(469\) | −13.5986 | −0.627926 | ||||||||
\(470\) | 0.431917 | 0.0199229 | ||||||||
\(471\) | 8.05405 | 0.371111 | ||||||||
\(472\) | −24.7392 | −1.13871 | ||||||||
\(473\) | 6.60038 | 0.303486 | ||||||||
\(474\) | −79.5403 | −3.65340 | ||||||||
\(475\) | −4.04223 | −0.185470 | ||||||||
\(476\) | −50.5976 | −2.31914 | ||||||||
\(477\) | −12.9244 | −0.591767 | ||||||||
\(478\) | −32.0405 | −1.46550 | ||||||||
\(479\) | 33.3439 | 1.52352 | 0.761761 | − | 0.647858i | \(-0.224335\pi\) | ||||
0.761761 | + | 0.647858i | \(0.224335\pi\) | |||||||
\(480\) | 6.46972 | 0.295301 | ||||||||
\(481\) | 2.07784 | 0.0947413 | ||||||||
\(482\) | 33.3281 | 1.51805 | ||||||||
\(483\) | −35.1396 | −1.59891 | ||||||||
\(484\) | 4.25662 | 0.193483 | ||||||||
\(485\) | −8.71708 | −0.395822 | ||||||||
\(486\) | −52.3901 | −2.37646 | ||||||||
\(487\) | −16.7072 | −0.757073 | −0.378537 | − | 0.925586i | \(-0.623573\pi\) | ||||
−0.378537 | + | 0.925586i | \(0.623573\pi\) | |||||||
\(488\) | 12.6115 | 0.570895 | ||||||||
\(489\) | −7.53829 | −0.340893 | ||||||||
\(490\) | 0.346188 | 0.0156392 | ||||||||
\(491\) | −23.4179 | −1.05684 | −0.528418 | − | 0.848984i | \(-0.677215\pi\) | ||||
−0.528418 | + | 0.848984i | \(0.677215\pi\) | |||||||
\(492\) | 53.3167 | 2.40370 | ||||||||
\(493\) | −28.9280 | −1.30285 | ||||||||
\(494\) | −35.2299 | −1.58507 | ||||||||
\(495\) | 2.60686 | 0.117169 | ||||||||
\(496\) | −16.5046 | −0.741081 | ||||||||
\(497\) | 10.4619 | 0.469279 | ||||||||
\(498\) | 50.6201 | 2.26834 | ||||||||
\(499\) | 32.7713 | 1.46704 | 0.733522 | − | 0.679665i | \(-0.237875\pi\) | ||||
0.733522 | + | 0.679665i | \(0.237875\pi\) | |||||||
\(500\) | 4.25662 | 0.190362 | ||||||||
\(501\) | 2.41918 | 0.108081 | ||||||||
\(502\) | −71.7099 | −3.20057 | ||||||||
\(503\) | 24.2802 | 1.08260 | 0.541301 | − | 0.840829i | \(-0.317932\pi\) | ||||
0.541301 | + | 0.840829i | \(0.317932\pi\) | |||||||
\(504\) | −39.3139 | −1.75118 | ||||||||
\(505\) | 3.41038 | 0.151760 | ||||||||
\(506\) | 13.8933 | 0.617634 | ||||||||
\(507\) | −2.03478 | −0.0903678 | ||||||||
\(508\) | 56.1432 | 2.49095 | ||||||||
\(509\) | 1.11035 | 0.0492154 | 0.0246077 | − | 0.999697i | \(-0.492166\pi\) | ||||
0.0246077 | + | 0.999697i | \(0.492166\pi\) | |||||||
\(510\) | 26.3508 | 1.16683 | ||||||||
\(511\) | −2.67178 | −0.118193 | ||||||||
\(512\) | −47.9657 | −2.11981 | ||||||||
\(513\) | 3.76299 | 0.166140 | ||||||||
\(514\) | 5.49077 | 0.242188 | ||||||||
\(515\) | −6.25577 | −0.275662 | ||||||||
\(516\) | 66.5263 | 2.92866 | ||||||||
\(517\) | 0.172675 | 0.00759426 | ||||||||
\(518\) | −3.98530 | −0.175104 | ||||||||
\(519\) | −7.73123 | −0.339363 | ||||||||
\(520\) | 19.6675 | 0.862478 | ||||||||
\(521\) | 15.8674 | 0.695162 | 0.347581 | − | 0.937650i | \(-0.387003\pi\) | ||||
0.347581 | + | 0.937650i | \(0.387003\pi\) | |||||||
\(522\) | −42.3975 | −1.85569 | ||||||||
\(523\) | −18.3366 | −0.801802 | −0.400901 | − | 0.916121i | \(-0.631303\pi\) | ||||
−0.400901 | + | 0.916121i | \(0.631303\pi\) | |||||||
\(524\) | −32.8133 | −1.43346 | ||||||||
\(525\) | −6.32645 | −0.276109 | ||||||||
\(526\) | 40.4739 | 1.76475 | ||||||||
\(527\) | −13.0994 | −0.570618 | ||||||||
\(528\) | 13.2733 | 0.577648 | ||||||||
\(529\) | 7.85123 | 0.341358 | ||||||||
\(530\) | −12.4012 | −0.538672 | ||||||||
\(531\) | −11.4255 | −0.495823 | ||||||||
\(532\) | 45.9712 | 1.99310 | ||||||||
\(533\) | 18.4315 | 0.798356 | ||||||||
\(534\) | −87.4649 | −3.78497 | ||||||||
\(535\) | −1.37862 | −0.0596031 | ||||||||
\(536\) | 28.7292 | 1.24091 | ||||||||
\(537\) | −39.4073 | −1.70055 | ||||||||
\(538\) | 19.4285 | 0.837624 | ||||||||
\(539\) | 0.138402 | 0.00596140 | ||||||||
\(540\) | −3.96257 | −0.170522 | ||||||||
\(541\) | 16.2518 | 0.698721 | 0.349360 | − | 0.936988i | \(-0.386399\pi\) | ||||
0.349360 | + | 0.936988i | \(0.386399\pi\) | |||||||
\(542\) | 32.4766 | 1.39499 | ||||||||
\(543\) | −14.1995 | −0.609357 | ||||||||
\(544\) | 12.1560 | 0.521184 | ||||||||
\(545\) | −16.4165 | −0.703207 | ||||||||
\(546\) | −55.1381 | −2.35969 | ||||||||
\(547\) | 3.90807 | 0.167097 | 0.0835485 | − | 0.996504i | \(-0.473375\pi\) | ||||
0.0835485 | + | 0.996504i | \(0.473375\pi\) | |||||||
\(548\) | 61.7562 | 2.63809 | ||||||||
\(549\) | 5.82444 | 0.248581 | ||||||||
\(550\) | 2.50132 | 0.106657 | ||||||||
\(551\) | 26.2829 | 1.11969 | ||||||||
\(552\) | 74.2377 | 3.15977 | ||||||||
\(553\) | 35.8805 | 1.52579 | ||||||||
\(554\) | 1.23015 | 0.0522643 | ||||||||
\(555\) | 1.41205 | 0.0599382 | ||||||||
\(556\) | 31.9768 | 1.35612 | ||||||||
\(557\) | 19.2238 | 0.814540 | 0.407270 | − | 0.913308i | \(-0.366481\pi\) | ||||
0.407270 | + | 0.913308i | \(0.366481\pi\) | |||||||
\(558\) | −19.1987 | −0.812748 | ||||||||
\(559\) | 22.9980 | 0.972712 | ||||||||
\(560\) | −14.9769 | −0.632888 | ||||||||
\(561\) | 10.5348 | 0.444778 | ||||||||
\(562\) | −7.18826 | −0.303218 | ||||||||
\(563\) | 6.97074 | 0.293782 | 0.146891 | − | 0.989153i | \(-0.453073\pi\) | ||||
0.146891 | + | 0.989153i | \(0.453073\pi\) | |||||||
\(564\) | 1.74042 | 0.0732851 | ||||||||
\(565\) | 16.6097 | 0.698776 | ||||||||
\(566\) | −77.2660 | −3.24773 | ||||||||
\(567\) | 26.7842 | 1.12483 | ||||||||
\(568\) | −22.1023 | −0.927392 | ||||||||
\(569\) | 40.8739 | 1.71352 | 0.856761 | − | 0.515714i | \(-0.172473\pi\) | ||||
0.856761 | + | 0.515714i | \(0.172473\pi\) | |||||||
\(570\) | −23.9414 | −1.00280 | ||||||||
\(571\) | 37.0955 | 1.55240 | 0.776199 | − | 0.630488i | \(-0.217145\pi\) | ||||
0.776199 | + | 0.630488i | \(0.217145\pi\) | |||||||
\(572\) | 14.8315 | 0.620138 | ||||||||
\(573\) | −49.1449 | −2.05306 | ||||||||
\(574\) | −35.3516 | −1.47555 | ||||||||
\(575\) | 5.55439 | 0.231634 | ||||||||
\(576\) | −11.4097 | −0.475406 | ||||||||
\(577\) | −10.1569 | −0.422838 | −0.211419 | − | 0.977396i | \(-0.567808\pi\) | ||||
−0.211419 | + | 0.977396i | \(0.567808\pi\) | |||||||
\(578\) | 6.98821 | 0.290671 | ||||||||
\(579\) | 25.6461 | 1.06581 | ||||||||
\(580\) | −27.6770 | −1.14922 | ||||||||
\(581\) | −22.8346 | −0.947339 | ||||||||
\(582\) | −51.6298 | −2.14013 | ||||||||
\(583\) | −4.95784 | −0.205333 | ||||||||
\(584\) | 5.64454 | 0.233573 | ||||||||
\(585\) | 9.08319 | 0.375544 | ||||||||
\(586\) | 66.2617 | 2.73724 | ||||||||
\(587\) | 22.4289 | 0.925739 | 0.462870 | − | 0.886426i | \(-0.346820\pi\) | ||||
0.462870 | + | 0.886426i | \(0.346820\pi\) | |||||||
\(588\) | 1.39498 | 0.0575279 | ||||||||
\(589\) | 11.9016 | 0.490398 | ||||||||
\(590\) | −10.9629 | −0.451337 | ||||||||
\(591\) | −18.2278 | −0.749793 | ||||||||
\(592\) | 3.34280 | 0.137388 | ||||||||
\(593\) | 37.6348 | 1.54547 | 0.772737 | − | 0.634726i | \(-0.218887\pi\) | ||||
0.772737 | + | 0.634726i | \(0.218887\pi\) | |||||||
\(594\) | −2.32853 | −0.0955408 | ||||||||
\(595\) | −11.8868 | −0.487311 | ||||||||
\(596\) | −23.9767 | −0.982124 | ||||||||
\(597\) | −33.5226 | −1.37199 | ||||||||
\(598\) | 48.4092 | 1.97960 | ||||||||
\(599\) | −27.0934 | −1.10701 | −0.553504 | − | 0.832846i | \(-0.686710\pi\) | ||||
−0.553504 | + | 0.832846i | \(0.686710\pi\) | |||||||
\(600\) | 13.3656 | 0.545648 | ||||||||
\(601\) | −2.74515 | −0.111977 | −0.0559884 | − | 0.998431i | \(-0.517831\pi\) | ||||
−0.0559884 | + | 0.998431i | \(0.517831\pi\) | |||||||
\(602\) | −44.1102 | −1.79780 | ||||||||
\(603\) | 13.2682 | 0.540322 | ||||||||
\(604\) | 101.076 | 4.11274 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 20.1991 | 0.820533 | ||||||||
\(607\) | 21.4316 | 0.869882 | 0.434941 | − | 0.900459i | \(-0.356769\pi\) | ||||
0.434941 | + | 0.900459i | \(0.356769\pi\) | |||||||
\(608\) | −11.0445 | −0.447914 | ||||||||
\(609\) | 41.1352 | 1.66688 | ||||||||
\(610\) | 5.58866 | 0.226278 | ||||||||
\(611\) | 0.601661 | 0.0243406 | ||||||||
\(612\) | 49.3681 | 1.99559 | ||||||||
\(613\) | 16.6985 | 0.674445 | 0.337222 | − | 0.941425i | \(-0.390513\pi\) | ||||
0.337222 | + | 0.941425i | \(0.390513\pi\) | |||||||
\(614\) | −56.4264 | −2.27718 | ||||||||
\(615\) | 12.5256 | 0.505081 | ||||||||
\(616\) | −15.0810 | −0.607629 | ||||||||
\(617\) | 18.1662 | 0.731345 | 0.365673 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365673 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(618\) | −37.0519 | −1.49045 | ||||||||
\(619\) | −28.5098 | −1.14590 | −0.572952 | − | 0.819589i | \(-0.694202\pi\) | ||||
−0.572952 | + | 0.819589i | \(0.694202\pi\) | |||||||
\(620\) | −12.5329 | −0.503333 | ||||||||
\(621\) | −5.17069 | −0.207493 | ||||||||
\(622\) | −6.55380 | −0.262783 | ||||||||
\(623\) | 39.4552 | 1.58074 | ||||||||
\(624\) | 46.2489 | 1.85144 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 59.5466 | 2.37996 | ||||||||
\(627\) | −9.57150 | −0.382249 | ||||||||
\(628\) | 14.4784 | 0.577750 | ||||||||
\(629\) | 2.65311 | 0.105786 | ||||||||
\(630\) | −17.4216 | −0.694092 | ||||||||
\(631\) | 35.0244 | 1.39430 | 0.697149 | − | 0.716926i | \(-0.254452\pi\) | ||||
0.697149 | + | 0.716926i | \(0.254452\pi\) | |||||||
\(632\) | −75.8029 | −3.01528 | ||||||||
\(633\) | 59.2061 | 2.35323 | ||||||||
\(634\) | −1.55700 | −0.0618362 | ||||||||
\(635\) | 13.1896 | 0.523414 | ||||||||
\(636\) | −49.9709 | −1.98148 | ||||||||
\(637\) | 0.482241 | 0.0191071 | ||||||||
\(638\) | −16.2638 | −0.643892 | ||||||||
\(639\) | −10.2077 | −0.403809 | ||||||||
\(640\) | −16.4124 | −0.648758 | ||||||||
\(641\) | 1.00090 | 0.0395334 | 0.0197667 | − | 0.999805i | \(-0.493708\pi\) | ||||
0.0197667 | + | 0.999805i | \(0.493708\pi\) | |||||||
\(642\) | −8.16536 | −0.322261 | ||||||||
\(643\) | 23.5361 | 0.928173 | 0.464087 | − | 0.885790i | \(-0.346383\pi\) | ||||
0.464087 | + | 0.885790i | \(0.346383\pi\) | |||||||
\(644\) | −63.1687 | −2.48919 | ||||||||
\(645\) | 15.6289 | 0.615387 | ||||||||
\(646\) | −44.9837 | −1.76986 | ||||||||
\(647\) | −11.3653 | −0.446816 | −0.223408 | − | 0.974725i | \(-0.571718\pi\) | ||||
−0.223408 | + | 0.974725i | \(0.571718\pi\) | |||||||
\(648\) | −56.5858 | −2.22290 | ||||||||
\(649\) | −4.38285 | −0.172042 | ||||||||
\(650\) | 8.71548 | 0.341849 | ||||||||
\(651\) | 18.6271 | 0.730055 | ||||||||
\(652\) | −13.5512 | −0.530706 | ||||||||
\(653\) | 1.63776 | 0.0640904 | 0.0320452 | − | 0.999486i | \(-0.489798\pi\) | ||||
0.0320452 | + | 0.999486i | \(0.489798\pi\) | |||||||
\(654\) | −97.2324 | −3.80209 | ||||||||
\(655\) | −7.70878 | −0.301207 | ||||||||
\(656\) | 29.6523 | 1.15773 | ||||||||
\(657\) | 2.60686 | 0.101703 | ||||||||
\(658\) | −1.15399 | −0.0449871 | ||||||||
\(659\) | −42.9468 | −1.67297 | −0.836484 | − | 0.547991i | \(-0.815393\pi\) | ||||
−0.836484 | + | 0.547991i | \(0.815393\pi\) | |||||||
\(660\) | 10.0792 | 0.392331 | ||||||||
\(661\) | −20.1232 | −0.782702 | −0.391351 | − | 0.920241i | \(-0.627992\pi\) | ||||
−0.391351 | + | 0.920241i | \(0.627992\pi\) | |||||||
\(662\) | −12.1407 | −0.471861 | ||||||||
\(663\) | 36.7067 | 1.42557 | ||||||||
\(664\) | 48.2416 | 1.87214 | ||||||||
\(665\) | 10.7999 | 0.418803 | ||||||||
\(666\) | 3.88846 | 0.150675 | ||||||||
\(667\) | −36.1152 | −1.39839 | ||||||||
\(668\) | 4.34884 | 0.168262 | ||||||||
\(669\) | −51.6889 | −1.99841 | ||||||||
\(670\) | 12.7311 | 0.491843 | ||||||||
\(671\) | 2.23428 | 0.0862534 | ||||||||
\(672\) | −17.2857 | −0.666809 | ||||||||
\(673\) | 18.6316 | 0.718196 | 0.359098 | − | 0.933300i | \(-0.383084\pi\) | ||||
0.359098 | + | 0.933300i | \(0.383084\pi\) | |||||||
\(674\) | 41.1275 | 1.58417 | ||||||||
\(675\) | −0.930919 | −0.0358311 | ||||||||
\(676\) | −3.65782 | −0.140686 | ||||||||
\(677\) | −20.1362 | −0.773895 | −0.386948 | − | 0.922102i | \(-0.626471\pi\) | ||||
−0.386948 | + | 0.922102i | \(0.626471\pi\) | |||||||
\(678\) | 98.3766 | 3.77813 | ||||||||
\(679\) | 23.2901 | 0.893792 | ||||||||
\(680\) | 25.1127 | 0.963027 | ||||||||
\(681\) | 64.3678 | 2.46658 | ||||||||
\(682\) | −7.36471 | −0.282009 | ||||||||
\(683\) | −32.8005 | −1.25508 | −0.627538 | − | 0.778586i | \(-0.715937\pi\) | ||||
−0.627538 | + | 0.778586i | \(0.715937\pi\) | |||||||
\(684\) | −44.8541 | −1.71504 | ||||||||
\(685\) | 14.5083 | 0.554332 | ||||||||
\(686\) | 45.8559 | 1.75079 | ||||||||
\(687\) | 23.8265 | 0.909038 | ||||||||
\(688\) | 36.9989 | 1.41057 | ||||||||
\(689\) | −17.2748 | −0.658119 | ||||||||
\(690\) | 32.8977 | 1.25239 | ||||||||
\(691\) | 2.43678 | 0.0926996 | 0.0463498 | − | 0.998925i | \(-0.485241\pi\) | ||||
0.0463498 | + | 0.998925i | \(0.485241\pi\) | |||||||
\(692\) | −13.8980 | −0.528324 | ||||||||
\(693\) | −6.96494 | −0.264576 | ||||||||
\(694\) | −62.1622 | −2.35965 | ||||||||
\(695\) | 7.51225 | 0.284956 | ||||||||
\(696\) | −86.9044 | −3.29410 | ||||||||
\(697\) | 23.5344 | 0.891429 | ||||||||
\(698\) | −19.0549 | −0.721239 | ||||||||
\(699\) | −59.4323 | −2.24793 | ||||||||
\(700\) | −11.3727 | −0.429849 | ||||||||
\(701\) | 15.6501 | 0.591095 | 0.295547 | − | 0.955328i | \(-0.404498\pi\) | ||||
0.295547 | + | 0.955328i | \(0.404498\pi\) | |||||||
\(702\) | −8.11341 | −0.306221 | ||||||||
\(703\) | −2.41052 | −0.0909146 | ||||||||
\(704\) | −4.37682 | −0.164958 | ||||||||
\(705\) | 0.408875 | 0.0153991 | ||||||||
\(706\) | 34.0664 | 1.28211 | ||||||||
\(707\) | −9.11179 | −0.342684 | ||||||||
\(708\) | −44.1755 | −1.66022 | ||||||||
\(709\) | 11.6826 | 0.438750 | 0.219375 | − | 0.975641i | \(-0.429598\pi\) | ||||
0.219375 | + | 0.975641i | \(0.429598\pi\) | |||||||
\(710\) | −9.79443 | −0.367578 | ||||||||
\(711\) | −35.0086 | −1.31292 | ||||||||
\(712\) | −83.3552 | −3.12387 | ||||||||
\(713\) | −16.3539 | −0.612460 | ||||||||
\(714\) | −70.4036 | −2.63479 | ||||||||
\(715\) | 3.48435 | 0.130307 | ||||||||
\(716\) | −70.8406 | −2.64744 | ||||||||
\(717\) | −30.3311 | −1.13274 | ||||||||
\(718\) | −56.5384 | −2.11000 | ||||||||
\(719\) | −10.4833 | −0.390960 | −0.195480 | − | 0.980708i | \(-0.562626\pi\) | ||||
−0.195480 | + | 0.980708i | \(0.562626\pi\) | |||||||
\(720\) | 14.6129 | 0.544592 | ||||||||
\(721\) | 16.7140 | 0.622463 | ||||||||
\(722\) | −6.65455 | −0.247657 | ||||||||
\(723\) | 31.5501 | 1.17336 | ||||||||
\(724\) | −25.5257 | −0.948654 | ||||||||
\(725\) | −6.50210 | −0.241482 | ||||||||
\(726\) | 5.92283 | 0.219817 | ||||||||
\(727\) | 40.0161 | 1.48412 | 0.742058 | − | 0.670336i | \(-0.233850\pi\) | ||||
0.742058 | + | 0.670336i | \(0.233850\pi\) | |||||||
\(728\) | −52.5473 | −1.94753 | ||||||||
\(729\) | −19.5205 | −0.722980 | ||||||||
\(730\) | 2.50132 | 0.0925781 | ||||||||
\(731\) | 29.3652 | 1.08611 | ||||||||
\(732\) | 22.5197 | 0.832351 | ||||||||
\(733\) | 21.8844 | 0.808320 | 0.404160 | − | 0.914688i | \(-0.367564\pi\) | ||||
0.404160 | + | 0.914688i | \(0.367564\pi\) | |||||||
\(734\) | 4.09389 | 0.151108 | ||||||||
\(735\) | 0.327719 | 0.0120881 | ||||||||
\(736\) | 15.1762 | 0.559401 | ||||||||
\(737\) | 5.08973 | 0.187482 | ||||||||
\(738\) | 34.4926 | 1.26969 | ||||||||
\(739\) | −11.5304 | −0.424153 | −0.212077 | − | 0.977253i | \(-0.568023\pi\) | ||||
−0.212077 | + | 0.977253i | \(0.568023\pi\) | |||||||
\(740\) | 2.53837 | 0.0933125 | ||||||||
\(741\) | −33.3504 | −1.22516 | ||||||||
\(742\) | 33.1332 | 1.21636 | ||||||||
\(743\) | 13.3300 | 0.489030 | 0.244515 | − | 0.969646i | \(-0.421371\pi\) | ||||
0.244515 | + | 0.969646i | \(0.421371\pi\) | |||||||
\(744\) | −39.3527 | −1.44274 | ||||||||
\(745\) | −5.63280 | −0.206370 | ||||||||
\(746\) | 18.5441 | 0.678947 | ||||||||
\(747\) | 22.2797 | 0.815173 | ||||||||
\(748\) | 18.9378 | 0.692435 | ||||||||
\(749\) | 3.68338 | 0.134588 | ||||||||
\(750\) | 5.92283 | 0.216271 | ||||||||
\(751\) | −27.9836 | −1.02114 | −0.510569 | − | 0.859837i | \(-0.670565\pi\) | ||||
−0.510569 | + | 0.859837i | \(0.670565\pi\) | |||||||
\(752\) | 0.967945 | 0.0352973 | ||||||||
\(753\) | −67.8842 | −2.47384 | ||||||||
\(754\) | −56.6689 | −2.06376 | ||||||||
\(755\) | 23.7457 | 0.864194 | ||||||||
\(756\) | 10.5871 | 0.385050 | ||||||||
\(757\) | −26.2443 | −0.953864 | −0.476932 | − | 0.878940i | \(-0.658251\pi\) | ||||
−0.476932 | + | 0.878940i | \(0.658251\pi\) | |||||||
\(758\) | 44.3681 | 1.61152 | ||||||||
\(759\) | 13.1521 | 0.477392 | ||||||||
\(760\) | −22.8165 | −0.827641 | ||||||||
\(761\) | 18.7033 | 0.677993 | 0.338997 | − | 0.940788i | \(-0.389912\pi\) | ||||
0.338997 | + | 0.940788i | \(0.389912\pi\) | |||||||
\(762\) | 78.1199 | 2.82999 | ||||||||
\(763\) | 43.8613 | 1.58789 | ||||||||
\(764\) | −88.3454 | −3.19622 | ||||||||
\(765\) | 11.5980 | 0.419325 | ||||||||
\(766\) | −37.5681 | −1.35739 | ||||||||
\(767\) | −15.2714 | −0.551417 | ||||||||
\(768\) | −76.4805 | −2.75975 | ||||||||
\(769\) | 8.51567 | 0.307083 | 0.153541 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153541 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(770\) | −6.68298 | −0.240838 | ||||||||
\(771\) | 5.19784 | 0.187196 | ||||||||
\(772\) | 46.1026 | 1.65927 | ||||||||
\(773\) | −1.52936 | −0.0550072 | −0.0275036 | − | 0.999622i | \(-0.508756\pi\) | ||||
−0.0275036 | + | 0.999622i | \(0.508756\pi\) | |||||||
\(774\) | 43.0383 | 1.54698 | ||||||||
\(775\) | −2.94433 | −0.105763 | ||||||||
\(776\) | −49.2039 | −1.76632 | ||||||||
\(777\) | −3.77269 | −0.135344 | ||||||||
\(778\) | 74.0496 | 2.65481 | ||||||||
\(779\) | −21.3825 | −0.766109 | ||||||||
\(780\) | 35.1193 | 1.25747 | ||||||||
\(781\) | −3.91570 | −0.140115 | ||||||||
\(782\) | 61.8117 | 2.21038 | ||||||||
\(783\) | 6.05293 | 0.216314 | ||||||||
\(784\) | 0.775823 | 0.0277080 | ||||||||
\(785\) | 3.40138 | 0.121400 | ||||||||
\(786\) | −45.6578 | −1.62856 | ||||||||
\(787\) | −6.31932 | −0.225259 | −0.112630 | − | 0.993637i | \(-0.535927\pi\) | ||||
−0.112630 | + | 0.993637i | \(0.535927\pi\) | |||||||
\(788\) | −32.7673 | −1.16729 | ||||||||
\(789\) | 38.3146 | 1.36404 | ||||||||
\(790\) | −33.5913 | −1.19513 | ||||||||
\(791\) | −44.3775 | −1.57788 | ||||||||
\(792\) | 14.7145 | 0.522857 | ||||||||
\(793\) | 7.78500 | 0.276454 | ||||||||
\(794\) | 39.8627 | 1.41468 | ||||||||
\(795\) | −11.7396 | −0.416360 | ||||||||
\(796\) | −60.2619 | −2.13593 | ||||||||
\(797\) | 12.9150 | 0.457473 | 0.228737 | − | 0.973488i | \(-0.426541\pi\) | ||||
0.228737 | + | 0.973488i | \(0.426541\pi\) | |||||||
\(798\) | 63.9662 | 2.26438 | ||||||||
\(799\) | 0.768237 | 0.0271783 | ||||||||
\(800\) | 2.73229 | 0.0966009 | ||||||||
\(801\) | −38.4965 | −1.36021 | ||||||||
\(802\) | −6.16857 | −0.217820 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 51.3002 | 1.80922 | ||||||||
\(805\) | −14.8401 | −0.523045 | ||||||||
\(806\) | −25.6612 | −0.903878 | ||||||||
\(807\) | 18.3920 | 0.647430 | ||||||||
\(808\) | 19.2500 | 0.677214 | ||||||||
\(809\) | 50.0904 | 1.76109 | 0.880543 | − | 0.473967i | \(-0.157178\pi\) | ||||
0.880543 | + | 0.473967i | \(0.157178\pi\) | |||||||
\(810\) | −25.0754 | −0.881061 | ||||||||
\(811\) | 21.8414 | 0.766954 | 0.383477 | − | 0.923550i | \(-0.374727\pi\) | ||||
0.383477 | + | 0.923550i | \(0.374727\pi\) | |||||||
\(812\) | 73.9467 | 2.59502 | ||||||||
\(813\) | 30.7440 | 1.07824 | ||||||||
\(814\) | 1.49163 | 0.0522815 | ||||||||
\(815\) | −3.18356 | −0.111515 | ||||||||
\(816\) | 59.0534 | 2.06728 | ||||||||
\(817\) | −26.6802 | −0.933422 | ||||||||
\(818\) | −0.951050 | −0.0332527 | ||||||||
\(819\) | −24.2683 | −0.848002 | ||||||||
\(820\) | 22.5166 | 0.786315 | ||||||||
\(821\) | −17.1885 | −0.599883 | −0.299942 | − | 0.953958i | \(-0.596967\pi\) | ||||
−0.299942 | + | 0.953958i | \(0.596967\pi\) | |||||||
\(822\) | 85.9300 | 2.99715 | ||||||||
\(823\) | −4.23255 | −0.147537 | −0.0737687 | − | 0.997275i | \(-0.523503\pi\) | ||||
−0.0737687 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(824\) | −35.3109 | −1.23011 | ||||||||
\(825\) | 2.36788 | 0.0824390 | ||||||||
\(826\) | 29.2905 | 1.01915 | ||||||||
\(827\) | −0.677290 | −0.0235517 | −0.0117758 | − | 0.999931i | \(-0.503748\pi\) | ||||
−0.0117758 | + | 0.999931i | \(0.503748\pi\) | |||||||
\(828\) | 61.6337 | 2.14192 | ||||||||
\(829\) | 0.823786 | 0.0286113 | 0.0143056 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143056 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(830\) | 21.3778 | 0.742034 | ||||||||
\(831\) | 1.16453 | 0.0403970 | ||||||||
\(832\) | −15.2504 | −0.528711 | ||||||||
\(833\) | 0.615754 | 0.0213346 | ||||||||
\(834\) | 44.4938 | 1.54070 | ||||||||
\(835\) | 1.02167 | 0.0353562 | ||||||||
\(836\) | −17.2062 | −0.595090 | ||||||||
\(837\) | 2.74093 | 0.0947404 | ||||||||
\(838\) | −66.4313 | −2.29483 | ||||||||
\(839\) | 9.57679 | 0.330627 | 0.165314 | − | 0.986241i | \(-0.447136\pi\) | ||||
0.165314 | + | 0.986241i | \(0.447136\pi\) | |||||||
\(840\) | −35.7099 | −1.23211 | ||||||||
\(841\) | 13.2773 | 0.457837 | ||||||||
\(842\) | 43.1515 | 1.48710 | ||||||||
\(843\) | −6.80477 | −0.234369 | ||||||||
\(844\) | 106.432 | 3.66354 | ||||||||
\(845\) | −0.859326 | −0.0295617 | ||||||||
\(846\) | 1.12595 | 0.0387108 | ||||||||
\(847\) | −2.67178 | −0.0918034 | ||||||||
\(848\) | −27.7916 | −0.954366 | ||||||||
\(849\) | −73.1439 | −2.51029 | ||||||||
\(850\) | 11.1284 | 0.381703 | ||||||||
\(851\) | 3.31228 | 0.113543 | ||||||||
\(852\) | −39.4670 | −1.35212 | ||||||||
\(853\) | 22.5458 | 0.771955 | 0.385978 | − | 0.922508i | \(-0.373864\pi\) | ||||
0.385978 | + | 0.922508i | \(0.373864\pi\) | |||||||
\(854\) | −14.9317 | −0.510951 | ||||||||
\(855\) | −10.5375 | −0.360375 | ||||||||
\(856\) | −7.78170 | −0.265973 | ||||||||
\(857\) | −33.1621 | −1.13280 | −0.566399 | − | 0.824131i | \(-0.691664\pi\) | ||||
−0.566399 | + | 0.824131i | \(0.691664\pi\) | |||||||
\(858\) | 20.6372 | 0.704543 | ||||||||
\(859\) | −12.7468 | −0.434915 | −0.217457 | − | 0.976070i | \(-0.569776\pi\) | ||||
−0.217457 | + | 0.976070i | \(0.569776\pi\) | |||||||
\(860\) | 28.0953 | 0.958042 | ||||||||
\(861\) | −33.4656 | −1.14051 | ||||||||
\(862\) | −4.14396 | −0.141144 | ||||||||
\(863\) | 55.2707 | 1.88144 | 0.940719 | − | 0.339188i | \(-0.110152\pi\) | ||||
0.940719 | + | 0.339188i | \(0.110152\pi\) | |||||||
\(864\) | −2.54354 | −0.0865329 | ||||||||
\(865\) | −3.26504 | −0.111015 | ||||||||
\(866\) | 36.0322 | 1.22443 | ||||||||
\(867\) | 6.61539 | 0.224671 | ||||||||
\(868\) | 33.4851 | 1.13656 | ||||||||
\(869\) | −13.4294 | −0.455562 | ||||||||
\(870\) | −38.5108 | −1.30564 | ||||||||
\(871\) | 17.7344 | 0.600906 | ||||||||
\(872\) | −92.6637 | −3.13799 | ||||||||
\(873\) | −22.7242 | −0.769097 | ||||||||
\(874\) | −56.1600 | −1.89964 | ||||||||
\(875\) | −2.67178 | −0.0903226 | ||||||||
\(876\) | 10.0792 | 0.340543 | ||||||||
\(877\) | −42.7001 | −1.44188 | −0.720940 | − | 0.692997i | \(-0.756290\pi\) | ||||
−0.720940 | + | 0.692997i | \(0.756290\pi\) | |||||||
\(878\) | 57.2599 | 1.93243 | ||||||||
\(879\) | 62.7267 | 2.11572 | ||||||||
\(880\) | 5.60558 | 0.188964 | ||||||||
\(881\) | 27.8217 | 0.937337 | 0.468669 | − | 0.883374i | \(-0.344734\pi\) | ||||
0.468669 | + | 0.883374i | \(0.344734\pi\) | |||||||
\(882\) | 0.902463 | 0.0303875 | ||||||||
\(883\) | 35.2179 | 1.18518 | 0.592588 | − | 0.805506i | \(-0.298106\pi\) | ||||
0.592588 | + | 0.805506i | \(0.298106\pi\) | |||||||
\(884\) | 65.9859 | 2.21935 | ||||||||
\(885\) | −10.3781 | −0.348855 | ||||||||
\(886\) | 30.1119 | 1.01163 | ||||||||
\(887\) | −49.1090 | −1.64892 | −0.824459 | − | 0.565922i | \(-0.808520\pi\) | ||||
−0.824459 | + | 0.565922i | \(0.808520\pi\) | |||||||
\(888\) | 7.97037 | 0.267468 | ||||||||
\(889\) | −35.2397 | −1.18190 | ||||||||
\(890\) | −36.9380 | −1.23817 | ||||||||
\(891\) | −10.0249 | −0.335846 | ||||||||
\(892\) | −92.9186 | −3.11115 | ||||||||
\(893\) | −0.697993 | −0.0233574 | ||||||||
\(894\) | −33.3622 | −1.11580 | ||||||||
\(895\) | −16.6425 | −0.556296 | ||||||||
\(896\) | 43.8504 | 1.46494 | ||||||||
\(897\) | 45.8266 | 1.53010 | ||||||||
\(898\) | 65.6639 | 2.19123 | ||||||||
\(899\) | 19.1443 | 0.638498 | ||||||||
\(900\) | 11.0964 | 0.369880 | ||||||||
\(901\) | −22.0576 | −0.734844 | ||||||||
\(902\) | 13.2315 | 0.440560 | ||||||||
\(903\) | −41.7570 | −1.38958 | ||||||||
\(904\) | 93.7542 | 3.11822 | ||||||||
\(905\) | −5.99670 | −0.199337 | ||||||||
\(906\) | 140.642 | 4.67251 | ||||||||
\(907\) | 17.0414 | 0.565849 | 0.282924 | − | 0.959142i | \(-0.408695\pi\) | ||||
0.282924 | + | 0.959142i | \(0.408695\pi\) | |||||||
\(908\) | 115.711 | 3.84000 | ||||||||
\(909\) | 8.89037 | 0.294875 | ||||||||
\(910\) | −23.2858 | −0.771918 | ||||||||
\(911\) | −46.5521 | −1.54234 | −0.771169 | − | 0.636630i | \(-0.780328\pi\) | ||||
−0.771169 | + | 0.636630i | \(0.780328\pi\) | |||||||
\(912\) | −53.6538 | −1.77666 | ||||||||
\(913\) | 8.54660 | 0.282851 | ||||||||
\(914\) | −4.62917 | −0.153119 | ||||||||
\(915\) | 5.29051 | 0.174899 | ||||||||
\(916\) | 42.8317 | 1.41520 | ||||||||
\(917\) | 20.5961 | 0.680145 | ||||||||
\(918\) | −10.3597 | −0.341921 | ||||||||
\(919\) | −23.3080 | −0.768860 | −0.384430 | − | 0.923154i | \(-0.625602\pi\) | ||||
−0.384430 | + | 0.923154i | \(0.625602\pi\) | |||||||
\(920\) | 31.3520 | 1.03364 | ||||||||
\(921\) | −53.4161 | −1.76012 | ||||||||
\(922\) | −91.6076 | −3.01694 | ||||||||
\(923\) | −13.6436 | −0.449086 | ||||||||
\(924\) | −26.9293 | −0.885909 | ||||||||
\(925\) | 0.596335 | 0.0196074 | ||||||||
\(926\) | −39.0965 | −1.28479 | ||||||||
\(927\) | −16.3079 | −0.535621 | ||||||||
\(928\) | −17.7656 | −0.583184 | ||||||||
\(929\) | 17.9792 | 0.589877 | 0.294939 | − | 0.955516i | \(-0.404701\pi\) | ||||
0.294939 | + | 0.955516i | \(0.404701\pi\) | |||||||
\(930\) | −17.4388 | −0.571839 | ||||||||
\(931\) | −0.559452 | −0.0183353 | ||||||||
\(932\) | −106.838 | −3.49961 | ||||||||
\(933\) | −6.20416 | −0.203115 | ||||||||
\(934\) | 39.6372 | 1.29697 | ||||||||
\(935\) | 4.44902 | 0.145499 | ||||||||
\(936\) | 51.2704 | 1.67583 | ||||||||
\(937\) | −0.0637686 | −0.00208323 | −0.00104161 | − | 0.999999i | \(-0.500332\pi\) | ||||
−0.00104161 | + | 0.999999i | \(0.500332\pi\) | |||||||
\(938\) | −34.0146 | −1.11061 | ||||||||
\(939\) | 56.3699 | 1.83956 | ||||||||
\(940\) | 0.735014 | 0.0239735 | ||||||||
\(941\) | −22.4057 | −0.730404 | −0.365202 | − | 0.930928i | \(-0.619000\pi\) | ||||
−0.365202 | + | 0.930928i | \(0.619000\pi\) | |||||||
\(942\) | 20.1458 | 0.656385 | ||||||||
\(943\) | 29.3816 | 0.956796 | ||||||||
\(944\) | −24.5684 | −0.799634 | ||||||||
\(945\) | 2.48721 | 0.0809090 | ||||||||
\(946\) | 16.5097 | 0.536776 | ||||||||
\(947\) | −44.7378 | −1.45378 | −0.726892 | − | 0.686752i | \(-0.759036\pi\) | ||||
−0.726892 | + | 0.686752i | \(0.759036\pi\) | |||||||
\(948\) | −135.357 | −4.39620 | ||||||||
\(949\) | 3.48435 | 0.113107 | ||||||||
\(950\) | −10.1109 | −0.328041 | ||||||||
\(951\) | −1.47393 | −0.0477955 | ||||||||
\(952\) | −67.0955 | −2.17458 | ||||||||
\(953\) | −6.96492 | −0.225616 | −0.112808 | − | 0.993617i | \(-0.535984\pi\) | ||||
−0.112808 | + | 0.993617i | \(0.535984\pi\) | |||||||
\(954\) | −32.3281 | −1.04666 | ||||||||
\(955\) | −20.7548 | −0.671610 | ||||||||
\(956\) | −54.5248 | −1.76346 | ||||||||
\(957\) | −15.3962 | −0.497688 | ||||||||
\(958\) | 83.4039 | 2.69466 | ||||||||
\(959\) | −38.7629 | −1.25172 | ||||||||
\(960\) | −10.3638 | −0.334490 | ||||||||
\(961\) | −22.3309 | −0.720353 | ||||||||
\(962\) | 5.19735 | 0.167569 | ||||||||
\(963\) | −3.59387 | −0.115811 | ||||||||
\(964\) | 56.7160 | 1.82670 | ||||||||
\(965\) | 10.8308 | 0.348656 | ||||||||
\(966\) | −87.8954 | −2.82799 | ||||||||
\(967\) | 17.6356 | 0.567122 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(968\) | 5.64454 | 0.181422 | ||||||||
\(969\) | −42.5838 | −1.36799 | ||||||||
\(970\) | −21.8042 | −0.700092 | ||||||||
\(971\) | 27.1151 | 0.870166 | 0.435083 | − | 0.900390i | \(-0.356719\pi\) | ||||
0.435083 | + | 0.900390i | \(0.356719\pi\) | |||||||
\(972\) | −89.1546 | −2.85964 | ||||||||
\(973\) | −20.0711 | −0.643449 | ||||||||
\(974\) | −41.7900 | −1.33904 | ||||||||
\(975\) | 8.25052 | 0.264228 | ||||||||
\(976\) | 12.5244 | 0.400897 | ||||||||
\(977\) | 20.3577 | 0.651300 | 0.325650 | − | 0.945490i | \(-0.394417\pi\) | ||||
0.325650 | + | 0.945490i | \(0.394417\pi\) | |||||||
\(978\) | −18.8557 | −0.602939 | ||||||||
\(979\) | −14.7674 | −0.471968 | ||||||||
\(980\) | 0.589125 | 0.0188189 | ||||||||
\(981\) | −42.7955 | −1.36636 | ||||||||
\(982\) | −58.5758 | −1.86923 | ||||||||
\(983\) | −17.3908 | −0.554679 | −0.277340 | − | 0.960772i | \(-0.589453\pi\) | ||||
−0.277340 | + | 0.960772i | \(0.589453\pi\) | |||||||
\(984\) | 70.7012 | 2.25387 | ||||||||
\(985\) | −7.69796 | −0.245277 | ||||||||
\(986\) | −72.3582 | −2.30436 | ||||||||
\(987\) | −1.09242 | −0.0347722 | ||||||||
\(988\) | −59.9524 | −1.90734 | ||||||||
\(989\) | 36.6611 | 1.16575 | ||||||||
\(990\) | 6.52059 | 0.207238 | ||||||||
\(991\) | −37.0023 | −1.17542 | −0.587709 | − | 0.809073i | \(-0.699970\pi\) | ||||
−0.587709 | + | 0.809073i | \(0.699970\pi\) | |||||||
\(992\) | −8.04474 | −0.255421 | ||||||||
\(993\) | −11.4930 | −0.364719 | ||||||||
\(994\) | 26.1685 | 0.830016 | ||||||||
\(995\) | −14.1572 | −0.448814 | ||||||||
\(996\) | 86.1426 | 2.72953 | ||||||||
\(997\) | −37.1654 | −1.17704 | −0.588520 | − | 0.808483i | \(-0.700289\pi\) | ||||
−0.588520 | + | 0.808483i | \(0.700289\pi\) | |||||||
\(998\) | 81.9716 | 2.59477 | ||||||||
\(999\) | −0.555140 | −0.0175639 |
(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 | 4015.2.a.h.1.34 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.34 | ✓ | 37 | 1.1 | even | 1 | trivial |