Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, 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("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(0\) |
Dimension: | \(287\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59707 | −1.83640 | −0.918202 | − | 0.396114i | \(-0.870359\pi\) | ||||
−0.918202 | + | 0.396114i | \(0.870359\pi\) | |||||||
\(3\) | −2.63415 | −1.52083 | −0.760414 | − | 0.649439i | \(-0.775004\pi\) | ||||
−0.760414 | + | 0.649439i | \(0.775004\pi\) | |||||||
\(4\) | 4.74475 | 2.37238 | ||||||||
\(5\) | −0.775653 | −0.346883 | −0.173441 | − | 0.984844i | \(-0.555489\pi\) | ||||
−0.173441 | + | 0.984844i | \(0.555489\pi\) | |||||||
\(6\) | 6.84106 | 2.79285 | ||||||||
\(7\) | 2.06715 | 0.781311 | 0.390655 | − | 0.920537i | \(-0.372248\pi\) | ||||
0.390655 | + | 0.920537i | \(0.372248\pi\) | |||||||
\(8\) | −7.12830 | −2.52024 | ||||||||
\(9\) | 3.93875 | 1.31292 | ||||||||
\(10\) | 2.01442 | 0.637016 | ||||||||
\(11\) | 0.868468 | 0.261853 | 0.130926 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130926 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(12\) | −12.4984 | −3.60797 | ||||||||
\(13\) | 5.42552 | 1.50477 | 0.752384 | − | 0.658725i | \(-0.228904\pi\) | ||||
0.752384 | + | 0.658725i | \(0.228904\pi\) | |||||||
\(14\) | −5.36854 | −1.43480 | ||||||||
\(15\) | 2.04319 | 0.527549 | ||||||||
\(16\) | 9.02317 | 2.25579 | ||||||||
\(17\) | −8.03282 | −1.94824 | −0.974122 | − | 0.226022i | \(-0.927428\pi\) | ||||
−0.974122 | + | 0.226022i | \(0.927428\pi\) | |||||||
\(18\) | −10.2292 | −2.41104 | ||||||||
\(19\) | −1.76967 | −0.405990 | −0.202995 | − | 0.979180i | \(-0.565068\pi\) | ||||
−0.202995 | + | 0.979180i | \(0.565068\pi\) | |||||||
\(20\) | −3.68028 | −0.822936 | ||||||||
\(21\) | −5.44520 | −1.18824 | ||||||||
\(22\) | −2.25547 | −0.480867 | ||||||||
\(23\) | −7.03750 | −1.46742 | −0.733710 | − | 0.679463i | \(-0.762213\pi\) | ||||
−0.733710 | + | 0.679463i | \(0.762213\pi\) | |||||||
\(24\) | 18.7770 | 3.83284 | ||||||||
\(25\) | −4.39836 | −0.879672 | ||||||||
\(26\) | −14.0904 | −2.76336 | ||||||||
\(27\) | −2.47280 | −0.475891 | ||||||||
\(28\) | 9.80814 | 1.85356 | ||||||||
\(29\) | −5.89931 | −1.09548 | −0.547738 | − | 0.836650i | \(-0.684511\pi\) | ||||
−0.547738 | + | 0.836650i | \(0.684511\pi\) | |||||||
\(30\) | −5.30629 | −0.968792 | ||||||||
\(31\) | −8.89929 | −1.59836 | −0.799180 | − | 0.601092i | \(-0.794732\pi\) | ||||
−0.799180 | + | 0.601092i | \(0.794732\pi\) | |||||||
\(32\) | −9.17716 | −1.62231 | ||||||||
\(33\) | −2.28767 | −0.398233 | ||||||||
\(34\) | 20.8618 | 3.57776 | ||||||||
\(35\) | −1.60339 | −0.271023 | ||||||||
\(36\) | 18.6884 | 3.11473 | ||||||||
\(37\) | 7.16902 | 1.17858 | 0.589290 | − | 0.807922i | \(-0.299408\pi\) | ||||
0.589290 | + | 0.807922i | \(0.299408\pi\) | |||||||
\(38\) | 4.59595 | 0.745562 | ||||||||
\(39\) | −14.2916 | −2.28849 | ||||||||
\(40\) | 5.52909 | 0.874226 | ||||||||
\(41\) | −7.11737 | −1.11155 | −0.555773 | − | 0.831334i | \(-0.687578\pi\) | ||||
−0.555773 | + | 0.831334i | \(0.687578\pi\) | |||||||
\(42\) | 14.1415 | 2.18209 | ||||||||
\(43\) | −11.7338 | −1.78938 | −0.894691 | − | 0.446686i | \(-0.852604\pi\) | ||||
−0.894691 | + | 0.446686i | \(0.852604\pi\) | |||||||
\(44\) | 4.12066 | 0.621214 | ||||||||
\(45\) | −3.05510 | −0.455428 | ||||||||
\(46\) | 18.2769 | 2.69477 | ||||||||
\(47\) | 6.17520 | 0.900746 | 0.450373 | − | 0.892840i | \(-0.351291\pi\) | ||||
0.450373 | + | 0.892840i | \(0.351291\pi\) | |||||||
\(48\) | −23.7684 | −3.43067 | ||||||||
\(49\) | −2.72687 | −0.389553 | ||||||||
\(50\) | 11.4228 | 1.61543 | ||||||||
\(51\) | 21.1596 | 2.96294 | ||||||||
\(52\) | 25.7427 | 3.56988 | ||||||||
\(53\) | −0.447451 | −0.0614622 | −0.0307311 | − | 0.999528i | \(-0.509784\pi\) | ||||
−0.0307311 | + | 0.999528i | \(0.509784\pi\) | |||||||
\(54\) | 6.42203 | 0.873928 | ||||||||
\(55\) | −0.673630 | −0.0908322 | ||||||||
\(56\) | −14.7353 | −1.96909 | ||||||||
\(57\) | 4.66158 | 0.617441 | ||||||||
\(58\) | 15.3209 | 2.01173 | ||||||||
\(59\) | −15.0907 | −1.96465 | −0.982323 | − | 0.187193i | \(-0.940061\pi\) | ||||
−0.982323 | + | 0.187193i | \(0.940061\pi\) | |||||||
\(60\) | 9.69442 | 1.25154 | ||||||||
\(61\) | 8.00322 | 1.02471 | 0.512354 | − | 0.858774i | \(-0.328774\pi\) | ||||
0.512354 | + | 0.858774i | \(0.328774\pi\) | |||||||
\(62\) | 23.1120 | 2.93523 | ||||||||
\(63\) | 8.14200 | 1.02580 | ||||||||
\(64\) | 5.78736 | 0.723419 | ||||||||
\(65\) | −4.20832 | −0.521978 | ||||||||
\(66\) | 5.94124 | 0.731316 | ||||||||
\(67\) | 3.38923 | 0.414061 | 0.207030 | − | 0.978335i | \(-0.433620\pi\) | ||||
0.207030 | + | 0.978335i | \(0.433620\pi\) | |||||||
\(68\) | −38.1137 | −4.62197 | ||||||||
\(69\) | 18.5378 | 2.23169 | ||||||||
\(70\) | 4.16412 | 0.497708 | ||||||||
\(71\) | −11.7111 | −1.38985 | −0.694925 | − | 0.719082i | \(-0.744563\pi\) | ||||
−0.694925 | + | 0.719082i | \(0.744563\pi\) | |||||||
\(72\) | −28.0766 | −3.30886 | ||||||||
\(73\) | 7.38827 | 0.864732 | 0.432366 | − | 0.901698i | \(-0.357679\pi\) | ||||
0.432366 | + | 0.901698i | \(0.357679\pi\) | |||||||
\(74\) | −18.6184 | −2.16435 | ||||||||
\(75\) | 11.5859 | 1.33783 | ||||||||
\(76\) | −8.39665 | −0.963162 | ||||||||
\(77\) | 1.79526 | 0.204589 | ||||||||
\(78\) | 37.1163 | 4.20260 | ||||||||
\(79\) | 1.72862 | 0.194485 | 0.0972427 | − | 0.995261i | \(-0.468998\pi\) | ||||
0.0972427 | + | 0.995261i | \(0.468998\pi\) | |||||||
\(80\) | −6.99885 | −0.782495 | ||||||||
\(81\) | −5.30251 | −0.589168 | ||||||||
\(82\) | 18.4843 | 2.04125 | ||||||||
\(83\) | 10.6809 | 1.17238 | 0.586189 | − | 0.810174i | \(-0.300627\pi\) | ||||
0.586189 | + | 0.810174i | \(0.300627\pi\) | |||||||
\(84\) | −25.8361 | −2.81895 | ||||||||
\(85\) | 6.23068 | 0.675812 | ||||||||
\(86\) | 30.4733 | 3.28603 | ||||||||
\(87\) | 15.5397 | 1.66603 | ||||||||
\(88\) | −6.19070 | −0.659931 | ||||||||
\(89\) | −7.32614 | −0.776570 | −0.388285 | − | 0.921539i | \(-0.626932\pi\) | ||||
−0.388285 | + | 0.921539i | \(0.626932\pi\) | |||||||
\(90\) | 7.93430 | 0.836349 | ||||||||
\(91\) | 11.2154 | 1.17569 | ||||||||
\(92\) | −33.3912 | −3.48127 | ||||||||
\(93\) | 23.4421 | 2.43083 | ||||||||
\(94\) | −16.0374 | −1.65413 | ||||||||
\(95\) | 1.37265 | 0.140831 | ||||||||
\(96\) | 24.1740 | 2.46725 | ||||||||
\(97\) | −2.48725 | −0.252542 | −0.126271 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126271 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(98\) | 7.08187 | 0.715377 | ||||||||
\(99\) | 3.42068 | 0.343791 | ||||||||
\(100\) | −20.8691 | −2.08691 | ||||||||
\(101\) | 12.0326 | 1.19729 | 0.598646 | − | 0.801013i | \(-0.295705\pi\) | ||||
0.598646 | + | 0.801013i | \(0.295705\pi\) | |||||||
\(102\) | −54.9530 | −5.44116 | ||||||||
\(103\) | −7.15520 | −0.705023 | −0.352512 | − | 0.935807i | \(-0.614672\pi\) | ||||
−0.352512 | + | 0.935807i | \(0.614672\pi\) | |||||||
\(104\) | −38.6747 | −3.79237 | ||||||||
\(105\) | 4.22358 | 0.412179 | ||||||||
\(106\) | 1.16206 | 0.112869 | ||||||||
\(107\) | −3.39159 | −0.327878 | −0.163939 | − | 0.986470i | \(-0.552420\pi\) | ||||
−0.163939 | + | 0.986470i | \(0.552420\pi\) | |||||||
\(108\) | −11.7328 | −1.12899 | ||||||||
\(109\) | −8.33494 | −0.798342 | −0.399171 | − | 0.916876i | \(-0.630702\pi\) | ||||
−0.399171 | + | 0.916876i | \(0.630702\pi\) | |||||||
\(110\) | 1.74946 | 0.166805 | ||||||||
\(111\) | −18.8843 | −1.79242 | ||||||||
\(112\) | 18.6523 | 1.76248 | ||||||||
\(113\) | 20.1472 | 1.89529 | 0.947645 | − | 0.319327i | \(-0.103457\pi\) | ||||
0.947645 | + | 0.319327i | \(0.103457\pi\) | |||||||
\(114\) | −12.1064 | −1.13387 | ||||||||
\(115\) | 5.45866 | 0.509023 | ||||||||
\(116\) | −27.9908 | −2.59888 | ||||||||
\(117\) | 21.3698 | 1.97563 | ||||||||
\(118\) | 39.1916 | 3.60788 | ||||||||
\(119\) | −16.6051 | −1.52218 | ||||||||
\(120\) | −14.5645 | −1.32955 | ||||||||
\(121\) | −10.2458 | −0.931433 | ||||||||
\(122\) | −20.7849 | −1.88178 | ||||||||
\(123\) | 18.7482 | 1.69047 | ||||||||
\(124\) | −42.2249 | −3.79191 | ||||||||
\(125\) | 7.28987 | 0.652026 | ||||||||
\(126\) | −21.1453 | −1.88377 | ||||||||
\(127\) | −3.45422 | −0.306512 | −0.153256 | − | 0.988186i | \(-0.548976\pi\) | ||||
−0.153256 | + | 0.988186i | \(0.548976\pi\) | |||||||
\(128\) | 3.32418 | 0.293819 | ||||||||
\(129\) | 30.9085 | 2.72134 | ||||||||
\(130\) | 10.9293 | 0.958562 | ||||||||
\(131\) | 16.4086 | 1.43363 | 0.716815 | − | 0.697264i | \(-0.245599\pi\) | ||||
0.716815 | + | 0.697264i | \(0.245599\pi\) | |||||||
\(132\) | −10.8544 | −0.944759 | ||||||||
\(133\) | −3.65818 | −0.317205 | ||||||||
\(134\) | −8.80206 | −0.760382 | ||||||||
\(135\) | 1.91804 | 0.165078 | ||||||||
\(136\) | 57.2604 | 4.91003 | ||||||||
\(137\) | 10.0916 | 0.862187 | 0.431094 | − | 0.902307i | \(-0.358128\pi\) | ||||
0.431094 | + | 0.902307i | \(0.358128\pi\) | |||||||
\(138\) | −48.1440 | −4.09829 | ||||||||
\(139\) | −8.65731 | −0.734304 | −0.367152 | − | 0.930161i | \(-0.619667\pi\) | ||||
−0.367152 | + | 0.930161i | \(0.619667\pi\) | |||||||
\(140\) | −7.60771 | −0.642969 | ||||||||
\(141\) | −16.2664 | −1.36988 | ||||||||
\(142\) | 30.4145 | 2.55233 | ||||||||
\(143\) | 4.71189 | 0.394028 | ||||||||
\(144\) | 35.5400 | 2.96167 | ||||||||
\(145\) | 4.57582 | 0.380001 | ||||||||
\(146\) | −19.1878 | −1.58800 | ||||||||
\(147\) | 7.18299 | 0.592443 | ||||||||
\(148\) | 34.0152 | 2.79603 | ||||||||
\(149\) | −12.9998 | −1.06499 | −0.532493 | − | 0.846435i | \(-0.678745\pi\) | ||||
−0.532493 | + | 0.846435i | \(0.678745\pi\) | |||||||
\(150\) | −30.0895 | −2.45679 | ||||||||
\(151\) | 5.44358 | 0.442992 | 0.221496 | − | 0.975161i | \(-0.428906\pi\) | ||||
0.221496 | + | 0.975161i | \(0.428906\pi\) | |||||||
\(152\) | 12.6148 | 1.02319 | ||||||||
\(153\) | −31.6392 | −2.55788 | ||||||||
\(154\) | −4.66240 | −0.375707 | ||||||||
\(155\) | 6.90276 | 0.554443 | ||||||||
\(156\) | −67.8103 | −5.42917 | ||||||||
\(157\) | −3.96128 | −0.316144 | −0.158072 | − | 0.987428i | \(-0.550528\pi\) | ||||
−0.158072 | + | 0.987428i | \(0.550528\pi\) | |||||||
\(158\) | −4.48935 | −0.357153 | ||||||||
\(159\) | 1.17865 | 0.0934734 | ||||||||
\(160\) | 7.11829 | 0.562751 | ||||||||
\(161\) | −14.5476 | −1.14651 | ||||||||
\(162\) | 13.7710 | 1.08195 | ||||||||
\(163\) | −3.96285 | −0.310395 | −0.155197 | − | 0.987883i | \(-0.549601\pi\) | ||||
−0.155197 | + | 0.987883i | \(0.549601\pi\) | |||||||
\(164\) | −33.7702 | −2.63701 | ||||||||
\(165\) | 1.77444 | 0.138140 | ||||||||
\(166\) | −27.7389 | −2.15296 | ||||||||
\(167\) | 2.82871 | 0.218892 | 0.109446 | − | 0.993993i | \(-0.465092\pi\) | ||||
0.109446 | + | 0.993993i | \(0.465092\pi\) | |||||||
\(168\) | 38.8150 | 2.99464 | ||||||||
\(169\) | 16.4363 | 1.26433 | ||||||||
\(170\) | −16.1815 | −1.24106 | ||||||||
\(171\) | −6.97029 | −0.533031 | ||||||||
\(172\) | −55.6738 | −4.24509 | ||||||||
\(173\) | −0.987860 | −0.0751056 | −0.0375528 | − | 0.999295i | \(-0.511956\pi\) | ||||
−0.0375528 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(174\) | −40.3576 | −3.05950 | ||||||||
\(175\) | −9.09209 | −0.687298 | ||||||||
\(176\) | 7.83633 | 0.590686 | ||||||||
\(177\) | 39.7513 | 2.98789 | ||||||||
\(178\) | 19.0265 | 1.42610 | ||||||||
\(179\) | 14.9924 | 1.12058 | 0.560292 | − | 0.828295i | \(-0.310689\pi\) | ||||
0.560292 | + | 0.828295i | \(0.310689\pi\) | |||||||
\(180\) | −14.4957 | −1.08045 | ||||||||
\(181\) | 5.09987 | 0.379070 | 0.189535 | − | 0.981874i | \(-0.439302\pi\) | ||||
0.189535 | + | 0.981874i | \(0.439302\pi\) | |||||||
\(182\) | −29.1271 | −2.15904 | ||||||||
\(183\) | −21.0817 | −1.55840 | ||||||||
\(184\) | 50.1654 | 3.69824 | ||||||||
\(185\) | −5.56067 | −0.408829 | ||||||||
\(186\) | −60.8806 | −4.46398 | ||||||||
\(187\) | −6.97624 | −0.510153 | ||||||||
\(188\) | 29.2998 | 2.13691 | ||||||||
\(189\) | −5.11167 | −0.371819 | ||||||||
\(190\) | −3.56487 | −0.258623 | ||||||||
\(191\) | 24.5268 | 1.77470 | 0.887348 | − | 0.461101i | \(-0.152545\pi\) | ||||
0.887348 | + | 0.461101i | \(0.152545\pi\) | |||||||
\(192\) | −15.2448 | −1.10020 | ||||||||
\(193\) | −0.556743 | −0.0400752 | −0.0200376 | − | 0.999799i | \(-0.506379\pi\) | ||||
−0.0200376 | + | 0.999799i | \(0.506379\pi\) | |||||||
\(194\) | 6.45956 | 0.463769 | ||||||||
\(195\) | 11.0854 | 0.793839 | ||||||||
\(196\) | −12.9383 | −0.924167 | ||||||||
\(197\) | −17.1379 | −1.22103 | −0.610513 | − | 0.792006i | \(-0.709037\pi\) | ||||
−0.610513 | + | 0.792006i | \(0.709037\pi\) | |||||||
\(198\) | −8.88372 | −0.631339 | ||||||||
\(199\) | −21.0085 | −1.48926 | −0.744628 | − | 0.667480i | \(-0.767373\pi\) | ||||
−0.744628 | + | 0.667480i | \(0.767373\pi\) | |||||||
\(200\) | 31.3529 | 2.21698 | ||||||||
\(201\) | −8.92775 | −0.629715 | ||||||||
\(202\) | −31.2496 | −2.19871 | ||||||||
\(203\) | −12.1948 | −0.855907 | ||||||||
\(204\) | 100.397 | 7.02922 | ||||||||
\(205\) | 5.52061 | 0.385576 | ||||||||
\(206\) | 18.5825 | 1.29471 | ||||||||
\(207\) | −27.7189 | −1.92660 | ||||||||
\(208\) | 48.9554 | 3.39445 | ||||||||
\(209\) | −1.53690 | −0.106310 | ||||||||
\(210\) | −10.9689 | −0.756928 | ||||||||
\(211\) | 16.1330 | 1.11064 | 0.555320 | − | 0.831637i | \(-0.312596\pi\) | ||||
0.555320 | + | 0.831637i | \(0.312596\pi\) | |||||||
\(212\) | −2.12305 | −0.145811 | ||||||||
\(213\) | 30.8488 | 2.11372 | ||||||||
\(214\) | 8.80820 | 0.602116 | ||||||||
\(215\) | 9.10133 | 0.620705 | ||||||||
\(216\) | 17.6269 | 1.19936 | ||||||||
\(217\) | −18.3962 | −1.24882 | ||||||||
\(218\) | 21.6464 | 1.46608 | ||||||||
\(219\) | −19.4618 | −1.31511 | ||||||||
\(220\) | −3.19621 | −0.215488 | ||||||||
\(221\) | −43.5822 | −2.93166 | ||||||||
\(222\) | 49.0437 | 3.29160 | ||||||||
\(223\) | 12.3540 | 0.827288 | 0.413644 | − | 0.910439i | \(-0.364256\pi\) | ||||
0.413644 | + | 0.910439i | \(0.364256\pi\) | |||||||
\(224\) | −18.9706 | −1.26753 | ||||||||
\(225\) | −17.3240 | −1.15494 | ||||||||
\(226\) | −52.3236 | −3.48052 | ||||||||
\(227\) | 23.0699 | 1.53120 | 0.765602 | − | 0.643315i | \(-0.222441\pi\) | ||||
0.765602 | + | 0.643315i | \(0.222441\pi\) | |||||||
\(228\) | 22.1180 | 1.46480 | ||||||||
\(229\) | −2.39061 | −0.157976 | −0.0789881 | − | 0.996876i | \(-0.525169\pi\) | ||||
−0.0789881 | + | 0.996876i | \(0.525169\pi\) | |||||||
\(230\) | −14.1765 | −0.934771 | ||||||||
\(231\) | −4.72898 | −0.311144 | ||||||||
\(232\) | 42.0521 | 2.76086 | ||||||||
\(233\) | 7.97759 | 0.522629 | 0.261315 | − | 0.965254i | \(-0.415844\pi\) | ||||
0.261315 | + | 0.965254i | \(0.415844\pi\) | |||||||
\(234\) | −55.4987 | −3.62806 | ||||||||
\(235\) | −4.78982 | −0.312453 | ||||||||
\(236\) | −71.6018 | −4.66088 | ||||||||
\(237\) | −4.55345 | −0.295779 | ||||||||
\(238\) | 43.1245 | 2.79534 | ||||||||
\(239\) | −14.8415 | −0.960015 | −0.480008 | − | 0.877264i | \(-0.659366\pi\) | ||||
−0.480008 | + | 0.877264i | \(0.659366\pi\) | |||||||
\(240\) | 18.4360 | 1.19004 | ||||||||
\(241\) | −7.06041 | −0.454801 | −0.227400 | − | 0.973801i | \(-0.573023\pi\) | ||||
−0.227400 | + | 0.973801i | \(0.573023\pi\) | |||||||
\(242\) | 26.6089 | 1.71049 | ||||||||
\(243\) | 21.3860 | 1.37191 | ||||||||
\(244\) | 37.9733 | 2.43099 | ||||||||
\(245\) | 2.11511 | 0.135129 | ||||||||
\(246\) | −48.6904 | −3.10439 | ||||||||
\(247\) | −9.60139 | −0.610922 | ||||||||
\(248\) | 63.4368 | 4.02824 | ||||||||
\(249\) | −28.1350 | −1.78299 | ||||||||
\(250\) | −18.9323 | −1.19738 | ||||||||
\(251\) | −6.33342 | −0.399762 | −0.199881 | − | 0.979820i | \(-0.564056\pi\) | ||||
−0.199881 | + | 0.979820i | \(0.564056\pi\) | |||||||
\(252\) | 38.6318 | 2.43357 | ||||||||
\(253\) | −6.11184 | −0.384248 | ||||||||
\(254\) | 8.97083 | 0.562880 | ||||||||
\(255\) | −16.4125 | −1.02779 | ||||||||
\(256\) | −20.2078 | −1.26299 | ||||||||
\(257\) | −29.6788 | −1.85131 | −0.925657 | − | 0.378364i | \(-0.876487\pi\) | ||||
−0.925657 | + | 0.378364i | \(0.876487\pi\) | |||||||
\(258\) | −80.2714 | −4.99748 | ||||||||
\(259\) | 14.8195 | 0.920837 | ||||||||
\(260\) | −19.9674 | −1.23833 | ||||||||
\(261\) | −23.2359 | −1.43827 | ||||||||
\(262\) | −42.6143 | −2.63272 | ||||||||
\(263\) | −1.71453 | −0.105722 | −0.0528611 | − | 0.998602i | \(-0.516834\pi\) | ||||
−0.0528611 | + | 0.998602i | \(0.516834\pi\) | |||||||
\(264\) | 16.3072 | 1.00364 | ||||||||
\(265\) | 0.347067 | 0.0213202 | ||||||||
\(266\) | 9.50055 | 0.582516 | ||||||||
\(267\) | 19.2982 | 1.18103 | ||||||||
\(268\) | 16.0811 | 0.982308 | ||||||||
\(269\) | 7.46245 | 0.454994 | 0.227497 | − | 0.973779i | \(-0.426946\pi\) | ||||
0.227497 | + | 0.973779i | \(0.426946\pi\) | |||||||
\(270\) | −4.98127 | −0.303150 | ||||||||
\(271\) | 17.1361 | 1.04094 | 0.520471 | − | 0.853880i | \(-0.325757\pi\) | ||||
0.520471 | + | 0.853880i | \(0.325757\pi\) | |||||||
\(272\) | −72.4815 | −4.39483 | ||||||||
\(273\) | −29.5430 | −1.78802 | ||||||||
\(274\) | −26.2087 | −1.58332 | ||||||||
\(275\) | −3.81984 | −0.230345 | ||||||||
\(276\) | 87.9574 | 5.29441 | ||||||||
\(277\) | 10.3103 | 0.619485 | 0.309743 | − | 0.950820i | \(-0.399757\pi\) | ||||
0.309743 | + | 0.950820i | \(0.399757\pi\) | |||||||
\(278\) | 22.4836 | 1.34848 | ||||||||
\(279\) | −35.0520 | −2.09851 | ||||||||
\(280\) | 11.4295 | 0.683042 | ||||||||
\(281\) | −9.91913 | −0.591726 | −0.295863 | − | 0.955230i | \(-0.595607\pi\) | ||||
−0.295863 | + | 0.955230i | \(0.595607\pi\) | |||||||
\(282\) | 42.2450 | 2.51565 | ||||||||
\(283\) | 4.21158 | 0.250352 | 0.125176 | − | 0.992135i | \(-0.460050\pi\) | ||||
0.125176 | + | 0.992135i | \(0.460050\pi\) | |||||||
\(284\) | −55.5662 | −3.29725 | ||||||||
\(285\) | −3.61577 | −0.214180 | ||||||||
\(286\) | −12.2371 | −0.723594 | ||||||||
\(287\) | −14.7127 | −0.868463 | ||||||||
\(288\) | −36.1465 | −2.12995 | ||||||||
\(289\) | 47.5261 | 2.79566 | ||||||||
\(290\) | −11.8837 | −0.697836 | ||||||||
\(291\) | 6.55179 | 0.384073 | ||||||||
\(292\) | 35.0555 | 2.05147 | ||||||||
\(293\) | 0.0522114 | 0.00305022 | 0.00152511 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152511 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(294\) | −18.6547 | −1.08796 | ||||||||
\(295\) | 11.7052 | 0.681502 | ||||||||
\(296\) | −51.1029 | −2.97030 | ||||||||
\(297\) | −2.14755 | −0.124613 | ||||||||
\(298\) | 33.7614 | 1.95574 | ||||||||
\(299\) | −38.1821 | −2.20813 | ||||||||
\(300\) | 54.9724 | 3.17384 | ||||||||
\(301\) | −24.2555 | −1.39806 | ||||||||
\(302\) | −14.1373 | −0.813512 | ||||||||
\(303\) | −31.6958 | −1.82088 | ||||||||
\(304\) | −15.9680 | −0.915830 | ||||||||
\(305\) | −6.20773 | −0.355453 | ||||||||
\(306\) | 82.1692 | 4.69730 | ||||||||
\(307\) | −14.4567 | −0.825088 | −0.412544 | − | 0.910938i | \(-0.635360\pi\) | ||||
−0.412544 | + | 0.910938i | \(0.635360\pi\) | |||||||
\(308\) | 8.51805 | 0.485361 | ||||||||
\(309\) | 18.8479 | 1.07222 | ||||||||
\(310\) | −17.9269 | −1.01818 | ||||||||
\(311\) | −12.5497 | −0.711629 | −0.355815 | − | 0.934557i | \(-0.615797\pi\) | ||||
−0.355815 | + | 0.934557i | \(0.615797\pi\) | |||||||
\(312\) | 101.875 | 5.76754 | ||||||||
\(313\) | −25.6393 | −1.44922 | −0.724609 | − | 0.689161i | \(-0.757979\pi\) | ||||
−0.724609 | + | 0.689161i | \(0.757979\pi\) | |||||||
\(314\) | 10.2877 | 0.580568 | ||||||||
\(315\) | −6.31537 | −0.355831 | ||||||||
\(316\) | 8.20189 | 0.461392 | ||||||||
\(317\) | 13.0472 | 0.732804 | 0.366402 | − | 0.930457i | \(-0.380589\pi\) | ||||
0.366402 | + | 0.930457i | \(0.380589\pi\) | |||||||
\(318\) | −3.06104 | −0.171655 | ||||||||
\(319\) | −5.12336 | −0.286853 | ||||||||
\(320\) | −4.48898 | −0.250942 | ||||||||
\(321\) | 8.93397 | 0.498646 | ||||||||
\(322\) | 37.7811 | 2.10546 | ||||||||
\(323\) | 14.2154 | 0.790969 | ||||||||
\(324\) | −25.1591 | −1.39773 | ||||||||
\(325\) | −23.8634 | −1.32370 | ||||||||
\(326\) | 10.2918 | 0.570010 | ||||||||
\(327\) | 21.9555 | 1.21414 | ||||||||
\(328\) | 50.7348 | 2.80136 | ||||||||
\(329\) | 12.7651 | 0.703763 | ||||||||
\(330\) | −4.60834 | −0.253681 | ||||||||
\(331\) | 4.19227 | 0.230428 | 0.115214 | − | 0.993341i | \(-0.463245\pi\) | ||||
0.115214 | + | 0.993341i | \(0.463245\pi\) | |||||||
\(332\) | 50.6781 | 2.78132 | ||||||||
\(333\) | 28.2370 | 1.54738 | ||||||||
\(334\) | −7.34635 | −0.401974 | ||||||||
\(335\) | −2.62887 | −0.143630 | ||||||||
\(336\) | −49.1329 | −2.68042 | ||||||||
\(337\) | 10.9409 | 0.595988 | 0.297994 | − | 0.954568i | \(-0.403682\pi\) | ||||
0.297994 | + | 0.954568i | \(0.403682\pi\) | |||||||
\(338\) | −42.6861 | −2.32182 | ||||||||
\(339\) | −53.0708 | −2.88241 | ||||||||
\(340\) | 29.5630 | 1.60328 | ||||||||
\(341\) | −7.72874 | −0.418535 | ||||||||
\(342\) | 18.1023 | 0.978860 | ||||||||
\(343\) | −20.1069 | −1.08567 | ||||||||
\(344\) | 83.6418 | 4.50966 | ||||||||
\(345\) | −14.3789 | −0.774135 | ||||||||
\(346\) | 2.56554 | 0.137924 | ||||||||
\(347\) | −16.7739 | −0.900469 | −0.450234 | − | 0.892910i | \(-0.648660\pi\) | ||||
−0.450234 | + | 0.892910i | \(0.648660\pi\) | |||||||
\(348\) | 73.7319 | 3.95245 | ||||||||
\(349\) | 10.7883 | 0.577485 | 0.288743 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288743 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(350\) | 23.6128 | 1.26216 | ||||||||
\(351\) | −13.4162 | −0.716106 | ||||||||
\(352\) | −7.97007 | −0.424806 | ||||||||
\(353\) | −2.37670 | −0.126499 | −0.0632495 | − | 0.997998i | \(-0.520146\pi\) | ||||
−0.0632495 | + | 0.997998i | \(0.520146\pi\) | |||||||
\(354\) | −103.237 | −5.48697 | ||||||||
\(355\) | 9.08374 | 0.482115 | ||||||||
\(356\) | −34.7607 | −1.84232 | ||||||||
\(357\) | 43.7403 | 2.31498 | ||||||||
\(358\) | −38.9362 | −2.05784 | ||||||||
\(359\) | 36.3997 | 1.92110 | 0.960551 | − | 0.278105i | \(-0.0897064\pi\) | ||||
0.960551 | + | 0.278105i | \(0.0897064\pi\) | |||||||
\(360\) | 21.7777 | 1.14779 | ||||||||
\(361\) | −15.8683 | −0.835172 | ||||||||
\(362\) | −13.2447 | −0.696126 | ||||||||
\(363\) | 26.9889 | 1.41655 | ||||||||
\(364\) | 53.2142 | 2.78918 | ||||||||
\(365\) | −5.73074 | −0.299960 | ||||||||
\(366\) | 54.7506 | 2.86186 | ||||||||
\(367\) | −3.07255 | −0.160386 | −0.0801929 | − | 0.996779i | \(-0.525554\pi\) | ||||
−0.0801929 | + | 0.996779i | \(0.525554\pi\) | |||||||
\(368\) | −63.5005 | −3.31019 | ||||||||
\(369\) | −28.0335 | −1.45937 | ||||||||
\(370\) | 14.4414 | 0.750774 | ||||||||
\(371\) | −0.924951 | −0.0480211 | ||||||||
\(372\) | 111.227 | 5.76684 | ||||||||
\(373\) | 4.38016 | 0.226796 | 0.113398 | − | 0.993550i | \(-0.463826\pi\) | ||||
0.113398 | + | 0.993550i | \(0.463826\pi\) | |||||||
\(374\) | 18.1178 | 0.936847 | ||||||||
\(375\) | −19.2026 | −0.991619 | ||||||||
\(376\) | −44.0187 | −2.27009 | ||||||||
\(377\) | −32.0068 | −1.64844 | ||||||||
\(378\) | 13.2753 | 0.682810 | ||||||||
\(379\) | −34.3109 | −1.76243 | −0.881216 | − | 0.472714i | \(-0.843274\pi\) | ||||
−0.881216 | + | 0.472714i | \(0.843274\pi\) | |||||||
\(380\) | 6.51289 | 0.334104 | ||||||||
\(381\) | 9.09893 | 0.466152 | ||||||||
\(382\) | −63.6977 | −3.25906 | ||||||||
\(383\) | −13.8511 | −0.707757 | −0.353878 | − | 0.935291i | \(-0.615137\pi\) | ||||
−0.353878 | + | 0.935291i | \(0.615137\pi\) | |||||||
\(384\) | −8.75638 | −0.446847 | ||||||||
\(385\) | −1.39250 | −0.0709682 | ||||||||
\(386\) | 1.44590 | 0.0735943 | ||||||||
\(387\) | −46.2163 | −2.34931 | ||||||||
\(388\) | −11.8014 | −0.599125 | ||||||||
\(389\) | 22.4250 | 1.13699 | 0.568495 | − | 0.822687i | \(-0.307526\pi\) | ||||
0.568495 | + | 0.822687i | \(0.307526\pi\) | |||||||
\(390\) | −28.7894 | −1.45781 | ||||||||
\(391\) | 56.5309 | 2.85889 | ||||||||
\(392\) | 19.4380 | 0.981766 | ||||||||
\(393\) | −43.2228 | −2.18030 | ||||||||
\(394\) | 44.5083 | 2.24230 | ||||||||
\(395\) | −1.34081 | −0.0674636 | ||||||||
\(396\) | 16.2303 | 0.815601 | ||||||||
\(397\) | 19.8719 | 0.997340 | 0.498670 | − | 0.866792i | \(-0.333822\pi\) | ||||
0.498670 | + | 0.866792i | \(0.333822\pi\) | |||||||
\(398\) | 54.5606 | 2.73487 | ||||||||
\(399\) | 9.63621 | 0.482414 | ||||||||
\(400\) | −39.6872 | −1.98436 | ||||||||
\(401\) | 17.3821 | 0.868019 | 0.434010 | − | 0.900908i | \(-0.357098\pi\) | ||||
0.434010 | + | 0.900908i | \(0.357098\pi\) | |||||||
\(402\) | 23.1860 | 1.15641 | ||||||||
\(403\) | −48.2833 | −2.40516 | ||||||||
\(404\) | 57.0919 | 2.84043 | ||||||||
\(405\) | 4.11291 | 0.204372 | ||||||||
\(406\) | 31.6707 | 1.57179 | ||||||||
\(407\) | 6.22606 | 0.308614 | ||||||||
\(408\) | −150.832 | −7.46732 | ||||||||
\(409\) | −12.2067 | −0.603581 | −0.301790 | − | 0.953374i | \(-0.597584\pi\) | ||||
−0.301790 | + | 0.953374i | \(0.597584\pi\) | |||||||
\(410\) | −14.3374 | −0.708073 | ||||||||
\(411\) | −26.5829 | −1.31124 | ||||||||
\(412\) | −33.9497 | −1.67258 | ||||||||
\(413\) | −31.1949 | −1.53500 | ||||||||
\(414\) | 71.9879 | 3.53801 | ||||||||
\(415\) | −8.28466 | −0.406678 | ||||||||
\(416\) | −49.7909 | −2.44120 | ||||||||
\(417\) | 22.8047 | 1.11675 | ||||||||
\(418\) | 3.99144 | 0.195228 | ||||||||
\(419\) | 16.0838 | 0.785745 | 0.392872 | − | 0.919593i | \(-0.371481\pi\) | ||||
0.392872 | + | 0.919593i | \(0.371481\pi\) | |||||||
\(420\) | 20.0399 | 0.977845 | ||||||||
\(421\) | 17.4473 | 0.850331 | 0.425166 | − | 0.905116i | \(-0.360216\pi\) | ||||
0.425166 | + | 0.905116i | \(0.360216\pi\) | |||||||
\(422\) | −41.8984 | −2.03958 | ||||||||
\(423\) | 24.3226 | 1.18260 | ||||||||
\(424\) | 3.18957 | 0.154899 | ||||||||
\(425\) | 35.3312 | 1.71382 | ||||||||
\(426\) | −80.1163 | −3.88165 | ||||||||
\(427\) | 16.5439 | 0.800615 | ||||||||
\(428\) | −16.0923 | −0.777850 | ||||||||
\(429\) | −12.4118 | −0.599249 | ||||||||
\(430\) | −23.6367 | −1.13987 | ||||||||
\(431\) | −0.628459 | −0.0302718 | −0.0151359 | − | 0.999885i | \(-0.504818\pi\) | ||||
−0.0151359 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(432\) | −22.3125 | −1.07351 | ||||||||
\(433\) | 17.2854 | 0.830684 | 0.415342 | − | 0.909665i | \(-0.363662\pi\) | ||||
0.415342 | + | 0.909665i | \(0.363662\pi\) | |||||||
\(434\) | 47.7761 | 2.29333 | ||||||||
\(435\) | −12.0534 | −0.577916 | ||||||||
\(436\) | −39.5472 | −1.89397 | ||||||||
\(437\) | 12.4541 | 0.595759 | ||||||||
\(438\) | 50.5436 | 2.41507 | ||||||||
\(439\) | 32.8972 | 1.57010 | 0.785049 | − | 0.619433i | \(-0.212638\pi\) | ||||
0.785049 | + | 0.619433i | \(0.212638\pi\) | |||||||
\(440\) | 4.80184 | 0.228919 | ||||||||
\(441\) | −10.7405 | −0.511451 | ||||||||
\(442\) | 113.186 | 5.38370 | ||||||||
\(443\) | −35.0305 | −1.66435 | −0.832175 | − | 0.554514i | \(-0.812904\pi\) | ||||
−0.832175 | + | 0.554514i | \(0.812904\pi\) | |||||||
\(444\) | −89.6012 | −4.25229 | ||||||||
\(445\) | 5.68255 | 0.269379 | ||||||||
\(446\) | −32.0843 | −1.51923 | ||||||||
\(447\) | 34.2434 | 1.61966 | ||||||||
\(448\) | 11.9634 | 0.565216 | ||||||||
\(449\) | 14.5810 | 0.688122 | 0.344061 | − | 0.938947i | \(-0.388197\pi\) | ||||
0.344061 | + | 0.938947i | \(0.388197\pi\) | |||||||
\(450\) | 44.9917 | 2.12093 | ||||||||
\(451\) | −6.18121 | −0.291062 | ||||||||
\(452\) | 95.5935 | 4.49634 | ||||||||
\(453\) | −14.3392 | −0.673714 | ||||||||
\(454\) | −59.9141 | −2.81191 | ||||||||
\(455\) | −8.69925 | −0.407827 | ||||||||
\(456\) | −33.2292 | −1.55610 | ||||||||
\(457\) | 14.5808 | 0.682059 | 0.341030 | − | 0.940053i | \(-0.389224\pi\) | ||||
0.341030 | + | 0.940053i | \(0.389224\pi\) | |||||||
\(458\) | 6.20858 | 0.290108 | ||||||||
\(459\) | 19.8636 | 0.927152 | ||||||||
\(460\) | 25.9000 | 1.20759 | ||||||||
\(461\) | −23.0210 | −1.07220 | −0.536099 | − | 0.844155i | \(-0.680102\pi\) | ||||
−0.536099 | + | 0.844155i | \(0.680102\pi\) | |||||||
\(462\) | 12.2815 | 0.571385 | ||||||||
\(463\) | 13.9624 | 0.648887 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(464\) | −53.2305 | −2.47116 | ||||||||
\(465\) | −18.1829 | −0.843212 | ||||||||
\(466\) | −20.7183 | −0.959758 | ||||||||
\(467\) | −4.86555 | −0.225151 | −0.112575 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112575 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(468\) | 101.394 | 4.68695 | ||||||||
\(469\) | 7.00607 | 0.323510 | ||||||||
\(470\) | 12.4395 | 0.573790 | ||||||||
\(471\) | 10.4346 | 0.480801 | ||||||||
\(472\) | 107.571 | 4.95137 | ||||||||
\(473\) | −10.1904 | −0.468555 | ||||||||
\(474\) | 11.8256 | 0.543169 | ||||||||
\(475\) | 7.78366 | 0.357139 | ||||||||
\(476\) | −78.7870 | −3.61119 | ||||||||
\(477\) | −1.76240 | −0.0806947 | ||||||||
\(478\) | 38.5443 | 1.76298 | ||||||||
\(479\) | 21.4660 | 0.980805 | 0.490402 | − | 0.871496i | \(-0.336850\pi\) | ||||
0.490402 | + | 0.871496i | \(0.336850\pi\) | |||||||
\(480\) | −18.7507 | −0.855846 | ||||||||
\(481\) | 38.8957 | 1.77349 | ||||||||
\(482\) | 18.3363 | 0.835197 | ||||||||
\(483\) | 38.3206 | 1.74365 | ||||||||
\(484\) | −48.6136 | −2.20971 | ||||||||
\(485\) | 1.92924 | 0.0876025 | ||||||||
\(486\) | −55.5409 | −2.51939 | ||||||||
\(487\) | −40.4414 | −1.83258 | −0.916288 | − | 0.400520i | \(-0.868829\pi\) | ||||
−0.916288 | + | 0.400520i | \(0.868829\pi\) | |||||||
\(488\) | −57.0494 | −2.58251 | ||||||||
\(489\) | 10.4388 | 0.472057 | ||||||||
\(490\) | −5.49307 | −0.248152 | ||||||||
\(491\) | −33.0060 | −1.48954 | −0.744769 | − | 0.667322i | \(-0.767440\pi\) | ||||
−0.744769 | + | 0.667322i | \(0.767440\pi\) | |||||||
\(492\) | 88.9557 | 4.01043 | ||||||||
\(493\) | 47.3881 | 2.13425 | ||||||||
\(494\) | 24.9354 | 1.12190 | ||||||||
\(495\) | −2.65326 | −0.119255 | ||||||||
\(496\) | −80.2998 | −3.60557 | ||||||||
\(497\) | −24.2086 | −1.08591 | ||||||||
\(498\) | 73.0686 | 3.27428 | ||||||||
\(499\) | −9.56933 | −0.428382 | −0.214191 | − | 0.976792i | \(-0.568711\pi\) | ||||
−0.214191 | + | 0.976792i | \(0.568711\pi\) | |||||||
\(500\) | 34.5886 | 1.54685 | ||||||||
\(501\) | −7.45125 | −0.332897 | ||||||||
\(502\) | 16.4483 | 0.734124 | ||||||||
\(503\) | 9.32185 | 0.415641 | 0.207820 | − | 0.978167i | \(-0.433363\pi\) | ||||
0.207820 | + | 0.978167i | \(0.433363\pi\) | |||||||
\(504\) | −58.0386 | −2.58525 | ||||||||
\(505\) | −9.33316 | −0.415320 | ||||||||
\(506\) | 15.8729 | 0.705635 | ||||||||
\(507\) | −43.2956 | −1.92282 | ||||||||
\(508\) | −16.3894 | −0.727162 | ||||||||
\(509\) | 34.1837 | 1.51516 | 0.757582 | − | 0.652740i | \(-0.226381\pi\) | ||||
0.757582 | + | 0.652740i | \(0.226381\pi\) | |||||||
\(510\) | 42.6245 | 1.88744 | ||||||||
\(511\) | 15.2727 | 0.675624 | ||||||||
\(512\) | 45.8327 | 2.02554 | ||||||||
\(513\) | 4.37605 | 0.193207 | ||||||||
\(514\) | 77.0779 | 3.39976 | ||||||||
\(515\) | 5.54996 | 0.244560 | ||||||||
\(516\) | 146.653 | 6.45604 | ||||||||
\(517\) | 5.36297 | 0.235863 | ||||||||
\(518\) | −38.4871 | −1.69103 | ||||||||
\(519\) | 2.60217 | 0.114223 | ||||||||
\(520\) | 29.9982 | 1.31551 | ||||||||
\(521\) | 17.5370 | 0.768310 | 0.384155 | − | 0.923269i | \(-0.374493\pi\) | ||||
0.384155 | + | 0.923269i | \(0.374493\pi\) | |||||||
\(522\) | 60.3452 | 2.64124 | ||||||||
\(523\) | 36.2892 | 1.58681 | 0.793407 | − | 0.608691i | \(-0.208305\pi\) | ||||
0.793407 | + | 0.608691i | \(0.208305\pi\) | |||||||
\(524\) | 77.8549 | 3.40111 | ||||||||
\(525\) | 23.9499 | 1.04526 | ||||||||
\(526\) | 4.45274 | 0.194149 | ||||||||
\(527\) | 71.4863 | 3.11399 | ||||||||
\(528\) | −20.6421 | −0.898331 | ||||||||
\(529\) | 26.5264 | 1.15332 | ||||||||
\(530\) | −0.901356 | −0.0391524 | ||||||||
\(531\) | −59.4386 | −2.57942 | ||||||||
\(532\) | −17.3572 | −0.752529 | ||||||||
\(533\) | −38.6154 | −1.67262 | ||||||||
\(534\) | −50.1186 | −2.16884 | ||||||||
\(535\) | 2.63070 | 0.113735 | ||||||||
\(536\) | −24.1595 | −1.04353 | ||||||||
\(537\) | −39.4922 | −1.70421 | ||||||||
\(538\) | −19.3805 | −0.835552 | ||||||||
\(539\) | −2.36820 | −0.102006 | ||||||||
\(540\) | 9.10061 | 0.391628 | ||||||||
\(541\) | 19.3552 | 0.832144 | 0.416072 | − | 0.909332i | \(-0.363406\pi\) | ||||
0.416072 | + | 0.909332i | \(0.363406\pi\) | |||||||
\(542\) | −44.5035 | −1.91159 | ||||||||
\(543\) | −13.4338 | −0.576501 | ||||||||
\(544\) | 73.7185 | 3.16065 | ||||||||
\(545\) | 6.46502 | 0.276931 | ||||||||
\(546\) | 76.7252 | 3.28353 | ||||||||
\(547\) | 26.3522 | 1.12674 | 0.563368 | − | 0.826206i | \(-0.309505\pi\) | ||||
0.563368 | + | 0.826206i | \(0.309505\pi\) | |||||||
\(548\) | 47.8823 | 2.04543 | ||||||||
\(549\) | 31.5227 | 1.34536 | ||||||||
\(550\) | 9.92037 | 0.423006 | ||||||||
\(551\) | 10.4398 | 0.444752 | ||||||||
\(552\) | −132.143 | −5.62439 | ||||||||
\(553\) | 3.57333 | 0.151954 | ||||||||
\(554\) | −26.7765 | −1.13762 | ||||||||
\(555\) | 14.6476 | 0.621758 | ||||||||
\(556\) | −41.0768 | −1.74204 | ||||||||
\(557\) | 37.8246 | 1.60268 | 0.801341 | − | 0.598208i | \(-0.204121\pi\) | ||||
0.801341 | + | 0.598208i | \(0.204121\pi\) | |||||||
\(558\) | 91.0325 | 3.85371 | ||||||||
\(559\) | −63.6617 | −2.69260 | ||||||||
\(560\) | −14.4677 | −0.611372 | ||||||||
\(561\) | 18.3765 | 0.775855 | ||||||||
\(562\) | 25.7606 | 1.08665 | ||||||||
\(563\) | 1.37711 | 0.0580382 | 0.0290191 | − | 0.999579i | \(-0.490762\pi\) | ||||
0.0290191 | + | 0.999579i | \(0.490762\pi\) | |||||||
\(564\) | −77.1801 | −3.24987 | ||||||||
\(565\) | −15.6272 | −0.657443 | ||||||||
\(566\) | −10.9377 | −0.459747 | ||||||||
\(567\) | −10.9611 | −0.460323 | ||||||||
\(568\) | 83.4802 | 3.50275 | ||||||||
\(569\) | 25.4686 | 1.06770 | 0.533849 | − | 0.845580i | \(-0.320745\pi\) | ||||
0.533849 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(570\) | 9.39039 | 0.393320 | ||||||||
\(571\) | −29.3389 | −1.22779 | −0.613897 | − | 0.789386i | \(-0.710399\pi\) | ||||
−0.613897 | + | 0.789386i | \(0.710399\pi\) | |||||||
\(572\) | 22.3567 | 0.934783 | ||||||||
\(573\) | −64.6072 | −2.69901 | ||||||||
\(574\) | 38.2099 | 1.59485 | ||||||||
\(575\) | 30.9535 | 1.29085 | ||||||||
\(576\) | 22.7949 | 0.949789 | ||||||||
\(577\) | −15.5966 | −0.649296 | −0.324648 | − | 0.945835i | \(-0.605246\pi\) | ||||
−0.324648 | + | 0.945835i | \(0.605246\pi\) | |||||||
\(578\) | −123.429 | −5.13395 | ||||||||
\(579\) | 1.46654 | 0.0609475 | ||||||||
\(580\) | 21.7111 | 0.901506 | ||||||||
\(581\) | 22.0790 | 0.915992 | ||||||||
\(582\) | −17.0154 | −0.705313 | ||||||||
\(583\) | −0.388597 | −0.0160940 | ||||||||
\(584\) | −52.6658 | −2.17933 | ||||||||
\(585\) | −16.5755 | −0.685313 | ||||||||
\(586\) | −0.135596 | −0.00560144 | ||||||||
\(587\) | −40.5404 | −1.67328 | −0.836641 | − | 0.547752i | \(-0.815484\pi\) | ||||
−0.836641 | + | 0.547752i | \(0.815484\pi\) | |||||||
\(588\) | 34.0815 | 1.40550 | ||||||||
\(589\) | 15.7488 | 0.648919 | ||||||||
\(590\) | −30.3991 | −1.25151 | ||||||||
\(591\) | 45.1438 | 1.85697 | ||||||||
\(592\) | 64.6873 | 2.65863 | ||||||||
\(593\) | −28.1266 | −1.15502 | −0.577510 | − | 0.816383i | \(-0.695976\pi\) | ||||
−0.577510 | + | 0.816383i | \(0.695976\pi\) | |||||||
\(594\) | 5.57733 | 0.228841 | ||||||||
\(595\) | 12.8798 | 0.528019 | ||||||||
\(596\) | −61.6809 | −2.52655 | ||||||||
\(597\) | 55.3396 | 2.26490 | ||||||||
\(598\) | 99.1614 | 4.05501 | ||||||||
\(599\) | −10.7550 | −0.439438 | −0.219719 | − | 0.975563i | \(-0.570514\pi\) | ||||
−0.219719 | + | 0.975563i | \(0.570514\pi\) | |||||||
\(600\) | −82.5881 | −3.37165 | ||||||||
\(601\) | −48.2605 | −1.96859 | −0.984293 | − | 0.176544i | \(-0.943508\pi\) | ||||
−0.984293 | + | 0.176544i | \(0.943508\pi\) | |||||||
\(602\) | 62.9931 | 2.56741 | ||||||||
\(603\) | 13.3493 | 0.543627 | ||||||||
\(604\) | 25.8284 | 1.05094 | ||||||||
\(605\) | 7.94716 | 0.323098 | ||||||||
\(606\) | 82.3161 | 3.34386 | ||||||||
\(607\) | 43.9992 | 1.78587 | 0.892936 | − | 0.450183i | \(-0.148641\pi\) | ||||
0.892936 | + | 0.450183i | \(0.148641\pi\) | |||||||
\(608\) | 16.2406 | 0.658642 | ||||||||
\(609\) | 32.1229 | 1.30169 | ||||||||
\(610\) | 16.1219 | 0.652756 | ||||||||
\(611\) | 33.5037 | 1.35541 | ||||||||
\(612\) | −150.120 | −6.06826 | ||||||||
\(613\) | 29.6653 | 1.19817 | 0.599085 | − | 0.800685i | \(-0.295531\pi\) | ||||
0.599085 | + | 0.800685i | \(0.295531\pi\) | |||||||
\(614\) | 37.5450 | 1.51519 | ||||||||
\(615\) | −14.5421 | −0.586395 | ||||||||
\(616\) | −12.7971 | −0.515611 | ||||||||
\(617\) | 25.0075 | 1.00677 | 0.503383 | − | 0.864064i | \(-0.332089\pi\) | ||||
0.503383 | + | 0.864064i | \(0.332089\pi\) | |||||||
\(618\) | −48.9492 | −1.96903 | ||||||||
\(619\) | 13.1365 | 0.528002 | 0.264001 | − | 0.964522i | \(-0.414958\pi\) | ||||
0.264001 | + | 0.964522i | \(0.414958\pi\) | |||||||
\(620\) | 32.7519 | 1.31535 | ||||||||
\(621\) | 17.4024 | 0.698332 | ||||||||
\(622\) | 32.5924 | 1.30684 | ||||||||
\(623\) | −15.1443 | −0.606742 | ||||||||
\(624\) | −128.956 | −5.16237 | ||||||||
\(625\) | 16.3374 | 0.653496 | ||||||||
\(626\) | 66.5869 | 2.66135 | ||||||||
\(627\) | 4.04843 | 0.161679 | ||||||||
\(628\) | −18.7953 | −0.750013 | ||||||||
\(629\) | −57.5874 | −2.29616 | ||||||||
\(630\) | 16.4014 | 0.653449 | ||||||||
\(631\) | −16.5689 | −0.659597 | −0.329799 | − | 0.944051i | \(-0.606981\pi\) | ||||
−0.329799 | + | 0.944051i | \(0.606981\pi\) | |||||||
\(632\) | −12.3222 | −0.490149 | ||||||||
\(633\) | −42.4967 | −1.68909 | ||||||||
\(634\) | −33.8845 | −1.34572 | ||||||||
\(635\) | 2.67928 | 0.106324 | ||||||||
\(636\) | 5.59242 | 0.221754 | ||||||||
\(637\) | −14.7947 | −0.586187 | ||||||||
\(638\) | 13.3057 | 0.526778 | ||||||||
\(639\) | −46.1270 | −1.82476 | ||||||||
\(640\) | −2.57841 | −0.101921 | ||||||||
\(641\) | 0.672540 | 0.0265637 | 0.0132819 | − | 0.999912i | \(-0.495772\pi\) | ||||
0.0132819 | + | 0.999912i | \(0.495772\pi\) | |||||||
\(642\) | −23.2021 | −0.915714 | ||||||||
\(643\) | 26.2009 | 1.03326 | 0.516632 | − | 0.856208i | \(-0.327186\pi\) | ||||
0.516632 | + | 0.856208i | \(0.327186\pi\) | |||||||
\(644\) | −69.0247 | −2.71996 | ||||||||
\(645\) | −23.9743 | −0.943986 | ||||||||
\(646\) | −36.9185 | −1.45254 | ||||||||
\(647\) | 2.85373 | 0.112192 | 0.0560958 | − | 0.998425i | \(-0.482135\pi\) | ||||
0.0560958 | + | 0.998425i | \(0.482135\pi\) | |||||||
\(648\) | 37.7979 | 1.48484 | ||||||||
\(649\) | −13.1058 | −0.514448 | ||||||||
\(650\) | 61.9748 | 2.43085 | ||||||||
\(651\) | 48.4584 | 1.89923 | ||||||||
\(652\) | −18.8028 | −0.736373 | ||||||||
\(653\) | 9.57456 | 0.374682 | 0.187341 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187341 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(654\) | −57.0198 | −2.22965 | ||||||||
\(655\) | −12.7274 | −0.497301 | ||||||||
\(656\) | −64.2212 | −2.50742 | ||||||||
\(657\) | 29.1005 | 1.13532 | ||||||||
\(658\) | −33.1518 | −1.29239 | ||||||||
\(659\) | −20.9439 | −0.815860 | −0.407930 | − | 0.913013i | \(-0.633749\pi\) | ||||
−0.407930 | + | 0.913013i | \(0.633749\pi\) | |||||||
\(660\) | 8.41929 | 0.327720 | ||||||||
\(661\) | 47.0866 | 1.83146 | 0.915729 | − | 0.401797i | \(-0.131614\pi\) | ||||
0.915729 | + | 0.401797i | \(0.131614\pi\) | |||||||
\(662\) | −10.8876 | −0.423158 | ||||||||
\(663\) | 114.802 | 4.45854 | ||||||||
\(664\) | −76.1365 | −2.95467 | ||||||||
\(665\) | 2.83748 | 0.110033 | ||||||||
\(666\) | −73.3333 | −2.84161 | ||||||||
\(667\) | 41.5164 | 1.60752 | ||||||||
\(668\) | 13.4215 | 0.519295 | ||||||||
\(669\) | −32.5424 | −1.25816 | ||||||||
\(670\) | 6.82735 | 0.263763 | ||||||||
\(671\) | 6.95054 | 0.268323 | ||||||||
\(672\) | 49.9714 | 1.92769 | ||||||||
\(673\) | 38.9569 | 1.50168 | 0.750838 | − | 0.660486i | \(-0.229650\pi\) | ||||
0.750838 | + | 0.660486i | \(0.229650\pi\) | |||||||
\(674\) | −28.4142 | −1.09447 | ||||||||
\(675\) | 10.8763 | 0.418628 | ||||||||
\(676\) | 77.9860 | 2.99946 | ||||||||
\(677\) | 15.6802 | 0.602638 | 0.301319 | − | 0.953523i | \(-0.402573\pi\) | ||||
0.301319 | + | 0.953523i | \(0.402573\pi\) | |||||||
\(678\) | 137.828 | 5.29326 | ||||||||
\(679\) | −5.14153 | −0.197314 | ||||||||
\(680\) | −44.4142 | −1.70321 | ||||||||
\(681\) | −60.7696 | −2.32870 | ||||||||
\(682\) | 20.0721 | 0.768599 | ||||||||
\(683\) | 6.83330 | 0.261469 | 0.130734 | − | 0.991417i | \(-0.458266\pi\) | ||||
0.130734 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(684\) | −33.0723 | −1.26455 | ||||||||
\(685\) | −7.82761 | −0.299078 | ||||||||
\(686\) | 52.2191 | 1.99373 | ||||||||
\(687\) | 6.29724 | 0.240255 | ||||||||
\(688\) | −105.876 | −4.03647 | ||||||||
\(689\) | −2.42766 | −0.0924863 | ||||||||
\(690\) | 37.3430 | 1.42162 | ||||||||
\(691\) | −19.8985 | −0.756974 | −0.378487 | − | 0.925607i | \(-0.623556\pi\) | ||||
−0.378487 | + | 0.925607i | \(0.623556\pi\) | |||||||
\(692\) | −4.68715 | −0.178179 | ||||||||
\(693\) | 7.07106 | 0.268608 | ||||||||
\(694\) | 43.5628 | 1.65362 | ||||||||
\(695\) | 6.71507 | 0.254717 | ||||||||
\(696\) | −110.772 | −4.19878 | ||||||||
\(697\) | 57.1725 | 2.16556 | ||||||||
\(698\) | −28.0180 | −1.06050 | ||||||||
\(699\) | −21.0142 | −0.794829 | ||||||||
\(700\) | −43.1397 | −1.63053 | ||||||||
\(701\) | 45.7263 | 1.72706 | 0.863529 | − | 0.504299i | \(-0.168249\pi\) | ||||
0.863529 | + | 0.504299i | \(0.168249\pi\) | |||||||
\(702\) | 34.8429 | 1.31506 | ||||||||
\(703\) | −12.6868 | −0.478492 | ||||||||
\(704\) | 5.02613 | 0.189429 | ||||||||
\(705\) | 12.6171 | 0.475187 | ||||||||
\(706\) | 6.17244 | 0.232303 | ||||||||
\(707\) | 24.8733 | 0.935458 | ||||||||
\(708\) | 188.610 | 7.08839 | ||||||||
\(709\) | −19.2019 | −0.721143 | −0.360571 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(710\) | −23.5911 | −0.885357 | ||||||||
\(711\) | 6.80861 | 0.255343 | ||||||||
\(712\) | 52.2230 | 1.95714 | ||||||||
\(713\) | 62.6287 | 2.34546 | ||||||||
\(714\) | −113.596 | −4.25124 | ||||||||
\(715\) | −3.65479 | −0.136681 | ||||||||
\(716\) | 71.1352 | 2.65845 | ||||||||
\(717\) | 39.0947 | 1.46002 | ||||||||
\(718\) | −94.5324 | −3.52792 | ||||||||
\(719\) | 26.5642 | 0.990677 | 0.495339 | − | 0.868700i | \(-0.335044\pi\) | ||||
0.495339 | + | 0.868700i | \(0.335044\pi\) | |||||||
\(720\) | −27.5667 | −1.02735 | ||||||||
\(721\) | −14.7909 | −0.550842 | ||||||||
\(722\) | 41.2109 | 1.53371 | ||||||||
\(723\) | 18.5982 | 0.691673 | ||||||||
\(724\) | 24.1976 | 0.899298 | ||||||||
\(725\) | 25.9473 | 0.963659 | ||||||||
\(726\) | −70.0919 | −2.60135 | ||||||||
\(727\) | −28.2304 | −1.04701 | −0.523503 | − | 0.852024i | \(-0.675375\pi\) | ||||
−0.523503 | + | 0.852024i | \(0.675375\pi\) | |||||||
\(728\) | −79.9467 | −2.96302 | ||||||||
\(729\) | −40.4265 | −1.49728 | ||||||||
\(730\) | 14.8831 | 0.550848 | ||||||||
\(731\) | 94.2551 | 3.48615 | ||||||||
\(732\) | −100.027 | −3.69712 | ||||||||
\(733\) | −42.7246 | −1.57807 | −0.789035 | − | 0.614348i | \(-0.789419\pi\) | ||||
−0.789035 | + | 0.614348i | \(0.789419\pi\) | |||||||
\(734\) | 7.97961 | 0.294533 | ||||||||
\(735\) | −5.57151 | −0.205508 | ||||||||
\(736\) | 64.5843 | 2.38061 | ||||||||
\(737\) | 2.94344 | 0.108423 | ||||||||
\(738\) | 72.8049 | 2.67999 | ||||||||
\(739\) | −36.7423 | −1.35159 | −0.675794 | − | 0.737091i | \(-0.736199\pi\) | ||||
−0.675794 | + | 0.737091i | \(0.736199\pi\) | |||||||
\(740\) | −26.3840 | −0.969896 | ||||||||
\(741\) | 25.2915 | 0.929106 | ||||||||
\(742\) | 2.40216 | 0.0881860 | ||||||||
\(743\) | −22.1036 | −0.810904 | −0.405452 | − | 0.914116i | \(-0.632886\pi\) | ||||
−0.405452 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(744\) | −167.102 | −6.12626 | ||||||||
\(745\) | 10.0833 | 0.369425 | ||||||||
\(746\) | −11.3756 | −0.416489 | ||||||||
\(747\) | 42.0693 | 1.53923 | ||||||||
\(748\) | −33.1005 | −1.21028 | ||||||||
\(749\) | −7.01095 | −0.256175 | ||||||||
\(750\) | 49.8705 | 1.82101 | ||||||||
\(751\) | 31.7198 | 1.15747 | 0.578735 | − | 0.815515i | \(-0.303546\pi\) | ||||
0.578735 | + | 0.815515i | \(0.303546\pi\) | |||||||
\(752\) | 55.7199 | 2.03190 | ||||||||
\(753\) | 16.6832 | 0.607969 | ||||||||
\(754\) | 83.1239 | 3.02719 | ||||||||
\(755\) | −4.22233 | −0.153666 | ||||||||
\(756\) | −24.2536 | −0.882094 | ||||||||
\(757\) | 28.3298 | 1.02966 | 0.514831 | − | 0.857292i | \(-0.327855\pi\) | ||||
0.514831 | + | 0.857292i | \(0.327855\pi\) | |||||||
\(758\) | 89.1076 | 3.23654 | ||||||||
\(759\) | 16.0995 | 0.584375 | ||||||||
\(760\) | −9.78467 | −0.354927 | ||||||||
\(761\) | 18.6435 | 0.675826 | 0.337913 | − | 0.941177i | \(-0.390279\pi\) | ||||
0.337913 | + | 0.941177i | \(0.390279\pi\) | |||||||
\(762\) | −23.6305 | −0.856044 | ||||||||
\(763\) | −17.2296 | −0.623753 | ||||||||
\(764\) | 116.374 | 4.21025 | ||||||||
\(765\) | 24.5411 | 0.887285 | ||||||||
\(766\) | 35.9721 | 1.29973 | ||||||||
\(767\) | −81.8751 | −2.95634 | ||||||||
\(768\) | 53.2304 | 1.92079 | ||||||||
\(769\) | 35.4371 | 1.27789 | 0.638947 | − | 0.769251i | \(-0.279370\pi\) | ||||
0.638947 | + | 0.769251i | \(0.279370\pi\) | |||||||
\(770\) | 3.61641 | 0.130326 | ||||||||
\(771\) | 78.1785 | 2.81553 | ||||||||
\(772\) | −2.64161 | −0.0950735 | ||||||||
\(773\) | 19.2193 | 0.691271 | 0.345636 | − | 0.938369i | \(-0.387663\pi\) | ||||
0.345636 | + | 0.938369i | \(0.387663\pi\) | |||||||
\(774\) | 120.027 | 4.31428 | ||||||||
\(775\) | 39.1423 | 1.40603 | ||||||||
\(776\) | 17.7299 | 0.636466 | ||||||||
\(777\) | −39.0367 | −1.40043 | ||||||||
\(778\) | −58.2391 | −2.08797 | ||||||||
\(779\) | 12.5954 | 0.451277 | ||||||||
\(780\) | 52.5972 | 1.88328 | ||||||||
\(781\) | −10.1707 | −0.363936 | ||||||||
\(782\) | −146.815 | −5.25008 | ||||||||
\(783\) | 14.5878 | 0.521327 | ||||||||
\(784\) | −24.6050 | −0.878751 | ||||||||
\(785\) | 3.07258 | 0.109665 | ||||||||
\(786\) | 112.253 | 4.00392 | ||||||||
\(787\) | −32.6004 | −1.16208 | −0.581039 | − | 0.813875i | \(-0.697354\pi\) | ||||
−0.581039 | + | 0.813875i | \(0.697354\pi\) | |||||||
\(788\) | −81.3151 | −2.89673 | ||||||||
\(789\) | 4.51632 | 0.160785 | ||||||||
\(790\) | 3.48218 | 0.123890 | ||||||||
\(791\) | 41.6474 | 1.48081 | ||||||||
\(792\) | −24.3836 | −0.866434 | ||||||||
\(793\) | 43.4217 | 1.54195 | ||||||||
\(794\) | −51.6085 | −1.83152 | ||||||||
\(795\) | −0.914227 | −0.0324243 | ||||||||
\(796\) | −99.6803 | −3.53307 | ||||||||
\(797\) | −18.0298 | −0.638648 | −0.319324 | − | 0.947646i | \(-0.603456\pi\) | ||||
−0.319324 | + | 0.947646i | \(0.603456\pi\) | |||||||
\(798\) | −25.0259 | −0.885906 | ||||||||
\(799\) | −49.6043 | −1.75487 | ||||||||
\(800\) | 40.3645 | 1.42710 | ||||||||
\(801\) | −28.8558 | −1.01957 | ||||||||
\(802\) | −45.1424 | −1.59403 | ||||||||
\(803\) | 6.41648 | 0.226433 | ||||||||
\(804\) | −42.3600 | −1.49392 | ||||||||
\(805\) | 11.2839 | 0.397705 | ||||||||
\(806\) | 125.395 | 4.41684 | ||||||||
\(807\) | −19.6572 | −0.691967 | ||||||||
\(808\) | −85.7723 | −3.01746 | ||||||||
\(809\) | 20.0714 | 0.705674 | 0.352837 | − | 0.935685i | \(-0.385217\pi\) | ||||
0.352837 | + | 0.935685i | \(0.385217\pi\) | |||||||
\(810\) | −10.6815 | −0.375309 | ||||||||
\(811\) | −46.3628 | −1.62802 | −0.814008 | − | 0.580853i | \(-0.802719\pi\) | ||||
−0.814008 | + | 0.580853i | \(0.802719\pi\) | |||||||
\(812\) | −57.8613 | −2.03053 | ||||||||
\(813\) | −45.1389 | −1.58309 | ||||||||
\(814\) | −16.1695 | −0.566741 | ||||||||
\(815\) | 3.07380 | 0.107671 | ||||||||
\(816\) | 190.927 | 6.68378 | ||||||||
\(817\) | 20.7649 | 0.726472 | ||||||||
\(818\) | 31.7015 | 1.10842 | ||||||||
\(819\) | 44.1746 | 1.54358 | ||||||||
\(820\) | 26.1939 | 0.914732 | ||||||||
\(821\) | −20.2018 | −0.705046 | −0.352523 | − | 0.935803i | \(-0.614676\pi\) | ||||
−0.352523 | + | 0.935803i | \(0.614676\pi\) | |||||||
\(822\) | 69.0376 | 2.40796 | ||||||||
\(823\) | −10.9908 | −0.383115 | −0.191557 | − | 0.981481i | \(-0.561354\pi\) | ||||
−0.191557 | + | 0.981481i | \(0.561354\pi\) | |||||||
\(824\) | 51.0045 | 1.77682 | ||||||||
\(825\) | 10.0620 | 0.350315 | ||||||||
\(826\) | 81.0152 | 2.81888 | ||||||||
\(827\) | −33.0782 | −1.15024 | −0.575120 | − | 0.818069i | \(-0.695045\pi\) | ||||
−0.575120 | + | 0.818069i | \(0.695045\pi\) | |||||||
\(828\) | −131.519 | −4.57062 | ||||||||
\(829\) | 18.0310 | 0.626242 | 0.313121 | − | 0.949713i | \(-0.398625\pi\) | ||||
0.313121 | + | 0.949713i | \(0.398625\pi\) | |||||||
\(830\) | 21.5158 | 0.746824 | ||||||||
\(831\) | −27.1589 | −0.942130 | ||||||||
\(832\) | 31.3994 | 1.08858 | ||||||||
\(833\) | 21.9045 | 0.758945 | ||||||||
\(834\) | −59.2252 | −2.05080 | ||||||||
\(835\) | −2.19410 | −0.0759299 | ||||||||
\(836\) | −7.29222 | −0.252207 | ||||||||
\(837\) | 22.0062 | 0.760645 | ||||||||
\(838\) | −41.7707 | −1.44294 | ||||||||
\(839\) | −38.7196 | −1.33675 | −0.668375 | − | 0.743824i | \(-0.733010\pi\) | ||||
−0.668375 | + | 0.743824i | \(0.733010\pi\) | |||||||
\(840\) | −30.1070 | −1.03879 | ||||||||
\(841\) | 5.80191 | 0.200066 | ||||||||
\(842\) | −45.3119 | −1.56155 | ||||||||
\(843\) | 26.1285 | 0.899913 | ||||||||
\(844\) | 76.5470 | 2.63486 | ||||||||
\(845\) | −12.7488 | −0.438573 | ||||||||
\(846\) | −63.1673 | −2.17174 | ||||||||
\(847\) | −21.1796 | −0.727739 | ||||||||
\(848\) | −4.03743 | −0.138646 | ||||||||
\(849\) | −11.0939 | −0.380742 | ||||||||
\(850\) | −91.7576 | −3.14726 | ||||||||
\(851\) | −50.4520 | −1.72947 | ||||||||
\(852\) | 146.370 | 5.01455 | ||||||||
\(853\) | −47.7349 | −1.63441 | −0.817206 | − | 0.576346i | \(-0.804478\pi\) | ||||
−0.817206 | + | 0.576346i | \(0.804478\pi\) | |||||||
\(854\) | −42.9656 | −1.47025 | ||||||||
\(855\) | 5.40653 | 0.184899 | ||||||||
\(856\) | 24.1763 | 0.826329 | ||||||||
\(857\) | −45.8957 | −1.56777 | −0.783883 | − | 0.620908i | \(-0.786764\pi\) | ||||
−0.783883 | + | 0.620908i | \(0.786764\pi\) | |||||||
\(858\) | 32.2343 | 1.10046 | ||||||||
\(859\) | −52.9776 | −1.80757 | −0.903786 | − | 0.427984i | \(-0.859224\pi\) | ||||
−0.903786 | + | 0.427984i | \(0.859224\pi\) | |||||||
\(860\) | 43.1835 | 1.47255 | ||||||||
\(861\) | 38.7555 | 1.32078 | ||||||||
\(862\) | 1.63215 | 0.0555912 | ||||||||
\(863\) | 18.3387 | 0.624256 | 0.312128 | − | 0.950040i | \(-0.398958\pi\) | ||||
0.312128 | + | 0.950040i | \(0.398958\pi\) | |||||||
\(864\) | 22.6933 | 0.772042 | ||||||||
\(865\) | 0.766237 | 0.0260528 | ||||||||
\(866\) | −44.8914 | −1.52547 | ||||||||
\(867\) | −125.191 | −4.25171 | ||||||||
\(868\) | −87.2854 | −2.96266 | ||||||||
\(869\) | 1.50125 | 0.0509265 | ||||||||
\(870\) | 31.3035 | 1.06129 | ||||||||
\(871\) | 18.3884 | 0.623066 | ||||||||
\(872\) | 59.4139 | 2.01201 | ||||||||
\(873\) | −9.79666 | −0.331567 | ||||||||
\(874\) | −32.3440 | −1.09405 | ||||||||
\(875\) | 15.0693 | 0.509435 | ||||||||
\(876\) | −92.3415 | −3.11993 | ||||||||
\(877\) | −40.6678 | −1.37325 | −0.686627 | − | 0.727010i | \(-0.740909\pi\) | ||||
−0.686627 | + | 0.727010i | \(0.740909\pi\) | |||||||
\(878\) | −85.4362 | −2.88333 | ||||||||
\(879\) | −0.137533 | −0.00463886 | ||||||||
\(880\) | −6.07828 | −0.204899 | ||||||||
\(881\) | −7.35756 | −0.247882 | −0.123941 | − | 0.992290i | \(-0.539553\pi\) | ||||
−0.123941 | + | 0.992290i | \(0.539553\pi\) | |||||||
\(882\) | 27.8937 | 0.939230 | ||||||||
\(883\) | −7.83441 | −0.263649 | −0.131824 | − | 0.991273i | \(-0.542083\pi\) | ||||
−0.131824 | + | 0.991273i | \(0.542083\pi\) | |||||||
\(884\) | −206.787 | −6.95499 | ||||||||
\(885\) | −30.8332 | −1.03645 | ||||||||
\(886\) | 90.9765 | 3.05642 | ||||||||
\(887\) | −1.00061 | −0.0335971 | −0.0167986 | − | 0.999859i | \(-0.505347\pi\) | ||||
−0.0167986 | + | 0.999859i | \(0.505347\pi\) | |||||||
\(888\) | 134.613 | 4.51731 | ||||||||
\(889\) | −7.14040 | −0.239481 | ||||||||
\(890\) | −14.7580 | −0.494688 | ||||||||
\(891\) | −4.60506 | −0.154275 | ||||||||
\(892\) | 58.6169 | 1.96264 | ||||||||
\(893\) | −10.9281 | −0.365694 | ||||||||
\(894\) | −88.9325 | −2.97435 | ||||||||
\(895\) | −11.6289 | −0.388711 | ||||||||
\(896\) | 6.87159 | 0.229564 | ||||||||
\(897\) | 100.577 | 3.35818 | ||||||||
\(898\) | −37.8679 | −1.26367 | ||||||||
\(899\) | 52.4997 | 1.75096 | ||||||||
\(900\) | −82.1983 | −2.73994 | ||||||||
\(901\) | 3.59430 | 0.119743 | ||||||||
\(902\) | 16.0530 | 0.534507 | ||||||||
\(903\) | 63.8926 | 2.12621 | ||||||||
\(904\) | −143.615 | −4.77658 | ||||||||
\(905\) | −3.95573 | −0.131493 | ||||||||
\(906\) | 37.2398 | 1.23721 | ||||||||
\(907\) | −25.3787 | −0.842686 | −0.421343 | − | 0.906901i | \(-0.638441\pi\) | ||||
−0.421343 | + | 0.906901i | \(0.638441\pi\) | |||||||
\(908\) | 109.461 | 3.63259 | ||||||||
\(909\) | 47.3936 | 1.57195 | ||||||||
\(910\) | 22.5925 | 0.748935 | ||||||||
\(911\) | −0.435314 | −0.0144226 | −0.00721130 | − | 0.999974i | \(-0.502295\pi\) | ||||
−0.00721130 | + | 0.999974i | \(0.502295\pi\) | |||||||
\(912\) | 42.0622 | 1.39282 | ||||||||
\(913\) | 9.27600 | 0.306991 | ||||||||
\(914\) | −37.8672 | −1.25254 | ||||||||
\(915\) | 16.3521 | 0.540583 | ||||||||
\(916\) | −11.3429 | −0.374779 | ||||||||
\(917\) | 33.9192 | 1.12011 | ||||||||
\(918\) | −51.5870 | −1.70263 | ||||||||
\(919\) | −21.1827 | −0.698752 | −0.349376 | − | 0.936983i | \(-0.613606\pi\) | ||||
−0.349376 | + | 0.936983i | \(0.613606\pi\) | |||||||
\(920\) | −38.9110 | −1.28286 | ||||||||
\(921\) | 38.0811 | 1.25482 | ||||||||
\(922\) | 59.7872 | 1.96899 | ||||||||
\(923\) | −63.5387 | −2.09140 | ||||||||
\(924\) | −22.4378 | −0.738150 | ||||||||
\(925\) | −31.5319 | −1.03676 | ||||||||
\(926\) | −36.2612 | −1.19162 | ||||||||
\(927\) | −28.1825 | −0.925636 | ||||||||
\(928\) | 54.1390 | 1.77720 | ||||||||
\(929\) | −30.1240 | −0.988336 | −0.494168 | − | 0.869366i | \(-0.664527\pi\) | ||||
−0.494168 | + | 0.869366i | \(0.664527\pi\) | |||||||
\(930\) | 47.2222 | 1.54848 | ||||||||
\(931\) | 4.82567 | 0.158155 | ||||||||
\(932\) | 37.8517 | 1.23987 | ||||||||
\(933\) | 33.0578 | 1.08227 | ||||||||
\(934\) | 12.6362 | 0.413468 | ||||||||
\(935\) | 5.41114 | 0.176963 | ||||||||
\(936\) | −152.330 | −4.97906 | ||||||||
\(937\) | −10.0826 | −0.329385 | −0.164693 | − | 0.986345i | \(-0.552663\pi\) | ||||
−0.164693 | + | 0.986345i | \(0.552663\pi\) | |||||||
\(938\) | −18.1952 | −0.594095 | ||||||||
\(939\) | 67.5377 | 2.20401 | ||||||||
\(940\) | −22.7265 | −0.741257 | ||||||||
\(941\) | 0.380700 | 0.0124105 | 0.00620523 | − | 0.999981i | \(-0.498025\pi\) | ||||
0.00620523 | + | 0.999981i | \(0.498025\pi\) | |||||||
\(942\) | −27.0993 | −0.882944 | ||||||||
\(943\) | 50.0885 | 1.63111 | ||||||||
\(944\) | −136.166 | −4.43183 | ||||||||
\(945\) | 3.96488 | 0.128978 | ||||||||
\(946\) | 26.4651 | 0.860455 | ||||||||
\(947\) | 45.5143 | 1.47902 | 0.739509 | − | 0.673147i | \(-0.235058\pi\) | ||||
0.739509 | + | 0.673147i | \(0.235058\pi\) | |||||||
\(948\) | −21.6050 | −0.701698 | ||||||||
\(949\) | 40.0852 | 1.30122 | ||||||||
\(950\) | −20.2147 | −0.655850 | ||||||||
\(951\) | −34.3683 | −1.11447 | ||||||||
\(952\) | 118.366 | 3.83626 | ||||||||
\(953\) | 53.0969 | 1.71998 | 0.859989 | − | 0.510313i | \(-0.170471\pi\) | ||||
0.859989 | + | 0.510313i | \(0.170471\pi\) | |||||||
\(954\) | 4.57707 | 0.148188 | ||||||||
\(955\) | −19.0243 | −0.615611 | ||||||||
\(956\) | −70.4191 | −2.27752 | ||||||||
\(957\) | 13.4957 | 0.436254 | ||||||||
\(958\) | −55.7485 | −1.80115 | ||||||||
\(959\) | 20.8610 | 0.673636 | ||||||||
\(960\) | 11.8247 | 0.381639 | ||||||||
\(961\) | 48.1973 | 1.55475 | ||||||||
\(962\) | −101.015 | −3.25684 | ||||||||
\(963\) | −13.3586 | −0.430476 | ||||||||
\(964\) | −33.4999 | −1.07896 | ||||||||
\(965\) | 0.431839 | 0.0139014 | ||||||||
\(966\) | −99.5210 | −3.20204 | ||||||||
\(967\) | −23.3007 | −0.749298 | −0.374649 | − | 0.927167i | \(-0.622237\pi\) | ||||
−0.374649 | + | 0.927167i | \(0.622237\pi\) | |||||||
\(968\) | 73.0349 | 2.34743 | ||||||||
\(969\) | −37.4456 | −1.20293 | ||||||||
\(970\) | −5.01038 | −0.160873 | ||||||||
\(971\) | 32.2438 | 1.03475 | 0.517376 | − | 0.855758i | \(-0.326909\pi\) | ||||
0.517376 | + | 0.855758i | \(0.326909\pi\) | |||||||
\(972\) | 101.471 | 3.25469 | ||||||||
\(973\) | −17.8960 | −0.573720 | ||||||||
\(974\) | 105.029 | 3.36535 | ||||||||
\(975\) | 62.8598 | 2.01312 | ||||||||
\(976\) | 72.2144 | 2.31153 | ||||||||
\(977\) | −9.10069 | −0.291157 | −0.145578 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145578 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(978\) | −27.1101 | −0.866886 | ||||||||
\(979\) | −6.36252 | −0.203347 | ||||||||
\(980\) | 10.0357 | 0.320577 | ||||||||
\(981\) | −32.8292 | −1.04816 | ||||||||
\(982\) | 85.7187 | 2.73539 | ||||||||
\(983\) | −41.6334 | −1.32790 | −0.663949 | − | 0.747778i | \(-0.731121\pi\) | ||||
−0.663949 | + | 0.747778i | \(0.731121\pi\) | |||||||
\(984\) | −133.643 | −4.26038 | ||||||||
\(985\) | 13.2931 | 0.423553 | ||||||||
\(986\) | −123.070 | −3.91935 | ||||||||
\(987\) | −33.6252 | −1.07030 | ||||||||
\(988\) | −45.5562 | −1.44934 | ||||||||
\(989\) | 82.5763 | 2.62577 | ||||||||
\(990\) | 6.89069 | 0.219000 | ||||||||
\(991\) | −25.4059 | −0.807044 | −0.403522 | − | 0.914970i | \(-0.632214\pi\) | ||||
−0.403522 | + | 0.914970i | \(0.632214\pi\) | |||||||
\(992\) | 81.6702 | 2.59303 | ||||||||
\(993\) | −11.0431 | −0.350441 | ||||||||
\(994\) | 62.8714 | 1.99416 | ||||||||
\(995\) | 16.2953 | 0.516597 | ||||||||
\(996\) | −133.494 | −4.22991 | ||||||||
\(997\) | −1.99317 | −0.0631243 | −0.0315621 | − | 0.999502i | \(-0.510048\pi\) | ||||
−0.0315621 | + | 0.999502i | \(0.510048\pi\) | |||||||
\(998\) | 24.8522 | 0.786682 | ||||||||
\(999\) | −17.7276 | −0.560876 |
(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 | 6047.2.a.b.1.14 | ✓ | 287 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.b.1.14 | ✓ | 287 | 1.1 | even | 1 | trivial |